Finite Group Databasebeta

← #26376492

Subgroups — #26376492

Order 12032.

3014 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D47C211yesmaximal, characteristic
2#20246336C212yesmaximal, complemented
3#20246316C214yesmaximal, complemented
4#20246289C212yesmaximal, complemented
5#20246264C212yesmaximal, complemented
6#20246232C214yesmaximal, complemented
7#20246209C212yesmaximal
8#20246031C211yesmaximal, characteristic, complemented
9#20246023C212yesmaximal, complemented
10#20246017C212yesmaximal, complemented
11#20245792C211yesmaximal, characteristic, complemented
12#20245780C211yesmaximal, characteristic, complemented
13#20245768C212yesmaximal, complemented
14#380×D47C212yesmaximal, complemented
15#20245750C211yesmaximal, characteristic, complemented
16#20245748C211yesmaximal, characteristic, complemented
17C47×#2319C211yesmaximal, characteristic, complemented
18C22×D4×D47C2211yescharacteristic
19C23×C4×D47C2212yes—
20C2×C4×D188C2212yes—
21C2×C4×D188C2211yescharacteristic
22C2×D4×Dic47C2211yescharacteristic
23C2×#13093986C2212yes—
24C2×#13093986C2211yescharacteristic
25C2×C4×C22⋊D47C2212yes—
26C2×(C22⋊D47)⋊C4C2212yes—
27C4×D4×D47C4116yescomplemented
28C2×#13093981C2212yes—
29C2×#13093980C2214yescomplemented
30C2×C4⋊C4×D47C2211yescharacteristic
31C2×C4⋊C4×D47C2214yescomplemented
32C2×C22⋊C4×D47C2214yes—
33C2×C22⋊C4×D47C2212yes—
34C2×C42×D47C2211yescharacteristic
35#15689026C2212yes—
36#15689022C2212yescomplemented
37#15689017C2214yescomplemented
38#15689016C2214yescomplemented
39#15689011C2214yescomplemented
40#15689010C2214yescomplemented
41#15689004C2214yescomplemented
42#15688999C2214yes—
43#15688999C2214yes—
44#15688997C2214yescomplemented
45#15688994C2214yescomplemented
46#15688992C2212yescomplemented
47#15688990C2211yescharacteristic, complemented
48#15688990C2211yescharacteristic, complemented
49#15688987C2212yescomplemented
50#15688987C2212yescomplemented
51#15688986C2212yescomplemented
52#15688985C2212yes—
53#15688983C2212yescomplemented
54#15688982C2211yescharacteristic
55#15688982C2212yes—
56#15688982C2211yescharacteristic
57#15688982C2214yescomplemented
58#15688981C2214yescomplemented
59#15688980C2212yes—
60#15688980C2214yes—
61#15688978C2214yes—
62C4⋊C4×Dic47C2212yescomplemented
63C4×Dic47⋊C4C2212yescomplemented
64C4×Dic47⋊C4C2212yescomplemented
65C4×C4⋊Dic47C2211yescharacteristic, complemented
66C4×C4⋊Dic47C2212yescomplemented
67C4×(C2×D47)⋊C4C2212yes—
68C4×(C2×D47)⋊C4C2214yescomplemented
69#15688970C2214yes—
70#15688970C2212yescomplemented
71#15688970C2212yescomplemented
72#15688970C2214yescomplemented
73#15688969C2211yescharacteristic, complemented
74#95×D47C2212yescomplemented
