Finite Group Databasebeta

← C2×#21456020 #30548262

Subgroups — C2×#21456020 #30548262

Order 15616.

2198 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840367C211yesmaximal, characteristic, complemented
2C2×#16840242C211yesmaximal, characteristic, complemented
3#21456020C2116yesmaximal, direct product factor
4C2×#16840081C211yesmaximal, characteristic, complemented
5C2×#16840076C211yesmaximal, characteristic, complemented
6C2×#16840070C211yesmaximal, characteristic, complemented
7C2×#16840063C211yesmaximal, characteristic, complemented
8C2×#16839963C211yesmaximal, characteristic, complemented
9C2×#16839958C211yesmaximal, characteristic, complemented
10C2×#16839909C211yesmaximal, characteristic, complemented
11C2×#16839909C211yesmaximal, characteristic, complemented
12C2×#16839875C211yesmaximal, characteristic, complemented
13C2×#16839864C211yesmaximal, characteristic, complemented
14C2×C4×#11758190C211yesmaximal, characteristic, complemented
15C2×C4×D488C211yesmaximal, characteristic, complemented
16C2×C61×#433C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C22×#11758190C2211yescharacteristic
19C22×#11758190C2211yescharacteristic
20C22×D488C2211yescharacteristic
21C22×D488C2211yescharacteristic
22#16840367—24no—
23#16840367C2218yescomplemented
24C2×#14519774C2211yescharacteristic
25C2×#14519769C2211yescharacteristic
26C2×#14519762—21no—
27C2×#14519762—21no—
28C2×#14519751C2211yescharacteristic
29C2×#14519751C2211yescharacteristic
30C2×#14519750—21no—
31C2×#14519750—21no—
32#16840242—24no—
33#16840242C2218yescomplemented
34C2×C4×Dic122C2211yescharacteristic
35C2×C4×Dic122C2211yescharacteristic
36C2×C4×D244C2211yescharacteristic
37C2×C4×D244C2211yescharacteristic
38C2×C4×D244C2211yescharacteristic
39C2×C4×D244C2211yescharacteristic
40C2×#14519737—21no—
41C2×#14519737—21no—
42C2×#14519735—21no—
43C22×C4⋊Dic61C2211yescharacteristic
44C2×C4⋊C4×D61—21no—
45#16840081C2218yescomplemented
46#16840076C2218yescomplemented
47#16840070C2218yescomplemented
48#16840063C2218yescomplemented
49#16839963C2218yescomplemented
50#16839958C2218yescomplemented
51#16839909C2218yescomplemented
52#16839909C2218yescomplemented
53#16839875C2218yescomplemented
54#16839864C2218yescomplemented
55C4×#11758190C2218yescomplemented
56C4×D488C2218yescomplemented
57C2×#14519711C2211yescharacteristic
58C2×#14519711C2211yescharacteristic
59C2×#14519709C2211yescharacteristic
60C2×#14519709C2211yescharacteristic
61C2×#14519702C2211yescharacteristic
62C2×#14519702C2211yescharacteristic
63C2×#14519699C2211yescharacteristic
64C2×#14519699C2211yescharacteristic
65C2×#14519699C2211yescharacteristic
66C2×#14519699C2211yescharacteristic
