Finite Group Databasebeta

← #35324769

Subgroups — #35324769

Order 21248.

318 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 71 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#24917863C211yesmaximal, characteristic
2#24909148C211yesmaximal, characteristic
3#24905635C214yesmaximal, complemented
4C83×#2132C211yesmaximal, characteristic
5C2×#14581784C411yescharacteristic
6#19128069C2212yes—
7#19128065C412yes—
8#19128055—21no—
9#19128055—21no—
10#19127702—21no—
11#19127702—21no—
12#19127685—21no—
13C4×#13050574C411yescharacteristic
14#19127500C2212yes—
15#19127498—21no—
16#532×C83C2211yescharacteristic
17#413×C83—21no—
18#356×C83C2212yes—
19#355×C83—21no—
20C2×#13050574—21no—
21C2×#13050574—41no—
22#14581784—21no—
23#14581784—41no—
24#14581784C2×C412yes—
25C2×C4⋊Dic83—21no—
26C2×Dic83⋊C4—41no—
27#14581716—22no—
28#14581716—22no—
29#14581713—22no—
30#14581713—22no—
31#14581711—22no—
32#14581709—41no—
33#14581703C2×C412yes—
34C4×C83⋊C8—21no—
35C2×#41×C83D411yescharacteristic
36C2×#41×C83D411yescharacteristic
37C2×M16×C83—41no—
38C4⋊Q8×C83C2311yescharacteristic
39#127×C83C2×C411yescharacteristic
40#124×C83D411yescharacteristic
41#124×C83D411yescharacteristic
42#121×C83—41no—
43C4×D4×C83—41no—
44C2×C42×C83C2×C411yescharacteristic
45#101×C83—22no—
46#100×C83—41no—
47C22×Dic83—41no—
48#13050574—41no—
49#13050574—41no—
50#13050574—42no—
51#13050574—81no—
52C2×C83⋊C8—22no—
53C2×C83⋊C8—81no—
54C4⋊Dic83—22no—
55C4⋊Dic83—41no—
56Dic83⋊C4—42no—
57Dic83⋊C4—42no—
58#41×C83—41no—
59#41×C83—41no—
60#41×C83—41no—
61#41×C83—41no—
62C2×Q8×C83C2×D411yescharacteristic
63C2×Q8×C83C2×D411yescharacteristic
64C2×D4×C83—21no—
65C2×D4×C83—21no—
66C2×D4×C83—41no—
67C2×D4×C83C22⋊C411yescharacteristic
68C2×D4×C83C22⋊C411yescharacteristic
69C22×C4×C83—21no—
70C22×C4×C83—21no—
71C22×C4×C83—21no—
72C22×C4×C83C22⋊C411yescharacteristic
73M16×C83—42no—
74M16×C83—81no—
75C2×C8×C83—81no—
76C4⋊C4×C83—41no—
77C22⋊C4×C83—41no—
78C22⋊C4×C83—41no—
79C42×C83—21no—
80C42×C83C22⋊C411yescharacteristic
81C42×C83C22×C411yescharacteristic
82C23×C83—21no—
83C23×C83—21no—
84C23×C83#9911yescharacteristic
85Q8×C83—41no—
86Q8×C83—41no—
87D4×C83—41no—
88D4×C83—41no—
89D4×C83—81no—
90D4×C83—81no—
91D4×C83—82no—
92C2×C4×C83—21no—
93C2×C4×C83—21no—
94C2×C4×C83—21no—
95C2×C4×C83—21no—
96C2×C4×C83—21no—
97C2×C4×C83—21no—
98C2×C4×C83—41no—
99C2×C4×C83—41no—
100C2×C4×C83—41no—
101C2×C4×C83—41no—
102C2×C4×C83—81no—
103C2×C4×C83#9911yescharacteristic
104C2×C4×C83C2×C22⋊C411yescharacteristic
105C2×Dic83—42no—
106C2×Dic83—82no—
107C8×C83—82no—
108C83⋊C8—42no—
109C83⋊C8—82no—
110C22×C83—21no—
111C22×C83—41no—
112C22×C83—41no—
113C22×C83—41no—
114C22×C83—81no—
115C22×C83—81no—
116C22×C83C2×#9911yescharacteristic
117C4×C83—21no—
118C4×C83—41no—
119C4×C83—41no—
120C4×C83—41no—
121C4×C83—41no—
122C4×C83#35411yescharacteristic
123C4×C83#35411yescharacteristic
124Dic83—82no—
125#13600—831nomaximal, Sylow
126C2×C83—21no—
127C2×C83—41no—
128C2×C83—81no—
