Finite Group Databasebeta

← C2×#21458895 #30561030

Subgroups — C2×#21458895 #30561030

Order 15616.

1938 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840486C211yesmaximal, characteristic, complemented
2C2×#16840481C211yesmaximal, characteristic, complemented
3#21458895C2116yesmaximal, direct product factor
4C2×#16840155C211yesmaximal, characteristic, complemented
5C2×#16840143C211yesmaximal, characteristic
6C2×#16839986C211yesmaximal, characteristic, complemented
7C2×#16839982C211yesmaximal, characteristic, complemented
8C2×#16839970C211yesmaximal, characteristic, complemented
9C2×#16839969C211yesmaximal, characteristic, complemented
10C2×#16839979C211yesmaximal, characteristic
11C2×#16839974C211yesmaximal, characteristic
12C2×#16839890C211yesmaximal, characteristic, complemented
13C2×#16839864C211yesmaximal, characteristic, complemented
14C2×#16839863C211yesmaximal, characteristic, complemented
15C2×Q16×Dic61C211yesmaximal, characteristic, complemented
16C2×C61×#497C211yesmaximal, characteristic, complemented
17C22×#11758202C2211yescharacteristic
18C22×#11758202C2211yescharacteristic
19C22×#11758190C2211yescharacteristic
20C22×#11758201C2211yescharacteristic
21C22×#11758199C2211yescharacteristic
22#16840486—24no—
23#16840486C2218yescomplemented
24#16840481—24no—
25#16840481C2218yescomplemented
26C2×#14519775C2211yescharacteristic
27C2×#14519772—21no—
28C2×#14519772—21no—
29C2×#14519770—21no—
30C2×#14519770—21no—
31C2×#14519766C2211yescharacteristic
32C2×#14519766C2211yescharacteristic
33C2×#14519764C2211yescharacteristic
34C2×#14519757—21no—
35C2×#14519754—21no—
36C2×Q8×Dic61C2211yescharacteristic
37C2×Q8×Dic61C2211yescharacteristic
38C2×Q8×Dic61C2211yescharacteristic
39C2×C4×Dic122C2211yescharacteristic
40C2×C4×Dic122C2211yescharacteristic
41C2×C4×D244C2211yescharacteristic
42C2×D4×Dic61C2211yescharacteristic
43C2×#14519735—21no—
44C2×#14519733—21no—
45#16840155C2218yescomplemented
46#16840143C2218yes—
47#16839986C2218yescomplemented
48#16839982C2218yescomplemented
49#16839979C2218yes—
50#16839974C2218yes—
51#16839970C2218yescomplemented
52#16839969C2218yescomplemented
53#16839890C2218yescomplemented
54#16839864C2218yescomplemented
55#16839863C2218yescomplemented
56Q16×Dic61C2218yescomplemented
57C2×#14519711C2211yescharacteristic
58C2×C4⋊#92418C2211yescharacteristic
59C2×#14519706C2211yescharacteristic
60C2×#14519706C2211yescharacteristic
61C2×#14519702C2211yescharacteristic
62C2×#14519701C2211yescharacteristic
63C2×#14519701C2211yescharacteristic
64C2×#14519701C2211yescharacteristic
65C2×#14519699C2211yescharacteristic
66C2×#14519698C2211yescharacteristic
67C2×#14519687C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C22×Q16×C61C2211yescharacteristic
70C22×Q16×C61C2211yescharacteristic
71C22×SD16×C61C2211yescharacteristic
72C22×SD16×C61C2211yescharacteristic
73C2×C4⋊Q8×C61C2211yescharacteristic
74C2×#124×C61C2211yescharacteristic
75C61×#497C2218yescomplemented
