Finite Group Databasebeta

← C2×#21455974 #30548144

Subgroups — C2×#21455974 #30548144

Order 15616.

2150 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840314C211yesmaximal, characteristic, complemented
2C2×#41×Dic61C211yesmaximal, characteristic
3#21455974C2116yesmaximal, direct product factor
4C2×#16840104C211yesmaximal, characteristic, complemented
5C2×#16840100C211yesmaximal, characteristic, complemented
6C2×#16840055C211yesmaximal, characteristic, complemented
7C2×#16840050C211yesmaximal, characteristic, complemented
8C2×#16839970C211yesmaximal, characteristic, complemented
9C2×#16839965C211yesmaximal, characteristic, complemented
10C2×#16839924C211yesmaximal, characteristic
11C2×#16839869C211yesmaximal, characteristic, complemented
12C2×#16839866C211yesmaximal, characteristic, complemented
13C2×#16839863C211yesmaximal, characteristic, complemented
14C2×#16839859C211yesmaximal, characteristic, complemented
15C2×#16839816C211yesmaximal, characteristic, complemented
16C2×C61×#452C211yesmaximal, characteristic
17C22×#11758202C2211yescharacteristic
18C22×#11758200C2211yescharacteristic
19#16840314—24no—
20#16840314C2218yescomplemented
21C2×#14519776C2211yescharacteristic
22C2×#14519775C2211yescharacteristic
23C2×#14519767—21no—
24C2×#14519756C2211yescharacteristic
25C2×#14519754—21no—
26#41×Dic61—24no—
27#41×Dic61C2218yes—
28C2×Q8×Dic61C2211yescharacteristic
29C2×Q8×Dic61C2211yescharacteristic
30C2×Q8×Dic61C2211yescharacteristic
31C2×#14519742—21no—
32C2×#14519742C2211yescharacteristic
33C2×D4×Dic61—21no—
34C2×D4×Dic61—21no—
35C2×D4×Dic61C2211yescharacteristic
36C2×D4×Dic61C2211yescharacteristic
37C2×#14519736—21no—
38C2×#14519736C2211yescharacteristic
39C2×#14519733—21no—
40C22×C4×Dic61—21no—
41C22×C4×Dic61C2211yescharacteristic
42#16840104C2218yescomplemented
43#16840100C2218yescomplemented
44#16840055C2218yescomplemented
45#16840050C2218yescomplemented
46#16839970C2218yescomplemented
47#16839965C2218yescomplemented
48#16839924C2218yes—
49#16839869C2218yescomplemented
50#16839866C2218yescomplemented
51#16839863C2218yescomplemented
52#16839859C2218yescomplemented
53#16839816C2218yescomplemented
54C2×#14519711C2211yescharacteristic
55C2×#14519710C2211yescharacteristic
56C2×#14519709C2211yescharacteristic
57C2×#14519708C2211yescharacteristic
58C2×#14519706C2211yescharacteristic
59C2×#14519706C2211yescharacteristic
60C2×#14519702C2211yescharacteristic
61C2×#14519702C2211yescharacteristic
62C2×#14519701C2211yescharacteristic
63C2×#14519701C2211yescharacteristic
64C2×#14519701C2211yescharacteristic
65C2×#14519698C2211yescharacteristic
66C2×C22⋊#92418C2211yescharacteristic
67C2×#14519687C2211yescharacteristic
68C2×#14519687C2211yescharacteristic
69C22×#41×C61C2211yescharacteristic
70C22×Q16×C61C2211yescharacteristic
71C22×SD16×C61C2211yescharacteristic
72C2×C22⋊Q8×C61C2211yescharacteristic
73C61×#452C2218yes—
74C2×#103×C61C2211yescharacteristic
