Finite Group Databasebeta

← #11801834

Subgroups — #11801834

Order 1152.

1477 conjugacy classes of subgroups.

The subgroup lattice has 371 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64086C211yesmaximal, characteristic
2C2×#63957C211yesmaximal, characteristic
3C22×Dic32C211yesmaximal, characteristic
4C3×#4946C212yesmaximal
5#10591718C212yesmaximal
6#10591256C214yesmaximal, complemented
7#10591241C214yesmaximal, complemented
8#74378—32nomaximal
9C23×C3⋊Dic3C2211yescharacteristic
10C23×C3×Dic3C2212yes—
11C2×C32×C22⋊C4C2211yescharacteristic
12C2×#3757C2211yescharacteristic
13C2×#3750C2212yes—
14C2×C4×C3⋊Dic3C2212yes—
15#64086—24no—
16C2×C3×#217C2212yes—
17C2×C3×Dic3⋊C4C2214yes—
18C2×#3724C2212yes—
19C2×Dic3⋊Dic3C2214yes—
20#63957C418yescomplemented
21C2×Dic32—24no—
22C2×Dic32C2212yes—
23C2×Dic32C2212yes—
24C2×Dic32C2212yes—
25C3×C3⋊#95C2214yes—
26#63579C2214yes—
27C22×C4×Dic3—32no—
28C2×#877—32no—
29C2×#877—32no—
30C2×#877—61no—
31C3×#385—32no—
32#5210—32no—
33#4976—34no—
34Dic3×C4⋊C4—34no—
35#4950—32no—
36#4946D312yes—
37#4649—34no—
38#4647—34no—
39C24×C32C2311yescharacteristic
40C22×C32×C4C2312yes—
41C22×C3⋊Dic3C2×C414yes—
42C22×C3⋊Dic3D414yes—
43C22×C3⋊Dic3Q814yes—
44C22×C3⋊Dic3C2312yes—
45C22×C3⋊Dic3C2311yescharacteristic
46C22×C3⋊Dic3C2311yescharacteristic
47C22×C3×Dic3—24no—
48C22×C3×Dic3—28no—
49C22×C3×Dic3C2314yes—
50C22×C3×Dic3C2314yes—
51C32×C22⋊C4—22no—
52#3757—22no—
53#3750—24no—
54C4×C3⋊Dic3—24no—
55C3×#217C2×C418yes—
56C3×Dic3⋊C4—28no—
57#3724C2×C418yescomplemented
58Dic3⋊Dic3—28no—
59Dic32—24no—
60Dic32—24no—
61Dic32C2×C418yescomplemented
62#2296—91noSylow
63C23×C3×C4—32no—
64C23×Dic3—32no—
65C23×Dic3—61no—
66C23×Dic3C2×D312yes—
67C2×C3×C4⋊C4—34no—
68C2×C3×C22⋊C4—21no—
69C2×C3×C22⋊C4—32no—
70C2×C3×C22⋊C4C2×D312yes—
71C2×#217—32no—
72C2×#217—61no—
73C2×#217C2×D312yes—
74C2×C4⋊Dic3—34no—
75C2×Dic3⋊C4—34no—
76C2×Dic3⋊C4—32no—
77C2×Dic3⋊C4—32no—
78C2×Dic3⋊C4—34no—
79C2×Dic3⋊C4—62no—
80C2×Dic3⋊C4C2×D314yes—
81C2×C4×Dic3—34no—
82C2×C4×Dic3—32no—
83C2×C4×Dic3—32no—
84C2×C4×Dic3—34no—
85C2×C4×Dic3—34no—
86C2×C4×Dic3—62no—
87C2×C4×Dic3—68no—
88#877—316no—
89#877—68no—
90#877—68no—
91C3×#95—34no—
92C3⋊#95—34no—
93C3⋊#95—34no—
94C3⋊#95C2×D314yes—
95C23×C32—24no—
96C23×C32C22×C412yes—
97C23×C32C2×D412yes—
98C23×C32C2×Q812yes—
99C23×C32C2411yescharacteristic
100C2×C32×C4—22no—
101C2×C32×C4—24no—
102C2×C3⋊Dic3—22no—
103C2×C3⋊Dic3—24no—
104C2×C3⋊Dic3C4⋊C4116yescomplemented
105C2×C3⋊Dic3C22×C412yes—
106C2×C3⋊Dic3C22×C412yes—
107C2×C3⋊Dic3C2×D412yes—
108C2×C3⋊Dic3C2×D412yes—
109C2×C3⋊Dic3C2×Q812yes—
110C2×C3⋊Dic3C2×Q812yes—
111C2×C3×Dic3—216no—
