Finite Group Databasebeta

← C2×#21457166 #30552830

Subgroups — C2×#21457166 #30552830

Order 15616.

1962 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×#16840296C211yesmaximal, characteristic, complemented
2#21457166C2116yesmaximal, direct product factor
3C2×#16840069C211yesmaximal, characteristic, complemented
4C2×#16840066C211yesmaximal, characteristic, complemented
5C2×#16840062C211yesmaximal, characteristic, complemented
6C2×#16840059C211yesmaximal, characteristic, complemented
7C2×#16840001C211yesmaximal, characteristic, complemented
8C2×#16839996C211yesmaximal, characteristic
9C2×#16839993C211yesmaximal, characteristic, complemented
10C2×#16839989C211yesmaximal, characteristic, complemented
11C2×#16839984C211yesmaximal, characteristic, complemented
12C2×#16839981C211yesmaximal, characteristic, complemented
13C2×#16839977C211yesmaximal, characteristic, complemented
14C2×#16839974C211yesmaximal, characteristic, complemented
15C22×C4⋊#92418C211yesmaximal, characteristic, complemented
16C2×C61×#529C211yesmaximal, characteristic, complemented
17C22×#11758202C2211yescharacteristic
18C22×#11758200C2211yescharacteristic
19C22×#11758201C2211yescharacteristic
20C22×#11758199C2211yescharacteristic
21C23×#92418C2211yescharacteristic
22C23×#92418C2211yescharacteristic
23#16840296—24no—
24#16840296C2218yescomplemented
25C2×#14519771—21no—
26C2×#14519769C2211yescharacteristic
27C2×#14519765C2211yescharacteristic
28C2×#14519760—21no—
29C2×#14519756C2211yescharacteristic
30C2×#14519751C2211yescharacteristic
31C2×C4×Dic122C2211yescharacteristic
32C2×C4×D244C2211yescharacteristic
33C2×C4×C22⋊D61—21no—
34C2×#14519734—21no—
35#16840069C2218yescomplemented
36#16840066C2218yescomplemented
37#16840062C2218yescomplemented
38#16840059C2218yescomplemented
39#16840001C2218yescomplemented
40#16839996C2218yes—
41#16839993C2218yescomplemented
42#16839989C2218yescomplemented
43#16839984C2218yescomplemented
44#16839981C2218yescomplemented
45#16839977C2218yescomplemented
46#16839974C2218yescomplemented
47C2×#14519710C2211yescharacteristic
48C2×#14519710C2211yescharacteristic
49C2×#14519708C2211yescharacteristic
50C2×#14519708C2211yescharacteristic
51C2×C4⋊#92418C2211yescharacteristic
52C2×C4⋊#92418C2211yescharacteristic
53C2×C4⋊#92418C2211yescharacteristic
54C2×C4⋊#92418C2211yescharacteristic
55C2×C4⋊#92418C2218yescomplemented
56C2×#14519701C2211yescharacteristic
57C2×#14519701C2211yescharacteristic
58C2×#14519700C2211yescharacteristic
59C2×#14519700C2211yescharacteristic
60C2×#14519698C2211yescharacteristic
61C2×#14519698C2211yescharacteristic
62C2×#14519697C2211yescharacteristic
63C2×#14519697C2211yescharacteristic
64C61×#529—24no—
65C61×#529C2218yescomplemented
66C2×#126×C61—21no—
67C2×#125×C61C2211yescharacteristic
68C2×#124×C61C2211yescharacteristic
69C2×#123×C61—21no—
70C2×C22⋊Q8×C61C2211yescharacteristic
71C2×#121×C61C2211yescharacteristic
72C2×C4×Q8×C61C2211yescharacteristic
73C2×C4×D4×C61—21no—
