Subgroups — C₂×#72236967 #72344183

Order 6144.

At least 14918 conjugacy classes of subgroups; only the 947 normal subgroups are shown.

The subgroup lattice has 332 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#72236796	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#72236792	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#72236797	C₂	1	2	yes	maximal, complemented
4	C₂×#72236787	C₂	1	2	yes	maximal, complemented
5	C₂×#11711590	C₂²	1	2	yes	complemented
6	C₂×#21484⋊C₃	C₂²	1	2	yes	complemented
7	C₂×#72236889	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#72236845	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#72236849	C₂	1	2	yes	maximal, complemented
10	C₂×#11715688	C₂²	1	2	yes	complemented
11	C₂×#11711589	C₂²	1	2	yes	complemented
12	C₂×#72215648	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#11715682	C₂²	1	2	yes	complemented
14	C₂×#72236846	C₂	1	2	yes	maximal, complemented
15	C₂×#11711588	C₂²	1	2	yes	complemented
16	C₂²×#11714162	C₂	1	1	yes	maximal, characteristic
17	C₂×#11711587	C₂²	1	2	yes	complemented
18	C₂²×#73025	C₄	1	1	yes	characteristic, complemented
19	C₂²×#3025⋊C₃	C₂²	1	1	yes	characteristic
20	C₂×#21483⋊C₃	C₂²	1	2	yes	complemented
21	C₂²×#73031	C₄	1	1	yes	characteristic, complemented
22	C₂×#72236738	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#11711597	C₂²	1	2	yes	complemented
24	C₂×#11711596	C₂²	1	2	yes	complemented
25	C₂×#11715661	C₂²	1	1	yes	characteristic, complemented
26	C₂×#20612⋊C₃	C₂²	1	1	yes	characteristic, complemented
27	C₂²×#87520	C₂²	1	1	yes	characteristic
28	C₂×#11710873	C₂²	1	1	yes	characteristic, complemented
29	C₂²×#73030	C₄	1	1	yes	characteristic, complemented
30	C₂×#11715667	C₂²	1	1	yes	characteristic, complemented
31	C₂×#6372744	D₃	1	1	yes	characteristic, complemented
32	C₂²×#87519	C₂²	1	1	yes	characteristic
33	C₂×#11715687	C₂²	1	2	yes	complemented
34	#72236967	C₂	1	16	yes	maximal, direct product factor
35	#72236889	C₂²	1	8	yes	complemented
36	#72236849	C₂²	1	16	yes	complemented
37	#72236846	C₂²	1	16	yes	complemented
38	#72236845	C₂²	1	8	yes	complemented
39	#72236797	C₂²	1	16	yes	complemented
40	#72236796	C₂²	1	8	yes	complemented
41	#72236792	C₂²	1	8	yes	complemented
42	#72236787	C₂²	1	16	yes	complemented
43	#72236738	C₂²	1	8	yes	complemented
