Finite Group Databasebeta

← #30620359

Subgroups — #30620359

Order 15616.

1258 conjugacy classes of subgroups.

The subgroup lattice has 1146 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#435C211yesmaximal, characteristic, complemented
2D4×C4⋊#6923C211yesmaximal, characteristic, complemented
3#21462002C211yesmaximal, characteristic, complemented
4#21461999C211yesmaximal, characteristic, complemented
5#21461835C211yesmaximal, characteristic, complemented
6#21461833C211yesmaximal, characteristic, complemented
7#21461806C211yesmaximal, characteristic, complemented
8#21461806C211yesmaximal, characteristic, complemented
9#21461724C211yesmaximal, characteristic, complemented
10#21461723C211yesmaximal, characteristic, complemented
11#21461687C211yesmaximal, characteristic, complemented
12#21461589C211yesmaximal, characteristic, complemented
13#21461508C211yesmaximal, characteristic, complemented
14C2×#16840635C211yesmaximal, characteristic, complemented
15#553×D61C211yesmaximal, characteristic
16C2×D61⋊M16C2211yescharacteristic
17C22×D61⋊C8C2211yescharacteristic
18C2×D4×#6923—21no—
19C22×C4⋊#6923C2211yescharacteristic
20C22×C4⋊#6923C2211yescharacteristic
21#16840794—21no—
22#16840793—21no—
23#16840792—21no—
24#16840791—21no—
25D61⋊(C4⋊C8)C2211yescharacteristic
26C2×#14519839C2211yescharacteristic
27C2×#14519839C2211yescharacteristic
28C2×#14519839C2211yescharacteristic
29C2×#14519839C2211yescharacteristic
30D61⋊(C22⋊C8)C2211yescharacteristic
31D61⋊(C22⋊C8)C2211yescharacteristic
32#16840721C2211yescharacteristic
33#16840713—21no—
34#16840709—21no—
35#16840709—21no—
36#16840708C2211yescharacteristic
37#16840704C2211yescharacteristic
38#16840704C2211yescharacteristic
39C4×C4⋊#6923C2211yescharacteristic
40#16840635C2211yescharacteristic
41#16840635C2211yescharacteristic
42#16840635C2211yescharacteristic
43#16840635C2211yescharacteristic
44#16840635C2211yescharacteristic
45#16840635C2211yescharacteristic
46#16840635C2211yescharacteristic
47#16840635C2211yescharacteristic
48#16840635C2211yescharacteristic
49#16840635C2211yescharacteristic
50#16840635C2211yescharacteristic
51#16840635C2211yescharacteristic
52#16840465C411yescharacteristic, complemented
53#16840464C411yescharacteristic, complemented
54#16840463—21no—
55#16840462C411yescharacteristic, complemented
56#16840461—21no—
57#16840460C411yescharacteristic, complemented
58#16840459C411yescharacteristic, complemented
59#16840458C411yescharacteristic, complemented
60#16840457—21no—
61#16840456C411yescharacteristic, complemented
62#16840455—21no—
63#126×D61—21no—
64#125×D61C2211yescharacteristic
65#123×D61—21no—
66#121×D61—21no—
67#121×D61C2211yescharacteristic
68#121×D61C2211yescharacteristic
69C4×D4×D61—21no—
70C4×D4×D61C2211yescharacteristic
71C4×D4×D61C2211yescharacteristic
72#117×D61C2211yescharacteristic
73C2×C4⋊C4×D61C2211yescharacteristic
74C61×#553C411yescharacteristic, complemented
75C23×#6923—21no—
76C23×#6923—21no—
77C2×#11758213—21no—
78D61⋊M16—22no—
79D61⋊M16—41no—
80C2×#11758217—21no—
81C2×D61⋊C8—22no—
82C2×D61⋊C8—21no—
83C2×D61⋊C8—41no—
84C2×D61⋊C8C2311yescharacteristic
85C2×D61⋊C8C2311yescharacteristic
86C2×D61⋊C8C2311yescharacteristic
87C2×D61⋊C8C2311yescharacteristic
88C22×#92420—21no—
89D4×#6923—44no—
90C2×C4⋊#6923—22no—
91C2×C4⋊#6923—22no—
92C2×C4⋊#6923—21no—
93C2×C4⋊#6923—21no—
94C2×C4⋊#6923—21no—
95C2×C4⋊#6923—21no—
