Finite Group Databasebeta

← #11805746

Subgroups — #11805746

Order 1152.

882 conjugacy classes of subgroups.

The subgroup lattice has 411 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#611C211yesmaximal, characteristic
2C9×#380C211yesmaximal, characteristic, complemented
3C2×C9⋊#95C211yesmaximal, characteristic, complemented
4#10588670C212yesmaximal, complemented
5#10588658C212yesmaximal, complemented
6#10588638C212yesmaximal
7C22⋊C4×Dic9C212yesmaximal, complemented
8#10588346C211yesmaximal, characteristic, complemented
9#10588344C211yesmaximal, characteristic, complemented
10#10588331C211yesmaximal, characteristic, complemented
11#10588328C211yesmaximal, characteristic, complemented
12#73884—31nomaximal
13C23×C4×C9C2211yescharacteristic
14C22×#611C2211yescharacteristic
15C23×Dic9C2212yes—
16C22×C4×D9C2211yescharacteristic
17C2×C9×C4⋊C4C2212yes—
18C2×C9×C22⋊C4C2212yes—
19C2×#3676C2211yescharacteristic
20C4×#611C418yescomplemented
21C2×(C2×D9)⋊C4C2212yes—
22C2×(C2×D9)⋊C4C2212yes—
23C2×(C2×D9)⋊C4C2211yescharacteristic
24C2×Dic9⋊C4C2211yescharacteristic
25C2×C4×Dic9C2212yes—
26C2×C4×Dic9C2212yes—
27C2×C4×Dic9C2211yescharacteristic
28C9×#95C2211yescharacteristic
29C9×#95C2211yescharacteristic
30C9⋊#95C2211yescharacteristic
31C9⋊#95C2212yes—
32C9⋊#95C2211yescharacteristic
33C9⋊#95C2212yes—
34C9⋊#95C2212yes—
35C9⋊#95C2212yes—
36C9⋊#95C2212yes—
37C2×C4×#67—31no—
38C3×#380D311yescharacteristic
39C2×C3⋊#95—31no—
40#4990—32no—
41#4978—32no—
42#4958—32no—
43Dic3×C22⋊C4—32no—
44#4666—31no—
45#4664—31no—
46#4651—31no—
47#4648—31no—
48C24×C9C2311yescharacteristic
49C23×D9C2311yescharacteristic
50C22×C4×C9—42no—
51C22×C4×C9C2×C414yes—
52C22×C4×C9C2312yes—
53C22×C4×C9C2312yes—
54C22×C4×C9C2311yescharacteristic
55C22×C4×C9C2311yescharacteristic
56C2×#611—22no—
57C2×#611—22no—
58C2×#611C2×C414yes—
59C22×Dic9—24no—
60C22×Dic9—24no—
61C22×Dic9—42no—
62C22×Dic9C2312yes—
63C22×Dic9C2311yescharacteristic
64C22×Dic9C2311yescharacteristic
65C22×Dic9C2311yescharacteristic
66C22×Dic9C2312yes—
67C2×C4×D9—42no—
68C2×C4×D9C2×C414yescomplemented
69C9×C4⋊C4—42no—
70C9×C22⋊C4—24no—
71#3676C2×C414yes—
72(C2×D9)⋊C4—24no—
73(C2×D9)⋊C4—42no—
74(C2×D9)⋊C4C2×C414yescomplemented
75Dic9⋊C4C2×C414yescomplemented
76C4×Dic9—24no—
77C4×Dic9—42no—
78C4×Dic9C2×C414yescomplemented
79#2353—91noSylow
80C23×C3×C4C2×D311yescharacteristic
81C22×#67—31no—
82C23×Dic3—32no—
83C22×C4×D3—31no—
84C2×C3×C4⋊C4C2×D312yes—
85C2×C3×C22⋊C4C2×D312yes—
86C2×#217—31no—
87C4×#67—38no—
88C2×(C2×D3)⋊C4—31no—
89C2×(C2×D3)⋊C4—32no—
90C2×(C2×D3)⋊C4—32no—
91C2×Dic3⋊C4—31no—
92C2×C4×Dic3—31no—
93C2×C4×Dic3—32no—
94C2×C4×Dic3—32no—
95C3×#95C2×D311yescharacteristic
96C3×#95C2×D311yescharacteristic
97C3⋊#95—31no—
98C3⋊#95—32no—
99C3⋊#95—31no—
100C3⋊#95—32no—
101C3⋊#95—32no—
102C3⋊#95—32no—
103C3⋊#95—32no—
104C23×C9—22no—
105C23×C9—22no—
106C23×C9C22×C412yes—
107C23×C9#4112yes—
108C23×C9#4112yes—
109C23×C9C2411yescharacteristic
110C22×D9—22no—
111C22×D9—21no—
112C22×D9—21no—
113C22×D9—22no—
114C22×D9C22×C412yes—
115C2×C4×C9—22no—
116C2×C4×C9—22no—
117C2×C4×C9—22no—
118C2×C4×C9—22no—
