Subgroups — C₉×#3196 #11767917

Order 1152.

621 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#525	C₂	1	1	yes	maximal, characteristic
2	C₂×C₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#485	C₂	1	2	yes	maximal, complemented
4	C₉×#484	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#481	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#470	C₂	1	2	yes	maximal, complemented
7	C₉×#468	C₂	1	2	yes	maximal, complemented
8	C₉×#452	C₂	1	2	yes	maximal, complemented
9	C₉×#451	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#448	C₂	1	1	yes	maximal, characteristic, complemented
11	C₉×#407	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3196	C₃	1	1	yes	maximal, characteristic
13	C₂×C₉×#41	C₂²	1	1	yes	characteristic
14	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic
15	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
16	C₂×C₉×Q₁₆	C₂²	1	2	yes	complemented
17	C₂×C₉×SD₁₆	C₂²	1	2	yes	complemented
18	C₂×C₉×M₁₆	C₂²	1	2	yes	—
19	C₉×#123	—	2	1	no	—
20	C₉×C₂²⋊Q₈	—	2	1	no	—
21	C₉×C₂²⋊Q₈	—	2	1	no	—
22	C₉×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₉×C₂²⋊Q₈	C₂²	1	2	yes	—
24	C₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
25	C₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₉×#121	C₂²	1	1	yes	characteristic
27	C₉×#121	C₂²	1	1	yes	characteristic
28	C₉×#120	—	2	1	no	—
29	C₄×D₄×C₉	—	2	1	no	—
30	C₄×D₄×C₉	—	2	1	no	—
31	C₉×#117	C₂²	1	1	yes	characteristic
32	C₂×C₉×C₄⋊C₄	—	2	1	no	—
33	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₉×C₂²⋊C₄	—	2	1	no	—
35	C₉×#107	C₂²	1	2	yes	complemented
36	C₉×#106	C₂²	1	2	yes	complemented
37	C₉×#103	C₂²	1	2	yes	complemented
38	C₉×#103	C₂²	1	2	yes	complemented
39	C₉×#103	C₂²	1	2	yes	complemented
40	C₉×#102	C₂²	1	2	yes	complemented
41	C₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
42	C₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
43	C₉×C₂²⋊C₈	C₂²	1	2	yes	—
44	C₃×#525	C₂×C₃	1	1	yes	characteristic
45	C₂×C₃×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
46	C₃×#485	C₂×C₃	1	2	yes	—
47	C₃×#484	C₂×C₃	1	1	yes	characteristic
48	C₃×#481	C₂×C₃	1	1	yes	characteristic
49	C₃×#470	C₂×C₃	1	2	yes	—
50	C₃×#468	C₂×C₃	1	2	yes	—
51	C₃×#452	C₂×C₃	1	2	yes	—
52	C₃×#451	C₂×C₃	1	1	yes	characteristic
53	C₃×#448	C₂×C₃	1	1	yes	characteristic
54	C₃×#407	C₂×C₃	1	1	yes	characteristic
55	C₂⁴×C₉	D₄	1	1	yes	characteristic
56	C₉×#41	—	4	2	no	—
57	C₂×Q₈×C₉	—	2	1	no	—
58	C₂×Q₈×C₉	—	4	2	no	—
59	C₂×Q₈×C₉	C₂³	1	2	yes	—
60	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
61	C₂×D₄×C₉	—	2	1	no	—
62	C₂×D₄×C₉	—	2	1	no	—
63	C₂×D₄×C₉	—	2	1	no	—
64	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
65	C₂²×C₄×C₉	—	2	1	no	—
66	C₂²×C₄×C₉	—	2	1	no	—
67	C₂²×C₄×C₉	—	2	1	no	—
68	C₂²×C₄×C₉	—	4	2	no	—
69	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
70	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
71	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
72	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
73	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
74	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
75	C₉×Q₁₆	—	4	2	no	—
76	C₉×SD₁₆	—	4	2	no	—
77	C₉×M₁₆	—	4	2	no	—
78	C₂×C₈×C₉	C₂³	1	2	yes	—
79	C₂×C₈×C₉	C₂³	1	2	yes	—
