Subgroups — C₂×#72219158 #72271257

Order 2048.

At least 8368 conjugacy classes of subgroups; only the 824 normal subgroups are shown.

The subgroup lattice has 416 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#7316	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#7310	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#382434	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#12705	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#12687	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#8541	C₂	1	1	yes	maximal, characteristic, complemented
7	#72219158	C₂	1	8	yes	maximal, direct product factor
8	C₂²×#23900	C₂	1	1	yes	maximal, characteristic
9	C₂²×#3484	C₂²	1	1	yes	characteristic
10	C₂⁴×#120	C₂²	1	1	yes	characteristic
11	C₂²×#2846	C₄	1	2	yes	complemented
12	C₂×#23900	C₄	1	4	yes	complemented
13	C₂×#23900	C₂²	1	4	yes	—
14	C₂²×#1898	C₄	1	2	yes	complemented
15	C₂²×#1783	C₂²	1	1	yes	characteristic
16	C₂²×#1781	C₂²	1	1	yes	characteristic
17	C₂²×#1781	C₂²	1	1	yes	characteristic
18	C₂²×#1781	C₂²	1	1	yes	characteristic
19	C₂²×#1781	C₂²	1	1	yes	characteristic
20	C₂×#12705	C₂²	1	4	yes	complemented
21	C₂×#12687	C₂²	1	4	yes	complemented
22	#382434	C₂²	1	4	yes	complemented
23	C₂×#8541	C₂²	1	4	yes	complemented
24	C₂×#7316	C₂²	1	4	yes	complemented
25	C₂×#7310	C₂²	1	4	yes	complemented
26	C₂⁸	C₂×C₄	1	1	yes	characteristic
27	C₂³×H(5,𝔽₂)	D₄	1	1	yes	characteristic
28	C₂⁵×D₄	C₂³	1	1	yes	characteristic
29	C₂×#3484	C₂×C₄	1	2	yes	—
30	C₂×#3484	D₄	1	2	yes	—
31	C₂×#3484	D₄	1	2	yes	—
32	C₂×#3484	C₂³	1	2	yes	—
33	C₂²×#534	D₄	1	2	yes	—
34	C₂³×#120	C₂×C₄	1	2	yes	—
35	C₂³×#120	C₂×C₄	1	2	yes	—
36	C₂³×#120	D₄	1	4	yes	—
37	C₂³×#120	D₄	1	4	yes	—
38	C₂³×#120	C₂³	1	2	yes	—
39	C₂²×#518	D₄	1	1	yes	characteristic
40	C₂⁴×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
41	C₂³×#99	D₄	1	2	yes	complemented
42	C₂×#2846	C₂×C₄	1	8	yes	complemented
43	C₂²×#379	C₂×C₄	1	2	yes	—
44	C₂²×#379	D₄	1	2	yes	complemented
45	C₂×#1898	C₂×C₄	1	8	yes	complemented
46	C₂×#1783	D₄	1	4	yes	complemented
47	C₂×#1783	C₂³	1	2	yes	—
48	C₂×#1781	C₂×C₄	1	2	yes	—
49	C₂×#1781	D₄	1	4	yes	—
50	C₂×#1781	D₄	1	4	yes	—
51	C₂×#1781	D₄	1	4	yes	complemented
52	C₂×#1781	D₄	1	2	yes	complemented
53	C₂×#1781	D₄	1	2	yes	complemented
54	C₂×#1781	C₂³	1	2	yes	—
55	C₂×#1781	C₂³	1	2	yes	—
56	C₂×#1781	C₂³	1	2	yes	—
57	C₂×#1781	C₂³	1	2	yes	—
58	C₂⁷	C₂²⋊C₄	1	4	yes	complemented
59	C₂⁷	C₂²×C₄	1	1	yes	characteristic
60	C₂⁷	C₂²×C₄	1	2	yes	—
61	C₂⁷	C₂×D₄	1	1	yes	characteristic
62	C₂²×H(5,𝔽₂)	C₂²⋊C₄	1	2	yes	—
63	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
64	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	—
65	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
66	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
