Finite Group Databasebeta

← #11786670

Subgroups — #11786670

Order 1152.

453 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 453 conjugacy classes of subgroups — too many to draw. Only its 110 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#10589606C211yesmaximal, characteristic
2C9×#384C211yesmaximal, characteristic, complemented
3#10588649C211yesmaximal, characteristic
4#10588644C211yesmaximal, characteristic, complemented
5C2×#63364C211yesmaximal, characteristic
6#10588207C211yesmaximal, characteristic, complemented
7#10588201C211yesmaximal, characteristic, complemented
8#69592—31nomaximal
9C2×#3697C2211yescharacteristic
10C2×C9×C4⋊C4—22no—
11C2×C9×C4⋊C4C2211yescharacteristic
12C2×C9×C4⋊C4C2211yescharacteristic
13C2×C42×C9C2211yescharacteristic
14C4×#611—22no—
15#63488C2211yescharacteristic
16C2×#3667C2211yescharacteristic
17C2×#3667C2211yescharacteristic
18#63455—21no—
19#63454—21no—
20C4⋊C4×D9—21no—
21#63449—21no—
22#63369—21no—
23#63368—21no—
24#63367—21no—
25#63366—21no—
26#63364C414yescomplemented
27#5504—31no—
28C3×#384D311yescharacteristic
29#4966—31no—
30#4964—31no—
31C2×#805—31no—
32#4530—31no—
33#4523—31no—
34C22×C4×C9—21no—
35C22×C4×C9—21no—
36C22×C4×C9D412yes—
37C22×C4×C9C2311yescharacteristic
38C2×#611—21no—
39#3697—21no—
40#3697—21no—
41#3697C2×C412yes—
42#3697Q812yes—
43C2×D36D411yescharacteristic
44C2×C4×D9—21no—
45C2×C4×D9—22no—
46C2×Dic18D411yescharacteristic
47C9×C4⋊C4—21no—
48C9×C4⋊C4—21no—
49C9×C4⋊C4—21no—
50C9×C4⋊C4—21no—
51C9×C4⋊C4—44no—
52C42×C9—21no—
53C42×C9C2×C412yescomplemented
54#3676—21no—
55(C2×D9)⋊C4—22no—
56C4⋊Dic9D411yescharacteristic
57C4⋊Dic9D411yescharacteristic
58Dic9⋊C4—22no—
59C4×Dic9—22no—
60C4×Dic9—21no—
61#3667—21no—
62#3667—21no—
63#3667—21no—
64#3667C2×C412yescomplemented
65C2×C9⋊C8—21no—
66C2×C9⋊C8—21no—
67#1859—91noSylow
68C2×#235—31no—
69C2×C3×C4⋊C4—22no—
70C2×C3×C4⋊C4C2×D311yescharacteristic
71C2×C3×C4⋊C4C2×D311yescharacteristic
72C2×C3×C42C2×D311yescharacteristic
73C4×#67—62no—
74#926—31no—
75C2×#208—31no—
76C2×#208—31no—
77#893—61no—
78#892—61no—
79D3×C4⋊C4—61no—
80#887—61no—
81#810—61no—
82#809—61no—
83#808—61no—
84#807—61no—
85#805—34no—
86C23×C9C2×D411yescharacteristic
87C22×D9—21no—
88C2×C4×C9—22no—
89C2×C4×C9—22no—
90C2×C4×C9—22no—
91C2×C4×C9—22no—
92C2×C4×C9—42no—
93C2×C4×C9—42no—
94C2×C4×C9—41no—
95C2×C4×C9C22×C411yescharacteristic
96C2×C4×C9C2×D411yescharacteristic
97C2×C4×C9C2×D411yescharacteristic
98C2×C4×C9C2×Q811yescharacteristic
99C2×C4×C9#4111yescharacteristic
100C2×C4×C9#4111yescharacteristic
101#611—22no—
102#611—22no—
103C2×Dic9—21no—
104C2×Dic9—21no—
105C2×Dic9—21no—
106D36—21no—
107D36C4⋊C412yescomplemented
