Finite Group Databasebeta

← #35304070

Subgroups — #35304070

Order 21248.

466 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 117 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
1C2×#19128080C211yesmaximal, characteristic
2#24908452C211yesmaximal, characteristic
3#24906218C211yesmaximal, characteristic
4#24906145C211yesmaximal, characteristic
5#24906144C211yesmaximal, characteristic
6#24905750C211yesmaximal, characteristic
7C83×#1997C211yesmaximal, characteristic
8C22×#13050580C414yes—
9C2×#14581792C2211yescharacteristic
10#19128080—21no—
11#19128080—21no—
12#19128080—22no—
13#19127754C2211yescharacteristic
14#19127725C2211yescharacteristic
15C2×C4×C83⋊C8C2211yescharacteristic
16#19127469—22no—
17#19127451—22no—
18#19127450—22no—
19#19127449—22no—
20#19127423—21no—
21#19127423—21no—
22C2×C4⋊Q8×C83C2211yescharacteristic
23#423×C83C2211yescharacteristic
24C4×M16×C83C2211yescharacteristic
25#343×C83—22no—
26C22×Dic166C2×C412yes—
27C2×#13050580—24no—
28C2×#13050580—24no—
29C2×#13050580—48no—
30C2×#13050574—21no—
31C22×C83⋊C8C2×C412yes—
32#14581792—21no—
33#14581792—21no—
34#14581792—21no—
35#14581792—21no—
36C2×C4⋊Dic83—21no—
37C2×C4⋊Dic83—21no—
38C4⋊(C83⋊C8)—21no—
39C4⋊(C83⋊C8)—21no—
40C4⋊(C83⋊C8)D412yes—
41C22⋊(C83⋊C8)—21no—
42C4×C83⋊C8—21no—
43C4×C83⋊C8D411yescharacteristic
44C4×C83⋊C8D411yescharacteristic
45C4×C83⋊C8D412yes—
46C22×Q8×C83C2×C412yes—
47C2×M16×C83—21no—
48C2×M16×C83D412yes—
49C4⋊Q8×C83—21no—
50C4⋊Q8×C83—21no—
51C4⋊Q8×C83—21no—
52C4⋊Q8×C83—21no—
53C2×C4⋊C4×C83—21no—
54C2×C4⋊C4×C83—21no—
55C2×C42×C83C2311yescharacteristic
56C4⋊C8×C83—21no—
57C4⋊C8×C83—21no—
58#97×C83—21no—
59C4×C8×C83—21no—
60C2×Dic166—22no—
61C2×Dic166—22no—
62C2×Dic166—44no—
63C22×Dic83—22no—
64#13050580—48no—
65#13050580—48no—
66#13050574—42no—
67C2×C83⋊C8—24no—
68C2×C83⋊C8—22no—
69C2×C83⋊C8—41no—
70C2×C83⋊C8C22⋊C412yes—
71C2×C83⋊C8C22⋊C412yes—
72C4⋊Dic83—41no—
73C4⋊Dic83—41no—
74C4⋊Dic83—41no—
75C4⋊Dic83—41no—
76C2×Q8×C83—22no—
77C2×Q8×C83—22no—
78C2×Q8×C83—44no—
79C22×C4×C83—22no—
80C22×C4×C83C22×C411yescharacteristic
81C22×C4×C83C2×D411yescharacteristic
82C22×C4×C83#4111yescharacteristic
83M16×C83—22no—
84M16×C83—22no—
85M16×C83—42no—
86C2×C8×C83—22no—
87C2×C8×C83—41no—
88C4⋊C4×C83—41no—
89C4⋊C4×C83—41no—
90C4⋊C4×C83—41no—
91C4⋊C4×C83—41no—
92C42×C83C2×D411yescharacteristic
93C42×C83C2×D411yescharacteristic
94C42×C83C2×D411yescharacteristic
95C42×C83#4111yescharacteristic
96C23×C83C4×D411yescharacteristic
97Q8×C83—44no—
98Q8×C83—82no—
99C2×C4×C83—22no—
100C2×C4×C83—22no—
101C2×C4×C83—42no—
102C2×C4×C83—82no—
103C2×C4×C83C2×C22⋊C411yescharacteristic
104C2×C4×C83C4×D411yescharacteristic
105C2×C4×C83#12111yescharacteristic
106C2×C4×C83#12111yescharacteristic
107C2×C4×C83#12411yescharacteristic
108C2×C4×C83#12711yescharacteristic
109C2×C4×C83#13712yes—
110C2×C4×C83#13712yes—
111C2×Dic83—42no—
112C2×Dic83—82no—
113Dic166—44no—
114Dic166—82no—
115C8×C83—42no—
116C8×C83—81no—
117C83⋊C8—22no—
118C83⋊C8—42no—
119C83⋊C8—81no—
120C83⋊C8#10014yes—
121C22×C83—21no—
122C22×C83—21no—
123C22×C83#39011yescharacteristic
124C22×C83#44112yes—
125C4×C83—21no—
126C4×C83—21no—
127C4×C83—82no—
128C4×C83C2×#10012yes—
129C4×C83#47012yes—
130C4×C83#47312yes—
131C4×C83#49711yescharacteristic
132C4×C83#49711yescharacteristic
133Dic83—82no—
134#9807—831nomaximal, Sylow
135C2×C83—22no—
136C2×C83#196511yescharacteristic
