Finite Group Databasebeta

← C103×#26925 #39932200

Subgroups — C103×#26925 #39932200

Order 26368.

714 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3082C212yesmaximal
2C103×#2950C212yesmaximal
3C103×#2047C212yesmaximal
4C103×#2028C211yesmaximal, characteristic
5C103×#2016C211yesmaximal, characteristic
6C103×#1930C212yesmaximal
7C103×#1922C212yesmaximal
8C103×#1886C212yesmaximal
9C103×#1857C211yesmaximal, characteristic
10C22×Q16×C103C2212yes—
11#544×C103C2211yescharacteristic
12C2×C4⋊Q8×C103C2211yescharacteristic
13#519×C103C2212yes—
14#519×C103C2211yescharacteristic
15#479×C103—22no—
16#479×C103—22no—
17#477×C103—22no—
18#475×C103—22no—
19#441×C103—22no—
20#441×C103—22no—
21C4×Q16×C103—22no—
22C4×Q16×C103—22no—
23#428×C103C2212yes—
24#427×C103C2212yes—
25#424×C103C2212yes—
26#419×C103C2212yes—
27#419×C103C2212yes—
28#419×C103C2212yes—
29C2×#103×C103C2212yes—
30C2×#101×C103C2212yes—
31C2×#101×C103C2211yescharacteristic
32#405×C103C2212yes—
33#391×C103C2211yescharacteristic
34#343×C103C2211yescharacteristic
35#341×C103C2212yes—
36#339×C103C2212yes—
37#339×C103C2212yes—
38#336×C103C2211yescharacteristic
39C22×Q8×C103C2311yescharacteristic
40C22×Q8×C103C2312yes—
41C2×Q16×C103—24no—
42C2×Q16×C103—24no—
43C2×Q16×C103—22no—
44C2×Q16×C103—22no—
45C2×M16×C103C2312yes—
46C2×M16×C103C2312yes—
47C22×C8×C103C2312yes—
48C4⋊Q8×C103—22no—
49C4⋊Q8×C103—24no—
50#125×C103—22no—
51C22⋊Q8×C103—41no—
52C4×Q8×C103—22no—
53C4×Q8×C103—22no—
54C4×Q8×C103—22no—
55C4×Q8×C103—22no—
56C4×Q8×C103—22no—
57C4×Q8×C103—22no—
58#117×C103—41no—
59#117×C103—42no—
60#117×C103C2312yes—
61#117×C103C2312yes—
62C2×C4⋊C4×C103—41no—
63C2×C4⋊C4×C103C2311yescharacteristic
64C2×C42×C103C2311yescharacteristic
65#107×C103—22no—
66#107×C103D412yes—
67#107×C103D412yes—
68#106×C103—22no—
69#106×C103D412yes—
70#106×C103D412yes—
71C4⋊C8×C103—22no—
72C4⋊C8×C103—22no—
73#103×C103—22no—
74#103×C103—22no—
75#103×C103—22no—
76#103×C103—22no—
77#103×C103—22no—
78#103×C103—22no—
79#103×C103—22no—
80#103×C103—22no—
81#101×C103—24no—
82#101×C103—22no—
83#97×C103—22no—
84C4×C8×C103—22no—
85#95×C103—41no—
86C2×Q8×C103—22no—
87C2×Q8×C103—21no—
88C2×Q8×C103—22no—
89C2×Q8×C103—22no—
90C2×Q8×C103—22no—
91C2×Q8×C103—22no—
92C2×Q8×C103—22no—
93C2×Q8×C103—22no—
94C2×Q8×C103—41no—
95C2×Q8×C103#4114yes—
96C2×Q8×C103#4112yes—
97C22×C4×C103—21no—
98C22×C4×C103—21no—
99C22×C4×C103—22no—
100C22×C4×C103—21no—
101C22×C4×C103C2411yescharacteristic
102Q16×C103—28no—
103Q16×C103—28no—
104M16×C103—22no—
105M16×C103—22no—
106M16×C103—22no—
107M16×C103—22no—
108C2×C8×C103—22no—
109C2×C8×C103—22no—
110C2×C8×C103—22no—
111C2×C8×C103—22no—
112C2×C8×C103C2×D412yes—
113C2×C8×C103C2×D412yes—
114C4⋊C4×C103—22no—
115C4⋊C4×C103—44no—
116C4⋊C4×C103—41no—
