Subgroups — #72313024

Order 2048.

At least 10582 conjugacy classes of subgroups; only the 1118 normal subgroups are shown.

The subgroup lattice has 730 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72312738	C₂	1	1	yes	maximal, characteristic, complemented
2	#72312666	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#6437986	C₂	1	1	yes	maximal, characteristic
4	#72312254	C₂	1	1	yes	maximal, characteristic, complemented
5	#72303723	C₂	1	1	yes	maximal, characteristic, complemented
6	#72303721	C₂	1	1	yes	maximal, characteristic, complemented
7	#72303719	C₂	1	1	yes	maximal, characteristic, complemented
8	#72303705	C₂	1	1	yes	maximal, characteristic, complemented
9	#72303318	C₂	1	1	yes	maximal, characteristic, complemented
10	#72303110	C₂	1	1	yes	maximal, characteristic, complemented
11	#72280707	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#494758	C₂	1	1	yes	maximal, characteristic, complemented
13	#72256633	C₂	1	1	yes	maximal, characteristic, complemented
14	#72255935	C₂	1	1	yes	maximal, characteristic, complemented
15	#72255896	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#3585	C₂²	1	1	yes	characteristic
17	C₂×#60367	C₂²	1	1	yes	characteristic
18	C₂×#60387	C₂²	1	1	yes	characteristic
19	C₂²×#2888	C₂²	1	1	yes	characteristic
20	C₂²×#2883	C₂²	1	1	yes	characteristic
21	#7625680	C₂²	1	1	yes	characteristic
22	C₂×#33358	C₂²	1	1	yes	characteristic
23	C₂×#33347	C₂²	1	1	yes	characteristic
24	C₂×#24421	C₄	1	4	yes	complemented
25	C₂×#24420	C₄	1	4	yes	complemented
26	#6374181	C₂²	1	1	yes	characteristic
27	#6374127	C₂²	1	1	yes	characteristic
28	C₂×#21017	C₂²	1	1	yes	characteristic
29	C₂×#20860	C₂²	1	1	yes	characteristic
30	C₂²×#1795	C₂²	1	1	yes	characteristic
31	C₂×#20620	C₂²	1	1	yes	characteristic
32	#6370746	C₂²	1	1	yes	characteristic
33	C₂×#20612	C₂²	1	1	yes	characteristic
34	#6370734	C₂²	1	1	yes	characteristic
35	#6370734	C₂²	1	1	yes	characteristic
36	#6370719	C₂²	1	1	yes	characteristic
37	C₂×#12589	C₂²	1	1	yes	characteristic
38	C₂×#12589	C₂²	1	1	yes	characteristic
39	#492906	C₂²	1	1	yes	characteristic
40	C₂×#12579	C₂²	1	1	yes	characteristic
41	C₂×#12577	C₂²	1	1	yes	characteristic
42	#492886	C₂²	1	1	yes	characteristic
43	#492886	C₂²	1	1	yes	characteristic
44	#492886	C₂²	1	1	yes	characteristic
45	#492886	C₂²	1	1	yes	characteristic
46	#492886	C₂²	1	1	yes	characteristic
47	#355933	C₂²	1	1	yes	characteristic
48	#355902	C₂²	1	1	yes	characteristic
49	#353434	C₂²	1	1	yes	characteristic
50	#353430	C₂²	1	1	yes	characteristic
51	#353422	C₂²	1	1	yes	characteristic
52	#353422	C₂²	1	1	yes	characteristic
53	C₂²×#585	C₂³	1	1	yes	characteristic
54	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
55	C₂×#3585	C₂×C₄	1	4	yes	—
56	C₂×#3585	D₄	1	4	yes	—
57	C₂×#3585	D₄	1	4	yes	—
58	C₂²×#575	D₄	1	1	yes	characteristic
59	C₂³×AGL(1,ℤ/8)	D₄	1	1	yes	characteristic
60	C₂²×#568	C₂³	1	1	yes	characteristic
61	C₂×#3449	C₂³	1	1	yes	characteristic
62	C₂²×#518	D₄	1	1	yes	characteristic
63	C₂²×#518	D₄	1	1	yes	characteristic
64	C₂×#3022	C₂×C₄	1	2	yes	complemented
65	C₂×#3021	C₂×C₄	1	2	yes	complemented
66	C₂×#3009	C₂×C₄	1	2	yes	—
67	C₂×#3009	D₄	1	2	yes	—
68	C₂×#3008	C₂×C₄	1	2	yes	—
69	C₂×#3008	D₄	1	2	yes	—
70	C₂×#2896	D₄	1	1	yes	characteristic
71	C₂×#2896	D₄	1	1	yes	characteristic
72	C₂×#2896	D₄	1	1	yes	characteristic
73	C₂²×#418	D₄	1	1	yes	characteristic
74	C₂²×#418	D₄	1	1	yes	characteristic
75	C₂²×#418	D₄	1	1	yes	characteristic
76	C₂×#2888	C₂×C₄	1	4	yes	—
77	C₂×#2888	D₄	1	4	yes	—
78	C₂×#2888	D₄	1	4	yes	—
79	C₂²×#413	C₂³	1	1	yes	characteristic
80	C₂²×#413	C₂³	1	1	yes	characteristic
81	C₂²×#413	C₂³	1	1	yes	characteristic
82	C₂×#2883	D₄	1	4	yes	—
83	C₂²×#410	C₂³	1	1	yes	characteristic
84	C₂²×#410	C₂³	1	1	yes	characteristic
