Finite Group Databasebeta

← #30620171

Subgroups — #30620171

Order 15616.

1446 conjugacy classes of subgroups.

The subgroup lattice has 1230 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#435C211yesmaximal, characteristic
2C2×#16840755C211yesmaximal, characteristic, complemented
3C22×#14519840C211yesmaximal, characteristic, complemented
4#21462335C211yesmaximal, characteristic
5#21461985C211yesmaximal, characteristic, complemented
6#21461950C211yesmaximal, characteristic, complemented
7#21461834C211yesmaximal, characteristic, complemented
8#21461832C211yesmaximal, characteristic, complemented
9#21461805C211yesmaximal, characteristic, complemented
10#21461804C211yesmaximal, characteristic, complemented
11#21461690C211yesmaximal, characteristic, complemented
12#21461658C211yesmaximal, characteristic, complemented
13#21461658C211yesmaximal, characteristic, complemented
14#21461591C211yesmaximal, characteristic, complemented
15D4×Q8×D61C211yesmaximal, characteristic
16C2×D61⋊M16C2211yescharacteristic
17C22×D61⋊C8C2211yescharacteristic
18C2×#14519856C2211yescharacteristic
19C22×C4⋊#6923C2211yescharacteristic
20#16840794—21no—
21#16840793—21no—
22#16840792—21no—
23#16840791—21no—
24D61⋊(C4⋊C8)C2211yescharacteristic
25#16840755—24no—
26C2×#14519840—24no—
27C2×#14519840C2211yescharacteristic
28C2×#14519840C2211yescharacteristic
29C2×#14519840C2211yescharacteristic
30C2×#14519840C2211yescharacteristic
31C2×#14519840C2211yescharacteristic
32C2×#14519840C2211yescharacteristic
33C2×#14519840C2211yescharacteristic
34C2×#14519840C2211yescharacteristic
35C2×#14519840C2211yescharacteristic
36C2×#14519840C2211yescharacteristic
37C2×#14519840C2211yescharacteristic
38C2×#14519840C2211yescharacteristic
39D61⋊(C22⋊C8)C2211yescharacteristic
40D61⋊(C22⋊C8)C2211yescharacteristic
41#16840721C2211yescharacteristic
42#16840712—21no—
43#16840711—21no—
44#16840710—21no—
45#16840706C2211yescharacteristic
46#16840704C2211yescharacteristic
47#16840704C2211yescharacteristic
48C4×C4⋊#6923C2211yescharacteristic
49C22⋊C4×#6923—21no—
50#16840635C2211yescharacteristic
51#16840635C2211yescharacteristic
52#16840635C2211yescharacteristic
53#16840635C2211yescharacteristic
54C22×Q8×D61C2211yescharacteristic
55C22×Q8×D61C2211yescharacteristic
56Q8×D244C411yescharacteristic, complemented
57D4×Dic122—21no—
58D4×Dic122C411yescharacteristic, complemented
59#16840427—21no—
60#16840427C411yescharacteristic, complemented
61Q8×C22⋊D61C411yescharacteristic, complemented
62Q8×C22⋊D61C411yescharacteristic, complemented
63#16840425—21no—
64#16840425—21no—
65#16840425C411yescharacteristic, complemented
66#16840425C411yescharacteristic, complemented
67C4⋊Q8×D61—21no—
68C4⋊Q8×D61C2211yescharacteristic
69C22⋊Q8×D61—21no—
70C22⋊Q8×D61—21no—
71C22⋊Q8×D61C2211yescharacteristic
72C22⋊Q8×D61C2211yescharacteristic
73C4×Q8×D61C2211yescharacteristic
74C4×D4×D61—21no—
75C4×D4×D61C2211yescharacteristic
76D4×Q8×C61C411yescharacteristic, complemented
77C23×#6923—21no—
78C2×#11758213—21no—
79D61⋊M16—22no—
80D61⋊M16—41no—
81C2×#11758217—21no—
82C2×D61⋊C8—22no—
83C2×D61⋊C8—21no—
84C2×D61⋊C8—41no—
85C2×D61⋊C8C2311yescharacteristic
86C2×D61⋊C8C2311yescharacteristic
87C2×D61⋊C8C2311yescharacteristic
88C2×D61⋊C8C2311yescharacteristic
89C22×#92420—21no—
90#14519856—22no—
91#14519856—41no—
92C2×C4⋊#6923—22no—
93C2×C4⋊#6923—21no—
94C2×C4⋊#6923—41no—
95C2×C4⋊#6923C2311yescharacteristic
96C2×C4⋊#6923C2311yescharacteristic
97C2×C4⋊#6923C2311yescharacteristic
98C2×C4⋊#6923C2311yescharacteristic
