Finite Group Databasebeta

← C2×#21456656 #30550639

Subgroups — C2×#21456656 #30550639

Order 15616.

2362 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840273C211yesmaximal, characteristic, complemented
2#21456656C2116yesmaximal, direct product factor
3C2×#16840103C211yesmaximal, characteristic, complemented
4C2×#16840100C211yesmaximal, characteristic, complemented
5C2×#16840086C211yesmaximal, characteristic, complemented
6C2×#16840083C211yesmaximal, characteristic, complemented
7C2×#16840018C211yesmaximal, characteristic, complemented
8C2×#16840013C211yesmaximal, characteristic, complemented
9C2×#16840010C211yesmaximal, characteristic, complemented
10C2×#16840006C211yesmaximal, characteristic, complemented
11C2×#16839924C211yesmaximal, characteristic, complemented
12C2×#16839922C211yesmaximal, characteristic, complemented
13C2×#16839907C211yesmaximal, characteristic, complemented
14C2×#16839905C211yesmaximal, characteristic, complemented
15C2×#16839726C211yesmaximal, characteristic, complemented
16C2×C61×#525C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C22×#11758202C2211yescharacteristic, complemented
19C22×#11758200C2211yescharacteristic, complemented
20C22×#11758201C2211yescharacteristic, complemented
21C22×#11758199C2211yescharacteristic, complemented
22C22×#11758194C2211yescharacteristic
23C22×#11758194C2211yescharacteristic
24#16840273—24no—
25#16840273C2218yescomplemented
26C2×#14519760—21no—
27C2×#14519756C2211yescharacteristic
28C2×#14519756C2211yescharacteristic
29C2×#14519751C2211yescharacteristic
30C2×#14519751C2211yescharacteristic
31C2×#14519746—21no—
32C2×C4×C22⋊D61—21no—
33C2×C4×C22⋊D61—21no—
34C2×#14519736C2211yescharacteristic
35#16840103C2218yescomplemented
36#16840100C2218yescomplemented
37#16840086C2218yescomplemented
38#16840083C2218yescomplemented
39#16840018C2218yescomplemented
40#16840013C2218yescomplemented
41#16840010C2218yescomplemented
42#16840006C2218yescomplemented
43#16839924C2218yescomplemented
44#16839922C2218yescomplemented
45#16839907C2218yescomplemented
46#16839905C2218yescomplemented
47C2×#14519710C2211yescharacteristic, complemented
48C2×#14519710C2211yescharacteristic, complemented
49C2×#14519708C2211yescharacteristic, complemented
50C2×#14519708C2211yescharacteristic, complemented
51C2×#14519701C2211yescharacteristic, complemented
52C2×#14519701C2211yescharacteristic, complemented
53C2×#14519700C2211yescharacteristic, complemented
54C2×#14519700C2211yescharacteristic, complemented
55C2×#14519698C2211yescharacteristic, complemented
56C2×#14519698C2211yescharacteristic, complemented
57C2×#14519697C2211yescharacteristic, complemented
58C2×#14519697C2211yescharacteristic, complemented
59#16839726C2218yescomplemented
60C2×C22⋊#92418C2211yescharacteristic
61C2×C22⋊#92418C2211yescharacteristic
62C2×C22⋊#92418C2211yescharacteristic
63C2×C22⋊#92418C2211yescharacteristic
64C22×#41×C61C2211yescharacteristic
65C24×C4×C61C2211yescharacteristic
66C61×#525—24no—
67C61×#525C2218yescomplemented
