Finite Group Databasebeta

← #26182509

Subgroups — #26182509

Order 12032.

944 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689806C211yesmaximal, characteristic
2#20252046C211yesmaximal, characteristic, complemented
3#20241758C211yesmaximal, characteristic, complemented
4#20241755C211yesmaximal, characteristic, complemented
5#20241745C211yesmaximal, characteristic, complemented
6#20241743C211yesmaximal, characteristic, complemented
7#20241737C211yesmaximal, characteristic
8#20241734C211yesmaximal, characteristic
9#20241731C211yesmaximal, characteristic, complemented
10#20241720C211yesmaximal, characteristic, complemented
11#20241717C211yesmaximal, characteristic, complemented
12#20241711C211yesmaximal, characteristic, complemented
13#20241700C211yesmaximal, characteristic, complemented
14C2×#15688848C211yesmaximal, characteristic, complemented
15C47×#2924C211yesmaximal, characteristic, complemented
16#15689806—21no—
17#15689806—21no—
18#15689806—21no—
19#15689806—21no—
20#15689806—21no—
21#15689806—21no—
22#15689806—21no—
23#15689806—21no—
24C2×#13094019C411yescharacteristic
25C2×#13094018C2211yescharacteristic
26C2×#13094016C2211yescharacteristic
27C2×#13094014C411yescharacteristic
28C2×#13094014C411yescharacteristic
29C2×#13094008C411yescharacteristic
30C2×#13094007C2211yescharacteristic
31C2×#13094002C411yescharacteristic
32C2×#13094001C411yescharacteristic
33C2×C4×Dic94C2211yescharacteristic
34C2×(C22⋊D47)⋊C4C411yescharacteristic
35C2×#13093981C2211yescharacteristic
36C2×#13093980C411yescharacteristic
37C22×Dic47⋊C4C2211yescharacteristic
38#15689184—21no—
39#15689184—21no—
40#15689180C2211yescharacteristic
41#15689180C2211yescharacteristic
42#15689176C2211yescharacteristic
43#15689176C2211yescharacteristic
44#15689150—21no—
45#15689087C2211yescharacteristic
46C2×C22⋊(C47⋊C8)C2211yescharacteristic
47#15689079—21no—
48#15688848C2211yescharacteristic
49#15688848C2211yescharacteristic
50#15688848C2211yescharacteristic
51#15688848C2211yescharacteristic
52#15688848C2211yescharacteristic
53#15688848C2211yescharacteristic
54#15688848C2211yescharacteristic
55#15688848C2211yescharacteristic
56#15688848C2211yescharacteristic
57#15688848C2211yescharacteristic
58#15688848C2211yescharacteristic
59#15688848C2211yescharacteristic
60#15688846C2211yescharacteristic
61#15688846C2211yescharacteristic
62#15688846C2211yescharacteristic
63#15688846C2211yescharacteristic
64C2×#117×C47C2211yescharacteristic
65C47×#433—21no—
66C47×#433—21no—
67C47×#432C2211yescharacteristic
68C47×#432C2211yescharacteristic
69C47×#431C2211yescharacteristic
70C47×#431C2211yescharacteristic
71C47×#424—21no—
72C47×#407C2211yescharacteristic
