Finite Group Databasebeta

← C2×#21456935 #30551413

Subgroups — C2×#21456935 #30551413

Order 15616.

2086 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840384C211yesmaximal, characteristic, complemented
2C2×#16840337C211yesmaximal, characteristic, complemented
3#21456935C2116yesmaximal, direct product factor
4C2×#16840155C211yesmaximal, characteristic, complemented
5C2×#16840147C211yesmaximal, characteristic, complemented
6C2×#16840123C211yesmaximal, characteristic, complemented
7C2×#16840111C211yesmaximal, characteristic, complemented
8C2×#16839984C211yesmaximal, characteristic, complemented
9C2×#16839978C211yesmaximal, characteristic, complemented
10C2×#16839964C211yesmaximal, characteristic, complemented
11C2×#16839923C211yesmaximal, characteristic, complemented
12C2×#16839910C211yesmaximal, characteristic
13C2×#16839916C211yesmaximal, characteristic, complemented
14C2×#16839902C211yesmaximal, characteristic, complemented
15C2×#16839822C211yesmaximal, characteristic, complemented
16C2×C61×#462C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C22×Q8×D61C2211yescharacteristic
19C22×#11758202C2211yescharacteristic
20C22×#11758190C2211yescharacteristic
21C22×#11758201C2211yescharacteristic
22C22×#11758201C2211yescharacteristic
23C22×#11758201C2211yescharacteristic
24C22×D488C2211yescharacteristic
25#16840384—24no—
26#16840384C2218yescomplemented
27#16840337—24no—
28#16840337C2218yescomplemented
29C2×#14519776C2211yescharacteristic
30C2×#14519775C2211yescharacteristic
31C2×#14519771—21no—
32C2×#14519766C2211yescharacteristic
33C2×#14519766C2211yescharacteristic
34C2×#14519765—21no—
35C2×#14519765C2211yescharacteristic
36C2×#14519762—21no—
37C2×#14519762—21no—
38C2×#14519762—21no—
39C2×#14519755—21no—
40C2×#14519755—21no—
41C2×#14519755—21no—
42C2×#14519753C2211yescharacteristic
43C2×#14519752C2211yescharacteristic
44C2×C4×D244C2211yescharacteristic
45C2×#14519734C2211yescharacteristic
46#16840155C2218yescomplemented
47#16840147C2218yescomplemented
48#16840123C2218yescomplemented
49#16840111C2218yescomplemented
50#16839984C2218yescomplemented
51#16839978C2218yescomplemented
52#16839964C2218yescomplemented
53#16839923C2218yescomplemented
54#16839916C2218yescomplemented
55#16839910C2218yes—
56#16839902C2218yescomplemented
57#16839822C2218yescomplemented
58C2×C4⋊#92418C2211yescharacteristic
59C2×#14519702C2211yescharacteristic
60C2×#14519701C2211yescharacteristic
61C2×#14519701C2211yescharacteristic
62C2×#14519700C2211yescharacteristic
63C2×#14519699C2211yescharacteristic
64C2×#14519697C2211yescharacteristic
65C2×#14519689C2211yescharacteristic
66C2×#14519689C2211yescharacteristic
