Finite Group Databasebeta

← #26379066

Subgroups — #26379066

Order 12032.

2586 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689630C211yesmaximal, characteristic
2#20246549C212yesmaximal, complemented
3#20246540C212yesmaximal, complemented
4#20246467C212yesmaximal, complemented
5#20246437C212yesmaximal, complemented
6#20246338C211yesmaximal, characteristic, complemented
7#20246332C211yesmaximal, characteristic, complemented
8#20246319C211yesmaximal, characteristic, complemented
9#20246318C211yesmaximal, characteristic, complemented
10#20246313C211yesmaximal, characteristic, complemented
11#20246310C211yesmaximal, characteristic, complemented
12C4⋊C4×C22⋊D47C211yesmaximal, characteristic, complemented
13#20246284C211yesmaximal, characteristic, complemented
14#20246179C212yesmaximal, complemented
15#20246175C212yesmaximal, complemented
16#20246047C212yesmaximal, complemented
17#20246044C212yesmaximal, complemented
18#20245995C211yesmaximal, characteristic, complemented
19#20245995C211yesmaximal, characteristic, complemented
20#20245980C211yesmaximal, characteristic, complemented
21#20245770C211yesmaximal, characteristic, complemented
22#380×D47C211yesmaximal, characteristic, complemented
23C47×#2311C211yesmaximal, characteristic, complemented
24C23×C4×D47C2211yescharacteristic
25#15689630C4116yescomplemented
26C2×#13094005C2211yescharacteristic
27C2×#13094005C2211yescharacteristic
28C2×#13094000C2211yescharacteristic
29C2×#13094000C2211yescharacteristic
30C2×#13093995C2211yescharacteristic
31C2×#13093995C2211yescharacteristic
32C2×#13093992C2211yescharacteristic
33C2×#13093992C2211yescharacteristic
34C2×C4×C22⋊D47C2212yes—
35C2×C4×C22⋊D47C2211yescharacteristic
36C2×C4×C22⋊D47C2211yescharacteristic
37C2×C4×C22⋊D47C2211yescharacteristic
38C2×C4×C22⋊D47C2211yescharacteristic
39C2×(C22⋊D47)⋊C4C2212yes—
40C2×#13093983C2211yescharacteristic
41C2×#13093983C2211yescharacteristic, complemented
42C2×#13093982C2211yescharacteristic
43C2×#13093982C2211yescharacteristic
44C22×C4⋊Dic47C2211yescharacteristic, complemented
45C2×C4⋊C4×D47C2211yescharacteristic
46C2×C4⋊C4×D47C2211yescharacteristic
47C2×C22⋊C4×D47C2212yes—
48#15689030C2212yescomplemented
49#15689026C2212yes—
50#15689023C2212yes—
51#15689023C2212yes—
52#15689020C2212yescomplemented
53#15689018C2212yescomplemented
54#15689017C2212yes—
55#15689017C2212yes—
56#15689017C2212yescomplemented
57#15689017C2212yescomplemented
58#15689015C2212yes—
59#15689014C2212yes—
60#15689013C2212yes—
61#15689012C2212yes—
62#15689011C2212yes—
63#15689011C2212yes—
64#15689011C2212yescomplemented
65#15689011C2212yescomplemented
66#15689010C2212yescomplemented
67#15689008C2212yescomplemented
68#15689008C2212yescomplemented
69#15689007C2212yescomplemented
70#15689006C2212yescomplemented
71#15689006C2212yescomplemented
72#15689005C2212yescomplemented
73#15689004C2212yescomplemented
74#15689003C2212yes—
75#15689003C2212yescomplemented
76#15689002C2212yes—
77#15689000C2212yes—
78#15688999C2212yes—
79#15688999C2212yes—
80#15688997C2212yes—
81#15688996C2212yescomplemented
82#15688995C2212yescomplemented
83#15688994C2212yes—
84#15688992C2211yescharacteristic, complemented
85#15688992C2211yescharacteristic, complemented
86#15688988C2211yescharacteristic, complemented
87#15688988C2211yescharacteristic, complemented
88#15688985C2212yes—
89#15688983C2211yescharacteristic
90#15688983C2211yescharacteristic
91#15688983C2211yescharacteristic, complemented
92#15688983C2211yescharacteristic, complemented
93#15688982C2212yes—
94#15688981C2212yes—
95#15688980C2211yescharacteristic
96#15688980C2211yescharacteristic
97#15688980C2211yescharacteristic