67C2×#14519699C2211yescharacteristic
68C2×#14519699C2211yescharacteristic
69C2×#117×C61C2211yescharacteristic
70C61×#433C2218yescomplemented
71C2×C4⋊C8×C61C2211yescharacteristic
72C2×C4⋊C8×C61C2211yescharacteristic
73C2×C22⋊C8×C61C2211yescharacteristic
74C2×C22⋊C8×C61C2211yescharacteristic
75C2×#97×C61C2211yescharacteristic
76C2×C4×C8×C61C2211yescharacteristic
77C2×#11758222—22no—
78C2×#11758222—24no—
79C2×#11758222—24no—
80C2×#11758222C2314yes—
81C22×Dic122C2311yescharacteristic
82C22×D244—21no—
83C22×D244—21no—
84C22×D244C2311yescharacteristic
85C22×D244C2311yescharacteristic
86C22×D244C2311yescharacteristic
87C22×C22⋊D61—21no—
88C22×C22⋊D61—21no—
89C22×C22⋊D61—21no—
90C23×Dic61—21no—
91C22×C4×D61—21no—
92C22×C4×D61—21no—
93C22×C4×D61—21no—
94C22×C4×D61—21no—
95C22×C4×D61—21no—
96C2×#11758190—24no—
97C2×#11758190—24no—
98C2×#11758190C2314yes—
99C2×#11758190C2314yes—
100C2×D488—24no—
101C2×D488—24no—
102C2×D488C2314yes—
103C2×D488C2314yes—
104#14519774—22no—
105#14519774C2314yes—
106#14519769—22no—
107#14519769C2314yes—
108#14519762—28no—
109#14519762—28no—
110#14519751—22no—
111#14519751—22no—
112#14519751C2314yes—
113#14519751C2314yes—
114#14519750—28no—
115#14519750—28no—
116C4×Dic122—22no—
117C4×Dic122—22no—
118C4×Dic122C2314yes—
119C4×Dic122C2314yes—
120C4×D244—22no—
121C4×D244—22no—
122C4×D244—22no—
123C4×D244—22no—
124C4×D244C2314yes—
125C4×D244C2314yes—
126C4×D244C2314yes—
127C4×D244C2314yes—
128#14519737—28no—
129#14519737—28no—
130#14519735—28no—
131C2×C4⋊Dic61—21no—
132C2×C4⋊Dic61—22no—
133C2×C4⋊Dic61C2311yescharacteristic
134C2×C4⋊Dic61C2311yescharacteristic
135C2×C4⋊Dic61C2314yes—
136C2×C4⋊Dic61C2311yescharacteristic
137C2×C4⋊Dic61C2311yescharacteristic
138C2×#11758196—21no—
139C2×#11758196—21no—
140C2×#11758196—21no—
141C2×#11758196—21no—
142C4⋊C4×D61—28no—
143C2×#11758198—21no—
144C2×#11758198—21no—
145C2×#11758198—21no—
146C2×#11758198—21no—
147C2×#11758198—21no—
148C2×#11758198—21no—
149C2×C4×Dic61—21no—
150C2×C4×Dic61—21no—
151#14519711C2314yes—
152#14519711C2314yes—
153#14519709C2314yes—
154#14519709C2314yes—
155#14519702C2314yes—
156#14519702C2314yes—
157#14519699C2314yes—
158#14519699C2314yes—
159#14519699C2314yes—
160#14519699C2314yes—
161#14519699C2314yes—
162#14519699C2314yes—
163C23×C4×C61C2311yescharacteristic
164C22×C8×C61C2311yescharacteristic
165C22×C8×C61C2311yescharacteristic
166C22×C8×C61C2311yescharacteristic
167C22×C8×C61C2311yescharacteristic
168#117×C61D414yes—
169#117×C61C2314yes—
170C2×C4⋊C4×C61D411yescharacteristic
171C2×C4⋊C4×C61D411yescharacteristic
172C2×C22⋊C4×C61D411yescharacteristic
173C2×C22⋊C4×C61D411yescharacteristic
174C2×C42×C61C2311yescharacteristic
