Finite Group Databasebeta

← #26183799

Subgroups — #26183799

Order 12032.

1060 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257420C211yesmaximal, characteristic
2#20252423C211yesmaximal, characteristic, complemented
3#20241963C211yesmaximal, characteristic, complemented
4#20241955C211yesmaximal, characteristic, complemented
5#20241947C211yesmaximal, characteristic, complemented
6#20241942C211yesmaximal, characteristic, complemented
7#20241934C211yesmaximal, characteristic, complemented
8#20241929C211yesmaximal, characteristic, complemented
9#20241924C211yesmaximal, characteristic, complemented
10#20241916C211yesmaximal, characteristic, complemented
11#20241903C211yesmaximal, characteristic, complemented
12#20241890C211yesmaximal, characteristic, complemented
13#20241877C211yesmaximal, characteristic, complemented
14C2×#15688856C211yesmaximal, characteristic, complemented
15C47×#2318C211yesmaximal, characteristic, complemented
16#15689838C411yescharacteristic, complemented
17#15689830C411yescharacteristic, complemented
18#15689821—21no—
19#15689819C411yescharacteristic, complemented
20#15689819C411yescharacteristic, complemented
21#15689794C411yescharacteristic, complemented
22#15689769C411yescharacteristic, complemented
23#15689769C411yescharacteristic, complemented
24#15689763—21no—
25#15689763—21no—
26D4×D188C411yescharacteristic, complemented
27D4×C22⋊D47—21no—
28#15689724—21no—
29#15689706—21no—
30#15689706—21no—
31#15689673C2211yescharacteristic
32#15689657C2211yescharacteristic
33#15689634C2211yescharacteristic
34#15689634C2211yescharacteristic
35C2×#13093998C2211yescharacteristic
36C2×#13093998C2211yescharacteristic
37#15689595—21no—
38#15689201—21no—
39#15689195—21no—
40#15689195—21no—
41D4×C47⋊C8—21no—
42#15689180C2211yescharacteristic, complemented
43#15689176C2211yescharacteristic, complemented
44#15689087C2211yescharacteristic, complemented
45#15689087C2211yescharacteristic, complemented
46C2×C22⋊(C47⋊C8)C2211yescharacteristic, complemented
47C2×C22⋊(C47⋊C8)C2211yescharacteristic, complemented
48#15688859C2211yescharacteristic, complemented
49#15688859C2211yescharacteristic, complemented
50#15688859C2211yescharacteristic, complemented
51#15688859C2211yescharacteristic, complemented
52#15688856C2211yescharacteristic
53#15688856C2211yescharacteristic
54#15688856C2211yescharacteristic
55#15688856C2211yescharacteristic
56#15688856C2211yescharacteristic, complemented
57#15688856C2211yescharacteristic, complemented
58#15688856C2211yescharacteristic, complemented
59#15688856C2211yescharacteristic, complemented
60#15688856C2211yescharacteristic, complemented
61#15688856C2211yescharacteristic, complemented
62#15688856C2211yescharacteristic, complemented
63#15688856C2211yescharacteristic, complemented
64C2×C4×D4×C47C2211yescharacteristic
65C47×#388—21no—
66C47×#387—21no—
67C47×#386—21no—
68C47×#385—21no—
69C47×#383C2211yescharacteristic, complemented
70C47×#382C2211yescharacteristic, complemented
71C47×#381C2211yescharacteristic, complemented
72C47×#380C2211yescharacteristic, complemented
73C4×C22⋊C4×C47C2211yescharacteristic, complemented
