Finite Group Databasebeta

← C2×#21456005 #30548246

Subgroups — C2×#21456005 #30548246

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×#16840383C211yesmaximal, characteristic, complemented
2C2×#16840236C211yesmaximal, characteristic, complemented
3#21456005C2116yesmaximal, direct product factor
4C2×#16840104C211yesmaximal, characteristic, complemented
5C2×#16840087C211yesmaximal, characteristic, complemented
6C2×#16840053C211yesmaximal, characteristic, complemented
7C2×#16840043C211yesmaximal, characteristic, complemented
8C2×#16839978C211yesmaximal, characteristic, complemented
9C2×#16839978C211yesmaximal, characteristic, complemented
10C2×#16839915C211yesmaximal, characteristic, complemented
11C2×#16839898C211yesmaximal, characteristic
12C2×#16839875C211yesmaximal, characteristic, complemented
13C2×#16839864C211yesmaximal, characteristic, complemented
14C2×C4×#11758190C211yesmaximal, characteristic, complemented
15C2×C4×D488C211yesmaximal, characteristic, complemented
16C2×C61×#433C211yesmaximal, characteristic, complemented
17C23×D244C2211yescharacteristic
18C22×#11758190C2211yescharacteristic
19C22×#11758190C2211yescharacteristic
20C22×D488C2211yescharacteristic
21C22×D488C2211yescharacteristic
22#16840383—24no—
23#16840383C2218yescomplemented
24C2×#14519777C2211yescharacteristic, complemented
25C2×#14519772—21no—
26C2×#14519765C2211yescharacteristic, complemented
27C2×#14519763—21no—
28C2×#14519759—21no—
29C2×#14519756C2211yescharacteristic
30C2×#14519755—21no—
31C2×#14519751C2211yescharacteristic
32#16840236—24no—
33#16840236C2218yescomplemented
34C2×C4×Dic122C2211yescharacteristic, complemented
35C2×C4×D244C2211yescharacteristic
36C2×C4×D244C2211yescharacteristic
37C2×C4×D244C2211yescharacteristic
38C2×C4×D244C2211yescharacteristic
39C2×C4×D244C2211yescharacteristic, complemented
40C2×#14519739—21no—
41C2×#14519739—21no—
42C2×#14519736C2211yescharacteristic
43C2×C22⋊C4×D61—21no—
44C2×C22⋊C4×D61—21no—
45#16840104C2218yescomplemented
46#16840087C2218yescomplemented
47#16840053C2218yescomplemented
48#16840043C2218yescomplemented
49#16839978C2218yescomplemented
50#16839978C2218yescomplemented
51#16839915C2218yescomplemented
52#16839898C2218yes—
53#16839875C2218yescomplemented
54#16839864C2218yescomplemented
55C4×#11758190C2218yescomplemented
56C4×D488C2218yescomplemented
57C2×#14519711C2211yescharacteristic, complemented
58C2×#14519711C2211yescharacteristic, complemented
59C2×#14519709C2211yescharacteristic, complemented
60C2×#14519709C2211yescharacteristic, complemented
61C2×#14519702C2211yescharacteristic, complemented
62C2×#14519702C2211yescharacteristic, complemented
63C2×#14519699C2211yescharacteristic
64C2×#14519699C2211yescharacteristic
65C2×#14519699C2211yescharacteristic
66C2×#14519699C2211yescharacteristic
67C2×#14519699C2211yescharacteristic, complemented
68C2×#14519699C2211yescharacteristic, complemented
69C2×#117×C61C2211yescharacteristic
