Finite Group Databasebeta

← C2×#21458773 #30560550

Subgroups — C2×#21458773 #30560550

Order 15616.

1898 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840472C211yesmaximal, characteristic, complemented
2#21458773C2116yesmaximal, direct product factor
3C2×#16840172C211yesmaximal, characteristic, complemented
4C2×#16840168C211yesmaximal, characteristic, complemented
5C2×#16840161C211yesmaximal, characteristic, complemented
6C2×#16840062C211yesmaximal, characteristic, complemented
7C2×#16840062C211yesmaximal, characteristic, complemented
8C2×#16840059C211yesmaximal, characteristic, complemented
9C2×#16840059C211yesmaximal, characteristic, complemented
10C2×#16840042C211yesmaximal, characteristic, complemented
11C2×#16840039C211yesmaximal, characteristic, complemented
12C2×#16839893C211yesmaximal, characteristic, complemented
13C2×#16839872C211yesmaximal, characteristic
14C2×#16839872C211yesmaximal, characteristic
15C2×C4×#11758199C211yesmaximal, characteristic
16C2×C61×#554C211yesmaximal, characteristic, complemented
17C22×#11758199C2211yescharacteristic
18#16840472—24no—
19#16840472C2218yescomplemented
20C2×#14519777C2211yescharacteristic
21C2×#14519769C2211yescharacteristic
22C2×#14519769C2211yescharacteristic
23C2×#14519755—21no—
24C2×#14519755—21no—
25C2×#14519753—21no—
26C2×C4×D244C2211yescharacteristic
27C2×C4×D244C2211yescharacteristic
28C2×C4×D244C2211yescharacteristic
29C2×C4⋊C4×D61—21no—
30#16840172C2218yescomplemented
31#16840168C2218yescomplemented
32#16840161C2218yescomplemented
33#16840062C2218yescomplemented
34#16840062C2218yescomplemented
35#16840059C2218yescomplemented
36#16840059C2218yescomplemented
37#16840042C2218yescomplemented
38#16840039C2218yescomplemented
39#16839893C2218yescomplemented
40#16839872C2218yes—
41#16839872C2218yes—
42C4×#11758199C2218yes—
43C2×#14519710C2211yescharacteristic
44C2×#14519710C2211yescharacteristic
45C2×#14519710C2211yescharacteristic
46C2×#14519710C2211yescharacteristic
47C2×#14519710C2211yescharacteristic
48C2×#14519708C2211yescharacteristic
49C2×#14519708C2211yescharacteristic
50C2×#14519708C2211yescharacteristic
51C2×#14519708C2211yescharacteristic
52C2×C4⋊#92418C2211yescharacteristic
53C2×C4⋊#92418C2211yescharacteristic
54C2×C4⋊#92418C2211yescharacteristic
55C2×#14519698C2211yescharacteristic
56C2×#14519698C2211yescharacteristic
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×Dic122—21no—
78C22×D244C2311yescharacteristic
79C22×C4×D61—21no—
80C22×C4×D61—21no—
81C22×C4×D61—21no—
82C2×#11758199Q818yescomplemented
83C2×#11758199C2314yes—
84C22×#92418C2311yescharacteristic
85C22×#92418C2311yescharacteristic
86C22×#92418C2311yescharacteristic
87C22×#92418C2311yescharacteristic
88#14519777—22no—
