Subgroups — #72284295

Order 2048.

At least 8447 conjugacy classes of subgroups; only the 482 normal subgroups are shown.

The subgroup lattice has 388 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72284262	C₂	1	1	yes	maximal, characteristic, complemented
2	#72284229	C₂	1	1	yes	maximal, characteristic, complemented
3	#72284212	C₂	1	1	yes	maximal, characteristic, complemented
4	#72284190	C₂	1	1	yes	maximal, characteristic, complemented
5	#72283946	C₂	1	1	yes	maximal, characteristic, complemented
6	#72283877	C₂	1	2	yes	maximal, complemented
7	C₂×#201462	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#130062	C₂	1	2	yes	maximal, complemented
9	#72283816	C₂	1	2	yes	maximal, complemented
10	#72283750	C₂	1	2	yes	maximal, complemented
11	#72283107	C₂	1	1	yes	maximal, characteristic
12	C₂×#46996	C₂²	1	1	yes	characteristic
13	C₂²×#2404	C₂²	1	1	yes	characteristic
14	C₂×#34176	C₂²	1	1	yes	characteristic, complemented
15	C₂²×#1462	C₂²	1	1	yes	characteristic, complemented
16	#4320282	C₂²	1	1	yes	characteristic
17	#4320266	C₂²	1	1	yes	characteristic
18	#4029469	C₄	1	1	yes	characteristic, complemented
19	#4028459	C₄	1	1	yes	characteristic, complemented
20	#3547665	C₄	1	1	yes	characteristic, complemented
21	#3546569	C₄	1	1	yes	characteristic, complemented
22	#2745485	C₄	1	1	yes	characteristic, complemented
23	#1039328	C₄	1	1	yes	characteristic, complemented
24	#1016675	C₄	1	1	yes	characteristic, complemented
25	#772778	C₄	1	1	yes	characteristic, complemented
26	#612425	C₂²	1	1	yes	characteristic
27	#580250	C₂²	1	1	yes	characteristic
28	#516383	C₂²	1	1	yes	characteristic
29	C₂×#11753	C₂²	1	2	yes	—
30	C₂×#11753	C₂²	1	2	yes	complemented
31	C₂×#11753	C₂²	1	2	yes	complemented
32	C₂×#11502	C₂²	1	2	yes	complemented
33	C₂×#10938	C₂²	1	2	yes	complemented
34	C₂×#10725	C₂²	1	1	yes	characteristic, complemented
35	C₂×#9475	C₂²	1	2	yes	—
36	C₂×#9475	C₂²	1	2	yes	complemented
37	C₂×#9475	C₂²	1	2	yes	complemented
38	#184773	C₂²	1	1	yes	characteristic, complemented
39	#127600	C₂²	1	2	yes	complemented
40	#126973	C₂²	1	2	yes	complemented
41	#123493	C₂²	1	2	yes	complemented
42	#108182	C₂²	1	2	yes	complemented
43	C₂⁴×#41	D₄	1	1	yes	characteristic
44	C₂²×#525	D₄	1	1	yes	characteristic
45	C₂³×#120	D₄	1	1	yes	characteristic
46	C₂⁴×C₂²⋊C₄	C₂³	1	1	yes	characteristic
47	C₂×#2760	C₂×C₄	1	1	yes	characteristic
48	C₂×#2760	C₂×C₄	1	1	yes	characteristic
49	C₂×#2840	C₂×C₄	1	1	yes	characteristic
50	C₂×#2404	C₂×C₄	1	1	yes	characteristic
51	C₂×#2404	C₂×C₄	1	1	yes	characteristic
52	C₂×#2404	D₄	1	1	yes	characteristic
53	C₂×#2404	D₄	1	1	yes	characteristic
54	C₂×#2404	D₄	1	1	yes	characteristic
55	C₂×#2404	D₄	1	1	yes	characteristic
56	C₂×#2404	D₄	1	1	yes	characteristic
57	C₂×#2404	C₂³	1	1	yes	characteristic
58	C₂×#2404	C₂³	1	1	yes	characteristic
59	C₂×#2404	C₂³	1	1	yes	characteristic
60	C₂×#2403	C₂×C₄	1	1	yes	characteristic
61	C₂²×#393	C₂×C₄	1	1	yes	characteristic
62	C₂²×#393	D₄	1	1	yes	characteristic
63	C₂²×#392	C₂×C₄	1	1	yes	characteristic
64	C₂²×#392	D₄	1	1	yes	characteristic
65	C₂×#2308	D₄	1	1	yes	characteristic