85	C₂²×#410	C₂³	1	1	yes	characteristic
86	C₂×#2879	C₂³	1	1	yes	characteristic
87	C₂×#2879	C₂³	1	1	yes	characteristic
88	#34044	D₄	1	1	yes	characteristic
89	#34044	D₄	1	1	yes	characteristic
90	#34044	C₂³	1	1	yes	characteristic
91	#34044	C₂³	1	1	yes	characteristic
92	#34044	C₂³	1	1	yes	characteristic
93	C₂×#1915	C₂×C₄	1	2	yes	complemented
94	C₂×#1914	C₂×C₄	1	2	yes	complemented
95	C₂×#1858	C₂×C₄	1	4	yes	complemented
96	C₂×#1795	D₄	1	4	yes	—
97	C₂×#1791	C₂×C₄	1	4	yes	complemented
98	#12574	D₄	1	4	yes	—
99	#12573	D₄	1	4	yes	—
100	C₂×#585	C₂²×C₄	1	2	yes	—
101	C₂×#585	C₂×D₄	1	2	yes	—
102	C₂×#585	C₂×D₄	1	2	yes	—
103	C₂²×H(5,𝔽₂)	C₂²×C₄	1	2	yes	—
104	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
105	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
106	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
107	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
108	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
109	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
110	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
111	C₂²×H(5,𝔽₂)	#41	1	2	yes	—
112	C₂²×H(5,𝔽₂)	#41	1	2	yes	—
113	C₂²×H(5,𝔽₂)	#41	1	2	yes	—
114	C₂²×H(5,𝔽₂)	#41	1	2	yes	—
115	C₂³×#41	C₂×D₄	1	1	yes	characteristic
116	C₂³×#41	C₂×D₄	1	1	yes	characteristic
117	C₂³×#41	C₂×D₄	1	1	yes	characteristic
118	C₂³×#41	C₂×D₄	1	1	yes	characteristic
119	C₂³×#41	C₂⁴	1	1	yes	characteristic
120	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
121	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
122	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
123	#3585	C₂²⋊C₄	1	16	yes	—
124	C₂²×#137	C₂²⋊C₄	1	2	yes	complemented
125	C₂²×AGL(1,ℤ/8)	C₂²⋊C₄	1	2	yes	complemented
126	C₂³×SD₁₆	C₂²⋊C₄	1	2	yes	complemented
127	C₂³×D₈	C₂²⋊C₄	1	2	yes	complemented
128	C₂×#568	C₂²×C₄	1	2	yes	—
129	C₂×#568	C₂×D₄	1	2	yes	—
130	C₂×#568	C₂×D₄	1	2	yes	—
131	C₂³×M₁₆	C₂×D₄	1	1	yes	characteristic
132	C₂³×M₁₆	C₂×D₄	1	1	yes	characteristic
133	C₂³×M₁₆	C₂×D₄	1	1	yes	characteristic
134	C₂³×M₁₆	C₂×D₄	1	1	yes	characteristic
135	C₂×#536	C₂²×C₄	1	1	yes	characteristic
136	C₂×#536	C₂×D₄	1	1	yes	characteristic
137	C₂×#535	C₂²×C₄	1	1	yes	characteristic
138	C₂×#535	C₂×D₄	1	1	yes	characteristic
139	C₂²×#117	C₂×D₄	1	1	yes	characteristic
140	C₂²×#117	C₂×D₄	1	1	yes	characteristic
141	C₂²×#117	C₂×D₄	1	1	yes	characteristic
142	C₂²×#117	C₂×D₄	1	1	yes	characteristic
143	C₂²×#117	C₂×D₄	1	1	yes	characteristic
144	C₂²×#117	C₂×D₄	1	1	yes	characteristic
145	C₂²×#117	C₂×D₄	1	1	yes	characteristic
146	C₂×#418	C₂²⋊C₄	1	2	yes	complemented
147	C₂×#418	C₂²⋊C₄	1	2	yes	complemented
148	C₂×#416	C₂²⋊C₄	1	2	yes	complemented
149	C₂×#416	C₂²⋊C₄	1	2	yes	complemented
150	#2888	C₂²⋊C₄	1	16	yes	complemented
151	C₂×#413	C₂²×C₄	1	2	yes	—
152	C₂×#413	C₂²×C₄	1	2	yes	—
153	C₂×#413	C₂×D₄	1	2	yes	—
154	C₂×#413	C₂×D₄	1	2	yes	—
155	C₂×#413	C₂×D₄	1	2	yes	—
156	C₂×#413	C₂×D₄	1	2	yes	—
157	C₂×#413	C₂×D₄	1	2	yes	—
158	C₂×#413	C₂×D₄	1	2	yes	—
159	C₂×#413	#41	1	2	yes	—
160	C₂×#413	#41	1	2	yes	—
161	C₂²×#100	C₂×D₄	1	2	yes	—
162	C₂×#410	C₂×D₄	1	2	yes	—
163	C₂×#410	C₂×D₄	1	2	yes	—
164	C₂×#410	C₂×D₄	1	2	yes	—
165	C₂×#410	C₂×D₄	1	2	yes	—
166	C₂×#410	#41	1	2	yes	—
167	C₂×#410	#41	1	2	yes	—
168	C₂²×#99	C₂×D₄	1	2	yes	—
169	C₂×#408	C₂²×C₄	1	2	yes	—
170	C₂×#408	C₂×D₄	1	2	yes	—
171	#2308	C₂×D₄	1	2	yes	—
172	#2308	#41	1	2	yes	—
173	#2297	C₂×D₄	1	2	yes	—
174	#2297	#41	1	2	yes	—
175	#585	C₂×C₂²⋊C₄	1	4	yes	—
176	C₂×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	4	yes	—
177	C₂×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	4	yes	—
178	C₂×H(5,𝔽₂)	C₄×D₄	1	4	yes	—
179	C₂×H(5,𝔽₂)	C₄×D₄	1	4	yes	—
180	C₂×H(5,𝔽₂)	#120	1	4	yes	—
181	C₂×H(5,𝔽₂)	#120	1	4	yes	—
182	C₂×H(5,𝔽₂)	#120	1	4	yes	—
183	C₂×H(5,𝔽₂)	#121	1	4	yes	—
184	C₂×H(5,𝔽₂)	#121	1	4	yes	—
