Finite Group Databasebeta

← C2×#21458646 #30559778

Subgroups — C2×#21458646 #30559778

Order 15616.

1886 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840485C211yesmaximal, characteristic, complemented
2#21458646C2116yesmaximal, direct product factor
3C2×#16840132C211yesmaximal, characteristic, complemented
4C2×#16840124C211yesmaximal, characteristic, complemented
5C2×#16840119C211yesmaximal, characteristic, complemented
6C2×#16840066C211yesmaximal, characteristic, complemented
7C2×#16840044C211yesmaximal, characteristic, complemented
8C2×#16840059C211yesmaximal, characteristic, complemented
9C2×#16839977C211yesmaximal, characteristic
10C2×#16839977C211yesmaximal, characteristic
11C2×#16839967C211yesmaximal, characteristic, complemented
12C2×#16839893C211yesmaximal, characteristic, complemented
13C2×#16839872C211yesmaximal, characteristic
14C2×#16839862C211yesmaximal, characteristic, complemented
15C2×C4×#11758200C211yesmaximal, characteristic, complemented
16C2×C61×#554C211yesmaximal, characteristic, complemented
17C22×#11758200C2211yescharacteristic
18C22×#11758200C2211yescharacteristic
19C22×#11758199C2211yescharacteristic
20#16840485—24no—
21#16840485C2218yescomplemented
22C2×#14519777C2211yescharacteristic
23C2×#14519772—21no—
24C2×#14519772—21no—
25C2×#14519765C2211yescharacteristic
26C2×#14519765C2211yescharacteristic
27C2×#14519753—21no—
28C2×C4×Dic122C2211yescharacteristic
29C2×C4×Dic122C2211yescharacteristic
30C2×C4×D244C2211yescharacteristic
31C2×#14519735—21no—
32#16840132C2218yescomplemented
33#16840124C2218yescomplemented
34#16840119C2218yescomplemented
35#16840066C2218yescomplemented
36#16840059C2218yescomplemented
37#16840044C2218yescomplemented
38#16839977C2218yes—
39#16839977C2218yes—
40#16839967C2218yescomplemented
41#16839893C2218yescomplemented
42#16839872C2218yes—
43#16839862C2218yescomplemented
44C4×#11758200C2218yescomplemented
45C2×#14519710C2211yescharacteristic
46C2×#14519708C2211yescharacteristic
47C2×#14519708C2211yescharacteristic
48C2×C4⋊#92418C2211yescharacteristic
49C2×C4⋊#92418C2211yescharacteristic
50C2×C4⋊#92418C2211yescharacteristic
51C2×#14519700C2211yescharacteristic
52C2×#14519700C2211yescharacteristic
53C2×#14519700C2211yescharacteristic
54C2×#14519700C2211yescharacteristic
55C2×#14519700C2211yescharacteristic
56C2×#14519700C2211yescharacteristic
57C2×#14519698C2211yescharacteristic
58C2×#14519697C2211yescharacteristic
59C2×#14519697C2211yescharacteristic
60C2×#14519697C2211yescharacteristic
61C2×#14519688C2211yescharacteristic
62C2×#14519688C2211yescharacteristic
63C2×C4×#92418C2211yescharacteristic
64C61×#554—24no—
65C61×#554C2218yescomplemented
66C2×C4⋊Q8×C61C2211yescharacteristic
67C2×#125×C61C2211yescharacteristic
68C2×#125×C61C2211yescharacteristic
69C2×C22⋊Q8×C61—21no—
70C2×C22⋊Q8×C61—21no—
71C2×C22⋊Q8×C61—21no—
72C2×C4×Q8×C61C2211yescharacteristic
