Finite Group Databasebeta

← C2×#21461791 #30615541

Subgroups — C2×#21461791 #30615541

Order 15616.

1342 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840840C211yesmaximal, characteristic
2C2×#16840768C212yesmaximal, complemented
3C2×#16840735C211yesmaximal, characteristic
4#21461791C218yesmaximal, direct product factor
5C2×#16840643C212yesmaximal, complemented
6C2×#16839734C211yesmaximal, characteristic
7#16840840—24no—
8#16840840—22no—
9#16840840C2214yes—
10C2×#14519864—22no—
11C2×#14519864—22no—
12C2×D61⋊M16—21no—
13C22×#11758217—21no—
14C22×#11758217C2211yescharacteristic
15C22×#11758217C2212yes—
16C23×#92420C2211yescharacteristic
17#16840768—24no—
18#16840768C2218yescomplemented
19C2×#14519844—22no—
20C2×C4⋊#92420—22no—
21#16840735—22no—
22#16840735C2214yes—
23C2×#14519834—21no—
24C2×C22⋊#92420—21no—
25#16840643C2218yescomplemented
26C22×#11758224C2211yescharacteristic
27C2×#14519733C2212yes—
28#16839734C414yes—
29#16839734C2214yes—
30C2×#14519692C411yescharacteristic
31C2×#14519691C412yes—
32C2×#99×C61C411yescharacteristic
33#14519864—28no—
34#14519864—28no—
35#14519864—28no—
36#14519864—28no—
37C2×#11758213—21no—
38C2×#11758213—21no—
39D61⋊M16—24no—
40D61⋊M16—24no—
41C2×#11758217—22no—
42C2×#11758217—24no—
43C2×#11758217—22no—
44C2×#11758217—24no—
45C2×#11758217—22no—
46C2×#11758217—22no—
47C2×#11758217—22no—
48C2×#11758217—21no—
49C2×#11758217—22no—
50C2×#11758217—22no—
51C2×#11758217D414yes—
52C2×#11758217C2312yes—
53C2×#11758217C2314yes—
54C2×D61⋊C8—22no—
55C22×#92420—21no—
56C22×#92420—21no—
57C22×#92420—21no—
58C22×#92420—21no—
59C22×#92420—21no—
60C22×#92420—22no—
61C22×#92420—22no—
62C22×#92420D412yes—
63C22×#92420D412yes—
64C22×#92420C2312yes—
65#14519844—28no—
66C4⋊#92420—28no—
67#14519834—24no—
68C22⋊#92420—24no—
69C2×#11758224—22no—
70C2×#11758224—22no—
71C2×#11758224—22no—
72C2×#11758224—22no—
73C2×#11758224C2×C412yes—
74C2×#11758224D412yes—
75C2×#11758224Q812yes—
76C2×#11758224C2312yes—
77C22×Dic122Q811yescharacteristic
78C22×C22⋊D61C2×C411yescharacteristic
79C22×C22⋊D61Q811yescharacteristic
80C23×Dic61D411yescharacteristic
81C23×Dic61C2311yescharacteristic
82C22×C4×D61D411yescharacteristic
83#14519733—22no—
84#14519733—22no—
85#14519733C2×C414yes—
86#14519733C2314yes—
87C2×#11758196—22no—
88C2×C22⋊Dic61C2×C412yes—
89C2×C4×Dic61—22no—
90#14519692C2×C414yes—
91#14519691C2×C418yes—
92C22×D4×C61C2×C411yescharacteristic
93C2×C22⋊C4×C61C2×C412yes—
94#99×C61C2×C414yes—
95C24×C61C4⋊C411yescharacteristic
96C24×C61C22×C411yescharacteristic
97C23×D61C4⋊C411yescharacteristic
98C2×D4×C61—22no—
99C2×D4×C61—22no—
100C2×D4×C61C4⋊C412yes—
101C2×D4×C61C22×C412yes—
102C22×C4×C61—22no—
103C22×C4×C61C4⋊C411yescharacteristic
104C2×C22⋊D61—22no—
105C2×C22⋊D61—22no—
106C2×C22⋊D61—22no—
107C2×C22⋊D61—22no—
108C2×C22⋊D61C4⋊C412yes—
109C2×C22⋊D61C4⋊C412yes—
110C2×C22⋊D61C22×C412yes—
111C2×C22⋊D61C2×Q812yes—
112C22×Dic61—21no—
113C22×Dic61—21no—
114C22×Dic61—21no—
115C22×Dic61—21no—
116C22×Dic61—22no—
117C22×Dic61C4⋊C411yescharacteristic
118C22×Dic61C4⋊C412yes—
