Finite Group Databasebeta

← #26379598

Subgroups — #26379598

Order 12032.

2586 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689634C211yesmaximal, characteristic
2#20246532C214yesmaximal, complemented
3#20246402C212yesmaximal, complemented
4#20246391C212yesmaximal, complemented
5#20246330C212yesmaximal, complemented
6#20246292C212yesmaximal, complemented
7#20246279C211yesmaximal, characteristic, complemented
8#20246271C211yesmaximal, characteristic, complemented
9#20246228C211yesmaximal, characteristic, complemented
10#20246219C211yesmaximal, characteristic, complemented
11#20246081C212yesmaximal, complemented
12#20246070C212yesmaximal, complemented
13#20246043C214yesmaximal, complemented
14#20246028C212yesmaximal, complemented
15#20246017C212yesmaximal, complemented
16C2×#15688983C211yesmaximal, characteristic, complemented
17C47×#2280C211yesmaximal, characteristic, complemented
18C22×#10625350C2211yescharacteristic
19#15689634C4116yescomplemented
20C2×#13094007C2212yes—
21C2×#13094003C2211yescharacteristic
22C2×#13094003C2211yescharacteristic
23C2×#13093998C2211yescharacteristic
24C2×#13093998C2211yescharacteristic
25C2×#13093993C2212yes—
26C2×C4×Dic94C2212yescomplemented
27C2×C4×D188C2212yescomplemented
28C2×C4×C22⋊D47C2212yes—
29C2×C4×C22⋊D47C2212yes—
30C2×(C22⋊D47)⋊C4C2214yes—
31C2×#13093983C2211yescharacteristic
32C22×C4⋊Dic47C2212yes—
33C22×C22⋊Dic47C2212yes—
34#15689029C2212yescomplemented
35#15689025C2212yescomplemented
36#15689023C2214yes—
37#15689023C2214yes—
38#15689021C2212yescomplemented
39#15689021C2212yescomplemented
40#15689020C2214yescomplemented
41#15689018C2214yescomplemented
42#15689017C2214yes—
43#15689017C2214yes—
44#15689015C2214yescomplemented
45#15689013C2214yescomplemented
46#15689011C2214yes—
47#15689011C2214yes—
48#15689010C2214yescomplemented
49#15689004C2214yescomplemented
50#15689000C2214yes—
51#15688999C2214yes—
52#15688999C2214yes—
53#15688997C2214yescomplemented
54#15688995C2214yes—
55#15688994C2214yescomplemented
56#15688990C2212yescomplemented
57#15688987C2212yescomplemented
58#15688985C2212yescomplemented
59#15688983C2212yes—
60#15688983C2212yes—
61#15688983C2211yescharacteristic
62#15688983C2212yes—
63#15688983C2211yescharacteristic
64#15688982C2212yescomplemented
65C4×C4⋊Dic47C2212yescomplemented
66C4×C4⋊Dic47C2212yescomplemented
67#15688974C2212yescomplemented
68C22⋊C4×Dic47C2214yes—
69#15688970C2212yescomplemented
70#15688968C2212yescomplemented
71C2×C47⋊#95C2212yes—
72#95×D47C2212yescomplemented
73C24×C4×C47C2211yescharacteristic
74C2×#117×C47C2212yes—
75C47×#381C2211yescharacteristic
