Finite Group Databasebeta

← #11775887

Subgroups — #11775887

Order 1152.

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

normal subgroups only

This group has 484 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
3C2×#63555C211yesmaximal, characteristic, complemented
4#10590035C214yesmaximal, complemented
5C2×#3805C412yes—
6C2×C4×C3⋊Dic3C2211yescharacteristic
7C3×#930—21no—
8C22×C3×C3⋊C8—21no—
9#63980—21no—
10#63919C411yescharacteristic
11#63915C2212yes—
12#63914C411yescharacteristic
13#63902—21no—
14#63898—21no—
15C22⋊#622—21no—
16#63777C2212yes—
17C4⋊#622—21no—
18#63555—21no—
19#63555C2212yes—
20#5596—61no—
21C2×#815—61no—
22C22×C32×C4D411yescharacteristic
23C22×C3⋊Dic3C2×C411yescharacteristic
24C22×C3⋊Dic3D411yescharacteristic
25C2×C3×#67—22no—
26C2×C3×D12—21no—
27C2×#627C2×C412yes—
28C2×#625—21no—
29C2×#625C2×C412yes—
30#3805—44no—
31C2×D3×Dic3—22no—
32C2×#622—22no—
33C4×C3⋊Dic3C2×C411yescharacteristic
34C4×C3⋊Dic3D411yescharacteristic
35C4×C3⋊Dic3D411yescharacteristic
36C4×C3⋊Dic3C2311yescharacteristic
37C3×(C2×D3)⋊C4—22no—
38C3×C4⋊Dic3—21no—
39C2×C3×C3⋊C8—24no—
40C2×C3×C3⋊C8—22no—
41#3724—21no—
42(C2×D3)⋊Dic3—22no—
43#1530—91nomaximal, Sylow
44C2×#237—62no—
45C22×C3×C8—61no—
46C3×#121—61no—
47#940—61no—
48#939—62no—
49D4×Dic3—61no—
50#930—21no—
51C2×C4×Dic3—61no—
52C2×C4×Dic3—61no—
53C22×C3⋊C8—21no—
54#893—61no—
55#888—61no—
56#885—62no—
57#67⋊C4—62no—
58#815—62no—
59#815—62no—
60C23×C32C22⋊C411yescharacteristic
61C22×C3×D3—22no—
62C2×C32×C4—22no—
63C2×C32×C4C22⋊C411yescharacteristic
64C2×C32×C4C2×D411yescharacteristic
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—22no—
73C3×D12—42no—
74#627—42no—
75#625—42no—
76#625—42no—
77D3×Dic3—44no—
78#622—42no—
79C3×C3⋊C8—24no—
80#532—91no—
81#432—91no—
82C2×#97—91no—
83#329—94no—
84C2×C3×D4—61no—
85C2×C3×D4—62no—
86C22×C3×C4—21no—
87C22×C3×C4—21no—
88C2×#67—22no—
89C2×#67—62no—
90C2×#67—62no—
91C22×Dic3—61no—
92C22×Dic3—61no—
93C22×Dic3—61no—
94C22×Dic3—61no—
95C22×Dic3—62no—
96#237—128no—
97C2×D12—21no—
98C2×C4×D3—62no—
99C2×Dic6—62no—
100C2×C3×C8—62no—
101C2×C3×C8—64no—
102C3×C4⋊C4—61no—
103C3×C22⋊C4—62no—
104#217—62no—
105(C2×D3)⋊C4—22no—
106(C2×D3)⋊C4—62no—
107C4⋊Dic3—21no—
108Dic3⋊C4—62no—
109C4×Dic3—61no—
110C4×Dic3—61no—
111C4×Dic3—61no—
112C4×Dic3—61no—
113C4×Dic3—61no—
114C4×Dic3—61no—
115C4×Dic3—61no—
116C4×Dic3—61no—
117C2×C3⋊C8—22no—
118C2×C3⋊C8—24no—
119C22×C32—21no—
120C22×C32—21no—
121C22×C32#10012yes—
122C22×C32C2×C22⋊C411yescharacteristic
123C2×C3×D3—42no—
124C2×C3×D3—42no—
125C2×C3×D3—42no—
126C32×C4—21no—
127C32×C4#10412yes—
128C3⋊Dic3—21no—
129C3⋊Dic3—21no—
130C3⋊Dic3—21no—
131C3⋊Dic3—21no—
132C3×Dic3—42no—
133C2×#41—92no—
134C22×C8—61no—
135C4⋊Q8—91no—
136#127—91no—
137#124—92no—
138#121—61no—
139#121—181no—
140C4×D4—181no—
141C4×D4—181no—
142C2×C42—91no—
143C4⋊C8—181no—
144C22⋊C8—181no—
145#97—92no—
