Finite Group Databasebeta

← C2×#21455736 #30547784

Subgroups — C2×#21455736 #30547784

Order 15616.

2378 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840274C211yesmaximal, characteristic
2C2×#117×D61C211yesmaximal, characteristic, complemented
3#21455736C2116yesmaximal, direct product factor
4C2×#16840099C211yesmaximal, characteristic, complemented
5C2×#16840082C211yesmaximal, characteristic, complemented
6C2×#16840106C211yesmaximal, characteristic, complemented
7C2×#16840105C211yesmaximal, characteristic, complemented
8C2×#16840089C211yesmaximal, characteristic, complemented
9C2×#16840088C211yesmaximal, characteristic, complemented
10C2×#16840094C211yesmaximal, characteristic, complemented
11C2×#16840077C211yesmaximal, characteristic, complemented
12C2×#16839798C211yesmaximal, characteristic, complemented
13C2×#16839759C211yesmaximal, characteristic, complemented
14C2×#16839756C211yesmaximal, characteristic, complemented
15C22×#14519689C211yesmaximal, characteristic, complemented
16C2×C61×#427C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C23×#92418C2211yescharacteristic
20#16840274—24no—
21#16840274C2218yes—
22C2×#14519761—21no—
23C2×#14519757C2211yescharacteristic
24C2×#14519757C2211yescharacteristic
25C2×#14519752C2211yescharacteristic
26C2×#14519752C2211yescharacteristic
27C2×#14519747—21no—
28C2×C4×D244—21no—
29C2×C4×D244—21no—
30C2×#14519736C2211yescharacteristic
31C2×#14519735C2211yescharacteristic
32C2×#14519735C2211yescharacteristic
33C2×#14519734—21no—
34C2×#14519733—21no—
35#117×D61—24no—
36#117×D61C2218yescomplemented
37C2×C4⋊C4×D61C2211yescharacteristic
38C2×C4⋊C4×D61C2211yescharacteristic
39C2×C22⋊C4×D61—21no—
40C2×C42×D61—21no—
41#16840106C2218yescomplemented
42#16840105C2218yescomplemented
43#16840099C2218yescomplemented
44#16840094C2218yescomplemented
45#16840089C2218yescomplemented
46#16840088C2218yescomplemented
47#16840082C2218yescomplemented
48#16840077C2218yescomplemented
49#16839798C2218yescomplemented
50C2×#14519710C2211yescharacteristic, complemented
51C2×#14519710C2211yescharacteristic, complemented
52C2×#14519708C2211yescharacteristic, complemented
53C2×#14519708C2211yescharacteristic, complemented
54#16839759C2218yescomplemented
55#16839756C2218yescomplemented
56C2×#14519702C2211yescharacteristic, complemented
57C2×#14519702C2211yescharacteristic, complemented
58C2×#14519700C2211yescharacteristic, complemented
59C2×#14519700C2211yescharacteristic, complemented
60C2×#14519699C2211yescharacteristic, complemented
61C2×#14519699C2211yescharacteristic, complemented
62C2×#14519697C2211yescharacteristic, complemented
63C2×#14519697C2211yescharacteristic, complemented
64C2×#14519689C2211yescharacteristic
65C2×#14519689C2211yescharacteristic
66C2×#14519689C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×#14519689C2218yescomplemented
69C23×C8×C61C2211yescharacteristic
