Finite Group Databasebeta

← #11775863

Subgroups — #11775863

Order 1152.

768 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 768 conjugacy classes of subgroups — too many to draw. Only its 121 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#10596139C211yesmaximal, characteristic
2#10592404C211yesmaximal, characteristic, complemented
3C3⋊D3×#97C211yesmaximal, characteristic, complemented
4C32×#329C211yesmaximal, characteristic, complemented
5#10589406C211yesmaximal, characteristic, complemented
6#10589330C211yesmaximal, characteristic, complemented
7#10589330C211yesmaximal, characteristic, complemented
8#68345—34nomaximal
9C2×#3832C411yescharacteristic
10C2×#3830C411yescharacteristic
11C32×#124C2211yescharacteristic
12#64153C411yescharacteristic
13#64149C411yescharacteristic
14C2×C8×C3⋊D3—21no—
15#64093—21no—
16#64093—21no—
17#64090—21no—
18#64090—21no—
19#64084C2211yescharacteristic
20C42×C3⋊D3C2211yescharacteristic
21C32×#97C2211yescharacteristic
22C32×#97C2211yescharacteristic
23#63647—21no—
24#63642—21no—
25#63641—21no—
26#63630C2211yescharacteristic
27#63630C2211yescharacteristic
28#5668—34no—
29#4705—34no—
30D3×#97—34no—
31C3×#329D314yescomplemented
32#4540—34no—
33#4464—34no—
34#4464—34no—
35C2×C32×Q8C2×C411yescharacteristic
36C2×C32×D4C2×C411yescharacteristic
37C2×#638—21no—
38C2×#638—21no—
39C2×#638—21no—
40C22×C3⋊Dic3—21no—
41#3832—42no—
42#3830—42no—
43C2×C4⋊(C3⋊D3)—21no—
44C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
45C2×C4×C3⋊D3—21no—
46C2×C4×C3⋊D3C2×C411yescharacteristic
47C2×C4×C3⋊D3D411yescharacteristic
48C2×C4×C3⋊D3D411yescharacteristic
49C2×#634C2×C411yescharacteristic
50C2×C32×C8—21no—
51C2×C32×C8—21no—
52C32×C22⋊C4—21no—
53C32×C22⋊C4—21no—
54C32×C42C2311yescharacteristic
55#3752—21no—
56#3752—21no—
57#3750—21no—
58#3750—21no—
59C4×C3⋊Dic3C2×C411yescharacteristic
60C4×C3⋊Dic3D411yescharacteristic
61C4×C3⋊Dic3D411yescharacteristic
62C2×C3⋊(C3⋊C8)—21no—
63C2×C3⋊(C3⋊C8)—21no—
64C8×C3⋊D3—24no—
65#1530—91noSylow
66C2×#239—34no—
67C2×#237—34no—
68C3×#124C2×D314yes—
69#944—34no—
70#940—34no—
71C2×D3×C8—64no—
72#884—64no—
73#884—64no—
74#67⋊C4—64no—
75#67⋊C4—64no—
76#875—34no—
77C42×D3—34no—
78C3×#97C2×D314yes—
79C3×#97C2×D314yes—
80(C2×D3)⋊C8—64no—
81#815—64no—
82Dic3⋊C8—64no—
83#803—34no—
84#803—34no—
85C23×C32—21no—
86C22×C3⋊D3—21no—
87C22×C3⋊D3C22⋊C411yescharacteristic
88C32×Q8—41no—
89C32×D4—41no—
90C2×C32×C4—21no—
91C2×C32×C4C22×C411yescharacteristic
92C2×C32×C4C2×D411yescharacteristic
