Finite Group Databasebeta

← C2×#21456008 #30548249

Subgroups — C2×#21456008 #30548249

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×#16840386C211yesmaximal, characteristic, complemented
2C2×#16840234C211yesmaximal, characteristic, complemented
3#21456008C2116yesmaximal, direct product factor
4C2×#16840106C211yesmaximal, characteristic, complemented
5C2×#16840088C211yesmaximal, characteristic, complemented
6C2×#16840039C211yesmaximal, characteristic, complemented
7C2×#16839978C211yesmaximal, characteristic, complemented
8C2×#16839977C211yesmaximal, characteristic, complemented
9C2×#16839914C211yesmaximal, characteristic, complemented
10C2×#16839897C211yesmaximal, characteristic
11C2×#16839873C211yesmaximal, characteristic, complemented
12C2×#16839859C211yesmaximal, characteristic, complemented
13C2×#16839849C211yesmaximal, characteristic, complemented
14C2×#16839842C211yesmaximal, characteristic, complemented
15C2×#16839822C211yesmaximal, characteristic, complemented
16C2×C61×#476C211yesmaximal, characteristic, complemented
17C22×D4×D61C2211yescharacteristic
18C22×#11758190C2211yescharacteristic
19C22×#11758200C2211yescharacteristic
20C22×D488C2211yescharacteristic
21C22×#11758199C2211yescharacteristic
22#16840386—24no—
23#16840386C2218yescomplemented
24C2×#14519772—21no—
25C2×#14519766—21no—
26C2×#14519765C2211yescharacteristic, complemented
27C2×#14519762—21no—
28C2×#14519757C2211yescharacteristic
29C2×#14519753—21no—
30C2×#14519752C2211yescharacteristic
31#16840234—24no—
32#16840234C2218yescomplemented
33C2×#14519742C2211yescharacteristic, complemented
34C2×C4×D244C2211yescharacteristic
35C2×D4×Dic61C2211yescharacteristic
36C2×#14519739C2211yescharacteristic
37C2×#14519739C2211yescharacteristic, complemented
38C2×C4×C22⋊D61—21no—
39C2×#14519737—21no—
40C2×#14519735C2211yescharacteristic
41C2×#14519734C2211yescharacteristic
42C22×#11758198—21no—
43C2×C22⋊C4×D61—21no—
44#16840106C2218yescomplemented
45#16840088C2218yescomplemented
46#16840039C2218yescomplemented
47#16839978C2218yescomplemented
48#16839977C2218yescomplemented
49#16839914C2218yescomplemented
50#16839897C2218yes—
51#16839873C2218yescomplemented
52#16839859C2218yescomplemented
53#16839849C2218yescomplemented
54#16839842C2218yescomplemented
55#16839822C2218yescomplemented
56C2×#14519710C2211yescharacteristic, complemented
57C2×#14519710C2211yescharacteristic, complemented
58C2×C4⋊#92418C2211yescharacteristic, complemented
59C2×#14519702C2211yescharacteristic, complemented
60C2×#14519700C2211yescharacteristic, complemented
61C2×#14519699C2211yescharacteristic, complemented
62C2×#14519697C2211yescharacteristic
63C2×#14519697C2211yescharacteristic
64C2×#14519697C2211yescharacteristic, complemented
65C2×#14519689C2211yescharacteristic
66C2×#14519689C2211yescharacteristic
67C2×#14519687C2211yescharacteristic, complemented
68C2×C8×Dic61C2211yescharacteristic, complemented
69C2×C4⋊Q8×C61C2211yescharacteristic, complemented
70C2×C4×D4×C61C2211yescharacteristic
71C61×#476C2218yescomplemented
72C2×#106×C61C2211yescharacteristic, complemented
