Finite Group Databasebeta

← C2×#21457275 #30552973

Subgroups — C2×#21457275 #30552973

Order 15616.

1882 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×#16840383C211yesmaximal, characteristic, complemented
2#21457275C2116yesmaximal, direct product factor
3C2×#16840057C211yesmaximal, characteristic, complemented
4C2×#16840054C211yesmaximal, characteristic, complemented
5C2×#16840042C211yesmaximal, characteristic, complemented
6C2×#16840039C211yesmaximal, characteristic, complemented
7C2×#16840010C211yesmaximal, characteristic, complemented
8C2×#16840006C211yesmaximal, characteristic, complemented
9C2×#16840001C211yesmaximal, characteristic, complemented
10C2×#16839996C211yesmaximal, characteristic
11C2×#16839984C211yesmaximal, characteristic, complemented
12C2×#16839981C211yesmaximal, characteristic, complemented
13C2×#16839977C211yesmaximal, characteristic, complemented
14C2×#16839974C211yesmaximal, characteristic, complemented
15C2×#16839789C211yesmaximal, characteristic, complemented
16C2×C61×#542C211yesmaximal, characteristic, complemented
17C22×#11758202C2211yescharacteristic
18C22×#11758200C2211yescharacteristic
19C22×#11758201C2211yescharacteristic
20C22×#11758199C2211yescharacteristic
21C22×#11758194C2211yescharacteristic
22C23×#92418C2211yescharacteristic
23#16840383—24no—
24#16840383C2218yescomplemented
25C2×#14519777C2211yescharacteristic
26C2×#14519772—21no—
27C2×#14519765C2211yescharacteristic
28C2×#14519763—21no—
29C2×#14519759—21no—
30C2×#14519756C2211yescharacteristic
31C2×#14519755—21no—
32C2×#14519751C2211yescharacteristic
33C2×C4×Dic122C2211yescharacteristic
34C2×C4×D244C2211yescharacteristic
35#16840057C2218yescomplemented
36#16840054C2218yescomplemented
37#16840042C2218yescomplemented
38#16840039C2218yescomplemented
39#16840010C2218yescomplemented
40#16840006C2218yescomplemented
41#16840001C2218yescomplemented
42#16839996C2218yes—
43#16839984C2218yescomplemented
44#16839981C2218yescomplemented
45#16839977C2218yescomplemented
46#16839974C2218yescomplemented
47C2×#14519710C2211yescharacteristic
48C2×#14519710C2211yescharacteristic
49C2×#14519710C2211yescharacteristic
50C2×#14519710C2211yescharacteristic
51#16839789C2218yescomplemented
52C2×C4⋊#92418C2211yescharacteristic
53C2×C4⋊#92418C2211yescharacteristic
54C2×C4⋊#92418C2211yescharacteristic
55C2×C4⋊#92418C2211yescharacteristic
56C2×#14519701C2211yescharacteristic
57C2×#14519701C2211yescharacteristic
58C2×#14519700C2211yescharacteristic
59C2×#14519700C2211yescharacteristic
60C2×#14519698C2211yescharacteristic
61C2×#14519698C2211yescharacteristic
62C2×#14519697C2211yescharacteristic
63C2×#14519697C2211yescharacteristic
64C61×#542—24no—
65C61×#542C2218yescomplemented
66C2×C4⋊Q8×C61C2211yescharacteristic
67C2×#126×C61—21no—
68C2×#124×C61—21no—
69C2×#124×C61C2211yescharacteristic
70C2×#123×C61—21no—
71C2×C22⋊Q8×C61—21no—
72C2×C22⋊Q8×C61C2211yescharacteristic
73C2×#121×C61C2211yescharacteristic
74C2×C4×Q8×C61C2211yescharacteristic
75C2×C4×D4×C61C2211yescharacteristic
76C2×#117×C61C2211yescharacteristic
77C22×Dic122—21no—
78C22×Dic122C2311yescharacteristic
79C22×D244C2311yescharacteristic
80C22×C22⋊D61—21no—
