Finite Group Databasebeta

← #11860921

Subgroups — #11860921

Order 1152.

726 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#520C211yesmaximal, characteristic, complemented
2C2×#63513C211yesmaximal, characteristic
3#10589625C211yesmaximal, characteristic, complemented
4#10588916C211yesmaximal, characteristic, complemented
5C4×#3675C212yesmaximal, complemented
6#10588706C212yesmaximal, complemented
7#10588697C212yesmaximal, complemented
8C4×#3672C212yesmaximal, complemented
9#10588675C211yesmaximal, characteristic, complemented
10#10588649C211yesmaximal, characteristic, complemented
11C2×#63367C211yesmaximal, characteristic, complemented
12#82558—31nomaximal
13C2×C9×#41C2211yescharacteristic
14C2×#3697C2211yescharacteristic
15C4×Q8×C9C2212yes—
16C4×D4×C9—22no—
17C4×D4×C9C2212yes—
18C9×#117—21no—
19C9×#117C2211yescharacteristic
20C2×C9×C4⋊C4—21no—
21C2×C9×C4⋊C4C2211yescharacteristic
22#63513C418yescomplemented
23C2×#3675C2211yescharacteristic
24C2×#3674C2211yescharacteristic
25C2×#3673C2211yescharacteristic
26C2×#3672C2211yescharacteristic
27C2×C4⋊Dic9C2211yescharacteristic
28C2×#3667C2211yescharacteristic
29C22×C9⋊C8C2211yescharacteristic
30#63454—21no—
31C4⋊C4×D9—21no—
32#611⋊C4—22no—
33C4×D36C2212yes—
34C4×Dic18C2212yes—
35#63395C2212yes—
36#63392C2212yes—
37#63369C2212yes—
38#63368C2212yes—
39#63367C2212yes—
40#63367C2212yes—
41#63362C2212yes—
42C4×C9⋊C8C2212yes—
43C3×#520D311yescharacteristic
44C2×#950—31no—
45#5523—31no—
46#5232—31no—
47#5030—32no—
48C4×#215—32no—
49C4×#214—32no—
50#5014—32no—
51#4997—31no—
52#4966—31no—
53C2×#808—31no—
54C9×#41—22no—
55C9×#41C2×C414yescomplemented
56C2×Q8×C9C2311yescharacteristic
57C2×D4×C9—21no—
58C2×D4×C9C2311yescharacteristic
59C22×C4×C9—21no—
60C22×C4×C9—21no—
61C22×C4×C9—22no—
62C22×C4×C9C2311yescharacteristic
63C2×#611—21no—
64C22×Dic9—21no—
65#3697—22no—
66#3697C2×C414yescomplemented
67C2×D36C2311yescharacteristic
68C2×C4×D9—21no—
69C2×C4×D9—22no—
70C2×Dic18C2311yescharacteristic
71C9×C4⋊C4—21no—
72C9×C4⋊C4—22no—
73C9×C4⋊C4D411yescharacteristic
74C9×C4⋊C4D411yescharacteristic
75C9×C4⋊C4C2312yes—
76C9×C22⋊C4—22no—
77C9×C22⋊C4D412yes—
78C42×C9—22no—
79C42×C9C2312yes—
80#3675C2×C414yescomplemented
81#3674C2×C414yescomplemented
82#3673C2×C414yescomplemented
83#3672C2×C414yescomplemented
84(C2×D9)⋊C4—22no—
85C4⋊Dic9—21no—
86C4⋊Dic9C2312yes—
87Dic9⋊C4—22no—
88C4×Dic9—22no—
89#3667—22no—
90C2×C9⋊C8C2×C414yescomplemented
91C2×C9⋊C8C2312yes—
