Finite Group Databasebeta

← C2×#21457257 #30552952

Subgroups — C2×#21457257 #30552952

Order 15616.

2010 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840368C211yesmaximal, characteristic, complemented
2C2×#16840363C211yesmaximal, characteristic, complemented
3#21457257C2116yesmaximal, direct product factor
4C2×#16840065C211yesmaximal, characteristic, complemented
5C2×#16840061C211yesmaximal, characteristic, complemented
6C2×#16840059C211yesmaximal, characteristic, complemented
7C2×#16840016C211yesmaximal, characteristic, complemented
8C2×#16840014C211yesmaximal, characteristic, complemented
9C2×#16839999C211yesmaximal, characteristic, complemented
10C2×#16839997C211yesmaximal, characteristic, complemented
11C2×#16839958C211yesmaximal, characteristic, complemented
12C2×#16839957C211yesmaximal, characteristic, complemented
13C2×#16839956C211yesmaximal, characteristic, complemented
14C2×#16839956C211yesmaximal, characteristic, complemented
15C2×#16839787C211yesmaximal, characteristic, complemented
16C2×C61×#478C211yesmaximal, characteristic, complemented
17C22×D488C2211yescharacteristic
18C22×D488C2211yescharacteristic
19C22×#11758199C2211yescharacteristic
20C22×#11758199C2211yescharacteristic
21C22×#11758189C2211yescharacteristic
22C22×C8×D61C2211yescharacteristic
23#16840368—24no—
24#16840368C2218yescomplemented
25#16840363—24no—
26#16840363C2218yescomplemented
27C2×#14519774C2211yescharacteristic
28C2×#14519773C2211yescharacteristic
29C2×#14519768C2211yescharacteristic
30C2×#14519762—21no—
31C2×#14519762—21no—
32C2×#14519760—21no—
33C2×#14519759—21no—
34C2×#14519752—21no—
35C2×#14519752—21no—
36C2×#14519752C2211yescharacteristic
37C2×#14519752C2211yescharacteristic
38C2×#14519752C2211yescharacteristic
39C2×#14519751—21no—
40C2×#14519750—21no—
41C2×#14519748C2211yescharacteristic
42C2×C4×D244C2211yescharacteristic
43C2×#14519739C2211yescharacteristic
44C2×#14519739C2211yescharacteristic
45C2×#14519734C2211yescharacteristic
46#16840065C2218yescomplemented
47#16840061C2218yescomplemented
48#16840059C2218yescomplemented
49#16840016C2218yescomplemented
50#16840014C2218yescomplemented
51#16839999C2218yescomplemented
52#16839997C2218yescomplemented
53#16839958C2218yescomplemented
54#16839957C2218yescomplemented
55#16839956C2218yescomplemented
56#16839956C2218yescomplemented
57C2×#14519710C2211yescharacteristic
58C2×#14519708C2211yescharacteristic
59#16839787C2218yescomplemented
60C2×C4⋊#92418C2211yescharacteristic
61C2×#14519706C2211yescharacteristic
62C2×#14519706C2211yescharacteristic
63C2×#14519699C2211yescharacteristic
64C2×#14519699C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×#14519697C2211yescharacteristic
67C2×#14519697C2211yescharacteristic
68C2×#14519697C2211yescharacteristic
69C2×#125×C61C2211yescharacteristic
70C2×C4×D4×C61C2211yescharacteristic
71C61×#478C2218yescomplemented
72C2×#107×C61C2211yescharacteristic
73C2×#106×C61C2211yescharacteristic
74C2×C4⋊C8×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C22×D244—21no—
78C22×D244—21no—
79C22×D244—21no—
80C22×D244—21no—
