Finite Group Databasebeta

← C2×#21457679 #30556391

Subgroups — C2×#21457679 #30556391

Order 15616.

2374 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840425C211yesmaximal, characteristic, complemented
2C2×#16840412C211yesmaximal, characteristic
3#21457679C2116yesmaximal, direct product factor
4C2×#16840111C211yesmaximal, characteristic, complemented
5C2×#16840094C211yesmaximal, characteristic, complemented
6C2×#16840090C211yesmaximal, characteristic, complemented
7C2×#16840046C211yesmaximal, characteristic, complemented
8C2×#16839990C211yesmaximal, characteristic, complemented
9C2×#16839965C211yesmaximal, characteristic, complemented
10C2×#16839900C211yesmaximal, characteristic, complemented
11C2×#16839899C211yesmaximal, characteristic, complemented
12C2×#16839853C211yesmaximal, characteristic, complemented
13C2×C8×C22⋊D61C211yesmaximal, characteristic, complemented
14C22×#14519702C211yesmaximal, characteristic, complemented
15C2×#103×D61C211yesmaximal, characteristic, complemented
16C2×C61×#465C211yesmaximal, characteristic, complemented
17C22×#11758224—21no—
18C23×Dic122C2211yescharacteristic
19C22×Q8×D61C2211yescharacteristic
20C22×#11758200C2211yescharacteristic
21C22×#11758200C2211yescharacteristic
22C22×C8×D61C2211yescharacteristic
23#16840425—24no—
24#16840425C2218yescomplemented
25#16840412—24no—
26#16840412C2218yes—
27C2×#14519776—21no—
28C2×#14519776C2211yescharacteristic
29C2×#14519775C2211yescharacteristic
30C2×#14519759—21no—
31C2×#14519758—21no—
32C2×#14519757C2211yescharacteristic
33C2×#14519755—21no—
34C2×#14519754—21no—
35C2×#14519754—21no—
36C2×#14519748C2211yescharacteristic
37C2×#14519742C2211yescharacteristic
38C2×D4×Dic61C2211yescharacteristic
39C2×C4×C22⋊D61C2211yescharacteristic
40C2×#14519737—21no—
41C22×C4⋊Dic61C2211yescharacteristic
42C2×C4⋊C4×D61C2211yescharacteristic
43#16840111C2218yescomplemented
44#16840094C2218yescomplemented
45#16840090C2218yescomplemented
46#16840046C2218yescomplemented
47#16839990C2218yescomplemented
48#16839965C2218yescomplemented
49#16839900C2218yescomplemented
50#16839899C2218yescomplemented
51#16839853C2218yescomplemented
52C8×C22⋊D61C2218yescomplemented
53C2×#14519708C2211yescharacteristic
54C2×#14519708C2211yescharacteristic
55C2×#14519706C2211yescharacteristic
56C2×#14519702C2211yescharacteristic
57C2×#14519702C2211yescharacteristic
58C2×#14519702C2211yescharacteristic
59C2×#14519702C2211yescharacteristic
60C2×#14519702C2218yescomplemented
61C2×#14519701C2211yescharacteristic
62C2×#14519701C2211yescharacteristic
63C2×#14519700C2211yescharacteristic
64C2×#14519700C2211yescharacteristic
65#103×D61C2218yescomplemented
