Finite Group Databasebeta

← #26232773

Subgroups — #26232773

Order 12032.

1148 conjugacy classes of subgroups.

The subgroup lattice has 1048 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20256946C211yesmaximal, characteristic
2D4×#10625329C211yesmaximal, characteristic, complemented
3#20244369C211yesmaximal, characteristic, complemented
4#20244331C211yesmaximal, characteristic, complemented
5#20243836C211yesmaximal, characteristic, complemented
6#20243831C211yesmaximal, characteristic, complemented
7#20243688C211yesmaximal, characteristic, complemented
8#20243688C211yesmaximal, characteristic, complemented
9#20243488C211yesmaximal, characteristic, complemented
10#20243488C211yesmaximal, characteristic, complemented
11#20243409C211yesmaximal, characteristic, complemented
12#20243199C211yesmaximal, characteristic, complemented
13#20243098C211yesmaximal, characteristic, complemented
14C2×#15688883C211yesmaximal, characteristic, complemented
15C47×#2290C211yesmaximal, characteristic, complemented
16C22×#10625329C2211yescharacteristic
17C22×#10625329C2211yescharacteristic
18#15689843C411yescharacteristic, complemented
19#15689838C411yescharacteristic, complemented
20#15689830C411yescharacteristic, complemented
21#15689819C411yescharacteristic, complemented
22#15689819C411yescharacteristic, complemented
23#15689813C411yescharacteristic, complemented
24#15689813C411yescharacteristic, complemented
25#15689808—21no—
26#15689799—21no—
27#15689799—21no—
28#15689777C411yescharacteristic, complemented
29#15689767—21no—
30#15689680C2211yescharacteristic
31#15689655—21no—
32#15689653—21no—
33#15689653—21no—
34#15689634C2211yescharacteristic
35#15689634C2211yescharacteristic
36C4×#10625350C2211yescharacteristic
37C4×#10625352—21no—
38C2×#13093983C2211yescharacteristic
39C2×#13093983C2211yescharacteristic
40#15689201—21no—
41#15689195—21no—
42#15689195—21no—
43D4×C47⋊C8—21no—
44#15689147C2211yescharacteristic
45C2×#13093952C2211yescharacteristic
46C2×#13093952C2211yescharacteristic
47C2×#13093952C2211yescharacteristic
48C2×#13093952C2211yescharacteristic
49#15689087C2211yescharacteristic
50#15689087C2211yescharacteristic
51C4×#10625329C2211yescharacteristic
52#15688883C2211yescharacteristic
53#15688883C2211yescharacteristic
54#15688883C2211yescharacteristic
55#15688883C2211yescharacteristic
56#15688883C2211yescharacteristic
57#15688883C2211yescharacteristic
58#15688883C2211yescharacteristic
59#15688883C2211yescharacteristic
60#15688883C2211yescharacteristic
61#15688883C2211yescharacteristic
62#15688883C2211yescharacteristic
63#15688883C2211yescharacteristic
64C2×C4×D4×C47C2211yescharacteristic
65C2×#117×C47C2211yescharacteristic
66C22×C42×C47C2211yescharacteristic
67C47×#388—21no—
68C47×#387—21no—
69C47×#386—21no—
70C47×#385—21no—
71C4×C4⋊C4×C47C2211yescharacteristic
72C4×C22⋊C4×C47C2211yescharacteristic
73C4×C22⋊C4×C47C2211yescharacteristic
74C47×#376C2211yescharacteristic
75C2×#10625350C2311yescharacteristic
76C2×#10625352—21no—
77C2×#10625329—21no—
78C2×#10625329—21no—
79C2×#10625329—22no—
80C2×#10625329—22no—
81C2×#10625329—41no—
82C2×#10625329—41no—
83C2×#10625329C2311yescharacteristic
