Finite Group Databasebeta

← C2×#21455903 #30548100

Subgroups — C2×#21455903 #30548100

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×#16840299C211yesmaximal, characteristic
2C2×C4×Q8×D61C211yesmaximal, characteristic, complemented
3#21455903C2116yesmaximal, direct product factor
4C2×#16840091C211yesmaximal, characteristic, complemented
5C2×#16840077C211yesmaximal, characteristic
6C2×#16840068C211yesmaximal, characteristic, complemented
7C2×#16840067C211yesmaximal, characteristic, complemented
8C2×#16839987C211yesmaximal, characteristic, complemented
9C2×#16839986C211yesmaximal, characteristic, complemented
10C2×#16839916C211yesmaximal, characteristic, complemented
11C2×#16839902C211yesmaximal, characteristic
12C2×C4×#11758202C211yesmaximal, characteristic, complemented
13C2×C4×#11758190C211yesmaximal, characteristic, complemented
14C2×C4×#11758201C211yesmaximal, characteristic, complemented
15C2×#16839813C211yesmaximal, characteristic, complemented
16C2×C4×Q16×C61C211yesmaximal, characteristic, complemented
17C22×Q8×D61C2211yescharacteristic
18C22×#11758202C2211yescharacteristic
19C22×#11758190C2211yescharacteristic
20C22×#11758201C2211yescharacteristic
21#16840299—24no—
22#16840299C2218yes—
23C2×#14519772—21no—
24C2×#14519768C2211yescharacteristic
25C2×#14519766C2211yescharacteristic
26C2×#14519762—21no—
27C2×#14519753C2211yescharacteristic
28C2×#14519752C2211yescharacteristic
29C2×Q8×Dic61C2211yescharacteristic
30C2×C4×Dic122—21no—
31C2×C4×Dic122C2211yescharacteristic
32C2×#14519742—21no—
33C2×#14519742C2211yescharacteristic
34C4×Q8×D61—24no—
35C4×Q8×D61C2218yescomplemented
36C2×C4×D244—21no—
37C2×C4×D244C2211yescharacteristic
38C2×#14519734—21no—
39C2×C4⋊C4×D61—21no—
40C2×C4⋊C4×D61C2211yescharacteristic
41C2×C42×D61—21no—
42C2×C42×D61C2211yescharacteristic
43#16840091C2218yescomplemented
44#16840077C2218yes—
45#16840068C2218yescomplemented
46#16840067C2218yescomplemented
47#16839987C2218yescomplemented
48#16839986C2218yescomplemented
49#16839916C2218yescomplemented
50#16839902C2218yes—
51C4×#11758202C2218yescomplemented
52C4×#11758190C2218yescomplemented
53C4×#11758201C2218yescomplemented
54#16839813C2218yescomplemented
55C2×#14519710C2211yescharacteristic
56C2×#14519709C2211yescharacteristic
57C2×#14519708C2211yescharacteristic
58C2×#14519706C2211yescharacteristic
59C2×#14519706C2211yescharacteristic
60C2×#14519702C2211yescharacteristic
61C2×#14519701C2211yescharacteristic
62C2×#14519701C2211yescharacteristic
63C2×#14519700C2211yescharacteristic
64C2×#14519699C2211yescharacteristic
65C2×#14519697C2211yescharacteristic
66C2×#14519689C2211yescharacteristic
67C2×#14519689C2211yescharacteristic
68C2×C4×#92418C2211yescharacteristic
69C22×Q16×C61C2211yescharacteristic
70C2×C4×Q8×C61C2211yescharacteristic
71C2×C4×Q8×C61C2211yescharacteristic
72C4×Q16×C61C2218yescomplemented
