Subgroups — #86177

Order 384.

1160 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	#5704	C₂	1	4	yes	maximal, complemented
3	#5700	C₂	1	2	yes	maximal, complemented
4	#5683	C₂	1	2	yes	maximal, complemented
5	#5654	C₂	1	4	yes	maximal, complemented
6	#5644	C₂	1	2	yes	maximal, complemented
7	#5605	C₂	1	2	yes	maximal, complemented
8	#5585	C₂	1	2	yes	maximal, complemented
9	#5552	C₂	1	2	yes	maximal, complemented
10	#5550	C₂	1	2	yes	maximal, complemented
11	D₄×D₁₂	C₂	1	2	yes	maximal, complemented
12	#5534	C₂	1	2	yes	maximal, complemented
13	#5525	C₂	1	2	yes	maximal, complemented
14	#5477	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#875	C₂	1	1	yes	maximal, characteristic, complemented
16	#3558	—	3	1	no	maximal, Sylow
17	C₂×D₃×D₄	C₂²	1	4	yes	complemented
18	C₂×#235	C₂²	1	2	yes	complemented
19	C₂×#235	C₂²	1	2	yes	complemented
20	C₂²×D₁₂	C₂²	1	1	yes	characteristic
21	C₂²×D₁₂	C₂²	1	2	yes	complemented
22	C₂²×Dic₆	C₂²	1	1	yes	characteristic, complemented
23	C₃×#126	C₂²	1	2	yes	complemented
24	C₃×#125	C₂²	1	1	yes	characteristic, complemented
25	C₃×#124	C₂²	1	1	yes	characteristic, complemented
26	C₃×#123	C₂²	1	2	yes	complemented
27	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
28	C₃×#121	C₂²	1	1	yes	characteristic
29	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
30	C₃×C₄×D₄	C₂²	1	2	yes	complemented
31	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
32	C₃×#117	C₂²	1	2	yes	complemented
33	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic, complemented
34	#947	C₂²	1	4	yes	complemented
35	#939	C₂²	1	4	yes	complemented
36	#937	C₂²	1	4	yes	complemented
37	#930	C₂²	1	2	yes	—
38	#930	C₂²	1	2	yes	complemented
39	#930	C₂²	1	2	yes	complemented
40	C₂×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
41	C₂×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
42	#924	C₂²	1	2	yes	complemented
43	#898	C₂²	1	4	yes	complemented
44	#896	C₂²	1	4	yes	complemented
45	#896	C₂²	1	4	yes	complemented
46	#895	C₂²	1	4	yes	complemented
47	#895	C₂²	1	4	yes	complemented
48	#895	C₂²	1	4	yes	complemented
49	#894	C₂²	1	4	yes	complemented
50	#894	C₂²	1	4	yes	complemented
51	#894	C₂²	1	4	yes	complemented
52	#893	C₂²	1	4	yes	complemented
53	#885	C₂²	1	4	yes	complemented
54	#885	C₂²	1	4	yes	complemented
55	#884	C₂²	1	4	yes	complemented
56	#883	C₂²	1	4	yes	complemented
57	#882	C₂²	1	4	yes	complemented
58	#882	C₂²	1	4	yes	complemented
59	#882	C₂²	1	4	yes	complemented
60	#882	C₂²	1	4	yes	complemented
61	#67⋊C₄	C₂²	1	4	yes	complemented
62	D₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
63	#875	C₂²	1	2	yes	complemented
64	#875	C₂²	1	2	yes	complemented
