Subgroups — #72313966

Order 2048.

At least 7792 conjugacy classes of subgroups; only the 1140 normal subgroups are shown.

The subgroup lattice has 650 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72313906	C₂	1	1	yes	maximal, characteristic, complemented
2	#72313847	C₂	1	4	yes	maximal, complemented
3	#72313565	C₂	1	4	yes	maximal, complemented
4	#72313477	C₂	1	4	yes	maximal, complemented
5	#72313437	C₂	1	4	yes	maximal, complemented
6	#72313372	C₂	1	8	yes	maximal, complemented
7	C₂×#495580	C₂	1	1	yes	maximal, characteristic, complemented
8	#72311821	C₂	1	1	yes	maximal, characteristic, complemented
9	#72311799	C₂	1	1	yes	maximal, characteristic, complemented
10	#72306049	C₂	1	1	yes	maximal, characteristic, complemented
11	#72285068	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#6346637	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#62812	C₂²	1	1	yes	characteristic
14	#7628665	C₂²	1	1	yes	characteristic
15	C₂×#34963	C₂²	1	1	yes	characteristic
16	#7512477	C₂²	1	4	yes	complemented
17	#6657540	C₂²	1	2	yes	complemented
18	#6653018	C₂²	1	2	yes	complemented
19	#6640543	C₂²	1	2	yes	complemented
20	#6632008	C₂²	1	2	yes	complemented
21	#6443331	C₂²	1	2	yes	complemented
22	#6443330	C₂²	1	2	yes	complemented
23	#6443328	C₂²	1	4	yes	—
24	#6443327	C₂²	1	4	yes	complemented
25	#6374572	C₂²	1	1	yes	characteristic
26	C₂×#20723	C₂²	1	1	yes	characteristic
27	C₂×C₄×#413	C₂²	1	1	yes	characteristic
28	#6346637	C₂²	1	4	yes	—
29	#6346637	C₂²	1	4	yes	complemented
30	C₂×#18203	C₂²	1	2	yes	complemented
31	C₂×#18194	C₂²	1	2	yes	complemented
32	C₂×#17363	C₂²	1	1	yes	characteristic
33	#495580	C₂²	1	4	yes	complemented
34	#495580	C₂²	1	4	yes	complemented
35	C₂×#13292	C₂²	1	2	yes	complemented
36	C₂×#13218	C₂²	1	2	yes	complemented
37	#482368	C₂²	1	4	yes	complemented
38	#482364	C₂²	1	2	yes	complemented
39	#482363	C₂²	1	2	yes	complemented
40	#482050	C₂²	1	4	yes	complemented
41	#185348	C₂²	1	4	yes	complemented
42	#185340	C₂²	1	4	yes	complemented
43	#185331	C₂²	1	4	yes	complemented
44	#142735	C₂²	1	16	yes	complemented
45	#142734	C₂²	1	16	yes	complemented
46	#142605	C₂²	1	16	yes	complemented
47	#142604	C₂²	1	16	yes	complemented
48	#127138	C₂²	1	4	yes	complemented
49	#127136	C₂²	1	4	yes	complemented
50	#127067	C₂²	1	4	yes	complemented
51	#62812	D₄	1	2	yes	—
52	#62812	D₄	1	2	yes	—
53	#62812	C₂³	1	2	yes	—
54	#62812	C₂³	1	2	yes	—
55	C₂×#3497	D₄	1	2	yes	—
56	C₂×#3496	C₂³	1	2	yes	—
57	C₂×#3449	D₄	1	2	yes	—
58	C₂²×#532	D₄	1	1	yes	characteristic
59	C₂²×C₄×#41	C₂³	1	1	yes	characteristic
60	C₂³×C₄×D₄	D₄	1	1	yes	characteristic
61	C₂²×#432	D₄	1	1	yes	characteristic
62	C₂²×#432	D₄	1	1	yes	characteristic
63	C₂²×#413	D₄	1	2	yes	—
64	#35316	D₄	1	1	yes	characteristic
65	#35316	C₂³	1	1	yes	characteristic
66	#35272	D₄	1	1	yes	characteristic
67	#35272	C₂³	1	1	yes	characteristic
68	#35178	D₄	1	2	yes	—
69	#35165	C₂³	1	2	yes	—
70	#34963	D₄	1	2	yes	—
71	#34963	D₄	1	2	yes	—
72	#34963	C₂³	1	2	yes	—
73	#34963	C₂³	1	2	yes	—
74	#34937	D₄	1	2	yes	—
75	#34937	C₂³	1	2	yes	—
76	C₂×#2487	D₄	1	1	yes	characteristic
77	C₂×#2487	C₂³	1	1	yes	characteristic
78	C₂×#2408	D₄	1	1	yes	characteristic
79	C₂×#2408	C₂³	1	1	yes	characteristic
80	C₂×#2285	D₄	1	1	yes	characteristic
81	C₂×#2283	D₄	1	1	yes	characteristic
82	#32260	C₂³	1	4	yes	complemented
83	#32028	C₂³	1	4	yes	complemented
84	#31260	C₂³	1	4	yes	complemented
85	#30499	C₂³	1	4	yes	complemented
86	#25739	C₂³	1	8	yes	—
87	#25738	C₂³	1	8	yes	—
88	#21851	D₄	1	2	yes	—
89	#21851	C₂³	1	2	yes	—
