Finite Group Databasebeta

← C2×#21455916 #30548180

Subgroups — C2×#21455916 #30548180

Order 15616.

2550 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×#16840316C211yesmaximal, characteristic, complemented
2C2×C4×D4×D61C211yesmaximal, characteristic
3#21455916C2116yesmaximal, direct product factor
4C2×#16840099C211yesmaximal, characteristic, complemented
5C2×#16840096C211yesmaximal, characteristic, complemented
6C2×#16840041C211yesmaximal, characteristic, complemented
7C2×#16840040C211yesmaximal, characteristic, complemented
8C2×#16839966C211yesmaximal, characteristic, complemented
9C2×#16839965C211yesmaximal, characteristic, complemented
10C2×#16839914C211yesmaximal, characteristic
11C2×#16839911C211yesmaximal, characteristic
12C2×#16839864C211yesmaximal, characteristic, complemented
13C2×#16839862C211yesmaximal, characteristic, complemented
14C2×#16839860C211yesmaximal, characteristic, complemented
15C2×#16839817C211yesmaximal, characteristic, complemented
16C2×C61×#440C211yesmaximal, characteristic, complemented
17C22×D4×D61C2211yescharacteristic
18C23×C4×D61—21no—
19C22×#11758190C2211yescharacteristic
20C22×#11758200C2211yescharacteristic
21C22×#11758201C2211yescharacteristic
22#16840316—24no—
23#16840316C2218yescomplemented
24C2×#14519776C2211yescharacteristic, complemented
25C2×#14519775C2211yescharacteristic, complemented
26C2×#14519767—21no—
27C2×#14519757C2211yescharacteristic
28C2×#14519755—21no—
29C2×#14519753C2211yescharacteristic
30C2×C4×Dic122—21no—
31C2×C4×Dic122C2211yescharacteristic, complemented
32C2×C4×D244C2211yescharacteristic
33C2×D4×Dic61C2211yescharacteristic
34C2×#14519739C2211yescharacteristic
35C2×C4×C22⋊D61—21no—
36C2×#14519737—21no—
37C4×D4×D61—24no—
38C4×D4×D61C2218yes—
39C2×#14519734—21no—
40C2×C4⋊C4×D61C2211yescharacteristic
41C2×C22⋊C4×D61—21no—
42C2×C42×D61C2211yescharacteristic
43#16840099C2218yescomplemented
44#16840096C2218yescomplemented
45#16840041C2218yescomplemented
46#16840040C2218yescomplemented
47#16839966C2218yescomplemented
48#16839965C2218yescomplemented
49#16839914C2218yes—
50#16839911C2218yes—
51#16839864C2218yescomplemented
52#16839862C2218yescomplemented
53#16839860C2218yescomplemented
54#16839817C2218yescomplemented
55C2×#14519711C2211yescharacteristic, complemented
56C2×#14519710C2211yescharacteristic, complemented
57C2×#14519710C2211yescharacteristic, complemented
58C2×#14519706C2211yescharacteristic, complemented
59C2×#14519706C2211yescharacteristic, complemented
60C2×#14519702C2211yescharacteristic, complemented
61C2×#14519701C2211yescharacteristic, complemented
62C2×#14519700C2211yescharacteristic, complemented
63C2×#14519699C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×#14519689C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×#14519688C2211yescharacteristic, complemented
69C22×SD16×C61C2211yescharacteristic
