Finite Group Databasebeta

← #11778738

Subgroups — #11778738

Order 1152.

624 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 624 conjugacy classes of subgroups — too many to draw. Only its 117 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#10596116C211yesmaximal, characteristic
2#10592743C211yesmaximal, characteristic, complemented
3#10592434C211yesmaximal, characteristic
4#10592358C211yesmaximal, characteristic, complemented
5C32×#328C211yesmaximal, characteristic, complemented
6#10589335C211yesmaximal, characteristic, complemented
7#10589317C211yesmaximal, characteristic
8#68330—34nomaximal
9C32×C22⋊Q8C2211yescharacteristic
10#64155—21no—
11#64139C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C2×#3750C2211yescharacteristic
14#64107—21no—
15#64103—21no—
16#64099—21no—
17#64095—21no—
18#64090—21no—
19C32×C22⋊C8C2211yescharacteristic
20C32×#95C2211yescharacteristic
21#63662—21no—
22#63658—21no—
23#63658—21no—
24#63657C2211yescharacteristic
25#63648—21no—
26#63644—21no—
27#63634—21no—
28#5645—34no—
29#5044—34no—
30#4735—34no—
31#4659—34no—
32C3×#328D314yescomplemented
33#4469—34no—
34#4451—34no—
35C2×C32×Q8D411yescharacteristic
36C22×C32×C4—21no—
37C22×C32×C4C2311yescharacteristic
38C2×#638—21no—
39C22×C3⋊Dic3—21no—
40C22×C3⋊Dic3D411yescharacteristic
41C22×C3⋊Dic3D411yescharacteristic
42C2×C4⋊(C3⋊D3)D411yescharacteristic
43C2×C4×C3⋊D3—21no—
44C2×C32×C8—21no—
45C32×C4⋊C4—21no—
46C32×C4⋊C4D411yescharacteristic
47C32×C22⋊C4—21no—
48#3752—21no—
49#3752—21no—
50#3752—21no—
51#3752—21no—
52C4⋊(C3⋊Dic3)—21no—
53C4⋊(C3⋊Dic3)—21no—
54C4⋊(C3⋊Dic3)—21no—
55C4⋊(C3⋊Dic3)—21no—
56C4⋊(C3⋊Dic3)D411yescharacteristic
57#3750—21no—
58#3750—21no—
59#3750—21no—
60C4×C3⋊Dic3—21no—
61C2×C3⋊(C3⋊C8)—21no—
62#1615—91noSylow
63C3×C22⋊Q8C2×D314yes—
64#946—64no—
65#930—34no—
66C2×C4⋊Dic3—34no—
67C2×Dic3⋊C4—34no—
68#898—64no—
69#894—64no—
70#890—64no—
71#886—64no—
72#67⋊C4—64no—
73C3×C22⋊C8C2×D314yes—
74C3×#95C2×D314yes—
75#835—64no—
76C3⋊#95—64no—
77C3⋊#95—64no—
78#830—34no—
79#821—64no—
80#817—64no—
81#807—64no—
82C23×C32C2×D411yescharacteristic
83C22×C3⋊D3—21no—
84C32×Q8—41no—
85C2×C32×C4—21no—
86C2×C32×C4—21no—
87C2×C32×C4—41no—
88C2×C32×C4—41no—
89C2×C32×C4—41no—
90C2×C32×C4—41no—
91C2×C32×C4C2×D411yescharacteristic
92C2×C32×C4C2×D411yescharacteristic
93#638—41no—
94#638—41no—
95C2×C3⋊Dic3—21no—
96C2×C3⋊Dic3—21no—
97C2×C3⋊Dic3—21no—
98C2×C3⋊Dic3—21no—
99C2×C3⋊Dic3—21no—
100C2×C3⋊Dic3—41no—
101C2×C3⋊Dic3—42no—
102C2×C3⋊Dic3—41no—
103C4⋊(C3⋊D3)—41no—
104C4×C3⋊D3—81no—
105C32×C8—41no—
106C3⋊(C3⋊C8)—41no—
107#539—91no—
108#484—91no—
109#481—91no—
110#400—91no—
111#328C3⋊D311yescharacteristic, complemented
112#327—91no—
113#324—91no—
114C2×C3×Q8D1214yes—
115C22×C3×C4—24no—
116C22×C3×C4C22×D314yes—
117C2×#67—64no—
118C22×Dic3—34no—
119C22×Dic3—34no—
120C22×Dic3—64no—
121C2×D12—34no—
122C2×C4×D3—64no—
123C2×C3×C8—24no—
124C3×C4⋊C4—24no—
125C3×C4⋊C4D1214yes—
126C3×C22⋊C4—24no—
127(C2×D3)⋊C4—64no—
128(C2×D3)⋊C4—64no—
129(C2×D3)⋊C4—64no—
130(C2×D3)⋊C4—64no—
131C4⋊Dic3—34no—
132C4⋊Dic3—64no—
133C4⋊Dic3—64no—
134C4⋊Dic3—64no—
135C4⋊Dic3—64no—
136Dic3⋊C4—64no—
137Dic3⋊C4—64no—
138Dic3⋊C4—64no—
139C4×Dic3—64no—
140C2×C3⋊C8—64no—
141C22×C32—21no—
142C22×C32—21no—
143C22×C32#12011yescharacteristic
144C22×C32#13511yescharacteristic
145C22×C32#13711yescharacteristic
146C2×C3⋊D3—41no—
147C2×C3⋊D3—41no—
148C2×C3⋊D3—41no—
149C32×C4—21no—
150C32×C4—21no—
151C32×C4—41no—