70C2×#117×C61C2211yescharacteristic
71C2×#117×C61C2211yescharacteristic
72C61×#427C2218yescomplemented
73C2×#107×C61C2211yescharacteristic, complemented
74C2×#107×C61C2211yescharacteristic, complemented
75C2×#106×C61C2211yescharacteristic, complemented
76C2×#106×C61C2211yescharacteristic, complemented
77C24×D61D411yescharacteristic
78C2×#11758222—22no—
79C2×#11758222—24no—
80C2×#11758222—24no—
81C2×#11758222C2314yes—
82C22×Dic122C2311yescharacteristic
83C22×D244—21no—
84C22×D244—21no—
85C22×D244C2311yescharacteristic
86C22×C22⋊D61—21no—
87C23×Dic61D411yescharacteristic
88C22×C4×D61—24no—
89C22×C4×D61—24no—
90C22×C4×D61—21no—
91C22×C4×D61—21no—
92C22×C4×D61—21no—
93C22×C4×D61D411yescharacteristic
94C22×C4×D61D414yes—
95C22×C4×D61D411yescharacteristic
96C22×C4×D61C2311yescharacteristic
97C22×C4×D61C2314yes—
98C22×C4×D61C2311yescharacteristic
99C22×#92418—24no—
100C22×#92418C2311yescharacteristic
101C22×#92418C2311yescharacteristic
102C22×#92418C2314yes—
103#14519761—28no—
104#14519757—22no—
105#14519757—22no—
106#14519757C2314yes—
107#14519757C2314yes—
108#14519752—22no—
109#14519752—22no—
110#14519752C2314yes—
111#14519752C2314yes—
112#14519747—28no—
113C4×D244—28no—
114C4×D244—28no—
115#14519736—22no—
116#14519736C2314yes—
117#14519735—22no—
118#14519735—22no—
119#14519735C2314yes—
120#14519735C2314yes—
121#14519734—28no—
122#14519733—28no—
123C2×C4⋊Dic61—21no—
124C2×C4⋊Dic61—21no—
125C2×C4⋊Dic61C2311yescharacteristic
126C2×C4⋊Dic61C2311yescharacteristic
127C2×#11758196—21no—
128C2×#11758196—21no—
129C4⋊C4×D61—22no—
130C4⋊C4×D61—22no—
131C4⋊C4×D61C2314yes—
132C4⋊C4×D61C2314yes—
133C2×C22⋊Dic61—21no—
134C2×#11758198—21no—
135C2×#11758198—21no—
136C2×#11758198—21no—
137C2×#11758198—21no—
138C2×#11758198—21no—
139C2×#11758198—21no—
140C22⋊C4×D61—28no—
141C2×C4×Dic61—21no—
142C2×C4×Dic61—21no—
143C2×C4×Dic61—21no—
144C42×D61—28no—
145#14519710C2314yescomplemented
146#14519710C2314yescomplemented
147#14519708C2314yescomplemented
148#14519708C2314yescomplemented
149#14519702C2314yescomplemented
150#14519702C2314yescomplemented
151#14519700C2314yescomplemented
152#14519700C2314yescomplemented
153#14519699C2314yescomplemented
154#14519699C2314yescomplemented
155#14519697C2314yescomplemented
156#14519697C2314yescomplemented
157#14519689C2314yes—
158#14519689C2314yes—
159#14519689C2314yes—
160#14519689C2314yes—
161C23×C4×C61C2311yescharacteristic
162C22×C8×C61—24no—
163C22×C8×C61C2311yescharacteristic
164C22×C8×C61C2311yescharacteristic
165C22×C8×C61C2314yes—
166#117×C61—22no—
167#117×C61—22no—
168#117×C61C2314yes—
169#117×C61C2314yes—
170C2×C4⋊C4×C61C2311yescharacteristic
171C2×C4⋊C4×C61C2311yescharacteristic
172C2×C4⋊C4×C61C2311yescharacteristic
173C2×C4⋊C4×C61C2311yescharacteristic
174C2×C22⋊C4×C61—21no—
175C2×C22⋊C4×C61—21no—
176C2×C42×C61—21no—
177C2×C42×C61—21no—
178#107×C61C2314yescomplemented
179#107×C61C2314yescomplemented