99C2×C22⋊#6923—21no—
100C2×C22⋊#6923—21no—
101C2×C22⋊#6923—21no—
102C2×C4×#6923—21no—
103C2×C4×#6923—21no—
104#14519844—21no—
105C4⋊#92420—21no—
106#14519840—22no—
107#14519840—22no—
108#14519840—22no—
109#14519840—22no—
110#14519840—22no—
111#14519840—22no—
112#14519840—22no—
113#14519840—41no—
114#14519840—41no—
115#14519840—41no—
116#14519840—41no—
117#14519840D414yescomplemented
118#14519834—21no—
119#14519834—21no—
120C22⋊#92420—21no—
121C22⋊#92420—21no—
122#14519832—21no—
123#14519832—21no—
124(C2×#6923)⋊C4—21no—
125(C2×#6923)⋊C4—21no—
126(C2×#6923)⋊C4—21no—
127(C2×#6923)⋊C4—21no—
128(C2×#6923)⋊C4—21no—
129C22×Dic122—21no—
130C22×Dic122—21no—
131C22×Dic122C2×C411yescharacteristic
132C22×Dic122C2×C411yescharacteristic, complemented
133C2×Q8×D61—21no—
134C2×Q8×D61—21no—
135C2×Q8×D61—21no—
136C2×Q8×D61—21no—
137C2×Q8×D61—22no—
138C2×Q8×D61—22no—
139C2×Q8×D61—22no—
140C2×Q8×D61—22no—
141C2×Q8×D61—41no—
142C2×Q8×D61—41no—
143C2×Q8×D61—41no—
144C2×Q8×D61—41no—
145C2×Q8×D61C2×C411yescharacteristic
146C2×Q8×D61C2×C411yescharacteristic
147C2×Q8×D61C2×C411yescharacteristic, complemented
148C2×Q8×D61C2×C411yescharacteristic, complemented
149C2×Q8×D61C2311yescharacteristic
150C2×Q8×D61C2311yescharacteristic
151C2×Q8×D61C2311yescharacteristic
152C2×D4×D61D411yescharacteristic
153C22×C4×D61—21no—
154C22×C4×D61—21no—
155C22×C4×D61C2311yescharacteristic
156C22×C4×D61C2311yescharacteristic
157#14519777—21no—
158#14519777C2×C411yescharacteristic, complemented
159#14519776—21no—
160#14519776—21no—
161#14519776—21no—
162#14519776—21no—
163#14519776—21no—
164#14519776—21no—
165#14519775—21no—
166#14519775—21no—
167#14519775C2×C411yescharacteristic, complemented
168#14519775C2×C411yescharacteristic, complemented
169#14519757—21no—
170#14519757—21no—
171#14519757C2×C411yescharacteristic
172#14519757C2×C411yescharacteristic, complemented
173#14519756—21no—
174#14519756—21no—
175#14519756C2×C411yescharacteristic
176#14519756C2×C411yescharacteristic, complemented
177#14519755—21no—
178#14519755—21no—
179#14519755—21no—
180#14519755—21no—
181#14519755—21no—
182#14519755—21no—
183#14519754—21no—
184#14519754—21no—
185#14519754—21no—
186#14519754—21no—
187#14519754—21no—
188#14519754—21no—
189#14519753—21no—
190#14519753—21no—
191#14519753C2×C411yescharacteristic
192#14519753C2×C411yescharacteristic, complemented
193Q8×Dic61C2×C411yescharacteristic, complemented
194C4×Dic122—21no—
195C4×Dic122C2×C411yescharacteristic, complemented
196#14519742—21no—
197#14519742C2×C411yescharacteristic, complemented
198C4×D244—21no—
199C4×D244C2×C411yescharacteristic
200D4×Dic61—21no—
201D4×Dic61D411yescharacteristic
202#14519739—21no—
203#14519739D411yescharacteristic
204C4×C22⋊D61—21no—
205C4×C22⋊D61—21no—
206C4×C22⋊D61C2×C411yescharacteristic
207C4×C22⋊D61C2×C411yescharacteristic
208#14519737—21no—
209#14519737—21no—
210#14519737D411yescharacteristic
211#14519737D411yescharacteristic
212C4⋊C4×D61—21no—
213C4⋊C4×D61—21no—
214C4⋊C4×D61—21no—
215C4⋊C4×D61—21no—
216C4⋊C4×D61—21no—
217C4⋊C4×D61D411yescharacteristic
218C4⋊C4×D61C2311yescharacteristic
219C22⋊C4×D61—21no—
220C22⋊C4×D61—21no—
221C22⋊C4×D61D411yescharacteristic
222C22⋊C4×D61D411yescharacteristic
223C42×D61—21no—
224C42×D61C2311yescharacteristic
225C22×Q8×C61C2×C411yescharacteristic
226C22×Q8×C61C2×C411yescharacteristic, complemented
227C4⋊Q8×C61—21no—
228C4⋊Q8×C61C2×C411yescharacteristic, complemented
229C22⋊Q8×C61—21no—
230C22⋊Q8×C61—21no—
231C22⋊Q8×C61C2×C411yescharacteristic
