Finite Group Databasebeta

← C103×#9576 #39914851

Subgroups — C103×#9576 #39914851

Order 26368.

370 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#1990C211yesmaximal, characteristic
2C103×#1987C211yesmaximal, characteristic
3C103×#1947C211yesmaximal, characteristic
4C103×#1770C211yesmaximal, characteristic
5C2×#333×C103C211yesmaximal, characteristic
6C103×#1296C211yesmaximal, characteristic
7C103×#1277C211yesmaximal, characteristic
8C2×C4⋊Q8×C103C2211yescharacteristic
9C2×#107×C103—21no—
10C2×C4⋊C8×C103C2211yescharacteristic
11C2×C4⋊C8×C103C2211yescharacteristic
12C2×C4⋊C8×C103C2211yescharacteristic
13C2×#97×C103—21no—
14C2×C4×C8×C103C2211yescharacteristic
15#384×C103C2211yescharacteristic
16C4×C4⋊C4×C103C2211yescharacteristic
17#340×C103—21no—
18#340×C103—21no—
19#340×C103—21no—
20#340×C103—21no—
21#340×C103—21no—
22#336×C103—21no—
23#333×C103C414yescomplemented
24C22×Q8×C103—21no—
25C22×C8×C103—21no—
26C22×C8×C103—21no—
27C22×C8×C103—21no—
28C22×C8×C103D411yescharacteristic
29C22×C8×C103D411yescharacteristic
30C4⋊Q8×C103—21no—
31C4⋊Q8×C103—21no—
32C4⋊Q8×C103—21no—
33C4⋊Q8×C103C2×C412yes—
34C2×C4⋊C4×C103—21no—
35C2×C4⋊C4×C103—21no—
36C2×C4⋊C4×C103—21no—
37C2×C4⋊C4×C103—21no—
38C2×C4⋊C4×C103—21no—
39C2×C4⋊C4×C103D411yescharacteristic
40C2×C4⋊C4×C103D411yescharacteristic
41C2×C42×C103—21no—
42C2×C42×C103C2311yescharacteristic
43#107×C103—42no—
44C4⋊C8×C103—21no—
45C4⋊C8×C103—21no—
46C4⋊C8×C103—21no—
47C4⋊C8×C103—21no—
48C4⋊C8×C103C2×C412yes—
49C4⋊C8×C103C2×C412yes—
50#97×C103—42no—
51C4×C8×C103—21no—
52C4×C8×C103—21no—
53#95×C103—21no—
54C2×Q8×C103—22no—
55C2×Q8×C103—41no—
56C2×Q8×C103—81no—
57C2×Q8×C103—81no—
58C22×C4×C103—21no—
59C22×C4×C103—21no—
60C22×C4×C103—41no—
61C22×C4×C103—41no—
62C22×C4×C103C2×D411yescharacteristic
63C22×C4×C103C2×D411yescharacteristic
64C22×C4×C103#4111yescharacteristic
65C2×C8×C103—21no—
66C2×C8×C103—21no—
67C2×C8×C103—22no—
68C2×C8×C103—22no—
69C2×C8×C103—21no—
70C2×C8×C103—21no—
71C2×C8×C103—21no—
72C2×C8×C103—41no—
73C2×C8×C103—41no—
74C2×C8×C103—41no—
75C2×C8×C103—41no—
76C2×C8×C103—41no—
77C2×C8×C103—41no—
78C2×C8×C103—41no—
79C2×C8×C103Q1612yes—
80C4⋊C4×C103—22no—
81C4⋊C4×C103—22no—
82C4⋊C4×C103—21no—
83C4⋊C4×C103—21no—
84C4⋊C4×C103—21no—
85C4⋊C4×C103—21no—
86C4⋊C4×C103—41no—
87C4⋊C4×C103—41no—
88C4⋊C4×C103—41no—
89C4⋊C4×C103—41no—
90C4⋊C4×C103—41no—
91C4⋊C4×C103—41no—
92C4⋊C4×C103—81no—
93C42×C103—41no—
94C42×C103—41no—
95C42×C103C22×C411yescharacteristic
96C42×C103#4111yescharacteristic
97C42×C103#4111yescharacteristic
98C42×C103#4111yescharacteristic
99C23×C103#12111yescharacteristic
100Q8×C103—82no—
101Q8×C103—82no—
102C2×C4×C103—21no—
103C2×C4×C103—21no—
104C2×C4×C103—42no—
105C2×C4×C103—41no—
106C2×C4×C103—41no—
107C2×C4×C103—41no—
108C2×C4×C103—41no—
109C2×C4×C103—41no—
110C2×C4×C103—41no—
111C2×C4×C103—81no—
112C2×C4×C103—81no—
