Finite Group Databasebeta

← C2×#21456899 #30551393

Subgroups — C2×#21456899 #30551393

Order 15616.

2022 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840370C211yesmaximal, characteristic, complemented
2C2×#16840332C211yesmaximal, characteristic
3#21456899C2116yesmaximal, direct product factor
4C2×#16840153C211yesmaximal, characteristic, complemented
5C2×#16840140C211yesmaximal, characteristic, complemented
6C2×#16840129C211yesmaximal, characteristic, complemented
7C2×#16840115C211yesmaximal, characteristic, complemented
8C2×#16839981C211yesmaximal, characteristic, complemented
9C2×#16839973C211yesmaximal, characteristic, complemented
10C2×#16839972C211yesmaximal, characteristic, complemented
11C2×#16839925C211yesmaximal, characteristic
12C2×#16839921C211yesmaximal, characteristic
13C2×#16839919C211yesmaximal, characteristic, complemented
14C2×#16839916C211yesmaximal, characteristic, complemented
15C2×#16839822C211yesmaximal, characteristic, complemented
16C2×C61×#464C211yesmaximal, characteristic, complemented
17C22×#11758224C2211yescharacteristic
18C22×Q8×D61C2211yescharacteristic
19C22×Dic244C2211yescharacteristic
20C22×Dic244C2211yescharacteristic
21C22×#11758202C2211yescharacteristic
22C22×#11758202C2211yescharacteristic
23C22×#11758202C2211yescharacteristic
24C22×#11758200C2211yescharacteristic
25#16840370—24no—
26#16840370C2218yescomplemented
27#16840332—24no—
28#16840332C2218yes—
29C2×#14519777C2211yescharacteristic
30C2×#14519775C2211yescharacteristic
31C2×#14519775C2211yescharacteristic
32C2×#14519772—21no—
33C2×#14519771—21no—
34C2×#14519769—21no—
35C2×#14519768C2211yescharacteristic
36C2×#14519767—21no—
37C2×#14519764C2211yescharacteristic
38C2×#14519759—21no—
39C2×#14519759—21no—
40C2×#14519757C2211yescharacteristic
41C2×#14519754—21no—
42C2×#14519754—21no—
43C2×#14519753C2211yescharacteristic
44C2×C4×Dic122C2211yescharacteristic
45C2×#14519734C2211yescharacteristic
46#16840153C2218yescomplemented
47#16840140C2218yescomplemented
48#16840129C2218yescomplemented
49#16840115C2218yescomplemented
50#16839981C2218yescomplemented
51#16839973C2218yescomplemented
52#16839972C2218yescomplemented
53#16839925C2218yes—
54#16839921C2218yes—
55#16839919C2218yescomplemented
56#16839916C2218yescomplemented
57#16839822C2218yescomplemented
58C2×C4⋊#92418C2211yescharacteristic
59C2×#14519702C2211yescharacteristic
60C2×#14519702C2211yescharacteristic
61C2×#14519701C2211yescharacteristic
62C2×#14519700C2211yescharacteristic
63C2×#14519700C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65C2×#14519689C2211yescharacteristic
66C2×#14519689C2211yescharacteristic
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
77C2×#11758224—22no—
78C2×#11758224—42no—
79C2×#11758224—42no—
80C2×#11758224C2314yes—
81C22×Dic122—21no—
82C22×Dic122C2311yescharacteristic
83C22×Dic122C2311yescharacteristic
84C22×Dic122C2311yescharacteristic
85C2×Q8×D61—22no—
86C2×Q8×D61—42no—
87C2×Q8×D61—42no—
