Finite Group Databasebeta

← C2×#21456074 #30548321

Subgroups — C2×#21456074 #30548321

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×#16840379C211yesmaximal, characteristic, complemented
2C2×#16840245C211yesmaximal, characteristic, complemented
3#21456074C2116yesmaximal, direct product factor
4C2×#16840098C211yesmaximal, characteristic, complemented
5C2×#16840073C211yesmaximal, characteristic, complemented
6C2×#16840055C211yesmaximal, characteristic, complemented
7C2×#16840040C211yesmaximal, characteristic, complemented
8C2×#16839982C211yesmaximal, characteristic, complemented
9C2×#16839975C211yesmaximal, characteristic, complemented
10C2×#16839924C211yesmaximal, characteristic, complemented
11C2×#16839863C211yesmaximal, characteristic, complemented
12C2×#16839859C211yesmaximal, characteristic, complemented
13C2×#16839854C211yesmaximal, characteristic, complemented
14C2×D8×Dic61C211yesmaximal, characteristic, complemented
15C2×#16839820C211yesmaximal, characteristic, complemented
16C2×C61×#449C211yesmaximal, characteristic
17C22×#11758202C2211yescharacteristic
18C22×#11758200C2211yescharacteristic
19#16840379—24no—
20#16840379C2218yescomplemented
21C2×#14519776C2211yescharacteristic
22C2×#14519770—21no—
23C2×#14519764—21no—
24C2×#14519764C2211yescharacteristic
25C2×#14519758—21no—
26C2×#14519756C2211yescharacteristic
27C2×#14519754—21no—
28#16840245—24no—
29#16840245C2218yescomplemented
30C2×Q8×Dic61C2211yescharacteristic
31C2×Q8×Dic61C2211yescharacteristic
32C2×#14519742C2211yescharacteristic
33C2×D4×Dic61—21no—
34C2×D4×Dic61—21no—
35C2×D4×Dic61C2211yescharacteristic
36C2×D4×Dic61C2211yescharacteristic
37C2×D4×Dic61C2211yescharacteristic
38C2×#14519736—21no—
39C2×#14519736C2211yescharacteristic
40C22×C4⋊Dic61—21no—
41C22×C4⋊Dic61C2211yescharacteristic
42#16840098C2218yescomplemented
43#16840073C2218yescomplemented
44#16840055C2218yescomplemented
45#16840040C2218yescomplemented
46#16839982C2218yescomplemented
47#16839975C2218yescomplemented
48#16839924C2218yescomplemented
49#16839863C2218yescomplemented
50#16839859C2218yescomplemented
51#16839854C2218yescomplemented
52D8×Dic61C2218yescomplemented
53#16839820C2218yescomplemented
54C2×#14519711C2211yescharacteristic
55C2×#14519711C2211yescharacteristic
56C2×#14519710C2211yescharacteristic
57C2×#14519710C2211yescharacteristic
58C2×#14519706C2211yescharacteristic
59C2×#14519706C2211yescharacteristic
60C2×#14519702C2211yescharacteristic
61C2×#14519702C2211yescharacteristic
62C2×#14519701C2211yescharacteristic
63C2×#14519698C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65C2×#14519698C2211yescharacteristic
66C2×C22⋊#92418C2211yescharacteristic
67C2×#14519687C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C22×#41×C61C2211yescharacteristic
