Finite Group Databasebeta

← C2×#21456373 #30549722

Subgroups — C2×#21456373 #30549722

Order 15616.

2286 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840314C211yesmaximal, characteristic, complemented
2C2×#16840307C211yesmaximal, characteristic
3#21456373C2116yesmaximal, direct product factor
4C2×#16840159C211yesmaximal, characteristic, complemented
5C2×#16840133C211yesmaximal, characteristic, complemented
6C2×#16840111C211yesmaximal, characteristic, complemented
7C2×#16840107C211yesmaximal, characteristic, complemented
8C2×#16839993C211yesmaximal, characteristic, complemented
9C2×#16839991C211yesmaximal, characteristic, complemented
10C2×#16839989C211yesmaximal, characteristic, complemented
11C2×#16839853C211yesmaximal, characteristic, complemented
12C2×SD16×Dic61C211yesmaximal, characteristic, complemented
13C2×#16839849C211yesmaximal, characteristic, complemented
14C2×#16839847C211yesmaximal, characteristic, complemented
15C22×C8×Dic61C211yesmaximal, characteristic, complemented
16C2×C61×#465C211yesmaximal, characteristic, complemented
17C22×#11758224—21no—
18C22×#11758190C2211yescharacteristic
19C22×#11758200C2211yescharacteristic
20C22×#11758201C2211yescharacteristic
21C23×#92418C2211yescharacteristic
22#16840314—24no—
23#16840314C2218yescomplemented
24#16840307—24no—
25#16840307C2218yes—
26C2×#14519776C2211yescharacteristic
27C2×#14519776C2211yescharacteristic
28C2×#14519775C2211yescharacteristic
29C2×#14519773C2211yescharacteristic
30C2×#14519767—21no—
31C2×#14519763—21no—
32C2×#14519756C2211yescharacteristic
33C2×#14519754—21no—
34C2×#14519751C2211yescharacteristic
35C2×#14519749—21no—
36C2×Q8×Dic61C2211yescharacteristic
37C2×#14519742—21no—
38C2×#14519742C2211yescharacteristic
39C2×D4×Dic61C2211yescharacteristic
40C2×#14519739C2211yescharacteristic
41C2×#14519737—21no—
42C2×#14519733—21no—
43C22×C4×Dic61C2211yescharacteristic
44#16840159C2218yescomplemented
45#16840133C2218yescomplemented
46#16840111C2218yescomplemented
47#16840107C2218yescomplemented
48#16839993C2218yescomplemented
49#16839991C2218yescomplemented
50#16839989C2218yescomplemented
51#16839853C2218yescomplemented
52SD16×Dic61C2218yescomplemented
53#16839849C2218yescomplemented
54#16839847C2218yescomplemented
55C2×#14519709C2211yescharacteristic
56C2×#14519708C2211yescharacteristic
57C2×#14519708C2211yescharacteristic
58C2×#14519702C2211yescharacteristic
59C2×#14519701C2211yescharacteristic
60C2×#14519700C2211yescharacteristic
61C2×#14519699C2211yescharacteristic
62C2×#14519698C2211yescharacteristic
63C2×#14519697C2211yescharacteristic
64C2×C8×Dic61C2211yescharacteristic
65C2×C8×Dic61C2211yescharacteristic
