Finite Group Databasebeta

← C2×#21461088 #30610046

Subgroups — C2×#21461088 #30610046

Order 15616.

1346 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840782C211yesmaximal, characteristic, complemented
2C2×#16840778C211yesmaximal, characteristic, complemented
3#21461088C218yesmaximal, direct product factor
4C2×#16840606C212yesmaximal, complemented
5C2×#16840605C212yesmaximal, complemented
6C22×#14519763C211yesmaximal, characteristic
7#16840782—22no—
8#16840782C2214yescomplemented
9#16840778—22no—
10#16840778C2214yescomplemented
11C2×#14519844—21no—
12C2×C4⋊#92420—21no—
13C2×C22⋊#92420C2212yes—
14C2×C22⋊#92420C2212yes—
15C2×#14519832—21no—
16C2×C4×#92420—21no—
17#16840606C2218yescomplemented
18#16840605C2218yescomplemented
19C23×Dic122C411yescharacteristic
20C23×C22⋊D61C411yescharacteristic
21C2×#14519763—21no—
22C2×#14519763—21no—
23C2×#14519763—21no—
24C2×#14519763—21no—
25C2×#14519763—22no—
26C2×#14519763—22no—
27C2×#14519763C414yes—
28C2×#14519763C2214yes—
29C22×C22⋊Dic61C2211yescharacteristic
30C22×#11758198C411yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×C4×Dic61C2211yescharacteristic
33C22×C22⋊C4×C61C411yescharacteristic
34C22×#92420—22no—
35C22×#92420—22no—
36#14519844—24no—
37C4⋊#92420—24no—
38C22⋊#92420—22no—
39C22⋊#92420—22no—
40C22⋊#92420C2314yes—
41C22⋊#92420C2314yes—
42#14519832—24no—
43C4×#92420—24no—
44C24×D61C2×C411yescharacteristic
45C22×Dic122—21no—
46C22×Dic122—22no—
47C22×Dic122—21no—
48C22×Dic122—44no—
49C22×Dic122C2×C414yes—
50C22×C22⋊D61—22no—
51C22×C22⋊D61—21no—
52C22×C22⋊D61—21no—
53C22×C22⋊D61—44no—
54C22×C22⋊D61C2×C414yes—
55C23×Dic61C2×C411yescharacteristic
56C23×Dic61C2×C411yescharacteristic
57C23×Dic61C2311yescharacteristic
58#14519763—24no—
59#14519763—24no—
60#14519763—24no—
61#14519763—24no—
62#14519763—24no—
63#14519763—24no—
64#14519763—24no—
65#14519763—24no—
66C2×C22⋊Dic61—21no—
67C2×C22⋊Dic61—21no—
68C2×C22⋊Dic61—21no—
69C2×C22⋊Dic61—21no—
70C2×C22⋊Dic61C2×C412yes—
71C2×C22⋊Dic61C2312yes—
72C2×#11758198—22no—
73C2×#11758198—21no—
74C2×#11758198—21no—
75C2×#11758198—21no—
76C2×#11758198—21no—
77C2×#11758198—21no—
78C2×#11758198—21no—
79C2×#11758198C2×C414yes—
80C2×#11758198C2×C412yes—
81C2×#11758198C2312yes—
82C2×C4×Dic61C2×C412yes—
83C2×C4×Dic61D411yescharacteristic
84C2×C4×Dic61D411yescharacteristic
85C2×C4×Dic61D411yescharacteristic
86C2×C4×Dic61D411yescharacteristic
87C2×C4×Dic61D412yes—
88C2×C4×Dic61D412yes—
89C2×C4×Dic61C2312yes—
90C25×C61C2×C411yescharacteristic
91C23×C4×C61C2×C411yescharacteristic
92C23×C4×C61C2×C411yescharacteristic
93C2×C22⋊C4×C61—22no—
94C2×C22⋊C4×C61—21no—
95C2×C22⋊C4×C61—21no—
96C2×C22⋊C4×C61C2×C414yes—
97C24×C61—21no—
98C24×C61—21no—
99C24×C61—24no—
100C24×C61—42no—
101C24×C61—42no—
102C24×C61C22×C411yescharacteristic
103C24×C61C22×C412yes—
104C23×D61—21no—
105C23×D61—21no—
106C23×D61—24no—
107C23×D61—42no—
108C23×D61—42no—
109C23×D61C22×C412yes—
110C22×C4×C61—24no—
111C22×C4×C61—21no—
112C22×C4×C61—21no—
113C22×C4×C61—42no—
114C22×C4×C61C22⋊C412yes—
115C22×C4×C61C22⋊C411yescharacteristic
