Finite Group Databasebeta

← C4⋊C4×#11758198 #29601426

Subgroups — C4⋊C4×#11758198 #29601426

Order 15616.

2574 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D61C211yesmaximal, characteristic
2C2×#16839619C211yesmaximal, characteristic
3C2×C4⋊C4×Dic61C211yesmaximal, characteristic, complemented
4C2×C4×#11758198C212yesmaximal
5C2×C4×#11758198C211yesmaximal, characteristic
6#21444054C212yesmaximal, complemented
7#21444052C212yesmaximal, complemented
8#21444049C211yesmaximal, characteristic, complemented
9#21444048C211yesmaximal, characteristic, complemented
10#21444040C212yesmaximal
11C2×C4×C4⋊C4×C61C211yesmaximal, characteristic, complemented
12C23×C4×D61C2212yes—
13C23×C4×D61C2211yescharacteristic
14C22×C4⋊Dic61C2211yescharacteristic
15C22×C4⋊Dic61C2211yescharacteristic
16C22×#11758196C2212yes—
17C2×C4⋊C4×D61—24no—
18C2×C4⋊C4×D61—24no—
19C2×C4⋊C4×D61C418yescomplemented
20C22×#11758198C2211yescharacteristic
21C22×#11758198C2212yes—
22C22×#11758198C2211yescharacteristic
23C22×C4×Dic61C2212yes—
24C22×C4×Dic61C2211yescharacteristic
25#16839619C418yescomplemented
26C4⋊C4×Dic61—24no—
27C4×#11758198—28no—
28C4×#11758198C418yescomplemented
29C2×#14519684C2212yes—
30C2×#14519684C2212yes—
31C2×#14519684C2212yes—
32C2×#14519684C2212yes—
33C2×#14519684C2212yes—
34C2×#14519684C2211yescharacteristic
35C2×#14519684C2212yes—
36C2×#14519684C2211yescharacteristic
37C22×C4⋊C4×C61C2211yescharacteristic
38C22×C4⋊C4×C61C2211yescharacteristic
39C22×C42×C61C2212yes—
40C22×C42×C61C2211yescharacteristic
41C4×C4⋊C4×C61—24no—
42C2×#95×C61C2212yes—
43C24×D61C2311yescharacteristic
44C23×Dic61C2312yes—
45C23×Dic61C2311yescharacteristic
46C23×Dic61C2312yes—
47C23×Dic61C2311yescharacteristic
48C23×Dic61C2311yescharacteristic
49C22×C4×D61—22no—
50C22×C4×D61—22no—
51C22×C4×D61—22no—
52C22×C4×D61—22no—
53C22×C4×D61—24no—
54C22×C4×D61—24no—
55C22×C4×D61—24no—
56C22×C4×D61—24no—
57C22×C4×D61—42no—
58C22×C4×D61—42no—
59C22×C4×D61C2×C418yes—
60C22×C4×D61C2×C414yes—
61C22×C4×D61C2×C414yes—
62C22×C4×D61C2×C414yes—
63C2×C4⋊Dic61—22no—
64C2×C4⋊Dic61—22no—
65C2×C4⋊Dic61—22no—
66C2×C4⋊Dic61—22no—
67C2×C4⋊Dic61C2×C414yes—
68C2×C4⋊Dic61C2×C414yescomplemented
69C2×#11758196—24no—
70C2×#11758196—24no—
71C2×#11758196C2×C418yes—
72C4⋊C4×D61—232no—
73C2×#11758198—24no—
74C2×#11758198—22no—
75C2×#11758198—22no—
76C2×#11758198—24no—
77C2×#11758198C2×C414yes—
78C2×#11758198C2×C418yes—
79C2×#11758198C2×C414yes—
80C2×#11758198D414yes—
81C2×#11758198Q814yes—
82C2×C4×Dic61—22no—
83C2×C4×Dic61—22no—
