Finite Group Databasebeta

← #26221997

Subgroups — #26221997

Order 12032.

1616 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689257C211yesmaximal, characteristic
2C2×#15689233C211yesmaximal, characteristic, complemented
3C2×C4×#10625334C211yesmaximal, characteristic, complemented
4#20246081C211yesmaximal, characteristic, complemented
5#20243736C211yesmaximal, characteristic, complemented
6#20243736C211yesmaximal, characteristic, complemented
7#20243710C211yesmaximal, characteristic, complemented
8#20243649C211yesmaximal, characteristic, complemented
9#20243635C211yesmaximal, characteristic, complemented
10#20243587C211yesmaximal, characteristic, complemented
11#20243319C211yesmaximal, characteristic, complemented
12#20243213C211yesmaximal, characteristic, complemented
13C4×#13093945C211yesmaximal, characteristic, complemented
14#20243154C211yesmaximal, characteristic, complemented
15C2×C47×#518C211yesmaximal, characteristic, complemented
16C22×#10625334C2211yescharacteristic
17C22×#10625334C2211yescharacteristic
18C2×#13093998C2211yescharacteristic
19C2×C4×D188C2211yescharacteristic, complemented
20#15689257C418yescomplemented
21#15689233—24no—
22C4×#10625334—24no—
23C2×#13093957C2211yescharacteristic, complemented
24C2×#13093955C2211yescharacteristic, complemented
25C2×#13093945C2211yescharacteristic
26C2×#13093945C2211yescharacteristic
27C2×#13093945C2211yescharacteristic
28C2×#13093945C2211yescharacteristic
29C2×#13093945C2211yescharacteristic
30C2×#13093945C2211yescharacteristic
31C2×#13093944C2211yescharacteristic, complemented
32C2×#13093944C2211yescharacteristic, complemented
33C2×C22⋊(C47⋊C8)C2211yescharacteristic
34C2×C22⋊(C47⋊C8)C2211yescharacteristic
35C2×#13093935C2211yescharacteristic, complemented
36C2×C4×C47⋊C8C2211yescharacteristic, complemented
37#15689025C2211yescharacteristic, complemented
38#15689023—21no—
39#15689021C2211yescharacteristic, complemented
40#15689013—21no—
41#15688999—21no—
42#15688994—21no—
43#15688983C2211yescharacteristic
44C4×C4⋊Dic47C2211yescharacteristic, complemented
45#15688885C2211yescharacteristic, complemented
46#15688885C2211yescharacteristic, complemented
47#15688885C2211yescharacteristic, complemented
48#15688885C2211yescharacteristic, complemented
49#15688878C2211yescharacteristic, complemented
50#15688878C2211yescharacteristic, complemented
51C23×D4×C47C2211yescharacteristic
52C47×#518—24no—
53C47×#518—24no—
54C2×C4×D4×C47—21no—
55C2×C4×D4×C47—21no—
56C2×C4×D4×C47C2211yescharacteristic
57C2×C4×D4×C47C2211yescharacteristic
58C2×C4×D4×C47C2211yescharacteristic
59C2×C4×D4×C47C2211yescharacteristic
60C2×#117×C47C2211yescharacteristic
61C2×#117×C47C2211yescharacteristic
62C22×C22⋊C4×C47—21no—
63C22×C22⋊C4×C47—21no—
64C22×D188C2311yescharacteristic
65C22×C22⋊D47—21no—
66C22×C4×D47—21no—
67C2×#10625334—22no—
