Finite Group Databasebeta

← #11785462

Subgroups — #11785462

Order 1152.

570 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 570 conjugacy classes of subgroups — too many to draw. Only its 76 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×M16×C3⋊D3C211yesmaximal, characteristic
2#10593803C212yesmaximal
3C2×#63771C211yesmaximal, characteristic, complemented
4C2×#63770C211yesmaximal, characteristic, complemented
5#10590185C212yesmaximal, complemented
6C22×C4×C3⋊D3C2211yescharacteristic
7C2×#3788C2212yes—
8C2×#3788C2212yes—
9C2×C32×M16C411yescharacteristic
10C2×#3748C411yescharacteristic
11M16×C3⋊D3—22no—
12M16×C3⋊D3—22no—
13C2×#3743C411yescharacteristic
14C2×#3743C411yescharacteristic
15C2×C8×C3⋊D3C2211yescharacteristic
16C2×C8×C3⋊D3C2211yescharacteristic
17C22⋊#622—22no—
18#63778—22no—
19#63771—22no—
20#63770—22no—
21C2×D3×M16—62no—
22C23×C3⋊D3Q811yescharacteristic
23C22×C32×C4C2×C411yescharacteristic
24C22×C3⋊Dic3D411yescharacteristic
25C2×C4×C3⋊D3—21no—
26C2×C4×C3⋊D3—21no—
27C2×C4×C3⋊D3—21no—
28C2×C4×C3⋊D3—21no—
29C2×C4×C3⋊D3C2×C411yescharacteristic
30C2×C4×C3⋊D3D411yescharacteristic
31C2×C4×C3⋊D3Q811yescharacteristic
32C2×C4×C3⋊D3C2311yescharacteristic
33C2×#622—22no—
34C2×#622—22no—
35#3788—22no—
36#3788—22no—
37#3788—22no—
38#3788—22no—
39C32×M16—22no—
40C2×C32×C8C2×C411yescharacteristic
41C2×C32×C8C2×C411yescharacteristic
42#3748—22no—
43C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
44C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
45#3743—22no—
46#3743—22no—
47C8×C3⋊D3—21no—
48C8×C3⋊D3—21no—
49C8×C3⋊D3D412yes—
50C8×C3⋊D3D412yes—
51#1811—91nomaximal, Sylow
52C22×C4×D3—62no—
53C2×C3×M16—22no—
54C2×#208—62no—
55D3×M16—68no—
56D3×M16—68no—
57C2×ΓL(1,𝔽25)—62no—
58C2×ΓL(1,𝔽25)—62no—
59C2×D3×C8—62no—
60C2×D3×C8—62no—
61C23×C32C4⋊C411yescharacteristic
62C22×C3⋊D3—21no—
63C22×C3⋊D3—21no—
64C22×C3⋊D3—42no—
65C22×C3⋊D3C4⋊C411yescharacteristic
66C22×C3⋊D3C2×Q811yescharacteristic
67C2×C32×C4—21no—
68C2×C32×C4—21no—
69C2×C32×C4C4⋊C411yescharacteristic
70C2×C32×C4C22×C411yescharacteristic
71C2×C3⋊Dic3—21no—
72C2×C3⋊Dic3—21no—
73C2×C3⋊Dic3C4⋊C411yescharacteristic
74C2×C3⋊Dic3C2×D411yescharacteristic
75C4×C3⋊D3—21no—
76C4×C3⋊D3—21no—
77C4×C3⋊D3—21no—
78C4×C3⋊D3—21no—
79C4×C3⋊D3—21no—
80C4×C3⋊D3—21no—
81C4×C3⋊D3C2×D411yescharacteristic
82C4×C3⋊D3C2×D411yescharacteristic
83C4×C3⋊D3#4111yescharacteristic
84C4×C3⋊D3#4111yescharacteristic
85#622—42no—
86#622—42no—
87C32×C8—21no—
88C32×C8C22⋊C412yes—
89C3⋊(C3⋊C8)—21no—
90C3⋊(C3⋊C8)C22⋊C412yes—
91C22×M16—91no—
92C2×#108—91no—
93C2×#108—91no—
94#407—92no—
95#341—92no—
96C23×D3—62no—
97C22×C3×C4—22no—
98C22×Dic3—62no—
99C2×C4×D3—62no—
100C2×C4×D3—62no—
101C2×C4×D3—62no—
102C2×C4×D3—62no—
103C2×C4×D3—64no—
104C2×C4×D3—64no—
105C2×C4×D3—64no—
106C2×C4×D3—64no—
107C3×M16—28no—
108C2×C3×C8—22no—
109C2×C3×C8—22no—
110#208—68no—
111C2×C3⋊C8—62no—
112C2×C3⋊C8—62no—
113ΓL(1,𝔽25)—68no—
114ΓL(1,𝔽25)—68no—
115D3×C8—64no—
116D3×C8—64no—
117D3×C8—64no—
118D3×C8—64no—
119C22×C32—21no—
120C22×C32—22no—
121C22×C32C2×C4⋊C411yescharacteristic
122C2×C3⋊D3—22no—
123C2×C3⋊D3—21no—
124C2×C3⋊D3—22no—
125C2×C3⋊D3—42no—
126C2×C3⋊D3—42no—
127C2×C3⋊D3C22⋊Q811yescharacteristic
128C2×C3⋊D3C22⋊Q811yescharacteristic
129C32×C4—21no—
130C32×C4C2×C22⋊C411yescharacteristic
