Finite Group Databasebeta

← C2×#21461291 #30611457

Subgroups — C2×#21461291 #30611457

Order 15616.

1050 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840782C211yesmaximal, characteristic
2C22×#14519832C211yesmaximal, characteristic
3#21461291C218yesmaximal, direct product factor
4C2×#16840619C212yesmaximal, complemented
5C2×#16840619C212yesmaximal, complemented
6C2×#16840315C211yesmaximal, characteristic
7C23×#92420—21no—
8#16840782—22no—
9#16840782C2214yes—
10C2×#14519844—21no—
11C2×C22⋊#92420—21no—
12C2×#14519832—21no—
13C2×#14519832—22no—
14C2×#14519832C2212yes—
15C2×#14519832C2212yes—
16C2×#14519832C2214yes—
17#16840619C2218yescomplemented
18#16840619C2218yescomplemented
19#16840315—22no—
20#16840315—22no—
21#16840315C414yes—
22#16840315C2214yes—
23C2×#14519776C411yescharacteristic
24C2×#14519776C411yescharacteristic
25C2×#14519768C2211yescharacteristic
26C2×#14519768C2211yescharacteristic
27C2×#14519754—21no—
28C2×#14519754—21no—
29C2×C4×Dic122—21no—
30C2×C4×Dic122—21no—
31C2×#14519736C411yescharacteristic
32C22×C4×Dic61C2211yescharacteristic
33C2×#117×C61C411yescharacteristic
34C22×#92420—28no—
35C22×#92420—22no—
36C22×#92420—24no—
37C22×#92420—22no—
38#14519844—24no—
39C22⋊#92420—24no—
40#14519832—24no—
41#14519832—22no—
42#14519832—22no—
43#14519832C2314yes—
44#14519832C2314yes—
45C22×Dic122—21no—
46C22×Dic122—21no—
47C23×Dic61D411yescharacteristic
48C23×Dic61D411yescharacteristic
49#14519776—22no—
50#14519776—22no—
51#14519776C2×C414yes—
52#14519776C2×C414yes—
53#14519768—21no—
54#14519768—21no—
55#14519768—21no—
56#14519768—21no—
57#14519768C2×C412yes—
58#14519768C2×C412yes—
59#14519768C2312yes—
60#14519768C2312yes—
61#14519754—24no—
62#14519754—24no—
63#14519754—24no—
64#14519754—24no—
65C4×Dic122—24no—
66C4×Dic122—24no—
67C4×Dic122—24no—
68C4×Dic122—24no—
69#14519736—22no—
70#14519736C2×C414yes—
71C2×C4⋊Dic61—21no—
72C2×C4⋊Dic61—21no—
73C2×C4⋊Dic61C2×C411yescharacteristic
74C2×C4⋊Dic61C2×C411yescharacteristic
75C2×#11758196—21no—
76C2×#11758196—21no—
77C2×#11758196—21no—
78C2×#11758196—21no—
79C2×C22⋊Dic61—21no—
80C2×C4×Dic61—21no—
81C2×C4×Dic61C2×C411yescharacteristic
82C2×C4×Dic61C2×C412yes—
83C2×C4×Dic61D411yescharacteristic
84C2×C4×Dic61D412yes—
85C2×C4×Dic61D411yescharacteristic
86C2×C4×Dic61D412yes—
87C2×C4×Dic61C2311yescharacteristic
88C2×C4×Dic61C2312yes—
89C23×C4×C61C2×C411yescharacteristic
90#117×C61—22no—
91#117×C61C2×C414yes—
92C2×C4⋊C4×C61C2×C411yescharacteristic
93C2×C4⋊C4×C61C2×C411yescharacteristic
94C2×C22⋊C4×C61—21no—
