Finite Group Databasebeta

← C2×#21457890 #30556752

Subgroups — C2×#21457890 #30556752

Order 15616.

2114 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840485C211yesmaximal, characteristic, complemented
2C2×#16840424C211yesmaximal, characteristic
3#21457890C2116yesmaximal, direct product factor
4C2×#16840122C211yesmaximal, characteristic, complemented
5C2×#16840106C211yesmaximal, characteristic, complemented
6C2×#16840088C211yesmaximal, characteristic, complemented
7C2×#16840057C211yesmaximal, characteristic, complemented
8C2×#16840011C211yesmaximal, characteristic, complemented
9C2×#16840002C211yesmaximal, characteristic, complemented
10C2×#16839984C211yesmaximal, characteristic, complemented
11C2×#16839923C211yesmaximal, characteristic, complemented
12C2×#16839916C211yesmaximal, characteristic, complemented
13C2×#16839835C211yesmaximal, characteristic, complemented
14C2×#16839769C211yesmaximal, characteristic, complemented
15C2×#16839757C211yesmaximal, characteristic, complemented
16C2×C61×#441C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C22×Q8×D61C2211yescharacteristic
19C22×#11758202C2211yescharacteristic
20C22×#11758201C2211yescharacteristic
21C22×#11758189C2211yescharacteristic
22C22×C8×D61C2211yescharacteristic
23#16840485—24no—
24#16840485C2218yescomplemented
25#16840424—24no—
26#16840424C2218yes—
27C2×#14519777C2211yescharacteristic
28C2×#14519772—21no—
29C2×#14519772—21no—
30C2×#14519765—21no—
31C2×#14519765—21no—
32C2×#14519765C2211yescharacteristic
33C2×#14519757—21no—
34C2×#14519757C2211yescharacteristic
35C2×#14519753C2211yescharacteristic
36C2×#14519753C2211yescharacteristic
37C2×#14519752—21no—
38C2×#14519752C2211yescharacteristic
39C2×C4×Dic122—21no—
40C2×C4×D244—21no—
41C2×C4×D244C2211yescharacteristic
42C2×#14519735C2211yescharacteristic
43C2×#14519735C2211yescharacteristic
44#16840122C2218yescomplemented
45#16840106C2218yescomplemented
46#16840088C2218yescomplemented
47#16840057C2218yescomplemented
48#16840011C2218yescomplemented
49#16840002C2218yescomplemented
50#16839984C2218yescomplemented
51#16839923C2218yescomplemented
52#16839916C2218yescomplemented
53#16839835C2218yescomplemented
54C2×#14519710C2211yescharacteristic
55C2×#14519710C2211yescharacteristic
56C2×C4⋊#92418C2211yescharacteristic
57#16839769C2218yescomplemented
58#16839757C2218yescomplemented
59C2×#14519702C2211yescharacteristic
60C2×#14519702C2211yescharacteristic
61C2×#14519701C2211yescharacteristic
62C2×#14519701C2211yescharacteristic
63C2×#14519700C2211yescharacteristic
64C2×#14519699C2211yescharacteristic
65C2×#14519699C2211yescharacteristic
66C2×#14519697C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×#14519689C2211yescharacteristic
69C22×Q16×C61C2211yescharacteristic
70C2×C4×Q8×C61C2211yescharacteristic
71C2×C4×Q8×C61C2211yescharacteristic
72C61×#441C2218yescomplemented
73C2×#106×C61C2211yescharacteristic
74C2×#103×C61C2211yescharacteristic
75C2×#103×C61C2211yescharacteristic
76C2×#97×C61C2211yescharacteristic