131C32×C4#11711yescharacteristic
132C3⋊Dic3—21no—
133C3⋊Dic3#12111yescharacteristic
134C3⋊Dic3#12111yescharacteristic
135C23×C4—91no—
136C2×M16—91no—
137C2×M16—91no—
138C2×M16—91no—
139C2×M16—92no—
140C2×M16—92no—
141C2×M16—182no—
142C2×M16—182no—
143C2×M16#15711yescharacteristic
144C22×C8—91no—
145C22×C8—91no—
146#108—182no—
147#108—182no—
148C22⋊C8—182no—
149C22⋊C8—182no—
150C23×C3—22no—
151C22×D3—62no—
152C22×D3—62no—
153C22×D3—64no—
154C22×D3—64no—
155C22×D3—128no—
156C2×C3×C4—24no—
157C2×C3×C4—24no—
158C2×C3×C4—22no—
159C2×C3×C4—22no—
160C2×Dic3—62no—
161C2×Dic3—62no—
162C2×Dic3—64no—
163C2×Dic3—64no—
164C4×D3—62no—
165C4×D3—62no—
166C4×D3—62no—
167C4×D3—62no—
168C4×D3—64no—
169C4×D3—64no—
170C4×D3—64no—
171C4×D3—64no—
172C4×D3—64no—
173C4×D3—64no—
174C3×C8—24no—
175C3×C8—24no—
176C3⋊C8—64no—
177C3⋊C8—64no—
178C2×C32—41no—
179C2×C32#38011yescharacteristic
180C2×C32#43012yes—
181C3⋊D3—21no—
182C3⋊D3—21no—
183C3⋊D3—41no—
184C24—91no—
185C22×C4—91no—
186C22×C4—91no—
187C22×C4—91no—
188C22×C4—91no—
189C22×C4—91no—
190C22×C4—181no—
191C22×C4—181no—
192C22×C4—181no—
193C22×C4—181no—
194C22×C4C2×#15711yescharacteristic
195M16—22no—
196M16—182no—
197M16—182no—
198M16—182no—
199M16—182no—
200M16—182no—
201M16—182no—
202M16—182no—
203C2×C8—91no—
204C2×C8—92no—
205C2×C8—92no—
206C2×C8—91no—
207C2×C8—181no—
208C2×C8—181no—
209C2×C8—182no—
210C2×C8—182no—
211C2×C8C2×#15711yescharacteristic
212C2×C8C2×#15711yescharacteristic
213C22×C3—24no—
214C22×C3—22no—
215C22×C3—44no—
216C2×D3—62no—
217C2×D3—62no—
218C2×D3—68no—
219C2×D3—64no—
220C2×D3—124no—
221C2×D3—128no—
222C2×D3—128no—
223C3×C4—24no—
224C3×C4—22no—
225C3×C4—22no—
226Dic3—62no—
227Dic3—62no—
228Dic3—64no—
229C32#181111yescharacteristic, complemented, Sylow
230C23—91no—
231C23—91no—
232C23—181no—
233C23—181no—
234C23—362no—
235C23C4⋊#15711yescharacteristic
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—91no—
239C2×C4—91no—
240C2×C4—91no—
241C2×C4—91no—
242C2×C4—91no—
243C2×C4—91no—
244C2×C4—181no—
245C2×C4—181no—
246C2×C4—181no—
247C2×C4—181no—
248C2×C4—181no—
249C2×C4—181no—
250C2×C4—181no—
251C2×C4—181no—
252C2×C4C4⋊#15711yescharacteristic
253C2×C4C22×#15711yescharacteristic
254C8—21no—
255C8—92no—
256C8—181no—
257C8—362no—
258C8—362no—
259C8C22⋊#15712yes—
260C2×C3—22no—
261C2×C3—24no—
262C2×C3—44no—
263D3—64no—
264D3—64no—
265D3—124no—
266C22—21no—
267C22—22no—
268C22—91no—
269C22—91no—
270C22—182no—
271C22—181no—
272C22—182no—
273C22—362no—
274C22—362no—
275C22C2×C4⋊#15711yescharacteristic
276C4—21no—
277C4—91no—
278C4—91no—
279C4—181no—
280C4#6428611yescharacteristic
281C4C2×C22⋊#15711yescharacteristic
282C3—22no—
283C2—41no—
284C2—181no—
285C2—181no—
286C2—361no—
287C2#1059377612yes—
288C2#1059381211yescharacteristic
subgroupG/H
centerC22C2×C4⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC2×C32×M16C4
socleC22×C32C2×C4⋊C4
prime radicalC23×C3⋊D3Q8
cosocleC2×C4×C3⋊D3C23
hypercenterC2×M16#157
hypocenterC32#1811
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
3. C2×#63771C2semidirect
4. C2×#63770C2semidirect
5. #10590185C2semidirect
229. C32#1811semidirect

Maximal subgroups

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

subgroupindex
C2×M16×C3⋊D32
#105938032
C2×#637712
C2×#637702
#105901852
#18119