68C2×#123×C61—21no—
69C2×C22⋊Q8×C61C2211yescharacteristic
70C2×C22⋊Q8×C61C2211yescharacteristic
71C2×#121×C61C2211yescharacteristic
72C2×#121×C61C2211yescharacteristic
73C2×#120×C61—21no—
74C2×C4×D4×C61—21no—
75C2×C4×D4×C61—21no—
76C2×#117×C61C2211yescharacteristic
77C2×#11758222—22no—
78C2×#11758222—42no—
79C2×#11758222—42no—
80C2×#11758222C2314yes—
81C22×Dic122C2311yescharacteristic
82C22×D244C2311yescharacteristic
83C22×C22⋊D61—21no—
84C22×C22⋊D61—21no—
85C22×C22⋊D61—21no—
86C22×C4×D61—21no—
87C2×#11758202—42no—
88C2×#11758202C2314yescomplemented
89C2×#11758200—42no—
90C2×#11758200C2314yescomplemented
91C2×#11758201—42no—
92C2×#11758201C2314yescomplemented
93C2×#11758199—42no—
94C2×#11758199C2314yescomplemented
95C2×#11758194—42no—
96C2×#11758194—42no—
97C2×#11758194C2314yes—
98C2×#11758194C2314yes—
99C22×#92418C2311yescharacteristic
100C22×#92418C2311yescharacteristic
101C22×#92418C2311yescharacteristic
102C22×#92418C2311yescharacteristic
103#14519760—28no—
104#14519756—22no—
105#14519756—22no—
106#14519756C2314yes—
107#14519756C2314yes—
108#14519751—22no—
109#14519751—22no—
110#14519751C2314yes—
111#14519751C2314yes—
112#14519746—28no—
113C4×C22⋊D61—28no—
114C4×C22⋊D61—28no—
115#14519736—22no—
116#14519736C2314yes—
117C2×C4⋊Dic61C2311yescharacteristic
118C2×C4⋊Dic61C2311yescharacteristic
119C2×#11758196—21no—
120C2×#11758196—21no—
121C2×C22⋊Dic61—21no—
122C2×C22⋊Dic61—21no—
123C2×C22⋊Dic61—21no—
124C2×#11758198—21no—
125C2×#11758198—21no—
126C2×C4×Dic61—21no—
127#14519710C2314yescomplemented
128#14519710C2314yescomplemented
129#14519708C2314yescomplemented
130#14519708C2314yescomplemented
131#14519701C2314yescomplemented
132#14519701C2314yescomplemented
133#14519700C2314yescomplemented
134#14519700C2314yescomplemented
135#14519698C2314yescomplemented
136#14519698C2314yescomplemented
137#14519697C2314yescomplemented
138#14519697C2314yescomplemented
139C22⋊#92418C2314yes—
140C22⋊#92418C2314yes—
141C22⋊#92418C2314yes—
142C22⋊#92418C2314yes—
143C25×C61D411yescharacteristic
144C2×#41×C61—22no—
145C2×#41×C61—42no—
146C2×#41×C61—42no—
147C2×#41×C61C2314yes—
148C22×Q8×C61C2311yescharacteristic
149C22×D4×C61—21no—
150C22×D4×C61—21no—
151C22×D4×C61—21no—
152C22×D4×C61C2311yescharacteristic
153C23×C4×C61—21no—
154C23×C4×C61—42no—
155C23×C4×C61—42no—
156C23×C4×C61D411yescharacteristic
157C23×C4×C61D411yescharacteristic
158C23×C4×C61D411yescharacteristic
159C23×C4×C61D414yes—
160C23×C4×C61C2311yescharacteristic
161C23×C4×C61C2311yescharacteristic
162C23×C4×C61C2311yescharacteristic
163C23×C4×C61C2314yes—
164#123×C61—28no—
165C22⋊Q8×C61—22no—
166C22⋊Q8×C61—22no—
167C22⋊Q8×C61C2314yes—
168C22⋊Q8×C61C2314yes—
169#121×C61—22no—
170#121×C61—22no—
171#121×C61C2314yes—
172#121×C61C2314yes—
173#120×C61—28no—
174C4×D4×C61—28no—
175C4×D4×C61—28no—
176#117×C61—22no—
177#117×C61C2314yes—
178C2×C4⋊C4×C61—21no—
179C2×C4⋊C4×C61—21no—
180C2×C4⋊C4×C61C2311yescharacteristic
181C2×C4⋊C4×C61C2311yescharacteristic
182C2×C22⋊C4×C61—21no—
183C2×C22⋊C4×C61—21no—