75C2×#102×C61C2211yescharacteristic
76C2×C22⋊C8×C61C2211yescharacteristic
77C22×Dic122—21no—
78C22×Dic122C2311yescharacteristic
79C23×Dic61—21no—
80C23×Dic61—21no—
81C23×Dic61D411yescharacteristic
82C23×Dic61D411yescharacteristic
83C2×#11758202—24no—
84C2×#11758202C2314yes—
85C2×#11758200—24no—
86C2×#11758200C2314yes—
87C22×#92418C2311yescharacteristic
88C22×#92418C2311yescharacteristic
89#14519776—22no—
90#14519776C2314yes—
91#14519775—22no—
92#14519775C2314yes—
93#14519767—28no—
94#14519756—22no—
95#14519756C2314yes—
96#14519754—28no—
97Q8×Dic61—22no—
98Q8×Dic61—22no—
99Q8×Dic61—22no—
100Q8×Dic61C2314yes—
101Q8×Dic61C2314yes—
102Q8×Dic61C2314yes—
103#14519742—28no—
104#14519742—22no—
105#14519742C2314yes—
106D4×Dic61—28no—
107D4×Dic61—28no—
108D4×Dic61—22no—
109D4×Dic61—22no—
110D4×Dic61C2314yes—
111D4×Dic61C2314yes—
112#14519736—22no—
113#14519736—28no—
114#14519736C2314yes—
115#14519733—28no—
116C2×C4⋊Dic61—21no—
117C2×C4⋊Dic61—21no—
118C2×C4⋊Dic61—21no—
119C2×C4⋊Dic61C2311yescharacteristic
120C2×C4⋊Dic61C2311yescharacteristic
121C2×C4⋊Dic61C2311yescharacteristic
122C2×#11758196—21no—
123C2×#11758196—21no—
124C2×#11758196—21no—
125C2×#11758196—21no—
126C2×#11758196—21no—
127C2×C22⋊Dic61—21no—
128C2×C22⋊Dic61—21no—
129C2×C22⋊Dic61—21no—
130C2×C22⋊Dic61—21no—
131C2×C4×Dic61—21no—
132C2×C4×Dic61—21no—
133C2×C4×Dic61—21no—
134C2×C4×Dic61—21no—
135C2×C4×Dic61—21no—
136C2×C4×Dic61—28no—
137C2×C4×Dic61D411yescharacteristic
138C2×C4×Dic61D411yescharacteristic
139C2×C4×Dic61D414yes—
140C2×C4×Dic61C2311yescharacteristic
141C2×C4×Dic61C2311yescharacteristic
142C2×C4×Dic61C2314yes—
143#14519711C2314yes—
144#14519710C2314yes—
145#14519709C2314yes—
146#14519708C2314yes—
147#14519706C2314yes—
148#14519706C2314yes—
149#14519702C2314yes—
150#14519702C2314yes—
151#14519701C2314yes—
152#14519701C2314yes—
153#14519701C2314yes—
154#14519698C2314yes—
155C22⋊#92418C2314yes—
156#14519687C2314yes—
157#14519687C2314yes—
158C2×#41×C61—24no—
159C2×#41×C61—24no—
160C2×#41×C61—22no—
161C2×#41×C61C2314yes—
162C22×Q8×C61C2311yescharacteristic
163C22×Q8×C61C2311yescharacteristic
164C22×D4×C61—21no—
165C22×D4×C61C2311yescharacteristic
166C23×C4×C61—21no—
167C23×C4×C61C2311yescharacteristic
168C2×Q16×C61—24no—
169C2×Q16×C61C2314yes—
170C2×SD16×C61—24no—
171C2×SD16×C61C2314yes—
172C22×C8×C61C2311yescharacteristic
173C22×C8×C61C2311yescharacteristic
174C22⋊Q8×C61—22no—
175C22⋊Q8×C61C2314yes—
176C2×C4⋊C4×C61—21no—
177C2×C4⋊C4×C61C2311yescharacteristic
178C2×C22⋊C4×C61—21no—
179#103×C61C2314yes—
180#102×C61C2314yes—
181C22⋊C8×C61C2314yes—
182C24×C61—21no—
183C24×C61C2×D411yescharacteristic
184#41×C61—216no—
185#41×C61—28no—
186#41×C61—28no—
187C2×Q8×C61—21no—
188C2×Q8×C61—21no—
189C2×Q8×C61—22no—
190C2×Q8×C61—22no—
191C2×Q8×C61—22no—
192C2×Q8×C61#4114yes—
193C2×Q8×C61C2412yes—
194C2×Q8×C61C2412yes—
195C2×D4×C61—28no—
196C2×D4×C61—24no—
197C2×D4×C61—21no—
198C2×D4×C61—22no—
199C2×D4×C61#4114yes—
200C2×D4×C61C2412yes—