73C2×C22⋊C8×C47C2211yescharacteristic
74C47×#405—21no—
75C22×Dic94C2×C411yescharacteristic
76C22×C22⋊D47C2×C411yescharacteristic
77C23×Dic47C2×C411yescharacteristic
78C23×Dic47C2×C411yescharacteristic
79C22×C4×D47C2×C411yescharacteristic
80C2×#10625329—21no—
81C22×C47⋊C8—21no—
82#13094019—21no—
83#13094019—21no—
84#13094019—21no—
85#13094019—21no—
86#13094018—21no—
87#13094018—21no—
88#13094018—21no—
89#13094018—21no—
90#13094016—21no—
91#13094016—21no—
92#13094016—21no—
93#13094016—21no—
94#13094014—21no—
95#13094014—21no—
96#13094014—21no—
97#13094014—21no—
98#13094014—21no—
99#13094014—21no—
100#13094014—21no—
101#13094014—21no—
102#13094008—21no—
103#13094008—21no—
104#13094008—21no—
105#13094008—21no—
106#13094007—21no—
107#13094007—21no—
108#13094007—21no—
109#13094007—21no—
110#13094002—21no—
111#13094002—21no—
112#13094002—21no—
113#13094002—21no—
114#13094001—21no—
115#13094001—21no—
116#13094001—21no—
117#13094001—21no—
118C4×Dic94—21no—
119C4×Dic94—21no—
120C4×Dic94—21no—
121C4×Dic94—21no—
122(C22⋊D47)⋊C4—21no—
123(C22⋊D47)⋊C4—21no—
124(C22⋊D47)⋊C4—21no—
125(C22⋊D47)⋊C4—21no—
126#13093981—21no—
127#13093981—21no—
128#13093981—21no—
129#13093981—21no—
130#13093980—21no—
131#13093980—21no—
132#13093980—21no—
133#13093980—21no—
134C2×C4⋊Dic47C2×C411yescharacteristic
135C2×C4⋊Dic47C2×C411yescharacteristic
136C2×C4⋊Dic47C2×C411yescharacteristic
137C2×Dic47⋊C4—21no—
138C2×Dic47⋊C4—21no—
139C2×Dic47⋊C4—21no—
140C2×Dic47⋊C4—21no—
141C2×Dic47⋊C4C2×C411yescharacteristic
142C2×Dic47⋊C4C2×C411yescharacteristic
143C2×Dic47⋊C4C2×C411yescharacteristic
144C2×Dic47⋊C4C2×C411yescharacteristic
145C2×Dic47⋊C4C2×C411yescharacteristic
146C2×Dic47⋊C4C2×C411yescharacteristic
147C2×Dic47⋊C4C2×C411yescharacteristic
148C2×Dic47⋊C4C2×C411yescharacteristic
149C2×Dic47⋊C4C2311yescharacteristic
150C2×Dic47⋊C4C2311yescharacteristic
151C2×Dic47⋊C4C2311yescharacteristic
152C2×C22⋊Dic47C2×C411yescharacteristic
153C2×(C2×D47)⋊C4C2×C411yescharacteristic
154C2×(C2×D47)⋊C4C2×C411yescharacteristic
155C2×(C2×D47)⋊C4C2×C411yescharacteristic
156C2×(C2×D47)⋊C4C2×C411yescharacteristic
157C2×(C2×D47)⋊C4C2311yescharacteristic
158C2×C4×Dic47C2×C411yescharacteristic
159C2×C4×Dic47C2×C411yescharacteristic
160C2×C4×Dic47C2×C411yescharacteristic
161C4⋊(C47⋊C8)—21no—
162C4⋊(C47⋊C8)—21no—
163C4⋊(C47⋊C8)—21no—
164C4⋊(C47⋊C8)—21no—
165C22⋊(C47⋊C8)—21no—
166C22⋊(C47⋊C8)—21no—
167C22⋊(C47⋊C8)C2311yescharacteristic
168C22⋊(C47⋊C8)C2311yescharacteristic
169C22⋊(C47⋊C8)C2311yescharacteristic
170C22⋊(C47⋊C8)C2311yescharacteristic
171#13093935—21no—
172#13093935—21no—
173C4×C47⋊C8—21no—
174C4×C47⋊C8—21no—
175C23×C4×C47C2311yescharacteristic
176C2×M16×C47—21no—
177C22×C8×C47—21no—