66C2×C8×Dic61C2211yescharacteristic
67C2×C8×Dic61C2211yescharacteristic
68C2×C8×Dic61C2218yescomplemented
69C22×SD16×C61C2211yescharacteristic
70C23×C8×C61C2211yescharacteristic
71C2×C22⋊Q8×C61C2211yescharacteristic
72C2×#121×C61C2211yescharacteristic
73C61×#465C2218yescomplemented
74C2×#106×C61C2211yescharacteristic
75C2×#103×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C2×#11758224—28no—
78C2×#11758224—48no—
79C22×Dic122—21no—
80C22×Dic122—21no—
81C22×Dic122C2311yescharacteristic
82C22×D244C2311yescharacteristic
83C22×C22⋊D61—21no—
84C22×C22⋊D61—21no—
85C22×C22⋊D61—21no—
86C23×Dic61—21no—
87C23×Dic61D411yescharacteristic
88C23×Dic61D411yescharacteristic
89C22×C4×D61—21no—
90C2×#11758190—24no—
91C2×#11758190C2314yes—
92C2×#11758200—24no—
93C2×#11758200C2314yes—
94C2×#11758201—24no—
95C2×#11758201C2314yes—
96C22×#92418—24no—
97C22×#92418C2311yescharacteristic
98C22×#92418C2314yes—
99C22×#92418C2311yescharacteristic
100#14519776—22no—
101#14519776—22no—
102#14519776C2314yes—
103#14519776C2314yes—
104#14519775—22no—
105#14519775C2314yes—
106#14519773—22no—
107#14519773C2314yes—
108#14519767—28no—
109#14519763—28no—
110#14519756—22no—
111#14519756C2314yes—
112#14519754—28no—
113#14519751—22no—
114#14519751C2314yes—
115#14519749—28no—
116Q8×Dic61—22no—
117Q8×Dic61C2314yes—
118#14519742—28no—
119#14519742—22no—
120#14519742C2314yes—
121D4×Dic61—22no—
122D4×Dic61C2314yes—
123#14519739—22no—
124#14519739C2314yes—
125#14519737—28no—
126#14519733—28no—
127C2×C4⋊Dic61—21no—
128C2×C4⋊Dic61C2311yescharacteristic
129C2×C4⋊Dic61C2311yescharacteristic
130C2×#11758196—21no—
131C2×#11758196—21no—
132C2×#11758196—21no—
133C2×#11758196—21no—
134C2×#11758196—21no—
135C2×#11758196—21no—
136C2×C22⋊Dic61—21no—
137C2×C22⋊Dic61—21no—
138C2×#11758198—21no—
139C2×#11758198—21no—
140C2×C4×Dic61—21no—
141C2×C4×Dic61—21no—
142C2×C4×Dic61D411yescharacteristic
143C2×C4×Dic61D411yescharacteristic
144C2×C4×Dic61D414yes—
145C2×C4×Dic61C2311yescharacteristic
146C2×C4×Dic61C2311yescharacteristic
147C2×C4×Dic61C2314yes—
148#14519709C2314yes—
149#14519708C2314yes—
150#14519708C2314yes—
151#14519702C2314yes—
152#14519701C2314yes—
153#14519700C2314yes—
154#14519699C2314yes—
155#14519698C2314yes—
156#14519697C2314yes—
157C8×Dic61C2314yes—
158C8×Dic61C2314yes—
159C8×Dic61C2314yes—
160C8×Dic61C2314yes—
161C22×Q8×C61C2311yescharacteristic
162C22×D4×C61—21no—
163C22×D4×C61C2311yescharacteristic
164C23×C4×C61C2311yescharacteristic
165C2×SD16×C61—24no—
166C2×SD16×C61C2314yes—
167C22×C8×C61—24no—
168C22×C8×C61C2311yescharacteristic
169C22×C8×C61C2314yes—
170C22×C8×C61C2311yescharacteristic
171C22⋊Q8×C61—22no—
172C22⋊Q8×C61C2314yes—
