Finite Group Databasebeta

← C2×#21458885 #30561019

Subgroups — C2×#21458885 #30561019

Order 15616.

2002 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840497C211yesmaximal, characteristic, complemented
2#21458885C2116yesmaximal, direct product factor
3C2×#16840154C211yesmaximal, characteristic, complemented
4C2×#16840152C211yesmaximal, characteristic
5C2×#16840144C211yesmaximal, characteristic, complemented
6C2×#16839984C211yesmaximal, characteristic, complemented
7C2×#16839981C211yesmaximal, characteristic, complemented
8C2×#16839962C211yesmaximal, characteristic, complemented
9C2×#16839977C211yesmaximal, characteristic, complemented
10C2×#16839974C211yesmaximal, characteristic, complemented
11C2×#16839964C211yesmaximal, characteristic, complemented
12C2×#16839893C211yesmaximal, characteristic, complemented
13C2×#16839872C211yesmaximal, characteristic, complemented
14C2×#16839867C211yesmaximal, characteristic, complemented
15C2×C4×#11758201C211yesmaximal, characteristic, complemented
16C2×C61×#556C211yesmaximal, characteristic, complemented
17C22×#11758202C2211yescharacteristic
18C22×#11758202C2211yescharacteristic
19C22×#11758200C2211yescharacteristic
20C22×#11758201C2211yescharacteristic
21C22×#11758201C2211yescharacteristic
22C22×#11758201C2211yescharacteristic
23C22×#11758201C2211yescharacteristic
24C22×#11758199C2211yescharacteristic
25C22×#11758199C2211yescharacteristic
26#16840497—24no—
27#16840497C2218yescomplemented
28C2×#14519774C2211yescharacteristic
29C2×#14519766—21no—
30C2×#14519765C2211yescharacteristic
31C2×#14519765C2211yescharacteristic
32C2×#14519762—21no—
33C2×#14519762—21no—
34C2×C4×Dic122C2211yescharacteristic
35C2×C4×D244C2211yescharacteristic
36C2×C4×D244C2211yescharacteristic
37C2×#14519739—21no—
38#16840154C2218yescomplemented
39#16840152C2218yes—
40#16840144C2218yescomplemented
41#16839984C2218yescomplemented
42#16839981C2218yescomplemented
43#16839977C2218yescomplemented
44#16839974C2218yescomplemented
45#16839964C2218yescomplemented
46#16839962C2218yescomplemented
47#16839893C2218yescomplemented
48#16839872C2218yescomplemented
49#16839867C2218yescomplemented
50C4×#11758201C2218yescomplemented
51C2×#14519708C2211yescharacteristic
52C2×C4⋊#92418C2211yescharacteristic
53C2×C4⋊#92418C2211yescharacteristic
54C2×C4⋊#92418C2211yescharacteristic
55C2×#14519701C2211yescharacteristic
56C2×#14519701C2211yescharacteristic
57C2×#14519700C2211yescharacteristic
58C2×#14519698C2211yescharacteristic
59C2×#14519697C2211yescharacteristic
60C2×#14519697C2211yescharacteristic
61C2×#14519688C2211yescharacteristic