44	C₂×#11714162	C₄	1	1	yes	characteristic, complemented
45	C₂×#11714162	C₄	1	1	yes	characteristic, complemented
46	C₂×#11714162	C₄	1	1	yes	characteristic, complemented
47	C₂×#11714162	C₄	1	1	yes	characteristic, complemented
48	C₂×#11714162	C₄	1	8	yes	complemented
49	C₂×#11714162	C₂²	1	1	yes	characteristic
50	C₂×#11714162	C₂²	1	1	yes	characteristic
51	C₂×#11714162	C₂²	1	1	yes	characteristic
52	C₂×#11714162	C₂²	1	1	yes	characteristic
53	C₂×#11714162	C₂²	1	8	yes	—
54	C₂²×#73026	C₄	1	1	yes	characteristic, complemented
55	C₂×#11715681	C₂²	1	2	yes	complemented
56	#72215648	C₂²	1	8	yes	complemented
57	C₂×#87519	C₂×C₄	1	1	yes	characteristic
58	C₂×#87519	C₂×C₄	1	4	yes	—
59	C₂×#87519	C₂×C₄	1	1	yes	characteristic
60	C₂×#87519	C₂³	1	4	yes	—
61	C₂×#87519	C₂³	1	1	yes	characteristic
62	C₂×#87519	C₂³	1	1	yes	characteristic
63	C₂²×#5932	C₂×C₄	1	1	yes	characteristic
64	C₂²×#5934	C₂×C₄	1	1	yes	characteristic
65	C₂×#87520	C₂×C₄	1	1	yes	characteristic
66	C₂×#87520	C₂×C₄	1	1	yes	characteristic
67	C₂×#87520	C₂×C₄	1	4	yes	—
68	C₂×#87520	C₂³	1	1	yes	characteristic
69	C₂×#87520	C₂³	1	1	yes	characteristic
70	C₂×#87520	C₂³	1	4	yes	—
71	C₂²×#5933	C₂×C₄	1	1	yes	characteristic
72	C₂²×#5935	C₂×C₄	1	1	yes	characteristic
73	#11715688	C₂³	1	8	yes	complemented
74	#11715687	C₂³	1	8	yes	complemented
75	#11715682	C₂³	1	8	yes	complemented
76	#11715681	C₂³	1	8	yes	complemented
77	#11715667	C₂³	1	4	yes	complemented
78	C₂×#85567	C₂³	1	2	yes	complemented
79	#11715661	C₂³	1	4	yes	complemented
80	C₂×#85566	C₂³	1	2	yes	complemented
81	#11714162	C₂×C₄	1	4	yes	complemented
82	#11714162	C₂×C₄	1	4	yes	complemented
83	#11714162	C₂×C₄	1	4	yes	complemented
84	#11714162	C₂×C₄	1	4	yes	complemented
85	#11714162	C₂×C₄	1	8	yes	complemented
86	#11714162	C₂×C₄	1	8	yes	complemented
87	#11714162	C₂×C₄	1	8	yes	complemented
88	#11714162	C₂×C₄	1	8	yes	complemented
89	#11714162	C₂³	1	4	yes	—
90	#11714162	C₂³	1	4	yes	—
91	#11714162	C₂³	1	4	yes	—
92	#11714162	C₂³	1	4	yes	—
93	C₂×#73031	C₂×C₄	1	1	yes	characteristic, complemented
94	C₂×#73031	C₂×C₄	1	1	yes	characteristic, complemented
95	C₂×#73031	C₂×C₄	1	1	yes	characteristic, complemented
96	C₂×#73031	C₂×C₄	1	1	yes	characteristic, complemented
97	C₂×#73031	C₂×C₄	1	8	yes	complemented
98	C₂×#73025	C₂×C₄	1	1	yes	characteristic, complemented
