Finite Group Databasebeta

← C103×#15197 #39920472

Subgroups — C103×#15197 #39920472

Order 26368.

1254 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#389×C103C211yesmaximal, characteristic
2C2×#384×C103C211yesmaximal, characteristic
3C103×#1442C214yesmaximal
4C103×#1441C214yesmaximal
5C103×C4⋊#95C212yesmaximal
6C103×C4⋊#95C212yesmaximal
7C4×#95×C103C211yesmaximal, characteristic
8C22×C4⋊C4×C103C2212yes—
9C22×C4⋊C4×C103C2211yescharacteristic
10C22×C4⋊C4×C103C2212yes—
11C22×C4⋊C4×C103C2211yescharacteristic
12C22×C4⋊C4×C103C2212yes—
13C22×C4⋊C4×C103C2212yes—
14C22×C42×C103C2212yes—
15C22×C42×C103C2211yescharacteristic
16#389×C103—24no—
17#384×C103—24no—
18C2×#95×C103C2212yes—
19C2×#95×C103C2212yes—
20C2×#95×C103C2218yes—
21C2×#95×C103C2218yes—
22C2×#95×C103C2212yes—
23C23×C4×C103C2312yes—
24C23×C4×C103C2314yes—
25C23×C4×C103C2314yes—
26C23×C4×C103C2312yes—
27C23×C4×C103C2311yescharacteristic
28C23×C4×C103C2311yescharacteristic
29C23×C4×C103C2311yescharacteristic
30C2×C4⋊C4×C103—22no—
31C2×C4⋊C4×C103—22no—
32C2×C4⋊C4×C103—24no—
33C2×C4⋊C4×C103—24no—
34C2×C4⋊C4×C103—24no—
35C2×C4⋊C4×C103—22no—
36C2×C4⋊C4×C103—24no—
37C2×C4⋊C4×C103—24no—
38C2×C4⋊C4×C103—28no—
39C2×C4⋊C4×C103—28no—
40C2×C4⋊C4×C103—44no—
41C2×C4⋊C4×C103—44no—
42C2×C4⋊C4×C103Q814yes—
43C2×C42×C103—24no—
44C2×C42×C103—24no—
45C2×C42×C103—24no—
46C2×C42×C103—24no—
47C2×C42×C103D414yes—
48#95×C103—24no—
49#95×C103—24no—
50#95×C103—48no—
51#95×C103—48no—
52#95×C103Q818yes—
53C24×C103C2411yescharacteristic
54C22×C4×C103—22no—
55C22×C4×C103—22no—
56C22×C4×C103—22no—
57C22×C4×C103—22no—
58C22×C4×C103—22no—
59C22×C4×C103—24no—
60C22×C4×C103—24no—
61C22×C4×C103—24no—
62C22×C4×C103—24no—
63C22×C4×C103—22no—
64C22×C4×C103—24no—
65C22×C4×C103—24no—
66C22×C4×C103—24no—
67C22×C4×C103—24no—
68C22×C4×C103—22no—
69C22×C4×C103—24no—
70C22×C4×C103—24no—
71C22×C4×C103—28no—
72C22×C4×C103—24no—
73C22×C4×C103—24no—
74C22×C4×C103—28no—
75C22×C4×C103—28no—
76C22×C4×C103C2×D412yes—
77C22×C4×C103C2×D412yes—
78C22×C4×C103C2×D412yes—
79C22×C4×C103C2×Q818yes—
80C22×C4×C103C2×Q814yes—
81C22×C4×C103C2×Q814yes—
82C22×C4×C103C2×Q812yes—
83C22×C4×C103#4114yes—
84C22×C4×C103#4112yes—
85C22×C4×C103#4114yes—
86C22×C4×C103#4114yes—
87C4⋊C4×C103—28no—
88C4⋊C4×C103—48no—
89C4⋊C4×C103—48no—
90C4⋊C4×C103—44no—
91C4⋊C4×C103—48no—
92C4⋊C4×C103—48no—
93C42×C103—28no—
94C42×C103—48no—
95C23×C103C22×D411yescharacteristic
96C23×C103C22×Q811yescharacteristic
97C23×C103C22×Q812yes—
98C23×C103C2×#4111yescharacteristic
99C23×C103C2×#4112yes—
100C23×C103C2×#4112yes—
101C23×C103C2×#4112yes—
102C23×C103H(5,𝔽2)12yes—
103C23×C103H(5,𝔽2)12yes—
104C2×C4×C103—22no—
105C2×C4×C103—22no—
106C2×C4×C103—22no—
107C2×C4×C103—22no—
108C2×C4×C103—28no—
109C2×C4×C103—28no—
110C2×C4×C103—24no—
111C2×C4×C103—28no—
112C2×C4×C103—28no—
113C2×C4×C103—28no—
