Finite Group Databasebeta

← #26383257

Subgroups — #26383257

Order 12032.

1536 conjugacy classes of subgroups.

The subgroup lattice has 1266 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20249571C211yesmaximal, characteristic, complemented
2#20249570C211yesmaximal, characteristic, complemented
3#20249549C211yesmaximal, characteristic
4#20249546C211yesmaximal, characteristic
5#20249483C211yesmaximal, characteristic, complemented
6#20249482C211yesmaximal, characteristic, complemented
7#20249481C211yesmaximal, characteristic, complemented
8#20249474C211yesmaximal, characteristic, complemented
9#20249469C211yesmaximal, characteristic
10#20249466C211yesmaximal, characteristic
11#20249408C211yesmaximal, characteristic
12#20249401C211yesmaximal, characteristic
13#20249295C211yesmaximal, characteristic
14#20249294C211yesmaximal, characteristic
15#20249263C211yesmaximal, characteristic, complemented
16#20246694C211yesmaximal, characteristic, complemented
17#20246694C211yesmaximal, characteristic, complemented
18#20246692C211yesmaximal, characteristic, complemented
19#20246687C211yesmaximal, characteristic
20#20246687C211yesmaximal, characteristic
21#20246678C211yesmaximal, characteristic, complemented
22#20246665C211yesmaximal, characteristic
23#20246659C211yesmaximal, characteristic
24#125×Dic47C211yesmaximal, characteristic, complemented
25#20245945C211yesmaximal, characteristic, complemented
26#20245938C211yesmaximal, characteristic
27#20245936C211yesmaximal, characteristic
28#20245880C211yesmaximal, characteristic
29#20245861C211yesmaximal, characteristic, complemented
30C4×Q8×Dic47C211yesmaximal, characteristic, complemented
31C47×#2634C211yesmaximal, characteristic, complemented
32C2×#13094019C2211yescharacteristic
33C2×#13094018C2211yescharacteristic
34C2×#13094014C2211yescharacteristic
35C2×Q8×Dic47C2211yescharacteristic
36C2×Q8×Dic47C2211yescharacteristic
37C2×#13093989C2211yescharacteristic
38C2×#13093982C2211yescharacteristic
39C47⋊#401C2211yescharacteristic
40C47⋊#401C2211yescharacteristic
41#15689065C2211yescharacteristic
42#15689065C2211yescharacteristic
43#15689065C2211yescharacteristic
44#15689065C2211yescharacteristic
45#15689065C2211yescharacteristic
46#15689065C2211yescharacteristic
47#15689064C2211yescharacteristic
48#15689064C2211yescharacteristic
49#15689064C2211yescharacteristic
50#15689064C2211yescharacteristic
51#15689063C2211yescharacteristic
52#15689063C2211yescharacteristic
53#15689063C2211yescharacteristic
54#15689062C2211yescharacteristic
55#15689062C2211yescharacteristic
56#15689061C2211yescharacteristic
57#15689060C2211yescharacteristic
58#15689058C2211yescharacteristic
59#15689057C2211yescharacteristic
60#15689057C2211yescharacteristic
61#15689057C2211yescharacteristic
62#15689057C2211yescharacteristic
63#15689056C2211yescharacteristic
64#15689056C2211yescharacteristic
65#15689056C2211yescharacteristic
66#15689056C2211yescharacteristic
67#15689056C2211yescharacteristic
68#15689056C2211yescharacteristic
69#15689055C2211yescharacteristic
70#15689055C2211yescharacteristic
71#15689055C2211yescharacteristic
72#15689055C2211yescharacteristic
73#15689054C2211yescharacteristic
74#15689054C2211yescharacteristic
75#15689053C2211yescharacteristic
76#15689053C2211yescharacteristic
77#15689052C2211yescharacteristic
78#15689052C2211yescharacteristic
79#15689050C2211yescharacteristic
80#15689050C2211yescharacteristic
81#15689049C2211yescharacteristic
82#15689049C2211yescharacteristic
83#15689045C2211yescharacteristic
84#15689045C2211yescharacteristic
85#15689045C2211yescharacteristic
86#15689045C2211yescharacteristic
87#15689045C2211yescharacteristic
88#15689045C2211yescharacteristic
89#15689044C2211yescharacteristic
90#15689044C2211yescharacteristic
91#15689044C2211yescharacteristic
92#15689042C2211yescharacteristic
93#15689036C2211yescharacteristic
94#15689034C2211yescharacteristic
95#15689027C2211yescharacteristic
