Finite Group Databasebeta

← C2×#21449720 #29848124

Subgroups — C2×#21449720 #29848124

Order 15616.

3438 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519759C211yesmaximal, characteristic, complemented
2#21449720C2116yesmaximal, direct product factor
3C2×#16839701C211yesmaximal, characteristic, complemented
4C2×#16839684C211yesmaximal, characteristic, complemented
5C2×#16839676C211yesmaximal, characteristic, complemented
6C2×#16839670C211yesmaximal, characteristic
7C2×#16839656C211yesmaximal, characteristic, complemented
8C2×#16839655C211yesmaximal, characteristic, complemented
9C2×#16839646C211yesmaximal, characteristic, complemented
10C2×#16839641C211yesmaximal, characteristic, complemented
11C2×#16839641C211yesmaximal, characteristic, complemented
12C2×#16839638C211yesmaximal, characteristic, complemented
13C2×#16839625C211yesmaximal, characteristic, complemented
14C2×#16839622C211yesmaximal, characteristic, complemented
15C2×C4×#11758198C211yesmaximal, characteristic, complemented
16C22×C4×D4×C61C211yesmaximal, characteristic, complemented
17C23×C22⋊D61C2211yescharacteristic
18C23×C22⋊D61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C2×#14519759—28no—
21C2×#14519759C2218yescomplemented
22C22×C4⋊Dic61C2211yescharacteristic
23C22×C4⋊Dic61C2211yescharacteristic
24C22×#11758196C2211yescharacteristic
25C22×#11758196C2211yescharacteristic
26C22×C22⋊Dic61C2211yescharacteristic
27C22×C22⋊Dic61C2211yescharacteristic
28C22×C22⋊Dic61C2211yescharacteristic
29C22×C22⋊Dic61C2211yescharacteristic
30C22×C22⋊Dic61C2211yescharacteristic
31C22×C22⋊Dic61C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×#11758198C2211yescharacteristic
35C22×#11758198C2211yescharacteristic
36C22×C4×Dic61C2211yescharacteristic
37#16839701C2218yescomplemented
38#16839684C2218yescomplemented
39#16839676C2218yescomplemented
40#16839670C2218yes—
41#16839656C2218yescomplemented
42#16839655C2218yescomplemented
43#16839646C2218yescomplemented
44#16839641C2218yescomplemented
45#16839641C2218yescomplemented
46#16839638C2218yescomplemented
47#16839625C2218yescomplemented
48#16839622C2218yescomplemented
49C4×#11758198C2218yescomplemented
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C2×#14519684C2211yescharacteristic
53C2×#14519684C2211yescharacteristic
54C2×#14519684C2211yescharacteristic
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C2×#14519684C2211yescharacteristic
60C23×D4×C61C2211yescharacteristic
61C24×C4×C61C2211yescharacteristic
62C24×C4×C61C2211yescharacteristic
63C2×C4×D4×C61—28no—
64C2×C4×D4×C61C2218yescomplemented
65C22×C4⋊C4×C61C2211yescharacteristic
66C22×C22⋊C4×C61C2211yescharacteristic
67C22×C22⋊C4×C61C2211yescharacteristic
68C22×C42×C61C2211yescharacteristic
69C24×D61C2311yescharacteristic
70C22×C22⋊D61—24no—
71C22×C22⋊D61—24no—