113C2×C4×C103—81no—
114C2×C4×C103—81no—
115C2×C4×C103—81no—
116C2×C4×C103#11711yescharacteristic
117C2×C4×C103C4×D411yescharacteristic
118C2×C4×C103C4×D411yescharacteristic
119C2×C4×C103#12311yescharacteristic
120C2×C4×C103#12411yescharacteristic
121C2×C4×C103#12611yescharacteristic
122C2×C4×C103C2×Q1611yescharacteristic
123C2×C4×C103#13511yescharacteristic
124C2×C4×C103AGL(1,ℤ/8)11yescharacteristic
125C2×C4×C103AGL(1,ℤ/8)11yescharacteristic
126C2×C4×C103#13711yescharacteristic
127C2×C4×C103#13711yescharacteristic
128C2×C4×C103#13711yescharacteristic
129C2×C4×C103#13711yescharacteristic
130C8×C103—22no—
131C8×C103—42no—
132C8×C103—42no—
133C8×C103—41no—
134C8×C103—81no—
135C22×C103#38811yescharacteristic
136C22×C103#46211yescharacteristic
137C22×C103#46311yescharacteristic
138C22×C103#46811yescharacteristic
139C22×C103#47011yescharacteristic
140C22×C103#47111yescharacteristic
141C22×C103#47211yescharacteristic
142C4×C103—21no—
143C4×C103—21no—
144C4×C103—82no—
145C4×C103—81no—
146C4×C103—81no—
147C4×C103—161no—
148C4×C103C4×Q1611yescharacteristic
149C4×C103#44011yescharacteristic
150C4×C103#44011yescharacteristic
151C4×C103#44111yescharacteristic
152C4×C103#48411yescharacteristic
153C4×C103#48511yescharacteristic
154C4×C103#48911yescharacteristic
155C4×C103#49111yescharacteristic
156#9576C10311yesmaximal, characteristic, direct product factor, Sylow
157C2×C103#169211yescharacteristic
158C2×C103#169611yescharacteristic
159C2×C103#169711yescharacteristic
160C2×C103#170311yescharacteristic
161C2×C103#192811yescharacteristic
162C2×C103#193111yescharacteristic
163C2×C103#193511yescharacteristic
164#1990C2×C10311yescharacteristic
165#1987C2×C10311yescharacteristic
166#1947C2×C10311yescharacteristic
167#1770C2×C10311yescharacteristic
168C2×#333C2×C10311yescharacteristic
169#1296C2×C10311yescharacteristic
170#1277C2×C10311yescharacteristic
171C103#957611yescharacteristic, direct product factor, Sylow
172C2×C4⋊Q8C22×C10311yescharacteristic
173C2×#107—21no—
174C2×C4⋊C8C22×C10311yescharacteristic
175C2×C4⋊C8C22×C10311yescharacteristic
176C2×C4⋊C8C22×C10311yescharacteristic
177C2×#97—21no—
178C2×C4×C8C22×C10311yescharacteristic
179#384C22×C10311yescharacteristic
180C4×C4⋊C4C22×C10311yescharacteristic
181#340—21no—
182#340—21no—
183#340—21no—
184#340—21no—
185#340—21no—
186#336—21no—
187#333C4×C10314yescomplemented
188C22×Q8—21no—
189C22×C8—21no—
190C22×C8—21no—
191C22×C8—21no—
192C22×C8D4×C10311yescharacteristic
193C22×C8D4×C10311yescharacteristic
194C4⋊Q8—21no—
195C4⋊Q8—21no—
196C4⋊Q8—21no—
197C4⋊Q8C2×C4×C10312yes—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4D4×C10311yescharacteristic
204C2×C4⋊C4D4×C10311yescharacteristic
205C2×C42—21no—
206C2×C42C23×C10311yescharacteristic
207#107—42no—
208C4⋊C8—21no—
209C4⋊C8—21no—
210C4⋊C8—21no—
211C4⋊C8—21no—
212C4⋊C8C2×C4×C10312yes—
213C4⋊C8C2×C4×C10312yes—