67	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
68	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
69	C₂⁴×D₄	C₂×D₄	1	2	yes	—
70	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
71	C₂⁴×D₄	C₂×D₄	1	2	yes	—
72	C₂⁴×D₄	C₂×D₄	1	2	yes	—
73	C₂⁴×D₄	C₂×D₄	1	2	yes	—
74	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
75	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
76	C₂⁴×D₄	C₂×D₄	1	2	yes	—
77	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
78	C₂⁴×D₄	C₂×D₄	1	2	yes	—
79	C₂⁴×D₄	#41	1	1	yes	characteristic
80	C₂⁴×D₄	#41	1	2	yes	—
81	C₂⁴×D₄	#41	1	1	yes	characteristic
82	C₂⁴×D₄	#41	1	2	yes	—
83	C₂⁴×D₄	#41	1	1	yes	characteristic
84	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
85	C₂⁵×C₄	#41	1	1	yes	characteristic
86	C₂×#534	C₂²⋊C₄	1	4	yes	—
87	C₂×#534	C₂×D₄	1	4	yes	—
88	C₂²×#120	C₂²⋊C₄	1	4	yes	—
89	C₂²×#120	C₂²⋊C₄	1	8	yes	complemented
90	C₂²×#120	C₂²×C₄	1	4	yes	—
91	C₂²×#120	C₂×D₄	1	4	yes	—
92	C₂²×#120	C₂×D₄	1	4	yes	—
93	C₂×#518	C₂²⋊C₄	1	2	yes	—
94	C₂×#518	C₂×D₄	1	2	yes	—
95	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
96	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	4	yes	complemented
97	C₂³×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
98	C₂²×#99	C₂×D₄	1	4	yes	complemented
99	C₂×#379	C₂²⋊C₄	1	8	yes	complemented
100	C₂×#379	C₂²×C₄	1	4	yes	—
101	C₂×#379	C₂×D₄	1	4	yes	complemented
102	#1783	C₂×D₄	1	4	yes	complemented
103	#1781	C₂²⋊C₄	1	8	yes	complemented
104	#1781	C₂×D₄	1	4	yes	—
105	#1781	C₂×D₄	1	4	yes	—
106	#1781	C₂×D₄	1	4	yes	complemented
107	C₂⁶	#99	1	2	yes	complemented
108	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
109	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
110	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
111	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
112	C₂⁶	C₂×C₂²⋊C₄	1	4	yes	complemented
113	C₂⁶	C₄×D₄	1	1	yes	characteristic
114	C₂⁶	C₄×D₄	1	1	yes	characteristic
115	C₂⁶	C₄×D₄	1	1	yes	characteristic
116	C₂⁶	C₄×D₄	1	1	yes	characteristic
117	C₂⁶	C₄×D₄	1	1	yes	characteristic
118	C₂⁶	C₄×D₄	1	2	yes	—
119	C₂⁶	C₄×D₄	1	2	yes	—
120	C₂⁶	#120	1	1	yes	characteristic
121	C₂⁶	#120	1	2	yes	—
122	C₂⁶	#120	1	1	yes	characteristic
123	C₂⁶	#121	1	1	yes	characteristic
124	C₂⁶	#121	1	2	yes	—
125	C₂⁶	#121	1	1	yes	characteristic
126	C₂⁶	#121	1	2	yes	—
127	C₂⁶	#127	1	2	yes	—
128	C₂⁶	C₂³×C₄	1	1	yes	characteristic
129	C₂⁶	C₂²×D₄	1	1	yes	characteristic
130	C₂³×D₄	#99	1	4	yes	complemented
131	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
132	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
133	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
134	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
135	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
136	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
