Subgroups — #72341846

Order 2048.

At least 6337 conjugacy classes of subgroups; only the 830 normal subgroups are shown.

The subgroup lattice has 371 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72341833	C₂	1	1	yes	maximal, characteristic, complemented
2	#72337559	C₂	1	4	yes	maximal, complemented
3	#72311883	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#128079	C₂	1	2	yes	maximal, complemented
5	#72256016	C₂	1	1	yes	maximal, characteristic
6	#72241079	C₂	1	4	yes	maximal, complemented
7	C₂×#392135	C₂	1	2	yes	maximal, complemented
8	C₂²×H(7,𝔽₂)	C₂²	1	1	yes	characteristic
9	C₂×#60387	C₄	1	2	yes	complemented
10	#7630502	C₂²	1	1	yes	characteristic
11	#6628873	C₄	1	2	yes	complemented
12	#6628873	C₂²	1	2	yes	—
13	#6628872	C₄	1	2	yes	complemented
14	#6628872	C₂²	1	2	yes	—
15	#6370746	C₄	1	2	yes	complemented
16	C₂×#20592	C₂²	1	1	yes	characteristic
17	C₂×#20585	C₂²	1	2	yes	—
18	C₂×#20585	C₂²	1	2	yes	—
19	#496205	C₂²	1	2	yes	complemented
20	#496203	C₂²	1	2	yes	complemented
21	#392135	C₂²	1	8	yes	—
22	#213862	C₂²	1	2	yes	complemented
23	#213860	C₂²	1	2	yes	complemented
24	#128079	C₂²	1	8	yes	complemented
25	C₂×H(7,𝔽₂)	C₂×C₄	1	2	yes	—
26	C₂×H(7,𝔽₂)	D₄	1	4	yes	—
27	C₂×H(7,𝔽₂)	C₂³	1	2	yes	—
28	C₂²×#585	C₂×C₄	1	2	yes	—
29	C₂³×H(5,𝔽₂)	D₄	1	4	yes	—
30	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
31	C₂×#3449	C₂×C₄	1	1	yes	characteristic
32	C₂×#3449	D₄	1	1	yes	characteristic
33	C₂²×#535	D₄	1	1	yes	characteristic
34	C₂×#3022	C₂×C₄	1	4	yes	complemented
35	C₂×#3021	C₂×C₄	1	4	yes	complemented
36	C₂²×#413	C₂×C₄	1	2	yes	—
37	C₂³×#99	D₄	1	4	yes	—
38	#35616	C₂×C₄	1	1	yes	characteristic
39	#35616	D₄	1	1	yes	characteristic
40	#35616	D₄	1	1	yes	characteristic
41	#35616	C₂³	1	1	yes	characteristic
42	#35527	C₂×C₄	1	1	yes	characteristic
43	#35527	D₄	1	1	yes	characteristic
44	#35527	D₄	1	1	yes	characteristic
45	#35527	C₂³	1	1	yes	characteristic
46	#34044	C₂×C₄	1	1	yes	characteristic
47	#34044	D₄	1	1	yes	characteristic
48	C₂×#2309	D₄	1	1	yes	characteristic
49	C₂×#2308	D₄	1	4	yes	—
50	#20615	C₂×C₄	1	4	yes	complemented
51	#20615	C₂×C₄	1	4	yes	complemented
52	#20592	C₂×C₄	1	2	yes	—
53	#20592	D₄	1	4	yes	—
54	#20592	C₂³	1	2	yes	—
55	C₂×#1785	D₄	1	4	yes	—
56	#20585	D₄	1	4	yes	—
57	#20585	D₄	1	4	yes	—
58	#20585	C₂³	1	4	yes	—
59	#20585	C₂³	1	4	yes	—
60	C₂×#585	C₂²⋊C₄	1	4	yes	—
61	C₂×#585	C₂²×C₄	1	4	yes	—
62	C₂²×H(5,𝔽₂)	C₂²⋊C₄	1	4	yes	—
63	C₂²×H(5,𝔽₂)	C₂²⋊C₄	1	8	yes	—
