Finite Group Databasebeta

← C103×#18402 #39923677

Subgroups — C103×#18402 #39923677

Order 26368.

1174 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3497C211yesmaximal, characteristic
2C103×#3206C212yesmaximal, complemented
3C103×#2567C211yesmaximal, characteristic, complemented
4C103×#1604C218yesmaximal, complemented
5C103×#1502C212yesmaximal, complemented
6C103×#1461C211yesmaximal, characteristic, complemented
7C2×2−1+4×C103—21no—
8#550×C103—22no—
9D4×Q8×C103—22no—
10#548×C103—24no—
11#537×C103—21no—
12#537×C103C2214yes—
13#532×C103—22no—
14#532×C103C2212yes—
15C2×C4⋊Q8×C103C2211yescharacteristic
16C2×C4×Q8×C103C2211yescharacteristic
17#492×C103—22no—
18#487×C103—22no—
19#461×C103—24no—
20#448×C103C2218yes—
21#431×C103C2212yes—
22#395×C103C2214yes—
23#391×C103—21no—
24#389×C103—22no—
25#384×C103—21no—
26C4×C4⋊C4×C103C2211yescharacteristic
27#327×C103C2218yes—
28#324×C103C2214yes—
292−1+4×C103—44no—
302−1+4×C103—44no—
31C2×#41×C103—24no—
32C2×#41×C103—24no—
33C2×#41×C103—22no—
34C22×Q8×C103—24no—
35C22×Q8×C103D411yescharacteristic
36C22×Q8×C103C2312yes—
37C2×SD16×C103—28no—
38C4⋊Q8×C103—22no—
39C4⋊Q8×C103—22no—
40C4⋊Q8×C103—22no—
41C4⋊Q8×C103D412yes—
42#127×C103—22no—
43#127×C103D412yes—
44#124×C103—24no—
45#124×C103—22no—
46C22⋊Q8×C103—24no—
47C22⋊Q8×C103—28no—
48#121×C103—24no—
49#121×C103—28no—
50#121×C103—22no—
51#121×C103—24no—
52#121×C103C2314yes—
53C4×Q8×C103—22no—
54C4×Q8×C103—22no—
55C4×D4×C103—24no—
56C4×D4×C103—24no—
57C4×D4×C103—22no—
58C4×D4×C103D414yes—
59C2×C4⋊C4×C103—21no—
60C2×C4⋊C4×C103—21no—
61C2×C4⋊C4×C103—21no—
62C2×C4⋊C4×C103—24no—
63C2×C4⋊C4×C103D411yescharacteristic
64C2×C4⋊C4×C103C2312yes—
65C2×C42×C103—21no—
66C2×C42×C103D412yes—
67C2×C42×C103C2311yescharacteristic
68C4⋊C8×C103—22no—
69#103×C103—28no—
70C22⋊C8×C103C2314yes—
71C4×C8×C103—22no—
72#95×C103—24no—
73#95×C103C2312yes—
74#41×C103—48no—
75#41×C103—416no—
76#41×C103—48no—
77#41×C103—44no—
78#41×C103—44no—
79C2×Q8×C103—24no—
80C2×Q8×C103—22no—
81C2×Q8×C103—22no—
82C2×Q8×C103—22no—
83C2×Q8×C103—24no—
84C2×Q8×C103—416no—
85C2×Q8×C103—82no—
86C2×Q8×C103SD1614yescomplemented
87C2×D4×C103—24no—
88C2×D4×C103—24no—
89C2×D4×C103—24no—
90C2×D4×C103—22no—
91C2×D4×C103—22no—
92C2×D4×C103C2×D414yes—
93C22×C4×C103—28no—
94C22×C4×C103—22no—
95C22×C4×C103—24no—
96C22×C4×C103—22no—
97C22×C4×C103C2×D411yescharacteristic
98C22×C4×C103C2×D412yes—
99C22×C4×C103C2×D412yes—
100C22×C4×C103C2×D411yescharacteristic
101C22×C4×C103C2411yescharacteristic
102SD16×C103—88no—
103C2×C8×C103—24no—
104C4⋊C4×C103—24no—
105C4⋊C4×C103—24no—
106C4⋊C4×C103—22no—
107C4⋊C4×C103—22no—
108C4⋊C4×C103—24no—
109C4⋊C4×C103—41no—
110C4⋊C4×C103—42no—
111C4⋊C4×C103—41no—
112C4⋊C4×C103—84no—
113C4⋊C4×C103C2×D414yes—
114C22⋊C4×C103—28no—
115C22⋊C4×C103—24no—
116C22⋊C4×C103—24no—
117C42×C103—22no—
118C42×C103—22no—
