Finite Group Databasebeta

← C2×#21451161 #29850214

Subgroups — C2×#21451161 #29850214

Order 15616.

3374 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519737C211yesmaximal, characteristic
2C22×C4⋊C4×D61C211yesmaximal, characteristic, complemented
3#21451161C2116yesmaximal, direct product factor
4C2×#16839695C211yesmaximal, characteristic, complemented
5C2×#16839692C211yesmaximal, characteristic, complemented
6C2×#16839685C211yesmaximal, characteristic, complemented
7C2×#16839648C211yesmaximal, characteristic, complemented
8C2×#16839644C211yesmaximal, characteristic, complemented
9C2×#16839638C211yesmaximal, characteristic
10C2×#16839638C211yesmaximal, characteristic
11C2×#16839637C211yesmaximal, characteristic, complemented
12C2×#16839636C211yesmaximal, characteristic, complemented
13C2×#16839634C211yesmaximal, characteristic, complemented
14C2×#16839633C211yesmaximal, characteristic, complemented
15C2×#16839619C211yesmaximal, characteristic, complemented
16C2×C61×#396C211yesmaximal, characteristic, complemented
17C23×C22⋊D61C2211yescharacteristic
18C24×Dic61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C23×C4×D61C2211yescharacteristic
21C23×C4×D61C2211yescharacteristic
22C2×#14519737—28no—
23C2×#14519737C2218yes—
24C22×C4⋊Dic61C2211yescharacteristic
25C22×C4⋊Dic61C2211yescharacteristic
26C22×C4⋊Dic61C2211yescharacteristic
27C22×#11758196C2211yescharacteristic
28C22×#11758196C2211yescharacteristic
29C22×#11758196C2211yescharacteristic
30C22×#11758196C2211yescharacteristic
31C22×#11758196C2211yescharacteristic
32C2×C4⋊C4×D61—28no—
33C2×C4⋊C4×D61C2218yescomplemented
34C22×C22⋊Dic61C2211yescharacteristic
35C22×C22⋊Dic61C2211yescharacteristic
36C22×#11758198C2211yescharacteristic
37C22×#11758198C2211yescharacteristic
38C22×#11758198C2211yescharacteristic
39C22×C4×Dic61C2211yescharacteristic
40#16839695C2218yescomplemented
41#16839692C2218yescomplemented
42#16839685C2218yescomplemented
43#16839648C2218yescomplemented
44#16839644C2218yescomplemented
45#16839638C2218yes—
46#16839638C2218yes—
47#16839637C2218yescomplemented
48#16839636C2218yescomplemented
49#16839634C2218yescomplemented
50#16839633C2218yescomplemented
51#16839619C2218yescomplemented
52C2×#14519684C2211yescharacteristic
53C2×#14519684C2211yescharacteristic
54C2×#14519684C2211yescharacteristic
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C2×#14519684C2211yescharacteristic
60C2×#14519684C2211yescharacteristic
61C22×C4⋊C4×C61C2211yescharacteristic
62C22×C4⋊C4×C61C2211yescharacteristic
63C22×C4⋊C4×C61C2211yescharacteristic
64C22×C22⋊C4×C61C2211yescharacteristic
65C22×C22⋊C4×C61C2211yescharacteristic
