Finite Group Databasebeta

← #35320411

Subgroups — #35320411

Order 21248.

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

normal subgroups only

This group has 480 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
1C2×#19127498C212yesmaximal
2#24907459C212yesmaximal, complemented
3#24905590C212yesmaximal, complemented
4C83×#2326C211yesmaximal, characteristic
5#19127725—22no—
6C2×#14581711C2214yes—
7#19127498—24no—
8#19127470—22no—
9C2×#124×C83C2211yescharacteristic
10C2×C4×Q8×C83C2211yescharacteristic
11C2×C4×D4×C83C411yescharacteristic
12#391×C83C2211yescharacteristic
13#390×C83C411yescharacteristic
14#388×C83—22no—
15#385×C83—22no—
16#384×C83C411yescharacteristic
17#376×C83C411yescharacteristic
18C2×#13050574—24no—
19C4⋊(C83⋊C8)—44no—
20#14581711—24no—
21#14581711—24no—
22C22×Q8×C83C2311yescharacteristic
23C22×D4×C83C2×C411yescharacteristic
24C23×C4×C83—21no—
25#124×C83—22no—
26#124×C83D412yes—
27#124×C83Q812yes—
28C4×Q8×C83—42no—
29C4×D4×C83—42no—
30C2×C4⋊C4×C83—22no—
31C2×C4⋊C4×C83C2×C411yescharacteristic
32C2×C4⋊C4×C83C2×C411yescharacteristic
33C2×C4⋊C4×C83D412yes—
34C2×C22⋊C4×C83—22no—
35C2×C22⋊C4×C83—21no—
36C2×C22⋊C4×C83—22no—
37C2×C42×C83C2×C411yescharacteristic
38C2×C42×C83C2×C411yescharacteristic
39C2×C42×C83C2×C411yescharacteristic
40C2×C42×C83D412yes—
41#95×C83—21no—
42#95×C83—21no—
43#95×C83—22no—
44#13050574—44no—
45#13050574—44no—
46C2×C83⋊C8—44no—
47C24×C83—21no—
48C2×Q8×C83—41no—
49C2×Q8×C83—41no—
50C2×Q8×C83C2×D411yescharacteristic
51C2×Q8×C83C2×Q811yescharacteristic
52C2×Q8×C83#4112yes—
53C2×D4×C83—21no—
54C2×D4×C83—41no—
55C2×D4×C83—41no—
56C2×D4×C83C4⋊C412yes—
57C22×C4×C83—21no—
58C22×C4×C83—21no—
59C22×C4×C83—21no—
60C22×C4×C83—42no—
61C22×C4×C83—82no—
62C22×C4×C83C22⋊C411yescharacteristic
63C22×C4×C83C22⋊C412yes—
64C22×C4×C83C22⋊C411yescharacteristic
65C22×C4×C83C22×C411yescharacteristic
66C22×C4×C83C2×D412yes—
67C4⋊C4×C83—41no—
68C4⋊C4×C83—42no—
69C4⋊C4×C83—41no—
70C4⋊C4×C83—82no—
71C22⋊C4×C83—24no—
72C22⋊C4×C83—24no—
73C22⋊C4×C83—42no—
74C22⋊C4×C83—82no—
75C42×C83—22no—
76C42×C83—24no—
77C42×C83—21no—
78C42×C83—41no—
79C42×C83C4⋊C412yes—
80C23×C83—22no—
81C23×C83—42no—
82C23×C83—42no—
83C23×C83—41no—
84C23×C83—41no—
85C23×C83C2×C22⋊C411yescharacteristic
86Q8×C83—41no—
87Q8×C83—41no—
88Q8×C83—42no—
89D4×C83—42no—
90D4×C83—42no—
91C2×C4×C83—21no—
92C2×C4×C83—22no—
93C2×C4×C83—21no—
94C2×C4×C83—22no—
95C2×C4×C83—22no—
96C2×C4×C83—21no—
97C2×C4×C83—22no—
98C2×C4×C83—41no—
99C2×C4×C83—41no—
100C2×C4×C83—41no—
101C2×C4×C83—42no—
102C2×C4×C83—41no—
103C2×C4×C83—41no—
104C2×C4×C83—42no—
105C2×C4×C83—41no—
106C2×C4×C83—41no—
107C2×C4×C83—41no—
108C2×C4×C83—84no—
109C2×C4×C83#9912yes—
110C2×C4×C83C2×C4⋊C411yescharacteristic
111C2×C4×C83#11711yescharacteristic
112C2×C4×C83#12112yes—
113C2×C4×C83C22⋊Q812yes—
114C83⋊C8—84no—
115C22×C83—21no—
116C22×C83—21no—
117C22×C83—44no—
118C22×C83—42no—
119C22×C83—82no—
120C22×C83—81no—
121C22×C83—81no—
122C22×C83#38011yescharacteristic
123C22×C83C2×#9911yescharacteristic
124C22×C83#41011yescharacteristic
125C4×C83—22no—
126C4×C83—21no—
127C4×C83—21no—
128C4×C83—22no—
129C4×C83—22no—
130C4×C83—42no—
131C4×C83—42no—
132C4×C83—41no—
133C4×C83—81no—
134C4×C83—81no—
135#12803—831nomaximal, Sylow
136C2×C83—21no—
137C2×C83—21no—
138C2×C83—82no—
139C2×C83#179911yescharacteristic
140C2×C83#213311yescharacteristic