95C2×C42×C61—21no—
96C24×C61C22⋊C411yescharacteristic
97C22×C4×C61—24no—
98C22×C4×C61—21no—
99C22×C4×C61—21no—
100C22×C4×C61C22⋊C411yescharacteristic
101C22×C4×C61C22⋊C412yes—
102C22×C4×C61C22×C411yescharacteristic
103C22×C4×C61C22×C412yes—
104C22×Dic61—24no—
105C22×Dic61—21no—
106C22×Dic61—21no—
107C22×Dic61—42no—
108C22×Dic61C22⋊C411yescharacteristic
109C22×Dic61C22⋊C412yes—
110C22×Dic61C22⋊C412yes—
111C22×Dic61C22⋊C411yescharacteristic
112C22×Dic61C2×D411yescharacteristic
113C22×Dic61C2×D411yescharacteristic
114C22×Dic61C2×D412yes—
115C22×Dic61C2×D412yes—
116C2×Dic122—24no—
117C2×Dic122—24no—
118C2×Dic122—44no—
119C2×Dic122—44no—
120C2×#92420—28no—
121C2×#92420—216no—
122C2×#92420—24no—
123C2×#92420—24no—
124C2×#92420—44no—
125C4⋊C4×C61—21no—
126C4⋊C4×C61—21no—
127C4⋊C4×C61C22×C412yes—
128C4⋊C4×C61C22×C412yes—
129C22⋊C4×C61—24no—
130C42×C61—24no—
131C22⋊Dic61—24no—
132C4⋊Dic61—21no—
133C4⋊Dic61—21no—
134C4⋊Dic61—22no—
135C4⋊Dic61—22no—
136C4⋊Dic61—22no—
137C4⋊Dic61—22no—
138C4⋊Dic61C22×C412yes—
139C4⋊Dic61C22×C412yes—
140#11758196—22no—
141#11758196—22no—
142#11758196—24no—
143#11758196—24no—
144#11758196—22no—
145#11758196—22no—
146C4×Dic61—24no—
147C4×Dic61C22⋊C412yes—
148C4×Dic61C22⋊C412yes—
149C4×Dic61C22⋊C412yes—
150C4×Dic61C22×C411yescharacteristic
151C4×Dic61C22×C412yes—
152C4×Dic61C2×D412yes—
153C4×Dic61C2×D411yescharacteristic
154C4×Dic61C2×D411yescharacteristic
155C4×Dic61C2×D412yes—
156C4×Dic61C2411yescharacteristic
157C23×C61—22no—
158C23×C61—22no—
159C23×C61#10114yes—
160C23×C61C2×C22⋊C412yes—
161C23×C61C2×C22⋊C411yescharacteristic
162C2×C4×C61—24no—
163C2×C4×C61—22no—
164C2×C4×C61—24no—
165C2×C4×C61—22no—
166C2×C4×C61—22no—
167C2×C4×C61—22no—
168C2×C4×C61—42no—
169C2×C4×C61—42no—
170C2×C4×C61C2×C22⋊C412yes—
171C2×C4×C61C2×C22⋊C411yescharacteristic
172C2×C4×C61C23×C411yescharacteristic
173C2×Dic61—22no—
174C2×Dic61—22no—
175C2×Dic61—22no—
176C2×Dic61—24no—
177C2×Dic61—24no—
178C2×Dic61—22no—
179C2×Dic61—22no—
180C2×Dic61—42no—
181C2×Dic61—42no—
182C2×Dic61—42no—
183C2×Dic61—42no—
184C2×Dic61#10414yes—
185C2×Dic61C2×C22⋊C411yescharacteristic
186C2×Dic61C2×C22⋊C411yescharacteristic
187C2×Dic61C2×C22⋊C412yes—
188C2×Dic61C2×C22⋊C412yes—
189C2×Dic61C22×D411yescharacteristic
190C2×Dic61C22×D411yescharacteristic
191Dic122—48no—
192Dic122—48no—
193#92420—28no—
194#92420—44no—
195C2×#1531—611nomaximal, Sylow
196C22×C61—22no—
197C22×C61—22no—
198C22×C61—28no—
199C22×C61C2×#10114yes—
200C22×C61C2×#10112yes—
201C22×C61C2×#10412yes—
202C22×C61#42112yes—
