Finite Group Databasebeta

← C2×#21456900 #30551394

Subgroups — C2×#21456900 #30551394

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×#16840372C211yesmaximal, characteristic, complemented
2C2×#16840333C211yesmaximal, characteristic
3#21456900C2116yesmaximal, direct product factor
4C2×#16840153C211yesmaximal, characteristic, complemented
5C2×#16840140C211yesmaximal, characteristic, complemented
6C2×#16840129C211yesmaximal, characteristic, complemented
7C2×#16840115C211yesmaximal, characteristic, complemented
8C2×#16839983C211yesmaximal, characteristic, complemented
9C2×#16839982C211yesmaximal, characteristic, complemented
10C2×#16839971C211yesmaximal, characteristic, complemented
11C2×#16839970C211yesmaximal, characteristic, complemented
12C2×#16839924C211yesmaximal, characteristic
13C2×#16839920C211yesmaximal, characteristic, complemented
14C2×#16839917C211yesmaximal, characteristic, complemented
15C2×#16839820C211yesmaximal, characteristic, complemented
16C2×C61×#452C211yesmaximal, characteristic
17C23×Dic122C2211yescharacteristic
18C22×Dic244C2211yescharacteristic
19C22×Dic244C2211yescharacteristic
20C22×#11758202C2211yescharacteristic
21C22×#11758202C2211yescharacteristic
22C22×#11758202C2211yescharacteristic
23C22×#11758200C2211yescharacteristic
24#16840372—24no—
25#16840372C2218yescomplemented
26#16840333—24no—
27#16840333C2218yes—
28C2×#14519775C2211yescharacteristic
29C2×#14519775C2211yescharacteristic
30C2×#14519775C2211yescharacteristic
31C2×#14519770—21no—
32C2×#14519770—21no—
33C2×#14519768—21no—
34C2×#14519768C2211yescharacteristic
35C2×#14519767—21no—
36C2×#14519764C2211yescharacteristic
37C2×#14519764C2211yescharacteristic
38C2×#14519758—21no—
39C2×#14519758—21no—
40C2×#14519756—21no—
41C2×#14519756—21no—
42C2×#14519756C2211yescharacteristic
43C2×Q8×Dic61C2211yescharacteristic
44C2×#14519742C2211yescharacteristic
45C2×#14519736C2211yescharacteristic
46#16840153C2218yescomplemented
47#16840140C2218yescomplemented
48#16840129C2218yescomplemented
49#16840115C2218yescomplemented
50#16839983C2218yescomplemented
51#16839982C2218yescomplemented
52#16839971C2218yescomplemented
53#16839970C2218yescomplemented
54#16839924C2218yes—
55#16839920C2218yescomplemented
56#16839917C2218yescomplemented
57#16839820C2218yescomplemented
58C2×#14519706C2211yescharacteristic
59C2×#14519706C2211yescharacteristic
60C2×#14519702C2211yescharacteristic
61C2×#14519702C2211yescharacteristic
62C2×#14519701C2211yescharacteristic
63C2×#14519700C2211yescharacteristic
64C2×#14519700C2211yescharacteristic
65C2×#14519698C2211yescharacteristic
66C2×C22⋊#92418C2211yescharacteristic
67C2×#14519687C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C22×#41×C61C2211yescharacteristic
70C22×Q16×C61C2211yescharacteristic
71C22×SD16×C61C2211yescharacteristic
72C2×C22⋊Q8×C61C2211yescharacteristic
73C61×#452C2218yes—
74C2×#103×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×C22⋊C8×C61C2211yescharacteristic