184C2×C22⋊C4×C61—21no—
185C2×C22⋊C4×C61—21no—
186C2×C22⋊C4×C61—21no—
187C2×C42×C61—21no—
188C24×C61—21no—
189C24×C61—42no—
190C24×C61—42no—
191C24×C61—42no—
192C24×C61C2×D411yescharacteristic
193C24×C61C2×D411yescharacteristic
194C24×C61C2×D411yescharacteristic
195C24×C61C2×D414yes—
196C23×D61—21no—
197#41×C61—44no—
198#41×C61—44no—
199#41×C61—48no—
200C2×Q8×C61—21no—
201C2×Q8×C61—22no—
202C2×Q8×C61—22no—
203C2×Q8×C61C2412yes—
204C2×D4×C61—24no—
205C2×D4×C61—24no—
206C2×D4×C61—24no—
207C2×D4×C61—21no—
208C2×D4×C61—22no—
209C2×D4×C61—22no—
210C2×D4×C61—44no—
211C2×D4×C61—44no—
212C2×D4×C61—44no—
213C2×D4×C61C2412yes—
214C22×C4×C61—22no—
215C22×C4×C61—22no—
216C22×C4×C61—22no—
217C22×C4×C61—22no—
218C22×C4×C61—22no—
219C22×C4×C61—22no—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61—24no—
224C22×C4×C61—48no—
225C22×C4×C61—44no—
226C22×C4×C61—44no—
227C22×C4×C61—42no—
228C22×C4×C61—42no—
229C22×C4×C61—42no—
230C22×C4×C61—44no—
231C22×C4×C61C2×D411yescharacteristic
232C22×C4×C61C2×D412yes—
233C22×C4×C61C2×D411yescharacteristic
234C22×C4×C61C2×D411yescharacteristic
235C22×C4×C61C2×D412yes—
236C22×C4×C61C2×D412yes—
237C22×C4×C61C2×D414yes—
238C22×C4×C61C2×D414yes—
239C22×C4×C61C2×D414yes—
240C22×C4×C61C2412yes—
241C22×C4×C61C2412yes—
242C22×C4×C61C2412yes—
243C22×C4×C61C2411yescharacteristic
244C2×C22⋊D61—24no—
245C2×C22⋊D61—24no—
246C2×C22⋊D61—24no—
247C2×C22⋊D61—44no—
248C2×C22⋊D61—44no—
249C2×C22⋊D61—44no—
250C22×Dic61—21no—
251C22×Dic61—21no—
252C22×Dic61—21no—
253#11758222—44no—
254#11758222—44no—
255#11758222—48no—
256C2×D244—22no—
257C2×D244—22no—
258C2×D244—21no—
259C2×D244C2412yes—
260C2×C4×D61—24no—
261C2×C4×D61—44no—
262C2×Dic122—22no—
263C2×Dic122—22no—
264C2×Dic122—21no—
265C2×Dic122C2412yes—
266C4⋊C4×C61—24no—
267C4⋊C4×C61—24no—
268C4⋊C4×C61—21no—
269C4⋊C4×C61—21no—
270C4⋊C4×C61C2412yes—
271C4⋊C4×C61C2412yes—
272C22⋊C4×C61—24no—
273C22⋊C4×C61—24no—
274C22⋊C4×C61—24no—
275C22⋊C4×C61—24no—
276C22⋊C4×C61—24no—
277C42×C61—24no—
278C22⋊Dic61—24no—
279C22⋊Dic61—24no—
280C22⋊Dic61—24no—
281#11758202—44no—
282#11758201—44no—
283#11758200—44no—
284#11758199—44no—
285#11758198—24no—
286#11758198—24no—
287C4⋊Dic61—21no—
288C4⋊Dic61—21no—
289C4⋊Dic61C2412yes—
290C4⋊Dic61C2412yes—
291#11758196—24no—
292#11758196—24no—
293C4×Dic61—24no—
294#11758194—44no—
295#11758194—44no—
296C2×#92418—22no—
297C2×#92418—22no—
298C2×#92418—22no—
299C2×#92418—22no—
300C2×#92418C2412yes—
301C2×#92418C2412yes—
302C2×#92418C2412yes—
303C2×#92418C2412yes—
304C23×C61—22no—
305C23×C61—22no—
306C23×C61—22no—
307C23×C61—22no—
308C23×C61—22no—
309C23×C61—22no—
310C23×C61—22no—
311C23×C61—22no—
312C23×C61—22no—
313C23×C61—22no—
314C23×C61—44no—
315C23×C61—44no—
316C23×C61—44no—
317C23×C61—416no—
318C23×C61—42no—
319C23×C61—42no—
320C23×C61—42no—
321C23×C61C22×D412yes—
322C23×C61C22×D412yes—
323C23×C61C22×D412yes—
324C23×C61C22×D411yescharacteristic
325C22×D61—22no—
326C22×D61—42no—
327C22×D61—42no—
328C22×D61—42no—
329Q8×C61—22no—
330Q8×C61—22no—
331Q8×C61—42no—
