Finite Group Databasebeta

← C2×#21448663 #29839222

Subgroups — C2×#21448663 #29839222

Order 15616.

4990 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519734C211yesmaximal, characteristic, complemented
2C22×C22⋊C4×D61C211yesmaximal, characteristic
3C22×C22⋊C4×D61C211yesmaximal, characteristic
4#21448663C2116yesmaximal, direct product factor
5C2×#16839656C211yesmaximal, characteristic, complemented
6C2×#16839655C211yesmaximal, characteristic, complemented
7C2×#16839650C211yesmaximal, characteristic, complemented
8C2×#16839636C211yesmaximal, characteristic, complemented
9C2×#16839633C211yesmaximal, characteristic, complemented
10C2×#16839624C211yesmaximal, characteristic, complemented
11C2×#16839619C211yesmaximal, characteristic, complemented
12C2×#16839617C211yesmaximal, characteristic
13C2×C4×#11758198C211yesmaximal, characteristic, complemented
14C2×#16839609C211yesmaximal, characteristic, complemented
15C2×#16839609C211yesmaximal, characteristic, complemented
16C2×C61×#388C211yesmaximal, characteristic, complemented
17C25×D61C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C23×C4×D61C2211yescharacteristic
21C23×C4×D61C2211yescharacteristic
22C2×#14519734—28no—
23C2×#14519734C2218yescomplemented
24C22×C4⋊Dic61C2211yescharacteristic, complemented
25C22×#11758196C2211yescharacteristic, complemented
26C22×#11758196C2211yescharacteristic, complemented
27C22×C22⋊Dic61C2211yescharacteristic
28C22×C22⋊Dic61C2211yescharacteristic
29C22×C22⋊Dic61C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×#11758198C2211yescharacteristic
35C22×#11758198C2211yescharacteristic
36C22×#11758198C2211yescharacteristic
37C22×#11758198C2211yescharacteristic
38C2×C22⋊C4×D61—28no—
39C2×C22⋊C4×D61C4116yescomplemented
40C2×C22⋊C4×D61C2218yes—
41C2×C22⋊C4×D61C2218yes—
42C22×C4×Dic61C2211yescharacteristic, complemented
43C22×C4×Dic61C2211yescharacteristic, complemented
44C22×C4×Dic61C2211yescharacteristic, complemented
45#16839656C2218yescomplemented
46#16839655C2218yescomplemented
47#16839650C2218yescomplemented
48#16839636C2218yescomplemented
49#16839633C2218yescomplemented
50#16839624C2218yescomplemented
51#16839619C2218yescomplemented
52#16839617C2218yes—
53C4×#11758198C2218yescomplemented
54#16839609C2218yescomplemented
55#16839609C2218yescomplemented
56C2×#14519684C2211yescharacteristic, complemented
57C2×#14519684C2211yescharacteristic, complemented
58C2×#14519684C2211yescharacteristic, complemented
59C2×#14519684C2211yescharacteristic, complemented
60C2×#14519684C2211yescharacteristic, complemented
61C2×#14519684C2211yescharacteristic, complemented
62C22×C4⋊C4×C61C2211yescharacteristic, complemented
63C22×C22⋊C4×C61C2211yescharacteristic
64C22×C22⋊C4×C61C2211yescharacteristic
65C22×C22⋊C4×C61C2211yescharacteristic
66C22×C42×C61C2211yescharacteristic, complemented
67C61×#388C2218yescomplemented
