Finite Group Databasebeta

← C2×#21456048 #30548292

Subgroups — C2×#21456048 #30548292

Order 15616.

2058 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840383C211yesmaximal, characteristic
2#21456048C2116yesmaximal, direct product factor
3C2×#16840103C211yesmaximal, characteristic, complemented
4C2×#16840086C211yesmaximal, characteristic
5C2×#16840057C211yesmaximal, characteristic, complemented
6C2×#16840047C211yesmaximal, characteristic, complemented
7C2×#16839984C211yesmaximal, characteristic, complemented
8C2×#16839984C211yesmaximal, characteristic, complemented
9C2×#16839918C211yesmaximal, characteristic, complemented
10C2×#16839901C211yesmaximal, characteristic
11C2×#16839867C211yesmaximal, characteristic, complemented
12C2×#16839860C211yesmaximal, characteristic, complemented
13C2×C4×#11758202C211yesmaximal, characteristic, complemented
14C2×C4×#11758201C211yesmaximal, characteristic, complemented
15C2×#16839823C211yesmaximal, characteristic, complemented
16C2×C61×#519C211yesmaximal, characteristic, complemented
17C22×#11758202C2211yescharacteristic
18C22×#11758202C2211yescharacteristic
19C22×#11758201C2211yescharacteristic
20C22×#11758201C2211yescharacteristic
21#16840383—24no—
22#16840383C2218yes—
23C2×#14519777C2211yescharacteristic
24C2×#14519772—21no—
25C2×#14519765C2211yescharacteristic
26C2×#14519763—21no—
27C2×#14519759—21no—
28C2×#14519756C2211yescharacteristic
29C2×#14519755—21no—
30C2×#14519751C2211yescharacteristic
31C2×C4×Dic122C2211yescharacteristic
32C2×C4×D244C2211yescharacteristic
33#16840103C2218yescomplemented
34#16840086C2218yes—
35#16840057C2218yescomplemented
36#16840047C2218yescomplemented
37#16839984C2218yescomplemented
38#16839984C2218yescomplemented
39#16839918C2218yescomplemented
40#16839901C2218yes—
41#16839867C2218yescomplemented
42#16839860C2218yescomplemented
43C4×#11758202C2218yescomplemented
44C4×#11758201C2218yescomplemented
45#16839823C2218yescomplemented
46C2×#14519710C2211yescharacteristic
47C2×#14519710C2211yescharacteristic
48C2×#14519708C2211yescharacteristic
49C2×#14519708C2211yescharacteristic
50C2×C4⋊#92418C2211yescharacteristic
51C2×C4⋊#92418C2211yescharacteristic
52C2×#14519701C2211yescharacteristic
53C2×#14519701C2211yescharacteristic
54C2×#14519701C2211yescharacteristic
55C2×#14519701C2211yescharacteristic
56C2×#14519700C2211yescharacteristic
57C2×#14519700C2211yescharacteristic
58C2×#14519697C2211yescharacteristic
59C2×#14519697C2211yescharacteristic
60C2×C22⋊#92418C2211yescharacteristic
61C2×C22⋊#92418C2211yescharacteristic
62C2×#14519688C2211yescharacteristic
63C2×C4×#92418C2211yescharacteristic
64C23×Q8×C61C2211yescharacteristic
65C61×#519—24no—
66C61×#519C2218yescomplemented
67C2×C4×Q8×C61—21no—
68C2×C4×Q8×C61—21no—
69C2×C4×Q8×C61C2211yescharacteristic
70C2×C4×Q8×C61C2211yescharacteristic
71C2×C4×Q8×C61C2211yescharacteristic
72C2×C4×Q8×C61C2211yescharacteristic
73C2×#117×C61—21no—
74C2×#117×C61—21no—
