Finite Group Databasebeta

← #11797930

Subgroups — #11797930

Order 1152.

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

normal subgroups only

This group has 307 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
1#10590920C211yesmaximal, characteristic
2#10590819C211yesmaximal, characteristic, complemented
3#10590636C211yesmaximal, characteristic
4#10589378C211yesmaximal, characteristic, complemented
5C3×#4518C211yesmaximal, characteristic
6C3×#4517C211yesmaximal, characteristic, complemented
7#10589138C211yesmaximal, characteristic, complemented
8#69264—31nomaximal
9#69248—31nomaximal
10C2×C3×Dic12C2211yescharacteristic
11C3×#904C2211yescharacteristic
12#63843—21no—
13#63815—21no—
14C32×M32C2211yescharacteristic
15#63642C2211yescharacteristic
16#63639C2211yescharacteristic
17C3×#819C2211yescharacteristic
18C3×#817C2211yescharacteristic
19#63568—21no—
20#63565—21no—
21#63550C412yescomplemented
22#63547C412yescomplemented
23#5197—31no—
24#5195—31no—
25#5184—31no—
26#5179—31no—
27#4894—31no—
28#4853—31no—
29C3×#362—31no—
30C3×#360—31no—
31#4518D311yescharacteristic
32#4517D311yescharacteristic, complemented
33#4512—31no—
34#4512—31no—
35#4512—61no—
36#4494—31no—
37#4487—31no—
38C3×#235—21no—
39C2×C3×Dic6—21no—
40C2×C32×C8C2311yescharacteristic
41C4×C3⋊Dic3D411yescharacteristic
42C2×C3⋊(C3⋊C8)D411yescharacteristic
43C3×C4⋊Dic3—21no—
44C3×#208—21no—
45C3×Dic12—21no—
46C3×Dic12C2×C411yescharacteristic
47C3×Dic12C2×C412yes—
48C3×D24C2×C411yescharacteristic
49C3×#204—21no—
50Dic3⋊Dic3—41no—
51Dic32—41no—
52#3711—41no—
53D3×C3⋊C8—41no—
54C32×C16—21no—
55C3⋊(C3⋊C16)C2×C412yes—
56#2180—91noSylow
57C3×#135—31no—
58C2×C3×Q16—31no—
59#948—61no—
60Q8×Dic3—61no—
61#907—61no—
62C2×Dic12C2×D311yescharacteristic
63#904C2×D311yescharacteristic
64#887—61no—
65C3×M32—21no—
66C3×M32C2×D311yescharacteristic
67C3×M32C2×D311yescharacteristic
68C3×#108—31no—
69C3×#106—31no—
70#837—61no—
71#835—61no—
72#829—32no—
73#829—32no—
74#828—32no—
75#827—32no—
76#825—61no—
77#819C2×D311yescharacteristic
78#817C2×D311yescharacteristic
79#815—31no—
80#815—31no—
81#815—61no—
82#812—31no—
83#812—31no—
84#812—61no—
85#810—61no—
86C2×C32×C4C2×D411yescharacteristic
87C2×C3⋊Dic3—21no—
88C3×#67—41no—
89C2×C3×Dic3—41no—
90C2×C3×Dic3—41no—
91C3×D12—21no—
92C3×C4×D3—41no—
93C3×Dic6—21no—
94C3×Dic6—22no—
95C3×Dic6—41no—
96C32×C8C22×C411yescharacteristic
97C32×C8#4111yescharacteristic
98C3⋊(C3⋊C8)—21no—
99C3×C3⋊C8—41no—
100#510—91no—
101#444—91no—
102#441—91no—
103#365—91no—
104#362—31no—
105#360—31no—
106#347—91no—
107C3×#41—61no—
108C2×C3×Q8—61no—
109#235—21no—
110C2×Dic6—21no—
111C3×Q16—32no—
112C3×Q16—31no—
113C3×Q16—61no—
114C3×SD16—61no—
115C3×D8—31no—
116C3×M16—61no—
117C2×C3×C8—21no—
118C2×C3×C8C22×D311yescharacteristic
119C2×C3×C8C22×D311yescharacteristic
120C3×C4⋊C4—61no—
121C4⋊Dic3—21no—
122C4⋊Dic3—121no—
123Dic3⋊C4—121no—
124C4×Dic3—31no—
125C4×Dic3—31no—
126C4×Dic3—61no—
127C4×Dic3—121no—
128C4×Dic3—121no—
129#208—21no—
130#208—121no—
131C2×C3⋊C8—31no—
132C2×C3⋊C8—31no—
133C2×C3⋊C8—61no—
134C2×C3⋊C8—121no—
135Dic12—21no—
136Dic12C4×D312yes—
137Dic12C4×D311yescharacteristic
138D24C4×D311yescharacteristic
139#204—21no—
140ΓL(1,𝔽25)—121no—
141D3×C8—121no—
142C3×C16—22no—
143C3×C16—21no—
144C3×C16—21no—
145C3⋊C16—32no—
146C3⋊C16—32no—
147C3⋊C16—62no—
