Finite Group Databasebeta

← C103×#9908 #39915183

Subgroups — C103×#9908 #39915183

Order 26368.

684 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#2857C211yesmaximal, characteristic
2C103×#1797C211yesmaximal, characteristic
3C4×#95×C103C211yesmaximal, characteristic
4C103×#1294C214yesmaximal
5C2×C4⋊Q8×C103C411yescharacteristic, complemented
6C2×C22⋊Q8×C103—21no—
7C22×C42×C103—21no—
8C22×C42×C103C2211yescharacteristic
9C2×C4⋊C8×C103—21no—
10C2×C22⋊C8×C103C2212yes—
11#391×C103—21no—
12#389×C103—21no—
13#389×C103C412yescomplemented
14#384×C103C411yescharacteristic, complemented
15#380×C103—21no—
16#380×C103C2212yes—
17C2×#95×C103—21no—
18C2×#95×C103C2212yes—
19#336×C103—21no—
20C22×Q8×C103—21no—
21C23×C4×C103—22no—
22C23×C4×C103D411yescharacteristic
23C23×C4×C103D411yescharacteristic
24C23×C4×C103C2311yescharacteristic
25C22×C8×C103—22no—
26C4⋊Q8×C103—42no—
27C22⋊Q8×C103—44no—
28C2×C4⋊C4×C103—21no—
29C2×C4⋊C4×C103—21no—
30C2×C4⋊C4×C103—21no—
31C2×C4⋊C4×C103—22no—
32C2×C4⋊C4×C103C2×C412yes—
33C2×C4⋊C4×C103C2×C412yes—
34C2×C22⋊C4×C103—22no—
35C2×C42×C103—24no—
36C2×C42×C103—42no—
37C2×C42×C103—42no—
38C2×C42×C103—42no—
39C2×C42×C103C2×C411yescharacteristic
40C2×C42×C103C2×C411yescharacteristic
41C2×C42×C103D411yescharacteristic
42C2×C42×C103D411yescharacteristic
43C4⋊C8×C103—42no—
44C22⋊C8×C103—24no—
45#95×C103—24no—
46#95×C103—22no—
47#95×C103—22no—
48#95×C103—22no—
49#95×C103Q814yescomplemented
50C24×C103C2×D411yescharacteristic
51C2×Q8×C103—42no—
52C2×Q8×C103—42no—
53C2×Q8×C103—42no—
54C22×C4×C103—22no—
55C22×C4×C103—22no—
56C22×C4×C103—24no—
57C22×C4×C103—24no—
58C22×C4×C103—24no—
59C22×C4×C103—22no—
60C22×C4×C103—22no—
61C22×C4×C103—22no—
62C22×C4×C103—22no—
63C22×C4×C103—41no—
64C22×C4×C103—41no—
65C22×C4×C103—41no—
66C22×C4×C103—42no—
67C22×C4×C103—42no—
68C22×C4×C103—42no—
69C22×C4×C103—42no—
70C22×C4×C103C22⋊C411yescharacteristic
71C22×C4×C103C22⋊C411yescharacteristic
72C22×C4×C103C22⋊C411yescharacteristic
73C22×C4×C103C22⋊C411yescharacteristic
74C22×C4×C103SD1612yes—
75C22×C4×C103Q1612yes—
76C22×C4×C103C22×C411yescharacteristic
77C22×C4×C103C2×D411yescharacteristic
78C22×C4×C103C2×Q812yes—
79C22×C4×C103#4112yes—
80C2×C8×C103—42no—
81C2×C8×C103—42no—
82C2×C8×C103—42no—
83C4⋊C4×C103—42no—
84C4⋊C4×C103—42no—
85C4⋊C4×C103—42no—
86C4⋊C4×C103—44no—
87C4⋊C4×C103—42no—
88C4⋊C4×C103—42no—
89C22⋊C4×C103—44no—
90C42×C103—22no—
91C42×C103—22no—
92C42×C103—41no—
93C42×C103—41no—
94C42×C103—48no—
95C23×C103—21no—
96C23×C103—21no—
97C23×C103—21no—
98C23×C103—21no—
99C23×C103C2×C22⋊C411yescharacteristic
100C23×C103C22⋊Q812yes—
101C23×C103C2×SD1611yescharacteristic
102C23×C103C2×Q1611yescharacteristic
103C23×C103AGL(1,ℤ/8)12yes—
104Q8×C103—84no—
105C2×C4×C103—21no—
106C2×C4×C103—21no—
107C2×C4×C103—21no—
108C2×C4×C103—21no—
109C2×C4×C103—21no—
110C2×C4×C103—21no—
111C2×C4×C103—21no—
112C2×C4×C103—21no—
113C2×C4×C103—24no—
114C2×C4×C103—24no—
115C2×C4×C103—28no—
