Finite Group Databasebeta

← #11808363

Subgroups — #11808363

Order 1152.

1549 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63900C212yesmaximal
2C2×#63900C211yesmaximal, characteristic
3C2×#63883C211yesmaximal, characteristic
4C3⋊D3×#95C211yesmaximal, characteristic
5C3×#4661C212yesmaximal, complemented
6#10591370C212yesmaximal
7#10591345C214yesmaximal, complemented
8#10591214C212yesmaximal, complemented
9D3×#398—32nomaximal
10C22×C4×C3⋊D3C2211yescharacteristic
11C22×C4×C3⋊D3C2212yes—
12C22×#624C2211yescharacteristic
13C22×#624C2212yes—
14C22×#624C2211yescharacteristic
15C2×C3×C4⋊Dic3C2214yes—
16C2×C3×C4⋊Dic3C2212yes—
17C2×C3×Dic3⋊C4C2212yes—
18C2×#3724C2212yes—
19C2×#3724C2214yes—
20C2×Dic3⋊Dic3C2212yes—
21#63900—24no—
22#63900—28no—
23#63883—24no—
24C32×#95C2211yescharacteristic
25#63658C2212yes—
26#63658C2211yescharacteristic
27C3×C3⋊#95C2214yes—
28#63579C2214yes—
29C2×D3×C4⋊C4—32no—
30C2×D3×C4⋊C4—34no—
31C2×D3×C4⋊C4—32no—
32C3×#398—32no—
33#4983—32no—
34#4982—34no—
35#4981—32no—
36D3×#95—32no—
37D3×#95—34no—
38D3×#95—61no—
39#4661D312yescomplemented
40#4657—34no—
41C23×C3⋊D3C2311yescharacteristic
42C22×C32×C4C2311yescharacteristic
43C22×C32×C4C2312yes—
44C22×C3⋊Dic3C2311yescharacteristic
45C22×C3⋊Dic3C2312yes—
46C2×C4×C3⋊D3—24no—
47C2×C4×C3⋊D3—24no—
48C2×C4×C3⋊D3—24no—
49C2×C4×C3⋊D3D414yes—
50C2×C4×C3⋊D3Q818yes—
51C22×C3×Dic3C2312yes—
52C22×C3×Dic3C2314yes—
53C22×C3×Dic3C2312yes—
54C2×#624—22no—
55C2×#624—22no—
56C2×#624—22no—
57C2×#624—24no—
58C2×#624—24no—
59C2×#624—24no—
60C2×#624—24no—
61C2×#624D414yes—
62C3×C4⋊Dic3—24no—
63C3×C4⋊Dic3—28no—
64C3×Dic3⋊C4—24no—
65#3724—24no—
66#3724—28no—
67Dic3⋊Dic3—24no—
68C2×#398—91noSylow
69C22×C4×D3—34no—
70C22×C4×D3—32no—
71C22×C4×D3—32no—
72C22×C4×D3—32no—
73C22×C4×D3—34no—
74C22×C4×D3—61no—
75C22×C4×D3—62no—
76C2×C3×C4⋊C4—32no—
77C2×C3×C4⋊C4—34no—
78C2×C3×C4⋊C4—32no—
79C2×C4⋊Dic3—32no—
80C2×C4⋊Dic3C2×D314yes—
81C2×C4⋊Dic3C2×D312yes—
82C2×Dic3⋊C4—32no—
83C2×Dic3⋊C4—34no—
84C2×Dic3⋊C4—34no—
85C2×Dic3⋊C4—34no—
86C2×Dic3⋊C4C2×D312yes—
87D3×C4⋊C4—68no—
88D3×C4⋊C4—68no—
89D3×C4⋊C4—616no—
90C3×#95—21no—
91C3×#95—34no—
92C3×#95C2×D312yes—
93C3⋊#95—34no—
94C3⋊#95—32no—
95C3⋊#95—34no—
96C3⋊#95—34no—
97C3⋊#95—62no—
98C3⋊#95—61no—
99C3⋊#95C2×D314yes—
100C23×C32C2411yescharacteristic
101C22×C3⋊D3C2×D412yes—
102C22×C3⋊D3C2×D412yes—
103C22×C3⋊D3C2×Q814yes—
104C22×C3⋊D3#4112yes—
105C22×C3⋊D3#4114yes—
106C2×C32×C4—22no—
107C2×C32×C4—22no—
108C2×C32×C4—22no—
109C2×C32×C4C2×D412yes—
110C2×C32×C4C2×Q814yes—
111C2×C3⋊Dic3—22no—
112C2×C3⋊Dic3—22no—
113C2×C3⋊Dic3—22no—
114C2×C3⋊Dic3C2×D412yes—
115C2×C3⋊Dic3C2×Q814yes—
116C4×C3⋊D3—216no—
117C4×C3⋊D3—28no—
118C2×C3×Dic3—22no—
119C2×C3×Dic3—22no—
120C2×C3×Dic3—22no—
121C2×C3×Dic3—24no—
122C2×C3×Dic3—24no—
123C2×C3×Dic3—24no—
124C2×C3×Dic3—24no—
125C2×C3×Dic3C2×D414yes—
126#624—28no—
