Finite Group Databasebeta

← C2×#21454085 #29886604

Subgroups — C2×#21454085 #29886604

Order 15616.

1806 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454085C2116yesmaximal, direct product factor
2C2×#16839703C212yesmaximal
3C2×#16839701C211yesmaximal, characteristic
4C2×#16839696C212yesmaximal
5C2×#16839695C212yesmaximal
6C2×#16839693C212yesmaximal
7C2×#16839681C212yesmaximal
8C2×#16839631C211yesmaximal, characteristic
9C2×#16839629C212yesmaximal
10C2×C61×#395C211yesmaximal, characteristic
11C22×C4⋊Dic61C2211yescharacteristic
12C22×C4⋊Dic61C2211yescharacteristic
13C22×#11758196C2212yes—
14C22×#11758196C2212yes—
15C22×#11758196C2212yes—
16C22×#11758196C2212yes—
17C22×#11758196C2212yes—
18C22×C4×Dic61C2211yescharacteristic
19#16839703C22116yes—
20#16839701C2218yes—
21#16839696C22116yes—
22#16839695C22116yes—
23#16839693C22116yes—
24#16839681C22116yes—
25#16839631C2218yes—
26#16839629C22116yes—
27C2×#14519684C2212yes—
28C2×#14519684C2212yes—
29C2×#14519684C2212yes—
30C2×#14519684C2212yes—
31C2×#14519684C2212yes—
32C2×#14519684C2212yes—
33C2×#14519684C2211yescharacteristic
34C2×#14519684C2212yes—
35C23×Q8×C61C2211yescharacteristic
36C22×C4⋊C4×C61C2211yescharacteristic
37C22×C4⋊C4×C61C2212yes—
38C61×#395C2218yes—
39C2×#95×C61C2212yes—
40C2×#95×C61C2211yescharacteristic
41C23×Dic61C2312yes—
42C23×Dic61C2312yes—
43C23×Dic61C2312yes—
44C23×Dic61C2312yes—
45C2×C4⋊Dic61—42no—
46C2×C4⋊Dic61—42no—
47C2×C4⋊Dic61C2314yes—
48C2×C4⋊Dic61C2314yes—
49C2×#11758196—44no—
50C2×#11758196—44no—
51C2×#11758196—44no—
52C2×#11758196—44no—
53C2×#11758196—44no—
54C2×#11758196C2318yes—
55C2×#11758196C2318yes—
56C2×#11758196C2318yes—
57C2×#11758196C2318yes—
58C2×#11758196C2318yes—
59C2×C4×Dic61Q818yescomplemented
60C2×C4×Dic61C2314yes—
61#14519684C2318yes—
62#14519684C2318yes—
63#14519684C2318yes—
64#14519684C2314yes—
65#14519684C2318yes—
66#14519684C2318yes—
67#14519684C2318yes—
68#14519684C2318yes—
69C22×Q8×C61—42no—
70C22×Q8×C61—44no—
71C22×Q8×C61C2314yes—
72C23×C4×C61C2311yescharacteristic
73C23×C4×C61C2311yescharacteristic
74C23×C4×C61C2312yes—
75C23×C4×C61C2312yes—
76C23×C4×C61C2311yescharacteristic
77C2×C4⋊C4×C61—42no—
78C2×C4⋊C4×C61—44no—
79C2×C4⋊C4×C61C2318yes—
80C2×C4⋊C4×C61C2314yes—
81#95×C61C2318yes—
82#95×C61C2314yes—
83C24×C61C2411yescharacteristic
84C2×Q8×C61—48no—
85C2×Q8×C61—44no—
86C2×Q8×C61—416no—
87C22×C4×C61—22no—
88C22×C4×C61—22no—
89C22×C4×C61—24no—
90C22×C4×C61—22no—
91C22×C4×C61—24no—
92C22×C4×C61—24no—
93C22×C4×C61—22no—
94C22×C4×C61—24no—
95C22×C4×C61—24no—
96C22×C4×C61—24no—
97C22×C4×C61—24no—
98C22×C4×C61—24no—
99C22×C4×C61C2×Q814yes—
100C22×C4×C61C2414yes—
101C22×C4×C61C2414yes—
102C22×C4×C61C2412yes—
103C22×C4×C61C2412yes—
104C22×C4×C61C2412yes—
105C22×Dic61—24no—
106C22×Dic61—24no—
107C22×Dic61—24no—
108C22×Dic61—24no—
109C22×Dic61—24no—
110C22×Dic61—24no—
111C22×Dic61—24no—
112C22×Dic61—24no—
113C22×Dic61—24no—
114C22×Dic61—28no—
115C22×Dic61C2×Q818yes—
116C22×Dic61C2414yes—
117C22×Dic61C2414yes—
118C22×Dic61C2414yes—
119C22×Dic61C2414yes—
120C4⋊C4×C61—44no—
121C4⋊C4×C61—48no—
