Finite Group Databasebeta

← #27185314

Subgroups — #27185314

Order 12928.

1166 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20265923C211yesmaximal, characteristic, complemented
2#20265921C211yesmaximal, characteristic, complemented
3#20265916C211yesmaximal, characteristic, complemented
4#20265915C211yesmaximal, characteristic, complemented
5#20265877C211yesmaximal, characteristic, complemented
6#20265872C211yesmaximal, characteristic, complemented
7#20265853C211yesmaximal, characteristic, complemented
8#20265850C211yesmaximal, characteristic, complemented
9#20265823C211yesmaximal, characteristic, complemented
10#20265817C211yesmaximal, characteristic, complemented
11#20265816C211yesmaximal, characteristic, complemented
12#20265815C211yesmaximal, characteristic, complemented
13#20265814C211yesmaximal, characteristic, complemented
14#20265811C211yesmaximal, characteristic, complemented
15D4×C22⋊D101C211yesmaximal, characteristic, complemented
16#20265779C211yesmaximal, characteristic, complemented
17#20265777C211yesmaximal, characteristic, complemented
18#20265773C211yesmaximal, characteristic, complemented
19#20265772C211yesmaximal, characteristic, complemented
20#20265769C211yesmaximal, characteristic, complemented
21#20265765C211yesmaximal, characteristic, complemented
22#20265761C211yesmaximal, characteristic, complemented
23#20265760C211yesmaximal, characteristic, complemented
24#20265756C211yesmaximal, characteristic, complemented
25#20265737C211yesmaximal, characteristic, complemented
26#20265737C211yesmaximal, characteristic, complemented
27#20265736C211yesmaximal, characteristic, complemented
28#20265684C211yesmaximal, characteristic, complemented
29#123×D101C211yesmaximal, characteristic, complemented
30C2×#15692228C211yesmaximal, characteristic, complemented
31#546×C101C211yesmaximal, characteristic, complemented
32C2×#13108074C2211yescharacteristic, complemented
33C2×#13108073C2211yescharacteristic, complemented
34C22×D404C2211yescharacteristic, complemented
35C22×C22⋊D101C2211yescharacteristic, complemented
36C22×C22⋊D101C2211yescharacteristic, complemented
37C22×C22⋊D101C2211yescharacteristic, complemented
38C2×D4×D101C2211yescharacteristic
39C2×D4×D101C2211yescharacteristic, complemented
40C2×D4×D101C2211yescharacteristic, complemented
41C22×C4×D101C2211yescharacteristic, complemented
42#15692251C2211yescharacteristic, complemented
43#15692251C2211yescharacteristic, complemented
44#15692250C2211yescharacteristic, complemented
45#15692250C2211yescharacteristic, complemented
46#15692249C2211yescharacteristic, complemented
47#15692248C2211yescharacteristic, complemented
48#15692248C2211yescharacteristic, complemented
49#15692248C2211yescharacteristic, complemented
50#15692248C2211yescharacteristic, complemented
51#15692248C2211yescharacteristic, complemented
52#15692247C2211yescharacteristic, complemented
53#15692245C2211yescharacteristic, complemented
54#15692245C2211yescharacteristic, complemented
55#15692245C2211yescharacteristic, complemented
56#15692244C2211yescharacteristic, complemented
57#15692243C2211yescharacteristic, complemented
58#15692241C2211yescharacteristic, complemented
59#15692241C2211yescharacteristic, complemented
60#15692241C2211yescharacteristic, complemented
61#15692240C2211yescharacteristic, complemented
62#15692240C2211yescharacteristic, complemented
63#15692240C2211yescharacteristic, complemented
64#15692240C2211yescharacteristic, complemented
65#15692239C2211yescharacteristic, complemented
66#15692239C2211yescharacteristic, complemented
67#15692239C2211yescharacteristic, complemented
68#15692239C2211yescharacteristic, complemented
69#15692238C2211yescharacteristic, complemented
70#15692238C2211yescharacteristic, complemented
71#15692238C2211yescharacteristic, complemented
