Finite Group Databasebeta

← #11774753

Subgroups — #11774753

Order 1152.

512 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 67 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#10593971C211yesmaximal, characteristic
2#10593729C211yesmaximal, characteristic, complemented
3C4×#3710C211yesmaximal, characteristic, complemented
4#10590030C214yesmaximal, complemented
5C2×#3796—21no—
6C2×#3788—21no—
7C42×C3⋊D3C2211yescharacteristic
8C3×#875—21no—
9#63914C411yescharacteristic
10#63912—21no—
11#63912C412yes—
12#63902—21no—
13#63902C2212yes—
14#63873C411yescharacteristic
15C2×#3710—21no—
16#63779—21no—
17#63779C2212yes—
18C3×C4×C3⋊C8—21no—
19#63553C2212yes—
20#5668—61no—
21C4×D3×C8—61no—
22C2×C4×C3⋊D3C2×C411yescharacteristic
23C2×C4×C3⋊D3D411yescharacteristic
24C2×C4×C3⋊D3D411yescharacteristic
25C2×C3×D12—21no—
26C2×C3×Dic6—21no—
27C2×#626—22no—
28C2×#625—21no—
29C2×#625C2×C412yes—
30C2×D3×Dic3—22no—
31#3796—42no—
32#3796—42no—
33C2×#622—22no—
34#3788—42no—
35C32×C42D411yescharacteristic
36C4×C3⋊Dic3C2×C411yescharacteristic
37C4×C3⋊Dic3D411yescharacteristic
38C4×C3⋊Dic3C2311yescharacteristic
39C3×(C2×D3)⋊C4—22no—
40C3×(C2×D3)⋊C4—22no—
41C2×C3×C3⋊C8—22no—
42#3724—21no—
43#3724C2×C412yes—
44#3710—24no—
45#1492—91nomaximal, Sylow
46C2×#239—61no—
47C2×#237—61no—
48C3×#124—61no—
49#944—61no—
50#940—61no—
51C2×D3×C8—62no—
52#884—62no—
53#884—62no—
54#67⋊C4—62no—
55#67⋊C4—62no—
56#875—21no—
57C42×D3—61no—
58C42×D3—61no—
59C3×C4×C8—61no—
60C8×Dic3—62no—
61C4×C3⋊C8—21no—
62C22×C3⋊D3C22⋊C411yescharacteristic
63C22×C3×D3—22no—
64C2×C32×C4C22⋊C411yescharacteristic
65C2×C32×C4C22⋊C411yescharacteristic
66C2×C32×C4C2×D411yescharacteristic
67C2×C3⋊Dic3C22⋊C411yescharacteristic
68C2×C3⋊Dic3C22×C411yescharacteristic
69C2×C3⋊Dic3C2×D411yescharacteristic
70C4×C3⋊D3—22no—
71C4×C3⋊D3—22no—
72C4×C3⋊D3D812yes—
73C4×C3⋊D3SD1612yes—
74C2×C3×Dic3—22no—
75C3×D12—42no—
76C3×Dic6—42no—
77#626—44no—
78#625—24no—
79#625—42no—
80D3×Dic3—42no—
81D3×Dic3—42no—
82#622—42no—
83C3×C3⋊C8—24no—
84#532—91no—
85#423—91no—
86C2×C4×C8—91no—
87D4⋊C8—94no—
88C2×C3×Q8—61no—
89C2×C3×D4—61no—
90C2×#67—62no—
91C2×#67—62no—
92C2×#67—62no—
93C22×Dic3—62no—
94#239—122no—
95#239—122no—
96#237—122no—
97#237—122no—
98C2×D12—21no—
99C2×D12—62no—
100C2×C4×D3—61no—
101C2×C4×D3—61no—
102C2×C4×D3—61no—
103C2×C4×D3—61no—
104C2×C4×D3—61no—
105C2×C4×D3—61no—
106C2×C4×D3—62no—
107C2×Dic6—21no—
108C2×C3×C8—62no—
109C3×C22⋊C4—62no—
110C3×C22⋊C4—62no—
111C3×C42—21no—
112C3×C42—21no—
113(C2×D3)⋊C4—22no—
114(C2×D3)⋊C4—22no—
115Dic3⋊C4—62no—
116Dic3⋊C4—62no—
117C4×Dic3—61no—
118C4×Dic3—61no—
119C4×Dic3—61no—
120C4×Dic3—61no—
121C4×Dic3—61no—
122C4×Dic3—61no—
123C2×C3⋊C8—22no—
124D3×C8—68no—
125C22×C32C2×C22⋊C411yescharacteristic
126C2×C3⋊D3—21no—
127C2×C3⋊D3—21no—
128C2×C3⋊D3#10212yes—
129C2×C3×D3—42no—
130C2×C3×D3—42no—
131C2×C3×D3—42no—
132C32×C4—21no—
133C32×C4—21no—
134C32×C4#10212yes—
135C3⋊Dic3#10412yes—
136C3⋊Dic3#13112yes—
137C3⋊Dic3C2×D811yescharacteristic
138C3⋊Dic3C2×SD1611yescharacteristic
139C3×Dic3—42no—
140C2×#41—181no—
141C2×M16—181no—
142C22×C8—181no—
143C4⋊Q8—91no—
144#127—91no—
145#124—61no—
