Finite Group Databasebeta

← C2×#21455781 #30547845

Subgroups — C2×#21455781 #30547845

Order 15616.

2170 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840335C211yesmaximal, characteristic
2C2×#16840243C211yesmaximal, characteristic
3#21455781C2116yesmaximal, direct product factor
4C2×#16840097C211yesmaximal, characteristic, complemented
5C2×#16840096C211yesmaximal, characteristic, complemented
6C2×#16840106C211yesmaximal, characteristic, complemented
7C2×#16840104C211yesmaximal, characteristic, complemented
8C2×#16840101C211yesmaximal, characteristic, complemented
9C2×#16840100C211yesmaximal, characteristic, complemented
10C2×#16840094C211yesmaximal, characteristic, complemented
11C2×#16839801C211yesmaximal, characteristic, complemented
12C2×#16839797C211yesmaximal, characteristic, complemented
13C2×#16839769C211yesmaximal, characteristic, complemented
14C2×#103×D61C211yesmaximal, characteristic, complemented
15C2×#16839727C211yesmaximal, characteristic
16C2×C61×#483C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C22×Q8×D61C2211yescharacteristic
19C22×#11758189C2211yescharacteristic
20C22×C8×D61C2211yescharacteristic
21#16840335—24no—
22#16840335C2218yes—
23C2×#14519776—21no—
24C2×#14519763—21no—
25C2×#14519762—21no—
26C2×#14519759—21no—
27C2×#14519757C2211yescharacteristic
28C2×#14519756C2211yescharacteristic
29C2×#14519753C2211yescharacteristic
30#16840243—24no—
31#16840243C2218yes—
32C2×#14519742—21no—
33C2×#14519739—21no—
34C2×C4×C22⋊D61—21no—
35C2×C4×C22⋊D61—21no—
36C2×#14519736C2211yescharacteristic
37C2×#14519735C2211yescharacteristic
38C2×#14519735C2211yescharacteristic
39C2×#14519735C2211yescharacteristic
40C2×C4⋊C4×D61C2211yescharacteristic
41C2×C4⋊C4×D61C2211yescharacteristic
42#16840106C2218yescomplemented
43#16840104C2218yescomplemented
44#16840101C2218yescomplemented
45#16840100C2218yescomplemented
46#16840097C2218yescomplemented
47#16840096C2218yescomplemented
48#16840094C2218yescomplemented
49#16839801C2218yescomplemented
50#16839797C2218yescomplemented
51C2×#14519711C2211yescharacteristic
52C2×#14519710C2211yescharacteristic
53C2×#14519710C2211yescharacteristic
54C2×#14519710C2211yescharacteristic
55C2×#14519709C2211yescharacteristic
56C2×#14519708C2211yescharacteristic
57#16839769C2218yescomplemented
58C2×#14519702C2211yescharacteristic
59C2×#14519702C2211yescharacteristic
60C2×#14519701C2211yescharacteristic
61C2×#14519701C2211yescharacteristic
62C2×#14519700C2211yescharacteristic
63C2×#14519700C2211yescharacteristic
64#103×D61C2218yescomplemented
65#16839727C2218yes—
66C2×C22⋊#92418C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×#14519689C2211yescharacteristic
69C2×C22⋊Q8×C61C2211yescharacteristic
70C22×C4⋊C4×C61C2211yescharacteristic
71C61×#483C2218yescomplemented
72C2×#106×C61C2211yescharacteristic
73C2×#106×C61C2211yescharacteristic
74C2×#103×C61C2211yescharacteristic
