Finite Group Databasebeta

← #27185156

Subgroups — #27185156

Order 12928.

1252 conjugacy classes of subgroups.

The subgroup lattice has 1096 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20265889C211yesmaximal, characteristic, complemented
2#20265881C211yesmaximal, characteristic, complemented
3#20265878C211yesmaximal, characteristic, complemented
4#20265878C211yesmaximal, characteristic, complemented
5#20265872C211yesmaximal, characteristic, complemented
6#20265870C211yesmaximal, characteristic, complemented
7#20265845C211yesmaximal, characteristic, complemented
8#20265820C211yesmaximal, characteristic, complemented
9#20265819C211yesmaximal, characteristic, complemented
10#20265818C211yesmaximal, characteristic, complemented
11#20265816C211yesmaximal, characteristic, complemented
12#20265814C211yesmaximal, characteristic, complemented
13#20265814C211yesmaximal, characteristic, complemented
14#20265811C211yesmaximal, characteristic, complemented
15#20265809C211yesmaximal, characteristic, complemented
16#20265809C211yesmaximal, characteristic, complemented
17#20265779C211yesmaximal, characteristic, complemented
18#20265777C211yesmaximal, characteristic, complemented
19#20265766C211yesmaximal, characteristic, complemented
20#20265761C211yesmaximal, characteristic, complemented
21#20265760C211yesmaximal, characteristic, complemented
22#20265726C211yesmaximal, characteristic, complemented
23#20265710C211yesmaximal, characteristic, complemented
24#20265686C211yesmaximal, characteristic, complemented
25#20265685C211yesmaximal, characteristic, complemented
26C2×#15692228C211yesmaximal, characteristic, complemented
27#121×D101C211yesmaximal, characteristic, complemented
28#20265650C211yesmaximal, characteristic, complemented
29#20265649C211yesmaximal, characteristic, complemented
30C4×D4×D101C211yesmaximal, characteristic, complemented
31#538×C101C211yesmaximal, characteristic, complemented
32C2×#13108075C2211yescharacteristic, complemented
33C2×#13108074C2211yescharacteristic, complemented
34C2×#13108073C2211yescharacteristic, complemented
35C2×#13108073C2211yescharacteristic, complemented
36C22×D404C2211yescharacteristic, complemented
37C22×C22⋊D101C2211yescharacteristic
38C22×C22⋊D101C2211yescharacteristic, complemented
39C22×C22⋊D101C2211yescharacteristic, complemented
40C2×D4×D101C2211yescharacteristic
41C2×D4×D101C2211yescharacteristic
42C2×D4×D101C2211yescharacteristic, complemented
43C2×D4×D101C2211yescharacteristic, complemented
44C2×D4×D101C2211yescharacteristic, complemented
45C22×C4×D101C2211yescharacteristic, complemented
46C22×C4×D101C2211yescharacteristic, complemented
47#15692253C2211yescharacteristic, complemented
48#15692251C2211yescharacteristic, complemented
49#15692251C2211yescharacteristic, complemented
50#15692251C2211yescharacteristic, complemented
51#15692250C2211yescharacteristic, complemented
52#15692250C2211yescharacteristic, complemented
53#15692249C2211yescharacteristic, complemented
54#15692248C2211yescharacteristic, complemented
55#15692245C2211yescharacteristic, complemented
56#15692245C2211yescharacteristic, complemented
57#15692245C2211yescharacteristic, complemented
58#15692244C2211yescharacteristic, complemented
59#15692243C2211yescharacteristic, complemented
60#15692241C2211yescharacteristic, complemented
61#15692241C2211yescharacteristic, complemented
62#15692241C2211yescharacteristic, complemented
63#15692240C2211yescharacteristic, complemented
64#15692240C2211yescharacteristic, complemented
65#15692240C2211yescharacteristic, complemented
66#15692240C2211yescharacteristic, complemented
67#15692239C2211yescharacteristic, complemented
68#15692239C2211yescharacteristic, complemented
69#15692238C2211yescharacteristic, complemented
70#15692237C2211yescharacteristic, complemented
71#15692237C2211yescharacteristic, complemented
72#15692237C2211yescharacteristic, complemented
73#15692237C2211yescharacteristic, complemented
74#15692236C2211yescharacteristic, complemented
75#15692233C2211yescharacteristic, complemented
76#15692233C2211yescharacteristic, complemented
77#15692233C2211yescharacteristic, complemented
78#15692232C2211yescharacteristic, complemented
79#15692232C2211yescharacteristic, complemented
80#15692231C2211yescharacteristic, complemented
81#15692230C2211yescharacteristic, complemented
82#15692230C2211yescharacteristic, complemented
83#15692230C2211yescharacteristic, complemented
84#15692230C2211yescharacteristic, complemented
