Finite Group Databasebeta

← C2×#21457945 #30556731

Subgroups — C2×#21457945 #30556731

Order 15616.

2178 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840452C211yesmaximal, characteristic, complemented
2#21457945C2116yesmaximal, direct product factor
3C2×#16840126C211yesmaximal, characteristic, complemented
4C2×#16840078C211yesmaximal, characteristic, complemented
5C2×#16840083C211yesmaximal, characteristic, complemented
6C2×#16840069C211yesmaximal, characteristic, complemented
7C2×#16840006C211yesmaximal, characteristic, complemented
8C2×#16839989C211yesmaximal, characteristic, complemented
9C2×#16839959C211yesmaximal, characteristic, complemented
10C2×#16839924C211yesmaximal, characteristic, complemented
11C2×#16839924C211yesmaximal, characteristic, complemented
12C2×#16839867C211yesmaximal, characteristic, complemented
13C2×#16839834C211yesmaximal, characteristic, complemented
14C2×#16839763C211yesmaximal, characteristic, complemented
15C2×#16839758C211yesmaximal, characteristic, complemented
16C2×C61×#550C211yesmaximal, characteristic
17C22×#11758202C2211yescharacteristic
18C22×#11758200C2211yescharacteristic
19C22×#11758200C2211yescharacteristic
20C22×#11758194C2211yescharacteristic
21C23×#92418C2211yescharacteristic
22#16840452—24no—
23#16840452C2218yescomplemented
24C2×#14519770—21no—
25C2×#14519769C2211yescharacteristic
26C2×#14519767—21no—
27C2×#14519758—21no—
28C2×#14519756C2211yescharacteristic
29C2×#14519756C2211yescharacteristic
30C2×C4×Dic122C2211yescharacteristic
31C2×#14519736C2211yescharacteristic
32C2×#14519733—21no—
33C22×C4⋊Dic61C2211yescharacteristic
34#16840126C2218yescomplemented
35#16840083C2218yescomplemented
36#16840078C2218yescomplemented
37#16840069C2218yescomplemented
38#16840006C2218yescomplemented
39#16839989C2218yescomplemented
40#16839959C2218yescomplemented
41#16839924C2218yescomplemented
42#16839924C2218yescomplemented
43#16839867C2218yescomplemented
44#16839834C2218yescomplemented
45C2×#14519710C2211yescharacteristic
46C2×#14519708C2211yescharacteristic
47C2×#14519708C2211yescharacteristic
48C2×C4⋊#92418C2211yescharacteristic
49#16839763C2218yescomplemented
50#16839758C2218yescomplemented
51C2×#14519701C2211yescharacteristic
52C2×#14519701C2211yescharacteristic
53C2×#14519701C2211yescharacteristic
54C2×#14519700C2211yescharacteristic
55C2×#14519698C2211yescharacteristic
56C2×#14519698C2211yescharacteristic
57C2×#14519698C2211yescharacteristic
58C2×#14519698C2211yescharacteristic
59C2×#14519698C2211yescharacteristic
60C2×#14519698C2211yescharacteristic
61C2×C22⋊#92418C2211yescharacteristic
62C2×C22⋊#92418C2211yescharacteristic
63C2×#14519688C2211yescharacteristic