84C2×C4×Dic61—24no—
85C2×C4×Dic61—24no—
86C2×C4×Dic61—42no—
87C2×C4×Dic61C2×C414yescomplemented
88#14519684—24no—
89#14519684—24no—
90#14519684—24no—
91#14519684—42no—
92#14519684—42no—
93#14519684C2×C414yescomplemented
94#14519684C2×C414yescomplemented
95#14519684C2×C418yescomplemented
96C23×C4×C61C2311yescharacteristic
97C23×C4×C61C2312yes—
98C23×C4×C61C2312yes—
99C23×C4×C61C2311yescharacteristic
100C23×C4×C61C2311yescharacteristic
101C2×C4⋊C4×C61—22no—
102C2×C4⋊C4×C61—22no—
103C2×C4⋊C4×C61C2×C414yes—
104C2×C4⋊C4×C61C2×C414yescomplemented
105C2×C4⋊C4×C61D414yes—
106C2×C4⋊C4×C61D414yes—
107C2×C42×C61—22no—
108C2×C42×C61—22no—
109C2×C42×C61—24no—
110C2×C42×C61—24no—
111C2×C42×C61—42no—
112C2×C42×C61C2×C414yescomplemented
113#95×C61—24no—
114C24×C61C2411yescharacteristic
115C23×D61—21no—
116C23×D61—21no—
117C23×D61—21no—
118C23×D61—21no—
119C23×D61—21no—
120C23×D61—21no—
121C23×D61—21no—
122C23×D61—21no—
123C23×D61C22×C412yes—
124C23×D61C22×C412yes—
125C23×D61C22×C412yes—
126C23×D61C2×D412yes—
127C23×D61C2×Q812yes—
128C23×D61#4112yes—
129C23×D61#4112yes—
130C22×C4×C61—22no—
131C22×C4×C61—21no—
132C22×C4×C61—22no—
133C22×C4×C61—21no—
134C22×C4×C61—22no—
135C22×C4×C61—22no—
136C22×C4×C61—21no—
137C22×C4×C61—21no—
138C22×C4×C61—21no—
139C22×C4×C61—22no—
140C22×C4×C61—22no—
141C22×C4×C61—21no—
142C22×C4×C61—22no—
143C22×C4×C61—21no—
144C22×C4×C61—21no—
145C22×C4×C61—22no—
146C22×C4×C61—22no—
147C22×C4×C61—21no—
148C22×C4×C61—22no—
149C22×C4×C61—21no—
150C22×C4×C61C22×C412yes—
151C22×C4×C61C22×C414yes—
152C22×C4×C61C22×C414yes—
153C22×C4×C61C22×C412yes—
154C22×C4×C61C22×C412yes—
155C22×C4×C61C22×C412yes—
156C22×C4×C61C22×C412yes—
157C22×C4×C61C2×D414yes—
158C22×C4×C61C2×D414yes—
159C22×C4×C61C2×D412yes—
160C22×C4×C61C2×D412yes—
161C22×C4×C61C2×D412yes—
162C22×C4×C61C2×Q812yes—
163C22×C4×C61#4112yes—
164C22×C4×C61#4112yes—
165C22×Dic61—21no—
166C22×Dic61—21no—
167C22×Dic61—21no—
168C22×Dic61—21no—
169C22×Dic61—21no—
170C22×Dic61—21no—
171C22×Dic61—21no—
172C22×Dic61—21no—
173C22×Dic61—22no—
174C22×Dic61—22no—
175C22×Dic61—22no—
176C22×Dic61—21no—
177C22×Dic61—22no—
178C22×Dic61—22no—
179C22×Dic61—22no—
180C22×Dic61—21no—
181C22×Dic61—21no—
182C22×Dic61—21no—
183C22×Dic61—22no—
184C22×Dic61—22no—
185C22×Dic61—22no—
186C22×Dic61—22no—
187C22×Dic61—21no—
188C22×Dic61—22no—
189C22×Dic61—22no—
190C22×Dic61—21no—
191C22×Dic61C22×C414yes—
192C22×Dic61C22×C412yes—
193C22×Dic61C22×C414yes—
194C22×Dic61C22×C412yes—
195C22×Dic61C22×C412yes—
196C22×Dic61C22×C412yes—
197C22×Dic61C22×C412yes—
