Subgroups — #72234059

Order 2048.

At least 7997 conjugacy classes of subgroups; only the 464 normal subgroups are shown.

The subgroup lattice has 362 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72234058	C₂	1	2	yes	maximal, complemented
2	#72234057	C₂	1	2	yes	maximal, complemented
3	#72233787	C₂	1	1	yes	maximal, characteristic
4	#72233223	C₂	1	1	yes	maximal, characteristic, complemented
5	#72233040	C₂	1	1	yes	maximal, characteristic, complemented
6	#72232773	C₂	1	1	yes	maximal, characteristic, complemented
7	#72232724	C₂	1	1	yes	maximal, characteristic, complemented
8	#72232722	C₂	1	1	yes	maximal, characteristic, complemented
9	#72232716	C₂	1	1	yes	maximal, characteristic, complemented
10	#72231764	C₂	1	2	yes	maximal, complemented
11	#72231013	C₂	1	2	yes	maximal, complemented
12	C₂×#46350	C₂²	1	1	yes	characteristic
13	C₂×#37644	C₂²	1	1	yes	characteristic
14	#6385983	C₂²	1	1	yes	characteristic, complemented
15	#6385983	C₂²	1	1	yes	characteristic, complemented
16	#6385971	C₂²	1	1	yes	characteristic, complemented
17	#5024691	C₄	1	1	yes	characteristic, complemented
18	#5020746	C₄	1	1	yes	characteristic, complemented
19	#4933002	C₄	1	1	yes	characteristic, complemented
20	#4932999	C₄	1	1	yes	characteristic, complemented
21	#4433768	C₄	1	1	yes	characteristic, complemented
22	#4341466	C₂²	1	1	yes	characteristic
23	#1495037	C₄	1	1	yes	characteristic, complemented
24	#1494104	C₄	1	1	yes	characteristic, complemented
25	#876092	C₂²	1	1	yes	characteristic
26	#719145	C₂²	1	1	yes	characteristic
27	#649038	C₂²	1	1	yes	characteristic
28	#648360	C₄	1	1	yes	characteristic, complemented
29	#513995	C₂²	1	1	yes	characteristic
30	#496333	C₂²	1	2	yes	complemented
31	#493998	C₂²	1	2	yes	—
32	#482377	C₂²	1	2	yes	complemented
33	#482360	C₂²	1	2	yes	complemented
34	#201876	C₂²	1	2	yes	complemented
35	#201549	C₂²	1	2	yes	complemented
36	#201386	C₂²	1	2	yes	complemented
37	#196338	C₂²	1	2	yes	—
38	#188087	C₂²	1	1	yes	characteristic, complemented
39	#127207	C₂²	1	2	yes	complemented
40	#127202	C₂²	1	2	yes	complemented
41	#106601	C₂²	1	2	yes	complemented
42	#106573	C₂²	1	2	yes	complemented
43	C₂²×D₄²	C₂³	1	1	yes	characteristic
44	C₂²×#534	D₄	1	1	yes	characteristic
45	C₂³×#127	D₄	1	1	yes	characteristic
46	C₂³×#120	D₄	1	1	yes	characteristic
47	C₂³×#120	D₄	1	1	yes	characteristic
48	#60230	C₂³	1	2	yes	—
49	C₂×#2693	C₂×C₄	1	1	yes	characteristic, complemented
50	C₂×#2675	C₂×C₄	1	1	yes	characteristic, complemented
51	C₂×#2812	C₂×C₄	1	1	yes	characteristic, complemented
52	C₂×#2846	C₂×C₄	1	1	yes	characteristic
53	C₂×#2541	D₄	1	1	yes	characteristic
54	C₂×#2535	C₂³	1	1	yes	characteristic
55	C₂×#2539	D₄	1	1	yes	characteristic
56	C₂×#2534	C₂³	1	1	yes	characteristic
57	C₂×#2433	D₄	1	1	yes	characteristic
58	C₂×#2408	C₂³	1	1	yes	characteristic
59	C₂×#2412	C₂×C₄	1	1	yes	characteristic
60	C₂×#2405	D₄	1	1	yes	characteristic
61	C₂×#2410	C₂×C₄	1	1	yes	characteristic
62	C₂×#2403	C₂×C₄	1	1	yes	characteristic, complemented
63	C₂×#2403	D₄	1	1	yes	characteristic
64	C₂×#2617	D₄	1	1	yes	characteristic
65	C₂×#2613	C₂×C₄	1	1	yes	characteristic
66	C₂×#2397	D₄	1	1	yes	characteristic
