Finite Group Databasebeta

← #11775160

Subgroups — #11775160

Order 1152.

516 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 59 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#10594929C211yesmaximal, characteristic
2#10593806C211yesmaximal, characteristic, complemented
3#10591222C211yesmaximal, characteristic, complemented
4#10590071C214yesmaximal, complemented
5C2×#3805—21no—
6C2×C4×C3⋊Dic3C2211yescharacteristic
7C3×#930—21no—
8C2×C3×C4×Dic3—21no—
9#63980C2212yes—
10#63919C411yescharacteristic, complemented
11#63915—21no—
12#63914C411yescharacteristic, complemented
13#63902C412yescomplemented
14#63898—21no—
15C22⋊#622C2212yes—
16#63777—21no—
17C4⋊#622—21no—
18#63579—21no—
19#63579C2212yes—
20#5596—61no—
21#4932—61no—
22C22×C32×C4D411yescharacteristic
23C22×C3⋊Dic3D411yescharacteristic
24C22×C3⋊Dic3C2311yescharacteristic
25C2×C3×#67—22no—
26C22×C3×Dic3—22no—
27C2×C3×D12—21no—
28C2×#627—21no—
29C2×#625—21no—
30C2×#625C2×C412yes—
31#3805—44no—
32C2×D3×Dic3—22no—
33C2×#622—22no—
34C4×C3⋊Dic3C2×C411yescharacteristic
35C4×C3⋊Dic3C2×C411yescharacteristic
36C4×C3⋊Dic3D411yescharacteristic
37C4×C3⋊Dic3D411yescharacteristic
38C3×(C2×D3)⋊C4—22no—
39C3×C4⋊Dic3—21no—
40C3×C4×Dic3—24no—
41#3724C2×C412yes—
42(C2×D3)⋊Dic3—22no—
43#1505—91nomaximal, Sylow
44C2×#237—62no—
45C3×#121—61no—
46C2×C3×C42—61no—
47#940—61no—
48#939—62no—
49D4×Dic3—61no—
50#930—21no—
51C2×C4×Dic3—21no—
52C2×C4×Dic3—61no—
53C2×C4×Dic3—61no—
54#893—61no—
55#888—61no—
56#885—62no—
57#67⋊C4—62no—
58C3⋊#95—62no—
59C3⋊#95—62no—
60C23×C32C2×D411yescharacteristic
61C22×C3×D3—22no—
62C2×C32×C4—22no—
63C2×C32×C4C22⋊C411yescharacteristic
64C2×C32×C4C22⋊C411yescharacteristic
65C2×C3⋊Dic3—22no—
66C2×C3⋊Dic3—41no—
67C2×C3⋊Dic3C22⋊C411yescharacteristic
68C2×C3⋊Dic3C22⋊C411yescharacteristic
69C2×C3⋊Dic3C22×C411yescharacteristic
70C2×C3⋊Dic3C2×D411yescharacteristic
71C3×#67—44no—
72C2×C3×Dic3—24no—
73C2×C3×Dic3—22no—
74C2×C3×Dic3—42no—
75C2×C3×Dic3—42no—
76C3×D12—42no—
77#627—42no—
78#625—42no—
79#625—42no—
80D3×Dic3—44no—
81#622—42no—
82#532—91no—
83#432—91no—
84#376—91no—
85#327—94no—
86C2×C3×D4—61no—
87C2×C3×D4—62no—
88C22×C3×C4—21no—
89C22×C3×C4—21no—
90C22×C3×C4—62no—
91C2×#67—22no—
92C2×#67—62no—
93C2×#67—62no—
94C22×Dic3—22no—
95C22×Dic3—61no—
96C22×Dic3—61no—
97C22×Dic3—61no—
98C22×Dic3—61no—
99C22×Dic3—62no—
100#237—128no—
101C2×D12—21no—
102C2×C4×D3—62no—
103C2×Dic6—62no—
104C3×C4⋊C4—61no—
105C3×C22⋊C4—62no—
106C3×C42—64no—
107#217—62no—
108(C2×D3)⋊C4—22no—
109(C2×D3)⋊C4—62no—
110C4⋊Dic3—21no—
111Dic3⋊C4—62no—
112C4×Dic3—24no—
113C4×Dic3—61no—
114C4×Dic3—61no—
115C4×Dic3—61no—
116C4×Dic3—61no—
117C4×Dic3—61no—
118C4×Dic3—61no—
119C4×Dic3—61no—
120C4×Dic3—61no—
121C22×C32—21no—
122C22×C32—21no—
123C22×C32C2×C22⋊C411yescharacteristic
124C22×C32AGL(1,ℤ/8)12yes—
125C2×C3×D3—42no—
126C2×C3×D3—42no—
127C2×C3×D3—42no—
128C32×C4—21no—
129C32×C4#10412yes—
130C3⋊Dic3—21no—
131C3⋊Dic3—21no—
132C3⋊Dic3—21no—
133C3⋊Dic3—21no—
134C3×Dic3—44no—
135C3×Dic3—42no—
136C2×#41—181no—
137C4⋊Q8—91no—
138#127—91no—
139#124—181no—
140#121—61no—
141#121—92no—
142C4×D4—92no—
143C4×D4—181no—
144C2×C42—61no—
145C2×C42—91no—
146C4⋊C8—181no—
147C22⋊C8—92no—
148#97—181no—
