Finite Group Databasebeta

← C2×#21457223 #30552916

Subgroups — C2×#21457223 #30552916

Order 15616.

1946 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×#16840379C211yesmaximal, characteristic, complemented
2C2×#16840365C211yesmaximal, characteristic, complemented
3#21457223C2116yesmaximal, direct product factor
4C2×#16840068C211yesmaximal, characteristic, complemented
5C2×#16840064C211yesmaximal, characteristic, complemented
6C2×#16840050C211yesmaximal, characteristic, complemented
7C2×#16840041C211yesmaximal, characteristic, complemented
8C2×#16840013C211yesmaximal, characteristic, complemented
9C2×#16840006C211yesmaximal, characteristic, complemented
10C2×#16839991C211yesmaximal, characteristic, complemented
11C2×#16839961C211yesmaximal, characteristic, complemented
12C2×#16839976C211yesmaximal, characteristic, complemented
13C2×#16839975C211yesmaximal, characteristic, complemented
14C2×#16839955C211yesmaximal, characteristic, complemented
15C2×#16839788C211yesmaximal, characteristic, complemented
16C2×C61×#466C211yesmaximal, characteristic, complemented
17C22×#11758190C2211yescharacteristic
18C22×#11758200C2211yescharacteristic
19C22×#11758199C2211yescharacteristic
20C22×#11758194C2211yescharacteristic
21#16840379—24no—
22#16840379C2218yescomplemented
23#16840365—24no—
24#16840365C2218yescomplemented
25C2×#14519776C2211yescharacteristic
26C2×#14519773C2211yescharacteristic
27C2×#14519770—21no—
28C2×#14519768C2211yescharacteristic
29C2×#14519764—21no—
30C2×#14519764C2211yescharacteristic
31C2×#14519761—21no—
32C2×#14519759—21no—
33C2×#14519758—21no—
34C2×#14519756C2211yescharacteristic
35C2×#14519754—21no—
36C2×#14519751C2211yescharacteristic
37C2×#14519749—21no—
38C2×#14519748—21no—
39C2×#14519742C2211yescharacteristic
40C2×D4×Dic61C2211yescharacteristic
41C2×D4×Dic61C2211yescharacteristic
42C2×#14519739C2211yescharacteristic
43C2×#14519736C2211yescharacteristic
44#16840068C2218yescomplemented
45#16840064C2218yescomplemented
46#16840050C2218yescomplemented
47#16840041C2218yescomplemented
48#16840013C2218yescomplemented
49#16840006C2218yescomplemented
50#16839991C2218yescomplemented
51#16839976C2218yescomplemented
52#16839975C2218yescomplemented
53#16839961C2218yescomplemented
54#16839955C2218yescomplemented
55C2×#14519710C2211yescharacteristic
56C2×#14519709C2211yescharacteristic
57C2×#14519708C2211yescharacteristic
58#16839788C2218yescomplemented
59C2×#14519706C2211yescharacteristic
60C2×#14519706C2211yescharacteristic
61C2×#14519706C2211yescharacteristic
62C2×#14519706C2211yescharacteristic
63C2×#14519702C2211yescharacteristic
64C2×#14519700C2211yescharacteristic
65C2×#14519699C2211yescharacteristic
66C2×#14519698C2211yescharacteristic
67C2×#14519698C2211yescharacteristic