67	C₂×D₄×C₂²⋊C₄	D₄	1	1	yes	characteristic
68	C₂×#2321	C₂³	1	1	yes	characteristic
69	#20726	C₂³	1	2	yes	—
70	#20722	C₂³	1	2	yes	—
71	#17362	C₂³	1	2	yes	—
72	#15561	C₂×C₄	1	1	yes	characteristic, complemented
73	#15561	C₂×C₄	1	1	yes	characteristic, complemented
74	#15561	C₂×C₄	1	1	yes	characteristic, complemented
75	#15539	C₂×C₄	1	1	yes	characteristic, complemented
76	#15480	C₂×C₄	1	1	yes	characteristic, complemented
77	#15310	D₄	1	1	yes	characteristic
78	#15310	D₄	1	1	yes	characteristic
79	#15310	D₄	1	1	yes	characteristic
80	#15310	D₄	1	1	yes	characteristic
81	#15283	C₂×C₄	1	1	yes	characteristic
82	#15283	C₂×C₄	1	1	yes	characteristic
83	#15283	D₄	1	1	yes	characteristic
84	#15283	D₄	1	1	yes	characteristic
85	#15267	C₂×C₄	1	1	yes	characteristic, complemented
86	#15267	C₂×C₄	1	1	yes	characteristic, complemented
87	#15267	C₂×C₄	1	1	yes	characteristic, complemented
88	#15258	C₂×C₄	1	1	yes	characteristic
89	#15258	C₂×C₄	1	1	yes	characteristic
90	#15258	C₂×C₄	1	1	yes	characteristic
91	#15258	C₂×C₄	1	1	yes	characteristic
92	#15258	C₂×C₄	1	1	yes	characteristic
93	#15258	C₂×C₄	1	1	yes	characteristic
94	#15258	D₄	1	1	yes	characteristic
95	#15258	D₄	1	1	yes	characteristic
96	#14698	D₄	1	1	yes	characteristic
97	#14272	D₄	1	1	yes	characteristic
98	#13905	D₄	1	1	yes	characteristic
99	#13902	D₄	1	1	yes	characteristic
100	#13831	C₂×C₄	1	1	yes	characteristic, complemented
101	#13827	C₂×C₄	1	1	yes	characteristic, complemented
102	#13823	C₂×C₄	1	1	yes	characteristic, complemented
103	C₂²⋊C₄²	C₂×C₄	1	1	yes	characteristic, complemented
104	#13785	C₂³	1	1	yes	characteristic
105	C₄×#386	C₂³	1	1	yes	characteristic
106	#12795	D₄	1	8	yes	complemented
107	C₂⁷	C₂²⋊C₄	1	1	yes	characteristic
108	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
109	C₂⁴×D₄	C₂²⋊C₄	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	C₂×D₄	1	1	yes	characteristic
115	C₂²×#127	C₂²⋊C₄	1	1	yes	characteristic
116	C₂²×#127	C₂²⋊C₄	1	1	yes	characteristic
117	C₂²×#127	C₂²⋊C₄	1	1	yes	characteristic
118	C₂²×#127	C₂²⋊C₄	1	1	yes	characteristic
119	C₂²×#127	C₂²⋊C₄	1	1	yes	characteristic
120	C₂²×#127	C₂²⋊C₄	1	1	yes	characteristic
121	C₂²×#127	C₂×D₄	1	1	yes	characteristic
122	C₂²×#123	C₂²⋊C₄	1	1	yes	characteristic
123	C₂²×#123	C₂²⋊C₄	1	1	yes	characteristic
124	C₂²×#123	C₂×D₄	1	1	yes	characteristic
125	C₂²×#121	C₂×D₄	1	1	yes	characteristic
126	C₂²×#121	C₂×D₄	1	1	yes	characteristic
127	C₂²×#121	C₂×D₄	1	1	yes	characteristic
128	C₂²×#121	C₂×D₄	1	1	yes	characteristic
129	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
130	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
131	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
132	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
133	C₂²×#120	C₂²×C₄	1	1	yes	characteristic
134	C₂²×#120	C₂²×C₄	1	1	yes	characteristic
135	C₂²×#120	C₂×D₄	1	1	yes	characteristic
136	C₂²×#120	C₂×D₄	1	1	yes	characteristic
137	C₂²×#120	C₂×D₄	1	1	yes	characteristic
138	C₂²×#120	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×D₄	C₂⁴	1	1	yes	characteristic
142	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
143	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