84C2×#10625329C2311yescharacteristic
85C2×#10625329C2311yescharacteristic
86C2×#10625329C2311yescharacteristic
87C22×C47⋊C8—21no—
88C22×C47⋊C8—21no—
89#13094024C2×C411yescharacteristic, complemented
90#13094024C2×C411yescharacteristic, complemented
91#13094019—21no—
92#13094019—21no—
93#13094017—21no—
94#13094017—21no—
95#13094017—21no—
96#13094017—21no—
97#13094016C2×C411yescharacteristic, complemented
98#13094016C2×C411yescharacteristic, complemented
99#13094015—21no—
100#13094014—21no—
101#13094014—21no—
102#13094011—21no—
103#13094010—21no—
104#13094010—21no—
105#13094008—21no—
106#13094008—21no—
107#13094007—21no—
108#13094007—21no—
109#13094006—21no—
110#13094006—21no—
111#13094005—21no—
112#13094005—21no—
113#13094004—21no—
114#13094003—21no—
115#13094003—21no—
116#13094003C2×C411yescharacteristic
117#13094003C2×C411yescharacteristic
118#13094003C2×C411yescharacteristic, complemented
119#13094003C2×C411yescharacteristic, complemented
120#13094001—21no—
121#13094001—21no—
122#13093998C2×C411yescharacteristic
123#13093998C2×C411yescharacteristic
124#13093998C2×C411yescharacteristic, complemented
125#13093998C2×C411yescharacteristic, complemented
126#13093996—21no—
127#13093996—21no—
128#13093995—21no—
129#13093993—21no—
130#13093993—21no—
131C4×Dic94—21no—
132C4×Dic94—21no—
133C4×Dic94C2×C411yescharacteristic, complemented
134C4×Dic94C2×C411yescharacteristic, complemented
135#13093989—21no—
136C4×D188C2×C411yescharacteristic, complemented
137C4×D188C2×C411yescharacteristic, complemented
138D4×Dic47—21no—
139C4×C22⋊D47—21no—
140C4×C22⋊D47—21no—
141C4×C22⋊D47—21no—
142C4×C22⋊D47—21no—
143C4×C22⋊D47—21no—
144C4×C22⋊D47—21no—
145(C22⋊D47)⋊C4—21no—
146(C22⋊D47)⋊C4—21no—
147#13093983—21no—
148#13093983—21no—
149#13093983—21no—
150#13093983—21no—
151#13093983C2×C411yescharacteristic
152#13093983C2×C411yescharacteristic
153#13093983C2×C411yescharacteristic, complemented
154#13093983C2×C411yescharacteristic, complemented
155#13093983C2311yescharacteristic
156#13093983C2311yescharacteristic
157#13093983C2311yescharacteristic
158#13093982—21no—
159#13093981—21no—
160#13093980—21no—
161#13093980—21no—
162C2×C4⋊Dic47C2×C411yescharacteristic
163C2×C4⋊Dic47C2×C411yescharacteristic
164C2×C4⋊Dic47C2×C411yescharacteristic, complemented
165C2×C4⋊Dic47C2×C411yescharacteristic, complemented
166C2×C22⋊Dic47—21no—
167C2×C22⋊Dic47—21no—
168C2×C4×Dic47—21no—
169C2×C4×Dic47—21no—
170C42×D47—21no—
171C4⋊(C47⋊C8)—21no—
172C4⋊(C47⋊C8)—21no—
173#13093952—22no—
174#13093952—22no—
175#13093952—41no—
176#13093952—41no—
177C22⋊(C47⋊C8)—21no—
178C22⋊(C47⋊C8)—21no—
179C22⋊(C47⋊C8)—21no—
180C22⋊(C47⋊C8)—21no—
181#13093935—21no—
182C4×C47⋊C8—21no—
183C22×D4×C47D411yescharacteristic
184C23×C4×C47—21no—
185C23×C4×C47C2311yescharacteristic
186C23×C4×C47C2311yescharacteristic
187C4×D4×C47C2×C411yescharacteristic
188C4×D4×C47C2×C411yescharacteristic
189C4×D4×C47C2×C411yescharacteristic
190C4×D4×C47C2×C411yescharacteristic
191C4×D4×C47D411yescharacteristic
192C4×D4×C47D411yescharacteristic
193C4×D4×C47D411yescharacteristic
194C4×D4×C47D411yescharacteristic
195#117×C47—22no—
196#117×C47—41no—