85#15692229C2211yescharacteristic, complemented
86#15692228C2211yescharacteristic
87#15692228C2211yescharacteristic, complemented
88#15692228C2211yescharacteristic, complemented
89#15692228C2211yescharacteristic, complemented
90#15692228C2211yescharacteristic, complemented
91#15692228C2211yescharacteristic, complemented
92#15692228C2211yescharacteristic, complemented
93#15692228C2211yescharacteristic, complemented
94#15692228C2211yescharacteristic, complemented
95#15692228C2211yescharacteristic, complemented
96#15692228C2211yescharacteristic, complemented
97#15692228C2211yescharacteristic, complemented
98#15692228C2211yescharacteristic, complemented
99#15692228C2211yescharacteristic, complemented
100#15692228C2211yescharacteristic, complemented
101#15692228C2211yescharacteristic, complemented
102#15692227C2211yescharacteristic, complemented
103#15692227C2211yescharacteristic, complemented
104#15692227C2211yescharacteristic, complemented
105#15692227C2211yescharacteristic, complemented
106#15692227C2211yescharacteristic, complemented
107#15692227C2211yescharacteristic, complemented
108#15692227C2211yescharacteristic, complemented
109#15692227C2211yescharacteristic, complemented
110#15692227C2211yescharacteristic, complemented
111#15692226C2211yescharacteristic, complemented
112#15692226C2211yescharacteristic, complemented
113#15692225C2211yescharacteristic, complemented
114#15692225C2211yescharacteristic, complemented
115#15692225C2211yescharacteristic, complemented
116#15692225C2211yescharacteristic, complemented
117#15692225C2211yescharacteristic, complemented
118#15692225C2211yescharacteristic, complemented
119#15692223C2211yescharacteristic, complemented
120#15692223C2211yescharacteristic, complemented
121#15692223C2211yescharacteristic, complemented
122#15692223C2211yescharacteristic, complemented
123#15692220C2211yescharacteristic, complemented
124C4×D404C2211yescharacteristic, complemented
125C4×D404C2211yescharacteristic, complemented
126C4×D404C2211yescharacteristic, complemented
127D4×Dic101C2211yescharacteristic, complemented
128D4×Dic101C2211yescharacteristic, complemented
129#15692217C2211yescharacteristic, complemented
130#15692217C2211yescharacteristic, complemented
131#15692217C2211yescharacteristic, complemented
132#15692217C2211yescharacteristic, complemented
133C4×C22⋊D101C2211yescharacteristic
134C4×C22⋊D101C2211yescharacteristic
135C4×C22⋊D101C2211yescharacteristic, complemented
136C4×C22⋊D101C2211yescharacteristic, complemented
137C4×C22⋊D101C2211yescharacteristic, complemented
138C4×C22⋊D101C2211yescharacteristic, complemented
139C4×C22⋊D101C2211yescharacteristic, complemented
140#15692215C2211yescharacteristic
141#15692215C2211yescharacteristic
142#15692215C2211yescharacteristic, complemented
143#15692215C2211yescharacteristic, complemented
144#15692215C2211yescharacteristic, complemented
145#15692215C2211yescharacteristic, complemented
146#15692215C2211yescharacteristic, complemented
147#15692215C2211yescharacteristic, complemented
148#15692215C2211yescharacteristic, complemented
149#15692215C2211yescharacteristic, complemented
150#15692215C2211yescharacteristic, complemented
151#15692215C2211yescharacteristic, complemented
152#15692215C2211yescharacteristic, complemented
153#15692213C2211yescharacteristic, complemented
154#15692212C2211yescharacteristic, complemented
155#15692212C2211yescharacteristic, complemented
156#15692211C2211yescharacteristic, complemented
157#15692211C2211yescharacteristic, complemented
158#15692211C2211yescharacteristic, complemented
159C2×#13108053C2211yescharacteristic, complemented
160C4⋊C4×D101C2211yescharacteristic, complemented
161C4⋊C4×D101C2211yescharacteristic, complemented
162C2×C22⋊Dic101C2211yescharacteristic, complemented
163C2×#13108051C2211yescharacteristic, complemented
164C2×#13108051C2211yescharacteristic, complemented
165C22⋊C4×D101C2211yescharacteristic, complemented
166C22⋊C4×D101C2211yescharacteristic, complemented
167C22⋊C4×D101C2211yescharacteristic, complemented
168C22⋊C4×D101C2211yescharacteristic, complemented
169C22⋊C4×D101C2211yescharacteristic, complemented
170C22⋊C4×D101C2211yescharacteristic, complemented
171C42×D101C2211yescharacteristic, complemented
172#126×C101C2211yescharacteristic, complemented
173#126×C101C2211yescharacteristic, complemented
174#124×C101C2211yescharacteristic, complemented
175#124×C101C2211yescharacteristic, complemented
176#123×C101C2211yescharacteristic, complemented
