Finite Group Databasebeta

← C103×#9879 #39915154

Subgroups — C103×#9879 #39915154

Order 26368.

616 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#389×C103C211yesmaximal, characteristic
2C103×#1797C211yesmaximal, characteristic
3C4×C22⋊C8×C103C211yesmaximal, characteristic
4C103×#1280C214yesmaximal
5C22×C4⋊C4×C103C411yescharacteristic
6C22×C4⋊C4×C103C412yes—
7C22×C4⋊C4×C103C411yescharacteristic
8C22×C42×C103C2211yescharacteristic
9C2×C4⋊C8×C103—21no—
10C2×C22⋊C8×C103C2212yes—
11C2×C22⋊C8×C103C2212yes—
12C2×C4×C8×C103—21no—
13#389×C103—21no—
14#389×C103—21no—
15#389×C103—21no—
16#389×C103—21no—
17C2×#95×C103C2212yes—
18#336×C103—21no—
19#336×C103—21no—
20C23×C4×C103C2×C411yescharacteristic
21C23×C4×C103C2×C411yescharacteristic
22C23×C4×C103C2×C412yes—
23C23×C4×C103C2×C412yes—
24C23×C4×C103C2311yescharacteristic
25C22×C8×C103—22no—
26C22×C8×C103—22no—
27C2×C4⋊C4×C103—21no—
28C2×C4⋊C4×C103—21no—
29C2×C4⋊C4×C103—22no—
30C2×C4⋊C4×C103—22no—
31C2×C4⋊C4×C103—21no—
32C2×C4⋊C4×C103—21no—
33C2×C4⋊C4×C103—22no—
34C2×C4⋊C4×C103—42no—
35C2×C4⋊C4×C103—44no—
36C2×C4⋊C4×C103C814yescomplemented
37C2×C42×C103—42no—
38C2×C42×C103D411yescharacteristic
39C2×C42×C103D411yescharacteristic
40C2×C42×C103D411yescharacteristic
41C2×C42×C103D411yescharacteristic
42C4⋊C8×C103—42no—
43C22⋊C8×C103—22no—
44C22⋊C8×C103—24no—
45C22⋊C8×C103Q814yes—
46C4×C8×C103—42no—
47#95×C103—22no—
48#95×C103—22no—
49C24×C103C22×C411yescharacteristic
50C22×C4×C103—22no—
51C22×C4×C103—22no—
52C22×C4×C103—22no—
53C22×C4×C103—22no—
54C22×C4×C103—22no—
55C22×C4×C103—22no—
56C22×C4×C103—22no—
57C22×C4×C103—24no—
58C22×C4×C103—41no—
59C22×C4×C103—41no—
60C22×C4×C103—41no—
61C22×C4×C103—42no—
62C22×C4×C103—42no—
63C22×C4×C103—42no—
64C22×C4×C103—42no—
65C22×C4×C103C22⋊C411yescharacteristic
66C22×C4×C103C22⋊C411yescharacteristic
67C22×C4×C103C22⋊C411yescharacteristic
68C22×C4×C103C22⋊C411yescharacteristic
69C22×C4×C103C2×C812yes—
70C22×C4×C103C2×C814yes—
71C22×C4×C103M1612yes—
72C22×C4×C103C2×D411yescharacteristic
73C22×C4×C103C2×D411yescharacteristic
74C22×C4×C103C2×Q812yes—
75C22×C4×C103#4112yes—
76C2×C8×C103—24no—
77C2×C8×C103—42no—
78C2×C8×C103—42no—
79C2×C8×C103—42no—
80C2×C8×C103—42no—
81C2×C8×C103—42no—
82C4⋊C4×C103—24no—
83C4⋊C4×C103—24no—
84C4⋊C4×C103—42no—
85C4⋊C4×C103—44no—
86C4⋊C4×C103—42no—
87C4⋊C4×C103—44no—
88C42×C103—22no—
89C42×C103—22no—
90C42×C103—41no—
91C42×C103—41no—
92C23×C103—21no—
93C23×C103—21no—
94C23×C103—21no—
95C23×C103—21no—
96C23×C103C2×C22⋊C411yescharacteristic
97C23×C103C4×Q812yes—
98C23×C103C22×C811yescharacteristic
99C23×C103C2×M1611yescharacteristic
100C23×C103#13112yes—
101C2×C4×C103—21no—
102C2×C4×C103—21no—
103C2×C4×C103—21no—
104C2×C4×C103—21no—
105C2×C4×C103—21no—
106C2×C4×C103—21no—
107C2×C4×C103—21no—
108C2×C4×C103—21no—
