Subgroups — #72260599

Order 2048.

At least 11364 conjugacy classes of subgroups; only the 1108 normal subgroups are shown.

The subgroup lattice has 672 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72260592	C₂	1	1	yes	maximal, characteristic, complemented
2	#72260589	C₂	1	1	yes	maximal, characteristic, complemented
3	#72260584	C₂	1	2	yes	maximal, complemented
4	#72260390	C₂	1	4	yes	maximal, complemented
5	#72252021	C₂	1	1	yes	maximal, characteristic, complemented
6	#72252020	C₂	1	1	yes	maximal, characteristic, complemented
7	#72237371	C₂	1	2	yes	maximal, complemented
8	#72233637	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#144386	C₂	1	2	yes	maximal, complemented
10	#72233342	C₂	1	4	yes	maximal, complemented
11	#72231750	C₂	1	4	yes	maximal, complemented
12	#72225655	C₂	1	1	yes	maximal, characteristic, complemented
13	#72219303	C₂	1	1	yes	maximal, characteristic, complemented
14	#72218215	C₂	1	2	yes	maximal, complemented
15	#72213293	C₂	1	4	yes	maximal, complemented
16	#10586066	C₂²	1	1	yes	characteristic
17	C₂²×#3498	C₂²	1	1	yes	characteristic
18	C₂×#35346	C₂²	1	1	yes	characteristic
19	#6470228	C₂²	1	4	yes	complemented
20	#6470225	C₂²	1	4	yes	complemented
21	#6440460	C₂²	1	2	yes	complemented
22	C₂×#23900	C₂²	1	2	yes	complemented
23	#6437449	C₂²	1	2	yes	complemented
24	#6437445	C₂²	1	2	yes	—
25	#6437445	C₂²	1	2	yes	complemented
26	#6437437	C₂²	1	2	yes	complemented
27	C₂×#23906	C₂²	1	2	yes	—
28	C₂×#23906	C₂²	1	2	yes	complemented
29	#6370704	C₂²	1	1	yes	characteristic
30	#6370693	C₂²	1	1	yes	characteristic
31	#6370693	C₂²	1	1	yes	characteristic
32	#4312024	C₂²	1	2	yes	complemented
33	#4312017	C₂²	1	2	yes	complemented
34	#850089	C₂²	1	2	yes	complemented
35	#846785	C₂²	1	2	yes	complemented
36	#763514	C₂²	1	1	yes	characteristic, complemented
37	#617875	C₂²	1	1	yes	characteristic, complemented
38	#616961	C₂²	1	1	yes	characteristic, complemented
39	C₂×#15258	C₂²	1	1	yes	characteristic, complemented
40	#517592	C₂²	1	1	yes	characteristic
41	#496228	C₂²	1	4	yes	complemented
42	#496225	C₂²	1	4	yes	complemented
43	#493879	C₂²	1	2	yes	complemented
44	#493372	C₂²	1	2	yes	complemented
45	#493370	C₂²	1	2	yes	complemented
46	#493370	C₂²	1	2	yes	complemented
47	#493365	C₂²	1	2	yes	complemented
48	C₂×#12693	C₂²	1	2	yes	complemented
49	C₂×#12693	C₂²	1	2	yes	complemented
50	C₂×#12687	C₂²	1	2	yes	complemented
51	#187944	C₂²	1	2	yes	complemented
52	#187931	C₂²	1	4	yes	complemented
53	#187928	C₂²	1	4	yes	complemented
54	C₂×#8534	C₂²	1	2	yes	complemented
55	#144415	C₂²	1	8	yes	complemented
56	#144414	C₂²	1	8	yes	complemented
57	#144414	C₂²	1	8	yes	complemented
58	#144414	C₂²	1	8	yes	complemented
59	#144388	C₂²	1	8	yes	complemented
60	#144386	C₂²	1	8	yes	complemented
61	#144386	C₂²	1	8	yes	complemented
62	#144386	C₂²	1	8	yes	complemented
63	#128074	C₂²	1	4	yes	complemented
64	#128073	C₂²	1	4	yes	complemented
65	#128033	C₂²	1	2	yes	complemented
66	C₂×#7304	C₂²	1	2	yes	complemented
67	C₂×H(7,𝔽₂)	D₄	1	1	yes	characteristic, complemented
68	C₂³×H(5,𝔽₂)	D₄	1	1	yes	characteristic, complemented
69	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
70	#62852	D₄	1	2	yes	complemented
71	#62842	D₄	1	2	yes	complemented
72	#62842	D₄	1	2	yes	complemented
73	#62811	C₂³	1	2	yes	—
74	C₂×#3484	C₂³	1	2	yes	—
75	C₂×#3484	C₂³	1	2	yes	—
76	C₂²×#535	D₄	1	1	yes	characteristic, complemented
77	C₂²×#535	D₄	1	1	yes	characteristic, complemented
78	C₂²×#535	D₄	1	1	yes	characteristic, complemented
79	C₂²×#535	C₂³	1	1	yes	characteristic
80	C₂²×#535	C₂³	1	1	yes	characteristic
81	C₂²×#535	C₂³	1	1	yes	characteristic
82	C₂²×#532	D₄	1	1	yes	characteristic, complemented
83	C₂²×#532	D₄	1	1	yes	characteristic, complemented
84	C₂²×#532	C₂³	1	1	yes	characteristic
85	C₂³×#127	D₄	1	1	yes	characteristic, complemented
86	C₂³×#127	C₂³	1	1	yes	characteristic
87	C₂³×#127	C₂³	1	1	yes	characteristic
88	C₂³×#120	D₄	1	1	yes	characteristic
89	C₂³×#120	D₄	1	1	yes	characteristic
90	C₂³×#120	C₂³	1	1	yes	characteristic