75C2×#103×C61C2211yescharacteristic
76C2×C22⋊C8×C61C2211yescharacteristic
77C2×#11758222—24no—
78C2×#11758222—24no—
79C2×#11758222D414yes—
80C2×#11758222C2314yes—
81C22×Dic122—21no—
82C22×Dic122D411yescharacteristic
83C22×Dic122C2311yescharacteristic
84C2×Q8×D61—22no—
85C2×Q8×D61—24no—
86C2×Q8×D61—24no—
87C2×Q8×D61C2314yes—
88C22×D244D411yescharacteristic
89C22×C22⋊D61D411yescharacteristic
90C22×C22⋊D61D411yescharacteristic
91C22×C4×D61—21no—
92C22×C4×D61—21no—
93C22×C4×D61—21no—
94C22×C4×D61C2311yescharacteristic
95C22×C4×D61C2311yescharacteristic
96C2×#11758189—24no—
97C2×#11758189C2314yes—
98C22×#92418C2311yescharacteristic
99C22×#92418C2311yescharacteristic
100C2×C8×D61—24no—
101C2×C8×D61C2314yes—
102#14519776—28no—
103#14519763—28no—
104#14519762—28no—
105#14519759—28no—
106#14519757—22no—
107#14519757C2314yes—
108#14519756—22no—
109#14519756C2314yes—
110#14519753—22no—
111#14519753C2314yes—
112#14519742—28no—
113#14519739—28no—
114C4×C22⋊D61—28no—
115C4×C22⋊D61—28no—
116#14519736—22no—
117#14519736C2314yes—
118#14519735—22no—
119#14519735—22no—
120#14519735—22no—
121#14519735C2314yes—
122#14519735C2314yes—
123#14519735C2314yes—
124C2×C4⋊Dic61—21no—
125C2×C4⋊Dic61C2311yescharacteristic
126C2×C4⋊Dic61C2311yescharacteristic
127C2×C4⋊Dic61C2311yescharacteristic
128C2×#11758196—21no—
129C2×#11758196—21no—
130C2×#11758196—21no—
131C2×#11758196—21no—
132C4⋊C4×D61—22no—
133C4⋊C4×D61—22no—
134C4⋊C4×D61C2314yes—
135C4⋊C4×D61C2314yes—
136C2×C22⋊Dic61—21no—
137C2×C22⋊Dic61—21no—
138C2×#11758198—21no—
139C2×#11758198—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—
147#14519711C2314yes—
148#14519710C2314yes—
149#14519710C2314yes—
150#14519710C2314yes—
151#14519709C2314yes—
152#14519708C2314yes—
153#14519702C2314yes—
154#14519702C2314yes—
155#14519701C2314yes—
156#14519701C2314yes—
157#14519700C2314yes—
158#14519700C2314yes—
159C22⋊#92418C2314yes—
160#14519689C2314yes—
161#14519689C2314yes—
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#106×C61C2314yes—
178#106×C61C2314yes—
179#103×C61C2314yes—
180#103×C61C2314yes—
181C22⋊C8×C61C2314yes—
182C24×C61C2×D411yescharacteristic
183C23×D61C2×D411yescharacteristic
184C23×D61C2×D411yescharacteristic
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—24no—
202C2×C22⋊D61—24no—
203C2×C22⋊D61C2×D414yes—
204C2×C22⋊D61C2×D414yes—
205C22×Dic61—21no—
206C22×Dic61—21no—
207C22×Dic61—21no—
208C22×Dic61—21no—
209C22×Dic61C2×D411yescharacteristic
210C22×Dic61C2×D411yescharacteristic
211Q8×D61—28no—
212Q8×D61—28no—
213Q8×D61—48no—
214#11758222—216no—
215#11758222—28no—
216#11758222—28no—
217C2×D244—24no—
218C2×D244C2×D414yes—
219C2×C4×D61—22no—
220C2×C4×D61—22no—
221C2×C4×D61—24no—
222C2×C4×D61—24no—
223C2×C4×D61—24no—
224C2×C4×D61—44no—
225C2×C4×D61—82no—
226C2×C4×D61—82no—
227C2×C4×D61C2×D412yes—
228C2×C4×D61C2×D412yes—
229C2×C4×D61#4114yes—
230C2×C4×D61#4114yes—