66C22×C22⋊C4×C61C2211yescharacteristic
67C61×#396C2218yescomplemented
68C2×#95×C61C2211yescharacteristic
69C24×D61C2311yescharacteristic
70C22×C22⋊D61—24no—
71C22×C22⋊D61—24no—
72C22×C22⋊D61Q818yes—
73C22×C22⋊D61C2314yes—
74C23×Dic61—24no—
75C23×Dic61—42no—
76C23×Dic61—42no—
77C23×Dic61C2311yescharacteristic
78C23×Dic61C2311yescharacteristic
79C23×Dic61C2311yescharacteristic
80C23×Dic61C2311yescharacteristic
81C23×Dic61C2311yescharacteristic
82C23×Dic61C2311yescharacteristic
83C23×Dic61C2311yescharacteristic
84C23×Dic61C2314yes—
85C22×C4×D61—24no—
86C22×C4×D61—24no—
87C22×C4×D61—24no—
88C22×C4×D61—24no—
89C22×C4×D61—42no—
90C22×C4×D61—42no—
91C22×C4×D61—42no—
92C22×C4×D61—42no—
93C22×C4×D61D418yes—
94C22×C4×D61C2314yes—
95C22×C4×D61C2314yes—
96C22×C4×D61C2314yes—
97#14519737—232no—
98C2×C4⋊Dic61—24no—
99C2×C4⋊Dic61—42no—
100C2×C4⋊Dic61—42no—
101C2×C4⋊Dic61C2314yes—
102C2×C4⋊Dic61C2314yes—
103C2×C4⋊Dic61C2314yes—
104C2×#11758196—24no—
105C2×#11758196—24no—
106C2×#11758196—24no—
107C2×#11758196—24no—
108C2×#11758196—42no—
109C2×#11758196C2314yes—
110C2×#11758196C2314yes—
111C2×#11758196C2314yes—
112C2×#11758196C2314yes—
113C2×#11758196C2314yes—
114C4⋊C4×D61—232no—
115C2×C22⋊Dic61—24no—
116C2×C22⋊Dic61—42no—
117C2×C22⋊Dic61C2314yes—
118C2×C22⋊Dic61C2314yes—
119C2×#11758198—24no—
120C2×#11758198—24no—
121C2×#11758198—24no—
122C2×#11758198C2314yes—
123C2×#11758198C2314yes—
124C2×#11758198C2314yes—
125C2×C4×Dic61—24no—
126C2×C4×Dic61C2314yes—
127#14519684C2314yes—
128#14519684C2314yes—
129#14519684C2314yes—
130#14519684C2314yes—
131#14519684C2314yes—
132#14519684C2314yes—
133#14519684C2314yes—
134#14519684C2314yes—
135#14519684C2314yes—
136C25×C61C2311yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C23×C4×C61C2311yescharacteristic
139C23×C4×C61C2311yescharacteristic
140C23×C4×C61C2311yescharacteristic
141C23×C4×C61C2311yescharacteristic
142C23×C4×C61C2311yescharacteristic
143C2×C4⋊C4×C61—24no—
144C2×C4⋊C4×C61—24no—
145C2×C4⋊C4×C61—42no—
146C2×C4⋊C4×C61C2314yes—
147C2×C4⋊C4×C61C2314yes—
148C2×C4⋊C4×C61C2314yes—
149C2×C22⋊C4×C61—24no—
150C2×C22⋊C4×C61—24no—
151C2×C22⋊C4×C61—42no—
152C2×C22⋊C4×C61C2314yes—
153C2×C22⋊C4×C61C2314yes—
154C2×C22⋊C4×C61C2314yes—
155#95×C61C2314yes—
156C24×C61—22no—
157C24×C61—22no—
158C24×C61—22no—
159C24×C61—22no—
160C24×C61—22no—
161C24×C61—22no—
162C24×C61C2×Q814yes—
163C24×C61C2412yes—
164C24×C61C2411yescharacteristic
165C23×D61—22no—
166C23×D61—22no—
167C23×D61—22no—
168C23×D61—22no—
169C23×D61C2×D414yes—
170C23×D61C2×Q814yes—
171C23×D61#4114yes—
172C23×D61C2412yes—
173C22×C4×C61—22no—
174C22×C4×C61—22no—
175C22×C4×C61—22no—
176C22×C4×C61—22no—
177C22×C4×C61—22no—