74C2×C4×D4×C61C2211yescharacteristic
75C2×#117×C61—21no—
76C22×C42×C61C2211yescharacteristic
77C22×Dic122C2311yescharacteristic
78C22×D244C2311yescharacteristic
79C22×C22⋊D61—21no—
80C22×C4×D61—21no—
81C2×#11758202—42no—
82C2×#11758202C2314yes—
83C2×#11758200—42no—
84C2×#11758200C2314yes—
85C2×#11758201—42no—
86C2×#11758201C2314yes—
87C2×#11758199—42no—
88C2×#11758199C2314yes—
89C22×#92418—42no—
90C22×#92418—42no—
91C22×#92418C2311yescharacteristic
92C22×#92418C2311yescharacteristic
93C22×#92418C2311yescharacteristic
94C22×#92418C2311yescharacteristic
95C22×#92418C2314yes—
96C22×#92418C2314yes—
97#14519771—28no—
98#14519769—22no—
99#14519769C2314yes—
100#14519765—22no—
101#14519765C2314yes—
102#14519760—28no—
103#14519756—22no—
104#14519756C2314yes—
105#14519751—22no—
106#14519751C2314yes—
107C4×Dic122—22no—
108C4×Dic122C2314yes—
109C4×D244—22no—
110C4×D244C2314yes—
111C4×C22⋊D61—28no—
112#14519734—28no—
113C2×C4⋊Dic61C2311yescharacteristic
114C2×C4⋊Dic61C2311yescharacteristic
115C2×#11758196—21no—
116C2×#11758196—21no—
117C2×#11758196—21no—
118C2×#11758196—21no—
119C2×C22⋊Dic61—21no—
120C2×#11758198—21no—
121C2×#11758198—21no—
122C2×#11758198—21no—
123C2×#11758198—21no—
124C2×C4×Dic61—21no—
125#14519710C2314yes—
126#14519710C2314yes—
127#14519708C2314yes—
128#14519708C2314yes—
129C4⋊#92418C2314yes—
130C4⋊#92418C2314yes—
131C4⋊#92418C2314yes—
132C4⋊#92418C2314yes—
133#14519701C2314yes—
134#14519701C2314yes—
135#14519700C2314yes—
136#14519700C2314yes—
137#14519698C2314yes—
138#14519698C2314yes—
139#14519697C2314yes—
140#14519697C2314yes—
141C22×Q8×C61C2311yescharacteristic
142C22×D4×C61—21no—
143C22×D4×C61C2311yescharacteristic
144C23×C4×C61—21no—
145C23×C4×C61D411yescharacteristic
146C23×C4×C61D411yescharacteristic
147C23×C4×C61C2311yescharacteristic
148#126×C61—28no—
149#125×C61—22no—
150#125×C61C2314yes—
151#124×C61—22no—
152#124×C61C2314yes—
153#123×C61—28no—
154C22⋊Q8×C61—22no—
155C22⋊Q8×C61C2314yes—
156#121×C61—22no—
157#121×C61C2314yes—
158C4×Q8×C61—22no—
159C4×Q8×C61C2314yes—
160C4×D4×C61—28no—
161C4×D4×C61—22no—
162C4×D4×C61C2314yes—
163#117×C61—28no—
164C2×C4⋊C4×C61—21no—
165C2×C4⋊C4×C61—21no—
166C2×C4⋊C4×C61—21no—
167C2×C4⋊C4×C61—21no—
168C2×C4⋊C4×C61C2311yescharacteristic
169C2×C4⋊C4×C61C2311yescharacteristic
170C2×C22⋊C4×C61—21no—
171C2×C22⋊C4×C61—21no—
172C2×C22⋊C4×C61—21no—
173C2×C22⋊C4×C61—21no—
174C2×C22⋊C4×C61—21no—
175C2×C42×C61—21no—
176C2×C42×C61D411yescharacteristic
177C2×C42×C61D411yescharacteristic
178C2×C42×C61D414yes—
179C2×C42×C61C2311yescharacteristic
180C2×C42×C61C2311yescharacteristic
181C2×C42×C61C2314yes—
182C24×C61—21no—
183C24×C61C2×D411yescharacteristic
184C23×D61—21no—
185C2×Q8×C61—21no—
186C2×Q8×C61—22no—
187C2×Q8×C61—22no—
188C2×Q8×C61C2412yes—
189C2×D4×C61—24no—
190C2×D4×C61—21no—
191C2×D4×C61—22no—
192C2×D4×C61—22no—
193C2×D4×C61—44no—
194C2×D4×C61C2412yes—
195C22×C4×C61—24no—
196C22×C4×C61—22no—
