Subgroups — #72251111

Order 2048.

At least 13266 conjugacy classes of subgroups; only the 1676 normal subgroups are shown.

The subgroup lattice has 748 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72238052	C₂	1	2	yes	maximal, complemented
2	#72238049	C₂	1	2	yes	maximal, complemented
3	#72238046	C₂	1	4	yes	maximal, complemented
4	#72238031	C₂	1	1	yes	maximal, characteristic, complemented
5	#72238021	C₂	1	4	yes	maximal, complemented
6	#72237398	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#6470225	C₂	1	1	yes	maximal, characteristic, complemented
8	#72236431	C₂	1	2	yes	maximal, complemented
9	C₂×#201664	C₂	1	1	yes	maximal, characteristic, complemented
10	#72235095	C₂	1	1	yes	maximal, characteristic, complemented
11	#72234629	C₂	1	2	yes	maximal, complemented
12	#72233895	C₂	1	4	yes	maximal, complemented
13	#72225665	C₂	1	1	yes	maximal, characteristic, complemented
14	#72219307	C₂	1	1	yes	maximal, characteristic, complemented
15	#72210600	C₂	1	4	yes	maximal, complemented
16	C₂²×#3484	C₂²	1	1	yes	characteristic
17	C₂³×D₄²	C₂²	1	1	yes	characteristic
18	#7642257	C₂²	1	2	yes	complemented
19	#7642244	C₂²	1	2	yes	complemented
20	#7641845	C₂²	1	2	yes	—
21	#7630942	C₂²	1	2	yes	complemented
22	#7630939	C₂²	1	2	yes	complemented
23	C₂×#34980	C₂²	1	2	yes	—
24	C₂×#34980	C₂²	1	2	yes	complemented
25	C₂×#34980	C₂²	1	1	yes	characteristic, complemented
26	C₂²×#2403	C₂²	1	1	yes	characteristic
27	C₂²×#2403	C₂²	1	1	yes	characteristic, complemented
28	C₂×#34171	C₂²	1	1	yes	characteristic
29	#6470225	C₂²	1	4	yes	—
30	#6470225	C₂²	1	4	yes	complemented
31	C₂×#21746	C₂²	1	2	yes	complemented
32	C₂×#21746	C₂²	1	2	yes	complemented
33	C₂×#21746	C₂²	1	2	yes	complemented
34	C₂×#21746	C₂²	1	2	yes	complemented
35	C₂²×#1781	C₂²	1	1	yes	characteristic
36	C₂²×#1781	C₂²	1	1	yes	characteristic
37	C₂²×#1781	C₂²	1	2	yes	complemented
38	#636791	C₂²	1	2	yes	complemented
39	#635984	C₂²	1	2	yes	complemented
40	#613191	C₂²	1	2	yes	complemented
41	#612424	C₂²	1	2	yes	complemented
42	#556752	C₂²	1	1	yes	characteristic, complemented
43	#517411	C₂²	1	1	yes	characteristic
44	#517411	C₂²	1	1	yes	characteristic, complemented
45	#517411	C₂²	1	2	yes	complemented
46	#405090	C₂²	1	8	yes	complemented
47	#394058	C₂²	1	8	yes	complemented
48	#392245	C₂²	1	2	yes	complemented
49	#392109	C₂²	1	2	yes	complemented
50	#382422	C₂²	1	2	yes	complemented
51	#382390	C₂²	1	2	yes	complemented
52	#355913	C₂²	1	2	yes	complemented
53	#233542	C₂²	1	8	yes	complemented
54	#233541	C₂²	1	8	yes	complemented
55	#201664	C₂²	1	4	yes	complemented
56	#201664	C₂²	1	4	yes	complemented
57	#187928	C₂²	1	4	yes	complemented
58	#187928	C₂²	1	4	yes	complemented
59	C₂×#8101	C₂²	1	2	yes	complemented
60	C₂×#8101	C₂²	1	2	yes	complemented
61	#115691	C₂²	1	8	yes	complemented
62	#115690	C₂²	1	8	yes	complemented
63	#115205	C₂²	1	8	yes	complemented
64	#115204	C₂²	1	8	yes	complemented
65	#106766	C₂²	1	4	yes	complemented
66	#106766	C₂²	1	4	yes	complemented
67	C₂³×H(5,𝔽₂)	D₄	1	1	yes	characteristic, complemented
68	C₂⁵×D₄	D₄	1	1	yes	characteristic, complemented
69	C₂⁵×D₄	C₂³	1	1	yes	characteristic
70	C₂⁵×D₄	C₂³	1	1	yes	characteristic
71	C₂⁵×D₄	C₂³	1	1	yes	characteristic
72	C₂⁵×D₄	C₂³	1	1	yes	characteristic
73	C₂×#3484	D₄	1	2	yes	complemented
74	C₂×#3484	D₄	1	2	yes	complemented
75	C₂×#3484	C₂³	1	2	yes	—
76	C₂×#3484	C₂³	1	2	yes	—
77	C₂²×#534	D₄	1	2	yes	complemented
78	C₂³×#127	D₄	1	1	yes	characteristic, complemented
79	C₂³×#121	D₄	1	1	yes	characteristic, complemented
80	C₂³×#121	D₄	1	1	yes	characteristic, complemented
81	C₂³×#121	D₄	1	1	yes	characteristic, complemented
82	C₂³×#121	C₂³	1	1	yes	characteristic
83	C₂³×#120	D₄	1	2	yes	complemented
84	C₂³×#120	D₄	1	1	yes	characteristic, complemented
85	C₂³×#120	D₄	1	1	yes	characteristic, complemented
86	C₂³×#120	C₂³	1	2	yes	—
87	C₂³×#120	C₂³	1	1	yes	characteristic
88	C₂³×#120	C₂³	1	1	yes	characteristic
89	C₂³×#120	C₂³	1	2	yes	complemented
90	C₂²×#518	D₄	1	1	yes	characteristic, complemented
