Finite Group Databasebeta

← C103×#33818 #39939093

Subgroups — C103×#33818 #39939093

Order 26368.

490 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3170C211yesmaximal, characteristic, complemented
2C103×#3168C211yesmaximal, characteristic
3C103×#2229C212yesmaximal, complemented
4C103×#2227C211yesmaximal, characteristic, complemented
5C103×#2226C211yesmaximal, characteristic, complemented
6C103×#2220C212yesmaximal
7C103×#2219C212yesmaximal, complemented
8C103×#2211C212yesmaximal, complemented
9C103×#2209C211yesmaximal, characteristic, complemented
10C103×#2208C211yesmaximal, characteristic, complemented
11C103×#2150C211yesmaximal, characteristic, complemented
12#533×C103—21no—
13#529×C103—21no—
14C2×Q32×C103C2212yes—
15C2×SD32×C103C2212yes—
16C2×M32×C103C2212yes—
17#500×C103C2211yescharacteristic
18#499×C103C2211yescharacteristic
19#495×C103C2211yescharacteristic
20#494×C103C2211yescharacteristic
21#488×C103—21no—
22#487×C103—21no—
23#467×C103—21no—
24#467×C103C2211yescharacteristic
25#467×C103C2212yes—
26#466×C103C2211yescharacteristic
27#465×C103—21no—
28C4×Q16×C103—21no—
29C4×Q16×C103C2211yescharacteristic
30C4×Q16×C103C2212yes—
31C4×SD16×C103—21no—
32C4×D8×C103C2211yescharacteristic
33C2×C4×C8×C103C2211yescharacteristic
34#367×C103C2212yes—
35#366×C103C2212yes—
36C4⋊C16×C103C2211yescharacteristic
37C4⋊C16×C103C2211yescharacteristic
38C4⋊C16×C103C2212yes—
39#358×C103C2212yes—
40#358×C103C2212yes—
41#358×C103C2212yes—
42#357×C103C2212yes—
43C2×Q16×C103—21no—
44C2×Q16×C103C2312yes—
45C2×Q16×C103C2311yescharacteristic
46C2×SD16×C103—21no—
47C2×D8×C103C2311yescharacteristic
48C22×C8×C103D411yescharacteristic
49C22×C8×C103C2311yescharacteristic
50C4⋊Q8×C103—21no—
51C4⋊Q8×C103—21no—
52#126×C103—41no—
53#125×C103—21no—
54#125×C103—41no—
55#124×C103—21no—
56#123×C103—41no—
57C22⋊Q8×C103—21no—
58C22⋊Q8×C103—22no—
59C22⋊Q8×C103—41no—
60#121×C103—21no—
61C4×Q8×C103—21no—
62C4×Q8×C103—22no—
63C4×Q8×C103—41no—
64C4×D4×C103—21no—
65C4×D4×C103—41no—
66#117×C103—41no—
67#117×C103—41no—
68C2×C42×C103D411yescharacteristic
69Q32×C103—42no—
70SD32×C103—42no—
71M32×C103—42no—
72C2×C16×C103C2312yes—
73C2×C16×C103C2312yes—
74#107×C103—21no—
75#107×C103C2312yes—
76#107×C103C2311yescharacteristic
77#107×C103C2311yescharacteristic
78#106×C103—21no—
79#103×C103—21no—
80#103×C103—22no—
81#103×C103—21no—
82#103×C103—22no—
83#102×C103—21no—
84#102×C103—21no—
85C4×C8×C103D411yescharacteristic
86C4×C8×C103D411yescharacteristic
87C4×C8×C103C2311yescharacteristic
88C4×C8×C103C2311yescharacteristic
89C2×Q8×C103—21no—
90C2×Q8×C103—22no—
91C2×Q8×C103—41no—
92C2×D4×C103—21no—
93C2×D4×C103—41no—
94C22×C4×C103—41no—
95C22×C4×C103D811yescharacteristic
96C22×C4×C103D811yescharacteristic
97C22×C4×C103C2×D411yescharacteristic
98Q16×C103—22no—
99Q16×C103—21no—
100Q16×C103—22no—
101Q16×C103—21no—
102Q16×C103—42no—
103SD16×C103—42no—
104D8×C103—21no—
105D8×C103—21no—
106C2×C8×C103—21no—
107C2×C8×C103—21no—
108C2×C8×C103—41no—
109C2×C8×C103C2×D411yescharacteristic
110C2×C8×C103C2×D411yescharacteristic
111C2×C8×C103C2×D411yescharacteristic
112C2×C8×C103C2411yescharacteristic
113C4⋊C4×C103—21no—
114C4⋊C4×C103—21no—
115C4⋊C4×C103—22no—
116C4⋊C4×C103—41no—
117C4⋊C4×C103—41no—
118C4⋊C4×C103—41no—
119C4⋊C4×C103—41no—
120C4⋊C4×C103—41no—
121C4⋊C4×C103—42no—
122C4⋊C4×C103—41no—
123C4⋊C4×C103—42no—
124C4⋊C4×C103—41no—
125C22⋊C4×C103—42no—
126C22⋊C4×C103—41no—
