Finite Group Databasebeta

← C2×#21458816 #30560932

Subgroups — C2×#21458816 #30560932

Order 15616.

2022 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840495C211yesmaximal, characteristic, complemented
2C2×#16840484C211yesmaximal, characteristic, complemented
3#21458816C2116yesmaximal, direct product factor
4C2×#16840146C211yesmaximal, characteristic, complemented
5C2×#16840143C211yesmaximal, characteristic, complemented
6C2×#16840133C211yesmaximal, characteristic, complemented
7C2×#16839984C211yesmaximal, characteristic, complemented
8C2×#16839983C211yesmaximal, characteristic, complemented
9C2×#16839971C211yesmaximal, characteristic, complemented
10C2×#16839980C211yesmaximal, characteristic, complemented
11C2×#16839977C211yesmaximal, characteristic, complemented
12C2×#16839956C211yesmaximal, characteristic
13C2×C8×Dic122C211yesmaximal, characteristic, complemented
14C2×#16839849C211yesmaximal, characteristic, complemented
15C2×#16839849C211yesmaximal, characteristic, complemented
16C2×C4×SD16×C61C211yesmaximal, characteristic, complemented
17C22×Dic244C2211yescharacteristic
18C22×#11758202C2211yescharacteristic
19C22×#11758190C2211yescharacteristic
20C22×#11758190C2211yescharacteristic
21C22×#11758200C2211yescharacteristic
22C22×#11758201C2211yescharacteristic
23C22×D488C2211yescharacteristic
24C22×#11758199C2211yescharacteristic
25#16840495—24no—
26#16840495C2218yescomplemented
27#16840484—24no—
28#16840484C2218yescomplemented
29C2×#14519775C2211yescharacteristic
30C2×#14519773C2211yescharacteristic
31C2×#14519772—21no—
32C2×#14519771—21no—
33C2×#14519766C2211yescharacteristic
34C2×#14519765C2211yescharacteristic
35C2×#14519765C2211yescharacteristic
36C2×#14519764C2211yescharacteristic
37C2×#14519763—21no—
38C2×#14519760—21no—
39C2×#14519759—21no—
40C2×#14519755—21no—
41C2×C4×Dic122C2211yescharacteristic
42C2×#14519742C2211yescharacteristic
43C2×#14519742C2211yescharacteristic
44C2×#14519739C2211yescharacteristic
45C2×#14519739C2211yescharacteristic
46C2×C4×C22⋊D61—21no—
47C2×#14519734—21no—
48#16840146C2218yescomplemented
49#16840143C2218yescomplemented
50#16840133C2218yescomplemented
51#16839984C2218yescomplemented
52#16839983C2218yescomplemented
53#16839980C2218yescomplemented
54#16839977C2218yescomplemented
55#16839971C2218yescomplemented
56#16839956C2218yes—
57C8×Dic122C2218yescomplemented
58#16839849C2218yescomplemented
59#16839849C2218yescomplemented
60C2×C4⋊#92418C2211yescharacteristic
61C2×#14519706C2211yescharacteristic
62C2×#14519706C2211yescharacteristic
63C2×#14519700C2211yescharacteristic
64C2×#14519700C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×#14519697C2211yescharacteristic
67C2×C8×Dic61C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C22×SD16×C61C2211yescharacteristic
70C2×C4×Q8×C61C2211yescharacteristic
71C2×C4×D4×C61C2211yescharacteristic
72C4×SD16×C61C2218yescomplemented
73C2×#106×C61C2211yescharacteristic
