Finite Group Databasebeta

← C2×#21456509 #30549904

Subgroups — C2×#21456509 #30549904

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×#16840386C211yesmaximal, characteristic, complemented
2C2×#16840366C211yesmaximal, characteristic, complemented
3#21456509C2116yesmaximal, direct product factor
4C2×#16840168C211yesmaximal, characteristic, complemented
5C2×#16840149C211yesmaximal, characteristic, complemented
6C2×#16840117C211yesmaximal, characteristic, complemented
7C2×#16840014C211yesmaximal, characteristic, complemented
8C2×#16840007C211yesmaximal, characteristic, complemented
9C2×#16839997C211yesmaximal, characteristic, complemented
10C2×#16839990C211yesmaximal, characteristic, complemented
11C2×#16839871C211yesmaximal, characteristic, complemented
12C2×#16839859C211yesmaximal, characteristic, complemented
13C2×#16839853C211yesmaximal, characteristic, complemented
14C2×#16839842C211yesmaximal, characteristic, complemented
15C2×#16839716C211yesmaximal, characteristic, complemented
16C2×C61×#486C211yesmaximal, characteristic, complemented
17C22×#11758200C2211yescharacteristic
18C22×#11758200C2211yescharacteristic
19C22×#11758199C2211yescharacteristic
20C22×#11758199C2211yescharacteristic
21C22×#11758189C2211yescharacteristic
22C22×C8×D61C2211yescharacteristic
23#16840386—24no—
24#16840386C2218yescomplemented
25#16840366—24no—
26#16840366C2218yescomplemented
27C2×#14519772—21no—
28C2×#14519769C2211yescharacteristic
29C2×#14519766—21no—
30C2×#14519765C2211yescharacteristic
31C2×#14519762—21no—
32C2×#14519758—21no—
33C2×#14519758—21no—
34C2×#14519757C2211yescharacteristic
35C2×#14519753—21no—
36C2×#14519752C2211yescharacteristic
37C2×#14519749—21no—
38C2×#14519749—21no—
39C2×#14519748C2211yescharacteristic
40C2×#14519748C2211yescharacteristic
41C2×#14519742C2211yescharacteristic
42C2×D4×Dic61C2211yescharacteristic
43C2×D4×Dic61C2211yescharacteristic
44C2×#14519739C2211yescharacteristic
45C2×#14519734C2211yescharacteristic
46#16840168C2218yescomplemented
47#16840149C2218yescomplemented
48#16840117C2218yescomplemented
49#16840014C2218yescomplemented
50#16840007C2218yescomplemented
51#16839997C2218yescomplemented
52#16839990C2218yescomplemented
53#16839871C2218yescomplemented
54#16839859C2218yescomplemented
55#16839853C2218yescomplemented
56#16839842C2218yescomplemented
57C2×#14519710C2211yescharacteristic
58C2×#14519710C2211yescharacteristic
59C2×#14519708C2211yescharacteristic
60C2×#14519708C2211yescharacteristic
61C2×#14519702C2211yescharacteristic
62C2×#14519702C2211yescharacteristic
63C2×#14519699C2211yescharacteristic
64C2×#14519699C2211yescharacteristic
65#16839716C2218yescomplemented
66C2×#14519688C2211yescharacteristic
67C2×#14519687C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C2×C4⋊Q8×C61C2211yescharacteristic
70C2×#127×C61C2211yescharacteristic
71C61×#486C2218yescomplemented
72C2×#102×C61C2211yescharacteristic
73C2×#102×C61C2211yescharacteristic
74C2×#102×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×C4×C8×C61C2211yescharacteristic
77C22×Dic122C2311yescharacteristic
78C22×D244—21no—
79C22×D244C2311yescharacteristic
80C22×C22⋊D61—21no—
81C22×C22⋊D61—21no—
82C23×Dic61—21no—
83C23×Dic61—21no—
84C22×C4×D61—21no—
85C22×C4×D61C2311yescharacteristic
86C2×#11758200—24no—
87C2×#11758200—24no—
88C2×#11758200C2314yes—
