Finite Group Databasebeta

← C2×#21456388 #30549738

Subgroups — C2×#21456388 #30549738

Order 15616.

2070 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840297C211yesmaximal, characteristic, complemented
2C2×#16840291C211yesmaximal, characteristic, complemented
3#21456388C2116yesmaximal, direct product factor
4C2×#16840161C211yesmaximal, characteristic, complemented
5C2×#16840144C211yesmaximal, characteristic, complemented
6C2×#16840117C211yesmaximal, characteristic, complemented
7C2×#16840002C211yesmaximal, characteristic, complemented
8C2×#16839997C211yesmaximal, characteristic
9C2×#16839994C211yesmaximal, characteristic, complemented
10C2×#16839990C211yesmaximal, characteristic, complemented
11C2×#16839854C211yesmaximal, characteristic, complemented
12C2×#16839853C211yesmaximal, characteristic, complemented
13C2×#16839847C211yesmaximal, characteristic, complemented
14C2×#16839842C211yesmaximal, characteristic, complemented
15C2×C4×C8×D61C211yesmaximal, characteristic, complemented
16C2×C61×#488C211yesmaximal, characteristic, complemented
17C22×#11758202C2211yescharacteristic
18C22×#11758200C2211yescharacteristic
19C22×#11758201C2211yescharacteristic
20C22×#11758199C2211yescharacteristic
21C22×C8×D61C2211yescharacteristic
22C22×C8×D61C2211yescharacteristic
23#16840297—24no—
24#16840297C2218yescomplemented
25#16840291—24no—
26#16840291C2218yescomplemented
27C2×#14519772—21no—
28C2×#14519770—21no—
29C2×#14519769C2211yescharacteristic
30C2×#14519765C2211yescharacteristic
31C2×#14519762—21no—
32C2×#14519759—21no—
33C2×#14519757C2211yescharacteristic
34C2×#14519753C2211yescharacteristic
35C2×#14519752C2211yescharacteristic
36C2×#14519748C2211yescharacteristic
37C2×Q8×Dic61C2211yescharacteristic
38C2×#14519742C2211yescharacteristic
39C2×D4×Dic61C2211yescharacteristic
40C2×#14519739—21no—
41C2×#14519739C2211yescharacteristic
42C2×#14519737—21no—
43C2×#14519735—21no—
44C2×#14519733—21no—
45C2×C42×D61C2211yescharacteristic
46#16840161C2218yescomplemented
47#16840144C2218yescomplemented
48#16840117C2218yescomplemented
49#16840002C2218yescomplemented
50#16839997C2218yes—
51#16839994C2218yescomplemented
52#16839990C2218yescomplemented
53#16839854C2218yescomplemented
54#16839853C2218yescomplemented
55#16839847C2218yescomplemented
56#16839842C2218yescomplemented
57C2×#14519710C2211yescharacteristic
58C2×#14519710C2211yescharacteristic
59C2×#14519708C2211yescharacteristic
60C2×#14519708C2211yescharacteristic
61C2×#14519702C2211yescharacteristic
62C2×#14519702C2211yescharacteristic
63C2×#14519699C2211yescharacteristic
64C2×#14519699C2211yescharacteristic
65C2×C4×#92418C2211yescharacteristic
66C2×C8×Dic61C2211yescharacteristic
67C2×C8×Dic61C2211yescharacteristic
68C4×C8×D61C2218yescomplemented
69C2×#125×C61C2211yescharacteristic
70C2×#124×C61C2211yescharacteristic
71C61×#488C2218yescomplemented
72C2×#103×C61C2211yescharacteristic
73C2×#103×C61C2211yescharacteristic
74C2×#102×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×C4×C8×C61C2211yescharacteristic
