Finite Group Databasebeta

← C2×#21456068 #30548314

Subgroups — C2×#21456068 #30548314

Order 15616.

2210 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840370C211yesmaximal, characteristic, complemented
2C2×#16840234C211yesmaximal, characteristic
3#21456068C2116yesmaximal, direct product factor
4C2×#16840106C211yesmaximal, characteristic, complemented
5C2×#16840101C211yesmaximal, characteristic, complemented
6C2×#16840064C211yesmaximal, characteristic, complemented
7C2×#16840061C211yesmaximal, characteristic, complemented
8C2×#16839966C211yesmaximal, characteristic, complemented
9C2×#16839965C211yesmaximal, characteristic, complemented
10C2×#16839914C211yesmaximal, characteristic
11C2×#16839911C211yesmaximal, characteristic
12C2×#16839862C211yesmaximal, characteristic, complemented
13C2×#16839860C211yesmaximal, characteristic, complemented
14C2×C4×#11758190C211yesmaximal, characteristic, complemented
15C2×#16839821C211yesmaximal, characteristic, complemented
16C2×C4×SD16×C61C211yesmaximal, characteristic, complemented
17C22×D4×D61C2211yescharacteristic
18C22×#11758190C2211yescharacteristic
19C22×#11758200C2211yescharacteristic
20C22×#11758201C2211yescharacteristic
21#16840370—24no—
22#16840370C2218yescomplemented
23C2×#14519775C2211yescharacteristic, complemented
24C2×#14519772—21no—
25C2×#14519771—21no—
26C2×#14519769—21no—
27C2×#14519768C2211yescharacteristic, complemented
28C2×#14519767—21no—
29C2×#14519757C2211yescharacteristic
30C2×#14519753C2211yescharacteristic
31#16840234—24no—
32#16840234C2218yes—
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#16840106C2218yescomplemented
44#16840101C2218yescomplemented
45#16840064C2218yescomplemented
46#16840061C2218yescomplemented
47#16839966C2218yescomplemented
48#16839965C2218yescomplemented
49#16839914C2218yes—
50#16839911C2218yes—
51#16839862C2218yescomplemented
52#16839860C2218yescomplemented
53C4×#11758190C2218yescomplemented
54#16839821C2218yescomplemented
55C2×#14519710C2211yescharacteristic, complemented
56C2×#14519710C2211yescharacteristic, complemented
57C2×#14519709C2211yescharacteristic, 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
72C4×SD16×C61C2218yescomplemented
73C2×#106×C61C2211yescharacteristic, complemented
74C2×#103×C61C2211yescharacteristic, complemented
75C2×#102×C61C2211yescharacteristic
76C2×C4×C8×C61C2211yescharacteristic, complemented
77C24×D61—21no—
78C22×Dic122C2311yescharacteristic
79C22×D244C2311yescharacteristic
80C22×C22⋊D61—21no—
81C2×D4×D61—24no—
82C2×D4×D61—24no—
83C2×D4×D61—22no—
84C2×D4×D61C2314yes—
85C23×Dic61—21no—
86C22×C4×D61—21no—
87C22×C4×D61—21no—
88C22×C4×D61C2311yescharacteristic
