Finite Group Databasebeta

← #26422198

Subgroups — #26422198

Order 12032.

3202 conjugacy classes of subgroups.

The subgroup lattice has 1212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689658C211yesmaximal, characteristic, complemented
2C22×C42×D47C211yesmaximal, characteristic, complemented
3#20251726C211yesmaximal, characteristic, complemented
4#20251721C211yesmaximal, characteristic, complemented
5#20251712C212yesmaximal, complemented
6#20251706C212yesmaximal, complemented
7#20251705C212yesmaximal, complemented
8#20251693C211yesmaximal, characteristic, complemented
9#20251690C211yesmaximal, characteristic, complemented
10#20251689C211yesmaximal, characteristic, complemented
11#20251683C212yesmaximal, complemented
12#20251676C211yesmaximal, characteristic, complemented
13#20251671C211yesmaximal, characteristic
14#20245918C211yesmaximal, characteristic, complemented
15#20245916C211yesmaximal, characteristic, complemented
16#20245909C212yesmaximal, complemented
17#20245896C211yesmaximal, characteristic, complemented
18#20245894C211yesmaximal, characteristic, complemented
19#20245889C212yesmaximal, complemented
20#20245826C212yesmaximal, complemented
21#20245824C212yesmaximal, complemented
22#20245781C211yesmaximal, characteristic, complemented
23C47×#2851C211yesmaximal, characteristic, complemented
24C23×C4×D47C2211yescharacteristic
25C23×C4×D47C2211yescharacteristic
26C23×C4×D47C2211yescharacteristic
27#15689658—28no—
28C2×#13094019C2212yescomplemented
29C2×#13094012C2211yescharacteristic, complemented
30C2×#13094009C2212yes—
31C2×#13094009C2212yes—
32C2×#13094004C2211yescharacteristic
33C2×#13094004C2211yescharacteristic
34C2×#13094003C2211yescharacteristic
35C2×#13093999C2211yescharacteristic
36C2×#13093999C2211yescharacteristic
37C2×#13093998C2211yescharacteristic
38C2×#13093994C2212yes—
39C2×#13093989C2211yescharacteristic, complemented
40C2×#13093986C2212yes—
41C2×#13093986C2212yes—
42C2×#13093986C2211yescharacteristic, complemented
43C2×(C22⋊D47)⋊C4C2212yes—
44C2×#13093982C2212yescomplemented
45C22×C4×Dic47C2211yescharacteristic
46C22×C4×Dic47C2211yescharacteristic
47C22×C4×Dic47C2211yescharacteristic
48C2×C42×D47—28no—
49C2×C42×D47C2211yescharacteristic
50C2×C42×D47C2211yescharacteristic
51C2×C42×D47C2211yescharacteristic
52C2×C42×D47C2211yescharacteristic
53C2×C42×D47C2211yescharacteristic
54C2×C42×D47C2211yescharacteristic
55C2×C42×D47C2211yescharacteristic
56C2×C42×D47C2211yescharacteristic
57#15689029C2211yescharacteristic, complemented
58#15689028C2211yescharacteristic, complemented
59#15689025C2211yescharacteristic, complemented
60#15689024C2211yescharacteristic, complemented
61#15689019C2211yescharacteristic, complemented
62#15689019C2211yescharacteristic, complemented
63#15689015C2212yescomplemented
64#15689015C2212yescomplemented
65#15689014C2212yescomplemented
66#15689014C2212yescomplemented
67#15689013C2212yescomplemented
68#15689013C2212yescomplemented
69#15689012C2212yescomplemented
70#15689012C2212yescomplemented
71#15689010C2212yescomplemented
72#15689009C2212yescomplemented
73#15689006C2212yescomplemented
74#15689005C2212yescomplemented
75#15689004C2212yescomplemented
76#15689004C2212yescomplemented
77#15689002C2212yes—
78#15689002C2212yes—
79#15689001C2212yes—
80#15689001C2212yes—
81#15689001C2212yes—
82#15689001C2212yes—
83#15689001C2212yes—
84#15689001C2212yes—
85#15689000C2212yes—
86#15689000C2212yes—
87#15688998C2212yes—
88#15688997C2212yes—
89#15688997C2212yes—
90#15688995C2212yes—
91#15688994C2212yes—
92#15688994C2212yes—
