Finite Group Databasebeta

← C2×#21450827 #29850052

Subgroups — C2×#21450827 #29850052

Order 15616.

3094 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519754C211yesmaximal, characteristic
2#21450827C2116yesmaximal, direct product factor
3C2×#16839693C211yesmaximal, characteristic, complemented
4C2×#16839692C211yesmaximal, characteristic, complemented
5C2×#16839682C211yesmaximal, characteristic, complemented
6C2×#16839681C211yesmaximal, characteristic, complemented
7C2×#16839669C211yesmaximal, characteristic, complemented
8C2×#16839667C211yesmaximal, characteristic, complemented
9C2×#16839657C211yesmaximal, characteristic, complemented
10C2×#16839657C211yesmaximal, characteristic, complemented
11C2×#16839635C211yesmaximal, characteristic
12C2×#16839634C211yesmaximal, characteristic
13C2×#16839620C211yesmaximal, characteristic
14C2×C22⋊C4×Dic61C211yesmaximal, characteristic
15C22×#14519684C211yesmaximal, characteristic
16C22×C22⋊Q8×C61C211yesmaximal, characteristic
17C23×Dic122C2211yescharacteristic
18C24×Dic61C2211yescharacteristic
19C24×Dic61C2211yescharacteristic
20C2×#14519754—28no—
21C2×#14519754C2218yes—
22C22×C4⋊Dic61C2211yescharacteristic
23C22×#11758196C2211yescharacteristic
24C22×#11758196C2211yescharacteristic
25C22×#11758196C2211yescharacteristic
26C22×#11758196C2211yescharacteristic
27C22×#11758196C2211yescharacteristic
28C22×#11758196C2211yescharacteristic
29C22×#11758196C2211yescharacteristic
30C22×#11758196C2211yescharacteristic
31C22×C22⋊Dic61C2211yescharacteristic
32C22×C22⋊Dic61C2211yescharacteristic
33C22×C4×Dic61C2211yescharacteristic
34C22×C4×Dic61C2211yescharacteristic
35#16839693C2218yescomplemented
36#16839692C2218yescomplemented
37#16839682C2218yescomplemented
38#16839681C2218yescomplemented
39#16839669C2218yescomplemented
40#16839667C2218yescomplemented
41#16839657C2218yescomplemented
42#16839657C2218yescomplemented
43#16839635C2218yes—
44#16839634C2218yes—
45#16839620C2218yes—
46C22⋊C4×Dic61C2218yes—
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C2×#14519684C2211yescharacteristic
53C2×#14519684C2211yescharacteristic
54C2×#14519684C2211yescharacteristic
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2218yes—
58C2×#14519684C2211yescharacteristic
59C2×#14519684C2211yescharacteristic
60C23×Q8×C61C2211yescharacteristic
61C24×C4×C61C2211yescharacteristic
62C2×C22⋊Q8×C61—28no—
63C2×C22⋊Q8×C61C2218yes—
64C22×C4⋊C4×C61C2211yescharacteristic
65C22×C4⋊C4×C61C2211yescharacteristic
66C22×C4⋊C4×C61C2211yescharacteristic
67C22×C22⋊C4×C61C2211yescharacteristic
68C22×C22⋊C4×C61C2211yescharacteristic
69C22×Dic122—24no—
70C22×Dic122—24no—
71C22×Dic122—42no—
72C22×Dic122C2314yes—
73C23×Dic61—24no—
74C23×Dic61—24no—
75C23×Dic61—42no—
76C23×Dic61—42no—
77C23×Dic61—42no—
78C23×Dic61Q818yescomplemented
79C23×Dic61C2311yescharacteristic
80C23×Dic61C2311yescharacteristic
