Finite Group Databasebeta

← #26225532

Subgroups — #26225532

Order 12032.

1882 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093998C211yesmaximal, characteristic
2#20245771C211yesmaximal, characteristic, complemented
3#20244224C214yesmaximal, complemented
4#20244223C214yesmaximal, complemented
5#20243302C214yesmaximal, complemented
6C47×#2280C211yesmaximal, characteristic, complemented
7C23×D188C411yescharacteristic, complemented
8C23×C22⋊D47C2212yes—
9C2×#13093998—21no—
10C2×#13093998—21no—
11C2×#13093998—21no—
12C2×#13093998—21no—
13C2×#13093998—21no—
14C2×#13093998—21no—
15C2×#13093998—21no—
16C2×#13093998—21no—
17C2×#13093998C412yescomplemented
18C2×#13093998C412yescomplemented
19C2×#13093998C2212yes—
20C2×#13093998C2212yes—
21C2×#13093983—21no—
22C22×C4⋊Dic47C411yescharacteristic, complemented
23C22×(C2×D47)⋊C4C412yescomplemented
24C2×#13093938C22116yescomplemented
25#15688986—21no—
26#15688983—21no—
27#15688983C2212yescomplemented
28#15688979C2212yes—
29C4×C22⋊Dic47—21no—
30C4×C22⋊Dic47C2212yescomplemented
31C24×C4×C47C2211yescharacteristic
32C2×#117×C47—21no—
33C47×#381—21no—
34C47×#380—21no—
35C47×#380C2212yescomplemented
36C47×#379C2212yes—
37C4×C22⋊C4×C47—21no—
38C4×C22⋊C4×C47C2212yescomplemented
39C24×D47C2×C412yes—
40C22×D188—21no—
41C22×D188—21no—
42C22×D188—21no—
43C22×D188—21no—
44C22×D188—44no—
45C22×D188C2×C412yes—
46C22×D188C2×C412yes—
47C22×C22⋊D47—22no—
48C22×C22⋊D47—22no—
49C22×C22⋊D47—22no—
50C22×C22⋊D47—22no—
51C22×C22⋊D47—48no—
52C22×C22⋊D47C2×C414yes—
53C22×C22⋊D47C2314yes—
54C23×Dic47C2×C412yes—
55#13093998—22no—
56#13093998—22no—
57#13093998—22no—
58#13093998—22no—
59#13093998—22no—
60#13093998—22no—
61#13093998—22no—
62#13093998—22no—
63#13093998—22no—
64#13093998—22no—
65#13093998—22no—
66#13093998—22no—
67#13093998—22no—
68#13093998—22no—
69#13093998—22no—
70#13093998—22no—
71#13093983—44no—
72C2×C4⋊Dic47—21no—
73C2×C4⋊Dic47—21no—
74C2×C4⋊Dic47—21no—
75C2×C4⋊Dic47—21no—
76C2×C4⋊Dic47—22no—
77C2×C4⋊Dic47C2×C412yes—
78C2×C4⋊Dic47C2×C412yes—
79C2×C22⋊Dic47—22no—
80C2×C22⋊Dic47—22no—
81C2×C22⋊Dic47C2314yes—
82C2×(C2×D47)⋊C4—22no—
83C2×(C2×D47)⋊C4—22no—
84C2×(C2×D47)⋊C4—22no—
85C2×(C2×D47)⋊C4—22no—
86C2×(C2×D47)⋊C4C2×C414yes—
87C2×(C2×D47)⋊C4C2×C414yes—
88C2×C4×Dic47—22no—
89#13093938—416no—
90C47⋊#95—22no—
91C47⋊#95—22no—
92C25×C47C2311yescharacteristic
93C23×C4×C47—44no—
94C23×C4×C47C2×C411yescharacteristic
95C23×C4×C47C2×C411yescharacteristic
96C23×C4×C47C2×C411yescharacteristic
97C23×C4×C47C2×C411yescharacteristic
98C23×C4×C47D411yescharacteristic
99C23×C4×C47D411yescharacteristic
100C23×C4×C47D411yescharacteristic
101C23×C4×C47D411yescharacteristic
102C23×C4×C47D411yescharacteristic
103C23×C4×C47D411yescharacteristic
104C23×C4×C47D411yescharacteristic
105C23×C4×C47D411yescharacteristic