70C61×#433C2218yescomplemented
71C2×C4⋊C8×C61C2211yescharacteristic, complemented
72C2×C4⋊C8×C61C2211yescharacteristic, complemented
73C2×C22⋊C8×C61C2211yescharacteristic
74C2×C22⋊C8×C61C2211yescharacteristic
75C2×#97×C61C2211yescharacteristic, complemented
76C2×C4×C8×C61C2211yescharacteristic, complemented
77C24×D61—21no—
78C22×Dic122—21no—
79C22×Dic122C2311yescharacteristic
80C22×D244—21no—
81C22×D244—22no—
82C22×D244—24no—
83C22×D244—24no—
84C22×D244C2311yescharacteristic
85C22×D244C2314yes—
86C22×D244C2311yescharacteristic
87C22×D244C2311yescharacteristic
88C22×C22⋊D61—21no—
89C22×C4×D61—21no—
90C22×C4×D61—21no—
91C22×C4×D61—21no—
92C22×C4×D61—21no—
93C22×C4×D61—21no—
94C2×#11758190—24no—
95C2×#11758190—24no—
96C2×#11758190C2314yes—
97C2×#11758190C2314yes—
98C2×D488—24no—
99C2×D488—24no—
100C2×D488C2314yes—
101C2×D488C2314yes—
102#14519777—22no—
103#14519777C2314yescomplemented
104#14519772—28no—
105#14519765—22no—
106#14519765C2314yescomplemented
107#14519763—28no—
108#14519759—28no—
109#14519756—22no—
110#14519756C2314yes—
111#14519755—28no—
112#14519751—22no—
113#14519751C2314yes—
114C4×Dic122—22no—
115C4×Dic122C2314yescomplemented
116C4×D244—22no—
117C4×D244—22no—
118C4×D244—22no—
119C4×D244—22no—
120C4×D244—22no—
121C4×D244C2314yes—
122C4×D244C2314yes—
123C4×D244C2314yes—
124C4×D244C2314yes—
125C4×D244C2314yescomplemented
126#14519739—28no—
127#14519739—28no—
128#14519736—22no—
129#14519736C2314yes—
130C2×C4⋊Dic61—21no—
131C2×C4⋊Dic61C2311yescharacteristic
132C2×C4⋊Dic61C2311yescharacteristic
133C2×C4⋊Dic61C2311yescharacteristic
134C2×C4⋊Dic61C2311yescharacteristic
135C2×#11758196—21no—
136C2×#11758196—21no—
137C2×C22⋊Dic61—21no—
138C2×C22⋊Dic61—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—
147C22⋊C4×D61—28no—
148C22⋊C4×D61—28no—
149C2×C4×Dic61—21no—
150C2×C4×Dic61—21no—
151#14519711C2314yescomplemented
152#14519711C2314yescomplemented
153#14519709C2314yescomplemented
154#14519709C2314yescomplemented
155#14519702C2314yescomplemented
156#14519702C2314yescomplemented
157#14519699C2314yes—
158#14519699C2314yes—
159#14519699C2314yes—
160#14519699C2314yes—
161#14519699C2314yescomplemented
162#14519699C2314yescomplemented
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×C61C2314yescomplemented
177C4⋊C8×C61C2314yescomplemented
178C22⋊C8×C61C2314yes—
179C22⋊C8×C61C2314yes—
180#97×C61C2314yescomplemented
181C4×C8×C61C2314yescomplemented
182C24×C61C2×D411yescharacteristic
183C23×D61—21no—
184C23×D61—21no—
185C23×D61—28no—
186C23×D61—24no—
187C23×D61—21no—
188C23×D61—82no—
189C23×D61—82no—
190C22×C4×C61—22no—
191C22×C4×C61—22no—
192C22×C4×C61C2×D411yescharacteristic
193C22×C4×C61C2×D411yescharacteristic
194C22×C4×C61C2×D411yescharacteristic
195C22×C4×C61C2×D411yescharacteristic
196C22×C4×C61C2×D411yescharacteristic
197C22×C4×C61C2×D412yes—
198C22×C4×C61C2412yes—
199C22×C4×C61C2411yescharacteristic
200C2×C22⋊D61—24no—
201C2×C22⋊D61—82no—
202C22×Dic61—21no—
