Subgroups — #72263039

Order 2048.

At least 7269 conjugacy classes of subgroups; only the 784 normal subgroups are shown.

The subgroup lattice has 444 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72263036	C₂	1	2	yes	maximal, complemented
2	#72263034	C₂	1	2	yes	maximal, complemented
3	#72263032	C₂	1	2	yes	maximal, complemented
4	#72250951	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#496228	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#128057	C₂	1	1	yes	maximal, characteristic, complemented
7	#72234296	C₂	1	1	yes	maximal, characteristic, complemented
8	#72233876	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#493352	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#850465	C₂	1	1	yes	maximal, characteristic
11	#72219162	C₂	1	2	yes	maximal, complemented
12	C₂³×#525	C₂²	1	1	yes	characteristic
13	C₂²×#2404	C₂²	1	1	yes	characteristic
14	#7625442	C₂²	1	1	yes	characteristic
15	C₂×#20591	C₂²	1	1	yes	characteristic
16	C₂×#20584	C₂²	1	1	yes	characteristic
17	C₂×#20584	C₂²	1	1	yes	characteristic
18	#850465	C₄	1	8	yes	complemented
19	C₂×#15948	C₂²	1	1	yes	characteristic
20	C₂×#15947	C₂²	1	1	yes	characteristic
21	C₂×#15463	C₂²	1	1	yes	characteristic
22	C₂×#15266	C₂²	1	1	yes	characteristic
23	C₂×#13956	C₂²	1	1	yes	characteristic
24	C₂×#12852	C₂²	1	2	yes	—
25	C₂×#12688	C₂²	1	2	yes	—
26	C₂×#12687	C₂²	1	2	yes	—
27	C₂×#12687	C₂²	1	2	yes	—
28	#359863	C₂²	1	2	yes	—
29	#359502	C₂²	1	2	yes	—
30	#359501	C₂²	1	2	yes	—
31	#359501	C₂²	1	2	yes	—
32	C₂×#7307	C₂²	1	2	yes	—
33	C₂×#7307	C₂²	1	2	yes	—
34	#107130	C₂²	1	2	yes	—
35	#107130	C₂²	1	2	yes	—
36	C₂⁴×#41	C₂³	1	1	yes	characteristic
37	C₂⁶×C₄	D₄	1	1	yes	characteristic
38	C₂²×#525	C₂×C₄	1	4	yes	—
39	C₂²×#525	D₄	1	4	yes	—
40	C₂³×#123	D₄	1	1	yes	characteristic
41	C₂³×#123	C₂³	1	1	yes	characteristic
42	C₂³×#120	D₄	1	1	yes	characteristic
43	C₂³×#120	D₄	1	1	yes	characteristic
44	C₂³×#120	C₂³	1	1	yes	characteristic
45	C₂³×#120	C₂³	1	1	yes	characteristic
46	C₂×#3428	D₄	1	2	yes	complemented
47	C₂³×#117	D₄	1	1	yes	characteristic
48	C₂⁴×C₂²⋊C₄	D₄	1	1	yes	characteristic
49	C₂²×#410	D₄	1	2	yes	complemented
50	C₂²×#410	D₄	1	2	yes	complemented
51	C₂×#2404	C₂×C₄	1	4	yes	—
52	C₂×#2404	D₄	1	4	yes	—
53	#34172	D₄	1	2	yes	complemented
54	#34171	C₂³	1	2	yes	—
55	C₂²×#386	D₄	1	1	yes	characteristic
56	C₂²×#386	C₂³	1	1	yes	characteristic
57	C₂²×#381	D₄	1	1	yes	characteristic
58	C₂²×#381	D₄	1	1	yes	characteristic
59	C₂³×#95	D₄	1	1	yes	characteristic
60	#20591	D₄	1	4	yes	complemented
61	C₂×#1783	C₂³	1	2	yes	—