119C2×C4×C9—22no—
120C2×C4×C9—22no—
121C2×C4×C9—22no—
122C2×C4×C9—22no—
123C2×C4×C9—44no—
124C2×C4×C9C22×C412yes—
125C2×C4×C9C22×C412yes—
126#611—28no—
127C2×Dic9—22no—
128C2×Dic9—22no—
129C2×Dic9—21no—
130C2×Dic9—21no—
131C2×Dic9—22no—
132C2×Dic9—22no—
133C2×Dic9—22no—
134C2×Dic9—22no—
135C2×Dic9—22no—
136C2×Dic9—48no—
137C2×Dic9C22×C412yes—
138C2×Dic9C22×C412yes—
139C2×Dic9C22×C412yes—
140C2×Dic9#4114yes—
141C4×D9—44no—
142C2×C4×D4—91no—
143#388—92no—
144#387—92no—
145#386—92no—
146#383—91no—
147#381—91no—
148#380D911yescharacteristic, complemented
149C4×C22⋊C4—92no—
150C4×C22⋊C4—91no—
151#376—91no—
152C2×#95—91no—
153C24×C3C22×D311yescharacteristic
154C23×D3—31no—
155C22×C3×C4—42no—
156C22×C3×C4C4×D314yes—
157C22×C3×C4C22×D312yes—
158C22×C3×C4C22×D312yes—
159C22×C3×C4C22×D311yescharacteristic
160C22×C3×C4C22×D311yescharacteristic
161C2×#67—34no—
162C2×#67—62no—
163C2×#67—62no—
164C22×Dic3—31no—
165C22×Dic3—32no—
166C22×Dic3—31no—
167C22×Dic3—31no—
168C22×Dic3—32no—
169C22×Dic3—64no—
170C22×Dic3—64no—
171C22×Dic3—122no—
172C2×C4×D3—34no—
173C2×C4×D3—122no—
174C3×C4⋊C4—42no—
175C3×C22⋊C4—24no—
176#217—34no—
177(C2×D3)⋊C4—34no—
178(C2×D3)⋊C4—64no—
179(C2×D3)⋊C4—122no—
180Dic3⋊C4—34no—
181C4×Dic3—34no—
182C4×Dic3—64no—
183C4×Dic3—122no—
184C22×C9—22no—
185C22×C9—22no—
186C22×C9—24no—
187C22×C9—24no—
188C22×C9#11714yes—
189C22×C9C23×C411yescharacteristic
190C22×C9C2×#4111yescharacteristic
191C22×C9C2×#4111yescharacteristic
192C22×C9C2×#4112yes—
193C22×C9H(5,𝔽2)12yes—
194C2×D9—22no—
195C2×D9—22no—
196C2×D9—22no—
197C2×D9—42no—
198C2×D9—42no—
199C4×C9—22no—
200C4×C9—22no—
201C4×C9—42no—
202C4×C9—42no—
203Dic9—22no—
204Dic9—22no—
205Dic9—22no—
206Dic9—24no—
207Dic9—42no—
208C22×D4—91no—
209C23×C4—91no—
210C23×C4—92no—
211C23×C4C2×D911yescharacteristic
212C4×D4—98no—
213C2×C4⋊C4—91no—
214C2×C4⋊C4C2×D912yes—
215C2×C22⋊C4—91no—
216C2×C22⋊C4—91no—
217C2×C22⋊C4—92no—
218C2×C22⋊C4—92no—
219C2×C22⋊C4C2×D912yes—
220C2×C42—91no—
221C2×C42—92no—
222C2×C42—92no—
223#95—91no—
224#95—91no—
225#95—92no—
226#95—92no—
227#95—92no—
228#95—92no—
229#95—92no—
230#95C2×D911yescharacteristic
231#95C2×D911yescharacteristic
232C23×C3—22no—
233C23×C3—22no—
234C23×C3C2×C4×D312yes—
235C23×C3#23712yes—
236C23×C3#23912yes—
237C23×C3C23×D311yescharacteristic
238C22×D3—32no—
239C22×D3—61no—
240C22×D3—62no—
241C22×D3—61no—
242C22×D3—62no—
243C2×C3×C4—22no—
244C2×C3×C4—22no—
245C2×C3×C4—22no—
246C2×C3×C4—22no—
247C2×C3×C4—22no—
248C2×C3×C4—22no—
249C2×C3×C4—22no—
250C2×C3×C4—22no—
251C2×C3×C4—44no—
252C2×C3×C4C2×C4×D312yes—
253C2×C3×C4C2×C4×D312yes—
254#67—68no—
255C2×Dic3—32no—
256C2×Dic3—32no—
257C2×Dic3—32no—
258C2×Dic3—34no—
259C2×Dic3—61no—
260C2×Dic3—62no—
261C2×Dic3—62no—
262C2×Dic3—62no—
263C2×Dic3—61no—
264C2×Dic3—62no—
265C2×Dic3—62no—
266C2×Dic3—62no—
267C2×Dic3—62no—
268C2×Dic3—128no—
269C4×D3—124no—
270C2×C9—24no—
271C2×C9C2×#11711yescharacteristic
272C2×C9C4×#4111yescharacteristic
273C2×C9#51811yescharacteristic
274C2×C9#55112yes—
275C2×C9#55312yes—
276D9—42no—
277C24—91no—
278C24C22×D911yescharacteristic
279C2×D4—94no—
280C2×D4—182no—
281C2×D4—182no—
