Finite Group Databasebeta

← #11802990

Subgroups — #11802990

Order 1152.

1365 conjugacy classes of subgroups.

The subgroup lattice has 351 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64101C211yesmaximal, characteristic
2C2×#63900C211yesmaximal, characteristic
3C2×#63874C211yesmaximal, characteristic
4C3×#4977C212yesmaximal, complemented
5#10591375C214yesmaximal
6#10591349C212yesmaximal, complemented
7#10591328C214yesmaximal, complemented
8#74225—32nomaximal
9C22×C4×C3⋊D3C2211yescharacteristic
10C22×#624C2212yes—
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×#3752C2212yes—
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C4×C3⋊Dic3C2212yes—
15#64101—24no—
16C2×C3×C4⋊Dic3C2212yes—
17C2×C3×C4×Dic3C2212yes—
18C2×#3724C2212yes—
19C2×#3724C2212yes—
20C2×Dic3⋊Dic3C2218yes—
21C2×#3722C2212yes—
22#63900—24no—
23#63874C418yescomplemented
24C3×C3⋊#95C2218yes—
25C2×#892—32no—
26C2×#892—61no—
27C2×D3×C4⋊C4—32no—
28C2×#872—32no—
29C3×#382—32no—
30#4977D312yescomplemented
31#4975—32no—
32#4935—32no—
33#4668—38no—
34#4647—38no—
35C23×C3⋊D3C2311yescharacteristic
36C22×C32×C4C2312yes—
37C22×C32×C4C2311yescharacteristic
38C22×C3⋊Dic3C2312yes—
39C22×C3⋊Dic3C2311yescharacteristic
40C2×C4×C3⋊D3C2×C414yes—
41C2×C4×C3⋊D3D414yes—
42C2×C4×C3⋊D3Q814yes—
43C22×C3×Dic3C2314yes—
44C22×C3×Dic3C2314yes—
45C2×#624—24no—
46C2×#624—44no—
47C32×C4⋊C4—22no—
48#3752—24no—
49C4⋊(C3⋊Dic3)—22no—
50C4×C3⋊Dic3—24no—
51C3×C4⋊Dic3—24no—
52C3×C4×Dic3C2×C418yescomplemented
53#3724—24no—
54#3724C2×C418yescomplemented
55Dic3⋊Dic3—48no—
56#3722C2×C418yes—
57#2317—91noSylow
58C22×C4×D3—32no—
59C22×C4×D3—34no—
60C22×C4×D3—61no—
61C2×C3×C4⋊C4—21no—
62C2×C3×C4⋊C4—32no—
63C2×C3×C4⋊C4C2×D312yes—
64C2×C3×C42—32no—
65C2×(C2×D3)⋊C4—34no—
66C2×(C2×D3)⋊C4—34no—
67C2×(C2×D3)⋊C4—62no—
68C2×C4⋊Dic3—32no—
69C2×C4⋊Dic3—38no—
70C2×C4⋊Dic3—61no—
71C2×C4⋊Dic3C2×D312yes—
72C2×Dic3⋊C4—34no—
73C2×Dic3⋊C4—34no—
74C2×Dic3⋊C4—38no—
75C2×C4×Dic3—34no—
76C2×C4×Dic3—62no—
77C2×C4×Dic3C2×D312yes—
78#892—68no—
79#892—68no—
80D3×C4⋊C4—68no—
81#872—316no—
82C3×#95—38no—
83C3⋊#95C2×D318yes—
84C23×C32C2411yescharacteristic
85C22×C3⋊D3—22no—
86C22×C3⋊D3—22no—
87C22×C3⋊D3C22×C412yes—
88C22×C3⋊D3C2×D412yes—
89C22×C3⋊D3C2×Q812yes—
90C2×C32×C4—22no—
91C2×C32×C4—24no—
92C2×C32×C4C22×C412yes—
93C2×C32×C4C2×D412yes—
94C2×C32×C4C2×Q812yes—
95C2×C3⋊Dic3—22no—
96C2×C3⋊Dic3—24no—
97C2×C3⋊Dic3C22×C412yes—
98C2×C3⋊Dic3C2×D412yes—
99C2×C3⋊Dic3C2×Q812yes—
100C4×C3⋊D3C4⋊C4116yescomplemented
101C2×C3×Dic3—24no—
102C2×C3×Dic3—24no—
103C2×C3×Dic3—24no—
104C2×C3×Dic3—28no—
