Finite Group Databasebeta

← #11774785

Subgroups — #11774785

Order 1152.

690 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 690 conjugacy classes of subgroups — too many to draw. Only its 143 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#10596028C211yesmaximal, characteristic
2#10592534C211yesmaximal, characteristic, complemented
3C4×C8×C3⋊D3C211yesmaximal, characteristic, complemented
4C32×D4⋊C8C211yesmaximal, characteristic, complemented
5D4⋊(C3⋊(C3⋊C8))C211yesmaximal, characteristic, complemented
6#10589350C211yesmaximal, characteristic, complemented
7#10589322C211yesmaximal, characteristic, complemented
8#68177—34nomaximal
9C32×C4×D4C2211yescharacteristic
10#64147C411yescharacteristic
11#64145C411yescharacteristic
12C4×#638—21no—
13#64135—21no—
14C2×C8×C3⋊D3—21no—
15#64106C411yescharacteristic
16#64099C411yescharacteristic
17#64092—21no—
18#64088—21no—
19C42×C3⋊D3C2211yescharacteristic
20C4×#634C2211yescharacteristic
21C32×C4⋊C8C2211yescharacteristic
22C32×C4×C8C2211yescharacteristic
23#63647—21no—
24#63642—21no—
25C8×C3⋊Dic3—21no—
26C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
27C4×C3⋊(C3⋊C8)C2211yescharacteristic
28#5557—34no—
29#4835—34no—
30C4×D3×C8—34no—
31C3×D4⋊C8D314yescomplemented
32D4⋊(C3⋊C8)—34no—
33#4484—34no—
34#4456—34no—
35C2×C32×D4C2×C411yescharacteristic
36C22×C32×C4—21no—
37C2×#638—21no—
38C2×C4×C3⋊D3C2×C411yescharacteristic
39C2×C4×C3⋊D3D411yescharacteristic
40C2×C4×C3⋊D3D411yescharacteristic
41C2×#634C2×C411yescharacteristic
42C2×C32×C8—21no—
43C2×C32×C8—21no—
44C32×C4⋊C4C2×C411yescharacteristic
45C32×C22⋊C4—21no—
46C32×C42C2311yescharacteristic
47#3757—21no—
48#3757—21no—
49#3757—21no—
50#3752—21no—
51C4⋊(C3⋊Dic3)—21no—
52C4⋊(C3⋊Dic3)—21no—
53C4⋊(C3⋊Dic3)C2×C411yescharacteristic
54#3750—21no—
55#3750—21no—
56C4×C3⋊Dic3—21no—
57C4×C3⋊Dic3C2×C411yescharacteristic
58C4×C3⋊Dic3D411yescharacteristic
59C4×C3⋊Dic3D411yescharacteristic
60C2×C3⋊(C3⋊C8)—21no—
61C2×C3⋊(C3⋊C8)—21no—
62C8×C3⋊D3—24no—
63#1494—91noSylow
64C3×C4×D4C2×D314yes—
65#938—34no—
66#936—34no—
67C4×#67—64no—
68#926—64no—
69C2×D3×C8—64no—
70#897—34no—
71#890—34no—
72#883—64no—
73#879—64no—
74C42×D3—34no—
75C4×Dic6—34no—
76C3×C4⋊C8C2×D314yes—
77C3×C4×C8C2×D314yes—
78(C2×D3)⋊C8—64no—
79#815—64no—
80C8×Dic3—64no—
81C4⋊(C3⋊C8)—34no—
82C4×C3⋊C8—34no—
83C23×C32—21no—
84C22×C3⋊D3C22⋊C411yescharacteristic
85C32×D4—21no—
86C32×D4—21no—
87C2×C32×C4—21no—
88C2×C32×C4—41no—
89C2×C32×C4—41no—
90C2×C32×C4C22×C411yescharacteristic