106C23×C4×C47C2311yescharacteristic
107C23×C4×C47C2311yescharacteristic
108#117×C47—44no—
109C2×C4⋊C4×C47—22no—
110C2×C22⋊C4×C47—22no—
111C2×C22⋊C4×C47—22no—
112C2×C22⋊C4×C47C2314yes—
113C2×C42×C47—22no—
114#95×C47—22no—
115#95×C47—22no—
116C24×C47—24no—
117C24×C47—42no—
118C24×C47—42no—
119C24×C47C22×C411yescharacteristic
120C24×C47C22×C411yescharacteristic
121C24×C47C2×D411yescharacteristic
122C24×C47C2×D411yescharacteristic
123C24×C47C2×D411yescharacteristic
124C24×C47C2×D411yescharacteristic
125C24×C47C2411yescharacteristic
126C23×D47—22no—
127C23×D47—22no—
128C23×D47—44no—
129C23×D47—44no—
130C23×D47—44no—
131C23×D47C22×C414yes—
132C22×C4×C47—24no—
133C22×C4×C47—24no—
134C22×C4×C47—24no—
135C22×C4×C47—24no—
136C22×C4×C47—42no—
137C22×C4×C47—42no—
138C22×C4×C47—42no—
139C22×C4×C47—42no—
140C22×C4×C47—42no—
141C22×C4×C47—42no—
142C22×C4×C47—42no—
143C22×C4×C47—42no—
144C22×C4×C47—42no—
145C22×C4×C47—42no—
146C22×C4×C47—42no—
147C22×C4×C47C22⋊C411yescharacteristic
148C22×C4×C47C22⋊C411yescharacteristic
149C22×C4×C47C22⋊C411yescharacteristic
150C22×C4×C47C22⋊C411yescharacteristic
151C22×C4×C47C22⋊C411yescharacteristic
152C22×C4×C47C22⋊C411yescharacteristic
153C22×C4×C47C22⋊C411yescharacteristic
154C22×C4×C47C22⋊C411yescharacteristic
155C22×C4×C47C22⋊C411yescharacteristic
156C22×C4×C47C22⋊C411yescharacteristic
157C22×C4×C47C22⋊C411yescharacteristic
158C22×C4×C47C22⋊C411yescharacteristic
159C22×C4×C47C22⋊C411yescharacteristic
160C22×C4×C47C22⋊C411yescharacteristic
161C22×C4×C47C22⋊C411yescharacteristic
162C22×C4×C47C22⋊C411yescharacteristic
163C22×C4×C47C22×C411yescharacteristic
164C22×C4×C47C22×C411yescharacteristic
165C22×C4×C47C22×C411yescharacteristic
166C22×C4×C47C22×C411yescharacteristic
167C22×C4×C47C2×D411yescharacteristic
168C22×C4×C47C2×D411yescharacteristic
169C22×C4×C47C2×D411yescharacteristic
170C22×C4×C47C2×D411yescharacteristic
171C22×C4×C47C2×D411yescharacteristic
172C22×C4×C47C2×D411yescharacteristic
173C22×C4×C47C2×D411yescharacteristic
174C22×C4×C47C2×D411yescharacteristic
175C2×C22⋊D47—24no—
176C2×C22⋊D47—24no—
177C2×C22⋊D47—24no—
178C2×C22⋊D47—24no—
179C2×C22⋊D47—216no—
180C2×C22⋊D47—48no—
181C2×C22⋊D47—48no—
182C2×C22⋊D47—48no—
183C2×C22⋊D47—48no—
184C2×C22⋊D47—48no—
185C22×Dic47—22no—
186C22×Dic47—22no—
187C22×Dic47—24no—
188C22×Dic47—44no—
189C22×Dic47C22×C414yes—
190C2×D188—22no—
191C2×D188—22no—
192C2×D188—22no—
193C2×D188—22no—
194C2×D188—44no—
195C2×D188—44no—
196C2×D188—44no—
197C2×D188—44no—
198C2×D188—44no—
199C2×D188—44no—
200C4⋊C4×C47—44no—
201C22⋊C4×C47—28no—
202C22⋊C4×C47—44no—
203C22⋊C4×C47—44no—
204C42×C47—44no—
205C22⋊Dic47—28no—
206C22⋊Dic47—44no—
207C22⋊Dic47—44no—
208(C2×D47)⋊C4—24no—
209(C2×D47)⋊C4—24no—
210(C2×D47)⋊C4—24no—
211(C2×D47)⋊C4—24no—
