Finite Group Databasebeta

← C4×#16840759 #30614116

Subgroups — C4×#16840759 #30614116

Order 15616.

1618 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840759C212yesmaximal
2C2×C4×#11758213C211yesmaximal, characteristic, complemented
3C4×#14519856C211yesmaximal, characteristic, complemented
4#21461583C212yesmaximal, complemented
5#21461582C212yesmaximal, complemented
6C4×#14519842C212yesmaximal, complemented
7C4×#14519841C212yesmaximal, complemented
8#21461499C212yesmaximal, complemented
9C4×#41×D61C211yesmaximal, characteristic
10C22×#11758213C2212yes—
11C2×#14519856C2212yes—
12#16840759C4116yesdirect product factor
13C2×#14519842C2214yes—
14C2×#14519841C2214yes—
15C4×#11758213—21no—
16C4×#11758213—21no—
17C4×#11758213C2212yescomplemented
18C4×#11758213C2212yescomplemented
19C2×#14519832—21no—
20C2×C4×#92420—21no—
21C4×C4⋊#6923—21no—
22C4×C4⋊#6923—21no—
23C4×C22⋊#6923—21no—
24C4×C22⋊#6923—21no—
25#16840698C2212yescomplemented
26C42×#6923C2212yescomplemented
27#16840632C2214yescomplemented
28#16840632C2214yescomplemented
29C2×#41×D61C2211yescharacteristic
30#41×Dic61C411yescharacteristic, complemented
31C4×#11758226C2211yescharacteristic
32C4×#11758226C2211yescharacteristic
33C4×#11758222—21no—
34C4×#11758222C411yescharacteristic, complemented
35#16840230—21no—
36#16840230C411yescharacteristic, complemented
37C4×#11758224—21no—
38C4×#11758224—21no—
39C4×#11758224C2211yescharacteristic
40C4×#11758224C2211yescharacteristic
41C4×Q8×D61C411yescharacteristic, complemented
42C4×Q8×D61C411yescharacteristic, complemented
43C4×D4×D61—21no—
44C4×D4×D61—21no—
45C4×D4×D61C411yescharacteristic, complemented
46C4×D4×D61C411yescharacteristic, complemented
47#117×D61—21no—
48#117×D61C2211yescharacteristic
49C2×C42×D61—21no—
50C2×C42×D61C2211yescharacteristic
51C4×#41×C61C411yescharacteristic, complemented
52C2×#11758213—22no—
53C2×#11758213—24no—
54C2×#11758213C2×C418yescomplemented
55C2×#11758213C2314yes—
56C22×#92420—22no—
57#14519856—24no—
58#14519856C2×C418yescomplemented
59C2×C4⋊#6923—22no—
60C2×C22⋊#6923—22no—
61C2×C4×#6923—22no—
62C2×C4×#6923—22no—
63C2×C4×#6923C2314yes—
64#14519842C2×C4116yescomplemented
65#14519841C2×C4116yescomplemented
66#14519832—22no—
67#14519832—22no—
68C4×#92420—22no—
69C4×#92420—22no—
70(C2×#6923)⋊C4—22no—
71(C2×#6923)⋊C4—22no—
72C2×#11758226C2311yescharacteristic
73C2×#11758222—21no—
74C2×#11758222C2×C411yescharacteristic
75C2×#11758224—21no—
76C2×#11758224C2311yescharacteristic
77#41×D61—24no—
78#41×D61C2×C418yes—
79C2×Q8×D61C2×C411yescharacteristic
80C2×D4×D61—21no—
