Subgroups — #72313204

Order 2048.

At least 7422 conjugacy classes of subgroups; only the 656 normal subgroups are shown.

The subgroup lattice has 356 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72313202	C₂	1	2	yes	maximal, complemented
2	#72311484	C₂	1	2	yes	maximal, complemented
3	#72311484	C₂	1	2	yes	maximal, complemented
4	#72311470	C₂	1	1	yes	maximal, characteristic, complemented
5	#72311456	C₂	1	1	yes	maximal, characteristic, complemented
6	#72311440	C₂	1	1	yes	maximal, characteristic, complemented
7	#72311433	C₂	1	1	yes	maximal, characteristic, complemented
8	#72311414	C₂	1	2	yes	maximal, complemented
9	#72298107	C₂	1	1	yes	maximal, characteristic, complemented
10	#72237676	C₂	1	1	yes	maximal, characteristic, complemented
11	#72237569	C₂	1	1	yes	maximal, characteristic
12	C₂³×D₄²	C₂²	1	1	yes	characteristic
13	C₂×#61559	C₄	1	2	yes	complemented
14	#7630940	C₂²	1	1	yes	characteristic
15	C₂²×D₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
16	C₂×#32878	C₂²	1	2	yes	—
17	#6470077	C₄	1	4	yes	complemented
18	#6469932	C₂²	1	2	yes	—
19	#6386001	C₄	1	2	yes	complemented
20	#6385945	C₂²	1	1	yes	characteristic
21	C₂×#13902	C₂²	1	1	yes	characteristic, complemented
22	#392978	C₂²	1	2	yes	complemented
23	#392978	C₂²	1	2	yes	complemented
24	#392147	C₂²	1	1	yes	characteristic
25	#392118	C₂²	1	2	yes	complemented
26	#196822	C₂²	1	2	yes	complemented
27	#196822	C₂²	1	2	yes	complemented
28	#185046	C₂²	1	2	yes	complemented
29	#184743	C₂²	1	1	yes	characteristic
30	#154384	C₂²	1	1	yes	characteristic, complemented
31	#154384	C₂²	1	1	yes	characteristic, complemented
32	#154168	C₂²	1	1	yes	characteristic
33	C₄×#1438	C₂²	1	1	yes	characteristic
34	#106256	C₂²	1	2	yes	complemented
35	#106256	C₂²	1	2	yes	complemented
36	#106244	C₂²	1	2	yes	complemented
37	#106244	C₂²	1	2	yes	complemented
38	C₂⁵×D₄	D₄	1	1	yes	characteristic
39	C₂⁵×D₄	C₂³	1	1	yes	characteristic
40	C₂×#3496	C₂×C₄	1	1	yes	characteristic, complemented
41	C₂²×D₄²	C₂×C₄	1	2	yes	—
42	C₂²×D₄²	C₂×C₄	1	2	yes	—
43	C₂²×D₄²	D₄	1	2	yes	—
44	C₂²×D₄²	D₄	1	2	yes	—
45	C₂³×#127	D₄	1	1	yes	characteristic
46	C₂³×#121	D₄	1	1	yes	characteristic
47	C₂³×#121	C₂³	1	1	yes	characteristic
48	C₂³×C₄×D₄	D₄	1	1	yes	characteristic
49	C₂³×C₄×D₄	C₂³	1	1	yes	characteristic
50	C₂×#3186	C₂×C₄	1	4	yes	complemented
51	C₂²×#447	C₂×C₄	1	4	yes	—
52	C₂²×#447	D₄	1	4	yes	—
53	C₂²×#447	D₄	1	4	yes	—
54	C₂×#2972	C₂×C₄	1	2	yes	complemented
55	C₂×#2847	C₂³	1	2	yes	—
56	#35000	C₂×C₄	1	2	yes	complemented
57	#34181	C₂×C₄	1	1	yes	characteristic, complemented
58	C₂²×#380	C₂³	1	1	yes	characteristic
59	C₂²×#380	C₂³	1	1	yes	characteristic
60	C₂²×C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
61	C₂²×C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
62	#21758	C₂×C₄	1	4	yes	complemented
63	#21738	C₂×C₄	1	2	yes	complemented
64	C₂×#1786	C₂×C₄	1	4	yes	—
65	C₂×#1786	D₄	1	4	yes	—
66	C₂×#1786	D₄	1	4	yes	—
67	C₂×#1779	C₂³	1	2	yes	—
68	C₂×#1779	C₂³	1	2	yes	—
69	#14680	C₂³	1	2	yes	—
70	C₂×#1438	D₄	1	1	yes	characteristic
71	C₂×#1438	D₄	1	1	yes	characteristic
72	#7557	D₄	1	2	yes	—
73	#7555	D₄	1	2	yes	—