180#106×C61C2314yescomplemented
181#106×C61C2314yescomplemented
182C24×C61C2×D411yescharacteristic
183C23×D61—24no—
184C23×D61—24no—
185C23×D61—21no—
186C23×D61—42no—
187C23×D61C2×D411yescharacteristic
188C23×D61C2×D414yes—
189C23×D61C2×D411yescharacteristic
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61C2×D412yes—
195C22×C4×C61C2×D411yescharacteristic
196C22×C4×C61#4114yes—
197C22×C4×C61#4114yes—
198C22×C4×C61C2411yescharacteristic
199C22×C4×C61C2412yes—
200C2×C22⋊D61—24no—
201C2×C22⋊D61—44no—
202C22×Dic61—24no—
203C22×Dic61—21no—
204C22×Dic61—21no—
205C22×Dic61—21no—
206C22×Dic61C2×D411yescharacteristic
207C22×Dic61C2×D411yescharacteristic
208C22×Dic61C2×D414yes—
209#11758222—28no—
210#11758222—28no—
211#11758222—48no—
212C2×D244—22no—
213C2×D244—22no—
214C2×D244—24no—
215C2×D244—24no—
216C2×D244—21no—
217C2×D244—44no—
218C2×D244—44no—
219C2×D244C2412yes—
220C2×C4×D61—24no—
221C2×C4×D61—24no—
222C2×C4×D61—216no—
223C2×C4×D61—22no—
224C2×C4×D61—22no—
225C2×C4×D61—28no—
226C2×C4×D61—22no—
227C2×C4×D61—22no—
228C2×C4×D61—28no—
229C2×C4×D61—24no—
230C2×C4×D61—24no—
231C2×C4×D61—24no—
232C2×C4×D61—44no—
233C2×C4×D61—44no—
234C2×C4×D61—44no—
235C2×C4×D61C2×D414yes—
236C2×C4×D61C2×D412yes—
237C2×C4×D61C2×D414yes—
238C2×C4×D61C2×D412yes—
239C2×C4×D61C2412yes—
240C2×C4×D61C2412yes—
241C2×Dic122—22no—
242C2×Dic122—22no—
243C2×Dic122—21no—
244C2×Dic122C2412yes—
245C2×C8×C61—22no—
246C2×C8×C61—22no—
247C2×C8×C61—28no—
248C2×C8×C61C2412yes—
249C2×C8×C61C2412yes—
250C4⋊C4×C61—21no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61—21no—
254C4⋊C4×C61C2412yes—
255C4⋊C4×C61C2412yes—
256C4⋊C4×C61C2412yes—
257C4⋊C4×C61C2412yes—
258C22⋊C4×C61—24no—
259C22⋊C4×C61—24no—
260C42×C61—24no—
261C42×C61—24no—
262C22⋊Dic61—24no—
263#11758198—24no—
264#11758198—24no—
265#11758198—24no—
266#11758198—24no—
267#11758198—24no—
268#11758198—24no—
269C4⋊Dic61—21no—
270C4⋊Dic61—21no—
271C4⋊Dic61—24no—
272C4⋊Dic61—24no—
273C4⋊Dic61C2412yes—
274C4⋊Dic61C2412yes—
275#11758196—24no—
276#11758196—24no—
277C4×Dic61—24no—
278C4×Dic61—24no—
279C4×Dic61—24no—
280C2×#92418—22no—
281C2×#92418—22no—
282C2×#92418—28no—
283C2×#92418C2412yes—
284C2×#92418C2412yes—
285C23×C61—22no—
286C23×C61—22no—
287C23×C61#12314yes—
288C23×C61C22×D412yes—
289C23×C61C22×D411yescharacteristic
290C22×D61—22no—
291C22×D61—22no—
292C22×D61—28no—
293C22×D61—22no—
294C22×D61—22no—
295C22×D61—22no—
296C22×D61—28no—
297C22×D61—22no—
298C22×D61—44no—
299C22×D61—416no—
300C22×D61—42no—
301C22×D61—42no—
302C22×D61—42no—
303C22×D61#13514yes—
304C22×D61C22×D412yes—
305C22×D61C22×D412yes—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—42no—
311C2×C4×C61—42no—
312C2×C4×C61—42no—
313C2×C4×C61—42no—
314C2×C4×C61#12314yes—
315C2×C4×C61#12318yes—
316C2×C4×C61C22×D412yes—
317C2×C4×C61C22×D411yescharacteristic
318C2×C4×C61C2×#4112yes—
319C2×C4×C61C2×#4114yes—
320C2×C4×C61C2×#4112yes—
321C2×C4×C61C2×#4114yes—
