Finite Group Databasebeta

← #11805292

Subgroups — #11805292

Order 1152.

1512 conjugacy classes of subgroups.

The subgroup lattice has 369 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64081C211yesmaximal, characteristic
2C32×#376C211yesmaximal, characteristic, complemented
3#10592639C212yesmaximal
4#10592635C211yesmaximal, characteristic, complemented
5C4×#3750C212yesmaximal, complemented
6#10592369C212yesmaximal
7#10592366C211yesmaximal, characteristic
8#10592365C211yesmaximal, characteristic
9#10592349C211yesmaximal, characteristic, complemented
10#10592347C211yesmaximal, characteristic, complemented
11#10592346C212yesmaximal, complemented
12#73392—34nomaximal
13C22×C4×C3⋊D3C2211yescharacteristic
14C2×C32×C42C2212yes—
15C2×C32×C42C2211yescharacteristic
16C2×#3752C2212yes—
17C2×#3752C2212yes—
18C2×#3752C2211yescharacteristic
19C2×#3752C2211yescharacteristic
20C2×C4⋊(C3⋊Dic3)C2212yes—
21C2×#3750C2212yes—
22C2×#3750C2212yes—
23C2×#3750C2211yescharacteristic
24C2×#3750C2211yescharacteristic
25C2×C4×C3⋊Dic3C2212yes—
26C2×C4×C3⋊Dic3C2212yes—
27C2×C4×C3⋊Dic3C2211yescharacteristic
28#64081C418yescomplemented
29C32×#95C2212yes—
30C32×#95C2211yescharacteristic
31C32×#95C2211yescharacteristic
32#63658C2212yes—
33#63658C2211yescharacteristic
34#63658C2211yescharacteristic
35#63658C2212yes—
36#63658C2212yes—
37C2×#872—34no—
38C3×#376D314yescomplemented
39#4940—38no—
40#4936—34no—
41C4×Dic3⋊C4—38no—
42#4670—38no—
43#4667—34no—
44#4666—34no—
45#4650—34no—
46#4648—34no—
47#4647—38no—
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⋊D3C2×C414yes—
61C32×C42—24no—
62C32×C42C2×C414yes—
63#3752—24no—
64#3752—42no—
65#3752C2×C414yes—
66#3752C2×C414yes—
67C4⋊(C3⋊Dic3)—42no—
68#3750—24no—
69#3750—42no—
70#3750C2×C414yes—
71#3750C2×C414yes—
72C4×C3⋊Dic3—24no—
73C4×C3⋊Dic3—24no—
74C4×C3⋊Dic3C2×C414yes—
75#2346—91noSylow
76C22×C4×D3—34no—
77C2×C3×C42C2×D318yes—
78C2×C3×C42C2×D314yes—
79C2×(C2×D3)⋊C4—34no—
80C2×(C2×D3)⋊C4—34no—
81C2×(C2×D3)⋊C4—38no—
82C2×(C2×D3)⋊C4—38no—
83C2×C4⋊Dic3—38no—
84C2×Dic3⋊C4—34no—
85C2×Dic3⋊C4—34no—
86C2×Dic3⋊C4—38no—
87C2×Dic3⋊C4—38no—
88C2×C4×Dic3—34no—
89C2×C4×Dic3—38no—
90C2×C4×Dic3—38no—
91#872—332no—
92C3×#95C2×D318yes—
93C3×#95C2×D314yes—
94C3×#95C2×D314yes—
95C3⋊#95—38no—
96C3⋊#95—34no—
97C3⋊#95—34no—
98C3⋊#95—38no—
99C3⋊#95—38no—
100C23×C32C2411yescharacteristic
101C22×C3⋊D3—22no—
102C22×C3⋊D3—22no—
103C22×C3⋊D3—21no—
104C22×C3⋊D3—21no—
105C22×C3⋊D3C22×C412yes—
106C2×C32×C4—22no—
107C2×C32×C4—22no—
108C2×C32×C4—22no—
109C2×C32×C4—21no—
110C2×C32×C4—21no—
111C2×C32×C4—22no—
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—21no—
121C2×C3⋊Dic3—21no—