74	#7555	D₄	1	1	yes	characteristic
75	#7555	D₄	1	1	yes	characteristic
76	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	—
77	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	—
78	C₂⁴×D₄	C₂²×C₄	1	2	yes	—
79	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
80	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
81	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
82	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
83	C₂⁴×D₄	C₂×D₄	1	4	yes	—
84	C₂⁴×D₄	C₂×D₄	1	2	yes	—
85	C₂⁴×D₄	C₂×D₄	1	4	yes	—
86	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
87	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
88	C₂³×D₈	C₂²⋊C₄	1	8	yes	complemented
89	C₂²×#127	C₂²⋊C₄	1	2	yes	—
90	C₂²×#127	C₂²⋊C₄	1	2	yes	—
91	C₂²×#121	C₂²⋊C₄	1	2	yes	—
92	C₂²×#121	C₂²⋊C₄	1	2	yes	—
93	C₂²×#121	C₂²×C₄	1	2	yes	—
94	C₂²×#121	C₂²×C₄	1	2	yes	—
95	C₂²×#121	C₂×D₄	1	2	yes	—
96	C₂²×#121	C₂×D₄	1	2	yes	—
97	C₂²×#121	C₂×D₄	1	2	yes	—
98	C₂²×C₄×D₄	C₂²⋊C₄	1	2	yes	—
99	C₂²×C₄×D₄	C₂²⋊C₄	1	2	yes	—
100	C₂²×C₄×D₄	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×D₄	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×D₄	#41	1	1	yes	characteristic
105	C₂²×C₄×D₄	#41	1	1	yes	characteristic
106	C₂²×C₄×D₄	#41	1	1	yes	characteristic
107	C₂²×C₄×D₄	#41	1	1	yes	characteristic
108	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
109	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
110	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
111	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
112	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
113	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
114	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
115	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
116	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
117	C₂²×#102	C₂²⋊C₄	1	8	yes	complemented
118	C₂²×#102	C₂²⋊C₄	1	8	yes	complemented
119	C₂²×#102	C₂²⋊C₄	1	8	yes	complemented
120	C₂²×C₂²⋊C₈	C₂²×C₄	1	4	yes	—
121	C₂²×C₂²⋊C₈	C₂×D₄	1	4	yes	—
122	C₂²×C₂²⋊C₈	C₂×D₄	1	4	yes	—
123	C₂×#380	C₂²×C₄	1	2	yes	—
124	C₂×#380	C₂×D₄	1	2	yes	—
125	C₂×#380	C₂×D₄	1	2	yes	—
126	C₂²×#95	C₂×D₄	1	2	yes	—
127	C₂²×#95	C₂×D₄	1	2	yes	—
128	#1438	D₈	1	4	yes	complemented
129	C₂⁶	#120	1	1	yes	characteristic
130	C₂⁶	C₂²×D₄	1	1	yes	characteristic
131	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
132	C₂³×D₄	C₂×C₂²⋊C₄	1	8	yes	—
133	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
134	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
135	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
136	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
137	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
138	C₂³×D₄	#120	1	2	yes	—
139	C₂³×D₄	#120	1	2	yes	—
140	C₂³×D₄	#120	1	2	yes	—
141	C₂³×D₄	#120	1	8	yes	—
142	C₂³×D₄	#120	1	2	yes	—
143	C₂³×D₄	#121	1	1	yes	characteristic
144	C₂³×D₄	#121	1	1	yes	characteristic
145	C₂³×D₄	C₂×D₈	1	2	yes	—
146	C₂³×D₄	#135	1	2	yes	—
147	C₂³×D₄	AGL(1,ℤ/8)	1	2	yes	—
148	C₂³×D₄	AGL(1,ℤ/8)	1	2	yes	—
149	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
150	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
