Finite Group Databasebeta

← C103×#33934 #39939209

Subgroups — C103×#33934 #39939209

Order 26368.

508 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×#3393C211yesmaximal, characteristic, complemented
2Q8×D8×C103C211yesmaximal, characteristic, complemented
3C103×#2243C212yesmaximal, complemented
4C103×#2241C211yesmaximal, characteristic, complemented
5C103×#2227C212yesmaximal, complemented
6C103×#2224C211yesmaximal, characteristic, complemented
7C103×#2210C212yesmaximal
8C103×#2208C211yesmaximal, characteristic, complemented
9C103×#2183C211yesmaximal, characteristic, complemented
10C103×#2175C212yesmaximal, complemented
11C4×D16×C103C211yesmaximal, characteristic
12#556×C103—21no—
13D4×Q8×C103—21no—
14C2×SD32×C103C2212yes—
15C2×D16×C103C2211yescharacteristic
16#500×C103C2211yescharacteristic
17#500×C103C2212yes—
18#495×C103C2212yes—
19#494×C103C2211yescharacteristic
20#474×C103—21no—
21#474×C103—22no—
22#464×C103—22no—
23#461×C103—21no—
24C8×Q8×C103C2211yescharacteristic
25C4×Q16×C103C2212yes—
26C4×D8×C103C2211yescharacteristic
27C4×D8×C103C2212yes—
28C4×D8×C103C2211yescharacteristic
29#366×C103C2212yes—
30#366×C103C2211yescharacteristic
31C4⋊C16×C103C2211yescharacteristic
32C4⋊C16×C103C2212yes—
33#358×C103C2212yes—
34#358×C103C2212yes—
35#358×C103C2212yes—
36#357×C103C2212yes—
37#357×C103C2211yescharacteristic
38#357×C103C2211yescharacteristic
39#346×C103C2212yes—
40C4×C16×C103C2211yescharacteristic
41C22×Q8×C103—41no—
42C2×Q16×C103—21no—
43C2×Q16×C103C2312yes—
44C2×SD16×C103—22no—
45C2×D8×C103C2311yescharacteristic
46C2×D8×C103C2311yescharacteristic
47C4⋊Q8×C103—21no—
48C4⋊Q8×C103—22no—
49C4⋊Q8×C103—21no—
50#126×C103—42no—
51#124×C103—22no—
52C22⋊Q8×C103—41no—
53C22⋊Q8×C103—41no—
54C22⋊Q8×C103—42no—
55C4×Q8×C103—22no—
56C4×Q8×C103D411yescharacteristic
57C4×D4×C103—21no—
58C4×D4×C103—21no—
59C4×D4×C103—22no—
60#117×C103—41no—
61SD32×C103—24no—
62D16×C103—22no—
63C2×C16×C103C2311yescharacteristic
64C2×C16×C103C2311yescharacteristic
65C2×C16×C103C2312yes—
66#107×C103—21no—
67#107×C103—22no—
68#107×C103C2312yes—
69#107×C103C2311yescharacteristic
70#107×C103C2311yescharacteristic
71C4⋊C8×C103D411yescharacteristic
72C4⋊C8×C103D412yes—
73#103×C103—22no—
74#102×C103—21no—
75#102×C103—21no—
76#102×C103—22no—
77C4×C8×C103C2311yescharacteristic
78C4×C8×C103C2312yes—
79C2×Q8×C103—22no—
80C2×Q8×C103—42no—
81C2×Q8×C103—41no—
82C2×Q8×C103—84no—
83C2×Q8×C103D811yescharacteristic
84C2×D4×C103—21no—
85C2×D4×C103—21no—
86C22×C4×C103—41no—
87C22×C4×C103—42no—
88C22×C4×C103—41no—
89Q16×C103—22no—
90Q16×C103—22no—
91Q16×C103—81no—
92SD16×C103—82no—
93D8×C103—21no—
94D8×C103—21no—
95D8×C103—21no—
96D8×C103#4112yes—
97C2×C8×C103C2×D411yescharacteristic
98C2×C8×C103C2×D412yes—
99C2×C8×C103C2411yescharacteristic
100C4⋊C4×C103—21no—
101C4⋊C4×C103—21no—
102C4⋊C4×C103—22no—
103C4⋊C4×C103—41no—
104C4⋊C4×C103—42no—
105C4⋊C4×C103—42no—
106C4⋊C4×C103—41no—
107C4⋊C4×C103—41no—
108C4⋊C4×C103D811yescharacteristic
109C4⋊C4×C103D812yes—
110C22⋊C4×C103—42no—
111C22⋊C4×C103—42no—
112C22⋊C4×C103—41no—
