Finite Group Databasebeta

← #11788561

Subgroups — #11788561

Order 1152.

498 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C9×#41C211yesmaximal, characteristic, complemented
2#10589925C211yesmaximal, characteristic
3#10588914C211yesmaximal, characteristic, complemented
4#10588686C211yesmaximal, characteristic, complemented
5C2×#63364C211yesmaximal, characteristic, complemented
6#10588209C211yesmaximal, characteristic, complemented
7#10588201C211yesmaximal, characteristic, complemented
8#71645—31nomaximal
9C2×C9×#41C2211yescharacteristic
10C2×#3697C2211yescharacteristic
11C4×Q8×C9—21no—
12C4×D4×C9—21no—
13C4×D4×C9—22no—
14C9×#117—21no—
15C9×#117C2211yescharacteristic
16C2×C42×C9—21no—
17C2×C42×C9C2211yescharacteristic
18#63513—22no—
19#63512C412yescomplemented
20#63511C412yescomplemented
21#63505—21no—
22#63495—21no—
23#63488C2211yescharacteristic
24C2×#3667C2211yescharacteristic
25C2×#3667C2211yescharacteristic
26#63396—22no—
27#63365—22no—
28#63364—21no—
29#63364—21no—
30C3×C4×#41D311yescharacteristic
31#5822—31no—
32#5236—31no—
33#5006—31no—
34C2×#805—31no—
35#4533—31no—
36#4523—31no—
37C9×#41—21no—
38C9×#41—21no—
39C9×#41C2×C412yes—
40C9×#41D412yes—
41C2×Q8×C9D411yescharacteristic
42C2×D4×C9—21no—
43C2×D4×C9D411yescharacteristic
44C22×C4×C9—21no—
45C22×C4×C9—22no—
46C22×C4×C9—21no—
47C22×C4×C9C2311yescharacteristic
48C2×#611—21no—
49#3697—21no—
50#3697—21no—
51#3697—21no—
52#3697—21no—
53C2×D36C2×C411yescharacteristic, complemented
54C2×C4×D9—21no—
55C2×Dic18C2×C411yescharacteristic, complemented
56C9×C4⋊C4—22no—
57C9×C4⋊C4—21no—
58C9×C22⋊C4—22no—
59C9×C22⋊C4D412yes—
60C42×C9—22no—
61C42×C9—21no—
62C42×C9—21no—
63C42×C9D411yescharacteristic
64C42×C9D411yescharacteristic
65#3676—21no—
66#3675—22no—
67#3674—22no—
68#3673—22no—
69#3672—22no—
70C4⋊Dic9—21no—
71C4×Dic9—21no—
72#3667—21no—
73#3667—21no—
74#3667—21no—
75#3667C2×C412yescomplemented
76C2×C9⋊C8—21no—
77C2×C9⋊C8—21no—
78#1906—91noSylow
79C2×C3×#41C2×D311yescharacteristic
80C2×#235—31no—
81C3×C4×Q8—21no—
82C3×C4×D4—21no—
83C3×C4×D4—22no—
84C3×#117—21no—
85C3×#117C2×D311yescharacteristic
86C2×C3×C42—21no—
87C2×C3×C42C2×D311yescharacteristic
88#951—32no—
89#950—62no—
90#949—32no—
91#942—61no—
92#932—61no—
93#926—31no—
94C2×#208—31no—
95C2×#208—31no—
96#837—62no—
97#806—62no—
98#805—61no—
99#805—61no—
100C23×C9—21no—
101C23×C9C2×D411yescharacteristic
102C22×D9—21no—
103Q8×C9—21no—
104Q8×C9C22⋊C412yes—
105D4×C9—22no—
106D4×C9—22no—
107D4×C9—21no—
108D4×C9C22⋊C412yes—
109C2×C4×C9—21no—
110C2×C4×C9—21no—
111C2×C4×C9—22no—
112C2×C4×C9—22no—
113C2×C4×C9—22no—
114C2×C4×C9—21no—
115C2×C4×C9—42no—
116C2×C4×C9—44no—
117C2×C4×C9C22×C411yescharacteristic
118C2×C4×C9C2×D411yescharacteristic
119C2×C4×C9C2×D411yescharacteristic
120C2×C4×C9C2×D411yescharacteristic
121C2×C4×C9#4111yescharacteristic
122C2×C4×C9#4111yescharacteristic
123#611—41no—
124#611—41no—
125C2×Dic9—21no—
126C2×Dic9—41no—