90	#21738	D₄	1	2	yes	—
91	#21738	C₂³	1	2	yes	—
92	#21379	D₄	1	2	yes	—
93	#21379	C₂³	1	2	yes	—
94	#20723	C₂³	1	2	yes	—
95	#20723	C₂³	1	2	yes	—
96	C₂×#1799	C₂³	1	2	yes	—
97	C₄×#413	D₄	1	2	yes	—
98	C₄×#413	D₄	1	2	yes	—
99	C₄×#413	C₂³	1	2	yes	—
100	C₄×#413	C₂³	1	2	yes	—
101	C₂×C₄×#100	D₄	1	2	yes	—
102	C₂×C₄×#100	C₂³	1	2	yes	—
103	#18203	C₂³	1	8	yes	—
104	#18194	C₂³	1	8	yes	—
105	#17363	D₄	1	2	yes	—
106	#17363	D₄	1	2	yes	—
107	#17363	C₂³	1	2	yes	—
108	#17363	C₂³	1	2	yes	—
109	C₂×#1466	D₄	1	2	yes	—
110	C₂×#1464	D₄	1	2	yes	—
111	C₂×#1459	C₂³	1	2	yes	—
112	#13292	C₂³	1	8	yes	complemented
113	#13218	C₂³	1	8	yes	complemented
114	#11878	C₂³	1	8	yes	complemented
115	#11877	C₂³	1	8	yes	complemented
116	#8350	C₂³	1	16	yes	—
117	#7203	C₂³	1	16	yes	complemented
118	C₂³×#41	C₂×D₄	1	1	yes	characteristic
119	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
120	#3497	C₂×D₄	1	4	yes	—
121	#3497	C₂×D₄	1	4	yes	—
122	#3496	C₂×D₄	1	4	yes	—
123	#3496	C₂⁴	1	4	yes	—
124	#3449	C₂×D₄	1	4	yes	—
125	#3449	C₂×D₄	1	4	yes	—
126	C₂×#537	C₂×D₄	1	4	yes	—
127	C₂×#532	C₂×D₄	1	2	yes	—
128	C₂×#532	C₂×D₄	1	2	yes	—
129	C₂²×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic
130	C₂²×#127	C₂×D₄	1	1	yes	characteristic
131	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
132	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
133	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
134	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
135	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
136	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
137	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
138	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
139	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
140	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
141	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
142	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
143	C₂×C₄×#41	#41	1	1	yes	characteristic
144	C₂×C₄×#41	#41	1	1	yes	characteristic
145	C₂×C₄×#41	C₂⁴	1	1	yes	characteristic
146	C₂×C₄×#41	C₂⁴	1	1	yes	characteristic
147	C₂²×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
150	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
151	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×D₄	#41	1	1	yes	characteristic
156	C₂²×C₄×D₄	C₂⁴	1	1	yes	characteristic
157	C₂²×#117	C₂×D₄	1	1	yes	characteristic
158	C₂²×#117	C₂×D₄	1	1	yes	characteristic
159	C₂²×#117	#41	1	1	yes	characteristic
160	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
161	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
162	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
163	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
164	C₂×#432	C₂×D₄	1	2	yes	—
165	C₂×#432	C₂×D₄	1	2	yes	—
166	C₂²×C₄⋊C₈	C₂×D₄	1	2	yes	—
167	C₂×#413	C₂×D₄	1	4	yes	—
168	C₂×#413	C₂×D₄	1	4	yes	—
169	C₂²×#100	C₂×D₄	1	4	yes	—
170	C₂²×C₂²⋊C₈	C₂×D₄	1	2	yes	—
171	C₂²×C₂²⋊C₈	C₂×D₄	1	2	yes	—
172	C₂²×#97	C₂×D₄	1	2	yes	—
173	#2548	C₂×D₄	1	2	yes	—
174	#2548	C₂×D₄	1	2	yes	—
175	#2547	C₂×D₄	1	2	yes	—
176	#2547	C₂⁴	1	2	yes	—
177	#2546	C₂×D₄	1	2	yes	—
178	#2546	C₂×D₄	1	2	yes	—
179	#2541	C₂×D₄	1	2	yes	—
180	#2541	C₂⁴	1	2	yes	—
181	#2487	C₂×D₄	1	2	yes	—
182	#2487	C₂×D₄	1	2	yes	—
183	#2487	C₂×D₄	1	2	yes	—
184	#2487	C₂⁴	1	2	yes	—
185	#2408	C₂×D₄	1	2	yes	—
186	#2408	C₂×D₄	1	2	yes	—
187	#2408	C₂×D₄	1	2	yes	—
188	#2408	C₂⁴	1	2	yes	—
189	#2285	C₂×D₄	1	2	yes	—
190	#2285	C₂×D₄	1	1	yes	characteristic
191	#2285	C₂×D₄	1	1	yes	characteristic
