Finite Group Databasebeta

← #11882290

Subgroups — #11882290

Order 1152.

597 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#532C211yesmaximal, characteristic, complemented
2#10589581C211yesmaximal, characteristic, complemented
3#10588769C211yesmaximal, characteristic, complemented
4#10588764C211yesmaximal, characteristic, complemented
5#10588754C211yesmaximal, characteristic, complemented
6#10588752C211yesmaximal, characteristic, complemented
7#10588721C212yesmaximal, complemented
8#10588717C212yesmaximal, complemented
9#10588699C212yesmaximal, complemented
10#10588692C212yesmaximal, complemented
11C2×C4⋊(C9⋊C8)C211yesmaximal, characteristic, complemented
12#83311—31nomaximal
13C2×C9×#41—21no—
14C9×C4⋊Q8C2211yescharacteristic
15C9×#127C2211yescharacteristic
16C9×#124—21no—
17C9×#121—21no—
18C9×#121C2212yes—
19C4×D4×C9—21no—
20C4×D4×C9C2212yes—
21C2×C42×C9C2211yescharacteristic
22C2×#3673C2212yes—
23C2×#3672C2212yes—
24#63492C2211yescharacteristic
25#63491—21no—
26C4×#611—21no—
27#63486C2211yescharacteristic
28C22×C9⋊C8C2212yes—
29#63438—21no—
30#63437C2211yescharacteristic
31C4×D36C2211yescharacteristic
32#63434—21no—
33#63432C2211yescharacteristic
34C4×Dic18C2211yescharacteristic
35#63392C2212yes—
36#63392C2212yes—
37#63369C2212yes—
38#63368C2212yes—
39#63367C2212yes—
40#63366C2212yes—
41C4⋊(C9⋊C8)C2212yes—
42C4⋊(C9⋊C8)C2211yescharacteristic
43C4⋊(C9⋊C8)C2211yescharacteristic
44C3×#532D311yescharacteristic
45#5479—31no—
46#5091—31no—
47#5084—31no—
48#5075—31no—
49#5072—31no—
50#5041—32no—
51#5038—32no—
52#5016—32no—
53#5009—32no—
54C2×C4⋊(C3⋊C8)—31no—
55C9×#41—44no—
56C2×Q8×C9—21no—
57C2×D4×C9—22no—
58C2×D4×C9—21no—
59C2×D4×C9—21no—
60C2×D4×C9C2312yes—
61C22×C4×C9—22no—
62C22×C4×C9D411yescharacteristic
63C22×C4×C9D411yescharacteristic
64C22×C4×C9C2311yescharacteristic
65C2×#611—21no—
66C2×D36C2311yescharacteristic
67C2×C4×D9—21no—
68C2×Dic18C2311yescharacteristic
69C9×C4⋊C4—21no—
70C9×C4⋊C4C2312yes—
71C9×C22⋊C4—22no—
72C9×C22⋊C4—22no—
73C42×C9D411yescharacteristic
74C42×C9D411yescharacteristic
75C42×C9C2311yescharacteristic
76C42×C9C2311yescharacteristic
77#3676—21no—
78#3673—42no—
79#3672—42no—
80(C2×D9)⋊C4—21no—
81(C2×D9)⋊C4—21no—
82(C2×D9)⋊C4—21no—
83(C2×D9)⋊C4—21no—
84C4⋊Dic9C2311yescharacteristic
85C4⋊Dic9C2311yescharacteristic
86Dic9⋊C4—21no—
87Dic9⋊C4—21no—
88Dic9⋊C4—21no—
89Dic9⋊C4—21no—
90C4×Dic9—21no—
91C2×C9⋊C8—42no—
92C2×C9⋊C8C2312yes—
93C2×C9⋊C8C2312yes—
94#3247—91noSylow
95C2×C3×#41—21no—
96C3×C4⋊Q8C2×D311yescharacteristic
97C3×#127C2×D311yescharacteristic
98C3×#124—21no—
99C3×#121—21no—
100C3×#121C2×D312yes—
101C3×C4×D4—21no—
102C3×C4×D4C2×D312yes—
103C2×C3×C42C2×D311yescharacteristic
104C2×#214—32no—
105C2×#213—32no—
106#930—31no—
107#929—61no—
108C4×#67—61no—
109#924—31no—
110C22×C3⋊C8—32no—
111#876—61no—
112#875—31no—
113C4×D12—31no—
114#872—61no—
115#870—31no—
116C4×Dic6—31no—
117#832—32no—