137	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
138	C₂³×D₄	C₄×D₄	1	2	yes	—
139	C₂³×D₄	C₄×D₄	1	2	yes	—
140	C₂³×D₄	#120	1	1	yes	characteristic
141	C₂³×D₄	#120	1	1	yes	characteristic
142	C₂³×D₄	#120	1	2	yes	—
143	C₂³×D₄	#120	1	2	yes	—
144	C₂³×D₄	#120	1	2	yes	—
145	C₂³×D₄	#120	1	2	yes	—
146	C₂³×D₄	#120	1	2	yes	—
147	C₂³×D₄	#120	1	2	yes	—
148	C₂³×D₄	#120	1	2	yes	—
149	C₂³×D₄	#120	1	2	yes	—
150	C₂³×D₄	#120	1	2	yes	—
151	C₂³×D₄	#120	1	2	yes	—
152	C₂³×D₄	#120	1	2	yes	—
153	C₂³×D₄	#120	1	2	yes	—
154	C₂³×D₄	#120	1	2	yes	—
155	C₂³×D₄	#121	1	1	yes	characteristic
156	C₂³×D₄	#121	1	1	yes	characteristic
157	C₂³×D₄	#121	1	2	yes	—
158	C₂³×D₄	#121	1	2	yes	—
159	C₂³×D₄	#121	1	1	yes	characteristic
160	C₂³×D₄	#121	1	1	yes	characteristic
161	C₂³×D₄	#121	1	2	yes	—
162	C₂³×D₄	#121	1	2	yes	—
163	C₂³×D₄	#121	1	2	yes	—
164	C₂³×D₄	#121	1	2	yes	—
165	C₂³×D₄	#121	1	2	yes	—
166	C₂³×D₄	#121	1	2	yes	—
167	C₂³×D₄	#121	1	2	yes	—
168	C₂³×D₄	#121	1	2	yes	—
169	C₂³×D₄	#121	1	2	yes	—
170	C₂³×D₄	#121	1	2	yes	—
171	C₂³×D₄	#121	1	2	yes	—
172	C₂³×D₄	#121	1	2	yes	—
173	C₂³×D₄	#121	1	2	yes	—
174	C₂³×D₄	#121	1	2	yes	—
175	C₂³×D₄	#123	1	1	yes	characteristic
176	C₂³×D₄	#123	1	1	yes	characteristic
177	C₂³×D₄	#123	1	2	yes	—
178	C₂³×D₄	#123	1	2	yes	—
179	C₂³×D₄	#123	1	2	yes	—
180	C₂³×D₄	#123	1	2	yes	—
181	C₂³×D₄	#123	1	2	yes	—
182	C₂³×D₄	#124	1	2	yes	—
183	C₂³×D₄	#124	1	2	yes	—
184	C₂³×D₄	#124	1	2	yes	—
185	C₂³×D₄	#127	1	2	yes	—
186	C₂³×D₄	#127	1	2	yes	—
187	C₂³×D₄	#127	1	2	yes	—
188	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
189	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
190	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
191	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
192	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
193	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
194	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
195	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
196	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
197	C₂³×D₄	C₂×#41	1	1	yes	characteristic
198	C₂³×D₄	C₂×#41	1	1	yes	characteristic
199	C₂³×D₄	C₂×#41	1	1	yes	characteristic
200	C₂⁴×C₄	#99	1	2	yes	complemented
201	C₂⁴×C₄	C₄×D₄	1	1	yes	characteristic
202	C₂⁴×C₄	#121	1	1	yes	characteristic
203	C₂⁴×C₄	#121	1	2	yes	—
204	C₂⁴×C₄	#121	1	1	yes	characteristic
205	C₂⁴×C₄	#121	1	2	yes	—
206	C₂⁴×C₄	#123	1	1	yes	characteristic
207	C₂⁴×C₄	#123	1	2	yes	—
208	C₂⁴×C₄	#123	1	1	yes	characteristic
209	C₂⁴×C₄	#124	1	2	yes	—
210	C₂⁴×C₄	C₂×#41	1	1	yes	characteristic
211	C₂²×C₂²⋊C₄	#99	1	8	yes	complemented
212	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	—
213	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	4	yes	complemented
214	#379	C₂×C₂²⋊C₄	1	8	yes	complemented
215	C₂⁵	#379	1	2	yes	—
