Group #13142967 — subgroups

Subgroups — C₃×#10588750 #13142967

Order 1728.

462 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 130 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×#127	C₂	1	1	yes	maximal, characteristic
2	C₃×#63431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#63392	C₂	1	4	yes	maximal, complemented
4	C₃×C₄×C₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5070	—	3	1	no	maximal
6	#10588750	C₃	1	1	yes	maximal, characteristic, direct product factor
7	C₂×C₃×D₄×C₉	—	2	1	no	—
8	C₂×C₃×D₄×C₉	—	2	1	no	—
9	C₂×C₃×D₄×C₉	C₂²	1	2	yes	—
10	C₂×C₃×Dic₁₈	—	2	1	no	—
11	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
12	C₃×C₄⋊Dic₉	—	2	1	no	—
13	C₃×C₄⋊Dic₉	C₂²	1	2	yes	—
14	C₂×C₃×C₉⋊C₈	C₂²	1	2	yes	—
15	C₃²×#127	D₃	1	1	yes	characteristic
16	C₃×#869	—	3	1	no	—
17	C₃×#832	—	3	4	no	—
18	C₃×C₄×C₃⋊C₈	—	3	1	no	—
19	C₉×#127	—	2	1	no	—
20	C₉×#127	C₂×C₃	1	1	yes	characteristic
21	#63431	C₂×C₃	1	1	yes	characteristic, complemented
22	#63392	C₂×C₃	1	4	yes	complemented
23	C₄×C₉⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
24	C₂³×C₃×C₉	—	2	2	no	—
25	C₃×D₄×C₉	—	2	4	no	—
26	C₃×D₄×C₉	—	4	2	no	—
27	C₃×D₄×C₉	—	4	2	no	—
28	C₂×C₃×C₄×C₉	D₄	1	1	yes	characteristic
29	C₂×C₃×C₄×C₉	D₄	1	1	yes	characteristic
30	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
31	C₂×C₃×Dic₉	—	2	2	no	—
32	C₃×Dic₁₈	—	4	2	no	—
33	C₃×C₉⋊C₈	—	2	2	no	—
34	C₃×#486	—	9	1	no	—
35	#5070	—	3	1	no	—
36	C₂×C₃²×D₄	—	2	1	no	—
37	C₂×C₃²×D₄	—	2	1	no	—
38	C₂×C₃²×D₄	C₂×D₃	1	2	yes	—
39	C₂×C₃×Dic₆	—	6	1	no	—
40	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
41	C₃×C₄⋊Dic₃	—	3	2	no	—
42	C₃×C₄⋊Dic₃	—	6	1	no	—
43	C₂×C₃×C₃⋊C₈	—	3	2	no	—
44	C₂×D₄×C₉	—	2	2	no	—
45	C₂×D₄×C₉	—	2	2	no	—
46	C₂×D₄×C₉	—	2	2	no	—
47	C₂×D₄×C₉	—	2	1	no	—
48	C₂×D₄×C₉	—	2	1	no	—
49	C₂×D₄×C₉	C₂²×C₃	1	2	yes	—
50	C₂×Dic₁₈	—	2	1	no	—
51	C₄²×C₉	—	2	1	no	—
52	C₄²×C₉	C₂²×C₃	1	1	yes	characteristic
53	C₄⋊Dic₉	—	2	1	no	—
54	C₄⋊Dic₉	C₂²×C₃	1	2	yes	—