282C22×C4—42no—
283C22×C4—91no—
284C22×C4—92no—
285C22×C4—91no—
286C22×C4—91no—
287C22×C4—94no—
288C22×C4—92no—
289C22×C4—184no—
290C22×C4—184no—
291C22×C4—362no—
292C22×C4—362no—
293C22×C4C4×D914yes—
294C22×C4C22×D912yes—
295C22×C4C22×D912yes—
296C22×C4C22×D911yescharacteristic
297C22×C4C22×D911yescharacteristic
298C4⋊C4—42no—
299C4⋊C4—94no—
300C22⋊C4—24no—
301C22⋊C4—94no—
302C22⋊C4—94no—
303C22⋊C4—184no—
304C22⋊C4—362no—
305C42—94no—
306C42—184no—
307C42—362no—
308C22×C3—24no—
309C22×C3—22no—
310C22×C3—22no—
311C22×C3—24no—
312C22×C3#89214yes—
313C22×C3C22×C4×D311yescharacteristic
314C22×C3C2×#23711yescharacteristic
315C22×C3#100412yes—
316C22×C3C2×#23911yescharacteristic
317C22×C3D3×#4112yes—
318C2×D3—62no—
319C2×D3—62no—
320C2×D3—62no—
321C2×D3—122no—
322C2×D3—122no—
323C3×C4—22no—
324C3×C4—22no—
325C3×C4—42no—
326C3×C4—42no—
327Dic3—64no—
328Dic3—62no—
329Dic3—62no—
330Dic3—62no—
331Dic3—122no—
332C9#235311yescharacteristic, complemented, Sylow
333C23—22no—
334C23—22no—
335C23—92no—
336C23—181no—
337C23—182no—
338C23—181no—
339C23—182no—
340C23C2×C4×D912yes—
341C23#369912yes—
342C23#370112yes—
343C23C23×D911yescharacteristic
344D4—188no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—44no—
354C2×C4—92no—
355C2×C4—92no—
356C2×C4—92no—
357C2×C4—94no—
358C2×C4—181no—
359C2×C4—182no—
360C2×C4—182no—
361C2×C4—182no—
362C2×C4—181no—
363C2×C4—182no—
364C2×C4—182no—
365C2×C4—182no—
366C2×C4—182no—
367C2×C4—364no—
368C2×C4—368no—
369C2×C4C2×C4×D912yes—
370C2×C4C2×C4×D912yes—
371C2×C3—24no—
372C2×C3#548611yescharacteristic
373C2×C3C2×#89211yescharacteristic
374C2×C3#552211yescharacteristic
375C2×C3#560112yes—
376C2×C3#563712yes—
377D3—122no—
378C22—24no—
379C22—24no—
380C22—22no—
381C22—22no—
382C22—182no—
383C22—182no—
384C22—182no—
385C22—362no—
386C22—362no—
387C22#6345414yes—
388C22C22×C4×D911yescharacteristic
389C22C2×#369911yescharacteristic
390C22#6371012yes—
391C22C2×#370111yescharacteristic
392C22#41×D912yes—
393C4—22no—
394C4—22no—
395C4—42no—
396C4—42no—
397C4—184no—
398C4—182no—
399C4—182no—
400C4—182no—
401C4—362no—
402C3#7388411yescharacteristic
403C2—24no—
404C2—362no—
405C2#1058958811yescharacteristic
406C2C2×#6345411yescharacteristic
407C2#1058962411yescharacteristic
408C2#1058970312yes—
409C2#1058973912yes—
subgroupG/H
centerC23C23×D9
commutatorC22×C9C23×C4
Frattini, socleC23×C3C23×D3
FittingC9×#380C2
prime radicalC22×#611C22
cosocleC23×C9C24
hypercenter#380D9
hypocenterC9#2353
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
2. C9×#380C2semidirect
3. C2×C9⋊#95C2semidirect
4. #10588670C2semidirect
5. #10588658C2semidirect
7. C22⋊C4×Dic9C2semidirect
8. #10588346C2semidirect
9. #10588344C2semidirect
10. #10588331C2semidirect
11. #10588328C2semidirect
20. C4×#611C4semidirect
68. C2×C4×D9C2×C4semidirect
74. (C2×D9)⋊C4C2×C4semidirect
75. Dic9⋊C4C2×C4semidirect
78. C4×Dic9C2×C4semidirect
148. #380D9semidirect
332. C9#2353semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6112
C9×#3802
C2×C9⋊#952
#105886702
#105886582
#105886382
C22⋊C4×Dic92
#105883462
#105883442
#105883312
#105883282
#738843