232C22⋊Q8×C61C2×C411yescharacteristic, complemented
233C4×Q8×C61C2×C411yescharacteristic, complemented
234C4×D4×C61—21no—
235C4×D4×C61C2×C411yescharacteristic
236C23×D61C2×D411yescharacteristic
237C23×D61C2×D411yescharacteristic
238C22×#6923—21no—
239C22×#6923—21no—
240C22×#6923—21no—
241C22×#6923—21no—
242C22×#6923—42no—
243C22×#6923—42no—
244C22×#6923—81no—
245C2×Q8×C61—21no—
246C2×Q8×C61—21no—
247C2×Q8×C61—22no—
248C2×Q8×C61—22no—
249C2×Q8×C61—41no—
250C2×Q8×C61—41no—
251C2×Q8×C61C22×C411yescharacteristic
252C2×Q8×C61C22×C411yescharacteristic
253C2×Q8×C61C22×C411yescharacteristic
254C2×D4×C61C22⋊C411yescharacteristic
255C22×C4×C61—21no—
256C22×C4×C61—21no—
257C22×C4×C61C22×C411yescharacteristic
258C22×C4×C61C22×C411yescharacteristic
259C2×C22⋊D61C22⋊C411yescharacteristic
260C2×C22⋊D61C22⋊C411yescharacteristic
261C22×Dic61—21no—
262C22×Dic61—21no—
263C22×Dic61C2×D411yescharacteristic
264C22×Dic61C2×D411yescharacteristic
265Q8×D61—21no—
266Q8×D61—21no—
267Q8×D61—22no—
268Q8×D61—22no—
269Q8×D61—21no—
270Q8×D61—21no—
271Q8×D61—21no—
272Q8×D61—21no—
273Q8×D61—21no—
274Q8×D61—21no—
275Q8×D61—21no—
276Q8×D61—21no—
277Q8×D61—22no—
278Q8×D61—22no—
279Q8×D61—41no—
280Q8×D61—41no—
281Q8×D61—41no—
282Q8×D61—41no—
283Q8×D61—42no—
284Q8×D61—42no—
285Q8×D61—42no—
286Q8×D61—42no—
287Q8×D61—42no—
288Q8×D61—42no—
289Q8×D61—42no—
290Q8×D61—42no—
291Q8×D61C2×D412yes—
292Q8×D61#4112yes—
293D4×D61—22no—
294D4×D61—22no—
295C2×D244C22⋊C411yescharacteristic
296C2×C4×D61—21no—
297C2×C4×D61—21no—
298C2×C4×D61—21no—
299C2×C4×D61—21no—
300C2×C4×D61—21no—
301C2×C4×D61—21no—
302C2×C4×D61—21no—
303C2×C4×D61—21no—
304C2×C4×D61—21no—
305C2×C4×D61—21no—
306C2×C4×D61—21no—
307C2×C4×D61—21no—
308C2×C4×D61—21no—
309C2×C4×D61—21no—
310C2×C4×D61—21no—
311C2×C4×D61—21no—
312C2×C4×D61—42no—
313C2×C4×D61—42no—
314C2×C4×D61—42no—
315C2×C4×D61—42no—
316C2×C4×D61C22×C411yescharacteristic
317C2×C4×D61C22×C411yescharacteristic
318C2×C4×D61C2×D411yescharacteristic
319C2×C4×D61C2×D411yescharacteristic
320C2×C4×D61C2×D411yescharacteristic
321C2×C4×D61C2×D411yescharacteristic
322C2×C4×D61C2×D411yescharacteristic
323C2×C4×D61C2×D411yescharacteristic
324C2×C4×D61C2411yescharacteristic
325C2×Dic122—21no—
326C2×Dic122—22no—
327C2×Dic122—22no—
328C2×Dic122—21no—
329C2×Dic122—21no—
330C2×Dic122—21no—
331C2×Dic122—21no—
332C2×Dic122—21no—
333C2×Dic122—21no—
334C2×Dic122—21no—
335C2×Dic122—21no—
336C2×Dic122—41no—
337C2×Dic122—41no—
338C2×Dic122—42no—
339C2×Dic122—42no—
340C2×Dic122—42no—
341C2×Dic122—42no—
342C2×Dic122C22×C411yescharacteristic
343C2×Dic122C22×C411yescharacteristic
344C2×Dic122C22×C411yescharacteristic
345C22⋊#6923—42no—
346C22⋊#6923—42no—
347C22⋊#6923—81no—
348#11758217—42no—
349C2×#92420—21no—
350C2×#92420—21no—
351C2×#92420—21no—
352C2×#92420—21no—
353C2×#92420—42no—
354C4⋊#6923—21no—
355C4⋊#6923—21no—
356C4⋊#6923—21no—
357C4⋊#6923—21no—
358C4⋊#6923—21no—
359C4⋊#6923—21no—
360C4⋊#6923—21no—
361C4⋊#6923—42no—
362C4⋊#6923C2×D412yes—
363C4×#6923—42no—
364C4×#6923—81no—
365#11758213—42no—
366D61⋊C8—21no—
367D61⋊C8—21no—
368D61⋊C8—21no—
369D61⋊C8—21no—
370D61⋊C8—21no—
371D61⋊C8—21no—
372D61⋊C8—21no—
373D61⋊C8—42no—
374D61⋊C8C2×D412yes—
375C4⋊C4×C61—21no—
376C4⋊C4×C61—21no—
377C4⋊C4×C61—21no—
378C4⋊C4×C61—21no—
379C4⋊C4×C61—21no—
380C4⋊C4×C61C22⋊C411yescharacteristic
381C4⋊C4×C61C22×C411yescharacteristic
382C22⋊C4×C61—21no—
383C22⋊C4×C61—21no—
384C22⋊C4×C61C22⋊C411yescharacteristic
385C22⋊C4×C61C22⋊C411yescharacteristic
386C42×C61—21no—