98#15688980C2211yescharacteristic
99#15688978C2212yes—
100C4⋊C4×Dic47C2211yescharacteristic, complemented
101C4⋊C4×Dic47C2211yescharacteristic, complemented
102C4⋊C4×Dic47C2211yescharacteristic, complemented
103C4⋊C4×Dic47C2211yescharacteristic, complemented
104C4×Dic47⋊C4C2212yescomplemented
105#15688974C2212yescomplemented
106C22⋊C4×Dic47C2212yes—
107C22⋊C4×Dic47C2212yescomplemented
108C4×(C2×D47)⋊C4C2212yes—
109C4×C22⋊Dic47C2212yescomplemented
110#15688970C2212yes—
111#15688970C2212yes—
112#95×D47C2212yes—
113C22×#41×C47C2211yescharacteristic
114C2×#117×C47C2211yescharacteristic, complemented
115C22×C4⋊C4×C47C2211yescharacteristic, complemented
116C47×#391C2212yescomplemented
117C47×#390C2212yes—
118C47×#386C2212yes—
119C47×#386C2212yescomplemented
120C47×#380C2211yescharacteristic
121C47×#380C2211yescharacteristic
122C47×#380C2211yescharacteristic, complemented
123C47×#380C2211yescharacteristic, complemented
124C24×D47C2311yescharacteristic
125C22×C22⋊D47C2311yescharacteristic
126C22×C22⋊D47C2311yescharacteristic
127C22×C22⋊D47C2311yescharacteristic
128C22×C22⋊D47C2311yescharacteristic
129C23×Dic47C2312yes—
130C23×Dic47C2311yescharacteristic
131C22×C4×D47—42no—
132C22×C4×D47—42no—
133C22×C4×D47C2×C418yescomplemented
134C22×C4×D47C2311yescharacteristic
135C22×C4×D47C2311yescharacteristic
136C22×C4×D47C2312yes—
137C22×C4×D47C2312yes—
138C22×C4×D47C2311yescharacteristic
139C22×C4×D47C2311yescharacteristic
140#13094005C2×C418yescomplemented
141#13094005C2×C418yescomplemented
142#13094000C2×C418yescomplemented
143#13094000C2×C418yescomplemented
144#13093995C2×C418yes—
145#13093995C2×C418yescomplemented
146#13093992C2×C418yescomplemented
147#13093992C2×C418yescomplemented
148C4×C22⋊D47—44no—
149C4×C22⋊D47C2×C418yescomplemented
150C4×C22⋊D47C2×C418yescomplemented
151C4×C22⋊D47C2×C418yescomplemented
152C4×C22⋊D47C2×C418yescomplemented
153(C22⋊D47)⋊C4—44no—
154#13093983—42no—
155#13093983C2×C418yescomplemented
156#13093982—42no—
157#13093982—42no—
158C2×C4⋊Dic47—42no—
159C2×C4⋊Dic47C2311yescharacteristic
160C2×C4⋊Dic47C2311yescharacteristic
161C2×C4⋊Dic47C2311yescharacteristic
162C2×C4⋊Dic47C2311yescharacteristic
163C2×C4⋊Dic47C2312yes—
164C2×C4⋊Dic47C2311yescharacteristic
165C2×C4⋊Dic47C2311yescharacteristic
166C2×Dic47⋊C4C2312yes—
167C2×Dic47⋊C4C2312yes—
168C2×Dic47⋊C4C2312yes—
169C2×Dic47⋊C4C2312yes—
170C2×Dic47⋊C4C2312yes—
171C2×Dic47⋊C4C2312yes—
172C2×Dic47⋊C4C2311yescharacteristic
173C2×Dic47⋊C4C2311yescharacteristic
174C2×Dic47⋊C4C2311yescharacteristic
175C2×Dic47⋊C4C2311yescharacteristic
176C4⋊C4×D47—42no—
177C4⋊C4×D47—42no—
178C2×C22⋊Dic47C2312yes—
179C2×C22⋊Dic47C2312yes—
180C2×C22⋊Dic47C2312yes—
181C2×C22⋊Dic47C2312yes—
182C2×C22⋊Dic47C2312yes—
183C2×C22⋊Dic47C2311yescharacteristic
184C2×C22⋊Dic47C2311yescharacteristic
185C2×C22⋊Dic47C2311yescharacteristic
186C2×C22⋊Dic47C2311yescharacteristic
187C2×C22⋊Dic47C2311yescharacteristic
188C2×C22⋊Dic47C2311yescharacteristic
189C2×(C2×D47)⋊C4C2312yes—
190C2×(C2×D47)⋊C4C2312yes—
191C2×(C2×D47)⋊C4C2312yes—
192C2×(C2×D47)⋊C4C2312yes—
193C2×(C2×D47)⋊C4C2312yes—
194C2×(C2×D47)⋊C4C2312yes—
195C2×(C2×D47)⋊C4C2311yescharacteristic
196C2×(C2×D47)⋊C4C2311yescharacteristic
197C2×(C2×D47)⋊C4C2311yescharacteristic
198C2×(C2×D47)⋊C4C2311yescharacteristic
199C22⋊C4×D47—44no—
200C2×C4×Dic47C2312yes—
201C2×C4×Dic47C2312yes—
202C2×C4×Dic47C2312yes—
203C2×C4×Dic47C2312yes—
204C2×C4×Dic47C2312yes—
205C2×C4×Dic47C2312yes—
206C2×C4×Dic47C2312yes—
207C2×C4×Dic47C2311yescharacteristic
208C2×C4×Dic47C2311yescharacteristic
209C47⋊#95C2312yes—
210C47⋊#95C2312yes—
211C47⋊#95C2312yes—
212C47⋊#95C2312yes—
