Finite Group Databasebeta

← C103×#12935 #39918210

Subgroups — C103×#12935 #39918210

Order 26368.

490 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D8×C103C211yesmaximal, characteristic
2C2×#366×C103C211yesmaximal, characteristic, complemented
3C2×#357×C103C211yesmaximal, characteristic
4C2×#357×C103C211yesmaximal, characteristic
5C103×#1942C211yesmaximal, characteristic, complemented
6C103×#1380C211yesmaximal, characteristic, complemented
7C103×#1374C211yesmaximal, characteristic, complemented
8C22×D8×C103C2211yescharacteristic
9C2×C4×D4×C103—21no—
10C22×C16×C103C2211yescharacteristic
11C22×C16×C103C2211yescharacteristic
12C4×D8×C103—22no—
13C4×D8×C103—22no—
14C2×#107×C103C2211yescharacteristic
15C2×#107×C103C2211yescharacteristic
16C2×#107×C103C2211yescharacteristic
17C2×#102×C103—21no—
18C2×C4×C8×C103C2211yescharacteristic
19#389×C103—21no—
20#366×C103—22no—
21#357×C103—22no—
22#357×C103C414yescomplemented
23#340×C103—21no—
24C22×D4×C103—21no—
25C23×C4×C103—41no—
26C2×D8×C103—21no—
27C2×D8×C103—21no—
28C2×D8×C103—21no—
29C2×D8×C103C2×C412yes—
30C2×D8×C103D412yes—
31C2×D8×C103Q812yes—
32C22×C8×C103D411yescharacteristic
33C22×C8×C103C2311yescharacteristic
34C4×D4×C103—24no—
35C4×D4×C103—42no—
36C2×C4⋊C4×C103—21no—
37C2×C4⋊C4×C103—21no—
38C2×C4⋊C4×C103—21no—
39C2×C4⋊C4×C103—41no—
40C2×C22⋊C4×C103—41no—
41C2×C42×C103D411yescharacteristic
42C2×C16×C103—21no—
43C2×C16×C103—21no—
44C2×C16×C103—21no—
45C2×C16×C103—21no—
46C2×C16×C103—21no—
47C2×C16×C103C2×C412yescomplemented
48#107×C103—21no—
49#107×C103—21no—
50#107×C103—21no—
51#107×C103—21no—
52#107×C103C2×C412yescomplemented
53#107×C103D412yes—
54#102×C103—24no—
55C4×C8×C103—21no—
56C4×C8×C103—21no—
57#95×C103—41no—
58C24×C103—41no—
59C2×D4×C103—22no—
60C2×D4×C103—22no—
61C2×D4×C103—22no—
62C2×D4×C103—41no—
63C2×D4×C103—41no—
64C2×D4×C103—41no—
65C22×C4×C103—44no—
66C22×C4×C103—41no—
67C22×C4×C103—41no—
68C22×C4×C103—41no—
69C22×C4×C103—82no—
70C22×C4×C103—82no—
71C22×C4×C103D811yescharacteristic
72C22×C4×C103D811yescharacteristic
73C22×C4×C103C2×D411yescharacteristic
74D8×C103—22no—
75D8×C103—22no—
76D8×C103—22no—
77D8×C103C4⋊C414yescomplemented
78C2×C8×C103—21no—
79C2×C8×C103—21no—
80C2×C8×C103—21no—
81C2×C8×C103C22×C411yescharacteristic
82C2×C8×C103C2×D411yescharacteristic
83C2×C8×C103C2×D411yescharacteristic
84C2×C8×C103C2×Q811yescharacteristic
85C2×C8×C103#4111yescharacteristic
86C2×C8×C103#4111yescharacteristic
87C4⋊C4×C103—22no—
88C4⋊C4×C103—22no—
89C4⋊C4×C103—41no—
90C4⋊C4×C103—41no—
91C4⋊C4×C103—41no—
92C4⋊C4×C103—41no—
93C4⋊C4×C103—82no—
94C22⋊C4×C103—44no—
95C42×C103—21no—
96C42×C103—21no—
97C16×C103—22no—
98C16×C103—41no—
99C23×C103—42no—
100C23×C103—42no—
101C23×C103—42no—
102C23×C103—81no—
103C23×C103—81no—
104C23×C103—81no—
105C23×C103—81no—
106C23×C103C2×D811yescharacteristic
107D4×C103—24no—
108D4×C103—42no—
109D4×C103—42no—
110D4×C103—42no—
111C2×C4×C103—21no—
112C2×C4×C103—21no—
113C2×C4×C103—21no—
114C2×C4×C103—21no—
115C2×C4×C103—21no—
116C2×C4×C103—42no—
117C2×C4×C103—42no—
118C2×C4×C103—88no—
119C2×C4×C103—81no—
120C2×C4×C103—81no—