77C2×#11758226—22no—
78C2×#11758226—24no—
79C2×#11758226—42no—
80C2×#11758226C2314yes—
81C22×Dic122—21no—
82C22×Dic122—21no—
83C22×Dic122C2311yescharacteristic
84C2×Q8×D61—22no—
85C2×Q8×D61—24no—
86C2×Q8×D61—42no—
87C2×Q8×D61C2314yes—
88C22×D244—21no—
89C22×D244—21no—
90C22×D244D411yescharacteristic
91C22×D244C2311yescharacteristic
92C22×C4×D61—21no—
93C22×C4×D61—21no—
94C22×C4×D61C2311yescharacteristic
95C22×C4×D61C2311yescharacteristic
96C2×#11758202—42no—
97C2×#11758202C2314yes—
98C2×#11758201—42no—
99C2×#11758201C2314yes—
100C2×#11758189—42no—
101C2×#11758189C2314yes—
102C22×#92418C2311yescharacteristic
103C22×#92418C2311yescharacteristic
104C2×C8×D61—42no—
105C2×C8×D61C2314yes—
106#14519777—22no—
107#14519777C2314yes—
108#14519772—28no—
109#14519772—28no—
110#14519765—28no—
111#14519765—22no—
112#14519765—28no—
113#14519765C2314yes—
114#14519757—22no—
115#14519757—28no—
116#14519757C2314yes—
117#14519753—22no—
118#14519753—22no—
119#14519753C2314yes—
120#14519753C2314yes—
121#14519752—28no—
122#14519752—22no—
123#14519752C2314yes—
124C4×Dic122—28no—
125C4×D244—28no—
126C4×D244D414yes—
127C4×D244C2314yes—
128#14519735—22no—
129#14519735—22no—
130#14519735C2314yes—
131#14519735C2314yes—
132C2×C4⋊Dic61—21no—
133C2×C4⋊Dic61—21no—
134C2×C4⋊Dic61D411yescharacteristic
135C2×C4⋊Dic61C2311yescharacteristic
136C2×C4⋊Dic61C2311yescharacteristic
137C2×#11758196—21no—
138C2×#11758196—21no—
139C2×#11758198—21no—
140C2×#11758198—21no—
141C2×#11758198—21no—
142C2×#11758198—21no—
143C2×#11758198—21no—
144C2×#11758198—21no—
145C2×#11758198—21no—
146C2×#11758198—21no—
147C2×#11758198D411yescharacteristic
148C2×#11758198D411yescharacteristic
149C2×C4×Dic61—21no—
150C2×C4×Dic61—21no—
151#14519710C2314yes—
152#14519710C2314yes—
153C4⋊#92418C2314yes—
154#14519702C2314yes—
155#14519702C2314yes—
156#14519701C2314yes—
157#14519701C2314yes—
158#14519700C2314yes—
159#14519699C2314yes—
160#14519699C2314yes—
161#14519697C2314yes—
162#14519689C2314yes—
163#14519689C2314yes—
164C22×Q8×C61C2311yescharacteristic
165C22×Q8×C61C2311yescharacteristic
166C2×Q16×C61—24no—
167C2×Q16×C61C2314yes—
168C22×C8×C61C2311yescharacteristic
169C22×C8×C61C2311yescharacteristic
170C4×Q8×C61—22no—
171C4×Q8×C61—22no—
172C4×Q8×C61C2314yes—
173C4×Q8×C61C2314yes—
174C2×C4⋊C4×C61—21no—
175C2×C4⋊C4×C61—21no—
176C2×C4⋊C4×C61C2311yescharacteristic
177C2×C4⋊C4×C61C2311yescharacteristic
178C2×C42×C61—21no—
179C2×C42×C61—21no—
180C2×C42×C61C2311yescharacteristic
181#106×C61C2314yes—
182#103×C61C2314yes—
183#103×C61C2314yes—
184#97×C61C2314yes—
185C23×D61—21no—
186C23×D61C2×D411yescharacteristic
187C23×D61C2×D411yescharacteristic
188C2×Q8×C61—21no—
189C2×Q8×C61—21no—
190C2×Q8×C61—22no—
191C2×Q8×C61—22no—
192C2×Q8×C61—22no—
193C2×Q8×C61#4114yes—
194C2×Q8×C61C2412yes—
195C2×Q8×C61C2412yes—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61C2×D411yescharacteristic
201C22×C4×C61C2×D411yescharacteristic
202C22×C4×C61C2411yescharacteristic
203C22×Dic61—21no—
204C22×Dic61—21no—