72#15692238C2211yescharacteristic, complemented
73#15692238C2211yescharacteristic, complemented
74#15692237C2211yescharacteristic, complemented
75#15692237C2211yescharacteristic, complemented
76#15692237C2211yescharacteristic, complemented
77#15692237C2211yescharacteristic, complemented
78#15692237C2211yescharacteristic, complemented
79#15692237C2211yescharacteristic, complemented
80#15692237C2211yescharacteristic, complemented
81#15692237C2211yescharacteristic, complemented
82#15692236C2211yescharacteristic, complemented
83#15692236C2211yescharacteristic, complemented
84#15692236C2211yescharacteristic, complemented
85#15692236C2211yescharacteristic, complemented
86#15692236C2211yescharacteristic, complemented
87#15692235C2211yescharacteristic, complemented
88#15692234C2211yescharacteristic, complemented
89#15692234C2211yescharacteristic, complemented
90#15692233C2211yescharacteristic, complemented
91#15692232C2211yescharacteristic, complemented
92#15692232C2211yescharacteristic, complemented
93#15692232C2211yescharacteristic, complemented
94#15692232C2211yescharacteristic, complemented
95#15692231C2211yescharacteristic, complemented
96#15692231C2211yescharacteristic, complemented
97#15692231C2211yescharacteristic, complemented
98#15692230C2211yescharacteristic, complemented
99#15692229C2211yescharacteristic, complemented
100#15692229C2211yescharacteristic, complemented
101#15692229C2211yescharacteristic, complemented
102#15692228C2211yescharacteristic
103#15692228C2211yescharacteristic, complemented
104#15692228C2211yescharacteristic, complemented
105#15692228C2211yescharacteristic, complemented
106#15692228C2211yescharacteristic, complemented
107#15692228C2211yescharacteristic, complemented
108#15692228C2211yescharacteristic, complemented
109#15692228C2211yescharacteristic, complemented
110#15692228C2211yescharacteristic, complemented
111#15692228C2211yescharacteristic, complemented
112#15692228C2211yescharacteristic, complemented
113#15692228C2211yescharacteristic, complemented
114#15692228C2211yescharacteristic, complemented
115#15692228C2211yescharacteristic, complemented
116#15692227C2211yescharacteristic
117#15692227C2211yescharacteristic, complemented
118#15692227C2211yescharacteristic, complemented
119#15692227C2211yescharacteristic, complemented
120#15692227C2211yescharacteristic, complemented
121#15692227C2211yescharacteristic, complemented
122#15692227C2211yescharacteristic, complemented
123#15692227C2211yescharacteristic, complemented
124#15692227C2211yescharacteristic, complemented
125#15692226C2211yescharacteristic, complemented
126#15692226C2211yescharacteristic, complemented
127#15692226C2211yescharacteristic, complemented
128#15692226C2211yescharacteristic, complemented
129#15692226C2211yescharacteristic, complemented
130#15692226C2211yescharacteristic, complemented
131#15692225C2211yescharacteristic, complemented
132#15692225C2211yescharacteristic, complemented
133#15692224C2211yescharacteristic
134#15692224C2211yescharacteristic, complemented
135#15692224C2211yescharacteristic, complemented
136#15692224C2211yescharacteristic, complemented
137#15692223C2211yescharacteristic
138#15692223C2211yescharacteristic, complemented
139#15692223C2211yescharacteristic, complemented
140#15692223C2211yescharacteristic, complemented
141#15692223C2211yescharacteristic, complemented
142#15692223C2211yescharacteristic, complemented
143#15692223C2211yescharacteristic, complemented
144#15692223C2211yescharacteristic, complemented
145C4×D404C2211yescharacteristic, complemented
146D4×Dic101C2211yescharacteristic, complemented
147D4×Dic101C2211yescharacteristic, complemented
148#15692217C2211yescharacteristic, complemented
149C4×C22⋊D101C2211yescharacteristic, complemented
150C4×C22⋊D101C2211yescharacteristic, complemented