93#15688994C2212yes—
94#15688994C2212yes—
95#15688990C2212yescomplemented
96#15688989C2211yescharacteristic, complemented
97#15688985C2212yes—
98#15688985C2212yes—
99#15688980C2211yescharacteristic
100#15688980C2211yescharacteristic
101#15688980C2211yescharacteristic
102#15688980C2211yescharacteristic
103#15688978C2212yes—
104C4⋊C4×Dic47C2211yescharacteristic, complemented
105C4⋊C4×Dic47C2211yescharacteristic, complemented
106C4⋊C4×Dic47C2212yescomplemented
107#15688974C2212yescomplemented
108C22⋊C4×Dic47C2212yes—
109#15688970C2212yes—
110#15688970C2212yes—
111#15688970C2212yescomplemented
112#15688970C2212yescomplemented
113#15688968C2212yescomplemented
114C2×#125×C47C2211yescharacteristic, complemented
115C22×C42×C47C2211yescharacteristic
116C47×#389C2211yescharacteristic, complemented
117C47×#389C2211yescharacteristic, complemented
118C47×#387C2212yescomplemented
119C47×#387C2212yescomplemented
120C47×#385C2212yes—
121C47×#385C2212yes—
122C47×#382C2211yescharacteristic, complemented
123C47×#380C2211yescharacteristic
124C47×#380C2211yescharacteristic
125C24×D47C2311yescharacteristic
126C22×Dic94C2311yescharacteristic
127C22×D188C2312yes—
128C22×D188C2312yes—
129C22×D188C2311yescharacteristic
130C22×C22⋊D47C2312yes—
131C23×Dic47C2311yescharacteristic
132C23×Dic47C2311yescharacteristic
133C23×Dic47C2311yescharacteristic
134C22×C4×D47—24no—
135C22×C4×D47—24no—
136C22×C4×D47—24no—
137C22×C4×D47—24no—
138C22×C4×D47—24no—
139C22×C4×D47—24no—
140C22×C4×D47—24no—
141C22×C4×D47—24no—
142C22×C4×D47—24no—
143C22×C4×D47C2312yes—
144C22×C4×D47C2311yescharacteristic
145C22×C4×D47C2311yescharacteristic
146C22×C4×D47C2311yescharacteristic
147C22×C4×D47C2311yescharacteristic
148C22×C4×D47C2311yescharacteristic
149C22×C4×D47C2311yescharacteristic
150C22×C4×D47C2311yescharacteristic
151C22×C4×D47C2311yescharacteristic
152C22×C4×D47C2311yescharacteristic
153C22×C4×D47C2311yescharacteristic
154C22×C4×D47C2311yescharacteristic
155C22×C4×D47C2311yescharacteristic
156#13094019—28no—
157#13094012—24no—
158#13094009—28no—
159#13094009—28no—
160#13094004—24no—
161#13094004—24no—
162#13094003—24no—
163#13093999—24no—
164#13093999—24no—
165#13093998—24no—
166#13093994—28no—
167#13093989—24no—
168#13093986—28no—
169#13093986—28no—
170#13093986—24no—
171(C22⋊D47)⋊C4—28no—
172#13093982—28no—
173C2×C4⋊Dic47C2311yescharacteristic
174C2×C4⋊Dic47C2311yescharacteristic
175C2×C4⋊Dic47C2312yes—
176C2×C4⋊Dic47C2312yes—
177C2×Dic47⋊C4C2312yes—
178C2×Dic47⋊C4C2312yes—
179C2×Dic47⋊C4C2312yes—
180C2×Dic47⋊C4C2312yes—
181C2×C22⋊Dic47C2312yes—
182C2×(C2×D47)⋊C4C2312yes—
183C2×(C2×D47)⋊C4C2312yes—
184C2×(C2×D47)⋊C4C2312yes—
185C2×(C2×D47)⋊C4C2312yes—
186C2×(C2×D47)⋊C4C2312yes—
187C2×(C2×D47)⋊C4C2312yes—
188C2×(C2×D47)⋊C4C2312yes—
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)⋊C4C2312yes—
196C2×(C2×D47)⋊C4C2312yes—
197C2×(C2×D47)⋊C4C2312yes—
198C2×C4×Dic47—24no—
199C2×C4×Dic47—24no—
200C2×C4×Dic47—24no—
201C2×C4×Dic47C2312yes—
202C2×C4×Dic47C2312yes—
203C2×C4×Dic47C2312yes—
204C2×C4×Dic47C2311yescharacteristic
205C2×C4×Dic47C2311yescharacteristic
206C2×C4×Dic47C2311yescharacteristic
207C2×C4×Dic47C2311yescharacteristic
208C2×C4×Dic47C2311yescharacteristic
209C2×C4×Dic47C2311yescharacteristic
210C2×C4×Dic47C2311yescharacteristic
211C2×C4×Dic47C2311yescharacteristic
212C2×C4×Dic47C2311yescharacteristic
213C2×C4×Dic47C2311yescharacteristic
214C2×C4×Dic47C2311yescharacteristic
215C2×C4×Dic47C2311yescharacteristic
216C42×D47—24no—
217C42×D47—24no—
218C42×D47—24no—
219C42×D47—24no—
220C42×D47—24no—
221C42×D47—24no—