203C22×Dic61—21no—
204C22×Dic61—21no—
205C22×Dic61—21no—
206C22×Dic61—21no—
207C2×D244—28no—
208C2×D244—216no—
209C2×D244—24no—
210C2×D244—21no—
211C2×D244—21no—
212C2×D244—22no—
213C2×D244—22no—
214C2×D244—28no—
215C2×D244—28no—
216C2×D244—22no—
217C2×D244—22no—
218C2×D244—21no—
219C2×D244#4114yes—
220C2×D244#4114yes—
221C2×D244C2412yes—
222C2×D244C2412yes—
223C2×D244C2412yes—
224C2×C4×D61—24no—
225C2×C4×D61—24no—
226C2×C4×D61—24no—
227C2×C4×D61—24no—
228C2×C4×D61—24no—
229C2×C4×D61—82no—
230C2×C4×D61—82no—
231C2×C4×D61—82no—
232C2×C4×D61—82no—
233C2×C4×D61—82no—
234C2×Dic122—22no—
235C2×Dic122—22no—
236C2×Dic122—21no—
237C2×Dic122—24no—
238C2×Dic122—82no—
239C2×Dic122C2412yes—
240C2×C8×C61—22no—
241C2×C8×C61—22no—
242C2×C8×C61—22no—
243C2×C8×C61—22no—
244C2×C8×C61C2412yes—
245C2×C8×C61C2412yes—
246C2×C8×C61C2412yes—
247C2×C8×C61C2412yes—
248C4⋊C4×C61C2×D414yes—
249C4⋊C4×C61C2×D414yes—
250C22⋊C4×C61C2×D414yes—
251C22⋊C4×C61C2×D414yes—
252C42×C61C2×D412yes—
253C42×C61C2×D412yes—
254C42×C61C2412yes—
255C42×C61C2412yes—
256C22⋊Dic61—24no—
257C22⋊Dic61—24no—
258#11758198—24no—
259#11758198—24no—
260#11758198—24no—
261#11758198—24no—
262#11758198—24no—
263#11758198—24no—
264#11758198—24no—
265#11758198—24no—
266C4⋊Dic61—24no—
267C4⋊Dic61—21no—
268C4⋊Dic61—21no—
269C4⋊Dic61—21no—
270C4⋊Dic61—21no—
271C4⋊Dic61C2412yes—
272C4⋊Dic61C2412yes—
273C4⋊Dic61C2412yes—
274C4⋊Dic61C2412yes—
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—24no—
290C22×D61—22no—
291C22×D61—22no—
292C22×D61—216no—
293C22×D61—22no—
294C22×D61—42no—
295C22×D61—42no—
296C22×D61—42no—
297C22×D61—42no—
298C22×D61—42no—
299C22×D61—42no—
300C22×D61—42no—
301C22×D61—84no—
302C22×D61—84no—
303C22×D61—816no—
304C2×C4×C61—22no—
305C2×C4×C61—22no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—24no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61C22×D412yes—
313C2×C4×C61C22×D412yes—
314C2×C4×C61C22×D412yes—
315C2×C4×C61C22×D412yes—
316C2×C4×C61C22×D412yes—
317C2×C4×C61C22×D411yescharacteristic
318C2×C4×C61C2×#4112yes—
319C2×C4×C61C2×#4112yes—
320C2×C4×C61C2511yescharacteristic
321C22⋊D61—84no—
322C2×Dic61—22no—
323C2×Dic61—22no—
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61—42no—
328C2×Dic61—42no—
329C2×Dic61—42no—
330C2×Dic61—42no—
331C2×Dic61—42no—
332D244—216no—
333D244—24no—
334D244—24no—
335D244—22no—
336D244—22no—
337D244—22no—
338D244—22no—
339D244—42no—
340D244C2×#4114yes—
341D244C2×#4114yes—
342C4×D61—84no—
343C4×D61—84no—
344C4×D61—84no—
345C4×D61—84no—
346C4×D61—84no—
347Dic122—22no—
348Dic122—22no—
349Dic122—42no—
350Dic122—84no—
351C8×C61—22no—
352C8×C61—22no—
353C8×C61—22no—
354C8×C61—22no—
355C2×#3118—611nomaximal, Sylow
356C22×C61—22no—
357C22×C61—22no—
358C22×C61—22no—
359C22×C61—44no—
360C22×C61#52512yes—
361C22×C61#57612yes—
362C22×C61#57712yes—
363C22×C61C23×D411yescharacteristic
364C2×D61—24no—
365C2×D61—24no—
366C2×D61—48no—
367C2×D61—48no—
368C2×D61—42no—