66C2×C22⋊#92418C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
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—24no—
80C22×Dic122—21no—
81C22×Dic122—22no—
82C22×Dic122—21no—
83C22×Dic122—21no—
84C22×Dic122—42no—
85C22×Dic122C2311yescharacteristic
86C22×Dic122C2314yes—
87C22×Dic122C2311yescharacteristic
88C2×Q8×D61—22no—
89C2×Q8×D61—24no—
90C2×Q8×D61—42no—
91C2×Q8×D61C2314yes—
92C22×C22⋊D61—21no—
93C22×C22⋊D61D411yescharacteristic
94C23×Dic61—21no—
95C23×Dic61—21no—
96C23×Dic61—21no—
97C22×C4×D61—21no—
98C22×C4×D61—21no—
99C22×C4×D61C2311yescharacteristic
100C2×#11758200—24no—
101C2×#11758200—42no—
102C2×#11758200C2314yes—
103C2×#11758200C2314yes—
104C22×#92418C2311yescharacteristic
105C22×#92418C2311yescharacteristic
106C2×C8×D61—42no—
107C2×C8×D61C2314yes—
108#14519776—28no—
109#14519776—22no—
110#14519776C2314yes—
111#14519775—22no—
112#14519775C2314yes—
113#14519759—28no—
114#14519758—28no—
115#14519757—22no—
116#14519757C2314yes—
117#14519755—28no—
118#14519754—28no—
119#14519754—28no—
120#14519748—22no—
121#14519748C2314yes—
122#14519742—22no—
123#14519742C2314yes—
124D4×Dic61—22no—
125D4×Dic61C2314yes—
126C4×C22⋊D61D414yes—
127C4×C22⋊D61C2314yes—
128#14519737—28no—
129C2×C4⋊Dic61—21no—
130C2×C4⋊Dic61—22no—
131C2×C4⋊Dic61—21no—
132C2×C4⋊Dic61C2311yescharacteristic
133C2×C4⋊Dic61C2311yescharacteristic
134C2×C4⋊Dic61C2314yes—
135C2×#11758196—21no—
136C2×#11758196—21no—
137C2×#11758196—21no—
138C2×#11758196—21no—
139C2×#11758196—21no—
140C2×#11758196D411yescharacteristic
141C4⋊C4×D61—22no—
142C4⋊C4×D61C2314yes—
143C2×C22⋊Dic61—21no—
144C2×C22⋊Dic61—21no—
145C2×C22⋊Dic61D411yescharacteristic
146C2×#11758198—21no—
147C2×#11758198D411yescharacteristic
148C2×C4×Dic61—21no—
149C2×C4×Dic61C2311yescharacteristic
150#14519708C2314yes—
151#14519708C2314yes—
152#14519706C2314yes—
153#14519702C2314yes—
154#14519702C2314yes—
155#14519702C2314yes—
156#14519702C2314yes—
157#14519701C2314yes—
158#14519701C2314yes—
159#14519700C2314yes—
160#14519700C2314yes—
161C22⋊#92418C2314yes—
162#14519689C2314yes—
163C8×Dic61C2314yes—
164C22×Q8×C61C2311yescharacteristic
165C22×D4×C61—21no—
166C22×D4×C61C2311yescharacteristic
167C23×C4×C61C2311yescharacteristic
168C2×SD16×C61—42no—
169C2×SD16×C61C2314yes—
170C22×C8×C61—42no—
171C22×C8×C61C2311yescharacteristic
172C22×C8×C61C2311yescharacteristic
173C22×C8×C61C2314yes—
174C22⋊Q8×C61—22no—
175C22⋊Q8×C61C2314yes—
176#121×C61—22no—
177#121×C61C2314yes—
178C2×C4⋊C4×C61—21no—
179C2×C4⋊C4×C61C2311yescharacteristic
180C2×C4⋊C4×C61C2311yescharacteristic
181C2×C22⋊C4×C61—21no—
182C2×C22⋊C4×C61—21no—
183#106×C61C2314yes—
184#103×C61C2314yes—
185#102×C61C2314yes—
186C24×C61—21no—
187C24×C61C2×D411yescharacteristic
