Finite Group Databasebeta

← C2×#21448547 #29838830

Subgroups — C2×#21448547 #29838830

Order 15616.

2982 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519754C211yesmaximal, characteristic
2#21448547C2116yesmaximal, direct product factor
3C2×#16839668C211yesmaximal, characteristic, complemented
4C2×#16839666C211yesmaximal, characteristic, complemented
5C2×#16839660C211yesmaximal, characteristic, complemented
6C2×#16839659C211yesmaximal, characteristic, complemented
7C2×#16839649C211yesmaximal, characteristic, complemented
8C2×#16839646C211yesmaximal, characteristic, complemented
9C2×#16839646C211yesmaximal, characteristic, complemented
10C2×#16839645C211yesmaximal, characteristic, complemented
11C2×#16839637C211yesmaximal, characteristic
12C2×#16839634C211yesmaximal, characteristic
13C2×#16839620C211yesmaximal, characteristic
14C2×C4×C22⋊Dic61C211yesmaximal, characteristic
15C22×#14519684C211yesmaximal, characteristic
16C2×C4×C22⋊C4×C61C211yesmaximal, characteristic
17C23×Dic122C2211yescharacteristic
18C24×Dic61C2211yescharacteristic
19C24×Dic61C2211yescharacteristic
20C2×#14519754C4116yescomplemented
21C2×#14519754C2218yes—
22C22×C4⋊Dic61C2211yescharacteristic
23C22×C4⋊Dic61C2211yescharacteristic
24C22×C4⋊Dic61C2211yescharacteristic
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#16839668C2218yescomplemented
36#16839666C2218yescomplemented
37#16839660C2218yescomplemented
38#16839659C2218yescomplemented
39#16839649C2218yescomplemented
40#16839646C2218yescomplemented
41#16839646C2218yescomplemented
42#16839645C2218yescomplemented
43#16839637C2218yes—
44#16839634C2218yes—
45#16839620C2218yes—
46C4×C22⋊Dic61C2218yes—
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C2×#14519684C2211yescharacteristic
53C2×#14519684C2211yescharacteristic
54C2×#14519684C2211yescharacteristic
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C2×#14519684C2218yes—
60C24×C4×C61C2211yescharacteristic
61C22×C22⋊C4×C61C2211yescharacteristic
62C22×C22⋊C4×C61C2211yescharacteristic
63C22×C42×C61C2211yescharacteristic
64C22×C42×C61C2211yescharacteristic
65C4×C22⋊C4×C61C2218yes—
66C2×#95×C61C2211yescharacteristic
67C2×#95×C61C2211yescharacteristic
68C22×Dic122—42no—
69C22×Dic122—42no—
70C22×Dic122C2×C418yescomplemented
71C22×Dic122C2314yes—
72C23×Dic61—24no—
73C23×Dic61—42no—
74C23×Dic61—42no—
75C23×Dic61—42no—
76C23×Dic61—42no—
77C23×Dic61C2×C418yes—
78C23×Dic61C2311yescharacteristic
79C23×Dic61C2311yescharacteristic
80C23×Dic61C2311yescharacteristic
81C23×Dic61C2311yescharacteristic
82C23×Dic61C2311yescharacteristic
83C23×Dic61C2311yescharacteristic
84C23×Dic61C2311yescharacteristic
85C23×Dic61C2311yescharacteristic
86C23×Dic61C2314yes—
87C23×Dic61C2314yes—
88#14519754C2×C4164yescomplemented
89C2×C4⋊Dic61—42no—
90C2×C4⋊Dic61—42no—
91C2×C4⋊Dic61C2×C418yescomplemented
92C2×C4⋊Dic61C2314yes—