75#95×D47C2212yescomplemented
76C2×C4×D4×C47C2211yescharacteristic
77C47×#390C2212yes—
78C47×#389C2212yescomplemented
79C47×#388C2214yescomplemented
80C47×#381C2212yescomplemented
81C47×#380C2212yescomplemented
82C4×C4⋊C4×C47C2211yescharacteristic, complemented
83C47×#376C2211yescharacteristic, complemented
84C24×D47C2312yes—
85C22×D188C2311yescharacteristic
86C22×C22⋊D47C2312yes—
87C2×D4×D47—28no—
88C2×D4×D47C2×C418yes—
89C23×Dic47C2312yes—
90C22×C4×D47—48no—
91C22×C4×D47C2×C4116yescomplemented
92C22×C4×D47C2311yescharacteristic
93C22×C4×D47C2311yescharacteristic
94C22×C4×D47C2312yes—
95C22×C4×D47C2311yescharacteristic
96C22×C4×D47C2314yes—
97C22×C4×D47C2314yes—
98C22×C4×D47C2312yes—
99C22×C4×D47C2312yes—
100C4×D188—28no—
101C4×D188C2×C418yes—
102D4×Dic47C2×C418yescomplemented
103#13093986—28no—
104#13093986C2×C418yes—
105C4×C22⋊D47C2×C4116yescomplemented
106(C22⋊D47)⋊C4C2×C4116yescomplemented
107#13093981—44no—
108#13093980—48no—
109C2×C4⋊Dic47C2312yes—
110C2×C4⋊Dic47C2314yes—
111C2×C4⋊Dic47C2311yescharacteristic
112C2×Dic47⋊C4C2312yes—
113C2×Dic47⋊C4C2314yes—
114C2×Dic47⋊C4C2312yes—
115C2×Dic47⋊C4C2314yes—
116C2×Dic47⋊C4C2312yes—
117C4⋊C4×D47—48no—
118C4⋊C4×D47C2×C418yescomplemented
119C2×C22⋊Dic47C2314yes—
120C2×C22⋊Dic47C2314yes—
121C2×C22⋊Dic47C2312yes—
122C2×(C2×D47)⋊C4C2312yes—
123C2×(C2×D47)⋊C4C2314yes—
124C2×(C2×D47)⋊C4C2314yes—
125C2×(C2×D47)⋊C4C2314yes—
126C2×(C2×D47)⋊C4C2312yes—
127C2×(C2×D47)⋊C4C2312yes—
128C2×(C2×D47)⋊C4C2312yes—
129C22⋊C4×D47—48no—
130C22⋊C4×D47C2×C4116yescomplemented
131C2×C4×Dic47C2312yes—
132C2×C4×Dic47C2314yes—
133C2×C4×Dic47C2314yes—
134C2×C4×Dic47C2312yes—
135C2×C4×Dic47C2311yescharacteristic
136C2×C4×Dic47C2311yescharacteristic
137C2×C4×Dic47C2311yescharacteristic
138C42×D47C2×C418yescomplemented
139C47⋊#95C2311yescharacteristic
140C47⋊#95C2314yes—
141C47⋊#95C2312yes—
142C47⋊#95C2314yes—
143C47⋊#95C2311yescharacteristic
144C47⋊#95C2312yes—
145C47⋊#95C2314yes—
146C47⋊#95C2312yes—
147C47⋊#95C2312yes—
148C47⋊#95C2314yes—
149C47⋊#95C2312yes—
150C47⋊#95C2312yes—
151C22×D4×C47C2311yescharacteristic
152C23×C4×C47C2312yes—
153C4×D4×C47C2×C418yescomplemented
154C2×C4⋊C4×C47C2312yes—
155C2×C4⋊C4×C47C2314yes—
156C2×C4⋊C4×C47C2311yescharacteristic
157C2×C22⋊C4×C47C2314yes—
158C2×C22⋊C4×C47C2314yes—
159C2×C22⋊C4×C47C2312yes—
160C2×C42×C47C2312yes—
161C2×C42×C47C2312yes—
162C2×C42×C47C2311yescharacteristic
163#95×C47C2311yescharacteristic
164#95×C47C2312yes—
165#95×C47C2314yes—
166#95×C47C2311yescharacteristic
167#95×C47C2312yes—
168C24×C47C2412yes—
169C23×D47—28no—
170C23×D47—24no—
171C23×D47—24no—
172C23×D47—44no—
173C23×D47C22×C418yes—
