Finite Group Databasebeta

← C2×#21455874 #30548069

Subgroups — C2×#21455874 #30548069

Order 15616.

2450 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×#16840307C211yesmaximal, characteristic, complemented
2C2×#16840230C211yesmaximal, characteristic, complemented
3#21455874C2116yesmaximal, direct product factor
4C2×#16840086C211yesmaximal, characteristic, complemented
5C2×#16840056C211yesmaximal, characteristic, complemented
6C2×#16840051C211yesmaximal, characteristic, complemented
7C2×#16839961C211yesmaximal, characteristic, complemented
8C2×#16839956C211yesmaximal, characteristic, complemented
9C2×#16839909C211yesmaximal, characteristic, complemented
10C2×#16839905C211yesmaximal, characteristic, complemented
11C2×#16839853C211yesmaximal, characteristic, complemented
12C2×#16839849C211yesmaximal, characteristic, complemented
13C2×#16839844C211yesmaximal, characteristic, complemented
14C2×#16839842C211yesmaximal, characteristic, complemented
15C2×#16839812C211yesmaximal, characteristic, complemented
16C2×C61×#482C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C22×#11758224—21no—
19C22×#11758190C2211yescharacteristic
20C22×#11758200C2211yescharacteristic
21C22×D488C2211yescharacteristic
22C22×#11758199C2211yescharacteristic
23#16840307—24no—
24#16840307C2218yescomplemented
25C2×#14519776C2211yescharacteristic
26C2×#14519773C2211yescharacteristic
27C2×#14519763—21no—
28C2×#14519751C2211yescharacteristic
29C2×#14519749—21no—
30#16840230—24no—
31#16840230C2218yescomplemented
32C2×#14519742C2211yescharacteristic
33C2×#14519742C2211yescharacteristic
34C2×D4×Dic61C2211yescharacteristic
35C2×#14519739C2211yescharacteristic
36C2×#14519739C2211yescharacteristic
37C2×#14519739C2211yescharacteristic
38C2×#14519737—21no—
39C2×#14519737—21no—
40C2×#14519737—21no—
41C2×#14519734—21no—
42C22×C4×Dic61C2211yescharacteristic
43C2×C42×D61—21no—
44#16840086C2218yescomplemented
45#16840056C2218yescomplemented
46#16840051C2218yescomplemented
47#16839961C2218yescomplemented
48#16839956C2218yescomplemented
49#16839909C2218yescomplemented
50#16839905C2218yescomplemented
51#16839853C2218yescomplemented
52#16839849C2218yescomplemented
53#16839844C2218yescomplemented
54#16839842C2218yescomplemented
55#16839812C2218yescomplemented
56C2×#14519710C2211yescharacteristic
57C2×#14519708C2211yescharacteristic
58C2×#14519706C2211yescharacteristic
59C2×#14519706C2211yescharacteristic
60C2×#14519702C2211yescharacteristic
61C2×#14519700C2211yescharacteristic
62C2×#14519699C2211yescharacteristic
63C2×#14519697C2211yescharacteristic
64C2×#14519697C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×C22⋊#92418C2211yescharacteristic
