Subgroups — #72241067

Order 2048.

At least 9663 conjugacy classes of subgroups; only the 792 normal subgroups are shown.

The subgroup lattice has 354 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72241065	C₂	1	1	yes	maximal, characteristic, complemented
2	#72241064	C₂	1	1	yes	maximal, characteristic, complemented
3	#72241063	C₂	1	1	yes	maximal, characteristic, complemented
4	#72241062	C₂	1	2	yes	maximal, complemented
5	#72234609	C₂	1	1	yes	maximal, characteristic, complemented
6	#72234106	C₂	1	2	yes	maximal, complemented
7	#72233379	C₂	1	4	yes	maximal, complemented
8	#72233365	C₂	1	4	yes	maximal, complemented
9	#72233165	C₂	1	4	yes	maximal, complemented
10	#72233043	C₂	1	2	yes	maximal, complemented
11	#72232536	C₂	1	1	yes	maximal, characteristic, complemented
12	#72231479	C₂	1	2	yes	maximal, complemented
13	#72227781	C₂	1	4	yes	maximal, complemented
14	C₂×#133822	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#6499867	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#62817	C₂²	1	1	yes	characteristic
17	C₂×#45438	C₂²	1	1	yes	characteristic, complemented
18	C₂²×#2846	C₂²	1	1	yes	characteristic
19	#6499867	C₂²	1	4	yes	—
20	#6499867	C₂²	1	4	yes	—
21	#6470226	C₂²	1	2	yes	complemented
22	#6470019	C₂²	1	2	yes	complemented
23	C₂×#23900	C₂²	1	2	yes	—
24	C₂×#23900	C₂²	1	2	yes	—
25	C₂×#21746	C₂²	1	1	yes	characteristic
26	#5021145	C₂²	1	2	yes	complemented
27	#5021139	C₂²	1	2	yes	complemented
28	#2032535	C₂²	1	2	yes	complemented
29	#2031998	C₂²	1	2	yes	complemented
30	#846057	C₂²	1	1	yes	characteristic, complemented
31	#845677	C₂²	1	1	yes	characteristic, complemented
32	#617359	C₂²	1	1	yes	characteristic
33	#617161	C₂²	1	1	yes	characteristic
34	#559835	C₂²	1	1	yes	characteristic, complemented
35	#512145	C₂²	1	4	yes	complemented
36	#511776	C₂²	1	4	yes	complemented
37	#508086	C₂²	1	4	yes	complemented
38	#508063	C₂²	1	4	yes	complemented
39	#496226	C₂²	1	2	yes	complemented
40	#496189	C₂²	1	2	yes	complemented
41	C₂×#12687	C₂²	1	2	yes	complemented
42	C₂×#12687	C₂²	1	2	yes	complemented
43	#347048	C₂²	1	4	yes	complemented
44	#347048	C₂²	1	4	yes	complemented
45	#346466	C₂²	1	4	yes	complemented
46	#346446	C₂²	1	4	yes	complemented
47	C₂×#8547	C₂²	1	1	yes	characteristic
48	C₂×#8541	C₂²	1	1	yes	characteristic
49	#187928	C₂²	1	2	yes	complemented
50	#186808	C₂²	1	2	yes	complemented
51	#144412	C₂²	1	8	yes	complemented
52	#144404	C₂²	1	8	yes	complemented
53	#144386	C₂²	1	8	yes	complemented
54	#144367	C₂²	1	8	yes	complemented
55	#139830	C₂²	1	4	yes	complemented
56	#139828	C₂²	1	4	yes	complemented
57	#139773	C₂²	1	8	yes	complemented
58	#139718	C₂²	1	4	yes	complemented
59	#139714	C₂²	1	4	yes	complemented
60	#139702	C₂²	1	8	yes	complemented
61	#133822	C₂²	1	4	yes	complemented
62	#133822	C₂²	1	4	yes	complemented
63	#128073	C₂²	1	2	yes	complemented
64	#128058	C₂²	1	2	yes	complemented
65	C₂⁸	D₄	1	1	yes	characteristic
66	#62817	C₂³	1	4	yes	—
67	C₂×#3484	C₂³	1	2	yes	—
68	C₂²×#560	C₂³	1	1	yes	characteristic, complemented
69	C₂³×#120	C₂³	1	1	yes	characteristic
70	C₂³×#120	C₂³	1	1	yes	characteristic
71	C₂³×#120	C₂³	1	1	yes	characteristic
