Finite Group Databasebeta

← C2×#21456088 #30548335

Subgroups — C2×#21456088 #30548335

Order 15616.

2134 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840386C211yesmaximal, characteristic, complemented
2C2×#16840244C211yesmaximal, characteristic, complemented
3#21456088C2116yesmaximal, direct product factor
4C2×#16840099C211yesmaximal, characteristic, complemented
5C2×#16840077C211yesmaximal, characteristic, complemented
6C2×#16840039C211yesmaximal, characteristic, complemented
7C2×#16839984C211yesmaximal, characteristic, complemented
8C2×#16839978C211yesmaximal, characteristic, complemented
9C2×#16839927C211yesmaximal, characteristic, complemented
10C2×#16839910C211yesmaximal, characteristic
11C2×#16839865C211yesmaximal, characteristic, complemented
12C2×#16839861C211yesmaximal, characteristic, complemented
13C2×#16839854C211yesmaximal, characteristic, complemented
14C2×#16839844C211yesmaximal, characteristic, complemented
15C2×#16839822C211yesmaximal, characteristic, complemented
16C2×C61×#477C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C22×#11758202C2211yescharacteristic
19C22×#11758190C2211yescharacteristic
20C22×#11758201C2211yescharacteristic
21C22×D488C2211yescharacteristic
22#16840386—24no—
23#16840386C2218yescomplemented
24C2×#14519772—21no—
25C2×#14519766—21no—
26C2×#14519765C2211yescharacteristic
27C2×#14519762—21no—
28C2×#14519757C2211yescharacteristic
29C2×#14519753—21no—
30C2×#14519752C2211yescharacteristic
31#16840244—24no—
32#16840244C2218yescomplemented
33C2×Q8×Dic61C2211yescharacteristic
34C2×#14519742C2211yescharacteristic
35C2×C4×D244—21no—
36C2×C4×D244C2211yescharacteristic
37C2×#14519739—21no—
38C2×#14519739C2211yescharacteristic
39C2×#14519739C2211yescharacteristic
40C2×#14519734—21no—
41C2×#14519734C2211yescharacteristic
42C2×C4⋊C4×D61—21no—
43C2×C4⋊C4×D61C2211yescharacteristic
44#16840099C2218yescomplemented
45#16840077C2218yescomplemented
46#16840039C2218yescomplemented
47#16839984C2218yescomplemented
48#16839978C2218yescomplemented
49#16839927C2218yescomplemented
50#16839910C2218yes—
51#16839865C2218yescomplemented
52#16839861C2218yescomplemented
53#16839854C2218yescomplemented
54#16839844C2218yescomplemented
55#16839822C2218yescomplemented
56C2×#14519710C2211yescharacteristic
57C2×#14519710C2211yescharacteristic
58C2×C4⋊#92418C2211yescharacteristic
59C2×#14519702C2211yescharacteristic
60C2×#14519700C2211yescharacteristic
61C2×#14519699C2211yescharacteristic
62C2×#14519697C2211yescharacteristic
63C2×#14519697C2211yescharacteristic
64C2×#14519697C2211yescharacteristic
65C2×#14519689C2211yescharacteristic
66C2×#14519689C2211yescharacteristic
67C2×#14519687C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C2×C4⋊Q8×C61C2211yescharacteristic
70C2×C4×Q8×C61C2211yescharacteristic
71C61×#477C2218yescomplemented
72C2×#107×C61C2211yescharacteristic
73C2×#107×C61C2211yescharacteristic
74C2×C4⋊C8×C61C2211yescharacteristic
75C2×#103×C61C2211yescharacteristic