67C2×#14519687C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C22×Q16×C61C2211yescharacteristic
70C22×Q16×C61C2211yescharacteristic
71C2×C4⋊Q8×C61C2211yescharacteristic
72C2×C4×Q8×C61C2211yescharacteristic
73C61×#462C2218yescomplemented
74C2×C4⋊C8×C61C2211yescharacteristic
75C2×#103×C61C2211yescharacteristic
76C2×#103×C61C2211yescharacteristic
77C2×#11758226—22no—
78C2×#11758226—42no—
79C2×#11758226—42no—
80C2×#11758226C2314yes—
81C22×Dic122—21no—
82C22×Dic122—21no—
83C22×Dic122C2311yescharacteristic
84C2×Q8×D61—22no—
85C2×Q8×D61—42no—
86C2×Q8×D61—42no—
87C2×Q8×D61C2314yes—
88C22×D244—21no—
89C22×D244—21no—
90C22×D244C2311yescharacteristic
91C22×D244C2311yescharacteristic
92C22×C4×D61—21no—
93C22×C4×D61—21no—
94C22×C4×D61—21no—
95C22×C4×D61C2311yescharacteristic
96C2×#11758202—42no—
97C2×#11758202C2314yes—
98C2×#11758190—42no—
99C2×#11758190C2314yes—
100C2×#11758201—42no—
101C2×#11758201—42no—
102C2×#11758201—42no—
103C2×#11758201C2314yes—
104C2×#11758201C2314yes—
105C2×#11758201C2314yes—
106C2×D488—42no—
107C2×D488C2314yes—
108C22×#92418C2311yescharacteristic
109C22×#92418C2311yescharacteristic
110#14519776—22no—
111#14519776C2314yes—
112#14519775—22no—
113#14519775C2314yes—
114#14519771—28no—
115#14519766—22no—
116#14519766—22no—
117#14519766C2314yes—
118#14519766C2314yes—
119#14519765—22no—
120#14519765—28no—
121#14519765C2314yes—
122#14519762—28no—
123#14519762—28no—
124#14519762—28no—
125#14519755—28no—
126#14519755—28no—
127#14519755—28no—
128#14519753—22no—
129#14519753C2314yes—
130#14519752—22no—
131#14519752C2314yes—
132C4×D244—22no—
133C4×D244C2314yes—
134#14519734D414yes—
135#14519734C2314yes—
136C2×C4⋊Dic61C2311yescharacteristic
137C2×#11758196—21no—
138C2×#11758196—21no—
139C2×#11758196—21no—
140C2×#11758196—21no—
141C2×#11758196D411yescharacteristic
142C2×#11758196D411yescharacteristic
143C2×#11758198—21no—
144C2×#11758198—21no—
145C2×#11758198—21no—
146C2×#11758198—21no—
147C2×#11758198—21no—
148C2×#11758198—21no—
149C2×#11758198—21no—
150C2×#11758198—21no—
151C2×#11758198—21no—
152C2×#11758198D411yescharacteristic
153C2×#11758198D411yescharacteristic
154C2×C4×Dic61C2311yescharacteristic
155C4⋊#92418C2314yes—
156#14519702C2314yes—
157#14519701C2314yes—
158#14519701C2314yes—
159#14519700C2314yes—
160#14519699C2314yes—
161#14519697C2314yes—
162#14519689C2314yes—
163#14519689C2314yes—
164#14519687C2314yes—
165C8×Dic61C2314yes—
166C22×Q8×C61C2311yescharacteristic
167C22×Q8×C61C2311yescharacteristic
168C22×Q8×C61C2311yescharacteristic
169C2×Q16×C61—42no—
170C2×Q16×C61—42no—
171C2×Q16×C61C2314yes—
172C2×Q16×C61C2314yes—
173C22×C8×C61C2311yescharacteristic