68C2×#95×C61C2211yescharacteristic, complemented
69C2×#95×C61C2211yescharacteristic, complemented
70C24×D61—24no—
71C24×D61—24no—
72C24×D61—24no—
73C24×D61—24no—
74C24×D61—42no—
75C24×D61—42no—
76C24×D61C2×C418yes—
77C24×D61C2314yes—
78C24×D61C2311yescharacteristic
79C24×D61C2311yescharacteristic
80C23×Dic61C2311yescharacteristic
81C23×Dic61C2311yescharacteristic
82C23×Dic61C2311yescharacteristic
83C23×Dic61C2311yescharacteristic
84C23×Dic61C2311yescharacteristic
85C23×Dic61C2311yescharacteristic
86C22×C4×D61—24no—
87C22×C4×D61—24no—
88C22×C4×D61—24no—
89C22×C4×D61—24no—
90C22×C4×D61—24no—
91C22×C4×D61—24no—
92C22×C4×D61—42no—
93C22×C4×D61—42no—
94C22×C4×D61—42no—
95C22×C4×D61—42no—
96C22×C4×D61C2×C418yescomplemented
97C22×C4×D61C2×C418yescomplemented
98C22×C4×D61C2314yes—
99C22×C4×D61C2314yes—
100C22×C4×D61C2314yes—
101C22×C4×D61C2314yes—
102#14519734—232no—
103C2×C4⋊Dic61—42no—
104C2×C4⋊Dic61C2314yescomplemented
105C2×#11758196—24no—
106C2×#11758196—24no—
107C2×#11758196C2314yescomplemented
108C2×#11758196C2314yescomplemented
109C2×C22⋊Dic61—24no—
110C2×C22⋊Dic61—42no—
111C2×C22⋊Dic61C2×C418yescomplemented
112C2×C22⋊Dic61C2314yes—
113C2×C22⋊Dic61C2314yes—
114C2×C22⋊Dic61C2314yes—
115C2×#11758198—24no—
116C2×#11758198—24no—
117C2×#11758198—24no—
118C2×#11758198—24no—
119C2×#11758198—24no—
120C2×#11758198C2×C418yes—
121C2×#11758198C2×C418yes—
122C2×#11758198D418yes—
123C2×#11758198C2314yes—
124C2×#11758198C2314yes—
125C2×#11758198C2314yes—
126C2×#11758198C2314yes—
127C2×#11758198C2314yes—
128C2×#11758198C2314yes—
129C2×#11758198C2314yes—
130C2×#11758198C2314yes—
131C22⋊C4×D61—232no—
132C22⋊C4×D61C2×C4164yescomplemented
133C2×C4×Dic61—24no—
134C2×C4×Dic61—42no—
135C2×C4×Dic61—42no—
136C2×C4×Dic61C2314yescomplemented
137C2×C4×Dic61C2314yescomplemented
138C2×C4×Dic61C2314yescomplemented
139#14519684C2314yescomplemented
140#14519684C2314yescomplemented
141#14519684C2314yescomplemented
142#14519684C2314yescomplemented
143#14519684C2314yescomplemented
144#14519684C2314yescomplemented
145C25×C61C2311yescharacteristic
146C23×C4×C61C2311yescharacteristic
147C23×C4×C61C2311yescharacteristic
148C23×C4×C61C2311yescharacteristic
149C23×C4×C61C2311yescharacteristic
150C23×C4×C61C2311yescharacteristic
151C23×C4×C61C2311yescharacteristic
152C2×C4⋊C4×C61—42no—
153C2×C4⋊C4×C61C2314yescomplemented
154C2×C22⋊C4×C61—24no—
155C2×C22⋊C4×C61—42no—
156C2×C22⋊C4×C61C2×C418yescomplemented
157C2×C22⋊C4×C61C2314yes—
158C2×C22⋊C4×C61C2314yes—
159C2×C22⋊C4×C61C2314yes—
160C2×C42×C61—24no—
161C2×C42×C61C2314yescomplemented
162#95×C61C2314yescomplemented
163#95×C61C2314yescomplemented
164C24×C61—22no—
165C24×C61—22no—
166C24×C61—22no—
167C24×C61—22no—
168C24×C61—22no—
169C24×C61—22no—
170C24×C61C22×C414yes—
171C24×C61C2412yes—
172C24×C61C2411yescharacteristic
173C23×D61—22no—
174C23×D61—22no—
175C23×D61—22no—
176C23×D61—22no—
