Subgroups — C₂²×#88663 #13164800

Order 1728.

2906 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃⋊Dic₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₉×#67	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×#611	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#6194	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#88663	C₂	1	24	yes	maximal, direct product factor
6	C₂²×D₃×Dic₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×Dic₃×D₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#6189	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#3805	—	3	1	no	maximal
10	C₂²×#3699	—	3	1	no	maximal
11	C₂⁴×C₃×C₉	C₂²	1	1	yes	characteristic
12	C₂³×D₃×C₉	C₂²	1	1	yes	characteristic
13	C₂³×C₃×D₉	C₂²	1	1	yes	characteristic
14	C₂²×C₃⋊Dic₉	C₂²	1	1	yes	characteristic
15	C₂²×C₃⋊Dic₉	C₂²	1	1	yes	characteristic
16	C₂²×C₃⋊Dic₉	C₂²	1	12	yes	complemented
17	C₂×C₉×#67	C₂²	1	12	yes	complemented
18	C₂×C₃×#611	C₂²	1	12	yes	complemented
19	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
20	C₂²×C₃×Dic₉	C₂²	1	1	yes	characteristic
21	C₂×#6194	C₂²	1	12	yes	complemented
22	#88663	C₂²	1	64	yes	direct product factor
23	C₂×D₃×Dic₉	C₂²	1	12	yes	complemented
24	C₂×Dic₃×D₉	C₂²	1	12	yes	complemented
25	C₂×#6189	C₂²	1	12	yes	complemented
26	C₂³×C₃⋊Dic₃	—	3	1	no	—
27	C₂²×C₃×#67	—	3	1	no	—
28	C₂²×C₃×#67	D₃	1	1	yes	characteristic
29	C₂²×#627	—	3	1	no	—
30	C₂²×#625	—	3	1	no	—
31	C₂×#3805	—	3	24	no	—
32	C₂²×D₃×Dic₃	—	3	1	no	—
33	C₂²×D₃×Dic₃	—	3	1	no	—
34	C₂²×D₄×C₉	—	3	1	no	—
35	C₂²×#611	—	3	1	no	—
36	C₂²×#611	D₃	1	1	yes	characteristic, complemented
37	C₂³×Dic₉	—	3	1	no	—
38	C₂³×Dic₉	—	3	1	no	—
39	C₂³×Dic₉	—	6	1	no	—
40	C₂×#3699	—	3	24	no	—
41	C₂²×C₄×D₉	—	3	1	no	—
42	C₂²×Dic₁₈	—	3	1	no	—
43	C₂³×C₃×C₉	—	2	4	no	—
44	C₂³×C₃×C₉	C₂³	1	6	yes	—
45	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
46	C₂²×D₃×C₉	—	2	4	no	—
47	C₂²×D₃×C₉	C₂³	1	6	yes	—
48	C₂²×C₃×D₉	—	2	4	no	—
49	C₂²×C₃×D₉	C₂³	1	6	yes	—
50	C₂×C₃⋊Dic₉	C₂³	1	6	yes	—
51	C₂×C₃⋊Dic₉	C₂³	1	6	yes	—
52	C₂×C₃⋊Dic₉	C₂³	1	16	yes	complemented
53	C₉×#67	C₂³	1	16	yes	complemented
54	C₃×#611	C₂³	1	16	yes	complemented
55	C₂×C₉×Dic₃	C₂³	1	6	yes	—