151C4×C22⋊D101C2211yescharacteristic, complemented
152C4×C22⋊D101C2211yescharacteristic, complemented
153C4×C22⋊D101C2211yescharacteristic, complemented
154C4×C22⋊D101C2211yescharacteristic, complemented
155C4×C22⋊D101C2211yescharacteristic, complemented
156#15692215C2211yescharacteristic, complemented
157#15692215C2211yescharacteristic, complemented
158#15692215C2211yescharacteristic, complemented
159#15692214C2211yescharacteristic, complemented
160#15692213C2211yescharacteristic, complemented
161#15692211C2211yescharacteristic, complemented
162C2×#13108053C2211yescharacteristic, complemented
163C4⋊C4×D101C2211yescharacteristic, complemented
164C4⋊C4×D101C2211yescharacteristic, complemented
165C2×C22⋊Dic101C2211yescharacteristic, complemented
166C2×#13108051C2211yescharacteristic, complemented
167C2×#13108051C2211yescharacteristic, complemented
168C22⋊C4×D101C2211yescharacteristic, complemented
169C22⋊C4×D101C2211yescharacteristic, complemented
170C22⋊C4×D101C2211yescharacteristic, complemented
171C22⋊C4×D101C2211yescharacteristic, complemented
172C2×#41×C101C2211yescharacteristic, complemented
173C22×D4×C101C2211yescharacteristic, complemented
174#124×C101C2211yescharacteristic, complemented
175#123×C101C2211yescharacteristic, complemented
176#123×C101C2211yescharacteristic, complemented
177C22⋊Q8×C101C2211yescharacteristic, complemented
178#121×C101C2211yescharacteristic
179#121×C101C2211yescharacteristic, complemented
180#121×C101C2211yescharacteristic, complemented
181#120×C101C2211yescharacteristic, complemented
182#120×C101C2211yescharacteristic, complemented
183C4×D4×C101C2211yescharacteristic, complemented
184C4×D4×C101C2211yescharacteristic, complemented
185C2×C22⋊C4×C101C2211yescharacteristic, complemented
186C2×C22⋊C4×C101C2211yescharacteristic, complemented
187C23×D101C2311yescharacteristic
188C23×D101C2311yescharacteristic
189C23×D101C2311yescharacteristic
190C23×D101C2311yescharacteristic
191#13108074—42no—
192#13108073—42no—
193C2×Dic202C2311yescharacteristic
194C2×Dic202C2311yescharacteristic
195C2×D404—42no—
196C2×D404C2311yescharacteristic
197C2×D404C2311yescharacteristic
198C2×D404C2311yescharacteristic
199C2×D404C2311yescharacteristic
200C2×D404C2311yescharacteristic
201C2×D404C2311yescharacteristic
202C2×C22⋊D101—42no—
203C2×C22⋊D101—42no—
204C2×C22⋊D101—42no—
205C2×C22⋊D101C2311yescharacteristic
206C2×C22⋊D101C2311yescharacteristic
207C2×C22⋊D101C2311yescharacteristic
208C2×C22⋊D101C2311yescharacteristic
209C2×C22⋊D101C2311yescharacteristic
210C2×C22⋊D101C2311yescharacteristic
211C2×C22⋊D101C2311yescharacteristic
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
227D4×D101—42no—
228D4×D101—42no—
229D4×D101—42no—
230C22×Dic101C2311yescharacteristic
231C22×Dic101C2311yescharacteristic
232C22×Dic101C2311yescharacteristic
233C22×Dic101C2311yescharacteristic
234C22×Dic101C2311yescharacteristic
235C22×Dic101C2311yescharacteristic
236C2×C4×D101—42no—
237C2×C4×D101C2311yescharacteristic
238C2×C4×D101C2311yescharacteristic
239C2×C4×D101C2311yescharacteristic
240C2×C4×D101C2311yescharacteristic
241C2×C4×D101C2311yescharacteristic
242C2×C4×D101C2311yescharacteristic
243C2×C4×D101C2311yescharacteristic
244C2×C4×D101C2311yescharacteristic
245C2×C4×D101C2311yescharacteristic
246C2×C4×D101C2311yescharacteristic
247C2×C4×D101C2311yescharacteristic
248C4⋊Dic101C2311yescharacteristic
249C4⋊Dic101C2311yescharacteristic
250C4⋊Dic101C2311yescharacteristic
251C4⋊Dic101C2311yescharacteristic
252C4⋊Dic101C2311yescharacteristic
253C4⋊Dic101C2311yescharacteristic
254C4⋊Dic101C2311yescharacteristic
255C4⋊Dic101C2311yescharacteristic
256#13108053C2311yescharacteristic
257#13108053C2311yescharacteristic
258#13108053C2311yescharacteristic
259#13108053C2311yescharacteristic
260#13108053C2311yescharacteristic