205C22×Dic61—21no—
206C22×Dic61C2×D411yescharacteristic
207C22×Dic61C2×D411yescharacteristic
208#11758226—28no—
209#11758226—44no—
210#11758226—48no—
211Q8×D61—28no—
212Q8×D61—44no—
213Q8×D61—48no—
214C2×D244—22no—
215C2×D244—22no—
216C2×D244—24no—
217C2×D244—24no—
218C2×D244—21no—
219C2×D244—42no—
220C2×D244—44no—
221C2×D244—44no—
222C2×D244C2×D414yes—
223C2×D244C2412yes—
224C2×C4×D61—22no—
225C2×C4×D61—22no—
226C2×C4×D61—22no—
227C2×C4×D61—22no—
228C2×C4×D61—24no—
229C2×C4×D61—24no—
230C2×C4×D61—44no—
231C2×C4×D61—44no—
232C2×C4×D61C2×D412yes—
233C2×C4×D61C2×D412yes—
234C2×C4×D61C2412yes—
235C2×C4×D61C2412yes—
236C2×Dic122—22no—
237C2×Dic122—22no—
238C2×Dic122—21no—
239C2×Dic122—24no—
240C2×Dic122—24no—
241C2×Dic122—44no—
242C2×Dic122—44no—
243C2×Dic122C2412yes—
244Q16×C61—28no—
245C2×C8×C61—22no—
246C2×C8×C61—22no—
247C2×C8×C61C2412yes—
248C2×C8×C61C2412yes—
249C4⋊C4×C61—24no—
250C4⋊C4×C61—24no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61C2412yes—
254C4⋊C4×C61C2412yes—
255C42×C61—24no—
256C42×C61—24no—
257C42×C61C2×D412yes—
258C42×C61C2412yes—
259#11758202—44no—
260#11758201—44no—
261#11758198—24no—
262#11758198—24no—
263#11758198—24no—
264#11758198—24no—
265#11758198—24no—
266#11758198—24no—
267#11758198—24no—
268#11758198—24no—
269#11758198C2×D414yes—
270#11758198C2×D414yes—
271C4⋊Dic61—24no—
272C4⋊Dic61—21no—
273C4⋊Dic61—21no—
274C4⋊Dic61—24no—
275C4⋊Dic61C2×D414yes—
276C4⋊Dic61C2412yes—
277C4⋊Dic61C2412yes—
278#11758196—24no—
279#11758196—24no—
280C4×Dic61—24no—
281C4×Dic61—24no—
282C2×#92418—22no—
283C2×#92418—22no—
284C2×#92418C2412yes—
285C2×#92418C2412yes—
286#11758189—44no—
287C8×D61—44no—
288C23×C61C22×D411yescharacteristic
289C22×D61—22no—
290C22×D61—22no—
291C22×D61—22no—
292C22×D61—22no—
293C22×D61—22no—
294C22×D61—22no—
295C22×D61—22no—
296C22×D61—42no—
297C22×D61—42no—
298C22×D61—42no—
299C22×D61C22×D412yes—
300C22×D61C22×D412yes—
301Q8×C61—24no—
302Q8×C61—22no—
303Q8×C61—22no—
304Q8×C61—22no—
305Q8×C61—42no—
306Q8×C61C2×#4114yes—
307C2×C4×C61—24no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—42no—
315C2×C4×C61—42no—
316C2×C4×C61—42no—
317C2×C4×C61C22×D412yes—
318C2×C4×C61C22×D412yes—
319C2×C4×C61C22×D411yescharacteristic
320C2×C4×C61C2×#4112yes—
321C2×C4×C61H(5,𝔽2)12yes—
322C2×C4×C61C2511yescharacteristic
323C2×Dic61—22no—
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—42no—
329C2×Dic61—42no—
330C2×Dic61—42no—
331C2×Dic61C22×D412yes—
332C2×Dic61C22×D412yes—
333D244—22no—
334D244—22no—
335D244—44no—
336D244—48no—
337D244—48no—
338D244—42no—
339C4×D61—24no—
340C4×D61—24no—
341C4×D61—22no—
342C4×D61—22no—
343C4×D61—22no—
344C4×D61—22no—
345C4×D61—48no—
346C4×D61—48no—
347Dic122—22no—
348Dic122—22no—
349Dic122—48no—
350Dic122—48no—
351Dic122—42no—
352C8×C61—22no—
353C8×C61—22no—
354#92418—22no—
355#92418—22no—
356C2×#3313—611nomaximal, Sylow
357C22×C61#54612yes—
358C22×C61#57512yes—
359C22×C61#57812yes—
360C22×C61C23×D411yescharacteristic
361C2×D61—22no—
362C2×D61—22no—
363C2×D61—22no—
