Finite Group Databasebeta

← C103×#9279 #39914554

Subgroups — C103×#9279 #39914554

Order 26368.

422 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3228C211yesmaximal, characteristic
2C103×#2981C211yesmaximal, characteristic
3C103×#1506C211yesmaximal, characteristic, complemented
4C103×#1505C211yesmaximal, characteristic
5C103×#1497C211yesmaximal, characteristic, complemented
6C103×#1287C211yesmaximal, characteristic, complemented
7C103×#1274C211yesmaximal, characteristic, complemented
8#533×C103C2211yescharacteristic
9#532×C103C2211yescharacteristic
10#500×C103C411yescharacteristic, complemented
11#498×C103C411yescharacteristic, complemented
12#486×C103C411yescharacteristic, complemented
13#486×C103C411yescharacteristic, complemented
14#482×C103—22no—
15#478×C103—22no—
16#436×C103—21no—
17#435×C103—22no—
18C8×D4×C103—21no—
19#432×C103C2211yescharacteristic
20#432×C103C2211yescharacteristic
21#431×C103C2211yescharacteristic
22#431×C103C2211yescharacteristic
23#408×C103—22no—
24#376×C103C2211yescharacteristic
25#328×C103—22no—
26#327×C103—22no—
27Q8⋊C8×C103—21no—
28Q8⋊C8×C103—21no—
29C2×#41×C103—21no—
30C2×M16×C103—22no—
31C22×C8×C103—22no—
32C4⋊Q8×C103C2×C411yescharacteristic
33C4⋊Q8×C103C2×C411yescharacteristic
34C4⋊Q8×C103C2×C411yescharacteristic
35#127×C103C2×C411yescharacteristic
36#125×C103—21no—
37#124×C103—21no—
38C22⋊Q8×C103—21no—
39C22⋊Q8×C103—21no—
40#121×C103—21no—
41#121×C103D412yes—
42C4×Q8×C103—21no—
43C4×Q8×C103—21no—
44C4×D4×C103—21no—
45C4×D4×C103D412yes—
46#117×C103—21no—
47C2×C42×C103—21no—
48C2×C42×C103C2311yescharacteristic
49#107×C103—22no—
50#106×C103—22no—
51C4⋊C8×C103—21no—
52C4⋊C8×C103—21no—
53C4⋊C8×C103—21no—
54C4⋊C8×C103—21no—
55#102×C103—22no—
56#102×C103—22no—
57C22⋊C8×C103—22no—
58C22⋊C8×C103—22no—
59C22⋊C8×C103—21no—
60C22⋊C8×C103—21no—
61C22⋊C8×C103—21no—
62C22⋊C8×C103D412yes—
63#97×C103—21no—
64#97×C103—21no—
65C4×C8×C103C2×C411yescharacteristic
66C4×C8×C103C2×C411yescharacteristic
67C4×C8×C103D411yescharacteristic
68C4×C8×C103D411yescharacteristic
69#95×C103—21no—
70#95×C103—21no—
71#41×C103—82no—
72C2×Q8×C103—21no—
73C2×Q8×C103—21no—
74C2×Q8×C103—21no—
75C2×D4×C103—22no—
76C2×D4×C103—21no—
77C2×D4×C103—21no—
78C2×D4×C103C22⋊C412yes—
79C22×C4×C103—22no—
80C22×C4×C103—41no—
81C22×C4×C103C2×D411yescharacteristic
82C22×C4×C103C2×D411yescharacteristic
83C22×C4×C103#4111yescharacteristic
84M16×C103—82no—
85C2×C8×C103—21no—
86C2×C8×C103—21no—
87C2×C8×C103—21no—
88C2×C8×C103—21no—
89C2×C8×C103—22no—
90C2×C8×C103—41no—
91C2×C8×C103—82no—
92C4⋊C4×C103—21no—
93C4⋊C4×C103—21no—
94C4⋊C4×C103—21no—
95C4⋊C4×C103—21no—
96C4⋊C4×C103—21no—
97C4⋊C4×C103—41no—
98C4⋊C4×C103—41no—
99C4⋊C4×C103C22⋊C412yes—
100C22⋊C4×C103—22no—
101C22⋊C4×C103—22no—
102C22⋊C4×C103—41no—
103C42×C103—22no—
104C42×C103—41no—
105C42×C103—41no—
106C42×C103C22×C411yescharacteristic
