Finite Group Databasebeta

← #11799030

Subgroups — #11799030

Order 1152.

361 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 361 conjugacy classes of subgroups — too many to draw. Only its 84 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
1C2×#63655C211yesmaximal, characteristic
2C3×Dic3×Q16C211yesmaximal, characteristic, complemented
3C2×C3×#829C211yesmaximal, characteristic, complemented
4#10590865C211yesmaximal, characteristic
5Dic3⋊(C3⋊C16)C211yesmaximal, characteristic, complemented
6#10589117C211yesmaximal, characteristic, complemented
7#10589116C211yesmaximal, characteristic
8#71498—31nomaximal
9#70915—31nomaximal
10C2×C32×Q16C2211yescharacteristic
11C2×#3745C2211yescharacteristic
12C3×Q8×Dic3—21no—
13C2×C3×Dic12C2211yescharacteristic
14#63864—21no—
15C2×#3717—21no—
16#63655—22no—
17C2×C3⋊(C3⋊C16)C2211yescharacteristic
18C3×#835—21no—
19C3×#829—22no—
20C3×#818C2211yescharacteristic
21C3×C8×Dic3C2211yescharacteristic
22C2×C3×C3⋊C16C2211yescharacteristic
23C2×C3×Q32—31no—
24C3×C4×Q16—31no—
25#5191—31no—
26Dic3×Q16D311yescharacteristic, complemented
27C2×#829D311yescharacteristic, complemented
28C2×#828—31no—
29C2×#828—31no—
30C2×#828—61no—
31#4696—31no—
32#4564—31no—
33#4509—31no—
34Dic3⋊C16—31no—
35#4492—31no—
36#4491—31no—
37C4⋊(C3⋊C16)—31no—
38C2×C32×Q8—21no—
39C2×C4⋊(C3⋊D3)—21no—
40C2×C3×Dic6—21no—
41C32×Q16—21no—
42C32×Q16D412yes—
43C2×C32×C8C2311yescharacteristic
44#3745—21no—
45#3745—21no—
46C3×C4⋊Dic3—21no—
47C3×C4⋊Dic3—41no—
48C3×C4×Dic3—41no—
49C3×C4×Dic3D411yescharacteristic
50C2×C3×C3⋊C8D411yescharacteristic
51C3×Dic12—21no—
52C3×Dic12—21no—
53#3722—41no—
54#3722—41no—
55#3717—42no—
56C3⋊(C3⋊C16)—21no—
57C3×C3⋊C16—21no—
58#2211—91noSylow
59C2×C3×Q16—21no—
60C2×C3×Q16—31no—
61C2×C3×Q16C2×D311yescharacteristic
62C2×C3×Q16C2×D311yescharacteristic
63C3×C4×Q8—61no—
64#947—61no—
65Q8×Dic3—21no—
66C2×#215—61no—
67C2×Dic12C2×D311yescharacteristic
68C2×D24—31no—
69C2×D24—31no—
70C2×D24—61no—
71C2×#204—61no—
72#875—61no—
73C3×Q32—62no—
74C2×C3×C16—31no—
75C3×#107—31no—
76C3×#103—61no—
77C3×C4×C8—31no—
78#835—21no—
79#829—22no—
80#828—64no—
81#828—62no—
82#828—62no—
83#818C2×D311yescharacteristic
84C8×Dic3C2×D311yescharacteristic
85C2×C3⋊C16—31no—
86C2×C3⋊C16—31no—
87C2×C3⋊C16—61no—
88C2×C3⋊C16C2×D311yescharacteristic
89C22×C3⋊D3—41no—
90C32×Q8—22no—
91C32×Q8—41no—
92C2×C32×C4—41no—
93C2×C32×C4C2×D411yescharacteristic
94C4⋊(C3⋊D3)—41no—
95C4⋊(C3⋊D3)—41no—
96C2×C3×Dic3—41no—
97C2×C3×Dic3—41no—
98C2×C3×Dic3D811yescharacteristic
99C2×C3×Dic3D811yescharacteristic
