Finite Group Databasebeta

← C2×#21456084 #30548331

Subgroups — C2×#21456084 #30548331

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×#16840385C211yesmaximal, characteristic, complemented
2C2×#16840243C211yesmaximal, characteristic, complemented
3#21456084C2116yesmaximal, direct product factor
4C2×#16840075C211yesmaximal, characteristic, complemented
5C2×#16840056C211yesmaximal, characteristic, complemented
6C2×#16840041C211yesmaximal, characteristic, complemented
7C2×#16839987C211yesmaximal, characteristic, complemented
8C2×#16839980C211yesmaximal, characteristic, complemented
9C2×#16839922C211yesmaximal, characteristic, complemented
10C2×#16839909C211yesmaximal, characteristic
11C2×#16839865C211yesmaximal, characteristic, complemented
12C2×#16839861C211yesmaximal, characteristic, complemented
13C2×#16839854C211yesmaximal, characteristic, complemented
14C2×#16839844C211yesmaximal, characteristic, complemented
15C2×#16839820C211yesmaximal, characteristic, complemented
16C2×C61×#484C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C22×#11758202C2211yescharacteristic
19C22×#11758190C2211yescharacteristic
20C22×#11758201C2211yescharacteristic
21C22×D488C2211yescharacteristic
22#16840385—24no—
23#16840385C2218yescomplemented
24C2×#14519776C2211yescharacteristic
25C2×#14519772—21no—
26C2×#14519766C2211yescharacteristic
27C2×#14519763—21no—
28C2×#14519759—21no—
29C2×#14519757—21no—
30C2×#14519751C2211yescharacteristic
31#16840243—24no—
32#16840243C2218yescomplemented
33C2×Q8×Dic61C2211yescharacteristic
34C2×#14519742C2211yescharacteristic
35C2×#14519742C2211yescharacteristic
36C2×#14519739C2211yescharacteristic
37C2×#14519739C2211yescharacteristic
38C2×#14519739C2211yescharacteristic
39C2×C4×C22⋊D61—21no—
40C2×C4×C22⋊D61—21no—
41C2×#14519736C2211yescharacteristic
42C2×#14519735—21no—
43C2×C4⋊C4×D61—21no—
44#16840075C2218yescomplemented
45#16840056C2218yescomplemented
46#16840041C2218yescomplemented
47#16839987C2218yescomplemented
48#16839980C2218yescomplemented
49#16839922C2218yescomplemented
50#16839909C2218yes—
51#16839865C2218yescomplemented
52#16839861C2218yescomplemented
53#16839854C2218yescomplemented
54#16839844C2218yescomplemented
55#16839820C2218yescomplemented
56C2×#14519710C2211yescharacteristic
57C2×#14519710C2211yescharacteristic
58C2×#14519706C2211yescharacteristic
59C2×#14519706C2211yescharacteristic
60C2×#14519702C2211yescharacteristic
61C2×#14519700C2211yescharacteristic
62C2×#14519699C2211yescharacteristic
63C2×#14519697C2211yescharacteristic
64C2×#14519697C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×C22⋊#92418C2211yescharacteristic
67C2×#14519687C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C2×C22⋊Q8×C61C2211yescharacteristic
70C22×C4⋊C4×C61C2211yescharacteristic
71C61×#484C2218yescomplemented
72C2×#107×C61C2211yescharacteristic
73C2×#107×C61C2211yescharacteristic
74C2×#103×C61C2211yescharacteristic
75C2×#103×C61C2211yescharacteristic
76C2×C22⋊C8×C61C2211yescharacteristic
77C2×#11758222—22no—
78C2×#11758222—24no—
79C2×#11758222—24no—
80C2×#11758222C2314yes—
81C22×Dic122—21no—
82C22×Dic122C2311yescharacteristic
83C22×D244C2311yescharacteristic
84C22×D244C2311yescharacteristic
85C22×C22⋊D61—21no—
86C22×C22⋊D61—21no—