177C23×D61—22no—
178C23×D61—22no—
179C23×D61—22no—
180C23×D61—22no—
181C23×D61—232no—
182C23×D61—232no—
183C23×D61—28no—
184C23×D61—28no—
185C23×D61—28no—
186C23×D61—28no—
187C23×D61—416no—
188C23×D61—44no—
189C23×D61—44no—
190C23×D61—416no—
191C23×D61—416no—
192C23×D61—416no—
193C23×D61—416no—
194C23×D61C22×C4116yes—
195C23×D61C22×C414yes—
196C23×D61C22×C414yes—
197C23×D61C2×D414yes—
198C23×D61#4114yes—
199C23×D61#4114yes—
200C23×D61#4114yes—
201C23×D61C2412yes—
202C23×D61C2412yes—
203C22×C4×C61—22no—
204C22×C4×C61—22no—
205C22×C4×C61—22no—
206C22×C4×C61—22no—
207C22×C4×C61—22no—
208C22×C4×C61—22no—
209C22×C4×C61—22no—
210C22×C4×C61—22no—
211C22×C4×C61—22no—
212C22×C4×C61—22no—
213C22×C4×C61—22no—
214C22×C4×C61—22no—
215C22×C4×C61—22no—
216C22×C4×C61—22no—
217C22×C4×C61—22no—
218C22×C4×C61C22×C414yes—
219C22×C4×C61C22×C414yes—
220C22×C4×C61C2×D414yes—
221C22×C4×C61C2412yes—
222C22×C4×C61C2412yes—
223C22×C4×C61C2412yes—
224C22×C4×C61C2412yes—
225C22×C4×C61C2412yes—
226C22×C4×C61C2412yes—
227C22×Dic61—22no—
228C22×Dic61—22no—
229C22×Dic61—22no—
230C22×Dic61—22no—
231C22×Dic61—22no—
232C22×Dic61—22no—
233C22×Dic61—22no—
234C22×Dic61—22no—
235C22×Dic61—22no—
236C22×Dic61—22no—
237C22×Dic61—22no—
238C22×Dic61—22no—
239C22×Dic61—22no—
240C22×Dic61—22no—
241C22×Dic61—22no—
242C22×Dic61C22×C414yes—
243C22×Dic61C22×C414yes—
244C22×Dic61C2×D414yes—
245C22×Dic61C2412yes—
246C22×Dic61C2412yes—
247C22×Dic61C2412yes—
248C22×Dic61C2412yes—
249C22×Dic61C2412yes—
250C22×Dic61C2412yes—
251C2×C4×D61—232no—
252C2×C4×D61—28no—
253C2×C4×D61—28no—
254C2×C4×D61—28no—
255C2×C4×D61—28no—
256C2×C4×D61—28no—
257C2×C4×D61—28no—
258C2×C4×D61—416no—
259C2×C4×D61—44no—
260C2×C4×D61—44no—
261C2×C4×D61—44no—
262C2×C4×D61—44no—
263C2×C4×D61—416no—
264C2×C4×D61—416no—
265C2×C4×D61C22×C4116yescomplemented
266C2×C4×D61C22×C4116yescomplemented
267C4⋊C4×C61—44no—
268C22⋊C4×C61—28no—
269C22⋊C4×C61—44no—
270C22⋊C4×C61C22×C4116yescomplemented
271C42×C61—28no—
272C22⋊Dic61—28no—
273C22⋊Dic61—44no—
274C22⋊Dic61C22×C4116yescomplemented
275#11758198—28no—
276#11758198—28no—
277#11758198—28no—
278#11758198—28no—
279#11758198—28no—
280#11758198C22×C4116yes—
281#11758198C22×C4116yes—
282#11758198C2×D4116yes—
283C4⋊Dic61—44no—
284#11758196—28no—
285#11758196—28no—
286C4×Dic61—28no—
287C4×Dic61—44no—
288C4×Dic61—44no—
289C23×C61—28no—
290C23×C61—28no—
291C23×C61—28no—
292C23×C61—22no—
293C23×C61—22no—
294C23×C61—22no—
295C23×C61—22no—
296C23×C61—22no—
297C23×C61—22no—
298C23×C61—44no—
299C23×C61—44no—
300C23×C61—44no—
301C23×C61—44no—
302C23×C61C23×C414yes—
303C23×C61C23×C412yes—
304C23×C61C22×D412yes—
305C23×C61C2×#4112yes—
306C23×C61C2×#4112yes—
307C23×C61C2×#4112yes—
308C23×C61H(5,𝔽2)12yes—
309C23×C61H(5,𝔽2)12yes—
310C23×C61C2511yescharacteristic
311C22×D61—28no—
312C22×D61—28no—
313C22×D61—28no—
314C22×D61—28no—
315C22×D61—28no—
316C22×D61—28no—