88C2×Q8×D61C2314yes—
89C22×C22⋊D61—21no—
90C23×Dic61—21no—
91C22×C4×D61—21no—
92C22×C4×D61C2311yescharacteristic
93C2×Dic244—42no—
94C2×Dic244—42no—
95C2×Dic244C2314yes—
96C2×Dic244C2314yes—
97C2×#11758202—42no—
98C2×#11758202—42no—
99C2×#11758202—42no—
100C2×#11758202C2314yes—
101C2×#11758202C2314yes—
102C2×#11758202C2314yes—
103C2×#11758200—42no—
104C2×#11758200C2314yes—
105C22×#92418C2311yescharacteristic
106C22×#92418C2311yescharacteristic
107#14519777—22no—
108#14519777C2314yes—
109#14519775—22no—
110#14519775—22no—
111#14519775C2314yes—
112#14519775C2314yes—
113#14519772—28no—
114#14519771—28no—
115#14519769—28no—
116#14519768—22no—
117#14519768C2314yes—
118#14519767—28no—
119#14519764—22no—
120#14519764C2314yes—
121#14519759—28no—
122#14519759—28no—
123#14519757—22no—
124#14519757C2314yes—
125#14519754—28no—
126#14519754—28no—
127#14519753—22no—
128#14519753C2314yes—
129C4×Dic122—22no—
130C4×Dic122C2314yes—
131#14519734D414yes—
132#14519734C2314yes—
133C2×C4⋊Dic61—21no—
134C2×C4⋊Dic61—21no—
135C2×C4⋊Dic61—21no—
136C2×C4⋊Dic61—21no—
137C2×C4⋊Dic61C2311yescharacteristic
138C2×#11758196—21no—
139C2×#11758196—21no—
140C2×#11758196—21no—
141C2×#11758196—21no—
142C2×#11758196—21no—
143C2×#11758196—21no—
144C2×#11758196—21no—
145C2×#11758196D411yescharacteristic
146C2×#11758196D411yescharacteristic
147C2×C22⋊Dic61—21no—
148C2×C22⋊Dic61—21no—
149C2×#11758198—21no—
150C2×#11758198—21no—
151C2×#11758198D411yescharacteristic
152C2×#11758198D411yescharacteristic
153C2×C4×Dic61—21no—
154C2×C4×Dic61C2311yescharacteristic
155C4⋊#92418C2314yes—
156#14519702C2314yes—
157#14519702C2314yes—
158#14519701C2314yes—
159#14519700C2314yes—
160#14519700C2314yes—
161#14519698C2314yes—
162#14519689C2314yes—
163#14519689C2314yes—
164#14519687C2314yes—
165C8×Dic61C2314yes—
166C22×Q8×C61C2311yescharacteristic
167C22×Q8×C61C2311yescharacteristic
168C22×D4×C61C2311yescharacteristic
169C2×Q16×C61—42no—
170C2×Q16×C61C2314yes—
171C2×SD16×C61—42no—
172C2×SD16×C61C2314yes—
173C22×C8×C61C2311yescharacteristic
174C22×C8×C61C2311yescharacteristic
175#124×C61—22no—
176#124×C61C2314yes—
177C4×Q8×C61—22no—
178C4×Q8×C61C2314yes—
179C2×C4⋊C4×C61—21no—
180C2×C4⋊C4×C61C2311yescharacteristic
181C2×C22⋊C4×C61—21no—
182C2×C22⋊C4×C61—21no—
183C2×C42×C61—21no—
184C2×C42×C61C2311yescharacteristic
185C4⋊C8×C61C2314yes—
186#103×C61C2314yes—
187#102×C61C2314yes—
188C24×C61—21no—
189C23×D61C2×D411yescharacteristic
190C2×Q8×C61—21no—
191C2×Q8×C61—21no—
192C2×Q8×C61—22no—
193C2×Q8×C61—22no—
194C2×Q8×C61—22no—
195C2×Q8×C61—22no—
196C2×Q8×C61C2412yes—
197C2×Q8×C61C2412yes—
198C2×D4×C61—21no—
199C2×D4×C61—22no—
200C2×D4×C61—22no—
201C2×D4×C61C2412yes—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61C2×D411yescharacteristic
206C22×C4×C61C2×D411yescharacteristic
207C22×C4×C61C2411yescharacteristic
208C2×C22⋊D61—24no—
209C2×C22⋊D61—44no—
210C22×Dic61—21no—
211C22×Dic61—21no—
212C22×Dic61—21no—
213C22×Dic61—21no—
214C22×Dic61—24no—
215C22×Dic61—44no—
