Finite Group Databasebeta

← #26424494

Subgroups — #26424494

Order 12032.

1494 conjugacy classes of subgroups.

The subgroup lattice has 1318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20251737C211yesmaximal, characteristic, complemented
2#20251729C211yesmaximal, characteristic, complemented
3#20251260C211yesmaximal, characteristic, complemented
4#20251192C211yesmaximal, characteristic, complemented
5#20251178C211yesmaximal, characteristic, complemented
6#20251126C211yesmaximal, characteristic, complemented
7#20251058C211yesmaximal, characteristic
8#20251016C211yesmaximal, characteristic
9#20250886C211yesmaximal, characteristic, complemented
10#20250756C211yesmaximal, characteristic, complemented
11#20250698C211yesmaximal, characteristic, complemented
12#20250586C211yesmaximal, characteristic, complemented
13#20250510C211yesmaximal, characteristic
14#20250214C211yesmaximal, characteristic, complemented
15#20250171C211yesmaximal, characteristic, complemented
16#20250019C211yesmaximal, characteristic
17#20249849C211yesmaximal, characteristic, complemented
18#20249314C211yesmaximal, characteristic
19#20249313C211yesmaximal, characteristic
20#20248857C211yesmaximal, characteristic, complemented
21#20248843C211yesmaximal, characteristic, complemented
22#20248830C211yesmaximal, characteristic, complemented
23#20248810C211yesmaximal, characteristic, complemented
24#20248268C211yesmaximal, characteristic, complemented
25#20248188C211yesmaximal, characteristic, complemented
26#20247608C211yesmaximal, characteristic, complemented
27#20247552C211yesmaximal, characteristic, complemented
28#20246143C211yesmaximal, characteristic, complemented
29#20246140C211yesmaximal, characteristic, complemented
30#20245826C211yesmaximal, characteristic
31C47×#2799C211yesmaximal, characteristic, complemented
32C2×#13094022C2211yescharacteristic
33C2×#13094018C2211yescharacteristic
34C2×#13094014C2211yescharacteristic
35C2×#13094004C2211yescharacteristic
36C2×#13094000C2211yescharacteristic
37C2×#13094000C2211yescharacteristic
38C2×#13093986C2211yescharacteristic
39C2×#13093982C2211yescharacteristic
40C2×C42×D47C2211yescharacteristic
41C47⋊#401C2211yescharacteristic
42#15689065C2211yescharacteristic
43#15689065C2211yescharacteristic
44#15689064C2211yescharacteristic
45#15689064C2211yescharacteristic
46#15689064C2211yescharacteristic
47#15689064C2211yescharacteristic
48#15689063C2211yescharacteristic
49#15689063C2211yescharacteristic
50#15689061C2211yescharacteristic
51#15689060C2211yescharacteristic
52#15689057C2211yescharacteristic
53#15689057C2211yescharacteristic
54#15689057C2211yescharacteristic
55#15689057C2211yescharacteristic
56#15689056C2211yescharacteristic
57#15689056C2211yescharacteristic
58#15689056C2211yescharacteristic
59#15689054C2211yescharacteristic
60#15689054C2211yescharacteristic
61#15689053C2211yescharacteristic
62#15689052C2211yescharacteristic
63#15689052C2211yescharacteristic
64#15689052C2211yescharacteristic
65#15689052C2211yescharacteristic
66#15689052C2211yescharacteristic
67#15689050C2211yescharacteristic
68#15689049C2211yescharacteristic
69#15689049C2211yescharacteristic
70#15689049C2211yescharacteristic
71#15689047C2211yescharacteristic
72#15689045C2211yescharacteristic
73#15689045C2211yescharacteristic
74#15689043C2211yescharacteristic
75#15689042C2211yescharacteristic
76#15689041C2211yescharacteristic
