Finite Group Databasebeta

← C2×#21458869 #30561002

Subgroups — C2×#21458869 #30561002

Order 15616.

1970 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840494C211yesmaximal, characteristic
2C2×#16840487C211yesmaximal, characteristic, complemented
3#21458869C2116yesmaximal, direct product factor
4C2×#16840155C211yesmaximal, characteristic, complemented
5C2×#16840133C211yesmaximal, characteristic
6C2×#16839986C211yesmaximal, characteristic, complemented
7C2×#16839981C211yesmaximal, characteristic, complemented
8C2×#16839970C211yesmaximal, characteristic, complemented
9C2×#16839960C211yesmaximal, characteristic
10C2×#16839965C211yesmaximal, characteristic, complemented
11C2×#16839964C211yesmaximal, characteristic, complemented
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×#11758190C2211yescharacteristic
19C22×#11758200C2211yescharacteristic
20C22×#11758201C2211yescharacteristic
21C22×#11758201C2211yescharacteristic
22#16840494—24no—
23#16840494C2218yes—
24#16840487—24no—
25#16840487C2218yescomplemented
26C2×#14519775C2211yescharacteristic
27C2×#14519775C2211yescharacteristic
28C2×#14519773C2211yescharacteristic
29C2×#14519768—21no—
30C2×#14519767—21no—
31C2×#14519767—21no—
32C2×#14519766C2211yescharacteristic
33C2×#14519763—21no—
34C2×#14519761—21no—
35C2×#14519759—21no—
36C2×Q8×Dic61C2211yescharacteristic
37C2×Q8×Dic61C2211yescharacteristic
38C2×Q8×Dic61C2211yescharacteristic
39C2×C4×Dic122C2211yescharacteristic
40C2×C4×Dic122C2211yescharacteristic
41C2×#14519742—21no—
42C2×C4×D244C2211yescharacteristic
43C2×D4×Dic61C2211yescharacteristic
44C2×#14519737—21no—
45#16840155C2218yescomplemented
46#16840133C2218yes—
47#16839986C2218yescomplemented
48#16839981C2218yescomplemented
49#16839970C2218yescomplemented
50#16839965C2218yescomplemented
51#16839964C2218yescomplemented
52#16839960C2218yes—
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
80C22×C22⋊D61—21no—
81C22×C22⋊D61—21no—
82C23×Dic61—21no—
83C22×C4×D61—21no—
84C2×#11758202—42no—
85C2×#11758202C2314yes—
86C2×#11758190—24no—
87C2×#11758190C2314yes—
88C2×#11758200—42no—
89C2×#11758200C2314yes—
90C2×#11758201—42no—
91C2×#11758201—42no—
92C2×#11758201C2314yes—
93C2×#11758201C2314yes—
94C22×#92418C2311yescharacteristic
95C22×#92418C2311yescharacteristic
96#14519775—22no—
97#14519775—22no—
98#14519775C2314yes—
99#14519775C2314yes—
100#14519773—22no—
101#14519773C2314yes—
102#14519768—28no—
103#14519767—28no—
104#14519767—28no—
105#14519766—22no—
106#14519766C2314yes—
107#14519763—28no—
108#14519761—28no—
109#14519759—28no—
110Q8×Dic61—22no—
111Q8×Dic61—22no—
112Q8×Dic61—22no—
113Q8×Dic61C2314yes—
114Q8×Dic61C2314yes—
115Q8×Dic61C2314yes—
116C4×Dic122—22no—
117C4×Dic122D414yes—
118C4×Dic122C2314yes—
119C4×Dic122C2314yes—
120#14519742—28no—
121C4×D244—22no—
122C4×D244C2314yes—
123D4×Dic61—22no—
124D4×Dic61C2314yes—
125#14519737—28no—
126C2×C4⋊Dic61—21no—
127C2×C4⋊Dic61—21no—
128C2×C4⋊Dic61—21no—
129C2×C4⋊Dic61D411yescharacteristic