76C2×#103×C61C2211yescharacteristic
77C2×#11758226—24no—
78C2×#11758226—24no—
79C2×#11758226—22no—
80C2×#11758226C2314yes—
81C22×Dic122C2311yescharacteristic
82C22×D244—21no—
83C22×D244—21no—
84C22×D244C2311yescharacteristic
85C22×D244C2311yescharacteristic
86C22×C4×D61—21no—
87C22×C4×D61—21no—
88C22×C4×D61—21no—
89C22×C4×D61—21no—
90C22×C4×D61—21no—
91C22×C4×D61C2311yescharacteristic
92C2×#11758202—24no—
93C2×#11758202C2314yes—
94C2×#11758190—24no—
95C2×#11758190C2314yes—
96C2×#11758201—24no—
97C2×#11758201C2314yes—
98C2×D488—24no—
99C2×D488C2314yes—
100C22×#92418C2311yescharacteristic
101C22×#92418C2311yescharacteristic
102#14519772—28no—
103#14519766—28no—
104#14519765—22no—
105#14519765C2314yes—
106#14519762—28no—
107#14519757—22no—
108#14519757C2314yes—
109#14519753—28no—
110#14519752—22no—
111#14519752C2314yes—
112Q8×Dic61—22no—
113Q8×Dic61C2314yes—
114#14519742—22no—
115#14519742C2314yes—
116C4×D244—22no—
117C4×D244—28no—
118C4×D244C2314yes—
119#14519739—28no—
120#14519739—22no—
121#14519739—22no—
122#14519739C2314yes—
123#14519739C2314yes—
124#14519734—28no—
125#14519734D414yes—
126#14519734C2314yes—
127C2×C4⋊Dic61—21no—
128C2×C4⋊Dic61—21no—
129C2×C4⋊Dic61C2311yescharacteristic
130C2×#11758196—21no—
131C2×#11758196—21no—
132C2×#11758196D411yescharacteristic
133C2×#11758196D411yescharacteristic
134C4⋊C4×D61—22no—
135C4⋊C4×D61—28no—
136C4⋊C4×D61C2314yes—
137C2×#11758198—21no—
138C2×#11758198—21no—
139C2×#11758198—21no—
140C2×#11758198—21no—
141C2×#11758198—21no—
142C2×#11758198—21no—
143C2×#11758198—21no—
144C2×#11758198D411yescharacteristic
145C2×#11758198D411yescharacteristic
146C2×C4×Dic61—21no—
147C2×C4×Dic61—21no—
148C2×C4×Dic61C2311yescharacteristic
149#14519710C2314yes—
150#14519710C2314yes—
151C4⋊#92418C2314yes—
152#14519702C2314yes—
153#14519700C2314yes—
154#14519699C2314yes—
155#14519697C2314yes—
156#14519697C2314yes—
157#14519697C2314yes—
158#14519689C2314yes—
159#14519689C2314yes—
160#14519687C2314yes—
161C8×Dic61C2314yes—
162C22×Q8×C61—21no—
163C22×Q8×C61C2311yescharacteristic
164C22×C8×C61C2311yescharacteristic
165C22×C8×C61C2311yescharacteristic
166C4⋊Q8×C61—22no—
167C4⋊Q8×C61C2314yes—
168C4×Q8×C61—22no—
169C4×Q8×C61C2314yes—
170C2×C4⋊C4×C61—21no—
171C2×C4⋊C4×C61—21no—
172C2×C4⋊C4×C61C2311yescharacteristic
173C2×C4⋊C4×C61C2311yescharacteristic
174C2×C4⋊C4×C61C2311yescharacteristic
175C2×C42×C61—21no—
176C2×C42×C61C2311yescharacteristic
177#107×C61C2314yes—
178#107×C61C2314yes—
179C4⋊C8×C61C2314yes—
180#103×C61C2314yes—
181#103×C61C2314yes—
182C23×D61—21no—
183C23×D61—21no—
184C23×D61C2×D411yescharacteristic
185C2×Q8×C61—21no—
186C2×Q8×C61—24no—
187C2×Q8×C61—22no—
188C2×Q8×C61—82no—
189C2×Q8×C61#4114yes—
190C2×Q8×C61C2412yes—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61C2×D411yescharacteristic
196C22×C4×C61C2×D411yescharacteristic
197C22×C4×C61C2411yescharacteristic
198C22×Dic61—21no—
199C22×Dic61—21no—
200C22×Dic61C2×D411yescharacteristic