387C42×C61C22×C411yescharacteristic
388C22⋊Dic61—21no—
389C22⋊Dic61—21no—
390C22⋊Dic61C22⋊C411yescharacteristic
391C22⋊Dic61C22⋊C411yescharacteristic
392#11758198—21no—
393#11758198—21no—
394#11758198—21no—
395#11758198—21no—
396#11758198C22⋊C411yescharacteristic
397#11758198C22⋊C411yescharacteristic
398#11758198C22⋊C411yescharacteristic
399#11758198C22⋊C411yescharacteristic
400C4⋊Dic61—21no—
401C4⋊Dic61—21no—
402C4⋊Dic61—21no—
403C4⋊Dic61—21no—
404C4⋊Dic61—21no—
405C4⋊Dic61C22⋊C411yescharacteristic
406C4⋊Dic61C22×C411yescharacteristic
407#11758196—21no—
408#11758196—21no—
409#11758196—21no—
410#11758196—21no—
411#11758196—21no—
412#11758196—21no—
413#11758196—21no—
414#11758196—21no—
415#11758196—21no—
416#11758196—21no—
417#11758196—21no—
418#11758196C22⋊C411yescharacteristic
419#11758196C22⋊C411yescharacteristic
420C4×Dic61—21no—
421C4×Dic61—21no—
422C4×Dic61—21no—
423C4×Dic61C22×C411yescharacteristic
424C4×Dic61C2×D411yescharacteristic
425C4×Dic61C2×D411yescharacteristic
426C23×C61C2×C22⋊C411yescharacteristic
427C23×C61C2×C22⋊C411yescharacteristic
428C22×D61—21no—
429C22×D61—21no—
430C22×D61—21no—
431C22×D61—21no—
432C22×D61—21no—
433C22×D61—21no—
434C22×D61—21no—
435C22×D61—21no—
436C22×D61—21no—
437C22×D61—21no—
438C22×D61C2×C22⋊C411yescharacteristic
439C22×D61C2×C22⋊C411yescharacteristic
440C22×D61#13712yes—
441C22×D61#13712yes—
442C22×D61C22×D411yescharacteristic
443C2×#6923—22no—
444C2×#6923—41no—
445C2×#6923—41no—
446C2×#6923—41no—
447C2×#6923—41no—
448C2×#6923—41no—
449C2×#6923—41no—
450C2×#6923—41no—
451C2×#6923—41no—
452C2×#6923—41no—
453C2×#6923—41no—
454C2×#6923—41no—
455C2×#6923—84no—
456Q8×C61—21no—
457Q8×C61—21no—
458Q8×C61—21no—
459Q8×C61—21no—
460Q8×C61—21no—
461Q8×C61—42no—
462Q8×C61—42no—
463Q8×C61C4×D412yes—
464D4×C61—22no—
465C2×C4×C61—21no—
466C2×C4×C61—21no—
467C2×C4×C61—21no—
468C2×C4×C61—21no—
469C2×C4×C61—21no—
470C2×C4×C61—21no—
471C2×C4×C61—21no—
472C2×C4×C61—21no—
473C2×C4×C61—42no—
474C2×C4×C61—42no—
475C2×C4×C61C2×C22⋊C411yescharacteristic
476C2×C4×C61C2×C22⋊C411yescharacteristic
477C2×C4×C61C2×C22⋊C411yescharacteristic
478C2×C4×C61C2×C22⋊C411yescharacteristic
479C2×C4×C61C23×C411yescharacteristic
480C22⋊D61—22no—
481C22⋊D61—22no—
482C2×Dic61—21no—
483C2×Dic61—21no—
484C2×Dic61—21no—
485C2×Dic61—21no—
486C2×Dic61—21no—
487C2×Dic61—21no—
488C2×Dic61—21no—
489C2×Dic61—21no—
490C2×Dic61—42no—
491C2×Dic61—42no—
492C2×Dic61C2×C22⋊C411yescharacteristic
493C2×Dic61C2×C22⋊C411yescharacteristic
494C2×Dic61C2×C22⋊C411yescharacteristic
495C2×Dic61C2×C22⋊C411yescharacteristic
496C2×Dic61C22×D411yescharacteristic
497D244—22no—
498C4×D61—21no—
499C4×D61—21no—
500C4×D61—22no—
501C4×D61—21no—
502C4×D61—21no—
503C4×D61—22no—
504C4×D61—21no—
505C4×D61—21no—
506C4×D61—21no—
507C4×D61—21no—
508C4×D61—21no—
509C4×D61—21no—
510C4×D61—21no—
511C4×D61—21no—
512C4×D61—21no—
513C4×D61—21no—
514C4×D61—21no—
515C4×D61—21no—
516C4×D61—42no—
517C4×D61—42no—
518C4×D61—42no—
519C4×D61—42no—
520C4×D61—41no—
521C4×D61—41no—
522C4×D61—41no—
523C4×D61—41no—
524C4×D61—41no—
525C4×D61—41no—
526C4×D61C22×D411yescharacteristic
527C4×D61C2×#4111yescharacteristic
528C4×D61H(5,𝔽2)11yescharacteristic
529C4×D61H(5,𝔽2)11yescharacteristic
530Dic122—21no—
531Dic122—22no—
532Dic122—22no—
533Dic122—21no—
534Dic122—21no—
535Dic122—21no—
536Dic122—21no—
537Dic122—42no—
538Dic122—42no—
539Dic122—42no—
540Dic122—42no—
541Dic122—42no—
542Dic122—42no—
543Dic122—41no—
544Dic122—41no—
545Dic122—41no—
546Dic122—41no—
547Dic122C4×D412yes—