201C22×C4×C61—28no—
202C22×C4×C61—21no—
203C22×C4×C61—24no—
204C22×C4×C61—22no—
205C22×C4×C61—22no—
206C22×C4×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61C2×D411yescharacteristic
209C22×C4×C61C2×D412yes—
210C22×C4×C61C2412yes—
211C22×C4×C61C2411yescharacteristic
212C22×Dic61—24no—
213C22×Dic61—21no—
214C22×Dic61—21no—
215C22×Dic61—21no—
216C22×Dic61—21no—
217C22×Dic61—24no—
218C22×Dic61—24no—
219C22×Dic61—42no—
220C22×Dic61—44no—
221C22×Dic61—44no—
222C22×Dic61C2×D411yescharacteristic
223C22×Dic61C2×D411yescharacteristic
224C22×Dic61C2×D411yescharacteristic
225C22×Dic61C2×D414yes—
226C22×Dic61C2×D414yes—
227C22×Dic61C2×D411yescharacteristic
228C2×Dic122—22no—
229C2×Dic122—22no—
230C2×Dic122—21no—
231C2×Dic122—24no—
232C2×Dic122—44no—
233C2×Dic122C2412yes—
234Q16×C61—28no—
235SD16×C61—28no—
236C2×C8×C61—22no—
237C2×C8×C61—22no—
238C2×C8×C61C2412yes—
239C2×C8×C61C2412yes—
240C4⋊C4×C61—24no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61C2412yes—
243C22⋊C4×C61—24no—
244C22⋊Dic61—24no—
245C22⋊Dic61—24no—
246C22⋊Dic61—24no—
247C22⋊Dic61—24no—
248#11758202—28no—
249#11758200—28no—
250C4⋊Dic61—21no—
251C4⋊Dic61—21no—
252C4⋊Dic61—21no—
253C4⋊Dic61—24no—
254C4⋊Dic61—24no—
255C4⋊Dic61—24no—
256C4⋊Dic61C2412yes—
257C4⋊Dic61C2412yes—
258C4⋊Dic61C2412yes—
259#11758196—24no—
260#11758196—24no—
261#11758196—24no—
262#11758196—24no—
263#11758196—24no—
264C4×Dic61—24no—
265C4×Dic61—24no—
266C4×Dic61—24no—
267C4×Dic61—24no—
268C4×Dic61—24no—
269C4×Dic61C2×D414yes—
270C4×Dic61C2×D414yes—
271C4×Dic61C2×D412yes—
272C4×Dic61C2×D412yes—
273C4×Dic61C2412yes—
274C4×Dic61C2412yes—
275C2×#92418—22no—
276C2×#92418—22no—
277C2×#92418C2412yes—
278C2×#92418C2412yes—
279C23×C61—22no—
280C23×C61—24no—
281C23×C61—22no—
282C23×C61—22no—
283C23×C61—22no—
284C23×C61—42no—
285C23×C61—42no—
286C23×C61C22×D412yes—
287C23×C61C22×D411yescharacteristic
288Q8×C61—24no—
289Q8×C61—22no—
290Q8×C61—22no—
291Q8×C61—22no—
292Q8×C61—42no—
293Q8×C61C2×#4114yes—
294D4×C61—216no—
295D4×C61—24no—
296D4×C61—22no—
297D4×C61C2×#4114yes—
298C2×C4×C61—216no—
299C2×C4×C61—22no—
300C2×C4×C61—24no—
301C2×C4×C61—22no—
302C2×C4×C61—24no—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61—22no—
306C2×C4×C61—22no—
307C2×C4×C61—42no—
308C2×C4×C61—42no—
309C2×C4×C61C22×D412yes—
310C2×C4×C61C22×D411yescharacteristic
311C2×C4×C61C2×#4112yes—
312C2×C4×C61C2×#4112yes—
313C2×C4×C61C2511yescharacteristic
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—28no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—44no—
323C2×Dic61—48no—
324C2×Dic61—42no—
325C2×Dic61—42no—
326C2×Dic61—42no—
327C2×Dic61—42no—
328C2×Dic61—48no—
329C2×Dic61#13714yes—
330C2×Dic61C22×D412yes—
331C2×Dic61C22×D412yes—
332C2×Dic61C22×D412yes—
333C2×Dic61C22×D412yes—
334Dic122—22no—
335Dic122—22no—
336Dic122—48no—
337Dic122—42no—
338C8×C61—22no—
339C8×C61—22no—
340#92418—22no—
341#92418—22no—
342C2×#3116—611nomaximal, Sylow
343C22×C61—22no—