178C22×C4×C61—22no—
179C22×C4×C61—22no—
180C22×C4×C61—22no—
181C22×C4×C61—22no—
182C22×C4×C61—22no—
183C22×C4×C61—22no—
184C22×C4×C61—22no—
185C22×C4×C61—22no—
186C22×C4×C61—22no—
187C22×C4×C61—22no—
188C22×C4×C61—22no—
189C22×C4×C61C2×D414yes—
190C22×C4×C61#4114yes—
191C22×C4×C61C2412yes—
192C22×C4×C61C2412yes—
193C22×C4×C61C2412yes—
194C22×C4×C61C2412yes—
195C22×C4×C61C2412yes—
196C22×C4×C61C2412yes—
197C2×C22⋊D61—232no—
198C2×C22⋊D61—28no—
199C2×C22⋊D61—28no—
200C2×C22⋊D61C2×Q8116yes—
201C22×Dic61—22no—
202C22×Dic61—22no—
203C22×Dic61—22no—
204C22×Dic61—22no—
205C22×Dic61—22no—
206C22×Dic61—22no—
207C22×Dic61—22no—
208C22×Dic61—22no—
209C22×Dic61—22no—
210C22×Dic61—22no—
211C22×Dic61—22no—
212C22×Dic61—22no—
213C22×Dic61—22no—
214C22×Dic61—22no—
215C22×Dic61—22no—
216C22×Dic61—22no—
217C22×Dic61—22no—
218C22×Dic61—22no—
219C22×Dic61—28no—
220C22×Dic61—44no—
221C22×Dic61—44no—
222C22×Dic61—416no—
223C22×Dic61C2×D414yes—
224C22×Dic61C2×Q814yes—
225C22×Dic61#4114yes—
226C22×Dic61C2412yes—
227C22×Dic61C2412yes—
228C22×Dic61C2412yes—
229C22×Dic61C2412yes—
230C22×Dic61C2412yes—
231C22×Dic61C2412yes—
232C22×Dic61C2412yes—
233C2×C4×D61—232no—
234C2×C4×D61—28no—
235C2×C4×D61—28no—
236C2×C4×D61—28no—
237C2×C4×D61—28no—
238C2×C4×D61—416no—
239C2×C4×D61—44no—
240C2×C4×D61—44no—
241C2×C4×D61—44no—
242C2×C4×D61—44no—
243C2×C4×D61—416no—
244C2×C4×D61C2×D4116yes—
245C4⋊C4×C61—28no—
246C4⋊C4×C61—28no—
247C4⋊C4×C61—44no—
248C22⋊C4×C61—28no—
249C22⋊C4×C61—28no—
250C22⋊C4×C61—44no—
251C22⋊Dic61—28no—
252C22⋊Dic61—44no—
253#11758198—28no—
254#11758198—28no—
255#11758198—28no—
256C4⋊Dic61—28no—
257C4⋊Dic61—44no—
258C4⋊Dic61—44no—
259#11758196—28no—
260#11758196—28no—
261#11758196—28no—
262#11758196—28no—
263#11758196—44no—
264C4×Dic61—28no—
265C23×C61—28no—
266C23×C61—28no—
267C23×C61—28no—
268C23×C61—22no—
269C23×C61—22no—
270C23×C61—22no—
271C23×C61—22no—
272C23×C61—22no—
273C23×C61—22no—
274C23×C61—44no—
275C23×C61—44no—
276C23×C61—44no—
277C23×C61—44no—
278C23×C61C22×D412yes—
279C23×C61C22×Q814yes—
280C23×C61C22×Q812yes—
281C23×C61C2×#4112yes—
282C23×C61C2×#4112yes—
283C23×C61C2×#4112yes—
284C23×C61H(5,𝔽2)12yes—
285C23×C61H(5,𝔽2)12yes—
286C23×C61C2511yescharacteristic
287C22×D61—28no—
288C22×D61—28no—
289C22×D61—28no—
290C22×D61—28no—
291C22×D61—28no—
292C22×D61—28no—
293C22×D61—22no—
294C22×D61—22no—
295C22×D61—22no—
296C22×D61—22no—
297C22×D61C22⋊Q8116yes—
298C22×D61C22×D414yes—
299C22×D61C22×Q814yes—
300C22×D61C2×#4114yes—
301C2×C4×C61—28no—
302C2×C4×C61—28no—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61—22no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—22no—
315C2×C4×C61—22no—
