Finite Group Databasebeta

← #10762162

Subgroups — #10762162

Order 768.

1096 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#86153C211yesmaximal, characteristic
2#79340C211yesmaximal, characteristic, complemented
3C4×#901C211yesmaximal, characteristic, complemented
4C3×#1494C211yesmaximal, characteristic, complemented
5#71751C211yesmaximal, characteristic, complemented
6#70799C211yesmaximal, characteristic, complemented
7C2×#4459C211yesmaximal, characteristic, complemented
8#68241C211yesmaximal, characteristic, complemented
9#68238C211yesmaximal, characteristic, complemented
10#68234C211yesmaximal, characteristic, complemented
11#68229C211yesmaximal, characteristic, complemented
12#68176C211yesmaximal, characteristic, complemented
13#68175C211yesmaximal, characteristic, complemented
14#68171C211yesmaximal, characteristic, complemented
15D3×D4⋊C8C211yesmaximal, characteristic, complemented
16#17517—31nomaximal, Sylow
17C3×#529C2211yescharacteristic
18C2×#901—21no—
19#5709—21no—
20#5705—21no—
21#5695C411yescharacteristic
22#5690C411yescharacteristic
23#5681C411yescharacteristic
24#5676C411yescharacteristic
25#5658—21no—
26#5654—21no—
27#5635C411yescharacteristic
28#5630C411yescharacteristic
29#5618C411yescharacteristic
30#5609C411yescharacteristic
31#5580C2211yescharacteristic
32C4×#239C2211yescharacteristic
33#5548C2211yescharacteristic
34#5547—21no—
35C4×D3×D4—21no—
36C4×D3×D4C2211yescharacteristic
37#5528—21no—
38#5524—21no—
39C4×#235C2211yescharacteristic
40C2×C4×D12C2211yescharacteristic
41C3×#432C2211yescharacteristic, complemented
42C2×C3×C4×C8C2211yescharacteristic, complemented
43#5101—21no—
44C2×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
45C4×#208C2211yescharacteristic, complemented
46#4837C2211yescharacteristic, complemented
47#4835C2211yescharacteristic, complemented
48#4833C2211yescharacteristic, complemented
49D3×C4⋊C8C2211yescharacteristic, complemented
50#4730—21no—
51#67⋊C8—21no—
52#4706—21no—
53#4701—21no—
54#4689—21no—
55#4689—21no—
56C4×ΓL(1,𝔽25)C2211yescharacteristic, complemented
57C4×ΓL(1,𝔽25)C2211yescharacteristic, complemented
58C4×D3×C8C2211yescharacteristic, complemented
59C4×D3×C8C2211yescharacteristic, complemented
60C3×Q8⋊C8C2211yescharacteristic, complemented
61C3×Q8⋊C8C2211yescharacteristic, complemented
62C3×D4⋊C8C2211yescharacteristic, complemented
63C3×D4⋊C8C2211yescharacteristic, complemented
64#4535C2211yescharacteristic, complemented
65#4535C2211yescharacteristic, complemented
66D4⋊(C3⋊C8)C2211yescharacteristic, complemented
67D4⋊(C3⋊C8)C2211yescharacteristic, complemented
68#4483C2211yescharacteristic
69#4483C2211yescharacteristic