89C2×#11758190—24no—
90C2×#11758190C2314yes—
91C2×#11758200—24no—
92C2×#11758200C2314yes—
93C2×#11758201—24no—
94C2×#11758201C2314yes—
95C22×#92418C2311yescharacteristic
96C22×#92418C2311yescharacteristic
97#14519775—22no—
98#14519775C2314yescomplemented
99#14519772—28no—
100#14519771—28no—
101#14519769—28no—
102#14519768—22no—
103#14519768C2314yescomplemented
104#14519767—28no—
105#14519757—22no—
106#14519757C2314yes—
107#14519753—22no—
108#14519753C2314yes—
109C4×Dic122—22no—
110C4×Dic122C2314yescomplemented
111C4×D244—22no—
112C4×D244C2314yes—
113D4×Dic61—22no—
114D4×Dic61C2314yes—
115#14519739—22no—
116#14519739C2314yes—
117C4×C22⋊D61—28no—
118#14519737—28no—
119#14519735—22no—
120#14519735C2314yes—
121#14519734D414yes—
122#14519734C2314yes—
123C2×C4⋊Dic61—21no—
124C2×C4⋊Dic61—21no—
125C2×C4⋊Dic61C2311yescharacteristic
126C2×C4⋊Dic61C2311yescharacteristic
127C2×#11758196—21no—
128C2×#11758196—21no—
129C2×#11758196—21no—
130C2×#11758196—21no—
131C2×#11758196—21no—
132C2×#11758196D411yescharacteristic
133C2×#11758196D411yescharacteristic
134C2×C22⋊Dic61—21no—
135C2×#11758198—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#14519710C2314yescomplemented
149#14519709C2314yescomplemented
150#14519706C2314yescomplemented
151#14519706C2314yescomplemented
152#14519702C2314yescomplemented
153#14519701C2314yescomplemented
154#14519700C2314yescomplemented
155#14519699C2314yes—
156#14519698C2314yes—
157#14519697C2314yes—
158#14519689C2314yes—
159#14519689C2314yes—
160#14519688C2314yescomplemented
161C22×Q8×C61C2311yescharacteristic
162C22×D4×C61C2311yescharacteristic
163C23×C4×C61—21no—
164C2×SD16×C61—24no—
165C2×SD16×C61C2314yes—
166C22×C8×C61C2311yescharacteristic
167C22×C8×C61C2311yescharacteristic
168C4×Q8×C61—22no—
169C4×Q8×C61C2314yescomplemented
170C4×D4×C61—22no—
171C4×D4×C61C2314yes—
172C2×C4⋊C4×C61—21no—
173C2×C4⋊C4×C61C2311yescharacteristic
174C2×C4⋊C4×C61C2311yescharacteristic
175C2×C22⋊C4×C61—21no—
176C2×C42×C61—21no—
177C2×C42×C61C2311yescharacteristic
178#106×C61C2314yescomplemented
179#103×C61C2314yescomplemented
180#102×C61C2314yes—
181C4×C8×C61C2314yescomplemented
182C24×C61—21no—
183C23×D61—21no—
184C23×D61—28no—
185C23×D61—24no—
186C23×D61—82no—
187C23×D61—82no—
188C23×D61C2×D411yescharacteristic
189C2×Q8×C61—21no—
190C2×Q8×C61—22no—
191C2×Q8×C61—22no—
192C2×Q8×C61C2412yes—
193C2×D4×C61—21no—
194C2×D4×C61—22no—
195C2×D4×C61#4114yes—
196C2×D4×C61C2412yes—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—24no—
201C22×C4×C61—82no—
202C22×C4×C61C2×D411yescharacteristic
203C22×C4×C61C2×D411yescharacteristic
204C22×C4×C61C2411yescharacteristic
205C2×C22⋊D61—28no—
206C2×C22⋊D61—24no—