70C2×C4×Q8×C61C2211yescharacteristic, complemented
71C2×C4×D4×C61C2211yescharacteristic
72C61×#440C2218yescomplemented
73C2×#107×C61C2211yescharacteristic, complemented
74C2×#103×C61C2211yescharacteristic, complemented
75C2×#102×C61C2211yescharacteristic
76C2×#97×C61C2211yescharacteristic, complemented
77C24×D61—21no—
78C22×Dic122—21no—
79C22×Dic122C2311yescharacteristic
80C22×D244C2311yescharacteristic
81C22×C22⋊D61—21no—
82C2×D4×D61—24no—
83C2×D4×D61—24no—
84C2×D4×D61—22no—
85C2×D4×D61C2314yes—
86C23×Dic61—21no—
87C22×C4×D61—21no—
88C22×C4×D61—21no—
89C22×C4×D61—21no—
90C22×C4×D61—28no—
91C22×C4×D61—48no—
92C22×C4×D61D411yescharacteristic
93C22×C4×D61D411yescharacteristic
94C22×C4×D61C2311yescharacteristic
95C2×#11758190—24no—
96C2×#11758190C2314yes—
97C2×#11758200—24no—
98C2×#11758200C2314yes—
99C2×#11758201—24no—
100C2×#11758201C2314yes—
101C22×#92418C2311yescharacteristic
102C22×#92418C2311yescharacteristic
103#14519776—22no—
104#14519776C2314yescomplemented
105#14519775—22no—
106#14519775C2314yescomplemented
107#14519767—28no—
108#14519757—22no—
109#14519757C2314yes—
110#14519755—28no—
111#14519753—22no—
112#14519753C2314yes—
113C4×Dic122—22no—
114C4×Dic122—28no—
115C4×Dic122C2314yescomplemented
116C4×D244—22no—
117C4×D244C2314yes—
118D4×Dic61—22no—
119D4×Dic61C2314yes—
120#14519739—22no—
121#14519739C2314yes—
122C4×C22⋊D61—28no—
123#14519737—28no—
124#14519734—28no—
125C2×C4⋊Dic61—21no—
126C2×C4⋊Dic61C2311yescharacteristic
127C2×C4⋊Dic61C2311yescharacteristic
128C2×#11758196—21no—
129C2×#11758196—21no—
130C2×#11758196—21no—
131C2×#11758196—21no—
132C2×#11758196—21no—
133C2×#11758196—21no—
134C4⋊C4×D61—22no—
135C4⋊C4×D61C2314yes—
136C2×C22⋊Dic61—21no—
137C2×#11758198—21no—
138C2×#11758198—21no—
139C2×#11758198—21no—
140C2×#11758198—21no—
141C22⋊C4×D61—28no—
142C2×C4×Dic61—21no—
143C2×C4×Dic61D411yescharacteristic
144C2×C4×Dic61D411yescharacteristic
145C2×C4×Dic61C2311yescharacteristic
146C42×D61D414yes—
147C42×D61C2314yes—
148#14519711C2314yescomplemented
149#14519710C2314yescomplemented
150#14519710C2314yescomplemented
151#14519706C2314yescomplemented
152#14519706C2314yescomplemented
153#14519702C2314yescomplemented
154#14519701C2314yescomplemented
155#14519700C2314yescomplemented
156#14519699C2314yes—
157#14519698C2314yes—
158#14519697C2314yes—
159#14519689C2314yes—
160#14519689C2314yes—
161#14519688C2314yescomplemented
162C22×Q8×C61C2311yescharacteristic
163C22×D4×C61C2311yescharacteristic
164C23×C4×C61—21no—
165C2×SD16×C61—24no—
166C2×SD16×C61C2314yes—
167C22×C8×C61C2311yescharacteristic
168C22×C8×C61C2311yescharacteristic
169C4×Q8×C61—22no—
170C4×Q8×C61C2314yescomplemented
171C4×D4×C61—22no—
172C4×D4×C61C2314yes—
173C2×C4⋊C4×C61—21no—
174C2×C4⋊C4×C61C2311yescharacteristic
175C2×C4⋊C4×C61C2311yescharacteristic
176C2×C22⋊C4×C61—21no—
177C2×C42×C61—21no—
