Finite Group Databasebeta

← #11783655

Subgroups — #11783655

Order 1152.

897 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C3⋊C8C211yesmaximal, characteristic
2C4×#3757C211yesmaximal, characteristic
3C2×C3×#830C211yesmaximal, characteristic
4C2×#63553C212yesmaximal, complemented
5#10589156C212yesmaximal, complemented
6C8×#217—31nomaximal
7#69947—31nomaximal
8C23×C32×C4C2211yescharacteristic
9C2×#3757C412yes—
10C2×C4×C3⋊Dic3C2212yes—
11C22×C3×C3⋊C8—24no—
12C22×C3×C3⋊C8C414yescomplemented
13C22×C3×C3⋊C8C2211yescharacteristic
14C22×C3×C3⋊C8C2212yes—
15C22×C3×C3⋊C8C2211yescharacteristic
16#63658C412yes—
17C3×#830C414yescomplemented
18#63553—24no—
19C23×C3×C8—31no—
20C23×C3⋊C8D311yescharacteristic
21C2×C3×C22⋊C8—31no—
22C4×#217—31no—
23C4×#217—31no—
24C4×#217—61no—
25C2×#830D311yescharacteristic
26C2×C8×Dic3—32no—
27C2×C8×Dic3—32no—
28#4550—32no—
29#4550—32no—
30C24×C32C2×C411yescharacteristic
31C22×C32×C4—22no—
32C22×C32×C4—22no—
33C22×C32×C4C2×C411yescharacteristic
34C22×C32×C4C2×C412yes—
35C22×C32×C4C2×C412yes—
36C22×C32×C4C2311yescharacteristic
37C22×C3⋊Dic3C2×C414yes—
38#3757C818yescomplemented
39C4×C3⋊Dic3—22no—
40C4×C3⋊Dic3—22no—
41C2×C3×C3⋊C8—22no—
42C2×C3×C3⋊C8—22no—
43C2×C3×C3⋊C8—22no—
44C2×C3×C3⋊C8—28no—
45C2×C3×C3⋊C8C2×C412yes—
46C2×C3×C3⋊C8C2×C414yes—
47C2×C3×C3⋊C8C2×C412yes—
48C2×C3×C3⋊C8D414yes—
49C8×C22⋊C4—91noSylow
50C23×C3×C4—21no—
51C23×C3×C4C2×D311yescharacteristic
52C23×C3×C4C2×D311yescharacteristic
53C22×C3×C8—31no—
54C22×C3×C8—34no—
55C22×C3×C8—31no—
56C22×C3×C8—32no—
57C22×C3×C8—64no—
58C2×#217—32no—
59C2×#217—32no—
60C2×#217—62no—
61C2×C4×Dic3—32no—
62C2×C4×Dic3—32no—
63C2×C4×Dic3—62no—
64C22×C3⋊C8—24no—
65C22×C3⋊C8Dic314yescomplemented
66C22×C3⋊C8C2×D312yes—
67C22×C3⋊C8C2×D311yescharacteristic
68C22×C3⋊C8C2×D311yescharacteristic
69C3×C22⋊C8—34no—
70C3⋊#95—32no—
71C3⋊#95—32no—
72C3⋊#95—62no—
73#830Dic314yescomplemented
74C8×Dic3—64no—
75C8×Dic3—64no—
76C23×C32—22no—
77C23×C32—22no—
78C23×C32C4212yes—
79C23×C32C2×C814yes—
80C23×C32C22×C411yescharacteristic
81C2×C32×C4—22no—
82C2×C32×C4—22no—
83C2×C32×C4—22no—
84C2×C32×C4—24no—
85C2×C32×C4C4212yes—
86C2×C32×C4C22×C411yescharacteristic
87C2×C32×C4C22×C411yescharacteristic
88C2×C32×C4C2×D412yes—
89C2×C32×C4#4112yes—
90C2×C3⋊Dic3—24no—
91C2×C3⋊Dic3—24no—
92C2×C3⋊Dic3C2×C818yescomplemented
93C3×C3⋊C8—22no—
94C3×C3⋊C8—24no—
95C3×C3⋊C8C22⋊C414yescomplemented
96C23×C8—31no—
97C2×C22⋊C8—31no—
98C2×C4×C8—92no—
99C4×C22⋊C4—91no—
100#336—92no—
101C24×C3—21no—
102C24×C3C4×D311yescharacteristic
103C24×C3C4×D311yescharacteristic
104C22×C3×C4—22no—
105C22×C3×C4—22no—
106C22×C3×C4—22no—
107C22×C3×C4—22no—
108C22×C3×C4—22no—
109C22×C3×C4—22no—
110C22×C3×C4—21no—
111C22×C3×C4—21no—
112C22×C3×C4—42no—
113C22×C3×C4—42no—
114C22×C3×C4C4×D312yes—
115C22×C3×C4C4×D312yes—
116C22×C3×C4C4×D311yescharacteristic
117C22×C3×C4C4×D311yescharacteristic
118C22×C3×C4C2×Dic312yes—