74C2×#95×C47C2211yescharacteristic, complemented
75C2×#10625350—21no—
76C2×#10625350C2×C411yescharacteristic
77C2×#10625350C2×C411yescharacteristic, complemented
78C22×D188C2×C411yescharacteristic
79C22×D188C2×C411yescharacteristic, complemented
80C22×C22⋊D47—21no—
81C22×C22⋊D47—21no—
82C2×D4×D47—21no—
83C2×#10625329—21no—
84C2×#10625329—21no—
85C22×C47⋊C8—21no—
86C22×C47⋊C8—21no—
87#13094024C2×C411yescharacteristic, complemented
88#13094021C2×C411yescharacteristic, complemented
89#13094020—21no—
90#13094019—21no—
91#13094019—21no—
92#13094018—21no—
93#13094016C2×C411yescharacteristic, complemented
94#13094015—21no—
95#13094012—21no—
96#13094012C2×C411yescharacteristic, complemented
97#13094010—21no—
98#13094010—21no—
99#13094009—21no—
100#13094009—21no—
101#13094007—21no—
102#13094007—21no—
103#13094007—21no—
104#13094006—21no—
105#13094006—21no—
106#13094003C2×C411yescharacteristic
107#13094003C2×C411yescharacteristic, complemented
108#13094003C2311yescharacteristic
109#13094001—21no—
110#13094001—21no—
111#13093999—21no—
112#13093998—21no—
113#13093998—21no—
114#13093998—21no—
115#13093998—21no—
116#13093998—21no—
117#13093998C2×C411yescharacteristic
118#13093998C2×C411yescharacteristic
119#13093998C2×C411yescharacteristic
120#13093998C2×C411yescharacteristic, complemented
121#13093998C2×C411yescharacteristic, complemented
122#13093998C2×C411yescharacteristic, complemented
123#13093998C2311yescharacteristic
124#13093998C2311yescharacteristic
125#13093998C2311yescharacteristic
126#13093997—21no—
127#13093997—21no—
128#13093997—21no—
129#13093997—21no—
130#13093996—21no—
131#13093996—21no—
132#13093995—21no—
133#13093994—21no—
134#13093994—21no—
135#13093993—21no—
136#13093993—21no—
137#13093992—21no—
138#13093992—21no—
139C4×Dic94C2×C411yescharacteristic, complemented
140C4×D188—21no—
141C4×D188C2×C411yescharacteristic, complemented
142C4×D188C2×C411yescharacteristic, complemented
143C4×D188C2×C411yescharacteristic, complemented
144D4×Dic47—21no—
145#13093986—21no—
146C4×C22⋊D47—21no—
147C4×C22⋊D47—21no—
148C4×C22⋊D47—21no—
149C4×C22⋊D47—21no—
150C4×C22⋊D47—21no—
151(C22⋊D47)⋊C4—21no—
152(C22⋊D47)⋊C4—21no—
153#13093983C2×C411yescharacteristic
154#13093983C2×C411yescharacteristic, complemented
155#13093982—21no—
156#13093981—21no—
157C2×C4⋊Dic47C2×C411yescharacteristic
158C2×C4⋊Dic47C2×C411yescharacteristic, complemented
159C2×(C2×D47)⋊C4—21no—
160C2×(C2×D47)⋊C4—21no—
161C22⋊C4×D47—21no—
162C22⋊C4×D47—21no—
163C4⋊(C47⋊C8)—21no—
164C4⋊(C47⋊C8)—21no—
165C22⋊(C47⋊C8)—21no—
166C22⋊(C47⋊C8)—21no—
167C22⋊(C47⋊C8)—21no—
168C22⋊(C47⋊C8)—21no—
169C22⋊(C47⋊C8)C2311yescharacteristic
170C22⋊(C47⋊C8)C2311yescharacteristic
171C22⋊(C47⋊C8)C2311yescharacteristic
172C22⋊(C47⋊C8)C2311yescharacteristic
173#13093935—21no—
174C4×C47⋊C8—21no—
175C22×D4×C47D411yescharacteristic
176C23×C4×C47—21no—
177C23×C4×C47C2311yescharacteristic
178C23×C4×C47C2311yescharacteristic
179C4×D4×C47C2×C411yescharacteristic
180C4×D4×C47C2×C411yescharacteristic
181C4×D4×C47C2×C411yescharacteristic
182C4×D4×C47C2×C411yescharacteristic
183C4×D4×C47D411yescharacteristic
