Finite Group Databasebeta

← C83×#9439 #35237263

Subgroups — C83×#9439 #35237263

Order 21248.

490 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 118 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×#3140C211yesmaximal, characteristic
2C83×#2372C211yesmaximal, characteristic
3C83×#1533C211yesmaximal, characteristic
4C83×#1506C212yesmaximal, complemented
5C83×#1300C212yesmaximal, complemented
6#533×C83C2211yescharacteristic
7C2×#124×C83C2211yescharacteristic
8#489×C83C414yescomplemented
9#488×C83—22no—
10#432×C83C2212yes—
11#419×C83—21no—
12#418×C83—21no—
13C4×M16×C83C2211yescharacteristic
14#391×C83—21no—
15#388×C83—22no—
16#386×C83—21no—
17C4×C22⋊C4×C83—22no—
18#376×C83C2212yes—
19#329×C83—22no—
20#328×C83—22no—
21#328×C83—22no—
22C22×Q8×C83D411yescharacteristic
23C22×D4×C83D411yescharacteristic
24C23×C4×C83—21no—
25C2×M16×C83—21no—
26C4⋊Q8×C83C2×C412yescomplemented
27#125×C83—21no—
28#124×C83—22no—
29#124×C83C2×C412yes—
30#124×C83D412yes—
31C22⋊Q8×C83—22no—
32C4×Q8×C83—22no—
33#117×C83—21no—
34C2×C4⋊C4×C83—21no—
35C2×C22⋊C4×C83—22no—
36C2×C22⋊C4×C83—22no—
37C2×C22⋊C4×C83—21no—
38C2×C42×C83—22no—
39C2×C42×C83—21no—
40C2×C42×C83C2311yescharacteristic
41C4⋊C8×C83—22no—
42#103×C83—24no—
43#102×C83—24no—
44C22⋊C8×C83—22no—
45#97×C83—22no—
46#97×C83C2×C412yescomplemented
47C4×C8×C83—21no—
48#95×C83—22no—
49#95×C83—22no—
50#95×C83D412yes—
51#95×C83D412yes—
52C24×C83—21no—
53C2×Q8×C83—21no—
54C2×Q8×C83—22no—
55C2×Q8×C83—41no—
56C2×Q8×C83—41no—
57C2×Q8×C83C22⋊C412yes—
58C2×D4×C83—21no—
59C2×D4×C83—41no—
60C2×D4×C83—41no—
61C2×D4×C83C22⋊C412yes—
62C22×C4×C83—22no—
63C22×C4×C83—21no—
64C22×C4×C83—22no—
65C22×C4×C83—44no—
66C22×C4×C83—81no—
67C22×C4×C83C2×D411yescharacteristic
68C22×C4×C83C2×D412yes—
69M16×C83—41no—
70M16×C83—41no—
71C2×C8×C83—22no—
72C2×C8×C83—42no—
73C4⋊C4×C83—22no—
74C4⋊C4×C83—22no—
75C4⋊C4×C83—42no—
76C4⋊C4×C83—81no—
77C22⋊C4×C83—24no—
78C22⋊C4×C83—24no—
79C22⋊C4×C83—44no—
80C22⋊C4×C83—41no—
81C22⋊C4×C83—81no—
82C42×C83—44no—
83C42×C83—41no—
84C42×C83—81no—
85C42×C83C22×C411yescharacteristic
86C42×C83C2×D411yescharacteristic
87C42×C83#4112yes—
88C23×C83—22no—
89C23×C83—42no—
90C23×C83—42no—
91C23×C83—41no—
92C23×C83—41no—
93C23×C83#12011yescharacteristic
94Q8×C83—42no—
95Q8×C83—81no—
96Q8×C83—82no—
97D4×C83—42no—
98D4×C83—81no—
99C2×C4×C83—21no—
100C2×C4×C83—21no—
101C2×C4×C83—24no—
102C2×C4×C83—22no—
103C2×C4×C83—42no—
104C2×C4×C83—42no—
105C2×C4×C83—42no—
106C2×C4×C83—41no—
107C2×C4×C83—41no—
108C2×C4×C83—42no—
109C2×C4×C83—42no—
110C2×C4×C83—42no—
111C2×C4×C83—42no—
112C2×C4×C83—84no—
113C2×C4×C83C2×C22⋊C411yescharacteristic
114C2×C4×C83C4×D412yes—
115C2×C4×C83#12112yes—
116C2×C4×C83#12311yescharacteristic
117C8×C83—42no—
118C8×C83—82no—
119C22×C83—22no—
120C22×C83—42no—
121C22×C83—44no—
122C22×C83—81no—
123C22×C83—81no—
124C22×C83—82no—
125C22×C83#38611yescharacteristic
126C22×C83#45511yescharacteristic
127C22×C83#45511yescharacteristic
128C4×C83—21no—
129C4×C83—21no—
130C4×C83—22no—
131C4×C83—22no—
132C4×C83—44no—
133C4×C83—42no—
134C4×C83—82no—
135C4×C83—82no—
136#9439C8311yesmaximal, characteristic, direct product factor, Sylow
137C2×C83—21no—
138C2×C83—21no—
139C2×C83—82no—
140C2×C83#188511yescharacteristic
141C2×C83#190612yes—
142#3140C2×C8311yescharacteristic
