Finite Group Databasebeta

← C83×#10518 #35238342

Subgroups — C83×#10518 #35238342

Order 21248.

478 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 114 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×#3245C211yesmaximal, characteristic
2C83×#1962C212yesmaximal, complemented
3C83×#1842C211yesmaximal, characteristic, complemented
4C83×#1547C212yesmaximal, complemented
5C83×#1292C211yesmaximal, characteristic, complemented
6#532×C83C2212yes—
7#474×C83—22no—
8#466×C83—22no—
9#459×C83—22no—
10#423×C83C2212yes—
11C2×C4⋊C8×C83—22no—
12C2×C4⋊C8×C83C2211yescharacteristic
13C2×C4⋊C8×C83C2211yescharacteristic
14C2×#104×C83—22no—
15C2×#104×C83—22no—
16C43×C83C2211yescharacteristic
17#332×C83—22no—
18#331×C83—22no—
19C2×#41×C83—22no—
20C2×D8×C83—22no—
21C2×M16×C83—22no—
22C22×C8×C83—21no—
23C22×C8×C83D412yes—
24C4⋊Q8×C83D412yes—
25#127×C83D412yes—
26#124×C83—22no—
27#121×C83—22no—
28#121×C83—22no—
29C4×D4×C83—22no—
30C4×D4×C83—22no—
31C2×C42×C83—21no—
32C2×C42×C83—21no—
33C2×C42×C83D411yescharacteristic
34C2×C42×C83D411yescharacteristic
35C2×C42×C83C2311yescharacteristic
36#107×C83—22no—
37C4⋊C8×C83—22no—
38C4⋊C8×C83—22no—
39C4⋊C8×C83—22no—
40C4⋊C8×C83—22no—
41C4⋊C8×C83—44no—
42#104×C83—44no—
43#104×C83—44no—
44#102×C83—24no—
45#41×C83—42no—
46#41×C83—42no—
47#41×C83—42no—
48#41×C83—42no—
49C2×Q8×C83—22no—
50C2×D4×C83—22no—
51C2×D4×C83—22no—
52C2×D4×C83—22no—
53C2×D4×C83—42no—
54C22×C4×C83—21no—
55C22×C4×C83—21no—
56C22×C4×C83—42no—
57C22×C4×C83C2×D411yescharacteristic
58C22×C4×C83C2×D411yescharacteristic
59C22×C4×C83#4111yescharacteristic
60D8×C83—82no—
61M16×C83—42no—
62M16×C83—42no—
63C2×C8×C83—22no—
64C2×C8×C83—42no—
65C2×C8×C83—42no—
66C2×C8×C83—41no—
67C2×C8×C83—42no—
68C4⋊C4×C83—22no—
69C4⋊C4×C83—22no—
70C22⋊C4×C83—42no—
71C22⋊C4×C83—42no—
72C42×C83—22no—
73C42×C83—22no—
74C42×C83—21no—
75C42×C83—22no—
76C42×C83—42no—
77C42×C83D812yescomplemented
78C42×C83C2×D412yes—
79C42×C83#4112yes—
80C23×C83—42no—
81C23×C83#12111yescharacteristic
82Q8×C83—42no—
83Q8×C83—42no—
84D4×C83—42no—
85D4×C83—42no—
86D4×C83—42no—
87D4×C83—42no—
88D4×C83—82no—
89D4×C83—82no—
90D4×C83—82no—
91C2×C4×C83—22no—
92C2×C4×C83—22no—
93C2×C4×C83—22no—
94C2×C4×C83—21no—
95C2×C4×C83—21no—
96C2×C4×C83—22no—
97C2×C4×C83—41no—
98C2×C4×C83—41no—
99C2×C4×C83—41no—
100C2×C4×C83—42no—
101C2×C4×C83—82no—
102C2×C4×C83—82no—
103C2×C4×C83#12011yescharacteristic
104C2×C4×C83#12112yes—
105C2×C4×C83#12312yes—
106C2×C4×C83#12411yescharacteristic
107C2×C4×C83C2×D811yescharacteristic
108C2×C4×C83#13511yescharacteristic
109C2×C4×C83AGL(1,ℤ/8)12yes—
110C8×C83—42no—
111C8×C83—81no—
112C8×C83—82no—
113C22×C83—21no—
114C22×C83—21no—
115C22×C83—82no—
116C22×C83—82no—
117C22×C83—82no—
118C22×C83#39411yescharacteristic
119C22×C83#46611yescharacteristic
120C22×C83#46911yescharacteristic
121C4×C83—24no—
122C4×C83—22no—
123C4×C83—21no—
124C4×C83—42no—
125C4×C83—82no—
126C4×C83#45311yescharacteristic
127C4×C83#45611yescharacteristic
128C4×C83#45912yes—
129C4×C83#46312yes—
130#10518C8311yesmaximal, characteristic, direct product factor, Sylow
131C2×C83—21no—
132C2×C83—21no—
133C2×C83—162no—
134C2×C83#203911yescharacteristic
135C2×C83#205011yescharacteristic
136C2×C83#205411yescharacteristic
137#3245C2×C8311yescharacteristic
138#1962C2×C8312yescomplemented
