Finite Group Databasebeta

← #11783741

Subgroups — #11783741

Order 1152.

618 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 618 conjugacy classes of subgroups — too many to draw. Only its 136 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
1C2×#611⋊C4C211yesmaximal, characteristic
2C2×#63365C212yesmaximal
3C22⋊C4×Dic9C212yesmaximal, complemented
4C9×#342C211yesmaximal, characteristic, complemented
5#10588203C211yesmaximal, characteristic, complemented
6#68952—31nomaximal
7C22×#611C2211yescharacteristic
8C23×Dic9C2211yescharacteristic
9C22×C4×D9C411yescharacteristic, complemented
10C2×C9×C22⋊C4C2211yescharacteristic
11C2×C9×C22⋊C4C2212yes—
12C2×#3676C2212yes—
13C2×(C2×D9)⋊C4C411yescharacteristic, complemented
14C2×Dic9⋊C4C411yescharacteristic, complemented
15C2×C4×Dic9—22no—
16C2×C4×Dic9C411yescharacteristic, complemented
17#611⋊C4—22no—
18#611⋊C4—22no—
19C9⋊#95—22no—
20#63365C418yescomplemented
21C2×#67⋊C4—31no—
22C2×#806—32no—
23Dic3×C22⋊C4—32no—
24C3×#342D311yescharacteristic
25#4526—31no—
26C24×C9C2311yescharacteristic
27C23×D9C2×C411yescharacteristic
28C22×C4×C9—22no—
29C22×C4×C9C2×C411yescharacteristic
30C22×C4×C9C2×C411yescharacteristic
31C2×#611—22no—
32C2×#611—21no—
33C2×#611—21no—
34C2×#611C2×C414yes—
35C22×Dic9—22no—
36C22×Dic9—42no—
37C22×Dic9C2×C411yescharacteristic
38C22×Dic9C2×C411yescharacteristic
39C22×Dic9C2×C411yescharacteristic
40C22×Dic9D412yes—
41C22×Dic9D412yes—
42C2×C4×D9—21no—
43C2×C4×D9—21no—
44C2×C4×D9—42no—
45C9×C22⋊C4—22no—
46C9×C22⋊C4—22no—
47C9×C22⋊C4C2×C414yescomplemented
48#3676—22no—
49#3676C2×C414yescomplemented
50(C2×D9)⋊C4—22no—
51Dic9⋊C4—22no—
52C4×Dic9—21no—
53C4×Dic9—21no—
54C4×Dic9—44no—
55C4×#99—91noSylow
56C22×#67—31no—
57C23×Dic3—31no—
58C22×C4×D3—31no—
59C2×C3×C22⋊C4C2×D311yescharacteristic
60C2×C3×C22⋊C4C2×D312yes—
61C2×#217—32no—
62C2×(C2×D3)⋊C4—31no—
63C2×Dic3⋊C4—31no—
64C2×C4×Dic3—31no—
65C2×C4×Dic3—62no—
66#67⋊C4—62no—
67#67⋊C4—62no—
68C3⋊#95—62no—
69#806—38no—
70C23×C9—41no—
71C23×C9—41no—
72C23×C9C22×C411yescharacteristic
73C23×C9C22×C412yes—
74C23×C9C2×D412yes—
75C23×C9#4111yescharacteristic
76C23×C9#4111yescharacteristic
77C22×D9—21no—
78C22×D9—21no—
79C22×D9—41no—
80C22×D9—41no—
81C22×D9C4212yescomplemented
82C2×C4×C9—21no—
83C2×C4×C9—21no—
84C2×C4×C9—24no—
85C2×C4×C9—42no—
86C2×C4×C9—42no—
87C2×C4×C9—41no—
88C2×C4×C9—41no—
89#611—24no—
90#611—24no—
91C2×Dic9—21no—
92C2×Dic9—21no—
93C2×Dic9—24no—
94C2×Dic9—22no—
95C2×Dic9—24no—
96C2×Dic9—41no—
97C2×Dic9—42no—
98C2×Dic9—42no—
99C2×Dic9—42no—
100C2×Dic9C4212yescomplemented
101C2×Dic9C22⋊C411yescharacteristic
102C2×Dic9C22⋊C412yes—
103C2×Dic9C22⋊C411yescharacteristic
104C4×D9—42no—
105C4×D9—42no—
106C2×C4×D4—91no—
107C2×#99—92no—
108C4×C22⋊C4—92no—
