Finite Group Databasebeta

← C2×#21456513 #30549920

Subgroups — C2×#21456513 #30549920

Order 15616.

2278 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840309C211yesmaximal, characteristic, complemented
2C2×#16840299C211yesmaximal, characteristic, complemented
3#21456513C2116yesmaximal, direct product factor
4C2×#16840170C211yesmaximal, characteristic, complemented
5C2×#16840148C211yesmaximal, characteristic, complemented
6C2×#16840125C211yesmaximal, characteristic, complemented
7C2×#16840123C211yesmaximal, characteristic, complemented
8C2×#16839999C211yesmaximal, characteristic, complemented
9C2×#16839997C211yesmaximal, characteristic, complemented
10C2×#16839994C211yesmaximal, characteristic, complemented
11C2×#16839988C211yesmaximal, characteristic, complemented
12C2×#16839875C211yesmaximal, characteristic, complemented
13C2×#16839872C211yesmaximal, characteristic, complemented
14C2×#16839860C211yesmaximal, characteristic, complemented
15C2×#97×D61C211yesmaximal, characteristic, complemented
16C2×C61×#440C211yesmaximal, characteristic, complemented
17C22×#11758222—21no—
18C22×#11758201C2211yescharacteristic
19C22×D488C2211yescharacteristic
20C22×#11758199C2211yescharacteristic
21C22×C8×D61C2211yescharacteristic
22C22×C8×D61C2211yescharacteristic
23#16840309—24no—
24#16840309C2218yescomplemented
25C2×#14519776C2211yescharacteristic
26C2×#14519773C2211yescharacteristic
27#16840299—24no—
28#16840299C2218yescomplemented
29C2×#14519772—21no—
30C2×#14519768C2211yescharacteristic
31C2×#14519766C2211yescharacteristic
32C2×#14519763—21no—
33C2×#14519762—21no—
34C2×#14519753C2211yescharacteristic
35C2×#14519752C2211yescharacteristic
36C2×#14519752C2211yescharacteristic
37C2×#14519750—21no—
38C2×#14519748C2211yescharacteristic
39C2×C4×D244—21no—
40C2×C4×D244C2211yescharacteristic
41C2×C4×D244C2211yescharacteristic
42C2×C4×C22⋊D61—21no—
43C2×#14519734—21no—
44C2×C42×D61C2211yescharacteristic
45#16840170C2218yescomplemented
46#16840148C2218yescomplemented
47#16840125C2218yescomplemented
48#16840123C2218yescomplemented
49#16839999C2218yescomplemented
50#16839997C2218yescomplemented
51#16839994C2218yescomplemented
52#16839988C2218yescomplemented
53#16839875C2218yescomplemented
54#16839872C2218yescomplemented
55#16839860C2218yescomplemented
56C2×#14519710C2211yescharacteristic
57C2×#14519709C2211yescharacteristic
58C2×#14519708C2211yescharacteristic
59C2×#14519701C2211yescharacteristic
60C2×#14519699C2211yescharacteristic
61C2×#14519699C2211yescharacteristic
62C2×#14519698C2211yescharacteristic
63C2×#14519697C2211yescharacteristic
64C2×#14519697C2211yescharacteristic
65C2×#14519688C2211yescharacteristic
66C2×#14519687C2211yescharacteristic
67C2×#14519687C2211yescharacteristic
68#97×D61C2218yescomplemented
69C22×SD16×C61C2211yescharacteristic
70C2×C4×Q8×C61C2211yescharacteristic
71C2×C4×D4×C61C2211yescharacteristic
72C61×#440C2218yescomplemented
73C2×#107×C61C2211yescharacteristic
74C2×#103×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×#97×C61C2211yescharacteristic
77C2×#11758222—28no—
78C2×#11758222—48no—
