Finite Group Databasebeta

← #11797924

Subgroups — #11797924

Order 1152.

336 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 86 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#10592896C211yesmaximal, characteristic
2C3×#5195C211yesmaximal, characteristic
3#10590819C211yesmaximal, characteristic, complemented
4C3×#4566C211yesmaximal, characteristic
5#10589136C211yesmaximal, characteristic, complemented
6#10589130C211yesmaximal, characteristic, complemented
7#10589106C211yesmaximal, characteristic, complemented
8#71521—31nomaximal
9#69248—31nomaximal
10C32×#135C2211yescharacteristic
11#64157—21no—
12C2×C3×Dic12C2211yescharacteristic
13#63843—21no—
14#63664—21no—
15#63646C2211yescharacteristic
16#63642C2211yescharacteristic
17C3×#829C412yescomplemented
18C3×#827C412yescomplemented
19C3×#817C2211yescharacteristic
20C3×#812C2211yescharacteristic
21C3×#812C2211yescharacteristic
22#63565—21no—
23C3×#510—31no—
24#5197—31no—
25#5197—31no—
26#5197—61no—
27#5195D311yescharacteristic
28#5184—31no—
29#4853—31no—
30C3×#360—31no—
31#4566D311yescharacteristic
32#4565—31no—
33#4517—31no—
34#4513—31no—
35#4512—31no—
36#4512—31no—
37#4487—31no—
38C32×#41—21no—
39C2×C3×Dic6—21no—
40C32×Q16C2×C411yescharacteristic
41C32×SD16—21no—
42C32×D8C2×C411yescharacteristic
43C2×C32×C8C2311yescharacteristic
44C4×C3⋊Dic3D411yescharacteristic
45#3748—21no—
46#3748—41no—
47C2×C3⋊(C3⋊C8)—41no—
48C2×C3⋊(C3⋊C8)D411yescharacteristic
49C3×C4⋊Dic3—21no—
50C3×Dic12—21no—
51C3×Dic12C2×C412yes—
52Dic3⋊Dic3—41no—
53Dic32—41no—
54C3×C3⋊C16—21no—
55C3×C3⋊C16C2×C412yes—
56#2180—91noSylow
57C3×#135—21no—
58C3×#135C2×D311yescharacteristic
59C3×#135C2×D311yescharacteristic
60C2×C3×Q16—31no—
61#948—61no—
62#948—61no—
63#948—62no—
64Q8×Dic3—61no—
65C2×Dic12C2×D311yescharacteristic
66#887—61no—
67C3×Q32—32no—
68C3×SD32—32no—
69C3×M32—31no—
70C3×M32—31no—
71C3×#106—31no—
72#837—61no—
73#837—61no—
74#837—62no—
75#835—61no—
76#829Dic312yescomplemented
77#827Dic312yescomplemented
78#819—31no—
79#819—31no—
80#819—61no—
81#817C2×D311yescharacteristic
82#815—31no—
83#815—31no—
84#815—61no—
85#812C2×D311yescharacteristic
86#812C2×D311yescharacteristic
87#810—61no—
88C32×Q8—21no—
89C32×D4—21no—
90C32×D4—41no—
91C2×C32×C4—41no—
92C2×C32×C4C2×D411yescharacteristic
93C2×C3⋊Dic3—21no—
94C2×C3×Dic3—41no—
95C2×C3×Dic3—41no—
96C3×Dic6—22no—
97C3×Dic6—41no—
98C32×C8C22×C411yescharacteristic
99C32×C8#4111yescharacteristic
100C3⋊(C3⋊C8)—21no—
101C3⋊(C3⋊C8)—41no—
102#510—31no—
103#444—91no—
104#441—91no—
105#365—91no—
106#362—91no—
107#360—31no—
108#347—91no—
109C3×#41—22no—
110C3×#41—21no—
111C3×#41—21no—
112C2×C3×Q8—61no—
113C2×Dic6—21no—
114C3×Q16—21no—
115C3×Q16—32no—
116C3×Q16—61no—
117C3×Q16C4×D311yescharacteristic
118C3×Q16C2×Dic311yescharacteristic
119C3×SD16—22no—
120C3×SD16—21no—
121C3×SD16—21no—
122C3×D8—21no—
123C3×D8C4×D311yescharacteristic
124C3×D8C2×Dic311yescharacteristic
125C2×C3×C8—21no—
126C2×C3×C8C22×D311yescharacteristic
127C2×C3×C8C22×D311yescharacteristic
128C3×C4⋊C4—61no—
129C4⋊Dic3—21no—
130C4⋊Dic3—121no—
131Dic3⋊C4—121no—
132C4×Dic3—31no—
133C4×Dic3—31no—
134C4×Dic3—61no—
135C4×Dic3—121no—
136C4×Dic3—121no—
137#208—62no—
138#208—61no—
139#208—61no—
140#208—122no—
141#208—121no—
142#208—121no—
143C2×C3⋊C8—31no—
144C2×C3⋊C8—31no—
145C2×C3⋊C8—61no—
146C2×C3⋊C8—122no—
147C2×C3⋊C8—121no—
148C2×C3⋊C8—121no—
149Dic12—21no—
150Dic12C2×Dic312yes—
151C3×C16—32no—
152C3×C16—61no—
153C3⋊C16—21no—
154C3⋊C16C2×Dic312yes—
155C22×C32—41no—