151	C₂⁴×C₄	#120	1	1	yes	characteristic
152	C₂⁴×C₄	#120	1	1	yes	characteristic
153	C₂⁴×C₄	#120	1	1	yes	characteristic
154	C₂⁴×C₄	#123	1	1	yes	characteristic
155	C₂⁴×C₄	#123	1	1	yes	characteristic
156	C₂⁴×C₄	C₂³×C₄	1	1	yes	characteristic
157	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
158	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
159	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
160	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
161	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
162	C₂⁴×C₄	C₂×#41	1	1	yes	characteristic
163	C₂⁴×C₄	C₂×#41	1	1	yes	characteristic
164	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
165	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
166	C₂³×C₈	C₂×C₂²⋊C₄	1	8	yes	—
167	C₂×#127	#99	1	8	yes	complemented
168	C₂×#121	#99	1	8	yes	complemented
169	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
170	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
171	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
172	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
173	C₂²×C₄⋊C₄	C₄×D₄	1	1	yes	characteristic
174	C₂²×C₄⋊C₄	C₄×D₄	1	1	yes	characteristic
175	C₂²×C₄⋊C₄	#121	1	1	yes	characteristic
176	C₂²×C₄⋊C₄	#121	1	1	yes	characteristic
177	C₂²×C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic
178	C₂²×C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic
179	C₂²×C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic
180	C₂²×C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic
181	C₂²×C₂²⋊C₄	#121	1	1	yes	characteristic
182	C₂²×C₂²⋊C₄	#121	1	1	yes	characteristic
183	C₂²×C₂²⋊C₄	#121	1	1	yes	characteristic
184	C₂²×C₂²⋊C₄	#121	1	1	yes	characteristic
185	C₂²×C₂²⋊C₄	C₂×D₈	1	2	yes	complemented
186	C₂²×C₂²⋊C₄	C₂×D₈	1	2	yes	complemented
187	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
188	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
189	C₂²×C₄²	#123	1	1	yes	characteristic
190	C₂²×C₄²	#123	1	1	yes	characteristic
191	C₂⁵	#386	1	1	yes	characteristic
192	C₂⁵	#386	1	1	yes	characteristic
193	C₂⁵	#447	1	2	yes	—
194	C₂⁵	#449	1	2	yes	—
195	C₂⁵	C₂×C₄×D₄	1	1	yes	characteristic
196	C₂⁵	C₂×#120	1	1	yes	characteristic
197	C₂⁵	C₂×#121	1	1	yes	characteristic
198	C₂⁵	D₄²	1	2	yes	—
199	C₂⁵	D₄²	1	2	yes	—
200	C₂⁵	C₂²×D₈	1	1	yes	characteristic
201	C₂⁵	C₂×#135	1	1	yes	characteristic
202	C₂⁵	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
203	C₂⁵	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
204	C₂⁵	#576	1	2	yes	—
205	C₂⁵	#576	1	2	yes	—
206	C₂²×D₄	#379	1	4	yes	—
207	C₂²×D₄	#379	1	4	yes	—
208	C₂²×D₄	C₂×#99	1	4	yes	—
209	C₂²×D₄	C₂×#99	1	4	yes	—
210	C₂²×D₄	C₂×#99	1	4	yes	—
211	C₂²×D₄	C₄×D₈	1	2	yes	—
212	C₂²×D₄	C₄×D₈	1	2	yes	—
213	C₂²×D₄	#442	1	2	yes	—
214	C₂²×D₄	#442	1	2	yes	—
215	C₂²×D₄	B(4,𝔽₂)	1	4	yes	—
216	C₂²×D₄	#458	1	4	yes	—
217	C₂²×D₄	#459	1	2	yes	—
218	C₂²×D₄	#459	1	2	yes	—
219	C₂²×D₄	#463	1	2	yes	—
220	C₂²×D₄	#463	1	2	yes	—
221	C₂³×C₄	#386	1	1	yes	characteristic
222	C₂³×C₄	#386	1	1	yes	characteristic
223	C₂³×C₄	#386	1	1	yes	characteristic
224	C₂³×C₄	#386	1	1	yes	characteristic
225	C₂³×C₄	#386	1	1	yes	characteristic
