Finite Group Databasebeta

← C83×#9983 #35237807

Subgroups — C83×#9983 #35237807

Order 21248.

602 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 602 conjugacy classes of subgroups — too many to draw. Only its 98 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×#3094C212yesmaximal, complemented
2C83×#2815C211yesmaximal, characteristic
3C83×#1820C211yesmaximal, characteristic, complemented
4C83×#1510C212yesmaximal, complemented
5C83×#1306C211yesmaximal, characteristic, complemented
6C2×#121×C83C2212yes—
7C2×#117×C83C2211yescharacteristic
8#482×C83—24no—
9#481×C83—22no—
10#480×C83—22no—
11#428×C83—22no—
12#418×C83—22no—
13#407×C83C2212yes—
14#397×C83—22no—
15#392×C83—22no—
16#392×C83—22no—
17#381×C83C2211yescharacteristic
18#381×C83C2211yescharacteristic
19#342×C83—22no—
20#327×C83—24no—
21C22×D4×C83—22no—
22C22×D4×C83—22no—
23C22×D4×C83D412yes—
24C23×C4×C83C2311yescharacteristic
25C2×M16×C83—22no—
26#121×C83—22no—
27#121×C83—22no—
28#121×C83—22no—
29#121×C83—22no—
30#117×C83—22no—
31#117×C83—22no—
32C2×C4⋊C4×C83D412yes—
33C2×C4⋊C4×C83D412yescomplemented
34C2×C22⋊C4×C83—21no—
35C2×C22⋊C4×C83—22no—
36C2×C22⋊C4×C83—21no—
37C2×C22⋊C4×C83—24no—
38C2×C22⋊C4×C83D412yes—
39C2×C42×C83—21no—
40#107×C83—24no—
41#106×C83—24no—
42#102×C83—24no—
43#102×C83—24no—
44C22⋊C8×C83—22no—
45C22⋊C8×C83D414yescomplemented
46#95×C83—22no—
47#95×C83—22no—
48#95×C83—22no—
49C24×C83—22no—
50C24×C83C2×D411yescharacteristic
51C2×D4×C83—22no—
52C2×D4×C83—22no—
53C2×D4×C83—44no—
54C2×D4×C83—42no—
55C2×D4×C83—42no—
56C2×D4×C83—84no—
57C2×D4×C83—84no—
58C2×D4×C83—82no—
59C22×C4×C83—22no—
60C22×C4×C83—22no—
61C22×C4×C83—22no—
62C22×C4×C83—42no—
63C22×C4×C83—41no—
64C22×C4×C83C2×D412yes—
65C22×C4×C83C2×D411yescharacteristic
66C22×C4×C83C2×D412yes—
67C22×C4×C83#4111yescharacteristic
68M16×C83—44no—
69C2×C8×C83—24no—
70C4⋊C4×C83—22no—
71C4⋊C4×C83—22no—
72C4⋊C4×C83—22no—
73C4⋊C4×C83—22no—
74C22⋊C4×C83—41no—
75C22⋊C4×C83—41no—
76C22⋊C4×C83—42no—
77C22⋊C4×C83—42no—
78C22⋊C4×C83—42no—
79C22⋊C4×C83—42no—
80C22⋊C4×C83—84no—
81C42×C83—42no—
82C23×C83—22no—
83C23×C83—42no—
84C23×C83—42no—
85C23×C83—42no—
86C23×C83—44no—
87C23×C83—42no—
88C23×C83—44no—
89C23×C83#12011yescharacteristic
90C23×C83#12111yescharacteristic
91C23×C83#12711yescharacteristic
92D4×C83—44no—
93D4×C83—82no—
94D4×C83—84no—
95D4×C83—84no—
96D4×C83—88no—
97C2×C4×C83—24no—
98C2×C4×C83—41no—
99C2×C4×C83—42no—
100C2×C4×C83—41no—
101C2×C4×C83—44no—
102C2×C4×C83—44no—
103C2×C4×C83—42no—
104C2×C4×C83—42no—
105C2×C4×C83—42no—
106C2×C4×C83—82no—
107C2×C4×C83—81no—
108C2×C4×C83—82no—
109C2×C4×C83#12012yes—
110C2×C4×C83#12112yes—
111C8×C83—44no—
112C22×C83—22no—
113C22×C83—22no—
114C22×C83—22no—
115C22×C83—21no—
116C22×C83—21no—
117C22×C83—82no—
118C22×C83—84no—
119C22×C83—84no—
120C22×C83—82no—
121C22×C83—82no—
122C22×C83—82no—
123C22×C83#39211yescharacteristic
124C22×C83#45812yes—
125C4×C83—22no—
126C4×C83—22no—
127C4×C83—82no—
128C4×C83—82no—
129C4×C83—82no—
130C4×C83—161no—
131#9983C8311yesmaximal, characteristic, direct product factor, Sylow
132C2×C83—22no—
133C2×C83—41no—
134C2×C83—41no—
135C2×C83—162no—
136C2×C83#200812yes—
137C2×C83#202211yescharacteristic
138#3094C2×C8312yescomplemented
139#2815C2×C8311yescharacteristic
