Subgroups — #72234066

Order 2048.

At least 6233 conjugacy classes of subgroups; only the 392 normal subgroups are shown.

The subgroup lattice has 341 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72234063	C₂	1	2	yes	maximal, complemented
2	#72234062	C₂	1	2	yes	maximal, complemented
3	#72234061	C₂	1	2	yes	maximal, complemented
4	#72234060	C₂	1	2	yes	maximal, complemented
5	#72233824	C₂	1	1	yes	maximal, characteristic
6	#72233277	C₂	1	1	yes	maximal, characteristic, complemented
7	#72233258	C₂	1	1	yes	maximal, characteristic, complemented
8	#72233224	C₂	1	1	yes	maximal, characteristic, complemented
9	#72233123	C₂	1	1	yes	maximal, characteristic, complemented
10	#72233041	C₂	1	1	yes	maximal, characteristic, complemented
11	#72232722	C₂	1	1	yes	maximal, characteristic, complemented
12	#6385983	C₂²	1	1	yes	characteristic
13	#6385971	C₂²	1	1	yes	characteristic
14	#6385971	C₂²	1	1	yes	characteristic
15	#5522295	C₄	1	1	yes	characteristic, complemented
16	#5519537	C₄	1	1	yes	characteristic, complemented
17	#5482155	C₄	1	1	yes	characteristic, complemented
18	#5119558	C₄	1	1	yes	characteristic, complemented
19	#5118168	C₄	1	1	yes	characteristic, complemented
20	#4861302	C₂²	1	1	yes	characteristic
21	#4417886	C₂²	1	1	yes	characteristic
22	#4123398	C₄	1	1	yes	characteristic, complemented
23	#2535814	C₄	1	1	yes	characteristic, complemented
24	#2177498	C₄	1	1	yes	characteristic, complemented
25	#878571	C₂²	1	1	yes	characteristic
26	#649038	C₂²	1	1	yes	characteristic
27	#587425	C₂²	1	1	yes	characteristic
28	#556476	C₂²	1	1	yes	characteristic
29	#553180	C₂²	1	1	yes	characteristic
30	#482357	C₂²	1	2	yes	—
31	#481961	C₂²	1	2	yes	—
32	#201386	C₂²	1	2	yes	—
33	#197340	C₂²	1	2	yes	—
34	#188151	C₂²	1	1	yes	characteristic
35	#128086	C₂²	1	2	yes	—
36	#128050	C₂²	1	2	yes	—
37	#127233	C₂²	1	2	yes	—
38	#127199	C₂²	1	2	yes	—
39	#108241	C₂²	1	2	yes	—
40	#106763	C₂²	1	2	yes	—
41	#106601	C₂²	1	2	yes	—
42	#106385	C₂²	1	2	yes	—
43	C₂²×D₄²	C₂³	1	1	yes	characteristic
44	C₂³×#127	D₄	1	1	yes	characteristic
45	#60230	C₂³	1	2	yes	—
46	C₂×#2815	D₄	1	1	yes	characteristic
47	C₂×#2433	D₄	1	1	yes	characteristic
48	C₂×#2433	D₄	1	1	yes	characteristic
49	C₂×#2408	C₂³	1	1	yes	characteristic
50	C₂×#2635	C₂³	1	1	yes	characteristic
51	C₂×#2353	D₄	1	1	yes	characteristic
52	C₂×#2318	D₄	1	1	yes	characteristic
53	#20722	C₂³	1	2	yes	—
54	#20722	C₂³	1	2	yes	—
55	#17364	C₂³	1	2	yes	—
56	#17141	C₂×C₄	1	1	yes	characteristic, complemented
57	#17141	C₂×C₄	1	1	yes	characteristic, complemented
58	#17082	C₂×C₄	1	1	yes	characteristic, complemented
59	#17082	C₂×C₄	1	1	yes	characteristic, complemented
60	#16242	C₂×C₄	1	1	yes	characteristic, complemented
61	#16186	C₂×C₄	1	1	yes	characteristic, complemented
62	#16171	C₂×C₄	1	1	yes	characteristic, complemented
63	#15964	C₂×C₄	1	1	yes	characteristic, complemented
64	#15674	C₂×C₄	1	1	yes	characteristic
65	#15674	C₂×C₄	1	1	yes	characteristic
66	#15310	C₂×C₄	1	1	yes	characteristic
67	#15310	C₂×C₄	1	1	yes	characteristic
68	#15310	C₂×C₄	1	1	yes	characteristic
69	#15310	C₂×C₄	1	1	yes	characteristic