185	C₂×H(5,𝔽₂)	#121	1	4	yes	—
186	C₂×H(5,𝔽₂)	#121	1	4	yes	—
187	C₂×H(5,𝔽₂)	#123	1	4	yes	—
188	C₂×H(5,𝔽₂)	#123	1	4	yes	—
189	C₂×H(5,𝔽₂)	#123	1	4	yes	—
190	C₂×H(5,𝔽₂)	#124	1	4	yes	—
191	C₂×H(5,𝔽₂)	#124	1	4	yes	—
192	C₂²×#41	C₂×C₂²⋊C₄	1	2	yes	—
193	C₂²×#41	C₄×D₄	1	2	yes	—
194	C₂²×#41	C₄×D₄	1	2	yes	—
195	C₂²×#41	#120	1	2	yes	—
196	C₂²×#41	#120	1	2	yes	—
197	C₂²×#41	#120	1	2	yes	—
198	C₂²×#41	#120	1	2	yes	—
199	C₂²×#41	#121	1	2	yes	—
200	C₂²×#41	#121	1	2	yes	—
201	C₂²×#41	#121	1	2	yes	—
202	C₂²×#41	#121	1	2	yes	—
203	C₂²×#41	#121	1	2	yes	—
204	C₂²×#41	#121	1	2	yes	—
205	C₂²×#41	#121	1	2	yes	—
206	C₂²×#41	#121	1	2	yes	—
207	C₂²×#41	#123	1	2	yes	—
208	C₂²×#41	#127	1	2	yes	—
209	C₂²×#41	#127	1	2	yes	—
210	C₂²×#41	C₂³×C₄	1	1	yes	characteristic
211	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
212	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
213	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
214	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
215	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
216	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
217	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
218	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
219	C₂²×#41	C₂×#41	1	1	yes	characteristic
220	C₂²×#41	C₂×#41	1	1	yes	characteristic
221	C₂²×#41	C₂×#41	1	1	yes	characteristic
222	C₂²×#41	C₂×#41	1	1	yes	characteristic
223	C₂²×#41	C₂×#41	1	1	yes	characteristic
224	C₂²×#41	C₂×#41	1	1	yes	characteristic
225	C₂²×#41	C₂×#41	1	1	yes	characteristic
226	C₂²×#41	C₂×#41	1	1	yes	characteristic
227	C₂²×#41	C₂×#41	1	1	yes	characteristic
228	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
229	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
230	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
231	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
232	C₂²×#41	2₋¹⁺⁴	1	1	yes	characteristic
233	C₂²×#41	2₋¹⁺⁴	1	1	yes	characteristic
234	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
235	C₂³×Q₈	#120	1	1	yes	characteristic
236	C₂³×Q₈	H(5,𝔽₂)	1	1	yes	characteristic
237	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
238	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
239	C₂³×D₄	C₄×D₄	1	2	yes	—
240	C₂³×D₄	C₄×D₄	1	2	yes	—
241	C₂³×D₄	#120	1	2	yes	—
242	C₂³×D₄	#120	1	2	yes	—
243	C₂³×D₄	#120	1	2	yes	—
244	C₂³×D₄	#120	1	2	yes	—
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	#121	1	2	yes	—
249	C₂³×D₄	#121	1	2	yes	—
250	C₂³×D₄	#121	1	2	yes	—
251	C₂³×D₄	#121	1	2	yes	—
252	C₂³×D₄	#121	1	2	yes	—
253	C₂³×D₄	#121	1	2	yes	—
254	C₂³×D₄	#121	1	2	yes	—
255	C₂³×D₄	#121	1	2	yes	—
256	C₂³×D₄	#123	1	2	yes	—
257	C₂³×D₄	#127	1	2	yes	—
258	C₂³×D₄	#127	1	2	yes	—
259	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
260	C₂³×D₄	C₂×#41	1	1	yes	characteristic
261	C₂³×D₄	H(5,𝔽₂)	1	1	yes	characteristic
262	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
263	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
264	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
265	#568	C₂×C₂²⋊C₄	1	4	yes	—
266	C₂²×M₁₆	C₂×C₂²⋊C₄	1	2	yes	—
267	C₂³×C₈	C₂×C₂²⋊C₄	1	2	yes	—
268	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
269	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
270	C₂×#117	#121	1	2	yes	—
271	C₂²×C₂²⋊C₄	#121	1	2	yes	—
272	C₂²×C₂²⋊C₄	#121	1	2	yes	—
273	C₂²×C₄²	#121	1	2	yes	—
274	#413	C₂×C₂²⋊C₄	1	4	yes	—
275	#413	C₂×C₂²⋊C₄	1	4	yes	—
276	#413	C₄×D₄	1	4	yes	—
277	#413	#121	1	4	yes	—
278	#413	#123	1	4	yes	—
279	C₂×#100	C₄×D₄	1	4	yes	—
280	C₂×#100	#120	1	4	yes	—
281	C₂×#100	#121	1	4	yes	—
282	#410	#121	1	4	yes	—
283	C₂×#99	#121	1	4	yes	—
284	C₂⁵	C₂×#121	1	1	yes	characteristic
285	C₂⁵	D₄²	1	1	yes	characteristic
286	C₂⁵	#546	1	1	yes	characteristic