67C2×C8×Dic61C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C2×#121×C61C2211yescharacteristic
70C2×#117×C61C2211yescharacteristic
71C61×#482C2218yescomplemented
72C2×#107×C61C2211yescharacteristic
73C2×#106×C61C2211yescharacteristic
74C2×#102×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×C22⋊C8×C61C2211yescharacteristic
77C2×#11758222—22no—
78C2×#11758222—24no—
79C2×#11758222—24no—
80C2×#11758222C2314yes—
81C2×#11758224—28no—
82C2×#11758224—48no—
83C22×Dic122—21no—
84C22×Dic122C2311yescharacteristic
85C22×D244C2311yescharacteristic
86C22×D244C2311yescharacteristic
87C22×C22⋊D61—21no—
88C22×C22⋊D61—21no—
89C22×C22⋊D61—21no—
90C22×C22⋊D61—21no—
91C23×Dic61—21no—
92C23×Dic61D411yescharacteristic
93C23×Dic61D411yescharacteristic
94C22×C4×D61—21no—
95C22×C4×D61—21no—
96C22×C4×D61—21no—
97C22×C4×D61—21no—
98C2×#11758190—24no—
99C2×#11758190C2314yes—
100C2×#11758200—24no—
101C2×#11758200C2314yes—
102C2×D488—24no—
103C2×D488C2314yes—
104C2×#11758199—24no—
105C2×#11758199C2314yes—
106C22×#92418C2311yescharacteristic
107C22×#92418C2311yescharacteristic
108#14519776—22no—
109#14519776C2314yes—
110#14519773—22no—
111#14519773C2314yes—
112#14519763—28no—
113#14519751—22no—
114#14519751C2314yes—
115#14519749—28no—
116#14519742—22no—
117#14519742—22no—
118#14519742C2314yes—
119#14519742C2314yes—
120D4×Dic61—22no—
121D4×Dic61C2314yes—
122#14519739—22no—
123#14519739—22no—
124#14519739—22no—
125#14519739C2314yes—
126#14519739C2314yes—
127#14519739C2314yes—
128#14519737—28no—
129#14519737—28no—
130#14519737—28no—
131#14519734—28no—
132C2×C4⋊Dic61C2311yescharacteristic
133C2×#11758196—21no—
134C2×#11758196—21no—
135C2×#11758196—21no—
136C2×C22⋊Dic61—21no—
137C2×#11758198—21no—
138C2×#11758198—21no—
139C2×#11758198—21no—
140C2×#11758198—21no—
141C2×C4×Dic61—21no—
142C2×C4×Dic61—21no—
143C2×C4×Dic61D411yescharacteristic
144C2×C4×Dic61D411yescharacteristic
145C2×C4×Dic61D414yes—
146C2×C4×Dic61C2311yescharacteristic
147C2×C4×Dic61C2311yescharacteristic
148C2×C4×Dic61C2314yes—
149C42×D61—28no—
150#14519710C2314yes—
151#14519708C2314yes—
152#14519706C2314yes—
153#14519706C2314yes—
154#14519702C2314yes—
155#14519700C2314yes—
156#14519699C2314yes—
157#14519697C2314yes—
158#14519697C2314yes—
159#14519697C2314yes—
160C22⋊#92418C2314yes—
161C8×Dic61C2314yes—
162C8×Dic61C2314yes—
163C22×D4×C61—21no—
164C22×D4×C61C2311yescharacteristic
165C23×C4×C61C2311yescharacteristic
166C22×C8×C61C2311yescharacteristic
167C22×C8×C61C2311yescharacteristic
168#121×C61—22no—
169#121×C61C2314yes—
170#117×C61—22no—
171#117×C61C2314yes—
172C2×C4⋊C4×C61C2311yescharacteristic
173C2×C4⋊C4×C61C2311yescharacteristic
174C2×C4⋊C4×C61C2311yescharacteristic