216C22×Dic61C2×D411yescharacteristic
217C22×Dic61C2×D411yescharacteristic
218C22×Dic61C2×D411yescharacteristic
219Q8×D61—44no—
220Q8×D61—44no—
221Q8×D61—48no—
222#11758224—44no—
223#11758224—44no—
224#11758224—48no—
225C2×C4×D61—22no—
226C2×C4×D61—22no—
227C2×C4×D61—24no—
228C2×C4×D61—44no—
229C2×C4×D61C2×D412yes—
230C2×C4×D61C2412yes—
231C2×Dic122—22no—
232C2×Dic122—22no—
233C2×Dic122—22no—
234C2×Dic122—22no—
235C2×Dic122—22no—
236C2×Dic122—22no—
237C2×Dic122—21no—
238C2×Dic122—21no—
239C2×Dic122—21no—
240C2×Dic122—24no—
241C2×Dic122—44no—
242C2×Dic122C2412yes—
243C2×Dic122C2412yes—
244C2×Dic122C2412yes—
245Q16×C61—44no—
246SD16×C61—44no—
247C2×C8×C61—22no—
248C2×C8×C61—22no—
249C2×C8×C61C2412yes—
250C2×C8×C61C2412yes—
251C4⋊C4×C61—24no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61C2412yes—
254C22⋊C4×C61—24no—
255C22⋊C4×C61—24no—
256C42×C61—24no—
257C42×C61C2×D412yes—
258C42×C61C2412yes—
259C22⋊Dic61—24no—
260C22⋊Dic61—24no—
261#11758202—44no—
262#11758202—44no—
263#11758202—44no—
264#11758200—44no—
265#11758198—24no—
266#11758198—24no—
267#11758198C2×D414yes—
268#11758198C2×D414yes—
269C4⋊Dic61—24no—
270C4⋊Dic61—24no—
271C4⋊Dic61—21no—
272C4⋊Dic61—24no—
273C4⋊Dic61—24no—
274C4⋊Dic61C2412yes—
275#11758196—24no—
276#11758196—24no—
277#11758196—24no—
278#11758196—24no—
279#11758196—24no—
280#11758196—24no—
281#11758196—24no—
282#11758196C2×D414yes—
283#11758196C2×D414yes—
284C4×Dic61—24no—
285C4×Dic61C2×D412yes—
286C4×Dic61C2412yes—
287C2×#92418—22no—
288C2×#92418—22no—
289C2×#92418C2412yes—
290C2×#92418C2412yes—
291Dic244—44no—
292Dic244—44no—
293C23×C61—22no—
294C23×C61—42no—
295C23×C61—42no—
296C23×C61—42no—
297C23×C61C22×D411yescharacteristic
298C22×D61—22no—
299C22×D61—22no—
300C22×D61—22no—
301C22×D61C22×D412yes—
302Q8×C61—22no—
303Q8×C61—22no—
304Q8×C61—22no—
305Q8×C61—22no—
306Q8×C61—42no—
307Q8×C61—42no—
308D4×C61—22no—
309D4×C61—22no—
310D4×C61—42no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—22no—
315C2×C4×C61—22no—
316C2×C4×C61—42no—
317C2×C4×C61—42no—
318C2×C4×C61—42no—
319C2×C4×C61C22×D412yes—
320C2×C4×C61C22×D412yes—
321C2×C4×C61C22×D411yescharacteristic
322C2×C4×C61H(5,𝔽2)12yes—
323C2×C4×C61H(5,𝔽2)12yes—
324C2×C4×C61C2511yescharacteristic
325C22⋊D61—48no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—48no—
334C2×Dic61—42no—
335C2×Dic61—42no—
336C2×Dic61—42no—
337C2×Dic61—42no—
338C2×Dic61C22×D412yes—
339C2×Dic61C22×D412yes—
340C2×Dic61C22×D412yes—
341C4×D61—24no—
342C4×D61—22no—
343C4×D61—22no—
344C4×D61—48no—
345Dic122—22no—
346Dic122—22no—
347Dic122—22no—
348Dic122—22no—
349Dic122—22no—
350Dic122—22no—
351Dic122—48no—
352Dic122—42no—
353Dic122—42no—
354Dic122—42no—
355C8×C61—22no—
356C8×C61—22no—
357#92418—22no—
358#92418—22no—
359C2×#3223—611nomaximal, Sylow
360C22×C61—42no—
361C22×C61—42no—
362C22×C61—42no—
363C22×C61—84no—
364C22×C61#53512yes—
365C22×C61#57812yes—
366C22×C61#57812yes—
367C22×C61C23×D411yescharacteristic
368C2×D61—22no—