72	C₂²×B(4,𝔽₂)	D₄	1	4	yes	complemented
73	C₂×#2697	C₂³	1	1	yes	characteristic, complemented
74	C₂×#2669	C₂³	1	1	yes	characteristic, complemented
75	C₂×#2846	D₄	1	2	yes	—
76	C₂×#2846	D₄	1	2	yes	—
77	C₂×#2846	C₂³	1	2	yes	—
78	C₂×#2846	C₂³	1	2	yes	—
79	C₂×#2539	D₄	1	1	yes	characteristic, complemented
80	C₂×#2433	C₂³	1	1	yes	characteristic
81	C₂×#2405	D₄	1	1	yes	characteristic, complemented
82	C₂×#2405	C₂³	1	1	yes	characteristic
83	C₂×#2617	D₄	1	1	yes	characteristic, complemented
84	C₂×#2375	C₂³	1	1	yes	characteristic, complemented
85	C₂×#2308	D₄	1	1	yes	characteristic, complemented
86	C₂²×#379	D₄	1	1	yes	characteristic
87	C₂²×#379	D₄	1	1	yes	characteristic
88	C₂²×#379	D₄	1	1	yes	characteristic
89	#24056	C₂³	1	4	yes	complemented
90	#24018	C₂³	1	4	yes	complemented
91	#23906	C₂³	1	4	yes	complemented
92	#23901	C₂³	1	4	yes	complemented
93	#23900	D₄	1	8	yes	complemented
94	#23900	C₂³	1	8	yes	—
95	#23900	C₂³	1	4	yes	—
96	#23900	C₂³	1	4	yes	—
97	#21746	C₂³	1	4	yes	—
98	C₂×#1889	D₄	1	4	yes	complemented
99	C₂×#1783	C₂³	1	2	yes	—
100	C₂×#1781	C₂³	1	2	yes	—
101	C₂×#1781	C₂³	1	2	yes	—
102	#15948	D₄	1	2	yes	complemented
103	#15948	D₄	1	2	yes	complemented
104	#15948	C₂³	1	2	yes	—
105	#15948	C₂³	1	2	yes	—
106	#15948	C₂³	1	2	yes	complemented
107	#15283	D₄	1	2	yes	complemented
108	#15283	C₂³	1	2	yes	—
109	#15281	C₂³	1	2	yes	complemented
110	#15266	C₂³	1	2	yes	complemented
111	#15258	D₄	1	2	yes	complemented
112	#15258	C₂³	1	2	yes	—
113	#15258	C₂³	1	2	yes	complemented
114	#14657	C₂³	1	2	yes	complemented
115	#14358	C₂³	1	2	yes	complemented
116	#14335	D₄	1	1	yes	characteristic, complemented
117	#13903	D₄	1	1	yes	characteristic, complemented
118	#13902	C₂³	1	1	yes	characteristic
119	#13867	D₄	1	1	yes	characteristic, complemented
120	#13867	C₂³	1	1	yes	characteristic
121	#13775	D₄	1	1	yes	characteristic, complemented
122	#12856	C₂³	1	4	yes	complemented
123	#12852	C₂³	1	4	yes	complemented
124	#12693	C₂³	1	4	yes	complemented
125	#12688	C₂³	1	4	yes	complemented
126	#12687	C₂³	1	4	yes	complemented
127	#12687	C₂³	1	4	yes	complemented
128	#12687	C₂³	1	8	yes	complemented
129	#8547	C₂³	1	4	yes	—
130	#8541	C₂³	1	4	yes	—
131	#8534	C₂³	1	8	yes	complemented
132	#8453	C₂³	1	8	yes	complemented
133	#7307	C₂³	1	8	yes	complemented
134	#7304	C₂³	1	8	yes	complemented
135	C₂⁷	C₂×D₄	1	1	yes	characteristic
136	C₂⁷	C₂×D₄	1	1	yes	characteristic
137	C₂⁷	C₂×D₄	1	2	yes	—
138	C₂⁷	C₂×D₄	1	2	yes	—
139	C₂⁷	C₂×D₄	1	1	yes	characteristic
140	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
141	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
142	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
143	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
144	#3484	C₂×D₄	1	4	yes	—
145	#3484	C₂⁴	1	4	yes	—
146	C₂²×#127	C₂×D₄	1	1	yes	characteristic, complemented
147	C₂²×#127	C₂⁴	1	1	yes	characteristic
148	C₂²×#123	C₂×D₄	1	1	yes	characteristic, complemented
149	C₂²×#123	C₂×D₄	1	2	yes	complemented
150	C₂²×#123	C₂⁴	1	1	yes	characteristic
151	C₂²×#121	C₂×D₄	1	1	yes	characteristic, complemented
152	C₂²×#120	C₂×D₄	1	4	yes	—
153	C₂²×#120	C₂×D₄	1	4	yes	—
154	C₂²×#120	C₂×D₄	1	2	yes	—