64C22×#41×C61C2211yescharacteristic
65C22×#41×C61C2211yescharacteristic
66C61×#550—24no—
67C61×#550C2218yes—
68C2×#127×C61—21no—
69C2×#127×C61C2211yescharacteristic
70C2×#121×C61—21no—
71C2×#121×C61—21no—
72C2×#121×C61C2211yescharacteristic
73C2×#121×C61C2211yescharacteristic
74C2×C4×Q8×C61C2211yescharacteristic
75C2×C4×D4×C61—21no—
76C2×C4×D4×C61C2211yescharacteristic
77C22×Dic122C2311yescharacteristic
78C23×Dic61—21no—
79C2×#11758202—24no—
80C2×#11758202C2314yes—
81C2×#11758200—42no—
82C2×#11758200—42no—
83C2×#11758200C2314yes—
84C2×#11758200C2314yes—
85C2×#11758194—42no—
86C2×#11758194C2314yes—
87C22×#92418—42no—
88C22×#92418C2311yescharacteristic
89C22×#92418C2311yescharacteristic
90C22×#92418C2311yescharacteristic
91C22×#92418C2311yescharacteristic
92C22×#92418C2314yes—
93#14519770—28no—
94#14519769—22no—
95#14519769C2314yes—
96#14519767—28no—
97#14519758—28no—
98#14519756—22no—
99#14519756—22no—
100#14519756C2314yes—
101#14519756C2314yes—
102C4×Dic122—22no—
103C4×Dic122C2314yes—
104#14519736—22no—
105#14519736C2314yes—
106#14519733—28no—
107C2×C4⋊Dic61—22no—
108C2×C4⋊Dic61—21no—
109C2×C4⋊Dic61C2314yes—
110C2×C4⋊Dic61C2311yescharacteristic
111C2×C4⋊Dic61C2311yescharacteristic
112C2×C4⋊Dic61C2311yescharacteristic
113C2×#11758196—21no—
114C2×#11758196—21no—
115C2×#11758196—21no—
116C2×#11758196—21no—
117C2×#11758196—21no—
118C2×C22⋊Dic61—21no—
119C2×C22⋊Dic61—21no—
120C2×C22⋊Dic61—21no—
121C2×C4×Dic61—21no—
122C2×C4×Dic61—21no—
123#14519710C2314yes—
124#14519708C2314yes—
125#14519708C2314yes—
126C4⋊#92418C2314yes—
127#14519701C2314yes—
128#14519701C2314yes—
129#14519701C2314yes—
130#14519700C2314yes—
131#14519698C2314yes—
132#14519698C2314yes—
133#14519698C2314yes—
134#14519698C2314yes—
135#14519698C2314yes—
136#14519698C2314yes—
137C22⋊#92418C2314yes—
138C22⋊#92418C2314yes—
139#14519688C2314yes—
140C2×#41×C61—22no—
141C2×#41×C61—22no—
142C2×#41×C61—24no—
143C2×#41×C61—24no—
144C2×#41×C61—42no—
145C2×#41×C61—42no—
146C2×#41×C61C2314yes—
147C2×#41×C61C2314yes—
148C22×Q8×C61C2311yescharacteristic
149C22×D4×C61—21no—
150C22×D4×C61—21no—
151C22×D4×C61—21no—
152C22×D4×C61—21no—
153C22×D4×C61—21no—
154C22×D4×C61—21no—
155C22×D4×C61D411yescharacteristic
156C22×D4×C61C2311yescharacteristic
157C22×D4×C61C2311yescharacteristic
158C23×C4×C61—21no—
159C23×C4×C61—21no—
160C23×C4×C61C2311yescharacteristic
161C23×C4×C61C2311yescharacteristic
162#127×C61—28no—
163#127×C61—22no—
164#127×C61C2314yes—
165#121×C61—22no—
166#121×C61—22no—
167#121×C61—28no—
168#121×C61—28no—
169#121×C61C2314yes—
170#121×C61C2314yes—
171C4×Q8×C61—22no—
172C4×Q8×C61C2314yes—
173C4×D4×C61—28no—
174C4×D4×C61D414yes—