81C22×D244—21no—
82C22×D244C2311yescharacteristic
83C22×D244C2311yescharacteristic
84C22×D244C2311yescharacteristic
85C22×C22⋊D61—21no—
86C22×C22⋊D61—21no—
87C22×C22⋊D61—21no—
88C22×C4×D61—21no—
89C22×C4×D61—21no—
90C22×C4×D61—21no—
91C22×C4×D61C2311yescharacteristic
92C2×D488—42no—
93C2×D488—42no—
94C2×D488C2314yes—
95C2×D488C2314yes—
96C2×#11758199—42no—
97C2×#11758199—42no—
98C2×#11758199C2314yes—
99C2×#11758199C2314yes—
100C2×#11758189—42no—
101C2×#11758189C2314yes—
102C22×#92418C2311yescharacteristic
103C22×#92418C2311yescharacteristic
104C2×C8×D61—42no—
105C2×C8×D61C2314yes—
106#14519774—22no—
107#14519774C2314yes—
108#14519773—22no—
109#14519773C2314yes—
110#14519768—22no—
111#14519768C2314yes—
112#14519762—28no—
113#14519762—28no—
114#14519760—28no—
115#14519759—28no—
116#14519752—22no—
117#14519752—22no—
118#14519752—22no—
119#14519752—28no—
120#14519752—28no—
121#14519752C2314yes—
122#14519752C2314yes—
123#14519752C2314yes—
124#14519751—28no—
125#14519750—28no—
126#14519748—22no—
127#14519748C2314yes—
128C4×D244—22no—
129C4×D244C2314yes—
130#14519739—22no—
131#14519739—22no—
132#14519739C2314yes—
133#14519739C2314yes—
134#14519734D414yes—
135#14519734C2314yes—
136C2×C4⋊Dic61—21no—
137C2×C4⋊Dic61C2311yescharacteristic
138C2×#11758196—21no—
139C2×#11758196D411yescharacteristic
140C2×#11758196D411yescharacteristic
141C2×C22⋊Dic61—21no—
142C2×#11758198—21no—
143C2×#11758198—21no—
144C2×#11758198—21no—
145C2×#11758198—21no—
146C2×#11758198—21no—
147C2×#11758198—21no—
148C2×#11758198D411yescharacteristic
149C2×#11758198D411yescharacteristic
150C2×C4×Dic61C2311yescharacteristic
151#14519710C2314yes—
152#14519708C2314yes—
153C4⋊#92418C2314yes—
154#14519706C2314yes—
155#14519706C2314yes—
156#14519699C2314yes—
157#14519699C2314yes—
158#14519697C2314yes—
159#14519697C2314yes—
160#14519697C2314yes—
161#14519697C2314yes—
162C22×D4×C61C2311yescharacteristic
163C23×C4×C61—21no—
164C22×C8×C61C2311yescharacteristic
165C22×C8×C61C2311yescharacteristic
166#125×C61—22no—
167#125×C61C2314yes—
168C4×D4×C61—22no—
169C4×D4×C61C2314yes—
170C2×C4⋊C4×C61—21no—
171C2×C4⋊C4×C61—21no—
172C2×C4⋊C4×C61C2311yescharacteristic
173C2×C4⋊C4×C61C2311yescharacteristic
174C2×C4⋊C4×C61C2311yescharacteristic
175C2×C22⋊C4×C61—21no—
176C2×C42×C61C2311yescharacteristic
177#107×C61C2314yes—
178#106×C61C2314yes—
179C4⋊C8×C61C2314yes—
180#102×C61C2314yes—
181#102×C61C2314yes—
182C24×C61—21no—
183C23×D61—21no—
184C23×D61—21no—
185C23×D61—21no—
186C23×D61C2×D411yescharacteristic
187C2×D4×C61—21no—
188C2×D4×C61—22no—
189C2×D4×C61—22no—
190C2×D4×C61C2412yes—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—24no—
195C22×C4×C61—82no—
196C22×C4×C61C2×D411yescharacteristic
197C22×C4×C61C2×D411yescharacteristic
198C22×C4×C61C2411yescharacteristic
199C2×C22⋊D61—24no—
200C2×C22⋊D61—24no—
201C2×C22⋊D61—24no—
202C2×C22⋊D61—82no—
203C2×C22⋊D61—82no—
204C2×C22⋊D61—82no—
205C22×Dic61—21no—
206C22×Dic61C2×D411yescharacteristic
207C22×Dic61C2×D411yescharacteristic
208C22×Dic61C2×D411yescharacteristic
209C2×D244—22no—
210C2×D244—22no—
