Finite Group Databasebeta

← C2×#21458826 #30560944

Subgroups — C2×#21458826 #30560944

Order 15616.

2086 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×#16840495C211yesmaximal, characteristic, complemented
2C2×#16840494C211yesmaximal, characteristic, complemented
3#21458826C2116yesmaximal, direct product factor
4C2×#16840144C211yesmaximal, characteristic, complemented
5C2×#16840143C211yesmaximal, characteristic, complemented
6C2×#16840137C211yesmaximal, characteristic
7C2×#16839961C211yesmaximal, characteristic, complemented
8C2×#16839960C211yesmaximal, characteristic, complemented
9C2×#16839980C211yesmaximal, characteristic, complemented
10C2×#16839978C211yesmaximal, characteristic, complemented
11C2×#16839975C211yesmaximal, characteristic, complemented
12C2×#16839886C211yesmaximal, characteristic, complemented
13C2×#16839854C211yesmaximal, characteristic, complemented
14C2×C4×#11758199C211yesmaximal, characteristic, complemented
15C2×#16839842C211yesmaximal, characteristic, complemented
16C2×C61×#463C211yesmaximal, characteristic, complemented
17C22×#11758202C2211yescharacteristic
18C22×#11758190C2211yescharacteristic
19C22×#11758200C2211yescharacteristic
20C22×#11758201C2211yescharacteristic
21C22×D488C2211yescharacteristic
22C22×#11758199C2211yescharacteristic
23C22×#11758199C2211yescharacteristic
24#16840495—24no—
25#16840495C2218yescomplemented
26#16840494—24no—
27#16840494C2218yescomplemented
28C2×#14519773C2211yescharacteristic
29C2×#14519773C2211yescharacteristic
30C2×#14519766C2211yescharacteristic
31C2×#14519765C2211yescharacteristic
32C2×#14519764C2211yescharacteristic
33C2×#14519763—21no—
34C2×#14519763—21no—
35C2×#14519761—21no—
36C2×#14519760—21no—
37C2×#14519759—21no—
38C2×#14519759—21no—
39C2×Q8×Dic61C2211yescharacteristic
40C2×C4×Dic122C2211yescharacteristic
41C2×#14519742C2211yescharacteristic
42C2×C4×D244C2211yescharacteristic
43C2×D4×Dic61C2211yescharacteristic
44C2×#14519739C2211yescharacteristic
45C2×C4×C22⋊D61—21no—
46C2×#14519737—21no—
47#16840144C2218yescomplemented
48#16840143C2218yescomplemented
49#16840137C2218yes—
50#16839980C2218yescomplemented
51#16839978C2218yescomplemented
52#16839975C2218yescomplemented
53#16839961C2218yescomplemented
54#16839960C2218yescomplemented
55#16839886C2218yescomplemented
56#16839854C2218yescomplemented
57C4×#11758199C2218yescomplemented
58#16839842C2218yescomplemented
59C2×#14519710C2211yescharacteristic
60C2×#14519706C2211yescharacteristic
61C2×#14519706C2211yescharacteristic
62C2×#14519702C2211yescharacteristic
63C2×#14519699C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×C4×#92418C2211yescharacteristic
67C2×C8×Dic61C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C22×SD16×C61C2211yescharacteristic