369C2×D61—42no—
370C2×D61—42no—
371C2×D61—42no—
372C2×D61—42no—
373C2×D61—42no—
374C2×D61—42no—
375C2×D61—816no—
376C2×D61—84no—
377C4×C61—22no—
378C4×C61—22no—
379C4×C61—22no—
380C4×C61—22no—
381C4×C61—22no—
382C4×C61#52512yes—
383C4×C61C22×#4111yescharacteristic
384C4×C61C22×#4111yescharacteristic
385Dic61—42no—
386Dic61—42no—
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×D8—611no—
405C2×#433D6111yescharacteristic, complemented
406C2×C61—42no—
407C2×C61#311814yescomplemented
408C2×C61C2×#52511yescharacteristic
409C2×C61C2×#57611yescharacteristic
410C2×C61C2×#57711yescharacteristic
411D61—44no—
412D61—44no—
413D61—82no—
414C23×D4—611no—
415C22×SD16—611no—
416C22×SD16—611no—
417C22×D8—611no—
418C22×D8—611no—
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—611no—
436C2×C4×D4—611no—
437C2×C4×D4—1221no—
438C2×C4×D4—1221no—
439C2×#117—611no—
440C2×#117C2×D6111yescharacteristic
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×D8—618no—
455#433C2×D6118yescomplemented
456C2×#107—611no—
457C2×#107—611no—
458C2×#106—611no—
459C2×#106—611no—
460C2×C4⋊C8C2×D6111yescharacteristic, complemented
461C2×C4⋊C8C2×D6111yescharacteristic, complemented
462C2×#103—611no—
463C2×#103—611no—
464C2×#102—611no—
465C2×#102—611no—
466C2×#102—611no—
467C2×#102—611no—
468C2×#102—611no—
469C2×#102—611no—
470C2×C22⋊C8C2×D6111yescharacteristic
471C2×C22⋊C8C2×D6111yescharacteristic
472C2×#97C2×D6111yescharacteristic, complemented
473C2×C4×C8C2×D6111yescharacteristic, complemented
474C61C2×#311811yescharacteristic, complemented, Sylow
475C25—1221no—
476C22×Q8—611no—
477C22×Q8—1221no—
478C22×D4—611no—
479C22×D4—611no—
480C22×D4—611no—
481C22×D4—614no—
482C22×D4—1224no—
483C22×D4—1224no—
484C22×D4—1221no—
485C22×D4—1221no—
486C22×D4—1222no—
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
505C4⋊Q8—614no—
506C4⋊Q8—1222no—
507#126—1228no—
508#124—614no—
509#124—1228no—
510#124—1222no—
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—614no—
520C4×D4—614no—
521C4×D4—614no—
522C4×D4—614no—
523C4×D4—614no—
524C4×D4—1228no—
525C4×D4—1228no—
526C4×D4—1222no—
527C4×D4—1222no—
528C4×D4—1222no—
529C4×D4—1222no—
530C4×D4—1222no—
531#117—614no—
532#117—1222no—
533#117D24414yes—
534#117C22×D6114yes—
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⋊C4D24411yescharacteristic
543C2×C4⋊C4D24411yescharacteristic
544C2×C22⋊C4—1221no—
545C2×C22⋊C4—1221no—
546C2×C22⋊C4—1221no—
547C2×C22⋊C4—1221no—
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⋊C4—1228no—
555C2×C22⋊C4—1228no—
556C2×C22⋊C4D24411yescharacteristic
557C2×C22⋊C4D24411yescharacteristic
558C2×C42—1221no—
559C2×C42—1221no—
560C2×C42C22×D6111yescharacteristic
561C2×C42C22×D6111yescharacteristic
562#107—614no—
563#107—614no—
564#106—614no—
565#106—614no—
566C4⋊C8C22×D6114yescomplemented
567C4⋊C8C22×D6114yescomplemented
568#103—614no—
569#103—614no—
570#102—614no—
571#102—614no—
572#102—614no—
573#102—614no—
574#102—614no—
575#102—614no—