65	#875	C₂²	1	2	yes	complemented
66	#875	C₂²	1	2	yes	complemented
67	#875	C₂²	1	2	yes	complemented
68	#875	C₂²	1	2	yes	complemented
69	#874	C₂²	1	2	yes	—
70	#874	C₂²	1	1	yes	characteristic, complemented
71	C₄×D₁₂	C₂²	1	2	yes	complemented
72	C₄×D₁₂	C₂²	1	2	yes	complemented
73	C₄×D₁₂	C₂²	1	2	yes	complemented
74	#869	C₂²	1	1	yes	characteristic, complemented
75	C₄×Dic₆	C₂²	1	2	yes	complemented
76	#562	—	3	2	no	—
77	H(3,𝔽₄)	—	3	2	no	—
78	#559	—	3	2	no	—
79	#548	—	3	2	no	—
80	#546	—	3	4	no	—
81	#546	—	3	2	no	—
82	D₄²	—	3	2	no	—
83	#542	—	3	2	no	—
84	#538	—	3	4	no	—
85	#538	—	3	2	no	—
86	#535	—	3	2	no	—
87	#534	—	3	2	no	—
88	#532	—	3	1	no	—
89	#529	D₃	1	1	yes	characteristic, complemented
90	C₂×#124	—	3	1	no	—
91	C₂³×D₃	C₂³	1	2	yes	—
92	C₂³×D₃	C₂³	1	4	yes	—
93	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
94	C₂×C₃×D₄	C₂³	1	2	yes	—
95	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
96	C₂²×C₃×C₄	C₂³	1	2	yes	—
97	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
98	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
99	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
100	C₂×#67	C₂³	1	4	yes	—
101	C₂×#67	C₂³	1	4	yes	—
102	C₂×#67	C₂³	1	4	yes	—
103	C₂²×Dic₃	C₂³	1	2	yes	—
104	D₃×D₄	—	4	8	no	—
105	#235	—	4	4	no	—
106	#235	—	4	4	no	—
107	C₂×D₁₂	—	4	2	no	—
108	C₂×D₁₂	—	4	4	no	—
109	C₂×D₁₂	C₂³	1	2	yes	—
110	C₂×D₁₂	C₂³	1	2	yes	—
111	C₂×D₁₂	C₂³	1	2	yes	—
112	C₂×D₁₂	C₂³	1	4	yes	—
113	C₂×D₁₂	C₂³	1	4	yes	—
114	C₂×D₁₂	C₂³	1	2	yes	—
115	C₂×D₁₂	C₂³	1	2	yes	—
116	C₂×D₁₂	C₂³	1	4	yes	—
117	C₂×C₄×D₃	C₂³	1	4	yes	—
118	C₂×C₄×D₃	C₂³	1	4	yes	—
119	C₂×C₄×D₃	C₂³	1	4	yes	—
120	C₂×Dic₆	—	4	2	no	—
121	C₂×Dic₆	C₂³	1	2	yes	—
122	C₂×Dic₆	C₂³	1	2	yes	—
123	C₂×Dic₆	C₂³	1	2	yes	—
124	C₃×C₄⋊C₄	C₂³	1	2	yes	—
125	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
126	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
127	C₃×C₄⋊C₄	C₂³	1	2	yes	—
128	C₃×C₄⋊C₄	C₂³	1	2	yes	—
129	C₃×C₄⋊C₄	C₂³	1	2	yes	—
130	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
131	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
132	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
133	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
134	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
135	C₃×C₄²	C₂³	1	2	yes	—
136	C₃×C₄²	C₂³	1	1	yes	characteristic
137	C₃×C₄²	C₂³	1	1	yes	characteristic
138	C₃×C₄²	C₂³	1	1	yes	characteristic
139	C₃×C₄²	C₂³	1	1	yes	characteristic
140	#217	C₂³	1	4	yes	—
141	(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
142	(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
143	(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
