Finite Group Databasebeta

← #11774569

Subgroups — #11774569

Order 1152.

372 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 100 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
1C4×Q8×D9C211yesmaximal, characteristic
2#10588521C211yesmaximal, characteristic
3#10588367C211yesmaximal, characteristic
4C9×Q8⋊C8C211yesmaximal, characteristic, complemented
5#10588212C211yesmaximal, characteristic, complemented
6#10588160C211yesmaximal, characteristic, complemented
7#10588133C211yesmaximal, characteristic, complemented
8#68236—31nomaximal
9C2×Q8×D9C411yescharacteristic
10C4×Q8×C9C2211yescharacteristic
11Q8×Dic9C411yescharacteristic
12C2×#3663—21no—
13C4⋊C4×D9—21no—
14C4⋊C4×D9C411yescharacteristic
15#63449—21no—
16#63449C411yescharacteristic
17C42×D9—21no—
18C42×D9C2211yescharacteristic
19C4×Dic18—21no—
20C4×Dic18C2211yescharacteristic
21C9×C4⋊C8C2211yescharacteristic
22C4×C8×C9C2211yescharacteristic
23(C2×D9)⋊C8—21no—
24Dic9⋊C8—21no—
25Dic9⋊C8—21no—
26C4⋊(C9⋊C8)C2211yescharacteristic
27C4×C9⋊C8C2211yescharacteristic
28C4×D3×Q8—31no—
29#4837—31no—
30#4685—31no—
31C3×Q8⋊C8D311yescharacteristic
32#4535—31no—
33#4484—31no—
34#4456—31no—
35C2×Q8×C9C2×C411yescharacteristic
36Q8×D9—22no—
37Q8×D9—22no—
38C2×C4×D9—21no—
39C2×C4×D9—21no—
40C2×C4×D9C2×C411yescharacteristic
41C2×C4×D9D411yescharacteristic
42C2×C4×D9D411yescharacteristic
43C2×Dic18—21no—
44C2×Dic18C2×C411yescharacteristic
45C2×C8×C9—21no—
46C2×C8×C9—21no—
47C9×C4⋊C4—21no—
48C9×C4⋊C4C2×C411yescharacteristic
49C42×C9—21no—
50C42×C9C2311yescharacteristic
51C4⋊Dic9—21no—
52C4⋊Dic9C2×C411yescharacteristic
53Dic9⋊C4—21no—
54Dic9⋊C4—21no—
55Dic9⋊C4—21no—
56C4×Dic9—21no—
57C4×Dic9—21no—
58C4×Dic9—21no—
59C4×Dic9C2×C411yescharacteristic
60C4×Dic9D411yescharacteristic
61C4×Dic9D411yescharacteristic
62C2×C9⋊C8—21no—
63C2×C9⋊C8—21no—
64#3663—42no—
65#1487—91noSylow
66C2×D3×Q8—31no—
67C3×C4×Q8C2×D311yescharacteristic
68Q8×Dic3—31no—
69C2×ΓL(1,𝔽25)—61no—
70D3×C4⋊C4—31no—
71D3×C4⋊C4—61no—
72#887—31no—
73#887—61no—
74C42×D3—31no—
75C42×D3—61no—
76C4×Dic6—31no—
77C4×Dic6—61no—
78C3×C4⋊C8C2×D311yescharacteristic
79C3×C4×C8C2×D311yescharacteristic
80(C2×D3)⋊C8—61no—
81Dic3⋊C8—61no—
82Dic3⋊C8—61no—
83C4⋊(C3⋊C8)—31no—
84C4×C3⋊C8—31no—
85C22×D9C22⋊C411yescharacteristic
86Q8×C9—21no—
87Q8×C9M1612yescomplemented
88C2×C4×C9—21no—
89C2×C4×C9—21no—
90C2×C4×C9C22×C411yescharacteristic
91C2×C4×C9C2×D411yescharacteristic
92C2×C4×C9C2×D411yescharacteristic
93C2×Dic9—21no—
94C2×Dic9—21no—
95C2×Dic9C22⋊C411yescharacteristic
