Finite Group Databasebeta

← #11807126

Subgroups — #11807126

Order 1152.

1089 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×#63919C211yesmaximal, characteristic
2C4⋊C4×C3⋊Dic3C211yesmaximal, characteristic
3C3×#4972C212yesmaximal
4#10591337C212yesmaximal
5C4×#3724C211yesmaximal, characteristic
6Dic3×C4⋊Dic3C212yesmaximal
7#10591257C212yesmaximal
8#10591235C214yesmaximal
9#75987—32nomaximal
10C22×#627C2212yes—
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C2×C4×C3⋊Dic3C2212yes—
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C2×C3×C4⋊Dic3C2212yes—
16C2×C3×Dic3⋊C4C2214yes—
17C2×C3×C4×Dic3C2212yes—
18C2×#3724C2211yescharacteristic
19C2×#3724C2212yes—
20C2×#3724C2211yescharacteristic
21C2×Dic32C2214yes—
22#63919C418yescomplemented
23#63658C2212yes—
24C3×C3⋊#95C2214yes—
25#63579C2212yes—
26#63579C2214yes—
27C2×#888—32no—
28C3×#389—32no—
29#4976—34no—
30Dic3×C4⋊C4—32no—
31Dic3×C4⋊C4—32no—
32Dic3×C4⋊C4—61no—
33#4973—34no—
34#4972D312yes—
35C4×C4⋊Dic3—32no—
36C4×Dic3⋊C4—32no—
37#4649—34no—
38#4646—34no—
39C22×C32×C4C2312yes—
40C22×C32×C4C2311yescharacteristic
41C22×C3⋊Dic3C2311yescharacteristic
42C22×C3⋊Dic3C2312yes—
43C22×C3⋊Dic3C2311yescharacteristic
44C22×C3×Dic3C2312yes—
45C22×C3×Dic3C2314yes—
46C22×C3×Dic3C2312yes—
47C2×#627—42no—
48C2×#627—42no—
49C2×#627C2×C418yes—
50C32×C4⋊C4—22no—
51C4⋊(C3⋊Dic3)Q814yescomplemented
52C4×C3⋊Dic3—24no—
53C4×C3⋊Dic3C2×C414yes—
54C3×C4⋊Dic3C2×C418yes—
55C3×Dic3⋊C4—44no—
56C3×C4×Dic3—24no—
57#3724—22no—
58#3724C2×C418yes—
59#3724Q814yescomplemented
60Dic32—44no—
61#2369—91noSylow
62C22×Dic6—34no—
63C2×C3×C4⋊C4—21no—
64C2×C3×C4⋊C4—32no—
65C2×C3×C4⋊C4—34no—
66C2×C3×C4⋊C4C2×D312yes—
67C2×C3×C42—32no—
68C2×C4⋊Dic3—32no—
69C2×C4⋊Dic3—61no—
70C2×C4⋊Dic3C2×D312yes—
71C2×Dic3⋊C4—32no—
72C2×Dic3⋊C4—34no—
73C2×Dic3⋊C4—32no—
74C2×Dic3⋊C4C2×D314yes—
75C2×C4×Dic3—32no—
76C2×C4×Dic3—34no—
77C2×C4×Dic3—34no—
78C2×C4×Dic3—34no—
79C2×C4×Dic3—61no—
80C2×C4×Dic3—62no—
81C2×C4×Dic3C2×D312yes—
82#888—316no—
83C3×#95—34no—
84C3⋊#95—34no—
85C3⋊#95—32no—
86C3⋊#95—34no—
87C3⋊#95—32no—
88C3⋊#95—34no—
89C3⋊#95—62no—
90C3⋊#95C2×D314yes—
91C23×C32C2411yescharacteristic
92C2×C32×C4—22no—
93C2×C32×C4—22no—
94C2×C32×C4—22no—
95C2×C32×C4C22×C412yes—
96C2×C32×C4C2×Q812yes—
97C2×C32×C4#4112yes—
98C2×C3⋊Dic3—22no—
99C2×C3⋊Dic3—22no—
100C2×C3⋊Dic3—21no—
101C2×C3⋊Dic3—21no—
102C2×C3⋊Dic3C22×C412yes—
103C2×C3⋊Dic3C22×C412yes—
104C2×C3⋊Dic3C2×Q814yes—
105C2×C3⋊Dic3C2×Q812yes—
106C2×C3⋊Dic3#4112yes—
107C2×C3×Dic3—22no—
108C2×C3×Dic3—22no—
109C2×C3×Dic3—24no—
110C2×C3×Dic3—24no—
111C2×C3×Dic3—22no—
112C2×C3×Dic3—22no—
113C2×C3×Dic3—22no—
114C2×C3×Dic3C22×C418yes—
115C2×C3×Dic3C2×Q814yes—
116#627—48no—