287	C₂×#41	#379	1	4	yes	—
288	C₂×#41	#386	1	4	yes	—
289	C₂×#41	#386	1	4	yes	—
290	C₂×#41	#386	1	4	yes	—
291	C₂×#41	#390	1	4	yes	—
292	C₂×#41	#390	1	4	yes	—
293	C₂×#41	#392	1	4	yes	—
294	C₂×#41	#392	1	4	yes	—
295	C₂×#41	#394	1	4	yes	—
296	C₂×#41	#394	1	4	yes	—
297	C₂×#41	#394	1	4	yes	—
298	C₂×#41	#394	1	4	yes	—
299	C₂×#41	C₂²×C₂²⋊C₄	1	1	yes	characteristic
300	C₂×#41	C₂²×C₂²⋊C₄	1	1	yes	characteristic
301	C₂×#41	C₂×C₄×D₄	1	1	yes	characteristic
302	C₂×#41	C₂×C₄×D₄	1	1	yes	characteristic
303	C₂×#41	C₂×C₄×D₄	1	1	yes	characteristic
304	C₂×#41	C₄×#41	1	1	yes	characteristic
305	C₂×#41	#518	1	1	yes	characteristic
306	C₂×#41	#520	1	1	yes	characteristic
307	C₂×#41	C₂×#120	1	1	yes	characteristic
308	C₂×#41	C₂×#120	1	1	yes	characteristic
309	C₂×#41	C₂×#120	1	1	yes	characteristic
310	C₂×#41	C₂×#121	1	1	yes	characteristic
311	C₂×#41	C₂×#121	1	1	yes	characteristic
312	C₂×#41	C₂×#121	1	1	yes	characteristic
313	C₂×#41	C₂×#121	1	1	yes	characteristic
314	C₂×#41	C₂×#121	1	1	yes	characteristic
315	C₂×#41	C₂×#121	1	1	yes	characteristic
316	C₂×#41	C₂×#123	1	1	yes	characteristic
317	C₂×#41	C₂×#123	1	1	yes	characteristic
318	C₂×#41	C₂×#123	1	1	yes	characteristic
319	C₂×#41	C₂×#123	1	1	yes	characteristic
320	C₂×#41	#525	1	1	yes	characteristic
321	C₂×#41	#525	1	1	yes	characteristic
322	C₂×#41	C₂×#124	1	1	yes	characteristic
323	C₂×#41	C₂×#124	1	1	yes	characteristic
324	C₂×#41	#529	1	1	yes	characteristic
325	C₂×#41	#529	1	1	yes	characteristic
326	C₂×#41	#529	1	1	yes	characteristic
327	C₂×#41	#532	1	1	yes	characteristic
328	C₂×#41	#532	1	1	yes	characteristic
329	C₂×#41	#534	1	1	yes	characteristic
330	C₂×#41	#534	1	1	yes	characteristic
331	C₂×#41	#534	1	1	yes	characteristic
332	C₂×#41	#536	1	1	yes	characteristic
333	C₂×#41	#537	1	1	yes	characteristic
334	C₂×#41	#537	1	1	yes	characteristic
335	C₂×#41	#538	1	1	yes	characteristic
336	C₂×#41	#539	1	1	yes	characteristic
337	C₂×#41	#539	1	1	yes	characteristic
338	C₂×#41	#539	1	1	yes	characteristic
339	C₂×#41	D₄²	1	1	yes	characteristic
340	C₂×#41	D₄²	1	1	yes	characteristic
341	C₂×#41	#546	1	1	yes	characteristic
342	C₂×#41	#546	1	1	yes	characteristic
343	C₂×#41	#546	1	1	yes	characteristic
344	C₂×#41	#546	1	1	yes	characteristic
345	C₂×#41	#546	1	1	yes	characteristic
346	C₂×#41	#546	1	1	yes	characteristic
347	C₂×#41	#546	1	1	yes	characteristic
348	C₂×#41	#546	1	1	yes	characteristic
349	C₂×#41	#547	1	1	yes	characteristic
350	C₂×#41	#547	1	1	yes	characteristic
351	C₂×#41	#547	1	1	yes	characteristic
352	C₂×#41	#547	1	1	yes	characteristic
353	C₂×#41	#547	1	1	yes	characteristic
354	C₂×#41	#547	1	1	yes	characteristic
355	C₂×#41	#548	1	1	yes	characteristic
356	C₂×#41	#548	1	1	yes	characteristic
357	C₂×#41	#553	1	1	yes	characteristic
358	C₂×#41	#553	1	1	yes	characteristic
359	C₂×#41	#553	1	1	yes	characteristic
360	C₂×#41	#553	1	1	yes	characteristic
361	C₂×#41	#553	1	1	yes	characteristic
362	C₂×#41	#553	1	1	yes	characteristic
363	C₂²×Q₈	#386	1	2	yes	—
364	C₂²×Q₈	#392	1	2	yes	—
365	C₂²×Q₈	#392	1	2	yes	—
366	C₂²×Q₈	#518	1	1	yes	characteristic
367	C₂²×Q₈	#534	1	1	yes	characteristic
368	C₂²×Q₈	#534	1	1	yes	characteristic
369	C₂²×Q₈	#537	1	1	yes	characteristic
370	C₂²×Q₈	#538	1	1	yes	characteristic
371	C₂²×Q₈	#539	1	1	yes	characteristic
372	C₂²×Q₈	D₄²	1	1	yes	characteristic
373	C₂²×Q₈	#546	1	1	yes	characteristic
374	C₂²×Q₈	#546	1	1	yes	characteristic
375	C₂²×Q₈	#546	1	1	yes	characteristic
376	C₂²×Q₈	#553	1	1	yes	characteristic
377	C₂²×Q₈	#553	1	1	yes	characteristic
378	C₂²×D₄	#379	1	4	yes	—
379	C₂²×D₄	#386	1	2	yes	—
380	C₂²×D₄	#386	1	2	yes	—
381	C₂²×D₄	#386	1	4	yes	—
382	C₂²×D₄	#386	1	4	yes	—
383	C₂²×D₄	#386	1	2	yes	—
384	C₂²×D₄	#386	1	4	yes	—
385	C₂²×D₄	#390	1	4	yes	—
386	C₂²×D₄	#390	1	4	yes	—
387	C₂²×D₄	#392	1	2	yes	—