76C2×#97×C61C2211yescharacteristic
77C22×Dic122D411yescharacteristic
78C22×Dic122C2311yescharacteristic
79C22×D244C2311yescharacteristic
80C23×Dic61—21no—
81C22×C4×D61—21no—
82C2×#11758202—42no—
83C2×#11758202—42no—
84C2×#11758202C2314yes—
85C2×#11758202C2314yes—
86C2×#11758190—24no—
87C2×#11758190C2314yes—
88C2×#11758201—42no—
89C2×#11758201C2314yes—
90C2×#11758199—42no—
91C2×#11758199C2314yes—
92C22×#92418C2311yescharacteristic
93C22×#92418C2311yescharacteristic
94#14519775—22no—
95#14519775C2314yes—
96#14519772—28no—
97#14519772—28no—
98#14519770—28no—
99#14519770—28no—
100#14519766—22no—
101#14519766—22no—
102#14519766C2314yes—
103#14519766C2314yes—
104#14519764—22no—
105#14519764C2314yes—
106#14519757—28no—
107#14519754—28no—
108Q8×Dic61—22no—
109Q8×Dic61—22no—
110Q8×Dic61—22no—
111Q8×Dic61C2314yes—
112Q8×Dic61C2314yes—
113Q8×Dic61C2314yes—
114C4×Dic122—22no—
115C4×Dic122D414yes—
116C4×Dic122C2314yes—
117C4×Dic122C2314yes—
118C4×D244—22no—
119C4×D244C2314yes—
120D4×Dic61—22no—
121D4×Dic61C2314yes—
122#14519735—28no—
123#14519733—28no—
124C2×C4⋊Dic61—21no—
125C2×C4⋊Dic61—21no—
126C2×C4⋊Dic61—21no—
127C2×C4⋊Dic61D411yescharacteristic
128C2×C4⋊Dic61C2311yescharacteristic
129C2×C4⋊Dic61C2311yescharacteristic
130C2×#11758196—21no—
131C2×#11758196—21no—
132C2×#11758196—21no—
133C2×#11758196D411yescharacteristic
134C2×#11758196D411yescharacteristic
135C2×C22⋊Dic61—21no—
136C2×C22⋊Dic61—21no—
137C2×C22⋊Dic61—21no—
138C2×#11758198—21no—
139C2×#11758198—21no—
140C2×#11758198—21no—
141C2×#11758198—21no—
142C2×#11758198—21no—
143C2×C4×Dic61—21no—
144C2×C4×Dic61—21no—
145C2×C4×Dic61—21no—
146C2×C4×Dic61—21no—
147C2×C4×Dic61C2311yescharacteristic
148C2×C4×Dic61C2311yescharacteristic
149#14519711C2314yes—
150C4⋊#92418C2314yes—
151#14519706C2314yes—
152#14519706C2314yes—
153#14519702C2314yes—
154#14519701C2314yes—
155#14519701C2314yes—
156#14519701C2314yes—
157#14519699C2314yes—
158#14519698C2314yes—
159#14519687C2314yes—
160C8×Dic61C2314yes—
161C22×Q8×C61C2311yescharacteristic
162C22×Q8×C61C2311yescharacteristic
163C22×Q8×C61C2311yescharacteristic
164C22×D4×C61C2311yescharacteristic
165C2×Q16×C61—24no—
166C2×Q16×C61—42no—
167C2×Q16×C61C2314yes—
168C2×Q16×C61C2314yes—
169C2×SD16×C61—24no—
170C2×SD16×C61—42no—
171C2×SD16×C61C2314yes—
172C2×SD16×C61C2314yes—
173C22×C8×C61C2311yescharacteristic
174C22×C8×C61C2311yescharacteristic
175C4⋊Q8×C61—22no—
176C4⋊Q8×C61C2314yes—
177#124×C61—22no—
178#124×C61C2314yes—
179C2×C4⋊C4×C61—21no—
180C2×C4⋊C4×C61—21no—
181C2×C22⋊C4×C61—21no—
182C2×C22⋊C4×C61—21no—
183C2×C42×C61C2311yescharacteristic
184#97×C61C2314yes—
185C24×C61—21no—
186C23×D61—21no—
187C2×Q8×C61—21no—
188C2×Q8×C61—21no—
189C2×Q8×C61—21no—
190C2×Q8×C61—22no—
191C2×Q8×C61—22no—
192C2×Q8×C61—22no—
193C2×Q8×C61—22no—
194C2×Q8×C61—22no—
195C2×Q8×C61—22no—
196C2×Q8×C61C2412yes—
197C2×Q8×C61C2412yes—
198C2×Q8×C61C2412yes—
199C2×D4×C61—21no—
200C2×D4×C61—22no—
201C2×D4×C61—22no—