62	C₂×#1782	D₄	1	2	yes	complemented
63	C₂×#1782	D₄	1	2	yes	complemented
64	C₂×#1781	C₂³	1	2	yes	—
65	C₂×#1781	C₂³	1	2	yes	—
66	#15948	C₂×C₄	1	4	yes	complemented
67	#15947	C₂×C₄	1	4	yes	complemented
68	#15463	C₂×C₄	1	4	yes	complemented
69	#15266	C₂×C₄	1	4	yes	complemented
70	#13956	C₂×C₄	1	4	yes	—
71	#13956	D₄	1	4	yes	—
72	C₂×#1446	D₄	1	1	yes	characteristic
73	C₂×#1446	D₄	1	1	yes	characteristic
74	C₂×#1438	C₂³	1	1	yes	characteristic
75	C₂×#1438	C₂³	1	1	yes	characteristic
76	C₂⁷	C₂×D₄	1	1	yes	characteristic
77	C₂⁷	C₂×D₄	1	1	yes	characteristic
78	C₂³×#41	C₂²×C₄	1	2	yes	—
79	C₂³×#41	C₂×D₄	1	2	yes	—
80	C₂³×#41	C₂×D₄	1	2	yes	—
81	C₂³×#41	C₂×D₄	1	2	yes	—
82	C₂³×#41	C₂×D₄	1	1	yes	characteristic
83	C₂³×#41	C₂×D₄	1	1	yes	characteristic
84	C₂³×#41	C₂×D₄	1	1	yes	characteristic
85	C₂³×#41	C₂×D₄	1	1	yes	characteristic
86	C₂³×#41	C₂×D₄	1	1	yes	characteristic
87	C₂³×#41	C₂×D₄	1	1	yes	characteristic
88	C₂³×#41	C₂×D₄	1	2	yes	—
89	C₂³×#41	#41	1	1	yes	characteristic
90	C₂³×#41	#41	1	1	yes	characteristic
91	C₂³×#41	#41	1	2	yes	—
92	C₂³×#41	#41	1	2	yes	—
93	C₂³×#41	#41	1	2	yes	—
94	C₂⁴×Q₈	C₂×D₄	1	1	yes	characteristic
95	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
96	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
97	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
98	C₂⁵×C₄	C₂²⋊C₄	1	4	yes	complemented
99	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
100	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
101	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
102	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
103	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
104	C₂²×#123	C₂²⋊C₄	1	4	yes	complemented
105	C₂²×#123	C₂²×C₄	1	2	yes	—
106	C₂²×#123	C₂×D₄	1	2	yes	—
107	C₂²×#120	C₂²⋊C₄	1	4	yes	complemented
108	C₂²×#120	C₂²⋊C₄	1	4	yes	complemented
109	C₂²×#120	C₂²×C₄	1	2	yes	—
110	C₂²×#120	C₂²×C₄	1	2	yes	—
111	C₂²×#120	C₂×D₄	1	2	yes	—
112	C₂²×#120	C₂×D₄	1	2	yes	—
113	C₂×#518	C₂×D₄	1	4	yes	—
114	C₂²×#117	C₂²⋊C₄	1	4	yes	complemented
115	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	4	yes	complemented
116	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
117	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
118	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
119	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
120	C₂²×#99	C₂×D₄	1	4	yes	—
121	C₂²×#99	C₂×D₄	1	4	yes	—
122	C₂×#386	C₂²⋊C₄	1	4	yes	complemented
123	C₂×#386	C₂²×C₄	1	2	yes	—
124	C₂×#386	C₂×D₄	1	2	yes	—
125	C₂×#381	C₂²⋊C₄	1	4	yes	complemented
