Finite Group Databasebeta

← C2×#21456172 #30549248

Subgroups — C2×#21456172 #30549248

Order 15616.

2262 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×#16840392C211yesmaximal, characteristic, complemented
2C2×#16840330C211yesmaximal, characteristic
3#21456172C2116yesmaximal, direct product factor
4C2×#16840128C211yesmaximal, characteristic, complemented
5C2×#16840125C211yesmaximal, characteristic, complemented
6C2×#16840123C211yesmaximal, characteristic, complemented
7C2×#16840121C211yesmaximal, characteristic, complemented
8C2×#16840118C211yesmaximal, characteristic, complemented
9C2×#16840109C211yesmaximal, characteristic, complemented
10C2×#16840107C211yesmaximal, characteristic, complemented
11C2×#16839762C211yesmaximal, characteristic, complemented
12C2×#16839765C211yesmaximal, characteristic, complemented
13C2×#16839757C211yesmaximal, characteristic, complemented
14C2×#102×D61C211yesmaximal, characteristic, complemented
15C2×#16839716C211yesmaximal, characteristic, complemented
16C2×C61×#488C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C22×D4×D61C2211yescharacteristic
19C22×#11758189C2211yescharacteristic
20C22×C8×D61C2211yescharacteristic
21#16840392—24no—
22#16840392C2218yescomplemented
23#16840330—24no—
24#16840330C2218yes—
25C2×#14519777C2211yescharacteristic, complemented
26C2×#14519776—21no—
27C2×#14519776C2211yescharacteristic, complemented
28C2×#14519774C2211yescharacteristic
29C2×#14519773C2211yescharacteristic
30C2×#14519768C2211yescharacteristic, complemented
31C2×#14519767—21no—
32C2×#14519766C2211yescharacteristic
33C2×#14519757—21no—
34C2×#14519755—21no—
35C2×#14519750—21no—
36C2×#14519750—21no—
37C2×#14519747—21no—
38C2×#14519747—21no—
39C2×#14519735C2211yescharacteristic
40C2×#14519734C2211yescharacteristic
41C2×C4⋊C4×D61C2211yescharacteristic
42#16840128C2218yescomplemented
43#16840125C2218yescomplemented
44#16840123C2218yescomplemented
45#16840121C2218yescomplemented
46#16840118C2218yescomplemented
47#16840109C2218yescomplemented
48#16840107C2218yescomplemented
49#16839765C2218yescomplemented
50#16839762C2218yescomplemented
51#16839757C2218yescomplemented
52C2×#14519701C2211yescharacteristic, complemented
53C2×#14519701C2211yescharacteristic, complemented
54C2×#14519699C2211yescharacteristic
55C2×#14519699C2211yescharacteristic
56C2×#14519699C2211yescharacteristic, complemented
57C2×#14519699C2211yescharacteristic, complemented
58C2×#14519698C2211yescharacteristic
59C2×#14519698C2211yescharacteristic
60C2×#14519697C2211yescharacteristic
61C2×#14519697C2211yescharacteristic
62C2×#14519697C2211yescharacteristic, complemented
63C2×#14519697C2211yescharacteristic, complemented
64#102×D61C2218yescomplemented
65#16839716C2218yescomplemented
66C2×#14519688C2211yescharacteristic, complemented
67C2×#14519687C2211yescharacteristic, complemented
68C2×C8×Dic61C2211yescharacteristic, complemented
