Finite Group Databasebeta

← C103×#11793 #39917068

Subgroups — C103×#11793 #39917068

Order 26368.

444 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#2564C211yesmaximal, characteristic
2C4×#100×C103C211yesmaximal, characteristic
3C103×#1465C211yesmaximal, characteristic
4C103×#1354C212yesmaximal, complemented
5C103×#1353C212yesmaximal, complemented
6C2×C22⋊Q8×C103C411yescharacteristic
7C2×C4×D4×C103C2211yescharacteristic
8C2×#100×C103—21no—
9#407×C103—21no—
10C4×M16×C103—21no—
11#400×C103C2211yescharacteristic
12#399×C103C411yescharacteristic
13#395×C103C2211yescharacteristic
14#393×C103C411yescharacteristic
15#387×C103—21no—
16#386×C103—21no—
17#385×C103—21no—
18#380×C103—21no—
19C2×#95×C103C411yescharacteristic
20#343×C103C2212yes—
21#324×C103C2212yes—
22#323×C103—21no—
23C22×Q8×C103C2×C411yescharacteristic
24C22×D4×C103D411yescharacteristic
25C23×C4×C103—21no—
26C23×C4×C103C2×C411yescharacteristic
27C23×C4×C103D411yescharacteristic
28C2×M16×C103—22no—
29C2×M16×C103—41no—
30C22⋊Q8×C103—41no—
31C22⋊Q8×C103—41no—
32C4×D4×C103—41no—
33C4×D4×C103—41no—
34C2×C4⋊C4×C103—21no—
35C2×C4⋊C4×C103—21no—
36C2×C4⋊C4×C103—21no—
37C2×C4⋊C4×C103C2×C411yescharacteristic
38C2×C4⋊C4×C103C2311yescharacteristic
39C2×C22⋊C4×C103—21no—
40C2×C22⋊C4×C103—21no—
41C2×C22⋊C4×C103—21no—
42C2×C22⋊C4×C103C2×C411yescharacteristic
43C2×C22⋊C4×C103D411yescharacteristic
44C2×C42×C103D411yescharacteristic
45#100×C103—24no—
46C22⋊C8×C103—22no—
47C22⋊C8×C103—41no—
48#97×C103—41no—
49C4×C8×C103—41no—
50#95×C103—21no—
51#95×C103—21no—
52#95×C103—21no—
53#95×C103—21no—
54#95×C103—21no—
55#95×C103C2×C411yescharacteristic
56#95×C103C2×C411yescharacteristic
57C24×C103C22⋊C411yescharacteristic
58C24×C103C22⋊C411yescharacteristic
59C2×Q8×C103—41no—
60C2×Q8×C103—81no—
61C2×D4×C103—22no—
62C2×D4×C103—22no—
63C2×D4×C103—41no—
64C22×C4×C103—21no—
65C22×C4×C103—21no—
66C22×C4×C103—21no—
67C22×C4×C103—21no—
68C22×C4×C103—21no—
69C22×C4×C103—21no—
70C22×C4×C103—21no—
71C22×C4×C103—21no—
72C22×C4×C103—42no—
73C22×C4×C103—42no—
74C22×C4×C103—81no—
75C22×C4×C103—81no—
76C22×C4×C103—81no—
77C22×C4×C103C22⋊C411yescharacteristic
78C22×C4×C103C22⋊C411yescharacteristic
79C22×C4×C103C22×C411yescharacteristic
80C22×C4×C103C2×D411yescharacteristic
81C22×C4×C103C2×D411yescharacteristic
82M16×C103—24no—
83M16×C103—42no—
84M16×C103—82no—
85C2×C8×C103—42no—
86C2×C8×C103—42no—
87C4⋊C4×C103—41no—
88C4⋊C4×C103—41no—
89C4⋊C4×C103—42no—
90C4⋊C4×C103—41no—
91C4⋊C4×C103—41no—
92C4⋊C4×C103—81no—
93C22⋊C4×C103—41no—
94C22⋊C4×C103—41no—
95C22⋊C4×C103—42no—
96C22⋊C4×C103—42no—
97C22⋊C4×C103—81no—
98C42×C103—21no—
99C42×C103—21no—
100C23×C103—21no—
101C23×C103—21no—
102C23×C103—21no—
103C23×C103—21no—
104C23×C103—21no—
105C23×C103—41no—
106C23×C103—41no—
107C23×C103—41no—
108C23×C103—41no—
109C23×C103#10412yes—
110C23×C103C2×C22⋊C411yescharacteristic
111Q8×C103—82no—
112D4×C103—44no—
113C2×C4×C103—21no—
114C2×C4×C103—21no—
115C2×C4×C103—22no—
116C2×C4×C103—21no—
117C2×C4×C103—21no—
118C2×C4×C103—21no—
119C2×C4×C103—41no—
120C2×C4×C103—42no—
121C2×C4×C103—41no—
122C2×C4×C103—41no—
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×C103—41no—
132C2×C4×C103—41no—
133C2×C4×C103—41no—
134C2×C4×C103—41no—
135C2×C4×C103—81no—
136C2×C4×C103—81no—
137C2×C4×C103—81no—
138C2×C4×C103—84no—
139C2×C4×C103#9911yescharacteristic
140C2×C4×C103#9911yescharacteristic
141C2×C4×C103#13712yes—
142C8×C103—44no—
143C8×C103—82no—
144C22×C103—21no—
145C22×C103—21no—
146C22×C103—22no—
147C22×C103—42no—
148C22×C103—42no—
149C22×C103—42no—
150C22×C103—41no—
151C22×C103—41no—
152C22×C103—41no—
153C22×C103—41no—
154C22×C103—41no—
155C22×C103—81no—
156C22×C103C2×#9911yescharacteristic
157C22×C103#41911yescharacteristic
158C22×C103C2×#10411yescharacteristic
159C4×C103—21no—
160C4×C103—21no—
161C4×C103—22no—
162C4×C103—42no—
163C4×C103—41no—
164C4×C103—41no—
165C4×C103—41no—
166C4×C103—81no—
167C4×C103—81no—