81C2×D4×D61C2×C411yescharacteristic
82C22×C4×D61—21no—
83C22×C4×D61—21no—
84C22×C4×D61—21no—
85C22×C4×D61D411yescharacteristic
86C22×C4×D61D411yescharacteristic
87C22×C4×D61C2311yescharacteristic
88Q8×Dic61C2×C411yescharacteristic
89Q8×Dic61C2×C411yescharacteristic
90C4×Dic122—21no—
91C4×Dic122—21no—
92C4×Dic122C2×C411yescharacteristic
93C4×Dic122C2×C411yescharacteristic
94#14519742—21no—
95#14519742—21no—
96#14519742C2×C411yescharacteristic
97#14519742C2×C411yescharacteristic
98C4×D244—21no—
99C4×D244—21no—
100C4×D244C2×C411yescharacteristic
101C4×D244C2×C411yescharacteristic
102D4×Dic61—21no—
103D4×Dic61—21no—
104D4×Dic61C2×C411yescharacteristic
105D4×Dic61C2×C411yescharacteristic
106#14519739—21no—
107#14519739—21no—
108#14519739C2×C411yescharacteristic
109#14519739C2×C411yescharacteristic
110C4×C22⋊D61—21no—
111C4×C22⋊D61—21no—
112C4×C22⋊D61—21no—
113C4×C22⋊D61—21no—
114C4×C22⋊D61—21no—
115C4×C22⋊D61—21no—
116#14519737—21no—
117#14519737—21no—
118#14519737—21no—
119#14519737—21no—
120#14519737—21no—
121#14519737—21no—
122#14519736—21no—
123#14519736C2×C411yescharacteristic
124#14519735—21no—
125#14519735—21no—
126#14519735C2311yescharacteristic
127#14519735C2311yescharacteristic
128#14519734—21no—
129#14519734—21no—
130#14519734—21no—
131#14519733—21no—
132#14519733—21no—
133#14519733—21no—
134C4⋊C4×D61—21no—
135C4⋊C4×D61—21no—
136C4⋊C4×D61C2×C411yescharacteristic
137C4⋊C4×D61C2×C411yescharacteristic
138C22⋊C4×D61—21no—
139C22⋊C4×D61—21no—
140C22⋊C4×D61—21no—
141C2×C4×Dic61—21no—
142C2×C4×Dic61—21no—
143C2×C4×Dic61—21no—
144C2×C4×Dic61C2×C411yescharacteristic
145C2×C4×Dic61D411yescharacteristic
146C2×C4×Dic61D411yescharacteristic
147C42×D61—21no—
148C42×D61—21no—
149C42×D61—21no—
150C42×D61—21no—
151C42×D61—21no—
152C42×D61—21no—
153C42×D61—21no—
154C42×D61C2×C411yescharacteristic
155C42×D61C2×C411yescharacteristic
156C42×D61D411yescharacteristic
157C42×D61D411yescharacteristic
158C42×D61D411yescharacteristic
159C42×D61D411yescharacteristic
160C42×D61C2311yescharacteristic
161C42×D61C2311yescharacteristic
162C2×#41×C61C2×C411yescharacteristic
163C4×Q8×C61C2×C411yescharacteristic
164C4×Q8×C61C2×C411yescharacteristic
165C4×D4×C61—21no—
166C4×D4×C61—21no—
167C4×D4×C61C2×C411yescharacteristic
168C4×D4×C61C2×C411yescharacteristic
169#117×C61—21no—
170#117×C61C2×C411yescharacteristic
171C2×C42×C61—21no—
172C2×C42×C61C2×C411yescharacteristic
173C23×D61—21no—
174C23×D61C2×D411yescharacteristic
175C22×#6923—24no—
176#41×C61—22no—
177#41×C61C4214yescomplemented
178C2×Q8×C61C22×C411yescharacteristic
179C2×D4×C61—21no—