108C4×D9—22no—
109C4×D9—22no—
110C4×D9—82no—
111Dic18—21no—
112Dic18C4⋊C412yescomplemented
113C9⋊C8—22no—
114C9⋊C8—41no—
115#520—91no—
116#428—91no—
117C2×#104—91no—
118#417—91no—
119#384D911yescharacteristic, complemented
120#343—91no—
121#339—91no—
122C22×C3×C4—21no—
123C22×C3×C4—21no—
124C22×C3×C4#6712yes—
125C22×C3×C4C22×D311yescharacteristic
126C2×#67—61no—
127#235—32no—
128#235—32no—
129#235—61no—
130#235—61no—
131C2×D12—31no—
132C2×C4×D3—61no—
133C2×C4×D3—62no—
134C2×Dic6—31no—
135C3×C4⋊C4—21no—
136C3×C4⋊C4—21no—
137C3×C4⋊C4—21no—
138C3×C4⋊C4—21no—
139C3×C4⋊C4—44no—
140C3×C42—21no—
141C3×C42C4×D312yes—
142#217—61no—
143(C2×D3)⋊C4—62no—
144C4⋊Dic3—31no—
145C4⋊Dic3—31no—
146Dic3⋊C4—62no—
147C4×Dic3—62no—
148C4×Dic3—61no—
149#208—32no—
150#208—61no—
151#208—61no—
152#208—61no—
153C2×C3⋊C8—61no—
154C2×C3⋊C8—61no—
155C22×C9—21no—
156C22×C9—21no—
157C22×C9C4×D411yescharacteristic
158C22×C9#12011yescharacteristic
159C22×C9C22⋊Q811yescharacteristic
160C2×D9—22no—
161C2×D9—41no—
162C2×D9—41no—
163C4×C9—24no—
164C4×C9—42no—
165C4×C9—81no—
166C4×C9C2×C4⋊C411yescharacteristic
167C4×C9C4×D411yescharacteristic
168C4×C9C22⋊Q811yescharacteristic
169C4×C9#12311yescharacteristic
170Dic9—22no—
171Dic9—41no—
172Dic9—41no—
173C2×#41—91no—
174C2×M16—91no—
175C2×M16—91no—
176C4×Q8—181no—
177C4×D4—181no—
178C4×D4—182no—
179#117—91no—
180#117—181no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—181no—
183C2×C4⋊C4C2×D911yescharacteristic
184C2×C4⋊C4C2×D911yescharacteristic
185C2×C42C2×D911yescharacteristic
186#107—181no—
187#106—181no—
188#104—94no—
189#103—181no—
190#102—181no—
191C23×C3C2×#6711yescharacteristic
192C22×D3—61no—
193C2×C3×C4—22no—
194C2×C3×C4—22no—
195C2×C3×C4—22no—
196C2×C3×C4—22no—
197C2×C3×C4—42no—
198C2×C3×C4—42no—
199C2×C3×C4—41no—
200C2×C3×C4C2×C4×D311yescharacteristic
201C2×C3×C4#23511yescharacteristic
202C2×C3×C4D3×D411yescharacteristic
203C2×C3×C4D3×D411yescharacteristic
204C2×C3×C4D3×Q811yescharacteristic
205C2×C3×C4#23911yescharacteristic
206#67—62no—
207#67—62no—
208C2×Dic3—61no—
209C2×Dic3—61no—
210C2×Dic3—61no—
211D12—32no—
212D12—61no—
213C4×D3—62no—
214C4×D3—62no—
215C4×D3—242no—
216Dic6—32no—
217Dic6—61no—
218C3⋊C8—62no—
219C3⋊C8—121no—
220C2×C9—21no—
221C2×C9—21no—
222C2×C9#38511yescharacteristic
223C2×C9#45311yescharacteristic
224C2×C9#45611yescharacteristic
225D9—42no—
226#41—92no—
227#41—92no—
228#41—181no—
229#41—181no—
230C2×Q8—91no—
231C2×D4—91no—
232C2×D4—181no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—182no—
236C22×C4—181no—
237C22×C4#61112yes—
238C22×C4C22×D911yescharacteristic
239M16—92no—
240M16—181no—
241M16—181no—
242M16—181no—
243C2×C8—181no—
