Finite Group Databasebeta

← #11784043

Subgroups — #11784043

Order 1152.

797 conjugacy classes of subgroups.

The subgroup lattice has 333 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64096C211yesmaximal, characteristic
2#10591274C211yesmaximal, characteristic
3C2×#63567C212yesmaximal
4C2×#63555C211yesmaximal, characteristic
5C3×#4529C212yesmaximal
6#68783—32nomaximal
7C22×#634C2211yescharacteristic
8C2×C32×C4⋊C4C2211yescharacteristic
9C2×#3750—21no—
10C2×C4×C3⋊Dic3—21no—
11C2×C4×C3⋊Dic3C2211yescharacteristic
12#64096—22no—
13#64096C414yescomplemented
14C2×C3×C4⋊Dic3C2212yes—
15C22×C3×C3⋊C8C2212yes—
16C2×Dic32—21no—
17#63579—21no—
18#63567C418yescomplemented
19#63555—22no—
20C2×#887—32no—
21C2×#887—61no—
22C2×#816—32no—
23C2×#815—32no—
24Dic3×C4⋊C4—32no—
25C2×#810—32no—
26C3×#340—32no—
27#4529D312yes—
28C22×C32×C4—21no—
29C22×C32×C4C2311yescharacteristic
30C22×C3⋊Dic3—21no—
31C22×C3⋊Dic3D411yescharacteristic
32C22×C3⋊Dic3D411yescharacteristic
33C2×#634—21no—
34C2×#634—22no—
35C2×#634C2×C414yes—
36C2×#634C2×C412yes—
37C22×C3×Dic3—22no—
38C32×C4⋊C4—21no—
39C32×C4⋊C4C2×C412yes—
40#3750—24no—
41C4×C3⋊Dic3—24no—
42C4×C3⋊Dic3C2×C412yes—
43C4×C3⋊Dic3D412yes—
44C3×C4⋊Dic3—22no—
45C3×C4⋊Dic3C2×C414yes—
46C2×C3×C3⋊C8—22no—
47C2×C3×C3⋊C8—22no—
48C2×C3×C3⋊C8C2×C414yes—
49Dic32—42no—
50#1763—91noSylow
51C22×Dic6—32no—
52C22×Dic6—61no—
53C22×C3×C8—32no—
54C2×C3×C4⋊C4—21no—
55C2×C3×C4⋊C4—32no—
56C2×C3×C4⋊C4C2×D312yes—
57C2×C4⋊Dic3C2×D312yes—
58C2×Dic3⋊C4—62no—
59C2×Dic3⋊C4—62no—
60C2×C4×Dic3—32no—
61C2×C4×Dic3—61no—
62C2×C4×Dic3—62no—
63C2×C4×Dic3—62no—
64C2×C4×Dic3—62no—
65C22×C3⋊C8C2×D312yes—
66#887—38no—
67#887—64no—
68#887—64no—
69#887—64no—
70C3⋊#95—62no—
71#816—38no—
72#815—64no—
73#810—38no—
74C23×C32C2×D411yescharacteristic
75C2×C32×C4—22no—
76C2×C32×C4—41no—
77C2×C32×C4—41no—
78C2×C32×C4C22×C411yescharacteristic
79C2×C32×C4C22×C412yes—
80C2×C32×C4C2×D411yescharacteristic
81C2×C32×C4#4112yes—
82C2×C3⋊Dic3—22no—
83C2×C3⋊Dic3—24no—
84C2×C3⋊Dic3—22no—
85C2×C3⋊Dic3—21no—
86C2×C3⋊Dic3—21no—
87C2×C3⋊Dic3C22⋊C412yes—
88C2×C3⋊Dic3C22⋊C412yes—
89#634—22no—
90#634—24no—
91#634C4214yescomplemented
92C2×C3×Dic3—24no—
93C2×C3×Dic3—42no—
94C2×C3×Dic3—42no—
95C3×C3⋊C8—24no—
96C2×C4×Q8—91no—
97C2×#103—92no—
98C2×#97—91no—
99C4×C4⋊C4—91no—
100#340—32no—
101C22×C3×C4—22no—
102C22×C3×C4—22no—
103C22×C3×C4—21no—
104C22×C3×C4—62no—
105C22×C3×C4C22×D312yes—
