Finite Group Databasebeta

← #35315895

Subgroups — #35315895

Order 21248.

306 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 85 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#24918050C211yesmaximal, characteristic
2C4⋊C16×D83C211yesmaximal, characteristic
3#24906225C211yesmaximal, characteristic
4#24905518C211yesmaximal, characteristic, complemented
5#24905513C211yesmaximal, characteristic, complemented
6#24905511C211yesmaximal, characteristic, complemented
7C83×#1364C211yesmaximal, characteristic, complemented
8#19128256—21no—
9C2×C16×D83—21no—
10#19128081C2211yescharacteristic
11#19128053—21no—
12#19127943—21no—
13#19127943C412yes—
14#19127795—21no—
15#19127795C412yes—
16#19127757—21no—
17C4×C8×D83C2211yescharacteristic
18C4⋊(C83⋊C16)C2211yescharacteristic
19Dic83⋊C16—21no—
20#19127454C2211yescharacteristic
21#19127451—21no—
22#500×C83C2211yescharacteristic
23C4⋊C16×C83C2211yescharacteristic
24#335×C83C2211yescharacteristic
25C2×Dic332—21no—
26C2×Dic332C2×C412yes—
27C2×C8×D83C2×C411yescharacteristic
28C2×C8×D83D411yescharacteristic
29#14581792—21no—
30#14581783—41no—
31#14581772—22no—
32#14581768—41no—
33Q8×Dic83—41no—
34#14581757—22no—
35#14581750—41no—
36C42×D83D411yescharacteristic
37C2×C83⋊C16—21no—
38C16×D83—42no—
39C4⋊(C83⋊C8)—21no—
40#14581715—22no—
41#14581715—22no—
42(C2×D83)⋊C8—41no—
43#14581702—41no—
44C4×C83⋊C8D411yescharacteristic
45C8×Dic83C2×C411yescharacteristic
46C8×Dic83D411yescharacteristic
47C4⋊Q8×C83—21no—
48C2×C16×C83—21no—
49#107×C83—21no—
50#107×C83C2×C412yes—
51C4⋊C8×C83—21no—
52C4×C8×C83C2311yescharacteristic
53C2×Dic166—22no—
54C2×C4×D83C22⋊C411yescharacteristic
55C2×C4×D83D811yescharacteristic
56C2×C4×D83SD1611yescharacteristic
57Dic332—42no—
58Dic332—41no—
59Dic332—41no—
60C2×C83⋊C8—41no—
61C2×C83⋊C8C22⋊C411yescharacteristic
62C2×C83⋊C8C22⋊C411yescharacteristic
63C8×D83—21no—
64C8×D83—21no—
65C8×D83—41no—
66C4⋊Dic83—41no—
67C4⋊Dic83—41no—
68C4⋊Dic83—42no—
69Dic83⋊C4—42no—
70(C2×D83)⋊C4—42no—
71C4×Dic83—42no—
72C4×Dic83C22⋊C411yescharacteristic
73C4×Dic83D811yescharacteristic
74C4×Dic83SD1611yescharacteristic
75C83⋊C16—41no—
76C2×Q8×C83—41no—
77C2×C8×C83—41no—
78C2×C8×C83C22×C411yescharacteristic
79C2×C8×C83C2×D411yescharacteristic
80C4⋊C4×C83—22no—
81C4⋊C4×C83—41no—
82C42×C83C2×D411yescharacteristic
83C16×C83—41no—
84C22×D83#10211yescharacteristic
85Q8×C83—81no—
86Q8×C83—81no—
87C2×C4×C83—42no—
88C2×C4×C83C2×C22⋊C411yescharacteristic
89C2×C4×C83C2×D811yescharacteristic
90C2×C4×C83C2×SD1611yescharacteristic
91C2×Dic83—42no—
92C2×Dic83#10211yescharacteristic
93C2×Dic83#10211yescharacteristic
94C2×Dic83#10211yescharacteristic
95C4×D83—22no—
96C4×D83—21no—
97C4×D83—21no—
98C4×D83—21no—
99C4×D83—21no—
100Dic166—42no—
101Dic166—42no—
102C8×C83—21no—
103C8×C83—81no—
104C8×C83AGL(1,ℤ/8)11yescharacteristic
105C8×C83#13711yescharacteristic
106C83⋊C8—21no—
107C83⋊C8—21no—
108C83⋊C8—81no—
109C22×C83C2×#10211yescharacteristic
110C2×D83—21no—
111C2×D83—21no—
112C2×D83#36212yes—
113C4×C83—21no—
114C4×C83—82no—
115C4×C83#41311yescharacteristic
116C4×C83#41711yescharacteristic
117C4×C83#50811yescharacteristic
118C4×C83#50811yescharacteristic
119Dic83—21no—
120Dic83—21no—
121Dic83—21no—
122Dic83—82no—
123#11984—831nomaximal, Sylow