322C2×C4×C61C2511yescharacteristic
323C22⋊D61—48no—
324C2×Dic61—28no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—42no—
331C2×Dic61—42no—
332C2×Dic61—42no—
333C2×Dic61C22×D412yes—
334C2×Dic61C22×D412yes—
335D244—22no—
336D244—22no—
337D244—48no—
338D244—48no—
339D244—42no—
340C4×D61—24no—
341C4×D61—24no—
342C4×D61—28no—
343C4×D61—28no—
344C4×D61—22no—
345C4×D61—22no—
346C4×D61—22no—
347C4×D61—22no—
348C4×D61—48no—
349C4×D61—48no—
350C4×D61—48no—
351Dic122—22no—
352Dic122—22no—
353Dic122—42no—
354C8×C61—22no—
355C8×C61—22no—
356#92418—22no—
357#92418—22no—
358C2×#3091—611nomaximal, Sylow
359C22×C61—28no—
360C22×C61—22no—
361C22×C61—22no—
362C22×C61C2×#12314yes—
363C22×C61C2×#12312yes—
364C22×C61C2×#13512yes—
365C22×C61#57512yes—
366C22×C61C23×D411yescharacteristic
367C2×D61—28no—
368C2×D61—22no—
369C2×D61—22no—
370C2×D61—22no—
371C2×D61—22no—
372C2×D61—22no—
373C2×D61—416no—
374C2×D61—44no—
375C2×D61—42no—
376C2×D61—42no—
377C2×D61—42no—
378C2×D61—84no—
379C2×D61C2×#13514yes—
380C4×C61—42no—
381C4×C61—42no—
382C4×C61—42no—
383C4×C61—42no—
384C4×C61C2×#12312yes—
385C4×C61C2×#12314yes—
386C4×C61C22×#4111yescharacteristic
387C4×C61C22×#4111yescharacteristic
388Dic61—22no—
389Dic61—22no—
390Dic61—42no—
391Dic61—42no—
392Dic61—42no—
393C2×#525—611no—
394C22×#117—611no—
395#3091—6116no—
396C2×#484—611no—
397C2×#481—611no—
398C2×#485—611no—
399C2×#485—611no—
400C2×#482—611no—
401C2×#482—611no—
402C2×#483—611no—
403C2×#480—611no—
404C2×#427—611no—
405C2×#427D6111yescharacteristic, complemented
406C2×#416—611no—
407C2×#416—611no—
408C22×C22⋊C8—611no—
409C2×C61—24no—
410C2×C61#309114yescomplemented
411C2×C61C22×#12311yescharacteristic
412C2×C61C22×#13511yescharacteristic
413C2×C61C2×#57511yescharacteristic
414D61—24no—
415D61—42no—
416D61—82no—
417C22×#41—611no—
418C24×C4—611no—
419C23×C8—611no—
420C23×C8C2×D6111yescharacteristic
421#525—618no—
422#525—1224no—
423C2×#123—1221no—
424C2×C22⋊Q8—611no—
425C2×C22⋊Q8—611no—
426C2×#121—611no—
427C2×#121—611no—
428C2×#120—1221no—
429C2×C4×D4—1221no—
430C2×C4×D4—1221no—
431C2×#117—611no—
432C2×#117—618no—
433C2×#117—611no—
434C2×#117—611no—
435C2×#117—1221no—
436C2×#117—1221no—
437C2×#117—1224no—
438C2×#117C2×D6111yescharacteristic
439C2×#117C2×D6111yescharacteristic
440C22×C4⋊C4—611no—
441C22×C4⋊C4—611no—
442C22×C22⋊C4—1221no—
443C22×C42—1221no—
444#485—618no—
445#485—618no—
446#484—618no—
447#483—618no—
448#482—618no—
449#482—618no—
450#481—618no—
451#480—618no—
452#427—618no—
453#427C2×D6118yescomplemented
454C2×#107—611no—
455C2×#107—611no—
456C2×#107C2×D6111yescharacteristic, complemented
457C2×#107C2×D6111yescharacteristic, complemented
458C2×#106—611no—
459C2×#106—611no—
460C2×#106C2×D6111yescharacteristic, complemented
461C2×#106C2×D6111yescharacteristic, complemented
462#416—618no—
463#416—618no—
464C2×#103—611no—
465C2×#103—611no—
466C2×#103—611no—
467C2×#103—611no—