198C22×Dic61C2×D412yes—
199C22×Dic61C2×Q812yes—
200C2×C4×D61—28no—
201C2×C4×D61—28no—
202C2×C4×D61—28no—
203C2×C4×D61—28no—
204C2×C4×D61—28no—
205C2×C4×D61—28no—
206C2×C4×D61—216no—
207C2×C4×D61—216no—
208C2×C4×D61—48no—
209C2×C4×D61—48no—
210C2×C4×D61—48no—
211C2×C4×D61—48no—
212C2×C4×D61—48no—
213C2×C4×D61C42116yescomplemented
214C4⋊C4×C61—28no—
215C4⋊C4×C61C22⋊C4116yescomplemented
216C42×C61—28no—
217C42×C61—48no—
218#11758198—28no—
219#11758198—216no—
220#11758198C4⋊C4116yesdirect product factor
221C4⋊Dic61—28no—
222C4⋊Dic61—28no—
223#11758196—216no—
224C4×Dic61—28no—
225C4×Dic61—48no—
226C23×C61C23×C411yescharacteristic
227C23×C61C23×C411yescharacteristic
228C23×C61C23×C411yescharacteristic
229C23×C61C22×D411yescharacteristic
230C23×C61C22×D411yescharacteristic
231C23×C61C22×D411yescharacteristic
232C23×C61C22×Q811yescharacteristic
233C23×C61C2×#4111yescharacteristic
234C23×C61C2×#4111yescharacteristic
235C23×C61C2×#4111yescharacteristic
236C23×C61C2×#4111yescharacteristic
237C23×C61H(5,𝔽2)11yescharacteristic
238C23×C61H(5,𝔽2)11yescharacteristic
239C23×C612−1+411yescharacteristic
240C23×C612−1+411yescharacteristic
241C22×D61—22no—
242C22×D61—22no—
243C22×D61—22no—
244C22×D61—22no—
245C22×D61—22no—
246C22×D61—22no—
247C22×D61—22no—
248C22×D61—22no—
249C22×D61—22no—
250C22×D61—22no—
251C22×D61—22no—
252C22×D61—22no—
253C22×D61—22no—
254C22×D61—22no—
255C22×D61—22no—
256C22×D61—22no—
257C22×D61—22no—
258C22×D61—22no—
259C22×D61—22no—
260C22×D61—22no—
261C22×D61—22no—
262C22×D61—22no—
263C22×D61—22no—
264C22×D61—22no—
265C22×D61—22no—
266C22×D61—22no—
267C22×D61—22no—
268C22×D61—22no—
269C22×D61C2×C4214yes—
270C22×D61C2×C4⋊C414yes—
271C22×D61#11714yes—
272C22×D61C4×D414yes—
273C22×D61C4×D414yes—
274C22×D61C4×Q814yes—
275C22×D61C4×Q814yes—
276C2×C4×C61—22no—
277C2×C4×C61—24no—
278C2×C4×C61—24no—
279C2×C4×C61—22no—
280C2×C4×C61—24no—
281C2×C4×C61—22no—
282C2×C4×C61—24no—
283C2×C4×C61—24no—
284C2×C4×C61—24no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—24no—
290C2×C4×C61—22no—
291C2×C4×C61—24no—
292C2×C4×C61—22no—
293C2×C4×C61—24no—
294C2×C4×C61—42no—
295C2×C4×C61—41no—
296C2×C4×C61—42no—
297C2×C4×C61—41no—
298C2×C4×C61—42no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61—42no—
302C2×C4×C61C2×C4214yes—
303C2×C4×C61C2×C22⋊C418yes—
304C2×C4×C61C2×C22⋊C414yes—
305C2×C4×C61C2×C4⋊C414yescomplemented
306C2×C4×C61#11714yes—
307C2×C4×C61C4×D414yes—
308C2×C4×C61C4×D414yes—
309C2×C4×C61C4×D414yes—
310C2×C4×C61C4×D414yes—
311C2×Dic61—22no—