130C2×C4⋊Dic61C2311yescharacteristic
131C2×C4⋊Dic61C2311yescharacteristic
132C2×#11758196—21no—
133C2×#11758196—21no—
134C2×#11758196—21no—
135C2×#11758196—21no—
136C2×#11758196—21no—
137C2×#11758196D411yescharacteristic
138C2×#11758196D411yescharacteristic
139C2×C22⋊Dic61—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
209C2×C22⋊D61—24no—
210C2×C22⋊D61—24no—
211C2×C22⋊D61—44no—
212C2×C22⋊D61—82no—
213C22×Dic61—21no—
214C22×Dic61—21no—
215C22×Dic61—21no—
216C22×Dic61—24no—
217C22×Dic61—82no—
218C22×Dic61C2×D411yescharacteristic
219C22×Dic61C2×D411yescharacteristic
220C22×Dic61C2×D411yescharacteristic
221C22×Dic61C2×D411yescharacteristic
222C2×D244—22no—
223C2×D244—22no—
224C2×D244—21no—
225C2×D244C2412yes—
226C2×C4×D61—24no—
227C2×C4×D61—82no—
228C2×Dic122—24no—
229C2×Dic122—22no—
230C2×Dic122—22no—
231C2×Dic122—21no—
232C2×Dic122C2×D414yes—
233C2×Dic122C2412yes—
234Q16×C61—28no—
235Q16×C61—44no—
236SD16×C61—28no—
237SD16×C61—44no—
238C2×C8×C61—22no—
239C2×C8×C61#4114yes—
240C2×C8×C61C2412yes—
241C2×C8×C61C2412yes—
242C4⋊C4×C61—24no—
243C4⋊C4×C61—24no—
244C22⋊C4×C61—24no—
245C22⋊C4×C61—24no—
246C42×C61C2×D412yes—
247C42×C61C2412yes—
248C22⋊Dic61—24no—
249#11758202—44no—
250#11758201—44no—
251#11758201—44no—
252#11758200—44no—
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#11758196—24no—
268#11758196—24no—
269#11758196C2×D414yes—
270#11758196C2×D414yes—
271C4×Dic61—24no—
272C4×Dic61—24no—
273C4×Dic61—24no—
274C4×Dic61—24no—
275C4×Dic61C2×D412yes—
276C4×Dic61C2×D412yes—
277C4×Dic61C2412yes—
278C4×Dic61C2412yes—
279C2×#92418—22no—
280C2×#92418—22no—
281C2×#92418C2412yes—
282C2×#92418C2412yes—
283#11758190—28no—
284C23×C61—22no—
285C23×C61—42no—
286C23×C61—42no—
287C23×C61—42no—
288C23×C61C22×D411yescharacteristic
289C22×D61—22no—
290C22×D61—42no—
291C22×D61—42no—
292C22×D61—42no—
293Q8×C61—22no—
294Q8×C61—22no—
295Q8×C61—22no—
296Q8×C61—22no—
297Q8×C61—22no—
298Q8×C61—22no—
299Q8×C61—42no—
300Q8×C61—42no—
301Q8×C61—42no—
302D4×C61—22no—
303D4×C61—22no—
304D4×C61—42no—
305C2×C4×C61—22no—
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×C61—42no—
313C2×C4×C61C22×D412yes—
314C2×C4×C61C22×D412yes—
315C2×C4×C61C22×D411yescharacteristic
316C2×C4×C61C2×#4112yes—
317C2×C4×C61H(5,𝔽2)12yes—
318C2×C4×C61C2511yescharacteristic
319C22⋊D61—48no—
320C22⋊D61—84no—
321C2×Dic61—22no—
322C2×Dic61—22no—
323C2×Dic61—22no—
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61—42no—
328C2×Dic61—42no—
329C2×Dic61—42no—
330C2×Dic61—84no—
331C2×Dic61#13714yes—
332C2×Dic61C22×D412yes—
333C2×Dic61C22×D412yes—
334C2×Dic61C22×D412yes—
335C2×Dic61C22×D412yes—
336D244—22no—
337D244—22no—
338D244—42no—
339C4×D61—84no—
340Dic122—28no—
341Dic122—22no—
342Dic122—22no—
343Dic122—42no—
344C8×C61—22no—
345C8×C61C2×#4114yes—
346#92418—22no—
347#92418—22no—
348C2×#3400—611nomaximal, Sylow
349C22×C61—42no—
350C22×C61—42no—
351C22×C61—42no—
352C22×C61—84no—
353C22×C61#55012yes—
354C22×C61C2×#13712yes—
