Finite Group Databasebeta

← #11799040

Subgroups — #11799040

Order 1152.

371 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 371 conjugacy classes of subgroups — too many to draw. Only its 74 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, complemented
2#10590869C211yesmaximal, characteristic
3C2×#63551C211yesmaximal, characteristic, complemented
4C2×#63548C211yesmaximal, characteristic
5C3×#4492C211yesmaximal, characteristic, complemented
6C3×#4491C211yesmaximal, characteristic
7#10589133C211yesmaximal, characteristic, complemented
8#69237—31nomaximal
9#69205—31nomaximal
10C2×#3746C2211yescharacteristic
11#64096—21no—
12C2×C3×Dic12C2211yescharacteristic
13C2×C3×D24C2211yescharacteristic
14#63863—21no—
15C2×#3715—21no—
16C32×#107C2211yescharacteristic
17C8×C3⋊Dic3C2211yescharacteristic
18#63637—21no—
19C2×C3×C3⋊C16C2211yescharacteristic
20C2×C3×C3⋊C16C2211yescharacteristic
21#63551—22no—
22#63548—22no—
23#5191—31no—
24C2×#829—31no—
25#5155—31no—
26C2×#827—31no—
27C2×Dic24—31no—
28C2×#800—31no—
29#4873—31no—
30#4873—31no—
31#4873—61no—
32C3×#358—31no—
33C3×#357—31no—
34Dic3⋊C16—31no—
35Dic3⋊C16—31no—
36#4492D311yescharacteristic, complemented
37#4491D311yescharacteristic
38C2×#634—21no—
39C2×C3×D12—21no—
40C2×C3×Dic6—21no—
41C2×C32×C8C2311yescharacteristic
42C32×C4⋊C4—21no—
43#3750—41no—
44C4×C3⋊Dic3—41no—
45C4×C3⋊Dic3D411yescharacteristic
46C2×C3⋊(C3⋊C8)D411yescharacteristic
47#3746—21no—
48#3746D412yes—
49C3×Dic12—21no—
50C3×Dic12—21no—
51C3×D24—21no—
52C3×D24—21no—
53(C2×D3)⋊Dic3—41no—
54(C2×D3)⋊Dic3—41no—
55#3715—42no—
56C3×C3⋊C16—21no—
57C3×C3⋊C16—21no—
58#2211—91noSylow
59C2×C3×Q16—31no—
60C2×C3×D8—31no—
61#947—61no—
62C2×#215—61no—
63#936—61no—
64C2×#214—61no—
65C2×Dic12—31no—
66C2×Dic12—31no—
67C2×Dic12—61no—
68C2×Dic12C2×D311yescharacteristic
69C2×D24C2×D311yescharacteristic
70#887—61no—
71#887—61no—
72#887—62no—
73C2×C3×C16—31no—
74C2×C3×C16—31no—
75C3×#107—21no—
76C3×#107C2×D311yescharacteristic
77C3×#107C2×D311yescharacteristic
78#829—62no—
79#827—62no—
80C8×Dic3—31no—
81C8×Dic3—31no—
82C8×Dic3—61no—
83C2×C3⋊C16C2×D311yescharacteristic
84C2×C3⋊C16C2×D311yescharacteristic
85#810—61no—
86#810—61no—
87#810—62no—
88Dic24—62no—
89#800—62no—
90C22×C3×D3—41no—
91C2×C32×C4—41no—
92C2×C32×C4C2×D411yescharacteristic
93C2×C3⋊Dic3—41no—
94C2×C3⋊Dic3D811yescharacteristic
95C2×C3⋊Dic3D811yescharacteristic
96#634—22no—
97#634—41no—
98C2×C3×Dic3—41no—
99C3×D12—41no—
100C3×D12—41no—
101C3×Dic6—41no—
102C3×Dic6—41no—
103C32×C8C2×D411yescharacteristic
104C32×C8#4111yescharacteristic
105C3⋊(C3⋊C8)—21no—
106C2×Q32—91no—
107C2×SD32—91no—
108#495—91no—
109C4×Q16—91no—
110C4⋊C16—91no—
111#358—31no—
112#357—31no—
113C2×C3×Q8—61no—
114C2×C3×D4—61no—
115C2×D12—21no—
116C2×Dic6—21no—
117C2×Dic6—62no—
118C2×Dic6—61no—
119C2×Dic6—61no—
120C3×Q16—61no—
121C3×Q16—61no—
122C3×D8—61no—
123C3×D8—61no—
124C2×C3×C8—21no—
125C2×C3×C8C22×D311yescharacteristic
126C2×C3×C8C22×D311yescharacteristic
127C3×C4⋊C4—22no—
128C3×C4⋊C4—21no—
129C3×C4⋊C4—21no—
130#217—121no—
131#217—121no—
132#215—122no—
133#214—122no—
134(C2×D3)⋊C4—121no—
135(C2×D3)⋊C4—121no—
136Dic3⋊C4—121no—
137Dic3⋊C4—121no—
138Dic3⋊C4—122no—
139C4×Dic3—31no—
140C4×Dic3—31no—
141C4×Dic3—61no—
142C4×Dic3—121no—
143C4×Dic3—121no—
144C4×Dic3—122no—
145C2×C3⋊C8—31no—
146C2×C3⋊C8—31no—
147C2×C3⋊C8—61no—
148Dic12—21no—
149Dic12—21no—
150Dic12—32no—
151Dic12—32no—
152Dic12—62no—
153Dic12—62no—
154Dic12—61no—
155Dic12—61no—
156D24—21no—
157D24—21no—
158C3×C16—61no—
159C3×C16—61no—
160C3⋊C16—21no—
161C3⋊C16—21no—
162C22×C32C2×D811yescharacteristic
163C2×C3×D3—81no—
164C2×C3×D3—81no—
165C2×C3×D3—81no—
166C32×C4—81no—
167C32×C4#12111yescharacteristic
168C32×C4AGL(1,ℤ/8)11yescharacteristic