68C2×#10625334—22no—
69C2×#10625334—22no—
70C2×#10625334—22no—
71C2×#10625334C2×C414yescomplemented
72C2×#10625334C2×C414yescomplemented
73C22×C47⋊C8C2311yescharacteristic
74C22×C47⋊C8C2311yescharacteristic
75C22×C47⋊C8C2311yescharacteristic
76C22×C47⋊C8C2311yescharacteristic
77#13093998—22no—
78#13093998C2×C414yescomplemented
79C4×D188—22no—
80C4×D188—22no—
81C2×C4⋊Dic47C2311yescharacteristic
82C2×C4⋊Dic47C2311yescharacteristic
83C2×C4⋊Dic47C2311yescharacteristic
84C2×Dic47⋊C4—21no—
85C2×C22⋊Dic47—21no—
86C2×(C2×D47)⋊C4—21no—
87C2×(C2×D47)⋊C4—21no—
88C2×(C2×D47)⋊C4—21no—
89C2×(C2×D47)⋊C4—21no—
90C2×C4×Dic47—21no—
91#13093957—22no—
92#13093955—22no—
93#13093945—22no—
94#13093945—22no—
95#13093945—22no—
96#13093945—22no—
97#13093945C2×C414yescomplemented
98#13093945C2×C414yescomplemented
99#13093944—22no—
100#13093944—22no—
101C22⋊(C47⋊C8)—22no—
102C22⋊(C47⋊C8)C2×C414yescomplemented
103#13093935—22no—
104C4×C47⋊C8—22no—
105C47⋊#95—21no—
106C47⋊#95—21no—
107C47⋊#95—21no—
108C25×C47—21no—
109C22×D4×C47—22no—
110C22×D4×C47—22no—
111C22×D4×C47—22no—
112C22×D4×C47—22no—
113C22×D4×C47—21no—
114C22×D4×C47—22no—
115C22×D4×C47C2×C414yescomplemented
116C22×D4×C47C2311yescharacteristic
117C22×D4×C47C2311yescharacteristic
118C23×C4×C47—21no—
119C23×C4×C47—21no—
120C23×C4×C47—21no—
121C23×C4×C47—21no—
122C23×C4×C47C2311yescharacteristic
123C4×D4×C47—28no—
124C4×D4×C47—28no—
125C4×D4×C47—22no—
126C4×D4×C47—22no—
127C4×D4×C47—22no—
128C4×D4×C47—22no—
129C4×D4×C47—22no—
130C4×D4×C47—22no—
131C4×D4×C47D414yescomplemented
132C4×D4×C47D414yescomplemented
133#117×C47—22no—
134#117×C47—22no—
135#117×C47—22no—
136#117×C47—22no—
137C2×C4⋊C4×C47D411yescharacteristic
138C2×C4⋊C4×C47D411yescharacteristic
139C2×C4⋊C4×C47C2311yescharacteristic
140C2×C4⋊C4×C47C2311yescharacteristic
141C2×C22⋊C4×C47—28no—
142C2×C22⋊C4×C47—28no—
143C2×C22⋊C4×C47—21no—
144C2×C22⋊C4×C47—21no—
145C2×C22⋊C4×C47—21no—
146C2×C22⋊C4×C47—21no—
147C2×C22⋊C4×C47—21no—
148C2×C22⋊C4×C47D411yescharacteristic
149C2×C22⋊C4×C47D411yescharacteristic
150C2×C42×C47—21no—
151C2×C42×C47C2311yescharacteristic
152C2×C42×C47C2311yescharacteristic
153C24×C47—24no—
154C24×C47—24no—
155C24×C47—21no—
156C24×C47—21no—
157C24×C47—24no—
158C24×C47—81no—
159C24×C47—81no—
160C24×C47—81no—
161C24×C47—81no—
162C24×C47C2×D411yescharacteristic
163C23×D47—21no—
164C2×D4×C47—24no—
165C2×D4×C47—24no—
166C2×D4×C47—28no—
167C2×D4×C47—28no—
168C2×D4×C47—28no—
169C2×D4×C47—28no—
170C2×D4×C47—24no—
171C2×D4×C47—21no—
172C2×D4×C47—21no—
173C2×D4×C47—21no—
174C2×D4×C47—21no—
175C2×D4×C47—21no—
176C2×D4×C47—21no—
177C2×D4×C47C22×C412yes—
178C2×D4×C47C22×C412yes—
179C2×D4×C47C2×D412yes—
180C2×D4×C47C2×D412yes—
181C2×D4×C47#4112yes—
182C2×D4×C47#4112yes—
183C22×C4×C47—21no—
184C22×C4×C47—21no—
185C22×C4×C47—21no—
186C22×C4×C47—21no—
187C22×C4×C47—21no—
