Finite Group Databasebeta

← C103×#8667 #39913942

Subgroups — C103×#8667 #39913942

Order 26368.

454 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C8×#41×C103C211yesmaximal, characteristic
2C103×#1806C212yesmaximal
3C4×#107×C103C211yesmaximal, characteristic, complemented
4C103×#1567C211yesmaximal, characteristic, complemented
5C103×#1303C212yesmaximal, complemented
6C4×#41×C103C2211yescharacteristic
7C8×Q8×C103C411yescharacteristic, complemented
8C8×Q8×C103C411yescharacteristic, complemented
9C8×D4×C103—21no—
10C8×D4×C103—21no—
11C8×D4×C103C411yescharacteristic, complemented
12C8×D4×C103C411yescharacteristic, complemented
13#431×C103—21no—
14#431×C103C2211yescharacteristic
15C2×#107×C103—21no—
16#423×C103C2212yes—
17C2×#104×C103—22no—
18C2×C4×C8×C103—21no—
19C2×C4×C8×C103C2211yescharacteristic
20C4×C4⋊C4×C103C2212yes—
21#340×C103—21no—
22#339×C103—22no—
23#335×C103—21no—
24#335×C103—21no—
25C2×#41×C103D411yescharacteristic
26C2×M16×C103—22no—
27C22×C8×C103—21no—
28C22×C8×C103—21no—
29C22×C8×C103D411yescharacteristic
30C22×C8×C103D411yescharacteristic
31C4×Q8×C103C2×C411yescharacteristic
32C4×Q8×C103Q811yescharacteristic
33C4×D4×C103—21no—
34C4×D4×C103—21no—
35C4×D4×C103C2×C411yescharacteristic
36C4×D4×C103Q811yescharacteristic
37#117×C103—21no—
38#117×C103D411yescharacteristic
39C2×C4⋊C4×C103—22no—
40C2×C42×C103—21no—
41C2×C42×C103—22no—
42C2×C42×C103C2311yescharacteristic
43#107×C103—24no—
44C4⋊C8×C103—21no—
45C4⋊C8×C103—21no—
46C4⋊C8×C103—22no—
47C4⋊C8×C103—22no—
48C4⋊C8×C103C2×C411yescharacteristic
49C4⋊C8×C103C2×C411yescharacteristic
50#104×C103—44no—
51C22⋊C8×C103—21no—
52C22⋊C8×C103—21no—
53C22⋊C8×C103—21no—
54C4×C8×C103—21no—
55C4×C8×C103—21no—
56C4×C8×C103—21no—
57C4×C8×C103C2×C411yescharacteristic
58C4×C8×C103C2×C411yescharacteristic
59C4×C8×C103D411yescharacteristic
60C4×C8×C103D411yescharacteristic
61#95×C103—22no—
62#41×C103—21no—
63#41×C103—21no—
64#41×C103D812yes—
65#41×C103Q1612yes—
66C2×Q8×C103C4⋊C411yescharacteristic
67C2×D4×C103—21no—
68C2×D4×C103C4⋊C411yescharacteristic
69C22×C4×C103—21no—
70C22×C4×C103—21no—
71C22×C4×C103—21no—
72C22×C4×C103—42no—
73C22×C4×C103C2×D411yescharacteristic
74C22×C4×C103C2×D411yescharacteristic
75C22×C4×C103#4111yescharacteristic
76M16×C103—42no—
77M16×C103—42no—
78C2×C8×C103—22no—
79C2×C8×C103—21no—
80C2×C8×C103—21no—
81C2×C8×C103—41no—
82C2×C8×C103—42no—
83C2×C8×C103—42no—
84C2×C8×C103—42no—
85C2×C8×C103C22⋊C411yescharacteristic
86C2×C8×C103C22⋊C411yescharacteristic
87C2×C8×C103C22⋊C411yescharacteristic
88C2×C8×C103C22⋊C411yescharacteristic
89C4⋊C4×C103—21no—
90C4⋊C4×C103—21no—
91C4⋊C4×C103—24no—
92C4⋊C4×C103—42no—
93C4⋊C4×C103C4⋊C411yescharacteristic
94C4⋊C4×C103C4⋊C411yescharacteristic
95C22⋊C4×C103—21no—
96C22⋊C4×C103—21no—
97C22⋊C4×C103—21no—
98C42×C103—21no—
99C42×C103—21no—
100C42×C103—21no—
101C42×C103—42no—
102C42×C103—42no—
103C42×C103C22×C411yescharacteristic
104C42×C103C2×D411yescharacteristic
105C42×C103C2×Q811yescharacteristic
106C42×C103#4111yescharacteristic
107C23×C103—21no—
108C23×C103#12111yescharacteristic
109Q8×C103—21no—
110Q8×C103#10712yescomplemented
111D4×C103—22no—
112D4×C103—22no—
113D4×C103—21no—
114D4×C103#10712yescomplemented
115C2×C4×C103—21no—
116C2×C4×C103—21no—
117C2×C4×C103—21no—
118C2×C4×C103—22no—
119C2×C4×C103—22no—
