Subgroups — #72263559

Order 2048.

At least 14186 conjugacy classes of subgroups; only the 1072 normal subgroups are shown.

The subgroup lattice has 701 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72263558	C₂	1	2	yes	maximal, complemented
2	#72263557	C₂	1	2	yes	maximal, complemented
3	#72263556	C₂	1	4	yes	maximal, complemented
4	#72263555	C₂	1	4	yes	maximal, complemented
5	#72263547	C₂	1	1	yes	maximal, characteristic, complemented
6	#72237398	C₂	1	1	yes	maximal, characteristic, complemented
7	#72236704	C₂	1	1	yes	maximal, characteristic, complemented
8	#72236701	C₂	1	1	yes	maximal, characteristic, complemented
9	#72236670	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#496225	C₂	1	1	yes	maximal, characteristic, complemented
11	#72236527	C₂	1	4	yes	maximal, complemented
12	C₂×#6470225	C₂	1	1	yes	maximal, characteristic, complemented
13	#72234544	C₂	1	2	yes	maximal, complemented
14	#72231479	C₂	1	2	yes	maximal, complemented
15	#72213293	C₂	1	4	yes	maximal, complemented
16	C₂²×#3484	C₂²	1	1	yes	characteristic
17	C₂×#35222	C₂²	1	1	yes	characteristic
18	C₂²×#2403	C₂²	1	1	yes	characteristic
19	#6470225	C₂²	1	4	yes	—
20	#6470225	C₂²	1	4	yes	—
21	#6470020	C₂²	1	2	yes	—
22	#6470020	C₂²	1	2	yes	complemented
23	#6470019	C₂²	1	2	yes	—
24	#6470019	C₂²	1	2	yes	complemented
25	C₂×#24056	C₂²	1	2	yes	—
26	#6440354	C₂²	1	2	yes	complemented
27	C₂×#23900	C₂²	1	2	yes	—
28	#6437445	C₂²	1	2	yes	complemented
29	C₂²×#1783	C₂²	1	1	yes	characteristic
30	C₂²×#1781	C₂²	1	1	yes	characteristic
31	C₂²×#1781	C₂²	1	1	yes	characteristic
32	#4866529	C₂²	1	2	yes	complemented
33	#4866528	C₂²	1	2	yes	complemented
34	#4327960	C₂²	1	2	yes	complemented
35	#4312024	C₂²	1	2	yes	complemented
36	#846393	C₂²	1	1	yes	characteristic, complemented
37	#846389	C₂²	1	1	yes	characteristic, complemented
38	#846061	C₂²	1	1	yes	characteristic, complemented
39	#846057	C₂²	1	1	yes	characteristic, complemented
40	#517411	C₂²	1	1	yes	characteristic
41	#496225	C₂²	1	4	yes	complemented
42	#496225	C₂²	1	4	yes	complemented
43	#496191	C₂²	1	2	yes	complemented
44	#496191	C₂²	1	2	yes	complemented
45	#496189	C₂²	1	2	yes	complemented
46	#496189	C₂²	1	2	yes	complemented
47	#493883	C₂²	1	2	yes	complemented
48	C₂×#12852	C₂²	1	2	yes	complemented
49	#493370	C₂²	1	2	yes	complemented
50	C₂×#12687	C₂²	1	2	yes	complemented
51	#187944	C₂²	1	4	yes	complemented
52	#187928	C₂²	1	2	yes	—
53	#187928	C₂²	1	2	yes	—
54	#187928	C₂²	1	4	yes	complemented
55	#144429	C₂²	1	8	yes	complemented
56	#144428	C₂²	1	8	yes	complemented
57	#144415	C₂²	1	8	yes	complemented
58	#144414	C₂²	1	8	yes	complemented
59	#144404	C₂²	1	8	yes	complemented
60	#144404	C₂²	1	8	yes	complemented
61	#144388	C₂²	1	8	yes	complemented
62	#144386	C₂²	1	8	yes	complemented
63	#128073	C₂²	1	4	yes	complemented
64	#128073	C₂²	1	2	yes	complemented
65	#128073	C₂²	1	2	yes	complemented
66	#128033	C₂²	1	4	yes	complemented
67	C₂³×H(5,𝔽₂)	D₄	1	1	yes	characteristic, complemented
68	C₂⁵×D₄	D₄	1	1	yes	characteristic
69	C₂⁵×D₄	C₂³	1	1	yes	characteristic
70	C₂×#3484	D₄	1	2	yes	complemented
71	C₂×#3484	D₄	1	2	yes	complemented
72	C₂×#3484	D₄	1	2	yes	complemented
73	C₂×#3484	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	C₂³	1	1	yes	characteristic
78	C₂²×#525	D₄	1	1	yes	characteristic, complemented