312C2×Dic61—22no—
313C2×Dic61—22no—
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—22no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—22no—
323C2×Dic61—24no—
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—24no—
327C2×Dic61—24no—
328C2×Dic61—24no—
329C2×Dic61—24no—
330C2×Dic61—22no—
331C2×Dic61—24no—
332C2×Dic61—42no—
333C2×Dic61—42no—
334C2×Dic61—42no—
335C2×Dic61—42no—
336C2×Dic61—42no—
337C2×Dic61—41no—
338C2×Dic61—42no—
339C2×Dic61—41no—
340C2×Dic61—42no—
341C2×Dic61—41no—
342C2×Dic61—41no—
343C2×Dic61—42no—
344C2×Dic61C2×C4214yes—
345C2×Dic61C2×C4⋊C414yescomplemented
346C4×D61—232no—
347C4×D61—432no—
348C22⋊C4×C4⋊C4—611nomaximal, Sylow
349C22×C61C22×C4211yescharacteristic
350C22×C61C22×C22⋊C411yescharacteristic
351C22×C61C22×C4⋊C411yescharacteristic
352C22×C61C2×#11711yescharacteristic
353C22×C61C2×#11711yescharacteristic
354C22×C61C2×C4×D411yescharacteristic
355C22×C61C2×C4×D411yescharacteristic
356C22×C61C2×C4×D411yescharacteristic
357C22×C61C2×C4×D411yescharacteristic
358C22×C61C2×C4×D411yescharacteristic
359C22×C61C2×C4×D411yescharacteristic
360C22×C61C2×C4×Q811yescharacteristic
361C22×C61C2×C4×Q811yescharacteristic
362C22×C61#51811yescharacteristic
363C22×C61#51911yescharacteristic
364C22×C61#52011yescharacteristic
365C22×C61#52011yescharacteristic
366C22×C61#52011yescharacteristic
367C22×C61#52011yescharacteristic
368C22×C61D4211yescharacteristic
369C22×C61D4211yescharacteristic
370C22×C61#54611yescharacteristic
371C22×C61#54611yescharacteristic
372C22×C61#54711yescharacteristic
373C22×C61#54711yescharacteristic
374C22×C61#54811yescharacteristic
375C22×C61#54811yescharacteristic
376C22×C61D4×Q811yescharacteristic
377C22×C61D4×Q811yescharacteristic
378C22×C61#55211yescharacteristic
379C22×C61#55211yescharacteristic
380C22×C61#55311yescharacteristic
381C22×C61#55311yescharacteristic
382C22×C61#55411yescharacteristic
383C22×C61#55411yescharacteristic
384C2×D61—24no—
385C2×D61—24no—
386C2×D61—24no—
387C2×D61—24no—
388C2×D61—24no—
389C2×D61—24no—
390C2×D61—24no—
391C2×D61—24no—
392C2×D61—24no—
393C2×D61—24no—
394C2×D61—24no—
395C2×D61—24no—
396C2×D61—24no—
397C2×D61—24no—
398C2×D61C4×C4⋊C418yescomplemented
399C4×C61—28no—
400C4×C61—24no—
401C4×C61—42no—
402C4×C61—44no—
403C4×C61C4×C22⋊C418yescomplemented
404Dic61—24no—
405Dic61—24no—
406Dic61—44no—
407Dic61—42no—
408Dic61—44no—
409C23×C4⋊C4—611no—
410C2×#380—611no—
411C2×C4×C4⋊C4—611no—
412C2×C4×C4⋊C4D6111yescharacteristic, complemented
413C2×C4×C22⋊C4—611no—
414C2×C4×C22⋊C4—612no—