127D36—21no—
128D36—21no—
129C4×D9—41no—
130C4×D9—41no—
131Dic18—21no—
132Dic18—21no—
133C9⋊C8—22no—
134C9⋊C8—41no—
135#575—91no—
136C4×#41D911yescharacteristic, complemented
137#421—91no—
138C2×#104—91no—
139#410—91no—
140#344—91no—
141#339—91no—
142C3×#41—21no—
143C3×#41—21no—
144C3×#41C4×D312yes—
145C3×#41D1212yes—
146C2×C3×Q8#6711yescharacteristic
147C2×C3×D4—21no—
148C2×C3×D4#6711yescharacteristic
149C22×C3×C4—21no—
150C22×C3×C4—22no—
151C22×C3×C4—21no—
152C22×C3×C4C22×D311yescharacteristic
153C2×#67—61no—
154#235—61no—
155#235—61no—
156#235—61no—
157#235—61no—
158C2×D12—31no—
159C2×C4×D3—61no—
160C2×Dic6—31no—
161C3×C4⋊C4—22no—
162C3×C4⋊C4—21no—
163C3×C22⋊C4—22no—
164C3×C22⋊C4#6712yes—
165C3×C42—22no—
166C3×C42—21no—
167C3×C42—21no—
168C3×C42#6711yescharacteristic
169C3×C42#6711yescharacteristic
170#217—61no—
171#216—62no—
172#215—62no—
173#214—62no—
174#213—62no—
175C4⋊Dic3—61no—
176C4×Dic3—61no—
177#208—32no—
178#208—61no—
179#208—61no—
180#208—61no—
181C2×C3⋊C8—61no—
182C2×C3⋊C8—61no—
183C22×C9—22no—
184C22×C9—41no—
185C22×C9—42no—
186C22×C9C4×D411yescharacteristic
187C22×C9#12011yescharacteristic
188C22×C9#12111yescharacteristic
189C2×D9—41no—
190C2×D9—81no—
191C4×C9—22no—
192C4×C9—22no—
193C4×C9—42no—
194C4×C9—41no—
195C4×C9C2×C22⋊C411yescharacteristic
196C4×C9C4×D411yescharacteristic
197C4×C9#12111yescharacteristic
198C4×C9#12311yescharacteristic
199Dic9—41no—
200Dic9—81no—
201C2×#41—91no—
202C2×#41C2×D911yescharacteristic
203#137—92no—
204#137—181no—
205AGL(1,ℤ/8)—92no—
206AGL(1,ℤ/8)—181no—
207#135—182no—
208C2×M16—91no—
209C2×M16—91no—
210C4×Q8—21no—
211C4×D4—21no—
212C4×D4—22no—
213#117—21no—
214#117—91no—
215#117C2×D911yescharacteristic
216C2×C42—21no—
217C2×C42C2×D911yescharacteristic
218#104—182no—
219#104—181no—
220#104—181no—
221#99—182no—
222C23×C3—21no—
223C23×C3C2×#6711yescharacteristic
224C22×D3—61no—
225C3×Q8—21no—
226C3×Q8(C2×D3)⋊C412yes—
227C3×D4—22no—
228C3×D4—22no—
229C3×D4—21no—
230C3×D4(C2×D3)⋊C412yes—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—22no—
234C2×C3×C4—22no—
235C2×C3×C4—22no—
236C2×C3×C4—21no—
237C2×C3×C4—42no—
238C2×C3×C4—44no—
239C2×C3×C4C2×C4×D311yescharacteristic
240C2×C3×C4C2×D1211yescharacteristic
241C2×C3×C4#23511yescharacteristic
242C2×C3×C4#23511yescharacteristic
243C2×C3×C4C2×#6711yescharacteristic
244C2×C3×C4C2×#6711yescharacteristic
245#67—121no—
246#67—121no—
247C2×Dic3—61no—
248C2×Dic3—121no—
249D12—61no—
250D12—61no—
251C4×D3—121no—
252C4×D3—121no—
253Dic6—61no—
254Dic6—61no—
255C3⋊C8—62no—
256C3⋊C8—121no—
257C2×C9—21no—
258C2×C9—21no—
259C2×C9—21no—
260C2×C9—42no—
261C2×C9#38611yescharacteristic
262D9—81no—
263#41—21no—
264#41—21no—
265#41—181no—
266#41—181no—
267#41—181no—
268#41—181no—
269#41C4×D912yes—
270#41D3612yes—
271C2×Q8—91no—
272C2×Q8#61111yescharacteristic
273C2×D4—21no—
274C2×D4—91no—
275C2×D4—181no—
276C2×D4#61111yescharacteristic
277C22×C4—21no—
278C22×C4—22no—
279C22×C4—21no—