178#117×C47D411yescharacteristic
179#117×C47D411yescharacteristic
180#117×C47D411yescharacteristic
181#117×C47D411yescharacteristic
182#117×C47D411yescharacteristic
183#117×C47D411yescharacteristic
184#117×C47D411yescharacteristic
185#117×C47D411yescharacteristic
186C2×C4⋊C4×C47C2×C411yescharacteristic
187C2×C4⋊C4×C47C2×C411yescharacteristic
188C2×C22⋊C4×C47C2×C411yescharacteristic
189C2×C22⋊C4×C47C2×C411yescharacteristic
190C2×C42×C47C2311yescharacteristic
191C2×C42×C47C2311yescharacteristic
192C4⋊C8×C47—21no—
193C4⋊C8×C47—21no—
194C4⋊C8×C47—21no—
195C4⋊C8×C47—21no—
196C22⋊C8×C47—21no—
197C22⋊C8×C47—21no—
198C22⋊C8×C47C2311yescharacteristic
199C22⋊C8×C47C2311yescharacteristic
200C22⋊C8×C47C2311yescharacteristic
201C22⋊C8×C47C2311yescharacteristic
202#97×C47—21no—
203#97×C47—21no—
204C4×C8×C47—21no—
205C4×C8×C47—21no—
206C24×C47C22×C411yescharacteristic
207C23×D47C22×C411yescharacteristic
208C22×C4×C47—42no—
209C22×C4×C47C22×C411yescharacteristic
210C22×C4×C47C22×C411yescharacteristic
211C22×C4×C47C22×C411yescharacteristic
212C22×C4×C47C22×C411yescharacteristic
213C22×C4×C47C22×C411yescharacteristic
214C22×C4×C47C2×D411yescharacteristic
215C22×C4×C47C2×D411yescharacteristic
216C22×C4×C47C2×D411yescharacteristic
217C22×C4×C47C2×D411yescharacteristic
218C22×C4×C47C2411yescharacteristic
219C2×C22⋊D47—21no—
220C2×C22⋊D47—21no—
221C2×C22⋊D47—42no—
222C22×Dic47—21no—
223C22×Dic47—21no—
224C22×Dic47—21no—
225C22×Dic47—21no—
226C22×Dic47—22no—
227C22×Dic47—41no—
228C22×Dic47—42no—
229C22×Dic47C22×C411yescharacteristic
230C22×Dic47C22×C411yescharacteristic
231C22×Dic47C22×C411yescharacteristic
232C22×Dic47C22×C411yescharacteristic
233C22×Dic47C22×C411yescharacteristic
234C22×Dic47C22×C411yescharacteristic
235C22×Dic47C22×C411yescharacteristic
236C2×C4×D47—21no—
237C2×C4×D47—21no—
238C2×C4×D47—22no—
239C2×C4×D47—41no—
240C2×Dic94—21no—
241C2×Dic94—21no—
242C2×Dic94—22no—
243C2×Dic94—41no—
244M16×C47—42no—
245C2×C8×C47—21no—
246C2×C8×C47—21no—
247C2×C8×C47—21no—
248C2×C8×C47—21no—
249C2×C8×C47—42no—
250C4⋊C4×C47C22⋊C411yescharacteristic
251C4⋊C4×C47C22⋊C411yescharacteristic
252C4⋊C4×C47C22⋊C411yescharacteristic
253C4⋊C4×C47C22⋊C411yescharacteristic
254C4⋊C4×C47C22⋊C411yescharacteristic
255C4⋊C4×C47C22⋊C411yescharacteristic
256C4⋊C4×C47C22⋊C411yescharacteristic
257C4⋊C4×C47C22⋊C411yescharacteristic
258C22⋊C4×C47C22⋊C411yescharacteristic
259C22⋊C4×C47C22⋊C411yescharacteristic
260C22⋊C4×C47C22⋊C411yescharacteristic
261C22⋊C4×C47C22⋊C411yescharacteristic
262C22⋊C4×C47C22⋊C411yescharacteristic
263C22⋊C4×C47C22⋊C411yescharacteristic
264C22⋊C4×C47C22⋊C411yescharacteristic
265C22⋊C4×C47C22⋊C411yescharacteristic
