Finite Group Databasebeta

← #35315558

Subgroups — #35315558

Order 21248.

372 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 103 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
2#24905787C211yesmaximal, characteristic
3#24905493C212yesmaximal
4#24905490C212yesmaximal
5C83×#2581C211yesmaximal, characteristic
6#19127754—21no—
7#19127725—21no—
8C2×#14581711—21no—
9#19127470C2212yes—
10#19127427—21no—
11#19127427C2212yes—
12C2×C4×Q8×C83C411yescharacteristic
13C2×C4×Q8×C83C2211yescharacteristic
14#400×C83C411yescharacteristic
15#400×C83C2211yescharacteristic
16#395×C83C411yescharacteristic
17#395×C83C2211yescharacteristic
18#391×C83—21no—
19#389×C83—21no—
20#387×C83—21no—
21#387×C83—21no—
22#382×C83C411yescharacteristic
23C2×#13050574—22no—
24C4⋊(C83⋊C8)—41no—
25C4⋊(C83⋊C8)—41no—
26C4⋊(C83⋊C8)—41no—
27#14581711—42no—
28C22⋊(C83⋊C8)—22no—
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×C83C2×C411yescharacteristic
41C2×C4⋊C4×C83C2×C411yescharacteristic
42C2×C4⋊C4×C83D411yescharacteristic
43C2×C4⋊C4×C83C2311yescharacteristic
44C2×C42×C83—21no—
45C2×C42×C83C2×C411yescharacteristic
46C2×C42×C83D411yescharacteristic
47C2×C42×C83D411yescharacteristic
48#95×C83—21no—
49#95×C83—21no—
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—42no—
58#13050574—42no—
59C2×C83⋊C8—42no—
60C2×C83⋊C8—42no—
61C2×Q8×C83—41no—
62C2×Q8×C83—41no—
63C2×Q8×C83—42no—
64C2×Q8×C83—41no—
65C2×Q8×C83SD1612yes—
66C2×Q8×C83Q1612yes—
67C22×C4×C83—21no—
68C22×C4×C83—21no—
69C22×C4×C83—21no—
70C22×C4×C83—21no—
71C22×C4×C83C22⋊C411yescharacteristic
72C22×C4×C83C22⋊C411yescharacteristic
73C22×C4×C83C22⋊C411yescharacteristic
74C22×C4×C83C22⋊C411yescharacteristic
75C22×C4×C83C22×C411yescharacteristic
76C22×C4×C83C2×D411yescharacteristic
77C22×C4×C83C2×D411yescharacteristic
78C4⋊C4×C83—41no—
79C4⋊C4×C83—41no—
80C4⋊C4×C83—41no—
81C4⋊C4×C83—41no—
82C4⋊C4×C83—42no—
83C4⋊C4×C83—42no—
84C4⋊C4×C83—42no—
85C4⋊C4×C83—41no—
86C4⋊C4×C83—41no—
87C42×C83—21no—
88C42×C83—21no—
89C42×C83—21no—
90C42×C83—21no—
91C42×C83—21no—
92C42×C83—21no—
93C42×C83—42no—
94C23×C83C2×C22⋊C411yescharacteristic
95Q8×C83—42no—
96Q8×C83—42no—
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—21no—
104C2×C4×C83—21no—
105C2×C4×C83—22no—
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—41no—
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—42no—
120C2×C4×C83—41no—
121C2×C4×C83—41no—
122C2×C4×C83—41no—
123C2×C4×C83#9911yescharacteristic
124C2×C4×C83#9911yescharacteristic
125C2×C4×C83#10312yes—
126C2×C4×C83#10312yes—
127C2×C4×C83C2×SD1611yescharacteristic
128C2×C4×C83C2×Q1611yescharacteristic
129C83⋊C8—82no—
130C83⋊C8—82no—
131C22×C83—21no—
132C22×C83—21no—
133C22×C83C2×#9911yescharacteristic
134C22×C83C2×#10311yescharacteristic
135C22×C83#42111yescharacteristic
136C4×C83—21no—
137C4×C83—21no—
138C4×C83—21no—
139C4×C83—22no—
140C4×C83—22no—
141C4×C83—21no—
142C4×C83—41no—
143C4×C83—41no—
144C4×C83—42no—
145C4×C83—41no—
146C4×C83—81no—
147C4×C83—81no—
148C4×C83—81no—
149#11905—831nomaximal, Sylow
150C2×C83—21no—
151C2×C83—21no—
152C2×C83#152011yescharacteristic
153C2×C83#212011yescharacteristic
154C2×C83#213311yescharacteristic