89#14519777C2314yes—
90#14519769—22no—
91#14519769—22no—
92#14519769C2314yes—
93#14519769C2314yes—
94#14519755—28no—
95#14519755—28no—
96#14519753—28no—
97C4×D244—22no—
98C4×D244—22no—
99C4×D244—22no—
100C4×D244C2314yes—
101C4×D244C2314yes—
102C4×D244C2314yes—
103C2×C4⋊Dic61—21no—
104C2×C4⋊Dic61C2311yescharacteristic
105C2×C4⋊Dic61C2311yescharacteristic
106C2×C4⋊Dic61C2311yescharacteristic
107C2×#11758196—21no—
108C2×#11758196—21no—
109C2×#11758196—21no—
110C2×#11758196—21no—
111C4⋊C4×D61—28no—
112C2×#11758198—21no—
113C2×#11758198—21no—
114C2×#11758198—21no—
115#14519710C2314yes—
116#14519710C2314yes—
117#14519710C2314yes—
118#14519710C2314yes—
119#14519710C2314yes—
120#14519708C2314yes—
121#14519708C2314yes—
122#14519708C2314yes—
123#14519708C2314yes—
124C4⋊#92418C2314yes—
125C4⋊#92418C2314yes—
126C4⋊#92418C2314yes—
127#14519698C2314yes—
128#14519698C2314yes—
129#14519698C2314yes—
130#14519697C2314yes—
131#14519697C2314yes—
132#14519697C2314yes—
133#14519688C2314yes—
134#14519688C2314yes—
135C4×#92418C2314yes—
136C22×Q8×C61—21no—
137C22×Q8×C61D411yescharacteristic
138C22×D4×C61C2311yescharacteristic
139C23×C4×C61—21no—
140C23×C4×C61—21no—
141C23×C4×C61—21no—
142C4⋊Q8×C61—22no—
143C4⋊Q8×C61C2314yes—
144#125×C61—22no—
145#125×C61—22no—
146#125×C61C2314yes—
147#125×C61C2314yes—
148C22⋊Q8×C61—28no—
149C22⋊Q8×C61—28no—
150C22⋊Q8×C61—28no—
151C4×Q8×C61D414yes—
152C4×Q8×C61C2314yes—
153C4×D4×C61—22no—
154C4×D4×C61—22no—
155C4×D4×C61—22no—
156C4×D4×C61C2314yes—
157C4×D4×C61C2314yes—
158C4×D4×C61C2314yes—
159C2×C4⋊C4×C61—21no—
160C2×C4⋊C4×C61—21no—
161C2×C4⋊C4×C61—21no—
162C2×C4⋊C4×C61—21no—
163C2×C4⋊C4×C61—21no—
164C2×C4⋊C4×C61—28no—
165C2×C4⋊C4×C61D411yescharacteristic
166C2×C4⋊C4×C61D411yescharacteristic
167C2×C4⋊C4×C61D411yescharacteristic
168C2×C4⋊C4×C61C2311yescharacteristic
169C2×C4⋊C4×C61C2311yescharacteristic
170C2×C4⋊C4×C61C2311yescharacteristic
171C2×C22⋊C4×C61—21no—
172C2×C22⋊C4×C61—21no—
173C2×C22⋊C4×C61—21no—
174C2×C42×C61C2311yescharacteristic
175C2×C42×C61C2311yescharacteristic
176C2×C42×C61C2311yescharacteristic
177C24×C61—21no—
178C23×D61—21no—
179C2×Q8×C61—24no—
180C2×Q8×C61—42no—
181C2×Q8×C61—82no—
182C2×Q8×C61C2×D414yes—
183C2×D4×C61—21no—
184C2×D4×C61—22no—
185C2×D4×C61C2×Q814yes—
186C2×D4×C61C2412yes—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—24no—
191C22×C4×C61—24no—
192C22×C4×C61—24no—
193C22×C4×C61—44no—
194C22×C4×C61—82no—
195C22×C4×C61—82no—
196C22×C4×C61C2×D411yescharacteristic
197C22×C4×C61C2×D411yescharacteristic
198C22×C4×C61C2×D411yescharacteristic
199C22×C4×C61C2×D411yescharacteristic
200C22×C4×C61C2×D411yescharacteristic
201C22×C4×C61C2×D411yescharacteristic
202C22×C4×C61C2411yescharacteristic
203C22×Dic61—21no—
204C22×Dic61—21no—