211C2×D244—22no—
212C2×D244—22no—
213C2×D244—22no—
214C2×D244—22no—
215C2×D244—21no—
216C2×D244—21no—
217C2×D244—21no—
218C2×D244—24no—
219C2×D244—24no—
220C2×D244—24no—
221C2×D244—24no—
222C2×D244—24no—
223C2×D244—82no—
224C2×D244—82no—
225C2×D244—82no—
226C2×D244—82no—
227C2×D244—82no—
228C2×D244C2412yes—
229C2×D244C2412yes—
230C2×D244C2412yes—
231C2×C4×D61—22no—
232C2×C4×D61—22no—
233C2×C4×D61—24no—
234C2×C4×D61—24no—
235C2×C4×D61—24no—
236C2×C4×D61—82no—
237C2×C4×D61—82no—
238C2×C4×D61—82no—
239C2×C4×D61C2×D412yes—
240C2×C4×D61C2412yes—
241C2×C8×C61—22no—
242C2×C8×C61—22no—
243C2×C8×C61C2412yes—
244C2×C8×C61C2412yes—
245C4⋊C4×C61—24no—
246C4⋊C4×C61—24no—
247C4⋊C4×C61—21no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61—21no—
250C4⋊C4×C61C2412yes—
251C4⋊C4×C61C2412yes—
252C4⋊C4×C61C2412yes—
253C22⋊C4×C61—24no—
254C42×C61C2×D412yes—
255C42×C61C2412yes—
256C22⋊Dic61—24no—
257#11758199—44no—
258#11758199—44no—
259#11758198—24no—
260#11758198—24no—
261#11758198—24no—
262#11758198—24no—
263#11758198—24no—
264#11758198—24no—
265#11758198C2×D414yes—
266#11758198C2×D414yes—
267C4⋊Dic61—21no—
268C4⋊Dic61—24no—
269C4⋊Dic61C2412yes—
270#11758196—24no—
271#11758196C2×D414yes—
272#11758196C2×D414yes—
273C4×Dic61C2×D412yes—
274C4×Dic61C2412yes—
275C2×#92418—22no—
276C2×#92418—22no—
277C2×#92418C2412yes—
278C2×#92418C2412yes—
279D488—44no—
280D488—44no—
281#11758189—44no—
282C8×D61—44no—
283C23×C61—22no—
284C23×C61—42no—
285C23×C61—42no—
286C23×C61—42no—
287C23×C61C22×D411yescharacteristic
288C22×D61—22no—
289C22×D61—22no—
290C22×D61—22no—
291C22×D61—22no—
292C22×D61—22no—
293C22×D61—22no—
294C22×D61—42no—
295C22×D61—42no—
296C22×D61—42no—
297C22×D61—42no—
298C22×D61—42no—
299C22×D61—42no—
300C22×D61—42no—
301C22×D61—42no—
302C22×D61—42no—
303C22×D61C22×D412yes—
304D4×C61—22no—
305D4×C61—22no—
306D4×C61—42no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—42no—
313C2×C4×C61—42no—
314C2×C4×C61—42no—
315C2×C4×C61—84no—
316C2×C4×C61C22×D412yes—
317C2×C4×C61C22×D412yes—
318C2×C4×C61C22×D411yescharacteristic
319C2×C4×C61H(5,𝔽2)12yes—
320C2×C4×C612−1+412yes—
321C2×C4×C61C2511yescharacteristic
322C22⋊D61—84no—
323C22⋊D61—84no—
324C22⋊D61—84no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—22no—
329C2×Dic61—42no—
330C2×Dic61C22×D412yes—
331C2×Dic61C22×D412yes—
332C2×Dic61C22×D412yes—
333D244—22no—
334D244—22no—
335D244—22no—
336D244—22no—
337D244—22no—
338D244—22no—
339D244—42no—
340D244—42no—
341D244—42no—
342D244—84no—
343D244—84no—
344D244—84no—
345D244—84no—
346D244—84no—
347C4×D61—24no—
348C4×D61—22no—
349C4×D61—22no—
350C4×D61—84no—
351C4×D61—84no—
352C4×D61—84no—
353C8×C61—22no—
354C8×C61—22no—
355#92418—22no—
356#92418—22no—
357C2×#3259—611nomaximal, Sylow
358C22×C61—42no—
359C22×C61—42no—
360C22×C61—42no—
361C22×C61—84no—
362C22×C61#53712yes—
363C22×C61#57612yes—
364C22×C61#57612yes—
365C22×C61C23×D411yescharacteristic
366C2×D61—22no—
367C2×D61—22no—
368C2×D61—22no—
369C2×D61—44no—
370C2×D61—42no—
371C2×D61—42no—
372C2×D61—42no—
373C2×D61—42no—
374C2×D61—42no—
375C2×D61—42no—
376C2×D61—42no—
