Finite Group Databasebeta

← C2×#21456497 #30549892

Subgroups — C2×#21456497 #30549892

Order 15616.

2034 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840385C211yesmaximal, characteristic, complemented
2C2×#16840365C211yesmaximal, characteristic, complemented
3#21456497C2116yesmaximal, direct product factor
4C2×#16840169C211yesmaximal, characteristic, complemented
5C2×#16840148C211yesmaximal, characteristic, complemented
6C2×#16840118C211yesmaximal, characteristic, complemented
7C2×#16840107C211yesmaximal, characteristic, complemented
8C2×#16840013C211yesmaximal, characteristic, complemented
9C2×#16840010C211yesmaximal, characteristic, complemented
10C2×#16839998C211yesmaximal, characteristic, complemented
11C2×#16839873C211yesmaximal, characteristic, complemented
12C2×#16839863C211yesmaximal, characteristic, complemented
13C2×#16839847C211yesmaximal, characteristic, complemented
14C2×#16839842C211yesmaximal, characteristic, complemented
15C2×#16839717C211yesmaximal, characteristic, complemented
16C2×C61×#465C211yesmaximal, characteristic, complemented
17C22×#11758201C2211yescharacteristic
18C22×D488C2211yescharacteristic
19C22×#11758199C2211yescharacteristic
20C22×#11758194C2211yescharacteristic
21#16840385—24no—
22#16840385C2218yescomplemented
23#16840365—24no—
24#16840365C2218yescomplemented
25C2×#14519776C2211yescharacteristic
26C2×#14519773C2211yescharacteristic
27C2×#14519772—21no—
28C2×#14519768C2211yescharacteristic
29C2×#14519766C2211yescharacteristic
30C2×#14519763—21no—
31C2×#14519761—21no—
32C2×#14519759—21no—
33C2×#14519759—21no—
34C2×#14519757—21no—
35C2×#14519751C2211yescharacteristic
36C2×#14519751C2211yescharacteristic
37C2×#14519749—21no—
38C2×#14519748—21no—
39C2×Q8×Dic61C2211yescharacteristic
40C2×D4×Dic61C2211yescharacteristic
41C2×#14519739C2211yescharacteristic
42C2×#14519739C2211yescharacteristic
43C2×#14519736C2211yescharacteristic
44#16840169C2218yescomplemented
45#16840148C2218yescomplemented
46#16840118C2218yescomplemented
47#16840107C2218yescomplemented
48#16840013C2218yescomplemented
49#16840010C2218yescomplemented
50#16839998C2218yescomplemented
51#16839873C2218yescomplemented
52#16839863C2218yescomplemented
53#16839847C2218yescomplemented
54#16839842C2218yescomplemented
55C2×#14519711C2211yescharacteristic
56C2×#14519710C2211yescharacteristic
57C2×#14519708C2211yescharacteristic
58C2×#14519701C2211yescharacteristic
59C2×#14519699C2211yescharacteristic
60C2×#14519699C2211yescharacteristic
61C2×#14519698C2211yescharacteristic
62C2×#14519697C2211yescharacteristic
63C2×#14519697C2211yescharacteristic
64#16839717C2218yescomplemented
65C2×#14519687C2211yescharacteristic
66C2×#14519687C2211yescharacteristic
67C2×C8×Dic61C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C22×SD16×C61C2211yescharacteristic
70C23×C8×C61C2211yescharacteristic
71C2×C22⋊Q8×C61C2211yescharacteristic
72C2×#121×C61C2211yescharacteristic
73C61×#465C2218yescomplemented
74C2×#106×C61C2211yescharacteristic