91	#62652	D₄	1	1	yes	characteristic, complemented
92	C₂²×C₄×#41	D₄	1	1	yes	characteristic, complemented
93	C₂×#2888	D₄	1	2	yes	complemented
94	C₂×#2883	D₄	1	2	yes	complemented
95	C₂×#2404	D₄	1	2	yes	—
96	C₂×#2404	C₂³	1	2	yes	—
97	C₂×#2403	D₄	1	2	yes	—
98	C₂×#2403	C₂³	1	2	yes	—
99	C₂×D₄×C₂²⋊C₄	D₄	1	2	yes	complemented
100	C₂×#2308	D₄	1	1	yes	characteristic
101	C₂×#2308	D₄	1	1	yes	characteristic
102	C₂×#2308	C₂³	1	1	yes	characteristic
103	#24056	C₂³	1	8	yes	—
104	#23907	C₂³	1	4	yes	—
105	#23906	C₂³	1	4	yes	—
106	#23906	C₂³	1	4	yes	—
107	#23906	C₂³	1	4	yes	—
108	#23900	C₂³	1	8	yes	—
109	#20592	D₄	1	2	yes	complemented
110	#20592	D₄	1	2	yes	complemented
111	#20592	D₄	1	2	yes	complemented
112	#20591	C₂³	1	2	yes	—
113	C₂×#1783	C₂³	1	2	yes	—
114	C₂×#1783	C₂³	1	2	yes	—
115	#20586	D₄	1	2	yes	complemented
116	#20585	D₄	1	2	yes	complemented
117	#20585	D₄	1	2	yes	complemented
118	#20584	C₂³	1	2	yes	—
119	#20584	C₂³	1	2	yes	—
120	C₂×#1781	C₂³	1	2	yes	—
121	C₂×#1781	C₂³	1	2	yes	—
122	C₂×#1781	C₂³	1	2	yes	—
123	C₂×#1781	C₂³	1	2	yes	—
124	#15784	C₂³	1	2	yes	complemented
125	#15313	C₂³	1	2	yes	complemented
126	#15313	C₂³	1	2	yes	complemented
127	#15313	C₂³	1	2	yes	complemented
128	#15259	C₂³	1	2	yes	complemented
129	#15258	C₂³	1	2	yes	complemented
130	#15258	C₂³	1	2	yes	complemented
131	#15258	C₂³	1	2	yes	complemented
132	#14337	D₄	1	1	yes	characteristic, complemented
133	#14335	D₄	1	1	yes	characteristic, complemented
134	#14335	C₂³	1	1	yes	characteristic
135	#13937	C₂³	1	2	yes	—
136	#13867	D₄	1	2	yes	complemented
137	#13867	C₂³	1	2	yes	—
138	#13851	D₄	1	1	yes	characteristic, complemented
139	C₂×#1438	D₄	1	1	yes	characteristic, complemented
140	C₂×#1438	C₂³	1	1	yes	characteristic
141	#12852	C₂³	1	8	yes	complemented
142	#12694	C₂³	1	4	yes	complemented
143	#12693	C₂³	1	4	yes	complemented
144	#12693	C₂³	1	4	yes	complemented
145	#12693	C₂³	1	4	yes	complemented
146	#12687	C₂³	1	8	yes	complemented
147	#8534	C₂³	1	8	yes	—
148	#8534	C₂³	1	8	yes	—
149	#7304	C₂³	1	8	yes	complemented
150	#7304	C₂³	1	8	yes	complemented
151	C₂⁷	C₂×D₄	1	1	yes	characteristic
152	C₂×#585	C₂×D₄	1	2	yes	complemented
153	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
154	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
155	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
156	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
157	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
158	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
159	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
160	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
161	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
162	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
163	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
164	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
165	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
166	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	complemented
167	C₂²×H(5,𝔽₂)	#41	1	1	yes	characteristic
168	C₂²×H(5,𝔽₂)	#41	1	1	yes	characteristic
169	C₂²×H(5,𝔽₂)	#41	1	1	yes	characteristic
170	C₂²×H(5,𝔽₂)	#41	1	1	yes	characteristic
171	C₂³×#41	C₂×D₄	1	1	yes	characteristic
172	C₂³×#41	C₂×D₄	1	1	yes	characteristic
173	C₂³×#41	C₂×D₄	1	1	yes	characteristic
174	C₂³×#41	C₂×D₄	1	1	yes	characteristic
175	C₂³×#41	C₂×D₄	1	1	yes	characteristic
176	C₂³×#41	C₂×D₄	1	1	yes	characteristic
177	C₂³×#41	C₂×D₄	1	1	yes	characteristic, complemented
178	C₂³×#41	C₂×D₄	1	1	yes	characteristic, complemented
179	C₂³×#41	C₂⁴	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	1	yes	characteristic
183	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
184	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
185	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
186	C₂⁴×D₄	C₂×D₄	1	2	yes	—
187	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
188	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
189	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
190	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