355C22×C61#57712yes—
356C22×C61C23×D411yescharacteristic
357C2×D61—42no—
358C2×D61—42no—
359C2×D61—42no—
360C2×D61—84no—
361C4×C61—22no—
362C4×C61—22no—
363C4×C61—42no—
364C4×C61—42no—
365C4×C61—42no—
366C4×C61#55012yes—
367C4×C61C22×#4111yescharacteristic
368C4×C61C2×H(5,𝔽2)11yescharacteristic
369Dic61—22no—
370Dic61—22no—
371Dic61—22no—
372Dic61—42no—
373Dic61—42no—
374Dic61—42no—
375Dic61C2×#13714yes—
376C2×#559—611no—
377C2×#557—611no—
378#3400—6116no—
379C2×#497—611no—
380C2×#497D6111yescharacteristic, complemented
381C2×#492—611no—
382C2×#464—611no—
383C2×#464—611no—
384C2×#462—611no—
385C2×#460—611no—
386C2×#461—611no—
387C2×#461—611no—
388C2×#446—611no—
389C2×#440—611no—
390C2×#440—611no—
391C2×C4×Q16—611no—
392C2×C61—82no—
393C2×C61#340014yescomplemented
394C2×C61C2×#55011yescharacteristic
395C2×C61C22×#13711yescharacteristic
396C2×C61C2×#57711yescharacteristic
397D61—82no—
398C22×Q16—611no—
399C22×Q16C2×D6111yescharacteristic
400C22×Q16C2×D6111yescharacteristic
401C22×SD16—611no—
402C22×SD16—611no—
403C22×SD16—611no—
404C22×SD16—611no—
405C22×SD16C2×D6111yescharacteristic
406C22×SD16C2×D6111yescharacteristic
407#559—618no—
408#559—1224no—
409#557—618no—
410#557—1224no—
411C2×C4⋊Q8—611no—
412C2×C4⋊Q8—611no—
413C2×C4⋊Q8C2×D6111yescharacteristic
414C2×#127—611no—
415C2×#125—1221no—
416C2×#125—1221no—
417C2×#125—1221no—
418C2×#124—611no—
419C2×#124—1221no—
420C2×#124C2×D6111yescharacteristic
421C2×#123—1221no—
422C2×#123—1221no—
423C2×C4×Q8—611no—
424C2×C4×Q8—611no—
425C2×C4×Q8—611no—
426C2×C4×Q8—611no—
427C2×C4×Q8—611no—
428C2×C4×Q8—1221no—
429C2×C4×D4—611no—
430C2×C4×D4—611no—
431C2×C4×D4—1221no—
432#497—618no—
433#497C2×D6118yescomplemented
434#492—618no—
435#464—618no—
436#464—618no—
437#462—618no—
438#461—618no—
439#461—618no—
440#460—618no—
441#446—618no—
442#440—618no—
443#440—618no—
444C4×Q16—618no—
445C2×#107—611no—
446C2×C4⋊C8—611no—
447C2×C4⋊C8—611no—
448C2×C4⋊C8—611no—
449C2×#103—611no—
450C2×#103—611no—
451C2×#103—611no—
452C2×#103—611no—
453C2×#102—611no—
454C2×#102—611no—
455C2×#97—611no—
456C2×#97C2×D6111yescharacteristic
457C2×C4×C8—611no—
458C61C2×#340011yescharacteristic, complemented, Sylow
459C22×Q8—611no—
460C22×Q8—611no—
461C22×Q8C22×D6111yescharacteristic
462C22×Q8C22×D6111yescharacteristic
463C22×Q8C22×D6111yescharacteristic
464C22×D4—611no—
465C22×D4—1221no—
466C22×D4—1221no—
467C22×D4C22×D6111yescharacteristic
468C23×C4—1221no—
469C23×C4—1221no—
470C2×Q16—24no—
471C2×Q16—42no—
472C2×Q16—614no—
473C2×Q16—2442no—
474C2×Q16C22×D6114yes—
475C2×Q16C22×D6114yes—
476C2×SD16—24no—
477C2×SD16—42no—
478C2×SD16—614no—
479C2×SD16—614no—
480C2×SD16—614no—
481C2×SD16—614no—
482C2×SD16—1224no—
483C2×SD16—2442no—
484C2×SD16—2442no—
485C2×SD16—2442no—
486C2×SD16C22×D6114yes—
487C2×SD16C22×D6114yes—
488C22×C8—611no—
489C22×C8—611no—
490C22×C8C22×D6111yescharacteristic
491C22×C8C22×D6111yescharacteristic
492C4⋊Q8—22no—
493C4⋊Q8—614no—
494C4⋊Q8—614no—
495C4⋊Q8—1222no—
496C4⋊Q8—1222no—