415#1436—612no—
416#1436—612no—
417C4⋊#95—611no—
418C4⋊#95—611no—
419C22⋊#95—612no—
420C2×C61C2×C4×C22⋊C411yescharacteristic
421C2×C61C2×C4×C4⋊C411yescharacteristic
422C2×C61#227411yescharacteristic
423C2×C61D4×C22⋊C411yescharacteristic
424C2×C61Q8×C22⋊C411yescharacteristic
425C2×C61#234411yescharacteristic
426C2×C61#234511yescharacteristic
427C2×C61D4×C4⋊C411yescharacteristic
428C2×C61D4×C4⋊C411yescharacteristic
429C2×C61#235211yescharacteristic
430C2×C61#235211yescharacteristic
431C2×C61#236011yescharacteristic
432C2×C61#236011yescharacteristic
433C2×C61#236111yescharacteristic
434C2×C61#236111yescharacteristic
435D61—28no—
436C24×C4—611no—
437C24×C4—612no—
438C22×C4⋊C4—612no—
439C22×C4⋊C4—611no—
440C22×C4⋊C4—611no—
441C22×C4⋊C4—618no—
442C22×C4⋊C4—1224no—
443C22×C4⋊C4—1224no—
444C22×C4⋊C4C2×D6111yescharacteristic
445C22×C4⋊C4C2×D6111yescharacteristic
446C22×C22⋊C4—611no—
447C22×C22⋊C4—611no—
448C22×C22⋊C4—612no—
449C22×C42—611no—
450C22×C42—612no—
451C22×C42C2×D6112yes—
452C22×C42C2×D6111yescharacteristic
453#380—618no—
454C4×C4⋊C4—24no—
455C4×C4⋊C4—1224no—
456C4×C22⋊C4—618no—
457C4×C22⋊C4—1228no—
458C2×#95—611no—
459C2×#95—611no—
460C2×#95—612no—
461C2×#95—612no—
462C2×#95—612no—
463C2×#95—612no—
464C2×#95—612no—
465C2×#95—612no—
466C2×#95C2×D6112yes—
467C61C22⋊C4×C4⋊C411yescharacteristic, complemented, Sylow
468C25—611no—
469C23×C4—611no—
470C23×C4—611no—
471C23×C4—614no—
472C23×C4—614no—
473C23×C4—614no—
474C23×C4—612no—
475C23×C4—611no—
476C23×C4—612no—
477C23×C4—618no—
478C23×C4—1224no—
479C23×C4—1224no—
480C23×C4—1222no—
481C23×C4—1222no—
482C23×C4—1222no—
483C23×C4—1222no—
484C23×C4—1224no—
485C23×C4—1224no—
486C23×C4—2442no—
487C23×C4—2442no—
488C23×C4C22×D6112yes—
489C23×C4C22×D6111yescharacteristic
490C23×C4C22×D6112yes—
491C23×C4C22×D6111yescharacteristic
492C23×C4C22×D6111yescharacteristic
493C2×C4⋊C4—22no—
494C2×C4⋊C4—22no—
495C2×C4⋊C4—618no—
496C2×C4⋊C4—614no—
497C2×C4⋊C4—614no—
498C2×C4⋊C4—1224no—
499C2×C4⋊C4—1222no—
500C2×C4⋊C4—1222no—
501C2×C4⋊C4—1222no—
502C2×C4⋊C4—1224no—
503C2×C4⋊C4—1222no—
504C2×C4⋊C4—12232no—
505C2×C4⋊C4C4×D6114yes—
506C2×C4⋊C4C4×D6114yescomplemented
507C2×C4⋊C4D24414yes—
508C2×C4⋊C4C22⋊D6114yes—
509C2×C22⋊C4—614no—
510C2×C22⋊C4—614no—
511C2×C22⋊C4—614no—
512C2×C22⋊C4—614no—
513C2×C22⋊C4—618no—
514C2×C22⋊C4—1224no—
515C2×C22⋊C4—1222no—
516C2×C22⋊C4—1224no—
517C2×C22⋊C4—1222no—
518C2×C42—22no—
519C2×C42—22no—
520C2×C42—24no—
521C2×C42—24no—
522C2×C42—42no—
523C2×C42—614no—
524C2×C42—1222no—
525C2×C42—1222no—
526C2×C42—1224no—
