Finite Group Databasebeta

← C103×#8093 #39913368

Subgroups — C103×#8093 #39913368

Order 26368.

608 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#2920C211yesmaximal, characteristic
2C2×#423×C103C211yesmaximal, characteristic
3C103×#2283C211yesmaximal, characteristic
4C103×#1303C214yesmaximal, complemented
5C22×M16×C103—21no—
6C22×C42×C103C2211yescharacteristic
7#432×C103—21no—
8#432×C103C412yescomplemented
9#431×C103—21no—
10#431×C103C2212yes—
11#423×C103—21no—
12#423×C103—21no—
13#423×C103C412yescomplemented
14#423×C103C412yescomplemented
15#423×C103C2212yes—
16C2×C4⋊C8×C103—21no—
17C2×C4⋊C8×C103C412yescomplemented
18#407×C103—21no—
19C4×M16×C103—21no—
20#383×C103C412yes—
21#382×C103—21no—
22#381×C103C412yes—
23#380×C103—21no—
24C4×C4⋊C4×C103C2212yes—
25C4×C22⋊C4×C103—21no—
26#376×C103—21no—
27C23×C4×C103C2×C411yescharacteristic
28C23×C4×C103D411yescharacteristic
29C23×C4×C103D411yescharacteristic
30C2×M16×C103—22no—
31C2×M16×C103—22no—
32C2×M16×C103—22no—
33C2×M16×C103—44no—
34C22×C8×C103—22no—
35C2×C4⋊C4×C103—22no—
36C2×C22⋊C4×C103—22no—
37C2×C42×C103—22no—
38C2×C42×C103C2×C411yescharacteristic
39C2×C42×C103C2×C411yescharacteristic
40C2×C42×C103C2×C411yescharacteristic
41C2×C42×C103C2×C411yescharacteristic
42C2×C42×C103C2×C411yescharacteristic
43C2×C42×C103D411yescharacteristic
44C2×C42×C103D411yescharacteristic
45C2×C42×C103D411yescharacteristic
46C2×C42×C103D411yescharacteristic
47C2×C42×C103Q811yescharacteristic
48C2×C42×C103Q811yescharacteristic
49C2×C42×C103C2311yescharacteristic
50C4⋊C8×C103—22no—
51C4⋊C8×C103—22no—
52C4⋊C8×C103—22no—
53C4⋊C8×C103—22no—
54C4⋊C8×C103C2×C414yes—
55C4⋊C8×C103C2×C414yes—
56C22⋊C8×C103—22no—
57C22⋊C8×C103—22no—
58#97×C103—22no—
59C4×C8×C103—22no—
60#95×C103—22no—
61#95×C103—22no—
62#95×C103—22no—
63#95×C103C2×C414yes—
64C24×C103C22⋊C411yescharacteristic
65C22×C4×C103—22no—
66C22×C4×C103—22no—
67C22×C4×C103—24no—
68C22×C4×C103—42no—
69C22×C4×C103—42no—
70C22×C4×C103C4211yescharacteristic
71C22×C4×C103C4211yescharacteristic
72C22×C4×C103C22⋊C411yescharacteristic
73C22×C4×C103C22⋊C411yescharacteristic
74C22×C4×C103C22⋊C411yescharacteristic
75C22×C4×C103C22⋊C411yescharacteristic
76C22×C4×C103C22⋊C411yescharacteristic
77C22×C4×C103C22⋊C411yescharacteristic
78C22×C4×C103C22⋊C411yescharacteristic
79C22×C4×C103C4⋊C411yescharacteristic
80C22×C4×C103C4⋊C411yescharacteristic
81C22×C4×C103C4⋊C411yescharacteristic
82C22×C4×C103C4⋊C411yescharacteristic
83C22×C4×C103C4⋊C411yescharacteristic
84C22×C4×C103C4⋊C411yescharacteristic
85C22×C4×C103C22×C411yescharacteristic
86C22×C4×C103C2×D411yescharacteristic
87C22×C4×C103C2×D411yescharacteristic
88M16×C103—44no—
89M16×C103—44no—
90M16×C103—44no—
91C2×C8×C103—24no—
92C2×C8×C103—24no—
93C2×C8×C103—44no—
94C4⋊C4×C103—44no—
95C22⋊C4×C103—44no—
96C42×C103—42no—
97C42×C103—42no—
98C42×C103C4211yescharacteristic
99C42×C103C4211yescharacteristic
100C42×C103C22⋊C411yescharacteristic
101C42×C103C22⋊C411yescharacteristic
102C42×C103C22⋊C411yescharacteristic
103C42×C103C22⋊C411yescharacteristic
104C42×C103C4⋊C411yescharacteristic
105C42×C103C4⋊C411yescharacteristic
106C42×C103C4⋊C411yescharacteristic
107C42×C103C4⋊C411yescharacteristic
108C42×C103C4⋊C411yescharacteristic
109C42×C103C4⋊C411yescharacteristic
110C42×C103C22×C411yescharacteristic
111C42×C103C22×C411yescharacteristic
112C42×C103C2×D411yescharacteristic
113C42×C103C2×Q811yescharacteristic
114C23×C103—22no—
115C23×C103—22no—
116C23×C103—41no—