216	C₂⁵	#379	1	2	yes	—
217	C₂⁵	#386	1	1	yes	characteristic
218	C₂⁵	#386	1	2	yes	—
219	C₂⁵	#386	1	2	yes	—
220	C₂⁵	#386	1	1	yes	characteristic
221	C₂⁵	#386	1	1	yes	characteristic
222	C₂⁵	#386	1	1	yes	characteristic
223	C₂⁵	#386	1	1	yes	characteristic
224	C₂⁵	#386	1	2	yes	—
225	C₂⁵	#386	1	2	yes	—
226	C₂⁵	#386	1	2	yes	—
227	C₂⁵	#386	1	2	yes	—
228	C₂⁵	#386	1	2	yes	—
229	C₂⁵	#386	1	1	yes	characteristic
230	C₂⁵	#390	1	2	yes	—
231	C₂⁵	#390	1	2	yes	—
232	C₂⁵	#390	1	2	yes	—
233	C₂⁵	#390	1	2	yes	—
234	C₂⁵	#390	1	2	yes	—
235	C₂⁵	#392	1	2	yes	—
236	C₂⁵	#392	1	2	yes	—
237	C₂⁵	#392	1	2	yes	—
238	C₂⁵	#392	1	2	yes	—
239	C₂⁵	#392	1	2	yes	—
240	C₂⁵	#392	1	2	yes	—
241	C₂⁵	#394	1	2	yes	—
242	C₂⁵	#394	1	2	yes	—
243	C₂⁵	C₂×#99	1	2	yes	—
244	C₂⁵	C₂×#99	1	2	yes	—
245	C₂⁵	C₂×#99	1	4	yes	—
246	C₂⁵	C₂×#99	1	4	yes	complemented
247	C₂⁵	B(4,𝔽₂)	1	2	yes	—
248	C₂⁵	B(4,𝔽₂)	1	2	yes	—
249	C₂⁵	B(4,𝔽₂)	1	4	yes	—
250	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
251	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
252	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
253	C₂⁵	C₂×C₄×D₄	1	1	yes	characteristic
254	C₂⁵	C₂×C₄×D₄	1	1	yes	characteristic
255	C₂⁵	C₂×C₄×D₄	1	1	yes	characteristic
256	C₂⁵	C₂×C₄×D₄	1	1	yes	characteristic
257	C₂⁵	C₂×#120	1	1	yes	characteristic
258	C₂⁵	C₂×#120	1	1	yes	characteristic
259	C₂⁵	C₂×#121	1	1	yes	characteristic
260	C₂⁵	C₂×#121	1	1	yes	characteristic
261	C₂⁵	C₂×#121	1	1	yes	characteristic
262	C₂⁵	C₂×#127	1	1	yes	characteristic
263	C₂²×D₄	#379	1	2	yes	—
264	C₂²×D₄	#379	1	2	yes	—
265	C₂²×D₄	#386	1	2	yes	—
266	C₂²×D₄	#386	1	2	yes	—
267	C₂²×D₄	#386	1	2	yes	—
268	C₂²×D₄	#386	1	2	yes	—
269	C₂²×D₄	#390	1	2	yes	—
270	C₂²×D₄	#390	1	2	yes	—
271	C₂²×D₄	#392	1	2	yes	—
272	C₂²×D₄	#392	1	2	yes	—
273	C₂²×D₄	#392	1	2	yes	—
274	C₂²×D₄	#392	1	2	yes	—
275	C₂²×D₄	#392	1	2	yes	—
276	C₂²×D₄	#392	1	2	yes	—
277	C₂²×D₄	#392	1	2	yes	—
278	C₂²×D₄	#392	1	2	yes	—
279	C₂²×D₄	#394	1	2	yes	—
280	C₂²×D₄	#394	1	2	yes	—
281	C₂²×D₄	#394	1	2	yes	—
282	C₂²×D₄	#394	1	2	yes	—
283	C₂²×D₄	#394	1	2	yes	—
284	C₂²×D₄	#394	1	2	yes	—
285	C₂²×D₄	#394	1	2	yes	—
286	C₂²×D₄	#394	1	2	yes	—
287	C₂²×D₄	C₂×#120	1	1	yes	characteristic
288	C₂²×D₄	C₂×#120	1	1	yes	characteristic
289	C₂²×D₄	C₂×#120	1	1	yes	characteristic
290	C₂²×D₄	C₂×#120	1	1	yes	characteristic
291	C₂²×D₄	C₂×#120	1	1	yes	characteristic
292	C₂²×D₄	C₂×#120	1	1	yes	characteristic
293	C₂²×D₄	C₂×#121	1	1	yes	characteristic
294	C₂²×D₄	C₂×#121	1	1	yes	characteristic
295	C₂²×D₄	C₂×#121	1	1	yes	characteristic
296	C₂²×D₄	C₂×#121	1	1	yes	characteristic
297	C₂²×D₄	C₂×#121	1	1	yes	characteristic
298	C₂²×D₄	C₂×#121	1	1	yes	characteristic
299	C₂²×D₄	C₂×#123	1	1	yes	characteristic
300	C₂²×D₄	C₂×#123	1	1	yes	characteristic
301	C₂²×D₄	C₂×#124	1	1	yes	characteristic
