Finite Group Databasebeta

← #11805342

Subgroups — #11805342

Order 1152.

756 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×#63454C211yesmaximal, characteristic
2C4×C9×C4⋊C4C211yesmaximal, characteristic, complemented
3#10588667C211yesmaximal, characteristic
4C4⋊C4×Dic9C211yesmaximal, characteristic, complemented
5#10588652C211yesmaximal, characteristic, complemented
6#10588620C212yesmaximal
7C4×(C2×D9)⋊C4C211yesmaximal, characteristic
8C4×Dic9⋊C4C212yesmaximal, complemented
9#10588608C211yesmaximal, characteristic, complemented
10#10588349C212yesmaximal
11#10588331C212yesmaximal, complemented
12#73634—31nomaximal
13C22×C4×D9C2211yescharacteristic
14C2×C9×C4⋊C4C2211yescharacteristic
15C2×C9×C4⋊C4C2211yescharacteristic
16C2×C42×C9C2211yescharacteristic
17C2×C42×C9C2212yes—
18C2×(C2×D9)⋊C4C2211yescharacteristic
19C2×(C2×D9)⋊C4C2211yescharacteristic
20C2×(C2×D9)⋊C4C2212yes—
21C2×(C2×D9)⋊C4C2212yes—
22C2×C4⋊Dic9C2211yescharacteristic
23C2×C4⋊Dic9C2211yescharacteristic
24C2×Dic9⋊C4C2212yes—
25C2×Dic9⋊C4C2212yes—
26C2×C4×Dic9C2211yescharacteristic
27C2×C4×Dic9C2212yes—
28C2×C4×Dic9C2212yes—
29#63454C418yescomplemented
30C9×#95C2212yes—
31C9⋊#95C2211yescharacteristic
32C9⋊#95C2212yes—
33C9⋊#95C2212yes—
34C9⋊#95C2212yes—
35C9⋊#95C2212yes—
36C9⋊#95C2211yescharacteristic
37C2×#892—31no—
38C3×C4×C4⋊C4D311yescharacteristic
39#4987—31no—
40Dic3×C4⋊C4—31no—
41#4972—31no—
42#4940—32no—
43C4×(C2×D3)⋊C4—31no—
44C4×Dic3⋊C4—32no—
45#4928—31no—
46#4669—32no—
47#4651—32no—
48C23×D9C2311yescharacteristic
49C22×C4×C9C2312yes—
50C22×C4×C9C2311yescharacteristic
51C22×C4×C9C2312yes—
52C22×C4×C9C2311yescharacteristic
53C22×C4×C9C2311yescharacteristic
54C22×Dic9C2311yescharacteristic
55C22×Dic9C2312yes—
56C22×Dic9C2312yes—
57C22×Dic9C2311yescharacteristic
58C22×Dic9C2311yescharacteristic
59C2×C4×D9—22no—
60C2×C4×D9—22no—
61C2×C4×D9C2×C414yes—
62C9×C4⋊C4—22no—
63C9×C4⋊C4C2×C414yes—
64C42×C9—22no—
65C42×C9—42no—
66(C2×D9)⋊C4—22no—
67(C2×D9)⋊C4—22no—
68(C2×D9)⋊C4—42no—
69(C2×D9)⋊C4C2×C418yes—
70C4⋊Dic9—22no—
71C4⋊Dic9C2×C414yes—
72Dic9⋊C4—24no—
73Dic9⋊C4—24no—
74C4×Dic9—22no—
75C4×Dic9—42no—
76C4×Dic9C2×C418yes—
77#2347—91noSylow
78C22×C4×D3—31no—
79C2×C3×C4⋊C4C2×D311yescharacteristic
80C2×C3×C4⋊C4C2×D311yescharacteristic
81C2×C3×C42C2×D311yescharacteristic
82C2×C3×C42C2×D312yes—
83C2×(C2×D3)⋊C4—32no—
84C2×(C2×D3)⋊C4—31no—
85C2×(C2×D3)⋊C4—31no—