87C22×C4×D61—21no—
88C22×C4×D61—21no—
89C22×C4×D61—21no—
90C22×C4×D61—21no—
91C2×#11758202—24no—
92C2×#11758202C2314yes—
93C2×#11758190—24no—
94C2×#11758190C2314yes—
95C2×#11758201—24no—
96C2×#11758201C2314yes—
97C2×D488—24no—
98C2×D488C2314yes—
99C22×#92418C2311yescharacteristic
100C22×#92418C2311yescharacteristic
101#14519776—22no—
102#14519776C2314yes—
103#14519772—28no—
104#14519766—22no—
105#14519766C2314yes—
106#14519763—28no—
107#14519759—28no—
108#14519757—28no—
109#14519751—22no—
110#14519751C2314yes—
111Q8×Dic61—22no—
112Q8×Dic61C2314yes—
113#14519742—22no—
114#14519742—22no—
115#14519742C2314yes—
116#14519742C2314yes—
117#14519739—22no—
118#14519739—22no—
119#14519739—22no—
120#14519739C2314yes—
121#14519739C2314yes—
122#14519739C2314yes—
123C4×C22⋊D61—28no—
124C4×C22⋊D61—28no—
125#14519736D414yes—
126#14519736C2314yes—
127#14519735—28no—
128C2×C4⋊Dic61—21no—
129C2×C4⋊Dic61D411yescharacteristic
130C2×C4⋊Dic61D411yescharacteristic
131C2×C4⋊Dic61C2311yescharacteristic
132C2×#11758196—21no—
133C2×#11758196—21no—
134C2×#11758196—21no—
135C4⋊C4×D61—28no—
136C2×C22⋊Dic61D411yescharacteristic
137C2×C22⋊Dic61D411yescharacteristic
138C2×#11758198—21no—
139C2×#11758198—21no—
140C2×#11758198—21no—
141C2×#11758198—21no—
142C2×#11758198—21no—
143C2×#11758198—21no—
144C2×C4×Dic61—21no—
145C2×C4×Dic61—21no—
146C2×C4×Dic61—21no—
147C2×C4×Dic61C2311yescharacteristic
148C2×C4×Dic61C2311yescharacteristic
149#14519710C2314yes—
150#14519710C2314yes—
151#14519706C2314yes—
152#14519706C2314yes—
153#14519702C2314yes—
154#14519700C2314yes—
155#14519699C2314yes—
156#14519697C2314yes—
157#14519697C2314yes—
158#14519697C2314yes—
159C22⋊#92418C2314yes—
160#14519687C2314yes—
161C8×Dic61C2314yes—
162C22×Q8×C61C2311yescharacteristic
163C23×C4×C61—21no—
164C23×C4×C61C2311yescharacteristic
165C22×C8×C61C2311yescharacteristic
166C22×C8×C61C2311yescharacteristic
167C22⋊Q8×C61—22no—
168C22⋊Q8×C61C2314yes—
169C2×C4⋊C4×C61—21no—
170C2×C4⋊C4×C61—22no—
171C2×C4⋊C4×C61—21no—
172C2×C4⋊C4×C61C2311yescharacteristic
173C2×C4⋊C4×C61C2311yescharacteristic
174C2×C4⋊C4×C61C2311yescharacteristic
175C2×C4⋊C4×C61C2314yes—
176C2×C22⋊C4×C61—21no—
177#107×C61C2314yes—
178#107×C61C2314yes—
179#103×C61C2314yes—
180#103×C61C2314yes—
181C22⋊C8×C61C2314yes—
182C24×C61C2×D411yescharacteristic
183C23×D61—21no—
184C23×D61—21no—
185C2×Q8×C61—21no—
186C2×Q8×C61—22no—
187C2×Q8×C61—22no—
188C2×Q8×C61C2412yes—
189C22×C4×C61—22no—
190C22×C4×C61—22no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—24no—
196C22×C4×C61—82no—
197C22×C4×C61C2×D411yescharacteristic
198C22×C4×C61C2×D412yes—
199C22×C4×C61C2412yes—
200C22×C4×C61C2411yescharacteristic
201C2×C22⋊D61—28no—
202C2×C22⋊D61—24no—
203C2×C22⋊D61—24no—
204C2×C22⋊D61—82no—
205C22×Dic61—21no—
206C22×Dic61—21no—
207C22×Dic61C2×D411yescharacteristic
208C22×Dic61C2×D411yescharacteristic
209C22×Dic61C2×D411yescharacteristic
210C22×Dic61C2×D411yescharacteristic
211#11758222—216no—
212#11758222—28no—
213#11758222—28no—
214C2×D244—21no—
215C2×D244—22no—
216C2×D244—22no—
217C2×D244—22no—
218C2×D244—21no—
219C2×D244#4114yes—
220C2×D244C2412yes—
221C2×D244C2412yes—
222C2×C4×D61—28no—
223C2×C4×D61—24no—
224C2×C4×D61—24no—
225C2×C4×D61—24no—
226C2×C4×D61—24no—
227C2×C4×D61—82no—