64	C₂²×H(5,𝔽₂)	C₂²×C₄	1	1	yes	characteristic
65	C₂²×H(5,𝔽₂)	C₂×D₄	1	8	yes	—
66	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
67	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
68	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
69	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
70	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
71	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
72	C₂²×H(5,𝔽₂)	#41	1	2	yes	—
73	C₂²×H(5,𝔽₂)	#41	1	2	yes	—
74	C₂²×H(5,𝔽₂)	C₂⁴	1	1	yes	characteristic
75	C₂³×#41	C₂²⋊C₄	1	1	yes	characteristic, complemented
76	C₂³×#41	C₂²×C₄	1	1	yes	characteristic
77	C₂³×#41	C₂×D₄	1	1	yes	characteristic
78	C₂³×#41	C₂×D₄	1	2	yes	—
79	C₂³×#41	#41	1	2	yes	—
80	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
81	C₂⁴×D₄	C₂×D₄	1	2	yes	—
82	C₂⁴×D₄	C₂×D₄	1	2	yes	—
83	C₂⁴×D₄	C₂×D₄	1	2	yes	—
84	C₂⁴×D₄	#41	1	2	yes	—
85	C₂×#536	C₂²⋊C₄	1	1	yes	characteristic, complemented
86	C₂×#536	C₂²⋊C₄	1	1	yes	characteristic, complemented
87	C₂×#536	C₂²×C₄	1	1	yes	characteristic
88	C₂×#536	C₂×D₄	1	1	yes	characteristic
89	C₂×#535	C₂²⋊C₄	1	1	yes	characteristic, complemented
90	C₂×#535	C₂²⋊C₄	1	1	yes	characteristic, complemented
91	C₂×#535	C₂²×C₄	1	1	yes	characteristic
92	C₂×#535	C₂×D₄	1	1	yes	characteristic
93	C₂²×#127	C₂²⋊C₄	1	1	yes	characteristic, complemented
94	C₂²×#127	C₂×D₄	1	1	yes	characteristic
95	C₂²×#124	C₂²⋊C₄	1	1	yes	characteristic, complemented
96	C₂²×#124	C₂×D₄	1	1	yes	characteristic
97	C₂²×#117	C₂²⋊C₄	1	1	yes	characteristic, complemented
98	C₂²×#117	C₂²⋊C₄	1	1	yes	characteristic, complemented
99	C₂²×#117	C₂²⋊C₄	1	1	yes	characteristic, complemented
100	C₂×#413	C₂²⋊C₄	1	4	yes	complemented
101	C₂×#413	C₂²×C₄	1	4	yes	—
102	C₂²×#101	C₂²⋊C₄	1	4	yes	complemented
103	C₂²×#99	C₂×D₄	1	8	yes	—
104	#2309	C₂²⋊C₄	1	1	yes	characteristic, complemented
105	#2309	C₂²⋊C₄	1	1	yes	characteristic, complemented
106	#2309	C₂×D₄	1	1	yes	characteristic
107	#2309	C₂×D₄	1	1	yes	characteristic
108	#2308	C₂×D₄	1	8	yes	—
109	#2297	C₂²⋊C₄	1	1	yes	characteristic, complemented
110	#2297	C₂²⋊C₄	1	1	yes	characteristic, complemented
111	#2297	C₂²⋊C₄	1	1	yes	characteristic, complemented
112	#2297	C₂²⋊C₄	1	1	yes	characteristic, complemented
113	#2297	C₂²×C₄	1	1	yes	characteristic
114	#2297	C₂²×C₄	1	1	yes	characteristic
115	#2297	C₂×D₄	1	1	yes	characteristic
116	#2297	C₂×D₄	1	1	yes	characteristic
117	#1785	C₂²⋊C₄	1	8	yes	complemented
118	#1785	C₂×D₄	1	8	yes	—
119	C₂⁶	#120	1	2	yes	—
