Finite Group Databasebeta

← #11870848

Subgroups — #11870848

Order 1152.

681 conjugacy classes of subgroups.

The subgroup lattice has 423 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×C9C211yesmaximal, characteristic, complemented
2#10589581C211yesmaximal, characteristic, complemented
3#10588898C211yesmaximal, characteristic
4#10588897C211yesmaximal, characteristic, complemented
5#10588699C212yesmaximal, complemented
6C4×#3673C212yesmaximal, complemented
7C4×#3672C212yesmaximal, complemented
8#10588692C212yesmaximal, complemented
9#10588651C211yesmaximal, characteristic, complemented
10#10588646C211yesmaximal, characteristic, complemented
11#10588605C211yesmaximal, characteristic, complemented
12#82309—31nomaximal
13C22×D4×C9C2211yescharacteristic
14C23×C4×C9—21no—
15C4×D4×C9—21no—
16C4×D4×C9—21no—
17C4×D4×C9C2212yes—
18C4×D4×C9C2212yes—
19C2×C9×C4⋊C4C2211yescharacteristic
20C2×C9×C22⋊C4—21no—
21C2×C42×C9C2211yescharacteristic
22C2×#3673C2212yes—
23C2×#3672C2212yes—
24#63492C2211yescharacteristic
25#63491—21no—
26C4×#611—21no—
27#63486C2211yescharacteristic
28#63438—21no—
29#63437C2211yescharacteristic, complemented
30C4×D36C2211yescharacteristic, complemented
31#63434—21no—
32#63432C2211yescharacteristic, complemented
33C4×Dic18C2211yescharacteristic, complemented
34#63392C2212yes—
35#63392C2212yes—
36#63389C2211yescharacteristic
37#63389C2211yescharacteristic
38#63369C2212yescomplemented
39#63368C2212yescomplemented
40#63367C2212yescomplemented
41#63366C2212yescomplemented
42C4⋊(C9⋊C8)C2212yescomplemented
43C4×C9⋊C8C2212yescomplemented
44C2×C3×C4×D4D311yescharacteristic
45#5479—31no—
46#5218—31no—
47#5217—31no—
48C4×#214—32no—
49#5016—32no—
50C4×#213—32no—
51#5009—32no—
52#4970—31no—
53#4968—31no—
54#4925—31no—
55C24×C9—21no—
56C2×D4×C9—24no—
57C2×D4×C9—21no—
58C2×D4×C9C2312yes—
59C22×C4×C9—21no—
60C22×C4×C9—22no—
61C22×C4×C9—22no—
62C22×C4×C9—44no—
63C22×C4×C9D411yescharacteristic
64C22×C4×C9D411yescharacteristic
65C22×C4×C9C2311yescharacteristic
66C2×#611—21no—
67C2×D36C2311yescharacteristic
68C2×C4×D9—21no—
69C2×Dic18C2311yescharacteristic
70C9×C4⋊C4—21no—
71C9×C4⋊C4C2312yes—
72C9×C22⋊C4—22no—
73C9×C22⋊C4—22no—
74C42×C9D411yescharacteristic
75C42×C9D411yescharacteristic
76C42×C9C2311yescharacteristic
77C42×C9C2311yescharacteristic
78#3676—21no—
79#3673—24no—
80#3672—24no—
81(C2×D9)⋊C4—21no—
82(C2×D9)⋊C4—21no—
83(C2×D9)⋊C4—21no—
84(C2×D9)⋊C4—21no—
85C4⋊Dic9C2311yescharacteristic
86C4⋊Dic9C2311yescharacteristic
87Dic9⋊C4—21no—
88Dic9⋊C4—21no—
89Dic9⋊C4—21no—
90Dic9⋊C4—21no—
91C4×Dic9—21no—
92C2×C9⋊C8C2312yes—
93C2×C9⋊C8C2312yes—
94#3105—91noSylow
95C22×C3×D4C2×D311yescharacteristic
96C23×C3×C4—21no—
97C3×C4×D4—21no—
98C3×C4×D4—21no—
99C3×C4×D4C2×D312yes—
100C3×C4×D4C2×D312yes—
101C2×C3×C4⋊C4C2×D311yescharacteristic
102C2×C3×C22⋊C4—21no—
103C2×C3×C42C2×D311yescharacteristic
104C2×#214—32no—
105C2×#213—32no—
106#930—31no—
107#929—61no—
108C4×#67—61no—
109#924—31no—
110#876—61no—
111#875—31no—
112C4×D12—31no—
113#872—61no—
114#870—31no—
115C4×Dic6—31no—
116#832—32no—
117#832—32no—
118#830—31no—
119#830—31no—
120#810—32no—
121#809—32no—
122#808—32no—
123#807—32no—
124C4⋊(C3⋊C8)—32no—
125C4×C3⋊C8—32no—
126C23×C9—24no—
127C23×C9—22no—
128C23×C9—42no—
129C23×C9—42no—
130C23×C9C2×D411yescharacteristic