222C42×D47—24no—
223C42×D47D418yescomplemented
224C47⋊#95C2312yes—
225C47⋊#95C2312yes—
226C47⋊#95C2312yes—
227C47⋊#95C2312yes—
228C47⋊#95C2312yes—
229C47⋊#95C2312yes—
230C47⋊#95C2312yes—
231C47⋊#95C2312yes—
232C47⋊#95C2312yes—
233C47⋊#95C2312yes—
234C47⋊#95C2312yes—
235C47⋊#95C2312yes—
236C47⋊#95C2312yes—
237C47⋊#95C2312yes—
238C23×C4×C47C2311yescharacteristic
239C23×C4×C47C2311yescharacteristic
240C23×C4×C47C2311yescharacteristic
241#125×C47—24no—
242C2×C4⋊C4×C47C2311yescharacteristic
243C2×C4⋊C4×C47C2311yescharacteristic
244C2×C4⋊C4×C47C2312yes—
245C2×C4⋊C4×C47C2311yescharacteristic
246C2×C4⋊C4×C47C2311yescharacteristic
247C2×C4⋊C4×C47C2312yes—
248C2×C4⋊C4×C47C2312yes—
249C2×C4⋊C4×C47C2312yes—
250C2×C22⋊C4×C47C2312yes—
251C2×C22⋊C4×C47C2312yes—
252C2×C42×C47—24no—
253C2×C42×C47C2311yescharacteristic
254C2×C42×C47C2311yescharacteristic
255C2×C42×C47C2311yescharacteristic
256C2×C42×C47C2311yescharacteristic
257#95×C47C2312yes—
258#95×C47C2312yes—
259#95×C47C2312yes—
260#95×C47C2312yes—
261#95×C47C2312yes—
262#95×C47C2312yes—
263C24×C47C2411yescharacteristic
264C23×D47—22no—
265C23×D47—22no—
266C23×D47—22no—
267C23×D47—22no—
268C23×D47—22no—
269C23×D47—22no—
270C23×D47#4114yes—
271C23×D47C2412yes—
272C23×D47C2411yescharacteristic
273C23×D47C2411yescharacteristic
274C22×C4×C47—22no—
275C22×C4×C47—22no—
276C22×C4×C47—22no—
277C22×C4×C47—22no—
278C22×C4×C47—22no—
279C22×C4×C47—22no—
280C22×C4×C47—22no—
281C22×C4×C47—22no—
282C22×C4×C47#4114yes—
283C22×C4×C47C2412yes—
284C22×C4×C47C2412yes—
285C22×C4×C47C2412yes—
286C22×C4×C47C2412yes—
287C22×C4×C47C2411yescharacteristic
288C22×C4×C47C2411yescharacteristic
289C22×C4×C47C2411yescharacteristic
290C22×C4×C47C2411yescharacteristic
291C22×C4×C47C2411yescharacteristic
292C22×C4×C47C2411yescharacteristic
293C2×C22⋊D47—24no—
294C2×C22⋊D47—24no—
295C2×C22⋊D47—24no—
296C22×Dic47—22no—
297C22×Dic47—22no—
298C22×Dic47—22no—
299C22×Dic47—22no—
300C22×Dic47—22no—
301C22×Dic47—22no—
302C22×Dic47—22no—
303C22×Dic47—22no—
304C22×Dic47#4114yes—
305C22×Dic47C2412yes—
306C22×Dic47C2412yes—
307C22×Dic47C2412yes—
308C22×Dic47C2411yescharacteristic
309C22×Dic47C2411yescharacteristic
310C22×Dic47C2411yescharacteristic
311C22×Dic47C2411yescharacteristic
312C22×Dic47C2411yescharacteristic
313C22×Dic47C2411yescharacteristic
314C2×D188—24no—
315C2×D188—24no—
316C2×D188—24no—
317C2×D188—24no—
318C2×D188—24no—
319C2×D188—24no—
320C2×D188—22no—
321C2×D188—22no—
322C2×D188—22no—
323C2×C4×D47—232no—
324C2×C4×D47—232no—
325C2×C4×D47—232no—
326C2×C4×D47—22no—
327C2×C4×D47—22no—
328C2×C4×D47—22no—
329C2×C4×D47—22no—
330C2×C4×D47—22no—
331C2×C4×D47—22no—
332C2×C4×D47—22no—
333C2×C4×D47—22no—
334C2×C4×D47—22no—
335C2×C4×D47—22no—
336C2×C4×D47—22no—
337C2×C4×D47—22no—
338C2×C4×D47—22no—
339C2×C4×D47—22no—
340C2×C4×D47—22no—
341C2×C4×D47—22no—
342C2×C4×D47—22no—
343C2×C4×D47—22no—
344C2×C4×D47—22no—
345C2×C4×D47—22no—
346C2×C4×D47—22no—
347C2×C4×D47—22no—
348C2×C4×D47—22no—
349C2×C4×D47—22no—
350C2×C4×D47—22no—
351C2×C4×D47—22no—
352C2×C4×D47—22no—
353C2×C4×D47—22no—
354C2×C4×D47—22no—
355C2×C4×D47—22no—
356C2×C4×D47—24no—
357C2×C4×D47—24no—
358C2×C4×D47—24no—
359C2×C4×D47C2×D414yes—
360C2×C4×D47C2×D414yes—
361C2×C4×D47C2×D414yes—
362C2×C4×D47#4114yes—
363C2×C4×D47#4114yes—
364C2×C4×D47#4114yes—
365C2×Dic94—22no—
366C2×Dic94—22no—
367C2×Dic94—22no—
368C4⋊C4×C47—24no—
369C4⋊C4×C47—22no—
370C4⋊C4×C47—24no—
371C4⋊C4×C47—22no—
372C4⋊C4×C47—24no—
373C4⋊C4×C47—22no—
374C4⋊C4×C47—22no—
375C4⋊C4×C47—24no—
376C22⋊C4×C47—24no—
377C22⋊C4×C47—24no—
378C42×C47—22no—
379C42×C47—22no—