73C2×#107×C61C2211yescharacteristic
74C2×#103×C61C2211yescharacteristic
75C2×#103×C61C2211yescharacteristic
76C2×C4×C8×C61C2211yescharacteristic
77C22×Dic122—21no—
78C22×Dic122C2311yescharacteristic
79C2×Q8×D61—24no—
80C2×Q8×D61—22no—
81C2×Q8×D61—24no—
82C2×Q8×D61C2314yes—
83C22×D244—21no—
84C22×D244C2311yescharacteristic
85C22×C4×D61—21no—
86C22×C4×D61—21no—
87C22×C4×D61—21no—
88C22×C4×D61D411yescharacteristic
89C22×C4×D61D411yescharacteristic
90C22×C4×D61C2311yescharacteristic
91C2×#11758202—24no—
92C2×#11758202C2314yes—
93C2×#11758190—24no—
94C2×#11758190C2314yes—
95C2×#11758201—24no—
96C2×#11758201C2314yes—
97C22×#92418C2311yescharacteristic
98C22×#92418C2311yescharacteristic
99#14519772—28no—
100#14519768—22no—
101#14519768C2314yes—
102#14519766—22no—
103#14519766C2314yes—
104#14519762—28no—
105#14519753—22no—
106#14519753C2314yes—
107#14519752—22no—
108#14519752C2314yes—
109Q8×Dic61—22no—
110Q8×Dic61C2314yes—
111C4×Dic122—22no—
112C4×Dic122—28no—
113C4×Dic122C2314yes—
114#14519742—22no—
115#14519742—28no—
116#14519742C2314yes—
117C4×D244—28no—
118C4×D244—22no—
119C4×D244C2314yes—
120#14519734—28no—
121C2×C4⋊Dic61—21no—
122C2×C4⋊Dic61—21no—
123C2×C4⋊Dic61C2311yescharacteristic
124C2×C4⋊Dic61C2311yescharacteristic
125C2×#11758196—21no—
126C2×#11758196—21no—
127C2×#11758196—21no—
128C2×#11758196—21no—
129C2×#11758196—21no—
130C4⋊C4×D61—28no—
131C4⋊C4×D61—22no—
132C4⋊C4×D61C2314yes—
133C2×#11758198—21no—
134C2×#11758198—21no—
135C2×#11758198—21no—
136C2×#11758198—21no—
137C2×#11758198—21no—
138C2×C4×Dic61—21no—
139C2×C4×Dic61—21no—
140C2×C4×Dic61—21no—
141C2×C4×Dic61D411yescharacteristic
142C2×C4×Dic61D411yescharacteristic
143C2×C4×Dic61C2311yescharacteristic
144C42×D61—28no—
145C42×D61D414yes—
146C42×D61C2314yes—
147#14519710C2314yes—
148#14519709C2314yes—
149#14519708C2314yes—
150#14519706C2314yes—
151#14519706C2314yes—
152#14519702C2314yes—
153#14519701C2314yes—
154#14519701C2314yes—
155#14519700C2314yes—
156#14519699C2314yes—
157#14519697C2314yes—
158#14519689C2314yes—
159#14519689C2314yes—
160C4×#92418C2314yes—
161C22×Q8×C61C2311yescharacteristic
162C22×Q8×C61C2311yescharacteristic
163C2×Q16×C61—24no—
164C2×Q16×C61C2314yes—
165C22×C8×C61C2311yescharacteristic
166C22×C8×C61C2311yescharacteristic
167C4×Q8×C61—22no—
168C4×Q8×C61—22no—
169C4×Q8×C61C2314yes—
170C4×Q8×C61C2314yes—
171C2×C4⋊C4×C61—21no—
172C2×C4⋊C4×C61—21no—
173C2×C4⋊C4×C61C2311yescharacteristic
174C2×C4⋊C4×C61C2311yescharacteristic
175C2×C42×C61—21no—
176C2×C42×C61—21no—
177C2×C42×C61C2311yescharacteristic
178#107×C61C2314yes—
179#103×C61C2314yes—
180#103×C61C2314yes—
181C4×C8×C61C2314yes—
182C23×D61—21no—
183C23×D61C2×D411yescharacteristic
184C2×Q8×C61—21no—
185C2×Q8×C61—21no—
186C2×Q8×C61—22no—
187C2×Q8×C61—22no—
188C2×Q8×C61—22no—
189C2×Q8×C61#4114yes—
190C2×Q8×C61C2412yes—
191C2×Q8×C61C2412yes—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61C2×D411yescharacteristic