180C2×D4×C61C22×C411yescharacteristic
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61C22⋊C411yescharacteristic
185C22×C4×C61C22⋊C411yescharacteristic
186C22×C4×C61C22×C411yescharacteristic
187C2×C22⋊D61—21no—
188C2×C22⋊D61—21no—
189C2×C22⋊D61—21no—
190C22×Dic61—21no—
191C22×Dic61—21no—
192C22×Dic61—21no—
193C22×Dic61C22⋊C411yescharacteristic
194C22×Dic61C22⋊C411yescharacteristic
195C22×Dic61C2×D411yescharacteristic
196#11758226—22no—
197#11758226C22×C414yes—
198Q8×D61—22no—
199Q8×D61C4214yescomplemented
200#11758224—28no—
201#11758224—22no—
202#11758224C22×C414yes—
203D4×D61—28no—
204D4×D61—22no—
205D4×D61C4214yescomplemented
206#11758222—22no—
207#11758222—28no—
208#11758222C4214yescomplemented
209C2×D244—21no—
210C2×D244C22×C411yescharacteristic
211C2×C4×D61—21no—
212C2×C4×D61—21no—
213C2×C4×D61—21no—
214C2×C4×D61—28no—
215C2×C4×D61—21no—
216C2×C4×D61—21no—
217C2×C4×D61—21no—
218C2×C4×D61—21no—
219C2×C4×D61—21no—
220C2×C4×D61—21no—
221C2×C4×D61—42no—
222C2×C4×D61—42no—
223C2×C4×D61—44no—
224C2×C4×D61—44no—
225C2×C4×D61C22⋊C411yescharacteristic
226C2×C4×D61C22⋊C411yescharacteristic
227C2×C4×D61C22⋊C411yescharacteristic
228C2×C4×D61C22⋊C411yescharacteristic
229C2×C4×D61C22×C411yescharacteristic
230C2×C4×D61C22×C414yes—
231C2×C4×D61C2×D411yescharacteristic
232C2×C4×D61C2×D411yescharacteristic
233C2×C4×D61C2×D411yescharacteristic
234C2×C4×D61C2×D411yescharacteristic
235C2×C4×D61C2×D411yescharacteristic
236C2×C4×D61C2×D411yescharacteristic
237C2×C4×D61#4114yes—
238C2×C4×D61C2411yescharacteristic
239C2×Dic122—21no—
240C2×Dic122C22×C411yescharacteristic
241C22⋊#6923—28no—
242C2×#92420—28no—
243C2×#92420—24no—
244C4⋊#6923—28no—
245C4×#6923—24no—
246C4×#6923—44no—
247C4×#6923—44no—
248C4×#6923C22×C418yescomplemented
249#11758213—28no—
250#11758213—24no—
251#11758213C22×C418yescomplemented
252C4⋊C4×C61—21no—
253C4⋊C4×C61—21no—
254C4⋊C4×C61C22×C411yescharacteristic
255C4⋊C4×C61C22×C411yescharacteristic
256C22⋊C4×C61—21no—
257C22⋊C4×C61—21no—
258C22⋊C4×C61—21no—
259C42×C61—21no—
260C42×C61—21no—
261C42×C61—21no—
262C42×C61C22⋊C411yescharacteristic
263C42×C61C22⋊C411yescharacteristic
264C42×C61C22×C411yescharacteristic
265C42×C61C22×C411yescharacteristic
266C22⋊Dic61—21no—
267C22⋊Dic61—21no—
268C22⋊Dic61—21no—
269#11758198—21no—
270#11758198—21no—
271#11758198—21no—
272#11758198—21no—
273#11758198—21no—
274#11758198—21no—
275C4⋊Dic61—21no—
276C4⋊Dic61—21no—
277C4⋊Dic61C22×C411yescharacteristic
278C4⋊Dic61C22×C411yescharacteristic
279#11758196—21no—
280#11758196—21no—
281#11758196—21no—
282#11758196—21no—
283#11758196—21no—