188C23×D61C2×D411yescharacteristic
189C2×Q8×C61—21no—
190C2×Q8×C61—22no—
191C2×Q8×C61—22no—
192C2×Q8×C61C2412yes—
193C2×D4×C61—24no—
194C2×D4×C61—21no—
195C2×D4×C61—22no—
196C2×D4×C61—22no—
197C2×D4×C61—44no—
198C2×D4×C61C2412yes—
199C22×C4×C61—22no—
200C22×C4×C61—22no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61C2×D411yescharacteristic
205C22×C4×C61C2×D412yes—
206C22×C4×C61C2412yes—
207C22×C4×C61C2411yescharacteristic
208C2×C22⋊D61—24no—
209C2×C22⋊D61—44no—
210C2×C22⋊D61SD1618yescomplemented
211C2×C22⋊D61C2×D414yes—
212C22×Dic61—21no—
213C22×Dic61—21no—
214C22×Dic61—21no—
215C22×Dic61—21no—
216C22×Dic61—24no—
217C22×Dic61—24no—
218C22×Dic61—24no—
219C22×Dic61—44no—
220C22×Dic61—44no—
221C22×Dic61—44no—
222C22×Dic61C2×D411yescharacteristic
223C22×Dic61C2×D411yescharacteristic
224C22×Dic61C2×D411yescharacteristic
225Q8×D61—28no—
226Q8×D61—44no—
227Q8×D61—48no—
228#11758224—432no—
229C2×C4×D61—22no—
230C2×C4×D61—22no—
231C2×C4×D61—24no—
232C2×C4×D61—24no—
233C2×C4×D61—44no—
234C2×C4×D61—44no—
235C2×C4×D61C2×D412yes—
236C2×C4×D61C2412yes—
237C2×Dic122—21no—
238C2×Dic122—22no—
239C2×Dic122—22no—
240C2×Dic122—22no—
241C2×Dic122—28no—
242C2×Dic122—24no—
243C2×Dic122—21no—
244C2×Dic122—24no—
245C2×Dic122—24no—
246C2×Dic122—44no—
247C2×Dic122—48no—
248C2×Dic122—44no—
249C2×Dic122—44no—
250C2×Dic122—44no—
251C2×Dic122#4114yescomplemented
252C2×Dic122C2412yes—
253C2×Dic122C2412yes—
254SD16×C61—44no—
255C2×C8×C61—22no—
256C2×C8×C61—22no—
257C2×C8×C61—44no—
258C2×C8×C61C2412yes—
259C2×C8×C61C2412yes—
260C4⋊C4×C61—24no—
261C4⋊C4×C61—21no—
262C4⋊C4×C61—21no—
263C4⋊C4×C61C2412yes—
264C4⋊C4×C61C2412yes—
265C22⋊C4×C61—24no—
266C22⋊C4×C61—24no—
267C22⋊Dic61—24no—
268C22⋊Dic61—24no—
269C22⋊Dic61C2×D414yes—
270#11758200—28no—
271#11758200—44no—
272#11758198—24no—
273#11758198C2×D414yes—
274C4⋊Dic61—21no—
275C4⋊Dic61—21no—
276C4⋊Dic61—24no—
277C4⋊Dic61—24no—
278C4⋊Dic61C2412yes—
279C4⋊Dic61C2412yes—
280#11758196—24no—
281#11758196—24no—
282#11758196—24no—
283#11758196—24no—
284#11758196—24no—
285#11758196C2×D414yes—
286C4×Dic61—24no—
287C4×Dic61C2×D412yes—
288C4×Dic61C2412yes—
289C2×#92418—22no—
290C2×#92418—22no—
291C2×#92418C2412yes—
292C2×#92418C2412yes—
293C8×D61—44no—
294C23×C61—22no—
295C23×C61—22no—
296C23×C61—22no—
297C23×C61—42no—
298C23×C61—42no—
299C23×C61—42no—
300C23×C61C2×SD1614yes—
301C23×C61C22×D412yes—
302C23×C61C22×D411yescharacteristic
303C22×D61—22no—
304C22×D61—22no—
305C22×D61C2×SD1614yes—
306C22×D61C22×D412yes—
307Q8×C61—22no—
308Q8×C61—22no—
309Q8×C61—42no—
310D4×C61—22no—
311D4×C61—22no—
312D4×C61—48no—
313D4×C61—42no—
314C2×C4×C61—22no—
315C2×C4×C61—24no—