72C22×C22⋊D61—24no—
73C22×C22⋊D61—24no—
74C22×C22⋊D61—42no—
75C22×C22⋊D61—42no—
76C22×C22⋊D61C2314yes—
77C22×C22⋊D61C2314yes—
78C23×Dic61C2311yescharacteristic
79C23×Dic61C2311yescharacteristic
80C23×Dic61C2311yescharacteristic
81C23×Dic61C2311yescharacteristic
82C23×Dic61C2311yescharacteristic
83C23×Dic61C2311yescharacteristic
84C23×Dic61C2311yescharacteristic
85C22×C4×D61—24no—
86C22×C4×D61—24no—
87C22×C4×D61—42no—
88C22×C4×D61C2314yes—
89#14519759—232no—
90C2×C4⋊Dic61—24no—
91C2×C4⋊Dic61—42no—
92C2×C4⋊Dic61C2314yes—
93C2×C4⋊Dic61C2314yes—
94C2×#11758196—24no—
95C2×#11758196—24no—
96C2×#11758196C2314yes—
97C2×#11758196C2314yes—
98C2×C22⋊Dic61—24no—
99C2×C22⋊Dic61—24no—
100C2×C22⋊Dic61—42no—
101C2×C22⋊Dic61—42no—
102C2×C22⋊Dic61—42no—
103C2×C22⋊Dic61—42no—
104C2×C22⋊Dic61C2314yes—
105C2×C22⋊Dic61C2314yes—
106C2×C22⋊Dic61C2314yes—
107C2×C22⋊Dic61C2314yes—
108C2×C22⋊Dic61C2314yes—
109C2×C22⋊Dic61C2314yes—
110C2×#11758198—24no—
111C2×#11758198—24no—
112C2×#11758198—24no—
113C2×#11758198—42no—
114C2×#11758198C2314yes—
115C2×#11758198C2314yes—
116C2×#11758198C2314yes—
117C2×#11758198C2314yes—
118C2×C4×Dic61—42no—
119C2×C4×Dic61C2314yes—
120#14519684C2314yes—
121#14519684C2314yes—
122#14519684C2314yes—
123#14519684C2314yes—
124#14519684C2314yes—
125#14519684C2314yes—
126#14519684C2314yes—
127#14519684C2314yes—
128#14519684C2314yes—
129#14519684C2314yes—
130C25×C61C2311yescharacteristic
131C25×C61C2311yescharacteristic
132C22×D4×C61—24no—
133C22×D4×C61—24no—
134C22×D4×C61—24no—
135C22×D4×C61C2314yes—
136C23×C4×C61—24no—
137C23×C4×C61—24no—
138C23×C4×C61—24no—
139C23×C4×C61—24no—
140C23×C4×C61—42no—
141C23×C4×C61—42no—
142C23×C4×C61C2311yescharacteristic
143C23×C4×C61C2314yes—
144C23×C4×C61C2314yes—
145C23×C4×C61C2311yescharacteristic
146C23×C4×C61C2311yescharacteristic
147C23×C4×C61C2311yescharacteristic
148C23×C4×C61C2311yescharacteristic
149C4×D4×C61—232no—
150C2×C4⋊C4×C61—24no—
151C2×C4⋊C4×C61C2314yes—
152C2×C22⋊C4×C61—24no—
153C2×C22⋊C4×C61D418yescomplemented
154C2×C22⋊C4×C61C2314yes—
155C2×C22⋊C4×C61C2314yes—
156C2×C42×C61—24no—
157C2×C42×C61C2314yes—
158C24×C61—22no—
159C24×C61—22no—
160C24×C61—22no—
161C24×C61—22no—
162C24×C61—22no—
163C24×C61—22no—
164C24×C61—22no—
165C24×C61—22no—
166C24×C61—22no—
167C24×C61—22no—
168C24×C61—22no—
169C24×C61—22no—
170C24×C61C2×D414yes—
171C24×C61#4114yes—
172C24×C61C2412yes—
173C24×C61C2412yes—
174C24×C61C2411yescharacteristic
175C23×D61—22no—
176C23×D61—22no—
177C23×D61—22no—
178C23×D61—22no—
179C23×D61—22no—
180C23×D61—22no—
181C23×D61#4114yes—
182C23×D61C2412yes—
183C2×D4×C61—232no—
184C2×D4×C61—28no—
185C2×D4×C61—28no—
186C2×D4×C61—28no—
187C22×C4×C61—22no—
188C22×C4×C61—22no—
189C22×C4×C61—22no—
190C22×C4×C61—22no—
191C22×C4×C61—22no—
192C22×C4×C61—22no—
193C22×C4×C61—22no—
194C22×C4×C61—22no—
195C22×C4×C61—22no—