77#15689041C2211yescharacteristic
78#15689040C2211yescharacteristic
79#15689040C2211yescharacteristic
80#15689036C2211yescharacteristic
81#15689034C2211yescharacteristic
82#15689034C2211yescharacteristic
83#15689030C2211yescharacteristic
84#15689030C2211yescharacteristic
85#15689029C2211yescharacteristic
86#15689027C2211yescharacteristic
87#15689027C2211yescharacteristic
88#15689022C2211yescharacteristic
89#15689021C2211yescharacteristic
90#15689020C2211yescharacteristic
91#15689020C2211yescharacteristic
92#15689020C2211yescharacteristic
93#15689020C2211yescharacteristic
94#15689019C2211yescharacteristic
95#15689019C2211yescharacteristic
96#15689018C2211yescharacteristic
97#15689018C2211yescharacteristic
98#15689015C2211yescharacteristic
99#15689015C2211yescharacteristic
100#15689015C2211yescharacteristic
101#15689014C2211yescharacteristic
102#15689014C2211yescharacteristic
103#15689014C2211yescharacteristic
104#15689014C2211yescharacteristic
105#15689013C2211yescharacteristic
106#15689013C2211yescharacteristic
107#15689013C2211yescharacteristic
108#15689012C2211yescharacteristic
109#15689012C2211yescharacteristic
110#15689012C2211yescharacteristic
111#15689012C2211yescharacteristic
112#15689012C2211yescharacteristic
113#15689012C2211yescharacteristic
114#15689012C2211yescharacteristic
115#15689010C2211yescharacteristic
116#15689010C2211yescharacteristic
117#15689010C2211yescharacteristic
118#15689009C2211yescharacteristic
119#15689009C2211yescharacteristic
120#15689009C2211yescharacteristic
121#15689009C2211yescharacteristic
122#15689008C2211yescharacteristic
123#15689008C2211yescharacteristic
124#15689008C2211yescharacteristic
125#15689008C2211yescharacteristic
126#15689007C2211yescharacteristic
127#15689007C2211yescharacteristic
128#15689006C2211yescharacteristic
129#15689006C2211yescharacteristic
130#15689006C2211yescharacteristic
131#15689006C2211yescharacteristic
132#15689006C2211yescharacteristic
133#15689006C2211yescharacteristic
134#15689006C2211yescharacteristic
135#15689006C2211yescharacteristic
136#15689005C2211yescharacteristic
137#15689005C2211yescharacteristic
138#15689005C2211yescharacteristic
139#15689005C2211yescharacteristic
140#15689005C2211yescharacteristic
141#15689004C2211yescharacteristic
142#15689004C2211yescharacteristic
143#15689004C2211yescharacteristic
144#15689001C2211yescharacteristic
145#15689001C2211yescharacteristic
146#15688997C2211yescharacteristic
147#15688997C2211yescharacteristic
148#15688997C2211yescharacteristic
149#15688997C2211yescharacteristic
150#15688997C2211yescharacteristic
151#15688994C2211yescharacteristic
152#15688994C2211yescharacteristic
153#15688994C2211yescharacteristic
154#15688992C2211yescharacteristic
155#15688990C2211yescharacteristic
156#15688987C2211yescharacteristic
157#15688985C2211yescharacteristic
158#15688985C2211yescharacteristic
159#15688982C2211yescharacteristic
160#15688982C2211yescharacteristic
161#15688982C2211yescharacteristic
162#15688982C2211yescharacteristic
163#15688980C2211yescharacteristic
164C4⋊C4×Dic47C2211yescharacteristic
165C4×Dic47⋊C4C2211yescharacteristic
166C4×C4⋊Dic47C2211yescharacteristic
167#15688974C2211yescharacteristic
168#15688974C2211yescharacteristic
169#15688970C2211yescharacteristic
170#15688970C2211yescharacteristic
171#15688968C2211yescharacteristic
172C47×#400C2211yescharacteristic
173C47×#400C2211yescharacteristic
174C47×#400C2211yescharacteristic