56	C₂×C₃×Dic₉	C₂³	1	6	yes	—
57	#6194	C₂³	1	16	yes	complemented
58	D₃×Dic₉	C₂³	1	16	yes	complemented
59	Dic₃×D₉	C₂³	1	16	yes	complemented
60	#6189	C₂³	1	16	yes	complemented
61	C₂²×#237	—	9	1	no	—
62	C₂²×#237	—	9	1	no	—
63	C₂⁴×C₃²	C₂×D₃	1	1	yes	characteristic
64	C₂³×C₃×D₃	—	3	1	no	—
65	C₂³×C₃×D₃	C₂×D₃	1	1	yes	characteristic
66	C₂²×C₃⋊Dic₃	—	3	1	no	—
67	C₂²×C₃⋊Dic₃	—	3	12	no	—
68	C₂²×C₃⋊Dic₃	—	3	1	no	—
69	C₂×C₃×#67	—	3	12	no	—
70	C₂×C₃×#67	C₂×D₃	1	12	yes	—
71	C₂²×C₃×Dic₃	—	3	1	no	—
72	C₂²×C₃×Dic₃	C₂×D₃	1	1	yes	characteristic
73	C₂×#627	—	3	12	no	—
74	C₂×#625	—	3	12	no	—
75	#3805	—	3	64	no	—
76	C₂×D₃×Dic₃	—	3	12	no	—
77	C₂×D₃×Dic₃	—	3	12	no	—
78	C₂⁴×C₉	—	2	1	no	—
79	C₂⁴×C₉	—	3	1	no	—
80	C₂⁴×C₉	C₂×D₃	1	1	yes	characteristic
81	C₂³×D₉	C₂×D₃	1	1	yes	characteristic
82	C₂×D₄×C₉	—	3	12	no	—
83	C₂²×C₄×C₉	—	3	1	no	—
84	C₂×#611	—	3	12	no	—
85	C₂×#611	C₂×D₃	1	12	yes	complemented
86	C₂²×Dic₉	—	3	1	no	—
87	C₂²×Dic₉	—	3	1	no	—
88	C₂²×Dic₉	—	3	12	no	—
89	C₂²×Dic₉	—	3	12	no	—
90	C₂²×Dic₉	—	6	1	no	—
91	C₂²×Dic₉	—	6	1	no	—
92	C₂²×Dic₉	—	6	12	no	—
93	C₂²×Dic₉	C₂×D₃	1	1	yes	characteristic
94	#3699	—	3	64	no	—
95	C₂×C₄×D₉	—	3	12	no	—
96	C₂×Dic₁₈	—	3	12	no	—
97	C₂²×C₃×C₉	—	2	12	no	—
98	C₂²×C₃×C₉	#41	1	4	yes	complemented
99	C₂²×C₃×C₉	C₂⁴	1	4	yes	—
100	C₂²×C₃×C₉	C₂⁴	1	3	yes	—
101	C₂×D₃×C₉	—	2	12	no	—
102	C₂×D₃×C₉	C₂⁴	1	4	yes	—
103	C₂×C₃×D₉	—	2	12	no	—
104	C₂×C₃×D₉	C₂⁴	1	4	yes	—
105	C₃⋊Dic₉	C₂⁴	1	4	yes	—
106	C₃⋊Dic₉	C₂⁴	1	4	yes	—
107	C₉×Dic₃	C₂⁴	1	4	yes	—
108	C₃×Dic₉	C₂⁴	1	4	yes	—
109	C₂²×C₃×D₄	—	3	1	no	—
110	C₂²×C₃×D₄	—	9	1	no	—
111	C₂²×#67	—	3	1	no	—
112	C₂²×#67	—	9	1	no	—
113	C₂²×#67	—	9	1	no	—
114	C₂²×#67	D₉	1	1	yes	characteristic, complemented
115	C₂³×Dic₃	—	9	1	no	—
116	C₂³×Dic₃	—	9	1	no	—
117	C₂³×Dic₃	—	9	1	no	—
118	C₂³×Dic₃	—	9	1	no	—
119	C₂³×Dic₃	—	18	1	no	—
120	C₂×#237	—	9	24	no	—
121	C₂×#237	—	9	24	no	—
122	C₂²×C₄×D₃	—	9	1	no	—
123	C₂²×C₄×D₃	—	9	1	no	—
124	C₂²×Dic₆	—	9	1	no	—
125	C₂²×Dic₆	—	9	1	no	—
126	C₂³×C₃²	—	2	4	no	—
127	C₂³×C₃²	C₂²×D₃	1	6	yes	—
128	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
129	C₂²×C₃×D₃	—	2	4	no	—
130	C₂²×C₃×D₃	—	3	6	no	—
131	C₂²×C₃×D₃	—	6	4	no	—
