Finite Group Databasebeta

← C103×#34192 #39939467

Subgroups — C103×#34192 #39939467

Order 26368.

2250 conjugacy classes of subgroups.

The subgroup lattice has 310 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×#2345C216yesmaximal
5Q8×C22⋊C4×C103C212yesmaximal
6C103×#2320C216yesmaximal, complemented
7C103×#2283C213yesmaximal
8C103×#2283C213yesmaximal
9C103×#2276C212yesmaximal, complemented
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—
17C22×C4⋊C4×C103C2213yes—
18C22×C42×C103C2213yes—
19#391×C103C22112yes—
20#389×C103C22112yes—
21#387×C103C22124yes—
22#383×C103C2216yes—
23#383×C103C2216yes—
24#382×C103C2216yes—
25#382×C103C2216yes—
26#381×C103C2211yescharacteristic
27#381×C103C2213yes—
28#380×C103C2216yes—
29#380×C103C2216yes—
30C4×C4⋊C4×C103C2216yes—
31C4×C4⋊C4×C103C22112yes—
32C4×C4⋊C4×C103C2216yes—
33C4×C22⋊C4×C103C2216yes—
34C4×C22⋊C4×C103C2216yes—
35#376×C103C2216yes—
36#376×C103C2216yes—
37C22×Q8×C103—28no—
38C22×Q8×C103C2×C418yes—
39C22×Q8×C103C2313yes—
40C22×Q8×C103C2311yescharacteristic
41C23×C4×C103C2313yes—
42C23×C4×C103C2311yescharacteristic
43C23×C4×C103C2313yes—
44C4×Q8×C103—216no—
45C4×Q8×C103C2×C4124yes—
46C4×Q8×C103C2×C4124yes—
47C4×Q8×C103C2×C418yes—
48C4×Q8×C103C2×C418yes—
49C2×C4⋊C4×C103C2×C4124yes—
50C2×C4⋊C4×C103C23112yes—
51C2×C4⋊C4×C103C23112yes—
52C2×C4⋊C4×C103C2313yes—
53C2×C4⋊C4×C103C2316yes—
54C2×C4⋊C4×C103C2313yes—
55C2×C22⋊C4×C103C2312yes—
56C2×C22⋊C4×C103C2316yes—
57C2×C42×C103C2×C4124yes—
58C2×C42×C103C23112yes—
59C2×C42×C103C23112yes—
60C2×C42×C103C2313yes—
61C2×C42×C103C2313yes—
62C2×C42×C103C2313yes—
63C2×C42×C103C2313yes—
64#95×C103C2312yes—
65#95×C103C2316yes—
66#95×C103C23112yes—
67#95×C103C2316yes—
68#95×C103C23112yes—
69#95×C103C23112yes—
70#95×C103C23112yes—
71#95×C103C2312yes—
72C24×C103C2411yescharacteristic
73C2×Q8×C103—232no—
74C2×Q8×C103—212no—
75C2×Q8×C103C22×C4112yes—
76C2×Q8×C103C22×C414yes—
77C2×Q8×C103#4118yes—
78C22×C4×C103—24no—
79C22×C4×C103—212no—
80C22×C4×C103—46no—
81C22×C4×C103C22×C414yes—
82C22×C4×C103C22×C4112yes—
83C22×C4×C103C22×C4112yes—
84C22×C4×C103C2414yes—
85C22×C4×C103C24112yes—
86C22×C4×C103C2411yescharacteristic
87C22×C4×C103C2411yescharacteristic
88C22×C4×C103C2413yes—
89C22×C4×C103C2413yes—
90C22×C4×C103C2413yes—
91C22×C4×C103C2413yes—
92C4⋊C4×C103—224no—
93C4⋊C4×C103—412no—
94C4⋊C4×C103C22×C4124yes—
95C4⋊C4×C103C22×C4112yes—
96C4⋊C4×C103C22×C4112yes—
97C22⋊C4×C103—24no—
98C22⋊C4×C103—212no—
99C42×C103—224no—
100C42×C103—412no—
101C42×C103C22×C4112yes—
102C42×C103C22×C4112yes—
103C42×C103C22×C4112yes—
104C42×C103C22×C4112yes—
105C23×C103—22no—
106C23×C103—22no—
107C23×C103C23×C412yes—
108C23×C1032−1+414yes—
109C23×C103C2511yescharacteristic