332D4×C61—22no—
333D4×C61—22no—
334D4×C61—48no—
335D4×C61—48no—
336D4×C61—48no—
337D4×C61—42no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
340C2×C4×C61—22no—
341C2×C4×C61—24no—
342C2×C4×C61—24no—
343C2×C4×C61—24no—
344C2×C4×C61—22no—
345C2×C4×C61—22no—
346C2×C4×C61—22no—
347C2×C4×C61—22no—
348C2×C4×C61—22no—
349C2×C4×C61—22no—
350C2×C4×C61—22no—
351C2×C4×C61—22no—
352C2×C4×C61—22no—
353C2×C4×C61—44no—
354C2×C4×C61—44no—
355C2×C4×C61—44no—
356C2×C4×C61—48no—
357C2×C4×C61—42no—
358C2×C4×C61—42no—
359C2×C4×C61—42no—
360C2×C4×C61C22×D412yes—
361C2×C4×C61C22×D412yes—
362C2×C4×C61C22×D412yes—
363C2×C4×C61C22×D411yescharacteristic
364C2×C4×C61H(5,𝔽2)12yes—
365C2×C4×C61H(5,𝔽2)12yes—
366C2×C4×C61C2511yescharacteristic
367C22⋊D61—48no—
368C22⋊D61—48no—
369C22⋊D61—48no—
370C2×Dic61—22no—
371C2×Dic61—22no—
372C2×Dic61—22no—
373C2×Dic61—42no—
374C2×Dic61—42no—
375C2×Dic61—42no—
376D244—22no—
377D244—22no—
378D244—42no—
379C4×D61—48no—
380Dic122—22no—
381Dic122—22no—
382Dic122—42no—
383#92418—22no—
384#92418—22no—
385#92418—22no—
386#92418—22no—
387C2×#3197—611nomaximal, Sylow
388C22×C61—22no—
389C22×C61—22no—
390C22×C61—22no—
391C22×C61—22no—
392C22×C61—22no—
393C22×C61—22no—
394C22×C61—22no—
395C22×C61—22no—
396C22×C61—22no—
397C22×C61—416no—
398C22×C61—44no—
399C22×C61—44no—
400C22×C61—44no—
401C22×C61—42no—
402C22×C61—42no—
403C22×C61—42no—
404C22×C61—84no—
405C22×C61#53412yes—
406C22×C61#57512yes—
407C22×C61#57512yes—
408C22×C61C23×D411yescharacteristic
409C2×D61—42no—
410C2×D61—42no—
411C2×D61—42no—
412C2×D61—84no—
413C4×C61—22no—
414C4×C61—22no—
415C4×C61—22no—
416C4×C61—42no—
417C4×C61—42no—
418C4×C61—42no—
419C4×C61#53412yes—
420C4×C61C2×H(5,𝔽2)11yescharacteristic
421C4×C61C2×H(5,𝔽2)11yescharacteristic
422Dic61—42no—
423Dic61—42no—
424Dic61—42no—
425C2×#525—611no—
426C2×#525D6111yescharacteristic, complemented
427#3197—6116no—
428C2×#485—611no—
429C2×#485—611no—
430C2×#482—611no—
431C2×#482—611no—
432C2×#470—611no—
433C2×#469—611no—
434C2×#468—611no—
435C2×#468—611no—
436C2×#452—611no—
437C2×#452—611no—
438C2×#449—611no—
439C2×#449—611no—
440C2×#407—611no—
441C2×C61—42no—
442C2×C61—42no—
443C2×C61—42no—
444C2×C61—82no—
445C2×C61#319714yescomplemented
446C2×C61C2×#53411yescharacteristic
447C2×C61C2×#57511yescharacteristic
448C2×C61C2×#57511yescharacteristic
449D61—82no—
450C22×#41—611no—
451C22×#41C2×D6111yescharacteristic
452C24×C4C2×D6111yescharacteristic
453C22×Q16—611no—
454C22×SD16—611no—
455C22×SD16—611no—
456C22×D8—611no—
457C22×M16—611no—
458C22×M16—611no—
459#525—24no—
460#525—618no—
461#525—1224no—
462#525C2×D6118yescomplemented
463C2×#123—21no—
464C2×#123—1221no—
465C2×C22⋊Q8—611no—
466C2×C22⋊Q8—611no—
467C2×C22⋊Q8C2×D6111yescharacteristic
468C2×C22⋊Q8C2×D6111yescharacteristic
469C2×#121—611no—
470C2×#121—611no—
471C2×#121C2×D6111yescharacteristic
472C2×#121C2×D6111yescharacteristic
473C2×#120—21no—
474C2×#120—1221no—
475C2×C4×D4—21no—
476C2×C4×D4—21no—
477C2×C4×D4—1221no—
478C2×C4×D4—1221no—
479C2×#117—611no—