120	C₂⁶	#120	1	1	yes	characteristic
121	C₂⁶	#121	1	2	yes	—
122	C₂⁶	#123	1	1	yes	characteristic
123	C₂×H(5,𝔽₂)	#99	1	16	yes	complemented
124	C₂×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	8	yes	—
125	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
126	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
127	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
128	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
129	C₂²×#41	C₂×C₂²⋊C₄	1	2	yes	—
130	C₂²×#41	C₄×D₄	1	2	yes	—
131	C₂²×#41	C₄×D₄	1	2	yes	—
132	C₂²×#41	C₄×D₄	1	2	yes	—
133	C₂²×#41	#120	1	2	yes	—
134	C₂²×#41	#120	1	2	yes	—
135	C₂²×#41	#120	1	2	yes	—
136	C₂²×#41	#120	1	1	yes	characteristic
137	C₂²×#41	#121	1	2	yes	—
138	C₂²×#41	#121	1	2	yes	—
139	C₂²×#41	#121	1	2	yes	—
140	C₂²×#41	#121	1	2	yes	—
141	C₂²×#41	#121	1	2	yes	—
142	C₂²×#41	#121	1	2	yes	—
143	C₂²×#41	#123	1	2	yes	—
144	C₂²×#41	#123	1	1	yes	characteristic
145	C₂²×#41	#123	1	2	yes	—
146	C₂²×#41	#124	1	2	yes	—
147	C₂²×#41	#124	1	2	yes	—
148	C₂²×#41	#127	1	2	yes	—
149	C₂²×#41	C₂³×C₄	1	1	yes	characteristic
150	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
151	C₂²×#41	C₂²×D₄	1	2	yes	—
152	C₂²×#41	C₂×#41	1	2	yes	—
153	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
154	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented
155	C₂³×Q₈	#123	1	1	yes	characteristic
156	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
157	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
158	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
159	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented
160	C₂³×D₄	C₄×D₄	1	2	yes	—
161	C₂³×D₄	C₄×D₄	1	2	yes	—
162	C₂³×D₄	C₄×D₄	1	2	yes	—
163	C₂³×D₄	C₄×D₄	1	2	yes	—
164	C₂³×D₄	#120	1	2	yes	—
165	C₂³×D₄	#120	1	2	yes	—
166	C₂³×D₄	#120	1	2	yes	—
167	C₂³×D₄	#120	1	2	yes	—
168	C₂³×D₄	#120	1	2	yes	—
169	C₂³×D₄	#120	1	1	yes	characteristic
170	C₂³×D₄	#120	1	2	yes	—
171	C₂³×D₄	#120	1	1	yes	characteristic
172	C₂³×D₄	#120	1	2	yes	—
173	C₂³×D₄	#120	1	2	yes	—
174	C₂³×D₄	#120	1	2	yes	—
175	C₂³×D₄	#121	1	2	yes	—
176	C₂³×D₄	#121	1	2	yes	—
177	C₂³×D₄	#121	1	2	yes	—
178	C₂³×D₄	#121	1	2	yes	—
179	C₂³×D₄	#121	1	2	yes	—
180	C₂³×D₄	#121	1	2	yes	—
181	C₂³×D₄	#121	1	2	yes	—
182	C₂³×D₄	#121	1	2	yes	—
183	C₂³×D₄	#121	1	2	yes	—
184	C₂³×D₄	#121	1	2	yes	—
185	C₂³×D₄	#121	1	2	yes	—
186	C₂³×D₄	#121	1	2	yes	—
187	C₂³×D₄	#121	1	2	yes	—
188	C₂³×D₄	#121	1	2	yes	—
189	C₂³×D₄	#121	1	2	yes	—
190	C₂³×D₄	#121	1	2	yes	—