129C2×C83—81no—
130C2×C83C2×#35411yescharacteristic
131#3142—831no—
132#2132—831no—
133#2132D8311yescharacteristic
134#1413—834no—
135C83#1360011yescharacteristic, complemented, Sylow
136#532C2×D8311yescharacteristic
137C2×#125—831no—
138#491—832no—
139#490—832no—
140#488—1661no—
141#488—1661no—
142#417—1661no—
143#417—1661no—
144#413—21no—
145#413—1661no—
146C4×M16—831no—
147#356—832no—
148#356C2×D8312yes—
149#355—21no—
150#355—1661no—
151C2×#41D33211yescharacteristic
152C2×#41C22⋊D8311yescharacteristic
153C2×M16—41no—
154C2×M16—3321no—
155C2×M16—1661no—
156C4⋊Q8C22×D8311yescharacteristic
157#127C4×D8311yescharacteristic
158#125—3321no—
159#125—832no—
160#125—1661no—
161#124D33211yescharacteristic
162#124C22⋊D8311yescharacteristic
163#121—41no—
164C4×D4—41no—
165C2×C4⋊C4—3321no—
166C2×C4⋊C4—1661no—
167C2×C42C4×D8311yescharacteristic
168#103—1662no—
169#103—1662no—
170#102—1662no—
171#102—1662no—
172#101—22no—
173#101—1662no—
174#100—41no—
175#100—3321no—
176#97—832no—
177C4×C8—1661no—
178#41—41no—
179#41—41no—
180#41—41no—
181#41—41no—
182C2×Q8C2×C22⋊D8311yescharacteristic
183C2×Q8C2×D33211yescharacteristic
184C2×D4—21no—
185C2×D4—21no—
186C2×D4—41no—
187C2×D4(C2×D83)⋊C411yescharacteristic
188C2×D4(C2×D83)⋊C411yescharacteristic
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—3321no—
193C22×C4(C2×D83)⋊C411yescharacteristic
194M16—42no—
195M16—81no—
196M16—3321no—
197M16—3321no—
198M16—3322no—
199M16—6641no—
200C2×C8—81no—
201C2×C8—6641no—
202C2×C8—1662no—
203C4⋊C4—41no—
204C4⋊C4—3322no—
205C4⋊C4—3322no—
206C4⋊C4—3321no—
207C4⋊C4—1662no—
208C22⋊C4—41no—
209C22⋊C4—41no—
210C42—21no—
211C42(C2×D83)⋊C411yescharacteristic
212C42C2×C4×D8311yescharacteristic
213C23—21no—
214C23—21no—
215C23#1458170611yescharacteristic
216Q8—41no—
217Q8—41no—
218D4—41no—
219D4—41no—
220D4—81no—
221D4—81no—
222D4—82no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—81no—
234C2×C4—3322no—
235C2×C4—6642no—
236C2×C4#1458170611yescharacteristic
237C2×C4C2×(C2×D83)⋊C411yescharacteristic
238C8—82no—
239C8—3322no—
240C8—6642no—
241C22—21no—
242C22—41no—
243C22—41no—
244C22—41no—
245C22—81no—
246C22—81no—
247C22C2×#1458170611yescharacteristic
248C4—21no—
249C4—41no—
250C4—41no—
251C4—41no—
252C4—41no—
253C4—6642no—
254C4#1912749511yescharacteristic
255C4#1912749511yescharacteristic
256C2—21no—
257C2—41no—
258C2—81no—
259C2—81no—
260C2C2×#1912749511yescharacteristic
subgroupG/H
centerC2C2×#19127495
commutatorC42×C83C22×C4
FrattiniC4⋊Q8C22×D83
FittingC83×#2132C2
socleC2×C83C2×#354
prime radical#532×C83C22
cosocleC4⋊Q8×C83C23
hypercenter#2132D83
hypocenterC83#13600
LCSG ▷ C42×C83 ▷ C2×C4×C83 ▷ C22×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ #532 ◁ #2132

Complements

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

NH ≅ G/Ntype
3. #24905635C2semidirect
135. C83#13600semidirect

Maximal subgroups

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

subgroupindex
#249178632
#249091482
#249056352
C83×#21322
#1360083