70	#15310	C₂×C₄	1	1	yes	characteristic
71	#15310	C₂×C₄	1	1	yes	characteristic
72	#15283	D₄	1	1	yes	characteristic
73	#15283	D₄	1	1	yes	characteristic
74	#15258	D₄	1	1	yes	characteristic
75	#15258	D₄	1	1	yes	characteristic
76	#15258	D₄	1	1	yes	characteristic
77	#15258	D₄	1	1	yes	characteristic
78	#15258	D₄	1	1	yes	characteristic
79	#15258	D₄	1	1	yes	characteristic
80	#14698	D₄	1	1	yes	characteristic
81	#14661	D₄	1	1	yes	characteristic
82	#14659	C₂×C₄	1	1	yes	characteristic
83	#14654	C₂×C₄	1	1	yes	characteristic, complemented
84	#14641	C₂×C₄	1	1	yes	characteristic, complemented
85	#14641	C₂×C₄	1	1	yes	characteristic, complemented
86	#14617	C₂×C₄	1	1	yes	characteristic, complemented
87	#14571	C₂×C₄	1	1	yes	characteristic, complemented
88	#14345	C₂³	1	1	yes	characteristic
89	#14335	D₄	1	1	yes	characteristic
90	#14335	D₄	1	1	yes	characteristic
91	#14290	C₂×C₄	1	1	yes	characteristic
92	#14290	D₄	1	1	yes	characteristic
93	#14272	D₄	1	1	yes	characteristic
94	#14271	C₂×C₄	1	1	yes	characteristic
95	#14252	C₂×C₄	1	1	yes	characteristic, complemented
96	#14181	C₂×C₄	1	1	yes	characteristic, complemented
97	#14181	C₂×C₄	1	1	yes	characteristic, complemented
98	#14152	C₂×C₄	1	1	yes	characteristic
99	#13959	C₂³	1	1	yes	characteristic
100	#13940	C₂³	1	1	yes	characteristic
101	#13902	D₄	1	1	yes	characteristic
102	#13902	D₄	1	1	yes	characteristic
103	#13902	D₄	1	1	yes	characteristic
104	C₂×#1438	D₄	1	1	yes	characteristic
105	C₄×#386	C₂³	1	1	yes	characteristic
106	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
107	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
108	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
109	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
110	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
111	C₂²×#127	C₂²⋊C₄	1	1	yes	characteristic
112	C₂²×#127	C₂²⋊C₄	1	1	yes	characteristic
113	C₂²×#127	C₂²⋊C₄	1	1	yes	characteristic
114	C₂²×#127	C₂²⋊C₄	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	C₂×D₄	1	1	yes	characteristic
118	C₂²×#121	C₂²×C₄	1	1	yes	characteristic
119	C₂²×#121	C₂²×C₄	1	1	yes	characteristic
120	C₂²×#121	C₂×D₄	1	1	yes	characteristic
121	C₂²×#121	C₂×D₄	1	1	yes	characteristic
122	C₂²×#121	C₂×D₄	1	1	yes	characteristic
123	C₂²×#120	C₂×D₄	1	1	yes	characteristic
124	C₂²×#120	C₂×D₄	1	1	yes	characteristic
125	C₂²×#120	C₂×D₄	1	1	yes	characteristic
126	C₂²×#120	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×D₄	C₂⁴	1	1	yes	characteristic
129	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
130	C₂×#400	C₂²×C₄	1	1	yes	characteristic
131	C₂×#399	C₂×D₄	1	1	yes	characteristic
132	C₂×#397	C₂²⋊C₄	1	1	yes	characteristic
133	C₂×#397	C₂²⋊C₄	1	1	yes	characteristic
134	C₂×#394	C₂²×C₄	1	1	yes	characteristic
135	C₂×#394	C₂²×C₄	1	1	yes	characteristic
136	C₂×#394	C₂²×C₄	1	1	yes	characteristic
137	C₂×#392	C₂²⋊C₄	1	1	yes	characteristic
138	C₂×#392	C₂²⋊C₄	1	1	yes	characteristic
139	C₂×#392	C₂²⋊C₄	1	1	yes	characteristic
140	C₂×#392	C₂²⋊C₄	1	1	yes	characteristic
141	C₂×#392	C₂²⋊C₄	1	1	yes	characteristic
142	C₂×#392	C₂²⋊C₄	1	1	yes	characteristic
143	C₂×#392	C₂×D₄	1	1	yes	characteristic