197C22×C4×C61—22no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—24no—
202C22×C4×C61—42no—
203C22×C4×C61—44no—
204C22×C4×C61C2×D411yescharacteristic
205C22×C4×C61C2×D411yescharacteristic
206C22×C4×C61C2×D411yescharacteristic
207C22×C4×C61C2×D412yes—
208C22×C4×C61C2×D411yescharacteristic
209C22×C4×C61C2×D411yescharacteristic
210C22×C4×C61C2×D414yes—
211C22×C4×C61C2×D414yes—
212C22×C4×C61C2412yes—
213C22×C4×C61C2411yescharacteristic
214C2×C22⋊D61—24no—
215C2×C22⋊D61—44no—
216C22×Dic61—21no—
217C22×Dic61—21no—
218C22×Dic61—21no—
219C2×D244—22no—
220C2×D244—22no—
221C2×D244—21no—
222C2×D244C2412yes—
223C2×C4×D61—24no—
224C2×C4×D61—44no—
225C2×Dic122—22no—
226C2×Dic122—22no—
227C2×Dic122—21no—
228C2×Dic122C2412yes—
229C4⋊C4×C61—24no—
230C4⋊C4×C61—24no—
231C4⋊C4×C61—24no—
232C4⋊C4×C61—24no—
233C4⋊C4×C61—21no—
234C4⋊C4×C61—21no—
235C4⋊C4×C61C2412yes—
236C4⋊C4×C61C2412yes—
237C22⋊C4×C61—24no—
238C22⋊C4×C61—24no—
239C22⋊C4×C61—24no—
240C22⋊C4×C61—24no—
241C22⋊C4×C61—24no—
242C42×C61—24no—
243C42×C61C2×D414yes—
244C42×C61C2×D412yes—
245C42×C61C2×D412yes—
246C42×C61C2×D414yes—
247C42×C61C2412yes—
248C42×C61C2412yes—
249C22⋊Dic61—24no—
250#11758202—44no—
251#11758201—44no—
252#11758200—44no—
253#11758199—44no—
254#11758198—24no—
255#11758198—24no—
256#11758198—24no—
257#11758198—24no—
258C4⋊Dic61—21no—
259C4⋊Dic61—21no—
260C4⋊Dic61C2412yes—
261C4⋊Dic61C2412yes—
262#11758196—24no—
263#11758196—24no—
264#11758196—24no—
265#11758196—24no—
266C4×Dic61—24no—
267C2×#92418—22no—
268C2×#92418—22no—
269C2×#92418—22no—
270C2×#92418—22no—
271C2×#92418—44no—
272C2×#92418—44no—
273C2×#92418C2412yes—
274C2×#92418C2412yes—
275C2×#92418C2412yes—
276C2×#92418C2412yes—
277C23×C61—22no—
278C23×C61—22no—
279C23×C61—22no—
280C23×C61—42no—
281C23×C61—42no—
282C23×C61—42no—
283C23×C61#13514yes—
284C23×C61C22×D412yes—
285C23×C61C22×D411yescharacteristic
286C22×D61—22no—
287C22×D61—42no—
288C22×D61—42no—
289C22×D61—42no—
290Q8×C61—22no—
291Q8×C61—22no—
292Q8×C61—42no—
293D4×C61—22no—
294D4×C61—22no—
295D4×C61—48no—
296D4×C61—42no—
297C2×C4×C61—22no—
298C2×C4×C61—28no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—24no—
304C2×C4×C61—22no—
305C2×C4×C61—22no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—44no—
310C2×C4×C61—48no—
311C2×C4×C61—42no—
312C2×C4×C61—42no—
313C2×C4×C61—42no—
314C2×C4×C61C22×D412yes—
315C2×C4×C61C22×D412yes—
316C2×C4×C61C22×D412yes—
317C2×C4×C61C22×D412yes—
318C2×C4×C61C22×D412yes—
319C2×C4×C61C22×D411yescharacteristic
320C2×C4×C61H(5,𝔽2)12yes—
321C2×C4×C612−1+412yes—
322C2×C4×C61C2511yescharacteristic
323C22⋊D61—48no—
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61—42no—
328C2×Dic61—42no—
329C2×Dic61—42no—
330D244—22no—
331D244—22no—
332D244—42no—
333C4×D61—48no—
334Dic122—22no—
335Dic122—22no—
336Dic122—42no—
337#92418—22no—
338#92418—22no—
339#92418—22no—
340#92418—22no—
341C2×#3250—611nomaximal, Sylow
342C22×C61—22no—
343C22×C61—28no—
344C22×C61—22no—
345C22×C61—42no—
346C22×C61—42no—
