Finite Group Databasebeta

← #11808739

Subgroups — #11808739

Order 1152.

2520 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×D4C211yesmaximal, characteristic, complemented
2C2×C4×#638C214yesmaximal, complemented
3C2×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
4#10592922C212yesmaximal, complemented
5#10592692C212yesmaximal, complemented
6#10592659C212yesmaximal, complemented
7#10592648C212yesmaximal, complemented
8#10592631C211yesmaximal, characteristic, complemented
9#82347—34nomaximal
10C22×C32×D4C2211yescharacteristic
11C23×C32×C4C2212yes—
12C22×#638C2214yes—
13C22×C4⋊(C3⋊D3)C2211yescharacteristic
14C22×C4×C3⋊D3C2212yes—
15C32×C4×D4—24no—
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×C32×C22⋊C4C2212yes—
18C2×C32×C42C2211yescharacteristic
19C2×#3757C2214yes—
20C4×#638—216no—
21C2×#3752C2212yes—
22C2×#3752C2214yes—
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C2×#3750C2214yes—
25C2×C4×C3⋊Dic3C2212yes—
26C4×C4⋊(C3⋊D3)—24no—
27#63658C2212yes—
28#63658C2212yes—
29C2×C3×C4×D4D314yescomplemented
30C2×C4×#67—316no—
31C2×C4×D12—34no—
32#5223—38no—
33#4993—38no—
34#4960—38no—
35#4949—38no—
36#4932—34no—
37C24×C32C2312yes—
38C23×C3⋊D3C2312yes—
39C2×C32×D4—24no—
40C2×C32×D4—22no—
41C22×C32×C4—28no—
42C22×C32×C4—24no—
43C22×C32×C4C2312yes—
44C22×C32×C4C2311yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C2×#638—28no—
48C2×#638—28no—
49C2×#638—28no—
50C22×C3⋊Dic3C2312yes—
51C22×C3⋊Dic3C2314yes—
52C2×C4⋊(C3⋊D3)—24no—
53C2×C4⋊(C3⋊D3)—22no—
54C2×C4×C3⋊D3—24no—
55C2×C4×C3⋊D3—28no—
56C32×C4⋊C4—22no—
57C32×C22⋊C4—24no—
58C32×C42D414yescomplemented
59#3757—28no—
60#3752—24no—
61#3752—28no—
62C4⋊(C3⋊Dic3)—22no—
63#3750—28no—
64C4×C3⋊Dic3D418yescomplemented
65#2397—91noSylow
66C22×C3×D4C2×D314yes—
67C23×C3×C4C2×D318yes—
68C22×#67—316no—
69C22×D12—34no—
70C22×C4×D3—38no—
71C3×C4×D4—216no—
72C2×C3×C4⋊C4C2×D314yes—
73C2×C3×C22⋊C4C2×D318yes—
74C2×C3×C42C2×D314yes—
75C2×#217—316no—
76C4×#67—664no—
77C2×(C2×D3)⋊C4—316no—
78C2×(C2×D3)⋊C4—38no—
79C2×C4⋊Dic3—34no—
80C2×Dic3⋊C4—316no—
81C2×C4×Dic3—38no—
82C4×D12—616no—
83C3⋊#95—38no—
84C3⋊#95—38no—
85C23×C32—24no—
86C23×C32—22no—
87C23×C32—24no—
88C23×C32—22no—
89C23×C32#4114yes—
90C23×C32C2411yescharacteristic
91C22×C3⋊D3—22no—
92C22×C3⋊D3—24no—
93C22×C3⋊D3—22no—
94C22×C3⋊D3—24no—
95C22×C3⋊D3#4114yes—
96C32×D4—28no—
97C2×C32×C4—22no—
98C2×C32×C4—22no—
99C2×C32×C4—24no—
100C2×C32×C4—22no—
101C2×C32×C4—48no—
102C2×C32×C4C2×D414yes—
103C2×C32×C4C2×D412yes—
104C2×C32×C4C2×D412yes—
105C2×C32×C4C2×D412yes—
106#638—232no—
107C2×C3⋊Dic3—24no—