302	C₂²×D₄	C₂×#127	1	1	yes	characteristic
303	C₂³×C₄	#386	1	1	yes	characteristic
304	C₂³×C₄	#386	1	1	yes	characteristic
305	C₂³×C₄	#386	1	2	yes	—
306	C₂³×C₄	#390	1	2	yes	—
307	C₂³×C₄	#392	1	2	yes	—
308	C₂³×C₄	#392	1	2	yes	—
309	C₂³×C₄	#394	1	2	yes	—
310	C₂³×C₄	#394	1	2	yes	—
311	C₂³×C₄	#394	1	2	yes	—
312	C₂³×C₄	#394	1	2	yes	—
313	C₂³×C₄	#394	1	2	yes	—
314	C₂³×C₄	#394	1	2	yes	—
315	C₂³×C₄	C₂×#99	1	4	yes	complemented
316	C₂³×C₄	C₂×#121	1	1	yes	characteristic
317	C₂³×C₄	C₂×#121	1	1	yes	characteristic
318	C₂³×C₄	C₂×#121	1	1	yes	characteristic
319	C₂³×C₄	C₂×#123	1	1	yes	characteristic
320	C₂³×C₄	C₂×#123	1	1	yes	characteristic
321	C₂³×C₄	C₂×#124	1	1	yes	characteristic
322	C₂×C₂²⋊C₄	C₂×#99	1	8	yes	complemented
323	C₂⁴	#1438	1	2	yes	—
324	C₂⁴	#1438	1	2	yes	—
325	C₂⁴	#1438	1	2	yes	—
326	C₂⁴	#1438	1	2	yes	—
327	C₂⁴	#1438	1	2	yes	—
328	C₂⁴	#1438	1	2	yes	—
329	C₂⁴	#1781	1	4	yes	—
330	C₂⁴	#1781	1	4	yes	—
331	C₂⁴	#1889	1	1	yes	characteristic
332	C₂⁴	#1889	1	2	yes	—
333	C₂⁴	#1889	1	2	yes	—
334	C₂⁴	#1889	1	1	yes	characteristic
335	C₂⁴	#1889	1	2	yes	—
336	C₂⁴	#1898	1	1	yes	characteristic
337	C₂⁴	#1898	1	4	yes	—
338	C₂⁴	#1898	1	2	yes	—
339	C₂⁴	#1898	1	2	yes	—
340	C₂⁴	#1898	1	4	yes	—
341	C₂⁴	#1898	1	1	yes	characteristic
342	C₂⁴	#1898	1	2	yes	—
343	C₂⁴	#1913	1	1	yes	characteristic
344	C₂⁴	#1913	1	1	yes	characteristic
345	C₂⁴	#1913	1	2	yes	—
346	C₂⁴	#2021	1	4	yes	—
347	C₂⁴	#2021	1	4	yes	—
348	C₂⁴	#2021	1	4	yes	—
349	C₂⁴	#2021	1	4	yes	—
350	C₂⁴	C₂×#379	1	1	yes	characteristic
351	C₂⁴	C₂×#386	1	1	yes	characteristic
352	C₂⁴	C₂×#386	1	1	yes	characteristic
353	C₂⁴	C₂×#386	1	1	yes	characteristic
354	C₂⁴	C₂×#386	1	1	yes	characteristic
355	C₂⁴	C₂×#390	1	1	yes	characteristic
356	C₂⁴	C₂×#390	1	1	yes	characteristic
357	C₂⁴	C₂×#392	1	1	yes	characteristic
358	C₂⁴	C₂×#392	1	1	yes	characteristic
359	C₂⁴	C₂×#392	1	1	yes	characteristic
360	C₂⁴	C₂×#394	1	1	yes	characteristic
361	C₂⁴	C₂²×#99	1	2	yes	—
362	C₂⁴	C₂²×#99	1	2	yes	—
363	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
364	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
365	C₂²×C₄	#1438	1	2	yes	—
366	C₂²×C₄	#1438	1	2	yes	—
367	C₂²×C₄	C₂×#392	1	1	yes	characteristic
368	C₂²×C₄	C₂×#394	1	1	yes	characteristic
369	C₂²×C₄	C₂×#394	1	1	yes	characteristic
370	C₂²×C₄	C₂×#394	1	1	yes	characteristic
371	C₂³	#9495	1	2	yes	—
372	C₂³	#9495	1	1	yes	characteristic
373	C₂³	#9495	1	1	yes	characteristic
374	C₂³	#9495	1	1	yes	characteristic
375	C₂³	#9495	1	2	yes	—
376	C₂³	#9495	1	1	yes	characteristic
377	C₂³	#9497	1	2	yes	—
378	C₂³	#9497	1	2	yes	—
379	C₂³	#9497	1	2	yes	—
380	C₂³	#9497	1	2	yes	—
381	C₂³	#10965	1	2	yes	—
382	C₂³	#10965	1	4	yes	—
383	C₂³	#10965	1	2	yes	—
384	C₂³	#10972	1	2	yes	—
385	C₂³	#10972	1	2	yes	—
386	C₂³	#10991	1	2	yes	—
387	C₂³	#10991	1	4	yes	—
388	C₂³	#10991	1	2	yes	—