266C42×C47C2×D411yescharacteristic
267C42×C47C2×D411yescharacteristic
268C42×C47C2×D411yescharacteristic
269C42×C47C2×D411yescharacteristic
270C42×C47C2×D411yescharacteristic
271C42×C47C2×D411yescharacteristic
272C42×C47C2×D411yescharacteristic
273C42×C47C2×D411yescharacteristic
274C22⋊Dic47—21no—
275C22⋊Dic47—21no—
276(C2×D47)⋊C4—21no—
277(C2×D47)⋊C4—21no—
278(C2×D47)⋊C4—21no—
279(C2×D47)⋊C4—21no—
280(C2×D47)⋊C4—21no—
281(C2×D47)⋊C4—21no—
282(C2×D47)⋊C4—21no—
283(C2×D47)⋊C4—21no—
284(C2×D47)⋊C4—21no—
285(C2×D47)⋊C4—21no—
286C4⋊Dic47—21no—
287C4⋊Dic47—21no—
288C4⋊Dic47—21no—
289C4⋊Dic47—21no—
290C4⋊Dic47—21no—
291C4⋊Dic47—21no—
292Dic47⋊C4—21no—
293Dic47⋊C4—21no—
294Dic47⋊C4—21no—
295Dic47⋊C4—21no—
296Dic47⋊C4—21no—
297Dic47⋊C4—21no—
298Dic47⋊C4—21no—
299Dic47⋊C4—21no—
300Dic47⋊C4—21no—
301Dic47⋊C4—21no—
302Dic47⋊C4—21no—
303Dic47⋊C4—21no—
304Dic47⋊C4—21no—
305Dic47⋊C4—21no—
306Dic47⋊C4—21no—
307Dic47⋊C4—21no—
308Dic47⋊C4—21no—
309Dic47⋊C4—21no—
310Dic47⋊C4—21no—
311Dic47⋊C4—21no—
312Dic47⋊C4—21no—
313Dic47⋊C4—21no—
314C4×Dic47—21no—
315C4×Dic47—21no—
316C4×Dic47—21no—
317C4×Dic47—21no—
318C4×Dic47—21no—
319C4×Dic47—21no—
320#10625329—42no—
321C2×C47⋊C8—21no—
322C2×C47⋊C8—21no—
323C2×C47⋊C8—21no—
324C2×C47⋊C8—21no—
325C2×C47⋊C8—42no—
326C23×C47—21no—
327C23×C47—21no—
328C23×C47—22no—
329C23×C47—41no—
330C23×C47C2×C22⋊C411yescharacteristic
331C23×C47C2×C22⋊C411yescharacteristic
332C23×C47C23×C411yescharacteristic
333C22×D47—21no—
334C22×D47—21no—
335C22×D47—21no—
336C22×D47—41no—
337C22×D47—41no—
338C2×C4×C47—21no—
339C2×C4×C47—21no—
340C2×C4×C47—21no—
341C2×C4×C47—21no—
342C2×C4×C47—22no—
343C2×C4×C47—22no—
344C2×C4×C47—41no—
345C2×C4×C47—41no—
346C2×C4×C47—41no—
347C2×C4×C47—41no—
348C2×C4×C47—41no—
349C2×C4×C47—41no—
350C2×C4×C47C2×C22⋊C411yescharacteristic
351C2×C4×C47C2×C22⋊C411yescharacteristic
352C2×C4×C47C2×C22⋊C411yescharacteristic
353C2×C4×C47C2×C22⋊C411yescharacteristic
354C2×C4×C47C2×C22⋊C411yescharacteristic
355C2×C4×C47C2×C22⋊C411yescharacteristic
356C2×C4×C47C2×C22⋊C411yescharacteristic
357C2×C4×C47C2×C22⋊C411yescharacteristic
358C2×C4×C47C2×C22⋊C411yescharacteristic
359C2×C4×C47C2×C22⋊C411yescharacteristic
360C2×C4×C47C22×D411yescharacteristic
361C2×C4×C47C22×D411yescharacteristic
362C22⋊D47—42no—
363C22⋊D47—42no—
364C2×Dic47—21no—
365C2×Dic47—21no—
366C2×Dic47—21no—
367C2×Dic47—21no—
368C2×Dic47—21no—
369C2×Dic47—21no—
370C2×Dic47—21no—
371C2×Dic47—21no—
372C2×Dic47—21no—
373C2×Dic47—21no—
374C2×Dic47—21no—
375C2×Dic47—21no—
376C2×Dic47—42no—
377C2×Dic47—42no—
378C2×Dic47—42no—
379C2×Dic47—42no—
380C2×Dic47—41no—
381C2×Dic47—41no—
382C2×Dic47—41no—
383C2×Dic47—41no—
384C2×Dic47#13112yes—
385C4×D47—42no—
386C4×D47—42no—
