Finite Group Databasebeta

← #11882311

Subgroups — #11882311

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
1#10589581C211yesmaximal, characteristic, complemented
2#10589579C211yesmaximal, characteristic, complemented
3C2×C9×C4⋊C8C211yesmaximal, characteristic, complemented
4#10588796C212yesmaximal, complemented
5#10588795C212yesmaximal, complemented
6#10588531C212yesmaximal, complemented
7#10588528C212yesmaximal, complemented
8#10588527C211yesmaximal, characteristic, complemented
9#10588526C211yesmaximal, characteristic, complemented
10#10588514C211yesmaximal, characteristic, complemented
11#10588512C211yesmaximal, characteristic, complemented
12#79028—31nomaximal
13C2×#3697—21no—
14C22×C8×C9C2212yes—
15C2×C42×C9C2211yescharacteristic
16#63492—21no—
17#63492C2212yes—
18#63492C2211yescharacteristic
19#63491—21no—
20C4×#611—21no—
21#63486C2211yescharacteristic
22C2×D72C2212yes—
23C2×#3664C2212yes—
24#63438—21no—
25#63437—21no—
26#63437C2211yescharacteristic
27#63436C2211yescharacteristic
28C4×D36—21no—
29C4×D36C2211yescharacteristic
30C4×D36C2212yes—
31#63434—21no—
32#63432C2211yescharacteristic
33#63431C2211yescharacteristic
34C4×Dic18C2211yescharacteristic
35C9×C4⋊C8C2211yescharacteristic
36C9×C4⋊C8C2211yescharacteristic
37C9×C4⋊C8C2212yes—
38#63380C2212yes—
39#63380C2212yes—
40#63380C2212yes—
41#63378C2212yes—
42#63377C2212yes—
43#63376C2212yes—
44#5479—31no—
45#5477—31no—
46C2×C3×C4⋊C8D311yescharacteristic
47#5115—32no—
48#5114—32no—
49#4850—31no—
50#4848—31no—
51#4847—32no—
52#4844—32no—
53#4843—31no—
54#4842—31no—
55C22×C4×C9D411yescharacteristic
56C22×C4×C9D411yescharacteristic
57C22×C4×C9C2311yescharacteristic
58C2×#611—21no—
59C2×#611—22no—
60#3697—44no—
61C2×D36—21no—
62C2×D36—21no—
63C2×D36C2312yes—
64C2×D36C2311yescharacteristic
65C2×C4×D9—21no—
66C2×C4×D9—22no—
67C2×Dic18—21no—
68C2×Dic18C2311yescharacteristic
69C2×C8×C9—42no—
70C2×C8×C9C2312yes—
71C2×C8×C9C2312yes—
72C42×C9D411yescharacteristic
73C42×C9D411yescharacteristic
74C42×C9C2311yescharacteristic
75C42×C9C2311yescharacteristic
76#3676—21no—
77(C2×D9)⋊C4—21no—
78(C2×D9)⋊C4—21no—
79(C2×D9)⋊C4—21no—
80(C2×D9)⋊C4—22no—
81(C2×D9)⋊C4—21no—
82(C2×D9)⋊C4—22no—
83C4⋊Dic9—21no—
84C4⋊Dic9C2312yes—
85C4⋊Dic9C2311yescharacteristic
86C4⋊Dic9C2311yescharacteristic
87Dic9⋊C4—21no—
88Dic9⋊C4—21no—
89Dic9⋊C4—21no—
90Dic9⋊C4—21no—
91C4×Dic9—21no—
92D72—42no—
93#3664—42no—
94#3247—91noSylow
95C2×#235—61no—
96C22×C3×C8C2×D312yes—
97C2×C3×C42C2×D311yescharacteristic
98#930—32no—
99#930—31no—
100#930—61no—
101#929—61no—
102C4×#67—61no—
103#924—31no—
104C2×D24—32no—
105C2×#204—32no—
106#876—61no—
107#875—31no—
108#875—61no—
109#874—31no—
110C4×D12—32no—
111C4×D12—31no—
112C4×D12—61no—
113#872—61no—
114#870—31no—
115#869—31no—
116C4×Dic6—31no—
117C3×C4⋊C8C2×D311yescharacteristic
118C3×C4⋊C8C2×D311yescharacteristic
119C3×C4⋊C8C2×D312yes—
120#821—32no—
121#821—32no—
122#821—32no—
123#818—32no—
124#817—32no—
125#816—32no—
126C23×C9C2×D411yescharacteristic
127C22×D9—21no—
128C22×D9—22no—
129C2×C4×C9—22no—
130C2×C4×C9—22no—
131C2×C4×C9—21no—
132C2×C4×C9—21no—
133C2×C4×C9C2×D411yescharacteristic
