Finite Group Databasebeta

← C103×#9034 #39914309

Subgroups — C103×#9034 #39914309

Order 26368.

482 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#2921C211yesmaximal, characteristic
2C103×#2396C211yesmaximal, characteristic
3C103×#1487C212yesmaximal, complemented
4C103×#1458C211yesmaximal, characteristic
5C103×#1303C212yesmaximal, complemented
6C2×C4×Q8×C103C2211yescharacteristic
7C2×#117×C103C2211yescharacteristic
8#433×C103—24no—
9#431×C103C2212yes—
10#423×C103C2212yes—
11#407×C103—21no—
12C4×M16×C103—21no—
13#400×C103C411yescharacteristic
14#399×C103C411yescharacteristic
15#398×C103—21no—
16#396×C103—21no—
17#395×C103C411yescharacteristic
18#393×C103C411yescharacteristic
19C4×C4⋊C4×C103—21no—
20C4×C4⋊C4×C103C2211yescharacteristic
21C4×C22⋊C4×C103—21no—
22Q8⋊C8×C103—24no—
23#324×C103—21no—
24#323×C103—21no—
25C22×Q8×C103C2×C411yescharacteristic
26C23×C4×C103D411yescharacteristic
27C2×M16×C103—22no—
28C4×Q8×C103—22no—
29C4×Q8×C103—22no—
30#117×C103—22no—
31#117×C103—22no—
32C2×C4⋊C4×C103—21no—
33C2×C4⋊C4×C103—21no—
34C2×C4⋊C4×C103—21no—
35C2×C4⋊C4×C103—21no—
36C2×C4⋊C4×C103C2×C411yescharacteristic
37C2×C4⋊C4×C103C2×C411yescharacteristic
38C2×C4⋊C4×C103D411yescharacteristic
39C2×C22⋊C4×C103—21no—
40C2×C22⋊C4×C103—21no—
41C2×C22⋊C4×C103C2×C411yescharacteristic
42C2×C22⋊C4×C103D411yescharacteristic
43C2×C42×C103—21no—
44C2×C42×C103—21no—
45C2×C42×C103D411yescharacteristic
46C2×C42×C103C2311yescharacteristic
47C4⋊C8×C103—22no—
48C4⋊C8×C103—22no—
49C4⋊C8×C103D414yes—
50C22⋊C8×C103—24no—
51C22⋊C8×C103—22no—
52#97×C103—22no—
53C4×C8×C103—22no—
54C4×C8×C103—22no—
55#95×C103—21no—
56#95×C103—21no—
57#95×C103—21no—
58#95×C103—21no—
59#95×C103C2×C411yescharacteristic
60#95×C103C2×C411yescharacteristic
61C24×C103C22⋊C411yescharacteristic
62C2×Q8×C103—22no—
63C2×Q8×C103—42no—
64C22×C4×C103—21no—
65C22×C4×C103—21no—
66C22×C4×C103—21no—
67C22×C4×C103—21no—
68C22×C4×C103—22no—
69C22×C4×C103—22no—
70C22×C4×C103—21no—
71C22×C4×C103—21no—
72C22×C4×C103C22⋊C411yescharacteristic
73C22×C4×C103C22⋊C411yescharacteristic
74C22×C4×C103C22⋊C411yescharacteristic
75C22×C4×C103C22×C411yescharacteristic
76C22×C4×C103C2×D411yescharacteristic
77C22×C4×C103C2×D411yescharacteristic
78M16×C103—42no—
79M16×C103—42no—
80C2×C8×C103—24no—
81C2×C8×C103—42no—
82C4⋊C4×C103—22no—
83C4⋊C4×C103—22no—
84C4⋊C4×C103—22no—
85C4⋊C4×C103—42no—
86C4⋊C4×C103—42no—
87C4⋊C4×C103—42no—
88C4⋊C4×C103—42no—
89C22⋊C4×C103—22no—
90C22⋊C4×C103—22no—
91C22⋊C4×C103—42no—
92C22⋊C4×C103—42no—
93C42×C103—21no—
94C42×C103—21no—
95C42×C103—41no—
96C42×C103—41no—
97C42×C103—42no—
98C42×C103C2×D412yes—
99C42×C103#4112yes—
100C23×C103—21no—
101C23×C103—21no—
102C23×C103—21no—
103C23×C103—41no—
104C23×C103—41no—
105C23×C103C2×C22⋊C411yescharacteristic
106Q8×C103—24no—
107Q8×C103—42no—
108C2×C4×C103—22no—
109C2×C4×C103—22no—
110C2×C4×C103—21no—
111C2×C4×C103—21no—
112C2×C4×C103—21no—
113C2×C4×C103—21no—
114C2×C4×C103—21no—
115C2×C4×C103—41no—
116C2×C4×C103—41no—
117C2×C4×C103—41no—
118C2×C4×C103—41no—
119C2×C4×C103—41no—
120C2×C4×C103—41no—
121C2×C4×C103—42no—
122C2×C4×C103—42no—
123C2×C4×C103—41no—
124C2×C4×C103—41no—
125C2×C4×C103—41no—
126C2×C4×C103—41no—
127C2×C4×C103—41no—
128C2×C4×C103—41no—
129C2×C4×C103—41no—
130C2×C4×C103—41no—
131C2×C4×C103C4×D412yes—
132C2×C4×C103#12011yescharacteristic
133C2×C4×C103#12112yes—
134C2×C4×C103#12311yescharacteristic
135C2×C4×C103#13512yes—
136C2×C4×C103#13712yes—
137C8×C103—44no—
138C8×C103—82no—
139C22×C103—21no—
140C22×C103—21no—
141C22×C103—42no—
142C22×C103—41no—
143C22×C103—41no—
144C22×C103—41no—
145C22×C103—81no—
146C22×C103#38611yescharacteristic
147C22×C103#41611yescharacteristic
148C22×C103#41911yescharacteristic
149C4×C103—22no—
150C4×C103—22no—
151C4×C103—42no—
152C4×C103—41no—
153C4×C103—41no—
154C4×C103—41no—
155C4×C103—42no—
156C4×C103—81no—