96C2×C4⋊#6923—41no—
97C2×C4⋊#6923—41no—
98C2×C4⋊#6923C2311yescharacteristic
99C2×C4⋊#6923C2311yescharacteristic
100C2×C4⋊#6923C2311yescharacteristic
101C2×C4⋊#6923C2311yescharacteristic
102C2×C22⋊#6923—21no—
103C2×C22⋊#6923—21no—
104C2×C4×#6923—21no—
105#14519844—21no—
106C4⋊#92420—21no—
107#14519839—22no—
108#14519839—22no—
109#14519839—41no—
110#14519839—41no—
111#14519834—21no—
112#14519834—21no—
113C22⋊#92420—21no—
114C22⋊#92420—21no—
115#14519832—21no—
116#14519832—21no—
117(C2×#6923)⋊C4—21no—
118(C2×#6923)⋊C4—21no—
119(C2×#6923)⋊C4—21no—
120C2×D4×D61—21no—
121C2×D4×D61—21no—
122C2×D4×D61D411yescharacteristic
123C2×D4×D61C2311yescharacteristic
124C22×C4×D61—21no—
125C22×C4×D61—21no—
126C22×C4×D61C2311yescharacteristic
127C22×C4×D61C2311yescharacteristic
128#14519772—21no—
129#14519772—21no—
130#14519772—21no—
131#14519771—21no—
132#14519770—21no—
133#14519770—21no—
134#14519770—21no—
135#14519769C2×C411yescharacteristic, complemented
136#14519768C2×C411yescharacteristic, complemented
137#14519768C2×C411yescharacteristic, complemented
138#14519767—21no—
139#14519767—21no—
140#14519762—21no—
141#14519762—21no—
142#14519761—21no—
143#14519760—21no—
144#14519759—21no—
145#14519759—21no—
146#14519758—21no—
147#14519752—21no—
148#14519752C2×C411yescharacteristic, complemented
149#14519752C2×C411yescharacteristic, complemented
150#14519751—21no—
151#14519751C2×C411yescharacteristic, complemented
152#14519751C2×C411yescharacteristic, complemented
153#14519750—21no—
154#14519750—21no—
155#14519750—21no—
156#14519750—21no—
157#14519749—21no—
158#14519749—21no—
159#14519749—21no—
160#14519749—21no—
161#14519748—21no—
162#14519748C2×C411yescharacteristic, complemented
163#14519748C2×C411yescharacteristic, complemented
164C4×D244—21no—
165C4×D244C2×C411yescharacteristic
166C4×D244C2×C411yescharacteristic, complemented
167D4×Dic61—21no—
168D4×Dic61C2×C411yescharacteristic, complemented
169D4×Dic61D411yescharacteristic
170#14519739—21no—
171#14519739C2×C411yescharacteristic, complemented
172#14519739D411yescharacteristic
173C4×C22⋊D61—21no—
174C4×C22⋊D61—21no—
175C4×C22⋊D61—21no—
176C4×C22⋊D61C2×C411yescharacteristic
177C4×C22⋊D61C2×C411yescharacteristic
178#14519737—21no—
179#14519737—21no—
180#14519737—21no—
181#14519737D411yescharacteristic
182#14519737D411yescharacteristic
183#14519736C2×C411yescharacteristic, complemented
184#14519735C2×C411yescharacteristic, complemented
185#14519735C2×C411yescharacteristic, complemented
186#14519734—21no—
187#14519733—21no—
188C2×C4⋊Dic61C2×C411yescharacteristic, complemented
189C2×#11758196—21no—
190C4⋊C4×D61—21no—
191C4⋊C4×D61—21no—
192C4⋊C4×D61—21no—
193C4⋊C4×D61—21no—
194C4⋊C4×D61C2×C411yescharacteristic, complemented
195C4⋊C4×D61C2×C411yescharacteristic, complemented
196C4⋊C4×D61D411yescharacteristic
197C4⋊C4×D61C2311yescharacteristic
198C4⋊C4×D61C2311yescharacteristic
199C4⋊C4×D61C2311yescharacteristic
200C22⋊C4×D61—21no—
201C22⋊C4×D61—21no—
202C22⋊C4×D61—21no—
203C22⋊C4×D61—21no—
204C22⋊C4×D61D411yescharacteristic
205C22⋊C4×D61D411yescharacteristic
206C42×D61—21no—
207C42×D61C2311yescharacteristic
208#126×C61—21no—
209#125×C61C2×C411yescharacteristic, complemented
210#123×C61—21no—
211#121×C61—21no—
212#121×C61C2×C411yescharacteristic, complemented
213#121×C61C2×C411yescharacteristic, complemented
214C4×D4×C61—21no—
215C4×D4×C61C2×C411yescharacteristic