92C2×C9⋊C8C2311yescharacteristic
93C2×C9⋊C8C2311yescharacteristic
94#2952—91noSylow
95C2×C3×#41C2×D311yescharacteristic
96C2×#235—31no—
97C3×C4×Q8C2×D312yes—
98C3×C4×D4—22no—
99C3×C4×D4C2×D312yes—
100C3×#117—21no—
101C3×#117C2×D311yescharacteristic
102C2×C3×C4⋊C4—21no—
103C2×C3×C4⋊C4C2×D311yescharacteristic
104#950—38no—
105C2×#216—31no—
106C2×#215—31no—
107C2×#214—31no—
108C2×#213—31no—
109C2×C4⋊Dic3—31no—
110C2×#208—31no—
111C22×C3⋊C8—31no—
112#892—61no—
113D3×C4⋊C4—61no—
114#67⋊C4—62no—
115C4×D12—32no—
116C4×Dic6—32no—
117#835—32no—
118#832—32no—
119#810—32no—
120#809—32no—
121#808—32no—
122#808—32no—
123#803—32no—
124C4×C3⋊C8—32no—
125C23×C9—21no—
126C23×C9C2×D411yescharacteristic
127C22×D9—21no—
128Q8×C9—21no—
129Q8×C9C22×C412yes—
130D4×C9—24no—
131D4×C9—21no—
132D4×C9C22×C412yes—
133C2×C4×C9—21no—
134C2×C4×C9—24no—
135C2×C4×C9—22no—
136C2×C4×C9—82no—
137C2×C4×C9—81no—
138C2×C4×C9C22×C412yes—
139C2×C4×C9C2×D412yes—
140C2×C4×C9C2×D412yes—
141C2×C4×C9C2×D411yescharacteristic
142C2×C4×C9#4112yes—
143C2×C4×C9C2411yescharacteristic
144#611—24no—
145C2×Dic9—21no—
146C2×Dic9—22no—
147C2×Dic9—81no—
148D36—21no—
149D36C22×C412yes—
150C4×D9—24no—
151C4×D9—82no—
152Dic18—21no—
153Dic18C22×C412yes—
154C9⋊C8—22no—
155C9⋊C8C22×C412yes—
156C9⋊C8C22×C412yes—
157C2×#135—91no—
158#520—91no—
159#520D911yescharacteristic, complemented
160#442—92no—
161#441—92no—
162C4×SD16—92no—
163C4×SD16—92no—
164C2×#106—91no—
165#417—91no—
166#417—91no—
167#405—91no—
168C3×#41—22no—
169C3×#41C4×D314yes—
170C2×C3×Q8C22×D311yescharacteristic
171C2×C3×D4—21no—
172C2×C3×D4C22×D311yescharacteristic
173C22×C3×C4—21no—
174C22×C3×C4—21no—
175C22×C3×C4—22no—
176C22×C3×C4C22×D311yescharacteristic
177C2×#67—61no—
178C22×Dic3—61no—
179#235—34no—
180#235—62no—
181C2×D12—31no—
182C2×C4×D3—61no—
183C2×C4×D3—62no—
184C2×Dic6—31no—
185C3×C4⋊C4—21no—
186C3×C4⋊C4—22no—
187C3×C4⋊C4#6711yescharacteristic
188C3×C4⋊C4#6711yescharacteristic
189C3×C4⋊C4C22×D312yes—
190C3×C22⋊C4—22no—
191C3×C22⋊C4#6712yes—
192C3×C42—22no—
193C3×C42C22×D312yes—
194#216—34no—
195#215—34no—
196#214—34no—
197#213—34no—
198(C2×D3)⋊C4—62no—
199C4⋊Dic3—32no—
200C4⋊Dic3—61no—
201Dic3⋊C4—62no—
202C4×Dic3—62no—
203#208—62no—
204C2×C3⋊C8—34no—
205C2×C3⋊C8—31no—
206C2×C3⋊C8—31no—
207C2×C3⋊C8—32no—
208C22×C9—21no—
209C22×C9—21no—
210C22×C9—22no—
211C22×C9—41no—
212C22×C9—41no—
213C22×C9C4×D412yes—
214C22×C9C22×D411yescharacteristic
215C2×D9—22no—
216C2×D9—41no—
217C2×D9—41no—
218C4×C9—22no—
