Finite Group Databasebeta

← #35314994

Subgroups — #35314994

Order 21248.

482 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 87 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
1#24912462C211yesmaximal, characteristic
2#24905807C211yesmaximal, characteristic, complemented
3#24905465C214yesmaximal, complemented
4C4×#101×C83C211yesmaximal, characteristic, complemented
5C2×#14581789C411yescharacteristic
6C2×#14581781—21no—
7#19127758—21no—
8#19127618C412yes—
9#19127618C2212yes—
10#19127603—21no—
11#19127603—21no—
12#19127602—21no—
13C4×C4⋊Dic83C411yescharacteristic
14#19127427—21no—
15#19127427C2212yes—
16C2×C4×Q8×C83C2211yescharacteristic
17C2×#101×C83—21no—
18C4×M16×C83—21no—
19#343×C83C2212yes—
20C22×D332—21no—
21C22×D332—21no—
22C22×D332C2×C412yes—
23#14581789—41no—
24#14581789—41no—
25#14581781—44no—
26C2×C4⋊Dic83—21no—
27C2×(C2×D83)⋊C4—22no—
28C2×(C2×D83)⋊C4—22no—
29C2×(C2×D83)⋊C4—22no—
30C2×(C2×D83)⋊C4—22no—
31C2×C4×Dic83—21no—
32C4⋊(C83⋊C8)—41no—
33C22⋊(C83⋊C8)—22no—
34#14581703—41no—
35C83⋊#95C2×C412yes—
36C22×Q8×C83D411yescharacteristic
37C2×M16×C83—22no—
38C4×Q8×C83—41no—
39C4×Q8×C83—41no—
40C2×C4⋊C4×C83C2×C411yescharacteristic
41C2×C4⋊C4×C83D411yescharacteristic
42C2×C4⋊C4×C83C2311yescharacteristic
43C2×C42×C83C2×C411yescharacteristic
44C2×C42×C83D411yescharacteristic
45C2×C42×C83D411yescharacteristic
46#101×C83—24no—
47#97×C83—41no—
48C4×C8×C83—41no—
49C23×D83—22no—
50C2×D332—42no—
51C2×D332—42no—
52C2×D332—42no—
53C2×D332—42no—
54C2×D332—42no—
55C2×D332—41no—
56C2×D332—41no—
57C2×D332—42no—
58C2×D332—82no—
59C22×Dic83—22no—
60C2×C83⋊C8—42no—
61C4⋊Dic83—42no—
62(C2×D83)⋊C4—44no—
63(C2×D83)⋊C4—44no—
64(C2×D83)⋊C4—82no—
65(C2×D83)⋊C4—82no—
66C4×Dic83—42no—
67C2×Q8×C83—22no—
68C2×Q8×C83—22no—
69C2×Q8×C83—41no—
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
77M16×C83—24no—
78M16×C83—42no—
79C2×C8×C83—42no—
80C4⋊C4×C83—41no—
81C4⋊C4×C83—41no—
82C4⋊C4×C83—41no—
83C42×C83—21no—
84C42×C83—21no—
85C42×C83—21no—
86C42×C83—21no—
87C42×C83—21no—
88C42×C83—21no—
89C23×C83C2×C22⋊C411yescharacteristic
90C22×D83—42no—
91C22×D83—42no—
92C22×D83—42no—
93C22×D83—42no—
94C22×D83—42no—
95C22×D83—42no—
96C22×D83—42no—
97Q8×C83—44no—
98C2×C4×C83—21no—
99C2×C4×C83—21no—
100C2×C4×C83—21no—
101C2×C4×C83—21no—
102C2×C4×C83—22no—
103C2×C4×C83—21no—
104C2×C4×C83—21no—
105C2×C4×C83—21no—
106C2×C4×C83—21no—
107C2×C4×C83—21no—
108C2×C4×C83—21no—
109C2×C4×C83—41no—
110C2×C4×C83—41no—
111C2×C4×C83—41no—
112C2×C4×C83#9911yescharacteristic
113C2×C4×C83#9911yescharacteristic
114C2×C4×C83#10412yes—
115C2×C4×C83AGL(1,ℤ/8)12yes—
116C2×Dic83—42no—
117C2×Dic83—42no—
118C2×Dic83—42no—
119D332—82no—
120D332—84no—
121D332—84no—
122D332—82no—
123C8×C83—44no—
124C83⋊C8—82no—
125C22×C83—21no—
126C22×C83—21no—
127C22×C83C2×#9911yescharacteristic
128C22×C83#41811yescharacteristic
129C22×C83C2×#10411yescharacteristic
130C2×D83—82no—
131C2×D83—82no—
132C2×D83—82no—
133C2×D83—82no—
134C2×D83—82no—
135C2×D83—82no—
136C2×D83—82no—
137C4×C83—21no—
138C4×C83—22no—
139C4×C83—22no—
140C4×C83—41no—
141C4×C83—41no—
142C4×C83—41no—
143C4×C83—41no—
144C4×C83#35512yes—
145Dic83—82no—
146#11781—831nomaximal, Sylow
147C2×C83—21no—
148C2×C83—21no—
149C2×C83#150711yescharacteristic
150C2×C83#212211yescharacteristic
151C2×C83C2×#35511yescharacteristic
152D83—162no—
153#2548—831no—
