Finite Group Databasebeta

← #11790821

Subgroups — #11790821

Order 1152.

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

normal subgroups only

This group has 564 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#10594929C211yesmaximal, characteristic
2#10593805C211yesmaximal, characteristic, complemented
3C2×#63741C214yesmaximal, complemented
4#10591252C211yesmaximal, characteristic, complemented
5C2×#3805C2212yes—
6C2×#3792C2212yes—
7C2×C4×C3⋊Dic3C2211yescharacteristic
8C3×#930—21no—
9#63980—21no—
10C2×Dic32C2212yes—
11#63919C411yescharacteristic, complemented
12#63915C412yescomplemented
13#63914C411yescharacteristic, complemented
14#63902—21no—
15#63898—21no—
16#63779—21no—
17C4⋊#622—21no—
18#63741—28no—
19C3×C3⋊#95—21no—
20#63579—21no—
21#5596—61no—
22#4648—61no—
23C22×C32×C4D411yescharacteristic
24C22×C3⋊Dic3D411yescharacteristic
25C22×C3⋊Dic3C2311yescharacteristic
26C2×C3×#67—22no—
27C22×C3×Dic3—22no—
28C2×C3×D12—21no—
29C2×#627C2×C412yes—
30C2×#625—21no—
31C2×#625C2×C412yes—
32#3805—24no—
33#3805—24no—
34C2×D3×Dic3—22no—
35#3792—24no—
36C2×#622—22no—
37C4×C3⋊Dic3C2×C411yescharacteristic
38C4×C3⋊Dic3C2×C411yescharacteristic
39C4×C3⋊Dic3D411yescharacteristic
40C4×C3⋊Dic3D411yescharacteristic
41C3×(C2×D3)⋊C4—22no—
42C3×C4⋊Dic3—21no—
43#3724—21no—
44(C2×D3)⋊Dic3—22no—
45Dic32—22no—
46Dic32D414yescomplemented
47#1963—91nomaximal, Sylow
48C2×#237—62no—
49C3×#121—61no—
50#940—61no—
51#939—62no—
52D4×Dic3—61no—
53#930—21no—
54C2×C4×Dic3—62no—
55C2×C4×Dic3—61no—
56C2×C4×Dic3—61no—
57#893—61no—
58#888—61no—
59#885—62no—
60#67⋊C4—62no—
61C3×#95—61no—
62C3⋊#95—21no—
63C3⋊#95—62no—
64C23×C32C2×D411yescharacteristic
65C22×C3×D3—22no—
66C2×C32×C4—41no—
67C2×C32×C4C22⋊C411yescharacteristic
68C2×C32×C4C22⋊C411yescharacteristic
69C2×C3⋊Dic3—41no—
70C2×C3⋊Dic3C22⋊C411yescharacteristic
71C2×C3⋊Dic3C22⋊C411yescharacteristic
72C2×C3⋊Dic3C22×C411yescharacteristic
73C2×C3⋊Dic3C2×D412yes—
74C2×C3⋊Dic3C2×D411yescharacteristic
75C2×C3⋊Dic3#4112yes—
76C3×#67—44no—
77C2×C3×Dic3—22no—
78C2×C3×Dic3—24no—
79C2×C3×Dic3—42no—
80C2×C3×Dic3—42no—
81C3×D12—42no—
82#627—24no—
83#625—24no—
84#625—42no—
85D3×Dic3—42no—
86D3×Dic3—42no—
87#622—42no—
88#532—91no—
89#423—91no—
90C2×#104—94no—
91#376—91no—
92C2×C3×D4—61no—
93C2×C3×D4—62no—
94C22×C3×C4—21no—
95C22×C3×C4—21no—
96C22×C3×C4—62no—
97C2×#67—22no—
98C2×#67—62no—
99C2×#67—62no—
100C22×Dic3—22no—
101C22×Dic3—61no—
102C22×Dic3—61no—
103C22×Dic3—61no—
104C22×Dic3—61no—
105C22×Dic3—62no—
106#237—124no—
107#237—124no—
108C2×D12—21no—
109C2×C4×D3—62no—
110C2×Dic6—62no—
111C3×C4⋊C4—61no—
112C3×C22⋊C4—62no—
113#217—62no—
114(C2×D3)⋊C4—22no—
115(C2×D3)⋊C4—62no—
116C4⋊Dic3—21no—
117Dic3⋊C4—62no—
118C4×Dic3—64no—
119C4×Dic3—61no—
120C4×Dic3—61no—
121C4×Dic3—61no—
122C4×Dic3—61no—
123C4×Dic3—61no—
124C4×Dic3—61no—
125C4×Dic3—61no—
126C4×Dic3—61no—
127C4×Dic3—64no—
128C22×C32—21no—
129C22×C32—21no—
130C22×C32C2×C22⋊C411yescharacteristic
131C22×C32#12112yes—
132C2×C3×D3—42no—
133C2×C3×D3—42no—
134C2×C3×D3—42no—
135C32×C4—21no—
136C32×C4—21no—
137C3⋊Dic3—21no—
138C3⋊Dic3—21no—
139C3⋊Dic3C4×D412yes—
140C3⋊Dic3#12411yescharacteristic
141C3⋊Dic3#12711yescharacteristic
142C3×Dic3—44no—
143C3×Dic3—42no—
144C2×#41—92no—
145C2×M16—92no—
146C4⋊Q8—91no—
147#127—91no—
148#124—92no—
149#121—61no—
150#121—181no—
151C4×D4—181no—
152C4×D4—181no—
153C2×C42—91no—
154C2×C42—92no—
155C4⋊C8—181no—