174C22×C8×C61C2311yescharacteristic
175C4⋊Q8×C61—22no—
176C4⋊Q8×C61C2314yes—
177C4×Q8×C61—22no—
178C4×Q8×C61C2314yes—
179C2×C4⋊C4×C61—21no—
180C2×C4⋊C4×C61—21no—
181C2×C4⋊C4×C61—21no—
182C2×C4⋊C4×C61C2311yescharacteristic
183C2×C42×C61—21no—
184C2×C42×C61C2311yescharacteristic
185C4⋊C8×C61C2314yes—
186#103×C61C2314yes—
187#103×C61C2314yes—
188C23×D61—21no—
189C23×D61—21no—
190C23×D61C2×D411yescharacteristic
191C2×Q8×C61—21no—
192C2×Q8×C61—21no—
193C2×Q8×C61—21no—
194C2×Q8×C61—22no—
195C2×Q8×C61—22no—
196C2×Q8×C61—22no—
197C2×Q8×C61—22no—
198C2×Q8×C61—22no—
199C2×Q8×C61—22no—
200C2×Q8×C61C2412yes—
201C2×Q8×C61C2412yes—
202C2×Q8×C61C2412yes—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61C2×D411yescharacteristic
208C22×C4×C61C2×D411yescharacteristic
209C22×C4×C61C2411yescharacteristic
210C22×Dic61—21no—
211C22×Dic61—21no—
212C22×Dic61C2×D411yescharacteristic
213C22×Dic61C2×D411yescharacteristic
214C22×Dic61C2×D411yescharacteristic
215#11758226—44no—
216#11758226—44no—
217#11758226—48no—
218Q8×D61—44no—
219Q8×D61—44no—
220Q8×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—44no—
230C2×D244—82no—
231C2×D244C2412yes—
232C2×D244C2412yes—
233C2×C4×D61—22no—
234C2×C4×D61—22no—
235C2×C4×D61—24no—
236C2×C4×D61—24no—
237C2×C4×D61—24no—
238C2×C4×D61—44no—
239C2×C4×D61—44no—
240C2×C4×D61—82no—
241C2×C4×D61C2×D412yes—
242C2×C4×D61C2412yes—
243C2×Dic122—22no—
244C2×Dic122—22no—
245C2×Dic122—21no—
246C2×Dic122—24no—
247C2×Dic122—24no—
248C2×Dic122—44no—
249C2×Dic122—82no—
250C2×Dic122C2412yes—
251Q16×C61—44no—
252Q16×C61—44no—
253C2×C8×C61—22no—
254C2×C8×C61—22no—
255C2×C8×C61C2412yes—
256C2×C8×C61C2412yes—
257C4⋊C4×C61—24no—
258C4⋊C4×C61—24no—
259C4⋊C4×C61—24no—
260C4⋊C4×C61—21no—
261C4⋊C4×C61C2412yes—
262C42×C61—24no—
263C42×C61C2×D412yes—
264C42×C61C2412yes—
265#11758202—44no—
266#11758201—44no—
267#11758201—44no—
268#11758201—44no—
269#11758198—24no—
270#11758198—24no—
271#11758198—24no—
272#11758198—24no—
273#11758198—24no—
274#11758198—24no—
275#11758198—24no—
276#11758198—24no—
277#11758198—24no—
278#11758198C2×D414yes—
279#11758198C2×D414yes—
280C4⋊Dic61—21no—
281C4⋊Dic61C2412yes—
282#11758196—24no—
283#11758196—24no—
284#11758196—24no—
285#11758196—24no—
286#11758196C2×D414yes—
287#11758196C2×D414yes—
288C4×Dic61C2×D412yes—
289C4×Dic61C2412yes—
290C2×#92418—22no—
291C2×#92418—22no—
292C2×#92418C2412yes—
293C2×#92418C2412yes—
294D488—44no—
295#11758190—44no—
296C23×C61C22×D411yescharacteristic
297C22×D61—22no—
298C22×D61—22no—
299C22×D61—22no—
300C22×D61—22no—
301C22×D61—22no—
302C22×D61—42no—
303C22×D61—42no—
304C22×D61—42no—
305C22×D61—42no—
306C22×D61—42no—
307C22×D61—42no—