70C22×SD16×C61C2211yescharacteristic
71C22×D8×C61C2211yescharacteristic
72C2×#121×C61C2211yescharacteristic
73C61×#449C2218yes—
74C2×#103×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×C22⋊C8×C61C2211yescharacteristic
77C22×Dic122—21no—
78C22×Dic122C2311yescharacteristic
79C23×Dic61—21no—
80C23×Dic61—21no—
81C23×Dic61—21no—
82C23×Dic61—21no—
83C2×#11758202—24no—
84C2×#11758202C2314yes—
85C2×#11758200—24no—
86C2×#11758200C2314yes—
87C22×#92418C2311yescharacteristic
88C22×#92418C2311yescharacteristic
89#14519776—22no—
90#14519776C2314yes—
91#14519770—28no—
92#14519764—28no—
93#14519764—22no—
94#14519764C2314yes—
95#14519758—28no—
96#14519756—22no—
97#14519756C2314yes—
98#14519754—28no—
99Q8×Dic61—22no—
100Q8×Dic61—22no—
101Q8×Dic61C2314yes—
102Q8×Dic61C2314yes—
103#14519742—22no—
104#14519742C2314yes—
105D4×Dic61—28no—
106D4×Dic61—28no—
107D4×Dic61—22no—
108D4×Dic61—22no—
109D4×Dic61—22no—
110D4×Dic61C2314yes—
111D4×Dic61C2314yes—
112D4×Dic61C2314yes—
113#14519736—28no—
114#14519736D414yes—
115#14519736C2314yes—
116C2×C4⋊Dic61—21no—
117C2×C4⋊Dic61—22no—
118C2×C4⋊Dic61—21no—
119C2×C4⋊Dic61—21no—
120C2×C4⋊Dic61—28no—
121C2×C4⋊Dic61D411yescharacteristic
122C2×C4⋊Dic61D411yescharacteristic
123C2×C4⋊Dic61C2311yescharacteristic
124C2×C4⋊Dic61C2311yescharacteristic
125C2×C4⋊Dic61C2314yes—
126C2×C4⋊Dic61C2311yescharacteristic
127C2×#11758196—21no—
128C2×#11758196—21no—
129C2×#11758196—21no—
130C2×C22⋊Dic61—21no—
131C2×C22⋊Dic61—21no—
132C2×C22⋊Dic61—21no—
133C2×C22⋊Dic61—21no—
134C2×C22⋊Dic61—21no—
135C2×C22⋊Dic61—21no—
136C2×C22⋊Dic61D411yescharacteristic
137C2×C22⋊Dic61D411yescharacteristic
138C2×C4×Dic61—21no—
139C2×C4×Dic61—21no—
140C2×C4×Dic61—21no—
141C2×C4×Dic61C2311yescharacteristic
142C2×C4×Dic61C2311yescharacteristic
143#14519711C2314yes—
144#14519711C2314yes—
145#14519710C2314yes—
146#14519710C2314yes—
147#14519706C2314yes—
148#14519706C2314yes—
149#14519702C2314yes—
150#14519702C2314yes—
151#14519701C2314yes—
152#14519698C2314yes—
153#14519698C2314yes—
154#14519698C2314yes—
155C22⋊#92418C2314yes—
156#14519687C2314yes—
157C8×Dic61C2314yes—
158C2×#41×C61—24no—
159C2×#41×C61—24no—
160C2×#41×C61—22no—
161C2×#41×C61C2314yes—
162C22×Q8×C61C2311yescharacteristic
163C22×D4×C61—21no—
164C22×D4×C61—21no—
165C22×D4×C61C2311yescharacteristic
166C22×D4×C61C2311yescharacteristic
167C23×C4×C61—21no—
168C23×C4×C61C2311yescharacteristic
169C2×SD16×C61—24no—
170C2×SD16×C61C2314yes—
171C2×D8×C61—24no—
172C2×D8×C61C2314yes—
173C22×C8×C61C2311yescharacteristic
174C22×C8×C61C2311yescharacteristic
175#121×C61—22no—
176#121×C61C2314yes—
177C2×C4⋊C4×C61C2311yescharacteristic
178C2×C22⋊C4×C61—21no—
179#103×C61C2314yes—