75C2×#117×C61C2211yescharacteristic
76C2×#117×C61C2211yescharacteristic
77C22×Dic122—21no—
78C22×Dic122C2311yescharacteristic
79C22×D244C2311yescharacteristic
80C22×C22⋊D61—21no—
81C22×C4×D61—21no—
82C2×#11758202—24no—
83C2×#11758202—24no—
84C2×#11758202C2314yes—
85C2×#11758202C2314yes—
86C2×#11758201—24no—
87C2×#11758201—24no—
88C2×#11758201C2314yes—
89C2×#11758201C2314yes—
90C22×#92418C2311yescharacteristic
91C22×#92418C2311yescharacteristic
92C22×#92418C2311yescharacteristic
93C22×#92418C2311yescharacteristic
94#14519777—22no—
95#14519777C2314yes—
96#14519772—28no—
97#14519765—22no—
98#14519765C2314yes—
99#14519763—28no—
100#14519759—28no—
101#14519756—22no—
102#14519756C2314yes—
103#14519755—28no—
104#14519751—22no—
105#14519751C2314yes—
106C4×Dic122—22no—
107C4×Dic122C2314yes—
108C4×D244—22no—
109C4×D244C2314yes—
110C2×C4⋊Dic61—21no—
111C2×C4⋊Dic61C2311yescharacteristic
112C2×C4⋊Dic61C2311yescharacteristic
113C2×#11758196—21no—
114C2×#11758196—21no—
115C2×C22⋊Dic61—21no—
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×#11758198—21no—
119C2×#11758198—21no—
120C2×C4×Dic61—21no—
121#14519710C2314yes—
122#14519710C2314yes—
123#14519708C2314yes—
124#14519708C2314yes—
125C4⋊#92418C2314yes—
126C4⋊#92418C2314yes—
127#14519701C2314yes—
128#14519701C2314yes—
129#14519701C2314yes—
130#14519701C2314yes—
131#14519700C2314yes—
132#14519700C2314yes—
133#14519697C2314yes—
134#14519697C2314yes—
135C22⋊#92418C2314yes—
136C22⋊#92418C2314yes—
137#14519688C2314yes—
138C4×#92418C2314yes—
139C22×Q8×C61—24no—
140C22×Q8×C61—24no—
141C22×Q8×C61—21no—
142C22×Q8×C61—22no—
143C22×Q8×C61C2314yes—
144C22×Q8×C61C2311yescharacteristic
145C22×Q8×C61C2311yescharacteristic
146C23×C4×C61—21no—
147C23×C4×C61C2311yescharacteristic
148C4×Q8×C61—28no—
149C4×Q8×C61—28no—
150C4×Q8×C61—22no—
151C4×Q8×C61—22no—
152C4×Q8×C61—22no—
153C4×Q8×C61—22no—
154C4×Q8×C61C2314yes—
155C4×Q8×C61C2314yes—
156C4×Q8×C61C2314yes—
157C4×Q8×C61C2314yes—
158#117×C61—22no—
159#117×C61—28no—
160#117×C61—28no—
161#117×C61D414yes—
162#117×C61C2314yes—
163#117×C61C2314yes—
164C2×C4⋊C4×C61—21no—
165C2×C4⋊C4×C61—21no—
166C2×C4⋊C4×C61—21no—
167C2×C4⋊C4×C61—21no—
168C2×C4⋊C4×C61D411yescharacteristic
169C2×C4⋊C4×C61D411yescharacteristic
170C2×C4⋊C4×C61C2311yescharacteristic
171C2×C4⋊C4×C61C2311yescharacteristic
172C2×C22⋊C4×C61—21no—
173C2×C22⋊C4×C61D411yescharacteristic
174C2×C22⋊C4×C61D411yescharacteristic
175C2×C42×C61—21no—
176C2×C42×C61—21no—
177C2×C42×C61—21no—
178C2×C42×C61—21no—
179C2×C42×C61—21no—
180C2×C42×C61C2311yescharacteristic
181C2×C42×C61C2311yescharacteristic
182C24×C61C2×D411yescharacteristic
183C23×D61—21no—
184C2×Q8×C61—216no—
185C2×Q8×C61—28no—
186C2×Q8×C61—28no—
187C2×Q8×C61—28no—
188C2×Q8×C61—24no—
189C2×Q8×C61—21no—
190C2×Q8×C61—21no—
191C2×Q8×C61—22no—
192C2×Q8×C61—22no—
193C2×Q8×C61#4114yes—
194C2×Q8×C61#4114yes—
195C2×Q8×C61C2412yes—
196C2×Q8×C61C2412yes—
197C22×C4×C61—28no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—24no—