66	C₂×#2308	C₂³	1	1	yes	characteristic
67	C₂²×#381	D₄	1	1	yes	characteristic
68	C₂²×#379	D₄	1	1	yes	characteristic
69	C₂×#2273	C₂³	1	2	yes	—
70	C₂²×#342	C₂³	1	2	yes	—
71	C₂×#1462	C₂³	1	2	yes	—
72	C₂×#1462	C₂³	1	2	yes	—
73	#16823	C₂×C₄	1	1	yes	characteristic
74	#16666	C₂×C₄	1	1	yes	characteristic
75	#16660	C₂×C₄	1	1	yes	characteristic
76	#16357	C₂×C₄	1	1	yes	characteristic
77	#16357	C₂×C₄	1	1	yes	characteristic
78	#16297	C₂×C₄	1	1	yes	characteristic
79	#16252	C₂×C₄	1	1	yes	characteristic
80	#16249	C₂×C₄	1	1	yes	characteristic
81	#14717	C₂×C₄	1	1	yes	characteristic
82	#14717	C₂×C₄	1	1	yes	characteristic
83	#14717	D₄	1	1	yes	characteristic
84	#14717	D₄	1	1	yes	characteristic
85	#14716	C₂×C₄	1	1	yes	characteristic
86	#14716	C₂×C₄	1	1	yes	characteristic
87	#14716	D₄	1	1	yes	characteristic
88	#14716	D₄	1	1	yes	characteristic
89	#14681	D₄	1	1	yes	characteristic
90	#14635	C₂×C₄	1	1	yes	characteristic
91	#14596	C₂×C₄	1	1	yes	characteristic
92	#14572	C₂×C₄	1	1	yes	characteristic
93	#14171	C₂×C₄	1	1	yes	characteristic
94	#13869	C₂×C₄	1	1	yes	characteristic
95	#13869	C₂×C₄	1	1	yes	characteristic
96	#13869	D₄	1	1	yes	characteristic
97	#13869	D₄	1	1	yes	characteristic
98	#13868	D₄	1	1	yes	characteristic
99	#13868	C₂³	1	1	yes	characteristic
100	#13867	C₂×C₄	1	1	yes	characteristic
101	#13867	C₂×C₄	1	1	yes	characteristic
102	#13867	D₄	1	1	yes	characteristic
103	#13867	D₄	1	1	yes	characteristic
104	#13794	D₄	1	1	yes	characteristic
105	#13794	C₂³	1	1	yes	characteristic
106	#9475	D₄	1	8	yes	complemented
107	C₂⁷	C₂×D₄	1	1	yes	characteristic
108	C₂³×#41	C₂²⋊C₄	1	1	yes	characteristic
109	C₂³×#41	C₂²⋊C₄	1	1	yes	characteristic
110	C₂³×#41	C₂×D₄	1	1	yes	characteristic
111	C₂³×#41	C₂×D₄	1	1	yes	characteristic
112	C₂³×#41	C₂×D₄	1	1	yes	characteristic
113	C₂⁴×Q₈	C₂²⋊C₄	1	1	yes	characteristic
114	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
115	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
116	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
117	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
118	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
119	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₂²⋊Q₈	C₂²⋊C₄	1	1	yes	characteristic
121	C₂²×C₂²⋊Q₈	C₂²⋊C₄	1	1	yes	characteristic
122	C₂²×#121	C₂²⋊C₄	1	1	yes	characteristic
123	C₂²×#121	C₂²⋊C₄	1	1	yes	characteristic
124	C₂²×#117	C₂×D₄	1	1	yes	characteristic
125	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
126	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
127	C₂³×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
128	C₂³×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
129	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
130	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
131	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
132	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
133	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
134	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
135	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