175C47×#398C2211yescharacteristic
176C47×#398C2211yescharacteristic
177C47×#395C2211yescharacteristic
178C47×#391C2211yescharacteristic
179C47×#391C2211yescharacteristic
180C47×#391C2211yescharacteristic
181C47×#391C2211yescharacteristic
182C47×#391C2211yescharacteristic
183C47×#387C2211yescharacteristic
184C47×#387C2211yescharacteristic
185C47×#387C2211yescharacteristic
186C47×#387C2211yescharacteristic
187C22×Dic94C2311yescharacteristic
188C22×D188C2311yescharacteristic
189C22×C4×D47C2311yescharacteristic
190C22×C4×D47C2311yescharacteristic
191C22×C4×D47C2311yescharacteristic
192C22×C4×D47C2311yescharacteristic
193#13094022—42no—
194#13094018—42no—
195#13094014—42no—
196#13094004—24no—
197#13094000—24no—
198#13094000—42no—
199#13093986—24no—
200#13093982—42no—
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×Dic47⋊C4C2311yescharacteristic
232C2×Dic47⋊C4C2311yescharacteristic
233C2×Dic47⋊C4C2311yescharacteristic
234C2×Dic47⋊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×(C2×D47)⋊C4C2311yescharacteristic
246C2×(C2×D47)⋊C4C2311yescharacteristic
247C2×(C2×D47)⋊C4C2311yescharacteristic
248C2×(C2×D47)⋊C4C2311yescharacteristic
249C2×(C2×D47)⋊C4C2311yescharacteristic
250C2×(C2×D47)⋊C4C2311yescharacteristic
251C2×(C2×D47)⋊C4C2311yescharacteristic
252C2×(C2×D47)⋊C4C2311yescharacteristic
253C2×(C2×D47)⋊C4C2311yescharacteristic
254C2×(C2×D47)⋊C4C2311yescharacteristic
255C2×(C2×D47)⋊C4C2311yescharacteristic
256C2×(C2×D47)⋊C4C2311yescharacteristic
257C2×(C2×D47)⋊C4C2311yescharacteristic
258C2×(C2×D47)⋊C4C2311yescharacteristic
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
268C2×C4×Dic47C2311yescharacteristic
269C2×C4×Dic47C2311yescharacteristic
270C2×C4×Dic47C2311yescharacteristic
271C42×D47—42no—
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
314C47⋊#95C2311yescharacteristic
315C47⋊#95C2311yescharacteristic
316C22×Q8×C47C2311yescharacteristic
317C22×Q8×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×C42×C47C2311yescharacteristic
329C2×C42×C47C2311yescharacteristic
330C2×C42×C47C2311yescharacteristic
331#95×C47C2311yescharacteristic
332#95×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
352C23×D47C2411yescharacteristic
353C2×Q8×C47—22no—
354C2×Q8×C47—22no—
355C2×Q8×C47—41no—
356C2×Q8×C47—41no—
357C2×Q8×C47—41no—
358C2×Q8×C47—41no—
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×C4×C47C2411yescharacteristic
371C22×C4×C47C2411yescharacteristic
372C22×C4×C47C2411yescharacteristic
373C22×C4×C47C2411yescharacteristic
374C22×Dic47C2411yescharacteristic
375C22×Dic47C2411yescharacteristic
376C22×Dic47C2411yescharacteristic
377C22×Dic47C2411yescharacteristic
378C22×Dic47C2411yescharacteristic
379C22×Dic47C2411yescharacteristic
380C22×Dic47C2411yescharacteristic
381C22×Dic47C2411yescharacteristic
382C22×Dic47C2411yescharacteristic
383C22×Dic47C2411yescharacteristic
384C22×Dic47C2411yescharacteristic
385C22×Dic47C2411yescharacteristic
386C22×Dic47C2411yescharacteristic
387C22×Dic47C2411yescharacteristic
388C2×D188—22no—
389C2×D188—41no—
390C2×D188—41no—
391C2×C4×D47—22no—
392C2×C4×D47—22no—
393C2×C4×D47—22no—
394C2×C4×D47—22no—
395C2×C4×D47—41no—
396C2×C4×D47—41no—
397C2×C4×D47—41no—
398C2×C4×D47—41no—
399C2×C4×D47—41no—
400C2×C4×D47—41no—
401C2×C4×D47—41no—
402C2×C4×D47#4114yes—
403C2×Dic94—22no—
404C2×Dic94—41no—
405C2×Dic94—41no—
406C4⋊C4×C47—22no—
407C4⋊C4×C47—22no—
408C4⋊C4×C47—41no—