73C2×C4×D4×C61C2211yescharacteristic
74C2×C4×D4×C61C2211yescharacteristic
75C2×C4×D4×C61C2211yescharacteristic
76C22×C4⋊C4×C61—21no—
77C22×Dic122C2311yescharacteristic
78C22×Dic122C2311yescharacteristic
79C22×D244C2311yescharacteristic
80C22×C4×D61—21no—
81C2×#11758200—24no—
82C2×#11758200—24no—
83C2×#11758200C2314yes—
84C2×#11758200C2314yes—
85C2×#11758199—24no—
86C2×#11758199C2314yes—
87C22×#92418C2311yescharacteristic
88C22×#92418C2311yescharacteristic
89C22×#92418C2311yescharacteristic
90C22×#92418C2311yescharacteristic
91#14519777—22no—
92#14519777C2314yes—
93#14519772—28no—
94#14519772—28no—
95#14519765—22no—
96#14519765—22no—
97#14519765C2314yes—
98#14519765C2314yes—
99#14519753—28no—
100C4×Dic122—22no—
101C4×Dic122—22no—
102C4×Dic122C2314yes—
103C4×Dic122C2314yes—
104C4×D244—22no—
105C4×D244C2314yes—
106#14519735—28no—
107C2×C4⋊Dic61—21no—
108C2×C4⋊Dic61—21no—
109C2×C4⋊Dic61C2311yescharacteristic
110C2×#11758196—21no—
111C2×#11758196—21no—
112C2×#11758198—21no—
113C2×#11758198—21no—
114C2×#11758198—21no—
115C2×#11758198—21no—
116C2×#11758198—21no—
117C2×C4×Dic61—21no—
118C2×C4×Dic61—21no—
119#14519710C2314yes—
120#14519708C2314yes—
121#14519708C2314yes—
122C4⋊#92418C2314yes—
123C4⋊#92418C2314yes—
124C4⋊#92418C2314yes—
125#14519700C2314yes—
126#14519700C2314yes—
127#14519700C2314yes—
128#14519700C2314yes—
129#14519700C2314yes—
130#14519700C2314yes—
131#14519698C2314yes—
132#14519697C2314yes—
133#14519697C2314yes—
134#14519697C2314yes—
135#14519688C2314yes—
136#14519688C2314yes—
137C4×#92418C2314yes—
138C22×Q8×C61—21no—
139C22×Q8×C61D411yescharacteristic
140C22×D4×C61C2311yescharacteristic
141C23×C4×C61—21no—
142C23×C4×C61—21no—
143C23×C4×C61—21no—
144C4⋊Q8×C61—22no—
145C4⋊Q8×C61C2314yes—
146#125×C61—22no—
147#125×C61—22no—
148#125×C61C2314yes—
149#125×C61C2314yes—
150C22⋊Q8×C61—28no—
151C22⋊Q8×C61—28no—
152C22⋊Q8×C61—28no—
153C4×Q8×C61D414yes—
154C4×Q8×C61C2314yes—
155C4×D4×C61—22no—
156C4×D4×C61—22no—
157C4×D4×C61—22no—
158C4×D4×C61C2314yes—
159C4×D4×C61C2314yes—
160C4×D4×C61C2314yes—
161C2×C4⋊C4×C61—21no—
162C2×C4⋊C4×C61—21no—
163C2×C4⋊C4×C61—21no—
164C2×C4⋊C4×C61—21no—
165C2×C4⋊C4×C61—21no—
166C2×C4⋊C4×C61—28no—
167C2×C4⋊C4×C61D411yescharacteristic
168C2×C4⋊C4×C61D411yescharacteristic
169C2×C4⋊C4×C61D411yescharacteristic
170C2×C4⋊C4×C61C2311yescharacteristic
171C2×C4⋊C4×C61C2311yescharacteristic
172C2×C4⋊C4×C61C2311yescharacteristic
173C2×C22⋊C4×C61—21no—
174C2×C22⋊C4×C61—21no—
175C2×C22⋊C4×C61—21no—
176C2×C42×C61C2311yescharacteristic
177C2×C42×C61C2311yescharacteristic
178C2×C42×C61C2311yescharacteristic
179C24×C61—21no—
180C23×D61—21no—
181C2×Q8×C61—24no—
182C2×Q8×C61—42no—
183C2×Q8×C61—82no—
184C2×Q8×C61C2×D414yes—
185C2×D4×C61—21no—
186C2×D4×C61—22no—
187C2×D4×C61#4114yes—
188C2×D4×C61C2412yes—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—24no—