212C4⋊Dic47—22no—
213C4⋊Dic47—22no—
214C4⋊Dic47—22no—
215C4⋊Dic47—22no—
216C4⋊Dic47—44no—
217C4×Dic47—44no—
218C23×C47—22no—
219C23×C47—22no—
220C23×C47—22no—
221C23×C47—22no—
222C23×C47—22no—
223C23×C47—22no—
224C23×C47—22no—
225C23×C47—22no—
226C23×C47—22no—
227C23×C47—22no—
228C23×C47—22no—
229C23×C47—22no—
230C23×C47—41no—
231C23×C47—41no—
232C23×C47—41no—
233C23×C47—41no—
234C23×C47—41no—
235C23×C47—41no—
236C23×C47—41no—
237C23×C47—41no—
238C23×C47—416no—
239C23×C47C2×C22⋊C411yescharacteristic
240C23×C47C2×C22⋊C411yescharacteristic
241C23×C47C2×C22⋊C411yescharacteristic
242C23×C47C2×C22⋊C411yescharacteristic
243C23×C47C23×C411yescharacteristic
244C23×C47C22×D411yescharacteristic
245C23×C47C22×D411yescharacteristic
246C23×C47H(5,𝔽2)14yes—
247C22×D47—24no—
248C22×D47—28no—
249C22×D47—44no—
250C22×D47—44no—
251C22×D47—44no—
252C22×D47—44no—
253C22×D47—44no—
254C22×D47—44no—
255C22×D47—44no—
256C22×D47—44no—
257C22×D47—816no—
258C2×C4×C47—22no—
259C2×C4×C47—22no—
260C2×C4×C47—22no—
261C2×C4×C47—22no—
262C2×C4×C47—22no—
263C2×C4×C47—22no—
264C2×C4×C47—22no—
265C2×C4×C47—22no—
266C2×C4×C47—22no—
267C2×C4×C47—22no—
268C2×C4×C47—22no—
269C2×C4×C47—22no—
270C2×C4×C47—22no—
271C2×C4×C47—22no—
272C2×C4×C47—22no—
273C2×C4×C47—41no—
274C2×C4×C47—41no—
275C2×C4×C47—41no—
276C2×C4×C47—41no—
277C2×C4×C47—41no—
278C2×C4×C47—41no—
279C2×C4×C47—41no—
280C2×C4×C47—41no—
281C2×C4×C47—41no—
282C2×C4×C47—41no—
283C2×C4×C47—41no—
284C2×C4×C47—41no—
285C2×C4×C47—44no—
286C2×C4×C47—44no—
287C2×C4×C47—44no—
288C2×C4×C47#9914yescomplemented
289C2×C4×C47C2×C22⋊C411yescharacteristic
290C2×C4×C47C2×C22⋊C411yescharacteristic
291C2×C4×C47C2×C22⋊C411yescharacteristic
292C2×C4×C47C2×C22⋊C411yescharacteristic
293C2×C4×C47C2×C22⋊C411yescharacteristic
294C2×C4×C47C2×C22⋊C411yescharacteristic
295C2×C4×C47C2×C22⋊C411yescharacteristic
296C2×C4×C47C2×C22⋊C411yescharacteristic
297C22⋊D47—48no—
298C22⋊D47—48no—
299C22⋊D47—48no—
300C22⋊D47—48no—
301C2×Dic47—24no—
302C2×Dic47—28no—
303C2×Dic47—44no—
304C2×Dic47—44no—
305C2×Dic47—44no—
306C2×Dic47—44no—
307C2×Dic47—44no—
308D188—44no—
309D188—44no—
310D188—44no—
311D188—44no—
312#21793—471nomaximal, Sylow
313C22×C47—28no—
314C22×C47—21no—
315C22×C47—21no—
316C22×C47—21no—
317C22×C47—21no—
318C22×C47—21no—
319C22×C47—21no—
320C22×C47—21no—
321C22×C47—21no—
322C22×C47—21no—
323C22×C47—21no—
324C22×C47—21no—
325C22×C47—21no—
326C22×C47—21no—
327C22×C47—21no—
328C22×C47—21no—
329C22×C47—21no—
330C22×C47—44no—
331C22×C47—44no—
332C22×C47—44no—
333C22×C47—44no—
334C22×C47—44no—
335C22×C47—44no—
336C22×C47C2×#9912yes—
337C22×C47#41012yes—
338C22×C47C22×C22⋊C411yescharacteristic
339C22×C47#51812yes—
340C22×C47#53512yes—
341C22×C47#53512yes—
342C2×D47—44no—
343C2×D47—44no—
344C2×D47—44no—
345C2×D47—88no—
346C2×D47—88no—