191	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
192	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
193	#3485	C₂×D₄	1	4	yes	complemented
194	#3484	C₂×D₄	1	4	yes	—
195	#3484	C₂×D₄	1	4	yes	complemented
196	#3484	C₂⁴	1	4	yes	—
197	C₂²×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic, complemented
198	C₂²×#127	C₂×D₄	1	1	yes	characteristic
199	C₂²×#127	C₂×D₄	1	1	yes	characteristic
200	C₂²×#127	C₂×D₄	1	1	yes	characteristic
201	C₂²×#127	C₂×D₄	1	1	yes	characteristic, complemented
202	C₂²×#127	C₂×D₄	1	1	yes	characteristic, complemented
203	C₂²×#127	C₂×D₄	1	1	yes	characteristic, complemented
204	C₂²×#127	C₂⁴	1	1	yes	characteristic
205	C₂²×#127	C₂⁴	1	1	yes	characteristic
206	C₂²×#127	C₂⁴	1	1	yes	characteristic
207	C₂²×#124	C₂×D₄	1	1	yes	characteristic
208	C₂²×#124	C₂×D₄	1	1	yes	characteristic, complemented
209	C₂²×#124	C₂×D₄	1	1	yes	characteristic, complemented
210	C₂²×#124	C₂×D₄	1	1	yes	characteristic, complemented
211	C₂²×#124	C₂×D₄	1	1	yes	characteristic, complemented
212	C₂²×#124	C₂⁴	1	1	yes	characteristic
213	C₂²×#120	C₂×D₄	1	2	yes	—
214	C₂²×#120	C₂×D₄	1	2	yes	—
215	C₂²×#120	C₂×D₄	1	2	yes	—
216	C₂²×#120	C₂⁴	1	2	yes	—
217	#3428	C₂×D₄	1	2	yes	complemented
218	C₂×#518	C₂×D₄	1	2	yes	—
219	C₂×#518	C₂×D₄	1	2	yes	complemented
220	C₂²×#117	C₂×D₄	1	1	yes	characteristic
221	C₂²×#117	C₂×D₄	1	1	yes	characteristic, complemented
222	C₂²×#117	C₂×D₄	1	1	yes	characteristic, complemented
223	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
224	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
225	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
226	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
227	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
228	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
229	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
230	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic, complemented
231	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic, complemented
232	C₂×#413	C₂×D₄	1	4	yes	complemented
233	C₂²×#100	C₂×D₄	1	4	yes	—
234	C₂²×#100	C₂×D₄	1	4	yes	complemented
235	C₂×#410	C₂×D₄	1	4	yes	complemented
236	C₂²×#99	C₂×D₄	1	4	yes	—
237	C₂²×#99	C₂×D₄	1	4	yes	complemented
238	C₂×#386	C₂×D₄	1	2	yes	—
239	C₂×#386	C₂×D₄	1	2	yes	—
240	C₂×#386	C₂×D₄	1	2	yes	—
241	C₂×#386	C₂⁴	1	2	yes	—
242	C₂×#381	C₂×D₄	1	2	yes	—
243	C₂×#380	C₂×D₄	1	2	yes	complemented
244	C₂×#379	C₂×D₄	1	2	yes	—
245	C₂×#379	C₂×D₄	1	2	yes	—
246	C₂×#379	C₂×D₄	1	2	yes	complemented
247	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
248	#1785	C₂×D₄	1	4	yes	complemented
249	#1783	C₂×D₄	1	4	yes	—
250	#1783	C₂×D₄	1	4	yes	complemented
251	#1783	C₂⁴	1	4	yes	—
252	#1782	C₂×D₄	1	4	yes	complemented
253	#1781	C₂×D₄	1	4	yes	—
254	#1781	C₂×D₄	1	4	yes	complemented
255	#1781	C₂⁴	1	4	yes	—
256	#1781	C₂⁴	1	4	yes	—
257	#1438	C₂×D₄	1	1	yes	characteristic
258	#1438	C₂×D₄	1	1	yes	characteristic
259	#1438	C₂×D₄	1	1	yes	characteristic
260	#1438	C₂×D₄	1	1	yes	characteristic
261	#1438	C₂×D₄	1	2	yes	complemented
262	#1438	C₂×D₄	1	2	yes	complemented
263	#1438	C₂×D₄	1	2	yes	complemented
264	#1438	C₂×D₄	1	2	yes	complemented
265	#1438	C₂⁴	1	2	yes	—
266	#1438	C₂⁴	1	2	yes	—
267	C₂⁶	#120	1	1	yes	characteristic
268	C₂⁶	#120	1	1	yes	characteristic
269	C₂⁶	C₂²×D₄	1	1	yes	characteristic
270	C₂⁶	C₂²×D₄	1	1	yes	characteristic
271	C₂⁶	C₂²×D₄	1	1	yes	characteristic
272	C₂⁶	C₂²×D₄	1	1	yes	characteristic
273	C₂⁶	C₂²×D₄	1	2	yes	—
274	C₂×H(5,𝔽₂)	C₂²×D₄	1	4	yes	—
275	C₂²×#41	#120	1	1	yes	characteristic
276	C₂²×#41	#120	1	1	yes	characteristic
277	C₂²×#41	#120	1	1	yes	characteristic
278	C₂²×#41	#120	1	1	yes	characteristic
279	C₂²×#41	#120	1	1	yes	characteristic
280	C₂²×#41	#120	1	1	yes	characteristic
281	C₂²×#41	#120	1	1	yes	characteristic
282	C₂²×#41	#120	1	1	yes	characteristic
283	C₂²×#41	#120	1	1	yes	characteristic
284	C₂²×#41	#120	1	1	yes	characteristic
285	C₂²×#41	#120	1	1	yes	characteristic
286	C₂²×#41	#120	1	1	yes	characteristic
287	C₂²×#41	#120	1	1	yes	characteristic