93C2×C4⋊Dic61C2314yes—
94C2×C4⋊Dic61C2314yes—
95C2×#11758196—42no—
96C2×#11758196—42no—
97C2×#11758196—42no—
98C2×#11758196—42no—
99C2×#11758196C2×C418yescomplemented
100C2×#11758196C2×C418yescomplemented
101C2×#11758196C2314yes—
102C2×#11758196C2314yes—
103C2×#11758196C2314yes—
104C2×#11758196C2314yes—
105C2×#11758196C2314yes—
106C2×#11758196C2314yes—
107C2×C22⋊Dic61—24no—
108C2×C22⋊Dic61C2×C418yes—
109C2×C22⋊Dic61C2314yes—
110C2×C22⋊Dic61C2314yes—
111C2×C4×Dic61—42no—
112C2×C4×Dic61—42no—
113C2×C4×Dic61C2314yes—
114C2×C4×Dic61C2314yes—
115#14519684C2314yes—
116#14519684C2314yes—
117#14519684C2314yes—
118#14519684C2314yes—
119#14519684C2314yes—
120#14519684C2314yes—
121#14519684C2314yes—
122#14519684C2314yes—
123#14519684C2314yes—
124#14519684C2314yes—
125#14519684C2314yes—
126#14519684C2314yes—
127C25×C61C2311yescharacteristic
128C23×C4×C61—42no—
129C23×C4×C61—42no—
130C23×C4×C61Q818yescomplemented
131C23×C4×C61C2311yescharacteristic
132C23×C4×C61C2311yescharacteristic
133C23×C4×C61C2311yescharacteristic
134C23×C4×C61C2311yescharacteristic
135C23×C4×C61C2311yescharacteristic
136C23×C4×C61C2311yescharacteristic
137C23×C4×C61C2314yes—
138C2×C22⋊C4×C61—24no—
139C2×C22⋊C4×C61C2×C418yes—
140C2×C22⋊C4×C61C2314yes—
141C2×C22⋊C4×C61C2314yes—
142C2×C42×C61—42no—
143C2×C42×C61—42no—
144C2×C42×C61C2314yes—
145C2×C42×C61C2314yes—
146#95×C61C2314yes—
147#95×C61C2314yes—
148C24×C61—22no—
149C24×C61—22no—
150C24×C61—22no—
151C24×C61—22no—
152C24×C61C22×C414yes—
153C24×C61C2×Q814yes—
154C24×C61#4114yes—
155C24×C61C2412yes—
156C24×C61C2411yescharacteristic
157C22×C4×C61—22no—
158C22×C4×C61—22no—
159C22×C4×C61—22no—
160C22×C4×C61—22no—
161C22×C4×C61—22no—
162C22×C4×C61—22no—
163C22×C4×C61—22no—
164C22×C4×C61—22no—
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—416no—
172C22×C4×C61—44no—
173C22×C4×C61—44no—
174C22×C4×C61C22×C414yes—
175C22×C4×C61C22×C414yes—
176C22×C4×C61C2×Q814yes—
177C22×C4×C61C2×Q814yes—
178C22×C4×C61C2×Q8116yescomplemented
179C22×C4×C61C2412yes—
180C22×C4×C61C2412yes—
181C22×C4×C61C2412yes—
182C22×C4×C61C2412yes—
183C22×C4×C61C2412yes—
184C22×C4×C61C2412yes—
185C22×Dic61—22no—
186C22×Dic61—22no—
187C22×Dic61—22no—
188C22×Dic61—22no—
189C22×Dic61—22no—
190C22×Dic61—22no—
191C22×Dic61—22no—
192C22×Dic61—22no—
193C22×Dic61—28no—
194C22×Dic61—22no—
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—416no—
207C22×Dic61—44no—
208C22×Dic61—44no—
209C22×Dic61—44no—
210C22×Dic61—44no—
211C22×Dic61—416no—
212C22×Dic61C22×C414yes—
213C22×Dic61C22×C414yes—
214C22×Dic61C22×C414yes—
215C22×Dic61C22×C414yes—
216C22×Dic61C22×C4116yes—
217C22×Dic61C2412yes—
218C22×Dic61C2412yes—
219C22×Dic61C2412yes—
220C22×Dic61C2412yes—
221C22×Dic61C2412yes—
222C22×Dic61C2412yes—
223C22×Dic61C2412yes—
224C22×Dic61C2412yes—
225C2×Dic122—416no—
226C2×Dic122—44no—
227C2×Dic122—44no—
