Finite Group Databasebeta

← C2×#21455999 #30548240

Subgroups — C2×#21455999 #30548240

Order 15616.

2274 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840377C211yesmaximal, characteristic, complemented
2C2×#16840234C211yesmaximal, characteristic, complemented
3#21455999C2116yesmaximal, direct product factor
4C2×#16840105C211yesmaximal, characteristic, complemented
5C2×#16840085C211yesmaximal, characteristic, complemented
6C2×#16840050C211yesmaximal, characteristic, complemented
7C2×#16840041C211yesmaximal, characteristic, complemented
8C2×#16839976C211yesmaximal, characteristic, complemented
9C2×#16839975C211yesmaximal, characteristic, complemented
10C2×#16839914C211yesmaximal, characteristic, complemented
11C2×#16839894C211yesmaximal, characteristic
12C2×#16839872C211yesmaximal, characteristic, complemented
13C2×#16839862C211yesmaximal, characteristic, complemented
14C2×C4×#11758190C211yesmaximal, characteristic, complemented
15C2×#16839821C211yesmaximal, characteristic, complemented
16C2×C4×D8×C61C211yesmaximal, characteristic, complemented
17C22×D4×D61C2211yescharacteristic
18C22×#11758190C2211yescharacteristic
19C22×#11758200C2211yescharacteristic
20C22×#11758199C2211yescharacteristic
21#16840377—24no—
22#16840377C2218yescomplemented
23C2×#14519776C2211yescharacteristic, complemented
24C2×#14519770—21no—
25C2×#14519764C2211yescharacteristic, complemented
26C2×#14519763—21no—
27C2×#14519760—21no—
28C2×#14519757C2211yescharacteristic
29C2×#14519756—21no—
30C2×#14519748C2211yescharacteristic
31#16840234—24no—
32#16840234C2218yescomplemented
33C2×C4×Dic122C2211yescharacteristic, complemented
34C2×C4×D244C2211yescharacteristic
35C2×D4×Dic61C2211yescharacteristic
36C2×#14519739C2211yescharacteristic
37C2×C4×C22⋊D61—21no—
38C2×#14519737—21no—
39C2×#14519735C2211yescharacteristic
40C2×#14519734C2211yescharacteristic
41C22×#11758198—21no—
42C2×C22⋊C4×D61—21no—
43#16840105C2218yescomplemented
44#16840085C2218yescomplemented
45#16840050C2218yescomplemented
46#16840041C2218yescomplemented
47#16839976C2218yescomplemented
48#16839975C2218yescomplemented
49#16839914C2218yescomplemented
50#16839894C2218yes—
51#16839872C2218yescomplemented
52#16839862C2218yescomplemented
53C4×#11758190C2218yescomplemented
54#16839821C2218yescomplemented
55C2×#14519710C2211yescharacteristic, complemented
56C2×#14519709C2211yescharacteristic, complemented
57C2×#14519708C2211yescharacteristic, complemented
58C2×#14519706C2211yescharacteristic, complemented
59C2×#14519706C2211yescharacteristic, complemented
60C2×#14519702C2211yescharacteristic, complemented
61C2×#14519700C2211yescharacteristic, complemented
62C2×#14519699C2211yescharacteristic
63C2×#14519698C2211yescharacteristic
64C2×#14519698C2211yescharacteristic, complemented