308C22×D61C22×D412yes—
309Q8×C61—22no—
310Q8×C61—22no—
311Q8×C61—22no—
312Q8×C61—22no—
313Q8×C61—22no—
314Q8×C61—22no—
315Q8×C61—42no—
316Q8×C61—42no—
317Q8×C61—42no—
318C2×C4×C61—22no—
319C2×C4×C61—22no—
320C2×C4×C61—22no—
321C2×C4×C61—22no—
322C2×C4×C61—22no—
323C2×C4×C61—22no—
324C2×C4×C61—42no—
325C2×C4×C61—42no—
326C2×C4×C61—42no—
327C2×C4×C61—42no—
328C2×C4×C61C22×D412yes—
329C2×C4×C61C22×D412yes—
330C2×C4×C61C22×D411yescharacteristic
331C2×C4×C61H(5,𝔽2)12yes—
332C2×C4×C61H(5,𝔽2)12yes—
333C2×C4×C61C2511yescharacteristic
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—22no—
337C2×Dic61—22no—
338C2×Dic61—22no—
339C2×Dic61—42no—
340C2×Dic61—42no—
341C2×Dic61C22×D412yes—
342C2×Dic61C22×D412yes—
343C2×Dic61C22×D412yes—
344D244—22no—
345D244—22no—
346D244—22no—
347D244—22no—
348D244—48no—
349D244—42no—
350D244—42no—
351D244—84no—
352C4×D61—24no—
353C4×D61—22no—
354C4×D61—22no—
355C4×D61—48no—
356C4×D61—48no—
357C4×D61—84no—
358Dic122—22no—
359Dic122—22no—
360Dic122—48no—
361Dic122—42no—
362Dic122—84no—
363C8×C61—22no—
364C8×C61—22no—
365#92418—22no—
366#92418—22no—
367C2×#3225—611nomaximal, Sylow
368C22×C61#53512yes—
369C22×C61#57712yes—
370C22×C61#57812yes—
371C22×C61C23×D411yescharacteristic
372C2×D61—22no—
373C2×D61—22no—
374C2×D61—22no—
375C2×D61—44no—
376C2×D61—42no—
377C2×D61—42no—
378C2×D61—42no—
379C2×D61—42no—
380C2×D61—42no—
381C2×D61—42no—
382C2×D61—84no—
383C2×D61—84no—
384C4×C61—22no—
385C4×C61—22no—
386C4×C61—42no—
387C4×C61—42no—
388C4×C61—42no—
389C4×C61—42no—
390C4×C61#53512yes—
391C4×C61C2×H(5,𝔽2)11yescharacteristic
392C4×C61C2×H(5,𝔽2)11yescharacteristic
393Dic61—22no—
394Dic61—22no—
395Dic61—22no—
396Dic61—42no—
397Dic61—42no—
398C2×#542—611no—
399C2×#536—611no—
400#3225—6116no—
401C2×#497—611no—
402C2×#495—611no—
403C2×#489—611no—
404C2×#487—611no—
405C2×#464—611no—
406C2×#462D6111yescharacteristic, complemented
407C2×#463—611no—
408C2×#461—611no—
409C2×#452—611no—
410C2×#449—611no—
411C2×#451—611no—
412C2×#448—611no—
413C2×#433—611no—
414C2×C61#322514yescomplemented
415C2×C61C2×#53511yescharacteristic
416C2×C61C2×#57711yescharacteristic
417C2×C61C2×#57811yescharacteristic
418D61—42no—
419D61—82no—
420D61—82no—
421C22×#41—611no—
422C23×Q8—611no—
423C22×Q16—611no—
424C22×Q16C2×D6111yescharacteristic
425C22×Q16C2×D6111yescharacteristic
426C22×SD16—611no—
427C22×SD16—611no—
428C22×SD16—611no—
429C22×SD16—611no—
430C22×D8—611no—
431#542—618no—
432#542—1224no—
433#536—618no—
434#536—1224no—
435C2×C4⋊Q8—611no—
436C2×C4⋊Q8—611no—
437C2×C4⋊Q8C2×D6111yescharacteristic
438C2×#126—1221no—
439C2×#124—611no—
440C2×#124—611no—
441C2×#124—611no—
442C2×#124—1221no—