116C22×C4×C61C22⋊C411yescharacteristic
117C22×C4×C61C22×C412yes—
118C22×C4×C61C22×C412yes—
119C2×C22⋊D61—24no—
120C2×C22⋊D61—24no—
121C2×C22⋊D61—44no—
122C2×C22⋊D61—48no—
123C2×C22⋊D61—48no—
124C2×C22⋊D61—44no—
125C22×Dic61—24no—
126C22×Dic61—21no—
127C22×Dic61—21no—
128C22×Dic61—42no—
129C22×Dic61—42no—
130C22×Dic61C22⋊C411yescharacteristic
131C22×Dic61C22⋊C412yes—
132C22×Dic61C22⋊C411yescharacteristic
133C22×Dic61C22×C412yes—
134C22×Dic61C22×C412yes—
135C22×Dic61C22×C411yescharacteristic
136C22×Dic61C2×D411yescharacteristic
137C22×Dic61C2×D411yescharacteristic
138C22×Dic61C2×D411yescharacteristic
139C22×Dic61C2×D411yescharacteristic
140C22×Dic61C2411yescharacteristic
141C2×Dic122—24no—
142C2×Dic122—24no—
143C2×Dic122—44no—
144C2×Dic122—48no—
145C2×Dic122—44no—
146C2×Dic122—48no—
147C2×#92420—24no—
148C2×#92420—24no—
149C2×#92420—44no—
150C2×#92420—44no—
151C22⋊C4×C61—24no—
152C22⋊C4×C61—24no—
153C22⋊Dic61—22no—
154C22⋊Dic61—22no—
155C22⋊Dic61—22no—
156C22⋊Dic61—22no—
157#11758198—24no—
158#11758198—24no—
159#11758198—22no—
160#11758198—22no—
161#11758198—22no—
162#11758198—22no—
163C4×Dic61C22⋊C412yes—
164C4×Dic61C22⋊C412yes—
165C4×Dic61C22⋊C412yes—
166C4×Dic61C22⋊C412yes—
167C4×Dic61C2×D412yes—
168C4×Dic61C2×D412yes—
169C4×Dic61C2×D412yes—
170C4×Dic61C2×D412yes—
171C23×C61—22no—
172C23×C61—22no—
173C23×C61—22no—
174C23×C61—24no—
175C23×C61—42no—
176C23×C61—42no—
177C23×C61—42no—
178C23×C61—42no—
179C23×C61—42no—
180C23×C61—42no—
181C23×C61—42no—
182C23×C61—42no—
183C23×C61—88no—
184C23×C61C2×C22⋊C411yescharacteristic
185C23×C61C2×C22⋊C411yescharacteristic
186C23×C61#13114yes—
187C23×C61C23×C411yescharacteristic
188C22×D61—22no—
189C22×D61—24no—
190C22×D61—42no—
191C22×D61—42no—
192C22×D61—42no—
193C22×D61—42no—
194C22×D61—42no—
195C22×D61—42no—
196C22×D61—42no—
197C22×D61—42no—
198C22×D61—88no—
199C2×C4×C61—24no—
200C2×C4×C61—24no—
201C2×C4×C61—22no—
202C2×C4×C61—22no—
203C2×C4×C61—22no—
204C2×C4×C61—42no—
205C2×C4×C61—42no—
206C2×C4×C61—42no—
207C2×C4×C61C2×C22⋊C412yes—
208C2×C4×C61C2×C22⋊C412yes—
209C22⋊D61—48no—
210C22⋊D61—48no—
211C2×Dic61—22no—
212C2×Dic61—22no—
213C2×Dic61—22no—
214C2×Dic61—24no—
215C2×Dic61—24no—
216C2×Dic61—22no—
217C2×Dic61—41no—
218C2×Dic61—41no—
219C2×Dic61—41no—
220C2×Dic61—41no—
221C2×Dic61—42no—
222C2×Dic61—42no—
223C2×Dic61—42no—
224C2×Dic61#10014yes—
225C2×Dic61C2×C22⋊C411yescharacteristic
226C2×Dic61C2×C22⋊C411yescharacteristic
227C2×Dic61C2×C22⋊C412yes—
228C2×Dic61C2×C22⋊C412yes—
229C2×Dic61C22×D411yescharacteristic
230C2×Dic61C22×D411yescharacteristic
231Dic122—48no—
232Dic122—48no—
233#92420—44no—
234#92420—44no—
235C2×#1469—611nomaximal, Sylow
236C22×C61—21no—
237C22×C61—21no—
238C22×C61—21no—
239C22×C61—21no—
240C22×C61—28no—
241C22×C61—42no—
242C22×C61—42no—
243C22×C61—42no—
244C22×C61—84no—
245C22×C61—84no—
246C22×C61—84no—
247C22×C61#40812yes—
248C22×C61#40812yes—
249C22×C61#41012yes—
250C22×C61C2×#10012yes—
251C22×C61C22×C22⋊C411yescharacteristic
252C22×C61C2×#13112yes—
253C2×D61—42no—
254C2×D61—42no—
255C2×D61—42no—
