Finite Group Databasebeta

← C103×#29306 #39934581

Subgroups — C103×#29306 #39934581

Order 26368.

702 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#2629C211yesmaximal, characteristic
2C103×#2316C211yesmaximal, characteristic
3C103×#2083C212yesmaximal, complemented
4C103×#2059C212yesmaximal, complemented
5C103×#1943C212yesmaximal, complemented
6C103×#1942C212yesmaximal, complemented
7C103×#1854C212yesmaximal
8C103×#1852C212yesmaximal
9C103×#1750C211yesmaximal, characteristic
10C2×#125×C103C2211yescharacteristic
11C2×#117×C103C2211yescharacteristic
12C2×#117×C103C2211yescharacteristic
13C22×C4⋊C4×C103C2211yescharacteristic
14C2×#107×C103C2212yes—
15C2×#107×C103C2212yes—
16C2×#107×C103C2212yes—
17C2×#106×C103C2212yes—
18C2×C22⋊C8×C103C2212yes—
19C2×#97×C103C2211yescharacteristic
20C2×C4×C8×C103C2211yescharacteristic
21#398×C103—22no—
22#396×C103—22no—
23#389×C103—22no—
24#389×C103C2212yes—
25#389×C103C2212yes—
26#389×C103C2212yes—
27#384×C103C2211yescharacteristic
28#380×C103—22no—
29#380×C103C2212yes—
30#340×C103C2212yes—
31#340×C103C2212yes—
32#340×C103C2212yes—
33#340×C103C2212yes—
34#336×C103C2212yes—
35C23×C4×C103—21no—
36C23×C4×C103C2311yescharacteristic
37C22×C8×C103C2312yes—
38C22×C8×C103C2312yes—
39#125×C103—41no—
40#125×C103—41no—
41#117×C103—41no—
42#117×C103—41no—
43#117×C103—41no—
44#117×C103—41no—
45C2×C4⋊C4×C103—21no—
46C2×C4⋊C4×C103—24no—
47C2×C4⋊C4×C103—22no—
48C2×C4⋊C4×C103—22no—
49C2×C4⋊C4×C103—22no—
50C2×C4⋊C4×C103—22no—
51C2×C4⋊C4×C103—22no—
52C2×C4⋊C4×C103D412yes—
53C2×C4⋊C4×C103C2312yes—
54C2×C4⋊C4×C103C2312yes—
55C2×C4⋊C4×C103C2312yes—
56C2×C4⋊C4×C103C2312yes—
57C2×C22⋊C4×C103—21no—
58C2×C22⋊C4×C103—22no—
59C2×C22⋊C4×C103D412yes—
60C2×C42×C103—21no—
61C2×C42×C103C2311yescharacteristic
62C2×C42×C103C2311yescharacteristic
63#107×C103—24no—
64#107×C103—24no—
65#107×C103—42no—
66#106×C103—42no—
67C22⋊C8×C103Q818yes—
68#97×C103—41no—
69C4×C8×C103—41no—
70#95×C103—22no—
71#95×C103—22no—
72#95×C103—22no—
73#95×C103—22no—
74C24×C103C2×D411yescharacteristic
75C22×C4×C103—22no—
76C22×C4×C103—21no—
77C22×C4×C103—21no—
78C22×C4×C103—22no—
79C22×C4×C103—24no—
80C22×C4×C103—22no—
81C22×C4×C103—22no—
82C22×C4×C103—22no—
83C22×C4×C103—82no—
84C22×C4×C103C2×D412yes—
85C22×C4×C103C2×D412yes—
86C22×C4×C103C2×D411yescharacteristic
87C22×C4×C103C2×Q814yes—
88C22×C4×C103C2411yescharacteristic
89C2×C8×C103—22no—
90C2×C8×C103—22no—
91C2×C8×C103—22no—
92C2×C8×C103—22no—
93C2×C8×C103C2×Q814yes—
94C2×C8×C103C2×Q814yes—
95C4⋊C4×C103—24no—
96C4⋊C4×C103—22no—
97C4⋊C4×C103—22no—
98C4⋊C4×C103—22no—
99C4⋊C4×C103—22no—
100C4⋊C4×C103—22no—
101C4⋊C4×C103—22no—
102C4⋊C4×C103—22no—
103C4⋊C4×C103—42no—
104C4⋊C4×C103—44no—
105C4⋊C4×C103—82no—
106C4⋊C4×C103—82no—
107C4⋊C4×C103—82no—
108C4⋊C4×C103—82no—
109C4⋊C4×C103#4114yes—
110C22⋊C4×C103—42no—
111C22⋊C4×C103—42no—
112C22⋊C4×C103—82no—
113C42×C103—21no—