380C42×C47—22no—
381C42×C47C2×D414yes—
382C22⋊Dic47—24no—
383(C2×D47)⋊C4—24no—
384(C2×D47)⋊C4—24no—
385(C2×D47)⋊C4—24no—
386(C2×D47)⋊C4—24no—
387(C2×D47)⋊C4—24no—
388(C2×D47)⋊C4—24no—
389(C2×D47)⋊C4—24no—
390(C2×D47)⋊C4—24no—
391(C2×D47)⋊C4—24no—
392(C2×D47)⋊C4—24no—
393(C2×D47)⋊C4—24no—
394(C2×D47)⋊C4—24no—
395(C2×D47)⋊C4—24no—
396(C2×D47)⋊C4—24no—
397(C2×D47)⋊C4—24no—
398(C2×D47)⋊C4—24no—
399C4⋊Dic47—22no—
400C4⋊Dic47—22no—
401C4⋊Dic47—24no—
402C4⋊Dic47—24no—
403Dic47⋊C4—24no—
404Dic47⋊C4—24no—
405Dic47⋊C4—24no—
406Dic47⋊C4—24no—
407C4×Dic47—22no—
408C4×Dic47—22no—
409C4×Dic47—22no—
410C4×Dic47—22no—
411C4×Dic47—22no—
412C4×Dic47—22no—
413C4×Dic47—22no—
414C4×Dic47—22no—
415C4×Dic47—22no—
416C4×Dic47—24no—
417C4×Dic47—24no—
418C4×Dic47—24no—
419C4×Dic47C2×D414yes—
420C4×Dic47C2×D414yes—
421C4×Dic47C2×D414yes—
422C23×C47—21no—
423C23×C47—21no—
424C23×C47—21no—
425C23×C47—21no—
426C23×C47C2×#4112yes—
427C23×C47C2×#4112yes—
428C23×C47C2×#4112yes—
429C23×C47C2511yescharacteristic
430C22×D47—28no—
431C22×D47—28no—
432C22×D47—28no—
433C22×D47—28no—
434C22×D47—28no—
435C22×D47—21no—
436C22×D47—21no—
437C22×D47—21no—
438C22×D47—21no—
439C22×D47—21no—
440C22×D47—21no—
441C22×D47—21no—
442C22×D47—21no—
443C22×D47—28no—
444C22×D47—28no—
445C22×D47—22no—
446C22×D47—22no—
447C22×D47—22no—
448C22×D47—22no—
449C22×D47—22no—
450C22×D47—22no—
451C22×D47—22no—
452C22×D47C22×D412yes—
453C22×D47C2×#4112yes—
454C22×D47C2×#4112yes—
455C22×D47C2×#4112yes—
456C22×D47C2×#4112yes—
457C22×D47C2×#4112yes—
458C2×C4×C47—28no—
459C2×C4×C47—28no—
460C2×C4×C47—21no—
461C2×C4×C47—21no—
462C2×C4×C47—21no—
463C2×C4×C47—21no—
464C2×C4×C47—21no—
465C2×C4×C47—21no—
466C2×C4×C47—21no—
467C2×C4×C47—21no—
468C2×C4×C47—21no—
469C2×C4×C47—21no—
470C2×C4×C47—28no—
471C2×C4×C47—22no—
472C2×C4×C47—22no—
473C2×C4×C47—22no—
474C2×C4×C47—22no—
475C2×C4×C47—22no—
476C2×C4×C47—22no—
477C2×C4×C47—22no—
478C2×C4×C47—22no—
479C2×C4×C47—22no—
480C2×C4×C47—22no—
481C2×C4×C47—22no—
482C2×C4×C47—22no—
483C2×C4×C47C22×D412yes—
484C2×C4×C47C22×D412yes—
485C2×C4×C47C22×D412yes—
486C2×C4×C47C2×#4112yes—
487C2×C4×C47C2×#4112yes—
488C2×C4×C47C2×#4112yes—
489C2×C4×C47C2×#4112yes—
490C2×C4×C47C2×#4112yes—
491C22⋊D47—48no—
492C2×Dic47—28no—
493C2×Dic47—28no—
494C2×Dic47—21no—
495C2×Dic47—21no—
496C2×Dic47—21no—
497C2×Dic47—21no—
498C2×Dic47—21no—
499C2×Dic47—21no—
500C2×Dic47—21no—
501C2×Dic47—21no—
502C2×Dic47—21no—
503C2×Dic47—21no—
504C2×Dic47—28no—
505C2×Dic47—22no—
506C2×Dic47—22no—
507C2×Dic47—22no—
508C2×Dic47—22no—
509C2×Dic47—22no—
510C2×Dic47—22no—
511C2×Dic47—22no—
512C2×Dic47—22no—
513C2×Dic47—22no—
514C2×Dic47C22×D412yes—
515C2×Dic47C22×D412yes—
516C2×Dic47C22×D412yes—
517C2×Dic47C2×#4112yes—
518C2×Dic47C2×#4112yes—
519C2×Dic47C2×#4112yes—
520C2×Dic47C2×#4112yes—
521C2×Dic47C2×#4112yes—
522D188—48no—
523D188—48no—
524D188—44no—
525C4×D47—28no—
526C4×D47—28no—
527C4×D47—28no—
528C4×D47—28no—
529C4×D47—28no—
530C4×D47—28no—
531C4×D47—28no—
532C4×D47—28no—
533C4×D47—28no—
534C4×D47—28no—
535C4×D47—28no—
536C4×D47—28no—
537C4×D47—48no—
538Dic94—44no—
539#36621—471nomaximal, Sylow
540C22×C47—22no—
541C22×C47—22no—
542C22×C47—22no—
543C22×C47—22no—
544C22×C47—22no—
545C22×C47—22no—
546C22×C47#52914yescomplemented
547C22×C47C23×D411yescharacteristic
548C22×C47C22×#4111yescharacteristic
549C22×C47C22×#4111yescharacteristic
550C22×C47C22×#4111yescharacteristic
551C22×C47C22×#4111yescharacteristic
552C22×C47C22×#4111yescharacteristic
553C22×C47C22×#4111yescharacteristic
554C2×D47—232no—
555C2×D47—22no—
556C2×D47—22no—
557C2×D47—22no—