146#97—92no—
147#97—181no—
148C23×C3—21no—
149C23×C3—21no—
150C23×C3—62no—
151C22×D3—22no—
152C3×D4—122no—
153C3×D4—124no—
154C2×C3×C4—22no—
155C2×C3×C4—22no—
156C2×C3×C4—21no—
157C2×C3×C4—21no—
158C2×C3×C4—21no—
159C2×C3×C4—21no—
160C2×C3×C4—42no—
161C2×C3×C4—62no—
162#67—44no—
163#67—124no—
164#67—124no—
165C2×Dic3—22no—
166C2×Dic3—61no—
167C2×Dic3—61no—
168C2×Dic3—61no—
169C2×Dic3—61no—
170C2×Dic3—61no—
171C2×Dic3—61no—
172C2×Dic3—61no—
173C2×Dic3—61no—
174C2×Dic3—64no—
175C2×Dic3—122no—
176C2×Dic3—124no—
177C2×Dic3—122no—
178C2×Dic3—122no—
179D12—42no—
180C4×D3—124no—
181Dic6—124no—
182C3×C8—64no—
183C3⋊C8—24no—
184C2×C32—22no—
185C2×C32C2×#10011yescharacteristic
186C2×C32C2×#10411yescharacteristic
187C2×C32#42111yescharacteristic
188C3×D3—82no—
189#41—364no—
190C2×Q8—92no—
191C2×D4—62no—
192C2×D4—61no—
193C2×D4—92no—
194C2×D4—181no—
195C22×C4—91no—
196C22×C4—91no—
197C22×C4—182no—
198C22×C4GO+(4,𝔽2)11yescharacteristic
199C2×C8—64no—
200C2×C8—62no—
201C2×C8—182no—
202C4⋊C4—61no—
203C4⋊C4—181no—
204C22⋊C4—62no—
205C22⋊C4—182no—
206C42—91no—
207C42—91no—
208C42—91no—
209C42—91no—
210C22×C3—22no—
211C22×C3—22no—
212C22×C3—21no—
213C22×C3—21no—
214C22×C3—22no—
215C22×C3—22no—
216C22×C3—41no—
217C22×C3—41no—
218C22×C3—122no—
219C22×C3—122no—
220C22×C3—122no—
221C2×D3—42no—
222C2×D3—42no—
223C2×D3—42no—
224C3×C4—21no—
225C3×C4—21no—
226C3×C4—22no—
227C3×C4—22no—
228C3×C4—41no—
229C3×C4—122no—
230Dic3—42no—
231Dic3—62no—
232Dic3—62no—
233Dic3—62no—
234Dic3—121no—
235Dic3—121no—
236Dic3—121no—
237Dic3—121no—
238Dic3—121no—
239C32#153011yescharacteristic, complemented, Sylow
240C23—62no—
241C23D32⋊C411yescharacteristic
242Q8—362no—
243D4—124no—
244D4—122no—
245D4—362no—
246D4—362no—
247C2×C4—22no—
248C2×C4—62no—
249C2×C4—91no—
250C2×C4—91no—
251C2×C4—91no—
252C2×C4—91no—
253C2×C4—182no—
254C2×C4—364no—
255C2×C4—361no—
256C2×C4D32⋊C411yescharacteristic
257C2×C4C2×GO+(4,𝔽2)11yescharacteristic
258C8—64no—
259C8—362no—
260C2×C3—24no—
261C2×C3—21no—
262C2×C3—21no—
263C2×C3—21no—
264C2×C3—21no—
265C2×C3—21no—
266C2×C3—21no—
267C2×C3—42no—
268C2×C3—242no—
269D3—82no—
270C22—21no—
271C22—21no—
272C22—122no—
273C22—122no—
274C22—122no—
275C22#6372712yes—
276C22C2×D32⋊C411yescharacteristic
277C4—21no—
278C4—122no—
279C4—181no—
280C4—181no—
281C4—181no—
282C4—181no—
283C4#6374112yes—
284C3—21no—
285C3—21no—
286C2—22no—
287C2—242no—
288C2C2×#6372711yescharacteristic
289C2#1059332411yescharacteristic
290C2C2×#6374111yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radical#10594929C2
cosocleC4×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1530
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. C2×#63555C2semidirect
4. #10590035C2semidirect
239. C32#1530semidirect

Maximal subgroups

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

subgroupindex
#105949292
#105938062
C2×#635552
#105900352
#15309