201C22×Dic61C2×D411yescharacteristic
202C22×Dic61C2×D411yescharacteristic
203#11758226—216no—
204#11758226—28no—
205#11758226—28no—
206C2×D244—28no—
207C2×D244—24no—
208C2×D244—21no—
209C2×D244—22no—
210C2×D244—22no—
211C2×D244—22no—
212C2×D244—21no—
213C2×D244—24no—
214C2×D244—82no—
215C2×D244#4114yes—
216C2×D244C2412yes—
217C2×D244C2412yes—
218C2×C4×D61—28no—
219C2×C4×D61—22no—
220C2×C4×D61—22no—
221C2×C4×D61—24no—
222C2×C4×D61—24no—
223C2×C4×D61—24no—
224C2×C4×D61—24no—
225C2×C4×D61—24no—
226C2×C4×D61—82no—
227C2×C4×D61—82no—
228C2×C4×D61—82no—
229C2×C4×D61—82no—
230C2×C4×D61C2×D412yes—
231C2×C4×D61C2412yes—
232C2×Dic122—22no—
233C2×Dic122—22no—
234C2×Dic122—21no—
235C2×Dic122C2412yes—
236C2×C8×C61—22no—
237C2×C8×C61—22no—
238C2×C8×C61C2412yes—
239C2×C8×C61C2412yes—
240C4⋊C4×C61—24no—
241C4⋊C4×C61—24no—
242C4⋊C4×C61—21no—
243C4⋊C4×C61—21no—
244C4⋊C4×C61—21no—
245C4⋊C4×C61C2412yes—
246C4⋊C4×C61C2412yes—
247C4⋊C4×C61C2412yes—
248C42×C61—24no—
249C42×C61C2×D412yes—
250C42×C61C2412yes—
251#11758202—28no—
252#11758201—28no—
253#11758198—24no—
254#11758198—24no—
255#11758198—24no—
256#11758198—24no—
257#11758198—24no—
258#11758198—24no—
259#11758198—24no—
260#11758198C2×D414yes—
261#11758198C2×D414yes—
262C4⋊Dic61—21no—
263C4⋊Dic61—24no—
264C4⋊Dic61—24no—
265C4⋊Dic61C2412yes—
266#11758196—24no—
267#11758196—24no—
268#11758196C2×D414yes—
269#11758196C2×D414yes—
270C4×Dic61—24no—
271C4×Dic61—24no—
272C4×Dic61C2×D412yes—
273C4×Dic61C2412yes—
274C2×#92418—22no—
275C2×#92418—22no—
276C2×#92418C2412yes—
277C2×#92418C2412yes—
278D488—28no—
279#11758190—28no—
280C23×C61C22×D411yescharacteristic
281C22×D61—22no—
282C22×D61—24no—
283C22×D61—22no—
284C22×D61—22no—
285C22×D61—22no—
286C22×D61—22no—
287C22×D61—42no—
288C22×D61—42no—
289C22×D61—42no—
290C22×D61—42no—
291C22×D61—42no—
292C22×D61C22×D412yes—
293Q8×C61—24no—
294Q8×C61—22no—
295Q8×C61—84no—
296Q8×C61C2×#4114yes—
297C2×C4×C61—24no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—22no—
304C2×C4×C61—42no—
305C2×C4×C61—42no—
306C2×C4×C61—42no—
307C2×C4×C61C22×D412yes—
308C2×C4×C61C22×D412yes—
309C2×C4×C61C22×D411yescharacteristic
310C2×C4×C61C2×#4112yes—
311C2×C4×C61C2×#4112yes—
312C2×C4×C61C2511yescharacteristic
313C2×Dic61—22no—
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—22no—
318C2×Dic61—42no—
319C2×Dic61—42no—
320C2×Dic61C22×D412yes—
321C2×Dic61C22×D412yes—
322C2×Dic61C22×D412yes—
323D244—216no—
324D244—24no—
325D244—22no—
326D244—22no—
327D244—22no—
328D244—42no—
329D244—84no—
330D244C2×#4114yes—
331C4×D61—216no—
332C4×D61—24no—
333C4×D61—22no—
334C4×D61—22no—
335C4×D61—84no—
336C4×D61—84no—
337C4×D61—84no—
338C4×D61—84no—
339Dic122—22no—
340Dic122—22no—
341Dic122—42no—
342C8×C61—22no—
343C8×C61—22no—
344#92418—22no—
345#92418—22no—
346C2×#3124—611nomaximal, Sylow
347C22×C61#52512yes—
348C22×C61#57612yes—
349C22×C61#57812yes—
350C22×C61C23×D411yescharacteristic
351C2×D61—22no—
352C2×D61—24no—
353C2×D61—22no—
354C2×D61—22no—
355C2×D61—44no—