317C22×D61—28no—
318C22×D61—28no—
319C22×D61—28no—
320C22×D61—28no—
321C22×D61—28no—
322C22×D61—28no—
323C22×D61—22no—
324C22×D61—22no—
325C22×D61—22no—
326C22×D61—22no—
327C22×D61—22no—
328C22×D61—22no—
329C22×D61—22no—
330C22×D61—22no—
331C22×D61—232no—
332C22×D61—232no—
333C22×D61—416no—
334C22×D61—4128no—
335C22×D61—416no—
336C22×D61—416no—
337C22×D61—416no—
338C22×D61—416no—
339C22×D61#117116yescomplemented
340C22×D61C4×D4116yes—
341C22×D61C23×C414yes—
342C22×D61C23×C414yes—
343C22×D61C22×D414yes—
344C22×D61C2×#4114yes—
345C22×D61C2×#4114yes—
346C22×D61C2×#4114yes—
347C2×C4×C61—28no—
348C2×C4×C61—28no—
349C2×C4×C61—28no—
350C2×C4×C61—22no—
351C2×C4×C61—22no—
352C2×C4×C61—22no—
353C2×C4×C61—22no—
354C2×C4×C61—22no—
355C2×C4×C61—22no—
356C2×C4×C61—22no—
357C2×C4×C61—22no—
358C2×C4×C61—22no—
359C2×C4×C61—22no—
360C2×C4×C61—22no—
361C2×C4×C61—22no—
362C2×C4×C61—22no—
363C2×C4×C61—22no—
364C2×C4×C61—22no—
365C2×C4×C61—44no—
366C2×C4×C61—44no—
367C2×C4×C61—44no—
368C2×C4×C61C23×C414yes—
369C2×C4×C61C23×C414yes—
370C2×C4×C61C22×D414yes—
371C2×Dic61—28no—
372C2×Dic61—28no—
373C2×Dic61—28no—
374C2×Dic61—22no—
375C2×Dic61—22no—
376C2×Dic61—22no—
377C2×Dic61—22no—
378C2×Dic61—22no—
379C2×Dic61—22no—
380C2×Dic61—22no—
381C2×Dic61—22no—
382C2×Dic61—22no—
383C2×Dic61—22no—
384C2×Dic61—22no—
385C2×Dic61—22no—
386C2×Dic61—22no—
387C2×Dic61—22no—
388C2×Dic61—22no—
389C2×Dic61—44no—
390C2×Dic61—44no—
391C2×Dic61—44no—
392C2×Dic61C23×C414yes—
393C2×Dic61C23×C414yes—
394C2×Dic61C22×D414yes—
395C4×D61—232no—
396C4×D61—416no—
397C4×D61—416no—
398C4×D61—416no—
399C2×#2342—611nomaximal, Sylow
400C22×C61—24no—
401C22×C61—24no—
402C22×C61—24no—
403C22×C61—416no—
404C22×C61—42no—
405C22×C61—42no—
406C22×C61—42no—
407C22×C61—42no—
408C22×C61C2×#11714yes—
409C22×C61C2×C4×D414yes—
410C22×C61#51814yes—
411C22×C61#54614yes—
412C22×C61#54614yes—
413C22×C61#55114yes—
414C22×C61#55114yes—
415C22×C61C24×C411yescharacteristic
416C22×C61C23×D411yescharacteristic
417C22×C61C22×#4111yescharacteristic
418C22×C61C22×#4111yescharacteristic
419C22×C61C22×#4111yescharacteristic
420C22×C61C2×H(5,𝔽2)11yescharacteristic
421C22×C61C2×H(5,𝔽2)11yescharacteristic
422C2×D61—232no—
423C2×D61—232no—
424C2×D61—24no—
425C2×D61—24no—
426C2×D61—24no—
427C2×D61—24no—
428C2×D61—24no—
429C2×D61—24no—
430C2×D61—24no—
431C2×D61—24no—
432C2×D61—24no—
433C2×D61—24no—
434C2×D61—24no—
435C2×D61—24no—
436C2×D61—464no—
437C2×D61C2×#11718yescomplemented
438C2×D61C2×C4×D418yes—
439C4×C61—24no—
440C4×C61—24no—
441C4×C61—24no—
442C4×C61—42no—
443C4×C61—42no—
444C4×C61—42no—
445Dic61—24no—
446Dic61—24no—
447Dic61—24no—
448Dic61—42no—
449Dic61—42no—
450Dic61—42no—
451C22×#117—611no—
452C23×C22⋊C4—611no—
453C23×C22⋊C4—611no—
454#2342—6116no—
455C2×#388—611no—
456C2×#388—611no—
457C2×#388—611no—
458C2×#388D6111yescharacteristic, complemented
459C2×#385—611no—
