Finite Group Databasebeta

← C2×#21456499 #30549894

Subgroups — C2×#21456499 #30549894

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×#16840381C211yesmaximal, characteristic, complemented
2C2×#16840366C211yesmaximal, characteristic, complemented
3#21456499C2116yesmaximal, direct product factor
4C2×#16840171C211yesmaximal, characteristic, complemented
5C2×#16840116C211yesmaximal, characteristic, complemented
6C2×#16840108C211yesmaximal, characteristic, complemented
7C2×#16840012C211yesmaximal, characteristic, complemented
8C2×#16840005C211yesmaximal, characteristic, complemented
9C2×#16839995C211yesmaximal, characteristic, complemented
10C2×#16839988C211yesmaximal, characteristic, complemented
11C2×#16839874C211yesmaximal, characteristic, complemented
12C2×#16839863C211yesmaximal, characteristic, complemented
13C2×SD16×Dic61C211yesmaximal, characteristic, complemented
14C2×D8×Dic61C211yesmaximal, characteristic, complemented
15C2×#16839719C211yesmaximal, characteristic, complemented
16C2×C61×#496C211yesmaximal, characteristic, complemented
17C22×#11758189C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19#16840381—24no—
20#16840381C2218yescomplemented
21#16840366—24no—
22#16840366C2218yescomplemented
23C2×#14519777C2211yescharacteristic
24C2×#14519770—21no—
25C2×#14519769C2211yescharacteristic
26C2×#14519763—21no—
27C2×#14519761—21no—
28C2×#14519758—21no—
29C2×#14519758—21no—
30C2×#14519754—21no—
31C2×#14519753C2211yescharacteristic
32C2×#14519749—21no—
33C2×#14519749—21no—
34C2×#14519748C2211yescharacteristic
35C2×#14519748C2211yescharacteristic
36C2×#14519748C2211yescharacteristic
37C2×Q8×Dic61C2211yescharacteristic
38C2×D4×Dic61C2211yescharacteristic
39C2×D4×Dic61C2211yescharacteristic
40C2×D4×Dic61C2211yescharacteristic
41C2×#14519734C2211yescharacteristic
42#16840171C2218yescomplemented
43#16840116C2218yescomplemented
44#16840108C2218yescomplemented
45#16840012C2218yescomplemented
46#16840005C2218yescomplemented
47#16839995C2218yescomplemented
48#16839988C2218yescomplemented
49#16839874C2218yescomplemented
50#16839863C2218yescomplemented
51SD16×Dic61C2218yescomplemented
52D8×Dic61C2218yescomplemented
53C2×#14519711C2211yescharacteristic
54C2×#14519711C2211yescharacteristic
55C2×#14519709C2211yescharacteristic
56C2×#14519709C2211yescharacteristic
57C2×#14519701C2211yescharacteristic
58C2×#14519701C2211yescharacteristic
59C2×#14519698C2211yescharacteristic
60C2×#14519698C2211yescharacteristic
61C2×#14519698C2211yescharacteristic
62C2×#14519698C2211yescharacteristic
63C2×#14519698C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65#16839719C2218yescomplemented
66C2×#14519687C2211yescharacteristic
67C2×C4×#92418C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C22×SD16×C61C2211yescharacteristic
70C22×SD16×C61C2211yescharacteristic
71C22×D8×C61C2211yescharacteristic
72C22×D8×C61C2211yescharacteristic
73C2×#127×C61C2211yescharacteristic
74C2×#124×C61C2211yescharacteristic
75C61×#496C2218yescomplemented
76C2×#97×C61C2211yescharacteristic
77C22×Dic122—21no—
78C22×C22⋊D61—21no—
79C22×C22⋊D61—21no—
80C22×C22⋊D61—21no—
81C23×Dic61—21no—
82C23×Dic61—21no—
83C23×Dic61—21no—
84C22×C4×D61C2311yescharacteristic
85C2×#11758189—24no—
86C2×#11758189C2314yes—