188C22×C4×C47—21no—
189C22×C4×C47—24no—
190C22×C4×C47—24no—
191C22×C4×C47—24no—
192C22×C4×C47—24no—
193C22×C4×C47—81no—
194C22×C4×C47—81no—
195C22×C4×C47—81no—
196C22×C4×C47—81no—
197C22×C4×C47—81no—
198C22×C4×C47—81no—
199C22×C4×C47—81no—
200C22×C4×C47—81no—
201C22×C4×C47C22×C412yes—
202C22×C4×C47C2×D411yescharacteristic
203C22×C4×C47C2×D411yescharacteristic
204C22×C4×C47C2×D411yescharacteristic
205C22×C4×C47C2×D411yescharacteristic
206C22×C4×C47C2×D411yescharacteristic
207C22×C4×C47#4112yes—
208C22×C4×C47C2411yescharacteristic
209C2×C22⋊D47—24no—
210C2×C22⋊D47—81no—
211C2×C22⋊D47—81no—
212C22×Dic47—21no—
213C22×Dic47—21no—
214C22×Dic47—21no—
215C2×D188—21no—
216C2×D188—21no—
217C2×D188—21no—
218C2×D188—21no—
219C2×D188—21no—
220C2×D188C22×C412yes—
221C2×C4×D47—42no—
222C2×C4×D47—81no—
223C2×C4×D47—81no—
224C4⋊C4×C47—22no—
225C4⋊C4×C47—22no—
226C4⋊C4×C47—21no—
227C4⋊C4×C47—21no—
228C4⋊C4×C47C2×D412yes—
229C4⋊C4×C47C2×D412yes—
230C22⋊C4×C47—24no—
231C22⋊C4×C47—24no—
232C22⋊C4×C47—24no—
233C22⋊C4×C47—22no—
234C22⋊C4×C47—22no—
235C22⋊C4×C47—24no—
236C22⋊C4×C47—24no—
237C42×C47—24no—
238C42×C47—21no—
239C42×C47—21no—
240C42×C47C2×D412yes—
241C42×C47C2×D412yes—
242C22⋊Dic47—81no—
243#10625334—28no—
244#10625334—28no—
245(C2×D47)⋊C4—24no—
246(C2×D47)⋊C4—42no—
247(C2×D47)⋊C4—81no—
248(C2×D47)⋊C4—81no—
249C4⋊Dic47—21no—
250C4⋊Dic47—21no—
251C4⋊Dic47—21no—
252C4⋊Dic47—21no—
253C4⋊Dic47—21no—
254C4⋊Dic47C22×C412yes—
255Dic47⋊C4—81no—
256C4×Dic47—81no—
257C2×C47⋊C8—21no—
258C2×C47⋊C8—21no—
259C2×C47⋊C8—21no—
260C2×C47⋊C8—21no—
261C2×C47⋊C8—21no—
262C2×C47⋊C8—21no—
263C2×C47⋊C8—21no—
264C2×C47⋊C8—21no—
265C2×C47⋊C8—21no—
266C2×C47⋊C8—21no—
267C2×C47⋊C8C22×C412yes—
268C2×C47⋊C8C22×C412yes—
269C23×C47—216no—
270C23×C47—22no—
271C23×C47—22no—
272C23×C47—21no—
273C23×C47—22no—
274C23×C47—22no—
275C23×C47—21no—
276C23×C47—22no—
277C23×C47—22no—
278C23×C47—21no—
279C23×C47—21no—
280C23×C47—21no—
281C23×C47—21no—
282C23×C47—41no—
283C23×C47—41no—
284C23×C47—41no—
285C23×C47—41no—
286C23×C47—41no—
287C23×C47—41no—
288C23×C47—41no—
289C23×C47—41no—
290C23×C47—84no—
291C23×C47—84no—
292C23×C47—84no—
293C23×C47—84no—
294C23×C47—84no—
295C23×C47—84no—
296C23×C47C4×D412yes—
297C23×C47C22×D411yescharacteristic
298C22×D47—22no—
299C22×D47—41no—
300C22×D47—41no—
301C22×D47—41no—
302C22×D47—41no—
303C22×D47—41no—
304C22×D47—41no—
305D4×C47—216no—
306D4×C47—22no—
307D4×C47—22no—
308D4×C47—22no—
309D4×C47—22no—
310D4×C47—22no—
311D4×C47—22no—
312D4×C47C4×D414yes—
313D4×C47C4×D414yes—
314C2×C4×C47—21no—
315C2×C4×C47—21no—
316C2×C4×C47—21no—
317C2×C4×C47—21no—
318C2×C4×C47—21no—
319C2×C4×C47—21no—
320C2×C4×C47—22no—
321C2×C4×C47—22no—
322C2×C4×C47—22no—
323C2×C4×C47—22no—
324C2×C4×C47—21no—
325C2×C4×C47—21no—
326C2×C4×C47—22no—
327C2×C4×C47—22no—
328C2×C4×C47—21no—
329C2×C4×C47—21no—
330C2×C4×C47—21no—