120C2×C4×C103—21no—
121C2×C4×C103—21no—
122C2×C4×C103—41no—
123C2×C4×C103—42no—
124C2×C4×C103—41no—
125C2×C4×C103—41no—
126C2×C4×C103—44no—
127C2×C4×C103—82no—
128C2×C4×C103—82no—
129C2×C4×C103C2×C22⋊C411yescharacteristic
130C2×C4×C103C2×C4⋊C411yescharacteristic
131C2×C4×C103#11711yescharacteristic
132C2×C4×C103#12111yescharacteristic
133C2×C4×C103C22⋊Q811yescharacteristic
134C2×C4×C103C22⋊Q811yescharacteristic
135C2×C4×C103C2×D811yescharacteristic
136C2×C4×C103C2×Q1611yescharacteristic
137C2×C4×C103#13511yescharacteristic
138C2×C4×C103#13511yescharacteristic
139C8×C103—21no—
140C8×C103—21no—
141C8×C103—21no—
142C8×C103—41no—
143C8×C103—41no—
144C8×C103—82no—
145C8×C103#10412yescomplemented
146C22×C103—21no—
147C22×C103—21no—
148C22×C103—22no—
149C22×C103—41no—
150C22×C103—41no—
151C22×C103#38011yescharacteristic
152C22×C103#46611yescharacteristic
153C22×C103#46711yescharacteristic
154C4×C103—21no—
155C4×C103—22no—
156C4×C103—21no—
157C4×C103—21no—
158C4×C103—41no—
159C4×C103—41no—
160C4×C103—84no—
161C4×C103C2×#10411yescharacteristic
162C4×C103#42111yescharacteristic
163C4×C103C2×#10711yescharacteristic
164C4×C103#42711yescharacteristic
165C4×C103#46611yescharacteristic
166C4×C103#46711yescharacteristic
167#8667C10311yesmaximal, characteristic, direct product factor, Sylow
168C2×C103—21no—
169C2×C103—21no—
170C2×C103—42no—
171C2×C103#180611yescharacteristic
172C2×C103#180811yescharacteristic
173C2×C103#181411yescharacteristic
174C8×#41C2×C10311yescharacteristic
175#1806C2×C10312yes—
176C4×#107C2×C10311yescharacteristic, complemented
177#1567C2×C10311yescharacteristic, complemented
178#1303C2×C10312yescomplemented
179C103#866711yescharacteristic, direct product factor, Sylow
180C4×#41C22×C10311yescharacteristic
181C8×Q8C4×C10311yescharacteristic, complemented
182C8×Q8C4×C10311yescharacteristic, complemented
183C8×D4—21no—
184C8×D4—21no—
185C8×D4C4×C10311yescharacteristic, complemented
186C8×D4C4×C10311yescharacteristic, complemented
187#431—21no—
188#431C22×C10311yescharacteristic
189C2×#107—21no—
190#423C22×C10312yes—
191C2×#104—22no—
192C2×C4×C8—21no—
193C2×C4×C8C22×C10311yescharacteristic
194C4×C4⋊C4C22×C10312yes—
195#340—21no—
196#339—22no—
197#335—21no—
198#335—21no—
199C2×#41D4×C10311yescharacteristic
200C2×M16—22no—
201C22×C8—21no—
202C22×C8—21no—
203C22×C8D4×C10311yescharacteristic
204C22×C8D4×C10311yescharacteristic
205C4×Q8C2×C4×C10311yescharacteristic
206C4×Q8Q8×C10311yescharacteristic
207C4×D4—21no—
208C4×D4—21no—
209C4×D4C2×C4×C10311yescharacteristic
210C4×D4Q8×C10311yescharacteristic
211#117—21no—
212#117D4×C10311yescharacteristic
213C2×C4⋊C4—22no—
214C2×C42—21no—
215C2×C42—22no—
216C2×C42C23×C10311yescharacteristic
217#107—24no—
218C4⋊C8—21no—
219C4⋊C8—21no—
220C4⋊C8—22no—
221C4⋊C8—22no—
222C4⋊C8C2×C4×C10311yescharacteristic
223C4⋊C8C2×C4×C10311yescharacteristic
224#104—44no—
225C22⋊C8—21no—
226C22⋊C8—21no—
227C22⋊C8—21no—
228C4×C8—21no—
229C4×C8—21no—
230C4×C8—21no—
231C4×C8C2×C4×C10311yescharacteristic
232C4×C8C2×C4×C10311yescharacteristic
233C4×C8D4×C10311yescharacteristic
234C4×C8D4×C10311yescharacteristic
235#95—22no—
236#41—21no—
237#41—21no—
238#41D8×C10312yes—
239#41Q16×C10312yes—
240C2×Q8C4⋊C4×C10311yescharacteristic
241C2×D4—21no—
242C2×D4C4⋊C4×C10311yescharacteristic