388	C₂²×D₄	#392	1	2	yes	—
389	C₂²×D₄	#392	1	2	yes	—
390	C₂²×D₄	#392	1	2	yes	—
391	C₂²×D₄	#392	1	4	yes	—
392	C₂²×D₄	#392	1	4	yes	—
393	C₂²×D₄	#392	1	2	yes	—
394	C₂²×D₄	#392	1	2	yes	—
395	C₂²×D₄	#394	1	4	yes	—
396	C₂²×D₄	#394	1	4	yes	—
397	C₂²×D₄	#394	1	4	yes	—
398	C₂²×D₄	#394	1	4	yes	—
399	C₂²×D₄	B(4,𝔽₂)	1	2	yes	—
400	C₂²×D₄	B(4,𝔽₂)	1	2	yes	—
401	C₂²×D₄	B(4,𝔽₂)	1	2	yes	—
402	C₂²×D₄	B(4,𝔽₂)	1	2	yes	—
403	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
404	C₂²×D₄	C₄×#41	1	1	yes	characteristic
405	C₂²×D₄	#520	1	1	yes	characteristic
406	C₂²×D₄	C₂×#120	1	1	yes	characteristic
407	C₂²×D₄	C₂×#121	1	1	yes	characteristic
408	C₂²×D₄	C₂×#121	1	1	yes	characteristic
409	C₂²×D₄	#525	1	1	yes	characteristic
410	C₂²×D₄	#525	1	1	yes	characteristic
411	C₂²×D₄	#525	1	1	yes	characteristic
412	C₂²×D₄	#525	1	1	yes	characteristic
413	C₂²×D₄	#529	1	1	yes	characteristic
414	C₂²×D₄	#532	1	1	yes	characteristic
415	C₂²×D₄	#532	1	1	yes	characteristic
416	C₂²×D₄	#534	1	1	yes	characteristic
417	C₂²×D₄	#535	1	1	yes	characteristic
418	C₂²×D₄	#537	1	1	yes	characteristic
419	C₂²×D₄	#538	1	1	yes	characteristic
420	C₂²×D₄	#538	1	1	yes	characteristic
421	C₂²×D₄	D₄²	1	1	yes	characteristic
422	C₂²×D₄	D₄²	1	1	yes	characteristic
423	C₂²×D₄	D₄²	1	1	yes	characteristic
424	C₂²×D₄	D₄²	1	1	yes	characteristic
425	C₂²×D₄	D₄²	1	1	yes	characteristic
426	C₂²×D₄	#546	1	1	yes	characteristic
427	C₂²×D₄	#546	1	1	yes	characteristic
428	C₂²×D₄	#546	1	1	yes	characteristic
429	C₂²×D₄	#546	1	1	yes	characteristic
430	C₂²×D₄	#546	1	1	yes	characteristic
431	C₂²×D₄	#547	1	1	yes	characteristic
432	C₂²×D₄	#547	1	1	yes	characteristic
433	C₂²×D₄	#548	1	1	yes	characteristic
434	C₂²×D₄	#548	1	1	yes	characteristic
435	C₂²×D₄	#553	1	1	yes	characteristic
436	C₂²×D₄	#553	1	1	yes	characteristic
437	C₂²×D₄	#553	1	1	yes	characteristic
438	C₂²×D₄	#553	1	1	yes	characteristic
439	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
440	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
441	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
442	C₂³×C₄	C₂×#120	1	1	yes	characteristic
443	C₂³×C₄	C₂×#120	1	1	yes	characteristic
444	C₂³×C₄	C₂×#120	1	1	yes	characteristic
445	C₂³×C₄	C₂×#120	1	1	yes	characteristic
446	C₂³×C₄	C₂×#120	1	1	yes	characteristic
447	C₂³×C₄	C₂×#121	1	1	yes	characteristic
448	C₂³×C₄	C₂×#121	1	1	yes	characteristic
449	C₂³×C₄	C₂×#121	1	1	yes	characteristic
450	C₂³×C₄	C₂×#121	1	1	yes	characteristic
451	C₂³×C₄	C₂×#121	1	1	yes	characteristic
452	C₂³×C₄	C₂×#121	1	1	yes	characteristic
453	C₂³×C₄	C₂×#121	1	1	yes	characteristic
454	C₂³×C₄	C₂×#121	1	1	yes	characteristic
455	C₂³×C₄	C₂×#121	1	1	yes	characteristic
456	C₂³×C₄	C₂×#123	1	1	yes	characteristic
457	C₂³×C₄	C₂×#127	1	1	yes	characteristic
458	C₂³×C₄	C₂×#127	1	1	yes	characteristic
459	C₂³×C₄	#532	1	1	yes	characteristic
460	C₂³×C₄	#532	1	1	yes	characteristic
461	C₂³×C₄	#534	1	1	yes	characteristic
462	C₂³×C₄	#534	1	1	yes	characteristic
463	C₂³×C₄	#537	1	1	yes	characteristic
464	C₂³×C₄	#537	1	1	yes	characteristic
465	C₂³×C₄	D₄²	1	1	yes	characteristic
466	C₂³×C₄	D₄²	1	1	yes	characteristic
467	C₂³×C₄	D₄²	1	1	yes	characteristic
468	C₂³×C₄	#546	1	1	yes	characteristic
469	C₂³×C₄	#546	1	1	yes	characteristic
470	C₂³×C₄	#546	1	1	yes	characteristic
471	C₂³×C₄	#546	1	1	yes	characteristic
472	C₂³×C₄	#546	1	1	yes	characteristic
473	C₂³×C₄	#546	1	1	yes	characteristic
474	C₂³×C₄	#546	1	1	yes	characteristic
475	C₂³×C₄	#547	1	1	yes	characteristic
476	C₂³×C₄	#547	1	1	yes	characteristic
477	C₂³×C₄	#547	1	1	yes	characteristic
478	C₂³×C₄	#547	1	1	yes	characteristic
479	#100	#386	1	8	yes	—
480	C₂⁴	C₄×#121	1	1	yes	characteristic
481	C₂⁴	#2339	1	1	yes	characteristic
482	C₂⁴	#2361	1	1	yes	characteristic
483	C₂⁴	#2404	1	1	yes	characteristic
