Finite Group Databasebeta

← #11876963

Subgroups — #11876963

Order 1152.

1338 conjugacy classes of subgroups.

The subgroup lattice has 363 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#532C211yesmaximal, characteristic, complemented
2#10595948C211yesmaximal, characteristic, complemented
3#10592787C211yesmaximal, characteristic, complemented
4#10592779C211yesmaximal, characteristic, complemented
5#10592772C211yesmaximal, characteristic, complemented
6#10592769C211yesmaximal, characteristic, complemented
7#10592738C214yesmaximal, complemented
8#10592713C214yesmaximal, complemented
9C4×#3748C211yesmaximal, characteristic, complemented
10#83295—34nomaximal
11C2×C32×#41—21no—
12C2×#3828—21no—
13C32×C4⋊Q8C2211yescharacteristic
14C32×#127C2211yescharacteristic
15C32×#124—21no—
16C32×#121—21no—
17C32×#121C2212yes—
18C32×C4×D4—21no—
19C32×C4×D4C2212yes—
20C2×C32×C42C2211yescharacteristic
21C2×#3753C2214yes—
22#64139—21no—
23#64139C2212yes—
24C2×#3748C2212yes—
25#64084—21no—
26#64083C2211yescharacteristic
27C4×C4⋊(C3⋊D3)—21no—
28C4×C4⋊(C3⋊D3)C2212yes—
29#64078C2211yescharacteristic
30#63659C2214yes—
31#63636C2214yes—
32#63635C2214yes—
33#63630C2212yes—
34C4×C3⋊(C3⋊C8)C2211yescharacteristic
35C4×C3⋊(C3⋊C8)C2211yescharacteristic
36C3×#532D314yescomplemented
37#5477—34no—
38#5088—34no—
39#5080—34no—
40#5073—34no—
41#5070—34no—
42#5039—316no—
43#5014—316no—
44C4×#208—34no—
45C32×#41—44no—
46C2×C32×Q8—21no—
47C2×C32×D4—22no—
48C2×C32×D4—21no—
49C2×C32×D4—21no—
50C2×C32×D4C2312yes—
51C22×C32×C4—22no—
52C22×C32×C4D411yescharacteristic
53C22×C32×C4D411yescharacteristic
54C22×C32×C4C2311yescharacteristic
55C2×#638—22no—
56#3828—44no—
57C2×C4⋊(C3⋊D3)—21no—
58C2×C4⋊(C3⋊D3)—21no—
59C2×C4⋊(C3⋊D3)C2312yes—
60C2×C4×C3⋊D3—22no—
61C2×#634—21no—
62C32×C4⋊C4—21no—
63C32×C4⋊C4C2312yes—
64C32×C22⋊C4—22no—
65C32×C22⋊C4—22no—
66C32×C42D411yescharacteristic
67C32×C42D411yescharacteristic
68C32×C42C2311yescharacteristic
69C32×C42C2311yescharacteristic
70#3753—28no—
71#3752—22no—
72#3752—22no—
73C4⋊(C3⋊Dic3)—21no—
74C4⋊(C3⋊Dic3)C2312yes—
75#3748—24no—
76C2×C3⋊(C3⋊C8)C2312yes—
77C2×C3⋊(C3⋊C8)C2312yes—
78#3184—91noSylow
79C2×C3×#41—24no—
80C2×#235—64no—
81C3×C4⋊Q8C2×D314yes—
82C3×#127C2×D314yes—
83C3×#124—24no—
84C3×#121—24no—
85C3×#121C2×D318yes—
86C3×C4×D4—24no—
87C3×C4×D4C2×D318yes—
88C2×C3×C42C2×D314yes—
89C2×#213—316no—
90#930—38no—
91#930—64no—
92C2×#208—38no—
93#875—64no—
94#874—34no—
95C4×D12—38no—
96C4×D12—64no—
97#869—34no—
98#832—316no—
99#809—316no—
100#808—316no—
101#803—38no—
102C4×C3⋊C8—34no—
103C4×C3⋊C8—34no—
104C23×C32—22no—
105C23×C32C2×D411yescharacteristic
106C22×C3⋊D3—22no—
107C32×Q8—42no—
108C32×D4—24no—
109C32×D4—44no—
110C32×D4—42no—
111C32×D4—42no—
112C2×C32×C4—22no—