201C22×C4×C61—22no—
202C22×C4×C61—22no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61C2×D411yescharacteristic
206C22×C4×C61C2×D411yescharacteristic
207C22×C4×C61C2×D411yescharacteristic
208C22×C4×C61C2×D411yescharacteristic
209C22×C4×C61C2×D411yescharacteristic
210C22×C4×C61C2×D412yes—
211C22×C4×C61C2412yes—
212C22×C4×C61C2411yescharacteristic
213C2×C22⋊D61—24no—
214C2×C22⋊D61—82no—
215C22×Dic61—21no—
216C22×Dic61—21no—
217C22×Dic61—21no—
218C2×D244—22no—
219C2×D244—22no—
220C2×D244—21no—
221C2×D244C2412yes—
222C2×C4×D61—24no—
223C2×C4×D61—82no—
224C2×Dic122—22no—
225C2×Dic122—22no—
226C2×Dic122—21no—
227C2×Dic122—24no—
228C2×Dic122—82no—
229C2×Dic122C2412yes—
230C4⋊C4×C61—24no—
231C4⋊C4×C61—24no—
232C4⋊C4×C61—24no—
233C4⋊C4×C61—24no—
234C4⋊C4×C61—21no—
235C4⋊C4×C61—21no—
236C4⋊C4×C61C2×D414yes—
237C4⋊C4×C61C2×D414yes—
238C4⋊C4×C61C2412yes—
239C4⋊C4×C61C2412yes—
240C22⋊C4×C61—24no—
241C22⋊C4×C61C2×D414yes—
242C22⋊C4×C61C2×D414yes—
243C42×C61—24no—
244C42×C61—24no—
245C42×C61—24no—
246C42×C61—24no—
247C42×C61—24no—
248C42×C61C2×D412yes—
249C42×C61C2×D412yes—
250C42×C61C2412yes—
251C42×C61C2412yes—
252C22⋊Dic61—24no—
253#11758202—28no—
254#11758202—28no—
255#11758201—28no—
256#11758201—28no—
257#11758198—24no—
258#11758198—24no—
259#11758198—24no—
260#11758198—24no—
261C4⋊Dic61—24no—
262C4⋊Dic61—21no—
263C4⋊Dic61—21no—
264C4⋊Dic61C2412yes—
265C4⋊Dic61C2412yes—
266#11758196—24no—
267#11758196—24no—
268C4×Dic61—24no—
269C2×#92418—22no—
270C2×#92418—22no—
271C2×#92418—22no—
272C2×#92418—22no—
273C2×#92418C2412yes—
274C2×#92418C2412yes—
275C2×#92418C2412yes—
276C2×#92418C2412yes—
277C23×C61—22no—
278C23×C61—22no—
279C23×C61—22no—
280C23×C61C22×D412yes—
281C23×C61C22×D411yescharacteristic
282C22×D61—22no—
283C22×D61—42no—
284C22×D61—42no—
285C22×D61—42no—
286Q8×C61—216no—
287Q8×C61—24no—
288Q8×C61—24no—
289Q8×C61—22no—
290Q8×C61—22no—
291Q8×C61C2×#4114yes—
292Q8×C61C2×#4114yes—
293C2×C4×C61—216no—
294C2×C4×C61—24no—
295C2×C4×C61—24no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—24no—
304C2×C4×C61—22no—
305C2×C4×C61—22no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—42no—
309C2×C4×C61—42no—
310C2×C4×C61C22×D412yes—
311C2×C4×C61C22×D412yes—
312C2×C4×C61C22×D412yes—
313C2×C4×C61C22×D412yes—
314C2×C4×C61C22×D412yes—
315C2×C4×C61C22×D411yescharacteristic
316C2×C4×C61C2×#4112yes—
317C2×C4×C61C2×#4112yes—
318C2×C4×C61C2511yescharacteristic
319C22⋊D61—84no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—22no—
323C2×Dic61—42no—
324C2×Dic61—42no—
325C2×Dic61—42no—
326D244—22no—
327D244—22no—
328D244—42no—
329C4×D61—84no—
330Dic122—22no—
331Dic122—22no—
332Dic122—42no—
333Dic122—84no—
334#92418—22no—
335#92418—22no—
336#92418—22no—
337#92418—22no—
338C2×#3121—611nomaximal, Sylow
339C22×C61—22no—
340C22×C61—22no—
341C22×C61—22no—
342C22×C61—44no—
343C22×C61#52512yes—
344C22×C61#57712yes—
345C22×C61#57812yes—