155	C₂²×#120	C₂×D₄	1	1	yes	characteristic
156	C₂²×#120	C₂×D₄	1	1	yes	characteristic
157	C₂²×#120	C₂×D₄	1	2	yes	—
158	C₂²×#120	C₂×D₄	1	2	yes	—
159	C₂²×#120	C₂×D₄	1	2	yes	—
160	C₂²×#120	C₂⁴	1	2	yes	—
161	C₂²×#120	C₂⁴	1	1	yes	characteristic
162	C₂²×#120	C₂⁴	1	1	yes	characteristic
163	C₂²×#120	C₂⁴	1	2	yes	—
164	C₂×#518	C₂×D₄	1	2	yes	—
165	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
166	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
167	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
168	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
169	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
170	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
171	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
172	C₂×B(4,𝔽₂)	C₂×D₄	1	8	yes	—
173	C₂×B(4,𝔽₂)	C₂×D₄	1	8	yes	—
174	C₂²×#99	C₂×D₄	1	4	yes	—
175	C₂×#399	C₂×D₄	1	2	yes	complemented
176	C₂×#397	C₂×D₄	1	2	yes	complemented
177	C₂×#392	C₂×D₄	1	2	yes	complemented
178	C₂×#392	C₂×D₄	1	2	yes	complemented
179	C₂×#390	C₂×D₄	1	1	yes	characteristic, complemented
180	C₂×#390	C₂⁴	1	1	yes	characteristic
181	C₂×#386	C₂×D₄	1	1	yes	characteristic, complemented
182	C₂×#386	C₂×D₄	1	2	yes	complemented
183	C₂×#386	C₂×D₄	1	2	yes	complemented
184	C₂×#386	C₂×D₄	1	2	yes	complemented
185	C₂×#386	C₂⁴	1	1	yes	characteristic
186	C₂×#380	C₂×D₄	1	1	yes	characteristic, complemented
187	C₂×#379	C₂×D₄	1	2	yes	—
188	C₂×#379	C₂×D₄	1	2	yes	—
189	C₂×#379	C₂×D₄	1	2	yes	—
190	C₂×#379	C₂×D₄	1	2	yes	—
191	C₂×#379	C₂×D₄	1	2	yes	—
192	C₂×#379	C₂×D₄	1	2	yes	—
193	C₂×#379	C₂×D₄	1	1	yes	characteristic, complemented
194	C₂×#379	C₂×D₄	1	1	yes	characteristic, complemented
195	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
196	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
197	#1889	C₂×D₄	1	8	yes	—
198	#1889	C₂×D₄	1	8	yes	—
199	#1783	C₂⁴	1	4	yes	—
200	#1781	C₂×D₄	1	4	yes	—
201	#1781	C₂⁴	1	4	yes	—
202	#1781	C₂⁴	1	4	yes	—
203	#1438	C₂×D₄	1	2	yes	complemented
204	#1438	C₂×D₄	1	2	yes	complemented
205	#1438	C₂×D₄	1	2	yes	complemented
206	#1438	C₂×D₄	1	2	yes	complemented
207	#1438	C₂×D₄	1	2	yes	complemented
208	#1438	C₂×D₄	1	2	yes	complemented
209	#1438	C₂⁴	1	2	yes	—
210	#1438	C₂⁴	1	2	yes	—
211	#1437	C₂×D₄	1	2	yes	complemented
212	#1437	C₂×D₄	1	2	yes	complemented
213	#1437	C₂×D₄	1	2	yes	complemented
214	#1437	C₂×D₄	1	2	yes	complemented
215	C₂⁶	#120	1	1	yes	characteristic
216	C₂⁶	#120	1	2	yes	—
217	C₂⁶	#120	1	1	yes	characteristic
218	C₂⁶	#120	1	2	yes	—
219	C₂⁶	#120	1	2	yes	—
220	C₂⁶	C₂²×D₄	1	2	yes	—
221	C₂⁶	C₂²×D₄	1	1	yes	characteristic
222	C₂⁶	C₂²×D₄	1	1	yes	characteristic
223	C₂⁶	C₂²×D₄	1	1	yes	characteristic
224	C₂⁶	C₂²×D₄	1	2	yes	—
225	C₂⁶	C₂²×D₄	1	1	yes	characteristic
226	C₂×H(5,𝔽₂)	C₂²×D₄	1	4	yes	—
227	C₂³×D₄	#120	1	2	yes	—
228	C₂³×D₄	#120	1	2	yes	—
229	C₂³×D₄	C₂²×D₄	1	2	yes	—
230	C₂³×D₄	C₂²×D₄	1	2	yes	—
231	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
232	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
233	C₂³×D₄	C₂²×D₄	1	2	yes	—
234	C₂³×D₄	C₂²×D₄	1	2	yes	—
235	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
236	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic, complemented