149#95—92no—
150#95—181no—
151C23×C3—21no—
152C23×C3—21no—
153C23×C3—62no—
154C22×D3—22no—
155C3×D4—122no—
156C3×D4—124no—
157C2×C3×C4—22no—
158C2×C3×C4—22no—
159C2×C3×C4—21no—
160C2×C3×C4—21no—
161C2×C3×C4—21no—
162C2×C3×C4—21no—
163C2×C3×C4—42no—
164C2×C3×C4—62no—
165C2×C3×C4—64no—
166C2×C3×C4—122no—
167C2×C3×C4—122no—
168#67—44no—
169#67—124no—
170#67—124no—
171C2×Dic3—24no—
172C2×Dic3—22no—
173C2×Dic3—42no—
174C2×Dic3—42no—
175C2×Dic3—61no—
176C2×Dic3—61no—
177C2×Dic3—61no—
178C2×Dic3—61no—
179C2×Dic3—61no—
180C2×Dic3—61no—
181C2×Dic3—61no—
182C2×Dic3—61no—
183C2×Dic3—64no—
184C2×Dic3—122no—
185C2×Dic3—124no—
186C2×Dic3—122no—
187C2×Dic3—122no—
188D12—42no—
189C4×D3—124no—
190Dic6—124no—
191C2×C32—22no—
192C2×C32#41011yescharacteristic
193C2×C32#41811yescharacteristic
194C2×C32C2×#10411yescharacteristic
195C3×D3—82no—
196#41—364no—
197C2×Q8—181no—
198C2×D4—62no—
199C2×D4—61no—
200C2×D4—92no—
201C2×D4—181no—
202C22×C4—62no—
203C22×C4—91no—
204C22×C4—91no—
205C22×C4—182no—
206C22×C4GO+(4,𝔽2)11yescharacteristic
207C2×C8—182no—
208C4⋊C4—61no—
209C4⋊C4—92no—
210C22⋊C4—62no—
211C22⋊C4—182no—
212C42—64no—
213C42—91no—
214C42—91no—
215C42—91no—
216C42—91no—
217C22×C3—21no—
218C22×C3—22no—
219C22×C3—21no—
220C22×C3—22no—
221C22×C3—22no—
222C22×C3—21no—
223C22×C3—21no—
224C22×C3—41no—
225C22×C3—41no—
226C22×C3—122no—
227C22×C3—122no—
228C22×C3—122no—
229C2×D3—42no—
230C2×D3—42no—
231C2×D3—42no—
232C3×C4—22no—
233C3×C4—22no—
234C3×C4—22no—
235C3×C4—41no—
236C3×C4—122no—
237C3×C4—124no—
238Dic3—42no—
239Dic3—44no—
240Dic3—62no—
241Dic3—62no—
242Dic3—62no—
243Dic3—121no—
244Dic3—121no—
245Dic3—121no—
246Dic3—121no—
247Dic3—121no—
248C32#150511yescharacteristic, complemented, Sylow
249C23—62no—
250C23C2×GO+(4,𝔽2)11yescharacteristic
251Q8—362no—
252D4—124no—
253D4—122no—
254D4—362no—
255D4—362no—
256C2×C4—22no—
257C2×C4—64no—
258C2×C4—62no—
259C2×C4—91no—
260C2×C4—91no—
261C2×C4—91no—
262C2×C4—91no—
263C2×C4—122no—
264C2×C4—122no—
265C2×C4—182no—
266C2×C4—364no—
267C2×C4—361no—
268C2×C4D32⋊C411yescharacteristic
269C2×C4D32⋊C411yescharacteristic
270C8—362no—
271C2×C3—22no—
272C2×C3—22no—
273C2×C3—21no—
274C2×C3—21no—
275C2×C3—21no—
276C2×C3—21no—
277C2×C3—21no—
278C2×C3—21no—
279C2×C3—42no—
280C2×C3—242no—
281D3—82no—
282C22—21no—
283C22—21no—
284C22—122no—
285C22—122no—
286C22—122no—
287C22#6422412yes—
288C22C2×D32⋊C411yescharacteristic
289C4—21no—
290C4—124no—
291C4—122no—
292C4—181no—
293C4—181no—
294C4—181no—
295C4—181no—
296C4#6374112yes—
297C3—21no—
298C3—21no—
299C2—22no—
300C2—242no—
301C2#1059334511yescharacteristic
302C2#1059336311yescharacteristic
303C2C2×#6374111yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC23C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radical#10594929C2
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1505
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #10593806C2semidirect
3. #10591222C2semidirect
4. #10590071C2semidirect
10. #63919C4semidirect
12. #63914C4semidirect
13. #63902C4semidirect
248. C32#1505semidirect

Maximal subgroups

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

subgroupindex
#105949292
#105938062
#105912222
#105900712
#15059