112C2×C3×Dic3—24no—
113C2×C3×Dic3—24no—
114C2×C3×Dic3—24no—
115C2×C3×Dic3—24no—
116C2×C3×Dic3C22×C418yes—
117C2×C3×Dic3#4118yes—
118C2×#117—91no—
119C2×#117—91no—
120C22×C42—91no—
121#389—94no—
122#385—32no—
123#385—92no—
124C4×C4⋊C4—94no—
125C24×C3—21no—
126C24×C3C22×D312yes—
127C22×C3×C4—22no—
128C22×C3×C4—34no—
129C22×C3×C4—34no—
130C22×C3×C4—68no—
131C22×C3×C4—64no—
132C22×C3×C4C22×D312yes—
133C22×C3×C4C22×D312yes—
134C22×Dic3—24no—
135C22×Dic3—28no—
136C22×Dic3—38no—
137C22×Dic3—38no—
138C22×Dic3—38no—
139C22×Dic3—32no—
140C22×Dic3—32no—
141C22×Dic3—32no—
142C22×Dic3—32no—
143C22×Dic3—64no—
144C22×Dic3—61no—
145C22×Dic3—61no—
146C22×Dic3—64no—
147C22×Dic3—64no—
148C22×Dic3—62no—
149C22×Dic3C22×D314yes—
150C22×Dic3C22×D314yes—
151C3×C4⋊C4—68no—
152C3×C22⋊C4—24no—
153C3×C22⋊C4—24no—
154C3×C22⋊C4—38no—
155#217—64no—
156#217—64no—
157#217C4×D318yes—
158C4⋊Dic3—68no—
159Dic3⋊C4—28no—
160Dic3⋊C4—316no—
161Dic3⋊C4—68no—
162Dic3⋊C4—64no—
163Dic3⋊C4—64no—
164Dic3⋊C4—68no—
165C4×Dic3—316no—
166C4×Dic3—68no—
167C4×Dic3—68no—
168C4×Dic3—64no—
169C4×Dic3—64no—
170C4×Dic3—68no—
171C22×C32—24no—
172C22×C32—24no—
173C22×C32—24no—
174C22×C32C2×C4⋊C414yes—
175C22×C32C23×C411yescharacteristic
176C22×C32C22×D411yescharacteristic
177C22×C32C22×Q811yescharacteristic
178C22×C32C2×#4114yes—
179C32×C4—42no—
180C3⋊Dic3—42no—
181C3⋊Dic3C2×C4⋊C414yes—
182C3⋊Dic3C2×C4⋊C414yes—
183C3×Dic3—28no—
184C3×Dic3—28no—
185C23×C4—32no—
186C23×C4—91no—
187#117—98no—
188#117—184no—
189C2×C4⋊C4—34no—
190C2×C4⋊C4—92no—
191C2×C4⋊C4—94no—
192C2×C4⋊C4—92no—
193C2×C22⋊C4—32no—
194C2×C22⋊C4—91no—
195C2×C22⋊C4D3211yescharacteristic
196C2×C42—92no—
197C2×C42—92no—
198C2×C42—92no—
199C2×C42—92no—
200C2×C42—184no—
201#95—34no—
202#95—94no—
203C23×C3—24no—
204C23×C3—24no—
205C23×C3—21no—
206C23×C3—22no—
207C23×C3—22no—
208C23×C3—22no—
209C23×C3—44no—
210C23×C3C2×C4×D314yes—
211C23×C3D3×D414yes—
212C23×C3D3×Q814yes—
213C23×C3C23×D312yes—
214C2×C3×C4—24no—
215C2×C3×C4—22no—
216C2×C3×C4—22no—
217C2×C3×C4—24no—
218C2×C3×C4—24no—
219C2×C3×C4—38no—
220C2×C3×C4—38no—
221C2×C3×C4—44no—
222C2×C3×C4—616no—
223C2×C3×C4—64no—
224C2×C3×C4—64no—
225C2×C3×C4—64no—
226C2×C3×C4—64no—
227C2×Dic3—216no—
228C2×Dic3—24no—
229C2×Dic3—24no—
230C2×Dic3—24no—
231C2×Dic3—24no—
232C2×Dic3—332no—
233C2×Dic3—34no—
234C2×Dic3—34no—
235C2×Dic3—34no—
236C2×Dic3—34no—
237C2×Dic3—34no—
238C2×Dic3—34no—
239C2×Dic3—616no—
240C2×Dic3—62no—
241C2×Dic3—62no—
242C2×Dic3—62no—
243C2×Dic3—62no—
244C2×Dic3—62no—
245C2×Dic3—62no—
246C2×Dic3—64no—
247C2×Dic3—62no—
248C2×Dic3—62no—
249C2×Dic3—64no—
250C2×Dic3—64no—
251C2×Dic3—124no—
252C2×Dic3C2×C4×D318yes—
