Finite Group Databasebeta

← C103×#8863 #39914138

Subgroups — C103×#8863 #39914138

Order 26368.

374 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×#2921C211yesmaximal, characteristic
2C103×#1798C211yesmaximal, characteristic
3C103×#1571C211yesmaximal, characteristic, complemented
4C103×#1570C211yesmaximal, characteristic, complemented
5C103×#1458C211yesmaximal, characteristic
6C103×#1301C211yesmaximal, characteristic, complemented
7C103×#1301C211yesmaximal, characteristic, complemented
8C2×#117×C103C2211yescharacteristic
9#433×C103—22no—
10#433×C103—22no—
11#431×C103C2211yescharacteristic
12#431×C103C2211yescharacteristic
13#423×C103C2211yescharacteristic
14#423×C103C2211yescharacteristic
15C2×C4⋊C8×C103C2211yescharacteristic
16C2×C4⋊C8×C103C2211yescharacteristic
17#407×C103—21no—
18C2×C22⋊C8×C103—21no—
19C4×M16×C103—21no—
20#336×C103—21no—
21#335×C103—22no—
22#334×C103—22no—
23#324×C103C412yes—
24#323×C103C412yes—
25C23×C4×C103D411yescharacteristic
26C2×M16×C103—21no—
27C2×M16×C103—21no—
28C22×C8×C103—21no—
29C22×C8×C103—21no—
30#117×C103—21no—
31#117×C103—21no—
32#117×C103—21no—
33#117×C103—21no—
34C2×C4⋊C4×C103C2×C411yescharacteristic
35C2×C4⋊C4×C103Q811yescharacteristic
36C2×C22⋊C4×C103C2×C411yescharacteristic
37C2×C22⋊C4×C103Q811yescharacteristic
38C2×C42×C103D411yescharacteristic
39C2×C42×C103C2311yescharacteristic
40C4⋊C8×C103—21no—
41C4⋊C8×C103—21no—
42C4⋊C8×C103—21no—
43C4⋊C8×C103—21no—
44C4⋊C8×C103—21no—
45C4⋊C8×C103—21no—
46C4⋊C8×C103—21no—
47C4⋊C8×C103—21no—
48C4⋊C8×C103D412yes—
49C4⋊C8×C103D412yes—
50C22⋊C8×C103—24no—
51C22⋊C8×C103—42no—
52C22⋊C8×C103C2×C412yes—
53C22⋊C8×C103C2×C412yes—
54#97×C103—22no—
55C4×C8×C103—22no—
56C4×C8×C103—21no—
57C4×C8×C103—21no—
58C24×C103C4⋊C411yescharacteristic
59C22×C4×C103—21no—
60C22×C4×C103—21no—
61C22×C4×C103—21no—
62C22×C4×C103—21no—
63C22×C4×C103—21no—
64C22×C4×C103—21no—
65C22×C4×C103C4⋊C411yescharacteristic
66C22×C4×C103C4⋊C411yescharacteristic
67C22×C4×C103C4⋊C411yescharacteristic
68C22×C4×C103C22×C411yescharacteristic
69C22×C4×C103C2×D411yescharacteristic
70C22×C4×C103C2×Q811yescharacteristic
71M16×C103—41no—
72M16×C103—41no—
73M16×C103—41no—
74M16×C103—41no—
75C2×C8×C103—22no—
76C2×C8×C103—22no—
77C2×C8×C103—22no—
78C2×C8×C103—22no—
79C2×C8×C103—41no—
80C2×C8×C103—41no—
81C2×C8×C103—41no—
82C2×C8×C103—41no—
83C2×C8×C103—41no—
84C2×C8×C103—41no—
85C4⋊C4×C103—21no—
86C4⋊C4×C103—21no—
87C4⋊C4×C103—21no—
88C4⋊C4×C103—21no—
89C22⋊C4×C103—21no—
90C22⋊C4×C103—21no—
91C22⋊C4×C103—21no—
92C22⋊C4×C103—21no—
93C42×C103—21no—
94C42×C103—21no—
95C42×C103C2×D411yescharacteristic
96C42×C103C2×D411yescharacteristic
97C42×C103#4111yescharacteristic
98C42×C103#4111yescharacteristic
99C23×C103—21no—
100C23×C103—21no—
101C23×C103—21no—
102C23×C103—41no—