387Dic94—42no—
388Dic94—42no—
389C8×C47—41no—
390C8×C47—41no—
391C8×C47—41no—
392C8×C47—41no—
393C47⋊C8—41no—
394C47⋊C8—41no—
395C47⋊C8—41no—
396C47⋊C8—41no—
397#17417—471nomaximal, Sylow
398C22×C47—21no—
399C22×C47—21no—
400C22×C47—21no—
401C22×C47—21no—
402C22×C47—21no—
403C22×C47—21no—
404C22×C47—21no—
405C22×C47—42no—
406C22×C47—42no—
407C22×C47#41012yes—
408C22×C47C22×C22⋊C411yescharacteristic
409C22×C47C2×#13111yescharacteristic
410C22×C47#56811yescharacteristic
411C2×D47—41no—
412C2×D47—41no—
413C2×D47—41no—
414C2×D47—81no—
415C2×D47—81no—
416C4×C47—21no—
417C4×C47—21no—
418C4×C47—21no—
419C4×C47—21no—
420C4×C47—21no—
421C4×C47—21no—
422C4×C47—21no—
423C4×C47—21no—
424C4×C47—21no—
425C4×C47—21no—
426C4×C47—21no—
427C4×C47—21no—
428Dic47—22no—
429Dic47—41no—
430Dic47—41no—
431Dic47—41no—
432Dic47—41no—
433Dic47—41no—
434Dic47—41no—
435C2×#552—471no—
436#2924—471no—
437#2924D4711yescharacteristic, complemented
438#1473—471no—
439#1473—471no—
440#1470—471no—
441#1470—471no—
442#1468—471no—
443#1468—471no—
444#1467—471no—
445#1464—471no—
446#1463—471no—
447#1461—471no—
448#1458—471no—
449C2×#324—471no—
450C2×C47—21no—
451C2×C47—21no—
452C2×C47—22no—
453C2×C47—41no—
454C2×C47#288011yescharacteristic
455C2×C47C2×#41011yescharacteristic
456C2×C47#288911yescharacteristic
457D47—81no—
458#552—941no—
459#552—941no—
460#552—941no—
461#552—941no—
462#552—941no—
463#552—941no—
464#552—941no—
465#552—941no—
466C2×#126—471no—
467C2×#126—471no—
468C2×#125—471no—
469C2×#125—471no—
470C2×#125—471no—
471C2×#123—471no—
472C2×#123—471no—
473C2×C22⋊Q8—471no—
474C2×C22⋊Q8—471no—
475C2×C4×Q8—471no—
476C2×C4×D4—471no—
477C2×#117—471no—
478C2×#117—471no—
479C2×#117C2×D4711yescharacteristic
480C22×C4⋊C4—471no—
481#433—21no—
482#433—21no—
483#433—941no—
484#433—941no—
485#432—471no—
486#432—471no—
487#432C2×D4711yescharacteristic
488#432C2×D4711yescharacteristic
489#431—471no—
490#431—471no—
491#431C2×D4711yescharacteristic
492#431C2×D4711yescharacteristic
493#424—21no—
494#424—941no—
495#407—471no—
496#407C2×D4711yescharacteristic
497C2×C22⋊C8—471no—
498C2×C22⋊C8C2×D4711yescharacteristic
499#405—21no—
500#405—941no—
501#324—471no—
502#324—471no—
503#324—471no—
504#324—471no—
505#324—471no—
506#324—471no—
507#324—471no—
508#324—471no—
509#324—471no—
510#324—471no—
511#324—471no—
512#324—471no—
513#323—471no—
514#323—471no—
515#323—471no—
516#323—471no—
517C47#1741711yescharacteristic, complemented, Sylow
518C22×Q8—471no—
519C22×D4—471no—
520C23×C4—471no—
521C23×C4—471no—
522C23×C4—471no—
523C23×C4C22×D4711yescharacteristic
524C2×M16—21no—
525C2×M16—941no—
526C22×C8—21no—
527C22×C8—941no—
528#126—941no—
529#126—941no—
530#126—941no—
