Finite Group Databasebeta

← C103×#9606 #39914881

Subgroups — C103×#9606 #39914881

Order 26368.

368 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#1831C211yesmaximal, characteristic
2C103×#1767C211yesmaximal, characteristic
3C4×C4⋊C8×C103C211yesmaximal, characteristic
4C2×#335×C103C211yesmaximal, characteristic
5C2×#334×C103C211yesmaximal, characteristic
6C103×#1277C211yesmaximal, characteristic
7C103×#1277C211yesmaximal, characteristic
8C2×C4⋊C8×C103C411yescharacteristic
9C2×C4⋊C8×C103C411yescharacteristic
10C2×C4⋊C8×C103C2211yescharacteristic
11C2×C4⋊C8×C103C2211yescharacteristic
12C2×C4⋊C8×C103C2211yescharacteristic
13C2×C4⋊C8×C103C2211yescharacteristic
14C2×#97×C103—21no—
15C2×C4×C8×C103C2211yescharacteristic
16C2×C4×C8×C103C2211yescharacteristic
17C43×C103C2211yescharacteristic
18#336×C103—21no—
19#336×C103—21no—
20#336×C103—21no—
21#336×C103C411yescharacteristic
22#336×C103C411yescharacteristic
23#335×C103—22no—
24#334×C103—22no—
25C22×C8×C103—21no—
26C22×C8×C103—21no—
27C22×C8×C103—21no—
28C22×C8×C103—21no—
29C22×C8×C103C2×C411yescharacteristic
30C22×C8×C103C2×C411yescharacteristic
31C22×C8×C103C2×C411yescharacteristic
32C22×C8×C103C2×C411yescharacteristic
33C2×C42×C103C2×C411yescharacteristic
34C2×C42×C103C2×C411yescharacteristic
35C2×C42×C103D411yescharacteristic
36C2×C42×C103D411yescharacteristic
37C2×C42×C103Q811yescharacteristic
38C2×C42×C103Q811yescharacteristic
39C2×C42×C103C2311yescharacteristic
40C4⋊C8×C103—22no—
41C4⋊C8×C103—22no—
42C4⋊C8×C103—21no—
43C4⋊C8×C103—21no—
44C4⋊C8×C103—21no—
45C4⋊C8×C103—21no—
46C4⋊C8×C103—21no—
47C4⋊C8×C103—21no—
48C4⋊C8×C103D412yes—
49C4⋊C8×C103Q812yes—
50#97×C103—42no—
51C4×C8×C103—21no—
52C4×C8×C103—21no—
53C4×C8×C103—21no—
54C4×C8×C103—21no—
55C22×C4×C103C4⋊C411yescharacteristic
56C22×C4×C103C4⋊C411yescharacteristic
57C22×C4×C103C4⋊C411yescharacteristic
58C22×C4×C103C4⋊C411yescharacteristic
59C22×C4×C103C22×C411yescharacteristic
60C22×C4×C103C2×D411yescharacteristic
61C22×C4×C103C2×Q811yescharacteristic
62C2×C8×C103—21no—
63C2×C8×C103—21no—
64C2×C8×C103—21no—
65C2×C8×C103—21no—
66C2×C8×C103—21no—
67C2×C8×C103—21no—
68C2×C8×C103—22no—
69C2×C8×C103—22no—
70C2×C8×C103—21no—
71C2×C8×C103—21no—
72C2×C8×C103—21no—
73C2×C8×C103—21no—
74C2×C8×C103—41no—
75C2×C8×C103—41no—
76C2×C8×C103—41no—
77C2×C8×C103—41no—
78C2×C8×C103—41no—
79C2×C8×C103—41no—
80C2×C8×C103—41no—
81C2×C8×C103—41no—
82C2×C8×C103—41no—
83C2×C8×C103—41no—
84C2×C8×C103M1612yes—
85C2×C8×C103M1612yes—
86C42×C103—22no—
87C42×C103—21no—
88C42×C103—21no—
89C42×C103—21no—
90C42×C103—21no—
91C42×C103—21no—
92C42×C103—21no—
93C42×C103—21no—
94C42×C103—21no—
95C42×C103—41no—
96C42×C103C2×D411yescharacteristic
97C42×C103C2×Q811yescharacteristic
98C42×C103#4111yescharacteristic
99C42×C103#4111yescharacteristic
100C23×C103C2×C4⋊C411yescharacteristic
101C2×C4×C103—21no—
102C2×C4×C103—21no—
103C2×C4×C103—21no—
104C2×C4×C103—21no—
105C2×C4×C103—21no—
106C2×C4×C103—21no—
107C2×C4×C103—21no—
108C2×C4×C103—21no—
109C2×C4×C103—21no—
110C2×C4×C103—21no—
111C2×C4×C103—21no—
112C2×C4×C103—21no—