69C2×#125×C61C2211yescharacteristic, complemented
70C2×#124×C61C2211yescharacteristic
71C61×#488C2218yescomplemented
72C2×#103×C61C2211yescharacteristic, complemented
73C2×#103×C61C2211yescharacteristic, complemented
74C2×#102×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×C4×C8×C61C2211yescharacteristic, complemented
77C24×D61—21no—
78C2×#11758226—22no—
79C2×#11758226—24no—
80C2×#11758226—24no—
81C2×#11758226C2314yes—
82C22×Dic122—21no—
83C22×Dic122—21no—
84C22×D244—21no—
85C22×D244—21no—
86C22×D244—21no—
87C22×D244C2311yescharacteristic
88C22×D244C2311yescharacteristic
89C22×C22⋊D61—21no—
90C22×C22⋊D61—21no—
91C22×C22⋊D61—21no—
92C2×D4×D61—22no—
93C2×D4×D61—24no—
94C2×D4×D61—24no—
95C2×D4×D61C2314yes—
96C22×C4×D61—21no—
97C22×C4×D61—21no—
98C22×C4×D61C2311yescharacteristic
99C2×#11758189—24no—
100C2×#11758189C2314yes—
101C22×#92418C2311yescharacteristic
102C22×#92418C2311yescharacteristic
103C2×C8×D61—24no—
104C2×C8×D61C2314yes—
105#14519777—22no—
106#14519777C2314yescomplemented
107#14519776—28no—
108#14519776—22no—
109#14519776C2314yescomplemented
110#14519774—22no—
111#14519774C2314yes—
112#14519773—22no—
113#14519773C2314yes—
114#14519768—22no—
115#14519768C2314yescomplemented
116#14519767—28no—
117#14519766—22no—
118#14519766C2314yes—
119#14519757—28no—
120#14519755—28no—
121#14519750—28no—
122#14519750—28no—
123#14519747—28no—
124#14519747—28no—
125#14519735—22no—
126#14519735C2314yes—
127#14519734D414yes—
128#14519734C2314yes—
129C2×C4⋊Dic61—21no—
130C2×C4⋊Dic61—21no—
131C2×C4⋊Dic61C2311yescharacteristic
132C2×C4⋊Dic61C2311yescharacteristic
133C2×#11758196—21no—
134C2×#11758196—21no—
135C2×#11758196—21no—
136C2×#11758196D411yescharacteristic
137C2×#11758196D411yescharacteristic
138C4⋊C4×D61—22no—
139C4⋊C4×D61C2314yes—
140C2×#11758198—21no—
141C2×#11758198—21no—
142C2×#11758198—21no—
143C2×#11758198D411yescharacteristic
144C2×#11758198D411yescharacteristic
145C2×C4×Dic61—21no—
146C2×C4×Dic61C2311yescharacteristic
147#14519701C2314yescomplemented
148#14519701C2314yescomplemented
149#14519699C2314yes—
150#14519699C2314yes—
151#14519699C2314yescomplemented
152#14519699C2314yescomplemented
153#14519698C2314yes—
154#14519698C2314yes—
155#14519697C2314yes—
156#14519697C2314yes—
157#14519697C2314yescomplemented
158#14519697C2314yescomplemented
159#14519688C2314yescomplemented
160#14519687C2314yescomplemented
161C8×Dic61C2314yescomplemented
162C22×Q8×C61C2311yescharacteristic
163C22×D4×C61C2311yescharacteristic
164C22×C8×C61C2311yescharacteristic
165C22×C8×C61C2311yescharacteristic
166#125×C61—22no—
167#125×C61C2314yescomplemented
168#124×C61—22no—
169#124×C61C2314yes—
170C2×C4⋊C4×C61—21no—
171C2×C4⋊C4×C61—21no—
172C2×C4⋊C4×C61C2311yescharacteristic
173C2×C4⋊C4×C61C2311yescharacteristic
174C2×C22⋊C4×C61—21no—
175C2×C22⋊C4×C61—21no—
176C2×C42×C61C2311yescharacteristic
177#103×C61C2314yescomplemented