226	C₂³×C₄	#386	1	1	yes	characteristic
227	C₂³×C₄	C₂×#99	1	4	yes	—
228	C₂³×C₄	#447	1	2	yes	—
229	C₂³×C₄	#449	1	2	yes	—
230	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
231	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
232	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
233	C₂³×C₄	#518	1	2	yes	—
234	C₂³×C₄	C₂×#120	1	2	yes	—
235	C₂³×C₄	C₂×#120	1	1	yes	characteristic
236	C₂³×C₄	C₂×#120	1	1	yes	characteristic
237	C₂³×C₄	C₂×#121	1	1	yes	characteristic
238	C₂³×C₄	C₂×#123	1	1	yes	characteristic
239	C₂³×C₄	#534	1	1	yes	characteristic
240	C₂³×C₄	#534	1	1	yes	characteristic
241	C₂³×C₄	#534	1	2	yes	—
242	C₂³×C₄	D₄²	1	2	yes	—
243	C₂³×C₄	D₄²	1	2	yes	—
244	C₂³×C₄	#546	1	2	yes	—
245	C₂³×C₄	#546	1	2	yes	—
246	C₂³×C₄	#546	1	2	yes	—
247	C₂³×C₄	#546	1	2	yes	—
248	C₂×C₄⋊C₄	C₂×#99	1	4	yes	—
249	C₂×C₄²	C₂×#99	1	4	yes	—
250	C₂⁴	#1879	1	2	yes	—
251	C₂⁴	#1879	1	2	yes	—
252	C₂⁴	#1898	1	2	yes	—
253	C₂⁴	#1904	1	2	yes	—
254	C₂⁴	C₂×#386	1	1	yes	characteristic
255	C₂⁴	D₄×C₂²⋊C₄	1	2	yes	—
256	C₂⁴	#2403	1	1	yes	characteristic
257	C₂⁴	#2403	1	1	yes	characteristic
258	C₂⁴	#2410	1	2	yes	—
259	C₂⁴	C₂×C₄×D₈	1	1	yes	characteristic
260	C₂⁴	C₂×#442	1	1	yes	characteristic
261	C₂⁴	#2948	1	2	yes	—
262	C₂⁴	C₂×#447	1	1	yes	characteristic
263	C₂⁴	C₂×#449	1	1	yes	characteristic
264	C₂⁴	#3008	1	1	yes	characteristic
265	C₂⁴	#3008	1	1	yes	characteristic
266	C₂⁴	C₂×#459	1	1	yes	characteristic
267	C₂⁴	C₂×#463	1	1	yes	characteristic
268	C₂⁴	#3041	1	2	yes	—
269	C₂⁴	#3264	1	2	yes	—
270	C₂⁴	#3264	1	2	yes	—
271	C₂⁴	#3264	1	2	yes	—
272	C₂⁴	#3264	1	2	yes	—
273	C₂⁴	D₄×D₈	1	2	yes	—
274	C₂⁴	D₄×D₈	1	2	yes	—
275	C₂⁴	#3280	1	2	yes	—
276	C₂⁴	#3280	1	2	yes	—
277	C₂×D₄	#1781	1	8	yes	—
278	C₂×D₄	#1790	1	8	yes	—
279	C₂²×C₄	#1879	1	2	yes	—
280	C₂²×C₄	#1879	1	2	yes	—
281	C₂²×C₄	#1898	1	2	yes	—
282	C₂²×C₄	#1898	1	2	yes	—
283	C₂²×C₄	#1898	1	2	yes	—
284	C₂²×C₄	#1904	1	2	yes	—
285	C₂²×C₄	C₂×#379	1	1	yes	characteristic
286	C₂²×C₄	#2308	1	1	yes	characteristic
287	C₂²×C₄	D₄×C₂²⋊C₄	1	2	yes	—
288	C₂²×C₄	#2405	1	1	yes	characteristic
289	C₂²×C₄	#2405	1	1	yes	characteristic
290	C₂²×C₄	#2410	1	2	yes	—
291	C₂²×C₄	C₂²×#99	1	2	yes	—
292	C₂²×C₄	C₂²×#99	1	2	yes	—
293	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
294	C₂²×C₄	C₂×#458	1	2	yes	—
295	C₂²×C₄	#3026	1	2	yes	—
296	C₂²×C₄	#3026	1	2	yes	—
297	C₂³	#9259	1	4	yes	complemented
298	C₂³	#13867	1	1	yes	characteristic
299	C₂³	C₂×#1879	1	1	yes	characteristic
300	C₂³	#20934	1	1	yes	characteristic
301	C₂³	C₂×#1898	1	1	yes	characteristic
302	C₂³	C₂×#1898	1	1	yes	characteristic
303	C₂³	C₂×#1904	1	1	yes	characteristic
304	C₂³	C₂×#1904	1	1	yes	characteristic
305	C₂³	#22436	1	2	yes	—
306	C₂³	C₂²⋊C₄×D₈	1	2	yes	—
307	C₂³	#23848	1	1	yes	characteristic
308	C₂³	#23848	1	1	yes	characteristic
309	C₂³	#23851	1	1	yes	characteristic
310	C₂³	#23851	1	1	yes	characteristic
311	C₂³	#23882	1	1	yes	characteristic
312	C₂³	#23882	1	1	yes	characteristic
313	C₂³	#23883	1	1	yes	characteristic
314	C₂³	#23883	1	1	yes	characteristic
315	C₂³	#23900	1	1	yes	characteristic
316	C₂³	#23901	1	1	yes	characteristic
317	C₂³	#23903	1	1	yes	characteristic