156C4⋊C8—181no—
157#104—188no—
158#95—61no—
159#95—181no—
160C23×C3—21no—
161C23×C3—21no—
162C23×C3—62no—
163C22×D3—22no—
164C3×D4—122no—
165C3×D4—124no—
166C2×C3×C4—21no—
167C2×C3×C4—21no—
168C2×C3×C4—21no—
169C2×C3×C4—21no—
170C2×C3×C4—42no—
171C2×C3×C4—42no—
172C2×C3×C4—64no—
173C2×C3×C4—62no—
174C2×C3×C4—122no—
175C2×C3×C4—122no—
176#67—44no—
177#67—124no—
178#67—124no—
179C2×Dic3—24no—
180C2×Dic3—22no—
181C2×Dic3—42no—
182C2×Dic3—42no—
183C2×Dic3—61no—
184C2×Dic3—61no—
185C2×Dic3—61no—
186C2×Dic3—61no—
187C2×Dic3—62no—
188C2×Dic3—61no—
189C2×Dic3—62no—
190C2×Dic3—62no—
191C2×Dic3—62no—
192C2×Dic3—61no—
193C2×Dic3—61no—
194C2×Dic3—61no—
195C2×Dic3—122no—
196C2×Dic3—122no—
197C2×Dic3—122no—
198C2×Dic3—121no—
199C2×Dic3—121no—
200D12—42no—
201C4×D3—122no—
202C4×D3—122no—
203Dic6—124no—
204C2×C32—22no—
205C2×C32#39011yescharacteristic
206C2×C32#42111yescharacteristic
207C2×C32#42111yescharacteristic
208C3×D3—82no—
209#41—184no—
210#41—184no—
211C2×Q8—92no—
212C2×D4—62no—
213C2×D4—61no—
214C2×D4—92no—
215C2×D4—181no—
216C22×C4—62no—
217C22×C4—91no—
218C22×C4—91no—
219C22×C4—182no—
220C22×C4GO+(4,𝔽2)11yescharacteristic
221M16—184no—
222C2×C8—182no—
223C4⋊C4—61no—
224C4⋊C4—181no—
225C22⋊C4—62no—
226C22⋊C4—182no—
227C42—94no—
228C42—91no—
229C42—91no—
230C42—91no—
231C42—91no—
232C42—182no—
233C22×C3—21no—
234C22×C3—22no—
235C22×C3—21no—
236C22×C3—22no—
237C22×C3—22no—
238C22×C3—21no—
239C22×C3—21no—
240C22×C3—41no—
241C22×C3—41no—
242C22×C3—122no—
243C22×C3—122no—
244C22×C3—122no—
245C2×D3—42no—
246C2×D3—42no—
247C2×D3—42no—
248C3×C4—22no—
249C3×C4—41no—
250C3×C4—41no—
251C3×C4—41no—
252C3×C4—122no—
253C3×C4—124no—
254Dic3—42no—
255Dic3—44no—
256Dic3—62no—
257Dic3—61no—
258Dic3—61no—
259Dic3—62no—
260Dic3—61no—
261Dic3—61no—
262Dic3—62no—
263Dic3—121no—
264Dic3—121no—
265Dic3—121no—
266C32#196311yescharacteristic, complemented, Sylow
267C23—62no—
268C23C2×GO+(4,𝔽2)11yescharacteristic
269Q8—184no—
270D4—122no—
271D4—124no—
272D4—184no—
273D4—362no—
274C2×C4—41no—
275C2×C4—64no—
276C2×C4—62no—
277C2×C4—92no—
278C2×C4—92no—
279C2×C4—91no—
280C2×C4—91no—
281C2×C4—91no—
282C2×C4—91no—
283C2×C4—122no—
284C2×C4—122no—
285C2×C4—362no—
286C2×C4—362no—
287C2×C4—361no—
288C2×C4D32⋊C411yescharacteristic
289C2×C4D32⋊C411yescharacteristic
290C8—362no—
291C2×C3—22no—
292C2×C3—22no—
293C2×C3—21no—
294C2×C3—21no—
295C2×C3—21no—
296C2×C3—21no—
297C2×C3—21no—
298C2×C3—21no—
299C2×C3—42no—
300C2×C3—242no—
301D3—82no—
302C22—21no—
303C22—21no—
304C22—122no—
305C22—122no—
306C22—122no—
307C22#6423012yes—
308C22C2×D32⋊C411yescharacteristic
309C4—21no—
310C4—21no—
311C4—91no—
312C4—91no—
313C4—92no—
314C4—124no—
315C4—122no—
316C4—181no—
317C4—181no—
318C3—21no—
319C3—21no—
320C2—22no—
321C2—242no—
322C2#1059338111yescharacteristic
323C2#1059340511yescharacteristic
324C2#1059350611yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC23C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radical#10594929C2
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1963
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #10593805C2semidirect
3. C2×#63741C2semidirect
4. #10591252C2semidirect
11. #63919C4semidirect
12. #63915C4semidirect
13. #63914C4semidirect
46. Dic32D4semidirect
266. C32#1963semidirect

Maximal subgroups

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

subgroupindex
#105949292
#105938052
C2×#637412
#105912522
#19639