409C4⋊C4×C47—41no—
410C4⋊C4×C47—41no—
411C4⋊C4×C47—41no—
412C4⋊C4×C47—41no—
413C4⋊C4×C47—41no—
414C4⋊C4×C47—41no—
415C4⋊C4×C47—41no—
416C42×C47—41no—
417C42×C47—41no—
418C42×C47—41no—
419(C2×D47)⋊C4—22no—
420(C2×D47)⋊C4—22no—
421(C2×D47)⋊C4—22no—
422(C2×D47)⋊C4—22no—
423(C2×D47)⋊C4—22no—
424(C2×D47)⋊C4—22no—
425(C2×D47)⋊C4—22no—
426(C2×D47)⋊C4—22no—
427(C2×D47)⋊C4—22no—
428(C2×D47)⋊C4—41no—
429(C2×D47)⋊C4—41no—
430(C2×D47)⋊C4—41no—
431(C2×D47)⋊C4—41no—
432(C2×D47)⋊C4—41no—
433(C2×D47)⋊C4—41no—
434(C2×D47)⋊C4—41no—
435(C2×D47)⋊C4—41no—
436(C2×D47)⋊C4—41no—
437(C2×D47)⋊C4—41no—
438(C2×D47)⋊C4—41no—
439(C2×D47)⋊C4—41no—
440(C2×D47)⋊C4—41no—
441(C2×D47)⋊C4—41no—
442(C2×D47)⋊C4—41no—
443C4⋊Dic47—22no—
444C4⋊Dic47—22no—
445C4⋊Dic47—22no—
446C4⋊Dic47—22no—
447C4⋊Dic47—22no—
448C4⋊Dic47—22no—
449C4⋊Dic47—22no—
450C4⋊Dic47—41no—
451C4⋊Dic47—41no—
452C4⋊Dic47—41no—
453Dic47⋊C4—22no—
454Dic47⋊C4—22no—
455Dic47⋊C4—22no—
456Dic47⋊C4—22no—
457Dic47⋊C4—22no—
458Dic47⋊C4—22no—
459Dic47⋊C4—22no—
460Dic47⋊C4—22no—
461Dic47⋊C4—41no—
462Dic47⋊C4—41no—
463Dic47⋊C4—41no—
464Dic47⋊C4—41no—
465Dic47⋊C4—41no—
466Dic47⋊C4—41no—
467Dic47⋊C4—41no—
468Dic47⋊C4—41no—
469Dic47⋊C4—41no—
470Dic47⋊C4—41no—
471Dic47⋊C4—41no—
472Dic47⋊C4—41no—
473Dic47⋊C4—41no—
474Dic47⋊C4—41no—
475Dic47⋊C4—41no—
476Dic47⋊C4—41no—
477C4×Dic47—22no—
478C4×Dic47—22no—
479C4×Dic47—22no—
480C4×Dic47—41no—
481C4×Dic47—41no—
482C4×Dic47—41no—
483C4×Dic47—41no—
484C4×Dic47—41no—
485C4×Dic47—41no—
486C4×Dic47—41no—
487C4×Dic47—41no—
488C4×Dic47—41no—
489C23×C47C2511yescharacteristic
490C22×D47—21no—
491C22×D47—21no—
492C22×D47—21no—
493C22×D47—21no—
494C22×D47—21no—
495C22×D47—21no—
496C22×D47—21no—
497C22×D47—21no—
498C22×D47—21no—
499C22×D47—21no—
500C22×D47—21no—
501C22×D47—21no—
502C22×D47—21no—
503C22×D47C2×#4112yes—
504Q8×C47—82no—
505Q8×C47—82no—
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×C47—21no—
529C2×C4×C47—21no—
530C2×C4×C47—21no—
531C2×C4×C47—21no—
532C2×C4×C47—21no—
533C2×C4×C47—21no—
534C2×C4×C47—21no—
535C2×C4×C47—21no—
536C2×C4×C47—21no—
537C2×C4×C47—21no—
538C2×C4×C47—21no—
539C2×C4×C47—21no—
540C2×C4×C47—21no—
541C2×C4×C47—21no—
542C2×C4×C47—21no—
543C2×C4×C47—21no—
544C2×C4×C47—21no—
545C2×C4×C47—21no—
546C2×C4×C47—21no—
547C2×C4×C47—21no—
548C2×C4×C47—21no—
549C2×C4×C47C2×#4112yes—
550C2×C4×C472−1+412yes—
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×Dic47—21no—
573C2×Dic47—21no—
574C2×Dic47—21no—
575C2×Dic47—21no—
576C2×Dic47—21no—
577C2×Dic47—21no—
578C2×Dic47—21no—
579C2×Dic47—21no—
580C2×Dic47—21no—
581C2×Dic47—21no—
582C2×Dic47—21no—
583C2×Dic47—21no—
584C2×Dic47—21no—
585C2×Dic47—21no—
586C2×Dic47—21no—
587C2×Dic47—21no—
588C2×Dic47—21no—
589C2×Dic47—21no—
590C2×Dic47C2×#4112yes—
591C2×Dic47H(5,𝔽2)12yes—
592C2×Dic472−1+412yes—
593D188—44no—
594C4×D47—44no—
595C4×D47—44no—
596C4×D47—44no—
597C4×D47—44no—
598Dic94—82no—
599#36772—471nomaximal, Sylow
600C22×C47C22×#4111yescharacteristic
601C22×C47C2×H(5,𝔽2)11yescharacteristic
602C22×C47C2×2−1+411yescharacteristic
603C22×C47C2×2−1+411yescharacteristic
604C22×C47#58511yescharacteristic
605C22×C47#58511yescharacteristic
606C22×C47#58511yescharacteristic
607C2×D47—22no—
608C2×D47—22no—
609C2×D47—22no—
610C2×D47—41no—
611C2×D47—41no—
612C2×D47—41no—
613C2×D47—41no—
614C2×D47—41no—
615C2×D47—41no—
616C2×D47—41no—
617C2×D47—41no—
618C2×D47—41no—
619C2×D47—41no—
620C2×D47—41no—
621C4×C47—22no—
622C4×C47—22no—