70#4483C2211yescharacteristic, complemented
71#4483C2211yescharacteristic, complemented
72#4459C2211yescharacteristic
73#4459C2211yescharacteristic
74#4459C2211yescharacteristic, complemented
75#4459C2211yescharacteristic, complemented
76#3481—31no—
77#2990—31no—
78C4×#131—31no—
79#1494—31no—
80#1494D311yescharacteristic, complemented
81#1492—31no—
82#1490—31no—
83#1490—31no—
84#1489—31no—
85#1484—31no—
86#1483—31no—
87#1483—31no—
88#1476—31no—
89C2×D4⋊C8—31no—
90C2×D4⋊C8—31no—
91C2×#239C2×C411yescharacteristic
92C2×D3×D4—21no—
93C2×D3×D4C2×C411yescharacteristic
94C2×#235—21no—
95C2×#235D411yescharacteristic
96C22×D12C2×C411yescharacteristic
97C22×C4×D3—21no—
98C22×C4×D3—21no—
99C22×C3×C8—21no—
100C3×#126—21no—
101C3×#125C2×C411yescharacteristic
102C3×#124C2×C411yescharacteristic
103C3×#123—21no—
104C3×C22⋊Q8C2×C411yescharacteristic
105C3×#121C2×C411yescharacteristic
106C3×C4×Q8C2311yescharacteristic
107C3×C4×D4—21no—
108C3×C4×D4C2311yescharacteristic
109C3×#117—21no—
110C2×C3×C42C2311yescharacteristic
111#947C2×C411yescharacteristic
112#946C2×C411yescharacteristic
113Q8×Dic3C2×C411yescharacteristic
114#940C2×C411yescharacteristic
115#939—21no—
116#938C2×C411yescharacteristic
117#937—21no—
118D4×Dic3—21no—
119D4×Dic3C2×C411yescharacteristic
120C4×#67—21no—
121C4×#67—21no—
122C4×#67C2×C411yescharacteristic
123C4×#67C2×C411yescharacteristic
124C4×#67D411yescharacteristic
125C4×#67D411yescharacteristic
126C2×(C2×D3)⋊C4—21no—
127#926D411yescharacteristic
128C2×C4⋊Dic3C2×C411yescharacteristic
129C2×#208—21no—
130C22×C3⋊C8—21no—
131#901—28no—
132C2×ΓL(1,𝔽25)—21no—
133C2×ΓL(1,𝔽25)—21no—
134C2×ΓL(1,𝔽25)—21no—
135C2×D3×C8—21no—
136C2×D3×C8—21no—
137C2×D3×C8—21no—
138#898—21no—
139#898—21no—
140#897—21no—
141#897—21no—
142#896—21no—
143#896—21no—
144#895—21no—
145#895—21no—
146#895C2×C411yescharacteristic
147#895C2×C411yescharacteristic
148#894—21no—
149#894—21no—
150#894—21no—
151#893—21no—
152#893—21no—
153#893C2×C411yescharacteristic
154#893C2×C411yescharacteristic
155#892—21no—
156#892C2×C411yescharacteristic
157D3×C4⋊C4—21no—
158D3×C4⋊C4C2×C411yescharacteristic
159#890C2×C411yescharacteristic
160#889—21no—
161#888C2×C411yescharacteristic
162#886—21no—
163#886—21no—
164#885—21no—
165#885—21no—
166#884—21no—
167#884—21no—
168#884—21no—
169#883—21no—
170#883—21no—
171#882—21no—
172#882—21no—
173#882—21no—
174#67⋊C4—21no—
175#67⋊C4—21no—
176#67⋊C4—21no—
177D3×C22⋊C4—21no—
178D3×C22⋊C4—21no—
179D3×C22⋊C4—21no—
180#879—21no—
181#878—21no—
182C4×D12—21no—
183C4×D12—21no—
184C4×D12—21no—
185C4×D12—21no—
186C4×D12C2×C411yescharacteristic
187C4×D12C2×C411yescharacteristic
188C4×D12C2×C411yescharacteristic
