Finite Group Databasebeta

← #11786607

Subgroups — #11786607

Order 1152.

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

normal subgroups only

This group has 408 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#10589618C211yesmaximal, characteristic
2C2×#63382C211yesmaximal, characteristic
3#10588805C211yesmaximal, characteristic
4#10588679C211yesmaximal, characteristic
5#10588609C211yesmaximal, characteristic
6C9×#339C211yesmaximal, characteristic
7#10588201C211yesmaximal, characteristic
8#68764—31nomaximal
9C22×Dic18C2211yescharacteristic
10C2×C9×M16C2211yescharacteristic
11C9×#117C2211yescharacteristic
12C2×C42×C9C2211yescharacteristic
13#63488C2211yescharacteristic
14C2×C4⋊Dic9C2211yescharacteristic
15C2×#3667C2211yescharacteristic
16#63449—21no—
17#63449—21no—
18#63439—22no—
19C4×Dic18—21no—
20C4×Dic18—21no—
21C9⋊#95—22no—
22#63382C414yescomplemented
23#63378—21no—
24#63377—21no—
25#63367—21no—
26#63366—21no—
27#5516—31no—
28C2×#824—31no—
29#5121—31no—
30#4995—31no—
31#4929—31no—
32C3×#339D311yescharacteristic
33#4523—31no—
34C22×C4×C9—21no—
35C22×C4×C9C2311yescharacteristic
36C22×Dic9—21no—
37C22×Dic9D412yes—
38C2×Dic18—21no—
39C2×Dic18—21no—
40C2×Dic18—21no—
41C2×Dic18—21no—
42C2×Dic18C2×C412yes—
43C2×Dic18Q812yes—
44C9×M16—21no—
45C9×M16C2×C412yes—
46C2×C8×C9—21no—
47C9×C4⋊C4D411yescharacteristic
48C9×C4⋊C4D411yescharacteristic
49C9×C22⋊C4—21no—
50C42×C9—21no—
51C42×C9—21no—
52C42×C9—21no—
53#3676—21no—
54C4⋊Dic9—21no—
55C4⋊Dic9—21no—
56C4⋊Dic9D411yescharacteristic
57C4⋊Dic9D411yescharacteristic
58Dic9⋊C4—22no—
59Dic9⋊C4—22no—
60C4×Dic9—22no—
61C4×Dic9—22no—
62C4×Dic9—21no—
63#3667—21no—
64#3667C2×C412yes—
65C2×C9⋊C8—21no—
66#1857—91noSylow
67C22×Dic6—31no—
68C2×C3×M16C2×D311yescharacteristic
69C3×#117C2×D311yescharacteristic
70C2×C3×C42C2×D311yescharacteristic
71#926—31no—
72C2×C4⋊Dic3—31no—
73C2×#208—31no—
74#887—61no—
75#887—61no—
76#877—62no—
77C4×Dic6—61no—
78C4×Dic6—61no—
79C3⋊#95—62no—
80#824—34no—
81#818—61no—
82#817—61no—
83#808—61no—
84#807—61no—
85C23×C9C2×D411yescharacteristic
86C2×C4×C9—22no—
87C2×C4×C9—21no—
88C2×C4×C9—21no—
89C2×C4×C9—41no—
90C2×C4×C9—41no—
91C2×C4×C9C22×C411yescharacteristic
92C2×C4×C9C2×D411yescharacteristic
93C2×C4×C9C2×D411yescharacteristic
94C2×C4×C9C2×Q811yescharacteristic
95C2×C4×C9#4111yescharacteristic
96C2×C4×C9#4111yescharacteristic
97C2×Dic9—22no—
98C2×Dic9—22no—
99C2×Dic9—21no—
100C2×Dic9—21no—
101C2×Dic9—42no—
102C2×Dic9—41no—
103C2×Dic9C4⋊C414yes—
104Dic18—22no—
105Dic18—22no—
106Dic18—22no—
107Dic18—22no—
108C8×C9—22no—
109C9⋊C8—22no—
110#519—91no—
111#428—91no—
112#428—91no—
113C2×#101—91no—
114#391—91no—
115#339—91no—
116#339D911yescharacteristic
117C22×C3×C4—21no—
118C22×C3×C4C22×D311yescharacteristic
119C22×Dic3—32no—
120C22×Dic3—61no—
121C2×Dic6—32no—
122C2×Dic6—32no—
123C2×Dic6—61no—
124C2×Dic6—61no—
125C2×Dic6—61no—
126C2×Dic6—61no—
127C3×M16—21no—
128C3×M16C4×D312yes—
129C2×C3×C8—21no—
130C3×C4⋊C4D1211yescharacteristic
131C3×C4⋊C4D1211yescharacteristic
132C3×C22⋊C4—21no—
133C3×C42—21no—
134C3×C42—21no—
135C3×C42—21no—
136#217—61no—
137C4⋊Dic3—31no—
138C4⋊Dic3—31no—
139C4⋊Dic3—61no—
140C4⋊Dic3—61no—
141Dic3⋊C4—62no—
142Dic3⋊C4—62no—
143C4×Dic3—62no—
144C4×Dic3—62no—
145C4×Dic3—61no—
146#208—32no—
147#208—61no—
148C2×C3⋊C8—61no—
149C22×C9—21no—
150C22×C9—21no—
151C22×C9C2×C4⋊C411yescharacteristic
152C22×C9#12011yescharacteristic
153C22×C9#12311yescharacteristic
154C4×C9—42no—
155C4×C9—41no—
156C4×C9—41no—
157C4×C9C4×D411yescharacteristic
158C4×C9C4×D411yescharacteristic
159C4×C9C22⋊Q811yescharacteristic
160C4×C9C22⋊Q811yescharacteristic