79C22×Dic122—21no—
80C22×D244—21no—
81C22×D244—21no—
82C22×D244C2311yescharacteristic
83C22×D244C2311yescharacteristic
84C22×C22⋊D61—21no—
85C22×C22⋊D61—21no—
86C22×C22⋊D61—21no—
87C22×C4×D61—21no—
88C22×C4×D61—21no—
89C22×C4×D61D411yescharacteristic
90C22×C4×D61D411yescharacteristic
91C22×C4×D61C2311yescharacteristic
92C2×#11758201—24no—
93C2×#11758201C2314yes—
94C2×D488—24no—
95C2×D488C2314yes—
96C2×#11758199—24no—
97C2×#11758199C2314yes—
98C22×#92418C2311yescharacteristic
99C22×#92418C2311yescharacteristic
100C2×C8×D61—24no—
101C2×C8×D61—24no—
102C2×C8×D61C2314yes—
103C2×C8×D61C2314yes—
104#14519776—22no—
105#14519776C2314yes—
106#14519773—22no—
107#14519773C2314yes—
108#14519772—28no—
109#14519768—22no—
110#14519768C2314yes—
111#14519766—22no—
112#14519766C2314yes—
113#14519763—28no—
114#14519762—28no—
115#14519753—22no—
116#14519753C2314yes—
117#14519752—22no—
118#14519752—22no—
119#14519752C2314yes—
120#14519752C2314yes—
121#14519750—28no—
122#14519748—22no—
123#14519748C2314yes—
124C4×D244—28no—
125C4×D244—22no—
126C4×D244—22no—
127C4×D244C2314yes—
128C4×D244C2314yes—
129C4×C22⋊D61—28no—
130#14519734—28no—
131C2×C4⋊Dic61—21no—
132C2×C4⋊Dic61C2311yescharacteristic
133C2×C4⋊Dic61C2311yescharacteristic
134C2×#11758196—21no—
135C2×#11758196—21no—
136C2×#11758196—21no—
137C2×C22⋊Dic61—21no—
138C2×#11758198—21no—
139C2×#11758198—21no—
140C2×#11758198—21no—
141C2×#11758198—21no—
142C2×#11758198—21no—
143C2×#11758198—21no—
144C2×#11758198—21no—
145C2×C4×Dic61D411yescharacteristic
146C2×C4×Dic61D411yescharacteristic
147C2×C4×Dic61C2311yescharacteristic
148C42×D61D414yes—
149C42×D61C2314yes—
150#14519710C2314yes—
151#14519709C2314yes—
152#14519708C2314yes—
153#14519701C2314yes—
154#14519699C2314yes—
155#14519699C2314yes—
156#14519698C2314yes—
157#14519697C2314yes—
158#14519697C2314yes—
159#14519688C2314yes—
160#14519687C2314yes—
161#14519687C2314yes—
162C22×Q8×C61C2311yescharacteristic
163C22×D4×C61C2311yescharacteristic
164C23×C4×C61—21no—
165C2×SD16×C61—24no—
166C2×SD16×C61C2314yes—
167C22×C8×C61C2311yescharacteristic
168C22×C8×C61C2311yescharacteristic
169C4×Q8×C61—22no—
170C4×Q8×C61C2314yes—
171C4×D4×C61—22no—
172C4×D4×C61C2314yes—
173C2×C4⋊C4×C61—21no—
174C2×C4⋊C4×C61C2311yescharacteristic
175C2×C4⋊C4×C61C2311yescharacteristic
176C2×C22⋊C4×C61—21no—
177C2×C42×C61—21no—
178C2×C42×C61C2311yescharacteristic
179#107×C61C2314yes—
180#103×C61C2314yes—
181#102×C61C2314yes—
182#97×C61C2314yes—
183C24×C61—21no—
184C23×D61—21no—
185C23×D61—21no—
186C23×D61C2×D411yescharacteristic
187C2×Q8×C61—21no—
188C2×Q8×C61—22no—
189C2×Q8×C61—22no—
190C2×Q8×C61C2412yes—
191C2×D4×C61—21no—
192C2×D4×C61—22no—
193C2×D4×C61—22no—
194C2×D4×C61C2412yes—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—24no—
199C22×C4×C61—44no—
200C22×C4×C61C2×D411yescharacteristic
201C22×C4×C61C2×D411yescharacteristic
202C22×C4×C61C2411yescharacteristic
203C2×C22⋊D61—24no—
204C2×C22⋊D61—24no—
205C2×C22⋊D61—24no—
206C2×C22⋊D61—44no—
207C2×C22⋊D61—44no—
208C2×C22⋊D61—44no—
209C22×Dic61—21no—
210C22×Dic61—21no—
211C22×Dic61C2×D411yescharacteristic
212C22×Dic61C2×D411yescharacteristic