548#92420—22no—
549#92420—41no—
550#92420—41no—
551#92420—41no—
552#22425—611nomaximal, Sylow
553C22×C61—21no—
554C22×C61—21no—
555C22×C61—21no—
556C22×C61—21no—
557C22×C61—21no—
558C22×C61#41912yescomplemented
559C22×C61C22×C22⋊C411yescharacteristic
560C2×D61—21no—
561C2×D61—21no—
562C2×D61—22no—
563C2×D61—22no—
564C2×D61—22no—
565C2×D61—22no—
566C2×D61—21no—
567C2×D61—21no—
568C2×D61—21no—
569C2×D61—41no—
570C2×D61—41no—
571C2×D61—41no—
572C2×D61—41no—
573C2×D61#41912yescomplemented
574C2×D61D4211yescharacteristic
575C2×D61#54611yescharacteristic
576C2×D61C2×#13711yescharacteristic
577C2×D61C2×#13711yescharacteristic
578C2×D61#57711yescharacteristic
579C2×D61#57811yescharacteristic
580#6923—42no—
581#6923—81no—
582#6923—81no—
583#6923—81no—
584C4×C61—22no—
585C4×C61—21no—
586C4×C61—21no—
587C4×C61—21no—
588C4×C61—21no—
589C4×C61—41no—
590C4×C61—41no—
591C4×C61—41no—
592C4×C61C2×C4×D411yescharacteristic
593C4×C61#51811yescharacteristic
594Dic61—22no—
595Dic61—21no—
596Dic61—21no—
597Dic61—21no—
598Dic61—21no—
599Dic61—41no—
600Dic61—41no—
601Dic61—41no—
602Dic61D4211yescharacteristic
603Dic61#54611yescharacteristic
604C2×D4×Q8—611no—
605C2×#435—611no—
606C2×#419—611no—
607C22×#103—611no—
608#2352—611no—
609#1981—611no—
610#1960—611no—
611#1894—611no—
612#1892—611no—
613#1873—611no—
614#1872—611no—
615#1805—611no—
616#1787—611no—
617#1787—611no—
618#1763—611no—
619C2×C61—22no—
620C2×C61—41no—
621C2×C61D4×C22⋊C411yescharacteristic
622C2×C61C2×#41911yescharacteristic
623C2×C61#289811yescharacteristic
624D61—22no—
625D61—41no—
626D61#326611yescharacteristic
627D61#327011yescharacteristic
628D61#331211yescharacteristic
629D61#332011yescharacteristic
630C23×Q8—611no—
631C23×Q8—611no—
632C22×M16—611no—
633C23×C8—611no—
634D4×Q8—611no—
635D4×Q8—611no—
636D4×Q8—611no—
637D4×Q8—611no—
638D4×Q8—611no—
639D4×Q8—611no—
640D4×Q8—611no—
641D4×Q8—1221no—
642D4×Q8—1221no—
643D4×Q8—1221no—
644D4×Q8—1221no—
645D4×Q8#692311yescharacteristic, complemented
646C2×C4⋊Q8—611no—
647C2×C4⋊Q8—1221no—
648C2×C22⋊Q8—611no—
649C2×C22⋊Q8—611no—
650C2×C22⋊Q8—1221no—
651C2×C22⋊Q8—1221no—
652C2×C4×Q8—611no—
653C2×C4×D4—611no—
654C2×C4×D4—1221no—
655C2×#117—611no—
656C22×C4⋊C4—611no—
657#435—1221no—
658#435—1221no—
659#435—1221no—
660#435—1221no—
661C2×C4⋊C8—611no—
662#419—1224no—
663C2×#103—611no—
664C2×#103—611no—
665C2×#103—611no—
666C2×#103—611no—
667C2×#103—611no—
668C2×#103—611no—
669C2×#103—611no—
670C2×#103—611no—
671C2×#103—611no—
672C2×#103—611no—
673C2×#103—611no—
674C2×#103—611no—
675C2×#103—1224no—
676C2×C22⋊C8—611no—
677C2×C22⋊C8—611no—
678C2×#97—611no—
679#388—1221no—
680#387—1221no—
681#386—1221no—
682#382—611no—
683#380—611no—
684#380—611no—
685C4×C4⋊C4—611no—
686C4×C22⋊C4—1221no—
687#340—611no—
688#340—611no—
689#340—611no—
690#340—611no—
691C61#2242511yescharacteristic, complemented, Sylow
692C22×Q8—611no—
693C22×Q8—611no—
694C22×Q8—611no—
695C22×Q8—611no—
696C22×Q8—611no—
697C22×Q8—611no—
698C22×Q8—611no—
699C22×Q8—611no—
700C22×Q8—611no—
701C22×Q8—1221no—
702C22×Q8—1221no—
703C22×Q8—1221no—
704C22×Q8—1221no—
705C22×Q8—1221no—
706C22×Q8—1221no—
707C22×Q8—1222no—
708C22×Q8—1222no—
709C22×Q8—1222no—
710C22×Q8—1222no—
711C22×Q8—2441no—
712C22×Q8—2441no—
713C22×Q8—2441no—
714C22×Q8—2441no—
715C22×Q8C2×#692311yescharacteristic
716C22×Q8C2×#692311yescharacteristic, complemented
717C22×D4—611no—
718C23×C4—611no—
719C23×C4—611no—
720C23×C4—1221no—
721C23×C4—1221no—
722C23×C4—1221no—
723C2×M16—1222no—
724C2×M16—1221no—
725C2×M16—1221no—