126	C₂×#381	C₂²⋊C₄	1	4	yes	complemented
127	C₂²×#95	C₂²⋊C₄	1	4	yes	complemented
128	C₂²×#95	C₂×D₄	1	1	yes	characteristic
129	C₂²×#95	C₂×D₄	1	1	yes	characteristic
130	C₂²×#95	C₂×D₄	1	1	yes	characteristic
131	C₂²×#95	C₂×D₄	1	1	yes	characteristic
132	#1783	C₂×D₄	1	4	yes	—
133	#1446	C₂²⋊C₄	1	4	yes	complemented
134	#1446	C₂²⋊C₄	1	4	yes	complemented
135	#1438	C₂²×C₄	1	2	yes	—
136	#1438	C₂²×C₄	1	2	yes	—
137	#1438	C₂×D₄	1	2	yes	—
138	#1438	C₂×D₄	1	2	yes	—
139	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
140	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
141	C₂⁶	#120	1	1	yes	characteristic
142	C₂⁶	C₂²×D₄	1	1	yes	characteristic
143	C₂⁶	C₂²×D₄	1	1	yes	characteristic
144	C₂²×#41	C₄×D₄	1	2	yes	—
145	C₂²×#41	C₄×D₄	1	2	yes	—
146	C₂²×#41	C₄×D₄	1	2	yes	—
147	C₂²×#41	C₄×D₄	1	2	yes	—
148	C₂²×#41	C₄×D₄	1	2	yes	—
149	C₂²×#41	C₄×D₄	1	2	yes	—
150	C₂²×#41	C₄×D₄	1	2	yes	—
151	C₂²×#41	C₄×D₄	1	2	yes	—
152	C₂²×#41	#120	1	2	yes	—
153	C₂²×#41	#120	1	2	yes	—
154	C₂²×#41	#120	1	2	yes	—
155	C₂²×#41	#120	1	2	yes	—
156	C₂²×#41	#121	1	2	yes	—
157	C₂²×#41	#121	1	2	yes	—
158	C₂²×#41	#121	1	2	yes	—
159	C₂²×#41	#121	1	2	yes	—
160	C₂²×#41	#121	1	2	yes	—
161	C₂²×#41	#121	1	2	yes	—
162	C₂²×#41	#121	1	2	yes	—
163	C₂²×#41	#121	1	2	yes	—
164	C₂²×#41	#121	1	2	yes	—
165	C₂²×#41	#121	1	2	yes	—
166	C₂²×#41	#121	1	2	yes	—
167	C₂²×#41	#121	1	2	yes	—
168	C₂²×#41	#123	1	2	yes	—
169	C₂²×#41	#123	1	2	yes	—
170	C₂²×#41	#123	1	2	yes	—
171	C₂²×#41	#123	1	2	yes	—
172	C₂²×#41	#124	1	2	yes	—
173	C₂²×#41	#124	1	2	yes	—
174	C₂²×#41	#127	1	2	yes	—
175	C₂²×#41	#127	1	2	yes	—
176	C₂³×Q₈	C₂×C₂²⋊C₄	1	2	yes	—
177	C₂³×Q₈	#120	1	2	yes	—
178	C₂³×Q₈	#121	1	1	yes	characteristic
179	C₂³×Q₈	#121	1	1	yes	characteristic
180	C₂³×Q₈	#121	1	2	yes	—
181	C₂³×Q₈	#124	1	2	yes	—
182	C₂³×Q₈	#127	1	1	yes	characteristic
183	C₂³×Q₈	#127	1	1	yes	characteristic
184	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
185	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
186	C₂³×D₄	#120	1	2	yes	—
187	C₂³×D₄	#120	1	2	yes	—
188	C₂³×D₄	#120	1	1	yes	characteristic
189	C₂³×D₄	#120	1	1	yes	characteristic
190	C₂³×D₄	#120	1	1	yes	characteristic
191	C₂³×D₄	#120	1	1	yes	characteristic
192	C₂³×D₄	#121	1	1	yes	characteristic
193	C₂³×D₄	#121	1	1	yes	characteristic
194	C₂³×D₄	#121	1	1	yes	characteristic
195	C₂³×D₄	#121	1	1	yes	characteristic
196	C₂³×D₄	#121	1	2	yes	—
197	C₂³×D₄	#121	1	2	yes	—
198	C₂³×D₄	#123	1	2	yes	—
199	C₂³×D₄	#123	1	2	yes	—
200	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