175C2×C22⋊C4×C61—21no—
176C2×C22⋊C4×C61—21no—
177C2×C42×C61—21no—
178#107×C61C2314yes—
179#106×C61C2314yes—
180#102×C61C2314yes—
181#102×C61C2314yes—
182C22⋊C8×C61C2314yes—
183C24×C61—21no—
184C24×C61C2×D411yescharacteristic
185C23×D61—21no—
186C23×D61—21no—
187C2×D4×C61—24no—
188C2×D4×C61—21no—
189C2×D4×C61—22no—
190C2×D4×C61—22no—
191C2×D4×C61—44no—
192C2×D4×C61C2412yes—
193C22×C4×C61—22no—
194C22×C4×C61—22no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61C2×D411yescharacteristic
199C22×C4×C61C2×D412yes—
200C22×C4×C61C2412yes—
201C22×C4×C61C2411yescharacteristic
202C2×C22⋊D61—28no—
203C2×C22⋊D61—24no—
204C2×C22⋊D61—24no—
205C2×C22⋊D61—24no—
206C2×C22⋊D61—24no—
207C2×C22⋊D61—44no—
208C2×C22⋊D61—44no—
209C2×C22⋊D61—44no—
210C22×Dic61—21no—
211C22×Dic61—24no—
212C22×Dic61—24no—
213C22×Dic61—21no—
214C22×Dic61—24no—
215C22×Dic61—44no—
216C22×Dic61C2×D411yescharacteristic
217C22×Dic61C2×D414yes—
218C22×Dic61C2×D411yescharacteristic
219C22×Dic61C2×D414yes—
220C22×Dic61C2×D411yescharacteristic
221C22×Dic61C2×D411yescharacteristic
222#11758224—432no—
223#11758222—216no—
224#11758222—28no—
225#11758222—28no—
226C2×D244—21no—
227C2×D244—22no—
228C2×D244—22no—
229C2×D244—22no—
230C2×D244—21no—
231C2×D244#4114yescomplemented
232C2×D244C2412yes—
233C2×D244C2412yes—
234C2×C4×D61—28no—
235C2×C4×D61—24no—
236C2×C4×D61—24no—
237C2×C4×D61—24no—
238C2×C4×D61—24no—
239C2×C4×D61—44no—
240C2×C4×D61—44no—
241C2×C4×D61—44no—
242C2×Dic122—21no—
243C2×Dic122—22no—
244C2×Dic122—24no—
245C2×Dic122—44no—
246C2×Dic122#4114yescomplemented
247C2×Dic122C2412yes—
248C2×C8×C61—22no—
249C2×C8×C61—22no—
250C2×C8×C61C2412yes—
251C2×C8×C61C2412yes—
252C4⋊C4×C61—21no—
253C4⋊C4×C61—21no—
254C4⋊C4×C61—21no—
255C4⋊C4×C61C2412yes—
256C4⋊C4×C61C2412yes—
257C4⋊C4×C61C2412yes—
258C22⋊C4×C61—24no—
259C22⋊C4×C61—24no—
260C42×C61—24no—
261C22⋊Dic61—24no—
262#11758200—28no—
263#11758199—28no—
264#11758198—24no—
265#11758198—24no—
266#11758198—24no—
267#11758198—24no—
268C4⋊Dic61—21no—
269C4⋊Dic61C2412yes—
270#11758196—24no—
271#11758196—24no—
272#11758196—24no—
273C4×Dic61—24no—
274C4×Dic61—24no—
275C4×Dic61C2×D414yes—
276C4×Dic61C2×D414yes—
277C4×Dic61C2×D412yes—
278C4×Dic61C2×D412yes—
279C4×Dic61C2412yes—
280C4×Dic61C2412yes—
281C2×#92418—22no—
282C2×#92418—22no—
283C2×#92418C2412yes—
284C2×#92418C2412yes—
285D488—28no—
286#11758190—28no—
287C23×C61—22no—
288C23×C61—22no—
289C23×C61—22no—
290C23×C61—22no—
291C23×C61—42no—
292C23×C61—42no—
293C23×C61—42no—
294C23×C61C22×D412yes—
295C23×C61C22×D411yescharacteristic
296C22×D61—24no—
297C22×D61—22no—
298C22×D61—22no—
299C22×D61—42no—
300C22×D61—42no—
301C22×D61—42no—
302C22×D61—42no—
303C22×D61—42no—