96C2×Dic9C22⋊C411yescharacteristic
97C2×Dic9C22⋊C411yescharacteristic
98C4×D9—24no—
99C4×D9—21no—
100C4×D9—21no—
101C4×D9—41no—
102C4×D9—42no—
103C4×D9SD1612yes—
104C4×D9Q1612yes—
105Dic18—24no—
106Dic18—21no—
107Dic18M1612yescomplemented
108C8×C9—41no—
109C8×C9—41no—
110C9⋊C8—41no—
111C9⋊C8—41no—
112C2×C4×Q8—91no—
113#431—91no—
114#423—91no—
115Q8⋊C8—91no—
116Q8⋊C8—91no—
117Q8⋊C8—91no—
118Q8⋊C8D911yescharacteristic, complemented
119C2×C3×Q8C4×D311yescharacteristic
120D3×Q8—62no—
121D3×Q8—62no—
122C2×C4×D3—31no—
123C2×C4×D3—31no—
124C2×C4×D3—31no—
125C2×C4×D3—61no—
126C2×C4×D3—61no—
127C2×Dic6—31no—
128C2×Dic6—61no—
129C2×C3×C8—21no—
130C2×C3×C8—21no—
131C3×C4⋊C4—21no—
132C3×C4⋊C4C4×D311yescharacteristic
133C3×C42—21no—
134C3×C42C22×D311yescharacteristic
135C4⋊Dic3—31no—
136C4⋊Dic3—61no—
137Dic3⋊C4—61no—
138Dic3⋊C4—61no—
139Dic3⋊C4—61no—
140C4×Dic3—31no—
141C4×Dic3—31no—
142C4×Dic3—31no—
143C4×Dic3—61no—
144C4×Dic3—61no—
145C4×Dic3—61no—
146C2×C3⋊C8—61no—
147C2×C3⋊C8—61no—
148ΓL(1,𝔽25)—122no—
149C22×C9C2×C22⋊C411yescharacteristic
150C2×D9—21no—
151C2×D9—21no—
152C2×D9#10312yes—
153C4×C9—22no—
154C4×C9—21no—
155C4×C9—41no—
156C4×C9C2×M1611yescharacteristic
157C4×C9C2×M1611yescharacteristic
158C4×C9C2×SD1611yescharacteristic
159C4×C9C2×Q1611yescharacteristic
160Dic9—21no—
161Dic9—22no—
162Dic9—21no—
163Dic9—41no—
164Dic9#10312yes—
165C22×Q8—91no—
166C2×M16—181no—
167C4×Q8—91no—
168C4×Q8—91no—
169C4×Q8—91no—
170C4×Q8—181no—
171C4×Q8—181no—
172C4×Q8C2×D911yescharacteristic
173C2×C4⋊C4—91no—
174C2×C4⋊C4—181no—
175C2×C42—91no—
176C2×C42—181no—
177C4⋊C8—91no—
178C4⋊C8—181no—
179C4⋊C8—181no—
180C4⋊C8C2×D911yescharacteristic
181C22⋊C8—181no—
182C4×C8—91no—
183C4×C8C2×D911yescharacteristic
184C22×D3—31no—
185C3×Q8—21no—
186C3×Q8ΓL(1,𝔽25)12yes—
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4C2×C4×D311yescharacteristic
190C2×C3×C4D3×D411yescharacteristic
191C2×C3×C4D3×D411yescharacteristic
192C2×Dic3—31no—
193C2×Dic3—31no—
194C2×Dic3—31no—
195C2×Dic3—61no—
196C2×Dic3—61no—
197C4×D3—32no—
198C4×D3—32no—
199C4×D3—64no—
200C4×D3—61no—
201C4×D3—61no—
202C4×D3—121no—
203C4×D3—122no—
204Dic6—32no—
205Dic6—64no—
206Dic6—61no—
207C3×C8—41no—
208C3×C8—41no—
209C3⋊C8—121no—
210C3⋊C8—121no—
211C2×C9#40711yescharacteristic
212C2×C9C2×#10311yescharacteristic
213C2×C9#42111yescharacteristic
214D9—22no—
215C2×Q8—91no—
216C2×Q8—181no—
217C2×Q8—182no—
218C2×Q8—182no—
219C2×Q8C4×D911yescharacteristic
220C22×C4—91no—
221C22×C4—91no—
222C22×C4—91no—