109#342—91no—
110#342D911yescharacteristic, complemented
111C24×C3C22×D311yescharacteristic
112C23×D3—31no—
113C22×C3×C4—22no—
114C22×C3×C4C4×D311yescharacteristic
115C22×C3×C4C4×D311yescharacteristic
116C2×#67—34no—
117C2×#67—62no—
118C2×#67—61no—
119C2×#67—61no—
120C22×Dic3—31no—
121C22×Dic3—31no—
122C22×Dic3—32no—
123C22×Dic3—31no—
124C22×Dic3—32no—
125C22×Dic3—62no—
126C22×Dic3—122no—
127C2×C4×D3—61no—
128C2×C4×D3—61no—
129C2×C4×D3—122no—
130C3×C22⋊C4—22no—
131C3×C22⋊C4—22no—
132C3×C22⋊C4C4×D314yes—
133#217—34no—
134#217—62no—
135(C2×D3)⋊C4—62no—
136Dic3⋊C4—62no—
137C4×Dic3—61no—
138C4×Dic3—61no—
139C4×Dic3—124no—
140C22×C9—22no—
141C22×C9—21no—
142C22×C9—22no—
143C22×C9—21no—
144C22×C9—42no—
145C22×C9—41no—
146C22×C9—41no—
147C22×C9C2×C4211yescharacteristic
148C22×C9C2×C22⋊C411yescharacteristic
149C22×C9#11711yescharacteristic
150C22×C9C4×D412yes—
151C22×C9C4×D412yes—
152C2×D9—22no—
153C2×D9—42no—
154C2×D9—41no—
155C2×D9—41no—
156C2×D9—42no—
157C4×C9—44no—
158C4×C9—41no—
159C4×C9—41no—
160Dic9—22no—
161Dic9—21no—
162Dic9—22no—
163Dic9—44no—
164Dic9#9912yescomplemented
165C22×D4—91no—
166C23×C4—91no—
167C23×C4—91no—
168C4×D4—182no—
169C4×D4—182no—
170C2×C4⋊C4—91no—
171C2×C22⋊C4—92no—
172C2×C22⋊C4—91no—
173C2×C22⋊C4C2×D911yescharacteristic
174C2×C22⋊C4C2×D912yes—
175C2×C42—91no—
176C2×C42—182no—
177#99—98no—
178#95—182no—
179C23×C3—41no—
180C23×C3—41no—
181C23×C3C2×C4×D311yescharacteristic
182C23×C3C2×C4×D312yes—
183C23×C3D3×D412yes—
184C23×C3#23711yescharacteristic
185C23×C3#23911yescharacteristic
186C22×D3—32no—
187C22×D3—61no—
188C22×D3—61no—
189C22×D3—121no—
190C22×D3—121no—
191C2×C3×C4—21no—
192C2×C3×C4—21no—
193C2×C3×C4—24no—
194C2×C3×C4—42no—
195C2×C3×C4—42no—
196C2×C3×C4—41no—
197C2×C3×C4—41no—
198#67—64no—
199#67—64no—
200C2×Dic3—31no—
201C2×Dic3—32no—
202C2×Dic3—31no—
203C2×Dic3—32no—
204C2×Dic3—64no—
205C2×Dic3—62no—
206C2×Dic3—61no—
207C2×Dic3—61no—
208C2×Dic3—64no—
209C2×Dic3—122no—
210C2×Dic3—121no—
211C2×Dic3—122no—
212C2×Dic3—122no—
213C4×D3—122no—
214C4×D3—122no—
215C2×C9—22no—
216C2×C9—22no—
217C2×C9—21no—
218C2×C9—21no—
219C2×C9C4×C22⋊C411yescharacteristic
220C2×C9C2×#9911yescharacteristic
221C2×C9#41011yescharacteristic
222D9—42no—
223C24—91no—
224C24C22×D911yescharacteristic
225C2×D4—94no—
226C2×D4—182no—
227C2×D4—181no—
228C2×D4—181no—
229C22×C4—22no—
230C22×C4—91no—
231C22×C4—91no—
232C22×C4—92no—
233C22×C4—91no—
234C22×C4—92no—
235C22×C4—181no—
236C22×C4—181no—
237C22×C4—182no—
238C22×C4—362no—
239C22×C4—362no—
240C22×C4C4×D911yescharacteristic
241C22×C4C4×D911yescharacteristic
242C4⋊C4—182no—
243C22⋊C4—22no—
244C22⋊C4—22no—
245C22⋊C4—94no—
246C22⋊C4—182no—
247C22⋊C4—182no—
248C22⋊C4C4×D914yescomplemented
249C42—181no—