316C2×C4×C61—22no—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61—22no—
320C2×C4×C61—22no—
321C2×C4×C61—42no—
322C2×C4×C61—42no—
323C2×C4×C61—42no—
324C2×C4×C61C22×D412yes—
325C2×C4×C61C22×D411yescharacteristic
326C2×C4×C61C2×#4112yes—
327C2×C4×C61H(5,𝔽2)12yes—
328C2×C4×C61C2511yescharacteristic
329C22⋊D61—48no—
330C22⋊D61C2×SD16116yescomplemented
331C2×Dic61—24no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—22no—
337C2×Dic61—22no—
338C2×Dic61—48no—
339C2×Dic61—42no—
340C2×Dic61—42no—
341C2×Dic61—42no—
342C2×Dic61—48no—
343C2×Dic61—48no—
344C2×Dic61C2×SD1614yes—
345C2×Dic61C22×D412yes—
346C2×Dic61C22×D412yes—
347C2×Dic61C22×D412yes—
348C4×D61—24no—
349C4×D61—22no—
350C4×D61—22no—
351C4×D61—48no—
352C4×D61—48no—
353Dic122—24no—
354Dic122—22no—
355Dic122—22no—
356Dic122—22no—
357Dic122—48no—
358Dic122—48no—
359Dic122—42no—
360Dic122—48no—
361Dic122C2×#4114yescomplemented
362C8×C61—22no—
363C8×C61—22no—
364#92418—22no—
365#92418—22no—
366C2×#3298—611nomaximal, Sylow
367C22×C61—22no—
368C22×C61—28no—
369C22×C61—22no—
370C22×C61—42no—
371C22×C61—42no—
372C22×C61—42no—
373C22×C61—84no—
374C22×C61#54612yes—
375C22×C61C22×SD1614yes—
376C22×C61C22×SD1612yes—
377C22×C61#57812yes—
378C22×C61C23×D411yescharacteristic
379C2×D61—22no—
380C2×D61—28no—
381C2×D61—22no—
382C2×D61C22×SD1614yes—
383C4×C61—22no—
384C4×C61—42no—
385C4×C61—42no—
386C4×C61—42no—
387C4×C61#54612yes—
388C4×C61C22×#4111yescharacteristic
389C4×C61C2×H(5,𝔽2)11yescharacteristic
390Dic61—24no—
391Dic61—22no—
392Dic61—22no—
393Dic61—42no—
394Dic61—42no—
395Dic61—42no—
396Dic61C22×SD1614yes—
397C2×D4×Q8—611no—
398C2×#547—611no—
399#3298—6116no—
400C2×#487—611no—
401C2×#483—611no—
402C2×#483—611no—
403C2×#475—611no—
404C2×#465—611no—
405C2×#465D6111yescharacteristic, complemented
406C2×#461—611no—
407C2×#448—611no—
408C2×#448—611no—
409C2×C4×SD16—611no—
410C2×C8×D4—611no—
411C22×#103—611no—
412C22×#103—611no—
413C2×C61—24no—
414C2×C61—82no—
415C2×C61#329814yescomplemented
416C2×C61C2×#54611yescharacteristic
417C2×C61C23×SD1611yescharacteristic
418C2×C61C2×#57811yescharacteristic
419D61—24no—
420C22×#41—1221no—
421C23×Q8—611no—
422C23×Q8—611no—
423C22×SD16—611no—
424C22×SD16—611no—
425C22×SD16C2×D6111yescharacteristic
426C23×C8—611no—
427C23×C8C2×D6111yescharacteristic
428D4×Q8—618no—
429D4×Q8—1224no—
430#547—618no—
431#547—1224no—
432C2×C4⋊Q8—611no—
433C2×C4⋊Q8—611no—
434C2×C4⋊Q8—1221no—
435C2×#123—1221no—
436C2×#123—1221no—
437C2×C22⋊Q8—611no—
438C2×C22⋊Q8—1221no—
439C2×C22⋊Q8—1221no—
440C2×C22⋊Q8—1221no—
441C2×C22⋊Q8C2×D6111yescharacteristic
442C2×#121—611no—
443C2×#121C2×D6111yescharacteristic
444C2×C4×Q8—611no—
445C2×C4×D4—611no—
446C2×C4×D4—611no—
447C2×C4×D4—1221no—
