Finite Group Databasebeta

← #11807111

Subgroups — #11807111

Order 1152.

1488 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64153C211yesmaximal, characteristic
2C32×#391C211yesmaximal, characteristic
3#10592928C211yesmaximal, characteristic
4#10592675C212yesmaximal
5C4×#3750C212yesmaximal
6#10592348C212yesmaximal
7#10592348C212yesmaximal
8#10592346C212yesmaximal
9#10592345C212yesmaximal
10#76494—34nomaximal
11C22×C32×Q8C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×C32×C42C2211yescharacteristic
15#64153C418yescomplemented
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×#3750C2212yes—
18C2×#3750C2212yes—
19C2×#3750C2212yes—
20C2×#3750C2212yes—
21C2×#3750C2212yes—
22C2×C4×C3⋊Dic3C2212yes—
23C2×C4×C3⋊Dic3C2212yes—
24C2×C4×C3⋊Dic3C2212yes—
25C2×C4×C3⋊Dic3C2211yescharacteristic
26C2×C4×C3⋊Dic3C2211yescharacteristic
27C32×#95C2212yes—
28C32×#95C2212yes—
29#63658C2212yes—
30#63658C2212yes—
31#63658C2212yes—
32#63658C2212yes—
33C2×#944—34no—
34C3×#391D314yes—
35#5229—34no—
36#4976—38no—
37C4×Dic3⋊C4—38no—
38#4649—38no—
39#4649—38no—
40#4647—38no—
41#4646—38no—
42C2×C32×Q8—41no—
43C2×C32×Q8—41no—
44C2×C32×Q8C2×C414yes—
45C22×C32×C4C2312yes—
46C22×C32×C4C2311yescharacteristic
47C22×C32×C4C2311yescharacteristic
48C22×C32×C4C2311yescharacteristic
49C22×C32×C4C2312yes—
50C22×C3⋊Dic3C2312yes—
51C22×C3⋊Dic3C2312yes—
52C22×C3⋊Dic3C2312yes—
53C22×C3⋊Dic3C2312yes—
54C2×#634—41no—
55C2×#634—41no—
56C2×#634C2×C414yes—
57C32×C4⋊C4—41no—
58C32×C42—41no—
59C4⋊(C3⋊Dic3)—41no—
60#3750—24no—
61#3750—42no—
62#3750C2×C418yes—
63#3750C2×C418yes—
64#3750Q818yescomplemented
65C4×C3⋊Dic3—24no—
66C4×C3⋊Dic3—24no—
67C4×C3⋊Dic3—41no—
68C4×C3⋊Dic3—42no—
69C4×C3⋊Dic3C2×C414yes—
70#2369—91noSylow
71C22×C3×Q8C2×D314yes—
72C22×Dic6—34no—
73C2×C3×C4⋊C4C2×D314yes—
74C2×C3×C42C2×D314yes—
75#944—332no—
76C2×C4⋊Dic3—34no—
77C2×Dic3⋊C4—38no—
78C2×Dic3⋊C4—38no—
79C2×Dic3⋊C4—38no—
80C2×Dic3⋊C4—38no—
81C2×Dic3⋊C4—38no—
82C2×C4×Dic3—34no—
83C2×C4×Dic3—38no—
84C2×C4×Dic3—38no—
85C2×C4×Dic3—38no—
86C2×C4×Dic3—34no—
87C3×#95C2×D318yes—
88C3×#95C2×D318yes—
89C3⋊#95—38no—
90C3⋊#95—38no—
91C3⋊#95—38no—
92C3⋊#95—38no—
93C23×C32C2411yescharacteristic
94C32×Q8—44no—
95C2×C32×C4—22no—
96C2×C32×C4—22no—
97C2×C32×C4—21no—
98C2×C32×C4—21no—
99C2×C32×C4—21no—
100C2×C32×C4—21no—
101C2×C32×C4—21no—
102C2×C32×C4—21no—
103C2×C32×C4—22no—
104C2×C32×C4—22no—
105C2×C32×C4—22no—