116C2×C4×C103—21no—
117C2×C4×C103—21no—
118C2×C4×C103—21no—
119C2×C4×C103—42no—
120C2×C4×C103—42no—
121C2×C4×C103—44no—
122C2×C4×C103—44no—
123C2×C4×C103—44no—
124C2×C4×C103—44no—
125C2×C4×C103—44no—
126C2×C4×C103—44no—
127C2×C4×C103—44no—
128C2×C4×C103—42no—
129C2×C4×C103—42no—
130C2×C4×C103—42no—
131C2×C4×C103—42no—
132C2×C4×C103—42no—
133C2×C4×C103—42no—
134C2×C4×C103#9912yes—
135C2×C4×C103#10312yes—
136C2×C4×C103#10312yes—
137C2×C4×C103#10412yes—
138C2×C4×C103#10412yes—
139C2×C4×C103C4×Q812yes—
140C2×C4×C103#12411yescharacteristic
141C2×C4×C103C4⋊Q811yescharacteristic
142C8×C103—82no—
143C22×C103—22no—
144C22×C103—22no—
145C22×C103—21no—
146C22×C103—21no—
147C22×C103—21no—
148C22×C103—21no—
149C22×C103—22no—
150C22×C103—22no—
151C22×C103#39111yescharacteristic
152C22×C103C2×#9911yescharacteristic
153C22×C103#41011yescharacteristic
154C22×C103C2×#10311yescharacteristic
155C22×C103#41811yescharacteristic
156C22×C103C2×#10411yescharacteristic
157C22×C103C2×#10411yescharacteristic
158C22×C103#47612yes—
159C22×C103#47712yes—
160C4×C103—21no—
161C4×C103—22no—
162C4×C103—21no—
163C4×C103—22no—
164C4×C103—22no—
165C4×C103—48no—
166C4×C103—41no—
167C4×C103—82no—
168C4×C103—82no—
169C4×C103#32814yes—
170#9908C10311yesmaximal, characteristic, direct product factor, Sylow
171C2×C103—22no—
172C2×C103—22no—
173C2×C103C2×#32811yescharacteristic
174C2×C103#150311yescharacteristic
175C2×C103#150511yescharacteristic
176C2×C103#150711yescharacteristic
177C2×C103#198711yescharacteristic
178C2×C103#199411yescharacteristic
179C2×C103#199611yescharacteristic
180#2857C2×C10311yescharacteristic
181#1797C2×C10311yescharacteristic
182C4×#95C2×C10311yescharacteristic
183#1294C2×C10314yes—
184C103#990811yescharacteristic, direct product factor, Sylow
185C2×C4⋊Q8C4×C10311yescharacteristic, complemented
186C2×C22⋊Q8—21no—
187C22×C42—21no—
188C22×C42C22×C10311yescharacteristic
189C2×C4⋊C8—21no—
190C2×C22⋊C8C22×C10312yes—
191#391—21no—
192#389—21no—
193#389C4×C10312yescomplemented
194#384C4×C10311yescharacteristic, complemented
195#380—21no—
196#380C22×C10312yes—
197C2×#95—21no—
198C2×#95C22×C10312yes—
199#336—21no—
200C22×Q8—21no—
201C23×C4—22no—
202C23×C4D4×C10311yescharacteristic
203C23×C4D4×C10311yescharacteristic
204C23×C4C23×C10311yescharacteristic
205C22×C8—22no—
206C4⋊Q8—42no—
207C22⋊Q8—44no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—22no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4C2×C4×C10312yes—
213C2×C4⋊C4C2×C4×C10312yes—
214C2×C22⋊C4—22no—
215C2×C42—24no—
216C2×C42—42no—
217C2×C42—42no—
218C2×C42—42no—
219C2×C42C2×C4×C10311yescharacteristic
220C2×C42C2×C4×C10311yescharacteristic
221C2×C42D4×C10311yescharacteristic
222C2×C42D4×C10311yescharacteristic
223C4⋊C8—42no—
224C22⋊C8—24no—
225#95—24no—
226#95—22no—
227#95—22no—
228#95—22no—
229#95Q8×C10314yescomplemented
230C24C2×D4×C10311yescharacteristic
231C2×Q8—42no—
232C2×Q8—42no—