192	#2283	C₂×D₄	1	2	yes	—
193	#2283	C₂×D₄	1	2	yes	—
194	C₂×#380	C₂×D₄	1	1	yes	characteristic
195	C₂×#380	C₂×D₄	1	1	yes	characteristic
196	C₂×C₄×C₄⋊C₄	C₂×D₄	1	2	yes	—
197	#1869	C₂×D₄	1	4	yes	—
198	#1869	C₂×D₄	1	4	yes	—
199	#1869	C₂×D₄	1	4	yes	—
200	#1869	C₂⁴	1	4	yes	—
201	#1799	C₂⁴	1	4	yes	—
202	C₄×#100	C₂×D₄	1	4	yes	—
203	C₄×#100	C₂×D₄	1	4	yes	—
204	C₄×#100	C₂×D₄	1	4	yes	—
205	C₄×#100	C₂⁴	1	4	yes	—
206	#1466	C₂×D₄	1	4	yes	—
207	#1466	C₂×D₄	1	4	yes	—
208	#1464	C₂×D₄	1	4	yes	—
209	#1464	C₂×D₄	1	4	yes	—
210	#1459	C₂×D₄	1	4	yes	—
211	#1459	C₂⁴	1	4	yes	—
212	C₂×#323	C₂×D₄	1	4	yes	—
213	C₂²×#41	#120	1	1	yes	characteristic
214	C₂²×#41	#120	1	1	yes	characteristic
215	C₂²×#41	#121	1	1	yes	characteristic
216	C₂²×#41	#121	1	1	yes	characteristic
217	C₂²×#41	#127	1	1	yes	characteristic
218	C₂²×#41	#127	1	1	yes	characteristic
219	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
220	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
221	C₂³×Q₈	#120	1	1	yes	characteristic
222	C₂³×D₄	#121	1	1	yes	characteristic
223	C₂³×D₄	#127	1	1	yes	characteristic
224	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
225	C₂³×D₄	C₂²×D₄	1	2	yes	—
226	C₂⁴×C₄	#120	1	1	yes	characteristic
227	C₂⁴×C₄	#120	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	#127	1	1	yes	characteristic
232	C₂⁴×C₄	#127	1	1	yes	characteristic
233	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
234	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
235	C₂³×C₈	C₂²×D₄	1	4	yes	—
236	#537	C₂²×D₄	1	8	yes	—
237	C₂×C₄⋊Q₈	C₂²×D₄	1	2	yes	—
238	C₂×#127	C₂²×D₄	1	2	yes	—
239	C₂×C₄×Q₈	#120	1	1	yes	characteristic
240	C₂×C₄×Q₈	#120	1	1	yes	characteristic
241	C₂×C₄×Q₈	#120	1	1	yes	characteristic
242	C₂×C₄×Q₈	#120	1	1	yes	characteristic
243	C₂×C₄×Q₈	#120	1	1	yes	characteristic
244	C₂×C₄×Q₈	#120	1	1	yes	characteristic
245	C₂×C₄×Q₈	#120	1	1	yes	characteristic
246	C₂×C₄×Q₈	#120	1	1	yes	characteristic
247	C₂×C₄×Q₈	#121	1	1	yes	characteristic
248	C₂×C₄×Q₈	#121	1	1	yes	characteristic
249	C₂×C₄×Q₈	#121	1	1	yes	characteristic
250	C₂×C₄×Q₈	#121	1	1	yes	characteristic
251	C₂×C₄×Q₈	C₂²×D₄	1	1	yes	characteristic
252	C₂×C₄×Q₈	C₂²×D₄	1	1	yes	characteristic
253	C₂×C₄×Q₈	C₂²×D₄	1	1	yes	characteristic
254	C₂×C₄×Q₈	C₂²×D₄	1	1	yes	characteristic
255	C₂×C₄×D₄	#120	1	1	yes	characteristic
256	C₂×C₄×D₄	#120	1	1	yes	characteristic
257	C₂×C₄×D₄	#120	1	1	yes	characteristic
258	C₂×C₄×D₄	#120	1	1	yes	characteristic
259	C₂×C₄×D₄	#120	1	1	yes	characteristic
260	C₂×C₄×D₄	#120	1	1	yes	characteristic
261	C₂×C₄×D₄	#120	1	1	yes	characteristic
262	C₂×C₄×D₄	#120	1	1	yes	characteristic
263	C₂×C₄×D₄	#120	1	1	yes	characteristic
264	C₂×C₄×D₄	#120	1	1	yes	characteristic
265	C₂×C₄×D₄	#121	1	1	yes	characteristic
266	C₂×C₄×D₄	#121	1	1	yes	characteristic
267	C₂×C₄×D₄	#121	1	1	yes	characteristic
268	C₂×C₄×D₄	#121	1	1	yes	characteristic
269	C₂×C₄×D₄	#121	1	1	yes	characteristic
270	C₂×C₄×D₄	#121	1	1	yes	characteristic
271	C₂×C₄×D₄	#121	1	1	yes	characteristic
272	C₂×C₄×D₄	#121	1	1	yes	characteristic
273	C₂×C₄×D₄	#121	1	1	yes	characteristic
274	C₂×C₄×D₄	#121	1	1	yes	characteristic
275	C₂×C₄×D₄	#121	1	1	yes	characteristic
276	C₂×C₄×D₄	#121	1	1	yes	characteristic
277	C₂×C₄×D₄	#121	1	1	yes	characteristic
278	C₂×C₄×D₄	#121	1	1	yes	characteristic
279	C₂×C₄×D₄	#127	1	1	yes	characteristic
280	C₂×C₄×D₄	#127	1	1	yes	characteristic
281	C₂×C₄×D₄	#127	1	1	yes	characteristic
282	C₂×C₄×D₄	#127	1	1	yes	characteristic
283	C₂×C₄×D₄	#127	1	1	yes	characteristic
284	C₂×C₄×D₄	#127	1	1	yes	characteristic
