Finite Group Databasebeta

← #10761663

Subgroups — #10761663

Order 768.

1222 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#1004C211yesmaximal, characteristic
2#79339C211yesmaximal, characteristic, complemented
3#78523C211yesmaximal, characteristic, complemented
4C3×#1490C211yesmaximal, characteristic, complemented
5#71598C211yesmaximal, characteristic, complemented
6#70798C211yesmaximal, characteristic, complemented
7#69854C211yesmaximal, characteristic, complemented
8#68175C211yesmaximal, characteristic, complemented
9#68174C211yesmaximal, characteristic, complemented
10#68173C211yesmaximal, characteristic, complemented
11#68172C211yesmaximal, characteristic, complemented
12#68167C211yesmaximal, characteristic, complemented
13#68166C211yesmaximal, characteristic, complemented
14#68165C211yesmaximal, characteristic, complemented
15D3×D4⋊C8C211yesmaximal, characteristic, complemented
16#17453—31nomaximal, Sylow
17C2×#1004C411yescharacteristic
18C2×C3×C4×D4C2211yescharacteristic
19#5798C411yescharacteristic
20C2×C4×#67—21no—
21C2×C4×#67—21no—
22#5546—21no—
23#5546C411yescharacteristic
24#5546C411yescharacteristic
25#5545—21no—
26#5545C411yescharacteristic
27#5545C411yescharacteristic
28C4×D3×D4—21no—
29C4×D3×D4C2211yescharacteristic
30C4×D3×D4C2211yescharacteristic
31C4×#237—21no—
32C4×#237C2211yescharacteristic
33C4×#237C2211yescharacteristic
34#5504C411yescharacteristic
35#5504C411yescharacteristic
36#5486—21no—
37#5486—21no—
38C4×#235C2211yescharacteristic
39C4×#235C2211yescharacteristic
40C3×#432C2211yescharacteristic, complemented
41C3×C4×M16C2211yescharacteristic, complemented
42#5128—21no—
43#5127—21no—
44#4925C2211yescharacteristic, complemented
45#4924C2211yescharacteristic, complemented
46#4837C2211yescharacteristic, complemented
47#4835C2211yescharacteristic, complemented
48#4833C2211yescharacteristic, complemented
49D3×C4⋊C8C2211yescharacteristic, complemented
50#4729—21no—
51#4728—21no—
52#4706—21no—
53#4706—21no—
54#4701—21no—
55#4701—21no—
56C4×ΓL(1,𝔽25)C2211yescharacteristic, complemented
57#4685C2211yescharacteristic, complemented
58#4685C2211yescharacteristic, complemented
59C4×D3×C8C2211yescharacteristic, complemented
60C3×D4⋊C8C2211yescharacteristic, complemented
61C3×D4⋊C8C2211yescharacteristic, complemented
62C3×D4⋊C8C2211yescharacteristic, complemented
63C3×D4⋊C8C2211yescharacteristic, complemented
64D4⋊(C3⋊C8)C2211yescharacteristic, complemented
65D4⋊(C3⋊C8)C2211yescharacteristic, complemented
66D4⋊(C3⋊C8)C2211yescharacteristic, complemented
67D4⋊(C3⋊C8)C2211yescharacteristic, complemented
68#4484C2211yescharacteristic, complemented
69#4484C2211yescharacteristic, complemented
70#4483C2211yescharacteristic, complemented