531#126—941no—
532#126—941no—
533#126—941no—
534#126—941no—
535#126—941no—
536#125—941no—
537#125—941no—
538#125—941no—
539#125—941no—
540#125—941no—
541#125—941no—
542#125—941no—
543#125—941no—
544#125—941no—
545#125—941no—
546#125—941no—
547#125—941no—
548#123—941no—
549#123—941no—
550#123—941no—
551#123—941no—
552#123—941no—
553#123—941no—
554#123—941no—
555#123—941no—
556C22⋊Q8—941no—
557C22⋊Q8—941no—
558C22⋊Q8—941no—
559C22⋊Q8—941no—
560C22⋊Q8—941no—
561C22⋊Q8—941no—
562C22⋊Q8—941no—
563C22⋊Q8—941no—
564C4×Q8—941no—
565C4×Q8—941no—
566C4×Q8—941no—
567C4×Q8—941no—
568C4×D4—941no—
569C4×D4—941no—
570C4×D4—941no—
571C4×D4—941no—
572#117—941no—
573#117—941no—
574#117—941no—
575#117—941no—
576#117—941no—
577#117—941no—
578#117—941no—
579#117—941no—
580#117D18811yescharacteristic
581#117D18811yescharacteristic
582#117D18811yescharacteristic
583#117D18811yescharacteristic
584#117C22⋊D4711yescharacteristic
585#117C22⋊D4711yescharacteristic
586#117C22⋊D4711yescharacteristic
587#117C22⋊D4711yescharacteristic
588C2×C4⋊C4—471no—
589C2×C4⋊C4—471no—
590C2×C4⋊C4—471no—
591C2×C4⋊C4—471no—
592C2×C4⋊C4—471no—
593C2×C4⋊C4—471no—
594C2×C4⋊C4—471no—
595C2×C4⋊C4—471no—
596C2×C4⋊C4—471no—
597C2×C4⋊C4—471no—
598C2×C4⋊C4—471no—
599C2×C4⋊C4—471no—
600C2×C4⋊C4—471no—
601C2×C4⋊C4—471no—
602C2×C4⋊C4—941no—
603C2×C4⋊C4—941no—
604C2×C4⋊C4—941no—
605C2×C4⋊C4—941no—
606C2×C4⋊C4C4×D4711yescharacteristic
607C2×C4⋊C4C4×D4711yescharacteristic
608C2×C22⋊C4—471no—
609C2×C22⋊C4—471no—
610C2×C22⋊C4—471no—
611C2×C22⋊C4—471no—
612C2×C22⋊C4—471no—
613C2×C22⋊C4—471no—
614C2×C22⋊C4C4×D4711yescharacteristic
615C2×C22⋊C4C4×D4711yescharacteristic
616C2×C42—471no—
617C2×C42—471no—
618C2×C42—471no—
619C2×C42C22×D4711yescharacteristic
620C2×C42C22×D4711yescharacteristic
621C4⋊C8—21no—
622C4⋊C8—21no—
623C4⋊C8—21no—
624C4⋊C8—21no—
625C4⋊C8—941no—
626C4⋊C8—941no—
627C4⋊C8—941no—
628C4⋊C8—941no—
629C22⋊C8—21no—
630C22⋊C8—21no—
631C22⋊C8—471no—
632C22⋊C8—471no—
633C22⋊C8—471no—
634C22⋊C8—471no—
635C22⋊C8—941no—
636C22⋊C8—941no—
637C22⋊C8C22×D4711yescharacteristic
638C22⋊C8C22×D4711yescharacteristic
639C22⋊C8C22×D4711yescharacteristic
640C22⋊C8C22×D4711yescharacteristic
641#97—21no—
642#97—21no—
643#97—941no—
644#97—941no—
645C4×C8—21no—
646C4×C8—21no—
647C4×C8—941no—
648C4×C8—941no—
649C24—471no—
650C24C2×C4×D4711yescharacteristic
651C2×Q8—942no—
652C2×Q8—941no—
653C2×Q8—941no—
654C2×Q8—1881no—
655C2×D4—941no—
656C2×D4—941no—
657C2×D4—1882no—
658C22×C4—42no—
659C22×C4—471no—
660C22×C4—471no—
661C22×C4—471no—
662C22×C4—471no—
663C22×C4—471no—
664C22×C4—471no—
665C22×C4—471no—
666C22×C4—942no—
667C22×C4—942no—
668C22×C4—941no—
669C22×C4—941no—
670C22×C4—941no—