216C4×D4×C61C2×C411yescharacteristic, complemented
217#117×C61C2×C411yescharacteristic, complemented
218C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
219C23×D61—21no—
220C23×D61C2×D411yescharacteristic
221C23×D61C2×D411yescharacteristic
222C22×#6923—21no—
223C22×#6923—21no—
224C22×#6923—21no—
225C22×#6923—21no—
226C22×#6923—42no—
227C22×#6923—42no—
228C22×#6923—42no—
229C22×#6923—42no—
230C22×#6923—81no—
231C22×#6923—81no—
232C2×D4×C61—21no—
233C2×D4×C61—21no—
234C2×D4×C61C22⋊C411yescharacteristic
235C2×D4×C61C22×C411yescharacteristic
236C22×C4×C61—21no—
237C22×C4×C61—21no—
238C22×C4×C61C22×C411yescharacteristic
239C22×C4×C61C22×C411yescharacteristic
240C2×C22⋊D61—21no—
241C2×C22⋊D61—21no—
242C2×C22⋊D61—21no—
243C2×C22⋊D61—21no—
244C2×C22⋊D61—21no—
245C2×C22⋊D61C22⋊C411yescharacteristic
246C2×C22⋊D61C22⋊C411yescharacteristic
247C22×Dic61—21no—
248C22×Dic61—21no—
249C22×Dic61C2×D411yescharacteristic
250C22×Dic61C2×D411yescharacteristic
251D4×D61—22no—
252D4×D61—22no—
253D4×D61—21no—
254D4×D61—21no—
255D4×D61—21no—
256D4×D61—21no—
257D4×D61—42no—
258D4×D61—42no—
259D4×D61—81no—
260D4×D61—81no—
261C2×D244—21no—
262C2×D244—21no—
263C2×D244C22⋊C411yescharacteristic
264C2×D244C22×C411yescharacteristic
265C2×C4×D61—21no—
266C2×C4×D61—21no—
267C2×C4×D61—21no—
268C2×C4×D61—21no—
269C2×C4×D61—21no—
270C2×C4×D61—21no—
271C2×C4×D61—21no—
272C2×C4×D61—21no—
273C2×C4×D61—21no—
274C2×C4×D61—21no—
275C2×C4×D61—21no—
276C2×C4×D61—21no—
277C2×C4×D61—21no—
278C2×C4×D61—21no—
279C2×C4×D61—21no—
280C2×C4×D61—81no—
281C2×C4×D61—81no—
282C2×C4×D61—81no—
283C2×C4×D61—81no—
284C2×C4×D61C22×C411yescharacteristic
285C2×C4×D61C22×C411yescharacteristic
286C2×C4×D61C2×D411yescharacteristic
287C2×C4×D61C2×D411yescharacteristic
288C2×C4×D61C2×D411yescharacteristic
289C2×C4×D61C2×D411yescharacteristic
290C2×C4×D61C2×D411yescharacteristic
291C2×C4×D61C2×D411yescharacteristic
292C2×C4×D61C2411yescharacteristic
293C22⋊#6923—42no—
294C22⋊#6923—42no—
295#11758217—42no—
296C2×#92420—21no—
297C2×#92420—21no—
298C2×#92420—21no—
299C2×#92420—21no—
300C2×#92420—42no—
301C4⋊#6923—21no—
302C4⋊#6923—21no—
303C4⋊#6923—21no—
304C4⋊#6923—21no—
305C4⋊#6923—21no—
306C4⋊#6923—21no—
307C4⋊#6923—21no—
308C4⋊#6923—42no—
309C4⋊#6923—42no—
310C4⋊#6923—42no—
311C4⋊#6923—81no—
312C4⋊#6923#4112yes—
313C4×#6923—42no—
314#11758213—42no—
315D61⋊C8—21no—
316D61⋊C8—21no—
317D61⋊C8—21no—
318D61⋊C8—21no—
319D61⋊C8—21no—
320D61⋊C8—21no—
321D61⋊C8—21no—
322D61⋊C8—42no—
323D61⋊C8#4112yes—
324C4⋊C4×C61—21no—
325C4⋊C4×C61—21no—
326C4⋊C4×C61—21no—
327C4⋊C4×C61C22⋊C411yescharacteristic
328C4⋊C4×C61C22×C411yescharacteristic
329C4⋊C4×C61C22×C411yescharacteristic
330C4⋊C4×C61C22×C411yescharacteristic
331C22⋊C4×C61—21no—
332C22⋊C4×C61—21no—
333C22⋊C4×C61—21no—
334C22⋊C4×C61—21no—
335C22⋊C4×C61C22⋊C411yescharacteristic
336C22⋊C4×C61C22⋊C411yescharacteristic
337C42×C61—21no—
338C42×C61C22×C411yescharacteristic
339C22⋊Dic61—21no—
340C22⋊Dic61—21no—
341C22⋊Dic61—21no—
342C22⋊Dic61—21no—
343C22⋊Dic61C22⋊C411yescharacteristic
344C22⋊Dic61C22⋊C411yescharacteristic
345#11758198—21no—
346#11758198—21no—
347#11758198—21no—
348#11758198—21no—
349#11758198—21no—
350#11758198—21no—
351#11758198—21no—
352#11758198—21no—
353#11758198C22⋊C411yescharacteristic
354#11758198C22⋊C411yescharacteristic
355#11758198C22⋊C411yescharacteristic
356#11758198C22⋊C411yescharacteristic