178C2×C42×C61C2311yescharacteristic
179#107×C61C2314yescomplemented
180#103×C61C2314yescomplemented
181#102×C61C2314yes—
182#97×C61C2314yescomplemented
183C24×C61—21no—
184C23×D61—28no—
185C23×D61—21no—
186C23×D61—24no—
187C23×D61—44no—
188C23×D61—44no—
189C23×D61C2×D411yescharacteristic
190C2×Q8×C61—21no—
191C2×Q8×C61—22no—
192C2×Q8×C61—22no—
193C2×Q8×C61C2412yes—
194C2×D4×C61—21no—
195C2×D4×C61—22no—
196C2×D4×C61#4114yes—
197C2×D4×C61C2412yes—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—24no—
202C22×C4×C61—44no—
203C22×C4×C61C2×D411yescharacteristic
204C22×C4×C61C2×D411yescharacteristic
205C22×C4×C61C2411yescharacteristic
206C2×C22⋊D61—28no—
207C2×C22⋊D61—24no—
208C22×Dic61—21no—
209C22×Dic61—21no—
210C22×Dic61—21no—
211C22×Dic61—24no—
212C22×Dic61—44no—
213C22×Dic61C2×D411yescharacteristic
214C22×Dic61C2×D411yescharacteristic
215C22×Dic61C2×D411yescharacteristic
216D4×D61—216no—
217D4×D61—28no—
218D4×D61—28no—
219C2×D244—21no—
220C2×D244—22no—
221C2×D244#4114yes—
222C2×D244C2412yes—
223C2×C4×D61—24no—
224C2×C4×D61—22no—
225C2×C4×D61—22no—
226C2×C4×D61—24no—
227C2×C4×D61—24no—
228C2×C4×D61—24no—
229C2×C4×D61—24no—
230C2×C4×D61—432no—
231C2×C4×D61—44no—
232C2×C4×D61—44no—
233C2×C4×D61—44no—
234C2×C4×D61C2×D414yes—
235C2×C4×D61C2×D414yes—
236C2×C4×D61C2×D412yes—
237C2×C4×D61C2412yes—
238C2×Dic122—22no—
239C2×Dic122—22no—
240C2×Dic122—21no—
241C2×Dic122—24no—
242C2×Dic122—44no—
243C2×Dic122C2412yes—
244SD16×C61—28no—
245C2×C8×C61—22no—
246C2×C8×C61—22no—
247C2×C8×C61C2412yes—
248C2×C8×C61C2412yes—
249C4⋊C4×C61—24no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61C2412yes—
253C4⋊C4×C61C2412yes—
254C22⋊C4×C61—24no—
255C42×C61—24no—
256C42×C61C2×D412yes—
257C42×C61C2412yes—
258C22⋊Dic61—24no—
259#11758201—28no—
260#11758200—28no—
261#11758198—24no—
262#11758198—24no—
263#11758198—24no—
264#11758198—24no—
265C4⋊Dic61—21no—
266C4⋊Dic61—21no—
267C4⋊Dic61—24no—
268C4⋊Dic61C2412yes—
269C4⋊Dic61C2412yes—
270#11758196—24no—
271#11758196—24no—
272#11758196—24no—
273#11758196—24no—
274#11758196—24no—
275#11758196—24no—
276C4×Dic61—24no—
277C4×Dic61C2×D412yes—
278C4×Dic61C2×D414yes—
279C4×Dic61C2×D414yes—
280C4×Dic61C2412yes—
281C2×#92418—22no—
282C2×#92418—22no—
283C2×#92418C2412yes—
284C2×#92418C2412yes—
285#11758190—28no—
286C23×C61—24no—
287C23×C61—22no—
288C23×C61—42no—
289C23×C61—42no—
290C23×C61C22×D411yescharacteristic
291C22×D61—22no—
292C22×D61—22no—
293C22×D61—216no—
294C22×D61—24no—
295C22×D61—22no—
296C22×D61—48no—
297C22×D61—432no—
298C22×D61—42no—
299C22×D61—42no—
300C22×D61—48no—
301C22×D61#13714yes—
302C22×D61C22×D412yes—
303Q8×C61—22no—
304Q8×C61—22no—
305Q8×C61—42no—
306D4×C61—24no—
307D4×C61—22no—
308D4×C61C2×#4114yes—
309C2×C4×C61—22no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—48no—
315C2×C4×C61—42no—
316C2×C4×C61—42no—
317C2×C4×C61—42no—
318C2×C4×C61C22×D412yes—