202C2×D4×C61C2412yes—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61C2×D411yescharacteristic
207C22×C4×C61C2×D411yescharacteristic
208C22×C4×C61C2411yescharacteristic
209C22×Dic61—21no—
210C22×Dic61—21no—
211C22×Dic61—21no—
212C22×Dic61—24no—
213C22×Dic61—44no—
214C22×Dic61C2×D411yescharacteristic
215C22×Dic61C2×D411yescharacteristic
216C22×Dic61C2×D411yescharacteristic
217C22×Dic61C2×D411yescharacteristic
218C2×D244—22no—
219C2×D244—22no—
220C2×D244—21no—
221C2×D244C2412yes—
222C2×C4×D61—24no—
223C2×C4×D61—44no—
224C2×Dic122—22no—
225C2×Dic122—22no—
226C2×Dic122—21no—
227C2×Dic122—42no—
228C2×Dic122C2×D414yes—
229C2×Dic122C2412yes—
230Q16×C61—28no—
231Q16×C61—44no—
232SD16×C61—28no—
233SD16×C61—44no—
234C2×C8×C61—22no—
235C2×C8×C61#4114yes—
236C2×C8×C61C2412yes—
237C2×C8×C61C2412yes—
238C4⋊C4×C61—24no—
239C4⋊C4×C61—24no—
240C22⋊C4×C61—24no—
241C22⋊C4×C61—24no—
242C42×C61C2×D412yes—
243C42×C61C2412yes—
244C22⋊Dic61—24no—
245C22⋊Dic61—24no—
246C22⋊Dic61—24no—
247#11758202—44no—
248#11758202—44no—
249#11758201—44no—
250#11758199—44no—
251#11758198—24no—
252#11758198—24no—
253#11758198—24no—
254#11758198—24no—
255#11758198—24no—
256C4⋊Dic61—21no—
257C4⋊Dic61—21no—
258C4⋊Dic61—24no—
259C4⋊Dic61—24no—
260C4⋊Dic61—24no—
261C4⋊Dic61C2×D414yes—
262C4⋊Dic61C2412yes—
263C4⋊Dic61C2412yes—
264#11758196—24no—
265#11758196—24no—
266#11758196—24no—
267#11758196C2×D414yes—
268#11758196C2×D414yes—
269C4×Dic61—24no—
270C4×Dic61—24no—
271C4×Dic61—24no—
272C4×Dic61—24no—
273C4×Dic61C2×D412yes—
274C4×Dic61C2×D412yes—
275C4×Dic61C2412yes—
276C4×Dic61C2412yes—
277C2×#92418—22no—
278C2×#92418—22no—
279C2×#92418C2412yes—
280C2×#92418C2412yes—
281#11758190—28no—
282C23×C61—22no—
283C23×C61—42no—
284C23×C61—42no—
285C23×C61—42no—
286C23×C61C22×D411yescharacteristic
287C22×D61—22no—
288C22×D61—42no—
289C22×D61—42no—
290C22×D61—42no—
291Q8×C61—22no—
292Q8×C61—22no—
293Q8×C61—22no—
294Q8×C61—22no—
295Q8×C61—22no—
296Q8×C61—22no—
297Q8×C61—42no—
298Q8×C61—42no—
299Q8×C61—42no—
300D4×C61—22no—
301D4×C61—22no—
302D4×C61—42no—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61—22no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—42no—
309C2×C4×C61—42no—
310C2×C4×C61—42no—
311C2×C4×C61C22×D412yes—
312C2×C4×C61C22×D412yes—
313C2×C4×C61C22×D411yescharacteristic
314C2×C4×C61C2×#4112yes—
315C2×C4×C61H(5,𝔽2)12yes—
316C2×C4×C61C2511yescharacteristic
317C2×Dic61—22no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—22no—
323C2×Dic61—22no—
324C2×Dic61—48no—
325C2×Dic61—42no—
326C2×Dic61—42no—
327C2×Dic61—42no—
328C2×Dic61C22×D412yes—
329C2×Dic61C22×D412yes—
330C2×Dic61C22×D412yes—
331C2×Dic61C22×D412yes—
332D244—22no—
333D244—22no—
334D244—42no—
335C4×D61—48no—
336Dic122—22no—
337Dic122—22no—
338Dic122—44no—
339Dic122—42no—
340C8×C61—22no—
341C8×C61C2×#4114yes—
342#92418—22no—
343#92418—22no—
344C2×#3402—611nomaximal, Sylow
345C22×C61—42no—
346C22×C61—42no—
347C22×C61—42no—
348C22×C61—84no—
349C22×C61#55012yes—
350C22×C61#57512yes—