99	C₂×#73025	C₂×C₄	1	1	yes	characteristic, complemented
100	C₂×#73025	C₂×C₄	1	1	yes	characteristic, complemented
101	C₂×#73025	C₂×C₄	1	1	yes	characteristic, complemented
102	C₂×#73025	C₂×C₄	1	8	yes	complemented
103	C₂×#73030	C₂×C₄	1	1	yes	characteristic, complemented
104	C₂×#73030	C₂×C₄	1	1	yes	characteristic, complemented
105	C₂×#73030	C₂×C₄	1	1	yes	characteristic, complemented
106	C₂×#73030	C₂×C₄	1	1	yes	characteristic, complemented
107	C₂×#73030	C₂×C₄	1	8	yes	complemented
108	C₂×#73026	C₂×C₄	1	1	yes	characteristic, complemented
109	C₂×#73026	C₂×C₄	1	1	yes	characteristic, complemented
110	C₂×#73026	C₂×C₄	1	1	yes	characteristic, complemented
111	C₂×#73026	C₂×C₄	1	1	yes	characteristic, complemented
112	C₂×#73026	C₂×C₄	1	8	yes	complemented
113	#11711597	C₂³	1	8	yes	complemented
114	#11711596	C₂³	1	8	yes	complemented
115	#11711590	C₂³	1	8	yes	complemented
116	#11711589	C₂³	1	8	yes	complemented
117	#11711588	C₂³	1	8	yes	complemented
118	#11711587	C₂³	1	8	yes	complemented
119	C₂²×#5950	C₂³	1	1	yes	characteristic
120	#11710873	C₂³	1	4	yes	complemented
121	C₂×#85666	C₂³	1	2	yes	complemented
122	C₂×#3025⋊C₃	C₂×C₄	1	1	yes	characteristic
123	C₂×#3025⋊C₃	C₂×C₄	1	1	yes	characteristic
124	C₂×#3025⋊C₃	C₂×C₄	1	4	yes	—
125	C₂×#3025⋊C₃	C₂³	1	1	yes	characteristic
126	C₂×#3025⋊C₃	C₂³	1	1	yes	characteristic
127	C₂×#3025⋊C₃	C₂³	1	4	yes	—
128	C₂²×#458⋊C₃	C₂×C₄	1	1	yes	characteristic
129	C₂²×B(4,𝔽₂)⋊C₃	C₂×C₄	1	1	yes	characteristic
130	#21484⋊C₃	C₂³	1	8	yes	complemented
131	#21483⋊C₃	C₂³	1	8	yes	complemented
132	#20612⋊C₃	C₂³	1	4	yes	complemented
133	C₂×#1791⋊C₃	C₂³	1	2	yes	complemented
134	C₂×#63076	C₂×D₃	1	1	yes	characteristic, complemented
135	C₂²×#3025	C₂×D₃	1	1	yes	characteristic
136	#6372744	C₂×D₃	1	8	yes	complemented
137	C₂×#21484	C₂×D₃	1	2	yes	complemented
138	C₂×#21483	C₂×D₃	1	2	yes	complemented
139	C₂×#20612	C₂×D₃	1	1	yes	characteristic, complemented
140	C₂×#5950	C₂²×C₄	1	1	yes	characteristic
141	C₂×#5950	C₂²×C₄	1	2	yes	—
142	C₂×#5950	C₂⁴	1	1	yes	characteristic
143	C₂×#5950	C₂⁴	1	2	yes	—
144	C₂²×#997	C₂²×C₄	1	1	yes	characteristic
145	#87520	C₂²×C₄	1	2	yes	—
146	#87520	C₂²×C₄	1	2	yes	—
147	#87520	C₂²×C₄	1	4	yes	—
148	#87520	C₂²×C₄	1	4	yes	—
149	#87520	C₂⁴	1	2	yes	—
150	#87520	C₂⁴	1	2	yes	—