140#1820C2×C8311yescharacteristic, complemented
141#1510C2×C8312yescomplemented
142#1306C2×C8311yescharacteristic, complemented
143C83#998311yescharacteristic, direct product factor, Sylow
144C2×#121C22×C8312yes—
145C2×#117C22×C8311yescharacteristic
146#482—24no—
147#481—22no—
148#480—22no—
149#428—22no—
150#418—22no—
151#407C22×C8312yes—
152#397—22no—
153#392—22no—
154#392—22no—
155#381C22×C8311yescharacteristic
156#381C22×C8311yescharacteristic
157#342—22no—
158#327—24no—
159C22×D4—22no—
160C22×D4—22no—
161C22×D4D4×C8312yes—
162C23×C4C23×C8311yescharacteristic
163C2×M16—22no—
164#121—22no—
165#121—22no—
166#121—22no—
167#121—22no—
168#117—22no—
169#117—22no—
170C2×C4⋊C4D4×C8312yes—
171C2×C4⋊C4D4×C8312yescomplemented
172C2×C22⋊C4—21no—
173C2×C22⋊C4—22no—
174C2×C22⋊C4—21no—
175C2×C22⋊C4—24no—
176C2×C22⋊C4D4×C8312yes—
177C2×C42—21no—
178#107—24no—
179#106—24no—
180#102—24no—
181#102—24no—
182C22⋊C8—22no—
183C22⋊C8D4×C8314yescomplemented
184#95—22no—
185#95—22no—
186#95—22no—
187C24—22no—
188C24C2×D4×C8311yescharacteristic
189C2×D4—22no—
190C2×D4—22no—
191C2×D4—44no—
192C2×D4—42no—
193C2×D4—42no—
194C2×D4—84no—
195C2×D4—84no—
196C2×D4—82no—
197C22×C4—22no—
198C22×C4—22no—
199C22×C4—22no—
200C22×C4—42no—
201C22×C4—41no—
202C22×C4C2×D4×C8312yes—
203C22×C4C2×D4×C8311yescharacteristic
204C22×C4C2×D4×C8312yes—
205C22×C4#41×C8311yescharacteristic
206M16—44no—
207C2×C8—24no—
208C4⋊C4—22no—
209C4⋊C4—22no—
210C4⋊C4—22no—
211C4⋊C4—22no—
212C22⋊C4—41no—
213C22⋊C4—41no—
214C22⋊C4—42no—
215C22⋊C4—42no—
216C22⋊C4—42no—
217C22⋊C4—42no—
218C22⋊C4—84no—
219C42—42no—
220C23—22no—
221C23—42no—
222C23—42no—
223C23—42no—
224C23—44no—
225C23—42no—
226C23—44no—
227C23#120×C8311yescharacteristic
228C23#121×C8311yescharacteristic
229C23#127×C8311yescharacteristic
230D4—44no—
231D4—82no—
232D4—84no—
233D4—84no—
234D4—88no—
235C2×C4—24no—
236C2×C4—41no—
237C2×C4—42no—
238C2×C4—41no—
239C2×C4—44no—
240C2×C4—44no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—82no—
245C2×C4—81no—
246C2×C4—82no—
247C2×C4#120×C8312yes—
248C2×C4#121×C8312yes—
249C8—44no—
250C22—22no—
251C22—22no—
252C22—22no—
253C22—21no—
254C22—21no—
255C22—82no—
256C22—84no—
257C22—84no—
258C22—82no—
259C22—82no—
260C22—82no—
261C22#392×C8311yescharacteristic
262C22#458×C8312yes—
263C4—22no—
264C4—22no—
265C4—82no—
266C4—82no—
267C4—82no—
268C4—161no—
269C2—22no—
270C2—41no—
271C2—41no—
272C2—162no—
273C2C83×#200812yes—
274C2C83×#202211yescharacteristic
subgroupG/H
center, socleC22×C83#392
commutator, Frattini, cosocleC23×C4C23×C83
prime radicalC83×#2815C2
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C83 ◁ C23×C4×C83 ◁ G

Complements

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

NH ≅ G/Ntype
1. C83×#3094C2semidirect
3. C83×#1820C2semidirect
4. C83×#1510C2semidirect
5. C83×#1306C2semidirect
33. C2×C4⋊C4×C83D4semidirect
45. C22⋊C8×C83D4semidirect
131. #9983C83direct (N × H)
138. #3094C2×C83semidirect
140. #1820C2×C83semidirect
141. #1510C2×C83semidirect
142. #1306C2×C83semidirect
143. C83#9983direct (N × H)
171. C2×C4⋊C4D4×C83semidirect
183. C22⋊C8D4×C83semidirect

Maximal subgroups

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

subgroupindex
C83×#30942
C83×#28152
C83×#18202
C83×#15102
C83×#13062
#998383