193C22×C4×C61—24no—
194C22×C4×C61—24no—
195C22×C4×C61—44no—
196C22×C4×C61—82no—
197C22×C4×C61—82no—
198C22×C4×C61C2×D411yescharacteristic
199C22×C4×C61C2×D411yescharacteristic
200C22×C4×C61C2×D411yescharacteristic
201C22×C4×C61C2×D411yescharacteristic
202C22×C4×C61C2×D411yescharacteristic
203C22×C4×C61C2×D411yescharacteristic
204C22×C4×C61C2411yescharacteristic
205C22×Dic61—21no—
206C22×Dic61—21no—
207C22×Dic61—21no—
208C2×D244—22no—
209C2×D244—22no—
210C2×D244—21no—
211C2×D244C2412yes—
212C2×C4×D61—24no—
213C2×C4×D61—44no—
214C2×Dic122—22no—
215C2×Dic122—22no—
216C2×Dic122—22no—
217C2×Dic122—22no—
218C2×Dic122—21no—
219C2×Dic122—21no—
220C2×Dic122C2412yes—
221C2×Dic122C2412yes—
222C4⋊C4×C61—24no—
223C4⋊C4×C61—24no—
224C4⋊C4×C61—24no—
225C4⋊C4×C61—24no—
226C4⋊C4×C61—24no—
227C4⋊C4×C61—21no—
228C4⋊C4×C61—21no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61C2×D414yes—
231C4⋊C4×C61C2×D414yes—
232C4⋊C4×C61C2×D414yes—
233C4⋊C4×C61C2412yes—
234C4⋊C4×C61C2412yes—
235C4⋊C4×C61C2412yes—
236C22⋊C4×C61—24no—
237C22⋊C4×C61—24no—
238C22⋊C4×C61—24no—
239C42×C61C2×D412yes—
240C42×C61C2×D412yes—
241C42×C61C2×D412yes—
242C42×C61C2412yes—
243C42×C61C2412yes—
244C42×C61C2412yes—
245#11758200—28no—
246#11758200—28no—
247#11758199—28no—
248#11758198—24no—
249#11758198—24no—
250#11758198—24no—
251#11758198—24no—
252#11758198—24no—
253C4⋊Dic61—24no—
254C4⋊Dic61—24no—
255C4⋊Dic61—21no—
256C4⋊Dic61C2412yes—
257#11758196—24no—
258#11758196—24no—
259C4×Dic61—24no—
260C4×Dic61—24no—
261C2×#92418—22no—
262C2×#92418—22no—
263C2×#92418—22no—
264C2×#92418—22no—
265C2×#92418C2412yes—
266C2×#92418C2412yes—
267C2×#92418C2412yes—
268C2×#92418C2412yes—
269C23×C61—24no—
270C23×C61—22no—
271C23×C61—42no—
272C23×C61—42no—
273C23×C61C22×D411yescharacteristic
274C22×D61—22no—
275C22×D61—42no—
276C22×D61—42no—
277C22×D61—42no—
278Q8×C61—44no—
279Q8×C61—84no—
280D4×C61—24no—
281D4×C61—22no—
282D4×C61C2×#4114yes—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—48no—
293C2×C4×C61—42no—
294C2×C4×C61—42no—
295C2×C4×C61—42no—
296C2×C4×C61—84no—
297C2×C4×C61—84no—
298C2×C4×C61C22×D412yes—
299C2×C4×C61C22×D412yes—
300C2×C4×C61C22×D412yes—
301C2×C4×C61C22×D412yes—
302C2×C4×C61C22×D412yes—
303C2×C4×C61C22×D412yes—
304C2×C4×C61C22×D411yescharacteristic
305C2×C4×C61C2×#4112yes—
306C2×C4×C612−1+412yes—
307C2×C4×C61C2511yescharacteristic
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—22no—
311C2×Dic61—42no—
312C2×Dic61—42no—
313C2×Dic61—42no—
314D244—22no—
315D244—22no—
316D244—42no—
317C4×D61—48no—
318Dic122—22no—
319Dic122—22no—
320Dic122—22no—
321Dic122—22no—
322Dic122—42no—
323Dic122—42no—
324#92418—22no—
325#92418—22no—
326#92418—22no—
327#92418—22no—
328C2×#3376—611nomaximal, Sylow
329C22×C61—24no—
330C22×C61—48no—
331C22×C61—42no—
332C22×C61—42no—
333C22×C61#54812yes—
334C22×C61#57512yes—
335C22×C61#57712yes—
