Finite Group Databasebeta

← #35301799

Subgroups — #35301799

Order 21248.

514 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 119 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#24912636C211yesmaximal, characteristic
2#24907455C211yesmaximal, characteristic
3#24906143C212yesmaximal, complemented
4#24905365C212yesmaximal, complemented
5C83×#2975C211yesmaximal, characteristic
6C2×#14581792C2211yescharacteristic
7#19127725C2212yes—
8C2×#14581709—21no—
9#19127613C414yes—
10#19127604—21no—
11#19127566—21no—
12#19127561—22no—
13C4×C4⋊Dic83C2211yescharacteristic
14#19127470—21no—
15#19127449—24no—
16C2×C4×D4×C83C2211yescharacteristic
17#436×C83—24no—
18#431×C83C2212yes—
19#407×C83—22no—
20C22×Dic166C2×C412yes—
21C2×#13050574—22no—
22#14581792—22no—
23#14581792—22no—
24C2×C4⋊Dic83—21no—
25C2×C4⋊Dic83—21no—
26C2×C4⋊Dic83—21no—
27C2×C22⋊Dic83—24no—
28C2×C4×Dic83—21no—
29C4⋊(C83⋊C8)—22no—
30C4⋊(C83⋊C8)—22no—
31#14581709—42no—
32C83⋊#95—24no—
33C83⋊#95C2×C412yes—
34C22×D4×C83D411yescharacteristic
35C23×C4×C83D412yes—
36C2×M16×C83—24no—
37C4×D4×C83—22no—
38C4×D4×C83—22no—
39C2×C4⋊C4×C83D411yescharacteristic
40C2×C22⋊C4×C83C2×C412yes—
41C2×C42×C83C2311yescharacteristic
42C4⋊C8×C83D414yes—
43C22⋊C8×C83—24no—
44C22⋊C8×C83—22no—
45C4×C8×C83—22no—
46C2×Dic166—24no—
47C2×Dic166—82no—
48C22×Dic83—22no—
49C22×Dic83—22no—
50#13050574—42no—
51#13050574—42no—
52C2×C83⋊C8—42no—
53C4⋊Dic83—42no—
54C4⋊Dic83—41no—
55C4⋊Dic83—42no—
56C4⋊Dic83—41no—
57C22⋊Dic83—84no—
58C4×Dic83—41no—
59C4×Dic83—41no—
60C24×C83C22⋊C412yes—
61C2×D4×C83—22no—
62C2×D4×C83—21no—
63C2×D4×C83—22no—
64C2×D4×C83—21no—
65C22×C4×C83—22no—
66C22×C4×C83—22no—
67C22×C4×C83—44no—
68C22×C4×C83C22⋊C412yes—
69C22×C4×C83C22×C411yescharacteristic
70C22×C4×C83C2×D411yescharacteristic
71C22×C4×C83C2×D411yescharacteristic
72M16×C83—84no—
73C2×C8×C83—24no—
74C4⋊C4×C83—22no—
75C22⋊C4×C83—24no—
76C42×C83C2×D412yes—
77C42×C83#4112yes—
78C23×C83—22no—
79C23×C83—22no—
80C23×C83—22no—
81C23×C83—42no—
82C23×C83—42no—
83C23×C83C2×C22⋊C411yescharacteristic
84D4×C83—42no—
85D4×C83—42no—
86C2×C4×C83—22no—
87C2×C4×C83—22no—
88C2×C4×C83—41no—
89C2×C4×C83—44no—
90C2×C4×C83—42no—
91C2×C4×C83—82no—
92C2×C4×C83C4×D412yes—
93C2×C4×C83#12011yescharacteristic
94C2×C4×C83#12112yes—
95C2×C4×C83#12311yescharacteristic
96C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
97C2×C4×C83#13712yes—
98C2×C4×C83#13711yescharacteristic
99C2×Dic83—42no—
100C2×Dic83—44no—
101C2×Dic83—42no—
102C2×Dic83—42no—
103C2×Dic83—42no—
104Dic166—84no—
105C8×C83—44no—
106C83⋊C8—82no—
107C22×C83—21no—
108C22×C83—21no—
109C22×C83—44no—
110C22×C83—42no—
111C22×C83—42no—
112C22×C83—42no—
113C22×C83—82no—
114C22×C83#38611yescharacteristic
115C22×C83#41711yescharacteristic
116C22×C83#41911yescharacteristic
117C4×C83—21no—
118C4×C83—22no—
119C4×C83—42no—
120C4×C83#45512yes—
121C4×C83#46812yes—
122C4×C83#47012yes—
123Dic83—82no—
124Dic83—82no—
125#9399—831nomaximal, Sylow
126C2×C83—21no—
127C2×C83—21no—
128C2×C83—82no—
129C2×C83#188511yescharacteristic
130C2×C83#189411yescharacteristic
131C2×C83#191411yescharacteristic
132#2975D8311yescharacteristic