261#13108053C2311yescharacteristic
262#13108053C2311yescharacteristic
263#13108053C2311yescharacteristic
264#13108053C2311yescharacteristic
265#13108053C2311yescharacteristic
266#13108053C2311yescharacteristic
267#13108053C2311yescharacteristic
268#13108053C2311yescharacteristic
269#13108053C2311yescharacteristic
270#13108053C2311yescharacteristic
271#13108053C2311yescharacteristic
272#13108053C2311yescharacteristic
273#13108053C2311yescharacteristic
274C22⋊Dic101C2311yescharacteristic
275C22⋊Dic101C2311yescharacteristic
276C22⋊Dic101C2311yescharacteristic
277C22⋊Dic101C2311yescharacteristic
278C22⋊Dic101C2311yescharacteristic
279C22⋊Dic101C2311yescharacteristic
280C22⋊Dic101C2311yescharacteristic
281C22⋊Dic101C2311yescharacteristic
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
312C4×Dic101C2311yescharacteristic
313C4×Dic101C2311yescharacteristic
314C4×Dic101C2311yescharacteristic
315C4×Dic101C2311yescharacteristic
316C4×Dic101C2311yescharacteristic
317C24×C101C2311yescharacteristic
318C24×C101C2311yescharacteristic
319#41×C101—42no—
320C2×Q8×C101C2311yescharacteristic
321C2×D4×C101—42no—
322C2×D4×C101C2311yescharacteristic
323C2×D4×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
335C22×C4×C101C2311yescharacteristic
336C22×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
353C42×C101C2311yescharacteristic
354C23×C101—22no—
355C23×C101—41no—
356C23×C101—41no—
357C23×C101—41no—
358C23×C101—41no—
359C23×C101—41no—
360C23×C101C2411yescharacteristic
361C23×C101C2411yescharacteristic
362C23×C101C2411yescharacteristic
363C23×C101C2411yescharacteristic
364C23×C101C2411yescharacteristic
365C23×C101C2411yescharacteristic
366C22×D101—22no—
367C22×D101—22no—
368C22×D101—22no—
369C22×D101—22no—
370C22×D101—41no—
371C22×D101—41no—
372C22×D101—41no—
373C22×D101—41no—
374C22×D101—41no—
375C22×D101—41no—
376C22×D101—41no—
377C22×D101—41no—
378C22×D101C2411yescharacteristic
379C22×D101C2411yescharacteristic
380C22×D101C2411yescharacteristic
381C22×D101C2411yescharacteristic
382C22×D101C2411yescharacteristic
383Q8×C101—41no—
384D4×C101—22no—
385D4×C101—22no—
386D4×C101—22no—
387D4×C101—41no—
388D4×C101—41no—
389D4×C101—41no—
390D4×C101—41no—
391D4×C101—41no—
392D4×C101—41no—
393C2×C4×C101—22no—
394C2×C4×C101—41no—
395C2×C4×C101—41no—
396C2×C4×C101—41no—
397C2×C4×C101—41no—
398C2×C4×C101—41no—
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—41no—
414C22⋊D101—41no—
415C22⋊D101—41no—
416C22⋊D101—41no—
417C22⋊D101—41no—
418C22⋊D101—41no—
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—41no—
428C22⋊D101—41no—
429C22⋊D101—41no—
430C2×Dic101—22no—
431C2×Dic101—41no—
432C2×Dic101—41no—
433C2×Dic101—41no—
434C2×Dic101—41no—
435C2×Dic101—41no—
436C2×Dic101C2411yescharacteristic
437C2×Dic101C2411yescharacteristic
438C2×Dic101C2411yescharacteristic
439C2×Dic101C2411yescharacteristic
440C2×Dic101C2411yescharacteristic
441C2×Dic101C2411yescharacteristic
442C2×Dic101C2411yescharacteristic
443C2×Dic101C2411yescharacteristic
444C2×Dic101C2411yescharacteristic
445C2×Dic101C2411yescharacteristic
446C2×Dic101C2411yescharacteristic
447D404—22no—
448D404—22no—
449D404—41no—
450D404—41no—
451D404—41no—
452D404—41no—
453C4×D101—22no—
454C4×D101—41no—
455C4×D101—41no—
456C4×D101—41no—
457C4×D101—41no—
458C4×D101—41no—
459C4×D101—41no—
460C4×D101—41no—
461C4×D101—41no—
462C4×D101—41no—
463C4×D101—41no—
464Dic202—41no—
465Dic202—41no—
466C22×C101—21no—
467C22×C101—21no—
468C22×C101—21no—
469C22×C101—21no—
470C22×C101—21no—
471C22×C101—21no—
472C22×C101—21no—
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—82no—
484C22×C101—82no—
485C22×C101H(5,𝔽2)12yes—
486C22×C101C2511yescharacteristic
487C2×D101—21no—
488C2×D101—21no—
489C2×D101—21no—
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—44no—
502C2×D101—82no—
503C2×D101—82no—