347C22×C61—42no—
348C22×C61—84no—
349C22×C61#53712yes—
350C22×C61C2×#13514yes—
351C22×C61C2×#13512yes—
352C22×C61#57512yes—
353C22×C61C23×D411yescharacteristic
354C2×D61—42no—
355C2×D61—42no—
356C2×D61—42no—
357C2×D61—84no—
358C4×C61—22no—
359C4×C61—22no—
360C4×C61—22no—
361C4×C61—22no—
362C4×C61—22no—
363C4×C61—42no—
364C4×C61—42no—
365C4×C61—42no—
366C4×C61#53712yes—
367C4×C61C2×H(5,𝔽2)11yescharacteristic
368C4×C61C2×2−1+411yescharacteristic
369Dic61—42no—
370Dic61—42no—
371Dic61—42no—
372C2×#529—611no—
373C2×#529D6111yescharacteristic, complemented
374#3250—6116no—
375C2×#479—611no—
376C2×#479—611no—
377C2×#478—611no—
378C2×#478—611no—
379C2×#467—611no—
380C2×#466—611no—
381C2×#465—611no—
382C2×#465—611no—
383C2×#464—611no—
384C2×#464—611no—
385C2×#463—611no—
386C2×#463—611no—
387C22×C4⋊C8—611no—
388C2×C61—24no—
389C2×C61—82no—
390C2×C61#325014yescomplemented
391C2×C61C2×#53711yescharacteristic
392C2×C61C22×#13511yescharacteristic
393C2×C61C2×#57511yescharacteristic
394D61—82no—
395C22×Q16—611no—
396C22×SD16—611no—
397C22×SD16—611no—
398C22×D8—611no—
399C23×C8—611no—
400C23×C8—611no—
401#529—24no—
402#529—618no—
403#529—1224no—
404#529C2×D6118yescomplemented
405C2×#126—21no—
406C2×#126—1221no—
407C2×#125—611no—
408C2×#125C2×D6111yescharacteristic
409C2×#124—611no—
410C2×#124C2×D6111yescharacteristic
411C2×#123—21no—
412C2×#123—1221no—
413C2×C22⋊Q8—611no—
414C2×C22⋊Q8C2×D6111yescharacteristic
415C2×#121—611no—
416C2×#121C2×D6111yescharacteristic
417C2×C4×Q8—611no—
418C2×C4×Q8C2×D6111yescharacteristic
419C2×C4×D4—21no—
420C2×C4×D4—611no—
421C2×C4×D4—1221no—
422C2×C4×D4C2×D6111yescharacteristic
423C2×#117—21no—
424C2×#117—1221no—
425C22×C42C2×D6111yescharacteristic
426#479—618no—
427#479—618no—
428#478—618no—
429#478—618no—
430#467—618no—
431#466—618no—
432#465—618no—
433#465—618no—
434#464—618no—
435#464—618no—
436#463—618no—
437#463—618no—
438C2×#107—611no—
439C2×#107—611no—
440C2×#106—611no—
441C2×#106—611no—
442C2×C4⋊C8—611no—
443C2×C4⋊C8—611no—
444C2×C4⋊C8—611no—
445C2×C4⋊C8—611no—
446C2×C4⋊C8—618no—
447C2×#103—611no—
448C2×#103—611no—
449C2×#103—611no—
450C2×#103—611no—
451C2×#102—611no—
452C2×#102—611no—
453C2×#102—611no—
454C2×#102—611no—
455C61C2×#325011yescharacteristic, complemented, Sylow
456C22×Q8—611no—
457C22×Q8C22×D6111yescharacteristic
458C22×D4—21no—
459C22×D4—611no—
460C22×D4—1221no—
461C22×D4C22×D6111yescharacteristic
462C23×C4—21no—
463C23×C4—1221no—
464C23×C4C22⋊D6111yescharacteristic
465C23×C4C22⋊D6111yescharacteristic
466C23×C4C22×D6111yescharacteristic
467C2×Q16—614no—
468C2×Q16—2442no—
469C2×SD16—614no—
470C2×SD16—614no—
471C2×SD16—2442no—
472C2×SD16—2442no—
473C2×D8—614no—
474C2×D8—2442no—
475C22×C8—611no—
476C22×C8—611no—
477C22×C8—611no—
478C22×C8—611no—
479C22×C8—614no—
480C22×C8—614no—
481C22×C8—2442no—
482C22×C8—2442no—
483#126—28no—
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—28no—
494#123—1228no—
495C22⋊Q8—22no—
496C22⋊Q8—614no—
497C22⋊Q8—1222no—