144	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
145	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
146	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
147	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
148	C₂×#399	C₂²⋊C₄	1	1	yes	characteristic
149	C₂×#399	C₂²⋊C₄	1	1	yes	characteristic
150	C₂×#397	C₂²×C₄	1	1	yes	characteristic
151	C₂×#397	C₂×D₄	1	1	yes	characteristic
152	C₂×#394	C₂×D₄	1	1	yes	characteristic
153	C₂×#394	C₂×D₄	1	1	yes	characteristic
154	C₂×#392	C₂²⋊C₄	1	1	yes	characteristic
155	C₂×#392	C₂²⋊C₄	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	C₂×D₄	1	1	yes	characteristic
164	#2321	C₂×D₄	1	4	yes	—
165	#2321	#41	1	4	yes	—
166	C₂×#390	C₂²⋊C₄	1	1	yes	characteristic
167	C₂×#390	C₂²⋊C₄	1	1	yes	characteristic
168	C₂×#386	C₂²⋊C₄	1	1	yes	characteristic
169	C₂×#386	C₂²⋊C₄	1	1	yes	characteristic
170	C₂×#386	C₂×D₄	1	1	yes	characteristic
171	C₂×#385	C₂²×C₄	1	1	yes	characteristic
172	C₂×#382	C₂×D₄	1	1	yes	characteristic
173	C₂×#381	C₂²×C₄	1	1	yes	characteristic
174	C₂×#380	C₂×D₄	1	1	yes	characteristic
175	C₂×#380	C₂×D₄	1	1	yes	characteristic
176	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
177	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
178	C₂×#379	C₂²×C₄	1	1	yes	characteristic
179	C₂×#379	C₂²×C₄	1	1	yes	characteristic
180	C₂×C₄×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
181	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
182	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
183	C₂×#376	C₂×D₄	1	1	yes	characteristic
184	#1800	C₂×D₄	1	4	yes	complemented
185	#1799	C₂×D₄	1	4	yes	complemented
186	#1438	C₂²⋊C₄	1	1	yes	characteristic
187	#1438	C₂²⋊C₄	1	1	yes	characteristic
188	#1438	C₂²⋊C₄	1	1	yes	characteristic
189	#1438	C₂²⋊C₄	1	1	yes	characteristic
190	#1438	C₂²⋊C₄	1	1	yes	characteristic
191	#1438	C₂²⋊C₄	1	1	yes	characteristic
192	#1438	C₂²⋊C₄	1	1	yes	characteristic
193	#1438	C₂²⋊C₄	1	1	yes	characteristic
194	#1437	C₂²⋊C₄	1	1	yes	characteristic
195	#1437	C₂²⋊C₄	1	1	yes	characteristic
196	#1437	C₂²⋊C₄	1	1	yes	characteristic
197	#1437	C₂²⋊C₄	1	1	yes	characteristic
198	#1437	C₂²⋊C₄	1	1	yes	characteristic
199	#1437	C₂²⋊C₄	1	1	yes	characteristic
200	#1437	C₂²⋊C₄	1	1	yes	characteristic
201	#1437	C₂²⋊C₄	1	1	yes	characteristic
202	#1437	C₂²×C₄	1	1	yes	characteristic
203	#1437	C₂²×C₄	1	1	yes	characteristic
204	#1437	C₂²×C₄	1	1	yes	characteristic
205	#1437	C₂²×C₄	1	1	yes	characteristic
206	#1437	C₂×D₄	1	1	yes	characteristic
207	#1437	C₂×D₄	1	1	yes	characteristic
208	#1436	C₂×D₄	1	1	yes	characteristic
209	#1436	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	C₂×C₂²⋊C₄	1	1	yes	characteristic
214	C₂⁶	#120	1	1	yes	characteristic
215	C₂⁶	#120	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	C₂×C₂²⋊C₄	1	1	yes	characteristic
222	C₂³×D₄	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	#120	1	1	yes	characteristic
226	C₂³×D₄	#120	1	1	yes	characteristic
227	C₂³×D₄	#120	1	1	yes	characteristic
228	C₂³×D₄	#120	1	1	yes	characteristic
229	C₂³×D₄	#120	1	1	yes	characteristic
230	C₂³×D₄	#120	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	C₂²×D₄	1	1	yes	characteristic
