Finite Group Databasebeta

← C2×#21455885 #30548081

Subgroups — C2×#21455885 #30548081

Order 15616.

2170 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×#16840230C211yesmaximal, characteristic
3#21455885C2116yesmaximal, direct product factor
4C2×#16840103C211yesmaximal, characteristic, complemented
5C2×#16840046C211yesmaximal, characteristic, complemented
6C2×#16840041C211yesmaximal, characteristic, complemented
7C2×#16839971C211yesmaximal, characteristic, complemented
8C2×#16839966C211yesmaximal, characteristic, complemented
9C2×#16839926C211yesmaximal, characteristic
10C2×#16839922C211yesmaximal, characteristic
11C2×#16839856C211yesmaximal, characteristic, complemented
12C2×#16839854C211yesmaximal, characteristic, complemented
13C2×#16839849C211yesmaximal, characteristic, complemented
14C2×#16839847C211yesmaximal, characteristic, complemented
15C2×#16839812C211yesmaximal, characteristic, complemented
16C2×C61×#485C211yesmaximal, characteristic, complemented
17C22×#11758222C2211yescharacteristic
18C22×Dic244C2211yescharacteristic
19C22×#11758202C2211yescharacteristic
20C22×#11758190C2211yescharacteristic
21C22×#11758201C2211yescharacteristic
22#16840314—24no—
23#16840314C2218yescomplemented
24C2×#14519776C2211yescharacteristic
25C2×#14519775C2211yescharacteristic
26C2×#14519767—21no—
27C2×#14519756C2211yescharacteristic
28C2×#14519754—21no—
29#16840230—24no—
30#16840230C2218yes—
31C2×Q8×Dic61C2211yescharacteristic
32C2×#14519742—21no—
33C2×#14519742C2211yescharacteristic
34C2×#14519742C2211yescharacteristic
35C2×#14519742C2211yescharacteristic
36C2×#14519739C2211yescharacteristic
37C2×#14519739C2211yescharacteristic
38C2×#14519737—21no—
39C2×#14519737—21no—
40C2×#14519734—21no—
41C2×#14519733—21no—
42C22×C4×Dic61C2211yescharacteristic
43C2×C42×D61—21no—
44#16840103C2218yescomplemented
45#16840046C2218yescomplemented
46#16840041C2218yescomplemented
47#16839971C2218yescomplemented
48#16839966C2218yescomplemented
49#16839926C2218yes—
50#16839922C2218yes—
51#16839856C2218yescomplemented
52#16839854C2218yescomplemented
53#16839849C2218yescomplemented
54#16839847C2218yescomplemented
55#16839812C2218yescomplemented
56C2×#14519710C2211yescharacteristic
57C2×#14519708C2211yescharacteristic
58C2×#14519706C2211yescharacteristic
59C2×#14519706C2211yescharacteristic
60C2×#14519702C2211yescharacteristic
61C2×#14519700C2211yescharacteristic
62C2×#14519700C2211yescharacteristic
63C2×#14519700C2211yescharacteristic
64C2×#14519699C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×C22⋊#92418C2211yescharacteristic
67C2×C8×Dic61C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic
69C2×C22⋊Q8×C61C2211yescharacteristic
70C2×#117×C61C2211yescharacteristic
71C61×#485C2218yescomplemented