76C47×#381C2211yescharacteristic
77C47×#380C2212yes—
78C47×#380C2211yescharacteristic
79C47×#380C2211yescharacteristic
80C47×#379C2212yes—
81C4×C22⋊C4×C47C2211yescharacteristic
82C4×C22⋊C4×C47C2212yes—
83C4×C22⋊C4×C47C2211yescharacteristic
84C2×#10625350—44no—
85C2×#10625350C2×C418yescomplemented
86C22×Dic94C2311yescharacteristic
87C22×D188C2311yescharacteristic
88C22×C22⋊D47C2312yes—
89C22×C22⋊D47C2312yes—
90C22×C22⋊D47C2312yes—
91C23×Dic47C2314yes—
92C22×C4×D47C2314yes—
93C22×C4×D47C2312yes—
94#13094007C2×C4116yescomplemented
95#13094003C2×C418yescomplemented
96#13094003C2×C418yescomplemented
97#13093998C2×C418yes—
98#13093998C2×C418yescomplemented
99#13093993C2×C4116yescomplemented
100C4×Dic94—44no—
101C4×D188—44no—
102C4×C22⋊D47C2×C4116yescomplemented
103C4×C22⋊D47C2×C4116yescomplemented
104(C22⋊D47)⋊C4—48no—
105#13093983C2×C418yescomplemented
106C2×C4⋊Dic47—44no—
107C2×C4⋊Dic47C2312yes—
108C2×C4⋊Dic47C2312yes—
109C2×C4⋊Dic47C2314yes—
110C2×C4⋊Dic47C2311yescharacteristic
111C2×C4⋊Dic47C2311yescharacteristic
112C2×Dic47⋊C4C2314yes—
113C2×Dic47⋊C4C2314yes—
114C2×Dic47⋊C4C2314yes—
115C2×Dic47⋊C4C2312yes—
116C2×Dic47⋊C4C2312yes—
117C2×C22⋊Dic47—44no—
118C2×C22⋊Dic47C2312yes—
119C2×C22⋊Dic47C2314yes—
120C2×C22⋊Dic47C2312yes—
121C2×C22⋊Dic47C2312yes—
122C2×C22⋊Dic47C2312yes—
123C2×C22⋊Dic47C2312yes—
124C2×(C2×D47)⋊C4C2314yes—
125C2×(C2×D47)⋊C4C2314yes—
126C2×(C2×D47)⋊C4C2314yes—
127C2×(C2×D47)⋊C4C2312yes—
128C2×(C2×D47)⋊C4C2312yes—
129C2×C4×Dic47C2314yes—
130C2×C4×Dic47C2314yes—
131C2×C4×Dic47C2314yes—
132C2×C4×Dic47C2312yes—
133C47⋊#95C2312yes—
134C47⋊#95C2314yes—
135C47⋊#95C2312yes—
136C47⋊#95C2314yes—
137C47⋊#95C2314yes—
138C47⋊#95C2314yes—
139C47⋊#95C2314yes—
140C47⋊#95C2314yes—
141C47⋊#95C2314yes—
142C25×C47C2311yescharacteristic
143C23×C4×C47—44no—
144C23×C4×C47C2×C418yescomplemented
145C23×C4×C47C2311yescharacteristic
146C23×C4×C47C2311yescharacteristic
147C23×C4×C47C2311yescharacteristic
148C23×C4×C47C2311yescharacteristic
149C23×C4×C47C2311yescharacteristic
150C23×C4×C47C2311yescharacteristic
151#117×C47—44no—
152C2×C4⋊C4×C47C2312yes—
153C2×C4⋊C4×C47C2312yes—
154C2×C22⋊C4×C47C2312yes—
155C2×C22⋊C4×C47C2312yes—
156C2×C22⋊C4×C47C2312yes—
157C2×C22⋊C4×C47C2312yes—
158C2×C22⋊C4×C47C2312yes—
159C2×C22⋊C4×C47C2312yes—
160C2×C42×C47C2312yes—
161C2×C42×C47C2312yes—
162#95×C47C2311yescharacteristic
163#95×C47C2311yescharacteristic
164#95×C47C2311yescharacteristic
165#95×C47C2311yescharacteristic
166#95×C47C2312yes—
167#95×C47C2312yes—
168C24×C47—22no—
169C24×C47—22no—
170C24×C47—42no—
171C24×C47—42no—
172C24×C47C22×C414yes—
173C24×C47C2411yescharacteristic