173#121×C61—22no—
174#121×C61C2314yes—
175C2×C4⋊C4×C61—21no—
176C2×C4⋊C4×C61C2311yescharacteristic
177C2×C4⋊C4×C61C2311yescharacteristic
178C2×C22⋊C4×C61—21no—
179C2×C22⋊C4×C61—21no—
180#106×C61C2314yes—
181#103×C61C2314yes—
182#102×C61C2314yes—
183C24×C61—21no—
184C24×C61C2×D411yescharacteristic
185C23×D61—21no—
186C2×Q8×C61—21no—
187C2×Q8×C61—22no—
188C2×Q8×C61—22no—
189C2×Q8×C61C2412yes—
190C2×D4×C61—24no—
191C2×D4×C61—21no—
192C2×D4×C61—22no—
193C2×D4×C61—22no—
194C2×D4×C61—44no—
195C2×D4×C61C2412yes—
196C22×C4×C61—22no—
197C22×C4×C61—22no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61C2×D411yescharacteristic
202C22×C4×C61C2×D412yes—
203C22×C4×C61C2412yes—
204C22×C4×C61C2411yescharacteristic
205C2×C22⋊D61—24no—
206C2×C22⋊D61—24no—
207C2×C22⋊D61—24no—
208C2×C22⋊D61—44no—
209C2×C22⋊D61—44no—
210C2×C22⋊D61—44no—
211C22×Dic61—24no—
212C22×Dic61—21no—
213C22×Dic61—21no—
214C22×Dic61—21no—
215C22×Dic61—24no—
216C22×Dic61—44no—
217C22×Dic61SD1618yescomplemented
218C22×Dic61C2×D411yescharacteristic
219C22×Dic61C2×D414yes—
220C22×Dic61C2×D411yescharacteristic
221C22×Dic61C2×D411yescharacteristic
222C22×Dic61C2×D414yes—
223C22×Dic61C2×D411yescharacteristic
224#11758224—432no—
225C2×D244—22no—
226C2×D244—22no—
227C2×D244—21no—
228C2×D244C2412yes—
229C2×C4×D61—24no—
230C2×C4×D61—44no—
231C2×Dic122—22no—
232C2×Dic122—22no—
233C2×Dic122—21no—
234C2×Dic122—24no—
235C2×Dic122—24no—
236C2×Dic122—44no—
237C2×Dic122—44no—
238C2×Dic122C2412yes—
239SD16×C61—28no—
240C2×C8×C61—22no—
241C2×C8×C61—28no—
242C2×C8×C61#4114yescomplemented
243C2×C8×C61C2412yes—
244C2×C8×C61C2412yes—
245C4⋊C4×C61—24no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61—21no—
248C4⋊C4×C61C2412yes—
249C4⋊C4×C61C2412yes—
250C22⋊C4×C61—24no—
251C22⋊C4×C61—24no—
252C22⋊Dic61—24no—
253C22⋊Dic61—24no—
254#11758201—28no—
255#11758200—28no—
256#11758198—24no—
257#11758198—24no—
258C4⋊Dic61—21no—
259C4⋊Dic61—21no—
260C4⋊Dic61—24no—
261C4⋊Dic61C2412yes—
262C4⋊Dic61C2412yes—
263#11758196—24no—
264#11758196—24no—
265#11758196—24no—
266#11758196—24no—
267#11758196—24no—
268#11758196—24no—
269C4×Dic61—24no—
270C4×Dic61—24no—
271C4×Dic61C2×D414yes—
272C4×Dic61C2×D412yes—
273C4×Dic61C2×D414yes—
274C4×Dic61C2×D412yes—
275C4×Dic61C2412yes—
276C4×Dic61C2412yes—
277C2×#92418—22no—
278C2×#92418—28no—
279C2×#92418#4114yescomplemented
280C2×#92418C2412yes—
281C2×#92418C2412yes—
282#11758190—28no—
283C23×C61—22no—
284C23×C61—22no—
285C23×C61—22no—
286C23×C61—42no—
287C23×C61—42no—
288C23×C61—42no—
289C23×C61C2×SD1614yes—
290C23×C61C22×D412yes—
291C23×C61C22×D411yescharacteristic
292C22×D61—22no—
293C22×D61—42no—
294C22×D61—42no—
295C22×D61—42no—
296Q8×C61—22no—