228C2×Dic122C22×C4116yescomplemented
229C22⋊C4×C61—28no—
230C22⋊C4×C61C22×C4116yes—
231C42×C61—44no—
232C42×C61—44no—
233C22⋊Dic61—28no—
234C22⋊Dic61C22×C4116yes—
235C4⋊Dic61—44no—
236C4⋊Dic61—44no—
237C4⋊Dic61C22×C4116yescomplemented
238#11758196—44no—
239#11758196—44no—
240#11758196—44no—
241#11758196—44no—
242#11758196C22×C4116yescomplemented
243#11758196C22×C4116yescomplemented
244C4×Dic61—44no—
245C4×Dic61—44no—
246C23×C61—28no—
247C23×C61—28no—
248C23×C61—28no—
249C23×C61—28no—
250C23×C61—28no—
251C23×C61—28no—
252C23×C61—22no—
253C23×C61—22no—
254C23×C61—22no—
255C23×C61—22no—
256C23×C61C4×Q8116yes—
257C23×C61C23×C414yes—
258C23×C61C23×C412yes—
259C23×C61C22×Q814yes—
260C23×C61C22×Q812yes—
261C23×C61C2×#4114yes—
262C23×C61C2×#4112yes—
263C23×C61H(5,𝔽2)12yes—
264C23×C61H(5,𝔽2)12yes—
265C23×C61H(5,𝔽2)12yes—
266C23×C612−1+412yes—
267C23×C61C2511yescharacteristic
268C2×C4×C61—28no—
269C2×C4×C61—28no—
270C2×C4×C61—28no—
271C2×C4×C61—28no—
272C2×C4×C61—22no—
273C2×C4×C61—22no—
274C2×C4×C61—22no—
275C2×C4×C61—22no—
276C2×C4×C61—22no—
277C2×C4×C61—22no—
278C2×C4×C61—22no—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
281C2×C4×C61—22no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—416no—
287C2×C4×C61—44no—
288C2×C4×C61—44no—
289C2×C4×C61C23×C414yes—
290C2×C4×C61C23×C414yes—
291C2×C4×C61C22×Q814yes—
292C2×C4×C61C22×Q814yes—
293C2×Dic61—28no—
294C2×Dic61—28no—
295C2×Dic61—28no—
296C2×Dic61—28no—
297C2×Dic61—22no—
298C2×Dic61—22no—
299C2×Dic61—22no—
300C2×Dic61—22no—
301C2×Dic61—22no—
302C2×Dic61—22no—
303C2×Dic61—22no—
304C2×Dic61—22no—
305C2×Dic61—22no—
306C2×Dic61—22no—
307C2×Dic61—22no—
308C2×Dic61—22no—
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—416no—
318C2×Dic61—416no—
319C2×Dic61—44no—
320C2×Dic61—44no—
321C2×Dic61—44no—
322C2×Dic61—44no—
323C2×Dic61C23×C414yes—
324C2×Dic61C23×C414yes—
325C2×Dic61C23×C414yes—
326C2×Dic61C23×C414yes—
327Dic122—416no—
328C2×#2329—611nomaximal, Sylow
329C22×C61—232no—
330C22×C61—24no—
331C22×C61—24no—
332C22×C61—24no—
333C22×C61—24no—
334C22×C61—24no—
335C22×C61—24no—
336C22×C61C2×C4×Q818yes—
337C22×C61C2×C4×Q814yes—
338C22×C61#51814yes—
339C22×C61#52014yes—
340C22×C61#53814yes—
341C22×C61#53914yes—
342C22×C61#54314yes—
343C22×C61#54414yes—
344C22×C61C24×C411yescharacteristic
345C22×C61C23×Q811yescharacteristic
346C22×C61C22×#4111yescharacteristic
347C22×C61C2×H(5,𝔽2)11yescharacteristic
348C22×C61C2×H(5,𝔽2)11yescharacteristic
349C22×C61C2×H(5,𝔽2)11yescharacteristic
350C22×C61C2×2−1+411yescharacteristic
351C4×C61—24no—
352C4×C61—24no—
353C4×C61—24no—
354C4×C61—24no—
355C4×C61—42no—
356C4×C61—42no—
357Dic61—24no—
358Dic61—24no—
359Dic61—24no—
360Dic61—24no—
361Dic61—42no—
362Dic61—42no—
363Dic61—42no—
364Dic61—42no—
365C22×C22⋊Q8—611no—
366#2329—6116no—
367C2×#391—611no—
368C2×#391—611no—
369C2×#389—611no—
370C2×#389—611no—