62C2×#14519688C2211yescharacteristic
63C2×C4×#92418C2211yescharacteristic
64C61×#556—24no—
65C61×#556C2218yescomplemented
66C2×C4⋊Q8×C61C2211yescharacteristic
67C2×#126×C61—21no—
68C2×#126×C61—21no—
69C2×#124×C61C2211yescharacteristic
70C2×#124×C61C2211yescharacteristic
71C2×C22⋊Q8×C61—21no—
72C2×C4×Q8×C61C2211yescharacteristic
73C2×C4×Q8×C61C2211yescharacteristic
74C2×C4×Q8×C61C2211yescharacteristic
75C2×C4×D4×C61C2211yescharacteristic
76C2×#117×C61—21no—
77C22×Dic122C2311yescharacteristic
78C22×D244—21no—
79C22×D244—21no—
80C22×D244C2311yescharacteristic
81C22×D244C2311yescharacteristic
82C22×C4×D61—21no—
83C22×C4×D61—21no—
84C2×#11758202—24no—
85C2×#11758202—42no—
86C2×#11758202C2314yes—
87C2×#11758202C2314yes—
88C2×#11758200—42no—
89C2×#11758200C2314yes—
90C2×#11758201—24no—
91C2×#11758201—42no—
92C2×#11758201—42no—
93C2×#11758201—42no—
94C2×#11758201C2314yes—
95C2×#11758201C2314yes—
96C2×#11758201C2314yes—
97C2×#11758201C2314yes—
98C2×#11758199—24no—
99C2×#11758199—42no—
100C2×#11758199C2314yes—
101C2×#11758199C2314yes—
102C22×#92418C2311yescharacteristic
103C22×#92418C2311yescharacteristic
104C22×#92418C2311yescharacteristic
105C22×#92418C2311yescharacteristic
106#14519774—22no—
107#14519774C2314yes—
108#14519766—28no—
109#14519765—22no—
110#14519765—22no—
111#14519765C2314yes—
112#14519765C2314yes—
113#14519762—28no—
114#14519762—28no—
115C4×Dic122—22no—
116C4×Dic122C2314yes—
117C4×D244—22no—
118C4×D244—22no—
119C4×D244C2314yes—
120C4×D244C2314yes—
121#14519739—28no—
122C2×C4⋊Dic61C2311yescharacteristic
123C2×#11758196—21no—
124C2×#11758198—21no—
125C2×#11758198—21no—
126C2×#11758198—21no—
127C2×#11758198—21no—
128C2×#11758198—21no—
129C2×#11758198—21no—
130C2×C4×Dic61—21no—
131#14519708C2314yes—
132C4⋊#92418C2314yes—
133C4⋊#92418C2314yes—
134C4⋊#92418C2314yes—
135#14519701C2314yes—
136#14519701C2314yes—
137#14519700C2314yes—
138#14519698C2314yes—
139#14519697C2314yes—
140#14519697C2314yes—
141#14519688C2314yes—
142#14519688C2314yes—
143C4×#92418C2314yes—
144C22×Q8×C61D411yescharacteristic
145C22×Q8×C61C2311yescharacteristic
146C22×Q8×C61C2311yescharacteristic
147C22×D4×C61C2311yescharacteristic
148C23×C4×C61—21no—
149C4⋊Q8×C61—22no—
150C4⋊Q8×C61C2314yes—
151#126×C61—28no—
152#126×C61—28no—
153#124×C61—22no—
154#124×C61—22no—
155#124×C61C2314yes—
156#124×C61C2314yes—
157C22⋊Q8×C61—28no—
158C4×Q8×C61—22no—
159C4×Q8×C61—22no—
160C4×Q8×C61D414yes—
161C4×Q8×C61C2314yes—
162C4×Q8×C61C2314yes—
163C4×Q8×C61C2314yes—
164C4×D4×C61—22no—
165C4×D4×C61C2314yes—
166#117×C61—28no—
167C2×C4⋊C4×C61—21no—
168C2×C4⋊C4×C61—21no—
169C2×C4⋊C4×C61—21no—
170C2×C4⋊C4×C61—21no—