168C4×C103—81no—
169#11793C10311yesmaximal, characteristic, direct product factor, Sylow
170C2×C103—21no—
171C2×C103—21no—
172C2×C103—42no—
173C2×C103—81no—
174C2×C103#150811yescharacteristic
175C2×C103#212111yescharacteristic
176C2×C103#213211yescharacteristic
177#2564C2×C10311yescharacteristic
178C4×#100C2×C10311yescharacteristic
179#1465C2×C10311yescharacteristic
180#1354C2×C10312yescomplemented
181#1353C2×C10312yescomplemented
182C103#1179311yescharacteristic, direct product factor, Sylow
183C2×C22⋊Q8C4×C10311yescharacteristic
184C2×C4×D4C22×C10311yescharacteristic
185C2×#100—21no—
186#407—21no—
187C4×M16—21no—
188#400C22×C10311yescharacteristic
189#399C4×C10311yescharacteristic
190#395C22×C10311yescharacteristic
191#393C4×C10311yescharacteristic
192#387—21no—
193#386—21no—
194#385—21no—
195#380—21no—
196C2×#95C4×C10311yescharacteristic
197#343C22×C10312yes—
198#324C22×C10312yes—
199#323—21no—
200C22×Q8C2×C4×C10311yescharacteristic
201C22×D4D4×C10311yescharacteristic
202C23×C4—21no—
203C23×C4C2×C4×C10311yescharacteristic
204C23×C4D4×C10311yescharacteristic
205C2×M16—22no—
206C2×M16—41no—
207C22⋊Q8—41no—
208C22⋊Q8—41no—
209C4×D4—41no—
210C4×D4—41no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4C2×C4×C10311yescharacteristic
215C2×C4⋊C4C23×C10311yescharacteristic
216C2×C22⋊C4—21no—
217C2×C22⋊C4—21no—
218C2×C22⋊C4—21no—
219C2×C22⋊C4C2×C4×C10311yescharacteristic
220C2×C22⋊C4D4×C10311yescharacteristic
221C2×C42D4×C10311yescharacteristic
222#100—24no—
223C22⋊C8—22no—
224C22⋊C8—41no—
225#97—41no—
226C4×C8—41no—
227#95—21no—
228#95—21no—
229#95—21no—
230#95—21no—
231#95—21no—
232#95C2×C4×C10311yescharacteristic
233#95C2×C4×C10311yescharacteristic
234C24C22⋊C4×C10311yescharacteristic
235C24C22⋊C4×C10311yescharacteristic
236C2×Q8—41no—
237C2×Q8—81no—
238C2×D4—22no—
239C2×D4—22no—
240C2×D4—41no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—42no—
250C22×C4—42no—
251C22×C4—81no—
252C22×C4—81no—
253C22×C4—81no—
254C22×C4C22⋊C4×C10311yescharacteristic
255C22×C4C22⋊C4×C10311yescharacteristic
256C22×C4C22×C4×C10311yescharacteristic
257C22×C4C2×D4×C10311yescharacteristic
258C22×C4C2×D4×C10311yescharacteristic
259M16—24no—
260M16—42no—
261M16—82no—
262C2×C8—42no—
263C2×C8—42no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—42no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—81no—
270C22⋊C4—41no—
271C22⋊C4—41no—
272C22⋊C4—42no—
273C22⋊C4—42no—
274C22⋊C4—81no—
275C42—21no—
276C42—21no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23#104×C10312yes—
287C23C2×C22⋊C4×C10311yescharacteristic
288Q8—82no—
289D4—44no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—41no—
297C2×C4—42no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—84no—
316C2×C4#99×C10311yescharacteristic
317C2×C4#99×C10311yescharacteristic
318C2×C4#137×C10312yes—
319C8—44no—
320C8—82no—
321C22—21no—
322C22—21no—
323C22—22no—
324C22—42no—
325C22—42no—
326C22—42no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—81no—
333C22C2×#99×C10311yescharacteristic
334C22#419×C10311yescharacteristic
335C22C2×#104×C10311yescharacteristic
336C4—22no—
337C4—21no—
338C4—21no—
339C4—42no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—81no—
344C4—81no—
345C4—81no—
346C2—21no—
347C2—21no—
348C2—42no—
349C2—81no—
350C2C103×#150811yescharacteristic
351C2C103×#212111yescharacteristic
352C2C103×#213211yescharacteristic
subgroupG/H
center, socleC22×C103C2×#99
commutatorC22×C4C22×C4×C103
Frattini, cosocleC2×C4⋊C4C23×C103
prime radicalC22×D4×C103D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C103 ◁ C22×C4×C103 ◁ C2×C4×D4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
4. C103×#1354C2semidirect
5. C103×#1353C2semidirect
169. #11793C103direct (N × H)
180. #1354C2×C103semidirect
181. #1353C2×C103semidirect
182. C103#11793direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#25642
C4×#100×C1032
C103×#14652
C103×#13542
C103×#13532
#11793103