Finite Group Databasebeta

← C2×#21448825 #29839531

Subgroups — C2×#21448825 #29839531

Order 15616.

3614 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
2C22×C4×Dic122C211yesmaximal, characteristic, complemented
3C23×#11758196C211yesmaximal, characteristic
4#21448825C2116yesmaximal, direct product factor
5C2×#16839666C211yesmaximal, characteristic, complemented
6C2×#16839660C211yesmaximal, characteristic, complemented
7C2×#16839659C211yesmaximal, characteristic, complemented
8C2×#16839659C211yesmaximal, characteristic, complemented
9C2×#16839646C211yesmaximal, characteristic, complemented
10C2×#16839645C211yesmaximal, characteristic, complemented
11C2×#16839637C211yesmaximal, characteristic
12C2×#16839635C211yesmaximal, characteristic
13C2×C4×#11758196C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×Dic61C211yesmaximal, characteristic
15C2×C22⋊C4×Dic61C211yesmaximal, characteristic
16C2×C4×C22⋊C4×C61C211yesmaximal, characteristic
17C23×Dic122C2211yescharacteristic
18C24×Dic61C2211yescharacteristic
19C24×Dic61C2211yescharacteristic
20C2×#14519754C4116yescomplemented
21C2×#14519754C2218yes—
22C2×C4×Dic122—28no—
23C2×C4×Dic122C2218yescomplemented
24C22×C4⋊Dic61C2211yescharacteristic
25C22×C4⋊Dic61C2211yescharacteristic
26C22×C4⋊Dic61C2211yescharacteristic
27C22×#11758196—28no—
28C22×#11758196C2211yescharacteristic
29C22×#11758196C2211yescharacteristic
30C22×#11758196C2211yescharacteristic
31C22×#11758196C2218yes—
32C22×#11758196C2211yescharacteristic
33C22×#11758196C2211yescharacteristic
34C22×#11758196C2211yescharacteristic
35C22×#11758196C2211yescharacteristic
36C22×#11758196C2211yescharacteristic
37C22×C22⋊Dic61C2211yescharacteristic
38C22×C22⋊Dic61C2211yescharacteristic
39C22×C4×Dic61C2211yescharacteristic
40C22×C4×Dic61C2211yescharacteristic
41C22×C4×Dic61C2211yescharacteristic
42C22×C4×Dic61C2211yescharacteristic
43#16839666C2218yescomplemented
44#16839660C2218yescomplemented
45#16839659C2218yescomplemented
46#16839659C2218yescomplemented
47#16839646C2218yescomplemented
48#16839645C2218yescomplemented
49#16839637C2218yes—
50#16839635C2218yes—
51C4×#11758196C2218yescomplemented
52C22⋊C4×Dic61C2218yes—
53C22⋊C4×Dic61C2218yes—
54C2×#14519684C2211yescharacteristic
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C2×#14519684C2211yescharacteristic
60C2×#14519684C2211yescharacteristic
61C2×#14519684C2211yescharacteristic
62C24×C4×C61C2211yescharacteristic
63C22×C22⋊C4×C61C2211yescharacteristic
64C22×C22⋊C4×C61C2211yescharacteristic
65C22×C42×C61C2211yescharacteristic
66C22×C42×C61C2211yescharacteristic
67C4×C22⋊C4×C61C2218yes—
68C2×#95×C61C2211yescharacteristic
69C2×#95×C61C2211yescharacteristic
70C22×Dic122—24no—
71C22×Dic122—24no—
72C22×Dic122C2×C418yescomplemented
73C22×Dic122C2314yes—
74C23×Dic61—24no—
75C23×Dic61—24no—
76C23×Dic61—24no—
77C23×Dic61—24no—
78C23×Dic61—42no—
79C23×Dic61C2×C418yes—
80C23×Dic61C2311yescharacteristic
81C23×Dic61C2311yescharacteristic
