Finite Group Databasebeta

← C83×#12804 #35240628

Subgroups — C83×#12804 #35240628

Order 21248.

432 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 130 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×#2327C211yesmaximal, characteristic
2C2×#356×C83C212yesmaximal
3C83×#1801C212yesmaximal
4C83×#1394C212yesmaximal
5C2×C4⋊Q8×C83C2211yescharacteristic
6C2×C4×Q8×C83C411yescharacteristic
7C2×C4×Q8×C83C2211yescharacteristic
8#423×C83—22no—
9C2×#101×C83C2214yes—
10#391×C83C411yescharacteristic
11#391×C83C2211yescharacteristic
12#387×C83—22no—
13#387×C83—22no—
14#382×C83C411yescharacteristic
15#376×C83C411yescharacteristic
16#356×C83—24no—
17#343×C83—22no—
18C22×Q8×C83C2×C411yescharacteristic
19C22×Q8×C83C2311yescharacteristic
20C2×M16×C83—24no—
21C4⋊Q8×C83—22no—
22C4⋊Q8×C83D412yes—
23C4⋊Q8×C83Q812yes—
24C4×Q8×C83—42no—
25C4×Q8×C83—42no—
26C2×C4⋊C4×C83—22no—
27C2×C4⋊C4×C83—21no—
28C2×C4⋊C4×C83C2×C411yescharacteristic
29C2×C4⋊C4×C83C2×C411yescharacteristic
30C2×C4⋊C4×C83D412yes—
31C2×C42×C83—21no—
32C2×C42×C83C2×C411yescharacteristic
33C2×C42×C83C2×C411yescharacteristic
34C2×C42×C83C2×C411yescharacteristic
35C2×C42×C83D412yes—
36C4⋊C8×C83—44no—
37#101×C83—24no—
38#101×C83—24no—
39#95×C83—21no—
40#95×C83—22no—
41#95×C83—22no—
42#95×C83—21no—
43#95×C83—22no—
44C2×Q8×C83—21no—
45C2×Q8×C83—41no—
46C2×Q8×C83—41no—
47C2×Q8×C83—41no—
48C2×Q8×C83—41no—
49C2×Q8×C83C4⋊C412yes—
50C2×Q8×C83C2×D411yescharacteristic
51C2×Q8×C83C2×Q811yescharacteristic
52C2×Q8×C83#4112yes—
53C22×C4×C83—21no—
54C22×C4×C83—21no—
55C22×C4×C83—21no—
56C22×C4×C83—21no—
57C22×C4×C83C22⋊C412yes—
58C22×C4×C83C22⋊C411yescharacteristic
59C22×C4×C83C22⋊C411yescharacteristic
60C22×C4×C83C22×C411yescharacteristic
61C22×C4×C83C2×D412yes—
62M16×C83—44no—
63M16×C83—44no—
64C2×C8×C83—44no—
65C4⋊C4×C83—24no—
66C4⋊C4×C83—24no—
67C4⋊C4×C83—41no—
68C4⋊C4×C83—42no—
69C4⋊C4×C83—41no—
70C4⋊C4×C83—42no—
71C42×C83—24no—
72C42×C83—22no—
73C42×C83—21no—
74C42×C83—41no—
75C42×C83—42no—
76C42×C83C4⋊C412yes—
77C23×C83C2×C22⋊C411yescharacteristic
78Q8×C83—41no—
79Q8×C83—41no—
80Q8×C83—42no—
81Q8×C83—42no—
82Q8×C83—42no—
83C2×C4×C83—21no—
84C2×C4×C83—22no—
85C2×C4×C83—21no—
86C2×C4×C83—22no—
87C2×C4×C83—22no—
88C2×C4×C83—22no—
89C2×C4×C83—21no—
90C2×C4×C83—22no—
91C2×C4×C83—41no—
92C2×C4×C83—41no—
93C2×C4×C83—41no—
94C2×C4×C83—41no—
95C2×C4×C83—41no—
96C2×C4×C83—42no—
97C2×C4×C83—41no—
98C2×C4×C83—41no—
99C2×C4×C83—41no—
100C2×C4×C83—42no—
101C2×C4×C83—41no—
102C2×C4×C83—41no—
103C2×C4×C83#9912yes—
104C2×C4×C83C2×C4⋊C411yescharacteristic
105C2×C4×C83#11711yescharacteristic
106C2×C4×C83#12112yes—
107C2×C4×C83C22⋊Q812yes—
108C8×C83—84no—
109C22×C83—21no—
110C22×C83—21no—
111C22×C83#38011yescharacteristic
112C22×C83C2×#9911yescharacteristic
113C22×C83#41011yescharacteristic
114C4×C83—22no—
115C4×C83—21no—
116C4×C83—21no—
117C4×C83—22no—
118C4×C83—22no—
119C4×C83—42no—
120C4×C83—42no—
121C4×C83—41no—
122C4×C83—42no—
123C4×C83—81no—
124C4×C83—81no—
125#12804C8311yesmaximal, characteristic, direct product factor, Sylow
126C2×C83—21no—
127C2×C83—21no—
