Finite Group Databasebeta

← #11878700

Subgroups — #11878700

Order 1152.

1284 conjugacy classes of subgroups; only the 241 normal subgroups are shown.

normal subgroups only

This group has 1284 conjugacy classes of subgroups — too many to draw. Only its 241 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#10596196C211yesmaximal, characteristic
2C3⋊D3×C4⋊Q8C211yesmaximal, characteristic, complemented
3C32×#487C211yesmaximal, characteristic, complemented
4#10592792C211yesmaximal, characteristic, complemented
5#10592784C211yesmaximal, characteristic, complemented
6#10592517C214yesmaximal, complemented
7#10592505C214yesmaximal, complemented
8#10592392C211yesmaximal, characteristic, complemented
9#10592384C211yesmaximal, characteristic, complemented
10#81602—34nomaximal
11C2×#3832—21no—
12C2×Q8×C3⋊D3C2212yes—
13C32×C4⋊Q8C2211yescharacteristic
14C32×C4⋊Q8C2211yescharacteristic
15#64156—21no—
16#64153C2212yes—
17C2×#3755C2214yes—
18C2×#3744C2214yes—
19#64104—21no—
20#64104C2212yes—
21#64102—21no—
22#64102C2212yes—
23C4⋊C4×C3⋊D3—21no—
24C4⋊C4×C3⋊D3—21no—
25#64097—21no—
26#64097—21no—
27#64083C2211yescharacteristic
28C42×C3⋊D3C2211yescharacteristic
29#64078C2211yescharacteristic
30C32×#103C2214yes—
31C32×C4×C8C2211yescharacteristic
32#63647C2212yes—
33#63641C2212yes—
34#63637C2214yes—
35C4×C3⋊(C3⋊C8)C2211yescharacteristic
36#5725—34no—
37D3×C4⋊Q8—34no—
38C3×#487D314yescomplemented
39#5093—34no—
40#5085—34no—
41#4818—316no—
42#4806—316no—
43#4693—34no—
44#4685—34no—
45C2×C32×Q8—21no—
46C2×C32×Q8C2312yes—
47#3832—44no—
48Q8×C3⋊D3—44no—
49C2×C4⋊(C3⋊D3)—22no—
50C2×C4⋊(C3⋊D3)—21no—
51C2×C4⋊(C3⋊D3)—21no—
52C2×C4⋊(C3⋊D3)C2312yes—
53C2×C4×C3⋊D3—22no—
54C2×C4×C3⋊D3—22no—
55C2×C4×C3⋊D3D411yescharacteristic
56C2×C4×C3⋊D3D411yescharacteristic
57C2×C4×C3⋊D3C2311yescharacteristic
58C2×#634—22no—
59C2×#634C2312yes—
60C2×C32×C8C2312yes—
61C32×C4⋊C4—21no—
62C32×C4⋊C4—21no—
63C32×C4⋊C4—21no—
64C32×C4⋊C4C2312yes—
65C32×C42C2311yescharacteristic
66#3755—44no—
67#3752—22no—
68#3752—22no—
69C4⋊(C3⋊Dic3)—21no—
70C4⋊(C3⋊Dic3)—21no—
71#3750—22no—
72#3750—22no—
73C4×C3⋊Dic3D411yescharacteristic
74C4×C3⋊Dic3D411yescharacteristic
75C4×C3⋊Dic3C2311yescharacteristic
76C2×C3⋊(C3⋊C8)C2312yes—
77#3744—44no—
78#3206—91noSylow
79C2×#239—64no—
80C2×D3×Q8—38no—
81C3×C4⋊Q8C2×D314yes—
82C3×C4⋊Q8C2×D314yes—
83#947—64no—
84#944—38no—
85C2×#215—316no—
86C2×#204—316no—
87#895—38no—
88#895—64no—
89#893—38no—
90#893—64no—
91D3×C4⋊C4—64no—
92D3×C4⋊C4—64no—
93#888—64no—
94#888—64no—
95#874—34no—
96C42×D3—34no—
97#869—34no—
98C3×#103C2×D3116yes—
99C3×C4×C8C2×D314yes—
100(C2×D3)⋊C8—38no—
101Dic3⋊C8—38no—
102#810—316no—