124C2×C83#154711yescharacteristic
125C2×C83#213811yescharacteristic
126C2×C83C2×#36211yescharacteristic
127D83—22no—
128#3170—831no—
129C2×C4⋊C16—831no—
130#1568—831no—
131#1364—831no—
132#1364D8311yescharacteristic, complemented
133#1362—831no—
134#1362—831no—
135C83#1198411yescharacteristic, complemented, Sylow
136#533—1661no—
137C22×C16—1661no—
138#500C2×D8311yescharacteristic
139#494—831no—
140#487—1661no—
141#467—832no—
142#467—1661no—
143C4×Q16—832no—
144C4×Q16—1661no—
145#432—1661no—
146C2×C4×C8—831no—
147C4⋊C16—831no—
148C4⋊C16—1661no—
149C4⋊C16C2×D8311yescharacteristic
150#335—831no—
151#335C2×D8311yescharacteristic
152#334—1661no—
153C2×Q16—832no—
154C2×Q16—1661no—
155C22×C8—831no—
156C22×C8—831no—
157C4⋊Q8—21no—
158C4⋊Q8—1661no—
159#125—3321no—
160C22⋊Q8—3321no—
161C22⋊Q8—1662no—
162C4×Q8—3321no—
163C4×Q8—1662no—
164#117—3321no—
165C2×C42—831no—
166C2×C16—21no—
167C2×C16—3322no—
168C2×C16—1661no—
169#107—21no—
170#107C4×D8312yes—
171C4⋊C8—21no—
172C4⋊C8—1661no—
173#103—1662no—
174#103—1662no—
175C22⋊C8—3321no—
176#97—3321no—
177C4×C8—831no—
178C4×C8—831no—
179C4×C8—831no—
180C4×C8C22×D8311yescharacteristic
181C2×Q8—41no—
182C2×Q8—1662no—
183C22×C4—831no—
184C22×C4—831no—
185C22×C4—831no—
186Q16—3322no—
187Q16—3321no—
188Q16—3321no—
189C2×C8—41no—
190C2×C8—3321no—
191C2×C8—3321no—
192C2×C8—831no—
193C2×C8—831no—
194C2×C8—1661no—
195C2×C8—1661no—
196C2×C8C2×C4×D8311yescharacteristic
197C2×C8D4×D8311yescharacteristic
198C4⋊C4—22no—
199C4⋊C4—41no—
200C4⋊C4—3322no—
201C4⋊C4—3322no—
202C4⋊C4—3321no—
203C4⋊C4—3321no—
204C22⋊C4—3322no—
205C42—3322no—
206C42—831no—
207C42—831no—
208C42—831no—
209C42D4×D8311yescharacteristic
210C16—41no—
211C16—3321no—
212C23—831no—
213Q8—81no—
214Q8—81no—
215Q8—3322no—
216Q8—3322no—
217C2×C4—42no—
218C2×C4—3322no—
219C2×C4—831no—
220C2×C4—831no—
221C2×C4—831no—
222C2×C4—1662no—
223C2×C4—1661no—
224C2×C4—1661no—
225C2×C4—1661no—
226C2×C4—1661no—
227C2×C4C22⋊C4×D8311yescharacteristic
228C2×C4D8×D8311yescharacteristic
229C2×C4SD16×D8311yescharacteristic
230C8—21no—
231C8—81no—
232C8—6641no—
233C8—1661no—
234C8—1661no—
235C8#1458181911yescharacteristic
236C8#1458182411yescharacteristic
237C22—832no—
238C22—1661no—
239C22—1661no—
240C22#102×D8311yescharacteristic
241C4—21no—
242C4—82no—
243C4—6642no—
244C4—1661no—
245C4—1661no—
246C4—1661no—
247C4#1912768411yescharacteristic
248C4#1912770111yescharacteristic
249C4#1912813011yescharacteristic
250C4#1912813211yescharacteristic
251C2—1662no—
252C2#2490613911yescharacteristic
253C2#2490916711yescharacteristic
254C2#362×D8311yescharacteristic
subgroupG/H
centerC22#102×D83
commutatorC2×C8×C83C22×C4
FrattiniC4×C8C22×D83
FittingC83×#1364C2
socleC22×C83C2×#102
prime radicalC22×D83#102
cosocleC4×C8×C83C23
hypercenter#1364D83
hypocenterC83#11984
LCSG ▷ C2×C8×C83 ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1364

Complements

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

NH ≅ G/Ntype
4. #24905518C2semidirect
5. #24905513C2semidirect
6. #24905511C2semidirect
7. C83×#1364C2semidirect
132. #1364D83semidirect
135. C83#11984semidirect

Maximal subgroups

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

subgroupindex
#249180502
C4⋊C16×D832
#249062252
#249055182
#249055132
#249055112
C83×#13642
#1198483