231C2×C4×D61C2412yes—
232C2×C4×D61C2412yes—
233C2×Dic122—24no—
234C2×Dic122—22no—
235C2×Dic122—22no—
236C2×Dic122—21no—
237C2×Dic122—24no—
238C2×Dic122—44no—
239C2×Dic122C2×D414yes—
240C2×Dic122C2412yes—
241C2×C8×C61—22no—
242C2×C8×C61—22no—
243C2×C8×C61C2412yes—
244C2×C8×C61C2412yes—
245C4⋊C4×C61—21no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61—24no—
248C4⋊C4×C61—24no—
249C4⋊C4×C61—21no—
250C4⋊C4×C61C2412yes—
251C4⋊C4×C61C2412yes—
252C4⋊C4×C61C2412yes—
253C22⋊C4×C61—24no—
254C22⋊Dic61—24no—
255C22⋊Dic61—24no—
256#11758198—24no—
257#11758198—24no—
258#11758198—24no—
259#11758198—24no—
260#11758198—24no—
261C4⋊Dic61—21no—
262C4⋊Dic61—21no—
263C4⋊Dic61—21no—
264C4⋊Dic61—24no—
265C4⋊Dic61C2412yes—
266C4⋊Dic61C2412yes—
267C4⋊Dic61C2412yes—
268#11758196—24no—
269#11758196—24no—
270#11758196—24no—
271#11758196—24no—
272C4×Dic61—24no—
273C4×Dic61—24no—
274C4×Dic61—24no—
275C4×Dic61—24no—
276C2×#92418—22no—
277C2×#92418—22no—
278C2×#92418C2412yes—
279C2×#92418C2412yes—
280#11758189—28no—
281C8×D61—28no—
282C23×C61—22no—
283C23×C61—22no—
284C23×C61—22no—
285C23×C61C22×D412yes—
286C23×C61C22×D411yescharacteristic
287C22×D61—22no—
288C22×D61—22no—
289C22×D61—22no—
290C22×D61—22no—
291C22×D61—22no—
292C22×D61#12314yes—
293C22×D61C22×D412yes—
294C22×D61C22×D412yes—
295Q8×C61—22no—
296Q8×C61—22no—
297Q8×C61—42no—
298C2×C4×C61—22no—
299C2×C4×C61—24no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61—22no—
306C2×C4×C61—42no—
307C2×C4×C61—42no—
308C2×C4×C61—42no—
309C2×C4×C61—42no—
310C2×C4×C61—84no—
311C2×C4×C61C22×D412yes—
312C2×C4×C61C22×D411yescharacteristic
313C2×C4×C61C2×#4112yes—
314C2×C4×C61C2×#4112yes—
315C2×C4×C61C2511yescharacteristic
316C22⋊D61—28no—
317C22⋊D61—28no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—22no—
323C2×Dic61—42no—
324C2×Dic61—42no—
325C2×Dic61—42no—
326C2×Dic61—42no—
327C2×Dic61#12314yes—
328C2×Dic61C22×D412yes—
329C2×Dic61C22×D412yes—
330D244—28no—
331C4×D61—24no—
332C4×D61—22no—
333C4×D61—22no—
334C4×D61—48no—
335C4×D61—84no—
336C4×D61—84no—
337C4×D61#12318yes—
338C4×D61C2×#4114yes—
339C4×D61C2×#4114yes—
340Dic122—28no—
341Dic122—22no—
342Dic122—22no—
343Dic122—42no—
344Dic122—48no—
345C8×C61—22no—
346C8×C61—22no—
347#92418—22no—
348#92418—22no—
349C2×#3097—611nomaximal, Sylow
350C22×C61—22no—
351C22×C61—22no—
352C22×C61—22no—
353C22×C61—44no—
354C22×C61C2×#12312yes—
355C22×C61#57712yes—
356C22×C61#57812yes—
357C22×C61C23×D411yescharacteristic
358C2×D61—28no—
359C2×D61—22no—
360C2×D61—22no—
361C2×D61—22no—
362C2×D61—22no—
363C2×D61—22no—
364C2×D61—44no—
365C2×D61C2×#12314yes—
366C4×C61—22no—
367C4×C61—42no—
368C4×C61—42no—
369C4×C61—42no—
370C4×C61—42no—
371C4×C61C2×#12312yes—
372C4×C61C22×#4111yescharacteristic
373C4×C61C22×#4111yescharacteristic
374Dic61—22no—
375Dic61—42no—
376Dic61—42no—
377Dic61—42no—
378Dic61—42no—
379Dic61C2×#12314yes—
380C2×#536—611no—