119C42×C103—42no—
120C42×C103C2×D412yes—
121C42×C103C2×D412yes—
122C23×C103—24no—
123C23×C103C22×D411yescharacteristic
124Q8×C103—28no—
125Q8×C103—48no—
126Q8×C103—48no—
127Q8×C103—44no—
128D4×C103—44no—
129D4×C103—48no—
130D4×C103—44no—
131D4×C103—44no—
132D4×C103—44no—
133D4×C103—44no—
134D4×C103—84no—
135C2×C4×C103—22no—
136C2×C4×C103—22no—
137C2×C4×C103—22no—
138C2×C4×C103—24no—
139C2×C4×C103—22no—
140C2×C4×C103—24no—
141C2×C4×C103—41no—
142C2×C4×C103—416no—
143C2×C4×C103—42no—
144C2×C4×C103—42no—
145C2×C4×C103—48no—
146C2×C4×C103—42no—
147C2×C4×C103—44no—
148C2×C4×C103—42no—
149C2×C4×C103#12011yescharacteristic
150C2×C4×C103#12012yes—
151C2×C4×C103#12011yescharacteristic
152C2×C4×C103C2×SD1614yes—
153C2×C4×C103C2×SD1612yes—
154C2×C4×C103AGL(1,ℤ/8)12yes—
155C2×C4×C103C22×D412yes—
156C8×C103—44no—
157C22×C103—21no—
158C22×C103—21no—
159C22×C103—44no—
160C22×C103—44no—
161C22×C103—44no—
162C22×C103C2×#12011yescharacteristic
163C22×C103C22×SD1611yescharacteristic
164C22×C103C2×AGL(1,ℤ/8)11yescharacteristic
165C4×C103—24no—
166C4×C103—21no—
167C4×C103—22no—
168C4×C103—44no—
169C4×C103—44no—
170C4×C103—42no—
171C4×C103—82no—
172C4×C103#45014yes—
173C4×C103#45612yes—
174#18402C10311yesmaximal, characteristic, direct product factor, Sylow
175C2×C103—21no—
176C2×C103—21no—
177C2×C103—84no—
178C2×C103C2×#45011yescharacteristic
179C2×C103C2×#45611yescharacteristic
180C2×C103#302711yescharacteristic
181#3497C2×C10311yescharacteristic
182#3206C2×C10312yescomplemented
183#2567C2×C10311yescharacteristic, complemented
184#1604C2×C10318yescomplemented
185#1502C2×C10312yescomplemented
186#1461C2×C10311yescharacteristic, complemented
187C103#1840211yescharacteristic, direct product factor, Sylow
188C2×2−1+4—21no—
189#550—22no—
190D4×Q8—22no—
191#548—24no—
192#537—21no—
193#537C22×C10314yes—
194#532—22no—
195#532C22×C10312yes—
196C2×C4⋊Q8C22×C10311yescharacteristic
197C2×C4×Q8C22×C10311yescharacteristic
198#492—22no—
199#487—22no—
200#461—24no—
201#448C22×C10318yes—
202#431C22×C10312yes—
203#395C22×C10314yes—
204#391—21no—
205#389—22no—
206#384—21no—
207C4×C4⋊C4C22×C10311yescharacteristic
208#327C22×C10318yes—
209#324C22×C10314yes—
2102−1+4—44no—
2112−1+4—44no—
212C2×#41—24no—
213C2×#41—24no—
214C2×#41—22no—
215C22×Q8—24no—
216C22×Q8D4×C10311yescharacteristic
217C22×Q8C23×C10312yes—
218C2×SD16—28no—
219C4⋊Q8—22no—
220C4⋊Q8—22no—
221C4⋊Q8—22no—
222C4⋊Q8D4×C10312yes—
223#127—22no—
224#127D4×C10312yes—
225#124—24no—
226#124—22no—
227C22⋊Q8—24no—
228C22⋊Q8—28no—
229#121—24no—
230#121—28no—
231#121—22no—
232#121—24no—
233#121C23×C10314yes—
234C4×Q8—22no—
235C4×Q8—22no—
236C4×D4—24no—
237C4×D4—24no—
238C4×D4—22no—
239C4×D4D4×C10314yes—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—24no—
244C2×C4⋊C4D4×C10311yescharacteristic
245C2×C4⋊C4C23×C10312yes—
246C2×C42—21no—
247C2×C42D4×C10312yes—