726C2×M16—2441no—
727C22×C8—611no—
728C22×C8—611no—
729C22×C8—611no—
730C22×C8—611no—
731C22×C8—1222no—
732C22×C8—1221no—
733C22×C8—1221no—
734C22×C8—2441no—
735C4⋊Q8—21no—
736C4⋊Q8—611no—
737C4⋊Q8—611no—
738C4⋊Q8—611no—
739C4⋊Q8—1221no—
740C4⋊Q8—1221no—
741C4⋊Q8—1221no—
742C4⋊Q8—1221no—
743C4⋊Q8—1221no—
744C4⋊Q8—1221no—
745C4⋊Q8—1221no—
746C4⋊Q8—1221no—
747C4⋊Q8—1221no—
748C4⋊Q8C2×#692311yescharacteristic, complemented
749C22⋊Q8—21no—
750C22⋊Q8—21no—
751C22⋊Q8—611no—
752C22⋊Q8—611no—
753C22⋊Q8—611no—
754C22⋊Q8—611no—
755C22⋊Q8—611no—
756C22⋊Q8—611no—
757C22⋊Q8—1221no—
758C22⋊Q8—1221no—
759C22⋊Q8—1221no—
760C22⋊Q8—1221no—
761C22⋊Q8—1221no—
762C22⋊Q8—1221no—
763C22⋊Q8—1221no—
764C22⋊Q8—1221no—
765C22⋊Q8—1221no—
766C22⋊Q8—1221no—
767C22⋊Q8—1221no—
768C22⋊Q8—1221no—
769C22⋊Q8—1221no—
770C22⋊Q8—1221no—
771C22⋊Q8—1221no—
772C22⋊Q8—1221no—
773C22⋊Q8—1221no—
774C22⋊Q8—1221no—
775C22⋊Q8C2×#692311yescharacteristic
776C22⋊Q8C2×#692311yescharacteristic, complemented
777C4×Q8—611no—
778C4×Q8—611no—
779C4×Q8—611no—
780C4×Q8—1221no—
781C4×Q8—1221no—
782C4×Q8C2×#692311yescharacteristic, complemented
783C4×D4—21no—
784C4×D4—611no—
785C4×D4—611no—
786C4×D4—611no—
787C4×D4—611no—
788C4×D4—611no—
789C4×D4—611no—
790C4×D4—611no—
791C4×D4—1221no—
792C4×D4—1221no—
793C4×D4—1221no—
794C4×D4—1221no—
795C4×D4—1221no—
796C4×D4—1221no—
797C4×D4—1221no—
798C4×D4C2×#692311yescharacteristic
799#117—1222no—
800#117—2441no—
801C2×C4⋊C4—611no—
802C2×C4⋊C4—611no—
803C2×C4⋊C4—611no—
804C2×C4⋊C4—611no—
805C2×C4⋊C4—611no—
806C2×C4⋊C4—611no—
807C2×C4⋊C4—1221no—
808C2×C4⋊C4—1221no—
809C2×C4⋊C4—1221no—
810C2×C4⋊C4—1221no—
811C2×C4⋊C4—1221no—
812C2×C4⋊C4—1222no—
813C2×C4⋊C4—1221no—
814C2×C4⋊C4—2441no—
815C2×C22⋊C4—611no—
816C2×C22⋊C4—611no—
817C2×C22⋊C4—1221no—
818C2×C22⋊C4—1221no—
819C2×C22⋊C4—1221no—
820C2×C22⋊C4—1221no—
821C2×C22⋊C4—1221no—
822C2×C42—611no—
823C2×C42—1221no—
824C2×C42—1221no—
825C2×C42—1221no—
826C4⋊C8—1221no—
827C4⋊C8—1221no—
828#103—614no—
829#103—1222no—
830#103—1222no—
831#103—1222no—
832#103—1222no—
833#103—1222no—
834#103—1222no—
835#103—1222no—
836#103—2441no—
837#103—2441no—
838#103—2441no—
839#103—2441no—
840C22⋊C8—1221no—
841C22⋊C8—1221no—
842C22⋊C8—1221no—
843C22⋊C8—1221no—
844#97—1221no—
845#97—1221no—
846#95—1221no—
847#95—1221no—
848#95—1221no—
849#95—1221no—
850#95—1221no—
851C24—611no—
852C24—611no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8—22no—
856C2×Q8—22no—
857C2×Q8—41no—
858C2×Q8—41no—
859C2×Q8—612no—
860C2×Q8—612no—
861C2×Q8—611no—
862C2×Q8—611no—
863C2×Q8—611no—
864C2×Q8—1221no—
865C2×Q8—1221no—
866C2×Q8—1221no—
867C2×Q8—1221no—
868C2×Q8—1221no—
869C2×Q8—1221no—
870C2×Q8—1221no—
871C2×Q8—1222no—
872C2×Q8—1222no—
873C2×Q8—1221no—
874C2×Q8—1221no—
875C2×Q8—1221no—
876C2×Q8—1221no—
877C2×Q8—1221no—
878C2×Q8—1221no—
879C2×Q8—1221no—
880C2×Q8—1221no—
881C2×Q8—1221no—
882C2×Q8—1221no—
883C2×Q8—1221no—
884C2×Q8—1221no—
885C2×Q8—1222no—
886C2×Q8—1222no—
887C2×Q8—1222no—
888C2×Q8—1222no—
889C2×Q8—2441no—
890C2×Q8—2441no—
891C2×Q8—2442no—
892C2×Q8—2442no—
893C2×Q8—2442no—
894C2×Q8—2442no—
895C2×Q8—2442no—
896C2×Q8—2442no—
897C2×Q8—2442no—
898C2×Q8—2442no—
899C2×Q8—2441no—
900C2×Q8—2441no—
901C2×Q8—2441no—
902C2×Q8—2441no—
903C2×Q8—2442no—
904C2×Q8—2442no—
905C2×Q8—2442no—
906C2×Q8—2442no—
907C2×Q8C22×#692311yescharacteristic
908C2×Q8C22×#692311yescharacteristic
909C2×Q8C22×#692311yescharacteristic
910C2×D4—611no—
911C2×D4—611no—
912C2×D4—611no—
913C2×D4—1222no—
914C2×D4—1222no—
915C2×D4C22⋊#692311yescharacteristic