109C2×C4×C103—24no—
110C2×C4×C103—24no—
111C2×C4×C103—24no—
112C2×C4×C103—21no—
113C2×C4×C103—21no—
114C2×C4×C103—21no—
115C2×C4×C103—42no—
116C2×C4×C103—42no—
117C2×C4×C103—44no—
118C2×C4×C103—44no—
119C2×C4×C103—42no—
120C2×C4×C103—42no—
121C2×C4×C103—44no—
122C2×C4×C103—42no—
123C2×C4×C103—42no—
124C2×C4×C103—42no—
125C2×C4×C103—84no—
126C2×C4×C103C22⋊C812yes—
127C2×C4×C103C22⋊C812yes—
128C2×C4×C103#9912yes—
129C2×C4×C103#10012yes—
130C2×C4×C103#10112yes—
131C2×C4×C103C22⋊Q812yes—
132C2×C4×C103#12411yescharacteristic
133C2×C4×C103C4⋊Q811yescharacteristic
134C8×C103—44no—
135C8×C103—82no—
136C22×C103—21no—
137C22×C103—21no—
138C22×C103—21no—
139C22×C103—21no—
140C22×C103—22no—
141C22×C103—22no—
142C22×C103—22no—
143C22×C103—22no—
144C22×C103#39111yescharacteristic
145C22×C103C2×C22⋊C811yescharacteristic
146C22×C103#40811yescharacteristic
147C22×C103C2×#9911yescharacteristic
148C22×C103#41011yescharacteristic
149C22×C103C2×#10011yescharacteristic
150C22×C103C2×#10111yescharacteristic
151C22×C103C8×Q812yes—
152C22×C103#44612yes—
153C4×C103—22no—
154C4×C103—22no—
155C4×C103—22no—
156C4×C103—21no—
157C4×C103—21no—
158C4×C103—44no—
159C4×C103—41no—
160C4×C103—82no—
161C4×C103#32414yes—
162#9879C10311yesmaximal, characteristic, direct product factor, Sylow
163C2×C103—22no—
164C2×C103—22no—
165C2×C103C2×#32411yescharacteristic
166C2×C103#146011yescharacteristic
167C2×C103#147011yescharacteristic
168C2×C103#147111yescharacteristic
169C2×C103#198411yescharacteristic
170C2×C103#199611yescharacteristic
171C2×C103#199711yescharacteristic
172C2×#389C2×C10311yescharacteristic
173#1797C2×C10311yescharacteristic
174C4×C22⋊C8C2×C10311yescharacteristic
175#1280C2×C10314yes—
176C103#987911yescharacteristic, direct product factor, Sylow
177C22×C4⋊C4C4×C10311yescharacteristic
178C22×C4⋊C4C4×C10312yes—
179C22×C4⋊C4C4×C10311yescharacteristic
180C22×C42C22×C10311yescharacteristic
181C2×C4⋊C8—21no—
182C2×C22⋊C8C22×C10312yes—
183C2×C22⋊C8C22×C10312yes—
184C2×C4×C8—21no—
185#389—21no—
186#389—21no—
187#389—21no—
188#389—21no—
189C2×#95C22×C10312yes—
190#336—21no—
191#336—21no—
192C23×C4C2×C4×C10311yescharacteristic
193C23×C4C2×C4×C10311yescharacteristic
194C23×C4C2×C4×C10312yes—
195C23×C4C2×C4×C10312yes—
196C23×C4C23×C10311yescharacteristic
197C22×C8—22no—
198C22×C8—22no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—22no—
202C2×C4⋊C4—22no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—22no—
206C2×C4⋊C4—42no—
207C2×C4⋊C4—44no—
208C2×C4⋊C4C8×C10314yescomplemented
209C2×C42—42no—
210C2×C42D4×C10311yescharacteristic
211C2×C42D4×C10311yescharacteristic
212C2×C42D4×C10311yescharacteristic
213C2×C42D4×C10311yescharacteristic
214C4⋊C8—42no—
215C22⋊C8—22no—
216C22⋊C8—24no—
217C22⋊C8Q8×C10314yes—
218C4×C8—42no—
219#95—22no—
220#95—22no—