71#4483C2211yescharacteristic, complemented
72#4459C2211yescharacteristic, complemented
73#4459C2211yescharacteristic, complemented
74#4456C2211yescharacteristic, complemented
75#4456C2211yescharacteristic, complemented
76C4×H(5,𝔽2)—31no—
77#2989—31no—
78#2965—31no—
79#1490—31no—
80#1490D311yescharacteristic, complemented
81#1489—31no—
82#1489—31no—
83#1488—31no—
84#1488—31no—
85#1486—31no—
86#1486—31no—
87#1478—31no—
88#1477—31no—
89#1476—31no—
90C2×D4⋊C8—31no—
91C22×C3×D4C2×C411yescharacteristic
92C23×C3×C4—21no—
93C22×#67—21no—
94C22×#67—21no—
95#1004—24no—
96#1004—24no—
97C2×#237—21no—
98C2×#237C2×C411yescharacteristic
99C2×#237C2×C411yescharacteristic
100C2×D3×D4—21no—
101C2×D3×D4C2×C411yescharacteristic
102C2×D3×D4C2×C411yescharacteristic
103C2×#235C2×C411yescharacteristic
104C2×#235C2×C411yescharacteristic
105C22×C4×D3—21no—
106C22×C4×D3—21no—
107C2×C3×M16—21no—
108C3×C4×D4—21no—
109C3×C4×D4—21no—
110C3×C4×D4C2×C411yescharacteristic
111C3×C4×D4C2×C411yescharacteristic
112C3×C4×D4C2311yescharacteristic
113C3×C4×D4C2311yescharacteristic
114C2×C3×C4⋊C4C2×C411yescharacteristic
115C2×C3×C22⋊C4—21no—
116C2×C3×C42C2311yescharacteristic
117C2×#217—21no—
118C2×#217—21no—
119D4×Dic3—21no—
120D4×Dic3—21no—
121D4×Dic3C2×C411yescharacteristic
122D4×Dic3C2×C411yescharacteristic
123D4×Dic3C2×C411yescharacteristic
124D4×Dic3C2×C411yescharacteristic
125C4×#67—21no—
126C4×#67—21no—
127C4×#67—21no—
128C4×#67—21no—
129C4×#67—21no—
130C4×#67—21no—
131C4×#67—21no—
132C4×#67—21no—
133C4×#67—21no—
134C4×#67—21no—
135C4×#67—21no—
136C4×#67—21no—
137C4×#67—21no—
138C4×#67—21no—
139C4×#67D411yescharacteristic
140C4×#67D411yescharacteristic
141C4×#67D411yescharacteristic
142C4×#67D411yescharacteristic
143C2×(C2×D3)⋊C4—21no—
144C2×(C2×D3)⋊C4—21no—
145#926C2×C411yescharacteristic
146#926C2×C411yescharacteristic
147C2×Dic3⋊C4—21no—
148C2×Dic3⋊C4—21no—
149C2×C4×Dic3—21no—
150C2×C4×Dic3—21no—
151C2×#208—21no—
152C2×ΓL(1,𝔽25)—21no—
153C2×ΓL(1,𝔽25)—21no—
154C2×D3×C8—21no—
155C2×D3×C8—21no—
156#893—21no—
157#893C2×C411yescharacteristic
158#893C2×C411yescharacteristic
159#892—21no—
160#892C2×C411yescharacteristic
161#892C2×C411yescharacteristic
162D3×C4⋊C4—21no—
163D3×C4⋊C4C2×C411yescharacteristic
164D3×C4⋊C4C2×C411yescharacteristic
165#887—21no—
166#887C2×C411yescharacteristic
167#887C2×C411yescharacteristic
168#67⋊C4—21no—
169#67⋊C4—21no—
170#67⋊C4—21no—
171#67⋊C4—21no—
172#67⋊C4—21no—
173#67⋊C4—21no—
174#67⋊C4—21no—
175#67⋊C4—21no—
176D3×C22⋊C4—21no—
177D3×C22⋊C4—21no—
178D3×C22⋊C4—21no—
179D3×C22⋊C4—21no—
180#877—21no—
181#877—21no—
182#877—21no—
183#877—21no—
184C4×D12C2×C411yescharacteristic
185C4×D12D411yescharacteristic
186C4×D12D411yescharacteristic
187C4×D12C2311yescharacteristic
