Finite Group Databasebeta

← #11774635

Subgroups — #11774635

Order 1152.

798 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 798 conjugacy classes of subgroups — too many to draw. Only its 157 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
1C4×#3830C211yesmaximal, characteristic
2#10592536C211yesmaximal, characteristic, complemented
3C4×#3743C211yesmaximal, characteristic, complemented
4C32×D4⋊C8C211yesmaximal, characteristic, complemented
5D4⋊(C3⋊(C3⋊C8))C211yesmaximal, characteristic, complemented
6#10589350C211yesmaximal, characteristic, complemented
7#10589322C211yesmaximal, characteristic, complemented
8#68174—34nomaximal
9C2×#3830C411yescharacteristic
10C32×C4×D4C2211yescharacteristic
11D4×C3⋊Dic3C411yescharacteristic
12C4×#638—21no—
13C2×C4×C3⋊Dic3—21no—
14C2×#3743—21no—
15C2×#3743—21no—
16#64101C411yescharacteristic
17#64096C411yescharacteristic
18#64090—21no—
19#64086—21no—
20C42×C3⋊D3C2211yescharacteristic
21C4×#634C2211yescharacteristic
22C32×C4⋊C8C2211yescharacteristic
23C32×C4×C8C2211yescharacteristic
24#63642—21no—
25#63641—21no—
26C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
27C4×C3⋊(C3⋊C8)C2211yescharacteristic
28C4×#237—34no—
29#4837—34no—
30C4×ΓL(1,𝔽25)—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—
38C22×C3⋊Dic3—21no—
39C22×C3⋊Dic3—21no—
40#3830—22no—
41#3830—22no—
42C2×C4×C3⋊D3C2×C411yescharacteristic
43C2×C4×C3⋊D3D411yescharacteristic
44C2×C4×C3⋊D3D411yescharacteristic
45C2×#634C2×C411yescharacteristic
46C2×C32×C8—21no—
47C2×C32×C8—21no—
48C32×C4⋊C4C2×C411yescharacteristic
49C32×C22⋊C4—21no—
50C32×C42C2311yescharacteristic
51#3757—21no—
52#3752—21no—
53C4⋊(C3⋊Dic3)C2×C411yescharacteristic
54#3750—21no—
55#3750—21no—
56C4×C3⋊Dic3—21no—
57C4×C3⋊Dic3—21no—
58C4×C3⋊Dic3—21no—
59C4×C3⋊Dic3C2×C411yescharacteristic
60C4×C3⋊Dic3D411yescharacteristic
61C4×C3⋊Dic3D411yescharacteristic
62C2×C3⋊(C3⋊C8)—21no—
63C2×C3⋊(C3⋊C8)—21no—
64#3743—24no—
65#3743—42no—
66#1489—91noSylow
67C2×#237—34no—
68C3×C4×D4C2×D314yes—
69D4×Dic3—34no—
70C4×#67—64no—
71C2×C4×Dic3—64no—
72C2×ΓL(1,𝔽25)—64no—
73C2×ΓL(1,𝔽25)—64no—
74#892—34no—
75#887—34no—
76#67⋊C4—64no—
77#877—64no—
78C42×D3—34no—
79C4×Dic6—34no—
80C3×C4⋊C8C2×D314yes—
81C3×C4×C8C2×D314yes—
82#815—64no—
83Dic3⋊C8—64no—
84C4⋊(C3⋊C8)—34no—
85C4×C3⋊C8—34no—
86C23×C32—21no—
87C22×C3⋊D3C22⋊C411yescharacteristic
88C32×D4—21no—
89C32×D4M1612yescomplemented
90C2×C32×C4—21no—
91C2×C32×C4—41no—
92C2×C32×C4—41no—
93C2×C32×C4C22×C411yescharacteristic
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4C2×D411yescharacteristic
96#638—24no—
97C2×C3⋊Dic3—24no—
98C2×C3⋊Dic3—21no—
99C2×C3⋊Dic3—21no—