347C2×D47—88no—
348C4×C47—21no—
349C4×C47—21no—
350C4×C47—21no—
351C4×C47—21no—
352C4×C47—21no—
353C4×C47—21no—
354C4×C47—84no—
355C4×C47C2×#9912yes—
356C4×C47C2×#9912yes—
357Dic47—44no—
358Dic47—84no—
359C22×#121—471no—
360#2280—471no—
361#2280D4711yescharacteristic, complemented
362#1964—474no—
363#1964—474no—
364#1781—474no—
365C2×C47—22no—
366C2×C47—22no—
367C2×C47—22no—
368C2×C47—22no—
369C2×C47—22no—
370C2×C47—41no—
371C2×C47—41no—
372C2×C47#230911yescharacteristic
373C2×C47C22×#9911yescharacteristic
374C2×C47C2×#41011yescharacteristic
375D47—84no—
376C23×D4—472no—
377C23×D4—471no—
378C24×C4C2×D4711yescharacteristic
379C2×#121—472no—
380C2×#121—472no—
381C2×#121—472no—
382C2×#121—472no—
383C2×#121—941no—
384C2×#121—941no—
385C2×#121—941no—
386C2×#121—941no—
387C2×#121—941no—
388C2×#121—941no—
389C2×#121—941no—
390C2×#121—941no—
391C2×#117—21no—
392C2×#117—941no—
393C22×C4⋊C4—471no—
394C22×C22⋊C4—472no—
395C2×#99—4716no—
396#381—21no—
397#381—941no—
398#380—21no—
399#380—472no—
400#380—941no—
401#380C2×D4712yescomplemented
402#379—472no—
403#379C2×D4712yes—
404C4×C22⋊C4—21no—
405C4×C22⋊C4—472no—
406C4×C22⋊C4—941no—
407C4×C22⋊C4C2×D4712yescomplemented
408C47#2179311yescharacteristic, complemented, Sylow
409C25—472no—
410C25C22×D4711yescharacteristic
411C22×D4—474no—
412C22×D4—474no—
413C22×D4—472no—
414C22×D4—472no—
415C22×D4—942no—
416C22×D4—942no—
417C22×D4—942no—
418C22×D4—942no—
419C22×D4—941no—
420C22×D4—941no—
421C22×D4—941no—
422C22×D4—941no—
423C22×D4—1884no—
424C22×D4—1888no—
425C23×C4—44no—
426C23×C4—472no—
427C23×C4C4×D4711yescharacteristic
428C23×C4C4×D4711yescharacteristic
429C23×C4C4×D4711yescharacteristic
430C23×C4C4×D4711yescharacteristic
431C23×C4D18811yescharacteristic
432C23×C4D18811yescharacteristic
433C23×C4D18811yescharacteristic
434C23×C4D18811yescharacteristic
435C23×C4C22⋊D4711yescharacteristic
436C23×C4C22⋊D4711yescharacteristic
437C23×C4C22⋊D4711yescharacteristic
438C23×C4C22⋊D4711yescharacteristic
439C23×C4C22×D4711yescharacteristic
440C23×C4C22×D4711yescharacteristic
441#121—942no—
442#121—942no—
443#121—942no—
444#121—942no—
445#121—942no—
446#121—942no—
447#121—942no—
448#121—942no—
449#121—942no—
450#121—942no—
451#121—942no—
452#121—942no—
453#121—942no—
454#121—942no—
455#121—942no—
456#121—942no—
457#117—44no—
458#117—1884no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—472no—
461C2×C4⋊C4—472no—
462C2×C4⋊C4—941no—
463C2×C4⋊C4—941no—
464C2×C4⋊C4—941no—
465C2×C4⋊C4—941no—
466C2×C4⋊C4—942no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—474no—
470C2×C22⋊C4—474no—
471C2×C22⋊C4—474no—
472C2×C22⋊C4—942no—
473C2×C22⋊C4—942no—
474C2×C22⋊C4—942no—
475C2×C22⋊C4—942no—
476C2×C22⋊C4—942no—
477C2×C22⋊C4—942no—
478C2×C22⋊C4C22×D4714yes—
479C2×C42—22no—
480C2×C42—942no—