117C2×C4⋊Q8—91no—
118#391—94no—
119#389—32no—
120#389—92no—
121C4×C4⋊C4—92no—
122C4×C4⋊C4—91no—
123C4×C4⋊C4—92no—
124C4×C4⋊C4—91no—
125C22×C3×C4—21no—
126C22×C3×C4—22no—
127C22×C3×C4—32no—
128C22×C3×C4—34no—
129C22×C3×C4—32no—
130C22×C3×C4C22×D314yes—
131C22×C3×C4C22×D312yes—
132C22×Dic3—32no—
133C22×Dic3—32no—
134C22×Dic3—34no—
135C22×Dic3—61no—
136C22×Dic3—61no—
137C22×Dic3—62no—
138C22×Dic3C22×D312yes—
139C22×Dic3C22×D314yes—
140C22×Dic3C22×D312yes—
141C2×Dic6—316no—
142C2×Dic6—124no—
143C2×Dic6—124no—
144C3×C4⋊C4—24no—
145C3×C4⋊C4—24no—
146C3×C4⋊C4—38no—
147C3×C4⋊C4—124no—
148C3×C42—64no—
149C4⋊Dic3—38no—
150C4⋊Dic3—64no—
151C4⋊Dic3C4×D318yes—
152Dic3⋊C4—316no—
153Dic3⋊C4—38no—
154Dic3⋊C4—44no—
155Dic3⋊C4—64no—
156C4×Dic3—24no—
157C4×Dic3—38no—
158C4×Dic3—64no—
159C4×Dic3—68no—
160C4×Dic3—124no—
161C4×Dic3—124no—
162C4×Dic3—124no—
163C22×C32C23×C411yescharacteristic
164C22×C32C22×Q811yescharacteristic
165C22×C32C22×Q811yescharacteristic
166C22×C32C2×#4111yescharacteristic
167C22×C32C2×#4111yescharacteristic
168C22×C32H(5,𝔽2)11yescharacteristic
169C22×C32H(5,𝔽2)11yescharacteristic
170C32×C4—42no—
171C32×C4C4×Q814yes—
172C3⋊Dic3—22no—
173C3⋊Dic3—24no—
174C3⋊Dic3C4×Q814yes—
175C3×Dic3—28no—
176C3×Dic3—24no—
177C3×Dic3—42no—
178C22×Q8—92no—
179C4⋊Q8—98no—
180C2×C4⋊C4—32no—
181C2×C4⋊C4—34no—
182C2×C4⋊C4—92no—
183C2×C4⋊C4—91no—
184C2×C4⋊C4—91no—
185C2×C4⋊C4—91no—
186C2×C4⋊C4D3211yescharacteristic
187C2×C42—32no—
188C2×C42—91no—
189C2×C42—92no—
190C2×C42—94no—
191#95—34no—
192#95—94no—
193#95—92no—
194#95—92no—
195C23×C3—21no—
196C23×C3C23×D312yes—
197C2×C3×C4—24no—
198C2×C3×C4—24no—
199C2×C3×C4—24no—
200C2×C3×C4—24no—
201C2×C3×C4—22no—
202C2×C3×C4—22no—
203C2×C3×C4—22no—
204C2×C3×C4—38no—
205C2×C3×C4—34no—
206C2×C3×C4—42no—
207C2×C3×C4—42no—
208C2×C3×C4—62no—
209C2×C3×C4—64no—
210C2×C3×C4—62no—
211C2×C3×C4—64no—
212C2×C3×C4—62no—
213C2×C3×C4—62no—
214C2×C3×C4—62no—
215C2×C3×C4C2×C4×D314yes—
216C2×C3×C4#23714yes—
217C2×C3×C4D3×Q814yes—
218C2×Dic3—22no—
219C2×Dic3—24no—
220C2×Dic3—22no—
221C2×Dic3—24no—
222C2×Dic3—22no—
223C2×Dic3—22no—
224C2×Dic3—22no—
225C2×Dic3—34no—
226C2×Dic3—34no—
227C2×Dic3—34no—
228C2×Dic3—34no—
229C2×Dic3—38no—
230C2×Dic3—62no—
231C2×Dic3—62no—
232C2×Dic3—62no—
233C2×Dic3—62no—
234C2×Dic3—64no—
235C2×Dic3—62no—
236C2×Dic3—64no—
237C2×Dic3—64no—
238C2×Dic3—62no—
239C2×Dic3—122no—
240C2×Dic3—121no—
241C2×Dic3—122no—
242C2×Dic3—121no—
243C2×Dic3C2×C4×D318yes—
244C2×Dic3D3×Q814yes—
245Dic6—1216no—
246C2×C32C2×C4×Q811yescharacteristic
247C2×C32C2×C4×Q811yescharacteristic
248C2×C32#51811yescharacteristic
249C2×C32#55411yescharacteristic
250C2×C32#55411yescharacteristic
251C2×C32#55511yescharacteristic