284#11758196—21no—
285C4×Dic61—21no—
286C4×Dic61—21no—
287C4×Dic61—21no—
288C4×Dic61—21no—
289C4×Dic61—21no—
290C4×Dic61—21no—
291C4×Dic61—21no—
292C4×Dic61—21no—
293C4×Dic61—21no—
294C4×Dic61C22⋊C411yescharacteristic
295C4×Dic61C22⋊C411yescharacteristic
296C4×Dic61C22⋊C411yescharacteristic
297C4×Dic61C22⋊C411yescharacteristic
298C4×Dic61C22⋊C411yescharacteristic
299C4×Dic61C22⋊C411yescharacteristic
300C4×Dic61C22×C411yescharacteristic
301C4×Dic61C22×C411yescharacteristic
302C4×Dic61C2×D411yescharacteristic
303C4×Dic61C2×D411yescharacteristic
304C4×Dic61C2×D411yescharacteristic
305C4×Dic61C2×D411yescharacteristic
306C23×C61—21no—
307C23×C61C2×C22⋊C411yescharacteristic
308C22×D61—21no—
309C22×D61—24no—
310C22×D61—41no—
311C22×D61—41no—
312C22×D61—42no—
313C22×D61—42no—
314C22×D61C2×C22⋊C411yescharacteristic
315C22×D61C4×D414yes—
316C22×D61C22×D411yescharacteristic
317C2×#6923—28no—
318C2×#6923—44no—
319C2×#6923—44no—
320Q8×C61—21no—
321Q8×C61C2×C4212yes—
322D4×C61—24no—
323D4×C61—21no—
324D4×C61C2×C4212yes—
325C2×C4×C61—21no—
326C2×C4×C61—24no—
327C2×C4×C61—22no—
328C2×C4×C61—21no—
329C2×C4×C61—21no—
330C2×C4×C61—41no—
331C2×C4×C61—42no—
332C2×C4×C61—42no—
333C2×C4×C61C2×C4212yes—
334C2×C4×C61C2×C22⋊C411yescharacteristic
335C2×C4×C61C2×C22⋊C411yescharacteristic
336C2×C4×C61C2×C22⋊C411yescharacteristic
337C2×C4×C61C2×C22⋊C411yescharacteristic
338C2×C4×C61C2×C22⋊C411yescharacteristic
339C2×C4×C61#11712yes—
340C2×C4×C61C23×C411yescharacteristic
341C22⋊D61—24no—
342C22⋊D61—24no—
343C22⋊D61—24no—
344C2×Dic61—21no—
345C2×Dic61—24no—
346C2×Dic61—22no—
347C2×Dic61—21no—
348C2×Dic61—21no—
349C2×Dic61—41no—
350C2×Dic61—42no—
351C2×Dic61—42no—
352C2×Dic61C2×C22⋊C411yescharacteristic
353C2×Dic61C2×C22⋊C411yescharacteristic
354C2×Dic61C2×C22⋊C411yescharacteristic
355C2×Dic61C2×C22⋊C411yescharacteristic
356C2×Dic61C2×C22⋊C411yescharacteristic
357C2×Dic61C4×D414yes—
358C2×Dic61C22×D411yescharacteristic
359D244—24no—
360D244—21no—
361D244C2×C4212yes—
362C4×D61—24no—
363C4×D61—24no—
364C4×D61—22no—
365C4×D61—22no—
366C4×D61—24no—
367C4×D61—22no—
368C4×D61—22no—
369C4×D61—41no—
370C4×D61—41no—
371C4×D61—41no—
372C4×D61—41no—
373C4×D61—42no—
374C4×D61—42no—
375C4×D61—42no—
376C4×D61—42no—
377C4×D61—42no—
378C4×D61—42no—
379C4×D61C2×C4212yes—
380C4×D61#11712yes—
381C4×D61C4×D414yes—
382C4×D61C4×D414yes—
383C4×D61C23×C412yes—
384C4×D61C2×#4112yes—
385Dic122—21no—
386Dic122—24no—
387Dic122C2×C4212yes—
388#92420—28no—
389C4×#421—611nomaximal, Sylow
390C22×C61—21no—
391C22×C61—21no—
392C22×C61—22no—
393C22×C61—41no—
394C22×C61—41no—