132	C₂²×C₃×D₃	C₂²×D₃	1	6	yes	—
133	C₂×C₃⋊Dic₃	—	3	6	no	—
134	C₂×C₃⋊Dic₃	—	3	6	no	—
135	C₂×C₃⋊Dic₃	—	3	16	no	—
136	C₃×#67	—	3	16	no	—
137	C₃×#67	C₂²×D₃	1	16	yes	—
138	C₂×C₃×Dic₃	—	3	6	no	—
139	C₂×C₃×Dic₃	C₂²×D₃	1	6	yes	—
140	#627	—	3	16	no	—
141	#625	—	3	16	no	—
142	D₃×Dic₃	—	3	16	no	—
143	D₃×Dic₃	—	3	16	no	—
144	C₂³×C₉	—	2	8	no	—
145	C₂³×C₉	—	2	4	no	—
146	C₂³×C₉	—	2	6	no	—
147	C₂³×C₉	—	2	1	no	—
148	C₂³×C₉	—	3	6	no	—
149	C₂³×C₉	—	6	4	no	—
150	C₂³×C₉	C₂²×D₃	1	6	yes	—
151	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
152	C₂²×D₉	—	2	4	no	—
153	C₂²×D₉	C₂²×D₃	1	6	yes	—
154	D₄×C₉	—	3	16	no	—
155	C₂×C₄×C₉	—	3	6	no	—
156	#611	—	3	16	no	—
157	#611	C₂²×D₃	1	16	yes	complemented
158	C₂×Dic₉	—	3	6	no	—
159	C₂×Dic₉	—	3	6	no	—
160	C₂×Dic₉	—	3	16	no	—
161	C₂×Dic₉	—	3	16	no	—
162	C₂×Dic₉	—	6	6	no	—
163	C₂×Dic₉	—	6	6	no	—
164	C₂×Dic₉	—	6	16	no	—
165	C₂×Dic₉	C₂²×D₃	1	6	yes	—
166	C₄×D₉	—	3	16	no	—
167	Dic₁₈	—	3	16	no	—
168	C₂²×#41	—	27	1	no	Sylow
169	C₂×C₃×C₉	—	2	4	no	—
170	C₂×C₃×C₉	C₂×#41	1	6	yes	complemented
171	C₂×C₃×C₉	C₂⁵	1	1	yes	characteristic
172	D₃×C₉	—	2	4	no	—
173	C₃×D₉	—	2	4	no	—
174	C₂⁴×C₃	—	2	1	no	—
175	C₂⁴×C₃	—	3	1	no	—
176	C₂⁴×C₃	—	9	1	no	—
177	C₂⁴×C₃	C₂×D₉	1	1	yes	characteristic
178	C₂⁴×C₃	D₃²	1	1	yes	characteristic
179	C₂³×D₃	—	3	1	no	—
180	C₂³×D₃	C₂×D₉	1	1	yes	characteristic
181	C₂×C₃×D₄	—	3	12	no	—
182	C₂×C₃×D₄	—	9	12	no	—
183	C₂²×C₃×C₄	—	3	1	no	—
184	C₂²×C₃×C₄	—	9	1	no	—
185	C₂×#67	—	3	12	no	—
186	C₂×#67	—	9	12	no	—
187	C₂×#67	—	9	12	no	—
188	C₂×#67	C₂×D₉	1	12	yes	complemented
189	C₂²×Dic₃	—	3	1	no	—
190	C₂²×Dic₃	—	9	12	no	—
191	C₂²×Dic₃	—	9	1	no	—
192	C₂²×Dic₃	—	9	1	no	—
193	C₂²×Dic₃	—	9	12	no	—
194	C₂²×Dic₃	—	9	1	no	—
195	C₂²×Dic₃	—	9	1	no	—
196	C₂²×Dic₃	—	9	12	no	—
197	C₂²×Dic₃	—	9	12	no	—
198	C₂²×Dic₃	—	18	12	no	—
199	C₂²×Dic₃	—	18	1	no	—
200	C₂²×Dic₃	—	18	1	no	—
201	C₂²×Dic₃	C₂×D₉	1	1	yes	characteristic
202	#237	—	9	64	no	—
203	#237	—	9	64	no	—
204	C₂×C₄×D₃	—	9	12	no	—
205	C₂×C₄×D₃	—	9	12	no	—
206	C₂×Dic₆	—	9	12	no	—
207	C₂×Dic₆	—	9	12	no	—
208	C₂²×C₃²	—	2	12	no	—
209	C₂²×C₃²	#237	1	4	yes	—
210	C₂²×C₃²	C₂³×D₃	1	4	yes	—
211	C₂²×C₃²	C₂³×D₃	1	3	yes	—
212	C₂×C₃×D₃	—	2	12	no	—