177#123×C101C2211yescharacteristic, complemented
178C22⋊Q8×C101C2211yescharacteristic, complemented
179#121×C101C2211yescharacteristic, complemented
180#121×C101C2211yescharacteristic, complemented
181#121×C101C2211yescharacteristic, complemented
182#120×C101C2211yescharacteristic, complemented
183#120×C101C2211yescharacteristic, complemented
184C4×D4×C101C2211yescharacteristic, complemented
185C4×D4×C101C2211yescharacteristic, complemented
186C2×C22⋊C4×C101C2211yescharacteristic, complemented
187C23×D101C2311yescharacteristic
188C23×D101C2311yescharacteristic
189C23×D101C2311yescharacteristic
190C23×D101C2311yescharacteristic
191C23×D101C2311yescharacteristic
192#13108075—42no—
193#13108074—42no—
194#13108073—42no—
195#13108073—42no—
196C2×Dic202C2311yescharacteristic
197C2×Dic202C2311yescharacteristic
198C2×D404—42no—
199C2×D404C2311yescharacteristic
200C2×D404C2311yescharacteristic
201C2×D404C2311yescharacteristic
202C2×D404C2311yescharacteristic
203C2×D404C2311yescharacteristic
204C2×D404C2311yescharacteristic
205C2×D404C2311yescharacteristic
206C2×D404C2311yescharacteristic
207C2×D404C2311yescharacteristic
208C2×D404C2311yescharacteristic
209C2×C22⋊D101—24no—
210C2×C22⋊D101—42no—
211C2×C22⋊D101—42no—
212C2×C22⋊D101C2311yescharacteristic
213C2×C22⋊D101C2311yescharacteristic
214C2×C22⋊D101C2311yescharacteristic
215C2×C22⋊D101C2311yescharacteristic
216C2×C22⋊D101C2311yescharacteristic
217C2×C22⋊D101C2311yescharacteristic
218C2×C22⋊D101C2311yescharacteristic
219C2×C22⋊D101C2311yescharacteristic
220C2×C22⋊D101C2311yescharacteristic
221C2×C22⋊D101C2311yescharacteristic
222C2×C22⋊D101C2311yescharacteristic
223C2×C22⋊D101C2311yescharacteristic
224C2×C22⋊D101C2311yescharacteristic
225C2×C22⋊D101C2311yescharacteristic
226C2×C22⋊D101C2311yescharacteristic
227C2×C22⋊D101C2311yescharacteristic
228C2×C22⋊D101C2311yescharacteristic
229C2×C22⋊D101C2311yescharacteristic
230C2×C22⋊D101C2311yescharacteristic
231C2×C22⋊D101C2311yescharacteristic
232D4×D101—24no—
233D4×D101—24no—
234D4×D101—42no—
235D4×D101—42no—
236D4×D101—42no—
237C22×Dic101C2311yescharacteristic
238C22×Dic101C2311yescharacteristic
239C22×Dic101C2311yescharacteristic
240C22×Dic101C2311yescharacteristic
241C22×Dic101C2311yescharacteristic
242C22×Dic101C2311yescharacteristic
243C22×Dic101C2311yescharacteristic
244C2×C4×D101—42no—
245C2×C4×D101—42no—
246C2×C4×D101C2311yescharacteristic
247C2×C4×D101C2311yescharacteristic
248C2×C4×D101C2311yescharacteristic
249C2×C4×D101C2311yescharacteristic
250C2×C4×D101C2311yescharacteristic
251C2×C4×D101C2311yescharacteristic
252C2×C4×D101C2311yescharacteristic
253C2×C4×D101C2311yescharacteristic
254C2×C4×D101C2311yescharacteristic
255C2×C4×D101C2311yescharacteristic
256C2×C4×D101C2311yescharacteristic
257C2×C4×D101C2311yescharacteristic
258C2×C4×D101C2311yescharacteristic
259C2×C4×D101C2311yescharacteristic
260C2×C4×D101C2311yescharacteristic
261C2×C4×D101C2311yescharacteristic
262C4⋊Dic101C2311yescharacteristic
263C4⋊Dic101C2311yescharacteristic
264C4⋊Dic101C2311yescharacteristic
265C4⋊Dic101C2311yescharacteristic
266#13108053C2311yescharacteristic
267#13108053C2311yescharacteristic
268#13108053C2311yescharacteristic
269#13108053C2311yescharacteristic
270#13108053C2311yescharacteristic
271#13108053C2311yescharacteristic
272#13108053C2311yescharacteristic
273#13108053C2311yescharacteristic
274#13108053C2311yescharacteristic
275#13108053C2311yescharacteristic
276#13108053C2311yescharacteristic
277#13108053C2311yescharacteristic
278#13108053C2311yescharacteristic
279#13108053C2311yescharacteristic
280#13108053C2311yescharacteristic
281#13108053C2311yescharacteristic
282C22⋊Dic101C2311yescharacteristic
283C22⋊Dic101C2311yescharacteristic
284C22⋊Dic101C2311yescharacteristic
285C22⋊Dic101C2311yescharacteristic
286C22⋊Dic101C2311yescharacteristic
287C22⋊Dic101C2311yescharacteristic
288C22⋊Dic101C2311yescharacteristic
289C22⋊Dic101C2311yescharacteristic
290#13108051C2311yescharacteristic
291#13108051C2311yescharacteristic
292#13108051C2311yescharacteristic
293#13108051C2311yescharacteristic
294#13108051C2311yescharacteristic
295#13108051C2311yescharacteristic
296#13108051C2311yescharacteristic
297#13108051C2311yescharacteristic
298#13108051C2311yescharacteristic
299#13108051C2311yescharacteristic
300#13108051C2311yescharacteristic
301#13108051C2311yescharacteristic
302#13108051C2311yescharacteristic
303#13108051C2311yescharacteristic
304#13108051C2311yescharacteristic
305#13108051C2311yescharacteristic
