Finite Group Databasebeta

← C2×#21458906 #30561042

Subgroups — C2×#21458906 #30561042

Order 15616.

2066 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840497C211yesmaximal, characteristic, complemented
2C2×#16840494C211yesmaximal, characteristic, complemented
3#21458906C2116yesmaximal, direct product factor
4C2×#16840152C211yesmaximal, characteristic, complemented
5C2×#16840148C211yesmaximal, characteristic, complemented
6C2×#16840147C211yesmaximal, characteristic, complemented
7C2×#16839986C211yesmaximal, characteristic, complemented
8C2×#16839980C211yesmaximal, characteristic, complemented
9C2×#16839979C211yesmaximal, characteristic, complemented
10C2×#16839958C211yesmaximal, characteristic, complemented
11C2×#16839956C211yesmaximal, characteristic, complemented
12C2×#16839891C211yesmaximal, characteristic, complemented
13C2×#16839865C211yesmaximal, characteristic, complemented
14C2×#16839860C211yesmaximal, characteristic, complemented
15C2×#16839842C211yesmaximal, characteristic, complemented
16C2×C61×#464C211yesmaximal, characteristic, complemented
17C22×#11758201C2211yescharacteristic
18C22×#11758201C2211yescharacteristic
19C22×#11758201C2211yescharacteristic
20C22×D488C2211yescharacteristic
21C22×D488C2211yescharacteristic
22C22×#11758199C2211yescharacteristic
23C22×#11758199C2211yescharacteristic
24#16840497—24no—
25#16840497C2218yescomplemented
26#16840494—24no—
27#16840494C2218yescomplemented
28C2×#14519774C2211yescharacteristic
29C2×#14519773C2211yescharacteristic
30C2×#14519766C2211yescharacteristic
31C2×#14519766C2211yescharacteristic
32C2×#14519766C2211yescharacteristic
33C2×#14519765—21no—
34C2×#14519763—21no—
35C2×#14519762—21no—
36C2×#14519762—21no—
37C2×#14519761—21no—
38C2×#14519759—21no—
39C2×Q8×Dic61C2211yescharacteristic
40C2×C4×Dic122C2211yescharacteristic
41C2×C4×D244—21no—
42C2×C4×D244C2211yescharacteristic
43C2×D4×Dic61C2211yescharacteristic
44C2×#14519739C2211yescharacteristic
45C2×#14519739C2211yescharacteristic
46C2×#14519737—21no—
47#16840152C2218yescomplemented
48#16840148C2218yescomplemented
49#16840147C2218yescomplemented
50#16839986C2218yescomplemented
51#16839980C2218yescomplemented
52#16839979C2218yescomplemented
53#16839958C2218yescomplemented
54#16839956C2218yescomplemented
55#16839891C2218yescomplemented
56#16839865C2218yescomplemented
57#16839860C2218yescomplemented
58#16839842C2218yescomplemented
59C2×#14519710C2211yescharacteristic
60C2×#14519706C2211yescharacteristic
61C2×#14519706C2211yescharacteristic
62C2×#14519701C2211yescharacteristic
63C2×#14519699C2211yescharacteristic
64C2×#14519699C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×#14519688C2211yescharacteristic
67C2×#14519687C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C22×Q16×C61C2211yescharacteristic
70C22×SD16×C61C2211yescharacteristic
71C2×#124×C61C2211yescharacteristic
72C2×C4×Q8×C61C2211yescharacteristic
73C61×#464C2218yescomplemented
74C2×C4⋊C8×C61C2211yescharacteristic
75C2×#103×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C22×Dic122D411yescharacteristic