184C4×D4×C47D411yescharacteristic
185C4×D4×C47D411yescharacteristic
186C4×D4×C47D411yescharacteristic
187C2×C4⋊C4×C47—21no—
188C2×C4⋊C4×C47—21no—
189C2×C4⋊C4×C47D411yescharacteristic
190C2×C22⋊C4×C47—21no—
191C2×C22⋊C4×C47—21no—
192C2×C22⋊C4×C47—21no—
193C2×C22⋊C4×C47D411yescharacteristic
194C2×C22⋊C4×C47D411yescharacteristic
195C2×C42×C47—21no—
196C2×C42×C47C2311yescharacteristic
197#95×C47—21no—
198#95×C47—21no—
199#95×C47—21no—
200#95×C47—21no—
201#95×C47—21no—
202#95×C47C2311yescharacteristic
203#95×C47C2311yescharacteristic
204#95×C47C2311yescharacteristic
205#95×C47C2311yescharacteristic
206C24×C47C2×D411yescharacteristic
207C24×C47C2×D411yescharacteristic
208C23×D47—21no—
209C23×D47—21no—
210C2×D4×C47—42no—
211C2×D4×C47C22⋊C411yescharacteristic
212C2×D4×C47C22⋊C411yescharacteristic
213C2×D4×C47C22⋊C411yescharacteristic
214C2×D4×C47C22⋊C411yescharacteristic
215C22×C4×C47—21no—
216C22×C4×C47—21no—
217C22×C4×C47—21no—
218C22×C4×C47—21no—
219C22×C4×C47—42no—
220C22×C4×C47—81no—
221C22×C4×C47—81no—
222C22×C4×C47—81no—
223C22×C4×C47—81no—
224C22×C4×C47C22×C411yescharacteristic
225C22×C4×C47C22×C411yescharacteristic
226C22×C4×C47C22×C411yescharacteristic
227C22×C4×C47C22×C411yescharacteristic
228C22×C4×C47C2×D411yescharacteristic
229C22×C4×C47C2×D411yescharacteristic
230C22×C4×C47C2×D411yescharacteristic
231C22×C4×C47C2×D411yescharacteristic
232C22×C4×C47C2×D411yescharacteristic
233C22×C4×C47C2×D411yescharacteristic
234C22×C4×C47C2×D411yescharacteristic
235C22×C4×C47C2×D411yescharacteristic
236C22×C4×C47C2411yescharacteristic
237C2×C22⋊D47—21no—
238C2×C22⋊D47—21no—
239C2×C22⋊D47—21no—
240C2×C22⋊D47—21no—
241C2×C22⋊D47—21no—
242C2×C22⋊D47—21no—
243C2×C22⋊D47—21no—
244C2×C22⋊D47—21no—
245C2×C22⋊D47—21no—
246C2×C22⋊D47—21no—
247C2×C22⋊D47—21no—
248C2×C22⋊D47—81no—
249C2×C22⋊D47—81no—
250C2×C22⋊D47—81no—
251C2×C22⋊D47—81no—
252C22×Dic47—21no—
253C22×Dic47—21no—
254D4×D47—44no—
255#10625350—81no—
256#10625350—81no—
257#10625350—81no—
258#10625350—81no—
259C2×D188—21no—
260C2×D188—21no—
261C2×D188—21no—
262C2×D188—21no—
263C2×D188—81no—
264C2×D188—81no—
265C2×D188C22×C411yescharacteristic
266C2×D188C22×C411yescharacteristic
267C2×D188C22×C411yescharacteristic
268C2×C4×D47—21no—
269C2×C4×D47—21no—
270C2×C4×D47—21no—
271C2×C4×D47—21no—
272C2×C4×D47—21no—
273C2×Dic94—21no—
274C2×Dic94C22×C411yescharacteristic
275C4⋊C4×C47—81no—
276C4⋊C4×C47—81no—
277C4⋊C4×C47C22⋊C411yescharacteristic
278C4⋊C4×C47C22⋊C411yescharacteristic
279C4⋊C4×C47C22⋊C411yescharacteristic
280C4⋊C4×C47C22⋊C411yescharacteristic
281C22⋊C4×C47—42no—
282C22⋊C4×C47—81no—
283C22⋊C4×C47—81no—
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
291C22⋊C4×C47C22⋊C411yescharacteristic
292C42×C47—81no—
293C42×C47C22×C411yescharacteristic
294C42×C47C22×C411yescharacteristic
295C42×C47C2×D411yescharacteristic
296C42×C47C2×D411yescharacteristic
297C22⋊Dic47—21no—
298C22⋊Dic47—21no—
299C22⋊Dic47—21no—
300C22⋊Dic47—21no—
301C22⋊Dic47—21no—
302(C2×D47)⋊C4—21no—
303(C2×D47)⋊C4—21no—
304(C2×D47)⋊C4—21no—
305(C2×D47)⋊C4—21no—
306(C2×D47)⋊C4—21no—
307(C2×D47)⋊C4—21no—
308(C2×D47)⋊C4—21no—
309(C2×D47)⋊C4—21no—
