Finite Group Databasebeta

← #11801811

Subgroups — #11801811

Order 1152.

984 conjugacy classes of subgroups.

The subgroup lattice has 399 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63434C211yesmaximal, characteristic
2C2×#63434C211yesmaximal, characteristic
3C2×C42×D9C211yesmaximal, characteristic
4C4×C9×C4⋊C4C211yesmaximal, characteristic, complemented
5#10588669C212yesmaximal
6#10588656C212yesmaximal, complemented
7C4×C4⋊Dic9C211yesmaximal, characteristic, complemented
8C4×Dic9⋊C4C211yesmaximal, characteristic, complemented
9C4×Dic9⋊C4C211yesmaximal, characteristic, complemented
10#10588348C212yesmaximal
11#10588327C212yesmaximal, complemented
12#73755—31nomaximal
13C22×C4×D9C2212yes—
14C22×C4×D9C2211yescharacteristic
15C2×C9×C4⋊C4C2212yes—
16C2×C42×C9C2211yescharacteristic
17C2×C42×C9C2211yescharacteristic
18C2×C42×C9C2211yescharacteristic
19C2×(C2×D9)⋊C4C2212yes—
20C2×(C2×D9)⋊C4C2211yescharacteristic
21C2×(C2×D9)⋊C4C2211yescharacteristic
22C2×C4⋊Dic9C2212yes—
23C2×Dic9⋊C4C2212yes—
24C2×Dic9⋊C4C2212yes—
25C2×Dic9⋊C4C2212yes—
26C2×Dic9⋊C4C2211yescharacteristic
27C2×Dic9⋊C4C2211yescharacteristic
28C2×C4×Dic9C2212yes—
29C2×C4×Dic9C2211yescharacteristic
30C2×C4×Dic9C2211yescharacteristic
31C2×C4×Dic9C2211yescharacteristic
32#63434—24no—
33#63434C418yescomplemented
34C42×D9—24no—
35C9×#95C2212yes—
36C9⋊#95C2212yes—
37C9⋊#95C2212yes—
38C9⋊#95C2212yes—
39C2×#872—31no—
40C2×#872—31no—
41C2×C42×D3—31no—
42C3×C4×C4⋊C4D311yescharacteristic
43#4989—32no—
44#4976—32no—
45C4×C4⋊Dic3—31no—
46C4×Dic3⋊C4—31no—
47C4×Dic3⋊C4—31no—
48#4668—32no—
49#4647—32no—
50C23×D9C2311yescharacteristic
51C22×C4×C9C2312yes—
52C22×C4×C9C2311yescharacteristic
53C22×C4×C9C2311yescharacteristic
54C22×C4×C9C2312yes—
55C22×C4×C9C2311yescharacteristic
56C22×Dic9C2312yes—
57C22×Dic9C2311yescharacteristic
58C22×Dic9C2311yescharacteristic
59C22×Dic9C2312yes—
60C22×Dic9C2311yescharacteristic
61C2×C4×D9—24no—
62C2×C4×D9—24no—
63C2×C4×D9—24no—
64C2×C4×D9C2×C414yes—
65C2×C4×D9D414yes—
66C2×C4×D9Q814yes—
67C9×C4⋊C4—24no—
68C42×C9—22no—
69C42×C9—22no—
70C42×C9C2×C414yescomplemented
71(C2×D9)⋊C4—24no—
72(C2×D9)⋊C4C2×C414yes—
73(C2×D9)⋊C4C2×C414yes—
74C4⋊Dic9—24no—
75Dic9⋊C4—24no—
76Dic9⋊C4—24no—
77Dic9⋊C4—24no—
78Dic9⋊C4C2×C414yescomplemented
79Dic9⋊C4C2×C414yescomplemented
80C4×Dic9—22no—
81C4×Dic9—22no—
82C4×Dic9—24no—
83C4×Dic9C2×C414yescomplemented
84#2296—91noSylow
85C22×C4×D3—31no—
86C22×C4×D3—32no—
87C2×C3×C4⋊C4C2×D312yes—
88C2×C3×C42C2×D311yescharacteristic
89C2×C3×C42C2×D311yescharacteristic
90C2×C3×C42C2×D311yescharacteristic
91C2×(C2×D3)⋊C4—31no—
92C2×(C2×D3)⋊C4—31no—
93C2×(C2×D3)⋊C4—32no—
94C2×C4⋊Dic3—32no—
95C2×Dic3⋊C4—31no—
96C2×Dic3⋊C4—31no—
97C2×Dic3⋊C4—32no—
98C2×Dic3⋊C4—32no—
99C2×Dic3⋊C4—32no—
100C2×C4×Dic3—31no—
101C2×C4×Dic3—32no—
102C2×C4×Dic3—31no—
103C2×C4×Dic3—31no—
104#872—38no—
105#872—64no—
106C42×D3—64no—
107C3×#95C2×D312yes—
108C3⋊#95—32no—
109C3⋊#95—32no—
110C3⋊#95—32no—
111C23×C9C2411yescharacteristic
112C22×D9—22no—
113C22×D9—22no—
114C22×D9C22×C412yes—
115C22×D9C2×D412yes—