91	C₂³×C₄×D₄	D₄	1	1	yes	characteristic, complemented
92	C₂³×C₄×D₄	C₂³	1	1	yes	characteristic
93	C₂³×#99	D₄	1	4	yes	complemented
94	#37436	D₄	1	8	yes	complemented
95	C₂×#2849	C₂³	1	4	yes	—
96	C₂×#2846	C₂³	1	4	yes	—
97	#34992	D₄	1	4	yes	complemented
98	#34992	C₂³	1	4	yes	—
99	#34980	D₄	1	4	yes	complemented
100	#34980	C₂³	1	4	yes	—
101	#34980	C₂³	1	8	yes	—
102	C₂×#2405	D₄	1	4	yes	complemented
103	C₂×#2405	C₂³	1	2	yes	complemented
104	C₂×#2410	D₄	1	8	yes	complemented
105	C₂×#2403	D₄	1	4	yes	complemented
106	C₂×#2403	D₄	1	4	yes	complemented
107	C₂×#2403	C₂³	1	2	yes	—
108	C₂×#2403	C₂³	1	2	yes	—
109	C₂×#2403	C₂³	1	2	yes	complemented
110	#34171	D₄	1	2	yes	complemented
111	#34171	D₄	1	2	yes	complemented
112	#34171	C₂³	1	2	yes	—
113	#34171	C₂³	1	2	yes	—
114	C₂×#2309	D₄	1	2	yes	complemented
115	C₂×#2308	D₄	1	2	yes	complemented
116	C₂²×#386	D₄	1	2	yes	complemented
117	C₂²×#386	C₂³	1	2	yes	complemented
118	C₂²×#379	C₂³	1	2	yes	—
119	C₂²×#379	C₂³	1	2	yes	—
120	C₂²×#379	C₂³	1	1	yes	characteristic
121	C₂²×#379	C₂³	1	1	yes	characteristic
122	C₂²×#379	C₂³	1	2	yes	—
123	C₂²×#379	C₂³	1	1	yes	characteristic
124	#21746	C₂³	1	8	yes	—
125	#21746	C₂³	1	8	yes	—
126	C₂×#1898	C₂³	1	8	yes	—
127	C₂×#1819	C₂³	1	4	yes	complemented
128	C₂×#1781	D₄	1	4	yes	complemented
129	C₂×#1781	C₂³	1	2	yes	—
130	C₂×#1781	C₂³	1	2	yes	—
131	C₂×#1781	C₂³	1	2	yes	—
132	C₂×#1781	C₂³	1	2	yes	—
133	C₂×#1781	C₂³	1	8	yes	complemented
134	C₂×#1781	C₂³	1	4	yes	complemented
135	#14681	C₂³	1	2	yes	complemented
136	#14681	C₂³	1	4	yes	complemented
137	#14679	C₂³	1	2	yes	complemented
138	#14679	C₂³	1	4	yes	complemented
139	#14335	D₄	1	4	yes	complemented
140	#13869	C₂³	1	2	yes	complemented
141	#13867	D₄	1	4	yes	complemented
142	#13867	C₂³	1	2	yes	—
143	#13867	C₂³	1	2	yes	—
144	#13867	C₂³	1	2	yes	complemented
145	#10735	C₂³	1	8	yes	complemented
146	#8101	C₂³	1	8	yes	complemented
147	#8101	C₂³	1	8	yes	complemented
148	C₂⁷	C₂×D₄	1	1	yes	characteristic
149	C₂⁷	C₂×D₄	1	1	yes	characteristic, complemented
150	C₂⁷	C₂×D₄	1	1	yes	characteristic, complemented
151	C₂⁷	C₂⁴	1	1	yes	characteristic
152	C₂⁷	C₂⁴	1	1	yes	characteristic
153	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
154	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
155	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
156	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
157	C₂⁴×D₄	C₂×D₄	1	2	yes	—
158	C₂⁴×D₄	C₂×D₄	1	2	yes	—
159	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
160	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
161	C₂⁴×D₄	C₂×D₄	1	2	yes	—
162	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
163	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
164	C₂⁴×D₄	C₂×D₄	1	2	yes	—
165	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
166	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
167	C₂⁴×D₄	C₂×D₄	1	2	yes	—
168	C₂⁴×D₄	C₂×D₄	1	2	yes	—
169	C₂⁴×D₄	C₂×D₄	1	2	yes	—
170	C₂⁴×D₄	C₂×D₄	1	2	yes	—
171	C₂⁴×D₄	C₂×D₄	1	2	yes	—
172	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
173	C₂⁴×D₄	C₂×D₄	1	4	yes	—
174	C₂⁴×D₄	C₂×D₄	1	4	yes	—
175	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
176	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
177	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
178	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
179	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
180	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
181	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
182	C₂⁴×D₄	C₂×D₄	1	2	yes	complemented
183	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
184	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
185	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
186	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
187	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
188	C₂⁴×D₄	#41	1	2	yes	—
189	C₂⁴×D₄	#41	1	2	yes	—
190	C₂⁴×D₄	C₂⁴	1	2	yes	—
191	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
192	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