623C4×C47—41no—
624C4×C47—41no—
625C4×C47—41no—
626C4×C47—41no—
627C4×C47—41no—
628C4×C47—41no—
629C4×C47—41no—
630C4×C47—41no—
631C4×C47—41no—
632C4×C47—41no—
633C4×C47—41no—
634C4×C47—41no—
635C4×C47—41no—
636Dic47—22no—
637Dic47—22no—
638Dic47—22no—
639Dic47—41no—
640Dic47—41no—
641Dic47—41no—
642Dic47—41no—
643Dic47—41no—
644Dic47—41no—
645Dic47—41no—
646Dic47—41no—
647Dic47—41no—
648Dic47—41no—
649Dic47—41no—
650#2857—471no—
651#2855—471no—
652#2799D4711yescharacteristic, complemented
653#2798—471no—
654#2793—471no—
655#2791—471no—
656#2787—471no—
657#2781—471no—
658#2779—471no—
659#2770—471no—
660#2759—471no—
661#2755—471no—
662#2747—471no—
663#2741—471no—
664#2716—471no—
665#2713—471no—
666#2702—471no—
667#2690—471no—
668#2638—471no—
669#2638—471no—
670#2590—471no—
671#2589—471no—
672#2588—471no—
673#2587—471no—
674#2533—471no—
675#2528—471no—
676#2478—471no—
677#2475—471no—
678#2332—471no—
679#2332—471no—
680#2290—471no—
681C2×C47#345511yescharacteristic
682C2×C47#350511yescharacteristic
683C2×C47#350911yescharacteristic
684C2×C47#353511yescharacteristic
685C2×C47#354111yescharacteristic
686C2×C47#355711yescharacteristic
687C2×C47#356511yescharacteristic
688D47—42no—
689D47—81no—
690C2×C4⋊Q8—471no—
691C2×#126—471no—
692C2×#125—471no—
693C2×C22⋊Q8—471no—
694C2×C22⋊Q8—471no—
695C2×C22⋊Q8—471no—
696C2×C4×D4—471no—
697C2×#117—471no—
698C22×C42—471no—
699#401—471no—
700#400—471no—
701#400—471no—
702#400—471no—
703#400—471no—
704#400—471no—
705#400—471no—
706#400—471no—
707#400—471no—
708#400—471no—
709#400C2×D4711yescharacteristic
710#400C2×D4711yescharacteristic
711#400C2×D4711yescharacteristic
712#399—471no—
713#398—471no—
714#398—471no—
715#398—471no—
716#398—471no—
717#398—471no—
718#398—471no—
719#398—471no—
720#398—471no—
721#398—471no—
722#398—471no—
723#398C2×D4711yescharacteristic
724#398C2×D4711yescharacteristic
725#397—471no—
726#397—471no—
727#397—471no—
728#397—471no—
729#397—471no—
730#397—471no—
731#397—471no—
732#397—471no—
733#397—471no—
734#396—471no—
735#396—471no—
736#396—471no—
737#395—471no—
738#395—471no—
739#395C2×D4711yescharacteristic
740#394—471no—
741#394—471no—
742#394—471no—
743#394—471no—
744#393—471no—
745#393—471no—
746#393—471no—
747#391—471no—
748#391—471no—
749#391—471no—
750#391—471no—
751#391—471no—
752#391C2×D4711yescharacteristic
753#391C2×D4711yescharacteristic
754#391C2×D4711yescharacteristic
755#391C2×D4711yescharacteristic
756#391C2×D4711yescharacteristic
757#389—471no—
758#389—471no—
759#389—471no—
760#389—471no—
761#389—471no—
762#389—471no—
763#389—471no—
764#389—471no—
765#389—471no—
766#389—471no—
767#388—471no—
768#388—471no—
769#388—471no—
770#388—471no—
771#388—471no—
772#388—471no—
773#388—471no—
774#388—471no—
775#388—471no—
776#388—471no—
777#388—471no—
778#388—471no—
779#388—471no—
780#388—471no—
781#388—471no—
782#388—471no—
783#388—471no—
784#387—471no—
785#387—471no—
786#387—471no—
787#387—471no—
788#387—471no—
789#387—471no—
790#387—471no—
791#387—471no—
792#387—471no—
793#387—471no—
794#387—471no—
795#387—471no—
796#387—471no—
797#387—471no—
798#387—471no—
799#387—471no—
800#387—471no—
801#387—471no—
802#387—471no—
803#387—471no—
804#387—471no—
805#387—471no—
806#387—471no—
807#387—471no—
808#387—471no—
809#387—471no—
810#387—471no—
811#387—471no—
812#387—471no—
813#387C2×D4711yescharacteristic
814#387C2×D4711yescharacteristic
815#387C2×D4711yescharacteristic