75C2×#103×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C22×Dic122—21no—
78C22×D244C2311yescharacteristic
79C22×D244C2311yescharacteristic
80C22×C22⋊D61—21no—
81C22×C22⋊D61—21no—
82C22×C22⋊D61—21no—
83C22×C22⋊D61—21no—
84C23×Dic61—21no—
85C22×C4×D61—21no—
86C22×C4×D61—21no—
87C2×#11758201—24no—
88C2×#11758201C2314yes—
89C2×D488—24no—
90C2×D488C2314yes—
91C2×#11758199—24no—
92C2×#11758199C2314yes—
93C2×#11758194—24no—
94C2×#11758194C2314yes—
95C22×#92418C2311yescharacteristic
96C22×#92418C2311yescharacteristic
97#14519776—22no—
98#14519776C2314yes—
99#14519773—22no—
100#14519773C2314yes—
101#14519772—28no—
102#14519768—22no—
103#14519768C2314yes—
104#14519766—22no—
105#14519766C2314yes—
106#14519763—28no—
107#14519761—28no—
108#14519759—28no—
109#14519759—28no—
110#14519757—28no—
111#14519751—22no—
112#14519751—22no—
113#14519751C2314yes—
114#14519751C2314yes—
115#14519749—28no—
116#14519748—28no—
117Q8×Dic61—22no—
118Q8×Dic61C2314yes—
119D4×Dic61—22no—
120D4×Dic61C2314yes—
121#14519739—22no—
122#14519739—22no—
123#14519739C2314yes—
124#14519739C2314yes—
125#14519736D414yes—
126#14519736C2314yes—
127C2×C4⋊Dic61—21no—
128C2×C4⋊Dic61—21no—
129C2×C4⋊Dic61D411yescharacteristic
130C2×C4⋊Dic61D411yescharacteristic
131C2×C4⋊Dic61C2311yescharacteristic
132C2×C4⋊Dic61C2311yescharacteristic
133C2×#11758196—21no—
134C2×#11758196—21no—
135C2×C22⋊Dic61—21no—
136C2×C22⋊Dic61D411yescharacteristic
137C2×C22⋊Dic61D411yescharacteristic
138C2×#11758198—21no—
139C2×#11758198—21no—
140C2×#11758198—21no—
141C2×#11758198—21no—
142C2×#11758198—21no—
143C2×#11758198—21no—
144C2×C4×Dic61—21no—
145C2×C4×Dic61C2311yescharacteristic
146C2×C4×Dic61C2311yescharacteristic
147#14519711C2314yes—
148#14519710C2314yes—
149#14519708C2314yes—
150#14519701C2314yes—
151#14519699C2314yes—
152#14519699C2314yes—
153#14519698C2314yes—
154#14519697C2314yes—
155#14519697C2314yes—
156#14519687C2314yes—
157#14519687C2314yes—
158C8×Dic61C2314yes—
159C8×Dic61C2314yes—
160C22×Q8×C61C2311yescharacteristic
161C22×D4×C61—21no—
162C22×D4×C61C2311yescharacteristic
163C23×C4×C61C2311yescharacteristic
164C2×SD16×C61—24no—
165C2×SD16×C61C2314yes—
166C22×C8×C61—24no—
167C22×C8×C61C2311yescharacteristic
168C22×C8×C61C2314yes—
169C22×C8×C61C2311yescharacteristic
170C22⋊Q8×C61—22no—
171C22⋊Q8×C61C2314yes—
172#121×C61—22no—
173#121×C61C2314yes—
174C2×C4⋊C4×C61—21no—
175C2×C4⋊C4×C61C2311yescharacteristic
176C2×C4⋊C4×C61C2311yescharacteristic
177C2×C22⋊C4×C61—21no—
178C2×C22⋊C4×C61—21no—
179#106×C61C2314yes—
180#103×C61C2314yes—
181#102×C61C2314yes—
182C24×C61—21no—
183C24×C61C2×D411yescharacteristic
184C23×D61—21no—
185C23×D61—21no—
186C2×Q8×C61—21no—
187C2×Q8×C61—22no—
188C2×Q8×C61—22no—
189C2×Q8×C61C2412yes—
190C2×D4×C61—24no—
191C2×D4×C61—21no—
192C2×D4×C61—22no—
193C2×D4×C61—22no—
194C2×D4×C61—82no—
195C2×D4×C61C2412yes—
196C22×C4×C61—22no—
197C22×C4×C61—22no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61C2×D411yescharacteristic
202C22×C4×C61C2×D412yes—
203C22×C4×C61C2412yes—
204C22×C4×C61C2411yescharacteristic
205C2×C22⋊D61—24no—