114C42×C103—21no—
115C42×C103—21no—
116C42×C103—21no—
117C42×C103—42no—
118C23×C103—21no—
119C23×C103—21no—
120C23×C103—22no—
121C23×C103—22no—
122C23×C103C4⋊Q812yes—
123C23×C103C22×D411yescharacteristic
124C2×C4×C103—21no—
125C2×C4×C103—21no—
126C2×C4×C103—24no—
127C2×C4×C103—24no—
128C2×C4×C103—24no—
129C2×C4×C103—22no—
130C2×C4×C103—22no—
131C2×C4×C103—22no—
132C2×C4×C103—22no—
133C2×C4×C103—22no—
134C2×C4×C103—22no—
135C2×C4×C103—42no—
136C2×C4×C103—42no—
137C2×C4×C103—42no—
138C2×C4×C103—42no—
139C2×C4×C103—42no—
140C2×C4×C103—42no—
141C2×C4×C103—42no—
142C2×C4×C103—42no—
143C2×C4×C103—42no—
144C2×C4×C103—42no—
145C2×C4×C103—42no—
146C2×C4×C103—84no—
147C2×C4×C103C4⋊Q812yes—
148C2×C4×C103C22×Q812yes—
149C2×C4×C103C2×#4112yes—
150C2×C4×C103H(5,𝔽2)11yescharacteristic
151C2×C4×C103H(5,𝔽2)11yescharacteristic
152C8×C103—24no—
153C8×C103—24no—
154C22×C103—22no—
155C22×C103—24no—
156C22×C103—41no—
157C22×C103—41no—
158C22×C103—42no—
159C22×C103#52511yescharacteristic
160C22×C103C2×C4⋊Q811yescharacteristic
161C22×C103#53411yescharacteristic
162C22×C103#57612yes—
163C22×C103#57812yes—
164C4×C103—22no—
165C4×C103—44no—
166C4×C103—42no—
167C4×C103—42no—
168C4×C103—82no—
169C4×C103—82no—
170C4×C103—82no—
171C4×C103#55412yes—
172C4×C103#55412yes—
173#29306C10311yesmaximal, characteristic, direct product factor, Sylow
174C2×C103—42no—
175C2×C103#258311yescharacteristic
176C2×C103#312211yescharacteristic
177C2×C103#312711yescharacteristic
178C2×C103#316412yes—
179C2×C103#320312yes—
180#2629C2×C10311yescharacteristic
181#2316C2×C10311yescharacteristic
182#2083C2×C10312yescomplemented
183#2059C2×C10312yescomplemented
184#1943C2×C10312yescomplemented
185#1942C2×C10312yescomplemented
186#1854C2×C10312yes—
187#1852C2×C10312yes—
188#1750C2×C10311yescharacteristic
189C103#2930611yescharacteristic, direct product factor, Sylow
190C2×#125C22×C10311yescharacteristic
191C2×#117C22×C10311yescharacteristic
192C2×#117C22×C10311yescharacteristic
193C22×C4⋊C4C22×C10311yescharacteristic
194C2×#107C22×C10312yes—
195C2×#107C22×C10312yes—
196C2×#107C22×C10312yes—
197C2×#106C22×C10312yes—
198C2×C22⋊C8C22×C10312yes—
199C2×#97C22×C10311yescharacteristic
200C2×C4×C8C22×C10311yescharacteristic
201#398—22no—
202#396—22no—
203#389—22no—
204#389C22×C10312yes—
205#389C22×C10312yes—
206#389C22×C10312yes—
207#384C22×C10311yescharacteristic
208#380—22no—
209#380C22×C10312yes—
210#340C22×C10312yes—
211#340C22×C10312yes—
212#340C22×C10312yes—
213#340C22×C10312yes—
214#336C22×C10312yes—
215C23×C4—21no—
216C23×C4C23×C10311yescharacteristic
217C22×C8C23×C10312yes—
218C22×C8C23×C10312yes—
219#125—41no—
220#125—41no—
221#117—41no—
222#117—41no—
223#117—41no—
224#117—41no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—24no—
227C2×C4⋊C4—22no—
228C2×C4⋊C4—22no—
229C2×C4⋊C4—22no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—22no—
232C2×C4⋊C4D4×C10312yes—