346C22×C61C23×D411yescharacteristic
347C2×D61—42no—
348C2×D61—42no—
349C2×D61—42no—
350C2×D61—84no—
351C4×C61—24no—
352C4×C61—24no—
353C4×C61—22no—
354C4×C61—22no—
355C4×C61—22no—
356C4×C61—22no—
357C4×C61—22no—
358C4×C61—42no—
359C4×C61—42no—
360C4×C61#52512yes—
361C4×C61C22×#4111yescharacteristic
362C4×C61C22×#4111yescharacteristic
363Dic61—42no—
364Dic61—42no—
365Dic61—42no—
366C2×#542—611no—
367C2×#519D6111yescharacteristic, complemented
368#3121—6116no—
369C2×#485—611no—
370C2×#482—611no—
371C2×#477—611no—
372C2×#475—611no—
373C2×#464—611no—
374C2×#464—611no—
375C2×#451—611no—
376C2×#448—611no—
377C2×#441—611no—
378C2×#440—611no—
379C2×C4×Q16—611no—
380C2×C4×SD16—611no—
381C2×#433—611no—
382C2×C61—42no—
383C2×C61#312114yescomplemented
384C2×C61C2×#52511yescharacteristic
385C2×C61C2×#57711yescharacteristic
386C2×C61C2×#57811yescharacteristic
387D61—82no—
388C23×Q8C2×D6111yescharacteristic
389C22×Q16—611no—
390C22×Q16—611no—
391C22×SD16—611no—
392C22×SD16—611no—
393#542—618no—
394#542—1224no—
395C2×C4⋊Q8—611no—
396C2×#126—1221no—
397C2×#124—611no—
398C2×#124—1221no—
399C2×#123—1221no—
400C2×C22⋊Q8—611no—
401C2×C22⋊Q8—1221no—
402C2×#121—611no—
403#519—24no—
404#519C2×D6118yescomplemented
405C2×C4×Q8—21no—
406C2×C4×Q8—21no—
407C2×C4×Q8—611no—
408C2×C4×Q8C2×D6111yescharacteristic
409C2×C4×Q8C2×D6111yescharacteristic
410C2×C4×Q8C2×D6111yescharacteristic
411C2×C4×Q8C2×D6111yescharacteristic
412C2×C4×D4—611no—
413C2×#117—21no—
414C2×#117—21no—
415C2×#117C2×D6111yescharacteristic
416C2×#117C2×D6111yescharacteristic
417#485—618no—
418#482—618no—
419#477—618no—
420#475—618no—
421#464—618no—
422#464—618no—
423#451—618no—
424#448—618no—
425#441—618no—
426#440—618no—
427C4×Q16—618no—
428C4×SD16—618no—
429#433—618no—
430C2×#107—611no—
431C2×#107—611no—
432C2×#106—611no—
433C2×#106—611no—
434C2×C4⋊C8—611no—
435C2×C4⋊C8—611no—
436C2×#103—611no—
437C2×#103—611no—
438C2×#103—611no—
439C2×#103—611no—
440C2×#103—611no—
441C2×#103—611no—
442C2×#102—611no—
443C2×#102—611no—
444C2×C22⋊C8—611no—
445C2×C22⋊C8—611no—
446C2×#97—611no—
447C2×C4×C8—611no—
448C61C2×#312111yescharacteristic, complemented, Sylow
449C22×Q8—24no—
450C22×Q8—24no—
451C22×Q8—21no—
452C22×Q8—22no—
453C22×Q8—611no—
454C22×Q8—1221no—
455C22×Q8C22×D6114yes—
456C22×Q8C22×D6111yescharacteristic
457C22×Q8C22×D6111yescharacteristic
458C22×D4—611no—
459C22×D4—1221no—
460C23×C4—21no—
461C23×C4—1221no—
462C23×C4C22×D6111yescharacteristic
463C2×Q16—614no—
464C2×Q16—614no—
465C2×Q16—1224no—
466C2×Q16—1224no—
467C2×SD16—614no—
468C2×SD16—614no—
469C2×SD16—1224no—
470C2×SD16—1224no—
471C22×C8—611no—
472C22×C8—611no—
473C22×C8—611no—
474C22×C8—611no—
475C4⋊Q8—614no—
476C4⋊Q8—1222no—
477#126—1228no—
478#124—614no—
479#124—1228no—
480#124—1222no—
481#123—1228no—
482C22⋊Q8—614no—
483C22⋊Q8—1222no—
484C22⋊Q8—1228no—
485#121—614no—
486#121—1222no—
487C4×Q8—28no—
488C4×Q8—28no—
489C4×Q8—22no—
490C4×Q8—22no—
491C4×Q8—22no—
492C4×Q8—22no—
