Subgroups — #72341588

Order 2048.

Only the 830 normal subgroups are shown; non-normal subgroups are omitted.

The subgroup lattice has 558 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72340216	C₂	1	1	yes	maximal, characteristic, complemented
2	#72311172	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#128079	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#128062	C₂	1	1	yes	maximal, characteristic, complemented
5	#72303055	C₂	1	4	yes	maximal, complemented
6	C₂×#392138	C₂	1	1	yes	maximal, characteristic, complemented
7	#72240597	C₂	1	1	yes	maximal, characteristic
8	C₂×#392135	C₂	1	1	yes	maximal, characteristic, complemented
9	#72238013	C₂	1	4	yes	maximal, complemented
10	C₂²×H(7,𝔽₂)	C₂²	1	1	yes	characteristic
11	C₂²×#3026	C₄	1	2	yes	complemented
12	#7630442	C₂²	1	1	yes	characteristic
13	#6628897	C₄	1	2	yes	complemented
14	#6628897	C₂²	1	2	yes	—
15	#6628896	C₄	1	2	yes	complemented
16	#6628896	C₂²	1	2	yes	—
17	C₂×#20609	C₄	1	2	yes	complemented
18	C₂×#20592	C₂²	1	1	yes	characteristic
19	C₂×#20586	C₂²	1	1	yes	characteristic
20	C₂×#20585	C₂²	1	1	yes	characteristic
21	C₂×#20585	C₂²	1	1	yes	characteristic
22	C₂×#20585	C₂²	1	1	yes	characteristic
23	#496241	C₂²	1	2	yes	complemented
24	#496240	C₂²	1	2	yes	complemented
25	#392138	C₂²	1	4	yes	—
26	#392135	C₂²	1	4	yes	—
27	#213855	C₂²	1	2	yes	complemented
28	#213854	C₂²	1	2	yes	complemented
29	#128079	C₂²	1	4	yes	complemented
30	#128062	C₂²	1	4	yes	complemented
31	C₂×H(7,𝔽₂)	C₂×C₄	1	2	yes	—
32	C₂×H(7,𝔽₂)	D₄	1	2	yes	—
33	C₂×H(7,𝔽₂)	D₄	1	2	yes	—
34	C₂×H(7,𝔽₂)	C₂³	1	2	yes	—
35	C₂²×#585	D₄	1	2	yes	—
36	C₂³×H(5,𝔽₂)	C₂×C₄	1	2	yes	—
37	C₂³×H(5,𝔽₂)	D₄	1	2	yes	—
38	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
39	C₂²×#534	C₂×C₄	1	1	yes	characteristic
40	C₂²×#534	D₄	1	1	yes	characteristic
41	C₂²×#534	D₄	1	1	yes	characteristic
42	C₂²×#458	C₂×C₄	1	4	yes	complemented
43	C₂²×B(4,𝔽₂)	C₂×C₄	1	4	yes	complemented
44	C₂²×#413	D₄	1	2	yes	complemented
45	C₂³×#99	C₂×C₄	1	2	yes	—
46	C₂³×#99	D₄	1	2	yes	complemented
47	#35446	C₂×C₄	1	1	yes	characteristic
48	#35446	D₄	1	1	yes	characteristic
49	#35446	D₄	1	1	yes	characteristic
50	#35446	C₂³	1	1	yes	characteristic
51	#35346	C₂×C₄	1	1	yes	characteristic
52	#35346	D₄	1	1	yes	characteristic
53	#35346	D₄	1	1	yes	characteristic
54	#35346	C₂³	1	1	yes	characteristic
55	C₂×#2309	D₄	1	2	yes	complemented
56	C₂×#2308	C₂×C₄	1	1	yes	characteristic
57	C₂×#2308	D₄	1	1	yes	characteristic
58	C₂×#2308	D₄	1	1	yes	characteristic
59	C₂×#2308	D₄	1	2	yes	complemented
60	#20609	C₂×C₄	1	4	yes	complemented
61	#20609	C₂×C₄	1	4	yes	complemented
62	#20592	D₄	1	2	yes	complemented
63	#20592	C₂³	1	2	yes	—
64	#20586	D₄	1	2	yes	complemented
65	#20586	C₂³	1	2	yes	—
66	#20585	C₂×C₄	1	2	yes	—
67	#20585	D₄	1	2	yes	—
68	#20585	D₄	1	2	yes	—
69	#20585	D₄	1	2	yes	complemented
70	#20585	D₄	1	2	yes	complemented
71	#20585	C₂³	1	2	yes	—
72	#20585	C₂³	1	2	yes	—
73	#20585	C₂³	1	2	yes	—
74	C₂×#1782	D₄	1	2	yes	—
75	C₂×#1781	D₄	1	2	yes	—
76	C₂×#585	C₂²⋊C₄	1	4	yes	—
77	C₂×#585	C₂×D₄	1	4	yes	—
78	C₂²×H(5,𝔽₂)	C₂²⋊C₄	1	4	yes	—
79	C₂²×H(5,𝔽₂)	C₂²⋊C₄	1	4	yes	—
80	C₂²×H(5,𝔽₂)	C₂²⋊C₄	1	4	yes	—
81	C₂²×H(5,𝔽₂)	C₂²×C₄	1	1	yes	characteristic
