Finite Group Databasebeta

← #11805065

Subgroups — #11805065

Order 1152.

1596 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64081C211yesmaximal, characteristic
2C32×#376C211yesmaximal, characteristic, complemented
3C4×#3752C212yesmaximal
4#10592635C211yesmaximal, characteristic, complemented
5#10592632C212yesmaximal, complemented
6#10592367C212yesmaximal
7#10592363C211yesmaximal, characteristic
8C3⋊D3×#95C211yesmaximal, characteristic
9#10592354C212yesmaximal, complemented
10#10592350C211yesmaximal, characteristic, complemented
11#10592348C211yesmaximal, characteristic, complemented
12#73416—34nomaximal
13C22×C4×C3⋊D3C2212yes—
14C22×C4×C3⋊D3C2211yescharacteristic
15C2×C32×C42C2212yes—
16C2×C32×C42C2211yescharacteristic
17C2×#3752C2212yes—
18C2×#3752C2211yescharacteristic
19C2×#3752C2211yescharacteristic
20C2×C4⋊(C3⋊Dic3)C2212yes—
21C2×#3750C2212yes—
22C2×#3750C2211yescharacteristic
23C2×#3750C2211yescharacteristic
24C2×C4×C3⋊Dic3C2212yes—
25C2×C4×C3⋊Dic3C2211yescharacteristic
26#64081C418yescomplemented
27C32×#95C2211yescharacteristic
28C32×#95C2211yescharacteristic
29C32×#95C2212yes—
30#63658C2211yescharacteristic
31#63658C2212yes—
32#63658C2211yescharacteristic
33#63658C2212yes—
34#63658C2212yes—
35#63658C2212yes—
36#63658C2212yes—
37C2×#872—34no—
38C3×#376D314yescomplemented
39C4×(C2×D3)⋊C4—38no—
40#4936—34no—
41#4933—38no—
42#4668—38no—
43#4664—34no—
44D3×#95—34no—
45#4655—38no—
46#4651—34no—
47#4649—34no—
48C23×C3⋊D3C2311yescharacteristic
49C22×C32×C4C2312yes—
50C22×C32×C4C2311yescharacteristic
51C22×C32×C4C2311yescharacteristic
52C22×C32×C4C2311yescharacteristic
53C22×C32×C4C2312yes—
54C22×C3⋊Dic3C2312yes—
55C22×C3⋊Dic3C2312yes—
56C22×C3⋊Dic3C2311yescharacteristic
57C22×C3⋊Dic3C2311yescharacteristic
58C22×C3⋊Dic3C2311yescharacteristic
59C2×C4×C3⋊D3—24no—
60C2×C4×C3⋊D3—24no—
61C2×C4×C3⋊D3—24no—
62C2×C4×C3⋊D3—42no—
63C2×C4×C3⋊D3C2×C414yes—
64C32×C42—24no—
65C32×C42C2×C414yescomplemented
66#3752—24no—
67#3752C2×C414yes—
68#3752C2×C414yes—
69C4⋊(C3⋊Dic3)—42no—
70#3750—24no—
71#3750C2×C414yescomplemented
72#3750C2×C414yescomplemented
73C4×C3⋊Dic3—42no—
74C4×C3⋊Dic3C2×C414yescomplemented
75#2343—91noSylow
76C22×C4×D3—34no—
77C22×C4×D3—38no—
78C2×C3×C42C2×D318yes—
79C2×C3×C42C2×D314yes—
80C2×(C2×D3)⋊C4—34no—
81C2×(C2×D3)⋊C4—34no—
82C2×(C2×D3)⋊C4—38no—
83C2×C4⋊Dic3—38no—
84C2×Dic3⋊C4—34no—
85C2×Dic3⋊C4—34no—
86C2×Dic3⋊C4—38no—
87C2×C4×Dic3—34no—
88C2×C4×Dic3—38no—
89#872—332no—
90C3×#95C2×D314yes—
91C3×#95C2×D314yes—
92C3×#95C2×D318yes—
93C3⋊#95—34no—
94C3⋊#95—38no—
95C3⋊#95—34no—
96C3⋊#95—38no—
97C3⋊#95—38no—
98C3⋊#95—38no—
99C3⋊#95—38no—
100C23×C32C2411yescharacteristic
101C22×C3⋊D3—22no—
102C22×C3⋊D3—21no—
103C22×C3⋊D3—21no—
104C22×C3⋊D3C22×C412yes—
105C22×C3⋊D3#4114yes—
106C2×C32×C4—22no—
107C2×C32×C4—22no—
108C2×C32×C4—22no—
109C2×C32×C4—22no—
110C2×C32×C4—21no—
111C2×C32×C4—21no—
112C2×C32×C4—22no—
113C2×C32×C4—22no—
114C2×C32×C4—22no—