235	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
236	C₂⁴×C₄	C₂×C₂²⋊C₄	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	C₂×#120	#120	1	2	yes	—
242	C₂×#120	#123	1	2	yes	—
243	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
244	C₂×C₄×D₄	C₂×#41	1	2	yes	—
245	C₂×C₄×D₄	H(5,𝔽₂)	1	2	yes	—
246	C₂×C₄×D₄	H(5,𝔽₂)	1	2	yes	—
247	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
248	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
249	C₂²×C₄⋊C₄	C₂²×D₄	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	C₂×C₂²⋊C₄	1	1	yes	characteristic
254	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
255	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
256	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
257	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
258	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
259	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
260	C₂²×C₂²⋊C₄	#121	1	4	yes	—
261	C₂²×C₂²⋊C₄	C₂³×C₄	1	1	yes	characteristic
262	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
263	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
264	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
265	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
266	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
267	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
268	#386	#120	1	2	yes	—
269	#386	#123	1	2	yes	—
270	#385	C₄×D₄	1	4	yes	—
271	#379	C₄×D₄	1	4	yes	—
272	C₄×C₂²⋊C₄	#121	1	4	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	#379	1	1	yes	characteristic
286	C₂⁵	#379	1	1	yes	characteristic
287	C₂⁵	#386	1	2	yes	—
288	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
289	C₂⁵	C₂×#120	1	1	yes	characteristic
290	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
291	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
292	C₂²×D₄	#458	1	1	yes	characteristic
293	C₂²×D₄	#458	1	1	yes	characteristic
294	C₂²×D₄	C₂×#120	1	1	yes	characteristic
295	C₂²×D₄	C₂×#123	1	1	yes	characteristic
296	C₂²×D₄	#534	1	1	yes	characteristic
297	C₂²×D₄	#534	1	1	yes	characteristic
298	C₂³×C₄	#379	1	1	yes	characteristic
299	C₂³×C₄	#379	1	1	yes	characteristic
300	C₂³×C₄	#386	1	2	yes	—
301	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
302	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
303	C₂³×C₄	C₂×#120	1	1	yes	characteristic
304	C₂³×C₄	C₂×#120	1	1	yes	characteristic
305	C₂³×C₄	C₂×#120	1	1	yes	characteristic
306	C₂³×C₄	C₂×#121	1	2	yes	—
307	C₂³×C₄	#534	1	2	yes	—
308	C₂³×C₄	D₄²	1	2	yes	—
309	C₂³×C₄	#546	1	2	yes	—
310	#120	#453	1	8	yes	—
311	C₂×C₄⋊C₄	D₄²	1	2	yes	—
312	C₂×C₄⋊C₄	#546	1	2	yes	—
313	C₂×C₂²⋊C₄	#386	1	2	yes	—
314	C₂×C₂²⋊C₄	#386	1	2	yes	—
315	C₂×C₂²⋊C₄	C₂×C₄×D₄	1	2	yes	—
316	C₂×C₂²⋊C₄	#518	1	2	yes	—
317	C₂×C₂²⋊C₄	D₄²	1	2	yes	—
318	C₂×C₂²⋊C₄	#546	1	2	yes	—
319	C₂×C₄²	D₄²	1	2	yes	—
320	C₂×C₄²	#546	1	2	yes	—
321	C₂⁴	#1790	1	1	yes	characteristic
322	C₂⁴	#1790	1	1	yes	characteristic
323	C₂⁴	#1790	1	1	yes	characteristic
324	C₂⁴	#1790	1	1	yes	characteristic
325	C₂⁴	#1887	1	4	yes	complemented
326	C₂⁴	C₂×#379	1	1	yes	characteristic
327	C₂⁴	C₂×#386	1	1	yes	characteristic
328	C₂⁴	#2308	1	1	yes	characteristic