174C24×C47C2411yescharacteristic
175C24×C47C2411yescharacteristic
176C23×D47C2412yes—
177C22×C4×C47—24no—
178C22×C4×C47—24no—
179C22×C4×C47—24no—
180C22×C4×C47—416no—
181C22×C4×C47—42no—
182C22×C4×C47—42no—
183C22×C4×C47—42no—
184C22×C4×C47C22×C414yes—
185C22×C4×C47C22×C414yes—
186C22×C4×C47C22×C414yes—
187C22×C4×C47C22×C414yes—
188C22×C4×C47C22×C414yes—
189C22×C4×C47C22×C414yes—
190C22×C4×C47C2412yes—
191C22×C4×C47C2412yes—
192C22×C4×C47C2412yes—
193C22×C4×C47C2412yes—
194C22×C4×C47C2411yescharacteristic
195C22×C4×C47C2411yescharacteristic
196C22×C4×C47C2411yescharacteristic
197C22×C4×C47C2411yescharacteristic
198C2×C22⋊D47—24no—
199C2×C22⋊D47—24no—
200C2×C22⋊D47—44no—
201C2×C22⋊D47—44no—
202C2×C22⋊D47C22×C418yes—
203C2×C22⋊D47C22×C418yes—
204C2×C22⋊D47C22×C418yes—
205C22×Dic47—28no—
206C22×Dic47—44no—
207C22×Dic47—44no—
208C22×Dic47C2414yes—
209C22×Dic47C2414yes—
210C22×Dic47C2412yes—
211C22×Dic47C2412yes—
212C22×Dic47C2412yes—
213#10625350—416no—
214C2×D188—24no—
215C2×D188C22×C414yes—
216C2×C4×D47—44no—
217C2×C4×D47—44no—
218C2×C4×D47—44no—
219C2×C4×D47—44no—
220C2×C4×D47C22×C418yes—
221C2×Dic94—24no—
222C2×Dic94C22×C414yes—
223C4⋊C4×C47—42no—
224C4⋊C4×C47—42no—
225C22⋊C4×C47—24no—
226C22⋊C4×C47—24no—
227C22⋊C4×C47—42no—
228C22⋊C4×C47—42no—
229C22⋊C4×C47—42no—
230C22⋊C4×C47—42no—
231C42×C47—24no—
232C42×C47—24no—
233C22⋊Dic47—42no—
234C22⋊Dic47—44no—
235C22⋊Dic47—42no—
236C22⋊Dic47C22×C418yes—
237C22⋊Dic47C22×C418yes—
238C22⋊Dic47C22×C418yes—
239(C2×D47)⋊C4—44no—
240(C2×D47)⋊C4—44no—
241(C2×D47)⋊C4—44no—
242(C2×D47)⋊C4C22×C418yes—
243(C2×D47)⋊C4C22×C418yes—
244C4⋊Dic47—24no—
245C4⋊Dic47—24no—
246C4⋊Dic47—44no—
247C4⋊Dic47C22×C414yes—
248C4⋊Dic47C22×C414yes—
249Dic47⋊C4—44no—
250Dic47⋊C4—44no—
251Dic47⋊C4—44no—
252Dic47⋊C4C22×C418yes—
253Dic47⋊C4C22×C418yes—
254C4×Dic47—44no—
255C4×Dic47—44no—
256C4×Dic47—44no—
257C4×Dic47C22×C418yes—
258C23×C47—22no—
259C23×C47—22no—
260C23×C47—28no—
261C23×C47—21no—
262C23×C47—21no—
263C23×C47—22no—
264C23×C47—22no—
265C23×C47—21no—
266C23×C47—21no—
267C23×C47—22no—
268C23×C47—22no—
269C23×C47—44no—
270C23×C47—44no—
271C23×C47—48no—
272C23×C47—48no—
273C23×C47C23×C412yes—
274C23×C47C23×C412yes—
275C23×C47C23×C412yes—
276C23×C47H(5,𝔽2)12yes—
277C23×C472−1+412yes—
278C23×C47C2511yescharacteristic
279C22×D47—22no—
280C22×D47—24no—
281C22×D47—22no—
282C22×D47—24no—
283C22×D47C23×C414yes—
284C2×C4×C47—22no—
285C2×C4×C47—22no—
286C2×C4×C47—22no—
287C2×C4×C47—28no—
288C2×C4×C47—28no—
289C2×C4×C47—28no—
290C2×C4×C47—22no—
291C2×C4×C47—22no—
292C2×C4×C47—22no—
293C2×C4×C47—22no—
294C2×C4×C47—22no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—22no—
