Finite Group Databasebeta

← C103×#34128 #39939403

Subgroups — C103×#34128 #39939403

Order 26368.

2446 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Q8×C103C211yesmaximal, characteristic
2C103×#2356C216yesmaximal, complemented
3C103×#2351C212yesmaximal, complemented
4C103×#2344C216yesmaximal
5Q8×C22⋊C4×C103C212yesmaximal
6C103×#2295C216yesmaximal, complemented
7C103×#2283C213yesmaximal
8C42×Q8×C103C212yesmaximal, complemented
9C4×#117×C103C213yesmaximal
10C23×Q8×C103C2211yescharacteristic
11C2×C4×Q8×C103C4116yescomplemented
12C2×C4×Q8×C103C2214yes—
13C2×C4×Q8×C103C2211yescharacteristic
14C2×C4×Q8×C103C2213yes—
15C2×C4×Q8×C103C2211yescharacteristic
16C2×C4×Q8×C103C2213yes—
17C2×#117×C103C2216yes—
18C22×C4⋊C4×C103C2213yes—
19C22×C42×C103C2213yes—
20#391×C103C22112yes—
21#389×C103C22112yes—
22#387×C103C22124yes—
23#383×C103C2216yes—
24#382×C103C2216yes—
25#381×C103C2216yes—
26#380×C103C2216yes—
27C4×C4⋊C4×C103C2216yes—
28C4×C4⋊C4×C103C2216yes—
29C4×C4⋊C4×C103C2216yes—
30C4×C4⋊C4×C103C22112yes—
31C4×C22⋊C4×C103C2211yescharacteristic
32C4×C22⋊C4×C103C2213yes—
33C4×C22⋊C4×C103C2216yes—
34#376×C103C2216yes—
35#376×C103C2216yes—
36C43×C103C2216yes—
37C22×Q8×C103—28no—
38C22×Q8×C103C2×C418yes—
39C22×Q8×C103C2313yes—
40C22×Q8×C103C2311yescharacteristic
41C23×C4×C103C2313yes—
42C23×C4×C103C2313yes—
43C23×C4×C103C2311yescharacteristic
44C4×Q8×C103—216no—
45C4×Q8×C103C2×C4124yes—
46C4×Q8×C103C2×C4124yes—
47C4×Q8×C103C2×C418yes—
48C4×Q8×C103C2×C418yes—
49#117×C103—224no—
50C2×C4⋊C4×C103C2×C4124yes—
51C2×C4⋊C4×C103C23112yes—
52C2×C4⋊C4×C103C23112yes—
53C2×C4⋊C4×C103C2313yes—
54C2×C4⋊C4×C103C2316yes—
55C2×C4⋊C4×C103C2313yes—
56C2×C22⋊C4×C103C2316yes—
57C2×C22⋊C4×C103C2312yes—
58C2×C42×C103C2×C4124yes—
59C2×C42×C103C23112yes—
60C2×C42×C103C23112yes—
61C2×C42×C103C2312yes—
62C2×C42×C103C2316yes—
63C2×C42×C103C2313yes—
64C2×C42×C103C2313yes—
65C2×C42×C103C2313yes—
66C2×C42×C103C2313yes—
67#95×C103C2312yes—
68#95×C103C2316yes—
69#95×C103C23112yes—
70#95×C103C23112yes—
71#95×C103C23112yes—
72#95×C103C23112yes—
73C24×C103C2411yescharacteristic
74C2×Q8×C103—232no—
75C2×Q8×C103—212no—
76C2×Q8×C103C22×C4112yes—
77C2×Q8×C103C22×C414yes—
78C2×Q8×C103#4118yes—
79C22×C4×C103—212no—
80C22×C4×C103—212no—
81C22×C4×C103—24no—
82C22×C4×C103C22×C414yes—
83C22×C4×C103C22×C4112yes—
84C22×C4×C103C22×C4112yes—
85C22×C4×C103C24112yes—
86C22×C4×C103C2411yescharacteristic
87C22×C4×C103C2413yes—
88C22×C4×C103C2413yes—
89C22×C4×C103C2413yes—
90C22×C4×C103C2414yes—
91C22×C4×C103C2413yes—
92C22×C4×C103C2411yescharacteristic
93C4⋊C4×C103—224no—
94C4⋊C4×C103—224no—
95C4⋊C4×C103C22×C4124yes—
96C4⋊C4×C103C22×C4112yes—
97C4⋊C4×C103C22×C4112yes—
98C22⋊C4×C103—212no—
99C22⋊C4×C103#4118yes—
100C42×C103—224no—
101C42×C103—224no—
102C42×C103—24no—
103C42×C103—212no—
104C42×C103C22×C4112yes—
105C42×C103C22×C4112yes—
106C42×C103C22×C4112yes—
107C42×C103C22×C4112yes—