207C22×Dic61—21no—
208C22×Dic61—21no—
209C22×Dic61—21no—
210C22×Dic61—24no—
211C22×Dic61—82no—
212C22×Dic61C2×D411yescharacteristic
213C22×Dic61C2×D411yescharacteristic
214C22×Dic61C2×D411yescharacteristic
215D4×D61—216no—
216D4×D61—28no—
217D4×D61—28no—
218C2×D244—21no—
219C2×D244—22no—
220C2×D244#4114yes—
221C2×D244C2412yes—
222C2×C4×D61—22no—
223C2×C4×D61—22no—
224C2×C4×D61—24no—
225C2×C4×D61—24no—
226C2×C4×D61—82no—
227C2×C4×D61—82no—
228C2×C4×D61C2×D412yes—
229C2×C4×D61C2412yes—
230C2×Dic122—22no—
231C2×Dic122—22no—
232C2×Dic122—21no—
233C2×Dic122C2412yes—
234SD16×C61—28no—
235C2×C8×C61—22no—
236C2×C8×C61—22no—
237C2×C8×C61C2412yes—
238C2×C8×C61C2412yes—
239C4⋊C4×C61—24no—
240C4⋊C4×C61—21no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61C2412yes—
243C4⋊C4×C61C2412yes—
244C22⋊C4×C61—24no—
245C42×C61—24no—
246C42×C61C2×D412yes—
247C42×C61C2412yes—
248C22⋊Dic61—24no—
249#11758201—28no—
250#11758200—28no—
251#11758198—24no—
252#11758198—24no—
253#11758198—24no—
254#11758198—24no—
255#11758198—24no—
256#11758198C2×D414yes—
257#11758198C2×D414yes—
258C4⋊Dic61—21no—
259C4⋊Dic61—21no—
260C4⋊Dic61—24no—
261C4⋊Dic61—24no—
262C4⋊Dic61C2412yes—
263C4⋊Dic61C2412yes—
264#11758196—24no—
265#11758196—24no—
266#11758196—24no—
267#11758196—24no—
268#11758196—24no—
269#11758196C2×D414yes—
270#11758196C2×D414yes—
271C4×Dic61—24no—
272C4×Dic61—24no—
273C4×Dic61C2×D412yes—
274C4×Dic61C2412yes—
275C2×#92418—22no—
276C2×#92418—22no—
277C2×#92418C2412yes—
278C2×#92418C2412yes—
279#11758190—28no—
280C23×C61—24no—
281C23×C61—22no—
282C23×C61—42no—
283C23×C61—42no—
284C23×C61C22×D411yescharacteristic
285C22×D61—22no—
286C22×D61—24no—
287C22×D61—22no—
288C22×D61—22no—
289C22×D61—22no—
290C22×D61—216no—
291C22×D61—42no—
292C22×D61—42no—
293C22×D61—84no—
294C22×D61—84no—
295C22×D61—816no—
296C22×D61C22×D412yes—
297Q8×C61—22no—
298Q8×C61—22no—
299Q8×C61—42no—
300D4×C61—24no—
301D4×C61—22no—
302D4×C61C2×#4114yes—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61—22no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—42no—
309C2×C4×C61—42no—
310C2×C4×C61—42no—
311C2×C4×C61—84no—
312C2×C4×C61C22×D412yes—
313C2×C4×C61C22×D412yes—
314C2×C4×C61C22×D411yescharacteristic
315C2×C4×C61C2×#4112yes—
316C2×C4×C61C2×#4112yes—
317C2×C4×C61C2511yescharacteristic
318C22⋊D61—216no—
319C2×Dic61—22no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—22no—
323C2×Dic61—22no—
324C2×Dic61—22no—
325C2×Dic61—42no—
326C2×Dic61—42no—
327C2×Dic61—42no—
328C2×Dic61—84no—
329C2×Dic61C22×D412yes—
330C2×Dic61C22×D412yes—
331C2×Dic61C22×D412yes—
332D244—24no—
333D244—22no—
334D244C2×#4114yes—
335C4×D61—24no—
336C4×D61—22no—
337C4×D61—22no—
338C4×D61—84no—