299C2×C4×C47—22no—
300C2×C4×C47—22no—
301C2×C4×C47—22no—
302C2×C4×C47—44no—
303C2×C4×C47—44no—
304C2×C4×C47—44no—
305C2×C4×C47C23×C412yes—
306C2×C4×C47C23×C412yes—
307C2×C4×C47C23×C412yes—
308C2×C4×C47C23×C412yes—
309C2×C4×C47H(5,𝔽2)14yes—
310C22⋊D47—216no—
311C22⋊D47—48no—
312C22⋊D47—48no—
313C2×Dic47—22no—
314C2×Dic47—24no—
315C2×Dic47—22no—
316C2×Dic47—24no—
317C2×Dic47—24no—
318C2×Dic47—24no—
319C2×Dic47—24no—
320C2×Dic47—24no—
321C2×Dic47—24no—
322C2×Dic47—24no—
323C2×Dic47—88no—
324C2×Dic47C23×C414yes—
325C2×Dic47C23×C414yes—
326C2×Dic47C23×C414yes—
327D188—28no—
328C4×D47—48no—
329C4×D47—88no—
330Dic94—28no—
331#34404—471nomaximal, Sylow
332C22×C47—22no—
333C22×C47—22no—
334C22×C47—24no—
335C22×C47—24no—
336C22×C47—22no—
337C22×C47—22no—
338C22×C47—22no—
339C22×C47—22no—
340C22×C47—22no—
341C22×C47—22no—
342C22×C47—416no—
343C22×C47—42no—
344C22×C47—42no—
345C22×C47—42no—
346C22×C47—42no—
347C22×C47#52014yes—
348C22×C47C24×C411yescharacteristic
349C22×C47C2×H(5,𝔽2)12yes—
350C22×C47C2×H(5,𝔽2)11yescharacteristic
351C22×C47C2×2−1+411yescharacteristic
352C22×C47#58512yes—
353C2×D47—24no—
354C2×D47—24no—
355C2×D47—24no—
356C2×D47—44no—
357C2×D47—44no—
358C4×C47—22no—
359C4×C47—22no—
360C4×C47—22no—
361C4×C47—42no—
362C4×C47—42no—
363C4×C47—42no—
364C4×C47—42no—
365C4×C47#51814yes—
366Dic47—24no—
367Dic47—24no—
368Dic47—24no—
369Dic47—44no—
370Dic47—44no—
371C2×#525—471no—
372#2376—474no—
373#2361—472no—
374#2360—472no—
375#2353—472no—
376#2349—472no—
377#2347—471no—
378#2346—471no—
379#2341—471no—
380#2339—471no—
381#2324—472no—
382#2323—472no—
383#2321—474no—
384#2319—472no—
385#2318—472no—
386#2280D4711yescharacteristic, complemented
387C2×#380—471no—
388C2×C47—24no—
389C2×C47—42no—
390C2×C47—42no—
391C2×C47C2×#51811yescharacteristic
392C2×C47C2×#52011yescharacteristic
393C2×C47#342811yescharacteristic
394C2×C47#354112yes—
395C2×C47#354212yes—
396D47—44no—
397C22×#41—471no—
398C24×C4C2×D4711yescharacteristic
399#525—4716no—
400C2×#123—472no—
401C2×C22⋊Q8—471no—
402C2×C22⋊Q8—471no—
403C2×#121—471no—
404C2×#121—471no—
405C2×#120—472no—
406C2×C4×Q8—472no—
407C2×C4×D4—472no—
408C2×C4×D4—472no—
409C2×C4×D4—474no—
410C2×C4×D4—472no—
411C2×#117—471no—
412C2×#117C2×D4712yes—
413C22×C4⋊C4—472no—
414C22×C22⋊C4—472no—
415#391—472no—
416#390—474no—
417#390—474no—
418#390—472no—
419#389—474no—
420#389—472no—
421#389—472no—
422#389—474no—
423#388—474no—
424#388—474no—
425#388—474no—
426#388—474no—
427#388—474no—
428#388—474no—
429#387—474no—
430#387—474no—
431#386—474no—
432#386—474no—
433#386—474no—
434#385—474no—