285	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
286	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
287	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
288	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
289	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
290	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
291	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
292	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
293	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
294	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
295	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
296	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
297	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
298	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
299	C₂×C₄×D₄	C₂×#41	1	1	yes	characteristic
300	C₂×C₄×D₄	C₂×#41	1	1	yes	characteristic
301	C₂×C₄×D₄	C₂×#41	1	1	yes	characteristic
302	C₂×C₄×D₄	C₂⁵	1	1	yes	characteristic
303	C₂×#117	#120	1	1	yes	characteristic
304	C₂×#117	#120	1	1	yes	characteristic
305	C₂×#117	#120	1	1	yes	characteristic
306	C₂×#117	#120	1	1	yes	characteristic
307	C₂×#117	#120	1	1	yes	characteristic
308	C₂×#117	#120	1	1	yes	characteristic
309	C₂×#117	#121	1	1	yes	characteristic
310	C₂×#117	#121	1	1	yes	characteristic
311	C₂×#117	#121	1	1	yes	characteristic
312	C₂×#117	#121	1	1	yes	characteristic
313	C₂×#117	#121	1	1	yes	characteristic
314	C₂×#117	#121	1	1	yes	characteristic
315	C₂×#117	#121	1	1	yes	characteristic
316	C₂×#117	#121	1	1	yes	characteristic
317	C₂×#117	#121	1	1	yes	characteristic
318	C₂×#117	#121	1	1	yes	characteristic
319	C₂×#117	#127	1	1	yes	characteristic
320	C₂×#117	#127	1	1	yes	characteristic
321	C₂×#117	C₂²×D₄	1	1	yes	characteristic
322	C₂×#117	C₂²×D₄	1	1	yes	characteristic
323	C₂×#117	C₂²×D₄	1	1	yes	characteristic
324	C₂×#117	C₂²×D₄	1	1	yes	characteristic
325	C₂×#117	C₂×#41	1	1	yes	characteristic
326	C₂×#117	C₂×#41	1	1	yes	characteristic
327	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
328	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
329	C₂²×C₄⋊C₄	#121	1	1	yes	characteristic
330	C₂²×C₄⋊C₄	#121	1	1	yes	characteristic
331	C₂²×C₄⋊C₄	#121	1	1	yes	characteristic
332	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
333	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
334	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
335	C₂²×C₂²⋊C₄	#121	1	1	yes	characteristic
336	C₂²×C₂²⋊C₄	#121	1	1	yes	characteristic
337	C₂²×C₂²⋊C₄	#127	1	1	yes	characteristic
338	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
339	C₂²×C₂²⋊C₄	C₂×#41	1	1	yes	characteristic
340	C₂²×C₄²	#120	1	1	yes	characteristic
341	C₂²×C₄²	#120	1	1	yes	characteristic
342	C₂²×C₄²	#120	1	1	yes	characteristic
343	C₂²×C₄²	#120	1	1	yes	characteristic
344	C₂²×C₄²	#120	1	1	yes	characteristic
345	C₂²×C₄²	#120	1	1	yes	characteristic
346	C₂²×C₄²	#120	1	1	yes	characteristic
347	C₂²×C₄²	#120	1	1	yes	characteristic
348	C₂²×C₄²	#120	1	1	yes	characteristic
349	C₂²×C₄²	#120	1	1	yes	characteristic
350	C₂²×C₄²	#120	1	1	yes	characteristic
351	C₂²×C₄²	#120	1	1	yes	characteristic
352	C₂²×C₄²	#120	1	1	yes	characteristic
353	C₂²×C₄²	#120	1	1	yes	characteristic
354	C₂²×C₄²	#120	1	1	yes	characteristic
355	C₂²×C₄²	#120	1	1	yes	characteristic
356	C₂²×C₄²	#121	1	1	yes	characteristic
357	C₂²×C₄²	#121	1	1	yes	characteristic
358	C₂²×C₄²	#121	1	1	yes	characteristic
359	C₂²×C₄²	#121	1	1	yes	characteristic
360	C₂²×C₄²	#121	1	1	yes	characteristic
