Finite Group Databasebeta

← #11805171

Subgroups — #11805171

Order 1152.

1337 conjugacy classes of subgroups.

The subgroup lattice has 391 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3724C211yesmaximal, characteristic
2C2×#63955C212yesmaximal
3C22⋊C4×C3⋊Dic3C211yesmaximal, characteristic
4C3×#4943C212yesmaximal
5#10591720C211yesmaximal, characteristic
6#10591328C212yesmaximal, complemented
7#10591257C212yesmaximal, complemented
8#10591249C214yesmaximal, complemented
9#74060—32nomaximal
10C23×C3⋊Dic3C2211yescharacteristic
11C23×C3×Dic3C2212yes—
12C2×C32×C22⋊C4C2211yescharacteristic
13C2×#3757C2211yescharacteristic
14C2×C4×C3⋊Dic3C2212yes—
15C2×C3×#217C2212yes—
16C2×#3724C418yescomplemented
17C2×#3724C2212yes—
18C2×#3724C2212yes—
19C2×#3724C2211yescharacteristic
20C2×#3724C2211yescharacteristic
21C2×Dic3⋊Dic3C2214yes—
22#63955—28no—
23C2×Dic32C2214yes—
24#63658C2212yes—
25C3×C3⋊#95C2214yes—
26C3×C3⋊#95C2214yes—
27#63579C2212yes—
28C2×#926—32no—
29C22×Dic3⋊C4—32no—
30C2×#877—32no—
31C3×#381—32no—
32#4943D312yes—
33#4942—32no—
34Dic3×C22⋊C4—32no—
35Dic3×C22⋊C4—61no—
36#4655—34no—
37#4652—34no—
38#4649—34no—
39#4647—34no—
40C24×C32C2311yescharacteristic
41C22×C32×C4C2312yes—
42C22×C3⋊Dic3—24no—
43C22×C3⋊Dic3C2×C414yes—
44C22×C3⋊Dic3C2311yescharacteristic
45C22×C3⋊Dic3C2312yes—
46C22×C3⋊Dic3C2311yescharacteristic
47C22×C3×Dic3—24no—
48C22×C3×Dic3—24no—
49C22×C3×Dic3C2×C418yes—
50C22×C3×Dic3C2314yes—
51C22×C3×Dic3C2312yes—
52C22×C3×Dic3C2312yes—
53C32×C22⋊C4—22no—
54#3757D414yes—
55C4×C3⋊Dic3—24no—
56C3×#217—24no—
57#3724—24no—
58#3724C2×C418yes—
59#3724C2×C414yes—
60#3724C2×C414yes—
61Dic3⋊Dic3—28no—
62Dic32—28no—
63#2344—91noSylow
64C23×C3×C4—32no—
65C23×Dic3—32no—
66C23×Dic3—61no—
67C23×Dic3C2×D312yes—
68C2×C3×C22⋊C4—21no—
69C2×C3×C22⋊C4—32no—
70C2×C3×C22⋊C4C2×D312yes—
71C2×#217—32no—
72C2×#217—61no—
73C2×#217C2×D312yes—
74#926—68no—
75C2×C4⋊Dic3—34no—
76C2×Dic3⋊C4—316no—
77C2×Dic3⋊C4—32no—
78C2×Dic3⋊C4—32no—
79C2×Dic3⋊C4—32no—
80C2×Dic3⋊C4—32no—
81C2×Dic3⋊C4—34no—
82C2×Dic3⋊C4—34no—
83C2×C4×Dic3—34no—
84C2×C4×Dic3—34no—
85C2×C4×Dic3—34no—
86C2×C4×Dic3—62no—
87#877—68no—
88C3×#95—34no—
89C3×#95—34no—
90C3⋊#95—34no—
91C3⋊#95—34no—
92C3⋊#95—62no—
93C3⋊#95C2×D314yes—
94C3⋊#95C2×D314yes—
95C23×C32—22no—
96C23×C32—22no—
97C23×C32C22×C412yes—
98C23×C32C2×D412yes—
99C23×C32#4112yes—
100C23×C32C2411yescharacteristic
101C2×C32×C4—22no—
102C2×C32×C4—22no—
103C2×C32×C4—22no—
104C2×C3⋊Dic3—22no—
105C2×C3⋊Dic3—22no—
106C2×C3⋊Dic3—22no—
107C2×C3⋊Dic3—28no—
108C2×C3⋊Dic3C22×C412yes—
109C2×C3⋊Dic3C22×C412yes—
110C2×C3⋊Dic3C2×D414yes—
111C2×C3⋊Dic3#4114yes—
112C2×C3×Dic3—216no—
113C2×C3×Dic3—22no—
114C2×C3×Dic3—22no—
115C2×C3×Dic3—22no—
116C2×C3×Dic3—22no—
117C2×C3×Dic3—24no—
118C2×C3×Dic3—24no—