89C2×#11758200C2314yes—
90C2×#11758199—24no—
91C2×#11758199—24no—
92C2×#11758199C2314yes—
93C2×#11758199C2314yes—
94C2×#11758189—24no—
95C2×#11758189C2314yes—
96C22×#92418C2311yescharacteristic
97C22×#92418C2311yescharacteristic
98C2×C8×D61—24no—
99C2×C8×D61C2314yes—
100#14519772—28no—
101#14519769—22no—
102#14519769C2314yes—
103#14519766—28no—
104#14519765—22no—
105#14519765C2314yes—
106#14519762—28no—
107#14519758—28no—
108#14519758—28no—
109#14519757—22no—
110#14519757C2314yes—
111#14519753—28no—
112#14519752—22no—
113#14519752C2314yes—
114#14519749—28no—
115#14519749—28no—
116#14519748—22no—
117#14519748—22no—
118#14519748C2314yes—
119#14519748C2314yes—
120#14519742—22no—
121#14519742C2314yes—
122D4×Dic61—22no—
123D4×Dic61—22no—
124D4×Dic61C2314yes—
125D4×Dic61C2314yes—
126#14519739—22no—
127#14519739C2314yes—
128#14519734D414yes—
129#14519734C2314yes—
130C2×C4⋊Dic61—21no—
131C2×C4⋊Dic61C2311yescharacteristic
132C2×C4⋊Dic61C2311yescharacteristic
133C2×#11758196—21no—
134C2×#11758196—21no—
135C2×#11758196—21no—
136C2×#11758196D411yescharacteristic
137C2×#11758196D411yescharacteristic
138C2×C22⋊Dic61—21no—
139C2×C22⋊Dic61—21no—
140C2×C22⋊Dic61—21no—
141C2×C22⋊Dic61—21no—
142C2×#11758198—21no—
143C2×#11758198—21no—
144C2×#11758198—21no—
145C2×#11758198—21no—
146C2×#11758198—21no—
147C2×#11758198D411yescharacteristic
148C2×#11758198D411yescharacteristic
149C2×C4×Dic61—21no—
150C2×C4×Dic61C2311yescharacteristic
151#14519710C2314yes—
152#14519710C2314yes—
153#14519708C2314yes—
154#14519708C2314yes—
155#14519702C2314yes—
156#14519702C2314yes—
157#14519699C2314yes—
158#14519699C2314yes—
159#14519688C2314yes—
160#14519687C2314yes—
161C8×Dic61C2314yes—
162C22×Q8×C61—21no—
163C22×D4×C61—21no—
164C22×D4×C61—21no—
165C22×D4×C61C2311yescharacteristic
166C22×D4×C61C2311yescharacteristic
167C22×C8×C61C2311yescharacteristic
168C22×C8×C61C2311yescharacteristic
169C4⋊Q8×C61—22no—
170C4⋊Q8×C61C2314yes—
171#127×C61—22no—
172#127×C61C2314yes—
173C2×C4⋊C4×C61—21no—
174C2×C4⋊C4×C61C2311yescharacteristic
175C2×C4⋊C4×C61C2311yescharacteristic
176C2×C42×C61C2311yescharacteristic
177#102×C61C2314yes—
178#102×C61C2314yes—
179#102×C61C2314yes—
180#102×C61C2314yes—
181C4×C8×C61C2314yes—
182C24×C61—21no—
183C24×C61—21no—
184C23×D61—21no—
185C23×D61C2×D411yescharacteristic
186C2×Q8×C61—24no—
187C2×Q8×C61—82no—
188C2×D4×C61—21no—
189C2×D4×C61—21no—
190C2×D4×C61—24no—
191C2×D4×C61—24no—
192C2×D4×C61—22no—
193C2×D4×C61—22no—
194C2×D4×C61—22no—
195C2×D4×C61—22no—
196C2×D4×C61—82no—
197C2×D4×C61—82no—
198C2×D4×C61C2412yes—
199C2×D4×C61C2412yes—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61C2×D411yescharacteristic
203C22×C4×C61C2×D411yescharacteristic
204C22×C4×C61C2411yescharacteristic
205C2×C22⋊D61—24no—
206C2×C22⋊D61—24no—
207C2×C22⋊D61—82no—
208C2×C22⋊D61—82no—
209C22×Dic61—21no—
210C22×Dic61—21no—
211C22×Dic61—21no—
212C22×Dic61—24no—
213C22×Dic61—24no—
214C22×Dic61—82no—
215C22×Dic61—82no—
216C22×Dic61C2×D411yescharacteristic
217C22×Dic61C2×D411yescharacteristic
218C22×Dic61C2×D411yescharacteristic
219C2×D244—22no—
220C2×D244—22no—
221C2×D244—21no—
222C2×D244—24no—
223C2×D244—82no—
224C2×D244C2412yes—
225C2×C4×D61—22no—
226C2×C4×D61—22no—
227C2×C4×D61—24no—
228C2×C4×D61—82no—
229C2×C4×D61C2×D412yes—
230C2×C4×D61C2412yes—
231C2×Dic122—22no—
232C2×Dic122—22no—