248C2×C42C23×C10311yescharacteristic
249C4⋊C8—22no—
250#103—28no—
251C22⋊C8C23×C10314yes—
252C4×C8—22no—
253#95—24no—
254#95C23×C10312yes—
255#41—48no—
256#41—416no—
257#41—48no—
258#41—44no—
259#41—44no—
260C2×Q8—24no—
261C2×Q8—22no—
262C2×Q8—22no—
263C2×Q8—22no—
264C2×Q8—24no—
265C2×Q8—416no—
266C2×Q8—82no—
267C2×Q8SD16×C10314yescomplemented
268C2×D4—24no—
269C2×D4—24no—
270C2×D4—24no—
271C2×D4—22no—
272C2×D4—22no—
273C2×D4C2×D4×C10314yes—
274C22×C4—28no—
275C22×C4—22no—
276C22×C4—24no—
277C22×C4—22no—
278C22×C4C2×D4×C10311yescharacteristic
279C22×C4C2×D4×C10312yes—
280C22×C4C2×D4×C10312yes—
281C22×C4C2×D4×C10311yescharacteristic
282C22×C4C24×C10311yescharacteristic
283SD16—88no—
284C2×C8—24no—
285C4⋊C4—24no—
286C4⋊C4—24no—
287C4⋊C4—22no—
288C4⋊C4—22no—
289C4⋊C4—24no—
290C4⋊C4—41no—
291C4⋊C4—42no—
292C4⋊C4—41no—
293C4⋊C4—84no—
294C4⋊C4C2×D4×C10314yes—
295C22⋊C4—28no—
296C22⋊C4—24no—
297C22⋊C4—24no—
298C42—22no—
299C42—22no—
300C42—42no—
301C42C2×D4×C10312yes—
302C42C2×D4×C10312yes—
303C23—24no—
304C23C22×D4×C10311yescharacteristic
305Q8—28no—
306Q8—48no—
307Q8—48no—
308Q8—44no—
309D4—44no—
310D4—48no—
311D4—44no—
312D4—44no—
313D4—44no—
314D4—44no—
315D4—84no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—24no—
320C2×C4—22no—
321C2×C4—24no—
322C2×C4—41no—
323C2×C4—416no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—48no—
327C2×C4—42no—
328C2×C4—44no—
329C2×C4—42no—
330C2×C4#120×C10311yescharacteristic
331C2×C4#120×C10312yes—
332C2×C4#120×C10311yescharacteristic
333C2×C4C2×SD16×C10314yes—
334C2×C4C2×SD16×C10312yes—
335C2×C4AGL(1,ℤ/8)×C10312yes—
336C2×C4C22×D4×C10312yes—
337C8—44no—
338C22—21no—
339C22—21no—
340C22—44no—
341C22—44no—
342C22—44no—
343C22C2×#120×C10311yescharacteristic
344C22C22×SD16×C10311yescharacteristic
345C22C2×AGL(1,ℤ/8)×C10311yescharacteristic
346C4—24no—
347C4—21no—
348C4—22no—
349C4—44no—
350C4—44no—
351C4—42no—
352C4—82no—
353C4#450×C10314yes—
354C4#456×C10312yes—
355C2—21no—
356C2—21no—
357C2—84no—
358C2C2×#450×C10311yescharacteristic
359C2C2×#456×C10311yescharacteristic
360C2C103×#302711yescharacteristic
subgroupG/H
center, socleC22×C103C2×#120
commutator, Frattini, cosocleC22×C4C24×C103
prime radicalC103×#3497C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C103 ◁ C2×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C103×#3206C2semidirect
3. C103×#2567C2semidirect
4. C103×#1604C2semidirect
5. C103×#1502C2semidirect
6. C103×#1461C2semidirect
86. C2×Q8×C103SD16semidirect
174. #18402C103direct (N × H)
182. #3206C2×C103semidirect
183. #2567C2×C103semidirect
184. #1604C2×C103semidirect
185. #1502C2×C103semidirect
186. #1461C2×C103semidirect
187. C103#18402direct (N × H)
267. C2×Q8SD16×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#34972
C103×#32062
C103×#25672
C103×#16042
C103×#15022
C103×#14612
#18402103