Finite Group Databasebeta

← #14518819

Subgroups — #14518819

Order 1944.

698 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 99 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×C3×C3⋊(C3⋊D9)C211yesmaximal, characteristic
2C3×C3⋊(C3⋊Dic9)C211yesmaximal, characteristic, complemented
3C3×C9×C3⋊Dic3C211yesmaximal, characteristic, complemented
4#10620154—31nomaximal
5#10619896—33nomaximal
6#10619872—31nomaximal
7Dic3×C3⋊D9—31nomaximal
8C2×C33×C9C2211yescharacteristic
9C3×C3⋊(C3⋊D9)C412yescomplemented
10C2×C3×C3⋊(C3⋊D3)—31no—
11C3×C3⋊(C3⋊Dic3)—31no—
12C32×C3⋊Dic3D311yescharacteristic
13C2×C3⋊(C3⋊D9)D311yescharacteristic
14C2×C3×C3⋊D9—31no—
15C2×C3×C3⋊D9—33no—
16C2×C3×C3⋊D9—63no—
17C2×C3×C3⋊D9—61no—
18C3⋊(C3⋊Dic9)D311yescharacteristic, complemented
19C9×C3⋊Dic3D313yescomplemented
20C3×C3⋊Dic9—31no—
21C3×C3⋊Dic9—33no—
22C3×C3⋊Dic9—63no—
23C3×C3⋊Dic9—61no—
24C3×C9×Dic3—31no—
25C3×C9×Dic3—31no—
26C3×C9×Dic3—61no—
27C33×C9C2×C411yescharacteristic, complemented, Sylow
28#6294—93no—
29#6294—91no—
30#6289—91no—
31Dic3×C3⋊D3—91no—
32C4×C3⋊D9—91no—
33(C3⋊D9)⋊C4—93no—
34Dic3×D9—93no—
35C2×C34C2×D311yescharacteristic
36C3×C3⋊(C3⋊D3)—32no—
37C2×C32×C9—21no—
38C2×C32×C9—21no—
39C2×C32×C9—21no—
40C2×C32×C9—23no—
41C2×C32×C9—23no—
42C2×C32×C9—43no—
43C2×C32×C9—41no—
44C2×C32×C9C2×D311yescharacteristic
45C2×C32×C9C2×D311yescharacteristic
46C2×C32×C9C2×D313yes—
47C3⋊(C3⋊D9)Dic312yescomplemented
48C3×C3⋊D9—32no—
49C3×C3⋊D9—36no—
50C3×C3⋊D9—66no—
51C3×C3⋊D9—62no—
52C2×C3⋊(C3⋊D3)—31no—
53C2×C3×C3⋊D3—93no—
54C2×C3×C3⋊D3—91no—
55C2×C3×C3⋊D3—91no—
56C2×C3×C3⋊D3—181no—
57C2×C3×C3⋊D3—183no—
58C3⋊(C3⋊Dic3)—31no—
59C3×C3⋊Dic3—93no—
60C3×C3⋊Dic3—91no—
61C3×C3⋊Dic3—91no—
62C3×C3⋊Dic3—181no—
63C3×C3⋊Dic3—183no—
64C3×C3⋊Dic3D913yescomplemented
65C3×C3⋊Dic3C3⋊D311yescharacteristic
66C32×Dic3—31no—
67C32×Dic3—31no—
68C32×Dic3—61no—
69C2×C3⋊D9—31no—
70C2×C3⋊D9—33no—
71C2×C3⋊D9—63no—
72C2×C3⋊D9—61no—
73C2×C3×D9—93no—
74C2×C3×D9—183no—
75C3×C4×C9—91no—
76C3⋊Dic9—31no—
77C3⋊Dic9—33no—
78C3⋊Dic9—63no—
79C3⋊Dic9—61no—
80C9×Dic3—33no—
81C9×Dic3—33no—
82C9×Dic3—63no—
83C3×Dic9—93no—
84C3×Dic9—183no—
85C34C4×D311yescharacteristic
86C32×C9—21no—
87C32×C9—21no—
88C32×C9—23no—
89C32×C9—21no—
90C32×C9—23no—
91C32×C9—43no—
92C32×C9—41no—
93C32×C9C4×D311yescharacteristic, complemented
94C32×C9C4×D313yescomplemented
95C32×C9C2×Dic311yescharacteristic, complemented
96C4×C3⋊D3—271no—
97#624—271no—
98#624—273no—
99D3×Dic3—271no—
100D3×Dic3—273no—
101D3×Dic3—271no—
102C4×D9—273no—
103C2×C33—23no—
104C2×C33—23no—