80	C₉×C₄⋊C₄	—	2	2	no	—
81	C₉×C₄⋊C₄	—	2	2	no	—
82	C₉×C₄⋊C₄	—	2	1	no	—
83	C₉×C₄⋊C₄	—	2	1	no	—
84	C₉×C₄⋊C₄	—	2	1	no	—
85	C₉×C₄⋊C₄	C₂³	1	2	yes	—
86	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
87	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
88	C₉×C₂²⋊C₄	—	2	2	no	—
89	C₉×C₂²⋊C₄	—	2	2	no	—
90	C₉×C₂²⋊C₄	—	2	1	no	—
91	C₉×C₂²⋊C₄	—	2	1	no	—
92	C₉×C₂²⋊C₄	—	2	1	no	—
93	C₉×C₂²⋊C₄	—	2	1	no	—
94	C₉×C₂²⋊C₄	—	2	1	no	—
95	C₄²×C₉	—	2	1	no	—
96	#3196	C₉	1	1	yes	characteristic, direct product factor, Sylow
97	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
98	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
99	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
100	C₂×C₃×Q₁₆	C₂²×C₃	1	2	yes	—
101	C₂×C₃×SD₁₆	C₂²×C₃	1	2	yes	—
102	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
103	C₃×#123	—	2	1	no	—
104	C₃×C₂²⋊Q₈	—	2	1	no	—
105	C₃×C₂²⋊Q₈	—	2	1	no	—
106	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
107	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
108	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
109	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
110	C₃×#121	C₂²×C₃	1	1	yes	characteristic
111	C₃×#121	C₂²×C₃	1	1	yes	characteristic
112	C₃×#120	—	2	1	no	—
113	C₃×C₄×D₄	—	2	1	no	—
114	C₃×C₄×D₄	—	2	1	no	—
115	C₃×#117	C₂²×C₃	1	1	yes	characteristic
116	C₂×C₃×C₄⋊C₄	—	2	1	no	—
117	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
118	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
119	C₃×#107	C₂²×C₃	1	2	yes	—
120	C₃×#106	C₂²×C₃	1	2	yes	—
121	C₃×#103	C₂²×C₃	1	2	yes	—
122	C₃×#103	C₂²×C₃	1	2	yes	—
123	C₃×#103	C₂²×C₃	1	2	yes	—
124	C₃×#102	C₂²×C₃	1	2	yes	—
125	C₃×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
126	C₃×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
127	C₃×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
128	C₂³×C₉	—	2	2	no	—
129	C₂³×C₉	—	2	1	no	—
130	C₂³×C₉	—	4	1	no	—
131	C₂³×C₉	—	4	1	no	—
132	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
133	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
134	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
135	Q₈×C₉	—	2	2	no	—
136	Q₈×C₉	—	2	2	no	—
137	Q₈×C₉	—	2	2	no	—
138	Q₈×C₉	—	4	2	no	—
139	D₄×C₉	—	2	2	no	—
140	D₄×C₉	—	4	2	no	—
141	D₄×C₉	—	4	2	no	—
142	D₄×C₉	—	4	2	no	—
143	C₂×C₄×C₉	—	2	2	no	—
144	C₂×C₄×C₉	—	2	2	no	—
145	C₂×C₄×C₉	—	2	2	no	—
146	C₂×C₄×C₉	—	2	1	no	—
147	C₂×C₄×C₉	—	2	1	no	—
148	C₂×C₄×C₉	—	2	2	no	—
149	C₂×C₄×C₉	—	2	1	no	—
150	C₂×C₄×C₉	—	2	2	no	—
151	C₂×C₄×C₉	—	4	1	no	—
152	C₂×C₄×C₉	—	4	1	no	—
153	C₂×C₄×C₉	—	4	1	no	—
154	C₂×C₄×C₉	—	4	2	no	—
155	C₂×C₄×C₉	—	4	2	no	—
156	C₂×C₄×C₉	—	4	2	no	—
157	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
158	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
159	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
160	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
161	C₈×C₉	—	2	2	no	—
162	C₈×C₉	—	2	2	no	—
163	#525	C₂×C₉	1	1	yes	characteristic
164	C₂×C₂²⋊Q₈	C₂×C₉	1	1	yes	characteristic, complemented
165	#485	C₂×C₉	1	2	yes	complemented
166	#484	C₂×C₉	1	1	yes	characteristic, complemented
167	#481	C₂×C₉	1	1	yes	characteristic, complemented
168	#470	C₂×C₉	1	2	yes	complemented
169	#468	C₂×C₉	1	2	yes	complemented
