Finite Group Databasebeta

← C2×#21457669 #30556380

Subgroups — C2×#21457669 #30556380

Order 15616.

2350 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840458C211yesmaximal, characteristic, complemented
2#21457669C2116yesmaximal, direct product factor
3C2×#16840116C211yesmaximal, characteristic, complemented
4C2×#16840095C211yesmaximal, characteristic, complemented
5C2×#16840083C211yesmaximal, characteristic, complemented
6C2×#16840062C211yesmaximal, characteristic, complemented
7C2×#16839996C211yesmaximal, characteristic, complemented
8C2×#16839993C211yesmaximal, characteristic, complemented
9C2×#16839974C211yesmaximal, characteristic, complemented
10C2×#16839907C211yesmaximal, characteristic, complemented
11C2×#16839896C211yesmaximal, characteristic, complemented
12C2×C4×#11758199C211yesmaximal, characteristic, complemented
13C2×D4×#92418C211yesmaximal, characteristic, complemented
14C2×#16839758C211yesmaximal, characteristic, complemented
15C22×#14519698C211yesmaximal, characteristic, complemented
16C2×C61×#546C211yesmaximal, characteristic, complemented
17C22×#11758201C2211yescharacteristic, complemented
18C22×#11758199C2211yescharacteristic
19C22×#11758199C2211yescharacteristic
20C23×#92418C2211yescharacteristic
21C23×#92418C2211yescharacteristic, complemented
22#16840458—24no—
23#16840458C2218yescomplemented
24C2×#14519772—21no—
25C2×#14519769C2211yescharacteristic, complemented
26C2×#14519759—21no—
27C2×#14519751C2211yescharacteristic
28C2×#14519751C2211yescharacteristic, complemented
29C2×#14519749—21no—
30C2×C4×D244C2211yescharacteristic, complemented
31C2×#14519737—21no—
32C2×#14519736C2211yescharacteristic, complemented
33C22×C4⋊Dic61C2211yescharacteristic
34#16840116C2218yescomplemented
35#16840095C2218yescomplemented
36#16840083C2218yescomplemented
37#16840062C2218yescomplemented
38#16839996C2218yescomplemented
39#16839993C2218yescomplemented
40#16839974C2218yescomplemented
41#16839907C2218yescomplemented
42#16839896C2218yescomplemented
43C4×#11758199C2218yescomplemented
44D4×#92418C2218yescomplemented
45C2×#14519710C2211yescharacteristic, complemented
46C2×#14519710C2211yescharacteristic, complemented
47C2×#14519708C2211yescharacteristic, complemented
48C2×C4⋊#92418C2211yescharacteristic, complemented
49#16839758C2218yescomplemented
50C2×#14519701C2211yescharacteristic, complemented
51C2×#14519701C2211yescharacteristic, complemented
52C2×#14519701C2211yescharacteristic, complemented
53C2×#14519698C2211yescharacteristic
54C2×#14519698C2211yescharacteristic
55C2×#14519698C2211yescharacteristic
56C2×#14519698C2211yescharacteristic
57C2×#14519698C2211yescharacteristic
58C2×#14519698C2211yescharacteristic
59C2×#14519698C2218yescomplemented
60C2×#14519697C2211yescharacteristic, complemented
61C2×C22⋊#92418C2211yescharacteristic
62C2×C22⋊#92418C2211yescharacteristic, complemented
63C2×C4×#92418C2211yescharacteristic, complemented
64C22×#41×C61C2211yescharacteristic