87C22×#92418C2311yescharacteristic
88C22×#92418C2311yescharacteristic
89C2×C8×D61—24no—
90C2×C8×D61C2314yes—
91#14519777—22no—
92#14519777C2314yes—
93#14519770—28no—
94#14519769—22no—
95#14519769C2314yes—
96#14519763—28no—
97#14519761—28no—
98#14519758—28no—
99#14519758—28no—
100#14519754—28no—
101#14519753—22no—
102#14519753C2314yes—
103#14519749—28no—
104#14519749—28no—
105#14519748—22no—
106#14519748—22no—
107#14519748—22no—
108#14519748C2314yes—
109#14519748C2314yes—
110#14519748C2314yes—
111Q8×Dic61—22no—
112Q8×Dic61C2314yes—
113D4×Dic61—22no—
114D4×Dic61—22no—
115D4×Dic61—22no—
116D4×Dic61C2314yes—
117D4×Dic61C2314yes—
118D4×Dic61C2314yes—
119#14519734D414yes—
120#14519734C2314yes—
121C2×C4⋊Dic61—21no—
122C2×C4⋊Dic61—21no—
123C2×C4⋊Dic61C2311yescharacteristic
124C2×C4⋊Dic61C2311yescharacteristic
125C2×C4⋊Dic61C2311yescharacteristic
126C2×C4⋊Dic61C2311yescharacteristic
127C2×#11758196—21no—
128C2×#11758196—21no—
129C2×#11758196—21no—
130C2×#11758196D411yescharacteristic
131C2×#11758196D411yescharacteristic
132C2×C22⋊Dic61—21no—
133C2×C22⋊Dic61—21no—
134C2×C22⋊Dic61—21no—
135C2×C22⋊Dic61—21no—
136C2×C22⋊Dic61—21no—
137C2×C22⋊Dic61—21no—
138C2×#11758198—21no—
139C2×#11758198D411yescharacteristic
140C2×#11758198D411yescharacteristic
141C2×C4×Dic61—21no—
142C2×C4×Dic61C2311yescharacteristic
143#14519711C2314yes—
144#14519711C2314yes—
145#14519709C2314yes—
146#14519709C2314yes—
147#14519701C2314yes—
148#14519701C2314yes—
149#14519698C2314yes—
150#14519698C2314yes—
151#14519698C2314yes—
152#14519698C2314yes—
153#14519698C2314yes—
154#14519698C2314yes—
155#14519687C2314yes—
156C4×#92418C2314yes—
157C8×Dic61C2314yes—
158C22×Q8×C61C2311yescharacteristic
159C22×D4×C61—21no—
160C22×D4×C61—21no—
161C22×D4×C61C2311yescharacteristic
162C22×D4×C61C2311yescharacteristic
163C22×D4×C61C2311yescharacteristic
164C2×SD16×C61—24no—
165C2×SD16×C61—24no—
166C2×SD16×C61C2314yes—
167C2×SD16×C61C2314yes—
168C2×D8×C61—24no—
169C2×D8×C61—24no—
170C2×D8×C61C2314yes—
171C2×D8×C61C2314yes—
172C22×C8×C61C2311yescharacteristic
173C22×C8×C61C2311yescharacteristic
174#127×C61—22no—
175#127×C61C2314yes—
176#124×C61—22no—
177#124×C61C2314yes—
178C2×C22⋊C4×C61—21no—
179C2×C22⋊C4×C61—21no—
180C2×C42×C61C2311yescharacteristic
181#97×C61C2314yes—
182C24×C61—21no—
183C24×C61—21no—
184C24×C61—21no—
185C23×D61C2×D411yescharacteristic
186C2×Q8×C61—21no—
187C2×Q8×C61—22no—
188C2×Q8×C61—22no—
189C2×Q8×C61C2412yes—
190C2×D4×C61—21no—
191C2×D4×C61—21no—
192C2×D4×C61—21no—
193C2×D4×C61—24no—
194C2×D4×C61—24no—
195C2×D4×C61—22no—
196C2×D4×C61—22no—
197C2×D4×C61—22no—
198C2×D4×C61—22no—
199C2×D4×C61—22no—
200C2×D4×C61—22no—
201C2×D4×C61—82no—
202C2×D4×C61—82no—
203C2×D4×C61C2412yes—
204C2×D4×C61C2412yes—
205C2×D4×C61C2412yes—
206C22×C4×C61—21no—
207C22×C4×C61C2×D411yescharacteristic
208C22×C4×C61C2×D411yescharacteristic
209C22×C4×C61C2411yescharacteristic
210C2×C22⋊D61—24no—
211C2×C22⋊D61—24no—
212C2×C22⋊D61—24no—
213C2×C22⋊D61—82no—
214C2×C22⋊D61—82no—
215C2×C22⋊D61—82no—
216C22×Dic61—21no—
217C22×Dic61—21no—
218C22×Dic61—21no—
219C22×Dic61—21no—
220C22×Dic61—24no—
221C22×Dic61—24no—
222C22×Dic61—24no—
223C22×Dic61—82no—
224C22×Dic61—82no—
225C22×Dic61—82no—
226C22×Dic61C2×D411yescharacteristic
227C22×Dic61C2×D411yescharacteristic