171C2×C4⋊C4×C61D411yescharacteristic
172C2×C4⋊C4×C61D411yescharacteristic
173C2×C4⋊C4×C61D411yescharacteristic
174C2×C4⋊C4×C61C2311yescharacteristic
175C2×C22⋊C4×C61—21no—
176C2×C22⋊C4×C61—21no—
177C2×C22⋊C4×C61—21no—
178C2×C22⋊C4×C61—21no—
179C2×C22⋊C4×C61—21no—
180C2×C42×C61—21no—
181C2×C42×C61—21no—
182C2×C42×C61C2311yescharacteristic
183C2×C42×C61C2311yescharacteristic
184C2×C42×C61C2311yescharacteristic
185C24×C61—21no—
186C23×D61—21no—
187C23×D61—21no—
188C2×Q8×C61—21no—
189C2×Q8×C61—21no—
190C2×Q8×C61—22no—
191C2×Q8×C61—22no—
192C2×Q8×C61—22no—
193C2×Q8×C61—22no—
194C2×Q8×C61—42no—
195C2×Q8×C61C2×D414yes—
196C2×Q8×C61C2412yes—
197C2×Q8×C61C2412yes—
198C2×D4×C61—21no—
199C2×D4×C61—22no—
200C2×D4×C61—22no—
201C2×D4×C61C2412yes—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—24no—
206C22×C4×C61—44no—
207C22×C4×C61C2×D411yescharacteristic
208C22×C4×C61C2×D411yescharacteristic
209C22×C4×C61C2×D411yescharacteristic
210C22×C4×C61C2×D411yescharacteristic
211C22×C4×C61C2×D411yescharacteristic
212C22×C4×C61C2×D411yescharacteristic
213C22×C4×C61C2411yescharacteristic
214C22×Dic61—21no—
215C22×Dic61—21no—
216C2×D244—22no—
217C2×D244—22no—
218C2×D244—22no—
219C2×D244—22no—
220C2×D244—24no—
221C2×D244—21no—
222C2×D244—21no—
223C2×D244—24no—
224C2×D244—44no—
225C2×D244—82no—
226C2×D244C2412yes—
227C2×D244C2412yes—
228C2×C4×D61—24no—
229C2×C4×D61—24no—
230C2×C4×D61—82no—
231C2×C4×D61—82no—
232C2×Dic122—22no—
233C2×Dic122—22no—
234C2×Dic122—21no—
235C2×Dic122C2412yes—
236C4⋊C4×C61—24no—
237C4⋊C4×C61—24no—
238C4⋊C4×C61—24no—
239C4⋊C4×C61—24no—
240C4⋊C4×C61—21no—
241C4⋊C4×C61C2×D414yes—
242C4⋊C4×C61C2×D414yes—
243C4⋊C4×C61C2×D414yes—
244C4⋊C4×C61C2412yes—
245C22⋊C4×C61—24no—
246C22⋊C4×C61—24no—
247C22⋊C4×C61—24no—
248C22⋊C4×C61—24no—
249C22⋊C4×C61—24no—
250C42×C61—24no—
251C42×C61—24no—
252C42×C61C2×D412yes—
253C42×C61C2×D412yes—
254C42×C61C2×D412yes—
255C42×C61C2412yes—
256C42×C61C2412yes—
257C42×C61C2412yes—
258#11758202—28no—
259#11758202—44no—
260#11758201—28no—
261#11758201—44no—
262#11758201—44no—
263#11758201—44no—
264#11758200—44no—
265#11758199—28no—
266#11758199—44no—
267#11758198—24no—
268#11758198—24no—
269#11758198—24no—
270#11758198—24no—
271#11758198—24no—
272#11758198—24no—
273C4⋊Dic61—21no—
274C4⋊Dic61C2412yes—
275#11758196—24no—
276C4×Dic61—24no—
277C2×#92418—22no—
278C2×#92418—22no—
279C2×#92418—22no—
280C2×#92418#4114yes—
281C2×#92418C2412yes—
282C2×#92418C2412yes—
283C2×#92418C2412yes—
284C2×#92418C2412yes—
285C23×C61—22no—
286C23×C61—42no—
287C23×C61—42no—
288C23×C61—42no—
289C23×C61C22×D411yescharacteristic
290C22×D61—22no—