197C22×C4×C61C2×D411yescharacteristic
198C22×C4×C61C2411yescharacteristic
199C22×Dic61—21no—
200C22×Dic61—21no—
201C22×Dic61—21no—
202C22×Dic61C2×D411yescharacteristic
203C22×Dic61C2×D411yescharacteristic
204C22×Dic61C2×D411yescharacteristic
205Q8×D61—216no—
206Q8×D61—28no—
207Q8×D61—28no—
208C2×D244—22no—
209C2×D244—22no—
210C2×D244—24no—
211C2×D244—21no—
212C2×D244—44no—
213C2×D244C2412yes—
214C2×C4×D61—28no—
215C2×C4×D61—24no—
216C2×C4×D61—24no—
217C2×C4×D61—24no—
218C2×C4×D61—22no—
219C2×C4×D61—22no—
220C2×C4×D61—24no—
221C2×C4×D61—24no—
222C2×C4×D61—44no—
223C2×C4×D61—44no—
224C2×C4×D61C2×D414yes—
225C2×C4×D61C2×D414yes—
226C2×C4×D61C2×D412yes—
227C2×C4×D61C2412yes—
228C2×Dic122—28no—
229C2×Dic122—21no—
230C2×Dic122—22no—
231C2×Dic122—24no—
232C2×Dic122#4114yes—
233C2×Dic122C2412yes—
234Q16×C61—28no—
235C2×C8×C61—22no—
236C2×C8×C61—22no—
237C2×C8×C61C2412yes—
238C2×C8×C61C2412yes—
239C4⋊C4×C61—24no—
240C4⋊C4×C61—24no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61—21no—
243C4⋊C4×C61C2412yes—
244C4⋊C4×C61C2412yes—
245C42×C61—24no—
246C42×C61—24no—
247C42×C61C2×D412yes—
248C42×C61C2412yes—
249#11758202—28no—
250#11758201—28no—
251#11758198—24no—
252#11758198—24no—
253#11758198—24no—
254#11758198—24no—
255#11758198—24no—
256C4⋊Dic61—21no—
257C4⋊Dic61—21no—
258C4⋊Dic61—24no—
259C4⋊Dic61—24no—
260C4⋊Dic61C2412yes—
261C4⋊Dic61C2412yes—
262#11758196—24no—
263#11758196—24no—
264#11758196—24no—
265#11758196—24no—
266#11758196—24no—
267C4×Dic61—24no—
268C4×Dic61—24no—
269C4×Dic61—24no—
270C4×Dic61C2×D412yes—
271C4×Dic61C2×D414yes—
272C4×Dic61C2×D414yes—
273C4×Dic61C2412yes—
274C2×#92418—22no—
275C2×#92418—22no—
276C2×#92418C2412yes—
277C2×#92418C2412yes—
278#11758190—28no—
279C23×C61C22×D411yescharacteristic
280C22×D61—22no—
281C22×D61—22no—
282C22×D61—22no—
283C22×D61—42no—
284C22×D61—42no—
285C22×D61—42no—
286C22×D61#13514yes—
287C22×D61C22×D412yes—
288Q8×C61—24no—
289Q8×C61—22no—
290Q8×C61—22no—
291Q8×C61—22no—
292Q8×C61—42no—
293Q8×C61C2×#4114yes—
294C2×C4×C61—24no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—42no—
301C2×C4×C61—42no—
302C2×C4×C61—42no—
303C2×C4×C61#13714yes—
304C2×C4×C61C22×D412yes—
305C2×C4×C61C22×D411yescharacteristic
306C2×C4×C61C22×D412yes—
307C2×C4×C61C2×#4112yes—
308C2×C4×C61C2×#4112yes—
309C2×C4×C61C2511yescharacteristic
310C2×Dic61—22no—
311C2×Dic61—24no—
312C2×Dic61—22no—
313C2×Dic61—22no—
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—42no—
318C2×Dic61—42no—
319C2×Dic61C22×D412yes—
320C2×Dic61C22×D412yes—
321C2×Dic61C22×D412yes—
322D244—22no—
323D244—22no—
324D244—48no—
325D244—42no—
326C4×D61—216no—
327C4×D61—28no—
328C4×D61—24no—
329C4×D61—28no—
330C4×D61—22no—
331C4×D61—22no—
332C4×D61—48no—
333C4×D61—48no—
334Dic122—216no—
335Dic122—24no—
336Dic122—22no—
337Dic122C2×#4114yes—
338C8×C61—22no—
339C8×C61—22no—