106C22×Dic3—22no—
107C22×Dic3—32no—
108C22×Dic3—32no—
109C22×Dic3—61no—
110C22×Dic3—61no—
111C22×Dic3—62no—
112C22×Dic3—62no—
113C2×Dic6—34no—
114C2×Dic6—34no—
115C2×Dic6—34no—
116C2×Dic6—62no—
117C2×Dic6—64no—
118C2×Dic6—62no—
119C2×Dic6—64no—
120C2×Dic6—62no—
121C2×Dic6—62no—
122C2×Dic6—62no—
123C2×C3×C8—34no—
124C2×C3×C8—62no—
125C2×C3×C8—62no—
126C3×C4⋊C4—22no—
127C3×C4⋊C4—22no—
128C3×C4⋊C4—22no—
129C3×C4⋊C4—34no—
130C3×C4⋊C4—62no—
131C3×C4⋊C4C4×D314yes—
132C4⋊Dic3—22no—
133C4⋊Dic3C4×D314yes—
134Dic3⋊C4—68no—
135Dic3⋊C4—68no—
136C4×Dic3—34no—
137C4×Dic3—34no—
138C4×Dic3—62no—
139C4×Dic3—62no—
140C4×Dic3—68no—
141C4×Dic3—68no—
142C4×Dic3—124no—
143C2×C3⋊C8—22no—
144C2×C3⋊C8—22no—
145C2×C3⋊C8C4×D314yes—
146C22×C32C2×C22⋊C411yescharacteristic
147C22×C32C4×D412yes—
148C22×C32AGL(1,ℤ/8)11yescharacteristic
149C22×C32#13711yescharacteristic
150C22×C32#13712yes—
151C32×C4—42no—
152C32×C4C2×C4211yescharacteristic
153C32×C4#11711yescharacteristic
154C32×C4C4×D412yes—
155C3⋊Dic3—24no—
156C3⋊Dic3—22no—
157C3⋊Dic3—22no—
158C3×Dic3—44no—
159C22×Q8—91no—
160C22×C8—32no—
161C4×Q8—94no—
162C4×Q8—182no—
163C2×C4⋊C4—32no—
164C2×C4⋊C4—181no—
165C2×C4⋊C4D3211yescharacteristic
166C2×C42—91no—
167C2×C42—181no—
168C2×C42—181no—
169#103—98no—
170#97—182no—
171#95—181no—
172C23×C3—21no—
173C23×C3D3×D412yes—
174C2×C3×C4—24no—
175C2×C3×C4—24no—
176C2×C3×C4—22no—
177C2×C3×C4—22no—
178C2×C3×C4—21no—
179C2×C3×C4—21no—
180C2×C3×C4—42no—
181C2×C3×C4—42no—
182C2×C3×C4—42no—
183C2×C3×C4—42no—
184C2×C3×C4—64no—
185C2×C3×C4—122no—
186C2×C3×C4—122no—
187C2×C3×C4C2×C4×D312yes—
188C2×C3×C4C2×C4×D312yes—
189C2×C3×C4C2×C4×D312yes—
190C2×C3×C4D3×D412yes—
191C2×C3×C4#23712yes—
192C2×C3×C4#23912yes—
193C2×Dic3—24no—
194C2×Dic3—34no—
195C2×Dic3—34no—
196C2×Dic3—42no—
197C2×Dic3—42no—
198C2×Dic3—62no—
199C2×Dic3—62no—
200C2×Dic3—64no—
201C2×Dic3—68no—
202C2×Dic3—64no—
203C2×Dic3—64no—
204C2×Dic3—64no—
205C2×Dic3—64no—
206C2×Dic3—62no—
207C2×Dic3—62no—
208C2×Dic3—62no—
209C2×Dic3—62no—
210C2×Dic3—121no—
211C2×Dic3—121no—
212Dic6—38no—
213Dic6—64no—
214Dic6—64no—
215Dic6—68no—
216Dic6—64no—
217Dic6—64no—
218Dic6—64no—
219C3×C8—64no—
220C3⋊C8—24no—
221C2×C32C4×C22⋊C411yescharacteristic
222C2×C32#41711yescharacteristic
223C2×C32#41911yescharacteristic
224C2×C32#44012yes—
225C2×C32#44112yes—
226C2×Q8—94no—
227C2×Q8—92no—
228C2×Q8—182no—
229C2×Q8—181no—
230C22×C4—21no—
231C22×C4—62no—