306#13108051C2311yescharacteristic
307#13108051C2311yescharacteristic
308#13108051C2311yescharacteristic
309#13108051C2311yescharacteristic
310#13108051C2311yescharacteristic
311#13108051C2311yescharacteristic
312#13108051C2311yescharacteristic
313#13108051C2311yescharacteristic
314C4×Dic101C2311yescharacteristic
315C4×Dic101C2311yescharacteristic
316C4×Dic101C2311yescharacteristic
317C4×Dic101C2311yescharacteristic
318C4×Dic101C2311yescharacteristic
319C4×Dic101C2311yescharacteristic
320C4×Dic101C2311yescharacteristic
321C4×Dic101C2311yescharacteristic
322C24×C101C2311yescharacteristic
323C2×Q8×C101C2311yescharacteristic
324C2×D4×C101C2311yescharacteristic
325C2×D4×C101C2311yescharacteristic
326C2×D4×C101C2311yescharacteristic
327C2×D4×C101C2311yescharacteristic
328C2×D4×C101C2311yescharacteristic
329C2×D4×C101C2311yescharacteristic
330C2×D4×C101C2311yescharacteristic
331C22×C4×C101C2311yescharacteristic
332C22×C4×C101C2311yescharacteristic
333C22×C4×C101C2311yescharacteristic
334C22×C4×C101C2311yescharacteristic
335C4⋊C4×C101C2311yescharacteristic
336C4⋊C4×C101C2311yescharacteristic
337C4⋊C4×C101C2311yescharacteristic
338C4⋊C4×C101C2311yescharacteristic
339C4⋊C4×C101C2311yescharacteristic
340C4⋊C4×C101C2311yescharacteristic
341C22⋊C4×C101C2311yescharacteristic
342C22⋊C4×C101C2311yescharacteristic
343C22⋊C4×C101C2311yescharacteristic
344C22⋊C4×C101C2311yescharacteristic
345C22⋊C4×C101C2311yescharacteristic
346C22⋊C4×C101C2311yescharacteristic
347C22⋊C4×C101C2311yescharacteristic
348C22⋊C4×C101C2311yescharacteristic
349C22⋊C4×C101C2311yescharacteristic
350C22⋊C4×C101C2311yescharacteristic
351C22⋊C4×C101C2311yescharacteristic
352C22⋊C4×C101C2311yescharacteristic
353C22⋊C4×C101C2311yescharacteristic
354C22⋊C4×C101C2311yescharacteristic
355C42×C101C2311yescharacteristic
356C42×C101C2311yescharacteristic
357C23×C101—22no—
358C23×C101—41no—
359C23×C101—41no—
360C23×C101C2411yescharacteristic
361C23×C101C2411yescharacteristic
362C23×C101C2411yescharacteristic
363C23×C101C2411yescharacteristic
364C23×C101C2411yescharacteristic
365C22×D101—22no—
366C22×D101—22no—
367C22×D101—22no—
368C22×D101—22no—
369C22×D101—22no—
370C22×D101—22no—
371C22×D101—22no—
372C22×D101—41no—
373C22×D101—41no—
374C22×D101—41no—
375C22×D101—41no—
376C22×D101—41no—
377C22×D101—41no—
378C22×D101—41no—
379C22×D101—41no—
380C22×D101C2411yescharacteristic
381C22×D101C2411yescharacteristic
382C22×D101C2411yescharacteristic
383C22×D101C2411yescharacteristic
384C22×D101C2411yescharacteristic
385C22×D101C2411yescharacteristic
386Q8×C101—41no—
387D4×C101—22no—
388D4×C101—22no—
389D4×C101—41no—
390D4×C101—41no—
391D4×C101—41no—
392D4×C101—41no—
393D4×C101—41no—
394C2×C4×C101—41no—
395C2×C4×C101—41no—
396C2×C4×C101—41no—
397C2×C4×C101—41no—
398C2×C4×C101C2411yescharacteristic
399C2×C4×C101C2411yescharacteristic
400C2×C4×C101C2411yescharacteristic
401C2×C4×C101C2411yescharacteristic
402C2×C4×C101C2411yescharacteristic
403C2×C4×C101C2411yescharacteristic
404C2×C4×C101C2411yescharacteristic
405C2×C4×C101C2411yescharacteristic
406C2×C4×C101C2411yescharacteristic
407C2×C4×C101C2411yescharacteristic
408C22⋊D101—22no—
409C22⋊D101—22no—
410C22⋊D101—22no—
411C22⋊D101—22no—
412C22⋊D101—22no—
413C22⋊D101—22no—
414C22⋊D101—22no—
415C22⋊D101—22no—
416C22⋊D101—22no—
417C22⋊D101—22no—
418C22⋊D101—22no—
419C22⋊D101—41no—
420C22⋊D101—41no—
421C22⋊D101—41no—
422C22⋊D101—41no—
423C22⋊D101—41no—
424C22⋊D101—41no—
425C22⋊D101—41no—
426C22⋊D101—41no—
427C22⋊D101#4114yescomplemented
428C2×Dic101—22no—
429C2×Dic101—22no—
430C2×Dic101—22no—
431C2×Dic101—41no—
432C2×Dic101—41no—
433C2×Dic101—41no—
434C2×Dic101—41no—
435C2×Dic101C2411yescharacteristic
436C2×Dic101C2411yescharacteristic
437C2×Dic101C2411yescharacteristic
438C2×Dic101C2411yescharacteristic
439C2×Dic101C2411yescharacteristic
440C2×Dic101C2411yescharacteristic
441C2×Dic101C2411yescharacteristic
442C2×Dic101C2411yescharacteristic
443C2×Dic101C2411yescharacteristic
444C2×Dic101C2411yescharacteristic
445D404—22no—
446D404—22no—
447D404—22no—
448D404—22no—
449D404—22no—
450D404—41no—
451D404—41no—
452D404—41no—
453D404—41no—
454D404—41no—
455C4×D101—22no—
456C4×D101—22no—
457C4×D101—22no—
458C4×D101—22no—
459C4×D101—22no—
460C4×D101—22no—
461C4×D101—41no—
462C4×D101—41no—
463C4×D101—41no—
464C4×D101—41no—
465C4×D101—41no—
466C4×D101—41no—
467C4×D101—41no—
468C4×D101—41no—
469C4×D101—41no—
470C4×D101—41no—
471Dic202—22no—
472Dic202—41no—
473C22×C101—21no—
474C22×C101—21no—
475C22×C101—21no—
476C22×C101—21no—
