Finite Group Databasebeta

← #35314783

Subgroups — #35314783

Order 21248.

402 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C4×#14581711C211yesmaximal, characteristic
2#24905787C211yesmaximal, characteristic
3#24905493C212yesmaximal
4#24905469C212yesmaximal
5C83×#2399C211yesmaximal, characteristic
6#19127754—21no—
7C2×#14581711—21no—
8C4×#13050574—21no—
9#19127470C2212yes—
10#19127427—21no—
11#19127427C2212yes—
12C2×C4×Q8×C83C411yescharacteristic
13C2×C4×Q8×C83C2211yescharacteristic
14#398×C83—21no—
15#398×C83C411yescharacteristic
16#398×C83C2211yescharacteristic
17#395×C83—21no—
18#395×C83C411yescharacteristic
19#395×C83C2211yescharacteristic
20C4×C4⋊C4×C83—21no—
21C4×C4⋊C4×C83—21no—
22#376×C83C411yescharacteristic
23C2×#13050574—22no—
24C4⋊(C83⋊C8)—41no—
25#14581711—24no—
26C22⋊(C83⋊C8)—22no—
27#14581703—41no—
28C4×C83⋊C8—41no—
29C4×C83⋊C8—41no—
30C22×Q8×C83C2×C411yescharacteristic
31C22×Q8×C83D411yescharacteristic
32C4×Q8×C83—41no—
33C4×Q8×C83—41no—
34C4×Q8×C83—41no—
35C4×Q8×C83—41no—
36C2×C4⋊C4×C83—21no—
37C2×C4⋊C4×C83—21no—
38C2×C4⋊C4×C83—21no—
39C2×C4⋊C4×C83—21no—
40C2×C4⋊C4×C83—21no—
41C2×C4⋊C4×C83C2×C411yescharacteristic
42C2×C4⋊C4×C83C2×C411yescharacteristic
43C2×C4⋊C4×C83D411yescharacteristic
44C2×C4⋊C4×C83C2311yescharacteristic
45C2×C42×C83—21no—
46C2×C42×C83—21no—
47C2×C42×C83C2×C411yescharacteristic
48C2×C42×C83D411yescharacteristic
49C2×C42×C83D411yescharacteristic
50#95×C83—21no—
51#95×C83—21no—
52#95×C83—21no—
53#95×C83—21no—
54#95×C83—21no—
55#95×C83C2×C411yescharacteristic
56#95×C83C2×C411yescharacteristic
57#13050574—24no—
58#13050574—42no—
59C2×C83⋊C8—42no—
60C2×C83⋊C8—42no—
61C2×Q8×C83—22no—
62C2×Q8×C83—22no—
63C2×Q8×C83—41no—
64C2×Q8×C83—42no—
65C2×Q8×C83—41no—
66C22×C4×C83—21no—
67C22×C4×C83—21no—
68C22×C4×C83—21no—
69C22×C4×C83—21no—
70C22×C4×C83C22⋊C411yescharacteristic
71C22×C4×C83C22⋊C411yescharacteristic
72C22×C4×C83C22⋊C411yescharacteristic
73C22×C4×C83C22⋊C411yescharacteristic
74C22×C4×C83C22×C411yescharacteristic
75C22×C4×C83C2×D411yescharacteristic
76C22×C4×C83C2×D411yescharacteristic
77C4⋊C4×C83—41no—
78C4⋊C4×C83—41no—
79C4⋊C4×C83—41no—
80C4⋊C4×C83—41no—
81C4⋊C4×C83—42no—
82C4⋊C4×C83—42no—
83C4⋊C4×C83—42no—
84C4⋊C4×C83—42no—
85C4⋊C4×C83—42no—
86C42×C83—24no—
87C42×C83—21no—
88C42×C83—21no—
89C42×C83—21no—
90C42×C83—21no—
91C42×C83—21no—
92C42×C83—21no—
93C42×C83—41no—
94C42×C83—41no—
95C23×C83C2×C22⋊C411yescharacteristic
96Q8×C83—44no—
97Q8×C83—42no—
98Q8×C83—42no—
99C2×C4×C83—21no—
100C2×C4×C83—21no—
101C2×C4×C83—21no—
102C2×C4×C83—21no—
103C2×C4×C83—22no—
104C2×C4×C83—22no—
105C2×C4×C83—22no—
106C2×C4×C83—22no—
107C2×C4×C83—21no—
108C2×C4×C83—21no—
109C2×C4×C83—21no—
110C2×C4×C83—21no—
111C2×C4×C83—21no—
112C2×C4×C83—21no—
113C2×C4×C83—41no—
114C2×C4×C83—41no—
115C2×C4×C83—41no—
116C2×C4×C83—41no—
117C2×C4×C83—41no—
118C2×C4×C83—41no—
119C2×C4×C83—41no—
120C2×C4×C83—41no—
121C2×C4×C83—41no—
122C2×C4×C83—41no—
123C2×C4×C83—41no—
124C2×C4×C83—41no—
125C2×C4×C83#9911yescharacteristic
126C2×C4×C83#9911yescharacteristic
127C2×C4×C83#10412yes—
128C2×C4×C83#13512yes—
129C83⋊C8—44no—
130C83⋊C8—82no—
131C22×C83—21no—
132C22×C83—21no—
133C22×C83C2×#9911yescharacteristic
134C22×C83#41611yescharacteristic
135C22×C83C2×#10411yescharacteristic
136C4×C83—21no—
137C4×C83—22no—
138C4×C83—22no—
139C4×C83—42no—
140C4×C83—42no—
141C4×C83—41no—
142C4×C83—41no—
143C4×C83—42no—
144C4×C83—41no—
145C4×C83—41no—
146C4×C83—81no—