79	C₂³×#120	D₄	1	1	yes	characteristic
80	C₂³×#120	C₂³	1	1	yes	characteristic
81	C₂²×#518	D₄	1	1	yes	characteristic, complemented
82	C₂³×#100	D₄	1	2	yes	complemented
83	C₂³×#99	D₄	1	2	yes	complemented
84	C₂×#2435	D₄	1	1	yes	characteristic, complemented
85	C₂×#2435	D₄	1	1	yes	characteristic, complemented
86	C₂×#2435	C₂³	1	1	yes	characteristic
87	C₂×#2435	C₂³	1	1	yes	characteristic
88	C₂×#2433	D₄	1	1	yes	characteristic, complemented
89	C₂×#2433	D₄	1	1	yes	characteristic, complemented
90	C₂×#2433	C₂³	1	1	yes	characteristic
91	C₂×#2433	C₂³	1	1	yes	characteristic
92	C₂×#2403	D₄	1	2	yes	—
93	C₂×#2403	D₄	1	2	yes	—
94	C₂×#2403	C₂³	1	2	yes	—
95	C₂×#2403	C₂³	1	2	yes	—
96	C₂×#2309	D₄	1	1	yes	characteristic, complemented
97	C₂×#2309	C₂³	1	1	yes	characteristic
98	C₂²×#386	D₄	1	1	yes	characteristic
99	C₂²×#386	C₂³	1	1	yes	characteristic
100	C₂×#2280	D₄	1	1	yes	characteristic, complemented
101	C₂²×#379	D₄	1	1	yes	characteristic
102	C₂²×#379	D₄	1	1	yes	characteristic, complemented
103	C₂²×#379	D₄	1	1	yes	characteristic, complemented
104	#24056	C₂³	1	8	yes	—
105	#24018	C₂³	1	4	yes	—
106	#24018	C₂³	1	4	yes	—
107	#23907	C₂³	1	4	yes	—
108	#23906	C₂³	1	4	yes	—
109	#23900	C₂³	1	8	yes	—
110	C₂×#1783	D₄	1	2	yes	complemented
111	C₂×#1783	D₄	1	2	yes	complemented
112	C₂×#1783	D₄	1	2	yes	complemented
113	C₂×#1783	C₂³	1	2	yes	—
114	C₂×#1783	C₂³	1	2	yes	—
115	C₂×#1783	C₂³	1	2	yes	—
116	C₂×#1781	D₄	1	2	yes	complemented
117	C₂×#1781	D₄	1	2	yes	complemented
118	C₂×#1781	D₄	1	2	yes	complemented
119	C₂×#1781	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	C₂×#1781	C₂³	1	2	yes	—
125	#16074	C₂³	1	2	yes	complemented
126	#15784	C₂³	1	2	yes	complemented
127	#15342	C₂³	1	2	yes	complemented
128	#15313	C₂³	1	2	yes	complemented
129	#15281	C₂³	1	2	yes	complemented
130	#15281	C₂³	1	2	yes	complemented
131	#15259	C₂³	1	2	yes	complemented
132	#15258	C₂³	1	2	yes	complemented
133	#14335	D₄	1	2	yes	complemented
134	#14335	C₂³	1	2	yes	—
135	#13867	D₄	1	1	yes	characteristic, complemented
136	#13867	D₄	1	1	yes	characteristic, complemented
137	#13867	D₄	1	2	yes	complemented
138	#13867	C₂³	1	1	yes	characteristic
139	#13867	C₂³	1	1	yes	characteristic
140	#13867	C₂³	1	2	yes	—
141	#12856	C₂³	1	4	yes	complemented
142	#12856	C₂³	1	4	yes	complemented
143	#12852	C₂³	1	8	yes	complemented
144	#12694	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	C₂⁷	C₂×D₄	1	1	yes	characteristic
153	C₂⁷	C₂×D₄	1	1	yes	characteristic
154	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
155	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
156	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
157	C₂³×#41	C₂×D₄	1	1	yes	characteristic, complemented
158	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
159	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
160	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
161	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
162	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
163	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
164	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
165	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
166	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
167	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
168	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