357C4⋊Dic61—21no—
358C4⋊Dic61—21no—
359C4⋊Dic61—21no—
360C4⋊Dic61C22⋊C411yescharacteristic
361C4⋊Dic61C22×C411yescharacteristic
362C4⋊Dic61C22×C411yescharacteristic
363C4⋊Dic61C22×C411yescharacteristic
364#11758196—21no—
365#11758196—21no—
366#11758196—21no—
367#11758196—21no—
368#11758196—21no—
369#11758196—21no—
370#11758196—21no—
371#11758196—21no—
372#11758196—21no—
373#11758196C22⋊C411yescharacteristic
374#11758196C22⋊C411yescharacteristic
375C4×Dic61—21no—
376C4×Dic61—21no—
377C4×Dic61—21no—
378C4×Dic61C22×C411yescharacteristic
379C4×Dic61C2×D411yescharacteristic
380C4×Dic61C2×D411yescharacteristic
381C23×C61—21no—
382C23×C61C2×C22⋊C411yescharacteristic
383C23×C61C2×C22⋊C411yescharacteristic
384C22×D61—21no—
385C22×D61—21no—
386C22×D61—21no—
387C22×D61—21no—
388C22×D61—21no—
389C22×D61—21no—
390C22×D61—21no—
391C22×D61—21no—
392C22×D61—21no—
393C22×D61—21no—
394C22×D61—21no—
395C22×D61—41no—
396C22×D61—41no—
397C22×D61—41no—
398C22×D61—41no—
399C22×D61—41no—
400C22×D61—41no—
401C22×D61C2×C22⋊C411yescharacteristic
402C22×D61C2×C22⋊C411yescharacteristic
403C22×D61AGL(1,ℤ/8)12yes—
404C22×D61#13712yes—
405C22×D61C22×D411yescharacteristic
406C2×#6923—22no—
407C2×#6923—41no—
408C2×#6923—41no—
409C2×#6923—41no—
410C2×#6923—41no—
411C2×#6923—41no—
412C2×#6923—41no—
413C2×#6923—41no—
414C2×#6923—41no—
415C2×#6923—41no—
416C2×#6923—41no—
417C2×#6923—41no—
418C2×#6923—84no—
419C2×#6923—84no—
420D4×C61—22no—
421D4×C61—21no—
422D4×C61—21no—
423D4×C61—42no—
424D4×C61—81no—
425C2×C4×C61—21no—
426C2×C4×C61—21no—
427C2×C4×C61—21no—
428C2×C4×C61—21no—
429C2×C4×C61—21no—
430C2×C4×C61—21no—
431C2×C4×C61—21no—
432C2×C4×C61—81no—
433C2×C4×C61—81no—
434C2×C4×C61C2×C22⋊C411yescharacteristic
435C2×C4×C61C2×C22⋊C411yescharacteristic
436C2×C4×C61C2×C22⋊C411yescharacteristic
437C2×C4×C61C2×C22⋊C411yescharacteristic
438C2×C4×C61C23×C411yescharacteristic
439C22⋊D61—22no—
440C22⋊D61—22no—
441C22⋊D61—42no—
442C22⋊D61—42no—
443C22⋊D61—41no—
444C22⋊D61—41no—
445C22⋊D61—81no—
446C22⋊D61—81no—
447C2×Dic61—21no—
448C2×Dic61—21no—
449C2×Dic61—21no—
450C2×Dic61—21no—
451C2×Dic61—21no—
452C2×Dic61—21no—
453C2×Dic61—21no—
454C2×Dic61—81no—
455C2×Dic61—81no—
456C2×Dic61C2×C22⋊C411yescharacteristic
457C2×Dic61C2×C22⋊C411yescharacteristic
458C2×Dic61C2×C22⋊C411yescharacteristic
459C2×Dic61C2×C22⋊C411yescharacteristic
460C2×Dic61C22×D411yescharacteristic
461D244—22no—
462D244—21no—
463D244—21no—
464D244—42no—
465D244—81no—
466C4×D61—21no—
467C4×D61—21no—
468C4×D61—21no—
469C4×D61—21no—
470C4×D61—21no—
471C4×D61—21no—
472C4×D61—21no—
473C4×D61—21no—
474C4×D61—21no—
475C4×D61—21no—
476C4×D61—21no—
477C4×D61—21no—
478C4×D61—21no—
479C4×D61—21no—
480C4×D61—21no—
481C4×D61—21no—
482C4×D61—41no—
483C4×D61—41no—
484C4×D61—41no—
485C4×D61—41no—
486C4×D61—41no—
487C4×D61—41no—
488C4×D61—81no—
489C4×D61—81no—
490C4×D61—81no—
491C4×D61—81no—
492C4×D61C2×#4111yescharacteristic
493C4×D61C2×#4111yescharacteristic
494C4×D61H(5,𝔽2)11yescharacteristic
495C4×D612−1+411yescharacteristic
496#92420—22no—
497#92420—41no—
498#92420—41no—
499#92420—41no—
500#22493—611nomaximal, Sylow
501C22×C61—21no—
502C22×C61—21no—
503C22×C61—21no—
504C22×C61—21no—
505C22×C61—21no—
506C22×C61—41no—
507C22×C61—41no—
508C22×C61—41no—
509C22×C61#41712yes—
510C22×C61C22×C22⋊C411yescharacteristic
511C2×D61—21no—
512C2×D61—21no—
513C2×D61—22no—