86C2×(C2×D3)⋊C4—32no—
87C2×C4⋊Dic3—31no—
88C2×C4⋊Dic3—31no—
89C2×Dic3⋊C4—32no—
90C2×Dic3⋊C4—32no—
91C2×C4×Dic3—32no—
92C2×C4×Dic3—31no—
93C2×C4×Dic3—32no—
94#892—38no—
95C3×#95C2×D312yes—
96C3⋊#95—31no—
97C3⋊#95—32no—
98C3⋊#95—32no—
99C3⋊#95—32no—
100C3⋊#95—32no—
101C3⋊#95—31no—
102C23×C9C2411yescharacteristic
103C22×D9—21no—
104C22×D9—21no—
105C22×D9—21no—
106C22×D9—21no—
107C22×D9—21no—
108C22×D9—21no—
109C22×D9C22×C412yes—
110C2×C4×C9—21no—
111C2×C4×C9—22no—
112C2×C4×C9—21no—
113C2×C4×C9—22no—
114C2×C4×C9—22no—
115C2×C4×C9—21no—
116C2×C4×C9—21no—
117C2×C4×C9—22no—
118C2×C4×C9—22no—
119C2×C4×C9—21no—
120C2×C4×C9C22×C414yes—
121C2×C4×C9C22×C412yes—
122C2×C4×C9#4112yes—
123C2×C4×C9#4112yes—
124C2×C4×C9#4112yes—
125C2×Dic9—21no—
126C2×Dic9—22no—
127C2×Dic9—22no—
128C2×Dic9—21no—
129C2×Dic9—21no—
130C2×Dic9—21no—
131C2×Dic9—21no—
132C2×Dic9—22no—
133C2×Dic9—22no—
134C2×Dic9—21no—
135C2×Dic9—22no—
136C2×Dic9—21no—
137C2×Dic9C22×C412yes—
138C2×Dic9C22×C414yes—
139C2×Dic9#4112yes—
140C4×D9—28no—
141C2×#117—91no—
142#389—91no—
143#389—91no—
144#388—92no—
145#388—92no—
146#383—92no—
147#380—91no—
148C4×C4⋊C4—91no—
149C4×C4⋊C4—92no—
150C4×C4⋊C4D911yescharacteristic, complemented
151C4×C22⋊C4—91no—
152C23×D3—31no—
153C22×C3×C4C22×D311yescharacteristic
154C22×C3×C4C22×D312yes—
155C22×C3×C4C22×D312yes—
156C22×C3×C4C22×D311yescharacteristic
157C22×C3×C4C22×D311yescharacteristic
158C22×Dic3—31no—
159C22×Dic3—32no—
160C22×Dic3—31no—
161C22×Dic3—31no—
162C22×Dic3—32no—
163C2×C4×D3—34no—
164C2×C4×D3—62no—
165C2×C4×D3—62no—
166C3×C4⋊C4—22no—
167C3×C4⋊C4C4×D314yes—
168C3×C42—22no—
169C3×C42—42no—
170(C2×D3)⋊C4—38no—
171(C2×D3)⋊C4—62no—
172(C2×D3)⋊C4—62no—
173(C2×D3)⋊C4—122no—
174C4⋊Dic3—34no—
175C4⋊Dic3—62no—
176Dic3⋊C4—64no—
177Dic3⋊C4—64no—
178C4×Dic3—38no—
179C4×Dic3—62no—
180C4×Dic3—122no—
181C22×C9C23×C411yescharacteristic
182C22×C9C2×#4111yescharacteristic
183C22×C9C2×#4111yescharacteristic
184C22×C9C2×#4111yescharacteristic
185C22×C9C2×#4111yescharacteristic
186C22×C9H(5,𝔽2)11yescharacteristic
187C22×C92−1+411yescharacteristic
188C2×D9—22no—
189C2×D9—22no—
190C2×D9—22no—
191C2×D9—41no—
192C2×D9—41no—
193C2×D9—41no—
194C2×D9—41no—
195C4×C9—24no—
196C4×C9—22no—
197C4×C9—42no—
198C4×C9—41no—
199C4×C9#11714yes—
200Dic9—22no—
201Dic9—24no—
202Dic9—22no—
203Dic9—42no—
204Dic9—41no—
205C23×C4—91no—
206#117—98no—
207C2×C4⋊C4—91no—
208C2×C4⋊C4—91no—