816#387C2×D4711yescharacteristic
817#386—471no—
818#386—471no—
819#385—471no—
820#385—471no—
821#385—471no—
822#385—471no—
823#385—471no—
824#385—471no—
825#385—471no—
826#385—471no—
827#384—471no—
828#383—471no—
829#382—471no—
830#381—471no—
831#381—471no—
832#380—471no—
833#380—471no—
834#380—471no—
835#380—471no—
836#380—471no—
837C4×C4⋊C4—471no—
838C4×C4⋊C4—471no—
839C4×C4⋊C4—471no—
840C4×C4⋊C4—471no—
841C4×C4⋊C4—471no—
842C4×C22⋊C4—471no—
843C4×C22⋊C4—471no—
844#376—471no—
845C47#3677211yescharacteristic, complemented, Sylow
846C22×Q8—471no—
847C22×Q8C22×D4711yescharacteristic
848C22×Q8C22×D4711yescharacteristic
849C22×D4—471no—
850C23×C4—471no—
851C23×C4—471no—
852C23×C4—471no—
853C23×C4—471no—
854C4⋊Q8—1882no—
855#126—1882no—
856#125—1882no—
857C22⋊Q8—944no—
858C22⋊Q8—944no—
859C22⋊Q8—1882no—
860C4×D4—944no—
861#117—1882no—
862C2×C4⋊C4—471no—
863C2×C4⋊C4—471no—
864C2×C4⋊C4—471no—
865C2×C4⋊C4—471no—
866C2×C4⋊C4—471no—
867C2×C4⋊C4—471no—
868C2×C4⋊C4—471no—
869C2×C4⋊C4—471no—
870C2×C4⋊C4—471no—
871C2×C4⋊C4—471no—
872C2×C4⋊C4—471no—
873C2×C4⋊C4—471no—
874C2×C4⋊C4—471no—
875C2×C4⋊C4—471no—
876C2×C4⋊C4—471no—
877C2×C4⋊C4—471no—
878C2×C4⋊C4—471no—
879C2×C4⋊C4—471no—
880C2×C4⋊C4—471no—
881C2×C4⋊C4—471no—
882C2×C4⋊C4—471no—
883C2×C4⋊C4—471no—
884C2×C4⋊C4—471no—
885C2×C4⋊C4—471no—
886C2×C4⋊C4—471no—
887C2×C4⋊C4—471no—
888C2×C4⋊C4—471no—
889C2×C4⋊C4—471no—
890C2×C4⋊C4—471no—
891C2×C4⋊C4—471no—
892C2×C4⋊C4—471no—
893C2×C4⋊C4—471no—
894C2×C4⋊C4—471no—
895C2×C4⋊C4—471no—
896C2×C4⋊C4C22×D4711yescharacteristic
897C2×C4⋊C4C22×D4711yescharacteristic
898C2×C4⋊C4C22×D4711yescharacteristic
899C2×C4⋊C4C22×D4711yescharacteristic
900C2×C4⋊C4C22×D4711yescharacteristic
901C2×C4⋊C4C22×D4711yescharacteristic
902C2×C4⋊C4C22×D4711yescharacteristic
903C2×C4⋊C4C22×D4711yescharacteristic
904C2×C4⋊C4C22×D4711yescharacteristic
905C2×C4⋊C4C22×D4711yescharacteristic
906C2×C22⋊C4—471no—
907C2×C22⋊C4—471no—
908C2×C22⋊C4—471no—
909C2×C22⋊C4—471no—
910C2×C22⋊C4—471no—
911C2×C22⋊C4—471no—
912C2×C22⋊C4—471no—
913C2×C22⋊C4—471no—
914C2×C22⋊C4—471no—
915C2×C22⋊C4—471no—
916C2×C22⋊C4—471no—
917C2×C22⋊C4—471no—
918C2×C22⋊C4—471no—
919C2×C22⋊C4—471no—
920C2×C22⋊C4—471no—
921C2×C22⋊C4—471no—
922C2×C22⋊C4—471no—
923C2×C22⋊C4—471no—
924C2×C22⋊C4—471no—
925C2×C22⋊C4—471no—
926C2×C22⋊C4—471no—
927C2×C22⋊C4—471no—
928C2×C22⋊C4—471no—
929C2×C22⋊C4—471no—
930C2×C42—471no—
931C2×C42—471no—
932C2×C42—471no—
933C2×C42—471no—
934C2×C42—471no—
935C2×C42—471no—
936C2×C42—471no—
937C2×C42—471no—
938C2×C42—471no—
939C2×C42—471no—
940C2×C42—471no—
941C2×C42—471no—
942C2×C42—1882no—
943C2×C42C22×D4711yescharacteristic
944C2×C42C22×D4711yescharacteristic
945C2×C42C22×D4711yescharacteristic
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#95—471no—
967#95—471no—
968#95—471no—
969#95—471no—
970#95—471no—
971#95—471no—
972#95—471no—
973#95—471no—
974#95—471no—
975#95—471no—
976#95—471no—
977#95—471no—
978#95—471no—
979#95—471no—
980#95—471no—
981#95—471no—
982#95—471no—
983#95—471no—
984#95—471no—
985#95—471no—
986#95—471no—
987#95—471no—
988#95—471no—
989#95—471no—
990#95C22×D4711yescharacteristic
991#95C22×D4711yescharacteristic
992#95C22×D4711yescharacteristic
993#95C22×D4711yescharacteristic
994#95C22×D4711yescharacteristic
995#95C22×D4711yescharacteristic
996#95C22×D4711yescharacteristic
997#95C22×D4711yescharacteristic
998#95C22×D4711yescharacteristic
999#95C22×D4711yescharacteristic