213C47⋊#95C2312yes—
214C47⋊#95C2312yes—
215C47⋊#95C2312yes—
216C47⋊#95C2312yes—
217C47⋊#95C2312yes—
218C47⋊#95C2312yes—
219C47⋊#95C2312yes—
220C47⋊#95C2312yes—
221C47⋊#95C2312yes—
222C47⋊#95C2312yes—
223C47⋊#95C2312yes—
224C47⋊#95C2312yes—
225C2×#41×C47—42no—
226C2×#41×C47—42no—
227C2×#41×C47C2×C418yescomplemented
228C22×Q8×C47C2311yescharacteristic
229C22×D4×C47C2311yescharacteristic
230C22×D4×C47C2311yescharacteristic
231C22×D4×C47C2311yescharacteristic
232C23×C4×C47C2311yescharacteristic
233C23×C4×C47C2311yescharacteristic
234C23×C4×C47C2311yescharacteristic
235C23×C4×C47C2312yes—
236#117×C47—42no—
237C2×C4⋊C4×C47—42no—
238C2×C4⋊C4×C47C2311yescharacteristic
239C2×C4⋊C4×C47C2311yescharacteristic
240C2×C4⋊C4×C47C2311yescharacteristic
241C2×C4⋊C4×C47C2311yescharacteristic
242C2×C4⋊C4×C47C2312yes—
243C2×C22⋊C4×C47C2312yes—
244C2×C22⋊C4×C47C2312yes—
245C2×C22⋊C4×C47C2312yes—
246C2×C22⋊C4×C47C2312yes—
247C2×C22⋊C4×C47C2312yes—
248C2×C42×C47C2312yes—
249#95×C47C2312yes—
250#95×C47C2312yes—
251#95×C47C2312yes—
252#95×C47C2312yes—
253C24×C47C2411yescharacteristic
254C24×C47C2411yescharacteristic
255C24×C47C2411yescharacteristic
256C23×D47—22no—
257C23×D47—22no—
258C23×D47—41no—
259C23×D47—41no—
260C23×D47—41no—
261C23×D47—41no—
262C23×D47C22×C414yes—
263C23×D47C2411yescharacteristic
264C23×D47C2411yescharacteristic
265#41×C47—416no—
266C2×Q8×C47—41no—
267C2×Q8×C47—41no—
268C2×Q8×C47C22×C414yes—
269C2×D4×C47—41no—
270C2×D4×C47—41no—
271C2×D4×C47—41no—
272C2×D4×C47—41no—
273C2×D4×C47—41no—
274C2×D4×C47—41no—
275C2×D4×C47C22×C414yes—
276C2×D4×C47C22×C414yes—
277C2×D4×C47C22×C414yes—
278C22×C4×C47—22no—
279C22×C4×C47—22no—
280C22×C4×C47—22no—
281C22×C4×C47—22no—
282C22×C4×C47—22no—
283C22×C4×C47—22no—
284C22×C4×C47—42no—
285C22×C4×C47—42no—
286C22×C4×C47—42no—
287C22×C4×C47C22×C414yes—
288C22×C4×C47C22×C414yes—
289C22×C4×C47C22×C414yes—
290C22×C4×C47C2412yes—
291C22×C4×C47C2412yes—
292C22×C4×C47C2412yes—
293C22×C4×C47C2412yes—
294C22×C4×C47C2411yescharacteristic
295C22×C4×C47C2411yescharacteristic
296C22×C4×C47C2411yescharacteristic
297C22×C4×C47C2411yescharacteristic
298C2×C22⋊D47—22no—
299C2×C22⋊D47—22no—
300C2×C22⋊D47—22no—
301C2×C22⋊D47—22no—
302C2×C22⋊D47—41no—
303C2×C22⋊D47—41no—
304C2×C22⋊D47—41no—
305C2×C22⋊D47—41no—
306C2×C22⋊D47C22×C414yes—
307C2×C22⋊D47C22×C414yes—
308C2×C22⋊D47C22×C414yes—
309C2×C22⋊D47C22×C414yes—
310C22×Dic47—41no—
311C22×Dic47—41no—
312C22×Dic47—42no—
313C22×Dic47—42no—
314C22×Dic47—42no—
315C22×Dic47C22×C414yes—
316C22×Dic47C2412yes—
317C22×Dic47C2412yes—
318C22×Dic47C2412yes—
319C22×Dic47C2412yes—
320C22×Dic47C2411yescharacteristic
321C22×Dic47C2411yescharacteristic
322C22×Dic47C2411yescharacteristic
323C22×Dic47C2411yescharacteristic
324C22×Dic47C2411yescharacteristic
325C22×Dic47C2411yescharacteristic
326C2×C4×D47—22no—
327C2×C4×D47—22no—
328C2×C4×D47—22no—
329C2×C4×D47—22no—
330C2×C4×D47—24no—
331C2×C4×D47—24no—
332C2×C4×D47—416no—
333C2×C4×D47—41no—
334C2×C4×D47—41no—
335C2×C4×D47—41no—
336C2×C4×D47—41no—
337C2×C4×D47—42no—
338C2×C4×D47—42no—
339C2×C4×D47—42no—
340C2×C4×D47—42no—
341C2×C4×D47C22×C414yes—
342C2×C4×D47C22×C414yes—
343C2×C4×D47C22×C414yes—
344C2×C4×D47C22×C414yes—
345C4⋊C4×C47—22no—
346C4⋊C4×C47—22no—
347C4⋊C4×C47—22no—
348C4⋊C4×C47—22no—
349C4⋊C4×C47—42no—
350C22⋊C4×C47—42no—
351C22⋊C4×C47—42no—
352C22⋊C4×C47—42no—
353C22⋊C4×C47—42no—
354C22⋊C4×C47—42no—
355C42×C47—42no—
356C22⋊Dic47—42no—
357C22⋊Dic47—42no—
358C22⋊Dic47—42no—
359C22⋊Dic47—42no—
360C22⋊Dic47—42no—
361C22⋊Dic47C22×C414yes—
362C22⋊Dic47C22×C414yes—
363C22⋊Dic47C22×C414yes—
364C22⋊Dic47C22×C414yes—
365C22⋊Dic47C22×C414yes—
366C22⋊Dic47C22×C414yes—