65C23×D4×C61C2211yescharacteristic
66C61×#546—24no—
67C61×#546C2218yescomplemented
68C2×#124×C61C2211yescharacteristic
69C2×#123×C61—21no—
70C2×C22⋊Q8×C61C2211yescharacteristic
71C2×#121×C61—21no—
72C2×#121×C61C2211yescharacteristic
73C2×#120×C61—21no—
74C2×C4×D4×C61C2211yescharacteristic
75C2×C4×D4×C61C2211yescharacteristic
76C22×C22⋊C4×C61—21no—
77C22×D244C2311yescharacteristic
78C22×C22⋊D61—21no—
79C22×C22⋊D61—21no—
80C23×Dic61—21no—
81C22×C4×D61—21no—
82C2×#11758201—42no—
83C2×#11758201C2314yescomplemented
84C2×#11758199—24no—
85C2×#11758199—42no—
86C2×#11758199C2314yes—
87C2×#11758199C2314yes—
88C22×#92418—42no—
89C22×#92418—42no—
90C22×#92418C2311yescharacteristic
91C22×#92418C2311yescharacteristic
92C22×#92418C2311yescharacteristic
93C22×#92418C2311yescharacteristic
94C22×#92418C2314yes—
95C22×#92418C2314yescomplemented
96#14519772—28no—
97#14519769—22no—
98#14519769C2314yescomplemented
99#14519759—28no—
100#14519751—22no—
101#14519751—22no—
102#14519751C2314yes—
103#14519751C2314yescomplemented
104#14519749—28no—
105C4×D244—22no—
106C4×D244C2314yescomplemented
107#14519737—28no—
108#14519736—22no—
109#14519736C2314yescomplemented
110C2×C4⋊Dic61—22no—
111C2×C4⋊Dic61—21no—
112C2×C4⋊Dic61C2314yes—
113C2×C4⋊Dic61C2311yescharacteristic
114C2×C4⋊Dic61C2311yescharacteristic
115C2×C4⋊Dic61C2311yescharacteristic
116C2×#11758196—21no—
117C2×#11758196—21no—
118C2×C22⋊Dic61—21no—
119C2×#11758198—21no—
120C2×#11758198—21no—
121C2×#11758198—21no—
122C2×C4×Dic61—21no—
123#14519710C2314yescomplemented
124#14519710C2314yescomplemented
125#14519708C2314yescomplemented
126C4⋊#92418C2314yescomplemented
127#14519701C2314yescomplemented
128#14519701C2314yescomplemented
129#14519701C2314yescomplemented
130#14519698C2314yes—
131#14519698C2314yes—
132#14519698C2314yes—
133#14519698C2314yes—
134#14519698C2314yes—
135#14519698C2314yes—
136#14519697C2314yescomplemented
137C22⋊#92418C2314yes—
138C22⋊#92418C2314yescomplemented
139C4×#92418C2314yescomplemented
140C25×C61—21no—
141C2×#41×C61—22no—
142C2×#41×C61—24no—
143C2×#41×C61—42no—
144C2×#41×C61C2314yes—
145C22×Q8×C61C2311yescharacteristic
146C22×D4×C61—24no—
147C22×D4×C61—21no—
148C22×D4×C61—21no—
149C22×D4×C61—22no—
150C22×D4×C61—21no—
151C22×D4×C61—42no—
152C22×D4×C61D411yescharacteristic
153C22×D4×C61C2311yescharacteristic
154C22×D4×C61C2314yes—
155C22×D4×C61C2311yescharacteristic
156C23×C4×C61—21no—
157C23×C4×C61—21no—
158C23×C4×C61C2311yescharacteristic
159C23×C4×C61C2311yescharacteristic
160#124×C61—22no—
161#124×C61C2314yes—
162#123×C61—28no—
163C22⋊Q8×C61—22no—
164C22⋊Q8×C61C2314yes—
165#121×C61—22no—
166#121×C61—28no—
167#121×C61C2314yes—
168#120×C61—28no—
169C4×D4×C61—22no—
170C4×D4×C61D414yes—
171C4×D4×C61C2314yes—
172C4×D4×C61C2314yes—
173C2×C4⋊C4×C61—21no—
174C2×C4⋊C4×C61D411yescharacteristic
175C2×C4⋊C4×C61C2311yescharacteristic
176C2×C22⋊C4×C61—21no—
177C2×C22⋊C4×C61—21no—
178C2×C22⋊C4×C61—21no—
179C2×C22⋊C4×C61—21no—
180C2×C22⋊C4×C61—21no—