82	C₂²×H(5,𝔽₂)	C₂²×C₄	1	4	yes	—
83	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
84	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
85	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
86	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
87	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
88	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
89	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
90	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
91	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
92	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
93	C₂²×H(5,𝔽₂)	C₂×D₄	1	4	yes	—
94	C₂²×H(5,𝔽₂)	#41	1	1	yes	characteristic
95	C₂²×H(5,𝔽₂)	#41	1	1	yes	characteristic
96	C₂²×H(5,𝔽₂)	#41	1	1	yes	characteristic
97	C₂²×H(5,𝔽₂)	#41	1	1	yes	characteristic
98	C₂²×H(5,𝔽₂)	C₂⁴	1	1	yes	characteristic
99	C₂³×#41	C₂×D₄	1	1	yes	characteristic
100	C₂³×#41	C₂×D₄	1	1	yes	characteristic
101	C₂³×#41	C₂×D₄	1	1	yes	characteristic
102	C₂³×#41	#41	1	1	yes	characteristic
103	C₂³×#41	#41	1	1	yes	characteristic
104	C₂³×#41	#41	1	1	yes	characteristic
105	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
106	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
107	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
108	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
109	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
110	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
111	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
112	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
113	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
114	C₂⁴×D₄	#41	1	1	yes	characteristic
115	C₂²×#123	C₂²⋊C₄	1	1	yes	characteristic, complemented
116	C₂²×#123	C₂²⋊C₄	1	1	yes	characteristic, complemented
117	C₂²×#123	C₂²⋊C₄	1	1	yes	characteristic, complemented
118	C₂²×#123	C₂²×C₄	1	1	yes	characteristic
119	C₂²×#123	C₂×D₄	1	1	yes	characteristic
120	C₂²×#123	C₂×D₄	1	1	yes	characteristic
121	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic, complemented
122	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic, complemented
123	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic, complemented
124	C₂²×#120	C₂²×C₄	1	1	yes	characteristic
125	C₂²×#120	C₂×D₄	1	1	yes	characteristic
126	C₂²×#120	C₂×D₄	1	1	yes	characteristic
127	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
128	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
129	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
130	C₂×#413	C₂×D₄	1	4	yes	—
131	C₂²×#99	C₂²⋊C₄	1	4	yes	complemented
132	C₂²×#99	C₂²⋊C₄	1	4	yes	complemented
133	C₂²×#99	C₂²×C₄	1	4	yes	—
134	C₂²×#99	C₂×D₄	1	4	yes	—
135	#2309	C₂×D₄	1	4	yes	—
136	#2308	C₂²⋊C₄	1	1	yes	characteristic, complemented
137	#2308	C₂²⋊C₄	1	1	yes	characteristic, complemented
138	#2308	C₂²⋊C₄	1	1	yes	characteristic, complemented
139	#2308	C₂²⋊C₄	1	1	yes	characteristic, complemented
140	#2308	C₂²⋊C₄	1	1	yes	characteristic, complemented
141	#2308	C₂²⋊C₄	1	1	yes	characteristic, complemented
142	#2308	C₂²×C₄	1	1	yes	characteristic
143	#2308	C₂²×C₄	1	1	yes	characteristic
144	#2308	C₂×D₄	1	1	yes	characteristic
145	#2308	C₂×D₄	1	1	yes	characteristic