331C2×C4×C47—21no—
332C2×C4×C47—41no—
333C2×C4×C47—41no—
334C2×C4×C47—41no—
335C2×C4×C47—41no—
336C2×C4×C47—84no—
337C2×C4×C47—84no—
338C2×C4×C47—84no—
339C2×C4×C47—84no—
340C2×C4×C47C4×D412yes—
341C2×C4×C47#12012yes—
342C2×C4×C47#12012yes—
343C2×C4×C47C23×C411yescharacteristic
344C2×C4×C47C22×D411yescharacteristic
345C2×C4×C47C22×D411yescharacteristic
346C2×C4×C47C2×#4111yescharacteristic
347C2×C4×C47C2×#4111yescharacteristic
348C2×C4×C47C2×#4111yescharacteristic
349C22⋊D47—84no—
350C2×Dic47—22no—
351C2×Dic47—41no—
352C2×Dic47—41no—
353C2×Dic47—41no—
354C2×Dic47—41no—
355C2×Dic47—41no—
356C2×Dic47—41no—
357C2×Dic47—41no—
358C2×Dic47—41no—
359D188—22no—
360D188—22no—
361D188—41no—
362D188—41no—
363C4×D47—84no—
364C47⋊C8—22no—
365C47⋊C8—22no—
366C47⋊C8—41no—
367C47⋊C8—41no—
368#21458—471nomaximal, Sylow
369C22×C47—22no—
370C22×C47—22no—
371C22×C47—22no—
372C22×C47—24no—
373C22×C47—24no—
374C22×C47—41no—
375C22×C47—42no—
376C22×C47—42no—
377C22×C47—41no—
378C22×C47—42no—
379C22×C47—42no—
380C22×C47—42no—
381C22×C47—42no—
382C22×C47—42no—
383C22×C47—42no—
384C22×C47—42no—
385C22×C47—42no—
386C22×C47—41no—
387C22×C47—42no—
388C22×C47—42no—
389C22×C47—41no—
390C22×C47—816no—
391C22×C47C2×C4×D411yescharacteristic
392C22×C47C2×#12011yescharacteristic
393C22×C47#52511yescharacteristic
394C22×C47#57611yescharacteristic
395C22×C47#57611yescharacteristic
396C22×C47#57611yescharacteristic
397C22×C47#57711yescharacteristic
398C2×D47—42no—
399C2×D47—42no—
400C2×D47—42no—
401C2×D47—81no—
402C2×D47—81no—
403C2×D47—81no—
404C2×D47—81no—
405C4×C47—22no—
406C4×C47—22no—
407C4×C47—22no—
408C4×C47—41no—
409C4×C47—42no—
410C4×C47—41no—
411C4×C47—42no—
412C4×C47C2×C4×D411yescharacteristic
413C4×C47C2×C4×D411yescharacteristic
414C4×C47#52511yescharacteristic
415C4×C47#52511yescharacteristic
416Dic47—42no—
417Dic47—81no—
418Dic47—81no—
419C2×#518D4711yescharacteristic, complemented
420C2×#447—471no—
421C2×#442—471no—
422C2×C4×D8—471no—
423#2324—471no—
424#1879—471no—
425#1879—471no—
426#1875—471no—
427#1864—471no—
428#1862—471no—
429#1854—471no—
430#1786—471no—
431#1762—471no—
432C4×#102—471no—
433#1750—471no—
434C2×C47—42no—
435C2×C47—44no—
436C2×C47—44no—
437C2×C47C4×#12011yescharacteristic
438C2×C47#294611yescharacteristic
439C2×C47#294811yescharacteristic
440C2×C47#300811yescharacteristic
441C2×C47#301211yescharacteristic
442C2×C47#311811yescharacteristic
443C2×C47#312211yescharacteristic
444D47—82no—
445C23×D4C2×D4711yescharacteristic
446C22×D8—471no—
447C22×D8—471no—
448C2×#121—471no—
449#518—24no—
450#518—24no—
451C2×C4×D4—21no—
452C2×C4×D4—21no—
453C2×C4×D4—471no—
454C2×C4×D4C2×D4711yescharacteristic
455C2×C4×D4C2×D4711yescharacteristic
456C2×C4×D4C2×D4711yescharacteristic
457C2×C4×D4C2×D4711yescharacteristic
458C2×#117C2×D4711yescharacteristic
459C2×#117C2×D4711yescharacteristic