189C4×D12D411yescharacteristic
190C4×D12C2311yescharacteristic
191C4×D12C2311yescharacteristic
192#872—21no—
193#872D411yescharacteristic
194#872D411yescharacteristic
195C42×D3—21no—
196C42×D3C2311yescharacteristic
197C42×D3C2311yescharacteristic
198C4×Dic6C2×C411yescharacteristic
199C4×Dic6D411yescharacteristic
200C3×C4⋊C8C2311yescharacteristic
201C3×C4⋊C8C2311yescharacteristic
202C3×C22⋊C8—21no—
203C3×#97—21no—
204C3×C4×C8—21no—
205C3×C4×C8C2311yescharacteristic
206C3×C4×C8C2311yescharacteristic
207(C2×D3)⋊C8—21no—
208(C2×D3)⋊C8—21no—
209#815—21no—
210#815—21no—
211#815—21no—
212Dic3⋊C8—21no—
213Dic3⋊C8—21no—
214C8×Dic3—21no—
215C8×Dic3—21no—
216C8×Dic3—21no—
217C4⋊(C3⋊C8)—21no—
218C4⋊(C3⋊C8)C2311yescharacteristic
219C4⋊(C3⋊C8)C2311yescharacteristic
220#803—21no—
221C4×C3⋊C8C2311yescharacteristic
222C4×C3⋊C8C2311yescharacteristic
223C2×#131—61no—
224#559—31no—
225#554—31no—
226#554—31no—
227#553—31no—
228#553—31no—
229#553—61no—
230#551—61no—
231#551—61no—
232#546—31no—
233#546—31no—
234#546—61no—
235D42—31no—
236#532—31no—
237#529—31no—
238#529—61no—
239#529C2×D311yescharacteristic
240#525—61no—
241#525—61no—
242C4×#41—31no—
243C4×#41—31no—
244C2×C4×D4—31no—
245C2×C4×D4—31no—
246C2×C4×D4—61no—
247#446—61no—
248#435—61no—
249#435—61no—
250C8×D4—61no—
251#432—31no—
252#432C2×D311yescharacteristic, complemented
253#431—31no—
254#423—31no—
255C2×C4⋊C8—31no—
256C2×C4⋊C8—31no—
257#405—61no—
258#405—61no—
259#405—61no—
260C4×M16—31no—
261C4×M16—31no—
262C4×M16—31no—
263C2×C4×C8—31no—
264C2×C4×C8—31no—
265C2×C4×C8C2×D311yescharacteristic, complemented
266Q8⋊C8—31no—
267Q8⋊C8—31no—
268Q8⋊C8C2×D311yescharacteristic, complemented
269Q8⋊C8C2×D311yescharacteristic, complemented
270D4⋊C8—31no—
271D4⋊C8—31no—
272D4⋊C8—31no—
273D4⋊C8—31no—
274D4⋊C8—31no—
275D4⋊C8—31no—
276D4⋊C8—31no—
277D4⋊C8—31no—
278D4⋊C8—31no—
279D4⋊C8—31no—
280D4⋊C8C2×D311yescharacteristic, complemented
281D4⋊C8C2×D311yescharacteristic, complemented
282C23×D3—21no—
283C23×D3—21no—
284C2×C3×Q8C22×C411yescharacteristic
285C2×C3×D4—21no—
286C2×C3×D4C22×C411yescharacteristic
287C22×C3×C4—21no—
288C22×C3×C4C22×C411yescharacteristic
289C22×C3×C4C2×D411yescharacteristic
290C22×C3×C4C2×D411yescharacteristic
291C2×#67—21no—
292C2×#67—21no—
293C2×#67—21no—
294C2×#67—21no—
295C2×#67C22⋊C411yescharacteristic
296C2×#67C22⋊C411yescharacteristic
297C22×Dic3—21no—
298C22×Dic3—21no—
299#239—22no—
300#239—41no—
301D3×D4—22no—
302D3×D4—41no—
303D3×D4—44no—
304#235—24no—
305#235—81no—
306#235—81no—
307C2×D12—22no—
308C2×D12—21no—
309C2×D12—21no—
310C2×D12—21no—
311C2×D12—21no—
312C2×D12—41no—
313C2×D12C22⋊C411yescharacteristic