288	C₂²×#41	#120	1	1	yes	characteristic
289	C₂²×#41	#120	1	1	yes	characteristic
290	C₂²×#41	#120	1	1	yes	characteristic
291	C₂²×#41	#121	1	1	yes	characteristic
292	C₂²×#41	#121	1	1	yes	characteristic
293	C₂²×#41	#121	1	1	yes	characteristic
294	C₂²×#41	#121	1	1	yes	characteristic
295	C₂²×#41	#121	1	1	yes	characteristic
296	C₂²×#41	#121	1	1	yes	characteristic
297	C₂²×#41	#121	1	1	yes	characteristic
298	C₂²×#41	#121	1	1	yes	characteristic
299	C₂²×#41	#121	1	1	yes	characteristic
300	C₂²×#41	#121	1	1	yes	characteristic
301	C₂²×#41	#121	1	1	yes	characteristic
302	C₂²×#41	#121	1	1	yes	characteristic
303	C₂²×#41	#121	1	1	yes	characteristic
304	C₂²×#41	#121	1	1	yes	characteristic
305	C₂²×#41	#121	1	1	yes	characteristic
306	C₂²×#41	#121	1	1	yes	characteristic
307	C₂²×#41	#121	1	1	yes	characteristic
308	C₂²×#41	#121	1	1	yes	characteristic
309	C₂²×#41	#121	1	1	yes	characteristic
310	C₂²×#41	#121	1	1	yes	characteristic
311	C₂²×#41	#127	1	1	yes	characteristic
312	C₂²×#41	#127	1	1	yes	characteristic
313	C₂²×#41	#127	1	1	yes	characteristic
314	C₂²×#41	#127	1	1	yes	characteristic
315	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
316	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
317	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
318	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
319	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
320	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
321	C₂²×#41	C₂×#41	1	1	yes	characteristic
322	C₂²×#41	C₂×#41	1	1	yes	characteristic
323	C₂³×Q₈	#120	1	1	yes	characteristic
324	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
325	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
326	C₂³×D₄	#120	1	1	yes	characteristic
327	C₂³×D₄	#120	1	1	yes	characteristic
328	C₂³×D₄	#120	1	1	yes	characteristic
329	C₂³×D₄	#120	1	1	yes	characteristic
330	C₂³×D₄	#120	1	1	yes	characteristic
331	C₂³×D₄	#120	1	1	yes	characteristic
332	C₂³×D₄	#120	1	1	yes	characteristic
333	C₂³×D₄	#120	1	1	yes	characteristic
334	C₂³×D₄	#120	1	1	yes	characteristic
335	C₂³×D₄	#120	1	1	yes	characteristic
336	C₂³×D₄	#120	1	1	yes	characteristic
337	C₂³×D₄	#120	1	1	yes	characteristic
338	C₂³×D₄	#120	1	1	yes	characteristic
339	C₂³×D₄	#120	1	1	yes	characteristic
340	C₂³×D₄	#120	1	1	yes	characteristic
341	C₂³×D₄	#120	1	1	yes	characteristic
342	C₂³×D₄	#120	1	1	yes	characteristic
343	C₂³×D₄	#120	1	1	yes	characteristic
344	C₂³×D₄	#120	1	1	yes	characteristic
345	C₂³×D₄	#120	1	1	yes	characteristic
346	C₂³×D₄	#120	1	1	yes	characteristic
347	C₂³×D₄	#120	1	1	yes	characteristic
348	C₂³×D₄	#120	1	1	yes	characteristic
349	C₂³×D₄	#120	1	1	yes	characteristic
350	C₂³×D₄	#120	1	1	yes	characteristic
351	C₂³×D₄	#121	1	1	yes	characteristic
352	C₂³×D₄	#121	1	1	yes	characteristic
353	C₂³×D₄	#121	1	1	yes	characteristic
354	C₂³×D₄	#121	1	1	yes	characteristic
355	C₂³×D₄	#121	1	1	yes	characteristic
356	C₂³×D₄	#121	1	1	yes	characteristic
357	C₂³×D₄	#121	1	1	yes	characteristic
358	C₂³×D₄	#121	1	1	yes	characteristic
359	C₂³×D₄	#121	1	1	yes	characteristic
360	C₂³×D₄	#121	1	1	yes	characteristic
361	C₂³×D₄	#121	1	1	yes	characteristic
362	C₂³×D₄	#121	1	1	yes	characteristic
363	C₂³×D₄	#121	1	1	yes	characteristic
364	C₂³×D₄	#121	1	1	yes	characteristic
365	C₂³×D₄	#121	1	1	yes	characteristic
366	C₂³×D₄	#121	1	1	yes	characteristic
367	C₂³×D₄	#121	1	1	yes	characteristic
368	C₂³×D₄	#121	1	1	yes	characteristic
369	C₂³×D₄	#121	1	1	yes	characteristic
370	C₂³×D₄	#121	1	1	yes	characteristic
371	C₂³×D₄	#121	1	1	yes	characteristic
372	C₂³×D₄	#121	1	1	yes	characteristic
373	C₂³×D₄	#121	1	1	yes	characteristic
374	C₂³×D₄	#121	1	1	yes	characteristic
375	C₂³×D₄	#121	1	1	yes	characteristic
376	C₂³×D₄	#121	1	1	yes	characteristic
377	C₂³×D₄	#121	1	1	yes	characteristic
378	C₂³×D₄	#121	1	1	yes	characteristic
379	C₂³×D₄	#127	1	1	yes	characteristic
380	C₂³×D₄	#127	1	1	yes	characteristic
381	C₂³×D₄	#127	1	1	yes	characteristic
382	C₂³×D₄	#127	1	1	yes	characteristic
383	C₂³×D₄	#127	1	1	yes	characteristic
384	C₂³×D₄	#127	1	1	yes	characteristic