460C22×C22⋊C4—21no—
461C22×C22⋊C4—21no—
462#447—478no—
463#442—944no—
464C4×D8—944no—
465C2×#107—471no—
466C2×#106—471no—
467C2×#102—471no—
468C2×#102—471no—
469C2×#102—471no—
470C2×#102—471no—
471C2×#102—471no—
472C2×#102—471no—
473C2×#102—471no—
474C2×#102—471no—
475C2×C22⋊C8—471no—
476C2×C22⋊C8—471no—
477C2×#97—471no—
478C2×C4×C8—471no—
479#390—471no—
480#390—941no—
481#389—471no—
482#388—941no—
483#386—941no—
484#385—941no—
485#380—471no—
486C4×C4⋊C4—471no—
487#340—471no—
488#340—471no—
489#340—471no—
490#340—471no—
491#336—471no—
492#336—471no—
493C47#2145811yescharacteristic, complemented, Sylow
494C25—21no—
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—22no—
498C22×D4—22no—
499C22×D4—22no—
500C22×D4—21no—
501C22×D4—471no—
502C22×D4—941no—
503C22×D4C4×D4714yescomplemented
504C22×D4C22×D4711yescharacteristic
505C22×D4C22×D4711yescharacteristic
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—941no—
511C23×C4C22×D4711yescharacteristic
512C2×D8—474no—
513C2×D8—474no—
514C2×D8—942no—
515C2×D8—942no—
516C2×D8—942no—
517C2×D8—942no—
518C22×C8—471no—
519C22×C8—471no—
520C22×C8—471no—
521C22×C8—471no—
522#121—474no—
523#121—942no—
524C4×D4—28no—
525C4×D4—28no—
526C4×D4—22no—
527C4×D4—22no—
528C4×D4—22no—
529C4×D4—22no—
530C4×D4—22no—
531C4×D4—22no—
532C4×D4—942no—
533C4×D4—942no—
534C4×D4C22⋊D4714yescomplemented
535C4×D4C22⋊D4714yescomplemented
536#117—22no—
537#117—22no—
538#117—22no—
539#117—22no—
540C2×C4⋊C4—471no—
541C2×C4⋊C4—471no—
542C2×C4⋊C4—471no—
543C2×C4⋊C4—941no—
544C2×C4⋊C4C22⋊D4711yescharacteristic
545C2×C4⋊C4C22⋊D4711yescharacteristic
546C2×C4⋊C4C22×D4711yescharacteristic
547C2×C4⋊C4C22×D4711yescharacteristic
548C2×C22⋊C4—28no—
549C2×C22⋊C4—28no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—941no—
556C2×C22⋊C4—941no—
557C2×C22⋊C4—941no—
558C2×C22⋊C4—941no—
559C2×C22⋊C4—941no—
560C2×C22⋊C4C22⋊D4711yescharacteristic
561C2×C22⋊C4C22⋊D4711yescharacteristic
562C2×C42—21no—
563C2×C42—941no—
564C2×C42C22×D4711yescharacteristic
565C2×C42C22×D4711yescharacteristic
566#107—942no—
567#106—942no—
568#102—474no—
569#102—474no—
570#102—942no—
571#102—942no—
572#102—942no—
573#102—942no—
574#102—942no—
575#102—942no—
576C22⋊C8—474no—
577C22⋊C8—942no—
578#97—942no—
579C4×C8—942no—
580#95—941no—
581#95—941no—
582#95—941no—
583C24—24no—
584C24—24no—
585C24—21no—
586C24—21no—
587C24—24no—
588C24—81no—
589C24—81no—
590C24—81no—
591C24—81no—
592C24—941no—
593C24C2×C22⋊D4711yescharacteristic
594C2×D4—24no—
595C2×D4—24no—
596C2×D4—28no—
597C2×D4—28no—
598C2×D4—28no—
599C2×D4—28no—
600C2×D4—24no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—472no—
608C2×D4—944no—
609C2×D4—941no—
610C2×D4—941no—
611C2×D4—941no—
612C2×D4—941no—
613C2×D4—941no—
614C2×D4—3761no—
615C2×D4—3761no—
616C2×D4C2×C4×D4712yes—
617C2×D4C2×C4×D4712yes—
618C2×D4#1062535012yes—