197C2×C4⋊C4×C47—21no—
198C2×C4⋊C4×C47—21no—
199C2×C4⋊C4×C47D411yescharacteristic
200C2×C22⋊C4×C47—21no—
201C2×C22⋊C4×C47—21no—
202C2×C22⋊C4×C47—21no—
203C2×C22⋊C4×C47D411yescharacteristic
204C2×C22⋊C4×C47D411yescharacteristic
205C2×C42×C47—22no—
206C2×C42×C47—21no—
207C2×C42×C47—41no—
208C2×C42×C47C2311yescharacteristic
209C2×C42×C47C2311yescharacteristic
210C2×C42×C47C2311yescharacteristic
211C2×C42×C47C2311yescharacteristic
212C2×C42×C47C2311yescharacteristic
213#95×C47—21no—
214#95×C47—21no—
215#95×C47—21no—
216#95×C47—21no—
217#95×C47—21no—
218C24×C47C2×D411yescharacteristic
219C24×C47C2×D411yescharacteristic
220C2×D4×C47—42no—
221C2×D4×C47C22⋊C411yescharacteristic
222C2×D4×C47C22⋊C411yescharacteristic
223C2×D4×C47C22⋊C411yescharacteristic
224C2×D4×C47C22⋊C411yescharacteristic
225C22×C4×C47—21no—
226C22×C4×C47—21no—
227C22×C4×C47—21no—
228C22×C4×C47—21no—
229C22×C4×C47—21no—
230C22×C4×C47—21no—
231C22×C4×C47—21no—
232C22×C4×C47—21no—
233C22×C4×C47—21no—
234C22×C4×C47—21no—
235C22×C4×C47—21no—
236C22×C4×C47—21no—
237C22×C4×C47—42no—
238C22×C4×C47—42no—
239C22×C4×C47—42no—
240C22×C4×C47C22×C411yescharacteristic
241C22×C4×C47C22×C411yescharacteristic
242C22×C4×C47C22×C411yescharacteristic
243C22×C4×C47C22×C411yescharacteristic
244C22×C4×C47C2×D411yescharacteristic
245C22×C4×C47C2×D411yescharacteristic
246C22×C4×C47C2×D411yescharacteristic
247C22×C4×C47C2×D411yescharacteristic
248C22×C4×C47C2×D411yescharacteristic
249C22×C4×C47C2×D411yescharacteristic
250C22×C4×C47C2×D411yescharacteristic
251C22×C4×C47C2×D411yescharacteristic
252C22×C4×C47C2411yescharacteristic
253C2×C22⋊D47—21no—
254C2×C22⋊D47—21no—
255C2×C22⋊D47—21no—
256C2×C22⋊D47—21no—
257C2×C22⋊D47—21no—
258C22×Dic47—21no—
259C22×Dic47—21no—
260C22×Dic47—21no—
261C22×Dic47—21no—
262#10625352—44no—
263#10625350—21no—
264#10625350—21no—
265#10625350—21no—
266#10625350—21no—
267C2×D188C22×C411yescharacteristic
268C2×C4×D47—21no—
269C2×C4×D47—21no—
270C2×C4×D47—21no—
271C2×Dic94—21no—
272C2×Dic94—21no—
273C2×Dic94C22×C411yescharacteristic
274C4⋊C4×C47—42no—
275C4⋊C4×C47—42no—
276C4⋊C4×C47C22⋊C411yescharacteristic
277C4⋊C4×C47C22⋊C411yescharacteristic
278C4⋊C4×C47C22⋊C411yescharacteristic
279C4⋊C4×C47C22⋊C411yescharacteristic
280C22⋊C4×C47—42no—
281C22⋊C4×C47—42no—
282C22⋊C4×C47—42no—
283C22⋊C4×C47C22⋊C411yescharacteristic
284C22⋊C4×C47C22⋊C411yescharacteristic
285C22⋊C4×C47C22⋊C411yescharacteristic
286C22⋊C4×C47C22⋊C411yescharacteristic
287C22⋊C4×C47C22⋊C411yescharacteristic
288C22⋊C4×C47C22⋊C411yescharacteristic
289C22⋊C4×C47C22⋊C411yescharacteristic
290C22⋊C4×C47C22⋊C411yescharacteristic
291C42×C47—21no—
292C42×C47—21no—
293C42×C47—21no—
294C42×C47—21no—
295C42×C47—21no—
296C42×C47—21no—
297C42×C47—21no—
298C42×C47—42no—
299C42×C47C22×C411yescharacteristic
300C42×C47C22×C411yescharacteristic
301C42×C47C2×D411yescharacteristic
302C42×C47C2×D411yescharacteristic
303C42×C47#4112yescomplemented
304C22⋊Dic47—21no—
305C22⋊Dic47—21no—
306C22⋊Dic47—21no—
307C22⋊Dic47—21no—
308C22⋊Dic47—21no—
309C22⋊Dic47—21no—
310C22⋊Dic47—21no—
311C22⋊Dic47—21no—
312C22⋊Dic47—21no—
313C22⋊Dic47—21no—
314C22⋊Dic47—21no—
315(C2×D47)⋊C4—21no—