233C2×Dic122—21no—
234C2×Dic122C2412yes—
235C2×C8×C61—22no—
236C2×C8×C61—22no—
237C2×C8×C61C2412yes—
238C2×C8×C61C2412yes—
239C4⋊C4×C61—24no—
240C4⋊C4×C61—21no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61C2412yes—
243C4⋊C4×C61C2412yes—
244C42×C61C2×D412yes—
245C42×C61C2412yes—
246C22⋊Dic61—24no—
247C22⋊Dic61—24no—
248C22⋊Dic61—24no—
249C22⋊Dic61—24no—
250#11758200—28no—
251#11758200—28no—
252#11758199—28no—
253#11758199—28no—
254#11758198—24no—
255#11758198—24no—
256#11758198—24no—
257#11758198—24no—
258#11758198—24no—
259#11758198C2×D414yes—
260#11758198C2×D414yes—
261C4⋊Dic61—21no—
262C4⋊Dic61—21no—
263C4⋊Dic61—24no—
264C4⋊Dic61C2412yes—
265C4⋊Dic61C2412yes—
266#11758196—24no—
267#11758196—24no—
268#11758196—24no—
269#11758196C2×D414yes—
270#11758196C2×D414yes—
271C4×Dic61—24no—
272C4×Dic61C2×D412yes—
273C4×Dic61C2412yes—
274C2×#92418#4114yes—
275C2×#92418#4114yes—
276C2×#92418C2412yes—
277C2×#92418C2412yes—
278#11758189—28no—
279C8×D61—28no—
280C23×C61—22no—
281C23×C61—22no—
282C23×C61—42no—
283C23×C61—42no—
284C23×C61—42no—
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×D61C22×D412yes—
297Q8×C61—84no—
298D4×C61—22no—
299D4×C61—22no—
300D4×C61—22no—
301D4×C61—22no—
302D4×C61—42no—
303D4×C61—42no—
304D4×C61—84no—
305D4×C61—84no—
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×C61C22×D412yes—
313C2×C4×C61C22×D412yes—
314C2×C4×C61C22×D411yescharacteristic
315C2×C4×C61C2×#4112yes—
316C2×C4×C61C2×#4112yes—
317C2×C4×C61C2511yescharacteristic
318C22⋊D61—84no—
319C22⋊D61—84no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—22no—
323C2×Dic61—22no—
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—42no—
327C2×Dic61—42no—
328C2×Dic61—42no—
329C2×Dic61—84no—
330C2×Dic61—84no—
331C2×Dic61C22×D412yes—
332C2×Dic61C22×D412yes—
333C2×Dic61C22×D412yes—
334D244—22no—
335D244—22no—
336D244—42no—
337D244—84no—
338C4×D61—24no—
339C4×D61—22no—
340C4×D61—22no—
341C4×D61—84no—
342Dic122—22no—
343Dic122—22no—
344Dic122—42no—
345C8×C61—22no—
346C8×C61—22no—
347#92418C2×#4114yes—
348#92418C2×#4114yes—
349C2×#3179—611nomaximal, Sylow
350C22×C61—42no—
351C22×C61—42no—
352C22×C61—42no—
353C22×C61—42no—
354C22×C61—42no—
355C22×C61—42no—
356C22×C61—84no—
357C22×C61—84no—
358C22×C61#53212yes—
359C22×C61#57612yes—
360C22×C61#57712yes—
361C22×C61C23×D411yescharacteristic
362C2×D61—22no—
363C2×D61—22no—
364C2×D61—22no—
365C2×D61—44no—
366C2×D61—42no—
367C2×D61—42no—
368C2×D61—42no—
369C2×D61—84no—
370C4×C61—22no—
371C4×C61—22no—
372C4×C61—42no—
373C4×C61—42no—
374C4×C61#53212yes—
375C4×C61C22×#4111yescharacteristic
376C4×C61C22×#4111yescharacteristic
377Dic61—22no—
378Dic61—22no—
379Dic61—22no—
380Dic61—42no—
381Dic61—42no—
382Dic61—42no—
383C2×#542—611no—
384C2×#540—611no—
385#3179—6116no—
386C2×#501—611no—
387C2×#496—611no—
388C2×#488—611no—
389C2×#486D6111yescharacteristic, complemented
390C2×#469—611no—
391C2×#468—611no—
392C2×#466—611no—
393C2×#465—611no—
394C2×#442—611no—
395C2×#440—611no—
396C2×C4×SD16—611no—
397C2×C4×D8—611no—
398C2×#405—611no—
399C2×C61—82no—
400C2×C61—82no—
401C2×C61#317914yescomplemented
402C2×C61C2×#53211yescharacteristic
403C2×C61C2×#57611yescharacteristic
404C2×C61C2×#57711yescharacteristic
405D61—42no—
406D61—82no—
407C22×SD16—611no—
408C22×SD16—611no—
409C22×D8—611no—
410C22×D8—611no—
411C22×M16—611no—
412C23×C8—611no—