82C23×Dic61C2311yescharacteristic
83C23×Dic61C2314yes—
84C23×Dic61C2311yescharacteristic
85C23×Dic61C2311yescharacteristic
86C23×Dic61C2311yescharacteristic
87C23×Dic61C2314yes—
88C23×Dic61C2311yescharacteristic
89C23×Dic61C2311yescharacteristic
90#14519754C2×C4164yescomplemented
91C4×Dic122—232no—
92C2×C4⋊Dic61—24no—
93C2×C4⋊Dic61—42no—
94C2×C4⋊Dic61C2×C418yescomplemented
95C2×C4⋊Dic61C2314yes—
96C2×C4⋊Dic61C2314yes—
97C2×C4⋊Dic61C2314yes—
98C2×#11758196—24no—
99C2×#11758196—24no—
100C2×#11758196—24no—
101C2×#11758196—24no—
102C2×#11758196—232no—
103C2×#11758196—42no—
104C2×#11758196C2×C418yescomplemented
105C2×#11758196C2×C418yescomplemented
106C2×#11758196D418yes—
107C2×#11758196C2314yes—
108C2×#11758196C2314yes—
109C2×#11758196C2314yes—
110C2×#11758196C2314yes—
111C2×#11758196C2314yes—
112C2×#11758196C2314yes—
113C2×#11758196C2314yes—
114C2×#11758196C2314yes—
115C2×C22⋊Dic61—24no—
116C2×C22⋊Dic61C2×C418yes—
117C2×C22⋊Dic61C2314yes—
118C2×C22⋊Dic61C2314yes—
119C2×C4×Dic61—24no—
120C2×C4×Dic61—24no—
121C2×C4×Dic61—24no—
122C2×C4×Dic61—42no—
123C2×C4×Dic61C2314yes—
124C2×C4×Dic61C2314yes—
125C2×C4×Dic61C2314yes—
126C2×C4×Dic61C2314yes—
127#14519684C2314yes—
128#14519684C2314yes—
129#14519684C2314yes—
130#14519684C2314yes—
131#14519684C2314yes—
132#14519684C2314yes—
133#14519684C2314yes—
134#14519684C2314yes—
135C25×C61C2311yescharacteristic
136C23×C4×C61—24no—
137C23×C4×C61—24no—
138C23×C4×C61—42no—
139C23×C4×C61C2311yescharacteristic
140C23×C4×C61C2314yes—
141C23×C4×C61C2311yescharacteristic
142C23×C4×C61C2311yescharacteristic
143C23×C4×C61C2311yescharacteristic
144C23×C4×C61C2311yescharacteristic
145C23×C4×C61C2311yescharacteristic
146C2×C22⋊C4×C61C2×C418yes—
147C2×C22⋊C4×C61Q818yescomplemented
148C2×C22⋊C4×C61C2314yes—
149C2×C22⋊C4×C61C2314yes—
150C2×C42×C61—24no—
151C2×C42×C61—42no—
152C2×C42×C61C2314yes—
153C2×C42×C61C2314yes—
154#95×C61C2314yes—
155#95×C61C2314yes—
156C24×C61—22no—
157C24×C61—22no—
158C24×C61—22no—
159C24×C61—22no—
160C24×C61C22×C414yes—
161C24×C61C2×Q814yes—
162C24×C61#4114yes—
163C24×C61C2412yes—
164C24×C61C2411yescharacteristic
165C22×C4×C61—22no—
166C22×C4×C61—22no—
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—28no—
180C22×C4×C61—44no—
181C22×C4×C61—416no—
182C22×C4×C61C22×C414yes—
183C22×C4×C61C22×C414yes—
184C22×C4×C61C2×D414yes—
185C22×C4×C61C2×Q814yes—
186C22×C4×C61C2×Q814yes—
187C22×C4×C61C2412yes—
188C22×C4×C61C2412yes—
189C22×C4×C61C2412yes—
190C22×C4×C61C2412yes—
191C22×C4×C61C2412yes—
192C22×C4×C61C2412yes—
193C22×Dic61—22no—
194C22×Dic61—22no—
195C22×Dic61—22no—
196C22×Dic61—22no—
197C22×Dic61—22no—
198C22×Dic61—22no—
199C22×Dic61—22no—
200C22×Dic61—22no—
201C22×Dic61—232no—
202C22×Dic61—28no—
203C22×Dic61—28no—
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—28no—
215C22×Dic61—44no—
216C22×Dic61—416no—
217C22×Dic61C22×C414yes—
218C22×Dic61C22×C4116yes—
219C22×Dic61C22×C414yes—
220C22×Dic61C22×C414yes—
221C22×Dic61C22×C414yes—