178#103×C61C2314yescomplemented
179#102×C61C2314yes—
180#102×C61C2314yes—
181C4×C8×C61C2314yescomplemented
182C24×C61—21no—
183C23×D61—21no—
184C23×D61—21no—
185C23×D61—24no—
186C23×D61—44no—
187C23×D61—82no—
188C23×D61—82no—
189C23×D61C2×D411yescharacteristic
190C2×Q8×C61—21no—
191C2×Q8×C61—22no—
192C2×Q8×C61—22no—
193C2×Q8×C61C2412yes—
194C2×D4×C61—21no—
195C2×D4×C61—22no—
196C2×D4×C61—22no—
197C2×D4×C61C2412yes—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61C2×D411yescharacteristic
202C22×C4×C61C2×D411yescharacteristic
203C22×C4×C61C2411yescharacteristic
204C2×C22⋊D61—24no—
205C2×C22⋊D61—24no—
206C2×C22⋊D61—24no—
207C2×C22⋊D61—44no—
208C2×C22⋊D61—82no—
209C2×C22⋊D61—82no—
210C22×Dic61—21no—
211C22×Dic61—21no—
212C22×Dic61C2×D411yescharacteristic
213C22×Dic61C2×D411yescharacteristic
214C22×Dic61C2×D411yescharacteristic
215#11758226—28no—
216#11758226—28no—
217#11758226—48no—
218D4×D61—28no—
219D4×D61—28no—
220D4×D61—48no—
221C2×D244—22no—
222C2×D244—22no—
223C2×D244—22no—
224C2×D244—22no—
225C2×D244—24no—
226C2×D244—21no—
227C2×D244—21no—
228C2×D244—24no—
229C2×D244—24no—
230C2×D244—44no—
231C2×D244—82no—
232C2×D244—82no—
233C2×D244C2412yes—
234C2×D244C2412yes—
235C2×C4×D61—24no—
236C2×C4×D61—24no—
237C2×C4×D61—44no—
238C2×C4×D61—82no—
239C2×C4×D61C2×D412yes—
240C2×C4×D61#4114yes—
241C2×C4×D61#4114yes—
242C2×C4×D61C2412yes—
243C2×Dic122—24no—
244C2×Dic122—24no—
245C2×Dic122—82no—
246C2×Dic122—82no—
247C2×C8×C61—22no—
248C2×C8×C61—22no—
249C2×C8×C61C2412yes—
250C2×C8×C61C2412yes—
251C4⋊C4×C61—24no—
252C4⋊C4×C61—24no—
253C4⋊C4×C61—21no—
254C4⋊C4×C61—21no—
255C4⋊C4×C61C2412yes—
256C4⋊C4×C61C2412yes—
257C22⋊C4×C61—24no—
258C22⋊C4×C61—24no—
259C42×C61C2×D412yes—
260C42×C61C2412yes—
261#11758198—24no—
262#11758198—24no—
263#11758198—24no—
264#11758198C2×D414yes—
265#11758198C2×D414yes—
266C4⋊Dic61—21no—
267C4⋊Dic61—24no—
268C4⋊Dic61—21no—
269C4⋊Dic61—24no—
270C4⋊Dic61C2412yes—
271C4⋊Dic61C2412yes—
272#11758196—24no—
273#11758196—24no—
274#11758196—24no—
275#11758196C2×D414yes—
276#11758196C2×D414yes—
277C4×Dic61—24no—
278C4×Dic61C2×D412yes—
279C4×Dic61C2412yes—
280C2×#92418—22no—
281C2×#92418—22no—
282C2×#92418C2412yes—
283C2×#92418C2412yes—
284#11758189—28no—
285C8×D61—28no—
286C23×C61—22no—
287C23×C61—42no—
288C23×C61—42no—
289C23×C61—42no—
290C23×C61C22×D411yescharacteristic
291C22×D61—22no—
292C22×D61—22no—
293C22×D61—22no—
294C22×D61—22no—
295C22×D61—42no—
296C22×D61—42no—
297C22×D61—42no—
298C22×D61—42no—
299C22×D61—42no—
300C22×D61—42no—
301C22×D61—48no—
302C22×D61—84no—
303C22×D61—84no—
304C22×D61—816no—
305C22×D61#12414yes—
306C22×D61C22×D412yes—
307Q8×C61—22no—
308Q8×C61—22no—
309Q8×C61—42no—
310D4×C61—22no—
311D4×C61—22no—
312D4×C61—42no—
313C2×C4×C61—22no—
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—42no—
321C2×C4×C61C22×D412yes—
322C2×C4×C61C22×D412yes—
323C2×C4×C61C22×D411yescharacteristic