113C22⋊C4×C103—41no—
114C22⋊C4×C103—42no—
115C42×C103—42no—
116C42×C103C2×D411yescharacteristic
117C42×C103C2×D412yes—
118C16×C103—21no—
119C16×C103—22no—
120C16×C103—21no—
121C23×C103—41no—
122C23×C103—41no—
123Q8×C103—22no—
124Q8×C103—42no—
125Q8×C103—42no—
126Q8×C103—84no—
127Q8×C103—82no—
128D4×C103—22no—
129D4×C103—41no—
130D4×C103—41no—
131D4×C103—41no—
132C2×C4×C103—41no—
133C2×C4×C103—42no—
134C2×C4×C103—42no—
135C2×C4×C103—41no—
136C2×C4×C103—84no—
137C2×C4×C103—82no—
138C2×C4×C103—82no—
139C2×C4×C103C2×D812yes—
140C2×C4×C103C2×D811yescharacteristic
141C2×C4×C103C2×D812yes—
142C2×C4×C103C2×D811yescharacteristic
143C2×C4×C103C22×D411yescharacteristic
144C8×C103—22no—
145C8×C103—21no—
146C8×C103C2×#4111yescharacteristic
147C8×C1032−1+411yescharacteristic
148C22×C103—42no—
149C22×C103—81no—
150C22×C103—81no—
151C22×C103—81no—
152C22×C103—81no—
153C22×C103—81no—
154C22×C103C22×D811yescharacteristic
155C4×C103—22no—
156C4×C103—22no—
157C4×C103—21no—
158C4×C103—82no—
159C4×C103—81no—
160C4×C103—82no—
161C4×C103—81no—
162C4×C103#50912yes—
163C4×C103#54811yescharacteristic
164C4×C103#57711yescharacteristic
165#33934C10311yesmaximal, characteristic, direct product factor, Sylow
166C2×C103—82no—
167C2×C103—161no—
168C2×C103#335811yescharacteristic
169C2×C103C2×#50911yescharacteristic
170C2×C103#341711yescharacteristic
171#3393C2×C10311yescharacteristic, complemented
172Q8×D8C2×C10311yescharacteristic, complemented
173#2243C2×C10312yescomplemented
174#2241C2×C10311yescharacteristic, complemented
175#2227C2×C10312yescomplemented
176#2224C2×C10311yescharacteristic, complemented
177#2210C2×C10312yes—
178#2208C2×C10311yescharacteristic, complemented
179#2183C2×C10311yescharacteristic, complemented
180#2175C2×C10312yescomplemented
181C4×D16C2×C10311yescharacteristic
182C103#3393411yescharacteristic, direct product factor, Sylow
183#556—21no—
184D4×Q8—21no—
185C2×SD32C22×C10312yes—
186C2×D16C22×C10311yescharacteristic
187#500C22×C10311yescharacteristic
188#500C22×C10312yes—
189#495C22×C10312yes—
190#494C22×C10311yescharacteristic
191#474—21no—
192#474—22no—
193#464—22no—
194#461—21no—
195C8×Q8C22×C10311yescharacteristic
196C4×Q16C22×C10312yes—
197C4×D8C22×C10311yescharacteristic
198C4×D8C22×C10312yes—
199C4×D8C22×C10311yescharacteristic
200#366C22×C10311yescharacteristic
201#366C22×C10312yes—
202C4⋊C16C22×C10311yescharacteristic
203C4⋊C16C22×C10312yes—
204#358C22×C10312yes—
205#358C22×C10312yes—
206#358C22×C10312yes—
207#357C22×C10311yescharacteristic
208#357C22×C10311yescharacteristic
209#357C22×C10312yes—
210#346C22×C10312yes—
211C4×C16C22×C10311yescharacteristic
212C22×Q8—41no—
213C2×Q16—21no—
214C2×Q16C23×C10312yes—
215C2×SD16—22no—
216C2×D8C23×C10311yescharacteristic
217C2×D8C23×C10311yescharacteristic
218C4⋊Q8—21no—
219C4⋊Q8—22no—
220C4⋊Q8—21no—
221#126—42no—
222#124—22no—
223C22⋊Q8—41no—
224C22⋊Q8—41no—
225C22⋊Q8—42no—
226C4×Q8—22no—
227C4×Q8D4×C10311yescharacteristic
228C4×D4—21no—
229C4×D4—22no—
230C4×D4—21no—
231#117—41no—
232SD32—24no—
233D16—22no—
234C2×C16C23×C10311yescharacteristic