280C22×C4—181no—
281C22×C4C22×D911yescharacteristic
282Q16—182no—
283SD16—182no—
284SD16—182no—
285D8—182no—
286M16—92no—
287M16—181no—
288M16—181no—
289M16—181no—
290C2×C8—181no—
291C2×C8—181no—
292C4⋊C4—22no—
293C4⋊C4—21no—
294C4⋊C4—181no—
295C22⋊C4—22no—
296C22⋊C4—181no—
297C22⋊C4#61112yes—
298C42—22no—
299C42—21no—
300C42—21no—
301C42—181no—
302C42#61111yescharacteristic
303C42#61111yescharacteristic
304C22×C3—22no—
305C22×C3—41no—
306C22×C3—42no—
307C22×C3C4×#6711yescharacteristic
308C22×C3#93011yescharacteristic
309C22×C3#95311yescharacteristic
310C2×D3—121no—
311C2×D3—241no—
312C3×C4—22no—
313C3×C4—22no—
314C3×C4—42no—
315C3×C4—41no—
316C3×C4C2×(C2×D3)⋊C411yescharacteristic
317C3×C4C4×#6711yescharacteristic
318C3×C4#92911yescharacteristic
319C3×C4#93011yescharacteristic
320Dic3—121no—
321Dic3—241no—
322C9#190611yescharacteristic, complemented, Sylow
323C23—21no—
324C23—181no—
325C23C2×#61111yescharacteristic
326Q8—21no—
327Q8—181no—
328Q8—181no—
329Q8(C2×D9)⋊C412yes—
330D4—22no—
331D4—22no—
332D4—21no—
333D4—181no—
334D4—181no—
335D4—361no—
336D4—361no—
337D4(C2×D9)⋊C412yes—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—21no—
344C2×C4—42no—
345C2×C4—44no—
346C2×C4—181no—
347C2×C4—361no—
348C2×C4—361no—
349C2×C4—361no—
350C2×C4C2×C4×D911yescharacteristic
351C2×C4C2×D3611yescharacteristic
352C2×C4#369711yescharacteristic
353C2×C4#369711yescharacteristic
354C2×C4C2×#61111yescharacteristic
355C2×C4C2×#61111yescharacteristic
356C8—182no—
357C8—361no—
358C2×C3—21no—
359C2×C3—21no—
360C2×C3—21no—
361C2×C3—42no—
362C2×C3#521311yescharacteristic
363D3—241no—
364C22—22no—
365C22—41no—
366C22—42no—
367C22—361no—
368C22—721no—
369C22C4×#61111yescharacteristic
370C22#6349211yescharacteristic
371C22#6351511yescharacteristic
372C4—22no—
373C4—22no—
374C4—42no—
375C4—41no—
376C4—361no—
377C4—721no—
378C4C2×(C2×D9)⋊C411yescharacteristic
379C4C4×#61111yescharacteristic
380C4#6349111yescharacteristic
381C4#6349211yescharacteristic
382C3#7164511yescharacteristic
383C2—21no—
384C2—21no—
385C2—21no—
386C2—42no—
387C2—721no—
388C2#1058889311yescharacteristic
subgroupG/H
centerC4#63492
commutatorC2×C4×C9C22×C4
FrattiniC22×C3×C4C22×D3
FittingC4×C9×#41C2
socleC2×C3#5213
prime radical#10589925C2
cosocleC22×C4×C9C23
hypercenterC4×#41D9
hypocenterC9#1906
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C4 ◁ C22×C4 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. C4×C9×#41C2semidirect
3. #10588914C2semidirect
4. #10588686C2semidirect
5. C2×#63364C2semidirect
6. #10588209C2semidirect
7. #10588201C2semidirect
19. #63512C4semidirect
20. #63511C4semidirect
53. C2×D36C2×C4semidirect
55. C2×Dic18C2×C4semidirect
75. #3667C2×C4semidirect
136. C4×#41D9semidirect
322. C9#1906semidirect

Maximal subgroups

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

subgroupindex
C4×C9×#412
#105899252
#105889142
#105886862
C2×#633642
#105882092
#105882012
#716453