Finite Group Databasebeta

← #11795192

Subgroups — #11795192

Order 1152.

672 conjugacy classes of subgroups.

The subgroup lattice has 294 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63641C211yesmaximal, characteristic
2#10592683C211yesmaximal, characteristic
3#10592671C211yesmaximal, characteristic
4C2×#63634C211yesmaximal, characteristic
5C32×#340C211yesmaximal, characteristic
6#10589417C211yesmaximal, characteristic
7#10589395C211yesmaximal, characteristic
8#68807—34nomaximal
9C22×C32×C8C2211yescharacteristic
10C2×C32×C4⋊C4C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)—21no—
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×#3750—21no—
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18#63658—21no—
19#63658—21no—
20#63641—22no—
21#63634—22no—
22C2×Dic3⋊C8—34no—
23#4984—34no—
24#4972—34no—
25C2×#807—34no—
26C3×#340D314yes—
27#4551—34no—
28#4529—34no—
29C22×C32×C4—21no—
30C22×C32×C4—21no—
31C22×C32×C4C2311yescharacteristic
32C22×C3⋊Dic3—21no—
33C22×C3⋊Dic3—21no—
34C22×C3⋊Dic3D411yescharacteristic
35C22×C3⋊Dic3D411yescharacteristic
36C2×C32×C8—21no—
37C2×C32×C8—21no—
38C2×C32×C8—21no—
39C32×C4⋊C4—21no—
40C32×C4⋊C4—21no—
41C32×C4⋊C4—21no—
42C32×C4⋊C4Q812yes—
43C4⋊(C3⋊Dic3)—21no—
44C4⋊(C3⋊Dic3)—21no—
45C4⋊(C3⋊Dic3)—21no—
46C4⋊(C3⋊Dic3)—42no—
47C4⋊(C3⋊Dic3)Q812yes—
48#3750—42no—
49C4×C3⋊Dic3—21no—
50C4×C3⋊Dic3—21no—
51C2×C3⋊(C3⋊C8)—21no—
52C2×C3⋊(C3⋊C8)—21no—
53C2×C3⋊(C3⋊C8)D412yes—
54#2086—91noSylow
55C22×C3×C8C2×D314yes—
56C2×C3×C4⋊C4C2×D314yes—
57C2×C3×C4⋊C4C2×D314yes—
58C2×C4⋊Dic3—34no—
59C2×C4⋊Dic3—34no—
60C2×C4⋊Dic3—64no—
61C2×Dic3⋊C4—64no—
62C2×C4×Dic3—34no—
63C22×C3⋊C8—34no—
64C3⋊#95—64no—
65C3⋊#95—64no—
66Dic3⋊C8—68no—
67#807—68no—
68C23×C32C2×D411yescharacteristic
69C2×C32×C4—22no—
70C2×C32×C4—41no—
71C2×C32×C4—41no—
72C2×C32×C4—41no—
73C2×C32×C4—41no—
74C2×C32×C4—41no—
75C2×C32×C4C2×D411yescharacteristic
76C2×C32×C4C2×Q811yescharacteristic
77C2×C32×C4C2×Q811yescharacteristic
78C2×C32×C4#4111yescharacteristic
79C2×C32×C4#4111yescharacteristic
80C2×C32×C4#4111yescharacteristic
81C2×C3⋊Dic3—21no—
82C2×C3⋊Dic3—21no—
83C2×C3⋊Dic3—21no—
84C2×C3⋊Dic3—22no—
85C2×C3⋊Dic3—21no—
86C2×C3⋊Dic3—21no—
87C2×C3⋊Dic3—41no—
88C2×C3⋊Dic3—41no—
89C2×C3⋊Dic3—41no—
90C2×C3⋊Dic3—41no—
91C2×C3⋊Dic3—41no—
92C2×C3⋊Dic3D812yes—
93C32×C8—41no—
94C3⋊(C3⋊C8)—22no—
95C2×#107—91no—
96C2×C4⋊C8—91no—
97#389—91no—
98#389—91no—
99#340—91no—
100#340—91no—
101#340C3⋊D311yescharacteristic
102C22×C3×C4—24no—
103C22×C3×C4—24no—
104C22×C3×C4C22×D314yes—
105C22×Dic3—34no—
106C22×Dic3—34no—
107C22×Dic3—64no—
108C22×Dic3—64no—
109C2×C3×C8—24no—
110C2×C3×C8—24no—
111C2×C3×C8—24no—
112C3×C4⋊C4—24no—
113C3×C4⋊C4—24no—
114C3×C4⋊C4—24no—
115C3×C4⋊C4Dic618yes—
116C4⋊Dic3—38no—
117C4⋊Dic3—64no—
118C4⋊Dic3—64no—
119C4⋊Dic3—64no—
120C4⋊Dic3—128no—
121Dic3⋊C4—128no—
122C4×Dic3—64no—
123C4×Dic3—64no—
124C2×C3⋊C8—38no—
125C2×C3⋊C8—64no—
126C2×C3⋊C8—64no—
127C22×C32#12111yescharacteristic
128C22×C32C22⋊Q811yescharacteristic
129C22×C32C22⋊Q811yescharacteristic
130C22×C32C2×D811yescharacteristic
131C22×C32#13511yescharacteristic
132C22×C32#13711yescharacteristic
133C22×C32#13711yescharacteristic
134C32×C4—42no—
135C32×C4—81no—
136C32×C4#12311yescharacteristic
137C32×C4#12511yescharacteristic
138C32×C4#12511yescharacteristic
139C32×C4C4⋊Q811yescharacteristic
140C3⋊Dic3—22no—
141C3⋊Dic3—41no—
142C3⋊Dic3—42no—
143C3⋊Dic3—81no—
144C22×C8—91no—
145C22×C8C2×C3⋊D311yescharacteristic
146C2×C4⋊C4—91no—
147C2×C4⋊C4—91no—