460C2×#385—611no—
461C2×#381—611no—
462C2×#380—611no—
463C2×#379—611no—
464C2×C4×C22⋊C4—611no—
465C2×C4×C22⋊C4—611no—
466C2×C4×C22⋊C4—611no—
467C2×C61—44no—
468C2×C61#234218yescomplemented
469C2×C61C22×#11711yescharacteristic
470C2×C61C22×C4×D411yescharacteristic
471C2×C61C2×#51811yescharacteristic
472C2×C61C2×#54611yescharacteristic
473C2×C61C2×#54611yescharacteristic
474C2×C61C2×#55111yescharacteristic
475C2×C61C2×#55111yescharacteristic
476D61—28no—
477D61—28no—
478C26—611no—
479C24×C4—611no—
480C24×C4—611no—
481C24×C4—611no—
482C24×C4—611no—
483C2×#117—618no—
484C2×#117—1228no—
485C22×C4⋊C4—611no—
486C22×C4⋊C4—611no—
487C22×C4⋊C4—611no—
488C22×C4⋊C4C2×D6111yescharacteristic, complemented
489C22×C22⋊C4—611no—
490C22×C22⋊C4—611no—
491C22×C22⋊C4—611no—
492C22×C22⋊C4—611no—
493C22×C22⋊C4—6116no—
494C22×C22⋊C4—618no—
495C22×C22⋊C4—611no—
496C22×C22⋊C4—611no—
497C22×C22⋊C4—611no—
498C22×C22⋊C4—611no—
499C22×C22⋊C4—611no—
500C22×C22⋊C4—611no—
501C22×C22⋊C4—611no—
502C22×C22⋊C4—618no—
503C22×C22⋊C4—1228no—
504C22×C22⋊C4C2×D6111yescharacteristic
505C22×C22⋊C4C2×D6111yescharacteristic
506C22×C22⋊C4C2×D6111yescharacteristic
507C22×C42—611no—
508C22×C42—611no—
509C22×C42—611no—
510C22×C42C2×D6111yescharacteristic, complemented
511#388—618no—
512#388—618no—
513#388—618no—
514#388C2×D6118yescomplemented
515#385—618no—
516#385—618no—
517#381—618no—
518#380—618no—
519#379—618no—
520C4×C22⋊C4—618no—
521C4×C22⋊C4—618no—
522C4×C22⋊C4—618no—
523C2×#95—611no—
524C2×#95—611no—
525C2×#95—611no—
526C2×#95—611no—
527C2×#95—611no—
528C2×#95—611no—
529C2×#95C2×D6111yescharacteristic, complemented
530C2×#95C2×D6111yescharacteristic, complemented
531C61C2×#234211yescharacteristic, complemented, Sylow
532C25—611no—
533C25—611no—
534C25—618no—
535C25—614no—
536C25—1224no—
537C25—1224no—
538C25—1224no—
539C25—1224no—
540C25—2442no—
541C25—2442no—
542C25C22×D6111yescharacteristic
543C23×C4—611no—
544C23×C4—611no—
545C23×C4—611no—
546C23×C4—618no—
547C23×C4—614no—
548C23×C4—618no—
549C23×C4—614no—
550C23×C4—611no—
551C23×C4—611no—
552C23×C4—611no—
553C23×C4—614no—
554C23×C4—614no—
555C23×C4—1224no—
556C23×C4—1224no—
557C23×C4—1224no—
558C23×C4—1224no—
559C23×C4—1224no—
560C23×C4—1224no—
561C23×C4—2442no—
562C23×C4—2442no—
563C23×C4—2442no—
564C23×C4—2442no—
565C23×C4C22×D6111yescharacteristic
566C23×C4C22×D6111yescharacteristic
567C23×C4C22×D6111yescharacteristic
568C23×C4C22×D6111yescharacteristic
569C23×C4C22×D6111yescharacteristic
570C23×C4C22×D6111yescharacteristic
571#117—12232no—
572C2×C4⋊C4—42no—
573C2×C4⋊C4—614no—
574C2×C4⋊C4—614no—
575C2×C4⋊C4—614no—
576C2×C4⋊C4—1224no—
577C2×C4⋊C4—1224no—
578C2×C4⋊C4—2442no—
579C2×C4⋊C4C22×D6114yescomplemented
580C2×C22⋊C4—24no—
581C2×C22⋊C4—42no—
582C2×C22⋊C4—618no—
583C2×C22⋊C4—614no—
584C2×C22⋊C4—618no—
585C2×C22⋊C4—618no—
586C2×C22⋊C4—618no—
587C2×C22⋊C4—614no—
588C2×C22⋊C4—614no—