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—42no—
247C22×C4C2×D4×C10311yescharacteristic
248C22×C4C2×D4×C10311yescharacteristic
249C22×C4#41×C10311yescharacteristic
250M16—42no—
251M16—42no—
252C2×C8—22no—
253C2×C8—21no—
254C2×C8—21no—
255C2×C8—41no—
256C2×C8—42no—
257C2×C8—42no—
258C2×C8—42no—
259C2×C8C22⋊C4×C10311yescharacteristic
260C2×C8C22⋊C4×C10311yescharacteristic
261C2×C8C22⋊C4×C10311yescharacteristic
262C2×C8C22⋊C4×C10311yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—24no—
266C4⋊C4—42no—
267C4⋊C4C4⋊C4×C10311yescharacteristic
268C4⋊C4C4⋊C4×C10311yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—21no—
272C42—21no—
273C42—21no—
274C42—21no—
275C42—42no—
276C42—42no—
277C42C22×C4×C10311yescharacteristic
278C42C2×D4×C10311yescharacteristic
279C42C2×Q8×C10311yescharacteristic
280C42#41×C10311yescharacteristic
281C23—21no—
282C23#121×C10311yescharacteristic
283Q8—21no—
284Q8#107×C10312yescomplemented
285D4—22no—
286D4—22no—
287D4—21no—
288D4#107×C10312yescomplemented
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—41no—
297C2×C4—42no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—44no—
301C2×C4—82no—
302C2×C4—82no—
303C2×C4C2×C22⋊C4×C10311yescharacteristic
304C2×C4C2×C4⋊C4×C10311yescharacteristic
305C2×C4#117×C10311yescharacteristic
306C2×C4#121×C10311yescharacteristic
307C2×C4C22⋊Q8×C10311yescharacteristic
308C2×C4C22⋊Q8×C10311yescharacteristic
309C2×C4C2×D8×C10311yescharacteristic
310C2×C4C2×Q16×C10311yescharacteristic
311C2×C4#135×C10311yescharacteristic
312C2×C4#135×C10311yescharacteristic
313C8—21no—
314C8—21no—
315C8—21no—
316C8—41no—
317C8—41no—
318C8—82no—
319C8#104×C10312yescomplemented
320C22—21no—
321C22—21no—
322C22—22no—
323C22—41no—
324C22—41no—
325C22#380×C10311yescharacteristic
326C22#466×C10311yescharacteristic
327C22#467×C10311yescharacteristic
328C4—21no—
329C4—22no—
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—84no—
335C4C2×#104×C10311yescharacteristic
336C4#421×C10311yescharacteristic
337C4C2×#107×C10311yescharacteristic
338C4#427×C10311yescharacteristic
339C4#466×C10311yescharacteristic
340C4#467×C10311yescharacteristic
341C2—21no—
342C2—21no—
343C2—42no—
344C2C103×#180611yescharacteristic
345C2C103×#180811yescharacteristic
346C2C103×#181411yescharacteristic
subgroupG/H
centerC2×C4×C103#121
commutatorC42C22×C4×C103
Frattini, cosocleC2×C42C23×C103
socleC22×C103#380
prime radicalC2×#41×C103D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C103 ◁ C2×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
3. C4×#107×C103C2semidirect
4. C103×#1567C2semidirect
5. C103×#1303C2semidirect
7. C8×Q8×C103C4semidirect
8. C8×Q8×C103C4semidirect
11. C8×D4×C103C4semidirect
12. C8×D4×C103C4semidirect
110. Q8×C103#107semidirect
114. D4×C103#107semidirect
145. C8×C103#104semidirect
167. #8667C103direct (N × H)
176. C4×#107C2×C103semidirect
177. #1567C2×C103semidirect
178. #1303C2×C103semidirect
179. C103#8667direct (N × H)
181. C8×Q8C4×C103semidirect
182. C8×Q8C4×C103semidirect
185. C8×D4C4×C103semidirect
186. C8×D4C4×C103semidirect
284. Q8#107×C103semidirect
288. D4#107×C103semidirect
319. C8#104×C103semidirect

Maximal subgroups

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

subgroupindex
C8×#41×C1032
C103×#18062
C4×#107×C1032
C103×#15672
C103×#13032
#8667103