206C2×C22⋊D61—24no—
207C2×C22⋊D61—24no—
208C2×C22⋊D61—24no—
209C2×C22⋊D61—82no—
210C2×C22⋊D61—82no—
211C2×C22⋊D61—82no—
212C2×C22⋊D61—82no—
213C22×Dic61—21no—
214C22×Dic61—21no—
215C22×Dic61—24no—
216C22×Dic61—82no—
217C22×Dic61C2×D411yescharacteristic
218C22×Dic61C2×D411yescharacteristic
219C22×Dic61C2×D411yescharacteristic
220C22×Dic61C2×D411yescharacteristic
221C2×D244—22no—
222C2×D244—22no—
223C2×D244—22no—
224C2×D244—22no—
225C2×D244—21no—
226C2×D244—21no—
227C2×D244C2412yes—
228C2×D244C2412yes—
229C2×C4×D61—24no—
230C2×C4×D61—24no—
231C2×C4×D61—82no—
232C2×C4×D61—82no—
233C2×Dic122—24no—
234C2×Dic122—82no—
235SD16×C61—28no—
236C2×C8×C61—22no—
237C2×C8×C61—28no—
238C2×C8×C61#4114yes—
239C2×C8×C61C2412yes—
240C2×C8×C61C2412yes—
241C4⋊C4×C61—24no—
242C4⋊C4×C61—21no—
243C4⋊C4×C61—21no—
244C4⋊C4×C61C2412yes—
245C4⋊C4×C61C2412yes—
246C22⋊C4×C61—24no—
247C22⋊C4×C61—24no—
248C22⋊Dic61—24no—
249C22⋊Dic61C2×D414yes—
250C22⋊Dic61C2×D414yes—
251#11758201—28no—
252#11758199—28no—
253#11758198—24no—
254#11758198—24no—
255#11758198—24no—
256#11758198—24no—
257#11758198—24no—
258#11758198—24no—
259C4⋊Dic61—21no—
260C4⋊Dic61—21no—
261C4⋊Dic61—24no—
262C4⋊Dic61—24no—
263C4⋊Dic61C2×D414yes—
264C4⋊Dic61C2×D414yes—
265C4⋊Dic61C2412yes—
266C4⋊Dic61C2412yes—
267#11758196—24no—
268#11758196—24no—
269C4×Dic61—24no—
270C4×Dic61C2×D412yes—
271C4×Dic61C2×D412yes—
272C4×Dic61C2412yes—
273C4×Dic61C2412yes—
274#11758194—28no—
275C2×#92418—22no—
276C2×#92418#4114yes—
277C2×#92418C2412yes—
278C2×#92418C2412yes—
279D488—28no—
280C23×C61—22no—
281C23×C61—22no—
282C23×C61—22no—
283C23×C61—22no—
284C23×C61—42no—
285C23×C61—42no—
286C23×C61—42no—
287C23×C61C22×D412yes—
288C23×C61C22×D411yescharacteristic
289C22×D61—22no—
290C22×D61—22no—
291C22×D61—42no—
292C22×D61—42no—
293C22×D61—42no—
294C22×D61—42no—
295C22×D61—42no—
296C22×D61—42no—
297Q8×C61—22no—
298Q8×C61—22no—
299Q8×C61—42no—
300D4×C61—22no—
301D4×C61—22no—
302D4×C61—42no—
303D4×C61—84no—
304C2×C4×C61—22no—
305C2×C4×C61—24no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—22no—
311C2×C4×C61—42no—
312C2×C4×C61—42no—
313C2×C4×C61—42no—
314C2×C4×C61C22×D412yes—
315C2×C4×C61C22×D411yescharacteristic
316C2×C4×C61C2×#4112yes—
317C2×C4×C61C2×#4112yes—
318C2×C4×C61C2511yescharacteristic
319C22⋊D61—84no—
320C22⋊D61—84no—
321C22⋊D61—84no—
322C22⋊D61—84no—
323C2×Dic61—22no—
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—22no—
329C2×Dic61—42no—
330C2×Dic61—42no—
331C2×Dic61—84no—
332C2×Dic61C22×D412yes—
333C2×Dic61C22×D412yes—
334C2×Dic61C22×D412yes—
335C2×Dic61C22×D412yes—
336D244—22no—
337D244—22no—
338D244—22no—
339D244—22no—
340D244—42no—
341D244—42no—
342C4×D61—84no—
343C4×D61—84no—
344Dic122—84no—
345C8×C61—22no—
346C8×C61C2×#4114yes—
347#92418—22no—
348#92418C2×#4114yes—
349C2×#3179—611nomaximal, Sylow
350C22×C61—22no—
351C22×C61—22no—
352C22×C61—22no—
353C22×C61—44no—
354C22×C61—42no—
355C22×C61—42no—
356C22×C61—42no—
357C22×C61—84no—
358C22×C61#53212yes—
359C22×C61#57612yes—
360C22×C61#57712yes—