65C2×#14519697C2211yescharacteristic
66C2×#14519689C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×#14519688C2211yescharacteristic, complemented
69C22×D8×C61C2211yescharacteristic
70C2×C4×D4×C61C2211yescharacteristic
71C2×C4×D4×C61C2211yescharacteristic, complemented
72C4×D8×C61C2218yescomplemented
73C2×#107×C61C2211yescharacteristic, complemented
74C2×#102×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic, complemented
76C2×C4×C8×C61C2211yescharacteristic, complemented
77C24×D61—21no—
78C22×Dic122—21no—
79C22×Dic122C2311yescharacteristic
80C22×D244C2311yescharacteristic
81C22×C22⋊D61—21no—
82C22×C22⋊D61—21no—
83C2×D4×D61—24no—
84C2×D4×D61—24no—
85C2×D4×D61—22no—
86C2×D4×D61C2314yes—
87C23×Dic61—21no—
88C22×C4×D61—21no—
89C22×C4×D61—21no—
90C22×C4×D61C2311yescharacteristic
91C2×#11758190—24no—
92C2×#11758190C2314yes—
93C2×#11758200—24no—
94C2×#11758200C2314yes—
95C2×#11758199—24no—
96C2×#11758199C2314yes—
97C22×#92418C2311yescharacteristic
98C22×#92418C2311yescharacteristic
99#14519776—22no—
100#14519776C2314yescomplemented
101#14519770—28no—
102#14519764—22no—
103#14519764C2314yescomplemented
104#14519763—28no—
105#14519760—28no—
106#14519757—22no—
107#14519757C2314yes—
108#14519756—28no—
109#14519748—22no—
110#14519748C2314yes—
111C4×Dic122—22no—
112C4×Dic122C2314yescomplemented
113C4×D244—22no—
114C4×D244C2314yes—
115D4×Dic61—22no—
116D4×Dic61C2314yes—
117#14519739—22no—
118#14519739C2314yes—
119C4×C22⋊D61—28no—
120#14519737—28no—
121#14519735—22no—
122#14519735C2314yes—
123#14519734D414yes—
124#14519734C2314yes—
125C2×C4⋊Dic61—21no—
126C2×C4⋊Dic61C2311yescharacteristic
127C2×C4⋊Dic61C2311yescharacteristic
128C2×#11758196—21no—
129C2×#11758196—21no—
130C2×#11758196D411yescharacteristic
131C2×#11758196D411yescharacteristic
132C2×C22⋊Dic61—21no—
133C2×C22⋊Dic61—21no—
134C2×C22⋊Dic61—21no—
135C2×C22⋊Dic61—21no—
136C2×#11758198—21no—
137C2×#11758198—21no—
138C2×#11758198—21no—
139C2×#11758198—21no—
140C2×#11758198—28no—
141C2×#11758198D411yescharacteristic
142C2×#11758198D411yescharacteristic
143C22⋊C4×D61—28no—
144C2×C4×Dic61—21no—
145C2×C4×Dic61—21no—
146C2×C4×Dic61C2311yescharacteristic
147#14519710C2314yescomplemented
148#14519709C2314yescomplemented
149#14519708C2314yescomplemented
150#14519706C2314yescomplemented
151#14519706C2314yescomplemented
152#14519702C2314yescomplemented
153#14519700C2314yescomplemented
154#14519699C2314yes—
155#14519698C2314yes—
156#14519698C2314yescomplemented
157#14519697C2314yes—
158#14519689C2314yes—
159#14519689C2314yes—
160#14519688C2314yescomplemented
161C22×D4×C61C2311yescharacteristic
162C22×D4×C61C2311yescharacteristic
163C23×C4×C61—21no—
164C23×C4×C61—21no—
165C2×D8×C61—24no—
166C2×D8×C61C2314yes—
167C22×C8×C61C2311yescharacteristic
168C22×C8×C61C2311yescharacteristic
