Finite Group Databasebeta

← #11773213

Subgroups — #11773213

Order 1152.

1561 conjugacy classes of subgroups.

The subgroup lattice has 347 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C3⋊Dic3C211yesmaximal, characteristic
2C22×C3×C4⋊Dic3C212yesmaximal
3C2×#63579C214yesmaximal
4#71563—32nomaximal
5C23×C32×C4C2211yescharacteristic
6C23×C3⋊Dic3C2212yes—
7C23×C3×Dic3C2214yes—
8C2×C4×C3⋊Dic3—24no—
9C2×C4×C3⋊Dic3C414yescomplemented
10C2×C3×C4⋊Dic3—24no—
11C2×C3×C4⋊Dic3—24no—
12C2×C3×C4⋊Dic3C418yescomplemented
13#63579—28no—
14C22×C3×C4⋊C4—32no—
15C22×C4⋊Dic3D312yes—
16C22×C4×Dic3—32no—
17C22×C4×Dic3—61no—
18C2×C3⋊#95—38no—
19C24×C32C2311yescharacteristic
20C22×C32×C4C2×C412yes—
21C22×C32×C4C2×C414yes—
22C22×C32×C4D414yes—
23C22×C32×C4D412yes—
24C22×C32×C4Q812yes—
25C22×C3⋊Dic3—24no—
26C22×C3⋊Dic3—24no—
27C22×C3⋊Dic3C2×C414yes—
28C22×C3⋊Dic3D414yes—
29C22×C3⋊Dic3Q814yes—
30C22×C3×Dic3—24no—
31C22×C3×Dic3—24no—
32C22×C3×Dic3—28no—
33C22×C3×Dic3—28no—
34C22×C3×Dic3C2×C418yes—
35C4×C3⋊Dic3—28no—
36C3×C4⋊Dic3—216no—
37C4⋊#95—91noSylow
38C23×C3×C4—21no—
39C23×C3×C4—34no—
40C23×C3×C4C2×D312yes—
41C23×Dic3—34no—
42C23×Dic3—62no—
43C23×Dic3C2×D314yes—
44C2×C3×C4⋊C4—38no—
45C2×C3×C4⋊C4—64no—
46C2×C3×C4⋊C4—64no—
47C2×C4⋊Dic3—24no—
48C2×C4⋊Dic3—24no—
49C2×C4⋊Dic3Dic318yescomplemented
50C2×C4×Dic3—38no—
51C2×C4×Dic3—64no—
52C2×C4×Dic3—68no—
53C2×C4×Dic3—64no—
54C2×C4×Dic3—64no—
55C3⋊#95—616no—
56C23×C32C22×C411yescharacteristic
57C23×C32C22×C412yes—
58C23×C32C2×D412yes—
59C23×C32C2×D412yes—
60C23×C32C2×D411yescharacteristic
61C23×C32C2×Q811yescharacteristic
62C23×C32C2×Q812yes—
63C23×C32#4114yes—
64C2×C32×C4C4214yes—
65C2×C32×C4C22⋊C414yes—
66C2×C32×C4C22⋊C418yes—
67C2×C32×C4C4⋊C414yes—
68C2×C32×C4C4⋊C418yes—
69C2×C3⋊Dic3—24no—
70C2×C3⋊Dic3—24no—
71C2×C3⋊Dic3—28no—
72C2×C3⋊Dic3—28no—
73C2×C3⋊Dic3C4⋊C418yescomplemented
74C2×C3×Dic3—28no—
75C2×C3×Dic3—216no—
76C2×C3×Dic3—48no—
77C2×C3×Dic3—44no—
78C2×C3×Dic3—44no—
79C22×C4⋊C4—32no—
80C22×C42—91no—
81C2×#95—94no—
82C24×C3—21no—
83C24×C3C22×D312yes—
84C22×C3×C4—24no—
85C22×C3×C4—22no—
86C22×C3×C4—22no—
87C22×C3×C4—24no—
88C22×C3×C4—22no—
89C22×C3×C4—38no—
90C22×C3×C4—64no—
91C22×C3×C4—68no—
92C22×C3×C4—68no—
93C22×C3×C4—64no—
94C22×C3×C4Dic614yes—
95C22×C3×C4C4×D314yes—
96C22×C3×C4C4×D314yes—
97C22×C3×C4D1214yes—
98C22×C3×C4C2×Dic314yes—
99C22×C3×C4#6714yes—
100C22×C3×C4#6714yes—
101C22×Dic3—28no—
102C22×Dic3—28no—
103C22×Dic3—24no—
104C22×Dic3—24no—
105C22×Dic3—38no—
106C22×Dic3—38no—
107C22×Dic3—38no—
108C22×Dic3—64no—
109C22×Dic3—64no—
110C22×Dic3—64no—
111C22×Dic3—68no—
112C22×Dic3—68no—
113C22×Dic3—64no—
114C22×Dic3—64no—
115C22×Dic3—64no—
116C22×Dic3—64no—