108C23×C103—22no—
109C23×C103—22no—
110C23×C103C23×C412yes—
111C23×C103C2×#4114yes—
112C23×C103C2511yescharacteristic
113Q8×C103—224no—
114Q8×C103#117116yescomplemented
115C2×C4×C103—224no—
116C2×C4×C103—24no—
117C2×C4×C103—26no—
118C2×C4×C103—26no—
119C2×C4×C103—26no—
120C2×C4×C103—24no—
121C2×C4×C103—22no—
122C2×C4×C103—224no—
123C2×C4×C103—28no—
124C2×C4×C103—212no—
125C2×C4×C103—212no—
126C2×C4×C103—212no—
127C2×C4×C103C23×C412yes—
128C2×C4×C103C23×C416yes—
129C2×C4×C103C23×C416yes—
130C2×C4×C103C23×C416yes—
131C2×C4×C103C23×C416yes—
132C2×C4×C103C23×C412yes—
133C2×C4×C103C2×#4118yes—
134C2×C4×C103C2×#41112yes—
135C2×C4×C1032−1+414yes—
136C22×C103—22no—
137C22×C103—22no—
138C22×C103—28no—
139C22×C103C4×#4114yes—
140C22×C103C24×C411yescharacteristic
141C22×C103C22×#4112yes—
142C22×C103C22×#4112yes—
143C22×C103C2×2−1+412yes—
144C4×C103—26no—
145C4×C103—26no—
146C4×C103—26no—
147C4×C103—22no—
148C4×C103—28no—
149C4×C103—412no—
150C4×C103C2×#117112yes—
151C4×C103#51914yes—
152#34128C10311yesmaximal, characteristic, direct product factor, Sylow
153C2×C103—24no—
154C2×C103C22×#11711yescharacteristic
155C2×C103C2×C4×#4111yescharacteristic
156C2×C103C2×#51911yescharacteristic
157C2×C103#348214yes—
158C22×C4×Q8C2×C10311yescharacteristic
159#2356C2×C10316yescomplemented
160#2351C2×C10312yescomplemented
161#2344C2×C10316yes—
162Q8×C22⋊C4C2×C10312yes—
163#2295C2×C10316yescomplemented
164#2283C2×C10313yes—
165C42×Q8C2×C10312yescomplemented
166C4×#117C2×C10313yes—
167C103#3412811yescharacteristic, direct product factor, Sylow
168C23×Q8C22×C10311yescharacteristic
169C2×C4×Q8C4×C103116yescomplemented
170C2×C4×Q8C22×C10314yes—
171C2×C4×Q8C22×C10311yescharacteristic
172C2×C4×Q8C22×C10313yes—
173C2×C4×Q8C22×C10311yescharacteristic
174C2×C4×Q8C22×C10313yes—
175C2×#117C22×C10316yes—
176C22×C4⋊C4C22×C10313yes—
177C22×C42C22×C10313yes—
178#391C22×C103112yes—
179#389C22×C103112yes—
180#387C22×C103124yes—
181#383C22×C10316yes—
182#382C22×C10316yes—
183#381C22×C10316yes—
184#380C22×C10316yes—
185C4×C4⋊C4C22×C103112yes—
186C4×C4⋊C4C22×C10316yes—
187C4×C4⋊C4C22×C10316yes—
188C4×C4⋊C4C22×C10316yes—
189C4×C22⋊C4C22×C10316yes—
190C4×C22⋊C4C22×C10311yescharacteristic
191C4×C22⋊C4C22×C10313yes—
192#376C22×C10316yes—
193#376C22×C10316yes—
194C43C22×C10316yes—
195C22×Q8—28no—
196C22×Q8C2×C4×C10318yes—
197C22×Q8C23×C10313yes—
198C22×Q8C23×C10311yescharacteristic
199C23×C4C23×C10313yes—
200C23×C4C23×C10313yes—
201C23×C4C23×C10311yescharacteristic
202C4×Q8—216no—
203C4×Q8C2×C4×C103124yes—
204C4×Q8C2×C4×C103124yes—
205C4×Q8C2×C4×C10318yes—
206C4×Q8C2×C4×C10318yes—
207#117—224no—
208C2×C4⋊C4C2×C4×C103124yes—
209C2×C4⋊C4C23×C103112yes—
210C2×C4⋊C4C23×C103112yes—
211C2×C4⋊C4C23×C10313yes—
212C2×C4⋊C4C23×C10316yes—
213C2×C4⋊C4C23×C10313yes—
214C2×C22⋊C4C23×C10316yes—
215C2×C22⋊C4C23×C10312yes—
216C2×C42C2×C4×C103124yes—
217C2×C42C23×C103112yes—