144	(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
145	(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
146	(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
147	(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
148	(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
149	(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
150	(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
151	C₄⋊Dic₃	C₂³	1	2	yes	—
152	C₄⋊Dic₃	C₂³	1	2	yes	—
153	Dic₃⋊C₄	C₂³	1	4	yes	—
154	Dic₃⋊C₄	C₂³	1	4	yes	—
155	C₄×Dic₃	C₂³	1	4	yes	—
156	C₂×#41	—	3	2	no	—
157	C₂×#41	—	3	2	no	—
158	C₂²×Q₈	—	3	1	no	—
159	C₂²×D₄	—	3	4	no	—
160	C₂²×D₄	—	3	1	no	—
161	C₂²×D₄	—	3	2	no	—
162	C₄⋊Q₈	—	3	1	no	—
163	#127	—	3	1	no	—
164	#127	—	3	2	no	—
165	#126	—	3	4	no	—
166	#126	C₂×D₃	1	2	yes	complemented
167	#125	C₂×D₃	1	1	yes	characteristic, complemented
168	#124	—	3	4	no	—
169	#124	—	3	4	no	—
170	#124	—	3	4	no	—
171	#124	—	3	2	no	—
172	#124	—	3	2	no	—
173	#124	—	3	2	no	—
174	#124	—	3	2	no	—
175	#124	—	3	2	no	—
176	#124	—	3	2	no	—
177	#124	C₂×D₃	1	1	yes	characteristic, complemented
178	#123	—	3	4	no	—
179	#123	—	3	4	no	—
180	#123	—	3	4	no	—
181	#123	—	3	4	no	—
182	#123	C₂×D₃	1	2	yes	complemented
183	C₂²⋊Q₈	—	3	2	no	—
184	C₂²⋊Q₈	—	3	4	no	—
185	C₂²⋊Q₈	—	3	4	no	—
186	C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
187	#121	—	3	4	no	—
188	#121	—	3	2	no	—
189	#121	—	3	2	no	—
190	#121	—	3	2	no	—
191	#121	—	3	4	no	—
192	#121	—	3	4	no	—
193	#121	—	3	4	no	—
194	#121	—	3	4	no	—
195	#121	C₂×D₃	1	1	yes	characteristic
196	#120	—	3	4	no	—
197	#120	—	3	4	no	—
198	#120	—	3	4	no	—
199	#120	—	3	4	no	—
200	#120	—	3	4	no	—
201	C₄×Q₈	—	3	2	no	—
202	C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
203	C₄×D₄	—	3	4	no	—
204	C₄×D₄	—	3	4	no	—
205	C₄×D₄	—	3	2	no	—
206	C₄×D₄	—	3	2	no	—
207	C₄×D₄	—	3	2	no	—
208	C₄×D₄	C₂×D₃	1	2	yes	complemented
209	C₄×D₄	C₂×D₃	1	1	yes	characteristic, complemented
210	#117	C₂×D₃	1	2	yes	complemented
211	C₂×C₂²⋊C₄	—	3	2	no	—
212	C₂×C₂²⋊C₄	—	3	2	no	—
213	C₂×C₂²⋊C₄	—	3	4	no	—
214	C₂×C₄²	C₂×D₃	1	1	yes	characteristic, complemented
215	C₂³×C₃	C₂⁴	1	2	yes	—
216	C₂³×C₃	C₂⁴	1	1	yes	characteristic
217	C₂²×D₃	—	2	4	no	—
218	C₂²×D₃	—	4	4	no	—
219	C₂²×D₃	—	4	2	no	—
220	C₂²×D₃	—	4	4	no	—
221	C₂²×D₃	—	4	4	no	—
222	C₂²×D₃	—	4	2	no	—
223	C₂²×D₃	C₂⁴	1	4	yes	—
224	C₂²×D₃	C₂⁴	1	4	yes	—
225	C₃×Q₈	—	4	1	no	—
226	C₃×D₄	—	2	4	no	—
227	C₃×D₄	—	4	1	no	—
228	C₂×C₃×C₄	—	2	2	no	—
229	C₂×C₃×C₄	—	2	2	no	—
230	C₂×C₃×C₄	—	2	4	no	—
231	C₂×C₃×C₄	—	4	1	no	—
232	C₂×C₃×C₄	C₂⁴	1	2	yes	—
233	C₂×C₃×C₄	C₂⁴	1	2	yes	—
234	C₂×C₃×C₄	C₂⁴	1	2	yes	—
235	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