497C4⋊Q8C22×D6114yes—
498#127—614no—
499#127—1222no—
500#125—1228no—
501#125—1228no—
502#125—1228no—
503#124—22no—
504#124—614no—
505#124—1222no—
506#124—1228no—
507#124C22×D6114yes—
508#123—1228no—
509#123—1228no—
510C4×Q8—614no—
511C4×Q8—614no—
512C4×Q8—614no—
513C4×Q8—614no—
514C4×Q8—614no—
515C4×Q8—614no—
516C4×Q8—1222no—
517C4×Q8—1222no—
518C4×Q8—1222no—
519C4×Q8—1228no—
520C4×Q8—1222no—
521C4×D4—614no—
522C4×D4—614no—
523C4×D4—1222no—
524C4×D4—1228no—
525C4×D4—1222no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—611no—
529C2×C4⋊C4—611no—
530C2×C4⋊C4—611no—
531C2×C4⋊C4—611no—
532C2×C4⋊C4—611no—
533C2×C4⋊C4—1221no—
534C2×C4⋊C4—1221no—
535C2×C4⋊C4—1221no—
536C2×C4⋊C4—1221no—
537C2×C4⋊C4—1221no—
538C2×C4⋊C4—1221no—
539C2×C4⋊C4—1221no—
540C2×C4⋊C4—1221no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—1221no—
544C2×C22⋊C4—1221no—
545C2×C22⋊C4—1221no—
546C2×C22⋊C4—1221no—
547C2×C42—611no—
548C2×C42—611no—
549C2×C42—1221no—
550C2×C42—1221no—
551C2×C42—1221no—
552C2×C42—1221no—
553C2×C42C22×D6111yescharacteristic
554#107—614no—
555C4⋊C8—614no—
556C4⋊C8—614no—
557C4⋊C8—614no—
558#103—614no—
559#103—614no—
560#103—614no—
561#103—614no—
562#102—614no—
563#102—614no—
564#97—614no—
565#97C22×D6114yes—
566C4×C8—614no—
567C24—21no—
568C24—1221no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—22no—
573C2×Q8—22no—
574C2×Q8—22no—
575C2×Q8—22no—
576C2×Q8—22no—
577C2×Q8—22no—
578C2×Q8—614no—
579C2×Q8—612no—
580C2×Q8—1224no—
581C2×Q8—1221no—
582C2×Q8—1222no—
583C2×Q8—1222no—
584C2×Q8C23×D6112yes—
585C2×Q8C23×D6112yes—
586C2×Q8C23×D6112yes—
587C2×D4—21no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—612no—
591C2×D4—1224no—
592C2×D4—1224no—
593C2×D4—1221no—
594C2×D4—1222no—
595C2×D4—1222no—
596C2×D4—4882no—
597C2×D4—2444no—
598C2×D4C23×D6112yes—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—611no—
603C22×C4—611no—
604C22×C4—611no—
605C22×C4—611no—
606C22×C4—1224no—
607C22×C4—1221no—
608C22×C4—1221no—
609C22×C4—1221no—
610C22×C4—1224no—
611C22×C4—4882no—
612C22×C4—4882no—
613C22×C4D4×D6111yescharacteristic
614C22×C4D4×D6111yescharacteristic
615C22×C4C23×D6111yescharacteristic
616Q16—28no—
617Q16—44no—
618Q16—2444no—
619SD16—28no—
620SD16—44no—
621SD16—1228no—
622SD16—2444no—
623SD16—2444no—
624SD16—2444no—
625C2×C8—22no—
626C2×C8—612no—
627C2×C8—612no—
628C2×C8—1222no—
629C2×C8—1222no—
630C2×C8#1175822414yes—
631C2×C8C23×D6112yes—
632C2×C8C23×D6112yes—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—614no—
636C4⋊C4—614no—
637C4⋊C4—614no—
638C4⋊C4—612no—
639C4⋊C4—612no—
640C4⋊C4—1224no—
641C4⋊C4—1224no—
642C4⋊C4—1224no—
643C4⋊C4—1224no—
644C4⋊C4—1224no—
645C4⋊C4—1224no—
646C4⋊C4—1224no—
647C4⋊C4—1221no—
648C4⋊C4—1221no—
649C4⋊C4—1224no—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—1224no—
653C22⋊C4—1224no—
654C22⋊C4—1224no—
655C22⋊C4—1224no—
656C42—612no—
657C42—612no—
658C42—612no—
659C42—612no—
660C42—1224no—
661C42—1224no—
662C42—1224no—
663C42—1224no—
