Subgroups — #72340859

Order 2048.

At least 7195 conjugacy classes of subgroups; only the 498 normal subgroups are shown.

The subgroup lattice has 345 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72340835	C₂	1	2	yes	maximal, complemented
2	#72340834	C₂	1	2	yes	maximal, complemented
3	#72339692	C₂	1	1	yes	maximal, characteristic, complemented
4	#72338294	C₂	1	1	yes	maximal, characteristic, complemented
5	#72312790	C₂	1	1	yes	maximal, characteristic
6	#72286416	C₂	1	2	yes	maximal, complemented
7	#72286280	C₂	1	2	yes	maximal, complemented
8	#72279597	C₂	1	1	yes	maximal, characteristic, complemented
9	#72279491	C₂	1	1	yes	maximal, characteristic, complemented
10	#72261405	C₂	1	1	yes	maximal, characteristic, complemented
11	#72252021	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#3498	C₂²	1	1	yes	characteristic
13	#10575509	C₂²	1	1	yes	characteristic
14	#10575094	C₄	1	1	yes	characteristic, complemented
15	#7641973	C₄	1	1	yes	characteristic, complemented
16	C₂×#33359	C₂²	1	2	yes	—
17	#6446716	C₄	1	1	yes	characteristic, complemented
18	#6446716	C₄	1	1	yes	characteristic, complemented
19	#6446716	C₂²	1	1	yes	characteristic
20	#6446716	C₂²	1	1	yes	characteristic
21	#6443311	C₄	1	1	yes	characteristic, complemented
22	#6443311	C₄	1	1	yes	characteristic, complemented
23	#6443311	C₂²	1	1	yes	characteristic
24	#6443311	C₂²	1	1	yes	characteristic
25	#6374317	C₂²	1	1	yes	characteristic
26	C₂×#21797	C₄	1	1	yes	characteristic, complemented
27	#6370997	C₄	1	1	yes	characteristic, complemented
28	#512635	C₂²	1	2	yes	complemented
29	#512625	C₂²	1	2	yes	complemented
30	#512601	C₂²	1	2	yes	complemented
31	#512594	C₂²	1	2	yes	complemented
32	#493431	C₂²	1	2	yes	—
33	C₂×#12718	C₂²	1	2	yes	—
34	C₂×#12718	C₂²	1	2	yes	—
35	#493378	C₂²	1	1	yes	characteristic
36	#493365	C₂²	1	1	yes	characteristic
37	#493365	C₂²	1	1	yes	characteristic
38	#493365	C₂²	1	1	yes	characteristic
39	#151864	C₂²	1	2	yes	complemented
40	#151858	C₂²	1	2	yes	complemented
41	#151854	C₂²	1	2	yes	complemented
42	#151842	C₂²	1	2	yes	complemented
43	C₂³×H(5,𝔽₂)	D₄	1	1	yes	characteristic
44	C₂³×H(5,𝔽₂)	D₄	1	1	yes	characteristic
45	C₂×#3498	C₂×C₄	1	1	yes	characteristic
46	C₂×#3498	C₂×C₄	1	1	yes	characteristic
47	C₂×#3498	D₄	1	1	yes	characteristic
48	C₂×#3498	D₄	1	1	yes	characteristic
49	C₂×#3498	D₄	1	1	yes	characteristic
50	C₂×#3498	D₄	1	1	yes	characteristic
51	C₂×#3498	C₂³	1	1	yes	characteristic
52	C₂×#3498	C₂³	1	1	yes	characteristic
53	C₂²×#535	D₄	1	1	yes	characteristic
54	C₂²×#535	D₄	1	1	yes	characteristic
55	C₂×#3444	C₂×C₄	1	1	yes	characteristic, complemented
56	C₂²×#532	C₂³	1	1	yes	characteristic
57	C₂³×#127	C₂×C₄	1	1	yes	characteristic
58	C₂²×C₄×#41	C₂×C₄	1	1	yes	characteristic
59	#60639	C₂×C₄	1	1	yes	characteristic, complemented
