Finite Group Databasebeta

← #11858536

Subgroups — #11858536

Order 1152.

714 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63469C211yesmaximal, characteristic
2#10589625C211yesmaximal, characteristic
3#10589606C211yesmaximal, characteristic
4C9×#428C211yesmaximal, characteristic, complemented
5#10588805C211yesmaximal, characteristic, complemented
6#10588676C211yesmaximal, characteristic, complemented
7C2×#63367C211yesmaximal, characteristic, complemented
8#10588561C212yesmaximal, complemented
9#10588560C212yesmaximal, complemented
10#10588541C212yesmaximal, complemented
11D9×#106C212yesmaximal, complemented
12#79209—31nomaximal
13C2×#3697C2211yescharacteristic
14C2×C9×M16C2211yescharacteristic
15C9×#117C2211yescharacteristic
16C2×C9×C4⋊C4C2211yescharacteristic
17C4×#611—22no—
18#63488C2211yescharacteristic
19C2×C4⋊Dic9C2211yescharacteristic
20C22×C9⋊C8C2211yescharacteristic
21#63469C418yescomplemented
22C2×#3663C2212yes—
23C2×C8×D9C2212yes—
24#63455—21no—
25#63454C2212yes—
26#63454C2212yes—
27C4⋊C4×D9C2212yes—
28C4⋊C4×D9C2212yes—
29#63449—21no—
30#611⋊C4—22no—
31C4×D36—21no—
32C4×Dic18—21no—
33C9×#107C2212yes—
34C9×#106C2212yes—
35#63378C2212yes—
36#63377C2212yes—
37#63367C2211yescharacteristic
38#63367C2211yescharacteristic
39#63367C2212yes—
40#63367C2212yes—
41#63366C2211yescharacteristic
42#63366C2211yescharacteristic
43C2×#907—31no—
44#5523—31no—
45#5504—31no—
46C3×#428D311yescharacteristic
47#5121—31no—
48#4998—31no—
49C2×#808—31no—
50#4881—32no—
51#4880—32no—
52#4861—32no—
53D3×#106—32no—
54C22×C4×C9—21no—
55C22×C4×C9C2311yescharacteristic
56C2×#611D412yes—
57C22×Dic9—21no—
58#3697C2×C414yes—
59#3697Q814yes—
60C2×D36D411yescharacteristic
61C2×C4×D9—22no—
62C2×C4×D9—22no—
63C2×C4×D9C2312yes—
64C2×Dic18D411yescharacteristic
65C9×M16C2×C414yescomplemented
66C2×C8×C9C2312yes—
67C9×C4⋊C4—21no—
68C9×C4⋊C4C2312yes—
69C9×C4⋊C4C2311yescharacteristic
70C9×C4⋊C4C2311yescharacteristic
71C9×C22⋊C4—21no—
72C42×C9—21no—
73#3676—21no—
74(C2×D9)⋊C4—22no—
75(C2×D9)⋊C4—22no—
76C4⋊Dic9—21no—
77C4⋊Dic9C2311yescharacteristic
78C4⋊Dic9C2311yescharacteristic
79C4⋊Dic9C2312yes—
80Dic9⋊C4—22no—
81Dic9⋊C4—22no—
82C4×Dic9—21no—
83C4×Dic9—22no—
84C4×Dic9—22no—
85C2×C9⋊C8C2×C414yescomplemented
86C2×C9⋊C8C2311yescharacteristic
87C2×C9⋊C8C2311yescharacteristic
88#3663C2×C418yescomplemented
89C8×D9C2×C418yescomplemented
90#2912—91noSylow
91C2×#235—31no—
92C2×C3×M16C2×D311yescharacteristic
93C3×#117C2×D311yescharacteristic
94C2×C3×C4⋊C4C2×D311yescharacteristic
95C4×#67—62no—
96#926—31no—
97C2×C4⋊Dic3—31no—
98C22×C3⋊C8—31no—
99#907—38no—
100C2×ΓL(1,𝔽25)—32no—
101C2×D3×C8—32no—
102#893—61no—
103#892—32no—
104#892—32no—
105D3×C4⋊C4—32no—
106D3×C4⋊C4—32no—
107#887—61no—
108#67⋊C4—62no—
109C4×D12—61no—
110C4×Dic6—61no—
111C3×#107C2×D312yes—
112C3×#106C2×D312yes—
113#818—32no—
114#817—32no—
115#808—31no—
116#808—32no—
117#808—32no—
118#808—31no—
119#807—31no—
120#807—31no—