316(C2×D47)⋊C4—21no—
317(C2×D47)⋊C4—21no—
318(C2×D47)⋊C4—21no—
319(C2×D47)⋊C4—21no—
320(C2×D47)⋊C4—21no—
321C4⋊Dic47—21no—
322C4⋊Dic47—21no—
323C4⋊Dic47—21no—
324C4⋊Dic47—21no—
325C4⋊Dic47—21no—
326C4⋊Dic47—21no—
327C4⋊Dic47C22×C411yescharacteristic
328C4⋊Dic47C22×C411yescharacteristic
329C4⋊Dic47C22×C411yescharacteristic
330C4⋊Dic47C22×C411yescharacteristic
331C4⋊Dic47C22×C411yescharacteristic
332C4⋊Dic47C22×C411yescharacteristic
333Dic47⋊C4—21no—
334Dic47⋊C4—21no—
335Dic47⋊C4—21no—
336Dic47⋊C4—21no—
337Dic47⋊C4—21no—
338Dic47⋊C4—21no—
339Dic47⋊C4—21no—
340Dic47⋊C4—21no—
341Dic47⋊C4—21no—
342Dic47⋊C4—21no—
343C4×Dic47—21no—
344C4×Dic47—21no—
345C4×Dic47—21no—
346C4×Dic47—21no—
347C4×Dic47—21no—
348C4×Dic47—21no—
349C4×Dic47—21no—
350C4×Dic47—21no—
351C4×Dic47—21no—
352#10625329—21no—
353#10625329—21no—
354#10625329—21no—
355#10625329—21no—
356#10625329—21no—
357#10625329—21no—
358#10625329—21no—
359#10625329—42no—
360#10625329—42no—
361#10625329#4112yescomplemented
362C2×C47⋊C8—21no—
363C2×C47⋊C8—21no—
364C2×C47⋊C8—21no—
365C2×C47⋊C8—21no—
366C2×C47⋊C8—42no—
367C2×C47⋊C8—42no—
368C23×C47—21no—
369C23×C47—21no—
370C23×C47—22no—
371C23×C47—21no—
372C23×C47—21no—
373C23×C47—41no—
374C23×C47—41no—
375C23×C47—41no—
376C23×C47C2×C22⋊C411yescharacteristic
377C23×C47C2×C22⋊C411yescharacteristic
378C23×C47C2×C22⋊C411yescharacteristic
379C23×C47C2×C22⋊C411yescharacteristic
380C23×C47C22×D411yescharacteristic
381C22×D47—21no—
382D4×C47—22no—
383D4×C47—22no—
384D4×C47—41no—
385D4×C47—41no—
386C2×C4×C47—21no—
387C2×C4×C47—21no—
388C2×C4×C47—21no—
389C2×C4×C47—21no—
390C2×C4×C47—21no—
391C2×C4×C47—21no—
392C2×C4×C47—21no—
393C2×C4×C47—21no—
394C2×C4×C47—21no—
395C2×C4×C47—21no—
396C2×C4×C47—21no—
397C2×C4×C47—21no—
398C2×C4×C47—21no—
399C2×C4×C47—21no—
400C2×C4×C47—21no—
401C2×C4×C47—21no—
402C2×C4×C47—21no—
403C2×C4×C47—21no—
404C2×C4×C47—21no—
405C2×C4×C47—21no—
406C2×C4×C47—22no—
407C2×C4×C47—22no—
408C2×C4×C47—41no—
409C2×C4×C47—41no—
410C2×C4×C47—41no—
411C2×C4×C47—41no—
412C2×C4×C47—41no—
413C2×C4×C47—48no—
414C2×C4×C47—41no—
415C2×C4×C47—41no—
416C2×C4×C47—41no—
417C2×C4×C47—41no—
418C2×C4×C47—41no—
419C2×C4×C47—41no—
420C2×C4×C47—41no—
421C2×C4×C47C2×C22⋊C411yescharacteristic
422C2×C4×C47C2×C22⋊C411yescharacteristic
423C2×C4×C47C2×C22⋊C411yescharacteristic
424C2×C4×C47C2×C22⋊C411yescharacteristic
425C2×C4×C47C2×C22⋊C411yescharacteristic
426C2×C4×C47C2×C22⋊C411yescharacteristic
427C2×C4×C47C2×C22⋊C411yescharacteristic
428C2×C4×C47C2×C22⋊C411yescharacteristic
429C2×C4×C47C23×C411yescharacteristic
430C2×C4×C47C22×D411yescharacteristic
431C2×C4×C47C2×#4111yescharacteristic
432C2×C4×C47C2×#4111yescharacteristic
433C2×C4×C47H(5,𝔽2)11yescharacteristic
434C2×C4×C472−1+411yescharacteristic
435C22⋊D47—42no—
436C22⋊D47—41no—
437C22⋊D47—41no—
438C22⋊D47—42no—
439C22⋊D47—81no—
440C22⋊D47—81no—
441C2×Dic47—21no—
442C2×Dic47—21no—
443C2×Dic47—21no—
444C2×Dic47—21no—
445C2×Dic47—21no—
446C2×Dic47—21no—
447C2×Dic47—21no—
448C2×Dic47—42no—
449C2×Dic47—42no—
450C2×Dic47—81no—
451C2×Dic47—81no—
452D188—21no—
453D188—21no—
454C4×D47—42no—
455C4×D47—41no—
456C4×D47—41no—
457C4×D47—81no—