68C2×#14519697C2211yescharacteristic
69C22×D8×C61C2211yescharacteristic
70C23×C8×C61C2211yescharacteristic
71C2×#121×C61C2211yescharacteristic
72C2×#121×C61C2211yescharacteristic
73C61×#466C2218yescomplemented
74C2×#107×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C22×Dic122—21no—
78C22×Dic122C2311yescharacteristic
79C22×D244C2311yescharacteristic
80C22×C22⋊D61—21no—
81C22×C22⋊D61—21no—
82C22×C22⋊D61—21no—
83C23×Dic61—21no—
84C23×Dic61—21no—
85C22×C4×D61—21no—
86C2×#11758190—42no—
87C2×#11758190C2314yes—
88C2×#11758200—42no—
89C2×#11758200C2314yes—
90C2×#11758199—42no—
91C2×#11758199C2314yes—
92C2×#11758194—42no—
93C2×#11758194C2314yes—
94C22×#92418C2311yescharacteristic
95C22×#92418C2311yescharacteristic
96#14519776—22no—
97#14519776C2314yes—
98#14519773—22no—
99#14519773C2314yes—
100#14519770—28no—
101#14519768—22no—
102#14519768C2314yes—
103#14519764—28no—
104#14519764—22no—
105#14519764C2314yes—
106#14519761—28no—
107#14519759—28no—
108#14519758—28no—
109#14519756—22no—
110#14519756C2314yes—
111#14519754—28no—
112#14519751—22no—
113#14519751C2314yes—
114#14519749—28no—
115#14519748—28no—
116#14519742—22no—
117#14519742C2314yes—
118D4×Dic61—22no—
119D4×Dic61—22no—
120D4×Dic61C2314yes—
121D4×Dic61C2314yes—
122#14519739—22no—
123#14519739C2314yes—
124#14519736D414yes—
125#14519736C2314yes—
126C2×C4⋊Dic61—21no—
127C2×C4⋊Dic61D411yescharacteristic
128C2×C4⋊Dic61D411yescharacteristic
129C2×C4⋊Dic61C2311yescharacteristic
130C2×C4⋊Dic61C2311yescharacteristic
131C2×#11758196—21no—
132C2×#11758196—21no—
133C2×#11758196—21no—
134C2×#11758196—21no—
135C2×C22⋊Dic61—21no—
136C2×C22⋊Dic61—21no—
137C2×C22⋊Dic61—21no—
138C2×C22⋊Dic61—21no—
139C2×C22⋊Dic61—21no—
140C2×C22⋊Dic61D411yescharacteristic
141C2×C22⋊Dic61D411yescharacteristic
142C2×#11758198—21no—
143C2×#11758198—21no—
144C2×C4×Dic61—21no—
145C2×C4×Dic61C2311yescharacteristic
146C2×C4×Dic61C2311yescharacteristic
147#14519710C2314yes—
148#14519709C2314yes—
149#14519708C2314yes—
150#14519706C2314yes—
151#14519706C2314yes—
152#14519706C2314yes—
153#14519706C2314yes—
154#14519702C2314yes—
155#14519700C2314yes—
156#14519699C2314yes—
157#14519698C2314yes—
158#14519698C2314yes—
159#14519697C2314yes—
160C22×D4×C61—21no—
161C22×D4×C61—21no—
162C22×D4×C61C2311yescharacteristic
163C22×D4×C61C2311yescharacteristic
164C23×C4×C61C2311yescharacteristic
165C2×D8×C61—42no—
166C2×D8×C61C2314yes—
167C22×C8×C61—42no—
168C22×C8×C61C2311yescharacteristic
169C22×C8×C61C2311yescharacteristic
170C22×C8×C61C2314yes—
171#121×C61—22no—
172#121×C61—22no—
173#121×C61C2314yes—
174#121×C61C2314yes—
175C2×C4⋊C4×C61C2311yescharacteristic
176C2×C4⋊C4×C61C2311yescharacteristic
177C2×C22⋊C4×C61—21no—
178C2×C22⋊C4×C61—21no—
179#107×C61C2314yes—
180#102×C61C2314yes—
181#102×C61C2314yes—
182C24×C61—21no—