72C2×#107×C61C2211yescharacteristic
73C2×#106×C61C2211yescharacteristic
74C2×#103×C61C2211yescharacteristic
75C2×#103×C61C2211yescharacteristic
76C2×C22⋊C8×C61C2211yescharacteristic
77C2×#11758222—22no—
78C2×#11758222—24no—
79C2×#11758222—24no—
80C2×#11758222C2314yes—
81C22×Dic122—21no—
82C22×Dic122C2311yescharacteristic
83C22×Dic122C2311yescharacteristic
84C22×D244C2311yescharacteristic
85C22×C22⋊D61—21no—
86C23×Dic61D411yescharacteristic
87C23×Dic61D411yescharacteristic
88C22×C4×D61—21no—
89C22×C4×D61—21no—
90C22×C4×D61—21no—
91C2×Dic244—24no—
92C2×Dic244C2314yes—
93C2×#11758202—24no—
94C2×#11758202C2314yes—
95C2×#11758190—24no—
96C2×#11758190C2314yes—
97C2×#11758201—24no—
98C2×#11758201C2314yes—
99C22×#92418C2311yescharacteristic
100C22×#92418C2311yescharacteristic
101#14519776—22no—
102#14519776C2314yes—
103#14519775—22no—
104#14519775C2314yes—
105#14519767—28no—
106#14519756—22no—
107#14519756C2314yes—
108#14519754—28no—
109Q8×Dic61—22no—
110Q8×Dic61C2314yes—
111#14519742—28no—
112#14519742—22no—
113#14519742—22no—
114#14519742—22no—
115#14519742C2314yes—
116#14519742C2314yes—
117#14519742C2314yes—
118#14519739—22no—
119#14519739—22no—
120#14519739C2314yes—
121#14519739C2314yes—
122#14519737—28no—
123#14519737—28no—
124#14519734—28no—
125#14519733—28no—
126C2×C4⋊Dic61—21no—
127C2×C4⋊Dic61C2311yescharacteristic
128C2×#11758196—21no—
129C2×#11758196—21no—
130C2×#11758196—21no—
131C2×#11758196—21no—
132C2×#11758196—21no—
133C2×#11758196—21no—
134C2×#11758196—21no—
135C2×C22⋊Dic61—21no—
136C2×#11758198—21no—
137C2×#11758198—21no—
138C2×C4×Dic61—21no—
139C2×C4×Dic61—21no—
140C2×C4×Dic61—21no—
141C2×C4×Dic61—21no—
142C2×C4×Dic61D411yescharacteristic
143C2×C4×Dic61D411yescharacteristic
144C2×C4×Dic61D414yes—
145C2×C4×Dic61C2311yescharacteristic
146C2×C4×Dic61C2311yescharacteristic
147C2×C4×Dic61C2314yes—
148C42×D61—28no—
149#14519710C2314yes—
150#14519708C2314yes—
151#14519706C2314yes—
152#14519706C2314yes—
153#14519702C2314yes—
154#14519700C2314yes—
155#14519700C2314yes—
156#14519700C2314yes—
157#14519699C2314yes—
158#14519697C2314yes—
159C22⋊#92418C2314yes—
160C8×Dic61C2314yes—
161C8×Dic61C2314yes—
162C22×Q8×C61C2311yescharacteristic
163C23×C4×C61C2311yescharacteristic
164C22×C8×C61C2311yescharacteristic
165C22×C8×C61C2311yescharacteristic
166C22⋊Q8×C61—22no—
167C22⋊Q8×C61C2314yes—
168#117×C61—22no—
169#117×C61C2314yes—
170C2×C4⋊C4×C61—21no—
171C2×C4⋊C4×C61C2311yescharacteristic
172C2×C4⋊C4×C61C2311yescharacteristic
173C2×C4⋊C4×C61C2311yescharacteristic
174C2×C22⋊C4×C61—21no—
175C2×C22⋊C4×C61—21no—
176C2×C42×C61—21no—
177#107×C61C2314yes—
178#106×C61C2314yes—
179#103×C61C2314yes—
180#103×C61C2314yes—
181C22⋊C8×C61C2314yes—
182C24×C61C2×D411yescharacteristic