371C2×#387—611no—
372C2×#387—611no—
373C2×#387—611no—
374C2×#387—611no—
375C2×#385—611no—
376C2×#385—611no—
377C2×#380—611no—
378C2×C4×C22⋊C4—611no—
379C2×C4×C22⋊C4D6111yescharacteristic
380C22×#95—611no—
381C2×C61—28no—
382C2×C61#232918yescomplemented
383C2×C61C22×C4×Q811yescharacteristic
384C2×C61C2×#51811yescharacteristic
385C2×C61C2×#52011yescharacteristic
386C2×C61C2×#53811yescharacteristic
387C2×C61C2×#53911yescharacteristic
388C2×C61C2×#54311yescharacteristic
389C2×C61C2×#54411yescharacteristic
390C23×Q8—611no—
391C24×C4—611no—
392C24×C4—611no—
393C24×C4C2×D6111yescharacteristic
394C2×C22⋊Q8—6116no—
395C2×C22⋊Q8—618no—
396C22×C4⋊C4—611no—
397C22×C4⋊C4—611no—
398C22×C4⋊C4—611no—
399C22×C4⋊C4—611no—
400C22×C4⋊C4—611no—
401C22×C4⋊C4—611no—
402C22×C4⋊C4—611no—
403C22×C4⋊C4—611no—
404C22×C4⋊C4—611no—
405C22×C22⋊C4—611no—
406C22×C22⋊C4—611no—
407C22×C22⋊C4C2×D6111yescharacteristic
408C22×C22⋊C4C2×D6111yescharacteristic
409C22×C42—611no—
410C22×C42—611no—
411C22×C42C2×D6111yescharacteristic
412C22×C42C2×D6111yescharacteristic
413#391—618no—
414#391—618no—
415#389—618no—
416#389—618no—
417#387—618no—
418#387—618no—
419#387—618no—
420#387—618no—
421#385—618no—
422#385—618no—
423#380—618no—
424C4×C22⋊C4—618no—
425C4×C22⋊C4C2×D6118yes—
426C2×#95—618no—
427C2×#95—611no—
428C2×#95—611no—
429C2×#95—611no—
430C2×#95—611no—
431C2×#95—611no—
432C2×#95—611no—
433C2×#95—611no—
434C2×#95—611no—
435C2×#95—611no—
436C2×#95—611no—
437C2×#95—611no—
438C2×#95—611no—
439C2×#95C2×D6111yescharacteristic
440C2×#95C2×D6111yescharacteristic
441C61C2×#232911yescharacteristic, complemented, Sylow
442C25C22×D6111yescharacteristic
443C22×Q8—618no—
444C22×Q8—614no—
445C22×Q8—2442no—
446C22×Q8—2442no—
447C23×C4—42no—
448C23×C4—42no—
449C23×C4—611no—
450C23×C4—611no—
451C23×C4—611no—
452C23×C4—611no—
453C23×C4—618no—
454C23×C4—614no—
455C23×C4—611no—
456C23×C4—611no—
457C23×C4—611no—
458C23×C4—611no—
459C23×C4—614no—
460C23×C4—1224no—
461C23×C4—2442no—
462C23×C4—2442no—
463C23×C4—2442no—
464C23×C4—2442no—
465C23×C4Dic12218yescomplemented
466C23×C4C22×D6111yescharacteristic
467C23×C4C22×D6111yescharacteristic
468C23×C4C22×D6111yescharacteristic
469C23×C4C22×D6111yescharacteristic
470C23×C4C22×D6111yescharacteristic
471C23×C4C22×D6111yescharacteristic
472C23×C4C22×D6114yes—
473C22⋊Q8—6164no—
474C2×C4⋊C4—618no—
475C2×C4⋊C4—618no—
476C2×C4⋊C4—618no—
477C2×C4⋊C4—614no—
478C2×C4⋊C4—614no—
479C2×C4⋊C4—614no—
480C2×C4⋊C4—614no—
481C2×C4⋊C4—614no—
482C2×C4⋊C4—614no—
483C2×C4⋊C4—614no—
484C2×C4⋊C4—614no—
485C2×C4⋊C4—614no—
486C2×C4⋊C4—2442no—
487C2×C4⋊C4—2442no—
488C2×C4⋊C4—2442no—
489C2×C4⋊C4—2442no—
490C2×C4⋊C4—2442no—
491C2×C4⋊C4—2442no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—618no—
494C2×C22⋊C4—614no—
495C2×C22⋊C4—614no—
496C2×C22⋊C4—1224no—
497C2×C22⋊C4C4×D6118yes—
498C2×C22⋊C4C22×D6114yes—
499C2×C22⋊C4C22×D6114yes—
