Finite Group Databasebeta

← C103×#12722 #39917997

Subgroups — C103×#12722 #39917997

Order 26368.

790 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 790 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3508C211yesmaximal, characteristic
2C103×#2134C211yesmaximal, characteristic, complemented
3C103×#2128C211yesmaximal, characteristic, complemented
4C103×#2122C212yesmaximal, complemented
5C103×#1827C212yesmaximal, complemented
6#559×C103—22no—
7#550×C103—22no—
8#546×C103—24no—
9#540×C103—22no—
10#535×C103C2211yescharacteristic
11#535×C103C2211yescharacteristic
12#533×C103C411yescharacteristic, complemented
13#532×C103—22no—
14C2×#127×C103C411yescharacteristic, complemented
15#518×C103C411yescharacteristic, complemented
16#518×C103C411yescharacteristic, complemented
17C4×#41×C103C2211yescharacteristic
18#413×C103C2212yes—
19#410×C103C2212yes—
20#355×C103—22no—
21#353×C103—22no—
22AΣL(1,𝔽16)×C103—24no—
23#339×C103—22no—
24H(3,ℤ/4)×C103—22no—
25C2×#41×C103—24no—
26C2×#41×C103C2311yescharacteristic
27C22×D4×C103—22no—
28C22×D4×C103C2×C411yescharacteristic
29C22×D4×C103C2×C411yescharacteristic
30C2×M16×C103—22no—
31C4⋊Q8×C103—21no—
32#127×C103—22no—
33#127×C103—21no—
34#127×C103—21no—
35#127×C103—21no—
36#127×C103D412yes—
37#125×C103—21no—
38#124×C103—24no—
39#124×C103—21no—
40#124×C103D412yes—
41#123×C103—24no—
42#123×C103—24no—
43C22⋊Q8×C103—22no—
44#121×C103—24no—
45#121×C103—24no—
46#121×C103—24no—
47#121×C103—22no—
48#121×C103—22no—
49#120×C103—22no—
50#120×C103D414yes—
51C4×Q8×C103—21no—
52C4×Q8×C103—22no—
53C4×D4×C103—24no—
54C4×D4×C103—22no—
55C4×D4×C103—22no—
56C4×D4×C103—21no—
57C4×D4×C103—22no—
58C4×D4×C103—22no—
59C4×D4×C103—22no—
60#117×C103—22no—
61#117×C103C2×C411yescharacteristic
62#117×C103C2×C411yescharacteristic
63#117×C103C2×C411yescharacteristic
64#117×C103D412yes—
65C2×C22⋊C4×C103—22no—
66C2×C22⋊C4×C103—22no—
67C2×C42×C103C2×C411yescharacteristic
68C2×C42×C103D412yes—
69#101×C103—22no—
70#100×C103—22no—
71#99×C103—22no—
72#99×C103—22no—
73C24×C103—21no—
74C24×C103C22⋊C412yes—
75#41×C103—42no—
76#41×C103—88no—
77C2×Q8×C103—22no—
78C2×Q8×C103C2×D411yescharacteristic
79C2×D4×C103—24no—
80C2×D4×C103—24no—
81C2×D4×C103—24no—
82C2×D4×C103—24no—
83C2×D4×C103—21no—
84C2×D4×C103—21no—
85C2×D4×C103—21no—
86C2×D4×C103—42no—
87C2×D4×C103—42no—
88C2×D4×C103—84no—
89C2×D4×C103C22⋊C412yes—
90C2×D4×C103C2×D411yescharacteristic
91C2×D4×C103C2×D412yes—
92C22×C4×C103—21no—
93C22×C4×C103—22no—
94C22×C4×C103—24no—
95C22×C4×C103—24no—
96C22×C4×C103C22×C411yescharacteristic
97C22×C4×C103C2×D412yes—
98M16×C103—42no—
99M16×C103—42no—
100C2×C8×C103—42no—
101C4⋊C4×C103—22no—
102C4⋊C4×C103—22no—
103C4⋊C4×C103—22no—
104C4⋊C4×C103—21no—
105C4⋊C4×C103—21no—
106C4⋊C4×C103—21no—
107C4⋊C4×C103—22no—
108C4⋊C4×C103—42no—
109C22⋊C4×C103—24no—
110C22⋊C4×C103—24no—
111C22⋊C4×C103—21no—
112C22⋊C4×C103—21no—
113C22⋊C4×C103—22no—
114C22⋊C4×C103—24no—
115C22⋊C4×C103—24no—
116C22⋊C4×C103—42no—
117C22⋊C4×C103C22⋊C412yes—
118C42×C103—21no—
119C42×C103—21no—