146	#2308	C₂×D₄	1	1	yes	characteristic
147	#2308	C₂×D₄	1	1	yes	characteristic
148	#2308	C₂×D₄	1	4	yes	—
149	#1782	C₂²⋊C₄	1	4	yes	complemented
150	#1782	C₂×D₄	1	4	yes	—
151	#1781	C₂²⋊C₄	1	4	yes	complemented
152	#1781	C₂×D₄	1	4	yes	—
153	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
154	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented
155	C₂⁶	C₄×D₄	1	1	yes	characteristic
156	C₂⁶	#120	1	1	yes	characteristic
157	C₂⁶	#120	1	1	yes	characteristic
158	C₂⁶	#120	1	1	yes	characteristic
159	C₂⁶	#121	1	1	yes	characteristic
160	C₂×H(5,𝔽₂)	#99	1	16	yes	complemented
161	C₂×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	8	yes	—
162	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
163	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
164	C₂²×#41	C₄×D₄	1	1	yes	characteristic
165	C₂²×#41	C₄×D₄	1	1	yes	characteristic
166	C₂²×#41	C₄×D₄	1	1	yes	characteristic
167	C₂²×#41	C₄×D₄	1	1	yes	characteristic
168	C₂²×#41	#120	1	1	yes	characteristic
169	C₂²×#41	#120	1	1	yes	characteristic
170	C₂²×#41	#120	1	1	yes	characteristic
171	C₂²×#41	#120	1	1	yes	characteristic
172	C₂²×#41	#120	1	1	yes	characteristic
173	C₂²×#41	#120	1	1	yes	characteristic
174	C₂²×#41	#120	1	1	yes	characteristic
175	C₂²×#41	#121	1	1	yes	characteristic
176	C₂²×#41	#121	1	1	yes	characteristic
177	C₂²×#41	#121	1	1	yes	characteristic
178	C₂²×#41	#121	1	1	yes	characteristic
179	C₂²×#41	#121	1	1	yes	characteristic
180	C₂²×#41	#121	1	1	yes	characteristic
181	C₂²×#41	#121	1	1	yes	characteristic
182	C₂²×#41	#121	1	1	yes	characteristic
183	C₂²×#41	#121	1	1	yes	characteristic
184	C₂²×#41	#121	1	1	yes	characteristic
185	C₂²×#41	#121	1	1	yes	characteristic
186	C₂²×#41	#121	1	1	yes	characteristic
187	C₂²×#41	#121	1	1	yes	characteristic
188	C₂²×#41	#121	1	1	yes	characteristic
189	C₂²×#41	#121	1	1	yes	characteristic
190	C₂²×#41	#121	1	1	yes	characteristic
191	C₂²×#41	#123	1	1	yes	characteristic
192	C₂²×#41	#123	1	1	yes	characteristic
193	C₂²×#41	#123	1	1	yes	characteristic
194	C₂²×#41	#123	1	1	yes	characteristic
195	C₂²×#41	#123	1	1	yes	characteristic
196	C₂²×#41	#123	1	1	yes	characteristic
197	C₂²×#41	#123	1	1	yes	characteristic
198	C₂²×#41	#124	1	1	yes	characteristic
199	C₂²×#41	#124	1	1	yes	characteristic
200	C₂²×#41	#124	1	1	yes	characteristic
201	C₂²×#41	#124	1	1	yes	characteristic
202	C₂²×#41	#127	1	1	yes	characteristic
203	C₂²×#41	#127	1	1	yes	characteristic
204	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
205	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
206	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
207	C₂²×#41	C₂×#41	1	1	yes	characteristic
208	C₂²×#41	C₂×#41	1	1	yes	characteristic
209	C₂²×#41	C₂×#41	1	1	yes	characteristic
210	C₂³×Q₈	#121	1	1	yes	characteristic
211	C₂³×Q₈	#123	1	1	yes	characteristic
212	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
213	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
214	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
215	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
216	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
217	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