253C2×Dic3#23718yes—
254C2×C32—24no—
255C2×C32C22×C4⋊C411yescharacteristic
256C2×C32C4×#4112yes—
257C2×C32#52512yes—
258C2×C32#53312yes—
259C24C2×D3211yescharacteristic
260C22×C4—34no—
261C22×C4—34no—
262C22×C4—68no—
263C22×C4—64no—
264C22×C4—91no—
265C22×C4—91no—
266C22×C4—94no—
267C22×C4—94no—
268C22×C4—94no—
269C22×C4—92no—
270C22×C4C2×D3212yes—
271C4⋊C4—68no—
272C4⋊C4—98no—
273C4⋊C4—184no—
274C4⋊C4—188no—
275C22⋊C4—22no—
276C22⋊C4—38no—
277C22⋊C4—182no—
278C42—98no—
279C42—184no—
280C42—184no—
281C42—184no—
282C22×C3—24no—
283C22×C3—28no—
284C22×C3—24no—
285C22×C3—28no—
286C22×C3—21no—
287C22×C3—21no—
288C22×C3—24no—
289C22×C3—21no—
290C22×C3—24no—
291C22×C3—44no—
292C22×C3—44no—
293C22×C3—44no—
294C22×C3D3×C4⋊C418yes—
295C22×C3C22×C4×D312yes—
296C22×C3C2×D3×D412yes—
297C22×C3C2×#23714yes—
298C22×C3C2×D3×Q812yes—
299C22×C3D3×#4114yes—
300C3×C4—44no—
301C3×C4—42no—
302C3×C4—42no—
303C3×C4—68no—
304C3×C4—68no—
305Dic3—28no—
306Dic3—28no—
307Dic3—38no—
308Dic3—38no—
309Dic3—64no—
310Dic3—64no—
311Dic3—124no—
312Dic3—122no—
313Dic3—122no—
314C32#229611yescharacteristic, complemented, Sylow
315C23—24no—
316C23#379712yes—
317C23C4×D3212yes—
318C23#381112yes—
319C23C22×D3211yescharacteristic
320C2×C4—24no—
321C2×C4—22no—
322C2×C4—38no—
323C2×C4—38no—
324C2×C4—616no—
325C2×C4—64no—
326C2×C4—64no—
327C2×C4—64no—
328C2×C4—64no—
329C2×C4—92no—
330C2×C4—92no—
331C2×C4—92no—
332C2×C4—92no—
333C2×C4—92no—
334C2×C4—92no—
335C2×C4—916no—
336C2×C4—184no—
337C2×C4—182no—
338C2×C3—28no—
339C2×C3—22no—
340C2×C3—21no—
341C2×C3—22no—
342C2×C3—22no—
343C2×C3—44no—
344C2×C3C2×D3×C4⋊C412yes—
345C2×C3C4×#23714yes—
346C2×C3#558612yes—
347C2×C3#562214yes—
348C2×C3#565612yes—
349C22—24no—
350C22—24no—
351C22—24no—
352C22#6388314yes—
353C22C2×#379711yescharacteristic
354C22C2×C4×D3211yescharacteristic
355C22D3×#23714yes—
356C22C2×#381111yescharacteristic
357C4—42no—
358C4—68no—
359C4—68no—
360C4—94no—
361C4—94no—
362C4—362no—
363C3—21no—
364C3#7437812yescomplemented
365C2—24no—
366C2#1059403012yes—
367C2#1059405012yes—
368C2C2×#6388311yescharacteristic
369C2#1059516012yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC24×C32C23
hypercenterC2×C22⋊C4D32
hypocenterC32#2296
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
6. #10591256C2semidirect
7. #10591241C2semidirect
20. #63957C4semidirect
57. #3724C2×C4semidirect
61. Dic32C2×C4semidirect
104. C2×C3⋊Dic3C4⋊C4semidirect
314. C32#2296semidirect
364. C3#74378semidirect

Maximal subgroups

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

subgroupindex
C2×#640862
C2×#639572
C22×Dic322
C3×#49462
#105917182
#105912562
#105912412
#743783