Finite Group Databasebeta

← #11801840

Subgroups — #11801840

Order 1152.

1477 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64081C211yesmaximal, characteristic
2C2×C4×#624C211yesmaximal, characteristic
3C2×#63874C211yesmaximal, characteristic
4C3×C4×Dic3⋊C4C212yesmaximal, complemented
5#10591375C212yesmaximal
6#10591374C212yesmaximal
7C4×Dic3⋊Dic3C212yesmaximal, complemented
8#10591256C214yesmaximal, complemented
9#73755—32nomaximal
10C22×C4×C3⋊D3C2211yescharacteristic
11C22×#624C2212yes—
12C2×C32×C42C2211yescharacteristic
13C2×#3752C2212yes—
14C2×#3750C2212yes—
15C2×C4×C3⋊Dic3C2211yescharacteristic
16#64081—24no—
17C2×C3×Dic3⋊C4C2214yes—
18C2×C3×C4×Dic3C2212yes—
19C2×C3×C4×Dic3C2212yes—
20C2×#3724C2212yes—
21C2×Dic3⋊Dic3C2214yes—
22C2×#3722C2211yescharacteristic
23C2×#3722C2211yescharacteristic
24C2×Dic32C2212yes—
25C4×#624—24no—
26#63874C418yescomplemented
27C3×C3⋊#95C2214yes—
28#63579C2214yes—
29C2×#872—32no—
30C2×#872—32no—
31C2×#872—61no—
32C2×C42×D3—32no—
33C3×C4×C4⋊C4—32no—
34#4989—34no—
35#4976—34no—
36C4×C4⋊Dic3—32no—
37C4×Dic3⋊C4—32no—
38C4×Dic3⋊C4D312yescomplemented
39#4668—34no—
40#4647—34no—
41C23×C3⋊D3C2311yescharacteristic
42C22×C32×C4C2312yes—
43C22×C32×C4C2311yescharacteristic
44C22×C3⋊Dic3C2312yes—
45C22×C3⋊Dic3C2311yescharacteristic
46C2×C4×C3⋊D3C2×C414yes—
47C2×C4×C3⋊D3D414yes—
48C2×C4×C3⋊D3Q814yes—
49C22×C3×Dic3C2312yes—
50C22×C3×Dic3C2312yes—
51C22×C3×Dic3C2314yes—
52C2×#624—24no—
53C2×#624—28no—
54C32×C42—22no—
55#3752—24no—
56#3750—24no—
57C4×C3⋊Dic3—22no—
58C3×Dic3⋊C4—28no—
59C3×C4×Dic3—24no—
60C3×C4×Dic3C2×C418yescomplemented
61#3724C2×C418yescomplemented
62Dic3⋊Dic3—28no—
63#3722C2×C414yes—
64#3722C2×C414yes—
65Dic32—24no—
66#2296—91noSylow
67C22×C4×D3—32no—
68C22×C4×D3—34no—
69C22×C4×D3—61no—
70C2×C3×C4⋊C4—34no—
71C2×C3×C42—21no—
72C2×C3×C42—32no—
73C2×C3×C42—32no—
74C2×C3×C42C2×D312yes—
75C2×(C2×D3)⋊C4—32no—
76C2×(C2×D3)⋊C4—32no—
77C2×(C2×D3)⋊C4—34no—
78C2×(C2×D3)⋊C4—62no—
79C2×C4⋊Dic3—34no—
80C2×Dic3⋊C4—32no—
81C2×Dic3⋊C4—32no—
82C2×Dic3⋊C4—34no—
83C2×Dic3⋊C4—34no—
84C2×Dic3⋊C4—62no—
85C2×Dic3⋊C4C2×D314yes—
86C2×C4×Dic3—32no—
87C2×C4×Dic3—34no—
88C2×C4×Dic3—61no—
89C2×C4×Dic3C2×D312yes—
90C2×C4×Dic3C2×D312yes—
91#872—316no—
92#872—68no—
93#872—68no—
94C42×D3—68no—
95C3×#95—34no—
96C3⋊#95—34no—
97C3⋊#95—34no—
98C3⋊#95C2×D314yes—
99C23×C32C2411yescharacteristic
100C22×C3⋊D3—24no—
101C22×C3⋊D3C22×C412yes—
102C22×C3⋊D3C2×D412yes—
103C22×C3⋊D3C2×Q812yes—
104C2×C32×C4—22no—
105C2×C32×C4—24no—
106C2×C32×C4C22×C412yes—
107C2×C32×C4C2×D412yes—
108C2×C32×C4C2×Q812yes—
109C2×C3⋊Dic3—22no—
110C2×C3⋊Dic3—24no—
111C2×C3⋊Dic3C22×C412yes—
112C2×C3⋊Dic3C2×D412yes—
113C2×C3⋊Dic3C2×Q812yes—
114C4×C3⋊D3C4⋊C4116yescomplemented
115C2×C3×Dic3—24no—
116C2×C3×Dic3—24no—
117C2×C3×Dic3—24no—