351C22×C61#57812yes—
352C22×C61C23×D411yescharacteristic
353C2×D61—42no—
354C2×D61—42no—
355C2×D61—42no—
356C2×D61—84no—
357C4×C61—22no—
358C4×C61—22no—
359C4×C61—42no—
360C4×C61—42no—
361C4×C61—42no—
362C4×C61#55012yes—
363C4×C61C22×#4111yescharacteristic
364C4×C61C2×H(5,𝔽2)11yescharacteristic
365Dic61—22no—
366Dic61—22no—
367Dic61—22no—
368Dic61—22no—
369Dic61—42no—
370Dic61—42no—
371Dic61—42no—
372C2×#556—611no—
373C2×#556—611no—
374#3402—6116no—
375C2×#497—611no—
376C2×#497D6111yescharacteristic, complemented
377C2×#495—611no—
378C2×#464—611no—
379C2×#464—611no—
380C2×#462—611no—
381C2×#462—611no—
382C2×#463—611no—
383C2×#463—611no—
384C2×#446—611no—
385C2×#440—611no—
386C2×#440—611no—
387C2×C4×Q16—611no—
388C2×C61—82no—
389C2×C61#340214yescomplemented
390C2×C61C2×#55011yescharacteristic
391C2×C61C2×#57511yescharacteristic
392C2×C61C2×#57811yescharacteristic
393D61—82no—
394C22×Q16—611no—
395C22×Q16—611no—
396C22×Q16C2×D6111yescharacteristic
397C22×Q16C2×D6111yescharacteristic
398C22×SD16—611no—
399C22×SD16—611no—
400C22×SD16C2×D6111yescharacteristic
401C22×SD16C2×D6111yescharacteristic
402C22×D8—611no—
403#556—618no—
404#556—618no—
405#556—1224no—
406#556—1224no—
407C2×C4⋊Q8—611no—
408C2×C4⋊Q8C2×D6111yescharacteristic
409C2×#126—1221no—
410C2×#126—1221no—
411C2×#126—1221no—
412C2×#126—1221no—
413C2×#124—611no—
414C2×#124—611no—
415C2×#124—611no—
416C2×#124C2×D6111yescharacteristic
417C2×C22⋊Q8—1221no—
418C2×C22⋊Q8—1221no—
419C2×C4×Q8—611no—
420C2×C4×Q8—611no—
421C2×C4×Q8—611no—
422C2×C4×Q8—611no—
423C2×C4×Q8—611no—
424C2×C4×D4—611no—
425C2×C4×D4—611no—
426C2×#117—1221no—
427C2×#117—1221no—
428#497—618no—
429#497C2×D6118yescomplemented
430#495—618no—
431#464—618no—
432#464—618no—
433#463—618no—
434#463—618no—
435#462—618no—
436#462—618no—
437#446—618no—
438#440—618no—
439#440—618no—
440C4×Q16—618no—
441C2×#107—611no—
442C2×C4⋊C8—611no—
443C2×C4⋊C8—611no—
444C2×C4⋊C8—611no—
445C2×#103—611no—
446C2×#103—611no—
447C2×#103—611no—
448C2×#103—611no—
449C2×#102—611no—
450C2×#102—611no—
451C2×#97—611no—
452C2×#97C2×D6111yescharacteristic
453C2×C4×C8—611no—
454C61C2×#340211yescharacteristic, complemented, Sylow
455C22×Q8—611no—
456C22×Q8—611no—
457C22×Q8C22×D6111yescharacteristic
458C22×Q8C22×D6111yescharacteristic
459C22×Q8C22×D6111yescharacteristic
460C22×D4—611no—
461C22×D4C22×D6111yescharacteristic
462C23×C4—1221no—
463C23×C4—1221no—
464C2×Q16—24no—
465C2×Q16—42no—
466C2×Q16—614no—
467C2×Q16—614no—
468C2×Q16—2442no—
469C2×Q16—2442no—
470C2×Q16C22×D6114yes—
471C2×Q16C22×D6114yes—
472C2×SD16—24no—
473C2×SD16—42no—
474C2×SD16—614no—
475C2×SD16—614no—
476C2×SD16—1224no—
477C2×SD16—2442no—
478C2×SD16C22×D6114yes—
479C2×SD16C22×D6114yes—
480C2×D8—614no—
481C2×D8—2442no—
482C22×C8—611no—
483C22×C8—611no—
484C22×C8C22×D6111yescharacteristic
485C22×C8C22×D6111yescharacteristic
486C4⋊Q8—22no—
487C4⋊Q8—614no—
488C4⋊Q8—1222no—
489C4⋊Q8C22×D6114yes—
490#126—1228no—
491#126—1228no—
492#126—1228no—