148C22×C32AGL(1,ℤ/8)11yescharacteristic
149C2×C3×D3—41no—
150C32×C4C4×D411yescharacteristic
151C32×C4AGL(1,ℤ/8)11yescharacteristic
152C3⋊Dic3—41no—
153C3×Dic3—42no—
154C3×Dic3—41no—
155C3×Dic3—81no—
156#135—31no—
157C2×Q16—31no—
158#131—181no—
159C4×Q8—181no—
160Q32—92no—
161SD32—92no—
162M32—91no—
163M32D3211yescharacteristic
164#108—31no—
165#106—31no—
166#104—181no—
167#103—181no—
168#97—91no—
169C3×Q8—61no—
170C3×Q8—62no—
171C3×Q8—121no—
172C3×D4—61no—
173C3×D4—121no—
174C2×C3×C4—21no—
175C2×C3×C4—121no—
176C2×C3×C4—121no—
177C2×C3×C4—121no—
178C2×C3×C4D3×D411yescharacteristic
179C2×C3×C4D3×D411yescharacteristic
180#67—41no—
181C2×Dic3—41no—
182C2×Dic3—41no—
183C2×Dic3—61no—
184C2×Dic3—61no—
185C2×Dic3—121no—
186D12—21no—
187C4×D3—41no—
188Dic6—21no—
189Dic6—22no—
190Dic6—41no—
191C3×C8—21no—
192C3×C8—21no—
193C3×C8—121no—
194C3×C8C2×C4×D311yescharacteristic
195C3×C8C2×C4×D311yescharacteristic
196C3×C8#23711yescharacteristic
197C3×C8#23711yescharacteristic
198C3⋊C8—41no—
199C3⋊C8—61no—
200C3⋊C8—61no—
201C3⋊C8—121no—
202C2×C32—21no—
203C2×C32#44211yescharacteristic
204C3×D3—81no—
205#41—61no—
206C2×Q8—61no—
207Q16—32no—
208Q16—31no—
209Q16—61no—
210SD16—61no—
211D8—31no—
212M16—61no—
213M16—361no—
214C2×C8—91no—
215C2×C8—361no—
216C2×C8C2×D3211yescharacteristic
217C4⋊C4—61no—
218C4⋊C4—361no—
219C42—91no—
220C42—361no—
221C16—21no—
222C16—92no—
223C22×C3—21no—
224C22×C3—121no—
225C22×C3#91111yescharacteristic
226C22×C3#91411yescharacteristic
227C2×D3—41no—
228C3×C4—21no—
229C3×C4—21no—
230C3×C4—121no—
231C3×C4—122no—
232C3×C4—241no—
233C3×C4#67⋊C411yescharacteristic
234C3×C4#67⋊C411yescharacteristic
235C3×C4#91111yescharacteristic
236C3×C4#91411yescharacteristic
237Dic3—42no—
238Dic3—41no—
239Dic3—81no—
240Dic3—121no—
241Dic3—121no—
242Dic3—241no—
243C32#218011yescharacteristic, complemented, Sylow
244Q8—61no—
245Q8—62no—
246Q8—121no—
247D4—61no—
248D4—121no—
249C2×C4—121no—
250C2×C4—121no—
251C2×C4—121no—
252C2×C4—181no—
253C2×C4#380211yescharacteristic
254C8—121no—
255C8—181no—
256C8C4×D3211yescharacteristic
257C8#380511yescharacteristic
258C2×C3—21no—
259C2×C3—21no—
260C2×C3—21no—
261C2×C3—41no—
262C2×C3—241no—
263C2×C3#478511yescharacteristic
264C2×C3#478511yescharacteristic
265D3—81no—
266C22—121no—
267C22#6379811yescharacteristic
268C4—121no—
269C4—122no—
270C4—241no—
271C4—361no—
272C4#6379811yescharacteristic
273C4#6390211yescharacteristic
274C3—21no—
275C3#6924811yescharacteristic, complemented
276C3#6926411yescharacteristic, complemented
277C2—21no—
278C2—241no—
279C2#1059074111yescharacteristic
subgroupG/H
centerC2#10590741
commutatorC32×C8C22×C4
FrattiniC2×C8C2×D32
FittingC32×M32C22
socleC2×C32#442
prime radicalC3×#904C22
cosocleC2×C32×C8C23
hypercenterM32D32
hypocenterC32#2180
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ M32

Complements

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

NH ≅ G/Ntype
2. #10590819C2semidirect
4. #10589378C2semidirect
6. C3×#4517C2semidirect
7. #10589138C2semidirect
21. #63550C4semidirect
22. #63547C4semidirect
32. #4517D3semidirect
243. C32#2180semidirect
275. C3#69248semidirect
276. C3#69264semidirect

Maximal subgroups

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

subgroupindex
#105909202
#105908192
#105906362
#105893782
C3×#45182
C3×#45172
#105891382
#692643
#692483