175C4×D4×C61C2314yes—
176C2×C4⋊C4×C61—21no—
177C2×C4⋊C4×C61D411yescharacteristic
178C2×C4⋊C4×C61C2311yescharacteristic
179C2×C22⋊C4×C61—21no—
180C2×C22⋊C4×C61—21no—
181C2×C22⋊C4×C61D411yescharacteristic
182C2×C22⋊C4×C61D411yescharacteristic
183C2×C42×C61—21no—
184C2×C42×C61C2311yescharacteristic
185C24×C61—21no—
186C24×C61—21no—
187C24×C61C2×D411yescharacteristic
188C24×C61C2×D411yescharacteristic
189#41×C61—28no—
190#41×C61—28no—
191#41×C61—44no—
192#41×C61—44no—
193#41×C61—48no—
194#41×C61—48no—
195C2×Q8×C61—21no—
196C2×Q8×C61—22no—
197C2×Q8×C61#4114yes—
198C2×Q8×C61C2412yes—
199C2×D4×C61—24no—
200C2×D4×C61—24no—
201C2×D4×C61—24no—
202C2×D4×C61—24no—
203C2×D4×C61—24no—
204C2×D4×C61—21no—
205C2×D4×C61—21no—
206C2×D4×C61—24no—
207C2×D4×C61—22no—
208C2×D4×C61—22no—
209C2×D4×C61—22no—
210C2×D4×C61—22no—
211C2×D4×C61—42no—
212C2×D4×C61—44no—
213C2×D4×C61—44no—
214C2×D4×C61—44no—
215C2×D4×C61—82no—
216C2×D4×C61—82no—
217C2×D4×C61—82no—
218C2×D4×C61C2×D414yes—
219C2×D4×C61C2412yes—
220C2×D4×C61C2412yes—
221C22×C4×C61—21no—
222C22×C4×C61—22no—
223C22×C4×C61—22no—
224C22×C4×C61—22no—
225C22×C4×C61—22no—
226C22×C4×C61—21no—
227C22×C4×C61—24no—
228C22×C4×C61—24no—
229C22×C4×C61—44no—
230C22×C4×C61—44no—
231C22×C4×C61C2×D411yescharacteristic
232C22×C4×C61C2×D411yescharacteristic
233C22×C4×C61C2×D411yescharacteristic
234C22×C4×C61C2×D411yescharacteristic
235C22×C4×C61C2×D412yes—
236C22×C4×C61C2×D412yes—
237C22×C4×C61C2412yes—
238C22×C4×C61C2412yes—
239C22×C4×C61C2411yescharacteristic
240C22×Dic61—21no—
241C22×Dic61—21no—
242C22×Dic61—24no—
243C22×Dic61—21no—
244C22×Dic61—21no—
245C22×Dic61—44no—
246C2×Dic122—22no—
247C2×Dic122—22no—
248C2×Dic122—21no—
249C2×Dic122C2412yes—
250C4⋊C4×C61—24no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61C2×D414yes—
253C4⋊C4×C61C2412yes—
254C22⋊C4×C61—24no—
255C22⋊C4×C61—24no—
256C22⋊C4×C61C2×D414yes—
257C22⋊C4×C61C2×D414yes—
258C42×C61—24no—
259C42×C61C2×D412yes—
260C42×C61C2412yes—
261C22⋊Dic61—24no—
262C22⋊Dic61—24no—
263C22⋊Dic61—24no—
264#11758202—28no—
265#11758200—44no—
266#11758200—44no—
267C4⋊Dic61—21no—
268C4⋊Dic61—21no—
269C4⋊Dic61—24no—
270C4⋊Dic61—21no—
271C4⋊Dic61C2412yes—
272C4⋊Dic61C2412yes—
273C4⋊Dic61C2412yes—
274#11758196—24no—
275#11758196—24no—
276#11758196—24no—
277#11758196—24no—
278#11758196—24no—
279C4×Dic61—24no—
280C4×Dic61—24no—
281#11758194—44no—
282C2×#92418—22no—
283C2×#92418—22no—
284C2×#92418—22no—
285C2×#92418—22no—
286C2×#92418—44no—
287C2×#92418C2412yes—
288C2×#92418C2412yes—
289C2×#92418C2412yes—
290C2×#92418C2412yes—
291C23×C61—22no—
292C23×C61—22no—
293C23×C61—22no—
294C23×C61—22no—
295C23×C61—22no—
296C23×C61—22no—
297C23×C61—22no—
