Finite Group Databasebeta

← C103×#11694 #39916969

Subgroups — C103×#11694 #39916969

Order 26368.

468 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#2621C211yesmaximal, characteristic
2C103×#1740C211yesmaximal, characteristic
3C103×#1458C211yesmaximal, characteristic
4C103×#1344C214yesmaximal
5C2×C4⋊Q8×C103C411yescharacteristic, complemented
6C2×C22⋊Q8×C103—21no—
7C2×#117×C103—21no—
8C2×#117×C103C2211yescharacteristic
9#431×C103—21no—
10#398×C103—21no—
11#398×C103C412yescomplemented
12#397×C103—21no—
13#397×C103C2212yes—
14#391×C103—21no—
15#382×C103C411yescharacteristic, complemented
16#342×C103—21no—
17#342×C103C2212yes—
18#324×C103—21no—
19#323×C103C2212yes—
20C22×Q8×C103—21no—
21C23×C4×C103D411yescharacteristic
22C4⋊Q8×C103—41no—
23C4⋊Q8×C103—41no—
24C22⋊Q8×C103—42no—
25C22⋊Q8×C103—42no—
26#117×C103—24no—
27#117×C103—41no—
28#117×C103—41no—
29#117×C103—42no—
30C2×C4⋊C4×C103—21no—
31C2×C4⋊C4×C103—22no—
32C2×C4⋊C4×C103—21no—
33C2×C4⋊C4×C103—41no—
34C2×C4⋊C4×C103C2×C412yes—
35C2×C4⋊C4×C103C2×C411yescharacteristic
36C2×C4⋊C4×C103D411yescharacteristic
37C2×C22⋊C4×C103—22no—
38C2×C22⋊C4×C103—22no—
39C2×C22⋊C4×C103D411yescharacteristic
40C2×C22⋊C4×C103C2311yescharacteristic
41C2×C42×C103—41no—
42C2×C42×C103C2×C411yescharacteristic
43C2×C42×C103D411yescharacteristic
44C4⋊C8×C103—41no—
45C22⋊C8×C103—22no—
46C4×C8×C103—41no—
47#95×C103—21no—
48#95×C103—22no—
49#95×C103—22no—
50#95×C103C2×C412yes—
51C24×C103C2×D411yescharacteristic
52C2×Q8×C103—41no—
53C2×Q8×C103—41no—
54C2×Q8×C103—42no—
55C2×Q8×C103—42no—
56C22×C4×C103—21no—
57C22×C4×C103—21no—
58C22×C4×C103—22no—
59C22×C4×C103—22no—
60C22×C4×C103—22no—
61C22×C4×C103—42no—
62C22×C4×C103C22⋊C411yescharacteristic
63C22×C4×C103C22⋊C411yescharacteristic
64C22×C4×C103C22⋊C411yescharacteristic
65C22×C4×C103C22⋊C411yescharacteristic
66C22×C4×C103D812yes—
67C22×C4×C103SD1612yes—
68C22×C4×C103C22×C411yescharacteristic
69C22×C4×C103C2×D411yescharacteristic
70C2×C8×C103—42no—
71C4⋊C4×C103—41no—
72C4⋊C4×C103—41no—
73C4⋊C4×C103—42no—
74C4⋊C4×C103—42no—
75C4⋊C4×C103—44no—
76C4⋊C4×C103—42no—
77C4⋊C4×C103—44no—
78C22⋊C4×C103—24no—
79C22⋊C4×C103—41no—
80C22⋊C4×C103—41no—
81C22⋊C4×C103—42no—
82C22⋊C4×C103—42no—
83C22⋊C4×C103—42no—
84C42×C103—21no—
85C42×C103—21no—
86C42×C103—21no—
87C42×C103—21no—
88C42×C103—44no—
89C23×C103—21no—
90C23×C103—21no—
91C23×C103—41no—
92C23×C103—41no—
93C23×C103C2×C22⋊C411yescharacteristic
94C23×C103C2×D811yescharacteristic
95C23×C103C2×SD1611yescharacteristic
96Q8×C103—82no—
97Q8×C103—82no—
98C2×C4×C103—21no—
99C2×C4×C103—21no—
100C2×C4×C103—22no—
101C2×C4×C103—22no—
102C2×C4×C103—22no—
103C2×C4×C103—22no—
104C2×C4×C103—21no—
105C2×C4×C103—21no—
106C2×C4×C103—21no—
107C2×C4×C103—21no—
108C2×C4×C103—41no—
109C2×C4×C103—41no—
110C2×C4×C103—41no—
111C2×C4×C103—41no—
112C2×C4×C103—44no—
113C2×C4×C103—42no—
114C2×C4×C103—42no—
115C2×C4×C103—42no—
116C2×C4×C103—42no—
117C2×C4×C103—42no—
118C2×C4×C103—42no—
119C2×C4×C103—82no—
120C2×C4×C103—82no—
121C2×C4×C103#9911yescharacteristic
122C2×C4×C103#9911yescharacteristic
123C2×C4×C103#10212yes—
124C2×C4×C103#10212yes—
125C2×C4×C103#10412yes—
126C8×C103—82no—
127C22×C103—21no—
128C22×C103—21no—
129C22×C103—21no—
130C22×C103—21no—
131C22×C103—41no—
132C22×C103—41no—
133C22×C103—41no—
134C22×C103—41no—
135C22×C103—81no—
136C22×C103C2×#9911yescharacteristic
137C22×C103C2×#10211yescharacteristic
138C22×C103C2×#10411yescharacteristic
139C4×C103—22no—
140C4×C103—41no—
141C4×C103—41no—
142C4×C103—41no—
143C4×C103—41no—
144C4×C103—82no—
145C4×C103—84no—
146C4×C103—82no—
147C4×C103#32712yes—
148C4×C103#32712yes—
149#11694C10311yesmaximal, characteristic, direct product factor, Sylow
150C2×C103—21no—
151C2×C103—21no—
152C2×C103—41no—