114C2×C4×C103—28no—
115C2×C4×C103—42no—
116C2×C4×C103—44no—
117C2×C4×C103—42no—
118C2×C4×C103—44no—
119C2×C4×C103—44no—
120C2×C4×C103—44no—
121C2×C4×C103—44no—
122C2×C4×C103—42no—
123C2×C4×C103—44no—
124C2×C4×C103—42no—
125C2×C4×C103—44no—
126C2×C4×C103—44no—
127C2×C4×C103—42no—
128C2×C4×C103—416no—
129C2×C4×C103—48no—
130C2×C4×C103C22⋊Q814yes—
131C2×C4×C103#12314yes—
132C2×C4×C103#12414yes—
133C2×C4×C103#12414yes—
134C2×C4×C103#12518yes—
135C2×C4×C103#12618yes—
136C2×C4×C103C4⋊Q814yes—
137C22×C103C2×C22⋊Q811yescharacteristic
138C22×C103C2×#12311yescharacteristic
139C22×C103C2×#12411yescharacteristic
140C22×C103C2×#12411yescharacteristic
141C22×C103C2×#12512yes—
142C22×C103C2×#12612yes—
143C22×C103C2×C4⋊Q811yescharacteristic
144C22×C103#53314yes—
145C22×C103#53511yescharacteristic
146C22×C103#53511yescharacteristic
147C22×C103#54014yes—
148C22×C103#55314yes—
149C22×C103#55412yes—
150C22×C103#55412yes—
151C22×C103#55414yes—
152C22×C103#55512yes—
153C22×C103Q8212yes—
154C4×C103—24no—
155C4×C103—24no—
156C4×C103—44no—
157C4×C103—48no—
158C4×C103—84no—
159C4×C103—82no—
160C4×C103#40018yes—
161#15197C10311yesmaximal, characteristic, direct product factor, Sylow
162C2×C103C2×#40011yescharacteristic
163C2×C103#249714yes—
164C2×C103#250211yescharacteristic
165C2×C103#250411yescharacteristic
166C2×C103#250714yes—
167C2×C103#256311yescharacteristic
168C2×C103#256711yescharacteristic
169C2×C103#264111yescharacteristic
170C2×C103#286211yescharacteristic
171C2×#389C2×C10311yescharacteristic
172C2×#384C2×C10311yescharacteristic
173#1442C2×C10314yes—
174#1441C2×C10314yes—
175C4⋊#95C2×C10312yes—
176C4⋊#95C2×C10312yes—
177C4×#95C2×C10311yescharacteristic
178C103#1519711yescharacteristic, direct product factor, Sylow
179C22×C4⋊C4C22×C10312yes—
180C22×C4⋊C4C22×C10311yescharacteristic
181C22×C4⋊C4C22×C10312yes—
182C22×C4⋊C4C22×C10311yescharacteristic
183C22×C4⋊C4C22×C10312yes—
184C22×C4⋊C4C22×C10312yes—
185C22×C42C22×C10312yes—
186C22×C42C22×C10311yescharacteristic
187#389—24no—
188#384—24no—
189C2×#95C22×C10312yes—
190C2×#95C22×C10312yes—
191C2×#95C22×C10318yes—
192C2×#95C22×C10318yes—
193C2×#95C22×C10312yes—
194C23×C4C23×C10314yes—
195C23×C4C23×C10312yes—
196C23×C4C23×C10312yes—
197C23×C4C23×C10314yes—
198C23×C4C23×C10311yescharacteristic
199C23×C4C23×C10311yescharacteristic
200C23×C4C23×C10311yescharacteristic
201C2×C4⋊C4—22no—
202C2×C4⋊C4—22no—
203C2×C4⋊C4—24no—
204C2×C4⋊C4—24no—
205C2×C4⋊C4—24no—
206C2×C4⋊C4—22no—
207C2×C4⋊C4—24no—
208C2×C4⋊C4—24no—
209C2×C4⋊C4—28no—
210C2×C4⋊C4—28no—
211C2×C4⋊C4—44no—
212C2×C4⋊C4—44no—
213C2×C4⋊C4Q8×C10314yes—
214C2×C42—24no—
215C2×C42—24no—
216C2×C42—24no—
217C2×C42—24no—
218C2×C42D4×C10314yes—
219#95—24no—
220#95—24no—
221#95—48no—
222#95—48no—
223#95Q8×C10318yes—
224C24C24×C10311yescharacteristic