117C4⋊C4×C103—41no—
118C4⋊C4×C103—42no—
119C4⋊C4×C103—42no—
120C4⋊C4×C103—41no—
121C4⋊C4×C103—42no—
122C4⋊C4×C103C2×D412yes—
123C4⋊C4×C103C2×D412yes—
124C4⋊C4×C103C2×D412yes—
125C4⋊C4×C103C2×D412yes—
126C22⋊C4×C103—22no—
127C22⋊C4×C103—22no—
128C42×C103—22no—
129C42×C103—22no—
130C42×C103—22no—
131C42×C103—42no—
132C42×C103—42no—
133C42×C103—42no—
134C23×C103H(5,𝔽2)11yescharacteristic
135Q8×C103—24no—
136Q8×C103—24no—
137Q8×C103—24no—
138Q8×C103—42no—
139Q8×C103—42no—
140Q8×C103—42no—
141Q8×C103—161no—
142C2×C4×C103—22no—
143C2×C4×C103—22no—
144C2×C4×C103—22no—
145C2×C4×C103—22no—
146C2×C4×C103—22no—
147C2×C4×C103—22no—
148C2×C4×C103—24no—
149C2×C4×C103—41no—
150C2×C4×C103—42no—
151C2×C4×C103—41no—
152C2×C4×C103—42no—
153C2×C4×C103—41no—
154C2×C4×C103—41no—
155C2×C4×C103—41no—
156C2×C4×C103—81no—
157C2×C4×C103C22×D412yes—
158C2×C4×C103C2×#4111yescharacteristic
159C2×C4×C103C2×#4112yes—
160C2×C4×C1032−1+411yescharacteristic
161C8×C103—22no—
162C8×C103—22no—
163C8×C103—42no—
164C8×C103—42no—
165C22×C103—21no—
166C22×C103—21no—
167C22×C103#53911yescharacteristic
168C22×C103D4211yescharacteristic
169C22×C103#55111yescharacteristic
170C4×C103—42no—
171C4×C103—42no—
172C4×C103—44no—
173C4×C103—42no—
174C4×C103—42no—
175C4×C103—42no—
176C4×C103—42no—
177C4×C103—81no—
178C4×C103#52512yes—
179C4×C103#54812yes—
180#26925C10311yesmaximal, characteristic, direct product factor, Sylow
181C2×C103—21no—
182C2×C103—21no—
183C2×C103#246311yescharacteristic
184C2×C103#328911yescharacteristic
185C2×C103#329311yescharacteristic
186#3082C2×C10312yes—
187#2950C2×C10312yes—
188#2047C2×C10312yes—
189#2028C2×C10311yescharacteristic
190#2016C2×C10311yescharacteristic
191#1930C2×C10312yes—
192#1922C2×C10312yes—
193#1886C2×C10312yes—
194#1857C2×C10311yescharacteristic
195C103#2692511yescharacteristic, direct product factor, Sylow
196C22×Q16C22×C10312yes—
197#544C22×C10311yescharacteristic
198C2×C4⋊Q8C22×C10311yescharacteristic
199#519C22×C10312yes—
200#519C22×C10311yescharacteristic
201#479—22no—
202#479—22no—
203#477—22no—
204#475—22no—
205#441—22no—
206#441—22no—
207C4×Q16—22no—
208C4×Q16—22no—
209#428C22×C10312yes—
210#427C22×C10312yes—
211#424C22×C10312yes—
212#419C22×C10312yes—
213#419C22×C10312yes—
214#419C22×C10312yes—
215C2×#103C22×C10312yes—
216C2×#101C22×C10311yescharacteristic
217C2×#101C22×C10312yes—
218#405C22×C10312yes—
219#391C22×C10311yescharacteristic
220#343C22×C10311yescharacteristic
221#341C22×C10312yes—
222#339C22×C10312yes—
223#339C22×C10312yes—
224#336C22×C10311yescharacteristic
225C22×Q8C23×C10312yes—
226C22×Q8C23×C10311yescharacteristic
227C2×Q16—24no—
228C2×Q16—24no—
229C2×Q16—22no—
230C2×Q16—22no—
231C2×M16C23×C10312yes—
232C2×M16C23×C10312yes—
233C22×C8C23×C10312yes—
