Finite Group Databasebeta

← C103×#34193 #39939468

Subgroups — C103×#34193 #39939468

Order 26368.

2414 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#41×C103C211yesmaximal, characteristic
2C103×#2354C216yesmaximal, complemented
3Q8×C4⋊C4×C103C212yesmaximal, complemented
4C103×#2347C216yesmaximal, complemented
5C103×#2341C212yesmaximal
6C103×#2319C216yesmaximal, complemented
7C103×#2285C213yesmaximal, complemented
8C103×#2283C213yesmaximal, complemented
9C103×#2276C212yesmaximal, complemented
10C22×#41×C103C2211yescharacteristic
11C4×#41×C103C4116yescomplemented
12C2×C4×Q8×C103C2214yes—
13C2×C4×Q8×C103C2211yescharacteristic
14C2×C4×Q8×C103C2211yescharacteristic
15C2×C4×D4×C103C2213yes—
16C2×C4×D4×C103C2213yes—
17C2×#117×C103C2216yes—
18C2×#117×C103C2213yes—
19C22×C42×C103C2213yes—
20#390×C103C22112yes—
21#389×C103C22112yes—
22#388×C103C22124yes—
23#384×C103C2216yes—
24#383×C103C2216yes—
25#382×C103C2211yescharacteristic
26#382×C103C2213yes—
27#381×C103C2216yes—
28#380×C103C2216yes—
29#380×C103C2216yes—
30#380×C103C2216yes—
31C4×C4⋊C4×C103C2216yes—
32C4×C4⋊C4×C103C22112yes—
33C4×C4⋊C4×C103C2216yes—
34C4×C4⋊C4×C103C2216yes—
35C4×C22⋊C4×C103C2216yes—
36#376×C103C2216yes—
37C2×#41×C103—28no—
38C2×#41×C103C2×C418yes—
39C22×Q8×C103C2311yescharacteristic
40C22×D4×C103C2313yes—
41C23×C4×C103C2313yes—
42C23×C4×C103C2313yes—
43C23×C4×C103C2313yes—
44C4×Q8×C103—216no—
45C4×Q8×C103C2×C418yes—
46C4×Q8×C103C2×C418yes—
47C4×D4×C103C2×C4124yes—
48C4×D4×C103C2×C4124yes—
49#117×C103—412no—
50#117×C103C2×C4124yes—
51C2×C4⋊C4×C103C2312yes—
52C2×C4⋊C4×C103C23112yes—
53C2×C4⋊C4×C103C2316yes—
54C2×C4⋊C4×C103C23112yes—
55C2×C4⋊C4×C103C2313yes—
56C2×C4⋊C4×C103C2313yes—
57C2×C22⋊C4×C103C23112yes—
58C2×C22⋊C4×C103C23112yes—
59C2×C22⋊C4×C103C2316yes—
60C2×C42×C103C2×C4124yes—
61C2×C42×C103C23112yes—
62C2×C42×C103C23112yes—
63C2×C42×C103C2313yes—
64C2×C42×C103C2313yes—
65C2×C42×C103C2313yes—
66C2×C42×C103C2311yescharacteristic
67#95×C103C2312yes—
68#95×C103C2316yes—
69#95×C103C23112yes—
70#95×C103C2312yes—
71#95×C103C2316yes—
72#95×C103C23112yes—
73C24×C103C2413yes—
74#41×C103—232no—
75C2×Q8×C103C22×C414yes—
76C2×Q8×C103#4118yes—
77C2×D4×C103—212no—
78C2×D4×C103C22×C4112yes—
79C22×C4×C103—212no—
80C22×C4×C103—26no—
81C22×C4×C103—26no—
82C22×C4×C103—46no—
83C22×C4×C103C22×C4112yes—
84C22×C4×C103C22×C4112yes—
85C22×C4×C103C22×C4112yes—
86C22×C4×C103C2414yes—
87C22×C4×C103C24112yes—
88C22×C4×C103C2411yescharacteristic
89C22×C4×C103C2411yescharacteristic
90C22×C4×C103C2413yes—
91C22×C4×C103C2413yes—
92C22×C4×C103C2413yes—
93C22×C4×C103C2411yescharacteristic
94C4⋊C4×C103—224no—
95C4⋊C4×C103—212no—
96C4⋊C4×C103—24no—
97C4⋊C4×C103—412no—
98C4⋊C4×C103C22×C4112yes—
99C4⋊C4×C103C22×C4112yes—
100C22⋊C4×C103—412no—
101C22⋊C4×C103—412no—
102C22⋊C4×C103C22×C4124yes—
103C42×C103—224no—
104C42×C103—412no—
105C42×C103C22×C414yes—
106C42×C103C22×C4112yes—
107C42×C103C22×C4112yes—
108C42×C103C22×C4112yes—
109C23×C103—26no—
110C23×C103—23no—
111C23×C103—23no—
112C23×C103—26no—
113C23×C103C23×C416yes—