356C2×D61—48no—
357C2×D61—42no—
358C2×D61—42no—
359C2×D61—42no—
360C2×D61—42no—
361C2×D61—42no—
362C2×D61—84no—
363C4×C61—24no—
364C4×C61—22no—
365C4×C61—22no—
366C4×C61—42no—
367C4×C61—42no—
368C4×C61—42no—
369C4×C61#52512yes—
370C4×C61C22×#4111yescharacteristic
371C4×C61C22×#4111yescharacteristic
372Dic61—22no—
373Dic61—22no—
374Dic61—22no—
375Dic61—42no—
376Dic61—42no—
377C2×#542—611no—
378C2×#520—611no—
379#3124—6116no—
380C2×#484—611no—
381C2×#480—611no—
382C2×#477D6111yescharacteristic, complemented
383C2×#474—611no—
384C2×#464—611no—
385C2×#463—611no—
386C2×#452—611no—
387C2×#449—611no—
388C2×#440—611no—
389C2×#440—611no—
390C2×C4×Q16—611no—
391C2×C4×D8—611no—
392C2×#433—611no—
393C2×C61#312414yescomplemented
394C2×C61C2×#52511yescharacteristic
395C2×C61C2×#57611yescharacteristic
396C2×C61C2×#57811yescharacteristic
397D61—42no—
398D61—44no—
399D61—82no—
400C22×#41—611no—
401C22×Q16—611no—
402C22×SD16—611no—
403C22×SD16—611no—
404C22×D8—611no—
405#542—618no—
406#542—1224no—
407C2×C4⋊Q8C2×D6111yescharacteristic
408C2×#126—1221no—
409C2×#124—611no—
410C2×#124—1221no—
411C2×#123—1221no—
412C2×C22⋊Q8—611no—
413C2×C22⋊Q8—1221no—
414C2×#121—611no—
415#520—618no—
416#520—1224no—
417C2×C4×Q8—611no—
418C2×C4×Q8—611no—
419C2×C4×Q8C2×D6111yescharacteristic
420C2×C4×D4—611no—
421C2×C4×D4—611no—
422C2×C4×D4—611no—
423C2×C4×D4—1221no—
424C2×C4×D4—1221no—
425C2×#117—611no—
426C2×#117—1221no—
427C22×C4⋊C4—611no—
428C22×C4⋊C4—1221no—
429#484—618no—
430#480—618no—
431#477C2×D6118yescomplemented
432#474—618no—
433#464—618no—
434#463—618no—
435#452—618no—
436#449—618no—
437#440—618no—
438#440—618no—
439C4×Q16—618no—
440C4×D8—618no—
441#433—618no—
442C2×#107—611no—
443C2×#107—611no—
444C2×#107C2×D6111yescharacteristic
445C2×#107C2×D6111yescharacteristic
446C2×C4⋊C8—611no—
447C2×C4⋊C8C2×D6111yescharacteristic
448C2×#103—611no—
449C2×#103—611no—
450C2×#103C2×D6111yescharacteristic
451C2×#103C2×D6111yescharacteristic
452C2×#102—611no—
453C2×#102—611no—
454C2×#102—611no—
455C2×#102—611no—
456C2×C22⋊C8—611no—
457C2×C22⋊C8—611no—
458C2×#97—611no—
459C2×C4×C8—611no—
460C61C2×#312411yescharacteristic, complemented, Sylow
461C2×#41—614no—
462C2×#41—1222no—
463C2×#41—1224no—
464C2×#41—1224no—
465C22×Q8—21no—
466C22×Q8—611no—
467C22×Q8C22×D6111yescharacteristic
468C22×D4—611no—
469C22×D4—611no—
470C22×D4—1221no—
471C22×D4—1221no—
472C23×C4—611no—
473C23×C4—1221no—
474C23×C4—1221no—
475C23×C4—1221no—
476C23×C4—1221no—
477C23×C4—1221no—
478C2×Q16—614no—
479C2×Q16—1224no—
480C2×SD16—614no—
481C2×SD16—614no—
482C2×SD16—1224no—
483C2×SD16—1224no—
484C2×D8—614no—
485C2×D8—1224no—
486C22×C8—611no—
487C22×C8—611no—
488C22×C8C22×D6111yescharacteristic
489C22×C8C22×D6111yescharacteristic
490C4⋊Q8—22no—
491C4⋊Q8C22×D6114yes—
492#126—1228no—
493#124—614no—
494#124—1228no—
495#124—1222no—
496#123—1228no—
497C22⋊Q8—614no—
498C22⋊Q8—1222no—
499C22⋊Q8—1228no—
500#121—614no—
501#121—1222no—
502C4×Q8—22no—
503C4×Q8—614no—