169C4×D4×C61—22no—
170C4×D4×C61—22no—
171C4×D4×C61C2314yes—
172C4×D4×C61C2314yescomplemented
173C2×C4⋊C4×C61C2311yescharacteristic
174C2×C4⋊C4×C61C2311yescharacteristic
175C2×C22⋊C4×C61—21no—
176C2×C22⋊C4×C61—21no—
177C2×C42×C61C2311yescharacteristic
178#107×C61C2314yescomplemented
179#102×C61C2314yes—
180#102×C61C2314yescomplemented
181C4×C8×C61C2314yescomplemented
182C24×C61—21no—
183C24×C61—21no—
184C23×D61—21no—
185C23×D61—28no—
186C23×D61—24no—
187C23×D61—82no—
188C23×D61—82no—
189C23×D61C2×D411yescharacteristic
190C2×D4×C61—21no—
191C2×D4×C61—21no—
192C2×D4×C61—22no—
193C2×D4×C61—22no—
194C2×D4×C61—22no—
195C2×D4×C61#4114yes—
196C2×D4×C61C2412yes—
197C2×D4×C61C2412yes—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—24no—
201C22×C4×C61—24no—
202C22×C4×C61—82no—
203C22×C4×C61—82no—
204C22×C4×C61C2×D411yescharacteristic
205C22×C4×C61C2×D411yescharacteristic
206C22×C4×C61C2411yescharacteristic
207C2×C22⋊D61—28no—
208C2×C22⋊D61—24no—
209C2×C22⋊D61—24no—
210C2×C22⋊D61—82no—
211C22×Dic61—21no—
212C22×Dic61—21no—
213C22×Dic61—21no—
214C22×Dic61—24no—
215C22×Dic61—82no—
216C22×Dic61C2×D411yescharacteristic
217C22×Dic61C2×D411yescharacteristic
218C22×Dic61C2×D411yescharacteristic
219D4×D61—216no—
220D4×D61—28no—
221D4×D61—28no—
222C2×D244—21no—
223C2×D244—22no—
224C2×D244#4114yes—
225C2×D244C2412yes—
226C2×C4×D61—22no—
227C2×C4×D61—22no—
228C2×C4×D61—24no—
229C2×C4×D61—24no—
230C2×C4×D61—82no—
231C2×C4×D61—82no—
232C2×C4×D61C2×D412yes—
233C2×C4×D61C2412yes—
234C2×Dic122—22no—
235C2×Dic122—22no—
236C2×Dic122—21no—
237C2×Dic122—24no—
238C2×Dic122—82no—
239C2×Dic122C2412yes—
240D8×C61—28no—
241C2×C8×C61—22no—
242C2×C8×C61—22no—
243C2×C8×C61C2412yes—
244C2×C8×C61C2412yes—
245C4⋊C4×C61—21no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61C2412yes—
248C4⋊C4×C61C2412yes—
249C22⋊C4×C61—24no—
250C22⋊C4×C61—24no—
251C42×C61C2×D412yes—
252C42×C61C2412yes—
253C22⋊Dic61—24no—
254C22⋊Dic61—24no—
255C22⋊Dic61—24no—
256C22⋊Dic61—24no—
257#11758200—28no—
258#11758199—28no—
259#11758198—24no—
260#11758198—24no—
261#11758198—24no—
262#11758198—24no—
263#11758198C2×D414yes—
264#11758198C2×D414yes—
265C4⋊Dic61—21no—
266C4⋊Dic61—21no—
267C4⋊Dic61—24no—
268C4⋊Dic61C2412yes—
269C4⋊Dic61C2412yes—
270#11758196—24no—
271#11758196—24no—
272#11758196C2×D414yes—
273#11758196C2×D414yes—
274C4×Dic61—24no—
275C4×Dic61—24no—
276C4×Dic61C2×D412yes—
277C4×Dic61C2412yes—
278C2×#92418—22no—
279C2×#92418—22no—
280C2×#92418C2412yes—
281C2×#92418C2412yes—
282#11758190—28no—
283C23×C61—24no—
284C23×C61—22no—
285C23×C61—22no—
286C23×C61—42no—
287C23×C61—42no—
288C23×C61—42no—
289C23×C61—42no—
290C23×C61—42no—
291C23×C61C22×D411yescharacteristic
292C22×D61—22no—
293C22×D61—24no—
294C22×D61—22no—
295C22×D61—22no—
296C22×D61—22no—
297C22×D61—216no—
298C22×D61—42no—