316C2×C4×C61—22no—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61—44no—
320C2×C4×C61—44no—
321C2×C4×C61—44no—
322C2×C4×C61—44no—
323C2×C4×C61C22×D414yes—
324C2×C4×C61C2×#4114yes—
325C22⋊D61—232no—
326C2×Dic61—28no—
327C2×Dic61—28no—
328C2×Dic61—28no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—22no—
337C2×Dic61—22no—
338C2×Dic61—22no—
339C2×Dic61—22no—
340C2×Dic61—22no—
341C2×Dic61—22no—
342C2×Dic61—22no—
343C2×Dic61—22no—
344C2×Dic61—22no—
345C2×Dic61—22no—
346C2×Dic61—22no—
347C2×Dic61—416no—
348C2×Dic61—44no—
349C2×Dic61—44no—
350C2×Dic61—44no—
351C2×Dic61—44no—
352C2×Dic61C22×D414yes—
353C2×Dic61C22×Q814yes—
354C2×Dic61C2×#4114yes—
355C4×D61—232no—
356C4×D61—416no—
357C4×D61—416no—
358C2×#2579—611nomaximal, Sylow
359C22×C61—24no—
360C22×C61—24no—
361C22×C61—24no—
362C22×C61—416no—
363C22×C61—42no—
364C22×C61—42no—
365C22×C61—42no—
366C22×C61—42no—
367C22×C61C2×C22⋊Q814yes—
368C22×C61#52514yes—
369C22×C61#53414yes—
370C22×C61#55314yes—
371C22×C61#55314yes—
372C22×C61#55414yes—
373C22×C61#55414yes—
374C22×C61C23×D411yescharacteristic
375C22×C61C23×Q811yescharacteristic
376C22×C61C22×#4111yescharacteristic
377C22×C61C22×#4111yescharacteristic
378C22×C61C22×#4111yescharacteristic
379C22×C61C2×H(5,𝔽2)11yescharacteristic
380C22×C61C2×H(5,𝔽2)11yescharacteristic
381C2×D61—232no—
382C2×D61—24no—
383C2×D61—24no—
384C2×D61—24no—
385C2×D61—24no—
386C2×D61—24no—
387C2×D61—24no—
388C2×D61C2×C22⋊Q818yes—
389C4×C61—24no—
390C4×C61—24no—
391C4×C61—42no—
392C4×C61—42no—
393C4×C61—42no—
394C4×C61—42no—
395Dic61—24no—
396Dic61—24no—
397Dic61—24no—
398Dic61—42no—
399Dic61—42no—
400Dic61—42no—
401Dic61—42no—
402C22×C4×D4—611no—
403C23×C4⋊C4—611no—
404#2579—6116no—
405C2×#398—611no—
406C2×#398—611no—
407C2×#396—611no—
408C2×#396D6111yescharacteristic, complemented
409C2×#387—611no—
410C2×#387—611no—
411C2×#386—611no—
412C2×#386—611no—
413C2×#385—611no—
414C2×#385—611no—
415C2×#385—611no—
416C2×#385—611no—
417C2×#380—611no—
418C2×C61—44no—
419C2×C61#257918yescomplemented
420C2×C61C22×C22⋊Q811yescharacteristic
421C2×C61C2×#52511yescharacteristic
422C2×C61C2×#53411yescharacteristic
423C2×C61C2×#55311yescharacteristic
424C2×C61C2×#55311yescharacteristic
425C2×C61C2×#55411yescharacteristic
426C2×C61C2×#55411yescharacteristic
427D61—28no—
428C23×D4—611no—
429C24×C4—611no—
430C24×C4—611no—
431C24×C4—611no—
432C24×C4—611no—
433C2×C4×D4—618no—
434C2×C4×D4—1228no—
435C22×C4⋊C4—611no—
436C22×C4⋊C4—611no—
437C22×C4⋊C4—611no—
438C22×C4⋊C4—611no—
439C22×C4⋊C4—611no—
440C22×C4⋊C4—611no—
441C22×C4⋊C4—611no—
442C22×C4⋊C4—611no—
443C22×C4⋊C4—618no—
444C22×C4⋊C4—1228no—
445C22×C4⋊C4C2×D6111yescharacteristic