298C23×C61—22no—
299C23×C61—42no—
300C23×C61—42no—
301C23×C61—42no—
302C23×C61—42no—
303C23×C61—42no—
304C23×C61—42no—
305C23×C61C22×D412yes—
306C23×C61C22×D412yes—
307C23×C61C22×D411yescharacteristic
308Q8×C61—24no—
309Q8×C61—22no—
310Q8×C61C2×#4114yes—
311D4×C61—22no—
312D4×C61—22no—
313D4×C61—22no—
314D4×C61—22no—
315D4×C61—44no—
316D4×C61—48no—
317D4×C61—48no—
318D4×C61—48no—
319D4×C61—42no—
320D4×C61—42no—
321D4×C61—84no—
322D4×C61—84no—
323D4×C61—84no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—24no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—24no—
331C2×C4×C61—24no—
332C2×C4×C61—22no—
333C2×C4×C61—22no—
334C2×C4×C61—22no—
335C2×C4×C61—22no—
336C2×C4×C61—22no—
337C2×C4×C61—48no—
338C2×C4×C61—48no—
339C2×C4×C61—42no—
340C2×C4×C61C22×D412yes—
341C2×C4×C61C22×D412yes—
342C2×C4×C61C22×D412yes—
343C2×C4×C61C22×D412yes—
344C2×C4×C61C22×D411yescharacteristic
345C2×C4×C61C2×#4112yes—
346C2×C4×C61H(5,𝔽2)12yes—
347C2×C4×C61C2511yescharacteristic
348C2×Dic61—22no—
349C2×Dic61—22no—
350C2×Dic61—22no—
351C2×Dic61—22no—
352C2×Dic61—48no—
353C2×Dic61—42no—
354C2×Dic61—42no—
355C2×Dic61—42no—
356C2×Dic61—42no—
357Dic122—22no—
358Dic122—22no—
359Dic122—42no—
360#92418—22no—
361#92418—22no—
362#92418—22no—
363#92418—22no—
364C2×#3317—611nomaximal, Sylow
365C22×C61—22no—
366C22×C61—22no—
367C22×C61—22no—
368C22×C61—22no—
369C22×C61—22no—
370C22×C61—22no—
371C22×C61—44no—
372C22×C61—44no—
373C22×C61—42no—
374C22×C61—42no—
375C22×C61—42no—
376C22×C61—42no—
377C22×C61—42no—
378C22×C61—42no—
379C22×C61—84no—
380C22×C61—84no—
381C22×C61#54612yes—
382C22×C61#57512yes—
383C22×C61#57712yes—
384C22×C61C23×D411yescharacteristic
385C4×C61—22no—
386C4×C61—22no—
387C4×C61—24no—
388C4×C61—22no—
389C4×C61—22no—
390C4×C61—42no—
391C4×C61#54612yes—
392C4×C61C22×#4111yescharacteristic
393C4×C61C2×H(5,𝔽2)11yescharacteristic
394Dic61—42no—
395Dic61—42no—
396Dic61—42no—
397Dic61—42no—
398C2×#552—611no—
399C2×#550D6111yescharacteristic
400#3317—6116no—
401C2×#490—611no—
402C2×#481—611no—
403C2×#482—611no—
404C2×#479—611no—
405C2×#468—611no—
406C2×#465—611no—
407C2×#460—611no—
408C2×#452—611no—
409C2×#452—611no—
410C2×#441—611no—
411C2×#435—611no—
412C2×#417—611no—
413C2×#416—611no—
414C2×C61—42no—
415C2×C61—42no—
416C2×C61—82no—
417C2×C61—82no—
418C2×C61#331714yescomplemented
419C2×C61C2×#54611yescharacteristic
420C2×C61C2×#57511yescharacteristic
421C2×C61C2×#57711yescharacteristic
422C22×#41C2×D6111yescharacteristic
423C22×#41C2×D6111yescharacteristic
424C22×Q16—611no—
425C22×SD16—611no—
426C22×SD16—611no—
427C22×M16—611no—
428C23×C8—611no—
429#552—618no—
430#552—1224no—
431#550—24no—
432#550C2×D6118yes—