110Q8×C103—224no—
111Q8×C103#117116yes—
112C2×C4×C103—28no—
113C2×C4×C103—26no—
114C2×C4×C103—22no—
115C2×C4×C103—22no—
116C2×C4×C103—26no—
117C2×C4×C103—26no—
118C2×C4×C103—224no—
119C2×C4×C103—24no—
120C2×C4×C103—212no—
121C2×C4×C103—24no—
122C2×C4×C103—212no—
123C2×C4×C103—212no—
124C2×C4×C103—24no—
125C2×C4×C103—412no—
126C2×C4×C103C23×C412yes—
127C2×C4×C103C23×C412yes—
128C2×C4×C103C23×C416yes—
129C2×C4×C103C23×C416yes—
130C2×C4×C103C23×C416yes—
131C2×C4×C103C23×C416yes—
132C2×C4×C103C2×#41112yes—
133C22×C103—22no—
134C22×C103—22no—
135C22×C103—28no—
136C22×C103#51914yes—
137C22×C103C24×C411yescharacteristic
138C22×C103C22×#4112yes—
139C22×C103C2×2−1+412yes—
140C22×C103#58512yes—
141C4×C103—26no—
142C4×C103—22no—
143C4×C103—22no—
144C4×C103—26no—
145C4×C103—26no—
146C4×C103—44no—
147C4×C103—412no—
148C4×C103C2×#117112yes—
149#34192C10311yesmaximal, characteristic, direct product factor, Sylow
150C2×C103—24no—
151C2×C103C22×#11711yescharacteristic
152C2×C103C2×#51911yescharacteristic
153C2×C103#342811yescharacteristic
154C2×C103#351614yes—
155C22×C4×Q8C2×C10311yescharacteristic
156#2356C2×C10316yescomplemented
157#2351C2×C10312yescomplemented
158#2345C2×C10316yes—
159Q8×C22⋊C4C2×C10312yes—
160#2320C2×C10316yescomplemented
161#2283C2×C10313yes—
162#2283C2×C10313yes—
163#2276C2×C10312yescomplemented
164C103#3419211yescharacteristic, direct product factor, Sylow
165C23×Q8C22×C10311yescharacteristic
166C2×C4×Q8C4×C103116yescomplemented
167C2×C4×Q8C22×C10314yes—
168C2×C4×Q8C22×C10313yes—
169C2×C4×Q8C22×C10311yescharacteristic
170C2×C4×Q8C22×C10313yes—
171C2×C4×Q8C22×C10311yescharacteristic
172C22×C4⋊C4C22×C10313yes—
173C22×C42C22×C10313yes—
174#391C22×C103112yes—
175#389C22×C103112yes—
176#387C22×C103124yes—
177#383C22×C10316yes—
178#383C22×C10316yes—
179#382C22×C10316yes—
180#382C22×C10316yes—
181#381C22×C10311yescharacteristic
182#381C22×C10313yes—
183#380C22×C10316yes—
184#380C22×C10316yes—
185C4×C4⋊C4C22×C10316yes—
186C4×C4⋊C4C22×C103112yes—
187C4×C4⋊C4C22×C10316yes—
188C4×C22⋊C4C22×C10316yes—
189C4×C22⋊C4C22×C10316yes—
190#376C22×C10316yes—
191#376C22×C10316yes—
192C22×Q8—28no—
193C22×Q8C2×C4×C10318yes—
194C22×Q8C23×C10313yes—
195C22×Q8C23×C10311yescharacteristic
196C23×C4C23×C10313yes—
197C23×C4C23×C10311yescharacteristic
198C23×C4C23×C10313yes—
199C4×Q8—216no—
200C4×Q8C2×C4×C103124yes—
201C4×Q8C2×C4×C103124yes—
202C4×Q8C2×C4×C10318yes—
203C4×Q8C2×C4×C10318yes—
204C2×C4⋊C4C2×C4×C103124yes—
205C2×C4⋊C4C23×C103112yes—
206C2×C4⋊C4C23×C103112yes—
207C2×C4⋊C4C23×C10313yes—
208C2×C4⋊C4C23×C10316yes—
209C2×C4⋊C4C23×C10313yes—
210C2×C22⋊C4C23×C10312yes—
211C2×C22⋊C4C23×C10316yes—
212C2×C42C2×C4×C103124yes—