228C22×Dic61C2×D411yescharacteristic
229C2×C4×D61—22no—
230C2×C4×D61—22no—
231C2×C4×D61C2×D412yes—
232C2×C4×D61C2412yes—
233C2×Dic122—24no—
234C2×Dic122—82no—
235SD16×C61—28no—
236SD16×C61—28no—
237D8×C61—28no—
238D8×C61—28no—
239C2×C8×C61#4114yes—
240C2×C8×C61#4114yes—
241C2×C8×C61C2412yes—
242C2×C8×C61C2412yes—
243C22⋊C4×C61—24no—
244C22⋊C4×C61—24no—
245C42×C61C2×D412yes—
246C42×C61C2412yes—
247C22⋊Dic61—24no—
248C22⋊Dic61—24no—
249C22⋊Dic61—24no—
250C22⋊Dic61—24no—
251C22⋊Dic61—24no—
252C22⋊Dic61—24no—
253#11758198—24no—
254#11758198C2×D414yes—
255#11758198C2×D414yes—
256C4⋊Dic61—24no—
257C4⋊Dic61—21no—
258C4⋊Dic61—21no—
259C4⋊Dic61—21no—
260C4⋊Dic61—21no—
261C4⋊Dic61—24no—
262C4⋊Dic61C2412yes—
263C4⋊Dic61C2412yes—
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—22no—
275C2×#92418—22no—
276C2×#92418C2412yes—
277C2×#92418C2412yes—
278#11758189—28no—
279C8×D61—28no—
280C23×C61—22no—
281C23×C61—22no—
282C23×C61—22no—
283C23×C61—42no—
284C23×C61—42no—
285C23×C61—42no—
286C23×C61—42no—
287C23×C61—42no—
288C23×C61—42no—
289C23×C61—42no—
290C23×C61—42no—
291C23×C61—42no—
292C23×C61C22×D411yescharacteristic
293C22×D61—22no—
294C22×D61—22no—
295C22×D61—22no—
296C22×D61C22×D412yes—
297Q8×C61—22no—
298Q8×C61—22no—
299Q8×C61—42no—
300D4×C61—22no—
301D4×C61—22no—
302D4×C61—22no—
303D4×C61—22no—
304D4×C61—22no—
305D4×C61—22no—
306D4×C61—42no—
307D4×C61—42no—
308D4×C61—42no—
309D4×C61—84no—
310D4×C61—84no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—42no—
315C2×C4×C61C22×D412yes—
316C2×C4×C61C22×D412yes—
317C2×C4×C61C22×D411yescharacteristic
318C2×C4×C61C2×#4112yes—
319C2×C4×C61C2×#4112yes—
320C2×C4×C61C2511yescharacteristic
321C22⋊D61—84no—
322C22⋊D61—84no—
323C22⋊D61—84no—
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—42no—
332C2×Dic61—42no—
333C2×Dic61—42no—
334C2×Dic61—42no—
335C2×Dic61—84no—
336C2×Dic61—84no—
337C2×Dic61—84no—
338C2×Dic61C22×D412yes—
339C2×Dic61C22×D412yes—
340C2×Dic61C22×D412yes—
341C4×D61—24no—
342C4×D61—22no—
343C4×D61—22no—
344Dic122—84no—
345C8×C61C2×#4114yes—
346C8×C61C2×#4114yes—
347#92418—22no—
348#92418—22no—
349C2×#3179—611nomaximal, Sylow
350C22×C61—42no—
351C22×C61—42no—
352C22×C61—42no—
353C22×C61—42no—
354C22×C61—42no—
355C22×C61—42no—
356C22×C61—42no—
357C22×C61—42no—
358C22×C61—42no—
359C22×C61—84no—
360C22×C61—84no—
361C22×C61—84no—
362C22×C61#53212yes—
363C22×C61#57612yes—
364C22×C61#57712yes—
365C22×C61C23×D411yescharacteristic
366C2×D61—22no—
367C2×D61—22no—
368C2×D61—22no—
369C2×D61—44no—
370C4×C61—22no—
371C4×C61—22no—
372C4×C61—42no—
373C4×C61#53212yes—
374C4×C61C22×#4111yescharacteristic
375C4×C61C22×#4111yescharacteristic
376Dic61—22no—
377Dic61—22no—
378Dic61—22no—
379Dic61—42no—
380Dic61—42no—
381Dic61—42no—
382Dic61—42no—
383C2×#542—611no—
384C2×#540—611no—
385#3179—6116no—
386C2×#501—611no—
387C2×#496D6111yescharacteristic, complemented
388C2×#488—611no—
389C2×#486—611no—
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—82no—
402C2×C61#317914yescomplemented
403C2×C61C2×#53211yescharacteristic
404C2×C61C2×#57611yescharacteristic
405C2×C61C2×#57711yescharacteristic
406D61—42no—
407C22×SD16C2×D6111yescharacteristic
408C22×SD16C2×D6111yescharacteristic
409C22×D8C2×D6111yescharacteristic