191	C₂³×D₄	#123	1	1	yes	characteristic
192	C₂³×D₄	#123	1	2	yes	—
193	C₂³×D₄	#123	1	2	yes	—
194	C₂³×D₄	#123	1	2	yes	—
195	C₂³×D₄	#123	1	2	yes	—
196	C₂³×D₄	#124	1	2	yes	—
197	C₂³×D₄	#127	1	2	yes	—
198	C₂³×D₄	#127	1	2	yes	—
199	C₂³×D₄	#127	1	2	yes	—
200	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
201	C₂³×D₄	C₂²×D₄	1	2	yes	—
202	C₂³×D₄	C₂²×D₄	1	2	yes	—
203	C₂³×D₄	C₂²×D₄	1	2	yes	—
204	C₂³×D₄	C₂×#41	1	2	yes	—
205	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
206	C₂⁴×C₄	C₄×D₄	1	2	yes	—
207	C₂⁴×C₄	#120	1	2	yes	—
208	C₂⁴×C₄	#121	1	2	yes	—
209	C₂⁴×C₄	#124	1	2	yes	—
210	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented
211	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented
212	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented
213	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented
214	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented
215	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented
216	C₂×#101	C₂×C₂²⋊C₄	1	8	yes	complemented
217	C₂⁵	#386	1	2	yes	—
218	C₂⁵	#386	1	2	yes	—
219	C₂⁵	#386	1	1	yes	characteristic
220	C₂⁵	#386	1	2	yes	—
221	C₂⁵	#386	1	1	yes	characteristic
222	C₂⁵	#386	1	1	yes	characteristic
223	C₂⁵	#392	1	2	yes	—
224	C₂⁵	#392	1	2	yes	—
225	C₂⁵	#392	1	2	yes	—
226	C₂⁵	#392	1	2	yes	—
227	C₂⁵	#392	1	2	yes	—
228	C₂⁵	#392	1	2	yes	—
229	C₂⁵	#394	1	2	yes	—
230	C₂⁵	#394	1	2	yes	—
231	C₂⁵	#394	1	2	yes	—
232	C₂⁵	B(4,𝔽₂)	1	8	yes	—
233	C₂⁵	C₂×#120	1	2	yes	—
234	C₂⁵	C₂×#120	1	1	yes	characteristic
235	C₂⁵	C₂×#121	1	2	yes	—
236	C₂⁵	C₂×#123	1	1	yes	characteristic
237	H(5,𝔽₂)	C₂×#99	1	16	yes	—
238	C₂²×Q₈	#379	1	1	yes	characteristic
239	C₂²×Q₈	#386	1	1	yes	characteristic
240	C₂²×Q₈	#390	1	2	yes	—
241	C₂²×Q₈	#394	1	2	yes	—
242	C₂²×Q₈	C₂²×C₂²⋊C₄	1	1	yes	characteristic
243	C₂²×Q₈	C₂×#123	1	1	yes	characteristic
244	C₂²×D₄	#379	1	2	yes	—
245	C₂²×D₄	#379	1	1	yes	characteristic
246	C₂²×D₄	#386	1	2	yes	—
247	C₂²×D₄	#386	1	2	yes	—
248	C₂²×D₄	#386	1	2	yes	—
249	C₂²×D₄	#386	1	2	yes	—
250	C₂²×D₄	#386	1	2	yes	—
251	C₂²×D₄	#386	1	2	yes	—
252	C₂²×D₄	#386	1	2	yes	—
253	C₂²×D₄	#386	1	1	yes	characteristic
254	C₂²×D₄	#390	1	2	yes	—
255	C₂²×D₄	#390	1	2	yes	—
256	C₂²×D₄	#390	1	2	yes	—
257	C₂²×D₄	#392	1	2	yes	—
258	C₂²×D₄	#392	1	2	yes	—
259	C₂²×D₄	#392	1	2	yes	—
260	C₂²×D₄	#392	1	2	yes	—
261	C₂²×D₄	#392	1	2	yes	—
262	C₂²×D₄	#392	1	2	yes	—
263	C₂²×D₄	#392	1	2	yes	—
264	C₂²×D₄	#392	1	2	yes	—
265	C₂²×D₄	#394	1	2	yes	—
266	C₂²×D₄	#394	1	2	yes	—
267	C₂²×D₄	#394	1	2	yes	—