527C2×C42—1224no—
528C2×C42—2442no—
529C2×C42C4×D6114yescomplemented
530#95—24no—
531#95—614no—
532#95—614no—
533#95—618no—
534#95—1224no—
535#95—1224no—
536#95—1224no—
537#95—2442no—
538#95—2442no—
539C24—612no—
540C24—612no—
541C24—612no—
542C24—612no—
543C24—612no—
544C24—612no—
545C24—612no—
546C24—1221no—
547C24—1221no—
548C24—1221no—
549C24—1221no—
550C24—1221no—
551C24—1221no—
552C24—1221no—
553C24—1221no—
554C24C23×D6111yescharacteristic
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—21no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—612no—
576C22×C4—612no—
577C22×C4—612no—
578C22×C4—612no—
579C22×C4—612no—
580C22×C4—612no—
581C22×C4—6116no—
582C22×C4—612no—
583C22×C4—614no—
584C22×C4—614no—
585C22×C4—12216no—
586C22×C4—1221no—
587C22×C4—1221no—
588C22×C4—1221no—
589C22×C4—1221no—
590C22×C4—1221no—
591C22×C4—1221no—
592C22×C4—1221no—
593C22×C4—1221no—
594C22×C4—1228no—
595C22×C4—1228no—
596C22×C4—1228no—
597C22×C4—1228no—
598C22×C4—1228no—
599C22×C4—1228no—
600C22×C4—1222no—
601C22×C4—1222no—
602C22×C4—1222no—
603C22×C4—1221no—
604C22×C4—1222no—
605C22×C4—1222no—
606C22×C4—1221no—
607C22×C4—1221no—
608C22×C4—1222no—
609C22×C4—1222no—
610C22×C4—1221no—
611C22×C4—1222no—
612C22×C4—1221no—
613C22×C4—1222no—
614C22×C4—1222no—
615C22×C4—1222no—
616C22×C4—1221no—
617C22×C4—1222no—
618C22×C4—12216no—
619C22×C4—2448no—
620C22×C4—2448no—
621C22×C4—2448no—
622C22×C4—2448no—
623C22×C4—2448no—
624C22×C4C2×C4×D6112yes—
625C22×C4C2×C4×D6114yes—
626C22×C4C2×C4×D6114yes—
627C22×C4C2×C4×D6112yes—
628C22×C4C2×C4×D6112yes—
629C22×C4C2×C4×D6112yes—
630C22×C4C2×C4×D6112yes—
631C22×C4C2×D24414yes—
632C22×C4C2×D24412yes—
633C22×C4#1175822212yes—
634C22×C4#1175822212yes—
635C22×C4D4×D6112yes—
636C22×C4Q8×D6112yes—
637C22×C4C2×C22⋊D6114yes—
638C22×C4C2×C22⋊D6112yes—
639C4⋊C4—28no—
640C4⋊C4—12216no—
641C4⋊C4—1228no—
642C4⋊C4—1228no—
643C4⋊C4#11758198116yesdirect product factor
644C22⋊C4—6116no—
645C22⋊C4—1228no—
646C22⋊C4—12216no—
647C42—28no—
648C42—48no—
649C42—1228no—
650C42—2448no—
651C23—614no—
652C23—614no—
653C23—614no—
654C23—614no—
655C23—614no—
656C23—614no—
657C23—614no—
658C23—1222no—
659C23—1222no—
660C23—1222no—
661C23—1222no—
662C23—1222no—
663C23—1222no—
664C23—1222no—
665C23—1222no—
666C23—1222no—
667C23—1222no—
668C23—1222no—
669C23—1222no—
670C23—1222no—
671C23—1222no—
672C23—1222no—
673C23—1222no—
674C23—1222no—
675C23—1222no—
676C23—1222no—
677C23—1222no—
678C23—1222no—
679C23—1222no—
680C23—1222no—
681C23—1222no—
682C23—1222no—