314C2×D12C22×C411yescharacteristic
315C2×D12C22×C411yescharacteristic
316C2×C4×D3—21no—
317C2×C4×D3—21no—
318C2×C4×D3—21no—
319C2×C4×D3—21no—
320C2×C4×D3—21no—
321C2×C4×D3—21no—
322C2×C4×D3—21no—
323C2×C4×D3—21no—
324C2×C4×D3—81no—
325C2×C4×D3—81no—
326C2×C4×D3—81no—
327C2×C4×D3—81no—
328C2×C4×D3C22×C411yescharacteristic
329C2×C4×D3C22×C411yescharacteristic
330C2×C4×D3C2×D411yescharacteristic
331C2×C4×D3C2×D411yescharacteristic
332C2×C4×D3C2×D411yescharacteristic
333C2×C4×D3C2×D411yescharacteristic
334C2×Dic6—21no—
335C2×Dic6C22⋊C411yescharacteristic
336C2×C3×C8—24no—
337C2×C3×C8—21no—
338C2×C3×C8—21no—
339C2×C3×C8—21no—
340C2×C3×C8—21no—
341C3×C4⋊C4—21no—
342C3×C4⋊C4—21no—
343C3×C4⋊C4—21no—
344C3×C4⋊C4—21no—
345C3×C4⋊C4C22×C411yescharacteristic
346C3×C4⋊C4C22×C411yescharacteristic
347C3×C22⋊C4—21no—
348C3×C22⋊C4—21no—
349C3×C22⋊C4—21no—
350C3×C22⋊C4—21no—
351C3×C22⋊C4—21no—
352C3×C42—21no—
353C3×C42C22×C411yescharacteristic
354C3×C42C2×D411yescharacteristic
355C3×C42C2×D411yescharacteristic
356C3×C42C2411yescharacteristic
357#217—21no—
358#217—21no—
359#217C22⋊C411yescharacteristic
360#217C22⋊C411yescharacteristic
361(C2×D3)⋊C4—21no—
362(C2×D3)⋊C4—21no—
363(C2×D3)⋊C4—21no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—21no—
366(C2×D3)⋊C4—21no—
367(C2×D3)⋊C4—21no—
368(C2×D3)⋊C4—21no—
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—21no—
371(C2×D3)⋊C4—21no—
372(C2×D3)⋊C4—21no—
373(C2×D3)⋊C4C22⋊C411yescharacteristic
374(C2×D3)⋊C4C22⋊C411yescharacteristic
375(C2×D3)⋊C4C22⋊C411yescharacteristic
376(C2×D3)⋊C4C22⋊C411yescharacteristic
377C4⋊Dic3—21no—
378C4⋊Dic3—21no—
379C4⋊Dic3—21no—
380C4⋊Dic3C22⋊C411yescharacteristic
381C4⋊Dic3C22⋊C411yescharacteristic
382C4⋊Dic3C22×C411yescharacteristic
383C4⋊Dic3C22×C411yescharacteristic
384Dic3⋊C4—21no—
385Dic3⋊C4—21no—
386Dic3⋊C4—21no—
387Dic3⋊C4—21no—
388Dic3⋊C4C22⋊C411yescharacteristic
389Dic3⋊C4C22⋊C411yescharacteristic
390Dic3⋊C4C22⋊C411yescharacteristic
391Dic3⋊C4C22⋊C411yescharacteristic
392C4×Dic3—21no—
393C4×Dic3—21no—
394C4×Dic3C22×C411yescharacteristic
395C4×Dic3C22×C411yescharacteristic
396C4×Dic3C2×D411yescharacteristic
397C4×Dic3C2×D411yescharacteristic
398C4×Dic3C2×D411yescharacteristic
399C4×Dic3C2×D411yescharacteristic
400#208—24no—
401C2×C3⋊C8—21no—
402C2×C3⋊C8—21no—
403C2×C3⋊C8—21no—
404C2×C3⋊C8—21no—
405C2×C3⋊C8—81no—
406ΓL(1,𝔽25)—24no—
407ΓL(1,𝔽25)—24no—
408ΓL(1,𝔽25)—81no—
409D3×C8—24no—
410D3×C8—24no—
411D3×C8—81no—
412C2×#41—31no—
413C2×#41—31no—
414C2×#41—61no—
415C22×D4—31no—
416C22×D4—31no—
417C22×D4—61no—
418C23×C4—61no—
419C23×C4—61no—
420#131—68no—
421C2×M16—61no—
422C2×M16—61no—
423C2×M16—61no—
424C2×M16—61no—
425C22×C8—21no—