201	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
202	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
203	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
204	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
205	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
206	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
207	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
208	C₂³×D₄	C₂×#41	1	1	yes	characteristic
209	C₂³×D₄	C₂×#41	1	1	yes	characteristic
210	C₂³×D₄	C₂×#41	1	1	yes	characteristic
211	C₂³×D₄	C₂×#41	1	1	yes	characteristic
212	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
213	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
214	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
215	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
216	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
217	C₂⁴×C₄	#120	1	1	yes	characteristic
218	C₂⁴×C₄	#120	1	1	yes	characteristic
219	C₂⁴×C₄	#120	1	1	yes	characteristic
220	C₂⁴×C₄	#120	1	1	yes	characteristic
221	C₂⁴×C₄	#120	1	1	yes	characteristic
222	C₂⁴×C₄	#120	1	2	yes	—
223	C₂⁴×C₄	#120	1	1	yes	characteristic
224	C₂⁴×C₄	#120	1	2	yes	—
225	C₂⁴×C₄	#120	1	2	yes	—
226	C₂⁴×C₄	#120	1	1	yes	characteristic
227	C₂⁴×C₄	#121	1	1	yes	characteristic
228	C₂⁴×C₄	#121	1	1	yes	characteristic
229	C₂⁴×C₄	#121	1	1	yes	characteristic
230	C₂⁴×C₄	#121	1	1	yes	characteristic
231	C₂⁴×C₄	#121	1	2	yes	—
232	C₂⁴×C₄	#121	1	1	yes	characteristic
233	C₂⁴×C₄	#121	1	1	yes	characteristic
234	C₂⁴×C₄	#121	1	2	yes	—
235	C₂⁴×C₄	#121	1	2	yes	—
236	C₂⁴×C₄	#123	1	2	yes	—
237	C₂⁴×C₄	#123	1	2	yes	—
238	C₂⁴×C₄	#124	1	2	yes	—
239	C₂⁴×C₄	#127	1	1	yes	characteristic
240	C₂⁴×C₄	#127	1	1	yes	characteristic
241	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
242	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
243	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
244	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
245	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
246	C₂×#95	C₂×C₂²⋊C₄	1	2	yes	—
247	C₂×#95	C₂×C₂²⋊C₄	1	2	yes	—
248	C₂×#95	C₂×C₂²⋊C₄	1	2	yes	—
249	C₂×#95	C₂×C₂²⋊C₄	1	2	yes	—
250	C₂⁵	#379	1	2	yes	—
251	C₂⁵	#392	1	1	yes	characteristic
252	C₂⁵	#392	1	1	yes	characteristic
253	C₂⁵	#394	1	2	yes	—
254	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
255	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
256	C₂⁵	C₂×#120	1	1	yes	characteristic
257	C₂⁵	C₂×#120	1	1	yes	characteristic
258	C₂⁵	C₂×#120	1	1	yes	characteristic
259	C₂⁵	C₂×#120	1	1	yes	characteristic
