Finite Group Databasebeta

← C103×#7726 #39913001

Subgroups — C103×#7726 #39913001

Order 26368.

400 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#2860C211yesmaximal, characteristic
2C103×#1839C211yesmaximal, characteristic, complemented
3C103×#1839C211yesmaximal, characteristic, complemented
4C103×#1271C212yesmaximal, complemented
5C103×#1270C212yesmaximal
6C2×#126×C103—21no—
7#390×C103C411yescharacteristic
8#390×C103C411yescharacteristic
9#390×C103C2211yescharacteristic
10#389×C103C411yescharacteristic
11#389×C103C411yescharacteristic
12#389×C103C2211yescharacteristic
13#388×C103—21no—
14#388×C103—21no—
15#388×C103—21no—
16C43×C103C2211yescharacteristic
17#336×C103—21no—
18#336×C103—21no—
19#336×C103—21no—
20#336×C103—21no—
21#336×C103C2212yes—
22#336×C103C2212yes—
23C22×D4×C103C2×C411yescharacteristic
24C22×C8×C103—22no—
25C22×C8×C103—22no—
26#126×C103—44no—
27C2×C4⋊C4×C103—21no—
28C2×C4⋊C4×C103—21no—
29C2×C4⋊C4×C103—21no—
30C2×C4⋊C4×C103C2×C411yescharacteristic
31C2×C4⋊C4×C103C2×C411yescharacteristic
32C2×C4⋊C4×C103C2×C411yescharacteristic
33C2×C22⋊C4×C103—21no—
34C2×C22⋊C4×C103—21no—
35C2×C22⋊C4×C103—21no—
36C2×C22⋊C4×C103—21no—
37C2×C22⋊C4×C103—21no—
38C2×C22⋊C4×C103—21no—
39C2×C42×C103C2×C411yescharacteristic
40C2×C42×C103C2×C411yescharacteristic
41C2×C42×C103D411yescharacteristic
42C2×C42×C103D411yescharacteristic
43C2×C42×C103D411yescharacteristic
44C2×C42×C103D411yescharacteristic
45C2×C42×C103C2311yescharacteristic
46#95×C103—21no—
47#95×C103—21no—
48#95×C103—21no—
49C24×C103—21no—
50C2×D4×C103—22no—
51C2×D4×C103—41no—
52C2×D4×C103—41no—
53C22×C4×C103—21no—
54C22×C4×C103—21no—
55C22×C4×C103—21no—
56C22×C4×C103C22⋊C411yescharacteristic
57C22×C4×C103C22⋊C411yescharacteristic
58C22×C4×C103C22⋊C411yescharacteristic
59C22×C4×C103C22⋊C411yescharacteristic
60C22×C4×C103C22×C411yescharacteristic
61C22×C4×C103C2×D411yescharacteristic
62C22×C4×C103C2×D411yescharacteristic
63C2×C8×C103—42no—
64C2×C8×C103—42no—
65C2×C8×C103—42no—
66C2×C8×C103—42no—
67C2×C8×C103—42no—
68C2×C8×C103—42no—
69C4⋊C4×C103—22no—
70C4⋊C4×C103—41no—
71C4⋊C4×C103—41no—
72C4⋊C4×C103—42no—
73C4⋊C4×C103—42no—
74C4⋊C4×C103—42no—
75C22⋊C4×C103—42no—
76C22⋊C4×C103—42no—
77C22⋊C4×C103—42no—
78C22⋊C4×C103—42no—
79C22⋊C4×C103—42no—
80C22⋊C4×C103—42no—
81C42×C103—22no—
82C42×C103—22no—
83C42×C103—22no—
84C42×C103—41no—
85C42×C103—41no—
86C42×C103—41no—
87C42×C103—41no—
88C23×C103—41no—
89C23×C103—41no—
90C23×C103—41no—
91C23×C103—41no—
92C23×C103—41no—
93C23×C103—41no—
94C23×C103—41no—
95C23×C103C2×C22⋊C411yescharacteristic
96D4×C103—82no—
97C2×C4×C103—21no—
98C2×C4×C103—21no—
99C2×C4×C103—21no—
100C2×C4×C103—21no—
101C2×C4×C103—21no—
102C2×C4×C103—21no—
103C2×C4×C103—21no—
104C2×C4×C103—21no—
105C2×C4×C103—21no—
106C2×C4×C103—21no—
107C2×C4×C103—21no—
108C2×C4×C103—21no—
109C2×C4×C103—21no—
110C2×C4×C103—21no—
111C2×C4×C103—21no—
112C2×C4×C103—21no—
113C2×C4×C103—21no—
114C2×C4×C103—21no—
115C2×C4×C103—41no—
116C2×C4×C103—41no—
117C2×C4×C103—41no—
118C2×C4×C103—41no—
119C2×C4×C103—41no—
120C2×C4×C103—41no—
121C2×C4×C103—41no—
122C2×C4×C103—41no—
123C2×C4×C103—41no—
124C2×C4×C103#13112yes—
125C2×C4×C103#13512yes—
126C2×C4×C103AGL(1,ℤ/8)12yes—
127C8×C103—82no—
128C8×C103—82no—
129C22×C103—81no—
130C22×C103—81no—
131C22×C103—81no—
132C22×C103—81no—
133C22×C103—81no—
134C22×C103—81no—
135C22×C103—81no—
136C22×C103#40811yescharacteristic
137C22×C103#41011yescharacteristic
138C22×C103#41311yescharacteristic
139C22×C103#41611yescharacteristic
140C22×C103#41811yescharacteristic
141C22×C103#42111yescharacteristic
142C22×C103#42111yescharacteristic
143C4×C103—22no—
144C4×C103—22no—
145C4×C103—22no—
146C4×C103—41no—
147C4×C103—41no—
148C4×C103—41no—
149C4×C103—41no—
150C4×C103—81no—
151C4×C103—81no—
152C4×C103—81no—
153#7726C10311yesmaximal, characteristic, direct product factor, Sylow
154C2×C103—161no—
155C2×C103#147311yescharacteristic