435#385—474no—
436#385—474no—
437#383—472no—
438#382—472no—
439#381—472no—
440#381C2×D4711yescharacteristic
441#381C2×D4711yescharacteristic
442#380—472no—
443#380—472no—
444#380—471no—
445#380—471no—
446#380—472no—
447#380—472no—
448#380C2×D4711yescharacteristic
449#380C2×D4711yescharacteristic
450#380C2×D4712yes—
451#379C2×D4712yes—
452C4×C4⋊C4—472no—
453C4×C4⋊C4—472no—
454C4×C4⋊C4—472no—
455C4×C22⋊C4—474no—
456C4×C22⋊C4—472no—
457C4×C22⋊C4C2×D4711yescharacteristic
458C4×C22⋊C4C2×D4711yescharacteristic
459C4×C22⋊C4C2×D4712yes—
460#376—472no—
461C2×#95—472no—
462C2×#95—472no—
463C47#3440411yescharacteristic, complemented, Sylow
464C25C22×D4711yescharacteristic
465C2×#41—478no—
466C2×#41—1884no—
467C22×Q8—471no—
468C22×D4—472no—
469C22×D4—472no—
470C22×D4—472no—
471C22×D4—471no—
472C23×C4—44no—
473C23×C4—472no—
474C23×C4—474no—
475C23×C4—474no—
476C23×C4C4×D4718yescomplemented
477C23×C4C22×D4711yescharacteristic
478C23×C4C22×D4711yescharacteristic
479C23×C4C22×D4711yescharacteristic
480C23×C4C22×D4711yescharacteristic
481C23×C4C22×D4711yescharacteristic
482C23×C4C22×D4711yescharacteristic
483#123—4716no—
484C22⋊Q8—478no—
485C22⋊Q8—478no—
486#121—478no—
487#121—478no—
488#120—4716no—
489C4×Q8—1884no—
490C4×D4—4716no—
491C4×D4—4716no—
492C4×D4—1884no—
493C4×D4—1888no—
494#117—44no—
495#117—478no—
496C2×C4⋊C4—471no—
497C2×C4⋊C4—471no—
498C2×C4⋊C4—472no—
499C2×C4⋊C4—472no—
500C2×C4⋊C4—472no—
501C2×C4⋊C4—472no—
502C2×C4⋊C4—474no—
503C2×C4⋊C4—474no—
504C2×C4⋊C4—474no—
505C2×C4⋊C4—474no—
506C2×C4⋊C4—1884no—
507C2×C4⋊C4C22×D4712yes—
508C2×C4⋊C4C22×D4712yes—
509C2×C22⋊C4—472no—
510C2×C22⋊C4—472no—
511C2×C22⋊C4—472no—
512C2×C22⋊C4—472no—
513C2×C22⋊C4—472no—
514C2×C22⋊C4—472no—
515C2×C22⋊C4—474no—
516C2×C22⋊C4—472no—
517C2×C22⋊C4—474no—
518C2×C22⋊C4—474no—
519C2×C22⋊C4—474no—
520C2×C22⋊C4—1884no—
521C2×C22⋊C4C22×D4712yes—
522C2×C22⋊C4C22×D4712yes—
523C2×C22⋊C4C22×D4712yes—
524C2×C22⋊C4C22×D4712yes—
525C2×C22⋊C4C22×D4712yes—
526C2×C22⋊C4C22×D4712yes—
527C2×C42—472no—
528C2×C42—474no—
529C2×C42—474no—
530C2×C42—474no—
531C2×C42C22×D4712yes—
532C2×C42C22×D4712yes—
533#95—472no—
534#95—472no—
535#95—474no—
536#95—474no—
537#95—474no—
538#95—474no—
539#95—474no—
540#95—474no—
541#95—474no—
542#95C22×D4711yescharacteristic
543#95C22×D4711yescharacteristic
544#95C22×D4711yescharacteristic
545#95C22×D4711yescharacteristic
546#95C22×D4712yes—
547#95C22×D4712yes—
548C24—22no—
549C24—22no—
550C24—42no—
551C24—42no—
552C24—472no—
553C24C2×C4×D4714yes—
554C24C23×D4711yescharacteristic
555C24C23×D4711yescharacteristic
556C24C23×D4711yescharacteristic
557#41—18816no—
558C2×Q8—474no—