157C4×C103—81no—
158C4×C103#45212yes—
159C4×C103#48512yes—
160#9034C10311yesmaximal, characteristic, direct product factor, Sylow
161C2×C103—21no—
162C2×C103—21no—
163C2×C103—81no—
164C2×C103#187311yescharacteristic
165C2×C103#188411yescharacteristic
166C2×C103#189111yescharacteristic
167#2921C2×C10311yescharacteristic
168#2396C2×C10311yescharacteristic
169#1487C2×C10312yescomplemented
170#1458C2×C10311yescharacteristic
171#1303C2×C10312yescomplemented
172C103#903411yescharacteristic, direct product factor, Sylow
173C2×C4×Q8C22×C10311yescharacteristic
174C2×#117C22×C10311yescharacteristic
175#433—24no—
176#431C22×C10312yes—
177#423C22×C10312yes—
178#407—21no—
179C4×M16—21no—
180#400C4×C10311yescharacteristic
181#399C4×C10311yescharacteristic
182#398—21no—
183#396—21no—
184#395C4×C10311yescharacteristic
185#393C4×C10311yescharacteristic
186C4×C4⋊C4—21no—
187C4×C4⋊C4C22×C10311yescharacteristic
188C4×C22⋊C4—21no—
189Q8⋊C8—24no—
190#324—21no—
191#323—21no—
192C22×Q8C2×C4×C10311yescharacteristic
193C23×C4D4×C10311yescharacteristic
194C2×M16—22no—
195C4×Q8—22no—
196C4×Q8—22no—
197#117—22no—
198#117—22no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4C2×C4×C10311yescharacteristic
204C2×C4⋊C4C2×C4×C10311yescharacteristic
205C2×C4⋊C4D4×C10311yescharacteristic
206C2×C22⋊C4—21no—
207C2×C22⋊C4—21no—
208C2×C22⋊C4C2×C4×C10311yescharacteristic
209C2×C22⋊C4D4×C10311yescharacteristic
210C2×C42—21no—
211C2×C42—21no—
212C2×C42D4×C10311yescharacteristic
213C2×C42C23×C10311yescharacteristic
214C4⋊C8—22no—
215C4⋊C8—22no—
216C4⋊C8D4×C10314yes—
217C22⋊C8—24no—
218C22⋊C8—22no—
219#97—22no—
220C4×C8—22no—
221C4×C8—22no—
222#95—21no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95C2×C4×C10311yescharacteristic
227#95C2×C4×C10311yescharacteristic
228C24C22⋊C4×C10311yescharacteristic
229C2×Q8—22no—
230C2×Q8—42no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4C22⋊C4×C10311yescharacteristic
240C22×C4C22⋊C4×C10311yescharacteristic
241C22×C4C22⋊C4×C10311yescharacteristic
242C22×C4C22×C4×C10311yescharacteristic
243C22×C4C2×D4×C10311yescharacteristic
244C22×C4C2×D4×C10311yescharacteristic
245M16—42no—
246M16—42no—
247C2×C8—24no—
248C2×C8—42no—
249C4⋊C4—22no—
250C4⋊C4—22no—
251C4⋊C4—22no—
252C4⋊C4—42no—
253C4⋊C4—42no—
254C4⋊C4—42no—
255C4⋊C4—42no—
256C22⋊C4—22no—
257C22⋊C4—22no—
258C22⋊C4—42no—
259C22⋊C4—42no—
260C42—21no—
261C42—21no—
262C42—41no—
263C42—41no—
264C42—42no—
265C42C2×D4×C10312yes—
266C42#41×C10312yes—
267C23—21no—
268C23—21no—
269C23—21no—
270C23—41no—
271C23—41no—
272C23C2×C22⋊C4×C10311yescharacteristic
273Q8—24no—
274Q8—42no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4C4×D4×C10312yes—
299C2×C4#120×C10311yescharacteristic
300C2×C4#121×C10312yes—
301C2×C4#123×C10311yescharacteristic
302C2×C4#135×C10312yes—
303C2×C4#137×C10312yes—
304C8—44no—
305C8—82no—
306C22—21no—
307C22—21no—
308C22—42no—
309C22—41no—
310C22—41no—
311C22—41no—
312C22—81no—
313C22#386×C10311yescharacteristic
314C22#416×C10311yescharacteristic
315C22#419×C10311yescharacteristic
316C4—22no—
317C4—22no—
318C4—42no—
319C4—41no—
320C4—41no—
321C4—42no—
322C4—41no—
323C4—81no—
324C4—81no—
325C4#452×C10312yes—
326C4#485×C10312yes—
327C2—21no—
328C2—21no—
329C2—81no—
330C2C103×#187311yescharacteristic
331C2C103×#188411yescharacteristic
332C2C103×#189111yescharacteristic
subgroupG/H
centerC2×C4×C103#120
commutatorC22×C4C22×C4×C103
Frattini, cosocleC2×C42C23×C103
socleC22×C103#386
prime radicalC24×C103C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C103 ◁ C2×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
3. C103×#1487C2semidirect
5. C103×#1303C2semidirect
160. #9034C103direct (N × H)
169. #1487C2×C103semidirect
171. #1303C2×C103semidirect
172. C103#9034direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#29212
C103×#23962
C103×#14872
C103×#14582
C103×#13032
#9034103