196C22×C4×C61—28no—
197C22×C4×C61—22no—
198C22×C4×C61—22no—
199C22×C4×C61—28no—
200C22×C4×C61—28no—
201C22×C4×C61—28no—
202C22×C4×C61—44no—
203C22×C4×C61—44no—
204C22×C4×C61—416no—
205C22×C4×C61—416no—
206C22×C4×C61C2×D414yes—
207C22×C4×C61C2×D414yes—
208C22×C4×C61#4114yes—
209C22×C4×C61#4114yes—
210C22×C4×C61C2412yes—
211C22×C4×C61C2412yes—
212C22×C4×C61C2412yes—
213C22×C4×C61C2412yes—
214C22×C4×C61C2412yes—
215C2×C22⋊D61—28no—
216C2×C22⋊D61—28no—
217C2×C22⋊D61—28no—
218C2×C22⋊D61—28no—
219C2×C22⋊D61—44no—
220C2×C22⋊D61—44no—
221C2×C22⋊D61—416no—
222C2×C22⋊D61—416no—
223C22×Dic61—22no—
224C22×Dic61—22no—
225C22×Dic61—22no—
226C22×Dic61—22no—
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×Dic61—22no—
243C22×Dic61—22no—
244C22×Dic61C2412yes—
245C22×Dic61C2412yes—
246C22×Dic61C2412yes—
247C22×Dic61C2412yes—
248C22×Dic61C2412yes—
249C22×Dic61C2412yes—
250C22×Dic61C2412yes—
251C2×C4×D61—28no—
252C2×C4×D61—28no—
253C2×C4×D61—44no—
254C2×C4×D61—416no—
255C4⋊C4×C61—28no—
256C22⋊C4×C61—28no—
257C22⋊C4×C61C2×D4116yescomplemented
258C42×C61—28no—
259C22⋊Dic61—28no—
260C22⋊Dic61—28no—
261C22⋊Dic61—44no—
262C22⋊Dic61—44no—
263C22⋊Dic61—44no—
264C22⋊Dic61—44no—
265#11758198—28no—
266#11758198—28no—
267#11758198—28no—
268#11758198—44no—
269C4⋊Dic61—28no—
270C4⋊Dic61—44no—
271#11758196—28no—
272#11758196—28no—
273C4×Dic61—44no—
274C23×C61—28no—
275C23×C61—28no—
276C23×C61—28no—
277C23×C61—28no—
278C23×C61—28no—
279C23×C61—28no—
280C23×C61—22no—
281C23×C61—22no—
282C23×C61—22no—
283C23×C61—22no—
284C23×C61—22no—
285C23×C61—22no—
286C23×C61—22no—
287C23×C61—22no—
288C23×C61—22no—
289C23×C61—22no—
290C23×C61—22no—
291C23×C61—22no—
292C23×C61—44no—
293C23×C61—44no—
294C23×C61—44no—
295C23×C61—44no—
296C23×C61—44no—
297C23×C61—44no—
298C23×C61—44no—
299C23×C61—44no—
300C23×C61C22×D414yes—
301C23×C61C22×D412yes—
302C23×C61C2×#4114yes—
303C23×C61C2×#4112yes—
304C23×C61C2×#4112yes—
305C23×C61C2×#4112yes—
306C23×C61C2×#4112yes—
307C23×C61H(5,𝔽2)12yes—
308C23×C61H(5,𝔽2)12yes—
309C23×C61C2511yescharacteristic
310C22×D61—28no—
311C22×D61—28no—
312C22×D61—28no—
313C22×D61—22no—
314C22×D61—22no—
315C22×D61—22no—
316C22×D61—22no—
317C22×D61—22no—
318C22×D61—22no—
319C22×D61—44no—
320C22×D61—44no—
321C22×D61—44no—
322C22×D61—44no—
323C22×D61C2×#4114yes—
324D4×C61—232no—
325C2×C4×C61—28no—
326C2×C4×C61—28no—
327C2×C4×C61—28no—
328C2×C4×C61—28no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—22no—
334C2×C4×C61—22no—
335C2×C4×C61—22no—
336C2×C4×C61—22no—
337C2×C4×C61—22no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
340C2×C4×C61—416no—
341C2×C4×C61—416no—
342C2×C4×C61—44no—
343C2×C4×C61C22×D414yes—
344C2×C4×C61C22×D414yes—
345C2×C4×C61C2×#4114yes—
346C2×C4×C61C2×#4114yes—
347C22⋊D61—416no—
348C22⋊D61—416no—
349C2×Dic61—22no—
350C2×Dic61—22no—
351C2×Dic61—22no—