120C42×C103—22no—
121C42×C103—42no—
122C42×C103C22⋊C412yes—
123C42×C103C22⋊C411yescharacteristic
124C42×C103C22⋊C411yescharacteristic
125C42×C103C22⋊C412yes—
126C23×C103—22no—
127C23×C103—22no—
128C23×C103—42no—
129C23×C103—42no—
130C23×C103—82no—
131C23×C103—82no—
132C23×C103C2×C22⋊C411yescharacteristic
133C23×C103#12012yes—
134Q8×C103—41no—
135Q8×C103—44no—
136D4×C103—42no—
137D4×C103—41no—
138D4×C103—42no—
139D4×C103—42no—
140D4×C103—48no—
141D4×C103—42no—
142D4×C103—42no—
143D4×C103—84no—
144D4×C103—84no—
145D4×C103—84no—
146C2×C4×C103—21no—
147C2×C4×C103—22no—
148C2×C4×C103—22no—
149C2×C4×C103—22no—
150C2×C4×C103—22no—
151C2×C4×C103—21no—
152C2×C4×C103—22no—
153C2×C4×C103—22no—
154C2×C4×C103—42no—
155C2×C4×C103—44no—
156C2×C4×C103—84no—
157C2×C4×C103—84no—
158C2×C4×C103—82no—
159C2×C4×C103C2×C22⋊C411yescharacteristic
160C2×C4×C103C2×C22⋊C411yescharacteristic
161C2×C4×C103#12012yes—
162C8×C103—82no—
163C22×C103—22no—
164C22×C103—21no—
165C22×C103—42no—
166C22×C103—41no—
167C22×C103—44no—
168C22×C103—44no—
169C22×C103—42no—
170C22×C103—42no—
171C22×C103—162no—
172C22×C103—162no—
173C22×C103#37911yescharacteristic
174C4×C103—22no—
175C4×C103—22no—
176C4×C103—21no—
177C4×C103—42no—
178C4×C103—41no—
179C4×C103—42no—
180C4×C103—42no—
181C4×C103—162no—
182C4×C103#41012yes—
183#12722C10311yesmaximal, characteristic, direct product factor, Sylow
184C2×C103—21no—
185C2×C103—42no—
186C2×C103—41no—
187C2×C103—82no—
188C2×C103—82no—
189C2×C103#178211yescharacteristic
190#3508C2×C10311yescharacteristic
191#2134C2×C10311yescharacteristic, complemented
192#2128C2×C10311yescharacteristic, complemented
193#2122C2×C10312yescomplemented
194#1827C2×C10312yescomplemented
195C103#1272211yescharacteristic, direct product factor, Sylow
196#559—22no—
197#550—22no—
198#546—24no—
199#540—22no—
200#535C22×C10311yescharacteristic
201#535C22×C10311yescharacteristic
202#533C4×C10311yescharacteristic, complemented
203#532—22no—
204C2×#127C4×C10311yescharacteristic, complemented
205#518C4×C10311yescharacteristic, complemented
206#518C4×C10311yescharacteristic, complemented
207C4×#41C22×C10311yescharacteristic
208#413C22×C10312yes—
209#410C22×C10312yes—
210#355—22no—
211#353—22no—
212AΣL(1,𝔽16)—24no—
213#339—22no—
214H(3,ℤ/4)—22no—
215C2×#41—24no—
216C2×#41C23×C10311yescharacteristic
217C22×D4—22no—
218C22×D4C2×C4×C10311yescharacteristic
219C22×D4C2×C4×C10311yescharacteristic
220C2×M16—22no—
221C4⋊Q8—21no—
222#127—22no—
223#127—21no—
224#127—21no—
225#127—21no—
226#127D4×C10312yes—
227#125—21no—
228#124—24no—
229#124—21no—
230#124D4×C10312yes—
231#123—24no—
232#123—24no—
233C22⋊Q8—22no—
234#121—24no—
235#121—24no—
236#121—24no—
237#121—22no—
238#121—22no—
239#120—22no—
240#120D4×C10314yes—
241C4×Q8—21no—
242C4×Q8—22no—
243C4×D4—24no—
244C4×D4—22no—
245C4×D4—22no—
246C4×D4—21no—
247C4×D4—22no—
248C4×D4—22no—
249C4×D4—22no—
250#117—22no—
251#117C2×C4×C10311yescharacteristic
252#117C2×C4×C10311yescharacteristic
253#117C2×C4×C10311yescharacteristic
254#117D4×C10312yes—