103C23×C103—41no—
104C23×C103C2×C4⋊C411yescharacteristic
105C2×C4×C103—21no—
106C2×C4×C103—21no—
107C2×C4×C103—21no—
108C2×C4×C103—21no—
109C2×C4×C103—21no—
110C2×C4×C103—41no—
111C2×C4×C103—41no—
112C2×C4×C103—41no—
113C2×C4×C103—41no—
114C2×C4×C103—41no—
115C2×C4×C103—41no—
116C2×C4×C103—41no—
117C2×C4×C103—41no—
118C2×C4×C103C4×D411yescharacteristic
119C2×C4×C103C4×D411yescharacteristic
120C2×C4×C103#12011yescharacteristic
121C2×C4×C103C22⋊Q811yescharacteristic
122C2×C4×C103C22⋊Q811yescharacteristic
123C2×C4×C103#12311yescharacteristic
124C2×C4×C103#13511yescharacteristic
125C2×C4×C103#13511yescharacteristic
126C2×C4×C103AGL(1,ℤ/8)11yescharacteristic
127C2×C4×C103#13711yescharacteristic
128C8×C103—42no—
129C8×C103—42no—
130C8×C103—42no—
131C8×C103—42no—
132C8×C103—81no—
133C8×C103—81no—
134C22×C103—21no—
135C22×C103—21no—
136C22×C103—42no—
137C22×C103—41no—
138C22×C103—41no—
139C22×C103—41no—
140C22×C103—81no—
141C22×C103#38511yescharacteristic
142C22×C103#42711yescharacteristic
143C22×C103#42811yescharacteristic
144C4×C103—21no—
145C4×C103—21no—
146C4×C103—21no—
147C4×C103—21no—
148C4×C103—41no—
149C4×C103—41no—
150C4×C103—41no—
151C4×C103#44911yescharacteristic
152C4×C103#45211yescharacteristic
153C4×C103#48211yescharacteristic
154C4×C103#48511yescharacteristic
155#8863C10311yesmaximal, characteristic, direct product factor, Sylow
156C2×C103—21no—
157C2×C103—21no—
158C2×C103—81no—
159C2×C103#185411yescharacteristic
160C2×C103#185811yescharacteristic
161C2×C103#186811yescharacteristic
162#2921C2×C10311yescharacteristic
163#1798C2×C10311yescharacteristic
164#1571C2×C10311yescharacteristic, complemented
165#1570C2×C10311yescharacteristic, complemented
166#1458C2×C10311yescharacteristic
167#1301C2×C10311yescharacteristic, complemented
168#1301C2×C10311yescharacteristic, complemented
169C103#886311yescharacteristic, direct product factor, Sylow
170C2×#117C22×C10311yescharacteristic
171#433—22no—
172#433—22no—
173#431C22×C10311yescharacteristic
174#431C22×C10311yescharacteristic
175#423C22×C10311yescharacteristic
176#423C22×C10311yescharacteristic
177C2×C4⋊C8C22×C10311yescharacteristic
178C2×C4⋊C8C22×C10311yescharacteristic
179#407—21no—
180C2×C22⋊C8—21no—
181C4×M16—21no—
182#336—21no—
183#335—22no—
184#334—22no—
185#324C4×C10312yes—
186#323C4×C10312yes—
187C23×C4D4×C10311yescharacteristic
188C2×M16—21no—
189C2×M16—21no—
190C22×C8—21no—
191C22×C8—21no—
192#117—21no—
193#117—21no—
194#117—21no—
195#117—21no—
196C2×C4⋊C4C2×C4×C10311yescharacteristic
197C2×C4⋊C4Q8×C10311yescharacteristic
198C2×C22⋊C4C2×C4×C10311yescharacteristic
199C2×C22⋊C4Q8×C10311yescharacteristic
200C2×C42D4×C10311yescharacteristic
201C2×C42C23×C10311yescharacteristic
202C4⋊C8—21no—
203C4⋊C8—21no—
204C4⋊C8—21no—
205C4⋊C8—21no—
206C4⋊C8—21no—