500C2×C42—42no—
501C2×C42—42no—
502C2×C42—614no—
503C2×C42—614no—
504C2×C42—2442no—
505C2×C42—2442no—
506C2×C42C22×D6114yes—
507C2×C42C22×D6114yes—
508#95—614no—
509#95—614no—
510#95—614no—
511#95—614no—
512#95—614no—
513#95—614no—
514#95—614no—
515#95—614no—
516#95—614no—
517#95—614no—
518#95—614no—
519#95—614no—
520#95C22×D6114yes—
521#95C22×D6114yes—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24C2×Dic12214yes—
527C24C2×C4×D6114yes—
528C24#1175822214yes—
529C24C23×D6112yes—
530C24C23×D6111yescharacteristic
531C2×Q8—6116no—
532C2×Q8—24416no—
533C2×Q8—2444no—
534C2×Q8—2444no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—416no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—614no—
553C22×C4—614no—
554C22×C4—614no—
555C22×C4—614no—
556C22×C4—612no—
557C22×C4—612no—
558C22×C4—612no—
559C22×C4—612no—
560C22×C4—6116no—
561C22×C4—612no—
562C22×C4—612no—
563C22×C4—612no—
564C22×C4—612no—
565C22×C4—1222no—
566C22×C4—1222no—
567C22×C4—1222no—
568C22×C4—1222no—
569C22×C4—1222no—
570C22×C4—1222no—
571C22×C4—1222no—
572C22×C4—1222no—
573C22×C4—1222no—
574C22×C4—1222no—
575C22×C4—1228no—
576C22×C4—1222no—
577C22×C4—1222no—
578C22×C4—1222no—
579C22×C4—1222no—
580C22×C4—1222no—
581C22×C4—1222no—
582C22×C4—1222no—
583C22×C4—1222no—
584C22×C4—1222no—
585C22×C4—1222no—
586C22×C4—24416no—
587C22×C4—2444no—
588C22×C4—2444no—
589C22×C4—2444no—
590C22×C4—2444no—
591C22×C4—24416no—
592C22×C4C2×Dic12214yes—
593C22×C4C2×Dic12214yes—
594C22×C4C2×Dic122116yescomplemented
595C22×C4C2×C4×D6114yes—
596C22×C4C2×C4×D6114yes—
597C22×C4C23×D6112yes—
598C22×C4C23×D6112yes—
599C22×C4C23×D6112yes—
600C22×C4C23×D6112yes—
601C22×C4C23×D6112yes—
602C22×C4C23×D6112yes—
603C4⋊C4—6116no—
604C4⋊C4—6116no—
605C4⋊C4—6116no—
606C4⋊C4—2444no—
607C4⋊C4—2444no—
608C4⋊C4—2444no—
609C4⋊C4—2444no—
610C4⋊C4—2444no—
611C4⋊C4—2444no—
612C22⋊C4—28no—
613C22⋊C4—6116no—
614C22⋊C4—1228no—
615C22⋊C4C2×C4×D61116yes—
616C42—44no—
617C42—44no—
618C42—2444no—
619C42—2444no—
620C23—28no—
621C23—28no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—28no—
627C23—28no—
628C23—28no—
629C23—28no—
630C23C4×Dic122116yes—
631C23C22×C4×D6114yes—
632C23C22×C4×D6112yes—
633C23C22×Dic12214yes—
634C23C22×Dic12212yes—
635C23C2×#1175822214yes—
636C23C2×#1175822212yes—
637C23#1451982212yes—
638C23#1451982212yes—
639C23#1451982312yes—
640C23#1451982412yes—
641C23C24×D6111yescharacteristic
642Q8—24416no—
643C2×C4—28no—
644C2×C4—28no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—28no—
654C2×C4—28no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—416no—
662C2×C4—44no—
663C2×C4—44no—
664C2×C4—614no—
665C2×C4—614no—
666C2×C4—614no—
667C2×C4—614no—
668C2×C4—1228no—
669C2×C4—1228no—
670C2×C4—1228no—
671C2×C4—1228no—
672C2×C4—1222no—
673C2×C4—1222no—
674C2×C4—1222no—
675C2×C4—1222no—
676C2×C4—1222no—
677C2×C4—1222no—