100C3×Dic6—41no—
101C3×Dic6—41no—
102C32×C8C2×D411yescharacteristic
103C32×C8#4111yescharacteristic
104C3×C3⋊C8—21no—
105C2×Q32—31no—
106C2×SD32—91no—
107#495—91no—
108C4×Q16—31no—
109C4⋊C16—91no—
110#358—91no—
111#357—91no—
112C2×C3×Q8—21no—
113C2×C3×Q8—21no—
114C2×C3×Q8—41no—
115C2×C3×Q8—61no—
116C2×D12—61no—
117C2×D12—61no—
118C2×D12—121no—
119C2×Dic6—21no—
120C3×Q16—21no—
121C3×Q16—21no—
122C3×Q16—22no—
123C3×Q16—41no—
124C3×Q16—61no—
125C3×Q16—61no—
126C3×Q16D1212yes—
127C3×Q16#6712yes—
128C2×C3×C8—21no—
129C2×C3×C8—31no—
130C2×C3×C8C22×D311yescharacteristic
131C2×C3×C8C22×D311yescharacteristic
132C3×C4⋊C4—61no—
133C3×C4⋊C4—121no—
134C3×C42—31no—
135C3×C42—121no—
136#215—122no—
137(C2×D3)⋊C4—121no—
138(C2×D3)⋊C4—121no—
139(C2×D3)⋊C4—121no—
140(C2×D3)⋊C4—121no—
141C4⋊Dic3—21no—
142C4⋊Dic3—41no—
143C4×Dic3—41no—
144C4×Dic3#6711yescharacteristic
145C2×C3⋊C8#6711yescharacteristic
146Dic12—21no—
147Dic12—21no—
148D24—62no—
149D24—61no—
150D24—61no—
151D24—61no—
152D24—61no—
153D24—121no—
154#204—122no—
155C3×C16—61no—
156C3⋊C16—21no—
157C3⋊C16—62no—
158C3⋊C16—61no—
159C3⋊C16—61no—
160C22×C32C2×D811yescharacteristic
161C2×C3⋊D3—81no—
162C2×C3⋊D3—81no—
163C2×C3⋊D3—81no—
164C32×C4—42no—
165C32×C4#12111yescharacteristic
166C32×C4AGL(1,ℤ/8)11yescharacteristic
167C3×Dic3—21no—
168C3×Dic3—21no—
169C3×Dic3—81no—
170C3×Dic3—81no—
171C2×Q16—31no—
172C2×Q16D3211yescharacteristic
173C2×SD16—181no—
174C2×D8—91no—
175#124—181no—
176C4×Q8—61no—
177Q32—62no—
178SD32—182no—
179C2×C16—31no—
180C2×C16—91no—
181#107—31no—
182#103—61no—
183C4×C8—31no—
184C22×D3—121no—
185C22×D3—121no—
186C22×D3—241no—
187C3×Q8—22no—
188C3×Q8—22no—
189C3×Q8—42no—
190C3×Q8—41no—
191C3×Q8—41no—
192C3×Q8—81no—
193C3×Q8—121no—
194C3×Q8—121no—
195C2×C3×C4—21no—
196C2×C3×C4—31no—
197C2×C3×C4—31no—
198C2×C3×C4—41no—
199C2×C3×C4—41no—
200C2×C3×C4—81no—
201C2×C3×C4—121no—
202C2×C3×C4—121no—
203C2×C3×C4D3×D411yescharacteristic
204C2×C3×C4C2×#6711yescharacteristic
205C2×Dic3—41no—
206C2×Dic3—41no—
207C2×Dic3#21311yescharacteristic
208C2×Dic3#21311yescharacteristic
209D12—122no—
210D12—121no—
211D12—121no—
212D12—121no—
213D12—121no—
214D12—241no—
215Dic6—41no—
216Dic6—41no—
217C3×C8—21no—
218C3×C8—21no—
219C3×C8—61no—
220C3×C8C2×D1211yescharacteristic
221C3×C8#23511yescharacteristic
222C3×C8#23711yescharacteristic
223C3×C8C2×#6711yescharacteristic
224C3⋊C8—21no—
225C2×C32#45911yescharacteristic
226C2×C32#50811yescharacteristic
227C2×C32#51011yescharacteristic
228C3⋊D3—161no—
229C2×Q8—21no—
230C2×Q8—61no—