81C23×Dic61C2311yescharacteristic
82C23×Dic61C2314yes—
83C23×Dic61C2311yescharacteristic
84C23×Dic61C2311yescharacteristic
85C23×Dic61C2311yescharacteristic
86C23×Dic61C2311yescharacteristic
87C23×Dic61C2311yescharacteristic
88C23×Dic61C2314yes—
89#14519754—232no—
90C2×C4⋊Dic61—24no—
91C2×C4⋊Dic61C2314yes—
92C2×#11758196—24no—
93C2×#11758196—24no—
94C2×#11758196—24no—
95C2×#11758196—24no—
96C2×#11758196—42no—
97C2×#11758196—42no—
98C2×#11758196—42no—
99C2×#11758196—42no—
100C2×#11758196C2314yes—
101C2×#11758196C2314yes—
102C2×#11758196C2314yes—
103C2×#11758196C2314yes—
104C2×#11758196C2314yes—
105C2×#11758196C2314yes—
106C2×#11758196C2314yes—
107C2×#11758196C2314yes—
108C2×C22⋊Dic61—24no—
109C2×C22⋊Dic61Q818yescomplemented
110C2×C22⋊Dic61C2314yes—
111C2×C22⋊Dic61C2314yes—
112C2×C4×Dic61—42no—
113C2×C4×Dic61—42no—
114C2×C4×Dic61C2314yes—
115C2×C4×Dic61C2314yes—
116#14519684C2314yes—
117#14519684C2314yes—
118#14519684C2314yes—
119#14519684C2314yes—
120#14519684C2314yes—
121#14519684C2314yes—
122#14519684C2314yes—
123#14519684C2314yes—
124#14519684C2314yes—
125#14519684C2314yes—
126#14519684C2314yes—
127#14519684C2314yes—
128C25×C61C2311yescharacteristic
129C22×Q8×C61—24no—
130C22×Q8×C61—24no—
131C22×Q8×C61—42no—
132C22×Q8×C61C2314yes—
133C23×C4×C61—24no—
134C23×C4×C61—24no—
135C23×C4×C61—42no—
136C23×C4×C61C2311yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C23×C4×C61C2311yescharacteristic
139C23×C4×C61C2314yes—
140C23×C4×C61C2311yescharacteristic
141C23×C4×C61C2311yescharacteristic
142C23×C4×C61C2311yescharacteristic
143C22⋊Q8×C61—232no—
144C2×C4⋊C4×C61—24no—
145C2×C4⋊C4×C61—24no—
146C2×C4⋊C4×C61—24no—
147C2×C4⋊C4×C61C2314yes—
148C2×C4⋊C4×C61C2314yes—
149C2×C4⋊C4×C61C2314yes—
150C2×C22⋊C4×C61—24no—
151C2×C22⋊C4×C61D418yes—
152C2×C22⋊C4×C61C2314yes—
153C2×C22⋊C4×C61C2314yes—
154C24×C61—22no—
155C24×C61—22no—
156C24×C61—22no—
157C24×C61—22no—
158C24×C61C2×D414yes—
159C24×C61C2×Q814yes—
160C24×C61C2×Q814yes—
161C24×C61C2412yes—
162C24×C61C2411yescharacteristic
163C2×Q8×C61—28no—
164C2×Q8×C61—28no—
165C2×Q8×C61—44no—
166C2×Q8×C61—416no—
167C22×C4×C61—22no—
168C22×C4×C61—22no—
169C22×C4×C61—22no—
170C22×C4×C61—22no—
171C22×C4×C61—22no—
172C22×C4×C61—22no—
173C22×C4×C61—22no—
174C22×C4×C61—22no—
175C22×C4×C61—22no—
176C22×C4×C61—28no—
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—28no—
184C22×C4×C61—44no—
185C22×C4×C61—416no—
186C22×C4×C61C2×D414yes—
187C22×C4×C61C2×D414yes—
188C22×C4×C61#4114yes—
189C22×C4×C61C2412yes—
190C22×C4×C61C2412yes—
191C22×C4×C61C2412yes—
192C22×C4×C61C2412yes—
193C22×C4×C61C2412yes—
194C22×C4×C61C2412yes—
195C22×Dic61—22no—
196C22×Dic61—22no—
197C22×Dic61—22no—
198C22×Dic61—22no—
199C22×Dic61—22no—
200C22×Dic61—22no—
201C22×Dic61—22no—
202C22×Dic61—22no—
203C22×Dic61—22no—
204C22×Dic61—22no—
205C22×Dic61—22no—
206C22×Dic61—28no—
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—28no—