77C22×Dic122—21no—
78C22×Dic122—22no—
79C22×Dic122—42no—
80C22×Dic122—42no—
81C22×Dic122C2311yescharacteristic
82C22×Dic122C2311yescharacteristic
83C22×Dic122C2311yescharacteristic
84C22×Dic122C2314yes—
85C23×Dic61—21no—
86C2×Dic244—42no—
87C2×Dic244—42no—
88C2×Dic244C2314yes—
89C2×Dic244C2314yes—
90C2×#11758202—42no—
91C2×#11758202—42no—
92C2×#11758202—42no—
93C2×#11758202C2314yes—
94C2×#11758202C2314yes—
95C2×#11758202C2314yes—
96C2×#11758200—42no—
97C2×#11758200C2314yes—
98C22×#92418C2311yescharacteristic
99C22×#92418C2311yescharacteristic
100#14519775—22no—
101#14519775—22no—
102#14519775—22no—
103#14519775C2314yes—
104#14519775C2314yes—
105#14519775C2314yes—
106#14519770—28no—
107#14519770—28no—
108#14519768—28no—
109#14519768—22no—
110#14519768C2314yes—
111#14519767—28no—
112#14519764—22no—
113#14519764—22no—
114#14519764C2314yes—
115#14519764C2314yes—
116#14519758—28no—
117#14519758—28no—
118#14519756—22no—
119#14519756—28no—
120#14519756—28no—
121#14519756C2314yes—
122Q8×Dic61—22no—
123Q8×Dic61C2314yes—
124#14519742—22no—
125#14519742C2314yes—
126#14519736D414yes—
127#14519736C2314yes—
128C2×C4⋊Dic61—21no—
129C2×C4⋊Dic61—21no—
130C2×C4⋊Dic61D411yescharacteristic
131C2×C4⋊Dic61D411yescharacteristic
132C2×C4⋊Dic61C2311yescharacteristic
133C2×#11758196—21no—
134C2×#11758196—21no—
135C2×#11758196—21no—
136C2×#11758196—21no—
137C2×#11758196—21no—
138C2×#11758196—21no—
139C2×#11758196—21no—
140C2×#11758196—21no—
141C2×#11758196—21no—
142C2×C22⋊Dic61—21no—
143C2×C22⋊Dic61—21no—
144C2×C22⋊Dic61—21no—
145C2×C22⋊Dic61—21no—
146C2×C22⋊Dic61—21no—
147C2×C22⋊Dic61D411yescharacteristic
148C2×C22⋊Dic61D411yescharacteristic
149C2×C4×Dic61—21no—
150C2×C4×Dic61—21no—
151C2×C4×Dic61C2311yescharacteristic
152C2×C4×Dic61C2311yescharacteristic
153#14519706C2314yes—
154#14519706C2314yes—
155#14519702C2314yes—
156#14519702C2314yes—
157#14519701C2314yes—
158#14519700C2314yes—
159#14519700C2314yes—
160#14519698C2314yes—
161C22⋊#92418C2314yes—
162#14519687C2314yes—
163C8×Dic61C2314yes—
164C2×#41×C61—22no—
165C2×#41×C61—42no—
166C2×#41×C61—42no—
167C2×#41×C61C2314yes—
168C22×Q8×C61C2311yescharacteristic
169C22×Q8×C61C2311yescharacteristic
170C22×D4×C61—21no—
171C22×D4×C61C2311yescharacteristic
172C23×C4×C61—21no—
173C23×C4×C61C2311yescharacteristic
174C2×Q16×C61—42no—
175C2×Q16×C61C2314yes—
176C2×SD16×C61—42no—
177C2×SD16×C61C2314yes—
178C22×C8×C61C2311yescharacteristic
179C22×C8×C61C2311yescharacteristic
180C22⋊Q8×C61—22no—
181C22⋊Q8×C61C2314yes—
182C2×C4⋊C4×C61—21no—
183C2×C4⋊C4×C61C2311yescharacteristic
184C2×C22⋊C4×C61—21no—
185#103×C61C2314yes—
186#102×C61C2314yes—
187C22⋊C8×C61C2314yes—
188C24×C61—21no—
189C24×C61C2×D411yescharacteristic
190#41×C61—44no—
191#41×C61—44no—
192#41×C61—48no—
193C2×Q8×C61—21no—
194C2×Q8×C61—21no—
195C2×Q8×C61—22no—
196C2×Q8×C61—22no—
197C2×Q8×C61—22no—
198C2×Q8×C61—22no—
199C2×Q8×C61C2412yes—
200C2×Q8×C61C2412yes—
201C2×D4×C61—24no—
202C2×D4×C61—21no—