55	C₂×C₉⋊C₈	C₂²×C₃	1	2	yes	—
56	C₂²×C₃×C₉	—	4	2	no	—
57	C₂²×C₃×C₉	—	4	2	no	—
58	C₂²×C₃×C₉	—	4	2	no	—
59	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
60	C₃×C₄×C₉	D₈	1	2	yes	—
61	C₃×C₄×C₉	SD₁₆	1	2	yes	—
62	C₃×C₄×C₉	#41	1	2	yes	—
63	C₃×Dic₉	—	4	2	no	—
64	C₃×C₄⋊Q₈	—	9	1	no	—
65	C₃×#127	—	2	1	no	—
66	C₃×#127	D₉	1	1	yes	characteristic
67	C₃×#127	C₃×D₃	1	1	yes	characteristic
68	#869	—	3	1	no	—
69	C₃×#102	—	9	4	no	—
70	C₃×C₄×C₈	—	9	1	no	—
71	#832	—	3	4	no	—
72	C₄×C₃⋊C₈	—	3	1	no	—
73	C₂³×C₃²	—	2	2	no	—
74	C₃²×D₄	—	2	4	no	—
75	C₃²×D₄	—	4	2	no	—
76	C₃²×D₄	—	4	2	no	—
77	C₂×C₃²×C₄	#67	1	1	yes	characteristic
78	C₂×C₃²×C₄	#67	1	1	yes	characteristic
79	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
80	C₂×C₃×Dic₃	—	6	2	no	—
81	C₃×Dic₆	—	12	2	no	—
82	C₂³×C₉	—	2	4	no	—
83	C₂³×C₉	—	2	2	no	—
84	C₃×C₃⋊C₈	—	6	2	no	—
85	D₄×C₉	—	2	4	no	—
86	D₄×C₉	—	4	4	no	—
87	D₄×C₉	—	4	4	no	—
88	D₄×C₉	—	4	4	no	—
89	D₄×C₉	—	4	2	no	—
90	D₄×C₉	—	4	2	no	—
91	C₂×C₄×C₉	—	2	1	no	—
92	C₂×C₄×C₉	—	2	1	no	—
93	C₂×C₄×C₉	—	2	1	no	—
94	C₂×C₄×C₉	C₃×D₄	1	1	yes	characteristic
95	C₂×C₄×C₉	C₃×D₄	1	1	yes	characteristic
96	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
97	C₂×Dic₉	—	2	2	no	—
98	Dic₁₈	—	4	2	no	—
99	C₉⋊C₈	—	2	2	no	—
100	#486	—	9	1	no	Sylow
101	C₂×C₃×C₉	—	8	2	no	—
102	C₂×C₃×C₉	#124	1	1	yes	characteristic
103	C₂×C₃×C₉	C₂×D₈	1	1	yes	characteristic
104	C₂×C₃×C₉	C₂×SD₁₆	1	1	yes	characteristic
105	C₂×C₃×Q₈	—	18	1	no	—
106	C₂×C₃×D₄	—	2	2	no	—
107	C₂×C₃×D₄	—	2	2	no	—
108	C₂×C₃×D₄	—	2	1	no	—
109	C₂×C₃×D₄	—	2	1	no	—
110	C₂×C₃×D₄	—	2	1	no	—
111	C₂×C₃×D₄	—	2	1	no	—
112	C₂×C₃×D₄	—	2	2	no	—
113	C₂×C₃×D₄	C₂×D₉	1	2	yes	—
114	C₂×C₃×D₄	C₂×C₃×D₃	1	2	yes	—
115	C₂×Dic₆	—	6	1	no	—
116	C₂×C₃×C₈	—	9	2	no	—
117	C₃×C₄⋊C₄	—	9	2	no	—
118	C₃×C₄⋊C₄	—	18	1	no	—
119	C₃×C₄²	—	2	1	no	—
120	C₃×C₄²	C₂×D₉	1	1	yes	characteristic
121	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
122	C₄⋊Dic₃	—	3	2	no	—
123	C₄⋊Dic₃	—	6	1	no	—
124	C₂×C₃⋊C₈	—	3	2	no	—
125	C₂²×C₃²	—	4	2	no	—