214#97—42no—
215C4×C8—21no—
216C4×C8—21no—
217#95—21no—
218C2×Q8—22no—
219C2×Q8—41no—
220C2×Q8—81no—
221C2×Q8—81no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—41no—
225C22×C4—41no—
226C22×C4C2×D4×C10311yescharacteristic
227C22×C4C2×D4×C10311yescharacteristic
228C22×C4#41×C10311yescharacteristic
229C2×C8—21no—
230C2×C8—21no—
231C2×C8—22no—
232C2×C8—22no—
233C2×C8—21no—
234C2×C8—21no—
235C2×C8—21no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8Q16×C10312yes—
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—81no—
257C42—41no—
258C42—41no—
259C42C22×C4×C10311yescharacteristic
260C42#41×C10311yescharacteristic
261C42#41×C10311yescharacteristic
262C42#41×C10311yescharacteristic
263C23#121×C10311yescharacteristic
264Q8—82no—
265Q8—82no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—42no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—81no—
276C2×C4—81no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—81no—
280C2×C4#117×C10311yescharacteristic
281C2×C4C4×D4×C10311yescharacteristic
282C2×C4C4×D4×C10311yescharacteristic
283C2×C4#123×C10311yescharacteristic
284C2×C4#124×C10311yescharacteristic
285C2×C4#126×C10311yescharacteristic
286C2×C4C2×Q16×C10311yescharacteristic
287C2×C4#135×C10311yescharacteristic
288C2×C4AGL(1,ℤ/8)×C10311yescharacteristic
289C2×C4AGL(1,ℤ/8)×C10311yescharacteristic
290C2×C4#137×C10311yescharacteristic
291C2×C4#137×C10311yescharacteristic
292C2×C4#137×C10311yescharacteristic
293C2×C4#137×C10311yescharacteristic
294C8—22no—
295C8—42no—
296C8—42no—
297C8—41no—
298C8—81no—
299C22#388×C10311yescharacteristic
300C22#462×C10311yescharacteristic
301C22#463×C10311yescharacteristic
302C22#468×C10311yescharacteristic
303C22#470×C10311yescharacteristic
304C22#471×C10311yescharacteristic
305C22#472×C10311yescharacteristic
306C4—21no—
307C4—21no—
308C4—82no—
309C4—81no—
310C4—81no—
311C4—161no—
312C4C4×Q16×C10311yescharacteristic
313C4#440×C10311yescharacteristic
314C4#440×C10311yescharacteristic
315C4#441×C10311yescharacteristic
316C4#484×C10311yescharacteristic
317C4#485×C10311yescharacteristic
318C4#489×C10311yescharacteristic
319C4#491×C10311yescharacteristic
320C2C103×#169211yescharacteristic
321C2C103×#169611yescharacteristic
322C2C103×#169711yescharacteristic
323C2C103×#170311yescharacteristic
324C2C103×#192811yescharacteristic
325C2C103×#193111yescharacteristic
326C2C103×#193511yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C103#121
commutatorC42C22×C4×C103
Frattini, cosocleC2×C42C23×C103
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C103 ◁ C2×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
23. #333×C103C4semidirect
156. #9576C103direct (N × H)
171. C103#9576direct (N × H)
187. #333C4×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#19902
C103×#19872
C103×#19472
C103×#17702
C2×#333×C1032
C103×#12962
C103×#12772
#9576103