256C2×D61—84no—
257C2×D61—84no—
258C2×D61—84no—
259C4×C61—22no—
260C4×C61—22no—
261C4×C61—42no—
262Dic61—21no—
263Dic61—21no—
264Dic61—21no—
265Dic61—21no—
266Dic61—22no—
267Dic61—42no—
268Dic61C2×#10014yes—
269C22×#124—611no—
270C2×#432—611no—
271C2×#431—611no—
272#1469—618no—
273C2×#323—612no—
274C2×#323—612no—
275C2×C61—22no—
276C2×C61—22no—
277C2×C61—82no—
278C2×C61#146914yescomplemented
279C2×C61C2×#40811yescharacteristic
280C2×C61C2×#41011yescharacteristic
281C2×C61C22×#10011yescharacteristic
282D61—82no—
283C23×Q8—611no—
284C23×D4—611no—
285C2×#124—614no—
286C2×#124—614no—
287C2×#124—1221no—
288C2×#124—1221no—
289C2×#124—1221no—
290C2×#124—1221no—
291C2×#124—1222no—
292C2×#124—1222no—
293C22×C22⋊C4—611no—
294C22×C22⋊C4—611no—
295C22×C22⋊C4—611no—
296C22×C22⋊C4#692311yescharacteristic
297C22×C42—611no—
298#432—614no—
299#432—1222no—
300#431—614no—
301#431—1222no—
302C2×C4⋊C8—1221no—
303C2×C4⋊C8—1221no—
304C2×C22⋊C8—612no—
305C2×C22⋊C8—612no—
306C2×#97—1221no—
307C2×C4×C8—1221no—
308#323—618no—
309#323—618no—
310C61C2×#146911yescharacteristic, complemented, Sylow
311C25—611no—
312C25C2×#692311yescharacteristic
313C22×Q8—614no—
314C22×Q8—1222no—
315C22×Q8—1221no—
316C22×Q8—1221no—
317C22×Q8—2444no—
318C22×D4—614no—
319C22×D4—1221no—
320C22×D4—1222no—
321C22×D4—1221no—
322C22×D4—2444no—
323C23×C4—611no—
324C23×C4—611no—
325C23×C4—611no—
326C23×C4C2×#692311yescharacteristic
327C23×C4C2×#692311yescharacteristic
328C22×C8—1222no—
329C22×C8—1222no—
330#124—1224no—
331#124—1224no—
332#124—1224no—
333#124—1224no—
334#124—1224no—
335#124—1224no—
336#124—1224no—
337#124—1224no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—612no—
342C2×C22⋊C4—612no—
343C2×C22⋊C4—612no—
344C2×C22⋊C4—612no—
345C2×C22⋊C4—614no—
346C2×C22⋊C4—1221no—
347C2×C22⋊C4—1221no—
348C2×C22⋊C4—1221no—
349C2×C22⋊C4—1221no—
350C2×C22⋊C4—1221no—
351C2×C22⋊C4—1221no—
352C2×C22⋊C4—1221no—
353C2×C22⋊C4—1221no—
354C2×C22⋊C4—1222no—
355C2×C22⋊C4—1221no—
356C2×C22⋊C4—1221no—
357C2×C22⋊C4C2×#692314yes—
358C2×C42—611no—
359C2×C42—611no—
360C2×C42—611no—
361C2×C42—611no—
362C2×C42—612no—
363C2×C42—612no—
364C2×C42—612no—
365C2×C42—612no—
366C4⋊C8—1224no—
367C4⋊C8—1224no—
368C22⋊C8—614no—
369C22⋊C8—614no—
370C22⋊C8—1222no—
371C22⋊C8—1222no—
372#97—1224no—
373C4×C8—1224no—
374C24—21no—
375C24—21no—
376C24—24no—
377C24—42no—
378C24—42no—
379C24—612no—
380C24—1224no—
381C24—1221no—
382C24—1221no—
383C24—2442no—
384C24—2442no—
385C24C22×#692311yescharacteristic
386C24C22×#692312yes—
387C2×Q8—1224no—
388C2×Q8—1224no—
389C2×Q8—2444no—
390C2×Q8—2448no—
391C2×Q8—2448no—
392C2×Q8—2444no—
393C2×D4—1224no—
394C2×D4—1224no—
395C2×D4—2444no—
396C2×D4—2448no—
397C2×D4—2444no—
398C2×D4—2448no—
399C22×C4—24no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—42no—
403C22×C4—611no—
404C22×C4—612no—
405C22×C4—611no—
406C22×C4—611no—
407C22×C4—611no—
408C22×C4—612no—
409C22×C4—611no—
410C22×C4—611no—
411C22×C4—611no—
412C22×C4—611no—
413C22×C4—612no—
414C22×C4—1224no—
415C22×C4—1221no—
416C22×C4—1221no—
417C22×C4—2442no—
418C22×C4—2442no—