155#2581D8311yescharacteristic
156#1801—831no—
157#1461—831no—
158#1354—832no—
159#1353—832no—
160C83#1190511yescharacteristic, complemented, Sylow
161C2×C4×Q8Dic8311yescharacteristic
162C2×C4×Q8C2×D8311yescharacteristic
163#431—1661no—
164#423—1661no—
165C2×#101—1661no—
166#400Dic8311yescharacteristic
167#400C2×D8311yescharacteristic
168#395Dic8311yescharacteristic
169#395C2×D8311yescharacteristic
170#391—21no—
171#389—21no—
172#387—21no—
173#387—21no—
174#382Dic8311yescharacteristic
175#343—832no—
176#324—832no—
177#324—1661no—
178C22×Q8C2×Dic8311yescharacteristic
179C22×Q8C22⋊D8311yescharacteristic
180C2×M16—1662no—
181C4×Q8—41no—
182C4×Q8—41no—
183C4×Q8—41no—
184C4×Q8—41no—
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×C42C2×Dic8311yescharacteristic
195C2×C42C22⋊D8311yescharacteristic
196C2×C42C22⋊D8311yescharacteristic
197C4⋊C8—3321no—
198C4⋊C8—3321no—
199C4⋊C8—3321no—
200#101—3322no—
201C22⋊C8—1662no—
202C4×C8—3321no—
203#95—21no—
204#95—21no—
205#95—21no—
206#95—21no—
207#95—21no—
208#95—21no—
209#95—21no—
210#95C2×Dic8311yescharacteristic
211#95C2×Dic8311yescharacteristic
212C2×Q8—41no—
213C2×Q8—41no—
214C2×Q8—42no—
215C2×Q8—41no—
216C2×Q8#1305057712yes—
217C2×Q8#1305058012yes—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4C22⋊Dic8311yescharacteristic
223C22×C4C22⋊Dic8311yescharacteristic
224C22×C4C22⋊Dic8311yescharacteristic
225C22×C4C22⋊Dic8311yescharacteristic
226C22×C4C22×Dic8311yescharacteristic
227C22×C4C2×C22⋊D8311yescharacteristic
228C22×C4C2×C22⋊D8311yescharacteristic
229M16—3322no—
230M16—3322no—
231C2×C8—3322no—
232C2×C8—3322no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—42no—
238C4⋊C4—42no—
239C4⋊C4—42no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C42—21no—
243C42—21no—
244C42—21no—
245C42—21no—
246C42—21no—
247C42—21no—
248C42—42no—
249C23C2×C22⋊Dic8311yescharacteristic
250Q8—42no—
251Q8—42no—
252Q8—42no—
253Q8—42no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4#1458170711yescharacteristic
279C2×C4#1458170711yescharacteristic
280C2×C4#1458171612yes—
281C2×C4#1458171612yes—
282C2×C4C2×#1305057711yescharacteristic
283C2×C4C2×#1305058011yescharacteristic
284C8—6642no—
285C8—6642no—
286C22—21no—
287C22—21no—
288C22C2×#1458170711yescharacteristic
289C22C2×#1458171611yescharacteristic
290C22#1912771811yescharacteristic
291C4—21no—
292C4—21no—
293C4—22no—
294C4—22no—
295C4—21no—
296C4—21no—
297C4—41no—
298C4—42no—
299C4—41no—
300C4—41no—
301C4—81no—
302C4—81no—
303C4—81no—
304C2—21no—
305C2—21no—
306C2#2490603511yescharacteristic
307C2#2490910411yescharacteristic
308C2#2490915211yescharacteristic
subgroupG/H
centerC22C2×#14581707
commutatorC22×C4×C83C22×C4
FrattiniC2×C4⋊C4C22×D83
FittingC83×#2581C2
socleC22×C83C2×#99
prime radicalC23×C83C2×C22⋊C4
cosocleC2×C4⋊C4×C83C23
hypercenter#2581D83
hypocenterC83#11905
LCSG ▷ C22×C4×C83 ▷ C23×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2581

Complements

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

NH ≅ G/Ntype
160. C83#11905semidirect

Maximal subgroups

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

subgroupindex
#249074592
#249057872
#249054932
#249054902
C83×#25812
#1190583