73C2×#106×C61C2211yescharacteristic, complemented
74C2×C4⋊C8×C61C2211yescharacteristic, complemented
75C2×#102×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C24×D61—21no—
78C22×Dic122C2311yescharacteristic
79C22×D244—21no—
80C22×D244C2311yescharacteristic
81C22×D244C2311yescharacteristic
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×D61—21no—
91C22×C4×D61C2311yescharacteristic
92C2×#11758190—24no—
93C2×#11758190C2314yes—
94C2×#11758200—24no—
95C2×#11758200C2314yes—
96C2×D488—24no—
97C2×D488C2314yes—
98C2×#11758199—24no—
99C2×#11758199C2314yes—
100C22×#92418C2311yescharacteristic
101C22×#92418C2311yescharacteristic
102#14519772—28no—
103#14519766—28no—
104#14519765—22no—
105#14519765C2314yescomplemented
106#14519762—28no—
107#14519757—22no—
108#14519757C2314yes—
109#14519753—28no—
110#14519752—22no—
111#14519752C2314yes—
112#14519742—22no—
113#14519742C2314yescomplemented
114C4×D244—22no—
115C4×D244C2314yes—
116D4×Dic61—22no—
117D4×Dic61C2314yes—
118#14519739—22no—
119#14519739—22no—
120#14519739C2314yes—
121#14519739C2314yescomplemented
122C4×C22⋊D61—28no—
123#14519737—28no—
124#14519735—22no—
125#14519735C2314yes—
126#14519734D414yes—
127#14519734C2314yes—
128C2×C4⋊Dic61—21no—
129C2×C4⋊Dic61C2311yescharacteristic
130C2×#11758196—21no—
131C2×#11758196D411yescharacteristic
132C2×#11758196D411yescharacteristic
133C2×C22⋊Dic61—21no—
134C2×#11758198—21no—
135C2×#11758198—21no—
136C2×#11758198—21no—
137C2×#11758198—21no—
138C2×#11758198—21no—
139C2×#11758198—21no—
140C2×#11758198—21no—
141C2×#11758198—21no—
142C2×#11758198—28no—
143C2×#11758198D411yescharacteristic
144C2×#11758198D411yescharacteristic
145C22⋊C4×D61—28no—
146C2×C4×Dic61—21no—
147C2×C4×Dic61—21no—
148C2×C4×Dic61C2311yescharacteristic
149#14519710C2314yescomplemented
150#14519710C2314yescomplemented
151C4⋊#92418C2314yescomplemented
152#14519702C2314yescomplemented
153#14519700C2314yescomplemented
154#14519699C2314yescomplemented
155#14519697C2314yes—
156#14519697C2314yes—
157#14519697C2314yescomplemented
158#14519689C2314yes—
159#14519689C2314yes—
160#14519687C2314yescomplemented
161C8×Dic61C2314yescomplemented
162C22×Q8×C61—21no—
163C22×D4×C61C2311yescharacteristic
164C23×C4×C61—21no—
165C22×C8×C61C2311yescharacteristic
166C22×C8×C61C2311yescharacteristic
167C4⋊Q8×C61—22no—
168C4⋊Q8×C61C2314yescomplemented
169C4×D4×C61—22no—
170C4×D4×C61C2314yes—
171C2×C4⋊C4×C61—21no—
172C2×C4⋊C4×C61C2311yescharacteristic
173C2×C4⋊C4×C61C2311yescharacteristic
174C2×C4⋊C4×C61C2311yescharacteristic
175C2×C22⋊C4×C61—21no—
176C2×C42×C61C2311yescharacteristic
177#106×C61C2314yescomplemented
178#106×C61C2314yescomplemented
179C4⋊C8×C61C2314yescomplemented
180#102×C61C2314yes—
181#102×C61C2314yes—
182C24×C61—21no—
183C23×D61—21no—
184C23×D61—28no—
185C23×D61—24no—
186C23×D61—21no—
187C23×D61—82no—
188C23×D61—82no—
189C23×D61C2×D411yescharacteristic
190C2×Q8×C61—24no—
191C2×Q8×C61—82no—
192C2×D4×C61—21no—
193C2×D4×C61—22no—
194C2×D4×C61#4114yes—
195C2×D4×C61C2412yes—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—24no—
200C22×C4×C61—82no—