219C4×C9—22no—
220C4×C9—22no—
221C4×C9—42no—
222C4×C9C4×D412yes—
223C4×C9C23×C411yescharacteristic
224C4×C9C2×#4111yescharacteristic
225Dic9—22no—
226Dic9—42no—
227C2×#41—91no—
228C2×#41C2×D911yescharacteristic
229#135—98no—
230C2×Q16—91no—
231C2×SD16—91no—
232C2×SD16—91no—
233C2×D8—91no—
234C2×M16—91no—
235C22×C8—91no—
236C4×Q8—92no—
237C4×Q8C2×D912yes—
238C4×D4—22no—
239C4×D4—92no—
240C4×D4—182no—
241C4×D4C2×D912yes—
242#117—21no—
243#117—181no—
244#117C2×D911yescharacteristic
245C2×C4⋊C4—21no—
246C2×C4⋊C4—91no—
247C2×C4⋊C4—181no—
248C2×C4⋊C4C2×D911yescharacteristic
249#106—92no—
250#106—92no—
251#103—92no—
252#103—92no—
253#102—92no—
254#102—92no—
255#97—92no—
256C4×C8—92no—
257C23×C3—21no—
258C23×C3C2×#6711yescharacteristic
259C22×D3—61no—
260C3×Q8—21no—
261C3×Q8C2×C4×D312yes—
262C3×D4—24no—
263C3×D4—21no—
264C3×D4C2×C4×D312yes—
265C2×C3×C4—21no—
266C2×C3×C4—24no—
267C2×C3×C4—22no—
268C2×C3×C4—82no—
269C2×C3×C4—81no—
270C2×C3×C4C2×C4×D312yes—
271C2×C3×C4#23512yes—
272C2×C3×C4C2×#6712yes—
273C2×C3×C4C2×#6712yes—
274C2×C3×C4C2×#6711yescharacteristic
275C2×C3×C4C23×D311yescharacteristic
276#67—64no—
277C2×Dic3—61no—
278C2×Dic3—62no—
279C2×Dic3—241no—
280D12—32no—
281D12—61no—
282C4×D3—64no—
283C4×D3—242no—
284Dic6—32no—
285Dic6—61no—
286C3⋊C8—32no—
287C3⋊C8—32no—
288C3⋊C8—62no—
289C2×C9—22no—
290C2×C9—42no—
291C2×C9C2×C4×D411yescharacteristic
292C2×C9#57711yescharacteristic
293C2×C9#57711yescharacteristic
294D9—42no—
295#41—22no—
296#41—94no—
297#41—182no—
298#41C4×D914yescomplemented
299C2×Q8—91no—
300C2×Q8C22×D911yescharacteristic
301C2×D4—21no—
302C2×D4—91no—
303C2×D4—181no—
304C2×D4C22×D911yescharacteristic
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—22no—
308C22×C4—181no—
309C22×C4—181no—
310C22×C4—182no—
311C22×C4C22×D911yescharacteristic
312Q16—94no—
313SD16—94no—
314SD16—94no—
315D8—94no—
316M16—182no—
317C2×C8—94no—
318C2×C8—91no—
319C2×C8—91no—
320C2×C8—92no—
321C4⋊C4—21no—
322C4⋊C4—22no—
323C4⋊C4—92no—
324C4⋊C4—181no—
325C4⋊C4—182no—
326C4⋊C4#61111yescharacteristic
327C4⋊C4#61111yescharacteristic
328C4⋊C4C22×D912yes—
329C22⋊C4—22no—
330C22⋊C4—182no—
331C22⋊C4#61112yes—
332C42—22no—
333C42—182no—
334C42C22×D912yes—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—22no—
338C22×C3—41no—
339C22×C3—41no—
340C22×C3C4×#6712yes—
341C22×C3C22×#6711yescharacteristic
342C2×D3—62no—
343C2×D3—121no—
344C2×D3—121no—
345C3×C4—22no—
346C3×C4—22no—
347C3×C4—22no—
348C3×C4—42no—