74C2×#103×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×C4×C8×C61C2211yescharacteristic
77C22×Dic122D411yescharacteristic
78C22×Dic122C2311yescharacteristic
79C22×Dic122C2311yescharacteristic
80C22×D244C2311yescharacteristic
81C22×D244C2311yescharacteristic
82C22×C22⋊D61—21no—
83C22×C22⋊D61—21no—
84C22×C4×D61—21no—
85C22×C4×D61—21no—
86C2×Dic244—42no—
87C2×Dic244C2314yes—
88C2×#11758202—42no—
89C2×#11758202C2314yes—
90C2×#11758190—24no—
91C2×#11758190—24no—
92C2×#11758190C2314yes—
93C2×#11758190C2314yes—
94C2×#11758200—42no—
95C2×#11758200C2314yes—
96C2×#11758201—42no—
97C2×#11758201C2314yes—
98C2×D488—42no—
99C2×D488C2314yes—
100C2×#11758199—42no—
101C2×#11758199C2314yes—
102C22×#92418C2311yescharacteristic
103C22×#92418C2311yescharacteristic
104#14519775—22no—
105#14519775C2314yes—
106#14519773—22no—
107#14519773C2314yes—
108#14519772—28no—
109#14519771—28no—
110#14519766—22no—
111#14519766C2314yes—
112#14519765—22no—
113#14519765—22no—
114#14519765C2314yes—
115#14519765C2314yes—
116#14519764—22no—
117#14519764C2314yes—
118#14519763—28no—
119#14519760—28no—
120#14519759—28no—
121#14519755—28no—
122C4×Dic122D414yes—
123C4×Dic122C2314yes—
124#14519742—22no—
125#14519742—22no—
126#14519742C2314yes—
127#14519742C2314yes—
128#14519739—22no—
129#14519739—22no—
130#14519739C2314yes—
131#14519739C2314yes—
132C4×C22⋊D61—28no—
133#14519734—28no—
134C2×C4⋊Dic61D411yescharacteristic
135C2×#11758196—21no—
136C2×#11758196—21no—
137C2×#11758196—21no—
138C2×#11758196—21no—
139C2×#11758196D411yescharacteristic
140C2×#11758196D411yescharacteristic
141C2×C22⋊Dic61—21no—
142C2×C22⋊Dic61—21no—
143C2×#11758198—21no—
144C2×#11758198—21no—
145C2×#11758198—21no—
146C2×#11758198—21no—
147C2×#11758198—21no—
148C2×#11758198—21no—
149C2×#11758198—21no—
150C2×#11758198—21no—
151C2×C4×Dic61—21no—
152C2×C4×Dic61—21no—
153C2×C4×Dic61C2311yescharacteristic
154C2×C4×Dic61C2311yescharacteristic
155C4⋊#92418C2314yes—
156#14519706C2314yes—
157#14519706C2314yes—
158#14519700C2314yes—
159#14519700C2314yes—
160#14519697C2314yes—
161#14519697C2314yes—
162C8×Dic61C2314yes—
163C8×Dic61C2314yes—
164C22×Q8×C61C2311yescharacteristic
165C22×D4×C61C2311yescharacteristic
166C23×C4×C61—21no—
167C2×SD16×C61—24no—
168C2×SD16×C61C2314yes—
169C22×C8×C61C2311yescharacteristic
170C22×C8×C61C2311yescharacteristic
171C4×Q8×C61—22no—
172C4×Q8×C61C2314yes—
173C4×D4×C61—22no—
174C4×D4×C61C2314yes—
175C2×C4⋊C4×C61—21no—
176C2×C4⋊C4×C61C2311yescharacteristic
177C2×C4⋊C4×C61C2311yescharacteristic
178C2×C22⋊C4×C61—21no—
179C2×C42×C61—21no—
180C2×C42×C61C2311yescharacteristic
181#106×C61C2314yes—
182#103×C61C2314yes—
183#102×C61C2314yes—
184C4×C8×C61C2314yes—
185C24×C61—21no—
186C23×D61—21no—
187C23×D61—21no—
188C2×Q8×C61—21no—
189C2×Q8×C61—22no—
190C2×Q8×C61—22no—
191C2×Q8×C61C2412yes—
192C2×D4×C61—21no—
193C2×D4×C61—22no—
194C2×D4×C61—22no—
195C2×D4×C61C2412yes—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—24no—
200C22×C4×C61—82no—
