Finite Group Databasebeta

← C103×#9296 #39914571

Subgroups — C103×#9296 #39914571

Order 26368.

470 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3229C211yesmaximal, characteristic
2C103×#2327C211yesmaximal, characteristic
3C103×#1995C211yesmaximal, characteristic
4C103×#1546C211yesmaximal, characteristic
5C103×#1518C211yesmaximal, characteristic
6C103×#1286C211yesmaximal, characteristic
7C103×#1274C211yesmaximal, characteristic
8#533×C103C2211yescharacteristic
9C2×C4⋊Q8×C103C2211yescharacteristic
10C2×C4×Q8×C103—21no—
11#498×C103C412yescomplemented
12#487×C103C412yescomplemented
13#483×C103—22no—
14#475×C103—22no—
15#431×C103C2211yescharacteristic
16#431×C103C2211yescharacteristic
17#423×C103C2211yescharacteristic
18#391×C103—21no—
19#387×C103—22no—
20#387×C103—22no—
21#382×C103C2211yescharacteristic
22#376×C103C2211yescharacteristic
23#339×C103—21no—
24#339×C103—21no—
25#332×C103—22no—
26#328×C103—22no—
27C22×Q8×C103—21no—
28C2×M16×C103—21no—
29C4⋊Q8×C103—21no—
30C4⋊Q8×C103—21no—
31C4⋊Q8×C103C2×C411yescharacteristic
32C4⋊Q8×C103C2×C411yescharacteristic
33C4⋊Q8×C103C2×C412yes—
34C4⋊Q8×C103D412yes—
35#125×C103—21no—
36C22⋊Q8×C103—21no—
37C22⋊Q8×C103—21no—
38C4×Q8×C103—21no—
39C4×Q8×C103—21no—
40C4×Q8×C103—42no—
41C4×Q8×C103—42no—
42#117×C103—21no—
43C2×C4⋊C4×C103—21no—
44C2×C4⋊C4×C103—22no—
45C2×C4⋊C4×C103—21no—
46C2×C4⋊C4×C103D412yes—
47C2×C42×C103—22no—
48C2×C42×C103D411yescharacteristic
49C2×C42×C103D411yescharacteristic
50C2×C42×C103C2311yescharacteristic
51#106×C103—24no—
52C4⋊C8×C103—21no—
53C4⋊C8×C103—21no—
54C4⋊C8×C103—21no—
55C4⋊C8×C103—21no—
56#103×C103—24no—
57C22⋊C8×C103—21no—
58C22⋊C8×C103—21no—
59C4×C8×C103—21no—
60C4×C8×C103C2×C412yes—
61#95×C103—24no—
62#95×C103—21no—
63#95×C103—21no—
64#95×C103—21no—
65#95×C103D412yes—
66C2×Q8×C103—22no—
67C2×Q8×C103—22no—
68C2×Q8×C103—21no—
69C2×Q8×C103—21no—
70C2×Q8×C103—41no—
71C2×Q8×C103—41no—
72C2×Q8×C103—41no—
73C2×Q8×C103—41no—
74C22×C4×C103—21no—
75C22×C4×C103—22no—
76C22×C4×C103—21no—
77C22×C4×C103—22no—
78C22×C4×C103C2×D411yescharacteristic
79C22×C4×C103C2×D411yescharacteristic
80C22×C4×C103C2×D411yescharacteristic
81M16×C103—41no—
82M16×C103—41no—
83C2×C8×C103—22no—
84C2×C8×C103—41no—
85C2×C8×C103—41no—
86C4⋊C4×C103—22no—
87C4⋊C4×C103—22no—
88C4⋊C4×C103—22no—
89C4⋊C4×C103—21no—
90C4⋊C4×C103—21no—
91C4⋊C4×C103—21no—
92C4⋊C4×C103—21no—
93C4⋊C4×C103—44no—
94C4⋊C4×C103—41no—
95C4⋊C4×C103—41no—
96C4⋊C4×C103—41no—
97C4⋊C4×C103—41no—
98C4⋊C4×C103C22⋊C414yes—
99C22⋊C4×C103—41no—
100C42×C103—21no—
101C42×C103—21no—
102C42×C103—21no—
103C42×C103—44no—
104C42×C103—41no—
105C42×C103SD1612yes—
106C42×C103C22×C411yescharacteristic
107C42×C103C2×D411yescharacteristic
108C42×C103#4111yescharacteristic
109C42×C103#4111yescharacteristic
110C23×C103#12011yescharacteristic
111Q8×C103—42no—
112Q8×C103—42no—