336C22×C61C23×D411yescharacteristic
337C2×D61—42no—
338C2×D61—42no—
339C2×D61—42no—
340C2×D61—84no—
341C4×C61—22no—
342C4×C61—22no—
343C4×C61—22no—
344C4×C61—22no—
345C4×C61—22no—
346C4×C61—22no—
347C4×C61—42no—
348C4×C61—42no—
349C4×C61—42no—
350C4×C61#54812yes—
351C4×C61C22×#4111yescharacteristic
352C4×C61C2×2−1+411yescharacteristic
353Dic61—42no—
354Dic61—42no—
355Dic61—42no—
356C2×#556—611no—
357C2×#554D6111yescharacteristic, complemented
358#3376—6116no—
359C2×#491—611no—
360C2×#489—611no—
361C2×#488—611no—
362C2×#479—611no—
363C2×#475—611no—
364C2×#478—611no—
365C2×#463—611no—
366C2×#463—611no—
367C2×#461—611no—
368C2×#446—611no—
369C2×#442—611no—
370C2×#440—611no—
371C2×C4×SD16—611no—
372C2×C61—44no—
373C2×C61#337614yescomplemented
374C2×C61C2×#54811yescharacteristic
375C2×C61C2×#57511yescharacteristic
376C2×C61C2×#57711yescharacteristic
377D61—82no—
378C22×SD16—611no—
379C22×SD16—611no—
380C22×D8—611no—
381#556—618no—
382#556—1224no—
383#554—24no—
384#554C2×D6118yescomplemented
385C2×C4⋊Q8—611no—
386C2×C4⋊Q8C2×D6111yescharacteristic
387C2×#126—1221no—
388C2×#126—1221no—
389C2×#125C2×D6111yescharacteristic
390C2×#125C2×D6111yescharacteristic
391C2×#124—611no—
392C2×#124—611no—
393C2×C22⋊Q8—21no—
394C2×C22⋊Q8—21no—
395C2×C22⋊Q8—21no—
396C2×C22⋊Q8—1221no—
397C2×C4×Q8—611no—
398C2×C4×Q8—611no—
399C2×C4×Q8C2×D6111yescharacteristic
400C2×C4×D4—611no—
401C2×C4×D4C2×D6111yescharacteristic
402C2×C4×D4C2×D6111yescharacteristic
403C2×C4×D4C2×D6111yescharacteristic
404C2×#117—1221no—
405C22×C4⋊C4—21no—
406#491—618no—
407#489—618no—
408#488—618no—
409#479—618no—
410#478—618no—
411#475—618no—
412#463—618no—
413#463—618no—
414#461—618no—
415#446—618no—
416#442—618no—
417#440—618no—
418C4×SD16—618no—
419C2×#107—611no—
420C2×#106—611no—
421C2×#106—611no—
422C2×C4⋊C8—611no—
423C2×C4⋊C8—611no—
424C2×C4⋊C8—611no—
425C2×#103—611no—
426C2×#103—611no—
427C2×#103—611no—
428C2×#103—611no—
429C2×#103—611no—
430C2×#103—611no—
431C2×#102—611no—
432C2×#102—611no—
433C2×#102—611no—
434C2×#102—611no—
435C2×#97—611no—
436C2×#97—611no—
437C2×C4×C8—611no—
438C61C2×#337611yescharacteristic, complemented, Sylow
439C22×Q8—21no—
440C22×Q8—611no—
441C22×Q8—611no—
442C22×Q8C22⋊D6111yescharacteristic
443C22×D4—611no—
444C22×D4C22×D6111yescharacteristic
445C23×C4—21no—
446C23×C4—21no—
447C23×C4—21no—
448C23×C4—1221no—
449C2×SD16—614no—
450C2×SD16—614no—
451C2×SD16—1224no—
452C2×SD16—1224no—
453C2×D8—614no—
454C2×D8—1224no—
455C22×C8—611no—
456C22×C8—611no—
457C22×C8—611no—
458C22×C8—611no—
459C4⋊Q8—22no—
460C4⋊Q8—614no—
461C4⋊Q8—1222no—
462C4⋊Q8C22×D6114yes—
463#126—1228no—
464#126—1228no—
465#125—22no—
466#125—22no—
467#125C22×D6114yes—
468#125C22×D6114yes—
469#124—614no—
470#124—614no—
471#124—1222no—
472#124—1222no—
473C22⋊Q8—28no—
474C22⋊Q8—28no—
475C22⋊Q8—28no—
476C22⋊Q8—1228no—
477C4×Q8—614no—
478C4×Q8—614no—
479C4×Q8—1222no—