122C2×C3⋊Dic3—22no—
123C2×C3⋊Dic3—22no—
124C2×C3⋊Dic3—22no—
125C2×C3⋊Dic3—22no—
126C2×C3⋊Dic3—22no—
127C2×C3⋊Dic3—22no—
128C2×C3⋊Dic3C22×C412yes—
129C2×C3⋊Dic3C22×C412yes—
130C2×C3⋊Dic3C22×C412yes—
131C2×C3⋊Dic3#4114yes—
132C4×C3⋊D3—28no—
133C2×#117—91no—
134#389—92no—
135#388—92no—
136#388—92no—
137#382—91no—
138#382—91no—
139#380—91no—
140C4×C4⋊C4—92no—
141C4×C22⋊C4—91no—
142#376—91no—
143#376C3⋊D311yescharacteristic, complemented
144C23×D3—34no—
145C22×C3×C4C22×D318yes—
146C22×C3×C4C22×D314yes—
147C22×C3×C4C22×D314yes—
148C22×C3×C4C22×D314yes—
149C22×C3×C4C22×D318yes—
150C22×Dic3—34no—
151C22×Dic3—34no—
152C22×Dic3—34no—
153C22×Dic3—38no—
154C22×Dic3—38no—
155C2×C4×D3—316no—
156C2×C4×D3—616no—
157C3×C42—216no—
158C3×C42C4×D3116yes—
159(C2×D3)⋊C4—316no—
160(C2×D3)⋊C4—316no—
161(C2×D3)⋊C4—616no—
162(C2×D3)⋊C4—128no—
163C4⋊Dic3—128no—
164Dic3⋊C4—316no—
165Dic3⋊C4—316no—
166Dic3⋊C4—616no—
167Dic3⋊C4—128no—
168C4×Dic3—316no—
169C4×Dic3—616no—
170C4×Dic3—616no—
171C22×C32C23×C411yescharacteristic
172C22×C32C2×#4112yes—
173C22×C32C2×#4112yes—
174C22×C32H(5,𝔽2)11yescharacteristic
175C22×C322−1+411yescharacteristic
176C2×C3⋊D3—22no—
177C2×C3⋊D3—22no—
178C2×C3⋊D3—22no—
179C2×C3⋊D3—42no—
180C2×C3⋊D3—42no—
181C32×C4—22no—
182C32×C4—22no—
183C32×C4—22no—
184C32×C4—24no—
185C32×C4—42no—
186C3⋊Dic3—22no—
187C3⋊Dic3—22no—
188C3⋊Dic3—42no—
189C3⋊Dic3—42no—
190C3⋊Dic3#11714yes—
191C23×C4—91no—
192#117—98no—
193C2×C4⋊C4—91no—
194C2×C4⋊C4—91no—
195C2×C4⋊C4—92no—
196C2×C4⋊C4—92no—
197C2×C4⋊C4—92no—
198C2×C22⋊C4—91no—
199C2×C22⋊C4—91no—
200C2×C22⋊C4—92no—
201C2×C22⋊C4—92no—
202C2×C42—91no—
203C2×C42—92no—
204C2×C42—92no—
205C2×C42C2×C3⋊D312yes—
206C2×C42C2×C3⋊D311yescharacteristic
207#95—91no—
208#95—92no—
209#95—91no—
210#95—92no—
211#95—92no—
212#95C2×C3⋊D311yescharacteristic
213#95C2×C3⋊D311yescharacteristic
214#95C2×C3⋊D312yes—
215C23×C3C23×D314yes—
216C22×D3—38no—
217C22×D3—68no—
218C22×D3—68no—
219C22×D3—64no—
220C22×D3—64no—
221C2×C3×C4—28no—
222C2×C3×C4—28no—
223C2×C3×C4—28no—
224C2×C3×C4—24no—
225C2×C3×C4—24no—
226C2×C3×C4—28no—
227C2×C3×C4—28no—
228C2×C3×C4—28no—
229C2×C3×C4—28no—
230C2×C3×C4C2×C4×D318yes—
231C2×C3×C4C2×C4×D318yes—
232C2×C3×C4C2×C4×D318yes—
233C2×C3×C4#235116yes—
234C2×Dic3—38no—
235C2×Dic3—316no—
236C2×Dic3—38no—
237C2×Dic3—38no—
238C2×Dic3—68no—
239C2×Dic3—64no—
240C2×Dic3—64no—
241C2×Dic3—68no—
242C2×Dic3—68no—
243C2×Dic3—68no—
244C2×Dic3—68no—
245C2×Dic3—68no—
246C2×Dic3—68no—
247C4×D3—632no—
248C2×C32C2×#11711yescharacteristic
249C2×C32C4×#4111yescharacteristic
250C2×C32#52011yescharacteristic
251C2×C32#55212yes—
252C2×C32#55512yes—
253C3⋊D3—42no—
254C24—91no—
255C22×C4—91no—
256C22×C4—91no—