484	C₂⁴	#2410	1	1	yes	characteristic
485	C₂⁴	#2410	1	1	yes	characteristic
486	C₂⁴	#2410	1	1	yes	characteristic
487	C₂⁴	#2416	1	1	yes	characteristic
488	C₂⁴	#2416	1	1	yes	characteristic
489	C₂⁴	#2416	1	1	yes	characteristic
490	C₂⁴	#2424	1	1	yes	characteristic
491	C₂⁴	#2424	1	1	yes	characteristic
492	C₂⁴	#2424	1	1	yes	characteristic
493	C₂⁴	#2430	1	1	yes	characteristic
494	C₂⁴	#2433	1	1	yes	characteristic
495	C₂⁴	#2444	1	1	yes	characteristic
496	C₂⁴	#2543	1	1	yes	characteristic
497	C₂⁴	#2847	1	1	yes	characteristic
498	C₂⁴	#2856	1	1	yes	characteristic
499	C₂×Q₈	#1438	1	4	yes	—
500	C₂×Q₈	#2308	1	1	yes	characteristic
501	C₂×Q₈	#2325	1	1	yes	characteristic
502	C₂×Q₈	D₄×C₂²⋊C₄	1	1	yes	characteristic
503	C₂×Q₈	#2364	1	1	yes	characteristic
504	C₂×Q₈	#2405	1	1	yes	characteristic
505	C₂×Q₈	#2410	1	1	yes	characteristic
506	C₂×Q₈	#2416	1	1	yes	characteristic
507	C₂×Q₈	#2425	1	1	yes	characteristic
508	C₂×Q₈	#2430	1	1	yes	characteristic
509	C₂×Q₈	#2443	1	1	yes	characteristic
510	C₂×Q₈	#2444	1	1	yes	characteristic
511	C₂×Q₈	#2444	1	1	yes	characteristic
512	C₂×Q₈	#2543	1	1	yes	characteristic
513	C₂×Q₈	#2591	1	1	yes	characteristic
514	C₂×Q₈	#2618	1	1	yes	characteristic
515	C₂×Q₈	#2639	1	1	yes	characteristic
516	C₂×D₄	#1438	1	4	yes	—
517	C₂×D₄	#1438	1	4	yes	—
518	C₂×D₄	#1438	1	4	yes	—
519	C₂×D₄	#1889	1	4	yes	—
520	C₂×D₄	#1889	1	4	yes	—
521	C₂×D₄	#2021	1	4	yes	—
522	C₂×D₄	#2021	1	4	yes	—
523	C₂×D₄	#2021	1	4	yes	—
524	C₂×D₄	#2021	1	4	yes	—
525	C₂×D₄	C₂×#386	1	1	yes	characteristic
526	C₂×D₄	#2297	1	1	yes	characteristic
527	C₂×D₄	C₄×#121	1	1	yes	characteristic
528	C₂×D₄	C₄×#121	1	1	yes	characteristic
529	C₂×D₄	#2311	1	1	yes	characteristic
530	C₂×D₄	#2325	1	1	yes	characteristic
531	C₂×D₄	D₄×C₂²⋊C₄	1	1	yes	characteristic
532	C₂×D₄	#2339	1	1	yes	characteristic
533	C₂×D₄	#2339	1	1	yes	characteristic
534	C₂×D₄	#2361	1	1	yes	characteristic
535	C₂×D₄	#2361	1	1	yes	characteristic
536	C₂×D₄	#2364	1	1	yes	characteristic
537	C₂×D₄	#2403	1	1	yes	characteristic
538	C₂×D₄	#2404	1	1	yes	characteristic
539	C₂×D₄	#2406	1	1	yes	characteristic
540	C₂×D₄	#2410	1	1	yes	characteristic
541	C₂×D₄	#2410	1	1	yes	characteristic
542	C₂×D₄	#2410	1	1	yes	characteristic
543	C₂×D₄	#2416	1	1	yes	characteristic
544	C₂×D₄	#2416	1	1	yes	characteristic
545	C₂×D₄	#2416	1	1	yes	characteristic
546	C₂×D₄	#2424	1	1	yes	characteristic
547	C₂×D₄	#2424	1	1	yes	characteristic
548	C₂×D₄	#2425	1	1	yes	characteristic
549	C₂×D₄	#2430	1	1	yes	characteristic
550	C₂×D₄	#2430	1	1	yes	characteristic
551	C₂×D₄	#2430	1	1	yes	characteristic
552	C₂×D₄	#2436	1	1	yes	characteristic
553	C₂×D₄	#2443	1	1	yes	characteristic
554	C₂×D₄	#2443	1	1	yes	characteristic
555	C₂×D₄	#2443	1	1	yes	characteristic
556	C₂×D₄	#2443	1	1	yes	characteristic
557	C₂×D₄	#2443	1	1	yes	characteristic
558	C₂×D₄	#2444	1	1	yes	characteristic
559	C₂×D₄	#2444	1	1	yes	characteristic
560	C₂×D₄	#2444	1	1	yes	characteristic
561	C₂×D₄	#2444	1	1	yes	characteristic
562	C₂×D₄	#2504	1	1	yes	characteristic
563	C₂×D₄	#2543	1	1	yes	characteristic
564	C₂×D₄	#2543	1	1	yes	characteristic
565	C₂×D₄	#2543	1	1	yes	characteristic
566	C₂×D₄	#2591	1	1	yes	characteristic
567	C₂×D₄	#2617	1	1	yes	characteristic
568	C₂×D₄	#2639	1	1	yes	characteristic
569	C₂×D₄	#2847	1	1	yes	characteristic
570	C₂×D₄	#2850	1	1	yes	characteristic
571	C₂×D₄	#2850	1	1	yes	characteristic
572	C₂×D₄	#2854	1	1	yes	characteristic
573	C₂²×C₄	C₂×#379	1	1	yes	characteristic
574	C₂²×C₄	C₂×#386	1	1	yes	characteristic
575	C₂²×C₄	C₂×#386	1	1	yes	characteristic
576	C₂²×C₄	C₂×#386	1	1	yes	characteristic
577	C₂²×C₄	C₂×#386	1	1	yes	characteristic
578	C₂²×C₄	C₂×#390	1	1	yes	characteristic
579	C₂²×C₄	C₂×#390	1	1	yes	characteristic
580	C₂²×C₄	C₄×#121	1	1	yes	characteristic
581	C₂²×C₄	#2325	1	1	yes	characteristic