121C23×C9C2×D411yescharacteristic
122C22×D9C2×D412yes—
123C2×C4×C9—21no—
124C2×C4×C9—22no—
125C2×C4×C9—21no—
126C2×C4×C9—81no—
127C2×C4×C9C22×C412yes—
128C2×C4×C9C2×D411yescharacteristic
129C2×C4×C9C2×Q812yes—
130C2×C4×C9C2411yescharacteristic
131#611C4⋊C418yes—
132C2×Dic9—21no—
133C2×Dic9—21no—
134C2×Dic9—22no—
135C2×Dic9—81no—
136C2×Dic9C2×D412yes—
137D36C4⋊C414yes—
138C4×D9—82no—
139C4×D9—82no—
140C4×D9C22×C414yes—
141C4×D9C2×Q814yes—
142Dic18C4⋊C414yes—
143C8×C9C22×C414yes—
144C9⋊C8C22×C412yes—
145C9⋊C8C22×C412yes—
146C2×#131—91no—
147#520—91no—
148#520—91no—
149#428—91no—
150#428—92no—
151#428—92no—
152#428D911yescharacteristic, complemented
153#427—91no—
154#427—92no—
155C2×#106—91no—
156C2×#106—92no—
157C22×C3×C4—21no—
158C22×C3×C4C22×D311yescharacteristic
159C2×#67—32no—
160C22×Dic3—61no—
161#235—34no—
162#235—34no—
163C2×D12—31no—
164C2×C4×D3—32no—
165C2×C4×D3—62no—
166C2×C4×D3—62no—
167C2×Dic6—31no—
168C3×M16C4×D314yes—
169C2×C3×C8C22×D312yes—
170C3×C4⋊C4—21no—
171C3×C4⋊C4C22×D311yescharacteristic
172C3×C4⋊C4C22×D311yescharacteristic
173C3×C4⋊C4C22×D312yes—
174C3×C22⋊C4—21no—
175C3×C42—21no—
176#217—61no—
177(C2×D3)⋊C4—62no—
178(C2×D3)⋊C4—62no—
179C4⋊Dic3—31no—
180C4⋊Dic3—31no—
181C4⋊Dic3—32no—
182C4⋊Dic3—61no—
183Dic3⋊C4—62no—
184Dic3⋊C4—62no—
185C4×Dic3—62no—
186C4×Dic3—62no—
187C4×Dic3—61no—
188C2×C3⋊C8—34no—
189C2×C3⋊C8—31no—
190C2×C3⋊C8—31no—
191ΓL(1,𝔽25)—38no—
192D3×C8—38no—
193C22×C9—21no—
194C22×C9—21no—
195C22×C9C2×C4⋊C412yes—
196C22×C9C22×D411yescharacteristic
197C2×D9—22no—
198C2×D9—22no—
199C2×D9C2×C4⋊C414yes—
200C4×C9—41no—
201C4×C9—42no—
202C4×C9—41no—
203C4×C9C2×C4⋊C412yes—
204C4×C9C23×C411yescharacteristic
205C4×C9C22×Q811yescharacteristic
206Dic9—41no—
207Dic9—42no—
208Dic9—41no—
209Dic9C2×C4⋊C414yes—
210C2×#41—91no—
211#131—98no—
212C2×M16—92no—
213C2×M16C2×D911yescharacteristic
214C22×C8—91no—
215C22×C8—92no—
216C4×Q8—181no—
217C4×Q8—181no—
218C4×D4—181no—
219C4×D4—182no—
220C4×D4—181no—
221C4×D4—182no—
222#117—91no—
223#117—92no—
224#117—92no—
225#117C2×D911yescharacteristic
226C2×C4⋊C4—91no—
227C2×C4⋊C4—92no—
228C2×C4⋊C4—92no—
229C2×C4⋊C4C2×D911yescharacteristic
230#107—92no—
231#107—91no—
232#107—91no—
233#107C2×D912yes—
234#106—92no—
235#106—92no—
236#106—91no—
237#106—92no—
238#106—91no—
239#106C2×D912yes—
240C23×C3D3×D411yescharacteristic
241C22×D3—32no—
242C2×C3×C4—21no—
243C2×C3×C4—22no—
244C2×C3×C4—21no—
245C2×C3×C4—81no—
246C2×C3×C4C2×C4×D312yes—
247C2×C3×C4D3×D411yescharacteristic
248C2×C3×C4D3×Q812yes—
249C2×C3×C4C23×D311yescharacteristic
250#67—38no—
251C2×Dic3—32no—
252C2×Dic3—61no—
253C2×Dic3—61no—
254C2×Dic3—62no—
255C2×Dic3—241no—
256D12—34no—
257C4×D3—34no—
258C4×D3—34no—
259C4×D3—242no—
260C4×D3—242no—
261Dic6—34no—
262C3×C8C2×C4×D314yes—
263C3⋊C8—32no—
264C3⋊C8—32no—
265C2×C9—22no—
266C2×C9C22×C4⋊C411yescharacteristic
267C2×C9#57711yescharacteristic
268C2×C9#57711yescharacteristic
269D9—24no—
270#41—94no—
