Finite Group Databasebeta

← #35314793

Subgroups — #35314793

Order 21248.

400 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 91 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, complemented
2#24905787C211yesmaximal, characteristic, complemented
3#24905493C212yesmaximal, complemented
4#24905466C212yesmaximal
5C83×#2632C211yesmaximal, characteristic
6#19127754—21no—
7C2×#14581711—21no—
8C4×#13050574—21no—
9#19127470C2212yes—
10#19127427—21no—
11#19127427C2212yes—
12C2×#124×C83C411yescharacteristic
13C2×C4×Q8×C83C2211yescharacteristic
14#399×C83—21no—
15#395×C83C411yescharacteristic
16#395×C83C2211yescharacteristic
17#394×C83C411yescharacteristic
18#394×C83C2211yescharacteristic
19#393×C83—21no—
20#388×C83—21no—
21#388×C83—21no—
22#383×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
32C22×D4×C83C2×C411yescharacteristic
33#124×C83—41no—
34#124×C83—41no—
35C4×Q8×C83—41no—
36C4×Q8×C83—41no—
37C2×C4⋊C4×C83—21no—
38C2×C4⋊C4×C83—21no—
39C2×C4⋊C4×C83C2×C411yescharacteristic
40C2×C4⋊C4×C83D411yescharacteristic
41C2×C4⋊C4×C83C2311yescharacteristic
42C2×C22⋊C4×C83—21no—
43C2×C22⋊C4×C83—21no—
44C2×C22⋊C4×C83—21no—
45C2×C22⋊C4×C83—21no—
46C2×C22⋊C4×C83—21no—
47C2×C22⋊C4×C83—21no—
48C2×C42×C83C2×C411yescharacteristic
49C2×C42×C83D411yescharacteristic
50C2×C42×C83D411yescharacteristic
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—
61C24×C83—21no—
62C2×Q8×C83—22no—
63C2×Q8×C83—22no—
64C2×Q8×C83—41no—
65C2×Q8×C83—41no—
66C2×Q8×C83—81no—
67C2×D4×C83—41no—
68C2×D4×C83—81no—
69C22×C4×C83—21no—
70C22×C4×C83—21no—
71C22×C4×C83—21no—
72C22×C4×C83C22⋊C411yescharacteristic
73C22×C4×C83C22⋊C411yescharacteristic
74C22×C4×C83C22⋊C411yescharacteristic
75C22×C4×C83C22⋊C411yescharacteristic
76C22×C4×C83C22×C411yescharacteristic
77C22×C4×C83C2×D411yescharacteristic
78C22×C4×C83C2×D411yescharacteristic
79C4⋊C4×C83—41no—
80C4⋊C4×C83—41no—
81C4⋊C4×C83—41no—
82C4⋊C4×C83—81no—
83C4⋊C4×C83—81no—
84C22⋊C4×C83—42no—
85C22⋊C4×C83—41no—
86C22⋊C4×C83—41no—
87C22⋊C4×C83—42no—
88C22⋊C4×C83—42no—
89C22⋊C4×C83—81no—
90C22⋊C4×C83—81no—
91C42×C83—21no—
92C42×C83—21no—
93C42×C83—21no—
94C42×C83—21no—
95C42×C83—21no—
96C42×C83—21no—
97C23×C83—41no—
98C23×C83—41no—
99C23×C83—41no—
100C23×C83—41no—
101C23×C83—41no—
102C23×C83—41no—
103C23×C83—41no—
104C23×C83C2×C22⋊C411yescharacteristic
105Q8×C83—44no—
106Q8×C83—82no—
107D4×C83—82no—
108C2×C4×C83—21no—
109C2×C4×C83—21no—
110C2×C4×C83—21no—
111C2×C4×C83—21no—
112C2×C4×C83—21no—
113C2×C4×C83—21no—
114C2×C4×C83—21no—
115C2×C4×C83—21no—
116C2×C4×C83—21no—
117C2×C4×C83—21no—
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—41no—
126C2×C4×C83—41no—
127C2×C4×C83—41no—
128C2×C4×C83—41no—
129C2×C4×C83—41no—
130C2×C4×C83—41no—
131C2×C4×C83#9911yescharacteristic
132C2×C4×C83#9911yescharacteristic
133C2×C4×C83#10412yes—
134C2×C4×C83#13512yes—
135C83⋊C8—44no—
136C83⋊C8—82no—
137C22×C83—21no—
138C22×C83—21no—
139C22×C83—81no—
140C22×C83—81no—
141C22×C83—81no—
142C22×C83—81no—
143C22×C83—81no—
144C22×C83—81no—
145C22×C83—81no—
146C22×C83C2×#9911yescharacteristic
147C22×C83#41611yescharacteristic
148C22×C83C2×#10411yescharacteristic
149C4×C83—21no—
150C4×C83—21no—
151C4×C83—22no—
152C4×C83—22no—
153C4×C83—41no—
154C4×C83—41no—
155C4×C83—41no—
156C4×C83—41no—
157C4×C83—81no—
158C4×C83—81no—
159C4×C83—81no—
160#11738—831nomaximal, Sylow
161C2×C83—21no—
162C2×C83—21no—
163C2×C83—161no—
164C2×C83#150111yescharacteristic
165C2×C83#212211yescharacteristic
166C2×C83#213311yescharacteristic
167#2632D8311yescharacteristic
168C4×#101—831no—