222C22×Dic61C2×D414yes—
223C22×Dic61C2×D414yes—
224C22×Dic61#4114yes—
225C22×Dic61C2412yes—
226C22×Dic61C2412yes—
227C22×Dic61C2412yes—
228C22×Dic61C2412yes—
229C22×Dic61C2412yes—
230C22×Dic61C2412yes—
231C22×Dic61C2412yes—
232C22×Dic61C2412yes—
233C2×Dic122—232no—
234C2×Dic122—28no—
235C2×Dic122—28no—
236C2×Dic122C22×C4116yescomplemented
237C22⋊C4×C61C22×C4116yes—
238C22⋊C4×C61C2×Q8116yescomplemented
239C42×C61—28no—
240C42×C61—44no—
241C22⋊Dic61—28no—
242C22⋊Dic61C22×C4116yes—
243C4⋊Dic61—28no—
244C4⋊Dic61—44no—
245C4⋊Dic61C22×C4116yescomplemented
246#11758196—28no—
247#11758196—28no—
248#11758196—28no—
249#11758196—28no—
250#11758196—44no—
251#11758196C22×C4116yescomplemented
252#11758196C22×C4116yescomplemented
253#11758196C2×D4116yes—
254C4×Dic61—28no—
255C4×Dic61—28no—
256C4×Dic61—28no—
257C4×Dic61—44no—
258C23×C61—28no—
259C23×C61—28no—
260C23×C61—28no—
261C23×C61—28no—
262C23×C61—28no—
263C23×C61—28no—
264C23×C61—22no—
265C23×C61—22no—
266C23×C61—22no—
267C23×C61—22no—
268C23×C61C4×Q8116yescomplemented
269C23×C61C23×C414yes—
270C23×C61C23×C412yes—
271C23×C61C22×D412yes—
272C23×C61C22×Q814yes—
273C23×C61C22×Q812yes—
274C23×C61C2×#4114yes—
275C23×C61C2×#4112yes—
276C23×C61C2×#4112yes—
277C23×C61H(5,𝔽2)12yes—
278C23×C612−1+412yes—
279C23×C61C2511yescharacteristic
280C2×C4×C61—28no—
281C2×C4×C61—28no—
282C2×C4×C61—28no—
283C2×C4×C61—28no—
284C2×C4×C61—28no—
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×C61C23×C414yes—
301C2×C4×C61C23×C414yes—
302C2×C4×C61C22×D414yes—
303C2×C4×C61C22×Q814yes—
304C2×C4×C61C22×Q814yes—
305C2×Dic61—28no—
306C2×Dic61—28no—
307C2×Dic61—28no—
308C2×Dic61—28no—
309C2×Dic61—22no—
310C2×Dic61—22no—
311C2×Dic61—22no—
312C2×Dic61—22no—
313C2×Dic61—22no—
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—232no—
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—416no—
328C2×Dic61—44no—
329C2×Dic61—44no—
330C2×Dic61—44no—
331C2×Dic61C4×D4116yes—
332C2×Dic61C23×C414yes—
333C2×Dic61C23×C414yes—
334C2×Dic61C23×C414yes—
335C2×Dic61C23×C414yes—
336C2×Dic61C22×D414yes—
337C2×Dic61C22×D414yes—
338C2×Dic61C2×#4114yes—
339Dic122—232no—
340C2×#2360—611nomaximal, Sylow
341C22×C61—232no—
342C22×C61—24no—
343C22×C61—24no—
344C22×C61—24no—
345C22×C61—24no—
346C22×C61—24no—
347C22×C61—24no—
348C22×C61C2×C4×D414yes—
349C22×C61C2×C4×Q814yes—
350C22×C61C2×C4×Q818yescomplemented
351C22×C61#52014yes—
352C22×C61#54614yes—
353C22×C61D4×Q814yes—
354C22×C61#55214yes—
355C22×C61#55414yes—
356C22×C61C24×C411yescharacteristic
357C22×C61C23×D411yescharacteristic
358C22×C61C23×Q811yescharacteristic
359C22×C61C22×#4111yescharacteristic
360C22×C61C22×#4111yescharacteristic
361C22×C61C2×H(5,𝔽2)11yescharacteristic
362C22×C61C2×2−1+411yescharacteristic
363C4×C61—24no—
364C4×C61—24no—
365C4×C61—24no—
366C4×C61—24no—
367C4×C61—24no—
368C4×C61—42no—
369Dic61—24no—
370Dic61—24no—
371Dic61—24no—
372Dic61—24no—
373Dic61—42no—
374Dic61—42no—
375Dic61—42no—
376Dic61C2×C4×D418yes—