78C22×D244—21no—
79C22×D244—21no—
80C22×D244C2311yescharacteristic
81C22×D244C2311yescharacteristic
82C22×D244C2311yescharacteristic
83C22×C22⋊D61—21no—
84C22×C22⋊D61—21no—
85C23×Dic61—21no—
86C22×C4×D61—21no—
87C22×C4×D61—21no—
88C22×C4×D61—21no—
89C2×#11758201—24no—
90C2×#11758201—24no—
91C2×#11758201—42no—
92C2×#11758201C2314yes—
93C2×#11758201C2314yes—
94C2×#11758201C2314yes—
95C2×D488—42no—
96C2×D488—42no—
97C2×D488C2314yes—
98C2×D488C2314yes—
99C2×#11758199—24no—
100C2×#11758199—42no—
101C2×#11758199C2314yes—
102C2×#11758199C2314yes—
103C22×#92418C2311yescharacteristic
104C22×#92418C2311yescharacteristic
105#14519774—22no—
106#14519774C2314yes—
107#14519773—22no—
108#14519773C2314yes—
109#14519766—22no—
110#14519766—22no—
111#14519766—22no—
112#14519766C2314yes—
113#14519766C2314yes—
114#14519766C2314yes—
115#14519765—28no—
116#14519763—28no—
117#14519762—28no—
118#14519762—28no—
119#14519761—28no—
120#14519759—28no—
121Q8×Dic61—22no—
122Q8×Dic61C2314yes—
123C4×Dic122D414yes—
124C4×Dic122C2314yes—
125C4×D244—22no—
126C4×D244—28no—
127C4×D244C2314yes—
128D4×Dic61—22no—
129D4×Dic61C2314yes—
130#14519739—22no—
131#14519739—22no—
132#14519739C2314yes—
133#14519739C2314yes—
134#14519737—28no—
135C2×C4⋊Dic61—21no—
136C2×C4⋊Dic61D411yescharacteristic
137C2×C4⋊Dic61C2311yescharacteristic
138C2×#11758196D411yescharacteristic
139C2×#11758196D411yescharacteristic
140C2×C22⋊Dic61—21no—
141C2×#11758198—21no—
142C2×#11758198—21no—
143C2×#11758198—21no—
144C2×#11758198—21no—
145C2×#11758198—21no—
146C2×#11758198—21no—
147C2×#11758198—21no—
148C2×#11758198—21no—
149C2×#11758198—21no—
150C2×C4×Dic61—21no—
151C2×C4×Dic61C2311yescharacteristic
152C2×C4×Dic61C2311yescharacteristic
153#14519710C2314yes—
154#14519706C2314yes—
155#14519706C2314yes—
156#14519701C2314yes—
157#14519699C2314yes—
158#14519699C2314yes—
159#14519697C2314yes—
160#14519688C2314yes—
161#14519687C2314yes—
162C8×Dic61C2314yes—
163C22×Q8×C61C2311yescharacteristic
164C22×Q8×C61C2311yescharacteristic
165C22×D4×C61C2311yescharacteristic
166C2×Q16×C61—42no—
167C2×Q16×C61C2314yes—
168C2×SD16×C61—42no—
169C2×SD16×C61C2314yes—
170C22×C8×C61C2311yescharacteristic
171C22×C8×C61C2311yescharacteristic
172#124×C61—22no—
173#124×C61C2314yes—
174C4×Q8×C61—22no—
175C4×Q8×C61C2314yes—
176C2×C4⋊C4×C61—21no—
177C2×C4⋊C4×C61C2311yescharacteristic
178C2×C22⋊C4×C61—21no—
179C2×C22⋊C4×C61—21no—
180C2×C42×C61—21no—
181C2×C42×C61C2311yescharacteristic
182C4⋊C8×C61C2314yes—
183#103×C61C2314yes—
184#102×C61C2314yes—
185C24×C61—21no—
186C23×D61—21no—
187C23×D61—21no—
188C23×D61—21no—
189C2×Q8×C61—21no—
190C2×Q8×C61—21no—
191C2×Q8×C61—22no—
192C2×Q8×C61—22no—
193C2×Q8×C61—22no—
194C2×Q8×C61—22no—
195C2×Q8×C61C2412yes—
196C2×Q8×C61C2412yes—
197C2×D4×C61—21no—
198C2×D4×C61—22no—
199C2×D4×C61—22no—
200C2×D4×C61C2412yes—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61C2×D411yescharacteristic
205C22×C4×C61C2×D411yescharacteristic
206C22×C4×C61C2411yescharacteristic
207C2×C22⋊D61—24no—