558C2×D47—22no—
559C2×D47—22no—
560C2×D47—22no—
561C2×D47—22no—
562C2×D47—22no—
563C2×D47—22no—
564C2×D47—22no—
565C2×D47—22no—
566C2×D47—22no—
567C2×D47—42no—
568C2×D47—42no—
569C2×D47—42no—
570C2×D47—42no—
571C2×D47—42no—
572C2×D47—42no—
573C2×D47—42no—
574C2×D47#52514yes—
575C2×D47#52914yescomplemented
576C4×C47—22no—
577C4×C47—22no—
578C4×C47—22no—
579C4×C47—22no—
580C4×C47—22no—
581C4×C47—42no—
582C4×C47—42no—
583C4×C47—42no—
584C4×C47—42no—
585C4×C47#52514yes—
586Dic47—22no—
587Dic47—22no—
588Dic47—22no—
589Dic47—22no—
590Dic47—22no—
591Dic47—42no—
592Dic47—42no—
593Dic47—42no—
594Dic47#52514yes—
595C2×#529—471no—
596C23×C42—471no—
597#2855—471no—
598#2854—471no—
599#2853—472no—
600#2852—472no—
601#2852—472no—
602#2851—471no—
603#2851D4711yescharacteristic, complemented
604#2850—471no—
605#2850—471no—
606#2849—472no—
607#2848—471no—
608#2847—471no—
609C4×C22⋊Q8—471no—
610C4×C22⋊Q8—471no—
611C4×#123—472no—
612C4×#121—471no—
613C4×#121—471no—
614C4×#120—472no—
615#2290—472no—
616#2290—472no—
617#2283—471no—
618C2×C47—24no—
619C2×C47C2×#52511yescharacteristic
620C2×C47C2×#52511yescharacteristic
621C2×C47C2×#52511yescharacteristic
622C2×C47C2×#52911yescharacteristic
623C2×C47C2×#52911yescharacteristic
624C2×C47#344411yescharacteristic
625C2×C47#344411yescharacteristic
626D47—24no—
627D47—24no—
628D47—82no—
629C24×C4—471no—
630C24×C4—471no—
631C24×C4—471no—
632#529—948no—
633C2×#126—472no—
634C2×#125C2×D4711yescharacteristic, complemented
635C2×#124—471no—
636C2×#123—472no—
637C2×#123—472no—
638C2×C22⋊Q8—471no—
639C2×C22⋊Q8—471no—
640C2×C22⋊Q8—471no—
641C2×#121—471no—
642C2×#121—471no—
643C2×#121—471no—
644C2×#120—472no—
645C2×C4×Q8—471no—
646C2×C4×D4—472no—
647C2×C4×D4—471no—
648C2×C4×D4—472no—
649C2×C4×D4—472no—
650C2×#117—472no—
651C22×C42—471no—
652C22×C42—471no—
653C22×C42—471no—
654C22×C42—471no—
655C22×C42—471no—
656C22×C42—471no—
657C22×C42—471no—
658C22×C42—471no—
659C22×C42—471no—
660C22×C42—471no—
661C22×C42—471no—
662C22×C42—948no—
663C22×C42C2×D4711yescharacteristic
664#391—471no—
665#391—471no—
666#390—471no—
667#390—471no—
668#389—471no—
669#389—471no—
670#389C2×D4711yescharacteristic, complemented
671#389C2×D4711yescharacteristic, complemented
672#388—472no—
673#388—472no—
674#388—472no—
675#388—472no—
676#388—472no—
677#388—472no—
678#388—472no—
679#388—472no—
680#387—472no—
681#387—472no—
682#387—472no—
683#387—472no—
684#387—472no—
685#387—472no—
686#387C2×D4712yescomplemented
687#387C2×D4712yescomplemented
688#386—472no—
689#386—472no—
690#386—472no—
691#386—472no—
692#386—472no—
693#386—472no—
694#386—472no—
695#386—472no—
696#386—472no—
697#386—472no—
698#385—472no—
699#385—472no—
700#385—472no—
701#385—472no—
702#385—472no—
703#385—472no—
704#385—472no—
705#385—472no—
706#385C2×D4712yes—
707#385C2×D4712yes—
708#383—472no—
709#382—471no—
710#382C2×D4711yescharacteristic, complemented
711#381—472no—
712#381—472no—
713#380—471no—
714#380—471no—
715#380—471no—
716#380—471no—
717#380C2×D4711yescharacteristic
718#380C2×D4711yescharacteristic
719#379—472no—
720C4×C4⋊C4—471no—
721C4×C4⋊C4—471no—
722C4×C4⋊C4—472no—
723C4×C4⋊C4—472no—
724C4×C22⋊C4—472no—
725C4×C22⋊C4—472no—
726C4×C22⋊C4—472no—
727C4×C22⋊C4—472no—
728C4×C22⋊C4—472no—
729#376—472no—
730C47#3662111yescharacteristic, complemented, Sylow
731C25—471no—
732C22×Q8—471no—
733C22×D4—472no—
734C22×D4—472no—
735C22×D4—472no—
736C22×D4—471no—
737C23×C4—471no—
738C23×C4—471no—
739C23×C4—471no—
740C23×C4—471no—
741C23×C4—471no—
742C23×C4—471no—
743C23×C4—471no—
744C23×C4—471no—
745C23×C4—471no—
