Finite Group Databasebeta

← #35324763

Subgroups — #35324763

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#24917808C211yesmaximal, characteristic
2#24909148C211yesmaximal, characteristic
3#24905635C214yesmaximal, complemented
4C83×#2132C211yesmaximal, characteristic
5#19128258C411yescharacteristic
6#19128069C2212yes—
7#19128065C412yes—
8#19128060—21no—
9#19128060—21no—
10#19127697—21no—
11#19127697—21no—
12#19127685—21no—
13C2×#14581703C411yescharacteristic
14#19127500C2212yes—
15#19127498—21no—
16#532×C83C2211yescharacteristic
17#413×C83—21no—
18#356×C83C2212yes—
19#355×C83—21no—
20C2×#13050574—41no—
21C22×C83⋊C8—21no—
22#14581792—21no—
23#14581784C2×C412yes—
24#14581771—41no—
25C4×Dic166—41no—
26#14581751—21no—
27#14581716—22no—
28#14581716—22no—
29#14581713—22no—
30#14581713—22no—
31#14581711—22no—
32#14581709—41no—
33#14581703—21no—
34#14581703C2×C412yes—
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—
47C2×Dic166—41no—
48#13050574—42no—
49#13050574—81no—
50C2×C83⋊C8—22no—
51C2×C83⋊C8—41no—
52C2×C83⋊C8—41no—
53C2×C83⋊C8—81no—
54C4⋊Dic83—22no—
55C4⋊Dic83—41no—
56Dic83⋊C4—42no—
57C22⋊Dic83—41no—
58C4×Dic83—41no—
59#41×C83—41no—
60#41×C83—41no—
61#41×C83—41no—
62#41×C83—41no—
63C2×Q8×C83C2×D411yescharacteristic
64C2×Q8×C83C2×D411yescharacteristic
65C2×D4×C83—21no—
66C2×D4×C83—21no—
67C2×D4×C83—41no—
68C2×D4×C83C22⋊C411yescharacteristic
69C2×D4×C83C22⋊C411yescharacteristic
70C22×C4×C83—21no—
71C22×C4×C83—21no—
72C22×C4×C83—21no—
73C22×C4×C83C22⋊C411yescharacteristic
74M16×C83—42no—
75M16×C83—81no—
76C2×C8×C83—81no—
77C4⋊C4×C83—41no—
78C22⋊C4×C83—41no—
79C22⋊C4×C83—41no—
80C42×C83—21no—
81C42×C83C22⋊C411yescharacteristic
82C42×C83C22×C411yescharacteristic
83C23×C83—21no—
84C23×C83—21no—
85C23×C83#9911yescharacteristic
86Q8×C83—41no—
87Q8×C83—41no—
88D4×C83—41no—
89D4×C83—41no—
90D4×C83—81no—
91D4×C83—81no—
92D4×C83—82no—
93C2×C4×C83—21no—
94C2×C4×C83—21no—
95C2×C4×C83—21no—
96C2×C4×C83—21no—
97C2×C4×C83—21no—
98C2×C4×C83—21no—
99C2×C4×C83—41no—
100C2×C4×C83—41no—
101C2×C4×C83—41no—
102C2×C4×C83—41no—
103C2×C4×C83—81no—
104C2×C4×C83#9911yescharacteristic
105C2×C4×C83C2×C22⋊C411yescharacteristic
106C2×Dic83—42no—
107Dic166—82no—
108C8×C83—82no—
109C83⋊C8—42no—
110C83⋊C8—82no—
111C22×C83—21no—
112C22×C83—41no—
113C22×C83—41no—
114C22×C83—41no—
115C22×C83—81no—
116C22×C83—81no—
117C22×C83C2×#9911yescharacteristic
118C4×C83—21no—
119C4×C83—41no—
120C4×C83—41no—
121C4×C83—41no—
122C4×C83—41no—
123C4×C83#35411yescharacteristic
124C4×C83#35411yescharacteristic
125Dic83—82no—
126#13598—831nomaximal, Sylow
127C2×C83—21no—
128C2×C83—41no—
129C2×C83—81no—
130C2×C83—81no—
131C2×C83C2×#35411yescharacteristic
132#3135—831no—
133#2132—831no—
134#2132D8311yescharacteristic
135#1413—834no—
136C83#1359811yescharacteristic, complemented, Sylow