126	C₂²×C₃²	—	4	2	no	—
127	C₂²×C₃²	—	4	2	no	—
128	C₂²×C₃²	C₂×#67	1	1	yes	characteristic
129	C₃²×C₄	#213	1	2	yes	—
130	C₃²×C₄	#214	1	2	yes	—
131	C₃²×C₄	#237	1	2	yes	—
132	C₃×Dic₃	—	12	2	no	—
133	C₂²×C₉	—	2	1	no	—
134	C₂²×C₉	—	4	4	no	—
135	C₂²×C₉	—	4	4	no	—
136	C₂²×C₉	—	4	4	no	—
137	C₂²×C₉	—	4	2	no	—
138	C₂²×C₉	—	4	2	no	—
139	C₂²×C₉	—	4	2	no	—
140	C₂²×C₉	C₂×C₃×D₄	1	1	yes	characteristic
141	C₄×C₉	—	2	2	no	—
142	C₄×C₉	—	2	2	no	—
143	C₄×C₉	—	2	2	no	—
144	C₄×C₉	C₃×D₈	1	2	yes	—
145	C₄×C₉	C₃×SD₁₆	1	2	yes	—
146	C₄×C₉	C₃×#41	1	2	yes	—
147	Dic₉	—	4	2	no	—
148	C₄⋊Q₈	—	9	1	no	—
149	#127	C₃×D₉	1	1	yes	characteristic
150	#102	—	9	4	no	—
151	C₄×C₈	—	9	1	no	—
152	C₃×C₉	#486	1	1	yes	characteristic, complemented, Sylow
153	C₂³×C₃	—	2	4	no	—
154	C₂³×C₃	—	2	2	no	—
155	C₂³×C₃	—	2	2	no	—
156	C₃×Q₈	—	36	2	no	—
157	C₃×D₄	—	2	4	no	—
158	C₃×D₄	—	2	4	no	—
159	C₃×D₄	—	4	4	no	—
160	C₃×D₄	—	4	4	no	—
161	C₃×D₄	—	4	4	no	—
162	C₃×D₄	—	4	2	no	—
163	C₃×D₄	—	4	2	no	—
164	C₃×D₄	—	4	2	no	—
165	C₃×D₄	—	4	2	no	—
166	C₂×C₃×C₄	—	2	1	no	—
167	C₂×C₃×C₄	—	2	1	no	—
168	C₂×C₃×C₄	—	2	1	no	—
169	C₂×C₃×C₄	—	18	2	no	—
170	C₂×C₃×C₄	#611	1	1	yes	characteristic
171	C₂×C₃×C₄	#611	1	1	yes	characteristic
172	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
173	C₂×C₃×C₄	C₃×#67	1	1	yes	characteristic
174	C₂×C₃×C₄	C₃×#67	1	1	yes	characteristic
175	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
176	C₂×Dic₃	—	6	2	no	—
177	Dic₆	—	12	2	no	—
178	C₃×C₈	—	18	2	no	—
179	C₃⋊C₈	—	6	2	no	—
180	C₂×C₃²	—	8	2	no	—
181	C₂×C₃²	C₂×#213	1	1	yes	characteristic
182	C₂×C₃²	C₂×#214	1	1	yes	characteristic
183	C₂×C₃²	#936	1	1	yes	characteristic
184	C₂×C₉	—	2	1	no	—
185	C₂×C₉	—	2	1	no	—
186	C₂×C₉	—	2	1	no	—
187	C₂×C₉	—	8	4	no	—
188	C₂×C₉	—	8	2	no	—
189	C₂×C₉	C₃×#124	1	1	yes	characteristic
190	C₂×C₉	C₂×C₃×D₈	1	1	yes	characteristic
191	C₂×C₉	C₂×C₃×SD₁₆	1	1	yes	characteristic
192	C₂×Q₈	—	18	1	no	—
193	C₂×D₄	—	2	1	no	—
194	C₂×D₄	—	2	1	no	—
195	C₂×D₄	C₂×C₃×D₉	1	2	yes	—