367(C2×D47)⋊C4—24no—
368(C2×D47)⋊C4—24no—
369(C2×D47)⋊C4—42no—
370(C2×D47)⋊C4—42no—
371(C2×D47)⋊C4—42no—
372(C2×D47)⋊C4—42no—
373(C2×D47)⋊C4C22×C414yes—
374(C2×D47)⋊C4C22×C414yes—
375(C2×D47)⋊C4C22×C414yes—
376(C2×D47)⋊C4C22×C414yes—
377C4⋊Dic47—22no—
378C4⋊Dic47—22no—
379C4⋊Dic47—22no—
380C4⋊Dic47—22no—
381C4⋊Dic47—42no—
382C4⋊Dic47C22×C414yes—
383C4⋊Dic47C22×C414yes—
384Dic47⋊C4—42no—
385Dic47⋊C4—42no—
386Dic47⋊C4—42no—
387Dic47⋊C4—42no—
388Dic47⋊C4—42no—
389Dic47⋊C4—42no—
390Dic47⋊C4C22×C414yes—
391Dic47⋊C4C22×C414yes—
392Dic47⋊C4C22×C414yes—
393Dic47⋊C4C22×C414yes—
394C4×Dic47—42no—
395C4×Dic47—42no—
396C4×Dic47—42no—
397C4×Dic47—42no—
398C4×Dic47—42no—
399C4×Dic47—42no—
400C4×Dic47—42no—
401C4×Dic47C22×C414yes—
402C4×Dic47C22×C414yes—
403C23×C47—21no—
404C23×C47—21no—
405C23×C47—21no—
406C23×C47—21no—
407C23×C47—21no—
408C23×C47—21no—
409C23×C47—21no—
410C23×C47—21no—
411C23×C47—21no—
412C23×C47—21no—
413C23×C47—21no—
414C23×C47—21no—
415C23×C47—21no—
416C23×C47—21no—
417C23×C47—21no—
418C23×C47—21no—
419C23×C47—21no—
420C23×C47—21no—
421C23×C47C23×C412yes—
422C23×C47C23×C412yes—
423C23×C47C23×C412yes—
424C23×C47C2511yescharacteristic
425C22×D47—21no—
426C22×D47—21no—
427C22×D47—21no—
428C22×D47—21no—
429C22×D47—21no—
430C22×D47—21no—
431C22×D47—21no—
432C22×D47—21no—
433C22×D47—21no—
434C22×D47—21no—
435C22×D47—28no—
436C22×D47—44no—
437C22×D47—44no—
438C22×D47—44no—
439C22×D47—44no—
440C22×D47—44no—
441C22×D47—44no—
442C22×D47C23×C412yes—
443C22×D47C23×C412yes—
444C22×D47H(5,𝔽2)12yes—
445C22×D472−1+412yes—
446Q8×C47—44no—
447D4×C47—44no—
448D4×C47—44no—
449D4×C47—44no—
450C2×C4×C47—21no—
451C2×C4×C47—21no—
452C2×C4×C47—21no—
453C2×C4×C47—21no—
454C2×C4×C47—21no—
455C2×C4×C47—21no—
456C2×C4×C47—28no—
457C2×C4×C47—28no—
458C2×C4×C47—28no—
459C2×C4×C47—22no—
460C2×C4×C47—22no—
461C2×C4×C47—22no—
462C2×C4×C47—22no—
463C2×C4×C47—22no—
464C2×C4×C47—22no—
465C2×C4×C47—22no—
466C2×C4×C47—22no—
467C2×C4×C47—22no—
468C2×C4×C47—22no—
469C2×C4×C47—22no—
470C2×C4×C47—22no—
471C2×C4×C47—84no—
472C2×C4×C47C23×C412yes—
473C2×C4×C47C23×C412yes—
474C2×C4×C47C23×C412yes—
475C2×C4×C47C23×C412yes—
476C2×C4×C47H(5,𝔽2)12yes—
477C2×C4×C47H(5,𝔽2)12yes—
478C22⋊D47—28no—
479C22⋊D47—28no—
480C22⋊D47—44no—
481C22⋊D47—44no—
482C2×Dic47—21no—
483C2×Dic47—21no—
484C2×Dic47—21no—
485C2×Dic47—21no—
486C2×Dic47—21no—
487C2×Dic47—21no—
488C2×Dic47—21no—
489C2×Dic47—21no—
490C2×Dic47—21no—
491C2×Dic47—21no—
492C2×Dic47—21no—
493C2×Dic47—21no—
494C2×Dic47—22no—
495C2×Dic47—22no—
496C2×Dic47—22no—
497C2×Dic47—22no—
498C2×Dic47—22no—
499C2×Dic47—22no—
500C2×Dic47—22no—
501C2×Dic47—22no—
502C2×Dic47—22no—
503C2×Dic47—22no—
504C2×Dic47—22no—
505C2×Dic47—22no—
506C2×Dic47—44no—
507C2×Dic47—84no—
508C2×Dic47C23×C412yes—
509C2×Dic47C23×C412yes—
510C2×Dic47C23×C412yes—
511C2×Dic47C23×C412yes—
512C2×Dic47C23×C412yes—
513C2×Dic47C23×C412yes—
514C4×D47—28no—
515C4×D47—28no—
516C4×D47—44no—
517C4×D47—44no—
518C4×D47—84no—
519C4×D47—84no—
520#34362—471nomaximal, Sylow
521C22×C47—22no—
522C22×C47—22no—
523C22×C47—22no—
524C22×C47—22no—
525C22×C47—22no—
526C22×C47—22no—
527C22×C47—22no—
528C22×C47—22no—
529C22×C47—22no—
530C22×C47—41no—
531C22×C47—41no—
532C22×C47—41no—
533C22×C47—41no—
534C22×C47—41no—
535C22×C47—41no—
536C22×C47—41no—
537C22×C47—41no—
538C22×C47—41no—
539C22×C47—41no—
540C22×C47—41no—
541C22×C47—41no—
542C22×C47C24×C411yescharacteristic
543C22×C47C2×H(5,𝔽2)11yescharacteristic
544C22×C47C2×H(5,𝔽2)11yescharacteristic
545C22×C47C2×H(5,𝔽2)11yescharacteristic
546C22×C47C2×2−1+411yescharacteristic
547C22×C47#58511yescharacteristic
548C22×C47#58511yescharacteristic