180#102×C61C2314yes—
181C22⋊C8×C61C2314yes—
182C24×C61—21no—
183C24×C61—21no—
184C24×C61C2×D411yescharacteristic
185#41×C61—216no—
186#41×C61—28no—
187#41×C61—28no—
188C2×Q8×C61—21no—
189C2×Q8×C61—22no—
190C2×Q8×C61#4114yes—
191C2×Q8×C61C2412yes—
192C2×D4×C61—28no—
193C2×D4×C61—24no—
194C2×D4×C61—24no—
195C2×D4×C61—21no—
196C2×D4×C61—21no—
197C2×D4×C61—22no—
198C2×D4×C61—22no—
199C2×D4×C61—22no—
200C2×D4×C61—82no—
201C2×D4×C61#4114yes—
202C2×D4×C61C2412yes—
203C2×D4×C61C2412yes—
204C22×C4×C61—28no—
205C22×C4×C61—21no—
206C22×C4×C61—24no—
207C22×C4×C61—22no—
208C22×C4×C61—22no—
209C22×C4×C61—21no—
210C22×C4×C61C2×D411yescharacteristic
211C22×C4×C61C2×D412yes—
212C22×C4×C61C2412yes—
213C22×C4×C61C2411yescharacteristic
214C22×Dic61—21no—
215C22×Dic61—21no—
216C22×Dic61—21no—
217C22×Dic61—21no—
218C22×Dic61—24no—
219C22×Dic61—24no—
220C22×Dic61—24no—
221C22×Dic61—24no—
222C22×Dic61—82no—
223C22×Dic61—82no—
224C22×Dic61—82no—
225C22×Dic61—82no—
226C22×Dic61C2×D411yescharacteristic
227C22×Dic61C2×D411yescharacteristic
228C22×Dic61C2×D411yescharacteristic
229C22×Dic61C2×D411yescharacteristic
230C2×Dic122—22no—
231C2×Dic122—22no—
232C2×Dic122—21no—
233C2×Dic122—24no—
234C2×Dic122—82no—
235C2×Dic122C2412yes—
236SD16×C61—28no—
237D8×C61—28no—
238C2×C8×C61—22no—
239C2×C8×C61—22no—
240C2×C8×C61C2412yes—
241C2×C8×C61C2412yes—
242C4⋊C4×C61—21no—
243C4⋊C4×C61C2412yes—
244C22⋊C4×C61—24no—
245C22⋊Dic61—24no—
246C22⋊Dic61—24no—
247C22⋊Dic61—24no—
248C22⋊Dic61—24no—
249C22⋊Dic61—24no—
250C22⋊Dic61—24no—
251C22⋊Dic61C2×D414yes—
252C22⋊Dic61C2×D414yes—
253#11758202—28no—
254#11758200—28no—
255C4⋊Dic61—24no—
256C4⋊Dic61—21no—
257C4⋊Dic61—21no—
258C4⋊Dic61—21no—
259C4⋊Dic61—24no—
260C4⋊Dic61—24no—
261C4⋊Dic61C2×D414yes—
262C4⋊Dic61C2×D414yes—
263C4⋊Dic61C2412yes—
264C4⋊Dic61C2412yes—
265C4⋊Dic61C2412yes—
266#11758196—24no—
267#11758196—24no—
268#11758196—24no—
269C4×Dic61—24no—
270C4×Dic61—24no—
271C4×Dic61—24no—
272C4×Dic61C2×D412yes—
273C4×Dic61C2×D412yes—
274C4×Dic61C2412yes—
275C4×Dic61C2412yes—
276C2×#92418—22no—
277C2×#92418—22no—
278C2×#92418C2412yes—
279C2×#92418C2412yes—
280C23×C61—22no—
281C23×C61—24no—
282C23×C61—22no—
283C23×C61—22no—
284C23×C61—22no—
285C23×C61—22no—
286C23×C61—42no—
287C23×C61—42no—
288C23×C61—42no—
289C23×C61—42no—
290C23×C61—42no—
291C23×C61C22×D412yes—
292C23×C61C22×D411yescharacteristic
293Q8×C61—24no—
294Q8×C61—22no—
295Q8×C61C2×#4114yes—
296D4×C61—216no—
297D4×C61—24no—
298D4×C61—22no—
299D4×C61—22no—
300D4×C61—22no—
301D4×C61—42no—
302D4×C61—84no—
303D4×C61C2×#4114yes—
304C2×C4×C61—216no—
305C2×C4×C61—22no—
306C2×C4×C61—24no—
307C2×C4×C61—22no—
308C2×C4×C61—24no—
309C2×C4×C61—22no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—42no—