589C2×C22⋊C4—614no—
590C2×C22⋊C4—6164no—
591C2×C22⋊C4—614no—
592C2×C22⋊C4—614no—
593C2×C22⋊C4—614no—
594C2×C22⋊C4—614no—
595C2×C22⋊C4—614no—
596C2×C22⋊C4—614no—
597C2×C22⋊C4—614no—
598C2×C22⋊C4—12232no—
599C2×C22⋊C4—1224no—
600C2×C22⋊C4—1224no—
601C2×C22⋊C4—1224no—
602C2×C22⋊C4—1224no—
603C2×C22⋊C4—1224no—
604C2×C22⋊C4—1224no—
605C2×C22⋊C4—2442no—
606C2×C22⋊C4C4×D6118yescomplemented
607C2×C22⋊C4C22×D6114yes—
608C2×C22⋊C4C22×D6114yes—
609C2×C22⋊C4C22×D6114yes—
610C2×C42—24no—
611C2×C42—614no—
612C2×C42—614no—
613C2×C42—614no—
614C2×C42—1224no—
615C2×C42—2442no—
616C2×C42—2442no—
617C2×C42C22×D6114yescomplemented
618#95—614no—
619#95—614no—
620#95—614no—
621#95—614no—
622#95—614no—
623#95—614no—
624#95C22×D6114yescomplemented
625#95C22×D6114yescomplemented
626C24—22no—
627C24—22no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—22no—
632C24—614no—
633C24—614no—
634C24—614no—
635C24—614no—
636C24—614no—
637C24—614no—
638C24—612no—
639C24—612no—
640C24—6116no—
641C24—1228no—
642C24—12232no—
643C24—12232no—
644C24—1228no—
645C24—1228no—
646C24—1228no—
647C24—1222no—
648C24—1222no—
649C24—1222no—
650C24—1222no—
651C24—1222no—
652C24—1222no—
653C24—1222no—
654C24—1222no—
655C24—24416no—
656C24—2444no—
657C24—2444no—
658C24—24416no—
659C24—24416no—
660C24—24416no—
661C24—24416no—
662C24C2×C4×D6114yes—
663C24C23×D6112yes—
664C24C23×D6111yescharacteristic
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—614no—
681C22×C4—614no—
682C22×C4—614no—
683C22×C4—612no—
684C22×C4—612no—
685C22×C4—612no—
686C22×C4—6116no—
687C22×C4—6116no—
688C22×C4—612no—
689C22×C4—612no—
690C22×C4—612no—
691C22×C4—1228no—
692C22×C4—1228no—
693C22×C4—12232no—
694C22×C4—1228no—
695C22×C4—1228no—
696C22×C4—1228no—
697C22×C4—1222no—
698C22×C4—1222no—
699C22×C4—1222no—
700C22×C4—1222no—
701C22×C4—1222no—
702C22×C4—1222no—
703C22×C4—1222no—
704C22×C4—1222no—
705C22×C4—1222no—
706C22×C4—1222no—
707C22×C4—1222no—
708C22×C4—1222no—
709C22×C4—1222no—
710C22×C4—1222no—
711C22×C4—1222no—
712C22×C4—1228no—
713C22×C4—24416no—
714C22×C4—2444no—
715C22×C4—2444no—
716C22×C4—2444no—
717C22×C4—2444no—
718C22×C4—24416no—
719C22×C4—24416no—
720C22×C4C2×C4×D6114yes—
721C22×C4C2×C4×D6114yes—
722C22×C4D4×D6114yes—
723C22×C4C23×D6112yes—
724C22×C4C23×D6112yes—
725C22×C4C23×D6112yes—
726C22×C4C23×D6112yes—
727C22×C4C23×D6112yes—
728C22×C4C23×D6112yes—
729C4⋊C4—44no—
730C4⋊C4—1228no—
731C4⋊C4—1228no—
732C4⋊C4—2444no—
733C22⋊C4—28no—
734C22⋊C4—44no—
735C22⋊C4—6116no—
736C22⋊C4—6116no—
737C22⋊C4—6116no—
738C22⋊C4—6116no—
739C22⋊C4—1228no—
740C22⋊C4—1228no—
741C22⋊C4—1228no—
742C22⋊C4—1228no—
743C22⋊C4—1228no—
744C22⋊C4—1228no—
745C22⋊C4—2444no—
746C22⋊C4C2×C4×D61116yescomplemented
747C42—28no—
748C42—1228no—
749C42—2444no—
750C42—2444no—
751C23—28no—
752C23—28no—
753C23—28no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—44no—
761C23—44no—