458Dic94—21no—
459Dic94—21no—
460Dic94—42no—
461Dic94—81no—
462C47⋊C8—22no—
463C47⋊C8—41no—
464C47⋊C8—41no—
465C47⋊C8—41no—
466#22506—471nomaximal, Sylow
467C22×C47—21no—
468C22×C47—21no—
469C22×C47—21no—
470C22×C47—21no—
471C22×C47—21no—
472C22×C47—21no—
473C22×C47—21no—
474C22×C47—21no—
475C22×C47—21no—
476C22×C47—21no—
477C22×C47—21no—
478C22×C47—21no—
479C22×C47—21no—
480C22×C47—42no—
481C22×C47—42no—
482C22×C47—81no—
483C22×C47—81no—
484C22×C47#42112yes—
485C22×C47C22×C22⋊C411yescharacteristic
486C22×C47#54611yescharacteristic
487C22×C47#54711yescharacteristic
488C2×D47—41no—
489C2×D47—41no—
490C2×D47—41no—
491C4×C47—21no—
492C4×C47—21no—
493C4×C47—21no—
494C4×C47—21no—
495C4×C47—21no—
496C4×C47—21no—
497C4×C47—21no—
498C4×C47—21no—
499C4×C47—42no—
500C4×C47—42no—
501C4×C47—81no—
502C4×C47—81no—
503C4×C47C4×#4111yescharacteristic
504C4×C47#52011yescharacteristic
505C4×C47#54611yescharacteristic
506C4×C47#54711yescharacteristic
507Dic47—41no—
508Dic47—41no—
509Dic47—41no—
510Dic47—41no—
511Dic47—41no—
512Dic47—41no—
513Dic47—41no—
514#3475—471no—
515D4×M16—471no—
516#2290D4711yescharacteristic, complemented
517#1995—471no—
518#1986—471no—
519#1897—471no—
520#1896—471no—
521#1871—471no—
522#1871—471no—
523#1826—471no—
524#1826—471no—
525#1806—471no—
526#1759—471no—
527#1733—471no—
528C2×#339—471no—
529C2×C47—21no—
530C2×C47—21no—
531C2×C47—22no—
532C2×C47—41no—
533C2×C47—41no—
534C2×C47—41no—
535C2×C47#233911yescharacteristic
536C2×C47C2×#42111yescharacteristic
537C2×C47#290111yescharacteristic
538D47—81no—
539C22×M16—471no—
540C22×M16—471no—
541#556—471no—
542#555—471no—
543#554—471no—
544#553—471no—
545#553—471no—
546#552—471no—
547#552—471no—
548#552—941no—
549#551—941no—
550#551—941no—
551#547—471no—
552#546—941no—
553#533—471no—
554#529—941no—
555#529—941no—
556#529—941no—
557#525—471no—
558#525—471no—
559C4×#41—471no—
560C4×#41—941no—
561C2×C4×D4C2×D4711yescharacteristic
562C2×#117—471no—
563C2×#117—471no—
564C2×#117C2×D4711yescharacteristic
565C22×C42C2×D4711yescharacteristic
566#436—941no—
567#435—941no—
568#435—941no—
569C8×D4—941no—
570#423—471no—
571C2×#104—471no—
572C2×#104—471no—
573C2×#104—471no—
574C2×#104—471no—
575#407—471no—
576#407—471no—
577C4×M16—471no—
578#388—21no—
579#387—21no—
580#386—21no—
581#385—21no—
582C4×C4⋊C4C2×D4711yescharacteristic
583C4×C22⋊C4C2×D4711yescharacteristic
584C4×C22⋊C4C2×D4711yescharacteristic
585#376C2×D4711yescharacteristic
586#339—471no—
587#339—471no—
588#339—471no—
589#339—471no—
590#339—471no—
591#339—471no—
592#339—471no—
593#339—471no—
594#339—471no—
595#339—471no—
596#339—471no—
597#339—471no—
598C47#2250611yescharacteristic, complemented, Sylow
599C2×#41—471no—
600C2×#41—941no—
601C22×D4C22⋊D4711yescharacteristic
602C23×C4—21no—
603C23×C4C22×D4711yescharacteristic
604C23×C4C22×D4711yescharacteristic
605C2×M16—471no—
606C2×M16—471no—
607C2×M16—471no—
608C2×M16—471no—
609C2×M16—941no—
610C2×M16—941no—
611C2×M16—942no—
612C2×M16—942no—
613C2×M16—1881no—
614C2×M16—1881no—
615C22×C8—941no—
616C22×C8—941no—
617C4⋊Q8—471no—
618C4⋊Q8—471no—
619#126—941no—
620#126—941no—
621#126—941no—
622#126—941no—
623#126—941no—
624#126—941no—