188#872—21no—
189#872C2×C411yescharacteristic
190#872C2×C411yescharacteristic
191C42×D3—21no—
192C42×D3C2311yescharacteristic
193C42×D3C2311yescharacteristic
194C4×Dic6C2×C411yescharacteristic
195C4×Dic6D411yescharacteristic
196C4×Dic6D411yescharacteristic
197C4×Dic6C2311yescharacteristic
198C3×C4⋊C8C2311yescharacteristic
199C3×C4⋊C8C2311yescharacteristic
200C3×C22⋊C8—21no—
201C3×#97—21no—
202C3×#97—21no—
203C3×C4×C8C2311yescharacteristic
204C3×C4×C8C2311yescharacteristic
205#830—21no—
206(C2×D3)⋊C8—21no—
207(C2×D3)⋊C8—21no—
208(C2×D3)⋊C8—21no—
209(C2×D3)⋊C8—21no—
210#815—21no—
211#815—21no—
212Dic3⋊C8—21no—
213Dic3⋊C8—21no—
214Dic3⋊C8—21no—
215Dic3⋊C8—21no—
216C8×Dic3—21no—
217C8×Dic3—21no—
218C4⋊(C3⋊C8)—21no—
219C4⋊(C3⋊C8)—21no—
220C4⋊(C3⋊C8)C2311yescharacteristic
221C4⋊(C3⋊C8)C2311yescharacteristic
222C4×C3⋊C8C2311yescharacteristic
223C4×C3⋊C8C2311yescharacteristic
224C2×H(5,𝔽2)—31no—
225#520—31no—
226#520—31no—
227#520—31no—
228#520—31no—
229#520—61no—
230#518—31no—
231#518—31no—
232#518—31no—
233#518—61no—
234#518—61no—
235#518—61no—
236C4×#41—31no—
237C4×#41—31no—
238C4×#41—31no—
239C4×#41—31no—
240C4×#41—61no—
241C2×C4×D4—31no—
242C2×C4×D4—31no—
243C2×C4×D4—61no—
244C2×C4×D4—61no—
245C2×C4×D4—61no—
246C2×C4×D4C2×D311yescharacteristic
247#446—61no—
248#446—61no—
249#436—61no—
250#436—61no—
251#435—61no—
252#435—61no—
253#435—61no—
254#435—61no—
255#432—31no—
256#432C2×D311yescharacteristic, complemented
257#431—31no—
258#431—31no—
259#431—31no—
260#431—31no—
261#423—31no—
262#423—31no—
263C2×C4⋊C8—31no—
264C4×M16—31no—
265C4×M16C2×D311yescharacteristic, complemented
266C2×C4×C8—31no—
267Q8⋊C8—31no—
268Q8⋊C8—31no—
269Q8⋊C8—31no—
270Q8⋊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⋊C8C2×D311yescharacteristic, complemented
280D4⋊C8C2×D311yescharacteristic, complemented
281D4⋊C8C2×D311yescharacteristic, complemented
282D4⋊C8C2×D311yescharacteristic, complemented
283C24×C3—21no—
284C23×D3—21no—
285C23×D3—21no—
286C2×C3×D4—22no—
287C2×C3×D4—22no—
288C2×C3×D4—21no—
289C2×C3×D4C22×C411yescharacteristic
290C2×C3×D4C22×C411yescharacteristic
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—81no—
297C22×C3×C4—81no—
298C22×C3×C4C22×C411yescharacteristic
299C22×C3×C4C2×D411yescharacteristic
300C22×C3×C4C2×D411yescharacteristic
301C2×#67—28no—
302C2×#67—28no—
303C2×#67—21no—
304C2×#67—21no—
305C2×#67—21no—
306C2×#67—21no—
307C2×#67—21no—
308C2×#67C22⋊C411yescharacteristic
309C2×#67C22⋊C411yescharacteristic
310C22×Dic3—21no—
311C22×Dic3—21no—
312C22×Dic3—21no—
313C22×Dic3—21no—
314C22×Dic3—21no—
315C22×Dic3—21no—
316#237—28no—
317#237—22no—
318#237—22no—
319#237—22no—
320#237M1614yescomplemented
321D3×D4—28no—
322D3×D4—22no—
323D3×D4—22no—
324D3×D4—22no—