144	C₂×#392	C₂×D₄	1	1	yes	characteristic
145	C₂×#392	C₂×D₄	1	1	yes	characteristic
146	C₂×#390	C₂²⋊C₄	1	1	yes	characteristic
147	C₂×#390	C₂²⋊C₄	1	1	yes	characteristic
148	C₂×#383	C₂×D₄	1	1	yes	characteristic
149	C₂×#383	C₂×D₄	1	1	yes	characteristic
150	C₂×#382	C₂×D₄	1	1	yes	characteristic
151	C₂×#381	C₂²⋊C₄	1	1	yes	characteristic
152	C₂×#381	C₂²⋊C₄	1	1	yes	characteristic
153	C₂×#381	C₂×D₄	1	1	yes	characteristic
154	C₂×#381	C₂×D₄	1	1	yes	characteristic
155	C₂×#380	C₂²⋊C₄	1	1	yes	characteristic
156	C₂×#380	C₂²⋊C₄	1	1	yes	characteristic
157	C₂×#380	C₂×D₄	1	1	yes	characteristic
158	C₂×C₄×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
161	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
162	C₂×#376	C₂×D₄	1	1	yes	characteristic
163	C₂²×#95	C₂²⋊C₄	1	1	yes	characteristic
164	C₂²×#95	C₂²⋊C₄	1	1	yes	characteristic
165	#1799	#41	1	4	yes	complemented
166	C₄×#99	#41	1	4	yes	complemented
167	#1445	C₂²×C₄	1	1	yes	characteristic
168	#1445	C₂²×C₄	1	1	yes	characteristic
169	#1445	C₂²×C₄	1	1	yes	characteristic
170	#1445	C₂²×C₄	1	1	yes	characteristic
171	#1438	C₂²⋊C₄	1	1	yes	characteristic
172	#1438	C₂²⋊C₄	1	1	yes	characteristic
173	#1438	C₂²⋊C₄	1	1	yes	characteristic
174	#1438	C₂²⋊C₄	1	1	yes	characteristic
175	#1438	C₂²⋊C₄	1	1	yes	characteristic
176	#1438	C₂²⋊C₄	1	1	yes	characteristic
177	#1438	C₂²⋊C₄	1	1	yes	characteristic
178	#1438	C₂²⋊C₄	1	1	yes	characteristic
179	#1438	C₂²⋊C₄	1	1	yes	characteristic
180	#1438	C₂²⋊C₄	1	1	yes	characteristic
181	#1438	C₂²⋊C₄	1	1	yes	characteristic
182	#1438	C₂²⋊C₄	1	1	yes	characteristic
183	#1438	C₂²⋊C₄	1	1	yes	characteristic
184	#1438	C₂²⋊C₄	1	1	yes	characteristic
185	#1438	C₂²⋊C₄	1	1	yes	characteristic
186	#1438	C₂²⋊C₄	1	1	yes	characteristic
187	#1438	C₂×D₄	1	1	yes	characteristic
188	#1438	C₂×D₄	1	1	yes	characteristic
189	#1438	C₂×D₄	1	1	yes	characteristic
190	#1438	C₂×D₄	1	1	yes	characteristic
191	#1437	C₂²⋊C₄	1	1	yes	characteristic
192	#1437	C₂²⋊C₄	1	1	yes	characteristic
193	#1437	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	C₂×D₄	1	1	yes	characteristic
200	#1437	C₂×D₄	1	1	yes	characteristic
201	#1437	C₂×D₄	1	1	yes	characteristic
202	#1437	C₂×D₄	1	1	yes	characteristic
203	#1436	C₂²×C₄	1	1	yes	characteristic
204	#1436	C₂²×C₄	1	1	yes	characteristic
205	#1436	C₂²×C₄	1	1	yes	characteristic
206	#1436	C₂²×C₄	1	1	yes	characteristic
207	C₂⁶	#120	1	1	yes	characteristic
208	C₂⁶	#120	1	1	yes	characteristic
209	C₂⁶	#120	1	1	yes	characteristic
210	C₂⁶	#120	1	1	yes	characteristic
211	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
212	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
213	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
214	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
215	C₂³×D₄	C₂×C₂²⋊C₄	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	#120	1	1	yes	characteristic
221	C₂³×D₄	#120	1	1	yes	characteristic
222	C₂³×D₄	#120	1	1	yes	characteristic
223	C₂³×D₄	#120	1	1	yes	characteristic
224	C₂³×D₄	#120	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	C₂²×D₄	1	1	yes	characteristic
230	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