377C2×D61—42no—
378C2×D61—42no—
379C2×D61—84no—
380C2×D61—84no—
381C2×D61—84no—
382C4×C61—22no—
383C4×C61—22no—
384C4×C61—42no—
385C4×C61—42no—
386C4×C61—42no—
387C4×C61#53712yes—
388C4×C61C2×H(5,𝔽2)11yescharacteristic
389C4×C61C2×2−1+411yescharacteristic
390Dic61—22no—
391Dic61—22no—
392Dic61—22no—
393Dic61—42no—
394C2×#540—611no—
395C2×#540—611no—
396#3259—6116no—
397C2×#478—611no—
398C2×#478—611no—
399C2×#478—611no—
400C2×#478D6111yescharacteristic, complemented
401C2×#469—611no—
402C2×#469—611no—
403C2×#466—611no—
404C2×#466—611no—
405C2×#459—611no—
406C2×#459—611no—
407C2×#459—611no—
408C2×#459—611no—
409C2×#424—611no—
410C2×C61—82no—
411C2×C61#325914yescomplemented
412C2×C61C2×#53711yescharacteristic
413C2×C61C2×#57611yescharacteristic
414C2×C61C2×#57611yescharacteristic
415D61—42no—
416D61—82no—
417D61—82no—
418D61—82no—
419C22×D8—611no—
420C22×D8—611no—
421C22×D8—611no—
422C22×D8—611no—
423C22×M16—611no—
424C23×C8—611no—
425#540—618no—
426#540—618no—
427#540—1224no—
428#540—1224no—
429C2×#127—611no—
430C2×#127—611no—
431C2×#125—611no—
432C2×#125C2×D6111yescharacteristic
433C2×#123—1221no—
434C2×#123—1221no—
435C2×#123—1221no—
436C2×#123—1221no—
437C2×#121—611no—
438C2×#121—611no—
439C2×#121—611no—
440C2×#121—611no—
441C2×#121—1221no—
442C2×#121—1221no—
443C2×#121—1221no—
444C2×#121—1221no—
445C2×C4×D4—611no—
446C2×C4×D4—611no—
447C2×C4×D4—611no—
448C2×C4×D4C2×D6111yescharacteristic
449C2×#117—611no—
450#478—618no—
451#478—618no—
452#478—618no—
453#478C2×D6118yescomplemented
454#469—618no—
455#469—618no—
456#466—618no—
457#466—618no—
458#459—618no—
459#459—618no—
460#459—618no—
461#459—618no—
462C2×#107—611no—
463C2×#107C2×D6111yescharacteristic
464C2×#106—611no—
465C2×#106C2×D6111yescharacteristic
466#424—618no—
467C2×C4⋊C8—611no—
468C2×C4⋊C8—611no—
469C2×C4⋊C8—611no—
470C2×C4⋊C8C2×D6111yescharacteristic
471C2×#102—611no—
472C2×#102—611no—
473C2×#102—611no—
474C2×#102—611no—
475C2×#102—611no—
476C2×#102—611no—
477C2×#102C2×D6111yescharacteristic
478C2×#102C2×D6111yescharacteristic
479C61C2×#325911yescharacteristic, complemented, Sylow
480C22×D4—611no—
481C22×D4—611no—
482C22×D4—611no—
483C22×D4—1221no—
484C22×D4—1221no—
485C22×D4—1221no—
486C22×D4—1221no—
487C22×D4—1221no—
488C22×D4—1221no—
489C22×D4—1221no—
490C22×D4—1221no—
491C22×D4C22×D6111yescharacteristic
492C23×C4—21no—
493C23×C4—611no—
494C23×C4—1221no—
495C23×C4—1221no—
496C23×C4—1221no—
497C2×D8—614no—
498C2×D8—614no—
499C2×D8—614no—
500C2×D8—614no—
501C2×D8—2442no—
502C2×D8—2442no—
503C2×D8—2442no—
504C2×D8—2442no—
505C2×M16—614no—
506C2×M16—2442no—
507C22×C8—611no—
508C22×C8—611no—
509C22×C8—614no—
510C22×C8—2442no—
511C22×C8C22×D6111yescharacteristic
512C22×C8C22×D6111yescharacteristic
513#127—614no—
514#127—614no—
515#127—1222no—
516#127—1222no—
517#125—22no—
518#125—614no—
519#125—1222no—
520#125C22×D6114yes—
521#123—1228no—
522#123—1228no—
523#123—1228no—
524#123—1228no—
525#121—614no—
526#121—614no—
527#121—614no—
528#121—614no—
529#121—1228no—
530#121—1228no—
531#121—1228no—
532#121—1228no—
533#121—1222no—
534#121—1222no—