174C23×D47C2412yes—
175C23×D47C2411yescharacteristic
176C2×D4×C47—24no—
177C2×D4×C47C22×C414yes—
178C22×C4×C47—44no—
179C22×C4×C47C22×C418yes—
180C22×C4×C47C2412yes—
181C22×C4×C47C2414yes—
182C22×C4×C47C2412yes—
183C22×C4×C47C2411yescharacteristic
184C22×C4×C47C2411yescharacteristic
185C22×C4×C47C2412yes—
186C22×C4×C47C2411yescharacteristic
187C2×C22⋊D47—28no—
188C2×C22⋊D47C22×C418yes—
189C22×Dic47—28no—
190C22×Dic47C22×C418yes—
191C22×Dic47C2412yes—
192C22×Dic47C2412yes—
193C22×Dic47C2414yes—
194C22×Dic47C2411yescharacteristic
195C22×Dic47C2412yes—
196C22×Dic47C2411yescharacteristic
197C22×Dic47C2411yescharacteristic
198D4×D47—232no—
199C2×D188C22×C414yes—
200C2×D188#4118yes—
201C2×C4×D47—22no—
202C2×C4×D47—22no—
203C2×C4×D47—24no—
204C2×C4×D47—28no—
205C2×C4×D47—24no—
206C2×C4×D47—28no—
207C2×C4×D47—28no—
208C2×C4×D47—432no—
209C2×C4×D47—44no—
210C2×C4×D47—44no—
211C2×C4×D47—44no—
212C2×C4×D47—44no—
213C2×C4×D47—44no—
214C2×C4×D47—44no—
215C2×C4×D47C22×C414yes—
216C2×C4×D47C22×C414yes—
217C2×C4×D47C22×C414yes—
218C2×C4×D47C22×C418yes—
219C2×C4×D47C22×C418yes—
220C2×C4×D47C22×C418yes—
221C4⋊C4×C47—24no—
222C4⋊C4×C47—44no—
223C4⋊C4×C47C22×C414yes—
224C22⋊C4×C47—44no—
225C22⋊C4×C47—44no—
226C22⋊C4×C47C22×C418yes—
227C42×C47—24no—
228C42×C47—42no—
229C42×C47C22×C414yes—
230C22⋊Dic47—44no—
231C22⋊Dic47—44no—
232C22⋊Dic47C22×C418yes—
233(C2×D47)⋊C4—28no—
234(C2×D47)⋊C4—28no—
235(C2×D47)⋊C4—24no—
236(C2×D47)⋊C4—28no—
237(C2×D47)⋊C4—24no—
238(C2×D47)⋊C4C22×C418yes—
239(C2×D47)⋊C4C22×C418yes—
240C4⋊Dic47—24no—
241C4⋊Dic47—44no—
242C4⋊Dic47C22×C414yes—
243Dic47⋊C4—24no—
244Dic47⋊C4—28no—
245Dic47⋊C4—24no—
246Dic47⋊C4—44no—
247Dic47⋊C4C22×C418yes—
248C4×Dic47—24no—
249C4×Dic47—44no—
250C4×Dic47—44no—
251C4×Dic47—42no—
252C4×Dic47C22×C414yes—
253C4×Dic47C22×C414yes—
254C4×Dic47C22×C414yes—
255C23×C47—24no—
256C23×C47—22no—
257C23×C47—24no—
258C23×C47—22no—
259C23×C47C23×C414yes—
260C23×C47C2511yescharacteristic
261C22×D47—22no—
262C22×D47—24no—
263C22×D47—22no—
264C22×D47—22no—
265C22×D47—22no—
266C22×D47—216no—
267C22×D47—216no—
268C22×D47—48no—
269C22×D47—416no—
270C22×D47—416no—
271C22×D47C23×C414yes—
272C22×D47C23×C412yes—
273C22×D47C2×#4118yes—
274C22×D47H(5,𝔽2)12yes—
275C22×D472−1+412yes—
276D4×C47—28no—
277C2×C4×C47—21no—
278C2×C4×C47—24no—
279C2×C4×C47—22no—
280C2×C4×C47—21no—
281C2×C4×C47—22no—
282C2×C4×C47—24no—
283C2×C4×C47—22no—
284C2×C4×C47—22no—
285C2×C4×C47—24no—
286C2×C4×C47—22no—
287C2×C4×C47—24no—
288C2×C4×C47—22no—
289C2×C4×C47—22no—
290C2×C4×C47—48no—
291C2×C4×C47C23×C412yes—
292C2×C4×C47C23×C412yes—
293C2×C4×C47C23×C414yes—
294C2×C4×C47C23×C412yes—
295C2×C4×C47C2×#4114yes—
296C22⋊D47—216no—