218	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
219	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
220	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
221	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
222	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
223	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
224	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
225	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
226	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
227	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
228	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
229	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
230	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
231	C₂³×D₄	#120	1	1	yes	characteristic
232	C₂³×D₄	#120	1	1	yes	characteristic
233	C₂³×D₄	#120	1	1	yes	characteristic
234	C₂³×D₄	#120	1	1	yes	characteristic
235	C₂³×D₄	#120	1	1	yes	characteristic
236	C₂³×D₄	#120	1	1	yes	characteristic
237	C₂³×D₄	#120	1	1	yes	characteristic
238	C₂³×D₄	#120	1	1	yes	characteristic
239	C₂³×D₄	#120	1	1	yes	characteristic
240	C₂³×D₄	#120	1	1	yes	characteristic
241	C₂³×D₄	#120	1	1	yes	characteristic
242	C₂³×D₄	#120	1	1	yes	characteristic
243	C₂³×D₄	#120	1	1	yes	characteristic
244	C₂³×D₄	#120	1	1	yes	characteristic
245	C₂³×D₄	#120	1	1	yes	characteristic
246	C₂³×D₄	#120	1	1	yes	characteristic
247	C₂³×D₄	#120	1	1	yes	characteristic
248	C₂³×D₄	#120	1	1	yes	characteristic
249	C₂³×D₄	#120	1	1	yes	characteristic
250	C₂³×D₄	#120	1	1	yes	characteristic
251	C₂³×D₄	#121	1	1	yes	characteristic
252	C₂³×D₄	#121	1	1	yes	characteristic
253	C₂³×D₄	#121	1	1	yes	characteristic
254	C₂³×D₄	#121	1	1	yes	characteristic
255	C₂³×D₄	#121	1	1	yes	characteristic
256	C₂³×D₄	#121	1	1	yes	characteristic
257	C₂³×D₄	#121	1	1	yes	characteristic
258	C₂³×D₄	#121	1	1	yes	characteristic
259	C₂³×D₄	#121	1	1	yes	characteristic
260	C₂³×D₄	#121	1	1	yes	characteristic
261	C₂³×D₄	#121	1	1	yes	characteristic
262	C₂³×D₄	#121	1	1	yes	characteristic
263	C₂³×D₄	#121	1	1	yes	characteristic
264	C₂³×D₄	#121	1	1	yes	characteristic
265	C₂³×D₄	#121	1	1	yes	characteristic
266	C₂³×D₄	#121	1	1	yes	characteristic
267	C₂³×D₄	#121	1	1	yes	characteristic
268	C₂³×D₄	#121	1	1	yes	characteristic
269	C₂³×D₄	#121	1	1	yes	characteristic
270	C₂³×D₄	#121	1	1	yes	characteristic
271	C₂³×D₄	#121	1	1	yes	characteristic
272	C₂³×D₄	#121	1	1	yes	characteristic
273	C₂³×D₄	#121	1	1	yes	characteristic
274	C₂³×D₄	#121	1	1	yes	characteristic
275	C₂³×D₄	#121	1	1	yes	characteristic
276	C₂³×D₄	#121	1	1	yes	characteristic
277	C₂³×D₄	#121	1	1	yes	characteristic
278	C₂³×D₄	#123	1	1	yes	characteristic
279	C₂³×D₄	#123	1	1	yes	characteristic
280	C₂³×D₄	#123	1	1	yes	characteristic
281	C₂³×D₄	#123	1	1	yes	characteristic
282	C₂³×D₄	#123	1	1	yes	characteristic
283	C₂³×D₄	#123	1	1	yes	characteristic
284	C₂³×D₄	#123	1	1	yes	characteristic
285	C₂³×D₄	#124	1	1	yes	characteristic
286	C₂³×D₄	#124	1	1	yes	characteristic
287	C₂³×D₄	#127	1	1	yes	characteristic
288	C₂³×D₄	#127	1	1	yes	characteristic
289	C₂³×D₄	#127	1	1	yes	characteristic
290	C₂³×D₄	#127	1	1	yes	characteristic
291	C₂³×D₄	#127	1	1	yes	characteristic
