Finite Group Databasebeta

← C83×#9979 #35237803

Subgroups — C83×#9979 #35237803

Order 21248.

492 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 102 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×#3189C211yesmaximal, characteristic
2C83×#3095C212yesmaximal
3C83×#1818C211yesmaximal, characteristic
4C83×#1472C212yesmaximal
5C83×#1293C211yesmaximal, characteristic
6C2×C22⋊Q8×C83C2212yes—
7C2×#117×C83C2211yescharacteristic
8#485×C83—24no—
9#484×C83—22no—
10#484×C83—22no—
11#483×C83—22no—
12#467×C83—22no—
13#451×C83—22no—
14#428×C83—22no—
15#419×C83—22no—
16#407×C83C2212yes—
17C2×C22⋊C8×C83C2211yescharacteristic
18C2×C22⋊C8×C83C2211yescharacteristic
19#336×C83—22no—
20#324×C83—24no—
21C22×Q8×C83D412yes—
22C23×C4×C83C2311yescharacteristic
23C2×Q16×C83—22no—
24C2×M16×C83—22no—
25C22×C8×C83—21no—
26C22×C8×C83D412yes—
27C22⋊Q8×C83—22no—
28C22⋊Q8×C83—22no—
29C22⋊Q8×C83—22no—
30C22⋊Q8×C83—22no—
31#117×C83—22no—
32#117×C83—22no—
33C2×C4⋊C4×C83—22no—
34C2×C4⋊C4×C83D411yescharacteristic
35C2×C4⋊C4×C83D411yescharacteristic
36C2×C4⋊C4×C83D412yes—
37C2×C22⋊C4×C83—21no—
38C2×C22⋊C4×C83—22no—
39C2×C42×C83—21no—
40#107×C83—22no—
41#107×C83—24no—
42#106×C83—24no—
43#103×C83—24no—
44#103×C83—24no—
45#103×C83—24no—
46C22⋊C8×C83—22no—
47C22⋊C8×C83—22no—
48C22⋊C8×C83—22no—
49C22⋊C8×C83D414yes—
50C24×C83#4111yescharacteristic
51C2×Q8×C83—22no—
52C2×Q8×C83—22no—
53C2×Q8×C83—44no—
54C22×C4×C83—21no—
55C22×C4×C83—21no—
56C22×C4×C83—22no—
57C22×C4×C83—22no—
58C22×C4×C83—42no—
59C22×C4×C83C2×D412yes—
60C22×C4×C83C2×D411yescharacteristic
61C22×C4×C83C2×D411yescharacteristic
62C22×C4×C83C2×D412yes—
63Q16×C83—82no—
64M16×C83—44no—
65C2×C8×C83—22no—
66C2×C8×C83—24no—
67C2×C8×C83—42no—
68C2×C8×C83—42no—
69C2×C8×C83—41no—
70C4⋊C4×C83—22no—
71C4⋊C4×C83—22no—
72C4⋊C4×C83—22no—
73C4⋊C4×C83—22no—
74C4⋊C4×C83—42no—
75C4⋊C4×C83—42no—
76C22⋊C4×C83—42no—
77C22⋊C4×C83—42no—
78C22⋊C4×C83—42no—
79C42×C83—41no—
80C42×C83—41no—
81C23×C83—22no—
82C23×C83—41no—
83C23×C83—41no—
84C23×C83#12112yes—
85C23×C83#12111yescharacteristic
86Q8×C83—44no—
87Q8×C83—44no—
88C2×C4×C83—22no—
89C2×C4×C83—24no—
90C2×C4×C83—41no—
91C2×C4×C83—42no—
92C2×C4×C83—42no—
93C2×C4×C83—44no—
94C2×C4×C83—41no—
95C2×C4×C83—41no—
96C2×C4×C83—42no—
97C2×C4×C83—42no—
98C2×C4×C83—42no—
99C2×C4×C83—82no—
100C2×C4×C83#12012yes—
101C2×C4×C83#12011yescharacteristic
102C2×C4×C83#12711yescharacteristic
103C8×C83—44no—
104C8×C83—42no—
105C8×C83—81no—
106C22×C83—21no—
107C22×C83—21no—
108C22×C83—22no—
109C22×C83—22no—
110C22×C83—22no—
111C22×C83—82no—
112C22×C83#39211yescharacteristic
113C22×C83#47312yes—
114C4×C83—22no—
115C4×C83—21no—
116C4×C83—81no—
117C4×C83—82no—
118C4×C83—81no—
119C4×C83—82no—
120C4×C83#45812yes—
121#9979C8311yesmaximal, characteristic, direct product factor, Sylow
122C2×C83—22no—
123C2×C83—42no—
124C2×C83#201711yescharacteristic