493#126—1228no—
494#124—22no—
495#124—614no—
496#124—614no—
497#124—614no—
498#124—1222no—
499#124—1222no—
500#124—1222no—
501#124C22×D6114yes—
502C22⋊Q8—1228no—
503C22⋊Q8—1228no—
504C4×Q8—614no—
505C4×Q8—614no—
506C4×Q8—614no—
507C4×Q8—614no—
508C4×Q8—614no—
509C4×Q8—614no—
510C4×Q8—1222no—
511C4×Q8—1222no—
512C4×Q8—1222no—
513C4×Q8—1222no—
514C4×D4—614no—
515C4×D4—614no—
516C4×D4—1222no—
517C4×D4—1222no—
518#117—1228no—
519#117—1228no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—611no—
523C2×C4⋊C4—611no—
524C2×C4⋊C4—611no—
525C2×C4⋊C4—611no—
526C2×C4⋊C4—611no—
527C2×C4⋊C4—1221no—
528C2×C4⋊C4—1221no—
529C2×C4⋊C4—1221no—
530C2×C4⋊C4—1221no—
531C2×C4⋊C4—1221no—
532C2×C4⋊C4—1221no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—1221no—
536C2×C22⋊C4—1221no—
537C2×C22⋊C4—1221no—
538C2×C22⋊C4—1221no—
539C2×C22⋊C4—1221no—
540C2×C22⋊C4—1221no—
541C2×C22⋊C4—1221no—
542C2×C22⋊C4—1221no—
543C2×C42—611no—
544C2×C42—611no—
545C2×C42—1221no—
546C2×C42—1221no—
547C2×C42—1221no—
548C2×C42—1221no—
549C2×C42C22×D6111yescharacteristic
550#107—614no—
551C4⋊C8—614no—
552C4⋊C8—614no—
553C4⋊C8—614no—
554#103—614no—
555#103—614no—
556#103—614no—
557#103—614no—
558#102—614no—
559#102—614no—
560#97—614no—
561#97C22×D6114yes—
562C4×C8—614no—
563C24—21no—
564C24—1221no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—22no—
571C2×Q8—22no—
572C2×Q8—22no—
573C2×Q8—22no—
574C2×Q8—614no—
575C2×Q8—612no—
576C2×Q8—1221no—
577C2×Q8—1222no—
578C2×Q8—1222no—
579C2×Q8—2442no—
580C2×Q8C23×D6112yes—
581C2×Q8C23×D6112yes—
582C2×Q8C23×D6112yes—
583C2×D4—21no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—612no—
587C2×D4—1221no—
588C2×D4—1222no—
589C2×D4—1222no—
590C2×D4C23×D6112yes—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—611no—
595C22×C4—611no—
596C22×C4—611no—
597C22×C4—611no—
598C22×C4—1224no—
599C22×C4—1221no—
600C22×C4—1221no—
601C22×C4—1221no—
602C22×C4—1224no—
603C22×C4—2444no—
604C22×C4—2444no—
605C22×C4D4×D6111yescharacteristic
606C22×C4D4×D6111yescharacteristic
607C22×C4C23×D6111yescharacteristic
608Q16—28no—
609Q16—44no—
610Q16—2444no—
611Q16—2444no—
612SD16—28no—
613SD16—44no—
614SD16—1228no—
615SD16—2444no—
616D8—2444no—
617C2×C8—22no—
618C2×C8—612no—
619C2×C8—612no—
620C2×C8—1222no—
621C2×C8—1222no—
622C2×C8#1175822414yes—
623C2×C8C23×D6112yes—
624C2×C8C23×D6112yes—
625C4⋊C4—24no—
626C4⋊C4—24no—
627C4⋊C4—614no—
628C4⋊C4—614no—
629C4⋊C4—614no—
630C4⋊C4—612no—
631C4⋊C4—612no—
632C4⋊C4—1224no—
633C4⋊C4—1224no—
634C4⋊C4—1224no—
635C4⋊C4—1224no—
636C4⋊C4—1224no—
637C4⋊C4—1221no—
638C4⋊C4—1221no—
639C4⋊C4—1224no—
640C22⋊C4—24no—
641C22⋊C4—24no—
642C22⋊C4—1224no—
643C22⋊C4—1224no—
644C22⋊C4—1224no—
645C22⋊C4—1224no—
646C22⋊C4—1224no—
647C22⋊C4—1224no—
648C22⋊C4—1224no—
649C22⋊C4—1224no—
650C42—612no—
651C42—612no—
652C42—612no—
653C42—612no—
654C42—1224no—
655C42—1224no—
656C42—1224no—
657C42—1224no—
658C42D4×D6112yes—
659C42C23×D6112yes—