183C23×D61—21no—
184C2×Q8×C61—21no—
185C2×Q8×C61—22no—
186C2×Q8×C61—22no—
187C2×Q8×C61C2412yes—
188C22×C4×C61—22no—
189C22×C4×C61—22no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61C2×D411yescharacteristic
195C22×C4×C61C2×D412yes—
196C22×C4×C61C2412yes—
197C22×C4×C61C2411yescharacteristic
198C2×C22⋊D61—28no—
199C2×C22⋊D61—24no—
200C22×Dic61—21no—
201C22×Dic61—24no—
202C22×Dic61—24no—
203C22×Dic61—21no—
204C22×Dic61—21no—
205C22×Dic61C2×D411yescharacteristic
206C22×Dic61C2×D411yescharacteristic
207C22×Dic61C2×D414yes—
208C22×Dic61C2×D414yes—
209C22×Dic61C2×D411yescharacteristic
210C22×Dic61C2×D411yescharacteristic
211#11758222—216no—
212#11758222—28no—
213#11758222—28no—
214C2×D244—21no—
215C2×D244—22no—
216C2×D244#4114yes—
217C2×D244C2412yes—
218C2×C4×D61—28no—
219C2×C4×D61—24no—
220C2×C4×D61—24no—
221C2×C4×D61—24no—
222C2×C4×D61—44no—
223C2×C4×D61—44no—
224C2×Dic122—21no—
225C2×Dic122—22no—
226C2×Dic122—22no—
227C2×Dic122—22no—
228C2×Dic122—21no—
229C2×Dic122—24no—
230C2×Dic122—44no—
231C2×Dic122#4114yes—
232C2×Dic122C2412yes—
233C2×Dic122C2412yes—
234C2×C8×C61—22no—
235C2×C8×C61—22no—
236C2×C8×C61C2412yes—
237C2×C8×C61C2412yes—
238C4⋊C4×C61—24no—
239C4⋊C4×C61—21no—
240C4⋊C4×C61—21no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61C2412yes—
243C4⋊C4×C61C2412yes—
244C4⋊C4×C61C2412yes—
245C22⋊C4×C61—24no—
246C22⋊C4×C61—24no—
247C42×C61—24no—
248C22⋊Dic61—24no—
249#11758202—28no—
250#11758201—28no—
251#11758198—24no—
252#11758198—24no—
253C4⋊Dic61—21no—
254C4⋊Dic61—24no—
255C4⋊Dic61C2412yes—
256#11758196—24no—
257#11758196—24no—
258#11758196—24no—
259#11758196—24no—
260#11758196—24no—
261#11758196—24no—
262#11758196—24no—
263C4×Dic61—24no—
264C4×Dic61—24no—
265C4×Dic61—24no—
266C4×Dic61—24no—
267C4×Dic61C2×D414yes—
268C4×Dic61C2×D414yes—
269C4×Dic61C2×D412yes—
270C4×Dic61C2×D412yes—
271C4×Dic61C2412yes—
272C4×Dic61C2412yes—
273C2×#92418—22no—
274C2×#92418—22no—
275C2×#92418C2412yes—
276C2×#92418C2412yes—
277Dic244—28no—
278#11758190—28no—
279C23×C61—22no—
280C23×C61—22no—
281C23×C61—22no—
282C23×C61C22×D412yes—
283C23×C61C22×D411yescharacteristic
284C22×D61—24no—
285C22×D61—22no—
286C22×D61—42no—
287C22×D61—42no—
288Q8×C61—22no—
289Q8×C61—22no—
290Q8×C61—42no—
291C2×C4×C61—22no—
292C2×C4×C61—24no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—42no—
300C2×C4×C61—42no—
301C2×C4×C61—42no—
302C2×C4×C61—42no—
303C2×C4×C61C22×D412yes—
304C2×C4×C61C22×D411yescharacteristic
305C2×C4×C61C2×#4112yes—
306C2×C4×C61C2×#4112yes—
307C2×C4×C61C2511yescharacteristic
308C22⋊D61—216no—
309C2×Dic61—24no—
310C2×Dic61—22no—
311C2×Dic61—22no—
312C2×Dic61—22no—
313C2×Dic61—28no—
314C2×Dic61—28no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—42no—
318C2×Dic61—42no—