216C22×Dic61—416no—
217C22×Dic61—44no—
218C22×Dic61—44no—
219C22×Dic61—44no—
220C22×Dic61—416no—
221C22×Dic61C2×Q814yes—
222C22×Dic61C2×Q814yes—
223C22×Dic61C2×Q814yes—
224C22×Dic61C2×Q814yes—
225C22×Dic61C2×Q8116yescomplemented
226C22×Dic61#4114yes—
227C22×Dic61C2412yes—
228C22×Dic61C2412yes—
229C22×Dic61C2412yes—
230C22×Dic61C2412yes—
231C22×Dic61C2412yes—
232C22×Dic61C2412yes—
233C22×Dic61C2412yes—
234C22×Dic61C2412yes—
235C2×Dic122—28no—
236C2×Dic122—28no—
237C2×Dic122—44no—
238C2×Dic122—416no—
239C4⋊C4×C61—28no—
240C4⋊C4×C61—28no—
241C4⋊C4×C61—28no—
242C22⋊C4×C61—28no—
243C22⋊C4×C61C2×D4116yes—
244C22⋊Dic61—28no—
245C22⋊Dic61C2×Q8116yescomplemented
246C4⋊Dic61—28no—
247#11758196—28no—
248#11758196—28no—
249#11758196—28no—
250#11758196—28no—
251#11758196—44no—
252#11758196—44no—
253#11758196—44no—
254#11758196—44no—
255C4×Dic61—44no—
256C4×Dic61—44no—
257C23×C61—28no—
258C23×C61—28no—
259C23×C61—28no—
260C23×C61—28no—
261C23×C61—28no—
262C23×C61—28no—
263C23×C61—22no—
264C23×C61—22no—
265C23×C61—22no—
266C23×C61—22no—
267C23×C61C4⋊Q8116yes—
268C23×C61C22×D414yes—
269C23×C61C22×D412yes—
270C23×C61C22×Q814yes—
271C23×C61C22×Q814yes—
272C23×C61C22×Q812yes—
273C23×C61C22×Q812yes—
274C23×C61C2×#4112yes—
275C23×C61C2×#4112yes—
276C23×C61H(5,𝔽2)12yes—
277C23×C61H(5,𝔽2)12yes—
278C23×C61C2511yescharacteristic
279Q8×C61—416no—
280C2×C4×C61—28no—
281C2×C4×C61—28no—
282C2×C4×C61—28no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—416no—
299C2×C4×C61—44no—
300C2×C4×C61—44no—
301C2×C4×C61—44no—
302C2×C4×C61C22×D414yes—
303C2×C4×C61C22×D414yes—
304C2×C4×C61C2×#4114yes—
305C2×Dic61—28no—
306C2×Dic61—28no—
307C2×Dic61—28no—
308C2×Dic61—28no—
309C2×Dic61—28no—
310C2×Dic61—22no—
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—22no—
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—22no—
329C2×Dic61—416no—
330C2×Dic61—416no—
331C2×Dic61—44no—
332C2×Dic61—44no—
333C2×Dic61—44no—
334C2×Dic61C22×Q814yes—
335C2×Dic61C22×Q814yes—
336C2×Dic61C22×Q814yes—
337C2×Dic61C22×Q814yes—
338C2×Dic61C2×#4114yes—
339Dic122—416no—
340C2×#2549—611nomaximal, Sylow
341C22×C61—24no—
342C22×C61—24no—
343C22×C61—24no—
344C22×C61—24no—
345C22×C61—24no—
346C22×C61—24no—
347C22×C61—232no—
348C22×C61C2×C4⋊Q818yes—
349C22×C61C2×C4⋊Q814yes—
350C22×C61#53314yes—
351C22×C61#54314yes—
352C22×C61#54614yes—
353C22×C61#54614yes—
354C22×C61#55414yes—
355C22×C61#55414yes—
356C22×C61C23×D411yescharacteristic
357C22×C61C23×Q811yescharacteristic
358C22×C61C23×Q811yescharacteristic
359C22×C61C22×#4111yescharacteristic
360C22×C61C22×#4111yescharacteristic
361C22×C61C2×H(5,𝔽2)11yescharacteristic
362C22×C61C2×H(5,𝔽2)11yescharacteristic
363C4×C61—24no—
364C4×C61—24no—
365C4×C61—24no—
366C4×C61—42no—
367C4×C61—42no—
368C4×C61—42no—
369Dic61—24no—
370Dic61—24no—
371Dic61—24no—
372Dic61—24no—
373Dic61—24no—
374Dic61—42no—
375Dic61—42no—
376Dic61—42no—