60	#60639	C₂³	1	1	yes	characteristic
61	#60618	C₂×C₄	1	1	yes	characteristic, complemented
62	#60618	C₂³	1	1	yes	characteristic
63	#60484	C₂×C₄	1	1	yes	characteristic
64	#60484	C₂×C₄	1	1	yes	characteristic, complemented
65	#60415	C₂×C₄	1	1	yes	characteristic
66	#60415	C₂×C₄	1	1	yes	characteristic, complemented
67	C₂×#2920	C₂×C₄	1	1	yes	characteristic, complemented
68	C₂×#2920	C₂×C₄	1	1	yes	characteristic, complemented
69	#35285	C₂×C₄	1	1	yes	characteristic
70	#35285	C₂×C₄	1	1	yes	characteristic, complemented
71	#35274	C₂×C₄	1	1	yes	characteristic
72	#35274	C₂×C₄	1	1	yes	characteristic, complemented
73	#34012	C₂×C₄	1	1	yes	characteristic, complemented
74	C₂×#2132	C₂³	1	2	yes	—
75	C₂×#2126	C₂³	1	2	yes	—
76	C₂×#2126	C₂³	1	2	yes	—
77	C₂×#2126	C₂³	1	2	yes	—
78	#25878	D₄	1	8	yes	—
79	#25747	D₄	1	4	yes	—
80	#25744	D₄	1	4	yes	—
81	C₂×#1965	C₂×C₄	1	1	yes	characteristic
82	C₂×#1965	C₂×C₄	1	1	yes	characteristic
83	C₂×#1965	C₂×C₄	1	1	yes	characteristic, complemented
84	C₂×#1965	C₂×C₄	1	1	yes	characteristic, complemented
85	#21209	C₂×C₄	1	1	yes	characteristic, complemented
86	#21209	C₂×C₄	1	1	yes	characteristic, complemented
87	#21209	C₂³	1	1	yes	characteristic
88	#21209	C₂³	1	1	yes	characteristic
89	C₄×#421	C₂×C₄	1	1	yes	characteristic
90	C₄×#421	C₂×C₄	1	1	yes	characteristic
91	C₄×#421	C₂×C₄	1	1	yes	characteristic, complemented
92	C₄×#421	C₂×C₄	1	1	yes	characteristic, complemented
93	#12695	D₄	1	2	yes	complemented
94	#12695	D₄	1	2	yes	complemented
95	#12694	D₄	1	2	yes	complemented
96	#12693	D₄	1	2	yes	complemented
97	C₂²×H(5,𝔽₂)	C₂²⋊C₄	1	1	yes	characteristic
98	C₂²×H(5,𝔽₂)	C₂²⋊C₄	1	1	yes	characteristic
99	C₂²×H(5,𝔽₂)	C₂²⋊C₄	1	1	yes	characteristic
100	C₂²×H(5,𝔽₂)	C₂²⋊C₄	1	1	yes	characteristic
101	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
102	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
103	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
104	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
105	C₂³×#41	C₂²⋊C₄	1	1	yes	characteristic
106	C₂³×#41	C₂×D₄	1	1	yes	characteristic
107	C₂³×#41	C₂×D₄	1	1	yes	characteristic
108	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
109	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
110	#3498	C₂×D₄	1	4	yes	—
111	#3498	C₂×D₄	1	4	yes	—
112	C₂×#535	C₂²⋊C₄	1	1	yes	characteristic
113	C₂×#535	C₂²⋊C₄	1	1	yes	characteristic
114	C₂×#535	C₂²⋊C₄	1	1	yes	characteristic
115	C₂×#535	C₂²⋊C₄	1	1	yes	characteristic
116	C₂×#535	C₂×D₄	1	1	yes	characteristic
117	C₂×#535	C₂×D₄	1	1	yes	characteristic
118	C₂×#535	C₂×D₄	1	1	yes	characteristic
119	C₂×#535	C₂×D₄	1	1	yes	characteristic
120	C₂×#533	C₂²×C₄	1	1	yes	characteristic
121	C₂×#532	C₂²×C₄	1	1	yes	characteristic
122	C₂×#532	C₂²×C₄	1	1	yes	characteristic