395C22×C61C4×C22⋊C412yes—
396C22×C61C22×C22⋊C411yescharacteristic
397C2×D61—21no—
398C2×D61—21no—
399C2×D61—21no—
400C2×D61—21no—
401C2×D61—22no—
402C2×D61—44no—
403C2×D61—48no—
404C2×D61—41no—
405C2×D61—41no—
406C2×D61C4×C22⋊C412yes—
407C2×D61C2×C4×D412yes—
408#6923—48no—
409C4×C61—21no—
410C4×C61—21no—
411C4×C61—21no—
412C4×C61—22no—
413C4×C61—41no—
414C4×C61—41no—
415C4×C61C4×C22⋊C412yes—
416C4×C61#42112yescomplemented
417C4×C61C22×C4211yescharacteristic
418C4×C61C2×#11711yescharacteristic
419Dic61—21no—
420Dic61—21no—
421Dic61—21no—
422Dic61—22no—
423Dic61—41no—
424Dic61—41no—
425Dic61C4×C22⋊C412yes—
426Dic61#42112yescomplemented
427Dic61C2×C4×D412yes—
428C2×C4×#41—611no—
429C2×#421—612no—
430C2×C4×M16—611no—
431C4×#117—611no—
432#1759—612no—
433#1759—612no—
434C4×#104—612no—
435C4×#104—612no—
436#1733—612no—
437C2×C61—22no—
438C2×C61—42no—
439C2×C61C2×C4×C22⋊C411yescharacteristic
440C2×C61C2×#42111yescharacteristic
441C2×C61C2×#42111yescharacteristic
442D61—22no—
443D61—22no—
444D61—42no—
445C22×#41—611no—
446C22×M16—612no—
447C4×#41—611no—
448C4×#41—611no—
449C4×#41—611no—
450C4×#41—611no—
451C4×#41—611no—
452C4×#41—611no—
453C4×#41—611no—
454C4×#41—1221no—
455C4×#41—1221no—
456C4×#41—1221no—
457C4×#41—1221no—
458C4×#41#692311yescharacteristic, complemented
459C2×C4×Q8—611no—
460C2×C4×Q8—611no—
461C2×C4×D4—611no—
462C2×C4×D4—611no—
463C2×C4×D4—1221no—
464C2×C4×D4—1221no—
465C2×#117—612no—
466C2×#117—611no—
467C2×#117—1221no—
468C22×C42—611no—
469C22×C42—1221no—
470#421—6116no—
471C2×#104—614no—
472C2×#104—614no—
473C4×M16—612no—
474C4×M16—612no—
475C4×M16—1221no—
476C4×M16—1221no—
477C2×#97—1221no—
478C2×C4×C8—1221no—
479C4×C4⋊C4—1221no—
480C4×C4⋊C4—1221no—
481C4×C22⋊C4—1221no—
482C4×C22⋊C4—1221no—
483#376—612no—
484C43—612no—
485#339—614no—
486#339—614no—
487C61C4×#42111yescharacteristic, complemented, Sylow
488C2×#41—618no—
489C2×#41—611no—
490C2×#41—611no—
491C2×#41—611no—
492C2×#41—1221no—
493C2×#41—1221no—
494C2×#41—1224no—
495C2×#41C2×#692311yescharacteristic
496C22×Q8—611no—
497C22×D4—611no—
498C22×D4—1221no—
499C23×C4—611no—
500C23×C4—611no—
501C23×C4—611no—
502C23×C4—1221no—
503C23×C4—1221no—
504C23×C4—1221no—
505C2×M16—618no—
506C2×M16—614no—
507C2×M16—1224no—
508C2×M16—1222no—
509C22×C8—1222no—
510C4×Q8—611no—
511C4×Q8—611no—
512C4×Q8—611no—
513C4×Q8—611no—
514C4×Q8—611no—
515C4×Q8—611no—
516C4×Q8—1221no—
517C4×Q8—1221no—
518C4×Q8—1221no—
519C4×Q8—1221no—
520C4×Q8C2×#692311yescharacteristic
521C4×Q8C2×#692311yescharacteristic
522C4×D4—21no—
523C4×D4—21no—
524C4×D4—611no—
525C4×D4—611no—
526C4×D4—611no—