223C22×C4—181no—
224C22×C4—181no—
225M16—362no—
226C2×C8—21no—
227C2×C8—21no—
228C2×C8—181no—
229C2×C8—181no—
230C4⋊C4—21no—
231C4⋊C4—91no—
232C4⋊C4—181no—
233C4⋊C4—181no—
234C4⋊C4—181no—
235C4⋊C4—181no—
236C4⋊C4C4×D911yescharacteristic
237C42—21no—
238C42—91no—
239C42—91no—
240C42—91no—
241C42—181no—
242C42—181no—
243C42—181no—
244C42C22×D911yescharacteristic
245C22×C3D3×C22⋊C411yescharacteristic
246C2×D3—32no—
247C2×D3—61no—
248C2×D3—61no—
249C3×C4—22no—
250C3×C4—21no—
251C3×C4—41no—
252C3×C4C2×ΓL(1,𝔽25)11yescharacteristic
253C3×C4D3×M1611yescharacteristic
254C3×C4D3×SD1611yescharacteristic
255C3×C4D3×Q1611yescharacteristic
256Dic3—32no—
257Dic3—62no—
258Dic3—61no—
259Dic3—61no—
260Dic3—121no—
261C9#148711yescharacteristic, complemented, Sylow
262C23—91no—
263Q8—21no—
264Q8—92no—
265Q8—184no—
266Q8—181no—
267Q8#366312yescomplemented
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—91no—
271C2×C4—92no—
272C2×C4—92no—
273C2×C4—91no—
274C2×C4—91no—
275C2×C4—184no—
276C2×C4—181no—
277C2×C4—181no—
278C2×C4—181no—
279C2×C4—181no—
280C2×C4—361no—
281C2×C4—362no—
282C2×C4C2×C4×D911yescharacteristic
283C2×C4D4×D911yescharacteristic
284C2×C4D4×D911yescharacteristic
285C8—41no—
286C8—41no—
287C8—361no—
288C8—361no—
289C2×C3#472611yescharacteristic
290C2×C3D3×#10311yescharacteristic
291C2×C3#482111yescharacteristic
292D3—62no—
293C22—92no—
294C22—181no—
295C22—181no—
296C22C22⋊C4×D911yescharacteristic
297C4—21no—
298C4—22no—
299C4—41no—
300C4—92no—
301C4—181no—
302C4—181no—
303C4—182no—
304C4—361no—
305C4C2×#366311yescharacteristic
306C4M16×D911yescharacteristic
307C4SD16×D911yescharacteristic
308C4Q16×D911yescharacteristic
309C3#6823611yescharacteristic
310C2—182no—
311C2#1058840811yescharacteristic
312C2D9×#10311yescharacteristic
313C2#1058850111yescharacteristic
subgroupG/H
centerC2×C4D4×D9
commutatorC2×C4×C9C22×C4
FrattiniC3×C42C22×D3
FittingC9×Q8⋊C8C2
socleC22×C3D3×C22⋊C4
prime radicalC22×D9C22⋊C4
cosocleC42×C9C23
hypercenterQ8⋊C8D9
hypocenterC9#1487
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2×C4 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
4. C9×Q8⋊C8C2semidirect
5. #10588212C2semidirect
6. #10588160C2semidirect
7. #10588133C2semidirect
87. Q8×C9M16semidirect
107. Dic18M16semidirect
118. Q8⋊C8D9semidirect
261. C9#1487semidirect
267. Q8#3663semidirect

Maximal subgroups

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

subgroupindex
C4×Q8×D92
#105885212
#105883672
C9×Q8⋊C82
#105882122
#105881602
#105881332
#682363