Finite Group Databasebeta

← C4×#21440632 #44510001

Subgroups — C4×#21440632 #44510001

Order 30848.

484 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#21440632C211yesmaximal, characteristic
2#29507614C211yesmaximal, characteristic
3#29507612C211yesmaximal, characteristic
4#29507603C211yesmaximal, characteristic
5#29507602C211yesmaximal, characteristic
6#29507599C211yesmaximal, characteristic
7#29507598C211yesmaximal, characteristic
8#29507581C211yesmaximal, characteristic
9C4×#16838749C211yesmaximal, characteristic
10C4×#16838749C211yesmaximal, characteristic
11C4×#16838749C211yesmaximal, characteristic
12C4×#16838749C211yesmaximal, characteristic
13C4×C4⋊Dic241C211yesmaximal, characteristic
14C42×Dic241C211yesmaximal, characteristic
15C4×C4⋊C4×C241C211yesmaximal, characteristic
16#21440632C418yesdirect product factor
17C2×C4⋊Dic241C2211yescharacteristic
18C2×C4⋊Dic241C2211yescharacteristic
19C2×#16838749C2211yescharacteristic
20C2×#16838749C2211yescharacteristic
21C2×#16838749C2211yescharacteristic
22C2×#16838749C2211yescharacteristic
23C2×#16838749C2211yescharacteristic
24C2×#16838749C2211yescharacteristic
25C2×#16838749C2211yescharacteristic
26C2×#16838749C2211yescharacteristic
27C2×C4×Dic241C2211yescharacteristic
28C2×C4×Dic241C2211yescharacteristic
29C2×C4×Dic241C2211yescharacteristic
30C2×C4×Dic241C2211yescharacteristic
31C2×C4×Dic241C2211yescharacteristic
32C2×C4×Dic241C2211yescharacteristic
33C2×C4×Dic241C2211yescharacteristic
34C2×C4×Dic241C2211yescharacteristic
35#21440549C2211yescharacteristic
36#21440549C2211yescharacteristic
37#21440549C2211yescharacteristic
38#21440549C2211yescharacteristic
39#21440549C2211yescharacteristic
40#21440549C2211yescharacteristic
41#21440549C2211yescharacteristic
42#21440549C2211yescharacteristic
43#21440549C2211yescharacteristic
44#21440549C2211yescharacteristic
45C2×C4⋊C4×C241C2211yescharacteristic
46C2×C4⋊C4×C241C2211yescharacteristic
47C2×C42×C241C2211yescharacteristic
48C2×C42×C241C2211yescharacteristic
49C2×C42×C241C2211yescharacteristic
50#95×C241C2211yescharacteristic
51#95×C241C2211yescharacteristic
52C22×Dic241C2311yescharacteristic
53C22×Dic241C2311yescharacteristic
54C22×Dic241C2311yescharacteristic
55C22×Dic241C2311yescharacteristic
56C22×Dic241C2311yescharacteristic
57C22×Dic241C2311yescharacteristic
58C22×Dic241C2311yescharacteristic
59C22×Dic241C2311yescharacteristic
60C4⋊Dic241—22no—
61C4⋊Dic241C2×C414yes—
62#16838749—22no—
63#16838749—22no—
64#16838749—22no—
65#16838749—22no—
66#16838749C2×C414yes—
67#16838749C2×C414yes—
68#16838749C2×C414yes—
69#16838749C2×C414yes—
70C4×Dic241—22no—
71C4×Dic241—22no—
72C4×Dic241—22no—
73C4×Dic241—22no—
74C4×Dic241—22no—
75C4×Dic241—22no—
76C4×Dic241C2×C414yes—
77C4×Dic241Q814yes—
78C22×C4×C241C2311yescharacteristic
79C22×C4×C241C2311yescharacteristic
80C22×C4×C241C2311yescharacteristic
81C22×C4×C241C2311yescharacteristic