477C22×C101—21no—
478C22×C101—21no—
479C22×C101—21no—
480C22×C101—21no—
481C22×C101—21no—
482C22×C101—21no—
483C22×C101—21no—
484C22×C101—21no—
485C22×C101—21no—
486C22×C101—21no—
487C22×C101—82no—
488C22×C101C2×#4112yes—
489C22×C101C2511yescharacteristic
490C2×D101—21no—
491C2×D101—21no—
492C2×D101—21no—
493C2×D101—21no—
494C2×D101—21no—
495C2×D101—21no—
496C2×D101—21no—
497C2×D101—21no—
498C2×D101—21no—
499C2×D101—21no—
500C2×D101—21no—
501C2×D101—21no—
502C2×D101—21no—
503C2×D101—21no—
504C2×D101—21no—
505C2×D101—21no—
506C2×D101—44no—
507C2×D101—44no—
508C2×D101—82no—
509C2×D101—82no—
510C2×D101—82no—
511C2×D101C2×#4112yes—
512C2×D101H(5,𝔽2)12yes—
513C4×C101—21no—
514C4×C101—21no—
515C4×C101—21no—
516C4×C101—21no—
517C4×C101—21no—
518C4×C101—21no—
519C4×C101—21no—
520C4×C101—21no—
521C4×C101—21no—
522C4×C101—21no—
523Dic101—21no—
524Dic101—21no—
525Dic101—21no—
526Dic101—21no—
527Dic101—21no—
528Dic101—21no—
529Dic101—21no—
530Dic101—21no—
531Dic101C2×#4112yes—
532Dic101H(5,𝔽2)12yes—
533C2×C101—22no—
534C2×C101—41no—
535C2×C101—41no—
536C2×C101—41no—
537C2×C101—41no—
538C2×C101C22×#4111yescharacteristic
539C2×C101C2×H(5,𝔽2)11yescharacteristic
540C2×C101C2×H(5,𝔽2)11yescharacteristic
541D101—22no—
542D101—22no—
543D101—41no—
544D101—41no—
545D101—41no—
546D101—41no—
547#3519—1011nomaximal, Sylow
548C101#351911yescharacteristic, complemented, Sylow
549#555—1011no—
550#554—1011no—
551#553—1011no—
552#553—1011no—
553#553—1011no—
554#553—1011no—
555#550—1011no—
556#546—1011no—
557#546—1011no—
558#546—1011no—
559#546—1011no—
560#546—1011no—
561#546—1011no—
562D42—1011no—
563D42—1011no—
564D42—1011no—
565#540—1011no—
566#540—1011no—
567#538—1011no—
568#538—1011no—
569#538—1011no—
570#538D10111yescharacteristic, complemented
571#532—1011no—
572#529—1011no—
573#525—1011no—
574#525—1011no—
575C2×#121—1011no—
576C2×#121—1011no—
577#518—1011no—
578#518—1011no—
579C2×C4×D4—1011no—
580C2×#41—1011no—
581C2×#41—1011no—
582C2×#41—1011no—
583C2×#41—1011no—
584C22×D4—1011no—
585C22×D4—1011no—
586C22×D4—1011no—
587C22×D4—1011no—
588C22×D4—1011no—
589C22×D4—1011no—
590C22×D4—1011no—
591C22×D4—1011no—
592C22×D4—1011no—
593C23×C4—1011no—
594C23×C4—1011no—
595C4⋊Q8—1011no—
596#127—1011no—
597#127—1011no—
598#127—1011no—
599#126—1011no—
600#126—1011no—
601#126—1011no—
602#126—1011no—
603#126C2×D10111yescharacteristic, complemented
604#126C2×D10111yescharacteristic, complemented
605#125—1011no—
606#125—1011no—
607#125—1011no—
608#124—1011no—
609#124—1011no—
610#124—1011no—
611#124—1011no—
612#124—1011no—
613#124C2×D10111yescharacteristic, complemented
614#124C2×D10111yescharacteristic, complemented
615#123—1011no—
616#123—1011no—
617#123—1011no—
618#123—1011no—
619#123—1011no—
620#123—1011no—
621#123—1011no—
622#123—1011no—
623#123—1011no—
624#123—1011no—
625#123—1011no—
626#123—1011no—
627#123C2×D10111yescharacteristic, complemented
628#123C2×D10111yescharacteristic, complemented
629C22⋊Q8—1011no—
630C22⋊Q8—1011no—
631C22⋊Q8—1011no—
632C22⋊Q8—1011no—
633C22⋊Q8—1011no—
634C22⋊Q8—1011no—
635C22⋊Q8C2×D10111yescharacteristic, complemented
636#121—1011no—
637#121—1011no—
638#121—1011no—
639#121—1011no—
640#121—1011no—
641#121—1011no—
642#121—1011no—
643#121—1011no—
644#121—1011no—
645#121—1011no—
646#121—1011no—
647#121—1011no—
648#121—1011no—
649#121—1011no—
650#121—1011no—
651#121—1011no—
652#121—1011no—
653#121—1011no—
654#121—1011no—
655#121—1011no—
656#121—1011no—
657#121—1011no—
658#121—1011no—
659#121—1011no—
660#121—1011no—
661#121—1011no—
662#121—1011no—
663#121—1011no—
664#121—1011no—
665#121—1011no—
666#121—1011no—
667#121—1011no—
668#121C2×D10111yescharacteristic, complemented
669#121C2×D10111yescharacteristic, complemented
670#121C2×D10111yescharacteristic, complemented
671#120—1011no—
672#120—1011no—
673#120—1011no—
674#120—1011no—
675#120—1011no—
676#120—1011no—
677#120—1011no—
678#120—1011no—
679#120—1011no—
680#120—1011no—
681#120C2×D10111yescharacteristic, complemented
682#120C2×D10111yescharacteristic, complemented
683C4×Q8—1011no—
684C4×D4—1011no—
685C4×D4—1011no—
686C4×D4—1011no—
687C4×D4—1011no—
688C4×D4—1011no—
689C4×D4—1011no—
690C4×D4—1011no—
691C4×D4—1011no—
692C4×D4—1011no—
693C4×D4—1011no—
694C4×D4—1011no—
695C4×D4—1011no—
696C4×D4—1011no—
697C4×D4—1011no—
698C4×D4—1011no—
699C4×D4—1011no—
700C4×D4—1011no—
701C4×D4—1011no—
702C4×D4—1011no—
703C4×D4—1011no—
704C4×D4—1011no—
705C4×D4—1011no—
706C4×D4—1011no—
707C4×D4—1011no—
708C4×D4—1011no—
709C4×D4—1011no—
710C4×D4—1011no—