115C2×C32×C4C22×C412yes—
116C2×C32×C4C22×C412yes—
117C2×C32×C4C22×C412yes—
118C2×C32×C4#4114yes—
119C2×C3⋊Dic3—22no—
120C2×C3⋊Dic3—22no—
121C2×C3⋊Dic3—21no—
122C2×C3⋊Dic3—21no—
123C2×C3⋊Dic3—22no—
124C2×C3⋊Dic3—22no—
125C2×C3⋊Dic3—22no—
126C2×C3⋊Dic3—22no—
127C2×C3⋊Dic3—22no—
128C2×C3⋊Dic3—22no—
129C2×C3⋊Dic3C22×C412yes—
130C2×C3⋊Dic3C22×C412yes—
131C2×C3⋊Dic3C22×C412yes—
132C4×C3⋊D3—28no—
133C4×C3⋊D3—48no—
134C2×#117—91no—
135#387—92no—
136#387—92no—
137#385—92no—
138#383—91no—
139#382—91no—
140#381—91no—
141C4×C4⋊C4—91no—
142C4×C22⋊C4—92no—
143#376C3⋊D311yescharacteristic, complemented
144C2×#95—91no—
145C23×D3—34no—
146C22×C3×C4C22×D318yes—
147C22×C3×C4C22×D314yes—
148C22×C3×C4C22×D314yes—
149C22×C3×C4C22×D314yes—
150C22×C3×C4C22×D318yes—
151C22×Dic3—34no—
152C22×Dic3—34no—
153C22×Dic3—34no—
154C22×Dic3—38no—
155C22×Dic3—38no—
156C2×C4×D3—316no—
157C2×C4×D3—616no—
158C2×C4×D3—616no—
159C2×C4×D3—616no—
160C2×C4×D3—128no—
161C3×C42—216no—
162C3×C42C4×D3116yescomplemented
163(C2×D3)⋊C4—316no—
164(C2×D3)⋊C4—316no—
165(C2×D3)⋊C4—616no—
166C4⋊Dic3—128no—
167Dic3⋊C4—316no—
168Dic3⋊C4—316no—
169Dic3⋊C4—616no—
170C4×Dic3—316no—
171C4×Dic3—128no—
172C22×C32C23×C411yescharacteristic
173C22×C32C2×#4112yes—
174C22×C32C2×#4112yes—
175C22×C32H(5,𝔽2)11yescharacteristic
176C22×C322−1+411yescharacteristic
177C2×C3⋊D3—22no—
178C2×C3⋊D3—22no—
179C2×C3⋊D3—24no—
180C2×C3⋊D3—24no—
181C2×C3⋊D3#11714yes—
182C32×C4—22no—
183C32×C4—22no—
184C32×C4—22no—
185C32×C4—24no—
186C32×C4—42no—
187C3⋊Dic3—22no—
188C3⋊Dic3—22no—
189C3⋊Dic3—22no—
190C3⋊Dic3—42no—
191C3⋊Dic3—42no—
192C23×C4—91no—
193C23×C4—92no—
194#117—98no—
195C2×C4⋊C4—91no—
196C2×C4⋊C4—91no—
197C2×C4⋊C4—92no—
198C2×C4⋊C4—92no—
199C2×C22⋊C4—91no—
200C2×C22⋊C4—91no—
201C2×C22⋊C4—92no—
202C2×C42—91no—
203C2×C42—92no—
204C2×C42C2×C3⋊D312yes—
205C2×C42C2×C3⋊D311yescharacteristic
206#95—91no—
207#95—92no—
208#95—92no—
209#95—92no—
210#95—91no—
211#95—92no—
212#95—92no—
213#95C2×C3⋊D311yescharacteristic
214#95C2×C3⋊D311yescharacteristic
215#95C2×C3⋊D312yes—
216C23×C3C23×D314yes—
217C22×D3—38no—
218C22×D3—316no—
219C22×D3—68no—
220C22×D3—64no—
221C22×D3—64no—
222C2×C3×C4—28no—
223C2×C3×C4—28no—
224C2×C3×C4—28no—
225C2×C3×C4—28no—
226C2×C3×C4—24no—
227C2×C3×C4—24no—
228C2×C3×C4—28no—
229C2×C3×C4—28no—
230C2×C3×C4—28no—
231C2×C3×C4C2×C4×D318yes—
232C2×C3×C4C2×C4×D318yes—
233C2×C3×C4C2×C4×D318yes—
234C2×C3×C4#235116yes—
235C2×Dic3—38no—
236C2×Dic3—38no—
237C2×Dic3—38no—
238C2×Dic3—68no—
239C2×Dic3—68no—
240C2×Dic3—64no—
241C2×Dic3—64no—
242C2×Dic3—68no—
243C2×Dic3—68no—
244C2×Dic3—68no—
245C2×Dic3—68no—
246C2×Dic3—68no—
247C2×Dic3—68no—
248C4×D3—632no—
249C4×D3—1232no—
250C2×C32C2×#11711yescharacteristic
251C2×C32C4×#4111yescharacteristic
252C2×C32#52011yescharacteristic
253C2×C32#55112yes—
254C2×C32#55212yes—
255C3⋊D3—24no—
256C24—91no—
257C22×C4—91no—
258C22×C4—91no—
259C22×C4—91no—
260C22×C4—94no—
261C22×C4—92no—
262C22×C4—92no—
