Finite Group Databasebeta

← #11799988

Subgroups — #11799988

Order 1152.

299 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 299 conjugacy classes of subgroups — too many to draw. Only its 68 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
1C3×#5159C211yesmaximal, characteristic
2#10590912C211yesmaximal, characteristic, complemented
3#10589429C211yesmaximal, characteristic, complemented
4C3×#4563C211yesmaximal, characteristic, complemented
5#10589138C211yesmaximal, characteristic, complemented
6#10589136C211yesmaximal, characteristic, complemented
7#10589109C211yesmaximal, characteristic, complemented
8#71088—31nomaximal
9#69257—31nomaximal
10C2×C32×D8C2211yescharacteristic
11C3×#938—21no—
12C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
13D3×#208—21no—
14#63646C2211yescharacteristic
15#63639C2211yescharacteristic
16C3×#832—21no—
17C3×#819C2211yescharacteristic
18C3×#817C2211yescharacteristic
19C3×#812C2211yescharacteristic
20#63577—21no—
21C3×#469—31no—
22#5159D311yescharacteristic
23#5125—31no—
24#4893—31no—
25C3×#361—31no—
26#4563—31no—
27#4563—31no—
28#4563—61no—
29#4563D311yescharacteristic, complemented
30#4553—31no—
31#4514—31no—
32#4513—31no—
33#4494—31no—
34#4487—31no—
35#4487—31no—
36C2×C32×D4—21no—
37C2×C3×#67—41no—
38C2×C3×C4×D3D411yescharacteristic
39C32×D8—21no—
40C32×D8—21no—
41C2×C32×C8C2311yescharacteristic
42#3748—21no—
43C3×#217—41no—
44C3×C4⋊Dic3—21no—
45C3×#208—21no—
46C2×C3×C3⋊C8D411yescharacteristic
47C3×ΓL(1,𝔽25)—21no—
48C3×ΓL(1,𝔽25)—21no—
49#3711—41no—
50D3×C3⋊C8—41no—
51C3⋊(C3⋊C16)—21no—
52C3×C3⋊C16—21no—
53#2238—91noSylow
54C2×C3×D8—21no—
55C2×C3×D8C2×D311yescharacteristic
56C2×C3×D8C2×D311yescharacteristic
57C2×C3×M16—31no—
58C3×#121—61no—
59#938—21no—
60C2×#208—61no—
61D3×M16—61no—
62C2×ΓL(1,𝔽25)C2×D311yescharacteristic
63C3×M32—31no—
64C3×#108—31no—
65C3×#106—31no—
66C3×#102—61no—
67#832—21no—
68#822—61no—
69#819—31no—
70#819—31no—
71#819—61no—
72#819—61no—
73#819C2×D311yescharacteristic
74#817C2×D311yescharacteristic
75#812—31no—
76#812—31no—
77#812—61no—
78#812C2×D311yescharacteristic
79C23×C32—41no—
80C22×C3×D3SD1611yescharacteristic
81C32×D4—41no—
82C32×D4—41no—
83C2×C32×C4C2×D411yescharacteristic
84C3×#67—82no—
85C2×C3×Dic3—41no—
86C2×C3×Dic3SD1611yescharacteristic
87C3×C4×D3—21no—
88C3×C4×D3—21no—
89C32×C8#4111yescharacteristic
90C32×C8#4111yescharacteristic
91C3⋊(C3⋊C8)—41no—
92C3×C3⋊C8—21no—
93C3×C3⋊C8—41no—
94#469—31no—
95#430—91no—
96#365—91no—
97#365—91no—
98#361—31no—
99#361—91no—
100#349—91no—
101C2×C3×D4—21no—
102C2×C3×D4—21no—
103C2×C3×D4—41no—
104C2×C3×D4—121no—
105C22×C3×C4—31no—
106C2×#67—41no—
107C2×C4×D3#6711yescharacteristic
108C3×D8—22no—
109C3×D8—21no—
110C3×D8—21no—
111C3×D8—21no—
112C3×D8—21no—
113C3×D8—41no—
114C3×M16—61no—
115C3×M16—61no—
116C3×M16—61no—
117C2×C3×C8—21no—
118C2×C3×C8—31no—
119C2×C3×C8C22×D311yescharacteristic
120C2×C3×C8C22×D311yescharacteristic
121C3×C4⋊C4—61no—
122C3×C22⋊C4—121no—
123#217—41no—
124C4⋊Dic3—21no—
125#208—21no—
126#208—61no—
127#208—61no—
128#208—121no—
129#208—121no—
130C2×C3⋊C8—121no—
131C2×C3⋊C8#6711yescharacteristic
132ΓL(1,𝔽25)—21no—
133ΓL(1,𝔽25)—21no—
134ΓL(1,𝔽25)—121no—
135D3×C8—121no—
136C3×C16—61no—
137C3⋊C16—21no—
138C3⋊C16—61no—
139C3⋊C16—61no—
140C3⋊C16—121no—
141C22×C32—81no—
142C22×C32—81no—
143C22×C32—81no—
144C22×C32C2×SD1611yescharacteristic
145C2×C3×D3—21no—
146C2×C3×D3—41no—