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—611no—
919C22×C4—611no—
920C22×C4—611no—
921C22×C4—611no—
922C22×C4—611no—
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—1221no—
942C22×C4—1221no—
943C22×C4—1221no—
944C22×C4—1221no—
945C22×C4—1221no—
946C22×C4—1221no—
947C22×C4—1221no—
948C22×C4—1221no—
949C22×C4—1221no—
950C22×C4—1221no—
951C22×C4—4881no—
952C22×C4—2442no—
953C22×C4—2442no—
954C22×C4—2442no—
955C22×C4—2442no—
956C22×C4—2442no—
957C22×C4—2442no—
958C22×C4C22×#692311yescharacteristic
959C22×C4C22×#692311yescharacteristic
960M16—2442no—
961M16—2442no—
962C2×C8—612no—
963C2×C8—1221no—
964C2×C8—1221no—
965C2×C8—1221no—
966C2×C8—1221no—
967C2×C8—1221no—
968C2×C8—1221no—
969C2×C8—1221no—
970C2×C8—1221no—
971C2×C8—1221no—
972C2×C8—1221no—
973C2×C8—1221no—
974C2×C8—2442no—
975C2×C8—2442no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—611no—
982C4⋊C4—611no—
983C4⋊C4—611no—
984C4⋊C4—612no—
985C4⋊C4—611no—
986C4⋊C4—1221no—
987C4⋊C4—1221no—
988C4⋊C4—1221no—
989C4⋊C4—1221no—
990C4⋊C4—1221no—
991C4⋊C4—1221no—
992C4⋊C4—1221no—
993C4⋊C4—1221no—
994C4⋊C4—1221no—
995C4⋊C4—1221no—
996C4⋊C4—1221no—
997C4⋊C4—1221no—
998C4⋊C4—1221no—
999C4⋊C4—1221no—
1000C4⋊C4—1221no—
1001C4⋊C4—1221no—
1002C4⋊C4—1221no—
1003C4⋊C4—1221no—
1004C4⋊C4—1221no—
1005C4⋊C4—1221no—
1006C4⋊C4—1221no—
1007C4⋊C4—1221no—
1008C4⋊C4—1221no—
1009C4⋊C4—2442no—
1010C4⋊C4C22⋊#692311yescharacteristic
1011C4⋊C4C22×#692311yescharacteristic
1012C22⋊C4—21no—
1013C22⋊C4—21no—
1014C22⋊C4—611no—
1015C22⋊C4—611no—
1016C22⋊C4—611no—
1017C22⋊C4—611no—
1018C22⋊C4—611no—
1019C22⋊C4—611no—
1020C22⋊C4—1221no—
1021C22⋊C4—1221no—
1022C22⋊C4—1221no—
1023C22⋊C4—1221no—
1024C22⋊C4—1221no—
1025C22⋊C4—1221no—
1026C22⋊C4—4881no—
1027C22⋊C4—2442no—
1028C22⋊C4—2442no—
1029C22⋊C4C22⋊#692311yescharacteristic
1030C22⋊C4C22⋊#692311yescharacteristic
1031C42—21no—
1032C42—611no—
1033C42—611no—
1034C42—611no—
1035C42—1221no—
1036C42—1221no—
1037C42—1221no—
1038C42—4881no—
1039C42—2442no—
1040C42C22×#692311yescharacteristic
1041C23—611no—
1042C23—612no—
1043C23—612no—
1044C23—611no—
1045C23—611no—
1046C23—1221no—
1047C23—1221no—
1048C23—1221no—
1049C23—1221no—
1050C23—1221no—
1051C23—1221no—
1052C23—1221no—
1053C23—1221no—
1054C23—1221no—
1055C23—1221no—
1056C23C2×C22⋊#692311yescharacteristic
1057C23C2×C22⋊#692311yescharacteristic
1058Q8—21no—
1059Q8—21no—
1060Q8—21no—
1061Q8—21no—
1062Q8—21no—
1063Q8—42no—
1064Q8—42no—
1065Q8—612no—
1066Q8—1222no—
1067Q8—1222no—
1068Q8—1221no—
1069Q8—1221no—
1070Q8—1221no—
1071Q8—1221no—
1072Q8—1221no—
1073Q8—2442no—
1074Q8—2442no—
1075Q8—2442no—
1076Q8—2442no—
1077Q8—2441no—
1078Q8—2441no—
1079Q8—2441no—
1080Q8—2441no—
1081Q8—2442no—
1082Q8—2442no—
1083Q8D4×#692312yes—
1084D4—22no—
1085D4—1222no—
1086D4—1222no—
1087D4—1222no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—42no—
1097C2×C4—42no—
1098C2×C4—611no—
1099C2×C4—611no—
1100C2×C4—611no—
1101C2×C4—611no—
1102C2×C4—611no—
1103C2×C4—611no—
1104C2×C4—611no—
1105C2×C4—611no—
1106C2×C4—611no—
1107C2×C4—1221no—
1108C2×C4—1221no—
1109C2×C4—1221no—
1110C2×C4—1221no—
1111C2×C4—1221no—
1112C2×C4—1221no—
1113C2×C4—1221no—
1114C2×C4—1221no—
1115C2×C4—1221no—
1116C2×C4—1221no—
1117C2×C4—1221no—
1118C2×C4—1221no—
1119C2×C4—1222no—
1120C2×C4—1222no—
1121C2×C4—1221no—
1122C2×C4—1221no—
1123C2×C4—1221no—
1124C2×C4—1221no—
1125C2×C4—1221no—
1126C2×C4—1221no—
1127C2×C4—1221no—
1128C2×C4—1221no—
1129C2×C4—1221no—
1130C2×C4—1222no—
1131C2×C4—1221no—
1132C2×C4—1221no—
1133C2×C4—1221no—
