Finite Group Databasebeta

← C83×#9985 #35237809

Subgroups — C83×#9985 #35237809

Order 21248.

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

normal subgroups only

This group has 502 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×#3095C212yesmaximal
2C83×#2817C211yesmaximal, characteristic
3C83×#1820C211yesmaximal, characteristic
4C83×#1511C212yesmaximal
5C83×#1306C211yesmaximal, characteristic
6C2×C22⋊Q8×C83C2212yes—
7C2×#117×C83C2211yescharacteristic
8#485×C83—24no—
9#484×C83—22no—
10#483×C83—22no—
11#428×C83—22no—
12#419×C83—22no—
13#407×C83C2212yes—
14#400×C83—22no—
15#397×C83—22no—
16#395×C83—22no—
17#381×C83C2211yescharacteristic
18#381×C83C2211yescharacteristic
19#342×C83—22no—
20#328×C83—24no—
21C22×Q8×C83D412yes—
22C23×C4×C83C2311yescharacteristic
23C2×M16×C83—22no—
24C22⋊Q8×C83—22no—
25C22⋊Q8×C83—22no—
26C22⋊Q8×C83—22no—
27C22⋊Q8×C83—22no—
28#117×C83—22no—
29#117×C83—22no—
30C2×C4⋊C4×C83—22no—
31C2×C4⋊C4×C83—22no—
32C2×C4⋊C4×C83D412yes—
33C2×C4⋊C4×C83D412yes—
34C2×C22⋊C4×C83—21no—
35C2×C22⋊C4×C83—22no—
36C2×C22⋊C4×C83—21no—
37C2×C22⋊C4×C83D412yes—
38C2×C42×C83—21no—
39#107×C83—24no—
40#106×C83—24no—
41#103×C83—24no—
42#103×C83—24no—
43C22⋊C8×C83—22no—
44C22⋊C8×C83D414yes—
45#95×C83—24no—
46#95×C83—22no—
47#95×C83—22no—
48#95×C83—22no—
49C24×C83C2×D411yescharacteristic
50C2×Q8×C83—22no—
51C2×Q8×C83—22no—
52C2×Q8×C83—44no—
53C22×C4×C83—22no—
54C22×C4×C83—22no—
55C22×C4×C83—22no—
56C22×C4×C83—22no—
57C22×C4×C83—42no—
58C22×C4×C83—41no—
59C22×C4×C83C2×D412yes—
60C22×C4×C83C2×D411yescharacteristic
61C22×C4×C83C2×D412yes—
62C22×C4×C83#4111yescharacteristic
63M16×C83—44no—
64C2×C8×C83—24no—
65C4⋊C4×C83—22no—
66C4⋊C4×C83—22no—
67C4⋊C4×C83—22no—
68C4⋊C4×C83—22no—
69C4⋊C4×C83—42no—
70C4⋊C4×C83—42no—
71C4⋊C4×C83—82no—
72C22⋊C4×C83—41no—
73C22⋊C4×C83—42no—
74C22⋊C4×C83—41no—
75C22⋊C4×C83—42no—
76C22⋊C4×C83—42no—
77C22⋊C4×C83—42no—
78C42×C83—42no—
79C23×C83—22no—
80C23×C83—42no—
81C23×C83#12011yescharacteristic
82C23×C83#12111yescharacteristic
83C23×C83#12711yescharacteristic
84Q8×C83—44no—
85Q8×C83—82no—
86C2×C4×C83—24no—
87C2×C4×C83—41no—
88C2×C4×C83—42no—
89C2×C4×C83—41no—
90C2×C4×C83—44no—
91C2×C4×C83—44no—
92C2×C4×C83—42no—
93C2×C4×C83—42no—
94C2×C4×C83—42no—
95C2×C4×C83—42no—
96C2×C4×C83—44no—
97C2×C4×C83—82no—
98C2×C4×C83—81no—
99C2×C4×C83—82no—
100C2×C4×C83#12012yes—
101C2×C4×C83#12112yes—
102C8×C83—44no—
103C22×C83—22no—
104C22×C83—22no—
105C22×C83—22no—
106C22×C83—21no—
107C22×C83—21no—
108C22×C83—82no—
109C22×C83#39211yescharacteristic
110C22×C83#45812yes—
111C4×C83—22no—
112C4×C83—22no—
113C4×C83—82no—
114C4×C83—82no—
115C4×C83—82no—
116C4×C83—82no—
117C4×C83—161no—
118#9985C8311yesmaximal, characteristic, direct product factor, Sylow