201C22×C4×C61C2×D411yescharacteristic
202C22×C4×C61C2×D411yescharacteristic
203C22×C4×C61C2411yescharacteristic
204C2×C22⋊D61—28no—
205C2×C22⋊D61—24no—
206C22×Dic61—21no—
207C22×Dic61—21no—
208C22×Dic61—24no—
209C22×Dic61—82no—
210C22×Dic61C2×D411yescharacteristic
211C22×Dic61C2×D411yescharacteristic
212C22×Dic61C2×D411yescharacteristic
213D4×D61—216no—
214D4×D61—28no—
215D4×D61—28no—
216C2×D244—21no—
217C2×D244—22no—
218C2×D244—22no—
219C2×D244—22no—
220C2×D244—21no—
221C2×D244—24no—
222C2×D244—82no—
223C2×D244#4114yes—
224C2×D244C2412yes—
225C2×D244C2412yes—
226C2×C4×D61—22no—
227C2×C4×D61—22no—
228C2×C4×D61—24no—
229C2×C4×D61—24no—
230C2×C4×D61—24no—
231C2×C4×D61—82no—
232C2×C4×D61—82no—
233C2×C4×D61—82no—
234C2×C4×D61C2×D412yes—
235C2×C4×D61C2412yes—
236C2×Dic122—22no—
237C2×Dic122—22no—
238C2×Dic122—21no—
239C2×Dic122C2412yes—
240C2×C8×C61—22no—
241C2×C8×C61—22no—
242C2×C8×C61C2412yes—
243C2×C8×C61C2412yes—
244C4⋊C4×C61—24no—
245C4⋊C4×C61—21no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61—21no—
248C4⋊C4×C61C2412yes—
249C4⋊C4×C61C2412yes—
250C4⋊C4×C61C2412yes—
251C22⋊C4×C61—24no—
252C42×C61C2×D412yes—
253C42×C61C2412yes—
254C22⋊Dic61—24no—
255#11758200—28no—
256#11758199—28no—
257#11758198—24no—
258#11758198—24no—
259#11758198—24no—
260#11758198—24no—
261#11758198—24no—
262#11758198—24no—
263#11758198—24no—
264#11758198—24no—
265#11758198C2×D414yes—
266#11758198C2×D414yes—
267C4⋊Dic61—21no—
268C4⋊Dic61—24no—
269C4⋊Dic61C2412yes—
270#11758196—24no—
271#11758196C2×D414yes—
272#11758196C2×D414yes—
273C4×Dic61—24no—
274C4×Dic61—24no—
275C4×Dic61C2×D412yes—
276C4×Dic61C2412yes—
277C2×#92418—22no—
278C2×#92418—22no—
279C2×#92418C2412yes—
280C2×#92418C2412yes—
281D488—28no—
282#11758190—28no—
283C23×C61—24no—
284C23×C61—22no—
285C23×C61—42no—
286C23×C61—42no—
287C23×C61C22×D411yescharacteristic
288C22×D61—22no—
289C22×D61—24no—
290C22×D61—22no—
291C22×D61—22no—
292C22×D61—22no—
293C22×D61—216no—
294C22×D61—22no—
295C22×D61—42no—
296C22×D61—42no—
297C22×D61—42no—
298C22×D61—42no—
299C22×D61—42no—
300C22×D61—84no—
301C22×D61—84no—
302C22×D61—816no—
303C22×D61C22×D412yes—
304Q8×C61—84no—
305D4×C61—24no—
306D4×C61—22no—
307D4×C61C2×#4114yes—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—42no—
314C2×C4×C61—42no—
315C2×C4×C61—42no—
316C2×C4×C61—84no—
317C2×C4×C61C22×D412yes—
318C2×C4×C61C22×D412yes—
319C2×C4×C61C22×D411yescharacteristic
320C2×C4×C61C2×#4112yes—
321C2×C4×C61C2×#4112yes—
322C2×C4×C61C2511yescharacteristic
323C22⋊D61—216no—
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—22no—
329C2×Dic61—42no—
330C2×Dic61—42no—
331C2×Dic61—84no—
332C2×Dic61C22×D412yes—
333C2×Dic61C22×D412yes—
334C2×Dic61C22×D412yes—
335D244—24no—
336D244—22no—
337D244—22no—
338D244—22no—
339D244—42no—
340D244—84no—
341D244C2×#4114yes—
342C4×D61—24no—
343C4×D61—22no—
344C4×D61—22no—
345C4×D61—84no—
346C4×D61—84no—
347C4×D61—84no—
348Dic122—22no—
349Dic122—22no—
350Dic122—42no—
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#52512yes—
361C22×C61#57612yes—
362C22×C61#57712yes—
363C22×C61C23×D411yescharacteristic
364C2×D61—22no—