514C2×D61—22no—
515C2×D61—22no—
516C2×D61—22no—
517C2×D61—21no—
518C2×D61—21no—
519C2×D61—21no—
520C2×D61—41no—
521C2×D61—41no—
522C2×D61—41no—
523C2×D61—41no—
524C2×D61—41no—
525C2×D61—41no—
526C2×D61—41no—
527C2×D61—81no—
528C2×D61—81no—
529C2×D61—81no—
530C2×D61—81no—
531C2×D61#41712yes—
532C2×D61#54611yescharacteristic
533C2×D61#54711yescharacteristic
534C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
535C2×D61C2×#13711yescharacteristic
536C2×D61#57611yescharacteristic
537C2×D61#57711yescharacteristic
538#6923—42no—
539#6923—81no—
540#6923—81no—
541#6923—81no—
542C4×C61—21no—
543C4×C61—21no—
544C4×C61—21no—
545C4×C61—21no—
546C4×C61—41no—
547C4×C61—41no—
548C4×C61—41no—
549C4×C61C4×#4111yescharacteristic
550C4×C61#52011yescharacteristic
551Dic61—21no—
552Dic61—21no—
553Dic61—21no—
554Dic61—21no—
555Dic61—41no—
556Dic61—41no—
557Dic61—41no—
558Dic61#54611yescharacteristic
559Dic61#54711yescharacteristic
560C2×#553—611no—
561C2×#435—611no—
562D4×C4⋊C4—611no—
563#1992—611no—
564#1989—611no—
565#1895—611no—
566#1893—611no—
567#1874—611no—
568#1874—611no—
569#1825—611no—
570#1824—611no—
571#1802—611no—
572#1762—611no—
573#1736—611no—
574C2×#340—611no—
575C2×C61—22no—
576C2×C61—41no—
577C2×C61—81no—
578C2×C61#233911yescharacteristic
579C2×C61C2×#41711yescharacteristic
580C2×C61#289711yescharacteristic
581D61—22no—
582D61—41no—
583D61—81no—
584D61#331811yescharacteristic
585D61#332011yescharacteristic
586D61#334511yescharacteristic
587D61#334611yescharacteristic
588C22×M16—611no—
589C23×C8—611no—
590#553—611no—
591#553—611no—
592#553—611no—
593#553—611no—
594#553—611no—
595#553—611no—
596#553—611no—
597#553—1221no—
598#553—1221no—
599#553—1221no—
600#553—1221no—
601#553#692311yescharacteristic, complemented
602C2×#126—1221no—
603C2×#125—611no—
604C2×#123—1221no—
605C2×#121—611no—
606C2×#121—611no—
607C2×#121—1221no—
608C2×C4×D4—611no—
609C2×C4×D4—611no—
610C2×C4×D4—1221no—
611C2×C4×D4—1221no—
612C2×#117—611no—
613C22×C4⋊C4—611no—
614C22×C4⋊C4—611no—
615C22×C4⋊C4—611no—
616#435—1221no—
617#435—1221no—
618#435—1221no—
619#435—1221no—
620C2×C4⋊C8—611no—
621C2×#102—611no—
622C2×#102—611no—
623C2×#102—611no—
624C2×#102—611no—
625C2×C22⋊C8—611no—
626C2×C22⋊C8—611no—
627C2×#97—611no—
628#389—1221no—
629#385—1221no—
630#385—1221no—
631#384—611no—
632#380—611no—
633#380—611no—
634C4×C4⋊C4—611no—
635#340—611no—
636#340—611no—
637#340—611no—
638#340—611no—
639#340—611no—
640#340—611no—
641#340—611no—
642#340—611no—
643#340—611no—
644#340—611no—
645#340—611no—
646#340—611no—
647C61#2249311yescharacteristic, complemented, Sylow
648C22×D4—611no—
649C22×D4—611no—
650C22×D4—1221no—
651C22×D4—1221no—
652C23×C4—611no—
653C23×C4—611no—
654C23×C4—1221no—
655C23×C4—1221no—
656C23×C4—1221no—
657C23×C4—1221no—
658C2×M16—1222no—
659C2×M16—1221no—
660C2×M16—1221no—
661C2×M16—2441no—
662C22×C8—611no—
663C22×C8—611no—
664C22×C8—611no—
665C22×C8—611no—
666C22×C8—1222no—
667C22×C8—1221no—
668C22×C8—1221no—
669C22×C8—2441no—
670#126—21no—
671#126—1221no—
672#126—1221no—
673#126—1221no—
674#126—1221no—
675#126—1221no—
676#126—1221no—
677#126—1221no—
678#125—611no—
679#125—611no—
680#125—611no—
681#125—1221no—
682#125—1221no—
683#125C2×#692311yescharacteristic, complemented
684#123—21no—
685#123—1221no—
686#123—1221no—
687#123—1221no—
688#123—1221no—
689#123—1221no—
690#123—1221no—
691#123—1221no—
692#121—21no—