292	C₂³×D₄	#127	1	1	yes	characteristic
293	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
294	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
295	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
296	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
297	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
298	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
299	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
300	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
301	C₂³×D₄	C₂×#41	1	1	yes	characteristic
302	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented
303	C₂⁴×C₄	C₄×D₄	1	1	yes	characteristic
304	C₂⁴×C₄	#120	1	1	yes	characteristic
305	C₂⁴×C₄	#120	1	1	yes	characteristic
306	C₂⁴×C₄	#121	1	1	yes	characteristic
307	C₂⁴×C₄	#121	1	1	yes	characteristic
308	C₂⁴×C₄	#121	1	1	yes	characteristic
309	C₂⁴×C₄	#123	1	1	yes	characteristic
310	C₂⁴×C₄	#124	1	1	yes	characteristic
311	C₂⁴×C₄	#124	1	1	yes	characteristic
312	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented
313	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented
314	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented
315	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented
316	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented
317	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented
318	C₂×#99	C₂×C₂²⋊C₄	1	8	yes	complemented
319	C₂⁵	#379	1	1	yes	characteristic
320	C₂⁵	#379	1	1	yes	characteristic
321	C₂⁵	#379	1	1	yes	characteristic
322	C₂⁵	#386	1	1	yes	characteristic
323	C₂⁵	#386	1	1	yes	characteristic
324	C₂⁵	#386	1	1	yes	characteristic
325	C₂⁵	#386	1	1	yes	characteristic
326	C₂⁵	#386	1	1	yes	characteristic
327	C₂⁵	#386	1	1	yes	characteristic
328	C₂⁵	#386	1	1	yes	characteristic
329	C₂⁵	#386	1	1	yes	characteristic
330	C₂⁵	#386	1	1	yes	characteristic
331	C₂⁵	#390	1	1	yes	characteristic
332	C₂⁵	#390	1	1	yes	characteristic
333	C₂⁵	#390	1	1	yes	characteristic
334	C₂⁵	#392	1	1	yes	characteristic
335	C₂⁵	#392	1	1	yes	characteristic
336	C₂⁵	#392	1	1	yes	characteristic
337	C₂⁵	#392	1	1	yes	characteristic
338	C₂⁵	#392	1	1	yes	characteristic
339	C₂⁵	#392	1	1	yes	characteristic
340	C₂⁵	#392	1	1	yes	characteristic
341	C₂⁵	#392	1	1	yes	characteristic
342	C₂⁵	#392	1	1	yes	characteristic
343	C₂⁵	#394	1	1	yes	characteristic
344	C₂⁵	#394	1	1	yes	characteristic
345	C₂⁵	#394	1	1	yes	characteristic
346	C₂⁵	B(4,𝔽₂)	1	8	yes	—
347	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
348	C₂⁵	C₂×C₄×D₄	1	1	yes	characteristic
349	C₂⁵	C₂×#120	1	1	yes	characteristic
350	C₂⁵	C₂×#120	1	1	yes	characteristic
351	C₂⁵	C₂×#120	1	1	yes	characteristic
352	C₂⁵	C₂×#121	1	1	yes	characteristic
353	H(5,𝔽₂)	C₂×#99	1	16	yes	—
354	C₂²×Q₈	#386	1	1	yes	characteristic
355	C₂²×Q₈	#390	1	1	yes	characteristic
356	C₂²×Q₈	#392	1	1	yes	characteristic
357	C₂²×Q₈	#394	1	1	yes	characteristic
358	C₂²×Q₈	#394	1	1	yes	characteristic
359	C₂²×Q₈	#394	1	1	yes	characteristic
360	C₂²×Q₈	C₂×#121	1	1	yes	characteristic
361	C₂²×Q₈	C₂×#123	1	1	yes	characteristic
362	C₂²×D₄	#379	1	1	yes	characteristic
363	C₂²×D₄	#379	1	1	yes	characteristic
364	C₂²×D₄	#379	1	1	yes	characteristic
365	C₂²×D₄	#379	1	1	yes	characteristic