209C2×C4⋊C4—92no—
210C2×C4⋊C4—92no—
211C2×C4⋊C4C2×D911yescharacteristic
212C2×C4⋊C4C2×D911yescharacteristic
213C2×C22⋊C4—92no—
214C2×C22⋊C4—91no—
215C2×C22⋊C4—91no—
216C2×C22⋊C4—92no—
217C2×C42—92no—
218C2×C42—91no—
219C2×C42—92no—
220C2×C42C2×D911yescharacteristic
221C2×C42C2×D912yes—
222#95—91no—
223#95—91no—
224#95—92no—
225#95—92no—
226#95—92no—
227#95—92no—
228#95C2×D912yes—
229C23×C3C23×D311yescharacteristic
230C22×D3—32no—
231C22×D3—61no—
232C22×D3—61no—
233C22×D3—61no—
234C22×D3—61no—
235C22×D3—61no—
236C22×D3—61no—
237C2×C3×C4—21no—
238C2×C3×C4—22no—
239C2×C3×C4—21no—
240C2×C3×C4—22no—
241C2×C3×C4—21no—
242C2×C3×C4—22no—
243C2×C3×C4—22no—
244C2×C3×C4—22no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4C2×C4×D314yes—
248C2×C3×C4C2×C4×D312yes—
249C2×C3×C4#23512yes—
250C2×C3×C4#23512yes—
251C2×C3×C4#23912yes—
252C2×Dic3—32no—
253C2×Dic3—34no—
254C2×Dic3—32no—
255C2×Dic3—61no—
256C2×Dic3—61no—
257C2×Dic3—61no—
258C2×Dic3—61no—
259C2×Dic3—62no—
260C2×Dic3—62no—
261C2×Dic3—61no—
262C2×Dic3—62no—
263C2×Dic3—62no—
264C2×Dic3—62no—
265C2×Dic3—61no—
266C2×Dic3—61no—
267C4×D3—68no—
268C2×C9C2×#11711yescharacteristic
269C2×C9C4×#4111yescharacteristic
270C2×C9#52011yescharacteristic
271C2×C9#55311yescharacteristic
272C2×C9#55311yescharacteristic
273C2×C9#55611yescharacteristic
274C2×C9#55611yescharacteristic
275D9—42no—
276C24—91no—
277C22×C4—91no—
278C22×C4—92no—
279C22×C4—91no—
280C22×C4—94no—
281C22×C4—91no—
282C22×C4—92no—
283C22×C4—182no—
284C22×C4—182no—
285C22×C4C22×D911yescharacteristic
286C22×C4C22×D912yes—
287C22×C4C22×D912yes—
288C22×C4C22×D911yescharacteristic
289C22×C4C22×D911yescharacteristic
290C4⋊C4—22no—
291C4⋊C4—94no—
292C4⋊C4—184no—
293C4⋊C4—182no—
294C4⋊C4—184no—
295C4⋊C4C4×D914yes—
296C22⋊C4—98no—
297C22⋊C4—182no—
298C22⋊C4—182no—
299C22⋊C4—362no—
300C42—22no—
301C42—42no—
302C42—98no—
303C42—182no—
304C42—362no—
305C22×C3C22×C4×D311yescharacteristic
306C22×C3C2×#23511yescharacteristic
307C22×C3C2×#23511yescharacteristic
308C22×C3#100411yescharacteristic
309C22×C3C2×#23911yescharacteristic
310C22×C3D3×#4111yescharacteristic
311C22×C3#101011yescharacteristic
312C2×D3—62no—
313C2×D3—62no—
314C2×D3—62no—
315C2×D3—121no—
316C2×D3—121no—
317C2×D3—121no—
318C2×D3—121no—
319C3×C4—22no—
320C3×C4—24no—
321C3×C4—41no—
322C3×C4—42no—
323C3×C4#87214yes—
324Dic3—62no—
325Dic3—62no—
326Dic3—64no—
327Dic3—122no—