183C24×C61—21no—
184C24×C61C2×D411yescharacteristic
185C23×D61—21no—
186C2×D4×C61—24no—
187C2×D4×C61—24no—
188C2×D4×C61—21no—
189C2×D4×C61—21no—
190C2×D4×C61—22no—
191C2×D4×C61—22no—
192C2×D4×C61—22no—
193C2×D4×C61—22no—
194C2×D4×C61—82no—
195C2×D4×C61—82no—
196C2×D4×C61C2412yes—
197C2×D4×C61C2412yes—
198C22×C4×C61—22no—
199C22×C4×C61—22no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61C2×D411yescharacteristic
203C22×C4×C61C2×D412yes—
204C22×C4×C61C2412yes—
205C22×C4×C61C2411yescharacteristic
206C2×C22⋊D61—24no—
207C2×C22⋊D61—24no—
208C2×C22⋊D61—24no—
209C2×C22⋊D61—82no—
210C2×C22⋊D61—82no—
211C2×C22⋊D61—82no—
212C22×Dic61—21no—
213C22×Dic61—21no—
214C22×Dic61—21no—
215C22×Dic61—24no—
216C22×Dic61—24no—
217C22×Dic61—82no—
218C22×Dic61—82no—
219C22×Dic61C2×D411yescharacteristic
220C22×Dic61C2×D411yescharacteristic
221C22×Dic61C2×D411yescharacteristic
222C22×Dic61C2×D411yescharacteristic
223C2×D244—22no—
224C2×D244—22no—
225C2×D244—21no—
226C2×D244C2412yes—
227C2×C4×D61—24no—
228C2×C4×D61—82no—
229C2×Dic122—22no—
230C2×Dic122—22no—
231C2×Dic122—21no—
232C2×Dic122—24no—
233C2×Dic122—82no—
234C2×Dic122C2412yes—
235D8×C61—44no—
236C2×C8×C61—22no—
237C2×C8×C61—22no—
238C2×C8×C61—44no—
239C2×C8×C61C2412yes—
240C2×C8×C61C2412yes—
241C4⋊C4×C61—21no—
242C4⋊C4×C61—21no—
243C4⋊C4×C61C2412yes—
244C4⋊C4×C61C2412yes—
245C22⋊C4×C61—24no—
246C22⋊C4×C61—24no—
247C22⋊Dic61—24no—
248C22⋊Dic61—24no—
249C22⋊Dic61—24no—
250C22⋊Dic61—24no—
251C22⋊Dic61—24no—
252C22⋊Dic61C2×D414yes—
253C22⋊Dic61C2×D414yes—
254#11758200—44no—
255#11758199—44no—
256#11758198—24no—
257#11758198—24no—
258C4⋊Dic61—21no—
259C4⋊Dic61—21no—
260C4⋊Dic61—24no—
261C4⋊Dic61C2×D414yes—
262C4⋊Dic61C2×D414yes—
263C4⋊Dic61C2412yes—
264C4⋊Dic61C2412yes—
265#11758196—24no—
266#11758196—24no—
267#11758196—24no—
268#11758196—24no—
269C4×Dic61—24no—
270C4×Dic61C2×D412yes—
271C4×Dic61C2×D412yes—
272C4×Dic61C2412yes—
273C4×Dic61C2412yes—
274#11758194—44no—
275C2×#92418—22no—
276C2×#92418—22no—
277C2×#92418C2412yes—
278C2×#92418C2412yes—
279#11758190—44no—
280C23×C61—22no—
281C23×C61—22no—
282C23×C61—22no—
283C23×C61—22no—
284C23×C61—22no—
285C23×C61—42no—
286C23×C61—42no—
287C23×C61—42no—
288C23×C61—42no—
289C23×C61—42no—
290C23×C61—42no—
291C23×C61C22×D412yes—
292C23×C61C22×D411yescharacteristic
293C22×D61—22no—
294C22×D61—42no—
295C22×D61—42no—
296C22×D61—42no—
297D4×C61—22no—
298D4×C61—22no—
299D4×C61—22no—
300D4×C61—22no—
301D4×C61—42no—
302D4×C61—42no—
303D4×C61—84no—
304D4×C61—84no—
305C2×C4×C61—22no—
306C2×C4×C61—24no—
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×C61C22×D412yes—
314C2×C4×C61C22×D411yescharacteristic
315C2×C4×C61H(5,𝔽2)12yes—
316C2×C4×C612−1+412yes—
317C2×C4×C61C2511yescharacteristic
318C22⋊D61—84no—
319C22⋊D61—84no—