154C4×#101D8311yescharacteristic, complemented
155#1467—831no—
156#1345—834no—
157C83#1178111yescharacteristic, complemented, Sylow
158C2×#127—831no—
159C2×#124—1661no—
160C2×C4×Q8C2×D8311yescharacteristic
161#432—1661no—
162C2×#101—21no—
163C4×M16—21no—
164#394—832no—
165#394—832no—
166#390—1661no—
167#390—1661no—
168#390—1661no—
169C4×C4⋊C4—831no—
170#343C2×D8312yes—
171#324—832no—
172#324—1661no—
173C22×Q8C22⋊D8311yescharacteristic
174C22×D4—832no—
175C22×D4—1661no—
176C22×D4—1661no—
177C2×M16—22no—
178#127—3321no—
179#127—3321no—
180#124—3324no—
181C4×Q8—41no—
182C4×Q8—41no—
183C2×C4⋊C4—1661no—
184C2×C4⋊C4C4×D8311yescharacteristic
185C2×C4⋊C4D33211yescharacteristic
186C2×C4⋊C4C22×D8311yescharacteristic
187C2×C22⋊C4—1662no—
188C2×C22⋊C4—1662no—
189C2×C22⋊C4—1662no—
190C2×C22⋊C4—1662no—
191C2×C42—1661no—
192C2×C42C4×D8311yescharacteristic
193C2×C42D33211yescharacteristic
194C2×C42C22⋊D8311yescharacteristic
195C4⋊C8—3321no—
196#101—24no—
197C22⋊C8—1662no—
198#97—41no—
199#97—3321no—
200C4×C8—41no—
201#95—832no—
202C24—1662no—
203C2×Q8—22no—
204C2×Q8—22no—
205C2×Q8—41no—
206C2×D4—3322no—
207C2×D4—3322no—
208C2×D4—3322no—
209C2×D4—3322no—
210C2×D4—3322no—
211C2×D4—3321no—
212C2×D4—3321no—
213C2×D4—3322no—
214C2×D4—6642no—
215C22×C4—1662no—
216C22×C4(C2×D83)⋊C411yescharacteristic
217C22×C4(C2×D83)⋊C411yescharacteristic
218C22×C4(C2×D83)⋊C411yescharacteristic
219C22×C4(C2×D83)⋊C411yescharacteristic
220C22×C4C2×C4×D8311yescharacteristic
221C22×C4C2×C22⋊D8311yescharacteristic
222C22×C4C2×D33211yescharacteristic
223M16—24no—
224M16—42no—
225C2×C8—42no—
226C2×C8—3322no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C4⋊C4—3322no—
231C22⋊C4—3324no—
232C22⋊C4—3324no—
233C22⋊C4—6642no—
234C22⋊C4—6642no—
235C42—21no—
236C42—21no—
237C42—21no—
238C42—21no—
239C42—21no—
240C42—21no—
241C42—3322no—
242C23—3322no—
243C23—3322no—
244C23—3322no—
245C23—3322no—
246C23—3322no—
247C23—3322no—
248C23—3322no—
249C23C2×(C2×D83)⋊C411yescharacteristic
250Q8—44no—
251D4—6642no—
252D4—6644no—
253D4—6644no—
254D4—6642no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—3322no—
270C2×C4—3322no—
271C2×C4—3322no—
272C2×C4#1458170611yescharacteristic
273C2×C4#1458170611yescharacteristic
274C2×C4#1458172012yes—
275C2×C4#1458181712yes—
276C8—44no—
277C8—6642no—
278C22—21no—
279C22—21no—
280C22—6642no—
281C22—6642no—
282C22—6642no—
283C22—6642no—
284C22—6642no—
285C22—6642no—
286C22—6642no—
287C22C2×#1458170611yescharacteristic
288C22#1912770511yescharacteristic
289C22C2×#1458172011yescharacteristic
290C4—21no—
291C4—22no—
292C4—22no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—6642no—
298C4#1912749712yes—
299C2—21no—
300C2—21no—
301C2—13282no—
302C2#2490597811yescharacteristic
303C2#2490911411yescharacteristic
304C2C2×#1912749711yescharacteristic
subgroupG/H
centerC22C2×#14581706
commutatorC22×C4×C83C22×C4
FrattiniC2×C4⋊C4C22×D83
FittingC4×#101×C83C2
socleC22×C83C2×#99
prime radicalC2×#14581789C4
cosocleC2×C4⋊C4×C83C23
hypercenterC4×#101D83
hypocenterC83#11781
LCSG ▷ C22×C4×C83 ▷ C23×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
2. #24905807C2semidirect
3. #24905465C2semidirect
4. C4×#101×C83C2semidirect
154. C4×#101D83semidirect
157. C83#11781semidirect

Maximal subgroups

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

subgroupindex
#249124622
#249058072
#249054652
C4×#101×C832
#1178183