504C4×Q8—614no—
505C4×Q8—1222no—
506C4×Q8—1222no—
507C4×Q8C22×D6114yes—
508C4×D4—614no—
509C4×D4—614no—
510C4×D4—614no—
511C4×D4—1228no—
512C4×D4—1222no—
513C4×D4—1222no—
514C4×D4—1228no—
515C4×D4—1222no—
516#117—614no—
517#117—614no—
518#117—1228no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—611no—
522C2×C4⋊C4—611no—
523C2×C4⋊C4—611no—
524C2×C4⋊C4—614no—
525C2×C4⋊C4—1228no—
526C2×C4⋊C4—1222no—
527C2×C4⋊C4—1221no—
528C2×C4⋊C4—1221no—
529C2×C4⋊C4—1221no—
530C2×C4⋊C4—1221no—
531C2×C4⋊C4C22×D6111yescharacteristic
532C2×C4⋊C4C22×D6111yescharacteristic
533C2×C4⋊C4C22×D6111yescharacteristic
534C2×C22⋊C4—611no—
535C2×C22⋊C4—611no—
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—21no—
544C2×C42—611no—
545C2×C42—1221no—
546C2×C42—1221no—
547C2×C42C22×D6111yescharacteristic
548#107—614no—
549#107—614no—
550#107C22×D6114yes—
551#107C22×D6114yes—
552C4⋊C8—614no—
553C4⋊C8C22×D6114yes—
554#103—614no—
555#103—614no—
556#103C22×D6114yes—
557#103C22×D6114yes—
558#102—614no—
559#102—614no—
560#102—614no—
561#102—614no—
562C22⋊C8—614no—
563C22⋊C8—614no—
564#97—614no—
565C4×C8—614no—
566C24—611no—
567C24—1221no—
568C24—1221no—
569#41—1228no—
570#41—12216no—
571#41—1228no—
572C2×Q8—21no—
573C2×Q8—24no—
574C2×Q8—22no—
575C2×Q8—82no—
576C2×Q8—612no—
577C2×Q8—1221no—
578C2×Q8—1222no—
579C2×Q8—1222no—
580C2×Q8#1175822614yes—
581C2×Q8C23×D6112yes—
582C2×D4—614no—
583C2×D4—612no—
584C2×D4—612no—
585C2×D4—1224no—
586C2×D4—1228no—
587C2×D4—1224no—
588C2×D4—1221no—
589C2×D4—1221no—
590C2×D4—1222no—
591C2×D4—1222no—
592C2×D4—1222no—
593C2×D4—4882no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—611no—
599C22×C4—611no—
600C22×C4—611no—
601C22×C4—612no—
602C22×C4—612no—
603C22×C4—1224no—
604C22×C4—1224no—
605C22×C4—1224no—
606C22×C4—1228no—
607C22×C4—1224no—
608C22×C4—1222no—
609C22×C4—1222no—
610C22×C4—1221no—
611C22×C4—1221no—
612C22×C4—1224no—
613C22×C4—4882no—
614C22×C4—4882no—
615C22×C4—4882no—
616C22×C4—4882no—
617C22×C4D4×D6111yescharacteristic
618C22×C4D4×D6111yescharacteristic
619C22×C4C23×D6111yescharacteristic
620Q16—1228no—
621SD16—1228no—
622SD16—1228no—
623D8—1228no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—612no—
627C2×C8—612no—
628C2×C8—1222no—
629C2×C8—1222no—
630C2×C8C23×D6112yes—
631C2×C8C23×D6112yes—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—614no—
638C4⋊C4—614no—
639C4⋊C4—612no—
640C4⋊C4—1224no—
641C4⋊C4—1224no—
642C4⋊C4—1224no—
643C4⋊C4—1224no—
644C4⋊C4—1221no—
645C4⋊C4C23×D6112yes—
646C4⋊C4C23×D6112yes—
647C4⋊C4C23×D6112yes—
648C22⋊C4—614no—
649C22⋊C4—614no—
650C22⋊C4—1224no—
651C22⋊C4—1224no—
652C22⋊C4—1224no—
653C22⋊C4—1224no—
654C22⋊C4—1224no—
655C22⋊C4—1224no—
656C22⋊C4—1224no—
657C42—24no—
658C42—612no—
659C42—612no—
660C42—1224no—
661C42—1224no—
662C42D4×D6112yes—
663C42C23×D6112yes—
664C23—612no—
665C23—1224no—
666C23—1222no—
667C23—1222no—
668C23—1222no—
669C23—1222no—
670C23—1222no—
671C23—2442no—
672C23—2442no—
673C23—2442no—
674C23—2442no—
