Finite Group Databasebeta

← C83×#11573 #35239397

Subgroups — C83×#11573 #35239397

Order 21248.

358 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 106 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×#2568C211yesmaximal, characteristic
2C83×#1467C211yesmaximal, characteristic
3C83×#1461C211yesmaximal, characteristic
4C83×#1324C214yesmaximal
5C2×C4⋊Q8×C83C411yescharacteristic
6C2×C4×Q8×C83C2211yescharacteristic
7#432×C83—21no—
8#431×C83—21no—
9#400×C83—21no—
10#400×C83—21no—
11#391×C83—21no—
12#391×C83—21no—
13#391×C83C412yes—
14#382×C83C2212yes—
15C4×C4⋊C4×C83C411yescharacteristic
16#324×C83—21no—
17#324×C83—21no—
18#324×C83C2212yes—
19#324×C83C2212yes—
20C22×Q8×C83—21no—
21C22×Q8×C83C2×C411yescharacteristic
22C4⋊Q8×C83—41no—
23C4⋊Q8×C83—41no—
24C4×Q8×C83—41no—
25C4×Q8×C83—41no—
26C2×C4⋊C4×C83—21no—
27C2×C4⋊C4×C83—21no—
28C2×C4⋊C4×C83C2×C412yes—
29C2×C4⋊C4×C83D411yescharacteristic
30C2×C4⋊C4×C83D411yescharacteristic
31C2×C4⋊C4×C83C2311yescharacteristic
32C2×C42×C83C2×C412yes—
33C2×C42×C83C2×C411yescharacteristic
34C2×C42×C83D411yescharacteristic
35C2×C42×C83D411yescharacteristic
36C4⋊C8×C83—41no—
37C4⋊C8×C83—41no—
38C22⋊C8×C83—22no—
39C22⋊C8×C83—22no—
40#97×C83—41no—
41C4×C8×C83—41no—
42#95×C83—21no—
43#95×C83—22no—
44#95×C83—22no—
45#95×C83—22no—
46#95×C83—22no—
47C2×Q8×C83—22no—
48C2×Q8×C83—22no—
49C2×Q8×C83—41no—
50C2×Q8×C83—44no—
51C2×Q8×C83—41no—
52C2×Q8×C83—41no—
53C22×C4×C83—22no—
54C22×C4×C83—22no—
55C22×C4×C83C22⋊C411yescharacteristic
56C22×C4×C83C22⋊C411yescharacteristic
57C22×C4×C83C22⋊C411yescharacteristic
58C22×C4×C83C22⋊C411yescharacteristic
59C22×C4×C83C22×C411yescharacteristic
60C22×C4×C83C2×D411yescharacteristic
61C22×C4×C83C2×D411yescharacteristic
62C2×C8×C83—42no—
63C2×C8×C83—42no—
64C4⋊C4×C83—41no—
65C4⋊C4×C83—41no—
66C4⋊C4×C83—41no—
67C4⋊C4×C83—42no—
68C4⋊C4×C83—42no—
69C4⋊C4×C83—42no—
70C42×C83—21no—
71C42×C83—21no—
72C42×C83—21no—
73C42×C83—21no—
74C42×C83—21no—
75C42×C83—21no—
76C42×C83—24no—
77C23×C83C2×C22⋊C411yescharacteristic
78Q8×C83—44no—
79Q8×C83—82no—
80Q8×C83—82no—
81C2×C4×C83—21no—
82C2×C4×C83—21no—
83C2×C4×C83—21no—
84C2×C4×C83—21no—
85C2×C4×C83—22no—
86C2×C4×C83—21no—
87C2×C4×C83—21no—
88C2×C4×C83—21no—
89C2×C4×C83—21no—
90C2×C4×C83—21no—
91C2×C4×C83—21no—
92C2×C4×C83—41no—
93C2×C4×C83—41no—
94C2×C4×C83—41no—
95C2×C4×C83—42no—
96C2×C4×C83—42no—
97C2×C4×C83—44no—
98C2×C4×C83—42no—
99C2×C4×C83—42no—
100C2×C4×C83#9911yescharacteristic
101C2×C4×C83#9911yescharacteristic
102C2×C4×C83#10112yes—
103C2×C4×C83#13112yes—
104C8×C83—82no—
105C8×C83—82no—
106C22×C83—21no—
107C22×C83—21no—
108C22×C83#40811yescharacteristic
109C22×C83C2×#9911yescharacteristic
110C22×C83C2×#10111yescharacteristic
111C4×C83—21no—
112C4×C83—22no—
113C4×C83—22no—
114C4×C83—41no—
115C4×C83—41no—
116C4×C83—41no—
117C4×C83—41no—
118C4×C83—82no—
119C4×C83—82no—
120C4×C83#35512yes—
121#11573C8311yesmaximal, characteristic, direct product factor, Sylow