480C2×#117C2×D6111yescharacteristic
481#485—618no—
482#485—618no—
483#482—618no—
484#482—618no—
485#470—618no—
486#469—618no—
487#468—618no—
488#468—618no—
489#452—618no—
490#452—618no—
491#449—618no—
492#449—618no—
493C2×#107—611no—
494C2×#107—611no—
495C2×#106—611no—
496C2×#106—611no—
497C2×#103—611no—
498C2×#103—611no—
499C2×#103—611no—
500C2×#103—611no—
501C2×#102—611no—
502C2×#102—611no—
503C2×#102—611no—
504C2×#102—611no—
505#407—618no—
506C2×C22⋊C8—611no—
507C2×C22⋊C8—611no—
508C2×C22⋊C8—611no—
509C2×C22⋊C8—611no—
510C61C2×#319711yescharacteristic, complemented, Sylow
511C25C22⋊D6111yescharacteristic
512C2×#41—22no—
513C2×#41—42no—
514C2×#41—42no—
515C2×#41—614no—
516C2×#41—1222no—
517C2×#41—2442no—
518C2×#41—2442no—
519C2×#41C22×D6114yes—
520C22×Q8—611no—
521C22×Q8C22×D6111yescharacteristic
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—611no—
526C22×D4—1221no—
527C22×D4—1221no—
528C22×D4—1221no—
529C22×D4C22×D6111yescharacteristic
530C23×C4—21no—
531C23×C4—42no—
532C23×C4—42no—
533C23×C4—1221no—
534C23×C4C22⋊D6111yescharacteristic
535C23×C4C22⋊D6111yescharacteristic
536C23×C4C22⋊D6111yescharacteristic
537C23×C4C22⋊D6114yes—
538C23×C4C22×D6111yescharacteristic
539C23×C4C22×D6111yescharacteristic
540C23×C4C22×D6111yescharacteristic
541C23×C4C22×D6114yes—
542C2×Q16—614no—
543C2×Q16—2442no—
544C2×SD16—614no—
545C2×SD16—614no—
546C2×SD16—2442no—
547C2×SD16—2442no—
548C2×D8—614no—
549C2×D8—2442no—
550C2×M16—614no—
551C2×M16—614no—
552C2×M16—2442no—
553C2×M16—2442no—
554C22×C8—611no—
555C22×C8—611no—
556C22×C8—611no—
557C22×C8—611no—
558#123—28no—
559#123—1228no—
560C22⋊Q8—22no—
561C22⋊Q8—22no—
562C22⋊Q8—614no—
563C22⋊Q8—614no—
564C22⋊Q8—1222no—
565C22⋊Q8—1222no—
566C22⋊Q8C22×D6114yes—
567C22⋊Q8C22×D6114yes—
568#121—22no—
569#121—22no—
570#121—614no—
571#121—614no—
572#121—1222no—
573#121—1222no—
574#121C22×D6114yes—
575#121C22×D6114yes—
576#120—28no—
577#120—1228no—
578C4×D4—28no—
579C4×D4—28no—
580C4×D4—1228no—
581C4×D4—1228no—
582#117—22no—
583#117—614no—
584#117—1222no—
585#117C22×D6114yes—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—611no—
589C2×C4⋊C4—611no—
590C2×C4⋊C4—1221no—
591C2×C4⋊C4—1221no—
592C2×C4⋊C4C22×D6111yescharacteristic
593C2×C4⋊C4C22×D6111yescharacteristic
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—1221no—
600C2×C22⋊C4—1221no—
601C2×C22⋊C4—1221no—
602C2×C22⋊C4—1221no—
603C2×C22⋊C4—1221no—
604C2×C42—21no—
605C2×C42—1221no—
606#107—614no—
607#107—614no—
608#106—614no—
609#106—614no—
610#103—614no—
611#103—614no—
612#103—614no—
613#103—614no—
614#102—614no—
615#102—614no—
616#102—614no—
617#102—614no—
618C22⋊C8—614no—
619C22⋊C8—614no—
620C22⋊C8—614no—
621C22⋊C8—614no—
622C24—21no—
623C24—42no—
624C24—42no—
625C24—42no—
626C24—1221no—
627C24C2×C22⋊D6111yescharacteristic
628C24C2×C22⋊D6111yescharacteristic
629C24C2×C22⋊D6111yescharacteristic
630C24C2×C22⋊D6114yes—
631#41—44no—
632#41—44no—
633#41—48no—
634#41—2444no—
635#41—2444no—
636#41—2448no—
637C2×Q8—21no—
638C2×Q8—22no—
639C2×Q8—22no—
640C2×Q8—612no—