152C32×C4—41no—
153C32×C4—81no—
154C3⋊Dic3—41no—
155C3⋊Dic3—41no—
156C3⋊Dic3—41no—
157C3⋊Dic3—81no—
158#126—181no—
159#125—181no—
160#123—181no—
161#123—181no—
162C22⋊Q8—181no—
163C22⋊Q8C2×C3⋊D311yescharacteristic
164#121—91no—
165C4×D4—181no—
166C2×C4⋊C4—91no—
167C2×C4⋊C4—91no—
168#107—181no—
169#106—181no—
170#103—181no—
171#102—181no—
172C22⋊C8—91no—
173C22⋊C8C2×C3⋊D311yescharacteristic
174#95—181no—
175#95—181no—
176#95C2×C3⋊D311yescharacteristic
177C23×C3D3×D414yes—
178C22×D3—64no—
179C3×Q8—44no—
180C2×C3×C4—24no—
181C2×C3×C4—24no—
182C2×C3×C4—44no—
183C2×C3×C4—44no—
184C2×C3×C4—44no—
185C2×C3×C4—44no—
186C2×C3×C4C2×D1214yes—
187C2×C3×C4D3×D414yes—
188#67—124no—
189#67—124no—
190C2×Dic3—64no—
191C2×Dic3—64no—
192C2×Dic3—64no—
193C2×Dic3—64no—
194C2×Dic3—64no—
195C2×Dic3—124no—
196C2×Dic3—128no—
197C2×Dic3—124no—
198D12—124no—
199C4×D3—244no—
200C3×C8—44no—
201C3⋊C8—124no—
202C2×C32—21no—
203C2×C32—21no—
204C2×C32#45211yescharacteristic
205C2×C32#45411yescharacteristic
206C2×C32#45811yescharacteristic
207C3⋊D3—81no—
208C2×Q8C4⋊(C3⋊D3)11yescharacteristic
209C2×D4—91no—
210C2×D4—181no—
211C22×C4—21no—
212C22×C4—91no—
213C22×C4—91no—
214C22×C4—181no—
215C22×C4—181no—
216C22×C4C22×C3⋊D311yescharacteristic
217C2×C8—21no—
218C2×C8—181no—
219C4⋊C4—21no—
220C4⋊C4—91no—
221C4⋊C4—181no—
222C4⋊C4—181no—
223C4⋊C4—181no—
224C4⋊C4—181no—
225C4⋊C4—181no—
226C4⋊C4—181no—
227C4⋊C4—181no—
228C4⋊C4C4⋊(C3⋊D3)11yescharacteristic
229C22⋊C4—21no—
230C22⋊C4—181no—
231C22⋊C4—181no—
232C22⋊C4—181no—
233C22⋊C4—181no—
234C42—181no—
235C22×C3—24no—
236C22×C3—24no—
237C22×C3#88214yes—
238C22×C3#91614yes—
239C22×C3#91814yes—
240C2×D3—124no—
241C2×D3—124no—
242C2×D3—124no—
243C3×C4—24no—
244C3×C4—24no—
245C3×C4—44no—
246C3×C4—44no—
247C3×C4—84no—
248Dic3—124no—
249Dic3—124no—
250Dic3—124no—
251Dic3—244no—
252C32#161511yescharacteristic, complemented, Sylow
253C23—181no—
254C23D4×C3⋊D311yescharacteristic
255Q8—41no—
256D4—361no—
257D4—361no—
258D4—361no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—181no—
266C2×C4—181no—
267C2×C4—181no—
268C2×C4—181no—
269C2×C4—181no—
270C2×C4—361no—
271C2×C4—362no—
272C2×C4—361no—
273C2×C4—721no—
274C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
275C2×C4D4×C3⋊D311yescharacteristic
276C8—41no—
277C8—361no—
278C2×C3—24no—
279C2×C3—24no—
280C2×C3#474214yes—
281C2×C3#480814yes—
282C2×C3#482714yes—
283D3—244no—
284C22—21no—
285C22—21no—
286C22—361no—
287C22—361no—
288C22—361no—
289C22#6409111yescharacteristic
290C22#6412511yescharacteristic
291C22#6412711yescharacteristic
292C4—21no—
293C4—21no—
294C4—41no—
295C4—41no—
296C4—81no—
297C4—361no—
298C4—361no—
299C4—361no—
300C4—721no—
301C3#6833014yescomplemented
302C2—21no—
303C2—21no—
304C2—721no—
305C2#1059244111yescharacteristic
306C2#1059250711yescharacteristic
307C2#1059252611yescharacteristic
subgroupG/H
centerC22#64091
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#328C2
socleC22×C32#120
prime radical#64139C22
hypercenter#328C3⋊D3
hypocenterC32#1615
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #10592743C2semidirect
4. #10592358C2semidirect
5. C32×#328C2semidirect
6. #10589335C2semidirect
32. C3×#328D3semidirect
111. #328C3⋊D3semidirect
252. C32#1615semidirect
301. C3#68330semidirect

Maximal subgroups

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

subgroupindex
#105961162
#105927432
#105924342
#105923582
C32×#3282
#105893352
#105893172
#683303