310(C2×D47)⋊C4—21no—
311(C2×D47)⋊C4—21no—
312(C2×D47)⋊C4—21no—
313(C2×D47)⋊C4—21no—
314(C2×D47)⋊C4—21no—
315(C2×D47)⋊C4—21no—
316C4⋊Dic47—21no—
317C4⋊Dic47—21no—
318C4⋊Dic47—21no—
319C4⋊Dic47C22×C411yescharacteristic
320C4⋊Dic47C22×C411yescharacteristic
321C4⋊Dic47C22×C411yescharacteristic
322C4⋊Dic47C22×C411yescharacteristic
323Dic47⋊C4—21no—
324Dic47⋊C4—21no—
325Dic47⋊C4—21no—
326Dic47⋊C4—21no—
327Dic47⋊C4—21no—
328Dic47⋊C4—21no—
329C4×Dic47—21no—
330C4×Dic47—21no—
331C4×Dic47—21no—
332#10625329—81no—
333#10625329—81no—
334C2×C47⋊C8—21no—
335C2×C47⋊C8—21no—
336C2×C47⋊C8—21no—
337C2×C47⋊C8—21no—
338C2×C47⋊C8—81no—
339C2×C47⋊C8—81no—
340C23×C47—21no—
341C23×C47—21no—
342C23×C47—22no—
343C23×C47—21no—
344C23×C47—21no—
345C23×C47—41no—
346C23×C47—41no—
347C23×C47—41no—
348C23×C47C2×C22⋊C411yescharacteristic
349C23×C47C2×C22⋊C411yescharacteristic
350C23×C47C2×C22⋊C411yescharacteristic
351C23×C47C2×C22⋊C411yescharacteristic
352C23×C47C22×D411yescharacteristic
353C22×D47—21no—
354C22×D47—21no—
355C22×D47—21no—
356C22×D47—42no—
357C22×D47—42no—
358C22×D47—81no—
359C22×D47—81no—
360C22×D47—81no—
361C22×D47—81no—
362D4×C47—22no—
363D4×C47—22no—
364D4×C47—41no—
365D4×C47—41no—
366C2×C4×C47—21no—
367C2×C4×C47—21no—
368C2×C4×C47—41no—
369C2×C4×C47—41no—
370C2×C4×C47—41no—
371C2×C4×C47—41no—
372C2×C4×C47—41no—
373C2×C4×C47—41no—
374C2×C4×C47—41no—
375C2×C4×C47—41no—
376C2×C4×C47—41no—
377C2×C4×C47—41no—
378C2×C4×C47—41no—
379C2×C4×C47—41no—
380C2×C4×C47—41no—
381C2×C4×C47—41no—
382C2×C4×C47—41no—
383C2×C4×C47—41no—
384C2×C4×C47—41no—
385C2×C4×C47—41no—
386C2×C4×C47—41no—
387C2×C4×C47—41no—
388C2×C4×C47—41no—
389C2×C4×C47—41no—
390C2×C4×C47—41no—
391C2×C4×C47—41no—
392C2×C4×C47—84no—
393C2×C4×C47C2×C22⋊C411yescharacteristic
394C2×C4×C47C2×C22⋊C411yescharacteristic
395C2×C4×C47C2×C22⋊C411yescharacteristic
396C2×C4×C47C2×C22⋊C411yescharacteristic
397C2×C4×C47C2×C22⋊C411yescharacteristic
398C2×C4×C47C2×C22⋊C411yescharacteristic
399C2×C4×C47C2×C22⋊C411yescharacteristic
400C2×C4×C47C2×C22⋊C411yescharacteristic
401C2×C4×C47C23×C411yescharacteristic
402C2×C4×C47C22×D411yescharacteristic
403C22⋊D47—42no—
404C22⋊D47—41no—
405C22⋊D47—41no—
406C22⋊D47—41no—
407C22⋊D47—41no—
408C22⋊D47—41no—
409C22⋊D47—41no—
410C22⋊D47—42no—
411C22⋊D47—81no—
412C22⋊D47—81no—
413C22⋊D47—81no—
414C22⋊D47—81no—
415C22⋊D47—81no—
416C22⋊D47—81no—
417C2×Dic47—21no—
418C2×Dic47—21no—
419C2×Dic47—21no—
420C2×Dic47—21no—
421C2×Dic47—21no—
422C2×Dic47—81no—
423C2×Dic47—81no—
424D188—41no—
425D188—41no—
426D188—41no—
427D188—42no—
428D188—81no—
429D188—81no—
430D188—81no—
431C4×D47—42no—
432C4×D47—81no—
433C4×D47—81no—
434C4×D47—81no—
435C4×D47—81no—
436Dic94—41no—
437Dic94—81no—
438C47⋊C8—41no—
439C47⋊C8—41no—
440C47⋊C8—41no—
441C47⋊C8—41no—
442#17597—471nomaximal, Sylow
443C22×C47—21no—
444C22×C47—21no—
445C22×C47—21no—
446C22×C47—21no—
447C22×C47—21no—
448C22×C47—21no—
449C22×C47—21no—
450C22×C47—21no—
451C22×C47—21no—
452C22×C47—21no—
453C22×C47—21no—
454C22×C47—21no—
455C22×C47—21no—
456C22×C47—42no—
457C22×C47—42no—
458C22×C47—81no—
459C22×C47—81no—
460C22×C47#42112yes—
461C22×C47C22×C22⋊C411yescharacteristic