181C2×C22⋊C4×C61—28no—
182C2×C22⋊C4×C61D411yescharacteristic
183C2×C22⋊C4×C61D411yescharacteristic
184C2×C42×C61C2311yescharacteristic
185C24×C61—21no—
186C24×C61—21no—
187C24×C61—24no—
188C24×C61—44no—
189C24×C61—44no—
190C24×C61—82no—
191C24×C61C2×D411yescharacteristic
192C24×C61C2×D411yescharacteristic
193C23×D61—21no—
194#41×C61—28no—
195#41×C61—44no—
196#41×C61—48no—
197C2×Q8×C61—21no—
198C2×Q8×C61—22no—
199C2×Q8×C61—22no—
200C2×Q8×C61C2412yes—
201C2×D4×C61—24no—
202C2×D4×C61—28no—
203C2×D4×C61—24no—
204C2×D4×C61—24no—
205C2×D4×C61—21no—
206C2×D4×C61—24no—
207C2×D4×C61—21no—
208C2×D4×C61—22no—
209C2×D4×C61—22no—
210C2×D4×C61—22no—
211C2×D4×C61—44no—
212C2×D4×C61—48no—
213C2×D4×C61—44no—
214C2×D4×C61—44no—
215C2×D4×C61—82no—
216C2×D4×C61C2×D414yes—
217C2×D4×C61#4114yes—
218C2×D4×C61C2412yes—
219C2×D4×C61C2412yes—
220C22×C4×C61—22no—
221C22×C4×C61—22no—
222C22×C4×C61—22no—
223C22×C4×C61—22no—
224C22×C4×C61—21no—
225C22×C4×C61—21no—
226C22×C4×C61—24no—
227C22×C4×C61—24no—
228C22×C4×C61—44no—
229C22×C4×C61—82no—
230C22×C4×C61C2×D411yescharacteristic
231C22×C4×C61C2×D411yescharacteristic
232C22×C4×C61C2×D411yescharacteristic
233C22×C4×C61C2×D411yescharacteristic
234C22×C4×C61C2×D412yes—
235C22×C4×C61C2×D412yes—
236C22×C4×C61C2412yes—
237C22×C4×C61C2412yes—
238C22×C4×C61C2411yescharacteristic
239C2×C22⋊D61—24no—
240C2×C22⋊D61—24no—
241C2×C22⋊D61—44no—
242C2×C22⋊D61—82no—
243C22×Dic61—21no—
244C22×Dic61—21no—
245C22×Dic61—21no—
246C22×Dic61—24no—
247C22×Dic61—82no—
248C2×D244—22no—
249C2×D244—22no—
250C2×D244—21no—
251C2×D244C2412yes—
252C2×C4×D61—24no—
253C2×C4×D61—82no—
254C4⋊C4×C61—24no—
255C4⋊C4×C61—21no—
256C4⋊C4×C61C2×D414yes—
257C4⋊C4×C61C2412yes—
258C22⋊C4×C61—24no—
259C22⋊C4×C61—24no—
260C22⋊C4×C61—24no—
261C22⋊C4×C61—24no—
262C22⋊C4×C61—24no—
263C22⋊C4×C61C2×D414yes—
264C22⋊C4×C61C2×D414yes—
265C42×C61C2×D412yes—
266C42×C61C2412yes—
267C22⋊Dic61—24no—
268#11758201—44no—
269#11758199—28no—
270#11758199—44no—
271#11758198—24no—
272#11758198—24no—
273#11758198—24no—
274C4⋊Dic61—21no—
275C4⋊Dic61—21no—
276C4⋊Dic61—24no—
277C4⋊Dic61—21no—
278C4⋊Dic61C2412yes—
279C4⋊Dic61C2412yes—
280C4⋊Dic61C2412yes—
281#11758196—24no—
282#11758196—24no—
283C4×Dic61—24no—
284C2×#92418—22no—
285C2×#92418—22no—
286C2×#92418—22no—
287C2×#92418—22no—
288C2×#92418—44no—
289C2×#92418—44no—
290C2×#92418C2412yes—
291C2×#92418C2412yes—
292C2×#92418C2412yes—
293C2×#92418C2412yes—
294C23×C61—22no—
295C23×C61—22no—
296C23×C61—22no—
297C23×C61—24no—
298C23×C61—22no—
299C23×C61—22no—
300C23×C61—22no—
301C23×C61—22no—
302C23×C61—48no—
303C23×C61—42no—
304C23×C61—42no—
305C23×C61—42no—
306C23×C61—48no—
307C23×C61—42no—
308C23×C61—42no—
309C23×C61—84no—
310C23×C61—816no—
311C23×C61#13514yes—
312C23×C61C22×D412yes—
313C23×C61C22×D412yes—
314C23×C61C22×D411yescharacteristic
315C22×D61—22no—
316C22×D61—42no—
317C22×D61—42no—
318C22×D61—42no—
319Q8×C61—22no—
320Q8×C61—22no—
321Q8×C61—42no—
322D4×C61—28no—
323D4×C61—24no—
324D4×C61—22no—