175C2×C42×C61C2311yescharacteristic
176C4⋊C8×C61C2314yes—
177C4⋊C8×C61C2314yes—
178C22⋊C8×C61C2314yes—
179C22⋊C8×C61C2314yes—
180#97×C61C2314yes—
181C4×C8×C61C2314yes—
182C24×C61C2×D411yescharacteristic
183C23×D61—21no—
184C23×D61—21no—
185C23×D61—21no—
186C22×C4×C61—22no—
187C22×C4×C61—22no—
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2×D411yescharacteristic
190C22×C4×C61C2×D411yescharacteristic
191C22×C4×C61C2×D411yescharacteristic
192C22×C4×C61C2×D411yescharacteristic
193C22×C4×C61C2×D412yes—
194C22×C4×C61C2412yes—
195C22×C4×C61C2411yescharacteristic
196C2×C22⋊D61—28no—
197C2×C22⋊D61—24no—
198C2×C22⋊D61—24no—
199C2×C22⋊D61—24no—
200C2×C22⋊D61—82no—
201C2×C22⋊D61—82no—
202C22×Dic61—21no—
203C22×Dic61—21no—
204C22×Dic61—21no—
205C22×Dic61—21no—
206C22×Dic61—21no—
207C22×Dic61—24no—
208C22×Dic61—82no—
209#11758222—216no—
210#11758222—28no—
211#11758222—28no—
212C2×D244—21no—
213C2×D244—22no—
214C2×D244—22no—
215C2×D244—22no—
216C2×D244—22no—
217C2×D244—22no—
218C2×D244—21no—
219C2×D244—21no—
220C2×D244—24no—
221C2×D244—24no—
222C2×D244—82no—
223C2×D244—82no—
224C2×D244#4114yes—
225C2×D244C2412yes—
226C2×D244C2412yes—
227C2×D244C2412yes—
228C2×C4×D61—28no—
229C2×C4×D61—24no—
230C2×C4×D61—24no—
231C2×C4×D61—24no—
232C2×C4×D61—24no—
233C2×C4×D61—24no—
234C2×C4×D61—82no—
235C2×C4×D61—82no—
236C2×C4×D61—82no—
237C2×C4×D61—82no—
238C2×Dic122—21no—
239C2×Dic122—22no—
240C2×Dic122#4114yes—
241C2×Dic122C2412yes—
242C2×C8×C61—22no—
243C2×C8×C61—22no—
244C2×C8×C61—22no—
245C2×C8×C61—22no—
246C2×C8×C61C2412yes—
247C2×C8×C61C2412yes—
248C2×C8×C61C2412yes—
249C2×C8×C61C2412yes—
250C4⋊C4×C61C2×D414yes—
251C4⋊C4×C61C2×D414yes—
252C22⋊C4×C61C2×D414yes—
253C22⋊C4×C61C2×D414yes—
254C42×C61C2×D412yes—
255C42×C61C2×D412yes—
256C42×C61C2412yes—
257C42×C61C2412yes—
258#11758198—24no—
259#11758198—24no—
260#11758198—24no—
261#11758198—24no—
262#11758198—24no—
263#11758198—24no—
264C4⋊Dic61—24no—
265C4⋊Dic61—21no—
266C4⋊Dic61—21no—
267C4⋊Dic61—21no—
268C4⋊Dic61—21no—
269C4⋊Dic61C2412yes—
270C4⋊Dic61C2412yes—
271C4⋊Dic61C2412yes—
272C4⋊Dic61C2412yes—
273#11758196—24no—
274#11758196—24no—
275#11758196—24no—
276#11758196—24no—
277C4×Dic61—24no—
278C4×Dic61—24no—
279D488—28no—
280D488—28no—
281#11758190—28no—
282#11758190—28no—
283C23×C61—22no—
284C23×C61—22no—
285C23×C61—22no—
286C23×C61C22×D412yes—
287C23×C61C22×D411yescharacteristic
288C22×D61—24no—
289C22×D61—22no—
290C22×D61—22no—
291C22×D61—22no—
292C22×D61—42no—
293C22×D61—42no—
294C22×D61—42no—
295C22×D61—42no—
296C22×D61—42no—
297C22×D61—42no—
298C22×D61—42no—
299C22×D61—42no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61—24no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61C22×D412yes—
