Finite Group Databasebeta

← C2×#21448736 #29839318

Subgroups — C2×#21448736 #29839318

Order 15616.

3158 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic122C211yesmaximal, characteristic
2C22×#14519742C212yesmaximal
3#21448736C2116yesmaximal, direct product factor
4C2×#16839659C214yesmaximal
5C2×#16839658C212yesmaximal
6C2×#16839626C212yesmaximal
7C2×C4×C4⋊Dic61C211yesmaximal, characteristic
8C2×#16839613C212yesmaximal
9C2×C61×#382C211yesmaximal, characteristic
10C23×Dic122C2211yescharacteristic
11C2×C4×Dic122C4116yescomplemented
12C2×C4×Dic122C2218yes—
13C2×#14519742—216no—
14C2×#14519742C22116yes—
15C22×C4⋊Dic61C2212yes—
16C22×C4⋊Dic61C2211yescharacteristic
17C22×#11758196C2214yes—
18C22×#11758196C2214yes—
19C22×#11758196C2212yes—
20C22×C4×Dic61C2212yes—
21C22×C4×Dic61C2214yes—
22C22×C4×Dic61C2212yes—
23#16839659C22132yes—
24#16839658C22116yes—
25#16839626C22116yes—
26C4×C4⋊Dic61C2218yes—
27#16839613C22116yes—
28C2×#14519684C2211yescharacteristic
29C2×#14519684C2214yes—
30C2×#14519684C2211yescharacteristic
31C22×C4⋊C4×C61C2212yes—
32C22×C42×C61C2211yescharacteristic
33C61×#382C2218yes—
34C2×#95×C61C2212yes—
35C2×#95×C61C2212yes—
36C22×Dic122C2×C418yes—
37C22×Dic122D418yes—
38C22×Dic122Q818yes—
39C22×Dic122C2314yes—
40C23×Dic61C2312yes—
41C23×Dic61C2312yes—
42C23×Dic61C2312yes—
43C23×Dic61C2312yes—
44C4×Dic122C2×C4164yescomplemented
45#14519742—264no—
46C2×C4⋊Dic61—28no—
47C2×C4⋊Dic61C2×C418yes—
48C2×C4⋊Dic61C2318yes—
49C2×C4⋊Dic61C2314yes—
50C2×#11758196—216no—
51C2×#11758196—216no—
52C2×#11758196C2×C4116yes—
53C2×#11758196C23116yes—
54C2×#11758196C23116yes—
55C2×#11758196C2318yes—
56C2×C4×Dic61—28no—
57C2×C4×Dic61—216no—
58C2×C4×Dic61C2×C4116yes—
59C2×C4×Dic61C23116yes—
60C2×C4×Dic61C2318yes—
61C2×C4×Dic61C2318yes—
62#14519684C2314yes—
63#14519684C2314yes—
64#14519684C23116yes—
65C23×C4×C61C2314yes—
66C23×C4×C61C2311yescharacteristic
67C23×C4×C61C2311yescharacteristic
68C23×C4×C61C2311yescharacteristic
69C2×C4⋊C4×C61—28no—
70C2×C4⋊C4×C61C2318yes—
71C2×C42×C61C2×C418yes—
72C2×C42×C61C2314yes—
73#95×C61C2318yes—
74#95×C61C2318yes—
75C24×C61C2411yescharacteristic
76C22×C4×C61—24no—
77C22×C4×C61—24no—
78C22×C4×C61—28no—
79C22×C4×C61—28no—
80C22×C4×C61—28no—
81C22×C4×C61C22×C414yes—
82C22×C4×C61C22×C414yes—
83C22×C4×C61C22×C414yes—
84C22×C4×C61C2×D414yes—
85C22×C4×C61C2×Q814yes—
86C22×C4×C61C2418yes—
87C22×C4×C61C2412yes—
88C22×C4×C61C2412yes—
89C22×C4×C61C2412yes—
90C22×Dic61—24no—
91C22×Dic61—28no—
92C22×Dic61—24no—
93C22×Dic61—24no—
94C22×Dic61—24no—
95C22×Dic61—24no—
96C22×Dic61C22×C418yes—
97C22×Dic61C22×C418yes—
98C22×Dic61C2×D418yes—
99C22×Dic61C2×Q818yes—
100C22×Dic61#4118yes—
101C22×Dic61C2414yes—
102C22×Dic61C2414yes—
103C22×Dic61C2414yes—
104C22×Dic61C2414yes—
105C2×Dic122C4⋊C4164yescomplemented
106C2×Dic122C22×C4116yes—
107C2×Dic122C2×D4116yes—
108C2×Dic122C2×Q8116yes—
109C4⋊C4×C61—216no—
110C42×C61C22×C4116yes—
111C4⋊Dic61—216no—
112C4⋊Dic61C22×C4116yes—
113#11758196—232no—