660C23—22no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—1222no—
665C23—2442no—
666C23—2442no—
667C23—2442no—
668C23C2×D4×D6111yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—22no—
672Q8—22no—
673Q8—22no—
674Q8—22no—
675Q8—42no—
676Q8—42no—
677Q8—42no—
678Q8—1222no—
679Q8—1222no—
680Q8—2444no—
681Q8—2442no—
682D4—22no—
683D4—22no—
684D4—42no—
685D4—1222no—
686D4—1222no—
687D4—2442no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—612no—
697C2×C4—612no—
698C2×C4—612no—
699C2×C4—612no—
700C2×C4—1222no—
701C2×C4—1222no—
702C2×C4—1222no—
703C2×C4—1222no—
704C2×C4—1222no—
705C2×C4—1222no—
706C2×C4—1222no—
707C2×C4—2448no—
708C2×C4—2448no—
709C2×C4—2442no—
710C2×C4—2442no—
711C2×C4—2442no—
712C2×C4C2×D4×D6112yes—
713C2×C4C2×D4×D6112yes—
714C2×C4C2×D4×D6111yescharacteristic
715C2×C4C2×#1175822412yes—
716C2×C4#1451982212yes—
717C2×C4C24×D6111yescharacteristic
718C8—22no—
719C8—1222no—
720C8—1222no—
721C8C2×#1175822414yes—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—84no—
726C22—4884no—
727C22—2442no—
728C22—2442no—
729C22—2442no—
730C22#1684043212yes—
731C22#1684056112yes—
732C22#1684057812yes—
733C22C22×D4×D6111yescharacteristic
734C4—22no—
735C4—22no—
736C4—42no—
737C4—42no—
738C4—42no—
739C4—1222no—
740C4—1222no—
741C4—1222no—
742C4—1222no—
743C4—2442no—
744C4—2442no—
745C4—2442no—
746C4#1684043212yes—
747C4C22×#1175822411yescharacteristic
748C4C2×#1451982211yescharacteristic
749C2—82no—
750C2—4882no—
751C2#2145889514yesdirect product factor
752C2C2×#1684043211yescharacteristic
753C2C2×#1684056111yescharacteristic
754C2C2×#1684057811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#497C2
socleC23×C61C22×D4
prime radicalC22×#11758199C22
hypercenterC2×#497D61
hypocenterC61C2×#3402
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#497

Complements

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

NH ≅ G/Ntype
1. C2×#16840486C2semidirect
2. C2×#16840481C2semidirect
3. #21458895C2direct (N × H)
4. C2×#16840155C2semidirect
6. C2×#16839986C2semidirect
7. C2×#16839982C2semidirect
8. C2×#16839970C2semidirect
9. C2×#16839969C2semidirect
12. C2×#16839890C2semidirect
13. C2×#16839864C2semidirect
14. C2×#16839863C2semidirect
15. C2×Q16×Dic61C2semidirect
16. C2×C61×#497C2semidirect
23. #16840486C22semidirect
25. #16840481C22semidirect
45. #16840155C22semidirect
47. #16839986C22semidirect
48. #16839982C22semidirect
51. #16839970C22semidirect
52. #16839969C22semidirect
53. #16839890C22semidirect
54. #16839864C22semidirect
55. #16839863C22semidirect
56. Q16×Dic61C22semidirect
75. C61×#497C22semidirect
376. C2×#497D61semidirect
389. C2×C61#3402semidirect
429. #497C2×D61semidirect
454. C61C2×#3402semidirect
751. C2#21458895direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404862
C2×#168404812
#214588952
C2×#168401552
C2×#168401432
C2×#168399862
C2×#168399822
C2×#168399702
C2×#168399692
C2×#168399792
C2×#168399742
C2×#168398902
C2×#168398642
C2×#168398632
C2×Q16×Dic612
C2×C61×#4972
C2×#340261