352C2×Dic61—22no—
353C2×Dic61—22no—
354C2×Dic61—22no—
355C2×Dic61—22no—
356C2×Dic61—22no—
357C2×Dic61—22no—
358C2×Dic61—22no—
359C2×Dic61—22no—
360C2×Dic61—22no—
361C2×Dic61—22no—
362C2×Dic61—22no—
363C2×Dic61—22no—
364C2×Dic61—22no—
365C2×Dic61—22no—
366C2×Dic61—22no—
367C2×Dic61—22no—
368C2×Dic61—22no—
369C2×Dic61—22no—
370C2×Dic61—44no—
371C2×Dic61—44no—
372C2×Dic61—44no—
373C2×Dic61—44no—
374C2×Dic61—44no—
375C2×Dic61—44no—
376C2×Dic61—44no—
377C4×D61—416no—
378C2×#2457—611nomaximal, Sylow
379C22×C61—24no—
380C22×C61—24no—
381C22×C61—24no—
382C22×C61—24no—
383C22×C61—24no—
384C22×C61—24no—
385C22×C61—42no—
386C22×C61—42no—
387C22×C61—42no—
388C22×C61—42no—
389C22×C61—42no—
390C22×C61—42no—
391C22×C61—42no—
392C22×C61—42no—
393C22×C61—416no—
394C22×C61—416no—
395C22×C61#52514yes—
396C22×C61#52914yes—
397C22×C61#54014yes—
398C22×C61#54614yes—
399C22×C61#54614yes—
400C22×C61#55114yes—
401C22×C61#55314yes—
402C22×C61C23×D411yescharacteristic
403C22×C61C22×#4111yescharacteristic
404C22×C61C22×#4111yescharacteristic
405C22×C61C22×#4111yescharacteristic
406C22×C61C22×#4111yescharacteristic
407C22×C61C2×H(5,𝔽2)11yescharacteristic
408C22×C61C2×H(5,𝔽2)11yescharacteristic
409C2×D61—24no—
410C2×D61—24no—
411C2×D61—24no—
412C2×D61—42no—
413C2×D61—42no—
414C2×D61—42no—
415C2×D61—42no—
416C2×D61—416no—
417C4×C61—24no—
418C4×C61—24no—
419C4×C61—24no—
420C4×C61—24no—
421C4×C61—42no—
422Dic61—42no—
423Dic61—42no—
424Dic61—42no—
425Dic61—42no—
426Dic61—42no—
427Dic61—42no—
428Dic61—42no—
429C22×#123—611no—
430C22×C4×D4D6111yescharacteristic, complemented
431#2457—6116no—
432C2×#400—611no—
433C2×#396—611no—
434C2×#394—611no—
435C2×#392—611no—
436C2×#388—611no—
437C2×#388—611no—
438C2×#387—611no—
439C2×#386—611no—
440C2×#386—611no—
441C2×#386—611no—
442C2×#381—611no—
443C2×#380—611no—
444C2×C4×C22⋊C4—611no—
445C2×C61—44no—
446C2×C61—44no—
447C2×C61#245718yescomplemented
448C2×C61C2×#52511yescharacteristic
449C2×C61C2×#52911yescharacteristic
450C2×C61C2×#54011yescharacteristic
451C2×C61C2×#54611yescharacteristic
452C2×C61C2×#54611yescharacteristic
453C2×C61C2×#55111yescharacteristic
454C2×C61C2×#55311yescharacteristic
455D61—44no—
456C23×D4—611no—
457C23×D4—611no—
458C23×D4C2×D6111yescharacteristic
459C24×C4—611no—
460C24×C4C2×D6111yescharacteristic
461C24×C4C2×D6111yescharacteristic
462C2×#123—618no—
463C2×#123—1228no—
464C2×C4×D4—28no—
465C2×C4×D4C2×D6118yescomplemented
466C22×C4⋊C4—611no—
467C22×C4⋊C4—611no—
468C22×C4⋊C4—611no—
469C22×C4⋊C4—611no—
470C22×C4⋊C4C2×D6111yescharacteristic
471C22×C22⋊C4—611no—
472C22×C22⋊C4—611no—
473C22×C22⋊C4—611no—
474C22×C22⋊C4—611no—
475C22×C22⋊C4—611no—
476C22×C22⋊C4—611no—
477C22×C22⋊C4—611no—
478C22×C22⋊C4—611no—
479C22×C22⋊C4—611no—
480C22×C22⋊C4—611no—
481C22×C22⋊C4C2×D6111yescharacteristic
482C22×C22⋊C4C2×D6111yescharacteristic