77C22×Dic122C2311yescharacteristic
78C22×D244—21no—
79C22×D244C2311yescharacteristic
80C22×C22⋊D61—21no—
81C23×Dic61—21no—
82C22×C4×D61—21no—
83C22×C4×D61D411yescharacteristic
84C22×C4×D61D411yescharacteristic
85C22×C4×D61C2311yescharacteristic
86C2×#11758202—24no—
87C2×#11758202C2314yes—
88C2×#11758200—24no—
89C2×#11758200C2314yes—
90C2×#11758201—24no—
91C2×#11758201C2314yes—
92C2×#11758199—24no—
93C2×#11758199C2314yes—
94C22×#92418C2311yescharacteristic
95C22×#92418C2311yescharacteristic
96C2×C8×D61—24no—
97C2×C8×D61—24no—
98C2×C8×D61C2314yes—
99C2×C8×D61C2314yes—
100#14519772—28no—
101#14519770—28no—
102#14519769—22no—
103#14519769C2314yes—
104#14519765—22no—
105#14519765C2314yes—
106#14519762—28no—
107#14519759—28no—
108#14519757—22no—
109#14519757C2314yes—
110#14519753—22no—
111#14519753C2314yes—
112#14519752—22no—
113#14519752C2314yes—
114#14519748—22no—
115#14519748C2314yes—
116Q8×Dic61—22no—
117Q8×Dic61C2314yes—
118#14519742—22no—
119#14519742C2314yes—
120D4×Dic61—22no—
121D4×Dic61C2314yes—
122#14519739—28no—
123#14519739—22no—
124#14519739C2314yes—
125#14519737—28no—
126#14519735—28no—
127#14519733—28no—
128C2×C4⋊Dic61—21no—
129C2×C4⋊Dic61—21no—
130C2×C4⋊Dic61C2311yescharacteristic
131C2×C4⋊Dic61C2311yescharacteristic
132C2×#11758196—21no—
133C2×#11758196—21no—
134C2×#11758196—21no—
135C2×#11758196—21no—
136C2×C22⋊Dic61—21no—
137C2×C22⋊Dic61—21no—
138C2×#11758198—21no—
139C2×#11758198—21no—
140C2×#11758198—21no—
141C2×#11758198—21no—
142C2×#11758198—21no—
143C2×#11758198—21no—
144C2×C4×Dic61—21no—
145C2×C4×Dic61—21no—
146C2×C4×Dic61D411yescharacteristic
147C2×C4×Dic61D411yescharacteristic
148C2×C4×Dic61C2311yescharacteristic
149C42×D61D414yes—
150C42×D61C2314yes—
151#14519710C2314yes—
152#14519710C2314yes—
153#14519708C2314yes—
154#14519708C2314yes—
155#14519702C2314yes—
156#14519702C2314yes—
157#14519699C2314yes—
158#14519699C2314yes—
159C4×#92418C2314yes—
160C8×Dic61C2314yes—
161C8×Dic61C2314yes—
162C22×Q8×C61C2311yescharacteristic
163C22×D4×C61C2311yescharacteristic
164C22×C8×C61C2311yescharacteristic
165C22×C8×C61C2311yescharacteristic
166#125×C61—22no—
167#125×C61C2314yes—
168#124×C61—22no—
169#124×C61C2314yes—
170C2×C4⋊C4×C61—21no—
171C2×C4⋊C4×C61—21no—
172C2×C4⋊C4×C61C2311yescharacteristic
173C2×C4⋊C4×C61C2311yescharacteristic
174C2×C22⋊C4×C61—21no—
175C2×C22⋊C4×C61—21no—
176C2×C42×C61C2311yescharacteristic
177#103×C61C2314yes—
178#103×C61C2314yes—
179#102×C61C2314yes—
180#102×C61C2314yes—
181C4×C8×C61C2314yes—
182C24×C61—21no—
183C23×D61—21no—
184C23×D61C2×D411yescharacteristic
185C2×Q8×C61—21no—
186C2×Q8×C61—22no—
187C2×Q8×C61—22no—
188C2×Q8×C61C2412yes—
189C2×D4×C61—21no—
190C2×D4×C61—22no—
191C2×D4×C61—22no—
192C2×D4×C61C2412yes—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61C2×D411yescharacteristic
197C22×C4×C61C2×D411yescharacteristic
198C22×C4×C61C2411yescharacteristic
199C2×C22⋊D61—24no—
200C2×C22⋊D61—44no—
201C22×Dic61—21no—
202C22×Dic61—21no—