361	C₂²×C₄²	#121	1	1	yes	characteristic
362	C₂²×C₄²	#121	1	1	yes	characteristic
363	C₂²×C₄²	#121	1	1	yes	characteristic
364	C₂²×C₄²	#121	1	1	yes	characteristic
365	C₂²×C₄²	#127	1	1	yes	characteristic
366	C₂²×C₄²	#127	1	1	yes	characteristic
367	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
368	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
369	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
370	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
371	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
372	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
373	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
374	C₂×#100	AGL(1,ℤ/8)	1	16	yes	—
375	C₂×#100	C₂²×D₄	1	8	yes	—
376	C₂×C₂²⋊C₈	C₂²×D₄	1	4	yes	—
377	#380	C₂²×D₄	1	2	yes	—
378	#380	C₂²×D₄	1	2	yes	—
379	C₄×C₄⋊C₄	C₂²×D₄	1	2	yes	—
380	C₄×C₄⋊C₄	C₂²×D₄	1	2	yes	—
381	#323	C₂²×D₄	1	8	yes	—
382	C₂⁵	#392	1	1	yes	characteristic
383	C₂⁵	C₂×#121	1	1	yes	characteristic
384	C₂⁵	C₂×#127	1	1	yes	characteristic
385	C₂²×Q₈	#392	1	1	yes	characteristic
386	C₂²×Q₈	#392	1	1	yes	characteristic
387	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
388	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
389	C₂²×D₄	#392	1	1	yes	characteristic
390	C₂²×D₄	#392	1	1	yes	characteristic
391	C₂²×D₄	#392	1	1	yes	characteristic
392	C₂²×D₄	#392	1	1	yes	characteristic
393	C₂²×D₄	C₂×#120	1	1	yes	characteristic
394	C₂²×D₄	C₂×#121	1	1	yes	characteristic
395	C₂²×D₄	C₂×#121	1	1	yes	characteristic
396	C₂²×D₄	C₂×#121	1	1	yes	characteristic
397	C₂²×D₄	C₂×#127	1	1	yes	characteristic
398	C₂²×D₄	C₂×#127	1	1	yes	characteristic
399	C₂²×D₄	C₂×#127	1	1	yes	characteristic
400	C₂²×D₄	C₂×AGL(1,ℤ/8)	1	8	yes	—
401	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
402	C₂³×C₄	#392	1	1	yes	characteristic
403	C₂³×C₄	#392	1	1	yes	characteristic
404	C₂³×C₄	#392	1	1	yes	characteristic
405	C₂³×C₄	#392	1	1	yes	characteristic
406	C₂³×C₄	#392	1	1	yes	characteristic
407	C₂³×C₄	#392	1	1	yes	characteristic
408	C₂³×C₄	#392	1	1	yes	characteristic
409	C₂³×C₄	#392	1	1	yes	characteristic
410	C₂³×C₄	#392	1	1	yes	characteristic
411	C₂³×C₄	#392	1	1	yes	characteristic
412	C₂³×C₄	#392	1	1	yes	characteristic
413	C₂³×C₄	#392	1	1	yes	characteristic
414	C₂³×C₄	#392	1	1	yes	characteristic
415	C₂³×C₄	#392	1	1	yes	characteristic
416	C₂³×C₄	#392	1	1	yes	characteristic
417	C₂³×C₄	#392	1	1	yes	characteristic
418	C₂³×C₄	#392	1	1	yes	characteristic
419	C₂³×C₄	#392	1	1	yes	characteristic
420	C₂³×C₄	#392	1	1	yes	characteristic
421	C₂³×C₄	#392	1	1	yes	characteristic
422	C₂³×C₄	#392	1	1	yes	characteristic
423	C₂³×C₄	C₂×#120	1	1	yes	characteristic
424	C₂³×C₄	C₂×#120	1	1	yes	characteristic
425	C₂³×C₄	C₂×#120	1	1	yes	characteristic
426	C₂³×C₄	C₂×#120	1	1	yes	characteristic
427	C₂³×C₄	C₂×#120	1	1	yes	characteristic
428	C₂³×C₄	C₂×#120	1	1	yes	characteristic
429	C₂³×C₄	C₂×#120	1	1	yes	characteristic
430	C₂³×C₄	C₂×#120	1	1	yes	characteristic
431	C₂³×C₄	C₂×#120	1	1	yes	characteristic
432	C₂³×C₄	C₂×#120	1	1	yes	characteristic
433	C₂³×C₄	C₂×#121	1	1	yes	characteristic
434	C₂³×C₄	C₂×#121	1	1	yes	characteristic
435	C₂³×C₄	C₂×#121	1	1	yes	characteristic
436	C₂³×C₄	C₂×#121	1	1	yes	characteristic
437	C₂³×C₄	C₂×#121	1	1	yes	characteristic
438	C₂³×C₄	C₂×#121	1	1	yes	characteristic
439	C₂³×C₄	C₂×#121	1	1	yes	characteristic
440	C₂³×C₄	C₂×#121	1	1	yes	characteristic
441	C₂³×C₄	C₂×#121	1	1	yes	characteristic
442	C₂³×C₄	C₂×#121	1	1	yes	characteristic
443	C₂³×C₄	C₂×#127	1	1	yes	characteristic
444	C₂³×C₄	C₂×#127	1	1	yes	characteristic