127#624—48no—
128#624—44no—
129C22×C4⋊C4—91no—
130C22×C4⋊C4—92no—
131C22×C4⋊C4—91no—
132#398—32no—
133#398—94no—
134#398—92no—
135C2×#95—92no—
136C2×#95—91no—
137C23×D3—32no—
138C23×D3—61no—
139C22×C3×C4—22no—
140C22×C3×C4—21no—
141C22×C3×C4—32no—
142C22×C3×C4—32no—
143C22×C3×C4—34no—
144C22×C3×C4C22×D312yes—
145C22×C3×C4C22×D314yes—
146C22×Dic3—34no—
147C22×Dic3—32no—
148C22×Dic3—62no—
149C22×Dic3—61no—
150C22×Dic3C22×D312yes—
151C22×Dic3C22×D314yes—
152C22×Dic3C22×D312yes—
153C2×C4×D3—38no—
154C2×C4×D3—316no—
155C2×C4×D3—38no—
156C2×C4×D3—64no—
157C2×C4×D3—68no—
158C2×C4×D3—64no—
159C2×C4×D3—64no—
160C2×C4×D3—68no—
161C2×C4×D3—68no—
162C2×C4×D3—68no—
163C2×C4×D3—64no—
164C2×C4×D3—68no—
165C2×C4×D3—68no—
166C2×C4×D3—68no—
167C2×C4×D3—68no—
168C2×C4×D3—124no—
169C2×C4×D3—124no—
170C2×C4×D3—124no—
171C3×C4⋊C4—68no—
172C3×C4⋊C4—64no—
173C3×C4⋊C4—64no—
174C4⋊Dic3—24no—
175C4⋊Dic3—28no—
176C4⋊Dic3—64no—
177Dic3⋊C4—24no—
178Dic3⋊C4—64no—
179Dic3⋊C4—68no—
180Dic3⋊C4—68no—
181Dic3⋊C4—68no—
182C22×C32C22×D411yescharacteristic
183C22×C32C22×D411yescharacteristic
184C22×C32C22×Q812yes—
185C22×C32C2×#4111yescharacteristic
186C22×C32C2×#4112yes—
187C2×C3⋊D3#12114yes—
188C2×C3⋊D3C22⋊Q818yes—
189C2×C3⋊D3#12314yes—
190C2×C3⋊D3#12518yes—
191C2×C3⋊D3C4⋊Q814yes—
192C32×C4—24no—
193C32×C4—22no—
194C3⋊Dic3—24no—
195C3⋊Dic3—22no—
196C3×Dic3—24no—
197C3×Dic3—44no—
198C3×Dic3—42no—
199C23×C4—91no—
200C23×C4—92no—
201C23×C4—91no—
202C23×C4—91no—
203C23×C4—92no—
204C2×C4⋊C4—32no—
205C2×C4⋊C4—34no—
206C2×C4⋊C4—32no—
207C2×C4⋊C4—94no—
208C2×C4⋊C4—92no—
209C2×C4⋊C4—92no—
210C2×C4⋊C4—188no—
211C2×C4⋊C4—184no—
212C2×C4⋊C4—184no—
213#95—34no—
214#95—94no—
215#95—91no—
216#95—92no—
217#95D3211yescharacteristic
218C23×C3—21no—
219C23×C3C23×D312yes—
220C22×D3—34no—
221C22×D3—34no—
222C22×D3—38no—
223C22×D3—38no—
224C22×D3—34no—
225C22×D3—62no—
226C22×D3—62no—
227C22×D3—64no—
228C22×D3—64no—
229C22×D3—62no—
230C2×C3×C4—24no—
231C2×C3×C4—24no—
232C2×C3×C4—24no—
233C2×C3×C4—24no—
234C2×C3×C4—22no—
235C2×C3×C4—34no—
236C2×C3×C4—42no—
237C2×C3×C4—42no—
238C2×C3×C4—42no—
239C2×C3×C4—62no—
240C2×C3×C4—62no—
241C2×C3×C4—62no—
242C2×C3×C4—64no—
243C2×C3×C4—64no—
244C2×C3×C4—64no—
245C2×C3×C4—64no—
246C2×C3×C4D3×D414yes—
247C2×C3×C4D3×Q818yes—
248C2×Dic3—22no—
249C2×Dic3—22no—
250C2×Dic3—22no—
251C2×Dic3—24no—
252C2×Dic3—24no—
253C2×Dic3—24no—
254C2×Dic3—24no—
255C2×Dic3—34no—
256C2×Dic3—38no—
257C2×Dic3—62no—
258C2×Dic3—64no—
259C2×Dic3—64no—
260C2×Dic3—64no—
261C2×Dic3—64no—
262C2×Dic3—122no—
263C2×Dic3—122no—
264C2×Dic3—122no—
265C2×Dic3D3×D414yes—
266C4×D3—616no—
267C4×D3—616no—
268C4×D3—632no—
269C4×D3—1216no—
270C4×D3—128no—
271C4×D3—128no—
272C4×D3—1216no—
273C2×C32C2×#12111yescharacteristic
274C2×C32C2×C22⋊Q812yes—
275C2×C32C2×#12311yescharacteristic
276C2×C32C2×#12512yes—