619C2×D4#1062535012yes—
620C2×D4C2×C22⋊D4712yes—
621C2×D4C2×C22⋊D4712yes—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—24no—
629C22×C4—24no—
630C22×C4—24no—
631C22×C4—24no—
632C22×C4—81no—
633C22×C4—81no—
634C22×C4—81no—
635C22×C4—81no—
636C22×C4—81no—
637C22×C4—81no—
638C22×C4—81no—
639C22×C4—81no—
640C22×C4—941no—
641C22×C4—941no—
642C22×C4—941no—
643C22×C4—3761no—
644C22×C4—3761no—
645C22×C4—1882no—
646C22×C4C2×C4×D4712yes—
647C22×C4#1062535012yes—
648C22×C4C2×C22⋊D4711yescharacteristic
649C22×C4C2×C22⋊D4711yescharacteristic
650C22×C4C2×C22⋊D4711yescharacteristic
651C22×C4C2×C22⋊D4711yescharacteristic
652C22×C4C2×C22⋊D4711yescharacteristic
653C22×C4C23×D4711yescharacteristic
654D8—948no—
655D8—948no—
656C2×C8—472no—
657C2×C8—472no—
658C2×C8—941no—
659C2×C8—941no—
660C2×C8—941no—
661C2×C8—941no—
662C2×C8—941no—
663C2×C8—941no—
664C2×C8—941no—
665C2×C8—941no—
666C2×C8—941no—
667C2×C8—941no—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—472no—
673C4⋊C4—941no—
674C4⋊C4—941no—
675C4⋊C4—941no—
676C4⋊C4—941no—
677C4⋊C4—941no—
678C4⋊C4—3761no—
679C4⋊C4C2×C22⋊D4712yes—
680C4⋊C4C2×C22⋊D4712yes—
681C22⋊C4—24no—
682C22⋊C4—24no—
683C22⋊C4—24no—
684C22⋊C4—22no—
685C22⋊C4—22no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—944no—
689C22⋊C4—3761no—
690C22⋊C4—3761no—
691C22⋊C4—3761no—
692C22⋊C4—1882no—
693C42—24no—
694C42—21no—
695C42—21no—
696C42—3761no—
697C42C2×C22⋊D4712yes—
698C42C2×C22⋊D4712yes—
699C23—216no—
700C23—22no—
701C23—22no—
702C23—21no—
703C23—22no—
704C23—22no—
705C23—21no—
706C23—22no—
707C23—22no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—84no—
721C23—84no—
722C23—84no—
723C23—84no—
724C23—84no—
725C23—84no—
726C23—942no—
727C23—1881no—
728C23—1881no—
729C23—1881no—
730C23—1881no—
731C23—1881no—
732C23—1881no—
733C23C4×C22⋊D4712yes—
734C23C22×C22⋊D4711yescharacteristic
735D4—216no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—22no—
742D4—942no—
743D4—942no—
744D4—3764no—
745D4—1881no—
746D4—1881no—
747D4C4×C22⋊D4714yes—
748D4C4×C22⋊D4714yes—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—84no—
772C2×C4—84no—
773C2×C4—84no—
774C2×C4—84no—
775C2×C4—942no—
776C2×C4—3764no—
777C2×C4—1881no—
778C2×C4—1881no—
779C2×C4—1881no—
780C2×C4—1881no—
781C2×C4—1881no—
782C2×C4—1881no—
783C2×C4—1881no—
784C2×C4—1881no—
785C2×C4C4×C22⋊D4712yes—
786C2×C4#1309399312yes—
787C2×C4#1309399312yes—
788C2×C4C22×C4×D4711yescharacteristic
789C2×C4C22×C22⋊D4711yescharacteristic
790C2×C4C22×C22⋊D4711yescharacteristic
791C2×C4C2×#1062535011yescharacteristic
792C2×C4C2×#1062535011yescharacteristic
793C2×C4C2×#1062535011yescharacteristic
794C8—942no—
795C8—942no—
796C8—1881no—
797C8—1881no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—24no—
802C22—24no—
803C22—42no—
804C22—42no—
805C22—41no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—41no—
