Finite Group Databasebeta

← #35315230

Subgroups — #35315230

Order 21248.

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

normal subgroups only

This group has 382 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#24907459C211yesmaximal, characteristic, complemented
2#24905807C211yesmaximal, characteristic, complemented
3#24905493C212yesmaximal, complemented
4#24905466C212yesmaximal
5C83×#2632C211yesmaximal, characteristic
6#19127758—21no—
7#19127725—21no—
8C2×#14581711—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—
25C4⋊(C83⋊C8)—41no—
26C4⋊(C83⋊C8)—41no—
27#14581711—42no—
28C22⋊(C83⋊C8)—22no—
29#14581703—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—42no—
58#13050574—42no—
59C2×C83⋊C8—42no—
60C2×C83⋊C8—42no—
61C24×C83—21no—
62C2×Q8×C83—21no—
63C2×Q8×C83—21no—
64C2×Q8×C83—41no—
65C2×Q8×C83—41no—
66C2×Q8×C83—41no—
67C2×Q8×C83—81no—
68C2×D4×C83—41no—
69C2×D4×C83—81no—
70C22×C4×C83—21no—
71C22×C4×C83—21no—
72C22×C4×C83—21no—
73C22×C4×C83C22⋊C411yescharacteristic
74C22×C4×C83C22⋊C411yescharacteristic
75C22×C4×C83C22⋊C411yescharacteristic
76C22×C4×C83C22⋊C411yescharacteristic
77C22×C4×C83C22×C411yescharacteristic
78C22×C4×C83C2×D411yescharacteristic
79C22×C4×C83C2×D411yescharacteristic
80C4⋊C4×C83—41no—
81C4⋊C4×C83—41no—
82C4⋊C4×C83—41no—
83C4⋊C4×C83—81no—
84C4⋊C4×C83—81no—
85C22⋊C4×C83—42no—
86C22⋊C4×C83—42no—
87C22⋊C4×C83—41no—
88C22⋊C4×C83—41no—
89C22⋊C4×C83—41no—
90C22⋊C4×C83—41no—
91C22⋊C4×C83—81no—
92C22⋊C4×C83—81no—
93C42×C83—21no—
94C42×C83—21no—
95C42×C83—21no—
96C42×C83—21no—
97C42×C83—21no—
98C42×C83—21no—
99C23×C83—41no—
100C23×C83—41no—
101C23×C83—41no—
102C23×C83—41no—
103C23×C83—41no—
104C23×C83—41no—
105C23×C83—41no—
106C23×C83C2×C22⋊C411yescharacteristic
107Q8×C83—42no—
108Q8×C83—42no—
109Q8×C83—82no—
110D4×C83—82no—
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—21no—
119C2×C4×C83—21no—
120C2×C4×C83—21no—
121C2×C4×C83—21no—
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—41no—
132C2×C4×C83—41no—
133C2×C4×C83—41no—
134C2×C4×C83—41no—
135C2×C4×C83#9911yescharacteristic
136C2×C4×C83#9911yescharacteristic
137C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C83#13711yescharacteristic
139C83⋊C8—82no—
140C83⋊C8—82no—
141C22×C83—21no—
142C22×C83—21no—
143C22×C83—81no—
144C22×C83—81no—
145C22×C83—81no—
146C22×C83—81no—
147C22×C83—81no—
148C22×C83—81no—
149C22×C83—81no—
150C22×C83C2×#9911yescharacteristic
151C22×C83#41711yescharacteristic
152C22×C83#42111yescharacteristic
153C4×C83—21no—
154C4×C83—21no—
155C4×C83—21no—
156C4×C83—21no—
157C4×C83—41no—
158C4×C83—41no—
159C4×C83—41no—
160C4×C83—41no—
161C4×C83—41no—
162C4×C83—81no—
163C4×C83—81no—
164C4×C83—81no—
165#11833—831nomaximal, Sylow
166C2×C83—21no—
167C2×C83—21no—
168C2×C83—161no—
169C2×C83#151311yescharacteristic
170C2×C83#212211yescharacteristic
171C2×C83#213311yescharacteristic
172#2632D8311yescharacteristic
173#1801—831no—
174#1467—831no—
175#1354—832no—
176#1345—832no—
177C83#1183311yescharacteristic, complemented, Sylow
178C2×#124Dic8311yescharacteristic
179C2×C4×Q8C2×D8311yescharacteristic