576C22⋊C8C22×D6114yes—
577C22⋊C8C22×D6114yes—
578#97C22×D6114yescomplemented
579C4×C8C22×D6114yescomplemented
580C24—1228no—
581C24—1224no—
582C24—1221no—
583C24—1221no—
584C24—1221no—
585C24—4882no—
586C24—4882no—
587C24C2×D24411yescharacteristic
588C2×Q8—612no—
589C2×Q8—1224no—
590C2×Q8—1221no—
591C2×Q8—1222no—
592C2×Q8—1222no—
593C2×Q8—4882no—
594C2×D4—614no—
595C2×D4—614no—
596C2×D4—612no—
597C2×D4—612no—
598C2×D4—612no—
599C2×D4—1228no—
600C2×D4—1228no—
601C2×D4—1228no—
602C2×D4—12216no—
603C2×D4—1224no—
604C2×D4—1224no—
605C2×D4—1221no—
606C2×D4—1221no—
607C2×D4—1221no—
608C2×D4—1222no—
609C2×D4—1222no—
610C2×D4—1222no—
611C2×D4—1222no—
612C2×D4—4882no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—1221no—
616C22×C4—1221no—
617C22×C4—1221no—
618C22×C4—1221no—
619C22×C4—1221no—
620C22×C4—1224no—
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—1221no—
655C4⋊C4—1221no—
656C4⋊C4—1221no—
657C4⋊C4—1221no—
658C4⋊C4—1224no—
659C4⋊C4—1224no—
660C4⋊C4—1224no—
661C4⋊C4C2×D24414yes—
662C4⋊C4C2×D24414yes—
663C22⋊C4—1224no—
664C22⋊C4—1224no—
665C22⋊C4—1224no—
666C22⋊C4—1224no—
667C22⋊C4—1224no—
668C22⋊C4—1224no—
669C22⋊C4—1224no—
670C22⋊C4—1224no—
671C22⋊C4—1224no—
672C22⋊C4—1224no—
673C22⋊C4C2×D24414yes—
674C22⋊C4C2×D24414yes—
675C42—1224no—
676C42—1224no—
677C42C2×D24412yes—
678C42C2×D24412yes—
679C42C23×D6112yes—
680C42C23×D6112yes—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—12216no—
685C23—1224no—
686C23—1224no—
687C23—1222no—
688C23—1222no—
689C23—1222no—
690C23—4884no—
691C23—4884no—
692C23—48816no—
693C23—2442no—
694C23—2442no—
695C23—2442no—
696C23—2442no—
697C23—2442no—
698C23—2442no—
699C23—2442no—
700C23C22×D24412yes—
701C23C22×D24411yescharacteristic
702Q8—1222no—
703Q8—1222no—
704Q8—4884no—
705Q8—2442no—
706D4—614no—
707D4—614no—
708D4—12216no—
709D4—1224no—
710D4—1224no—
711D4—1222no—
712D4—1222no—
713D4—1222no—
714D4—1222no—
715D4—4884no—
716D4—2442no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—1222no—
726C2×C4—1222no—
727C2×C4—1222no—
728C2×C4—1222no—
729C2×C4—1222no—
730C2×C4—4884no—
731C2×C4—4884no—
732C2×C4—4884no—
733C2×C4—4884no—
734C2×C4—4884no—
735C2×C4—2442no—
736C2×C4—2442no—
737C2×C4—2442no—
738C2×C4—2442no—
739C2×C4—2442no—
740C2×C4C22×D24412yes—
741C2×C4C22×D24412yes—
742C2×C4C22×D24412yes—
743C2×C4C22×D24412yes—
744C2×C4C22×D24412yes—
745C2×C4C22×D24411yescharacteristic
746C2×C4#41×D6112yes—
747C2×C4#41×D6112yes—
748C2×C4C24×D6111yescharacteristic
749C8—22no—
750C8—22no—
751C8—22no—
752C8—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—44no—
757C22—1224no—
758C22—1224no—
759C22—48816no—
760C22—4884no—
761C22—2442no—
762C22—2442no—
763C22—2442no—
764C22—2442no—
765C22—2442no—
766C22—2442no—
767C22—2442no—
768C22—2448no—
769C22—2448no—
770C22#1684027412yes—
771C22#1684056712yes—
772C22#1684057412yes—
773C22C23×D24411yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—22no—
778C4—22no—
779C4—2442no—