170	#452	C₂×C₉	1	2	yes	complemented
171	#451	C₂×C₉	1	1	yes	characteristic, complemented
172	#448	C₂×C₉	1	1	yes	characteristic, complemented
173	#407	C₂×C₉	1	1	yes	characteristic, complemented
174	C₂⁴×C₃	C₃×D₄	1	1	yes	characteristic
175	C₃×#41	—	4	2	no	—
176	C₂×C₃×Q₈	—	2	1	no	—
177	C₂×C₃×Q₈	—	4	2	no	—
178	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
179	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
180	C₂×C₃×D₄	—	2	1	no	—
181	C₂×C₃×D₄	—	2	1	no	—
182	C₂×C₃×D₄	—	2	1	no	—
183	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
184	C₂²×C₃×C₄	—	2	1	no	—
185	C₂²×C₃×C₄	—	2	1	no	—
186	C₂²×C₃×C₄	—	2	1	no	—
187	C₂²×C₃×C₄	—	4	2	no	—
188	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
189	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
190	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
191	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
192	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
193	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
194	C₃×Q₁₆	—	4	2	no	—
195	C₃×SD₁₆	—	4	2	no	—
196	C₃×M₁₆	—	4	2	no	—
197	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
198	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
199	C₃×C₄⋊C₄	—	2	2	no	—
200	C₃×C₄⋊C₄	—	2	2	no	—
201	C₃×C₄⋊C₄	—	2	1	no	—
202	C₃×C₄⋊C₄	—	2	1	no	—
203	C₃×C₄⋊C₄	—	2	1	no	—
204	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
205	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
206	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
207	C₃×C₂²⋊C₄	—	2	2	no	—
208	C₃×C₂²⋊C₄	—	2	2	no	—
209	C₃×C₂²⋊C₄	—	2	1	no	—
210	C₃×C₂²⋊C₄	—	2	1	no	—
211	C₃×C₂²⋊C₄	—	2	1	no	—
212	C₃×C₂²⋊C₄	—	2	1	no	—
213	C₃×C₂²⋊C₄	—	2	1	no	—
214	C₃×C₄²	—	2	1	no	—
215	C₂²×C₉	—	2	1	no	—
216	C₂²×C₉	—	2	1	no	—
217	C₂²×C₉	—	2	1	no	—
218	C₂²×C₉	—	2	1	no	—
219	C₂²×C₉	—	2	1	no	—
220	C₂²×C₉	—	2	1	no	—
221	C₂²×C₉	—	2	1	no	—
222	C₂²×C₉	—	2	1	no	—
223	C₂²×C₉	—	4	4	no	—
224	C₂²×C₉	—	4	1	no	—
225	C₂²×C₉	—	4	1	no	—
226	C₂²×C₉	—	4	1	no	—
227	C₂²×C₉	#137	1	2	yes	—
228	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
229	C₄×C₉	—	2	1	no	—
230	C₄×C₉	—	2	1	no	—
231	C₄×C₉	—	2	1	no	—
232	C₄×C₉	—	4	1	no	—
233	C₄×C₉	—	4	2	no	—
234	C₄×C₉	—	4	1	no	—
235	C₄×C₉	—	4	2	no	—
236	C₄×C₉	—	4	1	no	—
237	C₄×C₉	H(5,𝔽₂)	1	2	yes	—
238	C₂×#41	C₂²×C₉	1	1	yes	characteristic
239	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic
240	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
241	C₂×Q₁₆	C₂²×C₉	1	2	yes	complemented
242	C₂×SD₁₆	C₂²×C₉	1	2	yes	complemented
243	C₂×M₁₆	C₂²×C₉	1	2	yes	—
244	#123	—	2	1	no	—
245	C₂²⋊Q₈	—	2	1	no	—
246	C₂²⋊Q₈	—	2	1	no	—
247	C₂²⋊Q₈	C₂²×C₉	1	2	yes	—
248	C₂²⋊Q₈	C₂²×C₉	1	2	yes	—
249	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic
250	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic
251	#121	C₂²×C₉	1	1	yes	characteristic
252	#121	C₂²×C₉	1	1	yes	characteristic
253	#120	—	2	1	no	—
254	C₄×D₄	—	2	1	no	—
255	C₄×D₄	—	2	1	no	—
256	#117	C₂²×C₉	1	1	yes	characteristic
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
259	C₂×C₂²⋊C₄	—	2	1	no	—
260	#107	C₂²×C₉	1	2	yes	complemented
261	#106	C₂²×C₉	1	2	yes	complemented
262	#103	C₂²×C₉	1	2	yes	complemented
263	#103	C₂²×C₉	1	2	yes	complemented