119C22×C3×C4C2×Dic312yes—
120C22×C3×C4C22×D311yescharacteristic
121C22×C3×C4C22×D311yescharacteristic
122C22×Dic3—34no—
123C22×Dic3—34no—
124C22×Dic3—64no—
125C2×C3×C8—32no—
126C2×C3×C8—34no—
127C2×C3×C8—34no—
128C2×C3×C8—32no—
129C2×C3×C8—68no—
130C2×C3×C8—62no—
131C2×C3×C8—62no—
132C2×C3×C8—62no—
133#217—38no—
134#217—38no—
135#217—68no—
136C4×Dic3—62no—
137C4×Dic3—62no—
138C4×Dic3—62no—
139C4×Dic3—62no—
140C4×Dic3—122no—
141C4×Dic3—122no—
142C2×C3⋊C8—22no—
143C2×C3⋊C8—22no—
144C2×C3⋊C8—22no—
145C2×C3⋊C8—28no—
146C2×C3⋊C8C2×Dic314yes—
147C2×C3⋊C8C2×Dic312yes—
148C2×C3⋊C8C2×Dic312yes—
149C2×C3⋊C8#6714yes—
150C22×C32—22no—
151C22×C32—22no—
152C22×C32—28no—
153C22×C32C4×C814yescomplemented
154C22×C32C2×C4211yescharacteristic
155C22×C32C4×D412yes—
156C22×C32C22×C812yes—
157C22×C32#13112yes—
158C32×C4—22no—
159C32×C4C2×C22⋊C411yescharacteristic
160C32×C4#11711yescharacteristic
161C32×C4C4×D412yes—
162C3⋊Dic3—28no—
163C23×C4D3211yescharacteristic
164C22×C8—31no—
165C22×C8—34no—
166C22×C8—31no—
167C22×C8—32no—
168C22×C8—64no—
169C2×C22⋊C4—92no—
170C2×C42—92no—
171C22⋊C8—34no—
172C4×C8—184no—
173#95—92no—
174C23×C3—22no—
175C23×C3—22no—
176C23×C3—22no—
177C23×C3—22no—
178C23×C3—24no—
179C23×C3—22no—
180C23×C3—21no—
181C23×C3—42no—
182C23×C3—42no—
183C23×C3D3×C814yes—
184C23×C3D3×C814yes—
185C23×C3C4×Dic312yes—
186C23×C3C4×Dic312yes—
187C23×C3C2×C4×D311yescharacteristic
188C23×C3C2×C4×D311yescharacteristic
189C2×C3×C4—22no—
190C2×C3×C4—22no—
191C2×C3×C4—22no—
192C2×C3×C4—22no—
193C2×C3×C4—22no—
194C2×C3×C4—24no—
195C2×C3×C4—24no—
196C2×C3×C4—22no—
197C2×C3×C4—22no—
198C2×C3×C4—21no—
199C2×C3×C4—21no—
200C2×C3×C4—22no—
201C2×C3×C4—22no—
202C2×C3×C4—42no—
203C2×C3×C4—42no—
204C2×C3×C4—44no—
205C2×C3×C4—42no—
206C2×C3×C4C4×Dic312yes—
207C2×C3×C4C4×Dic312yes—
208C2×C3×C4C2×C4×D311yescharacteristic
209C2×C3×C4C2×C4×D311yescharacteristic
210C2×C3×C4#23512yes—
211C2×C3×C4D3×D412yes—
212C2×C3×C4#23712yes—
213C2×C3×C4C22×Dic311yescharacteristic
214C2×C3×C4C22×Dic311yescharacteristic
215C2×C3×C4C2×#6712yes—
216C2×Dic3—38no—
217C2×Dic3—38no—
218C2×Dic3—68no—
219C2×Dic3—64no—
220C2×Dic3—64no—
221C2×Dic3—64no—
222C2×Dic3—64no—
223C2×Dic3—124no—
224C2×Dic3—124no—
225C3×C8—34no—
226C3×C8—62no—
227C3×C8—64no—
228C3⋊C8—24no—
229C3⋊C8—22no—
230C3⋊C8#21714yescomplemented
231C2×C32—24no—
232C2×C32C4×C22⋊C411yescharacteristic
233C2×C32C2×C4×C811yescharacteristic
234C2×C32#40511yescharacteristic
235C2×C32C8×D414yes—
236C24#62411yescharacteristic
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—94no—
240C22×C4D3×Dic312yes—
241C22×C4D3×Dic312yes—
242C22×C4#62411yescharacteristic
243C22×C4C2×D3211yescharacteristic
244C2×C8—32no—
245C2×C8—34no—
246C2×C8—34no—
247C2×C8—32no—
248C2×C8—68no—
249C2×C8—62no—
250C2×C8—62no—
251C2×C8—62no—
252C22⋊C4—98no—
253C42—182no—
254C42—182no—
255C22×C3—22no—
256C22×C3—22no—
257C22×C3—22no—
258C22×C3—28no—
259C22×C3—22no—
260C22×C3—28no—