134C2×C4×C9C2×D411yescharacteristic
135C2×C4×C9C2×D411yescharacteristic
136C2×C4×C9C2×D411yescharacteristic
137C2×C4×C9C2×D411yescharacteristic
138C2×C4×C9C2411yescharacteristic
139#611—44no—
140#611—42no—
141C2×Dic9—21no—
142C2×Dic9—21no—
143C2×Dic9—21no—
144C2×Dic9—22no—
145D36—22no—
146D36—21no—
147D36—22no—
148D36—21no—
149D36—42no—
150D36—42no—
151C4×D9—44no—
152C4×D9—42no—
153Dic18—21no—
154Dic18—21no—
155Dic18—42no—
156C8×C9—22no—
157C8×C9—22no—
158#532—91no—
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⋊C8D911yescharacteristic, complemented
169C22×C3×C4D1211yescharacteristic
170C22×C3×C4D1211yescharacteristic
171C22×C3×C4C22×D311yescharacteristic
172C2×#67—61no—
173C2×#67—62no—
174#235—124no—
175C2×D12—32no—
176C2×D12—31no—
177C2×D12—61no—
178C2×D12—61no—
179C2×C4×D3—61no—
180C2×C4×D3—62no—
181C2×Dic6—31no—
182C2×Dic6—61no—
183C2×C3×C8—42no—
184C2×C3×C8C22×D312yes—
185C2×C3×C8C22×D312yes—
186C3×C42D1211yescharacteristic
187C3×C42D1211yescharacteristic
188C3×C42C22×D311yescharacteristic
189C3×C42C22×D311yescharacteristic
190#217—61no—
191(C2×D3)⋊C4—61no—
192(C2×D3)⋊C4—61no—
193(C2×D3)⋊C4—62no—
194(C2×D3)⋊C4—61no—
195(C2×D3)⋊C4—62no—
196(C2×D3)⋊C4—61no—
197C4⋊Dic3—32no—
198C4⋊Dic3—31no—
199C4⋊Dic3—31no—
200C4⋊Dic3—61no—
201Dic3⋊C4—61no—
202Dic3⋊C4—61no—
203Dic3⋊C4—61no—
204Dic3⋊C4—61no—
205C4×Dic3—61no—
206D24—122no—
207#204—122no—
208C22×C9—21no—
209C22×C9—21no—
210C22×C9AGL(1,ℤ/8)12yes—
211C22×C9C22×D411yescharacteristic
212C2×D9—42no—
213C2×D9—41no—
214C2×D9—41no—
215C2×D9—42no—
216C2×D9—42no—
217C2×D9—41no—
218C4×C9—21no—
219C4×C9—21no—
220C4×C9—21no—
221C4×C9—21no—
222C4×C9#13512yes—
223C4×C9H(5,𝔽2)11yescharacteristic
224C4×C92−1+411yescharacteristic
225Dic9—41no—
226Dic9—41no—
227Dic9—42no—
228Dic9—41no—
229C2×#41—181no—
230C2×SD16—92no—
231C2×D8—92no—
232C22×C8C2×D912yes—
233C4⋊Q8—91no—
234#127—91no—
235#126—181no—
236#125—91no—
237#124—91no—
238#124—181no—
239#123—181no—
240C22⋊Q8—91no—
241#121—91no—
242#121—92no—
243#121—181no—
244C4×Q8—91no—
245C4×D4—91no—
246C4×D4—92no—
247C4×D4—181no—
248C4×D4—181no—
249#117—181no—
250C2×C42C2×D911yescharacteristic
251#107—92no—
252#106—92no—
253C4⋊C8C2×D911yescharacteristic
254C4⋊C8C2×D911yescharacteristic
255C4⋊C8C2×D912yes—
256#103—92no—
257#102—92no—
258#102—92no—
259#102—92no—
260C23×C3C2×D1211yescharacteristic
261C22×D3—61no—
262C22×D3—62no—
263C2×C3×C4—22no—
264C2×C3×C4—22no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4C2×D1211yescharacteristic
268C2×C3×C4C2×D1211yescharacteristic
269C2×C3×C4C2×D1211yescharacteristic
270C2×C3×C4C2×D1211yescharacteristic
271C2×C3×C4C2×D1211yescharacteristic
272C2×C3×C4C23×D311yescharacteristic
273#67—124no—
274#67—122no—
275C2×Dic3—61no—
276C2×Dic3—61no—
277C2×Dic3—61no—
278C2×Dic3—62no—
279D12—62no—
280D12—61no—
281D12—62no—
282D12—61no—
283D12—122no—
284D12—122no—
285C4×D3—124no—
286C4×D3—122no—
287Dic6—61no—
288Dic6—61no—
289Dic6—122no—
290C3×C8—22no—
291C3×C8—22no—
292C2×C9—22no—
293C2×C9#53711yescharacteristic
294C2×C9C2×#13511yescharacteristic
295C2×C9C2×AGL(1,ℤ/8)11yescharacteristic
296D9—81no—
297D9—82no—
298#41—364no—
299C2×Q8—91no—
300C2×Q8—181no—
301C2×D4—91no—