377C22×C22⋊Q8—611no—
378C22×C4×Q8—611no—
379C23×C4⋊C4—611no—
380#2360—6116no—
381C2×#391—611no—
382C2×#389—611no—
383C2×#389—611no—
384C2×#389—611no—
385C2×#387—611no—
386C2×#387—611no—
387C2×#385—611no—
388C2×#385—611no—
389C2×C4×C4⋊C4—611no—
390C2×C4×C22⋊C4—611no—
391C2×C4×C22⋊C4—611no—
392C2×C4×C22⋊C4D6111yescharacteristic
393C2×C61—28no—
394C2×C61#236018yescomplemented
395C2×C61C22×C4×D411yescharacteristic
396C2×C61C22×C4×Q811yescharacteristic
397C2×C61C2×#52011yescharacteristic
398C2×C61C2×#54611yescharacteristic
399C2×C61C2×D4×Q811yescharacteristic
400C2×C61C2×#55211yescharacteristic
401C2×C61C2×#55411yescharacteristic
402C23×Q8—611no—
403C24×C4—611no—
404C24×C4—611no—
405C24×C4C2×D6111yescharacteristic
406C2×C22⋊Q8—6116no—
407C2×C22⋊Q8—618no—
408C2×C4×Q8—618no—
409C2×C4×Q8—1228no—
410C22×C4⋊C4—611no—
411C22×C4⋊C4—611no—
412C22×C4⋊C4—611no—
413C22×C4⋊C4—611no—
414C22×C4⋊C4—618no—
415C22×C4⋊C4—611no—
416C22×C4⋊C4—611no—
417C22×C4⋊C4—611no—
418C22×C4⋊C4—611no—
419C22×C4⋊C4—611no—
420C22×C4⋊C4—611no—
421C22×C4⋊C4—611no—
422C22×C4⋊C4—1228no—
423C22×C22⋊C4—611no—
424C22×C22⋊C4—611no—
425C22×C22⋊C4C2×D6111yescharacteristic
426C22×C22⋊C4C2×D6111yescharacteristic
427C22×C42—611no—
428C22×C42—611no—
429C22×C42—611no—
430C22×C42—611no—
431C22×C42C2×D6111yescharacteristic
432C22×C42C2×D6111yescharacteristic
433#391—618no—
434#389—618no—
435#389—618no—
436#389—618no—
437#387—618no—
438#387—618no—
439#385—618no—
440#385—618no—
441C4×C4⋊C4—618no—
442C4×C22⋊C4—618no—
443C4×C22⋊C4—618no—
444C4×C22⋊C4C2×D6118yes—
445C2×#95—611no—
446C2×#95—611no—
447C2×#95—611no—
448C2×#95—611no—
449C2×#95—611no—
450C2×#95—611no—
451C2×#95—611no—
452C2×#95—611no—
453C2×#95C2×D6111yescharacteristic
454C2×#95C2×D6111yescharacteristic
455C61C2×#236011yescharacteristic, complemented, Sylow
456C25C22×D6111yescharacteristic
457C22×Q8—618no—
458C22×Q8—614no—
459C22×Q8—1224no—
460C22×Q8—1224no—
461C23×C4—24no—
462C23×C4—24no—
463C23×C4—42no—
464C23×C4—611no—
465C23×C4—618no—
466C23×C4—614no—
467C23×C4—611no—
468C23×C4—611no—
469C23×C4—611no—
470C23×C4—611no—
471C23×C4—611no—
472C23×C4—611no—
473C23×C4—611no—
474C23×C4—614no—
475C23×C4—1224no—
476C23×C4—1224no—
477C23×C4—1224no—
478C23×C4—1224no—
479C23×C4—2442no—
480C23×C4C22×D6111yescharacteristic
481C23×C4C22×D6114yes—
482C23×C4C22×D6111yescharacteristic
483C23×C4C22×D6111yescharacteristic
484C23×C4C22×D6111yescharacteristic
485C23×C4C22×D6111yescharacteristic
486C23×C4C22×D6111yescharacteristic
487C22⋊Q8—6164no—
488C4×Q8—12232no—
489C2×C4⋊C4—618no—
490C2×C4⋊C4—618no—
491C2×C4⋊C4—618no—
492C2×C4⋊C4—618no—
493C2×C4⋊C4—614no—
494C2×C4⋊C4—614no—
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—12232no—
505C2×C4⋊C4—1224no—
506C2×C4⋊C4—1224no—
507C2×C4⋊C4—1224no—
508C2×C4⋊C4—1224no—
509C2×C4⋊C4—1224no—
510C2×C4⋊C4—2442no—
511C2×C4⋊C4—2442no—
512C2×C22⋊C4—618no—
513C2×C22⋊C4—614no—
514C2×C22⋊C4—614no—
515C2×C22⋊C4—1224no—
516C2×C22⋊C4Dic12218yescomplemented
