Finite Group Databasebeta

← C103×#9909 #39915184

Subgroups — C103×#9909 #39915184

Order 26368.

684 conjugacy classes of subgroups.

The subgroup lattice has 364 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—42no—
28C22⋊Q8×C103—42no—
29C2×C4⋊C4×C103—21no—
30C2×C4⋊C4×C103—21no—
31C2×C4⋊C4×C103—21no—
32C2×C4⋊C4×C103—22no—
33C2×C4⋊C4×C103C2×C412yes—
34C2×C4⋊C4×C103C2×C412yes—
35C2×C22⋊C4×C103—22no—
36C2×C42×C103—24no—
37C2×C42×C103—42no—
38C2×C42×C103—42no—
39C2×C42×C103—42no—
40C2×C42×C103C2×C411yescharacteristic
41C2×C42×C103C2×C411yescharacteristic
42C2×C42×C103D411yescharacteristic
43C2×C42×C103D411yescharacteristic
44C4⋊C8×C103—42no—
45C22⋊C8×C103—24no—
46#95×C103—24no—
47#95×C103—22no—
48#95×C103—22no—
49#95×C103—22no—
50#95×C103Q814yescomplemented
51C24×C103C2×D411yescharacteristic
52C2×Q8×C103—42no—
53C2×Q8×C103—42no—
54C2×Q8×C103—42no—
55C22×C4×C103—22no—
56C22×C4×C103—22no—
57C22×C4×C103—24no—
58C22×C4×C103—24no—
59C22×C4×C103—24no—
60C22×C4×C103—22no—
61C22×C4×C103—22no—
62C22×C4×C103—22no—
63C22×C4×C103—22no—
64C22×C4×C103—41no—
65C22×C4×C103—41no—
66C22×C4×C103—41no—
67C22×C4×C103—42no—
68C22×C4×C103—42no—
69C22×C4×C103—42no—
70C22×C4×C103—42no—
71C22×C4×C103C22⋊C411yescharacteristic
72C22×C4×C103C22⋊C411yescharacteristic
73C22×C4×C103C22⋊C411yescharacteristic
74C22×C4×C103C22⋊C411yescharacteristic
75C22×C4×C103D812yes—
76C22×C4×C103SD1612yes—
77C22×C4×C103C22×C411yescharacteristic
78C22×C4×C103C2×D411yescharacteristic
79C22×C4×C103C2×Q812yes—
80C22×C4×C103#4112yes—
81C2×C8×C103—42no—
82C2×C8×C103—42no—
83C2×C8×C103—42no—
84C4⋊C4×C103—42no—
85C4⋊C4×C103—42no—
86C4⋊C4×C103—42no—
87C4⋊C4×C103—42no—
88C4⋊C4×C103—44no—
89C4⋊C4×C103—42no—
90C22⋊C4×C103—42no—
91C22⋊C4×C103—42no—
92C42×C103—22no—
93C42×C103—22no—
94C42×C103—41no—
95C42×C103—41no—
96C42×C103—48no—
97C23×C103—21no—
98C23×C103—21no—
99C23×C103—21no—
100C23×C103—21no—
101C23×C103C2×C22⋊C411yescharacteristic
102C23×C103C22⋊Q812yes—
103C23×C103C2×D811yescharacteristic
104C23×C103C2×SD1611yescharacteristic
105C23×C103#13712yes—
106Q8×C103—84no—
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—21no—
114C2×C4×C103—21no—
115C2×C4×C103—24no—
116C2×C4×C103—24no—
117C2×C4×C103—28no—
118C2×C4×C103—21no—
119C2×C4×C103—21no—
120C2×C4×C103—21no—
121C2×C4×C103—42no—
122C2×C4×C103—42no—
123C2×C4×C103—44no—
124C2×C4×C103—44no—
125C2×C4×C103—44no—
126C2×C4×C103—44no—
127C2×C4×C103—44no—
128C2×C4×C103—44no—
129C2×C4×C103—44no—
130C2×C4×C103—42no—
131C2×C4×C103—42no—
132C2×C4×C103—42no—
133C2×C4×C103—42no—
134C2×C4×C103—42no—
135C2×C4×C103—42no—
136C2×C4×C103#9912yes—
137C2×C4×C103#10212yes—
138C2×C4×C103#10212yes—
139C2×C4×C103#10412yes—
140C2×C4×C103#10412yes—
141C2×C4×C103C4×Q812yes—
142C2×C4×C103#12411yescharacteristic
143C2×C4×C103C4⋊Q811yescharacteristic
144C8×C103—82no—
145C22×C103—22no—
146C22×C103—22no—
147C22×C103—21no—
148C22×C103—21no—
149C22×C103—21no—
150C22×C103—21no—
151C22×C103—22no—
152C22×C103—22no—
153C22×C103#39111yescharacteristic
154C22×C103C2×#9911yescharacteristic
155C22×C103#41011yescharacteristic
156C22×C103C2×#10211yescharacteristic
157C22×C103#41911yescharacteristic
158C22×C103C2×#10411yescharacteristic
159C22×C103C2×#10411yescharacteristic
160C22×C103#47412yes—
161C22×C103#47512yes—
162C4×C103—21no—
163C4×C103—22no—
164C4×C103—21no—
165C4×C103—22no—
166C4×C103—22no—
167C4×C103—48no—
168C4×C103—41no—
169C4×C103—82no—
170C4×C103—82no—
171C4×C103#32714yes—
172#9909C10311yesmaximal, characteristic, direct product factor, Sylow
173C2×C103—22no—
174C2×C103—22no—
175C2×C103C2×#32711yescharacteristic
176C2×C103#150211yescharacteristic
177C2×C103#150611yescharacteristic
178C2×C103#150811yescharacteristic
179C2×C103#198811yescharacteristic
180C2×C103#199411yescharacteristic
181C2×C103#199611yescharacteristic
182#2857C2×C10311yescharacteristic
183#1797C2×C10311yescharacteristic
184C4×#95C2×C10311yescharacteristic