260	C₂⁵	C₂×#120	1	1	yes	characteristic
261	C₂⁵	C₂×#121	1	1	yes	characteristic
262	C₂⁵	C₂×#121	1	1	yes	characteristic
263	C₂⁵	C₂×#121	1	1	yes	characteristic
264	C₂⁵	C₂×#121	1	1	yes	characteristic
265	C₂⁵	C₂×#123	1	1	yes	characteristic
266	C₂⁵	C₂×#123	1	1	yes	characteristic
267	C₂²×Q₈	#390	1	2	yes	—
268	C₂²×Q₈	#390	1	2	yes	—
269	C₂²×Q₈	#390	1	2	yes	—
270	C₂²×Q₈	#390	1	2	yes	—
271	C₂²×Q₈	#392	1	2	yes	—
272	C₂²×Q₈	#392	1	2	yes	—
273	C₂²×Q₈	#394	1	2	yes	—
274	C₂²×Q₈	#394	1	2	yes	—
275	C₂²×D₄	#386	1	2	yes	—
276	C₂²×D₄	#386	1	2	yes	—
277	C₂²×D₄	#386	1	2	yes	—
278	C₂²×D₄	#386	1	2	yes	—
279	C₂²×D₄	#386	1	2	yes	—
280	C₂²×D₄	#386	1	2	yes	—
281	C₂²×D₄	#386	1	2	yes	—
282	C₂²×D₄	#386	1	2	yes	—
283	C₂²×D₄	#392	1	2	yes	—
284	C₂²×D₄	#392	1	2	yes	—
285	C₂²×D₄	#392	1	2	yes	—
286	C₂²×D₄	#392	1	2	yes	—
287	C₂²×D₄	#394	1	2	yes	—
288	C₂²×D₄	#394	1	2	yes	—
289	C₂²×D₄	#394	1	2	yes	—
290	C₂²×D₄	#394	1	2	yes	—
291	C₂²×D₄	B(4,𝔽₂)	1	8	yes	—
292	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
293	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
294	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
295	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
296	C₂²×D₄	C₂×#120	1	1	yes	characteristic
297	C₂²×D₄	C₂×#120	1	1	yes	characteristic
298	C₂²×D₄	C₂×#121	1	1	yes	characteristic
299	C₂²×D₄	C₂×#121	1	1	yes	characteristic
300	C₂²×D₄	C₂×#121	1	1	yes	characteristic
301	C₂²×D₄	C₂×#121	1	1	yes	characteristic
302	C₂²×D₄	C₂×#121	1	1	yes	characteristic
303	C₂²×D₄	C₂×#121	1	1	yes	characteristic
304	C₂²×D₄	C₂×#123	1	1	yes	characteristic
305	C₂²×D₄	C₂×#123	1	1	yes	characteristic
306	C₂²×D₄	C₂×#124	1	1	yes	characteristic
307	C₂²×D₄	C₂×#127	1	1	yes	characteristic
308	C₂³×C₄	#379	1	2	yes	—
309	C₂³×C₄	#379	1	2	yes	—
310	C₂³×C₄	#379	1	2	yes	—
311	C₂³×C₄	#386	1	2	yes	—
312	C₂³×C₄	#386	1	2	yes	—
313	C₂³×C₄	#386	1	2	yes	—
314	C₂³×C₄	#386	1	2	yes	—
315	C₂³×C₄	#386	1	2	yes	—
316	C₂³×C₄	#386	1	2	yes	—
317	C₂³×C₄	#386	1	2	yes	—
318	C₂³×C₄	#386	1	2	yes	—
319	C₂³×C₄	#390	1	2	yes	—
320	C₂³×C₄	#390	1	2	yes	—
321	C₂³×C₄	#390	1	2	yes	—
322	C₂³×C₄	#390	1	2	yes	—
323	C₂³×C₄	#392	1	1	yes	characteristic
324	C₂³×C₄	#392	1	1	yes	characteristic
325	C₂³×C₄	#392	1	1	yes	characteristic
326	C₂³×C₄	#392	1	2	yes	—
327	C₂³×C₄	#392	1	2	yes	—
328	C₂³×C₄	#392	1	2	yes	—
329	C₂³×C₄	#392	1	2	yes	—
330	C₂³×C₄	#392	1	2	yes	—
331	C₂³×C₄	#392	1	1	yes	characteristic
332	C₂³×C₄	#392	1	1	yes	characteristic
333	C₂³×C₄	#392	1	1	yes	characteristic
334	C₂³×C₄	#392	1	2	yes	—
335	C₂³×C₄	#394	1	2	yes	—