369C2×D61—22no—
370C2×D61—22no—
371C2×D61—44no—
372C4×C61—22no—
373C4×C61—22no—
374C4×C61—42no—
375C4×C61—42no—
376C4×C61—42no—
377C4×C61#53512yes—
378C4×C61C2×H(5,𝔽2)11yescharacteristic
379C4×C61C2×H(5,𝔽2)11yescharacteristic
380Dic61—22no—
381Dic61—22no—
382Dic61—22no—
383Dic61—42no—
384Dic61—42no—
385Dic61—42no—
386Dic61—42no—
387C2×#541—611no—
388C2×#536—611no—
389#3223—6116no—
390C2×#497—611no—
391C2×#494—611no—
392C2×#491—611no—
393C2×#488—611no—
394C2×#464—611no—
395C2×#464D6111yescharacteristic, complemented
396C2×#462—611no—
397C2×#462—611no—
398C2×#452—611no—
399C2×#452—611no—
400C2×#451—611no—
401C2×#451—611no—
402C2×#433—611no—
403C2×C61—82no—
404C2×C61#322314yescomplemented
405C2×C61C2×#53511yescharacteristic
406C2×C61C2×#57811yescharacteristic
407C2×C61C2×#57811yescharacteristic
408D61—42no—
409C22×#41—611no—
410C23×Q8—611no—
411C22×Q16—611no—
412C22×Q16—611no—
413C22×Q16—611no—
414C22×Q16—611no—
415C22×Q16—611no—
416C22×Q16C2×D6111yescharacteristic
417C22×SD16—611no—
418C22×SD16C2×D6111yescharacteristic
419#541—618no—
420#541—1224no—
421#536—618no—
422#536—1224no—
423C2×C4⋊Q8—611no—
424C2×C4⋊Q8—611no—
425C2×C4⋊Q8—611no—
426C2×#126—1221no—
427C2×#126—1221no—
428C2×#125—611no—
429C2×#125—1221no—
430C2×#125—1221no—
431C2×#124—611no—
432C2×#124C2×D6111yescharacteristic
433C2×#123—1221no—
434C2×#123—1221no—
435C2×C22⋊Q8—611no—
436C2×C22⋊Q8—611no—
437C2×C22⋊Q8—1221no—
438C2×C22⋊Q8—1221no—
439C2×C4×Q8—611no—
440C2×C4×Q8C2×D6111yescharacteristic
441C2×#117—611no—
442#497—618no—
443#494—618no—
444#491—618no—
445#488—618no—
446#464—618no—
447#464C2×D6118yescomplemented
448#462—618no—
449#462—618no—
450#452—618no—
451#452—618no—
452#451—618no—
453#451—618no—
454#433—618no—
455C2×C4⋊C8—611no—
456C2×C4⋊C8C2×D6111yescharacteristic
457C2×#103—611no—
458C2×#103—611no—
459C2×#103—611no—
460C2×#103—611no—
461C2×#103—611no—
462C2×#103C2×D6111yescharacteristic
463C2×#102—611no—
464C2×#102C2×D6111yescharacteristic
465C2×C22⋊C8—611no—
466C2×C22⋊C8—611no—
467C2×#97—611no—
468C2×C4×C8—611no—
469C61C2×#322311yescharacteristic, complemented, Sylow
470C2×#41—614no—
471C2×#41—1222no—
472C2×#41—2442no—
473C2×#41—2442no—
474C22×Q8—614no—
475C22×Q8—611no—
476C22×Q8—611no—
477C22×Q8—611no—
478C22×Q8—1221no—
479C22×Q8—1222no—
480C22×Q8—2442no—
481C22×Q8—2442no—
482C22×Q8C22×D6111yescharacteristic
483C22×Q8C22×D6111yescharacteristic
484C22×D4—1221no—
485C22×D4C22×D6111yescharacteristic
486C23×C4—611no—
487C23×C4—1221no—
488C23×C4—1221no—
489C2×Q16—42no—
490C2×Q16—614no—
491C2×Q16—614no—
492C2×Q16—614no—
493C2×Q16—614no—
494C2×Q16—614no—
495C2×Q16—2442no—
496C2×Q16—2442no—
497C2×Q16—2442no—
498C2×Q16—2442no—
499C2×Q16—2442no—
500C2×Q16C22×D6114yes—
501C2×SD16—42no—
502C2×SD16—614no—
503C2×SD16—2442no—
504C2×SD16C22×D6114yes—
505C22×C8—611no—
506C22×C8—611no—
507C22×C8C22×D6111yescharacteristic
508C22×C8C22×D6111yescharacteristic
509C4⋊Q8—614no—
510C4⋊Q8—614no—
511C4⋊Q8—614no—
512C4⋊Q8—1222no—
513C4⋊Q8—1222no—