433C2×#127—21no—
434C2×#127C2×D6111yescharacteristic
435C2×#126—1221no—
436C2×#125—611no—
437C2×#125—1221no—
438C2×#123—1221no—
439C2×C22⋊Q8—611no—
440C2×C22⋊Q8—611no—
441C2×#121—21no—
442C2×#121—21no—
443C2×#121C2×D6111yescharacteristic
444C2×#121C2×D6111yescharacteristic
445C2×C4×Q8—611no—
446C2×C4×Q8C2×D6111yescharacteristic
447C2×C4×D4—21no—
448C2×C4×D4C2×D6111yescharacteristic
449C2×#117—611no—
450C2×#117—1221no—
451C22×C4⋊C4—611no—
452#490—618no—
453#482—618no—
454#481—618no—
455#479—618no—
456#468—618no—
457#465—618no—
458#460—618no—
459#452—618no—
460#452—618no—
461#441—618no—
462#435—618no—
463C2×#107—611no—
464C2×#106—611no—
465C2×#106—611no—
466C2×C4⋊C8—611no—
467#417—618no—
468#416—618no—
469C2×#103—611no—
470C2×#103—611no—
471C2×#103—611no—
472C2×#103—611no—
473C2×#102—611no—
474C2×#102—611no—
475C2×#102—611no—
476C2×#102—611no—
477C2×#102—611no—
478C2×#102—611no—
479C2×C22⋊C8—611no—
480C2×C22⋊C8—611no—
481C2×#97—611no—
482C61C2×#331711yescharacteristic, complemented, Sylow
483C2×#41—22no—
484C2×#41—22no—
485C2×#41—24no—
486C2×#41—24no—
487C2×#41—42no—
488C2×#41—42no—
489C2×#41C22×D6114yes—
490C2×#41C22×D6114yes—
491C22×Q8—611no—
492C22×Q8C22×D6111yescharacteristic
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4C22⋊D6111yescharacteristic
500C22×D4C22×D6111yescharacteristic
501C22×D4C22×D6111yescharacteristic
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—1221no—
505C23×C4C22×D6111yescharacteristic
506C23×C4C22×D6111yescharacteristic
507C2×Q16—614no—
508C2×Q16—1224no—
509C2×SD16—614no—
510C2×SD16—614no—
511C2×SD16—2442no—
512C2×SD16—2442no—
513C2×M16—614no—
514C2×M16—2442no—
515C22×C8—611no—
516C22×C8—611no—
517C22×C8—611no—
518C22×C8—611no—
519C22×C8—614no—
520C22×C8—2442no—
521#127—28no—
522#127—22no—
523#127C22×D6114yes—
524#126—1228no—
525#125—614no—
526#125—1228no—
527#125—1222no—
528#123—1228no—
529C22⋊Q8—614no—
530C22⋊Q8—614no—
531C22⋊Q8—1222no—
532C22⋊Q8—1222no—
533#121—22no—
534#121—22no—
535#121—28no—
536#121—28no—
537#121C22×D6114yes—
538#121C22×D6114yes—
539C4×Q8—22no—
540C4×Q8—614no—
541C4×Q8—1222no—
542C4×Q8C22×D6114yes—
543C4×D4—28no—
544C4×D4C22⋊D6114yes—
545C4×D4C22×D6114yes—
546#117—614no—
547#117—1222no—
548#117—1228no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—611no—
551C2×C4⋊C4—611no—
552C2×C4⋊C4—614no—
553C2×C4⋊C4—611no—
554C2×C4⋊C4—1221no—
555C2×C4⋊C4—1222no—
556C2×C4⋊C4—1221no—
557C2×C4⋊C4—1221no—
558C2×C4⋊C4—1221no—
559C2×C4⋊C4—1221no—
560C2×C4⋊C4—1221no—
561C2×C4⋊C4C22⋊D6111yescharacteristic
562C2×C4⋊C4C22×D6111yescharacteristic
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—1221no—
566C2×C22⋊C4—1221no—
567C2×C22⋊C4—1221no—