1000#95C22×D4711yescharacteristic
1001#95C22×D4711yescharacteristic
1002#95C22×D4711yescharacteristic
1003#95C22×D4711yescharacteristic
1004#95C22×D4711yescharacteristic
1005#95C22×D4711yescharacteristic
1006#95C22×D4711yescharacteristic
1007#95C22×D4711yescharacteristic
1008#95C22×D4711yescharacteristic
1009#95C22×D4711yescharacteristic
1010C24—471no—
1011C24—471no—
1012C2×Q8—22no—
1013C2×Q8—22no—
1014C2×Q8—41no—
1015C2×Q8—41no—
1016C2×Q8—41no—
1017C2×Q8—41no—
1018C2×Q8—942no—
1019C2×Q8—1881no—
1020C2×Q8—1881no—
1021C2×D4—942no—
1022C2×D4—1881no—
1023C2×D4—1881no—
1024C22×C4—471no—
1025C22×C4—471no—
1026C22×C4—471no—
1027C22×C4—474no—
1028C22×C4—471no—
1029C22×C4—471no—
1030C22×C4—471no—
1031C22×C4—471no—
1032C22×C4—471no—
1033C22×C4—471no—
1034C22×C4—471no—
1035C22×C4—471no—
1036C22×C4—471no—
1037C22×C4—471no—
1038C22×C4—471no—
1039C22×C4—942no—
1040C22×C4—942no—
1041C22×C4—942no—
1042C22×C4—942no—
1043C22×C4—1881no—
1044C22×C4—1881no—
1045C22×C4—1881no—
1046C22×C4—1881no—
1047C22×C4—1881no—
1048C22×C4—1881no—
1049C22×C4—1881no—
1050C22×C4C23×D4711yescharacteristic
1051C22×C4C23×D4711yescharacteristic
1052C22×C4C23×D4711yescharacteristic
1053C22×C4C23×D4711yescharacteristic
1054C22×C4C23×D4711yescharacteristic
1055C22×C4C23×D4711yescharacteristic
1056C22×C4C23×D4711yescharacteristic
1057C22×C4C23×D4711yescharacteristic
1058C22×C4C23×D4711yescharacteristic
1059C22×C4C23×D4711yescharacteristic
1060C22×C4C23×D4711yescharacteristic
1061C22×C4C23×D4711yescharacteristic
1062C22×C4C23×D4711yescharacteristic
1063C22×C4C23×D4711yescharacteristic
1064C22×C4C23×D4711yescharacteristic
1065C4⋊C4—22no—
1066C4⋊C4—22no—
1067C4⋊C4—41no—
1068C4⋊C4—41no—
1069C4⋊C4—41no—
1070C4⋊C4—41no—
1071C4⋊C4—41no—
1072C4⋊C4—41no—
1073C4⋊C4—41no—
1074C4⋊C4—41no—
1075C4⋊C4—942no—
1076C4⋊C4—942no—
1077C4⋊C4—942no—
1078C4⋊C4—942no—
1079C4⋊C4—942no—
1080C4⋊C4—942no—
1081C4⋊C4—942no—
1082C4⋊C4—942no—
1083C4⋊C4—942no—
1084C4⋊C4—942no—
1085C4⋊C4—942no—
1086C4⋊C4—942no—
1087C4⋊C4—942no—
1088C4⋊C4—942no—
1089C4⋊C4—942no—
1090C4⋊C4—1881no—
1091C4⋊C4—1881no—
1092C4⋊C4—1881no—
1093C4⋊C4—1881no—
1094C4⋊C4—1881no—
1095C4⋊C4—1881no—
1096C4⋊C4—1881no—
1097C4⋊C4—1881no—
1098C4⋊C4—1881no—
1099C4⋊C4—1881no—
1100C4⋊C4—1881no—
1101C4⋊C4—1881no—
1102C4⋊C4—1881no—
1103C4⋊C4—1881no—
1104C4⋊C4—1881no—
1105C4⋊C4—1881no—
1106C4⋊C4—1881no—
1107C4⋊C4—1881no—
1108C4⋊C4—1881no—
1109C22⋊C4—942no—
1110C22⋊C4—942no—
1111C22⋊C4—942no—
1112C22⋊C4—942no—
1113C22⋊C4—942no—
1114C22⋊C4—942no—
1115C22⋊C4—942no—
1116C22⋊C4—942no—
1117C22⋊C4—942no—
1118C22⋊C4—1881no—
1119C22⋊C4—1881no—
1120C22⋊C4—1881no—
1121C22⋊C4—1881no—
1122C22⋊C4—1881no—
1123C22⋊C4—1881no—
1124C22⋊C4—1881no—
1125C22⋊C4—1881no—
1126C22⋊C4—1881no—
1127C22⋊C4—1881no—
1128C22⋊C4—1881no—
1129C22⋊C4—1881no—
1130C22⋊C4—1881no—
1131C22⋊C4—1881no—
1132C22⋊C4—1881no—
1133C42—41no—
1134C42—41no—
1135C42—41no—
1136C42—942no—
1137C42—942no—
1138C42—942no—
1139C42—1881no—
1140C42—1881no—
1141C42—1881no—
1142C42—1881no—
1143C42—1881no—
1144C42—1881no—
1145C42—1881no—
1146C42—1881no—
1147C42—1881no—
1148C23—472no—
1149C23—941no—
1150C23—941no—
1151C23—941no—
1152C23—941no—
1153C23—941no—
1154C23—941no—
1155C23—941no—
1156C23—941no—
1157C23—941no—
1158C23—941no—
1159C23—941no—
1160C23—941no—
1161C23—941no—
1162C23C24×D4711yescharacteristic
1163Q8—82no—
1164Q8—82no—
1165Q8—3762no—
1166D4—1884no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—472no—