193	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
194	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
195	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic, complemented
196	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic, complemented
197	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic, complemented
198	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
199	C₂×#534	C₂×D₄	1	4	yes	—
200	C₂×#534	C₂×D₄	1	4	yes	—
201	C₂²×#120	C₂×D₄	1	4	yes	—
202	C₂²×#120	C₂×D₄	1	4	yes	—
203	C₂²×#120	C₂×D₄	1	4	yes	—
204	C₂²×#120	C₂×D₄	1	4	yes	—
205	C₂²×#120	C₂×D₄	1	4	yes	—
206	C₂²×#120	C₂×D₄	1	4	yes	—
207	C₂²×#120	C₂×D₄	1	8	yes	complemented
208	C₂²×#120	C₂×D₄	1	4	yes	complemented
209	C₂²×#120	C₂⁴	1	4	yes	—
210	C₂×#518	C₂×D₄	1	2	yes	—
211	C₂×#518	C₂×D₄	1	2	yes	—
212	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
213	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
214	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
215	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
216	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
217	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
218	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
219	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
220	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
221	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
222	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
223	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
224	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
225	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
226	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
227	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
228	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
229	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
230	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic, complemented
231	C₂²×#99	C₂×D₄	1	8	yes	—
232	C₂²×#99	C₂×D₄	1	8	yes	complemented
233	#2483	C₂×D₄	1	8	yes	complemented
234	#2405	C₂×D₄	1	8	yes	complemented
235	#2405	C₂×D₄	1	8	yes	complemented
236	#2403	C₂×D₄	1	8	yes	complemented
237	#2309	C₂×D₄	1	4	yes	complemented
238	#2309	C₂×D₄	1	4	yes	complemented
239	#2308	C₂×D₄	1	4	yes	complemented
240	#2308	C₂×D₄	1	4	yes	complemented
241	C₂×#386	C₂×D₄	1	4	yes	—
242	C₂×#386	C₂×D₄	1	8	yes	complemented
243	C₂×#386	C₂×D₄	1	4	yes	complemented
244	C₂×#385	C₂×D₄	1	8	yes	complemented
245	C₂×#379	C₂×D₄	1	4	yes	—
246	C₂×#379	C₂×D₄	1	4	yes	—
247	C₂×#379	C₂×D₄	1	4	yes	—
248	C₂×#379	C₂×D₄	1	4	yes	—
249	C₂×#379	C₂×D₄	1	4	yes	—
250	C₂×#379	C₂×D₄	1	8	yes	complemented
251	C₂×#379	C₂×D₄	1	2	yes	complemented
252	C₂×#379	C₂×D₄	1	4	yes	complemented
253	C₂×#379	C₂×D₄	1	2	yes	complemented
254	C₂×#379	C₂×D₄	1	2	yes	complemented
255	C₂×#379	C₂×D₄	1	2	yes	complemented
256	C₂×#379	C₂⁴	1	4	yes	—
257	C₂×#379	C₂⁴	1	2	yes	—
258	C₂×#379	C₂⁴	1	2	yes	—
259	C₂×#379	C₂⁴	1	4	yes	—
260	C₂×#379	C₂⁴	1	4	yes	—
261	#1438	C₂×D₄	1	8	yes	complemented
262	#1438	C₂×D₄	1	8	yes	complemented
263	C₂⁶	#120	1	2	yes	—
264	C₂⁶	#120	1	1	yes	characteristic
265	C₂⁶	#120	1	1	yes	characteristic
266	C₂⁶	#120	1	2	yes	—
267	C₂⁶	#120	1	1	yes	characteristic
268	C₂⁶	#120	1	1	yes	characteristic
269	C₂⁶	#120	1	2	yes	complemented
270	C₂⁶	#121	1	2	yes	—
271	C₂⁶	#121	1	2	yes	—
272	C₂⁶	C₂²×D₄	1	2	yes	—
273	C₂⁶	C₂²×D₄	1	1	yes	characteristic
274	C₂⁶	C₂²×D₄	1	4	yes	—
275	C₂⁶	C₂²×D₄	1	1	yes	characteristic
276	C₂⁶	C₂²×D₄	1	1	yes	characteristic
277	C₂⁶	C₂²×D₄	1	1	yes	characteristic
278	C₂⁶	C₂²×D₄	1	1	yes	characteristic
279	C₂⁶	C₂²×D₄	1	1	yes	characteristic
280	C₂⁶	C₂²×D₄	1	1	yes	characteristic
281	C₂⁶	C₂²×D₄	1	1	yes	characteristic
282	C₂⁶	C₂²×D₄	1	1	yes	characteristic
283	C₂⁶	C₂²×D₄	1	1	yes	characteristic
284	C₂⁶	C₂²×D₄	1	2	yes	—
285	C₂⁶	C₂²×D₄	1	2	yes	—
286	C₂⁶	C₂²×D₄	1	2	yes	—
287	C₂⁶	C₂²×D₄	1	1	yes	characteristic
288	C₂⁶	C₂²×D₄	1	1	yes	characteristic
289	C₂⁶	C₂²×D₄	1	1	yes	characteristic
290	C₂⁶	C₂²×D₄	1	1	yes	characteristic