549C2×D47—22no—
550C2×D47—22no—
551C2×D47—22no—
552C2×D47—22no—
553C2×D47—22no—
554C2×D47—22no—
555C2×D47—22no—
556C2×D47—22no—
557C2×D47—22no—
558C2×D47—416no—
559C2×D47—41no—
560C2×D47—41no—
561C2×D47—41no—
562C2×D47—41no—
563C2×D47#52014yes—
564C4×C47—22no—
565C4×C47—22no—
566C4×C47—22no—
567C4×C47—42no—
568C4×C47—42no—
569C4×C47—42no—
570C4×C47—42no—
571C4×C47#51814yes—
572Dic47—22no—
573Dic47—22no—
574Dic47—22no—
575Dic47—22no—
576Dic47—22no—
577Dic47—22no—
578Dic47—42no—
579Dic47—42no—
580Dic47—42no—
581Dic47—42no—
582C2×#525—471no—
583#2378—472no—
584#2377—472no—
585#2368—472no—
586#2364—472no—
587#2354—471no—
588#2354—471no—
589#2352—471no—
590#2352—471no—
591#2352—471no—
592#2352—471no—
593D4×C4⋊C4—471no—
594D4×C4⋊C4—471no—
595#2335—472no—
596#2335—472no—
597#2321—472no—
598#2321—472no—
599#2314—471no—
600#2314—471no—
601#2311—471no—
602#2311D4711yescharacteristic, complemented
603#2280—471no—
604C2×#380—471no—
605C2×C47—42no—
606C2×C47—42no—
607C2×C47—42no—
608C2×C47C2×#51811yescharacteristic
609C2×C47C2×#52011yescharacteristic
610C2×C47#342811yescharacteristic
611C2×C47#354111yescharacteristic
612C2×C47#354111yescharacteristic
613C2×C47#354211yescharacteristic
614C2×C47#354211yescharacteristic
615D47—24no—
616D47—42no—
617C22×#41C2×D4711yescharacteristic
618C24×C4—471no—
619#525—4716no—
620C2×#123—471no—
621C2×#123—471no—
622C2×C22⋊Q8—471no—
623C2×C22⋊Q8—471no—
624C2×#121—471no—
625C2×#121—471no—
626C2×#120—471no—
627C2×#120—471no—
628C2×C4×D4—471no—
629C2×C4×D4—471no—
630C2×C4×D4—471no—
631C2×C4×D4—471no—
632C2×C4×D4—472no—
633C2×C4×D4—472no—
634C2×#117—471no—
635C2×#117—471no—
636C2×#117—471no—
637C2×#117—471no—
638C2×#117C2×D4711yescharacteristic, complemented
639C22×C4⋊C4—471no—
640C22×C4⋊C4—471no—
641C22×C4⋊C4—471no—
642C22×C4⋊C4C2×D4711yescharacteristic, complemented
643C22×C22⋊C4—472no—
644#391—472no—
645#391C2×D4712yescomplemented
646#390—472no—
647#390—472no—
648#390—472no—
649#390C2×D4712yes—
650#389—472no—
651#389—472no—
652#388—472no—
653#388—472no—
654#388—472no—
655#388—472no—
656#388—472no—
657#388—472no—
658#388—472no—
659#388—472no—
660#388—472no—
661#388—472no—
662#388—472no—
663#388—472no—
664#387—472no—
665#387—472no—
666#387—472no—
667#387—472no—
668#387—472no—
669#387—472no—
670#387—472no—
671#387—472no—
672#386—472no—
673#386—472no—
674#386—472no—
675#386—472no—
676#386—472no—
677#386—472no—
678#386C2×D4712yes—
679#386C2×D4712yescomplemented
680#385—472no—
681#385—472no—
682#385—472no—
683#385—472no—
684#384—471no—
685#384—471no—
686#382—471no—
687#382—471no—
688#381—472no—
689#380—471no—
690#380—471no—
691#380—471no—
692#380—471no—
693#380—471no—
694#380—471no—
695#380—471no—
696#380—471no—
697#380—472no—
698#380—472no—
699#380C2×D4711yescharacteristic
700#380C2×D4711yescharacteristic
701#380C2×D4711yescharacteristic, complemented
702#380C2×D4711yescharacteristic, complemented
703#379—472no—
704C4×C4⋊C4—471no—
705C4×C4⋊C4—471no—
706C4×C4⋊C4—471no—
707C4×C4⋊C4—471no—
708C4×C4⋊C4—472no—
709C4×C4⋊C4—472no—
710C4×C22⋊C4—472no—
711C4×C22⋊C4—472no—
712C4×C22⋊C4—472no—
713C4×C22⋊C4—472no—
714C4×C22⋊C4—472no—
715C4×C22⋊C4—472no—
716C2×#95—472no—
717C47#3436211yescharacteristic, complemented, Sylow
718C25—471no—
719C2×#41—42no—
720C2×#41—42no—
721C2×#41C4×D4718yescomplemented
722C22×Q8C22×D4711yescharacteristic
723C22×D4—471no—
724C22×D4—471no—
725C22×D4—471no—
726C22×D4—471no—
727C22×D4C22×D4711yescharacteristic
728C22×D4C22×D4711yescharacteristic
729C22×D4C22×D4711yescharacteristic
730C23×C4—471no—
731C23×C4—471no—
732C23×C4—471no—
733C23×C4—478no—
734C23×C4—471no—
735C23×C4—471no—
736C23×C4—472no—
737C23×C4—472no—