325D4×C61—22no—
326D4×C61—22no—
327D4×C61—48no—
328D4×C61—48no—
329D4×C61—42no—
330D4×C61—84no—
331D4×C61C2×#4114yes—
332C2×C4×C61—22no—
333C2×C4×C61—22no—
334C2×C4×C61—22no—
335C2×C4×C61—22no—
336C2×C4×C61—24no—
337C2×C4×C61—24no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
340C2×C4×C61—22no—
341C2×C4×C61—22no—
342C2×C4×C61—22no—
343C2×C4×C61—22no—
344C2×C4×C61—48no—
345C2×C4×C61—42no—
346C2×C4×C61—42no—
347C2×C4×C61—84no—
348C2×C4×C61C22×D412yes—
349C2×C4×C61C22×D412yes—
350C2×C4×C61C22×D412yes—
351C2×C4×C61C22×D412yes—
352C2×C4×C61C22×D411yescharacteristic
353C2×C4×C61C2×#4112yes—
354C2×C4×C61H(5,𝔽2)12yes—
355C2×C4×C61C2511yescharacteristic
356C22⋊D61—48no—
357C22⋊D61—84no—
358C2×Dic61—22no—
359C2×Dic61—22no—
360C2×Dic61—22no—
361C2×Dic61—42no—
362C2×Dic61—42no—
363C2×Dic61—42no—
364C2×Dic61—84no—
365D244—22no—
366D244—22no—
367D244—42no—
368C4×D61—84no—
369#92418—22no—
370#92418—22no—
371#92418—22no—
372#92418—22no—
373C2×#3297—611nomaximal, Sylow
374C22×C61—22no—
375C22×C61—28no—
376C22×C61—22no—
377C22×C61—22no—
378C22×C61—24no—
379C22×C61—22no—
380C22×C61—22no—
381C22×C61—44no—
382C22×C61—48no—
383C22×C61—42no—
384C22×C61—42no—
385C22×C61—42no—
386C22×C61—42no—
387C22×C61—42no—
388C22×C61—816no—
389C22×C61—84no—
390C22×C61#54612yes—
391C22×C61C2×#13514yes—
392C22×C61C2×#13512yes—
393C22×C61#57612yes—
394C22×C61C23×D411yescharacteristic
395C2×D61—42no—
396C2×D61—42no—
397C2×D61—42no—
398C2×D61—84no—
399C4×C61—22no—
400C4×C61—22no—
401C4×C61—22no—
402C4×C61—22no—
403C4×C61—42no—
404C4×C61—42no—
405C4×C61#54612yes—
406C4×C61C22×#4111yescharacteristic
407C4×C61C2×H(5,𝔽2)11yescharacteristic
408Dic61—42no—
409Dic61—42no—
410Dic61—42no—
411C2×#553—611no—
412C2×#546D6111yescharacteristic, complemented
413#3297—6116no—
414C2×#488—611no—
415C2×#484—611no—
416C2×#482—611no—
417C2×#478—611no—
418C2×#466—611no—
419C2×#465—611no—
420C2×#463—611no—
421C2×#449—611no—
422C2×#447—611no—
423C2×C4×D8—611no—
424C2×C8×D4—611no—
425C2×#416—611no—
426C22×#102—611no—
427C2×C61—24no—
428C2×C61—42no—
429C2×C61—44no—
430C2×C61—82no—
431C2×C61#329714yescomplemented
432C2×C61C2×#54611yescharacteristic
433C2×C61C22×#13511yescharacteristic
434C2×C61C2×#57611yescharacteristic
435D61—82no—
436C22×#41C2×D6111yescharacteristic
437C23×D4C2×D6111yescharacteristic
438C22×SD16—611no—
439C22×D8—611no—
440C22×D8—611no—
441C23×C8—611no—
442C23×C8—611no—
443#553—618no—
444#553—1224no—
445#546—24no—
446#546C2×D6118yescomplemented
447C2×#126—1221no—
448C2×#125—611no—
449C2×#124C2×D6111yescharacteristic
450C2×#123—21no—
451C2×#123—1221no—
452C2×C22⋊Q8C2×D6111yescharacteristic
453C2×#121—21no—
454C2×#121—611no—
455C2×#121—611no—
456C2×#121—1221no—
457C2×#121C2×D6111yescharacteristic
458C2×#120—21no—
459C2×C4×D4—611no—
460C2×C4×D4—1221no—
461C2×C4×D4C2×D6111yescharacteristic
462C2×C4×D4C2×D6111yescharacteristic
463C2×#117—611no—
464C22×C4⋊C4—611no—
465C22×C22⋊C4—21no—
466#488—618no—
467#484—618no—
468#482—618no—