250C42—181no—
251C42—364no—
252C22×C3—22no—
253C22×C3—21no—
254C22×C3—22no—
255C22×C3—21no—
256C22×C3—42no—
257C22×C3—41no—
258C22×C3—41no—
259C22×C3C42×D311yescharacteristic
260C22×C3D3×C22⋊C411yescharacteristic
261C22×C3#67⋊C412yes—
262C22×C3#89211yescharacteristic
263C22×C3#89312yes—
264C2×D3—62no—
265C2×D3—122no—
266C2×D3—121no—
267C2×D3—121no—
268C2×D3—122no—
269C3×C4—44no—
270C3×C4—41no—
271C3×C4—41no—
272Dic3—32no—
273Dic3—62no—
274Dic3—61no—
275Dic3—62no—
276Dic3—124no—
277C9C4×#9911yescharacteristic, complemented, Sylow
278C23—41no—
279C23—41no—
280C23—92no—
281C23—181no—
282C23—181no—
283C23—361no—
284C23—361no—
285C23C2×C4×D911yescharacteristic
286C23C2×C4×D912yes—
287C23D4×D912yes—
288C23#369911yescharacteristic
289C23#370111yescharacteristic
290D4—184no—
291D4—184no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—24no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—91no—
300C2×C4—92no—
301C2×C4—91no—
302C2×C4—92no—
303C2×C4—184no—
304C2×C4—182no—
305C2×C4—181no—
306C2×C4—181no—
307C2×C4—184no—
308C2×C4—362no—
309C2×C4—362no—
310C2×C4—362no—
311C2×C4—361no—
312C2×C4—362no—
313C2×C4—362no—
314C2×C3—22no—
315C2×C3—22no—
316C2×C3—21no—
317C2×C3—21no—
318C2×C3#466611yescharacteristic
319C2×C3#474011yescharacteristic
320C2×C3D3×#9911yescharacteristic
321D3—122no—
322C22—22no—
323C22—21no—
324C22—22no—
325C22—21no—
326C22—42no—
327C22—41no—
328C22—41no—
329C22—182no—
330C22—362no—
331C22—362no—
332C22—361no—
333C22—361no—
334C22C42×D911yescharacteristic
335C22C22⋊C4×D911yescharacteristic
336C22#611⋊C412yes—
337C22#6345411yescharacteristic
338C22#6345512yes—
339C4—44no—
340C4—41no—
341C4—41no—
342C4—92no—
343C4—181no—
344C4—182no—
345C4—182no—
346C4—364no—
347C3#6895211yescharacteristic
348C2—22no—
349C2—22no—
350C2—21no—
351C2—21no—
352C2—362no—
353C2#1058834611yescharacteristic
354C2#1058842011yescharacteristic
355C2D9×#9911yescharacteristic
subgroupG/H
centerC22C22⋊C4×D9
commutatorC22×C9C2×C42
FrattiniC24×C3C22×D3
FittingC9×#342C2
socleC22×C3D3×C22⋊C4
prime radicalC22×#611C22
cosocleC24×C9C23
hypercenter#342D9
hypocenterC9C4×#99
LCSG ▷ C22×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
3. C22⋊C4×Dic9C2semidirect
4. C9×#342C2semidirect
5. #10588203C2semidirect
9. C22×C4×D9C4semidirect
13. C2×(C2×D9)⋊C4C4semidirect
14. C2×Dic9⋊C4C4semidirect
16. C2×C4×Dic9C4semidirect
20. #63365C4semidirect
47. C9×C22⋊C4C2×C4semidirect
49. #3676C2×C4semidirect
81. C22×D9C42semidirect
100. C2×Dic9C42semidirect
110. #342D9semidirect
164. Dic9#99semidirect
248. C22⋊C4C4×D9semidirect
277. C9C4×#99semidirect

Maximal subgroups

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

subgroupindex
C2×#611⋊C42
C2×#633652
C22⋊C4×Dic92
C9×#3422
#105882032
#689523