365C2×D61—24no—
366C2×D61—22no—
367C2×D61—22no—
368C2×D61—44no—
369C2×D61—48no—
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—42no—
380C4×C61—42no—
381C4×C61—42no—
382C4×C61#52512yes—
383C4×C61C22×#4111yescharacteristic
384C4×C61C22×#4111yescharacteristic
385Dic61—22no—
386Dic61—22no—
387Dic61—22no—
388Dic61—42no—
389Dic61—42no—
390C2×#542—611no—
391C2×#518—611no—
392#3118—6116no—
393C2×#485—611no—
394C2×#482—611no—
395C2×#476D6111yescharacteristic, complemented
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×#433—611no—
406C2×C61—44no—
407C2×C61#311814yescomplemented
408C2×C61C2×#52511yescharacteristic
409C2×C61C2×#57611yescharacteristic
410C2×C61C2×#57711yescharacteristic
411D61—42no—
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⋊Q8C2×D6111yescharacteristic, complemented
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—1221no—
437C2×C4×D4—1221no—
438C2×C4×D4C2×D6111yescharacteristic
439C2×#117—611no—
440C2×#117—611no—
441C22×C22⋊C4—1221no—
442C22×C22⋊C4—1221no—
443#485—618no—
444#482—618no—
445#476C2×D6118yescomplemented
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#433—618no—
456C2×#107—611no—
457C2×#107—611no—
458C2×#106C2×D6111yescharacteristic, complemented
459C2×#106C2×D6111yescharacteristic, complemented
460C2×C4⋊C8—611no—
461C2×C4⋊C8C2×D6111yescharacteristic, complemented
462C2×#103—611no—
463C2×#103—611no—
464C2×#102—611no—
465C2×#102—611no—
466C2×#102—611no—
467C2×#102—611no—
468C2×#102C2×D6111yescharacteristic
469C2×#102C2×D6111yescharacteristic
470C2×C22⋊C8—611no—
471C2×C22⋊C8—611no—
472C2×#97—611no—
473C2×C4×C8—611no—
474C61C2×#311811yescharacteristic, complemented, Sylow
475C25—1221no—
476C22×Q8—21no—
477C22×Q8—611no—
478C22×D4—614no—
479C22×D4—611no—
480C22×D4—611no—
481C22×D4—1221no—
482C22×D4—1222no—
483C22×D4—1221no—
484C22×D4—1224no—
485C22×D4—1224no—
486C22×D4C22×D6111yescharacteristic
487C23×C4—21no—
488C23×C4—611no—
489C23×C4—1221no—
490C23×C4—1221no—
491C23×C4—1221no—
492C23×C4—1221no—
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×C8—611no—
502C22×C8—611no—
503C22×C8C22×D6111yescharacteristic
504C22×C8C22×D6111yescharacteristic
505C4⋊Q8—22no—
506C4⋊Q8C22×D6114yescomplemented
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—22no—
520C4×D4—614no—
521C4×D4—614no—
522C4×D4—614no—
523C4×D4—614no—
524C4×D4—1222no—
525C4×D4—1222no—
526C4×D4—1222no—
527C4×D4—1228no—
528C4×D4—1228no—
529C4×D4—1222no—
530C4×D4C22×D6114yes—
531#117—614no—
532#117—614no—
533#117—614no—
534#117—1222no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—611no—
537C2×C4⋊C4—611no—
538C2×C4⋊C4—611no—
539C2×C4⋊C4—1221no—
540C2×C4⋊C4—1221no—
541C2×C4⋊C4C22×D6111yescharacteristic
542C2×C4⋊C4C22×D6111yescharacteristic
543C2×C4⋊C4C22×D6111yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—611no—
546C2×C22⋊C4—611no—
547C2×C22⋊C4—1228no—
548C2×C22⋊C4—1228no—
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×C22⋊C4—1221no—
558C2×C42—611no—
559C2×C42—1221no—
560C2×C42—1221no—
561C2×C42C22×D6111yescharacteristic
562#107—614no—
563#107—614no—
564#106C22×D6114yescomplemented