96#15689027C2211yescharacteristic
97#15689022C2211yescharacteristic
98#15689022C2211yescharacteristic
99#15689020C2211yescharacteristic
100#15689020C2211yescharacteristic
101#15689018C2211yescharacteristic
102#15689018C2211yescharacteristic
103#15689015C2211yescharacteristic
104#15689015C2211yescharacteristic
105#15689014C2211yescharacteristic
106#15689014C2211yescharacteristic
107#15689013C2211yescharacteristic
108#15689013C2211yescharacteristic
109#15689012C2211yescharacteristic
110#15689012C2211yescharacteristic
111#15689012C2211yescharacteristic
112#15689012C2211yescharacteristic
113#15689010C2211yescharacteristic
114#15689010C2211yescharacteristic
115#15689009C2211yescharacteristic
116#15689009C2211yescharacteristic
117#15689009C2211yescharacteristic
118#15689009C2211yescharacteristic
119#15689009C2211yescharacteristic
120#15689009C2211yescharacteristic
121#15689008C2211yescharacteristic
122#15689008C2211yescharacteristic
123#15689007C2211yescharacteristic
124#15689007C2211yescharacteristic
125#15689006C2211yescharacteristic
126#15689006C2211yescharacteristic
127#15689005C2211yescharacteristic
128#15689005C2211yescharacteristic
129#15689005C2211yescharacteristic
130#15689005C2211yescharacteristic
131#15688990C2211yescharacteristic
132#15688989C2211yescharacteristic
133#15688987C2211yescharacteristic
134C4⋊C4×Dic47C2211yescharacteristic
135C4⋊C4×Dic47C2211yescharacteristic
136C4⋊C4×Dic47C2211yescharacteristic
137C4⋊C4×Dic47C2211yescharacteristic
138C4⋊C4×Dic47C2211yescharacteristic
139C4⋊C4×Dic47C2211yescharacteristic
140C4⋊C4×Dic47C2211yescharacteristic
141C4⋊C4×Dic47C2211yescharacteristic
142C4⋊C4×Dic47C2211yescharacteristic
143C4⋊C4×Dic47C2211yescharacteristic
144C4⋊C4×Dic47C2211yescharacteristic
145C4⋊C4×Dic47C2211yescharacteristic
146C4⋊C4×Dic47C2211yescharacteristic
147C4⋊C4×Dic47C2211yescharacteristic
148C4×C4⋊Dic47C2211yescharacteristic
149C4×C4⋊Dic47C2211yescharacteristic
150C4×C4⋊Dic47C2211yescharacteristic
151#15688974C2211yescharacteristic
152#15688974C2211yescharacteristic
153#15688974C2211yescharacteristic
154#15688974C2211yescharacteristic
155#15688974C2211yescharacteristic
156#15688974C2211yescharacteristic
157#15688974C2211yescharacteristic
158#15688974C2211yescharacteristic
159#15688974C2211yescharacteristic
160#15688970C2211yescharacteristic
161#15688970C2211yescharacteristic
162#15688970C2211yescharacteristic
163#15688970C2211yescharacteristic
164#15688970C2211yescharacteristic
165#15688970C2211yescharacteristic
166#15688968C2211yescharacteristic
167#15688968C2211yescharacteristic
168#15688968C2211yescharacteristic
169C42×Dic47C2211yescharacteristic
170C42×Dic47C2211yescharacteristic
171C42×Dic47C2211yescharacteristic
172C2×#125×C47C2211yescharacteristic
173C2×C4×Q8×C47C2211yescharacteristic
174C47×#400C2211yescharacteristic
175C47×#400C2211yescharacteristic
176C47×#400C2211yescharacteristic
177C47×#400C2211yescharacteristic
178C47×#398C2211yescharacteristic
179C47×#398C2211yescharacteristic
180C47×#395C2211yescharacteristic
181C47×#395C2211yescharacteristic
182C47×#387C2211yescharacteristic
183C47×#387C2211yescharacteristic
184C47×#387C2211yescharacteristic
185C47×#387C2211yescharacteristic
186C47×#383C2211yescharacteristic
187C22×Dic94C2311yescharacteristic
188C22×C4×D47C2311yescharacteristic
189#13094019—24no—
190#13094018—24no—
191#13094014—24no—
192Q8×Dic47—24no—
193Q8×Dic47—24no—
194#13093989—24no—
195#13093982—24no—
196C2×C4⋊Dic47C2311yescharacteristic
197C2×C4⋊Dic47C2311yescharacteristic
198C2×C4⋊Dic47C2311yescharacteristic
199C2×C4⋊Dic47C2311yescharacteristic
200C2×C4⋊Dic47C2311yescharacteristic
201C2×C4⋊Dic47C2311yescharacteristic
202C2×C4⋊Dic47C2311yescharacteristic
203C2×C4⋊Dic47C2311yescharacteristic
204C2×C4⋊Dic47C2311yescharacteristic
205C2×C4⋊Dic47C2311yescharacteristic
206C2×C4⋊Dic47C2311yescharacteristic
207C2×C4⋊Dic47C2311yescharacteristic
208C2×C4⋊Dic47C2311yescharacteristic
209C2×C4⋊Dic47C2311yescharacteristic