483C22×C42—611no—
484C22×C42C2×D6111yescharacteristic
485#400—618no—
486#396—618no—
487#394—618no—
488#392—618no—
489#388—618no—
490#388—618no—
491#387—618no—
492#386—618no—
493#386—618no—
494#386—618no—
495#381—618no—
496#380—618no—
497C4×C22⋊C4—618no—
498C2×#95—611no—
499C2×#95—611no—
500C2×#95—611no—
501C2×#95—611no—
502C2×#95—611no—
503C2×#95—611no—
504C2×#95—611no—
505C2×#95—611no—
506C2×#95—611no—
507C2×#95—611no—
508C61C2×#245711yescharacteristic, complemented, Sylow
509C25—611no—
510C25C22×D6111yescharacteristic
511C25C22×D6111yescharacteristic
512C22×D4—24no—
513C22×D4—24no—
514C22×D4—24no—
515C22×D4—614no—
516C22×D4—614no—
517C22×D4—1224no—
518C22×D4—1224no—
519C22×D4—1224no—
520C22×D4—1224no—
521C22×D4—2442no—
522C22×D4—2442no—
523C22×D4C22×D6114yes—
524C23×C4—24no—
525C23×C4—24no—
526C23×C4—24no—
527C23×C4—24no—
528C23×C4—42no—
529C23×C4—42no—
530C23×C4—611no—
531C23×C4—611no—
532C23×C4—611no—
533C23×C4—611no—
534C23×C4—611no—
535C23×C4—611no—
536C23×C4—611no—
537C23×C4—614no—
538C23×C4—1224no—
539C23×C4—1224no—
540C23×C4—2442no—
541C23×C4C22×D6111yescharacteristic
542C23×C4C22×D6114yes—
543C23×C4C22×D6114yes—
544C23×C4C22×D6111yescharacteristic
545C23×C4C22×D6111yescharacteristic
546C23×C4C22×D6111yescharacteristic
547C23×C4C22×D6111yescharacteristic
548#123—12232no—
549C4×D4—232no—
550C2×C4⋊C4—24no—
551C2×C4⋊C4—614no—
552C2×C4⋊C4—614no—
553C2×C4⋊C4—614no—
554C2×C4⋊C4—614no—
555C2×C4⋊C4—1224no—
556C2×C4⋊C4—1224no—
557C2×C4⋊C4—1224no—
558C2×C4⋊C4—2442no—
559C2×C4⋊C4C22×D6114yes—
560C2×C22⋊C4—24no—
561C2×C22⋊C4—614no—
562C2×C22⋊C4—614no—
563C2×C22⋊C4—614no—
564C2×C22⋊C4—614no—
565C2×C22⋊C4—614no—
566C2×C22⋊C4—614no—
567C2×C22⋊C4—614no—
568C2×C22⋊C4—614no—
569C2×C22⋊C4—614no—
570C2×C22⋊C4—614no—
571C2×C22⋊C4—1224no—
572C2×C22⋊C4—1224no—
573C2×C22⋊C4—1224no—
574C2×C22⋊C4—1224no—
575C2×C22⋊C4—1224no—
576C2×C22⋊C4—2442no—
577C2×C22⋊C4—2442no—
578C2×C22⋊C4—2442no—
579C2×C22⋊C4—2442no—
580C2×C22⋊C4—2442no—
581C2×C22⋊C4C22⋊D6118yescomplemented
582C2×C22⋊C4C22×D6114yes—
583C2×C22⋊C4C22×D6114yes—
584C2×C42—24no—
585C2×C42—614no—
586C2×C42—2442no—
587C2×C42C22×D6114yes—
588#95—614no—
589#95—614no—
590#95—614no—
591#95—614no—
592#95—614no—
593#95—614no—
594#95—614no—
595#95—614no—
596#95—614no—
597#95—614no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24—22no—
604C24—22no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—614no—
611C24—612no—
612C24—1222no—
613C24—1222no—
614C24—1222no—
615C24—1222no—
616C24—1222no—
617C24—1222no—
618C24#1175822214yes—
619C24C2×C22⋊D6114yes—
620C24C23×D6112yes—
621C24C23×D6112yes—
622C24C23×D6111yescharacteristic
623C2×D4—232no—
624C2×D4—28no—
625C2×D4—28no—
626C2×D4—28no—
627C2×D4—1228no—
628C2×D4—1228no—
629C2×D4—1228no—
630C2×D4—1228no—
631C2×D4—2444no—
632C2×D4—2444no—
633C2×D4—24416no—