320C22⋊D61—84no—
321C2×Dic61—22no—
322C2×Dic61—22no—
323C2×Dic61—22no—
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—42no—
329C2×Dic61—42no—
330C2×Dic61—42no—
331C2×Dic61—84no—
332C2×Dic61—84no—
333C2×Dic61C22×D412yes—
334C2×Dic61C22×D412yes—
335C2×Dic61C22×D412yes—
336C2×Dic61C22×D412yes—
337D244—22no—
338D244—22no—
339D244—42no—
340C4×D61—84no—
341Dic122—22no—
342Dic122—22no—
343Dic122—42no—
344Dic122—84no—
345C8×C61—22no—
346C8×C61—22no—
347#92418—22no—
348#92418—22no—
349C2×#3257—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—42no—
358C22×C61—42no—
359C22×C61—42no—
360C22×C61—84no—
361C22×C61—84no—
362C22×C61#53712yes—
363C22×C61#57612yes—
364C22×C61#57712yes—
365C22×C61C23×D411yescharacteristic
366C2×D61—42no—
367C2×D61—42no—
368C2×D61—42no—
369C2×D61—84no—
370C4×C61—22no—
371C4×C61—42no—
372C4×C61—42no—
373C4×C61#53712yes—
374C4×C61C2×H(5,𝔽2)11yescharacteristic
375C4×C61C2×2−1+411yescharacteristic
376Dic61—22no—
377Dic61—22no—
378Dic61—22no—
379Dic61—22no—
380Dic61—42no—
381Dic61—42no—
382Dic61—42no—
383C2×#542—611no—
384C2×#540—611no—
385#3257—6116no—
386C2×#479—611no—
387C2×#478—611no—
388C2×#476—611no—
389C2×#474—611no—
390C2×#469—611no—
391C2×#468—611no—
392C2×#466D6111yescharacteristic, complemented
393C2×#465—611no—
394C2×#460—611no—
395C2×#463—611no—
396C2×#463—611no—
397C2×#459—611no—
398C2×#424—611no—
399C2×C61—42no—
400C2×C61—82no—
401C2×C61—82no—
402C2×C61#325714yescomplemented
403C2×C61C2×#53711yescharacteristic
404C2×C61C2×#57611yescharacteristic
405C2×C61C2×#57711yescharacteristic
406D61—82no—
407C22×SD16—611no—
408C22×SD16—611no—
409C22×D8—611no—
410C22×D8C2×D6111yescharacteristic
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—611no—
427C2×C22⋊Q8—1221no—
428C2×#121—611no—
429C2×#121—1221no—
430C2×#121—1221no—
431C2×#121C2×D6111yescharacteristic
432C2×#121C2×D6111yescharacteristic
433C2×C4×Q8—611no—
434C2×C4×D4—611no—
435C2×C4×D4—611no—
436C2×C4×D4—611no—
437C2×#117—611no—
438#479—618no—
439#478—618no—
440#476—618no—
441#474—618no—
442#469—618no—
443#468—618no—
444#466C2×D6118yescomplemented
445#465—618no—
446#463—618no—
447#463—618no—
448#460—618no—
449#459—618no—
450C2×#107—611no—
451C2×#107C2×D6111yescharacteristic
452C2×#106—611no—
453C2×#106—611no—
454#424—618no—
455C2×C4⋊C8—611no—
456C2×C4⋊C8—611no—
457C2×C4⋊C8—611no—
458C2×C4⋊C8—611no—
459C2×#103—611no—
460C2×#103—611no—
461C2×#102—611no—
462C2×#102—611no—
463C2×#102—611no—
464C2×#102—611no—
465C2×#102C2×D6111yescharacteristic
466C2×#102C2×D6111yescharacteristic
467C61C2×#325711yescharacteristic, complemented, Sylow
468C22×Q8—611no—
469C22×Q8—1221no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4—611no—
473C22×D4—1221no—
474C22×D4—1221no—
475C22×D4—1221no—
476C22×D4C22×D6111yescharacteristic