325D3×D4M1614yescomplemented
326#235—22no—
327#235—22no—
328#235—22no—
329#235—22no—
330C2×D12C22⋊C411yescharacteristic
331C2×D12C22×C411yescharacteristic
332C2×C4×D3—21no—
333C2×C4×D3—21no—
334C2×C4×D3—21no—
335C2×C4×D3—21no—
336C2×C4×D3—21no—
337C2×C4×D3—21no—
338C2×C4×D3—21no—
339C2×C4×D3—81no—
340C2×C4×D3—81no—
341C2×C4×D3—81no—
342C2×C4×D3—81no—
343C2×C4×D3C22×C411yescharacteristic
344C2×C4×D3C22×C411yescharacteristic
345C2×C4×D3C2×D411yescharacteristic
346C2×C4×D3C2×D411yescharacteristic
347C2×C4×D3C2×D411yescharacteristic
348C2×C4×D3C2×D411yescharacteristic
349C2×Dic6C22⋊C411yescharacteristic
350C2×Dic6C22×C411yescharacteristic
351C3×M16—42no—
352C2×C3×C8—21no—
353C2×C3×C8—21no—
354C2×C3×C8—21no—
355C2×C3×C8—21no—
356C3×C4⋊C4—21no—
357C3×C4⋊C4C22×C411yescharacteristic
358C3×C4⋊C4C22×C411yescharacteristic
359C3×C22⋊C4—21no—
360C3×C22⋊C4—21no—
361C3×C22⋊C4—21no—
362C3×C22⋊C4—21no—
363C3×C42C22×C411yescharacteristic
364C3×C42C2×D411yescharacteristic
365C3×C42C2×D411yescharacteristic
366C3×C42C2411yescharacteristic
367#217—21no—
368#217—21no—
369#217—21no—
370#217—21no—
371#217—21no—
372#217C22⋊C411yescharacteristic
373#217C22⋊C411yescharacteristic
374(C2×D3)⋊C4—21no—
375(C2×D3)⋊C4—21no—
376(C2×D3)⋊C4—21no—
377(C2×D3)⋊C4—21no—
378(C2×D3)⋊C4—21no—
379(C2×D3)⋊C4—21no—
380(C2×D3)⋊C4C22⋊C411yescharacteristic
381(C2×D3)⋊C4C22⋊C411yescharacteristic
382(C2×D3)⋊C4C22⋊C411yescharacteristic
383(C2×D3)⋊C4C22⋊C411yescharacteristic
384C4⋊Dic3C22⋊C411yescharacteristic
385C4⋊Dic3C22⋊C411yescharacteristic
386C4⋊Dic3C22×C411yescharacteristic
387C4⋊Dic3C22×C411yescharacteristic
388Dic3⋊C4—21no—
389Dic3⋊C4—21no—
390Dic3⋊C4—21no—
391Dic3⋊C4—21no—
392Dic3⋊C4—21no—
393Dic3⋊C4—21no—
394Dic3⋊C4C22⋊C411yescharacteristic
395Dic3⋊C4C22⋊C411yescharacteristic
396Dic3⋊C4C22⋊C411yescharacteristic
397Dic3⋊C4C22⋊C411yescharacteristic
398C4×Dic3—21no—
399C4×Dic3—21no—
400C4×Dic3—21no—
401C4×Dic3—21no—
402C4×Dic3—21no—
403C4×Dic3—21no—
404C4×Dic3—21no—
405C4×Dic3C22×C411yescharacteristic
406C4×Dic3C22×C411yescharacteristic
407C4×Dic3C2×D411yescharacteristic
408C4×Dic3C2×D411yescharacteristic
409C4×Dic3C2×D411yescharacteristic
410C4×Dic3C2×D411yescharacteristic
411#208—81no—
412C2×C3⋊C8—21no—
413C2×C3⋊C8—21no—
414C2×C3⋊C8—21no—
415C2×C3⋊C8—21no—
416ΓL(1,𝔽25)—42no—
417ΓL(1,𝔽25)—81no—
418D3×C8—42no—
419D3×C8—81no—
420H(5,𝔽2)—64no—
421H(5,𝔽2)—64no—
422C2×#41—31no—
423C2×#41—31no—
424C2×#41—31no—
425C2×#41—31no—
426C2×#41—61no—
427C22×D4—31no—
428C22×D4—31no—
429C22×D4—61no—
430C22×D4—61no—
431C22×D4—61no—
432C22×D4C4×D311yescharacteristic
433C23×C4—21no—
434C23×C4—61no—
435C23×C4—61no—
436C2×M16—21no—
437C2×M16—61no—
438C2×M16—61no—
439C2×M16—61no—
440C22×C8—61no—
441C22×C8—61no—
442C4×Q8—31no—