237	C₂³×D₄	H(5,𝔽₂)	1	2	yes	—
238	C₂³×D₄	H(5,𝔽₂)	1	2	yes	—
239	C₂³×D₄	C₂⁵	1	1	yes	characteristic
240	C₂⁴×C₄	#120	1	1	yes	characteristic
241	C₂⁴×C₄	#120	1	1	yes	characteristic
242	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
243	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic, complemented
244	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic, complemented
245	C₂×#120	#120	1	4	yes	—
246	C₂×#120	#120	1	4	yes	—
247	C₂×#120	C₂²×D₄	1	4	yes	—
248	C₂×#120	C₂²×D₄	1	4	yes	—
249	#518	C₂²×D₄	1	4	yes	—
250	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic, complemented
251	C₂²×C₂²⋊C₄	#120	1	2	yes	—
252	C₂²×C₂²⋊C₄	#120	1	2	yes	—
253	C₂²×C₂²⋊C₄	#120	1	2	yes	—
254	C₂²×C₂²⋊C₄	#120	1	2	yes	—
255	C₂²×C₂²⋊C₄	#120	1	2	yes	—
256	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
257	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
258	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
259	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
260	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
261	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
262	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic, complemented
263	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic, complemented
264	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	complemented
265	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	complemented
266	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic, complemented
267	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic, complemented
268	C₂×#99	C₂²×D₄	1	8	yes	—
269	C₂×#95	C₂²×D₄	1	2	yes	complemented
270	C₂×#95	C₂²×D₄	1	2	yes	complemented
271	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
272	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
273	C₂⁵	B(4,𝔽₂)	1	2	yes	—
274	C₂⁵	B(4,𝔽₂)	1	2	yes	—
275	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
276	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
277	C₂⁵	C₂×#120	1	1	yes	characteristic
278	C₂⁵	C₂×#120	1	1	yes	characteristic
279	C₂⁵	C₂×#120	1	2	yes	—
280	C₂⁵	C₂×#120	1	2	yes	—
281	C₂⁵	C₂×#120	1	1	yes	characteristic
282	C₂⁵	C₂×#120	1	2	yes	—
283	C₂⁵	C₂×#120	1	1	yes	characteristic
284	C₂⁵	C₂×#120	1	2	yes	—
285	C₂⁵	C₂×#120	1	1	yes	characteristic
286	C₂⁵	#534	1	1	yes	characteristic
287	C₂⁵	#534	1	1	yes	characteristic
288	C₂⁵	D₄²	1	2	yes	—
289	C₂⁵	D₄²	1	2	yes	—
290	C₂⁵	C₂³×D₄	1	1	yes	characteristic
291	C₂⁵	C₂³×D₄	1	1	yes	characteristic
292	C₂²×D₄	C₂×#120	1	2	yes	—
293	C₂²×D₄	#534	1	2	yes	—
294	C₂²×D₄	D₄²	1	2	yes	—
295	C₂²×D₄	D₄²	1	2	yes	—
296	C₂²×D₄	D₄²	1	2	yes	—
297	C₂²×D₄	D₄²	1	2	yes	—
298	C₂²×D₄	C₂³×D₄	1	2	yes	—
299	C₂²×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
300	C₂³×C₄	C₂×#120	1	2	yes	—
301	C₂³×C₄	C₂×#120	1	2	yes	—
302	C₂³×C₄	C₂×#120	1	1	yes	characteristic
303	C₂³×C₄	D₄²	1	2	yes	—
304	C₂³×C₄	D₄²	1	2	yes	—
305	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
306	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
307	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
308	C₂⁴	#2200	1	4	yes	complemented
309	C₂⁴	#2403	1	1	yes	characteristic
