Finite Group Databasebeta

← #11797925

Subgroups — #11797925

Order 1152.

325 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 325 conjugacy classes of subgroups — too many to draw. Only its 80 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#10592894C211yesmaximal, characteristic
2C3×#5197C211yesmaximal, characteristic
3#10590810C211yesmaximal, characteristic, complemented
4C3×#4566C211yesmaximal, characteristic
5#10589138C211yesmaximal, characteristic, complemented
6#10589131C211yesmaximal, characteristic, complemented
7#10589105C211yesmaximal, characteristic, complemented
8#70928—31nomaximal
9#69248—31nomaximal
10C32×#135C2211yescharacteristic
11C2×#3746C2211yescharacteristic
12C3×#948—21no—
13#63844—21no—
14#63656C412yescomplemented
15#63654C412yescomplemented
16#63639C2211yescharacteristic
17C3×#837—21no—
18C3×#819C2211yescharacteristic
19C3×#817C2211yescharacteristic
20C3×#815C2211yescharacteristic
21C3×#812C2211yescharacteristic
22#63567—21no—
23C3×#444—31no—
24#5197D311yescharacteristic
25#5195—31no—
26#5195—31no—
27#5195—61no—
28#4853—31no—
29#4716—31no—
30C3×#360—31no—
31#4566D311yescharacteristic
32#4517—31no—
33#4512—31no—
34#4496—31no—
35#4494—31no—
36#4487—31no—
37#4466—31no—
38C32×#41—21no—
39C2×#634—21no—
40C32×Q16C2×C411yescharacteristic
41C32×SD16—21no—
42C32×D8C2×C411yescharacteristic
43C2×C32×C8C2311yescharacteristic
44#3746—21no—
45#3746C2×C412yes—
46C3×C4⋊Dic3—21no—
47C3×C4×Dic3D411yescharacteristic
48C3×#208—21no—
49C3×#208—41no—
50C2×C3×C3⋊C8—41no—
51C2×C3×C3⋊C8D411yescharacteristic
52#3724—41no—
53Dic32—41no—
54C3⋊(C3⋊C16)C2×C412yes—
55C3×C3⋊C16—21no—
56#2180—91noSylow
57C3×#135—21no—
58C3×#135C2×D311yescharacteristic
59C3×#135C2×D311yescharacteristic
60C3×#131—61no—
61#948—21no—
62C2×Dic12—31no—
63C2×Dic12—31no—
64C2×Dic12—61no—
65#887—61no—
66C4×Dic6—61no—
67C3×M32—31no—
68C3×#108—31no—
69C3×#106—31no—
70C3×#104—61no—
71C3×#97—31no—
72#837—21no—
73#829—32no—
74#829—32no—
75#829—62no—
76#827—32no—
77#827—32no—
78#827—62no—
79#819C2×D311yescharacteristic
80#817C2×D311yescharacteristic
81#816—61no—
82#815C2×D311yescharacteristic
83#812—31no—
84#812—31no—
85#812—61no—
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—41no—
94#634—22no—
95#634—41no—
96C2×C3×Dic3—21no—
97C2×C3×Dic3—41no—
98C32×C8C22×C411yescharacteristic
99C32×C8#4111yescharacteristic
100C3×C3⋊C8—21no—
101C3×C3⋊C8—41no—
102#510—91no—
103#444—31no—
104#441—91no—
105#365—91no—
106#362—91no—
107#360—31no—
108#347—91no—
109C3×#41—21no—
110C3×#41—21no—
111C3×#41—41no—
112C2×Dic6—61no—
113C2×Dic6—61no—
114C2×Dic6—121no—
115C3×Q16—21no—
116C3×Q16C4×D311yescharacteristic
117C3×Q16C4×D311yescharacteristic
118C3×SD16—21no—
119C3×SD16—21no—
120C3×SD16—41no—
121C3×D8—21no—
122C3×D8C4×D311yescharacteristic
123C3×D8C4×D311yescharacteristic
124C3×M16—61no—
125C3×M16—121no—
126C2×C3×C8—21no—
127C2×C3×C8—31no—
128C2×C3×C8—121no—
129C2×C3×C8C22×D311yescharacteristic
130C2×C3×C8C22×D311yescharacteristic
131C3×C4⋊C4—61no—
132C3×C42—31no—
133C4⋊Dic3—21no—
134Dic3⋊C4—121no—
135Dic3⋊C4—121no—
136C4×Dic3—121no—
137C4×Dic3—121no—
138C4×Dic3#6711yescharacteristic
139#208—21no—
140#208—41no—
141C2×C3⋊C8—41no—
142C2×C3⋊C8#6711yescharacteristic
143Dic12—32no—
144Dic12—32no—
145Dic12—62no—
146Dic12—61no—
147Dic12—61no—
148Dic12—121no—