210C2×C4⋊Dic47C2311yescharacteristic
211C2×Dic47⋊C4C2311yescharacteristic
212C2×Dic47⋊C4C2311yescharacteristic
213C2×Dic47⋊C4C2311yescharacteristic
214C2×Dic47⋊C4C2311yescharacteristic
215C2×Dic47⋊C4C2311yescharacteristic
216C2×Dic47⋊C4C2311yescharacteristic
217C2×Dic47⋊C4C2311yescharacteristic
218C2×Dic47⋊C4C2311yescharacteristic
219C2×Dic47⋊C4C2311yescharacteristic
220C2×Dic47⋊C4C2311yescharacteristic
221C2×Dic47⋊C4C2311yescharacteristic
222C2×Dic47⋊C4C2311yescharacteristic
223C2×Dic47⋊C4C2311yescharacteristic
224C2×Dic47⋊C4C2311yescharacteristic
225C2×Dic47⋊C4C2311yescharacteristic
226C2×Dic47⋊C4C2311yescharacteristic
227C2×Dic47⋊C4C2311yescharacteristic
228C2×Dic47⋊C4C2311yescharacteristic
229C2×Dic47⋊C4C2311yescharacteristic
230C2×Dic47⋊C4C2311yescharacteristic
231C2×(C2×D47)⋊C4C2311yescharacteristic
232C2×(C2×D47)⋊C4C2311yescharacteristic
233C2×(C2×D47)⋊C4C2311yescharacteristic
234C2×(C2×D47)⋊C4C2311yescharacteristic
235C2×(C2×D47)⋊C4C2311yescharacteristic
236C2×(C2×D47)⋊C4C2311yescharacteristic
237C2×(C2×D47)⋊C4C2311yescharacteristic
238C2×(C2×D47)⋊C4C2311yescharacteristic
239C2×(C2×D47)⋊C4C2311yescharacteristic
240C2×(C2×D47)⋊C4C2311yescharacteristic
241C2×(C2×D47)⋊C4C2311yescharacteristic
242C2×(C2×D47)⋊C4C2311yescharacteristic
243C2×(C2×D47)⋊C4C2311yescharacteristic
244C2×(C2×D47)⋊C4C2311yescharacteristic
245C2×C4×Dic47C2311yescharacteristic
246C2×C4×Dic47C2311yescharacteristic
247C2×C4×Dic47C2311yescharacteristic
248C2×C4×Dic47C2311yescharacteristic
249C2×C4×Dic47C2311yescharacteristic
250C2×C4×Dic47C2311yescharacteristic
251C2×C4×Dic47C2311yescharacteristic
252C2×C4×Dic47C2311yescharacteristic
253C2×C4×Dic47C2311yescharacteristic
254C2×C4×Dic47C2311yescharacteristic
255C2×C4×Dic47C2311yescharacteristic
256C2×C4×Dic47C2311yescharacteristic
257C2×C4×Dic47C2311yescharacteristic
258C2×C4×Dic47C2311yescharacteristic
259C2×C4×Dic47C2311yescharacteristic
260C2×C4×Dic47C2311yescharacteristic
261C2×C4×Dic47C2311yescharacteristic
262C2×C4×Dic47C2311yescharacteristic
263C2×C4×Dic47C2311yescharacteristic
264C2×C4×Dic47C2311yescharacteristic
265C2×C4×Dic47C2311yescharacteristic
266C2×C4×Dic47C2311yescharacteristic
267C2×C4×Dic47C2311yescharacteristic
268C47⋊#95C2311yescharacteristic
269C47⋊#95C2311yescharacteristic
270C47⋊#95C2311yescharacteristic
271C47⋊#95C2311yescharacteristic
272C47⋊#95C2311yescharacteristic
273C47⋊#95C2311yescharacteristic
274C47⋊#95C2311yescharacteristic
275C47⋊#95C2311yescharacteristic
276C47⋊#95C2311yescharacteristic
277C47⋊#95C2311yescharacteristic
278C47⋊#95C2311yescharacteristic
279C47⋊#95C2311yescharacteristic
280C47⋊#95C2311yescharacteristic
281C47⋊#95C2311yescharacteristic
282C47⋊#95C2311yescharacteristic
283C47⋊#95C2311yescharacteristic
284C47⋊#95C2311yescharacteristic
285C47⋊#95C2311yescharacteristic
286C47⋊#95C2311yescharacteristic
287C47⋊#95C2311yescharacteristic
288C47⋊#95C2311yescharacteristic
289C47⋊#95C2311yescharacteristic
290C47⋊#95C2311yescharacteristic
291C47⋊#95C2311yescharacteristic
292C47⋊#95C2311yescharacteristic
293C47⋊#95C2311yescharacteristic
294C47⋊#95C2311yescharacteristic
295C47⋊#95C2311yescharacteristic
296C47⋊#95C2311yescharacteristic
297C47⋊#95C2311yescharacteristic
298C47⋊#95C2311yescharacteristic
299C47⋊#95C2311yescharacteristic
300C47⋊#95C2311yescharacteristic
301C47⋊#95C2311yescharacteristic
302C47⋊#95C2311yescharacteristic
303C47⋊#95C2311yescharacteristic
304C47⋊#95C2311yescharacteristic
305C47⋊#95C2311yescharacteristic
306C47⋊#95C2311yescharacteristic
307C47⋊#95C2311yescharacteristic
308C47⋊#95C2311yescharacteristic
309C47⋊#95C2311yescharacteristic
310C47⋊#95C2311yescharacteristic
311C47⋊#95C2311yescharacteristic
312C47⋊#95C2311yescharacteristic
313C47⋊#95C2311yescharacteristic
314C22×Q8×C47C2311yescharacteristic
315#125×C47—24no—
316C4×Q8×C47—24no—
317C2×C4⋊C4×C47C2311yescharacteristic
318C2×C4⋊C4×C47C2311yescharacteristic
319C2×C4⋊C4×C47C2311yescharacteristic