196	C₂×C₈	—	9	2	no	—
197	C₄⋊C₄	—	9	2	no	—
198	C₄⋊C₄	—	18	1	no	—
199	C₄²	C₂×C₃×D₉	1	1	yes	characteristic
200	C₂²×C₃	—	2	1	no	—
201	C₂²×C₃	—	4	4	no	—
202	C₂²×C₃	—	4	4	no	—
203	C₂²×C₃	—	4	4	no	—
204	C₂²×C₃	—	4	2	no	—
205	C₂²×C₃	—	4	2	no	—
206	C₂²×C₃	—	4	2	no	—
207	C₂²×C₃	—	4	2	no	—
208	C₂²×C₃	—	4	2	no	—
209	C₂²×C₃	—	4	2	no	—
210	C₂²×C₃	C₂×#611	1	1	yes	characteristic
211	C₂²×C₃	C₂×C₃×#67	1	1	yes	characteristic
212	C₃×C₄	—	2	2	no	—
213	C₃×C₄	—	2	2	no	—
214	C₃×C₄	—	2	2	no	—
215	C₃×C₄	—	36	2	no	—
216	C₃×C₄	#3672	1	2	yes	—
217	C₃×C₄	#3673	1	2	yes	—
218	C₃×C₄	#3699	1	2	yes	—
219	C₃×C₄	C₃×#213	1	2	yes	—
220	C₃×C₄	C₃×#214	1	2	yes	—
221	C₃×C₄	C₃×#237	1	2	yes	—
222	Dic₃	—	12	2	no	—
223	C₃²	#5070	1	1	yes	characteristic
224	C₉	—	2	1	no	—
225	C₉	C₃×#486	1	1	yes	characteristic, complemented
226	C₂³	—	2	2	no	—
227	Q₈	—	36	2	no	—
228	D₄	—	2	4	no	—
229	D₄	—	4	2	no	—
230	D₄	—	4	2	no	—
231	C₂×C₄	—	18	2	no	—
232	C₂×C₄	C₃×#611	1	1	yes	characteristic
233	C₂×C₄	C₃×#611	1	1	yes	characteristic
234	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
235	C₈	—	18	2	no	—
236	C₂×C₃	—	2	1	no	—
237	C₂×C₃	—	2	1	no	—
238	C₂×C₃	—	2	1	no	—
239	C₂×C₃	—	8	4	no	—
240	C₂×C₃	—	8	2	no	—
241	C₂×C₃	—	8	2	no	—
242	C₂×C₃	C₂×#3672	1	1	yes	characteristic
243	C₂×C₃	C₂×#3673	1	1	yes	characteristic
244	C₂×C₃	#63498	1	1	yes	characteristic
245	C₂×C₃	C₂×C₃×#213	1	1	yes	characteristic
246	C₂×C₃	C₂×C₃×#214	1	1	yes	characteristic
247	C₂×C₃	C₃×#936	1	1	yes	characteristic
248	C₂²	—	4	2	no	—
249	C₂²	—	4	2	no	—
250	C₂²	—	4	2	no	—
251	C₂²	C₂×C₃×#611	1	1	yes	characteristic
252	C₄	—	36	2	no	—
253	C₄	C₃×#3672	1	2	yes	—
254	C₄	C₃×#3673	1	2	yes	—
255	C₄	C₃×#3699	1	2	yes	—
256	C₃	—	2	1	no	—
257	C₃	#10588750	1	1	yes	characteristic, direct product factor
258	C₃	C₃×#5070	1	1	yes	characteristic
259	C₂	—	8	2	no	—
260	C₂	C₂×C₃×#3672	1	1	yes	characteristic
261	C₂	C₂×C₃×#3673	1	1	yes	characteristic
262	C₂	C₃×#63498	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×C₉×#127