711C4×D4—1011no—
712C4×D4—1011no—
713C4×D4C2×D10111yescharacteristic, complemented
714C4×D4C2×D10111yescharacteristic, complemented
715#117—1011no—
716#117—1011no—
717#117—1011no—
718#117—1011no—
719#117—1011no—
720#117—1011no—
721C2×C4⋊C4—1011no—
722C2×C4⋊C4—1011no—
723C2×C4⋊C4—1011no—
724C2×C22⋊C4—1011no—
725C2×C22⋊C4—1011no—
726C2×C22⋊C4—1011no—
727C2×C22⋊C4—1011no—
728C2×C22⋊C4—1011no—
729C2×C22⋊C4—1011no—
730C2×C22⋊C4—1011no—
731C2×C22⋊C4—1011no—
732C2×C22⋊C4—1011no—
733C2×C22⋊C4C2×D10111yescharacteristic, complemented
734C2×C42—1011no—
735C24—1011no—
736C24—1011no—
737C24—1011no—
738C24—1011no—
739C24—1011no—
740C24C22×D10111yescharacteristic
741#41—4042no—
742#41—4042no—
743#41—4042no—
744#41—4042no—
745C2×Q8—1011no—
746C2×Q8—1011no—
747C2×Q8C22×D10111yescharacteristic
748C2×D4—1011no—
749C2×D4—1011no—
750C2×D4—1011no—
751C2×D4—1011no—
752C2×D4—1011no—
753C2×D4—1011no—
754C2×D4—1011no—
755C2×D4—1011no—
756C2×D4—1011no—
757C2×D4—1011no—
758C2×D4—1011no—
759C2×D4—1011no—
760C2×D4—1011no—
761C2×D4—1011no—
762C2×D4—1011no—
763C2×D4—1011no—
764C2×D4—1011no—
765C2×D4—1011no—
766C2×D4—1011no—
767C2×D4—1011no—
768C2×D4—1011no—
769C2×D4—1011no—
770C2×D4—1011no—
771C2×D4—1011no—
772C2×D4—1011no—
773C2×D4—1011no—
774C2×D4—1011no—
775C2×D4—1011no—
776C2×D4—1011no—
777C2×D4—1011no—
778C2×D4—4042no—
779C2×D4—4042no—
780C2×D4—4042no—
781C2×D4—4042no—
782C2×D4—4042no—
783C2×D4—4042no—
784C2×D4—2024no—
785C2×D4—2024no—
786C2×D4—2024no—
787C2×D4C22×D10111yescharacteristic
788C2×D4C22×D10111yescharacteristic
789C2×D4C22×D10111yescharacteristic
790C2×D4C22×D10111yescharacteristic
791C2×D4C22×D10111yescharacteristic
792C2×D4C22×D10111yescharacteristic
793C2×D4C22×D10111yescharacteristic
794C22×C4—1011no—
795C22×C4—1011no—
796C22×C4—1011no—
797C22×C4—1011no—
798C22×C4—1011no—
799C22×C4—1011no—
800C22×C4—1011no—
801C22×C4—1011no—
802C22×C4—1011no—
803C22×C4—1011no—
804C22×C4—1011no—
805C22×C4—1011no—
806C22×C4—1011no—
807C22×C4—1011no—
808C22×C4—1011no—
809C22×C4—1011no—
810C22×C4—1011no—
811C22×C4—1011no—
812C22×C4—1011no—
813C22×C4—1011no—
814C22×C4—1011no—
815C22×C4—1011no—
816C22×C4—1011no—
817C22×C4—4042no—
818C22×C4—4042no—
819C22×C4C22×D10111yescharacteristic
820C22×C4C22×D10111yescharacteristic
821C22×C4C22×D10111yescharacteristic
822C22×C4C22×D10111yescharacteristic
823C4⋊C4—1011no—
824C4⋊C4—1011no—
825C4⋊C4—1011no—
826C4⋊C4—1011no—
827C4⋊C4—1011no—
828C4⋊C4—1011no—
829C4⋊C4—1011no—
830C4⋊C4—1011no—
831C4⋊C4—1011no—
832C4⋊C4—1011no—
833C4⋊C4—1011no—
834C4⋊C4—1011no—
835C4⋊C4—1011no—
836C4⋊C4—1011no—
837C4⋊C4—1011no—
838C4⋊C4—1011no—
839C4⋊C4—1011no—
840C4⋊C4—1011no—
841C4⋊C4—1011no—
842C4⋊C4—1011no—
843C4⋊C4C22×D10111yescharacteristic
844C4⋊C4C22×D10111yescharacteristic
845C4⋊C4C22×D10111yescharacteristic
846C4⋊C4C22×D10111yescharacteristic
847C4⋊C4C22×D10111yescharacteristic
848C4⋊C4C22×D10111yescharacteristic
849C22⋊C4—1011no—
850C22⋊C4—1011no—
851C22⋊C4—1011no—
852C22⋊C4—1011no—
853C22⋊C4—1011no—
854C22⋊C4—1011no—
855C22⋊C4—1011no—
856C22⋊C4—1011no—
857C22⋊C4—1011no—
858C22⋊C4—1011no—
859C22⋊C4—1011no—
860C22⋊C4—1011no—
861C22⋊C4—1011no—
862C22⋊C4—1011no—
863C22⋊C4—1011no—
864C22⋊C4—1011no—
865C22⋊C4—1011no—
866C22⋊C4—1011no—
867C22⋊C4—1011no—
868C22⋊C4—1011no—
869C22⋊C4—1011no—
870C22⋊C4—1011no—
871C22⋊C4—1011no—
872C22⋊C4—1011no—
873C22⋊C4—1011no—
874C22⋊C4—1011no—
875C22⋊C4—1011no—
876C22⋊C4—1011no—
877C22⋊C4—1011no—
878C22⋊C4—1011no—
879C22⋊C4—1011no—
880C22⋊C4—1011no—
881C22⋊C4C22×D10111yescharacteristic
882C22⋊C4C22×D10111yescharacteristic
883C22⋊C4C22×D10111yescharacteristic
884C22⋊C4C22×D10111yescharacteristic
885C22⋊C4C22×D10111yescharacteristic
886C22⋊C4C22×D10111yescharacteristic
887C22⋊C4C22×D10111yescharacteristic
888C22⋊C4C22×D10111yescharacteristic
889C22⋊C4C22×D10111yescharacteristic
890C22⋊C4C22×D10111yescharacteristic
891C22⋊C4C22×D10111yescharacteristic
892C22⋊C4C22×D10111yescharacteristic
893C22⋊C4C22×D10111yescharacteristic
894C22⋊C4C22×D10111yescharacteristic
895C42—1011no—
896C42—1011no—
897C42—1011no—
898C42—1011no—
899C42—1011no—
900C42—1011no—
901C42—1011no—
902C42—1011no—
903C42C22×D10111yescharacteristic
904C42C22×D10111yescharacteristic
905C23—22no—
906C23—41no—
907C23—41no—
908C23—1011no—
909C23—1011no—
910C23—1011no—
911C23—1011no—
912C23—1011no—
913C23—1011no—
914C23—4041no—
915C23—4041no—
916C23—4041no—
917C23—4041no—
918C23—4041no—
919C23—4041no—
920C23—4041no—
921C23—4041no—
922C23—2022no—
923C23—2022no—
924C23—2022no—
925C23—2022no—
926C23—2022no—