228C2×C4×D61—82no—
229C2×C4×D61—82no—
230C2×Dic122—21no—
231C2×Dic122—22no—
232C2×Dic122—24no—
233C2×Dic122—82no—
234C2×Dic122#4114yes—
235C2×Dic122C2412yes—
236C2×C8×C61—22no—
237C2×C8×C61—22no—
238C2×C8×C61C2412yes—
239C2×C8×C61C2412yes—
240C4⋊C4×C61—24no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61—21no—
243C4⋊C4×C61—24no—
244C4⋊C4×C61—21no—
245C4⋊C4×C61C2412yes—
246C4⋊C4×C61C2412yes—
247C4⋊C4×C61C2412yes—
248C22⋊C4×C61—24no—
249C22⋊Dic61C2×D414yes—
250C22⋊Dic61C2×D414yes—
251#11758202—28no—
252#11758201—28no—
253#11758198—24no—
254#11758198—24no—
255#11758198—24no—
256#11758198—24no—
257#11758198—24no—
258#11758198—24no—
259C4⋊Dic61—21no—
260C4⋊Dic61—24no—
261C4⋊Dic61C2×D414yes—
262C4⋊Dic61C2×D414yes—
263C4⋊Dic61C2412yes—
264#11758196—24no—
265#11758196—24no—
266#11758196—24no—
267C4×Dic61—24no—
268C4×Dic61—24no—
269C4×Dic61—24no—
270C4×Dic61C2×D412yes—
271C4×Dic61C2×D412yes—
272C4×Dic61C2412yes—
273C4×Dic61C2412yes—
274C2×#92418—22no—
275C2×#92418—22no—
276C2×#92418C2412yes—
277C2×#92418C2412yes—
278D488—28no—
279#11758190—28no—
280C23×C61—22no—
281C23×C61—22no—
282C23×C61—22no—
283C23×C61C22×D412yes—
284C23×C61C22×D411yescharacteristic
285C22×D61—24no—
286C22×D61—22no—
287C22×D61—22no—
288C22×D61—42no—
289C22×D61—42no—
290C22×D61—42no—
291C22×D61—42no—
292C22×D61—42no—
293Q8×C61—22no—
294Q8×C61—22no—
295Q8×C61—42no—
296C2×C4×C61—22no—
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×C61—42no—
308C2×C4×C61—84no—
309C2×C4×C61C22×D412yes—
310C2×C4×C61C22×D411yescharacteristic
311C2×C4×C61C2×#4112yes—
312C2×C4×C61C2×#4112yes—
313C2×C4×C61C2511yescharacteristic
314C22⋊D61—216no—
315C22⋊D61—84no—
316C2×Dic61—24no—
317C2×Dic61—22no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—22no—
323C2×Dic61—42no—
324C2×Dic61C22×D412yes—
325C2×Dic61C22×D412yes—
326C2×Dic61C22×D412yes—
327C2×Dic61C22×D412yes—
328D244—24no—
329D244—22no—
330D244—22no—
331D244—22no—
332D244—42no—
333D244C2×#4114yes—
334C4×D61—216no—
335C4×D61—84no—
336C4×D61—84no—
337C4×D61—84no—
338Dic122—24no—
339Dic122—22no—
340Dic122—84no—
341Dic122C2×#4114yes—
342C8×C61—22no—
343C8×C61—22no—
344#92418—22no—
345#92418—22no—
346C2×#3124—611nomaximal, Sylow
347C22×C61—22no—
348C22×C61—22no—
349C22×C61—22no—
350C22×C61—44no—
351C22×C61#52512yes—
352C22×C61#57612yes—
353C22×C61#57812yes—
354C22×C61C23×D411yescharacteristic
355C2×D61—24no—
356C2×D61—48no—
357C2×D61—42no—
358C2×D61—42no—
359C2×D61—42no—
360C2×D61—42no—
361C2×D61—42no—
362C2×D61—84no—
363C4×C61—22no—
364C4×C61—42no—
365C4×C61—42no—
366C4×C61—42no—
367C4×C61—42no—
368C4×C61#52512yes—
369C4×C61C22×#4111yescharacteristic
370C4×C61C22×#4111yescharacteristic
371Dic61—24no—
372Dic61—22no—
373Dic61—22no—
374Dic61—22no—
375Dic61—22no—
376Dic61—42no—
377C2×#542—611no—
378C2×#520—611no—
379#3124—6116no—
380C2×#484D6111yescharacteristic, complemented
381C2×#480—611no—
382C2×#477—611no—
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—42no—
394C2×C61#312414yescomplemented
395C2×C61C2×#52511yescharacteristic
396C2×C61C2×#57611yescharacteristic
397C2×C61C2×#57811yescharacteristic
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⋊Q8—611no—
408C2×#126—1221no—
409C2×#124—611no—
410C2×#124—1221no—
411C2×#123—1221no—
412C2×C22⋊Q8—1221no—