448C22×C4⋊C4—611no—
449C22×C4⋊C4—611no—
450#487—618no—
451#483—618no—
452#483—618no—
453#475—618no—
454#465—618no—
455#465C2×D6118yescomplemented
456#461—618no—
457#448—618no—
458#448—618no—
459C4×SD16—618no—
460C8×D4—618no—
461C2×#106—611no—
462C2×#106—611no—
463C2×#106C2×D6111yescharacteristic
464C2×C4⋊C8—611no—
465C2×#103—611no—
466C2×#103—611no—
467C2×#103—611no—
468C2×#103—611no—
469C2×#103—611no—
470C2×#103—611no—
471C2×#103—618no—
472C2×#103—611no—
473C2×#103—611no—
474C2×#103—618no—
475C2×#103C2×D6111yescharacteristic
476C2×#102C2×D6111yescharacteristic
477C2×C22⋊C8—611no—
478C2×C22⋊C8—611no—
479C2×C4×C8—611no—
480C61C2×#329811yescharacteristic, complemented, Sylow
481C2×#41—1228no—
482C2×#41—2448no—
483C22×Q8—614no—
484C22×Q8—611no—
485C22×Q8—611no—
486C22×Q8—614no—
487C22×Q8—1221no—
488C22×Q8—1221no—
489C22×Q8—1224no—
490C22×Q8—1222no—
491C22×Q8—1221no—
492C22×Q8—1222no—
493C22×Q8—1224no—
494C22×Q8—2442no—
495C22×Q8—2442no—
496C22×Q8C22×D6111yescharacteristic
497C22×D4—21no—
498C22×D4—611no—
499C22×D4—1221no—
500C22×D4C22×D6111yescharacteristic
501C23×C4—611no—
502C23×C4—1221no—
503C23×C4—1221no—
504C23×C4—1221no—
505C23×C4—1221no—
506C23×C4—1221no—
507C23×C4C22×D6111yescharacteristic
508C2×SD16—42no—
509C2×SD16—614no—
510C2×SD16—614no—
511C2×SD16—1224no—
512C2×SD16—2442no—
513C2×SD16C22×D6114yes—
514C22×C8—42no—
515C22×C8—611no—
516C22×C8—611no—
517C22×C8—614no—
518C22×C8—2442no—
519C22×C8C22×D6111yescharacteristic
520C22×C8C22×D6111yescharacteristic
521C22×C8C22×D6114yes—
522C4⋊Q8—614no—
523C4⋊Q8—614no—
524C4⋊Q8—1222no—
525C4⋊Q8—1222no—
526C4⋊Q8—1228no—
527#123—1228no—
528#123—1228no—
529C22⋊Q8—22no—
530C22⋊Q8—614no—
531C22⋊Q8—1228no—
532C22⋊Q8—1228no—
533C22⋊Q8—1228no—
534C22⋊Q8—1222no—
535C22⋊Q8C22×D6114yes—
536#121—22no—
537#121—614no—
538#121—1222no—
539#121C22×D6114yes—
540C4×Q8—614no—
541C4×Q8—1222no—
542C4×D4—614no—
543C4×D4—614no—
544C4×D4—614no—
545C4×D4—1222no—
546C4×D4—1228no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—611no—
549C2×C4⋊C4—611no—
550C2×C4⋊C4—611no—
551C2×C4⋊C4—614no—
552C2×C4⋊C4—614no—
553C2×C4⋊C4—1222no—
554C2×C4⋊C4—1221no—
555C2×C4⋊C4—1221no—
556C2×C4⋊C4—1221no—
557C2×C4⋊C4—1221no—
558C2×C4⋊C4—1221no—
559C2×C4⋊C4—1221no—
560C2×C4⋊C4—1221no—
561C2×C4⋊C4—1222no—
562C2×C4⋊C4C22×D6111yescharacteristic
563C2×C4⋊C4C22×D6111yescharacteristic
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—611no—
567C2×C22⋊C4—611no—
568C2×C22⋊C4—1221no—
569C2×C22⋊C4—1221no—
570C2×C22⋊C4—1221no—
571C2×C42—611no—
572C2×C42—1221no—
573#106—614no—
574#106—614no—
575#106C22×D6114yes—
576C4⋊C8—614no—
577#103—614no—
578#103—614no—
579#103—614no—
580#103—614no—
581#103—614no—
582#103—614no—