114C23×C103C2511yescharacteristic
115Q8×C103#117116yescomplemented
116D4×C103—224no—
117C2×C4×C103—22no—
118C2×C4×C103—23no—
119C2×C4×C103—23no—
120C2×C4×C103—26no—
121C2×C4×C103—22no—
122C2×C4×C103—224no—
123C2×C4×C103—224no—
124C2×C4×C103—24no—
125C2×C4×C103—212no—
126C2×C4×C103—212no—
127C2×C4×C103—24no—
128C2×C4×C103—24no—
129C2×C4×C103—212no—
130C2×C4×C103—412no—
131C2×C4×C103C23×C412yes—
132C2×C4×C103C23×C412yes—
133C2×C4×C103C23×C416yes—
134C2×C4×C103C23×C416yes—
135C2×C4×C103C23×C416yes—
136C2×C4×C103C23×C412yes—
137C2×C4×C103C2×#41112yes—
138C2×C4×C103H(5,𝔽2)12yes—
139C2×C4×C1032−1+412yes—
140C22×C103—26no—
141C22×C103—26no—
142C22×C103—26no—
143C22×C103—46no—
144C22×C103—46no—
145C22×C103C24×C411yescharacteristic
146C22×C103C22×#4112yes—
147C22×C103C2×H(5,𝔽2)11yescharacteristic
148C22×C103C2×2−1+411yescharacteristic
149C22×C103#58512yes—
150C4×C103—22no—
151C4×C103—26no—
152C4×C103—22no—
153C4×C103—26no—
154C4×C103—412no—
155C4×C103—44no—
156C4×C103C2×#117112yes—
157C4×C103#52014yes—
158#34193C10311yesmaximal, characteristic, direct product factor, Sylow
159C2×C103—46no—
160C2×C103C22×#11711yescharacteristic
161C2×C103C2×#52011yescharacteristic
162C2×C103#342811yescharacteristic
163C2×C103#351712yes—
164C2×C103#351812yes—
165C2×C4×#41C2×C10311yescharacteristic
166#2354C2×C10316yescomplemented
167Q8×C4⋊C4C2×C10312yescomplemented
168#2347C2×C10316yescomplemented
169#2341C2×C10312yes—
170#2319C2×C10316yescomplemented
171#2285C2×C10313yescomplemented
172#2283C2×C10313yescomplemented
173#2276C2×C10312yescomplemented
174C103#3419311yescharacteristic, direct product factor, Sylow
175C22×#41C22×C10311yescharacteristic
176C4×#41C4×C103116yescomplemented
177C2×C4×Q8C22×C10314yes—
178C2×C4×Q8C22×C10311yescharacteristic
179C2×C4×Q8C22×C10311yescharacteristic
180C2×C4×D4C22×C10313yes—
181C2×C4×D4C22×C10313yes—
182C2×#117C22×C10316yes—
183C2×#117C22×C10313yes—
184C22×C42C22×C10313yes—
185#390C22×C103112yes—
186#389C22×C103112yes—
187#388C22×C103124yes—
188#384C22×C10316yes—
189#383C22×C10316yes—
190#382C22×C10311yescharacteristic
191#382C22×C10313yes—
192#381C22×C10316yes—
193#380C22×C10316yes—
194#380C22×C10316yes—
195#380C22×C10316yes—
196C4×C4⋊C4C22×C10316yes—
197C4×C4⋊C4C22×C10316yes—
198C4×C4⋊C4C22×C103112yes—
199C4×C4⋊C4C22×C10316yes—
200C4×C22⋊C4C22×C10316yes—
201#376C22×C10316yes—
202C2×#41—28no—
203C2×#41C2×C4×C10318yes—
204C22×Q8C23×C10311yescharacteristic
205C22×D4C23×C10313yes—
206C23×C4C23×C10313yes—
207C23×C4C23×C10313yes—
208C23×C4C23×C10313yes—
209C4×Q8—216no—
210C4×Q8C2×C4×C10318yes—
211C4×Q8C2×C4×C10318yes—
212C4×D4C2×C4×C103124yes—
213C4×D4C2×C4×C103124yes—
214#117—412no—
215#117C2×C4×C103124yes—
216C2×C4⋊C4C23×C10316yes—
217C2×C4⋊C4C23×C103112yes—
218C2×C4⋊C4C23×C10312yes—
219C2×C4⋊C4C23×C103112yes—
220C2×C4⋊C4C23×C10313yes—
221C2×C4⋊C4C23×C10313yes—
222C2×C22⋊C4C23×C103112yes—
223C2×C22⋊C4C23×C103112yes—
224C2×C22⋊C4C23×C10316yes—
225C2×C42C2×C4×C103124yes—
226C2×C42C23×C103112yes—
227C2×C42C23×C103112yes—
228C2×C42C23×C10313yes—
229C2×C42C23×C10313yes—