634C2×D4—24416no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—28no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—28no—
648C22×C4—28no—
649C22×C4—28no—
650C22×C4—44no—
651C22×C4—44no—
652C22×C4—416no—
653C22×C4—416no—
654C22×C4—612no—
655C22×C4—612no—
656C22×C4—612no—
657C22×C4—612no—
658C22×C4—612no—
659C22×C4—612no—
660C22×C4—612no—
661C22×C4—1228no—
662C22×C4—1222no—
663C22×C4—1222no—
664C22×C4—1222no—
665C22×C4—1222no—
666C22×C4—1222no—
667C22×C4—1222no—
668C22×C4—1222no—
669C22×C4—1222no—
670C22×C4—1222no—
671C22×C4—1222no—
672C22×C4—1222no—
673C22×C4—1222no—
674C22×C4—1222no—
675C22×C4—1222no—
676C22×C4—1222no—
677C22×C4—1222no—
678C22×C4—1222no—
679C22×C4—1222no—
680C22×C4—1222no—
681C22×C4—1222no—
682C22×C4—1222no—
683C22×C4—1228no—
684C22×C4—2444no—
685C22×C4—24416no—
686C22×C4#1175822214yes—
687C22×C4#1175822414yes—
688C22×C4C2×C22⋊D6114yes—
689C22×C4C2×C22⋊D6114yes—
690C22×C4C23×D6112yes—
691C22×C4C23×D6112yes—
692C22×C4C23×D6112yes—
693C22×C4C23×D6112yes—
694C22×C4C23×D6112yes—
695C4⋊C4—28no—
696C4⋊C4—1228no—
697C4⋊C4—1228no—
698C4⋊C4—1228no—
699C4⋊C4—2444no—
700C22⋊C4—28no—
701C22⋊C4—1228no—
702C22⋊C4—1228no—
703C22⋊C4—1228no—
704C22⋊C4—1228no—
705C22⋊C4—1228no—
706C22⋊C4—2444no—
707C22⋊C4—2444no—
708C22⋊C4—2444no—
709C22⋊C4—2444no—
710C22⋊C4—2444no—
711C22⋊C4C2×C22⋊D61116yescomplemented
712C42—28no—
713C42—2444no—
714C23—28no—
715C23—28no—
716C23—28no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—28no—
730C23—28no—
731C23—28no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—44no—
739C23—44no—
740C23—614no—
741C23—1228no—
742C23—1222no—
743C23—1222no—
744C23—1222no—
745C23—1222no—
746C23—1222no—
747C23—1222no—
748C23—1228no—
749C23—1228no—
750C23—2444no—
751C23—2444no—
752C23—2444no—
753C23—2444no—
754C23C22×C22⋊D6114yes—
755C23C22×C22⋊D6112yes—
756C23#41×D6112yes—
757C23C2×#1175822412yes—
758C23C2×#1175822214yes—
759C23C2×#1175822212yes—
760C23C2×#1175822212yes—
761C23#1451982212yes—
762C23#1451982312yes—
763C23C24×D6111yescharacteristic
764D4—232no—
765D4—24416no—
766D4—24416no—
767C2×C4—28no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—28no—
777C2×C4—28no—
778C2×C4—28no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—416no—
783C2×C4—416no—
784C2×C4—44no—
785C2×C4—1222no—
786C2×C4—1222no—
787C2×C4—1222no—
788C2×C4—1222no—
789C2×C4—1222no—
790C2×C4—1222no—
791C2×C4—1222no—
792C2×C4—1222no—
793C2×C4—1222no—
794C2×C4—1222no—
795C2×C4—1222no—
796C2×C4—1222no—
797C2×C4—1222no—
798C2×C4—1222no—
799C2×C4—1222no—
800C2×C4—1222no—
801C2×C4—1222no—
802C2×C4—1222no—
803C2×C4—1222no—
804C2×C4—1222no—
805C2×C4—1222no—
806C2×C4—24416no—
807C2×C4—2444no—
808C2×C4—2444no—
809C2×C4—2444no—
810C2×C4—2444no—
811C2×C4—2444no—
812C2×C4—2444no—
813C2×C4—2444no—
814C2×C4C22×C22⋊D6114yes—
815C2×C4C22×C22⋊D6114yes—