568C2×C22⋊C4C22⋊D6111yescharacteristic
569C2×C22⋊C4C22⋊D6111yescharacteristic
570C2×C42—21no—
571C2×C42—1221no—
572C2×C42—1221no—
573C2×C42C22×D6111yescharacteristic
574#107—614no—
575#106—614no—
576#106—614no—
577C4⋊C8—614no—
578#103—614no—
579#103—614no—
580#103—614no—
581#103—614no—
582#102—614no—
583#102—614no—
584#102—614no—
585#102—614no—
586#102—614no—
587#102—614no—
588C22⋊C8—614no—
589C22⋊C8—614no—
590#97—614no—
591C24—21no—
592C24—21no—
593C24C2×C22⋊D6111yescharacteristic
594C24C2×C22⋊D6111yescharacteristic
595#41—28no—
596#41—28no—
597#41—44no—
598#41—44no—
599#41—48no—
600#41—48no—
601C2×Q8—21no—
602C2×Q8—22no—
603C2×Q8—612no—
604C2×Q8—1221no—
605C2×Q8—1222no—
606C2×Q8—1222no—
607C2×Q8#1175822414yes—
608C2×Q8C23×D6112yes—
609C2×D4—24no—
610C2×D4—24no—
611C2×D4—24no—
612C2×D4—24no—
613C2×D4—24no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—24no—
617C2×D4—22no—
618C2×D4—22no—
619C2×D4—22no—
620C2×D4—22no—
621C2×D4—42no—
622C2×D4—44no—
623C2×D4—44no—
624C2×D4—44no—
625C2×D4—82no—
626C2×D4—82no—
627C2×D4—82no—
628C2×D4C2×C22⋊D6114yes—
629C2×D4C23×D6112yes—
630C2×D4C23×D6112yes—
631C22×C4—21no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—21no—
637C22×C4—24no—
638C22×C4—24no—
639C22×C4—44no—
640C22×C4—44no—
641C22×C4—1224no—
642C22×C4—1221no—
643C22×C4—1221no—
644C22×C4—1221no—
645C22×C4—1221no—
646C22×C4—2444no—
647C22×C4C2×C22⋊D6112yes—
648C22×C4C2×C22⋊D6112yes—
649C22×C4C2×C22⋊D6111yescharacteristic
650C22×C4C2×C22⋊D6111yescharacteristic
651C22×C4C2×C22⋊D6111yescharacteristic
652C22×C4C2×C22⋊D6111yescharacteristic
653C22×C4C23×D6112yes—
654C22×C4C23×D6112yes—
655C22×C4C23×D6111yescharacteristic
656Q16—1228no—
657SD16—2444no—
658SD16—2444no—
659M16—2444no—
660C2×C8—612no—
661C2×C8—612no—
662C2×C8—612no—
663C2×C8—612no—
664C2×C8—1222no—
665C2×C8—1222no—
666C2×C8—1222no—
667C2×C8—1222no—
668C2×C8—2444no—
669C4⋊C4—24no—
670C4⋊C4—21no—
671C4⋊C4—612no—
672C4⋊C4—612no—
673C4⋊C4—612no—
674C4⋊C4—1221no—
675C4⋊C4—1221no—
676C4⋊C4—1224no—
677C4⋊C4—1221no—
678C4⋊C4—1224no—
679C4⋊C4—1224no—
680C4⋊C4—1224no—
681C4⋊C4—1224no—
682C4⋊C4—1224no—
683C4⋊C4C2×C22⋊D6114yes—
684C4⋊C4C23×D6112yes—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—1224no—
688C22⋊C4—1224no—
689C22⋊C4—1224no—
690C22⋊C4C2×C22⋊D6114yes—
691C22⋊C4C2×C22⋊D6114yes—
692C42—24no—
693C42—1224no—
694C42—1224no—
695C42C2×C22⋊D6112yes—
696C42C23×D6112yes—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23C22×C22⋊D6112yes—
712C23C22×C22⋊D6112yes—
713C23C22×C22⋊D6111yescharacteristic
714Q8—22no—
715Q8—24no—
716Q8—1222no—
717Q8—1222no—
718Q8—2442no—
719Q8C2×#1175822414yes—
720D4—22no—
721D4—22no—
722D4—22no—
723D4—22no—