82C22×C4×C241C2311yescharacteristic
83C22×C4×C241C2311yescharacteristic
84C22×C4×C241C2311yescharacteristic
85C4⋊C4×C241—22no—
86C4⋊C4×C241C2×C414yes—
87C42×C241—22no—
88C42×C241—22no—
89C42×C241—22no—
90C2×Dic241—21no—
91C2×Dic241—21no—
92C2×Dic241—21no—
93C2×Dic241—21no—
94C2×Dic241—21no—
95C2×Dic241—21no—
96C2×Dic241—21no—
97C2×Dic241—21no—
98C2×Dic241—21no—
99C2×Dic241—21no—
100C2×Dic241—21no—
101C2×Dic241—21no—
102C2×Dic241—21no—
103C2×Dic241—21no—
104C2×Dic241—21no—
105C2×Dic241—21no—
106C2×Dic241C22×C412yes—
107C2×Dic241C22×C412yes—
108C2×Dic241C22×C412yes—
109C2×Dic241C22×C412yes—
110C2×Dic241C2×Q812yes—
111C2×Dic241C2×Q812yes—
112C2×Dic241#4112yes—
113C2×Dic241#4112yes—
114C23×C241C2411yescharacteristic
115C2×C4×C241—21no—
116C2×C4×C241—21no—
117C2×C4×C241—21no—
118C2×C4×C241—21no—
119C2×C4×C241—21no—
120C2×C4×C241—21no—
121C2×C4×C241—21no—
122C2×C4×C241—21no—
123C2×C4×C241—21no—
124C2×C4×C241—21no—
125C2×C4×C241—21no—
126C2×C4×C241—21no—
127C2×C4×C241—21no—
128C2×C4×C241—21no—
129C2×C4×C241C22×C412yes—
130C2×C4×C241C22×C412yes—
131C2×C4×C241C22×C412yes—
132C2×C4×C241C2×Q812yes—
133C2×C4×C241#4112yes—
134C2×C4×C241#4112yes—
135C2×C4×C241#4112yes—
136C22×C241C23×C411yescharacteristic
137C22×C241C22×Q811yescharacteristic
138C22×C241C2×#4111yescharacteristic
139C22×C241C2×#4111yescharacteristic
140C22×C241C2×#4111yescharacteristic
141C22×C241C2×#4111yescharacteristic
142C22×C241C2×#4111yescharacteristic
143C4×C241—22no—
144C4×C241—22no—
145C4×C241—22no—
146C4×C241—22no—
147C4×C241—41no—
148C4×C241—41no—
149C4×C241#12514yescomplemented
150Dic241—22no—
151Dic241—22no—
152Dic241—22no—
153Dic241—22no—
154Dic241—22no—
155Dic241—41no—
156Dic241—41no—
157Dic241C4×Q814yes—
158C2×C241C2×C4×Q811yescharacteristic
159C2×C241C4×#4111yescharacteristic
160C2×C241C4×#4111yescharacteristic
161C2×C241C2×#12511yescharacteristic
162C2×C241#52911yescharacteristic
163C2×C241#52911yescharacteristic
164C2×C241#53311yescharacteristic
165C241C4×#12511yescharacteristic, complemented, Sylow
166C4×#125—2411nomaximal, Sylow
167C2×#125—2411no—
168#389—2411no—
169#389—2411no—
170#387—2411no—
171#387—2411no—
172#387—2411no—
173#387—2411no—
174#382—2411no—
175C4×C4⋊C4—2411no—
176C4×C4⋊C4—2411no—
177C4×C4⋊C4—2411no—
178C4×C4⋊C4—2411no—
179C4×C4⋊C4—2411no—
180C4×C4⋊C4D24111yescharacteristic
181C43—2411no—
182#125—2418no—
183C2×C4⋊C4—2411no—
184C2×C4⋊C4—2411no—
185C2×C4⋊C4—2411no—
186C2×C4⋊C4—2411no—
187C2×C4⋊C4—2411no—
188C2×C4⋊C4—2411no—
189C2×C4⋊C4—2411no—
190C2×C4⋊C4—2411no—
191C2×C4⋊C4—2411no—
192C2×C4⋊C4—2411no—
193C2×C4⋊C4C2×D24111yescharacteristic
194C2×C4⋊C4C2×D24111yescharacteristic
195C2×C42—2411no—
196C2×C42—2411no—
197C2×C42—2411no—
198C2×C42—2411no—
199C2×C42—2411no—
200C2×C42—2411no—
201C2×C42—2411no—
202C2×C42—2411no—
203C2×C42C2×D24111yescharacteristic
204C2×C42C2×D24111yescharacteristic
205C2×C42C2×D24111yescharacteristic
206#95—2411no—
207#95—2411no—
208#95—2411no—