136	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
137	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
138	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
139	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
140	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
141	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
142	#2404	C₂×D₄	1	4	yes	—
143	#2404	#41	1	4	yes	—
144	C₂×#393	C₂²⋊C₄	1	1	yes	characteristic
145	C₂×#393	C₂²⋊C₄	1	1	yes	characteristic
146	C₂×#393	C₂²⋊C₄	1	1	yes	characteristic
147	C₂×#393	C₂²⋊C₄	1	1	yes	characteristic
148	C₂×#393	C₂²⋊C₄	1	1	yes	characteristic
149	C₂×#393	C₂²⋊C₄	1	1	yes	characteristic
150	C₂×#393	C₂²×C₄	1	1	yes	characteristic
151	C₂×#393	C₂²×C₄	1	1	yes	characteristic
152	C₂×#393	C₂²×C₄	1	1	yes	characteristic
153	C₂×#393	C₂×D₄	1	1	yes	characteristic
154	C₂×#393	C₂×D₄	1	1	yes	characteristic
155	C₂×#393	C₂×D₄	1	1	yes	characteristic
156	C₂×#392	C₂²⋊C₄	1	1	yes	characteristic
157	C₂×#392	C₂²⋊C₄	1	1	yes	characteristic
158	C₂×#392	C₂²⋊C₄	1	1	yes	characteristic
159	C₂×#392	C₂²⋊C₄	1	1	yes	characteristic
160	C₂×#392	C₂²⋊C₄	1	1	yes	characteristic
161	C₂×#392	C₂²⋊C₄	1	1	yes	characteristic
162	C₂×#392	C₂²×C₄	1	1	yes	characteristic
163	C₂×#392	C₂²×C₄	1	1	yes	characteristic
164	C₂×#392	C₂²×C₄	1	1	yes	characteristic
165	C₂×#392	C₂×D₄	1	1	yes	characteristic
166	C₂×#392	C₂×D₄	1	1	yes	characteristic
167	C₂×#392	C₂×D₄	1	1	yes	characteristic
168	C₂×#381	C₂²⋊C₄	1	1	yes	characteristic
169	C₂×#381	C₂²⋊C₄	1	1	yes	characteristic
170	C₂×#381	C₂²⋊C₄	1	1	yes	characteristic
171	C₂×#381	C₂²⋊C₄	1	1	yes	characteristic
172	C₂×#381	C₂²×C₄	1	1	yes	characteristic
173	C₂×#381	C₂×D₄	1	1	yes	characteristic
174	C₂×#381	C₂×D₄	1	1	yes	characteristic
175	C₂×#381	C₂×D₄	1	1	yes	characteristic
176	C₂×#381	C₂×D₄	1	1	yes	characteristic
177	C₂×#381	C₂×D₄	1	1	yes	characteristic
178	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
179	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
180	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
181	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
182	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
183	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
184	C₂×#379	C₂²×C₄	1	1	yes	characteristic
185	C₂×#379	C₂×D₄	1	1	yes	characteristic
186	#2273	C₂×D₄	1	4	yes	complemented
187	C₂²×#95	C₂²⋊C₄	1	1	yes	characteristic
188	C₂²×#95	C₂²⋊C₄	1	1	yes	characteristic
189	#1462	C₂×D₄	1	4	yes	complemented
190	#1439	C₂²⋊C₄	1	1	yes	characteristic
191	#1439	C₂²⋊C₄	1	1	yes	characteristic
192	#1439	C₂²⋊C₄	1	1	yes	characteristic
193	#1439	C₂²⋊C₄	1	1	yes	characteristic
194	#1439	C₂²×C₄	1	1	yes	characteristic
195	#1439	C₂²×C₄	1	1	yes	characteristic
196	#1439	C₂×D₄	1	1	yes	characteristic
197	#1439	C₂×D₄	1	1	yes	characteristic
198	C₂²⋊#95	C₂²⋊C₄	1	1	yes	characteristic
199	C₂²⋊#95	C₂²⋊C₄	1	1	yes	characteristic
200	C₂²⋊#95	C₂²⋊C₄	1	1	yes	characteristic
201	C₂²⋊#95	C₂²⋊C₄	1	1	yes	characteristic
202	C₂²⋊#95	C₂²⋊C₄	1	1	yes	characteristic
203	C₂²⋊#95	C₂²⋊C₄	1	1	yes	characteristic
204	C₂²⋊#95	C₂²⋊C₄	1	1	yes	characteristic
205	C₂²⋊#95	C₂²⋊C₄	1	1	yes	characteristic
