Finite Group Databasebeta

← C83×#11425 #35239249

Subgroups — C83×#11425 #35239249

Order 21248.

678 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 678 conjugacy classes of subgroups — too many to draw. Only its 142 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
1C83×#2280C211yesmaximal, characteristic
2C83×#1458C212yesmaximal, complemented
3C83×#1317C212yesmaximal, complemented
4C83×#1316C212yesmaximal
5C24×C4×C83C411yescharacteristic
6C2×#117×C83C411yescharacteristic
7C2×#117×C83C2211yescharacteristic
8#431×C83—22no—
9#381×C83C411yescharacteristic
10#381×C83C2211yescharacteristic
11#380×C83—22no—
12#379×C83C411yescharacteristic
13#379×C83C2211yescharacteristic
14C4×C22⋊C4×C83—22no—
15#324×C83—22no—
16#323×C83C2214yes—
17C25×C83C2×C411yescharacteristic
18C23×C4×C83—21no—
19C23×C4×C83—21no—
20C23×C4×C83—22no—
21C23×C4×C83—41no—
22C23×C4×C83—41no—
23C23×C4×C83—42no—
24C23×C4×C83C814yescomplemented
25C23×C4×C83C2×C411yescharacteristic
26C23×C4×C83C2×C411yescharacteristic
27#117×C83—41no—
28#117×C83—41no—
29#117×C83—42no—
30C2×C4⋊C4×C83—21no—
31C2×C4⋊C4×C83D412yes—
32C2×C22⋊C4×C83—22no—
33C2×C22⋊C4×C83—22no—
34C2×C22⋊C4×C83C2×C411yescharacteristic
35C2×C22⋊C4×C83C2×C411yescharacteristic
36C2×C22⋊C4×C83C2×C411yescharacteristic
37C2×C22⋊C4×C83C2311yescharacteristic
38C2×C42×C83—21no—
39C2×C42×C83D412yes—
40C4⋊C8×C83—42no—
41C22⋊C8×C83—24no—
42C4×C8×C83—42no—
43#95×C83—22no—
44#95×C83—22no—
45C24×C83—21no—
46C24×C83—21no—
47C24×C83—41no—
48C24×C83—41no—
49C24×C83—44no—
50C24×C83C2×C812yes—
51C24×C83C22×C411yescharacteristic
52C22×C4×C83—21no—
53C22×C4×C83—21no—
54C22×C4×C83—22no—
55C22×C4×C83—21no—
56C22×C4×C83—21no—
57C22×C4×C83—24no—
58C22×C4×C83—24no—
59C22×C4×C83—21no—
60C22×C4×C83—21no—
61C22×C4×C83—42no—
62C22×C4×C83—42no—
63C22×C4×C83—44no—
64C22×C4×C83—44no—
65C22×C4×C83—44no—
66C22×C4×C83—44no—
67C22×C4×C83—41no—
68C22×C4×C83—41no—
69C22×C4×C83—42no—
70C22×C4×C83—41no—
71C22×C4×C83—41no—
72C22×C4×C83C22⋊C411yescharacteristic
73C22×C4×C83C22⋊C412yes—
74C22×C4×C83C22⋊C411yescharacteristic
75C22×C4×C83C2×C812yes—
76C22×C4×C83C2×C812yes—
77C22×C4×C83M1612yes—
78C22×C4×C83C2×D412yes—
79C2×C8×C83—44no—
80C4⋊C4×C83—42no—
81C4⋊C4×C83—42no—
82C22⋊C4×C83—41no—
83C22⋊C4×C83—41no—
84C22⋊C4×C83—44no—
85C22⋊C4×C83—44no—
86C22⋊C4×C83—41no—
87C22⋊C4×C83—41no—
88C42×C83—22no—
89C42×C83—22no—
90C42×C83—42no—
91C23×C83—24no—
92C23×C83—22no—
93C23×C83—21no—
94C23×C83—21no—
95C23×C83—42no—
96C23×C83—44no—
97C23×C83—42no—
98C23×C83—42no—
99C23×C83—42no—
100C23×C83—44no—
101C23×C83—44no—
102C23×C83—48no—
103C23×C83—44no—
104C23×C83—41no—
105C23×C83—41no—
106C23×C83C2×C22⋊C411yescharacteristic