410C22×D8C2×D6111yescharacteristic
411C22×M16—611no—
412C23×C8—611no—
413#542—618no—
414#542—1224no—
415#540—618no—
416#540—1224no—
417C2×C4⋊Q8—611no—
418C2×#127C2×D6111yescharacteristic
419C2×#126—1221no—
420C2×#125—611no—
421C2×#124—1221no—
422C2×#124C2×D6111yescharacteristic
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#496C2×D6118yescomplemented
440#488—618no—
441#486—618no—
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×#102—611no—
459C2×#102—611no—
460C2×#102—611no—
461C2×#102—611no—
462#405—618no—
463C2×#97—611no—
464C2×#97C2×D6111yescharacteristic
465C2×C4×C8—611no—
466C2×C4×C8—611no—
467C61C2×#317911yescharacteristic, complemented, Sylow
468C22×Q8—1221no—
469C22×Q8C22×D6111yescharacteristic
470C22×D4—21no—
471C22×D4—21no—
472C22×D4—1221no—
473C22×D4—1221no—
474C22×D4—1221no—
475C22×D4C22×D6111yescharacteristic
476C22×D4C22×D6111yescharacteristic
477C22×D4C22×D6111yescharacteristic
478C23×C4—611no—
479C23×C4—1221no—
480C23×C4—1221no—
481C23×C4—1221no—
482C2×SD16—24no—
483C2×SD16—24no—
484C2×SD16C22×D6114yes—
485C2×SD16C22×D6114yes—
486C2×D8—24no—
487C2×D8—24no—
488C2×D8C22×D6114yes—
489C2×D8C22×D6114yes—
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—614no—
499C4⋊Q8—1222no—
500#127—22no—
501#127C22×D6114yes—
502#126—1228no—
503#125—614no—
504#125—1222no—
505#124—22no—
506#124—1228no—
507#124C22×D6114yes—
508#123—1228no—
509#123—1228no—
510#123—1228no—
511C22⋊Q8—614no—
512C22⋊Q8—1228no—
513C22⋊Q8—1222no—
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—611no—
533C2×C4⋊C4—611no—
534C2×C4⋊C4—611no—
535C2×C4⋊C4—611no—
536C2×C4⋊C4—611no—
537C2×C4⋊C4—611no—
538C2×C4⋊C4—1221no—
539C2×C4⋊C4—1221no—
540C2×C4⋊C4—1221no—
541C2×C4⋊C4—1221no—
542C2×C4⋊C4—1221no—
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—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#102—614no—
566#102—614no—
567#102—614no—
568#102—614no—
569#97—614no—
570#97C22×D6114yes—
571C4×C8—614no—
572C4×C8—614no—
573C24—21no—
574C24—21no—
575C24—21no—
576C24—611no—
577C2×Q8—21no—
578C2×Q8—22no—
579C2×Q8—22no—
580C2×Q8—1224no—
581C2×Q8—4882no—
582C2×Q8C23×D6112yes—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—24no—
587C2×D4—24no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—82no—
595C2×D4—82no—
596C2×D4—1224no—
597C2×D4—1224no—
598C2×D4—1224no—
599C2×D4—4882no—
600C2×D4—4882no—
601C2×D4—4882no—
602C2×D4C23×D6112yes—
603C2×D4C23×D6112yes—
604C2×D4C23×D6112yes—
605C22×C4—21no—
606C22×C4—611no—
607C22×C4—611no—
608C22×C4—611no—
609C22×C4—612no—
610C22×C4—612no—
611C22×C4—1224no—
612C22×C4—1224no—
613C22×C4—1224no—
614C22×C4—1222no—
615C22×C4—1222no—
616C22×C4—1221no—
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—28no—
627SD16—28no—
628D8—28no—
629D8—28no—
630M16—1228no—
631C2×C8—612no—
632C2×C8—612no—
633C2×C8—1222no—
634C2×C8—1222no—
635C2×C8—1228no—
636C2×C8#1175822414yes—
637C2×C8#1175822414yes—
638C2×C8C23×D6112yes—
639C2×C8C23×D6112yes—
640C4⋊C4—614no—
641C4⋊C4—614no—
642C4⋊C4—612no—
643C4⋊C4—612no—
644C4⋊C4—612no—
645C4⋊C4—612no—
646C4⋊C4—1224no—
647C4⋊C4—1224no—
648C4⋊C4—1221no—
649C4⋊C4—1221no—
650C4⋊C4—1221no—
651C4⋊C4—1221no—
652C4⋊C4—1224no—
653C4⋊C4—1224no—
654C4⋊C4—1224no—
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—1224no—