339C4×D61—84no—
340Dic122—22no—
341Dic122—22no—
342Dic122—42no—
343C8×C61—22no—
344C8×C61—22no—
345#92418—22no—
346#92418—22no—
347C2×#3123—611nomaximal, Sylow
348C22×C61—24no—
349C22×C61—48no—
350C22×C61—42no—
351C22×C61—42no—
352C22×C61#52512yes—
353C22×C61#57712yes—
354C22×C61#57712yes—
355C22×C61C23×D411yescharacteristic
356C2×D61—22no—
357C2×D61—24no—
358C2×D61—22no—
359C2×D61—22no—
360C2×D61—44no—
361C2×D61—48no—
362C2×D61—42no—
363C2×D61—42no—
364C2×D61—816no—
365C4×C61—22no—
366C4×C61—22no—
367C4×C61—42no—
368C4×C61—42no—
369C4×C61—42no—
370C4×C61#52512yes—
371C4×C61C22×#4111yescharacteristic
372C4×C61C22×#4111yescharacteristic
373Dic61—22no—
374Dic61—22no—
375Dic61—22no—
376Dic61—42no—
377Dic61—42no—
378Dic61—42no—
379C2×#541—611no—
380C2×#518—611no—
381#3123—6116no—
382C2×#485—611no—
383C2×#485—611no—
384C2×#478—611no—
385C2×#478—611no—
386C2×#461—611no—
387C2×#461—611no—
388C2×#450—611no—
389C2×#450—611no—
390C2×#440—611no—
391C2×#440—611no—
392C2×C4×SD16—611no—
393C2×C4×SD16D6111yescharacteristic, complemented
394C2×#433—611no—
395C2×C61—44no—
396C2×C61#312314yescomplemented
397C2×C61C2×#52511yescharacteristic
398C2×C61C2×#57711yescharacteristic
399C2×C61C2×#57711yescharacteristic
400D61—42no—
401D61—44no—
402C23×D4—611no—
403C22×SD16—611no—
404C22×SD16—611no—
405C22×SD16—611no—
406C22×SD16C2×D6111yescharacteristic
407#541—618no—
408#541—1224no—
409C2×C4⋊Q8—611no—
410C2×#126—1221no—
411C2×#126—1221no—
412C2×#125—611no—
413C2×#125—1221no—
414C2×#125—1221no—
415C2×C22⋊Q8—611no—
416C2×C22⋊Q8—611no—
417#518—618no—
418#518—1224no—
419C2×C4×Q8—611no—
420C2×C4×Q8C2×D6111yescharacteristic, complemented
421C2×C4×D4—611no—
422C2×C4×D4—611no—
423C2×C4×D4—611no—
424C2×C4×D4—1221no—
425C2×C4×D4—1221no—
426C2×C4×D4C2×D6111yescharacteristic
427C2×#117—611no—
428C2×#117—611no—
429C22×C22⋊C4—1221no—
430C22×C22⋊C4—1221no—
431#485—618no—
432#485—618no—
433#478—618no—
434#478—618no—
435#461—618no—
436#461—618no—
437#450—618no—
438#450—618no—
439#440—618no—
440#440—618no—
441C4×SD16—618no—
442C4×SD16C2×D6118yescomplemented
443#433—618no—
444C2×#107—611no—
445C2×#107—611no—
446C2×#106—611no—
447C2×#106C2×D6111yescharacteristic, complemented
448C2×C4⋊C8—611no—
449C2×C4⋊C8—611no—
450C2×#103—611no—
451C2×#103—611no—
452C2×#103—611no—
453C2×#103C2×D6111yescharacteristic, complemented
454C2×#102—611no—
455C2×#102—611no—
456C2×#102—611no—
457C2×#102C2×D6111yescharacteristic
458C2×C22⋊C8—611no—
459C2×C22⋊C8—611no—
460C2×#97—611no—
461C2×C4×C8C2×D6111yescharacteristic, complemented
462C61C2×#312311yescharacteristic, complemented, Sylow
463C25—1221no—
464C22×Q8—611no—
465C22×Q8C22×D6111yescharacteristic
466C22×D4—614no—