582	C₂²×C₄	#2325	1	1	yes	characteristic
583	C₂²×C₄	D₄×C₂²⋊C₄	1	1	yes	characteristic
584	C₂²×C₄	D₄×C₂²⋊C₄	1	1	yes	characteristic
585	C₂²×C₄	#2339	1	1	yes	characteristic
586	C₂²×C₄	#2361	1	1	yes	characteristic
587	C₂²×C₄	#2364	1	1	yes	characteristic
588	C₂²×C₄	#2364	1	1	yes	characteristic
589	C₂²×C₄	C₂×#392	1	1	yes	characteristic
590	C₂²×C₄	C₂×#392	1	1	yes	characteristic
591	C₂²×C₄	C₂×#392	1	1	yes	characteristic
592	C₂²×C₄	C₂×#392	1	1	yes	characteristic
593	C₂²×C₄	C₂×#394	1	1	yes	characteristic
594	C₂²×C₄	C₂×#394	1	1	yes	characteristic
595	C₂²×C₄	C₂×#394	1	1	yes	characteristic
596	C₂²×C₄	C₂×#394	1	1	yes	characteristic
597	C₂²×C₄	#2403	1	1	yes	characteristic
598	C₂²×C₄	#2405	1	1	yes	characteristic
599	C₂²×C₄	#2406	1	1	yes	characteristic
600	C₂²×C₄	#2410	1	1	yes	characteristic
601	C₂²×C₄	#2410	1	1	yes	characteristic
602	C₂²×C₄	#2410	1	1	yes	characteristic
603	C₂²×C₄	#2410	1	1	yes	characteristic
604	C₂²×C₄	#2410	1	1	yes	characteristic
605	C₂²×C₄	#2416	1	1	yes	characteristic
606	C₂²×C₄	#2416	1	1	yes	characteristic
607	C₂²×C₄	#2416	1	1	yes	characteristic
608	C₂²×C₄	#2416	1	1	yes	characteristic
609	C₂²×C₄	#2416	1	1	yes	characteristic
610	C₂²×C₄	#2424	1	1	yes	characteristic
611	C₂²×C₄	#2424	1	1	yes	characteristic
612	C₂²×C₄	#2424	1	1	yes	characteristic
613	C₂²×C₄	#2425	1	1	yes	characteristic
614	C₂²×C₄	#2425	1	1	yes	characteristic
615	C₂²×C₄	#2425	1	1	yes	characteristic
616	C₂²×C₄	#2425	1	1	yes	characteristic
617	C₂²×C₄	#2425	1	1	yes	characteristic
618	C₂²×C₄	#2425	1	1	yes	characteristic
619	C₂²×C₄	#2430	1	1	yes	characteristic
620	C₂²×C₄	#2430	1	1	yes	characteristic
621	C₂²×C₄	#2430	1	1	yes	characteristic
622	C₂²×C₄	#2430	1	1	yes	characteristic
623	C₂²×C₄	#2430	1	1	yes	characteristic
624	C₂²×C₄	#2430	1	1	yes	characteristic
625	C₂²×C₄	#2430	1	1	yes	characteristic
626	C₂²×C₄	#2443	1	1	yes	characteristic
627	C₂²×C₄	#2443	1	1	yes	characteristic
628	C₂²×C₄	#2444	1	1	yes	characteristic
629	C₂²×C₄	#2501	1	1	yes	characteristic
630	C₂²×C₄	#2539	1	1	yes	characteristic
631	C₂²×C₄	#2539	1	1	yes	characteristic
632	C₂²×C₄	#2543	1	1	yes	characteristic
633	C₂²×C₄	#2543	1	1	yes	characteristic
634	C₂²×C₄	#2543	1	1	yes	characteristic
635	C₂²×C₄	#2543	1	1	yes	characteristic
636	C₂²×C₄	#2543	1	1	yes	characteristic
637	C₂²×C₄	#2543	1	1	yes	characteristic
638	C₂²×C₄	#2543	1	1	yes	characteristic
639	C₂²×C₄	#2617	1	1	yes	characteristic
640	C₂²×C₄	#2618	1	1	yes	characteristic
641	C₂²×C₄	#2656	1	1	yes	characteristic
642	C₂²×C₄	#2656	1	1	yes	characteristic
643	C₂²×C₄	#2854	1	1	yes	characteristic
644	C₂²×C₄	#2856	1	1	yes	characteristic
645	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
646	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
647	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
648	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
649	C₂²×C₄	#3026	1	1	yes	characteristic
650	C₂²×C₄	#3026	1	1	yes	characteristic
651	C₂²×C₄	#3026	1	1	yes	characteristic
652	C₂²×C₄	#3026	1	1	yes	characteristic
653	C₂³	#13956	1	1	yes	characteristic
654	C₂³	#14023	1	1	yes	characteristic
655	C₂³	#14023	1	1	yes	characteristic
656	C₂³	#14023	1	1	yes	characteristic
657	C₂³	#14023	1	1	yes	characteristic
658	C₂³	#14137	1	1	yes	characteristic
659	C₂³	#14698	1	1	yes	characteristic
660	C₂³	#14716	1	1	yes	characteristic
661	C₂³	#14716	1	1	yes	characteristic
662	C₂³	#14719	1	1	yes	characteristic
663	C₂³	#14747	1	1	yes	characteristic
664	C₂³	#14747	1	1	yes	characteristic
665	C₂³	#14757	1	1	yes	characteristic
666	C₂³	#14757	1	1	yes	characteristic
667	C₂³	#14913	1	1	yes	characteristic
668	C₂³	#24404	1	1	yes	characteristic
669	C₂³	#24404	1	1	yes	characteristic
670	C₂³	#24404	1	1	yes	characteristic
671	C₂³	#24404	1	1	yes	characteristic
