Finite Group Databasebeta

← C103×#10151 #39915426

Subgroups — C103×#10151 #39915426

Order 26368.

544 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3229C211yesmaximal, characteristic, complemented
2C103×#3138C211yesmaximal, characteristic
3C2×#486×C103C211yesmaximal, characteristic
4C103×#1966C211yesmaximal, characteristic, complemented
5C103×#1545C211yesmaximal, characteristic
6C103×#1493C211yesmaximal, characteristic, complemented
7C103×#1278C211yesmaximal, characteristic, complemented
8#533×C103C2211yescharacteristic
9C2×C4⋊Q8×C103C2211yescharacteristic
10C2×#127×C103C2211yescharacteristic
11#498×C103—21no—
12#490×C103—22no—
13#487×C103—21no—
14#486×C103—21no—
15#486×C103—21no—
16#486×C103—22no—
17#486×C103—22no—
18#483×C103—22no—
19#475×C103—22no—
20#431×C103C2211yescharacteristic
21#423×C103C2211yescharacteristic
22#418×C103—22no—
23C2×#102×C103—22no—
24C2×#101×C103—22no—
25C4×M16×C103C2211yescharacteristic
26C2×C4×C8×C103C2211yescharacteristic
27#331×C103—22no—
28Q8⋊C8×C103—22no—
29C22×Q8×C103—21no—
30C22×D4×C103—21no—
31C22×D4×C103—21no—
32C22×D4×C103—21no—
33C2×M16×C103—21no—
34C2×M16×C103D412yes—
35C22×C8×C103—21no—
36C4⋊Q8×C103—21no—
37C4⋊Q8×C103—21no—
38C4⋊Q8×C103—21no—
39C4⋊Q8×C103—21no—
40C4⋊Q8×C103D411yescharacteristic
41C4⋊Q8×C103D411yescharacteristic
42#127×C103—21no—
43#127×C103—21no—
44#127×C103—21no—
45#127×C103D412yes—
46#125×C103—21no—
47C22⋊Q8×C103—21no—
48C22⋊Q8×C103—21no—
49C4×Q8×C103—21no—
50C4×Q8×C103—21no—
51#117×C103—21no—
52C2×C4⋊C4×C103—21no—
53C2×C4⋊C4×C103D412yes—
54C2×C42×C103C2311yescharacteristic
55#106×C103—24no—
56C4⋊C8×C103—21no—
57C4⋊C8×C103—21no—
58C4⋊C8×C103D412yes—
59#103×C103—24no—
60#102×C103—28no—
61#102×C103—24no—
62#102×C103—24no—
63#101×C103—44no—
64C22⋊C8×C103—21no—
65#97×C103—21no—
66C4×C8×C103—21no—
67C4×C8×C103—21no—
68C4×C8×C103—21no—
69C4×C8×C103D412yes—
70C24×C103—41no—
71C2×Q8×C103—21no—
72C2×Q8×C103—21no—
73C2×Q8×C103—41no—
74C2×Q8×C103—41no—
75C2×Q8×C103—42no—
76C2×Q8×C103—42no—
77C2×D4×C103—22no—
78C2×D4×C103—22no—
79C2×D4×C103—22no—
80C2×D4×C103—44no—
81C2×D4×C103—41no—
82C2×D4×C103—41no—
83C2×D4×C103—41no—
84C2×D4×C103—42no—
85C2×D4×C103—42no—
86C2×D4×C103—82no—
87C22×C4×C103—22no—
88C22×C4×C103C2×D411yescharacteristic
89C22×C4×C103C2×D411yescharacteristic
90C22×C4×C103#4111yescharacteristic
91M16×C103—22no—
92M16×C103—22no—
93M16×C103—42no—
94C2×C8×C103—22no—
95C2×C8×C103—22no—
96C2×C8×C103—22no—
97C2×C8×C103—42no—
98C2×C8×C103—41no—
99C4⋊C4×C103—22no—
100C4⋊C4×C103—21no—
101C4⋊C4×C103—21no—
102C4⋊C4×C103—22no—
103C4⋊C4×C103—21no—
104C4⋊C4×C103—21no—
105C4⋊C4×C103—41no—
106C4⋊C4×C103—41no—
107C4⋊C4×C103—41no—
108C4⋊C4×C103—41no—
109C22⋊C4×C103—41no—
110C42×C103—41no—
111C42×C103C2×D411yescharacteristic
112C42×C103C2×D411yescharacteristic