209#95—2411no—
210#95—2411no—
211#95—2411no—
212#95—2411no—
213#95—2411no—
214#95—2411no—
215#95—2411no—
216#95C2×D24111yescharacteristic
217#95C2×D24111yescharacteristic
218C22×C4—2411no—
219C22×C4—2411no—
220C22×C4—2411no—
221C22×C4—2411no—
222C22×C4—2411no—
223C22×C4—2411no—
224C22×C4—2411no—
225C22×C4—2411no—
226C22×C4C22×D24111yescharacteristic
227C22×C4C22×D24111yescharacteristic
228C22×C4C22×D24111yescharacteristic
229C22×C4C22×D24111yescharacteristic
230C22×C4C22×D24111yescharacteristic
231C22×C4C22×D24111yescharacteristic
232C22×C4C22×D24111yescharacteristic
233C4⋊C4—22no—
234C4⋊C4—4822no—
235C4⋊C4—4822no—
236C4⋊C4—4822no—
237C4⋊C4—4822no—
238C4⋊C4—4822no—
239C4⋊C4—2414no—
240C4⋊C4—2414no—
241C4⋊C4—2414no—
242C4⋊C4—2414no—
243C4⋊C4—2414no—
244C4⋊C4C4×D24114yes—
245C42—22no—
246C42—22no—
247C42—22no—
248C42—4822no—
249C42—4822no—
250C42—4822no—
251C42—4822no—
252C42—4822no—
253C42—4822no—
254C42—2414no—
255C42—2414no—
256C23C23×D24111yescharacteristic
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—4821no—
272C2×C4—4821no—
273C2×C4—4821no—
274C2×C4—4821no—
275C2×C4—4821no—
276C2×C4—4821no—
277C2×C4—4821no—
278C2×C4—4821no—
279C2×C4—4821no—
280C2×C4—4821no—
281C2×C4—4821no—
282C2×C4—4821no—
283C2×C4—4821no—
284C2×C4—4821no—
285C2×C4—4821no—
286C2×C4—4821no—
287C2×C4—2412no—
288C2×C4—2412no—
289C2×C4—2412no—
290C2×C4—2412no—
291C2×C4—2412no—
292C2×C4—2412no—
293C2×C4—2412no—
294C2×C4—2412no—
295C2×C4C2×C4×D24112yes—
296C2×C4C2×C4×D24112yes—
297C2×C4C2×C4×D24112yes—
298C2×C4Q8×D24112yes—
299C2×C4#1683876912yes—
300C2×C4#1683877012yes—
301C2×C4#1683877012yes—
302C22C22×C4×D24111yescharacteristic
303C22C2×Q8×D24111yescharacteristic
304C22#41×D24111yescharacteristic
305C22#41×D24111yescharacteristic
306C22C2×#1683876911yescharacteristic
307C22C2×#1683877011yescharacteristic
308C22C2×#1683877011yescharacteristic
309C4—22no—
310C4—22no—
311C4—22no—
312C4—22no—
313C4—41no—
314C4—41no—
315C4—9641no—
316C4—9641no—
317C4—4822no—
318C4—4822no—
319C4—4822no—
320C4—4822no—
321C4—4822no—
322C4—2414no—
323C4#2144063214yesdirect product factor
324C2C4×Q8×D24111yescharacteristic
325C2C4×#1683876911yescharacteristic
326C2C4×#1683877011yescharacteristic
327C2C2×#2144063211yescharacteristic
328C2#2950824511yescharacteristic
329C2#2950824711yescharacteristic
330C2#2950827111yescharacteristic
subgroupG/H
centerC22×C4C22×D241
commutatorC22×C241C23×C4
FrattiniC23C23×D241
FittingC4×C4⋊C4×C241C2
socle, prime radical, cosocleC23×C241C24
hypercenterC4×C4⋊C4D241
hypocenterC241C4×#125
LCSG ▷ C22×C241 ▷ C241
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
16. #21440632C4direct (N × H)
149. C4×C241#125semidirect
165. C241C4×#125semidirect
323. C4#21440632direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#214406322
#295076142
#295076122
#295076032
#295076022
#295075992
#295075982
#295075812
C4×#168387492
C4×C4⋊Dic2412
C42×Dic2412
C4×C4⋊C4×C2412
C4×#125241