236	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
237	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
238	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
239	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
240	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
241	#67	—	2	8	no	—
242	#67	—	4	4	no	—
243	#67	—	4	4	no	—
244	C₂×Dic₃	—	4	2	no	—
245	C₂×Dic₃	C₂⁴	1	4	yes	—
246	C₂×Dic₃	C₂⁴	1	4	yes	—
247	D₁₂	—	2	4	no	—
248	D₁₂	—	2	4	no	—
249	D₁₂	—	4	2	no	—
250	D₁₂	—	4	4	no	—
251	D₁₂	—	4	2	no	—
252	D₁₂	—	4	4	no	—
253	D₁₂	—	4	2	no	—
254	D₁₂	—	4	4	no	—
255	C₄×D₃	—	4	4	no	—
256	C₄×D₃	—	4	4	no	—
257	C₄×D₃	—	4	4	no	—
258	Dic₆	—	2	4	no	—
259	Dic₆	—	4	2	no	—
260	Dic₆	—	4	2	no	—
261	C₂⁴	—	3	2	no	—
262	C₂⁴	—	3	4	no	—
263	#41	—	12	4	no	—
264	#41	—	12	4	no	—
265	C₂×Q₈	—	3	2	no	—
266	C₂×Q₈	—	3	2	no	—
267	C₂×Q₈	—	3	2	no	—
268	C₂×Q₈	—	12	2	no	—
269	C₂×Q₈	C₂²×D₃	1	1	yes	characteristic
270	C₂×D₄	—	3	4	no	—
271	C₂×D₄	—	3	4	no	—
272	C₂×D₄	—	3	4	no	—
273	C₂×D₄	—	3	2	no	—
274	C₂×D₄	—	3	2	no	—
275	C₂×D₄	—	3	4	no	—
276	C₂×D₄	—	3	2	no	—
277	C₂×D₄	—	3	2	no	—
278	C₂×D₄	—	3	2	no	—
279	C₂×D₄	—	3	4	no	—
280	C₂×D₄	—	3	4	no	—
281	C₂×D₄	—	12	2	no	—
282	C₂×D₄	—	12	4	no	—
283	C₂×D₄	—	12	8	no	—
284	C₂×D₄	C₂²×D₃	1	2	yes	—
285	C₂×D₄	C₂²×D₃	1	1	yes	characteristic
286	C₂²×C₄	—	3	2	no	—
287	C₂²×C₄	—	3	4	no	—
288	C₂²×C₄	—	3	4	no	—
289	C₂²×C₄	—	3	4	no	—
290	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
291	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
292	C₂²×C₄	C₂²×D₃	1	2	yes	—
293	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
294	C₄⋊C₄	—	3	2	no	—
295	C₄⋊C₄	—	3	4	no	—
296	C₄⋊C₄	—	3	2	no	—
297	C₄⋊C₄	—	3	4	no	—
298	C₄⋊C₄	C₂²×D₃	1	2	yes	—
299	C₄⋊C₄	C₂²×D₃	1	2	yes	—
300	C₄⋊C₄	C₂²×D₃	1	2	yes	—
301	C₄⋊C₄	C₂²×D₃	1	2	yes	—
302	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
303	C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
304	C₂²⋊C₄	—	3	4	no	—
305	C₂²⋊C₄	—	3	4	no	—
306	C₂²⋊C₄	—	3	4	no	—
307	C₂²⋊C₄	—	3	4	no	—
308	C₂²⋊C₄	—	3	4	no	—
309	C₂²⋊C₄	—	3	4	no	—
310	C₂²⋊C₄	—	3	4	no	—
311	C₂²⋊C₄	—	3	4	no	—
312	C₂²⋊C₄	—	3	4	no	—
313	C₂²⋊C₄	—	3	4	no	—
314	C₂²⋊C₄	—	3	4	no	—
315	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
316	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
317	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
318	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
319	C₂²⋊C₄	C₂²×D₃	1	2	yes	—
320	C₄²	—	3	4	no	—
321	C₄²	C₂²×D₃	1	1	yes	characteristic
322	C₄²	C₂²×D₃	1	1	yes	characteristic
323	C₄²	C₂²×D₃	1	1	yes	characteristic
324	C₄²	C₂²×D₃	1	1	yes	characteristic
325	C₄²	C₂²×D₃	1	2	yes	—
326	C₂²×C₃	—	2	1	no	—