133#2563—831no—
134#1800—831no—
135#1548—832no—
136#1303—832no—
137C83#939911yescharacteristic, complemented, Sylow
138C2×C4⋊Q8—831no—
139C2×C4×D4C2×D8311yescharacteristic
140#436—24no—
141#431C2×D8312yes—
142#423—832no—
143C2×#100—1661no—
144#407—22no—
145#393—834no—
146#390—1661no—
147#382—1661no—
148#380—1662no—
149C4×C4⋊C4—831no—
150#343—1661no—
151#333—1664no—
152C22×Q8—832no—
153C22×D4D33211yescharacteristic
154C23×C4C22⋊D8312yes—
155C2×M16—24no—
156C2×M16—1662no—
157C4⋊Q8—1662no—
158C4⋊Q8—1662no—
159C4×D4—22no—
160C4×D4—22no—
161C2×C4⋊C4—1661no—
162C2×C4⋊C4—1661no—
163C2×C4⋊C4—1661no—
164C2×C4⋊C4D33211yescharacteristic
165C2×C22⋊C4—1664no—
166C2×C22⋊C4C4×D8312yes—
167C2×C42—1661no—
168C2×C42C22×D8311yescharacteristic
169C4⋊C8—1662no—
170C4⋊C8—1662no—
171C4⋊C8C22⋊D8314yes—
172#100—3322no—
173C22⋊C8—24no—
174C22⋊C8—22no—
175C4×C8—22no—
176#95—832no—
177#95—1664no—
178C24(C2×D83)⋊C412yes—
179C2×Q8—6642no—
180C2×Q8—1664no—
181C2×D4—22no—
182C2×D4—21no—
183C2×D4—22no—
184C2×D4—21no—
185C22×C4—22no—
186C22×C4—22no—
187C22×C4—44no—
188C22×C4—1662no—
189C22×C4—1662no—
190C22×C4(C2×D83)⋊C412yes—
191C22×C4C2×C4×D8311yescharacteristic
192C22×C4C2×C22⋊D8311yescharacteristic
193C22×C4C2×D33211yescharacteristic
194M16—84no—
195M16—3322no—
196M16—3322no—
197C2×C8—24no—
198C2×C8—3322no—
199C4⋊C4—22no—
200C4⋊C4—3322no—
201C4⋊C4—3321no—
202C4⋊C4—3322no—
203C4⋊C4—3321no—
204C22⋊C4—24no—
205C22⋊C4—6644no—
206C42—3321no—
207C42—3321no—
208C42C2×C22⋊D8312yes—
209C42#1305059012yes—
210C23—22no—
211C23—22no—
212C23—22no—
213C23—42no—
214C23—42no—
215C23C2×(C2×D83)⋊C411yescharacteristic
216Q8—6644no—
217D4—42no—
218D4—42no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—41no—
222C2×C4—44no—
223C2×C4—42no—
224C2×C4—82no—
225C2×C4—3322no—
226C2×C4—3324no—
227C2×C4—3322no—
228C2×C4—3322no—
229C2×C4—3322no—
230C2×C4C4×C22⋊D8312yes—
231C2×C4#1458176111yescharacteristic
232C2×C4#1458176612yes—
233C2×C4#1458177511yescharacteristic
234C2×C4#1458182011yescharacteristic
235C2×C4#1458182512yes—
236C2×C4#1458182511yescharacteristic
237C8—44no—
238C8—6642no—
239C22—21no—
240C22—21no—
241C22—44no—
242C22—42no—
243C22—42no—
244C22—42no—
245C22—82no—
246C22#1912758011yescharacteristic
247C22#1912770311yescharacteristic
248C22#1912771111yescharacteristic
249C4—21no—
250C4—22no—
251C4—42no—
252C4—6642no—
253C4—6642no—
254C4#1912787912yes—
255C4#1912794712yes—
256C4#1912795912yes—
257C2—21no—
258C2—21no—
259C2—82no—
260C2#2490785111yescharacteristic
261C2#2490789611yescharacteristic
262C2#2490801011yescharacteristic
subgroupG/H
centerC22#19127580
commutatorC22×C4×C83C22×C4
FrattiniC2×C42C22×D83
FittingC83×#2975C2
socleC22×C83#386
prime radicalC22×D4×C83D4
cosocleC2×C42×C83C23
hypercenter#2975D83
hypocenterC83#9399
LCSG ▷ C22×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2975

Complements

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

NH ≅ G/Ntype
3. #24906143C2semidirect
4. #24905365C2semidirect
137. C83#9399semidirect

Maximal subgroups

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

subgroupindex
#249126362
#249074552
#249061432
#249053652
C83×#29752
#939983