297Q8×C61—22no—
298Q8×C61—42no—
299D4×C61—22no—
300D4×C61—22no—
301D4×C61—48no—
302D4×C61—42no—
303C2×C4×C61—22no—
304C2×C4×C61—24no—
305C2×C4×C61—22no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—42no—
311C2×C4×C61—42no—
312C2×C4×C61—42no—
313C2×C4×C61C22×D412yes—
314C2×C4×C61C22×D411yescharacteristic
315C2×C4×C61C2×#4112yes—
316C2×C4×C61C2×#4112yes—
317C2×C4×C61C2511yescharacteristic
318C22⋊D61—48no—
319C22⋊D61—48no—
320C22⋊D61—48no—
321C2×Dic61—22no—
322C2×Dic61—28no—
323C2×Dic61—22no—
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—42no—
327C2×Dic61—42no—
328C2×Dic61—42no—
329C2×Dic61—48no—
330C2×Dic61C2×SD1614yes—
331C2×Dic61C2×SD1614yes—
332C2×Dic61C2×SD16116yescomplemented
333C2×Dic61#13514yes—
334C2×Dic61C22×D412yes—
335C2×Dic61C22×D412yes—
336C2×Dic61C22×D412yes—
337C2×Dic61C22×D412yes—
338D244—22no—
339D244—22no—
340D244—42no—
341C4×D61—48no—
342Dic122—22no—
343Dic122—22no—
344Dic122—42no—
345Dic122—48no—
346Dic122—48no—
347C8×C61—22no—
348C8×C61C2×#4114yescomplemented
349#92418—22no—
350#92418C2×#4114yescomplemented
351C2×#3167—611nomaximal, Sylow
352C22×C61—28no—
353C22×C61—22no—
354C22×C61—22no—
355C22×C61—42no—
356C22×C61—42no—
357C22×C61—42no—
358C22×C61—84no—
359C22×C61#53212yes—
360C22×C61C22×SD1614yes—
361C22×C61C22×SD1612yes—
362C22×C61C2×#13512yes—
363C22×C61C23×D411yescharacteristic
364C2×D61—42no—
365C2×D61—42no—
366C2×D61—42no—
367C2×D61—84no—
368C4×C61—22no—
369C4×C61—42no—
370C4×C61—42no—
371C4×C61—42no—
372C4×C61#53212yes—
373C4×C61C22×#4111yescharacteristic
374C4×C61C22×#4111yescharacteristic
375Dic61—22no—
376Dic61—42no—
377Dic61—42no—
378Dic61—42no—
379Dic61C22×SD1614yes—
380Dic61C22×SD1614yes—
381Dic61C2×#13514yes—
382C2×#533—611no—
383C2×#532—611no—
384#3167—6116no—
385C2×#498—611no—
386C2×#492—611no—
387C2×#487—611no—
388C2×#486—611no—
389C2×#465—611no—
390C2×#465—611no—
391C2×#465—611no—
392C2×#465D6111yescharacteristic, complemented
393C2×C4×SD16—611no—
394C2×C4×SD16—611no—
395C2×C4×SD16—611no—
396C2×C4×SD16—611no—
397C22×C4×C8—611no—
398C2×C61—24no—
399C2×C61—82no—
400C2×C61#316714yescomplemented
401C2×C61C2×#53211yescharacteristic
402C2×C61C23×SD1611yescharacteristic
403C2×C61C22×#13511yescharacteristic
404D61—82no—
405C22×#41—1221no—
406C22×SD16—611no—
407C22×SD16—611no—
408C22×SD16—611no—
409C22×SD16C2×D6111yescharacteristic
410C23×C8—611no—
411C23×C8C2×D6111yescharacteristic
412#533—618no—
413#533—1224no—
414#532—618no—
415#532—1224no—
416C2×C4⋊Q8—611no—
417C2×C4⋊Q8—611no—
418C2×C4⋊Q8—611no—
419C2×#127—611no—
420C2×#125—1221no—
421C2×#124—1221no—
422C2×C22⋊Q8—611no—
423C2×C22⋊Q8—1221no—
424C2×C22⋊Q8C2×D6111yescharacteristic
425C2×#121—611no—