206	C₂²⋊#95	C₂²×C₄	1	1	yes	characteristic
207	C₂²⋊#95	C₂²×C₄	1	1	yes	characteristic
208	C₂²⋊#95	C₂×D₄	1	1	yes	characteristic
209	C₂²⋊#95	C₂×D₄	1	1	yes	characteristic
210	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
211	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
212	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
213	C₂⁶	#120	1	1	yes	characteristic
214	C₂⁶	#120	1	1	yes	characteristic
215	C₂⁶	#120	1	1	yes	characteristic
216	C₂⁶	#120	1	1	yes	characteristic
217	C₂⁶	C₂²×D₄	1	1	yes	characteristic
218	C₂²×#41	#120	1	2	yes	—
219	C₂²×#41	#123	1	2	yes	—
220	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
221	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
222	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
223	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
224	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
225	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
226	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
227	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
228	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
229	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
230	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
231	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
232	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
233	C₂⁴×C₄	#120	1	1	yes	characteristic
234	C₂⁴×C₄	#120	1	1	yes	characteristic
235	C₂⁴×C₄	#120	1	1	yes	characteristic
236	C₂⁴×C₄	#120	1	1	yes	characteristic
237	C₂⁴×C₄	#120	1	1	yes	characteristic
238	C₂⁴×C₄	#120	1	1	yes	characteristic
239	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
240	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
241	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
242	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
243	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
244	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
245	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
246	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
247	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
248	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
249	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
250	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
251	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
252	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
253	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
254	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
255	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
256	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
257	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
258	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
259	C₂²×C₂²⋊C₄	C₂³×C₄	1	1	yes	characteristic
260	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
261	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
262	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
263	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
264	C₂²×C₂²⋊C₄	C₂×#41	1	2	yes	—