107C42×C103C2×D411yescharacteristic
108C42×C103C2×D411yescharacteristic
109C42×C103#4111yescharacteristic
110C23×C103—22no—
111C23×C103#12111yescharacteristic
112Q8×C103—41no—
113Q8×C103—41no—
114Q8×C103—81no—
115Q8×C103—81no—
116D4×C103—42no—
117D4×C103—41no—
118D4×C103—41no—
119D4×C103—81no—
120D4×C103—82no—
121C2×C4×C103—21no—
122C2×C4×C103—21no—
123C2×C4×C103—22no—
124C2×C4×C103—41no—
125C2×C4×C103—41no—
126C2×C4×C103—42no—
127C2×C4×C103—42no—
128C2×C4×C103—42no—
129C2×C4×C103—41no—
130C2×C4×C103—41no—
131C2×C4×C103—81no—
132C2×C4×C103—81no—
133C2×C4×C103C2×C22⋊C411yescharacteristic
134C2×C4×C103C4×D411yescharacteristic
135C2×C4×C103C4×D411yescharacteristic
136C2×C4×C103#12011yescharacteristic
137C2×C4×C103#12111yescharacteristic
138C2×C4×C103#12311yescharacteristic
139C8×C103—41no—
140C8×C103—41no—
141C8×C103—41no—
142C8×C103—42no—
143C8×C103—41no—
144C8×C103—81no—
145C22×C103—21no—
146C22×C103—21no—
147C22×C103—21no—
148C22×C103—42no—
149C22×C103—42no—
150C22×C103—42no—
151C22×C103#38611yescharacteristic
152C4×C103—21no—
153C4×C103—21no—
154C4×C103—21no—
155C4×C103—21no—
156C4×C103—21no—
157C4×C103—42no—
158C4×C103—82no—
159C4×C103—81no—
160C4×C103—81no—
161C4×C103#44311yescharacteristic
162C4×C103#44411yescharacteristic
163#9279C10311yesmaximal, characteristic, direct product factor, Sylow
164C2×C103—41no—
165C2×C103—82no—
166C2×C103#187611yescharacteristic
167C2×C103#190411yescharacteristic
168C2×C103#190911yescharacteristic
169#3228C2×C10311yescharacteristic
170#2981C2×C10311yescharacteristic
171#1506C2×C10311yescharacteristic, complemented
172#1505C2×C10311yescharacteristic
173#1497C2×C10311yescharacteristic, complemented
174#1287C2×C10311yescharacteristic, complemented
175#1274C2×C10311yescharacteristic, complemented
176C103#927911yescharacteristic, direct product factor, Sylow
177#533C22×C10311yescharacteristic
178#532C22×C10311yescharacteristic
179#500C4×C10311yescharacteristic, complemented
180#498C4×C10311yescharacteristic, complemented
181#486C4×C10311yescharacteristic, complemented
182#486C4×C10311yescharacteristic, complemented
183#482—22no—
184#478—22no—
185#436—21no—
186#435—22no—
187C8×D4—21no—
188#432C22×C10311yescharacteristic
189#432C22×C10311yescharacteristic
190#431C22×C10311yescharacteristic
191#431C22×C10311yescharacteristic
192#408—22no—
193#376C22×C10311yescharacteristic
194#328—22no—
195#327—22no—
196Q8⋊C8—21no—
197Q8⋊C8—21no—
198C2×#41—21no—
199C2×M16—22no—
200C22×C8—22no—
201C4⋊Q8C2×C4×C10311yescharacteristic
202C4⋊Q8C2×C4×C10311yescharacteristic
203C4⋊Q8C2×C4×C10311yescharacteristic
204#127C2×C4×C10311yescharacteristic
205#125—21no—
206#124—21no—
207C22⋊Q8—21no—
208C22⋊Q8—21no—
209#121—21no—
210#121D4×C10312yes—
211C4×Q8—21no—
212C4×Q8—21no—
213C4×D4—21no—
214C4×D4D4×C10312yes—
215#117—21no—
216C2×C42—21no—
217C2×C42C23×C10311yescharacteristic