291	C₂⁶	C₂²×D₄	1	1	yes	characteristic
292	C₂⁶	C₂²×D₄	1	1	yes	characteristic
293	C₂⁶	C₂²×D₄	1	2	yes	—
294	C₂⁶	C₂²×D₄	1	1	yes	characteristic
295	C₂⁶	C₂×#41	1	1	yes	characteristic
296	C₂⁶	C₂×#41	1	1	yes	characteristic
297	C₂⁶	H(5,𝔽₂)	1	2	yes	—
298	C₂⁶	H(5,𝔽₂)	1	2	yes	—
299	C₂⁶	H(5,𝔽₂)	1	2	yes	—
300	C₂⁶	H(5,𝔽₂)	1	2	yes	—
301	C₂⁶	C₂⁵	1	1	yes	characteristic
302	C₂³×D₄	#120	1	2	yes	—
303	C₂³×D₄	#120	1	2	yes	—
304	C₂³×D₄	#120	1	2	yes	—
305	C₂³×D₄	#120	1	2	yes	—
306	C₂³×D₄	#120	1	2	yes	—
307	C₂³×D₄	#120	1	4	yes	—
308	C₂³×D₄	#120	1	4	yes	—
309	C₂³×D₄	#120	1	2	yes	—
310	C₂³×D₄	#120	1	4	yes	—
311	C₂³×D₄	#120	1	1	yes	characteristic
312	C₂³×D₄	#120	1	1	yes	characteristic
313	C₂³×D₄	#120	1	1	yes	characteristic
314	C₂³×D₄	#120	1	1	yes	characteristic
315	C₂³×D₄	#120	1	2	yes	—
316	C₂³×D₄	#120	1	2	yes	—
317	C₂³×D₄	#120	1	2	yes	—
318	C₂³×D₄	#120	1	2	yes	—
319	C₂³×D₄	#120	1	1	yes	characteristic
320	C₂³×D₄	#120	1	1	yes	characteristic
321	C₂³×D₄	#120	1	1	yes	characteristic
322	C₂³×D₄	#120	1	1	yes	characteristic
323	C₂³×D₄	#120	1	2	yes	—
324	C₂³×D₄	#120	1	2	yes	—
325	C₂³×D₄	#120	1	2	yes	—
326	C₂³×D₄	#120	1	2	yes	—
327	C₂³×D₄	#120	1	2	yes	—
328	C₂³×D₄	#120	1	2	yes	—
329	C₂³×D₄	#120	1	2	yes	—
330	C₂³×D₄	#120	1	2	yes	—
331	C₂³×D₄	#120	1	4	yes	complemented
332	C₂³×D₄	#120	1	4	yes	complemented
333	C₂³×D₄	#120	1	4	yes	complemented
334	C₂³×D₄	#121	1	2	yes	—
335	C₂³×D₄	#121	1	2	yes	—
336	C₂³×D₄	#121	1	2	yes	—
337	C₂³×D₄	#121	1	2	yes	—
338	C₂³×D₄	#121	1	2	yes	—
339	C₂³×D₄	#121	1	2	yes	—
340	C₂³×D₄	#121	1	2	yes	—
341	C₂³×D₄	#121	1	2	yes	—
342	C₂³×D₄	#121	1	2	yes	—
343	C₂³×D₄	#121	1	2	yes	—
344	C₂³×D₄	#121	1	2	yes	—
345	C₂³×D₄	#121	1	2	yes	—
346	C₂³×D₄	#121	1	2	yes	—
347	C₂³×D₄	#121	1	2	yes	—
348	C₂³×D₄	#121	1	2	yes	—
349	C₂³×D₄	#121	1	2	yes	—
350	C₂³×D₄	#121	1	2	yes	—
351	C₂³×D₄	#121	1	2	yes	—
352	C₂³×D₄	#121	1	2	yes	—
353	C₂³×D₄	#121	1	2	yes	—
354	C₂³×D₄	#127	1	2	yes	—
355	C₂³×D₄	#127	1	2	yes	—
356	C₂³×D₄	#127	1	2	yes	—
357	C₂³×D₄	#127	1	2	yes	—
358	C₂³×D₄	#127	1	2	yes	—
359	C₂³×D₄	#127	1	2	yes	—
360	C₂³×D₄	#127	1	2	yes	—
361	C₂³×D₄	#127	1	2	yes	—
362	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
363	C₂³×D₄	C₂²×D₄	1	2	yes	—
364	C₂³×D₄	C₂²×D₄	1	4	yes	—
365	C₂³×D₄	C₂²×D₄	1	4	yes	—
366	C₂³×D₄	C₂²×D₄	1	4	yes	—
367	C₂³×D₄	C₂²×D₄	1	4	yes	—
368	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
369	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
370	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
371	C₂³×D₄	C₂²×D₄	1	2	yes	—
372	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
373	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
374	C₂³×D₄	C₂²×D₄	1	2	yes	—
375	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
376	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
377	C₂³×D₄	C₂²×D₄	1	2	yes	—
378	C₂³×D₄	C₂²×D₄	1	2	yes	—
379	C₂³×D₄	C₂²×D₄	1	2	yes	—
380	C₂³×D₄	C₂×#41	1	2	yes	—
381	C₂³×D₄	C₂×#41	1	2	yes	—
382	C₂⁴×C₄	#120	1	1	yes	characteristic
383	C₂⁴×C₄	#120	1	1	yes	characteristic
384	C₂⁴×C₄	#120	1	2	yes	—
385	C₂⁴×C₄	#120	1	2	yes	—
386	C₂⁴×C₄	#120	1	1	yes	characteristic
387	C₂⁴×C₄	#120	1	1	yes	characteristic
388	C₂⁴×C₄	#120	1	2	yes	complemented
389	C₂⁴×C₄	#120	1	2	yes	complemented
390	C₂⁴×C₄	#120	1	2	yes	complemented
391	C₂⁴×C₄	#121	1	2	yes	—
392	C₂⁴×C₄	#121	1	2	yes	—
393	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
394	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
395	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
396	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
397	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
398	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
399	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
400	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
401	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
402	C₂²×C₂²⋊C₄	#120	1	2	yes	—
403	C₂²×C₂²⋊C₄	#120	1	4	yes	—
404	C₂²×C₂²⋊C₄	#120	1	2	yes	—
405	C₂²×C₂²⋊C₄	#120	1	4	yes	complemented
406	C₂²×C₂²⋊C₄	#120	1	4	yes	complemented