205C22×Dic61—21no—
206C2×D244—21no—
207C2×D244—22no—
208C2×D244C2×Q814yes—
209C2×D244C2412yes—
210C2×C4×D61—24no—
211C2×C4×D61—24no—
212C2×C4×D61—24no—
213C2×C4×D61—44no—
214C2×C4×D61—82no—
215C2×C4×D61—82no—
216C2×Dic122—24no—
217C2×Dic122—82no—
218C4⋊C4×C61—24no—
219C4⋊C4×C61—24no—
220C4⋊C4×C61—24no—
221C4⋊C4×C61—24no—
222C4⋊C4×C61—24no—
223C4⋊C4×C61—21no—
224C4⋊C4×C61—21no—
225C4⋊C4×C61—21no—
226C4⋊C4×C61C2×D414yes—
227C4⋊C4×C61C2×D414yes—
228C4⋊C4×C61C2×D414yes—
229C4⋊C4×C61C2412yes—
230C4⋊C4×C61C2412yes—
231C4⋊C4×C61C2412yes—
232C22⋊C4×C61—24no—
233C22⋊C4×C61—24no—
234C22⋊C4×C61—24no—
235C42×C61C2×D412yes—
236C42×C61C2×D412yes—
237C42×C61C2×D412yes—
238C42×C61C2412yes—
239C42×C61C2412yes—
240C42×C61C2412yes—
241#11758199C2×Q8116yescomplemented
242#11758198—24no—
243#11758198—24no—
244#11758198—24no—
245C4⋊Dic61—24no—
246C4⋊Dic61—21no—
247C4⋊Dic61—21no—
248C4⋊Dic61—21no—
249C4⋊Dic61C2412yes—
250C4⋊Dic61C2412yes—
251C4⋊Dic61C2412yes—
252#11758196—24no—
253#11758196—24no—
254#11758196—24no—
255#11758196—24no—
256C2×#92418—22no—
257C2×#92418—22no—
258C2×#92418—22no—
259C2×#92418C2×Q814yes—
260C2×#92418C2412yes—
261C2×#92418C2412yes—
262C2×#92418C2412yes—
263C2×#92418C2412yes—
264C23×C61—24no—
265C23×C61—22no—
266C23×C61—42no—
267C23×C61—42no—
268C23×C61C22×D411yescharacteristic
269C22×D61—24no—
270C22×D61—22no—
271C22×D61—42no—
272C22×D61—42no—
273Q8×C61—44no—
274Q8×C61—84no—
275D4×C61—24no—
276D4×C61—22no—
277D4×C61C22×Q814yes—
278C2×C4×C61—22no—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
281C2×C4×C61—22no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—48no—
288C2×C4×C61—42no—
289C2×C4×C61—42no—
290C2×C4×C61—42no—
291C2×C4×C61—84no—
292C2×C4×C61—84no—
293C2×C4×C61C22×D412yes—
294C2×C4×C61C22×D412yes—
295C2×C4×C61C22×D412yes—
296C2×C4×C61C22×D412yes—
297C2×C4×C61C22×D412yes—
298C2×C4×C61C22×D412yes—
299C2×C4×C61C22×D411yescharacteristic
300C2×C4×C61C22×Q812yes—
301C2×C4×C612−1+412yes—
302C2×C4×C61C2511yescharacteristic
303C2×Dic61—22no—
304C2×Dic61—22no—
305C2×Dic61—22no—
306C2×Dic61—42no—
307C2×Dic61—42no—
308C2×Dic61—42no—
309D244—24no—
310D244—22no—
311D244C22×Q814yes—
312C4×D61—48no—
313C4×D61—84no—
314C4×D61—84no—
315Dic122—84no—
316#92418—22no—
317#92418—22no—
318#92418—22no—
319#92418C22×Q814yes—
320C2×#3389—611nomaximal, Sylow
321C22×C61—24no—
322C22×C61—48no—
323C22×C61—42no—
324C22×C61—42no—
325C22×C61D4×Q812yes—
326C22×C61#57512yes—
327C22×C61#57612yes—
328C22×C61C23×D411yescharacteristic
329C2×D61—24no—
330C2×D61—48no—
331C2×D61—42no—
332C2×D61—42no—
333C4×C61—22no—
334C4×C61—22no—
335C4×C61—22no—
336C4×C61—22no—
337C4×C61—22no—
338C4×C61—22no—
339C4×C61—42no—
340C4×C61—42no—
341C4×C61—42no—
342C4×C61D4×Q812yes—