146#121—92no—
147#121—181no—
148C4×D4—92no—
149C4×D4—181no—
150C2×C42—91no—
151C4⋊C8—92no—
152C4⋊C8—181no—
153C4×C8—61no—
154C4×C8—92no—
155C23×C3—62no—
156C22×D3—22no—
157C22×D3—61no—
158C22×D3—61no—
159C3×Q8—122no—
160C3×D4—122no—
161C2×C3×C4—21no—
162C2×C3×C4—21no—
163C2×C3×C4—21no—
164C2×C3×C4—21no—
165C2×C3×C4—21no—
166C2×C3×C4—21no—
167C2×C3×C4—62no—
168#67—124no—
169#67—124no—
170#67—124no—
171C2×Dic3—22no—
172C2×Dic3—61no—
173C2×Dic3—61no—
174C2×Dic3—61no—
175C2×Dic3—61no—
176C2×Dic3—61no—
177C2×Dic3—61no—
178C2×Dic3—122no—
179C2×Dic3—122no—
180D12—42no—
181D12—124no—
182C4×D3—62no—
183C4×D3—62no—
184C4×D3—62no—
185C4×D3—62no—
186C4×D3—64no—
187C4×D3—64no—
188C4×D3—122no—
189C4×D3—122no—
190C4×D3—122no—
191C4×D3—122no—
192Dic6—42no—
193C3×C8—64no—
194C3⋊C8—24no—
195C2×C32#40811yescharacteristic
196C2×C32C2×#10211yescharacteristic
197C2×C32C2×#10411yescharacteristic
198C3⋊D3—22no—
199C3×D3—82no—
200#41—362no—
201#41—362no—
202C2×Q8—61no—
203C2×D4—61no—
204C2×D4—92no—
205C2×D4—182no—
206C2×D4—181no—
207C22×C4—91no—
208C22×C4—91no—
209C22×C4—91no—
210C22×C4—182no—
211M16—362no—
212C2×C8—62no—
213C2×C8—184no—
214C2×C8—182no—
215C4⋊C4—92no—
216C4⋊C4—181no—
217C22⋊C4—62no—
218C22⋊C4—62no—
219C42—91no—
220C42—91no—
221C42—91no—
222C42GO+(4,𝔽2)11yescharacteristic
223C22×C3—21no—
224C22×C3—21no—
225C22×C3—122no—
226C22×C3—122no—
227C22×C3—122no—
228C2×D3—42no—
229C2×D3—42no—
230C2×D3—42no—
231C2×D3—62no—
232C2×D3—62no—
233C2×D3—62no—
234C2×D3—62no—
235C2×D3—121no—
236C2×D3—121no—
237C3×C4—22no—
238C3×C4—22no—
239C3×C4—22no—
240C3×C4—22no—
241C3×C4—41no—
242C3×C4—41no—
243C3×C4—122no—
244Dic3—42no—
245Dic3—61no—
246Dic3—61no—
247Dic3—62no—
248Dic3—62no—
249Dic3—61no—
250Dic3—61no—
251Dic3—62no—
252Dic3—62no—
253C32#149211yescharacteristic, complemented, Sylow
254C23—62no—
255C23—91no—
256Q8—122no—
257D4—122no—
258D4—184no—
259D4—362no—
260D4—364no—
261C2×C4—62no—
262C2×C4—91no—
263C2×C4—91no—
264C2×C4—91no—
265C2×C4—92no—
266C2×C4—92no—
267C2×C4—182no—
268C2×C4—182no—
269C2×C4—362no—
270C2×C4—362no—
271C2×C4D32⋊C411yescharacteristic
272C2×C4D32⋊C411yescharacteristic
273C2×C4C2×GO+(4,𝔽2)11yescharacteristic
274C8—64no—
275C8—362no—
276C2×C3—21no—
277C2×C3—21no—
278C2×C3—21no—
279C2×C3—21no—
280C2×C3—21no—
281C2×C3—21no—
282C2×C3—242no—
283D3—64no—
284D3—82no—
285D3—122no—
286C22—92no—
287C22—122no—
288C22—122no—
289C22—122no—
290C22—181no—
291C22—181no—
292C22C2×D32⋊C411yescharacteristic
293C4—21no—
294C4—21no—
295C4—92no—
296C4—91no—
297C4—91no—
298C4—92no—
299C4—122no—
300C4#6372912yes—
301C3—21no—
302C3—21no—
303C2—182no—
304C2—242no—
305C2#1059330811yescharacteristic
306C2C2×#6372911yescharacteristic
307C2#1059338011yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radical#10593971C2
cosocleC4×C3⋊Dic3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1492
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
2. #10593729C2semidirect
3. C4×#3710C2semidirect
4. #10590030C2semidirect
253. C32#1492semidirect

Maximal subgroups

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

subgroupindex
#105939712
#105937292
C4×#37102
#105900302
#14929