302C2×D4—92no—
303C2×D4—181no—
304C2×D4—182no—
305C2×D4—181no—
306C2×D4—181no—
307C22×C4—181no—
308C22×C4—182no—
309C22×C4D3611yescharacteristic
310C22×C4D3611yescharacteristic
311C22×C4C22×D911yescharacteristic
312SD16—362no—
313D8—362no—
314C2×C8—42no—
315C2×C8C22×D912yes—
316C2×C8C22×D912yes—
317C4⋊C4—91no—
318C4⋊C4—91no—
319C4⋊C4—92no—
320C4⋊C4—181no—
321C4⋊C4—181no—
322C4⋊C4—181no—
323C4⋊C4—181no—
324C4⋊C4—181no—
325C22⋊C4—181no—
326C22⋊C4—181no—
327C22⋊C4—181no—
328C22⋊C4—182no—
329C22⋊C4—181no—
330C22⋊C4—182no—
331C22⋊C4—181no—
332C42—181no—
333C42D3611yescharacteristic
334C42D3611yescharacteristic
335C42C22×D911yescharacteristic
336C42C22×D911yescharacteristic
337C22×C3—21no—
338C22×C3—21no—
339C22×C3#90812yes—
340C22×C3C22×D1211yescharacteristic
341C2×D3—121no—
342C2×D3—122no—
343C2×D3—122no—
344C2×D3—121no—
345C2×D3—122no—
346C2×D3—121no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4#90412yes—
352C3×C4#100411yescharacteristic
353C3×C4#100711yescharacteristic
354Dic3—121no—
355Dic3—122no—
356Dic3—121no—
357Dic3—121no—
358C9#324711yescharacteristic, complemented, Sylow
359C23—181no—
360C23—182no—
361C23C2×D3611yescharacteristic
362Q8—181no—
363Q8—181no—
364Q8—362no—
365D4—181no—
366D4—182no—
367D4—181no—
368D4—182no—
369D4—362no—
370D4—364no—
371D4—362no—
372D4—362no—
373C2×C4—22no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—22no—
377C2×C4—181no—
378C2×C4—181no—
379C2×C4—181no—
380C2×C4—182no—
381C2×C4—364no—
382C2×C4—362no—
383C2×C4C2×D3611yescharacteristic
384C2×C4C2×D3611yescharacteristic
385C2×C4C2×D3611yescharacteristic
386C2×C4C2×D3611yescharacteristic
387C2×C4C2×D3611yescharacteristic
388C2×C4C23×D911yescharacteristic
389C8—22no—
390C8—22no—
391C2×C3—22no—
392C2×C3#551011yescharacteristic
393C2×C3C2×#90411yescharacteristic
394C2×C3C2×#90811yescharacteristic
395D3—241no—
396D3—242no—
397C22—21no—
398C22—21no—
399C22—361no—
400C22—362no—
401C22—362no—
402C22—361no—
403C22—361no—
404C22—362no—
405C22#6347012yes—
406C22C22×D3611yescharacteristic
407C4—21no—
408C4—21no—
409C4—21no—
410C4—21no—
411C4—361no—
412C4—362no—
413C4—361no—
414C4—361no—
415C4#6346712yes—
416C4#6371011yescharacteristic
417C4#6371311yescharacteristic
418C3#7902811yescharacteristic
419C2—22no—
420C2—721no—
421C2—722no—
422C2#1058961211yescharacteristic
423C2C2×#6346711yescharacteristic
424C2C2×#6347011yescharacteristic
subgroupG/H
centerC22C22×D36
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC2×C9×C4⋊C8C2
socleC22×C3C22×D12
hypercenterC2×C4⋊C8D9
hypocenterC9#3247
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
1. #10589581C2semidirect
2. #10589579C2semidirect
3. C2×C9×C4⋊C8C2semidirect
4. #10588796C2semidirect
5. #10588795C2semidirect
6. #10588531C2semidirect
7. #10588528C2semidirect
8. #10588527C2semidirect
9. #10588526C2semidirect
10. #10588514C2semidirect
11. #10588512C2semidirect
168. C2×C4⋊C8D9semidirect
358. C9#3247semidirect

Maximal subgroups

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

subgroupindex
#105895812
#105895792
C2×C9×C4⋊C82
#105887962
#105887952
#105885312
#105885282
#105885272
#105885262
#105885142
#105885122
#790283