319C2×C4×C61C22×D412yes—
320C2×C4×C61C22×D411yescharacteristic
321C2×C4×C61C2×#4112yes—
322C2×C4×C61C2×#4112yes—
323C2×C4×C61C2511yescharacteristic
324C22⋊D61—216no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—42no—
331C2×Dic61—42no—
332C2×Dic61—42no—
333C2×Dic61—48no—
334C2×Dic61AGL(1,ℤ/8)14yes—
335C2×Dic61C22×D412yes—
336C2×Dic61C22×D412yes—
337C2×Dic61C22×D412yes—
338D244—24no—
339D244—22no—
340D244C2×#4114yes—
341C4×D61—28no—
342C4×D61—24no—
343C4×D61—22no—
344C4×D61—22no—
345C4×D61—28no—
346C4×D61—48no—
347C4×D61—48no—
348C4×D61—48no—
349Dic122—22no—
350Dic122—22no—
351Dic122—42no—
352Dic122—48no—
353C8×C61—22no—
354C8×C61—22no—
355#92418—22no—
356#92418—22no—
357C2×#3110—611nomaximal, Sylow
358C22×C61—24no—
359C22×C61—48no—
360C22×C61—42no—
361C22×C61—42no—
362C22×C61#52512yes—
363C22×C61C2×AGL(1,ℤ/8)12yes—
364C22×C61C2×#13712yes—
365C22×C61C23×D411yescharacteristic
366C2×D61—28no—
367C2×D61—22no—
368C2×D61—22no—
369C2×D61—24no—
370C2×D61—432no—
371C2×D61—48no—
372C2×D61—42no—
373C2×D61—42no—
374C2×D61C2×#13714yes—
375C4×C61—22no—
376C4×C61—22no—
377C4×C61—42no—
378C4×C61—42no—
379C4×C61—42no—
380C4×C61#52512yes—
381C4×C61C22×#4111yescharacteristic
382C4×C61C22×#4111yescharacteristic
383Dic61—22no—
384Dic61—22no—
385Dic61—42no—
386Dic61—42no—
387Dic61—42no—
388Dic61C2×AGL(1,ℤ/8)14yes—
389C2×#533—611no—
390C22×C4×D4—611no—
391#3110—6116no—
392C2×#484—611no—
393C2×#484—611no—
394C2×#474—611no—
395C2×#474—611no—
396C2×#461—611no—
397C2×#461—611no—
398C2×#450—611no—
399C2×#450—611no—
400C2×#440—611no—
401C2×#440—611no—
402C2×#440—611no—
403C2×#440D6111yescharacteristic, complemented
404C2×#432—611no—
405C2×C61—44no—
406C2×C61#311014yescomplemented
407C2×C61C2×#52511yescharacteristic
408C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
409C2×C61C22×#13711yescharacteristic
410D61—24no—
411D61—44no—
412C23×D4—611no—
413C24×C4—1221no—
414C22×SD16—611no—
415C22×SD16—611no—
416C22×SD16—611no—
417C22×SD16C2×D6111yescharacteristic
418#533—618no—
419#533—1224no—
420C2×C4⋊Q8—611no—
421C2×C4⋊Q8—611no—
422C2×#125—1221no—
423C2×C22⋊Q8—611no—
424C2×C22⋊Q8—611no—
425C2×C22⋊Q8—1221no—
426C2×C4×Q8—611no—
427C2×C4×Q8—1221no—
428C2×C4×Q8C2×D6111yescharacteristic, complemented
429C2×C4×D4—611no—
430C2×C4×D4—618no—
431C2×C4×D4—611no—
432C2×C4×D4—611no—
433C2×C4×D4—1221no—
434C2×C4×D4—1224no—
435C2×C4×D4—1221no—
436C2×C4×D4C2×D6111yescharacteristic
437C2×#117—1221no—
438C22×C4⋊C4—611no—
439C22×C22⋊C4—1221no—
440C22×C42—611no—
441#484—618no—
442#484—618no—
443#474—618no—
444#474—618no—
445#461—618no—
446#461—618no—
447#450—618no—
448#450—618no—
449#440—618no—
450#440—618no—
451#440—618no—
452#440C2×D6118yescomplemented
453#432—618no—
454C2×#107—611no—
455C2×#107—611no—
456C2×#107—611no—
457C2×#107C2×D6111yescharacteristic, complemented
458C2×C4⋊C8—611no—
459C2×C4⋊C8—611no—
460C2×#103—611no—
