Finite Group Databasebeta

← #11797921

Subgroups — #11797921

Order 1152.

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

normal subgroups only

This group has 338 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#10592552C211yesmaximal, characteristic, complemented
2#10590920C211yesmaximal, characteristic
3#10590638C211yesmaximal, characteristic
4C3×#4488C211yesmaximal, characteristic
5C3×#4487C211yesmaximal, characteristic, complemented
6#10589131C211yesmaximal, characteristic, complemented
7#10589106C211yesmaximal, characteristic, complemented
8#69309—31nomaximal
9#69248—31nomaximal
10C2×#3746C2211yescharacteristic
11#64096—21no—
12C3×#904C2211yescharacteristic
13#63815—21no—
14C32×#106C2211yescharacteristic
15#63642C2211yescharacteristic
16#63637—21no—
17C3×#819C2211yescharacteristic
18C3×#812C2211yescharacteristic
19C3×#812C2211yescharacteristic
20#63568—21no—
21#63551C412yescomplemented
22#63548C412yescomplemented
23#5197—31no—
24#5195—31no—
25#4909—31no—
26#4894—31no—
27#4853—31no—
28#4853—31no—
29#4853—61no—
30C3×#365—31no—
31C3×#360—31no—
32#4517—31no—
33#4512—31no—
34#4512—31no—
35#4496—31no—
36#4488D311yescharacteristic
37#4487D311yescharacteristic, complemented
38C2×#634—21no—
39C3×#235—21no—
40C2×C32×C8C2311yescharacteristic
41C32×C4⋊C4—21no—
42#3750—41no—
43C4×C3⋊Dic3—41no—
44C4×C3⋊Dic3D411yescharacteristic
45C2×C3⋊(C3⋊C8)D411yescharacteristic
46#3746—21no—
47#3746C2×C412yes—
48C3×#208—21no—
49C3×Dic12C2×C411yescharacteristic
50C3×D24C2×C411yescharacteristic
51C3×#204—21no—
52#3711—41no—
53D3×C3⋊C8—41no—
54C3×C3⋊C16—21no—
55C3×C3⋊C16C2×C412yes—
56#2180—91noSylow
57C3×#135—31no—
58#948—61no—
59#907—61no—
60C2×Dic12—31no—
61C2×Dic12—31no—
62C2×Dic12—61no—
63#904C2×D311yescharacteristic
64#887—61no—
65#887—61no—
66#887—62no—
67C3×M32—31no—
68C3×M32—31no—
69C3×#108—31no—
70C3×#106—21no—
71C3×#106C2×D311yescharacteristic
72C3×#106C2×D311yescharacteristic
73#837—61no—
74#829—32no—
75#827—32no—
76#825—61no—
77#819C2×D311yescharacteristic
78#815—31no—
79#815—31no—
80#815—61no—
81#812C2×D311yescharacteristic
82#812C2×D311yescharacteristic
83#810—61no—
84#810—61no—
85#810—62no—
86Dic24—32no—
87#800—32no—
88C2×C32×C4—41no—
89C2×C32×C4C2×D411yescharacteristic
90C2×C3⋊Dic3—21no—
91C2×C3⋊Dic3—41no—
92#634—22no—
93#634—41no—
94C3×#67—41no—
95C3×D12—21no—
96C3×C4×D3—41no—
97C3×Dic6—21no—
98C32×C8C22×C411yescharacteristic
99C32×C8#4111yescharacteristic
100C3⋊(C3⋊C8)—21no—
101C3×C3⋊C8—41no—
102#510—91no—
103#444—91no—
104#441—91no—
105#365—31no—
106#362—91no—
107#360—31no—
108#347—91no—
109C3×#41—61no—
110#235—21no—
111C2×Dic6—62no—
112C2×Dic6—61no—
113C2×Dic6—61no—
114C3×Q16—31no—
115C3×SD16—61no—
116C3×D8—31no—
117C3×M16—61no—
118C2×C3×C8—21no—
119C2×C3×C8C22×D311yescharacteristic
120C2×C3×C8C22×D311yescharacteristic
121C3×C4⋊C4—22no—
122C3×C4⋊C4—21no—
123C3×C4⋊C4—21no—
124Dic3⋊C4—122no—
125Dic3⋊C4—121no—
126Dic3⋊C4—121no—
127C4×Dic3—31no—
128C4×Dic3—31no—
129C4×Dic3—61no—
130C4×Dic3—122no—
131C4×Dic3—121no—
132C4×Dic3—121no—
133#208—21no—
134#208—121no—
135C2×C3⋊C8—31no—
136C2×C3⋊C8—31no—
137C2×C3⋊C8—61no—
138C2×C3⋊C8—121no—
139Dic12—32no—
140Dic12—32no—
141Dic12—62no—
142Dic12—62no—
143Dic12—61no—
144Dic12—61no—
145Dic12C4×D311yescharacteristic
146D24C4×D311yescharacteristic
147#204—21no—
148ΓL(1,𝔽25)—121no—
149D3×C8—121no—
150C3×C16—32no—
151C3×C16—61no—
152C3⋊C16—21no—
153C3⋊C16C4×D312yes—