445	C₂³×C₄	C₂×#127	1	1	yes	characteristic
446	C₂³×C₄	C₂×#127	1	1	yes	characteristic
447	C₂³×C₄	C₂×#127	1	1	yes	characteristic
448	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
449	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
450	C₂×C₄⋊C₄	#392	1	1	yes	characteristic
451	C₂×C₄⋊C₄	#392	1	1	yes	characteristic
452	C₂×C₄⋊C₄	#392	1	1	yes	characteristic
453	C₂×C₄⋊C₄	#392	1	1	yes	characteristic
454	C₂×C₄⋊C₄	#392	1	1	yes	characteristic
455	C₂×C₄⋊C₄	#392	1	1	yes	characteristic
456	C₂×C₄⋊C₄	#392	1	1	yes	characteristic
457	C₂×C₄⋊C₄	#392	1	1	yes	characteristic
458	C₂×C₄⋊C₄	#392	1	1	yes	characteristic
459	C₂×C₄⋊C₄	#392	1	1	yes	characteristic
460	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
461	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
462	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
463	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
464	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
465	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
466	C₂×C₄⋊C₄	C₂×#121	1	1	yes	characteristic
467	C₂×C₄⋊C₄	C₂×#121	1	1	yes	characteristic
468	C₂×C₄⋊C₄	C₂×#121	1	1	yes	characteristic
469	C₂×C₄⋊C₄	C₂×#121	1	1	yes	characteristic
470	C₂×C₄⋊C₄	C₂×#121	1	1	yes	characteristic
471	C₂×C₄⋊C₄	C₂×#121	1	1	yes	characteristic
472	C₂×C₄⋊C₄	C₂×#121	1	1	yes	characteristic
473	C₂×C₄⋊C₄	C₂³×D₄	1	1	yes	characteristic
474	C₂×C₂²⋊C₄	#392	1	1	yes	characteristic
475	C₂×C₂²⋊C₄	#392	1	1	yes	characteristic
476	C₂×C₂²⋊C₄	#392	1	1	yes	characteristic
477	C₂×C₂²⋊C₄	#392	1	1	yes	characteristic
478	C₂×C₂²⋊C₄	#392	1	1	yes	characteristic
479	C₂×C₂²⋊C₄	#392	1	1	yes	characteristic
480	C₂×C₂²⋊C₄	#392	1	1	yes	characteristic
481	C₂×C₂²⋊C₄	#392	1	1	yes	characteristic
482	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
483	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
484	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
485	C₂×C₂²⋊C₄	C₂×#121	1	1	yes	characteristic
486	C₂×C₂²⋊C₄	C₂×#121	1	1	yes	characteristic
487	C₂×C₂²⋊C₄	C₂×#121	1	1	yes	characteristic
488	C₂×C₂²⋊C₄	C₂×#121	1	1	yes	characteristic
489	C₂×C₂²⋊C₄	C₂×#121	1	1	yes	characteristic
490	C₂×C₂²⋊C₄	C₂×#121	1	1	yes	characteristic
491	C₂×C₂²⋊C₄	C₂×#121	1	1	yes	characteristic
492	C₂×C₂²⋊C₄	C₂×#121	1	1	yes	characteristic
493	C₂×C₂²⋊C₄	C₂×#127	1	1	yes	characteristic
494	C₂×C₂²⋊C₄	C₂×#127	1	1	yes	characteristic
495	C₂×C₂²⋊C₄	C₂×#127	1	1	yes	characteristic
496	C₂×C₂²⋊C₄	C₂³×D₄	1	1	yes	characteristic
497	C₂×C₂²⋊C₄	C₂²×#41	1	1	yes	characteristic
498	C₂×C₄²	#392	1	1	yes	characteristic
499	C₂×C₄²	#392	1	1	yes	characteristic
500	C₂×C₄²	#392	1	1	yes	characteristic
501	C₂×C₄²	#392	1	1	yes	characteristic
502	C₂×C₄²	#392	1	1	yes	characteristic
503	C₂×C₄²	#392	1	1	yes	characteristic
504	C₂×C₄²	#392	1	1	yes	characteristic
505	C₂×C₄²	#392	1	1	yes	characteristic
506	C₂×C₄²	#392	1	1	yes	characteristic
507	C₂×C₄²	#392	1	1	yes	characteristic
508	C₂×C₄²	#392	1	1	yes	characteristic
509	C₂×C₄²	#392	1	1	yes	characteristic
510	C₂×C₄²	#392	1	1	yes	characteristic
511	C₂×C₄²	#392	1	1	yes	characteristic
512	C₂×C₄²	#392	1	1	yes	characteristic
513	C₂×C₄²	#392	1	1	yes	characteristic
514	C₂×C₄²	#392	1	1	yes	characteristic
515	C₂×C₄²	#392	1	1	yes	characteristic
516	C₂×C₄²	B(4,𝔽₂)	1	1	yes	characteristic
517	C₂×C₄²	B(4,𝔽₂)	1	1	yes	characteristic
518	C₂×C₄²	B(4,𝔽₂)	1	1	yes	characteristic
519	C₂×C₄²	B(4,𝔽₂)	1	1	yes	characteristic
520	C₂×C₄²	B(4,𝔽₂)	1	1	yes	characteristic
521	C₂×C₄²	B(4,𝔽₂)	1	1	yes	characteristic
522	C₂×C₄²	B(4,𝔽₂)	1	1	yes	characteristic