C₂

yes

maximal, characteristic

C₃×#63431

C₂

yes

maximal, characteristic, complemented

C₃×#63392

C₂

yes

maximal, complemented

C₃×C₄×C₉⋊C₈

C₂

yes

maximal, characteristic, complemented

C₃×#5070

—

maximal

#10588750

C₃

yes

maximal, characteristic, direct product factor

C₂×C₃×D₄×C₉

—

C₂×C₃×D₄×C₉

—

C₂×C₃×D₄×C₉

C₂²

yes

—

C₂×C₃×Dic₁₈

—

C₃×C₄²×C₉

C₂²

yes

characteristic

C₃×C₄⋊Dic₉

—

C₃×C₄⋊Dic₉

C₂²

yes

—

C₂×C₃×C₉⋊C₈

C₂²

yes

—

C₃²×#127

D₃

yes

characteristic

C₃×#869

—

C₃×#832

—

C₃×C₄×C₃⋊C₈

—

C₉×#127

—

C₉×#127

C₂×C₃

yes

characteristic

#63431

C₂×C₃

yes

characteristic, complemented

#63392

C₂×C₃

yes

complemented

C₄×C₉⋊C₈

C₂×C₃

yes

characteristic, complemented

C₂³×C₃×C₉

—

C₃×D₄×C₉

—

C₃×D₄×C₉

—

C₃×D₄×C₉

—

C₂×C₃×C₄×C₉

D₄

yes

characteristic

C₂×C₃×C₄×C₉

D₄

yes

characteristic

C₂×C₃×C₄×C₉

C₂³

yes

characteristic

C₂×C₃×Dic₉

—

C₃×Dic₁₈

—

C₃×C₉⋊C₈

—

C₃×#486

—

#5070

—

C₂×C₃²×D₄

—

C₂×C₃²×D₄

—

C₂×C₃²×D₄

C₂×D₃

yes

—

C₂×C₃×Dic₆

—

C₃²×C₄²

C₂×D₃

yes

characteristic

C₃×C₄⋊Dic₃

—

C₃×C₄⋊Dic₃

—

C₂×C₃×C₃⋊C₈

—

C₂×D₄×C₉

—

C₂×D₄×C₉

—

C₂×D₄×C₉

—

C₂×D₄×C₉

—

C₂×D₄×C₉

—

C₂×D₄×C₉

C₂²×C₃

yes

—

C₂×Dic₁₈

—

C₄²×C₉

—

C₄²×C₉

C₂²×C₃

yes

characteristic

C₄⋊Dic₉

—

C₄⋊Dic₉

C₂²×C₃

yes

—

C₂×C₉⋊C₈

C₂²×C₃

yes

—

C₂²×C₃×C₉

—

C₂²×C₃×C₉

—

C₂²×C₃×C₉

—

C₂²×C₃×C₉

C₂×D₄

yes

characteristic

C₃×C₄×C₉

D₈

yes

—

C₃×C₄×C₉

SD₁₆

yes

—

C₃×C₄×C₉

#41

yes

—

C₃×Dic₉

—

C₃×C₄⋊Q₈

—

C₃×#127

—

C₃×#127

D₉

yes

characteristic

C₃×#127

C₃×D₃

yes

characteristic

#869

—

C₃×#102

—

C₃×C₄×C₈

—

#832

—

C₄×C₃⋊C₈

—

C₂³×C₃²

—

C₃²×D₄

—

C₃²×D₄

—

C₃²×D₄

—

C₂×C₃²×C₄

yes

C₂×C₃²×C₄

yes

C₂×C₃²×C₄

C₂²×D₃

yes

characteristic

C₂×C₃×Dic₃

—

C₃×Dic₆

—

C₂³×C₉

—

C₂³×C₉

—

C₃×C₃⋊C₈

—

D₄×C₉

—

D₄×C₉

—

D₄×C₉

—

D₄×C₉

—

D₄×C₉

—

D₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

C₃×D₄

yes

characteristic

C₂×C₄×C₉

C₃×D₄

yes

characteristic

C₂×C₄×C₉

C₂³×C₃

yes

characteristic

C₂×Dic₉

—

Dic₁₈

—

C₉⋊C₈

—

100

#486

—

Sylow

101

C₂×C₃×C₉

—

102

C₂×C₃×C₉

#124

yes

characteristic

103

C₂×C₃×C₉

C₂×D₈

yes

characteristic

104

C₂×C₃×C₉

C₂×SD₁₆

yes

characteristic

105

C₂×C₃×Q₈

—

106

C₂×C₃×D₄

—

107

C₂×C₃×D₄

—

108

C₂×C₃×D₄

—

109

C₂×C₃×D₄

—

110

C₂×C₃×D₄

—

111

C₂×C₃×D₄

—

112

C₂×C₃×D₄

—

113

C₂×C₃×D₄

C₂×D₉

yes

—

114

C₂×C₃×D₄

C₂×C₃×D₃

yes

—

115

C₂×Dic₆

—

116

C₂×C₃×C₈

—

117

C₃×C₄⋊C₄

—

118

C₃×C₄⋊C₄

—

119

C₃×C₄²

—

120

C₃×C₄²