498C22⋊Q8C22×D6114yes—
499#121—22no—
500#121—614no—
501#121—1222no—
502#121C22×D6114yes—
503C4×Q8—22no—
504C4×Q8—614no—
505C4×Q8—1222no—
506C4×Q8C22×D6114yes—
507C4×D4—28no—
508C4×D4—22no—
509C4×D4—614no—
510C4×D4—1228no—
511C4×D4—1222no—
512C4×D4C22×D6114yes—
513#117—28no—
514#117—1228no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—611no—
520C2×C4⋊C4—611no—
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—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—1221no—
533C2×C22⋊C4—1221no—
534C2×C22⋊C4—1221no—
535C2×C22⋊C4—1221no—
536C2×C22⋊C4—1221no—
537C2×C42—21no—
538C2×C42—1221no—
539C2×C42C22⋊D6111yescharacteristic
540C2×C42C22⋊D6111yescharacteristic
541C2×C42C22⋊D6114yes—
542C2×C42C22×D6111yescharacteristic
543C2×C42C22×D6111yescharacteristic
544C2×C42C22×D6114yes—
545#107—614no—
546#107—614no—
547#106—614no—
548#106—614no—
549C4⋊C8—614no—
550C4⋊C8—614no—
551C4⋊C8—614no—
552C4⋊C8—614no—
553#103—614no—
554#103—614no—
555#103—614no—
556#103—614no—
557#102—614no—
558#102—614no—
559#102—614no—
560#102—614no—
561C24—21no—
562C24—1221no—
563C24C2×C22⋊D6111yescharacteristic
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—24no—
573C2×D4—21no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—44no—
577C2×D4—612no—
578C2×D4—1224no—
579C2×D4—1221no—
580C2×D4—1222no—
581C2×D4—1222no—
582C2×D4—2444no—
583C2×D4C23×D6112yes—
584C22×C4—24no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—24no—
591C22×C4—42no—
592C22×C4—44no—
593C22×C4—1221no—
594C22×C4—1221no—
595C22×C4—1221no—
596C22×C4—1224no—
597C22×C4—2444no—
598C22×C4C2×C22⋊D6112yes—
599C22×C4C2×C22⋊D6114yes—
600C22×C4C2×C22⋊D6111yescharacteristic
601C22×C4C2×C22⋊D6111yescharacteristic
602C22×C4C2×C22⋊D6111yescharacteristic
603C22×C4C2×C22⋊D6111yescharacteristic
604C22×C4C2×C22⋊D6111yescharacteristic
605C22×C4C2×C22⋊D6114yes—
606C22×C4C23×D6112yes—
607C22×C4C23×D6111yescharacteristic
608Q16—2444no—
609SD16—2444no—
610SD16—2444no—
611D8—2444no—
612C2×C8—612no—
613C2×C8—612no—
614C2×C8—612no—
615C2×C8—612no—
616C2×C8—1222no—
617C2×C8—1222no—
618C2×C8—1222no—
619C2×C8—1222no—
620C2×C8—2444no—
621C2×C8—2444no—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—24no—
625C4⋊C4—24no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—612no—
629C4⋊C4—612no—
630C4⋊C4—1221no—
631C4⋊C4—1221no—
632C4⋊C4—1224no—
633C4⋊C4—1224no—
634C4⋊C4—1224no—
635C4⋊C4—1224no—
636C4⋊C4C23×D6112yes—
637C4⋊C4C23×D6112yes—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—24no—
641C22⋊C4—24no—
642C22⋊C4—24no—
643C22⋊C4—1224no—
644C22⋊C4—1224no—
645C22⋊C4—1224no—
646C22⋊C4—1224no—
647C22⋊C4—1224no—
648C42—24no—
649C42—1224no—
650C42C2×C22⋊D6114yes—
651C42C2×C22⋊D6114yes—
652C42C2×C22⋊D6112yes—
653C42C2×C22⋊D6112yes—
654C42C23×D6112yes—
655C42C23×D6112yes—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—1222no—
663C23—2442no—
664C23—2442no—
665C23—2442no—
666C23#1451979714yes—
667C23C22×C22⋊D6112yes—