443C2×#123—1221no—
444C2×#123—1221no—
445C2×#123—1221no—
446C2×C22⋊Q8—611no—
447C2×C22⋊Q8—1221no—
448C2×C22⋊Q8—1221no—
449C2×C22⋊Q8—1221no—
450C2×#121—611no—
451C2×C4×Q8C2×D6111yescharacteristic
452C2×C4×D4—611no—
453C2×#117—611no—
454#497—618no—
455#495—618no—
456#489—618no—
457#487—618no—
458#464—618no—
459#463—618no—
460#462C2×D6118yescomplemented
461#461—618no—
462#452—618no—
463#451—618no—
464#449—618no—
465#448—618no—
466#433—618no—
467C2×C4⋊C8—611no—
468C2×C4⋊C8C2×D6111yescharacteristic
469C2×#103—611no—
470C2×#103—611no—
471C2×#103—611no—
472C2×#103—611no—
473C2×#103C2×D6111yescharacteristic
474C2×#103C2×D6111yescharacteristic
475C2×#102—611no—
476C2×#102—611no—
477C2×C22⋊C8—611no—
478C2×C22⋊C8—611no—
479C2×#97—611no—
480C2×C4×C8—611no—
481C61C2×#322511yescharacteristic, complemented, Sylow
482C2×#41—614no—
483C2×#41—1222no—
484C2×#41—2442no—
485C2×#41—2442no—
486C22×Q8—614no—
487C22×Q8—611no—
488C22×Q8—1221no—
489C22×Q8—1221no—
490C22×Q8—1222no—
491C22×Q8—2442no—
492C22×Q8—2442no—
493C22×Q8C22×D6111yescharacteristic
494C22×Q8C22×D6111yescharacteristic
495C22×Q8C22×D6111yescharacteristic
496C22×D4—611no—
497C22×D4—611no—
498C22×D4—1221no—
499C22×D4—1221no—
500C23×C4—611no—
501C23×C4—1221no—
502C23×C4—1221no—
503C23×C4—1221no—
504C2×Q16—42no—
505C2×Q16—42no—
506C2×Q16—614no—
507C2×Q16—2442no—
508C2×Q16C22×D6114yes—
509C2×Q16C22×D6114yes—
510C2×SD16—614no—
511C2×SD16—614no—
512C2×SD16—614no—
513C2×SD16—614no—
514C2×SD16—2442no—
515C2×SD16—2442no—
516C2×SD16—2442no—
517C2×SD16—2442no—
518C2×D8—614no—
519C2×D8—2442no—
520C22×C8—611no—
521C22×C8—611no—
522C22×C8C22×D6111yescharacteristic
523C22×C8C22×D6111yescharacteristic
524C4⋊Q8—22no—
525C4⋊Q8—614no—
526C4⋊Q8—614no—
527C4⋊Q8—1222no—
528C4⋊Q8—1222no—
529C4⋊Q8C22×D6114yes—
530#126—1228no—
531#124—614no—
532#124—614no—
533#124—614no—
534#124—1228no—
535#124—1222no—
536#124—1222no—
537#124—1222no—
538#123—1228no—
539#123—1228no—
540#123—1228no—
541C22⋊Q8—614no—
542C22⋊Q8—1228no—
543C22⋊Q8—1228no—
544C22⋊Q8—1228no—
545C22⋊Q8—1222no—
546#121—614no—
547#121—1222no—
548C4×Q8—22no—
549C4×Q8C22×D6114yes—
550C4×D4—614no—
551C4×D4—1222no—
552#117—614no—
553#117—614no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—611no—
558C2×C4⋊C4—611no—
559C2×C4⋊C4—611no—
560C2×C4⋊C4—1221no—
561C2×C4⋊C4—1221no—
562C2×C4⋊C4—1221no—
563C2×C4⋊C4—1221no—
564C2×C4⋊C4C22×D6111yescharacteristic
565C2×C22⋊C4—611no—
566C2×C22⋊C4—611no—
567C2×C22⋊C4—1221no—
568C2×C22⋊C4—1221no—
569C2×C22⋊C4—1221no—
570C2×C22⋊C4—1221no—
571C2×C22⋊C4—1221no—
572C2×C22⋊C4—1221no—
573C2×C22⋊C4—1221no—
574C2×C22⋊C4—1221no—
575C2×C22⋊C4—1221no—
576C2×C42—21no—
577C2×C42—611no—