265	C₂²×C₂²⋊C₄	H(5,𝔽₂)	1	2	yes	—
266	C₂²×C₂²⋊C₄	H(5,𝔽₂)	1	2	yes	—
267	#393	C₄×D₄	1	4	yes	—
268	#393	#121	1	4	yes	—
269	#392	C₄×D₄	1	4	yes	—
270	#392	#121	1	4	yes	—
271	#381	#120	1	2	yes	—
272	#381	#123	1	2	yes	—
273	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
274	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
275	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
276	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
277	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
278	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
279	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
280	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
281	C₂⁵	#379	1	1	yes	characteristic
282	C₂⁵	#379	1	1	yes	characteristic
283	C₂⁵	#379	1	1	yes	characteristic
284	C₂⁵	#379	1	1	yes	characteristic
285	C₂⁵	#421	1	2	yes	complemented
286	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
287	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
288	C₂⁵	#458	1	1	yes	characteristic
289	C₂⁵	#458	1	1	yes	characteristic
290	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
291	C₂⁵	C₂×#120	1	1	yes	characteristic
292	C₂⁵	C₂×#120	1	1	yes	characteristic
293	C₂⁵	D₄²	1	2	yes	—
294	C₂⁵	#546	1	2	yes	—
295	C₂²×Q₈	#386	1	2	yes	—
296	C₂²×D₄	#386	1	2	yes	—
297	C₂³×C₄	#379	1	1	yes	characteristic
298	C₂³×C₄	#379	1	1	yes	characteristic
299	C₂³×C₄	#379	1	1	yes	characteristic
300	C₂³×C₄	#379	1	1	yes	characteristic
301	C₂³×C₄	#421	1	2	yes	complemented
302	C₂³×C₄	B(4,𝔽₂)	1	2	yes	—
303	C₂³×C₄	#458	1	2	yes	—
304	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
305	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
306	C₂³×C₄	C₂×#120	1	1	yes	characteristic
307	C₂³×C₄	C₂×#120	1	1	yes	characteristic
308	C₂³×C₄	C₂×#120	1	1	yes	characteristic
309	C₂³×C₄	C₂×#123	1	1	yes	characteristic
310	C₂³×C₄	#534	1	1	yes	characteristic
311	C₂³×C₄	#534	1	1	yes	characteristic
312	C₂³×C₄	D₄²	1	2	yes	—
313	C₂³×C₄	#546	1	2	yes	—
314	C₂×C₂²⋊C₄	C₂×C₄×D₄	1	2	yes	—
315	C₂×C₂²⋊C₄	#518	1	2	yes	—
316	C₂×C₂²⋊C₄	C₂×#121	1	2	yes	—
317	C₂×C₂²⋊C₄	#534	1	2	yes	—
318	C₂×C₂²⋊C₄	D₄²	1	2	yes	—
319	C₂×C₂²⋊C₄	D₄²	1	2	yes	—
320	C₂×C₂²⋊C₄	#546	1	2	yes	—
321	C₂×C₂²⋊C₄	#546	1	2	yes	—
322	#95	#386	1	2	yes	—
323	#95	#386	1	2	yes	—
324	C₂⁴	#1790	1	1	yes	characteristic
325	C₂⁴	#1790	1	1	yes	characteristic
326	C₂⁴	#1790	1	1	yes	characteristic
327	C₂⁴	#1790	1	1	yes	characteristic
328	C₂⁴	C₂×#379	1	1	yes	characteristic
329	C₂⁴	D₄×C₂²⋊C₄	1	2	yes	—
330	C₂⁴	#2403	1	1	yes	characteristic
331	C₂⁴	#2405	1	1	yes	characteristic
332	C₂⁴	#2410	1	2	yes	—
333	C₂⁴	C₂×#421	1	1	yes	characteristic
334	C₂⁴	C₂×#421	1	1	yes	characteristic
335	C₂⁴	#2901	1	2	yes	—
336	C₂⁴	#3019	1	2	yes	—
337	C₂⁴	#3021	1	1	yes	characteristic
338	C₂⁴	#3022	1	1	yes	characteristic
339	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
340	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
341	C₂⁴	C₂×#458	1	1	yes	characteristic
342	C₂⁴	C₂×#458	1	1	yes	characteristic
343	C₂²×C₄	#1790	1	2	yes	—
344	C₂²×C₄	#1790	1	2	yes	—
345	C₂²×C₄	C₂×#386	1	1	yes	characteristic