169#1461—831no—
170#1354—832no—
171#1345—832no—
172C83#1173811yescharacteristic, complemented, Sylow
173C2×#124Dic8311yescharacteristic
174C2×C4×Q8C2×D8311yescharacteristic
175#431—1661no—
176C2×#101—1661no—
177C4×M16—1661no—
178#399—21no—
179#395Dic8311yescharacteristic
180#395C2×D8311yescharacteristic
181#394Dic8311yescharacteristic
182#394C2×D8311yescharacteristic
183#393—21no—
184#388—21no—
185#388—21no—
186#383Dic8311yescharacteristic
187#343—832no—
188#324—832no—
189#324—1661no—
190C22×Q8C2×Dic8311yescharacteristic
191C22×Q8C22⋊D8311yescharacteristic
192C22×D4C2×Dic8311yescharacteristic
193C2×M16—1662no—
194#124—41no—
195#124—41no—
196C4×Q8—41no—
197C4×Q8—41no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4C2×Dic8311yescharacteristic
201C2×C4⋊C4C22⋊D8311yescharacteristic
202C2×C4⋊C4C22×D8311yescharacteristic
203C2×C22⋊C4—21no—
204C2×C22⋊C4—21no—
205C2×C22⋊C4—21no—
206C2×C22⋊C4—21no—
207C2×C22⋊C4—21no—
208C2×C22⋊C4—21no—
209C2×C42C2×Dic8311yescharacteristic
210C2×C42C22⋊D8311yescharacteristic
211C2×C42C22⋊D8311yescharacteristic
212C4⋊C8—3321no—
213#101—1664no—
214C22⋊C8—1662no—
215#97—3321no—
216C4×C8—3321no—
217C4×C8—3321no—
218#95—21no—
219#95—21no—
220#95—21no—
221#95—21no—
222#95C2×Dic8311yescharacteristic
223#95C2×Dic8311yescharacteristic
224C24—21no—
225C2×Q8—22no—
226C2×Q8—22no—
227C2×Q8—41no—
228C2×Q8—41no—
229C2×Q8—81no—
230C2×D4—41no—
231C2×D4—81no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4C22⋊Dic8311yescharacteristic
236C22×C4C22⋊Dic8311yescharacteristic
237C22×C4C22⋊Dic8311yescharacteristic
238C22×C4C22⋊Dic8311yescharacteristic
239C22×C4C22×Dic8311yescharacteristic
240C22×C4C2×C22⋊D8311yescharacteristic
241C22×C4C2×C22⋊D8311yescharacteristic
242M16—3322no—
243M16—1664no—
244C2×C8—3322no—
245C2×C8—3322no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—81no—
250C4⋊C4—81no—
251C22⋊C4—42no—
252C22⋊C4—42no—
253C22⋊C4—41no—
254C22⋊C4—41no—
255C22⋊C4—42no—
256C22⋊C4—81no—
257C22⋊C4—81no—
258C42—21no—
259C42—21no—
260C42—21no—
261C42—21no—
262C42—21no—
263C42—21no—
264C23—41no—
265C23—41no—
266C23—41no—
267C23—41no—
268C23—41no—
269C23—41no—
270C23—41no—
271C23C2×C22⋊Dic8311yescharacteristic
272Q8—44no—
273Q8—82no—
274D4—82no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4#1458170711yescharacteristic
299C2×C4#1458170711yescharacteristic
300C2×C4#1458171912yes—
301C2×C4#1458181212yes—
302C8—3324no—
303C8—6642no—
304C22—21no—
305C22—21no—
306C22—81no—
307C22—81no—
308C22—81no—
309C22—81no—
310C22—81no—
311C22—81no—
312C22—81no—
313C22C2×#1458170711yescharacteristic
314C22#1912769711yescharacteristic
315C22C2×#1458171911yescharacteristic
316C4—21no—
317C4—21no—
318C4—22no—
319C4—22no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—81no—
325C4—81no—
326C4—81no—
327C2—21no—
328C2—21no—
329C2—161no—
330C2#2490595411yescharacteristic
331C2#2490911311yescharacteristic
332C2#2490915211yescharacteristic
subgroupG/H
centerC22C2×#14581707
commutatorC22×C4×C83C22×C4
FrattiniC2×C4⋊C4C22×D83
FittingC83×#2632C2
socleC22×C83C2×#99
prime radicalC22×D4×C83C2×C4
cosocleC2×C4⋊C4×C83C23
hypercenter#2632D83
hypocenterC83#11738
LCSG ▷ C22×C4×C83 ▷ C23×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2632

Complements

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

NH ≅ G/Ntype
1. C4×#14581711C2semidirect
2. #24905787C2semidirect
3. #24905493C2semidirect
172. C83#11738semidirect

Maximal subgroups

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

subgroupindex
C4×#145817112
#249057872
#249054932
#249054662
C83×#26322
#1173883