477C22×D4C22×D6111yescharacteristic
478C23×C4—1221no—
479C23×C4—1221no—
480C23×C4—1221no—
481C23×C4C22×D6111yescharacteristic
482C2×SD16—614no—
483C2×SD16—614no—
484C2×SD16—2442no—
485C2×SD16—2442no—
486C2×D8—42no—
487C2×D8—614no—
488C2×D8—2442no—
489C2×D8C22×D6114yes—
490C2×M16—614no—
491C2×M16—2442no—
492C22×C8—42no—
493C22×C8—611no—
494C22×C8—611no—
495C22×C8C22×D6111yescharacteristic
496C22×C8C22×D6111yescharacteristic
497C22×C8C22×D6114yes—
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—614no—
512C22⋊Q8—1228no—
513C22⋊Q8—1222no—
514#121—22no—
515#121—22no—
516#121—614no—
517#121—1228no—
518#121—1228no—
519#121—1222no—
520#121C22×D6114yes—
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—611no—
533C2×C4⋊C4—611no—
534C2×C4⋊C4—611no—
535C2×C4⋊C4—611no—
536C2×C4⋊C4—1221no—
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#107C22×D6114yes—
559#106—614no—
560#106—614no—
561C4⋊C8—614no—
562C4⋊C8—614no—
563C4⋊C8—614no—
564C4⋊C8—614no—
565#103—614no—
566#103—614no—
567#102—614no—
568#102—614no—
569#102—614no—
570#102—614no—
571#102C22×D6114yes—
572#102C22×D6114yes—
573C24—21no—
574C24—21no—
575C24—1221no—
576C24D4×D6111yescharacteristic
577C2×Q8—612no—
578C2×Q8—1224no—
579C2×Q8—1221no—
580C2×Q8—1222no—
581C2×Q8—1222no—
582C2×Q8—4882no—
583C2×D4—24no—
584C2×D4—24no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—22no—
591C2×D4—82no—
592C2×D4—82no—
593C2×D4—612no—
594C2×D4—1224no—
595C2×D4—1224no—
596C2×D4—1224no—
597C2×D4—1221no—
598C2×D4—1222no—
599C2×D4—1222no—
600C2×D4—4882no—
601C2×D4—4882no—
602C2×D4—4882no—
603C2×D4C23×D6112yes—
604C2×D4C23×D6112yes—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—611no—
610C22×C4—611no—
611C22×C4—611no—
612C22×C4—611no—
613C22×C4—1224no—
614C22×C4—1224no—
615C22×C4—1224no—
616C22×C4—1221no—
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—2444no—
627SD16—2444no—
628D8—44no—
629D8—2444no—
630M16—2444no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—44no—
634C2×C8—612no—
635C2×C8—612no—
636C2×C8—1222no—
637C2×C8—1222no—
638C2×C8C23×D6112yes—
639C2×C8C23×D6112yes—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—614no—
643C4⋊C4—614no—
644C4⋊C4—612no—
645C4⋊C4—612no—
646C4⋊C4—1224no—
647C4⋊C4—1224no—
648C4⋊C4—1224no—
649C4⋊C4—1224no—
650C4⋊C4—1221no—
651C4⋊C4—1221no—
652C4⋊C4—1224no—
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—22no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—1222no—
683C23—2442no—
684C23—2442no—
685C23—2442no—
686C23C2×D4×D6112yes—
687C23C2×D4×D6111yescharacteristic
688Q8—1222no—
689Q8—1222no—
690Q8—4884no—
691Q8—2442no—
692D4—22no—
693D4—22no—
694D4—22no—
695D4—22no—
696D4—42no—
697D4—42no—
698D4—84no—
699D4—84no—
700D4—1222no—
701D4—1222no—
702D4—4884no—
703D4—4884no—
704D4—4884no—