119C22×Dic61C22×C411yescharacteristic
120C22×Dic61C2×D412yes—
121C22×Dic61C2×D411yescharacteristic
122C22×Dic61C2×D411yescharacteristic
123C22×Dic61C2×D412yes—
124C22×Dic61C2×D412yes—
125C22×Dic61C2×Q811yescharacteristic
126C22×Dic61C2×Q811yescharacteristic
127C22×Dic61#4112yes—
128C22×Dic61#4112yes—
129C22×Dic61C2411yescharacteristic
130#11758224—24no—
131#11758224—24no—
132#11758224—24no—
133#11758224—24no—
134#11758224—24no—
135#11758224—24no—
136#11758224—24no—
137#11758224—24no—
138C2×C4×D61—21no—
139C2×C4×D61—21no—
140C2×C4×D61—21no—
141C2×C4×D61—21no—
142C2×C4×D61C4⋊C412yes—
143C2×C4×D61C2×D412yes—
144C2×Dic122—22no—
145C2×Dic122—22no—
146C2×Dic122C4⋊C412yes—
147C2×Dic122C2×Q812yes—
148#11758217—28no—
149#11758217—24no—
150#11758217—24no—
151#11758217—24no—
152#11758217—24no—
153#11758217—24no—
154#11758217—42no—
155C2×#92420—24no—
156C2×#92420—24no—
157C2×#92420—22no—
158C2×#92420—22no—
159C2×#92420—22no—
160C2×#92420—22no—
161C2×#92420—22no—
162C2×#92420—22no—
163C2×#92420—24no—
164C2×#92420—41no—
165C2×#92420—42no—
166C2×#92420—41no—
167C2×#92420—41no—
168C2×#92420—41no—
169C2×#92420C2×D414yes—
170C2×#92420C2×D414yes—
171#11758213—24no—
172#11758213—24no—
173D61⋊C8—28no—
174C22⋊C4×C61—22no—
175C22⋊C4×C61C22×C414yes—
176C22⋊Dic61—22no—
177C22⋊Dic61C22×C414yes—
178#11758196—24no—
179#11758196—24no—
180C4×Dic61—24no—
181C4×Dic61—24no—
182C23×C61—21no—
183C23×C61—21no—
184C23×C61—42no—
185C23×C61—42no—
186C23×C61C2×C4⋊C411yescharacteristic
187C23×C61C2×C4⋊C412yes—
188C23×C61C2×C4⋊C411yescharacteristic
189C23×C61C4×D412yes—
190C23×C61C4×D412yes—
191C23×C61C23×C411yescharacteristic
192C22×D61—21no—
193C22×D61—21no—
194C22×D61—42no—
195C22×D61C2×C4⋊C412yes—
196D4×C61—24no—
197D4×C61—24no—
198C2×C4×C61—21no—
199C2×C4×C61—21no—
200C2×C4×C61—24no—
201C2×C4×C61—44no—
202C2×C4×C61C2×C4⋊C412yes—
203C22⋊D61—24no—
204C22⋊D61—24no—
205C22⋊D61—24no—
206C22⋊D61—24no—
207C2×Dic61—21no—
208C2×Dic61—21no—
209C2×Dic61—22no—
210C2×Dic61—22no—
211C2×Dic61—22no—
212C2×Dic61—22no—
213C2×Dic61—24no—
214C2×Dic61—44no—
215C2×Dic61C2×C4⋊C412yes—
216C2×Dic61C2×C4⋊C411yescharacteristic
217C2×Dic61C2×C4⋊C411yescharacteristic
218C2×Dic61C4×D412yes—
219C2×Dic61C4×D412yes—
220C2×Dic61#12011yescharacteristic
221C2×Dic61#12012yes—
222C2×Dic61#12011yescharacteristic
223C2×Dic61C22⋊Q812yes—
224C2×Dic61C22⋊Q812yes—
225C2×Dic61C22⋊Q812yes—
226C2×Dic61C22⋊Q812yes—
227C2×Dic61#12311yescharacteristic
228C2×Dic61#12311yescharacteristic
229C2×Dic61#12312yes—
230C2×Dic61C22×D412yes—
231C2×Dic61C22×D411yescharacteristic
232C2×Dic61C22×Q811yescharacteristic
233C2×Dic61C2×#4112yes—
234C4×D61—22no—
235C4×D61—22no—
236C4×D61—22no—
237C4×D61—22no—
238Dic122—24no—
239Dic122—24no—
240#92420—24no—
241#92420—24no—
242#92420—42no—
243#92420—42no—
244C2×#1868—611nomaximal, Sylow
245C22×C61—24no—
246C22×C61—22no—
247C22×C61—22no—
248C22×C61—41no—
249C22×C61—42no—
250C22×C61—41no—
251C22×C61—42no—
252C22×C61—42no—
253C22×C61—81no—
254C22×C61#38511yescharacteristic
255C22×C61#38512yes—
256C22×C61#38511yescharacteristic