535#121—1222no—
536#121—1222no—
537C4×D4—22no—
538C4×D4—614no—
539C4×D4—614no—
540C4×D4—614no—
541C4×D4—1222no—
542C4×D4—1222no—
543C4×D4—1222no—
544C4×D4C22×D6114yes—
545#117—614no—
546#117—614no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—611no—
550C2×C4⋊C4—611no—
551C2×C4⋊C4—611no—
552C2×C4⋊C4—1221no—
553C2×C4⋊C4—1221no—
554C2×C4⋊C4C22×D6111yescharacteristic
555C2×C4⋊C4C22×D6111yescharacteristic
556C2×C4⋊C4C22×D6111yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—611no—
559C2×C22⋊C4—611no—
560C2×C22⋊C4—1221no—
561C2×C22⋊C4—1221no—
562C2×C22⋊C4—1221no—
563C2×C22⋊C4—1221no—
564C2×C22⋊C4—1221no—
565C2×C22⋊C4—1221no—
566C2×C22⋊C4—1221no—
567C2×C42—611no—
568C2×C42C22×D6111yescharacteristic
569#107—614no—
570#107C22×D6114yes—
571#106—614no—
572#106C22×D6114yes—
573C4⋊C8—614no—
574C4⋊C8—614no—
575C4⋊C8—614no—
576C4⋊C8C22×D6114yes—
577#102—614no—
578#102—614no—
579#102—614no—
580#102—614no—
581#102—614no—
582#102—614no—
583#102C22×D6114yes—
584#102C22×D6114yes—
585C24—21no—
586C24—611no—
587C24—1221no—
588C24—1221no—
589C24—1221no—
590C2×D4—21no—
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—612no—
594C2×D4—612no—
595C2×D4—612no—
596C2×D4—1224no—
597C2×D4—1224no—
598C2×D4—1224no—
599C2×D4—1224no—
600C2×D4—1224no—
601C2×D4—1224no—
602C2×D4—1224no—
603C2×D4—1224no—
604C2×D4—1221no—
605C2×D4—1221no—
606C2×D4—1221no—
607C2×D4—1222no—
608C2×D4—1222no—
609C2×D4—1222no—
610C2×D4—1222no—
611C2×D4—1222no—
612C2×D4—1222no—
613C2×D4—4882no—
614C2×D4—4882no—
615C2×D4—4882no—
616C2×D4—4882no—
617C2×D4—4882no—
618C2×D4—4882no—
619C2×D4—4882no—
620C2×D4—4882no—
621C2×D4C23×D6112yes—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—24no—
626C22×C4—82no—
627C22×C4—611no—
628C22×C4—611no—
629C22×C4—611no—
630C22×C4—612no—
631C22×C4—612no—
632C22×C4—1224no—
633C22×C4—1224no—
634C22×C4—1222no—
635C22×C4—1222no—
636C22×C4—1221no—
637C22×C4—1224no—
638C22×C4—4882no—
639C22×C4—4882no—
640C22×C4—4882no—
641C22×C4D4×D6111yescharacteristic
642C22×C4D4×D6111yescharacteristic
643C22×C4C23×D6111yescharacteristic
644D8—2444no—
645D8—2444no—
646D8—2444no—
647D8—2444no—
648M16—2444no—
649C2×C8—22no—
650C2×C8—22no—
651C2×C8—612no—
652C2×C8—612no—
653C2×C8—1222no—
654C2×C8—1222no—
655C2×C8—2444no—
656C2×C8C23×D6112yes—
657C2×C8C23×D6112yes—
658C4⋊C4—24no—
659C4⋊C4—24no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—614no—
664C4⋊C4—614no—
665C4⋊C4—612no—
666C4⋊C4—1224no—
667C4⋊C4—1224no—
668C4⋊C4—1221no—
669C4⋊C4C23×D6112yes—
670C4⋊C4C23×D6112yes—
671C4⋊C4C23×D6112yes—
672C22⋊C4—24no—
673C22⋊C4—614no—
674C22⋊C4—614no—
675C22⋊C4—1224no—
676C22⋊C4—1224no—
677C22⋊C4—1224no—
678C22⋊C4—1224no—
679C22⋊C4—1224no—
680C22⋊C4—1224no—
681C22⋊C4—1224no—
682C42—612no—
683C42—612no—
684C42D4×D6112yes—
685C42C23×D6112yes—
686C23—22no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—612no—
691C23—1222no—
692C23—1222no—
693C23—1222no—
694C23—1222no—
695C23—1222no—
696C23—1222no—
697C23—2442no—
698C23—2442no—
699C23—2442no—
700C23—2442no—
701C23—2442no—
702C23—2442no—
703C23—2442no—
704C23—2442no—
705C23—2442no—