291C22×D61—22no—
292C22×D61—42no—
293C22×D61—42no—
294C22×D61—42no—
295C22×D61—42no—
296C22×D61—42no—
297C22×D61—42no—
298Q8×C61—22no—
299Q8×C61—22no—
300Q8×C61—22no—
301Q8×C61—22no—
302Q8×C61—44no—
303Q8×C61—42no—
304Q8×C61—42no—
305D4×C61—22no—
306D4×C61—22no—
307D4×C61—42no—
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—48no—
318C2×C4×C61—42no—
319C2×C4×C61—42no—
320C2×C4×C61—42no—
321C2×C4×C61C22×D412yes—
322C2×C4×C61C22×D412yes—
323C2×C4×C61C22×D412yes—
324C2×C4×C61C22×D412yes—
325C2×C4×C61C22×D412yes—
326C2×C4×C61C22×D412yes—
327C2×C4×C61C22×D411yescharacteristic
328C2×C4×C61C2×#4112yes—
329C2×C4×C61H(5,𝔽2)12yes—
330C2×C4×C61C2511yescharacteristic
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—42no—
334C2×Dic61—42no—
335D244—22no—
336D244—22no—
337D244—22no—
338D244—22no—
339D244—48no—
340D244—42no—
341D244—42no—
342D244—84no—
343C4×D61—84no—
344C4×D61—84no—
345Dic122—22no—
346Dic122—22no—
347Dic122—42no—
348#92418—22no—
349#92418—22no—
350#92418—22no—
351#92418C2×#4114yes—
352C2×#3401—611nomaximal, Sylow
353C22×C61—42no—
354C22×C61—42no—
355C22×C61—42no—
356C22×C61—84no—
357C22×C61#55012yes—
358C22×C61#57512yes—
359C22×C61#57712yes—
360C22×C61C23×D411yescharacteristic
361C2×D61—42no—
362C2×D61—42no—
363C2×D61—42no—
364C2×D61—42no—
365C2×D61—42no—
366C2×D61—42no—
367C2×D61—84no—
368C2×D61—84no—
369C4×C61—22no—
370C4×C61—22no—
371C4×C61—22no—
372C4×C61—22no—
373C4×C61—22no—
374C4×C61—22no—
375C4×C61—42no—
376C4×C61—42no—
377C4×C61—42no—
378C4×C61#55012yes—
379C4×C61C22×#4111yescharacteristic
380C4×C61C2×H(5,𝔽2)11yescharacteristic
381Dic61—42no—
382Dic61—42no—
383C2×#559—611no—
384C2×#556D6111yescharacteristic, complemented
385#3401—6116no—
386C2×#497—611no—
387C2×#496—611no—
388C2×#495—611no—
389C2×#464—611no—
390C2×#464—611no—
391C2×#460—611no—
392C2×#463—611no—
393C2×#463—611no—
394C2×#461—611no—
395C2×#446—611no—
396C2×#442—611no—
397C2×#441—611no—
398C2×C4×SD16—611no—
399C2×C61—82no—
400C2×C61#340114yescomplemented
401C2×C61C2×#55011yescharacteristic
402C2×C61C2×#57511yescharacteristic
403C2×C61C2×#57711yescharacteristic
404D61—82no—
405D61—82no—
406C22×Q16—611no—
407C22×Q16—611no—
408C22×SD16—611no—
409C22×SD16—611no—
410C22×SD16—611no—
411C22×SD16—611no—
412C22×SD16—611no—
413C22×D8—611no—
414C22×D8—611no—
415#559—618no—
416#559—1224no—
417#556—24no—
418#556C2×D6118yescomplemented
419C2×C4⋊Q8C2×D6111yescharacteristic
420C2×#127—611no—
421C2×#126—21no—
422C2×#126—21no—
423C2×#124—611no—
424C2×#124—611no—
425C2×#124—1221no—
426C2×#124C2×D6111yescharacteristic
427C2×#124C2×D6111yescharacteristic
428C2×#123—1221no—
429C2×#123—1221no—