443C4×Q8—31no—
444C4×Q8—31no—
445C4×Q8—31no—
446C4×Q8—31no—
447C4×Q8—31no—
448C4×Q8—61no—
449C4×D4—21no—
450C4×D4—21no—
451C4×D4—31no—
452C4×D4—31no—
453C4×D4—31no—
454C4×D4—31no—
455C4×D4—31no—
456C4×D4—31no—
457C4×D4—31no—
458C4×D4—31no—
459C4×D4—31no—
460C4×D4—31no—
461C4×D4—31no—
462C4×D4—31no—
463C4×D4—31no—
464C4×D4—31no—
465C4×D4—61no—
466C4×D4—61no—
467C4×D4—61no—
468C4×D4—61no—
469C4×D4—61no—
470C4×D4—61no—
471C4×D4—61no—
472C4×D4—61no—
473C4×D4—61no—
474C4×D4—61no—
475C4×D4—61no—
476C4×D4—61no—
477C4×D4—61no—
478C4×D4—61no—
479C4×D4—61no—
480C4×D4—61no—
481C4×D4—61no—
482C4×D4—61no—
483C4×D4—61no—
484C4×D4—61no—
485C4×D4—61no—
486C4×D4—61no—
487C4×D4—61no—
488C4×D4—61no—
489C4×D4—61no—
490C4×D4C4×D311yescharacteristic
491C4×D4C4×D311yescharacteristic
492C4×D4C22×D311yescharacteristic
493C4×D4C22×D311yescharacteristic
494#117—31no—
495#117—31no—
496#117—31no—
497#117—31no—
498#117—31no—
499#117—31no—
500#117—61no—
501#117—61no—
502#117—61no—
503#117—61no—
504#117—61no—
505#117—61no—
506C2×C4⋊C4—31no—
507C2×C4⋊C4—31no—
508C2×C4⋊C4—61no—
509C2×C4⋊C4—61no—
510C2×C4⋊C4—61no—
511C2×C4⋊C4C4×D311yescharacteristic
512C2×C22⋊C4—21no—
513C2×C22⋊C4—61no—
514C2×C22⋊C4—61no—
515C2×C22⋊C4—61no—
516C2×C22⋊C4—61no—
517C2×C22⋊C4—61no—
518C2×C22⋊C4—61no—
519C2×C22⋊C4—61no—
520C2×C22⋊C4—61no—
521C2×C42—31no—
522C2×C42—31no—
523C2×C42—61no—
524C2×C42—61no—
525C2×C42—61no—
526C2×C42C22×D311yescharacteristic
527C4⋊C8—31no—
528C4⋊C8—31no—
529C4⋊C8—61no—
530C4⋊C8—61no—
531C4⋊C8—61no—
532C4⋊C8—61no—
533C4⋊C8—61no—
534C4⋊C8—61no—
535C4⋊C8C22×D311yescharacteristic
536C4⋊C8C22×D311yescharacteristic
537C22⋊C8—21no—
538C22⋊C8—61no—
539C22⋊C8—61no—
540C22⋊C8—61no—
541C22⋊C8—61no—
542C22⋊C8—61no—
543#97—21no—
544#97—21no—
545#97—61no—
546#97—61no—
547C4×C8—31no—
548C4×C8—31no—
549C4×C8—61no—
550C4×C8—61no—
551C4×C8C22×D311yescharacteristic
552C4×C8C22×D311yescharacteristic
553C23×C3—24no—
554C23×C3—21no—
555C23×C3—21no—
556C23×C3—81no—
557C23×C3—81no—
558C23×C3C2×C22⋊C411yescharacteristic
559C22×D3—21no—
560C22×D3—24no—
561C22×D3—24no—
562C22×D3—81no—
563C22×D3—81no—
564C22×D3—81no—
565C22×D3—81no—
566C22×D3C2×C22⋊C411yescharacteristic
567C22×D3C2×C22⋊C411yescharacteristic
568C3×D4—24no—
569C3×D4—21no—
570C3×D4—21no—
571C3×D4C2×M1612yes—
572C3×D4C2×M1612yes—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—41no—
580C2×C3×C4—41no—
581C2×C3×C4—41no—
582C2×C3×C4—41no—
583C2×C3×C4—41no—
584C2×C3×C4—81no—
585C2×C3×C4—81no—
586C2×C3×C4—81no—
587C2×C3×C4C2×C22⋊C411yescharacteristic
588C2×C3×C4C2×C22⋊C411yescharacteristic
589C2×C3×C4C2×C22⋊C411yescharacteristic
590C2×C3×C4C23×C411yescharacteristic
591C2×C3×C4C22×D411yescharacteristic
592C2×C3×C4C22×D411yescharacteristic
593#67—24no—
594#67—24no—