705D4—2442no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—612no—
715C2×C4—612no—
716C2×C4—612no—
717C2×C4—612no—
718C2×C4—1222no—
719C2×C4—1222no—
720C2×C4—1222no—
721C2×C4—1222no—
722C2×C4—1222no—
723C2×C4—1222no—
724C2×C4—1222no—
725C2×C4—4884no—
726C2×C4—4884no—
727C2×C4—4884no—
728C2×C4—2442no—
729C2×C4—2442no—
730C2×C4—2442no—
731C2×C4C2×D4×D6112yes—
732C2×C4C2×D4×D6111yescharacteristic
733C2×C4#1451982212yes—
734C2×C4#1451982412yes—
735C2×C4C24×D6111yescharacteristic
736C8—22no—
737C8—22no—
738C8—1222no—
739C8—1222no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—44no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—84no—
751C22—84no—
752C22—4884no—
753C22—2442no—
754C22—2442no—
755C22—2442no—
756C22#1684033912yes—
757C22#1684056312yes—
758C22#1684056912yes—
759C22C22×D4×D6111yescharacteristic
760C4—22no—
761C4—42no—
762C4—42no—
763C4—1222no—
764C4—1222no—
765C4—1222no—
766C4—1222no—
767C4—2442no—
768C4—2442no—
769C4—2442no—
770C4#1684033912yes—
771C4C2×#1451982211yescharacteristic
772C4C2×#1451982411yescharacteristic
773C2—42no—
774C2—82no—
775C2—82no—
776C2—4882no—
777C2#2145722314yesdirect product factor
778C2C2×#1684033911yescharacteristic
779C2C2×#1684056311yescharacteristic
780C2C2×#1684056911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#466C2
socleC23×C61C22×D4
hypercenterC2×#466D61
hypocenterC61C2×#3257
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#466

Complements

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

NH ≅ G/Ntype
1. C2×#16840379C2semidirect
2. C2×#16840365C2semidirect
3. #21457223C2direct (N × H)
4. C2×#16840068C2semidirect
5. C2×#16840064C2semidirect
6. C2×#16840050C2semidirect
7. C2×#16840041C2semidirect
8. C2×#16840013C2semidirect
9. C2×#16840006C2semidirect
10. C2×#16839991C2semidirect
11. C2×#16839961C2semidirect
12. C2×#16839976C2semidirect
13. C2×#16839975C2semidirect
14. C2×#16839955C2semidirect
15. C2×#16839788C2semidirect
16. C2×C61×#466C2semidirect
22. #16840379C22semidirect
24. #16840365C22semidirect
44. #16840068C22semidirect
45. #16840064C22semidirect
46. #16840050C22semidirect
47. #16840041C22semidirect
48. #16840013C22semidirect
49. #16840006C22semidirect
50. #16839991C22semidirect
51. #16839976C22semidirect
52. #16839975C22semidirect
53. #16839961C22semidirect
54. #16839955C22semidirect
58. #16839788C22semidirect
73. C61×#466C22semidirect
392. C2×#466D61semidirect
402. C2×C61#3257semidirect
444. #466C2×D61semidirect
467. C61C2×#3257semidirect
777. C2#21457223direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403792
C2×#168403652
#214572232
C2×#168400682
C2×#168400642
C2×#168400502
C2×#168400412
C2×#168400132
C2×#168400062
C2×#168399912
C2×#168399612
C2×#168399762
C2×#168399752
C2×#168399552
C2×#168397882
C2×C61×#4662
C2×#325761