201C22×C4×C61C2×D411yescharacteristic
202C22×C4×C61C2×D411yescharacteristic
203C22×C4×C61C2411yescharacteristic
204C2×C22⋊D61—24no—
205C2×C22⋊D61—24no—
206C2×C22⋊D61—44no—
207C2×C22⋊D61—82no—
208C22×Dic61—21no—
209C22×Dic61—21no—
210C22×Dic61C2×D411yescharacteristic
211C22×Dic61C2×D411yescharacteristic
212C22×Dic61C2×D411yescharacteristic
213C22×Dic61C2×D411yescharacteristic
214C2×D244—22no—
215C2×D244—22no—
216C2×D244—22no—
217C2×D244—22no—
218C2×D244—21no—
219C2×D244—21no—
220C2×D244C2412yes—
221C2×D244C2412yes—
222C2×C4×D61—24no—
223C2×C4×D61—24no—
224C2×C4×D61—44no—
225C2×C4×D61—82no—
226C2×Dic122—24no—
227C2×Dic122—22no—
228C2×Dic122—22no—
229C2×Dic122—22no—
230C2×Dic122—22no—
231C2×Dic122—21no—
232C2×Dic122—21no—
233C2×Dic122C2×D414yes—
234C2×Dic122C2412yes—
235C2×Dic122C2412yes—
236SD16×C61—28no—
237C2×C8×C61—22no—
238C2×C8×C61#4114yes—
239C2×C8×C61C2412yes—
240C2×C8×C61C2412yes—
241C4⋊C4×C61—24no—
242C4⋊C4×C61—21no—
243C4⋊C4×C61—21no—
244C4⋊C4×C61C2412yes—
245C4⋊C4×C61C2412yes—
246C22⋊C4×C61—24no—
247C42×C61—24no—
248C42×C61C2×D412yes—
249C42×C61C2412yes—
250C22⋊Dic61—24no—
251C22⋊Dic61—24no—
252#11758202—44no—
253#11758201—44no—
254#11758200—44no—
255#11758199—44no—
256#11758198—24no—
257#11758198—24no—
258#11758198—24no—
259#11758198—24no—
260#11758198—24no—
261#11758198—24no—
262#11758198—24no—
263#11758198—24no—
264C4⋊Dic61C2×D414yes—
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×Dic61C2×D412yes—
274C4×Dic61C2×D412yes—
275C4×Dic61C2412yes—
276C4×Dic61C2412yes—
277C2×#92418—22no—
278C2×#92418—22no—
279C2×#92418C2412yes—
280C2×#92418C2412yes—
281Dic244—44no—
282D488—44no—
283#11758190—28no—
284#11758190—28no—
285C23×C61—22no—
286C23×C61—42no—
287C23×C61—42no—
288C23×C61—42no—
289C23×C61C22×D411yescharacteristic
290C22×D61—22no—
291C22×D61—22no—
292C22×D61—42no—
293C22×D61—42no—
294C22×D61—42no—
295C22×D61—42no—
296C22×D61—42no—
297C22×D61—42no—
298Q8×C61—22no—
299Q8×C61—22no—
300Q8×C61—42no—
301D4×C61—22no—
302D4×C61—22no—
303D4×C61—42no—
304C2×C4×C61—22no—
305C2×C4×C61—22no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—42no—
310C2×C4×C61—42no—
311C2×C4×C61—42no—
312C2×C4×C61—84no—
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—42no—
327C2×Dic61—42no—
328C2×Dic61#13514yes—
329C2×Dic61C22×D412yes—
330C2×Dic61C22×D412yes—
331C2×Dic61C22×D412yes—
332C2×Dic61C22×D412yes—
333D244—22no—
334D244—22no—
335D244—22no—
336D244—22no—
337D244—42no—
338D244—42no—
339C4×D61—48no—
340C4×D61—84no—
341Dic122—28no—
342Dic122—22no—
343Dic122—22no—
344Dic122—22no—
345Dic122—22no—
346Dic122—42no—
347Dic122—42no—
348C8×C61—22no—
349C8×C61C2×#4114yes—
350#92418—22no—
351#92418—22no—
352C2×#3394—611nomaximal, Sylow
353C22×C61—42no—
354C22×C61—42no—
355C22×C61—42no—
356C22×C61—84no—
357C22×C61#55012yes—
358C22×C61C2×#13512yes—
359C22×C61#57712yes—
360C22×C61C23×D411yescharacteristic
361C2×D61—42no—
362C2×D61—42no—
363C2×D61—42no—
364C2×D61—42no—
365C2×D61—42no—
366C2×D61—42no—