578C2×C42C22×D6111yescharacteristic
579C4⋊C8—614no—
580C4⋊C8C22×D6114yes—
581#103—614no—
582#103—614no—
583#103—614no—
584#103—614no—
585#103C22×D6114yes—
586#103C22×D6114yes—
587#102—614no—
588#102—614no—
589C22⋊C8—614no—
590C22⋊C8—614no—
591#97—614no—
592C4×C8—614no—
593C24—611no—
594C24—1221no—
595C24—1221no—
596#41—2444no—
597#41—2444no—
598#41—2448no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—22no—
603C2×Q8—22no—
604C2×Q8—22no—
605C2×Q8—22no—
606C2×Q8—22no—
607C2×Q8—22no—
608C2×Q8—612no—
609C2×Q8—1224no—
610C2×Q8—1224no—
611C2×Q8—1221no—
612C2×Q8—1222no—
613C2×Q8—1222no—
614C2×Q8—4882no—
615C2×Q8—2444no—
616C2×Q8—2444no—
617C2×Q8—2444no—
618C2×Q8—2448no—
619C2×Q8C23×D6112yes—
620C2×Q8C23×D6112yes—
621C2×Q8C23×D6112yes—
622C2×D4—612no—
623C2×D4—612no—
624C2×D4—1224no—
625C2×D4—1224no—
626C2×D4—1221no—
627C2×D4—1221no—
628C2×D4—1222no—
629C2×D4—1222no—
630C2×D4—1222no—
631C2×D4—1222no—
632C2×D4—4882no—
633C2×D4—2444no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—611no—
639C22×C4—611no—
640C22×C4—611no—
641C22×C4—612no—
642C22×C4—612no—
643C22×C4—1224no—
644C22×C4—1224no—
645C22×C4—1222no—
646C22×C4—1222no—
647C22×C4—1221no—
648C22×C4—1221no—
649C22×C4—1224no—
650C22×C4—4882no—
651C22×C4—2444no—
652C22×C4—2444no—
653C22×C4D4×D6111yescharacteristic
654C22×C4D4×D6111yescharacteristic
655C22×C4C23×D6111yescharacteristic
656Q16—44no—
657Q16—44no—
658Q16—2444no—
659SD16—2444no—
660SD16—2444no—
661SD16—2444no—
662SD16—2444no—
663D8—2444no—
664C2×C8—22no—
665C2×C8—22no—
666C2×C8—612no—
667C2×C8—612no—
668C2×C8—1222no—
669C2×C8—1222no—
670C2×C8C23×D6112yes—
671C2×C8C23×D6112yes—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—24no—
675C4⋊C4—21no—
676C4⋊C4—614no—
677C4⋊C4—614no—
678C4⋊C4—612no—
679C4⋊C4—1224no—
680C4⋊C4—1224no—
681C4⋊C4—1224no—
682C4⋊C4—1224no—
683C4⋊C4—1221no—
684C4⋊C4C23×D6112yes—
685C22⋊C4—614no—
686C22⋊C4—614no—
687C22⋊C4—1224no—
688C22⋊C4—1224no—
689C22⋊C4—1224no—
690C22⋊C4—1224no—
691C22⋊C4—1224no—
692C22⋊C4—1224no—
693C22⋊C4—1224no—
694C22⋊C4—1224no—
695C22⋊C4—1224no—
696C42—24no—
697C42—612no—
698C42—612no—
699C42D4×D6112yes—
700C42C23×D6112yes—
701C23—612no—
702C23—1222no—
703C23—1222no—
704C23—1222no—
705C23—1222no—
706C23—1222no—
707C23—2442no—
708C23—2442no—
709C23—2442no—
710C23—2442no—
711C23—2442no—
712C23—2442no—
713C23C2×D4×D6111yescharacteristic
714Q8—22no—
715Q8—22no—
716Q8—22no—
717Q8—22no—
718Q8—22no—
719Q8—22no—
720Q8—42no—
721Q8—42no—
722Q8—42no—
723Q8—1222no—
724Q8—1222no—
725Q8—4884no—
726Q8—2448no—
727Q8—2442no—
728D4—1222no—
729D4—1222no—
730D4—1222no—
731D4—1222no—
732D4—4884no—
733D4—2448no—
734D4—2442no—