762C23—44no—
763C23—44no—
764C23—6116no—
765C23—6116no—
766C23—614no—
767C23—614no—
768C23—614no—
769C23—614no—
770C23—614no—
771C23—614no—
772C23—12232no—
773C23—12232no—
774C23—1228no—
775C23—1228no—
776C23—1228no—
777C23—1228no—
778C23—1222no—
779C23—1222no—
780C23—1222no—
781C23—1222no—
782C23—1222no—
783C23—1222no—
784C23—1222no—
785C23—1222no—
786C23—1228no—
787C23—1228no—
788C23—1228no—
789C23—1228no—
790C23—1228no—
791C23—1228no—
792C23—1228no—
793C23—1228no—
794C23—24416no—
795C23—24416no—
796C23—24416no—
797C23—24416no—
798C23—24416no—
799C23—244128no—
800C23C22×C4×D6114yes—
801C23C22×C4×D6112yes—
802C23C2×D4×D6112yes—
803C23#41×D6112yes—
804C23#41×D6112yes—
805C23#41×D6112yes—
806C23#1451982212yes—
807C23#1451982312yes—
808C23C24×D6111yescharacteristic
809C2×C4—28no—
810C2×C4—28no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—28no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—44no—
828C2×C4—44no—
829C2×C4—44no—
830C2×C4—614no—
831C2×C4—614no—
832C2×C4—614no—
833C2×C4—12232no—
834C2×C4—1228no—
835C2×C4—1228no—
836C2×C4—1222no—
837C2×C4—1222no—
838C2×C4—1222no—
839C2×C4—1222no—
840C2×C4—1222no—
841C2×C4—1222no—
842C2×C4—1228no—
843C2×C4—1222no—
844C2×C4—1222no—
845C2×C4—1222no—
846C2×C4—1222no—
847C2×C4—1222no—
848C2×C4—1222no—
849C2×C4—1222no—
850C2×C4—1222no—
851C2×C4—1222no—
852C2×C4—24416no—
853C2×C4—24416no—
854C2×C4—24416no—
855C2×C4—2444no—
856C2×C4—2444no—
857C2×C4—2444no—
858C2×C4C22×C4×D6114yes—
859C2×C4C22×C4×D6114yes—
860C2×C4C2×D4×D6114yes—
861C22—24no—
862C22—24no—
863C22—24no—
864C22—42no—
865C22—42no—
866C22—42no—
867C22—42no—
868C22—416no—
869C22—618no—
870C22—618no—
871C22—1224no—
872C22—1224no—
873C22—1224no—
874C22—1224no—
875C22—1224no—
876C22—1224no—
877C22—1224no—
878C22—1224no—
879C22—1224no—
880C22—1224no—
881C22—1224no—
882C22—1224no—
883C22—12232no—
884C22—12232no—
885C22—24464no—
886C22#117×D6114yes—
887C22C4×D4×D6114yes—
888C22#1684023414yes—
889C22#1684040414yes—
890C22#1684040914yes—
891C22#1684043714yes—
892C22#1684044214yes—
893C22C23×C4×D6111yescharacteristic
894C22C22×D4×D6111yescharacteristic
895C22C2×#41×D6111yescharacteristic
896C22C2×#41×D6111yescharacteristic
897C22C2×#41×D6111yescharacteristic
898C22C2×#1451982211yescharacteristic
899C22C2×#1451982311yescharacteristic
900C4—24no—
901C4—24no—
902C4—24no—
903C4—42no—
904C4—42no—
905C4—42no—
906C4—1224no—
907C4—1224no—
908C4—1224no—
909C4—2442no—
910C4—2442no—
911C4—2442no—
912C2—44no—
913C2—1228no—
914C2—1228no—
915C2#2144866318yesdirect product factor
916C2C2×#117×D6111yescharacteristic
917C2C2×C4×D4×D6111yescharacteristic
918C2C2×#1684023411yescharacteristic
919C2C2×#1684040411yescharacteristic
920C2C2×#1684040911yescharacteristic
921C2C2×#1684043711yescharacteristic
922C2C2×#1684044211yescharacteristic
subgroupG/H
centerC24C23×D61
commutatorC22×C61C24×C4
FrattiniC23C24×D61