113C2×C32×C4—22no—
114C2×C32×C4—22no—
115C2×C32×C4—22no—
116C2×C32×C4—44no—
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2411yescharacteristic
123#638—44no—
124C2×C3⋊Dic3—22no—
125C4⋊(C3⋊D3)—24no—
126C4⋊(C3⋊D3)—42no—
127C4⋊(C3⋊D3)—42no—
128C4×C3⋊D3—44no—
129#634—42no—
130C3⋊(C3⋊C8)—22no—
131C3⋊(C3⋊C8)#4114yescomplemented
132#532—91no—
133#532C3⋊D311yescharacteristic, complemented
134#498—91no—
135#493—91no—
136#486—91no—
137#486—91no—
138#469—94no—
139#442—94no—
140C4×M16—91no—
141C3×#41—416no—
142C2×C3×Q8—24no—
143C2×C3×D4—28no—
144C2×C3×D4—24no—
145C2×C3×D4—24no—
146C2×C3×D4C22×D318yes—
147C22×C3×C4—28no—
148C22×C3×C4#6714yes—
149C22×C3×C4#6714yes—
150C22×C3×C4C22×D314yes—
151C2×#67—68no—
152#235—1216no—
153C2×D12—38no—
154C2×D12—64no—
155C2×D12—64no—
156C2×C4×D3—68no—
157C2×Dic6—64no—
158C3×C4⋊C4—24no—
159C3×C4⋊C4C22×D318yes—
160C3×C22⋊C4—28no—
161C3×C22⋊C4—28no—
162C3×C42#6714yes—
163C3×C42#6714yes—
164C3×C42C22×D314yes—
165C3×C42C22×D314yes—
166#213—632no—
167(C2×D3)⋊C4—68no—
168(C2×D3)⋊C4—68no—
169C4⋊Dic3—38no—
170C4⋊Dic3—64no—
171#208—616no—
172C2×C3⋊C8—38no—
173C2×C3⋊C8—38no—
174C22×C32—21no—
175C22×C32—21no—
176C22×C32—21no—
177C22×C32—42no—
178C22×C32—42no—
179C22×C32—42no—
180C22×C32C22×D411yescharacteristic
181C2×C3⋊D3—42no—
182C2×C3⋊D3—42no—
183C2×C3⋊D3—42no—
184C32×C4—21no—
185C32×C4—21no—
186C32×C4—21no—
187C32×C4—42no—
188C32×C4AGL(1,ℤ/8)12yes—
189C32×C4AGL(1,ℤ/8)12yes—
190C32×C4C2×#4112yes—
191C3⋊Dic3—42no—
192C2×#41—21no—
193C2×#41—181no—
194C2×D8—94no—
195C2×M16—92no—
196C4⋊Q8—91no—
197C4⋊Q8C2×C3⋊D311yescharacteristic
198#127—91no—
199#127C2×C3⋊D311yescharacteristic
200#124—21no—
201#124—181no—
202#121—21no—
203#121—92no—
204#121—181no—
205#121C2×C3⋊D312yes—
206C4×D4—21no—
207C4×D4—92no—
208C4×D4—181no—
209C4×D4C2×C3⋊D312yes—
210C2×C42C2×C3⋊D311yescharacteristic
211#106—94no—
212#102—94no—
213#102—94no—
214#97—92no—
215C4×C8—91no—
216C4×C8—91no—
217C23×C3—28no—
218C23×C3C2×#6714yes—
219C22×D3—68no—
220C3×Q8—48no—
221C3×D4—216no—
222C3×D4—416no—
223C3×D4—48no—
224C3×D4—48no—
225C2×C3×C4—28no—
226C2×C3×C4—28no—
227C2×C3×C4—28no—
228C2×C3×C4—28no—
229C2×C3×C4—416no—
230C2×C3×C4C2×#6714yes—
231C2×C3×C4C2×#6714yes—
232C2×C3×C4C2×#6714yes—
233C2×C3×C4C2×#6714yes—
234C2×C3×C4C2×#6714yes—
235C2×C3×C4C23×D314yes—
236#67—1216no—
237C2×Dic3—68no—
238D12—616no—
239D12—128no—
240D12—128no—
241C4×D3—1216no—
242Dic6—128no—
243C3⋊C8—316no—
244C3⋊C8—68no—
245C2×C32—41no—
246C2×C32—82no—
247C2×C32#53211yescharacteristic
248C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
249C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
250C3⋊D3—82no—
251#41—44no—
252#41—364no—
253C2×Q8—21no—
254C2×Q8—181no—
255C2×D4—22no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—92no—