735D4—2442no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—612no—
747C2×C4—612no—
748C2×C4—612no—
749C2×C4—1222no—
750C2×C4—1222no—
751C2×C4—1222no—
752C2×C4—1224no—
753C2×C4—1222no—
754C2×C4—1222no—
755C2×C4—1222no—
756C2×C4—1222no—
757C2×C4—4884no—
758C2×C4—2448no—
759C2×C4—2448no—
760C2×C4—2442no—
761C2×C4—2442no—
762C2×C4C2×D4×D6112yes—
763C2×C4C2×D4×D6112yes—
764C2×C4C2×D4×D6111yescharacteristic
765C2×C4#1451982212yes—
766C2×C4#1451982312yes—
767C2×C4C24×D6111yescharacteristic
768C8—22no—
769C8—22no—
770C8—1222no—
771C8—1222no—
772C22—1222no—
773C22—1222no—
774C22—1222no—
775C22—4884no—
776C22—4884no—
777C22—2442no—
778C22—2442no—
779C22—2442no—
780C22—2442no—
781C22—2442no—
782C22—2442no—
783C22—2444no—
784C22#1684032812yes—
785C22#1684057112yes—
786C22#1684057512yes—
787C22C22×D4×D6111yescharacteristic
788C4—22no—
789C4—22no—
790C4—42no—
791C4—42no—
792C4—42no—
793C4—42no—
794C4—1222no—
795C4—1222no—
796C4—1222no—
797C4—2442no—
798C4—2442no—
799C4#1684032812yes—
800C4C2×#1451982211yescharacteristic
801C4C2×#1451982311yescharacteristic
802C2—4882no—
803C2—4882no—
804C2—2442no—
805C2#2145693514yesdirect product factor
806C2C2×#1684032811yescharacteristic
807C2C2×#1684057111yescharacteristic
808C2C2×#1684057511yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#462C2
socleC23×C61C22×D4
prime radicalC2×#16839910C2
hypercenterC2×#462D61
hypocenterC61C2×#3225
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
1. C2×#16840384C2semidirect
2. C2×#16840337C2semidirect
3. #21456935C2direct (N × H)
4. C2×#16840155C2semidirect
5. C2×#16840147C2semidirect
6. C2×#16840123C2semidirect
7. C2×#16840111C2semidirect
8. C2×#16839984C2semidirect
9. C2×#16839978C2semidirect
10. C2×#16839964C2semidirect
11. C2×#16839923C2semidirect
13. C2×#16839916C2semidirect
14. C2×#16839902C2semidirect
15. C2×#16839822C2semidirect
16. C2×C61×#462C2semidirect
26. #16840384C22semidirect
28. #16840337C22semidirect
46. #16840155C22semidirect
47. #16840147C22semidirect
48. #16840123C22semidirect
49. #16840111C22semidirect
50. #16839984C22semidirect
51. #16839978C22semidirect
52. #16839964C22semidirect
53. #16839923C22semidirect
54. #16839916C22semidirect
56. #16839902C22semidirect
57. #16839822C22semidirect
73. C61×#462C22semidirect
406. C2×#462D61semidirect
414. C2×C61#3225semidirect
460. #462C2×D61semidirect
481. C61C2×#3225semidirect
805. C2#21456935direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403842
C2×#168403372
#214569352
C2×#168401552
C2×#168401472
C2×#168401232
C2×#168401112
C2×#168399842
C2×#168399782
C2×#168399642
C2×#168399232
C2×#168399102
C2×#168399162
C2×#168399022
C2×#168398222
C2×C61×#4622
C2×#322561