367C2×D61—84no—
368C2×D61—84no—
369C4×C61—22no—
370C4×C61—22no—
371C4×C61—42no—
372C4×C61—42no—
373C4×C61—42no—
374C4×C61#55012yes—
375C4×C61C22×#4111yescharacteristic
376C4×C61C2×H(5,𝔽2)11yescharacteristic
377Dic61—22no—
378Dic61—22no—
379Dic61—22no—
380Dic61—42no—
381Dic61—42no—
382Dic61C2×#13514yes—
383C2×#559—611no—
384C2×#556—611no—
385#3394—6116no—
386C2×#495—611no—
387C2×#495—611no—
388C2×#492—611no—
389C2×#464—611no—
390C2×#464—611no—
391C2×#462—611no—
392C2×#463—611no—
393C2×#463—611no—
394C2×#459—611no—
395C2×C8×Q8—611no—
396C2×C4×SD16—611no—
397C2×C4×SD16—611no—
398C2×C4×SD16D6111yescharacteristic, complemented
399C2×C61—82no—
400C2×C61#339414yescomplemented
401C2×C61C2×#55011yescharacteristic
402C2×C61C22×#13511yescharacteristic
403C2×C61C2×#57711yescharacteristic
404D61—82no—
405D61—82no—
406C22×Q16—611no—
407C22×Q16—611no—
408C22×SD16—611no—
409C22×SD16—611no—
410C22×SD16—611no—
411C22×SD16—611no—
412C22×SD16C2×D6111yescharacteristic
413C22×D8—611no—
414C22×D8—611no—
415#559—618no—
416#559—1224no—
417#556—618no—
418#556—1224no—
419C2×C4⋊Q8—611no—
420C2×#127—611no—
421C2×#126—1221no—
422C2×#126—1221no—
423C2×#124—611no—
424C2×#124—611no—
425C2×#124—611no—
426C2×#124—611no—
427C2×#124—1221no—
428C2×#123—1221no—
429C2×#123—1221no—
430C2×C22⋊Q8—1221no—
431C2×C4×Q8—611no—
432C2×C4×Q8—611no—
433C2×C4×Q8—611no—
434C2×C4×Q8C2×D6111yescharacteristic
435C2×C4×D4—611no—
436C2×C4×D4—611no—
437C2×C4×D4—1221no—
438C2×C4×D4C2×D6111yescharacteristic
439C2×#117—1221no—
440#495—618no—
441#495—618no—
442#492—618no—
443#464—618no—
444#464—618no—
445#463—618no—
446#463—618no—
447#462—618no—
448#459—618no—
449C8×Q8—618no—
450C4×SD16—618no—
451C4×SD16—618no—
452C4×SD16C2×D6118yescomplemented
453C2×#106C2×D6111yescharacteristic
454C2×C4⋊C8—611no—
455C2×C4⋊C8—611no—
456C2×C4⋊C8—611no—
457C2×#103—611no—
458C2×#103—611no—
459C2×#103C2×D6111yescharacteristic
460C2×#102—611no—
461C2×#102—611no—
462C2×#102C2×D6111yescharacteristic
463C2×C4×C8—611no—
464C2×C4×C8—611no—
465C2×C4×C8C2×D6111yescharacteristic
466C61C2×#339411yescharacteristic, complemented, Sylow
467C22×Q8—611no—
468C22×Q8—611no—
469C22×Q8—611no—
470C22×Q8C22×D6111yescharacteristic
471C22×D4—611no—
472C22×D4—611no—
473C22×D4—1221no—
474C22×D4—1221no—
475C22×D4C22×D6111yescharacteristic
476C23×C4—21no—
477C23×C4—1221no—
478C23×C4—1221no—
479C2×Q16—614no—
480C2×Q16—614no—
481C2×Q16—2442no—
482C2×Q16—2442no—
483C2×SD16—24no—
484C2×SD16—614no—
485C2×SD16—614no—
486C2×SD16—614no—
487C2×SD16—614no—
488C2×SD16—1224no—
489C2×SD16—1224no—
490C2×SD16—2442no—
491C2×SD16—2442no—
492C2×SD16C22×D6114yes—
493C2×D8—614no—
494C2×D8—614no—
495C2×D8—2442no—
496C2×D8—2442no—
497C22×C8—611no—
498C22×C8—611no—
499C22×C8C22×D6111yescharacteristic
500C22×C8C22×D6111yescharacteristic
501C4⋊Q8—614no—
502C4⋊Q8—1222no—
503#127—614no—
504#127—1222no—
505#126—1228no—
506#126—1228no—
507#124—614no—
508#124—614no—
509#124—614no—
510#124—614no—
511#124—1222no—