329	C₂⁴	#2403	1	1	yes	characteristic
330	C₂⁴	#2405	1	1	yes	characteristic
331	C₂×D₄	C₂×#453	1	4	yes	—
332	C₂²×C₄	D₄×C₂²⋊C₄	1	2	yes	—
333	C₂²×C₄	D₄×C₂²⋊C₄	1	2	yes	—
334	C₂²×C₄	#2403	1	1	yes	characteristic
335	C₂²×C₄	#2405	1	1	yes	characteristic
336	C₂²×C₄	#2410	1	2	yes	—
337	C₂²×C₄	#2410	1	2	yes	—
338	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
339	C₂²×C₄	C₂×#458	1	1	yes	characteristic
340	C₂²×C₄	#3026	1	2	yes	—
341	C₂²⋊C₄	#1887	1	4	yes	complemented
342	C₂³	#12753	1	2	yes	—
343	C₂³	#13867	1	1	yes	characteristic
344	C₂³	C₂×#1790	1	1	yes	characteristic
345	C₂³	#20609	1	1	yes	characteristic
346	C₂³	C₂×#1887	1	2	yes	—
347	C₂³	#23906	1	2	yes	—
348	C₂×C₄	#23906	1	2	yes	—
349	C₂×C₄	#24404	1	2	yes	—
350	C₂×C₄	#24405	1	2	yes	—
351	C₂²	#359458	1	1	yes	characteristic
352	C₂²	#359531	1	1	yes	characteristic
353	C₂²	#359534	1	1	yes	characteristic
354	C₂²	C₂×#12753	1	1	yes	characteristic
355	C₂²	#493562	1	1	yes	characteristic
356	C₂²	#493641	1	1	yes	characteristic
357	C₂²	#493648	1	1	yes	characteristic
358	C₂	#72232729	1	1	yes	characteristic
359	C₂	#72232797	1	1	yes	characteristic
360	C₂	#72233196	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#359531
commutator	C₂²×C₂²⋊C₄	C₂³×C₄
Frattini, cosocle	C₂²×C₄×D₄	C₂⁴
prime radical	#72233787	C₂
LCS	G ▷ C₂²×C₂²⋊C₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂²×D₄² ◁ G
LECS	G ▷ C₂²×C₄×D₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72234058	C₂	semidirect
2. #72234057	C₂	semidirect
4. #72233223	C₂	semidirect
5. #72233040	C₂	semidirect
6. #72232773	C₂	semidirect
7. #72232724	C₂	semidirect
8. #72232722	C₂	semidirect
9. #72232716	C₂	semidirect
10. #72231764	C₂	semidirect
11. #72231013	C₂	semidirect
14. #6385983	C₂²	semidirect
15. #6385983	C₂²	semidirect
16. #6385971	C₂²	semidirect
17. #5024691	C₄	semidirect
18. #5020746	C₄	semidirect
19. #4933002	C₄	semidirect
20. #4932999	C₄	semidirect
21. #4433768	C₄	semidirect
23. #1495037	C₄	semidirect
24. #1494104	C₄	semidirect
28. #648360	C₄	semidirect
30. #496333	C₂²	semidirect
32. #482377	C₂²	semidirect
33. #482360	C₂²	semidirect
34. #201876	C₂²	semidirect
35. #201549	C₂²	semidirect
36. #201386	C₂²	semidirect
38. #188087	C₂²	semidirect
39. #127207	C₂²	semidirect
40. #127202	C₂²	semidirect
41. #106601	C₂²	semidirect
42. #106573	C₂²	semidirect
49. C₂×#2693	C₂×C₄	semidirect
50. C₂×#2675	C₂×C₄	semidirect
51. C₂×#2812	C₂×C₄	semidirect
62. C₂×#2403	C₂×C₄	semidirect
72. #15561	C₂×C₄	semidirect
73. #15561	C₂×C₄	semidirect
74. #15561	C₂×C₄	semidirect
75. #15539	C₂×C₄	semidirect
76. #15480	C₂×C₄	semidirect
85. #15267	C₂×C₄	semidirect
86. #15267	C₂×C₄	semidirect
87. #15267	C₂×C₄	semidirect
100. #13831	C₂×C₄	semidirect
101. #13827	C₂×C₄	semidirect
102. #13823	C₂×C₄	semidirect
103. C₂²⋊C₄²	C₂×C₄	semidirect
106. #12795	D₄	semidirect
184. #1800	C₂×D₄	semidirect
185. #1799	C₂×D₄	semidirect
325. C₂⁴	#1887	semidirect
341. C₂²⋊C₄	#1887	semidirect

Maximal subgroups

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

subgroup	index
#72234058	2
#72234057	2
#72233787	2
#72233223	2
#72233040	2
#72232773	2
#72232724	2
#72232722	2
#72232716	2
#72231764	2
#72231013	2