Finite Group Databasebeta

← #11797786

Subgroups — #11797786

Order 1152.

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

normal subgroups only

This group has 351 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#10592572C211yesmaximal, characteristic
2#10590818C211yesmaximal, characteristic
3C2×#63551C211yesmaximal, characteristic
4C3×#4492C211yesmaximal, characteristic
5C3×#4490C211yesmaximal, characteristic
6#10589119C211yesmaximal, characteristic
7#10589104C211yesmaximal, characteristic
8#69338—31nomaximal
9#69209—31nomaximal
10C2×#3746C2211yescharacteristic
11#64096—21no—
12C2×C3×Dic12C2211yescharacteristic
13#63843—21no—
14C32×#107C2211yescharacteristic
15C8×C3⋊Dic3C2211yescharacteristic
16#63637—21no—
17C3×#818C2211yescharacteristic
18C2×C3×C3⋊C16C2211yescharacteristic
19C2×C3×C3⋊C16C2211yescharacteristic
20#63565—21no—
21#63551C414yescomplemented
22Dic3×Q16—31no—
23C2×#829—31no—
24C2×Dic24—31no—
25#4873—31no—
26#4873—31no—
27#4873—31no—
28#4873—61no—
29C3×#367—31no—
30C3×#358—31no—
31#4503—31no—
32#4502—31no—
33#4502—31no—
34#4492—31no—
35#4492D311yescharacteristic
36#4490D311yescharacteristic
37C2×#634—21no—
38C2×C3×Dic6—21no—
39C2×C32×C8C2311yescharacteristic
40C32×C4⋊C4—21no—
41#3750—41no—
42C4×C3⋊Dic3—41no—
43C4×C3⋊Dic3D411yescharacteristic
44C2×C3⋊(C3⋊C8)D411yescharacteristic
45#3746—21no—
46#3746C2×C412yes—
47C3×C4⋊Dic3—21no—
48C3×Dic12—21no—
49C3×Dic12C2×C412yes—
50Dic3⋊Dic3—41no—
51Dic32—41no—
52C3×C3⋊C16—21no—
53C3×C3⋊C16C2×C412yes—
54#2176—91noSylow
55C2×C3×Q16—31no—
56Q8×Dic3—61no—
57C2×Dic12—31no—
58C2×Dic12—31no—
59C2×Dic12—61no—
60C2×Dic12C2×D311yescharacteristic
61#887—61no—
62#887—61no—
63#887—61no—
64#887—62no—
65C2×C3×C16—31no—
66C2×C3×C16—31no—
67C3×#107—21no—
68C3×#107—31no—
69C3×#107C2×D311yescharacteristic
70C3×#107C2×D311yescharacteristic
71#835—61no—
72#829—34no—
73#818C2×D311yescharacteristic
74C8×Dic3—31no—
75C8×Dic3—31no—
76C8×Dic3—61no—
77C2×C3⋊C16C2×D311yescharacteristic
78C2×C3⋊C16C2×D311yescharacteristic
79#810—61no—
80#810—61no—
81#810—61no—
82#810—62no—
83Dic24—34no—
84C2×C32×C4—41no—
85C2×C32×C4C2×D411yescharacteristic
86C2×C3⋊Dic3—41no—
87C2×C3⋊Dic3D811yescharacteristic
88C2×C3⋊Dic3D811yescharacteristic
89#634—22no—
90#634—41no—
91C2×C3×Dic3—41no—
92C2×C3×Dic3—41no—
93C3×Dic6—22no—
94C3×Dic6—41no—
95C32×C8C22×C411yescharacteristic
96C32×C8#4111yescharacteristic
97C3⋊(C3⋊C8)—21no—
98C2×Q32—91no—
99C4×Q16—91no—
100C4×Q16—91no—
101#367—31no—
102#358—31no—
103#358—91no—
104#346—91no—
105C2×C3×Q8—61no—
106C2×Dic6—21no—
107C2×Dic6—62no—
108C2×Dic6—61no—
109C2×Dic6—61no—
110C3×Q16—32no—
111C3×Q16—61no—
112C2×C3×C8—21no—
113C2×C3×C8C22×D311yescharacteristic
114C2×C3×C8C22×D311yescharacteristic
115C3×C4⋊C4—22no—
116C3×C4⋊C4—21no—
117C3×C4⋊C4—21no—
118C3×C4⋊C4—61no—
119C4⋊Dic3—21no—
120C4⋊Dic3—121no—
121Dic3⋊C4—121no—
122Dic3⋊C4—121no—
123Dic3⋊C4—121no—
124Dic3⋊C4—122no—
125C4×Dic3—31no—
126C4×Dic3—31no—
127C4×Dic3—61no—
128C4×Dic3—121no—
129C4×Dic3—121no—
130C4×Dic3—121no—
131C4×Dic3—121no—
132C4×Dic3—122no—
133C2×C3⋊C8—31no—
134C2×C3⋊C8—31no—
135C2×C3⋊C8—61no—
136Dic12—21no—
137Dic12—32no—
138Dic12—32no—
139Dic12—62no—
140Dic12—62no—
141Dic12—61no—
142Dic12—61no—
143Dic12C4×D312yes—
144C3×C16—32no—
145C3×C16—61no—
146C3⋊C16—21no—
147C3⋊C16C4×D312yes—
148C22×C32C2×D811yescharacteristic
149C32×C4—81no—
150C32×C4C4×D411yescharacteristic
151C32×C4#13511yescharacteristic