641C2×Q8—1221no—
642C2×Q8—1222no—
643C2×Q8—1222no—
644C2×Q8C23×D6112yes—
645C2×D4—24no—
646C2×D4—24no—
647C2×D4—24no—
648C2×D4—21no—
649C2×D4—22no—
650C2×D4—22no—
651C2×D4—44no—
652C2×D4—44no—
653C2×D4—44no—
654C2×D4—612no—
655C2×D4—1224no—
656C2×D4—1224no—
657C2×D4—1224no—
658C2×D4—1221no—
659C2×D4—1222no—
660C2×D4—1222no—
661C2×D4—2444no—
662C2×D4—2444no—
663C2×D4—2444no—
664C2×D4C23×D6112yes—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—24no—
675C22×C4—48no—
676C22×C4—44no—
677C22×C4—44no—
678C22×C4—42no—
679C22×C4—42no—
680C22×C4—42no—
681C22×C4—44no—
682C22×C4—1221no—
683C22×C4—1221no—
684C22×C4—1221no—
685C22×C4—1224no—
686C22×C4—2444no—
687C22×C4C2×C22⋊D6112yes—
688C22×C4C2×C22⋊D6112yes—
689C22×C4C2×C22⋊D6112yes—
690C22×C4C2×C22⋊D6111yescharacteristic
691C22×C4C2×C22⋊D6111yescharacteristic
692C22×C4C2×C22⋊D6111yescharacteristic
693C22×C4C2×C22⋊D6114yes—
694C22×C4C2×C22⋊D6114yes—
695C22×C4C2×C22⋊D6114yes—
696C22×C4C23×D6112yes—
697C22×C4C23×D6112yes—
698C22×C4C23×D6112yes—
699C22×C4C23×D6111yescharacteristic
700Q16—2444no—
701SD16—2444no—
702SD16—2444no—
703D8—2444no—
704M16—2444no—
705M16—2444no—
706C2×C8—612no—
707C2×C8—612no—
708C2×C8—612no—
709C2×C8—612no—
710C2×C8—1222no—
711C2×C8—1222no—
712C2×C8—1222no—
713C2×C8—1222no—
714C4⋊C4—24no—
715C4⋊C4—24no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—612no—
719C4⋊C4—612no—
720C4⋊C4—1221no—
721C4⋊C4—1221no—
722C4⋊C4—1224no—
723C4⋊C4—1224no—
724C4⋊C4C23×D6112yes—
725C4⋊C4C23×D6112yes—
726C22⋊C4—24no—
727C22⋊C4—24no—
728C22⋊C4—24no—
729C22⋊C4—24no—
730C22⋊C4—24no—
731C22⋊C4—1224no—
732C22⋊C4—1224no—
733C22⋊C4—1224no—
734C22⋊C4—1224no—
735C22⋊C4—1224no—
736C42—24no—
737C42—1224no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—44no—
749C23—44no—
750C23—44no—
751C23—416no—
752C23—42no—
753C23—42no—
754C23—42no—
755C23—1222no—
756C23—2442no—
757C23—2442no—
758C23—2442no—
759C23C22×C22⋊D6112yes—
760C23C22×C22⋊D6112yes—
761C23C22×C22⋊D6112yes—
762C23C22×C22⋊D6111yescharacteristic
763Q8—22no—
764Q8—22no—
765Q8—42no—
766Q8—1222no—
767Q8—1222no—
768Q8—2442no—
769D4—22no—
770D4—22no—
771D4—48no—
772D4—48no—
773D4—48no—
774D4—42no—
775D4—1222no—
776D4—1222no—
777D4—2448no—
778D4—2448no—
779D4—2448no—
780D4—2442no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—24no—
785C2×C4—24no—
786C2×C4—24no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—44no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—48no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—1222no—
804C2×C4—1222no—
805C2×C4—1222no—
806C2×C4—2448no—
807C2×C4—2442no—
808C2×C4—2442no—
809C2×C4—2442no—
810C2×C4C22×C22⋊D6112yes—
811C2×C4C22×C22⋊D6112yes—
812C2×C4C22×C22⋊D6112yes—
813C2×C4C22×C22⋊D6111yescharacteristic
814C2×C4#1451982212yes—
815C2×C4#1451982212yes—
816C2×C4C24×D6111yescharacteristic
817C8—1222no—
818C8—1222no—
819C8—1222no—
820C8—1222no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—22no—
828C22—22no—
829C22—22no—
830C22—416no—
831C22—44no—
832C22—44no—