310	C₂⁴	#2403	1	1	yes	characteristic
311	C₂⁴	#2403	1	1	yes	characteristic
312	C₂⁴	#2403	1	2	yes	—
313	C₂⁴	#2403	1	1	yes	characteristic
314	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
315	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
316	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
317	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
318	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
319	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
320	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
321	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
322	C₂⁴	#3026	1	4	yes	—
323	C₂⁴	C₂²×#120	1	1	yes	characteristic
324	C₂⁴	C₂²×#120	1	1	yes	characteristic
325	C₂⁴	C₂×#534	1	1	yes	characteristic
326	C₂⁴	C₂×D₄²	1	2	yes	—
327	C₂²×C₄	#2403	1	2	yes	—
328	C₂²×C₄	C₂×D₄²	1	2	yes	—
329	C₂³	#23895	1	2	yes	—
330	C₂³	#23900	1	1	yes	characteristic
331	C₂³	#23900	1	1	yes	characteristic
332	C₂³	#23900	1	1	yes	characteristic
333	C₂³	#23900	1	1	yes	characteristic
334	C₂³	C₂×#2200	1	4	yes	—
335	C₂³	C₂×#2200	1	2	yes	—
336	C₂³	#33551	1	4	yes	—
337	C₂³	#33551	1	2	yes	—
338	C₂³	C₂×#2403	1	1	yes	characteristic
339	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
340	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
341	C₂³	C₂×#3026	1	2	yes	—
342	C₂²	#499797	1	2	yes	—
343	C₂²	#499797	1	2	yes	—
344	C₂²	C₂×#23900	1	1	yes	characteristic
345	C₂²	#6437621	1	1	yes	characteristic
346	C₂²	C₂×#23895	1	1	yes	characteristic
347	C₂²	C₂²×#2200	1	1	yes	characteristic
348	C₂²	C₂×#33551	1	1	yes	characteristic
349	C₂²	C₂×#33551	1	2	yes	—
350	C₂	#72218077	1	1	yes	characteristic
351	C₂	#72233065	1	1	yes	characteristic
352	C₂	C₂×#499797	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×#23900
commutator, Frattini, cosocle	C₂³×D₄	C₂⁵
LCS	G ▷ C₂³×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ C₂³×#120 ◁ G
LECS	G ▷ C₂³×D₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72241065	C₂	semidirect
2. #72241064	C₂	semidirect
3. #72241063	C₂	semidirect
4. #72241062	C₂	semidirect
5. #72234609	C₂	semidirect
6. #72234106	C₂	semidirect
7. #72233379	C₂	semidirect
8. #72233365	C₂	semidirect
9. #72233165	C₂	semidirect
10. #72233043	C₂	semidirect
11. #72232536	C₂	semidirect
12. #72231479	C₂	semidirect
13. #72227781	C₂	semidirect
14. C₂×#133822	C₂	semidirect
15. C₂×#6499867	C₂	semidirect
17. C₂×#45438	C₂²	semidirect
21. #6470226	C₂²	semidirect
22. #6470019	C₂²	semidirect
26. #5021145	C₂²	semidirect
27. #5021139	C₂²	semidirect
28. #2032535	C₂²	semidirect
29. #2031998	C₂²	semidirect
30. #846057	C₂²	semidirect
31. #845677	C₂²	semidirect
34. #559835	C₂²	semidirect
35. #512145	C₂²	semidirect
36. #511776	C₂²	semidirect
37. #508086	C₂²	semidirect
38. #508063	C₂²	semidirect
39. #496226	C₂²	semidirect
40. #496189	C₂²	semidirect
41. C₂×#12687	C₂²	semidirect
42. C₂×#12687	C₂²	semidirect
43. #347048	C₂²	semidirect
44. #347048	C₂²	semidirect
45. #346466	C₂²	semidirect
46. #346446	C₂²	semidirect
49. #187928	C₂²	semidirect
50. #186808	C₂²	semidirect
51. #144412	C₂²	semidirect
52. #144404	C₂²	semidirect
53. #144386	C₂²	semidirect
54. #144367	C₂²	semidirect