467C22×D4—611no—
468C22×D4—1222no—
469C22×D4—1221no—
470C22×D4—1224no—
471C22×D4—1224no—
472C22×D4C22×D6111yescharacteristic
473C23×C4—21no—
474C23×C4—611no—
475C23×C4—1221no—
476C23×C4—1221no—
477C23×C4—1221no—
478C2×SD16—24no—
479C2×SD16—614no—
480C2×SD16—614no—
481C2×SD16—614no—
482C2×SD16—1224no—
483C2×SD16—1224no—
484C2×SD16—1224no—
485C2×SD16C22×D6114yes—
486C22×C8—611no—
487C22×C8—611no—
488C22×C8C22×D6111yescharacteristic
489C22×C8C22×D6111yescharacteristic
490C4⋊Q8—614no—
491C4⋊Q8—1222no—
492#126—1228no—
493#126—1228no—
494#125—614no—
495#125—1228no—
496#125—1222no—
497#125—1228no—
498C22⋊Q8—614no—
499C22⋊Q8—614no—
500C22⋊Q8—1222no—
501C22⋊Q8—1222no—
502C4×Q8—22no—
503C4×Q8—614no—
504C4×Q8—1222no—
505C4×Q8C22×D6114yescomplemented
506C4×D4—22no—
507C4×D4—614no—
508C4×D4—614no—
509C4×D4—614no—
510C4×D4—1222no—
511C4×D4—1222no—
512C4×D4—1228no—
513C4×D4—1228no—
514C4×D4—1222no—
515C4×D4C22×D6114yes—
516#117—614no—
517#117—614no—
518#117—614no—
519#117—1222no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—611no—
522C2×C4⋊C4—611no—
523C2×C4⋊C4—611no—
524C2×C4⋊C4—611no—
525C2×C4⋊C4—1221no—
526C2×C4⋊C4—1221no—
527C2×C4⋊C4—1221no—
528C2×C4⋊C4—1221no—
529C2×C4⋊C4—1221no—
530C2×C4⋊C4—1221no—
531C2×C4⋊C4—1221no—
532C2×C4⋊C4C22×D6111yescharacteristic
533C2×C4⋊C4C22×D6111yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—611no—
536C2×C22⋊C4—611no—
537C2×C22⋊C4—1228no—
538C2×C22⋊C4—1228no—
539C2×C22⋊C4—1221no—
540C2×C22⋊C4—1221no—
541C2×C22⋊C4—1221no—
542C2×C22⋊C4—1221no—
543C2×C22⋊C4—1221no—
544C2×C22⋊C4—1221no—
545C2×C42—21no—
546C2×C42—611no—
547C2×C42—1221no—
548C2×C42—1221no—
549C2×C42C22×D6111yescharacteristic
550#107—614no—
551#107—614no—
552#106—614no—
553#106C22×D6114yescomplemented
554C4⋊C8—614no—
555C4⋊C8—614no—
556#103—614no—
557#103—614no—
558#103—614no—
559#103C22×D6114yescomplemented
560#102—614no—
561#102—614no—
562#102—614no—
563#102C22×D6114yes—
564C22⋊C8—614no—
565C22⋊C8—614no—
566#97—614no—
567C4×C8C22×D6114yescomplemented
568C24—21no—
569C24—611no—
570C24—1224no—
571C24—1228no—
572C24—1221no—
573C24—4882no—
574C24—4882no—
575C2×Q8—21no—
576C2×Q8—22no—
577C2×Q8—22no—
578C2×Q8—612no—
579C2×Q8—1221no—
580C2×Q8—1222no—
581C2×Q8—1222no—
582C2×Q8C23×D6112yes—
583C2×D4—21no—
584C2×D4—22no—
585C2×D4—614no—
586C2×D4—612no—
587C2×D4—1224no—
588C2×D4—1228no—
589C2×D4—12216no—
590C2×D4—1228no—
591C2×D4—1228no—
592C2×D4—1221no—
593C2×D4—1222no—
594C2×D4#1175822214yes—
595C2×D4C23×D6112yes—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—24no—
600C22×C4—82no—
601C22×C4—611no—
602C22×C4—611no—
603C22×C4—611no—
604C22×C4—612no—
605C22×C4—612no—
606C22×C4—1224no—
607C22×C4—1224no—