469#478—618no—
470#466—618no—
471#465—618no—
472#463—618no—
473#449—618no—
474#447—618no—
475C4×D8—618no—
476C8×D4—618no—
477C2×#107—611no—
478C2×#107—611no—
479C2×#106—611no—
480C2×C4⋊C8—611no—
481#416—618no—
482C2×#103—611no—
483C2×#103—611no—
484C2×#103—611no—
485C2×#102—611no—
486C2×#102—611no—
487C2×#102—611no—
488C2×#102—611no—
489C2×#102—611no—
490C2×#102—611no—
491C2×#102—618no—
492C2×#102—611no—
493C2×C22⋊C8—611no—
494C2×C22⋊C8—611no—
495C2×C4×C8—611no—
496C61C2×#329711yescharacteristic, complemented, Sylow
497C25—21no—
498C2×#41—22no—
499C2×#41—24no—
500C2×#41—42no—
501C2×#41C22×D6114yes—
502C22×Q8C22×D6111yescharacteristic
503C22×D4—24no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—22no—
508C22×D4—42no—
509C22×D4—611no—
510C22×D4—1221no—
511C22×D4—1221no—
512C22×D4C22⋊D6111yescharacteristic
513C22×D4C22×D6111yescharacteristic
514C22×D4C22×D6114yes—
515C22×D4C22×D6111yescharacteristic
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—1221no—
519C23×C4—1221no—
520C23×C4C22×D6111yescharacteristic
521C23×C4C22×D6111yescharacteristic
522C2×SD16—614no—
523C2×SD16—2442no—
524C2×D8—614no—
525C2×D8—614no—
526C2×D8—1224no—
527C2×D8—2442no—
528C22×C8—611no—
529C22×C8—611no—
530C22×C8—611no—
531C22×C8—611no—
532C22×C8—614no—
533C22×C8—614no—
534C22×C8—2442no—
535C22×C8—2442no—
536#126—1228no—
537#125—614no—
538#125—1222no—
539#124—22no—
540#124C22×D6114yes—
541#123—28no—
542#123—1228no—
543C22⋊Q8—22no—
544C22⋊Q8C22×D6114yes—
545#121—22no—
546#121—28no—
547#121—614no—
548#121—614no—
549#121—1228no—
550#121—1222no—
551#121—1222no—
552#121C22×D6114yes—
553#120—28no—
554C4×D4—22no—
555C4×D4—614no—
556C4×D4—1228no—
557C4×D4—1222no—
558C4×D4C22⋊D6114yes—
559C4×D4C22×D6114yes—
560C4×D4C22×D6114yes—
561#117—614no—
562#117—1222no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—611no—
565C2×C4⋊C4—611no—
566C2×C4⋊C4—614no—
567C2×C4⋊C4—611no—
568C2×C4⋊C4—1221no—
569C2×C4⋊C4—1222no—
570C2×C4⋊C4—1221no—
571C2×C4⋊C4—1221no—
572C2×C4⋊C4C22⋊D6111yescharacteristic
573C2×C4⋊C4C22×D6111yescharacteristic
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4—28no—
580C2×C22⋊C4—1221no—
581C2×C22⋊C4—1221no—
582C2×C22⋊C4—1221no—
583C2×C22⋊C4—1221no—
584C2×C22⋊C4C22⋊D6111yescharacteristic
585C2×C22⋊C4C22⋊D6111yescharacteristic
586C2×C42—1221no—
587C2×C42C22×D6111yescharacteristic
588#107—614no—
589#107—614no—
590#106—614no—
591C4⋊C8—614no—
592#103—614no—
593#103—614no—
594#103—614no—
595#102—614no—
596#102—614no—
597#102—614no—
598#102—614no—
599#102—614no—
600#102—614no—
601#102—614no—
602C22⋊C8—614no—
603C22⋊C8—614no—
604C4×C8—614no—
605C24—21no—
606C24—21no—
607C24—24no—
608C24—44no—
609C24—44no—
610C24—82no—
611C24—1221no—
612C24C2×C22⋊D6111yescharacteristic
613C24C2×C22⋊D6111yescharacteristic
614#41—28no—
615#41—44no—
616#41—48no—
617C2×Q8—21no—
618C2×Q8—22no—
619C2×Q8—22no—
620C2×Q8C23×D6112yes—
621C2×D4—24no—
622C2×D4—28no—
623C2×D4—24no—
624C2×D4—24no—
625C2×D4—21no—
626C2×D4—24no—
627C2×D4—21no—