504C2×D101—82no—
505C2×D101H(5,𝔽2)12yes—
506C4×C101—21no—
507C4×C101—21no—
508C4×C101—21no—
509C4×C101—21no—
510C4×C101—21no—
511C4×C101—21no—
512C4×C101—21no—
513C4×C101—21no—
514C4×C101—21no—
515Dic101—21no—
516Dic101—21no—
517Dic101—21no—
518Dic101—21no—
519Dic101—21no—
520Dic101—21no—
521Dic101—21no—
522Dic101—21no—
523Dic101—21no—
524Dic101—21no—
525Dic101—21no—
526C2×C101—22no—
527C2×C101—41no—
528C2×C101—41no—
529C2×C101—41no—
530C2×C101—41no—
531C2×C101—41no—
532C2×C101C2×H(5,𝔽2)11yescharacteristic
533C2×C101C2×H(5,𝔽2)11yescharacteristic
534C2×C101#58511yescharacteristic
535D101—22no—
536D101—41no—
537D101—41no—
538D101—41no—
539D101—41no—
540#3534—1011nomaximal, Sylow
541C101#353411yescharacteristic, complemented, Sylow
542#562—1011no—
543#562—1011no—
544#560—1011no—
545#560—1011no—
546#553—1011no—
547#553—1011no—
548#551—1011no—
549#551—1011no—
550#546—1011no—
551#546—1011no—
552#546—1011no—
553#546—1011no—
554#546—1011no—
555#546D10111yescharacteristic, complemented
556D42—1011no—
557D42—1011no—
558#540—1011no—
559#540—1011no—
560#539—1011no—
561#539—1011no—
562#539—1011no—
563#538—1011no—
564#538—1011no—
565#538—1011no—
566#537—1011no—
567#534—1011no—
568#534—1011no—
569#534—1011no—
570#525—1011no—
571C2×#123—1011no—
572C2×#121—1011no—
573C2×#41—1011no—
574C2×#41—1011no—
575C2×#41C2×D10111yescharacteristic, complemented
576C22×D4—1011no—
577C22×D4—1011no—
578C22×D4—1011no—
579C22×D4—1011no—
580C22×D4—1011no—
581C22×D4—1011no—
582C22×D4—1011no—
583C22×D4C2×D10111yescharacteristic, complemented
584C23×C4—1011no—
585#127—1011no—
586#127—1011no—
587#126—1011no—
588#126—1011no—
589#126—1011no—
590#126—1011no—
591#126—1011no—
592#126—1011no—
593#126—1011no—
594#126—1011no—
595#125—1011no—
596#125—1011no—
597#125—1011no—
598#125—1011no—
599#124—1011no—
600#124—1011no—
601#124—1011no—
602#124—1011no—
603#124—1011no—
604#124C2×D10111yescharacteristic, complemented
605#123—1011no—
606#123—1011no—
607#123—1011no—
608#123—1011no—
609#123—1011no—
610#123—1011no—
611#123—1011no—
612#123—1011no—
613#123—1011no—
614#123—1011no—
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#123—1011no—
628#123—1011no—
629#123—1011no—
630#123—1011no—
631#123C2×D10111yescharacteristic, complemented
632#123C2×D10111yescharacteristic, complemented
633C22⋊Q8—1011no—
634C22⋊Q8—1011no—
635C22⋊Q8—1011no—
636C22⋊Q8—1011no—
637C22⋊Q8—1011no—
638C22⋊Q8—1011no—
639C22⋊Q8—1011no—
640C22⋊Q8—1011no—
641C22⋊Q8—1011no—
642C22⋊Q8—1011no—
643C22⋊Q8—1011no—
644C22⋊Q8C2×D10111yescharacteristic, complemented
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#121—1011no—
669#121—1011no—
670#121—1011no—
671#121—1011no—
672#121—1011no—
673#121—1011no—
674#121—1011no—
675#121—1011no—
676#121—1011no—
677#121—1011no—
678#121C2×D10111yescharacteristic
679#121C2×D10111yescharacteristic, complemented
680#121C2×D10111yescharacteristic, complemented
681#120—1011no—
682#120—1011no—
683#120—1011no—
684#120—1011no—
685#120—1011no—
686#120—1011no—
687#120—1011no—
688#120—1011no—
689#120—1011no—
690#120—1011no—
691#120—1011no—
692#120—1011no—
693#120—1011no—
694#120—1011no—
695#120C2×D10111yescharacteristic, complemented
696#120C2×D10111yescharacteristic, complemented
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×D4C2×D10111yescharacteristic, complemented
712C4×D4C2×D10111yescharacteristic, complemented
713#117—1011no—
714#117—1011no—
715#117—1011no—
716C2×C4⋊C4—1011no—
717C2×C4⋊C4—1011no—
718C2×C4⋊C4—1011no—
719C2×C22⋊C4—1011no—
720C2×C22⋊C4—1011no—
721C2×C22⋊C4—1011no—
722C2×C22⋊C4—1011no—
723C2×C22⋊C4—1011no—
724C2×C22⋊C4—1011no—
725C2×C22⋊C4—1011no—
726C2×C22⋊C4C2×D10111yescharacteristic, complemented
727C2×C22⋊C4C2×D10111yescharacteristic, complemented
728C24—1011no—
729C24—1011no—
730C24—1011no—
731C24—1011no—
732C24C22×D10111yescharacteristic