527C4×D4—611no—
528C4×D4—611no—
529C4×D4—611no—
530C4×D4—1221no—
531C4×D4—1221no—
532C4×D4—1221no—
533C4×D4—1221no—
534C4×D4—1221no—
535C4×D4—1221no—
536C4×D4—1221no—
537C4×D4—1221no—
538C4×D4—1221no—
539C4×D4—1221no—
540C4×D4—1221no—
541C4×D4—1221no—
542C4×D4—1221no—
543C4×D4—1221no—
544C4×D4—1221no—
545C4×D4—1221no—
546C4×D4—1221no—
547C4×D4—1221no—
548C4×D4C2×#692311yescharacteristic
549C4×D4C2×#692311yescharacteristic
550#117—21no—
551#117—618no—
552#117—611no—
553#117—611no—
554#117—611no—
555#117—1221no—
556#117—1221no—
557#117—1221no—
558#117—1221no—
559#117—1221no—
560#117—1221no—
561#117—1221no—
562#117—1221no—
563#117—1224no—
564#117—1221no—
565#117C2×#692311yescharacteristic
566C2×C4⋊C4—611no—
567C2×C4⋊C4—611no—
568C2×C4⋊C4—1221no—
569C2×C4⋊C4—1221no—
570C2×C4⋊C4—1222no—
571C2×C22⋊C4—1221no—
572C2×C22⋊C4—1221no—
573C2×C22⋊C4—1221no—
574C2×C22⋊C4—1222no—
575C2×C42—21no—
576C2×C42—611no—
577C2×C42—611no—
578C2×C42—611no—
579C2×C42—611no—
580C2×C42—611no—
581C2×C42—611no—
582C2×C42—611no—
583C2×C42—611no—
584C2×C42—611no—
585C2×C42—611no—
586C2×C42—611no—
587C2×C42—614no—
588C2×C42—1221no—
589C2×C42—1221no—
590C2×C42—1221no—
591C2×C42—1221no—
592C2×C42—1221no—
593C2×C42—1221no—
594C2×C42—1221no—
595C2×C42—1221no—
596C2×C42—1221no—
597C2×C42—1221no—
598C2×C42—1222no—
599C2×C42—1222no—
600C2×C42C2×#692311yescharacteristic
601#104—6116no—
602#104—6116no—
603#97—1222no—
604#97—1222no—
605C4×C8—1222no—
606C4×C8—1222no—
607#95—1222no—
608#95—1222no—
609C24—611no—
610C24—1221no—
611#41—22no—
612#41—614no—
613#41—614no—
614#41—614no—
615#41—1228no—
616#41—1228no—
617#41—1222no—
618#41—1222no—
619#41—1222no—
620#41C4×#692314yescomplemented
621C2×Q8—614no—
622C2×Q8—611no—
623C2×Q8—1221no—
624C2×Q8—1222no—
625C2×Q8C22×#692311yescharacteristic
626C2×D4—21no—
627C2×D4—614no—
628C2×D4—611no—
629C2×D4—1221no—
630C2×D4—1222no—
631C2×D4—1221no—
632C2×D4—1228no—
633C2×D4—1221no—
634C2×D4—1221no—
635C2×D4C22×#692311yescharacteristic
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—611no—
640C22×C4—614no—
641C22×C4—611no—
642C22×C4—611no—
643C22×C4—614no—
644C22×C4—611no—
645C22×C4—611no—
646C22×C4—611no—
647C22×C4—611no—
648C22×C4—611no—
649C22×C4—611no—
650C22×C4—611no—
651C22×C4—611no—
652C22×C4—611no—
653C22×C4—611no—
654C22×C4—611no—
655C22×C4—611no—
656C22×C4—1221no—
657C22×C4—1228no—
658C22×C4—1221no—
659C22×C4—1221no—
660C22×C4—1221no—
661C22×C4—1221no—
662C22×C4—1221no—
663C22×C4—1221no—
664C22×C4—1221no—
665C22×C4—1221no—
666C22×C4—1221no—
667C22×C4—1224no—
668C22×C4—1221no—
669C22×C4—1221no—
670C22×C4—2442no—