344C22×C61—24no—
345C22×C61—22no—
346C22×C61—22no—
347C22×C61—44no—
348C22×C61—48no—
349C22×C61—42no—
350C22×C61—42no—
351C22×C61#52512yes—
352C22×C61C2×#13712yes—
353C22×C61#57512yes—
354C22×C61C23×D411yescharacteristic
355C4×C61—22no—
356C4×C61—24no—
357C4×C61—42no—
358C4×C61—42no—
359C4×C61#52512yes—
360C4×C61C22×#4111yescharacteristic
361C4×C61C22×#4111yescharacteristic
362Dic61—22no—
363Dic61—22no—
364Dic61—22no—
365Dic61—42no—
366Dic61—42no—
367Dic61—42no—
368Dic61—42no—
369Dic61C2×#13714yes—
370C2×#533—611no—
371C2×C4×#41—611no—
372#3116—6116no—
373C2×#485—611no—
374C2×#485—611no—
375C2×#477—611no—
376C2×#476—611no—
377C2×#462—611no—
378C2×#461—611no—
379C2×#452—611no—
380C2×#452D6111yescharacteristic
381C2×#441—611no—
382C2×#441—611no—
383C2×#440—611no—
384C2×#440—611no—
385C2×#432—611no—
386C2×C61—42no—
387C2×C61—44no—
388C2×C61#311614yescomplemented
389C2×C61C2×#52511yescharacteristic
390C2×C61C22×#13711yescharacteristic
391C2×C61C2×#57511yescharacteristic
392C22×#41C2×D6111yescharacteristic
393C22×Q16—611no—
394C22×Q16C2×D6111yescharacteristic
395C22×SD16—611no—
396C22×SD16C2×D6111yescharacteristic
397#533—618no—
398#533—1224no—
399C2×C4⋊Q8—611no—
400C2×C4⋊Q8—611no—
401C2×#125—1221no—
402C2×C22⋊Q8—611no—
403C2×C22⋊Q8—1221no—
404C2×C22⋊Q8C2×D6111yescharacteristic
405C4×#41—618no—
406C4×#41—1224no—
407C2×C4×Q8—611no—
408C2×C4×Q8—611no—
409C2×C4×Q8—611no—
410C2×C4×Q8—611no—
411C2×C4×Q8—1221no—
412C2×C4×D4—611no—
413C2×C4×D4—611no—
414C2×C4×D4—1221no—
415C2×C4×D4—1221no—
416C2×#117—611no—
417C2×#117—1221no—
418C2×#117—1221no—
419C22×C42—611no—
420C22×C42—1221no—
421#485—618no—
422#485—618no—
423#477—618no—
424#476—618no—
425#462—618no—
426#461—618no—
427#452—618no—
428#452C2×D6118yes—
429#441—618no—
430#441—618no—
431#440—618no—
432#440—618no—
433#432—618no—
434C2×#107—611no—
435C2×#107—611no—
436C2×#106—611no—
437C2×#106—611no—
438C2×C4⋊C8—611no—
439C2×C4⋊C8—611no—
440C2×#103—611no—
441C2×#103—611no—
442C2×#103—611no—
443C2×#103—611no—
444C2×#103—611no—
445C2×#103C2×D6111yescharacteristic
446C2×#102—611no—
447C2×#102C2×D6111yescharacteristic
448C2×C22⋊C8—611no—
449C2×C22⋊C8C2×D6111yescharacteristic
450C2×#97—611no—
451C2×#97—611no—
452C61C2×#311611yescharacteristic, complemented, Sylow
453C2×#41—24no—
454C2×#41—24no—
455C2×#41—22no—
456C2×#41C22×D6114yes—
457C22×Q8—611no—
458C22×Q8—1221no—
459C22×Q8C22×D6111yescharacteristic
460C22×Q8C22×D6111yescharacteristic
461C22×D4—21no—
462C22×D4C22×D6111yescharacteristic
463C23×C4—21no—
464C23×C4—611no—
465C23×C4—611no—
466C23×C4—1221no—
467C23×C4—1221no—
468C23×C4C22×D6111yescharacteristic
469C2×Q16—24no—
470C2×Q16—614no—
471C2×Q16—1224no—
472C2×Q16C22×D6114yes—
473C2×SD16—24no—
474C2×SD16—614no—
475C2×SD16—1224no—
476C2×SD16C22×D6114yes—
477C22×C8—611no—
478C22×C8—611no—
479C22×C8C22×D6111yescharacteristic
480C22×C8C22×D6111yescharacteristic
481C4⋊Q8—614no—
482C4⋊Q8—614no—
483C4⋊Q8—1222no—
484C4⋊Q8—1222no—
485#125—1228no—