299C22×D61—42no—
300C22×D61—84no—
301C22×D61—84no—
302C22×D61—816no—
303C22×D61C22×D412yes—
304D4×C61—24no—
305D4×C61—22no—
306D4×C61—22no—
307D4×C61—22no—
308D4×C61—42no—
309D4×C61C2×#4114yes—
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—84no—
317C2×C4×C61—84no—
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—
325C22⋊D61—84no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—42no—
333C2×Dic61—42no—
334C2×Dic61—42no—
335C2×Dic61—84no—
336C2×Dic61C22×D412yes—
337C2×Dic61C22×D412yes—
338C2×Dic61C22×D412yes—
339D244—24no—
340D244—22no—
341D244C2×#4114yes—
342C4×D61—24no—
343C4×D61—22no—
344C4×D61—22no—
345C4×D61—84no—
346C4×D61—84no—
347Dic122—22no—
348Dic122—22no—
349Dic122—42no—
350Dic122—84no—
351C8×C61—22no—
352C8×C61—22no—
353#92418—22no—
354#92418—22no—
355C2×#3118—611nomaximal, Sylow
356C22×C61—24no—
357C22×C61—48no—
358C22×C61—42no—
359C22×C61—42no—
360C22×C61—42no—
361C22×C61—42no—
362C22×C61—42no—
363C22×C61—84no—
364C22×C61#52512yes—
365C22×C61#57612yes—
366C22×C61#57712yes—
367C22×C61C23×D411yescharacteristic
368C2×D61—22no—
369C2×D61—24no—
370C2×D61—22no—
371C2×D61—22no—
372C2×D61—44no—
373C2×D61—48no—
374C2×D61—42no—
375C2×D61—42no—
376C2×D61—816no—
377C4×C61—22no—
378C4×C61—22no—
379C4×C61—42no—
380C4×C61—42no—
381C4×C61#52512yes—
382C4×C61C22×#4111yescharacteristic
383C4×C61C22×#4111yescharacteristic
384Dic61—22no—
385Dic61—22no—
386Dic61—22no—
387Dic61—42no—
388Dic61—42no—
389Dic61—42no—
390C2×#542—611no—
391C2×#518—611no—
392#3118—6116no—
393C2×#485—611no—
394C2×#482—611no—
395C2×#476—611no—
396C2×#474—611no—
397C2×#463—611no—
398C2×#463—611no—
399C2×#450—611no—
400C2×#447—611no—
401C2×#442—611no—
402C2×#440—611no—
403C2×C4×SD16—611no—
404C2×C4×D8D6111yescharacteristic, complemented
405C2×#433—611no—
406C2×C61—44no—
407C2×C61—82no—
408C2×C61#311814yescomplemented
409C2×C61C2×#52511yescharacteristic
410C2×C61C2×#57611yescharacteristic
411C2×C61C2×#57711yescharacteristic
412D61—42no—
413D61—44no—
414C23×D4—611no—
415C22×SD16—611no—
416C22×SD16—611no—
417C22×D8—611no—
418C22×D8C2×D6111yescharacteristic
419#542—618no—
420#542—1224no—
421C2×C4⋊Q8—611no—
422C2×#126—1221no—
423C2×#124—611no—
424C2×#124—1221no—
425C2×#123—1221no—
426C2×C22⋊Q8—611no—
427C2×C22⋊Q8—1221no—
428C2×#121—611no—
429#518—618no—
430#518—1224no—
431C2×C4×Q8—611no—
432C2×C4×D4—611no—
433C2×C4×D4—611no—
434C2×C4×D4—611no—
435C2×C4×D4—1221no—
436C2×C4×D4—1221no—
437C2×C4×D4C2×D6111yescharacteristic
438C2×C4×D4C2×D6111yescharacteristic, complemented
439C2×#117—611no—
440C2×#117—611no—
441C22×C22⋊C4—1221no—
442C22×C22⋊C4—1221no—
443#485—618no—
444#482—618no—
445#476—618no—
446#474—618no—
447#463—618no—
448#463—618no—
449#450—618no—
450#447—618no—
451#442—618no—
452#440—618no—
453C4×SD16—618no—
454C4×D8C2×D6118yescomplemented