203C2×D4×C61—22no—
204C2×D4×C61—22no—
205C2×D4×C61—44no—
206C2×D4×C61C2412yes—
207C22×C4×C61—22no—
208C22×C4×C61—22no—
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—24no—
213C22×C4×C61—44no—
214C22×C4×C61C2×D411yescharacteristic
215C22×C4×C61C2×D412yes—
216C22×C4×C61C2412yes—
217C22×C4×C61C2411yescharacteristic
218C22×Dic61—21no—
219C22×Dic61—21no—
220C22×Dic61—24no—
221C22×Dic61—21no—
222C22×Dic61—21no—
223C22×Dic61—44no—
224C22×Dic61C2×D411yescharacteristic
225C22×Dic61C2×D411yescharacteristic
226C22×Dic61C2×D411yescharacteristic
227C22×Dic61C2×D411yescharacteristic
228C2×Dic122—22no—
229C2×Dic122—22no—
230C2×Dic122—22no—
231C2×Dic122—22no—
232C2×Dic122—22no—
233C2×Dic122—22no—
234C2×Dic122—24no—
235C2×Dic122—21no—
236C2×Dic122—21no—
237C2×Dic122—21no—
238C2×Dic122—44no—
239C2×Dic122—44no—
240C2×Dic122—44no—
241C2×Dic122—48no—
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⋊Dic61—24no—
256C22⋊Dic61—24no—
257C22⋊Dic61—24no—
258C22⋊Dic61—24no—
259C22⋊Dic61—24no—
260C22⋊Dic61C2×D414yes—
261C22⋊Dic61C2×D414yes—
262#11758202—44no—
263#11758202—44no—
264#11758202—44no—
265#11758200—44no—
266C4⋊Dic61—21no—
267C4⋊Dic61—24no—
268C4⋊Dic61—24no—
269C4⋊Dic61C2×D414yes—
270C4⋊Dic61C2×D414yes—
271C4⋊Dic61C2412yes—
272#11758196—24no—
273#11758196—24no—
274#11758196—24no—
275#11758196—24no—
276#11758196—24no—
277#11758196—24no—
278#11758196—24no—
279#11758196—24no—
280#11758196—24no—
281C4×Dic61—24no—
282C4×Dic61—24no—
283C4×Dic61C2×D412yes—
284C4×Dic61C2×D412yes—
285C4×Dic61C2412yes—
286C4×Dic61C2412yes—
287C2×#92418—22no—
288C2×#92418—22no—
289C2×#92418C2412yes—
290C2×#92418C2412yes—
291Dic244—44no—
292Dic244—44no—
293C23×C61—22no—
294C23×C61—22no—
295C23×C61—22no—
296C23×C61—22no—
297C23×C61—42no—
298C23×C61—42no—
299C23×C61—42no—
300C23×C61C22×D412yes—
301C23×C61C22×D411yescharacteristic
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—48no—
311D4×C61—42no—
312C2×C4×C61—22no—
313C2×C4×C61—24no—
314C2×C4×C61—22no—
315C2×C4×C61—22no—
316C2×C4×C61—22no—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61—48no—
320C2×C4×C61—42no—
321C2×C4×C61—42no—
322C2×C4×C61—42no—
323C2×C4×C61C22×D412yes—
324C2×C4×C61C22×D411yescharacteristic
325C2×C4×C61H(5,𝔽2)12yes—
326C2×C4×C61H(5,𝔽2)12yes—
327C2×C4×C61C2511yescharacteristic
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—48no—
337C2×Dic61—42no—
338C2×Dic61—42no—
339C2×Dic61—42no—
340C2×Dic61—42no—
341C2×Dic61C22×D412yes—
342C2×Dic61C22×D412yes—
343C2×Dic61C22×D412yes—
344C2×Dic61C22×D412yes—
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—22no—
361C22×C61—22no—
362C22×C61—22no—
363C22×C61—44no—
364C22×C61—42no—
365C22×C61—42no—
366C22×C61—42no—
367C22×C61—84no—
368C22×C61#53512yes—
369C22×C61#57812yes—
370C22×C61#57812yes—
371C22×C61C23×D411yescharacteristic
372C4×C61—22no—
373C4×C61—42no—
374C4×C61—42no—
375C4×C61—42no—
376C4×C61#53512yes—
377C4×C61C2×H(5,𝔽2)11yescharacteristic
378C4×C61C2×H(5,𝔽2)11yescharacteristic