324C2×C4×C61C2×#4112yes—
325C2×C4×C61C2×#4112yes—
326C2×C4×C61C2511yescharacteristic
327C22⋊D61—48no—
328C22⋊D61—84no—
329C22⋊D61—84no—
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—42no—
335C2×Dic61—42no—
336C2×Dic61#12414yes—
337C2×Dic61C22×D412yes—
338C2×Dic61C22×D412yes—
339C2×Dic61C22×D412yes—
340D244—22no—
341D244—22no—
342D244—22no—
343D244—22no—
344D244—48no—
345D244—42no—
346D244—42no—
347D244—84no—
348D244—84no—
349C4×D61—48no—
350C4×D61—84no—
351C4×D61#12418yes—
352C4×D61C2×#4114yes—
353C4×D61C2×#4114yes—
354Dic122—84no—
355Dic122—84no—
356C8×C61—22no—
357C8×C61—22no—
358#92418—22no—
359#92418—22no—
360C2×#3136—611nomaximal, Sylow
361C22×C61—42no—
362C22×C61—42no—
363C22×C61—42no—
364C22×C61—84no—
365C22×C61C2×#12412yes—
366C22×C61#57612yes—
367C22×C61#57712yes—
368C22×C61C23×D411yescharacteristic
369C2×D61—28no—
370C2×D61—22no—
371C2×D61—22no—
372C2×D61—42no—
373C2×D61—42no—
374C2×D61—42no—
375C2×D61—42no—
376C2×D61—42no—
377C2×D61—42no—
378C2×D61—816no—
379C2×D61—84no—
380C2×D61—84no—
381C2×D61C2×#12414yes—
382C4×C61—22no—
383C4×C61—22no—
384C4×C61—42no—
385C4×C61—42no—
386C4×C61—42no—
387C4×C61C2×#12412yes—
388C4×C61C22×#4111yescharacteristic
389C4×C61C22×#4111yescharacteristic
390Dic61—22no—
391Dic61—22no—
392Dic61—42no—
393Dic61—42no—
394Dic61C2×#12414yes—
395C2×#544—611no—
396C2×#535—611no—
397#3136—6116no—
398C2×#490—611no—
399C2×#490—611no—
400C2×#489—611no—
401C2×#489—611no—
402C2×#488—611no—
403C2×#488D6111yescharacteristic, complemented
404C2×#486—611no—
405C2×#486—611no—
406C2×#417—611no—
407C2×#418—611no—
408C2×#416—611no—
409C22×#102—611no—
410C2×#405—611no—
411C2×C61—82no—
412C2×C61#313614yescomplemented
413C2×C61C22×#12411yescharacteristic
414C2×C61C2×#57611yescharacteristic
415C2×C61C2×#57711yescharacteristic
416D61—24no—
417D61—82no—
418D61—82no—
419C22×#41—611no—
420C23×D4—611no—
421C22×M16—611no—
422C23×C8—611no—
423#544—618no—
424#544—1224no—
425#535—618no—
426#535—1224no—
427C2×C4⋊Q8—611no—
428C2×C4⋊Q8—611no—
429C2×C4⋊Q8—1221no—
430C2×#127—611no—
431C2×#127—611no—
432C2×#125—611no—
433C2×#125—1221no—
434C2×#125C2×D6111yescharacteristic, complemented
435C2×#124—611no—
436C2×#124C2×D6111yescharacteristic
437C2×C22⋊Q8—1221no—
438C2×C22⋊Q8—1221no—
439C2×#121—1221no—
440C2×#121—1221no—
441C2×#120—1221no—
442C2×#120—1221no—
443C2×#117—611no—
444C2×#117—611no—
445C22×C4⋊C4—611no—
446#490—618no—
447#490—618no—
448#489—618no—
449#489—618no—
450#488—618no—
451#488C2×D6118yescomplemented
452#486—618no—
453#486—618no—
454#418—618no—
455#417—618no—
456#416—618no—
457C2×#103—611no—
458C2×#103—611no—
459C2×#103C2×D6111yescharacteristic, complemented
460C2×#103C2×D6111yescharacteristic, complemented
461C2×#102—611no—
462C2×#102—611no—
463C2×#102—611no—
464C2×#102—611no—
465C2×#102—611no—
466C2×#102—611no—
467C2×#102—611no—
468C2×#102—611no—
469C2×#102—611no—
470C2×#102—611no—