218#107—22no—
219#106—22no—
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8—21no—
224#102—22no—
225#102—22no—
226C22⋊C8—22no—
227C22⋊C8—22no—
228C22⋊C8—21no—
229C22⋊C8—21no—
230C22⋊C8—21no—
231C22⋊C8D4×C10312yes—
232#97—21no—
233#97—21no—
234C4×C8C2×C4×C10311yescharacteristic
235C4×C8C2×C4×C10311yescharacteristic
236C4×C8D4×C10311yescharacteristic
237C4×C8D4×C10311yescharacteristic
238#95—21no—
239#95—21no—
240#41—82no—
241C2×Q8—21no—
242C2×Q8—21no—
243C2×Q8—21no—
244C2×D4—22no—
245C2×D4—21no—
246C2×D4—21no—
247C2×D4C22⋊C4×C10312yes—
248C22×C4—22no—
249C22×C4—41no—
250C22×C4C2×D4×C10311yescharacteristic
251C22×C4C2×D4×C10311yescharacteristic
252C22×C4#41×C10311yescharacteristic
253M16—82no—
254C2×C8—21no—
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—21no—
258C2×C8—22no—
259C2×C8—41no—
260C2×C8—82no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4C22⋊C4×C10312yes—
269C22⋊C4—22no—
270C22⋊C4—22no—
271C22⋊C4—41no—
272C42—22no—
273C42—41no—
274C42—41no—
275C42C22×C4×C10311yescharacteristic
276C42C2×D4×C10311yescharacteristic
277C42C2×D4×C10311yescharacteristic
278C42#41×C10311yescharacteristic
279C23—22no—
280C23#121×C10311yescharacteristic
281Q8—41no—
282Q8—41no—
283Q8—81no—
284Q8—81no—
285D4—42no—
286D4—41no—
287D4—41no—
288D4—81no—
289D4—82no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4C2×C22⋊C4×C10311yescharacteristic
303C2×C4C4×D4×C10311yescharacteristic
304C2×C4C4×D4×C10311yescharacteristic
305C2×C4#120×C10311yescharacteristic
306C2×C4#121×C10311yescharacteristic
307C2×C4#123×C10311yescharacteristic
308C8—41no—
309C8—42no—
310C8—41no—
311C8—41no—
312C8—41no—
313C8—81no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—42no—
318C22—42no—
319C22—42no—
320C22#386×C10311yescharacteristic
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—42no—
327C4—82no—
328C4—81no—
329C4—81no—
330C4#443×C10311yescharacteristic
331C4#444×C10311yescharacteristic
332C2—41no—
333C2—82no—
334C2C103×#187611yescharacteristic
335C2C103×#190411yescharacteristic
336C2C103×#190911yescharacteristic
subgroupG/H
center, socleC22×C103#386
commutatorC42C22×C4×C103
Frattini, cosocleC2×C42C23×C103
prime radical#532×C103C22
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
3. C103×#1506C2semidirect
5. C103×#1497C2semidirect
6. C103×#1287C2semidirect
7. C103×#1274C2semidirect
10. #500×C103C4semidirect
11. #498×C103C4semidirect
12. #486×C103C4semidirect
13. #486×C103C4semidirect
163. #9279C103direct (N × H)
171. #1506C2×C103semidirect
173. #1497C2×C103semidirect
174. #1287C2×C103semidirect
175. #1274C2×C103semidirect
176. C103#9279direct (N × H)
179. #500C4×C103semidirect
180. #498C4×C103semidirect
181. #486C4×C103semidirect
182. #486C4×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#32282
C103×#29812
C103×#15062
C103×#15052
C103×#14972
C103×#12872
C103×#12742
#9279103