678C2×C4—1222no—
679C2×C4—1222no—
680C2×C4—1222no—
681C2×C4—1222no—
682C2×C4—1222no—
683C2×C4—1222no—
684C2×C4—1222no—
685C2×C4—1222no—
686C2×C4—1222no—
687C2×C4—1222no—
688C2×C4—1222no—
689C2×C4—1222no—
690C2×C4—1222no—
691C2×C4—1222no—
692C2×C4—24416no—
693C2×C4—24416no—
694C2×C4—2444no—
695C2×C4—2444no—
696C2×C4—2444no—
697C2×C4—2444no—
698C2×C4C22×C4×D6114yes—
699C2×C4C22×C4×D6114yes—
700C2×C4C22×Dic12214yes—
701C2×C4C22×Dic12214yes—
702C22—24no—
703C22—24no—
704C22—24no—
705C22—24no—
706C22—232no—
707C22—24no—
708C22—24no—
709C22C2×C4×Dic12218yes—
710C22C2×C4×Dic12214yes—
711C22#1684023414yes—
712C22#1684024114yes—
713C22#1684034514yes—
714C22#1684035414yes—
715C22#1684038814yes—
716C22#1684039014yes—
717C22C23×C4×D6111yescharacteristic
718C22C23×Dic12211yescharacteristic
719C22C22×#1175822211yescharacteristic
720C22C2×#1451982211yescharacteristic
721C22C2×#1451982211yescharacteristic
722C22C2×#1451982311yescharacteristic
723C22C2×#1451982411yescharacteristic
724C4—24no—
725C4—24no—
726C4—24no—
727C4—24no—
728C4—42no—
729C4—42no—
730C4—1224no—
731C4—1224no—
732C4—1224no—
733C4—1224no—
734C4—2442no—
735C4—2442no—
736C4—2442no—
737C4—2442no—
738C2—28no—
739C2#2144854718yesdirect product factor
740C2C22×C4×Dic12211yescharacteristic
741C2C2×#1684023411yescharacteristic
742C2C2×#1684024111yescharacteristic
743C2C2×#1684034511yescharacteristic
744C2C2×#1684035411yescharacteristic
745C2C2×#1684038811yescharacteristic
746C2C2×#1684039011yescharacteristic
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×#2329
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. #21448547C2direct (N × H)
3. C2×#16839668C2semidirect
4. C2×#16839666C2semidirect
5. C2×#16839660C2semidirect
6. C2×#16839659C2semidirect
7. C2×#16839649C2semidirect
8. C2×#16839646C2semidirect
9. C2×#16839646C2semidirect
10. C2×#16839645C2semidirect
20. C2×#14519754C4semidirect
35. #16839668C22semidirect
36. #16839666C22semidirect
37. #16839660C22semidirect
38. #16839659C22semidirect
39. #16839649C22semidirect
40. #16839646C22semidirect
41. #16839646C22semidirect
42. #16839645C22semidirect
70. C22×Dic122C2×C4semidirect
88. #14519754C2×C4semidirect
91. C2×C4⋊Dic61C2×C4semidirect
99. C2×#11758196C2×C4semidirect
100. C2×#11758196C2×C4semidirect
130. C23×C4×C61Q8semidirect
178. C22×C4×C61C2×Q8semidirect
228. C2×Dic122C22×C4semidirect
237. C4⋊Dic61C22×C4semidirect
242. #11758196C22×C4semidirect
243. #11758196C22×C4semidirect
382. C2×C61#2329semidirect
441. C61C2×#2329semidirect
465. C23×C4Dic122semidirect
594. C22×C4C2×Dic122semidirect
739. C2#21448547direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197542
#214485472
C2×#168396682
C2×#168396662
C2×#168396602
C2×#168396592
C2×#168396492
C2×#168396462
C2×#168396452
C2×#168396372
C2×#168396342
C2×#168396202
C2×C4×C22⋊Dic612
C22×#145196842
C2×C4×C22⋊C4×C612
C2×#232961