127C22⋊C4×C103—41no—
128C22⋊C4×C103—41no—
129C22⋊C4×C103—41no—
130C22⋊C4×C103—41no—
131C42×C103—41no—
132C42×C103—42no—
133C42×C103D811yescharacteristic
134C42×C103D811yescharacteristic
135C42×C103C2×D411yescharacteristic
136C42×C103C2×D411yescharacteristic
137C16×C103—22no—
138C16×C103—22no—
139C23×C103—41no—
140C23×C103C2×D811yescharacteristic
141Q8×C103—42no—
142Q8×C103—41no—
143Q8×C103—41no—
144Q8×C103—42no—
145Q8×C103—82no—
146D4×C103—41no—
147D4×C103—41no—
148D4×C103—82no—
149C2×C4×C103—21no—
150C2×C4×C103—21no—
151C2×C4×C103—22no—
152C2×C4×C103—41no—
153C2×C4×C103—41no—
154C2×C4×C103—41no—
155C2×C4×C103—42no—
156C2×C4×C103—42no—
157C2×C4×C103—41no—
158C2×C4×C103—82no—
159C2×C4×C103C2×D811yescharacteristic
160C2×C4×C103C2×D811yescharacteristic
161C2×C4×C103C2×D811yescharacteristic
162C2×C4×C103C2×D811yescharacteristic
163C2×C4×C103C2×D811yescharacteristic
164C2×C4×C103C22×D411yescharacteristic
165C8×C103—21no—
166C8×C103—21no—
167C8×C103—21no—
168C8×C103H(5,𝔽2)11yescharacteristic
169C8×C1032−1+411yescharacteristic
170C22×C103—21no—
171C22×C103—21no—
172C22×C103—21no—
173C22×C103—81no—
174C22×C103—81no—
175C22×C103—81no—
176C22×C103C22×D811yescharacteristic
177C4×C103—21no—
178C4×C103—21no—
179C4×C103—21no—
180C4×C103—21no—
181C4×C103—81no—
182C4×C103—81no—
183C4×C103—82no—
184C4×C103—81no—
185C4×C103—82no—
186C4×C103#51012yes—
187C4×C103#53711yescharacteristic
188C4×C103#57511yescharacteristic
189#33818C10311yesmaximal, characteristic, direct product factor, Sylow
190C2×C103—41no—
191C2×C103—161no—
192C2×C103#324511yescharacteristic
193C2×C103C2×#51011yescharacteristic
194C2×C103#341411yescharacteristic
195#3170C2×C10311yescharacteristic, complemented
196#3168C2×C10311yescharacteristic
197#2229C2×C10312yescomplemented
198#2227C2×C10311yescharacteristic, complemented
199#2226C2×C10311yescharacteristic, complemented
200#2220C2×C10312yes—
201#2219C2×C10312yescomplemented
202#2211C2×C10312yescomplemented
203#2209C2×C10311yescharacteristic, complemented
204#2208C2×C10311yescharacteristic, complemented
205#2150C2×C10311yescharacteristic, complemented
206C103#3381811yescharacteristic, direct product factor, Sylow
207#533—21no—
208#529—21no—
209C2×Q32C22×C10312yes—
210C2×SD32C22×C10312yes—
211C2×M32C22×C10312yes—
212#500C22×C10311yescharacteristic
213#499C22×C10311yescharacteristic
214#495C22×C10311yescharacteristic
215#494C22×C10311yescharacteristic
216#488—21no—
217#487—21no—
218#467—21no—
219#467C22×C10311yescharacteristic
220#467C22×C10312yes—
221#466C22×C10311yescharacteristic
222#465—21no—
223C4×Q16—21no—
224C4×Q16C22×C10311yescharacteristic
225C4×Q16C22×C10312yes—
226C4×SD16—21no—
227C4×D8C22×C10311yescharacteristic
228C2×C4×C8C22×C10311yescharacteristic
229#367C22×C10312yes—
230#366C22×C10312yes—
231C4⋊C16C22×C10311yescharacteristic
232C4⋊C16C22×C10311yescharacteristic
233C4⋊C16C22×C10312yes—
234#358C22×C10312yes—
235#358C22×C10312yes—
236#358C22×C10312yes—
237#357C22×C10312yes—
238C2×Q16—21no—
239C2×Q16C23×C10312yes—
240C2×Q16C23×C10311yescharacteristic
241C2×SD16—21no—
242C2×D8C23×C10311yescharacteristic
243C22×C8D4×C10311yescharacteristic
244C22×C8C23×C10311yescharacteristic
245C4⋊Q8—21no—
246C4⋊Q8—21no—
247#126—41no—
248#125—21no—
249#125—41no—
250#124—21no—
251#123—41no—
252C22⋊Q8—21no—
253C22⋊Q8—22no—
254C22⋊Q8—41no—
255#121—21no—
256C4×Q8—21no—
257C4×Q8—22no—
258C4×Q8—41no—
259C4×D4—21no—
260C4×D4—41no—