565#106C22×D6114yescomplemented
566C4⋊C8—614no—
567C4⋊C8C22×D6114yescomplemented
568#103—614no—
569#103—614no—
570#102—614no—
571#102—614no—
572#102—614no—
573#102—614no—
574#102C22×D6114yes—
575#102C22×D6114yes—
576C22⋊C8—614no—
577C22⋊C8—614no—
578#97—614no—
579C4×C8—614no—
580C24—21no—
581C24—611no—
582C24—1224no—
583C24—1228no—
584C24—1221no—
585C24—1221no—
586C24—4882no—
587C24—4882no—
588C2×Q8—24no—
589C2×Q8—82no—
590C2×Q8—612no—
591C2×Q8—1221no—
592C2×Q8—1222no—
593C2×Q8—1222no—
594C2×D4—21no—
595C2×D4—22no—
596C2×D4—614no—
597C2×D4—612no—
598C2×D4—612no—
599C2×D4—1224no—
600C2×D4—1224no—
601C2×D4—1228no—
602C2×D4—12216no—
603C2×D4—1228no—
604C2×D4—1228no—
605C2×D4—1221no—
606C2×D4—1221no—
607C2×D4—1222no—
608C2×D4—1222no—
609C2×D4—1222no—
610C2×D4—4882no—
611C2×D4#1175822614yes—
612C2×D4C23×D6112yes—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—24no—
617C22×C4—82no—
618C22×C4—611no—
619C22×C4—611no—
620C22×C4—611no—
621C22×C4—612no—
622C22×C4—612no—
623C22×C4—1224no—
624C22×C4—1224no—
625C22×C4—1224no—
626C22×C4—1222no—
627C22×C4—1222no—
628C22×C4—1221no—
629C22×C4—1221no—
630C22×C4—1224no—
631C22×C4—4882no—
632C22×C4—4882no—
633C22×C4—4882no—
634C22×C4—4882no—
635C22×C4D4×D6111yescharacteristic
636C22×C4D4×D6111yescharacteristic
637C22×C4C23×D6111yescharacteristic
638SD16—1228no—
639SD16—1228no—
640D8—1228no—
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—24no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—614no—
655C4⋊C4—614no—
656C4⋊C4—612no—
657C4⋊C4—1224no—
658C4⋊C4—1224no—
659C4⋊C4—1221no—
660C4⋊C4C23×D6112yes—
661C4⋊C4C23×D6112yes—
662C4⋊C4C23×D6112yes—
663C22⋊C4—24no—
664C22⋊C4—614no—
665C22⋊C4—614no—
666C22⋊C4—1224no—
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—42no—
684C23—42no—
685C23—612no—
686C23—12216no—
687C23—1222no—
688C23—1224no—
689C23—1222no—
690C23—1222no—
691C23—1222no—
692C23—1222no—
693C23—4884no—
694C23—4884no—
695C23—48816no—
696C23—2442no—
697C23—2442no—
698C23—2442no—
699C23—2442no—
700C23—2442no—
701C23C2×D4×D6111yescharacteristic
702Q8—84no—
703Q8—1222no—
704Q8—1222no—
705Q8—2442no—
706D4—24no—
707D4—22no—
708D4—614no—
709D4—12216no—
710D4—1224no—
711D4—1222no—
712D4—1222no—
713D4—1222no—
714D4—4884no—
715D4—2442no—
716D4C2×#1175822614yes—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—84no—
726C2×C4—612no—
727C2×C4—612no—
728C2×C4—612no—
729C2×C4—1222no—
730C2×C4—1222no—
731C2×C4—1222no—
732C2×C4—1224no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—1222no—
737C2×C4—4884no—
738C2×C4—4884no—
739C2×C4—4884no—
740C2×C4—4884no—
741C2×C4—2442no—
742C2×C4—2442no—
743C2×C4C2×D4×D6112yes—
744C2×C4C2×D4×D6112yes—
745C2×C4C2×D4×D6111yescharacteristic
746C2×C4#41×D6112yes—
747C2×C4C2×#1175822612yes—
748C2×C4C24×D6111yescharacteristic
749C8—22no—
750C8—22no—
751C8—1222no—
752C8—1222no—
753C22—24no—
754C22—42no—
755C22—42no—
756C22—48no—
757C22—1222no—
758C22—1222no—
759C22—1222no—
760C22—1224no—
761C22—48816no—
762C22—4884no—
763C22—2442no—
764C22—2442no—
765C22—2442no—
766C22—2442no—
767C22—2442no—
768C22—2444no—
769C22—2448no—
770C22#1684027512yes—