336	C₂³×C₄	#394	1	2	yes	—
337	C₂³×C₄	#394	1	2	yes	—
338	C₂³×C₄	#394	1	2	yes	—
339	C₂³×C₄	#394	1	2	yes	—
340	C₂³×C₄	#394	1	2	yes	—
341	C₂³×C₄	#394	1	2	yes	—
342	C₂³×C₄	#394	1	2	yes	—
343	C₂³×C₄	#394	1	2	yes	—
344	C₂³×C₄	B(4,𝔽₂)	1	1	yes	characteristic
345	C₂³×C₄	B(4,𝔽₂)	1	1	yes	characteristic
346	C₂³×C₄	B(4,𝔽₂)	1	1	yes	characteristic
347	C₂³×C₄	B(4,𝔽₂)	1	1	yes	characteristic
348	C₂³×C₄	#458	1	2	yes	—
349	C₂³×C₄	#458	1	2	yes	—
350	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
351	C₂³×C₄	C₂×#120	1	1	yes	characteristic
352	C₂³×C₄	C₂×#121	1	1	yes	characteristic
353	C₂³×C₄	C₂×#121	1	1	yes	characteristic
354	C₂³×C₄	C₂×#124	1	1	yes	characteristic
355	C₂³×C₄	C₂×#127	1	1	yes	characteristic
356	C₂⁴	#1438	1	2	yes	—
357	C₂⁴	#1438	1	2	yes	—
358	C₂⁴	#2021	1	4	yes	—
359	C₂⁴	C₂×#379	1	1	yes	characteristic
360	C₂⁴	C₂×#386	1	1	yes	characteristic
361	C₂⁴	C₂×#386	1	1	yes	characteristic
362	C₂⁴	C₂×#386	1	1	yes	characteristic
363	C₂⁴	C₂×#386	1	1	yes	characteristic
364	C₂⁴	C₂×#392	1	1	yes	characteristic
365	C₂⁴	C₂×#392	1	1	yes	characteristic
366	C₂⁴	C₂×#392	1	1	yes	characteristic
367	C₂⁴	C₂×#394	1	1	yes	characteristic
368	C₂⁴	C₂×#394	1	1	yes	characteristic
369	C₂⁴	C₂×#394	1	1	yes	characteristic
370	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
371	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
372	C₂⁴	C₂×B(4,𝔽₂)	1	4	yes	—
373	C₂⁴	C₂×#458	1	1	yes	characteristic
374	C₂⁴	C₂×#458	1	1	yes	characteristic
375	C₂⁴	#3026	1	4	yes	—
376	C₂×D₄	#1889	1	8	yes	—
377	C₂×D₄	#2021	1	8	yes	—
378	C₂²×C₄	#1438	1	2	yes	—
379	C₂²×C₄	#1438	1	2	yes	—
380	C₂²×C₄	#1438	1	2	yes	—
381	C₂²×C₄	#1438	1	2	yes	—
382	C₂²×C₄	#1438	1	2	yes	—
383	C₂²×C₄	#1438	1	2	yes	—
384	C₂²×C₄	#1790	1	2	yes	—
385	C₂²×C₄	#1790	1	2	yes	—
386	C₂²×C₄	#1790	1	2	yes	—
387	C₂²×C₄	#1790	1	2	yes	—
388	C₂²×C₄	#2021	1	4	yes	—
389	C₂²×C₄	#2021	1	1	yes	characteristic
390	C₂²×C₄	#2021	1	1	yes	characteristic
391	C₂²×C₄	#2021	1	1	yes	characteristic
392	C₂²×C₄	#2021	1	1	yes	characteristic
393	C₂²×C₄	#2022	1	2	yes	—
394	C₂²×C₄	#2022	1	2	yes	—
395	C₂²×C₄	#2044	1	2	yes	—
396	C₂²×C₄	#2044	1	2	yes	—
397	C₂²×C₄	#2044	1	2	yes	—
398	C₂²×C₄	#2044	1	2	yes	—
399	C₂²×C₄	C₂×#390	1	1	yes	characteristic
400	C₂²×C₄	C₂×#390	1	1	yes	characteristic
401	C₂²×C₄	C₂×#392	1	1	yes	characteristic
402	C₂²×C₄	C₂×#394	1	1	yes	characteristic
403	C₂³	#10991	1	4	yes	—
404	C₂³	C₂×#1438	1	1	yes	characteristic
405	C₂³	C₂×#1790	1	1	yes	characteristic
406	C₂³	C₂×#1790	1	1	yes	characteristic
407	C₂³	C₂×#1889	1	2	yes	—
408	C₂³	#20960	1	2	yes	—