230C2×C42C23×C10313yes—
231C2×C42C23×C10311yescharacteristic
232#95C23×C10312yes—
233#95C23×C10316yes—
234#95C23×C103112yes—
235#95C23×C10312yes—
236#95C23×C10316yes—
237#95C23×C103112yes—
238C24C24×C10313yes—
239#41—232no—
240C2×Q8C22×C4×C10314yes—
241C2×Q8#41×C10318yes—
242C2×D4—212no—
243C2×D4C22×C4×C103112yes—
244C22×C4—212no—
245C22×C4—26no—
246C22×C4—26no—
247C22×C4—46no—
248C22×C4C22×C4×C103112yes—
249C22×C4C22×C4×C103112yes—
250C22×C4C22×C4×C103112yes—
251C22×C4C24×C10314yes—
252C22×C4C24×C103112yes—
253C22×C4C24×C10311yescharacteristic
254C22×C4C24×C10311yescharacteristic
255C22×C4C24×C10313yes—
256C22×C4C24×C10313yes—
257C22×C4C24×C10313yes—
258C22×C4C24×C10311yescharacteristic
259C4⋊C4—224no—
260C4⋊C4—212no—
261C4⋊C4—24no—
262C4⋊C4—412no—
263C4⋊C4C22×C4×C103112yes—
264C4⋊C4C22×C4×C103112yes—
265C22⋊C4—412no—
266C22⋊C4—412no—
267C22⋊C4C22×C4×C103124yes—
268C42—224no—
269C42—412no—
270C42C22×C4×C10314yes—
271C42C22×C4×C103112yes—
272C42C22×C4×C103112yes—
273C42C22×C4×C103112yes—
274C23—26no—
275C23—23no—
276C23—23no—
277C23—26no—
278C23C23×C4×C10316yes—
279C23C25×C10311yescharacteristic
280Q8#117×C103116yescomplemented
281D4—224no—
282C2×C4—22no—
283C2×C4—23no—
284C2×C4—23no—
285C2×C4—26no—
286C2×C4—22no—
287C2×C4—224no—
288C2×C4—224no—
289C2×C4—24no—
290C2×C4—212no—
291C2×C4—212no—
292C2×C4—24no—
293C2×C4—24no—
294C2×C4—212no—
295C2×C4—412no—
296C2×C4C23×C4×C10312yes—
297C2×C4C23×C4×C10312yes—
298C2×C4C23×C4×C10316yes—
299C2×C4C23×C4×C10316yes—
300C2×C4C23×C4×C10316yes—
301C2×C4C23×C4×C10312yes—
302C2×C4C2×#41×C103112yes—
303C2×C4H(5,𝔽2)×C10312yes—
304C2×C42−1+4×C10312yes—
305C22—26no—
306C22—26no—
307C22—26no—
308C22—46no—
309C22—46no—
310C22C24×C4×C10311yescharacteristic
311C22C22×#41×C10312yes—
312C22C2×H(5,𝔽2)×C10311yescharacteristic
313C22C2×2−1+4×C10311yescharacteristic
314C22#585×C10312yes—
315C4—22no—
316C4—26no—
317C4—22no—
318C4—26no—
319C4—412no—
320C4—44no—
321C4C2×#117×C103112yes—
322C4#520×C10314yes—
323C2—46no—
324C2C22×#117×C10311yescharacteristic
325C2C2×#520×C10311yescharacteristic
326C2C103×#342811yescharacteristic
327C2C103×#351712yes—
328C2C103×#351812yes—
subgroupG/H
center, socleC23×C103C25
commutatorC22C24×C4×C103
Frattini, cosocleC23C25×C103
prime radicalC22×#41×C103C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C103×#2354C2semidirect
3. Q8×C4⋊C4×C103C2semidirect
4. C103×#2347C2semidirect
6. C103×#2319C2semidirect
7. C103×#2285C2semidirect
8. C103×#2283C2semidirect
9. C103×#2276C2semidirect
11. C4×#41×C103C4semidirect
115. Q8×C103#117semidirect
158. #34193C103direct (N × H)
166. #2354C2×C103semidirect
167. Q8×C4⋊C4C2×C103semidirect
168. #2347C2×C103semidirect
170. #2319C2×C103semidirect
171. #2285C2×C103semidirect
172. #2283C2×C103semidirect
173. #2276C2×C103semidirect
174. C103#34193direct (N × H)
176. C4×#41C4×C103semidirect
280. Q8#117×C103semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#41×C1032
C103×#23542
Q8×C4⋊C4×C1032
C103×#23472
C103×#23412
C103×#23192
C103×#22852
C103×#22832
C103×#22762
#34193103