119C2×C83—22no—
120C2×C83—41no—
121C2×C83—41no—
122C2×C83#200912yes—
123C2×C83#202211yescharacteristic
124#3095C2×C8312yes—
125#2817C2×C8311yescharacteristic
126#1820C2×C8311yescharacteristic
127#1511C2×C8312yes—
128#1306C2×C8311yescharacteristic
129C83#998511yescharacteristic, direct product factor, Sylow
130C2×C22⋊Q8C22×C8312yes—
131C2×#117C22×C8311yescharacteristic
132#485—24no—
133#484—22no—
134#483—22no—
135#428—22no—
136#419—22no—
137#407C22×C8312yes—
138#400—22no—
139#397—22no—
140#395—22no—
141#381C22×C8311yescharacteristic
142#381C22×C8311yescharacteristic
143#342—22no—
144#328—24no—
145C22×Q8D4×C8312yes—
146C23×C4C23×C8311yescharacteristic
147C2×M16—22no—
148C22⋊Q8—22no—
149C22⋊Q8—22no—
150C22⋊Q8—22no—
151C22⋊Q8—22no—
152#117—22no—
153#117—22no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4D4×C8312yes—
157C2×C4⋊C4D4×C8312yes—
158C2×C22⋊C4—21no—
159C2×C22⋊C4—22no—
160C2×C22⋊C4—21no—
161C2×C22⋊C4D4×C8312yes—
162C2×C42—21no—
163#107—24no—
164#106—24no—
165#103—24no—
166#103—24no—
167C22⋊C8—22no—
168C22⋊C8D4×C8314yes—
169#95—24no—
170#95—22no—
171#95—22no—
172#95—22no—
173C24C2×D4×C8311yescharacteristic
174C2×Q8—22no—
175C2×Q8—22no—
176C2×Q8—44no—
177C22×C4—22no—
178C22×C4—22no—
179C22×C4—22no—
180C22×C4—22no—
181C22×C4—42no—
182C22×C4—41no—
183C22×C4C2×D4×C8312yes—
184C22×C4C2×D4×C8311yescharacteristic
185C22×C4C2×D4×C8312yes—
186C22×C4#41×C8311yescharacteristic
187M16—44no—
188C2×C8—24no—
189C4⋊C4—22no—
190C4⋊C4—22no—
191C4⋊C4—22no—
192C4⋊C4—22no—
193C4⋊C4—42no—
194C4⋊C4—42no—
195C4⋊C4—82no—
196C22⋊C4—41no—
197C22⋊C4—42no—
198C22⋊C4—41no—
199C22⋊C4—42no—
200C22⋊C4—42no—
201C22⋊C4—42no—
202C42—42no—
203C23—22no—
204C23—42no—
205C23#120×C8311yescharacteristic
206C23#121×C8311yescharacteristic
207C23#127×C8311yescharacteristic
208Q8—44no—
209Q8—82no—
210C2×C4—24no—
211C2×C4—41no—
212C2×C4—42no—
213C2×C4—41no—
214C2×C4—44no—
215C2×C4—44no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—44no—
221C2×C4—82no—
222C2×C4—81no—
223C2×C4—82no—
224C2×C4#120×C8312yes—
225C2×C4#121×C8312yes—
226C8—44no—
227C22—22no—
228C22—22no—
229C22—22no—
230C22—21no—
231C22—21no—
232C22—82no—
233C22#392×C8311yescharacteristic
234C22#458×C8312yes—
235C4—22no—
236C4—22no—
237C4—82no—
238C4—82no—
239C4—82no—
240C4—82no—
241C4—161no—
242C2—22no—
243C2—41no—
244C2—41no—
245C2C83×#200912yes—
246C2C83×#202211yescharacteristic
subgroupG/H
center, socleC22×C83#392
commutator, Frattini, cosocleC23×C4C23×C83
prime radicalC24×C83C2×D4
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
118. #9985C83direct (N × H)
129. C83#9985direct (N × H)

Maximal subgroups

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

subgroupindex
C83×#30952
C83×#28172
C83×#18202
C83×#15112
C83×#13062
#998583