523	C₂×C₄²	B(4,𝔽₂)	1	1	yes	characteristic
524	C₂×C₄²	C₂×#120	1	1	yes	characteristic
525	C₂×C₄²	C₂×#120	1	1	yes	characteristic
526	C₂×C₄²	C₂×#120	1	1	yes	characteristic
527	C₂×C₄²	C₂×#120	1	1	yes	characteristic
528	C₂×C₄²	C₂×#120	1	1	yes	characteristic
529	C₂×C₄²	C₂×#120	1	1	yes	characteristic
530	C₂×C₄²	C₂×#120	1	1	yes	characteristic
531	C₂×C₄²	C₂×#120	1	1	yes	characteristic
532	C₂×C₄²	C₂×#120	1	1	yes	characteristic
533	C₂×C₄²	C₂×#120	1	1	yes	characteristic
534	C₂×C₄²	C₂×#120	1	1	yes	characteristic
535	C₂×C₄²	C₂×#120	1	1	yes	characteristic
536	C₂×C₄²	C₂×#120	1	1	yes	characteristic
537	C₂×C₄²	C₂×#120	1	1	yes	characteristic
538	C₂×C₄²	C₂×#121	1	1	yes	characteristic
539	C₂×C₄²	C₂×#121	1	1	yes	characteristic
540	C₂×C₄²	C₂×#121	1	1	yes	characteristic
541	C₂×C₄²	C₂×#121	1	1	yes	characteristic
542	C₂×C₄²	C₂×#121	1	1	yes	characteristic
543	C₂×C₄²	C₂×#121	1	1	yes	characteristic
544	C₂×C₄²	C₂×#121	1	1	yes	characteristic
545	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
546	#100	C₂×AGL(1,ℤ/8)	1	16	yes	—
547	C₂⁴	#2008	1	4	yes	—
548	C₂⁴	C₂×#392	1	1	yes	characteristic
549	C₂⁴	C₂×#392	1	1	yes	characteristic
550	C₂⁴	C₂×#392	1	1	yes	characteristic
551	C₂⁴	C₂×#392	1	1	yes	characteristic
552	C₂⁴	C₂×#392	1	1	yes	characteristic
553	C₂⁴	#3038	1	4	yes	—
554	C₂⁴	#3151	1	4	yes	—
555	C₂⁴	C₂²×#121	1	1	yes	characteristic
556	C₂⁴	C₂²×#127	1	1	yes	characteristic
557	C₂×D₄	#3003	1	4	yes	—
558	C₂×D₄	#3038	1	4	yes	—
559	C₂×D₄	#3151	1	4	yes	—
560	C₂×D₄	C₂²×AGL(1,ℤ/8)	1	4	yes	—
561	C₂²×C₄	#2021	1	1	yes	characteristic
562	C₂²×C₄	#2021	1	1	yes	characteristic
563	C₂²×C₄	#2021	1	1	yes	characteristic
564	C₂²×C₄	#2021	1	1	yes	characteristic
565	C₂²×C₄	#2021	1	1	yes	characteristic
566	C₂²×C₄	#2021	1	1	yes	characteristic
567	C₂²×C₄	#2021	1	1	yes	characteristic
568	C₂²×C₄	#2021	1	1	yes	characteristic
569	C₂²×C₄	C₂×#392	1	1	yes	characteristic
570	C₂²×C₄	C₂×#392	1	1	yes	characteristic
571	C₂²×C₄	C₂×#392	1	1	yes	characteristic
572	C₂²×C₄	C₂×#392	1	1	yes	characteristic
573	C₂²×C₄	C₂×#392	1	1	yes	characteristic
574	C₂²×C₄	C₂×#392	1	1	yes	characteristic
575	C₂²×C₄	C₂×#392	1	1	yes	characteristic
576	C₂²×C₄	C₂×#392	1	1	yes	characteristic
577	C₂²×C₄	C₂×#392	1	1	yes	characteristic
578	C₂²×C₄	C₂×#392	1	1	yes	characteristic
579	C₂²×C₄	C₂×#392	1	1	yes	characteristic
580	C₂²×C₄	C₂×#392	1	1	yes	characteristic
581	C₂²×C₄	C₂×#392	1	1	yes	characteristic
582	C₂²×C₄	C₂×#392	1	1	yes	characteristic
583	C₂²×C₄	C₂×#392	1	1	yes	characteristic
584	C₂²×C₄	C₂×#392	1	1	yes	characteristic
585	C₂²×C₄	C₂×#392	1	1	yes	characteristic
586	C₂²×C₄	C₂×#392	1	1	yes	characteristic
587	C₂²×C₄	C₂×#392	1	1	yes	characteristic
588	C₂²×C₄	#3003	1	4	yes	—
589	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
590	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
591	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
592	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
593	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
594	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
595	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
596	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
597	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
598	C₄²	#2021	1	1	yes	characteristic
599	C₄²	#2021	1	1	yes	characteristic
600	C₄²	#2021	1	1	yes	characteristic
601	C₄²	#2021	1	1	yes	characteristic
602	C₄²	#2021	1	1	yes	characteristic
603	C₄²	#2021	1	1	yes	characteristic
604	C₄²	#2021	1	1	yes	characteristic
605	C₄²	#2021	1	1	yes	characteristic