468C2×#102—611no—
469C2×#102—611no—
470C2×#102—611no—
471C2×#102—611no—
472C2×C22⋊C8—611no—
473C2×C22⋊C8—611no—
474C2×C22⋊C8—611no—
475C2×C22⋊C8—611no—
476C2×C22⋊C8—618no—
477C61C2×#309111yescharacteristic, complemented, Sylow
478C25—611no—
479C2×#41—614no—
480C2×#41—1222no—
481C2×#41—1224no—
482C2×#41—1224no—
483C22×Q8—611no—
484C22×D4—611no—
485C22×D4—1221no—
486C22×D4—1221no—
487C22×D4—1221no—
488C23×C4—611no—
489C23×C4—614no—
490C23×C4—611no—
491C23×C4—611no—
492C23×C4—611no—
493C23×C4—611no—
494C23×C4—614no—
495C23×C4—1221no—
496C23×C4—1221no—
497C23×C4—1224no—
498C23×C4—1224no—
499C23×C4—1221no—
500C23×C4C22×D6111yescharacteristic
501C22×C8—24no—
502C22×C8—611no—
503C22×C8—611no—
504C22×C8—614no—
505C22×C8—1224no—
506C22×C8C22×D6111yescharacteristic
507C22×C8C22×D6111yescharacteristic
508C22×C8C22×D6114yes—
509#123—1228no—
510C22⋊Q8—614no—
511C22⋊Q8—614no—
512C22⋊Q8—1222no—
513C22⋊Q8—1222no—
514#121—614no—
515#121—614no—
516#121—1222no—
517#121—1222no—
518#120—1228no—
519C4×D4—1228no—
520C4×D4—1228no—
521#117—22no—
522#117—22no—
523#117—614no—
524#117—614no—
525#117—614no—
526#117—1228no—
527#117—1228no—
528#117—1222no—
529#117—1222no—
530#117—1222no—
531#117C22×D6114yes—
532#117C22×D6114yes—
533C2×C4⋊C4—611no—
534C2×C4⋊C4—611no—
535C2×C4⋊C4—614no—
536C2×C4⋊C4—614no—
537C2×C4⋊C4—1222no—
538C2×C4⋊C4—1222no—
539C2×C4⋊C4—1221no—
540C2×C4⋊C4—1221no—
541C2×C4⋊C4—1221no—
542C2×C4⋊C4—1221no—
543C2×C4⋊C4C22×D6111yescharacteristic
544C2×C4⋊C4C22×D6111yescharacteristic
545C2×C4⋊C4C22×D6111yescharacteristic
546C2×C4⋊C4C22×D6111yescharacteristic
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—1228no—
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×C22⋊C4—1221no—
557C2×C42—21no—
558C2×C42—21no—
559C2×C42—1228no—
560C2×C42—1221no—
561C2×C42—1221no—
562C2×C42—1221no—
563#107—614no—
564#107—614no—
565#107C22×D6114yescomplemented
566#107C22×D6114yescomplemented
567#106—614no—
568#106—614no—
569#106C22×D6114yescomplemented
570#106C22×D6114yescomplemented
571#103—614no—
572#103—614no—
573#103—614no—
574#103—614no—
575#102—614no—
576#102—614no—
577#102—614no—
578#102—614no—
579C22⋊C8—614no—
580C22⋊C8—614no—
581C22⋊C8—614no—
582C22⋊C8—614no—
583C24—611no—
584C24—611no—
585C24—614no—
586C24—1224no—
587C24—1224no—
588C24—1221no—
589C24—2442no—
590C24D4×D6111yescharacteristic
591#41—1228no—
592#41—1228no—
593#41—2448no—
594C2×Q8—612no—
595C2×Q8—1221no—
596C2×Q8—1222no—
597C2×Q8—1222no—
598C2×D4—612no—
599C2×D4—1224no—
600C2×D4—1224no—
601C2×D4—1224no—
602C2×D4—1221no—
603C2×D4—1222no—
604C2×D4—1222no—
605C2×D4—2444no—
606C2×D4—2444no—
607C2×D4—2444no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—611no—
613C22×C4—611no—
614C22×C4—614no—
615C22×C4—614no—
616C22×C4—612no—
617C22×C4—614no—
618C22×C4—612no—
619C22×C4—612no—
620C22×C4—612no—
621C22×C4—1224no—
622C22×C4—1224no—
623C22×C4—1224no—
624C22×C4—1222no—
625C22×C4—1222no—