366	C₂²×D₄	#386	1	1	yes	characteristic
367	C₂²×D₄	#386	1	1	yes	characteristic
368	C₂²×D₄	#386	1	1	yes	characteristic
369	C₂²×D₄	#386	1	1	yes	characteristic
370	C₂²×D₄	#386	1	1	yes	characteristic
371	C₂²×D₄	#386	1	1	yes	characteristic
372	C₂²×D₄	#386	1	1	yes	characteristic
373	C₂²×D₄	#386	1	1	yes	characteristic
374	C₂²×D₄	#386	1	1	yes	characteristic
375	C₂²×D₄	#386	1	1	yes	characteristic
376	C₂²×D₄	#386	1	1	yes	characteristic
377	C₂²×D₄	#386	1	1	yes	characteristic
378	C₂²×D₄	#386	1	1	yes	characteristic
379	C₂²×D₄	#386	1	1	yes	characteristic
380	C₂²×D₄	#386	1	1	yes	characteristic
381	C₂²×D₄	#390	1	1	yes	characteristic
382	C₂²×D₄	#390	1	1	yes	characteristic
383	C₂²×D₄	#390	1	1	yes	characteristic
384	C₂²×D₄	#390	1	1	yes	characteristic
385	C₂²×D₄	#390	1	1	yes	characteristic
386	C₂²×D₄	#390	1	1	yes	characteristic
387	C₂²×D₄	#390	1	1	yes	characteristic
388	C₂²×D₄	#392	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	#392	1	1	yes	characteristic
394	C₂²×D₄	#392	1	1	yes	characteristic
395	C₂²×D₄	#392	1	1	yes	characteristic
396	C₂²×D₄	#392	1	1	yes	characteristic
397	C₂²×D₄	#392	1	1	yes	characteristic
398	C₂²×D₄	#392	1	1	yes	characteristic
399	C₂²×D₄	#392	1	1	yes	characteristic
400	C₂²×D₄	#392	1	1	yes	characteristic
401	C₂²×D₄	#392	1	1	yes	characteristic
402	C₂²×D₄	#392	1	1	yes	characteristic
403	C₂²×D₄	#394	1	1	yes	characteristic
404	C₂²×D₄	#394	1	1	yes	characteristic
405	C₂²×D₄	#394	1	1	yes	characteristic
406	C₂²×D₄	#394	1	1	yes	characteristic
407	C₂²×D₄	#394	1	1	yes	characteristic
408	C₂²×D₄	#394	1	1	yes	characteristic
409	C₂²×D₄	#394	1	1	yes	characteristic
410	C₂²×D₄	#394	1	1	yes	characteristic
411	C₂²×D₄	#394	1	1	yes	characteristic
412	C₂²×D₄	#394	1	1	yes	characteristic
413	C₂²×D₄	#394	1	1	yes	characteristic
414	C₂²×D₄	#394	1	1	yes	characteristic
415	C₂²×D₄	#394	1	1	yes	characteristic
416	C₂²×D₄	C₂×#99	1	8	yes	—
417	C₂²×D₄	B(4,𝔽₂)	1	8	yes	—
418	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
419	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
420	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
421	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
422	C₂²×D₄	C₂×#120	1	1	yes	characteristic
423	C₂²×D₄	C₂×#120	1	1	yes	characteristic
424	C₂²×D₄	C₂×#120	1	1	yes	characteristic
425	C₂²×D₄	C₂×#121	1	1	yes	characteristic
426	C₂²×D₄	C₂×#121	1	1	yes	characteristic
427	C₂²×D₄	C₂×#121	1	1	yes	characteristic
428	C₂²×D₄	C₂×#121	1	1	yes	characteristic
429	C₂²×D₄	C₂×#121	1	1	yes	characteristic
430	C₂²×D₄	C₂×#121	1	1	yes	characteristic
431	C₂²×D₄	C₂×#121	1	1	yes	characteristic
432	C₂²×D₄	C₂×#123	1	1	yes	characteristic
433	C₂²×D₄	C₂×#123	1	1	yes	characteristic
434	C₂²×D₄	C₂×#127	1	1	yes	characteristic
435	C₂²×D₄	C₂×#127	1	1	yes	characteristic
436	C₂³×C₄	#379	1	1	yes	characteristic
437	C₂³×C₄	#386	1	1	yes	characteristic
438	C₂³×C₄	#386	1	1	yes	characteristic
439	C₂³×C₄	#386	1	1	yes	characteristic
440	C₂³×C₄	#386	1	1	yes	characteristic
441	C₂³×C₄	#386	1	1	yes	characteristic
442	C₂³×C₄	#386	1	1	yes	characteristic
443	C₂³×C₄	#386	1	1	yes	characteristic
444	C₂³×C₄	#390	1	1	yes	characteristic
445	C₂³×C₄	#390	1	1	yes	characteristic
446	C₂³×C₄	#390	1	1	yes	characteristic