213	C₂×C₃×D₃	—	3	4	no	—
214	C₂×C₃×D₃	—	6	12	no	—
215	C₂×C₃×D₃	C₂³×D₃	1	4	yes	—
216	C₃⋊Dic₃	—	3	4	no	—
217	C₃⋊Dic₃	—	3	4	no	—
218	C₃×Dic₃	—	3	4	no	—
219	C₃×Dic₃	C₂³×D₃	1	4	yes	—
220	C₂²×C₉	—	2	24	no	—
221	C₂²×C₉	—	2	12	no	—
222	C₂²×C₉	—	2	4	no	—
223	C₂²×C₉	—	2	3	no	—
224	C₂²×C₉	—	2	4	no	—
225	C₂²×C₉	—	3	4	no	—
226	C₂²×C₉	—	6	12	no	—
227	C₂²×C₉	#237	1	4	yes	complemented
228	C₂²×C₉	C₂³×D₃	1	4	yes	—
229	C₂²×C₉	C₂³×D₃	1	3	yes	—
230	C₂×D₉	—	2	12	no	—
231	C₂×D₉	C₂³×D₃	1	4	yes	—
232	C₄×C₉	—	3	4	no	—
233	Dic₉	—	3	4	no	—
234	Dic₉	—	3	4	no	—
235	Dic₉	—	6	4	no	—
236	Dic₉	—	6	4	no	—
237	Dic₉	C₂³×D₃	1	4	yes	—
238	C₂×#41	—	27	24	no	—
239	C₂²×Q₈	—	27	1	no	—
240	C₂²×D₄	—	3	1	no	—
241	C₂²×D₄	—	9	1	no	—
242	C₂²×D₄	—	27	1	no	—
243	C₂³×C₄	—	27	1	no	—
244	C₂³×C₄	—	27	1	no	—
245	C₂³×C₄	—	27	1	no	—
246	C₃×C₉	C₂²×#41	1	1	yes	characteristic, complemented, Sylow
247	C₂³×C₃	—	2	8	no	—
248	C₂³×C₃	—	2	4	no	—
249	C₂³×C₃	—	2	4	no	—
250	C₂³×C₃	—	2	6	no	—
251	C₂³×C₃	—	2	1	no	—
252	C₂³×C₃	—	3	6	no	—
253	C₂³×C₃	—	6	4	no	—
254	C₂³×C₃	—	9	6	no	—
255	C₂³×C₃	—	18	4	no	—
256	C₂³×C₃	C₂²×D₉	1	6	yes	—
257	C₂³×C₃	C₂²×D₉	1	1	yes	characteristic
258	C₂³×C₃	C₂×D₃²	1	6	yes	—
259	C₂³×C₃	C₂×D₃²	1	1	yes	characteristic
260	C₂²×D₃	—	2	4	no	—
261	C₂²×D₃	—	3	6	no	—
262	C₂²×D₃	—	6	4	no	—
263	C₂²×D₃	C₂²×D₉	1	6	yes	—
264	C₃×D₄	—	3	16	no	—
265	C₃×D₄	—	9	16	no	—
266	C₂×C₃×C₄	—	3	6	no	—
267	C₂×C₃×C₄	—	9	6	no	—
268	#67	—	3	16	no	—
269	#67	—	9	16	no	—
270	#67	—	9	16	no	—
271	#67	C₂²×D₉	1	16	yes	complemented
272	C₂×Dic₃	—	3	6	no	—
273	C₂×Dic₃	—	9	16	no	—
274	C₂×Dic₃	—	9	6	no	—
275	C₂×Dic₃	—	9	6	no	—
276	C₂×Dic₃	—	9	16	no	—
277	C₂×Dic₃	—	9	6	no	—
278	C₂×Dic₃	—	9	6	no	—
279	C₂×Dic₃	—	9	16	no	—
280	C₂×Dic₃	—	9	16	no	—
281	C₂×Dic₃	—	18	6	no	—
282	C₂×Dic₃	—	18	6	no	—
283	C₂×Dic₃	—	18	16	no	—
284	C₂×Dic₃	C₂²×D₉	1	6	yes	—
285	C₄×D₃	—	9	16	no	—
286	C₄×D₃	—	9	16	no	—
287	Dic₆	—	9	16	no	—
288	Dic₆	—	9	16	no	—
289	C₂×C₃²	—	2	4	no	—
290	C₂×C₃²	C₂×#237	1	6	yes	—
291	C₂×C₃²	C₂⁴×D₃	1	1	yes	characteristic
292	C₃×D₃	—	2	4	no	—
293	C₃×D₃	—	6	4	no	—
294	C₂×C₉	—	2	8	no	—
295	C₂×C₉	—	2	4	no	—
296	C₂×C₉	—	2	6	no	—
297	C₂×C₉	—	2	1	no	—
298	C₂×C₉	—	6	4	no	—