113Q8×C103—42no—
114Q8×C103—42no—
115Q8×C103—42no—
116Q8×C103—81no—
117C2×C4×C103—24no—
118C2×C4×C103—22no—
119C2×C4×C103—41no—
120C2×C4×C103—41no—
121C2×C4×C103—41no—
122C2×C4×C103—41no—
123C2×C4×C103—42no—
124C2×C4×C103—42no—
125C2×C4×C103—41no—
126C2×C4×C103—42no—
127C2×C4×C103—41no—
128C2×C4×C103—42no—
129C2×C4×C103—41no—
130C2×C4×C103—41no—
131C2×C4×C103—42no—
132C2×C4×C103—41no—
133C2×C4×C103C2×C22⋊C411yescharacteristic
134C2×C4×C103C4×D411yescharacteristic
135C2×C4×C103C4×D411yescharacteristic
136C2×C4×C103#12111yescharacteristic
137C2×C4×C103#12111yescharacteristic
138C2×C4×C103#12311yescharacteristic
139C2×C4×C103C2×SD1611yescharacteristic
140C2×C4×C103#13511yescharacteristic
141C2×C4×C103AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C103#13711yescharacteristic
143C8×C103—42no—
144C8×C103—81no—
145C8×C103—81no—
146C22×C103—21no—
147C22×C103—21no—
148C22×C103#38611yescharacteristic
149C22×C103#45011yescharacteristic
150C22×C103#45211yescharacteristic
151C4×C103—21no—
152C4×C103—21no—
153C4×C103—21no—
154C4×C103—21no—
155C4×C103—42no—
156C4×C103—44no—
157C4×C103—82no—
158C4×C103—81no—
159C4×C103—81no—
160C4×C103—81no—
161C4×C103C4×SD1611yescharacteristic
162C4×C103#44011yescharacteristic
163C4×C103#46111yescharacteristic
164C4×C103#46311yescharacteristic
165#9296C10311yesmaximal, characteristic, direct product factor, Sylow
166C2×C103—21no—
167C2×C103—21no—
168C2×C103#187711yescharacteristic
169C2×C103#190511yescharacteristic
170C2×C103#191211yescharacteristic
171#3229C2×C10311yescharacteristic
172#2327C2×C10311yescharacteristic
173#1995C2×C10311yescharacteristic
174#1546C2×C10311yescharacteristic
175#1518C2×C10311yescharacteristic
176#1286C2×C10311yescharacteristic
177#1274C2×C10311yescharacteristic
178C103#929611yescharacteristic, direct product factor, Sylow
179#533C22×C10311yescharacteristic
180C2×C4⋊Q8C22×C10311yescharacteristic
181C2×C4×Q8—21no—
182#498C4×C10312yescomplemented
183#487C4×C10312yescomplemented
184#483—22no—
185#475—22no—
186#431C22×C10311yescharacteristic
187#431C22×C10311yescharacteristic
188#423C22×C10311yescharacteristic
189#391—21no—
190#387—22no—
191#387—22no—
192#382C22×C10311yescharacteristic
193#376C22×C10311yescharacteristic
194#339—21no—
195#339—21no—
196#332—22no—
197#328—22no—
198C22×Q8—21no—
199C2×M16—21no—
200C4⋊Q8—21no—
201C4⋊Q8—21no—
202C4⋊Q8C2×C4×C10311yescharacteristic
203C4⋊Q8C2×C4×C10311yescharacteristic
204C4⋊Q8C2×C4×C10312yes—
205C4⋊Q8D4×C10312yes—
206#125—21no—
207C22⋊Q8—21no—
208C22⋊Q8—21no—
209C4×Q8—21no—
210C4×Q8—21no—
211C4×Q8—42no—
212C4×Q8—42no—
213#117—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—22no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4D4×C10312yes—
218C2×C42—22no—
219C2×C42D4×C10311yescharacteristic
220C2×C42D4×C10311yescharacteristic
221C2×C42C23×C10311yescharacteristic