118C2×C3×Dic3—24no—
119C2×C3×Dic3C22×C414yes—
120C2×C3×Dic3C22×C414yes—
121C2×C3×Dic3#4118yes—
122#624—216no—
123C2×#117—91no—
124C2×#117—91no—
125C22×C42—91no—
126#389—94no—
127#385—92no—
128#385—92no—
129C4×C4⋊C4—32no—
130C4×C4⋊C4—92no—
131C23×D3—32no—
132C23×D3—61no—
133C22×C3×C4—22no—
134C22×C3×C4—21no—
135C22×C3×C4—32no—
136C22×C3×C4—34no—
137C22×C3×C4—32no—
138C22×C3×C4C22×D314yes—
139C22×C3×C4C22×D312yes—
140C22×Dic3—32no—
141C22×Dic3—34no—
142C22×Dic3—61no—
143C22×Dic3—62no—
144C22×Dic3C22×D312yes—
145C22×Dic3C22×D312yes—
146C22×Dic3C22×D314yes—
147C2×C4×D3—38no—
148C2×C4×D3—38no—
149C2×C4×D3—38no—
150C2×C4×D3—64no—
151C2×C4×D3—64no—
152C2×C4×D3—64no—
153C2×C4×D3—68no—
154C2×C4×D3—68no—
155C2×C4×D3—68no—
156C3×C4⋊C4—68no—
157C3×C42—24no—
158C3×C42—24no—
159C3×C42—38no—
160C3×C42—64no—
161(C2×D3)⋊C4—38no—
162(C2×D3)⋊C4—38no—
163(C2×D3)⋊C4—68no—
164(C2×D3)⋊C4—68no—
165C4⋊Dic3—68no—
166Dic3⋊C4—28no—
167Dic3⋊C4—38no—
168Dic3⋊C4—38no—
169Dic3⋊C4—68no—
170Dic3⋊C4—68no—
171Dic3⋊C4—68no—
172C4×Dic3—24no—
173C4×Dic3—68no—
174C4×Dic3—64no—
175C4×Dic3—64no—
176C4×Dic3C4×D318yescomplemented
177C22×C32C23×C411yescharacteristic
178C22×C32C22×D411yescharacteristic
179C22×C32C22×Q811yescharacteristic
180C22×C32C2×#4114yes—
181C2×C3⋊D3—24no—
182C2×C3⋊D3—24no—
183C2×C3⋊D3—24no—
184C2×C3⋊D3C2×C4⋊C414yes—
185C32×C4—42no—
186C32×C4C2×C4⋊C414yes—
187C3⋊Dic3—42no—
188C3⋊Dic3C2×C4⋊C414yes—
189C3×Dic3—24no—
190C3×Dic3—24no—
191C3×Dic3—28no—
192C23×C4—92no—
193C23×C4—91no—
194#117—98no—
195#117—184no—
196C2×C4⋊C4—34no—
197C2×C4⋊C4—92no—
198C2×C4⋊C4—94no—
199C2×C4⋊C4—92no—
200C2×C22⋊C4—91no—
201C2×C22⋊C4—91no—
202C2×C22⋊C4—92no—
203C2×C42—32no—
204C2×C42—32no—
205C2×C42—92no—
206C2×C42—91no—
207C2×C42—184no—
208C2×C42D3211yescharacteristic
209#95—34no—
210#95—94no—
211C23×C3—21no—
212C23×C3C23×D312yes—
213C22×D3—34no—
214C22×D3—34no—
215C22×D3—34no—
216C22×D3—62no—
217C22×D3—62no—
218C22×D3—62no—
219C22×D3—64no—
220C22×D3—64no—
221C22×D3—124no—
222C2×C3×C4—24no—
223C2×C3×C4—24no—
224C2×C3×C4—24no—
225C2×C3×C4—24no—
226C2×C3×C4—22no—
227C2×C3×C4—22no—
228C2×C3×C4—22no—
229C2×C3×C4—34no—
230C2×C3×C4—34no—
231C2×C3×C4—38no—
232C2×C3×C4—44no—
233C2×C3×C4—64no—
234C2×C3×C4—64no—
235C2×C3×C4—64no—
236C2×C3×C4—64no—
237C2×C3×C4C2×C4×D314yes—
238C2×C3×C4D3×D414yes—
239C2×C3×C4D3×Q814yes—
240C2×Dic3—24no—
241C2×Dic3—24no—
242C2×Dic3—24no—
243C2×Dic3—24no—
244C2×Dic3—34no—
245C2×Dic3—34no—
246C2×Dic3—34no—
247C2×Dic3—62no—
248C2×Dic3—62no—
249C2×Dic3—62no—
250C2×Dic3—64no—
251C2×Dic3—64no—
252C2×Dic3—64no—
253C2×Dic3—64no—
254C2×Dic3—124no—
255C2×Dic3C2×C4×D314yes—
256C2×Dic3C2×C4×D314yes—
257C2×Dic3#23518yes—
258C4×D3—332no—
259C4×D3—616no—
260C4×D3—632no—
261C2×C32C22×C4⋊C411yescharacteristic
262C2×C32C4×#4112yes—