693#121—611no—
694#121—611no—
695#121—611no—
696#121—611no—
697#121—611no—
698#121—611no—
699#121—1221no—
700#121—1221no—
701#121—1221no—
702#121—1221no—
703#121—1221no—
704#121—1221no—
705#121—1221no—
706#121—1221no—
707#121—1221no—
708#121—1221no—
709#121—1221no—
710#121C2×#692311yescharacteristic, complemented
711#121C2×#692311yescharacteristic, complemented
712C4×D4—21no—
713C4×D4—611no—
714C4×D4—611no—
715C4×D4—611no—
716C4×D4—611no—
717C4×D4—611no—
718C4×D4—611no—
719C4×D4—611no—
720C4×D4—611no—
721C4×D4—611no—
722C4×D4—611no—
723C4×D4—1221no—
724C4×D4—1221no—
725C4×D4—1221no—
726C4×D4—1221no—
727C4×D4—1221no—
728C4×D4—1221no—
729C4×D4—1221no—
730C4×D4—1221no—
731C4×D4—1221no—
732C4×D4—2444no—
733C4×D4C2×#692311yescharacteristic
734C4×D4C2×#692311yescharacteristic, complemented
735#117—611no—
736#117—611no—
737#117—611no—
738#117—1221no—
739#117—1221no—
740#117C2×#692311yescharacteristic, complemented
741C2×C4⋊C4—611no—
742C2×C4⋊C4—611no—
743C2×C4⋊C4—611no—
744C2×C4⋊C4—611no—
745C2×C4⋊C4—611no—
746C2×C4⋊C4—611no—
747C2×C4⋊C4—611no—
748C2×C4⋊C4—611no—
749C2×C4⋊C4—611no—
750C2×C4⋊C4—611no—
751C2×C4⋊C4—611no—
752C2×C4⋊C4—1221no—
753C2×C4⋊C4—1221no—
754C2×C4⋊C4—1221no—
755C2×C4⋊C4—1221no—
756C2×C4⋊C4—1222no—
757C2×C4⋊C4—1222no—
758C2×C4⋊C4—1221no—
759C2×C4⋊C4—1221no—
760C2×C4⋊C4—1221no—
761C2×C4⋊C4—1221no—
762C2×C4⋊C4—1221no—
763C2×C4⋊C4—2441no—
764C2×C4⋊C4—2441no—
765C2×C4⋊C4C2×#692311yescharacteristic, complemented
766C2×C22⋊C4—611no—
767C2×C22⋊C4—611no—
768C2×C22⋊C4—1221no—
769C2×C22⋊C4—1221no—
770C2×C22⋊C4—1221no—
771C2×C22⋊C4—1221no—
772C2×C22⋊C4—1221no—
773C2×C22⋊C4—1221no—
774C2×C42—611no—
775C2×C42—1221no—
776C2×C42—1221no—
777C4⋊C8—1221no—
778C4⋊C8—1221no—
779#102—1222no—
780#102—1222no—
781#102—2441no—
782#102—2441no—
783C22⋊C8—1221no—
784C22⋊C8—1221no—
785C22⋊C8—1221no—
786C22⋊C8—1221no—
787#97—1221no—
788#97—1221no—
789#95—1221no—
790#95—1221no—
791#95—1221no—
792C24—611no—
793C24—611no—
794C24—1221no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—611no—
798C2×D4—611no—
799C2×D4—611no—
800C2×D4—611no—
801C2×D4—1221no—
802C2×D4—1221no—
803C2×D4—1221no—
804C2×D4—1221no—
805C2×D4—1221no—
806C2×D4—1221no—
807C2×D4—1221no—
808C2×D4—1222no—
809C2×D4—1222no—
810C2×D4—1221no—
811C2×D4—1221no—
812C2×D4—1221no—
813C2×D4—1221no—
814C2×D4—4881no—
815C2×D4—4881no—
816C2×D4—2442no—
817C2×D4—2442no—
818C2×D4C22⋊#692311yescharacteristic
819C2×D4C22×#692311yescharacteristic
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—611no—
823C22×C4—611no—
824C22×C4—611no—
825C22×C4—611no—
826C22×C4—611no—
827C22×C4—611no—
828C22×C4—611no—
829C22×C4—611no—
830C22×C4—611no—
831C22×C4—611no—
832C22×C4—611no—
833C22×C4—1221no—
834C22×C4—1221no—
835C22×C4—1221no—
836C22×C4—1221no—
837C22×C4—1221no—
838C22×C4—1221no—
839C22×C4—1221no—
840C22×C4—1221no—
841C22×C4—1221no—
842C22×C4—1221no—
843C22×C4—1221no—
844C22×C4—1221no—
845C22×C4—1221no—
846C22×C4—1221no—
847C22×C4—1221no—
848C22×C4—1221no—
849C22×C4—1221no—
850C22×C4—1221no—
851C22×C4—1221no—
852C22×C4—1221no—
853C22×C4—1221no—
854C22×C4—4881no—
855C22×C4—4881no—
856C22×C4—4881no—
857C22×C4—4881no—
858C22×C4—4881no—
859C22×C4—4881no—
860C22×C4—2442no—
861C22×C4—2442no—
862C22×C4—2442no—
863C22×C4—2442no—
864C22×C4C22×#692311yescharacteristic
865C22×C4C22×#692311yescharacteristic
866M16—2442no—
867M16—2442no—
868C2×C8—612no—
869C2×C8—1221no—