264	#103	C₂²×C₉	1	2	yes	complemented
265	#102	C₂²×C₉	1	2	yes	complemented
266	C₂²⋊C₈	C₂²×C₉	1	1	yes	characteristic
267	C₂²⋊C₈	C₂²×C₉	1	1	yes	characteristic
268	C₂²⋊C₈	C₂²×C₉	1	2	yes	—
269	C₂³×C₃	—	2	2	no	—
270	C₂³×C₃	—	2	1	no	—
271	C₂³×C₃	—	4	1	no	—
272	C₂³×C₃	—	4	1	no	—
273	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
274	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
275	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
276	C₃×Q₈	—	2	2	no	—
277	C₃×Q₈	—	2	2	no	—
278	C₃×Q₈	—	2	2	no	—
279	C₃×Q₈	—	4	2	no	—
280	C₃×D₄	—	2	2	no	—
281	C₃×D₄	—	4	2	no	—
282	C₃×D₄	—	4	2	no	—
283	C₃×D₄	—	4	2	no	—
284	C₂×C₃×C₄	—	2	2	no	—
285	C₂×C₃×C₄	—	2	2	no	—
286	C₂×C₃×C₄	—	2	2	no	—
287	C₂×C₃×C₄	—	2	1	no	—
288	C₂×C₃×C₄	—	2	1	no	—
289	C₂×C₃×C₄	—	2	2	no	—
290	C₂×C₃×C₄	—	2	1	no	—
291	C₂×C₃×C₄	—	2	2	no	—
292	C₂×C₃×C₄	—	4	1	no	—
293	C₂×C₃×C₄	—	4	1	no	—
294	C₂×C₃×C₄	—	4	1	no	—
295	C₂×C₃×C₄	—	4	2	no	—
296	C₂×C₃×C₄	—	4	2	no	—
297	C₂×C₃×C₄	—	4	2	no	—
298	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
299	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
300	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
301	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
302	C₃×C₈	—	2	2	no	—
303	C₃×C₈	—	2	2	no	—
304	C₂×C₉	—	2	2	no	—
305	C₂×C₉	—	4	1	no	—
306	C₂×C₉	—	4	1	no	—
307	C₂×C₉	—	8	1	no	—
308	C₂×C₉	#534	1	1	yes	characteristic
309	C₂×C₉	C₂×#137	1	1	yes	characteristic
310	C₂×C₉	#575	1	1	yes	characteristic
311	C₂⁴	D₄×C₉	1	1	yes	characteristic
312	#41	—	4	2	no	—
313	C₂×Q₈	—	2	1	no	—
314	C₂×Q₈	—	4	2	no	—
315	C₂×Q₈	C₂³×C₉	1	2	yes	—
316	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
317	C₂×D₄	—	2	1	no	—
318	C₂×D₄	—	2	1	no	—
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	4	2	no	—
325	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
326	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
327	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
328	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
329	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
330	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
331	Q₁₆	—	4	2	no	—
332	SD₁₆	—	4	2	no	—
333	M₁₆	—	4	2	no	—
334	C₂×C₈	C₂³×C₉	1	2	yes	—
335	C₂×C₈	C₂³×C₉	1	2	yes	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	1	no	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	C₂³×C₉	1	2	yes	—
342	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
343	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
344	C₂²⋊C₄	—	2	2	no	—
345	C₂²⋊C₄	—	2	2	no	—
346	C₂²⋊C₄	—	2	1	no	—
347	C₂²⋊C₄	—	2	1	no	—
348	C₂²⋊C₄	—	2	1	no	—
349	C₂²⋊C₄	—	2	1	no	—
350	C₂²⋊C₄	—	2	1	no	—
351	C₄²	—	2	1	no	—
352	C₂²×C₃	—	2	1	no	—
353	C₂²×C₃	—	2	1	no	—
354	C₂²×C₃	—	2	1	no	—
355	C₂²×C₃	—	2	1	no	—
356	C₂²×C₃	—	2	1	no	—
357	C₂²×C₃	—	2	1	no	—
358	C₂²×C₃	—	2	1	no	—
359	C₂²×C₃	—	2	1	no	—
360	C₂²×C₃	—	4	4	no	—
361	C₂²×C₃	—	4	1	no	—
362	C₂²×C₃	—	4	1	no	—
363	C₂²×C₃	—	4	1	no	—
364	C₂²×C₃	C₃×#137	1	2	yes	—
365	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
366	C₃×C₄	—	2	1	no	—
367	C₃×C₄	—	2	1	no	—
368	C₃×C₄	—	2	1	no	—
369	C₃×C₄	—	4	1	no	—
370	C₃×C₄	—	4	2	no	—
371	C₃×C₄	—	4	1	no	—
372	C₃×C₄	—	4	1	no	—
373	C₃×C₄	—	4	2	no	—
374	C₃×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
