Finite Group Databasebeta

← C83×#10566 #35238390

Subgroups — C83×#10566 #35238390

Order 21248.

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

normal subgroups only

This group has 490 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×#3189C211yesmaximal, characteristic
2C83×#1996C212yesmaximal
3C83×#1892C212yesmaximal
4C83×#1850C211yesmaximal, characteristic
5C83×#1289C211yesmaximal, characteristic
6C23×C8×C83C2211yescharacteristic
7C2×C22⋊Q8×C83C2212yes—
8#484×C83—22no—
9#467×C83—21no—
10#467×C83—21no—
11#451×C83—22no—
12C2×C4⋊C8×C83—21no—
13C2×#103×C83—22no—
14C2×C22⋊C8×C83C2211yescharacteristic
15#380×C83C2212yes—
16C4×C22⋊C4×C83C2211yescharacteristic
17#342×C83—22no—
18#342×C83—22no—
19#340×C83—22no—
20#336×C83—21no—
21C22×Q8×C83D412yes—
22C23×C4×C83C2311yescharacteristic
23C2×Q16×C83—21no—
24C2×Q16×C83—21no—
25C22×C8×C83—21no—
26C22×C8×C83—22no—
27C22×C8×C83—42no—
28C22×C8×C83D411yescharacteristic
29C22×C8×C83D411yescharacteristic
30C22⋊Q8×C83—22no—
31C22⋊Q8×C83—22no—
32C22⋊Q8×C83—22no—
33C22⋊Q8×C83—22no—
34C2×C4⋊C4×C83—22no—
35C2×C4⋊C4×C83—22no—
36C2×C4⋊C4×C83D412yes—
37C2×C22⋊C4×C83—22no—
38C2×C22⋊C4×C83—22no—
39C2×C22⋊C4×C83D411yescharacteristic
40C2×C22⋊C4×C83D411yescharacteristic
41C2×C42×C83—21no—
42#107×C83—21no—
43#107×C83—21no—
44C4⋊C8×C83—42no—
45#103×C83—22no—
46#103×C83—22no—
47#103×C83—44no—
48C22⋊C8×C83—22no—
49#95×C83—21no—
50#95×C83—22no—
51C24×C83C2×D411yescharacteristic
52C2×Q8×C83—22no—
53C2×Q8×C83—22no—
54C2×Q8×C83—42no—
55C2×Q8×C83—42no—
56C22×C4×C83—21no—
57C22×C4×C83—21no—
58C22×C4×C83—22no—
59C22×C4×C83—22no—
60C22×C4×C83—41no—
61C22×C4×C83—41no—
62C22×C4×C83—42no—
63C22×C4×C83C2×D412yes—
64C22×C4×C83C2×D411yescharacteristic
65C22×C4×C83#4111yescharacteristic
66C22×C4×C83#4112yes—
67Q16×C83—81no—
68Q16×C83—81no—
69C2×C8×C83—24no—
70C2×C8×C83—22no—
71C2×C8×C83—21no—
72C2×C8×C83—21no—
73C2×C8×C83—41no—
74C2×C8×C83—42no—
75C2×C8×C83—41no—
76C2×C8×C83—41no—
77C2×C8×C83—41no—
78C4⋊C4×C83—22no—
79C4⋊C4×C83—22no—
80C4⋊C4×C83—42no—
81C4⋊C4×C83—42no—
82C4⋊C4×C83—42no—
83C4⋊C4×C83—42no—
84C22⋊C4×C83—21no—
85C22⋊C4×C83—22no—
86C22⋊C4×C83—42no—
87C22⋊C4×C83—42no—
88C22⋊C4×C83—42no—
89C22⋊C4×C83—42no—
90C22⋊C4×C83Q1612yescomplemented
91C42×C83—41no—
92C42×C83—41no—
93C23×C83—41no—
94C23×C83—41no—
95C23×C83#12112yes—
96C23×C83#12111yescharacteristic
97C23×C83C2×Q1611yescharacteristic
98C23×C83#13511yescharacteristic
99C23×C83#13712yes—
100Q8×C83—44no—
101Q8×C83—42no—
102Q8×C83—42no—
103C2×C4×C83—21no—
104C2×C4×C83—22no—
105C2×C4×C83—21no—
106C2×C4×C83—22no—
107C2×C4×C83—22no—
108C2×C4×C83—41no—
109C2×C4×C83—42no—
110C2×C4×C83—41no—
111C2×C4×C83—41no—
112C2×C4×C83—41no—
113C2×C4×C83—41no—
114C2×C4×C83—42no—
115C2×C4×C83—42no—
116C2×C4×C83—41no—
117C2×C4×C83—82no—
118C2×C4×C83—82no—
119C2×C4×C83—82no—
120C2×C4×C83—82no—
121C2×C4×C83—82no—
122C2×C4×C83#12011yescharacteristic
123C2×C4×C83#12312yes—
124C2×C4×C83#12411yescharacteristic
125C8×C83—42no—
126C8×C83—41no—
127C8×C83—41no—
128C22×C83—21no—
129C22×C83—22no—
130C22×C83—21no—
131C22×C83—22no—
132C22×C83—41no—
133C22×C83—41no—
134C22×C83—42no—
135C22×C83#39411yescharacteristic
136C22×C83#46212yes—
137C22×C83#46412yes—
138C22×C83#46711yescharacteristic
139C22×C83#47011yescharacteristic
140C4×C83—22no—
141C4×C83—21no—
142C4×C83—42no—
143C4×C83—81no—
144C4×C83—82no—
145C4×C83—82no—
146C4×C83—162no—
147C4×C83B(4,𝔽2)11yescharacteristic
148C4×C83#45811yescharacteristic
149#10566C8311yesmaximal, characteristic, direct product factor, Sylow