208C2×C22⋊D61—24no—
209C2×C22⋊D61—44no—
210C2×C22⋊D61—82no—
211C22×Dic61—21no—
212C22×Dic61—24no—
213C22×Dic61—82no—
214C22×Dic61C2×D411yescharacteristic
215C22×Dic61C2×D411yescharacteristic
216C22×Dic61C2×D411yescharacteristic
217C22×Dic61C2×D411yescharacteristic
218C2×D244—22no—
219C2×D244—22no—
220C2×D244—22no—
221C2×D244—22no—
222C2×D244—22no—
223C2×D244—22no—
224C2×D244—24no—
225C2×D244—21no—
226C2×D244—21no—
227C2×D244—21no—
228C2×D244—24no—
229C2×D244—44no—
230C2×D244—82no—
231C2×D244C2412yes—
232C2×D244C2412yes—
233C2×D244C2412yes—
234C2×C4×D61—24no—
235C2×C4×D61—24no—
236C2×C4×D61—24no—
237C2×C4×D61—82no—
238C2×C4×D61—82no—
239C2×C4×D61—82no—
240C2×Dic122—42no—
241C2×Dic122C2×D414yes—
242Q16×C61—44no—
243SD16×C61—44no—
244C2×C8×C61—22no—
245C2×C8×C61—22no—
246C2×C8×C61C2412yes—
247C2×C8×C61C2412yes—
248C4⋊C4×C61—24no—
249C4⋊C4×C61—21no—
250C4⋊C4×C61C2412yes—
251C22⋊C4×C61—24no—
252C22⋊C4×C61—24no—
253C42×C61—24no—
254C42×C61C2×D412yes—
255C42×C61C2412yes—
256C22⋊Dic61—24no—
257#11758201—28no—
258#11758201—28no—
259#11758201—44no—
260#11758199—28no—
261#11758199—44no—
262#11758198—24no—
263#11758198—24no—
264#11758198—24no—
265#11758198—24no—
266#11758198—24no—
267#11758198—24no—
268#11758198—24no—
269#11758198—24no—
270#11758198—24no—
271C4⋊Dic61—21no—
272C4⋊Dic61—24no—
273C4⋊Dic61C2×D414yes—
274C4⋊Dic61C2412yes—
275#11758196C2×D414yes—
276#11758196C2×D414yes—
277C4×Dic61—24no—
278C4×Dic61C2×D412yes—
279C4×Dic61C2×D412yes—
280C4×Dic61C2412yes—
281C4×Dic61C2412yes—
282C2×#92418—22no—
283C2×#92418#4114yes—
284C2×#92418C2412yes—
285C2×#92418C2412yes—
286D488—44no—
287D488—44no—
288C23×C61—22no—
289C23×C61—42no—
290C23×C61—42no—
291C23×C61—42no—
292C23×C61C22×D411yescharacteristic
293C22×D61—22no—
294C22×D61—22no—
295C22×D61—22no—
296C22×D61—42no—
297C22×D61—42no—
298C22×D61—42no—
299C22×D61—42no—
300C22×D61—42no—
301C22×D61—42no—
302C22×D61—42no—
303C22×D61—42no—
304C22×D61—42no—
305Q8×C61—22no—
306Q8×C61—22no—
307Q8×C61—22no—
308Q8×C61—22no—
309Q8×C61—42no—
310Q8×C61—42no—
311D4×C61—22no—
312D4×C61—22no—
313D4×C61—42no—
314C2×C4×C61—22no—
315C2×C4×C61—22no—
316C2×C4×C61—22no—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61—42no—
320C2×C4×C61—42no—
321C2×C4×C61—42no—
322C2×C4×C61C22×D412yes—
323C2×C4×C61C22×D412yes—
324C2×C4×C61C22×D411yescharacteristic
325C2×C4×C61C2×#4112yes—
326C2×C4×C61H(5,𝔽2)12yes—
327C2×C4×C61C2511yescharacteristic
328C22⋊D61—48no—
329C22⋊D61—84no—
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—42no—
336C2×Dic61—84no—
337C2×Dic61C22×D412yes—
338C2×Dic61C22×D412yes—
339C2×Dic61C22×D412yes—
340C2×Dic61C22×D412yes—
341D244—22no—
342D244—22no—
343D244—22no—
344D244—22no—
345D244—22no—
346D244—22no—
347D244—48no—
348D244—42no—
349D244—42no—
350D244—42no—
351D244—84no—
352C4×D61—84no—
353C4×D61—84no—
354C4×D61—84no—
355Dic122—44no—
356C8×C61—22no—
357C8×C61—22no—
358#92418—22no—
359#92418C2×#4114yes—
360C2×#3403—611nomaximal, Sylow
361C22×C61—42no—
362C22×C61—42no—
363C22×C61—42no—
364C22×C61—84no—