105C2×C33—21no—
106C2×C33—21no—
107C2×C33—21no—
108C2×C33—41no—
109C2×C33—43no—
110C2×C33C2×D913yes—
111C2×C33D3211yescharacteristic
112C2×C33D3211yescharacteristic
113C2×C33C2×C3⋊D311yescharacteristic
114C3⋊(C3⋊D3)—32no—
115C3×C3⋊D3—92no—
116C3×C3⋊D3—96no—
117C3×C3⋊D3—92no—
118C3×C3⋊D3—182no—
119C3×C3⋊D3—186no—
120C2×C3×C9—21no—
121C2×C3×C9—21no—
122C2×C3×C9—23no—
123C2×C3×C9—23no—
124C2×C3×C9—23no—
125C2×C3×C9—23no—
126C2×C3×C9—23no—
127C2×C3×C9—43no—
128C2×C3×C9—46no—
129C2×C3×C9—43no—
130C2×C3×C9—43no—
131C2×C3×C9—41no—
132C2×C3×C9—43no—
133C2×C3×C9D3213yes—
134C2×C3×C9D3213yes—
135C2×C3×C9D3211yescharacteristic
136C3⋊D9—32no—
137C3⋊D9—36no—
138C3⋊D9—66no—
139C3⋊D9—62no—
140C3×D9—96no—
141C3×D9—186no—
142C2×C3⋊D3—91no—
143C2×C3⋊D3—93no—
144C2×C3⋊D3—91no—
145C2×C3⋊D3—181no—
146C2×C3⋊D3—183no—
147C2×C3×D3—273no—
148C2×C3×D3—271no—
149C2×C3×D3—271no—
150C2×C3×D3—543no—
151C2×C3×D3—541no—
152C32×C4—91no—
153C3⋊Dic3—91no—
154C3⋊Dic3—93no—
155C3⋊Dic3—91no—
156C3⋊Dic3—181no—
157C3⋊Dic3—183no—
158C3⋊Dic3C3⋊D911yescharacteristic, complemented
159C3×Dic3—33no—
160C3×Dic3—33no—
161C3×Dic3—31no—
162C3×Dic3—31no—
163C3×Dic3—61no—
164C3×Dic3—63no—
165C3×Dic3—273no—
166C3×Dic3—271no—
167C3×Dic3—271no—
168C3×Dic3—543no—
169C3×Dic3—541no—
170C2×D9—93no—
171C2×D9—183no—
172C4×C9—93no—
173Dic9—93no—
174Dic9—183no—
175C33—23no—
176C33—23no—
177C33—21no—
178C33—21no—
179C33—21no—
180C33—41no—
181C33—43no—
182C33C4×D913yescomplemented
183C33D3×Dic311yescharacteristic
184C33#62411yescharacteristic
185C33C4×C3⋊D311yescharacteristic
186C3×C9—21no—
187C3×C9—21no—
188C3×C9—23no—
189C3×C9—23no—
190C3×C9—23no—
191C3×C9—23no—
192C3×C9—23no—
193C3×C9—43no—
194C3×C9—46no—
195C3×C9—43no—
196C3×C9—43no—
197C3×C9—41no—
198C3×C9—43no—
199C3×C9D3×Dic313yescomplemented
200C3×C9D3×Dic311yescharacteristic, complemented
201C3×C9#62413yescomplemented
202C2×Dic3—811no—
203C4×D3—811no—
204C4×D3—811no—
205C4×D3—813no—
206C2×C32—23no—
207C2×C32—23no—
208C2×C32—21no—
209C2×C32—21no—
210C2×C32—23no—
211C2×C32—23no—
212C2×C32—21no—
213C2×C32—21no—
214C2×C32—23no—
215C2×C32—21no—
216C2×C32—43no—
217C2×C32—41no—
218C2×C32—46no—
219C2×C32—43no—
220C2×C32—43no—
221C2×C32—43no—
222C2×C32—41no—
223C2×C32D3×D913yes—
224C2×C32D3×D913yes—
225C2×C32C2×C3⋊D911yescharacteristic
226C2×C32D3×C3⋊D311yescharacteristic
227C2×C32D3×C3⋊D311yescharacteristic
228C2×C32#111311yescharacteristic
229C3⋊D3—92no—
230C3⋊D3—96no—
231C3⋊D3—92no—
232C3⋊D3—182no—
233C3⋊D3—186no—
234C3×D3—276no—
235C3×D3—272no—
236C3×D3—272no—
237C3×D3—546no—
238C3×D3—542no—