493C4×Q8—614no—
494C4×Q8—1222no—
495C4×Q8C22×D6114yes—
496C4×Q8C22×D6114yes—
497C4×Q8C22×D6114yes—
498C4×Q8C22×D6114yes—
499C4×D4—614no—
500C4×D4—1222no—
501#117—22no—
502#117—28no—
503#117—28no—
504#117C22⋊D6114yes—
505#117C22×D6114yes—
506#117C22×D6114yes—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—611no—
512C2×C4⋊C4—611no—
513C2×C4⋊C4—1221no—
514C2×C4⋊C4—1221no—
515C2×C4⋊C4—1221no—
516C2×C4⋊C4C22⋊D6111yescharacteristic
517C2×C4⋊C4C22⋊D6111yescharacteristic
518C2×C4⋊C4C22×D6111yescharacteristic
519C2×C4⋊C4C22×D6111yescharacteristic
520C2×C22⋊C4—21no—
521C2×C22⋊C4—1221no—
522C2×C22⋊C4—1221no—
523C2×C22⋊C4—1221no—
524C2×C22⋊C4—1221no—
525C2×C22⋊C4—1221no—
526C2×C22⋊C4C22⋊D6111yescharacteristic
527C2×C22⋊C4C22⋊D6111yescharacteristic
528C2×C42—21no—
529C2×C42—21no—
530C2×C42—21no—
531C2×C42—21no—
532C2×C42—21no—
533C2×C42—1221no—
534C2×C42C22×D6111yescharacteristic
535C2×C42C22×D6111yescharacteristic
536#107—614no—
537#107—614no—
538#106—614no—
539#106—614no—
540C4⋊C8—614no—
541C4⋊C8—614no—
542#103—614no—
543#103—614no—
544#103—614no—
545#103—614no—
546#103—614no—
547#103—614no—
548#102—614no—
549#102—614no—
550C22⋊C8—614no—
551C22⋊C8—614no—
552#97—614no—
553C4×C8—614no—
554C24—1221no—
555C24C2×C22⋊D6111yescharacteristic
556C2×Q8—216no—
557C2×Q8—28no—
558C2×Q8—28no—
559C2×Q8—28no—
560C2×Q8—24no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—22no—
564C2×Q8—22no—
565C2×Q8—612no—
566C2×Q8—1224no—
567C2×Q8—1221no—
568C2×Q8—1222no—
569C2×Q8—1222no—
570C2×Q8—4882no—
571C2×Q8#1175822214yes—
572C2×Q8#1175822214yes—
573C2×Q8C23×D6112yes—
574C2×Q8C23×D6112yes—
575C2×D4—612no—
576C2×D4—1224no—
577C2×D4—1221no—
578C2×D4—1222no—
579C2×D4—1222no—
580C2×D4—4882no—
581C22×C4—28no—
582C22×C4—24no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—1221no—
590C22×C4—1221no—
591C22×C4—1221no—
592C22×C4—1224no—
593C22×C4—4882no—
594C22×C4C2×C22⋊D6112yes—
595C22×C4C2×C22⋊D6111yescharacteristic
596C22×C4C2×C22⋊D6111yescharacteristic
597C22×C4C2×C22⋊D6111yescharacteristic
598C22×C4C2×C22⋊D6111yescharacteristic
599C22×C4C2×C22⋊D6111yescharacteristic
600C22×C4C23×D6112yes—
601C22×C4C23×D6111yescharacteristic
602Q16—1228no—
603Q16—1228no—
604SD16—1228no—
605SD16—1228no—
606C2×C8—612no—
607C2×C8—612no—
608C2×C8—612no—
609C2×C8—612no—
610C2×C8—1222no—
611C2×C8—1222no—
612C2×C8—1222no—
613C2×C8—1222no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—612no—
621C4⋊C4—612no—
622C4⋊C4—1221no—
623C4⋊C4—1221no—
624C4⋊C4—1224no—
625C4⋊C4—1224no—
626C4⋊C4—1224no—
627C4⋊C4C2×C22⋊D6114yes—
628C4⋊C4C2×C22⋊D6114yes—
629C4⋊C4C23×D6112yes—
630C4⋊C4C23×D6112yes—
631C22⋊C4—24no—
632C22⋊C4—1224no—
633C22⋊C4—1224no—
634C22⋊C4—1224no—
635C22⋊C4—1224no—
636C22⋊C4—1224no—
637C22⋊C4C2×C22⋊D6114yes—
638C22⋊C4C2×C22⋊D6114yes—
639C42—24no—
640C42—24no—
641C42—24no—
642C42—24no—
643C42—24no—
644C42—1224no—
645C42C2×C22⋊D6112yes—
646C42C2×C22⋊D6112yes—
647C42C23×D6112yes—