152C3⋊Dic3—21no—
153C3⋊Dic3—21no—
154C3⋊Dic3—42no—
155C3×Dic3—42no—
156C3×Dic3—81no—
157C2×Q16—31no—
158C2×Q16—91no—
159C4×Q8—181no—
160C4×Q8—181no—
161Q32—94no—
162C2×C16—31no—
163C2×C16—31no—
164#107—31no—
165#107D3211yescharacteristic
166#103—181no—
167#103—181no—
168C4×C8—91no—
169C3×Q8—62no—
170C3×Q8—121no—
171C2×C3×C4—21no—
172C2×C3×C4—42no—
173C2×C3×C4—41no—
174C2×C3×C4—41no—
175C2×C3×C4—121no—
176C2×C3×C4—121no—
177C2×C3×C4D3×D411yescharacteristic
178C2×C3×C4D3×D411yescharacteristic
179C2×Dic3—31no—
180C2×Dic3—31no—
181C2×Dic3—31no—
182C2×Dic3—31no—
183C2×Dic3—41no—
184C2×Dic3—41no—
185C2×Dic3—61no—
186C2×Dic3—61no—
187C2×Dic3—122no—
188C2×Dic3—121no—
189C2×Dic3—121no—
190Dic6—22no—
191Dic6—41no—
192Dic6—64no—
193Dic6—62no—
194Dic6—62no—
195Dic6—122no—
196Dic6—121no—
197Dic6—121no—
198C3×C8—21no—
199C3×C8—21no—
200C3×C8C2×C4×D311yescharacteristic
201C3×C8C2×C4×D311yescharacteristic
202C3×C8#23711yescharacteristic
203C3×C8#23911yescharacteristic
204C3⋊C8—61no—
205C3⋊C8—61no—
206C3⋊C8—121no—
207C2×C32C4×D811yescharacteristic
208C2×C32#51011yescharacteristic
209C2×C32#51011yescharacteristic
210C2×Q8—61no—
211C2×Q8—181no—
212Q16—32no—
213Q16—61no—
214Q16—92no—
215Q16—181no—
216C2×C8—91no—
217C2×C8C2×D3211yescharacteristic
218C4⋊C4—21no—
219C4⋊C4—61no—
220C4⋊C4—361no—
221C4⋊C4—361no—
222C42—91no—
223C42—361no—
224C42—361no—
225C16—32no—
226C16—61no—
227C22×C3—21no—
228C22×C3D3×D811yescharacteristic
229C22×C3D3×D811yescharacteristic
230C3×C4—21no—
231C3×C4—21no—
232C3×C4—82no—
233C3×C4—81no—
234C3×C4—81no—
235C3×C4—122no—
236C3×C4—241no—
237C3×C4#67⋊C411yescharacteristic
238C3×C4#89311yescharacteristic
239C3×C4#91611yescharacteristic
240C3×C4#91911yescharacteristic
241Dic3—42no—
242Dic3—62no—
243Dic3—61no—
244Dic3—61no—
245Dic3—61no—
246Dic3—61no—
247Dic3—81no—
248Dic3—121no—
249Dic3—124no—
250Dic3—122no—
251Dic3—122no—
252C32#217611yescharacteristic, complemented, Sylow
253Q8—62no—
254Q8—121no—
255Q8—182no—
256Q8—361no—
257C2×C4—41no—
258C2×C4—91no—
259C2×C4—91no—
260C2×C4—121no—
261C2×C4—121no—
262C2×C4—361no—
263C2×C4#381111yescharacteristic
264C8—181no—
265C8#379611yescharacteristic
266C8C4×D3211yescharacteristic
267C2×C3—21no—
268C2×C3—21no—
269C2×C3—21no—
270C2×C3#475611yescharacteristic
271C2×C3#487211yescharacteristic
272C2×C3#491511yescharacteristic
273C2×C3#491511yescharacteristic
274C2×C3#491511yescharacteristic
275C2×C3#491811yescharacteristic
276C22#6392611yescharacteristic
277C4—81no—
278C4—122no—
279C4—181no—
280C4—181no—
281C4—241no—
282C4—362no—
283C4#6388111yescharacteristic
284C4#6395011yescharacteristic
285C3—21no—
286C3#6920911yescharacteristic, complemented
287C3#6933811yescharacteristic, complemented
288C2#1059045911yescharacteristic
289C2#1059103011yescharacteristic
290C2#1059105011yescharacteristic
subgroupG/H
centerC22#63926
commutatorC32×C8C22×C4
FrattiniC2×C8C2×D32
FittingC32×#107C22
socle, prime radicalC22×C32C2×D8
cosocleC2×C32×C8C23
hypercenter#107D32
hypocenterC32#2176
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #107

Complements

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

NH ≅ G/Ntype
21. #63551C4semidirect
252. C32#2176semidirect
286. C3#69209semidirect
287. C3#69338semidirect

Maximal subgroups

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

subgroupindex
#105925722
#105908182
C2×#635512
C3×#44922
C3×#44902
#105891192
#105891042
#693383
#692093