207C4⋊C8—21no—
208C4⋊C8—21no—
209C4⋊C8—21no—
210C4⋊C8D4×C10312yes—
211C4⋊C8D4×C10312yes—
212C22⋊C8—24no—
213C22⋊C8—42no—
214C22⋊C8C2×C4×C10312yes—
215C22⋊C8C2×C4×C10312yes—
216#97—22no—
217C4×C8—22no—
218C4×C8—21no—
219C4×C8—21no—
220C24C4⋊C4×C10311yescharacteristic
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4C4⋊C4×C10311yescharacteristic
228C22×C4C4⋊C4×C10311yescharacteristic
229C22×C4C4⋊C4×C10311yescharacteristic
230C22×C4C22×C4×C10311yescharacteristic
231C22×C4C2×D4×C10311yescharacteristic
232C22×C4C2×Q8×C10311yescharacteristic
233M16—41no—
234M16—41no—
235M16—41no—
236M16—41no—
237C2×C8—22no—
238C2×C8—22no—
239C2×C8—22no—
240C2×C8—22no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—41no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C22⋊C4—21no—
252C22⋊C4—21no—
253C22⋊C4—21no—
254C22⋊C4—21no—
255C42—21no—
256C42—21no—
257C42C2×D4×C10311yescharacteristic
258C42C2×D4×C10311yescharacteristic
259C42#41×C10311yescharacteristic
260C42#41×C10311yescharacteristic
261C23—21no—
262C23—21no—
263C23—21no—
264C23—41no—
265C23—41no—
266C23C2×C4⋊C4×C10311yescharacteristic
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4C4×D4×C10311yescharacteristic
281C2×C4C4×D4×C10311yescharacteristic
282C2×C4#120×C10311yescharacteristic
283C2×C4C22⋊Q8×C10311yescharacteristic
284C2×C4C22⋊Q8×C10311yescharacteristic
285C2×C4#123×C10311yescharacteristic
286C2×C4#135×C10311yescharacteristic
287C2×C4#135×C10311yescharacteristic
288C2×C4AGL(1,ℤ/8)×C10311yescharacteristic
289C2×C4#137×C10311yescharacteristic
290C8—42no—
291C8—42no—
292C8—42no—
293C8—42no—
294C8—81no—
295C8—81no—
296C22—21no—
297C22—21no—
298C22—42no—
299C22—41no—
300C22—41no—
301C22—41no—
302C22—81no—
303C22#385×C10311yescharacteristic
304C22#427×C10311yescharacteristic
305C22#428×C10311yescharacteristic
306C4—21no—
307C4—21no—
308C4—21no—
309C4—21no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4#449×C10311yescharacteristic
314C4#452×C10311yescharacteristic
315C4#482×C10311yescharacteristic
316C4#485×C10311yescharacteristic
317C2—21no—
318C2—21no—
319C2—81no—
320C2C103×#185411yescharacteristic
321C2C103×#185811yescharacteristic
322C2C103×#186811yescharacteristic
subgroupG/H
centerC2×C4×C103#120
commutatorC22×C4C22×C4×C103
Frattini, cosocleC2×C42C23×C103
socleC22×C103#385
prime radicalC24×C103C4⋊C4
LCSG ▷ C22×C4 ▷ 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. C103×#1571C2semidirect
4. C103×#1570C2semidirect
6. C103×#1301C2semidirect
7. C103×#1301C2semidirect
155. #8863C103direct (N × H)
164. #1571C2×C103semidirect
165. #1570C2×C103semidirect
167. #1301C2×C103semidirect
168. #1301C2×C103semidirect
169. C103#8863direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#29212
C103×#17982
C103×#15712
C103×#15702
C103×#14582
C103×#13012
#8863103