389	C₂³	C₂×#1438	1	1	yes	characteristic
390	C₂³	C₂×#1781	1	2	yes	—
391	C₂³	C₂×#1889	1	1	yes	characteristic
392	C₂³	C₂×#1889	1	1	yes	characteristic
393	C₂³	C₂×#1898	1	1	yes	characteristic
394	C₂³	C₂×#1898	1	2	yes	—
395	C₂³	C₂×#1898	1	1	yes	characteristic
396	C₂³	C₂×#1913	1	1	yes	characteristic
397	C₂³	C₂×#1913	1	1	yes	characteristic
398	C₂³	C₂×#2021	1	2	yes	—
399	C₂³	C₂×#2021	1	2	yes	—
400	C₂²	#115133	1	2	yes	—
401	C₂²	#115133	1	2	yes	—
402	C₂²	#115133	1	2	yes	—
403	C₂²	#115133	1	2	yes	—
404	C₂²	#139750	1	4	yes	—
405	C₂²	C₂×#9495	1	1	yes	characteristic
406	C₂²	C₂×#9495	1	1	yes	characteristic
407	C₂²	C₂×#9497	1	1	yes	characteristic
408	C₂²	C₂×#9497	1	1	yes	characteristic
409	C₂²	C₂×#10965	1	1	yes	characteristic
410	C₂²	C₂×#10972	1	1	yes	characteristic
411	C₂²	C₂×#10991	1	1	yes	characteristic
412	C₂	C₂×#139750	1	2	yes	—
413	C₂	#72219158	1	4	yes	direct product factor
414	C₂	C₂×#115133	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	#9495
commutator	C₂⁶	C₂³×C₄
Frattini, cosocle	C₂⁴×D₄	C₂⁴
prime radical	C₂²×#23900	C₂
LCS	G ▷ C₂⁶ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂⁵ ◁ C₂⁵×D₄ ◁ G
LECS	G ▷ C₂⁴×D₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂²×#7316	C₂	semidirect
2. C₂²×#7310	C₂	semidirect
3. C₂×#382434	C₂	semidirect
4. C₂²×#12705	C₂	semidirect
5. C₂²×#12687	C₂	semidirect
6. C₂²×#8541	C₂	semidirect
7. #72219158	C₂	direct (N × H)
11. C₂²×#2846	C₄	semidirect
12. C₂×#23900	C₄	semidirect
14. C₂²×#1898	C₄	semidirect
20. C₂×#12705	C₂²	semidirect
21. C₂×#12687	C₂²	semidirect
22. #382434	C₂²	semidirect
23. C₂×#8541	C₂²	semidirect
24. C₂×#7316	C₂²	semidirect
25. C₂×#7310	C₂²	semidirect
41. C₂³×#99	D₄	semidirect
42. C₂×#2846	C₂×C₄	semidirect
44. C₂²×#379	D₄	semidirect
45. C₂×#1898	C₂×C₄	semidirect
46. C₂×#1783	D₄	semidirect
51. C₂×#1781	D₄	semidirect
52. C₂×#1781	D₄	semidirect
53. C₂×#1781	D₄	semidirect
58. C₂⁷	C₂²⋊C₄	semidirect
89. C₂²×#120	C₂²⋊C₄	semidirect
96. C₂³×C₂²⋊C₄	C₂²⋊C₄	semidirect
98. C₂²×#99	C₂×D₄	semidirect
99. C₂×#379	C₂²⋊C₄	semidirect
101. C₂×#379	C₂×D₄	semidirect
102. #1783	C₂×D₄	semidirect
103. #1781	C₂²⋊C₄	semidirect
106. #1781	C₂×D₄	semidirect
107. C₂⁶	#99	semidirect
112. C₂⁶	C₂×C₂²⋊C₄	semidirect
130. C₂³×D₄	#99	semidirect
200. C₂⁴×C₄	#99	semidirect
211. C₂²×C₂²⋊C₄	#99	semidirect
213. C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	semidirect
214. #379	C₂×C₂²⋊C₄	semidirect
246. C₂⁵	C₂×#99	semidirect
315. C₂³×C₄	C₂×#99	semidirect
322. C₂×C₂²⋊C₄	C₂×#99	semidirect
413. C₂	#72219158	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×#7316	2
C₂²×#7310	2
C₂×#382434	2
C₂²×#12705	2
C₂²×#12687	2
C₂²×#8541	2
#72219158	2
C₂²×#23900	2

Subgroups — C2×#72219158 #72271257

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#72219158 #72271257