257C22×C61C22×C4⋊C411yescharacteristic
258C22×C61C2×C4×D412yes—
259C2×D61—22no—
260C2×D61—42no—
261C2×D61—42no—
262C2×D61—81no—
263C4×C61—22no—
264C4×C61—44no—
265Dic61—22no—
266Dic61—44no—
267Dic61#38512yes—
268Dic61#38511yescharacteristic
269Dic61#38511yescharacteristic
270Dic61C2×#12011yescharacteristic
271Dic61C2×C22⋊Q812yes—
272Dic61C2×#12311yescharacteristic
273C2×#568—611no—
274C2×#424—612no—
275C2×#410—611no—
276C2×#408—611no—
277#1868—618no—
278C2×#344—612no—
279C2×C61—22no—
280C2×C61—21no—
281C2×C61—21no—
282C2×C61—22no—
283C2×C61—42no—
284C2×C61#186812yescomplemented
285C2×C61C2×#38511yescharacteristic
286D61—42no—
287C22×#41—611no—
288#568—614no—
289#568—1224no—
290#568—1222no—
291C2×#131—1222no—
292C2×#131—1222no—
293C22×M16—612no—
294C22×M16—611no—
295C22×M16—1221no—
296C22×M16—1221no—
297C23×C8—611no—
298C2×#117—612no—
299#424—618no—
300#424—1224no—
301C2×C4⋊C8—1222no—
302C2×C4⋊C8—1222no—
303#410—614no—
304#410—614no—
305C2×#99—611no—
306C2×#99—612no—
307C2×#99#692311yescharacteristic
308#408—614no—
309#408—1222no—
310C2×C22⋊C8—1221no—
311C2×C22⋊C8—1221no—
312#344—618no—
313C61C2×#186811yescharacteristic, complemented, Sylow
314C2×#41—612no—
315C2×#41—612no—
316C2×#41—612no—
317C2×#41—612no—
318C2×#41—1222no—
319C2×#41—1222no—
320C2×#41—1222no—
321C2×#41—1222no—
322C22×Q8—611no—
323C22×D4—611no—
324C22×D4—611no—
325C22×D4C2×#692311yescharacteristic
326C23×C4—611no—
327C23×C4—611no—
328C23×C4—611no—
329#131—1228no—
330#131—1228no—
331#131—1228no—
332#131—1228no—
333C2×M16—614no—
334C2×M16—614no—
335C2×M16—612no—
336C2×M16—1222no—
337C2×M16—1222no—
338C2×M16—1222no—
339C2×M16—1222no—
340C2×M16—1224no—
341C2×M16—1224no—
342C2×M16—1222no—
343C2×M16—1224no—
344C2×M16—1224no—
345C2×M16—1221no—
346C2×M16—1221no—
347C2×M16—1221no—
348C2×M16—1222no—
349C2×M16—1222no—
350C22×C8—612no—
351C22×C8—612no—
352C22×C8—612no—
353C22×C8—1221no—
354C22×C8—1221no—
355C22×C8—1222no—
356C22×C8—1221no—
357C22×C8—1221no—
358C22×C8—1222no—
359C22×C8—1222no—
360C22×C8—1221no—
361#117—614no—
362#117—614no—
363#117—1222no—
364#117—1222no—
365C2×C4⋊C4—1222no—
366C2×C22⋊C4—612no—
367C2×C22⋊C4C2×#692312yes—
368C2×C42—1222no—
369C4⋊C8—1228no—
370C4⋊C8—1228no—
371#99—614no—
372#99—618no—
373#99C2×#692314yes—
374C22⋊C8—1224no—
375C22⋊C8—1224no—
376C24—611no—
377C24C4⋊#692311yescharacteristic
378C24C22×#692311yescharacteristic
379#41—1224no—
380#41—1224no—
381#41—1224no—
382#41—1224no—
383#41—1224no—
384#41—1224no—
385#41—1224no—
386#41—1224no—
387C2×Q8—612no—
388C2×Q8—612no—
389C2×Q8—1222no—
390C2×Q8—1222no—
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—612no—
394C2×D4—612no—
395C2×D4—612no—
396C2×D4—612no—
397C2×D4—1222no—
398C2×D4—1222no—
399C2×D4—1222no—
400C2×D4—1222no—
401C2×D4C4⋊#692312yes—
402C2×D4C22×#692312yes—
403C22×C4—22no—
404C22×C4—611no—
405C22×C4—611no—
406C22×C4—611no—
407C22×C4—611no—
408C22×C4—612no—
409C22×C4—612no—
410C22×C4—612no—
411C22×C4—612no—
412C22×C4—611no—
413C22×C4—611no—
414C22×C4—612no—
415C22×C4—611no—
416C22×C4—612no—
417C22×C4—612no—
418C22×C4—612no—
419C22×C4—1221no—