70C22×D8×C61C2211yescharacteristic
71C2×#124×C61C2211yescharacteristic
72C2×C4×D4×C61C2211yescharacteristic
73C61×#463C2218yescomplemented
74C2×C4⋊C8×C61C2211yescharacteristic
75C2×#103×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C22×Dic122D411yescharacteristic
78C22×Dic122C2311yescharacteristic
79C22×D244C2311yescharacteristic
80C22×D244C2311yescharacteristic
81C22×C22⋊D61—21no—
82C22×C22⋊D61—21no—
83C22×C22⋊D61—21no—
84C22×C22⋊D61—21no—
85C23×Dic61—21no—
86C22×C4×D61—21no—
87C22×C4×D61—21no—
88C2×#11758202—24no—
89C2×#11758202C2314yes—
90C2×#11758190—42no—
91C2×#11758190C2314yes—
92C2×#11758200—42no—
93C2×#11758200C2314yes—
94C2×#11758201—42no—
95C2×#11758201C2314yes—
96C2×D488—42no—
97C2×D488C2314yes—
98C2×#11758199—24no—
99C2×#11758199—24no—
100C2×#11758199C2314yes—
101C2×#11758199C2314yes—
102C22×#92418C2311yescharacteristic
103C22×#92418C2311yescharacteristic
104#14519773—22no—
105#14519773—22no—
106#14519773C2314yes—
107#14519773C2314yes—
108#14519766—22no—
109#14519766C2314yes—
110#14519765—22no—
111#14519765C2314yes—
112#14519764—22no—
113#14519764C2314yes—
114#14519763—28no—
115#14519763—28no—
116#14519761—28no—
117#14519760—28no—
118#14519759—28no—
119#14519759—28no—
120Q8×Dic61—22no—
121Q8×Dic61C2314yes—
122C4×Dic122D414yes—
123C4×Dic122C2314yes—
124#14519742—22no—
125#14519742C2314yes—
126C4×D244—22no—
127C4×D244C2314yes—
128D4×Dic61—22no—
129D4×Dic61C2314yes—
130#14519739—22no—
131#14519739C2314yes—
132C4×C22⋊D61—28no—
133#14519737—28no—
134C2×C4⋊Dic61—21no—
135C2×C4⋊Dic61D411yescharacteristic
136C2×C4⋊Dic61C2311yescharacteristic
137C2×#11758196—21no—
138C2×#11758196D411yescharacteristic
139C2×#11758196D411yescharacteristic
140C2×C22⋊Dic61—21no—
141C2×C22⋊Dic61—21no—
142C2×C22⋊Dic61—21no—
143C2×#11758198—21no—
144C2×#11758198—21no—
145C2×#11758198—21no—
146C2×#11758198—21no—
147C2×#11758198—21no—
148C2×#11758198—21no—
149C2×C4×Dic61—21no—
150C2×C4×Dic61—21no—
151C2×C4×Dic61C2311yescharacteristic
152C2×C4×Dic61C2311yescharacteristic
153#14519710C2314yes—
154#14519706C2314yes—
155#14519706C2314yes—
156#14519702C2314yes—
157#14519699C2314yes—
158#14519698C2314yes—
159#14519697C2314yes—
160C4×#92418C2314yes—
161C8×Dic61C2314yes—
162C8×Dic61C2314yes—
163C22×Q8×C61C2311yescharacteristic
164C22×D4×C61C2311yescharacteristic
165C22×D4×C61C2311yescharacteristic
166C23×C4×C61—21no—
167C2×SD16×C61—42no—
168C2×SD16×C61C2314yes—
169C2×D8×C61—42no—
170C2×D8×C61C2314yes—
171C22×C8×C61C2311yescharacteristic
172C22×C8×C61C2311yescharacteristic
173#124×C61—22no—
174#124×C61C2314yes—
175C4×D4×C61—22no—
176C4×D4×C61C2314yes—
177C2×C4⋊C4×C61C2311yescharacteristic
178C2×C22⋊C4×C61—21no—
179C2×C22⋊C4×C61—21no—
180C2×C22⋊C4×C61—21no—
181C2×C42×C61C2311yescharacteristic
182C4⋊C8×C61C2314yes—
183#103×C61C2314yes—