268	C₂²×D₄	#394	1	2	yes	—
269	C₂²×D₄	#394	1	2	yes	—
270	C₂²×D₄	#394	1	2	yes	—
271	C₂²×D₄	#394	1	2	yes	—
272	C₂²×D₄	C₂×#99	1	8	yes	—
273	C₂²×D₄	B(4,𝔽₂)	1	4	yes	—
274	C₂²×D₄	B(4,𝔽₂)	1	4	yes	—
275	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
276	C₂²×D₄	C₂×C₄×D₄	1	2	yes	—
277	C₂²×D₄	C₂×#120	1	2	yes	—
278	C₂²×D₄	C₂×#120	1	1	yes	characteristic
279	C₂²×D₄	C₂×#121	1	2	yes	—
280	C₂²×D₄	C₂×#121	1	2	yes	—
281	C₂²×D₄	C₂×#121	1	2	yes	—
282	C₂²×D₄	C₂×#121	1	2	yes	—
283	C₂²×D₄	C₂×#123	1	2	yes	—
284	C₂²×D₄	C₂×#127	1	2	yes	—
285	C₂³×C₄	#379	1	1	yes	characteristic
286	C₂³×C₄	#379	1	2	yes	—
287	C₂³×C₄	#379	1	1	yes	characteristic
288	C₂³×C₄	#386	1	1	yes	characteristic
289	C₂³×C₄	#386	1	1	yes	characteristic
290	C₂³×C₄	#386	1	2	yes	—
291	C₂³×C₄	#386	1	2	yes	—
292	C₂³×C₄	#386	1	1	yes	characteristic
293	C₂³×C₄	#390	1	2	yes	—
294	C₂³×C₄	#390	1	2	yes	—
295	C₂³×C₄	#390	1	2	yes	—
296	C₂³×C₄	#390	1	2	yes	—
297	C₂³×C₄	#392	1	2	yes	—
298	C₂³×C₄	#392	1	2	yes	—
299	C₂³×C₄	#394	1	2	yes	—
300	C₂³×C₄	#394	1	2	yes	—
301	C₂³×C₄	#394	1	2	yes	—
302	C₂³×C₄	#394	1	2	yes	—
303	C₂³×C₄	#394	1	2	yes	—
304	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
305	C₂³×C₄	C₂×C₄×D₄	1	2	yes	—
306	C₂³×C₄	C₂×#120	1	2	yes	—
307	C₂³×C₄	C₂×#121	1	2	yes	—
308	C₂³×C₄	C₂×#124	1	2	yes	—
309	C₂⁴	#1438	1	2	yes	—
310	C₂⁴	#1438	1	2	yes	—
311	C₂⁴	#1438	1	2	yes	—
312	C₂⁴	#1438	1	2	yes	—
313	C₂⁴	#1438	1	1	yes	characteristic
314	C₂⁴	#1438	1	1	yes	characteristic
315	C₂⁴	#1889	1	4	yes	—
316	C₂⁴	#1889	1	4	yes	—
317	C₂⁴	#1898	1	4	yes	—
318	C₂⁴	#1898	1	4	yes	—
319	C₂⁴	#2021	1	4	yes	—
320	C₂⁴	#2021	1	4	yes	—
321	C₂⁴	#2021	1	4	yes	—
322	C₂⁴	#2021	1	4	yes	—
323	C₂⁴	#2021	1	8	yes	—
324	C₂⁴	C₂×#386	1	1	yes	characteristic
325	C₂⁴	C₂×#386	1	2	yes	—
326	C₂⁴	C₂×#392	1	2	yes	—
327	C₂⁴	C₂×#392	1	2	yes	—
328	C₂⁴	C₂×#394	1	2	yes	—
329	C₂⁴	C₂×B(4,𝔽₂)	1	4	yes	—
330	C₂×D₄	#1781	1	4	yes	—
331	C₂×D₄	#1889	1	4	yes	—
332	C₂×D₄	#1898	1	8	yes	—
333	C₂×D₄	#2021	1	8	yes	—
334	C₂×D₄	C₂²×#99	1	4	yes	—
335	C₂×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
336	C₂²×C₄	#1438	1	2	yes	—
337	C₂²×C₄	#1438	1	2	yes	—
338	C₂²×C₄	#1438	1	1	yes	characteristic
339	C₂²×C₄	#1438	1	1	yes	characteristic
340	C₂²×C₄	#1781	1	4	yes	—
341	C₂²×C₄	#1889	1	2	yes	—
342	C₂²×C₄	#1889	1	2	yes	—
343	C₂²×C₄	C₂×#379	1	1	yes	characteristic
344	C₂²×C₄	C₂×#386	1	1	yes	characteristic
345	C₂²×C₄	C₂×#390	1	2	yes	—
346	C₂²×C₄	C₂×#394	1	2	yes	—
347	C₂³	#10965	1	4	yes	—