672	D₄	#10991	1	8	yes	—
673	C₂×C₄	C₂×#1438	1	1	yes	characteristic
674	C₂×C₄	#13867	1	1	yes	characteristic
675	C₂×C₄	#14023	1	1	yes	characteristic
676	C₂×C₄	#14023	1	1	yes	characteristic
677	C₂×C₄	#14023	1	1	yes	characteristic
678	C₂×C₄	#14023	1	1	yes	characteristic
679	C₂×C₄	#14152	1	1	yes	characteristic
680	C₂×C₄	#14271	1	1	yes	characteristic
681	C₂×C₄	#14719	1	1	yes	characteristic
682	C₂×C₄	#14747	1	1	yes	characteristic
683	C₂×C₄	#14747	1	1	yes	characteristic
684	C₂×C₄	#14757	1	1	yes	characteristic
685	C₂×C₄	#14757	1	1	yes	characteristic
686	C₂×C₄	#14913	1	1	yes	characteristic
687	C₂×C₄	#14926	1	1	yes	characteristic
688	C₂×C₄	#14926	1	1	yes	characteristic
689	C₂×C₄	C₂×#1889	1	1	yes	characteristic
690	C₂×C₄	C₂×#1889	1	1	yes	characteristic
691	C₂×C₄	#20960	1	1	yes	characteristic
692	C₂×C₄	#20960	1	1	yes	characteristic
693	C₂×C₄	C₂×#2021	1	1	yes	characteristic
694	C₂×C₄	C₂×#2021	1	1	yes	characteristic
695	C₂×C₄	C₂×#2021	1	1	yes	characteristic
696	C₂×C₄	C₂×#2021	1	1	yes	characteristic
697	C₂×C₄	#23444	1	1	yes	characteristic
698	C₂×C₄	#23444	1	1	yes	characteristic
699	C₂×C₄	#23444	1	1	yes	characteristic
700	C₂×C₄	#23444	1	1	yes	characteristic
701	C₂×C₄	#24404	1	1	yes	characteristic
702	C₂×C₄	#24404	1	1	yes	characteristic
703	C₂×C₄	#24404	1	1	yes	characteristic
704	C₂×C₄	#24404	1	1	yes	characteristic
705	C₂×C₄	#25563	1	1	yes	characteristic
706	C₂×C₄	#25563	1	1	yes	characteristic
707	C₂×C₄	#25563	1	1	yes	characteristic
708	C₂×C₄	#25563	1	1	yes	characteristic
709	C₂×C₄	#25563	1	1	yes	characteristic
710	C₂×C₄	#25563	1	1	yes	characteristic
711	C₂×C₄	#25563	1	1	yes	characteristic
712	C₂×C₄	#25563	1	1	yes	characteristic
713	C₂²	#154255	1	1	yes	characteristic
714	C₂²	#368739	1	1	yes	characteristic
715	C₂²	#368739	1	1	yes	characteristic
716	C₂²	#394267	1	1	yes	characteristic
717	C₂²	#394267	1	1	yes	characteristic
718	C₂²	#397910	1	1	yes	characteristic
719	C₂²	#397910	1	1	yes	characteristic
720	C₄	C₂×#10991	1	1	yes	characteristic
721	C₄	#357530	1	1	yes	characteristic
722	C₄	#368739	1	1	yes	characteristic
723	C₄	#368739	1	1	yes	characteristic
724	C₄	#397910	1	1	yes	characteristic
725	C₄	#397910	1	1	yes	characteristic
726	C₄	#406272	1	1	yes	characteristic
727	C₄	#406272	1	1	yes	characteristic
728	C₂	#72260795	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	#72260795
commutator	C₂²×#41	C₂³×C₄
Frattini, cosocle	C₂³×#41	C₂⁴
prime radical	C₂×#6437986	C₂
LCS	G ▷ C₂²×#41 ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂³×C₄ ◁ C₂³×H(5,𝔽₂) ◁ G
LECS	G ▷ C₂³×#41 ▷ C₂² ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72312738	C₂	semidirect
2. #72312666	C₂	semidirect
4. #72312254	C₂	semidirect
5. #72303723	C₂	semidirect
6. #72303721	C₂	semidirect
7. #72303719	C₂	semidirect
8. #72303705	C₂	semidirect
9. #72303318	C₂	semidirect
10. #72303110	C₂	semidirect
11. #72280707	C₂	semidirect
12. C₂×#494758	C₂	semidirect
13. #72256633	C₂	semidirect
14. #72255935	C₂	semidirect
15. #72255896	C₂	semidirect
24. C₂×#24421	C₄	semidirect
25. C₂×#24420	C₄	semidirect
64. C₂×#3022	C₂×C₄	semidirect
65. C₂×#3021	C₂×C₄	semidirect
93. C₂×#1915	C₂×C₄	semidirect
94. C₂×#1914	C₂×C₄	semidirect
95. C₂×#1858	C₂×C₄	semidirect
97. C₂×#1791	C₂×C₄	semidirect
124. C₂²×#137	C₂²⋊C₄	semidirect
125. C₂²×AGL(1,ℤ/8)	C₂²⋊C₄	semidirect
126. C₂³×SD₁₆	C₂²⋊C₄	semidirect
127. C₂³×D₈	C₂²⋊C₄	semidirect
146. C₂×#418	C₂²⋊C₄	semidirect
147. C₂×#418	C₂²⋊C₄	semidirect
148. C₂×#416	C₂²⋊C₄	semidirect
149. C₂×#416	C₂²⋊C₄	semidirect
150. #2888	C₂²⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
#72312738	2
#72312666	2
C₂×#6437986	2
#72312254	2
#72303723	2
#72303721	2
#72303719	2
#72303705	2
#72303318	2
#72303110	2
#72280707	2
C₂×#494758	2
#72256633	2
#72255935	2
#72255896	2