137C2×C83#197111yescharacteristic
138C2×C83#197911yescharacteristic
139C2×#494—831no—
140#1997—831no—
141#1997D8311yescharacteristic
142#1566—831no—
143#1548—831no—
144#1548—831no—
145#1451—831no—
146C83#980711yescharacteristic, complemented, Sylow
147C22×Q16—834no—
148C2×C4⋊Q8—831no—
149C2×C4⋊Q8C2×D8311yescharacteristic
150#494—1661no—
151#494—1661no—
152#494—1662no—
153#431—831no—
154#423—831no—
155#423C2×D8311yescharacteristic
156C4×M16C2×D8311yescharacteristic
157C2×C4×C8—831no—
158#343—22no—
159#343—1662no—
160#334—1662no—
161#333—1662no—
162#333—1662no—
163#322—1661no—
164#322—1661no—
165C22×Q8—832no—
166C22×Q8C4×D8312yes—
167C2×Q16—3328no—
168C2×Q16—1664no—
169C2×Q16—1664no—
170C2×M16—21no—
171C2×M16—1661no—
172C2×M16C22⋊D8312yes—
173C22×C8—832no—
174C4⋊Q8—21no—
175C4⋊Q8—21no—
176C4⋊Q8—21no—
177C4⋊Q8—21no—
178C4⋊Q8—1661no—
179C4⋊Q8—1661no—
180C4⋊Q8—1661no—
181C4⋊Q8—1661no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—1661no—
185C2×C4⋊C4—1661no—
186C2×C42C22×D8311yescharacteristic
187C4⋊C8—21no—
188C4⋊C8—21no—
189C4⋊C8—832no—
190C4⋊C8—1661no—
191C4⋊C8—1661no—
192C22⋊C8—1661no—
193#97—21no—
194C4×C8—21no—
195C4×C8—831no—
196C4×C8—831no—
197C4×C8—832no—
198C4×C8—1661no—
199C2×Q8—22no—
200C2×Q8—22no—
201C2×Q8—44no—
202C2×Q8—3324no—
203C2×Q8—1662no—
204C2×Q8—1662no—
205C22×C4—22no—
206C22×C4—1662no—
207C22×C4C2×C4×D8311yescharacteristic
208C22×C4C2×C22⋊D8311yescharacteristic
209C22×C4#1305059011yescharacteristic
210Q16—3328no—
211Q16—3328no—
212M16—22no—
213M16—22no—
214M16—42no—
215M16—3322no—
216C2×C8—22no—
217C2×C8—41no—
218C2×C8—3321no—
219C2×C8—832no—
220C2×C8—832no—
221C2×C8—1662no—
222C2×C8—1664no—
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—41no—
227C4⋊C4—3321no—
228C4⋊C4—3321no—
229C4⋊C4—3321no—
230C4⋊C4—3321no—
231C42D4×D8311yescharacteristic
232C42D4×D8311yescharacteristic
233C42D4×D8311yescharacteristic
234C42#1305058911yescharacteristic
235C23C4×C22⋊D8311yescharacteristic
236Q8—44no—
237Q8—82no—
238Q8—3324no—
239Q8—6642no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—42no—
243C2×C4—82no—
244C2×C4—3322no—
245C2×C4—6642no—
246C2×C4C22⋊C4×D8311yescharacteristic
247C2×C4(C22⋊D83)⋊C411yescharacteristic
248C2×C4#1458176411yescharacteristic
249C2×C4#1458176511yescharacteristic
250C2×C4#1458177811yescharacteristic
251C2×C4#1458178811yescharacteristic
252C2×C4#1458182212yes—
253C2×C4#1458182312yes—
254C8—42no—
255C8—81no—
256C8—3322no—
257C8—834no—
258C8—6641no—
259C8—1662no—
260C22—21no—
261C22—21no—
262C22#1912760111yescharacteristic
263C22#1912780612yes—
264C4—21no—
265C4—21no—
266C4—82no—
267C4—6642no—
268C4#100×D8312yes—
269C4#1912795712yes—
270C4#1912797512yes—
271C4#1912809311yescharacteristic
272C4#1912809611yescharacteristic
273C2—22no—
274C2#2490830111yescharacteristic
275C2#2490833311yescharacteristic
276C2#2490837511yescharacteristic
subgroupG/H
centerC22#19127601
commutatorC22×C4×C83C22×C4
FrattiniC2×C42C22×D83
FittingC83×#1997C2
socleC22×C83#390
prime radicalC23×C83C4×D4
cosocleC2×C42×C83C23
hypercenter#1997D83
hypocenterC83#9807
LCSG ▷ C22×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1997

Complements

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

NH ≅ G/Ntype
146. C83#9807semidirect

Maximal subgroups

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

subgroupindex
C2×#191280802
#249084522
#249062182
#249061452
#249061442
#249057502
C83×#19972
#980783