327	C₂²×C₃	—	2	1	no	—
328	C₂²×C₃	—	2	2	no	—
329	C₂²×C₃	—	2	2	no	—
330	C₂²×C₃	—	2	2	no	—
331	C₂²×C₃	H(5,𝔽₂)	1	2	yes	—
332	C₂²×C₃	C₂⁵	1	1	yes	characteristic
333	C₂×D₃	—	2	4	no	—
334	C₂×D₃	—	2	4	no	—
335	C₂×D₃	—	2	4	no	—
336	C₂×D₃	—	2	4	no	—
337	C₂×D₃	—	2	4	no	—
338	C₂×D₃	—	2	4	no	—
339	C₂×D₃	—	8	4	no	—
340	C₂×D₃	—	8	8	no	—
341	C₃×C₄	—	2	1	no	—
342	C₃×C₄	—	2	1	no	—
343	C₃×C₄	—	2	1	no	—
344	C₃×C₄	—	2	2	no	—
345	C₃×C₄	—	2	2	no	—
346	C₃×C₄	—	2	1	no	—
347	C₃×C₄	—	2	2	no	—
348	C₃×C₄	—	2	1	no	—
349	C₃×C₄	H(5,𝔽₂)	1	2	yes	—
350	Dic₃	—	2	4	no	—
351	Dic₃	—	2	4	no	—
352	C₂³	—	3	4	no	—
353	C₂³	—	3	4	no	—
354	C₂³	—	6	4	no	—
355	C₂³	—	12	2	no	—
356	C₂³	—	12	4	no	—
357	C₂³	—	12	4	no	—
358	C₂³	—	12	2	no	—
359	C₂³	—	12	4	no	—
360	C₂³	C₂³×D₃	1	2	yes	—
361	C₂³	C₂³×D₃	1	1	yes	characteristic
362	Q₈	—	4	1	no	—
363	Q₈	—	6	4	no	—
364	Q₈	—	12	2	no	—
365	Q₈	—	12	2	no	—
366	D₄	—	2	4	no	—
367	D₄	—	4	1	no	—
368	D₄	—	6	8	no	—
369	D₄	—	6	4	no	—
370	D₄	—	6	4	no	—
371	D₄	—	12	4	no	—
372	D₄	—	12	2	no	—
373	D₄	—	12	4	no	—
374	D₄	—	12	2	no	—
375	D₄	—	12	2	no	—
376	D₄	—	12	4	no	—
377	D₄	—	12	4	no	—
378	D₄	—	12	4	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	3	4	no	—
383	C₂×C₄	—	3	4	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	12	4	no	—
386	C₂×C₄	—	12	4	no	—
387	C₂×C₄	—	12	4	no	—
388	C₂×C₄	—	12	2	no	—
389	C₂×C₄	C₂³×D₃	1	2	yes	—
390	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
391	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
392	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
393	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
394	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
395	C₂×C₄	C₂³×D₃	1	2	yes	—
396	C₂×C₄	C₂³×D₃	1	2	yes	—
397	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
398	C₂×C₃	—	2	2	no	—
399	C₂×C₃	—	4	2	no	—
400	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
401	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
402	C₂×C₃	#585	1	1	yes	characteristic
403	D₃	—	4	4	no	—
404	D₃	—	4	4	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	2	2	no	—
410	C₂²	—	6	4	no	—
411	C₂²	—	6	4	no	—
412	C₂²	—	6	4	no	—
413	C₂²	—	6	4	no	—
414	C₂²	—	6	4	no	—
415	C₂²	—	6	4	no	—
416	C₂²	—	24	4	no	—
417	C₂²	—	24	8	no	—
418	C₂²	#1009	1	2	yes	—
419	C₂²	C₂⁴×D₃	1	1	yes	characteristic
420	C₄	—	2	1	no	—
421	C₄	—	2	2	no	—
422	C₄	—	2	1	no	—
423	C₄	—	2	1	no	—
424	C₄	—	2	2	no	—
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	2	2	no	—
428	C₄	—	6	4	no	—
429	C₄	—	6	4	no	—
430	C₄	#1009	1	2	yes	—
431	C₃	#3558	1	1	yes	characteristic, complemented, Sylow
432	C₂	—	2	2	no	—
433	C₂	—	4	2	no	—
434	C₂	—	12	4	no	—
435	C₂	—	12	4	no	—