724D4—44no—
725D4—48no—
726D4—48no—
727D4—48no—
728D4—42no—
729D4—42no—
730D4—84no—
731D4—84no—
732D4—84no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—48no—
747C2×C4—48no—
748C2×C4—42no—
749C2×C4—1222no—
750C2×C4—1222no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—2448no—
754C2×C4—2442no—
755C2×C4—2442no—
756C2×C4—2442no—
757C2×C4—2442no—
758C2×C4C22×C22⋊D6112yes—
759C2×C4C22×C22⋊D6112yes—
760C2×C4C22×C22⋊D6112yes—
761C2×C4C22×C22⋊D6112yes—
762C2×C4C22×C22⋊D6111yescharacteristic
763C2×C4C2×#1175822412yes—
764C2×C4#1451982212yes—
765C2×C4C24×D6111yescharacteristic
766C8—1222no—
767C8—1222no—
768C8—1222no—
769C8—1222no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—44no—
777C22—44no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—84no—
785C22—84no—
786C22#1684040612yes—
787C22#1684056012yes—
788C22#1684057312yes—
789C22C23×C22⋊D6111yescharacteristic
790C4—22no—
791C4—22no—
792C4—24no—
793C4—22no—
794C4—22no—
795C4—42no—
796C4—2442no—
797C4—2442no—
798C4—2442no—
799C4—2442no—
800C4#1684040612yes—
801C4C22×#1175822411yescharacteristic
802C4C2×#1451982211yescharacteristic
803C2—42no—
804C2—42no—
805C2—82no—
806C2—82no—
807C2#2145794514yesdirect product factor
808C2C2×#1684040611yescharacteristic
809C2C2×#1684056011yescharacteristic
810C2C2×#1684057311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
Fitting, prime radicalC2×C61×#550C2
socleC23×C61C22×D4
hypercenterC2×#550D61
hypocenterC61C2×#3317
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C2×#16840452C2semidirect
2. #21457945C2direct (N × H)
3. C2×#16840126C2semidirect
4. C2×#16840078C2semidirect
5. C2×#16840083C2semidirect
6. C2×#16840069C2semidirect
7. C2×#16840006C2semidirect
8. C2×#16839989C2semidirect
9. C2×#16839959C2semidirect
10. C2×#16839924C2semidirect
11. C2×#16839924C2semidirect
12. C2×#16839867C2semidirect
13. C2×#16839834C2semidirect
14. C2×#16839763C2semidirect
15. C2×#16839758C2semidirect
23. #16840452C22semidirect
34. #16840126C22semidirect
35. #16840083C22semidirect
36. #16840078C22semidirect
37. #16840069C22semidirect
38. #16840006C22semidirect
39. #16839989C22semidirect
40. #16839959C22semidirect
41. #16839924C22semidirect
42. #16839924C22semidirect
43. #16839867C22semidirect
44. #16839834C22semidirect
49. #16839763C22semidirect
50. #16839758C22semidirect
418. C2×C61#3317semidirect
482. C61C2×#3317semidirect
807. C2#21457945direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404522
#214579452
C2×#168401262
C2×#168400782
C2×#168400832
C2×#168400692
C2×#168400062
C2×#168399892
C2×#168399592
C2×#168399242
C2×#168398672
C2×#168398342
C2×#168397632
C2×#168397582
C2×C61×#5502
C2×#331761