131C22×D9—21no—
132D4×C9—24no—
133D4×C9—22no—
134D4×C9#4114yes—
135C2×C4×C9—22no—
136C2×C4×C9—22no—
137C2×C4×C9—22no—
138C2×C4×C9—22no—
139C2×C4×C9—44no—
140C2×C4×C9—42no—
141C2×C4×C9—44no—
142C2×C4×C9C2×D411yescharacteristic
143C2×C4×C9C2×D411yescharacteristic
144C2×C4×C9C2×D411yescharacteristic
145C2×C4×C9C2×D411yescharacteristic
146C2×C4×C9C2×D411yescharacteristic
147C2×C4×C9C2411yescharacteristic
148#611—42no—
149C2×Dic9—21no—
150C2×Dic9—21no—
151C2×Dic9—21no—
152D36—22no—
153C4×D9—42no—
154Dic18—22no—
155C9⋊C8—22no—
156C9⋊C8—22no—
157#529—91no—
158C2×C4×D4D911yescharacteristic, complemented
159#484—91no—
160#481—91no—
161#478—92no—
162#463—92no—
163#450—91no—
164#447—91no—
165C4×SD16—92no—
166C4×D8—92no—
167#431—91no—
168C24×C3—21no—
169C2×C3×D4—24no—
170C2×C3×D4—21no—
171C2×C3×D4C22×D312yes—
172C22×C3×C4—21no—
173C22×C3×C4—22no—
174C22×C3×C4—22no—
175C22×C3×C4—44no—
176C22×C3×C4#6711yescharacteristic
177C22×C3×C4#6711yescharacteristic
178C22×C3×C4C22×D311yescharacteristic
179C2×#67—61no—
180C2×D12—31no—
181C2×C4×D3—61no—
182C2×Dic6—31no—
183C3×C4⋊C4—21no—
184C3×C4⋊C4C22×D312yes—
185C3×C22⋊C4—22no—
186C3×C22⋊C4—22no—
187C3×C42#6711yescharacteristic
188C3×C42#6711yescharacteristic
189C3×C42C22×D311yescharacteristic
190C3×C42C22×D311yescharacteristic
191#217—61no—
192#214—64no—
193#213—64no—
194(C2×D3)⋊C4—61no—
195(C2×D3)⋊C4—61no—
196(C2×D3)⋊C4—61no—
197(C2×D3)⋊C4—61no—
198C4⋊Dic3—31no—
199C4⋊Dic3—31no—
200Dic3⋊C4—61no—
201Dic3⋊C4—61no—
202Dic3⋊C4—61no—
203Dic3⋊C4—61no—
204C4×Dic3—61no—
205C2×C3⋊C8—32no—
206C2×C3⋊C8—32no—
207C22×C9—21no—
208C22×C9—21no—
209C22×C9—24no—
210C22×C9—48no—
211C22×C9—42no—
212C22×C9—42no—
213C22×C9#13512yes—
214C22×C9C22×D411yescharacteristic
215C2×D9—41no—
216C2×D9—41no—
217C2×D9—41no—
218C4×C9—21no—
219C4×C9—21no—
220C4×C9—21no—
221C4×C9—21no—
222C4×C9—42no—
223C4×C9AGL(1,ℤ/8)12yes—
224C4×C9C2×#4112yes—
225Dic9—41no—
226Dic9—41no—
227Dic9—41no—
228C22×D4C2×D911yescharacteristic
229C23×C4—21no—
230C2×SD16—92no—
231C2×D8—92no—
232#126—181no—
233#125—91no—
234#124—91no—
235#123—181no—
236C22⋊Q8—91no—
237#121—91no—
238C4×Q8—91no—
239C4×D4—21no—
240C4×D4—21no—
241C4×D4—91no—
242C4×D4—181no—
243C4×D4C2×D912yes—
244C4×D4C2×D912yes—
245#117—181no—
246C2×C4⋊C4C2×D911yescharacteristic
247C2×C22⋊C4—21no—
248C2×C42C2×D911yescharacteristic
249#107—92no—
250#106—92no—
251C4⋊C8—92no—
252#103—92no—
253#102—92no—
254#102—92no—
255#102—92no—
256C22⋊C8—91no—
257C22⋊C8—91no—
258C4×C8—92no—
259C23×C3—24no—
260C23×C3—22no—
261C23×C3—42no—
262C23×C3—42no—
263C23×C3C2×#6711yescharacteristic
264C22×D3—61no—
265C3×D4—24no—
266C3×D4—22no—
267C3×D4#23514yes—
268C2×C3×C4—22no—
269C2×C3×C4—22no—
270C2×C3×C4—22no—
271C2×C3×C4—22no—
272C2×C3×C4—44no—
273C2×C3×C4—42no—
274C2×C3×C4—44no—
275C2×C3×C4C2×#6711yescharacteristic
276C2×C3×C4C2×#6711yescharacteristic
277C2×C3×C4C2×#6711yescharacteristic
278C2×C3×C4C2×#6711yescharacteristic
279C2×C3×C4C2×#6711yescharacteristic
280C2×C3×C4C23×D311yescharacteristic
281#67—122no—
282C2×Dic3—61no—
283C2×Dic3—61no—
284C2×Dic3—61no—
285D12—62no—
286C4×D3—122no—
287Dic6—62no—
288C3⋊C8—62no—
289C3⋊C8—62no—
290C2×C9—22no—
291C2×C9—44no—
292C2×C9#52511yescharacteristic
293C2×C9C2×#13511yescharacteristic
294C2×C9C2×AGL(1,ℤ/8)11yescharacteristic
295D9—81no—
296C24—21no—
297C2×Q8—91no—