297C2×Dic47—22no—
298C2×Dic47—24no—
299C2×Dic47—21no—
300C2×Dic47—21no—
301C2×Dic47—216no—
302C2×Dic47—22no—
303C2×Dic47—22no—
304C2×Dic47—24no—
305C2×Dic47—22no—
306C2×Dic47—24no—
307C2×Dic47—24no—
308C2×Dic47—22no—
309C2×Dic47—22no—
310C2×Dic47—22no—
311C2×Dic47C23×C412yes—
312C2×Dic47C23×C412yes—
313C2×Dic47C23×C414yes—
314C2×Dic47C23×C412yes—
315C2×Dic47H(5,𝔽2)14yes—
316D188#117116yescomplemented
317C4×D47—28no—
318C4×D47—28no—
319C4×D47—28no—
320C4×D47—216no—
321C4×D47—48no—
322C4×D47—48no—
323C4×D47—88no—
324C4×D47—88no—
325#34194—471nomaximal, Sylow
326C22×C47—24no—
327C22×C47—24no—
328C22×C47—24no—
329C22×C47—44no—
330C22×C47—44no—
331C22×C47C24×C411yescharacteristic
332C22×C47C22×#4112yes—
333C22×C47C2×H(5,𝔽2)12yes—
334C22×C47C2×H(5,𝔽2)11yescharacteristic
335C22×C47C2×2−1+411yescharacteristic
336C2×D47—22no—
337C2×D47—22no—
338C2×D47—24no—
339C2×D47—24no—
340C2×D47—28no—
341C2×D47—24no—
342C2×D47—24no—
343C2×D47—28no—
344C2×D47—432no—
345C2×D47C2×#11718yes—
346C2×D47#52014yes—
347C4×C47—22no—
348C4×C47—24no—
349C4×C47—22no—
350C4×C47—42no—
351C4×C47—44no—
352C4×C47—42no—
353C4×C47C2×#11714yes—
354Dic47—22no—
355Dic47—24no—
356Dic47—22no—
357Dic47—42no—
358Dic47—44no—
359Dic47—42no—
360Dic47#51814yes—
361C22×C4×D4—471no—
362#2354—472no—
363#2352—474no—
364D4×C4⋊C4—472no—
365#2345—472no—
366#2342—474no—
367D4×C22⋊C4—472no—
368#2319—471no—
369#2319D4711yescharacteristic, complemented
370#2318—472no—
371#2318—472no—
372#2285—471no—
373#2283—471no—
374#2280—472no—
375C2×#380—472no—
376#2275—471no—
377#2275—471no—
378C2×C47—44no—
379C2×C47C22×#11711yescharacteristic
380C2×C47C2×#51811yescharacteristic
381C2×C47C2×#52011yescharacteristic
382C2×C47#351912yes—
383C2×C47#352012yes—
384D47—24no—
385D47—28no—
386C23×D4—471no—
387C24×C4—472no—
388C2×C4×D4—471no—
389C2×C4×D4—472no—
390C2×C4×D4—4716no—
391C2×C4×D4—471no—
392C2×C4×D4—472no—
393C2×C4×D4—472no—
394C2×C4×D4—471no—
395C2×C4×D4—472no—
396C2×C4×D4C2×D4711yescharacteristic
397C2×#117—474no—
398C2×#117—472no—
399C22×C4⋊C4—471no—
400C22×C4⋊C4—474no—
401C22×C22⋊C4—472no—
402C22×C22⋊C4—474no—
403C22×C42—471no—
404#390—472no—
405#390C2×D4712yes—
406#389—472no—
407#389C2×D4712yescomplemented
408#388—474no—
409#388—474no—
410#388—474no—
411#388C2×D4714yescomplemented
412#387—474no—
413#387—474no—
414#386—474no—
415#386—474no—
416#385—474no—
417#385—474no—
418#384—472no—
419#383—471no—
420#383—471no—
421#382—472no—
422#382—472no—
423#381—472no—
424#381—472no—
425#381C2×D4712yescomplemented
426#380—472no—
427#380—472no—
428#380—474no—
429#380—474no—
430#380—471no—
431#380—472no—
432#380—471no—
433#380—474no—
434#380C2×D4712yescomplemented