319C2×Dic61#13514yes—
320C2×Dic61#13714yes—
321C2×Dic61C22×D412yes—
322C2×Dic61C22×D412yes—
323C2×Dic61C22×D412yes—
324C2×Dic61C22×D412yes—
325D244—24no—
326D244—22no—
327D244C2×#4114yes—
328C4×D61—216no—
329C4×D61—48no—
330C4×D61—48no—
331Dic122—24no—
332Dic122—22no—
333Dic122—22no—
334Dic122—22no—
335Dic122—42no—
336Dic122—48no—
337Dic122C2×#4114yes—
338C8×C61—22no—
339C8×C61—22no—
340#92418—22no—
341#92418—22no—
342C2×#3107—611nomaximal, Sylow
343C22×C61—22no—
344C22×C61—22no—
345C22×C61—22no—
346C22×C61—44no—
347C22×C61#52512yes—
348C22×C61C2×#13512yes—
349C22×C61C2×#13712yes—
350C22×C61C23×D411yescharacteristic
351C2×D61—24no—
352C2×D61—48no—
353C2×D61—42no—
354C2×D61—42no—
355C4×C61—22no—
356C4×C61—42no—
357C4×C61—42no—
358C4×C61—42no—
359C4×C61—42no—
360C4×C61#52512yes—
361C4×C61C22×#4111yescharacteristic
362C4×C61C22×#4111yescharacteristic
363Dic61—24no—
364Dic61—22no—
365Dic61—22no—
366Dic61—42no—
367Dic61—42no—
368Dic61C2×#13514yes—
369Dic61C2×#13714yes—
370C2×#533—611no—
371C2×C4×#41—611no—
372#3107—6116no—
373C2×#485—611no—
374C2×#485D6111yescharacteristic, complemented
375C2×#475—611no—
376C2×#474—611no—
377C2×#462—611no—
378C2×#461—611no—
379C2×#452—611no—
380C2×#452—611no—
381C2×C4×Q16—611no—
382C2×C4×Q16—611no—
383C2×C4×SD16—611no—
384C2×C4×SD16—611no—
385C2×#431—611no—
386C2×C61—42no—
387C2×C61#310714yescomplemented
388C2×C61C2×#52511yescharacteristic
389C2×C61C22×#13511yescharacteristic
390C2×C61C22×#13711yescharacteristic
391D61—44no—
392C22×#41—611no—
393C22×Q16—611no—
394C22×Q16—611no—
395C22×SD16—611no—
396C22×SD16—611no—
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—1221no—
417C2×#117—1221no—
418C2×#117C2×D6111yescharacteristic
419C22×C42—611no—
420C22×C42—1221no—
421#485—618no—
422#485C2×D6118yescomplemented
423#475—618no—
424#474—618no—
425#462—618no—
426#461—618no—
427#452—618no—
428#452—618no—
429C4×Q16—618no—
430C4×Q16—618no—
431C4×SD16—618no—
432C4×SD16—618no—
433#431—618no—
434C2×#107—611no—
435C2×#107C2×D6111yescharacteristic
436C2×#106—611no—
437C2×#106C2×D6111yescharacteristic
438C2×C4⋊C8—611no—
439C2×C4⋊C8—611no—
440C2×#103—611no—
441C2×#103—611no—
442C2×#103—611no—
443C2×#103—611no—
444C2×#103C2×D6111yescharacteristic
445C2×#103C2×D6111yescharacteristic
446C2×#102—611no—
447C2×#102—611no—
448C2×C22⋊C8—611no—
449C2×C22⋊C8C2×D6111yescharacteristic
450C2×C4×C8—611no—
451C2×C4×C8—611no—
452C61C2×#310711yescharacteristic, complemented, Sylow
453C2×#41—614no—
454C2×#41—1224no—
455C2×#41—1224no—
456C2×#41—1222no—
457C22×Q8—611no—
458C22×Q8—611no—
459C22×Q8—1221no—
460C22×Q8C22×D6111yescharacteristic
461C22×D4—611no—
462C22×D4—1221no—
463C23×C4—611no—
464C23×C4—611no—
465C23×C4—1221no—
466C23×C4—1221no—
467C23×C4—1221no—