870C2×C8—1221no—
871C2×C8—1221no—
872C2×C8—1221no—
873C2×C8—1221no—
874C2×C8—1221no—
875C2×C8—1221no—
876C2×C8—1221no—
877C2×C8—1221no—
878C2×C8—1221no—
879C2×C8—1221no—
880C2×C8—2442no—
881C2×C8—2442no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—611no—
886C4⋊C4—611no—
887C4⋊C4—611no—
888C4⋊C4—612no—
889C4⋊C4—611no—
890C4⋊C4—611no—
891C4⋊C4—611no—
892C4⋊C4—1221no—
893C4⋊C4—1221no—
894C4⋊C4—1221no—
895C4⋊C4—1221no—
896C4⋊C4—1221no—
897C4⋊C4—1221no—
898C4⋊C4—1221no—
899C4⋊C4—1221no—
900C4⋊C4—1221no—
901C4⋊C4—1221no—
902C4⋊C4—1221no—
903C4⋊C4—1221no—
904C4⋊C4—1221no—
905C4⋊C4—1221no—
906C4⋊C4—1221no—
907C4⋊C4—1221no—
908C4⋊C4—1221no—
909C4⋊C4—1221no—
910C4⋊C4—1221no—
911C4⋊C4—4881no—
912C4⋊C4—2442no—
913C4⋊C4—2442no—
914C4⋊C4—2442no—
915C4⋊C4C22⋊#692311yescharacteristic
916C4⋊C4C22×#692311yescharacteristic
917C4⋊C4C22×#692311yescharacteristic
918C4⋊C4C22×#692311yescharacteristic
919C22⋊C4—21no—
920C22⋊C4—21no—
921C22⋊C4—21no—
922C22⋊C4—21no—
923C22⋊C4—611no—
924C22⋊C4—611no—
925C22⋊C4—611no—
926C22⋊C4—611no—
927C22⋊C4—611no—
928C22⋊C4—611no—
929C22⋊C4—1221no—
930C22⋊C4—1221no—
931C22⋊C4—1221no—
932C22⋊C4—1221no—
933C22⋊C4—1221no—
934C22⋊C4—1221no—
935C22⋊C4—1221no—
936C22⋊C4—1221no—
937C22⋊C4—1221no—
938C22⋊C4—1221no—
939C22⋊C4—1221no—
940C22⋊C4—1221no—
941C22⋊C4—2442no—
942C22⋊C4—2442no—
943C22⋊C4C22⋊#692311yescharacteristic
944C22⋊C4C22⋊#692311yescharacteristic
945C42—21no—
946C42—611no—
947C42—611no—
948C42—611no—
949C42—1221no—
950C42—1221no—
951C42—1221no—
952C42—2442no—
953C42C22×#692311yescharacteristic
954C23—21no—
955C23—611no—
956C23—612no—
957C23—612no—
958C23—611no—
959C23—611no—
960C23—1221no—
961C23—1221no—
962C23—1221no—
963C23—1221no—
964C23—1221no—
965C23—1221no—
966C23—1221no—
967C23—1221no—
968C23—1221no—
969C23—1221no—
970C23—1221no—
971C23—2441no—
972C23—2441no—
973C23—2441no—
974C23—2441no—
975C23—2441no—
976C23—2441no—
977C23C2×C22⋊#692311yescharacteristic
978C23C2×C22⋊#692311yescharacteristic
979D4—22no—
980D4—21no—
981D4—21no—
982D4—42no—
983D4—81no—
984D4—1222no—
985D4—1222no—
986D4—1222no—
987D4—1221no—
988D4—1221no—
989D4—4881no—
990D4—4881no—
991D4—4881no—
992D4—2442no—
993D4—2441no—
994D4—2441no—
995D4—2442no—
996D4—2442no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—81no—
1005C2×C4—81no—
1006C2×C4—611no—
1007C2×C4—611no—
1008C2×C4—611no—
1009C2×C4—611no—
1010C2×C4—611no—
1011C2×C4—611no—
1012C2×C4—611no—
1013C2×C4—611no—
1014C2×C4—611no—
1015C2×C4—1221no—
1016C2×C4—1221no—
1017C2×C4—1221no—
1018C2×C4—1221no—
1019C2×C4—1221no—
1020C2×C4—1221no—
1021C2×C4—1221no—
1022C2×C4—1221no—
1023C2×C4—1221no—
1024C2×C4—1221no—
1025C2×C4—1221no—
1026C2×C4—1221no—
1027C2×C4—1221no—
1028C2×C4—1221no—
1029C2×C4—1221no—
1030C2×C4—1221no—
1031C2×C4—1221no—
1032C2×C4—1221no—
1033C2×C4—1221no—
1034C2×C4—1221no—
1035C2×C4—1222no—
1036C2×C4—1221no—
1037C2×C4—1221no—
1038C2×C4—1221no—
1039C2×C4—4881no—
1040C2×C4—4881no—
1041C2×C4—4881no—
1042C2×C4—4881no—
1043C2×C4—4881no—
1044C2×C4—4884no—
1045C2×C4—4884no—
1046C2×C4—4881no—
1047C2×C4—2441no—
1048C2×C4—2441no—
1049C2×C4—2441no—
1050C2×C4—2441no—
1051C2×C4—2441no—
1052C2×C4—2441no—
1053C2×C4—2441no—
1054C2×C4—2441no—
1055C2×C4—2441no—
1056C2×C4—2441no—
1057C2×C4—2441no—
1058C2×C4—2441no—
1059C2×C4—2441no—
1060C2×C4—2441no—
1061C2×C4—2441no—
1062C2×C4—2441no—
1063C2×C4—2441no—
1064C2×C4C2×C22⋊#692311yescharacteristic