669C42D4×D6112yes—
670C42C23×D6112yes—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—612no—
684C23—1222no—
685C23—1222no—
686C23—1222no—
687C23C2×D4×D6111yescharacteristic
688Q8—22no—
689Q8—22no—
690Q8—42no—
691Q8—4884no—
692D4—22no—
693D4—22no—
694D4—22no—
695D4—22no—
696D4—22no—
697D4—22no—
698D4—42no—
699D4—42no—
700D4—42no—
701D4—84no—
702D4—84no—
703D4—4884no—
704D4—4884no—
705D4—4884no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—42no—
710C2×C4—612no—
711C2×C4—612no—
712C2×C4—612no—
713C2×C4—1222no—
714C2×C4—1222no—
715C2×C4—1222no—
716C2×C4—1224no—
717C2×C4—1222no—
718C2×C4—1222no—
719C2×C4—1222no—
720C2×C4—1222no—
721C2×C4—1222no—
722C2×C4—1222no—
723C2×C4—4884no—
724C2×C4—4884no—
725C2×C4—4884no—
726C2×C4—2442no—
727C2×C4—2442no—
728C2×C4—2442no—
729C2×C4—2442no—
730C2×C4C2×D4×D6112yes—
731C2×C4C2×D4×D6112yes—
732C2×C4C2×D4×D6111yescharacteristic
733C2×C4C2×#1175822412yes—
734C2×C4C2×#1175822412yes—
735C2×C4C24×D6111yescharacteristic
736C8—1222no—
737C8—1222no—
738C8C2×#1175822414yes—
739C8C2×#1175822414yes—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—84no—
750C22—84no—
751C22—84no—
752C22—1222no—
753C22—1222no—
754C22—1222no—
755C22—2444no—
756C22#1684031012yes—
757C22#1684056612yes—
758C22#1684057212yes—
759C22C22×D4×D6111yescharacteristic
760C4—22no—
761C4—22no—
762C4—42no—
763C4—1222no—
764C4—1222no—
765C4—1222no—
766C4—2442no—
767C4—2442no—
768C4—2442no—
769C4—2442no—
770C4#1684031012yes—
771C4C22×#1175822411yescharacteristic
772C4C22×#1175822411yescharacteristic
773C2—82no—
774C2—82no—
775C2—82no—
776C2—2442no—
777C2#2145649914yesdirect product factor
778C2C2×#1684031011yescharacteristic
779C2C2×#1684056611yescharacteristic
780C2C2×#1684057211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#496C2
socleC23×C61C22×D4
hypercenterC2×#496D61
hypocenterC61C2×#3179
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#496

Complements

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

NH ≅ G/Ntype
1. C2×#16840381C2semidirect
2. C2×#16840366C2semidirect
3. #21456499C2direct (N × H)
4. C2×#16840171C2semidirect
5. C2×#16840116C2semidirect
6. C2×#16840108C2semidirect
7. C2×#16840012C2semidirect
8. C2×#16840005C2semidirect
9. C2×#16839995C2semidirect
10. C2×#16839988C2semidirect
11. C2×#16839874C2semidirect
12. C2×#16839863C2semidirect
13. C2×SD16×Dic61C2semidirect
14. C2×D8×Dic61C2semidirect
15. C2×#16839719C2semidirect
16. C2×C61×#496C2semidirect
20. #16840381C22semidirect
22. #16840366C22semidirect
42. #16840171C22semidirect
43. #16840116C22semidirect
44. #16840108C22semidirect
45. #16840012C22semidirect
46. #16840005C22semidirect
47. #16839995C22semidirect
48. #16839988C22semidirect
49. #16839874C22semidirect
50. #16839863C22semidirect
51. SD16×Dic61C22semidirect
52. D8×Dic61C22semidirect
65. #16839719C22semidirect
75. C61×#496C22semidirect
387. C2×#496D61semidirect
402. C2×C61#3179semidirect
439. #496C2×D61semidirect
467. C61C2×#3179semidirect
777. C2#21456499direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403812
C2×#168403662
#214564992
C2×#168401712
C2×#168401162
C2×#168401082
C2×#168400122
C2×#168400052
C2×#168399952
C2×#168399882
C2×#168398742
C2×#168398632
C2×SD16×Dic612
C2×D8×Dic612
C2×#168397192
C2×C61×#4962
C2×#317961