426C2×#121—1221no—
427C2×#121C2×D6111yescharacteristic
428C2×C4×Q8—611no—
429C2×C4×Q8—611no—
430C2×C4×Q8—1221no—
431C2×C4×D4—611no—
432C2×C4×D4—611no—
433C2×C4×D4—1221no—
434C2×#117—1221no—
435C22×C42—611no—
436#498—618no—
437#492—618no—
438#487—618no—
439#486—618no—
440#465—618no—
441#465—618no—
442#465—618no—
443#465C2×D6118yescomplemented
444C4×SD16—618no—
445C4×SD16—618no—
446C4×SD16—618no—
447C4×SD16—618no—
448C2×#106—611no—
449C2×#106—611no—
450C2×#106—611no—
451C2×#106C2×D6111yescharacteristic
452C2×#103—611no—
453C2×#103—611no—
454C2×#103—611no—
455C2×#103C2×D6111yescharacteristic
456C2×#102—611no—
457C2×#102—611no—
458C2×#102—611no—
459C2×#102C2×D6111yescharacteristic
460C2×C4×C8—611no—
461C2×C4×C8—611no—
462C2×C4×C8—611no—
463C2×C4×C8—611no—
464C2×C4×C8—618no—
465C61C2×#316711yescharacteristic, complemented, Sylow
466C2×#41—1228no—
467C2×#41—2448no—
468C22×Q8—611no—
469C22×Q8—1221no—
470C22×Q8—1221no—
471C22×Q8C22×D6111yescharacteristic
472C22×D4—21no—
473C22×D4—611no—
474C22×D4—1221no—
475C22×D4—1221no—
476C22×D4—1221no—
477C22×D4C22×D6111yescharacteristic
478C23×C4—611no—
479C23×C4—611no—
480C23×C4—1221no—
481C23×C4—1221no—
482C23×C4C22×D6111yescharacteristic
483C2×SD16—24no—
484C2×SD16—614no—
485C2×SD16—614no—
486C2×SD16—614no—
487C2×SD16—1224no—
488C2×SD16—1224no—
489C2×SD16—1224no—
490C2×SD16C22×D6114yes—
491C22×C8—24no—
492C22×C8—611no—
493C22×C8—611no—
494C22×C8—614no—
495C22×C8—1224no—
496C22×C8C22×D6111yescharacteristic
497C22×C8C22×D6114yes—
498C22×C8C22×D6111yescharacteristic
499C4⋊Q8—614no—
500C4⋊Q8—614no—
501C4⋊Q8—614no—
502C4⋊Q8—1222no—
503C4⋊Q8—1222no—
504C4⋊Q8—1222no—
505#127—614no—
506#127—1222no—
507#125—1228no—
508#124—1228no—
509C22⋊Q8—22no—
510C22⋊Q8—614no—
511C22⋊Q8—1228no—
512C22⋊Q8—1222no—
513C22⋊Q8C22×D6114yes—
514#121—22no—
515#121—614no—
516#121—1228no—
517#121—1222no—
518#121C22×D6114yes—
519C4×Q8—614no—
520C4×Q8—614no—
521C4×Q8—1222no—
522C4×Q8—1228no—
523C4×Q8—1222no—
524C4×D4—614no—
525C4×D4—614no—
526C4×D4—1228no—
527C4×D4—1222no—
528C4×D4—1222no—
529#117—1228no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—611no—
532C2×C4⋊C4—611no—
533C2×C4⋊C4—1221no—
534C2×C4⋊C4—1221no—
535C2×C4⋊C4—1221no—
536C2×C4⋊C4—1221no—
537C2×C4⋊C4—1221no—
538C2×C4⋊C4—1221no—
539C2×C4⋊C4—1221no—
540C2×C4⋊C4C22×D6111yescharacteristic
541C2×C4⋊C4C22×D6111yescharacteristic
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—1221no—
545C2×C22⋊C4—1221no—
546C2×C22⋊C4—1221no—
547C2×C22⋊C4—1221no—
548C2×C42—611no—
549C2×C42—611no—
550C2×C42—614no—
551C2×C42—611no—
552C2×C42—611no—
553C2×C42—614no—
554C2×C42—1221no—
555C2×C42—1221no—
556#106—614no—
557#106—614no—