180#432—1661no—
181#423—1661no—
182C2×#101—1661no—
183#399—21no—
184#395Dic8311yescharacteristic
185#395C2×D8311yescharacteristic
186#394Dic8311yescharacteristic
187#394C2×D8311yescharacteristic
188#393—21no—
189#388—21no—
190#388—21no—
191#383Dic8311yescharacteristic
192#343—832no—
193#324—832no—
194#324—1661no—
195C22×Q8C2×Dic8311yescharacteristic
196C22×Q8C22⋊D8311yescharacteristic
197C22×D4C2×Dic8311yescharacteristic
198C2×M16—1662no—
199#124—41no—
200#124—41no—
201C4×Q8—41no—
202C4×Q8—41no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4C2×Dic8311yescharacteristic
206C2×C4⋊C4C22⋊D8311yescharacteristic
207C2×C4⋊C4C22×D8311yescharacteristic
208C2×C22⋊C4—21no—
209C2×C22⋊C4—21no—
210C2×C22⋊C4—21no—
211C2×C22⋊C4—21no—
212C2×C22⋊C4—21no—
213C2×C22⋊C4—21no—
214C2×C42C2×Dic8311yescharacteristic
215C2×C42C22⋊D8311yescharacteristic
216C2×C42C22⋊D8311yescharacteristic
217C4⋊C8—3321no—
218C4⋊C8—3321no—
219C4⋊C8—3321no—
220#101—3322no—
221C22⋊C8—1662no—
222#97—3321no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95C2×Dic8311yescharacteristic
228#95C2×Dic8311yescharacteristic
229C24—21no—
230C2×Q8—21no—
231C2×Q8—21no—
232C2×Q8—41no—
233C2×Q8—41no—
234C2×Q8—41no—
235C2×Q8—81no—
236C2×D4—41no—
237C2×D4—81no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4C22⋊Dic8311yescharacteristic
242C22×C4C22⋊Dic8311yescharacteristic
243C22×C4C22⋊Dic8311yescharacteristic
244C22×C4C22⋊Dic8311yescharacteristic
245C22×C4C22×Dic8311yescharacteristic
246C22×C4C2×C22⋊D8311yescharacteristic
247C22×C4C2×C22⋊D8311yescharacteristic
248M16—3322no—
249M16—3322no—
250C2×C8—3322no—
251C2×C8—3322no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—81no—
256C4⋊C4—81no—
257C22⋊C4—42no—
258C22⋊C4—42no—
259C22⋊C4—41no—
260C22⋊C4—41no—
261C22⋊C4—41no—
262C22⋊C4—41no—
263C22⋊C4—81no—
264C22⋊C4—81no—
265C42—21no—
266C42—21no—
267C42—21no—
268C42—21no—
269C42—21no—
270C42—21no—
271C23—41no—
272C23—41no—
273C23—41no—
274C23—41no—
275C23—41no—
276C23—41no—
277C23—41no—
278C23C2×C22⋊Dic8311yescharacteristic
279Q8—42no—
280Q8—42no—
281Q8—82no—
282D4—82no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4#1458170711yescharacteristic
308C2×C4#1458170711yescharacteristic
309C2×C4#1458181711yescharacteristic
310C2×C4#1458182211yescharacteristic
311C8—6642no—
312C8—6642no—
313C22—21no—
314C22—21no—
315C22—81no—
316C22—81no—
317C22—81no—
318C22—81no—
319C22—81no—
320C22—81no—
321C22—81no—
322C22C2×#1458170711yescharacteristic
323C22#1912770211yescharacteristic
324C22#1912771811yescharacteristic
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—81no—
335C4—81no—
336C4—81no—
337C2—21no—
338C2—21no—
339C2—161no—
340C2#2490600611yescharacteristic
341C2#2490911311yescharacteristic
342C2#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#11833
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. #24907459C2semidirect
2. #24905807C2semidirect
3. #24905493C2semidirect
177. C83#11833semidirect

Maximal subgroups

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

subgroupindex
#249074592
#249058072
#249054932
#249054662
C83×#26322
#1183383