151	#87519	C₂²×C₄	1	4	yes	—
152	#87519	C₂²×C₄	1	4	yes	—
153	#87519	C₂²×C₄	1	2	yes	—
154	#87519	C₂²×C₄	1	2	yes	—
155	#87519	C₂⁴	1	2	yes	—
156	#87519	C₂⁴	1	2	yes	—
157	C₂×#5935	C₂²×C₄	1	1	yes	characteristic
158	C₂×#5935	C₂²×C₄	1	1	yes	characteristic
159	C₂×#5935	C₂²×C₄	1	4	yes	—
160	C₂×#5934	C₂²×C₄	1	1	yes	characteristic
161	C₂×#5934	C₂²×C₄	1	4	yes	—
162	C₂×#5934	C₂²×C₄	1	1	yes	characteristic
163	C₂×#5933	C₂²×C₄	1	1	yes	characteristic
164	C₂×#5933	C₂²×C₄	1	1	yes	characteristic
165	C₂×#5933	C₂²×C₄	1	4	yes	—
166	C₂×#5932	C₂²×C₄	1	4	yes	—
167	C₂×#5932	C₂²×C₄	1	1	yes	characteristic
168	C₂×#5932	C₂²×C₄	1	1	yes	characteristic
169	#85666	C₂⁴	1	4	yes	complemented
170	#85567	C₂⁴	1	4	yes	complemented
171	#85566	C₂⁴	1	4	yes	complemented
172	#3025⋊C₃	C₂²×C₄	1	2	yes	—
173	#3025⋊C₃	C₂²×C₄	1	2	yes	—
174	#3025⋊C₃	C₂²×C₄	1	4	yes	—
175	#3025⋊C₃	C₂²×C₄	1	4	yes	—
176	#3025⋊C₃	C₂⁴	1	2	yes	—
177	#3025⋊C₃	C₂⁴	1	2	yes	—
178	C₂×#458⋊C₃	C₂²×C₄	1	1	yes	characteristic
179	C₂×#458⋊C₃	C₂²×C₄	1	1	yes	characteristic
180	C₂×#458⋊C₃	C₂²×C₄	1	4	yes	—
181	C₂×B(4,𝔽₂)⋊C₃	C₂²×C₄	1	1	yes	characteristic
182	C₂×B(4,𝔽₂)⋊C₃	C₂²×C₄	1	1	yes	characteristic
183	C₂×B(4,𝔽₂)⋊C₃	C₂²×C₄	1	4	yes	—
184	#73031	C₂²×C₄	1	4	yes	complemented
185	#73031	C₂²×C₄	1	4	yes	complemented
186	#73031	C₂²×C₄	1	4	yes	complemented
187	#73031	C₂²×C₄	1	4	yes	complemented
188	#73030	C₂²×C₄	1	4	yes	complemented
189	#73030	C₂²×C₄	1	4	yes	complemented
190	#73030	C₂²×C₄	1	4	yes	complemented
191	#73030	C₂²×C₄	1	4	yes	complemented
192	#73026	C₂²×C₄	1	4	yes	complemented
193	#73026	C₂²×C₄	1	4	yes	complemented
194	#73026	C₂²×C₄	1	4	yes	complemented
195	#73026	C₂²×C₄	1	4	yes	complemented
196	#73025	C₂²×C₄	1	4	yes	complemented
197	#73025	C₂²×C₄	1	4	yes	complemented
198	#73025	C₂²×C₄	1	4	yes	complemented
199	#73025	C₂²×C₄	1	4	yes	complemented
200	#1791⋊C₃	C₂⁴	1	4	yes	complemented
201	C₂²×#585	C₂²×D₃	1	1	yes	characteristic
202	#63076	C₂²×D₃	1	4	yes	complemented
203	C₂×#3573	C₂²×D₃	1	2	yes	complemented
204	C₂⁴×M₁₆	S₄	1	1	yes	characteristic, complemented
205	C₂×#3025	C₄×D₃	1	1	yes	characteristic
206	C₂×#3025	C₄×D₃	1	1	yes	characteristic
207	C₂×#3025	C₄×D₃	1	4	yes	—
208	C₂×#3025	C₂²×D₃	1	1	yes	characteristic
209	C₂×#3025	C₂²×D₃	1	1	yes	characteristic
210	C₂×#3025	C₂²×D₃	1	4	yes	—
211	C₂²×#458	C₄×D₃	1	1	yes	characteristic