309C2×C4×C61C22×D412yes—
310C2×C4×C61C22×D412yes—
311C2×C4×C61C22×D412yes—
312C2×C4×C61C22×D412yes—
313C2×C4×C61C22×D411yescharacteristic
314C2×C4×C61C2×#4112yes—
315C2×C4×C61C2×#4112yes—
316C2×C4×C61C2511yescharacteristic
317C22⋊D61—216no—
318C22⋊D61—84no—
319C22⋊D61—84no—
320C2×Dic61—24no—
321C2×Dic61—22no—
322C2×Dic61—22no—
323C2×Dic61—22no—
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—42no—
327C2×Dic61—42no—
328C2×Dic61—42no—
329C2×Dic61—42no—
330C2×Dic61—84no—
331D244—24no—
332D244—22no—
333D244—22no—
334D244—22no—
335D244—22no—
336D244—22no—
337D244—42no—
338D244—42no—
339D244—84no—
340D244—84no—
341D244C2×#4114yes—
342C4×D61—216no—
343C4×D61—84no—
344C4×D61—84no—
345C4×D61—84no—
346C4×D61—84no—
347Dic122—24no—
348Dic122—22no—
349Dic122C2×#4114yes—
350C8×C61—22no—
351C8×C61—22no—
352C8×C61—22no—
353C8×C61—22no—
354C2×#3119—611nomaximal, Sylow
355C22×C61—22no—
356C22×C61—22no—
357C22×C61—22no—
358C22×C61—44no—
359C22×C61#52512yes—
360C22×C61#57612yes—
361C22×C61#57712yes—
362C22×C61C23×D411yescharacteristic
363C2×D61—24no—
364C2×D61—48no—
365C2×D61—42no—
366C2×D61—42no—
367C2×D61—42no—
368C2×D61—42no—
369C2×D61—42no—
370C2×D61—42no—
371C2×D61—42no—
372C2×D61—42no—
373C2×D61—84no—
374C2×D61—84no—
375C4×C61—22no—
376C4×C61—22no—
377C4×C61—22no—
378C4×C61—22no—
379C4×C61—22no—
380C4×C61#52512yes—
381C4×C61C22×#4111yescharacteristic
382C4×C61C22×#4111yescharacteristic
383Dic61—24no—
384Dic61—42no—
385Dic61—42no—
386Dic61—42no—
387Dic61—42no—
388C2×#540—611no—
389C2×#520—611no—
390#3119—6116no—
391C2×#481—611no—
392C2×#480—611no—
393C2×#479—611no—
394C2×#478—611no—
395C2×#460—611no—
396C2×#459—611no—
397C2×#449—611no—
398C2×#449—611no—
399C2×#442—611no—
400C2×#440—611no—
401C2×C4×SD16—611no—
402C2×C4×D8—611no—
403C2×#433D6111yescharacteristic, complemented
404C2×C61—42no—
405C2×C61#311914yescomplemented
406C2×C61C2×#52511yescharacteristic
407C2×C61C2×#57611yescharacteristic
408C2×C61C2×#57711yescharacteristic
409D61—44no—
410D61—82no—
411D61—82no—
412C22×#41—611no—
413C22×SD16—611no—
414C22×SD16—611no—
415C22×D8—611no—
416C22×D8—611no—
417#540—618no—
418#540—1224no—
419C2×#127—611no—
420C2×#125—611no—
421C2×#123—1221no—
422C2×#123—1221no—
423C2×#121—611no—
424C2×#121—611no—
425C2×#121—1221no—
426C2×#121—1221no—
427#520—618no—
428#520—1224no—
429C2×C4×Q8—611no—
430C2×C4×Q8—611no—
431C2×C4×D4—611no—
432C2×C4×D4—611no—
433C2×C4×D4—611no—
434C2×C4×D4—611no—
435C2×C4×D4—1221no—
436C2×C4×D4—1221no—
437C2×#117—1221no—
438C2×#117C2×D6111yescharacteristic
439C22×C4⋊C4—611no—
440C22×C4⋊C4—1221no—
441#481—618no—
442#480—618no—
443#479—618no—