121C2×C4×C103—81no—
122C2×C4×C103—81no—
123C2×C4×C103—81no—
124C2×C4×C103—81no—
125C2×C4×C103—81no—
126C2×C4×C103D1612yes—
127C2×C4×C103C4×D411yescharacteristic
128C2×C4×C103#12011yescharacteristic
129C2×C4×C103C22⋊Q811yescharacteristic
130C2×C4×C103#13511yescharacteristic
131C2×C4×C103AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C103#13711yescharacteristic
133C8×C103—41no—
134C8×C103C2×C4⋊C411yescharacteristic
135C8×C103C4×D411yescharacteristic
136C8×C103C22⋊Q811yescharacteristic
137C8×C103#12311yescharacteristic
138C22×C103—44no—
139C22×C103—82no—
140C22×C103—82no—
141C22×C103—82no—
142C22×C103—82no—
143C22×C103—82no—
144C22×C103—82no—
145C22×C103C4×D811yescharacteristic
146C22×C103#44711yescharacteristic
147C22×C103#47411yescharacteristic
148C22×C103C2×D1611yescharacteristic
149C22×C103#50811yescharacteristic
150C22×C103#50911yescharacteristic
151C22×C103#51011yescharacteristic
152C4×C103—22no—
153C4×C103—41no—
154C4×C103—82no—
155C4×C103—82no—
156C4×C103—161no—
157C4×C103#38511yescharacteristic
158C4×C103#44011yescharacteristic
159C4×C103#45211yescharacteristic
160C4×C103#47811yescharacteristic
161#12935C10311yesmaximal, characteristic, direct product factor, Sylow
162C2×C103—84no—
163C2×C103#186211yescharacteristic
164C2×C103C4×D1611yescharacteristic
165C2×C103#217511yescharacteristic
166C2×C103#218411yescharacteristic
167C2×C103#218911yescharacteristic
168C2×C103#222411yescharacteristic
169C2×C103#222811yescharacteristic
170C2×C4×D8C2×C10311yescharacteristic
171C2×#366C2×C10311yescharacteristic, complemented
172C2×#357C2×C10311yescharacteristic
173C2×#357C2×C10311yescharacteristic
174#1942C2×C10311yescharacteristic, complemented
175#1380C2×C10311yescharacteristic, complemented
176#1374C2×C10311yescharacteristic, complemented
177C103#1293511yescharacteristic, direct product factor, Sylow
178C22×D8C22×C10311yescharacteristic
179C2×C4×D4—21no—
180C22×C16C22×C10311yescharacteristic
181C22×C16C22×C10311yescharacteristic
182C4×D8—22no—
183C4×D8—22no—
184C2×#107C22×C10311yescharacteristic
185C2×#107C22×C10311yescharacteristic
186C2×#107C22×C10311yescharacteristic
187C2×#102—21no—
188C2×C4×C8C22×C10311yescharacteristic
189#389—21no—
190#366—22no—
191#357—22no—
192#357C4×C10314yescomplemented
193#340—21no—
194C22×D4—21no—
195C23×C4—41no—
196C2×D8—21no—
197C2×D8—21no—
198C2×D8—21no—
199C2×D8C2×C4×C10312yes—
200C2×D8D4×C10312yes—
201C2×D8Q8×C10312yes—
202C22×C8D4×C10311yescharacteristic
203C22×C8C23×C10311yescharacteristic
204C4×D4—24no—
205C4×D4—42no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—41no—
210C2×C22⋊C4—41no—
211C2×C42D4×C10311yescharacteristic
212C2×C16—21no—
213C2×C16—21no—
214C2×C16—21no—
215C2×C16—21no—
216C2×C16—21no—
217C2×C16C2×C4×C10312yescomplemented
218#107—21no—
219#107—21no—
220#107—21no—
221#107—21no—
222#107C2×C4×C10312yescomplemented
223#107D4×C10312yes—
224#102—24no—
225C4×C8—21no—
226C4×C8—21no—
227#95—41no—
228C24—41no—
229C2×D4—22no—
230C2×D4—22no—
231C2×D4—22no—
232C2×D4—41no—
233C2×D4—41no—
234C2×D4—41no—
235C22×C4—44no—
236C22×C4—41no—
237C22×C4—41no—