738C23×C4—472no—
739C23×C4—1882no—
740C23×C4—1882no—
741C23×C4C22×D4711yescharacteristic
742C23×C4C22×D4711yescharacteristic
743C23×C4C22×D4711yescharacteristic
744C23×C4C22×D4712yes—
745#123—478no—
746#123—478no—
747C22⋊Q8—478no—
748C22⋊Q8—478no—
749#121—478no—
750#121—478no—
751#120—478no—
752#120—478no—
753C4×D4—478no—
754C4×D4—478no—
755C4×D4—478no—
756C4×D4—478no—
757C4×D4—1884no—
758C4×D4—1884no—
759#117—42no—
760#117—478no—
761#117—1882no—
762#117—1882no—
763#117—1882no—
764C2×C4⋊C4—42no—
765C2×C4⋊C4—471no—
766C2×C4⋊C4—471no—
767C2×C4⋊C4—471no—
768C2×C4⋊C4—471no—
769C2×C4⋊C4—471no—
770C2×C4⋊C4—471no—
771C2×C4⋊C4—471no—
772C2×C4⋊C4—471no—
773C2×C4⋊C4—471no—
774C2×C4⋊C4—471no—
775C2×C4⋊C4—472no—
776C2×C4⋊C4—472no—
777C2×C4⋊C4—472no—
778C2×C4⋊C4—472no—
779C2×C4⋊C4—472no—
780C2×C4⋊C4—472no—
781C2×C4⋊C4—472no—
782C2×C4⋊C4—1882no—
783C2×C4⋊C4—1882no—
784C2×C4⋊C4—1882no—
785C2×C4⋊C4C22×D4711yescharacteristic
786C2×C4⋊C4C22×D4711yescharacteristic
787C2×C4⋊C4C22×D4711yescharacteristic
788C2×C4⋊C4C22×D4711yescharacteristic
789C2×C4⋊C4C22×D4712yes—
790C2×C22⋊C4—471no—
791C2×C22⋊C4—471no—
792C2×C22⋊C4—471no—
793C2×C22⋊C4—471no—
794C2×C22⋊C4—471no—
795C2×C22⋊C4—471no—
796C2×C22⋊C4—471no—
797C2×C22⋊C4—471no—
798C2×C22⋊C4—471no—
799C2×C22⋊C4—471no—
800C2×C22⋊C4—472no—
801C2×C22⋊C4—472no—
802C2×C22⋊C4—472no—
803C2×C22⋊C4—472no—
804C2×C22⋊C4—472no—
805C2×C22⋊C4—472no—
806C2×C22⋊C4—472no—
807C2×C22⋊C4—472no—
808C2×C22⋊C4—472no—
809C2×C22⋊C4—472no—
810C2×C22⋊C4—472no—
811C2×C22⋊C4—1884no—
812C2×C22⋊C4C22×D4712yes—
813C2×C22⋊C4C22×D4712yes—
814C2×C22⋊C4C22×D4712yes—
815C2×C22⋊C4C22×D4712yes—
816C2×C22⋊C4C22×D4712yes—
817C2×C42—471no—
818C2×C42—471no—
819C2×C42—472no—
820C2×C42—472no—
821C2×C42—472no—
822C2×C42—472no—
823C2×C42—472no—
824C2×C42—472no—
825C2×C42—472no—
826C2×C42C22×D4712yes—
827#95—472no—
828#95—472no—
829#95—472no—
830#95—472no—
831#95—472no—
832#95—472no—
833#95—472no—
834#95—472no—
835#95—472no—
836#95—472no—
837#95—472no—
838#95—472no—
839#95—472no—
840#95—472no—
841#95—472no—
842#95—472no—
843#95C22×D4712yes—
844#95C22×D4712yes—
845#95C22×D4712yes—
846#95C22×D4712yes—
847C24—471no—
848C24—471no—
849C24—474no—
850C24—942no—
851C24—942no—
852C24—1881no—
853C24—1881no—
854C24—1881no—
855C24—1881no—
856C24C23×D4711yescharacteristic
857C24C23×D4711yescharacteristic
858C24C23×D4711yescharacteristic
859#41—416no—
860C2×Q8—41no—
861C2×Q8—41no—
862C2×Q8C2×C4×D4714yes—
863C2×D4—41no—
864C2×D4—41no—
865C2×D4—41no—
866C2×D4—41no—
867C2×D4—41no—
868C2×D4—41no—
869C2×D4—474no—
870C2×D4—474no—
871C2×D4—474no—
872C2×D4—474no—
873C2×D4—942no—
874C2×D4—942no—
875C2×D4—942no—
876C2×D4—942no—
877C2×D4—1881no—
878C2×D4—1881no—
879C2×D4—1881no—
880C2×D4—1881no—
881C2×D4C2×C4×D4714yes—
882C2×D4C2×C4×D4714yes—
883C2×D4C2×C4×D4714yes—
884C22×C4—22no—
885C22×C4—22no—
886C22×C4—22no—
887C22×C4—22no—
888C22×C4—22no—
889C22×C4—22no—
890C22×C4—42no—
891C22×C4—42no—
892C22×C4—42no—
893C22×C4—471no—
894C22×C4—471no—
895C22×C4—471no—
896C22×C4—471no—
897C22×C4—471no—
898C22×C4—471no—
899C22×C4—474no—
900C22×C4—474no—
901C22×C4—474no—
902C22×C4—474no—
903C22×C4—474no—
904C22×C4—472no—
905C22×C4—472no—
906C22×C4—472no—
907C22×C4—472no—
908C22×C4—944no—
909C22×C4—944no—
910C22×C4—942no—
911C22×C4—942no—
912C22×C4—942no—
913C22×C4—942no—
914C22×C4—18816no—
915C22×C4—1882no—
916C22×C4—1882no—
917C22×C4—1882no—
918C22×C4—1882no—
919C22×C4—1881no—
920C22×C4—1881no—
921C22×C4—1881no—
922C22×C4—1881no—
923C22×C4—1882no—
924C22×C4—1882no—
925C22×C4—1882no—
926C22×C4—1881no—
927C22×C4—1881no—
928C22×C4C2×C4×D4714yes—
929C22×C4C2×C4×D4714yes—
930C22×C4C2×C4×D4714yes—
931C22×C4C23×D4712yes—