235C2×C16C23×C10311yescharacteristic
236C2×C16C23×C10312yes—
237#107—21no—
238#107—22no—
239#107C23×C10311yescharacteristic
240#107C23×C10312yes—
241#107C23×C10311yescharacteristic
242C4⋊C8D4×C10311yescharacteristic
243C4⋊C8D4×C10312yes—
244#103—22no—
245#102—21no—
246#102—21no—
247#102—22no—
248C4×C8C23×C10311yescharacteristic
249C4×C8C23×C10312yes—
250C2×Q8—22no—
251C2×Q8—42no—
252C2×Q8—41no—
253C2×Q8—84no—
254C2×Q8D8×C10311yescharacteristic
255C2×D4—21no—
256C2×D4—21no—
257C22×C4—41no—
258C22×C4—42no—
259C22×C4—41no—
260Q16—22no—
261Q16—22no—
262Q16—81no—
263SD16—82no—
264D8—21no—
265D8—21no—
266D8—21no—
267D8#41×C10312yes—
268C2×C8C2×D4×C10311yescharacteristic
269C2×C8C2×D4×C10312yes—
270C2×C8C24×C10311yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—22no—
274C4⋊C4—41no—
275C4⋊C4—42no—
276C4⋊C4—42no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4D8×C10311yescharacteristic
280C4⋊C4D8×C10312yes—
281C22⋊C4—42no—
282C22⋊C4—42no—
283C22⋊C4—41no—
284C22⋊C4—41no—
285C22⋊C4—42no—
286C42—42no—
287C42C2×D4×C10311yescharacteristic
288C42C2×D4×C10312yes—
289C16—21no—
290C16—22no—
291C16—21no—
292C23—41no—
293C23—41no—
294Q8—22no—
295Q8—42no—
296Q8—42no—
297Q8—84no—
298Q8—82no—
299D4—22no—
300D4—41no—
301D4—41no—
302D4—41no—
303C2×C4—41no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—41no—
307C2×C4—84no—
308C2×C4—82no—
309C2×C4—82no—
310C2×C4C2×D8×C10312yes—
311C2×C4C2×D8×C10311yescharacteristic
312C2×C4C2×D8×C10312yes—
313C2×C4C2×D8×C10311yescharacteristic
314C2×C4C22×D4×C10311yescharacteristic
315C8—22no—
316C8—21no—
317C8C2×#41×C10311yescharacteristic
318C82−1+4×C10311yescharacteristic
319C22—42no—
320C22—81no—
321C22—81no—
322C22—81no—
323C22—81no—
324C22—81no—
325C22C22×D8×C10311yescharacteristic
326C4—22no—
327C4—22no—
328C4—21no—
329C4—82no—
330C4—82no—
331C4—81no—
332C4—81no—
333C4#509×C10312yes—
334C4#548×C10311yescharacteristic
335C4#577×C10311yescharacteristic
336C2—82no—
337C2—161no—
338C2C103×#335811yescharacteristic
339C2C2×#509×C10311yescharacteristic
340C2C103×#341711yescharacteristic
subgroupG/H
center, socleC22×C103C22×D8
commutator, Frattini, cosocleC2×C8C24×C103
prime radicalC2×D16×C103C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C103 ◁ C4×Q8×C103 ◁ C8×Q8×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C103×#3393C2semidirect
2. Q8×D8×C103C2semidirect
3. C103×#2243C2semidirect
4. C103×#2241C2semidirect
5. C103×#2227C2semidirect
6. C103×#2224C2semidirect
8. C103×#2208C2semidirect
9. C103×#2183C2semidirect
10. C103×#2175C2semidirect
165. #33934C103direct (N × H)
171. #3393C2×C103semidirect
172. Q8×D8C2×C103semidirect
173. #2243C2×C103semidirect
174. #2241C2×C103semidirect
175. #2227C2×C103semidirect
176. #2224C2×C103semidirect
178. #2208C2×C103semidirect
179. #2183C2×C103semidirect
180. #2175C2×C103semidirect
182. C103#33934direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#33932
Q8×D8×C1032
C103×#22432
C103×#22412
C103×#22272
C103×#22242
C103×#22102
C103×#22082
C103×#21832
C103×#21752
C4×D16×C1032
#33934103