81C22×C4×D61—21no—
82C2×#11758202—42no—
83C2×#11758202C2314yes—
84C2×#11758200—42no—
85C2×#11758200C2314yes—
86C2×#11758201—42no—
87C2×#11758201C2314yes—
88C2×#11758199—42no—
89C2×#11758199C2314yes—
90C2×#11758194—42no—
91C2×#11758194C2314yes—
92C22×#92418—42no—
93C22×#92418C2311yescharacteristic
94C22×#92418C2311yescharacteristic
95C22×#92418C2311yescharacteristic
96C22×#92418C2311yescharacteristic
97C22×#92418C2314yes—
98#14519777—22no—
99#14519777C2314yes—
100#14519772—28no—
101#14519765—22no—
102#14519765C2314yes—
103#14519763—28no—
104#14519759—28no—
105#14519756—22no—
106#14519756C2314yes—
107#14519755—28no—
108#14519751—22no—
109#14519751C2314yes—
110C4×Dic122—22no—
111C4×Dic122C2314yes—
112C4×D244—22no—
113C4×D244C2314yes—
114C2×C4⋊Dic61—21no—
115C2×C4⋊Dic61C2311yescharacteristic
116C2×C4⋊Dic61C2311yescharacteristic
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#14519710C2314yes—
128#14519710C2314yes—
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×C61—21no—
142C22×Q8×C61C2311yescharacteristic
143C22×D4×C61—21no—
144C22×D4×C61C2311yescharacteristic
145C23×C4×C61—21no—
146C23×C4×C61C2311yescharacteristic
147C4⋊Q8×C61—22no—
148C4⋊Q8×C61C2314yes—
149#126×C61—28no—
150#124×C61—28no—
151#124×C61—22no—
152#124×C61C2314yes—
153#123×C61—28no—
154C22⋊Q8×C61—22no—
155C22⋊Q8×C61—28no—
156C22⋊Q8×C61C2314yes—
157#121×C61—22no—
158#121×C61C2314yes—
159C4×Q8×C61—22no—
160C4×Q8×C61C2314yes—
161C4×D4×C61—22no—
162C4×D4×C61C2314yes—
163#117×C61D414yes—
164#117×C61C2314yes—
165C2×C4⋊C4×C61—21no—
166C2×C4⋊C4×C61—21no—
167C2×C4⋊C4×C61—21no—
168C2×C4⋊C4×C61D411yescharacteristic
169C2×C4⋊C4×C61D411yescharacteristic
170C2×C4⋊C4×C61C2311yescharacteristic
171C2×C4⋊C4×C61C2311yescharacteristic
172C2×C22⋊C4×C61—21no—
173C2×C22⋊C4×C61—21no—
174C2×C22⋊C4×C61—21no—
175C2×C22⋊C4×C61—21no—
176C2×C22⋊C4×C61—21no—
177C2×C22⋊C4×C61D411yescharacteristic
178C2×C22⋊C4×C61D411yescharacteristic
179C2×C42×C61—21no—
180C2×C42×C61C2311yescharacteristic
181C2×C42×C61C2311yescharacteristic
182C24×C61—21no—
183C24×C61C2×D411yescharacteristic
184C23×D61—21no—
185C2×Q8×C61—21no—
186C2×Q8×C61—24no—
187C2×Q8×C61—22no—
188C2×Q8×C61—22no—
189C2×Q8×C61—82no—
190C2×Q8×C61C2412yes—
191C2×D4×C61—24no—
192C2×D4×C61—21no—
193C2×D4×C61—22no—
194C2×D4×C61—22no—
195C2×D4×C61—82no—
196C2×D4×C61C2412yes—
197C22×C4×C61—22no—
198C22×C4×C61—22no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—24no—
203C22×C4×C61—82no—
204C22×C4×C61C2×D411yescharacteristic
205C22×C4×C61C2×D411yescharacteristic
206C22×C4×C61C2×D411yescharacteristic
207C22×C4×C61C2×D411yescharacteristic
208C22×C4×C61C2×D411yescharacteristic
209C22×C4×C61C2×D412yes—
210C22×C4×C61C2412yes—
211C22×C4×C61C2411yescharacteristic
212C2×C22⋊D61—24no—
213C2×C22⋊D61—82no—
214C22×Dic61—21no—
215C22×Dic61—21no—
216C22×Dic61—21no—
217C2×D244—22no—
218C2×D244—22no—
219C2×D244—21no—
220C2×D244C2412yes—
221C2×C4×D61—24no—
222C2×C4×D61—82no—
223C2×Dic122—22no—
224C2×Dic122—22no—
225C2×Dic122—21no—
226C2×Dic122—24no—
227C2×Dic122—82no—
228C2×Dic122C2412yes—
229C4⋊C4×C61—24no—
230C4⋊C4×C61—24no—
231C4⋊C4×C61—24no—
232C4⋊C4×C61—21no—
233C4⋊C4×C61—21no—
234C4⋊C4×C61C2×D414yes—