683C23—1222no—
684C23—1222no—
685C23—1222no—
686C23C22×C4×D6111yescharacteristic
687C23C22×C4×D6111yescharacteristic
688C23C22×C4×D6111yescharacteristic
689C23C2×D4×D6111yescharacteristic
690C23C22×C22⋊D6111yescharacteristic
691C23C22×D24411yescharacteristic
692C23C2×Q8×D6111yescharacteristic
693C23#41×D6111yescharacteristic
694C23#41×D6111yescharacteristic
695C23C2×#1175822211yescharacteristic
696C23C2×#1175822211yescharacteristic
697C23#1451982211yescharacteristic
698C23#1451982311yescharacteristic
699C23#1451982411yescharacteristic
700C23#1451982511yescharacteristic
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—41no—
724C2×C4—42no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—614no—
728C2×C4—614no—
729C2×C4—1222no—
730C2×C4—1222no—
731C2×C4—1222no—
732C2×C4—1222no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—1222no—
737C2×C4—1222no—
738C2×C4—1222no—
739C2×C4—1222no—
740C2×C4—1222no—
741C2×C4—12232no—
742C2×C4—1224no—
743C2×C4—1222no—
744C2×C4—1224no—
745C2×C4—1224no—
746C2×C4—1222no—
747C2×C4—1224no—
748C2×C4—1224no—
749C2×C4—1222no—
750C2×C4—1224no—
751C2×C4—24432no—
752C2×C4—2441no—
753C2×C4—2442no—
754C2×C4—2441no—
755C2×C4—2442no—
756C2×C4—2442no—
757C2×C4—2442no—
758C2×C4—2442no—
759C2×C4—2441no—
760C2×C4—2442no—
761C2×C4—2442no—
762C2×C4—2441no—
763C2×C4—2442no—
764C2×C4C42×D6114yes—
765C2×C4C2×#1175819818yes—
766C2×C4C2×#1175819814yes—
767C2×C4C4⋊C4×D6114yescomplemented
768C2×C4#1451973414yes—
769C2×C4C4×C22⋊D6114yes—
770C2×C4C4×C22⋊D6114yes—
771C2×C4C4×D24414yes—
772C2×C4C4×D24414yes—
773C22—618no—
774C22—1224no—
775C22—1224no—
776C22—1224no—
777C22—1224no—
778C22—1224no—
779C22—1224no—
780C22—1224no—
781C22—1224no—
782C22—1224no—
783C22—1224no—
784C22—1224no—
785C22—1224no—
786C22—1224no—
787C22—1224no—
788C22C2×C42×D6111yescharacteristic
789C22C22×#1175819811yescharacteristic
790C22C2×C4⋊C4×D6111yescharacteristic
791C22#117×D6111yescharacteristic
792C22C2×#1451973411yescharacteristic
793C22C4×D4×D6111yescharacteristic
794C22C4×D4×D6111yescharacteristic
795C22C2×C4×C22⋊D6111yescharacteristic
796C22C2×C4×C22⋊D6111yescharacteristic
797C22C2×C4×D24411yescharacteristic
798C22C2×C4×D24411yescharacteristic
799C22C4×Q8×D6111yescharacteristic
800C22C4×Q8×D6111yescharacteristic
801C22#1684023411yescharacteristic
802C22#1684023811yescharacteristic
803C22#1684024111yescharacteristic
804C22#1684024211yescharacteristic
805C22#1684024311yescharacteristic
806C22#1684024411yescharacteristic
807C22D4×C22⋊D6111yescharacteristic