299	C₂×C₉	C₂×#237	1	6	yes	complemented
300	C₂×C₉	C₂⁴×D₃	1	1	yes	characteristic
301	D₉	—	2	4	no	—
302	C₂⁴	—	3	1	no	—
303	C₂⁴	—	9	1	no	—
304	C₂⁴	D₃×D₉	1	1	yes	characteristic
305	#41	—	27	64	no	—
306	C₂×Q₈	—	27	12	no	—
307	C₂×D₄	—	3	12	no	—
308	C₂×D₄	—	9	12	no	—
309	C₂×D₄	—	27	12	no	—
310	C₂²×C₄	—	3	1	no	—
311	C₂²×C₄	—	9	1	no	—
312	C₂²×C₄	—	27	12	no	—
313	C₂²×C₄	—	27	12	no	—
314	C₂²×C₄	—	27	12	no	—
315	C₂²×C₄	—	27	1	no	—
316	C₂²×C₄	—	27	1	no	—
317	C₂²×C₃	—	2	24	no	—
318	C₂²×C₃	—	2	12	no	—
319	C₂²×C₃	—	2	12	no	—
320	C₂²×C₃	—	2	4	no	—
321	C₂²×C₃	—	2	3	no	—
322	C₂²×C₃	—	2	4	no	—
323	C₂²×C₃	—	3	4	no	—
324	C₂²×C₃	—	6	12	no	—
325	C₂²×C₃	—	9	4	no	—
326	C₂²×C₃	—	18	12	no	—
327	C₂²×C₃	#3699	1	4	yes	complemented
328	C₂²×C₃	C₂³×D₉	1	4	yes	—
329	C₂²×C₃	C₂³×D₉	1	3	yes	—
330	C₂²×C₃	#3805	1	4	yes	—
331	C₂²×C₃	C₂²×D₃²	1	4	yes	—
332	C₂²×C₃	C₂²×D₃²	1	3	yes	—
333	C₂×D₃	—	2	12	no	—
334	C₂×D₃	—	3	4	no	—
335	C₂×D₃	—	6	12	no	—
336	C₂×D₃	C₂³×D₉	1	4	yes	—
337	C₃×C₄	—	3	4	no	—
338	C₃×C₄	—	9	4	no	—
339	Dic₃	—	3	4	no	—
340	Dic₃	—	9	4	no	—
341	Dic₃	—	9	4	no	—
342	Dic₃	—	9	4	no	—
343	Dic₃	—	9	4	no	—
344	Dic₃	—	18	4	no	—
345	Dic₃	—	18	4	no	—
346	Dic₃	C₂³×D₉	1	4	yes	—
347	C₃²	C₂²×#237	1	1	yes	characteristic
348	C₉	—	2	1	no	—
349	C₉	C₂²×#237	1	1	yes	characteristic, complemented
350	C₂³	—	2	4	no	—
351	C₂³	—	3	6	no	—
352	C₂³	—	6	4	no	—
353	C₂³	—	9	6	no	—
354	C₂³	—	18	4	no	—
355	C₂³	C₂×D₃×D₉	1	6	yes	—
356	C₂³	C₂×D₃×D₉	1	1	yes	characteristic
357	Q₈	—	27	16	no	—
358	D₄	—	3	16	no	—
359	D₄	—	9	16	no	—
360	D₄	—	27	16	no	—
361	C₂×C₄	—	3	6	no	—
362	C₂×C₄	—	9	6	no	—
363	C₂×C₄	—	27	16	no	—
364	C₂×C₄	—	27	16	no	—
365	C₂×C₄	—	27	6	no	—
366	C₂×C₄	—	27	6	no	—
367	C₂×C₄	—	27	16	no	—
368	C₂×C₃	—	2	8	no	—
369	C₂×C₃	—	2	4	no	—
370	C₂×C₃	—	2	4	no	—
371	C₂×C₃	—	2	6	no	—
372	C₂×C₃	—	2	1	no	—
373	C₂×C₃	—	6	4	no	—
374	C₂×C₃	—	18	4	no	—
375	C₂×C₃	C₂×#3699	1	6	yes	complemented
376	C₂×C₃	C₂⁴×D₉	1	1	yes	characteristic
377	C₂×C₃	C₂×#3805	1	6	yes	—
378	C₂×C₃	C₂³×D₃²	1	1	yes	characteristic
379	D₃	—	2	4	no	—
380	D₃	—	6	4	no	—
381	C₂²	—	2	12	no	—
382	C₂²	—	3	4	no	—
383	C₂²	—	6	12	no	—
384	C₂²	—	9	4	no	—
385	C₂²	—	18	12	no	—