446C22×C4⋊C4C2×D6111yescharacteristic
447C22×C4⋊C4C2×D6111yescharacteristic
448C22×C22⋊C4—611no—
449C22×C22⋊C4—611no—
450C22×C22⋊C4—611no—
451C22×C22⋊C4—611no—
452C22×C22⋊C4—611no—
453C22×C22⋊C4C2×D6111yescharacteristic
454C22×C22⋊C4C2×D6111yescharacteristic
455C22×C22⋊C4C2×D6111yescharacteristic
456C22×C42—611no—
457#398—618no—
458#398—618no—
459#396—618no—
460#396C2×D6118yescomplemented
461#387—618no—
462#387—618no—
463#386—618no—
464#386—618no—
465#385—618no—
466#385—618no—
467#385—618no—
468#385—618no—
469#380—618no—
470C2×#95—611no—
471C2×#95—611no—
472C2×#95—611no—
473C2×#95—611no—
474C2×#95—611no—
475C2×#95—611no—
476C2×#95—611no—
477C2×#95—611no—
478C2×#95—611no—
479C2×#95C2×D6111yescharacteristic
480C61C2×#257911yescharacteristic, complemented, Sylow
481C25—611no—
482C25C22×D6111yescharacteristic
483C22×D4—618no—
484C22×D4—614no—
485C22×D4—1224no—
486C22×D4—1224no—
487C23×C4—611no—
488C23×C4—611no—
489C23×C4—611no—
490C23×C4—618no—
491C23×C4—614no—
492C23×C4—611no—
493C23×C4—611no—
494C23×C4—611no—
495C23×C4—611no—
496C23×C4—614no—
497C23×C4—614no—
498C23×C4—614no—
499C23×C4—1224no—
500C23×C4—1224no—
501C23×C4—1224no—
502C23×C4—1224no—
503C23×C4—1224no—
504C23×C4—2442no—
505C23×C4—2442no—
506C23×C4—2442no—
507C23×C4—2442no—
508C23×C4—2442no—
509C23×C4—2442no—
510C23×C4C22×D6111yescharacteristic
511C23×C4C22×D6111yescharacteristic
512C23×C4C22×D6111yescharacteristic
513C23×C4C22×D6111yescharacteristic
514C23×C4C22×D6111yescharacteristic
515C23×C4C22×D6111yescharacteristic
516C4×D4—12232no—
517C2×C4⋊C4—24no—
518C2×C4⋊C4—24no—
519C2×C4⋊C4—42no—
520C2×C4⋊C4—614no—
521C2×C4⋊C4—614no—
522C2×C4⋊C4—614no—
523C2×C4⋊C4—614no—
524C2×C4⋊C4—614no—
525C2×C4⋊C4—614no—
526C2×C4⋊C4—614no—
527C2×C4⋊C4—614no—
528C2×C4⋊C4—12232no—
529C2×C4⋊C4—1224no—
530C2×C4⋊C4—1224no—
531C2×C4⋊C4—1224no—
532C2×C4⋊C4—1224no—
533C2×C4⋊C4—1224no—
534C2×C4⋊C4—2442no—
535C2×C4⋊C4—2442no—
536C2×C4⋊C4—2442no—
537C2×C4⋊C4C22×D6114yes—
538C2×C4⋊C4C22×D6114yes—
539C2×C4⋊C4C22×D6114yes—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—24no—
542C2×C22⋊C4—42no—
543C2×C22⋊C4—614no—
544C2×C22⋊C4—614no—
545C2×C22⋊C4—614no—
546C2×C22⋊C4—614no—
547C2×C22⋊C4—614no—
548C2×C22⋊C4—1224no—
549C2×C22⋊C4—1224no—
550C2×C22⋊C4—1224no—
551C2×C22⋊C4—1224no—
552C2×C22⋊C4—2442no—
553C2×C22⋊C4C22×D6114yes—
554C2×C22⋊C4C22×D6114yes—
555C2×C22⋊C4C22×D6114yes—
556C2×C42—614no—
557C2×C42—1224no—
558#95—614no—
559#95—614no—
560#95—614no—
561#95—614no—
562#95—614no—
563#95—614no—
564#95—614no—
565#95—614no—
566#95—614no—
567#95C22×D6114yes—
568C24—22no—
569C24—22no—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—614no—
575C24—614no—
576C24—614no—