105C2×C3×Dic3C22×C418yes—
106#624—48no—
107C2×#117—91no—
108C2×#117—91no—
109C22×C4⋊C4—91no—
110#389—94no—
111#385—94no—
112#384—92no—
113#382—32no—
114C23×D3—32no—
115C23×D3—61no—
116C22×C3×C4—21no—
117C22×C3×C4—22no—
118C22×C3×C4—34no—
119C22×C3×C4—34no—
120C22×C3×C4C22×D314yes—
121C22×C3×C4C22×D312yes—
122C22×Dic3—32no—
123C22×Dic3—34no—
124C22×Dic3—61no—
125C22×Dic3—62no—
126C22×Dic3C22×D314yes—
127C22×Dic3C22×D314yes—
128C2×C4×D3—38no—
129C2×C4×D3—38no—
130C2×C4×D3—38no—
131C2×C4×D3—64no—
132C2×C4×D3—64no—
133C2×C4×D3—64no—
134C2×C4×D3—68no—
135C2×C4×D3—128no—
136C3×C4⋊C4—24no—
137C3×C4⋊C4—24no—
138C3×C4⋊C4—64no—
139C3×C42—38no—
140(C2×D3)⋊C4—316no—
141(C2×D3)⋊C4—68no—
142(C2×D3)⋊C4—68no—
143C4⋊Dic3—24no—
144C4⋊Dic3—64no—
145C4⋊Dic3—64no—
146C4⋊Dic3—128no—
147Dic3⋊C4—316no—
148Dic3⋊C4—68no—
149Dic3⋊C4—128no—
150C4×Dic3—68no—
151C4×Dic3—68no—
152C4×Dic3C4×D318yescomplemented
153C22×C32C23×C411yescharacteristic
154C22×C32C22×D411yescharacteristic
155C22×C32C22×Q811yescharacteristic
156C22×C32H(5,𝔽2)12yes—
157C22×C322−1+412yes—
158C2×C3⋊D3—24no—
159C2×C3⋊D3—22no—
160C2×C3⋊D3—22no—
161C2×C3⋊D3—24no—
162C2×C3⋊D3C2×C4⋊C414yes—
163C32×C4—42no—
164C32×C4C2×C4⋊C414yes—
165C3⋊Dic3—42no—
166C3⋊Dic3C2×C4⋊C414yes—
167C3×Dic3—28no—
168C3×Dic3—44no—
169C23×C4—92no—
170C23×C4—91no—
171#117—98no—
172#117—184no—
173C2×C4⋊C4—32no—
174C2×C4⋊C4—92no—
175C2×C4⋊C4—92no—
176C2×C4⋊C4—91no—
177C2×C4⋊C4—98no—
178C2×C4⋊C4—184no—
179C2×C4⋊C4D3211yescharacteristic
180C2×C22⋊C4—92no—
181C2×C22⋊C4—92no—
182C2×C42—32no—
183C2×C42—92no—
184#95—38no—
185C23×C3—21no—
186C23×C3C23×D312yes—
187C22×D3—34no—
188C22×D3—34no—
189C22×D3—34no—
190C22×D3—62no—
191C22×D3—62no—
192C22×D3—62no—
193C22×D3—64no—
194C22×D3—64no—
195C22×D3—122no—
196C22×D3—122no—
197C2×C3×C4—24no—
198C2×C3×C4—24no—
199C2×C3×C4—28no—
200C2×C3×C4—22no—
201C2×C3×C4—22no—
202C2×C3×C4—22no—
203C2×C3×C4—38no—
204C2×C3×C4—44no—
205C2×C3×C4—64no—
206C2×C3×C4—64no—
207C2×C3×C4—64no—
208C2×C3×C4—68no—
209C2×C3×C4C2×C4×D314yes—
210C2×C3×C4D3×D414yes—
211C2×C3×C4D3×Q814yes—
212C2×Dic3—24no—
213C2×Dic3—24no—
214C2×Dic3—24no—
215C2×Dic3—28no—
216C2×Dic3—34no—
217C2×Dic3—34no—
218C2×Dic3—34no—
219C2×Dic3—62no—
220C2×Dic3—62no—
221C2×Dic3—62no—
222C2×Dic3—64no—
223C2×Dic3—64no—
224C2×Dic3—68no—
225C2×Dic3—124no—
226C2×Dic3C2×C4×D318yes—
227C4×D3—332no—
228C4×D3—616no—
229C4×D3—1216no—
230C2×C32C22×C4⋊C411yescharacteristic
231C2×C32#52012yes—
232C2×C32#53511yescharacteristic
233C2×C32#53611yescharacteristic
234C2×C32#54412yes—
235C3⋊D3—24no—
236C24—91no—
237C22×C4—34no—
238C22×C4—34no—