413#542—618no—
414#542—1224no—
415#540—618no—
416#540—1224no—
417C2×C4⋊Q8C2×D6111yescharacteristic
418C2×#127C2×D6111yescharacteristic
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—611no—
430C2×#121—611no—
431C2×#121—1221no—
432C2×#121—1221no—
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#486C2×D6118yescomplemented
442#469—618no—
443#468—618no—
444#466—618no—
445#465—618no—
446#442—618no—
447#440—618no—
448C4×SD16—618no—
449C4×D8—618no—
450C2×#107—611no—
451C2×#107—611no—
452C2×#106—611no—
453C2×#106—611no—
454C2×#103—611no—
455C2×#103—611no—
456C2×#102—611no—
457C2×#102—611no—
458C2×#102C2×D6111yescharacteristic
459C2×#102C2×D6111yescharacteristic
460C2×#102C2×D6111yescharacteristic
461C2×#102C2×D6111yescharacteristic
462#405—618no—
463C2×#97—611no—
464C2×#97—611no—
465C2×C4×C8—611no—
466C2×C4×C8C2×D6111yescharacteristic
467C61C2×#317911yescharacteristic, complemented, Sylow
468C22×Q8—21no—
469C22×Q8—611no—
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—611no—
479C23×C4—1221no—
480C23×C4—1221no—
481C23×C4—1221no—
482C2×SD16—614no—
483C2×SD16—614no—
484C2×SD16—1224no—
485C2×SD16—1224no—
486C2×D8—614no—
487C2×D8—614no—
488C2×D8—1224no—
489C2×D8—1224no—
490C2×M16—614no—
491C2×M16—1224no—
492C22×C8—611no—
493C22×C8—611no—
494C22×C8—614no—
495C22×C8—1224no—
496C22×C8C22×D6111yescharacteristic
497C22×C8C22×D6111yescharacteristic
498C4⋊Q8—22no—
499C4⋊Q8C22×D6114yes—
500#127—22no—
501#127C22×D6114yes—
502#126—1228no—
503#125—614no—
504#125—1222no—
505#124—614no—
506#124—1228no—
507#124—1222no—
508#123—1228no—
509#123—1228no—
510#123—1228no—
511C22⋊Q8—614no—
512C22⋊Q8—1222no—
513C22⋊Q8—1228no—
514#121—614no—
515#121—614no—
516#121—614no—
517#121—1228no—
518#121—1228no—
519#121—1222no—
520#121—1222no—
521#121—1222no—
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—611no—
544C2×C22⋊C4—611no—
545C2×C22⋊C4—1221no—
546C2×C22⋊C4—1221no—
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—1221no—
556C2×C42C22×D6111yescharacteristic
557#107—614no—
558#107—614no—
559#106—614no—
560#106—614no—
561#103—614no—
562#103—614no—
563#102—614no—
564#102—614no—
565#102C22×D6114yes—
566#102C22×D6114yes—
567#102C22×D6114yes—
568#102C22×D6114yes—
569#97—614no—
570#97—614no—
571C4×C8—614no—
572C4×C8C22×D6114yes—
573C24—21no—
574C24—21no—
575C24—611no—
576C24—1221no—
577C2×Q8—24no—
578C2×Q8—82no—
579C2×Q8—612no—
580C2×Q8—1221no—
581C2×Q8—1222no—
582C2×Q8—1222no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—24no—
586C2×D4—24no—
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—21no—
606C22×C4—21no—
607C22×C4—611no—
608C22×C4—611no—
609C22×C4—611no—
610C22×C4—612no—
611C22×C4—612no—
612C22×C4—1224no—
613C22×C4—1224no—
614C22×C4—1224no—
615C22×C4—1222no—
616C22×C4—1222no—
617C22×C4—1221no—
618C22×C4—1221no—
619C22×C4—1221no—
620C22×C4—4882no—
621C22×C4—4882no—
622C22×C4—4882no—
623C22×C4D4×D6111yescharacteristic
624C22×C4D4×D6111yescharacteristic
625C22×C4C23×D6111yescharacteristic
626SD16—1228no—
627SD16—1228no—
628D8—1228no—
629D8—1228no—
630M16—1228no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—614no—
634C2×C8—614no—
635C2×C8—612no—
636C2×C8—612no—
637C2×C8—1228no—
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—1221no—
650C4⋊C4—1221no—
651C4⋊C4—1224no—
652C4⋊C4—1224no—
653C4⋊C4C23×D6112yes—
654C4⋊C4C23×D6112yes—