430C2×C22⋊Q8—21no—
431C2×C4×Q8—611no—
432C2×C4×Q8C2×D6111yescharacteristic
433C2×C4×Q8C2×D6111yescharacteristic
434C2×C4×Q8C2×D6111yescharacteristic
435C2×C4×D4—611no—
436C2×C4×D4—611no—
437C2×C4×D4—1221no—
438C2×C4×D4C2×D6111yescharacteristic
439C2×#117—21no—
440#497—618no—
441#496—618no—
442#495—618no—
443#464—618no—
444#464—618no—
445#463—618no—
446#463—618no—
447#461—618no—
448#460—618no—
449#446—618no—
450#442—618no—
451#441—618no—
452C4×SD16—618no—
453C2×#106—611no—
454C2×C4⋊C8—611no—
455C2×C4⋊C8—611no—
456C2×C4⋊C8—611no—
457C2×#103—611no—
458C2×#103—611no—
459C2×#103—611no—
460C2×#102—611no—
461C2×#102—611no—
462C2×#102—611no—
463C2×#97—611no—
464C2×#97—611no—
465C2×C4×C8—611no—
466C61C2×#340111yescharacteristic, complemented, Sylow
467C22×Q8—611no—
468C22×Q8C22⋊D6111yescharacteristic
469C22×Q8C22×D6111yescharacteristic
470C22×Q8C22×D6111yescharacteristic
471C22×D4—611no—
472C22×D4—611no—
473C22×D4—1221no—
474C22×D4—1221no—
475C22×D4C22×D6111yescharacteristic
476C23×C4—21no—
477C23×C4—1221no—
478C23×C4—1221no—
479C2×Q16—614no—
480C2×Q16—614no—
481C2×Q16—1224no—
482C2×Q16—2442no—
483C2×SD16—614no—
484C2×SD16—614no—
485C2×SD16—614no—
486C2×SD16—614no—
487C2×SD16—614no—
488C2×SD16—1224no—
489C2×SD16—2442no—
490C2×SD16—2442no—
491C2×SD16—2442no—
492C2×SD16—2442no—
493C2×D8—614no—
494C2×D8—614no—
495C2×D8—1224no—
496C2×D8—2442no—
497C22×C8—611no—
498C22×C8—611no—
499C22×C8—611no—
500C22×C8—611no—
501C4⋊Q8—22no—
502C4⋊Q8C22×D6114yes—
503#127—614no—
504#127—1222no—
505#126—28no—
506#126—28no—
507#124—22no—
508#124—22no—
509#124—614no—
510#124—614no—
511#124—1228no—
512#124—1222no—
513#124—1222no—
514#124C22×D6114yes—
515#124C22×D6114yes—
516#123—1228no—
517#123—1228no—
518C22⋊Q8—28no—
519C4×Q8—22no—
520C4×Q8—22no—
521C4×Q8—614no—
522C4×Q8—1222no—
523C4×Q8C22⋊D6114yes—
524C4×Q8C22×D6114yes—
525C4×Q8C22×D6114yes—
526C4×Q8C22×D6114yes—
527C4×D4—22no—
528C4×D4—614no—
529C4×D4—614no—
530C4×D4—1228no—
531C4×D4—1222no—
532C4×D4—1222no—
533C4×D4C22×D6114yes—
534#117—28no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—611no—
540C2×C4⋊C4—1221no—
541C2×C4⋊C4C22⋊D6111yescharacteristic
542C2×C4⋊C4C22⋊D6111yescharacteristic
543C2×C4⋊C4C22⋊D6111yescharacteristic
544C2×C4⋊C4C22×D6111yescharacteristic
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—1221no—
551C2×C22⋊C4—1221no—
552C2×C22⋊C4—1221no—
553C2×C22⋊C4—1221no—
554C2×C22⋊C4—1221no—
555C2×C22⋊C4—1221no—
556C2×C42—21no—
557C2×C42—21no—
558C2×C42—1221no—
559C2×C42C22×D6111yescharacteristic
560C2×C42C22×D6111yescharacteristic
561C2×C42C22×D6111yescharacteristic
562#106—614no—
563C4⋊C8—614no—