147C4×C83#35612yes—
148#11736—831nomaximal, Sylow
149C2×C83—21no—
150C2×C83—21no—
151C2×C83#150111yescharacteristic
152C2×C83#212011yescharacteristic
153C2×C83C2×#35611yescharacteristic
154#2399D8311yescharacteristic
155C4×#101—831no—
156#1461—831no—
157#1354—832no—
158#1346—832no—
159C83#1173611yescharacteristic, complemented, Sylow
160C2×C4×Q8Dic8311yescharacteristic
161C2×C4×Q8C2×D8311yescharacteristic
162#431—1661no—
163C2×#101—1661no—
164C4×M16—1661no—
165#398—21no—
166#398Dic8311yescharacteristic
167#398C2×D8311yescharacteristic
168#395—21no—
169#395Dic8311yescharacteristic
170#395C2×D8311yescharacteristic
171C4×C4⋊C4—21no—
172C4×C4⋊C4—21no—
173#376Dic8311yescharacteristic
174#343—832no—
175#324—832no—
176#324—1661no—
177C22×Q8C2×Dic8311yescharacteristic
178C22×Q8C22⋊D8311yescharacteristic
179C2×M16—1662no—
180C4×Q8—41no—
181C4×Q8—41no—
182C4×Q8—41no—
183C4×Q8—41no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4C2×Dic8311yescharacteristic
190C2×C4⋊C4C2×Dic8311yescharacteristic
191C2×C4⋊C4C22⋊D8311yescharacteristic
192C2×C4⋊C4C22×D8311yescharacteristic
193C2×C42—21no—
194C2×C42—21no—
195C2×C42C2×Dic8311yescharacteristic
196C2×C42C22⋊D8311yescharacteristic
197C2×C42C22⋊D8311yescharacteristic
198C4⋊C8—3321no—
199#101—1664no—
200C22⋊C8—1662no—
201#97—3321no—
202C4×C8—3321no—
203C4×C8—3321no—
204#95—21no—
205#95—21no—
206#95—21no—
207#95—21no—
208#95—21no—
209#95C2×Dic8311yescharacteristic
210#95C2×Dic8311yescharacteristic
211C2×Q8—22no—
212C2×Q8—22no—
213C2×Q8—41no—
214C2×Q8—42no—
215C2×Q8—41no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4C22⋊Dic8311yescharacteristic
221C22×C4C22⋊Dic8311yescharacteristic
222C22×C4C22⋊Dic8311yescharacteristic
223C22×C4C22⋊Dic8311yescharacteristic
224C22×C4C22×Dic8311yescharacteristic
225C22×C4C2×C22⋊D8311yescharacteristic
226C22×C4C2×C22⋊D8311yescharacteristic
227M16—3322no—
228M16—1664no—
229C2×C8—3322no—
230C2×C8—3322no—
231C4⋊C4—41no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—42no—
236C4⋊C4—42no—
237C4⋊C4—42no—
238C4⋊C4—42no—
239C4⋊C4—42no—
240C42—24no—
241C42—21no—
242C42—21no—
243C42—21no—
244C42—21no—
245C42—21no—
246C42—21no—
247C42—41no—
248C42—41no—
249C23C2×C22⋊Dic8311yescharacteristic
250Q8—44no—
251Q8—42no—
252Q8—42no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4#1458170711yescharacteristic
280C2×C4#1458170711yescharacteristic
281C2×C4#1458171912yes—
282C2×C4#1458181212yes—
283C8—3324no—
284C8—6642no—
285C22—21no—
286C22—21no—
287C22C2×#1458170711yescharacteristic
288C22#1912769711yescharacteristic
289C22C2×#1458171911yescharacteristic
290C4—21no—
291C4—22no—
292C4—22no—
293C4—42no—
294C4—42no—
295C4—41no—
296C4—42no—
297C4—41no—
298C4—41no—
299C4—41no—
300C4—81no—
301C4#1912750012yes—
302C2—21no—
303C2—21no—
304C2#2490595411yescharacteristic
305C2#2490910411yescharacteristic
306C2C2×#1912750011yescharacteristic
subgroupG/H
centerC2×C4#14581707
commutatorC22×C4×C83C22×C4
FrattiniC2×C4⋊C4C22×D83
FittingC83×#2399C2
socleC22×C83C2×#99
prime radicalC23×C83C2×C22⋊C4
cosocleC2×C4⋊C4×C83C23
hypercenter#2399D83
hypocenterC83#11736
LCSG ▷ C22×C4×C83 ▷ C23×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2399

Complements

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

NH ≅ G/Ntype
159. C83#11736semidirect

Maximal subgroups

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

subgroupindex
C4×#145817112
#249057872
#249054932
#249054692
C83×#23992
#1173683