119C2×C3×Dic3—24no—
120C2×C3×Dic3C22×C414yes—
121C2×C3×Dic3C22×C414yes—
122C2×#117—92no—
123C22×C4⋊C4—91no—
124#389—92no—
125#387—94no—
126#381—32no—
127#380—91no—
128C4×C4⋊C4—92no—
129C4×C22⋊C4—91no—
130C24×C3—21no—
131C24×C3C22×D312yes—
132C22×C3×C4—22no—
133C22×C3×C4—38no—
134C22×C3×C4—32no—
135C22×C3×C4—32no—
136C22×C3×C4—34no—
137C22×C3×C4—64no—
138C22×C3×C4—64no—
139C22×C3×C4C22×D314yes—
140C22×Dic3—24no—
141C22×Dic3—24no—
142C22×Dic3—32no—
143C22×Dic3—38no—
144C22×Dic3—32no—
145C22×Dic3—34no—
146C22×Dic3—61no—
147C22×Dic3—61no—
148C22×Dic3—62no—
149C22×Dic3—64no—
150C22×Dic3—68no—
151C22×Dic3—124no—
152C22×Dic3C4×D318yes—
153C22×Dic3C22×D314yes—
154C22×Dic3C22×D312yes—
155C22×Dic3C22×D312yes—
156C3×C22⋊C4—24no—
157C3×C22⋊C4—24no—
158C3×C22⋊C4—64no—
159#217—24no—
160#217—38no—
161#217—64no—
162C4⋊Dic3—68no—
163Dic3⋊C4—38no—
164Dic3⋊C4—38no—
165Dic3⋊C4—38no—
166Dic3⋊C4—38no—
167Dic3⋊C4—68no—
168Dic3⋊C4—68no—
169C4×Dic3—68no—
170C4×Dic3—68no—
171C4×Dic3—68no—
172C4×Dic3—124no—
173C22×C32—22no—
174C22×C32—22no—
175C22×C32—24no—
176C22×C32—24no—
177C22×C32C4×D414yes—
178C22×C32C23×C411yescharacteristic
179C22×C32C22×D411yescharacteristic
180C22×C32C2×#4111yescharacteristic
181C22×C32C2×#4112yes—
182C22×C322−1+412yes—
183C32×C4—42no—
184C3⋊Dic3—22no—
185C3⋊Dic3—24no—
186C3⋊Dic3#11714yescomplemented
187C3×Dic3—24no—
188C3×Dic3—24no—
189C3×Dic3—44no—
190C23×C4—32no—
191C23×C4—91no—
192#117—188no—
193C2×C4⋊C4—91no—
194C2×C4⋊C4—92no—
195C2×C4⋊C4—91no—
196C2×C4⋊C4—98no—
197C2×C4⋊C4—94no—
198C2×C4⋊C4—92no—
199C2×C22⋊C4—32no—
200C2×C22⋊C4—91no—
201C2×C22⋊C4D3211yescharacteristic
202C2×C42—94no—
203C2×C42—92no—
204#95—34no—
205#95—34no—
206#95—92no—
207#95—92no—
208C23×C3—24no—
209C23×C3—24no—
210C23×C3—21no—
211C23×C3—22no—
212C23×C3—22no—
213C23×C3—22no—
214C23×C3—42no—
215C23×C3—42no—
216C23×C3C2×C4×D314yes—
217C23×C3D3×D414yes—
218C23×C3#23714yes—
219C23×C3C23×D312yes—
220C2×C3×C4—24no—
221C2×C3×C4—24no—
222C2×C3×C4—24no—
223C2×C3×C4—24no—
224C2×C3×C4—34no—
225C2×C3×C4—34no—
226C2×C3×C4—42no—
227C2×C3×C4—42no—
228C2×C3×C4—616no—
229C2×C3×C4—62no—
230C2×C3×C4—62no—
231C2×C3×C4—62no—
232C2×C3×C4—62no—
233C2×C3×C4—64no—
234C2×C3×C4—64no—
235C2×C3×C4—64no—
236C2×Dic3—216no—
237C2×Dic3—22no—
238C2×Dic3—22no—
239C2×Dic3—22no—
240C2×Dic3—22no—
241C2×Dic3—24no—
242C2×Dic3—24no—
243C2×Dic3—24no—
244C2×Dic3—34no—
245C2×Dic3—38no—
246C2×Dic3—34no—
247C2×Dic3—38no—
248C2×Dic3—62no—
249C2×Dic3—64no—
250C2×Dic3—62no—
251C2×Dic3—64no—
252C2×Dic3—616no—
253C2×Dic3—64no—
254C2×Dic3—64no—
255C2×Dic3—64no—
256C2×Dic3—128no—
257C2×Dic3—122no—
258C2×Dic3—122no—
259C2×Dic3—122no—
260C2×Dic3C2×C4×D314yes—
261C2×Dic3C2×C4×D314yes—
262C2×C32—24no—
263C2×C32C2×#11711yescharacteristic
264C2×C32C2×C4×D411yescharacteristic
