Finite Group Databasebeta

← #11805917

Subgroups — #11805917

Order 1152.

1057 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×C4×#627C211yesmaximal, characteristic
2C4⋊C4×C3⋊Dic3C211yesmaximal, characteristic
3C3×#4977C212yesmaximal
4#10591396C212yesmaximal
5#10591359C211yesmaximal, characteristic
6Dic3×C4⋊Dic3C212yesmaximal
7#10591257C212yesmaximal
8#10591250C214yesmaximal
9#74158—32nomaximal
10C22×#627C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C2×C4×C3⋊Dic3C2212yes—
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C2×C3×C4⋊Dic3C2212yes—
16C2×C3×C4×Dic3C2212yes—
17C2×#3724C2212yes—
18C2×#3724C2212yes—
19C2×#3724C2211yescharacteristic
20C2×Dic3⋊Dic3C2212yes—
21C2×Dic32C2214yes—
22C4×#627C418yescomplemented
23#63658C2212yes—
24C3×C3⋊#95C2214yes—
25C3×C3⋊#95C2214yes—
26#63579C2214yes—
27C2×C4×Dic6—32no—
28C3×#382—32no—
29#4977D312yes—
30#4975—32no—
31Dic3×C4⋊C4—32no—
32Dic3×C4⋊C4—32no—
33Dic3×C4⋊C4—61no—
34C4×C4⋊Dic3—32no—
35#4653—34no—
36#4652—34no—
37#4649—34no—
38#4646—34no—
39C22×C32×C4C2312yes—
40C22×C32×C4C2311yescharacteristic
41C22×C3⋊Dic3C2311yescharacteristic
42C22×C3⋊Dic3C2312yes—
43C22×C3⋊Dic3C2311yescharacteristic
44C22×C3×Dic3C2314yes—
45C22×C3×Dic3C2312yes—
46C22×C3×Dic3C2312yes—
47C2×#627—22no—
48C2×#627—22no—
49C2×#627C2×C414yes—
50C32×C4⋊C4—22no—
51C4⋊(C3⋊Dic3)Q814yescomplemented
52C4×C3⋊Dic3—24no—
53C4×C3⋊Dic3C2×C414yes—
54C3×C4⋊Dic3—24no—
55C3×C4×Dic3C2×C418yes—
56#3724—24no—
57#3724—42no—
58#3724C2×C414yes—
59Dic3⋊Dic3C2×C418yes—
60Dic32—44no—
61#2355—91noSylow
62C22×Dic6—32no—
63C2×C3×C4⋊C4—21no—
64C2×C3×C4⋊C4—32no—
65C2×C3×C4⋊C4C2×D312yes—
66C2×C3×C42—32no—
67C2×C4⋊Dic3—32no—
68C2×C4⋊Dic3—32no—
69C2×C4⋊Dic3—61no—
70C2×C4⋊Dic3C2×D312yes—
71C2×Dic3⋊C4—32no—
72C2×Dic3⋊C4—32no—
73C2×Dic3⋊C4—34no—
74C2×Dic3⋊C4—34no—
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—
82C4×Dic6—316no—
83C3×#95—34no—
84C3×#95—34no—
85C3⋊#95—34no—
86C3⋊#95—34no—
87C3⋊#95—34no—
88C3⋊#95—62no—
89C3⋊#95C2×D314yes—
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⋊Dic3#4112yes—
106C2×C3⋊Dic3#4112yes—
107C2×C3×Dic3—22no—
108C2×C3×Dic3—22no—
109C2×C3×Dic3—22no—
110C2×C3×Dic3—22no—
111C2×C3×Dic3—24no—
112C2×C3×Dic3—24no—
113C2×C3×Dic3—24no—
114C2×C3×Dic3C22×C414yes—
115C2×C3×Dic3C22×C414yes—
116#627—28no—
117C2×C4×Q8—91no—
118#391—92no—
119#387—94no—
120#384—91no—
121#382—32no—
122C4×C4⋊C4—92no—
123C4×C4⋊C4—92no—
124C4×C4⋊C4—91no—
125C22×C3×C4—21no—
126C22×C3×C4—22no—
127C22×C3×C4—32no—
128C22×C3×C4—32no—
129C22×C3×C4—34no—
130C22×C3×C4C22×D314yes—
131C22×C3×C4C22×D312yes—
132C22×Dic3—32no—
133C22×Dic3—34no—
134C22×Dic3—32no—
135C22×Dic3—61no—
136C22×Dic3—61no—
137C22×Dic3—62no—
138C22×Dic3C22×D314yes—
139C22×Dic3C22×D312yes—
140C22×Dic3C22×D312yes—
141C2×Dic6—38no—
142C2×Dic6—64no—
143C2×Dic6—64no—
144C3×C4⋊C4—24no—
145C3×C4⋊C4—24no—
146C3×C4⋊C4—64no—
147C3×C42—38no—
148C4⋊Dic3—24no—
149C4⋊Dic3—38no—
150C4⋊Dic3—38no—
151C4⋊Dic3—64no—
152Dic3⋊C4—38no—
153Dic3⋊C4—38no—
154Dic3⋊C4—68no—
155Dic3⋊C4—124no—
156C4×Dic3—38no—
157C4×Dic3—64no—
158C4×Dic3—68no—
159C4×Dic3—124no—
160C4×Dic3—124no—
161C4×Dic3—124no—
162C4×Dic3C4×D318yes—
163C22×C32C23×C411yescharacteristic
164C22×C32C22×Q811yescharacteristic
165C22×C32C2×#4111yescharacteristic
166C22×C32C2×#4111yescharacteristic
167C22×C32C2×#4111yescharacteristic
168C22×C32H(5,𝔽2)11yescharacteristic
169C22×C322−1+411yescharacteristic
170C32×C4—42no—
171C32×C4C4×Q814yes—
172C3⋊Dic3—22no—
173C3⋊Dic3—24no—
174C3⋊Dic3#11714yes—
175C3×Dic3—24no—