365C22×C61#55012yes—
366C22×C61#57512yes—
367C22×C61#57612yes—
368C22×C61C23×D411yescharacteristic
369C2×D61—42no—
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—84no—
379C2×D61—84no—
380C2×D61—84no—
381C4×C61—22no—
382C4×C61—22no—
383C4×C61—42no—
384C4×C61—42no—
385C4×C61—42no—
386C4×C61#55012yes—
387C4×C61C22×#4111yescharacteristic
388C4×C61C2×H(5,𝔽2)11yescharacteristic
389Dic61—22no—
390Dic61—22no—
391Dic61—22no—
392Dic61—22no—
393Dic61—42no—
394C2×#559—611no—
395C2×#559—611no—
396#3403—6116no—
397C2×#496—611no—
398C2×#496—611no—
399C2×#495—611no—
400C2×#464—611no—
401C2×#464D6111yescharacteristic, complemented
402C2×#463—611no—
403C2×#463—611no—
404C2×#459—611no—
405C2×#459—611no—
406C2×#446—611no—
407C2×#440—611no—
408C2×#440—611no—
409C2×C4×D8—611no—
410C2×C61—82no—
411C2×C61#340314yescomplemented
412C2×C61C2×#55011yescharacteristic
413C2×C61C2×#57511yescharacteristic
414C2×C61C2×#57611yescharacteristic
415D61—82no—
416D61—82no—
417D61—82no—
418C22×Q16C2×D6111yescharacteristic
419C22×SD16—611no—
420C22×SD16—611no—
421C22×SD16—611no—
422C22×SD16C2×D6111yescharacteristic
423C22×D8—611no—
424C22×D8—611no—
425C22×D8—611no—
426C22×D8—611no—
427#559—618no—
428#559—618no—
429#559—1224no—
430#559—1224no—
431C2×#127—611no—
432C2×#127—611no—
433C2×#124—611no—
434C2×#124—611no—
435C2×#124—611no—
436C2×#124—1221no—
437C2×#124—1221no—
438C2×#124C2×D6111yescharacteristic
439C2×#123—1221no—
440C2×#123—1221no—
441C2×#123—1221no—
442C2×#123—1221no—
443C2×C4×Q8—611no—
444C2×C4×Q8—611no—
445C2×C4×Q8C2×D6111yescharacteristic
446C2×C4×D4—611no—
447C2×C4×D4—611no—
448C2×C4×D4—611no—
449C2×C4×D4—611no—
450C2×C4×D4—1221no—
451C2×C4×D4—1221no—
452#496—618no—
453#496—618no—
454#495—618no—
455#464—618no—
456#464C2×D6118yescomplemented
457#463—618no—
458#463—618no—
459#459—618no—
460#459—618no—
461#446—618no—
462#440—618no—
463#440—618no—
464C4×D8—618no—
465C2×#107—611no—
466C2×C4⋊C8—611no—
467C2×C4⋊C8—611no—
468C2×C4⋊C8C2×D6111yescharacteristic
469C2×#103—611no—
470C2×#103C2×D6111yescharacteristic
471C2×#102—611no—
472C2×#102—611no—
473C2×#102—611no—
474C2×#102C2×D6111yescharacteristic
475C2×#97—611no—
476C2×#97—611no—
477C2×C4×C8—611no—
478C61C2×#340311yescharacteristic, complemented, Sylow
479C22×Q8—611no—
480C22×Q8C22×D6111yescharacteristic
481C22×Q8C22×D6111yescharacteristic
482C22×D4—611no—
483C22×D4—611no—
484C22×D4—611no—
485C22×D4—1221no—
486C22×D4—1221no—
487C22×D4—1221no—
488C22×D4—1221no—
489C22×D4C22×D6111yescharacteristic
490C23×C4—1221no—
491C23×C4—1221no—
492C23×C4—1221no—
493C23×C4—1221no—
494C2×Q16—42no—
495C2×Q16C22×D6114yes—
496C2×SD16—42no—
497C2×SD16—614no—
498C2×SD16—614no—
499C2×SD16—614no—
500C2×SD16—1224no—
501C2×SD16—1224no—
502C2×SD16—2442no—
503C2×SD16C22×D6114yes—
504C2×D8—614no—
505C2×D8—614no—
506C2×D8—614no—
507C2×D8—614no—
508C2×D8—1224no—
509C2×D8—2442no—
510C2×D8—2442no—
511C2×D8—2442no—
512C22×C8—611no—
513C22×C8—611no—
514C22×C8C22×D6111yescharacteristic
515C22×C8C22×D6111yescharacteristic
516#127—614no—
517#127—614no—
518#127—1222no—