213C22×Dic61C2×D411yescharacteristic
214#11758222—432no—
215C2×D244—22no—
216C2×D244—22no—
217C2×D244—22no—
218C2×D244—22no—
219C2×D244—24no—
220C2×D244—24no—
221C2×D244—21no—
222C2×D244—21no—
223C2×D244—44no—
224C2×D244—44no—
225C2×D244C2412yes—
226C2×D244C2412yes—
227C2×C4×D61—24no—
228C2×C4×D61—22no—
229C2×C4×D61—22no—
230C2×C4×D61—24no—
231C2×C4×D61—24no—
232C2×C4×D61—42no—
233C2×C4×D61—44no—
234C2×C4×D61—44no—
235C2×C4×D61C2×D414yes—
236C2×C4×D61C2×D412yes—
237C2×C4×D61C2×D414yes—
238C2×C4×D61C2412yes—
239C2×Dic122—24no—
240C2×Dic122—44no—
241SD16×C61—28no—
242C2×C8×C61—22no—
243C2×C8×C61#4114yescomplemented
244C2×C8×C61C2412yes—
245C2×C8×C61C2412yes—
246C4⋊C4×C61—24no—
247C4⋊C4×C61—21no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61C2412yes—
250C4⋊C4×C61C2412yes—
251C22⋊C4×C61—24no—
252C42×C61—24no—
253C42×C61C2×D412yes—
254C42×C61C2412yes—
255C22⋊Dic61—24no—
256#11758201—28no—
257#11758199—28no—
258#11758198—24no—
259#11758198—24no—
260#11758198—24no—
261#11758198—24no—
262#11758198—24no—
263#11758198—24no—
264#11758198—24no—
265C4⋊Dic61—21no—
266C4⋊Dic61—21no—
267C4⋊Dic61—24no—
268C4⋊Dic61C2412yes—
269C4⋊Dic61C2412yes—
270#11758196—24no—
271#11758196—24no—
272#11758196—24no—
273C4×Dic61C2×D412yes—
274C4×Dic61C2×D414yes—
275C4×Dic61C2×D414yes—
276C4×Dic61C2412yes—
277C2×#92418—22no—
278C2×#92418#4114yescomplemented
279C2×#92418C2412yes—
280C2×#92418C2412yes—
281D488—28no—
282C8×D61—28no—
283C8×D61—28no—
284C23×C61—22no—
285C23×C61—42no—
286C23×C61—42no—
287C23×C61—42no—
288C23×C61C22×D411yescharacteristic
289C22×D61—22no—
290C22×D61—22no—
291C22×D61—22no—
292C22×D61—22no—
293C22×D61—42no—
294C22×D61—42no—
295C22×D61—42no—
296C22×D61—42no—
297C22×D61—42no—
298C22×D61—42no—
299C22×D61AGL(1,ℤ/8)14yes—
300C22×D61C22×D412yes—
301Q8×C61—22no—
302Q8×C61—22no—
303Q8×C61—42no—
304D4×C61—22no—
305D4×C61—22no—
306D4×C61—42no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—48no—
313C2×C4×C61—42no—
314C2×C4×C61—42no—
315C2×C4×C61—42no—
316C2×C4×C61C22×D412yes—
317C2×C4×C61C22×D412yes—
318C2×C4×C61C22×D411yescharacteristic
319C2×C4×C61C2×#4112yes—
320C2×C4×C61C2×#4112yes—
321C2×C4×C61C2511yescharacteristic
322C22⋊D61—48no—
323C22⋊D61—48no—
324C22⋊D61—48no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—42no—
331C2×Dic61—42no—
332C2×Dic61C22×D412yes—
333C2×Dic61C22×D412yes—
334C2×Dic61C22×D412yes—
335D244—22no—
336D244—22no—
337D244—22no—
338D244—22no—
339D244—48no—
340D244—48no—
341D244—42no—
342D244—42no—
343C4×D61—28no—
344C4×D61—24no—
345C4×D61—22no—
346C4×D61—22no—
347C4×D61—44no—
348C4×D61—48no—
349C4×D61—48no—
350Dic122—48no—
351C8×C61—22no—
352C8×C61C2×#4114yescomplemented
353#92418—22no—
354#92418C2×#4114yescomplemented
355C2×#3180—611nomaximal, Sylow
356C22×C61—42no—
357C22×C61—42no—
358C22×C61—42no—
359C22×C61—84no—
360C22×C61#53212yes—
361C22×C61C2×AGL(1,ℤ/8)12yes—
362C22×C61#57512yes—
363C22×C61C23×D411yescharacteristic
364C2×D61—28no—
365C2×D61—22no—
366C2×D61—22no—
367C2×D61—42no—
368C2×D61—42no—
369C2×D61—42no—
370C2×D61—42no—
371C2×D61—42no—
372C2×D61—42no—
373C2×D61—84no—