364C2×D61—22no—
365C2×D61—22no—
366C2×D61—22no—
367C2×D61—44no—
368C2×D61—44no—
369C2×D61—42no—
370C2×D61—42no—
371C2×D61—42no—
372C2×D61—84no—
373C4×C61—24no—
374C4×C61—22no—
375C4×C61—22no—
376C4×C61—42no—
377C4×C61—42no—
378C4×C61—42no—
379C4×C61#54612yes—
380C4×C61C22×#4111yescharacteristic
381C4×C61C2×H(5,𝔽2)11yescharacteristic
382Dic61—22no—
383Dic61—22no—
384Dic61—42no—
385Dic61—42no—
386Dic61—42no—
387C2×#556—611no—
388C2×#548—611no—
389#3313—6116no—
390C2×#489—611no—
391C2×#485—611no—
392C2×#482—611no—
393C2×#477—611no—
394C2×#468—611no—
395C2×#467—611no—
396C2×#464—611no—
397C2×#452—611no—
398C2×#451—611no—
399C2×#441D6111yescharacteristic, complemented
400C2×#435—611no—
401C2×#419—611no—
402C2×#416—611no—
403C2×C61#331314yescomplemented
404C2×C61C2×#54611yescharacteristic
405C2×C61C2×#57511yescharacteristic
406C2×C61C2×#57811yescharacteristic
407D61—42no—
408D61—42no—
409D61—82no—
410C22×#41—611no—
411C23×Q8—611no—
412C22×Q16—611no—
413C22×Q16C2×D6111yescharacteristic
414C22×SD16—611no—
415C22×M16—611no—
416C23×C8—611no—
417#556—618no—
418#556—1224no—
419#548—618no—
420#548—1224no—
421C2×C4⋊Q8—611no—
422C2×#126—1221no—
423C2×#126—1221no—
424C2×#124—611no—
425C2×#124—1221no—
426C2×#124—1221no—
427C2×C22⋊Q8—611no—
428C2×C22⋊Q8—611no—
429C2×C22⋊Q8—611no—
430C2×C22⋊Q8—1221no—
431C2×#121—611no—
432C2×#121—1221no—
433C2×C4×Q8—1221no—
434C2×C4×Q8C2×D6111yescharacteristic
435C2×C4×Q8C2×D6111yescharacteristic
436C2×C4×D4—611no—
437C2×C4×D4—1221no—
438C2×#117—611no—
439C2×#117—611no—
440#489—618no—
441#485—618no—
442#482—618no—
443#477—618no—
444#468—618no—
445#467—618no—
446#464—618no—
447#452—618no—
448#451—618no—
449#441C2×D6118yescomplemented
450#435—618no—
451C2×#107—611no—
452C2×#107—611no—
453C2×#106C2×D6111yescharacteristic
454C2×C4⋊C8—611no—
455#419—618no—
456#416—618no—
457C2×#103—611no—
458C2×#103—611no—
459C2×#103—611no—
460C2×#103—611no—
461C2×#103—611no—
462C2×#103C2×D6111yescharacteristic
463C2×#103C2×D6111yescharacteristic
464C2×#102—611no—
465C2×#102—611no—
466C2×#102—611no—
467C2×C22⋊C8—611no—
468C2×C22⋊C8—611no—
469C2×#97C2×D6111yescharacteristic
470C61C2×#331311yescharacteristic, complemented, Sylow
471C2×#41—614no—
472C2×#41—1222no—
473C2×#41—1224no—
474C2×#41—2442no—
475C22×Q8—614no—
476C22×Q8—611no—
477C22×Q8—1221no—
478C22×Q8—1222no—
479C22×Q8—1221no—
480C22×Q8—1224no—
481C22×Q8—2442no—
482C22×Q8C22×D6111yescharacteristic
483C22×Q8C22×D6111yescharacteristic
484C22×D4—611no—
485C22×D4—611no—
486C22×D4—1221no—
487C22×D4—1221no—
488C23×C4—611no—
489C23×C4—611no—
490C23×C4—1221no—
491C23×C4—1221no—
492C2×Q16—24no—
493C2×Q16—614no—
494C2×Q16—2442no—
495C2×Q16C22×D6114yes—
496C2×SD16—614no—
497C2×SD16—2442no—
498C2×M16—614no—
499C2×M16—2442no—
500C22×C8—611no—
501C22×C8—611no—
502C22×C8—614no—
503C22×C8—2442no—
504C22×C8C22×D6111yescharacteristic
505C22×C8C22×D6111yescharacteristic
506C4⋊Q8—614no—
507C4⋊Q8—1222no—
508#126—1228no—
509#126—1228no—
510#124—614no—
511#124—1228no—
512#124—1228no—
513#124—1222no—