203C22×Dic61—21no—
204C22×Dic61—24no—
205C22×Dic61—44no—
206C22×Dic61C2×D411yescharacteristic
207C22×Dic61C2×D411yescharacteristic
208C22×Dic61C2×D411yescharacteristic
209C2×D244—22no—
210C2×D244—22no—
211C2×D244—24no—
212C2×D244—21no—
213C2×D244—44no—
214C2×D244C2412yes—
215C2×C4×D61—24no—
216C2×C4×D61—22no—
217C2×C4×D61—22no—
218C2×C4×D61—24no—
219C2×C4×D61—24no—
220C2×C4×D61—44no—
221C2×C4×D61C2×D414yes—
222C2×C4×D61C2×D414yes—
223C2×C4×D61C2×D412yes—
224C2×C4×D61C2412yes—
225C2×Dic122—22no—
226C2×Dic122—22no—
227C2×Dic122—21no—
228C2×Dic122C2412yes—
229C2×C8×C61—22no—
230C2×C8×C61—22no—
231C2×C8×C61C2412yes—
232C2×C8×C61C2412yes—
233C4⋊C4×C61—24no—
234C4⋊C4×C61—24no—
235C4⋊C4×C61—21no—
236C4⋊C4×C61—21no—
237C4⋊C4×C61C2412yes—
238C4⋊C4×C61C2412yes—
239C22⋊C4×C61—24no—
240C22⋊C4×C61—24no—
241C42×C61C2×D412yes—
242C42×C61C2412yes—
243C22⋊Dic61—24no—
244C22⋊Dic61—24no—
245#11758202—28no—
246#11758201—28no—
247#11758200—28no—
248#11758199—28no—
249#11758198—24no—
250#11758198—24no—
251#11758198—24no—
252#11758198—24no—
253#11758198—24no—
254#11758198—24no—
255C4⋊Dic61—21no—
256C4⋊Dic61—21no—
257C4⋊Dic61—24no—
258C4⋊Dic61—24no—
259C4⋊Dic61C2412yes—
260C4⋊Dic61C2412yes—
261#11758196—24no—
262#11758196—24no—
263#11758196—24no—
264#11758196—24no—
265C4×Dic61—24no—
266C4×Dic61—24no—
267C4×Dic61C2×D412yes—
268C4×Dic61C2×D414yes—
269C4×Dic61C2×D414yes—
270C4×Dic61C2412yes—
271C2×#92418#4114yes—
272C2×#92418#4114yes—
273C2×#92418C2412yes—
274C2×#92418C2412yes—
275C8×D61—28no—
276C8×D61—28no—
277C23×C61—22no—
278C23×C61—42no—
279C23×C61—42no—
280C23×C61—42no—
281C23×C61C22×D411yescharacteristic
282C22×D61—22no—
283C22×D61—22no—
284C22×D61—22no—
285C22×D61—42no—
286C22×D61—42no—
287C22×D61—42no—
288C22×D61#13514yes—
289C22×D61C22×D412yes—
290Q8×C61—22no—
291Q8×C61—22no—
292Q8×C61—42no—
293D4×C61—22no—
294D4×C61—22no—
295D4×C61—42no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—42no—
302C2×C4×C61—42no—
303C2×C4×C61—42no—
304C2×C4×C61C22×D412yes—
305C2×C4×C61C22×D412yes—
306C2×C4×C61C22×D411yescharacteristic
307C2×C4×C61C2×#4112yes—
308C2×C4×C61C2×#4112yes—
309C2×C4×C61C2511yescharacteristic
310C22⋊D61—48no—
311C2×Dic61—22no—
312C2×Dic61—22no—
313C2×Dic61—22no—
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—42no—
317C2×Dic61—42no—
318C2×Dic61—42no—
319C2×Dic61—48no—
320C2×Dic61#13514yes—
321C2×Dic61C22×D412yes—
322C2×Dic61C22×D412yes—
323C2×Dic61C22×D412yes—
324D244—22no—
325D244—22no—
326D244—48no—
327D244—42no—
328C4×D61—28no—
329C4×D61—24no—
330C4×D61—22no—
331C4×D61—22no—
332C4×D61—28no—
333C4×D61—48no—
334Dic122—22no—
335Dic122—22no—
336Dic122—42no—
337C8×C61—22no—
338C8×C61—22no—
339#92418C2×#4114yes—
340#92418C2×#4114yes—
341C2×#3168—611nomaximal, Sylow
342C22×C61—42no—
343C22×C61—42no—
344C22×C61—42no—
345C22×C61—84no—
346C22×C61#53212yes—
347C22×C61C2×#13512yes—
348C22×C61C2×#13512yes—
349C22×C61C23×D411yescharacteristic
350C2×D61—28no—
351C2×D61—22no—
352C2×D61—22no—
353C2×D61—42no—
354C2×D61—42no—