361C22×C61C23×D411yescharacteristic
362C2×D61—42no—
363C2×D61—42no—
364C2×D61—42no—
365C2×D61—42no—
366C2×D61—42no—
367C2×D61—42no—
368C2×D61—84no—
369C2×D61—84no—
370C4×C61—22no—
371C4×C61—42no—
372C4×C61—42no—
373C4×C61—42no—
374C4×C61#53212yes—
375C4×C61C22×#4111yescharacteristic
376C4×C61C22×#4111yescharacteristic
377Dic61—22no—
378Dic61—22no—
379Dic61—22no—
380Dic61—22no—
381Dic61—42no—
382Dic61—42no—
383C2×#542—611no—
384C2×#540—611no—
385#3179—6116no—
386C2×#501—611no—
387C2×#496—611no—
388C2×#488—611no—
389C2×#486—611no—
390C2×#469—611no—
391C2×#468—611no—
392C2×#466—611no—
393C2×#465D6111yescharacteristic, complemented
394C2×#442—611no—
395C2×#440—611no—
396C2×C4×SD16—611no—
397C2×C4×D8—611no—
398C2×#405—611no—
399C2×C61—42no—
400C2×C61—82no—
401C2×C61#317914yescomplemented
402C2×C61C2×#53211yescharacteristic
403C2×C61C2×#57611yescharacteristic
404C2×C61C2×#57711yescharacteristic
405D61—82no—
406D61—82no—
407C22×SD16—611no—
408C22×SD16C2×D6111yescharacteristic
409C22×D8—611no—
410C22×D8—611no—
411C22×M16—611no—
412C23×C8C2×D6111yescharacteristic
413#542—618no—
414#542—1224no—
415#540—618no—
416#540—1224no—
417C2×C4⋊Q8—611no—
418C2×#127—611no—
419C2×#126—1221no—
420C2×#125—611no—
421C2×#124—611no—
422C2×#124—1221no—
423C2×#123—1221no—
424C2×#123—1221no—
425C2×#123—1221no—
426C2×C22⋊Q8—1221no—
427C2×C22⋊Q8C2×D6111yescharacteristic
428C2×#121—611no—
429C2×#121—611no—
430C2×#121—1221no—
431C2×#121—1221no—
432C2×#121C2×D6111yescharacteristic
433C2×C4×Q8—611no—
434C2×C4×D4—611no—
435C2×C4×D4—611no—
436C2×C4×D4—611no—
437C2×#117—611no—
438#501—618no—
439#496—618no—
440#488—618no—
441#486—618no—
442#469—618no—
443#468—618no—
444#466—618no—
445#465C2×D6118yescomplemented
446#442—618no—
447#440—618no—
448C4×SD16—618no—
449C4×D8—618no—
450C2×#107—611no—
451C2×#107—611no—
452C2×#106—611no—
453C2×#106C2×D6111yescharacteristic
454C2×#103—611no—
455C2×#103C2×D6111yescharacteristic
456C2×#102—611no—
457C2×#102—611no—
458C2×#102—611no—
459C2×#102—611no—
460C2×#102—611no—
461C2×#102C2×D6111yescharacteristic
462#405—618no—
463C2×#97—611no—
464C2×#97—611no—
465C2×C4×C8—611no—
466C2×C4×C8—611no—
467C61C2×#317911yescharacteristic, complemented, Sylow
468C22×Q8—1221no—
469C22×Q8C22×D6111yescharacteristic
470C22×D4—21no—
471C22×D4—611no—
472C22×D4—611no—
473C22×D4—1221no—
474C22×D4—1221no—
475C22×D4—1221no—
476C22×D4—1221no—
477C22×D4C22×D6111yescharacteristic
478C23×C4—1221no—
479C23×C4—1221no—
480C23×C4—1221no—
481C23×C4C22×D6111yescharacteristic
482C2×SD16—24no—
483C2×SD16—614no—
484C2×SD16—1224no—
485C2×SD16C22×D6114yes—
486C2×D8—614no—
487C2×D8—614no—
488C2×D8—1224no—
489C2×D8—1224no—
490C2×M16—614no—
491C2×M16—1224no—
492C22×C8—24no—
493C22×C8—611no—
494C22×C8—611no—
495C22×C8C22×D6111yescharacteristic
496C22×C8C22×D6114yes—
497C22×C8C22×D6111yescharacteristic
498C4⋊Q8—614no—
499C4⋊Q8—1222no—
500#127—614no—
501#127—1222no—
502#126—1228no—
503#125—614no—
504#125—1222no—
505#124—614no—
506#124—1222no—
507#124—1228no—
508#123—1228no—
509#123—1228no—
510#123—1228no—