517C2×C22⋊C4C4×D6118yes—
518C2×C22⋊C4C22×D6114yes—
519C2×C22⋊C4C22×D6114yes—
520C2×C42—24no—
521C2×C42—42no—
522C2×C42—614no—
523C2×C42—614no—
524C2×C42—614no—
525C2×C42—614no—
526C2×C42—1224no—
527C2×C42—1224no—
528C2×C42—1224no—
529C2×C42—2442no—
530C2×C42C22×D6114yes—
531C2×C42C22×D6114yes—
532#95—614no—
533#95—614no—
534#95—614no—
535#95—614no—
536#95—614no—
537#95—614no—
538#95—614no—
539#95—614no—
540#95C22×D6114yes—
541#95C22×D6114yes—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24C2×Dic12214yes—
547C24C2×C4×D6114yes—
548C24#1175822214yes—
549C24C23×D6112yes—
550C24C23×D6111yescharacteristic
551C2×Q8—6116no—
552C2×Q8—1228no—
553C2×Q8—12232no—
554C2×Q8—1228no—
555C22×C4—22no—
556C22×C4—22no—
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—28no—
570C22×C4—44no—
571C22×C4—416no—
572C22×C4—614no—
573C22×C4—614no—
574C22×C4—614no—
575C22×C4—612no—
576C22×C4—614no—
577C22×C4—614no—
578C22×C4—614no—
579C22×C4—6116no—
580C22×C4—614no—
581C22×C4—612no—
582C22×C4—612no—
583C22×C4—612no—
584C22×C4—612no—
585C22×C4—612no—
586C22×C4—612no—
587C22×C4—612no—
588C22×C4—1228no—
589C22×C4—12232no—
590C22×C4—1228no—
591C22×C4—1228no—
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—1222no—
605C22×C4—1228no—
606C22×C4—1222no—
607C22×C4—1222no—
608C22×C4—1222no—
609C22×C4—1222no—
610C22×C4—2444no—
611C22×C4—24416no—
612C22×C4C2×Dic12214yes—
613C22×C4C2×Dic12214yes—
614C22×C4C2×C4×D6114yes—
615C22×C4C2×C4×D6114yes—
616C22×C4D4×D6114yes—
617C22×C4C23×D6112yes—
618C22×C4C23×D6112yes—
619C22×C4C23×D6112yes—
620C22×C4C23×D6112yes—
621C22×C4C23×D6112yes—
622C22×C4C23×D6112yes—
623C4⋊C4—6116no—
624C4⋊C4—6116no—
625C4⋊C4—6116no—
626C4⋊C4—6116no—
627C4⋊C4—1228no—
628C4⋊C4—1228no—
629C4⋊C4—1228no—
630C4⋊C4—1228no—
631C4⋊C4—1228no—
632C4⋊C4—2444no—
633C4⋊C4—2444no—
634C22⋊C4—6116no—
635C22⋊C4—1228no—
636C22⋊C4C2×Dic122116yescomplemented
637C22⋊C4C2×C4×D61116yes—
638C42—28no—
639C42—44no—
640C42—1228no—
641C42—1228no—
642C42—1228no—
643C42—2444no—
644C23—28no—
645C23—28no—
646C23—28no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—28no—
652C23—28no—
653C23—28no—
654C23C4×Dic122116yescomplemented
655C23C22×C4×D6114yes—
656C23C22×C4×D6112yes—
657C23C2×D4×D6112yes—
658C23C22×Dic12214yes—
659C23C22×Dic12212yes—
660C23#41×D6112yes—
661C23C2×#1175822214yes—
662C23C2×#1175822212yes—
663C23#1451982212yes—
664C23#1451982412yes—
665C23C24×D6111yescharacteristic
666Q8—12232no—
667C2×C4—28no—
668C2×C4—28no—
669C2×C4—28no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—28no—
681C2×C4—28no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—416no—
686C2×C4—44no—
687C2×C4—6116no—
688C2×C4—614no—
689C2×C4—614no—
690C2×C4—614no—
691C2×C4—614no—
692C2×C4—614no—
693C2×C4—614no—
694C2×C4—614no—
695C2×C4—12232no—
696C2×C4—1228no—
697C2×C4—1228no—
698C2×C4—1228no—
699C2×C4—1222no—
700C2×C4—1222no—
701C2×C4—1222no—
702C2×C4—1222no—
703C2×C4—1222no—
704C2×C4—1222no—
705C2×C4—1222no—
706C2×C4—1222no—