106C2×C32×C4C22×C412yes—
107C2×C32×C4C22×C412yes—
108C2×C32×C4C22×C412yes—
109C2×C32×C4C2×Q814yes—
110C2×C3⋊Dic3—22no—
111C2×C3⋊Dic3—22no—
112C2×C3⋊Dic3—22no—
113C2×C3⋊Dic3—22no—
114C2×C3⋊Dic3—22no—
115C2×C3⋊Dic3—22no—
116C2×C3⋊Dic3—22no—
117C2×C3⋊Dic3C22×C414yes—
118C2×C3⋊Dic3C22×C414yes—
119C2×C3⋊Dic3C2×Q814yes—
120C2×C3⋊Dic3C2×Q814yes—
121C2×C3⋊Dic3#4114yes—
122#634—44no—
123C2×C4⋊Q8—91no—
124#391—91no—
125#391—92no—
126#391C3⋊D311yescharacteristic
127#389—92no—
128#389—92no—
129C4×C4⋊C4—92no—
130C4×C4⋊C4—92no—
131C4×C4⋊C4—92no—
132C2×C3×Q8—44no—
133C2×C3×Q8—44no—
134C2×C3×Q8C4×D3116yes—
135C22×C3×C4C22×D318yes—
136C22×C3×C4C22×D314yes—
137C22×C3×C4C22×D314yes—
138C22×C3×C4C22×D314yes—
139C22×C3×C4C22×D318yes—
140C22×Dic3—38no—
141C22×Dic3—38no—
142C22×Dic3—38no—
143C22×Dic3—38no—
144C2×Dic6—316no—
145C2×Dic6—124no—
146C2×Dic6—124no—
147C3×C4⋊C4—44no—
148C3×C42—44no—
149C4⋊Dic3—124no—
150Dic3⋊C4—332no—
151Dic3⋊C4—332no—
152Dic3⋊C4—332no—
153Dic3⋊C4—616no—
154Dic3⋊C4—128no—
155C4×Dic3—316no—
156C4×Dic3—616no—
157C4×Dic3—616no—
158C4×Dic3—124no—
159C4×Dic3—128no—
160C22×C32C23×C411yescharacteristic
161C22×C32C22×Q812yes—
162C22×C32C2×#4112yes—
163C22×C32H(5,𝔽2)11yescharacteristic
164C22×C32H(5,𝔽2)11yescharacteristic
165C32×C4—22no—
166C32×C4—22no—
167C32×C4—22no—
168C32×C4—24no—
169C32×C4—42no—
170C3⋊Dic3—24no—
171C3⋊Dic3—24no—
172C3⋊Dic3—42no—
173C3⋊Dic3C4×Q818yes—
174C22×Q8—91no—
175C22×Q8C2×C3⋊D311yescharacteristic
176C4⋊Q8—98no—
177C2×C4⋊C4—92no—
178C2×C4⋊C4—92no—
179C2×C4⋊C4—92no—
180C2×C4⋊C4—92no—
181C2×C4⋊C4—92no—
182C2×C4⋊C4—91no—
183C2×C4⋊C4C2×C3⋊D311yescharacteristic
184C2×C42—91no—
185C2×C42—92no—
186C2×C42—92no—
187C2×C42—91no—
188C2×C42—92no—
189C2×C42C2×C3⋊D311yescharacteristic
190#95—92no—
191#95—92no—
192#95—92no—
193#95—92no—
194#95C2×C3⋊D312yes—
195#95C2×C3⋊D312yes—
196C23×C3C23×D314yes—
197C3×Q8—416no—
198C2×C3×C4—28no—
199C2×C3×C4—24no—
200C2×C3×C4—24no—
201C2×C3×C4—24no—
202C2×C3×C4—24no—
203C2×C3×C4—24no—
204C2×C3×C4—24no—
205C2×C3×C4—28no—
206C2×C3×C4—28no—
207C2×C3×C4—28no—
208C2×C3×C4—28no—
209C2×C3×C4C2×C4×D318yes—
210C2×C3×C4C2×C4×D318yes—
211C2×C3×C4C2×C4×D318yes—
212C2×C3×C4D3×Q8116yes—
213C2×Dic3—316no—
214C2×Dic3—316no—
215C2×Dic3—316no—
216C2×Dic3—316no—
217C2×Dic3—316no—
218C2×Dic3—68no—
219C2×Dic3—68no—
220C2×Dic3—68no—
221C2×Dic3—68no—
222C2×Dic3—68no—
223C2×Dic3—68no—
224C2×Dic3—68no—
225Dic6—1216no—