374C2×D61—84no—
375C2×D61C2×AGL(1,ℤ/8)14yes—
376C4×C61—22no—
377C4×C61—22no—
378C4×C61—42no—
379C4×C61—42no—
380C4×C61—42no—
381C4×C61#53212yes—
382C4×C61C22×#4111yescharacteristic
383C4×C61C22×#4111yescharacteristic
384Dic61—22no—
385Dic61—22no—
386Dic61—22no—
387Dic61—42no—
388Dic61—42no—
389C2×#532—611no—
390C2×#529—611no—
391#3180—6116no—
392C2×#501—611no—
393C2×#496—611no—
394C2×#490—611no—
395C2×#489—611no—
396C2×#466—611no—
397C2×#466—611no—
398C2×#465—611no—
399C2×#465—611no—
400C2×#442—611no—
401C2×#442—611no—
402C2×#440—611no—
403C2×#440D6111yescharacteristic, complemented
404C22×#97—611no—
405C2×C61—82no—
406C2×C61#318014yescomplemented
407C2×C61C2×#53211yescharacteristic
408C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
409C2×C61C2×#57511yescharacteristic
410D61—24no—
411D61—82no—
412D61—82no—
413C22×#41—1221no—
414C22×SD16—611no—
415C22×SD16C2×D6111yescharacteristic
416C22×D8—611no—
417C22×D8—611no—
418C23×C8—611no—
419C23×C8—611no—
420#532—618no—
421#532—1224no—
422C2×C4⋊Q8—611no—
423C2×#127—611no—
424#529—618no—
425#529—1224no—
426C2×#126—1221no—
427C2×#125—611no—
428C2×#124—611no—
429C2×#124—1221no—
430C2×#123—1221no—
431C2×C22⋊Q8—611no—
432C2×#121—611no—
433C2×#121—611no—
434C2×#121—611no—
435C2×#121—1221no—
436C2×C4×Q8C2×D6111yescharacteristic
437C2×C4×D4—611no—
438C2×C4×D4—611no—
439C2×C4×D4—1221no—
440C2×C4×D4—1221no—
441C2×C4×D4C2×D6111yescharacteristic
442C2×#117—1221no—
443C22×C42—611no—
444#501—618no—
445#496—618no—
446#490—618no—
447#489—618no—
448#466—618no—
449#466—618no—
450#465—618no—
451#465—618no—
452#442—618no—
453#442—618no—
454#440—618no—
455#440C2×D6118yescomplemented
456C2×#107—611no—
457C2×#107C2×D6111yescharacteristic
458C2×#106—611no—
459C2×#106—611no—
460C2×#103—611no—
461C2×#103C2×D6111yescharacteristic
462C2×#102—611no—
463C2×#102—611no—
464C2×#102—611no—
465C2×#102—611no—
466C2×#102—611no—
467C2×#102C2×D6111yescharacteristic
468C2×#97—611no—
469C2×#97—611no—
470C2×#97—611no—
471C2×#97—618no—
472C2×#97C2×D6111yescharacteristic
473C61C2×#318011yescharacteristic, complemented, Sylow
474C2×#41—1228no—
475C2×#41—2448no—
476C22×Q8—1221no—
477C22×Q8C22×D6111yescharacteristic
478C22×D4—611no—
479C22×D4—611no—
480C22×D4—1221no—
481C22×D4—1221no—
482C22×D4—1221no—
483C22×D4—1221no—
484C22×D4—1221no—
485C22×D4C22×D6111yescharacteristic
486C23×C4—21no—
487C23×C4—611no—
488C23×C4—611no—
489C23×C4—611no—
490C23×C4—1221no—
491C23×C4—1221no—
492C2×SD16—24no—
493C2×SD16—614no—
494C2×SD16—1224no—
495C2×SD16C22×D6114yes—
496C2×D8—614no—
497C2×D8—614no—
498C2×D8—1224no—
499C2×D8—1224no—
500C22×C8—611no—
501C22×C8—611no—
502C22×C8—614no—
503C22×C8—614no—
504C22×C8—1224no—
505C22×C8—1224no—
506C22×C8C22×D6111yescharacteristic
507C22×C8C22×D6111yescharacteristic
508C4⋊Q8—614no—
509C4⋊Q8—1222no—
510#127—614no—
511#127—1222no—
512#126—1228no—
513#125—614no—
514#125—1222no—
515#124—614no—
516#124—1228no—
517#124—1222no—
518#123—1228no—
519C22⋊Q8—614no—
520C22⋊Q8—1222no—
521#121—614no—
522#121—614no—
523#121—614no—
524#121—1228no—
525#121—1222no—
526#121—1222no—
527#121—1222no—
528C4×Q8—22no—