328Dic3—121no—
329C9#234711yescharacteristic, complemented, Sylow
330C23—92no—
331C23—181no—
332C23—181no—
333C23—181no—
334C23—181no—
335C23—181no—
336C23—181no—
337C23C23×D911yescharacteristic
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—21no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—21no—
346C2×C4—22no—
347C2×C4—21no—
348C2×C4—92no—
349C2×C4—94no—
350C2×C4—92no—
351C2×C4—181no—
352C2×C4—181no—
353C2×C4—181no—
354C2×C4—181no—
355C2×C4—182no—
356C2×C4—182no—
357C2×C4—188no—
358C2×C4—181no—
359C2×C4—182no—
360C2×C4—182no—
361C2×C4—181no—
362C2×C4—182no—
363C2×C4—181no—
364C2×C4C2×C4×D914yes—
365C2×C4C2×C4×D912yes—
366C2×C4#369712yes—
367C2×C4#369712yes—
368C2×C4#370112yes—
369C2×C3C2×#87211yescharacteristic
370C2×C3#551411yescharacteristic
371C2×C3#553311yescharacteristic
372C2×C3#554611yescharacteristic
373C2×C3#555811yescharacteristic
374C2×C3C4×#23911yescharacteristic
375C2×C3#558411yescharacteristic
376D3—122no—
377C22—182no—
378C22—182no—
379C22—182no—
380C22—361no—
381C22—361no—
382C22—361no—
383C22—361no—
384C22C22×C4×D911yescharacteristic
385C22C2×#369711yescharacteristic
386C22C2×#369711yescharacteristic
387C22#6371011yescharacteristic
388C22C2×#370111yescharacteristic
389C22#41×D911yescharacteristic
390C22#6371611yescharacteristic
391C4—22no—
392C4—24no—
393C4—41no—
394C4—42no—
395C4—182no—
396C4—182no—
397C4—184no—
398C4—362no—
399C4—361no—
400C4#6343414yes—
401C3#7363411yescharacteristic
402C2—362no—
403C2C2×#6343411yescharacteristic
404C2#1058961611yescharacteristic
405C2#1058963511yescharacteristic
406C2#1058964811yescharacteristic
407C2#1058966011yescharacteristic
408C2C4×#370111yescharacteristic
409C2#1058968611yescharacteristic
subgroupG/H
centerC23C23×D9
commutatorC22×C9C23×C4
Frattini, socleC23×C3C23×D3
FittingC4×C9×C4⋊C4C2
prime radicalC23×D9C23
cosocleC23×C9C24
hypercenterC4×C4⋊C4D9
hypocenterC9#2347
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C4×C9×C4⋊C4C2semidirect
4. C4⋊C4×Dic9C2semidirect
5. #10588652C2semidirect
8. C4×Dic9⋊C4C2semidirect
9. #10588608C2semidirect
11. #10588331C2semidirect
29. #63454C4semidirect
150. C4×C4⋊C4D9semidirect
329. C9#2347semidirect

Maximal subgroups

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

subgroupindex
C2×#634542
C4×C9×C4⋊C42
#105886672
C4⋊C4×Dic92
#105886522
#105886202
C4×(C2×D9)⋊C42
C4×Dic9⋊C42
#105886082
#105883492
#105883312
#736343