231	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
232	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
233	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×D₄	C₂×#41	1	2	yes	—
235	C₂×C₄×D₄	C₂×#41	1	2	yes	—
236	C₂×C₄×D₄	H(5,𝔽₂)	1	2	yes	—
237	C₂×C₄×D₄	2₋¹⁺⁴	1	2	yes	—
238	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
239	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
240	C₂²×C₄⋊C₄	C₂³×C₄	1	1	yes	characteristic
241	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
242	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
243	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
244	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
245	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
246	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
247	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
248	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
249	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
250	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
251	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
252	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
253	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
254	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
255	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
256	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
257	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
258	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
259	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
260	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
261	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
262	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
263	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
264	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
265	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
266	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
267	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
268	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
269	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
270	C₂⁵	#379	1	1	yes	characteristic
271	C₂⁵	#379	1	1	yes	characteristic
272	C₂⁵	#379	1	1	yes	characteristic
273	C₂⁵	#379	1	1	yes	characteristic
274	C₂⁵	#379	1	1	yes	characteristic
275	C₂⁵	#379	1	1	yes	characteristic
276	C₂⁵	C₂×#120	1	1	yes	characteristic
277	C₂⁵	C₂×#120	1	1	yes	characteristic
278	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
279	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
280	C₂²×D₄	#458	1	1	yes	characteristic
281	C₂²×D₄	#458	1	1	yes	characteristic
282	C₂²×D₄	#525	1	1	yes	characteristic
283	C₂²×D₄	#525	1	1	yes	characteristic
284	C₂²×D₄	#535	1	1	yes	characteristic
285	C₂²×D₄	#536	1	1	yes	characteristic
286	C₂³×C₄	#379	1	1	yes	characteristic
287	C₂³×C₄	#379	1	1	yes	characteristic
288	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
289	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
290	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
291	C₂³×C₄	C₂×#120	1	1	yes	characteristic