564C4⋊C8—614no—
565C4⋊C8—614no—
566#103—614no—
567#103—614no—
568#103—614no—
569#102—614no—
570#102—614no—
571#102—614no—
572#97—614no—
573#97—614no—
574C4×C8—614no—
575C24—21no—
576C24—1221no—
577C24—1221no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—22no—
581C2×Q8—22no—
582C2×Q8—22no—
583C2×Q8—22no—
584C2×Q8—42no—
585C2×Q8—612no—
586C2×Q8—1221no—
587C2×Q8—1222no—
588C2×Q8—1222no—
589C2×Q8C2×C22⋊D6114yes—
590C2×Q8C23×D6112yes—
591C2×Q8C23×D6112yes—
592C2×D4—21no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—612no—
596C2×D4—612no—
597C2×D4—1224no—
598C2×D4—1224no—
599C2×D4—1221no—
600C2×D4—1221no—
601C2×D4—1222no—
602C2×D4—1222no—
603C2×D4—1222no—
604C2×D4—1222no—
605C2×D4—4882no—
606C2×D4—2444no—
607C2×D4C23×D6112yes—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—24no—
612C22×C4—44no—
613C22×C4—1221no—
614C22×C4—1221no—
615C22×C4—1224no—
616C22×C4—1224no—
617C22×C4—4882no—
618C22×C4—4882no—
619C22×C4C2×C22⋊D6111yescharacteristic
620C22×C4C2×C22⋊D6111yescharacteristic
621C22×C4C2×C22⋊D6111yescharacteristic
622C22×C4C2×C22⋊D6111yescharacteristic
623C22×C4C2×C22⋊D6111yescharacteristic
624C22×C4C2×C22⋊D6111yescharacteristic
625C22×C4C23×D6111yescharacteristic
626Q16—1228no—
627Q16—2444no—
628SD16—1228no—
629SD16—2444no—
630SD16—2444no—
631SD16—2444no—
632SD16—2444no—
633D8—1228no—
634D8—2444no—
635C2×C8—614no—
636C2×C8—612no—
637C2×C8—612no—
638C2×C8—612no—
639C2×C8—612no—
640C2×C8—1222no—
641C2×C8—1222no—
642C2×C8—1222no—
643C4⋊C4—24no—
644C4⋊C4—24no—
645C4⋊C4—24no—
646C4⋊C4—24no—
647C4⋊C4—21no—
648C4⋊C4—612no—
649C4⋊C4—1221no—
650C4⋊C4—1224no—
651C4⋊C4C2×C22⋊D6114yes—
652C4⋊C4C2×C22⋊D6114yes—
653C4⋊C4C2×C22⋊D6114yes—
654C4⋊C4C23×D6112yes—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—24no—
658C22⋊C4—24no—
659C22⋊C4—24no—
660C22⋊C4—1224no—
661C22⋊C4—1224no—
662C22⋊C4—1224no—
663C22⋊C4—1224no—
664C22⋊C4—1224no—
665C22⋊C4—1224no—
666C42—24no—
667C42—24no—
668C42—1224no—
669C42C2×C22⋊D6112yes—
670C42C2×C22⋊D6112yes—
671C42C2×C22⋊D6112yes—
672C42C23×D6112yes—
673C42C23×D6112yes—
674C42C23×D6112yes—
675C23—22no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—1222no—
680C23—1222no—
681C23—2442no—
682C23—2442no—
683C23—2442no—
684C23—2442no—
685C23—2442no—
686C23—2442no—
687C23C22×C22⋊D6111yescharacteristic
688Q8—22no—
689Q8—22no—
690Q8—22no—
691Q8—22no—
692Q8—44no—
693Q8—42no—
694Q8—42no—
695Q8—1222no—
696Q8—1222no—
697Q8—2442no—
698D4—22no—
699D4—22no—
700D4—42no—
701D4—1222no—
702D4—1222no—
703D4—1222no—
704D4—1222no—
705D4—4884no—
706D4—2448no—
707D4—2442no—