113C42×C103C2×D411yescharacteristic
114C42×C103C2×D411yescharacteristic
115C23×C103—42no—
116C23×C103—82no—
117C23×C103—82no—
118C23×C103—82no—
119C23×C103#12111yescharacteristic
120Q8×C103—42no—
121Q8×C103—42no—
122Q8×C103—82no—
123Q8×C103—81no—
124Q8×C103—81no—
125D4×C103—44no—
126D4×C103—44no—
127D4×C103—82no—
128D4×C103—82no—
129D4×C103—82no—
130D4×C103—81no—
131D4×C103—81no—
132C2×C4×C103—22no—
133C2×C4×C103—22no—
134C2×C4×C103—41no—
135C2×C4×C103—41no—
136C2×C4×C103—42no—
137C2×C4×C103—44no—
138C2×C4×C103#12011yescharacteristic
139C2×C4×C103#12011yescharacteristic
140C2×C4×C103#12011yescharacteristic
141C2×C4×C103#12111yescharacteristic
142C2×C4×C103#12111yescharacteristic
143C2×C4×C103#12711yescharacteristic
144C2×C4×C103#13512yes—
145C2×C4×C103AGL(1,ℤ/8)12yes—
146C8×C103—42no—
147C8×C103—42no—
148C8×C103—42no—
149C8×C103—81no—
150C22×C103—21no—
151C22×C103—21no—
152C22×C103—82no—
153C22×C103—82no—
154C22×C103—82no—
155C22×C103—164no—
156C22×C103#39211yescharacteristic
157C22×C103#46312yes—
158C4×C103—21no—
159C4×C103—21no—
160C4×C103—81no—
161C4×C103—82no—
162C4×C103—81no—
163C4×C103#44912yes—
164C4×C103#45412yes—
165C4×C103#47112yes—
166C4×C103#49511yescharacteristic
167C4×C103#49611yescharacteristic
168#10151C10311yesmaximal, characteristic, direct product factor, Sylow
169C2×C103—22no—
170C2×C103—162no—
171C2×C103#200311yescharacteristic
172C2×C103#201211yescharacteristic
173C2×C103#201911yescharacteristic
174#3229C2×C10311yescharacteristic, complemented
175#3138C2×C10311yescharacteristic
176C2×#486C2×C10311yescharacteristic
177#1966C2×C10311yescharacteristic, complemented
178#1545C2×C10311yescharacteristic
179#1493C2×C10311yescharacteristic, complemented
180#1278C2×C10311yescharacteristic, complemented
181C103#1015111yescharacteristic, direct product factor, Sylow
182#533C22×C10311yescharacteristic
183C2×C4⋊Q8C22×C10311yescharacteristic
184C2×#127C22×C10311yescharacteristic
185#498—21no—
186#490—22no—
187#487—21no—
188#486—21no—
189#486—21no—
190#486—22no—
191#486—22no—
192#483—22no—
193#475—22no—
194#431C22×C10311yescharacteristic
195#423C22×C10311yescharacteristic
196#418—22no—
197C2×#102—22no—
198C2×#101—22no—
199C4×M16C22×C10311yescharacteristic
200C2×C4×C8C22×C10311yescharacteristic
201#331—22no—
202Q8⋊C8—22no—
203C22×Q8—21no—
204C22×D4—21no—
205C22×D4—21no—
206C22×D4—21no—
207C2×M16—21no—
208C2×M16D4×C10312yes—
209C22×C8—21no—
210C4⋊Q8—21no—
211C4⋊Q8—21no—
212C4⋊Q8—21no—
213C4⋊Q8—21no—
214C4⋊Q8D4×C10311yescharacteristic
215C4⋊Q8D4×C10311yescharacteristic
216#127—21no—
217#127—21no—
218#127—21no—
219#127D4×C10312yes—
220#125—21no—
221C22⋊Q8—21no—
222C22⋊Q8—21no—
223C4×Q8—21no—
224C4×Q8—21no—
225#117—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4D4×C10312yes—