100C2×C3⋊Dic3—42no—
101C2×C3⋊Dic3C22⋊C411yescharacteristic
102C2×C3⋊Dic3C22⋊C411yescharacteristic
103C2×C3⋊Dic3C22⋊C411yescharacteristic
104C4×C3⋊D3—21no—
105C4×C3⋊D3—21no—
106C4×C3⋊D3—21no—
107C4×C3⋊D3—21no—
108C4×C3⋊D3—22no—
109#634—21no—
110#634M1612yescomplemented
111C32×C8—22no—
112C32×C8—41no—
113C3⋊(C3⋊C8)—22no—
114C3⋊(C3⋊C8)—41no—
115C4×#41—91no—
116#423—91no—
117C4×M16—91no—
118Q8⋊C8—91no—
119Q8⋊C8—91no—
120D4⋊C8—91no—
121D4⋊C8C3⋊D311yescharacteristic, complemented
122C2×C3×D4C4×D314yes—
123C22×C3×C4—24no—
124C2×#67—64no—
125C22×Dic3—64no—
126C22×Dic3—64no—
127#237—68no—
128#237—68no—
129C2×C4×D3—34no—
130C2×C4×D3—34no—
131C2×C4×D3—34no—
132C2×Dic6—34no—
133C2×C3×C8—24no—
134C2×C3×C8—24no—
135C3×C4⋊C4C4×D314yes—
136C3×C22⋊C4—24no—
137C3×C42C22×D314yes—
138#217—64no—
139(C2×D3)⋊C4—64no—
140C4⋊Dic3—34no—
141Dic3⋊C4—64no—
142Dic3⋊C4—64no—
143C4×Dic3—34no—
144C4×Dic3—34no—
145C4×Dic3—34no—
146C4×Dic3—64no—
147C4×Dic3—64no—
148C4×Dic3—64no—
149C2×C3⋊C8—64no—
150C2×C3⋊C8—64no—
151ΓL(1,𝔽25)—616no—
152ΓL(1,𝔽25)—128no—
153C22×C32—22no—
154C22×C32—41no—
155C22×C32—41no—
156C22×C32C2×C22⋊C411yescharacteristic
157C2×C3⋊D3—21no—
158C2×C3⋊D3—21no—
159C2×C3⋊D3—21no—
160C32×C4—21no—
161C32×C4—41no—
162C32×C4C2×M1611yescharacteristic
163C32×C4C2×M1611yescharacteristic
164C32×C4AGL(1,ℤ/8)11yescharacteristic
165C32×C4#13711yescharacteristic
166C3⋊Dic3—22no—
167C3⋊Dic3—21no—
168C3⋊Dic3—21no—
169C3⋊Dic3—41no—
170C3⋊Dic3#10412yes—
171C2×#41—91no—
172C2×M16—181no—
173C2×M16—181no—
174C4×Q8—91no—
175C4×Q8—91no—
176C4×D4—91no—
177C4×D4—181no—
178C4×D4—181no—
179C4×D4C2×C3⋊D311yescharacteristic
180#117—91no—
181#117—181no—
182C2×C42—91no—
183C2×C42—181no—
184C4⋊C8—91no—
185C4⋊C8—181no—
186C4⋊C8C2×C3⋊D311yescharacteristic
187#97—181no—
188C4×C8—91no—
189C4×C8C2×C3⋊D311yescharacteristic
190C23×C3—24no—
191C22×D3—34no—
192C3×D4—24no—
193C3×D4ΓL(1,𝔽25)18yescomplemented
194C2×C3×C4—24no—
195C2×C3×C4—44no—
196C2×C3×C4—44no—
197C2×C3×C4C2×C4×D314yes—
198C2×C3×C4D3×D414yes—
199C2×C3×C4D3×D414yes—
200#67—616no—
201C2×Dic3—34no—
202C2×Dic3—34no—
203C2×Dic3—34no—
204C2×Dic3—616no—
205C2×Dic3—64no—
206C2×Dic3—64no—
207C2×Dic3—128no—
208C4×D3—68no—
209C4×D3—64no—
210C4×D3—64no—
211C4×D3—64no—
212C4×D3—64no—
213Dic6—38no—
214Dic6—64no—
215C3×C8—28no—
216C3×C8—44no—
217C3⋊C8—68no—
218C3⋊C8—124no—
219C2×C32—42no—
220C2×C32#40711yescharacteristic
221C2×C32#41711yescharacteristic
222C2×C32C2×#10411yescharacteristic
223C3⋊D3—41no—
224#41—182no—
225#41—182no—
226C2×Q8—91no—
227C2×D4—181no—
228C2×D4C4×C3⋊D311yescharacteristic
229C22×C4—21no—
230C22×C4—91no—
231C22×C4—91no—
232C22×C4—91no—
233C22×C4—181no—