529C4×Q8C22×D6114yes—
530C4×D4—22no—
531C4×D4—614no—
532C4×D4—614no—
533C4×D4—1228no—
534C4×D4—1228no—
535C4×D4—1222no—
536C4×D4—1222no—
537C4×D4C22×D6114yes—
538#117—1228no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—611no—
541C2×C4⋊C4—611no—
542C2×C4⋊C4—1221no—
543C2×C4⋊C4—1221no—
544C2×C4⋊C4—1221no—
545C2×C4⋊C4—1221no—
546C2×C4⋊C4C22×D6111yescharacteristic
547C2×C4⋊C4C22×D6111yescharacteristic
548C2×C22⋊C4—21no—
549C2×C22⋊C4—1221no—
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—611no—
559C2×C42—611no—
560C2×C42—611no—
561C2×C42—614no—
562C2×C42—614no—
563C2×C42C22×D6111yescharacteristic
564#107—614no—
565#107C22×D6114yes—
566#106—614no—
567#106—614no—
568#103—614no—
569#103C22×D6114yes—
570#102—614no—
571#102—614no—
572#102—614no—
573#102—614no—
574#102—614no—
575#102C22×D6114yes—
576#97—614no—
577#97—614no—
578#97—614no—
579#97C22×D6114yes—
580C24—21no—
581C24—611no—
582C24—1221no—
583C24—1221no—
584#41—24432no—
585C2×Q8—21no—
586C2×Q8—22no—
587C2×Q8—22no—
588C2×Q8—1224no—
589C2×Q8—2444no—
590C2×Q8C23×D6112yes—
591C2×D4—21no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—612no—
595C2×D4—612no—
596C2×D4—1224no—
597C2×D4—1224no—
598C2×D4—1224no—
599C2×D4—1224no—
600C2×D4—1224no—
601C2×D4—1221no—
602C2×D4—1221no—
603C2×D4—1222no—
604C2×D4—1222no—
605C2×D4—1222no—
606C2×D4—1222no—
607C2×D4—2444no—
608C2×D4—2444no—
609C2×D4—2444no—
610C2×D4—2444no—
611C2×D4—2444no—
612C2×D4C23×D6112yes—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—24no—
617C22×C4—44no—
618C22×C4—611no—
619C22×C4—611no—
620C22×C4—611no—
621C22×C4—612no—
622C22×C4—614no—
623C22×C4—612no—
624C22×C4—614no—
625C22×C4—1224no—
626C22×C4—1222no—
627C22×C4—1222no—
628C22×C4—1221no—
629C22×C4—1221no—
630C22×C4—1224no—
631C22×C4—1224no—
632C22×C4—2442no—
633C22×C4—2444no—
634C22×C4—2444no—
635C22×C4D4×D6111yescharacteristic
636C22×C4D4×D6111yescharacteristic
637C22×C4C23×D6111yescharacteristic
638SD16—28no—
639SD16—1228no—
640D8—1228no—
641D8—1228no—
642C2×C8—22no—
643C2×C8—614no—
644C2×C8—612no—
645C2×C8—612no—
646C2×C8—1228no—
647C2×C8—1222no—
648C2×C8—1228no—
649C2×C8#1175822214yescomplemented
650C2×C8C23×D6112yes—
651C2×C8C23×D6112yes—
652C4⋊C4—24no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—612no—
656C4⋊C4—612no—
657C4⋊C4—1224no—
658C4⋊C4—1224no—
659C4⋊C4—1224no—
660C4⋊C4—1224no—
661C4⋊C4—1221no—
662C4⋊C4—1221no—
663C4⋊C4C23×D6112yes—
664C4⋊C4C23×D6112yes—
665C22⋊C4—24no—
666C22⋊C4—1224no—
667C22⋊C4—1224no—
668C22⋊C4—1224no—
669C22⋊C4—1224no—
670C22⋊C4—1224no—
671C22⋊C4—1224no—
672C22⋊C4—1224no—
673C22⋊C4—1224no—
674C42—24no—
675C42—614no—
676C42—614no—
677C42—612no—
678C42—612no—
679C42D4×D6112yes—
680C42C23×D6112yes—
681C23—22no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—614no—
686C23—612no—
687C23—1222no—
688C23—1222no—
689C23—1222no—
690C23—1222no—
691C23—2442no—
692C23—2442no—
693C23—2442no—
694C23—2442no—
695C23—2442no—
696C23—2442no—
697C23C2×D4×D6111yescharacteristic
698Q8—22no—
699Q8—22no—
700Q8—42no—
701Q8—2448no—
702D4—22no—
703D4—22no—
704D4—42no—
705D4—1222no—
706D4—1222no—
707D4—1222no—
708D4—1222no—