514C22⋊Q8—614no—
515C22⋊Q8—614no—
516C22⋊Q8—614no—
517C22⋊Q8—1228no—
518C22⋊Q8—1222no—
519C22⋊Q8—1222no—
520C22⋊Q8—1222no—
521#121—614no—
522#121—1222no—
523#121—1228no—
524C4×Q8—22no—
525C4×Q8—22no—
526C4×Q8—1228no—
527C4×Q8C22×D6114yes—
528C4×Q8C22×D6114yes—
529C4×D4—614no—
530C4×D4—614no—
531C4×D4—1228no—
532#117—614no—
533#117—614no—
534#117—1222no—
535#117—1222no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—611no—
539C2×C4⋊C4—611no—
540C2×C4⋊C4—611no—
541C2×C4⋊C4—1221no—
542C2×C4⋊C4—1221no—
543C2×C4⋊C4—1221no—
544C2×C4⋊C4—1221no—
545C2×C4⋊C4C22×D6111yescharacteristic
546C2×C4⋊C4C22×D6111yescharacteristic
547C2×C22⋊C4—611no—
548C2×C22⋊C4—611no—
549C2×C22⋊C4—1221no—
550C2×C22⋊C4—1221no—
551C2×C22⋊C4—1221no—
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—21no—
559C2×C42—1221no—
560C2×C42—1221no—
561C2×C42C22×D6111yescharacteristic
562#107—614no—
563#107—614no—
564#106C22×D6114yes—
565C4⋊C8—614no—
566#103—614no—
567#103—614no—
568#103—614no—
569#103—614no—
570#103—614no—
571#103C22×D6114yes—
572#103C22×D6114yes—
573#102—614no—
574#102—614no—
575#102—614no—
576C22⋊C8—614no—
577C22⋊C8—614no—
578#97C22×D6114yes—
579C24—611no—
580C24—611no—
581C24—1221no—
582#41—1228no—
583#41—2444no—
584#41—2448no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—22no—
588C2×Q8—22no—
589C2×Q8—22no—
590C2×Q8—612no—
591C2×Q8—1224no—
592C2×Q8—1224no—
593C2×Q8—1221no—
594C2×Q8—1228no—
595C2×Q8—1222no—
596C2×Q8—1222no—
597C2×Q8—2444no—
598C2×Q8—2444no—
599C2×Q8—2444no—
600C2×Q8—2448no—
601C2×Q8#1175822214yes—
602C2×Q8C23×D6112yes—
603C2×Q8C23×D6112yes—
604C2×D4—614no—
605C2×D4—612no—
606C2×D4—1224no—
607C2×D4—1224no—
608C2×D4—1221no—
609C2×D4—1222no—
610C2×D4—1222no—
611C2×D4—2442no—
612C2×D4—2444no—
613C2×D4—2444no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—611no—
619C22×C4—611no—
620C22×C4—612no—
621C22×C4—612no—
622C22×C4—612no—
623C22×C4—612no—
624C22×C4—1224no—
625C22×C4—1224no—
626C22×C4—1222no—
627C22×C4—1222no—
628C22×C4—1222no—
629C22×C4—1222no—
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—28no—
639Q16—2444no—
640SD16—2444no—
641M16—2444no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—612no—
645C2×C8—612no—
646C2×C8—1222no—
647C2×C8—1222no—
648C2×C8—2444no—
649C2×C8C23×D6112yes—
650C2×C8C23×D6112yes—
651C4⋊C4—24no—
652C4⋊C4—24no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—614no—
656C4⋊C4—612no—
657C4⋊C4—612no—
658C4⋊C4—1224no—
659C4⋊C4—1224no—
660C4⋊C4—1224no—
661C4⋊C4—1221no—
662C4⋊C4—1221no—
663C4⋊C4—1224no—
664C4⋊C4C23×D6112yes—
665C4⋊C4C23×D6112yes—
666C22⋊C4—614no—
667C22⋊C4—614no—
668C22⋊C4—1224no—
669C22⋊C4—1224no—
670C22⋊C4—1224no—
671C22⋊C4—1224no—
672C22⋊C4—1224no—
673C22⋊C4—1224no—
674C22⋊C4—1224no—
675C22⋊C4—1224no—
676C42—24no—
677C42—24no—
678C42—1224no—
679C42—1224no—
680C42D4×D6112yes—
681C42C23×D6112yes—
682C23—612no—
683C23—612no—
684C23—1222no—
685C23—1222no—
686C23—1222no—
687C23—1222no—
688C23—1222no—
689C23—1222no—
690C23—1222no—
691C23—2442no—
692C23—2442no—