343C4×C61C23×Q811yescharacteristic
344C4×C61C2×2−1+411yescharacteristic
345Dic61—42no—
346Dic61—42no—
347Dic61—42no—
348C2×#554—611no—
349C2×#554D6111yescharacteristic, complemented
350#3389—6116no—
351C2×#501—611no—
352C2×#501—611no—
353C2×#499—611no—
354C2×#478—611no—
355C2×#478—611no—
356C2×#478—611no—
357C2×#478—611no—
358C2×#474—611no—
359C2×#474—611no—
360C2×#446—611no—
361C2×#442—611no—
362C2×#442—611no—
363C2×C4×D8—611no—
364C2×C61—44no—
365C2×C61#338914yescomplemented
366C2×C61C2×D4×Q811yescharacteristic
367C2×C61C2×#57511yescharacteristic
368C2×C61C2×#57611yescharacteristic
369D61—44no—
370C22×D8—611no—
371#554—24no—
372#554—618no—
373#554—1224no—
374#554C2×D6118yescomplemented
375C2×C4⋊Q8—611no—
376C2×C4⋊Q8C2×D6111yescharacteristic
377C2×#125—611no—
378C2×#125—611no—
379C2×#125C2×D6111yescharacteristic
380C2×#125C2×D6111yescharacteristic
381C2×C22⋊Q8—21no—
382C2×C22⋊Q8—21no—
383C2×C22⋊Q8—21no—
384C2×C22⋊Q8—1221no—
385C2×C22⋊Q8—1221no—
386C2×C22⋊Q8—1221no—
387C2×C4×Q8C2×D6111yescharacteristic
388C2×C4×D4—611no—
389C2×C4×D4—611no—
390C2×C4×D4—611no—
391C2×C4×D4C2×D6111yescharacteristic
392C2×C4×D4C2×D6111yescharacteristic
393C2×C4×D4C2×D6111yescharacteristic
394C22×C4⋊C4—21no—
395C22×C4⋊C4—1221no—
396#501—618no—
397#501—618no—
398#499—618no—
399#478—618no—
400#478—618no—
401#478—618no—
402#478—618no—
403#474—618no—
404#474—618no—
405#446—618no—
406#442—618no—
407#442—618no—
408C4×D8—618no—
409C2×#107—611no—
410C2×#107—611no—
411C2×#107—611no—
412C2×#107—611no—
413C2×#107—611no—
414C2×#106—611no—
415C2×#106—611no—
416C2×#106—611no—
417C2×#106—611no—
418C2×C4⋊C8—611no—
419C2×C4⋊C8—611no—
420C2×C4⋊C8—611no—
421C2×#102—611no—
422C2×#102—611no—
423C2×#102—611no—
424C2×#102—611no—
425C2×#102—611no—
426C2×#102—611no—
427C2×#97—611no—
428C2×#97—611no—
429C2×C4×C8—611no—
430C61C2×#338911yescharacteristic, complemented, Sylow
431C22×Q8—21no—
432C22×Q8—1221no—
433C22×Q8C22⋊D6111yescharacteristic
434C22×D4—611no—
435C22×D4C22×D6111yescharacteristic
436C23×C4—21no—
437C23×C4—21no—
438C23×C4—21no—
439C23×C4—1221no—
440C23×C4—1221no—
441C23×C4—1221no—
442C2×D8—618no—
443C2×D8—614no—
444C22×C8—611no—
445C22×C8—611no—
446C22×C8—611no—
447C22×C8—611no—
448C4⋊Q8—22no—
449C4⋊Q8—614no—
450C4⋊Q8—1222no—
451C4⋊Q8C22×D6114yes—
452#125—22no—
453#125—22no—
454#125—614no—
455#125—614no—
456#125—1222no—
457#125—1222no—
458#125C22×D6114yes—
459#125C22×D6114yes—
460C22⋊Q8—28no—
461C22⋊Q8—28no—
462C22⋊Q8—28no—
463C22⋊Q8—1228no—
464C22⋊Q8—1228no—
465C22⋊Q8—1228no—
466C4×Q8C22⋊D6114yes—
467C4×Q8C22×D6114yes—
468C4×D4—22no—
469C4×D4—22no—
470C4×D4—22no—
471C4×D4—614no—
472C4×D4—614no—
473C4×D4—614no—
474C4×D4—1222no—
475C4×D4—1222no—
476C4×D4—1222no—
477C4×D4C22×D6114yes—
478C4×D4C22×D6114yes—
