Finite Group Databasebeta

← C103×#33927 #39939202

Subgroups — C103×#33927 #39939202

Order 26368.

486 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3393C211yesmaximal, characteristic, complemented
2C103×#3380C211yesmaximal, characteristic, complemented
3C103×#2242C212yesmaximal, complemented
4C103×#2241C211yesmaximal, characteristic, complemented
5C103×#2229C212yesmaximal, complemented
6C103×#2226C211yesmaximal, characteristic, complemented
7C103×#2210C212yesmaximal
8C103×#2208C211yesmaximal, characteristic, complemented
9Q8×C16×C103C211yesmaximal, characteristic, complemented
10C4×SD32×C103C212yesmaximal, complemented
11C4×D16×C103C211yesmaximal, characteristic
12#556×C103—21no—
13#554×C103—21no—
14C2×SD32×C103C2212yes—
15C2×D16×C103C2211yescharacteristic
16#500×C103C2211yescharacteristic
17#499×C103C2212yes—
18#495×C103C2212yes—
19#494×C103C2211yescharacteristic
20#478×C103—22no—
21#476×C103—21no—
22#464×C103—22no—
23#461×C103—21no—
24C8×Q8×C103C2211yescharacteristic
25C4×Q16×C103C2212yes—
26C4×D8×C103C2211yescharacteristic
27C4×D8×C103C2212yes—
28C4×D8×C103C2211yescharacteristic
29#367×C103C2212yes—
30#366×C103C2211yescharacteristic
31C4⋊C16×C103C2211yescharacteristic
32C4⋊C16×C103C2212yes—
33#358×C103C2212yes—
34#358×C103C2212yes—
35#358×C103C2212yes—
36#357×C103C2212yes—
37#357×C103C2211yescharacteristic
38#357×C103C2211yescharacteristic
39C4×C16×C103C2211yescharacteristic
40C4×C16×C103C2212yes—
41C2×Q16×C103—21no—
42C2×Q16×C103C2312yes—
43C2×SD16×C103—22no—
44C2×D8×C103C2311yescharacteristic
45C2×D8×C103C2311yescharacteristic
46C4⋊Q8×C103—21no—
47C4⋊Q8×C103—21no—
48#126×C103—42no—
49#125×C103—22no—
50#124×C103—22no—
51C22⋊Q8×C103—41no—
52C22⋊Q8×C103—41no—
53C22⋊Q8×C103—42no—
54C4×Q8×C103—22no—
55C4×Q8×C103D411yescharacteristic
56C4×D4×C103—21no—
57C4×D4×C103—21no—
58C4×D4×C103—22no—
59#117×C103—41no—
60C2×C4⋊C4×C103—41no—
61SD32×C103—24no—
62D16×C103—22no—
63C2×C16×C103C2311yescharacteristic
64C2×C16×C103C2312yes—
65C2×C16×C103C2311yescharacteristic
66#107×C103—21no—
67#107×C103C2311yescharacteristic
68#107×C103C2312yes—
69#107×C103C2311yescharacteristic
70#106×C103—22no—
71C4⋊C8×C103D411yescharacteristic
72C4⋊C8×C103D412yes—
73#103×C103—22no—
74#102×C103—21no—
75#102×C103—22no—
76#102×C103—21no—
77C4×C8×C103C2311yescharacteristic
78C4×C8×C103C2312yes—
79C2×Q8×C103—22no—
80C2×Q8×C103—41no—
81C2×Q8×C103D811yescharacteristic
82C2×D4×C103—21no—
83C2×D4×C103—21no—
84C22×C4×C103—41no—
85C22×C4×C103—41no—
86C22×C4×C103—42no—
87Q16×C103—22no—
88Q16×C103—22no—
89Q16×C103—81no—
90SD16×C103—82no—
91D8×C103—21no—
92D8×C103—21no—
93D8×C103—21no—
94D8×C103#4112yes—
95C2×C8×C103C2×D411yescharacteristic
96C2×C8×C103C2×D412yes—
97C2×C8×C103C2411yescharacteristic
98C4⋊C4×C103—21no—
99C4⋊C4×C103—21no—
100C4⋊C4×C103—22no—
101C4⋊C4×C103—42no—
102C4⋊C4×C103—41no—
103C4⋊C4×C103—41no—
104C4⋊C4×C103—42no—
105C4⋊C4×C103—42no—
106C4⋊C4×C103—41no—
107C4⋊C4×C103D811yescharacteristic
108C4⋊C4×C103D812yes—
109C22⋊C4×C103—42no—
110C22⋊C4×C103—41no—
111C22⋊C4×C103—42no—