91C2×C32×C4C2×D411yescharacteristic
92C2×C32×C4C2×D411yescharacteristic
93#638—42no—
94C2×C3⋊Dic3—21no—
95C2×C3⋊Dic3—21no—
96C2×C3⋊Dic3C22⋊C411yescharacteristic
97C2×C3⋊Dic3C22⋊C411yescharacteristic
98C2×C3⋊Dic3C22⋊C411yescharacteristic
99C4×C3⋊D3—22no—
100C4×C3⋊D3—21no—
101C4×C3⋊D3—21no—
102C4×C3⋊D3—21no—
103C4×C3⋊D3—21no—
104#634—21no—
105#634—21no—
106C32×C8—22no—
107C32×C8—41no—
108C3⋊(C3⋊C8)—22no—
109C3⋊(C3⋊C8)—41no—
110#529—91no—
111#432—91no—
112C2×C4×C8—91no—
113Q8⋊C8—91no—
114Q8⋊C8—91no—
115D4⋊C8—91no—
116D4⋊C8C3⋊D311yescharacteristic, complemented
117C2×C3×D4C4×D314yes—
118C22×C3×C4—24no—
119C2×#67—64no—
120C2×C4×D3—34no—
121C2×C4×D3—34no—
122C2×C4×D3—34no—
123C2×Dic6—34no—
124C2×C3×C8—24no—
125C2×C3×C8—24no—
126C3×C4⋊C4C4×D314yes—
127C3×C22⋊C4—24no—
128C3×C42C22×D314yes—
129#217—64no—
130#217—64no—
131#217—64no—
132(C2×D3)⋊C4—64no—
133C4⋊Dic3—34no—
134C4⋊Dic3—64no—
135C4⋊Dic3—64no—
136Dic3⋊C4—64no—
137Dic3⋊C4—64no—
138C4×Dic3—34no—
139C4×Dic3—34no—
140C4×Dic3—34no—
141C4×Dic3—64no—
142C2×C3⋊C8—64no—
143C2×C3⋊C8—64no—
144D3×C8—616no—
145C22×C32—41no—
146C22×C32—41no—
147C22×C32—41no—
148C22×C32C2×C22⋊C411yescharacteristic
149C2×C3⋊D3—21no—
150C2×C3⋊D3—21no—
151C2×C3⋊D3#10412yes—
152C32×C4—21no—
153C32×C4—41no—
154C32×C4#13111yescharacteristic
155C32×C4#13111yescharacteristic
156C32×C4#13511yescharacteristic
157C32×C4#13511yescharacteristic
158C3⋊Dic3—21no—
159C3⋊Dic3—21no—
160C3⋊Dic3—21no—
161C3⋊Dic3—41no—
162C3⋊Dic3—41no—
163C22×C8—181no—
164#126—181no—
165#125—91no—
166#124—91no—
167#123—181no—
168C22⋊Q8—91no—
169#121—91no—
170C4×Q8—91no—
171C4×D4—181no—
172C4×D4C2×C3⋊D311yescharacteristic
173#117—181no—
174C2×C42—91no—
175C4⋊C8—91no—
176C4⋊C8C2×C3⋊D311yescharacteristic
177C22⋊C8—181no—
178#97—181no—
179C4×C8—91no—
180C4×C8—181no—
181C4×C8C2×C3⋊D311yescharacteristic
182C23×C3—24no—
183C22×D3—34no—
184C3×D4—24no—
185C3×D4—24no—
186C2×C3×C4—24no—
187C2×C3×C4—44no—
188C2×C3×C4—44no—
189C2×C3×C4C2×C4×D314yes—
190C2×C3×C4D3×D414yes—
191C2×C3×C4D3×D414yes—
192#67—128no—
193C2×Dic3—34no—
194C2×Dic3—34no—
195C2×Dic3—34no—
196C2×Dic3—64no—
197C2×Dic3—64no—
198C4×D3—68no—
199C4×D3—64no—
200C4×D3—64no—
201C4×D3—64no—
202C4×D3—64no—
203Dic6—64no—
204Dic6—64no—
205C3×C8—28no—
206C3×C8—44no—
207C3⋊C8—68no—
208C3⋊C8—124no—
209C2×C32—81no—
210C2×C32#40811yescharacteristic
211C2×C32#41611yescharacteristic
212C2×C32C2×#10411yescharacteristic
213C3⋊D3—22no—
214C2×Q8—91no—
215C2×D4—181no—
216C2×D4C4×C3⋊D311yescharacteristic
217C22×C4—21no—
218C22×C4—91no—