385	C₂³×D₄	#127	1	1	yes	characteristic
386	C₂³×D₄	#127	1	1	yes	characteristic
387	C₂³×D₄	#127	1	1	yes	characteristic
388	C₂³×D₄	#127	1	1	yes	characteristic
389	C₂³×D₄	#127	1	1	yes	characteristic
390	C₂³×D₄	#127	1	1	yes	characteristic
391	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
392	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
393	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
394	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
395	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
396	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
397	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
398	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
399	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
400	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
401	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
402	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
403	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
404	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
405	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
406	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
407	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
408	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
409	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
410	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
411	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
412	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
413	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
414	C₂³×D₄	C₂×#41	1	1	yes	characteristic
415	C₂³×D₄	C₂×#41	1	1	yes	characteristic
416	C₂³×D₄	C₂×#41	1	1	yes	characteristic
417	C₂³×D₄	C₂×#41	1	1	yes	characteristic
418	C₂³×D₄	C₂⁵	1	1	yes	characteristic
419	C₂⁴×C₄	#120	1	1	yes	characteristic
420	C₂⁴×C₄	#120	1	1	yes	characteristic
421	C₂⁴×C₄	#120	1	1	yes	characteristic
422	C₂⁴×C₄	#120	1	1	yes	characteristic
423	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
424	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
425	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
426	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
427	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
428	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
429	#518	C₂²×D₄	1	4	yes	—
430	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
431	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
432	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
433	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
434	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
435	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
436	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
437	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
438	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
439	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
440	C₂×#100	C₂²×D₄	1	8	yes	—
441	C₂×#99	C₂²×D₄	1	8	yes	—
442	C₂⁵	#392	1	1	yes	characteristic
443	C₂⁵	#392	1	1	yes	characteristic
444	C₂⁵	#392	1	1	yes	characteristic
445	C₂⁵	#392	1	1	yes	characteristic
446	C₂⁵	#392	1	1	yes	characteristic
447	C₂⁵	#392	1	1	yes	characteristic
448	C₂⁵	#392	1	1	yes	characteristic
449	C₂⁵	#392	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	1	yes	characteristic
453	C₂⁵	C₂×#120	1	1	yes	characteristic
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	1	yes	characteristic
460	C₂⁵	C₂×#120	1	1	yes	characteristic
461	C₂⁵	C₂×#121	1	1	yes	characteristic
462	C₂⁵	C₂×#121	1	1	yes	characteristic
463	C₂⁵	C₂×#121	1	1	yes	characteristic
464	C₂⁵	C₂×#121	1	1	yes	characteristic
465	C₂⁵	C₂×#121	1	1	yes	characteristic
466	C₂⁵	C₂×#121	1	1	yes	characteristic
467	C₂⁵	C₂×#121	1	1	yes	characteristic
468	C₂⁵	C₂×#121	1	1	yes	characteristic
469	C₂⁵	C₂×#127	1	1	yes	characteristic
470	C₂⁵	C₂×#127	1	1	yes	characteristic
471	C₂⁵	C₂×#127	1	1	yes	characteristic
472	C₂⁵	C₂×#127	1	1	yes	characteristic
473	C₂⁵	C₂³×D₄	1	1	yes	characteristic