608C22×C4—1222no—
609C22×C4—1222no—
610C22×C4—1221no—
611C22×C4—1221no—
612C22×C4—1221no—
613C22×C4—1224no—
614C22×C4—4882no—
615C22×C4—4882no—
616C22×C4—4882no—
617C22×C4D4×D6111yescharacteristic
618C22×C4D4×D6111yescharacteristic
619C22×C4C23×D6111yescharacteristic
620SD16—28no—
621SD16—1228no—
622SD16—1228no—
623SD16—1228no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—612no—
627C2×C8—612no—
628C2×C8—1222no—
629C2×C8—1222no—
630C2×C8C23×D6112yes—
631C2×C8C23×D6112yes—
632C4⋊C4—24no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—614no—
636C4⋊C4—614no—
637C4⋊C4—612no—
638C4⋊C4—612no—
639C4⋊C4—1224no—
640C4⋊C4—1224no—
641C4⋊C4—1224no—
642C4⋊C4—1224no—
643C4⋊C4—1224no—
644C4⋊C4—1224no—
645C4⋊C4—1221no—
646C4⋊C4—1221no—
647C4⋊C4—1224no—
648C4⋊C4C23×D6112yes—
649C4⋊C4C23×D6112yes—
650C22⋊C4—24no—
651C22⋊C4—614no—
652C22⋊C4—614no—
653C22⋊C4—1224no—
654C22⋊C4—1224no—
655C22⋊C4—1224no—
656C22⋊C4—1224no—
657C22⋊C4—1224no—
658C22⋊C4—1224no—
659C42—24no—
660C42—612no—
661C42—612no—
662C42—1224no—
663C42—1224no—
664C42D4×D6112yes—
665C42C23×D6112yes—
666C23—24no—
667C23—22no—
668C23—42no—
669C23—42no—
670C23—612no—
671C23—12216no—
672C23—1222no—
673C23—1224no—
674C23—1222no—
675C23—1222no—
676C23—1222no—
677C23—4884no—
678C23—4884no—
679C23—48816no—
680C23—2442no—
681C23—2442no—
682C23C2×D4×D6111yescharacteristic
683Q8—22no—
684Q8—22no—
685Q8—42no—
686Q8—1222no—
687Q8—1222no—
688Q8—2442no—
689D4—24no—
690D4—22no—
691D4—614no—
692D4—12216no—
693D4—1224no—
694D4—1222no—
695D4C2×#1175822214yes—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—84no—
705C2×C4—612no—
706C2×C4—612no—
707C2×C4—612no—
708C2×C4—1222no—
709C2×C4—1222no—
710C2×C4—1222no—
711C2×C4—1224no—
712C2×C4—1222no—
713C2×C4—1222no—
714C2×C4—1222no—
715C2×C4—1222no—
716C2×C4—1222no—
717C2×C4—4884no—
718C2×C4—4884no—
719C2×C4—4884no—
720C2×C4—2442no—
721C2×C4—2442no—
722C2×C4—2442no—
723C2×C4C2×D4×D6112yes—
724C2×C4C2×D4×D6112yes—
725C2×C4C2×D4×D6111yescharacteristic
726C2×C4#41×D6112yes—
727C2×C4C2×#1175822212yes—
728C2×C4C24×D6111yescharacteristic
729C8—22no—
730C8—22no—
731C8—1222no—
732C8—1222no—
733C22—24no—
734C22—42no—
735C22—42no—
736C22—48no—
737C22—1222no—
738C22—1222no—
739C22—1222no—
740C22—1224no—
741C22—48816no—
742C22—2442no—
743C22—2442no—
744C22—2444no—
745C22—2448no—
746C22#1684027112yes—
747C22#1684056812yes—
748C22#1684056912yes—
749C22C22×D4×D6111yescharacteristic
750C4—22no—
751C4—22no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—1222no—
756C4—1222no—
757C4—1222no—
758C4—2442no—
759C4—2442no—
760C4—2442no—
761C4#1684027112yes—
762C4C2×#41×D6111yescharacteristic
763C4C22×#1175822211yescharacteristic