113C2×C4×C103—21no—
114C2×C4×C103#10812yes—
115C2×C4×C103C4×D411yescharacteristic
116C2×C4×C103C4×Q811yescharacteristic
117C2×C4×C103#12111yescharacteristic
118C2×C4×C103C22⋊Q811yescharacteristic
119C2×C4×C103#12511yescharacteristic
120C2×C4×C103C4⋊Q811yescharacteristic
121C2×C4×C103C2×M1611yescharacteristic
122C2×C4×C103C2×M1611yescharacteristic
123C2×C4×C103#13111yescharacteristic
124C2×C4×C103#13111yescharacteristic
125C2×C4×C103#13511yescharacteristic
126C2×C4×C103#13511yescharacteristic
127C2×C4×C103AGL(1,ℤ/8)11yescharacteristic
128C2×C4×C103#13711yescharacteristic
129C8×C103—22no—
130C8×C103—22no—
131C8×C103—41no—
132C8×C103—41no—
133C8×C103—42no—
134C8×C103—42no—
135C8×C103—81no—
136C8×C103—81no—
137C22×C103#38911yescharacteristic
138C22×C103#42311yescharacteristic
139C22×C103#42411yescharacteristic
140C22×C103#42711yescharacteristic
141C22×C103#42811yescharacteristic
142C22×C103C2×#10811yescharacteristic
143C22×C103#43011yescharacteristic
144C4×C103—22no—
145C4×C103—21no—
146C4×C103—21no—
147C4×C103—41no—
148C4×C103—41no—
149C4×C103—41no—
150C4×C103#43511yescharacteristic
151C4×C103#43511yescharacteristic
152C4×C103#44611yescharacteristic
153C4×C103#44611yescharacteristic
154C4×C103#46311yescharacteristic
155C4×C103#46411yescharacteristic
156C4×C103#47811yescharacteristic
157C4×C103#47911yescharacteristic
158#9606C10311yesmaximal, characteristic, direct product factor, Sylow
159C2×C103#156811yescharacteristic
160C2×C103#156911yescharacteristic
161C2×C103#157211yescharacteristic
162C2×C103#157411yescharacteristic
163C2×C103#194011yescharacteristic
164C2×C103#194911yescharacteristic
165C2×C103#195011yescharacteristic
166#1831C2×C10311yescharacteristic
167#1767C2×C10311yescharacteristic
168C4×C4⋊C8C2×C10311yescharacteristic
169C2×#335C2×C10311yescharacteristic
170C2×#334C2×C10311yescharacteristic
171#1277C2×C10311yescharacteristic
172#1277C2×C10311yescharacteristic
173C103#960611yescharacteristic, direct product factor, Sylow
174C2×C4⋊C8C4×C10311yescharacteristic
175C2×C4⋊C8C4×C10311yescharacteristic
176C2×C4⋊C8C22×C10311yescharacteristic
177C2×C4⋊C8C22×C10311yescharacteristic
178C2×C4⋊C8C22×C10311yescharacteristic
179C2×C4⋊C8C22×C10311yescharacteristic
180C2×#97—21no—
181C2×C4×C8C22×C10311yescharacteristic
182C2×C4×C8C22×C10311yescharacteristic
183C43C22×C10311yescharacteristic
184#336—21no—
185#336—21no—
186#336—21no—
187#336C4×C10311yescharacteristic
188#336C4×C10311yescharacteristic
189#335—22no—
190#334—22no—
191C22×C8—21no—
192C22×C8—21no—
193C22×C8—21no—
194C22×C8—21no—
195C22×C8C2×C4×C10311yescharacteristic
196C22×C8C2×C4×C10311yescharacteristic
197C22×C8C2×C4×C10311yescharacteristic
198C22×C8C2×C4×C10311yescharacteristic
199C2×C42C2×C4×C10311yescharacteristic
200C2×C42C2×C4×C10311yescharacteristic
201C2×C42D4×C10311yescharacteristic
202C2×C42D4×C10311yescharacteristic
203C2×C42Q8×C10311yescharacteristic
204C2×C42Q8×C10311yescharacteristic
205C2×C42C23×C10311yescharacteristic
206C4⋊C8—22no—
207C4⋊C8—22no—
208C4⋊C8—21no—
209C4⋊C8—21no—
210C4⋊C8—21no—