746C23×C4—472no—
747C23×C4—471no—
748C23×C4—471no—
749C23×C4—471no—
750C23×C4—471no—
751C23×C4—471no—
752C23×C4—471no—
753C23×C4—944no—
754C23×C4—944no—
755C23×C4—944no—
756C23×C4—944no—
757C23×C4—944no—
758C23×C4—944no—
759C23×C4—944no—
760C23×C4—944no—
761C23×C4—944no—
762C23×C4C22×D4711yescharacteristic
763C23×C4C22×D4711yescharacteristic
764C23×C4C22×D4711yescharacteristic
765#126—948no—
766#125—24no—
767#124—944no—
768#123—948no—
769#123—948no—
770C22⋊Q8—944no—
771C22⋊Q8—944no—
772C22⋊Q8—944no—
773#121—944no—
774#121—944no—
775#121—944no—
776#120—948no—
777C4×Q8—944no—
778C4×D4—944no—
779C4×D4—948no—
780C4×D4—948no—
781C4×D4—948no—
782#117—948no—
783C2×C4⋊C4—472no—
784C2×C4⋊C4—472no—
785C2×C4⋊C4—472no—
786C2×C4⋊C4—471no—
787C2×C4⋊C4—472no—
788C2×C4⋊C4—471no—
789C2×C4⋊C4—472no—
790C2×C4⋊C4—472no—
791C2×C4⋊C4C22×D4712yes—
792C2×C4⋊C4C22×D4711yescharacteristic
793C2×C4⋊C4C22×D4712yes—
794C2×C4⋊C4C22×D4712yes—
795C2×C4⋊C4C22×D4711yescharacteristic
796C2×C4⋊C4C22×D4711yescharacteristic
797C2×C4⋊C4C22×D4711yescharacteristic
798C2×C4⋊C4C22×D4712yes—
799C2×C22⋊C4—472no—
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—472no—
812C2×C22⋊C4—472no—
813C2×C22⋊C4—472no—
814C2×C22⋊C4—472no—
815C2×C22⋊C4—472no—
816C2×C22⋊C4C22×D4712yes—
817C2×C22⋊C4C22×D4712yes—
818C2×C42—24no—
819C2×C42—471no—
820C2×C42—471no—
821C2×C42—471no—
822C2×C42—478no—
823C2×C42—472no—
824C2×C42—472no—
825C2×C42—472no—
826C2×C42—471no—
827C2×C42—471no—
828C2×C42—471no—
829C2×C42—471no—
830C2×C42—471no—
831C2×C42—471no—
832C2×C42—471no—
833C2×C42—471no—
834C2×C42—471no—
835C2×C42—944no—
836C2×C42—944no—
837C2×C42—944no—
838C2×C42—944no—
839C2×C42—944no—
840C2×C42—944no—
841C2×C42—944no—
842C2×C42—944no—
843C2×C42—944no—
844C2×C42—944no—
845C2×C42C22×D4711yescharacteristic
846C2×C42C22×D4711yescharacteristic
847C2×C42C22×D4711yescharacteristic
848C2×C42C22×D4711yescharacteristic
849#95—472no—
850#95—472no—
851#95—472no—
852#95—472no—
853#95—472no—
854#95—472no—
855#95—472no—
856#95—472no—
857#95—472no—
858#95—472no—
859#95—472no—
860#95—472no—
861#95—472no—
862#95—472no—
863#95C22×D4712yes—
864#95C22×D4712yes—
865#95C22×D4712yes—
866#95C22×D4712yes—
867#95C22×D4712yes—
868#95C22×D4712yes—
869C24—471no—
870C24—471no—
871C24—474no—
872C24—472no—
873C24—942no—
874C24—942no—
875C24—942no—
876C24—942no—
877C24—942no—
878C24—942no—
879C24C23×D4711yescharacteristic
880C2×Q8—942no—
881C2×Q8—942no—
882C2×Q8—942no—
883C2×D4—944no—
884C2×D4—944no—
885C2×D4—944no—
886C2×D4—944no—
887C2×D4—944no—
888C2×D4—944no—
889C2×D4—944no—
890C2×D4—944no—
891C2×D4—944no—
892C2×D4—942no—
893C2×D4—942no—
894C2×D4—942no—
895C22×C4—22no—
896C22×C4—22no—
897C22×C4—22no—
898C22×C4—22no—
899C22×C4—22no—
900C22×C4—22no—
901C22×C4—22no—
902C22×C4—22no—
903C22×C4—471no—
904C22×C4—474no—
905C22×C4—471no—
906C22×C4—471no—
907C22×C4—471no—
908C22×C4—471no—
909C22×C4—471no—
910C22×C4—474no—
911C22×C4—474no—
912C22×C4—474no—
913C22×C4—474no—
914C22×C4—474no—
915C22×C4—474no—
916C22×C4—472no—
917C22×C4—472no—
918C22×C4—472no—
919C22×C4—942no—
920C22×C4—942no—
921C22×C4—942no—
922C22×C4—942no—
923C22×C4—942no—
924C22×C4—942no—
925C22×C4—942no—
926C22×C4—942no—
927C22×C4—942no—
928C22×C4—942no—
929C22×C4—944no—
930C22×C4—944no—
931C22×C4—944no—
932C22×C4—942no—
933C22×C4—942no—
934C22×C4—942no—
935C22×C4—942no—
936C22×C4—942no—
937C22×C4—942no—
938C22×C4—942no—
939C22×C4—942no—
940C22×C4—942no—
941C22×C4—942no—
942C22×C4—9432no—
943C22×C4—9432no—
944C22×C4—9432no—
945C22×C4—942no—
946C22×C4—942no—
947C22×C4—942no—
948C22×C4—942no—
949C22×C4—942no—