320C2×C4⋊C4×C47C2311yescharacteristic
321C2×C4⋊C4×C47C2311yescharacteristic
322C2×C4⋊C4×C47C2311yescharacteristic
323C2×C4⋊C4×C47C2311yescharacteristic
324C2×C4⋊C4×C47C2311yescharacteristic
325C2×C4⋊C4×C47C2311yescharacteristic
326C2×C4⋊C4×C47C2311yescharacteristic
327C2×C4⋊C4×C47C2311yescharacteristic
328C2×C4⋊C4×C47C2311yescharacteristic
329C2×C4⋊C4×C47C2311yescharacteristic
330C2×C42×C47C2311yescharacteristic
331C2×C42×C47C2311yescharacteristic
332C2×C42×C47C2311yescharacteristic
333#95×C47C2311yescharacteristic
334#95×C47C2311yescharacteristic
335#95×C47C2311yescharacteristic
336#95×C47C2311yescharacteristic
337#95×C47C2311yescharacteristic
338#95×C47C2311yescharacteristic
339#95×C47C2311yescharacteristic
340#95×C47C2311yescharacteristic
341#95×C47C2311yescharacteristic
342#95×C47C2311yescharacteristic
343#95×C47C2311yescharacteristic
344#95×C47C2311yescharacteristic
345#95×C47C2311yescharacteristic
346#95×C47C2311yescharacteristic
347#95×C47C2311yescharacteristic
348#95×C47C2311yescharacteristic
349#95×C47C2311yescharacteristic
350#95×C47C2311yescharacteristic
351C23×D47C2411yescharacteristic
352C2×Q8×C47—22no—
353C2×Q8×C47—22no—
354C2×Q8×C47—22no—
355C22×C4×C47C2411yescharacteristic
356C22×C4×C47C2411yescharacteristic
357C22×C4×C47C2411yescharacteristic
358C22×C4×C47C2411yescharacteristic
359C22×C4×C47C2411yescharacteristic
360C22×C4×C47C2411yescharacteristic
361C22×C4×C47C2411yescharacteristic
362C22×C4×C47C2411yescharacteristic
363C22×C4×C47C2411yescharacteristic
364C22×C4×C47C2411yescharacteristic
365C22×C4×C47C2411yescharacteristic
366C22×C4×C47C2411yescharacteristic
367C22×C4×C47C2411yescharacteristic
368C22×C4×C47C2411yescharacteristic
369C22×C4×C47C2411yescharacteristic
370C22×Dic47C2411yescharacteristic
371C22×Dic47C2411yescharacteristic
372C22×Dic47C2411yescharacteristic
373C22×Dic47C2411yescharacteristic
374C22×Dic47C2411yescharacteristic
375C22×Dic47C2411yescharacteristic
376C22×Dic47C2411yescharacteristic
377C22×Dic47C2411yescharacteristic
378C22×Dic47C2411yescharacteristic
379C22×Dic47C2411yescharacteristic
380C22×Dic47C2411yescharacteristic
381C22×Dic47C2411yescharacteristic
382C22×Dic47C2411yescharacteristic
383C22×Dic47C2411yescharacteristic
384C22×Dic47C2411yescharacteristic
385C2×C4×D47—22no—
386C2×C4×D47—22no—
387C2×C4×D47—22no—
388C2×Dic94—22no—
389C2×Dic94—41no—
390C2×Dic94—41no—
391C4⋊C4×C47—22no—
392C4⋊C4×C47—22no—
393C4⋊C4×C47—22no—
394C4⋊C4×C47—22no—
395C4⋊C4×C47—22no—
396C4⋊C4×C47—22no—
397C4⋊C4×C47—22no—
398C4⋊C4×C47—22no—
399C4⋊C4×C47—22no—
400C4⋊C4×C47—22no—
401C4⋊C4×C47—22no—
402C4⋊C4×C47—22no—
403C4⋊C4×C47—22no—
404C42×C47—22no—
405C42×C47—22no—
406C42×C47#4114yes—
407(C2×D47)⋊C4—22no—
408(C2×D47)⋊C4—22no—
409(C2×D47)⋊C4—22no—
410(C2×D47)⋊C4—22no—
411(C2×D47)⋊C4—22no—
412(C2×D47)⋊C4—22no—
413(C2×D47)⋊C4—22no—
414(C2×D47)⋊C4—22no—
415(C2×D47)⋊C4—41no—
416(C2×D47)⋊C4—41no—
417(C2×D47)⋊C4—41no—
418(C2×D47)⋊C4—41no—
419(C2×D47)⋊C4—41no—
420(C2×D47)⋊C4—41no—
421C4⋊Dic47—22no—
422C4⋊Dic47—22no—
423C4⋊Dic47—22no—
424C4⋊Dic47—22no—
425C4⋊Dic47—22no—
426C4⋊Dic47—22no—
427C4⋊Dic47—22no—
428C4⋊Dic47—22no—
429C4⋊Dic47—22no—
430C4⋊Dic47—41no—
431C4⋊Dic47—41no—
432C4⋊Dic47—41no—
433C4⋊Dic47—41no—
434C4⋊Dic47—41no—
435C4⋊Dic47—41no—
436Dic47⋊C4—22no—
437Dic47⋊C4—22no—
438Dic47⋊C4—22no—
439Dic47⋊C4—22no—
440Dic47⋊C4—22no—
441Dic47⋊C4—22no—
442Dic47⋊C4—22no—
443Dic47⋊C4—22no—
444Dic47⋊C4—22no—
445Dic47⋊C4—22no—
446Dic47⋊C4—41no—
447Dic47⋊C4—41no—
448Dic47⋊C4—41no—
449Dic47⋊C4—41no—
450Dic47⋊C4—41no—
451Dic47⋊C4—41no—
452Dic47⋊C4—41no—
453Dic47⋊C4—41no—
454Dic47⋊C4—41no—
455Dic47⋊C4—41no—
456C4×Dic47—22no—
457C4×Dic47—22no—
458C4×Dic47—22no—
459C4×Dic47—22no—
460C4×Dic47—22no—
461C4×Dic47—22no—
462C4×Dic47—22no—
463C4×Dic47—22no—
464C4×Dic47—22no—
465C4×Dic47—22no—
466C4×Dic47—22no—
467C4×Dic47—22no—
468C4×Dic47—22no—
469C4×Dic47—22no—
470C4×Dic47—22no—
471C4×Dic47—41no—
472C4×Dic47—41no—
473C4×Dic47—41no—
474C4×Dic47—41no—