108C2×C3⋊Dic3—24no—
109C2×C3⋊Dic3—24no—
110C2×C3⋊Dic3—22no—
111C2×C3⋊Dic3C2×D418yes—
112C4⋊(C3⋊D3)—28no—
113C4×C3⋊D3—48no—
114C2×C4×D4—94no—
115C2×C4×D4—91no—
116C2×C4×D4C3⋊D311yescharacteristic, complemented
117#399—92no—
118#399—92no—
119#392—92no—
120#392—92no—
121#376—91no—
122C24×C3C22×D318yes—
123C23×D3—38no—
124C2×C3×D4—216no—
125C2×C3×D4—28no—
126C22×C3×C4—232no—
127C22×C3×C4—216no—
128C22×C3×C4C22×D318yes—
129C22×C3×C4C22×D314yes—
130C22×C3×C4C22×D314yes—
131C22×C3×C4C22×D314yes—
132C2×#67—632no—
133C2×#67—632no—
134C2×#67—632no—
135C22×Dic3—316no—
136C22×Dic3—38no—
137C2×D12—616no—
138C2×D12—68no—
139C2×C4×D3—632no—
140C2×C4×D3—616no—
141C3×C4⋊C4—28no—
142C3×C22⋊C4—216no—
143C3×C42#67116yescomplemented
144#217—632no—
145(C2×D3)⋊C4—632no—
146(C2×D3)⋊C4—616no—
147C4⋊Dic3—68no—
148Dic3⋊C4—632no—
149C4×Dic3—332no—
150C22×C32—28no—
151C22×C32—24no—
152C22×C32—44no—
153C22×C32—42no—
154C22×C32—42no—
155C22×C32C22×D412yes—
156C22×C32C22×D411yescharacteristic
157C22×C32C2×#4112yes—
158C22×C32C2×#4112yes—
159C2×C3⋊D3—24no—
160C2×C3⋊D3—28no—
161C2×C3⋊D3—42no—
162C2×C3⋊D3—44no—
163C2×C3⋊D3—42no—
164C32×C4—22no—
165C32×C4—22no—
166C32×C4—42no—
167C32×C4#12714yes—
168C3⋊Dic3—28no—
169C3⋊Dic3—42no—
170C22×D4—94no—
171C22×D4—91no—
172C22×D4C2×C3⋊D311yescharacteristic
173C23×C4—92no—
174C23×C4C2×C3⋊D312yes—
175C4×D4—24no—
176C4×D4—1816no—
177C4×D4—184no—
178C2×C4⋊C4—94no—
179C2×C4⋊C4—91no—
180C2×C4⋊C4C2×C3⋊D311yescharacteristic
181C2×C22⋊C4—94no—
182C2×C22⋊C4—94no—
183C2×C22⋊C4—92no—
184C2×C22⋊C4C2×C3⋊D312yes—
185C2×C42—92no—
186C2×C42C2×C3⋊D311yescharacteristic
187#95—92no—
188#95—92no—
189C23×C3—28no—
190C23×C3—216no—
191C23×C3—216no—
192C23×C3—28no—
193C23×C3#235116yes—
194C23×C3C23×D314yes—
195C22×D3—316no—
196C22×D3—616no—
197C22×D3—616no—
198C22×D3—68no—
199C22×D3—68no—
200C3×D4—232no—
201C2×C3×C4—28no—
202C2×C3×C4—28no—
203C2×C3×C4—216no—
204C2×C3×C4—28no—
205C2×C3×C4—432no—
206C2×C3×C4D3×D4116yes—
207C2×C3×C4C2×#6718yes—
208C2×C3×C4C2×#6718yes—
209C2×C3×C4C2×#6718yes—
210#67—6128no—
211C2×Dic3—332no—
212C2×Dic3—616no—
213C2×Dic3—616no—
214C2×Dic3—616no—
215C2×Dic3—68no—
216D12—632no—
217C4×D3—1232no—
218C2×C32—44no—
219C2×C32#52511yescharacteristic
220C2×C32#52514yes—
221C2×C32#52511yescharacteristic
222C2×C32C2×#12711yescharacteristic
223C3⋊D3—44no—
224C24—92no—
225C24C22×C3⋊D312yes—
226C2×D4—24no—
227C2×D4—22no—
228C2×D4—184no—
229C2×D4—188no—
230C2×D4—188no—
231C2×D4—188no—
232C2×D4—182no—
233C22×C4—28no—
234C22×C4—24no—
235C22×C4—94no—
236C22×C4—92no—
237C22×C4—188no—
238C22×C4—184no—