771C22#1684056612yes—
772C22#1684056812yes—
773C22C22×D4×D6111yescharacteristic
774C4—22no—
775C4—22no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—1222no—
780C4—1222no—
781C4—1222no—
782C4—2442no—
783C4—2442no—
784C4#1684027512yes—
785C4C2×#41×D6111yescharacteristic
786C4C22×#1175822611yescharacteristic
787C2—44no—
788C2—4882no—
789C2—2442no—
790C2—2444no—
791C2#2145600814yesdirect product factor
792C2C2×#1684027511yescharacteristic
793C2C2×#1684056611yescharacteristic
794C2C2×#1684056811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#476C2
socleC23×C61C22×D4
prime radicalC2×#16839897C2
hypercenterC2×#476D61
hypocenterC61C2×#3118
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#16840386C2semidirect
2. C2×#16840234C2semidirect
3. #21456008C2direct (N × H)
4. C2×#16840106C2semidirect
5. C2×#16840088C2semidirect
6. C2×#16840039C2semidirect
7. C2×#16839978C2semidirect
8. C2×#16839977C2semidirect
9. C2×#16839914C2semidirect
11. C2×#16839873C2semidirect
12. C2×#16839859C2semidirect
13. C2×#16839849C2semidirect
14. C2×#16839842C2semidirect
15. C2×#16839822C2semidirect
16. C2×C61×#476C2semidirect
23. #16840386C22semidirect
26. C2×#14519765C22semidirect
32. #16840234C22semidirect
33. C2×#14519742C22semidirect
37. C2×#14519739C22semidirect
44. #16840106C22semidirect
45. #16840088C22semidirect
46. #16840039C22semidirect
47. #16839978C22semidirect
48. #16839977C22semidirect
49. #16839914C22semidirect
51. #16839873C22semidirect
52. #16839859C22semidirect
53. #16839849C22semidirect
54. #16839842C22semidirect
55. #16839822C22semidirect
56. C2×#14519710C22semidirect
57. C2×#14519710C22semidirect
58. C2×C4⋊#92418C22semidirect
59. C2×#14519702C22semidirect
60. C2×#14519700C22semidirect
61. C2×#14519699C22semidirect
64. C2×#14519697C22semidirect
67. C2×#14519687C22semidirect
68. C2×C8×Dic61C22semidirect
69. C2×C4⋊Q8×C61C22semidirect
71. C61×#476C22semidirect
72. C2×#106×C61C22semidirect
73. C2×#106×C61C22semidirect
74. C2×C4⋊C8×C61C22semidirect
105. #14519765C23semidirect
113. #14519742C23semidirect
121. #14519739C23semidirect
149. #14519710C23semidirect
150. #14519710C23semidirect
151. C4⋊#92418C23semidirect
152. #14519702C23semidirect
153. #14519700C23semidirect
154. #14519699C23semidirect
157. #14519697C23semidirect
160. #14519687C23semidirect
161. C8×Dic61C23semidirect
168. C4⋊Q8×C61C23semidirect
177. #106×C61C23semidirect
178. #106×C61C23semidirect
179. C4⋊C8×C61C23semidirect
395. C2×#476D61semidirect
407. C2×C61#3118semidirect
421. C2×C4⋊Q8C2×D61semidirect
445. #476C2×D61semidirect
458. C2×#106C2×D61semidirect
459. C2×#106C2×D61semidirect
461. C2×C4⋊C8C2×D61semidirect
474. C61C2×#3118semidirect
506. C4⋊Q8C22×D61semidirect
564. #106C22×D61semidirect
565. #106C22×D61semidirect
567. C4⋊C8C22×D61semidirect
791. C2#21456008direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403862
C2×#168402342
#214560082
C2×#168401062
C2×#168400882
C2×#168400392
C2×#168399782
C2×#168399772
C2×#168399142
C2×#168398972
C2×#168398732
C2×#168398592
C2×#168398492
C2×#168398422
C2×#168398222
C2×C61×#4762
C2×#311861