462C22×C47#57611yescharacteristic
463C22×C47#57711yescharacteristic
464C2×D47—41no—
465C2×D47—41no—
466C2×D47—41no—
467C2×D47—41no—
468C2×D47—41no—
469C2×D47—41no—
470C2×D47—41no—
471C2×D47—41no—
472C2×D47—41no—
473C2×D47—162no—
474C2×D47—162no—
475C4×C47—21no—
476C4×C47—21no—
477C4×C47—21no—
478C4×C47—21no—
479C4×C47—21no—
480C4×C47—21no—
481C4×C47—21no—
482C4×C47—21no—
483C4×C47—21no—
484C4×C47—21no—
485C4×C47—81no—
486C4×C47—81no—
487C4×C47—81no—
488C4×C47—81no—
489Dic47—41no—
490Dic47—41no—
491Dic47—41no—
492Dic47—41no—
493Dic47—41no—
494#3519—471no—
495#2974—471no—
496#2318D4711yescharacteristic, complemented
497#1521—471no—
498#1519—471no—
499#1517—471no—
500#1516—471no—
501#1514—471no—
502#1513—471no—
503#1512—471no—
504#1510—471no—
505#1507—471no—
506#1504—471no—
507#1501—471no—
508C2×#327—471no—
509C2×C47—21no—
510C2×C47—21no—
511C2×C47—22no—
512C2×C47—41no—
513C2×C47—41no—
514C2×C47—41no—
515C2×C47#288311yescharacteristic
516C2×C47#289711yescharacteristic
517C2×C47C2×#42111yescharacteristic
518D47—81no—
519D47—81no—
520D47—81no—
521#555—471no—
522#554—471no—
523#553—471no—
524#553—471no—
525#553—941no—
526#550—471no—
527#546—471no—
528#546—471no—
529#546—941no—
530#546—941no—
531D42—471no—
532D42—941no—
533#540—941no—
534#538—941no—
535#538—941no—
536#532—471no—
537#529—471no—
538#525—471no—
539#525—471no—
540C2×#121—471no—
541C2×#121—471no—
542#518—941no—
543C2×C4×D4C2×D4711yescharacteristic
544#436—941no—
545#435—941no—
546#435—941no—
547C8×D4—941no—
548#432—471no—
549#431—471no—
550#407—471no—
551#407—471no—
552C2×C22⋊C8—471no—
553C2×C22⋊C8—471no—
554#388—21no—
555#387—21no—
556#386—21no—
557#385—21no—
558#383C2×D4711yescharacteristic, complemented
559#382C2×D4711yescharacteristic, complemented
560#381C2×D4711yescharacteristic, complemented
561#380C2×D4711yescharacteristic, complemented
562C4×C22⋊C4C2×D4711yescharacteristic, complemented
563C2×#95C2×D4711yescharacteristic, complemented
564#328—471no—
565#328—471no—
566#328—471no—
567#328—471no—
568#327—471no—
569#327—471no—
570#327—471no—
571#327—471no—
572#327—471no—
573#327—471no—
574#327—471no—
575#327—471no—
576#327—471no—
577#327—471no—
578#327—471no—
579#327—471no—
580C47#1759711yescharacteristic, complemented, Sylow
581C2×#41—471no—
582C2×#41—471no—
583C2×#41—941no—
584C22×D4—471no—
585C22×D4—471no—
586C22×D4—941no—
587C22×D4—941no—
588C22×D4—941no—
589C22×D4C22⋊D4711yescharacteristic
590C23×C4—21no—
591C23×C4C22×D4711yescharacteristic
592C23×C4C22×D4711yescharacteristic
593C2×M16—941no—
594C2×M16—941no—
595C22×C8—941no—
596C22×C8—941no—
597C4⋊Q8—471no—
598#127—471no—
599#127—941no—
600#126—941no—
601#126—941no—
602#126—941no—
603#125—471no—
604#125—941no—
605#124—471no—
606#124—941no—
607#124—941no—
608#124—941no—
609#123—941no—
610#123—941no—
611#123—941no—
612#123—941no—
613#123—941no—
614#123—941no—
615#123—941no—
616C22⋊Q8—471no—
617C22⋊Q8—471no—
618C22⋊Q8—471no—
619C22⋊Q8—941no—
620C22⋊Q8—941no—
621#121—471no—
622#121—471no—
623#121—471no—
624#121—471no—
625#121—471no—
626#121—471no—
627#121—471no—
628#121—471no—
629#121—471no—
630#121—941no—
631#121—941no—