263C22×C4—184no—
264C22×C4—184no—
265C22×C4—184no—
266C22×C4—362no—
267C22×C4C22×C3⋊D312yes—
268C22×C4C22×C3⋊D311yescharacteristic
269C22×C4C22×C3⋊D311yescharacteristic
270C22×C4C22×C3⋊D311yescharacteristic
271C22×C4C22×C3⋊D312yes—
272C4⋊C4—94no—
273C4⋊C4—94no—
274C4⋊C4—184no—
275C4⋊C4—362no—
276C22⋊C4—94no—
277C22⋊C4—94no—
278C22⋊C4—184no—
279C42—24no—
280C42—94no—
281C42—362no—
282C42C4×C3⋊D314yescomplemented
283C22×C3C22×C4×D314yes—
284C22×C3C2×#23518yes—
285C22×C3D3×#4118yes—
286C22×C3#100914yes—
287C22×C3#101014yes—
288C2×D3—316no—
289C2×D3—68no—
290C2×D3—68no—
291C2×D3—616no—
292C2×D3—616no—
293C3×C4—28no—
294C3×C4—28no—
295C3×C4—28no—
296C3×C4—216no—
297C3×C4—48no—
298Dic3—68no—
299Dic3—68no—
300Dic3—68no—
301Dic3—128no—
302Dic3—128no—
303C32#234311yescharacteristic, complemented, Sylow
304C23—92no—
305C23—94no—
306C23—182no—
307C23—181no—
308C23—181no—
309C23C23×C3⋊D311yescharacteristic
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—92no—
320C2×C4—92no—
321C2×C4—92no—
322C2×C4—188no—
323C2×C4—182no—
324C2×C4—182no—
325C2×C4—181no—
326C2×C4—181no—
327C2×C4—182no—
328C2×C4—182no—
329C2×C4—182no—
330C2×C4—182no—
331C2×C4—182no—
332C2×C4—182no—
333C2×C4—368no—
334C2×C4C2×C4×C3⋊D312yes—
335C2×C4C2×C4×C3⋊D312yes—
336C2×C4C2×C4×C3⋊D312yes—
337C2×C4#382814yes—
338C2×C3C4×#23514yes—
339C2×C3D3×#11714yes—
340C2×C3#552314yes—
341C2×C3#552718yes—
342C2×C3#552918yes—
343D3—616no—
344C22—94no—
345C22—182no—
346C22—182no—
347C22—184no—
348C22—184no—
349C22C22×C4×C3⋊D311yescharacteristic
350C22C2×#382812yes—
351C22#41×C3⋊D312yes—
352C22#6436611yescharacteristic
353C22#6436711yescharacteristic
354C4—22no—
355C4—22no—
356C4—22no—
357C4—24no—
358C4—42no—
359C4—182no—
360C4—182no—
361C4—182no—
362C4—362no—
363C4—362no—
364C3#7341614yescomplemented
365C2—184no—
366C2C4×#382811yescharacteristic
367C2C3⋊D3×#11711yescharacteristic
368C2#1059599411yescharacteristic
369C2#1059599812yes—
370C2#1059600012yes—
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutatorC22×C32C23×C4
FittingC32×#376C2
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenter#376C3⋊D3
hypocenterC32#2343
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #376

Complements

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

NH ≅ G/Ntype
2. C32×#376C2semidirect
4. #10592635C2semidirect
5. #10592632C2semidirect
9. #10592354C2semidirect
10. #10592350C2semidirect
11. #10592348C2semidirect
26. #64081C4semidirect
38. C3×#376D3semidirect
65. C32×C42C2×C4semidirect
71. #3750C2×C4semidirect
72. #3750C2×C4semidirect
74. C4×C3⋊Dic3C2×C4semidirect
143. #376C3⋊D3semidirect
162. C3×C42C4×D3semidirect
282. C42C4×C3⋊D3semidirect
303. C32#2343semidirect
364. C3#73416semidirect

Maximal subgroups

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

subgroupindex
C2×#640812
C32×#3762
C4×#37522
#105926352
#105926322
#105923672
#105923632
C3⋊D3×#952
#105923542
#105923502
#105923482
#734163