816C2×C4C2×#1175822414yes—
817C2×C4C2×#1175822214yes—
818C22—24no—
819C22—24no—
820C22—24no—
821C22—24no—
822C22—24no—
823C22—24no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—416no—
833C22—416no—
834C22—1224no—
835C22—1224no—
836C22—1224no—
837C22—2442no—
838C22—2442no—
839C22—2442no—
840C22—2442no—
841C22—24416no—
842C22#1684027314yes—
843C22#1684029414yes—
844C22#1684036314yes—
845C22#1684040014yes—
846C22#1684040614yes—
847C22#1684044114yes—
848C22#1684045814yes—
849C22C23×C22⋊D6111yescharacteristic
850C22C2×#41×D6111yescharacteristic
851C22C22×#1175822411yescharacteristic
852C22C22×#1175822211yescharacteristic
853C22C22×#1175822211yescharacteristic
854C22C2×#1451982211yescharacteristic
855C22C2×#1451982311yescharacteristic
856C4—24no—
857C4—24no—
858C4—24no—
859C4—24no—
860C4—42no—
861C4—2442no—
862C4—2442no—
863C4—2442no—
864C4—2442no—
865C4—2442no—
866C4—2442no—
867C4—2442no—
868C2—44no—
869C2—44no—
870C2—2444no—
871C2#2144972018yesdirect product factor
872C2C2×#1684027311yescharacteristic
873C2C2×#1684029411yescharacteristic
874C2C2×#1684036311yescharacteristic
875C2C2×#1684040011yescharacteristic
876C2C2×#1684040611yescharacteristic
877C2C2×#1684044111yescharacteristic
878C2C2×#1684045811yescharacteristic
subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC22×C4×D4×C61C2
socleC24×C61C24
prime radicalC2×#16839670C2
hypercenterC22×C4×D4D61
hypocenterC61C2×#2457
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×#14519759C2semidirect
2. #21449720C2direct (N × H)
3. C2×#16839701C2semidirect
4. C2×#16839684C2semidirect
5. C2×#16839676C2semidirect
7. C2×#16839656C2semidirect
8. C2×#16839655C2semidirect
9. C2×#16839646C2semidirect
10. C2×#16839641C2semidirect
11. C2×#16839641C2semidirect
12. C2×#16839638C2semidirect
13. C2×#16839625C2semidirect
14. C2×#16839622C2semidirect
15. C2×C4×#11758198C2semidirect
16. C22×C4×D4×C61C2semidirect
21. C2×#14519759C22semidirect
37. #16839701C22semidirect
38. #16839684C22semidirect
39. #16839676C22semidirect
41. #16839656C22semidirect
42. #16839655C22semidirect
43. #16839646C22semidirect
44. #16839641C22semidirect
45. #16839641C22semidirect
46. #16839638C22semidirect
47. #16839625C22semidirect
48. #16839622C22semidirect
49. C4×#11758198C22semidirect
64. C2×C4×D4×C61C22semidirect
153. C2×C22⋊C4×C61D4semidirect
257. C22⋊C4×C61C2×D4semidirect
430. C22×C4×D4D61semidirect
447. C2×C61#2457semidirect
465. C2×C4×D4C2×D61semidirect
508. C61C2×#2457semidirect
581. C2×C22⋊C4C22⋊D61semidirect
711. C22⋊C4C2×C22⋊D61semidirect
871. C2#21449720direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197592
#214497202
C2×#168397012
C2×#168396842
C2×#168396762
C2×#168396702
C2×#168396562
C2×#168396552
C2×#168396462
C2×#168396412
C2×#168396382
C2×#168396252
C2×#168396222
C2×C4×#117581982
C22×C4×D4×C612
C2×#245761