407	C₂²×C₂²⋊C₄	#120	1	4	yes	complemented
408	C₂²×C₂²⋊C₄	#120	1	8	yes	complemented
409	C₂²×C₂²⋊C₄	#120	1	8	yes	complemented
410	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
411	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
412	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
413	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
414	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
415	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
416	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
417	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
418	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
419	#379	#120	1	8	yes	complemented
420	#379	#120	1	8	yes	complemented
421	#379	C₂²×D₄	1	8	yes	—
422	#379	C₂²×D₄	1	8	yes	—
423	C₂⁵	#392	1	2	yes	—
424	C₂⁵	#392	1	2	yes	—
425	C₂⁵	#392	1	2	yes	—
426	C₂⁵	#392	1	2	yes	—
427	C₂⁵	#392	1	2	yes	—
428	C₂⁵	#392	1	2	yes	—
429	C₂⁵	#392	1	2	yes	—
430	C₂⁵	#392	1	2	yes	—
431	C₂⁵	C₂×#120	1	2	yes	—
432	C₂⁵	C₂×#120	1	2	yes	—
433	C₂⁵	C₂×#120	1	1	yes	characteristic
434	C₂⁵	C₂×#120	1	2	yes	—
435	C₂⁵	C₂×#120	1	1	yes	characteristic
436	C₂⁵	C₂×#120	1	1	yes	characteristic
437	C₂⁵	C₂×#120	1	1	yes	characteristic
438	C₂⁵	C₂×#120	1	1	yes	characteristic
439	C₂⁵	C₂×#120	1	1	yes	characteristic
440	C₂⁵	C₂×#120	1	1	yes	characteristic
441	C₂⁵	C₂×#120	1	2	yes	—
442	C₂⁵	C₂×#120	1	1	yes	characteristic
443	C₂⁵	C₂×#120	1	1	yes	characteristic
444	C₂⁵	C₂×#120	1	4	yes	—
445	C₂⁵	C₂×#120	1	2	yes	—
446	C₂⁵	C₂×#120	1	2	yes	—
447	C₂⁵	C₂×#120	1	1	yes	characteristic
448	C₂⁵	C₂×#120	1	1	yes	characteristic
449	C₂⁵	C₂×#120	1	1	yes	characteristic
450	C₂⁵	C₂×#120	1	1	yes	characteristic
451	C₂⁵	C₂×#120	1	1	yes	characteristic
452	C₂⁵	C₂×#120	1	2	yes	—
453	C₂⁵	C₂×#120	1	2	yes	—
454	C₂⁵	C₂×#120	1	1	yes	characteristic
455	C₂⁵	C₂×#120	1	1	yes	characteristic
456	C₂⁵	C₂×#120	1	1	yes	characteristic
457	C₂⁵	C₂×#120	1	1	yes	characteristic
458	C₂⁵	C₂×#120	1	1	yes	characteristic
459	C₂⁵	C₂×#120	1	2	yes	—
460	C₂⁵	C₂×#120	1	2	yes	—
461	C₂⁵	C₂×#120	1	2	yes	—
462	C₂⁵	C₂×#120	1	1	yes	characteristic
463	C₂⁵	C₂×#120	1	2	yes	—
464	C₂⁵	C₂×#120	1	2	yes	—
465	C₂⁵	C₂×#120	1	2	yes	—
466	C₂⁵	C₂×#120	1	2	yes	—
467	C₂⁵	C₂×#121	1	2	yes	—
468	C₂⁵	C₂×#121	1	2	yes	—
469	C₂⁵	C₂×#121	1	1	yes	characteristic
470	C₂⁵	C₂×#121	1	1	yes	characteristic
471	C₂⁵	C₂×#121	1	1	yes	characteristic
472	C₂⁵	C₂×#121	1	1	yes	characteristic
473	C₂⁵	C₂×#121	1	1	yes	characteristic
474	C₂⁵	C₂×#121	1	1	yes	characteristic
475	C₂⁵	C₂×#121	1	1	yes	characteristic
476	C₂⁵	C₂×#121	1	1	yes	characteristic
477	C₂⁵	C₂×#121	1	1	yes	characteristic
478	C₂⁵	C₂×#121	1	1	yes	characteristic
479	C₂⁵	C₂×#121	1	1	yes	characteristic
480	C₂⁵	C₂×#121	1	1	yes	characteristic
481	C₂⁵	C₂×#127	1	1	yes	characteristic
482	C₂⁵	C₂×#127	1	1	yes	characteristic
483	C₂⁵	C₂×#127	1	1	yes	characteristic
484	C₂⁵	C₂×#127	1	1	yes	characteristic
485	C₂⁵	#534	1	1	yes	characteristic
486	C₂⁵	#534	1	2	yes	—
487	C₂⁵	#534	1	2	yes	—
488	C₂⁵	#534	1	1	yes	characteristic
489	C₂⁵	#534	1	1	yes	characteristic
490	C₂⁵	#534	1	1	yes	characteristic
491	C₂⁵	#534	1	2	yes	—
492	C₂⁵	#534	1	2	yes	—
493	C₂⁵	#534	1	2	yes	—
494	C₂⁵	#534	1	2	yes	—
495	C₂⁵	#535	1	2	yes	—
496	C₂⁵	#535	1	2	yes	—
497	C₂⁵	#535	1	2	yes	—
498	C₂⁵	#535	1	2	yes	—
499	C₂⁵	D₄²	1	2	yes	—
500	C₂⁵	D₄²	1	2	yes	—
501	C₂⁵	D₄²	1	2	yes	—
502	C₂⁵	D₄²	1	2	yes	—
503	C₂⁵	D₄²	1	2	yes	—
504	C₂⁵	D₄²	1	2	yes	—
505	C₂⁵	D₄²	1	2	yes	—
506	C₂⁵	D₄²	1	2	yes	—
507	C₂⁵	D₄²	1	2	yes	—
508	C₂⁵	D₄²	1	2	yes	—
509	C₂⁵	D₄²	1	2	yes	—
510	C₂⁵	D₄²	1	2	yes	—
511	C₂⁵	D₄²	1	2	yes	—
512	C₂⁵	D₄²	1	2	yes	—
513	C₂⁵	D₄²	1	2	yes	—
514	C₂⁵	D₄²	1	2	yes	—
515	C₂⁵	D₄²	1	2	yes	—
516	C₂⁵	D₄²	1	2	yes	—
517	C₂⁵	D₄²	1	2	yes	—
518	C₂⁵	D₄²	1	2	yes	—
519	C₂⁵	D₄²	1	2	yes	—
520	C₂⁵	D₄²	1	2	yes	—
521	C₂⁵	D₄²	1	2	yes	—
522	C₂⁵	D₄²	1	2	yes	—
523	C₂⁵	#546	1	2	yes	—
524	C₂⁵	#546	1	2	yes	—
525	C₂⁵	#546	1	2	yes	—
526	C₂⁵	#546	1	2	yes	—
527	C₂⁵	#546	1	2	yes	—
528	C₂⁵	#546	1	2	yes	—
529	C₂⁵	#546	1	2	yes	—
530	C₂⁵	#546	1	2	yes	—
531	C₂⁵	C₂³×D₄	1	1	yes	characteristic