122C2×C83—21no—
123C2×C83—21no—
124C2×C83#147211yescharacteristic
125C2×C83#212911yescharacteristic
126C2×C83C2×#35511yescharacteristic
127#2568C2×C8311yescharacteristic
128#1467C2×C8311yescharacteristic
129#1461C2×C8311yescharacteristic
130#1324C2×C8314yes—
131C83#1157311yescharacteristic, direct product factor, Sylow
132C2×C4⋊Q8C4×C8311yescharacteristic
133C2×C4×Q8C22×C8311yescharacteristic
134#432—21no—
135#431—21no—
136#400—21no—
137#400—21no—
138#391—21no—
139#391—21no—
140#391C4×C8312yes—
141#382C22×C8312yes—
142C4×C4⋊C4C4×C8311yescharacteristic
143#324—21no—
144#324—21no—
145#324C22×C8312yes—
146#324C22×C8312yes—
147C22×Q8—21no—
148C22×Q8C2×C4×C8311yescharacteristic
149C4⋊Q8—41no—
150C4⋊Q8—41no—
151C4×Q8—41no—
152C4×Q8—41no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4C2×C4×C8312yes—
156C2×C4⋊C4D4×C8311yescharacteristic
157C2×C4⋊C4D4×C8311yescharacteristic
158C2×C4⋊C4C23×C8311yescharacteristic
159C2×C42C2×C4×C8312yes—
160C2×C42C2×C4×C8311yescharacteristic
161C2×C42D4×C8311yescharacteristic
162C2×C42D4×C8311yescharacteristic
163C4⋊C8—41no—
164C4⋊C8—41no—
165C22⋊C8—22no—
166C22⋊C8—22no—
167#97—41no—
168C4×C8—41no—
169#95—21no—
170#95—22no—
171#95—22no—
172#95—22no—
173#95—22no—
174C2×Q8—22no—
175C2×Q8—22no—
176C2×Q8—41no—
177C2×Q8—44no—
178C2×Q8—41no—
179C2×Q8—41no—
180C22×C4—22no—
181C22×C4—22no—
182C22×C4C22⋊C4×C8311yescharacteristic
183C22×C4C22⋊C4×C8311yescharacteristic
184C22×C4C22⋊C4×C8311yescharacteristic
185C22×C4C22⋊C4×C8311yescharacteristic
186C22×C4C22×C4×C8311yescharacteristic
187C22×C4C2×D4×C8311yescharacteristic
188C22×C4C2×D4×C8311yescharacteristic
189C2×C8—42no—
190C2×C8—42no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C4⋊C4—41no—
194C4⋊C4—42no—
195C4⋊C4—42no—
196C4⋊C4—42no—
197C42—21no—
198C42—21no—
199C42—21no—
200C42—21no—
201C42—21no—
202C42—21no—
203C42—24no—
204C23C2×C22⋊C4×C8311yescharacteristic
205Q8—44no—
206Q8—82no—
207Q8—82no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—42no—
223C2×C4—44no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4#99×C8311yescharacteristic
228C2×C4#99×C8311yescharacteristic
229C2×C4#101×C8312yes—
230C2×C4#131×C8312yes—
231C8—82no—
232C8—82no—
233C22—21no—
234C22—21no—
235C22#408×C8311yescharacteristic
236C22C2×#99×C8311yescharacteristic
237C22C2×#101×C8311yescharacteristic
238C4—21no—
239C4—22no—
240C4—22no—
241C4—41no—
242C4—41no—
243C4—41no—
244C4—41no—
245C4—82no—
246C4—82no—
247C4#355×C8312yes—
248C2—21no—
249C2—21no—
250C2C83×#147211yescharacteristic
251C2C83×#212911yescharacteristic
252C2C2×#355×C8311yescharacteristic
subgroupG/H
center, socleC22×C83C2×#99
commutatorC22×C4C22×C4×C83
Frattini, cosocleC2×C4⋊C4C23×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
121. #11573C83direct (N × H)
131. C83#11573direct (N × H)

Maximal subgroups

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

subgroupindex
C83×#25682
C83×#14672
C83×#14612
C83×#13242
#1157383