184#102×C61C2314yes—
185C24×C61—21no—
186C24×C61—21no—
187C23×D61—21no—
188C23×D61—21no—
189C2×Q8×C61—21no—
190C2×Q8×C61—22no—
191C2×Q8×C61—22no—
192C2×Q8×C61C2412yes—
193C2×D4×C61—21no—
194C2×D4×C61—21no—
195C2×D4×C61—22no—
196C2×D4×C61—22no—
197C2×D4×C61—22no—
198C2×D4×C61—22no—
199C2×D4×C61C2412yes—
200C2×D4×C61C2412yes—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—24no—
204C22×C4×C61—82no—
205C22×C4×C61C2×D411yescharacteristic
206C22×C4×C61C2×D411yescharacteristic
207C22×C4×C61C2411yescharacteristic
208C2×C22⋊D61—24no—
209C2×C22⋊D61—24no—
210C2×C22⋊D61—24no—
211C2×C22⋊D61—24no—
212C2×C22⋊D61—44no—
213C2×C22⋊D61—44no—
214C2×C22⋊D61—82no—
215C2×C22⋊D61—82no—
216C22×Dic61—21no—
217C22×Dic61—21no—
218C22×Dic61—24no—
219C22×Dic61—82no—
220C22×Dic61C2×D411yescharacteristic
221C22×Dic61C2×D411yescharacteristic
222C22×Dic61C2×D411yescharacteristic
223C22×Dic61C2×D411yescharacteristic
224C2×D244—22no—
225C2×D244—22no—
226C2×D244—22no—
227C2×D244—22no—
228C2×D244—21no—
229C2×D244—21no—
230C2×D244C2412yes—
231C2×D244C2412yes—
232C2×C4×D61—24no—
233C2×C4×D61—24no—
234C2×C4×D61—82no—
235C2×C4×D61—82no—
236C2×Dic122—24no—
237C2×Dic122—22no—
238C2×Dic122—22no—
239C2×Dic122—21no—
240C2×Dic122C2×D414yes—
241C2×Dic122C2412yes—
242SD16×C61—44no—
243D8×C61—44no—
244C2×C8×C61—22no—
245C2×C8×C61—22no—
246C2×C8×C61C2412yes—
247C2×C8×C61C2412yes—
248C4⋊C4×C61—21no—
249C4⋊C4×C61C2412yes—
250C22⋊C4×C61—24no—
251C22⋊C4×C61—24no—
252C22⋊C4×C61—24no—
253C42×C61C2×D412yes—
254C42×C61C2412yes—
255C22⋊Dic61—24no—
256C22⋊Dic61—24no—
257C22⋊Dic61—24no—
258#11758202—28no—
259#11758201—44no—
260#11758200—44no—
261#11758199—28no—
262#11758199—28no—
263#11758198—24no—
264#11758198—24no—
265#11758198—24no—
266#11758198—24no—
267#11758198—24no—
268#11758198—24no—
269C4⋊Dic61—21no—
270C4⋊Dic61—24no—
271C4⋊Dic61C2×D414yes—
272C4⋊Dic61C2412yes—
273#11758196—24no—
274#11758196C2×D414yes—
275#11758196C2×D414yes—
276C4×Dic61—24no—
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—
287#11758190—44no—
288C23×C61—22no—
289C23×C61—22no—
290C23×C61—42no—
291C23×C61—42no—
292C23×C61—42no—
293C23×C61—42no—
294C23×C61—42no—
295C23×C61—42no—
296C23×C61C22×D411yescharacteristic
297C22×D61—22no—
298C22×D61—22no—
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—42no—
308D4×C61—22no—
309D4×C61—22no—
310D4×C61—22no—
311D4×C61—22no—
312D4×C61—42no—
313D4×C61—42no—
314C2×C4×C61—22no—
315C2×C4×C61—22no—
316C2×C4×C61—22no—
317C2×C4×C61—22no—
318C2×C4×C61—42no—
319C2×C4×C61—42no—
320C2×C4×C61—84no—
321C2×C4×C61C22×D412yes—
322C2×C4×C61C22×D412yes—
323C2×C4×C61C22×D411yescharacteristic
324C2×C4×C61C2×#4112yes—
325C2×C4×C61H(5,𝔽2)12yes—
326C2×C4×C61C2511yescharacteristic
327C22⋊D61—48no—
328C22⋊D61—48no—
329C22⋊D61—84no—