625#125—471no—
626#125—471no—
627#125—941no—
628#125—941no—
629#125—941no—
630#124—941no—
631#124—941no—
632#124—941no—
633#123—941no—
634#123—941no—
635#123—941no—
636#123—941no—
637#123—941no—
638#123—941no—
639#123—941no—
640#123—941no—
641C22⋊Q8—471no—
642C22⋊Q8—471no—
643C22⋊Q8—471no—
644C22⋊Q8—471no—
645C22⋊Q8—941no—
646C22⋊Q8—941no—
647C22⋊Q8—941no—
648C22⋊Q8—941no—
649C22⋊Q8—941no—
650#121—471no—
651#121—471no—
652#121—471no—
653#121—471no—
654#121—941no—
655#121—941no—
656#121—941no—
657#120—941no—
658#120—941no—
659C4×Q8—471no—
660C4×Q8—471no—
661C4×Q8—941no—
662C4×Q8—941no—
663C4×Q8—941no—
664C4×D4—471no—
665C4×D4—471no—
666C4×D4—941no—
667C4×D4—941no—
668C4×D4—941no—
669C4×D4—941no—
670C4×D4—941no—
671C4×D4—941no—
672C4×D4—941no—
673C4×D4—941no—
674C4×D4—941no—
675C4×D4C4×D4711yescharacteristic
676C4×D4C4×D4711yescharacteristic
677C4×D4C4×D4711yescharacteristic
678C4×D4C4×D4711yescharacteristic
679C4×D4D18811yescharacteristic
680C4×D4D18811yescharacteristic
681C4×D4D18811yescharacteristic
682C4×D4D18811yescharacteristic
683#117—22no—
684#117—41no—
685#117—471no—
686#117—471no—
687#117—471no—
688#117—471no—
689#117—471no—
690#117—471no—
691#117—471no—
692#117—941no—
693#117—941no—
694#117—941no—
695#117—941no—
696#117—941no—
697#117—941no—
698#117—941no—
699#117—941no—
700C2×C4⋊C4—21no—
701C2×C4⋊C4—21no—
702C2×C4⋊C4—471no—
703C2×C4⋊C4—471no—
704C2×C4⋊C4—471no—
705C2×C4⋊C4—471no—
706C2×C4⋊C4C22⋊D4711yescharacteristic
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—941no—
711C2×C22⋊C4—941no—
712C2×C22⋊C4C22⋊D4711yescharacteristic
713C2×C22⋊C4C22⋊D4711yescharacteristic
714C2×C42—22no—
715C2×C42—21no—
716C2×C42—41no—
717C2×C42—941no—
718C2×C42—941no—
719C2×C42—941no—
720C2×C42C22×D4711yescharacteristic
721C2×C42C22×D4711yescharacteristic
722C2×C42C22×D4711yescharacteristic
723C2×C42C22×D4711yescharacteristic
724C2×C42C22×D4711yescharacteristic
725C4⋊C8—941no—
726C4⋊C8—941no—
727#104—942no—
728#104—942no—
729#104—1881no—
730#104—1881no—
731C22⋊C8—941no—
732C22⋊C8—941no—
733C22⋊C8—941no—
734C22⋊C8—941no—
735#97—941no—
736C4×C8—941no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742C24C2×C22⋊D4711yescharacteristic
743C24C2×C22⋊D4711yescharacteristic
744#41—941no—
745#41—941no—
746#41—941no—
747#41—941no—
748#41—1884no—
749C2×Q8—471no—
750C2×Q8—941no—
751C2×Q8—941no—
752C2×D4—42no—
753C2×D4—471no—
754C2×D4—941no—
755C2×D4—941no—
756C2×D4—941no—
757C2×D4—941no—
758C2×D4—941no—
759C2×D4(C2×D47)⋊C411yescharacteristic
760C2×D4(C2×D47)⋊C411yescharacteristic
761C2×D4(C2×D47)⋊C411yescharacteristic
762C2×D4(C2×D47)⋊C411yescharacteristic
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—42no—
776C22×C4—42no—
777C22×C4—42no—
778C22×C4—941no—
779C22×C4—941no—
780C22×C4—941no—
781C22×C4—941no—
782C22×C4—941no—
783C22×C4—941no—
784C22×C4—941no—
785C22×C4C2×C4×D4711yescharacteristic
786C22×C4C2×C4×D4711yescharacteristic
787C22×C4C2×C4×D4711yescharacteristic
788C22×C4C2×C4×D4711yescharacteristic
789C22×C4C2×D18811yescharacteristic
790C22×C4C2×D18811yescharacteristic
791C22×C4C2×D18811yescharacteristic
792C22×C4C2×D18811yescharacteristic
793C22×C4C2×C22⋊D4711yescharacteristic