455#433—618no—
456C2×#107—611no—
457C2×#107C2×D6111yescharacteristic, complemented
458C2×#106—611no—
459C2×#106—611no—
460C2×C4⋊C8—611no—
461C2×C4⋊C8—611no—
462C2×#103—611no—
463C2×#103—611no—
464C2×#102—611no—
465C2×#102—611no—
466C2×#102—611no—
467C2×#102—611no—
468C2×#102C2×D6111yescharacteristic
469C2×#102C2×D6111yescharacteristic, complemented
470C2×C22⋊C8—611no—
471C2×C22⋊C8—611no—
472C2×#97—611no—
473C2×C4×C8C2×D6111yescharacteristic, complemented
474C61C2×#311811yescharacteristic, complemented, Sylow
475C25—1221no—
476C22×Q8—611no—
477C22×Q8—1221no—
478C22×D4—614no—
479C22×D4—611no—
480C22×D4—1222no—
481C22×D4—1221no—
482C22×D4—1224no—
483C22×D4—1224no—
484C22×D4—1221no—
485C22×D4C22×D6111yescharacteristic
486C22×D4C22×D6111yescharacteristic
487C23×C4—21no—
488C23×C4—21no—
489C23×C4—611no—
490C23×C4—1221no—
491C23×C4—1221no—
492C23×C4—1221no—
493C2×SD16—614no—
494C2×SD16—614no—
495C2×SD16—1224no—
496C2×SD16—1224no—
497C2×D8—24no—
498C2×D8—614no—
499C2×D8—1224no—
500C2×D8C22×D6114yes—
501C22×C8—611no—
502C22×C8—611no—
503C22×C8C22×D6111yescharacteristic
504C22×C8C22×D6111yescharacteristic
505C4⋊Q8—614no—
506C4⋊Q8—1222no—
507#126—1228no—
508#124—614no—
509#124—1222no—
510#124—1228no—
511#123—1228no—
512C22⋊Q8—614no—
513C22⋊Q8—1222no—
514C22⋊Q8—1228no—
515#121—614no—
516#121—1222no—
517C4×Q8—614no—
518C4×Q8—1222no—
519C4×D4—22no—
520C4×D4—22no—
521C4×D4—614no—
522C4×D4—614no—
523C4×D4—614no—
524C4×D4—1222no—
525C4×D4—1222no—
526C4×D4—1228no—
527C4×D4—1228no—
528C4×D4—1222no—
529C4×D4C22×D6114yes—
530C4×D4C22×D6114yescomplemented
531#117—614no—
532#117—614no—
533#117—614no—
534#117—1222no—
535C2×C4⋊C4—611no—
536C2×C4⋊C4—611no—
537C2×C4⋊C4—611no—
538C2×C4⋊C4—611no—
539C2×C4⋊C4—1221no—
540C2×C4⋊C4—1221no—
541C2×C4⋊C4—1221no—
542C2×C4⋊C4C22×D6111yescharacteristic
543C2×C4⋊C4C22×D6111yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—611no—
547C2×C22⋊C4—611no—
548C2×C22⋊C4—1228no—
549C2×C22⋊C4—1228no—
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×C22⋊C4—1221no—
558C2×C42—611no—
559C2×C42—1221no—
560C2×C42—1221no—
561C2×C42C22×D6111yescharacteristic
562#107—614no—
563#107C22×D6114yescomplemented
564#106—614no—
565#106—614no—
566C4⋊C8—614no—
567C4⋊C8—614no—
568#103—614no—
569#103—614no—
570#102—614no—
571#102—614no—
572#102—614no—
573#102—614no—
574#102C22×D6114yes—
575#102C22×D6114yescomplemented
576C22⋊C8—614no—
577C22⋊C8—614no—
578#97—614no—
579C4×C8C22×D6114yescomplemented
580C24—21no—
581C24—21no—
582C24—611no—
583C24—1224no—
584C24—1228no—
585C24—1221no—
586C24—4882no—
587C24—4882no—
588C2×Q8—612no—
589C2×Q8—1224no—
590C2×Q8—1221no—
591C2×Q8—1222no—
592C2×Q8—1222no—
593C2×Q8—4882no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—614no—
600C2×D4—612no—
601C2×D4—1224no—
602C2×D4—1228no—
