Finite Group Databasebeta

← #11878643

Subgroups — #11878643

Order 1152.

798 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 798 conjugacy classes of subgroups — too many to draw. Only its 154 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10589827C211yesmaximal, characteristic, complemented
2D9×#127C211yesmaximal, characteristic, complemented
3C9×#486C211yesmaximal, characteristic, complemented
4#10588773C211yesmaximal, characteristic, complemented
5#10588755C211yesmaximal, characteristic, complemented
6#10588466C214yesmaximal, complemented
7#10588453C214yesmaximal, complemented
8#10588377C211yesmaximal, characteristic, complemented
9#10588367C211yesmaximal, characteristic, complemented
10#81566—31nomaximal
11C2×#3701—21no—
12C2×D4×D9—21no—
13C2×D4×D9—21no—
14C2×D4×D9C2212yes—
15C9×C4⋊Q8C2211yescharacteristic, complemented
16C9×#127C2211yescharacteristic
17#63509—21no—
18#63502—21no—
19#63502—21no—
20#63502C2212yes—
21C2×#3673C2214yescomplemented
22C2×D72C2214yescomplemented
23#63457—21no—
24#63457C2212yes—
25#63455—21no—
26#63455C2212yescomplemented
27#63436C2211yescharacteristic
28#63436C2211yescharacteristic, complemented
29C42×D9C2211yescharacteristic
30C9×#102C2214yescomplemented
31C4×C8×C9C2211yescharacteristic, complemented
32(C2×D9)⋊C8C2212yes—
33Dic9⋊C8C2212yescomplemented
34#63369C2214yescomplemented
35C4×C9⋊C8C2211yescharacteristic, complemented
36#5725—31no—
37D3×#127—31no—
38C3×#486D311yescharacteristic
39#5088—31no—
40#5073—31no—
41#4786—34no—
42#4773—34no—
43#4695—31no—
44#4685—31no—
45C23×D9—22no—
46C2×Q8×C9—21no—
47C2×D4×C9—21no—
48C2×D4×C9—21no—
49C2×D4×C9C2312yes—
50C2×#611—22no—
51C2×#611—22no—
52C2×#611—22no—
53#3701—44no—
54D4×D9—44no—
55D4×D9—44no—
56D4×D9—44no—
57C2×D36—22no—
58C2×D36—21no—
59C2×D36—21no—
60C2×D36—21no—
61C2×D36—21no—
62C2×D36C2312yes—
63C2×D36C2312yes—
64C2×C4×D9—22no—
65C2×C4×D9D411yescharacteristic
66C2×C4×D9D411yescharacteristic
67C2×C4×D9C2311yescharacteristic
68C2×C8×C9C2312yes—
69C9×C4⋊C4—21no—
70C9×C4⋊C4C2312yes—
71C42×C9C2311yescharacteristic
72#3673—44no—
73(C2×D9)⋊C4—22no—
74(C2×D9)⋊C4—22no—
75C4×Dic9D411yescharacteristic
76C4×Dic9D411yescharacteristic
77C4×Dic9C2311yescharacteristic
78C2×C9⋊C8C2312yes—
79D72—44no—
80#3205—91noSylow
81C2×#239—61no—
82C2×D3×D4—32no—
83C2×D3×D4—61no—
84C2×D3×D4—61no—
85C3×C4⋊Q8C2×D311yescharacteristic
86C3×#127C2×D311yescharacteristic
87#947—61no—
88#940—32no—
89#940—61no—
90#940—61no—
91C2×#213—34no—
92C2×D24—34no—
93#895—32no—
94#895—61no—
95#893—32no—
96#893—61no—
97#874—31no—
98#874—31no—
99C42×D3—31no—
100C3×#102C2×D314yes—
101C3×C4×C8C2×D311yescharacteristic
102(C2×D3)⋊C8—32no—
103Dic3⋊C8—32no—
104#809—34no—
105C4×C3⋊C8—31no—
106C23×C9—22no—
107C22×D9—22no—
108C22×D9—22no—
109C22×D9—44no—
110C22×D9—44no—
111C22×D9—44no—
112C22×D9C2×D411yescharacteristic
113Q8×C9—42no—
114D4×C9—24no—
115D4×C9—42no—
116D4×C9—42no—
117C2×C4×C9—22no—
118C2×C4×C9C2×D411yescharacteristic