212	C₂²×B(4,𝔽₂)	C₄×D₃	1	1	yes	characteristic
213	#21484	C₂²×D₃	1	8	yes	complemented
214	#21483	C₂²×D₃	1	8	yes	complemented
215	#20612	C₂²×D₃	1	4	yes	complemented
216	C₂×#1791	C₂²×D₃	1	2	yes	complemented
217	#5950	C₂³×C₄	1	1	yes	characteristic
218	#5950	C₂³×C₄	1	2	yes	—
219	#5950	C₂⁵	1	1	yes	characteristic
220	C₂×#997	C₂³×C₄	1	1	yes	characteristic
221	C₂×#997	C₂³×C₄	1	2	yes	—
222	#5935	C₂³×C₄	1	2	yes	—
223	#5935	C₂³×C₄	1	2	yes	—
224	#5934	C₂³×C₄	1	2	yes	—
225	#5934	C₂³×C₄	1	2	yes	—
226	#5933	C₂³×C₄	1	2	yes	—
227	#5933	C₂³×C₄	1	2	yes	—
228	#5932	C₂³×C₄	1	2	yes	—
229	#5932	C₂³×C₄	1	2	yes	—
230	#458⋊C₃	C₂³×C₄	1	2	yes	—
231	#458⋊C₃	C₂³×C₄	1	2	yes	—
232	B(4,𝔽₂)⋊C₃	C₂³×C₄	1	2	yes	—
233	B(4,𝔽₂)⋊C₃	C₂³×C₄	1	2	yes	—
234	C₂×#585	C₂×C₄×D₃	1	1	yes	characteristic
235	C₂×#585	C₂×C₄×D₃	1	2	yes	—
236	C₂×#585	C₂³×D₃	1	1	yes	characteristic
237	C₂×#585	C₂³×D₃	1	2	yes	—
238	C₂²×H(5,𝔽₂)	C₂×C₄×D₃	1	1	yes	characteristic
239	C₂⁵×C₄	C₂×S₄	1	1	yes	characteristic
240	#3573	C₂³×D₃	1	4	yes	complemented
241	C₂³×M₁₆	C₂×S₄	1	1	yes	characteristic
242	C₂³×M₁₆	C₂×S₄	1	1	yes	characteristic
243	C₂³×M₁₆	C₂×S₄	1	2	yes	complemented
244	C₂³×M₁₆	C₂×S₄	1	8	yes	complemented
245	C₂⁴×C₈	C₂×S₄	1	2	yes	complemented
246	#3025	C₂×C₄×D₃	1	2	yes	—
247	#3025	C₂×C₄×D₃	1	2	yes	—
248	#3025	C₂×C₄×D₃	1	4	yes	—
249	#3025	C₂×C₄×D₃	1	4	yes	—
250	#3025	C₂³×D₃	1	2	yes	—
251	#3025	C₂³×D₃	1	2	yes	—
252	C₂×#458	C₂×C₄×D₃	1	1	yes	characteristic
253	C₂×#458	C₂×C₄×D₃	1	1	yes	characteristic
254	C₂×#458	C₂×C₄×D₃	1	4	yes	—
255	C₂×B(4,𝔽₂)	C₂×C₄×D₃	1	1	yes	characteristic
256	C₂×B(4,𝔽₂)	C₂×C₄×D₃	1	1	yes	characteristic
257	C₂×B(4,𝔽₂)	C₂×C₄×D₃	1	4	yes	—
258	#1791	C₂³×D₃	1	4	yes	complemented
259	#997	C₂⁴×C₄	1	1	yes	characteristic
260	C₂⁶	C₄×S₄	1	1	yes	characteristic
261	#585	C₂²×C₄×D₃	1	1	yes	characteristic
262	#585	C₂²×C₄×D₃	1	2	yes	—
263	#585	C₂⁴×D₃	1	1	yes	characteristic
264	C₂×H(5,𝔽₂)	C₂²×C₄×D₃	1	1	yes	characteristic
265	C₂×H(5,𝔽₂)	C₂²×C₄×D₃	1	2	yes	—
266	C₂⁴×C₄	C₄×S₄	1	1	yes	characteristic
267	C₂⁴×C₄	C₄×S₄	1	1	yes	characteristic
268	C₂⁴×C₄	C₄×S₄	1	1	yes	characteristic
269	C₂⁴×C₄	C₄×S₄	1	4	yes	—
270	C₂⁴×C₄	C₂²×S₄	1	1	yes	characteristic
271	C₂⁴×C₄	C₂²×S₄	1	1	yes	characteristic
272	C₂⁴×C₄	C₂²×S₄	1	1	yes	characteristic
273	C₂⁴×C₄	C₂²×S₄	1	4	yes	—
274	C₂²×M₁₆	C₂²×S₄	1	4	yes	—