481#99—18816no—
482#95—22no—
483#95—22no—
484#95—942no—
485#95—942no—
486C24—24no—
487C24—42no—
488C24—42no—
489C24—474no—
490C24—942no—
491C24—942no—
492C24—1884no—
493C24—1884no—
494C24—1884no—
495C24C2×C4×D4711yescharacteristic
496C24C2×C4×D4711yescharacteristic
497C24C2×D18811yescharacteristic
498C24C2×D18811yescharacteristic
499C24C2×C22⋊D4711yescharacteristic
500C24C2×C22⋊D4711yescharacteristic
501C24C23×D4711yescharacteristic
502C2×D4—944no—
503C2×D4—944no—
504C2×D4—944no—
505C2×D4—944no—
506C2×D4—9416no—
507C2×D4—942no—
508C2×D4—942no—
509C2×D4—942no—
510C2×D4—942no—
511C2×D4—1884no—
512C2×D4—1884no—
513C2×D4—1884no—
514C2×D4—1884no—
515C2×D4—1884no—
516C2×D4—1888no—
517C2×D4—1888no—
518C2×D4—1888no—
519C2×D4—1888no—
520C2×D4—1888no—
521C2×D4—1884no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—474no—
538C22×C4—942no—
539C22×C4—942no—
540C22×C4—944no—
541C22×C4—1884no—
542C22×C4(C2×D47)⋊C411yescharacteristic
543C22×C4(C2×D47)⋊C411yescharacteristic
544C22×C4(C2×D47)⋊C411yescharacteristic
545C22×C4(C2×D47)⋊C411yescharacteristic
546C22×C4(C2×D47)⋊C411yescharacteristic
547C22×C4(C2×D47)⋊C411yescharacteristic
548C22×C4(C2×D47)⋊C411yescharacteristic
549C22×C4(C2×D47)⋊C411yescharacteristic
550C22×C4(C2×D47)⋊C411yescharacteristic
551C22×C4(C2×D47)⋊C411yescharacteristic
552C22×C4(C2×D47)⋊C411yescharacteristic
553C22×C4(C2×D47)⋊C411yescharacteristic
554C22×C4(C2×D47)⋊C411yescharacteristic
555C22×C4(C2×D47)⋊C411yescharacteristic
556C22×C4(C2×D47)⋊C411yescharacteristic
557C22×C4(C2×D47)⋊C411yescharacteristic
558C22×C4C2×C4×D4711yescharacteristic
559C22×C4C2×C4×D4711yescharacteristic
560C22×C4C2×C4×D4711yescharacteristic
561C22×C4C2×C4×D4711yescharacteristic
562C22×C4C2×D18811yescharacteristic
563C22×C4C2×D18811yescharacteristic
564C22×C4C2×D18811yescharacteristic
565C22×C4C2×D18811yescharacteristic
566C22×C4C2×C22⋊D4711yescharacteristic
567C22×C4C2×C22⋊D4711yescharacteristic
568C22×C4C2×C22⋊D4711yescharacteristic
569C22×C4C2×C22⋊D4711yescharacteristic
570C4⋊C4—44no—
571C4⋊C4—942no—
572C4⋊C4—942no—
573C4⋊C4—942no—
574C4⋊C4—942no—
575C4⋊C4—1884no—
576C22⋊C4—28no—
577C22⋊C4—44no—
578C22⋊C4—44no—
579C22⋊C4—944no—
580C22⋊C4—944no—
581C22⋊C4—944no—
582C22⋊C4—944no—
583C22⋊C4—948no—
584C22⋊C4—1884no—
585C22⋊C4—1884no—
586C42—44no—
587C42—1884no—
588C23—22no—
589C23—22no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—416no—
609C23—948no—
610C23—944no—
611C23—37616no—
612C23—1884no—
613C23—1884no—
614C23—1884no—
615C23—1884no—
616C23—1884no—
617C23—1884no—
618C23—1884no—
619C23—1884no—
620C23C2×(C2×D47)⋊C411yescharacteristic
621C23C2×(C2×D47)⋊C411yescharacteristic
622C23C2×(C2×D47)⋊C411yescharacteristic
623C23C2×(C2×D47)⋊C411yescharacteristic
624C23C22×C4×D4711yescharacteristic
625C23C22×C22⋊D4711yescharacteristic