379Dic61—22no—
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×#464—611no—
396C2×#462—611no—
397C2×#462—611no—
398C2×#452—611no—
399C2×#452D6111yescharacteristic
400C2×#451—611no—
401C2×#451—611no—
402C2×#433—611no—
403C2×C61—42no—
404C2×C61—82no—
405C2×C61#322314yescomplemented
406C2×C61C2×#53511yescharacteristic
407C2×C61C2×#57811yescharacteristic
408C2×C61C2×#57811yescharacteristic
409C22×#41C2×D6111yescharacteristic
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×#124—611no—
433C2×#123—1221no—
434C2×#123—1221no—
435C2×C22⋊Q8—611no—
436C2×C22⋊Q8—1221no—
437C2×C22⋊Q8—1221no—
438C2×C22⋊Q8C2×D6111yescharacteristic
439C2×C4×Q8—611no—
440C2×C4×Q8—611no—
441C2×#117—611no—
442#497—618no—
443#494—618no—
444#491—618no—
445#488—618no—
446#464—618no—
447#464—618no—
448#462—618no—
449#462—618no—
450#452—618no—
451#452C2×D6118yes—
452#451—618no—
453#451—618no—
454#433—618no—
455C2×C4⋊C8—611no—
456C2×C4⋊C8—611no—
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⋊C8C2×D6111yescharacteristic
467C2×#97—611no—
468C2×C4×C8—611no—
469C61C2×#322311yescharacteristic, complemented, Sylow
470C2×#41—22no—
471C2×#41—42no—
472C2×#41—42no—
473C2×#41C22×D6114yes—
474C22×Q8—611no—
475C22×Q8—611no—
476C22×Q8—611no—
477C22×Q8—614no—
478C22×Q8—1221no—
479C22×Q8—1222no—
480C22×Q8—2442no—
481C22×Q8—2442no—
482C22×Q8C22×D6111yescharacteristic
483C22×Q8C22×D6111yescharacteristic
484C22×D4—21no—
485C22×D4C22×D6111yescharacteristic
486C23×C4—21no—
487C23×C4—1221no—
488C23×C4C22×D6111yescharacteristic
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—1222no—
519#125—1228no—
520#125—1228no—
521#124—614no—
522#124—614no—
523#124—1222no—
524#124—1222no—
525#123—1228no—
526#123—1228no—
527C22⋊Q8—22no—
528C22⋊Q8—614no—
529C22⋊Q8—1228no—
530C22⋊Q8—1228no—
531C22⋊Q8—1222no—
532C22⋊Q8C22×D6114yes—
533C4×Q8—614no—
534C4×Q8—614no—
535C4×Q8—1222no—
536C4×Q8—1222no—
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—611no—
557C2×C22⋊C4—611no—
558C2×C22⋊C4—1221no—
559C2×C22⋊C4—1221no—
560C2×C22⋊C4—1221no—
561C2×C22⋊C4—1221no—
562C2×C22⋊C4—1221no—
563C2×C42—611no—
564C2×C42—611no—
565C2×C42—1221no—
566C2×C42—1221no—
567C4⋊C8—614no—
568C4⋊C8—614no—
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⋊C8C22×D6114yes—
579#97—614no—
580C4×C8—614no—
581C24—21no—
582C24D4×D6111yescharacteristic
583#41—44no—
584#41—44no—
585#41—48no—
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—1221no—
596C2×Q8—1224no—
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—24no—
612C2×D4—21no—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—44no—
616C2×D4C23×D6112yes—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—24no—
623C22×C4—44no—
624C22×C4—611no—
625C22×C4—611no—
626C22×C4—611no—
627C22×C4—611no—
628C22×C4—1224no—
629C22×C4—1221no—
630C22×C4—1221no—
631C22×C4—1221no—
632C22×C4—1221no—
633C22×C4—2444no—
634C22×C4D4×D6112yes—
635C22×C4D4×D6111yescharacteristic
636C22×C4C23×D6112yes—