330C22⋊D61—84no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—42no—
337C2×Dic61—42no—
338C2×Dic61—84no—
339C2×Dic61#13514yes—
340C2×Dic61C22×D412yes—
341C2×Dic61C22×D412yes—
342C2×Dic61C22×D412yes—
343C2×Dic61C22×D412yes—
344D244—22no—
345D244—22no—
346D244—22no—
347D244—22no—
348D244—42no—
349D244—42no—
350C4×D61—84no—
351C4×D61—84no—
352Dic122—28no—
353Dic122—22no—
354Dic122—22no—
355Dic122—42no—
356C8×C61—22no—
357C8×C61—22no—
358#92418—22no—
359#92418C2×#4114yes—
360C2×#3396—611nomaximal, Sylow
361C22×C61—42no—
362C22×C61—42no—
363C22×C61—42no—
364C22×C61—42no—
365C22×C61—42no—
366C22×C61—42no—
367C22×C61—84no—
368C22×C61—84no—
369C22×C61#55012yes—
370C22×C61C2×#13512yes—
371C22×C61#57612yes—
372C22×C61C23×D411yescharacteristic
373C2×D61—42no—
374C2×D61—42no—
375C2×D61—42no—
376C2×D61—42no—
377C2×D61—42no—
378C2×D61—42no—
379C2×D61—84no—
380C2×D61—84no—
381C4×C61—22no—
382C4×C61—22no—
383C4×C61—42no—
384C4×C61—42no—
385C4×C61#55012yes—
386C4×C61C22×#4111yescharacteristic
387C4×C61C2×H(5,𝔽2)11yescharacteristic
388Dic61—22no—
389Dic61—22no—
390Dic61—22no—
391Dic61—42no—
392Dic61—42no—
393Dic61C2×#13514yes—
394C2×#559—611no—
395C2×#559—611no—
396#3396—6116no—
397C2×#495—611no—
398C2×#495—611no—
399C2×#493—611no—
400C2×#460—611no—
401C2×#460—611no—
402C2×#463—611no—
403C2×#463—611no—
404C2×#463—611no—
405C2×#463D6111yescharacteristic, complemented
406C2×C8×Q8—611no—
407C2×C4×Q16—611no—
408C2×C4×D8—611no—
409C2×C4×D8—611no—
410C2×C61—82no—
411C2×C61—82no—
412C2×C61#339614yescomplemented
413C2×C61C2×#55011yescharacteristic
414C2×C61C22×#13511yescharacteristic
415C2×C61C2×#57611yescharacteristic
416D61—82no—
417D61—82no—
418C22×Q16—611no—
419C22×SD16—611no—
420C22×SD16—611no—
421C22×SD16—611no—
422C22×SD16C2×D6111yescharacteristic
423C22×D8—611no—
424C22×D8—611no—
425C22×D8—611no—
426C22×D8C2×D6111yescharacteristic
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×Q8—611no—
446C2×C4×D4—611no—
447C2×C4×D4—611no—
448C2×C4×D4—611no—
449C2×C4×D4—1221no—
450C2×C4×D4—1221no—
451C2×C4×D4C2×D6111yescharacteristic
452#495—618no—
453#495—618no—
454#493—618no—
455#463—618no—
456#463—618no—
457#463—618no—
458#463C2×D6118yescomplemented
459#460—618no—
460#460—618no—
461C8×Q8—618no—
462C4×Q16—618no—
463C4×D8—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×C4×C8—611no—
476C2×C4×C8—611no—
477C2×C4×C8—611no—
478C61C2×#339611yescharacteristic, complemented, Sylow
479C22×Q8—611no—
480C22×Q8—611no—
481C22×Q8C22×D6111yescharacteristic
482C22×D4—611no—
483C22×D4—611no—
484C22×D4—1221no—
485C22×D4—1221no—
486C22×D4—1221no—
487C22×D4—1221no—
488C22×D4C22×D6111yescharacteristic
489C22×D4C22×D6111yescharacteristic
490C23×C4—21no—
491C23×C4—1221no—
492C23×C4—1221no—
493C23×C4—1221no—
494C2×Q16—614no—
495C2×Q16—1224no—