444#478—618no—
445#460—618no—
446#459—618no—
447#449—618no—
448#449—618no—
449#442—618no—
450#440—618no—
451C4×SD16—618no—
452C4×D8—618no—
453#433C2×D6118yescomplemented
454C2×#107—611no—
455C2×#107—611no—
456C2×#106—611no—
457C2×#106—611no—
458C2×C4⋊C8C2×D6111yescharacteristic
459C2×C4⋊C8C2×D6111yescharacteristic
460C2×#103—611no—
461C2×#103—611no—
462C2×#102—611no—
463C2×#102—611no—
464C2×#102—611no—
465C2×#102—611no—
466C2×#102—611no—
467C2×#102—611no—
468C2×C22⋊C8C2×D6111yescharacteristic
469C2×C22⋊C8C2×D6111yescharacteristic
470C2×#97C2×D6111yescharacteristic
471C2×C4×C8C2×D6111yescharacteristic
472C61C2×#311911yescharacteristic, complemented, Sylow
473C2×#41—614no—
474C2×#41—1224no—
475C2×#41—1224no—
476C2×#41—1222no—
477C22×Q8—611no—
478C22×D4—611no—
479C22×D4—611no—
480C22×D4—611no—
481C22×D4—1221no—
482C22×D4—1221no—
483C22×D4—1221no—
484C22×D4—1221no—
485C22×D4—1221no—
486C23×C4—1221no—
487C23×C4—1221no—
488C23×C4—1221no—
489C23×C4—1221no—
490C23×C4—1221no—
491C23×C4—1221no—
492C23×C4C22×D6111yescharacteristic
493C2×SD16—614no—
494C2×SD16—614no—
495C2×SD16—1224no—
496C2×SD16—1224no—
497C2×D8—614no—
498C2×D8—614no—
499C2×D8—1224no—
500C2×D8—1224no—
501C22×C8C22×D6111yescharacteristic
502C22×C8C22×D6111yescharacteristic
503C22×C8C22×D6111yescharacteristic
504C22×C8C22×D6111yescharacteristic
505#127—614no—
506#127—1222no—
507#125—614no—
508#125—1222no—
509#123—1228no—
510#123—1228no—
511#121—614no—
512#121—614no—
513#121—1222no—
514#121—1222no—
515#121—1228no—
516#121—1228no—
517C4×Q8—614no—
518C4×Q8—614no—
519C4×Q8—1222no—
520C4×Q8—1222no—
521C4×D4—614no—
522C4×D4—614no—
523C4×D4—614no—
524C4×D4—614no—
525C4×D4—1228no—
526C4×D4—1228no—
527C4×D4—1222no—
528C4×D4—1222no—
529C4×D4—1222no—
530C4×D4—1222no—
531#117—1228no—
532#117D24414yes—
533#117C22×D6114yes—
534C2×C4⋊C4—611no—
535C2×C4⋊C4—611no—
536C2×C4⋊C4—614no—
537C2×C4⋊C4—611no—
538C2×C4⋊C4—611no—
539C2×C4⋊C4—1221no—
540C2×C4⋊C4—1222no—
541C2×C4⋊C4—1221no—
542C2×C4⋊C4—1221no—
543C2×C4⋊C4—1221no—
544C2×C4⋊C4—1221no—
545C2×C4⋊C4—1228no—
546C2×C4⋊C4D24411yescharacteristic
547C2×C4⋊C4D24411yescharacteristic
548C2×C22⋊C4—1221no—
549C2×C22⋊C4—1221no—
550C2×C22⋊C4—1221no—
551C2×C22⋊C4—1221no—
552C2×C22⋊C4—1221no—
553C2×C22⋊C4—1221no—
554C2×C22⋊C4D24411yescharacteristic
555C2×C22⋊C4D24411yescharacteristic
556C2×C42—1221no—
557C2×C42—1221no—
558C2×C42C22×D6111yescharacteristic
559C2×C42C22×D6111yescharacteristic
560#107—614no—
561#107—614no—
562#106—614no—
563#106—614no—
564C4⋊C8C22×D6114yes—
565C4⋊C8C22×D6114yes—
566#103—614no—
567#103—614no—
568#102—614no—
569#102—614no—
570#102—614no—
571#102—614no—
572#102—614no—
573#102—614no—
574C22⋊C8C22×D6114yes—