648C42C23×D6112yes—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—1222no—
653C23—2442no—
654C23—2442no—
655C23—2442no—
656C23C22×C22⋊D6112yes—
657C23C22×C22⋊D6111yescharacteristic
658Q8—216no—
659Q8—24no—
660Q8—24no—
661Q8—22no—
662Q8—22no—
663Q8—1222no—
664Q8—1222no—
665Q8—4884no—
666Q8—2442no—
667Q8C2×#1175822214yes—
668Q8C2×#1175822214yes—
669D4—1222no—
670D4—1222no—
671D4—4884no—
672D4—2442no—
673C2×C4—216no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—24no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—1222no—
691C2×C4—1222no—
692C2×C4—1222no—
693C2×C4—4884no—
694C2×C4—2442no—
695C2×C4—2442no—
696C2×C4—2442no—
697C2×C4C22×C22⋊D6112yes—
698C2×C4C22×C22⋊D6112yes—
699C2×C4C22×C22⋊D6112yes—
700C2×C4C22×C22⋊D6112yes—
701C2×C4C22×C22⋊D6112yes—
702C2×C4C22×C22⋊D6111yescharacteristic
703C2×C4C2×#1175822212yes—
704C2×C4C2×#1175822212yes—
705C2×C4C24×D6111yescharacteristic
706C8—1222no—
707C8—1222no—
708C8—1222no—
709C8—1222no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—4884no—
715C22—2442no—
716C22—2442no—
717C22—2442no—
718C22#1684027312yes—
719C22#1684057012yes—
720C22#1684057712yes—
721C22C23×C22⋊D6111yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—24no—
727C4—24no—
728C4—22no—
729C4—42no—
730C4—42no—
731C4—2442no—
732C4—2442no—
733C4—2442no—
734C4#1684027312yes—
735C4C22×#1175822211yescharacteristic
736C4C22×#1175822211yescharacteristic
737C2—42no—
738C2—4882no—
739C2#2145604814yesdirect product factor
740C2C2×#1684027311yescharacteristic
741C2C2×#1684057011yescharacteristic
742C2C2×#1684057711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#519C2
socleC23×C61C22×D4
prime radicalC2×#14519751C22
hypercenterC2×#519D61
hypocenterC61C2×#3121
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#519

Complements

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

NH ≅ G/Ntype
2. #21456048C2direct (N × H)
3. C2×#16840103C2semidirect
5. C2×#16840057C2semidirect
6. C2×#16840047C2semidirect
7. C2×#16839984C2semidirect
8. C2×#16839984C2semidirect
9. C2×#16839918C2semidirect
11. C2×#16839867C2semidirect
12. C2×#16839860C2semidirect
13. C2×C4×#11758202C2semidirect
14. C2×C4×#11758201C2semidirect
15. C2×#16839823C2semidirect
16. C2×C61×#519C2semidirect
33. #16840103C22semidirect
35. #16840057C22semidirect
36. #16840047C22semidirect
37. #16839984C22semidirect
38. #16839984C22semidirect
39. #16839918C22semidirect
41. #16839867C22semidirect
42. #16839860C22semidirect
43. C4×#11758202C22semidirect
44. C4×#11758201C22semidirect
45. #16839823C22semidirect
66. C61×#519C22semidirect
367. C2×#519D61semidirect
383. C2×C61#3121semidirect
404. #519C2×D61semidirect
448. C61C2×#3121semidirect
739. C2#21456048direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403832
#214560482
C2×#168401032
C2×#168400862
C2×#168400572
C2×#168400472
C2×#168399842
C2×#168399182
C2×#168399012
C2×#168398672
C2×#168398602
C2×C4×#117582022
C2×C4×#117582012
C2×#168398232
C2×C61×#5192
C2×#312161