474	C₂⁵	C₂³×D₄	1	1	yes	characteristic
475	C₂²×Q₈	#392	1	1	yes	characteristic
476	C₂²×Q₈	#392	1	1	yes	characteristic
477	C₂²×Q₈	#392	1	1	yes	characteristic
478	C₂²×Q₈	#392	1	1	yes	characteristic
479	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
480	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
481	C₂²×Q₈	C₂×#121	1	1	yes	characteristic
482	C₂²×Q₈	C₂×#121	1	1	yes	characteristic
483	C₂²×D₄	#392	1	1	yes	characteristic
484	C₂²×D₄	#392	1	1	yes	characteristic
485	C₂²×D₄	#392	1	1	yes	characteristic
486	C₂²×D₄	#392	1	1	yes	characteristic
487	C₂²×D₄	#392	1	1	yes	characteristic
488	C₂²×D₄	#392	1	1	yes	characteristic
489	C₂²×D₄	#392	1	1	yes	characteristic
490	C₂²×D₄	#392	1	1	yes	characteristic
491	C₂²×D₄	#392	1	1	yes	characteristic
492	C₂²×D₄	#392	1	1	yes	characteristic
493	C₂²×D₄	#392	1	1	yes	characteristic
494	C₂²×D₄	#392	1	1	yes	characteristic
495	C₂²×D₄	#392	1	1	yes	characteristic
496	C₂²×D₄	#392	1	1	yes	characteristic
497	C₂²×D₄	#392	1	1	yes	characteristic
498	C₂²×D₄	#392	1	1	yes	characteristic
499	C₂²×D₄	#392	1	1	yes	characteristic
500	C₂²×D₄	#392	1	1	yes	characteristic
501	C₂²×D₄	#392	1	1	yes	characteristic
502	C₂²×D₄	#392	1	1	yes	characteristic
503	C₂²×D₄	#392	1	1	yes	characteristic
504	C₂²×D₄	#392	1	1	yes	characteristic
505	C₂²×D₄	#392	1	1	yes	characteristic
506	C₂²×D₄	#392	1	1	yes	characteristic
507	C₂²×D₄	#392	1	1	yes	characteristic
508	C₂²×D₄	#392	1	1	yes	characteristic
509	C₂²×D₄	#392	1	1	yes	characteristic
510	C₂²×D₄	#392	1	1	yes	characteristic
511	C₂²×D₄	#392	1	1	yes	characteristic
512	C₂²×D₄	#392	1	1	yes	characteristic
513	C₂²×D₄	#392	1	1	yes	characteristic
514	C₂²×D₄	#392	1	1	yes	characteristic
515	C₂²×D₄	#392	1	1	yes	characteristic
516	C₂²×D₄	#392	1	1	yes	characteristic
517	C₂²×D₄	#392	1	1	yes	characteristic
518	C₂²×D₄	#392	1	1	yes	characteristic
519	C₂²×D₄	B(4,𝔽₂)	1	8	yes	—
520	C₂²×D₄	B(4,𝔽₂)	1	8	yes	—
521	C₂²×D₄	C₂×#120	1	1	yes	characteristic
522	C₂²×D₄	C₂×#120	1	1	yes	characteristic
523	C₂²×D₄	C₂×#120	1	1	yes	characteristic
524	C₂²×D₄	C₂×#120	1	1	yes	characteristic
525	C₂²×D₄	C₂×#120	1	1	yes	characteristic
526	C₂²×D₄	C₂×#120	1	1	yes	characteristic
527	C₂²×D₄	C₂×#120	1	1	yes	characteristic
528	C₂²×D₄	C₂×#120	1	1	yes	characteristic
529	C₂²×D₄	C₂×#120	1	1	yes	characteristic
530	C₂²×D₄	C₂×#120	1	1	yes	characteristic
531	C₂²×D₄	C₂×#121	1	1	yes	characteristic
532	C₂²×D₄	C₂×#121	1	1	yes	characteristic
533	C₂²×D₄	C₂×#121	1	1	yes	characteristic
534	C₂²×D₄	C₂×#121	1	1	yes	characteristic
535	C₂²×D₄	C₂×#121	1	1	yes	characteristic
536	C₂²×D₄	C₂×#121	1	1	yes	characteristic
537	C₂²×D₄	C₂×#121	1	1	yes	characteristic
538	C₂²×D₄	C₂×#121	1	1	yes	characteristic
539	C₂²×D₄	C₂×#121	1	1	yes	characteristic
540	C₂²×D₄	C₂×#121	1	1	yes	characteristic
541	C₂²×D₄	C₂×#121	1	1	yes	characteristic
542	C₂²×D₄	C₂×#121	1	1	yes	characteristic
543	C₂²×D₄	C₂×#121	1	1	yes	characteristic
544	C₂²×D₄	C₂×#121	1	1	yes	characteristic
545	C₂²×D₄	C₂×#121	1	1	yes	characteristic
546	C₂²×D₄	C₂×#121	1	1	yes	characteristic
547	C₂²×D₄	C₂×#127	1	1	yes	characteristic
548	C₂²×D₄	C₂×#127	1	1	yes	characteristic
549	C₂²×D₄	C₂×#127	1	1	yes	characteristic
550	C₂²×D₄	C₂×#127	1	1	yes	characteristic
551	C₂²×D₄	C₂×#127	1	1	yes	characteristic
552	C₂²×D₄	C₂×#127	1	1	yes	characteristic
553	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
554	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
555	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
556	C₂²×D₄	C₂²×#41	1	1	yes	characteristic
557	C₂³×C₄	#392	1	1	yes	characteristic
558	C₂³×C₄	#392	1	1	yes	characteristic
559	C₂³×C₄	#392	1	1	yes	characteristic
560	C₂³×C₄	#392	1	1	yes	characteristic
561	C₂³×C₄	#392	1	1	yes	characteristic
562	C₂³×C₄	#392	1	1	yes	characteristic
563	C₂³×C₄	#392	1	1	yes	characteristic
564	C₂³×C₄	#392	1	1	yes	characteristic
565	C₂³×C₄	#392	1	1	yes	characteristic
566	C₂³×C₄	#392	1	1	yes	characteristic
567	C₂³×C₄	#392	1	1	yes	characteristic
568	C₂³×C₄	#392	1	1	yes	characteristic
569	C₂³×C₄	#392	1	1	yes	characteristic
570	C₂³×C₄	#392	1	1	yes	characteristic