693C23—2442no—
694C23C2×D4×D6111yescharacteristic
695Q8—22no—
696Q8—24no—
697Q8—22no—
698Q8—22no—
699Q8—42no—
700Q8—1222no—
701Q8—1222no—
702Q8—2448no—
703Q8—2448no—
704Q8—2442no—
705Q8C2×#1175822214yes—
706D4—1222no—
707D4—1222no—
708D4—2444no—
709D4—2448no—
710D4—2448no—
711D4—2442no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—612no—
723C2×C4—612no—
724C2×C4—1222no—
725C2×C4—1222no—
726C2×C4—1222no—
727C2×C4—1222no—
728C2×C4—1222no—
729C2×C4—1222no—
730C2×C4—1224no—
731C2×C4—1224no—
732C2×C4—1222no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—2448no—
736C2×C4—2448no—
737C2×C4—2442no—
738C2×C4—2442no—
739C2×C4—2442no—
740C2×C4C2×D4×D6112yes—
741C2×C4C2×D4×D6112yes—
742C2×C4C2×D4×D6111yescharacteristic
743C2×C4C2×#1175822212yes—
744C2×C4#1451982312yes—
745C2×C4C24×D6111yescharacteristic
746C8—22no—
747C8—22no—
748C8—1222no—
749C8—1222no—
750C22—1222no—
751C22—1222no—
752C22—1222no—
753C22—1222no—
754C22—1222no—
755C22—1222no—
756C22—4884no—
757C22—2442no—
758C22—2442no—
759C22—2442no—
760C22—2444no—
761C22—2444no—
762C22#1684040812yes—
763C22#1684056112yes—
764C22#1684057812yes—
765C22C22×D4×D6111yescharacteristic
766C4—24no—
767C4—22no—
768C4—22no—
769C4—42no—
770C4—42no—
771C4—42no—
772C4—1222no—
773C4—1222no—
774C4—2442no—
775C4—2442no—
776C4—2442no—
777C4#1684040812yes—
778C4C22×#1175822211yescharacteristic
779C4C2×#1451982311yescharacteristic
780C2—4882no—
781C2—2442no—
782C2—2442no—
783C2#2145789014yesdirect product factor
784C2C2×#1684040811yescharacteristic
785C2C2×#1684056111yescharacteristic
786C2C2×#1684057811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#441C2
socleC23×C61C22×D4
prime radicalC2×#16840424C2
hypercenterC2×#441D61
hypocenterC61C2×#3313
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
1. C2×#16840485C2semidirect
3. #21457890C2direct (N × H)
4. C2×#16840122C2semidirect
5. C2×#16840106C2semidirect
6. C2×#16840088C2semidirect
7. C2×#16840057C2semidirect
8. C2×#16840011C2semidirect
9. C2×#16840002C2semidirect
10. C2×#16839984C2semidirect
11. C2×#16839923C2semidirect
12. C2×#16839916C2semidirect
13. C2×#16839835C2semidirect
14. C2×#16839769C2semidirect
15. C2×#16839757C2semidirect
16. C2×C61×#441C2semidirect
24. #16840485C22semidirect
44. #16840122C22semidirect
45. #16840106C22semidirect
46. #16840088C22semidirect
47. #16840057C22semidirect
48. #16840011C22semidirect
49. #16840002C22semidirect
50. #16839984C22semidirect
51. #16839923C22semidirect
52. #16839916C22semidirect
53. #16839835C22semidirect
57. #16839769C22semidirect
58. #16839757C22semidirect
72. C61×#441C22semidirect
399. C2×#441D61semidirect
403. C2×C61#3313semidirect
449. #441C2×D61semidirect
470. C61C2×#3313semidirect
783. C2#21457890direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404852
C2×#168404242
#214578902
C2×#168401222
C2×#168401062
C2×#168400882
C2×#168400572
C2×#168400112
C2×#168400022
C2×#168399842
C2×#168399232
C2×#168399162
C2×#168398352
C2×#168397692
C2×#168397572
C2×C61×#4412
C2×#331361