628C2×D4—22no—
629C2×D4—22no—
630C2×D4—22no—
631C2×D4—44no—
632C2×D4—48no—
633C2×D4—44no—
634C2×D4—44no—
635C2×D4—82no—
636C2×D4—612no—
637C2×D4—1224no—
638C2×D4—1224no—
639C2×D4—1221no—
640C2×D4—1222no—
641C2×D4—1222no—
642C2×D4—4882no—
643C2×D4—2444no—
644C2×D4#1175822414yes—
645C2×D4C2×C22⋊D6114yes—
646C2×D4C23×D6112yes—
647C2×D4C23×D6112yes—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—24no—
655C22×C4—24no—
656C22×C4—44no—
657C22×C4—82no—
658C22×C4—1224no—
659C22×C4—1221no—
660C22×C4—1221no—
661C22×C4—1221no—
662C22×C4—1224no—
663C22×C4—4882no—
664C22×C4—4882no—
665C22×C4C2×C22⋊D6112yes—
666C22×C4C2×C22⋊D6112yes—
667C22×C4C2×C22⋊D6111yescharacteristic
668C22×C4C2×C22⋊D6111yescharacteristic
669C22×C4C2×C22⋊D6111yescharacteristic
670C22×C4C2×C22⋊D6111yescharacteristic
671C22×C4C23×D6112yes—
672C22×C4C23×D6112yes—
673C22×C4C23×D6111yescharacteristic
674SD16—2444no—
675D8—1228no—
676D8—2444no—
677C2×C8—612no—
678C2×C8—612no—
679C2×C8—612no—
680C2×C8—612no—
681C2×C8—1222no—
682C2×C8—1222no—
683C2×C8—1222no—
684C2×C8—1222no—
685C2×C8—2444no—
686C2×C8—2444no—
687C4⋊C4—24no—
688C4⋊C4—21no—
689C4⋊C4—612no—
690C4⋊C4—612no—
691C4⋊C4—612no—
692C4⋊C4—1221no—
693C4⋊C4—1221no—
694C4⋊C4—1224no—
695C4⋊C4—1221no—
696C4⋊C4—1224no—
697C4⋊C4—1224no—
698C4⋊C4C2×C22⋊D6114yes—
699C4⋊C4C23×D6112yes—
700C22⋊C4—24no—
701C22⋊C4—24no—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—24no—
705C22⋊C4—1224no—
706C22⋊C4—1224no—
707C22⋊C4—1224no—
708C22⋊C4—1224no—
709C22⋊C4C2×C22⋊D6114yes—
710C22⋊C4C2×C22⋊D6114yes—
711C42—1224no—
712C42C2×C22⋊D6112yes—
713C42C23×D6112yes—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—24no—
721C23—22no—
722C23—48no—
723C23—42no—
724C23—42no—
725C23—48no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—84no—
730C23—816no—
731C23—1222no—
732C23—2442no—
733C23—2442no—
734C23—2442no—
735C23#1451979714yes—
736C23C22×C22⋊D6112yes—
737C23C22×C22⋊D6112yes—
738C23C22×C22⋊D6111yescharacteristic
739Q8—22no—
740Q8—22no—
741Q8—42no—
742D4—28no—
743D4—22no—
744D4—22no—
745D4—22no—
746D4—24no—
747D4—48no—
748D4—48no—
749D4—42no—
750D4—84no—
751D4—1222no—
752D4—1222no—
753D4—4884no—
754D4—2448no—
755D4—2442no—
756D4C2×#1175822414yes—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—48no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—84no—
773C2×C4—1222no—
774C2×C4—1222no—
775C2×C4—1222no—
776C2×C4—4884no—
777C2×C4—4884no—
778C2×C4—2442no—
779C2×C4—2442no—
780C2×C4—2442no—
781C2×C4C22×C22⋊D6112yes—
782C2×C4C22×C22⋊D6112yes—
783C2×C4C22×C22⋊D6112yes—
784C2×C4C22×C22⋊D6112yes—
785C2×C4C22×C22⋊D6111yescharacteristic
786C2×C4C2×#1175822412yes—
787C2×C4#1451982212yes—
788C2×C4C24×D6111yescharacteristic
789C8—1222no—
790C8—1222no—
791C8—1222no—
792C8—1222no—
793C22—28no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—24no—
799C22—22no—
800C22—44no—
801C22—48no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22—816no—
808C22—84no—
809C22—4884no—
810C22—2442no—