313C2×C4×C61C22×D412yes—
314C2×C4×C61C22×D411yescharacteristic
315C2×C4×C61C2×#4112yes—
316C2×C4×C61C2×#4112yes—
317C2×C4×C61C2511yescharacteristic
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—22no—
323C2×Dic61—22no—
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—42no—
327C2×Dic61—42no—
328C2×Dic61—42no—
329C2×Dic61—42no—
330C2×Dic61—84no—
331C2×Dic61—84no—
332C2×Dic61—84no—
333C2×Dic61—84no—
334C2×Dic61C22×D412yes—
335C2×Dic61C22×D412yes—
336C2×Dic61C22×D412yes—
337C2×Dic61C22×D412yes—
338Dic122—22no—
339Dic122—22no—
340Dic122—42no—
341Dic122—84no—
342C8×C61—22no—
343C8×C61—22no—
344#92418—22no—
345#92418—22no—
346C2×#3124—611nomaximal, Sylow
347C22×C61—22no—
348C22×C61—24no—
349C22×C61—22no—
350C22×C61—22no—
351C22×C61—44no—
352C22×C61—48no—
353C22×C61—42no—
354C22×C61—42no—
355C22×C61—42no—
356C22×C61—42no—
357C22×C61—42no—
358C22×C61—84no—
359C22×C61#52512yes—
360C22×C61#57612yes—
361C22×C61#57812yes—
362C22×C61C23×D411yescharacteristic
363C4×C61—22no—
364C4×C61—24no—
365C4×C61—42no—
366C4×C61#52512yes—
367C4×C61C22×#4111yescharacteristic
368C4×C61C22×#4111yescharacteristic
369Dic61—22no—
370Dic61—22no—
371Dic61—22no—
372Dic61—22no—
373Dic61—42no—
374Dic61—42no—
375Dic61—42no—
376Dic61—42no—
377C2×#542—611no—
378C2×#520—611no—
379#3124—6116no—
380C2×#484—611no—
381C2×#480—611no—
382C2×#477—611no—
383C2×#474—611no—
384C2×#464—611no—
385C2×#463—611no—
386C2×#452—611no—
387C2×#449D6111yescharacteristic
388C2×#440—611no—
389C2×#440—611no—
390C2×C4×Q16—611no—
391C2×C4×D8—611no—
392C2×#433—611no—
393C2×C61—42no—
394C2×C61—44no—
395C2×C61—82no—
396C2×C61#312414yescomplemented
397C2×C61C2×#52511yescharacteristic
398C2×C61C2×#57611yescharacteristic
399C2×C61C2×#57811yescharacteristic
400C22×#41C2×D6111yescharacteristic
401C22×Q16—611no—
402C22×SD16—611no—
403C22×SD16C2×D6111yescharacteristic
404C22×D8C2×D6111yescharacteristic
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—611no—
413C2×C22⋊Q8—1221no—
414C2×#121C2×D6111yescharacteristic
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—611no—
428C22×C4⋊C4—1221no—
429#484—618no—
430#480—618no—
431#477—618no—
432#474—618no—
433#464—618no—
434#463—618no—
435#452—618no—
436#449C2×D6118yes—
437#440—618no—
438#440—618no—
439C4×Q16—618no—
440C4×D8—618no—
441#433—618no—
442C2×#107—611no—
443C2×#107—611no—
444C2×#107—611no—
445C2×#107—611no—
446C2×C4⋊C8—611no—
447C2×C4⋊C8—611no—
448C2×#103—611no—
449C2×#103—611no—
450C2×#103—611no—
451C2×#103C2×D6111yescharacteristic
452C2×#102—611no—
453C2×#102—611no—
454C2×#102—611no—
455C2×#102C2×D6111yescharacteristic
456C2×C22⋊C8—611no—
457C2×C22⋊C8C2×D6111yescharacteristic
458C2×#97—611no—
459C2×C4×C8—611no—
460C61C2×#312411yescharacteristic, complemented, Sylow
