Finite Group Databasebeta

← #35308347

Subgroups — #35308347

Order 21248.

344 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 83 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#24918604C211yesmaximal, characteristic
2#24908452C211yesmaximal, characteristic
3#24906252C211yesmaximal, characteristic
4#24906201C211yesmaximal, characteristic
5#24906147C211yesmaximal, characteristic
6#24905353C211yesmaximal, characteristic
7C83×#1485C211yesmaximal, characteristic
8C2×#14581792C2211yescharacteristic
9#19128097—21no—
10#19128051—21no—
11#19128029—22no—
12#19127986—21no—
13#19127986—21no—
14#19127754C2211yescharacteristic
15#19127725C2211yescharacteristic
16#19127725C2211yescharacteristic
17#19127469—22no—
18#19127454—21no—
19#19127452—21no—
20#19127448—22no—
21#19127447—21no—
22#19127447—21no—
23#533×C83C2211yescharacteristic
24#431×C83C2211yescharacteristic
25C4×M16×C83C2211yescharacteristic
26Q8⋊C8×C83—22no—
27C22×Dic166—21no—
28C2×#13050574—21no—
29C2×#13050574—21no—
30#14581792—21no—
31#14581792—21no—
32#14581792—21no—
33#14581792—21no—
34C2×C4⋊Dic83—21no—
35C2×C4⋊Dic83D412yes—
36#14581723—22no—
37#14581723—22no—
38C4⋊(C83⋊C8)—21no—
39C4⋊(C83⋊C8)—21no—
40C4⋊(C83⋊C8)—21no—
41C4⋊(C83⋊C8)—21no—
42C4⋊(C83⋊C8)D411yescharacteristic
43C4⋊(C83⋊C8)D411yescharacteristic
44#14581716—22no—
45#14581716—22no—
46C22⋊(C83⋊C8)—21no—
47C4×C83⋊C8—21no—
48C2×M16×C83—21no—
49C4⋊Q8×C83D411yescharacteristic
50C4⋊Q8×C83D411yescharacteristic
51#125×C83—21no—
52C22⋊Q8×C83—21no—
53C22⋊Q8×C83—21no—
54C4×Q8×C83—21no—
55C4×Q8×C83—21no—
56#117×C83—21no—
57C2×C42×C83C2311yescharacteristic
58C4⋊C8×C83D412yes—
59C22⋊C8×C83—21no—
60#97×C83—21no—
61C4×C8×C83—21no—
62C4×C8×C83—21no—
63C2×Dic166—41no—
64C2×Dic166—41no—
65C2×Dic166—82no—
66C22×Dic83—22no—
67#13050574—42no—
68#13050574—81no—
69C2×C83⋊C8—21no—
70C2×C83⋊C8—21no—
71C2×C83⋊C8—41no—
72C2×C83⋊C8—41no—
73C4⋊Dic83—22no—
74C4⋊Dic83—22no—
75C4⋊Dic83—41no—
76C4⋊Dic83—41no—
77C2×Q8×C83—21no—
78C2×Q8×C83—21no—
79C22×C4×C83C2×D411yescharacteristic
80C22×C4×C83#4111yescharacteristic
81C22×C4×C83#4111yescharacteristic
82M16×C83—22no—
83M16×C83—41no—
84C2×C8×C83—22no—
85C2×C8×C83—41no—
86C4⋊C4×C83—21no—
87C4⋊C4×C83—21no—
88C4⋊C4×C83—21no—
89C4⋊C4×C83—21no—
90C4⋊C4×C83—41no—
91C4⋊C4×C83—41no—
92C22⋊C4×C83—41no—
93C42×C83—41no—
94C42×C83C2×D411yescharacteristic
95C42×C83C2×D411yescharacteristic
96C42×C83C2×D411yescharacteristic
97C42×C83#4111yescharacteristic
98C23×C83#12311yescharacteristic
99Q8×C83—41no—
100Q8×C83—41no—
101Q8×C83—41no—
102Q8×C83—41no—
103C2×C4×C83—21no—
104C2×C4×C83—21no—
105C2×C4×C83—21no—
106C2×C4×C83—22no—
107C2×C4×C83—21no—
108C2×C4×C83—41no—
109C2×C4×C83—41no—
110C2×C4×C83#12011yescharacteristic
111C2×C4×C83#12111yescharacteristic
112C2×C4×C83#12111yescharacteristic
113C2×C4×C83#12111yescharacteristic
114C2×C4×C83#12311yescharacteristic
115C2×C4×C83#12411yescharacteristic
116C2×Dic83—42no—
117C2×Dic83—82no—
118Dic166—82no—
119Dic166—82no—
120C8×C83—42no—
121C8×C83—42no—
122C83⋊C8—41no—
123C83⋊C8—41no—
124C83⋊C8—81no—
125C83⋊C8—81no—
126C22×C83—21no—
127C22×C83—21no—
128C22×C83—21no—
129C22×C83#39411yescharacteristic
130C4×C83—21no—
131C4×C83—21no—
132C4×C83—21no—
133C4×C83—81no—
134C4×C83—81no—
135C4×C83#45411yescharacteristic
136C4×C83#45611yescharacteristic
137C4×C83#47111yescharacteristic
138C4×C83#47112yes—
139C4×C83#47311yescharacteristic
140Dic83—82no—
141#10494—831nomaximal, Sylow
142C2×C83—41no—