577C24—612no—
578C24—1222no—
579C24—1222no—
580C24—1222no—
581C24—1222no—
582C24Q8×D6114yes—
583C24C23×D6112yes—
584C24C23×D6111yescharacteristic
585C2×D4—6116no—
586C2×D4—1228no—
587C2×D4—12232no—
588C2×D4—1228no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—614no—
606C22×C4—614no—
607C22×C4—614no—
608C22×C4—612no—
609C22×C4—612no—
610C22×C4—612no—
611C22×C4—6116no—
612C22×C4—612no—
613C22×C4—612no—
614C22×C4—612no—
615C22×C4—612no—
616C22×C4—1228no—
617C22×C4—1228no—
618C22×C4—12232no—
619C22×C4—1228no—
620C22×C4—1228no—
621C22×C4—1222no—
622C22×C4—1222no—
623C22×C4—1222no—
624C22×C4—1222no—
625C22×C4—1222no—
626C22×C4—1222no—
627C22×C4—1228no—
628C22×C4—1222no—
629C22×C4—1222no—
630C22×C4—1222no—
631C22×C4—1222no—
632C22×C4—1222no—
633C22×C4—1222no—
634C22×C4—1222no—
635C22×C4—1222no—
636C22×C4—1222no—
637C22×C4—1222no—
638C22×C4—1222no—
639C22×C4—1222no—
640C22×C4—24416no—
641C22×C4—2444no—
642C22×C4—2444no—
643C22×C4—2444no—
644C22×C4—2444no—
645C22×C4—24416no—
646C22×C4—2444no—
647C22×C4—2444no—
648C22×C4—24416no—
649C22×C4D4×D6114yes—
650C22×C4#1175822414yes—
651C22×C4C23×D6112yes—
652C22×C4C23×D6112yes—
653C22×C4C23×D6112yes—
654C22×C4C23×D6112yes—
655C22×C4C23×D6112yes—
656C22×C4C23×D6112yes—
657C4⋊C4—28no—
658C4⋊C4—28no—
659C4⋊C4—44no—
660C4⋊C4—1228no—
661C4⋊C4—1228no—
662C4⋊C4—1228no—
663C4⋊C4—1228no—
664C4⋊C4—1228no—
665C4⋊C4—2444no—
666C4⋊C4—2444no—
667C4⋊C4—2444no—
668C22⋊C4—28no—
669C22⋊C4—28no—
670C22⋊C4—44no—
671C22⋊C4—1228no—
672C22⋊C4—1228no—
673C22⋊C4—1228no—
674C22⋊C4—1228no—
675C22⋊C4—2444no—
676C42—1228no—
677C23—28no—
678C23—28no—
679C23—28no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—44no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—6116no—
691C23—614no—
692C23—614no—
693C23—614no—
694C23—1228no—
695C23—1228no—
696C23—1228no—
697C23—1228no—
698C23—1228no—
699C23—1228no—
700C23—1222no—
701C23—1222no—
702C23—1222no—
703C23—1222no—
704C23C2×D4×D6112yes—
705C23C2×Q8×D6114yes—
706C23C2×Q8×D6112yes—
707C23#41×D6112yes—
708C23#41×D6112yes—
709C23C2×#1175822412yes—
710C23#1451982212yes—
711C23#1451982312yes—
712C23C24×D6111yescharacteristic
713D4—12232no—
714C2×C4—28no—
715C2×C4—28no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—614no—
737C2×C4—614no—
738C2×C4—614no—
739C2×C4—12232no—
740C2×C4—1228no—
741C2×C4—1228no—
742C2×C4—1228no—
743C2×C4—1222no—
744C2×C4—1222no—
745C2×C4—1222no—
746C2×C4—1222no—
747C2×C4—1222no—
748C2×C4—1222no—
749C2×C4—1222no—
750C2×C4—1222no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—1222no—
754C2×C4—1222no—
755C2×C4—1222no—
756C2×C4—1222no—
757C2×C4—1222no—
758C2×C4—1222no—
759C2×C4—1222no—