426C22×C8—61no—
427C22×C8—61no—
428C22×C8—61no—
429C22×C8—61no—
430C4⋊Q8—31no—
431#127—31no—
432#126—21no—
433#126—61no—
434#126—61no—
435#126—61no—
436#125—31no—
437#125—61no—
438#125C4×D311yescharacteristic
439#124—31no—
440#124—61no—
441#124—61no—
442#124C4×D311yescharacteristic
443#123—21no—
444#123—61no—
445#123—61no—
446#123—61no—
447#123—61no—
448#123—61no—
449#123—61no—
450#123—61no—
451C22⋊Q8—31no—
452C22⋊Q8—61no—
453C22⋊Q8—61no—
454C22⋊Q8—61no—
455C22⋊Q8—61no—
456C22⋊Q8—61no—
457C22⋊Q8C4×D311yescharacteristic
458#121—31no—
459#121—31no—
460#121—31no—
461#121—61no—
462#121—61no—
463#121—61no—
464#121—61no—
465#121—61no—
466#121—61no—
467#121C4×D311yescharacteristic
468#120—61no—
469#120—61no—
470#120—61no—
471#120—61no—
472C4×Q8—31no—
473C4×Q8—31no—
474C4×Q8—31no—
475C4×Q8C22×D311yescharacteristic
476C4×D4—21no—
477C4×D4—31no—
478C4×D4—31no—
479C4×D4—31no—
480C4×D4—31no—
481C4×D4—31no—
482C4×D4—31no—
483C4×D4—31no—
484C4×D4—31no—
485C4×D4—31no—
486C4×D4—31no—
487C4×D4—31no—
488C4×D4—31no—
489C4×D4—31no—
490C4×D4—61no—
491C4×D4—61no—
492C4×D4—61no—
493C4×D4—61no—
494C4×D4—61no—
495C4×D4—61no—
496C4×D4—61no—
497C4×D4—61no—
498C4×D4—61no—
499C4×D4—61no—
500C4×D4—61no—
501C4×D4—61no—
502C4×D4C22×D311yescharacteristic
503#117—21no—
504#117—31no—
505#117—31no—
506#117—31no—
507#117—31no—
508#117—61no—
509#117—61no—
510C2×C4⋊C4—31no—
511C2×C4⋊C4—31no—
512C2×C4⋊C4—61no—
513C2×C22⋊C4—61no—
514C2×C22⋊C4—61no—
515C2×C22⋊C4—61no—
516C2×C22⋊C4—61no—
517C2×C42—31no—
518C2×C42—31no—
519C2×C42—61no—
520C2×C42C22×D311yescharacteristic
521C4⋊C8—31no—
522C4⋊C8—31no—
523C4⋊C8—61no—
524C4⋊C8—61no—
525C4⋊C8—61no—
526C4⋊C8C22×D311yescharacteristic
527C4⋊C8C22×D311yescharacteristic
528C22⋊C8—21no—
529C22⋊C8—61no—
530C22⋊C8—61no—
531#97—21no—
532#97—61no—
533#97—61no—
534#97—61no—
535#97—61no—
536C4×C8—21no—
537C4×C8—31no—
538C4×C8—31no—
539C4×C8—61no—
540C4×C8—61no—
541C4×C8—61no—
542C4×C8C22×D311yescharacteristic
543C4×C8C22×D311yescharacteristic
544C23×C3—21no—
545C23×C3C2×C22⋊C411yescharacteristic
546C22×D3—21no—
547C22×D3—21no—
548C22×D3—42no—
549C22×D3—42no—
550C22×D3—42no—
551C22×D3—42no—
552C22×D3—81no—
553C22×D3—81no—
554C22×D3C2×C22⋊C411yescharacteristic
555C22×D3C2×C22⋊C411yescharacteristic
556C3×Q8—21no—
557C3×Q8—21no—
558C3×D4—21no—
559C3×D4—21no—
560C3×D4—42no—
561C2×C3×C4—22no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—41no—
570C2×C3×C4—41no—
571C2×C3×C4C2×C22⋊C411yescharacteristic
572C2×C3×C4C2×C22⋊C411yescharacteristic
573C2×C3×C4C2×C22⋊C411yescharacteristic
574C2×C3×C4C23×C411yescharacteristic
575C2×C3×C4C22×D411yescharacteristic
576C2×C3×C4C22×D411yescharacteristic
