Finite Group Databasebeta

← C103×#29132 #39934407

Subgroups — C103×#29132 #39934407

Order 26368.

710 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#2859C211yesmaximal, characteristic
2C4×C4⋊Q8×C103C211yesmaximal, characteristic
3C103×#2099C212yesmaximal
4C103×#2043C212yesmaximal
5C103×#1935C214yesmaximal
6C103×#1803C212yesmaximal
7C103×#1803C212yesmaximal
8C103×#1767C211yesmaximal, characteristic
9C2×C4⋊Q8×C103C2211yescharacteristic
10C2×#125×C103—21no—
11C2×C4×Q8×C103C2212yes—
12C2×C4⋊C8×C103C2212yes—
13C2×#103×C103C2214yes—
14C2×#103×C103C2214yes—
15C2×#97×C103C2212yes—
16#391×C103C2212yes—
17#389×C103—21no—
18#389×C103—21no—
19#389×C103—21no—
20#389×C103—21no—
21#389×C103C2212yes—
22#389×C103C2212yes—
23#384×C103C2211yescharacteristic
24#384×C103C2211yescharacteristic
25#384×C103C2211yescharacteristic
26#382×C103—21no—
27C4×C4⋊C4×C103—21no—
28C4×C4⋊C4×C103—21no—
29C43×C103C2211yescharacteristic
30#340×C103C2214yes—
31#340×C103C2214yes—
32#336×C103C2212yes—
33C22×Q8×C103C2312yes—
34C22×C8×C103C2314yes—
35C4⋊Q8×C103—24no—
36#125×C103—44no—
37C4×Q8×C103—24no—
38C4×Q8×C103—24no—
39C2×C4⋊C4×C103—21no—
40C2×C4⋊C4×C103—21no—
41C2×C4⋊C4×C103—21no—
42C2×C4⋊C4×C103—21no—
43C2×C4⋊C4×C103—21no—
44C2×C4⋊C4×C103—21no—
45C2×C4⋊C4×C103—21no—
46C2×C4⋊C4×C103—21no—
47C2×C4⋊C4×C103—22no—
48C2×C4⋊C4×C103—22no—
49C2×C4⋊C4×C103—22no—
50C2×C4⋊C4×C103C2312yes—
51C2×C4⋊C4×C103C2312yes—
52C2×C4⋊C4×C103C2312yes—
53C2×C42×C103—22no—
54C2×C42×C103D411yescharacteristic
55C2×C42×C103D411yescharacteristic
56C2×C42×C103D411yescharacteristic
57C2×C42×C103D411yescharacteristic
58C2×C42×C103C2311yescharacteristic
59C2×C42×C103C2311yescharacteristic
60C2×C42×C103C2311yescharacteristic
61C4⋊C8×C103—24no—
62#103×C103—28no—
63#103×C103—44no—
64#97×C103—42no—
65#95×C103—22no—
66#95×C103—22no—
67#95×C103—22no—
68#95×C103—22no—
69C2×Q8×C103—22no—
70C2×Q8×C103—22no—
71C2×Q8×C103—22no—
72C2×Q8×C103—22no—
73C2×Q8×C103—22no—
74C2×Q8×C103#4114yes—
75C22×C4×C103—22no—
76C22×C4×C103—22no—
77C22×C4×C103—22no—
78C22×C4×C103—22no—
79C22×C4×C103C2×D411yescharacteristic
80C22×C4×C103C2×D411yescharacteristic
81C22×C4×C103C2×D411yescharacteristic
82C22×C4×C103C2×D411yescharacteristic
83C22×C4×C103C2×D411yescharacteristic
84C22×C4×C103C2×D411yescharacteristic
85C22×C4×C103C2411yescharacteristic
86C2×C8×C103—24no—
87C2×C8×C103—24no—
88C2×C8×C103—24no—
89C4⋊C4×C103—24no—
90C4⋊C4×C103—24no—
91C4⋊C4×C103—24no—
92C4⋊C4×C103—22no—
93C4⋊C4×C103—22no—
94C4⋊C4×C103—22no—
95C4⋊C4×C103—22no—
96C4⋊C4×C103—42no—
97C4⋊C4×C103—42no—
98C4⋊C4×C103—44no—
99C4⋊C4×C103—44no—
100C4⋊C4×C103—42no—
101C4⋊C4×C103—44no—
102C4⋊C4×C103—42no—
103C4⋊C4×C103—42no—
104C4⋊C4×C103—42no—
105C42×C103—22no—
106C42×C103—22no—
107C42×C103—22no—
108C42×C103—22no—
109C42×C103—22no—
110C42×C103—21no—
111C42×C103—21no—
112C42×C103—44no—