559C2×Q8—944no—
560C2×D4—478no—
561C2×D4—478no—
562C2×D4—478no—
563C2×D4—474no—
564C2×D4—944no—
565C2×D4—944no—
566C2×D4—944no—
567C2×D4—1884no—
568C2×D4—1884no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—416no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—472no—
577C22×C4—472no—
578C22×C4—472no—
579C22×C4—478no—
580C22×C4—474no—
581C22×C4—474no—
582C22×C4—948no—
583C22×C4—1884no—
584C22×C4—1884no—
585C22×C4—1884no—
586C22×C4—1884no—
587C22×C4—1884no—
588C22×C4—1884no—
589C22×C4C2×C4×D4714yes—
590C22×C4C2×C4×D4714yes—
591C22×C4C2×C4×D4714yes—
592C22×C4C2×C4×D4714yes—
593C22×C4C2×C4×D4714yes—
594C22×C4C2×C4×D4714yes—
595C22×C4C23×D4712yes—
596C22×C4C23×D4712yes—
597C22×C4C23×D4712yes—
598C22×C4C23×D4712yes—
599C22×C4C23×D4711yescharacteristic
600C22×C4C23×D4711yescharacteristic
601C22×C4C23×D4711yescharacteristic
602C22×C4C23×D4711yescharacteristic
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4—478no—
606C4⋊C4—478no—
607C4⋊C4—474no—
608C4⋊C4—474no—
609C4⋊C4—944no—
610C4⋊C4—944no—
611C4⋊C4—1884no—
612C4⋊C4—1884no—
613C4⋊C4—1884no—
614C4⋊C4—1884no—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—478no—
622C22⋊C4—478no—
623C22⋊C4—478no—
624C22⋊C4—478no—
625C22⋊C4—478no—
626C22⋊C4—1884no—
627C22⋊C4—1884no—
628C22⋊C4—1884no—
629C22⋊C4—1882no—
630C22⋊C4—1884no—
631C22⋊C4—1882no—
632C42—24no—
633C42—24no—
634C42—478no—
635C42—1884no—
636C42—1884no—
637C42—1884no—
638C23—22no—
639C23—22no—
640C23—28no—
641C23—22no—
642C23—22no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—22no—
648C23—22no—
649C23—44no—
650C23—44no—
651C23—48no—
652C23—48no—
653C23—474no—
654C23—944no—
655C23—942no—
656C23—942no—
657C23—944no—
658C23C22×C4×D4712yes—
659C23C22×C4×D4712yes—
660C23C22×C4×D4712yes—
661C23#1309407012yes—
662C23#1309407112yes—
663C23C24×D4711yescharacteristic
664Q8—948no—
665D4—9416no—
666D4—948no—
667D4—1888no—
668D4—1888no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—28no—
673C2×C4—28no—
674C2×C4—28no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—474no—
691C2×C4—474no—
692C2×C4—474no—
693C2×C4—944no—
694C2×C4—942no—
695C2×C4—942no—
696C2×C4—944no—
697C2×C4—944no—
698C2×C4—944no—
699C2×C4—944no—
700C2×C4—944no—
701C2×C4—944no—
702C2×C4—944no—
703C2×C4—3768no—
704C2×C4—3768no—
705C2×C4—1888no—
706C2×C4C22×C4×D4712yes—
707C2×C4C22×C4×D4712yes—
708C2×C4C22×C4×D4712yes—
709C2×C4C22×C4×D4712yes—
710C2×C4#1309406914yes—
711C22—22no—
712C22—22no—
713C22—24no—
714C22—24no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—416no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—944no—
727C22—944no—
728C22—944no—