238C22×C4—41no—
239C22×C4—82no—
240C22×C4—82no—
241C22×C4D8×C10311yescharacteristic
242C22×C4D8×C10311yescharacteristic
243C22×C4C2×D4×C10311yescharacteristic
244D8—22no—
245D8—22no—
246D8—22no—
247D8C4⋊C4×C10314yescomplemented
248C2×C8—21no—
249C2×C8—21no—
250C2×C8—21no—
251C2×C8C22×C4×C10311yescharacteristic
252C2×C8C2×D4×C10311yescharacteristic
253C2×C8C2×D4×C10311yescharacteristic
254C2×C8C2×Q8×C10311yescharacteristic
255C2×C8#41×C10311yescharacteristic
256C2×C8#41×C10311yescharacteristic
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—82no—
264C22⋊C4—44no—
265C42—21no—
266C42—21no—
267C16—22no—
268C16—41no—
269C23—42no—
270C23—42no—
271C23—42no—
272C23—81no—
273C23—81no—
274C23—81no—
275C23—81no—
276C23C2×D8×C10311yescharacteristic
277D4—24no—
278D4—42no—
279D4—42no—
280D4—42no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—88no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4—81no—
293C2×C4—81no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4D16×C10312yes—
297C2×C4C4×D4×C10311yescharacteristic
298C2×C4#120×C10311yescharacteristic
299C2×C4C22⋊Q8×C10311yescharacteristic
300C2×C4#135×C10311yescharacteristic
301C2×C4AGL(1,ℤ/8)×C10311yescharacteristic
302C2×C4#137×C10311yescharacteristic
303C8—41no—
304C8C2×C4⋊C4×C10311yescharacteristic
305C8C4×D4×C10311yescharacteristic
306C8C22⋊Q8×C10311yescharacteristic
307C8#123×C10311yescharacteristic
308C22—44no—
309C22—82no—
310C22—82no—
311C22—82no—
312C22—82no—
313C22—82no—
314C22—82no—
315C22C4×D8×C10311yescharacteristic
316C22#447×C10311yescharacteristic
317C22#474×C10311yescharacteristic
318C22C2×D16×C10311yescharacteristic
319C22#508×C10311yescharacteristic
320C22#509×C10311yescharacteristic
321C22#510×C10311yescharacteristic
322C4—22no—
323C4—41no—
324C4—82no—
325C4—82no—
326C4—161no—
327C4#385×C10311yescharacteristic
328C4#440×C10311yescharacteristic
329C4#452×C10311yescharacteristic
330C4#478×C10311yescharacteristic
331C2—84no—
332C2C103×#186211yescharacteristic
333C2C4×D16×C10311yescharacteristic
334C2C103×#217511yescharacteristic
335C2C103×#218411yescharacteristic
336C2C103×#218911yescharacteristic
337C2C103×#222411yescharacteristic
338C2C103×#222811yescharacteristic
subgroupG/H
center, socleC23×C103C2×D8
commutatorC2×C8C22×C4×C103
Frattini, cosocleC22×C8C23×C103
prime radicalC22×D8×C103C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C103 ◁ C2×C42×C103 ◁ C2×C4×C8×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#366×C103C2semidirect
5. C103×#1942C2semidirect
6. C103×#1380C2semidirect
7. C103×#1374C2semidirect
22. #357×C103C4semidirect
47. C2×C16×C103C2×C4semidirect
52. #107×C103C2×C4semidirect
77. D8×C103C4⋊C4semidirect
161. #12935C103direct (N × H)
171. C2×#366C2×C103semidirect
174. #1942C2×C103semidirect
175. #1380C2×C103semidirect
176. #1374C2×C103semidirect
177. C103#12935direct (N × H)
192. #357C4×C103semidirect
217. C2×C16C2×C4×C103semidirect
222. #107C2×C4×C103semidirect
247. D8C4⋊C4×C103semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D8×C1032
C2×#366×C1032
C2×#357×C1032
C103×#19422
C103×#13802
C103×#13742
#12935103