122C4⋊Dic61—44no—
123C4⋊Dic61—44no—
124#11758196—48no—
125#11758196—48no—
126#11758196—48no—
127#11758196—48no—
128#11758196—48no—
129C4×Dic61C2×Q8116yescomplemented
130C23×C61C22×Q812yes—
131C23×C61H(5,𝔽2)14yes—
132C23×C61H(5,𝔽2)12yes—
133C23×C612−1+412yes—
134C23×C612−1+414yes—
135C23×C61C2511yescharacteristic
136Q8×C61—416no—
137C2×C4×C61—28no—
138C2×C4×C61—22no—
139C2×C4×C61—22no—
140C2×C4×C61—24no—
141C2×C4×C61—24no—
142C2×C4×C61—24no—
143C2×C4×C61—24no—
144C2×C4×C61—24no—
145C2×C4×C61—22no—
146C2×C4×C61—24no—
147C2×C4×C61—22no—
148C2×C4×C61—24no—
149C2×C4×C61—24no—
150C2×C4×C61—44no—
151C2×C4×C61—44no—
152C2×C4×C61—48no—
153C2×C4×C61—48no—
154C2×C4×C61C22×Q814yes—
155C2×Dic61—216no—
156C2×Dic61—24no—
157C2×Dic61—24no—
158C2×Dic61—24no—
159C2×Dic61—24no—
160C2×Dic61—24no—
161C2×Dic61—24no—
162C2×Dic61—24no—
163C2×Dic61—24no—
164C2×Dic61—24no—
165C2×Dic61—28no—
166C2×Dic61—48no—
167C2×Dic61—48no—
168C2×Dic61—48no—
169C2×Dic61C22×Q818yes—
170C2×#2843—611nomaximal, Sylow
171C22×C61#54418yes—
172C22×C61#54414yes—
173C22×C61#56014yes—
174C22×C61#56314yes—
175C22×C61#56318yes—
176C22×C61C23×Q811yescharacteristic
177C22×C61C2×H(5,𝔽2)12yes—
178C22×C61C2×H(5,𝔽2)11yescharacteristic
179C22×C61C2×2−1+411yescharacteristic
180C22×C61C2×2−1+412yes—
181C4×C61—24no—
182C4×C61—42no—
183C4×C61—44no—
184C4×C61—42no—
185C4×C61—44no—
186Dic61—28no—
187Dic61—44no—
188Dic61—44no—
189Dic61—44no—
190#2843—6116no—
191C2×#400—612no—
192C2×#400—611no—
193C2×#398—612no—
194C2×#398—612no—
195C2×#398—612no—
196C2×#395—612no—
197C2×#395D6111yescharacteristic
198C2×#384—611no—
199C2×#383—612no—
200C2×C61#284318yescomplemented
201C2×C61C2×#54412yes—
202C2×C61C2×#54411yescharacteristic
203C2×C61C2×#56011yescharacteristic
204C2×C61C2×#56311yescharacteristic
205C2×C61C2×#56312yes—
206C23×Q8C2×D6111yescharacteristic
207C22×C4⋊C4—612no—
208C22×C4⋊C4—612no—
209C22×C4⋊C4—612no—
210C22×C4⋊C4—612no—
211C22×C4⋊C4—612no—
212C22×C4⋊C4—611no—
213C22×C4⋊C4—611no—
214C22×C4⋊C4C2×D6112yes—
215C22×C4⋊C4C2×D6111yescharacteristic
216C22×C42—611no—
217#400—618no—
218#400—6116no—
219#398—6116no—
220#398—6116no—
221#398—6116no—
222#395—6116no—
223#395C2×D6118yes—
224#384—618no—
225#383—6116no—
226C2×#95—612no—
227C2×#95—612no—
228C2×#95—612no—
229C2×#95—612no—
230C2×#95—611no—
231C2×#95—612no—
232C2×#95—612no—
233C2×#95—612no—
234C2×#95C2×D6112yes—
235C2×#95C2×D6111yescharacteristic
236C61C2×#284311yescharacteristic, complemented, Sylow
237C22×Q8—42no—
238C22×Q8—44no—
239C22×Q8C22×D6114yes—
240C23×C4—612no—
241C23×C4—612no—
242C23×C4—612no—
243C23×C4—612no—
244C23×C4C22×D6111yescharacteristic
245C23×C4C22×D6112yes—
246C23×C4C22×D6111yescharacteristic
247C23×C4C22×D6112yes—
248C23×C4C22×D6111yescharacteristic
249C2×C4⋊C4—42no—
250C2×C4⋊C4—44no—
251C2×C4⋊C4—618no—
252C2×C4⋊C4—618no—
253C2×C4⋊C4—614no—
254C2×C4⋊C4—618no—
255C2×C4⋊C4—618no—
256C2×C4⋊C4—618no—
257C2×C4⋊C4—614no—
258C2×C4⋊C4—2444no—
259C2×C4⋊C4—2444no—
260C2×C4⋊C4—2444no—
261C2×C4⋊C4—2444no—
262C2×C4⋊C4—2444no—
263C2×C4⋊C4—2442no—
264C2×C4⋊C4—2442no—