950C22×C4—942no—
951C22×C4—942no—
952C22×C4—942no—
953C22×C4—942no—
954C22×C4—942no—
955C22×C4—942no—
956C22×C4—942no—
957C22×C4—942no—
958C22×C4—942no—
959C22×C4—942no—
960C22×C4—942no—
961C22×C4—942no—
962C22×C4—942no—
963C22×C4#1062535414yes—
964C22×C4C23×D4712yes—
965C22×C4C23×D4712yes—
966C22×C4C23×D4712yes—
967C22×C4C23×D4712yes—
968C22×C4C23×D4711yescharacteristic
969C22×C4C23×D4711yescharacteristic
970C22×C4C23×D4711yescharacteristic
971C22×C4C23×D4711yescharacteristic
972C22×C4C23×D4711yescharacteristic
973C22×C4C23×D4711yescharacteristic
974C4⋊C4—24no—
975C4⋊C4—22no—
976C4⋊C4—24no—
977C4⋊C4—22no—
978C4⋊C4—24no—
979C4⋊C4—22no—
980C4⋊C4—22no—
981C4⋊C4—24no—
982C4⋊C4—944no—
983C4⋊C4—944no—
984C4⋊C4—944no—
985C4⋊C4—944no—
986C4⋊C4—944no—
987C4⋊C4—944no—
988C4⋊C4—942no—
989C4⋊C4—942no—
990C22⋊C4—24no—
991C22⋊C4—24no—
992C22⋊C4—944no—
993C22⋊C4—944no—
994C22⋊C4—944no—
995C22⋊C4—944no—
996C22⋊C4—944no—
997C22⋊C4—944no—
998C22⋊C4—944no—
999C22⋊C4—944no—
1000C22⋊C4—944no—
1001C22⋊C4—944no—
1002C22⋊C4—944no—
1003C22⋊C4—944no—
1004C22⋊C4—944no—
1005C22⋊C4—944no—
1006C22⋊C4—944no—
1007C22⋊C4—944no—
1008C22⋊C4—944no—
1009C42—22no—
1010C42—22no—
1011C42—22no—
1012C42—474no—
1013C42—474no—
1014C42—474no—
1015C42—942no—
1016C42—942no—
1017C42—942no—
1018C42—942no—
1019C42—942no—
1020C42—942no—
1021C42—944no—
1022C42—944no—
1023C42—944no—
1024C42—942no—
1025C42—942no—
1026C42—942no—
1027C42D4×D4714yes—
1028C23—21no—
1029C23—21no—
1030C23—21no—
1031C23—21no—
1032C23—472no—
1033C23—472no—
1034C23—472no—
1035C23—472no—
1036C23—472no—
1037C23—472no—
1038C23—948no—
1039C23—948no—
1040C23—948no—
1041C23—948no—
1042C23—948no—
1043C23—948no—
1044C23—948no—
1045C23—941no—
1046C23—941no—
1047C23—941no—
1048C23—941no—
1049C23—941no—
1050C23—941no—
1051C23—941no—
1052C23—941no—
1053C23—942no—
1054C23—942no—
1055C23—942no—
1056C23—942no—
1057C23—942no—
1058C23—942no—
1059C23—942no—
1060C23#41×D4712yes—
1061C23#41×D4712yes—
1062C23C2×#1062535412yes—
1063C23C24×D4711yescharacteristic
1064Q8—1884no—
1065D4—1888no—
1066D4—1888no—
1067D4—1888no—
1068D4—1884no—
1069C2×C4—28no—
1070C2×C4—28no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—28no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—472no—
1095C2×C4—472no—
1096C2×C4—472no—
1097C2×C4—472no—
1098C2×C4—472no—
1099C2×C4—472no—
1100C2×C4—472no—
1101C2×C4—472no—
1102C2×C4—948no—
1103C2×C4—948no—
1104C2×C4—948no—
1105C2×C4—948no—
1106C2×C4—948no—
1107C2×C4—948no—
1108C2×C4—948no—
1109C2×C4—948no—
1110C2×C4—948no—
1111C2×C4—948no—
1112C2×C4—948no—
1113C2×C4—948no—
1114C2×C4—948no—
1115C2×C4—941no—
1116C2×C4—941no—
1117C2×C4—941no—
1118C2×C4—941no—
1119C2×C4—941no—
1120C2×C4—941no—
1121C2×C4—941no—
1122C2×C4—941no—
1123C2×C4—941no—
1124C2×C4—941no—
1125C2×C4—948no—
1126C2×C4—948no—
1127C2×C4—942no—
1128C2×C4—942no—
1129C2×C4—942no—
1130C2×C4—942no—
1131C2×C4—942no—
1132C2×C4—942no—
1133C2×C4—942no—
1134C2×C4—942no—
1135C2×C4—942no—
1136C2×C4—1888no—
1137C2×C4C2×D4×D4712yes—
1138C2×C4C2×D4×D4712yes—
1139C2×C4C2×D4×D4712yes—
1140C2×C4#41×D4712yes—
1141C2×C4#41×D4712yes—
1142C2×C4#41×D4712yes—
1143C2×C4C2×#1062535412yes—
1144C2×C4C2×#1062535412yes—
1145C22—22no—
1146C22—22no—
1147C22—22no—
1148C22—22no—
1149C22—22no—
1150C22—22no—
1151C22—474no—
1152C22—474no—
1153C22—9432no—
1154C22—942no—
1155C22—942no—
1156C22—942no—
1157C22—942no—
1158C22—942no—
1159C22—942no—
1160C22—942no—
1161C22—942no—
1162C22—942no—
1163C22—942no—
1164C22—942no—
1165C22—942no—
1166C22—1882no—
1167C22—1882no—
1168C22—1882no—
1169C22—1882no—
1170C22—1882no—
1171C22—1882no—