114#11758196—232no—
115#11758196C22×C4132yes—
116C4×Dic61—216no—
117C4×Dic61—232no—
118C4×Dic61C22×C4132yes—
119C23×C61C23×C412yes—
120C23×C61C22×D412yes—
121C23×C61C22×Q812yes—
122C23×C61C2×#4114yes—
123C23×C612−1+414yes—
124C23×C61C2511yescharacteristic
125C2×C4×C61—28no—
126C2×C4×C61—28no—
127C2×C4×C61—24no—
128C2×C4×C61—24no—
129C2×C4×C61—28no—
130C2×C4×C61—28no—
131C2×C4×C61—28no—
132C2×C4×C61—416no—
133C2×C4×C61C2×C4⋊C4116yes—
134C2×C4×C61C23×C414yes—
135C2×C4×C61C23×C414yes—
136C2×C4×C61C23×C414yes—
137C2×C4×C61C22×D414yes—
138C2×C4×C61C22×Q814yes—
139C2×Dic61—216no—
140C2×Dic61—216no—
141C2×Dic61—24no—
142C2×Dic61—28no—
143C2×Dic61—24no—
144C2×Dic61—24no—
145C2×Dic61—24no—
146C2×Dic61—24no—
147C2×Dic61—48no—
148C2×Dic61C2×C4⋊C4132yes—
149C2×Dic61C23×C418yes—
150C2×Dic61C23×C418yes—
151C2×Dic61C22×D418yes—
152C2×Dic61C22×Q818yes—
153C2×Dic61C2×#4118yes—
154Dic122C2×C4⋊C4164yescomplemented
155C2×#2351—611nomaximal, Sylow
156C22×C61C22×C4⋊C414yes—
157C22×C61C4×#4114yes—
158C22×C61#51914yes—
159C22×C61#54818yes—
160C22×C61#55718yes—
161C22×C61C24×C411yescharacteristic
162C22×C61C23×D411yescharacteristic
163C22×C61C23×Q811yescharacteristic
164C22×C61C22×#4112yes—
165C22×C61C2×2−1+412yes—
166C4×C61—24no—
167C4×C61—24no—
168C4×C61—48no—
169C4×C61C22×C4⋊C418yes—
170Dic61—28no—
171Dic61—28no—
172Dic61—44no—
173Dic61C22×C4⋊C4116yes—
174C22×C4×Q8—611no—
175C22×C4×Q8—612no—
176#2351—6116no—
177C2×#389—614no—
178C2×#389—612no—
179C2×#382—612no—
180C2×#382D6111yescharacteristic
181C2×C4×C4⋊C4—611no—
182C2×C4×C4⋊C4—612no—
183C2×C61#235118yescomplemented
184C2×C61C23×C4⋊C411yescharacteristic
185C2×C61C2×C4×#4111yescharacteristic
186C2×C61C2×#51911yescharacteristic
187C2×C61C2×#54812yes—
188C2×C61C2×#55712yes—
189C23×Q8—611no—
190C2×C4×Q8—6116no—
191C2×C4×Q8—6116no—
192C2×C4×Q8—618no—
193C2×C4×Q8—12216no—
194C22×C4⋊C4—612no—
195C22×C4⋊C4—611no—
196C22×C4⋊C4—614no—
197C22×C4⋊C4—614no—
198C22×C4⋊C4—612no—
199C22×C4⋊C4C2×D6112yes—
200C22×C42—612no—
201C22×C42—614no—
202C22×C42—612no—
203C22×C42C2×D6111yescharacteristic
204#389—6116no—
205#389—6132no—
206#382—6116no—
207#382C2×D6118yes—
208C4×C4⋊C4—618no—
209C4×C4⋊C4—6116no—
210C2×#95—611no—
211C2×#95—611no—
212C2×#95—614no—
213C2×#95C2×D6112yes—
214C2×#95C2×D6112yes—
215C61C2×#235111yescharacteristic, complemented, Sylow
216C22×Q8—618no—
217C22×Q8—618no—
218C22×Q8—618no—
219C22×Q8—614no—
220C23×C4—612no—
221C23×C4—612no—
222C23×C4—612no—
223C23×C4—612no—
224C23×C4C22×D6114yes—
225C23×C4C22×D6111yescharacteristic
226C23×C4C22×D6111yescharacteristic
227C23×C4C22×D6111yescharacteristic
228C4×Q8—6164no—
229C4×Q8—12264no—
230C2×C4⋊C4—28no—
231C2×C4⋊C4—6116no—
232C2×C4⋊C4—618no—
233C2×C4⋊C4—618no—
234C2×C4⋊C4—614no—
235C2×C4⋊C4—6116no—
236C2×C4⋊C4—6116no—
237C2×C4⋊C4—618no—
238C2×C4⋊C4—12216no—
239C2×C4⋊C4—12216no—
240C2×C4⋊C4—1228no—
241C2×C4⋊C4C22×D6118yes—
242C2×C42—6116no—
243C2×C42—618no—
244C2×C42—6116no—
245C2×C42—618no—
246C2×C42—12216no—
247C2×C42—1228no—