143#2372C2×C8311yescharacteristic
144#1533C2×C8311yescharacteristic
145#1506C2×C8312yescomplemented
146#1300C2×C8312yescomplemented
147C83#943911yescharacteristic, direct product factor, Sylow
148#533C22×C8311yescharacteristic
149C2×#124C22×C8311yescharacteristic
150#489C4×C8314yescomplemented
151#488—22no—
152#432C22×C8312yes—
153#419—21no—
154#418—21no—
155C4×M16C22×C8311yescharacteristic
156#391—21no—
157#388—22no—
158#386—21no—
159C4×C22⋊C4—22no—
160#376C22×C8312yes—
161#329—22no—
162#328—22no—
163#328—22no—
164C22×Q8D4×C8311yescharacteristic
165C22×D4D4×C8311yescharacteristic
166C23×C4—21no—
167C2×M16—21no—
168C4⋊Q8C2×C4×C8312yescomplemented
169#125—21no—
170#124—22no—
171#124C2×C4×C8312yes—
172#124D4×C8312yes—
173C22⋊Q8—22no—
174C4×Q8—22no—
175#117—21no—
176C2×C4⋊C4—21no—
177C2×C22⋊C4—22no—
178C2×C22⋊C4—22no—
179C2×C22⋊C4—21no—
180C2×C42—22no—
181C2×C42—21no—
182C2×C42C23×C8311yescharacteristic
183C4⋊C8—22no—
184#103—24no—
185#102—24no—
186C22⋊C8—22no—
187#97—22no—
188#97C2×C4×C8312yescomplemented
189C4×C8—21no—
190#95—22no—
191#95—22no—
192#95D4×C8312yes—
193#95D4×C8312yes—
194C24—21no—
195C2×Q8—21no—
196C2×Q8—22no—
197C2×Q8—41no—
198C2×Q8—41no—
199C2×Q8C22⋊C4×C8312yes—
200C2×D4—21no—
201C2×D4—41no—
202C2×D4—41no—
203C2×D4C22⋊C4×C8312yes—
204C22×C4—22no—
205C22×C4—21no—
206C22×C4—22no—
207C22×C4—44no—
208C22×C4—81no—
209C22×C4C2×D4×C8311yescharacteristic
210C22×C4C2×D4×C8312yes—
211M16—41no—
212M16—41no—
213C2×C8—22no—
214C2×C8—42no—
215C4⋊C4—22no—
216C4⋊C4—22no—
217C4⋊C4—42no—
218C4⋊C4—81no—
219C22⋊C4—24no—
220C22⋊C4—24no—
221C22⋊C4—44no—
222C22⋊C4—41no—
223C22⋊C4—81no—
224C42—44no—
225C42—41no—
226C42—81no—
227C42C22×C4×C8311yescharacteristic
228C42C2×D4×C8311yescharacteristic
229C42#41×C8312yes—
230C23—22no—
231C23—42no—
232C23—42no—
233C23—41no—
234C23—41no—
235C23#120×C8311yescharacteristic
236Q8—42no—
237Q8—81no—
238Q8—82no—
239D4—42no—
240D4—81no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—24no—
244C2×C4—22no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—84no—
255C2×C4C2×C22⋊C4×C8311yescharacteristic
256C2×C4C4×D4×C8312yes—
257C2×C4#121×C8312yes—
258C2×C4#123×C8311yescharacteristic
259C8—42no—
260C8—82no—
261C22—22no—
262C22—42no—
263C22—44no—
264C22—81no—
265C22—81no—
266C22—82no—
267C22#386×C8311yescharacteristic
268C22#455×C8311yescharacteristic
269C22#455×C8311yescharacteristic
270C4—21no—
271C4—21no—
272C4—22no—
273C4—22no—
274C4—44no—
275C4—42no—
276C4—82no—
277C4—82no—
278C2—21no—
279C2—21no—
280C2—82no—
281C2C83×#188511yescharacteristic
282C2C83×#190612yes—
subgroupG/H
center, socleC22×C83#386
commutatorC42C22×C4×C83
Frattini, cosocleC2×C42C23×C83
prime radicalC22×D4×C83D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C83 ◁ C2×C42×C83 ◁ G

Complements

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

NH ≅ G/Ntype
4. C83×#1506C2semidirect
5. C83×#1300C2semidirect
8. #489×C83C4semidirect
26. C4⋊Q8×C83C2×C4semidirect
46. #97×C83C2×C4semidirect
136. #9439C83direct (N × H)
145. #1506C2×C83semidirect
146. #1300C2×C83semidirect
147. C83#9439direct (N × H)
150. #489C4×C83semidirect
168. C4⋊Q8C2×C4×C83semidirect
188. #97C2×C4×C83semidirect

Maximal subgroups

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

subgroupindex
C83×#31402
C83×#23722
C83×#15332
C83×#15062
C83×#13002
#943983