103C4×C3⋊C8—34no—
104C22×C3⋊D3—22no—
105C22×C3⋊D3C2×D411yescharacteristic
106C32×Q8—24no—
107C32×Q8—42no—
108C2×C32×C4—22no—
109C2×C32×C4—22no—
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2411yescharacteristic
113C2×C3⋊Dic3—22no—
114C2×C3⋊Dic3C2×D411yescharacteristic
115C2×C3⋊Dic3C2×D411yescharacteristic
116C2×C3⋊Dic3C2×D411yescharacteristic
117C4⋊(C3⋊D3)—24no—
118C4⋊(C3⋊D3)—44no—
119C4⋊(C3⋊D3)—42no—
120C4⋊(C3⋊D3)—42no—
121C4×C3⋊D3—22no—
122C4×C3⋊D3—22no—
123C4×C3⋊D3—44no—
124C4×C3⋊D3—44no—
125C4×C3⋊D3SD1614yescomplemented
126#634—24no—
127#634—44no—
128C32×C8—22no—
129C3⋊(C3⋊C8)—22no—
130#532—91no—
131C2×C4⋊Q8—91no—
132#492—91no—
133#492—91no—
134#487—91no—
135#487C3⋊D311yescharacteristic, complemented
136#461—94no—
137#448—94no—
138#431—91no—
139C2×C3×Q8—24no—
140C2×C3×Q8C22×D318yes—
141#239—1216no—
142D3×Q8—1216no—
143C2×D12—38no—
144C2×D12—68no—
145C2×D12—64no—
146C2×D12—64no—
147C2×C4×D3—34no—
148C2×C4×D3—34no—
149C2×C4×D3—34no—
150C2×C4×D3—68no—
151C2×C4×D3—68no—
152C2×Dic6—38no—
153C2×Dic6—68no—
154C2×C3×C8C22×D318yes—
155C3×C4⋊C4—24no—
156C3×C4⋊C4—24no—
157C3×C4⋊C4—24no—
158C3×C4⋊C4C22×D318yes—
159C3×C42C22×D314yes—
160#215—1216no—
161(C2×D3)⋊C4—68no—
162(C2×D3)⋊C4—68no—
163C4⋊Dic3—64no—
164C4⋊Dic3—64no—
165Dic3⋊C4—68no—
166Dic3⋊C4—68no—
167C4×Dic3—34no—
168C4×Dic3—34no—
169C4×Dic3—34no—
170C2×C3⋊C8—38no—
171#204—1216no—
172C22×C32C22×D411yescharacteristic
173C2×C3⋊D3—21no—
174C2×C3⋊D3—21no—
175C2×C3⋊D3—42no—
176C2×C3⋊D3—42no—
177C2×C3⋊D3—42no—
178C2×C3⋊D3C2×SD1612yes—
179C32×C4—42no—
180C32×C4—42no—
181C32×C4C2×SD1612yes—
182C32×C4#13712yes—
183C32×C4H(5,𝔽2)12yes—
184C3⋊Dic3—21no—
185C3⋊Dic3—21no—
186C3⋊Dic3—42no—
187C3⋊Dic3C2×SD1612yes—
188C2×#41—181no—
189C22×Q8—92no—
190C2×SD16—94no—
191C2×SD16—94no—
192C4⋊Q8—92no—
193C4⋊Q8—91no—
194C4⋊Q8—181no—
195C4⋊Q8—181no—
196C4⋊Q8C2×C3⋊D311yescharacteristic
197C4⋊Q8C2×C3⋊D311yescharacteristic
198#127—91no—
199#124—181no—
200#121—92no—
201#121—181no—
202C4×D4—92no—
203C4×D4—181no—
204C2×C4⋊C4—181no—
205C2×C4⋊C4—181no—
206C2×C42—91no—
207C4⋊C8—92no—
208#103—94no—
209#103C2×C3⋊D314yes—
210C22⋊C8—92no—
211C4×C8—91no—
212C4×C8C2×C3⋊D311yescharacteristic
213C22×D3—34no—
214C22×D3—68no—
215C3×Q8—216no—
216C3×Q8—48no—
217C2×C3×C4—28no—
218C2×C3×C4—28no—
219C2×C3×C4D3×D414yes—
220C2×C3×C4D3×D414yes—
221C2×C3×C4C23×D314yes—
222C2×Dic3—34no—
223C2×Dic3—34no—
224C2×Dic3—34no—
225C2×Dic3—68no—
226D12—616no—
227D12—1216no—
228D12—128no—
229D12—128no—
230C4×D3—316no—
231C4×D3—68no—
232C4×D3—68no—
233C4×D3—1216no—
234C4×D3—1216no—
235Dic6—616no—
236Dic6—1216no—
237C3×C8—28no—
238C3⋊C8—68no—
239C2×C32#53511yescharacteristic