340#92418—22no—
341#92418—22no—
342C2×#3108—611nomaximal, Sylow
343C22×C61#52512yes—
344C22×C61C2×#13512yes—
345C22×C61C2×#13712yes—
346C22×C61C23×D411yescharacteristic
347C2×D61—28no—
348C2×D61—22no—
349C2×D61—22no—
350C2×D61—42no—
351C2×D61—42no—
352C2×D61—42no—
353C2×D61—84no—
354C2×D61C2×#13514yes—
355C4×C61—24no—
356C4×C61—22no—
357C4×C61—42no—
358C4×C61—42no—
359C4×C61—42no—
360C4×C61#52512yes—
361C4×C61C2×#13714yes—
362C4×C61C22×#4111yescharacteristic
363C4×C61C22×#4111yescharacteristic
364Dic61—22no—
365Dic61—24no—
366Dic61—22no—
367Dic61—22no—
368Dic61—42no—
369Dic61—42no—
370C2×#529—611no—
371C22×C4×Q8—611no—
372#3108—6116no—
373C2×#483—611no—
374C2×#480—611no—
375C2×#479—611no—
376C2×#479—611no—
377C2×#464—611no—
378C2×#464—611no—
379C2×#451—611no—
380C2×#448—611no—
381C2×C4×Q16—611no—
382C2×C4×Q16D6111yescharacteristic, complemented
383C2×C4×SD16—611no—
384C2×C4×SD16—611no—
385C2×#431—611no—
386C2×C61#310814yescomplemented
387C2×C61C2×#52511yescharacteristic
388C2×C61C22×#13511yescharacteristic
389C2×C61C22×#13711yescharacteristic
390D61—24no—
391D61—82no—
392C23×Q8—611no—
393C22×Q16—611no—
394C22×Q16C2×D6111yescharacteristic
395C22×SD16—611no—
396C22×SD16—611no—
397#529—618no—
398#529—1224no—
399C2×#126—1221no—
400C2×#125—611no—
401C2×#124—611no—
402C2×#123—1221no—
403C2×C22⋊Q8—611no—
404C2×#121—611no—
405C2×C4×Q8—611no—
406C2×C4×Q8—618no—
407C2×C4×Q8—611no—
408C2×C4×Q8—611no—
409C2×C4×Q8—1221no—
410C2×C4×Q8—1221no—
411C2×C4×Q8—1224no—
412C2×C4×Q8C2×D6111yescharacteristic
413C2×C4×Q8C2×D6111yescharacteristic
414C2×C4×D4—611no—
415C2×C4×D4—1221no—
416C2×#117—1221no—
417C22×C4⋊C4—611no—
418C22×C4⋊C4—1221no—
419C22×C42—611no—
420C22×C42—1221no—
421#483—618no—
422#480—618no—
423#479—618no—
424#479—618no—
425#464—618no—
426#464—618no—
427#451—618no—
428#448—618no—
429C4×Q16—618no—
430C4×Q16C2×D6118yescomplemented
431C4×SD16—618no—
432C4×SD16—618no—
433#431—618no—
434C2×#107—611no—
435C2×#107C2×D6111yescharacteristic
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×#103C2×D6111yescharacteristic
445C2×#103C2×D6111yescharacteristic
446C2×#102—611no—
447C2×#102—611no—
448C2×C22⋊C8—611no—
449C2×C22⋊C8—611no—
450C2×C4×C8—611no—
451C2×C4×C8C2×D6111yescharacteristic
452C61C2×#310811yescharacteristic, complemented, Sylow
453C22×Q8—614no—
454C22×Q8—611no—
455C22×Q8—1221no—
456C22×Q8—1222no—
457C22×Q8—1224no—
458C22×Q8—1224no—
459C22×Q8C22×D6111yescharacteristic
460C22×Q8C22×D6111yescharacteristic
461C22×D4—611no—
462C22×D4—1221no—
463C23×C4—611no—
464C23×C4—611no—
465C23×C4—611no—
466C23×C4—1221no—
467C23×C4—1221no—
468C23×C4—1221no—
469C2×Q16—24no—
470C2×Q16—614no—
471C2×Q16—1224no—
472C2×Q16C22×D6114yes—
473C2×SD16—614no—
474C2×SD16—614no—
475C2×SD16—1224no—
476C2×SD16—1224no—
477C22×C8—611no—
478C22×C8—611no—
479C22×C8C22×D6111yescharacteristic
480C22×C8C22×D6111yescharacteristic
481#126—1228no—