113C42×C103#4114yes—
114C23×C103C22×D411yescharacteristic
115Q8×C103—24no—
116Q8×C103—24no—
117Q8×C103—42no—
118Q8×C103—42no—
119C2×C4×C103—21no—
120C2×C4×C103—21no—
121C2×C4×C103—21no—
122C2×C4×C103—21no—
123C2×C4×C103—21no—
124C2×C4×C103—21no—
125C2×C4×C103—24no—
126C2×C4×C103—21no—
127C2×C4×C103—21no—
128C2×C4×C103—21no—
129C2×C4×C103—21no—
130C2×C4×C103—21no—
131C2×C4×C103—21no—
132C2×C4×C103—42no—
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—42no—
143C2×C4×C103#12412yes—
144C2×C4×C103#12412yes—
145C2×C4×C103AGL(1,ℤ/8)12yes—
146C2×C4×C103#13712yes—
147C2×C4×C103#13712yes—
148C2×C4×C103#13712yes—
149C2×C4×C103C2×#4112yes—
150C2×C4×C103C2×#4112yes—
151C2×C4×C103H(5,𝔽2)11yescharacteristic
152C2×C4×C1032−1+411yescharacteristic
153C8×C103—44no—
154C22×C103#52511yescharacteristic
155C22×C103C2×#12411yescharacteristic
156C22×C103#53711yescharacteristic
157C22×C103C2×AGL(1,ℤ/8)11yescharacteristic
158C22×C103C2×#13711yescharacteristic
159C22×C103C2×#13711yescharacteristic
160C22×C103C2×#13711yescharacteristic
161C4×C103—22no—
162C4×C103—22no—
163C4×C103—22no—
164C4×C103—44no—
165C4×C103—41no—
166C4×C103—41no—
167C4×C103—82no—
168C4×C103—82no—
169C4×C103—82no—
170C4×C103#49114yes—
171C4×C103#55212yes—
172C4×C103#55312yes—
173#29132C10311yesmaximal, characteristic, direct product factor, Sylow
174C2×C103#256211yescharacteristic
175C2×C103#311211yescharacteristic
176C2×C103#311311yescharacteristic
177C2×C103C2×#49111yescharacteristic
178C2×C103#314111yescharacteristic
179C2×C103#325411yescharacteristic
180C2×C103#325511yescharacteristic
181#2859C2×C10311yescharacteristic
182C4×C4⋊Q8C2×C10311yescharacteristic
183#2099C2×C10312yes—
184#2043C2×C10312yes—
185#1935C2×C10314yes—
186#1803C2×C10312yes—
187#1803C2×C10312yes—
188#1767C2×C10311yescharacteristic
189C103#2913211yescharacteristic, direct product factor, Sylow
190C2×C4⋊Q8C22×C10311yescharacteristic
191C2×#125—21no—
192C2×C4×Q8C22×C10312yes—
193C2×C4⋊C8C22×C10312yes—
194C2×#103C22×C10314yes—
195C2×#103C22×C10314yes—
196C2×#97C22×C10312yes—
197#391C22×C10312yes—
198#389—21no—
199#389—21no—
200#389—21no—
201#389—21no—
202#389C22×C10312yes—
203#389C22×C10312yes—
204#384C22×C10311yescharacteristic
205#384C22×C10311yescharacteristic
206#384C22×C10311yescharacteristic
207#382—21no—
208C4×C4⋊C4—21no—
209C4×C4⋊C4—21no—
210C43C22×C10311yescharacteristic
211#340C22×C10314yes—
212#340C22×C10314yes—
213#336C22×C10312yes—
214C22×Q8C23×C10312yes—
215C22×C8C23×C10314yes—
216C4⋊Q8—24no—
217#125—44no—
218C4×Q8—24no—
219C4×Q8—24no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—22no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—22no—
226C2×C4⋊C4—22no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4C23×C10312yes—
232C2×C4⋊C4C23×C10312yes—
233C2×C4⋊C4C23×C10312yes—
234C2×C42—22no—
235C2×C42D4×C10311yescharacteristic