169C3⋊Dic3—21no—
170C3⋊Dic3—21no—
171C3⋊Dic3—42no—
172C3×Dic3—81no—
173C2×Q16—31no—
174C2×Q16—91no—
175C2×SD16—181no—
176C2×D8—31no—
177#124—181no—
178C4×Q8—181no—
179Q32—182no—
180SD32—182no—
181C2×C16—31no—
182C2×C16—31no—
183#107D3211yescharacteristic
184#103—181no—
185C4×C8—91no—
186C23×C3—121no—
187C22×D3—41no—
188C3×Q8—121no—
189C3×Q8—121no—
190C3×D4—121no—
191C3×D4—121no—
192C2×C3×C4—21no—
193C2×C3×C4—42no—
194C2×C3×C4—41no—
195C2×C3×C4—41no—
196C2×C3×C4—121no—
197C2×C3×C4D3×D411yescharacteristic
198C2×C3×C4D3×D411yescharacteristic
199C2×Dic3—31no—
200C2×Dic3—31no—
201C2×Dic3—31no—
202C2×Dic3—31no—
203C2×Dic3—41no—
204C2×Dic3—61no—
205C2×Dic3—61no—
206C2×Dic3—122no—
207C2×Dic3—121no—
208C2×Dic3—121no—
209D12—41no—
210D12—41no—
211Dic6—41no—
212Dic6—41no—
213Dic6—64no—
214Dic6—62no—
215Dic6—62no—
216Dic6—122no—
217Dic6—121no—
218Dic6—121no—
219C3×C8—21no—
220C3×C8—21no—
221C3×C8#23511yescharacteristic
222C3×C8#23511yescharacteristic
223C3×C8D3×D411yescharacteristic
224C3×C8D3×D411yescharacteristic
225C3⋊C8—61no—
226C3⋊C8—61no—
227C3⋊C8—121no—
228C2×C32#45911yescharacteristic
229C2×C32#50811yescharacteristic
230C2×C32#51011yescharacteristic
231C3×D3—161no—
232C2×Q8—61no—
233C2×Q8—181no—
234C2×D4—61no—
235Q16—61no—
236Q16—61no—
237Q16—92no—
238Q16—181no—
239SD16—362no—
240D8—61no—
241D8—61no—
242C2×C8—91no—
243C2×C8C2×D3211yescharacteristic
244C4⋊C4—21no—
245C4⋊C4—361no—
246C22⋊C4—361no—
247C22⋊C4—361no—
248C42—91no—
249C42—361no—
250C16—61no—
251C16—61no—
252C22×C3—21no—
253C22×C3—241no—
254C22×C3—241no—
255C22×C3—241no—
256C22×C3D3×D811yescharacteristic
257C22×C3D3×D811yescharacteristic
258C2×D3—81no—
259C2×D3—81no—
260C2×D3—81no—
261C3×C4—21no—
262C3×C4—21no—
263C3×C4—82no—
264C3×C4—81no—
265C3×C4—81no—
266C3×C4—241no—
267C3×C4#88411yescharacteristic
268C3×C4#88411yescharacteristic
269C3×C4#91411yescharacteristic
270C3×C4#91411yescharacteristic
271Dic3—62no—
272Dic3—61no—
273Dic3—61no—
274Dic3—61no—
275Dic3—61no—
276Dic3—81no—
277Dic3—121no—
278Dic3—124no—
279Dic3—122no—
280Dic3—122no—
281C32#221111yescharacteristic, complemented, Sylow
282C23—121no—
283Q8—121no—
284Q8—121no—
285Q8—182no—
286Q8—361no—
287D4—121no—
288D4—121no—
289C2×C4—41no—
290C2×C4—91no—
291C2×C4—91no—
292C2×C4—121no—
293C2×C4—361no—
294C2×C4#381111yescharacteristic
295C8—181no—
296C8#379811yescharacteristic
297C8#380211yescharacteristic
298C2×C3—21no—
299C2×C3—21no—
300C2×C3—21no—
301C2×C3—481no—
302C2×C3#478611yescharacteristic
303C2×C3#478611yescharacteristic
304C2×C3#491211yescharacteristic
305C2×C3#491511yescharacteristic
306C2×C3#491611yescharacteristic
307C2×C3#491811yescharacteristic
308D3—161no—
309C22—241no—
310C22—241no—
311C22—241no—
312C22#6392611yescharacteristic
313C4—81no—
314C4—181no—
315C4—181no—
316C4—241no—
317C4—362no—
318C4#6391211yescharacteristic
319C4#6394111yescharacteristic
320C3—21no—
321C3#6920511yescharacteristic, complemented
322C3#6923711yescharacteristic, complemented
323C2—481no—
324C2#1059055111yescharacteristic
325C2#1059103511yescharacteristic
326C2#1059105011yescharacteristic
subgroupG/H
centerC22#63926
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC32×#107C22
socleC22×C32C2×D8
prime radicalC2×C3×D24C22
hypercenter#107D32
hypocenterC32#2211
LCSG ▷ C2×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
1. #10592572C2semidirect
3. C2×#63551C2semidirect
5. C3×#4492C2semidirect
7. #10589133C2semidirect
36. #4492D3semidirect
281. C32#2211semidirect
321. C3#69205semidirect
322. C3#69237semidirect

Maximal subgroups

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

subgroupindex
#105925722
#105908692
C2×#635512
C2×#635482
C3×#44922
C3×#44912
#105891332
#692373
#692053