265C2×C32#51911yescharacteristic
266C2×C32#54712yes—
267C2×C32#55212yes—
268C24C2×D3211yescharacteristic
269C22×C4—32no—
270C22×C4—32no—
271C22×C4—38no—
272C22×C4—34no—
273C22×C4—64no—
274C22×C4—64no—
275C22×C4—91no—
276C22×C4—91no—
277C22×C4—92no—
278C22×C4—94no—
279C22×C4—184no—
280C22×C4C2×D3212yes—
281C4⋊C4—94no—
282C4⋊C4—94no—
283C4⋊C4—98no—
284C4⋊C4—188no—
285C4⋊C4—184no—
286C22⋊C4—22no—
287C22⋊C4—64no—
288C22⋊C4—94no—
289C42—184no—
290C42—188no—
291C22×C3—28no—
292C22×C3—28no—
293C22×C3—24no—
294C22×C3—24no—
295C22×C3—21no—
296C22×C3—21no—
297C22×C3—22no—
298C22×C3—22no—
299C22×C3—21no—
300C22×C3—24no—
301C22×C3—42no—
302C22×C3—44no—
303C22×C3—44no—
304C22×C3—42no—
305C22×C3#67⋊C418yes—
306C22×C3C22×C4×D312yes—
307C22×C3C2×D3×D412yes—
308C22×C3C2×#23712yes—
309C22×C3D3×#4114yes—
310C22×C3#101014yes—
311C3×C4—44no—
312C3×C4—44no—
313C3×C4—64no—
314C3×C4—64no—
315C3×C4—124no—
316Dic3—24no—
317Dic3—24no—
318Dic3—38no—
319Dic3—44no—
320Dic3—64no—
321Dic3—68no—
322Dic3—64no—
323Dic3—122no—
324Dic3—124no—
325C32#234411yescharacteristic, complemented, Sylow
326C23—22no—
327C23—22no—
328C23C4×D3212yes—
329C23#380212yes—
330C23#380512yes—
331C23C22×D3211yescharacteristic
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—34no—
336C2×C4—34no—
337C2×C4—62no—
338C2×C4—62no—
339C2×C4—62no—
340C2×C4—62no—
341C2×C4—616no—
342C2×C4—64no—
343C2×C4—64no—
344C2×C4—64no—
345C2×C4—92no—
346C2×C4—94no—
347C2×C4—92no—
348C2×C4—94no—
349C2×C4—188no—
350C2×C4—182no—
351C2×C4—182no—
352C2×C4—182no—
353C2×C3—28no—
354C2×C3—21no—
355C2×C3—22no—
356C2×C3—22no—
357C2×C3—21no—
358C2×C3—21no—
359C2×C3—44no—
360C2×C3C2×#67⋊C412yes—
361C2×C3#551612yes—
362C2×C3D3×#11712yes—
363C2×C3#565014yes—
364C2×C3#565514yes—
365C22—22no—
366C22—24no—
367C22—24no—
368C22—22no—
369C22#6390214yes—
370C22C2×C4×D3211yescharacteristic
371C22C2×#380211yescharacteristic
372C22#6430912yes—
373C22#6431212yes—
374C22C2×#380511yescharacteristic
375C4—42no—
376C4—64no—
377C4—64no—
378C4—94no—
379C4—124no—
380C4—182no—
381C4—184no—
382C3—21no—
383C3#7406012yescomplemented
384C2—24no—
385C2#1059405211yescharacteristic
386C2#1059408312yes—
387C2#1059424511yescharacteristic
388C2C2×#6390211yescharacteristic
389C2#1059512012yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC24×C32C23
hypercenterC2×C22⋊C4D32
hypocenterC32#2344
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
6. #10591328C2semidirect
7. #10591257C2semidirect
8. #10591249C2semidirect
16. C2×#3724C4semidirect
186. C3⋊Dic3#117semidirect
325. C32#2344semidirect
383. C3#74060semidirect

Maximal subgroups

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

subgroupindex
C22×#37242
C2×#639552
C22⋊C4×C3⋊Dic32
C3×#49432
#105917202
#105913282
#105912572
#105912492
#740603