475C4×Dic47—41no—
476C4×Dic47—41no—
477C4×Dic47#4114yes—
478C4×Dic47#4114yes—
479C23×C47C2511yescharacteristic
480C22×D47—21no—
481C22×D47—21no—
482C22×D47—21no—
483C22×D47—21no—
484C22×D47—21no—
485C22×D47—21no—
486C22×D47—21no—
487Q8×C47—28no—
488C2×C4×C47—21no—
489C2×C4×C47—21no—
490C2×C4×C47—21no—
491C2×C4×C47—21no—
492C2×C4×C47—21no—
493C2×C4×C47—21no—
494C2×C4×C47—21no—
495C2×C4×C47—21no—
496C2×C4×C47—21no—
497C2×C4×C47—21no—
498C2×C4×C47—21no—
499C2×C4×C47—21no—
500C2×C4×C47—21no—
501C2×C4×C47—21no—
502C2×C4×C47—21no—
503C2×C4×C47—21no—
504C2×C4×C47—21no—
505C2×C4×C47—21no—
506C2×C4×C47—21no—
507C2×C4×C47—21no—
508C2×C4×C47—21no—
509C2×C4×C47—21no—
510C2×C4×C47—21no—
511C2×C4×C47—21no—
512C2×C4×C47—21no—
513C2×C4×C47—21no—
514C2×C4×C47—21no—
515C2×C4×C47—21no—
516C2×C4×C47—21no—
517C2×C4×C47—21no—
518C2×C4×C47—21no—
519C2×C4×C47—21no—
520C2×C4×C47—21no—
521C2×C4×C47—21no—
522C2×C4×C47—21no—
523C2×C4×C47—21no—
524C2×C4×C47—21no—
525C2×C4×C47—21no—
526C2×C4×C47—21no—
527C2×C4×C47—21no—
528C2×C4×C47C2×#4112yes—
529C2×C4×C47C2×#4112yes—
530C2×C4×C47C2×#4112yes—
531C2×C4×C47C2×#4112yes—
532C2×C4×C47C2×#4112yes—
533C2×Dic47—21no—
534C2×Dic47—21no—
535C2×Dic47—21no—
536C2×Dic47—21no—
537C2×Dic47—21no—
538C2×Dic47—21no—
539C2×Dic47—21no—
540C2×Dic47—21no—
541C2×Dic47—21no—
542C2×Dic47—21no—
543C2×Dic47—21no—
544C2×Dic47—21no—
545C2×Dic47—21no—
546C2×Dic47—21no—
547C2×Dic47—21no—
548C2×Dic47—21no—
549C2×Dic47—21no—
550C2×Dic47—21no—
551C2×Dic47—21no—
552C2×Dic47—21no—
553C2×Dic47—21no—
554C2×Dic47—21no—
555C2×Dic47—21no—
556C2×Dic47—21no—
557C2×Dic47—21no—
558C2×Dic47—21no—
559C2×Dic47—21no—
560C2×Dic47—21no—
561C2×Dic47—21no—
562C2×Dic47—21no—
563C2×Dic47—21no—
564C2×Dic47—21no—
565C2×Dic47—21no—
566C2×Dic47—21no—
567C2×Dic47—21no—
568C2×Dic47—21no—
569C2×Dic47—21no—
570C2×Dic47—21no—
571C2×Dic47—21no—
572C2×Dic47C2×#4112yes—
573C2×Dic47C2×#4112yes—
574C2×Dic47C2×#4112yes—
575C2×Dic47C2×#4112yes—
576C2×Dic472−1+412yes—
577C2×Dic472−1+412yes—
578C4×D47—44no—
579Dic94—44no—
580#34604—471nomaximal, Sylow
581C22×C47C22×#4111yescharacteristic
582C22×C47C22×#4111yescharacteristic
583C22×C47C22×#4111yescharacteristic
584C22×C47C2×2−1+411yescharacteristic
585C22×C47C2×2−1+411yescharacteristic
586C22×C47#58511yescharacteristic
587C22×C47#58511yescharacteristic
588C2×D47—41no—
589C2×D47—41no—
590C2×D47—41no—
591C2×D47—41no—
592C2×D47—41no—
593C2×D47—41no—
594C2×D47—41no—
595C4×C47—22no—
596C4×C47—22no—
597C4×C47—22no—
598C4×C47—22no—
599C4×C47—22no—
600C4×C47—41no—
601C4×C47—41no—
602C4×C47—41no—
603C4×C47—41no—
604C4×C47—41no—
605C4×C47—41no—
606C4×C47—41no—
607C4×C47—41no—
608C4×C47—41no—
609C4×C47—41no—
610Dic47—22no—
611Dic47—22no—
612Dic47—22no—
613Dic47—41no—
614Dic47—41no—
615Dic47—41no—
616Dic47—41no—
617Dic47—41no—
618Dic47—41no—
619Dic47—41no—
620Dic47—41no—
621Dic47—41no—
622Dic47—41no—
623Dic47—41no—
624Dic47#54114yes—
625#2666—471no—
626#2666—471no—
627#2664—471no—
628#2664—471no—
629#2655—471no—
630#2655—471no—
631#2655—471no—
632#2655—471no—
633#2654—471no—
634#2654—471no—
635#2650—471no—
636#2650—471no—
637#2637—471no—
638#2637—471no—
639#2634—471no—
640#2634D4711yescharacteristic, complemented
641#2402—471no—
642#2402—471no—
643#2402—471no—
644#2401—471no—
645#2401—471no—
646#2399—471no—
647#2396—471no—
648#2396—471no—
649C4×#125—471no—
650C4×#125—471no—
651C4×#126—471no—
652C4×#126—471no—
653#2298—471no—
654#2295—471no—
655C42×Q8—471no—
656C2×C47#344411yescharacteristic
657C2×C47C2×#54111yescharacteristic
658C2×C47#345511yescharacteristic
659C2×C47#346111yescharacteristic
660C2×C47#346111yescharacteristic
661C2×C47#346111yescharacteristic
662C2×C47#346111yescharacteristic
663D47—81no—
664C2×#126—471no—
665C2×#126—471no—
666C2×#125—471no—
667C2×#125C2×D4711yescharacteristic
668C2×C4×Q8—471no—
669C2×C4×Q8—471no—
670C2×C4×Q8—471no—
671C2×C4×Q8C2×D4711yescharacteristic
672C2×#117—471no—
673#401—471no—
674#401—471no—
675#400—471no—
676#400—471no—