55. #139830	C₂²	semidirect
56. #139828	C₂²	semidirect
57. #139773	C₂²	semidirect
58. #139718	C₂²	semidirect
59. #139714	C₂²	semidirect
60. #139702	C₂²	semidirect
61. #133822	C₂²	semidirect
62. #133822	C₂²	semidirect
63. #128073	C₂²	semidirect
64. #128058	C₂²	semidirect
68. C₂²×#560	C₂³	semidirect
72. C₂²×B(4,𝔽₂)	D₄	semidirect
73. C₂×#2697	C₂³	semidirect
74. C₂×#2669	C₂³	semidirect
79. C₂×#2539	D₄	semidirect
81. C₂×#2405	D₄	semidirect
83. C₂×#2617	D₄	semidirect
84. C₂×#2375	C₂³	semidirect
85. C₂×#2308	D₄	semidirect
89. #24056	C₂³	semidirect
90. #24018	C₂³	semidirect
91. #23906	C₂³	semidirect
92. #23901	C₂³	semidirect
93. #23900	D₄	semidirect
98. C₂×#1889	D₄	semidirect
102. #15948	D₄	semidirect
103. #15948	D₄	semidirect
106. #15948	C₂³	semidirect
107. #15283	D₄	semidirect
109. #15281	C₂³	semidirect
110. #15266	C₂³	semidirect
111. #15258	D₄	semidirect
113. #15258	C₂³	semidirect
114. #14657	C₂³	semidirect
115. #14358	C₂³	semidirect
116. #14335	D₄	semidirect
117. #13903	D₄	semidirect
119. #13867	D₄	semidirect
121. #13775	D₄	semidirect
122. #12856	C₂³	semidirect
123. #12852	C₂³	semidirect
124. #12693	C₂³	semidirect
125. #12688	C₂³	semidirect
126. #12687	C₂³	semidirect
127. #12687	C₂³	semidirect
128. #12687	C₂³	semidirect
131. #8534	C₂³	semidirect
132. #8453	C₂³	semidirect
133. #7307	C₂³	semidirect
134. #7304	C₂³	semidirect
146. C₂²×#127	C₂×D₄	semidirect
148. C₂²×#123	C₂×D₄	semidirect
149. C₂²×#123	C₂×D₄	semidirect
151. C₂²×#121	C₂×D₄	semidirect
170. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
171. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
175. C₂×#399	C₂×D₄	semidirect
176. C₂×#397	C₂×D₄	semidirect
177. C₂×#392	C₂×D₄	semidirect
178. C₂×#392	C₂×D₄	semidirect
179. C₂×#390	C₂×D₄	semidirect
181. C₂×#386	C₂×D₄	semidirect
182. C₂×#386	C₂×D₄	semidirect
183. C₂×#386	C₂×D₄	semidirect
184. C₂×#386	C₂×D₄	semidirect
186. C₂×#380	C₂×D₄	semidirect
193. C₂×#379	C₂×D₄	semidirect
194. C₂×#379	C₂×D₄	semidirect
195. C₂×C₄×C₂²⋊C₄	C₂×D₄	semidirect
196. C₂×C₄×C₂²⋊C₄	C₂×D₄	semidirect
203. #1438	C₂×D₄	semidirect
204. #1438	C₂×D₄	semidirect
205. #1438	C₂×D₄	semidirect
206. #1438	C₂×D₄	semidirect
207. #1438	C₂×D₄	semidirect
208. #1438	C₂×D₄	semidirect
211. #1437	C₂×D₄	semidirect
212. #1437	C₂×D₄	semidirect
213. #1437	C₂×D₄	semidirect
214. #1437	C₂×D₄	semidirect
236. C₂³×D₄	C₂²×D₄	semidirect
243. C₂⁴×C₄	C₂²×D₄	semidirect
244. C₂⁴×C₄	C₂²×D₄	semidirect
250. C₂²×C₄⋊C₄	C₂²×D₄	semidirect
262. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
263. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
264. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
265. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
266. C₂²×C₄²	C₂²×D₄	semidirect
267. C₂²×C₄²	C₂²×D₄	semidirect
269. C₂×#95	C₂²×D₄	semidirect
270. C₂×#95	C₂²×D₄	semidirect
308. C₂⁴	#2200	semidirect

Maximal subgroups

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

subgroup	index
#72241065	2
#72241064	2
#72241063	2
#72241062	2
#72234609	2
#72234106	2
#72233379	2
#72233365	2
#72233165	2
#72233043	2
#72232536	2
#72231479	2
#72227781	2
C₂×#133822	2
C₂×#6499867	2