235C4⋊C4×C61C2×D414yes—
236C4⋊C4×C61C2412yes—
237C4⋊C4×C61C2412yes—
238C22⋊C4×C61—24no—
239C22⋊C4×C61—24no—
240C22⋊C4×C61—24no—
241C22⋊C4×C61—24no—
242C22⋊C4×C61—24no—
243C22⋊C4×C61C2×D414yes—
244C22⋊C4×C61C2×D414yes—
245C42×C61—24no—
246C42×C61C2×D412yes—
247C42×C61C2×D412yes—
248C42×C61C2412yes—
249C42×C61C2412yes—
250C22⋊Dic61—24no—
251#11758202—44no—
252#11758201—44no—
253#11758200—44no—
254#11758199—44no—
255#11758198—24no—
256#11758198—24no—
257#11758198—24no—
258#11758198—24no—
259C4⋊Dic61—24no—
260C4⋊Dic61—21no—
261C4⋊Dic61—21no—
262C4⋊Dic61C2412yes—
263C4⋊Dic61C2412yes—
264#11758196—24no—
265#11758196—24no—
266C4×Dic61—24no—
267#11758194—44no—
268C2×#92418—22no—
269C2×#92418—22no—
270C2×#92418—22no—
271C2×#92418—22no—
272C2×#92418—44no—
273C2×#92418C2412yes—
274C2×#92418C2412yes—
275C2×#92418C2412yes—
276C2×#92418C2412yes—
277C23×C61—22no—
278C23×C61—22no—
279C23×C61—22no—
280C23×C61—22no—
281C23×C61—42no—
282C23×C61—42no—
283C23×C61—42no—
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—
293Q8×C61—84no—
294D4×C61—22no—
295D4×C61—22no—
296D4×C61—42no—
297D4×C61—84no—
298C2×C4×C61—22no—
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—42no—
310C2×C4×C61—42no—
311C2×C4×C61—42no—
312C2×C4×C61—84no—
313C2×C4×C61C22×D412yes—
314C2×C4×C61C22×D412yes—
315C2×C4×C61C22×D412yes—
316C2×C4×C61C22×D412yes—
317C2×C4×C61C22×D412yes—
318C2×C4×C61C22×D411yescharacteristic
319C2×C4×C61H(5,𝔽2)12yes—
320C2×C4×C612−1+412yes—
321C2×C4×C61C2511yescharacteristic
322C22⋊D61—84no—
323C2×Dic61—22no—
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—42no—
327C2×Dic61—42no—
328C2×Dic61—42no—
329D244—22no—
330D244—22no—
331D244—42no—
332C4×D61—84no—
333Dic122—22no—
334Dic122—22no—
335Dic122—42no—
336Dic122—84no—
337#92418—22no—
338#92418—22no—
339#92418—22no—
340#92418—22no—
341C2×#3262—611nomaximal, Sylow
342C22×C61—22no—
343C22×C61—22no—
344C22×C61—22no—
345C22×C61—44no—
346C22×C61—42no—
347C22×C61—42no—
348C22×C61—42no—
349C22×C61—84no—
350C22×C61#53712yes—
351C22×C61#57612yes—
352C22×C61#57812yes—
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×#542—611no—
373C2×#542D6111yescharacteristic, complemented
374#3262—6116no—
375C2×#477—611no—
376C2×#477—611no—
377C2×#474—611no—
378C2×#474—611no—
379C2×#468—611no—
380C2×#468—611no—
381C2×#467—611no—
382C2×#466—611no—
383C2×#464—611no—
384C2×#464—611no—
385C2×#463—611no—
386C2×#463—611no—
387C2×#424—611no—
388C2×C61—42no—
389C2×C61—82no—
390C2×C61#326214yescomplemented
391C2×C61C2×#53711yescharacteristic
392C2×C61C2×#57611yescharacteristic
393C2×C61C2×#57811yescharacteristic
394D61—82no—
395C22×Q16—611no—
396C22×SD16—611no—
397C22×SD16—611no—
398C22×D8—611no—
399C22×M16—611no—
400C23×C8—611no—
401#542—24no—
402#542—618no—
403#542—1224no—
404#542C2×D6118yescomplemented
405C2×C4⋊Q8—611no—
406C2×C4⋊Q8C2×D6111yescharacteristic
407C2×#126—21no—
408C2×#126—1221no—
409C2×#124—21no—
410C2×#124—611no—
411C2×#124—1221no—
412C2×#124C2×D6111yescharacteristic
413C2×#123—21no—
414C2×#123—1221no—
415C2×C22⋊Q8—21no—
416C2×C22⋊Q8—611no—
417C2×C22⋊Q8—1221no—
418C2×C22⋊Q8C2×D6111yescharacteristic
419C2×#121—611no—
420C2×#121C2×D6111yescharacteristic