112C22⋊C4×C103—41no—
113C22⋊C4×C103—42no—
114C42×C103—42no—
115C42×C103C2×D411yescharacteristic
116C42×C103C2×D412yes—
117C16×C103—21no—
118C16×C103—22no—
119C16×C103—21no—
120C23×C103—41no—
121C23×C103—41no—
122Q8×C103—22no—
123Q8×C103—42no—
124Q8×C103—42no—
125Q8×C103—161no—
126D4×C103—22no—
127D4×C103—41no—
128D4×C103—41no—
129D4×C103—41no—
130C2×C4×C103—41no—
131C2×C4×C103—42no—
132C2×C4×C103—41no—
133C2×C4×C103—42no—
134C2×C4×C103—82no—
135C2×C4×C103—82no—
136C2×C4×C103—162no—
137C2×C4×C103C2×D812yes—
138C2×C4×C103C2×D812yes—
139C2×C4×C103C2×D811yescharacteristic
140C2×C4×C103C2×D811yescharacteristic
141C2×C4×C103C22×D411yescharacteristic
142C8×C103—22no—
143C8×C103—21no—
144C8×C103C2×#4111yescharacteristic
145C8×C1032−1+411yescharacteristic
146C22×C103—42no—
147C22×C103—81no—
148C22×C103—81no—
149C22×C103—81no—
150C22×C103—81no—
151C22×C103—81no—
152C22×C103C22×D811yescharacteristic
153C4×C103—22no—
154C4×C103—22no—
155C4×C103—21no—
156C4×C103—82no—
157C4×C103—81no—
158C4×C103—81no—
159C4×C103—82no—
160C4×C103#50812yes—
161C4×C103#54811yescharacteristic
162C4×C103#57711yescharacteristic
163#33927C10311yesmaximal, characteristic, direct product factor, Sylow
164C2×C103—82no—
165C2×C103—161no—
166C2×C103#335811yescharacteristic
167C2×C103C2×#50811yescharacteristic
168C2×C103#341611yescharacteristic
169#3393C2×C10311yescharacteristic, complemented
170#3380C2×C10311yescharacteristic, complemented
171#2242C2×C10312yescomplemented
172#2241C2×C10311yescharacteristic, complemented
173#2229C2×C10312yescomplemented
174#2226C2×C10311yescharacteristic, complemented
175#2210C2×C10312yes—
176#2208C2×C10311yescharacteristic, complemented
177Q8×C16C2×C10311yescharacteristic, complemented
178C4×SD32C2×C10312yescomplemented
179C4×D16C2×C10311yescharacteristic
180C103#3392711yescharacteristic, direct product factor, Sylow
181#556—21no—
182#554—21no—
183C2×SD32C22×C10312yes—
184C2×D16C22×C10311yescharacteristic
185#500C22×C10311yescharacteristic
186#499C22×C10312yes—
187#495C22×C10312yes—
188#494C22×C10311yescharacteristic
189#478—22no—
190#476—21no—
191#464—22no—
192#461—21no—
193C8×Q8C22×C10311yescharacteristic
194C4×Q16C22×C10312yes—
195C4×D8C22×C10311yescharacteristic
196C4×D8C22×C10312yes—
197C4×D8C22×C10311yescharacteristic
198#367C22×C10312yes—
199#366C22×C10311yescharacteristic
200C4⋊C16C22×C10311yescharacteristic
201C4⋊C16C22×C10312yes—
202#358C22×C10312yes—
203#358C22×C10312yes—
204#358C22×C10312yes—
205#357C22×C10311yescharacteristic
206#357C22×C10311yescharacteristic
207#357C22×C10312yes—
208C4×C16C22×C10311yescharacteristic
209C4×C16C22×C10312yes—
210C2×Q16—21no—
211C2×Q16C23×C10312yes—
212C2×SD16—22no—
213C2×D8C23×C10311yescharacteristic
214C2×D8C23×C10311yescharacteristic
215C4⋊Q8—21no—
216C4⋊Q8—21no—
217#126—42no—
218#125—22no—
219#124—22no—
220C22⋊Q8—41no—
221C22⋊Q8—41no—
222C22⋊Q8—42no—
223C4×Q8—22no—
224C4×Q8D4×C10311yescharacteristic
225C4×D4—21no—
226C4×D4—22no—
227C4×D4—21no—
228#117—41no—
229C2×C4⋊C4—41no—
230SD32—24no—
231D16—22no—
232C2×C16C23×C10311yescharacteristic