927C23—2022no—
928C23—2022no—
929C23C23×D10111yescharacteristic
930C23C23×D10111yescharacteristic
931C23C23×D10111yescharacteristic
932C23C23×D10111yescharacteristic
933C23C23×D10111yescharacteristic
934Q8—41no—
935Q8—4041no—
936Q8—2022no—
937D4—22no—
938D4—22no—
939D4—41no—
940D4—41no—
941D4—41no—
942D4—41no—
943D4—41no—
944D4—1014no—
945D4—4041no—
946D4—4041no—
947D4—4041no—
948D4—4041no—
949D4—4041no—
950D4—4041no—
951D4—4041no—
952D4—4041no—
953D4—4041no—
954D4—4041no—
955D4—4041no—
956D4—4041no—
957D4—4041no—
958D4—2022no—
959D4—2022no—
960D4—2022no—
961D4—2022no—
962D4—2022no—
963D4—2022no—
964D4—2022no—
965D4—2022no—
966D4—2022no—
967D4—2022no—
968D4—2022no—
969D4—2022no—
970D4—2022no—
971D4—2022no—
972D4—2022no—
973D4—2022no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—1011no—
979C2×C4—1011no—
980C2×C4—1011no—
981C2×C4—1011no—
982C2×C4—1011no—
983C2×C4—1011no—
984C2×C4—1011no—
985C2×C4—1011no—
986C2×C4—1011no—
987C2×C4—1011no—
988C2×C4—4041no—
989C2×C4—4041no—
990C2×C4—4041no—
991C2×C4—4041no—
992C2×C4—4041no—
993C2×C4—4041no—
994C2×C4—4041no—
995C2×C4—4041no—
996C2×C4—4041no—
997C2×C4—4041no—
998C2×C4—4041no—
999C2×C4—4041no—
1000C2×C4—4041no—
1001C2×C4—4041no—
1002C2×C4—2022no—
1003C2×C4—2022no—
1004C2×C4—2022no—
1005C2×C4—2022no—
1006C2×C4—2022no—
1007C2×C4—2022no—
1008C2×C4—2022no—
1009C2×C4—2022no—
1010C2×C4—2022no—
1011C2×C4C23×D10111yescharacteristic
1012C2×C4C23×D10111yescharacteristic
1013C2×C4C23×D10111yescharacteristic
1014C2×C4C23×D10111yescharacteristic
1015C2×C4C23×D10111yescharacteristic
1016C2×C4C23×D10111yescharacteristic
1017C2×C4C23×D10111yescharacteristic
1018C2×C4C23×D10111yescharacteristic
1019C2×C4C23×D10111yescharacteristic
1020C2×C4C23×D10111yescharacteristic
1021C22—21no—
1022C22—21no—
1023C22—21no—
1024C22—21no—
1025C22—21no—
1026C22—21no—
1027C22—21no—
1028C22—21no—
1029C22—21no—
1030C22—21no—
1031C22—21no—
1032C22—21no—
1033C22—21no—
1034C22—21no—
1035C22—82no—
1036C22—8082no—
1037C22—8082no—
1038C22—8082no—
1039C22—1012no—
1040C22—1012no—
1041C22—4044no—
1042C22—4044no—
1043C22—2021no—
1044C22—2021no—
1045C22—2021no—
1046C22—2021no—
1047C22—2021no—
1048C22—2021no—
1049C22—2021no—
1050C22—2021no—
1051C22—2021no—
1052C22—2021no—
1053C22—2021no—
1054C22—2021no—
1055C22—2021no—
1056C22—2021no—
1057C22—2021no—
1058C22—2021no—
1059C22#41×D10112yes—
1060C22C24×D10111yescharacteristic
1061C4—21no—
1062C4—21no—
1063C4—21no—
1064C4—21no—
1065C4—21no—
1066C4—21no—
1067C4—21no—
1068C4—21no—
1069C4—21no—
1070C4—21no—
1071C4—1012no—
1072C4—1012no—
1073C4—2021no—
1074C4—2021no—
1075C4—2021no—
1076C4—2021no—
1077C4—2021no—
1078C4—2021no—
1079C4—2021no—
1080C4—2021no—
1081C2—22no—
1082C2—41no—
1083C2—41no—
1084C2—41no—
1085C2—41no—
1086C2—4041no—
1087C2—4041no—
1088C2—4041no—
1089C2—4041no—
1090C2—2022no—
1091C2—2022no—
1092C2C2×#41×D10111yescharacteristic
1093C2H(5,𝔽2)×D10111yescharacteristic
1094C2H(5,𝔽2)×D10111yescharacteristic
subgroupG/H
center, FrattiniC22C24×D101
commutator, socle, cosocleC22×C101C25
Fitting#538×C101C2
hypercenter#538D101
hypocenterC101#3519
LCSG ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ #538

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #20265889C2semidirect
2. #20265881C2semidirect
3. #20265878C2semidirect
4. #20265878C2semidirect
5. #20265872C2semidirect
6. #20265870C2semidirect
7. #20265845C2semidirect
8. #20265820C2semidirect
9. #20265819C2semidirect
10. #20265818C2semidirect
11. #20265816C2semidirect
12. #20265814C2semidirect
13. #20265814C2semidirect
14. #20265811C2semidirect
15. #20265809C2semidirect
16. #20265809C2semidirect
17. #20265779C2semidirect
18. #20265777C2semidirect
19. #20265766C2semidirect
20. #20265761C2semidirect
21. #20265760C2semidirect
22. #20265726C2semidirect
23. #20265710C2semidirect
24. #20265686C2semidirect
25. #20265685C2semidirect
26. C2×#15692228C2semidirect
27. #121×D101C2semidirect
28. #20265650C2semidirect
29. #20265649C2semidirect
30. C4×D4×D101C2semidirect
31. #538×C101C2semidirect
32. C2×#13108075C22semidirect
33. C2×#13108074C22semidirect
34. C2×#13108073C22semidirect
35. C2×#13108073C22semidirect
36. C22×D404C22semidirect
38. C22×C22⋊D101C22semidirect
39. C22×C22⋊D101C22semidirect
42. C2×D4×D101C22semidirect
43. C2×D4×D101C22semidirect
44. C2×D4×D101C22semidirect
45. C22×C4×D101C22semidirect
46. C22×C4×D101C22semidirect
47. #15692253C22semidirect
48. #15692251C22semidirect
49. #15692251C22semidirect
50. #15692251C22semidirect
51. #15692250C22semidirect
52. #15692250C22semidirect