107C23×C83C22×C811yescharacteristic
108C23×C83C2×M1611yescharacteristic
109C2×C4×C83—21no—
110C2×C4×C83—21no—
111C2×C4×C83—22no—
112C2×C4×C83—22no—
113C2×C4×C83—22no—
114C2×C4×C83—22no—
115C2×C4×C83—22no—
116C2×C4×C83—22no—
117C2×C4×C83—22no—
118C2×C4×C83—48no—
119C2×C4×C83—42no—
120C2×C4×C83—41no—
121C2×C4×C83—41no—
122C2×C4×C83—44no—
123C2×C4×C83—44no—
124C2×C4×C83—42no—
125C2×C4×C83—42no—
126C2×C4×C83—42no—
127C2×C4×C83—42no—
128C2×C4×C83—42no—
129C2×C4×C83—41no—
130C2×C4×C83—41no—
131C2×C4×C83C22⋊C812yes—
132C2×C4×C83C22⋊C812yes—
133C2×C4×C83#9911yescharacteristic
134C2×C4×C83#9911yescharacteristic
135C2×C4×C83#10012yes—
136C8×C83—84no—
137C22×C83—22no—
138C22×C83—24no—
139C22×C83—21no—
140C22×C83—21no—
141C22×C83—41no—
142C22×C83—41no—
143C22×C83—44no—
144C22×C83—42no—
145C22×C83—42no—
146C22×C83—44no—
147C22×C83—44no—
148C22×C83—48no—
149C22×C83—44no—
150C22×C83—42no—
151C22×C83—42no—
152C22×C83C2×C22⋊C811yescharacteristic
153C22×C83C2×#9911yescharacteristic
154C22×C83C2×#10011yescharacteristic
155C4×C83—22no—
156C4×C83—42no—
157C4×C83—42no—
158C4×C83—42no—
159C4×C83—81no—
160C4×C83—81no—
161C4×C83#32312yes—
162C4×C83#32312yes—
163#11425C8311yesmaximal, characteristic, direct product factor, Sylow
164C2×C83—21no—
165C2×C83—21no—
166C2×C83—44no—
167C2×C83—41no—
168C2×C83—41no—
169C2×C83C2×#32311yescharacteristic
170C2×C83#212012yes—
171#2280C2×C8311yescharacteristic
172#1458C2×C8312yescomplemented
173#1317C2×C8312yescomplemented
174#1316C2×C8312yes—
175C83#1142511yescharacteristic, direct product factor, Sylow
176C24×C4C4×C8311yescharacteristic
177C2×#117C4×C8311yescharacteristic
178C2×#117C22×C8311yescharacteristic
179#431—22no—
180#381C4×C8311yescharacteristic
181#381C22×C8311yescharacteristic
182#380—22no—
183#379C4×C8311yescharacteristic
184#379C22×C8311yescharacteristic
185C4×C22⋊C4—22no—
186#324—22no—
187#323C22×C8314yes—
188C25C2×C4×C8311yescharacteristic
189C23×C4—21no—
190C23×C4—21no—
191C23×C4—22no—
192C23×C4—41no—
193C23×C4—41no—
194C23×C4—42no—
195C23×C4C8×C8314yescomplemented
196C23×C4C2×C4×C8311yescharacteristic
197C23×C4C2×C4×C8311yescharacteristic
198#117—41no—
199#117—41no—
200#117—42no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4D4×C8312yes—
203C2×C22⋊C4—22no—
204C2×C22⋊C4—22no—
205C2×C22⋊C4C2×C4×C8311yescharacteristic
206C2×C22⋊C4C2×C4×C8311yescharacteristic
207C2×C22⋊C4C2×C4×C8311yescharacteristic
208C2×C22⋊C4C23×C8311yescharacteristic
209C2×C42—21no—
210C2×C42D4×C8312yes—
211C4⋊C8—42no—
212C22⋊C8—24no—
213C4×C8—42no—
214#95—22no—
215#95—22no—
216C24—21no—
217C24—21no—
218C24—41no—
219C24—41no—
220C24—44no—
221C24C2×C8×C8312yes—