161Dic9—24no—
162Dic9—41no—
163Dic9—41no—
164Dic9—81no—
165C22×Q8—91no—
166C2×M16—91no—
167C2×M16C2×D911yescharacteristic
168C4×Q8—181no—
169C4×Q8—181no—
170C4×Q8—181no—
171C4×Q8—181no—
172#117—91no—
173#117—182no—
174#117C2×D911yescharacteristic
175C2×C4⋊C4—91no—
176C2×C42C2×D911yescharacteristic
177#107—181no—
178#107—181no—
179#106—181no—
180#106—181no—
181#101—94no—
182#95—182no—
183C23×C3D3×D411yescharacteristic
184C2×C3×C4—22no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4—41no—
188C2×C3×C4—41no—
189C2×C3×C4C2×C4×D311yescharacteristic
190C2×C3×C4C2×D1211yescharacteristic
191C2×C3×C4#23511yescharacteristic
192C2×C3×C4D3×D411yescharacteristic
193C2×C3×C4#23711yescharacteristic
194C2×C3×C4D3×Q811yescharacteristic
195C2×Dic3—34no—
196C2×Dic3—62no—
197C2×Dic3—62no—
198C2×Dic3—61no—
199C2×Dic3—61no—
200C2×Dic3—122no—
201C2×Dic3—121no—
202Dic6—62no—
203Dic6—62no—
204Dic6—62no—
205Dic6—62no—
206C3×C8—22no—
207C3⋊C8—62no—
208C2×C9—21no—
209C2×C9—21no—
210C2×C9#38511yescharacteristic
211C2×C9#45411yescharacteristic
212C2×C9#45611yescharacteristic
213C2×Q8—92no—
214C2×Q8—92no—
215C2×Q8—181no—
216C2×Q8—181no—
217C2×Q8—181no—
218C2×Q8—181no—
219C22×C4—21no—
220C22×C4—92no—
221C22×C4—181no—
222C22×C4C22×D911yescharacteristic
223M16—21no—
224M16—92no—
225M16—181no—
226M16C4×D912yes—
227C2×C8—21no—
228C2×C8—181no—
229C4⋊C4—91no—
230C4⋊C4—91no—
231C4⋊C4—182no—
232C4⋊C4—182no—
233C4⋊C4—181no—
234C4⋊C4—181no—
235C4⋊C4D3611yescharacteristic
236C4⋊C4D3611yescharacteristic
237C22⋊C4—21no—
238C22⋊C4—181no—
239C42—21no—
240C42—21no—
241C42—21no—
242C42—182no—
243C42—182no—
244C42—181no—
245C22×C3—21no—
246C22×C3—21no—
247C22×C3#88211yescharacteristic
248C22×C3#88311yescharacteristic
249C22×C3D3×C4⋊C411yescharacteristic
250C3×C4—42no—
251C3×C4—41no—
252C3×C4—41no—
253C3×C4C4×D1211yescharacteristic
254C3×C4#67⋊C411yescharacteristic
255C3×C4#89611yescharacteristic
256C3×C4#89711yescharacteristic
257Dic3—64no—
258Dic3—121no—
259Dic3—121no—
260Dic3—241no—
261C9#185711yescharacteristic, complemented, Sylow
262C23D4×D911yescharacteristic
263Q8—182no—
264Q8—182no—
265Q8—182no—
266Q8—182no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—94no—
273C2×C4—182no—
274C2×C4—182no—
275C2×C4—181no—
276C2×C4—181no—
277C2×C4—362no—
278C2×C4—361no—
279C2×C4C2×C4×D911yescharacteristic
280C2×C4C2×D3611yescharacteristic
281C2×C4#369711yescharacteristic
282C2×C4D4×D911yescharacteristic
283C2×C4#369911yescharacteristic
284C2×C4Q8×D911yescharacteristic
285C8—22no—
286C8—182no—
287C2×C3—21no—
288C2×C3—21no—
289C2×C3#466811yescharacteristic
290C2×C3#482611yescharacteristic
291C2×C3#482711yescharacteristic
292C22—21no—
293C22—21no—
294C22#6344411yescharacteristic
295C22#6344511yescharacteristic
296C22C4⋊C4×D911yescharacteristic
297C4—42no—
298C4—41no—
299C4—41no—
300C4—184no—
301C4—361no—
302C4—361no—
303C4—721no—
304C4C4×D3611yescharacteristic
305C4#611⋊C411yescharacteristic
306C4#6345811yescharacteristic
307C4#6345911yescharacteristic
308C3#6876411yescharacteristic
309C2—21no—
310C2—21no—
311C2#1058834811yescharacteristic
312C2#1058850611yescharacteristic
313C2#1058850711yescharacteristic
subgroupG/H
centerC22#63444
commutatorC2×C4×C9C22×C4
FrattiniC22×C3×C4C22×D3
FittingC9×#339C2
socleC22×C3#882
prime radicalC23×C3D3×D4
cosocleC22×C4×C9C23
hypercenter#339D9
hypocenterC9#1857
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
22. #63382C4semidirect
261. C9#1857semidirect

Maximal subgroups

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

subgroupindex
#105896182
C2×#633822
#105888052
#105886792
#105886092
C9×#3392
#105882012
#687643