263C2×C32#52512yes—
264C2×C32#53312yes—
265C3⋊D3—24no—
266C24—91no—
267C22×C4—32no—
268C22×C4—34no—
269C22×C4—32no—
270C22×C4—91no—
271C22×C4—94no—
272C22×C4—94no—
273C22×C4—94no—
274C22×C4—92no—
275C22×C4—188no—
276C22×C4—184no—
277C22×C4C2×D3212yes—
278C22×C4C2×D3211yescharacteristic
279C4⋊C4—68no—
280C4⋊C4—98no—
281C4⋊C4—184no—
282C4⋊C4—188no—
283C22⋊C4—94no—
284C22⋊C4—94no—
285C22⋊C4—184no—
286C42—22no—
287C42—38no—
288C42—64no—
289C42—184no—
290C42—182no—
291C22×C3—21no—
292C22×C3—21no—
293C22×C3—24no—
294C22×C3—21no—
295C22×C3C22×C4×D312yes—
296C22×C3C2×#23514yes—
297C22×C3C2×D3×D412yes—
298C22×C3C2×D3×Q812yes—
299C22×C3D3×#4114yes—
300C2×D3—38no—
301C2×D3—64no—
302C2×D3—64no—
303C2×D3—64no—
304C2×D3—68no—
305C2×D3—68no—
306C2×D3—124no—
307C2×D3—124no—
308C2×D3—124no—
309C3×C4—24no—
310C3×C4—44no—
311C3×C4—44no—
312C3×C4—64no—
313C3×C4—64no—
314C3×C4—68no—
315C3×C4D3×C4⋊C418yes—
316Dic3—24no—
317Dic3—24no—
318Dic3—28no—
319Dic3—38no—
320Dic3—64no—
321Dic3—124no—
322Dic3—124no—
323C32#229611yescharacteristic, complemented, Sylow
324C23—92no—
325C23—92no—
326C23—92no—
327C23—184no—
328C23C22×D3211yescharacteristic
329C2×C4—24no—
330C2×C4—22no—
331C2×C4—34no—
332C2×C4—34no—
333C2×C4—38no—
334C2×C4—64no—
335C2×C4—64no—
336C2×C4—64no—
337C2×C4—64no—
338C2×C4—92no—
339C2×C4—92no—
340C2×C4—92no—
341C2×C4—916no—
342C2×C4—1816no—
343C2×C4—184no—
344C2×C4—182no—
345C2×C4#379712yes—
346C2×C4C4×D3212yes—
347C2×C4#381112yes—
348C2×C3—22no—
349C2×C3—21no—
350C2×C3—22no—
351C2×C3—22no—
352C2×C3C4×#23512yes—
353C2×C3C2×D3×C4⋊C412yes—
354C2×C3#552212yes—
355C2×C3#554714yes—
356C2×C3#557814yes—
357D3—68no—
358D3—124no—
359C22—94no—
360C22—184no—
361C22—184no—
362C22—184no—
363C22C2×#379711yescharacteristic
364C22C2×C4×D3211yescharacteristic
365C22D3×#23514yes—
366C22C2×#381111yescharacteristic
367C4—42no—
368C4—68no—
369C4—64no—
370C4—64no—
371C4—94no—
372C4—362no—
373C4#6388314yes—
374C3—21no—
375C3#7375512yescomplemented
376C2—184no—
377C2#1059393512yes—
378C2#1059396512yes—
379C2C2×#6388311yescharacteristic
380C2#1059507612yes—
subgroupG/H
centerC22×C4C2×D32
commutatorC22×C32C23×C4
FrattiniC23C22×D32
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC2×C42D32
hypocenterC32#2296
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
4. C3×C4×Dic3⋊C4C2semidirect
7. C4×Dic3⋊Dic3C2semidirect
8. #10591256C2semidirect
26. #63874C4semidirect
38. C4×Dic3⋊C4D3semidirect
60. C3×C4×Dic3C2×C4semidirect
61. #3724C2×C4semidirect
114. C4×C3⋊D3C4⋊C4semidirect
176. C4×Dic3C4×D3semidirect
323. C32#2296semidirect
375. C3#73755semidirect

Maximal subgroups

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

subgroupindex
C2×#640812
C2×C4×#6242
C2×#638742
C3×C4×Dic3⋊C42
#105913752
#105913742
C4×Dic3⋊Dic32
#105912562
#737553