219C22×C4—91no—
220C22×C4—91no—
221C2×C8—21no—
222C2×C8—21no—
223C2×C8—184no—
224C2×C8—181no—
225C2×C8—181no—
226C4⋊C4—91no—
227C4⋊C4—181no—
228C4⋊C4—181no—
229C4⋊C4—181no—
230C4⋊C4—181no—
231C4⋊C4C4×C3⋊D311yescharacteristic
232C22⋊C4—21no—
233C22⋊C4—181no—
234C22⋊C4—181no—
235C22⋊C4—181no—
236C22⋊C4—181no—
237C42—91no—
238C42—91no—
239C42—91no—
240C42—181no—
241C42C22×C3⋊D311yescharacteristic
242C22×C3—44no—
243C22×C3—44no—
244C22×C3—44no—
245C22×C3D3×C22⋊C414yes—
246C2×D3—38no—
247C2×D3—64no—
248C2×D3—64no—
249C3×C4—24no—
250C3×C4—44no—
251C3×C4#90114yes—
252C3×C4#90714yes—
253C3×C4#91214yes—
254C3×C4#91614yes—
255Dic3—64no—
256Dic3—64no—
257Dic3—64no—
258Dic3—124no—
259Dic3—124no—
260C32#149411yescharacteristic, complemented, Sylow
261C23—21no—
262C23—91no—
263Q8—181no—
264Q8—181no—
265D4—21no—
266D4—21no—
267D4—362no—
268C2×C4—21no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—91no—
272C2×C4—91no—
273C2×C4—91no—
274C2×C4—182no—
275C2×C4—181no—
276C2×C4—181no—
277C2×C4—181no—
278C2×C4—181no—
279C2×C4—181no—
280C2×C4—181no—
281C2×C4C2×C4×C3⋊D311yescharacteristic
282C2×C4D4×C3⋊D311yescharacteristic
283C2×C4D4×C3⋊D311yescharacteristic
284C8—22no—
285C8—41no—
286C8—182no—
287C8—361no—
288C2×C3—84no—
289C2×C3#472714yes—
290C2×C3#477214yes—
291C2×C3D3×#10414yes—
292D3—68no—
293C22—41no—
294C22—41no—
295C22—41no—
296C22—92no—
297C22—181no—
298C22—181no—
299C22C22⋊C4×C3⋊D311yescharacteristic
300C4—21no—
301C4—41no—
302C4—181no—
303C4—181no—
304C4—181no—
305C4—361no—
306C4—361no—
307C4#6411011yescharacteristic
308C4#6411611yescharacteristic
309C4#6412111yescharacteristic
310C4#6412511yescharacteristic
311C3#6817714yescomplemented
312C2—81no—
313C2—182no—
314C2#1059242611yescharacteristic
315C2#1059247111yescharacteristic
316C2C3⋊D3×#10411yescharacteristic
subgroupG/H
centerC2×C4D4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC42C22×C3⋊D3
FittingC32×D4⋊C8C2
socleC22×C32C2×C22⋊C4
prime radical#64147C4
cosocleC32×C42C23
hypercenterD4⋊C8C3⋊D3
hypocenterC32#1494
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10592534C2semidirect
3. C4×C8×C3⋊D3C2semidirect
4. C32×D4⋊C8C2semidirect
5. D4⋊(C3⋊(C3⋊C8))C2semidirect
6. #10589350C2semidirect
7. #10589322C2semidirect
31. C3×D4⋊C8D3semidirect
116. D4⋊C8C3⋊D3semidirect
260. C32#1494semidirect
311. C3#68177semidirect

Maximal subgroups

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

subgroupindex
#105960282
#105925342
C4×C8×C3⋊D32
C32×D4⋊C82
D4⋊(C3⋊(C3⋊C8))2
#105893502
#105893222
#681773