811C22—2442no—
812C22—2442no—
813C22#1684040612yes—
814C22C2×#1451979714yes—
815C22C2×#1451979712yes—
816C22#1684056512yes—
817C22C23×C22⋊D6111yescharacteristic
818C4—22no—
819C4—22no—
820C4—22no—
821C4—22no—
822C4—42no—
823C4—42no—
824C4—2442no—
825C4—2442no—
826C4—2442no—
827C4#1684040612yes—
828C4C22×#1175822411yescharacteristic
829C4C2×#1451982211yescharacteristic
830C2—24no—
831C2—42no—
832C2—44no—
833C2—82no—
834C2—4882no—
835C2#2145766914yesdirect product factor
836C2C2×#1684040611yescharacteristic
837C2C22×#1451979711yescharacteristic
838C2C2×#1684056511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#546C2
socleC23×C61C22×D4
hypercenterC2×#546D61
hypocenterC61C2×#3297
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. C2×#16840458C2semidirect
2. #21457669C2direct (N × H)
3. C2×#16840116C2semidirect
4. C2×#16840095C2semidirect
5. C2×#16840083C2semidirect
6. C2×#16840062C2semidirect
7. C2×#16839996C2semidirect
8. C2×#16839993C2semidirect
9. C2×#16839974C2semidirect
10. C2×#16839907C2semidirect
11. C2×#16839896C2semidirect
12. C2×C4×#11758199C2semidirect
13. C2×D4×#92418C2semidirect
14. C2×#16839758C2semidirect
15. C22×#14519698C2semidirect
16. C2×C61×#546C2semidirect
17. C22×#11758201C22semidirect
21. C23×#92418C22semidirect
23. #16840458C22semidirect
25. C2×#14519769C22semidirect
28. C2×#14519751C22semidirect
30. C2×C4×D244C22semidirect
32. C2×#14519736C22semidirect
34. #16840116C22semidirect
35. #16840095C22semidirect
36. #16840083C22semidirect
37. #16840062C22semidirect
38. #16839996C22semidirect
39. #16839993C22semidirect
40. #16839974C22semidirect
41. #16839907C22semidirect
42. #16839896C22semidirect
43. C4×#11758199C22semidirect
44. D4×#92418C22semidirect
45. C2×#14519710C22semidirect
46. C2×#14519710C22semidirect
47. C2×#14519708C22semidirect
48. C2×C4⋊#92418C22semidirect
49. #16839758C22semidirect
50. C2×#14519701C22semidirect
51. C2×#14519701C22semidirect
52. C2×#14519701C22semidirect
59. C2×#14519698C22semidirect
60. C2×#14519697C22semidirect
62. C2×C22⋊#92418C22semidirect
63. C2×C4×#92418C22semidirect
67. C61×#546C22semidirect
83. C2×#11758201C23semidirect
95. C22×#92418C23semidirect
98. #14519769C23semidirect
103. #14519751C23semidirect
106. C4×D244C23semidirect
109. #14519736C23semidirect
123. #14519710C23semidirect
124. #14519710C23semidirect
125. #14519708C23semidirect
126. C4⋊#92418C23semidirect
127. #14519701C23semidirect
128. #14519701C23semidirect
129. #14519701C23semidirect
136. #14519697C23semidirect
138. C22⋊#92418C23semidirect
139. C4×#92418C23semidirect
412. C2×#546D61semidirect
431. C2×C61#3297semidirect
446. #546C2×D61semidirect
496. C61C2×#3297semidirect
835. C2#21457669direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404582
#214576692
C2×#168401162
C2×#168400952
C2×#168400832
C2×#168400622
C2×#168399962
C2×#168399932
C2×#168399742
C2×#168399072
C2×#168398962
C2×C4×#117581992
C2×D4×#924182
C2×#168397582
C22×#145196982
C2×C61×#5462
C2×#329761