421C2×C4×Q8—611no—
422C2×C4×Q8C2×D6111yescharacteristic
423C2×C4×D4—611no—
424C2×C4×D4C2×D6111yescharacteristic
425C2×#117C2×D6111yescharacteristic
426#477—618no—
427#477—618no—
428#474—618no—
429#474—618no—
430#468—618no—
431#468—618no—
432#467—618no—
433#466—618no—
434#464—618no—
435#464—618no—
436#463—618no—
437#463—618no—
438C2×#107—611no—
439C2×#107—611no—
440C2×#107—611no—
441C2×#107—611no—
442#424—618no—
443C2×C4⋊C8—611no—
444C2×C4⋊C8—611no—
445C2×C4⋊C8—611no—
446C2×C4⋊C8—611no—
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×#326211yescharacteristic, complemented, Sylow
456C22×Q8—21no—
457C22×Q8—611no—
458C22×Q8—1221no—
459C22×Q8C22×D6111yescharacteristic
460C22×D4—21no—
461C22×D4—611no—
462C22×D4—1221no—
463C22×D4C22×D6111yescharacteristic
464C23×C4—21no—
465C23×C4—1221no—
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—
475C2×M16—614no—
476C2×M16—2442no—
477C22×C8—611no—
478C22×C8—611no—
479C22×C8—611no—
480C22×C8—611no—
481C22×C8—614no—
482C22×C8—2442no—
483C4⋊Q8—22no—
484C4⋊Q8—614no—
485C4⋊Q8—1222no—
486C4⋊Q8C22×D6114yes—
487#126—28no—
488#126—1228no—
489#124—28no—
490#124—22no—
491#124—614no—
492#124—1228no—
493#124—1222no—
494#124C22×D6114yes—
495#123—28no—
496#123—1228no—
497C22⋊Q8—22no—
498C22⋊Q8—28no—
499C22⋊Q8—614no—
500C22⋊Q8—1222no—
501C22⋊Q8—1228no—
502C22⋊Q8C22×D6114yes—
503#121—22no—
504#121—614no—
505#121—1222no—
506#121C22×D6114yes—
507C4×Q8—22no—
508C4×Q8—614no—
509C4×Q8—1222no—
510C4×Q8C22×D6114yes—
511C4×D4—22no—
512C4×D4—614no—
513C4×D4—1222no—
514C4×D4C22×D6114yes—
515#117C22⋊D6114yes—
516#117C22×D6114yes—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—611no—
521C2×C4⋊C4—611no—
522C2×C4⋊C4—1221no—
523C2×C4⋊C4—1221no—
524C2×C4⋊C4—1221no—
525C2×C4⋊C4C22⋊D6111yescharacteristic
526C2×C4⋊C4C22⋊D6111yescharacteristic
527C2×C4⋊C4C22×D6111yescharacteristic
528C2×C4⋊C4C22×D6111yescharacteristic
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—1221no—
535C2×C22⋊C4—1221no—
536C2×C22⋊C4—1221no—
537C2×C22⋊C4—1221no—
538C2×C22⋊C4—1221no—
539C2×C22⋊C4C22⋊D6111yescharacteristic
540C2×C22⋊C4C22⋊D6111yescharacteristic
541C2×C42—21no—
542C2×C42—1221no—
543C2×C42C22×D6111yescharacteristic
544C2×C42C22×D6111yescharacteristic
545#107—614no—
546#107—614no—
547#107—614no—
548#107—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—24no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—82no—
569C2×Q8—612no—
570C2×Q8—1224no—
571C2×Q8—1221no—
572C2×Q8—1222no—
573C2×Q8—1222no—
574C2×Q8—4882no—
575C2×Q8C23×D6112yes—
576C2×D4—24no—
577C2×D4—21no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—82no—
581C2×D4—612no—
582C2×D4—1224no—
583C2×D4—1221no—
584C2×D4—1222no—
585C2×D4—1222no—
586C2×D4—4882no—
587C2×D4C23×D6112yes—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—24no—
594C22×C4—82no—
595C22×C4—1221no—
596C22×C4—1221no—
597C22×C4—1221no—
598C22×C4—1224no—
599C22×C4—4882no—
600C22×C4C2×C22⋊D6112yes—
601C22×C4C2×C22⋊D6111yescharacteristic
602C22×C4C2×C22⋊D6111yescharacteristic
603C22×C4C2×C22⋊D6111yescharacteristic
604C22×C4C2×C22⋊D6111yescharacteristic
605C22×C4C2×C22⋊D6111yescharacteristic
606C22×C4C23×D6112yes—
607C22×C4C23×D6111yescharacteristic