512#124—1222no—
513#124—1228no—
514#124—1222no—
515#124—1222no—
516#123—1228no—
517#123—1228no—
518C22⋊Q8—1228no—
519C4×Q8—22no—
520C4×Q8—614no—
521C4×Q8—614no—
522C4×Q8—614no—
523C4×Q8—614no—
524C4×Q8—1222no—
525C4×Q8—1222no—
526C4×Q8C22×D6114yes—
527C4×D4—22no—
528C4×D4—614no—
529C4×D4—614no—
530C4×D4—1222no—
531C4×D4—1222no—
532C4×D4—1228no—
533C4×D4C22×D6114yes—
534#117—1228no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—611no—
537C2×C4⋊C4—611no—
538C2×C4⋊C4—611no—
539C2×C4⋊C4—1221no—
540C2×C4⋊C4—1221no—
541C2×C4⋊C4—1221no—
542C2×C4⋊C4—1221no—
543C2×C4⋊C4C22×D6111yescharacteristic
544C2×C4⋊C4C22×D6111yescharacteristic
545C2×C22⋊C4—21no—
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×C22⋊C4—1221no—
555C2×C22⋊C4—1221no—
556C2×C42—21no—
557C2×C42—611no—
558C2×C42—611no—
559C2×C42—1221no—
560C2×C42—1221no—
561C2×C42C22×D6111yescharacteristic
562#106C22×D6114yes—
563C4⋊C8—614no—
564C4⋊C8—614no—
565C4⋊C8—614no—
566#103—614no—
567#103—614no—
568#103C22×D6114yes—
569#102—614no—
570#102—614no—
571#102C22×D6114yes—
572C4×C8—614no—
573C4×C8—614no—
574C4×C8C22×D6114yes—
575C24—21no—
576C24—1221no—
577C24—1221no—
578C2×Q8—21no—
579C2×Q8—22no—
580C2×Q8—22no—
581C2×Q8—614no—
582C2×Q8—612no—
583C2×Q8—612no—
584C2×Q8—1224no—
585C2×Q8—1221no—
586C2×Q8—1221no—
587C2×Q8—1222no—
588C2×Q8—1222no—
589C2×Q8—1222no—
590C2×Q8—1222no—
591C2×Q8C23×D6112yes—
592C2×D4—21no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—612no—
596C2×D4—612no—
597C2×D4—1224no—
598C2×D4—1224no—
599C2×D4—1221no—
600C2×D4—1221no—
601C2×D4—1222no—
602C2×D4—1222no—
603C2×D4—1222no—
604C2×D4—1222no—
605C2×D4—4882no—
606C2×D4—2444no—
607C2×D4C23×D6112yes—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—24no—
612C22×C4—82no—
613C22×C4—611no—
614C22×C4—611no—
615C22×C4—611no—
616C22×C4—611no—
617C22×C4—1224no—
618C22×C4—1224no—
619C22×C4—1221no—
620C22×C4—1221no—
621C22×C4—4882no—
622C22×C4—2444no—
623C22×C4D4×D6111yescharacteristic
624C22×C4D4×D6111yescharacteristic
625C22×C4C23×D6111yescharacteristic
626Q16—2444no—
627Q16—2444no—
628SD16—28no—
629SD16—1228no—
630SD16—1228no—
631SD16—2444no—
632SD16—2444no—
633D8—2444no—
634D8—2444no—
635C2×C8—22no—
636C2×C8—612no—
637C2×C8—612no—
638C2×C8—1222no—
639C2×C8—1222no—
640C2×C8#1175822214yes—
641C2×C8C23×D6112yes—
642C2×C8C23×D6112yes—
643C4⋊C4—24no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—614no—
647C4⋊C4—614no—
648C4⋊C4—614no—
649C4⋊C4—1224no—
650C4⋊C4—1224no—
651C4⋊C4—1224no—
652C4⋊C4—1224no—
653C4⋊C4C23×D6112yes—
654C4⋊C4C23×D6112yes—
655C22⋊C4—24no—
656C22⋊C4—1224no—
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—24no—
667C42—612no—
668C42—612no—
669C42—612no—
670C42—612no—
671C42—1224no—
672C42—1224no—
673C42D4×D6112yes—
674C42C23×D6112yes—
675C23—22no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—1222no—
680C23—1222no—
681C23—2442no—
682C23—2442no—
683C23—2442no—
684C23—2442no—
685C23—2442no—
686C23—2442no—
687C23C2×D4×D6111yescharacteristic