381C2×#520—611no—
382#3097—6116no—
383C2×#484—611no—
384C2×#484—611no—
385C2×#485—611no—
386C2×#485—611no—
387C2×#485—611no—
388C2×#485—611no—
389C2×#483—611no—
390C2×#483D6111yescharacteristic, complemented
391C2×#428—611no—
392C2×#427—611no—
393C2×#419—611no—
394C22×#103—611no—
395C2×#408—611no—
396C2×C61—42no—
397C2×C61#309714yescomplemented
398C2×C61C22×#12311yescharacteristic
399C2×C61C2×#57711yescharacteristic
400C2×C61C2×#57811yescharacteristic
401D61—24no—
402D61—42no—
403C22×#41—611no—
404C23×Q8—611no—
405C22×M16—611no—
406C23×C8—611no—
407#536—618no—
408#536—1224no—
409C2×C4⋊Q8—1221no—
410C2×#124—1221no—
411C2×#123—1221no—
412C2×#123—1221no—
413C2×C22⋊Q8—611no—
414C2×C22⋊Q8—611no—
415C2×C22⋊Q8—611no—
416C2×C22⋊Q8C2×D6111yescharacteristic
417#520—618no—
418#520—1224no—
419C2×C4×Q8—1221no—
420C2×C4×D4—1221no—
421C2×C4×D4—1221no—
422C2×C4×D4—1221no—
423C2×#117—611no—
424C2×#117—611no—
425C2×#117—611no—
426C2×#117—611no—
427C22×C4⋊C4—611no—
428C22×C4⋊C4—611no—
429C22×C4⋊C4C2×D6111yescharacteristic
430#485—618no—
431#485—618no—
432#485—618no—
433#485—618no—
434#484—618no—
435#484—618no—
436#483—618no—
437#483C2×D6118yescomplemented
438#428—618no—
439#427—618no—
440C2×#107—611no—
441C2×#107—611no—
442C2×#107—611no—
443C2×#107—611no—
444C2×#106—611no—
445C2×#106—611no—
446C2×#106C2×D6111yescharacteristic
447C2×#106C2×D6111yescharacteristic
448#419—618no—
449C2×#103—611no—
450C2×#103—611no—
451C2×#103—611no—
452C2×#103—611no—
453C2×#103—611no—
454C2×#103—611no—
455C2×#103—618no—
456C2×#103C2×D6111yescharacteristic
457C2×#103C2×D6111yescharacteristic
458#408—618no—
459C2×C22⋊C8—611no—
460C2×C22⋊C8—611no—
461C2×C22⋊C8—611no—
462C2×C22⋊C8C2×D6111yescharacteristic
463C61C2×#309711yescharacteristic, complemented, Sylow
464C2×#41—614no—
465C2×#41—614no—
466C2×#41—1224no—
467C2×#41—1224no—
468C22×Q8—611no—
469C22×Q8—614no—
470C22×Q8—611no—
471C22×Q8—1221no—
472C22×Q8—1222no—
473C22×Q8—1224no—
474C22×Q8—1224no—
475C22×Q8C22×D6111yescharacteristic
476C22×D4—611no—
477C22×D4—611no—
478C22×D4—611no—
479C23×C4—21no—
480C23×C4—611no—
481C23×C4—611no—
482C23×C4—1221no—
483C23×C4—1221no—
484C23×C4—1221no—
485C23×C4C22×D6111yescharacteristic
486C2×M16—614no—
487C2×M16—1224no—
488C22×C8—611no—
489C22×C8—611no—
490C22×C8—614no—
491C22×C8—1224no—
492C22×C8C22×D6111yescharacteristic
493C22×C8C22×D6111yescharacteristic
494C4⋊Q8—1228no—
495#124—1228no—
496#123—1228no—
497#123—1228no—
498C22⋊Q8—22no—
499C22⋊Q8—614no—
500C22⋊Q8—614no—
501C22⋊Q8—614no—
502C22⋊Q8—1222no—
503C22⋊Q8—1222no—
504C22⋊Q8—1222no—
505C22⋊Q8C22×D6114yes—
506C4×Q8—1228no—
507C4×D4—1228no—
508C4×D4—1228no—
509C4×D4—1228no—
510#117—614no—
511#117—614no—
512#117—614no—
513#117—614no—
514#117—1222no—
515#117—1222no—
516#117—1222no—
517#117—1222no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—611no—
522C2×C4⋊C4—611no—
523C2×C4⋊C4—611no—
524C2×C4⋊C4—614no—