706C23C2×D4×D6111yescharacteristic
707D4—22no—
708D4—22no—
709D4—42no—
710D4—1222no—
711D4—1222no—
712D4—1222no—
713D4—1222no—
714D4—1222no—
715D4—1222no—
716D4—4884no—
717D4—4884no—
718D4—4884no—
719D4—4884no—
720D4—4884no—
721D4—4884no—
722D4—4884no—
723D4—4884no—
724D4—2442no—
725D4—2442no—
726D4—2442no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—84no—
736C2×C4—612no—
737C2×C4—612no—
738C2×C4—612no—
739C2×C4—1222no—
740C2×C4—1222no—
741C2×C4—1222no—
742C2×C4—1222no—
743C2×C4—1222no—
744C2×C4—1224no—
745C2×C4—1222no—
746C2×C4—4884no—
747C2×C4—4884no—
748C2×C4—4884no—
749C2×C4—2442no—
750C2×C4C2×D4×D6112yes—
751C2×C4C2×D4×D6112yes—
752C2×C4C2×D4×D6111yescharacteristic
753C2×C4#1451982312yes—
754C2×C4#1451982512yes—
755C2×C4C24×D6111yescharacteristic
756C8—22no—
757C8—22no—
758C8—1222no—
759C8—1222no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—84no—
764C22—1222no—
765C22—1222no—
766C22—1222no—
767C22—4884no—
768C22—4884no—
769C22—4884no—
770C22—2442no—
771C22—2442no—
772C22—2442no—
773C22—2442no—
774C22—2442no—
775C22—2442no—
776C22—2442no—
777C22—2442no—
778C22—2442no—
779C22—2444no—
780C22#1684034212yes—
781C22#1684056412yes—
782C22#1684056612yes—
783C22C22×D4×D6111yescharacteristic
784C4—22no—
785C4—22no—
786C4—42no—
787C4—42no—
788C4—42no—
789C4—1222no—
790C4—1222no—
791C4—1222no—
792C4—2442no—
793C4#1684034212yes—
794C4C2×#1451982311yescharacteristic
795C4C2×#1451982511yescharacteristic
796C2—82no—
797C2—4882no—
798C2—4882no—
799C2—4882no—
800C2—2442no—
801C2#2145725714yesdirect product factor
802C2C2×#1684034211yescharacteristic
803C2C2×#1684056411yescharacteristic
804C2C2×#1684056611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#478C2
socleC23×C61C22×D4
hypercenterC2×#478D61
hypocenterC61C2×#3259
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#16840368C2semidirect
2. C2×#16840363C2semidirect
3. #21457257C2direct (N × H)
4. C2×#16840065C2semidirect
5. C2×#16840061C2semidirect
6. C2×#16840059C2semidirect
7. C2×#16840016C2semidirect
8. C2×#16840014C2semidirect
9. C2×#16839999C2semidirect
10. C2×#16839997C2semidirect
11. C2×#16839958C2semidirect
12. C2×#16839957C2semidirect
13. C2×#16839956C2semidirect
14. C2×#16839956C2semidirect
15. C2×#16839787C2semidirect
16. C2×C61×#478C2semidirect
24. #16840368C22semidirect
26. #16840363C22semidirect
46. #16840065C22semidirect
47. #16840061C22semidirect
48. #16840059C22semidirect
49. #16840016C22semidirect
50. #16840014C22semidirect
51. #16839999C22semidirect
52. #16839997C22semidirect
53. #16839958C22semidirect
54. #16839957C22semidirect
55. #16839956C22semidirect
56. #16839956C22semidirect
59. #16839787C22semidirect
71. C61×#478C22semidirect
400. C2×#478D61semidirect
411. C2×C61#3259semidirect
453. #478C2×D61semidirect
479. C61C2×#3259semidirect
801. C2#21457257direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403682
C2×#168403632
#214572572
C2×#168400652
C2×#168400612
C2×#168400592
C2×#168400162
C2×#168400142
C2×#168399992
C2×#168399972
C2×#168399582
C2×#168399572
C2×#168399562
C2×#168397872
C2×C61×#4782
C2×#325961