486C22⋊Q8—22no—
487C22⋊Q8—614no—
488C22⋊Q8—1228no—
489C22⋊Q8—1222no—
490C22⋊Q8C22×D6114yes—
491C4×Q8—614no—
492C4×Q8—614no—
493C4×Q8—614no—
494C4×Q8—614no—
495C4×Q8—1222no—
496C4×Q8—1228no—
497C4×Q8—1222no—
498C4×Q8—1222no—
499C4×Q8—1222no—
500C4×D4—614no—
501C4×D4—614no—
502C4×D4—1222no—
503C4×D4—1222no—
504C4×D4—1228no—
505C4×D4—1228no—
506#117—614no—
507#117—1228no—
508#117—1228no—
509#117—1222no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—611no—
512C2×C4⋊C4—611no—
513C2×C4⋊C4—611no—
514C2×C4⋊C4—1221no—
515C2×C4⋊C4—1221no—
516C2×C4⋊C4—1221no—
517C2×C4⋊C4—1221no—
518C2×C4⋊C4—1221no—
519C2×C4⋊C4—1221no—
520C2×C4⋊C4—1221no—
521C2×C4⋊C4—1221no—
522C2×C4⋊C4C22×D6111yescharacteristic
523C2×C22⋊C4—21no—
524C2×C22⋊C4—1221no—
525C2×C22⋊C4—1221no—
526C2×C22⋊C4—1221no—
527C2×C22⋊C4—1221no—
528C2×C42—611no—
529C2×C42—614no—
530C2×C42—611no—
531C2×C42—611no—
532C2×C42—611no—
533C2×C42—614no—
534C2×C42—1228no—
535C2×C42—1221no—
536C2×C42—1221no—
537C2×C42—1221no—
538C2×C42—1221no—
539C2×C42—1221no—
540#107—614no—
541#107—614no—
542#106—614no—
543#106—614no—
544C4⋊C8—614no—
545C4⋊C8—614no—
546#103—614no—
547#103—614no—
548#103—614no—
549#103—614no—
550#103—614no—
551#103C22×D6114yes—
552#102—614no—
553#102C22×D6114yes—
554C22⋊C8—614no—
555C22⋊C8C22×D6114yes—
556#97—614no—
557#97—614no—
558C24—21no—
559C24D4×D6111yescharacteristic
560#41—216no—
561#41—28no—
562#41—28no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—612no—
569C2×Q8—1224no—
570C2×Q8—1221no—
571C2×Q8—1222no—
572C2×Q8—1222no—
573C2×Q8—2444no—
574C2×Q8#1175822414yes—
575C2×Q8C23×D6112yes—
576C2×Q8C23×D6112yes—
577C2×D4—28no—
578C2×D4—24no—
579C2×D4—21no—
580C2×D4—22no—
581C2×D4#1175822414yes—
582C2×D4C23×D6112yes—
583C22×C4—28no—
584C22×C4—21no—
585C22×C4—24no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—611no—
591C22×C4—614no—
592C22×C4—611no—
593C22×C4—611no—
594C22×C4—611no—
595C22×C4—614no—
596C22×C4—1224no—
597C22×C4—1224no—
598C22×C4—1224no—
599C22×C4—1221no—
600C22×C4—1221no—
601C22×C4—1221no—
602C22×C4—1221no—
603C22×C4—2444no—
604C22×C4—2442no—
605C22×C4—2444no—
606C22×C4D4×D6112yes—
607C22×C4D4×D6111yescharacteristic
608C22×C4C23×D6112yes—
609C22×C4C23×D6111yescharacteristic
610Q16—28no—
611Q16—1228no—
612SD16—28no—
613SD16—1228no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—612no—
617C2×C8—612no—
618C2×C8—1222no—
619C2×C8—1222no—
620C2×C8C23×D6112yes—
621C2×C8C23×D6112yes—
622C4⋊C4—24no—
623C4⋊C4—21no—
624C4⋊C4—612no—
625C4⋊C4—612no—
626C4⋊C4—612no—
627C4⋊C4—1224no—
628C4⋊C4—1224no—
629C4⋊C4—1224no—
630C4⋊C4—1224no—
631C4⋊C4—1224no—
632C4⋊C4—1224no—
633C4⋊C4—1224no—
634C4⋊C4—1221no—
635C4⋊C4—1221no—
636C4⋊C4—1221no—
637C4⋊C4—1224no—
638C4⋊C4C23×D6112yes—
639C22⋊C4—24no—
640C22⋊C4—1224no—
641C22⋊C4—1224no—
642C22⋊C4—1224no—
643C22⋊C4—1224no—
644C42—614no—
645C42—614no—
646C42—612no—
647C42—612no—
648C42—612no—
649C42—612no—
650C42—1224no—
651C42—1224no—
652C42—1224no—