386	C₂²	#88663	1	4	yes	direct product factor
387	C₂²	C₂²×D₃×D₉	1	4	yes	—
388	C₂²	C₂²×D₃×D₉	1	3	yes	—
389	C₄	—	3	4	no	—
390	C₄	—	9	4	no	—
391	C₄	—	27	4	no	—
392	C₄	—	27	4	no	—
393	C₃	—	2	1	no	—
394	C₃	C₂²×#3699	1	1	yes	characteristic, complemented
395	C₃	C₂²×#3805	1	1	yes	characteristic
396	C₂	—	2	4	no	—
397	C₂	—	6	4	no	—
398	C₂	—	18	4	no	—
399	C₂	C₂×#88663	1	6	yes	direct product factor
400	C₂	C₂³×D₃×D₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₃×D₉
commutator, cosocle	C₂×C₃×C₉	C₂⁵
Frattini	C₂×C₃	C₂³×D₃²
Fitting	C₂⁴×C₃×C₉	C₂²
socle	C₂³×C₃²	C₂²×D₃
hypercenter	C₂⁴	D₃×D₉
hypocenter	C₃×C₉	C₂²×#41
LCS	G ▷ C₂×C₃×C₉ ▷ C₃×C₉
UCS	C₁ ◁ C₂³ ◁ C₂⁴

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃⋊Dic₉	C₂	semidirect
2. C₂²×C₉×#67	C₂	semidirect
3. C₂²×C₃×#611	C₂	semidirect
4. C₂²×#6194	C₂	semidirect
5. C₂×#88663	C₂	direct (N × H)
6. C₂²×D₃×Dic₉	C₂	semidirect
7. C₂²×Dic₃×D₉	C₂	semidirect
8. C₂²×#6189	C₂	semidirect
16. C₂²×C₃⋊Dic₉	C₂²	semidirect
17. C₂×C₉×#67	C₂²	semidirect
18. C₂×C₃×#611	C₂²	semidirect
21. C₂×#6194	C₂²	semidirect
22. #88663	C₂²	direct (N × H)
23. C₂×D₃×Dic₉	C₂²	semidirect
24. C₂×Dic₃×D₉	C₂²	semidirect
25. C₂×#6189	C₂²	semidirect
36. C₂²×#611	D₃	semidirect
52. C₂×C₃⋊Dic₉	C₂³	semidirect
53. C₉×#67	C₂³	semidirect
54. C₃×#611	C₂³	semidirect
57. #6194	C₂³	semidirect
58. D₃×Dic₉	C₂³	semidirect
59. Dic₃×D₉	C₂³	semidirect
60. #6189	C₂³	semidirect
85. C₂×#611	C₂×D₃	semidirect
98. C₂²×C₃×C₉	#41	semidirect
114. C₂²×#67	D₉	semidirect
157. #611	C₂²×D₃	semidirect
170. C₂×C₃×C₉	C₂×#41	semidirect
188. C₂×#67	C₂×D₉	semidirect
227. C₂²×C₉	#237	semidirect
246. C₃×C₉	C₂²×#41	semidirect
271. #67	C₂²×D₉	semidirect
299. C₂×C₉	C₂×#237	semidirect
327. C₂²×C₃	#3699	semidirect
349. C₉	C₂²×#237	semidirect
375. C₂×C₃	C₂×#3699	semidirect
386. C₂²	#88663	direct (N × H)
394. C₃	C₂²×#3699	semidirect
399. C₂	C₂×#88663	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃⋊Dic₉	2
C₂²×C₉×#67	2
C₂²×C₃×#611	2
C₂²×#6194	2
C₂×#88663	2
C₂²×D₃×Dic₉	2
C₂²×Dic₃×D₉	2
C₂²×#6189	2
C₂²×#3805	3
C₂²×#3699	3

Subgroups — C22×#88663 #13164800

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#88663 #13164800