671C22×C4—2442no—
672C22×C4—2444no—
673C22×C4—2444no—
674C22×C4C22⋊#692311yescharacteristic
675C22×C4C22⋊#692311yescharacteristic
676C22×C4C22×#692311yescharacteristic
677M16—618no—
678M16—1224no—
679M16—1228no—
680C2×C8—1224no—
681C2×C8—1228no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—611no—
685C4⋊C4—611no—
686C4⋊C4—1221no—
687C4⋊C4—1221no—
688C4⋊C4—1221no—
689C4⋊C4—1221no—
690C4⋊C4—1221no—
691C4⋊C4—1221no—
692C4⋊C4—1228no—
693C4⋊C4—1221no—
694C4⋊C4—1221no—
695C4⋊C4C22×#692311yescharacteristic
696C4⋊C4C22×#692311yescharacteristic
697C22⋊C4—21no—
698C22⋊C4—21no—
699C22⋊C4—21no—
700C22⋊C4—1221no—
701C22⋊C4—1221no—
702C22⋊C4—1221no—
703C22⋊C4—1221no—
704C22⋊C4—1221no—
705C22⋊C4—1221no—
706C22⋊C4—1228no—
707C22⋊C4—1221no—
708C22⋊C4—1221no—
709C22⋊C4—1221no—
710C42—21no—
711C42—21no—
712C42—21no—
713C42—611no—
714C42—611no—
715C42—611no—
716C42—611no—
717C42—611no—
718C42—611no—
719C42—611no—
720C42—611no—
721C42—611no—
722C42—611no—
723C42—611no—
724C42—611no—
725C42—618no—
726C42—1221no—
727C42—1221no—
728C42—1221no—
729C42—1221no—
730C42—1221no—
731C42—1221no—
732C42—1224no—
733C42—1221no—
734C42—1221no—
735C42—1221no—
736C42—2444no—
737C42—2444no—
738C42C22⋊#692311yescharacteristic
739C42C22⋊#692311yescharacteristic
740C42C22×#692311yescharacteristic
741C42C22×#692311yescharacteristic
742C23—21no—
743C23—611no—
744C23—611no—
745C23—614no—
746C23—1224no—
747C23—1221no—
748C23—2441no—
749C23—2441no—
750C23—2442no—
751C23—2442no—
752C23C2×C22⋊#692311yescharacteristic
753Q8—21no—
754Q8—612no—
755Q8—1224no—
756Q8—1221no—
757Q8C2×C4×#692312yes—
758D4—24no—
759D4—21no—
760D4—612no—
761D4—1224no—
762D4—1224no—
763D4—1224no—
764D4—1224no—
765D4—1221no—
766D4C2×C4×#692312yes—
767C2×C4—21no—
768C2×C4—22no—
769C2×C4—24no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—41no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—611no—
776C2×C4—611no—
777C2×C4—611no—
778C2×C4—614no—
779C2×C4—612no—
780C2×C4—612no—
781C2×C4—612no—
782C2×C4—612no—
783C2×C4—614no—
784C2×C4—614no—
785C2×C4—611no—
786C2×C4—611no—
787C2×C4—611no—
788C2×C4—1222no—
789C2×C4—1222no—
790C2×C4—1224no—
791C2×C4—1224no—
792C2×C4—1222no—
793C2×C4—1224no—
794C2×C4—1221no—
795C2×C4—1222no—
796C2×C4—1222no—
797C2×C4—1224no—
798C2×C4—1228no—
799C2×C4—1221no—
800C2×C4—1221no—
801C2×C4—2441no—
802C2×C4—2441no—
803C2×C4—2441no—
804C2×C4—2441no—
805C2×C4—2442no—
806C2×C4—2442no—
807C2×C4—2442no—
808C2×C4—2442no—
809C2×C4—2442no—
810C2×C4—2442no—
811C2×C4—2441no—
812C2×C4—2442no—
813C2×C4—2444no—
814C2×C4—2444no—
815C2×C4—2442no—
816C2×C4C2×C4×#692312yes—