447	C₂³×C₄	#390	1	1	yes	characteristic
448	C₂³×C₄	#390	1	1	yes	characteristic
449	C₂³×C₄	#392	1	1	yes	characteristic
450	C₂³×C₄	#392	1	1	yes	characteristic
451	C₂³×C₄	#392	1	1	yes	characteristic
452	C₂³×C₄	#392	1	1	yes	characteristic
453	C₂³×C₄	#392	1	1	yes	characteristic
454	C₂³×C₄	#392	1	1	yes	characteristic
455	C₂³×C₄	#392	1	1	yes	characteristic
456	C₂³×C₄	#394	1	1	yes	characteristic
457	C₂³×C₄	#394	1	1	yes	characteristic
458	C₂³×C₄	#394	1	1	yes	characteristic
459	C₂³×C₄	#394	1	1	yes	characteristic
460	C₂³×C₄	#394	1	1	yes	characteristic
461	C₂³×C₄	#394	1	1	yes	characteristic
462	C₂³×C₄	#394	1	1	yes	characteristic
463	C₂³×C₄	#394	1	1	yes	characteristic
464	C₂³×C₄	#394	1	1	yes	characteristic
465	C₂³×C₄	#394	1	1	yes	characteristic
466	C₂³×C₄	#394	1	1	yes	characteristic
467	C₂³×C₄	#394	1	1	yes	characteristic
468	C₂³×C₄	#394	1	1	yes	characteristic
469	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
470	C₂³×C₄	C₂×#120	1	1	yes	characteristic
471	C₂³×C₄	C₂×#120	1	1	yes	characteristic
472	C₂³×C₄	C₂×#121	1	1	yes	characteristic
473	C₂³×C₄	C₂×#121	1	1	yes	characteristic
474	C₂³×C₄	C₂×#121	1	1	yes	characteristic
475	C₂³×C₄	C₂×#123	1	1	yes	characteristic
476	C₂³×C₄	C₂×#124	1	1	yes	characteristic
477	C₂³×C₄	C₂×#124	1	1	yes	characteristic
478	C₂⁴	#1438	1	1	yes	characteristic
479	C₂⁴	#1438	1	1	yes	characteristic
480	C₂⁴	#1438	1	1	yes	characteristic
481	C₂⁴	#1438	1	1	yes	characteristic
482	C₂⁴	#1438	1	1	yes	characteristic
483	C₂⁴	#1438	1	1	yes	characteristic
484	C₂⁴	#1438	1	1	yes	characteristic
485	C₂⁴	#1438	1	1	yes	characteristic
486	C₂⁴	#1438	1	1	yes	characteristic
487	C₂⁴	#1438	1	1	yes	characteristic
488	C₂⁴	#1781	1	4	yes	—
489	C₂⁴	#1889	1	4	yes	—
490	C₂⁴	#1889	1	4	yes	—
491	C₂⁴	#1889	1	4	yes	—
492	C₂⁴	#1898	1	4	yes	—
493	C₂⁴	#2021	1	4	yes	—
494	C₂⁴	#2021	1	4	yes	—
495	C₂⁴	#2021	1	4	yes	—
496	C₂⁴	#2021	1	4	yes	—
497	C₂⁴	#2021	1	4	yes	—
498	C₂⁴	C₂×#379	1	1	yes	characteristic
499	C₂⁴	C₂×#386	1	1	yes	characteristic
500	C₂⁴	C₂×#386	1	1	yes	characteristic
501	C₂⁴	C₂×#386	1	1	yes	characteristic
502	C₂⁴	C₂×#390	1	1	yes	characteristic
503	C₂⁴	C₂×#392	1	1	yes	characteristic
504	C₂⁴	C₂×#392	1	1	yes	characteristic
505	C₂⁴	C₂×#392	1	1	yes	characteristic
506	C₂⁴	C₂×#394	1	1	yes	characteristic
507	C₂⁴	C₂×B(4,𝔽₂)	1	4	yes	—
508	C₂×D₄	#1781	1	4	yes	—
509	C₂×D₄	#1889	1	4	yes	—
510	C₂×D₄	#1898	1	4	yes	—
511	C₂×D₄	#1898	1	4	yes	—
512	C₂×D₄	#2021	1	4	yes	—
513	C₂×D₄	#2021	1	4	yes	—
514	C₂×D₄	C₂²×#99	1	4	yes	—
515	C₂×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
516	C₂²×C₄	#1438	1	1	yes	characteristic
517	C₂²×C₄	#1438	1	1	yes	characteristic
518	C₂²×C₄	#1438	1	1	yes	characteristic
519	C₂²×C₄	#1438	1	1	yes	characteristic
520	C₂²×C₄	#1438	1	1	yes	characteristic
521	C₂²×C₄	#1438	1	1	yes	characteristic
522	C₂²×C₄	#1898	1	4	yes	—
523	C₂²×C₄	#2021	1	4	yes	—
524	C₂²×C₄	C₂×#386	1	1	yes	characteristic
525	C₂²×C₄	C₂×#390	1	1	yes	characteristic
526	C₂²×C₄	C₂×#392	1	1	yes	characteristic
527	C₂²×C₄	C₂×#394	1	1	yes	characteristic
528	C₂²×C₄	C₂×#394	1	1	yes	characteristic
529	C₂²×C₄	C₂×#394	1	1	yes	characteristic
530	C₂³	#10965	1	2	yes	—
531	C₂³	#10965	1	2	yes	—
532	C₂³	#10965	1	2	yes	—