471C2×#102—618no—
472C2×#102C2×D6111yescharacteristic
473C2×#102C2×D6111yescharacteristic
474#405—618no—
475C2×#97—611no—
476C2×#97—611no—
477C2×C4×C8—611no—
478C2×C4×C8C2×D6111yescharacteristic, complemented
479C61C2×#313611yescharacteristic, complemented, Sylow
480C25—1221no—
481C2×#41—614no—
482C2×#41—1222no—
483C2×#41—1224no—
484C2×#41—1224no—
485C22×Q8—1221no—
486C22×Q8—1221no—
487C22×Q8C22×D6111yescharacteristic
488C22×D4—614no—
489C22×D4—611no—
490C22×D4—611no—
491C22×D4—1221no—
492C22×D4—1224no—
493C22×D4—1224no—
494C22×D4—1222no—
495C22×D4—1221no—
496C22×D4—1221no—
497C22×D4—1221no—
498C22×D4—1221no—
499C22×D4—1221no—
500C22×D4C22×D6111yescharacteristic
501C23×C4—611no—
502C23×C4—1221no—
503C23×C4—1221no—
504C2×M16—614no—
505C2×M16—1224no—
506C22×C8—611no—
507C22×C8—611no—
508C22×C8—614no—
509C22×C8—1224no—
510C22×C8C22×D6111yescharacteristic
511C22×C8C22×D6111yescharacteristic
512C4⋊Q8—614no—
513C4⋊Q8—614no—
514C4⋊Q8—1222no—
515C4⋊Q8—1228no—
516C4⋊Q8—1222no—
517#127—614no—
518#127—614no—
519#127—1222no—
520#127—1222no—
521#125—22no—
522#125—614no—
523#125—1222no—
524#125—1228no—
525#125C22×D6114yescomplemented
526#124—22no—
527#124—614no—
528#124—1222no—
529#124C22×D6114yes—
530C22⋊Q8—1228no—
531C22⋊Q8—1228no—
532#121—1228no—
533#121—1228no—
534#120—1228no—
535#120—1228no—
536#117—614no—
537#117—614no—
538#117—614no—
539#117—1222no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—611no—
543C2×C4⋊C4—611no—
544C2×C4⋊C4—611no—
545C2×C4⋊C4—611no—
546C2×C4⋊C4—614no—
547C2×C4⋊C4—1222no—
548C2×C4⋊C4—1221no—
549C2×C4⋊C4—1221no—
550C2×C4⋊C4—1221no—
551C2×C4⋊C4—1221no—
552C2×C4⋊C4—1221no—
553C2×C4⋊C4C22×D6111yescharacteristic
554C2×C4⋊C4C22×D6111yescharacteristic
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—611no—
558C2×C22⋊C4—611no—
559C2×C22⋊C4—1221no—
560C2×C22⋊C4—1221no—
561C2×C22⋊C4—1221no—
562C2×C42—611no—
563C2×C42—1221no—
564C2×C42C22×D6111yescharacteristic
565#103—614no—
566#103—614no—
567#103C22×D6114yescomplemented
568#103C22×D6114yescomplemented
569#102—614no—
570#102—614no—
571#102—614no—
572#102—614no—
573#102—614no—
574#102—614no—
575#102—614no—
576#102—614no—
577#102—614no—
578#102—614no—
579#102C22×D6114yes—
580#102C22×D6114yes—
581#97—614no—
582#97—614no—
583C4×C8—614no—
584C4×C8C22×D6114yescomplemented
585C24—21no—
586C24—611no—
587C24—1224no—
588C24—1221no—
589C24—1221no—
590C24—4882no—
591C24—4882no—
592C24—2444no—
593#41—1228no—
594#41—1228no—
595#41—2448no—
596C2×Q8—21no—
597C2×Q8—22no—
598C2×Q8—22no—
599C2×Q8—1224no—
600C2×Q8—1224no—
601C2×Q8—4882no—
602C2×Q8—4882no—
603C2×Q8C23×D6112yes—
604C2×D4—21no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—612no—
608C2×D4—612no—
609C2×D4—1224no—
610C2×D4—1228no—
611C2×D4—1228no—
612C2×D4—1224no—
613C2×D4—1224no—
614C2×D4—1224no—
615C2×D4—1224no—
616C2×D4—1224no—
617C2×D4—1221no—
618C2×D4—1221no—
619C2×D4—1222no—
620C2×D4—1222no—