583#103—614no—
584#103—614no—
585#103C22×D6114yes—
586#102C22×D6114yes—
587C22⋊C8—614no—
588C22⋊C8—614no—
589C4×C8—614no—
590C24—21no—
591C24—611no—
592C24D4×D6111yescharacteristic
593#41—24432no—
594C2×Q8—21no—
595C2×Q8—22no—
596C2×Q8—22no—
597C2×Q8—614no—
598C2×Q8—612no—
599C2×Q8—612no—
600C2×Q8—1224no—
601C2×Q8—1224no—
602C2×Q8—1228no—
603C2×Q8—1221no—
604C2×Q8—1224no—
605C2×Q8—1221no—
606C2×Q8—1222no—
607C2×Q8—1228no—
608C2×Q8—1222no—
609C2×Q8—1222no—
610C2×Q8—2444no—
611C2×Q8—2444no—
612C2×Q8—2448no—
613C2×Q8—2444no—
614C2×Q8—2444no—
615C2×Q8—2444no—
616C2×Q8—2448no—
617C2×Q8C23×D6112yes—
618C2×D4—24no—
619C2×D4—21no—
620C2×D4—22no—
621C2×D4—22no—
622C2×D4—44no—
623C2×D4—614no—
624C2×D4—618no—
625C2×D4—1224no—
626C2×D4—2444no—
627C2×D4C23×D6112yes—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—611no—
634C22×C4—611no—
635C22×C4—611no—
636C22×C4—612no—
637C22×C4—612no—
638C22×C4—1224no—
639C22×C4—1224no—
640C22×C4—1224no—
641C22×C4—1221no—
642C22×C4—1222no—
643C22×C4—1222no—
644C22×C4—1224no—
645C22×C4—1224no—
646C22×C4—1221no—
647C22×C4—1221no—
648C22×C4—1221no—
649C22×C4—2444no—
650C22×C4—2444no—
651C22×C4—2444no—
652C22×C4—2444no—
653C22×C4—2444no—
654C22×C4D4×D6112yes—
655C22×C4D4×D6111yescharacteristic
656C22×C4C23×D6112yes—
657C22×C4C23×D6111yescharacteristic
658SD16—44no—
659SD16—1228no—
660SD16—2444no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—44no—
664C2×C8—612no—
665C2×C8—612no—
666C2×C8—1222no—
667C2×C8—1222no—
668C2×C8—2444no—
669C2×C8C23×D6112yes—
670C2×C8C23×D6112yes—
671C4⋊C4—24no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—614no—
675C4⋊C4—612no—
676C4⋊C4—612no—
677C4⋊C4—1224no—
678C4⋊C4—1224no—
679C4⋊C4—1224no—
680C4⋊C4—1224no—
681C4⋊C4—1224no—
682C4⋊C4—1224no—
683C4⋊C4—1221no—
684C4⋊C4—1221no—
685C4⋊C4—1224no—
686C4⋊C4C23×D6112yes—
687C4⋊C4C23×D6112yes—
688C22⋊C4—24no—
689C22⋊C4—24no—
690C22⋊C4—614no—
691C22⋊C4—614no—
692C22⋊C4—1224no—
693C22⋊C4—1224no—
694C22⋊C4—1224no—
695C42—612no—
696C42—612no—
697C42—1224no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—614no—
705C23—612no—
706C23—1222no—
707C23—1222no—
708C23SD16×D6114yes—
709C23C2×D4×D6112yes—
710C23C2×D4×D6111yescharacteristic
711Q8—22no—
712Q8—22no—
713Q8—42no—
714Q8—614no—
715Q8—1222no—
716Q8—1224no—
717Q8—1222no—
718Q8—1222no—
719Q8—2448no—
720Q8—2448no—
721Q8—2448no—
722Q8—2442no—
723D4—22no—
724D4—22no—
725D4—48no—
726D4—42no—
727D4—6116no—
728D4—2448no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—24no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—614no—
740C2×C4—612no—
741C2×C4—612no—
742C2×C4—612no—
743C2×C4—1222no—
744C2×C4—1222no—
745C2×C4—1222no—
746C2×C4—1224no—