675C23—2442no—
676C23C2×D4×D6111yescharacteristic
677Q8—24no—
678Q8—22no—
679Q8—84no—
680Q8—1222no—
681Q8—1222no—
682Q8—2442no—
683Q8C2×#1175822614yes—
684D4—614no—
685D4—12216no—
686D4—1224no—
687D4—1222no—
688D4—1222no—
689D4—1222no—
690D4—4884no—
691D4—2442no—
692C2×C4—24no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—612no—
703C2×C4—612no—
704C2×C4—612no—
705C2×C4—12216no—
706C2×C4—1222no—
707C2×C4—1222no—
708C2×C4—1222no—
709C2×C4—1224no—
710C2×C4—1222no—
711C2×C4—1222no—
712C2×C4—1222no—
713C2×C4—1222no—
714C2×C4—4884no—
715C2×C4—4884no—
716C2×C4—4884no—
717C2×C4—4884no—
718C2×C4—2442no—
719C2×C4—2442no—
720C2×C4C2×D4×D6112yes—
721C2×C4C2×D4×D6112yes—
722C2×C4C2×D4×D6111yescharacteristic
723C2×C4#41×D6112yes—
724C2×C4C2×#1175822612yes—
725C2×C4C24×D6111yescharacteristic
726C8—22no—
727C8—22no—
728C8—1222no—
729C8—1222no—
730C22—1222no—
731C22—1222no—
732C22—1224no—
733C22—1222no—
734C22—4884no—
735C22—2442no—
736C22—2442no—
737C22—2442no—
738C22—2442no—
739C22—2442no—
740C22—2444no—
741C22—2448no—
742C22#1684027512yes—
743C22#1684056612yes—
744C22#1684057512yes—
745C22C22×D4×D6111yescharacteristic
746C4—22no—
747C4—22no—
748C4—24no—
749C4—42no—
750C4—42no—
751C4—42no—
752C4—1222no—
753C4—1222no—
754C4—1222no—
755C4—2442no—
756C4—2442no—
757C4#1684027512yes—
758C4C2×#41×D6111yescharacteristic
759C4C22×#1175822611yescharacteristic
760C2—4882no—
761C2—2442no—
762C2—2444no—
763C2#2145608814yesdirect product factor
764C2C2×#1684027511yescharacteristic
765C2C2×#1684056611yescharacteristic
766C2C2×#1684057511yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#477C2
socleC23×C61C22×D4
prime radicalC2×#16839910C2
hypercenterC2×#477D61
hypocenterC61C2×#3124
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
1. C2×#16840386C2semidirect
2. C2×#16840244C2semidirect
3. #21456088C2direct (N × H)
4. C2×#16840099C2semidirect
5. C2×#16840077C2semidirect
6. C2×#16840039C2semidirect
7. C2×#16839984C2semidirect
8. C2×#16839978C2semidirect
9. C2×#16839927C2semidirect
11. C2×#16839865C2semidirect
12. C2×#16839861C2semidirect
13. C2×#16839854C2semidirect
14. C2×#16839844C2semidirect
15. C2×#16839822C2semidirect
16. C2×C61×#477C2semidirect
23. #16840386C22semidirect
32. #16840244C22semidirect
44. #16840099C22semidirect
45. #16840077C22semidirect
46. #16840039C22semidirect
47. #16839984C22semidirect
48. #16839978C22semidirect
49. #16839927C22semidirect
51. #16839865C22semidirect
52. #16839861C22semidirect
53. #16839854C22semidirect
54. #16839844C22semidirect
55. #16839822C22semidirect
71. C61×#477C22semidirect
382. C2×#477D61semidirect
393. C2×C61#3124semidirect
431. #477C2×D61semidirect
460. C61C2×#3124semidirect
763. C2#21456088direct (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×#168402442
#214560882
C2×#168400992
C2×#168400772
C2×#168400392
C2×#168399842
C2×#168399782
C2×#168399272
C2×#168399102
C2×#168398652
C2×#168398612
C2×#168398542
C2×#168398442
C2×#168398222
C2×C61×#4772
C2×#312461