156C2×C103#148211yescharacteristic
157C2×C103#149611yescharacteristic
158C2×C103#151411yescharacteristic
159C2×C103#152111yescharacteristic
160C2×C103#153511yescharacteristic
161C2×C103#155311yescharacteristic
162#2860C2×C10311yescharacteristic
163#1839C2×C10311yescharacteristic, complemented
164#1839C2×C10311yescharacteristic, complemented
165#1271C2×C10312yescomplemented
166#1270C2×C10312yes—
167C103#772611yescharacteristic, direct product factor, Sylow
168C2×#126—21no—
169#390C4×C10311yescharacteristic
170#390C4×C10311yescharacteristic
171#390C22×C10311yescharacteristic
172#389C4×C10311yescharacteristic
173#389C4×C10311yescharacteristic
174#389C22×C10311yescharacteristic
175#388—21no—
176#388—21no—
177#388—21no—
178C43C22×C10311yescharacteristic
179#336—21no—
180#336—21no—
181#336—21no—
182#336—21no—
183#336C22×C10312yes—
184#336C22×C10312yes—
185C22×D4C2×C4×C10311yescharacteristic
186C22×C8—22no—
187C22×C8—22no—
188#126—44no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4C2×C4×C10311yescharacteristic
193C2×C4⋊C4C2×C4×C10311yescharacteristic
194C2×C4⋊C4C2×C4×C10311yescharacteristic
195C2×C22⋊C4—21no—
196C2×C22⋊C4—21no—
197C2×C22⋊C4—21no—
198C2×C22⋊C4—21no—
199C2×C22⋊C4—21no—
200C2×C22⋊C4—21no—
201C2×C42C2×C4×C10311yescharacteristic
202C2×C42C2×C4×C10311yescharacteristic
203C2×C42D4×C10311yescharacteristic
204C2×C42D4×C10311yescharacteristic
205C2×C42D4×C10311yescharacteristic
206C2×C42D4×C10311yescharacteristic
207C2×C42C23×C10311yescharacteristic
208#95—21no—
209#95—21no—
210#95—21no—
211C24—21no—
212C2×D4—22no—
213C2×D4—41no—
214C2×D4—41no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4C22⋊C4×C10311yescharacteristic
219C22×C4C22⋊C4×C10311yescharacteristic
220C22×C4C22⋊C4×C10311yescharacteristic
221C22×C4C22⋊C4×C10311yescharacteristic
222C22×C4C22×C4×C10311yescharacteristic
223C22×C4C2×D4×C10311yescharacteristic
224C22×C4C2×D4×C10311yescharacteristic
225C2×C8—42no—
226C2×C8—42no—
227C2×C8—42no—
228C2×C8—42no—
229C2×C8—42no—
230C2×C8—42no—
231C4⋊C4—22no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—42no—
235C4⋊C4—42no—
236C4⋊C4—42no—
237C22⋊C4—42no—
238C22⋊C4—42no—
239C22⋊C4—42no—
240C22⋊C4—42no—
241C22⋊C4—42no—
242C22⋊C4—42no—
243C42—22no—
244C42—22no—
245C42—22no—
246C42—41no—
247C42—41no—
248C42—41no—
249C42—41no—
250C23—41no—
251C23—41no—
252C23—41no—
253C23—41no—
254C23—41no—
255C23—41no—
256C23—41no—
257C23C2×C22⋊C4×C10311yescharacteristic
258D4—82no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4#131×C10312yes—
287C2×C4#135×C10312yes—
288C2×C4AGL(1,ℤ/8)×C10312yes—
289C8—82no—
290C8—82no—
291C22—81no—
292C22—81no—
293C22—81no—
294C22—81no—
295C22—81no—
296C22—81no—
297C22—81no—
298C22#408×C10311yescharacteristic
299C22#410×C10311yescharacteristic
300C22#413×C10311yescharacteristic
301C22#416×C10311yescharacteristic
302C22#418×C10311yescharacteristic
303C22#421×C10311yescharacteristic
304C22#421×C10311yescharacteristic
305C4—22no—
306C4—22no—
307C4—22no—
308C4—41no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—81no—
313C4—81no—
314C4—81no—
315C2—161no—
316C2C103×#147311yescharacteristic
317C2C103×#148211yescharacteristic
318C2C103×#149611yescharacteristic
319C2C103×#151411yescharacteristic
320C2C103×#152111yescharacteristic
321C2C103×#153511yescharacteristic
322C2C103×#155311yescharacteristic
subgroupG/H
center, socleC23×C103C2×C22⋊C4
commutatorC22×C4C22×C4×C103
Frattini, cosocleC2×C42C23×C103
prime radicalC22×D4×C103C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C103 ◁ C43×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C103×#1839C2semidirect
3. C103×#1839C2semidirect
4. C103×#1271C2semidirect
153. #7726C103direct (N × H)
163. #1839C2×C103semidirect
164. #1839C2×C103semidirect
165. #1271C2×C103semidirect
167. C103#7726direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#28602
C103×#18392
C103×#12712
C103×#12702
#7726103