608Q16—2444no—
609SD16—2444no—
610SD16—2444no—
611D8—2444no—
612M16—2444no—
613C2×C8—612no—
614C2×C8—612no—
615C2×C8—612no—
616C2×C8—612no—
617C2×C8—1222no—
618C2×C8—1222no—
619C2×C8—1222no—
620C2×C8—1222no—
621C2×C8—2444no—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—24no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—612no—
628C4⋊C4—612no—
629C4⋊C4—1221no—
630C4⋊C4—1221no—
631C4⋊C4—1224no—
632C4⋊C4—1224no—
633C4⋊C4—1224no—
634C4⋊C4C2×C22⋊D6114yes—
635C4⋊C4C2×C22⋊D6114yes—
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—
648C22⋊C4C2×C22⋊D6114yes—
649C22⋊C4C2×C22⋊D6114yes—
650C42—24no—
651C42—1224no—
652C42C2×C22⋊D6112yes—
653C42C2×C22⋊D6112yes—
654C42C23×D6112yes—
655C42C23×D6112yes—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—1222no—
664C23—2442no—
665C23—2442no—
666C23—2442no—
667C23C22×C22⋊D6112yes—
668C23C22×C22⋊D6111yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—42no—
672Q8—84no—
673Q8—1222no—
674Q8—1222no—
675Q8—4884no—
676Q8—2442no—
677D4—22no—
678D4—22no—
679D4—42no—
680D4—84no—
681D4—1222no—
682D4—1222no—
683D4—4884no—
684D4—2442no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—84no—
700C2×C4—1222no—
701C2×C4—1222no—
702C2×C4—1222no—
703C2×C4—4884no—
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—22no—
721C22—22no—
722C22—22no—
723C22—44no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—84no—
728C22—4884no—
729C22—2442no—
730C22—2442no—
731C22—2442no—
732C22#1684034012yes—
733C22#1684056512yes—
734C22#1684057712yes—
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—42no—
751C2—82no—
752C2—4882no—
753C2#2145727514yesdirect product factor
754C2C2×#1684034011yescharacteristic
755C2C2×#1684056511yescharacteristic
756C2C2×#1684057711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#542C2
socleC23×C61C22×D4
prime radicalC2×#16839996C2
hypercenterC2×#542D61
hypocenterC61C2×#3262
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#16840383C2semidirect
2. #21457275C2direct (N × H)
3. C2×#16840057C2semidirect
4. C2×#16840054C2semidirect
5. C2×#16840042C2semidirect
6. C2×#16840039C2semidirect
7. C2×#16840010C2semidirect
8. C2×#16840006C2semidirect
9. C2×#16840001C2semidirect
11. C2×#16839984C2semidirect
12. C2×#16839981C2semidirect
13. C2×#16839977C2semidirect
14. C2×#16839974C2semidirect
15. C2×#16839789C2semidirect
16. C2×C61×#542C2semidirect
24. #16840383C22semidirect
35. #16840057C22semidirect
36. #16840054C22semidirect
37. #16840042C22semidirect
38. #16840039C22semidirect
39. #16840010C22semidirect
40. #16840006C22semidirect
41. #16840001C22semidirect
43. #16839984C22semidirect
44. #16839981C22semidirect
45. #16839977C22semidirect
46. #16839974C22semidirect
51. #16839789C22semidirect
65. C61×#542C22semidirect
373. C2×#542D61semidirect
390. C2×C61#3262semidirect
404. #542C2×D61semidirect
455. C61C2×#3262semidirect
753. C2#21457275direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403832
#214572752
C2×#168400572
C2×#168400542
C2×#168400422
C2×#168400392
C2×#168400102
C2×#168400062
C2×#168400012
C2×#168399962
C2×#168399842
C2×#168399812
C2×#168399772
C2×#168399742
C2×#168397892
C2×C61×#5422
C2×#326261