355C2×D61—42no—
356C2×D61—84no—
357C2×D61C2×#13514yes—
358C4×C61—22no—
359C4×C61—22no—
360C4×C61—42no—
361C4×C61—42no—
362C4×C61—42no—
363C4×C61#53212yes—
364C4×C61C22×#4111yescharacteristic
365C4×C61C22×#4111yescharacteristic
366Dic61—22no—
367Dic61—22no—
368Dic61—42no—
369Dic61—42no—
370Dic61—42no—
371Dic61C2×#13514yes—
372C2×#529—611no—
373C2×#529—611no—
374#3168—6116no—
375C2×#499—611no—
376C2×#495—611no—
377C2×#488—611no—
378C2×#488D6111yescharacteristic, complemented
379C2×#467—611no—
380C2×#466—611no—
381C2×#465—611no—
382C2×#465—611no—
383C2×C4×Q16—611no—
384C2×C4×SD16—611no—
385C2×C4×SD16—611no—
386C2×C4×D8—611no—
387C22×C4×C8—611no—
388C2×C61—82no—
389C2×C61#316814yescomplemented
390C2×C61C2×#53211yescharacteristic
391C2×C61C22×#13511yescharacteristic
392C2×C61C22×#13511yescharacteristic
393D61—24no—
394D61—82no—
395C22×Q16—611no—
396C22×SD16—611no—
397C22×SD16—611no—
398C22×D8—611no—
399C23×C8—611no—
400C23×C8—611no—
401#529—618no—
402#529—618no—
403#529—1224no—
404#529—1224no—
405C2×#126—1221no—
406C2×#126—1221no—
407C2×#125—611no—
408C2×#125C2×D6111yescharacteristic
409C2×#124—611no—
410C2×#124C2×D6111yescharacteristic
411C2×#123—1221no—
412C2×#123—1221no—
413C2×C22⋊Q8—611no—
414C2×C22⋊Q8—611no—
415C2×#121—611no—
416C2×#121—611no—
417C2×C4×Q8—611no—
418C2×C4×Q8—611no—
419C2×C4×D4—611no—
420C2×C4×D4—611no—
421C2×C4×D4—1221no—
422C2×C4×D4—1221no—
423C2×#117—1221no—
424C2×#117—1221no—
425C22×C42—611no—
426#499—618no—
427#495—618no—
428#488—618no—
429#488C2×D6118yescomplemented
430#467—618no—
431#466—618no—
432#465—618no—
433#465—618no—
434C4×Q16—618no—
435C4×SD16—618no—
436C4×SD16—618no—
437C4×D8—618no—
438C2×#107—611no—
439C2×#107—611no—
440C2×#106—611no—
441C2×#106—611no—
442C2×#103—611no—
443C2×#103—611no—
444C2×#103C2×D6111yescharacteristic
445C2×#103C2×D6111yescharacteristic
446C2×#102—611no—
447C2×#102—611no—
448C2×#102C2×D6111yescharacteristic
449C2×#102C2×D6111yescharacteristic
450C2×C4×C8—611no—
451C2×C4×C8—611no—
452C2×C4×C8—611no—
453C2×C4×C8—618no—
454C2×C4×C8C2×D6111yescharacteristic
455C61C2×#316811yescharacteristic, complemented, Sylow
456C22×Q8—611no—
457C22×Q8C22×D6111yescharacteristic
458C22×D4—611no—
459C22×D4—1221no—
460C22×D4—1221no—
461C22×D4C22×D6111yescharacteristic
462C23×C4—611no—
463C23×C4—611no—
464C23×C4—611no—
465C23×C4—1221no—
466C23×C4—1221no—
467C2×Q16—614no—
468C2×Q16—1224no—
469C2×SD16—614no—
470C2×SD16—614no—
471C2×SD16—1224no—
472C2×SD16—1224no—
473C2×D8—614no—
474C2×D8—1224no—
475C22×C8—611no—
476C22×C8—611no—
477C22×C8—614no—
478C22×C8—614no—
479C22×C8—1224no—
480C22×C8—1224no—
481C22×C8C22×D6111yescharacteristic
482C22×C8C22×D6111yescharacteristic
483#126—1228no—
484#126—1228no—
485#125—22no—
486#125—614no—
487#125—1222no—
488#125C22×D6114yes—
489#124—22no—
490#124—614no—
491#124—1222no—
492#124C22×D6114yes—
493#123—1228no—
494#123—1228no—
495C22⋊Q8—614no—
496C22⋊Q8—614no—
497C22⋊Q8—1222no—
498C22⋊Q8—1222no—
499#121—614no—
500#121—614no—
501#121—1222no—
502#121—1222no—