595#67—24no—
596#67—22no—
597#67—24no—
598#67—22no—
599#67—24no—
600C2×Dic3—24no—
601C2×Dic3—21no—
602C2×Dic3—24no—
603C2×Dic3—21no—
604C2×Dic3—21no—
605C2×Dic3—81no—
606C2×Dic3—81no—
607C2×Dic3—81no—
608C2×Dic3—81no—
609C2×Dic3C2×C22⋊C411yescharacteristic
610C2×Dic3C2×C22⋊C411yescharacteristic
611C2×Dic3C2×C22⋊C411yescharacteristic
612C2×Dic3C2×C22⋊C411yescharacteristic
613C2×Dic3C2×C22⋊C411yescharacteristic
614C2×Dic3C2×C22⋊C411yescharacteristic
615D12—22no—
616D12—21no—
617D12C2×M1612yes—
618C4×D3—24no—
619C4×D3—21no—
620C4×D3—21no—
621C4×D3—21no—
622C4×D3—21no—
623C4×D3—21no—
624C4×D3—21no—
625C4×D3—41no—
626C4×D3—41no—
627C4×D3—41no—
628C4×D3—41no—
629C4×D3—81no—
630C4×D3—81no—
631C4×D3—81no—
632C4×D3—81no—
633C4×D3—81no—
634C4×D3C2×M1612yes—
635C4×D3C2×M1612yes—
636Dic6—21no—
637Dic6—22no—
638Dic6C2×M1612yes—
639C3×C8—22no—
640C3×C8—41no—
641C3×C8—41no—
642C3×C8—41no—
643C3⋊C8—41no—
644C3⋊C8—41no—
645C3⋊C8—41no—
646C3⋊C8—41no—
647C24—21no—
648C24—61no—
649C24—61no—
650#41—34no—
651#41—62no—
652#41—62no—
653#41—62no—
654#41—62no—
655#41—62no—
656#41—62no—
657#41—68no—
658#41—62no—
659C2×Q8—31no—
660C2×Q8—31no—
661C2×D4—22no—
662C2×D4—22no—
663C2×D4—21no—
664C2×D4—34no—
665C2×D4—31no—
666C2×D4—31no—
667C2×D4—31no—
668C2×D4—31no—
669C2×D4—62no—
670C2×D4—61no—
671C2×D4—61no—
672C2×D4—62no—
673C2×D4—68no—
674C2×D4—61no—
675C2×D4—61no—
676C2×D4—68no—
677C2×D4—68no—
678C2×D4—61no—
679C2×D4—62no—
680C2×D4C2×C4×D311yescharacteristic
681C2×D4C2×C4×D311yescharacteristic
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—31no—
688C22×C4—31no—
689C22×C4—31no—
690C22×C4—31no—
691C22×C4—31no—
692C22×C4—31no—
693C22×C4—61no—
694C22×C4—61no—
695C22×C4—61no—
696C22×C4—61no—
697C22×C4—61no—
698C22×C4—61no—
699C22×C4—61no—
700C22×C4—61no—
701C22×C4—61no—
702C22×C4—61no—
703C22×C4—61no—
704C22×C4—61no—
705C22×C4—61no—
706C22×C4—81no—
707C22×C4—81no—
708C22×C4—241no—
709C22×C4—241no—
710C22×C4—241no—
711C22×C4—241no—
712C22×C4C2×C4×D311yescharacteristic
713C22×C4D3×D411yescharacteristic
714C22×C4D3×D411yescharacteristic
715M16—42no—
716M16—122no—
717M16—241no—
718M16—241no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—61no—
724C2×C8—61no—
725C2×C8—61no—
726C2×C8—61no—
727C2×C8—122no—
728C2×C8—241no—
729C4⋊C4—21no—
730C4⋊C4—31no—
731C4⋊C4—31no—
732C4⋊C4—31no—
733C4⋊C4—31no—
734C4⋊C4—31no—
735C4⋊C4—31no—
736C4⋊C4—31no—
737C4⋊C4—31no—
738C4⋊C4—61no—
739C4⋊C4—61no—
740C4⋊C4—61no—
741C4⋊C4—61no—
742C4⋊C4—61no—
743C4⋊C4—61no—
744C4⋊C4C2×C4×D311yescharacteristic
745C4⋊C4C2×C4×D311yescharacteristic
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—31no—
751C22⋊C4—31no—
752C22⋊C4—31no—
753C22⋊C4—31no—
754C22⋊C4—31no—
755C22⋊C4—31no—
756C22⋊C4—61no—
757C22⋊C4—61no—