277C2×C32C2×C4⋊Q811yescharacteristic
278C3⋊D3#39818yescomplemented
279C24—91no—
280C22×C4—32no—
281C22×C4—32no—
282C22×C4—34no—
283C22×C4—94no—
284C22×C4—92no—
285C22×C4—91no—
286C22×C4—98no—
287C22×C4—94no—
288C22×C4—184no—
289C22×C4—184no—
290C22×C4—184no—
291C22×C4—182no—
292C22×C4—182no—
293C22×C4—184no—
294C22×C4—182no—
295C22×C4—184no—
296C22×C4—184no—
297C22×C4—184no—
298C22×C4C2×D3212yes—
299C22×C4C2×D3211yescharacteristic
300C4⋊C4—68no—
301C4⋊C4—64no—
302C4⋊C4—64no—
303C4⋊C4—188no—
304C4⋊C4—184no—
305C4⋊C4—184no—
306C22×C3—22no—
307C22×C3—21no—
308C22×C3—21no—
309C22×C3—22no—
310C22×C3—21no—
311C22×C3C2×D3×D412yes—
312C22×C3C2×D3×D412yes—
313C22×C3C2×D3×Q814yes—
314C22×C3D3×#4114yes—
315C22×C3D3×#4112yes—
316C2×D3—38no—
317C2×D3—316no—
318C2×D3—38no—
319C2×D3—38no—
320C2×D3—316no—
321C2×D3—68no—
322C2×D3—64no—
323C2×D3—64no—
324C2×D3—68no—
325C2×D3—64no—
326C3×C4—24no—
327C3×C4—28no—
328C3×C4—44no—
329C3×C4—42no—
330C3×C4—64no—
331C3×C4—122no—
332C3×C4—124no—
333Dic3—24no—
334Dic3—42no—
335Dic3—44no—
336Dic3—64no—
337Dic3—68no—
338Dic3—124no—
339Dic3—122no—
340C32C2×#39811yescharacteristic, complemented, Sylow
341C23—94no—
342C23—92no—
343C23—92no—
344C23—94no—
345C23—92no—
346C23C22×D3211yescharacteristic
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—22no—
350C2×C4—34no—
351C2×C4—62no—
352C2×C4—62no—
353C2×C4—64no—
354C2×C4—62no—
355C2×C4—64no—
356C2×C4—64no—
357C2×C4—64no—
358C2×C4—94no—
359C2×C4—92no—
360C2×C4—1816no—
361C2×C4—188no—
362C2×C4—188no—
363C2×C4—182no—
364C2×C4—182no—
365C2×C4—182no—
366C2×C4—368no—
367C2×C4—364no—
368C2×C4#379714yes—
369C2×C4#380212yes—
370C2×C3—22no—
371C2×C3—21no—
372C2×C3—21no—
373C2×C3—22no—
374C2×C3—21no—
375C2×C3D3×#12112yes—
376C2×C3D3×C22⋊Q814yes—
377C2×C3D3×#12312yes—
378C2×C3D3×#12514yes—
379C2×C3D3×C4⋊Q812yes—
380D3—316no—
381D3—68no—
382C22—98no—
383C22—94no—
384C22—94no—
385C22—98no—
386C22—94no—
387C22C2×#379712yes—
388C22C2×#380211yescharacteristic
389C22D32×D411yescharacteristic
390C22#6431212yes—
391C22#6431911yescharacteristic
392C4—24no—
393C4—22no—
394C4—64no—
395C4—124no—
396C4—122no—
397C4—184no—
398C4—182no—
399C3—21no—
400C3D3×#39812yescomplemented
401C2—98no—
402C2#1059390911yescharacteristic
403C2#1059406712yes—
404C2#1059429511yescharacteristic
405C2#1059448212yes—
406C2#1059461211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC32×#95C22
prime radicalC23×C3⋊D3C23
hypercenter#95D32
hypocenterC32C2×#398
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
5. C3×#4661C2semidirect
7. #10591345C2semidirect
8. #10591214C2semidirect
39. #4661D3semidirect
278. C3⋊D3#398semidirect
340. C32C2×#398semidirect
400. C3D3×#398semidirect

Maximal subgroups

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

subgroupindex
C2×#639002
C2×#638832
C3⋊D3×#952
C3×#46612
#105913702
#105913452
#105912142
D3×#3983