503C4×Q8—614no—
504C4×Q8—614no—
505C4×Q8—1222no—
506C4×Q8—1222no—
507C4×D4—614no—
508C4×D4—614no—
509C4×D4—1222no—
510C4×D4—1222no—
511C4×D4—1228no—
512C4×D4—1228no—
513#117—1228no—
514#117—1228no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—611no—
518C2×C4⋊C4—611no—
519C2×C4⋊C4—1221no—
520C2×C4⋊C4—1221no—
521C2×C4⋊C4—1221no—
522C2×C4⋊C4—1221no—
523C2×C4⋊C4—1221no—
524C2×C4⋊C4—1221no—
525C2×C4⋊C4C22×D6111yescharacteristic
526C2×C4⋊C4C22×D6111yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—1221no—
530C2×C22⋊C4—1221no—
531C2×C22⋊C4—1221no—
532C2×C22⋊C4—1221no—
533C2×C22⋊C4—1221no—
534C2×C22⋊C4—1221no—
535C2×C22⋊C4—1221no—
536C2×C22⋊C4—1221no—
537C2×C42—611no—
538C2×C42—611no—
539C2×C42—611no—
540C2×C42—614no—
541C2×C42—614no—
542C2×C42—1221no—
543C2×C42—1221no—
544C2×C42C22×D6111yescharacteristic
545#107—614no—
546#107—614no—
547#106—614no—
548#106—614no—
549#103—614no—
550#103—614no—
551#103C22×D6114yes—
552#103C22×D6114yes—
553#102—614no—
554#102—614no—
555#102C22×D6114yes—
556#102C22×D6114yes—
557C4×C8—614no—
558C4×C8—614no—
559C4×C8—614no—
560C4×C8C22×D6114yes—
561C24—21no—
562C24—611no—
563C24—1221no—
564C2×Q8—21no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—612no—
568C2×Q8—1221no—
569C2×Q8—1222no—
570C2×Q8—1222no—
571C2×Q8C23×D6112yes—
572C2×D4—21no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—612no—
576C2×D4—1224no—
577C2×D4—1224no—
578C2×D4—1221no—
579C2×D4—1222no—
580C2×D4—1222no—
581C2×D4—2444no—
582C2×D4—2444no—
583C2×D4C23×D6112yes—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—611no—
588C22×C4—611no—
589C22×C4—611no—
590C22×C4—614no—
591C22×C4—612no—
592C22×C4—614no—
593C22×C4—612no—
594C22×C4—1224no—
595C22×C4—1224no—
596C22×C4—1224no—
597C22×C4—1224no—
598C22×C4—1222no—
599C22×C4—1222no—
600C22×C4—1221no—
601C22×C4—1221no—
602C22×C4—1221no—
603C22×C4—2444no—
604C22×C4—2444no—
605C22×C4D4×D6111yescharacteristic
606C22×C4D4×D6111yescharacteristic
607C22×C4C23×D6111yescharacteristic
608Q16—1228no—
609SD16—1228no—
610SD16—1228no—
611D8—1228no—
612C2×C8—22no—
613C2×C8—22no—
614C2×C8—614no—
615C2×C8—614no—
616C2×C8—612no—
617C2×C8—612no—
618C2×C8—1228no—
619C2×C8—1228no—
620C2×C8C23×D6112yes—
621C2×C8C23×D6112yes—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—612no—
627C4⋊C4—612no—
628C4⋊C4—1224no—
629C4⋊C4—1224no—
630C4⋊C4—1224no—
631C4⋊C4—1224no—
632C4⋊C4—1221no—
633C4⋊C4—1221no—
634C4⋊C4—1224no—
635C4⋊C4—1224no—
636C4⋊C4C23×D6112yes—
637C4⋊C4C23×D6112yes—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—1224no—
641C22⋊C4—1224no—
642C22⋊C4—1224no—
643C22⋊C4—1224no—
644C22⋊C4—1224no—
645C22⋊C4—1224no—
646C22⋊C4—1224no—
647C22⋊C4—1224no—
648C42—614no—
649C42—612no—
650C42—614no—
651C42—612no—
652C42—1224no—
653C42—1224no—
654C42D4×D6112yes—
655C42C23×D6112yes—
656C23—22no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—614no—
661C23—612no—
662C23—1222no—
663C23—1222no—
664C23—1222no—
665C23—2442no—
666C23—2442no—
667C23—2442no—