525C2×C4⋊C4—614no—
526C2×C4⋊C4—1222no—
527C2×C4⋊C4—1222no—
528C2×C4⋊C4—1221no—
529C2×C4⋊C4—1221no—
530C2×C4⋊C4—1221no—
531C2×C4⋊C4—1221no—
532C2×C4⋊C4—1221no—
533C2×C4⋊C4C22×D6111yescharacteristic
534C2×C4⋊C4C22×D6111yescharacteristic
535C2×C4⋊C4C22×D6114yes—
536C2×C4⋊C4C22×D6111yescharacteristic
537C2×C22⋊C4—21no—
538C2×C22⋊C4—1221no—
539C2×C22⋊C4—1221no—
540C2×C22⋊C4—1221no—
541C2×C22⋊C4—1221no—
542C2×C22⋊C4—1221no—
543C2×C22⋊C4—1221no—
544C2×C22⋊C4—1221no—
545C2×C42—1221no—
546C2×C42—1221no—
547C2×C42—1221no—
548C2×C42—1221no—
549#107—614no—
550#107—614no—
551#107—614no—
552#107—614no—
553#106—614no—
554#106—614no—
555#106C22×D6114yes—
556#106C22×D6114yes—
557#103—614no—
558#103—614no—
559#103—614no—
560#103—614no—
561#103—614no—
562#103—614no—
563#103C22×D6114yes—
564#103C22×D6114yes—
565C22⋊C8—614no—
566C22⋊C8—614no—
567C22⋊C8—614no—
568C22⋊C8C22×D6114yes—
569C24—611no—
570C24—611no—
571C24D4×D6111yescharacteristic
572#41—12216no—
573#41—1228no—
574#41—1228no—
575C2×Q8—21no—
576C2×Q8—22no—
577C2×Q8—22no—
578C2×Q8—614no—
579C2×Q8—612no—
580C2×Q8—1224no—
581C2×Q8—1224no—
582C2×Q8—1228no—
583C2×Q8—1228no—
584C2×Q8—1221no—
585C2×Q8—1222no—
586C2×Q8—1222no—
587C2×Q8—2444no—
588C2×Q8—2448no—
589C2×Q8C23×D6112yes—
590C2×D4—614no—
591C2×D4—614no—
592C2×D4—614no—
593C2×D4—1224no—
594C2×D4—1224no—
595C2×D4—1224no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—24no—
603C22×C4—82no—
604C22×C4—611no—
605C22×C4—612no—
606C22×C4—614no—
607C22×C4—614no—
608C22×C4—612no—
609C22×C4—611no—
610C22×C4—612no—
611C22×C4—612no—
612C22×C4—1224no—
613C22×C4—1224no—
614C22×C4—1224no—
615C22×C4—1222no—
616C22×C4—1222no—
617C22×C4—1221no—
618C22×C4—1221no—
619C22×C4—1221no—
620C22×C4—1221no—
621C22×C4—4882no—
622C22×C4—4882no—
623C22×C4—2444no—
624C22×C4D4×D6112yes—
625C22×C4D4×D6111yescharacteristic
626C22×C4C23×D6112yes—
627C22×C4C23×D6111yescharacteristic
628M16—1228no—
629C2×C8—22no—
630C2×C8—22no—
631C2×C8—612no—
632C2×C8—612no—
633C2×C8—1228no—
634C2×C8—1222no—
635C2×C8—1222no—
636C2×C8C23×D6112yes—
637C2×C8C23×D6112yes—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—24no—
641C4⋊C4—24no—
642C4⋊C4—21no—
643C4⋊C4—612no—
644C4⋊C4—612no—
645C4⋊C4—612no—
646C4⋊C4—1224no—
647C4⋊C4—1224no—
648C4⋊C4—1224no—
649C4⋊C4—1224no—
650C4⋊C4—1221no—
651C4⋊C4—1221no—
652C4⋊C4—1221no—
653C4⋊C4—1224no—
654C4⋊C4C23×D6112yes—
655C4⋊C4C23×D6112yes—
656C4⋊C4C23×D6112yes—
657C22⋊C4—24no—
658C22⋊C4—1224no—
659C22⋊C4—1224no—
660C22⋊C4—1224no—
661C22⋊C4—1224no—
662C22⋊C4—1224no—
663C22⋊C4—1224no—
664C22⋊C4—1224no—
665C42—1224no—
666C42—1224no—
667C42—1224no—
668C42—1224no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—614no—
673C23—612no—
674C23—612no—
675C23—1222no—
676C23—1222no—
677C23—1222no—
678C23—1222no—
679C23—1222no—
680C23C2×D4×D6112yes—
681C23C2×D4×D6111yescharacteristic
682Q8—22no—
683Q8—22no—
684Q8—42no—