688Q8—22no—
689Q8—22no—
690Q8—42no—
691Q8—1228no—
692Q8—1222no—
693Q8—1222no—
694Q8—1222no—
695Q8—1222no—
696Q8—2442no—
697Q8—2442no—
698D4—22no—
699D4—22no—
700D4—42no—
701D4—1222no—
702D4—1222no—
703D4—1222no—
704D4—1222no—
705D4—4884no—
706D4—2448no—
707D4—2442no—
708D4—2442no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—84no—
718C2×C4—614no—
719C2×C4—612no—
720C2×C4—612no—
721C2×C4—612no—
722C2×C4—612no—
723C2×C4—1222no—
724C2×C4—1222no—
725C2×C4—1222no—
726C2×C4—1222no—
727C2×C4—1222no—
728C2×C4—4884no—
729C2×C4—2448no—
730C2×C4—2442no—
731C2×C4—2442no—
732C2×C4C2×D4×D6112yes—
733C2×C4C2×D4×D6112yes—
734C2×C4C2×D4×D6111yescharacteristic
735C2×C4C2×#1175822212yes—
736C2×C4#1451982312yes—
737C2×C4C24×D6111yescharacteristic
738C8—22no—
739C8—1222no—
740C8—1222no—
741C8C2×#1175822214yes—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—84no—
746C22—4884no—
747C22—4884no—
748C22—2442no—
749C22—2442no—
750C22—2442no—
751C22—2442no—
752C22—2442no—
753C22—2442no—
754C22#1684043312yes—
755C22#135×D6112yes—
756C22#1684056812yes—
757C22C22×D4×D6111yescharacteristic
758C4—22no—
759C4—22no—
760C4—42no—
761C4—42no—
762C4—42no—
763C4—614no—
764C4—1222no—
765C4—1222no—
766C4—1222no—
767C4—2442no—
768C4—2442no—
769C4#1684043312yes—
770C4C22×#1175822211yescharacteristic
771C4C2×#1451982311yescharacteristic
772C2—82no—
773C2—4882no—
774C2—4882no—
775C2#2145881614yesdirect product factor
776C2C2×#1684043311yescharacteristic
777C2C2×#135×D6111yescharacteristic
778C2C2×#1684056811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C4×SD16×C61C2
socleC23×C61C22×D4
prime radicalC2×#16839956C2
hypercenterC2×C4×SD16D61
hypocenterC61C2×#3394
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#16840495C2semidirect
2. C2×#16840484C2semidirect
3. #21458816C2direct (N × H)
4. C2×#16840146C2semidirect
5. C2×#16840143C2semidirect
6. C2×#16840133C2semidirect
7. C2×#16839984C2semidirect
8. C2×#16839983C2semidirect
9. C2×#16839971C2semidirect
10. C2×#16839980C2semidirect
11. C2×#16839977C2semidirect
13. C2×C8×Dic122C2semidirect
14. C2×#16839849C2semidirect
15. C2×#16839849C2semidirect
16. C2×C4×SD16×C61C2semidirect
26. #16840495C22semidirect
28. #16840484C22semidirect
48. #16840146C22semidirect
49. #16840143C22semidirect
50. #16840133C22semidirect
51. #16839984C22semidirect
52. #16839983C22semidirect
53. #16839980C22semidirect
54. #16839977C22semidirect
55. #16839971C22semidirect
57. C8×Dic122C22semidirect
58. #16839849C22semidirect
59. #16839849C22semidirect
72. C4×SD16×C61C22semidirect
398. C2×C4×SD16D61semidirect
400. C2×C61#3394semidirect
452. C4×SD16C2×D61semidirect
466. C61C2×#3394semidirect
775. C2#21458816direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404952
C2×#168404842
#214588162
C2×#168401462
C2×#168401432
C2×#168401332
C2×#168399842
C2×#168399832
C2×#168399712
C2×#168399802
C2×#168399772
C2×#168399562
C2×C8×Dic1222
C2×#168398492
C2×C4×SD16×C612
C2×#339461