420C22×C4—1221no—
421C22×C4—1221no—
422C22×C4—1221no—
423C22×C4—1221no—
424C22×C4—1221no—
425C22×C4—1221no—
426C22×C4—1221no—
427C22×C4—1222no—
428C22×C4C4⋊#692311yescharacteristic
429M16—1224no—
430M16—1224no—
431M16—1224no—
432M16—1224no—
433M16—1224no—
434M16—1224no—
435M16—1228no—
436M16—1224no—
437M16—2442no—
438C2×C8—614no—
439C2×C8—614no—
440C2×C8—1222no—
441C2×C8—1222no—
442C2×C8—1222no—
443C2×C8—1222no—
444C2×C8—1228no—
445C2×C8—1224no—
446C2×C8—1224no—
447C2×C8—1222no—
448C2×C8—1222no—
449C2×C8—1224no—
450C2×C8—2442no—
451C2×C8—2441no—
452C2×C8—2441no—
453C2×C8—2441no—
454C2×C8—2441no—
455C4⋊C4—1224no—
456C4⋊C4—1224no—
457C22⋊C4—22no—
458C22⋊C4—614no—
459C22⋊C4—1222no—
460C22⋊C4C22×#692314yes—
461C42—1224no—
462C42—1224no—
463C23—21no—
464C23—21no—
465C23—42no—
466C23—42no—
467C23—612no—
468C23—1221no—
469C23—1221no—
470C23—2442no—
471C23C2×C4⋊#692311yescharacteristic
472C23C2×C4⋊#692312yes—
473C23C2×C4⋊#692311yescharacteristic
474C23D4×#692312yes—
475C23D4×#692312yes—
476C23C23×#692311yescharacteristic
477Q8—1224no—
478Q8—1224no—
479D4—24no—
480D4—24no—
481D4—1224no—
482D4—1224no—
483D4—1224no—
484D4—1224no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—24no—
488C2×C4—44no—
489C2×C4—612no—
490C2×C4—611no—
491C2×C4—612no—
492C2×C4—612no—
493C2×C4—612no—
494C2×C4—611no—
495C2×C4—612no—
496C2×C4—611no—
497C2×C4—612no—
498C2×C4—611no—
499C2×C4—611no—
500C2×C4—611no—
501C2×C4—611no—
502C2×C4—611no—
503C2×C4—612no—
504C2×C4—612no—
505C2×C4—612no—
506C2×C4—612no—
507C2×C4—612no—
508C2×C4—1222no—
509C2×C4—1222no—
510C2×C4—1222no—
511C2×C4—1222no—
512C2×C4—1222no—
513C2×C4—1222no—
514C2×C4—1222no—
515C2×C4—1222no—
516C2×C4—1221no—
517C2×C4—1221no—
518C2×C4—1224no—
519C2×C4—2444no—
520C2×C4C2×C4⋊#692312yes—
521C8—1224no—
522C8—1224no—
523C8—2442no—
524C8—2442no—
525C22—24no—
526C22—22no—
527C22—22no—
528C22—41no—
529C22—42no—
530C22—41no—
531C22—42no—
532C22—42no—
533C22—81no—
534C22—1222no—
535C22—4881no—
536C22—2442no—
537C22—2442no—
538C22#1684070911yescharacteristic
539C22#1684070912yes—
540C22#1684070911yescharacteristic
541C22C22×C4⋊#692311yescharacteristic
542C22C2×D4×#692312yes—
543C4—22no—
544C4—44no—
545C4—611no—
546C4—612no—
547C4—611no—
548C4—611no—
549C4—611no—
550C4—612no—
551C4—1222no—
552C4—2444no—
553C2—22no—
554C2—21no—
555C2—21no—
556C2—22no—
557C2—42no—
558C2—2442no—
559C2#2146179112yesdirect product factor
560C2C2×#1684070911yescharacteristic
subgroupG/H
centerC22#16840709
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×#99×C61C4
socleC22×C61#385
prime radicalC22×#11758224C22
cosocleC22×Dic61C24
hypercenterC2×#99#6923
hypocenterC61C2×#1868
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
2. C2×#16840768C2semidirect
4. #21461791C2direct (N × H)
5. C2×#16840643C2semidirect
18. #16840768C22semidirect
25. #16840643C22semidirect
284. C2×C61#1868semidirect
313. C61C2×#1868semidirect
559. C2#21461791direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168408402
C2×#168407682
C2×#168407352
#214617912
C2×#168406432
C2×#168397342
C2×#186861