248C2×C42C4×D6118yes—
249C2×C42C22×D6114yes—
250#95—614no—
251#95—614no—
252#95—6116no—
253#95C22×D6118yes—
254#95C22×D6118yes—
255C24C23×D6111yescharacteristic
256C2×Q8—6116no—
257C2×Q8—6116no—
258C2×Q8—6116no—
259C2×Q8—6164no—
260C22×C4—24no—
261C22×C4—24no—
262C22×C4—28no—
263C22×C4—28no—
264C22×C4—28no—
265C22×C4—618no—
266C22×C4—618no—
267C22×C4—618no—
268C22×C4—614no—
269C22×C4—618no—
270C22×C4—618no—
271C22×C4—614no—
272C22×C4—614no—
273C22×C4—614no—
274C22×C4—1224no—
275C22×C4—1228no—
276C22×C4—1224no—
277C22×C4—1224no—
278C22×C4—1224no—
279C22×C4—1224no—
280C22×C4C2×C4×D6114yes—
281C22×C4C2×C4×D6114yes—
282C22×C4C2×C4×D6114yes—
283C22×C4D4×D6114yes—
284C22×C4Q8×D6114yes—
285C22×C4C23×D6118yes—
286C22×C4C23×D6112yes—
287C22×C4C23×D6112yes—
288C22×C4C23×D6112yes—
289C4⋊C4—216no—
290C4⋊C4—6132no—
291C4⋊C4—6116no—
292C4⋊C4—12232no—
293C4⋊C4—12232no—
294C4⋊C4—12216no—
295C42—6132no—
296C42—12232no—
297C42—12216no—
298C42C2×C4×D61116yes—
299C23C22×C4×D6112yes—
300C23C2×D4×D6112yes—
301C23C2×Q8×D6112yes—
302C23#41×D6114yes—
303C23#1451982414yes—
304C23C24×D6111yescharacteristic
305Q8—6164no—
306C2×C4—28no—
307C2×C4—28no—
308C2×C4—24no—
309C2×C4—24no—
310C2×C4—28no—
311C2×C4—28no—
312C2×C4—28no—
313C2×C4—416no—
314C2×C4—6132no—
315C2×C4—618no—
316C2×C4—618no—
317C2×C4—618no—
318C2×C4—618no—
319C2×C4—618no—
320C2×C4—12216no—
321C2×C4—1224no—
322C2×C4—1228no—
323C2×C4—1224no—
324C2×C4—12216no—
325C2×C4—1224no—
326C2×C4—1224no—
327C2×C4—1224no—
328C2×C4—2448no—
329C2×C4C4⋊C4×D61116yes—
330C2×C4C22×C4×D6114yes—
331C2×C4C22×C4×D6114yes—
332C2×C4C22×C4×D6114yes—
333C2×C4C2×D4×D6114yes—
334C2×C4C2×Q8×D6114yes—
335C22C2×C4⋊C4×D6114yes—
336C22#1684023014yes—
337C22#1684023914yes—
338C22#1684042018yes—
339C22#1684048918yes—
340C22C23×C4×D6111yescharacteristic
341C22C22×D4×D6111yescharacteristic
342C22C22×Q8×D6111yescharacteristic
343C22C2×#41×D6112yes—
344C22C2×#1451982412yes—
345C4—24no—
346C4—24no—
347C4—48no—
348C4—6116no—
349C4—1228no—
350C4—1228no—
351C4—2444no—
352C4C2×C4⋊C4×D6118yes—
353C2#2144873618yesdirect product factor
354C2C22×C4⋊C4×D6111yescharacteristic
355C2C2×#1684023011yescharacteristic
356C2C2×#1684023911yescharacteristic
357C2C2×#1684042012yes—
358C2C2×#1684048912yes—
subgroupG/H
centerC24C23×D61
commutatorC22×C61C24×C4
FrattiniC23C24×D61
FittingC2×C61×#382C2
socle, prime radicalC24×C61C24
cosocleC23×C61C25
hypercenterC2×#382D61
hypocenterC61C2×#2351
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#382

Complements

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

NH ≅ G/Ntype
3. #21448736C2direct (N × H)
11. C2×C4×Dic122C4semidirect
44. C4×Dic122C2×C4semidirect
105. C2×Dic122C4⋊C4semidirect
154. Dic122C2×C4⋊C4semidirect
183. C2×C61#2351semidirect
215. C61C2×#2351semidirect
353. C2#21448736direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×Dic1222
C22×#145197422
#214487362
C2×#168396592
C2×#168396582
C2×#168396262
C2×C4×C4⋊Dic612
C2×#168396132
C2×C61×#3822
C2×#235161