233C2×C16C23×C10312yes—
234C2×C16C23×C10311yescharacteristic
235#107—21no—
236#107C23×C10311yescharacteristic
237#107C23×C10312yes—
238#107C23×C10311yescharacteristic
239#106—22no—
240C4⋊C8D4×C10311yescharacteristic
241C4⋊C8D4×C10312yes—
242#103—22no—
243#102—21no—
244#102—22no—
245#102—21no—
246C4×C8C23×C10311yescharacteristic
247C4×C8C23×C10312yes—
248C2×Q8—22no—
249C2×Q8—41no—
250C2×Q8D8×C10311yescharacteristic
251C2×D4—21no—
252C2×D4—21no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—42no—
256Q16—22no—
257Q16—22no—
258Q16—81no—
259SD16—82no—
260D8—21no—
261D8—21no—
262D8—21no—
263D8#41×C10312yes—
264C2×C8C2×D4×C10311yescharacteristic
265C2×C8C2×D4×C10312yes—
266C2×C8C24×C10311yescharacteristic
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—22no—
270C4⋊C4—42no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—42no—
274C4⋊C4—42no—
275C4⋊C4—41no—
276C4⋊C4D8×C10311yescharacteristic
277C4⋊C4D8×C10312yes—
278C22⋊C4—42no—
279C22⋊C4—41no—
280C22⋊C4—42no—
281C22⋊C4—41no—
282C22⋊C4—42no—
283C42—42no—
284C42C2×D4×C10311yescharacteristic
285C42C2×D4×C10312yes—
286C16—21no—
287C16—22no—
288C16—21no—
289C23—41no—
290C23—41no—
291Q8—22no—
292Q8—42no—
293Q8—42no—
294Q8—161no—
295D4—22no—
296D4—41no—
297D4—41no—
298D4—41no—
299C2×C4—41no—
300C2×C4—42no—
301C2×C4—41no—
302C2×C4—42no—
303C2×C4—82no—
304C2×C4—82no—
305C2×C4—162no—
306C2×C4C2×D8×C10312yes—
307C2×C4C2×D8×C10312yes—
308C2×C4C2×D8×C10311yescharacteristic
309C2×C4C2×D8×C10311yescharacteristic
310C2×C4C22×D4×C10311yescharacteristic
311C8—22no—
312C8—21no—
313C8C2×#41×C10311yescharacteristic
314C82−1+4×C10311yescharacteristic
315C22—42no—
316C22—81no—
317C22—81no—
318C22—81no—
319C22—81no—
320C22—81no—
321C22C22×D8×C10311yescharacteristic
322C4—22no—
323C4—22no—
324C4—21no—
325C4—82no—
326C4—81no—
327C4—81no—
328C4—82no—
329C4#508×C10312yes—
330C4#548×C10311yescharacteristic
331C4#577×C10311yescharacteristic
332C2—82no—
333C2—161no—
334C2C103×#335811yescharacteristic
335C2C2×#508×C10311yescharacteristic
336C2C103×#341611yescharacteristic
subgroupG/H
center, socleC22×C103C22×D8
commutator, Frattini, cosocleC2×C8C24×C103
prime radicalC2×D16×C103C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C103 ◁ C4×Q8×C103 ◁ C8×Q8×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C103×#3393C2semidirect
2. C103×#3380C2semidirect
3. C103×#2242C2semidirect
4. C103×#2241C2semidirect
5. C103×#2229C2semidirect
6. C103×#2226C2semidirect
8. C103×#2208C2semidirect
9. Q8×C16×C103C2semidirect
10. C4×SD32×C103C2semidirect
163. #33927C103direct (N × H)
169. #3393C2×C103semidirect
170. #3380C2×C103semidirect
171. #2242C2×C103semidirect
172. #2241C2×C103semidirect
173. #2229C2×C103semidirect
174. #2226C2×C103semidirect
176. #2208C2×C103semidirect
177. Q8×C16C2×C103semidirect
178. C4×SD32C2×C103semidirect
180. C103#33927direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#33932
C103×#33802
C103×#22422
C103×#22412
C103×#22292
C103×#22262
C103×#22102
C103×#22082
Q8×C16×C1032
C4×SD32×C1032
C4×D16×C1032
#33927103