632#121—941no—
633#121—941no—
634#121—941no—
635#121—941no—
636#121—941no—
637#121—941no—
638#121—941no—
639#121—941no—
640#121—941no—
641#121—941no—
642#121—941no—
643#120—941no—
644#120—941no—
645#120—941no—
646#120—941no—
647#120—941no—
648#120—941no—
649C4×Q8—471no—
650C4×D4—471no—
651C4×D4—471no—
652C4×D4—471no—
653C4×D4—941no—
654C4×D4—941no—
655C4×D4—941no—
656C4×D4—941no—
657C4×D4—941no—
658C4×D4—941no—
659C4×D4—941no—
660C4×D4—941no—
661C4×D4—941no—
662C4×D4—941no—
663C4×D4C4×D4711yescharacteristic
664C4×D4C4×D4711yescharacteristic
665C4×D4C4×D4711yescharacteristic
666C4×D4C4×D4711yescharacteristic
667C4×D4D18811yescharacteristic
668C4×D4D18811yescharacteristic
669C4×D4D18811yescharacteristic
670C4×D4D18811yescharacteristic
671#117—471no—
672#117—471no—
673#117—941no—
674#117—941no—
675C2×C4⋊C4—21no—
676C2×C4⋊C4—21no—
677C2×C4⋊C4—471no—
678C2×C4⋊C4—471no—
679C2×C4⋊C4C22⋊D4711yescharacteristic
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—941no—
684C2×C22⋊C4—941no—
685C2×C22⋊C4—941no—
686C2×C22⋊C4—941no—
687C2×C22⋊C4C22⋊D4711yescharacteristic
688C2×C22⋊C4C22⋊D4711yescharacteristic
689C2×C42—21no—
690C2×C42C22×D4711yescharacteristic
691C4⋊C8—941no—
692C4⋊C8—941no—
693C22⋊C8—471no—
694C22⋊C8—471no—
695C22⋊C8—471no—
696C22⋊C8—471no—
697C22⋊C8—941no—
698C22⋊C8—941no—
699C22⋊C8—941no—
700C22⋊C8—941no—
701#97—941no—
702C4×C8—941no—
703#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95C22×D4711yescharacteristic
709#95C22×D4711yescharacteristic
710#95C22×D4711yescharacteristic
711#95C22×D4711yescharacteristic
712C24—941no—
713C24—941no—
714C24C2×C22⋊D4711yescharacteristic
715C24C2×C22⋊D4711yescharacteristic
716#41—3761no—
717#41—3761no—
718#41—3761no—
719#41—3761no—
720C2×Q8—471no—
721C2×Q8—941no—
722C2×D4—42no—
723C2×D4—471no—
724C2×D4—471no—
725C2×D4—471no—
726C2×D4—941no—
727C2×D4—941no—
728C2×D4—941no—
729C2×D4—941no—
730C2×D4—941no—
731C2×D4—941no—
732C2×D4—941no—
733C2×D4—941no—
734C2×D4—941no—
735C2×D4—941no—
736C2×D4—941no—
737C2×D4—941no—
738C2×D4—941no—
739C2×D4—941no—
740C2×D4—941no—
741C2×D4—3761no—
742C2×D4—3761no—
743C2×D4—3761no—
744C2×D4—3761no—
745C2×D4—3761no—
746C2×D4—3761no—
747C2×D4—1884no—
748C2×D4(C2×D47)⋊C411yescharacteristic
749C2×D4(C2×D47)⋊C411yescharacteristic
750C2×D4(C2×D47)⋊C411yescharacteristic
751C2×D4(C2×D47)⋊C411yescharacteristic
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—42no—
757C22×C4—81no—
758C22×C4—81no—
759C22×C4—81no—
760C22×C4—81no—
761C22×C4—941no—
762C22×C4—941no—
763C22×C4—941no—
764C22×C4—941no—
765C22×C4—941no—
766C22×C4—941no—
767C22×C4—941no—
768C22×C4C2×C4×D4711yescharacteristic
769C22×C4C2×C4×D4711yescharacteristic
770C22×C4C2×C4×D4711yescharacteristic
771C22×C4C2×C4×D4711yescharacteristic
772C22×C4C2×D18811yescharacteristic
773C22×C4C2×D18811yescharacteristic
774C22×C4C2×D18811yescharacteristic
775C22×C4C2×D18811yescharacteristic
776C22×C4C2×C22⋊D4711yescharacteristic
777C22×C4C2×C22⋊D4711yescharacteristic
778C22×C4C2×C22⋊D4711yescharacteristic
779C22×C4C2×C22⋊D4711yescharacteristic
780C22×C4C23×D4711yescharacteristic
781M16—3761no—
782M16—3761no—
783C2×C8—941no—