117C22×Dic3C2×Dic318yes—
118C3×C4⋊C4—616no—
119C4⋊Dic3—216no—
120C4×Dic3—616no—
121C4×Dic3—616no—
122C22×C32C2×C4211yescharacteristic
123C22×C32C2×C22⋊C411yescharacteristic
124C22×C32C2×C22⋊C412yes—
125C22×C32C2×C4⋊C412yes—
126C22×C32C2×C4⋊C411yescharacteristic
127C22×C32C2×C4⋊C412yes—
128C22×C32#11712yes—
129C22×C32C4×D414yes—
130C22×C32C4×Q814yes—
131C22×C32#12114yes—
132C22×C32C22⋊Q814yes—
133C22×C32#12412yes—
134C22×C32#12512yes—
135C22×C32#12711yescharacteristic
136C22×C32C4⋊Q812yes—
137C22×C32C4⋊Q811yescharacteristic
138C32×C4#9518yescomplemented
139C3⋊Dic3—28no—
140C3×Dic3—48no—
141C23×C4—34no—
142C23×C4—92no—
143C23×C4D3211yescharacteristic
144C2×C4⋊C4—38no—
145C2×C4⋊C4—64no—
146C2×C4⋊C4—64no—
147C2×C42—94no—
148C2×C42—184no—
149#95—188no—
150C23×C3—24no—
151C23×C3—22no—
152C23×C3—22no—
153C23×C3—22no—
154C23×C3—21no—
155C23×C3—21no—
156C23×C3—22no—
157C23×C3—21no—
158C23×C3C2×Dic612yes—
159C23×C3C2×C4×D312yes—
160C23×C3C2×C4×D312yes—
161C23×C3C2×D1212yes—
162C23×C3D3×D414yes—
163C23×C3#23714yes—
164C23×C3D3×Q814yes—
165C23×C3#23914yes—
166C23×C3C22×Dic312yes—
167C23×C3C2×#6712yes—
168C23×C3C2×#6712yes—
169C2×C3×C4—24no—
170C2×C3×C4—28no—
171C2×C3×C4—24no—
172C2×C3×C4—28no—
173C2×C3×C4—24no—
174C2×C3×C4—616no—
175C2×C3×C4—68no—
176C2×C3×C4—128no—
177C2×C3×C4—124no—
178C2×C3×C4—124no—
179C2×C3×C4C4×Dic318yes—
180C2×C3×C4Dic3⋊C418yes—
181C2×C3×C4Dic3⋊C418yes—
182C2×C3×C4C4⋊Dic318yes—
183C2×C3×C4(C2×D3)⋊C418yes—
184C2×C3×C4(C2×D3)⋊C418yes—
185C2×C3×C4#21718yes—
186C2×Dic3—216no—
187C2×Dic3—28no—
188C2×Dic3—316no—
189C2×Dic3—44no—
190C2×Dic3—48no—
191C2×Dic3—44no—
192C2×Dic3—68no—
193C2×Dic3—68no—
194C2×Dic3—68no—
195C2×Dic3—616no—
196C2×Dic3—616no—
197C2×Dic3—68no—
198C2×Dic3—68no—
199C2×Dic3—68no—
200C2×Dic3—68no—
201C2×Dic3—68no—
202C2×Dic3—68no—
203C2×C32C2×#9511yescharacteristic
204C2×C32C4×C4⋊C412yes—
205C2×C32#38012yes—
206C2×C32#38211yescharacteristic
207C2×C32#38411yescharacteristic
208C2×C32#38914yes—
209C2×C32#39012yes—
210C2×C32#39112yes—
211C24C2×D3211yescharacteristic
212C22×C4—38no—
213C22×C4—68no—
214C22×C4—68no—
215C22×C4—64no—
216C22×C4—64no—
217C22×C4—94no—
218C22×C4—94no—
219C22×C4—94no—
220C22×C4—184no—
221C22×C4—184no—
222C22×C4D3×Dic314yes—
223C22×C4#62412yes—
224C22×C4#62512yes—
225C22×C4#62614yes—
226C22×C4#62712yes—
227C4⋊C4—616no—
228C42—188no—
229C22×C3—24no—
230C22×C3—22no—
231C22×C3—22no—
232C22×C3—24no—
233C22×C3—22no—
234C22×C3—21no—
235C22×C3—24no—
236C22×C3—22no—
237C22×C3—21no—
238C22×C3—24no—
239C22×C3—22no—
240C22×C3—21no—
241C22×C3—22no—
242C22×C3—21no—
243C22×C3—22no—
244C22×C3—21no—
245C22×C3#88714yes—
246C22×C3#88814yes—
247C22×C3#89014yes—
248C22×C3D3×C4⋊C414yes—