218C2×C42C23×C103112yes—
219C2×C42C23×C10312yes—
220C2×C42C23×C10316yes—
221C2×C42C23×C10313yes—
222C2×C42C23×C10313yes—
223C2×C42C23×C10313yes—
224C2×C42C23×C10313yes—
225#95C23×C10312yes—
226#95C23×C10316yes—
227#95C23×C103112yes—
228#95C23×C103112yes—
229#95C23×C103112yes—
230#95C23×C103112yes—
231C24C24×C10311yescharacteristic
232C2×Q8—232no—
233C2×Q8—212no—
234C2×Q8C22×C4×C103112yes—
235C2×Q8C22×C4×C10314yes—
236C2×Q8#41×C10318yes—
237C22×C4—212no—
238C22×C4—212no—
239C22×C4—24no—
240C22×C4C22×C4×C10314yes—
241C22×C4C22×C4×C103112yes—
242C22×C4C22×C4×C103112yes—
243C22×C4C24×C103112yes—
244C22×C4C24×C10311yescharacteristic
245C22×C4C24×C10313yes—
246C22×C4C24×C10313yes—
247C22×C4C24×C10313yes—
248C22×C4C24×C10314yes—
249C22×C4C24×C10313yes—
250C22×C4C24×C10311yescharacteristic
251C4⋊C4—224no—
252C4⋊C4—224no—
253C4⋊C4C22×C4×C103124yes—
254C4⋊C4C22×C4×C103112yes—
255C4⋊C4C22×C4×C103112yes—
256C22⋊C4—212no—
257C22⋊C4#41×C10318yes—
258C42—224no—
259C42—224no—
260C42—24no—
261C42—212no—
262C42C22×C4×C103112yes—
263C42C22×C4×C103112yes—
264C42C22×C4×C103112yes—
265C42C22×C4×C103112yes—
266C23—22no—
267C23—22no—
268C23C23×C4×C10312yes—
269C23C2×#41×C10314yes—
270C23C25×C10311yescharacteristic
271Q8—224no—
272Q8#117×C103116yescomplemented
273C2×C4—224no—
274C2×C4—24no—
275C2×C4—26no—
276C2×C4—26no—
277C2×C4—26no—
278C2×C4—24no—
279C2×C4—22no—
280C2×C4—224no—
281C2×C4—28no—
282C2×C4—212no—
283C2×C4—212no—
284C2×C4—212no—
285C2×C4C23×C4×C10312yes—
286C2×C4C23×C4×C10316yes—
287C2×C4C23×C4×C10316yes—
288C2×C4C23×C4×C10316yes—
289C2×C4C23×C4×C10316yes—
290C2×C4C23×C4×C10312yes—
291C2×C4C2×#41×C10318yes—
292C2×C4C2×#41×C103112yes—
293C2×C42−1+4×C10314yes—
294C22—28no—
295C22—22no—
296C22—22no—
297C22C4×#41×C10314yes—
298C22C24×C4×C10311yescharacteristic
299C22C22×#41×C10312yes—
300C22C22×#41×C10312yes—
301C22C2×2−1+4×C10312yes—
302C4—28no—
303C4—26no—
304C4—26no—
305C4—26no—
306C4—22no—
307C4—412no—
308C4C2×#117×C103112yes—
309C4#519×C10314yes—
310C2—24no—
311C2C22×#117×C10311yescharacteristic
312C2C2×C4×#41×C10311yescharacteristic
313C2C2×#519×C10311yescharacteristic
314C2C103×#348214yes—
subgroupG/H
centerC22×C4×C103C24
commutatorC22C24×C4×C103
Frattini, cosocleC23C25×C103
socleC23×C103C25
prime radicalC24×C103C24
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C103×#2356C2semidirect
3. C103×#2351C2semidirect
6. C103×#2295C2semidirect
8. C42×Q8×C103C2semidirect
11. C2×C4×Q8×C103C4semidirect
114. Q8×C103#117semidirect
152. #34128C103direct (N × H)
159. #2356C2×C103semidirect
160. #2351C2×C103semidirect
163. #2295C2×C103semidirect
165. C42×Q8C2×C103semidirect
167. C103#34128direct (N × H)
169. C2×C4×Q8C4×C103semidirect
272. Q8#117×C103semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Q8×C1032
C103×#23562
C103×#23512
C103×#23442
Q8×C22⋊C4×C1032
C103×#22952
C103×#22832
C42×Q8×C1032
C4×#117×C1032
#34128103