239C22×C4C22×C3⋊D312yes—
240C22×C4C22×C3⋊D311yescharacteristic
241C22×C4C22×C3⋊D311yescharacteristic
242C22×C4C22×C3⋊D311yescharacteristic
243C4⋊C4—22no—
244C4⋊C4—188no—
245C4⋊C4—182no—
246C22⋊C4—24no—
247C22⋊C4—188no—
248C22⋊C4—188no—
249C22⋊C4—184no—
250C42—98no—
251C42#63814yescomplemented
252C22×C3—216no—
253C22×C3—232no—
254C22×C3—416no—
255C22×C3—48no—
256C22×C3—48no—
257C22×C3C2×#23518yes—
258C22×C3C2×D3×D418yes—
259C22×C3D3×#4118yes—
260C22×C3C22×#6714yes—
261C2×D3—632no—
262C2×D3—616no—
263C2×D3—128no—
264C2×D3—1216no—
265C2×D3—128no—
266C3×C4—28no—
267C3×C4—28no—
268C3×C4—48no—
269C3×C4#940116yes—
270Dic3—632no—
271Dic3—128no—
272C32#239711yescharacteristic, complemented, Sylow
273C23—22no—
274C23—24no—
275C23—24no—
276C23—22no—
277C23—94no—
278C23—184no—
279C23—184no—
280C23—182no—
281C23—182no—
282C23#382814yes—
283C23C23×C3⋊D311yescharacteristic
284D4—28no—
285D4—188no—
286D4—1832no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—24no—
290C2×C4—22no—
291C2×C4—48no—
292C2×C4—98no—
293C2×C4—184no—
294C2×C4—184no—
295C2×C4—184no—
296C2×C4—182no—
297C2×C4—368no—
298C2×C4D4×C3⋊D314yes—
299C2×C4C2×#63812yes—
300C2×C4C2×#63812yes—
301C2×C4C2×#63812yes—
302C2×C3—416no—
303C2×C3#5547116yes—
304C2×C3#579114yes—
305C2×C3C2×#94014yes—
306C2×C3#582814yes—
307D3—1216no—
308C22—24no—
309C22—28no—
310C22—44no—
311C22—42no—
312C22—42no—
313C22—188no—
314C22—184no—
315C22—362no—
316C22—364no—
317C22—362no—
318C22C2×#382812yes—
319C22C2×D4×C3⋊D312yes—
320C22#41×C3⋊D312yes—
321C22C22×#63811yescharacteristic
322C4—22no—
323C4—22no—
324C4—42no—
325C4—188no—
326C4—362no—
327C4#6414914yes—
328C3#8234714yescomplemented
329C2—44no—
330C2—364no—
331C2#1059601814yes—
332C2#1059626211yescharacteristic
333C2C2×#6414911yescharacteristic
334C2#1059629911yescharacteristic
subgroupG/H
centerC22×C4C22×C3⋊D3
commutator, socle, cosocleC23×C32C24
FrattiniC23C23×C3⋊D3
FittingC2×C32×C4×D4C2
hypercenterC2×C4×D4C3⋊D3
hypocenterC32#2397
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×C4×D4C2semidirect
2. C2×C4×#638C2semidirect
3. C2×C4×C4⋊(C3⋊D3)C2semidirect
4. #10592922C2semidirect
5. #10592692C2semidirect
6. #10592659C2semidirect
7. #10592648C2semidirect
8. #10592631C2semidirect
29. C2×C3×C4×D4D3semidirect
58. C32×C42D4semidirect
64. C4×C3⋊Dic3D4semidirect
116. C2×C4×D4C3⋊D3semidirect
143. C3×C42#67semidirect
251. C42#638semidirect
272. C32#2397semidirect
328. C3#82347semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×D42
C2×C4×#6382
C2×C4×C4⋊(C3⋊D3)2
#105929222
#105926922
#105926592
#105926482
#105926312
#823473