169	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
170	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
171	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
172	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
173	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
174	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
175	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
176	C₂⁴×D₄	C₂×D₄	1	2	yes	—
177	C₂⁴×D₄	C₂×D₄	1	2	yes	—
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	#41	1	1	yes	characteristic
182	C₂⁴×D₄	#41	1	1	yes	characteristic
183	C₂⁴×D₄	#41	1	1	yes	characteristic
184	C₂⁴×D₄	#41	1	1	yes	characteristic
185	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
186	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
187	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
188	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
189	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
190	#3484	C₂×D₄	1	4	yes	—
191	#3484	C₂×D₄	1	4	yes	—
192	#3484	C₂×D₄	1	4	yes	—
193	#3484	C₂⁴	1	4	yes	—
194	C₂²×#127	C₂×D₄	1	1	yes	characteristic
195	C₂²×#127	C₂×D₄	1	1	yes	characteristic, complemented
196	C₂²×#127	C₂×D₄	1	1	yes	characteristic, complemented
197	C₂²×#127	C₂⁴	1	1	yes	characteristic
198	C₂²×#124	C₂×D₄	1	1	yes	characteristic
199	C₂²×#124	C₂×D₄	1	1	yes	characteristic, complemented
200	C₂²×#124	C₂×D₄	1	1	yes	characteristic, complemented
201	C₂²×#124	C₂⁴	1	1	yes	characteristic
202	C₂²×C₂²⋊Q₈	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₂²⋊Q₈	C₂×D₄	1	1	yes	characteristic, complemented
204	C₂²×#121	C₂×D₄	1	1	yes	characteristic
205	C₂²×#121	C₂×D₄	1	1	yes	characteristic, complemented
206	C₂²×#120	C₂×D₄	1	2	yes	—
207	C₂²×#120	C₂×D₄	1	2	yes	—
208	C₂²×#120	C₂×D₄	1	2	yes	—
209	C₂²×#120	C₂⁴	1	2	yes	—
210	C₂×#518	C₂×D₄	1	2	yes	—
211	C₂×#518	C₂×D₄	1	2	yes	—
212	C₂×#518	C₂×D₄	1	2	yes	—
213	C₂²×#117	C₂×D₄	1	1	yes	characteristic, complemented
214	C₂²×#117	C₂×D₄	1	1	yes	characteristic, complemented
215	C₂²×#117	C₂×D₄	1	1	yes	characteristic, complemented
216	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
217	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
218	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
219	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
220	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
221	C₂²×#100	C₂×D₄	1	4	yes	—
222	C₂²×#100	C₂×D₄	1	4	yes	complemented
223	C₂²×#100	C₂×D₄	1	4	yes	complemented
224	C₂²×#99	C₂×D₄	1	4	yes	—
225	C₂²×#99	C₂×D₄	1	4	yes	—
226	C₂²×#99	C₂×D₄	1	4	yes	—
227	C₂×#390	C₂×D₄	1	1	yes	characteristic
228	C₂×#390	C₂×D₄	1	1	yes	characteristic
229	C₂×#390	C₂×D₄	1	1	yes	characteristic, complemented
230	C₂×#390	C₂×D₄	1	1	yes	characteristic, complemented
231	C₂×#390	C₂×D₄	1	1	yes	characteristic, complemented
232	C₂×#390	C₂×D₄	1	1	yes	characteristic, complemented
233	C₂×#390	C₂⁴	1	1	yes	characteristic
234	C₂×#390	C₂⁴	1	1	yes	characteristic
235	C₂×#386	C₂×D₄	1	2	yes	—
236	C₂×#386	C₂×D₄	1	2	yes	—
237	C₂×#386	C₂×D₄	1	2	yes	—
238	C₂×#386	C₂⁴	1	2	yes	—
239	C₂×#379	C₂×D₄	1	2	yes	—
240	C₂×#379	C₂×D₄	1	2	yes	—
241	C₂×#379	C₂×D₄	1	1	yes	characteristic
242	C₂×#379	C₂×D₄	1	1	yes	characteristic
243	C₂×#379	C₂×D₄	1	2	yes	complemented
244	C₂×#379	C₂×D₄	1	2	yes	complemented
