Finite Group Databasebeta

← #11805612

Subgroups — #11805612

Order 1152.

1253 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64096C211yesmaximal, characteristic
2C2×#63844C212yesmaximal
3C3×#4984C212yesmaximal
4#10591360C212yesmaximal
5C4×#3724C211yesmaximal, characteristic
6#10591274C212yesmaximal
7#10591264C214yesmaximal
8#10591230C211yesmaximal, characteristic
9#75982—32nomaximal
10C22×#634C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×#3750C2212yes—
13C2×C4×C3⋊Dic3C2212yes—
14C2×C4×C3⋊Dic3C2211yescharacteristic
15#64096C418yescomplemented
16C2×C3×C4⋊Dic3C2212yes—
17C2×C3×C4⋊Dic3C2214yes—
18C2×C3×C4×Dic3C2212yes—
19C2×#3724C2214yes—
20C2×#3724C2212yes—
21C2×Dic32C2214yes—
22#63844—28no—
23C3×C3⋊#95C2214yes—
24#63579C2212yes—
25#63579C2211yescharacteristic
26#63579C2212yes—
27#63579C2211yescharacteristic
28C2×#887—32no—
29C2×#887—32no—
30C2×#887—61no—
31C2×C4×Dic6—32no—
32C3×#389—32no—
33#4984D312yes—
34#4977—32no—
35#4976—34no—
36Dic3×C4⋊C4—34no—
37C4×Dic3⋊C4—32no—
38#4650—34no—
39#4647—34no—
40C22×C32×C4C2312yes—
41C22×C32×C4C2311yescharacteristic
42C22×C3⋊Dic3C2311yescharacteristic
43C22×C3⋊Dic3C2311yescharacteristic
44C22×C3⋊Dic3C2312yes—
45C2×#634C2×C414yes—
46C2×#634D414yes—
47C2×#634Q814yes—
48C22×C3×Dic3C2312yes—
49C22×C3×Dic3C2314yes—
50C22×C3×Dic3C2312yes—
51C32×C4⋊C4C2×C414yes—
52#3750C2×C418yes—
53C4×C3⋊Dic3C2×C414yes—
54C4×C3⋊Dic3C2×C418yes—
55C3×C4⋊Dic3—24no—
56C3×C4⋊Dic3—28no—
57C3×C4×Dic3—24no—
58#3724—28no—
59#3724—24no—
60Dic32—28no—
61#2351—91noSylow
62C22×Dic6—32no—
63C22×Dic6—61no—
64C2×C3×C4⋊C4—21no—
65C2×C3×C4⋊C4—34no—
66C2×C3×C4⋊C4—32no—
67C2×C3×C4⋊C4C2×D312yes—
68C2×C3×C42—32no—
69C2×C4⋊Dic3C2×D314yes—
70C2×C4⋊Dic3C2×D312yes—
71C2×Dic3⋊C4—34no—
72C2×Dic3⋊C4—32no—
73C2×Dic3⋊C4—34no—
74C2×Dic3⋊C4—34no—
75C2×Dic3⋊C4—32no—
76C2×Dic3⋊C4—62no—
77C2×C4×Dic3—34no—
78C2×C4×Dic3—32no—
79C2×C4×Dic3—34no—
80C2×C4×Dic3—34no—
81C2×C4×Dic3—62no—
82C2×C4×Dic3—61no—
83C2×C4×Dic3C2×D312yes—
84#887—316no—
85#887—68no—
86#887—68no—
87C4×Dic6—68no—
88C3×#95—34no—
89C3⋊#95—34no—
90C3⋊#95—32no—
91C3⋊#95—34no—
92C3⋊#95—32no—
93C3⋊#95C2×D314yes—
94C23×C32C2411yescharacteristic
95C2×C32×C4—24no—
96C2×C32×C4C22×C414yes—
97C2×C32×C4C22×C412yes—
98C2×C32×C4C2×D412yes—
99C2×C32×C4C2×Q812yes—
100C2×C3⋊Dic3—22no—
101C2×C3⋊Dic3—22no—
102C2×C3⋊Dic3C22×C412yes—
103C2×C3⋊Dic3C22×C412yes—
104C2×C3⋊Dic3C22×C414yes—
105C2×C3⋊Dic3C2×D414yes—
106C2×C3⋊Dic3C2×Q814yes—
107#634C4⋊C4116yescomplemented
108C2×C3×Dic3—22no—
109C2×C3×Dic3—22no—
110C2×C3×Dic3—24no—