377C22×C22⋊Q8—611no—
378C22×C22⋊Q8D6111yescharacteristic
379#2549—6116no—
380C2×#398—611no—
381C2×#398—611no—
382C2×#395—611no—
383C2×#395—611no—
384C2×#391—611no—
385C2×#391—611no—
386C2×#389—611no—
387C2×#389—611no—
388C2×#385—611no—
389C2×#385—611no—
390C2×#380—611no—
391C2×C4×C22⋊C4—611no—
392C22×#95—611no—
393C2×C61—28no—
394C2×C61#254918yescomplemented
395C2×C61C22×C4⋊Q811yescharacteristic
396C2×C61C2×#53311yescharacteristic
397C2×C61C2×#54311yescharacteristic
398C2×C61C2×#54611yescharacteristic
399C2×C61C2×#54611yescharacteristic
400C2×C61C2×#55411yescharacteristic
401C2×C61C2×#55411yescharacteristic
402C23×Q8—611no—
403C23×Q8C2×D6111yescharacteristic
404C24×C4—611no—
405C24×C4—611no—
406C24×C4C2×D6111yescharacteristic
407C2×C22⋊Q8—28no—
408C2×C22⋊Q8—618no—
409C2×C22⋊Q8—1228no—
410C2×C22⋊Q8C2×D6118yes—
411C22×C4⋊C4—611no—
412C22×C4⋊C4—611no—
413C22×C4⋊C4—611no—
414C22×C4⋊C4—611no—
415C22×C4⋊C4—611no—
416C22×C4⋊C4—611no—
417C22×C4⋊C4—611no—
418C22×C4⋊C4—611no—
419C22×C4⋊C4—611no—
420C22×C4⋊C4C2×D6111yescharacteristic
421C22×C4⋊C4C2×D6111yescharacteristic
422C22×C4⋊C4C2×D6111yescharacteristic
423C22×C22⋊C4—611no—
424C22×C22⋊C4—611no—
425C22×C22⋊C4C2×D6111yescharacteristic
426C22×C22⋊C4C2×D6111yescharacteristic
427C22×C42—611no—
428C22×C42—611no—
429#398—618no—
430#398—618no—
431#395—618no—
432#395—618no—
433#391—618no—
434#391—618no—
435#389—618no—
436#389—618no—
437#385—618no—
438#385—618no—
439#380—618no—
440C4×C22⋊C4—618no—
441C2×#95—611no—
442C2×#95—611no—
443C2×#95—611no—
444C2×#95—611no—
445C2×#95—611no—
446C2×#95—611no—
447C2×#95—611no—
448C2×#95—611no—
449C2×#95—611no—
450C2×#95—611no—
451C2×#95—618no—
452C2×#95—611no—
453C2×#95—611no—
454C61C2×#254911yescharacteristic, complemented, Sylow
455C25C22×D6111yescharacteristic
456C22×Q8—24no—
457C22×Q8—24no—
458C22×Q8—42no—
459C22×Q8—614no—
460C22×Q8—1224no—
461C22×Q8—1224no—
462C22×Q8—2442no—
463C22×Q8C22×D6114yes—
464C23×C4—24no—
465C23×C4—24no—
466C23×C4—42no—
467C23×C4—611no—
468C23×C4—611no—
469C23×C4—611no—
470C23×C4—611no—
471C23×C4—611no—
472C23×C4—618no—
473C23×C4—614no—
474C23×C4—611no—
475C23×C4—611no—
476C23×C4—611no—
477C23×C4—614no—
478C23×C4—1224no—
479C23×C4—1224no—
480C23×C4—2442no—
481C23×C4—2442no—
482C23×C4—2442no—
483C23×C4C22×D6111yescharacteristic
484C23×C4C22×D6111yescharacteristic
485C23×C4C22×D6111yescharacteristic
486C23×C4C22×D6114yes—
487C23×C4C22×D6111yescharacteristic
488C23×C4C22×D6111yescharacteristic
489C23×C4C22×D6111yescharacteristic
490C22⋊Q8—232no—
491C22⋊Q8—12232no—
492C2×C4⋊C4—24no—
493C2×C4⋊C4—24no—
494C2×C4⋊C4—24no—
495C2×C4⋊C4—614no—
496C2×C4⋊C4—614no—
497C2×C4⋊C4—614no—
498C2×C4⋊C4—614no—
499C2×C4⋊C4—614no—
500C2×C4⋊C4—614no—
501C2×C4⋊C4—614no—
502C2×C4⋊C4—614no—
503C2×C4⋊C4—614no—
504C2×C4⋊C4—1224no—
505C2×C4⋊C4—1224no—
506C2×C4⋊C4—1224no—
507C2×C4⋊C4—1224no—
508C2×C4⋊C4—1224no—
509C2×C4⋊C4—2442no—