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—1224no—
668C4⋊C4—1224no—
669C4⋊C4—1221no—
670C4⋊C4—1224no—
671C4⋊C4C23×D6112yes—
672C22⋊C4—24no—
673C22⋊C4—614no—
674C22⋊C4—614no—
675C22⋊C4—1224no—
676C22⋊C4—1224no—
677C22⋊C4—1224no—
678C22⋊C4—1224no—
679C22⋊C4—1224no—
680C42—612no—
681C42—612no—
682C42—612no—
683C42—612no—
684C42—1224no—
685C42—1224no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23C2×D4×D6112yes—
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—48no—
714D4—42no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—48no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—612no—
727C2×C4—612no—
728C2×C4—612no—
729C2×C4—612no—
730C2×C4—1222no—
731C2×C4—1222no—
732C2×C4—1222no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—1222no—
737C2×C4—1222no—
738C2×C4—2448no—
739C2×C4—2442no—
740C2×C4—2442no—
741C2×C4—2442no—
742C2×C4—2442no—
743C2×C4C2×D4×D6112yes—
744C2×C4C2×D4×D6111yescharacteristic
745C2×C4#1451982212yes—
746C2×C4#1451982212yes—
747C2×C4C24×D6111yescharacteristic
748C8—22no—
749C8—22no—
750C8—1222no—
751C8—1222no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—44no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—84no—
760C22#1684032712yes—
761C22#1684057612yes—
762C22#1684057812yes—
763C22C22×D4×D6111yescharacteristic
764C4—22no—
765C4—42no—
766C4—42no—
767C4—42no—
768C4—1222no—
769C4—1222no—
770C4—1222no—
771C4—1222no—
772C4—2442no—
773C4—2442no—
774C4—2442no—
775C4—2442no—
776C4#1684032712yes—
777C4C2×#1451982211yescharacteristic
778C4C2×#1451982211yescharacteristic
779C2—42no—
780C2—82no—
781C2#2145690014yesdirect product factor
782C2C2×#1684032711yescharacteristic
783C2C2×#1684057611yescharacteristic
784C2C2×#1684057811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#452C2
socleC23×C61C22×D4
prime radicalC22×#41×C61C22
hypercenterC2×#452D61
hypocenterC61C2×#3223
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C2×#16840372C2semidirect
3. #21456900C2direct (N × H)
4. C2×#16840153C2semidirect
5. C2×#16840140C2semidirect
6. C2×#16840129C2semidirect
7. C2×#16840115C2semidirect
8. C2×#16839983C2semidirect
9. C2×#16839982C2semidirect
10. C2×#16839971C2semidirect
11. C2×#16839970C2semidirect
13. C2×#16839920C2semidirect
14. C2×#16839917C2semidirect
15. C2×#16839820C2semidirect
25. #16840372C22semidirect
46. #16840153C22semidirect
47. #16840140C22semidirect
48. #16840129C22semidirect
49. #16840115C22semidirect
50. #16839983C22semidirect
51. #16839982C22semidirect
52. #16839971C22semidirect
53. #16839970C22semidirect
55. #16839920C22semidirect
56. #16839917C22semidirect
57. #16839820C22semidirect
405. C2×C61#3223semidirect
469. C61C2×#3223semidirect
781. C2#21456900direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403722
C2×#168403332
#214569002
C2×#168401532
C2×#168401402
C2×#168401292
C2×#168401152
C2×#168399832
C2×#168399822
C2×#168399712
C2×#168399702
C2×#168399242
C2×#168399202
C2×#168399172
C2×#168398202
C2×C61×#4522
C2×#322361