116C22×D9C2×Q812yes—
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—22no—
124C2×C4×C9C22×C412yes—
125C2×C4×C9C22×C412yes—
126C2×C4×C9C22×C412yes—
127C2×C4×C9C2×D412yes—
128C2×C4×C9C2×Q812yes—
129C2×C4×C9#4114yes—
130C2×Dic9—22no—
131C2×Dic9—22no—
132C2×Dic9—22no—
133C2×Dic9—22no—
134C2×Dic9—22no—
135C2×Dic9—22no—
136C2×Dic9—22no—
137C2×Dic9C22×C412yes—
138C2×Dic9C22×C412yes—
139C2×Dic9C22×C412yes—
140C2×Dic9C2×D412yes—
141C2×Dic9C2×Q812yes—
142C2×Dic9#4114yes—
143C4×D9—216no—
144C4×D9C4⋊C4116yescomplemented
145C2×#117—91no—
146C2×#117—91no—
147C22×C42—91no—
148#389—92no—
149#389—92no—
150#385—92no—
151#385—92no—
152C4×C4⋊C4—91no—
153C4×C4⋊C4—91no—
154C4×C4⋊C4—91no—
155C4×C4⋊C4D911yescharacteristic, complemented
156C23×D3—31no—
157C22×C3×C4C22×D312yes—
158C22×C3×C4C22×D311yescharacteristic
159C22×C3×C4C22×D311yescharacteristic
160C22×C3×C4C22×D312yes—
161C22×C3×C4C22×D311yescharacteristic
162C22×Dic3—31no—
163C22×Dic3—32no—
164C22×Dic3—31no—
165C22×Dic3—31no—
166C22×Dic3—32no—
167C2×C4×D3—34no—
168C2×C4×D3—34no—
169C2×C4×D3—34no—
170C2×C4×D3—64no—
171C2×C4×D3—64no—
172C2×C4×D3—64no—
173C3×C4⋊C4—24no—
174C3×C42—22no—
175C3×C42—22no—
176C3×C42C4×D314yes—
177(C2×D3)⋊C4—34no—
178(C2×D3)⋊C4—34no—
179(C2×D3)⋊C4—64no—
180C4⋊Dic3—64no—
181Dic3⋊C4—34no—
182Dic3⋊C4—34no—
183Dic3⋊C4—64no—
184Dic3⋊C4—64no—
185Dic3⋊C4—64no—
186C4×Dic3—34no—
187C4×Dic3—64no—
188C4×Dic3—62no—
189C4×Dic3—62no—
190C22×C9C23×C411yescharacteristic
191C22×C9C22×D411yescharacteristic
192C22×C9C22×Q811yescharacteristic
193C22×C9C2×#4112yes—
194C22×C9C2×#4112yes—
195C2×D9—22no—
196C2×D9—22no—
197C2×D9—24no—
198C2×D9—24no—
199C2×D9C2×C4⋊C414yes—
200C4×C9—22no—
201C4×C9—22no—
202C4×C9—24no—
203C4×C9—42no—
204C4×C9C2×C4⋊C414yes—
205Dic9—22no—
206Dic9—22no—
207Dic9—24no—
208Dic9—42no—
209Dic9C2×C4⋊C414yes—
210C23×C4—91no—
211C23×C4—92no—
212#117—98no—
213#117—184no—
214C2×C4⋊C4—91no—
215C2×C4⋊C4—91no—
216C2×C4⋊C4—92no—
217C2×C4⋊C4—92no—
218C2×C4⋊C4—92no—
219C2×C4⋊C4—92no—
220C2×C4⋊C4C2×D912yes—
221C2×C22⋊C4—91no—
222C2×C22⋊C4—91no—
223C2×C22⋊C4—92no—
224C2×C42—91no—
225C2×C42—92no—
226C2×C42—91no—
227C2×C42—91no—
228C2×C42—184no—
229C2×C42C2×D911yescharacteristic
230C2×C42C2×D911yescharacteristic
231C2×C42C2×D911yescharacteristic
232#95—92no—
233#95—92no—
234#95—92no—
235#95C2×D912yes—
236C23×C3C23×D311yescharacteristic
237C22×D3—32no—
238C22×D3—32no—
239C22×D3—32no—
240C22×D3—62no—
241C22×D3—62no—
242C2×C3×C4—22no—
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×C4C2×C4×D312yes—
250C2×C3×C4C2×C4×D312yes—
251C2×C3×C4C2×C4×D312yes—
252C2×C3×C4#23514yes—
253C2×C3×C4D3×D412yes—
254C2×C3×C4D3×Q812yes—
255C2×Dic3—32no—
256C2×Dic3—32no—
257C2×Dic3—32no—
258C2×Dic3—32no—
259C2×Dic3—32no—
260C2×Dic3—34no—
261C2×Dic3—62no—
262C2×Dic3—62no—
263C2×Dic3—62no—
264C2×Dic3—62no—
265C2×Dic3—62no—
266C2×Dic3—62no—
267C2×Dic3—62no—
268C4×D3—316no—
269C4×D3—616no—
270C2×C9C22×C4⋊C411yescharacteristic
271C2×C9C4×#4111yescharacteristic
272C2×C9C4×#4111yescharacteristic
273C2×C9#52512yes—
274C2×C9#53312yes—
275D9—24no—
276C24—91no—
277C22×C4—91no—