784C2×C8—941no—
785C2×C8—941no—
786C2×C8—941no—
787C2×C8—3761no—
788C2×C8—3761no—
789C4⋊C4—81no—
790C4⋊C4—81no—
791C4⋊C4—471no—
792C4⋊C4—471no—
793C4⋊C4—471no—
794C4⋊C4—471no—
795C4⋊C4—941no—
796C4⋊C4—941no—
797C4⋊C4—941no—
798C4⋊C4—941no—
799C4⋊C4—941no—
800C4⋊C4—941no—
801C4⋊C4—941no—
802C4⋊C4—941no—
803C4⋊C4—941no—
804C4⋊C4(C2×D47)⋊C411yescharacteristic
805C4⋊C4(C2×D47)⋊C411yescharacteristic
806C4⋊C4(C2×D47)⋊C411yescharacteristic
807C4⋊C4(C2×D47)⋊C411yescharacteristic
808C22⋊C4—42no—
809C22⋊C4—81no—
810C22⋊C4—81no—
811C22⋊C4—941no—
812C22⋊C4—941no—
813C22⋊C4—941no—
814C22⋊C4—941no—
815C22⋊C4—941no—
816C22⋊C4—941no—
817C22⋊C4—941no—
818C22⋊C4—941no—
819C22⋊C4—941no—
820C22⋊C4—941no—
821C22⋊C4—941no—
822C22⋊C4—941no—
823C22⋊C4—941no—
824C22⋊C4—941no—
825C22⋊C4—941no—
826C22⋊C4—941no—
827C22⋊C4—941no—
828C22⋊C4—941no—
829C22⋊C4—941no—
830C22⋊C4(C2×D47)⋊C411yescharacteristic
831C22⋊C4(C2×D47)⋊C411yescharacteristic
832C22⋊C4(C2×D47)⋊C411yescharacteristic
833C22⋊C4(C2×D47)⋊C411yescharacteristic
834C22⋊C4(C2×D47)⋊C411yescharacteristic
835C22⋊C4(C2×D47)⋊C411yescharacteristic
836C22⋊C4(C2×D47)⋊C411yescharacteristic
837C22⋊C4(C2×D47)⋊C411yescharacteristic
838C42—81no—
839C42—941no—
840C42—941no—
841C42—941no—
842C42C2×C4×D4711yescharacteristic
843C42C2×C4×D4711yescharacteristic
844C42C2×D18811yescharacteristic
845C42C2×D18811yescharacteristic
846C23—22no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—941no—
855C23—941no—
856C23—941no—
857C23—3761no—
858C23—3761no—
859C23—3761no—
860C23—3761no—
861C23—1882no—
862C23—1882no—
863C23C2×(C2×D47)⋊C411yescharacteristic
864C23C2×(C2×D47)⋊C411yescharacteristic
865C23C2×(C2×D47)⋊C411yescharacteristic
866C23C2×(C2×D47)⋊C411yescharacteristic
867C23C22×C22⋊D4711yescharacteristic
868Q8—3761no—
869Q8—1881no—
870D4—22no—
871D4—22no—
872D4—41no—
873D4—41no—
874D4—3761no—
875D4—3761no—
876D4—3761no—
877D4—3761no—
878D4—3761no—
879D4—3761no—
880D4—3761no—
881D4—3761no—
882D4—3761no—
883D4—1881no—
884D4—1881no—
885D4—1881no—
886D4—1882no—
887D4—1882no—
888D4—1882no—
889D4—1881no—
890D4—1881no—
891D4—1881no—
892D4—1881no—
893D4—1881no—
894D4—1881no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—84no—
922C2×C4—941no—
923C2×C4—941no—
924C2×C4—941no—
925C2×C4—941no—
926C2×C4—941no—
927C2×C4—3761no—
928C2×C4—3761no—
929C2×C4—3761no—
930C2×C4—3761no—
931C2×C4—3761no—
932C2×C4—3761no—
933C2×C4—1882no—
934C2×C4C2×(C2×D47)⋊C411yescharacteristic
935C2×C4C2×(C2×D47)⋊C411yescharacteristic
936C2×C4C2×(C2×D47)⋊C411yescharacteristic
937C2×C4C2×(C2×D47)⋊C411yescharacteristic
938C2×C4C2×(C2×D47)⋊C411yescharacteristic
939C2×C4C2×(C2×D47)⋊C411yescharacteristic
940C2×C4C2×(C2×D47)⋊C411yescharacteristic
941C2×C4C2×(C2×D47)⋊C411yescharacteristic
942C2×C4C22×C4×D4711yescharacteristic
943C2×C4C22×D18811yescharacteristic
944C8—1881no—
945C8—1881no—
946C8—1881no—
947C8—1881no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—21no—
961C22—42no—
962C22—42no—
963C22—81no—
964C22—81no—
965C22—1881no—
966C22—1881no—
967C22—1881no—
968C22—1881no—
969C22—1881no—
970C22—1881no—
971C22—1881no—
972C22—1881no—
973C22—1881no—
974C22—7522no—
975C22—7522no—