685Q8—1228no—
686Q8—1222no—
687Q8—1222no—
688Q8—2448no—
689Q8—2442no—
690D4—1228no—
691D4—1228no—
692D4—1228no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—22no—
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—42no—
705C2×C4—84no—
706C2×C4—614no—
707C2×C4—612no—
708C2×C4—618no—
709C2×C4—614no—
710C2×C4—614no—
711C2×C4—612no—
712C2×C4—1222no—
713C2×C4—1224no—
714C2×C4—1222no—
715C2×C4—1222no—
716C2×C4—1222no—
717C2×C4—1222no—
718C2×C4—1222no—
719C2×C4—1222no—
720C2×C4—4884no—
721C2×C4—4884no—
722C2×C4—2448no—
723C2×C4—2442no—
724C2×C4—2442no—
725C2×C4—2442no—
726C2×C4—2442no—
727C2×C4C2×D4×D6112yes—
728C2×C4C2×D4×D6111yescharacteristic
729C2×C4#41×D6112yes—
730C2×C4#41×D6112yes—
731C2×C4C24×D6111yescharacteristic
732C8—22no—
733C8—22no—
734C8—1222no—
735C8—1222no—
736C22—22no—
737C22—22no—
738C22—22no—
739C22—44no—
740C22—614no—
741C22—1222no—
742C22—1222no—
743C22—1228no—
744C22—1222no—
745C22—1222no—
746C22—1222no—
747C22—2444no—
748C22#123×D6112yes—
749C22#1684056812yes—
750C22#1684057812yes—
751C22C22×D4×D6111yescharacteristic
752C4—22no—
753C4—42no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—614no—
758C4—1222no—
759C4—2442no—
760C4—2442no—
761C4—2442no—
762C4—2442no—
763C4#123×D6112yes—
764C4C2×#41×D6111yescharacteristic
765C4C2×#41×D6111yescharacteristic
766C2—42no—
767C2—1224no—
768C2—2442no—
769C2#2145578114yesdirect product factor
770C2C2×#123×D6111yescharacteristic
771C2C2×#1684056811yescharacteristic
772C2C2×#1684057811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#483C2
socleC23×C61C22×D4
prime radicalC22×#11758222C22
hypercenterC2×#483D61
hypocenterC61C2×#3097
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#483

Complements

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

NH ≅ G/Ntype
3. #21455781C2direct (N × H)
4. C2×#16840097C2semidirect
5. C2×#16840096C2semidirect
6. C2×#16840106C2semidirect
7. C2×#16840104C2semidirect
8. C2×#16840101C2semidirect
9. C2×#16840100C2semidirect
10. C2×#16840094C2semidirect
11. C2×#16839801C2semidirect
12. C2×#16839797C2semidirect
13. C2×#16839769C2semidirect
14. C2×#103×D61C2semidirect
16. C2×C61×#483C2semidirect
42. #16840106C22semidirect
43. #16840104C22semidirect
44. #16840101C22semidirect
45. #16840100C22semidirect
46. #16840097C22semidirect
47. #16840096C22semidirect
48. #16840094C22semidirect
49. #16839801C22semidirect
50. #16839797C22semidirect
57. #16839769C22semidirect
64. #103×D61C22semidirect
71. C61×#483C22semidirect
390. C2×#483D61semidirect
397. C2×C61#3097semidirect
437. #483C2×D61semidirect
463. C61C2×#3097semidirect
769. C2#21455781direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403352
C2×#168402432
#214557812
C2×#168400972
C2×#168400962
C2×#168401062
C2×#168401042
C2×#168401012
C2×#168401002
C2×#168400942
C2×#168398012
C2×#168397972
C2×#168397692
C2×#103×D612
C2×#168397272
C2×C61×#4832
C2×#309761