FittingC2×C61×#388C2
socleC24×C61C24
prime radicalC25×D61C22
cosocleC23×C61C25
hypercenterC2×#388D61
hypocenterC61C2×#2342
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#14519734C2semidirect
4. #21448663C2direct (N × H)
5. C2×#16839656C2semidirect
6. C2×#16839655C2semidirect
7. C2×#16839650C2semidirect
8. C2×#16839636C2semidirect
9. C2×#16839633C2semidirect
10. C2×#16839624C2semidirect
11. C2×#16839619C2semidirect
13. C2×C4×#11758198C2semidirect
14. C2×#16839609C2semidirect
15. C2×#16839609C2semidirect
16. C2×C61×#388C2semidirect
23. C2×#14519734C22semidirect
24. C22×C4⋊Dic61C22semidirect
25. C22×#11758196C22semidirect
26. C22×#11758196C22semidirect
39. C2×C22⋊C4×D61C4semidirect
42. C22×C4×Dic61C22semidirect
43. C22×C4×Dic61C22semidirect
44. C22×C4×Dic61C22semidirect
45. #16839656C22semidirect
46. #16839655C22semidirect
47. #16839650C22semidirect
48. #16839636C22semidirect
49. #16839633C22semidirect
50. #16839624C22semidirect
51. #16839619C22semidirect
53. C4×#11758198C22semidirect
54. #16839609C22semidirect
55. #16839609C22semidirect
56. C2×#14519684C22semidirect
57. C2×#14519684C22semidirect
58. C2×#14519684C22semidirect
59. C2×#14519684C22semidirect
60. C2×#14519684C22semidirect
61. C2×#14519684C22semidirect
62. C22×C4⋊C4×C61C22semidirect
66. C22×C42×C61C22semidirect
67. C61×#388C22semidirect
68. C2×#95×C61C22semidirect
69. C2×#95×C61C22semidirect
96. C22×C4×D61C2×C4semidirect
97. C22×C4×D61C2×C4semidirect
104. C2×C4⋊Dic61C23semidirect
107. C2×#11758196C23semidirect
108. C2×#11758196C23semidirect
111. C2×C22⋊Dic61C2×C4semidirect
132. C22⋊C4×D61C2×C4semidirect
136. C2×C4×Dic61C23semidirect
137. C2×C4×Dic61C23semidirect
138. C2×C4×Dic61C23semidirect
139. #14519684C23semidirect
140. #14519684C23semidirect
141. #14519684C23semidirect
142. #14519684C23semidirect
143. #14519684C23semidirect
144. #14519684C23semidirect
153. C2×C4⋊C4×C61C23semidirect
156. C2×C22⋊C4×C61C2×C4semidirect
161. C2×C42×C61C23semidirect
162. #95×C61C23semidirect
163. #95×C61C23semidirect
265. C2×C4×D61C22×C4semidirect
266. C2×C4×D61C22×C4semidirect
270. C22⋊C4×C61C22×C4semidirect
274. C22⋊Dic61C22×C4semidirect
339. C22×D61#117semidirect
437. C2×D61C2×#117semidirect
458. C2×#388D61semidirect
468. C2×C61#2342semidirect
488. C22×C4⋊C4C2×D61semidirect
510. C22×C42C2×D61semidirect
514. #388C2×D61semidirect
529. C2×#95C2×D61semidirect
530. C2×#95C2×D61semidirect
531. C61C2×#2342semidirect
579. C2×C4⋊C4C22×D61semidirect
606. C2×C22⋊C4C4×D61semidirect
617. C2×C42C22×D61semidirect
624. #95C22×D61semidirect
625. #95C22×D61semidirect
746. C22⋊C4C2×C4×D61semidirect
915. C2#21448663direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197342
C22×C22⋊C4×D612
#214486632
C2×#168396562
C2×#168396552
C2×#168396502
C2×#168396362
C2×#168396332
C2×#168396242
C2×#168396192
C2×#168396172
C2×C4×#117581982
C2×#168396092
C2×C61×#3882
C2×#234261