141C2×C83#213411yescharacteristic
142#2326D8311yescharacteristic
143C2×#355—832no—
144#1801—832no—
145#1394—832no—
146C83#1280311yescharacteristic, complemented, Sylow
147C2×#124C2×D8311yescharacteristic
148C2×C4×Q8C2×D8311yescharacteristic
149C2×C4×D4Dic8311yescharacteristic
150#423—1662no—
151C2×#101—834no—
152#391C2×D8311yescharacteristic
153#390Dic8311yescharacteristic
154#388—22no—
155#385—22no—
156#384Dic8311yescharacteristic
157#376Dic8311yescharacteristic
158#355—1664no—
159#343—1662no—
160C22×Q8C22×D8311yescharacteristic
161C22×D4C2×Dic8311yescharacteristic
162C23×C4—21no—
163C2×M16—1664no—
164#124—22no—
165#124Dic16612yes—
166#124D33212yes—
167C4×Q8—42no—
168C4×D4—42no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4C2×Dic8311yescharacteristic
171C2×C4⋊C4C2×Dic8311yescharacteristic
172C2×C4⋊C4C22⋊D8312yes—
173C2×C22⋊C4—22no—
174C2×C22⋊C4—21no—
175C2×C22⋊C4—22no—
176C2×C42C2×Dic8311yescharacteristic
177C2×C42C2×Dic8311yescharacteristic
178C2×C42C2×Dic8311yescharacteristic
179C2×C42C22⋊D8312yes—
180C4⋊C8—3324no—
181#101—1664no—
182#101—1664no—
183#95—21no—
184#95—21no—
185#95—22no—
186C24—21no—
187C2×Q8—41no—
188C2×Q8—41no—
189C2×Q8C2×D33211yescharacteristic
190C2×Q8C2×Dic16611yescharacteristic
191C2×Q8#1305059012yes—
192C2×D4—21no—
193C2×D4—41no—
194C2×D4—41no—
195C2×D4C4⋊Dic8312yes—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—42no—
200C22×C4—82no—
201C22×C4C22⋊Dic8311yescharacteristic
202C22×C4C22⋊Dic8312yes—
203C22×C4C22⋊Dic8311yescharacteristic
204C22×C4C22×Dic8311yescharacteristic
205C22×C4C2×C22⋊D8312yes—
206M16—3324no—
207M16—3324no—
208C2×C8—3324no—
209C4⋊C4—41no—
210C4⋊C4—42no—
211C4⋊C4—41no—
212C4⋊C4—82no—
213C22⋊C4—24no—
214C22⋊C4—24no—
215C22⋊C4—42no—
216C22⋊C4—82no—
217C42—24no—
218C42—22no—
219C42—21no—
220C42—41no—
221C42C4⋊Dic8312yes—
222C23—22no—
223C23—42no—
224C23—42no—
225C23—41no—
226C23—41no—
227C23C2×C22⋊Dic8311yescharacteristic
228Q8—41no—
229Q8—41no—
230Q8—42no—
231D4—42no—
232D4—42no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—42no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—42no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—84no—
251C2×C4#1458170712yes—
252C2×C4C2×C4⋊Dic8311yescharacteristic
253C2×C4#1458175111yescharacteristic
254C2×C4#1458176612yes—
255C2×C4#1458177112yes—
256C8—6644no—
257C22—21no—
258C22—21no—
259C22—44no—
260C22—42no—
261C22—82no—
262C22—81no—
263C22—81no—
264C22#1912756111yescharacteristic
265C22C2×#1458170711yescharacteristic
266C22#1912767511yescharacteristic
267C4—22no—
268C4—22no—
269C4—22no—
270C4—21no—
271C4—21no—
272C4—42no—
273C4—41no—
274C4—42no—
275C4—81no—
276C4—81no—
277C2—21no—
278C2—21no—
279C2—82no—
280C2#2490745111yescharacteristic
281C2#2490915211yescharacteristic
282C2#2490915511yescharacteristic
subgroupG/H
centerC22C2×#14581707
commutatorC22×C4×C83C22×C4
FrattiniC22×Q8C22×D83
FittingC83×#2326C2
socleC22×C83C2×#99
prime radicalC22×D4×C83C2×C4
cosocleC22×Q8×C83C23
hypercenter#2326D83
hypocenterC83#12803
LCSG ▷ C22×C4×C83 ▷ C22×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2326

Complements

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

NH ≅ G/Ntype
2. #24907459C2semidirect
3. #24905590C2semidirect
146. C83#12803semidirect

Maximal subgroups

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

subgroupindex
C2×#191274982
#249074592
#249055902
C83×#23262
#1280383