245	C₂×#379	C₂×D₄	1	2	yes	complemented
246	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
247	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
248	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
249	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
250	#1783	C₂×D₄	1	4	yes	—
251	#1783	C₂×D₄	1	4	yes	complemented
252	#1783	C₂×D₄	1	4	yes	complemented
253	#1783	C₂⁴	1	4	yes	—
254	#1781	C₂×D₄	1	4	yes	—
255	#1781	C₂×D₄	1	4	yes	—
256	#1781	C₂×D₄	1	4	yes	—
257	#1781	C₂⁴	1	4	yes	—
258	#1781	C₂⁴	1	4	yes	—
259	#1438	C₂×D₄	1	2	yes	—
260	#1438	C₂×D₄	1	2	yes	—
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	#120	1	1	yes	characteristic
270	C₂⁶	#120	1	1	yes	characteristic
271	C₂⁶	#120	1	1	yes	characteristic
272	C₂⁶	#120	1	1	yes	characteristic
273	C₂⁶	#120	1	1	yes	characteristic
274	C₂⁶	#120	1	1	yes	characteristic
275	C₂⁶	#120	1	1	yes	characteristic
276	C₂⁶	#120	1	1	yes	characteristic
277	C₂⁶	#120	1	1	yes	characteristic
278	C₂⁶	#121	1	1	yes	characteristic
279	C₂⁶	#121	1	1	yes	characteristic
280	C₂⁶	#121	1	1	yes	characteristic
281	C₂⁶	#121	1	1	yes	characteristic
282	C₂⁶	#121	1	1	yes	characteristic
283	C₂⁶	#121	1	1	yes	characteristic
284	C₂⁶	#121	1	1	yes	characteristic
285	C₂⁶	#121	1	1	yes	characteristic
286	C₂⁶	#127	1	1	yes	characteristic
287	C₂⁶	#127	1	1	yes	characteristic
288	C₂⁶	#127	1	1	yes	characteristic
289	C₂⁶	#127	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	1	yes	characteristic
294	C₂⁶	C₂²×D₄	1	1	yes	characteristic
295	C₂⁶	C₂²×D₄	1	1	yes	characteristic
296	C₂⁶	C₂²×D₄	1	2	yes	—
297	C₂×H(5,𝔽₂)	C₂²×D₄	1	4	yes	—
298	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
299	C₂³×D₄	#120	1	1	yes	characteristic
300	C₂³×D₄	#120	1	1	yes	characteristic
301	C₂³×D₄	#120	1	1	yes	characteristic
302	C₂³×D₄	#120	1	1	yes	characteristic
303	C₂³×D₄	#120	1	1	yes	characteristic
304	C₂³×D₄	#120	1	1	yes	characteristic
305	C₂³×D₄	#120	1	1	yes	characteristic
306	C₂³×D₄	#120	1	1	yes	characteristic
307	C₂³×D₄	#120	1	1	yes	characteristic
308	C₂³×D₄	#120	1	1	yes	characteristic
309	C₂³×D₄	#120	1	1	yes	characteristic
310	C₂³×D₄	#120	1	1	yes	characteristic
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	1	yes	characteristic
316	C₂³×D₄	#120	1	1	yes	characteristic
317	C₂³×D₄	#120	1	1	yes	characteristic
318	C₂³×D₄	#120	1	1	yes	characteristic
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	1	yes	characteristic
324	C₂³×D₄	#120	1	1	yes	characteristic
325	C₂³×D₄	#120	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	#121	1	1	yes	characteristic
330	C₂³×D₄	#121	1	1	yes	characteristic
331	C₂³×D₄	#121	1	1	yes	characteristic
332	C₂³×D₄	#121	1	1	yes	characteristic
333	C₂³×D₄	#121	1	1	yes	characteristic
334	C₂³×D₄	#121	1	1	yes	characteristic
335	C₂³×D₄	#121	1	1	yes	characteristic
336	C₂³×D₄	#121	1	1	yes	characteristic
337	C₂³×D₄	#121	1	1	yes	characteristic
338	C₂³×D₄	#121	1	1	yes	characteristic
339	C₂³×D₄	#121	1	1	yes	characteristic
340	C₂³×D₄	#121	1	1	yes	characteristic
341	C₂³×D₄	#121	1	1	yes	characteristic
342	C₂³×D₄	#121	1	1	yes	characteristic
343	C₂³×D₄	#121	1	1	yes	characteristic
344	C₂³×D₄	#121	1	1	yes	characteristic
345	C₂³×D₄	#121	1	1	yes	characteristic
346	C₂³×D₄	#121	1	1	yes	characteristic
347	C₂³×D₄	#121	1	1	yes	characteristic
348	C₂³×D₄	#121	1	1	yes	characteristic
349	C₂³×D₄	#121	1	1	yes	characteristic