571	C₂³×C₄	#392	1	1	yes	characteristic
572	C₂³×C₄	#392	1	1	yes	characteristic
573	C₂³×C₄	C₂×#120	1	1	yes	characteristic
574	C₂³×C₄	C₂×#120	1	1	yes	characteristic
575	C₂³×C₄	C₂×#120	1	1	yes	characteristic
576	C₂³×C₄	C₂×#120	1	1	yes	characteristic
577	C₂³×C₄	C₂×#120	1	1	yes	characteristic
578	C₂³×C₄	C₂×#120	1	1	yes	characteristic
579	C₂³×C₄	C₂×#120	1	1	yes	characteristic
580	C₂³×C₄	C₂×#120	1	1	yes	characteristic
581	C₂³×C₄	C₂×#120	1	1	yes	characteristic
582	C₂³×C₄	C₂×#120	1	1	yes	characteristic
583	C₂³×C₄	C₂×#120	1	1	yes	characteristic
584	C₂³×C₄	C₂×#120	1	1	yes	characteristic
585	C₂³×C₄	C₂×#120	1	1	yes	characteristic
586	C₂³×C₄	C₂×#121	1	1	yes	characteristic
587	C₂³×C₄	C₂×#121	1	1	yes	characteristic
588	C₂³×C₄	C₂×#121	1	1	yes	characteristic
589	C₂³×C₄	C₂×#121	1	1	yes	characteristic
590	C₂³×C₄	C₂×#121	1	1	yes	characteristic
591	C₂³×C₄	C₂×#121	1	1	yes	characteristic
592	C₂³×C₄	C₂×#121	1	1	yes	characteristic
593	C₂³×C₄	C₂×#121	1	1	yes	characteristic
594	C₂³×C₄	C₂×#121	1	1	yes	characteristic
595	C₂³×C₄	C₂×#121	1	1	yes	characteristic
596	C₂³×C₄	C₂×#127	1	1	yes	characteristic
597	C₂³×C₄	C₂×#127	1	1	yes	characteristic
598	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
599	C₂⁴	#2021	1	4	yes	—
600	C₂⁴	C₂×#392	1	1	yes	characteristic
601	C₂⁴	C₂×#392	1	1	yes	characteristic
602	C₂⁴	C₂×#392	1	1	yes	characteristic
603	C₂⁴	C₂×#392	1	1	yes	characteristic
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	1	yes	characteristic
611	C₂⁴	C₂×#392	1	1	yes	characteristic
612	C₂⁴	C₂×#392	1	1	yes	characteristic
613	C₂⁴	C₂×#392	1	1	yes	characteristic
614	C₂⁴	C₂×B(4,𝔽₂)	1	4	yes	—
615	C₂⁴	C₂×B(4,𝔽₂)	1	4	yes	—
616	C₂⁴	C₂×B(4,𝔽₂)	1	4	yes	—
617	C₂⁴	C₂²×#120	1	1	yes	characteristic
618	C₂⁴	C₂²×#120	1	1	yes	characteristic
619	C₂⁴	C₂²×#121	1	1	yes	characteristic
620	C₂⁴	C₂²×#121	1	1	yes	characteristic
621	C₂⁴	C₂²×#127	1	1	yes	characteristic
622	C₂×D₄	#2021	1	4	yes	—
623	C₂×D₄	#2021	1	4	yes	—
624	C₂×D₄	#2021	1	4	yes	—
625	C₂×D₄	#2021	1	4	yes	—
626	C₂×D₄	#2021	1	4	yes	—
627	C₂×D₄	#2021	1	4	yes	—
628	C₂×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
629	C₂×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
630	C₂²×C₄	#2021	1	4	yes	—
631	C₂²×C₄	C₂×#392	1	1	yes	characteristic
632	C₂²×C₄	C₂×#392	1	1	yes	characteristic
633	C₂²×C₄	C₂×#392	1	1	yes	characteristic
634	C₂²×C₄	C₂×#392	1	1	yes	characteristic
635	C₂²×C₄	C₂×#392	1	1	yes	characteristic
636	C₂²×C₄	C₂×#392	1	1	yes	characteristic
637	C₂²×C₄	C₂×#392	1	1	yes	characteristic
638	C₂²×C₄	C₂×#392	1	1	yes	characteristic
639	C₂²×C₄	C₂×#392	1	1	yes	characteristic
640	C₂²×C₄	C₂×#392	1	1	yes	characteristic
641	C₂²×C₄	C₂×B(4,𝔽₂)	1	4	yes	—
642	C₂²×C₄	#3026	1	4	yes	—
643	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
644	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
645	C₂³	C₂×#2021	1	2	yes	—
646	C₂³	C₂×#2021	1	2	yes	—
647	C₂³	C₂×#2021	1	2	yes	—
648	C₂³	C₂×#2021	1	2	yes	—
649	C₂³	C₂×#2021	1	2	yes	—
650	C₂³	C₂×#2021	1	2	yes	—
651	C₂³	C₂×#2021	1	2	yes	—
652	C₂³	C₂×#2021	1	2	yes	—
653	C₂³	#23444	1	2	yes	—
654	C₂³	C₂²×#392	1	1	yes	characteristic
655	C₂³	C₂²×B(4,𝔽₂)	1	2	yes	—
656	C₂³	C₂²×B(4,𝔽₂)	1	2	yes	—
657	C₂×C₄	C₂×#2021	1	2	yes	—
658	C₂×C₄	C₂×#2021	1	2	yes	—
659	C₂×C₄	C₂×#2021	1	2	yes	—
660	C₂×C₄	C₂×#2021	1	2	yes	—
661	C₂×C₄	#23444	1	2	yes	—
662	C₂×C₄	C₂×#3026	1	2	yes	—
663	C₂²	#233541	1	4	yes	—
664	C₂²	C₂²×#2021	1	1	yes	characteristic
665	C₂²	C₂²×#2021	1	1	yes	characteristic
666	C₂²	C₂×#23444	1	1	yes	characteristic
667	C₂²	#7622880	1	2	yes	—
668	C₂²	#7622887	1	2	yes	—
669	C₂	#72234696	1	2	yes	—
670	C₂	C₂×#233541	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂²×#2021
commutator, Frattini, cosocle	C₂³×D₄	C₂⁵
LCS	G ▷ C₂³×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂³×D₄ ◁ C₂³×H(5,𝔽₂) ◁ 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. #72260592	C₂	semidirect
2. #72260589	C₂	semidirect
3. #72260584	C₂	semidirect
4. #72260390	C₂	semidirect
5. #72252021	C₂	semidirect
6. #72252020	C₂	semidirect
7. #72237371	C₂	semidirect
8. #72233637	C₂	semidirect