413C2×C22⋊Q8C2×D6111yescharacteristic
414C2×#121—611no—
415#520—618no—
416#520—1224no—
417C2×C4×Q8—611no—
418C2×C4×Q8—611no—
419C2×C4×Q8—611no—
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—1221no—
428C22×C4⋊C4C2×D6111yescharacteristic
429#484C2×D6118yescomplemented
430#480—618no—
431#477—618no—
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⋊C8—611no—
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⋊C8C2×D6111yescharacteristic
458C2×#97—611no—
459C2×C4×C8—611no—
460C61C2×#312411yescharacteristic, complemented, Sylow
461C2×#41—614no—
462C2×#41—1224no—
463C2×#41—1224no—
464C2×#41—1222no—
465C22×Q8—611no—
466C22×Q8—1221no—
467C22×Q8C22×D6111yescharacteristic
468C22×D4—611no—
469C22×D4—611no—
470C22×D4—1221no—
471C22×D4—1221no—
472C23×C4—21no—
473C23×C4—1221no—
474C23×C4—1221no—
475C23×C4—1221no—
476C23×C4—1221no—
477C23×C4C22×D6111yescharacteristic
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—614no—
491C4⋊Q8—1222no—
492#126—1228no—
493#124—614no—
494#124—1222no—
495#124—1228no—
496#123—1228no—
497C22⋊Q8—22no—
498C22⋊Q8—1228no—
499C22⋊Q8C22×D6114yes—
500#121—614no—
501#121—1222no—
502C4×Q8—614no—
503C4×Q8—614no—
504C4×Q8—614no—
505C4×Q8—1222no—
506C4×Q8—1222no—
507C4×Q8—1222no—
508C4×D4—614no—
509C4×D4—614no—
510C4×D4—614no—
511C4×D4—1222no—
512C4×D4—1222no—
513C4×D4—1222no—
514C4×D4—1228no—
515C4×D4—1228no—
516#117—614no—
517#117—614no—
518#117—1228no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—22no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—611no—
523C2×C4⋊C4—611no—
524C2×C4⋊C4—611no—
525C2×C4⋊C4—1228no—
526C2×C4⋊C4—1221no—
527C2×C4⋊C4—1221no—
528C2×C4⋊C4—1221no—
529C2×C4⋊C4—1221no—
530C2×C4⋊C4C22×D6111yescharacteristic
531C2×C4⋊C4C22×D6111yescharacteristic
532C2×C4⋊C4C22×D6114yes—
533C2×C4⋊C4C22×D6111yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—611no—
536C2×C22⋊C4—611no—
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—
548#107—614no—
549#107—614no—
550#107C22×D6114yes—
551#107C22×D6114yes—
552C4⋊C8—614no—
553C4⋊C8—614no—
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⋊C8C22×D6114yes—
564#97—614no—
565C4×C8—614no—
566C24—1221no—
567C24—1221no—
568C24D4×D6111yescharacteristic
569#41—1228no—
570#41—1228no—
571#41—12216no—
572C2×Q8—21no—
573C2×Q8—22no—
574C2×Q8—22no—
575C2×Q8—614no—
576C2×Q8—612no—
577C2×Q8—1224no—
578C2×Q8—1221no—
579C2×Q8—1222no—
580C2×Q8—4882no—
581C2×Q8C23×D6112yes—
582C2×D4—614no—
583C2×D4—612no—
584C2×D4—612no—
585C2×D4—1228no—
586C2×D4—1224no—
587C2×D4—1224no—
588C2×D4—1221no—
589C2×D4—1221no—
590C2×D4—1222no—
591C2×D4—1222no—
592C2×D4—1222no—
593C2×D4—4882no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—24no—
601C22×C4—82no—
602C22×C4—611no—
603C22×C4—611no—
604C22×C4—611no—
605C22×C4—611no—
606C22×C4—1224no—
607C22×C4—1224no—
608C22×C4—1224no—
609C22×C4—1228no—
610C22×C4—1221no—
611C22×C4—1224no—
612C22×C4—1221no—
613C22×C4—4882no—
614C22×C4—4882no—
615C22×C4—4882no—
616C22×C4D4×D6112yes—
617C22×C4D4×D6111yescharacteristic
618C22×C4C23×D6112yes—
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—21no—
634C4⋊C4—21no—
635C4⋊C4—24no—
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—24no—
649C22⋊C4—614no—
650C22⋊C4—614no—
651C22⋊C4—1224no—
652C22⋊C4—1224no—