671C22×C4—941no—
672C22×C4—941no—
673C22×C4—941no—
674C22×C4—1881no—
675C22×C4—1881no—
676C22×C4—1882no—
677C22×C4C2×C4×D4711yescharacteristic
678C22×C4C2×C4×D4711yescharacteristic
679C22×C4C2×C4×D4711yescharacteristic
680C22×C4C2×C4×D4711yescharacteristic
681C22×C4C2×C4×D4711yescharacteristic
682C22×C4C2×D18811yescharacteristic
683C22×C4C2×D18811yescharacteristic
684C22×C4C2×C22⋊D4711yescharacteristic
685C22×C4C2×C22⋊D4711yescharacteristic
686C22×C4C23×D4711yescharacteristic
687M16—42no—
688M16—1882no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—42no—
694C2×C8—941no—
695C2×C8—941no—
696C2×C8—941no—
697C2×C8—941no—
698C2×C8—1882no—
699C4⋊C4—941no—
700C4⋊C4—941no—
701C4⋊C4—941no—
702C4⋊C4—941no—
703C4⋊C4—941no—
704C4⋊C4—941no—
705C4⋊C4—941no—
706C4⋊C4—941no—
707C4⋊C4—941no—
708C4⋊C4—941no—
709C4⋊C4—941no—
710C4⋊C4—941no—
711C4⋊C4—941no—
712C4⋊C4—941no—
713C4⋊C4—941no—
714C4⋊C4—941no—
715C4⋊C4—941no—
716C4⋊C4—941no—
717C4⋊C4—941no—
718C4⋊C4—941no—
719C4⋊C4—941no—
720C4⋊C4—941no—
721C4⋊C4—941no—
722C4⋊C4—941no—
723C4⋊C4—941no—
724C4⋊C4—941no—
725C4⋊C4—941no—
726C4⋊C4—941no—
727C4⋊C4(C2×D47)⋊C411yescharacteristic
728C4⋊C4(C2×D47)⋊C411yescharacteristic
729C4⋊C4(C2×D47)⋊C411yescharacteristic
730C4⋊C4(C2×D47)⋊C411yescharacteristic
731C4⋊C4(C2×D47)⋊C411yescharacteristic
732C4⋊C4(C2×D47)⋊C411yescharacteristic
733C4⋊C4(C2×D47)⋊C411yescharacteristic
734C4⋊C4(C2×D47)⋊C411yescharacteristic
735C22⋊C4—941no—
736C22⋊C4—941no—
737C22⋊C4—941no—
738C22⋊C4—941no—
739C22⋊C4—941no—
740C22⋊C4—941no—
741C22⋊C4—941no—
742C22⋊C4—941no—
743C22⋊C4—941no—
744C22⋊C4—941no—
745C22⋊C4—941no—
746C22⋊C4—941no—
747C22⋊C4(C2×D47)⋊C411yescharacteristic
748C22⋊C4(C2×D47)⋊C411yescharacteristic
749C22⋊C4(C2×D47)⋊C411yescharacteristic
750C22⋊C4(C2×D47)⋊C411yescharacteristic
751C22⋊C4(C2×D47)⋊C411yescharacteristic
752C22⋊C4(C2×D47)⋊C411yescharacteristic
753C22⋊C4(C2×D47)⋊C411yescharacteristic
754C22⋊C4(C2×D47)⋊C411yescharacteristic
755C42—941no—
756C42—941no—
757C42—941no—
758C42—941no—
759C42—941no—
760C42—941no—
761C42C2×D18811yescharacteristic
762C42C2×D18811yescharacteristic
763C42C2×D18811yescharacteristic
764C42C2×D18811yescharacteristic
765C42C2×C22⋊D4711yescharacteristic
766C42C2×C22⋊D4711yescharacteristic
767C42C2×C22⋊D4711yescharacteristic
768C42C2×C22⋊D4711yescharacteristic
769C23—22no—
770C23—21no—
771C23—21no—
772C23—41no—
773C23—941no—
774C23—941no—
775C23—941no—
776C23—1881no—
777C23—1881no—
778C23C2×(C2×D47)⋊C411yescharacteristic
779C23C2×(C2×D47)⋊C411yescharacteristic
780C23C22×C4×D4711yescharacteristic
781Q8—1882no—
782Q8—1882no—
783D4—1882no—
784D4—1882no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—472no—
798C2×C4—941no—