346	C₂²×C₄	#2308	1	1	yes	characteristic
347	C₂²×C₄	D₄×C₂²⋊C₄	1	2	yes	—
348	C₂²×C₄	#2403	1	1	yes	characteristic
349	C₂²×C₄	#2405	1	1	yes	characteristic
350	C₂²×C₄	#2410	1	2	yes	—
351	C₂³	#12753	1	2	yes	—
352	C₂³	#12753	1	2	yes	—
353	C₂³	#12753	1	2	yes	—
354	C₂³	#13867	1	1	yes	characteristic
355	C₂³	#20605	1	1	yes	characteristic
356	C₂³	#20606	1	1	yes	characteristic
357	C₂³	C₂×#1790	1	1	yes	characteristic
358	C₂³	C₂×#1790	1	1	yes	characteristic
359	C₂³	#20616	1	1	yes	characteristic
360	C₂³	#20618	1	1	yes	characteristic
361	C₂³	#22434	1	2	yes	—
362	C₂³	#22435	1	2	yes	—
363	C₂³	#23900	1	1	yes	characteristic
364	C₂³	#23901	1	1	yes	characteristic
365	C₂³	#24056	1	1	yes	characteristic
366	C₂³	#24056	1	1	yes	characteristic
367	C₂³	#24468	1	2	yes	—
368	C₂³	#24471	1	2	yes	—
369	C₂²	#185255	1	1	yes	characteristic
370	C₂²	#185258	1	1	yes	characteristic
371	C₂²	#185267	1	1	yes	characteristic
372	C₂²	#185270	1	1	yes	characteristic
373	C₂²	#359552	1	1	yes	characteristic
374	C₂²	#359638	1	1	yes	characteristic
375	C₂²	#359658	1	1	yes	characteristic
376	C₂²	C₂×#12753	1	1	yes	characteristic
377	C₂²	C₂×#12753	1	1	yes	characteristic
378	C₂²	C₂×#12753	1	1	yes	characteristic
379	C₂²	#493562	1	1	yes	characteristic
380	C₂	#72218088	1	1	yes	characteristic
381	C₂	#72231809	1	1	yes	characteristic
382	C₂	#72235402	1	1	yes	characteristic
383	C₂	#72282993	1	1	yes	characteristic
384	C₂	#72283182	1	1	yes	characteristic
385	C₂	#72283413	1	1	yes	characteristic
386	C₂	#72283617	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂×#1790
commutator	C₂²×C₂²⋊C₄	C₂³×C₄
Frattini, cosocle	C₂³×C₂²⋊C₄	C₂⁴
prime radical	#72283107	C₂
LCS	G ▷ C₂²×C₂²⋊C₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂⁶ ◁ C₂⁴×C₂²⋊C₄ ◁ G
LECS	G ▷ C₂³×C₂²⋊C₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72284262	C₂	semidirect
2. #72284229	C₂	semidirect
3. #72284212	C₂	semidirect
4. #72284190	C₂	semidirect
5. #72283946	C₂	semidirect
6. #72283877	C₂	semidirect
7. C₂×#201462	C₂	semidirect
8. C₂×#130062	C₂	semidirect
9. #72283816	C₂	semidirect
10. #72283750	C₂	semidirect
14. C₂×#34176	C₂²	semidirect
15. C₂²×#1462	C₂²	semidirect
18. #4029469	C₄	semidirect
19. #4028459	C₄	semidirect
20. #3547665	C₄	semidirect
21. #3546569	C₄	semidirect
22. #2745485	C₄	semidirect
23. #1039328	C₄	semidirect
24. #1016675	C₄	semidirect
25. #772778	C₄	semidirect
30. C₂×#11753	C₂²	semidirect
31. C₂×#11753	C₂²	semidirect
32. C₂×#11502	C₂²	semidirect
33. C₂×#10938	C₂²	semidirect
34. C₂×#10725	C₂²	semidirect
36. C₂×#9475	C₂²	semidirect
37. C₂×#9475	C₂²	semidirect
38. #184773	C₂²	semidirect
39. #127600	C₂²	semidirect
40. #126973	C₂²	semidirect
41. #123493	C₂²	semidirect
42. #108182	C₂²	semidirect
106. #9475	D₄	semidirect
186. #2273	C₂×D₄	semidirect
189. #1462	C₂×D₄	semidirect
285. C₂⁵	#421	semidirect
301. C₂³×C₄	#421	semidirect

Maximal subgroups

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

subgroup	index
#72284262	2
#72284229	2
#72284212	2
#72284190	2
#72283946	2
#72283877	2
C₂×#201462	2
C₂×#130062	2
#72283816	2
#72283750	2
#72283107	2