511C22⋊Q8—22no—
512C22⋊Q8—1228no—
513C22⋊Q8C22×D6114yes—
514#121—22no—
515#121—614no—
516#121—614no—
517#121—1228no—
518#121—1228no—
519#121—1222no—
520#121—1222no—
521#121C22×D6114yes—
522C4×Q8—614no—
523C4×Q8—1222no—
524C4×D4—614no—
525C4×D4—614no—
526C4×D4—614no—
527C4×D4—1222no—
528C4×D4—1222no—
529C4×D4—1222no—
530#117—614no—
531#117—614no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—611no—
534C2×C4⋊C4—611no—
535C2×C4⋊C4—611no—
536C2×C4⋊C4—611no—
537C2×C4⋊C4—1221no—
538C2×C4⋊C4—1221no—
539C2×C4⋊C4—1221no—
540C2×C4⋊C4—1221no—
541C2×C4⋊C4C22×D6111yescharacteristic
542C2×C4⋊C4C22×D6111yescharacteristic
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—611no—
546C2×C22⋊C4—611no—
547C2×C22⋊C4—1221no—
548C2×C22⋊C4—1221no—
549C2×C22⋊C4—1221no—
550C2×C22⋊C4—1221no—
551C2×C22⋊C4—1221no—
552C2×C22⋊C4—1221no—
553C2×C22⋊C4—1221no—
554C2×C42—611no—
555C2×C42—611no—
556C2×C42—1221no—
557#107—614no—
558#107—614no—
559#106—614no—
560#106C22×D6114yes—
561#103—614no—
562#103C22×D6114yes—
563#102—614no—
564#102—614no—
565#102—614no—
566#102—614no—
567#102—614no—
568#102C22×D6114yes—
569#97—614no—
570#97—614no—
571C4×C8—614no—
572C4×C8—614no—
573C24—21no—
574C24—1221no—
575C24—1221no—
576C24D4×D6111yescharacteristic
577C2×Q8—21no—
578C2×Q8—22no—
579C2×Q8—22no—
580C2×Q8—1224no—
581C2×Q8—4882no—
582C2×Q8C23×D6112yes—
583C2×D4—24no—
584C2×D4—21no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—82no—
588C2×D4—612no—
589C2×D4—612no—
590C2×D4—1224no—
591C2×D4—1224no—
592C2×D4—1224no—
593C2×D4—1224no—
594C2×D4—1221no—
595C2×D4—1221no—
596C2×D4—1222no—
597C2×D4—1222no—
598C2×D4—1222no—
599C2×D4—1222no—
600C2×D4—4882no—
601C2×D4—4882no—
602C2×D4—4882no—
603C2×D4—4882no—
604C2×D4C23×D6112yes—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—611no—
611C22×C4—611no—
612C22×C4—611no—
613C22×C4—611no—
614C22×C4—1224no—
615C22×C4—1224no—
616C22×C4—1224no—
617C22×C4—1221no—
618C22×C4—1221no—
619C22×C4—4882no—
620C22×C4—4882no—
621C22×C4—4882no—
622C22×C4D4×D6112yes—
623C22×C4D4×D6111yescharacteristic
624C22×C4C23×D6112yes—
625C22×C4C23×D6111yescharacteristic
626SD16—28no—
627SD16—1228no—
628D8—1228no—
629D8—1228no—
630M16—1228no—
631C2×C8—22no—
632C2×C8—28no—
633C2×C8—614no—
634C2×C8—612no—
635C2×C8—612no—
636C2×C8—1222no—
637C2×C8#1175822414yes—
638C2×C8C23×D6112yes—
639C2×C8C23×D6112yes—
640C4⋊C4—24no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—614no—
644C4⋊C4—614no—
645C4⋊C4—612no—
646C4⋊C4—612no—
647C4⋊C4—1224no—
648C4⋊C4—1224no—
649C4⋊C4—1224no—
650C4⋊C4—1224no—
651C4⋊C4—1221no—
652C4⋊C4—1221no—
653C4⋊C4C23×D6112yes—
654C4⋊C4C23×D6112yes—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—614no—
658C22⋊C4—614no—
659C22⋊C4—1224no—
660C22⋊C4—1224no—
661C22⋊C4—1224no—
662C22⋊C4—1224no—
663C22⋊C4—1224no—
664C22⋊C4—1224no—
665C22⋊C4—1224no—
666C42—612no—
667C42—612no—
668C42—612no—
669C42—612no—
670C42—1224no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—1222no—
679C23—1222no—
680C23—2442no—
681C23—2442no—
682C23—2442no—
683C23—2442no—
684C23—2442no—