558#106—614no—
559#106C22×D6114yes—
560#103—614no—
561#103—614no—
562#103—614no—
563#103C22×D6114yes—
564#102—614no—
565#102—614no—
566#102—614no—
567#102C22×D6114yes—
568C4×C8—614no—
569C4×C8—614no—
570C4×C8—614no—
571C4×C8—614no—
572C24—21no—
573C24—1221no—
574C24D4×D6111yescharacteristic
575#41—24432no—
576C2×Q8—21no—
577C2×Q8—22no—
578C2×Q8—22no—
579C2×Q8—612no—
580C2×Q8—1224no—
581C2×Q8—1224no—
582C2×Q8—1221no—
583C2×Q8—1222no—
584C2×Q8—1222no—
585C2×Q8—2444no—
586C2×Q8—2444no—
587C2×Q8C23×D6112yes—
588C2×D4—24no—
589C2×D4—21no—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—44no—
593C2×D4—612no—
594C2×D4—1224no—
595C2×D4—1224no—
596C2×D4—1224no—
597C2×D4—1221no—
598C2×D4—1222no—
599C2×D4—1222no—
600C2×D4—2444no—
601C2×D4—2444no—
602C2×D4—2444no—
603C2×D4C23×D6112yes—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—614no—
610C22×C4—611no—
611C22×C4—611no—
612C22×C4—611no—
613C22×C4—618no—
614C22×C4—614no—
615C22×C4—611no—
616C22×C4—1224no—
617C22×C4—1224no—
618C22×C4—1224no—
619C22×C4—1221no—
620C22×C4—1221no—
621C22×C4—1221no—
622C22×C4—2444no—
623C22×C4—2444no—
624C22×C4D4×D6112yes—
625C22×C4D4×D6111yescharacteristic
626C22×C4C23×D6112yes—
627C22×C4C23×D6111yescharacteristic
628SD16—28no—
629SD16—1228no—
630SD16—1228no—
631SD16—1228no—
632C2×C8—22no—
633C2×C8—28no—
634C2×C8—614no—
635C2×C8—612no—
636C2×C8—612no—
637C2×C8—1228no—
638C2×C8—1222no—
639C2×C8#1175822414yescomplemented
640C2×C8C23×D6112yes—
641C2×C8C23×D6112yes—
642C4⋊C4—24no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—612no—
646C4⋊C4—612no—
647C4⋊C4—1224no—
648C4⋊C4—1224no—
649C4⋊C4—1224no—
650C4⋊C4—1224no—
651C4⋊C4—1224no—
652C4⋊C4—1224no—
653C4⋊C4—1221no—
654C4⋊C4—1221no—
655C4⋊C4—1224no—
656C4⋊C4C23×D6112yes—
657C4⋊C4C23×D6112yes—
658C22⋊C4—24no—
659C22⋊C4—24no—
660C22⋊C4—1224no—
661C22⋊C4—1224no—
662C22⋊C4—1224no—
663C22⋊C4—1224no—
664C42—614no—
665C42—612no—
666C42—614no—
667C42—612no—
668C42—612no—
669C42—612no—
670C42—1224no—
671C42—1224no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—1222no—
679C23—2442no—
680C23—2442no—
681C23—2442no—
682C23SD16×D6114yes—
683C23C2×D4×D6112yes—
684C23C2×D4×D6111yescharacteristic
685Q8—22no—
686Q8—22no—
687Q8—42no—
688Q8—1222no—
689Q8—1222no—
690Q8—2448no—
691Q8—2448no—
692Q8—2442no—
693D4—22no—
694D4—22no—
695D4—48no—
696D4—42no—
697D4—1222no—
698D4—1222no—
699D4—2448no—
700D4—2448no—
701D4—2448no—
702D4—2442no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—614no—
714C2×C4—614no—
715C2×C4—6116no—
716C2×C4—614no—
717C2×C4—612no—
718C2×C4—612no—
719C2×C4—612no—
720C2×C4—612no—
721C2×C4—1228no—
722C2×C4—1222no—
723C2×C4—1222no—
724C2×C4—1222no—
725C2×C4—1222no—