808C22D4×D24411yescharacteristic
809C22#1684040011yescharacteristic
810C22#1684040711yescharacteristic
811C22#1684041311yescharacteristic
812C22#1684041711yescharacteristic
813C22#1684041911yescharacteristic
814C22#1684042411yescharacteristic
815C22Q8×C22⋊D6111yescharacteristic
816C22Q8×D24411yescharacteristic
817C22#1684045111yescharacteristic
818C22#1684045311yescharacteristic
819C22#1684045611yescharacteristic
820C22#1684046211yescharacteristic
821C22#1684046711yescharacteristic
822C22#1684047211yescharacteristic
823C4—24no—
824C4—28no—
825C4—42no—
826C4—44no—
827C4—1224no—
828C4—1224no—
829C4—2442no—
830C4—2444no—
831C4—2444no—
832C4C4×#1175819818yescomplemented
833C2—1228no—
834C2C2×C4×#1175819811yescharacteristic
835C2C4×C4⋊C4×D6111yescharacteristic
836C2#2144817311yescharacteristic
837C2D4×#1175819811yescharacteristic
838C2Q8×#1175819811yescharacteristic
839C2#2144868411yescharacteristic
840C2#2144869211yescharacteristic
841C2C4⋊C4×C22⋊D6111yescharacteristic
842C2C4⋊C4×D24411yescharacteristic
843C2#2144874911yescharacteristic
844C2#2144875111yescharacteristic
845C2#2144882011yescharacteristic
846C2#2144882611yescharacteristic
847C2#2144883111yescharacteristic
848C2#2144883711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC22×C61C22×C42
FittingC2×C4×C4⋊C4×C61C2
socle, cosocleC24×C61C24
prime radicalC24×D61C23
hypercenterC2×C4×C4⋊C4D61
hypocenterC61C22⋊C4×C4⋊C4
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C4⋊C4×Dic61C2semidirect
6. #21444054C2semidirect
7. #21444052C2semidirect
8. #21444049C2semidirect
9. #21444048C2semidirect
11. C2×C4×C4⋊C4×C61C2semidirect
19. C2×C4⋊C4×D61C4semidirect
25. #16839619C4semidirect
28. C4×#11758198C4semidirect
68. C2×C4⋊Dic61C2×C4semidirect
87. C2×C4×Dic61C2×C4semidirect
93. #14519684C2×C4semidirect
94. #14519684C2×C4semidirect
95. #14519684C2×C4semidirect
104. C2×C4⋊C4×C61C2×C4semidirect
112. C2×C42×C61C2×C4semidirect
213. C2×C4×D61C42semidirect
215. C4⋊C4×C61C22⋊C4semidirect
220. #11758198C4⋊C4direct (N × H)
305. C2×C4×C61C2×C4⋊C4semidirect
345. C2×Dic61C2×C4⋊C4semidirect
398. C2×D61C4×C4⋊C4semidirect
403. C4×C61C4×C22⋊C4semidirect
412. C2×C4×C4⋊C4D61semidirect
467. C61C22⋊C4×C4⋊C4semidirect
506. C2×C4⋊C4C4×D61semidirect
529. C2×C42C4×D61semidirect
643. C4⋊C4#11758198direct (N × H)
767. C2×C4C4⋊C4×D61semidirect
832. C4C4×#11758198semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D612
C2×#168396192
C2×C4⋊C4×Dic612
C2×C4×#117581982
#214440542
#214440522
#214440492
#214440482
#214440402
C2×C4×C4⋊C4×C612
C22⋊C4×C4⋊C461