606	C₄²	C₂×B(4,𝔽₂)	1	1	yes	characteristic
607	C₄²	C₂×B(4,𝔽₂)	1	1	yes	characteristic
608	C₄²	C₂×B(4,𝔽₂)	1	1	yes	characteristic
609	C₄²	C₂×B(4,𝔽₂)	1	1	yes	characteristic
610	C₄²	C₂×B(4,𝔽₂)	1	1	yes	characteristic
611	C₄²	C₂×B(4,𝔽₂)	1	1	yes	characteristic
612	C₄²	C₂×B(4,𝔽₂)	1	1	yes	characteristic
613	C₄²	C₂×B(4,𝔽₂)	1	1	yes	characteristic
614	C₂³	C₂×#2008	1	2	yes	—
615	C₂³	C₂×#2008	1	2	yes	—
616	C₂³	C₂×#2008	1	2	yes	—
617	C₂³	#23430	1	2	yes	—
618	C₂³	#23430	1	2	yes	—
619	C₂³	#23430	1	2	yes	—
620	C₂³	C₂×#2021	1	1	yes	characteristic
621	C₂³	C₂×#2021	1	1	yes	characteristic
622	C₂³	C₂²×#392	1	1	yes	characteristic
623	C₂³	C₂×#3038	1	2	yes	—
624	C₂³	C₂×#3151	1	2	yes	—
625	C₂×C₄	#23430	1	2	yes	—
626	C₂×C₄	C₂×#2021	1	1	yes	characteristic
627	C₂×C₄	C₂×#2021	1	1	yes	characteristic
628	C₂×C₄	C₂×#2021	1	1	yes	characteristic
629	C₂×C₄	C₂×#2021	1	1	yes	characteristic
630	C₂×C₄	C₂×#2021	1	1	yes	characteristic
631	C₂×C₄	C₂×#2021	1	1	yes	characteristic
632	C₂×C₄	C₂×#2021	1	1	yes	characteristic
633	C₂×C₄	C₂×#2021	1	1	yes	characteristic
634	C₂×C₄	C₂×#2021	1	1	yes	characteristic
635	C₂×C₄	C₂×#2021	1	1	yes	characteristic
636	C₂×C₄	C₂×#3003	1	2	yes	—
637	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
638	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
639	C₂²	#235099	1	2	yes	—
640	C₂²	#235099	1	2	yes	—
641	C₂²	C₂²×#2008	1	1	yes	characteristic
642	C₂²	C₂×#23430	1	1	yes	characteristic
643	C₂²	C₂²×#2021	1	1	yes	characteristic
644	C₄	#498916	1	2	yes	—
645	C₄	#7622868	1	2	yes	—
646	C₂	C₂×#235099	1	1	yes	characteristic
647	C₂	#72256636	1	1	yes	characteristic
648	C₂	C₂×#498916	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂²×#2021
commutator, Frattini, cosocle	C₂×C₄×D₄	C₂⁵
LCS	G ▷ C₂×C₄×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄² ◁ C₂²×C₄×#41 ◁ G
LECS	G ▷ C₂×C₄×D₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72313906	C₂	semidirect
2. #72313847	C₂	semidirect
3. #72313565	C₂	semidirect
4. #72313477	C₂	semidirect
5. #72313437	C₂	semidirect
6. #72313372	C₂	semidirect
7. C₂×#495580	C₂	semidirect
8. #72311821	C₂	semidirect
9. #72311799	C₂	semidirect
10. #72306049	C₂	semidirect
11. #72285068	C₂	semidirect
12. C₂×#6346637	C₂	semidirect
16. #7512477	C₂²	semidirect
17. #6657540	C₂²	semidirect
18. #6653018	C₂²	semidirect
19. #6640543	C₂²	semidirect
20. #6632008	C₂²	semidirect
21. #6443331	C₂²	semidirect
22. #6443330	C₂²	semidirect
24. #6443327	C₂²	semidirect
29. #6346637	C₂²	semidirect
30. C₂×#18203	C₂²	semidirect
31. C₂×#18194	C₂²	semidirect
33. #495580	C₂²	semidirect
34. #495580	C₂²	semidirect
35. C₂×#13292	C₂²	semidirect
36. C₂×#13218	C₂²	semidirect
37. #482368	C₂²	semidirect
38. #482364	C₂²	semidirect
39. #482363	C₂²	semidirect
40. #482050	C₂²	semidirect
41. #185348	C₂²	semidirect
42. #185340	C₂²	semidirect
43. #185331	C₂²	semidirect
44. #142735	C₂²	semidirect
45. #142734	C₂²	semidirect
46. #142605	C₂²	semidirect
47. #142604	C₂²	semidirect
48. #127138	C₂²	semidirect
49. #127136	C₂²	semidirect
50. #127067	C₂²	semidirect
82. #32260	C₂³	semidirect
83. #32028	C₂³	semidirect
84. #31260	C₂³	semidirect
85. #30499	C₂³	semidirect
112. #13292	C₂³	semidirect
113. #13218	C₂³	semidirect
114. #11878	C₂³	semidirect
115. #11877	C₂³	semidirect
117. #7203	C₂³	semidirect

Maximal subgroups

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

subgroup	index
#72313906	2
#72313847	2
#72313565	2
#72313477	2
#72313437	2
#72313372	2
C₂×#495580	2
#72311821	2
#72311799	2
#72306049	2
#72285068	2
C₂×#6346637	2