435#379—474no—
436C4×C4⋊C4—472no—
437C4×C4⋊C4—471no—
438C4×C4⋊C4—472no—
439C4×C4⋊C4—472no—
440C4×C4⋊C4—472no—
441C4×C4⋊C4C2×D4711yescharacteristic, complemented
442C4×C22⋊C4—472no—
443C4×C22⋊C4—474no—
444C4×C22⋊C4—474no—
445C4×C22⋊C4—472no—
446C4×C22⋊C4—472no—
447C4×C22⋊C4—474no—
448#376—471no—
449#376C2×D4711yescharacteristic, complemented
450C2×#95—472no—
451C2×#95—472no—
452C47#3419411yescharacteristic, complemented, Sylow
453C25—472no—
454C22×D4—472no—
455C22×D4—478no—
456C22×D4—471no—
457C22×D4—948no—
458C22×D4C22×D4711yescharacteristic
459C23×C4—472no—
460C23×C4—471no—
461C23×C4—472no—
462C23×C4—471no—
463C23×C4—471no—
464C23×C4—4716no—
465C23×C4—472no—
466C23×C4—472no—
467C23×C4—474no—
468C23×C4—474no—
469C23×C4—1888no—
470C23×C4C22×D4712yes—
471C4×D4—478no—
472C4×D4—4716no—
473C4×D4—478no—
474C4×D4—4716no—
475C4×D4—478no—
476C4×D4—948no—
477C4×D4—948no—
478C4×D4C4×D4718yescomplemented
479#117—1884no—
480#117—1888no—
481C2×C4⋊C4—472no—
482C2×C4⋊C4—471no—
483C2×C4⋊C4—478no—
484C2×C4⋊C4—472no—
485C2×C4⋊C4—474no—
486C2×C4⋊C4—472no—
487C2×C4⋊C4—472no—
488C2×C4⋊C4—474no—
489C2×C4⋊C4—474no—
490C2×C4⋊C4—1888no—
491C2×C4⋊C4C22×D4712yes—
492C2×C4⋊C4C22×D4714yes—
493C2×C4⋊C4C22×D4711yescharacteristic
494C2×C22⋊C4—472no—
495C2×C22⋊C4—472no—
496C2×C22⋊C4—472no—
497C2×C22⋊C4—4716no—
498C2×C22⋊C4—472no—
499C2×C22⋊C4—474no—
500C2×C22⋊C4—474no—
501C2×C22⋊C4—474no—
502C2×C22⋊C4—472no—
503C2×C22⋊C4—474no—
504C2×C22⋊C4—474no—
505C2×C22⋊C4—1888no—
506C2×C22⋊C4C22×D4714yes—
507C2×C22⋊C4C22×D4714yes—
508C2×C22⋊C4C22×D4712yes—
509C2×C42—471no—
510C2×C42—471no—
511C2×C42—471no—
512C2×C42—478no—
513C2×C42—472no—
514C2×C42—474no—
515C2×C42—474no—
516C2×C42—472no—
517C2×C42C22×D4712yes—
518C2×C42C22×D4712yes—
519C2×C42C22×D4711yescharacteristic
520#95—471no—
521#95—472no—
522#95—474no—
523#95—474no—
524#95—471no—
525#95—472no—
526#95—474no—
527#95—472no—
528#95—472no—
529#95—474no—
530#95—472no—
531#95—472no—
532#95C22×D4711yescharacteristic
533#95C22×D4712yes—
534#95C22×D4711yescharacteristic
535#95C22×D4712yes—
536#95C22×D4714yes—
537C24—471no—
538C24—472no—
539C24—478no—
540C24—944no—
541C24—948no—
542C24—944no—
543C24—1884no—
544C24C23×D4712yes—
545C2×D4—24no—
546C2×D4—478no—
547C2×D4—474no—
548C2×D4—478no—
549C2×D4—9432no—
550C2×D4—948no—
551C2×D4C2×C4×D4714yes—
552C22×C4—44no—
553C22×C4—471no—
554C22×C4—478no—
555C22×C4—471no—
556C22×C4—472no—
557C22×C4—471no—
558C22×C4—474no—
559C22×C4—474no—
560C22×C4—474no—
561C22×C4—478no—
562C22×C4—478no—
563C22×C4—478no—
564C22×C4—472no—
565C22×C4—472no—
566C22×C4—474no—
567C22×C4—948no—
568C22×C4—944no—
569C22×C4—942no—
570C22×C4—942no—
571C22×C4—948no—