304D4×C61—22no—
305D4×C61—22no—
306D4×C61—48no—
307D4×C61—42no—
308C2×C4×C61—22no—
309C2×C4×C61—24no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—22no—
315C2×C4×C61—42no—
316C2×C4×C61—42no—
317C2×C4×C61—42no—
318C2×C4×C61C22×D412yes—
319C2×C4×C61C22×D411yescharacteristic
320C2×C4×C61C2×#4112yes—
321C2×C4×C61C2×#4112yes—
322C2×C4×C61C2511yescharacteristic
323C22⋊D61—216no—
324C22⋊D61—48no—
325C22⋊D61—48no—
326C22⋊D61—48no—
327C2×Dic61—24no—
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—28no—
332C2×Dic61—28no—
333C2×Dic61—22no—
334C2×Dic61—42no—
335C2×Dic61—48no—
336C2×Dic61#13514yes—
337C2×Dic61AGL(1,ℤ/8)14yes—
338C2×Dic61C22×D412yes—
339C2×Dic61C22×D412yes—
340C2×Dic61C22×D412yes—
341C2×Dic61C22×D412yes—
342D244—24no—
343D244—22no—
344D244—22no—
345D244—22no—
346D244—42no—
347D244C2×#4114yescomplemented
348C4×D61—216no—
349C4×D61—48no—
350C4×D61—48no—
351C4×D61—48no—
352Dic122—24no—
353Dic122—22no—
354Dic122—48no—
355Dic122C2×#4114yescomplemented
356C8×C61—22no—
357C8×C61—22no—
358#92418—22no—
359#92418—22no—
360C2×#3106—611nomaximal, Sylow
361C22×C61—22no—
362C22×C61—22no—
363C22×C61—22no—
364C22×C61—44no—
365C22×C61—42no—
366C22×C61—42no—
367C22×C61—42no—
368C22×C61—84no—
369C22×C61#52512yes—
370C22×C61C2×#13512yes—
371C22×C61C2×AGL(1,ℤ/8)12yes—
372C22×C61C23×D411yescharacteristic
373C2×D61—24no—
374C2×D61—48no—
375C2×D61—42no—
376C2×D61—42no—
377C2×D61—42no—
378C2×D61—42no—
379C2×D61—42no—
380C2×D61—84no—
381C4×C61—22no—
382C4×C61—42no—
383C4×C61—42no—
384C4×C61—42no—
385C4×C61#52512yes—
386C4×C61C22×#4111yescharacteristic
387C4×C61C22×#4111yescharacteristic
388Dic61—24no—
389Dic61—22no—
390Dic61—22no—
391Dic61—42no—
392Dic61C2×#13514yes—
393Dic61C2×AGL(1,ℤ/8)14yes—
394C2×#532—611no—
395C2×C4×#41—611no—
396#3106—6116no—
397C2×#482—611no—
398C2×#482D6111yescharacteristic, complemented
399C2×#477—611no—
400C2×#476—611no—
401C2×#460—611no—
402C2×#459—611no—
403C2×#449—611no—
404C2×#449—611no—
405C2×C4×SD16—611no—
406C2×C4×SD16—611no—
407C2×C4×D8—611no—
408C2×C4×D8—611no—
409C2×#431—611no—
410C2×C61—42no—
411C2×C61—82no—
412C2×C61#310614yescomplemented
413C2×C61C2×#52511yescharacteristic
414C2×C61C22×#13511yescharacteristic
415C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
416D61—44no—
417D61—82no—
418C22×#41—611no—
419C22×#41—1221no—
420C22×SD16—611no—
421C22×SD16—611no—
422C22×D8—611no—
423C22×D8—611no—
424#532—618no—
425#532—1224no—
426C2×C4⋊Q8—611no—
427C2×#127—611no—
428C2×#124—1221no—
429C2×#121—611no—
430C2×#121—1221no—
431C2×#121C2×D6111yescharacteristic
432C4×#41—618no—
433C4×#41—1224no—
434C2×C4×Q8—611no—
435C2×C4×Q8—611no—
436C2×C4×D4—611no—
437C2×C4×D4—611no—
438C2×C4×D4—611no—