655C22⋊C4—614no—
656C22⋊C4—614no—
657C22⋊C4—1224no—
658C22⋊C4—1224no—
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—1224no—
669C42D4×D6112yes—
670C42C23×D6112yes—
671C23—22no—
672C23—22no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—612no—
680C23—1222no—
681C23—1222no—
682C23—1222no—
683C23—1222no—
684C23—2442no—
685C23—2442no—
686C23—2442no—
687C23C2×D4×D6111yescharacteristic
688Q8—84no—
689Q8—1222no—
690Q8—1222no—
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—22no—
709C2×C4—22no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—612no—
713C2×C4—612no—
714C2×C4—612no—
715C2×C4—1222no—
716C2×C4—1222no—
717C2×C4—1222no—
718C2×C4—1224no—
719C2×C4—1222no—
720C2×C4—1222no—
721C2×C4—1222no—
722C2×C4—1222no—
723C2×C4—1222no—
724C2×C4—4884no—
725C2×C4—4884no—
726C2×C4—4884no—
727C2×C4—2442no—
728C2×C4—2442no—
729C2×C4—2442no—
730C2×C4C2×D4×D6112yes—
731C2×C4C2×D4×D6112yes—
732C2×C4C2×D4×D6111yescharacteristic
733C2×C4#41×D6112yes—
734C2×C4#41×D6112yes—
735C2×C4C24×D6111yescharacteristic
736C8—22no—
737C8—22no—
738C8—614no—
739C8—614no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—84no—
747C22—84no—
748C22—1222no—
749C22—1222no—
750C22—1222no—
751C22—4884no—
752C22—2442no—
753C22—2442no—
754C22—2442no—
755C22—2444no—
756C22#1684031112yes—
757C22#1684056312yes—
758C22#1684056812yes—
759C22C22×D4×D6111yescharacteristic
760C4—22no—
761C4—22no—
762C4—42no—
763C4—42no—
764C4—1222no—
765C4—1222no—
766C4—1222no—
767C4—2442no—
768C4—2442no—
769C4—2442no—
770C4#1684031112yes—
771C4C2×#41×D6111yescharacteristic
772C4C2×#41×D6111yescharacteristic
773C2—82no—
774C2—82no—
775C2—4882no—
776C2—2442no—
777C2#2145650914yesdirect product factor
778C2C2×#1684031111yescharacteristic
779C2C2×#1684056311yescharacteristic
780C2C2×#1684056811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#486C2
socleC23×C61C22×D4
hypercenterC2×#486D61
hypocenterC61C2×#3179
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#486

Complements

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

NH ≅ G/Ntype
1. C2×#16840386C2semidirect
2. C2×#16840366C2semidirect
3. #21456509C2direct (N × H)
4. C2×#16840168C2semidirect
5. C2×#16840149C2semidirect
6. C2×#16840117C2semidirect
7. C2×#16840014C2semidirect
8. C2×#16840007C2semidirect
9. C2×#16839997C2semidirect
10. C2×#16839990C2semidirect
11. C2×#16839871C2semidirect
12. C2×#16839859C2semidirect
13. C2×#16839853C2semidirect
14. C2×#16839842C2semidirect
15. C2×#16839716C2semidirect
16. C2×C61×#486C2semidirect
24. #16840386C22semidirect
26. #16840366C22semidirect
46. #16840168C22semidirect
47. #16840149C22semidirect
48. #16840117C22semidirect
49. #16840014C22semidirect
50. #16840007C22semidirect
51. #16839997C22semidirect
52. #16839990C22semidirect
53. #16839871C22semidirect
54. #16839859C22semidirect
55. #16839853C22semidirect
56. #16839842C22semidirect
65. #16839716C22semidirect
71. C61×#486C22semidirect
389. C2×#486D61semidirect
401. C2×C61#3179semidirect
441. #486C2×D61semidirect
467. C61C2×#3179semidirect
777. C2#21456509direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403862
C2×#168403662
#214565092
C2×#168401682
C2×#168401492
C2×#168401172
C2×#168400142
C2×#168400072
C2×#168399972
C2×#168399902
C2×#168398712
C2×#168398592
C2×#168398532
C2×#168398422
C2×#168397162
C2×C61×#4862
C2×#317961