626C22×C4—1228no—
627C22×C4—1222no—
628C22×C4—1222no—
629C22×C4—1228no—
630C22×C4—1224no—
631C22×C4—1224no—
632C22×C4—12216no—
633C22×C4—1221no—
634C22×C4—1221no—
635C22×C4—1221no—
636C22×C4—1224no—
637C22×C4—2444no—
638C22×C4—2444no—
639C22×C4—2444no—
640C22×C4#1175822214yes—
641C22×C4D4×D6112yes—
642C22×C4D4×D6111yescharacteristic
643C22×C4#1175822614yes—
644C22×C4C23×D6111yescharacteristic
645C22×C4C23×D6112yes—
646C2×C8—22no—
647C2×C8—22no—
648C2×C8—28no—
649C2×C8—612no—
650C2×C8—612no—
651C2×C8—1222no—
652C2×C8—1222no—
653C2×C8—1228no—
654C2×C8C23×D6112yes—
655C2×C8C23×D6112yes—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—612no—
661C4⋊C4—612no—
662C4⋊C4—1224no—
663C4⋊C4—1224no—
664C4⋊C4—1224no—
665C4⋊C4—1224no—
666C4⋊C4—1221no—
667C4⋊C4—1221no—
668C4⋊C4C23×D6112yes—
669C4⋊C4C23×D6112yes—
670C4⋊C4C23×D6112yes—
671C4⋊C4C23×D6112yes—
672C22⋊C4—24no—
673C22⋊C4—24no—
674C22⋊C4—1224no—
675C22⋊C4—1224no—
676C22⋊C4—1224no—
677C22⋊C4—1224no—
678C22⋊C4—1224no—
679C22⋊C4—1224no—
680C22⋊C4—1224no—
681C42—24no—
682C42—24no—
683C42—1224no—
684C42—1224no—
685C42—1224no—
686C23—22no—
687C23—22no—
688C23—614no—
689C23—612no—
690C23—612no—
691C23—1228no—
692C23—1222no—
693C23—1222no—
694C23—1228no—
695C23—1222no—
696C23—1222no—
697C23—1222no—
698C23—1222no—
699C23—2444no—
700C23—24416no—
701C23—2442no—
702C23—2442no—
703C23—2442no—
704C23#1451976214yes—
705C23C2×D4×D6112yes—
706C23C2×D4×D6111yescharacteristic
707Q8—1222no—
708Q8—1222no—
709Q8—2442no—
710D4—1222no—
711D4—1222no—
712D4—2448no—
713D4—2448no—
714D4—2448no—
715D4—2442no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—612no—
725C2×C4—612no—
726C2×C4—1228no—
727C2×C4—1222no—
728C2×C4—1222no—
729C2×C4—1228no—
730C2×C4—1228no—
731C2×C4—1224no—
732C2×C4—1224no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—1222no—
737C2×C4—1222no—
738C2×C4—1222no—
739C2×C4—1222no—
740C2×C4—2448no—
741C2×C4—2448no—
742C2×C4—2442no—
743C2×C4—2442no—
744C2×C4—2442no—
745C2×C4—2448no—
746C2×C4#1451976214yes—
747C2×C4#1451976218yes—
748C2×C4C2×D4×D6112yes—
749C2×C4C2×D4×D6111yescharacteristic
750C2×C4C2×#1175822212yes—
751C2×C4C2×#1175822214yes—
752C2×C4C2×#1175822612yes—
753C2×C4C2×#1175822614yes—
754C2×C4C24×D6111yescharacteristic
755C8—22no—
756C8—22no—
757C8—1222no—
758C8—1222no—
759C22—22no—
760C22—22no—
761C22—28no—
762C22—614no—
763C22—1222no—
764C22—1222no—
765C22—1228no—
766C22—1222no—
767C22—1222no—
768C22—1222no—
769C22—4884no—
770C22—24416no—
771C22—2442no—
772C22—2442no—
773C22—2442no—
774C22—2444no—
775C22C2×#1451976214yes—
776C22C2×#1451976212yes—
777C22#135×D6112yes—
778C22#1684055912yes—
779C22C22×D4×D6111yescharacteristic
780C4—42no—
781C4—42no—
782C4—42no—
783C4—42no—
784C4—1222no—
785C4—1222no—
786C4—2442no—
787C4—2442no—
788C4—2442no—
789C4C2×#1451976214yes—
790C4C2×#1451976212yes—
791C4C22×#1175822211yescharacteristic
792C4C22×#1175822611yescharacteristic