468C23×C4C22×D6111yescharacteristic
469C2×Q16—614no—
470C2×Q16—614no—
471C2×Q16—1224no—
472C2×Q16—1224no—
473C2×SD16—614no—
474C2×SD16—614no—
475C2×SD16—1224no—
476C2×SD16—1224no—
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—1222no—
497C4×Q8—1222no—
498C4×Q8—1228no—
499C4×Q8—1222no—
500C4×D4—614no—
501C4×D4—614no—
502C4×D4—1222no—
503C4×D4—1222no—
504C4×D4—1228no—
505C4×D4—1228no—
506#117—22no—
507#117—1228no—
508#117—1228no—
509#117C22×D6114yes—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—611no—
512C2×C4⋊C4—1221no—
513C2×C4⋊C4—1221no—
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⋊C4C22×D6111yescharacteristic
521C2×C4⋊C4C22×D6111yescharacteristic
522C2×C4⋊C4C22×D6111yescharacteristic
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—1221no—
526C2×C22⋊C4—1221no—
527C2×C22⋊C4—1221no—
528C2×C42—21no—
529C2×C42—611no—
530C2×C42—611no—
531C2×C42—614no—
532C2×C42—611no—
533C2×C42—611no—
534C2×C42—614no—
535C2×C42—1228no—
536C2×C42—1221no—
537C2×C42—1221no—
538C2×C42—1221no—
539C2×C42—1221no—
540#107—614no—
541#107C22×D6114yes—
542#106—614no—
543#106C22×D6114yes—
544C4⋊C8—614no—
545C4⋊C8—614no—
546#103—614no—
547#103—614no—
548#103—614no—
549#103—614no—
550#103C22×D6114yes—
551#103C22×D6114yes—
552#102—614no—
553#102—614no—
554C22⋊C8—614no—
555C22⋊C8C22×D6114yes—
556C4×C8—614no—
557C4×C8—614no—
558C24—1221no—
559C24D4×D6111yescharacteristic
560#41—1228no—
561#41—1228no—
562#41—12216no—
563C2×Q8—21no—
564C2×Q8—22no—
565C2×Q8—22no—
566C2×Q8—614no—
567C2×Q8—612no—
568C2×Q8—612no—
569C2×Q8—1224no—
570C2×Q8—1221no—
571C2×Q8—1221no—
572C2×Q8—1222no—
573C2×Q8—1222no—
574C2×Q8—1222no—
575C2×Q8—2444no—
576C2×Q8C23×D6112yes—
577C2×D4—614no—
578C2×D4—612no—
579C2×D4—1228no—
580C2×D4—1224no—
581C2×D4—1221no—
582C2×D4—1222no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—611no—
590C22×C4—611no—
591C22×C4—614no—
592C22×C4—614no—
593C22×C4—611no—
594C22×C4—611no—
595C22×C4—1224no—
596C22×C4—1224no—
597C22×C4—1228no—
598C22×C4—1224no—
599C22×C4—1224no—
600C22×C4—1221no—
601C22×C4—1224no—
602C22×C4—1221no—
603C22×C4—1221no—
604C22×C4—2444no—
605C22×C4—2444no—
606C22×C4D4×D6112yes—
607C22×C4D4×D6111yescharacteristic
608C22×C4C23×D6112yes—
609C22×C4C23×D6111yescharacteristic
610Q16—1228no—
611Q16—1228no—
612SD16—1228no—
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—21no—
625C4⋊C4—21no—
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—1224no—
636C4⋊C4C23×D6112yes—
637C4⋊C4C23×D6112yes—
638C4⋊C4C23×D6112yes—
639C22⋊C4—24no—
640C22⋊C4—24no—
641C22⋊C4—1224no—
642C22⋊C4—1224no—
643C22⋊C4—1224no—
644C42—24no—
645C42—614no—
646C42—614no—
647C42—612no—
648C42—612no—
649C42—612no—
650C42—612no—
651C42—1224no—
652C42—1224no—
653C42—1224no—