275	C₂²×M₁₆	C₂²×S₄	1	4	yes	—
276	C₂²×M₁₆	C₂²×S₄	1	8	yes	complemented
277	C₂³×C₈	C₂²×S₄	1	2	yes	—
278	C₂³×C₈	C₂²×S₄	1	2	yes	—
279	C₂³×C₈	C₂²×S₄	1	8	yes	complemented
280	#458	C₂²×C₄×D₃	1	2	yes	—
281	#458	C₂²×C₄×D₃	1	2	yes	—
282	B(4,𝔽₂)	C₂²×C₄×D₃	1	2	yes	—
283	B(4,𝔽₂)	C₂²×C₄×D₃	1	2	yes	—
284	C₂⁵	C₂×C₄×S₄	1	1	yes	characteristic
285	C₂⁵	C₂×C₄×S₄	1	1	yes	characteristic
286	C₂⁵	C₂×C₄×S₄	1	1	yes	characteristic
287	C₂⁵	C₂×C₄×S₄	1	4	yes	—
288	H(5,𝔽₂)	C₂³×C₄×D₃	1	1	yes	characteristic
289	C₂³×C₄	C₂×C₄×S₄	1	1	yes	characteristic
290	C₂³×C₄	C₂×C₄×S₄	1	2	yes	—
291	C₂³×C₄	C₂×C₄×S₄	1	1	yes	characteristic
292	C₂³×C₄	C₂×C₄×S₄	1	1	yes	characteristic
293	C₂³×C₄	C₂×C₄×S₄	1	4	yes	—
294	C₂³×C₄	C₂×C₄×S₄	1	2	yes	—
295	C₂³×C₄	C₂×C₄×S₄	1	4	yes	—
296	C₂³×C₄	C₂×C₄×S₄	1	2	yes	—
297	C₂³×C₄	C₂×C₄×S₄	1	4	yes	—
298	C₂³×C₄	C₂³×S₄	1	1	yes	characteristic
299	C₂³×C₄	C₂³×S₄	1	2	yes	—
300	C₂³×C₄	C₂³×S₄	1	2	yes	—
301	C₂³×C₄	C₂³×S₄	1	2	yes	—
302	C₂×M₁₆	#1020⋊C₂	1	1	yes	characteristic
303	C₂²×C₈	C₂³×S₄	1	4	yes	—
304	C₂²×C₈	C₂³×S₄	1	4	yes	—
305	C₂⁴	C₂²×C₄×S₄	1	1	yes	characteristic
306	C₂⁴	C₂²×C₄×S₄	1	2	yes	—
307	C₂⁴	C₂²×C₄×S₄	1	2	yes	—
308	C₂⁴	C₂²×C₄×S₄	1	2	yes	—
309	C₂²×C₄	C₂×#1020⋊C₂	1	1	yes	characteristic
310	C₂²×C₄	C₂²×C₄×S₄	1	1	yes	characteristic
311	C₂²×C₄	C₂²×C₄×S₄	1	2	yes	—
312	C₂²×C₄	C₂²×C₄×S₄	1	2	yes	—
313	C₂²×C₄	C₂²×C₄×S₄	1	2	yes	—
314	C₂²×C₄	C₂⁴×S₄	1	1	yes	characteristic
315	M₁₆	C₂×#1020⋊C₂	1	4	yes	—
316	C₂×C₈	C₂×#1020⋊C₂	1	2	yes	—
317	C₂³	C₄×#1020⋊C₂	1	1	yes	characteristic
318	C₂³	C₂³×C₄×S₄	1	1	yes	characteristic
319	C₂×C₄	C₄×#1020⋊C₂	1	1	yes	characteristic
320	C₂×C₄	C₄×#1020⋊C₂	1	2	yes	—
321	C₂×C₄	C₂²×#1020⋊C₂	1	2	yes	—
322	C₂×C₄	C₂²×#1020⋊C₂	1	1	yes	characteristic
323	C₈	C₂²×#1020⋊C₂	1	4	yes	—
324	C₂²	C₂×C₄×#1020⋊C₂	1	2	yes	—
325	C₂²	C₂×C₄×#1020⋊C₂	1	1	yes	characteristic
326	C₄	C₂³×#1020⋊C₂	1	1	yes	characteristic
327	C₄	C₂×C₄×#1020⋊C₂	1	2	yes	—
328	C₄	C₂×C₄×#1020⋊C₂	1	1	yes	characteristic
329	C₂	#72236967	1	2	yes	direct product factor
330	C₂	C₂²×C₄×#1020⋊C₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×#1020⋊C₂
commutator, hypocenter	#997	C₂⁴×C₄
Frattini	C₂²×C₄	C₂⁴×S₄
Fitting	C₂×#6372744	D₃
socle	C₂²	C₂×C₄×#1020⋊C₂
prime radical	C₂²×#11714162	C₂
cosocle	#5950	C₂⁵
hypercenter	C₂×M₁₆	#1020⋊C₂
LCS	G ▷ #997