480C4×Q8—1222no—
481C4×Q8C22⋊D6114yes—
482C4×Q8C22×D6114yes—
483C4×D4—22no—
484C4×D4—22no—
485C4×D4—22no—
486C4×D4—614no—
487C4×D4—1222no—
488C4×D4C22×D6114yes—
489C4×D4C22×D6114yes—
490C4×D4C22×D6114yes—
491#117—1228no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—28no—
498C2×C4⋊C4—611no—
499C2×C4⋊C4—1221no—
500C2×C4⋊C4—1221no—
501C2×C4⋊C4—1221no—
502C2×C4⋊C4—1221no—
503C2×C4⋊C4C22⋊D6111yescharacteristic
504C2×C4⋊C4C22⋊D6111yescharacteristic
505C2×C4⋊C4C22⋊D6111yescharacteristic
506C2×C4⋊C4C22×D6111yescharacteristic
507C2×C4⋊C4C22×D6111yescharacteristic
508C2×C4⋊C4C22×D6111yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—1221no—
513C2×C22⋊C4—1221no—
514C2×C22⋊C4—1221no—
515C2×C22⋊C4—1221no—
516C2×C22⋊C4—1221no—
517C2×C42—1221no—
518C2×C42—1221no—
519C2×C42C22×D6111yescharacteristic
520C2×C42C22×D6111yescharacteristic
521C2×C42C22×D6111yescharacteristic
522#107—614no—
523#106—614no—
524#106—614no—
525C4⋊C8—614no—
526C4⋊C8—614no—
527C4⋊C8—614no—
528#103—614no—
529#103—614no—
530#103—614no—
531#103—614no—
532#103—614no—
533#103—614no—
534#102—614no—
535#102—614no—
536#102—614no—
537#102—614no—
538#97—614no—
539#97—614no—
540C4×C8—614no—
541C24—21no—
542C24—1221no—
543C2×Q8—24no—
544C2×Q8—42no—
545C2×Q8—82no—
546C2×Q8—612no—
547C2×Q8—612no—
548C2×Q8—1221no—
549C2×Q8—1221no—
550C2×Q8—1222no—
551C2×Q8—1222no—
552C2×Q8—1222no—
553C2×Q8—1222no—
554C2×Q8C2×C22⋊D6114yes—
555C2×D4—21no—
556C2×D4—22no—
557C2×D4—612no—
558C2×D4—1221no—
559C2×D4—1222no—
560C2×D4—1222no—
561C2×D4#1175822614yes—
562C2×D4C23×D6112yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—24no—
569C22×C4—44no—
570C22×C4—82no—
571C22×C4—82no—
572C22×C4—1221no—
573C22×C4—1221no—
574C22×C4—1221no—
575C22×C4—1224no—
576C22×C4—2444no—
577C22×C4C2×C22⋊D6111yescharacteristic
578C22×C4C2×C22⋊D6111yescharacteristic
579C22×C4C2×C22⋊D6111yescharacteristic
580C22×C4C2×C22⋊D6111yescharacteristic
581C22×C4C2×C22⋊D6111yescharacteristic
582C22×C4C2×C22⋊D6111yescharacteristic
583C22×C4C23×D6111yescharacteristic
584SD16—1228no—
585SD16—1228no—
586D8—1228no—
587C2×C8—612no—
588C2×C8—612no—
589C2×C8—612no—
590C2×C8—612no—
591C2×C8—1222no—
592C2×C8—1222no—
593C2×C8—1222no—
594C2×C8—1222no—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—24no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—612no—
604C4⋊C4—1221no—
605C4⋊C4—1224no—
606C4⋊C4—1224no—
607C4⋊C4—1224no—
608C4⋊C4—1224no—
609C4⋊C4C2×C22⋊D6114yes—
610C4⋊C4C2×C22⋊D6114yes—
611C4⋊C4C2×C22⋊D6114yes—
612C4⋊C4C23×D6112yes—
613C4⋊C4C23×D6112yes—
614C4⋊C4C23×D6112yes—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—24no—
618C22⋊C4—1224no—
619C22⋊C4—1224no—
620C22⋊C4—1224no—
621C22⋊C4—1224no—
622C22⋊C4—1224no—
623C42—1224no—
624C42—1224no—
625C42C2×C22⋊D6112yes—
626C42C2×C22⋊D6112yes—
627C42C2×C22⋊D6112yes—
628C42C23×D6112yes—
629C42C23×D6112yes—
630C42C23×D6112yes—
631C23—22no—