1134C2×C4—4884no—
1135C2×C4—2442no—
1136C2×C4—2442no—
1137C2×C4—2442no—
1138C2×C4—2442no—
1139C2×C4—2441no—
1140C2×C4—2441no—
1141C2×C4—2441no—
1142C2×C4—2441no—
1143C2×C4—2441no—
1144C2×C4—2441no—
1145C2×C4—2442no—
1146C2×C4—2442no—
1147C2×C4—2441no—
1148C2×C4—2441no—
1149C2×C4—2441no—
1150C2×C4—2441no—
1151C2×C4—2441no—
1152C2×C4—2441no—
1153C2×C4—2441no—
1154C2×C4—2441no—
1155C2×C4—2441no—
1156C2×C4—2441no—
1157C2×C4—2441no—
1158C2×C4C2×C22⋊#692311yescharacteristic
1159C2×C4C2×C22⋊#692311yescharacteristic
1160C2×C4C2×C22⋊#692311yescharacteristic
1161C2×C4C2×C22⋊#692311yescharacteristic
1162C2×C4C23×#692311yescharacteristic
1163C8—1222no—
1164C8—2441no—
1165C8—2441no—
1166C8—2441no—
1167C22—21no—
1168C22—21no—
1169C22—21no—
1170C22—21no—
1171C22—21no—
1172C22—611no—
1173C22—611no—
1174C22—611no—
1175C22—611no—
1176C22—611no—
1177C22—611no—
1178C22—612no—
1179C22—1222no—
1180C22—1222no—
1181C22—1222no—
1182C22—1222no—
1183C22—1221no—
1184C22—1221no—
1185C22—1221no—
1186C22—1221no—
1187C22—1221no—
1188C22—2441no—
1189C22—2441no—
1190C22—2441no—
1191C22—2441no—
1192C22#1684075512yescomplemented
1193C22C22×C22⋊#692311yescharacteristic
1194C4—21no—
1195C4—21no—
1196C4—22no—
1197C4—21no—
1198C4—21no—
1199C4—41no—
1200C4—41no—
1201C4—41no—
1202C4—611no—
1203C4—611no—
1204C4—1221no—
1205C4—1221no—
1206C4—1222no—
1207C4—1221no—
1208C4—1221no—
1209C4—4881no—
1210C4—4881no—
1211C4—4881no—
1212C4—2442no—
1213C4—2441no—
1214C4—2441no—
1215C4—2441no—
1216C4C2×D4×#692311yescharacteristic
1217C4#1684082911yescharacteristic
1218C2—22no—
1219C2—41no—
1220C2—611no—
1221C2—611no—
1222C2—611no—
1223C2—611no—
1224C2—1222no—
1225C2—2441no—
1226C2D4×C22⋊#692311yescharacteristic
1227C2C2×#1684075511yescharacteristic
1228C2#2146244111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingD4×Q8×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×D4×D61D4
cosocleC2×C4×D61C24
hypercenterD4×Q8#6923
hypocenterC61#22425
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
2. C2×#16840755C2semidirect
3. C22×#14519840C2semidirect
5. #21461985C2semidirect
6. #21461950C2semidirect
7. #21461834C2semidirect
8. #21461832C2semidirect
9. #21461805C2semidirect
10. #21461804C2semidirect
11. #21461690C2semidirect
12. #21461658C2semidirect
13. #21461658C2semidirect
14. #21461591C2semidirect
56. Q8×D244C4semidirect
58. D4×Dic122C4semidirect
60. #16840427C4semidirect
61. Q8×C22⋊D61C4semidirect
62. Q8×C22⋊D61C4semidirect
65. #16840425C4semidirect
66. #16840425C4semidirect
76. D4×Q8×C61C4semidirect
117. #14519840D4semidirect
132. C22×Dic122C2×C4semidirect
147. C2×Q8×D61C2×C4semidirect
148. C2×Q8×D61C2×C4semidirect
158. #14519777C2×C4semidirect
167. #14519775C2×C4semidirect
168. #14519775C2×C4semidirect
172. #14519757C2×C4semidirect
176. #14519756C2×C4semidirect
192. #14519753C2×C4semidirect
193. Q8×Dic61C2×C4semidirect
195. C4×Dic122C2×C4semidirect
197. #14519742C2×C4semidirect
226. C22×Q8×C61C2×C4semidirect
228. C4⋊Q8×C61C2×C4semidirect
232. C22⋊Q8×C61C2×C4semidirect
233. C4×Q8×C61C2×C4semidirect
558. C22×C61#419semidirect
573. C2×D61#419semidirect
645. D4×Q8#6923semidirect
691. C61#22425semidirect
716. C22×Q8C2×#6923semidirect
748. C4⋊Q8C2×#6923semidirect
776. C22⋊Q8C2×#6923semidirect
782. C4×Q8C2×#6923semidirect
1192. C22#16840755semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4352
C2×#168407552
C22×#145198402
#214623352
#214619852
#214619502
#214618342
#214618322
#214618052
#214618042
#214616902
#214616582
#214615912
D4×Q8×D612
#2242561