780C4—2442no—
781C4—2442no—
782C4—2442no—
783C4—2442no—
784C4#1684027412yes—
785C4C2×#41×D6111yescharacteristic
786C4C2×#41×D6111yescharacteristic
787C2—42no—
788C2—4882no—
789C2—2444no—
790C2—2444no—
791C2#2145600514yesdirect product factor
792C2C2×#1684027411yescharacteristic
793C2C2×#1684056711yescharacteristic
794C2C2×#1684057411yescharacteristic
subgroupG/H
centerC23C22×D244
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#433C2
socleC23×C61C22×D4
prime radicalC2×#16839898C2
hypercenterC2×#433D61
hypocenterC61C2×#3118
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×#16840383C2semidirect
2. C2×#16840236C2semidirect
3. #21456005C2direct (N × H)
4. C2×#16840104C2semidirect
5. C2×#16840087C2semidirect
6. C2×#16840053C2semidirect
7. C2×#16840043C2semidirect
8. C2×#16839978C2semidirect
9. C2×#16839978C2semidirect
10. C2×#16839915C2semidirect
12. C2×#16839875C2semidirect
13. C2×#16839864C2semidirect
14. C2×C4×#11758190C2semidirect
15. C2×C4×D488C2semidirect
16. C2×C61×#433C2semidirect
23. #16840383C22semidirect
24. C2×#14519777C22semidirect
26. C2×#14519765C22semidirect
33. #16840236C22semidirect
34. C2×C4×Dic122C22semidirect
39. C2×C4×D244C22semidirect
45. #16840104C22semidirect
46. #16840087C22semidirect
47. #16840053C22semidirect
48. #16840043C22semidirect
49. #16839978C22semidirect
50. #16839978C22semidirect
51. #16839915C22semidirect
53. #16839875C22semidirect
54. #16839864C22semidirect
55. C4×#11758190C22semidirect
56. C4×D488C22semidirect
57. C2×#14519711C22semidirect
58. C2×#14519711C22semidirect
59. C2×#14519709C22semidirect
60. C2×#14519709C22semidirect
61. C2×#14519702C22semidirect
62. C2×#14519702C22semidirect
67. C2×#14519699C22semidirect
68. C2×#14519699C22semidirect
70. C61×#433C22semidirect
71. C2×C4⋊C8×C61C22semidirect
72. C2×C4⋊C8×C61C22semidirect
75. C2×#97×C61C22semidirect
76. C2×C4×C8×C61C22semidirect
103. #14519777C23semidirect
106. #14519765C23semidirect
115. C4×Dic122C23semidirect
125. C4×D244C23semidirect
151. #14519711C23semidirect
152. #14519711C23semidirect
153. #14519709C23semidirect
154. #14519709C23semidirect
155. #14519702C23semidirect
156. #14519702C23semidirect
161. #14519699C23semidirect
162. #14519699C23semidirect
176. C4⋊C8×C61C23semidirect
177. C4⋊C8×C61C23semidirect
180. #97×C61C23semidirect
181. C4×C8×C61C23semidirect
405. C2×#433D61semidirect
407. C2×C61#3118semidirect
455. #433C2×D61semidirect
460. C2×C4⋊C8C2×D61semidirect
461. C2×C4⋊C8C2×D61semidirect
472. C2×#97C2×D61semidirect
473. C2×C4×C8C2×D61semidirect
474. C61C2×#3118semidirect
566. C4⋊C8C22×D61semidirect
567. C4⋊C8C22×D61semidirect
578. #97C22×D61semidirect
579. C4×C8C22×D61semidirect
791. C2#21456005direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403832
C2×#168402362
#214560052
C2×#168401042
C2×#168400872
C2×#168400532
C2×#168400432
C2×#168399782
C2×#168399152
C2×#168398982
C2×#168398752
C2×#168398642
C2×C4×#117581902
C2×C4×D4882
C2×C61×#4332
C2×#311861