118#832—32no—
119#810—32no—
120#809—32no—
121#808—32no—
122#807—32no—
123C4⋊(C3⋊C8)—32no—
124C4⋊(C3⋊C8)—31no—
125C4⋊(C3⋊C8)—31no—
126C23×C9—22no—
127C23×C9C2×D411yescharacteristic
128C22×D9—21no—
129Q8×C9—42no—
130D4×C9—22no—
131D4×C9—22no—
132D4×C9—42no—
133D4×C9—44no—
134D4×C9—42no—
135C2×C4×C9—22no—
136C2×C4×C9—22no—
137C2×C4×C9—21no—
138C2×C4×C9—21no—
139C2×C4×C9—22no—
140C2×C4×C9—44no—
141C2×C4×C9C2×D411yescharacteristic
142C2×C4×C9C2×D411yescharacteristic
143C2×C4×C9C2×D411yescharacteristic
144C2×C4×C9C2×D411yescharacteristic
145C2×C4×C9C2×D411yescharacteristic
146C2×C4×C9C2411yescharacteristic
147#611—42no—
148C2×Dic9—21no—
149C2×Dic9—21no—
150C2×Dic9—21no—
151D36—21no—
152D36—21no—
153C4×D9—42no—
154Dic18—21no—
155Dic18—21no—
156C9⋊C8—22no—
157C9⋊C8—22no—
158#532D911yescharacteristic, complemented
159#529—91no—
160#478—92no—
161#477—91no—
162#476—91no—
163#466—92no—
164#465—92no—
165#463—92no—
166#460—91no—
167#459—91no—
168C2×C4⋊C8—91no—
169C3×#41—44no—
170C2×C3×Q8—21no—
171C2×C3×D4—22no—
172C2×C3×D4—21no—
173C2×C3×D4—21no—
174C2×C3×D4C22×D312yes—
175C22×C3×C4—22no—
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—122no—
193#213—122no—
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—
207C2×C3⋊C8—122no—
208C22×C9—21no—
209C22×C9—21no—
210C22×C9—42no—
211C22×C9—42no—
212C22×C9—42no—
213C22×C9AGL(1,ℤ/8)12yes—
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×C9#13512yes—
224C4×C9H(5,𝔽2)11yescharacteristic
225C4×C92−1+411yescharacteristic
226Dic9—41no—
227Dic9—41no—
228Dic9—41no—
229C2×#41—21no—
230C2×SD16—92no—
231C2×D8—92no—
232C22×C8—92no—
233C4⋊Q8C2×D911yescharacteristic
234#127C2×D911yescharacteristic
235#126—181no—
236#125—91no—
237#124—21no—
238#124—91no—
239#123—181no—
240C22⋊Q8—91no—
241#121—21no—
242#121—91no—
243#121C2×D912yes—
244C4×Q8—91no—
245C4×D4—21no—
246C4×D4—91no—
247C4×D4—181no—
248C4×D4C2×D912yes—
249#117—181no—
250C2×C42C2×D911yescharacteristic
251#107—92no—
252#106—92no—
253C4⋊C8—91no—
254C4⋊C8—91no—
255C4⋊C8—92no—
256#103—92no—
257#102—92no—
258#102—92no—
259#102—92no—
260C23×C3—22no—
261C23×C3C2×#6711yescharacteristic
262C22×D3—61no—
263C3×Q8—42no—
264C3×D4—22no—
265C3×D4—22no—
266C3×D4—42no—
267C3×D4—44no—
268C3×D4—42no—
269C2×C3×C4—22no—
270C2×C3×C4—22no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—22no—
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—61no—
286D12—61no—
287C4×D3—122no—
288Dic6—61no—
289Dic6—61no—
290C3⋊C8—62no—
291C3⋊C8—62no—
292C2×C9—22no—
293C2×C9—82no—
294C2×C9#53711yescharacteristic
295C2×C9C2×#13511yescharacteristic
296C2×C9C2×AGL(1,ℤ/8)11yescharacteristic
297D9—81no—
298#41—44no—
299C2×Q8—21no—
300C2×Q8—91no—
301C2×D4—22no—
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—91no—
305C2×D4—181no—
306C2×D4C22×D912yes—
307C22×C4—22no—
308C22×C4—181no—
309C22×C4#61111yescharacteristic
310C22×C4#61111yescharacteristic