143C2×C83#203811yescharacteristic
144C2×C83#204611yescharacteristic
145C2×C83#205211yescharacteristic
146#3229—831no—
147#1997—831no—
148#1574—831no—
149#1561—831no—
150#1549—831no—
151#1485D8311yescharacteristic
152#1299—831no—
153C83#1049411yescharacteristic, complemented, Sylow
154#533C2×D8311yescharacteristic
155C2×C4⋊Q8—831no—
156#498—1661no—
157#487—1661no—
158#483—1662no—
159#475—1661no—
160#475—1661no—
161#431—831no—
162#431C2×D8311yescharacteristic
163#423—831no—
164#423—831no—
165C4×M16C2×D8311yescharacteristic
166#343—1662no—
167#335—1661no—
168#334—1661no—
169#332—1661no—
170#332—1661no—
171#332—1662no—
172Q8⋊C8—22no—
173C22×Q8—1661no—
174C2×M16—21no—
175C2×M16—1661no—
176C2×M16—1661no—
177C4⋊Q8—1661no—
178C4⋊Q8—1661no—
179C4⋊Q8—1661no—
180C4⋊Q8—1661no—
181C4⋊Q8D33211yescharacteristic
182C4⋊Q8D33211yescharacteristic
183#125—21no—
184C22⋊Q8—21no—
185C22⋊Q8—21no—
186C4×Q8—21no—
187C4×Q8—21no—
188#117—21no—
189C2×C4⋊C4—832no—
190C2×C4⋊C4—1661no—
191C2×C42C22×D8311yescharacteristic
192#106—1662no—
193#106—1662no—
194C4⋊C8—831no—
195C4⋊C8—831no—
196C4⋊C8—1661no—
197C4⋊C8—1661no—
198C4⋊C8—1661no—
199C4⋊C8—1661no—
200C4⋊C8C22⋊D8312yes—
201#103—1662no—
202#103—1662no—
203C22⋊C8—21no—
204C22⋊C8—1661no—
205#97—21no—
206C4×C8—21no—
207C4×C8—21no—
208C4×C8—1661no—
209C2×Q8—21no—
210C2×Q8—21no—
211C2×Q8—3321no—
212C2×Q8—3321no—
213C2×Q8—6642no—
214C22×C4—1662no—
215C22×C4D4×D8311yescharacteristic
216C22×C4#1305058911yescharacteristic
217C22×C4#1305059011yescharacteristic
218M16—22no—
219M16—41no—
220M16—3322no—
221M16—6641no—
222C2×C8—22no—
223C2×C8—41no—
224C2×C8—3321no—
225C2×C8—3321no—
226C2×C8—1661no—
227C2×C8—1661no—
228C4⋊C4—21no—
229C4⋊C4—21no—
230C4⋊C4—21no—
231C4⋊C4—21no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—3321no—
235C4⋊C4—3321no—
236C4⋊C4—1662no—
237C4⋊C4—1662no—
238C22⋊C4—41no—
239C42—41no—
240C42D4×D8311yescharacteristic
241C42C2×C22⋊D8311yescharacteristic
242C42C2×D33211yescharacteristic
243C42#1305058911yescharacteristic
244C23#1458177411yescharacteristic
245Q8—41no—
246Q8—41no—
247Q8—41no—
248Q8—41no—
249Q8—6642no—
250Q8—6642no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—3322no—
259C2×C4—6642no—
260C2×C4#1458176211yescharacteristic
261C2×C4#1458176311yescharacteristic
262C2×C4#1458176411yescharacteristic
263C2×C4#1458176611yescharacteristic
264C2×C4#1458177611yescharacteristic
265C2×C4#1458177811yescharacteristic
266C8—42no—
267C8—42no—
268C8—3321no—
269C8—3321no—
270C8—6641no—
271C8—6641no—
272C22—21no—
273C22—21no—
274C22—21no—
275C22#1912761711yescharacteristic
276C4—21no—
277C4—21no—
278C4—21no—
279C4—81no—
280C4—81no—
281C4—6642no—
282C4#1912787511yescharacteristic
283C4#1912788511yescharacteristic
284C4#1912796411yescharacteristic
285C4#1912796612yes—
286C4#1912797611yescharacteristic
287C2—41no—
288C2#2490867911yescharacteristic
289C2#2490872311yescharacteristic
290C2#2490876111yescharacteristic
subgroupG/H
centerC22#19127617
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1485C2
socleC22×C83#394
prime radicalC23×C83#123
hypercenter#1485D83
hypocenterC83#10494
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1485

Complements

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

NH ≅ G/Ntype
153. C83#10494semidirect

Maximal subgroups

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

subgroupindex
#249186042
#249084522
#249062522
#249062012
#249061472
#249053532
C83×#14852
#1049483