348	C₂³	#10965	1	2	yes	—
349	C₂³	#10991	1	4	yes	—
350	C₂³	#10991	1	2	yes	—
351	C₂³	#10991	1	4	yes	—
352	C₂³	#10991	1	2	yes	—
353	C₂³	#10991	1	1	yes	characteristic
354	C₂³	#10991	1	1	yes	characteristic
355	C₂³	C₂×#1438	1	1	yes	characteristic
356	C₂³	C₂×#1889	1	2	yes	—
357	C₂³	C₂×#1898	1	4	yes	—
358	C₂³	C₂×#2021	1	4	yes	—
359	C₂³	C₂×#2021	1	4	yes	—
360	C₂×C₄	#10965	1	2	yes	—
361	C₂×C₄	#10991	1	2	yes	—
362	C₂×C₄	C₂×#1781	1	2	yes	—
363	C₂×C₄	C₂×#1889	1	2	yes	—
364	C₂²	#115690	1	2	yes	—
365	C₂²	#115690	1	2	yes	—
366	C₂²	C₂×#10965	1	1	yes	characteristic
367	C₂²	C₂×#10991	1	1	yes	characteristic
368	C₂²	C₂×#10991	1	1	yes	characteristic
369	C₂	C₂×#115690	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	C₂×#115690
commutator	C₂²×#41	C₂³×C₄
Frattini, cosocle	C₂²×H(5,𝔽₂)	C₂⁴
prime radical	#72256016	C₂
LCS	G ▷ C₂²×#41 ▷ 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. #72341833	C₂	semidirect
2. #72337559	C₂	semidirect
3. #72311883	C₂	semidirect
4. C₂×#128079	C₂	semidirect
6. #72241079	C₂	semidirect
7. C₂×#392135	C₂	semidirect
9. C₂×#60387	C₄	semidirect
11. #6628873	C₄	semidirect
13. #6628872	C₄	semidirect
15. #6370746	C₄	semidirect
19. #496205	C₂²	semidirect
20. #496203	C₂²	semidirect
22. #213862	C₂²	semidirect
23. #213860	C₂²	semidirect
24. #128079	C₂²	semidirect
34. C₂×#3022	C₂×C₄	semidirect
35. C₂×#3021	C₂×C₄	semidirect
50. #20615	C₂×C₄	semidirect
51. #20615	C₂×C₄	semidirect
75. C₂³×#41	C₂²⋊C₄	semidirect
85. C₂×#536	C₂²⋊C₄	semidirect
86. C₂×#536	C₂²⋊C₄	semidirect
89. C₂×#535	C₂²⋊C₄	semidirect
90. C₂×#535	C₂²⋊C₄	semidirect
93. C₂²×#127	C₂²⋊C₄	semidirect
95. C₂²×#124	C₂²⋊C₄	semidirect
97. C₂²×#117	C₂²⋊C₄	semidirect
98. C₂²×#117	C₂²⋊C₄	semidirect
99. C₂²×#117	C₂²⋊C₄	semidirect
100. C₂×#413	C₂²⋊C₄	semidirect
102. C₂²×#101	C₂²⋊C₄	semidirect
104. #2309	C₂²⋊C₄	semidirect
105. #2309	C₂²⋊C₄	semidirect
109. #2297	C₂²⋊C₄	semidirect
110. #2297	C₂²⋊C₄	semidirect
111. #2297	C₂²⋊C₄	semidirect
112. #2297	C₂²⋊C₄	semidirect
117. #1785	C₂²⋊C₄	semidirect
123. C₂×H(5,𝔽₂)	#99	semidirect
154. C₂³×Q₈	C₂×C₂²⋊C₄	semidirect
159. C₂³×D₄	C₂×C₂²⋊C₄	semidirect
210. C₂×#117	C₂×C₂²⋊C₄	semidirect
211. C₂×#117	C₂×C₂²⋊C₄	semidirect
212. C₂×#117	C₂×C₂²⋊C₄	semidirect
213. C₂×#117	C₂×C₂²⋊C₄	semidirect
214. C₂²×C₄²	C₂×C₂²⋊C₄	semidirect
215. C₂²×C₄²	C₂×C₂²⋊C₄	semidirect
216. C₂×#101	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
#72341833	2
#72337559	2
#72311883	2
C₂×#128079	2
#72256016	2
#72241079	2
C₂×#392135	2