240C2×C32C22×SD1611yescharacteristic
241C2×C32C2×#13711yescharacteristic
242C3⋊D3—22no—
243C3⋊D3—82no—
244#41—364no—
245C2×Q8—21no—
246C2×Q8—92no—
247C2×Q8—182no—
248C2×Q8—364no—
249C2×Q8C22×C3⋊D312yes—
250C2×D4—92no—
251C2×D4—182no—
252C2×D4—181no—
253C2×D4—181no—
254C22×C4—91no—
255C22×C4—91no—
256C22×C4—91no—
257C22×C4—182no—
258C22×C4—182no—
259SD16—364no—
260SD16—364no—
261C2×C8—92no—
262C2×C8C22×C3⋊D312yes—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—182no—
267C4⋊C4—182no—
268C4⋊C4—181no—
269C4⋊C4—181no—
270C4⋊C4C22×C3⋊D312yes—
271C22⋊C4—182no—
272C22⋊C4—182no—
273C42—91no—
274C42—91no—
275C42—91no—
276C42C22×C3⋊D311yescharacteristic
277C22×C3C2×D3×D414yes—
278C2×D3—38no—
279C2×D3—64no—
280C2×D3—64no—
281C2×D3—128no—
282C2×D3—128no—
283C2×D3—128no—
284C3×C4—48no—
285C3×C4—48no—
286C3×C4D3×SD1618yes—
287C3×C4#91818yes—
288C3×C4#100918yes—
289Dic3—38no—
290Dic3—64no—
291Dic3—64no—
292Dic3—128no—
293C32#320611yescharacteristic, complemented, Sylow
294C23—91no—
295C23—182no—
296Q8—24no—
297Q8—42no—
298Q8—184no—
299Q8—364no—
300D4—184no—
301D4—364no—
302D4—362no—
303D4—362no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—91no—
307C2×C4—94no—
308C2×C4—91no—
309C2×C4—91no—
310C2×C4—182no—
311C2×C4—182no—
312C2×C4—182no—
313C2×C4—364no—
314C2×C4—364no—
315C2×C4D4×C3⋊D311yescharacteristic
316C2×C4D4×C3⋊D311yescharacteristic
317C2×C4C23×C3⋊D311yescharacteristic
318C8—22no—
319C8—182no—
320C2×C3#567414yes—
321C2×C3C2×D3×SD1614yes—
322C2×C3C2×#91814yes—
323D3—68no—
324D3—248no—
325C22—92no—
326C22—181no—
327C22—181no—
328C22—362no—
329C22—362no—
330C22—362no—
331C22C2×D4×C3⋊D311yescharacteristic
332C4—42no—
333C4—42no—
334C4—92no—
335C4—181no—
336C4—181no—
337C4—362no—
338C4SD16×C3⋊D312yes—
339C4#6412712yes—
340C4#6436612yes—
341C3#8160214yescomplemented
342C2—182no—
343C2—722no—
344C2#1059614511yescharacteristic
345C2C2×SD16×C3⋊D311yescharacteristic
346C2C2×#6412711yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#487C2
socleC22×C32C22×D4
prime radical#10596196C2
hypercenter#487C3⋊D3
hypocenterC32#3206
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. C3⋊D3×C4⋊Q8C2semidirect
3. C32×#487C2semidirect
4. #10592792C2semidirect
5. #10592784C2semidirect
6. #10592517C2semidirect
7. #10592505C2semidirect
8. #10592392C2semidirect
9. #10592384C2semidirect
38. C3×#487D3semidirect
125. C4×C3⋊D3SD16semidirect
135. #487C3⋊D3semidirect
293. C32#3206semidirect
341. C3#81602semidirect

Maximal subgroups

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

subgroupindex
#105961962
C3⋊D3×C4⋊Q82
C32×#4872
#105927922
#105927842
#105925172
#105925052
#105923922
#105923842
#816023