213C2×C42C23×C103112yes—
214C2×C42C23×C103112yes—
215C2×C42C23×C10313yes—
216C2×C42C23×C10313yes—
217C2×C42C23×C10313yes—
218C2×C42C23×C10313yes—
219#95C23×C10312yes—
220#95C23×C10316yes—
221#95C23×C103112yes—
222#95C23×C10316yes—
223#95C23×C103112yes—
224#95C23×C103112yes—
225#95C23×C103112yes—
226#95C23×C10312yes—
227C24C24×C10311yescharacteristic
228C2×Q8—232no—
229C2×Q8—212no—
230C2×Q8C22×C4×C103112yes—
231C2×Q8C22×C4×C10314yes—
232C2×Q8#41×C10318yes—
233C22×C4—24no—
234C22×C4—212no—
235C22×C4—46no—
236C22×C4C22×C4×C10314yes—
237C22×C4C22×C4×C103112yes—
238C22×C4C22×C4×C103112yes—
239C22×C4C24×C10314yes—
240C22×C4C24×C103112yes—
241C22×C4C24×C10311yescharacteristic
242C22×C4C24×C10311yescharacteristic
243C22×C4C24×C10313yes—
244C22×C4C24×C10313yes—
245C22×C4C24×C10313yes—
246C22×C4C24×C10313yes—
247C4⋊C4—224no—
248C4⋊C4—412no—
249C4⋊C4C22×C4×C103124yes—
250C4⋊C4C22×C4×C103112yes—
251C4⋊C4C22×C4×C103112yes—
252C22⋊C4—24no—
253C22⋊C4—212no—
254C42—224no—
255C42—412no—
256C42C22×C4×C103112yes—
257C42C22×C4×C103112yes—
258C42C22×C4×C103112yes—
259C42C22×C4×C103112yes—
260C23—22no—
261C23—22no—
262C23C23×C4×C10312yes—
263C232−1+4×C10314yes—
264C23C25×C10311yescharacteristic
265Q8—224no—
266Q8#117×C103116yes—
267C2×C4—28no—
268C2×C4—26no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—26no—
272C2×C4—26no—
273C2×C4—224no—
274C2×C4—24no—
275C2×C4—212no—
276C2×C4—24no—
277C2×C4—212no—
278C2×C4—212no—
279C2×C4—24no—
280C2×C4—412no—
281C2×C4C23×C4×C10312yes—
282C2×C4C23×C4×C10312yes—
283C2×C4C23×C4×C10316yes—
284C2×C4C23×C4×C10316yes—
285C2×C4C23×C4×C10316yes—
286C2×C4C23×C4×C10316yes—
287C2×C4C2×#41×C103112yes—
288C22—28no—
289C22—22no—
290C22—22no—
291C22#519×C10314yes—
292C22C24×C4×C10311yescharacteristic
293C22C22×#41×C10312yes—
294C22C2×2−1+4×C10312yes—
295C22#585×C10312yes—
296C4—26no—
297C4—22no—
298C4—22no—
299C4—26no—
300C4—26no—
301C4—44no—
302C4—412no—
303C4C2×#117×C103112yes—
304C2—24no—
305C2C22×#117×C10311yescharacteristic
306C2C2×#519×C10311yescharacteristic
307C2C103×#342811yescharacteristic
308C2C103×#351614yes—
subgroupG/H
center, socleC23×C103C25
commutatorC22C24×C4×C103
Frattini, cosocleC23C25×C103
prime radicalC24×C103C24
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C103×#2356C2semidirect
3. C103×#2351C2semidirect
6. C103×#2320C2semidirect
9. C103×#2276C2semidirect
11. C2×C4×Q8×C103C4semidirect
149. #34192C103direct (N × H)
156. #2356C2×C103semidirect
157. #2351C2×C103semidirect
160. #2320C2×C103semidirect
163. #2276C2×C103semidirect
164. C103#34192direct (N × H)
166. C2×C4×Q8C4×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×#23452
Q8×C22⋊C4×C1032
C103×#23202
C103×#22832
C103×#22762
#34192103