794C22×C4C2×C22⋊D4711yescharacteristic
795C22×C4C2×C22⋊D4711yescharacteristic
796C22×C4C2×C22⋊D4711yescharacteristic
797C22×C4C23×D4711yescharacteristic
798M16—472no—
799M16—941no—
800M16—941no—
801M16—941no—
802M16—941no—
803M16—941no—
804M16—941no—
805M16—941no—
806M16—1882no—
807M16—1882no—
808C2×C8—941no—
809C2×C8—941no—
810C2×C8—941no—
811C2×C8—941no—
812C2×C8—1882no—
813C2×C8—1882no—
814C4⋊C4—42no—
815C4⋊C4—42no—
816C4⋊C4—471no—
817C4⋊C4—471no—
818C4⋊C4—471no—
819C4⋊C4—471no—
820C4⋊C4—471no—
821C4⋊C4—471no—
822C4⋊C4—941no—
823C4⋊C4—941no—
824C4⋊C4—941no—
825C4⋊C4—941no—
826C4⋊C4—941no—
827C4⋊C4—941no—
828C4⋊C4—941no—
829C4⋊C4—941no—
830C4⋊C4—941no—
831C4⋊C4—941no—
832C4⋊C4—941no—
833C4⋊C4—941no—
834C4⋊C4—941no—
835C4⋊C4—941no—
836C4⋊C4—941no—
837C4⋊C4—941no—
838C4⋊C4(C2×D47)⋊C411yescharacteristic
839C4⋊C4(C2×D47)⋊C411yescharacteristic
840C4⋊C4(C2×D47)⋊C411yescharacteristic
841C4⋊C4(C2×D47)⋊C411yescharacteristic
842C22⋊C4—42no—
843C22⋊C4—42no—
844C22⋊C4—42no—
845C22⋊C4—941no—
846C22⋊C4—941no—
847C22⋊C4—941no—
848C22⋊C4—941no—
849C22⋊C4—941no—
850C22⋊C4—941no—
851C22⋊C4—941no—
852C22⋊C4—941no—
853C22⋊C4—941no—
854C22⋊C4—941no—
855C22⋊C4—941no—
856C22⋊C4—941no—
857C22⋊C4—941no—
858C22⋊C4—941no—
859C22⋊C4—941no—
860C22⋊C4—941no—
861C22⋊C4—941no—
862C22⋊C4(C2×D47)⋊C411yescharacteristic
863C22⋊C4(C2×D47)⋊C411yescharacteristic
864C22⋊C4(C2×D47)⋊C411yescharacteristic
865C22⋊C4(C2×D47)⋊C411yescharacteristic
866C22⋊C4(C2×D47)⋊C411yescharacteristic
867C22⋊C4(C2×D47)⋊C411yescharacteristic
868C22⋊C4(C2×D47)⋊C411yescharacteristic
869C22⋊C4(C2×D47)⋊C411yescharacteristic
870C42—21no—
871C42—21no—
872C42—21no—
873C42—21no—
874C42—21no—
875C42—21no—
876C42—21no—
877C42—42no—
878C42—941no—
879C42—941no—
880C42—941no—
881C42—941no—
882C42—941no—
883C42—941no—
884C42—941no—
885C42—941no—
886C42—941no—
887C42C2×C4×D4711yescharacteristic
888C42C2×C4×D4711yescharacteristic
889C42C2×D18811yescharacteristic
890C42C2×D18811yescharacteristic
891C42#1062535212yescomplemented
892C23—21no—
893C23—21no—
894C23—22no—
895C23—21no—
896C23—21no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—941no—
901C23C2×(C2×D47)⋊C411yescharacteristic
902C23C2×(C2×D47)⋊C411yescharacteristic
903C23C2×(C2×D47)⋊C411yescharacteristic
904C23C2×(C2×D47)⋊C411yescharacteristic
905C23C22×C22⋊D4711yescharacteristic
906Q8—941no—
907Q8—941no—
908Q8—3761no—
909Q8—1882no—
910D4—22no—
911D4—22no—
912D4—41no—
913D4—41no—
914D4—941no—
915D4—941no—
916D4—3761no—
917D4—3761no—
918D4—1882no—
919D4—1881no—
920D4—1881no—
921D4—1882no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—48no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—941no—
958C2×C4—941no—
959C2×C4—941no—
960C2×C4—941no—
961C2×C4—941no—
962C2×C4—941no—
963C2×C4—941no—
964C2×C4—3761no—
965C2×C4—3761no—
966C2×C4—3761no—
967C2×C4—1882no—
968C2×C4—1882no—
969C2×C4—1882no—
970C2×C4—1881no—
971C2×C4—1881no—
972C2×C4C2×(C2×D47)⋊C411yescharacteristic
973C2×C4C2×(C2×D47)⋊C411yescharacteristic
974C2×C4C2×(C2×D47)⋊C411yescharacteristic
975C2×C4C2×(C2×D47)⋊C411yescharacteristic
976C2×C4C2×(C2×D47)⋊C411yescharacteristic
977C2×C4C2×(C2×D47)⋊C411yescharacteristic