249C22×C3#89214yes—
250C22×C3#89314yes—
251C22×C3#89514yes—
252C22×C3#89714yes—
253C22×C3C2×C4×Dic312yes—
254C22×C3C2×Dic3⋊C412yes—
255C22×C3C2×Dic3⋊C412yes—
256C22×C3C2×C4⋊Dic312yes—
257C22×C3C2×(C2×D3)⋊C412yes—
258C22×C3C2×(C2×D3)⋊C412yes—
259C22×C3D4×Dic314yes—
260C22×C3#93612yes—
261C22×C3#93814yes—
262C22×C3#94012yes—
263C22×C3#94412yes—
264C22×C3Q8×Dic314yes—
265C22×C3#94614yes—
266C22×C3#94712yes—
267C22×C3C2×#21712yes—
268C3×C4—28no—
269C3×C4—128no—
270C3×C4C3⋊#95116yescomplemented
271Dic3—48no—
272Dic3—616no—
273Dic3—616no—
274C32C4⋊#9511yescharacteristic, complemented, Sylow
275C23#379614yes—
276C23#379712yes—
277C23#380212yes—
278C23C2×D3×Dic312yes—
279C23C2×#62411yescharacteristic
280C23C2×#62511yescharacteristic
281C23C2×#62612yes—
282C23C2×#62711yescharacteristic
283C2×C4—616no—
284C2×C4—68no—
285C2×C4—98no—
286C2×C4—124no—
287C2×C4—124no—
288C2×C4—128no—
289C2×C4—184no—
290C2×C4—188no—
291C2×C4—188no—
292C2×C4—184no—
293C2×C4Dic3214yes—
294C2×C4(C2×D3)⋊Dic318yes—
295C2×C4#372214yes—
296C2×C4Dic3⋊Dic318yes—
297C2×C4#372414yes—
298C2×C3—22no—
299C2×C3—22no—
300C2×C3—22no—
301C2×C3—24no—
302C2×C3—21no—
303C2×C3—21no—
304C2×C3—22no—
305C2×C3—21no—
306C2×C3#497214yes—
307C2×C3#497312yes—
308C2×C3Dic3×C4⋊C414yes—
309C2×C3#497512yes—
310C2×C3#497712yes—
311C2×C3#498414yes—
312C2×C3#498714yes—
313C2×C3#498812yes—
314C2×C3C2×C3⋊#9512yes—
315C2×C3#522112yes—
316C2×C3#522912yes—
317C22#6384314yes—
318C22#6384912yes—
319C22#6386312yes—
320C22#6387114yes—
321C22#6387212yes—
322C22#6387311yescharacteristic
323C22#6389814yes—
324C22#6390012yes—
325C22#6391411yescharacteristic
326C22#6391614yes—
327C22#6391912yes—
328C22C2×Dic3211yescharacteristic
329C22C2×(C2×D3)⋊Dic312yes—
330C22C2×#372211yescharacteristic
331C22C2×Dic3⋊Dic312yes—
332C22C2×#372411yescharacteristic
333C4—128no—
334C4—188no—
335C4#6357918yescomplemented
336C3—21no—
337C3#7156312yescomplemented
338C2#1059122112yes—
339C2#1059123011yescharacteristic
340C2#1059127412yes—
341C2#1059132312yes—
342C2#1059132512yes—
343C2#1059135714yes—
344C2#1059135911yescharacteristic
345C2C2×#6357911yescharacteristic
subgroupG/H
center, FrattiniC24C2×D32
commutatorC22×C32C2×C42
FittingC23×C32×C4C22
socle, prime radical, cosocleC24×C32C23
hypercenterC23×C4D32
hypocenterC32C4⋊#95
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
9. C2×C4×C3⋊Dic3C4semidirect
12. C2×C3×C4⋊Dic3C4semidirect
49. C2×C4⋊Dic3Dic3semidirect
73. C2×C3⋊Dic3C4⋊C4semidirect
138. C32×C4#95semidirect
270. C3×C4C3⋊#95semidirect
274. C32C4⋊#95semidirect
335. C4#63579semidirect
337. C3#71563semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C3⋊Dic32
C22×C3×C4⋊Dic32
C2×#635792
#715633