575C22⋊C8C22×D6114yes—
576#97C22×D6114yes—
577C4×C8C22×D6114yes—
578C24—1221no—
579C24—1221no—
580C24—1221no—
581C24C2×D24411yescharacteristic
582#41—1228no—
583#41—1228no—
584#41—12216no—
585C2×Q8—614no—
586C2×Q8—612no—
587C2×Q8—1221no—
588C2×Q8—1222no—
589C2×D4—614no—
590C2×D4—612no—
591C2×D4—612no—
592C2×D4—612no—
593C2×D4—1228no—
594C2×D4—1224no—
595C2×D4—1224no—
596C2×D4—1224no—
597C2×D4—1221no—
598C2×D4—1224no—
599C2×D4—1224no—
600C2×D4—1221no—
601C2×D4—1221no—
602C2×D4—1222no—
603C2×D4—1222no—
604C2×D4—1222no—
605C2×D4—1222no—
606C2×D4—1222no—
607C2×D4—4882no—
608C2×D4—4882no—
609C2×D4—4882no—
610C2×D4—4882no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—1228no—
614C22×C4—1221no—
615C22×C4—1224no—
616C22×C4—1224no—
617C22×C4—1221no—
618C22×C4—1221no—
619C22×C4—1221no—
620C22×C4—1221no—
621C22×C4—1224no—
622C22×C4—1224no—
623C22×C4—1224no—
624C22×C4—1224no—
625C22×C4—4882no—
626C22×C4—4882no—
627C22×C4—4882no—
628C22×C4—4882no—
629C22×C4—4882no—
630C22×C4C2×D24412yes—
631C22×C4C2×D24411yescharacteristic
632C22×C4C2×D24411yescharacteristic
633C22×C4C2×D24411yescharacteristic
634C22×C4C2×D24411yescharacteristic
635C22×C4C2×D24411yescharacteristic
636C22×C4C23×D6112yes—
637C22×C4C23×D6111yescharacteristic
638SD16—1228no—
639SD16—1228no—
640D8—1228no—
641D8—1228no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8C23×D6112yes—
647C2×C8C23×D6112yes—
648C2×C8C23×D6112yes—
649C2×C8C23×D6112yes—
650C4⋊C4—612no—
651C4⋊C4—612no—
652C4⋊C4—612no—
653C4⋊C4—612no—
654C4⋊C4—1224no—
655C4⋊C4—1221no—
656C4⋊C4—1221no—
657C4⋊C4—1221no—
658C4⋊C4—1221no—
659C4⋊C4—1224no—
660C4⋊C4—1224no—
661C4⋊C4—1224no—
662C4⋊C4—1224no—
663C4⋊C4C2×D24414yes—
664C4⋊C4C2×D24414yes—
665C22⋊C4—1224no—
666C22⋊C4—1224no—
667C22⋊C4—1224no—
668C22⋊C4—1224no—
669C22⋊C4—1224no—
670C22⋊C4—1224no—
671C22⋊C4C2×D24414yes—
672C22⋊C4C2×D24414yes—
673C42—1224no—
674C42—1224no—
675C42C2×D24412yes—
676C42C2×D24412yes—
677C42C23×D6112yes—
678C42C23×D6112yes—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—1224no—
683C23—1222no—
684C23—1222no—
685C23—1222no—
686C23—2442no—
687C23—2442no—
688C23—2442no—
689C23—2442no—
690C23—2442no—
691C23—2442no—
692C23—2442no—
693C23—2442no—
694C23C22×D24412yes—
695C23C22×D24411yescharacteristic
696Q8—614no—
697Q8—1224no—
698Q8—1222no—
699D4—614no—
700D4—12216no—
701D4—1224no—
702D4—1222no—
703D4—1222no—
704D4—1222no—
705D4—1222no—
706D4—1222no—
707D4—4884no—
708D4—4884no—
709D4—4884no—
710D4—4884no—
711D4—2442no—
712D4—2442no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—12216no—
722C2×C4—1224no—
723C2×C4—1222no—
724C2×C4—1222no—
725C2×C4—1222no—
726C2×C4—1222no—
727C2×C4—1222no—