244C2×C8—181no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—44no—
250C4⋊C4—91no—
251C4⋊C4—91no—
252C4⋊C4—182no—
253C22⋊C4—182no—
254C22⋊C4—181no—
255C42—21no—
256C42—182no—
257C42—181no—
258C42C4×D912yescomplemented
259C22×C3—21no—
260C22×C3—21no—
261C22×C3C4×#6711yescharacteristic
262C22×C3#93711yescharacteristic
263C22×C3#94611yescharacteristic
264C2×D3—62no—
265C2×D3—121no—
266C2×D3—121no—
267C3×C4—24no—
268C3×C4—42no—
269C3×C4—81no—
270C3×C4D3×C4⋊C411yescharacteristic
271C3×C4#89311yescharacteristic
272C3×C4#89411yescharacteristic
273C3×C4#89611yescharacteristic
274Dic3—62no—
275Dic3—121no—
276Dic3—121no—
277C9#185911yescharacteristic, complemented, Sylow
278C23—181no—
279C23C2×#61111yescharacteristic
280Q8—92no—
281Q8—181no—
282D4—92no—
283D4—182no—
284D4—182no—
285D4—181no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—181no—
294C2×C4—182no—
295C2×C4—182no—
296C2×C4—181no—
297C2×C4—181no—
298C2×C4—722no—
299C2×C4C2×C4×D911yescharacteristic
300C2×C4#369711yescharacteristic
301C2×C4D4×D911yescharacteristic
302C2×C4D4×D911yescharacteristic
303C2×C4Q8×D911yescharacteristic
304C2×C4#370111yescharacteristic
305C8—182no—
306C8—361no—
307C2×C3—21no—
308C2×C3—21no—
309C2×C3#498911yescharacteristic
310C2×C3#507711yescharacteristic
311C2×C3#509511yescharacteristic
312D3—122no—
313C22—21no—
314C22—21no—
315C22—182no—
316C22—361no—
317C22—361no—
318C22C4×#61111yescharacteristic
319C22#6349911yescharacteristic
320C22#6350811yescharacteristic
321C4—24no—
322C4—42no—
323C4—81no—
324C4—182no—
325C4—361no—
326C4—361no—
327C4C4⋊C4×D911yescharacteristic
328C4#6345511yescharacteristic
329C4#6345611yescharacteristic
330C4#6345811yescharacteristic
331C3#6959211yescharacteristic
332C2—21no—
333C2—21no—
334C2—362no—
335C2#1058866911yescharacteristic
336C2#1058875711yescharacteristic
337C2#1058877511yescharacteristic
subgroupG/H
centerC22#63499
commutatorC2×C4×C9C22×C4
FrattiniC22×C3×C4C22×D3
FittingC9×#384C2
socleC22×C3#937
prime radicalC2×#3697C22
cosocleC22×C4×C9C23
hypercenter#384D9
hypocenterC9#1859
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #384

Complements

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

NH ≅ G/Ntype
2. C9×#384C2semidirect
4. #10588644C2semidirect
6. #10588207C2semidirect
7. #10588201C2semidirect
26. #63364C4semidirect
53. C42×C9C2×C4semidirect
64. #3667C2×C4semidirect
107. D36C4⋊C4semidirect
112. Dic18C4⋊C4semidirect
119. #384D9semidirect
258. C42C4×D9semidirect
277. C9#1859semidirect

Maximal subgroups

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

subgroupindex
#105896062
C9×#3842
#105886492
#105886442
C2×#633642
#105882072
#105882012
#695923