677#400—471no—
678#400—471no—
679#400—471no—
680#400—471no—
681#400—471no—
682#400—471no—
683#400—471no—
684#400—471no—
685#400—471no—
686#400—471no—
687#400—471no—
688#400—471no—
689#400—471no—
690#400—471no—
691#400C2×D4711yescharacteristic
692#400C2×D4711yescharacteristic
693#400C2×D4711yescharacteristic
694#400C2×D4711yescharacteristic
695#399—471no—
696#399—471no—
697#398—471no—
698#398—471no—
699#398—471no—
700#398—471no—
701#398—471no—
702#398—471no—
703#398—471no—
704#398—471no—
705#398—471no—
706#398—471no—
707#398—471no—
708#398—471no—
709#398—471no—
710#398—471no—
711#398—471no—
712#398—471no—
713#398—471no—
714#398—471no—
715#398C2×D4711yescharacteristic
716#398C2×D4711yescharacteristic
717#397—471no—
718#397—471no—
719#397—471no—
720#397—471no—
721#397—471no—
722#397—471no—
723#396—471no—
724#396—471no—
725#396—471no—
726#396—471no—
727#396—471no—
728#396—471no—
729#395—471no—
730#395—471no—
731#395—471no—
732#395—471no—
733#395C2×D4711yescharacteristic
734#395C2×D4711yescharacteristic
735#393—471no—
736#393—471no—
737#391—471no—
738#391—471no—
739#389—471no—
740#389—471no—
741#389—471no—
742#389—471no—
743#389—471no—
744#389—471no—
745#388—471no—
746#388—471no—
747#388—471no—
748#388—471no—
749#388—471no—
750#388—471no—
751#388—471no—
752#388—471no—
753#388—471no—
754#388—471no—
755#387—471no—
756#387—471no—
757#387—471no—
758#387—471no—
759#387—471no—
760#387—471no—
761#387—471no—
762#387—471no—
763#387—471no—
764#387—471no—
765#387—471no—
766#387—471no—
767#387—471no—
768#387—471no—
769#387—471no—
770#387—471no—
771#387—471no—
772#387—471no—
773#387C2×D4711yescharacteristic
774#387C2×D4711yescharacteristic
775#387C2×D4711yescharacteristic
776#387C2×D4711yescharacteristic
777#383—471no—
778#383C2×D4711yescharacteristic
779#382—471no—
780#382—471no—
781C4×C4⋊C4—471no—
782C4×C4⋊C4—471no—
783C4×C4⋊C4—471no—
784C4×C4⋊C4—471no—
785C4×C4⋊C4—471no—
786C4×C4⋊C4—471no—
787C4×C4⋊C4—471no—
788C4×C4⋊C4—471no—
789C4×C4⋊C4—471no—
790C4×C4⋊C4—471no—
791C4×C4⋊C4—471no—
792C4×C4⋊C4—471no—
793C4×C4⋊C4—471no—
794C4×C4⋊C4—471no—
795C4×C4⋊C4—471no—
796C4×C4⋊C4—471no—
797C4×C4⋊C4—471no—
798C4×C4⋊C4—471no—
799C4×C4⋊C4—471no—
800C4×C4⋊C4—471no—
801C4×C4⋊C4—471no—
802C4×C4⋊C4—471no—
803C4×C4⋊C4—471no—
804C4×C4⋊C4—471no—
805C4×C4⋊C4—471no—
806C4×C4⋊C4—471no—
807C4×C22⋊C4—471no—
808C4×C22⋊C4—471no—
809C4×C22⋊C4—471no—
810C4×C22⋊C4—471no—
811C4×C22⋊C4—471no—
812C4×C22⋊C4—471no—
813#376—471no—
814#376—471no—
815#376—471no—
816C43—471no—
817C43—471no—
818C43—471no—
819C47#3460411yescharacteristic, complemented, Sylow
820C22×Q8—471no—
821C22×Q8C22×D4711yescharacteristic
822C23×C4—471no—
823#126—944no—
824#126—944no—
825#125—24no—
826#125—944no—
827C4×Q8—24no—
828C4×Q8—944no—
829C4×Q8—944no—
830C4×Q8—944no—
831#117—944no—
832C2×C4⋊C4—471no—
833C2×C4⋊C4—471no—
834C2×C4⋊C4—471no—
835C2×C4⋊C4—471no—
836C2×C4⋊C4—471no—
837C2×C4⋊C4—471no—
838C2×C4⋊C4—471no—
839C2×C4⋊C4—471no—
840C2×C4⋊C4—471no—
841C2×C4⋊C4—471no—
842C2×C4⋊C4—471no—
843C2×C4⋊C4—471no—
844C2×C4⋊C4—471no—
845C2×C4⋊C4—471no—
846C2×C4⋊C4—471no—
847C2×C4⋊C4—471no—
848C2×C4⋊C4—471no—
849C2×C4⋊C4—471no—
850C2×C4⋊C4—471no—
851C2×C4⋊C4—471no—
852C2×C4⋊C4—471no—
853C2×C4⋊C4—471no—
854C2×C4⋊C4—471no—
855C2×C4⋊C4—471no—
856C2×C4⋊C4—471no—
857C2×C4⋊C4—471no—
858C2×C4⋊C4—471no—
859C2×C4⋊C4—471no—
860C2×C4⋊C4—471no—
861C2×C4⋊C4—471no—
862C2×C4⋊C4—471no—
863C2×C4⋊C4—471no—
864C2×C4⋊C4—471no—
865C2×C4⋊C4—471no—
866C2×C4⋊C4—471no—
867C2×C4⋊C4C22×D4711yescharacteristic
868C2×C4⋊C4C22×D4711yescharacteristic
869C2×C4⋊C4C22×D4711yescharacteristic
870C2×C4⋊C4C22×D4711yescharacteristic
871C2×C4⋊C4C22×D4711yescharacteristic
872C2×C4⋊C4C22×D4711yescharacteristic
873C2×C4⋊C4C22×D4711yescharacteristic
874C2×C4⋊C4C22×D4711yescharacteristic
875C2×C4⋊C4C22×D4711yescharacteristic
876C2×C4⋊C4C22×D4711yescharacteristic
877C2×C4⋊C4C22×D4711yescharacteristic
878C2×C4⋊C4C22×D4711yescharacteristic
879C2×C4⋊C4C22×D4711yescharacteristic