758C22⋊C4—61no—
759C22⋊C4—61no—
760C22⋊C4—61no—
761C22⋊C4—61no—
762C22⋊C4—61no—
763C22⋊C4—61no—
764C22⋊C4—61no—
765C22⋊C4—61no—
766C22⋊C4—61no—
767C42—31no—
768C42—31no—
769C42—31no—
770C42—31no—
771C42—31no—
772C42—31no—
773C42—61no—
774C42—61no—
775C42—61no—
776C42—61no—
777C42—61no—
778C42—61no—
779C42—61no—
780C42C2×C4×D311yescharacteristic
781C42D3×D411yescharacteristic
782C42D3×D411yescharacteristic
783C42C23×D311yescharacteristic
784C22×C3—22no—
785C22×C3—22no—
786C22×C3—21no—
787C22×C3—21no—
788C22×C3—21no—
789C22×C3—41no—
790C22×C3—41no—
791C22×C3—41no—
792C22×C3—41no—
793C22×C3—84no—
794C22×C3C22×C22⋊C411yescharacteristic
795C2×D3—21no—
796C2×D3—21no—
797C2×D3—21no—
798C2×D3—22no—
799C2×D3—21no—
800C2×D3—21no—
801C2×D3—41no—
802C2×D3—41no—
803C2×D3—84no—
804C2×D3—84no—
805C2×D3#40712yes—
806C3×C4—21no—
807C3×C4—21no—
808C3×C4—21no—
809C3×C4—21no—
810C3×C4—41no—
811C3×C4—41no—
812C3×C4C22×M1611yescharacteristic
813C3×C4C22×M1611yescharacteristic
814C3×C4#57611yescharacteristic
815C3×C4#57711yescharacteristic
816Dic3—21no—
817Dic3—22no—
818Dic3—21no—
819Dic3—21no—
820Dic3—21no—
821Dic3—21no—
822Dic3—41no—
823Dic3—41no—
824Dic3#40712yes—
825C23—24no—
826C23—21no—
827C23—21no—
828C23—31no—
829C23—31no—
830C23—64no—
831C23—64no—
832C23—61no—
833C23—81no—
834C23—81no—
835C23—241no—
836C23—241no—
837C23—241no—
838C23—241no—
839C23D3×C22⋊C411yescharacteristic
840Q8—32no—
841Q8—62no—
842Q8—61no—
843D4—24no—
844D4—21no—
845D4—21no—
846D4—32no—
847D4—62no—
848D4—62no—
849D4—64no—
850D4—62no—
851D4—64no—
852D4—64no—
853D4—64no—
854D4—64no—
855D4—61no—
856D4D3×M1612yes—
857D4D3×M1612yes—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—31no—
865C2×C4—32no—
866C2×C4—32no—
867C2×C4—31no—
868C2×C4—31no—
869C2×C4—31no—
870C2×C4—31no—
871C2×C4—31no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—64no—
878C2×C4—64no—
879C2×C4—64no—
880C2×C4—61no—
881C2×C4—61no—
882C2×C4—61no—
883C2×C4—61no—
884C2×C4—61no—
885C2×C4—61no—
886C2×C4—61no—
887C2×C4—61no—
888C2×C4—61no—
889C2×C4—81no—
890C2×C4—81no—
891C2×C4—81no—
892C2×C4—121no—
893C2×C4—121no—
894C2×C4—121no—
895C2×C4—121no—
896C2×C4—241no—
897C2×C4—241no—
898C2×C4—241no—
899C2×C4—241no—
900C2×C4—241no—
901C2×C4—241no—
902C2×C4—241no—
903C2×C4—241no—
904C2×C4—241no—
905C2×C4D3×C22⋊C411yescharacteristic
906C2×C4D3×C22⋊C411yescharacteristic
907C2×C4D3×C22⋊C411yescharacteristic
908C2×C4C22×C4×D311yescharacteristic
909C2×C4C2×D3×D411yescharacteristic
910C2×C4C2×D3×D411yescharacteristic
911C8—22no—
912C8—41no—
913C8—41no—
914C8—41no—
915C8—121no—
916C8—121no—
917C8—121no—
918C8—121no—
919C2×C3—42no—
920C2×C3—42no—
921C2×C3—41no—
922C2×C3C2×#40711yescharacteristic
923C2×C3#289711yescharacteristic
924C2×C3#290111yescharacteristic