148C2×C4⋊C4—181no—
149C2×C4⋊C4—181no—
150C2×C4⋊C4C2×C3⋊D311yescharacteristic
151C2×C4⋊C4C2×C3⋊D311yescharacteristic
152C2×C42—91no—
153#107—182no—
154C4⋊C8—182no—
155#95—181no—
156#95—181no—
157C23×C3D3×D414yes—
158C2×C3×C4—28no—
159C2×C3×C4—44no—
160C2×C3×C4—44no—
161C2×C3×C4—44no—
162C2×C3×C4—44no—
163C2×C3×C4—44no—
164C2×C3×C4C2×Dic614yes—
165C2×C3×C4#23514yes—
166C2×C3×C4#23514yes—
167C2×C3×C4D3×D414yes—
168C2×C3×C4#23714yes—
169C2×C3×C4D3×Q814yes—
170C2×Dic3—38no—
171C2×Dic3—64no—
172C2×Dic3—64no—
173C2×Dic3—64no—
174C2×Dic3—68no—
175C2×Dic3—64no—
176C2×Dic3—64no—
177C2×Dic3—124no—
178C2×Dic3—124no—
179C2×Dic3—124no—
180C2×Dic3—124no—
181C2×Dic3—124no—
182C3×C8—44no—
183C3⋊C8—68no—
184C2×C32#39811yescharacteristic
185C2×C32#46611yescharacteristic
186C2×C32#47011yescharacteristic
187C2×C32#47411yescharacteristic
188C2×C32#47411yescharacteristic
189C2×C32#47911yescharacteristic
190C2×C32#47911yescharacteristic
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—91no—
194C22×C4—91no—
195C22×C4—181no—
196C22×C4—181no—
197C22×C4C22×C3⋊D311yescharacteristic
198C2×C8—21no—
199C2×C8—21no—
200C2×C8—21no—
201C2×C8—92no—
202C2×C8—181no—
203C2×C8—181no—
204C4⋊C4—21no—
205C4⋊C4—21no—
206C4⋊C4—21no—
207C4⋊C4—92no—
208C4⋊C4—181no—
209C4⋊C4—181no—
210C4⋊C4—181no—
211C4⋊C4—362no—
212C4⋊C4—362no—
213C4⋊C4#63412yes—
214C42—181no—
215C42—181no—
216C22×C3#87814yes—
217C22×C3#88414yes—
218C22×C3#89614yes—
219C22×C3D3×D814yes—
220C22×C3#91514yes—
221C22×C3#91614yes—
222C22×C3#91814yes—
223C3×C4—48no—
224C3×C4—84no—
225C3×C4#87014yes—
226C3×C4#88314yes—
227C3×C4#88814yes—
228C3×C4#88914yes—
229Dic3—68no—
230Dic3—128no—
231Dic3—124no—
232Dic3—244no—
233C32#208611yescharacteristic, complemented, Sylow
234C23D4×C3⋊D311yescharacteristic
235C2×C4—22no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—92no—
242C2×C4—181no—
243C2×C4—181no—
244C2×C4—181no—
245C2×C4—182no—
246C2×C4—181no—
247C2×C4—181no—
248C2×C4—361no—
249C2×C4—361no—
250C2×C4—361no—
251C2×C4—361no—
252C2×C4—361no—
253C2×C4C2×#63411yescharacteristic
254C2×C4#382811yescharacteristic
255C2×C4#382811yescharacteristic
256C2×C4D4×C3⋊D311yescharacteristic
257C2×C4#383011yescharacteristic
258C2×C4Q8×C3⋊D311yescharacteristic
259C8—41no—
260C8—182no—
261C2×C3#465714yes—
262C2×C3#475914yes—
263C2×C3#477514yes—
264C2×C3#479914yes—
265C2×C3#481614yes—
266C2×C3#485714yes—
267C2×C3#489014yes—
268C22#6408711yescharacteristic
269C22#6409311yescharacteristic
270C22#6410511yescharacteristic
271C22D8×C3⋊D311yescharacteristic
272C22#6412411yescharacteristic
273C22#6412511yescharacteristic
274C22#6412711yescharacteristic
275C4—42no—
276C4—81no—
277C4—182no—
278C4—361no—
279C4—362no—
280C4—721no—
281C4#6407911yescharacteristic
282C4#6409211yescharacteristic
283C4#6409711yescharacteristic
284C4#6409811yescharacteristic
285C3#6880714yescomplemented
286C2#1059235611yescharacteristic
287C2#1059245811yescharacteristic
288C2#1059247411yescharacteristic
289C2#1059249811yescharacteristic
290C2#1059251511yescharacteristic
291C2#1059255611yescharacteristic
292C2#1059258911yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#340C2
socle, prime radicalC23×C32C2×D4
hypercenter#340C3⋊D3
hypocenterC32#2086
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
233. C32#2086semidirect
285. C3#68807semidirect

Maximal subgroups

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

subgroupindex
C2×#636412
#105926832
#105926712
C2×#636342
C32×#3402
#105894172
#105893952
#688073