318	C₂³	#23903	1	1	yes	characteristic
319	C₂³	#24354	1	2	yes	—
320	C₂³	#24355	1	2	yes	—
321	C₂×C₄	#9259	1	4	yes	complemented
322	C₂×C₄	C₂×#1781	1	2	yes	—
323	C₂×C₄	C₂×#1790	1	2	yes	—
324	C₂×C₄	#20609	1	2	yes	—
325	C₂×C₄	#21746	1	2	yes	—
326	C₂×C₄	#24056	1	2	yes	—
327	C₂×C₄	#24058	1	2	yes	—
328	C₂²	C₂×#9259	1	1	yes	characteristic
329	C₂²	C₂×#9259	1	1	yes	characteristic
330	C₂²	#198463	1	1	yes	characteristic
331	C₂²	#198463	1	1	yes	characteristic
332	C₂²	#248455	1	1	yes	characteristic
333	C₂²	#248458	1	1	yes	characteristic
334	C₂²	#248467	1	1	yes	characteristic
335	C₂²	#248470	1	1	yes	characteristic
336	C₂²	#248503	1	1	yes	characteristic
337	C₂²	#248506	1	1	yes	characteristic
338	C₂²	#248515	1	1	yes	characteristic
339	C₂²	#248518	1	1	yes	characteristic
340	C₂²	#359428	1	1	yes	characteristic
341	C₂²	#359472	1	1	yes	characteristic
342	C₂²	#359487	1	1	yes	characteristic
343	C₂²	#359552	1	1	yes	characteristic
344	C₂²	#359554	1	1	yes	characteristic
345	C₂²	#359576	1	1	yes	characteristic
346	C₂²	#359576	1	1	yes	characteristic
347	C₄	#187928	1	4	yes	—
348	C₂	#72214400	1	1	yes	characteristic
349	C₂	#72214493	1	1	yes	characteristic
350	C₂	#72236440	1	1	yes	characteristic
351	C₂	#72264018	1	1	yes	characteristic
352	C₂	#72264272	1	1	yes	characteristic
353	C₂	#72313095	1	1	yes	characteristic
354	C₂	#72313181	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	#13867
commutator	C₂⁴×C₄	C₂³×C₄
Frattini, cosocle	C₂⁵×C₄	C₂⁴
prime radical	#72237569	C₂
LCS	G ▷ C₂⁴×C₄ ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂⁵×C₄ ◁ G
LECS	G ▷ C₂⁵×C₄ ▷ C₂³ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72313202	C₂	semidirect
2. #72311484	C₂	semidirect
3. #72311484	C₂	semidirect
4. #72311470	C₂	semidirect
5. #72311456	C₂	semidirect
6. #72311440	C₂	semidirect
7. #72311433	C₂	semidirect
8. #72311414	C₂	semidirect
9. #72298107	C₂	semidirect
10. #72237676	C₂	semidirect
13. C₂×#61559	C₄	semidirect
15. C₂²×D₄×C₂²⋊C₄	C₂²	semidirect
17. #6470077	C₄	semidirect
19. #6386001	C₄	semidirect
21. C₂×#13902	C₂²	semidirect
22. #392978	C₂²	semidirect
23. #392978	C₂²	semidirect
25. #392118	C₂²	semidirect
26. #196822	C₂²	semidirect
27. #196822	C₂²	semidirect
28. #185046	C₂²	semidirect
30. #154384	C₂²	semidirect
31. #154384	C₂²	semidirect
34. #106256	C₂²	semidirect
35. #106256	C₂²	semidirect
36. #106244	C₂²	semidirect
37. #106244	C₂²	semidirect
40. C₂×#3496	C₂×C₄	semidirect
50. C₂×#3186	C₂×C₄	semidirect
54. C₂×#2972	C₂×C₄	semidirect
56. #35000	C₂×C₄	semidirect
57. #34181	C₂×C₄	semidirect
62. #21758	C₂×C₄	semidirect
63. #21738	C₂×C₄	semidirect
88. C₂³×D₈	C₂²⋊C₄	semidirect
117. C₂²×#102	C₂²⋊C₄	semidirect
118. C₂²×#102	C₂²⋊C₄	semidirect
119. C₂²×#102	C₂²⋊C₄	semidirect
128. #1438	D₈	semidirect
167. C₂×#127	#99	semidirect
168. C₂×#121	#99	semidirect
185. C₂²×C₂²⋊C₄	C₂×D₈	semidirect
186. C₂²×C₂²⋊C₄	C₂×D₈	semidirect
297. C₂³	#9259	semidirect
321. C₂×C₄	#9259	semidirect

Maximal subgroups

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

subgroup	index
#72313202	2
#72311484	2
#72311470	2
#72311456	2
#72311440	2
#72311433	2
#72311414	2
#72298107	2
#72237676	2
#72237569	2