Finite Group Databasebeta

← C103×#29136 #39934411

Subgroups — C103×#29136 #39934411

Order 26368.

754 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#2647C211yesmaximal, characteristic, complemented
2C103×#2328C211yesmaximal, characteristic
3C103×#2101C212yesmaximal, complemented
4C103×#2041C212yesmaximal
5C103×#1936C212yesmaximal, complemented
6C103×#1934C212yesmaximal, complemented
7C103×#1804C212yesmaximal, complemented
8C103×#1802C212yesmaximal, complemented
9C103×#1768C211yesmaximal, characteristic, complemented
10C2×#127×C103C2211yescharacteristic
11C2×C4×D4×C103C2212yes—
12C2×C4⋊C8×C103C2212yes—
13C2×#102×C103C2212yes—
14C2×#102×C103C2212yes—
15C2×#102×C103C2212yes—
16C2×#102×C103C2212yes—
17C2×#97×C103C2211yescharacteristic
18C2×C4×C8×C103C2211yescharacteristic
19#400×C103—22no—
20#398×C103—22no—
21#390×C103C2212yes—
22#389×C103C2212yes—
23#389×C103C2212yes—
24#386×C103—22no—
25#386×C103—22no—
26#384×C103C2211yescharacteristic
27#382×C103C2211yescharacteristic
28#382×C103C2211yescharacteristic
29#376×C103C2211yescharacteristic
30#340×C103C2212yes—
31#340×C103C2212yes—
32#340×C103C2212yes—
33#340×C103C2212yes—
34#336×C103C2212yes—
35C22×D4×C103—22no—
36C22×D4×C103C2312yes—
37C23×C4×C103—22no—
38C22×C8×C103C2312yes—
39C22×C8×C103C2312yes—
40#127×C103—24no—
41C4×D4×C103—24no—
42C4×D4×C103—24no—
43C2×C4⋊C4×C103—22no—
44C2×C4⋊C4×C103—22no—
45C2×C4⋊C4×C103—22no—
46C2×C4⋊C4×C103C2312yes—
47C2×C4⋊C4×C103C2312yes—
48C2×C4⋊C4×C103C2312yes—
49C2×C22⋊C4×C103—22no—
50C2×C22⋊C4×C103—22no—
51C2×C22⋊C4×C103—22no—
52C2×C42×C103C2311yescharacteristic
53C2×C42×C103C2311yescharacteristic
54C2×C42×C103C2311yescharacteristic
55C4⋊C8×C103—24no—
56#102×C103—24no—
57#102×C103—24no—
58#102×C103—42no—
59#102×C103—42no—
60#97×C103—41no—
61C4×C8×C103—41no—
62#95×C103—22no—
63#95×C103—22no—
64#95×C103—22no—
65#95×C103—22no—
66#95×C103D412yes—
67#95×C103D412yes—
68C24×C103—22no—
69C2×D4×C103—28no—
70C2×D4×C103—22no—
71C2×D4×C103—22no—
72C2×D4×C103—22no—
73C2×D4×C103—22no—
74C2×D4×C103—22no—
75C2×D4×C103—82no—
76C2×D4×C103—82no—
77C2×D4×C103#4114yes—
78C22×C4×C103—22no—
79C22×C4×C103—22no—
80C22×C4×C103—22no—
81C22×C4×C103—44no—
82C22×C4×C103—82no—
83C22×C4×C103—82no—
84C22×C4×C103C2×D411yescharacteristic
85C22×C4×C103C2×D412yes—
86C22×C4×C103C2×D411yescharacteristic
87C22×C4×C103C2×D412yes—
88C22×C4×C103C2411yescharacteristic
89C2×C8×C103—22no—
90C2×C8×C103—22no—
91C2×C8×C103—22no—
92C2×C8×C103—22no—
93C2×C8×C103—22no—
94C2×C8×C103—22no—
95C4⋊C4×C103—22no—
96C4⋊C4×C103—22no—
97C4⋊C4×C103—22no—
98C4⋊C4×C103—22no—
99C4⋊C4×C103—22no—
100C4⋊C4×C103—22no—
101C4⋊C4×C103—82no—
102C4⋊C4×C103—82no—
103C4⋊C4×C103—82no—
104C22⋊C4×C103—44no—
105C22⋊C4×C103—82no—
106C22⋊C4×C103—82no—
107C42×C103—22no—
108C42×C103—21no—
109C42×C103—21no—