439C2×C4×D4—611no—
440C2×C4×D4—1221no—
441C2×C4×D4—1221no—
442C2×C4×D4—1221no—
443C2×#117—1221no—
444C2×#117C2×D6111yescharacteristic
445C22×C42—611no—
446C22×C42—1221no—
447#482—618no—
448#482C2×D6118yescomplemented
449#477—618no—
450#476—618no—
451#460—618no—
452#459—618no—
453#449—618no—
454#449—618no—
455C4×SD16—618no—
456C4×SD16—618no—
457C4×D8—618no—
458C4×D8—618no—
459#431—618no—
460C2×#107—611no—
461C2×#107C2×D6111yescharacteristic
462C2×#106—611no—
463C2×#106C2×D6111yescharacteristic
464C2×C4⋊C8—611no—
465C2×C4⋊C8—611no—
466C2×#103—611no—
467C2×#103—611no—
468C2×#102—611no—
469C2×#102—611no—
470C2×#102—611no—
471C2×#102—611no—
472C2×#102C2×D6111yescharacteristic
473C2×#102C2×D6111yescharacteristic
474C2×C22⋊C8—611no—
475C2×C22⋊C8C2×D6111yescharacteristic
476C2×C4×C8—611no—
477C2×C4×C8—611no—
478C61C2×#310611yescharacteristic, complemented, Sylow
479C2×#41—614no—
480C2×#41—1224no—
481C2×#41—1224no—
482C2×#41—1228no—
483C2×#41—1222no—
484C2×#41—2448no—
485C22×Q8—611no—
486C22×Q8—1221no—
487C22×D4—21no—
488C22×D4—611no—
489C22×D4—611no—
490C22×D4—1221no—
491C22×D4—1221no—
492C22×D4—1221no—
493C22×D4—1221no—
494C22×D4C22×D6111yescharacteristic
495C23×C4—611no—
496C23×C4—611no—
497C23×C4—1221no—
498C23×C4—1221no—
499C23×C4—1221no—
500C23×C4—1221no—
501C23×C4—1221no—
502C23×C4C22×D6111yescharacteristic
503C2×SD16—614no—
504C2×SD16—614no—
505C2×SD16—1224no—
506C2×SD16—1224no—
507C2×D8—614no—
508C2×D8—614no—
509C2×D8—1224no—
510C2×D8—1224no—
511C22×C8—611no—
512C22×C8—611no—
513C22×C8C22×D6111yescharacteristic
514C22×C8C22×D6111yescharacteristic
515C4⋊Q8—614no—
516C4⋊Q8—1222no—
517#127—614no—
518#127—1222no—
519#124—1228no—
520#121—22no—
521#121—614no—
522#121—1228no—
523#121—1222no—
524#121C22×D6114yes—
525C4×Q8—614no—
526C4×Q8—614no—
527C4×Q8—1222no—
528C4×Q8—1222no—
529C4×D4—614no—
530C4×D4—614no—
531C4×D4—614no—
532C4×D4—614no—
533C4×D4—1228no—
534C4×D4—1222no—
535C4×D4—1222no—
536C4×D4—1222no—
537C4×D4—1222no—
538C4×D4—1228no—
539C4×D4—1228no—
540#117—22no—
541#117—1228no—
542#117C22×D6114yes—
543C2×C4⋊C4—611no—
544C2×C4⋊C4—1221no—
545C2×C4⋊C4—1221no—
546C2×C4⋊C4—1221no—
547C2×C4⋊C4C22×D6111yescharacteristic
548C2×C4⋊C4C22×D6111yescharacteristic
549C2×C4⋊C4C22×D6111yescharacteristic
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—1221no—
553C2×C22⋊C4—1221no—
554C2×C22⋊C4—1221no—
555C2×C22⋊C4—1221no—
556C2×C22⋊C4—1221no—
557C2×C42—21no—
558C2×C42—611no—
559C2×C42—611no—
560C2×C42—614no—
561C2×C42—611no—
562C2×C42—611no—
563C2×C42—614no—
564C2×C42—1228no—
565C2×C42—1221no—
566C2×C42—1221no—
567#107—614no—
568#107C22×D6114yes—
569#106—614no—
570#106C22×D6114yes—
571C4⋊C8—614no—
572C4⋊C8—614no—