119C2×C4×C9C2×D411yescharacteristic
120C2×C4×C9C2411yescharacteristic
121#611—44no—
122#611—44no—
123#611—44no—
124C2×Dic9C2×D411yescharacteristic
125C2×Dic9C2×D411yescharacteristic
126C2×Dic9C2×D411yescharacteristic
127D36—24no—
128D36—24no—
129D36—44no—
130D36—42no—
131D36—42no—
132D36—42no—
133D36—42no—
134C4×D9—22no—
135C4×D9—22no—
136C4×D9—44no—
137C4×D9D814yescomplemented
138C8×C9—22no—
139C9⋊C8—22no—
140#532—91no—
141C2×#127—91no—
142#493—91no—
143#493—91no—
144#486—91no—
145#486D911yescharacteristic, complemented
146#459—94no—
147#447—94no—
148#431—91no—
149C23×D3—62no—
150C2×C3×Q8—21no—
151C2×C3×D4—21no—
152C2×C3×D4—21no—
153C2×C3×D4C22×D312yes—
154C2×#67—62no—
155C2×#67—62no—
156C2×#67—62no—
157#239—124no—
158D3×D4—124no—
159D3×D4—124no—
160D3×D4—124no—
161C2×D12—32no—
162C2×D12—32no—
163C2×D12—62no—
164C2×D12—61no—
165C2×D12—61no—
166C2×D12—61no—
167C2×D12—61no—
168C2×C4×D3—31no—
169C2×C4×D3—31no—
170C2×C4×D3—31no—
171C2×C4×D3—62no—
172C2×C3×C8C22×D312yes—
173C3×C4⋊C4—21no—
174C3×C4⋊C4C22×D312yes—
175C3×C42C22×D311yescharacteristic
176#213—124no—
177(C2×D3)⋊C4—62no—
178(C2×D3)⋊C4—62no—
179C4×Dic3—31no—
180C4×Dic3—31no—
181C4×Dic3—31no—
182C2×C3⋊C8—32no—
183D24—124no—
184C22×C9—42no—
185C22×C9—42no—
186C22×C9—42no—
187C22×C9C22×D411yescharacteristic
188C2×D9—21no—
189C2×D9—21no—
190C2×D9—42no—
191C2×D9—42no—
192C2×D9—42no—
193C2×D9—42no—
194C2×D9—42no—
195C2×D9—42no—
196C2×D9—88no—
197C2×D9C2×D812yes—
198C4×C9—42no—
199C4×C9C2×D812yes—
200C4×C9AGL(1,ℤ/8)12yes—
201C4×C9H(5,𝔽2)12yes—
202Dic9—21no—
203Dic9—21no—
204Dic9C2×D812yes—
205C2×#41—181no—
206C22×D4—92no—
207C22×D4—181no—
208C22×D4—181no—
209C2×D8—94no—
210C2×D8—94no—
211C4⋊Q8C2×D911yescharacteristic, complemented
212#127—92no—
213#127—91no—
214#127—91no—
215#127—181no—
216#127—181no—
217#127C2×D911yescharacteristic
218#124—181no—
219#121—92no—
220#121—181no—
221C4×D4—92no—
222C4×D4—181no—
223C2×C42—91no—
224C4⋊C8—92no—
225#102—94no—
226#102C2×D914yescomplemented
227C22⋊C8—92no—
228C4×C8—91no—
229C4×C8C2×D911yescharacteristic, complemented
230C23×C3—22no—
231C22×D3—31no—
232C22×D3—62no—
233C22×D3—62no—
234C22×D3—124no—
235C22×D3—124no—
236C22×D3—124no—
237C3×Q8—42no—
238C3×D4—24no—
239C3×D4—42no—
240C3×D4—42no—
241C2×C3×C4—22no—
242C2×C3×C4D3×D411yescharacteristic
243C2×C3×C4D3×D411yescharacteristic
244C2×C3×C4C23×D311yescharacteristic
245#67—124no—
246#67—124no—
247#67—124no—
248C2×Dic3—31no—
249C2×Dic3—31no—
250C2×Dic3—31no—
251D12—64no—
252D12—64no—
253D12—124no—
254D12—122no—
255D12—122no—
256D12—122no—
257D12—122no—
258C4×D3—34no—
259C4×D3—62no—
260C4×D3—62no—
261C4×D3—124no—
262C3×C8—22no—
263C3⋊C8—62no—
264C2×C9—82no—
265C2×C9#53511yescharacteristic
266C2×C9C22×D811yescharacteristic
267C2×C9C2×AGL(1,ℤ/8)11yescharacteristic
268D9—22no—
269D9—82no—
270D9—82no—
271C24—182no—
272#41—364no—
273C2×Q8—21no—
274C2×D4—21no—
275C2×D4—21no—
276C2×D4—92no—
277C2×D4—92no—
278C2×D4—182no—
279C2×D4—182no—
280C2×D4—182no—
281C2×D4—182no—