496C2×SD16—42no—
497C2×SD16—614no—
498C2×SD16—614no—
499C2×SD16—614no—
500C2×SD16—2442no—
501C2×SD16—2442no—
502C2×SD16—2442no—
503C2×SD16C22×D6114yes—
504C2×D8—42no—
505C2×D8—614no—
506C2×D8—614no—
507C2×D8—614no—
508C2×D8—1224no—
509C2×D8—1224no—
510C2×D8—2442no—
511C2×D8C22×D6114yes—
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—1222no—
525#124—1222no—
526#124—1228no—
527#124—1228no—
528#124—1222no—
529#124C22×D6114yes—
530#123—1228no—
531#123—1228no—
532#123—1228no—
533#123—1228no—
534C4×Q8—614no—
535C4×Q8—614no—
536C4×Q8—614no—
537C4×Q8—614no—
538C4×Q8—1222no—
539C4×Q8—1222no—
540C4×D4—22no—
541C4×D4—614no—
542C4×D4—614no—
543C4×D4—614no—
544C4×D4—1222no—
545C4×D4—1222no—
546C4×D4—1228no—
547C4×D4—1228no—
548C4×D4—1222no—
549C4×D4C22×D6114yes—
550C2×C4⋊C4—611no—
551C2×C4⋊C4—611no—
552C2×C4⋊C4—611no—
553C2×C4⋊C4—611no—
554C2×C4⋊C4—1221no—
555C2×C4⋊C4—1221no—
556C2×C4⋊C4C22×D6111yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
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—611no—
570C2×C42—611no—
571C2×C42—1221no—
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—
584C4×C8—614no—
585C4×C8—614no—
586C4×C8—614no—
587C24—21no—
588C24—21no—
589C24—1221no—
590C24—1221no—
591C2×Q8—21no—
592C2×Q8—22no—
593C2×Q8—22no—
594C2×Q8—614no—
595C2×Q8—612no—
596C2×Q8—1224no—
597C2×Q8—1221no—
598C2×Q8—1222no—
599C2×Q8—1222no—
600C2×Q8C23×D6112yes—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—612no—
608C2×D4—612no—
609C2×D4—1224no—
610C2×D4—1224no—
611C2×D4—1224no—
612C2×D4—1224no—
613C2×D4—1221no—
614C2×D4—1221no—
615C2×D4—1222no—
616C2×D4—1222no—
617C2×D4—1222no—
618C2×D4—1222no—
619C2×D4—4882no—
620C2×D4—4882no—
621C2×D4—2444no—
622C2×D4—2444no—
623C2×D4C23×D6112yes—
624C2×D4C23×D6112yes—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—24no—
628C22×C4—82no—
629C22×C4—611no—
630C22×C4—611no—
631C22×C4—611no—
632C22×C4—611no—
633C22×C4—1224no—
634C22×C4—1224no—
635C22×C4—1221no—
636C22×C4—1221no—
637C22×C4—1224no—
638C22×C4—4882no—
639C22×C4—4882no—
640C22×C4—4882no—
641C22×C4D4×D6111yescharacteristic
642C22×C4D4×D6111yescharacteristic
643C22×C4C23×D6111yescharacteristic
644Q16—1228no—
645SD16—44no—
646SD16—2444no—
647SD16—2444no—
648SD16—2444no—
649D8—44no—
650D8—1228no—
651D8—1228no—
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—21no—
662C4⋊C4—614no—
663C4⋊C4—614no—
664C4⋊C4—614no—
665C4⋊C4—612no—
666C4⋊C4—1224no—
667C4⋊C4—1224no—
668C4⋊C4—1221no—
669C4⋊C4C23×D6112yes—
670C22⋊C4—24no—
671C22⋊C4—24no—
672C22⋊C4—24no—
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—612no—
683C42—612no—
684C42—612no—
685C42—612no—
686C42—1224no—
687C42—1224no—
688C42D4×D6112yes—
689C42C23×D6112yes—
690C23—22no—
691C23—22no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—1222no—