111C2×C3×Dic3—22no—
112C2×C3×Dic3—22no—
113C2×C3×Dic3—24no—
114C2×C3×Dic3—22no—
115C2×C3×Dic3—24no—
116C2×C3×Dic3#4114yes—
117C2×C4×Q8—92no—
118C2×C4×Q8—91no—
119#389—32no—
120#389—94no—
121#382—92no—
122#382—91no—
123C4×C4⋊C4—91no—
124C4×C4⋊C4—92no—
125C22×C3×C4—21no—
126C22×C3×C4—22no—
127C22×C3×C4—32no—
128C22×C3×C4—34no—
129C22×C3×C4—32no—
130C22×C3×C4C22×D314yes—
131C22×C3×C4C22×D312yes—
132C22×Dic3—34no—
133C22×Dic3—32no—
134C22×Dic3—32no—
135C22×Dic3—61no—
136C22×Dic3—62no—
137C22×Dic3—61no—
138C22×Dic3C22×D314yes—
139C22×Dic3C22×D312yes—
140C22×Dic3C22×D312yes—
141C2×Dic6—38no—
142C2×Dic6—38no—
143C2×Dic6—38no—
144C2×Dic6—64no—
145C2×Dic6—64no—
146C2×Dic6—64no—
147C3×C4⋊C4—24no—
148C3×C4⋊C4—68no—
149C3×C4⋊C4—64no—
150C3×C4⋊C4C4×D318yes—
151C3×C42—64no—
152C4⋊Dic3—24no—
153C4⋊Dic3—28no—
154Dic3⋊C4—316no—
155Dic3⋊C4—68no—
156Dic3⋊C4—68no—
157Dic3⋊C4—68no—
158Dic3⋊C4—64no—
159Dic3⋊C4—64no—
160C4×Dic3—24no—
161C4×Dic3—316no—
162C4×Dic3—38no—
163C4×Dic3—68no—
164C4×Dic3—64no—
165C4×Dic3—68no—
166C4×Dic3—68no—
167C22×C32C23×C411yescharacteristic
168C22×C32C22×D411yescharacteristic
169C22×C32C22×Q811yescharacteristic
170C22×C32C2×#4112yes—
171C22×C322−1+412yes—
172C32×C4—24no—
173C32×C4C2×C4⋊C414yes—
174C3⋊Dic3—22no—
175C3⋊Dic3—22no—
176C3⋊Dic3C2×C4⋊C418yes—
177C3×Dic3—24no—
178C3×Dic3—42no—
179C3×Dic3—44no—
180C22×Q8—91no—
181C4×Q8—98no—
182C4×Q8—188no—
183C2×C4⋊C4—32no—
184C2×C4⋊C4—34no—
185C2×C4⋊C4—92no—
186C2×C4⋊C4—94no—
187C2×C4⋊C4—92no—
188C2×C4⋊C4D3211yescharacteristic
189C2×C42—32no—
190C2×C42—92no—
191C2×C42—91no—
192C2×C42—94no—
193#95—34no—
194#95—91no—
195#95—91no—
196#95—92no—
197#95—92no—
198C23×C3—21no—
199C23×C3C23×D312yes—
200C2×C3×C4—24no—
201C2×C3×C4—24no—
202C2×C3×C4—22no—
203C2×C3×C4—22no—
204C2×C3×C4—22no—
205C2×C3×C4—24no—
206C2×C3×C4—34no—
207C2×C3×C4—44no—
208C2×C3×C4—62no—
209C2×C3×C4—62no—
210C2×C3×C4—64no—
211C2×C3×C4—62no—
212C2×C3×C4—62no—
213C2×C3×C4—64no—
214C2×C3×C4—64no—
215C2×C3×C4—62no—
216C2×C3×C4C2×C4×D318yes—
217C2×C3×C4C2×C4×D314yes—
218C2×C3×C4D3×D414yes—
219C2×C3×C4D3×Q814yes—
220C2×Dic3—22no—
221C2×Dic3—22no—
222C2×Dic3—22no—
223C2×Dic3—24no—
224C2×Dic3—24no—
225C2×Dic3—22no—
226C2×Dic3—22no—
227C2×Dic3—24no—
228C2×Dic3—38no—
229C2×Dic3—38no—
230C2×Dic3—38no—
231C2×Dic3—34no—
232C2×Dic3—34no—
233C2×Dic3—62no—
234C2×Dic3—64no—
235C2×Dic3—64no—
236C2×Dic3—64no—
237C2×Dic3—62no—
238C2×Dic3—64no—
239C2×Dic3—62no—
240C2×Dic3—62no—
241C2×Dic3—62no—
242C2×Dic3—62no—
243C2×Dic3—122no—
244C2×Dic3#23714yes—