9. C₂×#144386	C₂	semidirect
10. #72233342	C₂	semidirect
11. #72231750	C₂	semidirect
12. #72225655	C₂	semidirect
13. #72219303	C₂	semidirect
14. #72218215	C₂	semidirect
15. #72213293	C₂	semidirect
19. #6470228	C₂²	semidirect
20. #6470225	C₂²	semidirect
21. #6440460	C₂²	semidirect
22. C₂×#23900	C₂²	semidirect
23. #6437449	C₂²	semidirect
25. #6437445	C₂²	semidirect
26. #6437437	C₂²	semidirect
28. C₂×#23906	C₂²	semidirect
32. #4312024	C₂²	semidirect
33. #4312017	C₂²	semidirect
34. #850089	C₂²	semidirect
35. #846785	C₂²	semidirect
36. #763514	C₂²	semidirect
37. #617875	C₂²	semidirect
38. #616961	C₂²	semidirect
39. C₂×#15258	C₂²	semidirect
41. #496228	C₂²	semidirect
42. #496225	C₂²	semidirect
43. #493879	C₂²	semidirect
44. #493372	C₂²	semidirect
45. #493370	C₂²	semidirect
46. #493370	C₂²	semidirect
47. #493365	C₂²	semidirect
48. C₂×#12693	C₂²	semidirect
49. C₂×#12693	C₂²	semidirect
50. C₂×#12687	C₂²	semidirect
51. #187944	C₂²	semidirect
52. #187931	C₂²	semidirect
53. #187928	C₂²	semidirect
54. C₂×#8534	C₂²	semidirect
55. #144415	C₂²	semidirect
56. #144414	C₂²	semidirect
57. #144414	C₂²	semidirect
58. #144414	C₂²	semidirect
59. #144388	C₂²	semidirect
60. #144386	C₂²	semidirect
61. #144386	C₂²	semidirect
62. #144386	C₂²	semidirect
63. #128074	C₂²	semidirect
64. #128073	C₂²	semidirect
65. #128033	C₂²	semidirect
66. C₂×#7304	C₂²	semidirect
67. C₂×H(7,𝔽₂)	D₄	semidirect
68. C₂³×H(5,𝔽₂)	D₄	semidirect
70. #62852	D₄	semidirect
71. #62842	D₄	semidirect
72. #62842	D₄	semidirect
76. C₂²×#535	D₄	semidirect
77. C₂²×#535	D₄	semidirect
78. C₂²×#535	D₄	semidirect
82. C₂²×#532	D₄	semidirect
83. C₂²×#532	D₄	semidirect
85. C₂³×#127	D₄	semidirect
91. #62652	D₄	semidirect
92. C₂²×C₄×#41	D₄	semidirect
93. C₂×#2888	D₄	semidirect
94. C₂×#2883	D₄	semidirect
99. C₂×D₄×C₂²⋊C₄	D₄	semidirect
109. #20592	D₄	semidirect
110. #20592	D₄	semidirect
111. #20592	D₄	semidirect
115. #20586	D₄	semidirect
116. #20585	D₄	semidirect
117. #20585	D₄	semidirect
124. #15784	C₂³	semidirect
125. #15313	C₂³	semidirect
126. #15313	C₂³	semidirect
127. #15313	C₂³	semidirect
128. #15259	C₂³	semidirect
129. #15258	C₂³	semidirect
130. #15258	C₂³	semidirect
131. #15258	C₂³	semidirect
132. #14337	D₄	semidirect
133. #14335	D₄	semidirect
136. #13867	D₄	semidirect
138. #13851	D₄	semidirect
139. C₂×#1438	D₄	semidirect
141. #12852	C₂³	semidirect
142. #12694	C₂³	semidirect
143. #12693	C₂³	semidirect
144. #12693	C₂³	semidirect
145. #12693	C₂³	semidirect
146. #12687	C₂³	semidirect
149. #7304	C₂³	semidirect
150. #7304	C₂³	semidirect
152. C₂×#585	C₂×D₄	semidirect
166. C₂²×H(5,𝔽₂)	C₂×D₄	semidirect
177. C₂³×#41	C₂×D₄	semidirect
178. C₂³×#41	C₂×D₄	semidirect
189. C₂⁴×D₄	C₂×D₄	semidirect
190. C₂⁴×D₄	C₂×D₄	semidirect
193. #3485	C₂×D₄	semidirect
195. #3484	C₂×D₄	semidirect
197. C₂²×C₄⋊Q₈	C₂×D₄	semidirect
201. C₂²×#127	C₂×D₄	semidirect
202. C₂²×#127	C₂×D₄	semidirect
203. C₂²×#127	C₂×D₄	semidirect
208. C₂²×#124	C₂×D₄	semidirect
209. C₂²×#124	C₂×D₄	semidirect
210. C₂²×#124	C₂×D₄	semidirect
211. C₂²×#124	C₂×D₄	semidirect
217. #3428	C₂×D₄	semidirect
219. C₂×#518	C₂×D₄	semidirect
221. C₂²×#117	C₂×D₄	semidirect
222. C₂²×#117	C₂×D₄	semidirect
228. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
230. C₂³×C₄²	C₂×D₄	semidirect
231. C₂³×C₄²	C₂×D₄	semidirect
232. C₂×#413	C₂×D₄	semidirect
234. C₂²×#100	C₂×D₄	semidirect
235. C₂×#410	C₂×D₄	semidirect
237. C₂²×#99	C₂×D₄	semidirect
243. C₂×#380	C₂×D₄	semidirect
246. C₂×#379	C₂×D₄	semidirect
247. C₂×C₄×C₂²⋊C₄	C₂×D₄	semidirect
248. #1785	C₂×D₄	semidirect
250. #1783	C₂×D₄	semidirect
252. #1782	C₂×D₄	semidirect
254. #1781	C₂×D₄	semidirect
261. #1438	C₂×D₄	semidirect
262. #1438	C₂×D₄	semidirect
263. #1438	C₂×D₄	semidirect
264. #1438	C₂×D₄	semidirect

Maximal subgroups

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

subgroup	index
#72260592	2
#72260589	2
#72260584	2
#72260390	2
#72252021	2
#72252020	2
#72237371	2
#72233637	2
C₂×#144386	2
#72233342	2
#72231750	2
#72225655	2
#72219303	2
#72218215	2
#72213293	2