156C22×C32AGL(1,ℤ/8)11yescharacteristic
157C32×C4—41no—
158C32×C4C4×D411yescharacteristic
159C32×C4AGL(1,ℤ/8)11yescharacteristic
160C3⋊Dic3—41no—
161C3×Dic3—42no—
162C3×Dic3—81no—
163#135D3211yescharacteristic
164C2×Q16—31no—
165#131—181no—
166C4×Q8—181no—
167Q32—32no—
168SD32—32no—
169M32—31no—
170M32—31no—
171#108—91no—
172#106—31no—
173#104—181no—
174#103—181no—
175#97—91no—
176C3×Q8—22no—
177C3×Q8—21no—
178C3×Q8—21no—
179C3×Q8—62no—
180C3×Q8—121no—
181C3×D4—22no—
182C3×D4—21no—
183C3×D4—21no—
184C3×D4—42no—
185C3×D4—41no—
186C3×D4—41no—
187C2×C3×C4—21no—
188C2×C3×C4—42no—
189C2×C3×C4—41no—
190C2×C3×C4—41no—
191C2×C3×C4—121no—
192C2×C3×C4—121no—
193C2×C3×C4D3×D411yescharacteristic
194C2×C3×C4D3×D411yescharacteristic
195C2×Dic3—41no—
196C2×Dic3—41no—
197C2×Dic3—61no—
198C2×Dic3—61no—
199C2×Dic3—121no—
200Dic6—22no—
201Dic6—41no—
202C3×C8—21no—
203C3×C8—21no—
204C3×C8C2×C4×D311yescharacteristic
205C3×C8#23711yescharacteristic
206C3×C8#23711yescharacteristic
207C3×C8C22×Dic311yescharacteristic
208C3⋊C8—62no—
209C3⋊C8—61no—
210C3⋊C8—61no—
211C3⋊C8—122no—
212C3⋊C8—121no—
213C3⋊C8—121no—
214C2×C32—21no—
215C2×C32—81no—
216C2×C32#44211yescharacteristic
217#41—21no—
218C2×Q8—61no—
219Q16—32no—
220Q16—61no—
221Q16D3×Dic311yescharacteristic
222SD16—21no—
223D8D3×Dic311yescharacteristic
224M16—181no—
225M16—361no—
226C2×C8—91no—
227C2×C8—361no—
228C2×C8C2×D3211yescharacteristic
229C4⋊C4—61no—
230C4⋊C4—361no—
231C42—91no—
232C42—361no—
233C16—32no—
234C16—61no—
235C22×C3—21no—
236C22×C3—42no—
237C22×C3—41no—
238C22×C3—41no—
239C22×C3#91111yescharacteristic
240C22×C3#91111yescharacteristic
241C3×C4—21no—
242C3×C4—21no—
243C3×C4—42no—
244C3×C4—41no—
245C3×C4—41no—
246C3×C4—122no—
247C3×C4—241no—
248C3×C4#67⋊C411yescharacteristic
249C3×C4#91111yescharacteristic
250C3×C4#91411yescharacteristic
251C3×C4D4×Dic311yescharacteristic
252Dic3—42no—
253Dic3—81no—
254Dic3—121no—
255Dic3—121no—
256Dic3—241no—
257C32#218011yescharacteristic, complemented, Sylow
258Q8—21no—
259Q8—62no—
260Q8—121no—
261D4—21no—
262D4—41no—
263C2×C4—41no—
264C2×C4—121no—
265C2×C4—121no—
266C2×C4—181no—
267C2×C4#381111yescharacteristic
268C8—181no—
269C8—361no—
270C8C2×D3×Dic311yescharacteristic
271C8#380511yescharacteristic
272C2×C3—21no—
273C2×C3—21no—
274C2×C3—21no—
275C2×C3—41no—
276C2×C3—82no—
277C2×C3—81no—
278C2×C3—81no—
279C2×C3#478511yescharacteristic
280C2×C3#515211yescharacteristic
281C22—41no—
282C22#6392711yescharacteristic
283C4—41no—
284C4—122no—
285C4—241no—
286C4—361no—
287C4#6393711yescharacteristic
288C4#67⋊Dic311yescharacteristic
289C3—21no—
290C3#6924811yescharacteristic, complemented
291C3#7152111yescharacteristic, complemented
292C2—21no—
293C2—81no—
294C2#1059143611yescharacteristic
subgroupG/H
centerC2#10591436
commutatorC32×C8C22×C4
FrattiniC2×C8C2×D32
Fitting, prime radicalC32×#135C22
socleC2×C32#442
cosocleC2×C32×C8C23
hypercenter#135D32
hypocenterC32#2180
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #135

Complements

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

NH ≅ G/Ntype
3. #10590819C2semidirect
5. #10589136C2semidirect
6. #10589130C2semidirect
7. #10589106C2semidirect
17. C3×#829C4semidirect
18. C3×#827C4semidirect
76. #829Dic3semidirect
77. #827Dic3semidirect
257. C32#2180semidirect
290. C3#69248semidirect
291. C3#71521semidirect

Maximal subgroups

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

subgroupindex
#105928962
C3×#51952
#105908192
C3×#45662
#105891362
#105891302
#105891062
#715213
#692483