514C4⋊Q8—1222no—
515#126—1228no—
516#126—1228no—
517#125—614no—
518#125—1228no—
519#125—1222no—
520#125—1228no—
521#124—22no—
522#124—614no—
523#124—1222no—
524#124C22×D6114yes—
525#123—1228no—
526#123—1228no—
527C22⋊Q8—614no—
528C22⋊Q8—614no—
529C22⋊Q8—1228no—
530C22⋊Q8—1228no—
531C22⋊Q8—1222no—
532C22⋊Q8—1222no—
533C4×Q8—22no—
534C4×Q8—614no—
535C4×Q8—1222no—
536C4×Q8C22×D6114yes—
537#117—614no—
538#117—614no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—611no—
541C2×C4⋊C4—611no—
542C2×C4⋊C4—611no—
543C2×C4⋊C4—1221no—
544C2×C4⋊C4—1221no—
545C2×C4⋊C4—1221no—
546C2×C4⋊C4—1221no—
547C2×C4⋊C4—1221no—
548C2×C4⋊C4—1221no—
549C2×C4⋊C4—1221no—
550C2×C4⋊C4—1221no—
551C2×C4⋊C4—1221no—
552C2×C4⋊C4—1221no—
553C2×C4⋊C4—1221no—
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×C22⋊C4—1221no—
563C2×C42—21no—
564C2×C42—611no—
565C2×C42—1221no—
566C2×C42C22×D6111yescharacteristic
567C4⋊C8—614no—
568C4⋊C8C22×D6114yes—
569#103—614no—
570#103—614no—
571#103—614no—
572#103—614no—
573#103—614no—
574#103C22×D6114yes—
575#102—614no—
576#102C22×D6114yes—
577C22⋊C8—614no—
578C22⋊C8—614no—
579#97—614no—
580C4×C8—614no—
581C24—21no—
582C24—611no—
583#41—2444no—
584#41—2444no—
585#41—2448no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—22no—
589C2×Q8—22no—
590C2×Q8—22no—
591C2×Q8—22no—
592C2×Q8—612no—
593C2×Q8—612no—
594C2×Q8—612no—
595C2×Q8—1224no—
596C2×Q8—1221no—
597C2×Q8—1221no—
598C2×Q8—1221no—
599C2×Q8—1222no—
600C2×Q8—1222no—
601C2×Q8—1222no—
602C2×Q8—1222no—
603C2×Q8—1222no—
604C2×Q8—1222no—
605C2×Q8—2444no—
606C2×Q8—2444no—
607C2×Q8—2444no—
608C2×Q8—2448no—
609C2×Q8C23×D6112yes—
610C2×Q8C23×D6112yes—
611C2×D4—21no—
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—1224no—
615C2×D4—2444no—
616C2×D4C23×D6112yes—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—611no—
621C22×C4—611no—
622C22×C4—611no—
623C22×C4—612no—
624C22×C4—612no—
625C22×C4—1224no—
626C22×C4—1224no—
627C22×C4—1222no—
628C22×C4—1222no—
629C22×C4—1221no—
630C22×C4—1221no—
631C22×C4—1221no—
632C22×C4—1221no—
633C22×C4—2444no—
634C22×C4—2444no—
635C22×C4D4×D6111yescharacteristic
636C22×C4D4×D6111yescharacteristic
637C22×C4C23×D6111yescharacteristic
638Q16—44no—
639Q16—2444no—
640Q16—2444no—
641Q16—2444no—
642Q16—2444no—
643Q16—2444no—
644SD16—44no—
645SD16—2444no—
646C2×C8—22no—
647C2×C8—22no—
648C2×C8—612no—
649C2×C8—612no—
650C2×C8—1222no—
651C2×C8—1222no—
652C2×C8C23×D6112yes—
653C2×C8C23×D6112yes—
654C4⋊C4—24no—
655C4⋊C4—21no—
656C4⋊C4—614no—
657C4⋊C4—614no—
658C4⋊C4—612no—
659C4⋊C4—1224no—
660C4⋊C4—1224no—
661C4⋊C4—1224no—
662C4⋊C4—1224no—
663C4⋊C4—1224no—
664C4⋊C4—1224no—
665C4⋊C4—1224no—
666C4⋊C4—1224no—
667C4⋊C4—1221no—
668C4⋊C4—1224no—
669C4⋊C4—1224no—
670C4⋊C4—1224no—
671C4⋊C4C23×D6112yes—
672C22⋊C4—24no—
673C22⋊C4—24no—
674C22⋊C4—614no—
675C22⋊C4—614no—
676C22⋊C4—1224no—
677C22⋊C4—1224no—
678C22⋊C4—1224no—
679C22⋊C4—1224no—
680C42—24no—
681C42—612no—
682C42—612no—
683C42—1224no—
684C42D4×D6112yes—