729C22—1884no—
730C22—1884no—
731C22#1568960314yes—
732C22C23×C4×D4711yescharacteristic
733C22C2×#1309406912yes—
734C22C2×#1309407011yescharacteristic
735C22C2×#1309407111yescharacteristic
736C22#1568995912yes—
737C4—22no—
738C4—22no—
739C4—22no—
740C4—42no—
741C4—42no—
742C4—42no—
743C4—42no—
744C4—944no—
745C4—944no—
746C4—944no—
747C4—1884no—
748C4—1884no—
749C4#1568959614yes—
750C2—24no—
751C2—42no—
752C2—42no—
753C2—1884no—
754C2C2×#1568959611yescharacteristic
755C2C2×#1568960311yescharacteristic
756C2#2025658911yescharacteristic
757C2#2025768112yes—
758C2#2025770412yes—
subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingC47×#2280C2
socle, cosocleC23×C47C25
prime radicalC2×#15689634C2
hypercenter#2280D47
hypocenterC47#34404
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2280

Complements

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

NH ≅ G/Ntype
2. #20246532C2semidirect
3. #20246402C2semidirect
4. #20246391C2semidirect
5. #20246330C2semidirect
6. #20246292C2semidirect
7. #20246279C2semidirect
8. #20246271C2semidirect
9. #20246228C2semidirect
10. #20246219C2semidirect
11. #20246081C2semidirect
12. #20246070C2semidirect
13. #20246043C2semidirect
14. #20246028C2semidirect
15. #20246017C2semidirect
16. C2×#15688983C2semidirect
17. C47×#2280C2semidirect
19. #15689634C4semidirect
26. C2×C4×Dic94C22semidirect
27. C2×C4×D188C22semidirect
34. #15689029C22semidirect
35. #15689025C22semidirect
38. #15689021C22semidirect
39. #15689021C22semidirect
40. #15689020C22semidirect
41. #15689018C22semidirect
44. #15689015C22semidirect
45. #15689013C22semidirect
48. #15689010C22semidirect
49. #15689004C22semidirect
53. #15688997C22semidirect
55. #15688994C22semidirect
56. #15688990C22semidirect
57. #15688987C22semidirect
58. #15688985C22semidirect
64. #15688982C22semidirect
65. C4×C4⋊Dic47C22semidirect
66. C4×C4⋊Dic47C22semidirect
67. #15688974C22semidirect
69. #15688970C22semidirect
70. #15688968C22semidirect
72. #95×D47C22semidirect
85. C2×#10625350C2×C4semidirect
94. #13094007C2×C4semidirect
95. #13094003C2×C4semidirect
96. #13094003C2×C4semidirect
98. #13093998C2×C4semidirect
99. #13093993C2×C4semidirect
102. C4×C22⋊D47C2×C4semidirect
103. C4×C22⋊D47C2×C4semidirect
105. #13093983C2×C4semidirect
144. C23×C4×C47C2×C4semidirect
386. #2280D47semidirect
463. C47#34404semidirect
476. C23×C4C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156896342
#202465322
#202464022
#202463912
#202463302
#202462922
#202462792
#202462712
#202462282
#202462192
#202460812
#202460702
#202460432
#202460282
#202460172
C2×#156889832
C47×#22802
#3440447