234C4⋊Q8—22no—
235C4⋊Q8—24no—
236#125—22no—
237C22⋊Q8—41no—
238C4×Q8—22no—
239C4×Q8—22no—
240C4×Q8—22no—
241C4×Q8—22no—
242C4×Q8—22no—
243C4×Q8—22no—
244#117—41no—
245#117—42no—
246#117C23×C10312yes—
247#117C23×C10312yes—
248C2×C4⋊C4—41no—
249C2×C4⋊C4C23×C10311yescharacteristic
250C2×C42C23×C10311yescharacteristic
251#107—22no—
252#107D4×C10312yes—
253#107D4×C10312yes—
254#106—22no—
255#106D4×C10312yes—
256#106D4×C10312yes—
257C4⋊C8—22no—
258C4⋊C8—22no—
259#103—22no—
260#103—22no—
261#103—22no—
262#103—22no—
263#103—22no—
264#103—22no—
265#103—22no—
266#103—22no—
267#101—24no—
268#101—22no—
269#97—22no—
270C4×C8—22no—
271#95—41no—
272C2×Q8—22no—
273C2×Q8—21no—
274C2×Q8—22no—
275C2×Q8—22no—
276C2×Q8—22no—
277C2×Q8—22no—
278C2×Q8—22no—
279C2×Q8—22no—
280C2×Q8—41no—
281C2×Q8#41×C10314yes—
282C2×Q8#41×C10312yes—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—22no—
286C22×C4—21no—
287C22×C4C24×C10311yescharacteristic
288Q16—28no—
289Q16—28no—
290M16—22no—
291M16—22no—
292M16—22no—
293M16—22no—
294C2×C8—22no—
295C2×C8—22no—
296C2×C8—22no—
297C2×C8—22no—
298C2×C8C2×D4×C10312yes—
299C2×C8C2×D4×C10312yes—
300C4⋊C4—22no—
301C4⋊C4—44no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—42no—
305C4⋊C4—42no—
306C4⋊C4—41no—
307C4⋊C4—42no—
308C4⋊C4C2×D4×C10312yes—
309C4⋊C4C2×D4×C10312yes—
310C4⋊C4C2×D4×C10312yes—
311C4⋊C4C2×D4×C10312yes—
312C22⋊C4—22no—
313C22⋊C4—22no—
314C42—22no—
315C42—22no—
316C42—22no—
317C42—42no—
318C42—42no—
319C42—42no—
320C23H(5,𝔽2)×C10311yescharacteristic
321Q8—24no—
322Q8—24no—
323Q8—24no—
324Q8—42no—
325Q8—42no—
326Q8—42no—
327Q8—161no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—24no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—81no—
343C2×C4C22×D4×C10312yes—
344C2×C4C2×#41×C10311yescharacteristic
345C2×C4C2×#41×C10312yes—
346C2×C42−1+4×C10311yescharacteristic
347C8—22no—
348C8—22no—
349C8—42no—
350C8—42no—
351C22—21no—
352C22—21no—
353C22#539×C10311yescharacteristic
354C22D42×C10311yescharacteristic
355C22#551×C10311yescharacteristic
356C4—42no—
357C4—42no—
358C4—44no—
359C4—42no—
360C4—42no—
361C4—42no—
362C4—42no—
363C4—81no—
364C4#525×C10312yes—
365C4#548×C10312yes—
366C2—21no—
367C2—21no—
368C2C103×#246311yescharacteristic
369C2C103×#328911yescharacteristic
370C2C103×#329311yescharacteristic
subgroupG/H
center, socleC22×C103D42
commutator, Frattini, cosocleC22×C4C24×C103
prime radicalC23×C103H(5,𝔽2)
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C103 ◁ C22×C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
180. #26925C103direct (N × H)
195. C103#26925direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#30822
C103×#29502
C103×#20472
C103×#20282
C103×#20162
C103×#19302
C103×#19222
C103×#18862
C103×#18572
#26925103