252C2×C32Q8211yescharacteristic
253C2×Q8—98no—
254C2×Q8—362no—
255C2×Q8—362no—
256C22×C4—32no—
257C22×C4—34no—
258C22×C4—32no—
259C22×C4—91no—
260C22×C4—91no—
261C22×C4—92no—
262C22×C4C2×D3212yes—
263C22×C4C2×D3211yescharacteristic
264C4⋊C4—22no—
265C4⋊C4—38no—
266C4⋊C4—98no—
267C4⋊C4—94no—
268C4⋊C4—94no—
269C4⋊C4—124no—
270C4⋊C4—182no—
271C42—64no—
272C42—94no—
273C42—184no—
274C42—364no—
275C22×C3—21no—
276C22×C3—21no—
277C22×C3—21no—
278C22×C3—21no—
279C22×C3—21no—
280C22×C3—21no—
281C22×C3—21no—
282C22×C3C22×C4×D312yes—
283C22×C3C2×#23712yes—
284C22×C3#100412yes—
285C22×C3C2×D3×Q812yes—
286C22×C3C2×D3×Q812yes—
287C22×C3D3×#4112yes—
288C22×C3#100912yes—
289C3×C4—24no—
290C3×C4—44no—
291C3×C4—44no—
292C3×C4—64no—
293C3×C4—68no—
294C3×C4—122no—
295C3×C4#88718yes—
296Dic3—24no—
297Dic3—28no—
298Dic3—38no—
299Dic3—42no—
300Dic3—64no—
301Dic3—68no—
302Dic3—64no—
303Dic3—122no—
304Dic3—124no—
305C32#236911yescharacteristic, complemented, Sylow
306C23C22×D3211yescharacteristic
307Q8—368no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—38no—
312C2×C4—34no—
313C2×C4—64no—
314C2×C4—62no—
315C2×C4—64no—
316C2×C4—62no—
317C2×C4—62no—
318C2×C4—62no—
319C2×C4—62no—
320C2×C4—92no—
321C2×C4—92no—
322C2×C4—92no—
323C2×C4—94no—
324C2×C4—92no—
325C2×C4—182no—
326C2×C4—181no—
327C2×C4—182no—
328C2×C4—181no—
329C2×C4#379712yes—
330C2×C4C4×D3212yes—
331C2×C4#380512yes—
332C2×C3—21no—
333C2×C3—21no—
334C2×C3—21no—
335C2×C3—21no—
336C2×C3—21no—
337C2×C3—21no—
338C2×C3—21no—
339C2×C3C2×#88712yes—
340C2×C3#554512yes—
341C2×C3C4×D3×Q812yes—
342C2×C3#561612yes—
343C2×C3#563512yes—
344C2×C3#569012yes—
345C2×C3#572212yes—
346C22C2×#379711yescharacteristic
347C22C2×C4×D3211yescharacteristic
348C22#6431211yescharacteristic
349C22#6431311yescharacteristic
350C22D32×Q811yescharacteristic
351C22#6432011yescharacteristic
352C22C2×#380511yescharacteristic
353C4—42no—
354C4—68no—
355C4—64no—
356C4—94no—
357C4—122no—
358C4—182no—
359C4—184no—
360C4#6383814yes—
361C3—21no—
362C3#7598712yescomplemented
363C2#1059431311yescharacteristic
364C2#1059436311yescharacteristic
365C2#1059448411yescharacteristic
366C2#1059460611yescharacteristic
367C2C2×#6383811yescharacteristic
368C2#1059525311yescharacteristic
369C2#1059540711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C4⋊C4D32
hypocenterC32#2369
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
22. #63919C4semidirect
51. C4⋊(C3⋊Dic3)Q8semidirect
59. #3724Q8semidirect
305. C32#2369semidirect
362. C3#75987semidirect

Maximal subgroups

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

subgroupindex
C2×#639192
C4⋊C4×C3⋊Dic32
C3×#49722
#105913372
C4×#37242
Dic3×C4⋊Dic32
#105912572
#105912352
#759873