93C2×C32×C4C2×D411yescharacteristic
94#638—42no—
95#638—42no—
96#638—42no—
97C2×C3⋊Dic3—21no—
98C2×C3⋊Dic3—42no—
99C2×C3⋊Dic3C22⋊C411yescharacteristic
100C2×C3⋊Dic3C22⋊C411yescharacteristic
101C2×C3⋊Dic3C22⋊C411yescharacteristic
102C4⋊(C3⋊D3)—41no—
103C4⋊(C3⋊D3)—42no—
104C4×C3⋊D3—22no—
105C4×C3⋊D3—22no—
106C4×C3⋊D3—41no—
107C4×C3⋊D3—42no—
108#634—41no—
109C32×C8—22no—
110C32×C8—41no—
111C3⋊(C3⋊C8)—22no—
112C3⋊(C3⋊C8)—41no—
113#532—91no—
114#432—91no—
115C2×#97—91no—
116#329—91no—
117#329—91no—
118#329—91no—
119#329C3⋊D311yescharacteristic, complemented
120C2×C3×Q8C4×D314yes—
121C2×C3×D4C4×D314yes—
122C2×#67—64no—
123C2×#67—64no—
124C2×#67—64no—
125C22×Dic3—64no—
126#239—128no—
127#237—128no—
128C2×D12—34no—
129C2×D12—64no—
130C2×C4×D3—34no—
131C2×C4×D3—34no—
132C2×C4×D3—34no—
133C2×C4×D3—64no—
134C2×Dic6—34no—
135C2×C3×C8—24no—
136C2×C3×C8—24no—
137C3×C22⋊C4—24no—
138C3×C22⋊C4—24no—
139C3×C42C22×D314yes—
140(C2×D3)⋊C4—64no—
141(C2×D3)⋊C4—64no—
142Dic3⋊C4—64no—
143Dic3⋊C4—64no—
144C4×Dic3—34no—
145C4×Dic3—34no—
146C4×Dic3—34no—
147C2×C3⋊C8—64no—
148C2×C3⋊C8—64no—
149D3×C8—616no—
150C22×C32—41no—
151C22×C32—41no—
152C22×C32—41no—
153C22×C32C2×C22⋊C411yescharacteristic
154C2×C3⋊D3—21no—
155C2×C3⋊D3—21no—
156C2×C3⋊D3—41no—
157C2×C3⋊D3—41no—
158C2×C3⋊D3—41no—
159C2×C3⋊D3#10012yes—
160C32×C4—21no—
161C32×C4—21no—
162C32×C4—21no—
163C32×C4—41no—
164C3⋊Dic3—21no—
165C3⋊Dic3—21no—
166C3⋊Dic3—41no—
167C3⋊Dic3#10412yes—
168C2×#41—91no—
169C2×#41—91no—
170C22×C8—181no—
171C4⋊Q8—91no—
172#127—91no—
173#124—91no—
174#124C2×C3⋊D311yescharacteristic
175#121—181no—
176#121—181no—
177C4×D4—181no—
178C4×D4—181no—
179C2×C42—91no—
180C4⋊C8—181no—
181C22⋊C8—181no—
182#97—91no—
183#97—91no—
184#97—181no—
185#97C2×C3⋊D311yescharacteristic
186#97C2×C3⋊D311yescharacteristic
187C23×C3—24no—
188C22×D3—34no—
189C22×D3—64no—
190C3×Q8—44no—
191C3×D4—44no—
192C2×C3×C4—24no—
193C2×C3×C4C2×C4×D314yes—
194C2×C3×C4D3×D414yes—
195C2×C3×C4D3×D414yes—
196#67—128no—
197#67—128no—
198#67—128no—
199C2×Dic3—34no—
200C2×Dic3—34no—
201C2×Dic3—34no—
202C2×Dic3—64no—
203C2×Dic3—128no—
204D12—124no—
205D12—128no—
206C4×D3—68no—
207C4×D3—68no—
208C4×D3—124no—
209C4×D3—128no—
210Dic6—124no—
211C3×C8—28no—
212C3×C8—44no—
213C3⋊C8—68no—
214C3⋊C8—124no—
215C2×C32—81no—
216C2×C32C2×#10011yescharacteristic
217C2×C32C2×#10411yescharacteristic
218C2×C32#42111yescharacteristic
219C3⋊D3—22no—
220C3⋊D3—81no—
221#41—362no—
222#41—362no—
223C2×Q8—91no—
224C2×Q8C4×C3⋊D311yescharacteristic