233C2×C4⋊C4C23×C10312yes—
234C2×C4⋊C4C23×C10312yes—
235C2×C4⋊C4C23×C10312yes—
236C2×C4⋊C4C23×C10312yes—
237C2×C22⋊C4—21no—
238C2×C22⋊C4—22no—
239C2×C22⋊C4D4×C10312yes—
240C2×C42—21no—
241C2×C42C23×C10311yescharacteristic
242C2×C42C23×C10311yescharacteristic
243#107—24no—
244#107—24no—
245#107—42no—
246#106—42no—
247C22⋊C8Q8×C10318yes—
248#97—41no—
249C4×C8—41no—
250#95—22no—
251#95—22no—
252#95—22no—
253#95—22no—
254C24C2×D4×C10311yescharacteristic
255C22×C4—22no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—22no—
259C22×C4—24no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—82no—
264C22×C4C2×D4×C10312yes—
265C22×C4C2×D4×C10312yes—
266C22×C4C2×D4×C10311yescharacteristic
267C22×C4C2×Q8×C10314yes—
268C22×C4C24×C10311yescharacteristic
269C2×C8—22no—
270C2×C8—22no—
271C2×C8—22no—
272C2×C8—22no—
273C2×C8C2×Q8×C10314yes—
274C2×C8C2×Q8×C10314yes—
275C4⋊C4—24no—
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—22no—
280C4⋊C4—22no—
281C4⋊C4—22no—
282C4⋊C4—22no—
283C4⋊C4—42no—
284C4⋊C4—44no—
285C4⋊C4—82no—
286C4⋊C4—82no—
287C4⋊C4—82no—
288C4⋊C4—82no—
289C4⋊C4#41×C10314yes—
290C22⋊C4—42no—
291C22⋊C4—42no—
292C22⋊C4—82no—
293C42—21no—
294C42—21no—
295C42—21no—
296C42—21no—
297C42—42no—
298C23—21no—
299C23—21no—
300C23—22no—
301C23—22no—
302C23C4⋊Q8×C10312yes—
303C23C22×D4×C10311yescharacteristic
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—24no—
307C2×C4—24no—
308C2×C4—24no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—84no—
327C2×C4C4⋊Q8×C10312yes—
328C2×C4C22×Q8×C10312yes—
329C2×C4C2×#41×C10312yes—
330C2×C4H(5,𝔽2)×C10311yescharacteristic
331C2×C4H(5,𝔽2)×C10311yescharacteristic
332C8—24no—
333C8—24no—
334C22—22no—
335C22—24no—
336C22—41no—
337C22—41no—
338C22—42no—
339C22#525×C10311yescharacteristic
340C22C2×C4⋊Q8×C10311yescharacteristic
341C22#534×C10311yescharacteristic
342C22#576×C10312yes—
343C22#578×C10312yes—
344C4—22no—
345C4—44no—
346C4—42no—
347C4—42no—
348C4—82no—
349C4—82no—
350C4—82no—
351C4#554×C10312yes—
352C4#554×C10312yes—
353C2—42no—
354C2C103×#258311yescharacteristic
355C2C103×#312211yescharacteristic
356C2C103×#312711yescharacteristic
357C2C103×#316412yes—
358C2C103×#320312yes—
subgroupG/H
center, socleC23×C103C22×D4
commutator, Frattini, cosocleC22×C4C24×C103
prime radicalC24×C103C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C103 ◁ C2×#117×C103 ◁ G

Complements

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

NH ≅ G/Ntype
3. C103×#2083C2semidirect
4. C103×#2059C2semidirect
5. C103×#1943C2semidirect
6. C103×#1942C2semidirect
173. #29306C103direct (N × H)
182. #2083C2×C103semidirect
183. #2059C2×C103semidirect
184. #1943C2×C103semidirect
185. #1942C2×C103semidirect
189. C103#29306direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#26292
C103×#23162
C103×#20832
C103×#20592
C103×#19432
C103×#19422
C103×#18542
C103×#18522
C103×#17502
#29306103