125C2×C83#202011yescharacteristic
126C2×C83#202211yescharacteristic
127#3189C2×C8311yescharacteristic
128#3095C2×C8312yes—
129#1818C2×C8311yescharacteristic
130#1472C2×C8312yes—
131#1293C2×C8311yescharacteristic
132C83#997911yescharacteristic, direct product factor, Sylow
133C2×C22⋊Q8C22×C8312yes—
134C2×#117C22×C8311yescharacteristic
135#485—24no—
136#484—22no—
137#484—22no—
138#483—22no—
139#467—22no—
140#451—22no—
141#428—22no—
142#419—22no—
143#407C22×C8312yes—
144C2×C22⋊C8C22×C8311yescharacteristic
145C2×C22⋊C8C22×C8311yescharacteristic
146#336—22no—
147#324—24no—
148C22×Q8D4×C8312yes—
149C23×C4C23×C8311yescharacteristic
150C2×Q16—22no—
151C2×M16—22no—
152C22×C8—21no—
153C22×C8D4×C8312yes—
154C22⋊Q8—22no—
155C22⋊Q8—22no—
156C22⋊Q8—22no—
157C22⋊Q8—22no—
158#117—22no—
159#117—22no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4D4×C8311yescharacteristic
162C2×C4⋊C4D4×C8311yescharacteristic
163C2×C4⋊C4D4×C8312yes—
164C2×C22⋊C4—21no—
165C2×C22⋊C4—22no—
166C2×C42—21no—
167#107—24no—
168#107—22no—
169#106—24no—
170#103—24no—
171#103—24no—
172#103—24no—
173C22⋊C8—22no—
174C22⋊C8—22no—
175C22⋊C8—22no—
176C22⋊C8D4×C8314yes—
177C24#41×C8311yescharacteristic
178C2×Q8—22no—
179C2×Q8—22no—
180C2×Q8—44no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—22no—
184C22×C4—22no—
185C22×C4—42no—
186C22×C4C2×D4×C8312yes—
187C22×C4C2×D4×C8311yescharacteristic
188C22×C4C2×D4×C8311yescharacteristic
189C22×C4C2×D4×C8312yes—
190Q16—82no—
191M16—44no—
192C2×C8—22no—
193C2×C8—24no—
194C2×C8—42no—
195C2×C8—42no—
196C2×C8—41no—
197C4⋊C4—22no—
198C4⋊C4—22no—
199C4⋊C4—22no—
200C4⋊C4—22no—
201C4⋊C4—42no—
202C4⋊C4—42no—
203C22⋊C4—42no—
204C22⋊C4—42no—
205C22⋊C4—42no—
206C42—41no—
207C42—41no—
208C23—22no—
209C23—41no—
210C23—41no—
211C23#121×C8312yes—
212C23#121×C8311yescharacteristic
213Q8—44no—
214Q8—44no—
215C2×C4—22no—
216C2×C4—24no—
217C2×C4—41no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—44no—
221C2×C4—42no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—82no—
227C2×C4#120×C8312yes—
228C2×C4#120×C8311yescharacteristic
229C2×C4#127×C8311yescharacteristic
230C8—44no—
231C8—42no—
232C8—81no—
233C22—21no—
234C22—21no—
235C22—22no—
236C22—22no—
237C22—22no—
238C22—82no—
239C22#392×C8311yescharacteristic
240C22#473×C8312yes—
241C4—22no—
242C4—21no—
243C4—81no—
244C4—82no—
245C4—81no—
246C4—82no—
247C4#458×C8312yes—
248C2—22no—
249C2—42no—
250C2C83×#201711yescharacteristic
251C2C83×#202011yescharacteristic
252C2C83×#202211yescharacteristic
subgroupG/H
center, socleC22×C83#392
commutator, Frattini, cosocleC23×C4C23×C83
prime radicalC24×C83#41
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
121. #9979C83direct (N × H)
132. C83#9979direct (N × H)

Maximal subgroups

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

subgroupindex
C83×#31892
C83×#30952
C83×#18182
C83×#14722
C83×#12932
#997983