1065C2×C4C2×C22⋊#692311yescharacteristic
1066C2×C4C2×C22⋊#692311yescharacteristic
1067C2×C4C2×C22⋊#692311yescharacteristic
1068C2×C4C23×#692311yescharacteristic
1069C8—1222no—
1070C8—2441no—
1071C8—2441no—
1072C8—2441no—
1073C22—21no—
1074C22—21no—
1075C22—21no—
1076C22—21no—
1077C22—21no—
1078C22—41no—
1079C22—41no—
1080C22—41no—
1081C22—611no—
1082C22—611no—
1083C22—611no—
1084C22—611no—
1085C22—611no—
1086C22—611no—
1087C22—612no—
1088C22—1222no—
1089C22—1222no—
1090C22—1222no—
1091C22—1222no—
1092C22—1221no—
1093C22—1221no—
1094C22—1221no—
1095C22—1221no—
1096C22—1221no—
1097C22—4881no—
1098C22—4881no—
1099C22—4881no—
1100C22—4881no—
1101C22—2441no—
1102C22—2441no—
1103C22—2441no—
1104C22—2441no—
1105C22—2441no—
1106C22—2441no—
1107C22—2441no—
1108C22#1684075312yes—
1109C22C22×C22⋊#692311yescharacteristic
1110C4—21no—
1111C4—21no—
1112C4—21no—
1113C4—21no—
1114C4—41no—
1115C4—41no—
1116C4—41no—
1117C4—611no—
1118C4—611no—
1119C4—1221no—
1120C4—1221no—
1121C4—1221no—
1122C4—1221no—
1123C4—4881no—
1124C4—4881no—
1125C4—4881no—
1126C4—2442no—
1127C4—2441no—
1128C4—2441no—
1129C4—2441no—
1130C4#41×#692311yescharacteristic
1131C4#1684083111yescharacteristic
1132C2—22no—
1133C2—41no—
1134C2—81no—
1135C2—611no—
1136C2—611no—
1137C2—611no—
1138C2—611no—
1139C2—1222no—
1140C2—4881no—
1141C2—2441no—
1142C2#2146232211yescharacteristic
1143C2C2×#1684075311yescharacteristic
1144C2#2146244011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#553C4
socleC22×C61C22×C22⋊C4
prime radical#553×D61C2
cosocleC2×C4×D61C24
hypercenter#553#6923
hypocenterC61#22493
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. D61⋊#435C2semidirect
2. D4×C4⋊#6923C2semidirect
3. #21462002C2semidirect
4. #21461999C2semidirect
5. #21461835C2semidirect
6. #21461833C2semidirect
7. #21461806C2semidirect
8. #21461806C2semidirect
9. #21461724C2semidirect
10. #21461723C2semidirect
11. #21461687C2semidirect
12. #21461589C2semidirect
13. #21461508C2semidirect
14. C2×#16840635C2semidirect
52. #16840465C4semidirect
53. #16840464C4semidirect
55. #16840462C4semidirect
57. #16840460C4semidirect
58. #16840459C4semidirect
59. #16840458C4semidirect
61. #16840456C4semidirect
74. C61×#553C4semidirect
135. #14519769C2×C4semidirect
136. #14519768C2×C4semidirect
137. #14519768C2×C4semidirect
148. #14519752C2×C4semidirect
149. #14519752C2×C4semidirect
151. #14519751C2×C4semidirect
152. #14519751C2×C4semidirect
162. #14519748C2×C4semidirect
163. #14519748C2×C4semidirect
166. C4×D244C2×C4semidirect
168. D4×Dic61C2×C4semidirect
171. #14519739C2×C4semidirect
183. #14519736C2×C4semidirect
184. #14519735C2×C4semidirect
185. #14519735C2×C4semidirect
188. C2×C4⋊Dic61C2×C4semidirect
194. C4⋊C4×D61C2×C4semidirect
195. C4⋊C4×D61C2×C4semidirect
209. #125×C61C2×C4semidirect
212. #121×C61C2×C4semidirect
213. #121×C61C2×C4semidirect
216. C4×D4×C61C2×C4semidirect
217. #117×C61C2×C4semidirect
218. C2×C4⋊C4×C61C2×C4semidirect
601. #553#6923semidirect
647. C61#22493semidirect
683. #125C2×#6923semidirect
710. #121C2×#6923semidirect
711. #121C2×#6923semidirect
734. C4×D4C2×#6923semidirect
740. #117C2×#6923semidirect
765. C2×C4⋊C4C2×#6923semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4352
D4×C4⋊#69232
#214620022
#214619992
#214618352
#214618332
#214618062
#214617242
#214617232
#214616872
#214615892
#214615082
C2×#168406352
#553×D612
#2249361