265C2×C4⋊C4C22×D6114yes—
266C2×C4⋊C4C22×D6118yes—
267C2×C42—618no—
268C2×C42—614no—
269#95—618no—
270#95—618no—
271#95—618no—
272#95—618no—
273#95—618no—
274#95—618no—
275#95—614no—
276#95—618no—
277#95C22×D6118yes—
278#95C22×D6114yes—
279C24C23×D6111yescharacteristic
280C2×Q8—48no—
281C2×Q8—44no—
282C2×Q8—416no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—24no—
287C22×C4—24no—
288C22×C4—22no—
289C22×C4—24no—
290C22×C4—24no—
291C22×C4—24no—
292C22×C4—24no—
293C22×C4—24no—
294C22×C4—24no—
295C22×C4—618no—
296C22×C4—614no—
297C22×C4—614no—
298C22×C4—614no—
299C22×C4—614no—
300C22×C4—1224no—
301C22×C4—1224no—
302C22×C4—1224no—
303C22×C4—1224no—
304C22×C4—1224no—
305C22×C4—1224no—
306C22×C4—1224no—
307C22×C4—1224no—
308C22×C4—1228no—
309C22×C4—1224no—
310C22×C4Q8×D6114yes—
311C22×C4C23×D6114yes—
312C22×C4C23×D6114yes—
313C22×C4C23×D6112yes—
314C22×C4C23×D6112yes—
315C22×C4C23×D6112yes—
316C4⋊C4—44no—
317C4⋊C4—48no—
318C4⋊C4—2448no—
319C4⋊C4—2448no—
320C4⋊C4—2448no—
321C4⋊C4—2448no—
322C4⋊C4—2448no—
323C4⋊C4—2444no—
324C4⋊C4—2444no—
325C42—6116no—
326C23C2×Q8×D6112yes—
327C23#1451982212yes—
328C23#1451982214yes—
329C23#1451982412yes—
330C23#1451982514yes—
331C23C24×D6111yescharacteristic
332Q8—416no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—28no—
336C2×C4—24no—
337C2×C4—22no—
338C2×C4—24no—
339C2×C4—24no—
340C2×C4—22no—
341C2×C4—24no—
342C2×C4—24no—
343C2×C4—24no—
344C2×C4—24no—
345C2×C4—24no—
346C2×C4—44no—
347C2×C4—44no—
348C2×C4—48no—
349C2×C4—48no—
350C2×C4—618no—
351C2×C4—1224no—
352C2×C4—1224no—
353C2×C4—12216no—
354C2×C4—1224no—
355C2×C4—1224no—
356C2×C4—1224no—
357C2×C4—1224no—
358C2×C4—1224no—
359C2×C4—1224no—
360C2×C4—1228no—
361C2×C4—1224no—
362C2×C4—2448no—
363C2×C4—2448no—
364C2×C4—2448no—
365C2×C4C2×Q8×D6114yes—
366C22#1684038918yes—
367C22#1684039114yes—
368C22#1684050114yes—
369C22#1684051114yes—
370C22#1684051318yes—
371C22C22×Q8×D6111yescharacteristic
372C22C2×#1451982212yes—
373C22C2×#1451982211yescharacteristic
374C22C2×#1451982411yescharacteristic
375C22C2×#1451982512yes—
376C4—24no—
377C4—42no—
378C4—44no—
379C4—42no—
380C4—44no—
381C4—1228no—
382C4—2444no—
383C4—2444no—
384C4—2444no—
385C2#2145408518yesdirect product factor
386C2C2×#1684038912yes—
387C2C2×#1684039111yescharacteristic
388C2C2×#1684050111yescharacteristic
389C2C2×#1684051111yescharacteristic
390C2C2×#1684051312yes—
subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC2×C61×#395C2
socle, prime radicalC24×C61C24
hypercenterC2×#395D61
hypocenterC61C2×#2843
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#395

Complements

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

NH ≅ G/Ntype
1. #21454085C2direct (N × H)
59. C2×C4×Dic61Q8semidirect
129. C4×Dic61C2×Q8semidirect
200. C2×C61#2843semidirect
236. C61C2×#2843semidirect
385. C2#21454085direct (N × H)

Maximal subgroups

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

subgroupindex
#214540852
C2×#168397032
C2×#168397012
C2×#168396962
C2×#168396952
C2×#168396932
C2×#168396812
C2×#168396312
C2×#168396292
C2×C61×#3952
C2×#284361