621C2×D4—1222no—
622C2×D4—1222no—
623C2×D4—4882no—
624C2×D4—4882no—
625C2×D4—4882no—
626C2×D4—4882no—
627C2×D4—2444no—
628C2×D4—2448no—
629C2×D4—2444no—
630C2×D4C23×D6112yes—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—611no—
635C22×C4—612no—
636C22×C4—614no—
637C22×C4—614no—
638C22×C4—612no—
639C22×C4—611no—
640C22×C4—611no—
641C22×C4—1224no—
642C22×C4—1224no—
643C22×C4—1221no—
644C22×C4—1221no—
645C22×C4—4882no—
646C22×C4—2444no—
647C22×C4D4×D6111yescharacteristic
648C22×C4D4×D6111yescharacteristic
649C22×C4C23×D6111yescharacteristic
650M16—1228no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—612no—
654C2×C8—612no—
655C2×C8—1228no—
656C2×C8—1222no—
657C2×C8—1222no—
658C2×C8C23×D6112yes—
659C2×C8C23×D6112yes—
660C4⋊C4—24no—
661C4⋊C4—24no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—614no—
665C4⋊C4—614no—
666C4⋊C4—612no—
667C4⋊C4—612no—
668C4⋊C4—1224no—
669C4⋊C4—1224no—
670C4⋊C4—1224no—
671C4⋊C4—1224no—
672C4⋊C4—1221no—
673C4⋊C4—1221no—
674C4⋊C4—1224no—
675C4⋊C4C23×D6112yes—
676C4⋊C4C23×D6112yes—
677C22⋊C4—24no—
678C22⋊C4—24no—
679C22⋊C4—614no—
680C22⋊C4—614no—
681C22⋊C4—1224no—
682C22⋊C4—1224no—
683C22⋊C4—1224no—
684C42—612no—
685C42—612no—
686C42—1224no—
687C42D4×D6112yes—
688C42C23×D6112yes—
689C23—22no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—614no—
694C23—612no—
695C23—1222no—
696C23—1222no—
697C23—1222no—
698C23—1222no—
699C23—4884no—
700C23—4884no—
701C23—48816no—
702C23—2448no—
703C23—2442no—
704C23—2442no—
705C23—2442no—
706C23—2442no—
707C23—2442no—
708C23—2442no—
709C23C2×D4×D6111yescharacteristic
710Q8—22no—
711Q8—22no—
712Q8—42no—
713Q8—4884no—
714Q8—4884no—
715D4—22no—
716D4—22no—
717D4—42no—
718D4—1222no—
719D4—1222no—
720D4—1222no—
721D4—1222no—
722D4—4884no—
723D4—4884no—
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—22no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—614no—
739C2×C4—612no—
740C2×C4—618no—
741C2×C4—614no—
742C2×C4—614no—
743C2×C4—612no—
744C2×C4—612no—
745C2×C4—1222no—
746C2×C4—1222no—
747C2×C4—1222no—
748C2×C4—1222no—
749C2×C4—4884no—
750C2×C4—2448no—
751C2×C4—2442no—
752C2×C4—2442no—
753C2×C4C2×D4×D6112yes—
754C2×C4C2×D4×D6112yes—
755C2×C4C2×D4×D6111yescharacteristic
756C2×C4#41×D6112yes—
757C2×C4#41×D6112yes—
758C2×C4C24×D6111yescharacteristic
759C8—22no—
760C8—22no—
761C8—1222no—
762C8—1222no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—84no—
767C22—614no—
768C22—1228no—
769C22—1222no—
770C22—1222no—
771C22—48816no—
772C22—4884no—
773C22—4884no—
774C22—2442no—
775C22—2442no—
776C22—2442no—
777C22—2442no—
778C22—2442no—
779C22—2442no—
780C22#124×D6112yes—
781C22#1684056412yes—
782C22#1684056912yes—
783C22C22×D4×D6111yescharacteristic
784C4—22no—
785C4—22no—
786C4—42no—
787C4—42no—
788C4—42no—
789C4—614no—
790C4—1222no—
791C4—1222no—
792C4—2442no—
793C4—2442no—
794C4#124×D6112yes—
795C4C2×#41×D6111yescharacteristic