482#125—614no—
483#125—1222no—
484#124—614no—
485#124—1222no—
486#123—1228no—
487C22⋊Q8—614no—
488C22⋊Q8—1222no—
489#121—614no—
490#121—1222no—
491C4×Q8—22no—
492C4×Q8—22no—
493C4×Q8—614no—
494C4×Q8—614no—
495C4×Q8—614no—
496C4×Q8—1228no—
497C4×Q8—1222no—
498C4×Q8—1228no—
499C4×Q8—1222no—
500C4×Q8—1222no—
501C4×Q8C22×D6114yes—
502C4×Q8C22×D6114yes—
503C4×D4—614no—
504C4×D4—1228no—
505C4×D4—1222no—
506#117—1228no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—611no—
510C2×C4⋊C4—611no—
511C2×C4⋊C4—614no—
512C2×C4⋊C4—1222no—
513C2×C4⋊C4—1228no—
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⋊C4C22×D6111yescharacteristic
522C2×C4⋊C4C22×D6111yescharacteristic
523C2×C22⋊C4—1221no—
524C2×C22⋊C4—1221no—
525C2×C22⋊C4—1221no—
526C2×C22⋊C4—1221no—
527C2×C22⋊C4—1221no—
528C2×C42—21no—
529C2×C42—21no—
530C2×C42—611no—
531C2×C42—611no—
532C2×C42—611no—
533C2×C42—614no—
534C2×C42—614no—
535C2×C42—1228no—
536C2×C42—1221no—
537C2×C42—1221no—
538C2×C42—1221no—
539C2×C42C22×D6111yescharacteristic
540#107—614no—
541#107C22×D6114yes—
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#103C22×D6114yes—
551#103C22×D6114yes—
552#102—614no—
553#102—614no—
554C22⋊C8—614no—
555C22⋊C8—614no—
556C4×C8—614no—
557C4×C8C22×D6114yes—
558C24—611no—
559C24—1221no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—22no—
563C2×Q8—22no—
564C2×Q8—22no—
565C2×Q8—614no—
566C2×Q8—612no—
567C2×Q8—1224no—
568C2×Q8—1228no—
569C2×Q8—1228no—
570C2×Q8—12216no—
571C2×Q8—1228no—
572C2×Q8—1221no—
573C2×Q8—1222no—
574C2×Q8#1175822214yes—
575C2×Q8C23×D6112yes—
576C2×Q8C23×D6112yes—
577C2×D4—612no—
578C2×D4—1224no—
579C2×D4—1221no—
580C2×D4—1222no—
581C2×D4—1222no—
582C2×D4—2444no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—611no—
588C22×C4—611no—
589C22×C4—611no—
590C22×C4—614no—
591C22×C4—614no—
592C22×C4—612no—
593C22×C4—612no—
594C22×C4—1224no—
595C22×C4—1224no—
596C22×C4—1228no—
597C22×C4—1224no—
598C22×C4—1221no—
599C22×C4—1224no—
600C22×C4—1222no—
601C22×C4—1222no—
602C22×C4—1221no—
603C22×C4—1221no—
604C22×C4—1224no—
605C22×C4—2444no—
606C22×C4—2444no—
607C22×C4D4×D6111yescharacteristic
608C22×C4D4×D6111yescharacteristic
609C22×C4C23×D6111yescharacteristic
610Q16—28no—
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—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—1224no—
633C4⋊C4—1224no—
634C4⋊C4—1221no—
635C4⋊C4—1221no—
636C4⋊C4—1224no—
637C4⋊C4C23×D6112yes—
638C4⋊C4C23×D6112yes—
639C22⋊C4—1224no—
640C22⋊C4—1224no—
641C22⋊C4—1224no—
642C22⋊C4—1224no—
643C22⋊C4—1224no—
644C42—24no—
645C42—24no—
646C42—614no—
647C42—612no—
648C42—614no—
649C42—612no—
650C42—1224no—
651C42—1224no—
652C42—1224no—
653C42D4×D6112yes—
654C42C23×D6112yes—
655C23—614no—
656C23—612no—
657C23—1222no—
658C23—1222no—
659C23—1222no—
660C23—2442no—
661C23—2442no—
662C23—2442no—
663C23C2×D4×D6111yescharacteristic
664Q8—24no—