117C23×C103#9511yescharacteristic
118C23×C103#9511yescharacteristic
119C23×C103C2×C22⋊C411yescharacteristic
120C2×C4×C103—22no—
121C2×C4×C103—22no—
122C2×C4×C103—22no—
123C2×C4×C103—21no—
124C2×C4×C103—21no—
125C2×C4×C103—21no—
126C2×C4×C103—21no—
127C2×C4×C103—22no—
128C2×C4×C103—22no—
129C2×C4×C103—22no—
130C2×C4×C103—22no—
131C2×C4×C103—22no—
132C2×C4×C103—41no—
133C2×C4×C103—41no—
134C2×C4×C103—41no—
135C2×C4×C103—41no—
136C2×C4×C103—41no—
137C2×C4×C103—41no—
138C2×C4×C103—41no—
139C2×C4×C103—44no—
140C2×C4×C103—44no—
141C2×C4×C103—44no—
142C2×C4×C103#9511yescharacteristic
143C2×C4×C103#9511yescharacteristic
144C2×C4×C103#9511yescharacteristic
145C2×C4×C103#9511yescharacteristic
146C2×C4×C103#9511yescharacteristic
147C2×C4×C103#9511yescharacteristic
148C2×C4×C103C2×C4211yescharacteristic
149C2×C4×C103C2×C22⋊C411yescharacteristic
150C2×C4×C103C2×C22⋊C411yescharacteristic
151C2×C4×C103C2×C4⋊C411yescharacteristic
152C2×C4×C103C2×C4⋊C411yescharacteristic
153C2×C4×C103C2×C4⋊C411yescharacteristic
154C2×C4×C103AGL(1,ℤ/8)12yes—
155C2×C4×C103#13712yes—
156C8×C103—44no—
157C8×C103—44no—
158C22×C103—21no—
159C22×C103—21no—
160C22×C103—21no—
161C22×C103—21no—
162C22×C103—21no—
163C22×C103—21no—
164C22×C103—21no—
165C22×C103—44no—
166C22×C103#34412yes—
167C22×C103C2×#9511yescharacteristic
168C22×C103#41712yes—
169C4×C103—21no—
170C4×C103—21no—
171C4×C103—21no—
172C4×C103—21no—
173C4×C103—21no—
174C4×C103—21no—
175C4×C103—21no—
176C4×C103—21no—
177C4×C103—21no—
178C4×C103—84no—
179C4×C103#41811yescharacteristic
180C4×C103#41911yescharacteristic
181C4×C103#42112yes—
182C4×C103#42812yes—
183#8093C10311yesmaximal, characteristic, direct product factor, Sylow
184C2×C103—22no—
185C2×C103—22no—
186C2×C103—41no—
187C2×C103#173311yescharacteristic
188C2×C103#173611yescharacteristic
189C2×C103C2×#34411yescharacteristic
190#2920C2×C10311yescharacteristic
191C2×#423C2×C10311yescharacteristic
192#2283C2×C10311yescharacteristic
193#1303C2×C10314yescomplemented
194C103#809311yescharacteristic, direct product factor, Sylow
195C22×M16—21no—
196C22×C42C22×C10311yescharacteristic
197#432—21no—
198#432C4×C10312yescomplemented
199#431—21no—
200#431C22×C10312yes—
201#423—21no—
202#423—21no—
203#423C4×C10312yescomplemented
204#423C4×C10312yescomplemented
205#423C22×C10312yes—
206C2×C4⋊C8—21no—
207C2×C4⋊C8C4×C10312yescomplemented
208#407—21no—
209C4×M16—21no—
210#383C4×C10312yes—
211#382—21no—
212#381C4×C10312yes—
213#380—21no—
214C4×C4⋊C4C22×C10312yes—
215C4×C22⋊C4—21no—
216#376—21no—
217C23×C4C2×C4×C10311yescharacteristic
218C23×C4D4×C10311yescharacteristic
219C23×C4D4×C10311yescharacteristic
220C2×M16—22no—
221C2×M16—22no—
222C2×M16—22no—
223C2×M16—44no—
224C22×C8—22no—
225C2×C4⋊C4—22no—
226C2×C22⋊C4—22no—
227C2×C42—22no—
228C2×C42C2×C4×C10311yescharacteristic
229C2×C42C2×C4×C10311yescharacteristic
230C2×C42C2×C4×C10311yescharacteristic
231C2×C42C2×C4×C10311yescharacteristic
232C2×C42C2×C4×C10311yescharacteristic
233C2×C42D4×C10311yescharacteristic
234C2×C42D4×C10311yescharacteristic
235C2×C42D4×C10311yescharacteristic
236C2×C42D4×C10311yescharacteristic
237C2×C42Q8×C10311yescharacteristic
238C2×C42Q8×C10311yescharacteristic
239C2×C42C23×C10311yescharacteristic
240C4⋊C8—22no—
241C4⋊C8—22no—
242C4⋊C8—22no—
243C4⋊C8—22no—
244C4⋊C8C2×C4×C10314yes—
245C4⋊C8C2×C4×C10314yes—
246C22⋊C8—22no—
247C22⋊C8—22no—
248#97—22no—
249C4×C8—22no—
250#95—22no—
251#95—22no—
252#95—22no—
253#95C2×C4×C10314yes—
254C24C22⋊C4×C10311yescharacteristic