139#1842C2×C8311yescharacteristic, complemented
140#1547C2×C8312yescomplemented
141#1292C2×C8311yescharacteristic, complemented
142C83#1051811yescharacteristic, direct product factor, Sylow
143#532C22×C8312yes—
144#474—22no—
145#466—22no—
146#459—22no—
147#423C22×C8312yes—
148C2×C4⋊C8—22no—
149C2×C4⋊C8C22×C8311yescharacteristic
150C2×C4⋊C8C22×C8311yescharacteristic
151C2×#104—22no—
152C2×#104—22no—
153C43C22×C8311yescharacteristic
154#332—22no—
155#331—22no—
156C2×#41—22no—
157C2×D8—22no—
158C2×M16—22no—
159C22×C8—21no—
160C22×C8D4×C8312yes—
161C4⋊Q8D4×C8312yes—
162#127D4×C8312yes—
163#124—22no—
164#121—22no—
165#121—22no—
166C4×D4—22no—
167C4×D4—22no—
168C2×C42—21no—
169C2×C42—21no—
170C2×C42D4×C8311yescharacteristic
171C2×C42D4×C8311yescharacteristic
172C2×C42C23×C8311yescharacteristic
173#107—22no—
174C4⋊C8—22no—
175C4⋊C8—22no—
176C4⋊C8—22no—
177C4⋊C8—22no—
178C4⋊C8—44no—
179#104—44no—
180#104—44no—
181#102—24no—
182#41—42no—
183#41—42no—
184#41—42no—
185#41—42no—
186C2×Q8—22no—
187C2×D4—22no—
188C2×D4—22no—
189C2×D4—22no—
190C2×D4—42no—
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—42no—
194C22×C4C2×D4×C8311yescharacteristic
195C22×C4C2×D4×C8311yescharacteristic
196C22×C4#41×C8311yescharacteristic
197D8—82no—
198M16—42no—
199M16—42no—
200C2×C8—22no—
201C2×C8—42no—
202C2×C8—42no—
203C2×C8—41no—
204C2×C8—42no—
205C4⋊C4—22no—
206C4⋊C4—22no—
207C22⋊C4—42no—
208C22⋊C4—42no—
209C42—22no—
210C42—22no—
211C42—21no—
212C42—22no—
213C42—42no—
214C42D8×C8312yescomplemented
215C42C2×D4×C8312yes—
216C42#41×C8312yes—
217C23—42no—
218C23#121×C8311yescharacteristic
219Q8—42no—
220Q8—42no—
221D4—42no—
222D4—42no—
223D4—42no—
224D4—42no—
225D4—82no—
226D4—82no—
227D4—82no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—42no—
238C2×C4—82no—
239C2×C4—82no—
240C2×C4#120×C8311yescharacteristic
241C2×C4#121×C8312yes—
242C2×C4#123×C8312yes—
243C2×C4#124×C8311yescharacteristic
244C2×C4C2×D8×C8311yescharacteristic
245C2×C4#135×C8311yescharacteristic
246C2×C4AGL(1,ℤ/8)×C8312yes—
247C8—42no—
248C8—81no—
249C8—82no—
250C22—21no—
251C22—21no—
252C22—82no—
253C22—82no—
254C22—82no—
255C22#394×C8311yescharacteristic
256C22#466×C8311yescharacteristic
257C22#469×C8311yescharacteristic
258C4—24no—
259C4—21no—
260C4—22no—
261C4—42no—
262C4—82no—
263C4#453×C8311yescharacteristic
264C4#456×C8311yescharacteristic
265C4#459×C8312yes—
266C4#463×C8312yes—
267C2—21no—
268C2—21no—
269C2—162no—
270C2C83×#203911yescharacteristic
271C2C83×#205011yescharacteristic
272C2C83×#205411yescharacteristic
subgroupG/H
center, socleC22×C83#394
commutator, Frattini, cosocleC2×C42C23×C83
prime radicalC83×#3245C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C83 ◁ C2×C42×C83 ◁ G

Complements

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

NH ≅ G/Ntype
2. C83×#1962C2semidirect
3. C83×#1842C2semidirect
4. C83×#1547C2semidirect
5. C83×#1292C2semidirect
77. C42×C83D8semidirect
130. #10518C83direct (N × H)
138. #1962C2×C83semidirect
139. #1842C2×C83semidirect
140. #1547C2×C83semidirect
141. #1292C2×C83semidirect
142. C83#10518direct (N × H)
214. C42D8×C83semidirect

Maximal subgroups

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

subgroupindex
C83×#32452
C83×#19622
C83×#18422
C83×#15472
C83×#12922
#1051883