278C22×C4—94no—
279C22×C4—94no—
280C22×C4—94no—
281C22×C4—92no—
282C22×C4—91no—
283C22×C4—91no—
284C22×C4—92no—
285C22×C4—184no—
286C22×C4—184no—
287C22×C4—184no—
288C22×C4C22×D912yes—
289C22×C4C22×D911yescharacteristic
290C22×C4C22×D911yescharacteristic
291C22×C4C22×D912yes—
292C22×C4C22×D911yescharacteristic
293C4⋊C4—24no—
294C4⋊C4—94no—
295C4⋊C4—94no—
296C4⋊C4—184no—
297C4⋊C4—184no—
298C4⋊C4—184no—
299C4⋊C4—184no—
300C22⋊C4—94no—
301C22⋊C4—94no—
302C22⋊C4—184no—
303C42—22no—
304C42—22no—
305C42—94no—
306C42—184no—
307C42—182no—
308C42—182no—
309C42C4×D914yescomplemented
310C22×C3C22×C4×D311yescharacteristic
311C22×C3C2×#23512yes—
312C22×C3C2×D3×D411yescharacteristic
313C22×C3C2×D3×Q811yescharacteristic
314C22×C3D3×#4112yes—
315C2×D3—34no—
316C2×D3—62no—
317C2×D3—62no—
318C2×D3—64no—
319C2×D3—64no—
320C3×C4—22no—
321C3×C4—22no—
322C3×C4—24no—
323C3×C4—42no—
324C3×C4D3×C4⋊C414yes—
325Dic3—34no—
326Dic3—62no—
327Dic3—62no—
328Dic3—64no—
329Dic3—122no—
330C9#229611yescharacteristic, complemented, Sylow
331C23—92no—
332C23—92no—
333C23—92no—
334C23—182no—
335C23—182no—
336C23C23×D911yescharacteristic
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—92no—
345C2×C4—92no—
346C2×C4—92no—
347C2×C4—916no—
348C2×C4—92no—
349C2×C4—92no—
350C2×C4—94no—
351C2×C4—1816no—
352C2×C4—182no—
353C2×C4—182no—
354C2×C4—182no—
355C2×C4—182no—
356C2×C4—182no—
357C2×C4—182no—
358C2×C4—182no—
359C2×C4C2×C4×D912yes—
360C2×C4C2×C4×D912yes—
361C2×C4C2×C4×D912yes—
362C2×C4#369714yes—
363C2×C4D4×D912yes—
364C2×C4Q8×D912yes—
365C2×C3C4×#23511yescharacteristic
366C2×C3C2×D3×C4⋊C411yescharacteristic
367C2×C3#552211yescharacteristic
368C2×C3#554712yes—
369C2×C3#557812yes—
370D3—64no—
371C22—94no—
372C22—182no—
373C22—182no—
374C22—184no—
375C22—184no—
376C22C22×C4×D911yescharacteristic
377C22C2×#369712yes—
378C22C2×D4×D911yescharacteristic
379C22C2×Q8×D911yescharacteristic
380C22#41×D912yes—
381C4—22no—
382C4—22no—
383C4—24no—
384C4—42no—
385C4—94no—
386C4—182no—
387C4—182no—
388C4—184no—
389C4—362no—
390C4C4⋊C4×D914yes—
391C3#7375511yescharacteristic
392C2—184no—
393C2C4×#369711yescharacteristic
394C2C2×C4⋊C4×D911yescharacteristic
395C2#1058962411yescharacteristic
396C2#1058964912yes—
397C2#1058968012yes—
subgroupG/H
centerC22×C4C22×D9
commutatorC22×C9C23×C4
Frattini, socleC23×C3C23×D3
FittingC4×C9×C4⋊C4C2
prime radicalC23×D9C23
cosocleC23×C9C24
hypercenterC4×C4⋊C4D9
hypocenterC9#2296
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. C4×C9×C4⋊C4C2semidirect
6. #10588656C2semidirect
7. C4×C4⋊Dic9C2semidirect
8. C4×Dic9⋊C4C2semidirect
9. C4×Dic9⋊C4C2semidirect
11. #10588327C2semidirect
33. #63434C4semidirect
70. C42×C9C2×C4semidirect
78. Dic9⋊C4C2×C4semidirect
79. Dic9⋊C4C2×C4semidirect
83. C4×Dic9C2×C4semidirect
144. C4×D9C4⋊C4semidirect
155. C4×C4⋊C4D9semidirect
309. C42C4×D9semidirect
330. C9#2296semidirect

Maximal subgroups

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

subgroupindex
C2×#634342
C2×C42×D92
C4×C9×C4⋊C42
#105886692
#105886562
C4×C4⋊Dic92
C4×Dic9⋊C42
#105883482
#105883272
#737553