533	C₂³	#10991	1	2	yes	—
534	C₂³	#10991	1	2	yes	—
535	C₂³	#10991	1	2	yes	—
536	C₂³	#10991	1	2	yes	—
537	C₂³	#10991	1	2	yes	—
538	C₂³	#10991	1	2	yes	—
539	C₂³	#10991	1	2	yes	—
540	C₂³	C₂×#1438	1	1	yes	characteristic
541	C₂³	C₂×#1781	1	2	yes	—
542	C₂³	C₂×#1889	1	2	yes	—
543	C₂³	C₂×#1889	1	2	yes	—
544	C₂³	C₂×#1898	1	2	yes	—
545	C₂³	C₂×#2021	1	2	yes	—
546	C₂³	C₂×#2021	1	2	yes	—
547	C₂³	C₂×#2021	1	2	yes	—
548	C₂×C₄	#10965	1	2	yes	—
549	C₂×C₄	#10991	1	2	yes	—
550	C₂×C₄	C₂×#1898	1	2	yes	—
551	C₂×C₄	C₂×#2021	1	2	yes	—
552	C₂²	#115690	1	4	yes	—
553	C₂²	C₂×#10965	1	1	yes	characteristic
554	C₂²	C₂×#10991	1	1	yes	characteristic
555	C₂²	C₂×#10991	1	1	yes	characteristic
556	C₂	C₂×#115690	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	C₂×#115690
commutator	C₂³×D₄	C₂³×C₄
Frattini, cosocle	C₂²×H(5,𝔽₂)	C₂⁴
prime radical	#72240597	C₂
LCS	G ▷ C₂³×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂⁴ ◁ C₂³×H(5,𝔽₂) ◁ G
LECS	G ▷ C₂²×H(5,𝔽₂) ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72340216	C₂	semidirect
2. #72311172	C₂	semidirect
3. C₂×#128079	C₂	semidirect
4. C₂×#128062	C₂	semidirect
5. #72303055	C₂	semidirect
6. C₂×#392138	C₂	semidirect
8. C₂×#392135	C₂	semidirect
9. #72238013	C₂	semidirect
11. C₂²×#3026	C₄	semidirect
13. #6628897	C₄	semidirect
15. #6628896	C₄	semidirect
17. C₂×#20609	C₄	semidirect
23. #496241	C₂²	semidirect
24. #496240	C₂²	semidirect
27. #213855	C₂²	semidirect
28. #213854	C₂²	semidirect
29. #128079	C₂²	semidirect
30. #128062	C₂²	semidirect
42. C₂²×#458	C₂×C₄	semidirect
43. C₂²×B(4,𝔽₂)	C₂×C₄	semidirect
44. C₂²×#413	D₄	semidirect
46. C₂³×#99	D₄	semidirect
55. C₂×#2309	D₄	semidirect
59. C₂×#2308	D₄	semidirect
60. #20609	C₂×C₄	semidirect
61. #20609	C₂×C₄	semidirect
62. #20592	D₄	semidirect
64. #20586	D₄	semidirect
69. #20585	D₄	semidirect
70. #20585	D₄	semidirect
105. C₂⁴×D₄	C₂²⋊C₄	semidirect
115. C₂²×#123	C₂²⋊C₄	semidirect
116. C₂²×#123	C₂²⋊C₄	semidirect
117. C₂²×#123	C₂²⋊C₄	semidirect
121. C₂²×#120	C₂²⋊C₄	semidirect
122. C₂²×#120	C₂²⋊C₄	semidirect
123. C₂²×#120	C₂²⋊C₄	semidirect
127. C₂³×C₂²⋊C₄	C₂²⋊C₄	semidirect
128. C₂³×C₂²⋊C₄	C₂²⋊C₄	semidirect
129. C₂³×C₂²⋊C₄	C₂²⋊C₄	semidirect
131. C₂²×#99	C₂²⋊C₄	semidirect
132. C₂²×#99	C₂²⋊C₄	semidirect
136. #2308	C₂²⋊C₄	semidirect
137. #2308	C₂²⋊C₄	semidirect
138. #2308	C₂²⋊C₄	semidirect
139. #2308	C₂²⋊C₄	semidirect
140. #2308	C₂²⋊C₄	semidirect
141. #2308	C₂²⋊C₄	semidirect
149. #1782	C₂²⋊C₄	semidirect
151. #1781	C₂²⋊C₄	semidirect
154. C₂⁶	C₂×C₂²⋊C₄	semidirect
160. C₂×H(5,𝔽₂)	#99	semidirect
302. C₂⁴×C₄	C₂×C₂²⋊C₄	semidirect
312. C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	semidirect
313. C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	semidirect
314. C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	semidirect
315. C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	semidirect
316. C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	semidirect
317. C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	semidirect
318. C₂×#99	C₂×C₂²⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
#72340216	2
#72311172	2
C₂×#128079	2
C₂×#128062	2
#72303055	2
C₂×#392138	2
#72240597	2
C₂×#392135	2
#72238013	2