685C23—2442no—
686C23C2×D4×D6112yes—
687C23C2×D4×D6111yescharacteristic
688Q8—22no—
689Q8—22no—
690Q8—42no—
691Q8—4884no—
692D4—22no—
693D4—22no—
694D4—42no—
695D4—84no—
696D4—1222no—
697D4—1222no—
698D4—1222no—
699D4—1222no—
700D4—4884no—
701D4—4884no—
702D4—4884no—
703D4—4884no—
704D4—2442no—
705D4—2442no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—612no—
717C2×C4—612no—
718C2×C4—612no—
719C2×C4—612no—
720C2×C4—1222no—
721C2×C4—1222no—
722C2×C4—1222no—
723C2×C4—1222no—
724C2×C4—1222no—
725C2×C4—1222no—
726C2×C4—4884no—
727C2×C4—4884no—
728C2×C4—4884no—
729C2×C4—2442no—
730C2×C4—2442no—
731C2×C4C2×D4×D6112yes—
732C2×C4C2×D4×D6111yescharacteristic
733C2×C4#41×D6112yes—
734C2×C4C2×#1175822412yes—
735C2×C4C24×D6111yescharacteristic
736C8—22no—
737C8—614no—
738C8—1222no—
739C8C2×#1175822414yes—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—44no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—84no—
748C22—4884no—
749C22—4884no—
750C22—2442no—
751C22—2442no—
752C22—2442no—
753C22—2442no—
754C22—2442no—
755C22—2442no—
756C22#1684030712yes—
757C22#1684056412yes—
758C22#1684056812yes—
759C22C22×D4×D6111yescharacteristic
760C4—22no—
761C4—42no—
762C4—42no—
763C4—42no—
764C4—1222no—
765C4—1222no—
766C4—1222no—
767C4—1222no—
768C4—2442no—
769C4—2442no—
770C4#1684030712yes—
771C4C2×#41×D6111yescharacteristic
772C4C22×#1175822411yescharacteristic
773C2—42no—
774C2—82no—
775C2—4882no—
776C2—4882no—
777C2#2145649714yesdirect product factor
778C2C2×#1684030711yescharacteristic
779C2C2×#1684056411yescharacteristic
780C2C2×#1684056811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#465C2
socleC23×C61C22×D4
hypercenterC2×#465D61
hypocenterC61C2×#3179
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×#16840385C2semidirect
2. C2×#16840365C2semidirect
3. #21456497C2direct (N × H)
4. C2×#16840169C2semidirect
5. C2×#16840148C2semidirect
6. C2×#16840118C2semidirect
7. C2×#16840107C2semidirect
8. C2×#16840013C2semidirect
9. C2×#16840010C2semidirect
10. C2×#16839998C2semidirect
11. C2×#16839873C2semidirect
12. C2×#16839863C2semidirect
13. C2×#16839847C2semidirect
14. C2×#16839842C2semidirect
15. C2×#16839717C2semidirect
16. C2×C61×#465C2semidirect
22. #16840385C22semidirect
24. #16840365C22semidirect
44. #16840169C22semidirect
45. #16840148C22semidirect
46. #16840118C22semidirect
47. #16840107C22semidirect
48. #16840013C22semidirect
49. #16840010C22semidirect
50. #16839998C22semidirect
51. #16839873C22semidirect
52. #16839863C22semidirect
53. #16839847C22semidirect
54. #16839842C22semidirect
64. #16839717C22semidirect
73. C61×#465C22semidirect
393. C2×#465D61semidirect
401. C2×C61#3179semidirect
445. #465C2×D61semidirect
467. C61C2×#3179semidirect
777. C2#21456497direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403852
C2×#168403652
#214564972
C2×#168401692
C2×#168401482
C2×#168401182
C2×#168401072
C2×#168400132
C2×#168400102
C2×#168399982
C2×#168398732
C2×#168398632
C2×#168398472
C2×#168398422
C2×#168397172
C2×C61×#4652
C2×#317961