796C4C2×#41×D6111yescharacteristic
797C2—82no—
798C2—1224no—
799C2—4882no—
800C2—4882no—
801C2#2145617214yesdirect product factor
802C2C2×#124×D6111yescharacteristic
803C2C2×#1684056411yescharacteristic
804C2C2×#1684056911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#488C2
socleC23×C61C22×D4
prime radicalC2×#16840330C2
hypercenterC2×#488D61
hypocenterC61C2×#3136
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#488

Complements

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

NH ≅ G/Ntype
1. C2×#16840392C2semidirect
3. #21456172C2direct (N × H)
4. C2×#16840128C2semidirect
5. C2×#16840125C2semidirect
6. C2×#16840123C2semidirect
7. C2×#16840121C2semidirect
8. C2×#16840118C2semidirect
9. C2×#16840109C2semidirect
10. C2×#16840107C2semidirect
11. C2×#16839762C2semidirect
12. C2×#16839765C2semidirect
13. C2×#16839757C2semidirect
14. C2×#102×D61C2semidirect
15. C2×#16839716C2semidirect
16. C2×C61×#488C2semidirect
22. #16840392C22semidirect
25. C2×#14519777C22semidirect
27. C2×#14519776C22semidirect
30. C2×#14519768C22semidirect
42. #16840128C22semidirect
43. #16840125C22semidirect
44. #16840123C22semidirect
45. #16840121C22semidirect
46. #16840118C22semidirect
47. #16840109C22semidirect
48. #16840107C22semidirect
49. #16839765C22semidirect
50. #16839762C22semidirect
51. #16839757C22semidirect
52. C2×#14519701C22semidirect
53. C2×#14519701C22semidirect
56. C2×#14519699C22semidirect
57. C2×#14519699C22semidirect
62. C2×#14519697C22semidirect
63. C2×#14519697C22semidirect
64. #102×D61C22semidirect
65. #16839716C22semidirect
66. C2×#14519688C22semidirect
67. C2×#14519687C22semidirect
68. C2×C8×Dic61C22semidirect
69. C2×#125×C61C22semidirect
71. C61×#488C22semidirect
72. C2×#103×C61C22semidirect
73. C2×#103×C61C22semidirect
76. C2×C4×C8×C61C22semidirect
106. #14519777C23semidirect
109. #14519776C23semidirect
115. #14519768C23semidirect
147. #14519701C23semidirect
148. #14519701C23semidirect
151. #14519699C23semidirect
152. #14519699C23semidirect
157. #14519697C23semidirect
158. #14519697C23semidirect
159. #14519688C23semidirect
160. #14519687C23semidirect
161. C8×Dic61C23semidirect
167. #125×C61C23semidirect
177. #103×C61C23semidirect
178. #103×C61C23semidirect
181. C4×C8×C61C23semidirect
403. C2×#488D61semidirect
412. C2×C61#3136semidirect
434. C2×#125C2×D61semidirect
451. #488C2×D61semidirect
459. C2×#103C2×D61semidirect
460. C2×#103C2×D61semidirect
478. C2×C4×C8C2×D61semidirect
479. C61C2×#3136semidirect
525. #125C22×D61semidirect
567. #103C22×D61semidirect
568. #103C22×D61semidirect
584. C4×C8C22×D61semidirect
801. C2#21456172direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403922
C2×#168403302
#214561722
C2×#168401282
C2×#168401252
C2×#168401232
C2×#168401212
C2×#168401182
C2×#168401092
C2×#168401072
C2×#168397622
C2×#168397652
C2×#168397572
C2×#102×D612
C2×#168397162
C2×C61×#4882
C2×#313661