668C23C2×D4×D6111yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—42no—
672Q8—1222no—
673Q8—1222no—
674Q8—2442no—
675D4—22no—
676D4—22no—
677D4—42no—
678D4—1222no—
679D4—1222no—
680D4—2448no—
681D4—2448no—
682D4—2442no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—614no—
692C2×C4—612no—
693C2×C4—612no—
694C2×C4—612no—
695C2×C4—1228no—
696C2×C4—1228no—
697C2×C4—1222no—
698C2×C4—1222no—
699C2×C4—1224no—
700C2×C4—1222no—
701C2×C4—1222no—
702C2×C4—1222no—
703C2×C4—1222no—
704C2×C4—1222no—
705C2×C4—2448no—
706C2×C4—2448no—
707C2×C4—2442no—
708C2×C4—2442no—
709C2×C4—2442no—
710C2×C4C2×D4×D6112yes—
711C2×C4C2×D4×D6112yes—
712C2×C4C2×D4×D6111yescharacteristic
713C2×C4#41×D6112yes—
714C2×C4#41×D6112yes—
715C2×C4C24×D6111yescharacteristic
716C8—22no—
717C8—22no—
718C8—614no—
719C8—614no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—84no—
724C22—614no—
725C22—1228no—
726C22—1222no—
727C22—1222no—
728C22—4884no—
729C22—2442no—
730C22—2442no—
731C22—2442no—
732C22#1684031112yes—
733C22#135×D6112yes—
734C22#135×D6112yes—
735C22C22×D4×D6111yescharacteristic
736C4—22no—
737C4—22no—
738C4—42no—
739C4—42no—
740C4—42no—
741C4—614no—
742C4—1222no—
743C4—1222no—
744C4—2442no—
745C4—2442no—
746C4—2442no—
747C4#1684031112yes—
748C4C2×#41×D6111yescharacteristic
749C4C2×#41×D6111yescharacteristic
750C2—82no—
751C2—1224no—
752C2—4882no—
753C2#2145638814yesdirect product factor
754C2C2×#1684031111yescharacteristic
755C2C2×#135×D6111yescharacteristic
756C2C2×#135×D6111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#488C2
socleC23×C61C22×D4
prime radicalC2×#16839997C2
hypercenterC2×#488D61
hypocenterC61C2×#3168
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#488

Complements

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

NH ≅ G/Ntype
1. C2×#16840297C2semidirect
2. C2×#16840291C2semidirect
3. #21456388C2direct (N × H)
4. C2×#16840161C2semidirect
5. C2×#16840144C2semidirect
6. C2×#16840117C2semidirect
7. C2×#16840002C2semidirect
9. C2×#16839994C2semidirect
10. C2×#16839990C2semidirect
11. C2×#16839854C2semidirect
12. C2×#16839853C2semidirect
13. C2×#16839847C2semidirect
14. C2×#16839842C2semidirect
15. C2×C4×C8×D61C2semidirect
16. C2×C61×#488C2semidirect
24. #16840297C22semidirect
26. #16840291C22semidirect
46. #16840161C22semidirect
47. #16840144C22semidirect
48. #16840117C22semidirect
49. #16840002C22semidirect
51. #16839994C22semidirect
52. #16839990C22semidirect
53. #16839854C22semidirect
54. #16839853C22semidirect
55. #16839847C22semidirect
56. #16839842C22semidirect
68. C4×C8×D61C22semidirect
71. C61×#488C22semidirect
378. C2×#488D61semidirect
389. C2×C61#3168semidirect
429. #488C2×D61semidirect
455. C61C2×#3168semidirect
753. C2#21456388direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168402972
C2×#168402912
#214563882
C2×#168401612
C2×#168401442
C2×#168401172
C2×#168400022
C2×#168399972
C2×#168399942
C2×#168399902
C2×#168398542
C2×#168398532
C2×#168398472
C2×#168398422
C2×C4×C8×D612
C2×C61×#4882
C2×#316861