764C2—44no—
765C2—2442no—
766C2—2444no—
767C2#2145606814yesdirect product factor
768C2C2×#1684027111yescharacteristic
769C2C2×#1684056811yescharacteristic
770C2C2×#1684056911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C4×SD16×C61C2
socleC23×C61C22×D4
prime radicalC22×D4×D61C22
hypercenterC2×C4×SD16D61
hypocenterC61C2×#3123
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#16840370C2semidirect
3. #21456068C2direct (N × H)
4. C2×#16840106C2semidirect
5. C2×#16840101C2semidirect
6. C2×#16840064C2semidirect
7. C2×#16840061C2semidirect
8. C2×#16839966C2semidirect
9. C2×#16839965C2semidirect
12. C2×#16839862C2semidirect
13. C2×#16839860C2semidirect
14. C2×C4×#11758190C2semidirect
15. C2×#16839821C2semidirect
16. C2×C4×SD16×C61C2semidirect
22. #16840370C22semidirect
23. C2×#14519775C22semidirect
27. C2×#14519768C22semidirect
33. C2×C4×Dic122C22semidirect
43. #16840106C22semidirect
44. #16840101C22semidirect
45. #16840064C22semidirect
46. #16840061C22semidirect
47. #16839966C22semidirect
48. #16839965C22semidirect
51. #16839862C22semidirect
52. #16839860C22semidirect
53. C4×#11758190C22semidirect
54. #16839821C22semidirect
55. C2×#14519710C22semidirect
56. C2×#14519710C22semidirect
57. C2×#14519709C22semidirect
58. C2×#14519706C22semidirect
59. C2×#14519706C22semidirect
60. C2×#14519702C22semidirect
61. C2×#14519701C22semidirect
62. C2×#14519700C22semidirect
68. C2×#14519688C22semidirect
70. C2×C4×Q8×C61C22semidirect
72. C4×SD16×C61C22semidirect
73. C2×#106×C61C22semidirect
74. C2×#103×C61C22semidirect
76. C2×C4×C8×C61C22semidirect
98. #14519775C23semidirect
103. #14519768C23semidirect
110. C4×Dic122C23semidirect
147. #14519710C23semidirect
148. #14519710C23semidirect
149. #14519709C23semidirect
150. #14519706C23semidirect
151. #14519706C23semidirect
152. #14519702C23semidirect
153. #14519701C23semidirect
154. #14519700C23semidirect
160. #14519688C23semidirect
169. C4×Q8×C61C23semidirect
178. #106×C61C23semidirect
179. #103×C61C23semidirect
181. C4×C8×C61C23semidirect
393. C2×C4×SD16D61semidirect
396. C2×C61#3123semidirect
420. C2×C4×Q8C2×D61semidirect
442. C4×SD16C2×D61semidirect
447. C2×#106C2×D61semidirect
453. C2×#103C2×D61semidirect
461. C2×C4×C8C2×D61semidirect
462. C61C2×#3123semidirect
505. C4×Q8C22×D61semidirect
553. #106C22×D61semidirect
559. #103C22×D61semidirect
567. C4×C8C22×D61semidirect
767. C2#21456068direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403702
C2×#168402342
#214560682
C2×#168401062
C2×#168401012
C2×#168400642
C2×#168400612
C2×#168399662
C2×#168399652
C2×#168399142
C2×#168399112
C2×#168398622
C2×#168398602
C2×C4×#117581902
C2×#168398212
C2×C4×SD16×C612
C2×#312361