572C22×C4—948no—
573C22×C4—948no—
574C22×C4—944no—
575C22×C4—1884no—
576C22×C4—1884no—
577C22×C4—1884no—
578C22×C4—1884no—
579C22×C4—1884no—
580C22×C4—1884no—
581C22×C4—18832no—
582C22×C4C2×C4×D4718yes—
583C22×C4C23×D4712yes—
584C22×C4C23×D4712yes—
585C22×C4C23×D4714yes—
586C22×C4C23×D4711yescharacteristic
587C22×C4C23×D4711yescharacteristic
588C22×C4C23×D4712yes—
589C22×C4C23×D4711yescharacteristic
590C4⋊C4—24no—
591C4⋊C4—44no—
592C4⋊C4—478no—
593C4⋊C4—474no—
594C4⋊C4—944no—
595C4⋊C4—948no—
596C4⋊C4—944no—
597C4⋊C4—944no—
598C4⋊C4—1884no—
599C4⋊C4—1884no—
600C4⋊C4C2×C4×D4714yes—
601C22⋊C4—44no—
602C22⋊C4—44no—
603C22⋊C4—478no—
604C22⋊C4—478no—
605C22⋊C4—478no—
606C22⋊C4—944no—
607C22⋊C4—944no—
608C22⋊C4—948no—
609C22⋊C4—948no—
610C22⋊C4—948no—
611C22⋊C4—1884no—
612C22⋊C4—1884no—
613C22⋊C4C2×C4×D4718yes—
614C42—24no—
615C42—42no—
616C42—474no—
617C42—474no—
618C42—474no—
619C42—944no—
620C42—1882no—
621C42—1884no—
622C42—1884no—
623C42C2×C4×D4714yes—
624C23—24no—
625C23—22no—
626C23—24no—
627C23—22no—
628C23—474no—
629C23—472no—
630C23—478no—
631C23—472no—
632C23—472no—
633C23—9416no—
634C23—9416no—
635C23—942no—
636C23—944no—
637C23—942no—
638C23—942no—
639C23—942no—
640C23—1888no—
641C23—18816no—
642C23—18816no—
643C23C22×C4×D4714yes—
644C23C24×D4711yescharacteristic
645D4—28no—
646D4—4716no—
647D4—9416no—
648C2×C4—21no—
649C2×C4—24no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—24no—
655C2×C4—24no—
656C2×C4—22no—
657C2×C4—24no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—48no—
662C2×C4—472no—
663C2×C4—474no—
664C2×C4—472no—
665C2×C4—472no—
666C2×C4—474no—
667C2×C4—9416no—
668C2×C4—948no—
669C2×C4—948no—
670C2×C4—9416no—
671C2×C4—942no—
672C2×C4—944no—
673C2×C4—941no—
674C2×C4—941no—
675C2×C4—948no—
676C2×C4—942no—
677C2×C4—942no—
678C2×C4—944no—
679C2×C4—942no—
680C2×C4—944no—
681C2×C4—944no—
682C2×C4—942no—
683C2×C4—942no—
684C2×C4—942no—
685C2×C4—3768no—
686C2×C4—3768no—
687C2×C4—1888no—
688C2×C4—1888no—
689C2×C4C22×C4×D4712yes—
690C2×C4C22×C4×D4712yes—
691C2×C4C22×C4×D4714yes—
692C2×C4C22×C4×D4712yes—
693C2×C4#41×D4714yes—
694C22—24no—
695C22—24no—
696C22—24no—
697C22—44no—
698C22—44no—
699C22—478no—
700C22—474no—
701C22—942no—
702C22—942no—
703C22—944no—
704C22—944no—
705C22—948no—
706C22—944no—
707C22—944no—
708C22—948no—
709C22—18832no—
710C22C23×C4×D4711yescharacteristic
711C22C2×#41×D4712yes—
712C22H(5,𝔽2)×D4712yes—
713C22H(5,𝔽2)×D4711yescharacteristic
714C222−1+4×D4711yescharacteristic
715C4—22no—
716C4—24no—
717C4—22no—
718C4—42no—
719C4—44no—
720C4—42no—
721C4—474no—
722C4—942no—
723C4—944no—
724C4—942no—
725C4—1882no—
726C4—1884no—
727C4—1882no—
728C4#117×D4714yes—