726C2×C4—2448no—
727C2×C4—2448no—
728C2×C4—2442no—
729C2×C4—2442no—
730C2×C4—2442no—
731C2×C4C2×D4×D6112yes—
732C2×C4C2×D4×D6111yescharacteristic
733C2×C4#41×D6112yes—
734C2×C4C2×#1175822412yes—
735C2×C4C24×D6111yescharacteristic
736C8—22no—
737C8—614no—
738C8—1222no—
739C8C2×#1175822414yescomplemented
740C22—22no—
741C22—22no—
742C22—28no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—84no—
747C22—4884no—
748C22—2442no—
749C22—2442no—
750C22—2442no—
751C22#1684030712yes—
752C22C2×SD16×D6114yes—
753C22C2×SD16×D6112yes—
754C22#135×D6112yes—
755C22C22×D4×D6111yescharacteristic
756C4—22no—
757C4—42no—
758C4—42no—
759C4—42no—
760C4—614no—
761C4—614no—
762C4—614no—
763C4—1222no—
764C4—2442no—
765C4—2442no—
766C4—2442no—
767C4#1684030712yes—
768C4C2×#41×D6111yescharacteristic
769C4C22×#1175822411yescharacteristic
770C2—24no—
771C2—82no—
772C2—4882no—
773C2#2145637314yesdirect product factor
774C2C2×#1684030711yescharacteristic
775C2C22×SD16×D6111yescharacteristic
776C2C2×#135×D6111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#465C2
socleC23×C61C22×D4
prime radicalC2×#16840307C2
hypercenterC2×#465D61
hypocenterC61C2×#3167
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×#16840314C2semidirect
3. #21456373C2direct (N × H)
4. C2×#16840159C2semidirect
5. C2×#16840133C2semidirect
6. C2×#16840111C2semidirect
7. C2×#16840107C2semidirect
8. C2×#16839993C2semidirect
9. C2×#16839991C2semidirect
10. C2×#16839989C2semidirect
11. C2×#16839853C2semidirect
12. C2×SD16×Dic61C2semidirect
13. C2×#16839849C2semidirect
14. C2×#16839847C2semidirect
15. C22×C8×Dic61C2semidirect
16. C2×C61×#465C2semidirect
23. #16840314C22semidirect
44. #16840159C22semidirect
45. #16840133C22semidirect
46. #16840111C22semidirect
47. #16840107C22semidirect
48. #16839993C22semidirect
49. #16839991C22semidirect
50. #16839989C22semidirect
51. #16839853C22semidirect
52. SD16×Dic61C22semidirect
53. #16839849C22semidirect
54. #16839847C22semidirect
68. C2×C8×Dic61C22semidirect
73. C61×#465C22semidirect
217. C22×Dic61SD16semidirect
242. C2×C8×C61#41semidirect
279. C2×#92418#41semidirect
332. C2×Dic61C2×SD16semidirect
348. C8×C61C2×#41semidirect
350. #92418C2×#41semidirect
392. C2×#465D61semidirect
400. C2×C61#3167semidirect
443. #465C2×D61semidirect
465. C61C2×#3167semidirect
639. C2×C8#11758224semidirect
739. C8C2×#11758224semidirect
773. C2#21456373direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403142
C2×#168403072
#214563732
C2×#168401592
C2×#168401332
C2×#168401112
C2×#168401072
C2×#168399932
C2×#168399912
C2×#168399892
C2×#168398532
C2×SD16×Dic612
C2×#168398492
C2×#168398472
C22×C8×Dic612
C2×C61×#4652
C2×#316761