976C22#1568914112yes—
977C22C22×(C2×D47)⋊C411yescharacteristic
978C22#1568992611yescharacteristic
979C22#1568993111yescharacteristic
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—21no—
987C4—21no—
988C4—21no—
989C4—21no—
990C4—81no—
991C4—81no—
992C4—81no—
993C4—81no—
994C4—1881no—
995C4—1881no—
996C4—1881no—
997C4—1881no—
998C4—1881no—
999C2—21no—
1000C2—21no—
1001C2—22no—
1002C2—41no—
1003C2—41no—
1004C2—41no—
1005C2—3761no—
1006C2—3761no—
1007C2—3761no—
1008C2#2025184811yescharacteristic
1009C2#2025191111yescharacteristic
1010C2C2×#1568914111yescharacteristic
subgroupG/H
centerC22C22×(C2×D47)⋊C4
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2318C2
socleC22×C47C22×C22⋊C4
prime radical#20257420C2
cosocleC22×C4×C47C24
hypercenter#2318D47
hypocenterC47#17597
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2318

Complements

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

NH ≅ G/Ntype
2. #20252423C2semidirect
3. #20241963C2semidirect
4. #20241955C2semidirect
5. #20241947C2semidirect
6. #20241942C2semidirect
7. #20241934C2semidirect
8. #20241929C2semidirect
9. #20241924C2semidirect
10. #20241916C2semidirect
11. #20241903C2semidirect
12. #20241890C2semidirect
13. #20241877C2semidirect
14. C2×#15688856C2semidirect
15. C47×#2318C2semidirect
16. #15689838C4semidirect
17. #15689830C4semidirect
19. #15689819C4semidirect
20. #15689819C4semidirect
21. #15689794C4semidirect
22. #15689769C4semidirect
23. #15689769C4semidirect
26. D4×D188C4semidirect
42. #15689180C22semidirect
43. #15689176C22semidirect
44. #15689087C22semidirect
45. #15689087C22semidirect
46. C2×C22⋊(C47⋊C8)C22semidirect
47. C2×C22⋊(C47⋊C8)C22semidirect
48. #15688859C22semidirect
49. #15688859C22semidirect
50. #15688859C22semidirect
51. #15688859C22semidirect
56. #15688856C22semidirect
57. #15688856C22semidirect
58. #15688856C22semidirect
59. #15688856C22semidirect
60. #15688856C22semidirect
61. #15688856C22semidirect
62. #15688856C22semidirect
63. #15688856C22semidirect
69. C47×#383C22semidirect
70. C47×#382C22semidirect
71. C47×#381C22semidirect
72. C47×#380C22semidirect
73. C4×C22⋊C4×C47C22semidirect
74. C2×#95×C47C22semidirect
77. C2×#10625350C2×C4semidirect
79. C22×D188C2×C4semidirect
87. #13094024C2×C4semidirect
88. #13094021C2×C4semidirect
93. #13094016C2×C4semidirect
96. #13094012C2×C4semidirect
107. #13094003C2×C4semidirect
120. #13093998C2×C4semidirect
121. #13093998C2×C4semidirect
122. #13093998C2×C4semidirect
139. C4×Dic94C2×C4semidirect
141. C4×D188C2×C4semidirect
142. C4×D188C2×C4semidirect
143. C4×D188C2×C4semidirect
154. #13093983C2×C4semidirect
158. C2×C4⋊Dic47C2×C4semidirect
496. #2318D47semidirect
558. #383C2×D47semidirect
559. #382C2×D47semidirect
560. #381C2×D47semidirect
561. #380C2×D47semidirect
562. C4×C22⋊C4C2×D47semidirect
563. C2×#95C2×D47semidirect
580. C47#17597semidirect

Maximal subgroups

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

subgroupindex
#202574202
#202524232
#202419632
#202419552
#202419472
#202419422
#202419342
#202419292
#202419242
#202419162
#202419032
#202418902
#202418772
C2×#156888562
C47×#23182
#1759747