147C32×C4#12311yescharacteristic
148C32×C4AGL(1,ℤ/8)11yescharacteristic
149C3×Dic3—21no—
150C3×Dic3—81no—
151C2×D8D3211yescharacteristic
152C2×M16—31no—
153C2×M16—181no—
154#121—61no—
155M32—31no—
156M32—91no—
157#108—31no—
158#108—91no—
159#108—181no—
160#106—31no—
161#102—61no—
162C23×C3—31no—
163C23×C3—41no—
164C23×C3—41no—
165C23×C3—81no—
166C22×D3#21411yescharacteristic
167C3×D4—42no—
168C3×D4—41no—
169C3×D4—41no—
170C3×D4—41no—
171C3×D4—41no—
172C3×D4—81no—
173C3×D4—242no—
174C2×C3×C4—21no—
175C2×C3×C4—31no—
176C2×C3×C4—61no—
177C2×C3×C4—61no—
178C2×C3×C4—121no—
179C2×C3×C4D3×D411yescharacteristic
180C2×C3×C4C2×#6711yescharacteristic
181#67—82no—
182C2×Dic3—41no—
183C2×Dic3#21411yescharacteristic
184C4×D3—21no—
185C4×D3—21no—
186C3×C8—21no—
187C3×C8—21no—
188C3×C8—61no—
189C3×C8—121no—
190C3×C8#23511yescharacteristic
191C3×C8#23711yescharacteristic
192C3×C8#23711yescharacteristic
193C3×C8#23711yescharacteristic
194C3⋊C8—21no—
195C3⋊C8—41no—
196C3⋊C8—121no—
197C3⋊C8—121no—
198C3⋊C8—241no—
199C2×C32—21no—
200C2×C32—161no—
201C2×C32#48111yescharacteristic
202C3×D3—41no—
203C2×D4—21no—
204C2×D4—121no—
205C22×C4—31no—
206D8—21no—
207D8—21no—
208M16—61no—
209M16—61no—
210M16—61no—
211M16—181no—
212M16—361no—
213C2×C8—31no—
214C2×C8—361no—
215C2×C8C2×D3211yescharacteristic
216C4⋊C4—61no—
217C22⋊C4—121no—
218C16—61no—
219C16—181no—
220C22×C3—21no—
221C22×C3—61no—
222C22×C3—81no—
223C22×C3—82no—
224C22×C3—81no—
225C22×C3—81no—
226C22×C3—81no—
227C22×C3—81no—
228C22×C3—81no—
229C22×C3—121no—
230C22×C3—161no—
231C22×C3—161no—
232C22×C3D3×SD1611yescharacteristic
233C22×C3C2×#21411yescharacteristic
234C2×D3—21no—
235C2×D3—41no—
236C3×C4—21no—
237C3×C4—21no—
238C3×C4—61no—
239C3×C4—241no—
240C3×C4#88311yescharacteristic
241C3×C4#91111yescharacteristic
242C3×C4#93511yescharacteristic
243C3×C4#94911yescharacteristic
244Dic3—21no—
245Dic3—81no—
246C32#223811yescharacteristic, complemented, Sylow
247C23—31no—
248C23—41no—
249D4—41no—
250D4—41no—
251D4—242no—
252C2×C4—31no—
253C2×C4—61no—
254C2×C4—61no—
255C2×C4—121no—
256C2×C4D3×#6711yescharacteristic
257C8—61no—
258C8—121no—
259C8—361no—
260C8#380411yescharacteristic
261C8#380511yescharacteristic
262C2×C3—21no—
263C2×C3—21no—
264C2×C3—21no—
265C2×C3—41no—
266C2×C3—121no—
267C2×C3—162no—
268C2×C3—161no—
269C2×C3—161no—
270C2×C3#477711yescharacteristic
271C2×C3#503411yescharacteristic
272D3—41no—
273C22—61no—
274C22—81no—
275C22—81no—
276C22—81no—
277C22—121no—
278C22D3×#21411yescharacteristic
279C4—61no—
280C4—241no—
281C4#6392511yescharacteristic
282C4#6396911yescharacteristic
283C3—21no—
284C3#6925711yescharacteristic, complemented
285C3#7108811yescharacteristic, complemented
286C2—21no—
287C2—121no—
288C2—161no—
289C2#1059141511yescharacteristic
subgroupG/H
centerC2#10591415
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC2×C32×D8C22
socleC2×C32#481
prime radicalC3×#5159C2
hypercenterC2×D8D32
hypocenterC32#2238
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
2. #10590912C2semidirect
3. #10589429C2semidirect
4. C3×#4563C2semidirect
5. #10589138C2semidirect
6. #10589136C2semidirect
7. #10589109C2semidirect
29. #4563D3semidirect
246. C32#2238semidirect
284. C3#69257semidirect
285. C3#71088semidirect

Maximal subgroups

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

subgroupindex
C3×#51592
#105909122
#105894292
C3×#45632
#105891382
#105891362
#105891092
#710883
#692573