123	C₂×#532	C₂×D₄	1	1	yes	characteristic
124	C₂×#532	C₂×D₄	1	1	yes	characteristic
125	C₂×#532	C₂×D₄	1	1	yes	characteristic
126	C₂×#532	C₂×D₄	1	1	yes	characteristic
127	C₂×#532	#41	1	1	yes	characteristic
128	C₂×#532	#41	1	1	yes	characteristic
129	C₂×#532	C₂⁴	1	1	yes	characteristic
130	C₂²×C₄⋊Q₈	#41	1	1	yes	characteristic
131	C₂²×#127	C₂²⋊C₄	1	1	yes	characteristic
132	C₂²×#127	C₂²⋊C₄	1	1	yes	characteristic
133	C₂²×#127	C₂²×C₄	1	1	yes	characteristic
134	C₂²×#127	C₂²×C₄	1	1	yes	characteristic
135	C₂²×#127	C₂×D₄	1	1	yes	characteristic
136	C₂²×#124	C₂×D₄	1	1	yes	characteristic
137	C₂²×#124	#41	1	1	yes	characteristic
138	C₂×C₄×#41	C₂²⋊C₄	1	1	yes	characteristic
139	C₂×C₄×#41	C₂²⋊C₄	1	1	yes	characteristic
140	C₂×C₄×#41	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₄×#41	C₂²×C₄	1	1	yes	characteristic
142	C₂²×#117	C₂²⋊C₄	1	1	yes	characteristic
143	C₂³×C₄²	C₂²×C₄	1	1	yes	characteristic
144	#3152	C₂×D₄	1	2	yes	—
145	#3151	C₂×D₄	1	2	yes	—
146	#3142	C₂×D₄	1	4	yes	—
147	#3080	C₂²⋊C₄	1	4	yes	complemented
148	#3039	C₂²⋊C₄	1	2	yes	complemented
149	#3038	C₂²⋊C₄	1	2	yes	complemented
150	C₂×#423	C₂²×C₄	1	1	yes	characteristic
151	C₂×#423	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₄×M₁₆	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₄×M₁₆	C₂²×C₄	1	1	yes	characteristic
154	#2867	C₂²⋊C₄	1	2	yes	complemented
155	#2858	C₂²⋊C₄	1	2	yes	complemented
156	#2641	C₂²⋊C₄	1	4	yes	complemented
157	C₄×#117	C₂²×C₄	1	1	yes	characteristic
158	C₄×#117	C₂²×C₄	1	1	yes	characteristic
159	C₂×#354	C₂×D₄	1	4	yes	—
160	C₂×#353	C₂×D₄	1	4	yes	—
161	#1965	C₂²⋊C₄	1	4	yes	complemented
162	#1965	C₂²⋊C₄	1	4	yes	complemented
163	#1963	C₂×D₄	1	4	yes	—
164	#1962	C₂×D₄	1	4	yes	—
165	#1759	C₂²⋊C₄	1	4	yes	complemented
166	C₄×#104	C₂²⋊C₄	1	4	yes	complemented
167	C₂⁶	#99	1	2	yes	—
168	C₂×H(5,𝔽₂)	#120	1	4	yes	—
169	C₂×H(5,𝔽₂)	#120	1	4	yes	—
170	C₂²×#41	#99	1	1	yes	characteristic
171	C₂²×#41	#99	1	1	yes	characteristic
172	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
173	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
174	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
175	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
176	C₂²×#41	#120	1	1	yes	characteristic
177	C₂²×#41	#121	1	1	yes	characteristic
178	C₂²×#41	#121	1	1	yes	characteristic
179	C₂²×#41	#123	1	1	yes	characteristic
180	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
181	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
182	C₂³×Q₈	#99	1	1	yes	characteristic
183	C₂³×Q₈	#121	1	1	yes	characteristic
184	C₂³×Q₈	#123	1	1	yes	characteristic
185	C₂³×D₄	#99	1	1	yes	characteristic
186	C₂³×D₄	#99	1	2	yes	—
187	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
188	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