C₂×D₉

yes

characteristic

121

C₃×C₄²

C₂×C₃×D₃

yes

characteristic

122

C₄⋊Dic₃

—

123

C₄⋊Dic₃

—

124

C₂×C₃⋊C₈

—

125

C₂²×C₃²

—

126

C₂²×C₃²

—

127

C₂²×C₃²

—

128

C₂²×C₃²

C₂×#67

yes

characteristic

129

C₃²×C₄

#213

yes

—

130

C₃²×C₄

#214

yes

—

131

C₃²×C₄

#237

yes

—

132

C₃×Dic₃

—

133

C₂²×C₉

—

134

C₂²×C₉

—

135

C₂²×C₉

—

136

C₂²×C₉

—

137

C₂²×C₉

—

138

C₂²×C₉

—

139

C₂²×C₉

—

140

C₂²×C₉

C₂×C₃×D₄

yes

characteristic

141

C₄×C₉

—

142

C₄×C₉

—

143

C₄×C₉

—

144

C₄×C₉

C₃×D₈

yes

—

145

C₄×C₉

C₃×SD₁₆

yes

—

146

C₄×C₉

C₃×#41

yes

—

147

Dic₉

—

148

C₄⋊Q₈

—

149

#127

C₃×D₉

yes

characteristic

150

#102

—

151

C₄×C₈

—

152

C₃×C₉

#486

yes

characteristic, complemented, Sylow

153

C₂³×C₃

—

154

C₂³×C₃

—

155

C₂³×C₃

—

156

C₃×Q₈

—

157

C₃×D₄

—

158

C₃×D₄

—

159

C₃×D₄

—

160

C₃×D₄

—

161

C₃×D₄

—

162

C₃×D₄

—

163

C₃×D₄

—

164

C₃×D₄

—

165

C₃×D₄

—

166

C₂×C₃×C₄

—

167

C₂×C₃×C₄

—

168

C₂×C₃×C₄

—

169

C₂×C₃×C₄

—

170

C₂×C₃×C₄

#611

yes

characteristic

171

C₂×C₃×C₄

#611

yes

characteristic

172

C₂×C₃×C₄

C₂²×D₉

yes

characteristic

173

C₂×C₃×C₄

C₃×#67

yes

characteristic

174

C₂×C₃×C₄

C₃×#67

yes

characteristic

175

C₂×C₃×C₄

C₂²×C₃×D₃

yes

characteristic

176

C₂×Dic₃

—

177

Dic₆

—

178

C₃×C₈

—

179

C₃⋊C₈

—

180

C₂×C₃²

—

181

C₂×C₃²

C₂×#213

yes

characteristic

182

C₂×C₃²

C₂×#214

yes

characteristic

183

C₂×C₃²

#936

yes

characteristic

184

C₂×C₉

—

185

C₂×C₉

—

186

C₂×C₉

—

187

C₂×C₉

—

188

C₂×C₉

—

189

C₂×C₉

C₃×#124

yes

characteristic

190

C₂×C₉

C₂×C₃×D₈

yes

characteristic

191

C₂×C₉

C₂×C₃×SD₁₆

yes

characteristic

192

C₂×Q₈

—

193

C₂×D₄

—

194

C₂×D₄

—

195

C₂×D₄

C₂×C₃×D₉

yes

—

196

C₂×C₈

—

197

C₄⋊C₄

—

198

C₄⋊C₄

—

199

C₄²

C₂×C₃×D₉

yes

characteristic

200

C₂²×C₃

—

201

C₂²×C₃

—

202

C₂²×C₃

—

203

C₂²×C₃

—

204

C₂²×C₃

—

205

C₂²×C₃

—

206

C₂²×C₃

—

207

C₂²×C₃

—

208

C₂²×C₃

—

209

C₂²×C₃

—

210

C₂²×C₃

C₂×#611

yes

characteristic

211

C₂²×C₃

C₂×C₃×#67

yes

characteristic

212

C₃×C₄

—

213

C₃×C₄

—

214

C₃×C₄

—

215

C₃×C₄

—

216

C₃×C₄

#3672

yes

—

217

C₃×C₄

#3673

yes

—

218

C₃×C₄

#3699

yes

—

219

C₃×C₄

C₃×#213

yes

—

220

C₃×C₄

C₃×#214

yes

—

221

C₃×C₄

C₃×#237

yes

—

222

Dic₃

—

223

C₃²

#5070

yes

characteristic

224

C₉

—

225

C₉

C₃×#486

yes

characteristic, complemented

226

C₂³

—

227

Q₈

—

228

D₄

—

229

D₄

—

230

D₄

—

231

C₂×C₄

—