149C3×C16—61no—
150C3⋊C16—21no—
151C3⋊C16—32no—
152C3⋊C16—32no—
153C3⋊C16—62no—
154C22×C32—41no—
155C22×C32AGL(1,ℤ/8)11yescharacteristic
156C32×C4—41no—
157C32×C4C4×D411yescharacteristic
158C32×C4AGL(1,ℤ/8)11yescharacteristic
159C3⋊Dic3—42no—
160C3×Dic3—41no—
161C3×Dic3—81no—
162#135D3211yescharacteristic
163C2×Q16—91no—
164#131—61no—
165C4×Q8—181no—
166Q32—92no—
167SD32—92no—
168M32—31no—
169M32—91no—
170#108—31no—
171#106—31no—
172#104—61no—
173#103—181no—
174#97—31no—
175C3×Q8—21no—
176C3×Q8—21no—
177C3×Q8—41no—
178C3×D4—21no—
179C3×D4—21no—
180C3×D4—41no—
181C3×D4—41no—
182C3×D4—41no—
183C3×D4—81no—
184C2×C3×C4—21no—
185C2×C3×C4—41no—
186C2×C3×C4—41no—
187C2×C3×C4—61no—
188C2×C3×C4—81no—
189C2×C3×C4—121no—
190C2×C3×C4D3×D411yescharacteristic
191C2×C3×C4C2×#6711yescharacteristic
192C2×Dic3—21no—
193C2×Dic3—41no—
194C2×Dic3—121no—
195C2×Dic3—121no—
196C2×Dic3—241no—
197Dic6—62no—
198Dic6—62no—
199Dic6—122no—
200Dic6—121no—
201Dic6—121no—
202Dic6—241no—
203C3×C8—21no—
204C3×C8—21no—
205C3×C8—61no—
206C3×C8—121no—
207C3×C8C2×C4×D311yescharacteristic
208C3×C8C2×C4×D311yescharacteristic
209C3×C8#23511yescharacteristic
210C3×C8#23711yescharacteristic
211C3⋊C8—21no—
212C3⋊C8—41no—
213C2×C32—21no—
214C2×C32—81no—
215C2×C32#44211yescharacteristic
216#41—21no—
217C2×Q8—181no—
218Q16—92no—
219Q16—181no—
220Q16#62411yescharacteristic
221SD16—21no—
222D8#62411yescharacteristic
223M16—61no—
224M16—121no—
225C2×C8—31no—
226C2×C8—121no—
227C2×C8C2×D3211yescharacteristic
228C4⋊C4—61no—
229C4⋊C4—361no—
230C42—31no—
231C42—361no—
232C16—61no—
233C16—92no—
234C22×C3—21no—
235C22×C3—41no—
236C22×C3—41no—
237C22×C3—81no—
238C22×C3#91111yescharacteristic
239C22×C3#94911yescharacteristic
240C3×C4—21no—
241C3×C4—21no—
242C3×C4—41no—
243C3×C4—41no—
244C3×C4—81no—
245C3×C4—121no—
246C3×C4—241no—
247C3×C4#67⋊C411yescharacteristic
248C3×C4#91411yescharacteristic
249C3×C4C4×#6711yescharacteristic
250C3×C4#93211yescharacteristic
251Dic3—41no—
252Dic3—81no—
253Dic3—122no—
254Dic3—122no—
255Dic3—242no—
256C32#218011yescharacteristic, complemented, Sylow
257Q8—21no—
258Q8—182no—
259Q8—361no—
260D4—21no—
261D4—41no—
262C2×C4—41no—
263C2×C4—61no—
264C2×C4—121no—
265C2×C4—361no—
266C2×C4D3×#6711yescharacteristic
267C8—61no—
268C8—121no—
269C8#380411yescharacteristic
270C8C2×#62411yescharacteristic
271C2×C3—21no—
272C2×C3—21no—
273C2×C3—21no—
274C2×C3—41no—
275C2×C3—81no—
276C2×C3—81no—
277C2×C3—161no—
278C2×C3#478511yescharacteristic
279C2×C3#501411yescharacteristic
280C22—41no—
281C22#6392511yescharacteristic
282C4—41no—
283C4—121no—
284C4—241no—
285C4—362no—
286C4#6393411yescharacteristic
287C4#6395211yescharacteristic
288C3—21no—
289C3#6924811yescharacteristic, complemented
290C3#7092811yescharacteristic, complemented
291C2—21no—
292C2—81no—
293C2#1059140411yescharacteristic
subgroupG/H
centerC2#10591404
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. #10590810C2semidirect
5. #10589138C2semidirect
6. #10589131C2semidirect
7. #10589105C2semidirect
14. #63656C4semidirect
15. #63654C4semidirect
256. C32#2180semidirect
289. C3#69248semidirect
290. C3#70928semidirect

Maximal subgroups

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

subgroupindex
#105928942
C3×#51972
#105908102
C3×#45662
#105891382
#105891312
#105891052
#709283
#692483