225C2×D4—91no—
226C2×D4—181no—
227C2×D4—181no—
228C2×D4—181no—
229C2×D4—181no—
230C2×D4C4×C3⋊D311yescharacteristic
231C22×C4—91no—
232C22×C4—91no—
233C22×C4—91no—
234C22×C4—181no—
235C22×C4—181no—
236C2×C8—21no—
237C2×C8—21no—
238C2×C8—184no—
239C2×C8—181no—
240C2×C8—181no—
241C4⋊C4—181no—
242C4⋊C4—181no—
243C22⋊C4—21no—
244C22⋊C4—21no—
245C22⋊C4—181no—
246C22⋊C4—181no—
247C42—91no—
248C42—91no—
249C42—91no—
250C42C22×C3⋊D311yescharacteristic
251C22×C3—44no—
252C22×C3—44no—
253C22×C3—44no—
254C22×C3D3×C22⋊C414yes—
255C2×D3—38no—
256C2×D3—64no—
257C2×D3—64no—
258C2×D3—124no—
259C2×D3—124no—
260C2×D3—124no—
261C3×C4—24no—
262C3×C4—24no—
263C3×C4—24no—
264C3×C4—44no—
265Dic3—38no—
266Dic3—64no—
267Dic3—64no—
268Dic3—124no—
269C32#153011yescharacteristic, complemented, Sylow
270C23—21no—
271C23—91no—
272C23—181no—
273Q8—41no—
274Q8—361no—
275D4—41no—
276D4—361no—
277D4—362no—
278D4—362no—
279D4—362no—
280D4—362no—
281C2×C4—21no—
282C2×C4—91no—
283C2×C4—91no—
284C2×C4—91no—
285C2×C4—182no—
286C2×C4—182no—
287C2×C4—181no—
288C2×C4—361no—
289C2×C4—362no—
290C2×C4—362no—
291C2×C4C2×C4×C3⋊D311yescharacteristic
292C2×C4D4×C3⋊D311yescharacteristic
293C2×C4D4×C3⋊D311yescharacteristic
294C8—22no—
295C8—41no—
296C8—182no—
297C8—361no—
298C2×C3—84no—
299C2×C3D3×#10014yes—
300C2×C3D3×#10414yes—
301C2×C3#482114yes—
302D3—68no—
303D3—244no—
304C22—41no—
305C22—41no—
306C22—41no—
307C22—92no—
308C22—181no—
309C22—181no—
310C22—361no—
311C22—361no—
312C22—361no—
313C22C22⋊C4×C3⋊D311yescharacteristic
314C4—21no—
315C4—21no—
316C4—21no—
317C4—41no—
318C4—92no—
319C4—181no—
320C4—181no—
321C4—361no—
322C3#6834514yescomplemented
323C2—81no—
324C2—182no—
325C2—721no—
326C2C3⋊D3×#10011yescharacteristic
327C2C3⋊D3×#10411yescharacteristic
328C2#1059252011yescharacteristic
subgroupG/H
centerC22C22⋊C4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC42C22×C3⋊D3
FittingC32×#329C2
socleC22×C32C2×C22⋊C4
prime radical#10596139C2
cosocleC32×C42C23
hypercenter#329C3⋊D3
hypocenterC32#1530
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #10592404C2semidirect
3. C3⋊D3×#97C2semidirect
4. C32×#329C2semidirect
5. #10589406C2semidirect
6. #10589330C2semidirect
7. #10589330C2semidirect
31. C3×#329D3semidirect
119. #329C3⋊D3semidirect
269. C32#1530semidirect
322. C3#68345semidirect

Maximal subgroups

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

subgroupindex
#105961392
#105924042
C3⋊D3×#972
C32×#3292
#105894062
#105893302
#683453