461C2×#103—611no—
462C2×#103—611no—
463C2×#103C2×D6111yescharacteristic, complemented
464C2×#102—611no—
465C2×#102—611no—
466C2×#102—611no—
467C2×#102C2×D6111yescharacteristic
468C2×C22⋊C8—611no—
469C2×C22⋊C8—611no—
470C2×#97—611no—
471C2×#97C2×D6111yescharacteristic, complemented
472C61C2×#311011yescharacteristic, complemented, Sylow
473C25—1221no—
474C22×Q8—611no—
475C22×Q8—1221no—
476C22×Q8C22×D6111yescharacteristic
477C22×D4—614no—
478C22×D4—611no—
479C22×D4—1222no—
480C22×D4—1221no—
481C22×D4—1224no—
482C22×D4—1224no—
483C22×D4C22×D6111yescharacteristic
484C23×C4—21no—
485C23×C4—611no—
486C23×C4—611no—
487C23×C4—611no—
488C23×C4—1221no—
489C23×C4—1228no—
490C23×C4—1221no—
491C23×C4—1221no—
492C23×C4—1221no—
493C23×C4—2448no—
494C2×SD16—24no—
495C2×SD16—614no—
496C2×SD16—614no—
497C2×SD16—614no—
498C2×SD16—1224no—
499C2×SD16—1224no—
500C2×SD16—1224no—
501C2×SD16C22×D6114yes—
502C22×C8—611no—
503C22×C8—611no—
504C22×C8C22×D6111yescharacteristic
505C22×C8C22×D6111yescharacteristic
506C4⋊Q8—614no—
507C4⋊Q8—614no—
508C4⋊Q8—1222no—
509C4⋊Q8—1222no—
510#125—1228no—
511C22⋊Q8—614no—
512C22⋊Q8—614no—
513C22⋊Q8—1222no—
514C22⋊Q8—1228no—
515C22⋊Q8—1222no—
516C4×Q8—22no—
517C4×Q8—614no—
518C4×Q8—1228no—
519C4×Q8—1222no—
520C4×Q8C22×D6114yescomplemented
521C4×D4—22no—
522C4×D4—614no—
523C4×D4—614no—
524C4×D4—614no—
525C4×D4—1228no—
526C4×D4—1222no—
527C4×D4—1228no—
528C4×D4—1222no—
529C4×D4—1222no—
530C4×D4C22×D6114yes—
531#117—1228no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—611no—
534C2×C4⋊C4—611no—
535C2×C4⋊C4—614no—
536C2×C4⋊C4—1222no—
537C2×C4⋊C4—1221no—
538C2×C4⋊C4—1221no—
539C2×C4⋊C4—1221no—
540C2×C4⋊C4—1221no—
541C2×C4⋊C4—1221no—
542C2×C4⋊C4—1221no—
543C2×C4⋊C4—1221no—
544C2×C4⋊C4C22×D6111yescharacteristic
545C2×C4⋊C4C22×D6111yescharacteristic
546C2×C22⋊C4—21no—
547C2×C22⋊C4—1228no—
548C2×C22⋊C4—1221no—
549C2×C22⋊C4—1221no—
550C2×C22⋊C4—1221no—
551C2×C22⋊C4—1221no—
552C2×C22⋊C4—1221no—
553C2×C42—21no—
554C2×C42—611no—
555C2×C42—611no—
556C2×C42—611no—
557C2×C42—614no—
558C2×C42—614no—
559C2×C42—1221no—
560C2×C42C22×D6111yescharacteristic
561#107—614no—
562#107—614no—
563#107—614no—
564#107C22×D6114yescomplemented
565C4⋊C8—614no—
566C4⋊C8—614no—
567#103—614no—
568#103—614no—
569#103—614no—
570#103C22×D6114yescomplemented
571#102—614no—
572#102—614no—
573#102—614no—
574#102C22×D6114yes—
575C22⋊C8—614no—
576C22⋊C8—614no—
577#97—614no—
578#97C22×D6114yescomplemented
579C24—21no—
580C24—611no—
581C24—1224no—
582C24—1228no—
583C24—1221no—
584C24—2444no—
585C24—2444no—
586C2×Q8—21no—
587C2×Q8—22no—
588C2×Q8—22no—
589C2×Q8—612no—
590C2×Q8—1224no—
591C2×Q8—1221no—
592C2×Q8—1222no—
593C2×Q8—1222no—
594C2×Q8—2444no—
595C2×Q8C23×D6112yes—
596C2×D4—21no—
597C2×D4—22no—
598C2×D4—614no—
599C2×D4—612no—
600C2×D4—1224no—
601C2×D4—1228no—
602C2×D4—12216no—
603C2×D4—1228no—
604C2×D4—1228no—