833C22—44no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—84no—
838C22—4884no—
839C22—2442no—
840C22—2442no—
841C22—2442no—
842C22#1684032112yes—
843C22#1684056012yes—
844C22#1684056012yes—
845C22C23×C22⋊D6111yescharacteristic
846C4—22no—
847C4—22no—
848C4—22no—
849C4—42no—
850C4—42no—
851C4—42no—
852C4—2442no—
853C4—2442no—
854C4—2442no—
855C4#1684032112yes—
856C4C2×#1451982211yescharacteristic
857C4C2×#1451982211yescharacteristic
858C2—42no—
859C2—42no—
860C2—42no—
861C2—82no—
862C2—4882no—
863C2#2145665614yesdirect product factor
864C2C2×#1684032111yescharacteristic
865C2C2×#1684056011yescharacteristic
866C2C2×#1684056011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#525C2
socleC23×C61C22×D4
hypercenterC2×#525D61
hypocenterC61C2×#3197
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C2×#16840273C2semidirect
2. #21456656C2direct (N × H)
3. C2×#16840103C2semidirect
4. C2×#16840100C2semidirect
5. C2×#16840086C2semidirect
6. C2×#16840083C2semidirect
7. C2×#16840018C2semidirect
8. C2×#16840013C2semidirect
9. C2×#16840010C2semidirect
10. C2×#16840006C2semidirect
11. C2×#16839924C2semidirect
12. C2×#16839922C2semidirect
13. C2×#16839907C2semidirect
14. C2×#16839905C2semidirect
15. C2×#16839726C2semidirect
16. C2×C61×#525C2semidirect
18. C22×#11758202C22semidirect
19. C22×#11758200C22semidirect
20. C22×#11758201C22semidirect
21. C22×#11758199C22semidirect
25. #16840273C22semidirect
35. #16840103C22semidirect
36. #16840100C22semidirect
37. #16840086C22semidirect
38. #16840083C22semidirect
39. #16840018C22semidirect
40. #16840013C22semidirect
41. #16840010C22semidirect
42. #16840006C22semidirect
43. #16839924C22semidirect
44. #16839922C22semidirect
45. #16839907C22semidirect
46. #16839905C22semidirect
47. C2×#14519710C22semidirect
48. C2×#14519710C22semidirect
49. C2×#14519708C22semidirect
50. C2×#14519708C22semidirect
51. C2×#14519701C22semidirect
52. C2×#14519701C22semidirect
53. C2×#14519700C22semidirect
54. C2×#14519700C22semidirect
55. C2×#14519698C22semidirect
56. C2×#14519698C22semidirect
57. C2×#14519697C22semidirect
58. C2×#14519697C22semidirect
59. #16839726C22semidirect
67. C61×#525C22semidirect
88. C2×#11758202C23semidirect
90. C2×#11758200C23semidirect
92. C2×#11758201C23semidirect
94. C2×#11758199C23semidirect
127. #14519710C23semidirect
128. #14519710C23semidirect
129. #14519708C23semidirect
130. #14519708C23semidirect
131. #14519701C23semidirect
132. #14519701C23semidirect
133. #14519700C23semidirect
134. #14519700C23semidirect
135. #14519698C23semidirect
136. #14519698C23semidirect
137. #14519697C23semidirect
138. #14519697C23semidirect
426. C2×#525D61semidirect
445. C2×C61#3197semidirect
462. #525C2×D61semidirect
510. C61C2×#3197semidirect
863. C2#21456656direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168402732
#214566562
C2×#168401032
C2×#168401002
C2×#168400862
C2×#168400832
C2×#168400182
C2×#168400132
C2×#168400102
C2×#168400062
C2×#168399242
C2×#168399222
C2×#168399072
C2×#168399052
C2×#168397262
C2×C61×#5252
C2×#319761