245Dic6—332no—
246Dic6—616no—
247C2×C32C22×C4⋊C411yescharacteristic
248C2×C32C4×#4111yescharacteristic
249C2×C32#51911yescharacteristic
250C2×C32#54812yes—
251C2×C32#55712yes—
252C2×Q8—94no—
253C2×Q8—94no—
254C2×Q8—94no—
255C22×C4—32no—
256C22×C4—32no—
257C22×C4—34no—
258C22×C4—92no—
259C22×C4—91no—
260C22×C4—91no—
261C22×C4C2×D3212yes—
262C22×C4C2×D3211yescharacteristic
263C4⋊C4—68no—
264C4⋊C4—64no—
265C4⋊C4—98no—
266C4⋊C4—184no—
267C4⋊C4—188no—
268C4⋊C4#62414yes—
269C42—64no—
270C42—98no—
271C42—94no—
272C42—188no—
273C22×C3—21no—
274C22×C3—21no—
275C22×C3—22no—
276C22×C3—22no—
277C22×C3—21no—
278C22×C3C22×C4×D312yes—
279C22×C3C2×D3×D412yes—
280C22×C3C2×#23712yes—
281C22×C3C2×D3×Q812yes—
282C22×C3#100712yes—
283C22×C3D3×#4112yes—
284C22×C3#101012yes—
285C3×C4—28no—
286C3×C4—24no—
287C3×C4—44no—
288C3×C4—64no—
289C3×C4—124no—
290C3×C4—122no—
291C3×C4D3×C4⋊C418yes—
292Dic3—24no—
293Dic3—316no—
294Dic3—42no—
295Dic3—44no—
296Dic3—68no—
297Dic3—64no—
298Dic3—64no—
299Dic3—64no—
300Dic3—122no—
301C32#235111yescharacteristic, complemented, Sylow
302C23C22×D3211yescharacteristic
303Q8—916no—
304C2×C4—24no—
305C2×C4—34no—
306C2×C4—62no—
307C2×C4—62no—
308C2×C4—62no—
309C2×C4—64no—
310C2×C4—64no—
311C2×C4—62no—
312C2×C4—62no—
313C2×C4—64no—
314C2×C4—94no—
315C2×C4—94no—
316C2×C4—94no—
317C2×C4—92no—
318C2×C4—92no—
319C2×C4—182no—
320C2×C4—182no—
321C2×C4#379712yes—
322C2×C4#380212yes—
323C2×C4C2×#62414yes—
324C2×C4C2×#62412yes—
325C2×C3—21no—
326C2×C3—22no—
327C2×C3—21no—
328C2×C3—21no—
329C2×C3—22no—
330C2×C3C2×D3×C4⋊C412yes—
331C2×C3C4×#23712yes—
332C2×C3#557212yes—
333C2×C3#559812yes—
334C2×C3#563312yes—
335C2×C3#568512yes—
336C2×C3#572112yes—
337C22C2×#379711yescharacteristic
338C22C2×#380211yescharacteristic
339C22D3×#23712yes—
340C22#6431512yes—
341C22C22×#62411yescharacteristic
342C4—24no—
343C4—64no—
344C4—98no—
345C4—122no—
346C4—124no—
347C4—182no—
348C4—182no—
349C4#6390014yes—
350C3—21no—
351C3#7598212yescomplemented
352C2#1059431812yes—
353C2#1059452512yes—
354C2C2×#6390011yescharacteristic
355C2#1059519011yescharacteristic
356C2#1059533911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C4⋊C4D32
hypocenterC32#2351
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
15. #64096C4semidirect
107. #634C4⋊C4semidirect
301. C32#2351semidirect
351. C3#75982semidirect

Maximal subgroups

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

subgroupindex
C2×#640962
C2×#638442
C3×#49842
#105913602
C4×#37242
#105912742
#105912642
#105912302
#759823