532	C₂⁵	C₂³×D₄	1	1	yes	characteristic
533	C₂⁵	C₂³×D₄	1	1	yes	characteristic
534	C₂⁵	C₂³×D₄	1	2	yes	—
535	C₂⁵	C₂³×D₄	1	1	yes	characteristic
536	C₂⁵	C₂³×D₄	1	2	yes	—
537	C₂⁵	C₂³×D₄	1	1	yes	characteristic
538	C₂⁵	C₂³×D₄	1	1	yes	characteristic
539	C₂⁵	C₂²×#41	1	1	yes	characteristic
540	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
541	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
542	C₂²×D₄	#392	1	2	yes	—
543	C₂²×D₄	#392	1	2	yes	—
544	C₂²×D₄	#392	1	2	yes	—
545	C₂²×D₄	#392	1	2	yes	—
546	C₂²×D₄	#392	1	2	yes	—
547	C₂²×D₄	#392	1	2	yes	—
548	C₂²×D₄	#392	1	2	yes	—
549	C₂²×D₄	#392	1	2	yes	—
550	C₂²×D₄	#392	1	2	yes	—
551	C₂²×D₄	#392	1	2	yes	—
552	C₂²×D₄	#392	1	2	yes	—
553	C₂²×D₄	#392	1	2	yes	—
554	C₂²×D₄	#392	1	2	yes	—
555	C₂²×D₄	#392	1	2	yes	—
556	C₂²×D₄	#392	1	2	yes	—
557	C₂²×D₄	#392	1	2	yes	—
558	C₂²×D₄	C₂×#120	1	2	yes	—
559	C₂²×D₄	C₂×#120	1	2	yes	—
560	C₂²×D₄	C₂×#120	1	2	yes	—
561	C₂²×D₄	C₂×#120	1	2	yes	—
562	C₂²×D₄	C₂×#121	1	2	yes	—
563	C₂²×D₄	C₂×#121	1	2	yes	—
564	C₂²×D₄	C₂×#121	1	2	yes	—
565	C₂²×D₄	C₂×#121	1	2	yes	—
566	C₂²×D₄	C₂×#121	1	2	yes	—
567	C₂²×D₄	C₂×#121	1	2	yes	—
568	C₂²×D₄	C₂×#121	1	2	yes	—
569	C₂²×D₄	C₂×#121	1	2	yes	—
570	C₂²×D₄	C₂×#127	1	2	yes	—
571	C₂²×D₄	C₂×#127	1	2	yes	—
572	C₂²×D₄	C₂×#127	1	2	yes	—
573	C₂²×D₄	C₂×#127	1	2	yes	—
574	C₂³×C₄	#392	1	2	yes	—
575	C₂³×C₄	#392	1	2	yes	—
576	C₂³×C₄	#392	1	2	yes	—
577	C₂³×C₄	#392	1	2	yes	—
578	C₂³×C₄	#392	1	2	yes	—
579	C₂³×C₄	#392	1	2	yes	—
580	C₂³×C₄	#392	1	2	yes	—
581	C₂³×C₄	#392	1	2	yes	—
582	C₂³×C₄	C₂×#120	1	1	yes	characteristic
583	C₂³×C₄	C₂×#120	1	2	yes	—
584	C₂³×C₄	C₂×#120	1	2	yes	—
585	C₂³×C₄	C₂×#120	1	4	yes	—
586	C₂³×C₄	C₂×#120	1	4	yes	—
587	C₂³×C₄	C₂×#120	1	2	yes	—
588	C₂³×C₄	C₂×#120	1	2	yes	—
589	C₂³×C₄	C₂×#120	1	2	yes	—
590	C₂³×C₄	C₂×#120	1	4	yes	—
591	C₂³×C₄	C₂×#120	1	2	yes	—
592	C₂³×C₄	C₂×#120	1	2	yes	—
593	C₂³×C₄	C₂×#120	1	1	yes	characteristic
594	C₂³×C₄	C₂×#120	1	1	yes	characteristic
595	C₂³×C₄	C₂×#120	1	1	yes	characteristic
596	C₂³×C₄	C₂×#121	1	2	yes	—
597	C₂³×C₄	C₂×#121	1	2	yes	—
598	C₂×C₂²⋊C₄	C₂×#120	1	16	yes	—
599	C₂⁴	C₂×#392	1	1	yes	characteristic
600	C₂⁴	C₂×#392	1	1	yes	characteristic
601	C₂⁴	C₂×#392	1	2	yes	—
602	C₂⁴	C₂×#392	1	2	yes	—
603	C₂⁴	C₂×#392	1	2	yes	—
604	C₂⁴	C₂×#392	1	1	yes	characteristic
605	C₂⁴	C₂×#392	1	1	yes	characteristic
606	C₂⁴	C₂×#392	1	1	yes	characteristic
607	C₂⁴	C₂×#392	1	1	yes	characteristic
608	C₂⁴	C₂×#392	1	1	yes	characteristic
609	C₂⁴	C₂×#392	1	1	yes	characteristic
610	C₂⁴	C₂×#392	1	2	yes	—
611	C₂⁴	#2403	1	2	yes	—
612	C₂⁴	#2403	1	1	yes	characteristic
613	C₂⁴	#2403	1	1	yes	characteristic
614	C₂⁴	#2403	1	2	yes	—
615	C₂⁴	#2403	1	1	yes	characteristic
616	C₂⁴	#2403	1	2	yes	—
617	C₂⁴	#2403	1	2	yes	—
618	C₂⁴	#2403	1	2	yes	—
619	C₂⁴	#2403	1	1	yes	characteristic
620	C₂⁴	#2403	1	1	yes	characteristic
621	C₂⁴	#2403	1	2	yes	—
622	C₂⁴	#2403	1	2	yes	—
623	C₂⁴	#2403	1	2	yes	—
624	C₂⁴	#2403	1	2	yes	—
625	C₂⁴	#2403	1	1	yes	characteristic
626	C₂⁴	#2403	1	2	yes	—
627	C₂⁴	#2403	1	2	yes	—
628	C₂⁴	#2403	1	1	yes	characteristic
629	C₂⁴	#2403	1	2	yes	—
630	C₂⁴	#2403	1	1	yes	characteristic
631	C₂⁴	#2408	1	2	yes	—
632	C₂⁴	#2408	1	2	yes	—
633	C₂⁴	#2408	1	2	yes	—
634	C₂⁴	#2408	1	2	yes	—
635	C₂⁴	#2408	1	2	yes	—
636	C₂⁴	#2408	1	2	yes	—
637	C₂⁴	#2408	1	2	yes	—
638	C₂⁴	#2408	1	2	yes	—
639	C₂⁴	#2410	1	1	yes	characteristic
640	C₂⁴	#2410	1	1	yes	characteristic
641	C₂⁴	#2410	1	1	yes	characteristic
642	C₂⁴	#2410	1	1	yes	characteristic
643	C₂⁴	#2410	1	2	yes	—
644	C₂⁴	#2410	1	1	yes	characteristic
645	C₂⁴	#2410	1	2	yes	—
646	C₂⁴	#2410	1	2	yes	—
647	C₂⁴	#2410	1	1	yes	characteristic
648	C₂⁴	#2410	1	2	yes	—
649	C₂⁴	#2410	1	2	yes	—
650	C₂⁴	#2410	1	2	yes	—
651	C₂⁴	#2410	1	2	yes	—
652	C₂⁴	#2410	1	2	yes	—
653	C₂⁴	#2410	1	1	yes	characteristic
654	C₂⁴	#2410	1	1	yes	characteristic
655	C₂⁴	#2410	1	2	yes	—
656	C₂⁴	#2410	1	2	yes	—
657	C₂⁴	#2410	1	2	yes	—
658	C₂⁴	#2410	1	2	yes	—
659	C₂⁴	#2433	1	2	yes	—
660	C₂⁴	#2433	1	2	yes	—
661	C₂⁴	#2433	1	2	yes	—
662	C₂⁴	#2433	1	2	yes	—
663	C₂⁴	#2433	1	2	yes	—