793C2—24no—
794C2—1224no—
795C2—4882no—
796C2—2442no—
797C2#2145573614yesdirect product factor
798C2C22×#1451976211yescharacteristic
799C2C2×#135×D6111yescharacteristic
800C2C2×#1684055911yescharacteristic
subgroupG/H
centerC22×C4D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#427C2
socleC23×C61C22×D4
prime radicalC2×#16840274C2
hypercenterC2×#427D61
hypocenterC61C2×#3091
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#427

Complements

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

NH ≅ G/Ntype
2. C2×#117×D61C2semidirect
3. #21455736C2direct (N × H)
4. C2×#16840099C2semidirect
5. C2×#16840082C2semidirect
6. C2×#16840106C2semidirect
7. C2×#16840105C2semidirect
8. C2×#16840089C2semidirect
9. C2×#16840088C2semidirect
10. C2×#16840094C2semidirect
11. C2×#16840077C2semidirect
12. C2×#16839798C2semidirect
13. C2×#16839759C2semidirect
14. C2×#16839756C2semidirect
15. C22×#14519689C2semidirect
16. C2×C61×#427C2semidirect
36. #117×D61C22semidirect
41. #16840106C22semidirect
42. #16840105C22semidirect
43. #16840099C22semidirect
44. #16840094C22semidirect
45. #16840089C22semidirect
46. #16840088C22semidirect
47. #16840082C22semidirect
48. #16840077C22semidirect
49. #16839798C22semidirect
50. C2×#14519710C22semidirect
51. C2×#14519710C22semidirect
52. C2×#14519708C22semidirect
53. C2×#14519708C22semidirect
54. #16839759C22semidirect
55. #16839756C22semidirect
56. C2×#14519702C22semidirect
57. C2×#14519702C22semidirect
58. C2×#14519700C22semidirect
59. C2×#14519700C22semidirect
60. C2×#14519699C22semidirect
61. C2×#14519699C22semidirect
62. C2×#14519697C22semidirect
63. C2×#14519697C22semidirect
68. C2×#14519689C22semidirect
72. C61×#427C22semidirect
73. C2×#107×C61C22semidirect
74. C2×#107×C61C22semidirect
75. C2×#106×C61C22semidirect
76. C2×#106×C61C22semidirect
145. #14519710C23semidirect
146. #14519710C23semidirect
147. #14519708C23semidirect
148. #14519708C23semidirect
149. #14519702C23semidirect
150. #14519702C23semidirect
151. #14519700C23semidirect
152. #14519700C23semidirect
153. #14519699C23semidirect
154. #14519699C23semidirect
155. #14519697C23semidirect
156. #14519697C23semidirect
178. #107×C61C23semidirect
179. #107×C61C23semidirect
180. #106×C61C23semidirect
181. #106×C61C23semidirect
405. C2×#427D61semidirect
410. C2×C61#3091semidirect
453. #427C2×D61semidirect
456. C2×#107C2×D61semidirect
457. C2×#107C2×D61semidirect
460. C2×#106C2×D61semidirect
461. C2×#106C2×D61semidirect
477. C61C2×#3091semidirect
565. #107C22×D61semidirect
566. #107C22×D61semidirect
569. #106C22×D61semidirect
570. #106C22×D61semidirect
797. C2#21455736direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168402742
C2×#117×D612
#214557362
C2×#168400992
C2×#168400822
C2×#168401062
C2×#168401052
C2×#168400892
C2×#168400882
C2×#168400942
C2×#168400772
C2×#168397982
C2×#168397592
C2×#168397562
C22×#145196892
C2×C61×#4272
C2×#309161