699C23—1222no—
700C23—2442no—
701C23—2442no—
702C23—2442no—
703C23—2442no—
704C23—2442no—
705C23—2442no—
706C23C2×D4×D6111yescharacteristic
707Q8—22no—
708Q8—22no—
709Q8—42no—
710Q8—1228no—
711Q8—1222no—
712Q8—1222no—
713Q8—2442no—
714D4—22no—
715D4—22no—
716D4—22no—
717D4—22no—
718D4—42no—
719D4—42no—
720D4—1222no—
721D4—1222no—
722D4—1222no—
723D4—1222no—
724D4—4884no—
725D4—4884no—
726D4—2448no—
727D4—2448no—
728D4—2442no—
729D4—2442no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—84no—
737C2×C4—614no—
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—2442no—
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—42no—
766C22—42no—
767C22—42no—
768C22—84no—
769C22—84no—
770C22—4884no—
771C22—4884no—
772C22—2442no—
773C22—2442no—
774C22—2442no—
775C22—2442no—
776C22—2442no—
777C22—2442no—
778C22#1684043012yes—
779C22#135×D6112yes—
780C22#1684056612yes—
781C22C22×D4×D6111yescharacteristic
782C4—22no—
783C4—22no—
784C4—42no—
785C4—42no—
786C4—614no—
787C4—1222no—
788C4—1222no—
789C4—1222no—
790C4—2442no—
791C4—2442no—
792C4#1684043012yes—
793C4C2×#41×D6111yescharacteristic
794C4C2×#1451982211yescharacteristic
795C2—82no—
796C2—82no—
797C2—4882no—
798C2—4882no—
799C2#2145882614yesdirect product factor
800C2C2×#1684043011yescharacteristic
801C2C2×#135×D6111yescharacteristic
802C2C2×#1684056611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#463C2
socleC23×C61C22×D4
prime radicalC2×#16840137C2
hypercenterC2×#463D61
hypocenterC61C2×#3396
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C2×#16840495C2semidirect
2. C2×#16840494C2semidirect
3. #21458826C2direct (N × H)
4. C2×#16840144C2semidirect
5. C2×#16840143C2semidirect
7. C2×#16839961C2semidirect
8. C2×#16839960C2semidirect
9. C2×#16839980C2semidirect
10. C2×#16839978C2semidirect
11. C2×#16839975C2semidirect
12. C2×#16839886C2semidirect
13. C2×#16839854C2semidirect
14. C2×C4×#11758199C2semidirect
15. C2×#16839842C2semidirect
16. C2×C61×#463C2semidirect
25. #16840495C22semidirect
27. #16840494C22semidirect
47. #16840144C22semidirect
48. #16840143C22semidirect
50. #16839980C22semidirect
51. #16839978C22semidirect
52. #16839975C22semidirect
53. #16839961C22semidirect
54. #16839960C22semidirect
55. #16839886C22semidirect
56. #16839854C22semidirect
57. C4×#11758199C22semidirect
58. #16839842C22semidirect
73. C61×#463C22semidirect
405. C2×#463D61semidirect
412. C2×C61#3396semidirect
458. #463C2×D61semidirect
478. C61C2×#3396semidirect
799. C2#21458826direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404952
C2×#168404942
#214588262
C2×#168401442
C2×#168401432
C2×#168401372
C2×#168399612
C2×#168399602
C2×#168399802
C2×#168399782
C2×#168399752
C2×#168398862
C2×#168398542
C2×C4×#117581992
C2×#168398422
C2×C61×#4632
C2×#339661