128C2×C83#179911yescharacteristic
129C2×C83#213311yescharacteristic
130C2×C83#213511yescharacteristic
131#2327C2×C8311yescharacteristic
132C2×#356C2×C8312yes—
133#1801C2×C8312yes—
134#1394C2×C8312yes—
135C83#1280411yescharacteristic, direct product factor, Sylow
136C2×C4⋊Q8C22×C8311yescharacteristic
137C2×C4×Q8C4×C8311yescharacteristic
138C2×C4×Q8C22×C8311yescharacteristic
139#423—22no—
140C2×#101C22×C8314yes—
141#391C4×C8311yescharacteristic
142#391C22×C8311yescharacteristic
143#387—22no—
144#387—22no—
145#382C4×C8311yescharacteristic
146#376C4×C8311yescharacteristic
147#356—24no—
148#343—22no—
149C22×Q8C2×C4×C8311yescharacteristic
150C22×Q8C23×C8311yescharacteristic
151C2×M16—24no—
152C4⋊Q8—22no—
153C4⋊Q8D4×C8312yes—
154C4⋊Q8Q8×C8312yes—
155C4×Q8—42no—
156C4×Q8—42no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4C2×C4×C8311yescharacteristic
160C2×C4⋊C4C2×C4×C8311yescharacteristic
161C2×C4⋊C4D4×C8312yes—
162C2×C42—21no—
163C2×C42C2×C4×C8311yescharacteristic
164C2×C42C2×C4×C8311yescharacteristic
165C2×C42C2×C4×C8311yescharacteristic
166C2×C42D4×C8312yes—
167C4⋊C8—44no—
168#101—24no—
169#101—24no—
170#95—21no—
171#95—21no—
172#95—22no—
173#95—22no—
174#95—22no—
175C2×Q8—21no—
176C2×Q8—41no—
177C2×Q8—41no—
178C2×Q8—41no—
179C2×Q8—41no—
180C2×Q8C4⋊C4×C8312yes—
181C2×Q8C2×D4×C8311yescharacteristic
182C2×Q8C2×Q8×C8311yescharacteristic
183C2×Q8#41×C8312yes—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—21no—
188C22×C4C22⋊C4×C8312yes—
189C22×C4C22⋊C4×C8311yescharacteristic
190C22×C4C22⋊C4×C8311yescharacteristic
191C22×C4C22×C4×C8311yescharacteristic
192C22×C4C2×D4×C8312yes—
193M16—44no—
194M16—44no—
195C2×C8—44no—
196C4⋊C4—24no—
197C4⋊C4—24no—
198C4⋊C4—41no—
199C4⋊C4—42no—
200C4⋊C4—41no—
201C4⋊C4—42no—
202C42—24no—
203C42—22no—
204C42—21no—
205C42—41no—
206C42—42no—
207C42C4⋊C4×C8312yes—
208C23C2×C22⋊C4×C8311yescharacteristic
209Q8—41no—
210Q8—41no—
211Q8—42no—
212Q8—42no—
213Q8—42no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—42no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4#99×C8312yes—
235C2×C4C2×C4⋊C4×C8311yescharacteristic
236C2×C4#117×C8311yescharacteristic
237C2×C4#121×C8312yes—
238C2×C4C22⋊Q8×C8312yes—
239C8—84no—
240C22—21no—
241C22—21no—
242C22#380×C8311yescharacteristic
243C22C2×#99×C8311yescharacteristic
244C22#410×C8311yescharacteristic
245C4—22no—
246C4—21no—
247C4—21no—
248C4—22no—
249C4—22no—
250C4—42no—
251C4—42no—
252C4—41no—
253C4—42no—
254C4—81no—
255C4—81no—
256C2—21no—
257C2—21no—
258C2C83×#179911yescharacteristic
259C2C83×#213311yescharacteristic
260C2C83×#213511yescharacteristic
subgroupG/H
center, socleC22×C83C2×#99
commutatorC22×C4C22×C4×C83
Frattini, cosocleC22×Q8C23×C83
prime radicalC23×C83C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C83 ◁ C22×C4×C83 ◁ C2×C4×Q8×C83 ◁ G

Complements

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

NH ≅ G/Ntype
125. #12804C83direct (N × H)
135. C83#12804direct (N × H)

Maximal subgroups

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

subgroupindex
C83×#23272
C2×#356×C832
C83×#18012
C83×#13942
#1280483