461C2×#41—24no—
462C2×#41—24no—
463C2×#41—22no—
464C2×#41C22×D6114yes—
465C22×Q8—611no—
466C22×Q8—1221no—
467C22×Q8C22×D6111yescharacteristic
468C22×D4—21no—
469C22×D4—21no—
470C22×D4C22×D6111yescharacteristic
471C22×D4C22×D6111yescharacteristic
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—24no—
481C2×SD16—614no—
482C2×SD16—1224no—
483C2×SD16C22×D6114yes—
484C2×D8—24no—
485C2×D8C22×D6114yes—
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—614no—
498C22⋊Q8—1228no—
499C22⋊Q8—1222no—
500#121—22no—
501#121C22×D6114yes—
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—611no—
520C2×C4⋊C4—611no—
521C2×C4⋊C4—611no—
522C2×C4⋊C4—611no—
523C2×C4⋊C4—614no—
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⋊C4—1221no—
531C2×C4⋊C4—1222no—
532C2×C4⋊C4—1221no—
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#107—614no—
551#107—614no—
552C4⋊C8—614no—
553C4⋊C8—614no—
554#103—614no—
555#103—614no—
556#103—614no—
557#103C22×D6114yes—
558#102—614no—
559#102—614no—
560#102—614no—
561#102C22×D6114yes—
562C22⋊C8—614no—
563C22⋊C8C22×D6114yes—
564#97—614no—
565C4×C8—614no—
566C24—21no—
567C24—21no—
568C24D4×D6111yescharacteristic
569#41—216no—
570#41—28no—
571#41—28no—
572C2×Q8—21no—
573C2×Q8—22no—
574C2×Q8—612no—
575C2×Q8—1224no—
576C2×Q8—1221no—
577C2×Q8—1222no—
578C2×Q8—1222no—
579C2×Q8—4882no—
580C2×Q8#1175822414yes—
581C2×Q8C23×D6112yes—
582C2×D4—28no—
583C2×D4—24no—
584C2×D4—24no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—82no—
591C2×D4#1175822414yes—
592C2×D4C23×D6112yes—
593C2×D4C23×D6112yes—
594C22×C4—28no—
595C22×C4—21no—
596C22×C4—24no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—21no—
600C22×C4—611no—
601C22×C4—611no—
602C22×C4—611no—
603C22×C4—611no—
604C22×C4—1224no—
605C22×C4—1224no—
606C22×C4—1224no—
607C22×C4—1224no—
608C22×C4—1221no—
609C22×C4—1221no—
610C22×C4—1221no—
611C22×C4—1221no—
612C22×C4—4882no—
613C22×C4—4882no—
614C22×C4—4882no—
615C22×C4—4882no—
616C22×C4D4×D6112yes—
617C22×C4D4×D6111yescharacteristic
618C22×C4C23×D6112yes—
619C22×C4C23×D6111yescharacteristic
620Q16—1228no—
621SD16—28no—
622SD16—1228no—
623D8—28no—
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—21no—
633C4⋊C4—614no—
634C4⋊C4—614no—
635C4⋊C4—612no—
636C4⋊C4—612no—
637C4⋊C4—612no—
638C4⋊C4—1224no—
639C4⋊C4—1224no—
640C4⋊C4—1224no—
641C4⋊C4—1224no—
642C4⋊C4—1224no—
643C4⋊C4—1221no—
644C4⋊C4—1221no—
645C4⋊C4—1221no—
646C4⋊C4—1224no—
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—24no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23C2×D4×D6112yes—
676C23C2×D4×D6111yescharacteristic
677Q8—24no—
678Q8—22no—
679Q8—1222no—
680Q8—1222no—
681Q8—4884no—
682Q8—2442no—
683Q8C2×#1175822414yes—
684D4—216no—
685D4—24no—
686D4—22no—
687D4—22no—