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8—21no—
214C4⋊C8D4×C10312yes—
215C4⋊C8Q8×C10312yes—
216#97—42no—
217C4×C8—21no—
218C4×C8—21no—
219C4×C8—21no—
220C4×C8—21no—
221C22×C4C4⋊C4×C10311yescharacteristic
222C22×C4C4⋊C4×C10311yescharacteristic
223C22×C4C4⋊C4×C10311yescharacteristic
224C22×C4C4⋊C4×C10311yescharacteristic
225C22×C4C22×C4×C10311yescharacteristic
226C22×C4C2×D4×C10311yescharacteristic
227C22×C4C2×Q8×C10311yescharacteristic
228C2×C8—21no—
229C2×C8—21no—
230C2×C8—21no—
231C2×C8—21no—
232C2×C8—21no—
233C2×C8—21no—
234C2×C8—22no—
235C2×C8—22no—
236C2×C8—21no—
237C2×C8—21no—
238C2×C8—21no—
239C2×C8—21no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—41no—
249C2×C8—41no—
250C2×C8M16×C10312yes—
251C2×C8M16×C10312yes—
252C42—22no—
253C42—21no—
254C42—21no—
255C42—21no—
256C42—21no—
257C42—21no—
258C42—21no—
259C42—21no—
260C42—21no—
261C42—41no—
262C42C2×D4×C10311yescharacteristic
263C42C2×Q8×C10311yescharacteristic
264C42#41×C10311yescharacteristic
265C42#41×C10311yescharacteristic
266C23C2×C4⋊C4×C10311yescharacteristic
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4#108×C10312yes—
281C2×C4C4×D4×C10311yescharacteristic
282C2×C4C4×Q8×C10311yescharacteristic
283C2×C4#121×C10311yescharacteristic
284C2×C4C22⋊Q8×C10311yescharacteristic
285C2×C4#125×C10311yescharacteristic
286C2×C4C4⋊Q8×C10311yescharacteristic
287C2×C4C2×M16×C10311yescharacteristic
288C2×C4C2×M16×C10311yescharacteristic
289C2×C4#131×C10311yescharacteristic
290C2×C4#131×C10311yescharacteristic
291C2×C4#135×C10311yescharacteristic
292C2×C4#135×C10311yescharacteristic
293C2×C4AGL(1,ℤ/8)×C10311yescharacteristic
294C2×C4#137×C10311yescharacteristic
295C8—22no—
296C8—22no—
297C8—41no—
298C8—41no—
299C8—42no—
300C8—42no—
301C8—81no—
302C8—81no—
303C22#389×C10311yescharacteristic
304C22#423×C10311yescharacteristic
305C22#424×C10311yescharacteristic
306C22#427×C10311yescharacteristic
307C22#428×C10311yescharacteristic
308C22C2×#108×C10311yescharacteristic
309C22#430×C10311yescharacteristic
310C4—21no—
311C4—21no—
312C4—22no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4#435×C10311yescharacteristic
317C4#435×C10311yescharacteristic
318C4#446×C10311yescharacteristic
319C4#446×C10311yescharacteristic
320C4#463×C10311yescharacteristic
321C4#464×C10311yescharacteristic
322C4#478×C10311yescharacteristic
323C4#479×C10311yescharacteristic
324C2C103×#156811yescharacteristic
325C2C103×#156911yescharacteristic
326C2C103×#157211yescharacteristic
327C2C103×#157411yescharacteristic
328C2C103×#194011yescharacteristic
329C2C103×#194911yescharacteristic
330C2C103×#195011yescharacteristic
subgroupG/H
centerC22×C4×C103C2×D4
commutatorC22×C4C22×C4×C103
Frattini, cosocleC2×C42C23×C103
socle, prime radicalC23×C103C2×C4⋊C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C103 ◁ C43×C103 ◁ G

Complements

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

NH ≅ G/Ntype
158. #9606C103direct (N × H)
173. C103#9606direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#18312
C103×#17672
C4×C4⋊C8×C1032
C2×#335×C1032
C2×#334×C1032
C103×#12772
#9606103