203C22×C61C22×C22⋊C411yescharacteristic
204C4×C61—22no—
205C4×C61—21no—
206C4×C61—21no—
207C4×C61—42no—
208C4×C61—42no—
209Dic61—21no—
210Dic61—21no—
211Dic61—21no—
212Dic61—22no—
213Dic61—21no—
214Dic61—42no—
215Dic61—42no—
216Dic61C2×#10414yes—
217C2×#533—611no—
218C2×#432—611no—
219C22×#97—611no—
220#1531—618no—
221C2×#330—612no—
222C2×#330—612no—
223C2×C61—24no—
224C2×C61#153114yescomplemented
225C2×C61C22×#10111yescharacteristic
226C2×C61C22×#10411yescharacteristic
227C2×C61C2×#42111yescharacteristic
228C23×C8—1221no—
229#533—614no—
230#533—614no—
231#533—1222no—
232#533—1222no—
233C2×C4⋊Q8—611no—
234C2×C4⋊Q8—611no—
235C2×#125—611no—
236C2×#125—611no—
237C2×C22⋊Q8—1221no—
238C2×C22⋊Q8—1221no—
239C2×C4×Q8—1221no—
240C2×C4×Q8—1221no—
241C2×#117—611no—
242C2×#117#692311yescharacteristic
243C22×C42—611no—
244#432—614no—
245#432—1222no—
246C2×C4⋊C8—1221no—
247C2×C22⋊C8—1221no—
248C2×#97—612no—
249C2×#97—614no—
250C2×#97—612no—
251C2×#97—1221no—
252C2×#97—1222no—
253#330—618no—
254#330—618no—
255C61C2×#153111yescharacteristic, complemented, Sylow
256C22×Q8—1221no—
257C22×Q8—1221no—
258C23×C4—611no—
259C23×C4—611no—
260C23×C4C2×#692311yescharacteristic
261C22×C8—1224no—
262C22×C8—1222no—
263C22×C8—1228no—
264C22×C8—1222no—
265C4⋊Q8—614no—
266C4⋊Q8—614no—
267C4⋊Q8—1222no—
268C4⋊Q8—1222no—
269#125—612no—
270#125—612no—
271#125—612no—
272#125—612no—
273#125—1221no—
274#125—1221no—
275#125—1221no—
276#125—1221no—
277C22⋊Q8—1224no—
278C22⋊Q8—1224no—
279C22⋊Q8—1224no—
280C22⋊Q8—1224no—
281C4×Q8—1224no—
282C4×Q8—1224no—
283C4×Q8—1224no—
284C4×Q8—1224no—
285#117—22no—
286#117—614no—
287#117—1222no—
288#117C2×#692314yes—
289C2×C4⋊C4—611no—
290C2×C4⋊C4—611no—
291C2×C4⋊C4—1221no—
292C2×C4⋊C4—1221no—
293C2×C4⋊C4—1221no—
294C2×C4⋊C4—1221no—
295C2×C4⋊C4—1221no—
296C2×C4⋊C4—1221no—
297C2×C4⋊C4C2×#692311yescharacteristic
298C2×C4⋊C4C2×#692311yescharacteristic
299C2×C22⋊C4—21no—
300C2×C22⋊C4—1221no—
301C2×C42—21no—
302C2×C42—611no—
303C2×C42—611no—
304C2×C42—612no—
305C2×C42—612no—
306C2×C42—611no—
307C2×C42—611no—
308C2×C42—612no—
309C2×C42—612no—
310C2×C42—1221no—
311C4⋊C8—1224no—
312C22⋊C8—1224no—
313#97—614no—
314#97—614no—
315#97—1224no—
316#97—1222no—
317#97—1222no—
318C24C22⋊#692311yescharacteristic
319C2×Q8—1224no—
320C2×Q8—1224no—
321C2×Q8—2444no—
322C2×Q8—2444no—
323C22×C4—24no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—611no—
327C22×C4—612no—
328C22×C4—612no—
329C22×C4—611no—
330C22×C4—611no—
331C22×C4—611no—
332C22×C4—612no—
333C22×C4—612no—
334C22×C4—1224no—