733C24C22×D10111yescharacteristic
734#41—42no—
735#41—4042no—
736#41—4042no—
737C2×Q8—1011no—
738C2×Q8—1011no—
739C2×Q8C22×D10111yescharacteristic
740C2×D4—42no—
741C2×D4—1011no—
742C2×D4—1011no—
743C2×D4—1011no—
744C2×D4—1011no—
745C2×D4—1011no—
746C2×D4—1011no—
747C2×D4—1011no—
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—4042no—
770C2×D4—4042no—
771C2×D4—4042no—
772C2×D4—4042no—
773C2×D4—4042no—
774C2×D4—4042no—
775C2×D4—4042no—
776C2×D4C22×D10111yescharacteristic
777C2×D4C22×D10111yescharacteristic
778C2×D4C22×D10111yescharacteristic
779C2×D4C22×D10111yescharacteristic
780C2×D4C22×D10111yescharacteristic
781C2×D4C22×D10111yescharacteristic
782C2×D4C22×D10111yescharacteristic
783C2×D4C22×D10111yescharacteristic
784C2×D4C22×D10111yescharacteristic
785C22×C4—1011no—
786C22×C4—1011no—
787C22×C4—1011no—
788C22×C4—1011no—
789C22×C4—1011no—
790C22×C4—1011no—
791C22×C4—1011no—
792C22×C4—1011no—
793C22×C4—1011no—
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—4042no—
803C22×C4C22×D10111yescharacteristic
804C22×C4C22×D10111yescharacteristic
805C22×C4C22×D10111yescharacteristic
806C22×C4C22×D10111yescharacteristic
807C22×C4C22×D10111yescharacteristic
808C22×C4C22×D10111yescharacteristic
809C4⋊C4—1011no—
810C4⋊C4—1011no—
811C4⋊C4—1011no—
812C4⋊C4—1011no—
813C4⋊C4—1011no—
814C4⋊C4—1011no—
815C4⋊C4—1011no—
816C4⋊C4—1011no—
817C4⋊C4—1011no—
818C4⋊C4—1011no—
819C4⋊C4—1011no—
820C4⋊C4—1011no—
821C4⋊C4—1011no—
822C4⋊C4—1011no—
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⋊C4C22×D10111yescharacteristic
836C4⋊C4C22×D10111yescharacteristic
837C4⋊C4C22×D10111yescharacteristic
838C4⋊C4C22×D10111yescharacteristic
839C22⋊C4—1011no—
840C22⋊C4—1011no—
841C22⋊C4—1011no—
842C22⋊C4—1011no—
843C22⋊C4—1011no—
844C22⋊C4—1011no—
845C22⋊C4—1011no—
846C22⋊C4—1011no—
847C22⋊C4—1011no—
848C22⋊C4—1011no—
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⋊C4C22×D10111yescharacteristic
878C22⋊C4C22×D10111yescharacteristic
879C22⋊C4C22×D10111yescharacteristic
880C22⋊C4C22×D10111yescharacteristic
881C22⋊C4C22×D10111yescharacteristic
882C22⋊C4C22×D10111yescharacteristic
883C22⋊C4C22×D10111yescharacteristic
884C22⋊C4C22×D10111yescharacteristic
885C22⋊C4C22×D10111yescharacteristic
886C22⋊C4C22×D10111yescharacteristic
887C22⋊C4C22×D10111yescharacteristic
888C22⋊C4C22×D10111yescharacteristic
889C42—1011no—
890C42—1011no—
891C42—1011no—
892C42—1011no—
893C42—1011no—
894C42C22×D10111yescharacteristic
895C23—22no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—1011no—
902C23—1011no—
903C23—1011no—
904C23—1011no—
905C23—1011no—
906C23—4041no—
907C23—4041no—
908C23—4041no—
909C23—4041no—
910C23—4041no—
911C23—4041no—
912C23—4041no—
913C23—4041no—
914C23—2022no—
915C23—2022no—
916C23—2022no—
917C23—2022no—
918C23C23×D10111yescharacteristic
919C23C23×D10111yescharacteristic
920C23C23×D10111yescharacteristic
921C23C23×D10111yescharacteristic
922C23C23×D10111yescharacteristic
923C23C23×D10111yescharacteristic
924Q8—41no—
925Q8—4041no—
926Q8—4041no—
927D4—22no—
928D4—22no—
929D4—22no—
930D4—41no—
931D4—41no—
932D4—41no—
933D4—41no—
934D4—41no—
935D4—41no—
936D4—4041no—
937D4—4041no—
938D4—4041no—
939D4—4041no—
940D4—4041no—
941D4—4041no—
942D4—4041no—
943D4—4041no—
944D4—4041no—
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—2022no—
958D4—2022no—
959D4—2022no—
960D4—2022no—
961D4—2022no—
962D4—2022no—
963D4—2022no—
964C2×C4—22no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—1011no—
971C2×C4—1011no—
972C2×C4—1011no—
973C2×C4—1011no—
974C2×C4—1011no—
975C2×C4—1011no—
976C2×C4—1011no—
977C2×C4—1011no—
978C2×C4—1011no—
979C2×C4—1011no—
980C2×C4—1011no—
981C2×C4—4041no—
982C2×C4—4041no—
983C2×C4—4041no—
984C2×C4—4041no—
985C2×C4—4041no—
986C2×C4—4041no—
987C2×C4—4041no—
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—2022no—