375	C₉	#3196	1	1	yes	characteristic, direct product factor, Sylow
376	C₂³	—	2	2	no	—
377	C₂³	—	2	1	no	—
378	C₂³	—	4	1	no	—
379	C₂³	—	4	1	no	—
380	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
381	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
382	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
383	Q₈	—	2	2	no	—
384	Q₈	—	2	2	no	—
385	Q₈	—	2	2	no	—
386	Q₈	—	4	2	no	—
387	D₄	—	2	2	no	—
388	D₄	—	4	2	no	—
389	D₄	—	4	2	no	—
390	D₄	—	4	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
406	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
407	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
408	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
409	C₈	—	2	2	no	—
410	C₈	—	2	2	no	—
411	C₂×C₃	—	2	2	no	—
412	C₂×C₃	—	4	1	no	—
413	C₂×C₃	—	4	1	no	—
414	C₂×C₃	—	8	1	no	—
415	C₂×C₃	C₃×#534	1	1	yes	characteristic
416	C₂×C₃	C₂×C₃×#137	1	1	yes	characteristic
417	C₂×C₃	C₃×#575	1	1	yes	characteristic
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	2	1	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	2	1	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	4	4	no	—
427	C₂²	—	4	1	no	—
428	C₂²	—	4	1	no	—
429	C₂²	—	4	1	no	—
430	C₂²	C₉×#137	1	2	yes	—
431	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	4	1	no	—
436	C₄	—	4	2	no	—
437	C₄	—	4	1	no	—
438	C₄	—	4	2	no	—
439	C₄	—	4	1	no	—
440	C₄	C₉×H(5,𝔽₂)	1	2	yes	—
441	C₃	C₃×#3196	1	1	yes	characteristic
442	C₂	—	2	2	no	—
443	C₂	—	4	1	no	—
444	C₂	—	4	1	no	—
445	C₂	—	8	1	no	—
446	C₂	C₉×#534	1	1	yes	characteristic
447	C₂	C₂×C₉×#137	1	1	yes	characteristic
448	C₂	C₉×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	C₂²×D₄
commutator	C₂×C₄	C₂⁴×C₉
Frattini, cosocle	C₂×C₃×C₄	C₂⁴×C₃
socle	C₂²×C₃	C₂²×C₃×D₄
prime radical	C₃×#525	C₂×C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₂³×C₄×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₉×C₂²⋊Q₈	C₂	semidirect
3. C₉×#485	C₂	semidirect
4. C₉×#484	C₂	semidirect
5. C₉×#481	C₂	semidirect
6. C₉×#470	C₂	semidirect
7. C₉×#468	C₂	semidirect
8. C₉×#452	C₂	semidirect
9. C₉×#451	C₂	semidirect
10. C₉×#448	C₂	semidirect
11. C₉×#407	C₂	semidirect
16. C₂×C₉×Q₁₆	C₂²	semidirect
17. C₂×C₉×SD₁₆	C₂²	semidirect
35. C₉×#107	C₂²	semidirect
36. C₉×#106	C₂²	semidirect
37. C₉×#103	C₂²	semidirect
38. C₉×#103	C₂²	semidirect
39. C₉×#103	C₂²	semidirect
40. C₉×#102	C₂²	semidirect
96. #3196	C₉	direct (N × H)
164. C₂×C₂²⋊Q₈	C₂×C₉	semidirect
165. #485	C₂×C₉	semidirect
166. #484	C₂×C₉	semidirect
167. #481	C₂×C₉	semidirect
168. #470	C₂×C₉	semidirect
169. #468	C₂×C₉	semidirect
170. #452	C₂×C₉	semidirect
171. #451	C₂×C₉	semidirect
172. #448	C₂×C₉	semidirect
173. #407	C₂×C₉	semidirect
241. C₂×Q₁₆	C₂²×C₉	semidirect
242. C₂×SD₁₆	C₂²×C₉	semidirect
260. #107	C₂²×C₉	semidirect
261. #106	C₂²×C₉	semidirect
262. #103	C₂²×C₉	semidirect
263. #103	C₂²×C₉	semidirect
264. #103	C₂²×C₉	semidirect
265. #102	C₂²×C₉	semidirect
375. C₉	#3196	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉×#525	2
C₂×C₉×C₂²⋊Q₈	2
C₉×#485	2
C₉×#484	2
C₉×#481	2
C₉×#470	2
C₉×#468	2
C₉×#452	2
C₉×#451	2
C₉×#448	2
C₉×#407	2
C₃×#3196	3

Subgroups — C9×#3196 #11767917

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3196 #11767917