577#67—22no—
578#67—42no—
579#67—42no—
580#67—81no—
581#67—81no—
582#67#10414yes—
583C2×Dic3—21no—
584C2×Dic3—21no—
585C2×Dic3—81no—
586C2×Dic3—81no—
587C2×Dic3C2×C22⋊C411yescharacteristic
588C2×Dic3C2×C22⋊C411yescharacteristic
589C2×Dic3C2×C22⋊C411yescharacteristic
590C2×Dic3C2×C22⋊C411yescharacteristic
591C2×Dic3C2×C22⋊C411yescharacteristic
592C2×Dic3C2×C22⋊C411yescharacteristic
593D12—22no—
594D12—21no—
595D12—21no—
596D12—21no—
597D12—42no—
598D12—42no—
599D12—42no—
600D12—81no—
601D12#13112yescomplemented
602C4×D3—22no—
603C4×D3—21no—
604C4×D3—21no—
605C4×D3—21no—
606C4×D3—21no—
607C4×D3—21no—
608C4×D3—21no—
609C4×D3—21no—
610C4×D3—21no—
611C4×D3—22no—
612C4×D3—42no—
613C4×D3—41no—
614C4×D3—41no—
615C4×D3—41no—
616C4×D3—41no—
617C4×D3—42no—
618C4×D3—81no—
619C4×D3—81no—
620C4×D3—81no—
621C4×D3—81no—
622Dic6—22no—
623Dic6—81no—
624C3×C8—22no—
625C3×C8—22no—
626C3×C8—41no—
627C3×C8—41no—
628C3⋊C8—22no—
629C3⋊C8—22no—
630C3⋊C8—41no—
631C3⋊C8—41no—
632C24—61no—
633C24—61no—
634#41—64no—
635#41—62no—
636#41—121no—
637#41—241no—
638#41—241no—
639C2×Q8—31no—
640C2×Q8—61no—
641C2×Q8C2×C4×D311yescharacteristic
642C2×D4—21no—
643C2×D4—31no—
644C2×D4—31no—
645C2×D4—31no—
646C2×D4—31no—
647C2×D4—31no—
648C2×D4—62no—
649C2×D4—61no—
650C2×D4—61no—
651C2×D4—61no—
652C2×D4—61no—
653C2×D4—61no—
654C2×D4—61no—
655C2×D4—62no—
656C2×D4—61no—
657C2×D4—61no—
658C2×D4—121no—
659C2×D4—121no—
660C2×D4—124no—
661C2×D4C2×C4×D311yescharacteristic
662C22×C4—21no—
663C22×C4—31no—
664C22×C4—31no—
665C22×C4—31no—
666C22×C4—31no—
667C22×C4—31no—
668C22×C4—31no—
669C22×C4—61no—
670C22×C4—61no—
671C22×C4—61no—
672C22×C4—61no—
673C22×C4—61no—
674C22×C4—61no—
675C22×C4—61no—
676C22×C4—61no—
677C22×C4—61no—
678C22×C4—61no—
679C22×C4—241no—
680C22×C4—241no—
681C22×C4—241no—
682C22×C4—241no—
683C22×C4C2×C4×D311yescharacteristic
684C22×C4D3×D411yescharacteristic
685C22×C4D3×D411yescharacteristic
686M16—64no—
687M16—64no—
688M16—64no—
689M16—241no—
690C2×C8—24no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—64no—
696C2×C8—64no—
697C2×C8—61no—
698C2×C8—61no—
699C2×C8—61no—
700C2×C8—61no—
701C2×C8—241no—
702C2×C8—241no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—31no—
708C4⋊C4—31no—
709C4⋊C4—31no—
710C4⋊C4—31no—
711C4⋊C4—31no—
712C4⋊C4—31no—
713C4⋊C4—31no—
714C4⋊C4—31no—
715C4⋊C4—61no—
716C4⋊C4—61no—
717C4⋊C4—61no—
718C4⋊C4—61no—
719C4⋊C4—61no—
720C4⋊C4—61no—
721C4⋊C4—61no—
722C4⋊C4C2×C4×D311yescharacteristic
723C4⋊C4C2×C4×D311yescharacteristic
724C22⋊C4—21no—
725C22⋊C4—21no—
726C22⋊C4—21no—
727C22⋊C4—21no—
728C22⋊C4—21no—
729C22⋊C4—31no—
730C22⋊C4—31no—
731C22⋊C4—31no—
732C22⋊C4—31no—
733C22⋊C4—31no—
