Finite Group Databasebeta

← #11805313

Subgroups — #11805313

Order 1152.

1137 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63874C211yesmaximal, characteristic
2#10592365C211yesmaximal, characteristic
3C3×#4648C212yesmaximal, complemented
4#10591355C211yesmaximal, characteristic
5C4×#3724C212yesmaximal, complemented
6#10591328C212yesmaximal, complemented
7#10591206C212yesmaximal, complemented
8#10591194C214yesmaximal
9#73392—32nomaximal
10C22×C4×C3⋊D3C2211yescharacteristic
11C2×#3752C2212yes—
12C2×C4×C3⋊Dic3C2212yes—
13C2×C3×C4×Dic3C2214yes—
14C2×C3×C4×Dic3C2212yes—
15C2×#3724C2212yes—
16C2×#3724C2211yescharacteristic
17C2×#3724C2211yescharacteristic
18C2×Dic3⋊Dic3C2214yes—
19C2×#3722C2212yes—
20C2×#3722C2212yes—
21#63874C418yescomplemented
22C32×#95C2211yescharacteristic
23#63658C2211yescharacteristic
24C3×C3⋊#95C2214yes—
25C3×C3⋊#95C2212yes—
26#63579C2214yes—
27C2×#872—32no—
28C3×#376—32no—
29#4940—34no—
30#4936—32no—
31C4×Dic3⋊C4—34no—
32#4670—34no—
33#4667—32no—
34#4666—32no—
35#4666—61no—
36#4650—32no—
37#4648D312yescomplemented
38#4647—34no—
39C23×C3⋊D3C2311yescharacteristic
40C22×C32×C4C2311yescharacteristic
41C22×C32×C4C2312yes—
42C22×C3⋊Dic3C2312yes—
43C22×C3⋊Dic3C2311yescharacteristic
44C2×C4×C3⋊D3—24no—
45C2×C4×C3⋊D3C2×C414yes—
46C22×C3×Dic3C2314yes—
47C22×C3×Dic3C2312yes—
48C22×C3×Dic3C2312yes—
49#3752—24no—
50C4×C3⋊Dic3—24no—
51C3×C4×Dic3—28no—
52C3×C4×Dic3C2×C418yes—
53#3724—24no—
54#3724C2×C414yes—
55#3724C2×C414yes—
56Dic3⋊Dic3—44no—
57#3722—42no—
58#3722C2×C418yes—
59#2346—91noSylow
60C22×C4×D3—32no—
61C22×C4×D3—61no—
62C2×C3×C42—32no—
63C2×C3×C42—34no—
64C2×(C2×D3)⋊C4—32no—
65C2×(C2×D3)⋊C4—32no—
66C2×(C2×D3)⋊C4—34no—
67C2×(C2×D3)⋊C4—34no—
68C2×(C2×D3)⋊C4—62no—
69C2×C4⋊Dic3—34no—
70C2×Dic3⋊C4—32no—
71C2×Dic3⋊C4—32no—
72C2×Dic3⋊C4—34no—
73C2×Dic3⋊C4—34no—
74C2×C4×Dic3—34no—
75C2×C4×Dic3—62no—
76C2×C4×Dic3C2×D314yes—
77C2×C4×Dic3C2×D312yes—
78#872—316no—
79C3×#95—21no—
80C3×#95—34no—
81C3×#95—32no—
82C3×#95C2×D312yes—
83C3⋊#95—32no—
84C3⋊#95—34no—
85C3⋊#95—34no—
86C3⋊#95—61no—
87C3⋊#95C2×D314yes—
88C3⋊#95C2×D312yes—
89C23×C32C2411yescharacteristic
90C22×C3⋊D3—22no—
91C22×C3⋊D3—22no—
92C22×C3⋊D3—21no—
93C22×C3⋊D3—21no—
94C22×C3⋊D3C22×C412yes—
95C2×C32×C4—22no—
96C2×C32×C4—22no—
97C2×C32×C4—22no—
98C2×C32×C4C22×C412yes—
99C2×C32×C4#4114yes—
100C2×C3⋊Dic3—22no—
101C2×C3⋊Dic3—22no—
102C2×C3⋊Dic3—22no—
103C2×C3⋊Dic3C22×C412yes—
104C2×C3⋊Dic3#4114yes—
105C4×C3⋊D3—28no—
106C2×C3×Dic3—24no—
107C2×C3×Dic3—22no—
108C2×C3×Dic3—22no—
109C2×C3×Dic3—24no—
110C2×C3×Dic3—24no—
111C2×C3×Dic3—24no—