709D4—2448no—
710D4—2448no—
711D4—2448no—
712D4—2448no—
713D4—2448no—
714D4—2442no—
715D4—2442no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—48no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—612no—
726C2×C4—612no—
727C2×C4—612no—
728C2×C4—1228no—
729C2×C4—1222no—
730C2×C4—1222no—
731C2×C4—1222no—
732C2×C4—1224no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—1222no—
737C2×C4—2444no—
738C2×C4—2448no—
739C2×C4—2448no—
740C2×C4—2442no—
741C2×C4—2442no—
742C2×C4C2×D4×D6112yes—
743C2×C4C2×D4×D6112yes—
744C2×C4C2×D4×D6111yescharacteristic
745C2×C4#41×D6112yes—
746C2×C4C2×#1175822212yes—
747C2×C4C24×D6111yescharacteristic
748C8—22no—
749C8—614no—
750C8—1222no—
751C8C2×#1175822214yescomplemented
752C22—42no—
753C22—42no—
754C22—42no—
755C22—84no—
756C22—614no—
757C22—1222no—
758C22—1228no—
759C22—1222no—
760C22—4884no—
761C22—4884no—
762C22—2442no—
763C22—2442no—
764C22—2442no—
765C22—2442no—
766C22—2442no—
767C22—2442no—
768C22#1684030912yes—
769C22AGL(1,ℤ/8)×D6112yes—
770C22#1684056112yes—
771C22C22×D4×D6111yescharacteristic
772C4—22no—
773C4—22no—
774C4—42no—
775C4—42no—
776C4—42no—
777C4—1222no—
778C4—1222no—
779C4—1222no—
780C4—2442no—
781C4—2442no—
782C4#1684030912yes—
783C4C2×#41×D6111yescharacteristic
784C4C22×#1175822211yescharacteristic
785C2—82no—
786C2—1224no—
787C2—4882no—
788C2—4882no—
789C2#2145651314yesdirect product factor
790C2C2×#1684030911yescharacteristic
791C2C2×AGL(1,ℤ/8)×D6111yescharacteristic
792C2C2×#1684056111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#440C2
socleC23×C61C22×D4
hypercenterC2×#440D61
hypocenterC61C2×#3180
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C2×#16840309C2semidirect
2. C2×#16840299C2semidirect
3. #21456513C2direct (N × H)
4. C2×#16840170C2semidirect
5. C2×#16840148C2semidirect
6. C2×#16840125C2semidirect
7. C2×#16840123C2semidirect
8. C2×#16839999C2semidirect
9. C2×#16839997C2semidirect
10. C2×#16839994C2semidirect
11. C2×#16839988C2semidirect
12. C2×#16839875C2semidirect
13. C2×#16839872C2semidirect
14. C2×#16839860C2semidirect
15. C2×#97×D61C2semidirect
16. C2×C61×#440C2semidirect
24. #16840309C22semidirect
28. #16840299C22semidirect
45. #16840170C22semidirect
46. #16840148C22semidirect
47. #16840125C22semidirect
48. #16840123C22semidirect
49. #16839999C22semidirect
50. #16839997C22semidirect
51. #16839994C22semidirect
52. #16839988C22semidirect
53. #16839875C22semidirect
54. #16839872C22semidirect
55. #16839860C22semidirect
68. #97×D61C22semidirect
72. C61×#440C22semidirect
243. C2×C8×C61#41semidirect
278. C2×#92418#41semidirect
352. C8×C61C2×#41semidirect
354. #92418C2×#41semidirect
403. C2×#440D61semidirect
406. C2×C61#3180semidirect
455. #440C2×D61semidirect
473. C61C2×#3180semidirect
649. C2×C8#11758222semidirect
751. C8C2×#11758222semidirect
789. C2#21456513direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403092
C2×#168402992
#214565132
C2×#168401702
C2×#168401482
C2×#168401252
C2×#168401232
C2×#168399992
C2×#168399972
C2×#168399942
C2×#168399882
C2×#168398752
C2×#168398722
C2×#168398602
C2×#97×D612
C2×C61×#4402
C2×#318061