234C22×C4—181no—
235M16—184no—
236M16—362no—
237C2×C8—21no—
238C2×C8—21no—
239C2×C8—181no—
240C2×C8—181no—
241C4⋊C4—91no—
242C4⋊C4—181no—
243C4⋊C4—181no—
244C4⋊C4C4×C3⋊D311yescharacteristic
245C22⋊C4—21no—
246C22⋊C4—181no—
247C22⋊C4—181no—
248C42—91no—
249C42—91no—
250C42—91no—
251C42—181no—
252C42—181no—
253C42—181no—
254C42C22×C3⋊D311yescharacteristic
255C22×C3—28no—
256C22×C3—44no—
257C22×C3—44no—
258C22×C3D3×C22⋊C414yes—
259C2×D3—64no—
260C2×D3—64no—
261C2×D3—64no—
262C3×C4—24no—
263C3×C4—44no—
264C3×C4C2×ΓL(1,𝔽25)14yes—
265C3×C4D3×M1614yes—
266C3×C4#91114yes—
267C3×C4#91514yes—
268Dic3—38no—
269Dic3—68no—
270Dic3—64no—
271Dic3—64no—
272Dic3—124no—
273C32#148911yescharacteristic, complemented, Sylow
274C23—21no—
275C23—91no—
276Q8—92no—
277Q8—181no—
278D4—21no—
279D4—184no—
280D4#374312yescomplemented
281C2×C4—21no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—91no—
285C2×C4—91no—
286C2×C4—91no—
287C2×C4—182no—
288C2×C4—184no—
289C2×C4—181no—
290C2×C4—181no—
291C2×C4—181no—
292C2×C4—181no—
293C2×C4—181no—
294C2×C4—181no—
295C2×C4—362no—
296C2×C4C2×C4×C3⋊D311yescharacteristic
297C2×C4D4×C3⋊D311yescharacteristic
298C2×C4D4×C3⋊D311yescharacteristic
299C8—22no—
300C8—41no—
301C8—182no—
302C8—361no—
303C2×C3—48no—
304C2×C3#472614yes—
305C2×C3#477114yes—
306C2×C3D3×#10414yes—
307D3—124no—
308C22—22no—
309C22—41no—
310C22—41no—
311C22—181no—
312C22—181no—
313C22—181no—
314C22C22⋊C4×C3⋊D311yescharacteristic
315C4—21no—
316C4—41no—
317C4—92no—
318C4—181no—
319C4—182no—
320C4—181no—
321C4—361no—
322C4C2×#374311yescharacteristic
323C4M16×C3⋊D311yescharacteristic
324C4#6412011yescharacteristic
325C4#6412411yescharacteristic
326C3#6817414yescomplemented
327C2—42no—
328C2—361no—
329C2#1059242511yescharacteristic
330C2#1059247011yescharacteristic
331C2C3⋊D3×#10411yescharacteristic
subgroupG/H
centerC2×C4D4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC42C22×C3⋊D3
FittingC32×D4⋊C8C2
socleC22×C32C2×C22⋊C4
prime radicalC2×#3830C4
cosocleC32×C42C23
hypercenterD4⋊C8C3⋊D3
hypocenterC32#1489
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. #10592536C2semidirect
3. C4×#3743C2semidirect
4. C32×D4⋊C8C2semidirect
5. D4⋊(C3⋊(C3⋊C8))C2semidirect
6. #10589350C2semidirect
7. #10589322C2semidirect
31. C3×D4⋊C8D3semidirect
89. C32×D4M16semidirect
110. #634M16semidirect
121. D4⋊C8C3⋊D3semidirect
193. C3×D4ΓL(1,𝔽25)semidirect
273. C32#1489semidirect
280. D4#3743semidirect
326. C3#68174semidirect

Maximal subgroups

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

subgroupindex
C4×#38302
#105925362
C4×#37432
C32×D4⋊C82
D4⋊(C3⋊(C3⋊C8))2
#105893502
#105893222
#681743