112C2×C3×Dic3C22×C414yes—
113C2×C3×Dic3C22×C414yes—
114C2×#117—91no—
115#389—92no—
116#388—94no—
117#382—92no—
118#380—91no—
119C4×C4⋊C4—92no—
120C4×C22⋊C4—91no—
121#376—32no—
122C23×D3—32no—
123C23×D3—61no—
124C22×C3×C4—21no—
125C22×C3×C4—22no—
126C22×C3×C4—32no—
127C22×C3×C4—32no—
128C22×C3×C4—34no—
129C22×C3×C4C22×D312yes—
130C22×C3×C4C22×D314yes—
131C22×Dic3—32no—
132C22×Dic3—34no—
133C22×Dic3—61no—
134C22×Dic3—62no—
135C22×Dic3C22×D314yes—
136C22×Dic3C22×D312yes—
137C22×Dic3C22×D312yes—
138C2×C4×D3—38no—
139C2×C4×D3—64no—
140C2×C4×D3—68no—
141C2×C4×D3—124no—
142C3×C42—38no—
143C3×C42—68no—
144(C2×D3)⋊C4—38no—
145(C2×D3)⋊C4—38no—
146(C2×D3)⋊C4—68no—
147(C2×D3)⋊C4—68no—
148(C2×D3)⋊C4—124no—
149C4⋊Dic3—124no—
150Dic3⋊C4—38no—
151Dic3⋊C4—38no—
152Dic3⋊C4—68no—
153Dic3⋊C4—124no—
154C4×Dic3—28no—
155C4×Dic3—68no—
156C4×Dic3—124no—
157C4×Dic3C4×D318yes—
158C22×C32C23×C411yescharacteristic
159C22×C32C2×#4112yes—
160C22×C32C2×#4112yes—
161C22×C32H(5,𝔽2)11yescharacteristic
162C22×C322−1+411yescharacteristic
163C2×C3⋊D3—22no—
164C2×C3⋊D3—22no—
165C2×C3⋊D3—22no—
166C2×C3⋊D3—42no—
167C2×C3⋊D3—42no—
168C32×C4—22no—
169C32×C4—24no—
170C3⋊Dic3—42no—
171C3⋊Dic3#11714yes—
172C3×Dic3—24no—
173C3×Dic3—24no—
174C3×Dic3—44no—
175C23×C4—91no—
176#117—98no—
177C2×C4⋊C4—91no—
178C2×C4⋊C4—91no—
179C2×C4⋊C4—92no—
180C2×C4⋊C4—94no—
181C2×C22⋊C4—92no—
182C2×C22⋊C4—92no—
183C2×C22⋊C4—92no—
184C2×C42—32no—
185C2×C42—34no—
186C2×C42—92no—
187#95—32no—
188#95—34no—
189#95—94no—
190#95—91no—
191#95D3211yescharacteristic
192C23×C3—21no—
193C23×C3C23×D312yes—
194C22×D3—34no—
195C22×D3—62no—
196C22×D3—64no—
197C22×D3—64no—
198C22×D3—64no—
199C22×D3—62no—
200C22×D3—62no—
201C22×D3—122no—
202C22×D3—121no—
203C22×D3—121no—
204C2×C3×C4—24no—
205C2×C3×C4—24no—
206C2×C3×C4—24no—
207C2×C3×C4—24no—
208C2×C3×C4—22no—
209C2×C3×C4—34no—
210C2×C3×C4—34no—
211C2×C3×C4—42no—
212C2×C3×C4—42no—
213C2×C3×C4—42no—
214C2×C3×C4—64no—
215C2×C3×C4—62no—
216C2×C3×C4—62no—
217C2×C3×C4—64no—
218C2×C3×C4—64no—
219C2×C3×C4—64no—
220C2×C3×C4C2×C4×D314yes—
221C2×C3×C4#23518yes—
222C2×Dic3—24no—
223C2×Dic3—22no—
224C2×Dic3—22no—
225C2×Dic3—24no—
226C2×Dic3—24no—
227C2×Dic3—24no—
228C2×Dic3—34no—
229C2×Dic3—38no—
230C2×Dic3—62no—
231C2×Dic3—64no—
232C2×Dic3—64no—
233C2×Dic3—64no—
234C2×Dic3—64no—
235C2×Dic3—64no—
236C2×Dic3—122no—
237C2×Dic3—122no—
238C2×Dic3C2×C4×D314yes—
239C2×Dic3C2×C4×D314yes—
240C4×D3—616no—
241C4×D3—128no—
242C2×C32C2×#11711yescharacteristic
243C2×C32C4×#4111yescharacteristic
244C2×C32#52011yescharacteristic
245C2×C32#55212yes—
246C2×C32#55512yes—