255C2×C22⋊C4—22no—
256C2×C22⋊C4—22no—
257C2×C42C2×C4×C10311yescharacteristic
258C2×C42D4×C10312yes—
259#101—22no—
260#100—22no—
261#99—22no—
262#99—22no—
263C24—21no—
264C24C22⋊C4×C10312yes—
265#41—42no—
266#41—88no—
267C2×Q8—22no—
268C2×Q8C2×D4×C10311yescharacteristic
269C2×D4—24no—
270C2×D4—24no—
271C2×D4—24no—
272C2×D4—24no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—21no—
276C2×D4—42no—
277C2×D4—42no—
278C2×D4—84no—
279C2×D4C22⋊C4×C10312yes—
280C2×D4C2×D4×C10311yescharacteristic
281C2×D4C2×D4×C10312yes—
282C22×C4—21no—
283C22×C4—22no—
284C22×C4—24no—
285C22×C4—24no—
286C22×C4C22×C4×C10311yescharacteristic
287C22×C4C2×D4×C10312yes—
288M16—42no—
289M16—42no—
290C2×C8—42no—
291C4⋊C4—22no—
292C4⋊C4—22no—
293C4⋊C4—22no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—22no—
298C4⋊C4—42no—
299C22⋊C4—24no—
300C22⋊C4—24no—
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—22no—
304C22⋊C4—24no—
305C22⋊C4—24no—
306C22⋊C4—42no—
307C22⋊C4C22⋊C4×C10312yes—
308C42—21no—
309C42—21no—
310C42—22no—
311C42—42no—
312C42C22⋊C4×C10311yescharacteristic
313C42C22⋊C4×C10311yescharacteristic
314C42C22⋊C4×C10312yes—
315C42C22⋊C4×C10312yes—
316C23—22no—
317C23—22no—
318C23—42no—
319C23—42no—
320C23—82no—
321C23—82no—
322C23C2×C22⋊C4×C10311yescharacteristic
323C23#120×C10312yes—
324Q8—41no—
325Q8—44no—
326D4—42no—
327D4—41no—
328D4—42no—
329D4—42no—
330D4—48no—
331D4—42no—
332D4—42no—
333D4—84no—
334D4—84no—
335D4—84no—
336C2×C4—21no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—21no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—42no—
345C2×C4—44no—
346C2×C4—84no—
347C2×C4—84no—
348C2×C4—82no—
349C2×C4C2×C22⋊C4×C10311yescharacteristic
350C2×C4C2×C22⋊C4×C10311yescharacteristic
351C2×C4#120×C10312yes—
352C8—82no—
353C22—22no—
354C22—21no—
355C22—42no—
356C22—41no—
357C22—44no—
358C22—44no—
359C22—42no—
360C22—42no—
361C22—162no—
362C22—162no—
363C22#379×C10311yescharacteristic
364C4—22no—
365C4—22no—
366C4—21no—
367C4—42no—
368C4—41no—
369C4—42no—
370C4—42no—
371C4—162no—
372C4#410×C10312yes—
373C2—21no—
374C2—42no—
375C2—41no—
376C2—82no—
377C2—82no—
378C2C103×#178211yescharacteristic
subgroupG/H
center, socleC2×C103#1782
commutatorC22×C4C22×C4×C103
Frattini, cosocleC2×#41C23×C103
prime radicalC103×#3508C2
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C103 ◁ C2×C4×C103 ◁ C4×#41×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C103×#2134C2semidirect
3. C103×#2128C2semidirect
4. C103×#2122C2semidirect
5. C103×#1827C2semidirect
12. #533×C103C4semidirect
14. C2×#127×C103C4semidirect
15. #518×C103C4semidirect
16. #518×C103C4semidirect
183. #12722C103direct (N × H)
191. #2134C2×C103semidirect
192. #2128C2×C103semidirect
193. #2122C2×C103semidirect
194. #1827C2×C103semidirect
195. C103#12722direct (N × H)
202. #533C4×C103semidirect
204. C2×#127C4×C103semidirect
205. #518C4×C103semidirect
206. #518C4×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#35082
C103×#21342
C103×#21282
C103×#21222
C103×#18272
#12722103