605C2×D4—1221no—
606C2×D4—1222no—
607C2×D4#1175822214yes—
608C2×D4C23×D6112yes—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—24no—
613C22×C4—44no—
614C22×C4—611no—
615C22×C4—611no—
616C22×C4—611no—
617C22×C4—614no—
618C22×C4—612no—
619C22×C4—614no—
620C22×C4—612no—
621C22×C4—1224no—
622C22×C4—1224no—
623C22×C4—1224no—
624C22×C4—1224no—
625C22×C4—1224no—
626C22×C4—1222no—
627C22×C4—1222no—
628C22×C4—1221no—
629C22×C4—1221no—
630C22×C4—1221no—
631C22×C4—1224no—
632C22×C4—2444no—
633C22×C4—2444no—
634C22×C4—24432no—
635C22×C4—2444no—
636C22×C4—2444no—
637C22×C4D4×D6111yescharacteristic
638C22×C4D4×D6111yescharacteristic
639C22×C4C23×D6111yescharacteristic
640SD16—28no—
641SD16—1228no—
642SD16—1228no—
643SD16—1228no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8—612no—
647C2×C8—612no—
648C2×C8—1222no—
649C2×C8—1222no—
650C2×C8C23×D6112yes—
651C2×C8C23×D6112yes—
652C4⋊C4—24no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—612no—
656C4⋊C4—612no—
657C4⋊C4—1224no—
658C4⋊C4—1224no—
659C4⋊C4—1224no—
660C4⋊C4—1224no—
661C4⋊C4—1224no—
662C4⋊C4—1224no—
663C4⋊C4—1221no—
664C4⋊C4—1221no—
665C4⋊C4—1224no—
666C4⋊C4C23×D6112yes—
667C4⋊C4C23×D6112yes—
668C22⋊C4—24no—
669C22⋊C4—1224no—
670C22⋊C4—1224no—
671C22⋊C4—1224no—
672C22⋊C4—1224no—
673C22⋊C4—1224no—
674C42—24no—
675C42—614no—
676C42—614no—
677C42—612no—
678C42—612no—
679C42—1224no—
680C42D4×D6112yes—
681C42C23×D6112yes—
682C23—24no—
683C23—22no—
684C23—42no—
685C23—42no—
686C23—614no—
687C23—612no—
688C23—12216no—
689C23—1222no—
690C23—1222no—
691C23—1224no—
692C23—1222no—
693C23—2448no—
694C23—2448no—
695C23—24432no—
696C23—2442no—
697C23—2442no—
698C23C2×D4×D6111yescharacteristic
699Q8—22no—
700Q8—22no—
701Q8—42no—
702Q8—1222no—
703Q8—1222no—
704Q8—2448no—
705Q8—2442no—
706D4—24no—
707D4—22no—
708D4—614no—
709D4—12216no—
710D4—1224no—
711D4—1222no—
712D4C2×#1175822214yes—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—48no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—614no—
723C2×C4—612no—
724C2×C4—612no—
725C2×C4—612no—
726C2×C4—1228no—
727C2×C4—1228no—
728C2×C4—1222no—
729C2×C4—1222no—
730C2×C4—1224no—
731C2×C4—1222no—
732C2×C4—1222no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—2448no—
737C2×C4—2448no—
738C2×C4—2448no—
739C2×C4—2448no—
740C2×C4—2442no—
741C2×C4—2442no—
742C2×C4—2442no—
743C2×C4C2×D4×D6112yes—
744C2×C4C2×D4×D6112yes—
745C2×C4C2×D4×D6111yescharacteristic
746C2×C4#41×D6112yes—
747C2×C4C2×#1175822212yes—
748C2×C4C24×D6111yescharacteristic
749C8—22no—
750C8—22no—
751C8—1222no—
752C8—1222no—
753C22—24no—
754C22—48no—
755C22—42no—
756C22—42no—
757C22—614no—
758C22—1228no—
759C22—1222no—
760C22—1222no—
761C22—1224no—
762C22—24432no—
763C22—2448no—
764C22—2442no—
765C22—2442no—
766C22#1684027112yes—
767C22AGL(1,ℤ/8)×D6112yes—
768C22#137×D6112yes—
769C22C22×D4×D6111yescharacteristic
770C4—22no—