708D4—2442no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—48no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—1222no—
723C2×C4—1222no—
724C2×C4—4884no—
725C2×C4—4884no—
726C2×C4—2442no—
727C2×C4—2442no—
728C2×C4C22×C22⋊D6112yes—
729C2×C4C22×C22⋊D6112yes—
730C2×C4C22×C22⋊D6112yes—
731C2×C4C22×C22⋊D6112yes—
732C2×C4C22×C22⋊D6112yes—
733C2×C4C22×C22⋊D6112yes—
734C2×C4C22×C22⋊D6111yescharacteristic
735C2×C4#41×D6112yes—
736C2×C4#1451982312yes—
737C2×C4C24×D6111yescharacteristic
738C8—614no—
739C8—1222no—
740C8—1222no—
741C8—1222no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—84no—
746C22—4884no—
747C22—4884no—
748C22—2442no—
749C22—2442no—
750C22—2442no—
751C22—2442no—
752C22—2442no—
753C22—2442no—
754C22#1684043112yes—
755C22#1684056012yes—
756C22#1684057012yes—
757C22C23×C22⋊D6111yescharacteristic
758C4—22no—
759C4—22no—
760C4—22no—
761C4—22no—
762C4—22no—
763C4—22no—
764C4—42no—
765C4—42no—
766C4—42no—
767C4—2442no—
768C4—2442no—
769C4#1684043112yes—
770C4C2×#41×D6111yescharacteristic
771C4C2×#1451982311yescharacteristic
772C2—82no—
773C2—4882no—
774C2—4882no—
775C2#2145888514yesdirect product factor
776C2C2×#1684043111yescharacteristic
777C2C2×#1684056011yescharacteristic
778C2C2×#1684057011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#556C2
socleC23×C61C22×D4
prime radicalC2×#16840152C2
hypercenterC2×#556D61
hypocenterC61C2×#3401
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. C2×#16840497C2semidirect
2. #21458885C2direct (N × H)
3. C2×#16840154C2semidirect
5. C2×#16840144C2semidirect
6. C2×#16839984C2semidirect
7. C2×#16839981C2semidirect
8. C2×#16839962C2semidirect
9. C2×#16839977C2semidirect
10. C2×#16839974C2semidirect
11. C2×#16839964C2semidirect
12. C2×#16839893C2semidirect
13. C2×#16839872C2semidirect
14. C2×#16839867C2semidirect
15. C2×C4×#11758201C2semidirect
16. C2×C61×#556C2semidirect
27. #16840497C22semidirect
38. #16840154C22semidirect
40. #16840144C22semidirect
41. #16839984C22semidirect
42. #16839981C22semidirect
43. #16839977C22semidirect
44. #16839974C22semidirect
45. #16839964C22semidirect
46. #16839962C22semidirect
47. #16839893C22semidirect
48. #16839872C22semidirect
49. #16839867C22semidirect
50. C4×#11758201C22semidirect
65. C61×#556C22semidirect
384. C2×#556D61semidirect
400. C2×C61#3401semidirect
418. #556C2×D61semidirect
466. C61C2×#3401semidirect
775. C2#21458885direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404972
#214588852
C2×#168401542
C2×#168401522
C2×#168401442
C2×#168399842
C2×#168399812
C2×#168399622
C2×#168399772
C2×#168399742
C2×#168399642
C2×#168398932
C2×#168398722
C2×#168398672
C2×C4×#117582012
C2×C61×#5562
C2×#340161