997C2×C4—2022no—
998C2×C4C23×D10111yescharacteristic
999C2×C4C23×D10111yescharacteristic
1000C2×C4C23×D10111yescharacteristic
1001C2×C4C23×D10111yescharacteristic
1002C2×C4C23×D10111yescharacteristic
1003C2×C4C23×D10111yescharacteristic
1004C2×C4C23×D10111yescharacteristic
1005C2×C4C23×D10111yescharacteristic
1006C2×C4C23×D10111yescharacteristic
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—21no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—21no—
1016C22—21no—
1017C22—21no—
1018C22—21no—
1019C22—21no—
1020C22—21no—
1021C22—21no—
1022C22—21no—
1023C22—21no—
1024C22—82no—
1025C22—82no—
1026C22—8082no—
1027C22—8082no—
1028C22—8082no—
1029C22—1012no—
1030C22—4044no—
1031C22—2021no—
1032C22—2021no—
1033C22—2021no—
1034C22—2021no—
1035C22—2021no—
1036C22—2021no—
1037C22—2021no—
1038C22—2021no—
1039C22—2021no—
1040C22—2021no—
1041C22—2021no—
1042C22—2021no—
1043C22—2021no—
1044C22—2021no—
1045C22#1569230012yes—
1046C22C24×D10111yescharacteristic
1047C4—21no—
1048C4—21no—
1049C4—21no—
1050C4—21no—
1051C4—21no—
1052C4—21no—
1053C4—21no—
1054C4—21no—
1055C4—21no—
1056C4—2021no—
1057C4—2021no—
1058C4—2021no—
1059C4—2021no—
1060C4—2021no—
1061C4—2021no—
1062C4—2021no—
1063C4—2021no—
1064C4—2021no—
1065C4—2021no—
1066C4—2021no—
1067C2—22no—
1068C2—41no—
1069C2—41no—
1070C2—41no—
1071C2—41no—
1072C2—41no—
1073C2—4041no—
1074C2—4041no—
1075C2—4041no—
1076C2—4041no—
1077C2—2022no—
1078C2H(5,𝔽2)×D10111yescharacteristic
1079C2C2×#1569230011yescharacteristic
1080C2#2026601311yescharacteristic
subgroupG/H
center, FrattiniC22C24×D101
commutator, socle, cosocleC22×C101C25
Fitting#546×C101C2
hypercenter#546D101
hypocenterC101#3534
LCSG ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #20265923C2semidirect
2. #20265921C2semidirect
3. #20265916C2semidirect
4. #20265915C2semidirect
5. #20265877C2semidirect
6. #20265872C2semidirect
7. #20265853C2semidirect
8. #20265850C2semidirect
9. #20265823C2semidirect
10. #20265817C2semidirect
11. #20265816C2semidirect
12. #20265815C2semidirect
13. #20265814C2semidirect
14. #20265811C2semidirect
15. D4×C22⋊D101C2semidirect
16. #20265779C2semidirect
17. #20265777C2semidirect
18. #20265773C2semidirect
19. #20265772C2semidirect
20. #20265769C2semidirect
21. #20265765C2semidirect
22. #20265761C2semidirect
23. #20265760C2semidirect
24. #20265756C2semidirect
25. #20265737C2semidirect
26. #20265737C2semidirect
27. #20265736C2semidirect
28. #20265684C2semidirect
29. #123×D101C2semidirect
30. C2×#15692228C2semidirect
31. #546×C101C2semidirect
32. C2×#13108074C22semidirect
33. C2×#13108073C22semidirect
34. C22×D404C22semidirect
35. C22×C22⋊D101C22semidirect
36. C22×C22⋊D101C22semidirect
37. C22×C22⋊D101C22semidirect
39. C2×D4×D101C22semidirect
40. C2×D4×D101C22semidirect
41. C22×C4×D101C22semidirect
42. #15692251C22semidirect
43. #15692251C22semidirect
44. #15692250C22semidirect
45. #15692250C22semidirect
46. #15692249C22semidirect
47. #15692248C22semidirect
48. #15692248C22semidirect
49. #15692248C22semidirect
50. #15692248C22semidirect
51. #15692248C22semidirect
52. #15692247C22semidirect
53. #15692245C22semidirect
54. #15692245C22semidirect
55. #15692245C22semidirect
56. #15692244C22semidirect
57. #15692243C22semidirect
58. #15692241C22semidirect
59. #15692241C22semidirect
60. #15692241C22semidirect
61. #15692240C22semidirect
62. #15692240C22semidirect
63. #15692240C22semidirect
64. #15692240C22semidirect
65. #15692239C22semidirect
66. #15692239C22semidirect
67. #15692239C22semidirect
68. #15692239C22semidirect
69. #15692238C22semidirect
70. #15692238C22semidirect
71. #15692238C22semidirect
72. #15692238C22semidirect
73. #15692238C22semidirect
74. #15692237C22semidirect
75. #15692237C22semidirect
76. #15692237C22semidirect
77. #15692237C22semidirect
78. #15692237C22semidirect