932C22×C4C23×D4712yes—
933C22×C4C23×D4712yes—
934C22×C4C23×D4712yes—
935C22×C4C23×D4711yescharacteristic
936C22×C4C23×D4711yescharacteristic
937C22×C4C23×D4711yescharacteristic
938C22×C4C23×D4711yescharacteristic
939C4⋊C4—22no—
940C4⋊C4—22no—
941C4⋊C4—22no—
942C4⋊C4—22no—
943C4⋊C4—42no—
944C4⋊C4—474no—
945C4⋊C4—474no—
946C4⋊C4—474no—
947C4⋊C4—474no—
948C4⋊C4—474no—
949C4⋊C4—474no—
950C4⋊C4—942no—
951C4⋊C4—942no—
952C4⋊C4—942no—
953C4⋊C4—942no—
954C4⋊C4—1882no—
955C4⋊C4—1882no—
956C4⋊C4—1882no—
957C4⋊C4—1882no—
958C4⋊C4—1882no—
959C4⋊C4—1882no—
960C4⋊C4—1882no—
961C22⋊C4—42no—
962C22⋊C4—42no—
963C22⋊C4—42no—
964C22⋊C4—42no—
965C22⋊C4—42no—
966C22⋊C4—474no—
967C22⋊C4—474no—
968C22⋊C4—474no—
969C22⋊C4—474no—
970C22⋊C4—474no—
971C22⋊C4—474no—
972C22⋊C4—474no—
973C22⋊C4—474no—
974C22⋊C4—474no—
975C22⋊C4—474no—
976C22⋊C4—944no—
977C22⋊C4—944no—
978C22⋊C4—1882no—
979C22⋊C4—1882no—
980C22⋊C4—1882no—
981C22⋊C4—1882no—
982C22⋊C4—1882no—
983C22⋊C4—1882no—
984C22⋊C4—1882no—
985C22⋊C4—1882no—
986C22⋊C4—1882no—
987C42—42no—
988C42—474no—
989C42—474no—
990C42—1882no—
991C42—1882no—
992C42—1882no—
993C42—1882no—
994C42—1882no—
995C42—1882no—
996C42—1882no—
997C23—21no—
998C23—21no—
999C23—21no—
1000C23—21no—
1001C23—21no—
1002C23—21no—
1003C23—21no—
1004C23—21no—
1005C23—21no—
1006C23—21no—
1007C23—21no—
1008C23—21no—
1009C23—21no—
1010C23—21no—
1011C23—21no—
1012C23—21no—
1013C23—21no—
1014C23—21no—
1015C23—472no—
1016C23—472no—
1017C23—472no—
1018C23—472no—
1019C23—948no—
1020C23—941no—
1021C23—941no—
1022C23—941no—
1023C23—941no—
1024C23—941no—
1025C23—941no—
1026C23—941no—
1027C23—941no—
1028C23—941no—
1029C23—941no—
1030C23—1884no—
1031C23—1884no—
1032C23—1884no—
1033C23—1884no—
1034C23—1884no—
1035C23—1884no—
1036C23C22×C4×D4712yes—
1037C23C22×C4×D4712yes—
1038C23C22×C4×D4712yes—
1039C23C24×D4711yescharacteristic
1040Q8—44no—
1041D4—44no—
1042D4—44no—
1043D4—44no—
1044D4—948no—
1045D4—948no—
1046D4—1884no—
1047D4—1884no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—28no—
1055C2×C4—28no—
1056C2×C4—28no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—84no—
1070C2×C4—472no—
1071C2×C4—472no—
1072C2×C4—472no—
1073C2×C4—472no—
1074C2×C4—472no—
1075C2×C4—472no—
1076C2×C4—941no—
1077C2×C4—941no—
1078C2×C4—941no—
1079C2×C4—941no—
1080C2×C4—941no—
1081C2×C4—941no—
1082C2×C4—941no—
1083C2×C4—941no—
1084C2×C4—941no—
1085C2×C4—941no—
1086C2×C4—941no—
1087C2×C4—941no—
1088C2×C4—948no—
1089C2×C4—948no—
1090C2×C4—942no—
1091C2×C4—942no—
1092C2×C4—942no—
1093C2×C4—942no—
1094C2×C4—942no—
1095C2×C4—942no—
1096C2×C4—942no—
1097C2×C4—942no—
1098C2×C4—942no—
1099C2×C4—942no—
1100C2×C4—942no—
1101C2×C4—942no—
1102C2×C4—3764no—
1103C2×C4—3764no—
1104C2×C4—3764no—
1105C2×C4—1884no—
1106C2×C4—1884no—
1107C2×C4—1884no—
1108C2×C4C22×C4×D4712yes—
1109C2×C4C22×C4×D4712yes—
1110C2×C4C22×C4×D4712yes—
1111C2×C4C22×C4×D4712yes—
1112C2×C4#1309406912yes—
1113C2×C4#1309406912yes—
1114C22—22no—
1115C22—22no—
1116C22—22no—
1117C22—22no—
1118C22—22no—
1119C22—22no—
1120C22—22no—
1121C22—22no—
1122C22—22no—
1123C22—41no—
1124C22—41no—
1125C22—41no—
1126C22—41no—
1127C22—41no—
1128C22—41no—
1129C22—41no—
1130C22—41no—
1131C22—41no—
1132C22—41no—
1133C22—41no—
1134C22—41no—
1135C22—474no—
1136C22—942no—
1137C22—942no—
1138C22—942no—
1139C22—942no—
1140C22—942no—
1141C22—942no—
1142C22—942no—
1143C22—942no—
1144C22—942no—
1145C22—18816no—
1146C22—1881no—
1147C22—1881no—
1148C22—1881no—
1149C22—1881no—
1150C22C23×C4×D4711yescharacteristic
1151C22H(5,𝔽2)×D4711yescharacteristic
1152C22C2×#1309406911yescharacteristic
1153C22C2×#1309406911yescharacteristic
1154C222−1+4×D4711yescharacteristic