734C22⋊C4—31no—
735C22⋊C4—61no—
736C22⋊C4—61no—
737C22⋊C4—61no—
738C22⋊C4—61no—
739C22⋊C4—61no—
740C22⋊C4—61no—
741C22⋊C4—61no—
742C22⋊C4—61no—
743C22⋊C4—61no—
744C22⋊C4—61no—
745C22⋊C4—61no—
746C22⋊C4—61no—
747C22⋊C4—61no—
748C22⋊C4—61no—
749C42—21no—
750C42—31no—
751C42—31no—
752C42—31no—
753C42—31no—
754C42—31no—
755C42—31no—
756C42—61no—
757C42—61no—
758C42C2×C4×D311yescharacteristic
759C42D3×D411yescharacteristic
760C42D3×D411yescharacteristic
761C42C23×D311yescharacteristic
762C22×C3—21no—
763C22×C3—21no—
764C22×C3—41no—
765C22×C3—41no—
766C22×C3—41no—
767C22×C3C2×#10412yes—
768C22×C3C22×C22⋊C411yescharacteristic
769C2×D3—21no—
770C2×D3—21no—
771C2×D3—21no—
772C2×D3—22no—
773C2×D3—21no—
774C2×D3—21no—
775C2×D3—41no—
776C2×D3—41no—
777C2×D3—41no—
778C2×D3—41no—
779C2×D3—41no—
780C2×D3—84no—
781C2×D3—84no—
782C2×D3C2×#10412yes—
783C3×C4—21no—
784C3×C4—21no—
785C3×C4—21no—
786C3×C4—21no—
787C3×C4—41no—
788C3×C4—41no—
789C3×C4—41no—
790C3×C4C2×#13111yescharacteristic
791C3×C4#56811yescharacteristic
792C3×C4#57611yescharacteristic
793C3×C4#57711yescharacteristic
794Dic3—21no—
795Dic3—21no—
796Dic3—21no—
797Dic3—21no—
798Dic3—21no—
799Dic3—41no—
800Dic3—41no—
801Dic3C2×#10412yes—
802C23—21no—
803C23—31no—
804C23—31no—
805C23—61no—
806C23—61no—
807C23—122no—
808C23—122no—
809C23—122no—
810C23—122no—
811C23—241no—
812C23—241no—
813C23D3×C22⋊C411yescharacteristic
814Q8—21no—
815Q8—21no—
816Q8—62no—
817Q8—241no—
818D4—21no—
819D4—21no—
820D4—34no—
821D4—32no—
822D4—42no—
823D4—62no—
824D4—62no—
825D4—61no—
826D4—61no—
827D4—61no—
828D4—122no—
829D4—122no—
830D4—122no—
831D4—122no—
832D4—122no—
833D4—241no—
834D4—241no—
835D4—241no—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—31no—
845C2×C4—31no—
846C2×C4—31no—
847C2×C4—31no—
848C2×C4—31no—
849C2×C4—31no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—62no—
853C2×C4—62no—
854C2×C4—61no—
855C2×C4—61no—
856C2×C4—61no—
857C2×C4—61no—
858C2×C4—61no—
859C2×C4—61no—
860C2×C4—61no—
861C2×C4—61no—
862C2×C4—61no—
863C2×C4—61no—
864C2×C4—122no—
865C2×C4—122no—
866C2×C4—121no—
867C2×C4—121no—
868C2×C4—121no—
869C2×C4—121no—
870C2×C4—241no—
871C2×C4—241no—
872C2×C4—241no—
873C2×C4—241no—
874C2×C4—241no—
875C2×C4—241no—
876C2×C4D3×C22⋊C411yescharacteristic
877C2×C4D3×C22⋊C411yescharacteristic
878C2×C4D3×C22⋊C411yescharacteristic
879C2×C4C22×C4×D311yescharacteristic
880C2×C4C2×D3×D411yescharacteristic
881C2×C4C2×D3×D411yescharacteristic
882C8—22no—
883C8—22no—
884C8—41no—
885C8—41no—
886C8—62no—
887C8—62no—
888C8—121no—
889C8—121no—
890C2×C3—22no—
891C2×C3—81no—
892C2×C3#288011yescharacteristic
893C2×C3#289711yescharacteristic