226C2×C32C2×C4×Q812yes—
227C2×C32#51811yescharacteristic
228C2×C32#55412yes—
229C2×C32#55511yescharacteristic
230C2×C32Q8211yescharacteristic
231C2×Q8—41no—
232C2×Q8—41no—
233C2×Q8—94no—
234C2×Q8—361no—
235C2×Q8—361no—
236C2×Q8C4×C3⋊D314yes—
237C22×C4—92no—
238C22×C4—92no—
239C22×C4—92no—
240C22×C4—92no—
241C22×C4C22×C3⋊D312yes—
242C22×C4C22×C3⋊D311yescharacteristic
243C22×C4C22×C3⋊D311yescharacteristic
244C22×C4C22×C3⋊D311yescharacteristic
245C22×C4C22×C3⋊D312yes—
246C4⋊C4—41no—
247C4⋊C4—98no—
248C4⋊C4—98no—
249C4⋊C4—98no—
250C4⋊C4—184no—
251C4⋊C4—362no—
252C4⋊C4—361no—
253C42—41no—
254C42—94no—
255C42—184no—
256C42—184no—
257C42—362no—
258C42—361no—
259C22×C3C22×C4×D314yes—
260C22×C3#100414yes—
261C22×C3#100414yes—
262C22×C3C2×D3×Q818yes—
263C22×C3D3×#4118yes—
264C3×C4—216no—
265C3×C4—28no—
266C3×C4—28no—
267C3×C4—28no—
268C3×C4—48no—
269Dic3—332no—
270Dic3—616no—
271Dic3—616no—
272Dic3—128no—
273C32#236911yescharacteristic, complemented, Sylow
274C23C23×C3⋊D311yescharacteristic
275Q8—44no—
276Q8—364no—
277C2×C4—22no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—94no—
289C2×C4—94no—
290C2×C4—94no—
291C2×C4—94no—
292C2×C4—94no—
293C2×C4—182no—
294C2×C4—182no—
295C2×C4—182no—
296C2×C4—182no—
297C2×C4—182no—
298C2×C4—182no—
299C2×C4—182no—
300C2×C4C2×C4×C3⋊D312yes—
301C2×C4C2×C4×C3⋊D312yes—
302C2×C4C2×C4×C3⋊D312yes—
303C2×C4Q8×C3⋊D314yes—
304C2×C3#548614yes—
305C2×C3C4×D3×Q818yes—
306C2×C3#563618yes—
307C2×C3#567014yes—
308C2×C3#572214yes—
309C22C22×C4×C3⋊D311yescharacteristic
310C22#6436111yescharacteristic
311C22#6436111yescharacteristic
312C22C2×Q8×C3⋊D312yes—
313C22#41×C3⋊D312yes—
314C4—24no—
315C4—22no—
316C4—22no—
317C4—22no—
318C4—42no—
319C4—98no—
320C4—184no—
321C4—184no—
322C4—362no—
323C3#7649414yescomplemented
324C2#1059595711yescharacteristic
325C2C4×Q8×C3⋊D312yes—
326C2#1059610712yes—
327C2#1059614111yescharacteristic
328C2#1059619311yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutatorC22×C32C23×C4
FittingC32×#391C2
socle, prime radical, cosocleC23×C32C24
hypercenter#391C3⋊D3
hypocenterC32#2369
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
15. #64153C4semidirect
64. #3750Q8semidirect
273. C32#2369semidirect
323. C3#76494semidirect

Maximal subgroups

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

subgroupindex
C2×#641532
C32×#3912
#105929282
#105926752
C4×#37502
#105923482
#105923462
#105923452
#764943