436	C₂	C₂×#1009	1	1	yes	characteristic
437	C₂	C₂×#1009	1	1	yes	characteristic
438	C₂	#5964	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₃
commutator, socle, cosocle	C₂²×C₃	C₂⁵
Fitting	C₃×#529	C₂
hypercenter	#529	D₃
hypocenter	C₃	#3558
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. C₃×#529	C₂	semidirect
2. #5704	C₂	semidirect
3. #5700	C₂	semidirect
4. #5683	C₂	semidirect
5. #5654	C₂	semidirect
6. #5644	C₂	semidirect
7. #5605	C₂	semidirect
8. #5585	C₂	semidirect
9. #5552	C₂	semidirect
10. #5550	C₂	semidirect
11. D₄×D₁₂	C₂	semidirect
12. #5534	C₂	semidirect
13. #5525	C₂	semidirect
14. #5477	C₂	semidirect
15. C₂×#875	C₂	semidirect
17. C₂×D₃×D₄	C₂²	semidirect
18. C₂×#235	C₂²	semidirect
19. C₂×#235	C₂²	semidirect
21. C₂²×D₁₂	C₂²	semidirect
22. C₂²×Dic₆	C₂²	semidirect
23. C₃×#126	C₂²	semidirect
24. C₃×#125	C₂²	semidirect
25. C₃×#124	C₂²	semidirect
26. C₃×#123	C₂²	semidirect
27. C₃×C₂²⋊Q₈	C₂²	semidirect
29. C₃×C₄×Q₈	C₂²	semidirect
30. C₃×C₄×D₄	C₂²	semidirect
31. C₃×C₄×D₄	C₂²	semidirect
32. C₃×#117	C₂²	semidirect
33. C₂×C₃×C₄²	C₂²	semidirect
34. #947	C₂²	semidirect
35. #939	C₂²	semidirect
36. #937	C₂²	semidirect
38. #930	C₂²	semidirect
39. #930	C₂²	semidirect
40. C₂×(C₂×D₃)⋊C₄	C₂²	semidirect
41. C₂×(C₂×D₃)⋊C₄	C₂²	semidirect
42. #924	C₂²	semidirect
43. #898	C₂²	semidirect
44. #896	C₂²	semidirect
45. #896	C₂²	semidirect
46. #895	C₂²	semidirect
47. #895	C₂²	semidirect
48. #895	C₂²	semidirect
49. #894	C₂²	semidirect
50. #894	C₂²	semidirect
51. #894	C₂²	semidirect
52. #893	C₂²	semidirect
53. #885	C₂²	semidirect
54. #885	C₂²	semidirect
55. #884	C₂²	semidirect
56. #883	C₂²	semidirect
57. #882	C₂²	semidirect
58. #882	C₂²	semidirect
59. #882	C₂²	semidirect
60. #882	C₂²	semidirect
61. #67⋊C₄	C₂²	semidirect
62. D₃×C₂²⋊C₄	C₂²	semidirect
63. #875	C₂²	semidirect
64. #875	C₂²	semidirect
65. #875	C₂²	semidirect
66. #875	C₂²	semidirect
67. #875	C₂²	semidirect
68. #875	C₂²	semidirect
70. #874	C₂²	semidirect
71. C₄×D₁₂	C₂²	semidirect
72. C₄×D₁₂	C₂²	semidirect
73. C₄×D₁₂	C₂²	semidirect
74. #869	C₂²	semidirect
75. C₄×Dic₆	C₂²	semidirect
89. #529	D₃	semidirect
166. #126	C₂×D₃	semidirect
167. #125	C₂×D₃	semidirect
177. #124	C₂×D₃	semidirect
182. #123	C₂×D₃	semidirect
186. C₂²⋊Q₈	C₂×D₃	semidirect
202. C₄×Q₈	C₂×D₃	semidirect
208. C₄×D₄	C₂×D₃	semidirect
209. C₄×D₄	C₂×D₃	semidirect
210. #117	C₂×D₃	semidirect
214. C₂×C₄²	C₂×D₃	semidirect
431. C₃	#3558	semidirect

Maximal subgroups

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

subgroup	index
C₃×#529	2
#5704	2
#5700	2
#5683	2
#5654	2
#5644	2
#5605	2
#5585	2
#5552	2
#5550	2
D₄×D₁₂	2
#5534	2
#5525	2
#5477	2
C₂×#875	2
#3558	3