Finite Group Databasebeta

← #11774599

Subgroups — #11774599

Order 1152.

738 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 155 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#10592534C211yesmaximal, characteristic, complemented
3#10592384C211yesmaximal, characteristic, complemented
4C32×D4⋊C8C211yesmaximal, characteristic, complemented
5D4⋊(C3⋊(C3⋊C8))C211yesmaximal, characteristic, complemented
6#10589350C211yesmaximal, characteristic, complemented
7#10589322C211yesmaximal, characteristic, complemented
8#68173—34nomaximal
9C2×#3830C411yescharacteristic
10C32×C4×D4C2211yescharacteristic
11D4×C3⋊Dic3C411yescharacteristic
12C4×#638—21no—
13C2×C4×C3⋊Dic3—21no—
14#64101C411yescharacteristic
15#64096C411yescharacteristic
16#64090—21no—
17#64086—21no—
18C42×C3⋊D3C2211yescharacteristic
19C4×#634C2211yescharacteristic
20C32×C4⋊C8C2211yescharacteristic
21C32×C4×C8C2211yescharacteristic
22#63647—21no—
23#63647—21no—
24#63642—21no—
25#63641—21no—
26C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
27C4×C3⋊(C3⋊C8)C2211yescharacteristic
28C4×#237—34no—
29#4835—34no—
30#4685—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#1488—91noSylow
65C2×#237—34no—
66C3×C4×D4C2×D314yes—
67D4×Dic3—34no—
68C4×#67—64no—
69C2×C4×Dic3—64no—
70#892—34no—
71#887—34no—
72#67⋊C4—64no—
73#877—64no—
74C42×D3—34no—
75C4×Dic6—34no—
76C3×C4⋊C8C2×D314yes—
77C3×C4×C8C2×D314yes—
78(C2×D3)⋊C8—64no—
79(C2×D3)⋊C8—64no—
80#815—64no—
81Dic3⋊C8—64no—
82C4⋊(C3⋊C8)—34no—
83C4×C3⋊C8—34no—
84C23×C32—21no—
85C22×C3⋊D3C22⋊C411yescharacteristic
86C32×D4—21no—
87C32×D4M1612yes—
88C2×C32×C4—21no—
89C2×C32×C4—41no—
90C2×C32×C4—41no—
91C2×C32×C4C22×C411yescharacteristic
92C2×C32×C4C2×D411yescharacteristic
93C2×C32×C4C2×D411yescharacteristic
94#638—24no—
95C2×C3⋊Dic3—24no—
96C2×C3⋊Dic3—21no—
97C2×C3⋊Dic3—21no—
98C2×C3⋊Dic3—42no—
99C2×C3⋊Dic3C22⋊C411yescharacteristic
100C2×C3⋊Dic3C22⋊C411yescharacteristic
101C2×C3⋊Dic3C22⋊C411yescharacteristic
102C4×C3⋊D3—21no—
103C4×C3⋊D3—21no—
104C4×C3⋊D3—21no—
105C4×C3⋊D3—21no—
106C4×C3⋊D3—41no—
107#634—21no—
108#634M1612yes—
109C32×C8—41no—
110C32×C8—41no—
111C3⋊(C3⋊C8)—41no—
112C3⋊(C3⋊C8)—41no—
113C4×#41—91no—
114#432—91no—
115#431—91no—
116Q8⋊C8—91no—
117Q8⋊C8—91no—
118D4⋊C8—91no—
119D4⋊C8C3⋊D311yescharacteristic, complemented
120C2×C3×D4C4×D314yes—
121C22×C3×C4—24no—
122C2×#67—64no—
123C22×Dic3—64no—
124C22×Dic3—64no—
125#237—68no—
126#237—68no—
127C2×C4×D3—34no—
128C2×C4×D3—34no—
129C2×C4×D3—34no—
130C2×Dic6—34no—
131C2×C3×C8—24no—
132C2×C3×C8—24no—
133C3×C4⋊C4C4×D314yes—
134C3×C22⋊C4—24no—
135C3×C42C22×D314yes—
136#217—64no—
137(C2×D3)⋊C4—64no—
138C4⋊Dic3—34no—
139Dic3⋊C4—64no—
140Dic3⋊C4—64no—
141C4×Dic3—34no—
142C4×Dic3—34no—
143C4×Dic3—34no—
144C4×Dic3—64no—
145C4×Dic3—64no—
146C4×Dic3—64no—
147C2×C3⋊C8—64no—
148C2×C3⋊C8—64no—
149C22×C32—22no—
150C22×C32—41no—
151C22×C32—41no—
152C22×C32C2×C22⋊C411yescharacteristic
153C2×C3⋊D3—21no—
154C2×C3⋊D3—21no—
155C2×C3⋊D3—21no—
156C32×C4—21no—
157C32×C4—41no—
158C32×C4C2×M1611yescharacteristic
159C32×C4C2×M1611yescharacteristic
160C32×C4#13511yescharacteristic
161C32×C4#13511yescharacteristic
162C3⋊Dic3—22no—
163C3⋊Dic3—21no—
164C3⋊Dic3—21no—
165C3⋊Dic3—21no—
166C3⋊Dic3—41no—
167C2×#41—91no—
168C4×Q8—91no—
169C4×Q8—91no—
170C4×D4—91no—
171C4×D4—181no—
172C4×D4—181no—
173C4×D4C2×C3⋊D311yescharacteristic