729C2—44no—
730C2—944no—
731C2—948no—
732C2C2×#117×D4711yescharacteristic
733C2#518×D4711yescharacteristic
734C2#520×D4711yescharacteristic
735C2#2025741812yes—
736C2#2025743512yes—
subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingC47×#2319C2
socle, cosocleC23×C47C25
prime radicalC22×D4×D47C22
hypercenter#2319D47
hypocenterC47#34194
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2319

Complements

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

NH ≅ G/Ntype
2. #20246336C2semidirect
3. #20246316C2semidirect
4. #20246289C2semidirect
5. #20246264C2semidirect
6. #20246232C2semidirect
8. #20246031C2semidirect
9. #20246023C2semidirect
10. #20246017C2semidirect
11. #20245792C2semidirect
12. #20245780C2semidirect
13. #20245768C2semidirect
14. #380×D47C2semidirect
15. #20245750C2semidirect
16. #20245748C2semidirect
17. C47×#2319C2semidirect
27. C4×D4×D47C4semidirect
29. C2×#13093980C22semidirect
31. C2×C4⋊C4×D47C22semidirect
36. #15689022C22semidirect
37. #15689017C22semidirect
38. #15689016C22semidirect
39. #15689011C22semidirect
40. #15689010C22semidirect
41. #15689004C22semidirect
44. #15688997C22semidirect
45. #15688994C22semidirect
46. #15688992C22semidirect
47. #15688990C22semidirect
48. #15688990C22semidirect
49. #15688987C22semidirect
50. #15688987C22semidirect
51. #15688986C22semidirect
53. #15688983C22semidirect
57. #15688982C22semidirect
58. #15688981C22semidirect
62. C4⋊C4×Dic47C22semidirect
63. C4×Dic47⋊C4C22semidirect
64. C4×Dic47⋊C4C22semidirect
65. C4×C4⋊Dic47C22semidirect
66. C4×C4⋊Dic47C22semidirect
68. C4×(C2×D47)⋊C4C22semidirect
70. #15688970C22semidirect
71. #15688970C22semidirect
72. #15688970C22semidirect
73. #15688969C22semidirect
74. #95×D47C22semidirect
75. #95×D47C22semidirect
78. C47×#389C22semidirect
79. C47×#388C22semidirect
80. C47×#381C22semidirect
81. C47×#380C22semidirect
82. C4×C4⋊C4×C47C22semidirect
83. C47×#376C22semidirect
91. C22×C4×D47C2×C4semidirect
102. D4×Dic47C2×C4semidirect
105. C4×C22⋊D47C2×C4semidirect
106. (C22⋊D47)⋊C4C2×C4semidirect
118. C4⋊C4×D47C2×C4semidirect
130. C22⋊C4×D47C2×C4semidirect
138. C42×D47C2×C4semidirect
153. C4×D4×C47C2×C4semidirect
316. D188#117semidirect
369. #2319D47semidirect
407. #389C2×D47semidirect
411. #388C2×D47semidirect
425. #381C2×D47semidirect
434. #380C2×D47semidirect
441. C4×C4⋊C4C2×D47semidirect
449. #376C2×D47semidirect
452. C47#34194semidirect
478. C4×D4C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×D472
#202463362
#202463162
#202462892
#202462642
#202462322
#202462092
#202460312
#202460232
#202460172
#202457922
#202457802
#202457682
#380×D472
#202457502
#202457482
C47×#23192
#3419447