232C22×C4—91no—
233C22×C4—91no—
234C22×C4—181no—
235C22×C4C2×D3211yescharacteristic
236C2×C8—34no—
237C2×C8—62no—
238C2×C8—62no—
239C4⋊C4—21no—
240C4⋊C4—34no—
241C4⋊C4—62no—
242C4⋊C4—184no—
243C4⋊C4#62412yes—
244C42—92no—
245C42—92no—
246C42—184no—
247C42—362no—
248C22×C3—22no—
249C22×C3—21no—
250C22×C3—21no—
251C22×C3—22no—
252C22×C3—21no—
253C22×C3D3×C22⋊C412yes—
254C22×C3#67⋊C412yes—
255C22×C3#89312yes—
256C22×C3#91112yes—
257C22×C3#91512yes—
258C22×C3#91512yes—
259C22×C3#91812yes—
260C3×C4—21no—
261C3×C4—22no—
262C3×C4—21no—
263C3×C4—44no—
264C3×C4—44no—
265C3×C4—124no—
266C3×C4C42×D312yes—
267C3×C4#67⋊C412yes—
268C3×C4#89212yes—
269C3×C4#89312yes—
270Dic3—44no—
271Dic3—68no—
272Dic3—64no—
273Dic3—68no—
274Dic3—64no—
275Dic3—64no—
276Dic3—122no—
277C32#176311yescharacteristic, complemented, Sylow
278C23#381111yescharacteristic
279Q8—94no—
280Q8—182no—
281Q8—184no—
282C2×C4—22no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—64no—
286C2×C4—92no—
287C2×C4—92no—
288C2×C4—122no—
289C2×C4—122no—
290C2×C4—184no—
291C2×C4—181no—
292C2×C4—181no—
293C2×C4—182no—
294C2×C4—182no—
295C2×C4#379612yes—
296C2×C4C4×D3212yes—
297C2×C4C2×#62411yescharacteristic
298C2×C4#381111yescharacteristic
299C8—64no—
300C2×C3—22no—
301C2×C3—21no—
302C2×C3—21no—
303C2×C3—21no—
304C2×C3—22no—
305C2×C3#466612yes—
306C2×C3#475712yes—
307C2×C3#477112yes—
308C2×C3#478912yes—
309C2×C3#480212yes—
310C2×C3#485312yes—
311C2×C3#488912yes—
312C22#6388112yes—
313C22#6392711yescharacteristic
314C22#6393111yescharacteristic
315C22#6395112yes—
316C22#6397411yescharacteristic
317C4—42no—
318C4—124no—
319C4—184no—
320C4—182no—
321C4—182no—
322C4#6384911yescharacteristic
323C4#6388112yes—
324C4C4×#62411yescharacteristic
325C3—21no—
326C3#6878312yescomplemented
327C2#1059046112yes—
328C2#1059048512yes—
329C2#1059126011yescharacteristic
330C2#1059141811yescharacteristic
331C2#1059156211yescharacteristic
subgroupG/H
centerC23#3811
commutatorC32×C4C2×C42
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socle, prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1763
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
13. #64096C4semidirect
18. #63567C4semidirect
91. #634C42semidirect
277. C32#1763semidirect
326. C3#68783semidirect

Maximal subgroups

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

subgroupindex
C2×#640962
#105912742
C2×#635672
C2×#635552
C3×#45292
#687833