603C2×D4—12216no—
604C2×D4—1228no—
605C2×D4—1228no—
606C2×D4—1224no—
607C2×D4—1221no—
608C2×D4—1222no—
609C2×D4—4882no—
610C2×D4#1175822214yes—
611C2×D4C23×D6112yes—
612C2×D4C23×D6112yes—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—24no—
616C22×C4—24no—
617C22×C4—82no—
618C22×C4—82no—
619C22×C4—611no—
620C22×C4—611no—
621C22×C4—611no—
622C22×C4—612no—
623C22×C4—612no—
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—4882no—
633C22×C4—4882no—
634C22×C4—4882no—
635C22×C4D4×D6111yescharacteristic
636C22×C4D4×D6111yescharacteristic
637C22×C4C23×D6111yescharacteristic
638SD16—1228no—
639SD16—1228no—
640D8—28no—
641D8—1228no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—612no—
645C2×C8—612no—
646C2×C8—1222no—
647C2×C8—1222no—
648C2×C8C23×D6112yes—
649C2×C8C23×D6112yes—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—614no—
653C4⋊C4—614no—
654C4⋊C4—612no—
655C4⋊C4—612no—
656C4⋊C4—1224no—
657C4⋊C4—1224no—
658C4⋊C4—1221no—
659C4⋊C4—1221no—
660C4⋊C4—1224no—
661C4⋊C4C23×D6112yes—
662C4⋊C4C23×D6112yes—
663C22⋊C4—24no—
664C22⋊C4—24no—
665C22⋊C4—614no—
666C22⋊C4—614no—
667C22⋊C4—1224no—
668C22⋊C4—1224no—
669C22⋊C4—1224no—
670C22⋊C4—1224no—
671C22⋊C4—1224no—
672C22⋊C4—1224no—
673C22⋊C4—1224no—
674C22⋊C4—1224no—
675C42—612no—
676C42—612no—
677C42—1224no—
678C42—1224no—
679C42D4×D6112yes—
680C42C23×D6112yes—
681C23—24no—
682C23—22no—
683C23—22no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—612no—
690C23—12216no—
691C23—1222no—
692C23—1224no—
693C23—1222no—
694C23—1222no—
695C23—1222no—
696C23—4884no—
697C23—4884no—
698C23—48816no—
699C23—2442no—
700C23—2442no—
701C23C2×D4×D6111yescharacteristic
702Q8—1222no—
703Q8—1222no—
704Q8—4884no—
705Q8—2442no—
706D4—24no—
707D4—22no—
708D4—22no—
709D4—22no—
710D4—42no—
711D4—614no—
712D4—12216no—
713D4—1224no—
714D4—1222no—
715D4—4884no—
716D4C2×#1175822214yes—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—84no—
724C2×C4—84no—
725C2×C4—612no—
726C2×C4—612no—
727C2×C4—612no—
728C2×C4—1222no—
729C2×C4—1222no—
730C2×C4—1222no—
731C2×C4—1224no—
732C2×C4—1222no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—1222no—
737C2×C4—4884no—
738C2×C4—4884no—
739C2×C4—4884no—
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—42no—
755C22—42no—
756C22—48no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—84no—
761C22—1222no—
762C22—1222no—
763C22—1222no—
764C22—1224no—
765C22—48816no—
766C22—2442no—
767C22—2442no—
768C22—2444no—
769C22—2448no—
770C22#1684027112yes—
771C22#1684056312yes—
772C22#1684056912yes—
773C22C22×D4×D6111yescharacteristic
774C4—22no—
775C4—22no—
776C4—42no—
777C4—42no—
778C4—1222no—
779C4—1222no—
780C4—1222no—
781C4—2442no—
782C4—2442no—
783C4—2442no—
784C4#1684027112yes—
785C4C2×#41×D6111yescharacteristic
786C4C22×#1175822211yescharacteristic