257C22×C4—91no—
258C22×C4—94no—
259C22×C4—92no—
260C22×C4—92no—
261C22×C4—184no—
262C22×C4C22×C3⋊D312yes—
263C22×C4C22×C3⋊D311yescharacteristic
264C22×C4C22×C3⋊D311yescharacteristic
265C22×C4C22×C3⋊D311yescharacteristic
266C22×C4C22×C3⋊D312yes—
267C4⋊C4—94no—
268C4⋊C4—94no—
269C4⋊C4—184no—
270C4⋊C4—362no—
271C4⋊C4—362no—
272C22⋊C4—94no—
273C22⋊C4—94no—
274C22⋊C4—184no—
275C22⋊C4—362no—
276C42—24no—
277C42—94no—
278C42—184no—
279C42—184no—
280C42C4×C3⋊D314yes—
281C22×C3C22×C4×D314yes—
282C22×C3C2×#23518yes—
283C22×C3D3×#4118yes—
284C22×C3#100914yes—
285C22×C3#101014yes—
286C2×D3—68no—
287C2×D3—68no—
288C2×D3—68no—
289C2×D3—128no—
290C2×D3—128no—
291C3×C4—28no—
292C3×C4—28no—
293C3×C4—28no—
294C3×C4—216no—
295C3×C4—48no—
296Dic3—316no—
297Dic3—68no—
298Dic3—68no—
299Dic3—128no—
300Dic3—128no—
301C32#234611yescharacteristic, complemented, Sylow
302C23—92no—
303C23—182no—
304C23—182no—
305C23—181no—
306C23—181no—
307C23C23×C3⋊D311yescharacteristic
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—92no—
318C2×C4—94no—
319C2×C4—92no—
320C2×C4—92no—
321C2×C4—188no—
322C2×C4—182no—
323C2×C4—181no—
324C2×C4—181no—
325C2×C4—182no—
326C2×C4—182no—
327C2×C4—182no—
328C2×C4—182no—
329C2×C4—182no—
330C2×C4—182no—
331C2×C4C2×C4×C3⋊D312yes—
332C2×C4C2×C4×C3⋊D312yes—
333C2×C4C2×C4×C3⋊D312yes—
334C2×C4#382814yes—
335C2×C3C4×#23514yes—
336C2×C3D3×#11714yes—
337C2×C3#552314yes—
338C2×C3#553118yes—
339C2×C3#553218yes—
340D3—128no—
341C22—182no—
342C22—182no—
343C22—182no—
344C22—362no—
345C22—362no—
346C22C22×C4×C3⋊D311yescharacteristic
347C22C2×#382812yes—
348C22#41×C3⋊D312yes—
349C22#6436611yescharacteristic
350C22#6436711yescharacteristic
351C4—22no—
352C4—22no—
353C4—22no—
354C4—24no—
355C4—42no—
356C4—94no—
357C4—182no—
358C4—182no—
359C4—362no—
360C4—362no—
361C3#7339214yescomplemented
362C2—362no—
363C2C4×#382811yescharacteristic
364C2C3⋊D3×#11711yescharacteristic
365C2#1059599411yescharacteristic
366C2#1059600212yes—
367C2#1059600312yes—
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutatorC22×C32C23×C4
FittingC32×#376C2
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenter#376C3⋊D3
hypocenterC32#2346
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. C4×#3750C2semidirect
9. #10592349C2semidirect
10. #10592347C2semidirect
11. #10592346C2semidirect
28. #64081C4semidirect
38. C3×#376D3semidirect
143. #376C3⋊D3semidirect
301. C32#2346semidirect
361. C3#73392semidirect

Maximal subgroups

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

subgroupindex
C2×#640812
C32×#3762
#105926392
#105926352
C4×#37502
#105923692
#105923662
#105923652
#105923492
#105923472
#105923462
#733923