233C2×Q8—42no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—24no—
237C22×C4—24no—
238C22×C4—24no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4—42no—
247C22×C4—42no—
248C22×C4—42no—
249C22×C4—42no—
250C22×C4C22⋊C4×C10311yescharacteristic
251C22×C4C22⋊C4×C10311yescharacteristic
252C22×C4C22⋊C4×C10311yescharacteristic
253C22×C4C22⋊C4×C10311yescharacteristic
254C22×C4SD16×C10312yes—
255C22×C4Q16×C10312yes—
256C22×C4C22×C4×C10311yescharacteristic
257C22×C4C2×D4×C10311yescharacteristic
258C22×C4C2×Q8×C10312yes—
259C22×C4#41×C10312yes—
260C2×C8—42no—
261C2×C8—42no—
262C2×C8—42no—
263C4⋊C4—42no—
264C4⋊C4—42no—
265C4⋊C4—42no—
266C4⋊C4—44no—
267C4⋊C4—42no—
268C4⋊C4—42no—
269C22⋊C4—44no—
270C42—22no—
271C42—22no—
272C42—41no—
273C42—41no—
274C42—48no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23C2×C22⋊C4×C10311yescharacteristic
280C23C22⋊Q8×C10312yes—
281C23C2×SD16×C10311yescharacteristic
282C23C2×Q16×C10311yescharacteristic
283C23AGL(1,ℤ/8)×C10312yes—
284Q8—84no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—24no—
294C2×C4—24no—
295C2×C4—28no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—44no—
302C2×C4—44no—
303C2×C4—44no—
304C2×C4—44no—
305C2×C4—44no—
306C2×C4—44no—
307C2×C4—44no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4#99×C10312yes—
315C2×C4#103×C10312yes—
316C2×C4#103×C10312yes—
317C2×C4#104×C10312yes—
318C2×C4#104×C10312yes—
319C2×C4C4×Q8×C10312yes—
320C2×C4#124×C10311yescharacteristic
321C2×C4C4⋊Q8×C10311yescharacteristic
322C8—82no—
323C22—22no—
324C22—22no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—21no—
329C22—22no—
330C22—22no—
331C22#391×C10311yescharacteristic
332C22C2×#99×C10311yescharacteristic
333C22#410×C10311yescharacteristic
334C22C2×#103×C10311yescharacteristic
335C22#418×C10311yescharacteristic
336C22C2×#104×C10311yescharacteristic
337C22C2×#104×C10311yescharacteristic
338C22#476×C10312yes—
339C22#477×C10312yes—
340C4—21no—
341C4—22no—
342C4—21no—
343C4—22no—
344C4—22no—
345C4—48no—
346C4—41no—
347C4—82no—
348C4—82no—
349C4#328×C10314yes—
350C2—22no—
351C2—22no—
352C2C2×#328×C10311yescharacteristic
353C2C103×#150311yescharacteristic
354C2C103×#150511yescharacteristic
355C2C103×#150711yescharacteristic
356C2C103×#198711yescharacteristic
357C2C103×#199411yescharacteristic
358C2C103×#199611yescharacteristic
subgroupG/H
center, socleC23×C103C2×C22⋊C4
commutatorC22×C4C22×C4×C103
Frattini, cosocleC23×C4C23×C103
prime radicalC24×C103C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C103 ◁ C22×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
5. C2×C4⋊Q8×C103C4semidirect
13. #389×C103C4semidirect
14. #384×C103C4semidirect
49. #95×C103Q8semidirect
170. #9908C103direct (N × H)
184. C103#9908direct (N × H)
185. C2×C4⋊Q8C4×C103semidirect
193. #389C4×C103semidirect
194. #384C4×C103semidirect
229. #95Q8×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#28572
C103×#17972
C4×#95×C1032
C103×#12942
#9908103