259C2×D4—182no—
260C2×D4—181no—
261C2×D4—181no—
262C2×D4C22×C3⋊D312yes—
263C22×C4—22no—
264C22×C4—182no—
265C22×C4#63811yescharacteristic
266C22×C4#63811yescharacteristic
267C22×C4C22×C3⋊D311yescharacteristic
268D8—188no—
269M16—184no—
270C2×C8—92no—
271C2×C8—92no—
272C4⋊C4—21no—
273C4⋊C4—92no—
274C4⋊C4—181no—
275C4⋊C4C22×C3⋊D312yes—
276C22⋊C4—22no—
277C22⋊C4—22no—
278C22⋊C4—182no—
279C22⋊C4—182no—
280C42#63811yescharacteristic
281C42#63811yescharacteristic
282C42C22×C3⋊D311yescharacteristic
283C42C22×C3⋊D311yescharacteristic
284C22×C3—24no—
285C22×C3—24no—
286C22×C3—24no—
287C22×C3—48no—
288C22×C3—48no—
289C22×C3—48no—
290C22×C3C22×#6714yes—
291C2×D3—128no—
292C2×D3—128no—
293C2×D3—128no—
294C3×C4—24no—
295C3×C4—24no—
296C3×C4—24no—
297C3×C4—48no—
298C3×C4#93218yes—
299C3×C4#94918yes—
300C3×C4D3×#4118yes—
301Dic3—128no—
302C32#318411yescharacteristic, complemented, Sylow
303C23—22no—
304C23—182no—
305C23C2×#63811yescharacteristic
306Q8—42no—
307Q8—362no—
308D4—24no—
309D4—44no—
310D4—42no—
311D4—42no—
312D4—184no—
313D4—364no—
314D4—362no—
315D4—362no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—44no—
321C2×C4—182no—
322C2×C4—364no—
323C2×C4C2×#63811yescharacteristic
324C2×C4C2×#63811yescharacteristic
325C2×C4C2×#63811yescharacteristic
326C2×C4C2×#63811yescharacteristic
327C2×C4C2×#63811yescharacteristic
328C2×C4C23×C3⋊D311yescharacteristic
329C8—94no—
330C8—182no—
331C2×C3—44no—
332C2×C3—88no—
333C2×C3C2×#93214yes—
334C2×C3C2×#94914yes—
335C2×C3#583214yes—
336D3—248no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—42no—
341C22—42no—
342C22—42no—
343C22—362no—
344C22—362no—
345C22—362no—
346C22C22×#63811yescharacteristic
347C4—21no—
348C4—21no—
349C4—21no—
350C4—42no—
351C4—362no—
352C4#6414112yes—
353C4#6415812yes—
354C4#41×C3⋊D312yes—
355C3#8329514yescomplemented
356C2—41no—
357C2—82no—
358C2—722no—
359C2C2×#6414111yescharacteristic
360C2C2×#6415811yescharacteristic
361C2#1059630311yescharacteristic
subgroupG/H
centerC22C22×#638
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#532C2
socleC22×C32C22×D4
hypercenter#532C3⋊D3
hypocenterC32#3184
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. C32×#532C2semidirect
2. #10595948C2semidirect
3. #10592787C2semidirect
4. #10592779C2semidirect
5. #10592772C2semidirect
6. #10592769C2semidirect
7. #10592738C2semidirect
8. #10592713C2semidirect
9. C4×#3748C2semidirect
36. C3×#532D3semidirect
131. C3⋊(C3⋊C8)#41semidirect
133. #532C3⋊D3semidirect
302. C32#3184semidirect
355. C3#83295semidirect

Maximal subgroups

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

subgroupindex
C32×#5322
#105959482
#105927872
#105927792
#105927722
#105927692
#105927382
#105927132
C4×#37482
#832953