271#41—94no—
272C2×Q8—91no—
273C2×D4—92no—
274C2×D4—91no—
275C22×C4—21no—
276C22×C4—92no—
277C22×C4—182no—
278C22×C4—182no—
279C22×C4—181no—
280C22×C4C22×D911yescharacteristic
281M16—98no—
282M16C4×D914yescomplemented
283C2×C8—94no—
284C2×C8—91no—
285C2×C8—91no—
286C2×C8—98no—
287C2×C8C22×D912yes—
288C4⋊C4—21no—
289C4⋊C4—91no—
290C4⋊C4—92no—
291C4⋊C4—91no—
292C4⋊C4—182no—
293C4⋊C4—182no—
294C4⋊C4—181no—
295C4⋊C4C22×D912yes—
296C4⋊C4C22×D911yescharacteristic
297C4⋊C4C22×D911yescharacteristic
298C22⋊C4—21no—
299C22⋊C4—182no—
300C22⋊C4—182no—
301C22⋊C4—181no—
302C42—21no—
303C42—182no—
304C42—182no—
305C42—181no—
306C22×C3—21no—
307C22×C3—21no—
308C22×C3D3×C4⋊C412yes—
309C22×C3C2×D3×D411yescharacteristic
310C2×D3—34no—
311C2×D3—62no—
312C2×D3—62no—
313C3×C4—42no—
314C3×C4—41no—
315C3×C4—41no—
316C3×C4D3×C4⋊C412yes—
317C3×C4C22×C4×D311yescharacteristic
318C3×C4C2×D3×Q811yescharacteristic
319Dic3—34no—
320Dic3—121no—
321Dic3—122no—
322Dic3—121no—
323C9#291211yescharacteristic, complemented, Sylow
324C23—92no—
325C23D4×D911yescharacteristic
326Q8—94no—
327D4—98no—
328D4—94no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—22no—
332C2×C4—81no—
333C2×C4—92no—
334C2×C4—94no—
335C2×C4—94no—
336C2×C4—181no—
337C2×C4—181no—
338C2×C4—182no—
339C2×C4—722no—
340C2×C4—722no—
341C2×C4—721no—
342C2×C4C2×C4×D912yes—
343C2×C4D4×D911yescharacteristic
344C2×C4Q8×D912yes—
345C2×C4C23×D911yescharacteristic
346C8—92no—
347C8—92no—
348C8C2×C4×D914yes—
349C2×C3—22no—
350C2×C3C2×D3×C4⋊C411yescharacteristic
351C2×C3#577511yescharacteristic
352C2×C3#577811yescharacteristic
353D3—64no—
354C22—21no—
355C22—21no—
356C22—94no—
357C22—182no—
358C22—182no—
359C22C4⋊C4×D912yes—
360C22C2×D4×D911yescharacteristic
361C4—42no—
362C4—41no—
363C4—41no—
364C4—94no—
365C4—361no—
366C4—362no—
367C4—361no—
368C4C4⋊C4×D912yes—
369C4C22×C4×D911yescharacteristic
370C4C2×Q8×D911yescharacteristic
371C3#7920911yescharacteristic
372C2—22no—
373C2—184no—
374C2C2×C4⋊C4×D911yescharacteristic
375C2#1058987711yescharacteristic
376C2#1058988011yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutatorC4×C9C23×C4
FrattiniC2×C3×C4C23×D3
FittingC9×#428C2
socleC22×C3C2×D3×D4
prime radicalC2×#3697C22
cosocleC2×C4×C9C24
hypercenter#428D9
hypocenterC9#2912
LCSG ▷ C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
4. C9×#428C2semidirect
5. #10588805C2semidirect
6. #10588676C2semidirect
7. C2×#63367C2semidirect
8. #10588561C2semidirect
9. #10588560C2semidirect
10. #10588541C2semidirect
11. D9×#106C2semidirect
21. #63469C4semidirect
65. C9×M16C2×C4semidirect
85. C2×C9⋊C8C2×C4semidirect
88. #3663C2×C4semidirect
89. C8×D9C2×C4semidirect
152. #428D9semidirect
282. M16C4×D9semidirect
323. C9#2912semidirect

Maximal subgroups

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

subgroupindex
C2×#634692
#105896252
#105896062
C9×#4282
#105888052
#105886762
C2×#633672
#105885612
#105885602
#105885412
D9×#1062
#792093