185#1294C2×C10314yes—
186C103#990911yescharacteristic, direct product factor, Sylow
187C2×C4⋊Q8C4×C10311yescharacteristic, complemented
188C2×C22⋊Q8—21no—
189C22×C42—21no—
190C22×C42C22×C10311yescharacteristic
191C2×C4⋊C8—21no—
192C2×C22⋊C8C22×C10312yes—
193#391—21no—
194#389—21no—
195#389C4×C10312yescomplemented
196#384C4×C10311yescharacteristic, complemented
197#380—21no—
198#380C22×C10312yes—
199C2×#95—21no—
200C2×#95C22×C10312yes—
201#336—21no—
202C22×Q8—21no—
203C23×C4—22no—
204C23×C4D4×C10311yescharacteristic
205C23×C4D4×C10311yescharacteristic
206C23×C4C23×C10311yescharacteristic
207C22×C8—22no—
208C4⋊Q8—42no—
209C22⋊Q8—42no—
210C22⋊Q8—42no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—22no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4C2×C4×C10312yes—
216C2×C4⋊C4C2×C4×C10312yes—
217C2×C22⋊C4—22no—
218C2×C42—24no—
219C2×C42—42no—
220C2×C42—42no—
221C2×C42—42no—
222C2×C42C2×C4×C10311yescharacteristic
223C2×C42C2×C4×C10311yescharacteristic
224C2×C42D4×C10311yescharacteristic
225C2×C42D4×C10311yescharacteristic
226C4⋊C8—42no—
227C22⋊C8—24no—
228#95—24no—
229#95—22no—
230#95—22no—
231#95—22no—
232#95Q8×C10314yescomplemented
233C24C2×D4×C10311yescharacteristic
234C2×Q8—42no—
235C2×Q8—42no—
236C2×Q8—42no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—24no—
240C22×C4—24no—
241C22×C4—24no—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—22no—
245C22×C4—22no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—42no—
250C22×C4—42no—
251C22×C4—42no—
252C22×C4—42no—
253C22×C4C22⋊C4×C10311yescharacteristic
254C22×C4C22⋊C4×C10311yescharacteristic
255C22×C4C22⋊C4×C10311yescharacteristic
256C22×C4C22⋊C4×C10311yescharacteristic
257C22×C4D8×C10312yes—
258C22×C4SD16×C10312yes—
259C22×C4C22×C4×C10311yescharacteristic
260C22×C4C2×D4×C10311yescharacteristic
261C22×C4C2×Q8×C10312yes—
262C22×C4#41×C10312yes—
263C2×C8—42no—
264C2×C8—42no—
265C2×C8—42no—
266C4⋊C4—42no—
267C4⋊C4—42no—
268C4⋊C4—42no—
269C4⋊C4—42no—
270C4⋊C4—44no—
271C4⋊C4—42no—
272C22⋊C4—42no—
273C22⋊C4—42no—
274C42—22no—
275C42—22no—
276C42—41no—
277C42—41no—
278C42—48no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23C2×C22⋊C4×C10311yescharacteristic
284C23C22⋊Q8×C10312yes—
285C23C2×D8×C10311yescharacteristic
286C23C2×SD16×C10311yescharacteristic
287C23#137×C10312yes—
288Q8—84no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—24no—
298C2×C4—24no—
299C2×C4—28no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—44no—
306C2×C4—44no—
307C2×C4—44no—
308C2×C4—44no—
309C2×C4—44no—
310C2×C4—44no—
311C2×C4—44no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4#99×C10312yes—
319C2×C4#102×C10312yes—
320C2×C4#102×C10312yes—
321C2×C4#104×C10312yes—
322C2×C4#104×C10312yes—
323C2×C4C4×Q8×C10312yes—
324C2×C4#124×C10311yescharacteristic
325C2×C4C4⋊Q8×C10311yescharacteristic
326C8—82no—
327C22—22no—
328C22—22no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—22no—
334C22—22no—
335C22#391×C10311yescharacteristic
336C22C2×#99×C10311yescharacteristic
337C22#410×C10311yescharacteristic
338C22C2×#102×C10311yescharacteristic
339C22#419×C10311yescharacteristic
340C22C2×#104×C10311yescharacteristic
341C22C2×#104×C10311yescharacteristic
342C22#474×C10312yes—
343C22#475×C10312yes—
344C4—21no—
345C4—22no—
346C4—21no—
347C4—22no—
348C4—22no—
349C4—48no—
350C4—41no—
351C4—82no—
352C4—82no—
353C4#327×C10314yes—
354C2—22no—
355C2—22no—
356C2C2×#327×C10311yescharacteristic
357C2C103×#150211yescharacteristic
358C2C103×#150611yescharacteristic
359C2C103×#150811yescharacteristic
360C2C103×#198811yescharacteristic
361C2C103×#199411yescharacteristic
362C2C103×#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
50. #95×C103Q8semidirect
172. #9909C103direct (N × H)
186. C103#9909direct (N × H)
187. C2×C4⋊Q8C4×C103semidirect
195. #389C4×C103semidirect
196. #384C4×C103semidirect
232. #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
#9909103