664C42D4×D6112yes—
665C42C23×D6112yes—
666C23—22no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—1222no—
671C23—2442no—
672C23—2442no—
673C23—2442no—
674C23C2×D4×D6111yescharacteristic
675Q8—22no—
676Q8—22no—
677Q8—22no—
678Q8—22no—
679Q8—22no—
680Q8—22no—
681Q8—42no—
682Q8—42no—
683Q8—42no—
684Q8—1228no—
685Q8—1222no—
686Q8—1222no—
687Q8—2442no—
688D4—22no—
689D4—22no—
690D4—42no—
691D4—1222no—
692D4—1222no—
693D4—4884no—
694D4—2448no—
695D4—2442no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—614no—
705C2×C4—612no—
706C2×C4—612no—
707C2×C4—612no—
708C2×C4—612no—
709C2×C4—1222no—
710C2×C4—1222no—
711C2×C4—1222no—
712C2×C4—1222no—
713C2×C4—1222no—
714C2×C4—1222no—
715C2×C4—4884no—
716C2×C4—4884no—
717C2×C4—2442no—
718C2×C4—2442no—
719C2×C4—2442no—
720C2×C4C2×D4×D6112yes—
721C2×C4C2×D4×D6112yes—
722C2×C4C2×D4×D6111yescharacteristic
723C2×C4C2×#1175822412yes—
724C2×C4#1451982212yes—
725C2×C4C24×D6111yescharacteristic
726C8—22no—
727C8—1222no—
728C8—1222no—
729C8C2×#1175822414yes—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—84no—
734C22—4884no—
735C22—2442no—
736C22—2442no—
737C22—2442no—
738C22#1684043212yes—
739C22#137×D6112yes—
740C22#1684057112yes—
741C22C22×D4×D6111yescharacteristic
742C4—22no—
743C4—22no—
744C4—42no—
745C4—42no—
746C4—42no—
747C4—614no—
748C4—1222no—
749C4—1222no—
750C4—1222no—
751C4—2442no—
752C4—2442no—
753C4—2442no—
754C4#1684043212yes—
755C4C22×#1175822411yescharacteristic
756C4C2×#1451982211yescharacteristic
757C2—82no—
758C2—4882no—
759C2#2145886914yesdirect product factor
760C2C2×#1684043211yescharacteristic
761C2C2×#137×D6111yescharacteristic
762C2C2×#1684057111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#497C2
socleC23×C61C22×D4
prime radicalC2×#14519773C22
hypercenterC2×#497D61
hypocenterC61C2×#3400
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
2. C2×#16840487C2semidirect
3. #21458869C2direct (N × H)
4. C2×#16840155C2semidirect
6. C2×#16839986C2semidirect
7. C2×#16839981C2semidirect
8. C2×#16839970C2semidirect
10. C2×#16839965C2semidirect
11. C2×#16839964C2semidirect
12. C2×#16839890C2semidirect
13. C2×#16839864C2semidirect
14. C2×#16839863C2semidirect
15. C2×Q16×Dic61C2semidirect
16. C2×C61×#497C2semidirect
25. #16840487C22semidirect
45. #16840155C22semidirect
47. #16839986C22semidirect
48. #16839981C22semidirect
49. #16839970C22semidirect
50. #16839965C22semidirect
51. #16839964C22semidirect
53. #16839890C22semidirect
54. #16839864C22semidirect
55. #16839863C22semidirect
56. Q16×Dic61C22semidirect
75. C61×#497C22semidirect
380. C2×#497D61semidirect
393. C2×C61#3400semidirect
433. #497C2×D61semidirect
458. C61C2×#3400semidirect
759. C2#21458869direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404942
C2×#168404872
#214588692
C2×#168401552
C2×#168401332
C2×#168399862
C2×#168399812
C2×#168399702
C2×#168399602
C2×#168399652
C2×#168399642
C2×#168398902
C2×#168398642
C2×#168398632
C2×Q16×Dic612
C2×C61×#4972
C2×#340061