110C42×C103#4114yes—
111C23×C103—24no—
112C23×C103—42no—
113C23×C103—42no—
114C23×C103—42no—
115C23×C103—42no—
116C23×C103—42no—
117C23×C103—42no—
118C23×C103C22×D411yescharacteristic
119D4×C103—24no—
120D4×C103—24no—
121D4×C103—42no—
122D4×C103—42no—
123D4×C103—88no—
124C2×C4×C103—22no—
125C2×C4×C103—22no—
126C2×C4×C103—22no—
127C2×C4×C103—21no—
128C2×C4×C103—21no—
129C2×C4×C103—22no—
130C2×C4×C103—22no—
131C2×C4×C103—22no—
132C2×C4×C103—22no—
133C2×C4×C103—42no—
134C2×C4×C103—42no—
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—88no—
143C2×C4×C103#12414yes—
144C2×C4×C103C2×#4112yes—
145C2×C4×C103C2×#4112yes—
146C2×C4×C103H(5,𝔽2)11yescharacteristic
147C2×C4×C1032−1+411yescharacteristic
148C8×C103—42no—
149C8×C103—42no—
150C22×C103—44no—
151C22×C103—44no—
152C22×C103—44no—
153C22×C103—82no—
154C22×C103—82no—
155C22×C103—82no—
156C22×C103—82no—
157C22×C103#52511yescharacteristic
158C22×C103C2×#12411yescharacteristic
159C22×C103#53711yescharacteristic
160C22×C103#57612yes—
161C22×C103#57712yes—
162C4×C103—24no—
163C4×C103—42no—
164C4×C103—41no—
165C4×C103—41no—
166C4×C103—82no—
167C4×C103—82no—
168C4×C103—82no—
169C4×C103#55212yes—
170C4×C103#55312yes—
171#29136C10311yesmaximal, characteristic, direct product factor, Sylow
172C2×C103—84no—
173C2×C103#256211yescharacteristic
174C2×C103#311812yes—
175C2×C103#313612yes—
176C2×C103#325911yescharacteristic
177C2×C103#326011yescharacteristic
178#2647C2×C10311yescharacteristic, complemented
179#2328C2×C10311yescharacteristic
180#2101C2×C10312yescomplemented
181#2041C2×C10312yes—
182#1936C2×C10312yescomplemented
183#1934C2×C10312yescomplemented
184#1804C2×C10312yescomplemented
185#1802C2×C10312yescomplemented
186#1768C2×C10311yescharacteristic, complemented
187C103#2913611yescharacteristic, direct product factor, Sylow
188C2×#127C22×C10311yescharacteristic
189C2×C4×D4C22×C10312yes—
190C2×C4⋊C8C22×C10312yes—
191C2×#102C22×C10312yes—
192C2×#102C22×C10312yes—
193C2×#102C22×C10312yes—
194C2×#102C22×C10312yes—
195C2×#97C22×C10311yescharacteristic
196C2×C4×C8C22×C10311yescharacteristic
197#400—22no—
198#398—22no—
199#390C22×C10312yes—
200#389C22×C10312yes—
201#389C22×C10312yes—
202#386—22no—
203#386—22no—
204#384C22×C10311yescharacteristic
205#382C22×C10311yescharacteristic
206#382C22×C10311yescharacteristic
207#376C22×C10311yescharacteristic
208#340C22×C10312yes—
209#340C22×C10312yes—
210#340C22×C10312yes—
211#340C22×C10312yes—
212#336C22×C10312yes—
213C22×D4—22no—
214C22×D4C23×C10312yes—
215C23×C4—22no—
216C22×C8C23×C10312yes—
217C22×C8C23×C10312yes—
218#127—24no—
219C4×D4—24no—
220C4×D4—24no—
221C2×C4⋊C4—22no—
222C2×C4⋊C4—22no—
223C2×C4⋊C4—22no—
224C2×C4⋊C4C23×C10312yes—
225C2×C4⋊C4C23×C10312yes—
226C2×C4⋊C4C23×C10312yes—
227C2×C22⋊C4—22no—
228C2×C22⋊C4—22no—
229C2×C22⋊C4—22no—