53. #15692249C22semidirect
54. #15692248C22semidirect
55. #15692245C22semidirect
56. #15692245C22semidirect
57. #15692245C22semidirect
58. #15692244C22semidirect
59. #15692243C22semidirect
60. #15692241C22semidirect
61. #15692241C22semidirect
62. #15692241C22semidirect
63. #15692240C22semidirect
64. #15692240C22semidirect
65. #15692240C22semidirect
66. #15692240C22semidirect
67. #15692239C22semidirect
68. #15692239C22semidirect
69. #15692238C22semidirect
70. #15692237C22semidirect
71. #15692237C22semidirect
72. #15692237C22semidirect
73. #15692237C22semidirect
74. #15692236C22semidirect
75. #15692233C22semidirect
76. #15692233C22semidirect
77. #15692233C22semidirect
78. #15692232C22semidirect
79. #15692232C22semidirect
80. #15692231C22semidirect
81. #15692230C22semidirect
82. #15692230C22semidirect
83. #15692230C22semidirect
84. #15692230C22semidirect
85. #15692229C22semidirect
87. #15692228C22semidirect
88. #15692228C22semidirect
89. #15692228C22semidirect
90. #15692228C22semidirect
91. #15692228C22semidirect
92. #15692228C22semidirect
93. #15692228C22semidirect
94. #15692228C22semidirect
95. #15692228C22semidirect
96. #15692228C22semidirect
97. #15692228C22semidirect
98. #15692228C22semidirect
99. #15692228C22semidirect
100. #15692228C22semidirect
101. #15692228C22semidirect
102. #15692227C22semidirect
103. #15692227C22semidirect
104. #15692227C22semidirect
105. #15692227C22semidirect
106. #15692227C22semidirect
107. #15692227C22semidirect
108. #15692227C22semidirect
109. #15692227C22semidirect
110. #15692227C22semidirect
111. #15692226C22semidirect
112. #15692226C22semidirect
113. #15692225C22semidirect
114. #15692225C22semidirect
115. #15692225C22semidirect
116. #15692225C22semidirect
117. #15692225C22semidirect
118. #15692225C22semidirect
119. #15692223C22semidirect
120. #15692223C22semidirect
121. #15692223C22semidirect
122. #15692223C22semidirect
123. #15692220C22semidirect
124. C4×D404C22semidirect
125. C4×D404C22semidirect
126. C4×D404C22semidirect
127. D4×Dic101C22semidirect
128. D4×Dic101C22semidirect
129. #15692217C22semidirect
130. #15692217C22semidirect
131. #15692217C22semidirect
132. #15692217C22semidirect
135. C4×C22⋊D101C22semidirect
136. C4×C22⋊D101C22semidirect
137. C4×C22⋊D101C22semidirect
138. C4×C22⋊D101C22semidirect
139. C4×C22⋊D101C22semidirect
142. #15692215C22semidirect
143. #15692215C22semidirect
144. #15692215C22semidirect
145. #15692215C22semidirect
146. #15692215C22semidirect
147. #15692215C22semidirect
148. #15692215C22semidirect
149. #15692215C22semidirect
150. #15692215C22semidirect
151. #15692215C22semidirect
152. #15692215C22semidirect
153. #15692213C22semidirect
154. #15692212C22semidirect
155. #15692212C22semidirect
156. #15692211C22semidirect
157. #15692211C22semidirect
158. #15692211C22semidirect
159. C2×#13108053C22semidirect
160. C4⋊C4×D101C22semidirect
161. C4⋊C4×D101C22semidirect
162. C2×C22⋊Dic101C22semidirect
163. C2×#13108051C22semidirect
164. C2×#13108051C22semidirect
165. C22⋊C4×D101C22semidirect
166. C22⋊C4×D101C22semidirect
167. C22⋊C4×D101C22semidirect
168. C22⋊C4×D101C22semidirect
169. C22⋊C4×D101C22semidirect
170. C22⋊C4×D101C22semidirect
171. C42×D101C22semidirect
172. #126×C101C22semidirect
173. #126×C101C22semidirect
174. #124×C101C22semidirect
175. #124×C101C22semidirect
176. #123×C101C22semidirect
177. #123×C101C22semidirect
178. C22⋊Q8×C101C22semidirect
179. #121×C101C22semidirect
180. #121×C101C22semidirect
181. #121×C101C22semidirect
182. #120×C101C22semidirect
183. #120×C101C22semidirect
184. C4×D4×C101C22semidirect
185. C4×D4×C101C22semidirect
186. C2×C22⋊C4×C101C22semidirect
427. C22⋊D101#41semidirect
548. C101#3519semidirect
570. #538D101semidirect
603. #126C2×D101semidirect
604. #126C2×D101semidirect
613. #124C2×D101semidirect
614. #124C2×D101semidirect
627. #123C2×D101semidirect
628. #123C2×D101semidirect
635. C22⋊Q8C2×D101semidirect
668. #121C2×D101semidirect
669. #121C2×D101semidirect
670. #121C2×D101semidirect
681. #120C2×D101semidirect
682. #120C2×D101semidirect
713. C4×D4C2×D101semidirect
714. C4×D4C2×D101semidirect
733. C2×C22⋊C4C2×D101semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202658892
#202658812
#202658782
#202658722
#202658702
#202658452
#202658202
#202658192
#202658182
#202658162
#202658142
#202658112
#202658092
#202657792
#202657772
#202657662
#202657612
#202657602
#202657262
#202657102
#202656862
#202656852
C2×#156922282
#121×D1012
#202656502
#202656492
C4×D4×D1012
#538×C1012
#3519101