479C4×D4C22×D6114yes—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—28no—
486C2×C4⋊C4—611no—
487C2×C4⋊C4—611no—
488C2×C4⋊C4—611no—
489C2×C4⋊C4—1221no—
490C2×C4⋊C4—1221no—
491C2×C4⋊C4—1221no—
492C2×C4⋊C4—1221no—
493C2×C4⋊C4—1221no—
494C2×C4⋊C4—1228no—
495C2×C4⋊C4C22⋊D6111yescharacteristic
496C2×C4⋊C4C22⋊D6111yescharacteristic
497C2×C4⋊C4C22⋊D6111yescharacteristic
498C2×C4⋊C4C22×D6111yescharacteristic
499C2×C4⋊C4C22×D6111yescharacteristic
500C2×C4⋊C4C22×D6111yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—1221no—
505C2×C22⋊C4—1221no—
506C2×C22⋊C4—1221no—
507C2×C42C22×D6111yescharacteristic
508C2×C42C22×D6111yescharacteristic
509C2×C42C22×D6111yescharacteristic
510#107—614no—
511#107—614no—
512#107—614no—
513#107—614no—
514#107—614no—
515#106—614no—
516#106—614no—
517#106—614no—
518#106—614no—
519C4⋊C8—614no—
520C4⋊C8—614no—
521C4⋊C8—614no—
522#102—614no—
523#102—614no—
524#102—614no—
525#102—614no—
526#102—614no—
527#102—614no—
528#97—614no—
529#97—614no—
530C4×C8—614no—
531C24—21no—
532C24—1221no—
533C2×Q8—24no—
534C2×Q8—42no—
535C2×Q8—82no—
536C2×Q8—1224no—
537C2×Q8—4882no—
538C2×Q8C2×C22⋊D6114yes—
539C2×D4—21no—
540C2×D4—22no—
541C2×D4—614no—
542C2×D4—612no—
543C2×D4—1221no—
544C2×D4—1222no—
545C2×D4Q8×D6114yes—
546C2×D4C23×D6112yes—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—44no—
554C22×C4—82no—
555C22×C4—82no—
556C22×C4—1221no—
557C22×C4—1221no—
558C22×C4—1221no—
559C22×C4—1224no—
560C22×C4—1224no—
561C22×C4—1224no—
562C22×C4—4882no—
563C22×C4—4882no—
564C22×C4—2444no—
565C22×C4C2×C22⋊D6111yescharacteristic
566C22×C4C2×C22⋊D6111yescharacteristic
567C22×C4C2×C22⋊D6111yescharacteristic
568C22×C4C2×C22⋊D6111yescharacteristic
569C22×C4C2×C22⋊D6111yescharacteristic
570C22×C4C2×C22⋊D6111yescharacteristic
571C22×C4C23×D6111yescharacteristic
572D8—6116no—
573C2×C8—614no—
574C2×C8—612no—
575C2×C8—612no—
576C2×C8—612no—
577C2×C8—612no—
578C2×C8—1222no—
579C2×C8—1222no—
580C2×C8—1222no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—24no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—612no—
590C4⋊C4—612no—
591C4⋊C4—612no—
592C4⋊C4—1221no—
593C4⋊C4—1221no—
594C4⋊C4—1221no—
595C4⋊C4—1224no—
596C4⋊C4—1224no—
597C4⋊C4—1224no—
598C4⋊C4—1224no—
599C4⋊C4—1224no—
600C4⋊C4C2×C22⋊D6114yes—
601C4⋊C4C2×C22⋊D6114yes—
602C4⋊C4C2×C22⋊D6114yes—
603C4⋊C4C23×D6112yes—
604C4⋊C4C23×D6112yes—
605C4⋊C4C23×D6112yes—
606C22⋊C4—24no—
607C22⋊C4—24no—
608C22⋊C4—24no—
609C22⋊C4—1224no—
610C22⋊C4—1224no—
611C22⋊C4—1224no—
612C42C2×C22⋊D6112yes—
613C42C2×C22⋊D6112yes—
614C42C2×C22⋊D6112yes—
615C42C23×D6112yes—
616C42C23×D6112yes—
617C42C23×D6112yes—
618C23—22no—
619C23—24no—
620C23—42no—
621C23—42no—
622C23—1222no—
623C23—1224no—
624C23—2442no—
625C23—2442no—