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—24no—
258C22×C4—42no—
259C22×C4—42no—
260C22×C4C42×C10311yescharacteristic
261C22×C4C42×C10311yescharacteristic
262C22×C4C22⋊C4×C10311yescharacteristic
263C22×C4C22⋊C4×C10311yescharacteristic
264C22×C4C22⋊C4×C10311yescharacteristic
265C22×C4C22⋊C4×C10311yescharacteristic
266C22×C4C22⋊C4×C10311yescharacteristic
267C22×C4C22⋊C4×C10311yescharacteristic
268C22×C4C22⋊C4×C10311yescharacteristic
269C22×C4C4⋊C4×C10311yescharacteristic
270C22×C4C4⋊C4×C10311yescharacteristic
271C22×C4C4⋊C4×C10311yescharacteristic
272C22×C4C4⋊C4×C10311yescharacteristic
273C22×C4C4⋊C4×C10311yescharacteristic
274C22×C4C4⋊C4×C10311yescharacteristic
275C22×C4C22×C4×C10311yescharacteristic
276C22×C4C2×D4×C10311yescharacteristic
277C22×C4C2×D4×C10311yescharacteristic
278M16—44no—
279M16—44no—
280M16—44no—
281C2×C8—24no—
282C2×C8—24no—
283C2×C8—44no—
284C4⋊C4—44no—
285C22⋊C4—44no—
286C42—42no—
287C42—42no—
288C42C42×C10311yescharacteristic
289C42C42×C10311yescharacteristic
290C42C22⋊C4×C10311yescharacteristic
291C42C22⋊C4×C10311yescharacteristic
292C42C22⋊C4×C10311yescharacteristic
293C42C22⋊C4×C10311yescharacteristic
294C42C4⋊C4×C10311yescharacteristic
295C42C4⋊C4×C10311yescharacteristic
296C42C4⋊C4×C10311yescharacteristic
297C42C4⋊C4×C10311yescharacteristic
298C42C4⋊C4×C10311yescharacteristic
299C42C4⋊C4×C10311yescharacteristic
300C42C22×C4×C10311yescharacteristic
301C42C22×C4×C10311yescharacteristic
302C42C2×D4×C10311yescharacteristic
303C42C2×Q8×C10311yescharacteristic
304C23—22no—
305C23—22no—
306C23—41no—
307C23#95×C10311yescharacteristic
308C23#95×C10311yescharacteristic
309C23C2×C22⋊C4×C10311yescharacteristic
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—44no—
330C2×C4—44no—
331C2×C4—44no—
332C2×C4#95×C10311yescharacteristic
333C2×C4#95×C10311yescharacteristic
334C2×C4#95×C10311yescharacteristic
335C2×C4#95×C10311yescharacteristic
336C2×C4#95×C10311yescharacteristic
337C2×C4#95×C10311yescharacteristic
338C2×C4C2×C42×C10311yescharacteristic
339C2×C4C2×C22⋊C4×C10311yescharacteristic
340C2×C4C2×C22⋊C4×C10311yescharacteristic
341C2×C4C2×C4⋊C4×C10311yescharacteristic
342C2×C4C2×C4⋊C4×C10311yescharacteristic
343C2×C4C2×C4⋊C4×C10311yescharacteristic
344C2×C4AGL(1,ℤ/8)×C10312yes—
345C2×C4#137×C10312yes—
346C8—44no—
347C8—44no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—44no—
356C22#344×C10312yes—
357C22C2×#95×C10311yescharacteristic
358C22#417×C10312yes—
359C4—21no—
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—84no—
369C4#418×C10311yescharacteristic
370C4#419×C10311yescharacteristic
371C4#421×C10312yes—
372C4#428×C10312yes—
373C2—22no—
374C2—22no—
375C2—41no—
376C2C103×#173311yescharacteristic
377C2C103×#173611yescharacteristic
378C2C2×#344×C10311yescharacteristic
subgroupG/H
centerC2×C4×C103C2×C22⋊C4
commutatorC2×C4C2×C42×C103
Frattini, cosocleC2×C42C23×C103
socleC22×C103C2×#95
prime radicalC24×C103C22⋊C4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C103 ◁ C22×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
4. C103×#1303C2semidirect
8. #432×C103C4semidirect
13. #423×C103C4semidirect
14. #423×C103C4semidirect
17. C2×C4⋊C8×C103C4semidirect
183. #8093C103direct (N × H)
193. #1303C2×C103semidirect
194. C103#8093direct (N × H)
198. #432C4×C103semidirect
203. #423C4×C103semidirect
204. #423C4×C103semidirect
207. C2×C4⋊C8C4×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#29202
C2×#423×C1032
C103×#22832
C103×#13032
#8093103