632C23—24no—
633C23—42no—
634C23—42no—
635C23—1222no—
636C23—2442no—
637C23—2442no—
638C23—2442no—
639C23C22×C22⋊D6111yescharacteristic
640Q8—44no—
641Q8—84no—
642Q8—1222no—
643Q8—1222no—
644Q8—1222no—
645Q8—1222no—
646Q8—2442no—
647Q8—2442no—
648D4—22no—
649D4—24no—
650D4—1222no—
651D4—1222no—
652D4—2442no—
653D4C2×#1175822614yes—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—48no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—84no—
668C2×C4—84no—
669C2×C4—1222no—
670C2×C4—1222no—
671C2×C4—1222no—
672C2×C4—2448no—
673C2×C4—2442no—
674C2×C4—2442no—
675C2×C4—2442no—
676C2×C4C22×C22⋊D6112yes—
677C2×C4C22×C22⋊D6112yes—
678C2×C4C22×C22⋊D6112yes—
679C2×C4C22×C22⋊D6112yes—
680C2×C4C22×C22⋊D6112yes—
681C2×C4C22×C22⋊D6112yes—
682C2×C4C22×C22⋊D6111yescharacteristic
683C2×C4C2×#1175822612yes—
684C2×C4#1451982512yes—
685C2×C4C24×D6111yescharacteristic
686C8—1222no—
687C8—1222no—
688C8—1222no—
689C8—1222no—
690C22—24no—
691C22—42no—
692C22—42no—
693C22—48no—
694C22—4884no—
695C22—2442no—
696C22—2442no—
697C22—2442no—
698C22#1684042312yes—
699C22#1684056012yes—
700C22#1684057312yes—
701C22C23×C22⋊D6111yescharacteristic
702C4—22no—
703C4—22no—
704C4—22no—
705C4—22no—
706C4—22no—
707C4—22no—
708C4—42no—
709C4—42no—
710C4—42no—
711C4—2442no—
712C4—2442no—
713C4—2442no—
714C4#1684042312yes—
715C4C22×#1175822611yescharacteristic
716C4C2×#1451982511yescharacteristic
717C2—44no—
718C2—4882no—
719C2#2145864614yesdirect product factor
720C2C2×#1684042311yescharacteristic
721C2C2×#1684056011yescharacteristic
722C2C2×#1684057311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#554C2
socleC23×C61C22×D4
prime radicalC22×#11758199C22
hypercenterC2×#554D61
hypocenterC61C2×#3376
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×#16840485C2semidirect
2. #21458646C2direct (N × H)
3. C2×#16840132C2semidirect
4. C2×#16840124C2semidirect
5. C2×#16840119C2semidirect
6. C2×#16840066C2semidirect
7. C2×#16840044C2semidirect
8. C2×#16840059C2semidirect
11. C2×#16839967C2semidirect
12. C2×#16839893C2semidirect
14. C2×#16839862C2semidirect
15. C2×C4×#11758200C2semidirect
16. C2×C61×#554C2semidirect
21. #16840485C22semidirect
32. #16840132C22semidirect
33. #16840124C22semidirect
34. #16840119C22semidirect
35. #16840066C22semidirect
36. #16840059C22semidirect
37. #16840044C22semidirect
40. #16839967C22semidirect
41. #16839893C22semidirect
43. #16839862C22semidirect
44. C4×#11758200C22semidirect
65. C61×#554C22semidirect
357. C2×#554D61semidirect
373. C2×C61#3376semidirect
384. #554C2×D61semidirect
438. C61C2×#3376semidirect
719. C2#21458646direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404852
#214586462
C2×#168401322
C2×#168401242
C2×#168401192
C2×#168400662
C2×#168400442
C2×#168400592
C2×#168399772
C2×#168399672
C2×#168398932
C2×#168398722
C2×#168398622
C2×C4×#117582002
C2×C61×#5542
C2×#337661