1172C22—1882no—
1173C22#1568965814yescomplemented
1174C22C22×D4×D4711yescharacteristic
1175C22C2×#41×D4711yescharacteristic
1176C22C2×#41×D4711yescharacteristic
1177C22C2×#41×D4711yescharacteristic
1178C22C2×#41×D4711yescharacteristic
1179C22C2×#41×D4711yescharacteristic
1180C22C22×#1062535411yescharacteristic
1181C4—22no—
1182C4—22no—
1183C4—22no—
1184C4—22no—
1185C4—22no—
1186C4—42no—
1187C4—42no—
1188C4—42no—
1189C4—42no—
1190C4—474no—
1191C4—942no—
1192C4—942no—
1193C4—942no—
1194C4—942no—
1195C4—942no—
1196C4—1882no—
1197C4—1882no—
1198C4—1882no—
1199C4#1568963614yes—
1200C2—24no—
1201C2—944no—
1202C2—944no—
1203C2—3762no—
1204C2#525×D4711yescharacteristic
1205C2#525×D4711yescharacteristic
1206C2C2×#1568963611yescharacteristic
1207C2#529×D4711yescharacteristic
1208C2C2×#1568965811yescharacteristic
1209C2#2025668211yescharacteristic
1210C2#2025668511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D47
commutator, socle, cosocleC23×C47C25
FittingC47×#2851C2
prime radical#20251671C2
hypercenter#2851D47
hypocenterC47#36621
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2851

Complements

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

NH ≅ G/Ntype
1. C2×#15689658C2semidirect
2. C22×C42×D47C2semidirect
3. #20251726C2semidirect
4. #20251721C2semidirect
5. #20251712C2semidirect
6. #20251706C2semidirect
7. #20251705C2semidirect
8. #20251693C2semidirect
9. #20251690C2semidirect
10. #20251689C2semidirect
11. #20251683C2semidirect
12. #20251676C2semidirect
14. #20245918C2semidirect
15. #20245916C2semidirect
16. #20245909C2semidirect
17. #20245896C2semidirect
18. #20245894C2semidirect
19. #20245889C2semidirect
20. #20245826C2semidirect
21. #20245824C2semidirect
22. #20245781C2semidirect
23. C47×#2851C2semidirect
28. C2×#13094019C22semidirect
29. C2×#13094012C22semidirect
39. C2×#13093989C22semidirect
42. C2×#13093986C22semidirect
44. C2×#13093982C22semidirect
57. #15689029C22semidirect
58. #15689028C22semidirect
59. #15689025C22semidirect
60. #15689024C22semidirect
61. #15689019C22semidirect
62. #15689019C22semidirect
63. #15689015C22semidirect
64. #15689015C22semidirect
65. #15689014C22semidirect
66. #15689014C22semidirect
67. #15689013C22semidirect
68. #15689013C22semidirect
69. #15689012C22semidirect
70. #15689012C22semidirect
71. #15689010C22semidirect
72. #15689009C22semidirect
73. #15689006C22semidirect
74. #15689005C22semidirect
75. #15689004C22semidirect
76. #15689004C22semidirect
95. #15688990C22semidirect
96. #15688989C22semidirect
104. C4⋊C4×Dic47C22semidirect
105. C4⋊C4×Dic47C22semidirect
106. C4⋊C4×Dic47C22semidirect
107. #15688974C22semidirect
111. #15688970C22semidirect
112. #15688970C22semidirect
113. #15688968C22semidirect
114. C2×#125×C47C22semidirect
116. C47×#389C22semidirect
117. C47×#389C22semidirect
118. C47×#387C22semidirect
119. C47×#387C22semidirect
122. C47×#382C22semidirect
223. C42×D47D4semidirect
546. C22×C47#529semidirect
575. C2×D47#529semidirect
603. #2851D47semidirect
634. C2×#125C2×D47semidirect
670. #389C2×D47semidirect
671. #389C2×D47semidirect
686. #387C2×D47semidirect
687. #387C2×D47semidirect
710. #382C2×D47semidirect
730. C47#36621semidirect
1173. C22#15689658semidirect

Maximal subgroups

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

subgroupindex
C2×#156896582
C22×C42×D472
#202517262
#202517212
#202517122
#202517062
#202517052
#202516932
#202516902
#202516892
#202516832
#202516762
#202516712
#202459182
#202459162
#202459092
#202458962
#202458942
#202458892
#202458262
#202458242
#202457812
C47×#28512
#3662147