419C22×C4C22⋊#692312yes—
420C22×C4C22⋊#692311yescharacteristic
421C22×C4C22⋊#692311yescharacteristic
422C22×C4C22×#692312yes—
423C22×C4C22×#692312yes—
424C2×C8—1224no—
425C2×C8—1224no—
426C2×C8—2444no—
427C2×C8—2444no—
428C22⋊C4—24no—
429C22⋊C4—24no—
430C22⋊C4—1222no—
431C22⋊C4—1222no—
432C22⋊C4—1222no—
433C22⋊C4—1222no—
434C22⋊C4—1222no—
435C22⋊C4—1222no—
436C22⋊C4—1222no—
437C22⋊C4—1222no—
438C22⋊C4—1224no—
439C22⋊C4—1224no—
440C42—612no—
441C42—612no—
442C42—612no—
443C42—612no—
444C42—612no—
445C42—612no—
446C42—612no—
447C42—612no—
448C23—22no—
449C23—22no—
450C23—22no—
451C23—24no—
452C23—42no—
453C23—42no—
454C23—42no—
455C23—42no—
456C23—42no—
457C23—42no—
458C23—42no—
459C23—42no—
460C23—88no—
461C23—1224no—
462C23—1222no—
463C23—4888no—
464C23—2442no—
465C23—2442no—
466C23—2442no—
467C23—2442no—
468C23—2442no—
469C23—2442no—
470C23—2442no—
471C23—2442no—
472C23C2×C22⋊#692311yescharacteristic
473C23C2×C22⋊#692311yescharacteristic
474C23#1451986414yes—
475C23C23×#692311yescharacteristic
476Q8—2448no—
477Q8—2448no—
478D4—2448no—
479D4—2448no—
480C2×C4—24no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—24no—
484C2×C4—22no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—614no—
489C2×C4—612no—
490C2×C4—611no—
491C2×C4—611no—
492C2×C4—612no—
493C2×C4—611no—
494C2×C4—611no—
495C2×C4—1224no—
496C2×C4—1224no—
497C2×C4—1222no—
498C2×C4—1222no—
499C2×C4—1222no—
500C2×C4—1222no—
501C2×C4—2441no—
502C2×C4—2441no—
503C2×C4—2441no—
504C2×C4—2441no—
505C2×C4—2442no—
506C2×C4—2442no—
507C2×C4—2442no—
508C2×C4C2×C22⋊#692312yes—
509C2×C4C2×C22⋊#692312yes—
510C8—2444no—
511C8—2444no—
512C22—28no—
513C22—21no—
514C22—21no—
515C22—21no—
516C22—21no—
517C22—42no—
518C22—42no—
519C22—42no—
520C22—84no—
521C22—84no—
522C22—84no—
523C22—4884no—
524C22—4884no—
525C22—4884no—
526C22—2442no—
527C22—2442no—
528C22—2442no—
529C22#1684073512yes—
530C22#1684073512yes—
531C22#1684074112yes—
532C22D61⋊#10012yes—
533C22C22×C22⋊#692311yescharacteristic
534C22C2×#1451986412yes—
535C4—22no—
536C4—22no—
537C4—42no—
538C4—614no—
539C4—1221no—
540C4—1221no—
541C4—1221no—
542C4—1221no—
543C4—1222no—
544C4—2442no—
545C2—22no—
546C2—22no—
547C2—82no—
548C2—4882no—
549C2#2146108814yesdirect product factor
550C2C2×#1684073511yescharacteristic
551C2C2×#1684074111yescharacteristic
552C2C2×D61⋊#10011yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC22×C22⋊C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC23×C22⋊D61C4
cosocleC22×Dic61C24
hypercenterC22×C22⋊C4#6923
hypocenterC61C2×#1469
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#16840782C2semidirect
2. C2×#16840778C2semidirect
3. #21461088C2direct (N × H)
4. C2×#16840606C2semidirect
5. C2×#16840605C2semidirect
8. #16840782C22semidirect
10. #16840778C22semidirect
17. #16840606C22semidirect
18. #16840605C22semidirect
278. C2×C61#1469semidirect
310. C61C2×#1469semidirect
549. C2#21461088direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407822
C2×#168407782
#214610882
C2×#168406062
C2×#168406052
C22×#145197632
C2×#146961