282C2×D4—181no—
283C2×D4—181no—
284C2×D4—181no—
285C2×D4—181no—
286C2×D4—364no—
287C2×D4—364no—
288C2×D4—364no—
289C2×D4C22×D912yes—
290C22×C4—91no—
291C22×C4—91no—
292C22×C4—91no—
293C22×C4—182no—
294D8—364no—
295D8—364no—
296C2×C8—92no—
297C2×C8C22×D912yes—
298C4⋊C4—21no—
299C4⋊C4C22×D912yes—
300C22⋊C4—182no—
301C22⋊C4—182no—
302C42—91no—
303C42—91no—
304C42—91no—
305C42C22×D911yescharacteristic
306C22×C3—42no—
307C22×C3—42no—
308C22×C3—42no—
309C22×C3C2×D3×D411yescharacteristic
310C2×D3—32no—
311C2×D3—61no—
312C2×D3—61no—
313C2×D3—122no—
314C2×D3—122no—
315C2×D3—122no—
316C2×D3—122no—
317C2×D3—122no—
318C2×D3—122no—
319C2×D3—248no—
320C3×C4—42no—
321C3×C4D3×D812yes—
322C3×C4#91412yes—
323C3×C4#100912yes—
324Dic3—32no—
325Dic3—61no—
326Dic3—61no—
327C9#320511yescharacteristic, complemented, Sylow
328C23—22no—
329C23—91no—
330C23—182no—
331C23—182no—
332C23—364no—
333C23—364no—
334C23—364no—
335Q8—42no—
336D4—24no—
337D4—42no—
338D4—42no—
339D4—184no—
340D4—184no—
341D4—364no—
342D4—364no—
343D4—364no—
344D4—364no—
345D4—362no—
346D4—362no—
347D4—362no—
348D4—362no—
349C2×C4—22no—
350C2×C4—91no—
351C2×C4—94no—
352C2×C4—91no—
353C2×C4—91no—
354C2×C4—182no—
355C2×C4—182no—
356C2×C4—364no—
357C2×C4D4×D911yescharacteristic
358C2×C4D4×D911yescharacteristic
359C2×C4C23×D911yescharacteristic
360C8—22no—
361C8—182no—
362C2×C3—82no—
363C2×C3#567411yescharacteristic
364C2×C3C2×D3×D811yescharacteristic
365C2×C3C2×#91411yescharacteristic
366D3—62no—
367D3—242no—
368D3—242no—
369C22—42no—
370C22—42no—
371C22—42no—
372C22—92no—
373C22—181no—
374C22—181no—
375C22—362no—
376C22—362no—
377C22—362no—
378C22—362no—
379C22—362no—
380C22—362no—
381C22—728no—
382C22C2×D4×D911yescharacteristic
383C4—42no—
384C4—92no—
385C4—181no—
386C4—181no—
387C4D8×D912yes—
388C4#6347612yes—
389C4#6371512yes—
390C3#8156611yescharacteristic
391C2—82no—
392C2—182no—
393C2—722no—
394C2—722no—
395C2#1058977611yescharacteristic
396C2C2×D8×D911yescharacteristic
397C2C2×#6347611yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#486C2
socleC22×C3C2×D3×D4
hypercenter#486D9
hypocenterC9#3205
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #10589827C2semidirect
2. D9×#127C2semidirect
3. C9×#486C2semidirect
4. #10588773C2semidirect
5. #10588755C2semidirect
6. #10588466C2semidirect
7. #10588453C2semidirect
8. #10588377C2semidirect
9. #10588367C2semidirect
15. C9×C4⋊Q8C22semidirect
21. C2×#3673C22semidirect
22. C2×D72C22semidirect
26. #63455C22semidirect
28. #63436C22semidirect
30. C9×#102C22semidirect
31. C4×C8×C9C22semidirect
33. Dic9⋊C8C22semidirect
34. #63369C22semidirect
35. C4×C9⋊C8C22semidirect
137. C4×D9D8semidirect
145. #486D9semidirect
211. C4⋊Q8C2×D9semidirect
226. #102C2×D9semidirect
229. C4×C8C2×D9semidirect
327. C9#3205semidirect

Maximal subgroups

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

subgroupindex
#105898272
D9×#1272
C9×#4862
#105887732
#105887552
#105884662
#105884532
#105883772
#105883672
#815663