154C22×C32AGL(1,ℤ/8)11yescharacteristic
155C2×C3×D3—41no—
156C32×C4—81no—
157C32×C4C4×D411yescharacteristic
158C32×C4AGL(1,ℤ/8)11yescharacteristic
159C3⋊Dic3—41no—
160C3⋊Dic3—42no—
161C3×Dic3—41no—
162#135—31no—
163C2×Q16—91no—
164#131—181no—
165C4×Q8—181no—
166Q32—92no—
167SD32—92no—
168M32—31no—
169M32—31no—
170#108—31no—
171#106D3211yescharacteristic
172#104—181no—
173#103—181no—
174#97—91no—
175C3×Q8—61no—
176C3×D4—61no—
177C3×D4—121no—
178C2×C3×C4—21no—
179C2×C3×C4—42no—
180C2×C3×C4—41no—
181C2×C3×C4—41no—
182C2×C3×C4—121no—
183C2×C3×C4D3×D411yescharacteristic
184C2×C3×C4D3×D411yescharacteristic
185#67—41no—
186C2×Dic3—62no—
187C2×Dic3—61no—
188C2×Dic3—61no—
189C2×Dic3—122no—
190C2×Dic3—121no—
191C2×Dic3—121no—
192D12—21no—
193C4×D3—41no—
194Dic6—21no—
195Dic6—64no—
196Dic6—62no—
197Dic6—62no—
198Dic6—122no—
199Dic6—121no—
200Dic6—121no—
201C3×C8—21no—
202C3×C8—21no—
203C3×C8—121no—
204C3×C8C2×C4×D311yescharacteristic
205C3×C8C2×C4×D311yescharacteristic
206C3×C8#23711yescharacteristic
207C3×C8#23911yescharacteristic
208C3⋊C8—41no—
209C3⋊C8—61no—
210C3⋊C8—61no—
211C3⋊C8—121no—
212C2×C32—21no—
213C2×C32#44211yescharacteristic
214C3×D3—81no—
215#41—61no—
216C2×Q8—181no—
217Q16—31no—
218Q16—92no—
219Q16—181no—
220SD16—61no—
221D8—31no—
222M16—61no—
223M16—361no—
224C2×C8—91no—
225C2×C8—361no—
226C2×C8C2×D3211yescharacteristic
227C4⋊C4—21no—
228C4⋊C4—361no—
229C42—91no—
230C42—361no—
231C16—32no—
232C16—61no—
233C22×C3—21no—
234C22×C3—121no—
235C22×C3#91111yescharacteristic
236C22×C3#91411yescharacteristic
237C2×D3—41no—
238C3×C4—21no—
239C3×C4—21no—
240C3×C4—82no—
241C3×C4—81no—
242C3×C4—81no—
243C3×C4—121no—
244C3×C4#67⋊C411yescharacteristic
245C3×C4#89311yescharacteristic
246C3×C4#91411yescharacteristic
247C3×C4#91411yescharacteristic
248Dic3—41no—
249Dic3—124no—
250Dic3—122no—
251Dic3—121no—
252Dic3—121no—
253Dic3—122no—
254Dic3—122no—
255C32#218011yescharacteristic, complemented, Sylow
256Q8—61no—
257Q8—182no—
258Q8—361no—
259D4—61no—
260D4—121no—
261C2×C4—41no—
262C2×C4—121no—
263C2×C4—181no—
264C2×C4—361no—
265C2×C4#381111yescharacteristic
266C8—121no—
267C8—181no—
268C8#379611yescharacteristic
269C8C4×D3211yescharacteristic
270C2×C3—22no—
271C2×C3—21no—
272C2×C3—21no—
273C2×C3—21no—
274C2×C3—241no—
275C2×C3#478511yescharacteristic
276C2×C3#486911yescharacteristic
277D3—81no—
278C22—121no—
279C22#6393711yescharacteristic
280C4—81no—
281C4—121no—
282C4—361no—
283C4—362no—
284C4#6388111yescharacteristic
285C4#6394111yescharacteristic
286C3—21no—
287C3#6924811yescharacteristic, complemented
288C3#6930911yescharacteristic, complemented
289C2—21no—
290C2—241no—
291C2#1059046211yescharacteristic
subgroupG/H
centerC2#10590462
commutatorC32×C8C22×C4
FrattiniC2×C8C2×D32
FittingC32×#106C22
socleC2×C32#442
prime radicalC3×#904C22
cosocleC2×C32×C8C23
hypercenter#106D32
hypocenterC32#2180
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #106

Complements

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

NH ≅ G/Ntype
1. #10592552C2semidirect
5. C3×#4487C2semidirect
6. #10589131C2semidirect
7. #10589106C2semidirect
21. #63551C4semidirect
22. #63548C4semidirect
37. #4487D3semidirect
255. C32#2180semidirect
287. C3#69248semidirect
288. C3#69309semidirect

Maximal subgroups

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

subgroupindex
#105925522
#105909202
#105906382
C3×#44882
C3×#44872
#105891312
#105891062
#693093
#692483