799C2×C4—941no—
800C2×C4—941no—
801C2×C4—941no—
802C2×C4—941no—
803C2×C4—941no—
804C2×C4—941no—
805C2×C4—941no—
806C2×C4—941no—
807C2×C4—941no—
808C2×C4—941no—
809C2×C4—941no—
810C2×C4—1882no—
811C2×C4—1882no—
812C2×C4—1882no—
813C2×C4—1882no—
814C2×C4—1882no—
815C2×C4—1882no—
816C2×C4—1881no—
817C2×C4—1881no—
818C2×C4—1881no—
819C2×C4—1881no—
820C2×C4C2×(C2×D47)⋊C411yescharacteristic
821C2×C4C2×(C2×D47)⋊C411yescharacteristic
822C2×C4C2×(C2×D47)⋊C411yescharacteristic
823C2×C4C2×(C2×D47)⋊C411yescharacteristic
824C2×C4C2×(C2×D47)⋊C411yescharacteristic
825C2×C4C2×(C2×D47)⋊C411yescharacteristic
826C2×C4C2×(C2×D47)⋊C411yescharacteristic
827C2×C4C2×(C2×D47)⋊C411yescharacteristic
828C2×C4C2×(C2×D47)⋊C411yescharacteristic
829C2×C4C2×(C2×D47)⋊C411yescharacteristic
830C2×C4C22×C22⋊D4711yescharacteristic
831C2×C4C22×D18811yescharacteristic
832C8—41no—
833C8—41no—
834C8—41no—
835C8—41no—
836C8—1881no—
837C8—1881no—
838C8—1881no—
839C8—1881no—
840C22—21no—
841C22—21no—
842C22—21no—
843C22—21no—
844C22—21no—
845C22—21no—
846C22—21no—
847C22—42no—
848C22—42no—
849C22—3761no—
850C22—3761no—
851C22—1881no—
852C22—1881no—
853C22—1881no—
854C22#1568909612yes—
855C22C22×(C2×D47)⋊C411yescharacteristic
856C22#131×D4711yescharacteristic
857C22#1568988811yescharacteristic
858C4—21no—
859C4—21no—
860C4—21no—
861C4—21no—
862C4—21no—
863C4—21no—
864C4—21no—
865C4—21no—
866C4—21no—
867C4—21no—
868C4—21no—
869C4—21no—
870C4—942no—
871C4—1881no—
872C4—1881no—
873C4—1881no—
874C4—1881no—
875C4—1881no—
876C4—1881no—
877C2—21no—
878C2—21no—
879C2—22no—
880C2—41no—
881C2—3761no—
882C2#2025183511yescharacteristic
883C2C2×#1568909611yescharacteristic
884C2#2025187011yescharacteristic
subgroupG/H
centerC22C22×(C2×D47)⋊C4
commutatorC23×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2924C2
socleC22×C47C22×C22⋊C4
prime radicalC22×C22⋊D47C2×C4
cosocleC22×C4×C47C24
hypercenter#2924D47
hypocenterC47#17417
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2924

Complements

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

NH ≅ G/Ntype
2. #20252046C2semidirect
3. #20241758C2semidirect
4. #20241755C2semidirect
5. #20241745C2semidirect
6. #20241743C2semidirect
9. #20241731C2semidirect
10. #20241720C2semidirect
11. #20241717C2semidirect
12. #20241711C2semidirect
13. #20241700C2semidirect
14. C2×#15688848C2semidirect
15. C47×#2924C2semidirect
437. #2924D47semidirect
517. C47#17417semidirect

Maximal subgroups

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

subgroupindex
C2×#156898062
#202520462
#202417582
#202417552
#202417452
#202417432
#202417372
#202417342
#202417312
#202417202
#202417172
#202417112
#202417002
C2×#156888482
C47×#29242
#1741747