747C2×C4—1222no—
748C2×C4—1222no—
749C2×C4—1224no—
750C2×C4—1222no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—2448no—
754C2×C4—2448no—
755C2×C4—2448no—
756C2×C4—2448no—
757C2×C4—2442no—
758C2×C4—2442no—
759C2×C4—2448no—
760C2×C4—2442no—
761C2×C4C2×D4×D6112yes—
762C2×C4C2×D4×D6111yescharacteristic
763C2×C4#41×D6112yes—
764C2×C4#1451982212yes—
765C2×C4C24×D6111yescharacteristic
766C8—22no—
767C8—22no—
768C8—1222no—
769C8—1222no—
770C22—28no—
771C22—22no—
772C22—22no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—84no—
777C22—614no—
778C22—1228no—
779C22—1222no—
780C22—1222no—
781C22#1684040112yes—
782C22C2×SD16×D6114yes—
783C22C2×SD16×D6112yes—
784C22#1684057612yes—
785C22C22×D4×D6111yescharacteristic
786C4—22no—
787C4—42no—
788C4—42no—
789C4—42no—
790C4—614no—
791C4—1222no—
792C4—1224no—
793C4—1222no—
794C4—2442no—
795C4—2442no—
796C4—2442no—
797C4#1684040112yes—
798C4C2×#41×D6111yescharacteristic
799C4C2×#1451982211yescharacteristic
800C2—24no—
801C2—82no—
802C2—1224no—
803C2#2145767914yesdirect product factor
804C2C2×#1684040111yescharacteristic
805C2C22×SD16×D6111yescharacteristic
806C2C2×#1684057611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#465C2
socleC23×C61C22×D4
prime radicalC2×#16840412C2
hypercenterC2×#465D61
hypocenterC61C2×#3298
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×#16840425C2semidirect
3. #21457679C2direct (N × H)
4. C2×#16840111C2semidirect
5. C2×#16840094C2semidirect
6. C2×#16840090C2semidirect
7. C2×#16840046C2semidirect
8. C2×#16839990C2semidirect
9. C2×#16839965C2semidirect
10. C2×#16839900C2semidirect
11. C2×#16839899C2semidirect
12. C2×#16839853C2semidirect
13. C2×C8×C22⋊D61C2semidirect
14. C22×#14519702C2semidirect
15. C2×#103×D61C2semidirect
16. C2×C61×#465C2semidirect
24. #16840425C22semidirect
43. #16840111C22semidirect
44. #16840094C22semidirect
45. #16840090C22semidirect
46. #16840046C22semidirect
47. #16839990C22semidirect
48. #16839965C22semidirect
49. #16839900C22semidirect
50. #16839899C22semidirect
51. #16839853C22semidirect
52. C8×C22⋊D61C22semidirect
60. C2×#14519702C22semidirect
65. #103×D61C22semidirect
73. C61×#465C22semidirect
210. C2×C22⋊D61SD16semidirect
251. C2×Dic122#41semidirect
330. C22⋊D61C2×SD16semidirect
361. Dic122C2×#41semidirect
405. C2×#465D61semidirect
415. C2×C61#3298semidirect
455. #465C2×D61semidirect
480. C61C2×#3298semidirect
803. C2#21457679direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404252
C2×#168404122
#214576792
C2×#168401112
C2×#168400942
C2×#168400902
C2×#168400462
C2×#168399902
C2×#168399652
C2×#168399002
C2×#168398992
C2×#168398532
C2×C8×C22⋊D612
C22×#145197022
C2×#103×D612
C2×C61×#4652
C2×#329861