UCS	C₁ ◁ C₂×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×#72236796	C₂	semidirect
2. C₂×#72236792	C₂	semidirect
3. C₂×#72236797	C₂	semidirect
4. C₂×#72236787	C₂	semidirect
5. C₂×#11711590	C₂²	semidirect
6. C₂×#21484⋊C₃	C₂²	semidirect
7. C₂×#72236889	C₂	semidirect
8. C₂×#72236845	C₂	semidirect
9. C₂×#72236849	C₂	semidirect
10. C₂×#11715688	C₂²	semidirect
11. C₂×#11711589	C₂²	semidirect
12. C₂×#72215648	C₂	semidirect
13. C₂×#11715682	C₂²	semidirect
14. C₂×#72236846	C₂	semidirect
15. C₂×#11711588	C₂²	semidirect
17. C₂×#11711587	C₂²	semidirect
18. C₂²×#73025	C₄	semidirect
20. C₂×#21483⋊C₃	C₂²	semidirect
21. C₂²×#73031	C₄	semidirect
22. C₂×#72236738	C₂	semidirect
23. C₂×#11711597	C₂²	semidirect
24. C₂×#11711596	C₂²	semidirect
25. C₂×#11715661	C₂²	semidirect
26. C₂×#20612⋊C₃	C₂²	semidirect
28. C₂×#11710873	C₂²	semidirect
29. C₂²×#73030	C₄	semidirect
30. C₂×#11715667	C₂²	semidirect
31. C₂×#6372744	D₃	semidirect
33. C₂×#11715687	C₂²	semidirect
34. #72236967	C₂	direct (N × H)
35. #72236889	C₂²	semidirect
36. #72236849	C₂²	semidirect
37. #72236846	C₂²	semidirect
38. #72236845	C₂²	semidirect
39. #72236797	C₂²	semidirect
40. #72236796	C₂²	semidirect
41. #72236792	C₂²	semidirect
42. #72236787	C₂²	semidirect
43. #72236738	C₂²	semidirect
44. C₂×#11714162	C₄	semidirect
45. C₂×#11714162	C₄	semidirect
46. C₂×#11714162	C₄	semidirect
47. C₂×#11714162	C₄	semidirect
48. C₂×#11714162	C₄	semidirect
54. C₂²×#73026	C₄	semidirect
55. C₂×#11715681	C₂²	semidirect
56. #72215648	C₂²	semidirect
73. #11715688	C₂³	semidirect
74. #11715687	C₂³	semidirect
75. #11715682	C₂³	semidirect
76. #11715681	C₂³	semidirect
77. #11715667	C₂³	semidirect
78. C₂×#85567	C₂³	semidirect
79. #11715661	C₂³	semidirect
80. C₂×#85566	C₂³	semidirect
81. #11714162	C₂×C₄	semidirect
82. #11714162	C₂×C₄	semidirect
83. #11714162	C₂×C₄	semidirect
84. #11714162	C₂×C₄	semidirect
85. #11714162	C₂×C₄	semidirect
86. #11714162	C₂×C₄	semidirect
87. #11714162	C₂×C₄	semidirect
88. #11714162	C₂×C₄	semidirect
93. C₂×#73031	C₂×C₄	semidirect
94. C₂×#73031	C₂×C₄	semidirect
95. C₂×#73031	C₂×C₄	semidirect
96. C₂×#73031	C₂×C₄	semidirect
97. C₂×#73031	C₂×C₄	semidirect
98. C₂×#73025	C₂×C₄	semidirect
99. C₂×#73025	C₂×C₄	semidirect
100. C₂×#73025	C₂×C₄	semidirect
101. C₂×#73025	C₂×C₄	semidirect
102. C₂×#73025	C₂×C₄	semidirect