189	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
190	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
191	C₂³×D₄	#120	1	1	yes	characteristic
192	C₂³×D₄	#121	1	1	yes	characteristic
193	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
194	#535	#120	1	4	yes	—
195	#535	#120	1	4	yes	—
196	#532	C₂²×D₄	1	2	yes	—
197	#532	C₂²×D₄	1	2	yes	—
198	#532	H(5,𝔽₂)	1	2	yes	—
199	#532	H(5,𝔽₂)	1	2	yes	—
200	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented
201	C₂×C₄⋊Q₈	C₄×D₄	1	1	yes	characteristic
202	C₂×C₄⋊Q₈	#121	1	1	yes	characteristic
203	C₂×C₄⋊Q₈	#123	1	1	yes	characteristic
204	C₂×C₄⋊Q₈	C₂×#41	1	1	yes	characteristic
205	C₂×#127	#99	1	2	yes	—
206	C₂×#127	#99	1	2	yes	—
207	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
208	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
209	C₂×#127	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented
210	C₂×#127	C₄×D₄	1	1	yes	characteristic
211	C₂×#127	#120	1	1	yes	characteristic
212	C₂×#127	#121	1	1	yes	characteristic
213	C₂×#127	C₂²×D₄	1	1	yes	characteristic
214	C₂×#125	C₂×C₂²⋊C₄	1	2	yes	complemented
215	C₂×#124	C₄×D₄	1	1	yes	characteristic
216	C₂×#124	C₄×D₄	1	1	yes	characteristic
217	C₂×#124	#120	1	1	yes	characteristic
218	C₂×#124	#121	1	1	yes	characteristic
219	C₂×#124	#121	1	1	yes	characteristic
220	C₂×#124	#123	1	1	yes	characteristic
221	C₂×#124	C₂²×D₄	1	1	yes	characteristic
222	C₂×#124	C₂×#41	1	1	yes	characteristic
223	C₄×#41	#99	1	2	yes	—
224	C₄×#41	#99	1	2	yes	—
225	C₄×#41	C₂×C₂²⋊C₄	1	2	yes	—
226	C₄×#41	C₂×C₂²⋊C₄	1	2	yes	—
227	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
228	C₂×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
229	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
230	C₂²×C₄²	C₄×D₄	1	1	yes	characteristic
231	C₂²×C₄²	C₄×D₄	1	1	yes	characteristic
232	C₂²×C₄²	C₄×D₄	1	1	yes	characteristic
233	C₂²×C₄²	C₄×D₄	1	1	yes	characteristic
234	C₂²×C₄²	C₂³×C₄	1	1	yes	characteristic
235	#423	C₂×C₂²⋊C₄	1	2	yes	complemented
236	#423	C₂×C₂²⋊C₄	1	2	yes	complemented
237	C₄×M₁₆	C₂×C₂²⋊C₄	1	2	yes	complemented
238	C₄×M₁₆	C₂×C₂²⋊C₄	1	2	yes	complemented
239	#376	C₂×C₂²⋊C₄	1	2	yes	complemented
240	C₄³	C₂×C₂²⋊C₄	1	2	yes	complemented
241	C₂⁵	C₂×#99	1	2	yes	—
242	C₂⁵	C₂×#99	1	1	yes	characteristic
243	C₂⁵	C₂×#99	1	2	yes	—
244	C₂×#41	#379	1	2	yes	—
245	C₂×#41	C₂×#99	1	2	yes	—
246	C₂×#41	C₂×#120	1	2	yes	—
247	C₂×#41	C₂×#120	1	2	yes	—
248	C₂×#41	#534	1	2	yes	—
249	C₂×#41	#534	1	2	yes	—
250	C₂²×Q₈	#386	1	1	yes	characteristic
251	C₂²×Q₈	#386	1	1	yes	characteristic
252	C₂²×Q₈	C₂×#99	1	1	yes	characteristic
253	C₂²×Q₈	C₂×#99	1	1	yes	characteristic
254	C₂²×Q₈	C₂×#121	1	1	yes	characteristic
255	C₂²×Q₈	C₂×#123	1	1	yes	characteristic
256	C₂²×D₄	#379	1	2	yes	—
257	C₂²×D₄	#379	1	2	yes	—
258	C₂²×D₄	#386	1	1	yes	characteristic