728C2×C4—4884no—
729C2×C4—4884no—
730C2×C4—4884no—
731C2×C4—4884no—
732C2×C4—4884no—
733C2×C4—2442no—
734C2×C4—2442no—
735C2×C4—2442no—
736C2×C4—2442no—
737C2×C4C22×D24412yes—
738C2×C4C22×D24412yes—
739C2×C4C22×D24412yes—
740C2×C4C22×D24412yes—
741C2×C4C22×D24412yes—
742C2×C4C22×D24411yescharacteristic
743C2×C4#41×D6112yes—
744C2×C4#41×D6112yes—
745C2×C4C24×D6111yescharacteristic
746C8—22no—
747C8—22no—
748C8—22no—
749C8—22no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—44no—
754C22—1224no—
755C22—4884no—
756C22—4884no—
757C22—2442no—
758C22—2442no—
759C22—2442no—
760C22—2442no—
761C22—2442no—
762C22—2442no—
763C22—2442no—
764C22—2442no—
765C22—2448no—
766C22#1684027412yes—
767C22#1684056712yes—
768C22#1684057412yes—
769C22C23×D24411yescharacteristic
770C4—22no—
771C4—22no—
772C4—22no—
773C4—22no—
774C4—22no—
775C4—1224no—
776C4—2442no—
777C4—2442no—
778C4—2442no—
779C4—2442no—
780C4#1684027412yes—
781C4C2×#41×D6111yescharacteristic
782C4C2×#41×D6111yescharacteristic
783C2—42no—
784C2—4882no—
785C2—4882no—
786C2—2444no—
787C2#2145602014yesdirect product factor
788C2C2×#1684027411yescharacteristic
789C2C2×#1684056711yescharacteristic
790C2C2×#1684057411yescharacteristic
subgroupG/H
centerC23C22×D244
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#433C2
socleC23×C61C22×D4
hypercenterC2×#433D61
hypocenterC61C2×#3119
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
1. C2×#16840367C2semidirect
2. C2×#16840242C2semidirect
3. #21456020C2direct (N × H)
4. C2×#16840081C2semidirect
5. C2×#16840076C2semidirect
6. C2×#16840070C2semidirect
7. C2×#16840063C2semidirect
8. C2×#16839963C2semidirect
9. C2×#16839958C2semidirect
10. C2×#16839909C2semidirect
11. C2×#16839909C2semidirect
12. C2×#16839875C2semidirect
13. C2×#16839864C2semidirect
14. C2×C4×#11758190C2semidirect
15. C2×C4×D488C2semidirect
16. C2×C61×#433C2semidirect
23. #16840367C22semidirect
33. #16840242C22semidirect
45. #16840081C22semidirect
46. #16840076C22semidirect
47. #16840070C22semidirect
48. #16840063C22semidirect
49. #16839963C22semidirect
50. #16839958C22semidirect
51. #16839909C22semidirect
52. #16839909C22semidirect
53. #16839875C22semidirect
54. #16839864C22semidirect
55. C4×#11758190C22semidirect
56. C4×D488C22semidirect
70. C61×#433C22semidirect
403. C2×#433D61semidirect
405. C2×C61#3119semidirect
453. #433C2×D61semidirect
472. C61C2×#3119semidirect
787. C2#21456020direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403672
C2×#168402422
#214560202
C2×#168400812
C2×#168400762
C2×#168400702
C2×#168400632
C2×#168399632
C2×#168399582
C2×#168399092
C2×#168398752
C2×#168398642
C2×C4×#117581902
C2×C4×D4882
C2×C61×#4332
C2×#311961