880C2×C22⋊C4—471no—
881C2×C22⋊C4—471no—
882C2×C22⋊C4—471no—
883C2×C22⋊C4—471no—
884C2×C22⋊C4—471no—
885C2×C22⋊C4—471no—
886C2×C22⋊C4—471no—
887C2×C22⋊C4—471no—
888C2×C22⋊C4—471no—
889C2×C22⋊C4—471no—
890C2×C22⋊C4—471no—
891C2×C22⋊C4—471no—
892C2×C22⋊C4—471no—
893C2×C22⋊C4—471no—
894C2×C42—471no—
895C2×C42—471no—
896C2×C42—471no—
897C2×C42—471no—
898C2×C42—471no—
899C2×C42—471no—
900C2×C42—471no—
901C2×C42—471no—
902C2×C42—471no—
903C2×C42—471no—
904C2×C42—471no—
905C2×C42—471no—
906C2×C42—471no—
907C2×C42—471no—
908C2×C42—471no—
909C2×C42—471no—
910C2×C42—471no—
911C2×C42—471no—
912C2×C42—471no—
913C2×C42—471no—
914C2×C42—471no—
915C2×C42—471no—
916C2×C42—471no—
917C2×C42C22×D4711yescharacteristic
918C2×C42C22×D4711yescharacteristic
919C2×C42C22×D4711yescharacteristic
920#95—471no—
921#95—471no—
922#95—471no—
923#95—471no—
924#95—471no—
925#95—471no—
926#95—471no—
927#95—471no—
928#95—471no—
929#95—471no—
930#95—471no—
931#95—471no—
932#95—471no—
933#95—471no—
934#95—471no—
935#95—471no—
936#95—471no—
937#95—471no—
938#95—471no—
939#95—471no—
940#95—471no—
941#95—471no—
942#95—471no—
943#95—471no—
944#95—471no—
945#95—471no—
946#95—471no—
947#95—471no—
948#95—471no—
949#95—471no—
950#95—471no—
951#95—471no—
952#95—471no—
953#95—471no—
954#95—471no—
955#95—471no—
956#95—471no—
957#95—471no—
958#95—471no—
959#95—471no—
960#95—471no—
961#95—471no—
962#95—471no—
963#95—471no—
964#95—471no—
965#95—471no—
966#95C22×D4711yescharacteristic
967#95C22×D4711yescharacteristic
968#95C22×D4711yescharacteristic
969#95C22×D4711yescharacteristic
970#95C22×D4711yescharacteristic
971#95C22×D4711yescharacteristic
972#95C22×D4711yescharacteristic
973#95C22×D4711yescharacteristic
974#95C22×D4711yescharacteristic
975#95C22×D4711yescharacteristic
976#95C22×D4711yescharacteristic
977#95C22×D4711yescharacteristic
978#95C22×D4711yescharacteristic
979#95C22×D4711yescharacteristic
980#95C22×D4711yescharacteristic
981#95C22×D4711yescharacteristic
982#95C22×D4711yescharacteristic
983#95C22×D4711yescharacteristic
984C24—471no—
985C2×Q8—22no—
986C2×Q8—22no—
987C2×Q8—22no—
988C2×Q8—942no—
989C2×Q8—1881no—
990C2×Q8—1881no—
991C22×C4—471no—
992C22×C4—471no—
993C22×C4—471no—
994C22×C4—471no—
995C22×C4—471no—
996C22×C4—471no—
997C22×C4—471no—
998C22×C4—471no—
999C22×C4—471no—
1000C22×C4—471no—
1001C22×C4—471no—
1002C22×C4—471no—
1003C22×C4—471no—
1004C22×C4—471no—
1005C22×C4—471no—
1006C22×C4—942no—
1007C22×C4—942no—
1008C22×C4—942no—
1009C22×C4C23×D4711yescharacteristic
1010C22×C4C23×D4711yescharacteristic
1011C22×C4C23×D4711yescharacteristic
1012C22×C4C23×D4711yescharacteristic
1013C22×C4C23×D4711yescharacteristic
1014C22×C4C23×D4711yescharacteristic
1015C22×C4C23×D4711yescharacteristic
1016C22×C4C23×D4711yescharacteristic
1017C22×C4C23×D4711yescharacteristic
1018C22×C4C23×D4711yescharacteristic
1019C22×C4C23×D4711yescharacteristic
1020C22×C4C23×D4711yescharacteristic
1021C22×C4C23×D4711yescharacteristic
1022C22×C4C23×D4711yescharacteristic
1023C22×C4C23×D4711yescharacteristic
1024C4⋊C4—22no—
1025C4⋊C4—22no—
1026C4⋊C4—22no—
1027C4⋊C4—22no—
1028C4⋊C4—22no—
1029C4⋊C4—22no—
1030C4⋊C4—22no—
1031C4⋊C4—22no—
1032C4⋊C4—22no—
1033C4⋊C4—22no—
1034C4⋊C4—22no—
1035C4⋊C4—22no—
1036C4⋊C4—22no—
1037C4⋊C4—942no—
1038C4⋊C4—942no—
1039C4⋊C4—942no—
1040C4⋊C4—942no—
1041C4⋊C4—942no—
1042C4⋊C4—942no—
1043C4⋊C4—942no—
1044C4⋊C4—942no—
1045C4⋊C4—942no—
1046C4⋊C4—942no—
1047C4⋊C4—942no—
1048C4⋊C4—942no—
1049C4⋊C4—942no—
1050C4⋊C4—942no—
1051C4⋊C4—942no—
1052C4⋊C4—942no—
1053C4⋊C4—942no—
1054C4⋊C4—942no—
1055C4⋊C4—942no—
1056C4⋊C4—1881no—
1057C4⋊C4—1881no—
1058C4⋊C4—1881no—
1059C4⋊C4—1881no—
1060C4⋊C4—1881no—
1061C4⋊C4—1881no—
1062C4⋊C4—1881no—
1063C4⋊C4—1881no—
1064C4⋊C4—1881no—
1065C4⋊C4—1881no—
1066C4⋊C4—1881no—
1067C4⋊C4—1881no—
1068C4⋊C4—1881no—
1069C4⋊C4—1881no—
1070C4⋊C4—1881no—
1071C4⋊C4—1881no—
1072C22⋊C4—942no—
1073C22⋊C4—942no—
1074C22⋊C4—942no—
1075C22⋊C4—942no—
1076C22⋊C4—942no—