222#106—24no—
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8—21no—
226C4⋊C8—21no—
227#103—24no—
228C22⋊C8—21no—
229C22⋊C8—21no—
230C4×C8—21no—
231C4×C8C2×C4×C10312yes—
232#95—24no—
233#95—21no—
234#95—21no—
235#95—21no—
236#95D4×C10312yes—
237C2×Q8—22no—
238C2×Q8—22no—
239C2×Q8—21no—
240C2×Q8—21no—
241C2×Q8—41no—
242C2×Q8—41no—
243C2×Q8—41no—
244C2×Q8—41no—
245C22×C4—21no—
246C22×C4—22no—
247C22×C4—21no—
248C22×C4—22no—
249C22×C4C2×D4×C10311yescharacteristic
250C22×C4C2×D4×C10311yescharacteristic
251C22×C4C2×D4×C10311yescharacteristic
252M16—41no—
253M16—41no—
254C2×C8—22no—
255C2×C8—41no—
256C2×C8—41no—
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—22no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—44no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4C22⋊C4×C10314yes—
270C22⋊C4—41no—
271C42—21no—
272C42—21no—
273C42—21no—
274C42—44no—
275C42—41no—
276C42SD16×C10312yes—
277C42C22×C4×C10311yescharacteristic
278C42C2×D4×C10311yescharacteristic
279C42#41×C10311yescharacteristic
280C42#41×C10311yescharacteristic
281C23#120×C10311yescharacteristic
282Q8—42no—
283Q8—42no—
284Q8—42no—
285Q8—42no—
286Q8—42no—
287Q8—81no—
288C2×C4—24no—
289C2×C4—22no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—41no—
297C2×C4—42no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—42no—
303C2×C4—41no—
304C2×C4C2×C22⋊C4×C10311yescharacteristic
305C2×C4C4×D4×C10311yescharacteristic
306C2×C4C4×D4×C10311yescharacteristic
307C2×C4#121×C10311yescharacteristic
308C2×C4#121×C10311yescharacteristic
309C2×C4#123×C10311yescharacteristic
310C2×C4C2×SD16×C10311yescharacteristic
311C2×C4#135×C10311yescharacteristic
312C2×C4AGL(1,ℤ/8)×C10311yescharacteristic
313C2×C4#137×C10311yescharacteristic
314C8—42no—
315C8—81no—
316C8—81no—
317C22—21no—
318C22—21no—
319C22#386×C10311yescharacteristic
320C22#450×C10311yescharacteristic
321C22#452×C10311yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—42no—
327C4—44no—
328C4—82no—
329C4—81no—
330C4—81no—
331C4—81no—
332C4C4×SD16×C10311yescharacteristic
333C4#440×C10311yescharacteristic
334C4#461×C10311yescharacteristic
335C4#463×C10311yescharacteristic
336C2—21no—
337C2—21no—
338C2C103×#187711yescharacteristic
339C2C103×#190511yescharacteristic
340C2C103×#191211yescharacteristic
subgroupG/H
center, socleC22×C103#386
commutatorC42C22×C4×C103
Frattini, cosocleC2×C42C23×C103
prime radicalC23×C103#120
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C103 ◁ C2×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
11. #498×C103C4semidirect
12. #487×C103C4semidirect
165. #9296C103direct (N × H)
178. C103#9296direct (N × H)
182. #498C4×C103semidirect
183. #487C4×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#32292
C103×#23272
C103×#19952
C103×#15462
C103×#15182
C103×#12862
C103×#12742
#9296103