176C3×Dic3—24no—
177C3×Dic3—44no—
178C22×Q8—91no—
179C4×Q8—98no—
180C2×C4⋊C4—32no—
181C2×C4⋊C4—91no—
182C2×C4⋊C4—92no—
183C2×C4⋊C4—91no—
184C2×C4⋊C4—92no—
185C2×C4⋊C4—92no—
186C2×C4⋊C4D3211yescharacteristic
187C2×C42—32no—
188C2×C42—91no—
189C2×C42—92no—
190C2×C42—94no—
191#95—34no—
192#95—34no—
193#95—94no—
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—34no—
205C2×C3×C4—34no—
206C2×C3×C4—42no—
207C2×C3×C4—42no—
208C2×C3×C4—62no—
209C2×C3×C4—62no—
210C2×C3×C4—62no—
211C2×C3×C4—62no—
212C2×C3×C4—64no—
213C2×C3×C4—64no—
214C2×C3×C4—64no—
215C2×C3×C4C2×C4×D314yes—
216C2×C3×C4#23714yes—
217C2×C3×C4D3×Q814yes—
218C2×Dic3—22no—
219C2×Dic3—22no—
220C2×Dic3—22no—
221C2×Dic3—22no—
222C2×Dic3—24no—
223C2×Dic3—24no—
224C2×Dic3—24no—
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—64no—
236C2×Dic3—64no—
237C2×Dic3—62no—
238C2×Dic3—62no—
239C2×Dic3—122no—
240C2×Dic3—121no—
241C2×Dic3—122no—
242C2×Dic3—121no—
243C2×Dic3C2×C4×D314yes—
244C2×Dic3C2×C4×D314yes—
245Dic6—616no—
246C2×C32C2×#11711yescharacteristic
247C2×C32C2×C4×Q811yescharacteristic
248C2×C32#52011yescharacteristic
249C2×C32#55411yescharacteristic
250C2×C32#55611yescharacteristic
251C2×C32#55711yescharacteristic
252C2×C32#55911yescharacteristic
253C2×Q8—94no—
254C2×Q8—182no—
255C2×Q8—182no—
256C22×C4—32no—
257C22×C4—32no—
258C22×C4—34no—
259C22×C4—91no—
260C22×C4—92no—
261C22×C4—91no—
262C22×C4C2×D3212yes—
263C22×C4C2×D3211yescharacteristic
264C4⋊C4—22no—
265C4⋊C4—64no—
266C4⋊C4—94no—
267C4⋊C4—98no—
268C4⋊C4—94no—
269C4⋊C4—184no—
270C4⋊C4—362no—
271C42—38no—
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×C3C2×D3×Q812yes—
285C22×C3D3×#4112yes—
286C22×C3D3×#4112yes—
287C22×C3#100912yes—
288C22×C3#101012yes—
289C3×C4—24no—
290C3×C4—44no—
291C3×C4—44no—
292C3×C4—64no—
293C3×C4—64no—
294C3×C4—124no—
295C3×C4#88718yes—
296Dic3—24no—
297Dic3—24no—
298Dic3—38no—
299Dic3—44no—
300Dic3—64no—
301Dic3—68no—
302Dic3—64no—
303Dic3—124no—
304Dic3—122no—
305C32#235511yescharacteristic, complemented, Sylow
306C23C22×D3211yescharacteristic
307Q8—188no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—34no—
312C2×C4—34no—
313C2×C4—62no—
314C2×C4—62no—
315C2×C4—62no—
316C2×C4—62no—
317C2×C4—64no—
318C2×C4—64no—
319C2×C4—64no—
320C2×C4—92no—
321C2×C4—92no—
322C2×C4—92no—
323C2×C4—94no—
324C2×C4—92no—
325C2×C4—181no—
326C2×C4—182no—
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×C3D3×#11712yes—
341C2×C3#552312yes—
342C2×C3#567112yes—
343C2×C3#568112yes—
344C2×C3#568512yes—
345C2×C3#569012yes—
346C22C2×#379711yescharacteristic
347C22C2×C4×D3211yescharacteristic
348C22#6430911yescharacteristic
349C22#6431211yescharacteristic
350C22#6431911yescharacteristic
351C22#6432011yescharacteristic
352C22C2×#380511yescharacteristic
353C4—42no—
354C4—64no—
355C4—64no—
356C4—94no—
357C4—124no—
358C4—184no—
359C4—182no—
360C4#6383814yes—
361C3—21no—
362C3#7415812yescomplemented
363C2#1059432411yescharacteristic
364C2#1059448411yescharacteristic
365C2#1059451111yescharacteristic
366C2#1059460211yescharacteristic
367C2C2×#6383811yescharacteristic
368C2#1059511911yescharacteristic
369C2#1059539211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C4⋊C4D32
hypocenterC32#2355
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
22. C4×#627C4semidirect
51. C4⋊(C3⋊Dic3)Q8semidirect
305. C32#2355semidirect
362. C3#74158semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6272
C4⋊C4×C3⋊Dic32
C3×#49772
#105913962
#105913592
Dic3×C4⋊Dic32
#105912572
#105912502
#741583