247C3⋊D3—42no—
248C24—91no—
249C22×C4—32no—
250C22×C4—32no—
251C22×C4—34no—
252C22×C4—91no—
253C22×C4—94no—
254C22×C4—92no—
255C22×C4—184no—
256C22×C4C2×D3212yes—
257C22×C4C2×D3211yescharacteristic
258C4⋊C4—94no—
259C4⋊C4—94no—
260C4⋊C4—184no—
261C4⋊C4—364no—
262C22⋊C4—98no—
263C22⋊C4—184no—
264C22⋊C4—362no—
265C42—38no—
266C42—68no—
267C42—184no—
268C22×C3—22no—
269C22×C3—21no—
270C22×C3—21no—
271C22×C3—22no—
272C22×C3—21no—
273C22×C3C22×C4×D312yes—
274C22×C3C2×#23514yes—
275C22×C3D3×#4114yes—
276C22×C3#100912yes—
277C22×C3#101012yes—
278C2×D3—64no—
279C2×D3—64no—
280C2×D3—64no—
281C2×D3—64no—
282C2×D3—122no—
283C2×D3—122no—
284C2×D3—124no—
285C2×D3—124no—
286C2×D3—124no—
287C2×D3—124no—
288C3×C4—24no—
289C3×C4—28no—
290C3×C4—42no—
291C3×C4—44no—
292C3×C4—64no—
293C3×C4—64no—
294C3×C4—124no—
295Dic3—24no—
296Dic3—24no—
297Dic3—38no—
298Dic3—44no—
299Dic3—64no—
300Dic3—124no—
301Dic3—124no—
302C32#234611yescharacteristic, complemented, Sylow
303C23—92no—
304C23—182no—
305C23—181no—
306C23—182no—
307C23—181no—
308C23C22×D3211yescharacteristic
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—34no—
313C2×C4—34no—
314C2×C4—64no—
315C2×C4—62no—
316C2×C4—62no—
317C2×C4—64no—
318C2×C4—64no—
319C2×C4—64no—
320C2×C4—92no—
321C2×C4—94no—
322C2×C4—188no—
323C2×C4—182no—
324C2×C4—182no—
325C2×C4—182no—
326C2×C4#379814yes—
327C2×C4C4×D3212yes—
328C2×C3—21no—
329C2×C3—22no—
330C2×C3—21no—
331C2×C3—21no—
332C2×C3—22no—
333C2×C3C4×#23512yes—
334C2×C3D3×#11712yes—
335C2×C3#552312yes—
336C2×C3#553114yes—
337C2×C3#553214yes—
338D3—124no—
339D3—124no—
340C22—182no—
341C22—182no—
342C22—182no—
343C22—362no—
344C22—362no—
345C22C2×#379812yes—
346C22C2×C4×D3211yescharacteristic
347C22#6430911yescharacteristic
348C22#6431212yes—
349C22#6432011yescharacteristic
350C4—22no—
351C4—24no—
352C4—64no—
353C4—64no—
354C4—94no—
355C4—124no—
356C4—362no—
357C3—21no—
358C3#7339212yescomplemented
359C2—362no—
360C2C4×#379811yescharacteristic
361C2#1059404612yes—
362C2#1059405211yescharacteristic
363C2#1059451111yescharacteristic
364C2#1059457512yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenter#95D32
hypocenterC32#2346
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
3. C3×#4648C2semidirect
5. C4×#3724C2semidirect
6. #10591328C2semidirect
7. #10591206C2semidirect
21. #63874C4semidirect
37. #4648D3semidirect
302. C32#2346semidirect
358. C3#73392semidirect

Maximal subgroups

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

subgroupindex
C2×#638742
#105923652
C3×#46482
#105913552
C4×#37242
#105913282
#105912062
#105911942
#733923