298C2×D4—24no—
299C2×D4—21no—
300C2×D4—91no—
301C2×D4—181no—
302C2×D4C22×D912yes—
303C22×C4—21no—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—44no—
307C22×C4—181no—
308C22×C4#61111yescharacteristic
309C22×C4#61111yescharacteristic
310C22×C4C22×D911yescharacteristic
311SD16—184no—
312D8—184no—
313C2×C8—92no—
314C2×C8—92no—
315C4⋊C4—21no—
316C4⋊C4—91no—
317C4⋊C4—91no—
318C4⋊C4—181no—
319C4⋊C4—181no—
320C4⋊C4—181no—
321C4⋊C4—181no—
322C4⋊C4C22×D912yes—
323C22⋊C4—22no—
324C22⋊C4—22no—
325C22⋊C4—181no—
326C22⋊C4—181no—
327C22⋊C4—181no—
328C22⋊C4—181no—
329C22⋊C4—181no—
330C42—181no—
331C42#61111yescharacteristic
332C42#61111yescharacteristic
333C42C22×D911yescharacteristic
334C42C22×D911yescharacteristic
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—24no—
338C22×C3—48no—
339C22×C3—42no—
340C22×C3—42no—
341C22×C3#95012yes—
342C22×C3C22×#6711yescharacteristic
343C2×D3—121no—
344C2×D3—121no—
345C2×D3—121no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—42no—
351C3×C4#93212yes—
352C3×C4C2×#23512yes—
353Dic3—121no—
354Dic3—121no—
355Dic3—121no—
356C9#310511yescharacteristic, complemented, Sylow
357C23—24no—
358C23—22no—
359C23—42no—
360C23—42no—
361C23—181no—
362C23C2×#61111yescharacteristic
363Q8—182no—
364D4—24no—
365D4—22no—
366D4—182no—
367D4—362no—
368D4#369714yes—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—44no—
374C2×C4—42no—
375C2×C4—44no—
376C2×C4—181no—
377C2×C4—181no—
378C2×C4—181no—
379C2×C4—362no—
380C2×C4C2×#61111yescharacteristic
381C2×C4C2×#61111yescharacteristic
382C2×C4C2×#61111yescharacteristic
383C2×C4C2×#61111yescharacteristic
384C2×C4C2×#61111yescharacteristic
385C2×C4C23×D911yescharacteristic
386C8—182no—
387C8—182no—
388C2×C3—22no—
389C2×C3—44no—
390C2×C3#579111yescharacteristic
391C2×C3C2×#93211yescharacteristic
392C2×C3C2×#95011yescharacteristic
393D3—241no—
394C22—21no—
395C22—21no—
396C22—24no—
397C22—48no—
398C22—42no—
399C22—42no—
400C22—361no—
401C22—361no—
402C22—361no—
403C22#6351312yes—
404C22C22×#61111yescharacteristic
405C4—21no—
406C4—21no—
407C4—21no—
408C4—21no—
409C4—42no—
410C4—361no—
411C4—361no—
412C4—361no—
413C4#6349512yes—
414C4C2×#369712yes—
415C3#8230911yescharacteristic
416C2—22no—
417C2—44no—
418C2—721no—
419C2#1058989311yescharacteristic
420C2C2×#6349511yescharacteristic
421C2C2×#6351311yescharacteristic
subgroupG/H
centerC2×C4C2×#611
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC2×C4×D4×C9C2
socleC22×C3C22×#67
prime radical#10588898C2
hypercenterC2×C4×D4D9
hypocenterC9#3105
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C4×D4×C9C2semidirect
2. #10589581C2semidirect
4. #10588897C2semidirect
5. #10588699C2semidirect
6. C4×#3673C2semidirect
7. C4×#3672C2semidirect
8. #10588692C2semidirect
9. #10588651C2semidirect
10. #10588646C2semidirect
11. #10588605C2semidirect
29. #63437C22semidirect
30. C4×D36C22semidirect
32. #63432C22semidirect
33. C4×Dic18C22semidirect
38. #63369C22semidirect
39. #63368C22semidirect
40. #63367C22semidirect
41. #63366C22semidirect
42. C4⋊(C9⋊C8)C22semidirect
43. C4×C9⋊C8C22semidirect
158. C2×C4×D4D9semidirect
356. C9#3105semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×C92
#105895812
#105888982
#105888972
#105886992
C4×#36732
C4×#36722
#105886922
#105886512
#105886462
#105886052
#823093