510C2×C4⋊C4—2442no—
511C2×C4⋊C4—2442no—
512C2×C4⋊C4—2442no—
513C2×C4⋊C4C22×D6114yes—
514C2×C4⋊C4C22×D6114yes—
515C2×C4⋊C4C22×D6114yes—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—618no—
518C2×C22⋊C4—614no—
519C2×C22⋊C4—614no—
520C2×C22⋊C4—1224no—
521C2×C22⋊C4C22⋊D6118yes—
522C2×C22⋊C4C22×D6114yes—
523C2×C22⋊C4C22×D6114yes—
524C2×C42—614no—
525C2×C42—614no—
526C2×C42—2442no—
527C2×C42—2442no—
528#95—614no—
529#95—614no—
530#95—614no—
531#95—614no—
532#95—614no—
533#95—614no—
534#95—614no—
535#95—614no—
536#95—614no—
537#95—614no—
538#95—614no—
539#95—614no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24Q8×D6114yes—
545C24Q8×D6114yes—
546C24C2×C22⋊D6114yes—
547C24C23×D6112yes—
548C24C23×D6111yescharacteristic
549C2×Q8—28no—
550C2×Q8—28no—
551C2×Q8—44no—
552C2×Q8—416no—
553C2×Q8—1228no—
554C2×Q8—1228no—
555C2×Q8—2444no—
556C2×Q8—24416no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—28no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—28no—
574C22×C4—44no—
575C22×C4—416no—
576C22×C4—614no—
577C22×C4—614no—
578C22×C4—614no—
579C22×C4—614no—
580C22×C4—614no—
581C22×C4—612no—
582C22×C4—612no—
583C22×C4—612no—
584C22×C4—612no—
585C22×C4—612no—
586C22×C4—6116no—
587C22×C4—612no—
588C22×C4—612no—
589C22×C4—612no—
590C22×C4—1228no—
591C22×C4—1222no—
592C22×C4—1222no—
593C22×C4—1222no—
594C22×C4—1222no—
595C22×C4—1222no—
596C22×C4—1222no—
597C22×C4—1222no—
598C22×C4—1222no—
599C22×C4—1222no—
600C22×C4—1222no—
601C22×C4—1222no—
602C22×C4—1222no—
603C22×C4—1222no—
604C22×C4—1228no—
605C22×C4—1222no—
606C22×C4—1222no—
607C22×C4—1222no—
608C22×C4—1222no—
609C22×C4—1222no—
610C22×C4—1222no—
611C22×C4—2444no—
612C22×C4—2444no—
613C22×C4—2444no—
614C22×C4—24416no—
615C22×C4—24416no—
616C22×C4#1175822414yes—
617C22×C4C2×C22⋊D6114yes—
618C22×C4C2×C22⋊D6114yes—
619C22×C4C23×D6112yes—
620C22×C4C23×D6112yes—
621C22×C4C23×D6112yes—
622C22×C4C23×D6112yes—
623C22×C4C23×D6112yes—
624C22×C4C23×D6112yes—
625C4⋊C4—28no—
626C4⋊C4—28no—
627C4⋊C4—28no—
628C4⋊C4—1228no—
629C4⋊C4—1228no—
630C4⋊C4—1228no—
631C4⋊C4—1228no—
632C4⋊C4—1228no—
633C4⋊C4—2444no—
634C4⋊C4—2444no—
635C4⋊C4—2444no—
636C4⋊C4—2444no—
637C22⋊C4—28no—
638C22⋊C4—6116no—
639C22⋊C4—1228no—
640C22⋊C4C2×C22⋊D61116yes—
641C42—2444no—
642C42—2444no—
643C23—28no—
644C23—28no—
645C23—28no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—28no—
651C23—28no—
652C23—28no—
653C23#14519775116yes—
654C23C22×C22⋊D6114yes—
655C23C22×C22⋊D6112yes—
656C23C2×Q8×D6114yes—
657C23C2×Q8×D6114yes—
658C23C2×Q8×D6112yes—
659C23C2×Q8×D6112yes—
660C23#41×D6112yes—
661C23C2×#1175822412yes—
662C23#1451982212yes—
663C23#1451982312yes—
664C23C24×D6111yescharacteristic
665Q8—416no—
666Q8—24416no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—28no—
674C2×C4—28no—
675C2×C4—28no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—416no—