978C2×C4C2×(C2×D47)⋊C411yescharacteristic
979C2×C4C2×(C2×D47)⋊C411yescharacteristic
980C2×C4C22×C4×D4711yescharacteristic
981C2×C4C22×D18811yescharacteristic
982C2×C4#41×D4711yescharacteristic
983C2×C4C2×#1062535211yescharacteristic
984C2×C4#1309406911yescharacteristic
985C2×C4#1309407111yescharacteristic
986C8—942no—
987C8—1881no—
988C8—1881no—
989C8—1881no—
990C22—21no—
991C22—21no—
992C22—21no—
993C22—21no—
994C22—21no—
995C22—21no—
996C22—21no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—42no—
1004C22—42no—
1005C22—81no—
1006C22—81no—
1007C22—1881no—
1008C22—1881no—
1009C22—1881no—
1010C22#1568914112yes—
1011C22C22×(C2×D47)⋊C411yescharacteristic
1012C22#1568976711yescharacteristic
1013C22#1568977211yescharacteristic
1014C4—21no—
1015C4—21no—
1016C4—21no—
1017C4—21no—
1018C4—21no—
1019C4—21no—
1020C4—21no—
1021C4—21no—
1022C4—42no—
1023C4—42no—
1024C4—81no—
1025C4—81no—
1026C4—1881no—
1027C4—1881no—
1028C4—1881no—
1029C4—1881no—
1030C4—1881no—
1031C4—1881no—
1032C4—1881no—
1033C4C4×#1062535211yescharacteristic
1034C4#1568960211yescharacteristic
1035C4#1568976811yescharacteristic
1036C4#1568977711yescharacteristic
1037C2—21no—
1038C2—21no—
1039C2—22no—
1040C2—41no—
1041C2—41no—
1042C2—41no—
1043C2—3761no—
1044C2#2024621311yescharacteristic
1045C2C2×#1568914111yescharacteristic
1046C2#2025193611yescharacteristic
subgroupG/H
centerC2×C4C22×D188
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2290C2
socleC22×C47C22×C22⋊C4
prime radical#20256946C2
cosocleC22×C4×C47C24
hypercenter#2290D47
hypocenterC47#22506
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C4×D4 ◁ #2290

Complements

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

NH ≅ G/Ntype
2. D4×#10625329C2semidirect
3. #20244369C2semidirect
4. #20244331C2semidirect
5. #20243836C2semidirect
6. #20243831C2semidirect
7. #20243688C2semidirect
8. #20243688C2semidirect
9. #20243488C2semidirect
10. #20243488C2semidirect
11. #20243409C2semidirect
12. #20243199C2semidirect
13. #20243098C2semidirect
14. C2×#15688883C2semidirect
15. C47×#2290C2semidirect
18. #15689843C4semidirect
19. #15689838C4semidirect
20. #15689830C4semidirect
21. #15689819C4semidirect
22. #15689819C4semidirect
23. #15689813C4semidirect
24. #15689813C4semidirect
28. #15689777C4semidirect
89. #13094024C2×C4semidirect
90. #13094024C2×C4semidirect
97. #13094016C2×C4semidirect
98. #13094016C2×C4semidirect
118. #13094003C2×C4semidirect
119. #13094003C2×C4semidirect
124. #13093998C2×C4semidirect
125. #13093998C2×C4semidirect
133. C4×Dic94C2×C4semidirect
134. C4×Dic94C2×C4semidirect
136. C4×D188C2×C4semidirect
137. C4×D188C2×C4semidirect
153. #13093983C2×C4semidirect
154. #13093983C2×C4semidirect
164. C2×C4⋊Dic47C2×C4semidirect
165. C2×C4⋊Dic47C2×C4semidirect
303. C42×C47#41semidirect
361. #10625329#41semidirect
516. #2290D47semidirect
598. C47#22506semidirect
891. C42#10625352semidirect

Maximal subgroups

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

subgroupindex
#202569462
D4×#106253292
#202443692
#202443312
#202438362
#202438312
#202436882
#202434882
#202434092
#202431992
#202430982
C2×#156888832
C47×#22902
#2250647