1077C22⋊C4—942no—
1078C22⋊C4—942no—
1079C22⋊C4—942no—
1080C22⋊C4—1881no—
1081C22⋊C4—1881no—
1082C22⋊C4—1881no—
1083C22⋊C4—1881no—
1084C22⋊C4—1881no—
1085C22⋊C4—1881no—
1086C42—22no—
1087C42—22no—
1088C42—474no—
1089C42—474no—
1090C42—942no—
1091C42—942no—
1092C42—942no—
1093C42—942no—
1094C42—942no—
1095C42—942no—
1096C42—942no—
1097C42—942no—
1098C42—942no—
1099C42—942no—
1100C42—942no—
1101C42—942no—
1102C42—942no—
1103C42—942no—
1104C42—942no—
1105C42—1881no—
1106C42—1881no—
1107C42—1881no—
1108C42—1881no—
1109C42—1881no—
1110C42—1881no—
1111C42#1062535214yes—
1112C23—941no—
1113C23—941no—
1114C23—941no—
1115C23—941no—
1116C23—941no—
1117C23—941no—
1118C23—941no—
1119C23C24×D4711yescharacteristic
1120Q8—28no—
1121Q8—1884no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—472no—
1163C2×C4—472no—
1164C2×C4—472no—
1165C2×C4—472no—
1166C2×C4—472no—
1167C2×C4—472no—
1168C2×C4—941no—
1169C2×C4—941no—
1170C2×C4—941no—
1171C2×C4—941no—
1172C2×C4—941no—
1173C2×C4—941no—
1174C2×C4—941no—
1175C2×C4—941no—
1176C2×C4—941no—
1177C2×C4—941no—
1178C2×C4—941no—
1179C2×C4—941no—
1180C2×C4—941no—
1181C2×C4—941no—
1182C2×C4—941no—
1183C2×C4—941no—
1184C2×C4—941no—
1185C2×C4—941no—
1186C2×C4—941no—
1187C2×C4—941no—
1188C2×C4—941no—
1189C2×C4—941no—
1190C2×C4—941no—
1191C2×C4—941no—
1192C2×C4—941no—
1193C2×C4—941no—
1194C2×C4—941no—
1195C2×C4—941no—
1196C2×C4—941no—
1197C2×C4—941no—
1198C2×C4—941no—
1199C2×C4—941no—
1200C2×C4—941no—
1201C2×C4—941no—
1202C2×C4—941no—
1203C2×C4—941no—
1204C2×C4—941no—
1205C2×C4—941no—
1206C2×C4—941no—
1207C2×C4—1884no—
1208C2×C4#41×D4712yes—
1209C2×C4#41×D4712yes—
1210C2×C4C2×#1062535212yes—
1211C2×C4C2×#1062535212yes—
1212C2×C4C2×#1062535212yes—
1213C22—1881no—
1214C22—1881no—
1215C22—1881no—
1216C22—1881no—
1217C22—1881no—
1218C22—1881no—
1219C22—1881no—
1220C22C2×#41×D4711yescharacteristic
1221C22C2×#41×D4711yescharacteristic
1222C22C22×#1062535211yescharacteristic
1223C222−1+4×D4711yescharacteristic
1224C222−1+4×D4711yescharacteristic
1225C22#1568996011yescharacteristic
1226C22#1568996011yescharacteristic
1227C4—22no—
1228C4—22no—
1229C4—22no—
1230C4—22no—
1231C4—22no—
1232C4—41no—
1233C4—41no—
1234C4—41no—
1235C4—41no—
1236C4—41no—
1237C4—41no—
1238C4—41no—
1239C4—41no—
1240C4—41no—
1241C4—41no—
1242C4—474no—
1243C4—942no—
1244C4—942no—
1245C4—942no—
1246C4—1881no—
1247C4—1881no—
1248C4—1881no—
1249C4—1881no—
1250C4—1881no—
1251C4—1881no—
1252C4—1881no—
1253C4—1881no—
1254C4—1881no—
1255C4—1881no—
1256C4—1881no—
1257C2—3761no—
1258C2#2025668011yescharacteristic
1259C2#541×D4711yescharacteristic
1260C2#2025677911yescharacteristic
1261C2#2025681211yescharacteristic
1262C2#2025681211yescharacteristic
1263C2#2025682011yescharacteristic
1264C2#2025682011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D47
commutator, socle, cosocleC23×C47C25
FittingC47×#2634C2
prime radicalC23×D47C24
hypercenter#2634D47
hypocenterC47#34604
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2634

Complements

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

NH ≅ G/Ntype
1. #20249571C2semidirect
2. #20249570C2semidirect
5. #20249483C2semidirect
6. #20249482C2semidirect
7. #20249481C2semidirect
8. #20249474C2semidirect
15. #20249263C2semidirect
16. #20246694C2semidirect
17. #20246694C2semidirect
18. #20246692C2semidirect
21. #20246678C2semidirect
24. #125×Dic47C2semidirect
25. #20245945C2semidirect
29. #20245861C2semidirect
30. C4×Q8×Dic47C2semidirect
31. C47×#2634C2semidirect
640. #2634D47semidirect
819. C47#34604semidirect

Maximal subgroups

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

subgroupindex
#202495712
#202495702
#202495492
#202495462
#202494832
#202494822
#202494812
#202494742
#202494692
#202494662
#202494082
#202494012
#202492952
#202492942
#202492632
#202466942
#202466922
#202466872
#202466782
#202466652
#202466592
#125×Dic472
#202459452
#202459382
#202459362
#202458802
#202458612
C4×Q8×Dic472
C47×#26342
#3460447