222C24C22×C4×C8311yescharacteristic
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—22no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—24no—
229C22×C4—24no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—42no—
233C22×C4—42no—
234C22×C4—44no—
235C22×C4—44no—
236C22×C4—44no—
237C22×C4—44no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—42no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4C22⋊C4×C8311yescharacteristic
244C22×C4C22⋊C4×C8312yes—
245C22×C4C22⋊C4×C8311yescharacteristic
246C22×C4C2×C8×C8312yes—
247C22×C4C2×C8×C8312yes—
248C22×C4M16×C8312yes—
249C22×C4C2×D4×C8312yes—
250C2×C8—44no—
251C4⋊C4—42no—
252C4⋊C4—42no—
253C22⋊C4—41no—
254C22⋊C4—41no—
255C22⋊C4—44no—
256C22⋊C4—44no—
257C22⋊C4—41no—
258C22⋊C4—41no—
259C42—22no—
260C42—22no—
261C42—42no—
262C23—24no—
263C23—22no—
264C23—21no—
265C23—21no—
266C23—42no—
267C23—44no—
268C23—42no—
269C23—42no—
270C23—42no—
271C23—44no—
272C23—44no—
273C23—48no—
274C23—44no—
275C23—41no—
276C23—41no—
277C23C2×C22⋊C4×C8311yescharacteristic
278C23C22×C8×C8311yescharacteristic
279C23C2×M16×C8311yescharacteristic
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—48no—
290C2×C4—42no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—44no—
294C2×C4—44no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4C22⋊C8×C8312yes—
303C2×C4C22⋊C8×C8312yes—
304C2×C4#99×C8311yescharacteristic
305C2×C4#99×C8311yescharacteristic
306C2×C4#100×C8312yes—
307C8—84no—
308C22—22no—
309C22—24no—
310C22—21no—
311C22—21no—
312C22—41no—
313C22—41no—
314C22—44no—
315C22—42no—
316C22—42no—
317C22—44no—
318C22—44no—
319C22—48no—
320C22—44no—
321C22—42no—
322C22—42no—
323C22C2×C22⋊C8×C8311yescharacteristic
324C22C2×#99×C8311yescharacteristic
325C22C2×#100×C8311yescharacteristic
326C4—22no—
327C4—42no—
328C4—42no—
329C4—42no—
330C4—81no—
331C4—81no—
332C4#323×C8312yes—
333C4#323×C8312yes—
334C2—21no—
335C2—21no—
336C2—44no—
337C2—41no—
338C2—41no—
339C2C2×#323×C8311yescharacteristic
340C2C83×#212012yes—
subgroupG/H
centerC2×C4×C83#99
commutatorC23C22×C8×C83
Frattini, cosocleC2×C22⋊C4C23×C83
socleC22×C83C2×#99
prime radicalC25×C83C2×C4
LCSG ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C83 ◁ C22×C4×C83 ◁ C2×#117×C83 ◁ G

Complements

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

NH ≅ G/Ntype
2. C83×#1458C2semidirect
3. C83×#1317C2semidirect
24. C23×C4×C83C8semidirect
163. #11425C83direct (N × H)
172. #1458C2×C83semidirect
173. #1317C2×C83semidirect
175. C83#11425direct (N × H)
195. C23×C4C8×C83semidirect

Maximal subgroups

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

subgroupindex
C83×#22802
C83×#14582
C83×#13172
C83×#13162
#1142583