232

C₂×C₄

C₃×#611

yes

characteristic

233

C₂×C₄

C₃×#611

yes

characteristic

234

C₂×C₄

C₂²×C₃×D₉

yes

characteristic

235

C₈

—

236

C₂×C₃

—

237

C₂×C₃

—

238

C₂×C₃

—

239

C₂×C₃

—

240

C₂×C₃

—

241

C₂×C₃

—

242

C₂×C₃

C₂×#3672

yes

characteristic

243

C₂×C₃

C₂×#3673

yes

characteristic

244

C₂×C₃

#63498

yes

characteristic

245

C₂×C₃

C₂×C₃×#213

yes

characteristic

246

C₂×C₃

C₂×C₃×#214

yes

characteristic

247

C₂×C₃

C₃×#936

yes

characteristic

248

C₂²

—

249

C₂²

—

250

C₂²

—

251

C₂²

C₂×C₃×#611

yes

characteristic

252

C₄

—

253

C₄

C₃×#3672

yes

—

254

C₄

C₃×#3673

yes

—

255

C₄

C₃×#3699

yes

—

256

C₃

—

257

C₃

#10588750

yes

characteristic, direct product factor

258

C₃

C₃×#5070

yes

characteristic

259

C₂

—

260

C₂

C₂×C₃×#3672

yes

characteristic

261

C₂

C₂×C₃×#3673

yes

characteristic

262

C₂

C₃×#63498

yes

characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×#611
commutator, cosocle	C₂×C₄×C₉	C₂³×C₃
Frattini	C₂×C₃×C₄	C₂²×C₃×D₃
Fitting	C₃×C₉×#127	C₂
socle	C₂²×C₃²	C₂×#67
prime radical	C₃²×#127	D₃
hypercenter	C₃×#127	D₉
hypocenter	C₉	C₃×#486
LCS	G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#127

subgroup

G/H

center

C₂²×C₃

C₂×#611

commutator, cosocle

C₂×C₄×C₉

C₂³×C₃

Frattini

C₂×C₃×C₄

C₂²×C₃×D₃

Fitting

C₃×C₉×#127

C₂

socle

C₂²×C₃²

C₂×#67

prime radical

C₃²×#127

D₃

D₉

C₉

G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉

UCS

C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#127

N	H ≅ G/N	type
2. C₃×#63431	C₂	semidirect
3. C₃×#63392	C₂	semidirect
4. C₃×C₄×C₉⋊C₈	C₂	semidirect
6. #10588750	C₃	direct (N × H)
21. #63431	C₂×C₃	semidirect
22. #63392	C₂×C₃	semidirect
23. C₄×C₉⋊C₈	C₂×C₃	semidirect
152. C₃×C₉	#486	semidirect
225. C₉	C₃×#486	semidirect
257. C₃	#10588750	direct (N × H)

H ≅ G/N

type

2. C₃×#63431

C₂

semidirect

3. C₃×#63392

C₂

semidirect

4. C₃×C₄×C₉⋊C₈

C₂

semidirect

6. #10588750

C₃

direct (N × H)

21. #63431

C₂×C₃

semidirect

22. #63392

C₂×C₃

semidirect

23. C₄×C₉⋊C₈

C₂×C₃

semidirect

152. C₃×C₉

#486

semidirect

225. C₉

C₃×#486

semidirect

257. C₃

#10588750

direct (N × H)

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

subgroup	index
C₃×C₉×#127	2
C₃×#63431	2
C₃×#63392	2
C₃×C₄×C₉⋊C₈	2
C₃×#5070	3
#10588750	3

subgroup

index

C₃×C₉×#127

C₃×C₄×C₉⋊C₈

Subgroups — C₃×#10588750 #13142967

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C3×#10588750 #13142967

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10588750 #13142967