573#103—614no—
574#103—614no—
575#102—614no—
576#102—614no—
577#102—614no—
578#102—614no—
579#102C22×D6114yes—
580#102C22×D6114yes—
581C22⋊C8—614no—
582C22⋊C8C22×D6114yes—
583C4×C8—614no—
584C4×C8—614no—
585C24—21no—
586C24—1221no—
587C24—1221no—
588C24D4×D6111yescharacteristic
589#41—1228no—
590#41—1228no—
591#41—12216no—
592#41—24432no—
593C2×Q8—614no—
594C2×Q8—612no—
595C2×Q8—1224no—
596C2×Q8—1221no—
597C2×Q8—1222no—
598C2×Q8—2444no—
599C2×D4—24no—
600C2×D4—21no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—44no—
604C2×D4—614no—
605C2×D4—612no—
606C2×D4—612no—
607C2×D4—1224no—
608C2×D4—1224no—
609C2×D4—1228no—
610C2×D4—1224no—
611C2×D4—1224no—
612C2×D4—1221no—
613C2×D4—1221no—
614C2×D4—1222no—
615C2×D4—1222no—
616C2×D4—1222no—
617C2×D4—2444no—
618C2×D4—2444no—
619C2×D4—2444no—
620C2×D4C23×D6112yes—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—611no—
627C22×C4—611no—
628C22×C4—614no—
629C22×C4—614no—
630C22×C4—611no—
631C22×C4—611no—
632C22×C4—1224no—
633C22×C4—1224no—
634C22×C4—1224no—
635C22×C4—1228no—
636C22×C4—1224no—
637C22×C4—1224no—
638C22×C4—1224no—
639C22×C4—1221no—
640C22×C4—1224no—
641C22×C4—1221no—
642C22×C4—2444no—
643C22×C4—2444no—
644C22×C4—2444no—
645C22×C4—2444no—
646C22×C4D4×D6112yes—
647C22×C4D4×D6111yescharacteristic
648C22×C4C23×D6112yes—
649C22×C4C23×D6111yescharacteristic
650SD16—1228no—
651SD16—1228no—
652D8—1228no—
653D8—1228no—
654C2×C8—22no—
655C2×C8—22no—
656C2×C8—612no—
657C2×C8—612no—
658C2×C8—1222no—
659C2×C8—1222no—
660C2×C8C23×D6112yes—
661C2×C8C23×D6112yes—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—612no—
666C4⋊C4—1224no—
667C4⋊C4—1224no—
668C4⋊C4—1224no—
669C4⋊C4—1221no—
670C4⋊C4C23×D6112yes—
671C4⋊C4C23×D6112yes—
672C4⋊C4C23×D6112yes—
673C22⋊C4—24no—
674C22⋊C4—24no—
675C22⋊C4—1224no—
676C22⋊C4—1224no—
677C22⋊C4—1224no—
678C22⋊C4—1224no—
679C22⋊C4—1224no—
680C42—24no—
681C42—614no—
682C42—614no—
683C42—612no—
684C42—612no—
685C42—612no—
686C42—612no—
687C42—1224no—
688C42—1224no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—1224no—
697C23—1222no—
698C23—1222no—
699C23—2442no—
700C23—2442no—
701C23—2442no—
702C23—2442no—
703C23—2442no—
704C23C2×D4×D6112yes—
705C23C2×D4×D6111yescharacteristic
706Q8—614no—
707Q8—1224no—
708Q8—1222no—
709Q8—2448no—
710D4—22no—
711D4—22no—
712D4—48no—
713D4—42no—
714D4—614no—
715D4—12216no—
716D4—1224no—
717D4—1222no—
718D4—1222no—
719D4—1222no—
720D4—2448no—
721D4—2448no—
722D4—2448no—
723D4—2442no—
724C2×C4—22no—
725C2×C4—24no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—614no—
735C2×C4—614no—
736C2×C4—612no—
737C2×C4—612no—
738C2×C4—612no—
739C2×C4—612no—
740C2×C4—12216no—
741C2×C4—1228no—
742C2×C4—1228no—