239C22×C4—91no—
240C22×C4—94no—
241C22×C4—94no—
242C22×C4—94no—
243C22×C4—92no—
244C22×C4—184no—
245C22×C4—364no—
246C22×C4C2×D3212yes—
247C22×C4C2×D3211yescharacteristic
248C4⋊C4—22no—
249C4⋊C4—64no—
250C4⋊C4—98no—
251C4⋊C4—184no—
252C4⋊C4—182no—
253C4⋊C4—368no—
254C22⋊C4—98no—
255C22⋊C4—184no—
256C42—38no—
257C42—184no—
258C22×C3—21no—
259C22×C3—21no—
260C22×C3—22no—
261C22×C3—22no—
262C22×C3—21no—
263C22×C3C22×C4×D312yes—
264C22×C3C2×D3×D412yes—
265C22×C3C2×D3×Q812yes—
266C22×C3#100914yes—
267C22×C3#101014yes—
268C2×D3—38no—
269C2×D3—64no—
270C2×D3—64no—
271C2×D3—64no—
272C2×D3—68no—
273C2×D3—68no—
274C2×D3—122no—
275C2×D3—122no—
276C2×D3—124no—
277C2×D3—124no—
278C3×C4—24no—
279C3×C4—44no—
280C3×C4—44no—
281C3×C4—68no—
282C3×C4—124no—
283C3×C4D3×C4⋊C418yes—
284Dic3—28no—
285Dic3—38no—
286Dic3—44no—
287Dic3—64no—
288Dic3—124no—
289Dic3—124no—
290C32#231711yescharacteristic, complemented, Sylow
291C23—92no—
292C23—92no—
293C23—92no—
294C23—182no—
295C23—182no—
296C23C22×D3211yescharacteristic
297C2×C4—24no—
298C2×C4—22no—
299C2×C4—38no—
300C2×C4—64no—
301C2×C4—64no—
302C2×C4—68no—
303C2×C4—64no—
304C2×C4—92no—
305C2×C4—92no—
306C2×C4—92no—
307C2×C4—916no—
308C2×C4—184no—
309C2×C4—182no—
310C2×C4—368no—
311C2×C4#379712yes—
312C2×C4C4×D3212yes—
313C2×C4#381112yes—
314C2×C3—21no—
315C2×C3—21no—
316C2×C3—21no—
317C2×C3—22no—
318C2×C3—22no—
319C2×C3C2×D3×C4⋊C412yes—
320C2×C3#552314yes—
321C2×C3#567412yes—
322C2×C3#567512yes—
323C2×C3#568914yes—
324D3—68no—
325D3—124no—
326C22—94no—
327C22—182no—
328C22—182no—
329C22—184no—
330C22—184no—
331C22C2×#379711yescharacteristic
332C22C2×C4×D3211yescharacteristic
333C22#6430912yes—
334C22#6432012yes—
335C22C2×#381111yescharacteristic
336C4—42no—
337C4—68no—
338C4—94no—
339C4—124no—
340C4—362no—
341C4#6388314yes—
342C3—21no—
343C3#7422512yescomplemented
344C2—184no—
345C2#1059450812yes—
346C2#1059451112yes—
347C2C2×#6388311yescharacteristic
348C2#1059517111yescharacteristic
349C2#1059543311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC2×C4⋊C4D32
hypocenterC32#2317
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. C3×#4977C2semidirect
6. #10591349C2semidirect
7. #10591328C2semidirect
23. #63874C4semidirect
30. #4977D3semidirect
52. C3×C4×Dic3C2×C4semidirect
54. #3724C2×C4semidirect
100. C4×C3⋊D3C4⋊C4semidirect
152. C4×Dic3C4×D3semidirect
290. C32#2317semidirect
343. C3#74225semidirect

Maximal subgroups

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

subgroupindex
C2×#641012
C2×#639002
C2×#638742
C3×#49772
#105913752
#105913492
#105913282
#742253