817C2×C4C2×C22⋊#692311yescharacteristic
818C2×C4C2×C22⋊#692311yescharacteristic
819C2×C4C2×C22⋊#692311yescharacteristic
820C2×C4C2×C22⋊#692311yescharacteristic
821C2×C4C2×C22⋊#692311yescharacteristic
822C2×C4#1451985612yes—
823C2×C4C23×#692311yescharacteristic
824C8—1228no—
825C22—21no—
826C22—21no—
827C22—22no—
828C22—41no—
829C22—41no—
830C22—612no—
831C22—612no—
832C22—1221no—
833C22—1221no—
834C22—1221no—
835C22—1221no—
836C22—1222no—
837C22—2444no—
838C22—2448no—
839C22—2441no—
840C22—2441no—
841C22C4×C22⋊#692312yes—
842C22C22×C22⋊#692311yescharacteristic
843C4—21no—
844C4—21no—
845C4—21no—
846C4—22no—
847C4—41no—
848C4—41no—
849C4—612no—
850C4—612no—
851C4—612no—
852C4—1221no—
853C4—1221no—
854C4—1221no—
855C4—1222no—
856C4—2448no—
857C4—2441no—
858C4—2441no—
859C4C4×C22⋊#692312yes—
860C4#1684075912yesdirect product factor
861C4C22×C4×#692311yescharacteristic
862C4C2×#1451985611yescharacteristic
863C2—22no—
864C2—42no—
865C2—1222no—
866C2—1222no—
867C2—2442no—
868C2C2×C4×C22⋊#692311yescharacteristic
869C2D61⋊#42111yescharacteristic
870C2C2×#1684075911yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC4×C61C22×C42
FrattiniC2×C4C23×#6923
FittingC4×#41×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#41×D61C22
cosocleC2×C4×D61C24
hypercenterC4×#41#6923
hypocenterC61C4×#421
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11758213C2semidirect
3. C4×#14519856C2semidirect
4. #21461583C2semidirect
5. #21461582C2semidirect
6. C4×#14519842C2semidirect
7. C4×#14519841C2semidirect
8. #21461499C2semidirect
12. #16840759C4direct (N × H)
17. C4×#11758213C22semidirect
18. C4×#11758213C22semidirect
25. #16840698C22semidirect
26. C42×#6923C22semidirect
27. #16840632C22semidirect
28. #16840632C22semidirect
30. #41×Dic61C4semidirect
34. C4×#11758222C4semidirect
36. #16840230C4semidirect
41. C4×Q8×D61C4semidirect
42. C4×Q8×D61C4semidirect
45. C4×D4×D61C4semidirect
46. C4×D4×D61C4semidirect
51. C4×#41×C61C4semidirect
54. C2×#11758213C2×C4semidirect
58. #14519856C2×C4semidirect
64. #14519842C2×C4semidirect
65. #14519841C2×C4semidirect
177. #41×C61C42semidirect
199. Q8×D61C42semidirect
205. D4×D61C42semidirect
208. #11758222C42semidirect
248. C4×#6923C22×C4semidirect
251. #11758213C22×C4semidirect
416. C4×C61#421semidirect
426. Dic61#421semidirect
458. C4×#41#6923semidirect
487. C61C4×#421semidirect
620. #41C4×#6923semidirect
860. C4#16840759direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407592
C2×C4×#117582132
C4×#145198562
#214615832
#214615822
C4×#145198422
C4×#145198412
#214614992
C4×#41×D612
C4×#42161