519#127—1222no—
520#124—22no—
521#124—614no—
522#124—614no—
523#124—614no—
524#124—1228no—
525#124—1222no—
526#124—1222no—
527#124—1222no—
528#124—1228no—
529#124C22×D6114yes—
530#123—1228no—
531#123—1228no—
532#123—1228no—
533#123—1228no—
534C4×Q8—22no—
535C4×Q8—614no—
536C4×Q8—614no—
537C4×Q8—614no—
538C4×Q8—1222no—
539C4×Q8C22×D6114yes—
540C4×D4—614no—
541C4×D4—614no—
542C4×D4—614no—
543C4×D4—614no—
544C4×D4—1228no—
545C4×D4—1222no—
546C4×D4—1222no—
547C4×D4—1222no—
548C4×D4—1228no—
549C4×D4—1222no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—611no—
552C2×C4⋊C4—611no—
553C2×C4⋊C4—611no—
554C2×C4⋊C4—611no—
555C2×C4⋊C4—1221no—
556C2×C4⋊C4C22×D6111yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—1221no—
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×C22⋊C4—1221no—
568C2×C22⋊C4—1221no—
569C2×C42—21no—
570C2×C42—611no—
571C2×C42—611no—
572C2×C42—1221no—
573C2×C42C22×D6111yescharacteristic
574#107—614no—
575C4⋊C8—614no—
576C4⋊C8—614no—
577C4⋊C8C22×D6114yes—
578#103—614no—
579#103C22×D6114yes—
580#102—614no—
581#102—614no—
582#102—614no—
583#102C22×D6114yes—
584#97—614no—
585#97—614no—
586C4×C8—614no—
587C24—21no—
588C24—1221no—
589C24—1221no—
590C24—1221no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—22no—
594C2×Q8—22no—
595C2×Q8—22no—
596C2×Q8—22no—
597C2×Q8—614no—
598C2×Q8—2442no—
599C2×Q8C23×D6112yes—
600C2×Q8C23×D6112yes—
601C2×D4—21no—
602C2×D4—22no—
603C2×D4—22no—
604C2×D4—612no—
605C2×D4—612no—
606C2×D4—612no—
607C2×D4—1224no—
608C2×D4—1224no—
609C2×D4—1224no—
610C2×D4—1224no—
611C2×D4—1221no—
612C2×D4—1221no—
613C2×D4—1221no—
614C2×D4—1222no—
615C2×D4—1222no—
616C2×D4—1222no—
617C2×D4—1222no—
618C2×D4—1222no—
619C2×D4—1222no—
620C2×D4—4882no—
621C2×D4—4882no—
622C2×D4—2444no—
623C2×D4—2444no—
624C2×D4C23×D6112yes—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—611no—
629C22×C4—611no—
630C22×C4—611no—
631C22×C4—611no—
632C22×C4—1224no—
633C22×C4—1224no—
634C22×C4—1224no—
635C22×C4—1221no—
636C22×C4—1224no—
637C22×C4—4882no—
638C22×C4—4882no—
639C22×C4—4882no—
640C22×C4—4882no—
641C22×C4D4×D6111yescharacteristic
642C22×C4D4×D6111yescharacteristic
643C22×C4C23×D6111yescharacteristic
644Q16—44no—
645SD16—44no—
646SD16—1228no—
647SD16—1228no—
648SD16—2444no—
649D8—1228no—
650D8—2444no—
651D8—2444no—
652D8—2444no—
653C2×C8—22no—
654C2×C8—22no—
655C2×C8—614no—
656C2×C8—612no—
657C2×C8—612no—
658C2×C8—1222no—
659C2×C8C23×D6112yes—
660C2×C8C23×D6112yes—
661C4⋊C4—24no—
662C4⋊C4—21no—
663C4⋊C4—614no—
664C4⋊C4—614no—
665C4⋊C4—614no—
666C4⋊C4—612no—
667C4⋊C4—1224no—
668C4⋊C4—1221no—
669C4⋊C4C23×D6112yes—
670C22⋊C4—24no—
671C22⋊C4—24no—
672C22⋊C4—1224no—
673C22⋊C4—1224no—
674C22⋊C4—1224no—
675C22⋊C4—1224no—
676C22⋊C4—1224no—
677C22⋊C4—1224no—
678C22⋊C4—1224no—
679C22⋊C4—1224no—
680C22⋊C4—1224no—
681C22⋊C4—1224no—
682C42—24no—
683C42—612no—
684C42—612no—
685C42—612no—
686C42—612no—
687C42—1224no—
688C42D4×D6112yes—
689C42C23×D6112yes—
690C23—22no—
691C23—42no—
692C23—42no—
693C23—42no—
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