787C2—44no—
788C2—82no—
789C2—2442no—
790C2—2444no—
791C2#2145599914yesdirect product factor
792C2C2×#1684027111yescharacteristic
793C2C2×#1684056311yescharacteristic
794C2C2×#1684056911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C4×D8×C61C2
socleC23×C61C22×D4
prime radicalC2×#16839894C2
hypercenterC2×C4×D8D61
hypocenterC61C2×#3118
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#16840377C2semidirect
2. C2×#16840234C2semidirect
3. #21455999C2direct (N × H)
4. C2×#16840105C2semidirect
5. C2×#16840085C2semidirect
6. C2×#16840050C2semidirect
7. C2×#16840041C2semidirect
8. C2×#16839976C2semidirect
9. C2×#16839975C2semidirect
10. C2×#16839914C2semidirect
12. C2×#16839872C2semidirect
13. C2×#16839862C2semidirect
14. C2×C4×#11758190C2semidirect
15. C2×#16839821C2semidirect
16. C2×C4×D8×C61C2semidirect
22. #16840377C22semidirect
23. C2×#14519776C22semidirect
25. C2×#14519764C22semidirect
32. #16840234C22semidirect
33. C2×C4×Dic122C22semidirect
43. #16840105C22semidirect
44. #16840085C22semidirect
45. #16840050C22semidirect
46. #16840041C22semidirect
47. #16839976C22semidirect
48. #16839975C22semidirect
49. #16839914C22semidirect
51. #16839872C22semidirect
52. #16839862C22semidirect
53. C4×#11758190C22semidirect
54. #16839821C22semidirect
55. C2×#14519710C22semidirect
56. C2×#14519709C22semidirect
57. C2×#14519708C22semidirect
58. C2×#14519706C22semidirect
59. C2×#14519706C22semidirect
60. C2×#14519702C22semidirect
61. C2×#14519700C22semidirect
64. C2×#14519698C22semidirect
68. C2×#14519688C22semidirect
71. C2×C4×D4×C61C22semidirect
72. C4×D8×C61C22semidirect
73. C2×#107×C61C22semidirect
75. C2×#102×C61C22semidirect
76. C2×C4×C8×C61C22semidirect
100. #14519776C23semidirect
103. #14519764C23semidirect
112. C4×Dic122C23semidirect
147. #14519710C23semidirect
148. #14519709C23semidirect
149. #14519708C23semidirect
150. #14519706C23semidirect
151. #14519706C23semidirect
152. #14519702C23semidirect
153. #14519700C23semidirect
156. #14519698C23semidirect
160. #14519688C23semidirect
172. C4×D4×C61C23semidirect
178. #107×C61C23semidirect
180. #102×C61C23semidirect
181. C4×C8×C61C23semidirect
404. C2×C4×D8D61semidirect
408. C2×C61#3118semidirect
438. C2×C4×D4C2×D61semidirect
454. C4×D8C2×D61semidirect
457. C2×#107C2×D61semidirect
469. C2×#102C2×D61semidirect
473. C2×C4×C8C2×D61semidirect
474. C61C2×#3118semidirect
530. C4×D4C22×D61semidirect
563. #107C22×D61semidirect
575. #102C22×D61semidirect
579. C4×C8C22×D61semidirect
791. C2#21455999direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403772
C2×#168402342
#214559992
C2×#168401052
C2×#168400852
C2×#168400502
C2×#168400412
C2×#168399762
C2×#168399752
C2×#168399142
C2×#168398942
C2×#168398722
C2×#168398622
C2×C4×#117581902
C2×#168398212
C2×C4×D8×C612
C2×#311861