653C42—1224no—
654C42—1224no—
655C23—22no—
656C23—24no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—42no—
661C23—42no—
662C23C2×D4×D6112yes—
663C23C2×D4×D6111yescharacteristic
664Q8—24no—
665Q8—22no—
666Q8—22no—
667Q8—22no—
668Q8—42no—
669Q8—1222no—
670Q8—1222no—
671Q8—2448no—
672Q8—2442no—
673Q8C2×#1175822414yes—
674D4—216no—
675D4—24no—
676D4—22no—
677D4C2×#1175822414yes—
678C2×C4—216no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—22no—
682C2×C4—24no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—614no—
690C2×C4—612no—
691C2×C4—612no—
692C2×C4—612no—
693C2×C4—612no—
694C2×C4—1228no—
695C2×C4—1222no—
696C2×C4—1222no—
697C2×C4—1222no—
698C2×C4—1222no—
699C2×C4—1222no—
700C2×C4—1222no—
701C2×C4—1222no—
702C2×C4—2448no—
703C2×C4—2444no—
704C2×C4—2448no—
705C2×C4—2442no—
706C2×C4—2442no—
707C2×C4—2442no—
708C2×C4—2442no—
709C2×C4C2×D4×D6112yes—
710C2×C4C2×D4×D6111yescharacteristic
711C2×C4C2×#1175822412yes—
712C2×C4C2×#1175822412yes—
713C2×C4C24×D6111yescharacteristic
714C8—22no—
715C8—22no—
716C8—1222no—
717C8—1222no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—24no—
722C22—42no—
723C22—42no—
724C22—44no—
725C22—48no—
726C22#1684026812yes—
727C22#137×D6112yes—
728C22#1684055912yes—
729C22C22×D4×D6111yescharacteristic
730C4—22no—
731C4—24no—
732C4—42no—
733C4—42no—
734C4—614no—
735C4—1222no—
736C4—1222no—
737C4—1222no—
738C4—2442no—
739C4—2442no—
740C4—2442no—
741C4—2442no—
742C4#1684026812yes—
743C4C22×#1175822411yescharacteristic
744C4C22×#1175822411yescharacteristic
745C2—42no—
746C2—44no—
747C2#2145597414yesdirect product factor
748C2C2×#1684026811yescharacteristic
749C2C2×#137×D6111yescharacteristic
750C2C2×#1684055911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#452C2
socleC23×C61C22×D4
prime radicalC22×#41×C61C22
hypercenterC2×#452D61
hypocenterC61C2×#3116
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C2×#16840314C2semidirect
3. #21455974C2direct (N × H)
4. C2×#16840104C2semidirect
5. C2×#16840100C2semidirect
6. C2×#16840055C2semidirect
7. C2×#16840050C2semidirect
8. C2×#16839970C2semidirect
9. C2×#16839965C2semidirect
11. C2×#16839869C2semidirect
12. C2×#16839866C2semidirect
13. C2×#16839863C2semidirect
14. C2×#16839859C2semidirect
15. C2×#16839816C2semidirect
20. #16840314C22semidirect
42. #16840104C22semidirect
43. #16840100C22semidirect
44. #16840055C22semidirect
45. #16840050C22semidirect
46. #16839970C22semidirect
47. #16839965C22semidirect
49. #16839869C22semidirect
50. #16839866C22semidirect
51. #16839863C22semidirect
52. #16839859C22semidirect
53. #16839816C22semidirect
388. C2×C61#3116semidirect
452. C61C2×#3116semidirect
747. C2#21455974direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403142
C2×#41×Dic612
#214559742
C2×#168401042
C2×#168401002
C2×#168400552
C2×#168400502
C2×#168399702
C2×#168399652
C2×#168399242
C2×#168398692
C2×#168398662
C2×#168398632
C2×#168398592
C2×#168398162
C2×C61×#4522
C2×#311661