292	C₂³×C₄	C₂×#120	1	1	yes	characteristic
293	C₂³×C₄	#546	1	2	yes	—
294	C₂³×C₄	#546	1	2	yes	—
295	C₂³×C₄	#547	1	2	yes	—
296	C₂³×C₄	#547	1	2	yes	—
297	C₂×C₄⋊C₄	C₄×#41	1	2	yes	—
298	C₂×C₄⋊C₄	#520	1	2	yes	—
299	C₂×C₂²⋊C₄	#546	1	2	yes	—
300	C₂×C₂²⋊C₄	#546	1	2	yes	—
301	C₂×C₂²⋊C₄	#547	1	2	yes	—
302	C₂×C₂²⋊C₄	#547	1	2	yes	—
303	C₂×C₄²	#532	1	2	yes	—
304	C₂×C₄²	#537	1	2	yes	—
305	C₂⁴	#1790	1	1	yes	characteristic
306	C₂⁴	#1790	1	1	yes	characteristic
307	C₂⁴	#1790	1	1	yes	characteristic
308	C₂⁴	#1790	1	1	yes	characteristic
309	C₂⁴	C₂×#379	1	1	yes	characteristic
310	C₂⁴	#2404	1	1	yes	characteristic
311	C₂⁴	#2404	1	1	yes	characteristic
312	C₂⁴	#2406	1	1	yes	characteristic
313	C₂⁴	#2406	1	1	yes	characteristic
314	C₂²×C₄	#2297	1	1	yes	characteristic
315	C₂²×C₄	#2311	1	1	yes	characteristic
316	C₂²×C₄	#2339	1	2	yes	—
317	C₂²×C₄	#2339	1	2	yes	—
318	C₂²×C₄	#2430	1	2	yes	—
319	C₂²×C₄	#2430	1	2	yes	—
320	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
321	C₂²×C₄	C₂×#458	1	1	yes	characteristic
322	C₂²×C₄	#3026	1	2	yes	—
323	C₂³	#12753	1	2	yes	—
324	C₂³	#13956	1	1	yes	characteristic
325	C₂³	C₂×#1790	1	1	yes	characteristic
326	C₂³	#20609	1	1	yes	characteristic
327	C₂³	#23998	1	2	yes	—
328	C₂×C₄	#25563	1	2	yes	—
329	C₂×C₄	#25565	1	2	yes	—
330	C₂²	#363895	1	1	yes	characteristic
331	C₂²	#363956	1	1	yes	characteristic
332	C₂²	#363972	1	1	yes	characteristic
333	C₂²	C₂×#12753	1	1	yes	characteristic
334	C₂²	#493562	1	1	yes	characteristic
335	C₂²	#493656	1	1	yes	characteristic
336	C₂²	#493660	1	1	yes	characteristic
337	C₂	#72233200	1	1	yes	characteristic
338	C₂	#72234064	1	1	yes	characteristic
339	C₂	#72234065	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#363895
commutator	C₂²×C₄⋊C₄	C₂³×C₄
Frattini, cosocle	C₂²×C₄×D₄	C₂⁴
prime radical	#72233824	C₂
LCS	G ▷ C₂²×C₄⋊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. #72234063	C₂	semidirect
2. #72234062	C₂	semidirect
3. #72234061	C₂	semidirect
4. #72234060	C₂	semidirect
6. #72233277	C₂	semidirect
7. #72233258	C₂	semidirect
8. #72233224	C₂	semidirect
9. #72233123	C₂	semidirect
10. #72233041	C₂	semidirect
11. #72232722	C₂	semidirect
15. #5522295	C₄	semidirect
16. #5519537	C₄	semidirect
17. #5482155	C₄	semidirect
18. #5119558	C₄	semidirect
19. #5118168	C₄	semidirect
22. #4123398	C₄	semidirect
23. #2535814	C₄	semidirect
24. #2177498	C₄	semidirect
56. #17141	C₂×C₄	semidirect
57. #17141	C₂×C₄	semidirect
58. #17082	C₂×C₄	semidirect
59. #17082	C₂×C₄	semidirect
60. #16242	C₂×C₄	semidirect
61. #16186	C₂×C₄	semidirect
62. #16171	C₂×C₄	semidirect
63. #15964	C₂×C₄	semidirect
83. #14654	C₂×C₄	semidirect
84. #14641	C₂×C₄	semidirect
85. #14641	C₂×C₄	semidirect
86. #14617	C₂×C₄	semidirect
87. #14571	C₂×C₄	semidirect
95. #14252	C₂×C₄	semidirect
96. #14181	C₂×C₄	semidirect
97. #14181	C₂×C₄	semidirect
165. #1799	#41	semidirect
166. C₄×#99	#41	semidirect

Maximal subgroups

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

subgroup	index
#72234063	2
#72234062	2
#72234061	2
#72234060	2
#72233824	2
#72233277	2
#72233258	2
#72233224	2
#72233123	2
#72233041	2
#72232722	2