79. #15692237C22semidirect
80. #15692237C22semidirect
81. #15692237C22semidirect
82. #15692236C22semidirect
83. #15692236C22semidirect
84. #15692236C22semidirect
85. #15692236C22semidirect
86. #15692236C22semidirect
87. #15692235C22semidirect
88. #15692234C22semidirect
89. #15692234C22semidirect
90. #15692233C22semidirect
91. #15692232C22semidirect
92. #15692232C22semidirect
93. #15692232C22semidirect
94. #15692232C22semidirect
95. #15692231C22semidirect
96. #15692231C22semidirect
97. #15692231C22semidirect
98. #15692230C22semidirect
99. #15692229C22semidirect
100. #15692229C22semidirect
101. #15692229C22semidirect
103. #15692228C22semidirect
104. #15692228C22semidirect
105. #15692228C22semidirect
106. #15692228C22semidirect
107. #15692228C22semidirect
108. #15692228C22semidirect
109. #15692228C22semidirect
110. #15692228C22semidirect
111. #15692228C22semidirect
112. #15692228C22semidirect
113. #15692228C22semidirect
114. #15692228C22semidirect
115. #15692228C22semidirect
117. #15692227C22semidirect
118. #15692227C22semidirect
119. #15692227C22semidirect
120. #15692227C22semidirect
121. #15692227C22semidirect
122. #15692227C22semidirect
123. #15692227C22semidirect
124. #15692227C22semidirect
125. #15692226C22semidirect
126. #15692226C22semidirect
127. #15692226C22semidirect
128. #15692226C22semidirect
129. #15692226C22semidirect
130. #15692226C22semidirect
131. #15692225C22semidirect
132. #15692225C22semidirect
134. #15692224C22semidirect
135. #15692224C22semidirect
136. #15692224C22semidirect
138. #15692223C22semidirect
139. #15692223C22semidirect
140. #15692223C22semidirect
141. #15692223C22semidirect
142. #15692223C22semidirect
143. #15692223C22semidirect
144. #15692223C22semidirect
145. C4×D404C22semidirect
146. D4×Dic101C22semidirect
147. D4×Dic101C22semidirect
148. #15692217C22semidirect
149. C4×C22⋊D101C22semidirect
150. C4×C22⋊D101C22semidirect
151. C4×C22⋊D101C22semidirect
152. C4×C22⋊D101C22semidirect
153. C4×C22⋊D101C22semidirect
154. C4×C22⋊D101C22semidirect
155. C4×C22⋊D101C22semidirect
156. #15692215C22semidirect
157. #15692215C22semidirect
158. #15692215C22semidirect
159. #15692214C22semidirect
160. #15692213C22semidirect
161. #15692211C22semidirect
162. C2×#13108053C22semidirect
163. C4⋊C4×D101C22semidirect
164. C4⋊C4×D101C22semidirect
165. C2×C22⋊Dic101C22semidirect
166. C2×#13108051C22semidirect
167. C2×#13108051C22semidirect
168. C22⋊C4×D101C22semidirect
169. C22⋊C4×D101C22semidirect
170. C22⋊C4×D101C22semidirect
171. C22⋊C4×D101C22semidirect
172. C2×#41×C101C22semidirect
173. C22×D4×C101C22semidirect
174. #124×C101C22semidirect
175. #123×C101C22semidirect
176. #123×C101C22semidirect
177. C22⋊Q8×C101C22semidirect
179. #121×C101C22semidirect
180. #121×C101C22semidirect
181. #120×C101C22semidirect
182. #120×C101C22semidirect
183. C4×D4×C101C22semidirect
184. C4×D4×C101C22semidirect
185. C2×C22⋊C4×C101C22semidirect
186. C2×C22⋊C4×C101C22semidirect
541. C101#3534semidirect
555. #546D101semidirect
575. C2×#41C2×D101semidirect
583. C22×D4C2×D101semidirect
604. #124C2×D101semidirect
631. #123C2×D101semidirect
632. #123C2×D101semidirect
644. C22⋊Q8C2×D101semidirect
679. #121C2×D101semidirect
680. #121C2×D101semidirect
695. #120C2×D101semidirect
696. #120C2×D101semidirect
711. C4×D4C2×D101semidirect
712. C4×D4C2×D101semidirect
726. C2×C22⋊C4C2×D101semidirect
727. C2×C22⋊C4C2×D101semidirect

Maximal subgroups

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

subgroupindex
#202659232
#202659212
#202659162
#202659152
#202658772
#202658722
#202658532
#202658502
#202658232
#202658172
#202658162
#202658152
#202658142
#202658112
D4×C22⋊D1012
#202657792
#202657772
#202657732
#202657722
#202657692
#202657652
#202657612
#202657602
#202657562
#202657372
#202657362
#202656842
#123×D1012
C2×#156922282
#546×C1012
#3534101