409	C₂³	C₂×#2021	1	2	yes	—
410	C₂³	C₂×#2021	1	2	yes	—
411	C₂³	C₂×#2021	1	1	yes	characteristic
412	C₂³	C₂×#2022	1	1	yes	characteristic
413	C₂³	#23444	1	2	yes	—
414	C₂³	#23444	1	2	yes	—
415	C₂³	C₂×#2044	1	1	yes	characteristic
416	C₂³	C₂×#2044	1	1	yes	characteristic
417	C₂³	#33546	1	2	yes	—
418	C₂³	#33550	1	2	yes	—
419	C₂³	#33553	1	2	yes	—
420	C₂³	#33555	1	2	yes	—
421	C₂×C₄	#10991	1	4	yes	—
422	C₂×C₄	#10995	1	2	yes	—
423	C₂×C₄	#10995	1	2	yes	—
424	C₂×C₄	#10995	1	2	yes	—
425	C₂×C₄	#10995	1	2	yes	—
426	C₂²	#233541	1	2	yes	—
427	C₂²	#233542	1	2	yes	—
428	C₂²	C₂×#10995	1	1	yes	characteristic
429	C₂²	C₂×#10991	1	1	yes	characteristic
430	C₂²	#357530	1	1	yes	characteristic
431	C₂²	#493577	1	1	yes	characteristic
432	C₂²	#493581	1	1	yes	characteristic
433	C₂²	#493584	1	1	yes	characteristic
434	C₂²	#493587	1	1	yes	characteristic
435	C₂²	#498885	1	2	yes	—
436	C₂²	#498888	1	2	yes	—
437	C₂²	#499095	1	2	yes	—
438	C₂²	#499098	1	2	yes	—
439	C₂	#72215545	1	4	yes	—
440	C₂	#72250323	1	1	yes	characteristic
441	C₂	#72261819	1	1	yes	characteristic
442	C₂	#72261903	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂×#2021
commutator	C₂³×D₄	C₂³×C₄
Frattini, cosocle	C₂⁴×D₄	C₂⁴
prime radical	C₂×#850465	C₂
LCS	G ▷ C₂³×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂⁴×C₄ ◁ C₂⁴×#41 ◁ 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. #72263036	C₂	semidirect
2. #72263034	C₂	semidirect
3. #72263032	C₂	semidirect
4. #72250951	C₂	semidirect
5. C₂×#496228	C₂	semidirect
6. C₂×#128057	C₂	semidirect
7. #72234296	C₂	semidirect
8. #72233876	C₂	semidirect
9. C₂×#493352	C₂	semidirect
11. #72219162	C₂	semidirect
18. #850465	C₄	semidirect
46. C₂×#3428	D₄	semidirect
49. C₂²×#410	D₄	semidirect
50. C₂²×#410	D₄	semidirect
53. #34172	D₄	semidirect
60. #20591	D₄	semidirect
62. C₂×#1782	D₄	semidirect
63. C₂×#1782	D₄	semidirect
66. #15948	C₂×C₄	semidirect
67. #15947	C₂×C₄	semidirect
68. #15463	C₂×C₄	semidirect
69. #15266	C₂×C₄	semidirect
98. C₂⁵×C₄	C₂²⋊C₄	semidirect
104. C₂²×#123	C₂²⋊C₄	semidirect
107. C₂²×#120	C₂²⋊C₄	semidirect
108. C₂²×#120	C₂²⋊C₄	semidirect
114. C₂²×#117	C₂²⋊C₄	semidirect
115. C₂³×C₂²⋊C₄	C₂²⋊C₄	semidirect
122. C₂×#386	C₂²⋊C₄	semidirect
125. C₂×#381	C₂²⋊C₄	semidirect
126. C₂×#381	C₂²⋊C₄	semidirect
127. C₂²×#95	C₂²⋊C₄	semidirect
133. #1446	C₂²⋊C₄	semidirect
134. #1446	C₂²⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
#72263036	2
#72263034	2
#72263032	2
#72250951	2
C₂×#496228	2
C₂×#128057	2
#72234296	2
#72233876	2
C₂×#493352	2
C₂×#850465	2
#72219162	2