626C23C22×C22⋊D6111yescharacteristic
627Q8—44no—
628Q8—84no—
629Q8—4884no—
630D4—22no—
631D4—24no—
632D4—614no—
633D4—1222no—
634D4—1224no—
635D4C2×Q8×D6114yes—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—48no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—84no—
650C2×C4—84no—
651C2×C4—1222no—
652C2×C4—1222no—
653C2×C4—1222no—
654C2×C4—4884no—
655C2×C4—4884no—
656C2×C4—2448no—
657C2×C4—2442no—
658C2×C4—2442no—
659C2×C4—2442no—
660C2×C4C22×C22⋊D6112yes—
661C2×C4C22×C22⋊D6112yes—
662C2×C4C22×C22⋊D6112yes—
663C2×C4C22×C22⋊D6112yes—
664C2×C4C22×C22⋊D6112yes—
665C2×C4C22×C22⋊D6112yes—
666C2×C4C22×C22⋊D6111yescharacteristic
667C2×C4C2×Q8×D6112yes—
668C2×C4#1451982512yes—
669C2×C4C24×D6111yescharacteristic
670C8—614no—
671C8—1222no—
672C8—1222no—
673C8—1222no—
674C22—24no—
675C22—42no—
676C22—48no—
677C22—42no—
678C22—1224no—
679C22—2442no—
680C22—2448no—
681C22—2442no—
682C22Q8×C22⋊D6112yes—
683C22#1684056012yes—
684C22#1684056512yes—
685C22C23×C22⋊D6111yescharacteristic
686C4—22no—
687C4—22no—
688C4—22no—
689C4—22no—
690C4—22no—
691C4—22no—
692C4—42no—
693C4—42no—
694C4—42no—
695C4—2442no—
696C4—2442no—
697C4—2442no—
698C4Q8×C22⋊D6112yes—
699C4C22×Q8×D6111yescharacteristic
700C4C2×#1451982511yescharacteristic
701C2—44no—
702C2—2444no—
703C2#2145877314yesdirect product factor
704C2C2×Q8×C22⋊D6111yescharacteristic
705C2C2×#1684056011yescharacteristic
706C2C2×#1684056511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#554C2
socleC23×C61C22×D4
prime radicalC22×#11758199C22
hypercenterC2×#554D61
hypocenterC61C2×#3389
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×#16840472C2semidirect
2. #21458773C2direct (N × H)
3. C2×#16840172C2semidirect
4. C2×#16840168C2semidirect
5. C2×#16840161C2semidirect
6. C2×#16840062C2semidirect
7. C2×#16840062C2semidirect
8. C2×#16840059C2semidirect
9. C2×#16840059C2semidirect
10. C2×#16840042C2semidirect
11. C2×#16840039C2semidirect
12. C2×#16839893C2semidirect
16. C2×C61×#554C2semidirect
19. #16840472C22semidirect
30. #16840172C22semidirect
31. #16840168C22semidirect
32. #16840161C22semidirect
33. #16840062C22semidirect
34. #16840062C22semidirect
35. #16840059C22semidirect
36. #16840059C22semidirect
37. #16840042C22semidirect
38. #16840039C22semidirect
39. #16839893C22semidirect
65. C61×#554C22semidirect
82. C2×#11758199Q8semidirect
241. #11758199C2×Q8semidirect
349. C2×#554D61semidirect
365. C2×C61#3389semidirect
374. #554C2×D61semidirect
430. C61C2×#3389semidirect
703. C2#21458773direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404722
#214587732
C2×#168401722
C2×#168401682
C2×#168401612
C2×#168400622
C2×#168400592
C2×#168400422
C2×#168400392
C2×#168398932
C2×#168398722
C2×C4×#117581992
C2×C61×#5542
C2×#338961