707Q8—22no—
708Q8—22no—
709Q8—22no—
710Q8—22no—
711Q8—42no—
712Q8—42no—
713Q8—2444no—
714D4—22no—
715D4—22no—
716D4—42no—
717D4—1222no—
718D4—1222no—
719D4—1222no—
720D4—1222no—
721D4—1222no—
722D4—1222no—
723D4—4884no—
724D4—4884no—
725D4—2448no—
726D4—2448no—
727D4—2442no—
728D4—2442no—
729D4—2442no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—612no—
739C2×C4—612no—
740C2×C4—612no—
741C2×C4—612no—
742C2×C4—1222no—
743C2×C4—1222no—
744C2×C4—1222no—
745C2×C4—1222no—
746C2×C4—1222no—
747C2×C4—4884no—
748C2×C4—4884no—
749C2×C4—4884no—
750C2×C4—4884no—
751C2×C4—2442no—
752C2×C4C2×D4×D6112yes—
753C2×C4C2×D4×D6112yes—
754C2×C4C2×D4×D6111yescharacteristic
755C2×C4#41×D6112yes—
756C2×C4#1451982212yes—
757C2×C4C24×D6111yescharacteristic
758C8—22no—
759C8—22no—
760C8—614no—
761C8—1222no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—84no—
766C22—4884no—
767C22—4884no—
768C22—4884no—
769C22—2442no—
770C22—2442no—
771C22—2442no—
772C22—2442no—
773C22—2442no—
774C22—2442no—
775C22—2442no—
776C22—2442no—
777C22—2442no—
778C22#1684043012yes—
779C22#1684056112yes—
780C22#1684056412yes—
781C22C22×D4×D6111yescharacteristic
782C4—22no—
783C4—22no—
784C4—42no—
785C4—42no—
786C4—42no—
787C4—1222no—
788C4—1222no—
789C4—1222no—
790C4—1222no—
791C4—2442no—
792C4#1684043012yes—
793C4C2×#41×D6111yescharacteristic
794C4C2×#1451982211yescharacteristic
795C2—82no—
796C2—4882no—
797C2—4882no—
798C2—4882no—
799C2#2145890614yesdirect product factor
800C2C2×#1684043011yescharacteristic
801C2C2×#1684056111yescharacteristic
802C2C2×#1684056411yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#464C2
socleC23×C61C22×D4
hypercenterC2×#464D61
hypocenterC61C2×#3403
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
1. C2×#16840497C2semidirect
2. C2×#16840494C2semidirect
3. #21458906C2direct (N × H)
4. C2×#16840152C2semidirect
5. C2×#16840148C2semidirect
6. C2×#16840147C2semidirect
7. C2×#16839986C2semidirect
8. C2×#16839980C2semidirect
9. C2×#16839979C2semidirect
10. C2×#16839958C2semidirect
11. C2×#16839956C2semidirect
12. C2×#16839891C2semidirect
13. C2×#16839865C2semidirect
14. C2×#16839860C2semidirect
15. C2×#16839842C2semidirect
16. C2×C61×#464C2semidirect
25. #16840497C22semidirect
27. #16840494C22semidirect
47. #16840152C22semidirect
48. #16840148C22semidirect
49. #16840147C22semidirect
50. #16839986C22semidirect
51. #16839980C22semidirect
52. #16839979C22semidirect
53. #16839958C22semidirect
54. #16839956C22semidirect
55. #16839891C22semidirect
56. #16839865C22semidirect
57. #16839860C22semidirect
58. #16839842C22semidirect
73. C61×#464C22semidirect
401. C2×#464D61semidirect
411. C2×C61#3403semidirect
456. #464C2×D61semidirect
478. C61C2×#3403semidirect
799. C2#21458906direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404972
C2×#168404942
#214589062
C2×#168401522
C2×#168401482
C2×#168401472
C2×#168399862
C2×#168399802
C2×#168399792
C2×#168399582
C2×#168399562
C2×#168398912
C2×#168398652
C2×#168398602
C2×#168398422
C2×C61×#4642
C2×#340361