925D3—22no—
926D3—41no—
927D3—42no—
928C22—21no—
929C22—22no—
930C22—22no—
931C22—21no—
932C22—21no—
933C22—32no—
934C22—41no—
935C22—41no—
936C22—41no—
937C22—41no—
938C22—61no—
939C22—61no—
940C22—62no—
941C22—61no—
942C22—61no—
943C22—61no—
944C22—84no—
945C22—121no—
946C22—121no—
947C22—244no—
948C22—244no—
949C22C2×D3×C22⋊C411yescharacteristic
950C4—21no—
951C4—21no—
952C4—21no—
953C4—21no—
954C4—32no—
955C4—41no—
956C4—41no—
957C4—61no—
958C4—62no—
959C4—61no—
960C4—61no—
961C4—61no—
962C4—61no—
963C4—121no—
964C4—121no—
965C4C2×D3×M1611yescharacteristic
966C4C2×D3×M1611yescharacteristic
967C4#577411yescharacteristic
968C4#577511yescharacteristic
969C3#1745311yescharacteristic, complemented, Sylow
970C2—41no—
971C2—42no—
972C2—42no—
973C2—62no—
974C2—121no—
975C2—122no—
976C2D3×#40711yescharacteristic
977C2#7892511yescharacteristic
978C2#7898311yescharacteristic
subgroupG/H
centerC2×C4C2×D3×D4
commutatorC2×C3×C4C23×C4
FrattiniC42C23×D3
FittingC3×#1490C2
socleC22×C3C22×C22⋊C4
prime radicalC2×#1004C4
cosocleC3×C42C24
hypercenter#1490D3
hypocenterC3#17453
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1490

Complements

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

NH ≅ G/Ntype
2. #79339C2semidirect
3. #78523C2semidirect
4. C3×#1490C2semidirect
5. #71598C2semidirect
6. #70798C2semidirect
7. #69854C2semidirect
8. #68175C2semidirect
9. #68174C2semidirect
10. #68173C2semidirect
11. #68172C2semidirect
12. #68167C2semidirect
13. #68166C2semidirect
14. #68165C2semidirect
15. D3×D4⋊C8C2semidirect
40. C3×#432C22semidirect
41. C3×C4×M16C22semidirect
44. #4925C22semidirect
45. #4924C22semidirect
46. #4837C22semidirect
47. #4835C22semidirect
48. #4833C22semidirect
49. D3×C4⋊C8C22semidirect
56. C4×ΓL(1,𝔽25)C22semidirect
57. #4685C22semidirect
58. #4685C22semidirect
59. C4×D3×C8C22semidirect
60. C3×D4⋊C8C22semidirect
61. C3×D4⋊C8C22semidirect
62. C3×D4⋊C8C22semidirect
63. C3×D4⋊C8C22semidirect
64. D4⋊(C3⋊C8)C22semidirect
65. D4⋊(C3⋊C8)C22semidirect
66. D4⋊(C3⋊C8)C22semidirect
67. D4⋊(C3⋊C8)C22semidirect
68. #4484C22semidirect
69. #4484C22semidirect
70. #4483C22semidirect
71. #4483C22semidirect
72. #4459C22semidirect
73. #4459C22semidirect
74. #4456C22semidirect
75. #4456C22semidirect
80. #1490D3semidirect
256. #432C2×D3semidirect
265. C4×M16C2×D3semidirect
279. D4⋊C8C2×D3semidirect
280. D4⋊C8C2×D3semidirect
281. D4⋊C8C2×D3semidirect
282. D4⋊C8C2×D3semidirect
320. #237M16semidirect
325. D3×D4M16semidirect
969. C3#17453semidirect

Maximal subgroups

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

subgroupindex
C4×#10042
#793392
#785232
C3×#14902
#715982
#707982
#698542
#681752
#681742
#681732
#681722
#681672
#681662
#681652
D3×D4⋊C82
#174533