259	C₂²×D₄	#386	1	1	yes	characteristic
260	C₂²×D₄	C₂×#99	1	2	yes	—
261	C₂²×D₄	C₂×#99	1	2	yes	—
262	C₂²×D₄	C₂×#99	1	1	yes	characteristic
263	C₂²×D₄	C₂×#99	1	1	yes	characteristic
264	C₂²×D₄	C₂×#120	1	1	yes	characteristic
265	C₂²×D₄	C₂×#121	1	1	yes	characteristic
266	C₂³×C₄	#386	1	1	yes	characteristic
267	C₂³×C₄	#386	1	1	yes	characteristic
268	C₂³×C₄	C₂×#99	1	1	yes	characteristic
269	C₂³×C₄	C₂×#99	1	1	yes	characteristic
270	C₂³×C₄	C₂×#99	1	1	yes	characteristic
271	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
272	C₄⋊Q₈	#546	1	2	yes	—
273	C₄⋊Q₈	#546	1	2	yes	—
274	#127	D₄²	1	2	yes	—
275	#127	D₄²	1	2	yes	—
276	#124	D₄²	1	2	yes	—
277	#124	D₄²	1	2	yes	—
278	#124	#546	1	2	yes	—
279	#124	#546	1	2	yes	—
280	#117	#379	1	2	yes	—
281	#117	C₂×#99	1	2	yes	—
282	C₂×C₄²	#386	1	1	yes	characteristic
283	C₂×C₄²	#386	1	1	yes	characteristic
284	C₂×C₄²	C₂×#99	1	1	yes	characteristic
285	C₂×C₄²	C₂×#99	1	1	yes	characteristic
286	C₂×C₄²	C₂×#99	1	1	yes	characteristic
287	C₂×C₄²	C₂×#99	1	1	yes	characteristic
288	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
289	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
290	C₂×C₄²	C₂×C₄×D₄	1	1	yes	characteristic
291	C₂×C₄²	C₂×C₄×D₄	1	1	yes	characteristic
292	C₂×C₄²	#518	1	1	yes	characteristic
293	C₂×C₄²	#518	1	1	yes	characteristic
294	C₂⁴	#1781	1	4	yes	—
295	C₂⁴	#1898	1	1	yes	characteristic
296	C₂⁴	#1898	1	1	yes	characteristic
297	C₂⁴	C₂²×#99	1	1	yes	characteristic
298	C₂×Q₈	#1781	1	2	yes	—
299	C₂×Q₈	#2127	1	2	yes	—
300	C₂×Q₈	#2405	1	2	yes	—
301	C₂×Q₈	#2410	1	2	yes	—
302	C₂×D₄	#1781	1	2	yes	—
303	C₂×D₄	#2127	1	2	yes	—
304	C₂×D₄	#2127	1	2	yes	—
305	C₂×D₄	#2127	1	2	yes	—
306	C₂×D₄	#2403	1	2	yes	—
307	C₂×D₄	#2410	1	2	yes	—
308	C₂²×C₄	#1898	1	1	yes	characteristic
309	C₂²×C₄	#1898	1	1	yes	characteristic
310	C₂²×C₄	C₂×#379	1	1	yes	characteristic
311	C₂²×C₄	C₂×#386	1	1	yes	characteristic
312	C₂²×C₄	#2308	1	1	yes	characteristic
313	C₂²×C₄	C₂²×#99	1	1	yes	characteristic
314	C₂²×C₄	C₂²×#99	1	1	yes	characteristic
315	C₂²×C₄	C₂²×#99	1	1	yes	characteristic
316	C₄²	#1898	1	1	yes	characteristic
317	C₄²	#1898	1	1	yes	characteristic
318	C₄²	#1898	1	1	yes	characteristic
319	C₄²	#1898	1	1	yes	characteristic
320	C₄²	D₄×C₂²⋊C₄	1	1	yes	characteristic
321	C₄²	D₄×C₂²⋊C₄	1	1	yes	characteristic
322	C₄²	D₄×C₂²⋊C₄	1	1	yes	characteristic
323	C₄²	D₄×C₂²⋊C₄	1	1	yes	characteristic
324	C₂³	C₂×#1781	1	1	yes	characteristic
325	C₂³	C₂×#1898	1	1	yes	characteristic
326	C₂³	#21746	1	1	yes	characteristic
327	D₄	#12696	1	4	yes	—
328	C₂×C₄	#13867	1	1	yes	characteristic
329	C₂×C₄	C₂×#1781	1	1	yes	characteristic
330	C₂×C₄	C₂×#1898	1	1	yes	characteristic
331	C₂×C₄	#21746	1	1	yes	characteristic
332	C₂×C₄	C₂×#2127	1	1	yes	characteristic
333	C₂×C₄	C₂×#2127	1	1	yes	characteristic