261C22×C3—24no—
262C22×C3—22no—
263C22×C3—22no—
264C22×C3—22no—
265C22×C3—21no—
266C22×C3—42no—
267C22×C3—42no—
268C22×C3—48no—
269C22×C3C8×Dic314yescomplemented
270C22×C3C8×Dic314yescomplemented
271C22×C3#67⋊C412yes—
272C22×C3C2×D3×C812yes—
273C22×C3C2×D3×C812yes—
274C22×C3#90112yes—
275C22×C3#90712yes—
276C22×C3C2×C4×Dic311yescharacteristic
277C22×C3C2×C4×Dic311yescharacteristic
278C22×C3C4×#6712yes—
279C3×C4—22no—
280C3×C4—22no—
281C3×C4—21no—
282C3×C4—21no—
283C3×C4—22no—
284C3×C4—42no—
285C3×C4#87711yescharacteristic
286C3×C4D3×C22⋊C411yescharacteristic
287C3×C4#92611yescharacteristic
288C3×C4C4×#6712yes—
289C3×C4D4×Dic312yes—
290C3×C4C2×#21711yescharacteristic
291Dic3—68no—
292Dic3—68no—
293Dic3—128no—
294C32C8×C22⋊C411yescharacteristic, complemented, Sylow
295C23—22no—
296C23—22no—
297C23#371014yes—
298C23Dic3212yes—
299C23C2×#62411yescharacteristic
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—24no—
304C2×C4—98no—
305C2×C4—184no—
306C2×C4—184no—
307C2×C4Dic3212yes—
308C2×C4C2×D3×Dic311yescharacteristic
309C2×C4C2×D3×Dic311yescharacteristic
310C2×C4#380412yes—
311C2×C4D3×#6712yes—
312C8—34no—
313C8—62no—
314C8—64no—
315C2×C3—24no—
316C2×C3—24no—
317C2×C3—21no—
318C2×C3—21no—
319C2×C3—24no—
320C2×C3—21no—
321C2×C3—44no—
322C2×C3#67⋊C814yes—
323C2×C3Dic3×C22⋊C411yescharacteristic
324C2×C3C2×C8×Dic311yescharacteristic
325C2×C3C2×C8×Dic311yescharacteristic
326C2×C3#510111yescharacteristic
327C2×C3C8×#6714yes—
328C2×C3#512211yescharacteristic
329C2×C3C4×#21711yescharacteristic
330C22—22no—
331C22—28no—
332C22—22no—
333C22#6355314yescomplemented
334C22C2×#371012yes—
335C22#6381712yes—
336C22#6395212yes—
337C22C2×Dic3211yescharacteristic
338C4—22no—
339C4—188no—
340C4#6395511yescharacteristic
341C4D3×#21711yescharacteristic
342C4Dic3×#6712yes—
343C3—21no—
344C3#6994711yescharacteristic, complemented
345C3C8×#21711yescharacteristic, complemented
346C2—24no—
347C2C2×#6355311yescharacteristic
348C2#1059105911yescharacteristic
349C2#1059114814yes—
350C2Dic3×#21711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C2×D32
commutatorC2×C32C2×C4×C8
FittingC23×C32×C4C22
socleC23×C32C22×C4
prime radicalC24×C32C2×C4
cosocleC22×C32×C4C23
hypercenterC23×C4D32
hypocenterC32C8×C22⋊C4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
4. C2×#63553C2semidirect
5. #10589156C2semidirect
12. C22×C3×C3⋊C8C4semidirect
17. C3×#830C4semidirect
38. #3757C8semidirect
65. C22×C3⋊C8Dic3semidirect
73. #830Dic3semidirect
92. C2×C3⋊Dic3C2×C8semidirect
95. C3×C3⋊C8C22⋊C4semidirect
153. C22×C32C4×C8semidirect
230. C3⋊C8#217semidirect
269. C22×C3C8×Dic3semidirect
270. C22×C3C8×Dic3semidirect
294. C32C8×C22⋊C4semidirect
333. C22#63553semidirect
344. C3#69947semidirect
345. C3C8×#217semidirect

Maximal subgroups

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

subgroupindex
C23×C3×C3⋊C82
C4×#37572
C2×C3×#8302
C2×#635532
#105891562
C8×#2173
#699473