137#533—831no—
138#532C2×D8311yescharacteristic
139#491—832no—
140#490—832no—
141#489—1661no—
142#489—1661no—
143#416—1661no—
144#416—1661no—
145#413—21no—
146#413—1661no—
147C2×#97—831no—
148#356—832no—
149#356C2×D8312yes—
150#355—21no—
151#355—1661no—
152C2×#41D33211yescharacteristic
153C2×#41C22⋊D8311yescharacteristic
154C2×M16—41no—
155C2×M16—3321no—
156C22×C8—1661no—
157C4⋊Q8—1661no—
158C4⋊Q8C22×D8311yescharacteristic
159#127C4×D8311yescharacteristic
160#125—832no—
161#124D33211yescharacteristic
162#124C22⋊D8311yescharacteristic
163C22⋊Q8—3321no—
164#121—41no—
165C4×Q8—3321no—
166C4×D4—41no—
167#117—1661no—
168C2×C42C4×D8311yescharacteristic
169#103—1662no—
170#103—1662no—
171#102—1662no—
172#102—1662no—
173#101—22no—
174#101—1662no—
175#100—41no—
176#100—3321no—
177#97—832no—
178#97—1661no—
179#41—41no—
180#41—41no—
181#41—41no—
182#41—41no—
183C2×Q8—3321no—
184C2×Q8C2×C22⋊D8311yescharacteristic
185C2×Q8C2×D33211yescharacteristic
186C2×D4—21no—
187C2×D4—21no—
188C2×D4—41no—
189C2×D4(C2×D83)⋊C411yescharacteristic
190C2×D4(C2×D83)⋊C411yescharacteristic
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4(C2×D83)⋊C411yescharacteristic
195M16—42no—
196M16—81no—
197M16—3322no—
198M16—6641no—
199C2×C8—81no—
200C2×C8—3321no—
201C2×C8—3321no—
202C2×C8—6641no—
203C2×C8—1662no—
204C4⋊C4—41no—
205C4⋊C4—3322no—
206C4⋊C4—3321no—
207C4⋊C4—1662no—
208C22⋊C4—41no—
209C22⋊C4—41no—
210C22⋊C4—3321no—
211C42—21no—
212C42—3321no—
213C42(C2×D83)⋊C411yescharacteristic
214C42C2×C4×D8311yescharacteristic
215C23—21no—
216C23—21no—
217C23#1458170611yescharacteristic
218Q8—41no—
219Q8—41no—
220Q8—6642no—
221D4—41no—
222D4—41no—
223D4—81no—
224D4—81no—
225D4—82no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—81no—
237C2×C4—3322no—
238C2×C4#1458170611yescharacteristic
239C2×C4C2×(C2×D83)⋊C411yescharacteristic
240C8—82no—
241C8—3322no—
242C8—6642no—
243C22—21no—
244C22—41no—
245C22—41no—
246C22—41no—
247C22—81no—
248C22—81no—
249C22C2×#1458170611yescharacteristic
250C4—21no—
251C4—41no—
252C4—41no—
253C4—41no—
254C4—41no—
255C4—6642no—
256C4#1912749511yescharacteristic
257C4#1912749511yescharacteristic
258C2—21no—
259C2—41no—
260C2—81no—
261C2—81no—
262C2C2×#1912749511yescharacteristic
subgroupG/H
centerC4#19127495
commutatorC42×C83C22×C4
FrattiniC4⋊Q8C22×D83
FittingC83×#2132C2
socleC2×C83C2×#354
prime radical#532×C83C22
cosocleC4⋊Q8×C83C23
hypercenter#2132D83
hypocenterC83#13598
LCSG ▷ C42×C83 ▷ C2×C4×C83 ▷ C22×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ #532 ◁ #2132

Complements

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

NH ≅ G/Ntype
3. #24905635C2semidirect
136. C83#13598semidirect

Maximal subgroups

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

subgroupindex
#249178082
#249091482
#249056352
C83×#21322
#1359883