626C23C22×D18811yescharacteristic
627C23#1309407014yes—
628D4—1884no—
629D4—1884no—
630D4—1888no—
631D4—1888no—
632D4—1888no—
633D4—1888no—
634D4—1884no—
635D4—1884no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—44no—
664C2×C4—44no—
665C2×C4—44no—
666C2×C4—944no—
667C2×C4—948no—
668C2×C4—1884no—
669C2×C4—1884no—
670C2×C4—1884no—
671C2×C4—1884no—
672C2×C4—1884no—
673C2×C4#1309393814yescomplemented
674C2×C4C2×(C2×D47)⋊C411yescharacteristic
675C2×C4C2×(C2×D47)⋊C411yescharacteristic
676C2×C4C2×(C2×D47)⋊C411yescharacteristic
677C2×C4C2×(C2×D47)⋊C411yescharacteristic
678C2×C4C2×(C2×D47)⋊C411yescharacteristic
679C2×C4C2×(C2×D47)⋊C411yescharacteristic
680C2×C4C2×(C2×D47)⋊C411yescharacteristic
681C2×C4C2×(C2×D47)⋊C411yescharacteristic
682C22—28no—
683C22—21no—
684C22—21no—
685C22—21no—
686C22—21no—
687C22—21no—
688C22—21no—
689C22—21no—
690C22—21no—
691C22—21no—
692C22—21no—
693C22—21no—
694C22—21no—
695C22—21no—
696C22—21no—
697C22—21no—
698C22—21no—
699C22—44no—
700C22—44no—
701C22—44no—
702C22—44no—
703C22—44no—
704C22—44no—
705C22—3768no—
706C22—3768no—
707C22—3768no—
708C22—1884no—
709C22—1884no—
710C22—1884no—
711C22C2×#1309393812yes—
712C22#1568909612yes—
713C22C22×(C2×D47)⋊C411yescharacteristic
714C22#1568959712yes—
715C22#1568968712yes—
716C22#1568969212yes—
717C4—21no—
718C4—21no—
719C4—21no—
720C4—21no—
721C4—21no—
722C4—21no—
723C4—84no—
724C4—3764no—
725C4—1884no—
726C4C2×#1309393812yes—
727C4C2×#1309393812yes—
728C2—22no—
729C2—22no—
730C2—22no—
731C2—22no—
732C2—22no—
733C2—41no—
734C2—41no—
735C2—3764no—
736C2#2024596811yescharacteristic
737C2C22×#1309393811yescharacteristic
738C2C2×#1568909611yescharacteristic
subgroupG/H
centerC22C22×(C2×D47)⋊C4
commutatorC23×C47C23×C4
FrattiniC24C23×D47
FittingC47×#2280C2
socleC22×C47C22×C22⋊C4
prime radicalC22×#13093998C2
cosocleC24×C47C24
hypercenter#2280D47
hypocenterC47#21793
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C24×C4 ◁ #2280

Complements

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

NH ≅ G/Ntype
2. #20245771C2semidirect
3. #20244224C2semidirect
4. #20244223C2semidirect
5. #20243302C2semidirect
6. C47×#2280C2semidirect
7. C23×D188C4semidirect
17. C2×#13093998C4semidirect
18. C2×#13093998C4semidirect
22. C22×C4⋊Dic47C4semidirect
23. C22×(C2×D47)⋊C4C4semidirect
24. C2×#13093938C22semidirect
27. #15688983C22semidirect
30. C4×C22⋊Dic47C22semidirect
35. C47×#380C22semidirect
38. C4×C22⋊C4×C47C22semidirect
288. C2×C4×C47#99semidirect
361. #2280D47semidirect
401. #380C2×D47semidirect
407. C4×C22⋊C4C2×D47semidirect
408. C47#21793semidirect
673. C2×C4#13093938semidirect

Maximal subgroups

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

subgroupindex
C22×#130939982
#202457712
#202442242
#202442232
#202433022
C47×#22802
#2179347