228C2×C42C23×C10311yescharacteristic
229#106—24no—
230C4⋊C8—21no—
231C4⋊C8—21no—
232C4⋊C8D4×C10312yes—
233#103—24no—
234#102—28no—
235#102—24no—
236#102—24no—
237#101—44no—
238C22⋊C8—21no—
239#97—21no—
240C4×C8—21no—
241C4×C8—21no—
242C4×C8—21no—
243C4×C8D4×C10312yes—
244C24—41no—
245C2×Q8—21no—
246C2×Q8—21no—
247C2×Q8—41no—
248C2×Q8—41no—
249C2×Q8—42no—
250C2×Q8—42no—
251C2×D4—22no—
252C2×D4—22no—
253C2×D4—22no—
254C2×D4—44no—
255C2×D4—41no—
256C2×D4—41no—
257C2×D4—41no—
258C2×D4—42no—
259C2×D4—42no—
260C2×D4—82no—
261C22×C4—22no—
262C22×C4C2×D4×C10311yescharacteristic
263C22×C4C2×D4×C10311yescharacteristic
264C22×C4#41×C10311yescharacteristic
265M16—22no—
266M16—22no—
267M16—42no—
268C2×C8—22no—
269C2×C8—22no—
270C2×C8—22no—
271C2×C8—42no—
272C2×C8—41no—
273C4⋊C4—22no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—22no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C22⋊C4—41no—
284C42—41no—
285C42C2×D4×C10311yescharacteristic
286C42C2×D4×C10311yescharacteristic
287C42C2×D4×C10311yescharacteristic
288C42C2×D4×C10311yescharacteristic
289C23—42no—
290C23—82no—
291C23—82no—
292C23—82no—
293C23#121×C10311yescharacteristic
294Q8—42no—
295Q8—42no—
296Q8—82no—
297Q8—81no—
298Q8—81no—
299D4—44no—
300D4—44no—
301D4—82no—
302D4—82no—
303D4—82no—
304D4—81no—
305D4—81no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—44no—
312C2×C4#120×C10311yescharacteristic
313C2×C4#120×C10311yescharacteristic
314C2×C4#120×C10311yescharacteristic
315C2×C4#121×C10311yescharacteristic
316C2×C4#121×C10311yescharacteristic
317C2×C4#127×C10311yescharacteristic
318C2×C4#135×C10312yes—
319C2×C4AGL(1,ℤ/8)×C10312yes—
320C8—42no—
321C8—42no—
322C8—42no—
323C8—81no—
324C22—21no—
325C22—21no—
326C22—82no—
327C22—82no—
328C22—82no—
329C22—164no—
330C22#392×C10311yescharacteristic
331C22#463×C10312yes—
332C4—21no—
333C4—21no—
334C4—81no—
335C4—82no—
336C4—81no—
337C4#449×C10312yes—
338C4#454×C10312yes—
339C4#471×C10312yes—
340C4#495×C10311yescharacteristic
341C4#496×C10311yescharacteristic
342C2—22no—
343C2—162no—
344C2C103×#200311yescharacteristic
345C2C103×#201211yescharacteristic
346C2C103×#201911yescharacteristic
subgroupG/H
center, socleC22×C103#392
commutator, Frattini, cosocleC2×C42C23×C103
prime radicalC2×#127×C103C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C103 ◁ C2×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C103×#3229C2semidirect
4. C103×#1966C2semidirect
6. C103×#1493C2semidirect
7. C103×#1278C2semidirect
168. #10151C103direct (N × H)
174. #3229C2×C103semidirect
177. #1966C2×C103semidirect
179. #1493C2×C103semidirect
180. #1278C2×C103semidirect
181. C103#10151direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#32292
C103×#31382
C2×#486×C1032
C103×#19662
C103×#15452
C103×#14932
C103×#12782
#10151103