239C2×C9—23no—
240C2×C9—23no—
241C2×C9—43no—
242C2×C9#111313yes—
243D9—96no—
244D9—186no—
245C22×C3—811no—
246C2×D3—271no—
247C2×D3—273no—
248C2×D3—271no—
249C2×D3—543no—
250C2×D3—541no—
251C3×C4—93no—
252C3×C4—91no—
253C3×C4—811no—
254Dic3—31no—
255Dic3—31no—
256Dic3—61no—
257Dic3—271no—
258Dic3—273no—
259Dic3—271no—
260Dic3—543no—
261Dic3—541no—
262C32—23no—
263C32—23no—
264C32—21no—
265C32—21no—
266C32—23no—
267C32—21no—
268C32—23no—
269C32—21no—
270C32—23no—
271C32—21no—
272C32—43no—
273C32—41no—
274C32—46no—
275C32—43no—
276C32—43no—
277C32—43no—
278C32—41no—
279C32Dic3×D913yescomplemented
280C32(C3⋊D9)⋊C413yescomplemented
281C32C4×C3⋊D911yescharacteristic, complemented
282C32Dic3×C3⋊D311yescharacteristic
283C32#628911yescharacteristic
284C32#629411yescharacteristic
285C9—23no—
286C9—23no—
287C9—43no—
288C9#629413yescomplemented
289C2×C4—2431noSylow
290C2×C3—21no—
291C2×C3—23no—
292C2×C3—21no—
293C2×C3—23no—
294C2×C3—21no—
295C2×C3—43no—
296C2×C3—41no—
297C2×C3—812no—
298C2×C3D3×C3⋊D911yescharacteristic
299C2×C3D3×C3⋊D911yescharacteristic
300C2×C3#6643113yes—
301C2×C3C3⋊#111311yescharacteristic
302D3—272no—
303D3—276no—
304D3—272no—
305D3—546no—
306D3—542no—
307C22—811no—
308C4—91no—
309C4—811no—
310C3—23no—
311C3—21no—
312C3—23no—
313C3—21no—
314C3—21no—
315C3—43no—
316C3—41no—
317C3Dic3×C3⋊D911yescharacteristic, complemented
318C3#1061987211yescharacteristic, complemented
319C3#1061989613yescomplemented
320C3#1062015411yescharacteristic
321C2—812no—
322C2C9⋊#111311yescharacteristic
subgroupG/H
center, hypercenterC2C9⋊#1113
commutator, hypocenterC33×C9C2×C4
FrattiniC2×C3C3⋊#1113
Fitting, cosocleC2×C33×C9C22
socleC2×C34C2×D3
prime radicalC2×C3×C3⋊(C3⋊D9)C2
LCSG ▷ C33×C9
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. C3×C3⋊(C3⋊Dic9)C2semidirect
3. C3×C9×C3⋊Dic3C2semidirect
9. C3×C3⋊(C3⋊D9)C4semidirect
18. C3⋊(C3⋊Dic9)D3semidirect
19. C9×C3⋊Dic3D3semidirect
27. C33×C9C2×C4semidirect
47. C3⋊(C3⋊D9)Dic3semidirect
64. C3×C3⋊Dic3D9semidirect
93. C32×C9C4×D3semidirect
94. C32×C9C4×D3semidirect
95. C32×C9C2×Dic3semidirect
158. C3⋊Dic3C3⋊D9semidirect
182. C33C4×D9semidirect
199. C3×C9D3×Dic3semidirect
200. C3×C9D3×Dic3semidirect
201. C3×C9#624semidirect
279. C32Dic3×D9semidirect
280. C32(C3⋊D9)⋊C4semidirect
281. C32C4×C3⋊D9semidirect
288. C9#6294semidirect
317. C3Dic3×C3⋊D9semidirect
318. C3#10619872semidirect
319. C3#10619896semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C3⋊(C3⋊D9)2
C3×C3⋊(C3⋊Dic9)2
C3×C9×C3⋊Dic32
#106201543
#106198963
#106198723
Dic3×C3⋊D93