688D4—22no—
689D4—42no—
690D4—84no—
691D4C2×#1175822414yes—
692C2×C4—216no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—42no—
701C2×C4—612no—
702C2×C4—612no—
703C2×C4—612no—
704C2×C4—612no—
705C2×C4—1222no—
706C2×C4—1222no—
707C2×C4—1222no—
708C2×C4—1222no—
709C2×C4—1222no—
710C2×C4—1222no—
711C2×C4—1222no—
712C2×C4—1222no—
713C2×C4—4884no—
714C2×C4—4884no—
715C2×C4—4884no—
716C2×C4—4884no—
717C2×C4—2442no—
718C2×C4—2442no—
719C2×C4—2442no—
720C2×C4—2442no—
721C2×C4C2×D4×D6112yes—
722C2×C4C2×D4×D6111yescharacteristic
723C2×C4C2×#1175822412yes—
724C2×C4C2×#1175822412yes—
725C2×C4C24×D6111yescharacteristic
726C8—22no—
727C8—22no—
728C8—1222no—
729C8—1222no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—24no—
734C22—42no—
735C22—42no—
736C22—44no—
737C22—48no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—84no—
742C22#1684026812yes—
743C22#1684056612yes—
744C22#1684057612yes—
745C22C22×D4×D6111yescharacteristic
746C4—22no—
747C4—24no—
748C4—42no—
749C4—1222no—
750C4—1222no—
751C4—1222no—
752C4—1222no—
753C4—2442no—
754C4—2442no—
755C4—2442no—
756C4—2442no—
757C4#1684026812yes—
758C4C22×#1175822411yescharacteristic
759C4C22×#1175822411yescharacteristic
760C2—42no—
761C2—44no—
762C2—82no—
763C2#2145607414yesdirect product factor
764C2C2×#1684026811yescharacteristic
765C2C2×#1684056611yescharacteristic
766C2C2×#1684057611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
Fitting, prime radicalC2×C61×#449C2
socleC23×C61C22×D4
hypercenterC2×#449D61
hypocenterC61C2×#3124
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#16840379C2semidirect
2. C2×#16840245C2semidirect
3. #21456074C2direct (N × H)
4. C2×#16840098C2semidirect
5. C2×#16840073C2semidirect
6. C2×#16840055C2semidirect
7. C2×#16840040C2semidirect
8. C2×#16839982C2semidirect
9. C2×#16839975C2semidirect
10. C2×#16839924C2semidirect
11. C2×#16839863C2semidirect
12. C2×#16839859C2semidirect
13. C2×#16839854C2semidirect
14. C2×D8×Dic61C2semidirect
15. C2×#16839820C2semidirect
20. #16840379C22semidirect
29. #16840245C22semidirect
42. #16840098C22semidirect
43. #16840073C22semidirect
44. #16840055C22semidirect
45. #16840040C22semidirect
46. #16839982C22semidirect
47. #16839975C22semidirect
48. #16839924C22semidirect
49. #16839863C22semidirect
50. #16839859C22semidirect
51. #16839854C22semidirect
52. D8×Dic61C22semidirect
53. #16839820C22semidirect
396. C2×C61#3124semidirect
460. C61C2×#3124semidirect
763. C2#21456074direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403792
C2×#168402452
#214560742
C2×#168400982
C2×#168400732
C2×#168400552
C2×#168400402
C2×#168399822
C2×#168399752
C2×#168399242
C2×#168398632
C2×#168398592
C2×#168398542
C2×D8×Dic612
C2×#168398202
C2×C61×#4492
C2×#312461