664	C₂⁴	#2433	1	2	yes	—
665	C₂⁴	#2433	1	2	yes	—
666	C₂⁴	#2433	1	2	yes	—
667	C₂⁴	#2613	1	1	yes	characteristic
668	C₂⁴	#2613	1	1	yes	characteristic
669	C₂⁴	#2613	1	1	yes	characteristic
670	C₂⁴	#2613	1	2	yes	—
671	C₂⁴	#2613	1	1	yes	characteristic
672	C₂⁴	#2613	1	2	yes	—
673	C₂⁴	#2846	1	1	yes	characteristic
674	C₂⁴	#2846	1	1	yes	characteristic
675	C₂⁴	#2846	1	1	yes	characteristic
676	C₂⁴	#2846	1	1	yes	characteristic
677	C₂⁴	#2846	1	2	yes	—
678	C₂⁴	#2846	1	2	yes	—
679	C₂⁴	C₂²×#120	1	1	yes	characteristic
680	C₂⁴	C₂²×#120	1	1	yes	characteristic
681	C₂⁴	C₂²×#120	1	2	yes	—
682	C₂⁴	C₂²×#120	1	1	yes	characteristic
683	C₂⁴	C₂²×#120	1	2	yes	—
684	C₂⁴	C₂²×#120	1	1	yes	characteristic
685	C₂⁴	C₂²×#120	1	1	yes	characteristic
686	C₂⁴	C₂²×#121	1	1	yes	characteristic
687	C₂⁴	C₂²×#121	1	1	yes	characteristic
688	C₂⁴	C₂²×#121	1	1	yes	characteristic
689	C₂⁴	C₂²×#127	1	1	yes	characteristic
690	C₂⁴	C₂×#534	1	1	yes	characteristic
691	C₂⁴	C₂×#534	1	2	yes	—
692	C₂⁴	C₂×#534	1	1	yes	characteristic
693	C₂⁴	C₂×#535	1	2	yes	—
694	C₂⁴	C₂×D₄²	1	2	yes	—
695	C₂⁴	C₂×D₄²	1	2	yes	—
696	C₂⁴	C₂×D₄²	1	2	yes	—
697	C₂⁴	C₂×D₄²	1	2	yes	—
698	C₂⁴	C₂×D₄²	1	2	yes	—
699	C₂⁴	C₂×D₄²	1	2	yes	—
700	C₂⁴	C₂×#546	1	2	yes	—
701	C₂⁴	C₂×#546	1	2	yes	—
702	C₂×D₄	#3026	1	8	yes	—
703	C₂²×C₄	C₂×#392	1	2	yes	—
704	C₂²×C₄	C₂×#392	1	2	yes	—
705	C₂²×C₄	C₂×#392	1	2	yes	—
706	C₂²×C₄	C₂×#392	1	2	yes	—
707	C₂³	#14715	1	1	yes	characteristic
708	C₂³	#14715	1	1	yes	characteristic
709	C₂³	#14715	1	1	yes	characteristic
710	C₂³	#14715	1	1	yes	characteristic
711	C₂³	#14715	1	1	yes	characteristic
712	C₂³	#14715	1	2	yes	—
713	C₂³	#14715	1	2	yes	—
714	C₂³	#14715	1	2	yes	—
715	C₂³	#14715	1	2	yes	—
716	C₂³	#14715	1	1	yes	characteristic
717	C₂³	#14715	1	1	yes	characteristic
718	C₂³	#14715	1	1	yes	characteristic
719	C₂³	#23444	1	4	yes	—
720	C₂³	#23895	1	4	yes	—
721	C₂³	C₂²×#392	1	1	yes	characteristic
722	C₂³	C₂×#2613	1	1	yes	characteristic
723	C₂³	C₂×#2403	1	1	yes	characteristic
724	C₂³	C₂×#2403	1	2	yes	—
725	C₂³	C₂×#2403	1	1	yes	characteristic
726	C₂³	C₂×#2410	1	1	yes	characteristic
727	C₂³	C₂×#2410	1	2	yes	—
728	C₂³	C₂×#2410	1	1	yes	characteristic
729	C₂³	C₂×#2408	1	2	yes	—
730	C₂³	C₂×#2433	1	2	yes	—
731	C₂³	C₂×#2846	1	1	yes	characteristic
732	C₂³	C₂×#3026	1	4	yes	—
733	C₂³	#60399	1	4	yes	—
734	C₂×C₄	#23444	1	4	yes	—
735	C₂²	#394064	1	2	yes	—
736	C₂²	#394064	1	2	yes	—
737	C₂²	C₂×#14715	1	1	yes	characteristic
738	C₂²	C₂×#23444	1	2	yes	—
739	C₂²	#6437621	1	4	yes	—
740	C₂²	C₂×#23895	1	2	yes	—
741	C₂²	#6437632	1	2	yes	—
742	C₂²	#6437999	1	2	yes	—
743	C₂²	#6628896	1	2	yes	—
744	C₂	C₂×#394064	1	1	yes	characteristic
745	C₂	#72238078	1	1	yes	characteristic
746	C₂	#72238085	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×#14715
commutator, Frattini, cosocle	C₂⁶	C₂⁵
LCS	G ▷ C₂⁶ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁷ ◁ G
LECS	G ▷ C₂⁶ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72238052	C₂	semidirect
2. #72238049	C₂	semidirect
3. #72238046	C₂	semidirect
4. #72238031	C₂	semidirect
5. #72238021	C₂	semidirect
6. #72237398	C₂	semidirect
7. C₂×#6470225	C₂	semidirect
8. #72236431	C₂	semidirect
9. C₂×#201664	C₂	semidirect
10. #72235095	C₂	semidirect
11. #72234629	C₂	semidirect
12. #72233895	C₂	semidirect
13. #72225665	C₂	semidirect
14. #72219307	C₂	semidirect
15. #72210600	C₂	semidirect
18. #7642257	C₂²	semidirect
19. #7642244	C₂²	semidirect
21. #7630942	C₂²	semidirect
22. #7630939	C₂²	semidirect
24. C₂×#34980	C₂²	semidirect
25. C₂×#34980	C₂²	semidirect
27. C₂²×#2403	C₂²	semidirect
30. #6470225	C₂²	semidirect
31. C₂×#21746	C₂²	semidirect
32. C₂×#21746	C₂²	semidirect
33. C₂×#21746	C₂²	semidirect
34. C₂×#21746	C₂²	semidirect
37. C₂²×#1781	C₂²	semidirect
38. #636791	C₂²	semidirect
39. #635984	C₂²	semidirect
40. #613191	C₂²	semidirect
41. #612424	C₂²	semidirect
42. #556752	C₂²	semidirect
44. #517411	C₂²	semidirect
45. #517411	C₂²	semidirect
46. #405090	C₂²	semidirect
47. #394058	C₂²	semidirect
48. #392245	C₂²	semidirect