811C22—42no—
812C22—42no—
813C22—41no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—41no—
819C22—816no—
820C22—3761no—
821C22—3761no—
822C22—3761no—
823C22—3761no—
824C22—1882no—
825C22—1882no—
826C22—1882no—
827C22C2×C4×C22⋊D4711yescharacteristic
828C22C2×#1309399311yescharacteristic
829C22#1568963411yescharacteristic
830C22#1568992611yescharacteristic
831C22#1568992611yescharacteristic
832C22#1568992611yescharacteristic
833C22#1568993411yescharacteristic
834C4—22no—
835C4—22no—
836C4—22no—
837C4—41no—
838C4—42no—
839C4—41no—
840C4—42no—
841C4—3761no—
842C4—3761no—
843C4—1882no—
844C4C2×C4×C22⋊D4711yescharacteristic
845C4C2×C4×C22⋊D4711yescharacteristic
846C4#1568963411yescharacteristic
847C4#1568963411yescharacteristic
848C2—42no—
849C2—44no—
850C2—44no—
851C2—3762no—
852C2C4×#1309399311yescharacteristic
853C2#2025222011yescharacteristic
854C2#2025223811yescharacteristic
855C2#2025265611yescharacteristic
856C2#2025269211yescharacteristic
857C2#2025357211yescharacteristic
858C2#2025363111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#518C2
socleC23×C47C22×D4
prime radicalC2×#15689257C2
cosocleC22×C4×C47C24
hypercenterC2×#518D47
hypocenterC47#21458
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#518

Complements

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

NH ≅ G/Ntype
2. C2×#15689233C2semidirect
3. C2×C4×#10625334C2semidirect
4. #20246081C2semidirect
5. #20243736C2semidirect
6. #20243736C2semidirect
7. #20243710C2semidirect
8. #20243649C2semidirect
9. #20243635C2semidirect
10. #20243587C2semidirect
11. #20243319C2semidirect
12. #20243213C2semidirect
13. C4×#13093945C2semidirect
14. #20243154C2semidirect
15. C2×C47×#518C2semidirect
19. C2×C4×D188C22semidirect
20. #15689257C4semidirect
23. C2×#13093957C22semidirect
24. C2×#13093955C22semidirect
31. C2×#13093944C22semidirect
32. C2×#13093944C22semidirect
35. C2×#13093935C22semidirect
36. C2×C4×C47⋊C8C22semidirect
37. #15689025C22semidirect
39. #15689021C22semidirect
44. C4×C4⋊Dic47C22semidirect
45. #15688885C22semidirect
46. #15688885C22semidirect
47. #15688885C22semidirect
48. #15688885C22semidirect
49. #15688878C22semidirect
50. #15688878C22semidirect
71. C2×#10625334C2×C4semidirect
72. C2×#10625334C2×C4semidirect
78. #13093998C2×C4semidirect
97. #13093945C2×C4semidirect
98. #13093945C2×C4semidirect
102. C22⋊(C47⋊C8)C2×C4semidirect
115. C22×D4×C47C2×C4semidirect
131. C4×D4×C47D4semidirect
132. C4×D4×C47D4semidirect
419. C2×#518D47semidirect
493. C47#21458semidirect
503. C22×D4C4×D47semidirect
534. C4×D4C22⋊D47semidirect
535. C4×D4C22⋊D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156892572
C2×#156892332
C2×C4×#106253342
#202460812
#202437362
#202437102
#202436492
#202436352
#202435872
#202433192
#202432132
C4×#130939452
#202431542
C2×C47×#5182
#2145847