349C3×C4C4×#6712yes—
350C3×C4C22×C4×D311yescharacteristic
351C3×C4C2×#23511yescharacteristic
352Dic3—62no—
353Dic3—122no—
354C9#295211yescharacteristic, complemented, Sylow
355C23—21no—
356C23—181no—
357C23C2×#61111yescharacteristic
358Q8—21no—
359Q8—92no—
360Q8—181no—
361Q8C2×C4×D912yes—
362D4—24no—
363D4—21no—
364D4—92no—
365D4—184no—
366D4—181no—
367D4C2×C4×D912yes—
368C2×C4—21no—
369C2×C4—24no—
370C2×C4—22no—
371C2×C4—82no—
372C2×C4—81no—
373C2×C4—181no—
374C2×C4—184no—
375C2×C4—182no—
376C2×C4—722no—
377C2×C4—721no—
378C2×C4C2×C4×D912yes—
379C2×C4#369712yes—
380C2×C4C2×#61112yes—
381C2×C4C2×#61112yes—
382C2×C4C2×#61111yescharacteristic
383C2×C4C23×D911yescharacteristic
384C8—92no—
385C8—92no—
386C8—182no—
387C2×C3—22no—
388C2×C3—42no—
389C2×C3C2×C4×#6711yescharacteristic
390C2×C3#583611yescharacteristic
391C2×C3#583711yescharacteristic
392D3—122no—
393C22—21no—
394C22—21no—
395C22—22no—
396C22—41no—
397C22—41no—
398C22—182no—
399C22—361no—
400C22—361no—
401C22C4×#61112yes—
402C22C22×#61111yescharacteristic
403C4—22no—
404C4—22no—
405C4—22no—
406C4—42no—
407C4—182no—
408C4—362no—
409C4C4×#61112yes—
410C4C22×C4×D911yescharacteristic
411C4C2×#369711yescharacteristic
412C3#8255811yescharacteristic
413C2—22no—
414C2—42no—
415C2—362no—
416C2C2×C4×#61111yescharacteristic
417C2#1058993811yescharacteristic
418C2#1058993911yescharacteristic
subgroupG/H
centerC22C22×#611
commutatorC4×C9C23×C4
FrattiniC2×C3×C4C23×D3
FittingC9×#520C2
socleC22×C3C22×#67
prime radicalC2×#63513C2
cosocleC2×C4×C9C24
hypercenter#520D9
hypocenterC9#2952
LCSG ▷ C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ #117 ◁ #520

Complements

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

NH ≅ G/Ntype
1. C9×#520C2semidirect
3. #10589625C2semidirect
4. #10588916C2semidirect
5. C4×#3675C2semidirect
6. #10588706C2semidirect
7. #10588697C2semidirect
8. C4×#3672C2semidirect
9. #10588675C2semidirect
10. #10588649C2semidirect
11. C2×#63367C2semidirect
22. #63513C4semidirect
55. C9×#41C2×C4semidirect
66. #3697C2×C4semidirect
80. #3675C2×C4semidirect
81. #3674C2×C4semidirect
82. #3673C2×C4semidirect
83. #3672C2×C4semidirect
90. C2×C9⋊C8C2×C4semidirect
159. #520D9semidirect
298. #41C4×D9semidirect
354. C9#2952semidirect

Maximal subgroups

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

subgroupindex
C9×#5202
C2×#635132
#105896252
#105889162
C4×#36752
#105887062
#105886972
C4×#36722
#105886752
#105886492
C2×#633672
#825583