103. C₂×#73030	C₂×C₄	semidirect
104. C₂×#73030	C₂×C₄	semidirect
105. C₂×#73030	C₂×C₄	semidirect
106. C₂×#73030	C₂×C₄	semidirect
107. C₂×#73030	C₂×C₄	semidirect
108. C₂×#73026	C₂×C₄	semidirect
109. C₂×#73026	C₂×C₄	semidirect
110. C₂×#73026	C₂×C₄	semidirect
111. C₂×#73026	C₂×C₄	semidirect
112. C₂×#73026	C₂×C₄	semidirect
113. #11711597	C₂³	semidirect
114. #11711596	C₂³	semidirect
115. #11711590	C₂³	semidirect
116. #11711589	C₂³	semidirect
117. #11711588	C₂³	semidirect
118. #11711587	C₂³	semidirect
120. #11710873	C₂³	semidirect
121. C₂×#85666	C₂³	semidirect
130. #21484⋊C₃	C₂³	semidirect
131. #21483⋊C₃	C₂³	semidirect
132. #20612⋊C₃	C₂³	semidirect
133. C₂×#1791⋊C₃	C₂³	semidirect
134. C₂×#63076	C₂×D₃	semidirect
136. #6372744	C₂×D₃	semidirect
137. C₂×#21484	C₂×D₃	semidirect
138. C₂×#21483	C₂×D₃	semidirect
139. C₂×#20612	C₂×D₃	semidirect
169. #85666	C₂⁴	semidirect
170. #85567	C₂⁴	semidirect
171. #85566	C₂⁴	semidirect
184. #73031	C₂²×C₄	semidirect
185. #73031	C₂²×C₄	semidirect
186. #73031	C₂²×C₄	semidirect
187. #73031	C₂²×C₄	semidirect
188. #73030	C₂²×C₄	semidirect
189. #73030	C₂²×C₄	semidirect
190. #73030	C₂²×C₄	semidirect
191. #73030	C₂²×C₄	semidirect
192. #73026	C₂²×C₄	semidirect
193. #73026	C₂²×C₄	semidirect
194. #73026	C₂²×C₄	semidirect
195. #73026	C₂²×C₄	semidirect
196. #73025	C₂²×C₄	semidirect
197. #73025	C₂²×C₄	semidirect
198. #73025	C₂²×C₄	semidirect
199. #73025	C₂²×C₄	semidirect
200. #1791⋊C₃	C₂⁴	semidirect
202. #63076	C₂²×D₃	semidirect
203. C₂×#3573	C₂²×D₃	semidirect
204. C₂⁴×M₁₆	S₄	semidirect
213. #21484	C₂²×D₃	semidirect
214. #21483	C₂²×D₃	semidirect
215. #20612	C₂²×D₃	semidirect
216. C₂×#1791	C₂²×D₃	semidirect
240. #3573	C₂³×D₃	semidirect
243. C₂³×M₁₆	C₂×S₄	semidirect
244. C₂³×M₁₆	C₂×S₄	semidirect
245. C₂⁴×C₈	C₂×S₄	semidirect
258. #1791	C₂³×D₃	semidirect
276. C₂²×M₁₆	C₂²×S₄	semidirect
279. C₂³×C₈	C₂²×S₄	semidirect
329. C₂	#72236967	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×M₁₆×S₄	4
C₂×#72236796	2
C₂×#72236792	2
C₂×#72236797	2
C₂×#72236787	2
C₂×#72236889	2
C₂×#72236845	2
C₂×#72236849	2
C₂×#72215648	2
C₂×#72236846	2
C₂²×#11714162	2
C₂×#72236738	2
C₂×#72236884	3
#72236967	2

Subgroups — C2×#72236967 #72344183

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#72236967 #72344183