334	C₂×C₄	C₂×#2127	1	1	yes	characteristic
335	C₂×C₄	C₂×#2127	1	1	yes	characteristic
336	C₂²	#359428	1	1	yes	characteristic
337	C₂²	#494713	1	1	yes	characteristic
338	C₂²	#494713	1	1	yes	characteristic
339	C₄	C₂×#12696	1	1	yes	characteristic
340	C₄	#493370	1	1	yes	characteristic
341	C₄	#496194	1	1	yes	characteristic
342	C₄	#496194	1	1	yes	characteristic
343	C₂	#72340830	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	#72340830
commutator	C₂²×C₄²	C₂³×C₄
Frattini, cosocle	C₂×#532	C₂⁴
prime radical	#72312790	C₂
LCS	G ▷ C₂²×C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂³×#41 ◁ C₂²×#3498 ◁ G
LECS	G ▷ C₂×#532 ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72340835	C₂	semidirect
2. #72340834	C₂	semidirect
3. #72339692	C₂	semidirect
4. #72338294	C₂	semidirect
6. #72286416	C₂	semidirect
7. #72286280	C₂	semidirect
8. #72279597	C₂	semidirect
9. #72279491	C₂	semidirect
10. #72261405	C₂	semidirect
11. #72252021	C₂	semidirect
14. #10575094	C₄	semidirect
15. #7641973	C₄	semidirect
17. #6446716	C₄	semidirect
18. #6446716	C₄	semidirect
21. #6443311	C₄	semidirect
22. #6443311	C₄	semidirect
26. C₂×#21797	C₄	semidirect
27. #6370997	C₄	semidirect
28. #512635	C₂²	semidirect
29. #512625	C₂²	semidirect
30. #512601	C₂²	semidirect
31. #512594	C₂²	semidirect
39. #151864	C₂²	semidirect
40. #151858	C₂²	semidirect
41. #151854	C₂²	semidirect
42. #151842	C₂²	semidirect
55. C₂×#3444	C₂×C₄	semidirect
59. #60639	C₂×C₄	semidirect
61. #60618	C₂×C₄	semidirect
64. #60484	C₂×C₄	semidirect
66. #60415	C₂×C₄	semidirect
67. C₂×#2920	C₂×C₄	semidirect
68. C₂×#2920	C₂×C₄	semidirect
70. #35285	C₂×C₄	semidirect
72. #35274	C₂×C₄	semidirect
73. #34012	C₂×C₄	semidirect
83. C₂×#1965	C₂×C₄	semidirect
84. C₂×#1965	C₂×C₄	semidirect
85. #21209	C₂×C₄	semidirect
86. #21209	C₂×C₄	semidirect
91. C₄×#421	C₂×C₄	semidirect
92. C₄×#421	C₂×C₄	semidirect
93. #12695	D₄	semidirect
94. #12695	D₄	semidirect
95. #12694	D₄	semidirect
96. #12693	D₄	semidirect
147. #3080	C₂²⋊C₄	semidirect
148. #3039	C₂²⋊C₄	semidirect
149. #3038	C₂²⋊C₄	semidirect
154. #2867	C₂²⋊C₄	semidirect
155. #2858	C₂²⋊C₄	semidirect
156. #2641	C₂²⋊C₄	semidirect
161. #1965	C₂²⋊C₄	semidirect
162. #1965	C₂²⋊C₄	semidirect
165. #1759	C₂²⋊C₄	semidirect
166. C₄×#104	C₂²⋊C₄	semidirect
200. C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	semidirect
209. C₂×#127	C₂×C₂²⋊C₄	semidirect
214. C₂×#125	C₂×C₂²⋊C₄	semidirect
235. #423	C₂×C₂²⋊C₄	semidirect
236. #423	C₂×C₂²⋊C₄	semidirect
237. C₄×M₁₆	C₂×C₂²⋊C₄	semidirect
238. C₄×M₁₆	C₂×C₂²⋊C₄	semidirect
239. #376	C₂×C₂²⋊C₄	semidirect
240. C₄³	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
#72340835	2
#72340834	2
#72339692	2
#72338294	2
#72312790	2
#72286416	2
#72286280	2
#72279597	2
#72279491	2
#72261405	2
#72252021	2