335C22×C4—1221no—
336C22×C4—1221no—
337C22×C4—2442no—
338C22×C4C22⋊#692312yes—
339C22×C4C22⋊#692311yescharacteristic
340C22×C4C22×#692312yes—
341C22×C4C22×#692311yescharacteristic
342C2×C8—1224no—
343C2×C8—12216no—
344C2×C8—1228no—
345C2×C8—1224no—
346C2×C8—2444no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—612no—
350C4⋊C4—612no—
351C4⋊C4—1222no—
352C4⋊C4—1222no—
353C4⋊C4—1222no—
354C4⋊C4—1222no—
355C4⋊C4—1224no—
356C4⋊C4—1224no—
357C4⋊C4—1222no—
358C4⋊C4—1222no—
359C4⋊C4—1222no—
360C4⋊C4—1222no—
361C4⋊C4—1221no—
362C4⋊C4—1221no—
363C4⋊C4C22×#692312yes—
364C4⋊C4C22×#692312yes—
365C22⋊C4—24no—
366C22⋊C4—1224no—
367C42—24no—
368C42—612no—
369C42—611no—
370C42—611no—
371C42—612no—
372C42—612no—
373C42—612no—
374C42—612no—
375C42—611no—
376C42—611no—
377C42—612no—
378C42—1224no—
379C23—22no—
380C23—22no—
381C23#1451983814yes—
382C23C2×C22⋊#692312yes—
383C23C2×C22⋊#692311yescharacteristic
384Q8—2448no—
385Q8—2448no—
386C2×C4—24no—
387C2×C4—22no—
388C2×C4—24no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—614no—
395C2×C4—612no—
396C2×C4—611no—
397C2×C4—611no—
398C2×C4—612no—
399C2×C4—611no—
400C2×C4—611no—
401C2×C4—1224no—
402C2×C4—1224no—
403C2×C4—1222no—
404C2×C4—1222no—
405C2×C4—1222no—
406C2×C4—1222no—
407C2×C4—1222no—
408C2×C4—2442no—
409C2×C4—2442no—
410C2×C4—2442no—
411C2×C4—2442no—
412C2×C4C2×C22⋊#692312yes—
413C2×C4C2×C22⋊#692311yescharacteristic
414C2×C4C23×#692311yescharacteristic
415C8—1228no—
416C8—2444no—
417C22—28no—
418C22—22no—
419C22—22no—
420C22C2×#1451983814yes—
421C22C2×#1451983812yes—
422C22D61⋊#10412yes—
423C22#1684075912yes—
424C22C22×C22⋊#692311yescharacteristic
425C4—22no—
426C4—21no—
427C4—21no—
428C4—42no—
429C4—42no—
430C4—614no—
431C4—1221no—
432C4—1221no—
433C4—1221no—
434C4—1221no—
435C4—1222no—
436C4—2442no—
437C4—2442no—
438C2—24no—
439C2#2146129114yesdirect product factor
440C2C22×#1451983811yescharacteristic
441C2C2×D61⋊#10411yescharacteristic
442C2C2×#1684075911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×#117×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22⋊C4
cosocleC4×Dic61C24
hypercenterC2×#117#6923
hypocenterC61C2×#1531
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
3. #21461291C2direct (N × H)
4. C2×#16840619C2semidirect
5. C2×#16840619C2semidirect
17. #16840619C22semidirect
18. #16840619C22semidirect
224. C2×C61#1531semidirect
255. C61C2×#1531semidirect
439. C2#21461291direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407822
C22×#145198322
#214612912
C2×#168406192
C2×#168403152
C2×#153161