174#117—91no—
175#117—181no—
176C2×C42—91no—
177C2×C42—181no—
178C4⋊C8—91no—
179C4⋊C8—181no—
180C4⋊C8C2×C3⋊D311yescharacteristic
181C22⋊C8—181no—
182C22⋊C8—181no—
183#97—181no—
184C4×C8—91no—
185C4×C8C2×C3⋊D311yescharacteristic
186C23×C3—24no—
187C22×D3—34no—
188C3×D4—24no—
189C3×D4ΓL(1,𝔽25)18yes—
190C2×C3×C4—24no—
191C2×C3×C4—44no—
192C2×C3×C4—44no—
193C2×C3×C4C2×C4×D314yes—
194C2×C3×C4D3×D414yes—
195C2×C3×C4D3×D414yes—
196#67—616no—
197C2×Dic3—34no—
198C2×Dic3—34no—
199C2×Dic3—34no—
200C2×Dic3—616no—
201C2×Dic3—64no—
202C2×Dic3—64no—
203C2×Dic3—128no—
204C4×D3—64no—
205C4×D3—64no—
206C4×D3—64no—
207C4×D3—64no—
208C4×D3—124no—
209Dic6—38no—
210Dic6—64no—
211C3×C8—44no—
212C3×C8—44no—
213C3⋊C8—124no—
214C3⋊C8—124no—
215C2×C32—42no—
216C2×C32#40711yescharacteristic
217C2×C32#41611yescharacteristic
218C2×C32#42111yescharacteristic
219C3⋊D3—41no—
220#41—182no—
221#41—182no—
222C2×Q8—91no—
223C2×D4—181no—
224C2×D4C4×C3⋊D311yescharacteristic
225C22×C4—21no—
226C22×C4—91no—
227C22×C4—91no—
228C22×C4—91no—
229C22×C4—181no—
230C22×C4—181no—
231C2×C8—21no—
232C2×C8—21no—
233C2×C8—181no—
234C2×C8—181no—
235C4⋊C4—91no—
236C4⋊C4—181no—
237C4⋊C4—181no—
238C4⋊C4C4×C3⋊D311yescharacteristic
239C22⋊C4—21no—
240C22⋊C4—181no—
241C22⋊C4—181no—
242C42—91no—
243C42—91no—
244C42—91no—
245C42—181no—
246C42—181no—
247C42—181no—
248C42C22×C3⋊D311yescharacteristic
249C22×C3—28no—
250C22×C3—44no—
251C22×C3—44no—
252C22×C3D3×C22⋊C414yes—
253C2×D3—64no—
254C2×D3—64no—
255C2×D3—64no—
256C3×C4—24no—
257C3×C4—44no—
258C3×C4C2×ΓL(1,𝔽25)14yes—
259C3×C4D3×M1614yes—
260C3×C4#91214yes—
261C3×C4#91614yes—
262Dic3—68no—
263Dic3—64no—
264Dic3—64no—
265Dic3—64no—
266Dic3—124no—
267C32#148811yescharacteristic, complemented, Sylow
268C23—21no—
269C23—91no—
270Q8—92no—
271Q8—181no—
272D4—21no—
273D4—184no—
274D4#374312yes—
275C2×C4—21no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—91no—
279C2×C4—91no—
280C2×C4—91no—
281C2×C4—184no—
282C2×C4—181no—
283C2×C4—181no—
284C2×C4—181no—
285C2×C4—181no—
286C2×C4—181no—
287C2×C4—181no—
288C2×C4—361no—
289C2×C4—362no—
290C2×C4C2×C4×C3⋊D311yescharacteristic
291C2×C4D4×C3⋊D311yescharacteristic
292C2×C4D4×C3⋊D311yescharacteristic
293C8—41no—
294C8—41no—
295C8—361no—
296C8—361no—
297C2×C3—48no—
298C2×C3#472614yes—
299C2×C3#477214yes—
300C2×C3#482114yes—
301D3—124no—
302C22—22no—
303C22—41no—
304C22—41no—
305C22—181no—
306C22—181no—
307C22—181no—
308C22C22⋊C4×C3⋊D311yescharacteristic
309C4—21no—
310C4—41no—
311C4—181no—
312C4—181no—
313C4—182no—
314C4—181no—
315C4—361no—
316C4C2×#374311yescharacteristic
317C4M16×C3⋊D311yescharacteristic
318C4#6412111yescharacteristic
319C4#6412511yescharacteristic
320C3#6817314yescomplemented
321C2—42no—
322C2—361no—
323C2#1059242511yescharacteristic
324C2#1059247111yescharacteristic
325C2#1059252011yescharacteristic
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#1488
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. #10592384C2semidirect
4. C32×D4⋊C8C2semidirect
5. D4⋊(C3⋊(C3⋊C8))C2semidirect
6. #10589350C2semidirect
7. #10589322C2semidirect
31. C3×D4⋊C8D3semidirect
119. D4⋊C8C3⋊D3semidirect
267. C32#1488semidirect
320. C3#68173semidirect

Maximal subgroups

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

subgroupindex
C4×#38302
#105925342
#105923842
C32×D4⋊C82
D4⋊(C3⋊(C3⋊C8))2
#105893502
#105893222
#681733