153C2×C103—41no—
154C2×C103C2×#32711yescharacteristic
155C2×C103#212311yescharacteristic
156C2×C103#212911yescharacteristic
157#2621C2×C10311yescharacteristic
158#1740C2×C10311yescharacteristic
159#1458C2×C10311yescharacteristic
160#1344C2×C10314yes—
161C103#1169411yescharacteristic, direct product factor, Sylow
162C2×C4⋊Q8C4×C10311yescharacteristic, complemented
163C2×C22⋊Q8—21no—
164C2×#117—21no—
165C2×#117C22×C10311yescharacteristic
166#431—21no—
167#398—21no—
168#398C4×C10312yescomplemented
169#397—21no—
170#397C22×C10312yes—
171#391—21no—
172#382C4×C10311yescharacteristic, complemented
173#342—21no—
174#342C22×C10312yes—
175#324—21no—
176#323C22×C10312yes—
177C22×Q8—21no—
178C23×C4D4×C10311yescharacteristic
179C4⋊Q8—41no—
180C4⋊Q8—41no—
181C22⋊Q8—42no—
182C22⋊Q8—42no—
183#117—24no—
184#117—41no—
185#117—41no—
186#117—42no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—41no—
191C2×C4⋊C4C2×C4×C10312yes—
192C2×C4⋊C4C2×C4×C10311yescharacteristic
193C2×C4⋊C4D4×C10311yescharacteristic
194C2×C22⋊C4—22no—
195C2×C22⋊C4—22no—
196C2×C22⋊C4D4×C10311yescharacteristic
197C2×C22⋊C4C23×C10311yescharacteristic
198C2×C42—41no—
199C2×C42C2×C4×C10311yescharacteristic
200C2×C42D4×C10311yescharacteristic
201C4⋊C8—41no—
202C22⋊C8—22no—
203C4×C8—41no—
204#95—21no—
205#95—22no—
206#95—22no—
207#95C2×C4×C10312yes—
208C24C2×D4×C10311yescharacteristic
209C2×Q8—41no—
210C2×Q8—41no—
211C2×Q8—42no—
212C2×Q8—42no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—42no—
219C22×C4C22⋊C4×C10311yescharacteristic
220C22×C4C22⋊C4×C10311yescharacteristic
221C22×C4C22⋊C4×C10311yescharacteristic
222C22×C4C22⋊C4×C10311yescharacteristic
223C22×C4D8×C10312yes—
224C22×C4SD16×C10312yes—
225C22×C4C22×C4×C10311yescharacteristic
226C22×C4C2×D4×C10311yescharacteristic
227C2×C8—42no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C4⋊C4—42no—
231C4⋊C4—42no—
232C4⋊C4—44no—
233C4⋊C4—42no—
234C4⋊C4—44no—
235C22⋊C4—24no—
236C22⋊C4—41no—
237C22⋊C4—41no—
238C22⋊C4—42no—
239C22⋊C4—42no—
240C22⋊C4—42no—
241C42—21no—
242C42—21no—
243C42—21no—
244C42—21no—
245C42—44no—
246C23—21no—
247C23—21no—
248C23—41no—
249C23—41no—
250C23C2×C22⋊C4×C10311yescharacteristic
251C23C2×D8×C10311yescharacteristic
252C23C2×SD16×C10311yescharacteristic
253Q8—82no—
254Q8—82no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—44no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—82no—
277C2×C4—82no—
278C2×C4#99×C10311yescharacteristic
279C2×C4#99×C10311yescharacteristic
280C2×C4#102×C10312yes—
281C2×C4#102×C10312yes—
282C2×C4#104×C10312yes—
283C8—82no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22—21no—
288C22—41no—
289C22—41no—
290C22—41no—
291C22—41no—
292C22—81no—
293C22C2×#99×C10311yescharacteristic
294C22C2×#102×C10311yescharacteristic
295C22C2×#104×C10311yescharacteristic
296C4—22no—
297C4—41no—
298C4—41no—
299C4—41no—
300C4—41no—
301C4—82no—
302C4—84no—
303C4—82no—
304C4#327×C10312yes—
305C4#327×C10312yes—
306C2—21no—
307C2—21no—
308C2—41no—
309C2—41no—
310C2C2×#327×C10311yescharacteristic
311C2C103×#212311yescharacteristic
312C2C103×#212911yescharacteristic
subgroupG/H
center, socleC22×C103C2×#99
commutatorC22×C4C22×C4×C103
Frattini, cosocleC2×C22⋊C4C23×C103
prime radicalC24×C103C2×D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C103 ◁ C22×C4×C103 ◁ C2×#117×C103 ◁ G

Complements

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

NH ≅ G/Ntype
5. C2×C4⋊Q8×C103C4semidirect
11. #398×C103C4semidirect
15. #382×C103C4semidirect
149. #11694C103direct (N × H)
161. C103#11694direct (N × H)
162. C2×C4⋊Q8C4×C103semidirect
168. #398C4×C103semidirect
172. #382C4×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#26212
C103×#17402
C103×#14582
C103×#13442
#11694103