654C42—1224no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—1224no—
659C23—1222no—
660C23—2442no—
661C23—2442no—
662C23C2×D4×D6112yes—
663C23C2×D4×D6111yescharacteristic
664Q8—22no—
665Q8—22no—
666Q8—42no—
667Q8—614no—
668Q8—1224no—
669Q8—1222no—
670Q8—1222no—
671Q8—1222no—
672Q8—2448no—
673Q8—2442no—
674D4—614no—
675D4—12216no—
676D4—1224no—
677D4—1222no—
678C2×C4—22no—
679C2×C4—24no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—614no—
691C2×C4—614no—
692C2×C4—612no—
693C2×C4—612no—
694C2×C4—612no—
695C2×C4—612no—
696C2×C4—12216no—
697C2×C4—1228no—
698C2×C4—1228no—
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×C4C2×D4×D6112yes—
710C2×C4C2×D4×D6111yescharacteristic
711C2×C4#41×D6112yes—
712C2×C4#41×D6112yes—
713C2×C4C24×D6111yescharacteristic
714C8—22no—
715C8—22no—
716C8—1222no—
717C8—1222no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—44no—
722C22—1224no—
723C22—2448no—
724C22—2442no—
725C22—2442no—
726C22#1684027012yes—
727C22#135×D6112yes—
728C22#137×D6112yes—
729C22C22×D4×D6111yescharacteristic
730C4—22no—
731C4—42no—
732C4—42no—
733C4—42no—
734C4—42no—
735C4—614no—
736C4—614no—
737C4—1222no—
738C4—1222no—
739C4—1224no—
740C4—2442no—
741C4—2442no—
742C4#1684027012yes—
743C4C2×#41×D6111yescharacteristic
744C4C2×#41×D6111yescharacteristic
745C2—42no—
746C2—2444no—
747C2#2145588514yesdirect product factor
748C2C2×#1684027011yescharacteristic
749C2C2×#135×D6111yescharacteristic
750C2C2×#137×D6111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#485C2
socleC23×C61C22×D4
prime radicalC22×#11758222C22
hypercenterC2×#485D61
hypocenterC61C2×#3107
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
1. C2×#16840314C2semidirect
3. #21455885C2direct (N × H)
4. C2×#16840103C2semidirect
5. C2×#16840046C2semidirect
6. C2×#16840041C2semidirect
7. C2×#16839971C2semidirect
8. C2×#16839966C2semidirect
11. C2×#16839856C2semidirect
12. C2×#16839854C2semidirect
13. C2×#16839849C2semidirect
14. C2×#16839847C2semidirect
15. C2×#16839812C2semidirect
16. C2×C61×#485C2semidirect
23. #16840314C22semidirect
44. #16840103C22semidirect
45. #16840046C22semidirect
46. #16840041C22semidirect
47. #16839971C22semidirect
48. #16839966C22semidirect
51. #16839856C22semidirect
52. #16839854C22semidirect
53. #16839849C22semidirect
54. #16839847C22semidirect
55. #16839812C22semidirect
71. C61×#485C22semidirect
374. C2×#485D61semidirect
387. C2×C61#3107semidirect
422. #485C2×D61semidirect
452. C61C2×#3107semidirect
747. C2#21455885direct (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×#168402302
#214558852
C2×#168401032
C2×#168400462
C2×#168400412
C2×#168399712
C2×#168399662
C2×#168399262
C2×#168399222
C2×#168398562
C2×#168398542
C2×#168398492
C2×#168398472
C2×#168398122
C2×C61×#4852
C2×#310761