1155C22#1568995811yescharacteristic
1156C22#1568996011yescharacteristic
1157C4—22no—
1158C4—22no—
1159C4—22no—
1160C4—42no—
1161C4—42no—
1162C4—42no—
1163C4—42no—
1164C4—942no—
1165C4—942no—
1166C4—942no—
1167C4—942no—
1168C4—942no—
1169C4—942no—
1170C4—1882no—
1171C4—1882no—
1172C4—1882no—
1173C4—1882no—
1174C4#1568959614yes—
1175C2—42no—
1176C2—42no—
1177C2—42no—
1178C2—944no—
1179C2—1882no—
1180C2C2×#1568959611yescharacteristic
1181C2#520×D4711yescharacteristic
1182C2#2025658811yescharacteristic
1183C2#2025766911yescharacteristic
1184C2#2025768311yescharacteristic
1185C2#2025769211yescharacteristic
1186C2#2025770611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingC47×#2311C2
socle, cosocleC23×C47C25
prime radicalC2×#15689630C2
hypercenter#2311D47
hypocenterC47#34362
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2311

Complements

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

NH ≅ G/Ntype
2. #20246549C2semidirect
3. #20246540C2semidirect
4. #20246467C2semidirect
5. #20246437C2semidirect
6. #20246338C2semidirect
7. #20246332C2semidirect
8. #20246319C2semidirect
9. #20246318C2semidirect
10. #20246313C2semidirect
11. #20246310C2semidirect
12. C4⋊C4×C22⋊D47C2semidirect
13. #20246284C2semidirect
14. #20246179C2semidirect
15. #20246175C2semidirect
16. #20246047C2semidirect
17. #20246044C2semidirect
18. #20245995C2semidirect
19. #20245995C2semidirect
20. #20245980C2semidirect
21. #20245770C2semidirect
22. #380×D47C2semidirect
23. C47×#2311C2semidirect
25. #15689630C4semidirect
41. C2×#13093983C22semidirect
44. C22×C4⋊Dic47C22semidirect
48. #15689030C22semidirect
52. #15689020C22semidirect
53. #15689018C22semidirect
56. #15689017C22semidirect
57. #15689017C22semidirect
64. #15689011C22semidirect
65. #15689011C22semidirect
66. #15689010C22semidirect
67. #15689008C22semidirect
68. #15689008C22semidirect
69. #15689007C22semidirect
70. #15689006C22semidirect
71. #15689006C22semidirect
72. #15689005C22semidirect
73. #15689004C22semidirect
75. #15689003C22semidirect
81. #15688996C22semidirect
82. #15688995C22semidirect
84. #15688992C22semidirect
85. #15688992C22semidirect
86. #15688988C22semidirect
87. #15688988C22semidirect
91. #15688983C22semidirect
92. #15688983C22semidirect
100. C4⋊C4×Dic47C22semidirect
101. C4⋊C4×Dic47C22semidirect
102. C4⋊C4×Dic47C22semidirect
103. C4⋊C4×Dic47C22semidirect
104. C4×Dic47⋊C4C22semidirect
105. #15688974C22semidirect
107. C22⋊C4×Dic47C22semidirect
109. C4×C22⋊Dic47C22semidirect
114. C2×#117×C47C22semidirect
115. C22×C4⋊C4×C47C22semidirect
116. C47×#391C22semidirect
119. C47×#386C22semidirect
122. C47×#380C22semidirect
123. C47×#380C22semidirect
133. C22×C4×D47C2×C4semidirect
140. #13094005C2×C4semidirect
141. #13094005C2×C4semidirect
142. #13094000C2×C4semidirect
143. #13094000C2×C4semidirect
145. #13093995C2×C4semidirect
146. #13093992C2×C4semidirect
147. #13093992C2×C4semidirect
149. C4×C22⋊D47C2×C4semidirect
150. C4×C22⋊D47C2×C4semidirect
151. C4×C22⋊D47C2×C4semidirect
152. C4×C22⋊D47C2×C4semidirect
155. #13093983C2×C4semidirect
227. C2×#41×C47C2×C4semidirect
602. #2311D47semidirect
638. C2×#117C2×D47semidirect
642. C22×C4⋊C4C2×D47semidirect
645. #391C2×D47semidirect
679. #386C2×D47semidirect
701. #380C2×D47semidirect
702. #380C2×D47semidirect
717. C47#34362semidirect
721. C2×#41C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156896302
#202465492
#202465402
#202464672
#202464372
#202463382
#202463322
#202463192
#202463182
#202463132
#202463102
C4⋊C4×C22⋊D472
#202462842
#202461792
#202461752
#202460472
#202460442
#202459952
#202459802
#202457702
#380×D472
C47×#23112
#3436247