261#117—41no—
262#117—41no—
263C2×C42D4×C10311yescharacteristic
264Q32—42no—
265SD32—42no—
266M32—42no—
267C2×C16C23×C10312yes—
268C2×C16C23×C10312yes—
269#107—21no—
270#107C23×C10312yes—
271#107C23×C10311yescharacteristic
272#107C23×C10311yescharacteristic
273#106—21no—
274#103—21no—
275#103—22no—
276#103—21no—
277#103—22no—
278#102—21no—
279#102—21no—
280C4×C8D4×C10311yescharacteristic
281C4×C8D4×C10311yescharacteristic
282C4×C8C23×C10311yescharacteristic
283C4×C8C23×C10311yescharacteristic
284C2×Q8—21no—
285C2×Q8—22no—
286C2×Q8—41no—
287C2×D4—21no—
288C2×D4—41no—
289C22×C4—41no—
290C22×C4D8×C10311yescharacteristic
291C22×C4D8×C10311yescharacteristic
292C22×C4C2×D4×C10311yescharacteristic
293Q16—22no—
294Q16—21no—
295Q16—22no—
296Q16—21no—
297Q16—42no—
298SD16—42no—
299D8—21no—
300D8—21no—
301C2×C8—21no—
302C2×C8—21no—
303C2×C8—41no—
304C2×C8C2×D4×C10311yescharacteristic
305C2×C8C2×D4×C10311yescharacteristic
306C2×C8C2×D4×C10311yescharacteristic
307C2×C8C24×C10311yescharacteristic
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—22no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—42no—
317C4⋊C4—41no—
318C4⋊C4—42no—
319C4⋊C4—41no—
320C22⋊C4—42no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—41no—
326C42—41no—
327C42—42no—
328C42D8×C10311yescharacteristic
329C42D8×C10311yescharacteristic
330C42C2×D4×C10311yescharacteristic
331C42C2×D4×C10311yescharacteristic
332C16—22no—
333C16—22no—
334C23—41no—
335C23C2×D8×C10311yescharacteristic
336Q8—42no—
337Q8—41no—
338Q8—41no—
339Q8—42no—
340Q8—82no—
341D4—41no—
342D4—41no—
343D4—82no—
344C2×C4—22no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—41no—
353C2×C4—82no—
354C2×C4C2×D8×C10311yescharacteristic
355C2×C4C2×D8×C10311yescharacteristic
356C2×C4C2×D8×C10311yescharacteristic
357C2×C4C2×D8×C10311yescharacteristic
358C2×C4C2×D8×C10311yescharacteristic
359C2×C4C22×D4×C10311yescharacteristic
360C8—21no—
361C8—21no—
362C8—21no—
363C8H(5,𝔽2)×C10311yescharacteristic
364C82−1+4×C10311yescharacteristic
365C22—21no—
366C22—21no—
367C22—21no—
368C22—81no—
369C22—81no—
370C22—81no—
371C22C22×D8×C10311yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—81no—
377C4—82no—
378C4—81no—
379C4—81no—
380C4—82no—
381C4#510×C10312yes—
382C4#537×C10311yescharacteristic
383C4#575×C10311yescharacteristic
384C2—41no—
385C2—161no—
386C2C103×#324511yescharacteristic
387C2C2×#510×C10311yescharacteristic
388C2C103×#341411yescharacteristic
subgroupG/H
center, socleC22×C103C22×D8
commutator, Frattini, cosocleC2×C8C24×C103
prime radical#466×C103C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C103 ◁ C2×C42×C103 ◁ C2×C4×C8×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C103×#3170C2semidirect
3. C103×#2229C2semidirect
4. C103×#2227C2semidirect
5. C103×#2226C2semidirect
7. C103×#2219C2semidirect
8. C103×#2211C2semidirect
9. C103×#2209C2semidirect
10. C103×#2208C2semidirect
11. C103×#2150C2semidirect
189. #33818C103direct (N × H)
195. #3170C2×C103semidirect
197. #2229C2×C103semidirect
198. #2227C2×C103semidirect
199. #2226C2×C103semidirect
201. #2219C2×C103semidirect
202. #2211C2×C103semidirect
203. #2209C2×C103semidirect
204. #2208C2×C103semidirect
205. #2150C2×C103semidirect
206. C103#33818direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#31702
C103×#31682
C103×#22292
C103×#22272
C103×#22262
C103×#22202
C103×#22192
C103×#22112
C103×#22092
C103×#22082
C103×#21502
#33818103