686C2×C4—44no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—614no—
690C2×C4—614no—
691C2×C4—614no—
692C2×C4—614no—
693C2×C4—614no—
694C2×C4—1228no—
695C2×C4—1228no—
696C2×C4—1222no—
697C2×C4—1222no—
698C2×C4—1222no—
699C2×C4—1222no—
700C2×C4—1222no—
701C2×C4—1222no—
702C2×C4—1222no—
703C2×C4—1222no—
704C2×C4—1222no—
705C2×C4—1222no—
706C2×C4—1228no—
707C2×C4—1228no—
708C2×C4—1228no—
709C2×C4—1222no—
710C2×C4—1222no—
711C2×C4—1222no—
712C2×C4—1222no—
713C2×C4—1222no—
714C2×C4—1222no—
715C2×C4—1222no—
716C2×C4—1222no—
717C2×C4—1222no—
718C2×C4—24416no—
719C2×C4—24416no—
720C2×C4—2444no—
721C2×C4—2444no—
722C2×C4—2444no—
723C2×C4C22×C22⋊D6114yes—
724C2×C4C22×C22⋊D6114yes—
725C2×C4C2×#1175822414yes—
726C22—24no—
727C22—24no—
728C22—24no—
729C22—232no—
730C22—24no—
731C22—24no—
732C22—24no—
733C22C2×#1451977518yes—
734C22C2×#1451977514yes—
735C22#1684031414yes—
736C22#1684038714yes—
737C22#1684040014yes—
738C22#1684040614yes—
739C22#1684046614yes—
740C22#1684047014yes—
741C22C23×C22⋊D6111yescharacteristic
742C22C22×Q8×D6111yescharacteristic
743C22C22×Q8×D6111yescharacteristic
744C22C2×#41×D6111yescharacteristic
745C22C22×#1175822411yescharacteristic
746C22C2×#1451982211yescharacteristic
747C22C2×#1451982311yescharacteristic
748C4—24no—
749C4—24no—
750C4—24no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—1224no—
755C4—1224no—
756C4—1224no—
757C4—1224no—
758C4—1224no—
759C4—2442no—
760C4—2442no—
761C4—2442no—
762C2—28no—
763C2#2145082718yesdirect product factor
764C2C22×#1451977511yescharacteristic
765C2C2×#1684031411yescharacteristic
766C2C2×#1684038711yescharacteristic
767C2C2×#1684040011yescharacteristic
768C2C2×#1684040611yescharacteristic
769C2C2×#1684046611yescharacteristic
770C2C2×#1684047011yescharacteristic
subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC22×C22⋊Q8×C61C2
socleC24×C61C24
prime radicalC25×C61C23
hypercenterC22×C22⋊Q8D61
hypocenterC61C2×#2549
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #21450827C2direct (N × H)
3. C2×#16839693C2semidirect
4. C2×#16839692C2semidirect
5. C2×#16839682C2semidirect
6. C2×#16839681C2semidirect
7. C2×#16839669C2semidirect
8. C2×#16839667C2semidirect
9. C2×#16839657C2semidirect
10. C2×#16839657C2semidirect
35. #16839693C22semidirect
36. #16839692C22semidirect
37. #16839682C22semidirect
38. #16839681C22semidirect
39. #16839669C22semidirect
40. #16839667C22semidirect
41. #16839657C22semidirect
42. #16839657C22semidirect
78. C23×Dic61Q8semidirect
109. C2×C22⋊Dic61Q8semidirect
225. C22×Dic61C2×Q8semidirect
245. C22⋊Dic61C2×Q8semidirect
394. C2×C61#2549semidirect
454. C61C2×#2549semidirect
763. C2#21450827direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197542
#214508272
C2×#168396932
C2×#168396922
C2×#168396822
C2×#168396812
C2×#168396692
C2×#168396672
C2×#168396572
C2×#168396352
C2×#168396342
C2×#168396202
C2×C22⋊C4×Dic612
C22×#145196842
C22×C22⋊Q8×C612
C2×#254961