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—24no—
231C22×C4—24no—
232C22×C4—24no—
233C22×C4—24no—
234C22×C4—22no—
235C22×C4—24no—
236C22×C4—24no—
237C22×C4—24no—
238C22×C4—24no—
239C22×C4—22no—
240C22×C4—24no—
241C22×C4—24no—
242C22×C4—28no—
243C22×C4—24no—
244C22×C4—24no—
245C22×C4—28no—
246C22×C4—28no—
247C22×C4C2×D4×C10312yes—
248C22×C4C2×D4×C10312yes—
249C22×C4C2×D4×C10312yes—
250C22×C4C2×Q8×C10318yes—
251C22×C4C2×Q8×C10314yes—
252C22×C4C2×Q8×C10314yes—
253C22×C4C2×Q8×C10312yes—
254C22×C4#41×C10314yes—
255C22×C4#41×C10312yes—
256C22×C4#41×C10314yes—
257C22×C4#41×C10314yes—
258C4⋊C4—28no—
259C4⋊C4—48no—
260C4⋊C4—48no—
261C4⋊C4—44no—
262C4⋊C4—48no—
263C4⋊C4—48no—
264C42—28no—
265C42—48no—
266C23C22×D4×C10311yescharacteristic
267C23C22×Q8×C10311yescharacteristic
268C23C22×Q8×C10312yes—
269C23C2×#41×C10311yescharacteristic
270C23C2×#41×C10312yes—
271C23C2×#41×C10312yes—
272C23C2×#41×C10312yes—
273C23H(5,𝔽2)×C10312yes—
274C23H(5,𝔽2)×C10312yes—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—28no—
280C2×C4—28no—
281C2×C4—24no—
282C2×C4—28no—
283C2×C4—28no—
284C2×C4—28no—
285C2×C4—28no—
286C2×C4—42no—
287C2×C4—44no—
288C2×C4—42no—
289C2×C4—44no—
290C2×C4—44no—
291C2×C4—44no—
292C2×C4—44no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—44no—
296C2×C4—44no—
297C2×C4—44no—
298C2×C4—42no—
299C2×C4—416no—
300C2×C4—48no—
301C2×C4C22⋊Q8×C10314yes—
302C2×C4#123×C10314yes—
303C2×C4#124×C10314yes—
304C2×C4#124×C10314yes—
305C2×C4#125×C10318yes—
306C2×C4#126×C10318yes—
307C2×C4C4⋊Q8×C10314yes—
308C22C2×C22⋊Q8×C10311yescharacteristic
309C22C2×#123×C10311yescharacteristic
310C22C2×#124×C10311yescharacteristic
311C22C2×#124×C10311yescharacteristic
312C22C2×#125×C10312yes—
313C22C2×#126×C10312yes—
314C22C2×C4⋊Q8×C10311yescharacteristic
315C22#533×C10314yes—
316C22#535×C10311yescharacteristic
317C22#535×C10311yescharacteristic
318C22#540×C10314yes—
319C22#553×C10314yes—
320C22#554×C10312yes—
321C22#554×C10314yes—
322C22#554×C10312yes—
323C22#555×C10312yes—
324C22Q82×C10312yes—
325C4—24no—
326C4—24no—
327C4—48no—
328C4—44no—
329C4—82no—
330C4—84no—
331C4#400×C10318yes—
332C2C2×#400×C10311yescharacteristic
333C2C103×#249714yes—
334C2C103×#250211yescharacteristic
335C2C103×#250411yescharacteristic
336C2C103×#250714yes—
337C2C103×#256311yescharacteristic
338C2C103×#256711yescharacteristic
339C2C103×#264111yescharacteristic
340C2C103×#286211yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C103C24
commutator, Frattini, cosocleC24C24×C103
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C103 ◁ G

Complements

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

NH ≅ G/Ntype
161. #15197C103direct (N × H)
178. C103#15197direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#389×C1032
C2×#384×C1032
C103×#14422
C103×#14412
C103×C4⋊#952
C4×#95×C1032
#15197103