668C23C22×C22⋊D6111yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—42no—
672Q8—1222no—
673Q8—1222no—
674Q8—2442no—
675D4—22no—
676D4—22no—
677D4—48no—
678D4—42no—
679D4—1222no—
680D4—1222no—
681D4—2448no—
682D4—2442no—
683C2×C4—28no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—24no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—44no—
696C2×C4—48no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—1222no—
701C2×C4—1222no—
702C2×C4—1222no—
703C2×C4—2448no—
704C2×C4—2442no—
705C2×C4—2442no—
706C2×C4—2442no—
707C2×C4C22×C22⋊D6112yes—
708C2×C4C22×C22⋊D6112yes—
709C2×C4C22×C22⋊D6112yes—
710C2×C4C22×C22⋊D6112yes—
711C2×C4C22×C22⋊D6112yes—
712C2×C4C22×C22⋊D6111yescharacteristic
713C2×C4#1451982312yes—
714C2×C4#1451982412yes—
715C2×C4C24×D6111yescharacteristic
716C8—1222no—
717C8—1222no—
718C8—1222no—
719C8—1222no—
720C22—28no—
721C22—22no—
722C22—22no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—84no—
727C22—4884no—
728C22—2442no—
729C22—2442no—
730C22—2442no—
731C22#1684034012yes—
732C22C2×#1451979714yes—
733C22C2×#1451979712yes—
734C22#1684056012yes—
735C22C23×C22⋊D6111yescharacteristic
736C4—22no—
737C4—22no—
738C4—22no—
739C4—22no—
740C4—22no—
741C4—42no—
742C4—42no—
743C4—42no—
744C4—2442no—
745C4—2442no—
746C4—2442no—
747C4#1684034012yes—
748C4C2×#1451982311yescharacteristic
749C4C2×#1451982411yescharacteristic
750C2—24no—
751C2—82no—
752C2—4882no—
753C2#2145716614yesdirect product factor
754C2C2×#1684034011yescharacteristic
755C2C22×#1451979711yescharacteristic
756C2C2×#1684056011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#529C2
socleC23×C61C22×D4
prime radicalC2×#16839996C2
hypercenterC2×#529D61
hypocenterC61C2×#3250
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. C2×#16840296C2semidirect
2. #21457166C2direct (N × H)
3. C2×#16840069C2semidirect
4. C2×#16840066C2semidirect
5. C2×#16840062C2semidirect
6. C2×#16840059C2semidirect
7. C2×#16840001C2semidirect
9. C2×#16839993C2semidirect
10. C2×#16839989C2semidirect
11. C2×#16839984C2semidirect
12. C2×#16839981C2semidirect
13. C2×#16839977C2semidirect
14. C2×#16839974C2semidirect
15. C22×C4⋊#92418C2semidirect
16. C2×C61×#529C2semidirect
24. #16840296C22semidirect
35. #16840069C22semidirect
36. #16840066C22semidirect
37. #16840062C22semidirect
38. #16840059C22semidirect
39. #16840001C22semidirect
41. #16839993C22semidirect
42. #16839989C22semidirect
43. #16839984C22semidirect
44. #16839981C22semidirect
45. #16839977C22semidirect
46. #16839974C22semidirect
55. C2×C4⋊#92418C22semidirect
65. C61×#529C22semidirect
373. C2×#529D61semidirect
390. C2×C61#3250semidirect
404. #529C2×D61semidirect
455. C61C2×#3250semidirect
753. C2#21457166direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168402962
#214571662
C2×#168400692
C2×#168400662
C2×#168400622
C2×#168400592
C2×#168400012
C2×#168399962
C2×#168399932
C2×#168399892
C2×#168399842
C2×#168399812
C2×#168399772
C2×#168399742
C22×C4⋊#924182
C2×C61×#5292
C2×#325061