743C2×C4—1224no—
744C2×C4—1222no—
745C2×C4—1222no—
746C2×C4—1222no—
747C2×C4—1222no—
748C2×C4—2448no—
749C2×C4—2448no—
750C2×C4—2448no—
751C2×C4—2448no—
752C2×C4—2442no—
753C2×C4C2×D4×D6112yes—
754C2×C4C2×D4×D6111yescharacteristic
755C2×C4#41×D6112yes—
756C2×C4#41×D6112yes—
757C2×C4C24×D6111yescharacteristic
758C8—22no—
759C8—22no—
760C8—1222no—
761C8—1222no—
762C22—22no—
763C22—22no—
764C22—22no—
765C22—44no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—84no—
770C22—1224no—
771C22—4884no—
772C22—2442no—
773C22—2442no—
774C22—2442no—
775C22—2448no—
776C22—2442no—
777C22—2442no—
778C22#1684027012yes—
779C22#135×D6112yes—
780C22AGL(1,ℤ/8)×D6112yes—
781C22C22×D4×D6111yescharacteristic
782C4—22no—
783C4—42no—
784C4—42no—
785C4—42no—
786C4—614no—
787C4—614no—
788C4—1222no—
789C4—1222no—
790C4—1224no—
791C4—2442no—
792C4#1684027012yes—
793C4C2×#41×D6111yescharacteristic
794C4C2×#41×D6111yescharacteristic
795C2—42no—
796C2—82no—
797C2—4882no—
798C2—2444no—
799C2#2145587414yesdirect product factor
800C2C2×#1684027011yescharacteristic
801C2C2×#135×D6111yescharacteristic
802C2C2×AGL(1,ℤ/8)×D6111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#482C2
socleC23×C61C22×D4
hypercenterC2×#482D61
hypocenterC61C2×#3106
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
1. C2×#16840307C2semidirect
2. C2×#16840230C2semidirect
3. #21455874C2direct (N × H)
4. C2×#16840086C2semidirect
5. C2×#16840056C2semidirect
6. C2×#16840051C2semidirect
7. C2×#16839961C2semidirect
8. C2×#16839956C2semidirect
9. C2×#16839909C2semidirect
10. C2×#16839905C2semidirect
11. C2×#16839853C2semidirect
12. C2×#16839849C2semidirect
13. C2×#16839844C2semidirect
14. C2×#16839842C2semidirect
15. C2×#16839812C2semidirect
16. C2×C61×#482C2semidirect
24. #16840307C22semidirect
31. #16840230C22semidirect
44. #16840086C22semidirect
45. #16840056C22semidirect
46. #16840051C22semidirect
47. #16839961C22semidirect
48. #16839956C22semidirect
49. #16839909C22semidirect
50. #16839905C22semidirect
51. #16839853C22semidirect
52. #16839849C22semidirect
53. #16839844C22semidirect
54. #16839842C22semidirect
55. #16839812C22semidirect
71. C61×#482C22semidirect
231. C2×D244#41semidirect
246. C2×Dic122#41semidirect
347. D244C2×#41semidirect
355. Dic122C2×#41semidirect
398. C2×#482D61semidirect
412. C2×C61#3106semidirect
448. #482C2×D61semidirect
478. C61C2×#3106semidirect
799. C2#21455874direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403072
C2×#168402302
#214558742
C2×#168400862
C2×#168400562
C2×#168400512
C2×#168399612
C2×#168399562
C2×#168399092
C2×#168399052
C2×#168398532
C2×#168398492
C2×#168398442
C2×#168398422
C2×#168398122
C2×C61×#4822
C2×#310661