1211C2×C4—472no—
1212C2×C4—472no—
1213C2×C4—941no—
1214C2×C4—941no—
1215C2×C4—941no—
1216C2×C4—941no—
1217C2×C4—941no—
1218C2×C4—941no—
1219C2×C4—941no—
1220C2×C4—941no—
1221C2×C4—941no—
1222C2×C4—941no—
1223C2×C4—941no—
1224C2×C4—941no—
1225C2×C4—941no—
1226C2×C4—941no—
1227C2×C4—941no—
1228C2×C4—941no—
1229C2×C4—941no—
1230C2×C4—941no—
1231C2×C4—941no—
1232C2×C4—941no—
1233C2×C4—941no—
1234C2×C4—941no—
1235C2×C4—941no—
1236C2×C4—941no—
1237C2×C4—941no—
1238C2×C4—941no—
1239C2×C4—941no—
1240C2×C4—941no—
1241C2×C4—941no—
1242C2×C4—941no—
1243C2×C4—941no—
1244C2×C4—941no—
1245C2×C4—941no—
1246C2×C4—941no—
1247C2×C4—941no—
1248C2×C4—941no—
1249C2×C4—941no—
1250C2×C4—941no—
1251C2×C4—941no—
1252C2×C4—1884no—
1253C2×C4—1884no—
1254C2×C4—1884no—
1255C2×C4—1884no—
1256C2×C4#41×D4712yes—
1257C2×C4#1309407212yes—
1258C22—942no—
1259C22—942no—
1260C22—942no—
1261C22—1881no—
1262C22—1881no—
1263C22—1881no—
1264C22—1881no—
1265C22—1881no—
1266C22—1881no—
1267C22—1881no—
1268C22—1881no—
1269C22—1881no—
1270C22—1881no—
1271C22—1881no—
1272C22C2×#41×D4711yescharacteristic
1273C22H(5,𝔽2)×D4711yescharacteristic
1274C222−1+4×D4711yescharacteristic
1275C22C2×#1309407211yescharacteristic
1276C22#1568995811yescharacteristic
1277C22#1568995911yescharacteristic
1278C22#1568996011yescharacteristic
1279C4—22no—
1280C4—22no—
1281C4—41no—
1282C4—41no—
1283C4—41no—
1284C4—41no—
1285C4—41no—
1286C4—41no—
1287C4—41no—
1288C4—41no—
1289C4—41no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—41no—
1294C4—942no—
1295C4—942no—
1296C4—942no—
1297C4—1881no—
1298C4—1881no—
1299C4—1881no—
1300C4—1881no—
1301C4—1881no—
1302C4—1881no—
1303C4—1881no—
1304C4—1881no—
1305C4—1881no—
1306C4—1881no—
1307C4—1881no—
1308C2—3761no—
1309C2—1882no—
1310C2#2025677511yescharacteristic
1311C2#2025721911yescharacteristic
1312C2#2025727111yescharacteristic
1313C2#2025760211yescharacteristic
1314C2#2025767811yescharacteristic
1315C2#2025789511yescharacteristic
1316C2#2025802011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D47
commutator, socle, cosocleC23×C47C25
FittingC47×#2799C2
prime radicalC22×D188C23
hypercenter#2799D47
hypocenterC47#36772
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2799

Complements

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

NH ≅ G/Ntype
1. #20251737C2semidirect
2. #20251729C2semidirect
3. #20251260C2semidirect
4. #20251192C2semidirect
5. #20251178C2semidirect
6. #20251126C2semidirect
9. #20250886C2semidirect
10. #20250756C2semidirect
11. #20250698C2semidirect
12. #20250586C2semidirect
14. #20250214C2semidirect
15. #20250171C2semidirect
17. #20249849C2semidirect
20. #20248857C2semidirect
21. #20248843C2semidirect
22. #20248830C2semidirect
23. #20248810C2semidirect
24. #20248268C2semidirect
25. #20248188C2semidirect
26. #20247608C2semidirect
27. #20247552C2semidirect
28. #20246143C2semidirect
29. #20246140C2semidirect
31. C47×#2799C2semidirect
652. #2799D47semidirect
845. C47#36772semidirect

Maximal subgroups

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

subgroupindex
#202517372
#202517292
#202512602
#202511922
#202511782
#202511262
#202510582
#202510162
#202508862
#202507562
#202506982
#202505862
#202505102
#202502142
#202501712
#202500192
#202498492
#202493142
#202493132
#202488572
#202488432
#202488302
#202488102
#202482682
#202481882
#202476082
#202475522
#202461432
#202461402
#202458262
C47×#27992
#3677247