230C2×C42C23×C10311yescharacteristic
231C2×C42C23×C10311yescharacteristic
232C2×C42C23×C10311yescharacteristic
233C4⋊C8—24no—
234#102—24no—
235#102—24no—
236#102—42no—
237#102—42no—
238#97—41no—
239C4×C8—41no—
240#95—22no—
241#95—22no—
242#95—22no—
243#95—22no—
244#95D4×C10312yes—
245#95D4×C10312yes—
246C24—22no—
247C2×D4—28no—
248C2×D4—22no—
249C2×D4—22no—
250C2×D4—22no—
251C2×D4—22no—
252C2×D4—22no—
253C2×D4—82no—
254C2×D4—82no—
255C2×D4#41×C10314yes—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—44no—
260C22×C4—82no—
261C22×C4—82no—
262C22×C4C2×D4×C10311yescharacteristic
263C22×C4C2×D4×C10312yes—
264C22×C4C2×D4×C10311yescharacteristic
265C22×C4C2×D4×C10312yes—
266C22×C4C24×C10311yescharacteristic
267C2×C8—22no—
268C2×C8—22no—
269C2×C8—22no—
270C2×C8—22no—
271C2×C8—22no—
272C2×C8—22no—
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—82no—
280C4⋊C4—82no—
281C4⋊C4—82no—
282C22⋊C4—44no—
283C22⋊C4—82no—
284C22⋊C4—82no—
285C42—22no—
286C42—21no—
287C42—21no—
288C42#41×C10314yes—
289C23—24no—
290C23—42no—
291C23—42no—
292C23—42no—
293C23—42no—
294C23—42no—
295C23—42no—
296C23C22×D4×C10311yescharacteristic
297D4—24no—
298D4—24no—
299D4—42no—
300D4—42no—
301D4—88no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—88no—
321C2×C4#124×C10314yes—
322C2×C4C2×#41×C10312yes—
323C2×C4C2×#41×C10312yes—
324C2×C4H(5,𝔽2)×C10311yescharacteristic
325C2×C42−1+4×C10311yescharacteristic
326C8—42no—
327C8—42no—
328C22—44no—
329C22—44no—
330C22—44no—
331C22—82no—
332C22—82no—
333C22—82no—
334C22—82no—
335C22#525×C10311yescharacteristic
336C22C2×#124×C10311yescharacteristic
337C22#537×C10311yescharacteristic
338C22#576×C10312yes—
339C22#577×C10312yes—
340C4—24no—
341C4—41no—
342C4—41no—
343C4—42no—
344C4—82no—
345C4—82no—
346C4—82no—
347C4#552×C10312yes—
348C4#553×C10312yes—
349C2—84no—
350C2C103×#256211yescharacteristic
351C2C103×#311812yes—
352C2C103×#313612yes—
353C2C103×#325911yescharacteristic
354C2C103×#326011yescharacteristic
subgroupG/H
center, socleC23×C103C22×D4
commutator, Frattini, cosocleC22×C4C24×C103
prime radicalC2×#127×C103C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C103 ◁ #376×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C103×#2647C2semidirect
3. C103×#2101C2semidirect
5. C103×#1936C2semidirect
6. C103×#1934C2semidirect
7. C103×#1804C2semidirect
8. C103×#1802C2semidirect
9. C103×#1768C2semidirect
171. #29136C103direct (N × H)
178. #2647C2×C103semidirect
180. #2101C2×C103semidirect
182. #1936C2×C103semidirect
183. #1934C2×C103semidirect
184. #1804C2×C103semidirect
185. #1802C2×C103semidirect
186. #1768C2×C103semidirect
187. C103#29136direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#26472
C103×#23282
C103×#21012
C103×#20412
C103×#19362
C103×#19342
C103×#18042
C103×#18022
C103×#17682
#29136103