49. #392109	C₂²	semidirect
50. #382422	C₂²	semidirect
51. #382390	C₂²	semidirect
52. #355913	C₂²	semidirect
53. #233542	C₂²	semidirect
54. #233541	C₂²	semidirect
55. #201664	C₂²	semidirect
56. #201664	C₂²	semidirect
57. #187928	C₂²	semidirect
58. #187928	C₂²	semidirect
59. C₂×#8101	C₂²	semidirect
60. C₂×#8101	C₂²	semidirect
61. #115691	C₂²	semidirect
62. #115690	C₂²	semidirect
63. #115205	C₂²	semidirect
64. #115204	C₂²	semidirect
65. #106766	C₂²	semidirect
66. #106766	C₂²	semidirect
67. C₂³×H(5,𝔽₂)	D₄	semidirect
68. C₂⁵×D₄	D₄	semidirect
73. C₂×#3484	D₄	semidirect
74. C₂×#3484	D₄	semidirect
77. C₂²×#534	D₄	semidirect
78. C₂³×#127	D₄	semidirect
79. C₂³×#121	D₄	semidirect
80. C₂³×#121	D₄	semidirect
81. C₂³×#121	D₄	semidirect
83. C₂³×#120	D₄	semidirect
84. C₂³×#120	D₄	semidirect
85. C₂³×#120	D₄	semidirect
89. C₂³×#120	C₂³	semidirect
90. C₂²×#518	D₄	semidirect
91. C₂³×C₄×D₄	D₄	semidirect
93. C₂³×#99	D₄	semidirect
94. #37436	D₄	semidirect
97. #34992	D₄	semidirect
99. #34980	D₄	semidirect
102. C₂×#2405	D₄	semidirect
103. C₂×#2405	C₂³	semidirect
104. C₂×#2410	D₄	semidirect
105. C₂×#2403	D₄	semidirect
106. C₂×#2403	D₄	semidirect
109. C₂×#2403	C₂³	semidirect
110. #34171	D₄	semidirect
111. #34171	D₄	semidirect
114. C₂×#2309	D₄	semidirect
115. C₂×#2308	D₄	semidirect
116. C₂²×#386	D₄	semidirect
117. C₂²×#386	C₂³	semidirect
127. C₂×#1819	C₂³	semidirect
128. C₂×#1781	D₄	semidirect
133. C₂×#1781	C₂³	semidirect
134. C₂×#1781	C₂³	semidirect
135. #14681	C₂³	semidirect
136. #14681	C₂³	semidirect
137. #14679	C₂³	semidirect
138. #14679	C₂³	semidirect
139. #14335	D₄	semidirect
140. #13869	C₂³	semidirect
141. #13867	D₄	semidirect
144. #13867	C₂³	semidirect
145. #10735	C₂³	semidirect
146. #8101	C₂³	semidirect
147. #8101	C₂³	semidirect
149. C₂⁷	C₂×D₄	semidirect
150. C₂⁷	C₂×D₄	semidirect
182. C₂⁴×D₄	C₂×D₄	semidirect
183. C₂⁴×D₄	C₂×D₄	semidirect
184. C₂⁴×D₄	C₂×D₄	semidirect
185. C₂⁴×D₄	C₂×D₄	semidirect
186. C₂⁴×D₄	C₂×D₄	semidirect
187. C₂⁴×D₄	C₂×D₄	semidirect
195. C₂⁵×C₄	C₂×D₄	semidirect
196. C₂⁵×C₄	C₂×D₄	semidirect
197. C₂⁵×C₄	C₂×D₄	semidirect
207. C₂²×#120	C₂×D₄	semidirect
208. C₂²×#120	C₂×D₄	semidirect
212. C₂³×C₄⋊C₄	C₂×D₄	semidirect
213. C₂³×C₄⋊C₄	C₂×D₄	semidirect
220. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
221. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
222. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
223. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
224. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
225. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
226. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
227. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
230. C₂³×C₄²	C₂×D₄	semidirect
232. C₂²×#99	C₂×D₄	semidirect
233. #2483	C₂×D₄	semidirect
234. #2405	C₂×D₄	semidirect
235. #2405	C₂×D₄	semidirect
236. #2403	C₂×D₄	semidirect
237. #2309	C₂×D₄	semidirect
238. #2309	C₂×D₄	semidirect
239. #2308	C₂×D₄	semidirect
240. #2308	C₂×D₄	semidirect
242. C₂×#386	C₂×D₄	semidirect
243. C₂×#386	C₂×D₄	semidirect
244. C₂×#385	C₂×D₄	semidirect
250. C₂×#379	C₂×D₄	semidirect
251. C₂×#379	C₂×D₄	semidirect
252. C₂×#379	C₂×D₄	semidirect
253. C₂×#379	C₂×D₄	semidirect
254. C₂×#379	C₂×D₄	semidirect
255. C₂×#379	C₂×D₄	semidirect
261. #1438	C₂×D₄	semidirect
262. #1438	C₂×D₄	semidirect
269. C₂⁶	#120	semidirect
331. C₂³×D₄	#120	semidirect
332. C₂³×D₄	#120	semidirect
333. C₂³×D₄	#120	semidirect
388. C₂⁴×C₄	#120	semidirect
389. C₂⁴×C₄	#120	semidirect
390. C₂⁴×C₄	#120	semidirect
405. C₂²×C₂²⋊C₄	#120	semidirect
406. C₂²×C₂²⋊C₄	#120	semidirect
407. C₂²×C₂²⋊C₄	#120	semidirect
408. C₂²×C₂²⋊C₄	#120	semidirect
409. C₂²×C₂²⋊C₄	#120	semidirect
419. #379	#120	semidirect
420. #379	#120	semidirect

Maximal subgroups

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

subgroup	index
#72238052	2
#72238049	2
#72238046	2
#72238031	2
#72238021	2
#72237398	2
C₂×#6470225	2
#72236431	2
C₂×#201664	2
#72235095	2
#72234629	2
#72233895	2
#72225665	2
#72219307	2
#72210600	2