707C2×C4—1228no—
708C2×C4—1222no—
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—24416no—
718C2×C4—2444no—
719C2×C4—2444no—
720C2×C4—2444no—
721C2×C4C22×C4×D6114yes—
722C2×C4C22×C4×D6114yes—
723C2×C4C2×D4×D6114yes—
724C2×C4C22×Dic12214yes—
725C2×C4C22×Dic12214yes—
726C22—24no—
727C22—24no—
728C22—24no—
729C22—24no—
730C22—232no—
731C22—24no—
732C22—24no—
733C22C4×D4×D6114yes—
734C22C2×C4×Dic12214yes—
735C22C2×C4×Dic12218yescomplemented
736C22#1684024114yes—
737C22#1684040214yes—
738C22D4×Dic12214yes—
739C22#1684044514yes—
740C22#1684047114yes—
741C22C23×C4×D6111yescharacteristic
742C22C22×D4×D6111yescharacteristic
743C22C23×Dic12211yescharacteristic
744C22C2×#41×D6111yescharacteristic
745C22C22×#1175822211yescharacteristic
746C22C2×#1451982211yescharacteristic
747C22C2×#1451982411yescharacteristic
748C4—24no—
749C4—24no—
750C4—24no—
751C4—24no—
752C4—24no—
753C4—42no—
754C4—618no—
755C4—1224no—
756C4—1224no—
757C4—1224no—
758C4—1224no—
759C4—2442no—
760C4—2442no—
761C4—2442no—
762C2—28no—
763C2#2144882518yesdirect product factor
764C2C2×C4×D4×D6111yescharacteristic
765C2C22×C4×Dic12211yescharacteristic
766C2C2×#1684024111yescharacteristic
767C2C2×#1684040211yescharacteristic
768C2C2×D4×Dic12211yescharacteristic
769C2C2×#1684044511yescharacteristic
770C2C2×#1684047111yescharacteristic
subgroupG/H
centerC24C23×D61
commutatorC22×C61C24×C4
FrattiniC23C24×D61
FittingC2×C4×C22⋊C4×C61C2
socleC24×C61C24
prime radicalC25×C61C23
cosocleC23×C61C25
hypercenterC2×C4×C22⋊C4D61
hypocenterC61C2×#2360
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic122C2semidirect
4. #21448825C2direct (N × H)
5. C2×#16839666C2semidirect
6. C2×#16839660C2semidirect
7. C2×#16839659C2semidirect
8. C2×#16839659C2semidirect
9. C2×#16839646C2semidirect
10. C2×#16839645C2semidirect
13. C2×C4×#11758196C2semidirect
20. C2×#14519754C4semidirect
23. C2×C4×Dic122C22semidirect
43. #16839666C22semidirect
44. #16839660C22semidirect
45. #16839659C22semidirect
46. #16839659C22semidirect
47. #16839646C22semidirect
48. #16839645C22semidirect
51. C4×#11758196C22semidirect
72. C22×Dic122C2×C4semidirect
90. #14519754C2×C4semidirect
94. C2×C4⋊Dic61C2×C4semidirect
104. C2×#11758196C2×C4semidirect
105. C2×#11758196C2×C4semidirect
147. C2×C22⋊C4×C61Q8semidirect
236. C2×Dic122C22×C4semidirect
238. C22⋊C4×C61C2×Q8semidirect
245. C4⋊Dic61C22×C4semidirect
251. #11758196C22×C4semidirect
252. #11758196C22×C4semidirect
268. C23×C61C4×Q8semidirect
350. C22×C61C2×C4×Q8semidirect
394. C2×C61#2360semidirect
455. C61C2×#2360semidirect
516. C2×C22⋊C4Dic122semidirect
636. C22⋊C4C2×Dic122semidirect
654. C23C4×Dic122semidirect
735. C22C2×C4×Dic122semidirect
763. C2#21448825direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197542
C22×C4×Dic1222
C23×#117581962
#214488252
C2×#168396662
C2×#168396602
C2×#168396592
C2×#168396462
C2×#168396452
C2×#168396372
C2×#168396352
C2×C4×#117581962
C2×C22⋊C4×Dic612
C2×C4×C22⋊C4×C612
C2×#236061