771C4—22no—
772C4—42no—
773C4—42no—
774C4—42no—
775C4—614no—
776C4—1222no—
777C4—1222no—
778C4—2442no—
779C4—2442no—
780C4—2442no—
781C4#1684027112yes—
782C4C2×#41×D6111yescharacteristic
783C4C22×#1175822211yescharacteristic
784C2—44no—
785C2—1224no—
786C2—2444no—
787C2#2145591614yesdirect product factor
788C2C2×#1684027111yescharacteristic
789C2C2×AGL(1,ℤ/8)×D6111yescharacteristic
790C2C2×#137×D6111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#440C2
socleC23×C61C22×D4
prime radicalC22×D4×D61C22
hypercenterC2×#440D61
hypocenterC61C2×#3110
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C2×#16840316C2semidirect
3. #21455916C2direct (N × H)
4. C2×#16840099C2semidirect
5. C2×#16840096C2semidirect
6. C2×#16840041C2semidirect
7. C2×#16840040C2semidirect
8. C2×#16839966C2semidirect
9. C2×#16839965C2semidirect
12. C2×#16839864C2semidirect
13. C2×#16839862C2semidirect
14. C2×#16839860C2semidirect
15. C2×#16839817C2semidirect
16. C2×C61×#440C2semidirect
23. #16840316C22semidirect
24. C2×#14519776C22semidirect
25. C2×#14519775C22semidirect
31. C2×C4×Dic122C22semidirect
43. #16840099C22semidirect
44. #16840096C22semidirect
45. #16840041C22semidirect
46. #16840040C22semidirect
47. #16839966C22semidirect
48. #16839965C22semidirect
51. #16839864C22semidirect
52. #16839862C22semidirect
53. #16839860C22semidirect
54. #16839817C22semidirect
55. C2×#14519711C22semidirect
56. C2×#14519710C22semidirect
57. C2×#14519710C22semidirect
58. C2×#14519706C22semidirect
59. C2×#14519706C22semidirect
60. C2×#14519702C22semidirect
61. C2×#14519701C22semidirect
62. C2×#14519700C22semidirect
68. C2×#14519688C22semidirect
70. C2×C4×Q8×C61C22semidirect
72. C61×#440C22semidirect
73. C2×#107×C61C22semidirect
74. C2×#103×C61C22semidirect
76. C2×#97×C61C22semidirect
104. #14519776C23semidirect
106. #14519775C23semidirect
115. C4×Dic122C23semidirect
148. #14519711C23semidirect
149. #14519710C23semidirect
150. #14519710C23semidirect
151. #14519706C23semidirect
152. #14519706C23semidirect
153. #14519702C23semidirect
154. #14519701C23semidirect
155. #14519700C23semidirect
161. #14519688C23semidirect
170. C4×Q8×C61C23semidirect
179. #107×C61C23semidirect
180. #103×C61C23semidirect
182. #97×C61C23semidirect
403. C2×#440D61semidirect
406. C2×C61#3110semidirect
428. C2×C4×Q8C2×D61semidirect
452. #440C2×D61semidirect
457. C2×#107C2×D61semidirect
463. C2×#103C2×D61semidirect
471. C2×#97C2×D61semidirect
472. C61C2×#3110semidirect
520. C4×Q8C22×D61semidirect
564. #107C22×D61semidirect
570. #103C22×D61semidirect
578. #97C22×D61semidirect
787. C2#21455916direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403162
C2×C4×D4×D612
#214559162
C2×#168400992
C2×#168400962
C2×#168400412
C2×#168400402
C2×#168399662
C2×#168399652
C2×#168399142
C2×#168399112
C2×#168398642
C2×#168398622
C2×#168398602
C2×#168398172
C2×C61×#4402
C2×#311061