685C42C23×D6112yes—
686C23—22no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—612no—
691C23—1222no—
692C23—1222no—
693C23—1222no—
694C23C2×D4×D6111yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—22no—
698Q8—22no—
699Q8—42no—
700Q8—42no—
701Q8—1222no—
702Q8—1222no—
703Q8—1222no—
704Q8—1222no—
705Q8—1222no—
706Q8—1222no—
707Q8—2448no—
708Q8—2442no—
709Q8—2442no—
710Q8—2442no—
711D4—22no—
712D4—22no—
713D4—42no—
714D4—2448no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—612no—
724C2×C4—612no—
725C2×C4—612no—
726C2×C4—1222no—
727C2×C4—1222no—
728C2×C4—1222no—
729C2×C4—1224no—
730C2×C4—1222no—
731C2×C4—1222no—
732C2×C4—1222no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—2448no—
737C2×C4—2448no—
738C2×C4—2442no—
739C2×C4—2442no—
740C2×C4—2442no—
741C2×C4—2442no—
742C2×C4C2×D4×D6112yes—
743C2×C4C2×D4×D6112yes—
744C2×C4C2×D4×D6111yescharacteristic
745C2×C4#1451982212yes—
746C2×C4#1451982312yes—
747C2×C4C24×D6111yescharacteristic
748C8—22no—
749C8—22no—
750C8—1222no—
751C8—1222no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—84no—
756C22—1222no—
757C22—1222no—
758C22—1222no—
759C22—2444no—
760C22#1684032812yes—
761C22#1684057612yes—
762C22#1684057812yes—
763C22C22×D4×D6111yescharacteristic
764C4—22no—
765C4—22no—
766C4—42no—
767C4—42no—
768C4—42no—
769C4—1222no—
770C4—1222no—
771C4—1222no—
772C4—2442no—
773C4—2442no—
774C4—2442no—
775C4—2442no—
776C4#1684032812yes—
777C4C2×#1451982211yescharacteristic
778C4C2×#1451982311yescharacteristic
779C2—82no—
780C2—2442no—
781C2#2145689914yesdirect product factor
782C2C2×#1684032811yescharacteristic
783C2C2×#1684057611yescharacteristic
784C2C2×#1684057811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#464C2
socleC23×C61C22×D4
prime radicalC22×#11758224C22
hypercenterC2×#464D61
hypocenterC61C2×#3223
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×#16840370C2semidirect
3. #21456899C2direct (N × H)
4. C2×#16840153C2semidirect
5. C2×#16840140C2semidirect
6. C2×#16840129C2semidirect
7. C2×#16840115C2semidirect
8. C2×#16839981C2semidirect
9. C2×#16839973C2semidirect
10. C2×#16839972C2semidirect
13. C2×#16839919C2semidirect
14. C2×#16839916C2semidirect
15. C2×#16839822C2semidirect
16. C2×C61×#464C2semidirect
26. #16840370C22semidirect
46. #16840153C22semidirect
47. #16840140C22semidirect
48. #16840129C22semidirect
49. #16840115C22semidirect
50. #16839981C22semidirect
51. #16839973C22semidirect
52. #16839972C22semidirect
55. #16839919C22semidirect
56. #16839916C22semidirect
57. #16839822C22semidirect
73. C61×#464C22semidirect
395. C2×#464D61semidirect
404. C2×C61#3223semidirect
447. #464C2×D61semidirect
469. C61C2×#3223semidirect
781. C2#21456899direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403702
C2×#168403322
#214568992
C2×#168401532
C2×#168401402
C2×#168401292
C2×#168401152
C2×#168399812
C2×#168399732
C2×#168399722
C2×#168399252
C2×#168399212
C2×#168399192
C2×#168399162
C2×#168398222
C2×C61×#4642
C2×#322361