236C2×C42D4×C10311yescharacteristic
237C2×C42D4×C10311yescharacteristic
238C2×C42D4×C10311yescharacteristic
239C2×C42C23×C10311yescharacteristic
240C2×C42C23×C10311yescharacteristic
241C2×C42C23×C10311yescharacteristic
242C4⋊C8—24no—
243#103—28no—
244#103—44no—
245#97—42no—
246#95—22no—
247#95—22no—
248#95—22no—
249#95—22no—
250C2×Q8—22no—
251C2×Q8—22no—
252C2×Q8—22no—
253C2×Q8—22no—
254C2×Q8—22no—
255C2×Q8#41×C10314yes—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4C2×D4×C10311yescharacteristic
261C22×C4C2×D4×C10311yescharacteristic
262C22×C4C2×D4×C10311yescharacteristic
263C22×C4C2×D4×C10311yescharacteristic
264C22×C4C2×D4×C10311yescharacteristic
265C22×C4C2×D4×C10311yescharacteristic
266C22×C4C24×C10311yescharacteristic
267C2×C8—24no—
268C2×C8—24no—
269C2×C8—24no—
270C4⋊C4—24no—
271C4⋊C4—24no—
272C4⋊C4—24no—
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—42no—
278C4⋊C4—42no—
279C4⋊C4—44no—
280C4⋊C4—44no—
281C4⋊C4—42no—
282C4⋊C4—44no—
283C4⋊C4—42no—
284C4⋊C4—42no—
285C4⋊C4—42no—
286C42—22no—
287C42—22no—
288C42—22no—
289C42—22no—
290C42—22no—
291C42—21no—
292C42—21no—
293C42—44no—
294C42#41×C10314yes—
295C23C22×D4×C10311yescharacteristic
296Q8—24no—
297Q8—24no—
298Q8—42no—
299Q8—42no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—24no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—42no—
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#124×C10312yes—
325C2×C4#124×C10312yes—
326C2×C4AGL(1,ℤ/8)×C10312yes—
327C2×C4#137×C10312yes—
328C2×C4#137×C10312yes—
329C2×C4#137×C10312yes—
330C2×C4C2×#41×C10312yes—
331C2×C4C2×#41×C10312yes—
332C2×C4H(5,𝔽2)×C10311yescharacteristic
333C2×C42−1+4×C10311yescharacteristic
334C8—44no—
335C22#525×C10311yescharacteristic
336C22C2×#124×C10311yescharacteristic
337C22#537×C10311yescharacteristic
338C22C2×AGL(1,ℤ/8)×C10311yescharacteristic
339C22C2×#137×C10311yescharacteristic
340C22C2×#137×C10311yescharacteristic
341C22C2×#137×C10311yescharacteristic
342C4—22no—
343C4—22no—
344C4—22no—
345C4—41no—
346C4—41no—
347C4—44no—
348C4—82no—
349C4—82no—
350C4—82no—
351C4#491×C10314yes—
352C4#552×C10312yes—
353C4#553×C10312yes—
354C2C103×#256211yescharacteristic
355C2C103×#311211yescharacteristic
356C2C103×#311311yescharacteristic
357C2C2×#491×C10311yescharacteristic
358C2C103×#314111yescharacteristic
359C2C103×#325411yescharacteristic
360C2C103×#325511yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C103C22×D4
commutator, Frattini, cosocleC22×C4C24×C103
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C103 ◁ C43×C103 ◁ G

Complements

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

NH ≅ G/Ntype
173. #29132C103direct (N × H)
189. C103#29132direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#28592
C4×C4⋊Q8×C1032
C103×#20992
C103×#20432
C103×#19352
C103×#18032
C103×#17672
#29132103