653C22⋊C4—1224no—
654C22⋊C4—1224no—
655C22⋊C4—1224no—
656C22⋊C4—1224no—
657C42—612no—
658C42—612no—
659C42—612no—
660C42—612no—
661C42—1224no—
662C42—1224no—
663C42—1224no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—1224no—
668C23—1222no—
669C23—1222no—
670C23—2442no—
671C23—2442no—
672C23—2442no—
673C23—2442no—
674C23—2442no—
675C23C2×D4×D6112yes—
676C23C2×D4×D6111yescharacteristic
677Q8—22no—
678Q8—22no—
679Q8—42no—
680Q8—614no—
681Q8—1224no—
682Q8—1222no—
683Q8—4884no—
684D4—614no—
685D4—12216no—
686D4—1224no—
687D4—1222no—
688D4—1222no—
689D4—1222no—
690D4—4884no—
691D4—2442no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—84no—
705C2×C4—612no—
706C2×C4—612no—
707C2×C4—612no—
708C2×C4—612no—
709C2×C4—12216no—
710C2×C4—1224no—
711C2×C4—1222no—
712C2×C4—1222no—
713C2×C4—1222no—
714C2×C4—1222no—
715C2×C4—1222no—
716C2×C4—1222no—
717C2×C4—4884no—
718C2×C4—4884no—
719C2×C4—4884no—
720C2×C4—2442no—
721C2×C4C2×D4×D6112yes—
722C2×C4C2×D4×D6111yescharacteristic
723C2×C4#41×D6112yes—
724C2×C4#41×D6112yes—
725C2×C4C24×D6111yescharacteristic
726C8—22no—
727C8—22no—
728C8—1222no—
729C8—1222no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—44no—
734C22—1224no—
735C22—4884no—
736C22—2442no—
737C22—2442no—
738C22—2442no—
739C22—2442no—
740C22—2442no—
741C22—2448no—
742C22#1684027012yes—
743C22#1684056612yes—
744C22#1684057512yes—
745C22C22×D4×D6111yescharacteristic
746C4—22no—
747C4—42no—
748C4—42no—
749C4—42no—
750C4—42no—
751C4—1222no—
752C4—1222no—
753C4—1222no—
754C4—1222no—
755C4—1224no—
756C4—2442no—
757C4#1684027012yes—
758C4C2×#41×D6111yescharacteristic
759C4C2×#41×D6111yescharacteristic
760C2—42no—
761C2—4882no—
762C2—2444no—
763C2#2145608414yesdirect product factor
764C2C2×#1684027011yescharacteristic
765C2C2×#1684056611yescharacteristic
766C2C2×#1684057511yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#484C2
socleC23×C61C22×D4
prime radicalC2×#16839909C2
hypercenterC2×#484D61
hypocenterC61C2×#3124
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
1. C2×#16840385C2semidirect
2. C2×#16840243C2semidirect
3. #21456084C2direct (N × H)
4. C2×#16840075C2semidirect
5. C2×#16840056C2semidirect
6. C2×#16840041C2semidirect
7. C2×#16839987C2semidirect
8. C2×#16839980C2semidirect
9. C2×#16839922C2semidirect
11. C2×#16839865C2semidirect
12. C2×#16839861C2semidirect
13. C2×#16839854C2semidirect
14. C2×#16839844C2semidirect
15. C2×#16839820C2semidirect
16. C2×C61×#484C2semidirect
23. #16840385C22semidirect
32. #16840243C22semidirect
44. #16840075C22semidirect
45. #16840056C22semidirect
46. #16840041C22semidirect
47. #16839987C22semidirect
48. #16839980C22semidirect
49. #16839922C22semidirect
51. #16839865C22semidirect
52. #16839861C22semidirect
53. #16839854C22semidirect
54. #16839844C22semidirect
55. #16839820C22semidirect
71. C61×#484C22semidirect
380. C2×#484D61semidirect
394. C2×C61#3124semidirect
429. #484C2×D61semidirect
460. C61C2×#3124semidirect
763. C2#21456084direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403852
C2×#168402432
#214560842
C2×#168400752
C2×#168400562
C2×#168400412
C2×#168399872
C2×#168399802
C2×#168399222
C2×#168399092
C2×#168398652
C2×#168398612
C2×#168398542
C2×#168398442
C2×#168398202
C2×C61×#4842
C2×#312461