760C2×C4—1222no—
761C2×C4—24416no—
762C2×C4—24416no—
763C2×C4—24416no—
764C2×C4—2444no—
765C2×C4—2444no—
766C2×C4—2444no—
767C2×C4—2444no—
768C2×C4C2×D4×D6114yes—
769C2×C4C2×#1175822414yes—
770C22—24no—
771C22—24no—
772C22—24no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—416no—
777C22—42no—
778C22—618no—
779C22—1224no—
780C22—1224no—
781C22—1224no—
782C22—1224no—
783C22—1224no—
784C22—12232no—
785C22—1224no—
786C22C22⋊Q8×D6114yes—
787C22#1684027214yes—
788C22#1684032014yes—
789C22#1684045914yes—
790C22#1684046314yes—
791C22#1684046614yes—
792C22#1684047014yes—
793C22C22×D4×D6111yescharacteristic
794C22C22×Q8×D6111yescharacteristic
795C22C2×#41×D6111yescharacteristic
796C22C2×#41×D6111yescharacteristic
797C22C22×#1175822411yescharacteristic
798C22C2×#1451982211yescharacteristic
799C22C2×#1451982311yescharacteristic
800C4—24no—
801C4—24no—
802C4—42no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—1224no—
807C4—1224no—
808C4—1224no—
809C4—2442no—
810C4—2442no—
811C4—2442no—
812C4—2442no—
813C2—44no—
814C2—1228no—
815C2#2145116118yesdirect product factor
816C2C2×C22⋊Q8×D6111yescharacteristic
817C2C2×#1684027211yescharacteristic
818C2C2×#1684032011yescharacteristic
819C2C2×#1684045911yescharacteristic
820C2C2×#1684046311yescharacteristic
821C2C2×#1684046611yescharacteristic
822C2C2×#1684047011yescharacteristic
subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC2×C61×#396C2
socleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenterC2×#396D61
hypocenterC61C2×#2579
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊C4×D61C2semidirect
3. #21451161C2direct (N × H)
4. C2×#16839695C2semidirect
5. C2×#16839692C2semidirect
6. C2×#16839685C2semidirect
7. C2×#16839648C2semidirect
8. C2×#16839644C2semidirect
11. C2×#16839637C2semidirect
12. C2×#16839636C2semidirect
13. C2×#16839634C2semidirect
14. C2×#16839633C2semidirect
15. C2×#16839619C2semidirect
16. C2×C61×#396C2semidirect
33. C2×C4⋊C4×D61C22semidirect
40. #16839695C22semidirect
41. #16839692C22semidirect
42. #16839685C22semidirect
43. #16839648C22semidirect
44. #16839644C22semidirect
47. #16839637C22semidirect
48. #16839636C22semidirect
49. #16839634C22semidirect
50. #16839633C22semidirect
51. #16839619C22semidirect
67. C61×#396C22semidirect
408. C2×#396D61semidirect
419. C2×C61#2579semidirect
460. #396C2×D61semidirect
480. C61C2×#2579semidirect
815. C2#21451161direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197372
C22×C4⋊C4×D612
#214511612
C2×#168396952
C2×#168396922
C2×#168396852
C2×#168396482
C2×#168396442
C2×#168396382
C2×#168396372
C2×#168396362
C2×#168396342
C2×#168396332
C2×#168396192
C2×C61×#3962
C2×#257961