894C2×C3C22×#10411yescharacteristic
895D3—22no—
896D3—41no—
897D3—42no—
898D3—81no—
899C22—21no—
900C22—21no—
901C22—32no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—61no—
906C22—61no—
907C22—61no—
908C22—62no—
909C22—61no—
910C22—61no—
911C22—121no—
912C22—121no—
913C22—121no—
914C22—121no—
915C22—121no—
916C22—244no—
917C22—244no—
918C22D3×#10412yes—
919C22C2×D3×C22⋊C411yescharacteristic
920C4—21no—
921C4—21no—
922C4—21no—
923C4—21no—
924C4—32no—
925C4—41no—
926C4—41no—
927C4—41no—
928C4—61no—
929C4—61no—
930C4—61no—
931C4—61no—
932C4—61no—
933C4—121no—
934C4—121no—
935C4D3×#13111yescharacteristic
936C4#575011yescharacteristic
937C4#576911yescharacteristic
938C4#577011yescharacteristic
939C3#1751711yescharacteristic, complemented, Sylow
940C2—22no—
941C2—62no—
942C2—81no—
943C2—121no—
944C2—122no—
945C2—241no—
946C2#7866311yescharacteristic
947C2#7883111yescharacteristic
948C2C2×D3×#10411yescharacteristic
subgroupG/H
centerC2×C4C2×D3×D4
commutatorC2×C3×C4C23×C4
FrattiniC42C23×D3
FittingC3×#1494C2
socleC22×C3C22×C22⋊C4
prime radical#86153C2
cosocleC3×C42C24
hypercenter#1494D3
hypocenterC3#17517
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1494

Complements

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

NH ≅ G/Ntype
2. #79340C2semidirect
3. C4×#901C2semidirect
4. C3×#1494C2semidirect
5. #71751C2semidirect
6. #70799C2semidirect
7. C2×#4459C2semidirect
8. #68241C2semidirect
9. #68238C2semidirect
10. #68234C2semidirect
11. #68229C2semidirect
12. #68176C2semidirect
13. #68175C2semidirect
14. #68171C2semidirect
15. D3×D4⋊C8C2semidirect
41. C3×#432C22semidirect
42. C2×C3×C4×C8C22semidirect
44. C2×C4⋊(C3⋊C8)C22semidirect
45. C4×#208C22semidirect
46. #4837C22semidirect
47. #4835C22semidirect
48. #4833C22semidirect
49. D3×C4⋊C8C22semidirect
56. C4×ΓL(1,𝔽25)C22semidirect
57. C4×ΓL(1,𝔽25)C22semidirect
58. C4×D3×C8C22semidirect
59. C4×D3×C8C22semidirect
60. C3×Q8⋊C8C22semidirect
61. C3×Q8⋊C8C22semidirect
62. C3×D4⋊C8C22semidirect
63. C3×D4⋊C8C22semidirect
64. #4535C22semidirect
65. #4535C22semidirect
66. D4⋊(C3⋊C8)C22semidirect
67. D4⋊(C3⋊C8)C22semidirect
70. #4483C22semidirect
71. #4483C22semidirect
74. #4459C22semidirect
75. #4459C22semidirect
80. #1494D3semidirect
252. #432C2×D3semidirect
265. C2×C4×C8C2×D3semidirect
268. Q8⋊C8C2×D3semidirect
269. Q8⋊C8C2×D3semidirect
280. D4⋊C8C2×D3semidirect
281. D4⋊C8C2×D3semidirect
601. D12#131semidirect
939. C3#17517semidirect

Maximal subgroups

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

subgroupindex
#861532
#793402
C4×#9012
C3×#14942
#717512
#707992
C2×#44592
#682412
#682382
#682342
#682292
#681762
#681752
#681712
D3×D4⋊C82
#175173