311C22×C4C22×D911yescharacteristic
312SD16—362no—
313D8—362no—
314C2×C8—92no—
315C2×C8—92no—
316C2×C8—362no—
317C4⋊C4—21no—
318C4⋊C4—91no—
319C4⋊C4—91no—
320C4⋊C4—181no—
321C4⋊C4—181no—
322C4⋊C4—181no—
323C4⋊C4—181no—
324C4⋊C4C22×D912yes—
325C22⋊C4—22no—
326C22⋊C4—22no—
327C22⋊C4—181no—
328C22⋊C4—181no—
329C22⋊C4—181no—
330C22⋊C4—181no—
331C22⋊C4—181no—
332C42—181no—
333C42#61111yescharacteristic
334C42#61111yescharacteristic
335C42C22×D911yescharacteristic
336C42C22×D911yescharacteristic
337C22×C3—21no—
338C22×C3—21no—
339C22×C3—42no—
340C22×C3—42no—
341C22×C3—42no—
342C22×C3#93212yes—
343C22×C3C22×#6711yescharacteristic
344C2×D3—121no—
345C2×D3—121no—
346C2×D3—121no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—42no—
352C3×C4#95012yes—
353C3×C4#100911yescharacteristic
354C3×C4#101011yescharacteristic
355Dic3—121no—
356Dic3—121no—
357Dic3—121no—
358C9#324711yescharacteristic, complemented, Sylow
359C23—22no—
360C23—181no—
361C23C2×#61111yescharacteristic
362Q8—42no—
363Q8—181no—
364Q8—181no—
365D4—22no—
366D4—22no—
367D4—42no—
368D4—44no—
369D4—42no—
370D4—181no—
371D4—181no—
372D4—362no—
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—22no—
378C2×C4—44no—
379C2×C4—181no—
380C2×C4—181no—
381C2×C4—181no—
382C2×C4—362no—
383C2×C4C2×#61111yescharacteristic
384C2×C4C2×#61111yescharacteristic
385C2×C4C2×#61111yescharacteristic
386C2×C4C2×#61111yescharacteristic
387C2×C4C2×#61111yescharacteristic
388C2×C4C23×D911yescharacteristic
389C8—182no—
390C8—182no—
391C2×C3—22no—
392C2×C3—82no—
393C2×C3C2×#93211yescharacteristic
394C2×C3C2×#95011yescharacteristic
395C2×C3#583311yescharacteristic
396D3—241no—
397C22—21no—
398C22—21no—
399C22—42no—
400C22—42no—
401C22—42no—
402C22—361no—
403C22—361no—
404C22—361no—
405C22#6349512yes—
406C22C22×#61111yescharacteristic
407C4—21no—
408C4—21no—
409C4—21no—
410C4—21no—
411C4—42no—
412C4—361no—
413C4—361no—
414C4—361no—
415C4#6351312yes—
416C4#6371511yescharacteristic
417C4#6371611yescharacteristic
418C3#8331111yescharacteristic
419C2—22no—
420C2—82no—
421C2—721no—
422C2C2×#6349511yescharacteristic
423C2C2×#6351311yescharacteristic
424C2#1058993511yescharacteristic
subgroupG/H
centerC22C22×#611
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#532C2
socleC22×C3C22×#67
hypercenter#532D9
hypocenterC9#3247
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. C9×#532C2semidirect
2. #10589581C2semidirect
3. #10588769C2semidirect
4. #10588764C2semidirect
5. #10588754C2semidirect
6. #10588752C2semidirect
7. #10588721C2semidirect
8. #10588717C2semidirect
9. #10588699C2semidirect
10. #10588692C2semidirect
11. C2×C4⋊(C9⋊C8)C2semidirect
158. #532D9semidirect
358. C9#3247semidirect

Maximal subgroups

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

subgroupindex
C9×#5322
#105895812
#105887692
#105887642
#105887542
#105887522
#105887212
#105887172
#105886992
#105886922
C2×C4⋊(C9⋊C8)2
#833113