231C2×D4—181no—
232Q16—21no—
233Q16—61no—
234Q16—61no—
235Q16#62612yes—
236SD16—362no—
237D8—181no—
238D8—181no—
239C2×C8—31no—
240C2×C8C2×D3211yescharacteristic
241C4⋊C4—61no—
242C4⋊C4—121no—
243C22⋊C4—361no—
244C22⋊C4—361no—
245C42—31no—
246C42—121no—
247C16—61no—
248C16—181no—
249C22×C3—21no—
250C22×C3D3×D811yescharacteristic
251C22×C3C2×#21311yescharacteristic
252C2×D3—242no—
253C2×D3—241no—
254C2×D3—241no—
255C2×D3—241no—
256C2×D3—241no—
257C2×D3—241no—
258C2×D3—241no—
259C2×D3—481no—
260C2×D3—481no—
261C3×C4—21no—
262C3×C4—21no—
263C3×C4—42no—
264C3×C4—42no—
265C3×C4—61no—
266C3×C4—61no—
267C3×C4—82no—
268C3×C4—241no—
269C3×C4—241no—
270C3×C4#91111yescharacteristic
271C3×C4#93011yescharacteristic
272C3×C4#93911yescharacteristic
273C3×C4#94911yescharacteristic
274Dic3—21no—
275Dic3—21no—
276Dic3—81no—
277Dic3—81no—
278C32#221111yescharacteristic, complemented, Sylow
279C23—361no—
280Q8—22no—
281Q8—41no—
282Q8—121no—
283Q8—121no—
284D4—361no—
285D4—361no—
286C2×C4—31no—
287C2×C4—31no—
288C2×C4—41no—
289C2×C4—121no—
290C2×C4—121no—
291C2×C4D3×#6711yescharacteristic
292C8—61no—
293C8#380411yescharacteristic
294C8C2×#62611yescharacteristic
295C2×C3—21no—
296C2×C3—21no—
297C2×C3—21no—
298C2×C3#491811yescharacteristic
299C2×C3#491911yescharacteristic
300C2×C3#501511yescharacteristic
301C2×C3#515011yescharacteristic
302C2×C3#517911yescharacteristic
303C2×C3#519411yescharacteristic
304D3—482no—
305D3—481no—
306D3—481no—
307C22—721no—
308C22—721no—
309C22—721no—
310C22D3×#21311yescharacteristic
311C4—42no—
312C4—61no—
313C4—61no—
314C4—241no—
315C4—241no—
316C4#6392511yescharacteristic
317C4#6397811yescharacteristic
318C3—21no—
319C3#7091511yescharacteristic, complemented
320C3#7149811yescharacteristic, complemented
321C2—1441no—
322C2#1059104711yescharacteristic
323C2#1059104811yescharacteristic
324C2#1059148111yescharacteristic
subgroupG/H
centerC22D3×#213
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC2×C32×Q16C22
socleC22×C32C2×D8
prime radicalC2×#3745C22
hypercenterC2×Q16D32
hypocenterC32#2211
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
2. C3×Dic3×Q16C2semidirect
3. C2×C3×#829C2semidirect
5. Dic3⋊(C3⋊C16)C2semidirect
6. #10589117C2semidirect
26. Dic3×Q16D3semidirect
27. C2×#829D3semidirect
278. C32#2211semidirect
319. C3#70915semidirect
320. C3#71498semidirect

Maximal subgroups

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

subgroupindex
C2×#636552
C3×Dic3×Q162
C2×C3×#8292
#105908652
Dic3⋊(C3⋊C16)2
#105891172
#105891162
#714983
#709153