221C24C22×C4×C10311yescharacteristic
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—24no—
230C22×C4—41no—
231C22×C4—41no—
232C22×C4—41no—
233C22×C4—42no—
234C22×C4—42no—
235C22×C4—42no—
236C22×C4—42no—
237C22×C4C22⋊C4×C10311yescharacteristic
238C22×C4C22⋊C4×C10311yescharacteristic
239C22×C4C22⋊C4×C10311yescharacteristic
240C22×C4C22⋊C4×C10311yescharacteristic
241C22×C4C2×C8×C10312yes—
242C22×C4C2×C8×C10314yes—
243C22×C4M16×C10312yes—
244C22×C4C2×D4×C10311yescharacteristic
245C22×C4C2×D4×C10311yescharacteristic
246C22×C4C2×Q8×C10312yes—
247C22×C4#41×C10312yes—
248C2×C8—24no—
249C2×C8—42no—
250C2×C8—42no—
251C2×C8—42no—
252C2×C8—42no—
253C2×C8—42no—
254C4⋊C4—24no—
255C4⋊C4—24no—
256C4⋊C4—42no—
257C4⋊C4—44no—
258C4⋊C4—42no—
259C4⋊C4—44no—
260C42—22no—
261C42—22no—
262C42—41no—
263C42—41no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23C2×C22⋊C4×C10311yescharacteristic
269C23C4×Q8×C10312yes—
270C23C22×C8×C10311yescharacteristic
271C23C2×M16×C10311yescharacteristic
272C23#131×C10312yes—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—24no—
282C2×C4—24no—
283C2×C4—24no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—44no—
290C2×C4—44no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—44no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—84no—
298C2×C4C22⋊C8×C10312yes—
299C2×C4C22⋊C8×C10312yes—
300C2×C4#99×C10312yes—
301C2×C4#100×C10312yes—
302C2×C4#101×C10312yes—
303C2×C4C22⋊Q8×C10312yes—
304C2×C4#124×C10311yescharacteristic
305C2×C4C4⋊Q8×C10311yescharacteristic
306C8—44no—
307C8—82no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—22no—
313C22—22no—
314C22—22no—
315C22—22no—
316C22#391×C10311yescharacteristic
317C22C2×C22⋊C8×C10311yescharacteristic
318C22#408×C10311yescharacteristic
319C22C2×#99×C10311yescharacteristic
320C22#410×C10311yescharacteristic
321C22C2×#100×C10311yescharacteristic
322C22C2×#101×C10311yescharacteristic
323C22C8×Q8×C10312yes—
324C22#446×C10312yes—
325C4—22no—
326C4—22no—
327C4—22no—
328C4—21no—
329C4—21no—
330C4—44no—
331C4—41no—
332C4—82no—
333C4#324×C10314yes—
334C2—22no—
335C2—22no—
336C2C2×#324×C10311yescharacteristic
337C2C103×#146011yescharacteristic
338C2C103×#147011yescharacteristic
339C2C103×#147111yescharacteristic
340C2C103×#198411yescharacteristic
341C2C103×#199611yescharacteristic
342C2C103×#199711yescharacteristic
subgroupG/H
center, socleC23×C103C2×C22⋊C4
commutatorC23C22×C8×C103
Frattini, cosocleC23×C4C23×C103
prime radicalC24×C103C22×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C103 ◁ C22×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
36. C2×C4⋊C4×C103C8semidirect
162. #9879C103direct (N × H)
176. C103#9879direct (N × H)
208. C2×C4⋊C4C8×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#389×C1032
C103×#17972
C4×C22⋊C8×C1032
C103×#12802
#9879103