665Q8—22no—
666Q8—22no—
667Q8—22no—
668Q8—42no—
669Q8—614no—
670Q8—12216no—
671Q8—1224no—
672Q8—1222no—
673Q8C2×#1175822214yes—
674D4—1222no—
675D4—1222no—
676D4—2448no—
677D4—2442no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—612no—
688C2×C4—612no—
689C2×C4—612no—
690C2×C4—1228no—
691C2×C4—12216no—
692C2×C4—1222no—
693C2×C4—1224no—
694C2×C4—1222no—
695C2×C4—1222no—
696C2×C4—1222no—
697C2×C4—1224no—
698C2×C4—1228no—
699C2×C4—1222no—
700C2×C4—1222no—
701C2×C4—1222no—
702C2×C4—1222no—
703C2×C4—2448no—
704C2×C4—2442no—
705C2×C4—2442no—
706C2×C4—2448no—
707C2×C4#1451980914yes—
708C2×C4C2×D4×D6112yes—
709C2×C4C2×D4×D6111yescharacteristic
710C2×C4C2×D4×D6112yes—
711C2×C4#41×D6112yes—
712C2×C4C2×#1175822212yes—
713C2×C4C24×D6111yescharacteristic
714C8—22no—
715C8—22no—
716C8—1222no—
717C8—1222no—
718C22—614no—
719C22—1228no—
720C22—1222no—
721C22—1222no—
722C22—4884no—
723C22—2442no—
724C22—2442no—
725C22—2442no—
726C22#1684027112yes—
727C22#135×D6112yes—
728C22C2×#1451980912yes—
729C22C22×D4×D6111yescharacteristic
730C4—22no—
731C4—24no—
732C4—42no—
733C4—42no—
734C4—42no—
735C4—1222no—
736C4—1222no—
737C4—1222no—
738C4—1224no—
739C4—2442no—
740C4—2442no—
741C4#1684027112yes—
742C4C2×#1451980914yes—
743C4C2×#41×D6111yescharacteristic
744C4C22×#1175822211yescharacteristic
745C2—1224no—
746C2—4882no—
747C2#2145590314yesdirect product factor
748C2C2×#1684027111yescharacteristic
749C2C2×#135×D6111yescharacteristic
750C2C22×#1451980911yescharacteristic
subgroupG/H
centerC22×C4D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C4×Q16×C61C2
socleC23×C61C22×D4
prime radicalC2×#14519752C22
hypercenterC2×C4×Q16D61
hypocenterC61C2×#3108
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
2. C2×C4×Q8×D61C2semidirect
3. #21455903C2direct (N × H)
4. C2×#16840091C2semidirect
6. C2×#16840068C2semidirect
7. C2×#16840067C2semidirect
8. C2×#16839987C2semidirect
9. C2×#16839986C2semidirect
10. C2×#16839916C2semidirect
12. C2×C4×#11758202C2semidirect
13. C2×C4×#11758190C2semidirect
14. C2×C4×#11758201C2semidirect
15. C2×#16839813C2semidirect
16. C2×C4×Q16×C61C2semidirect
35. C4×Q8×D61C22semidirect
43. #16840091C22semidirect
45. #16840068C22semidirect
46. #16840067C22semidirect
47. #16839987C22semidirect
48. #16839986C22semidirect
49. #16839916C22semidirect
51. C4×#11758202C22semidirect
52. C4×#11758190C22semidirect
53. C4×#11758201C22semidirect
54. #16839813C22semidirect
72. C4×Q16×C61C22semidirect
382. C2×C4×Q16D61semidirect
386. C2×C61#3108semidirect
430. C4×Q16C2×D61semidirect
452. C61C2×#3108semidirect
747. C2#21455903direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168402992
C2×C4×Q8×D612
#214559032
C2×#168400912
C2×#168400772
C2×#168400682
C2×#168400672
C2×#168399872
C2×#168399862
C2×#168399162
C2×#168399022
C2×C4×#117582022
C2×C4×#117581902
C2×C4×#117582012
C2×#168398132
C2×C4×Q16×C612
C2×#310861