150C2×C83—21no—
151C2×C83—21no—
152C2×C83—22no—
153C2×C83—22no—
154C2×C83#204411yescharacteristic
155C2×C83#205311yescharacteristic
156C2×C83#205611yescharacteristic
157#3189C2×C8311yescharacteristic
158#1996C2×C8312yes—
159#1892C2×C8312yes—
160#1850C2×C8311yescharacteristic
161#1289C2×C8311yescharacteristic
162C83#1056611yescharacteristic, direct product factor, Sylow
163C23×C8C22×C8311yescharacteristic
164C2×C22⋊Q8C22×C8312yes—
165#484—22no—
166#467—21no—
167#467—21no—
168#451—22no—
169C2×C4⋊C8—21no—
170C2×#103—22no—
171C2×C22⋊C8C22×C8311yescharacteristic
172#380C22×C8312yes—
173C4×C22⋊C4C22×C8311yescharacteristic
174#342—22no—
175#342—22no—
176#340—22no—
177#336—21no—
178C22×Q8D4×C8312yes—
179C23×C4C23×C8311yescharacteristic
180C2×Q16—21no—
181C2×Q16—21no—
182C22×C8—21no—
183C22×C8—22no—
184C22×C8—42no—
185C22×C8D4×C8311yescharacteristic
186C22×C8D4×C8311yescharacteristic
187C22⋊Q8—22no—
188C22⋊Q8—22no—
189C22⋊Q8—22no—
190C22⋊Q8—22no—
191C2×C4⋊C4—22no—
192C2×C4⋊C4—22no—
193C2×C4⋊C4D4×C8312yes—
194C2×C22⋊C4—22no—
195C2×C22⋊C4—22no—
196C2×C22⋊C4D4×C8311yescharacteristic
197C2×C22⋊C4D4×C8311yescharacteristic
198C2×C42—21no—
199#107—21no—
200#107—21no—
201C4⋊C8—42no—
202#103—22no—
203#103—22no—
204#103—44no—
205C22⋊C8—22no—
206#95—21no—
207#95—22no—
208C24C2×D4×C8311yescharacteristic
209C2×Q8—22no—
210C2×Q8—22no—
211C2×Q8—42no—
212C2×Q8—42no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—41no—
218C22×C4—41no—
219C22×C4—42no—
220C22×C4C2×D4×C8312yes—
221C22×C4C2×D4×C8311yescharacteristic
222C22×C4#41×C8311yescharacteristic
223C22×C4#41×C8312yes—
224Q16—81no—
225Q16—81no—
226C2×C8—24no—
227C2×C8—22no—
228C2×C8—21no—
229C2×C8—21no—
230C2×C8—41no—
231C2×C8—42no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—41no—
235C4⋊C4—22no—
236C4⋊C4—22no—
237C4⋊C4—42no—
238C4⋊C4—42no—
239C4⋊C4—42no—
240C4⋊C4—42no—
241C22⋊C4—21no—
242C22⋊C4—22no—
243C22⋊C4—42no—
244C22⋊C4—42no—
245C22⋊C4—42no—
246C22⋊C4—42no—
247C22⋊C4Q16×C8312yescomplemented
248C42—41no—
249C42—41no—
250C23—41no—
251C23—41no—
252C23#121×C8312yes—
253C23#121×C8311yescharacteristic
254C23C2×Q16×C8311yescharacteristic
255C23#135×C8311yescharacteristic
256C23#137×C8312yes—
257Q8—44no—
258Q8—42no—
259Q8—42no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—41no—
266C2×C4—42no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—82no—
275C2×C4—82no—
276C2×C4—82no—
277C2×C4—82no—
278C2×C4—82no—
279C2×C4#120×C8311yescharacteristic
280C2×C4#123×C8312yes—
281C2×C4#124×C8311yescharacteristic
282C8—42no—
283C8—41no—
284C8—41no—
285C22—21no—
286C22—22no—
287C22—21no—
288C22—22no—
289C22—41no—
290C22—41no—
291C22—42no—
292C22#394×C8311yescharacteristic
293C22#462×C8312yes—
294C22#464×C8312yes—
295C22#467×C8311yescharacteristic
296C22#470×C8311yescharacteristic
297C4—22no—
298C4—21no—
299C4—42no—
300C4—81no—
301C4—82no—
302C4—82no—
303C4—162no—
304C4B(4,𝔽2)×C8311yescharacteristic
305C4#458×C8311yescharacteristic
306C2—21no—
307C2—21no—
308C2—22no—
309C2—22no—
310C2C83×#204411yescharacteristic
311C2C83×#205311yescharacteristic
312C2C83×#205611yescharacteristic
subgroupG/H
center, socleC22×C83#394
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
90. C22⋊C4×C83Q16semidirect
149. #10566C83direct (N × H)
162. C83#10566direct (N × H)
247. C22⋊C4Q16×C83semidirect

Maximal subgroups

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

subgroupindex
C83×#31892
C83×#19962
C83×#18922
C83×#18502
C83×#12892
#1056683