350	C₂³×D₄	#121	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	#127	1	1	yes	characteristic
366	C₂³×D₄	#127	1	1	yes	characteristic
367	C₂³×D₄	#127	1	1	yes	characteristic
368	C₂³×D₄	#127	1	1	yes	characteristic
369	C₂³×D₄	#127	1	1	yes	characteristic
370	C₂³×D₄	#127	1	1	yes	characteristic
371	C₂³×D₄	#127	1	1	yes	characteristic
372	C₂³×D₄	#127	1	1	yes	characteristic
373	C₂³×D₄	#127	1	1	yes	characteristic
374	C₂³×D₄	#127	1	1	yes	characteristic
375	C₂³×D₄	#127	1	1	yes	characteristic
376	C₂³×D₄	#127	1	1	yes	characteristic
377	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
378	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
379	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
380	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
381	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
382	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
383	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
384	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
385	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
386	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
387	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
388	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
389	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
390	C₂³×D₄	C₂²×D₄	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	C₂×#41	1	1	yes	characteristic
406	C₂³×D₄	C₂×#41	1	1	yes	characteristic
407	C₂³×D₄	C₂×#41	1	1	yes	characteristic
408	C₂³×D₄	C₂×#41	1	1	yes	characteristic
409	C₂³×D₄	C₂×#41	1	1	yes	characteristic
410	C₂³×D₄	C₂×#41	1	1	yes	characteristic
411	C₂³×D₄	C₂⁵	1	1	yes	characteristic
412	C₂⁴×C₄	#120	1	1	yes	characteristic
413	C₂⁴×C₄	#120	1	1	yes	characteristic
414	C₂⁴×C₄	#120	1	1	yes	characteristic
415	C₂⁴×C₄	#120	1	1	yes	characteristic
416	C₂⁴×C₄	#120	1	1	yes	characteristic
417	C₂⁴×C₄	#120	1	1	yes	characteristic
418	C₂⁴×C₄	#120	1	1	yes	characteristic
419	C₂⁴×C₄	#121	1	1	yes	characteristic
420	C₂⁴×C₄	#121	1	1	yes	characteristic
421	C₂⁴×C₄	#121	1	1	yes	characteristic
422	C₂⁴×C₄	#121	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	2	yes	—
427	#518	C₂²×D₄	1	4	yes	—
428	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
429	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
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	#392	1	1	yes	characteristic
451	C₂⁵	#392	1	1	yes	characteristic
452	C₂⁵	#392	1	1	yes	characteristic
453	C₂⁵	#392	1	1	yes	characteristic
454	C₂⁵	#392	1	1	yes	characteristic
455	C₂⁵	#392	1	1	yes	characteristic
456	C₂⁵	#392	1	1	yes	characteristic
457	C₂⁵	#392	1	1	yes	characteristic
458	C₂⁵	#392	1	1	yes	characteristic
459	C₂⁵	#392	1	1	yes	characteristic
460	C₂⁵	#392	1	1	yes	characteristic
461	C₂⁵	#392	1	1	yes	characteristic
462	C₂⁵	#392	1	1	yes	characteristic
463	C₂⁵	#392	1	1	yes	characteristic
464	C₂⁵	#392	1	1	yes	characteristic
465	C₂⁵	#392	1	1	yes	characteristic
466	C₂⁵	#392	1	1	yes	characteristic
467	C₂⁵	#392	1	1	yes	characteristic
468	C₂⁵	#392	1	1	yes	characteristic
469	C₂⁵	#392	1	1	yes	characteristic
470	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
471	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
472	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
473	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
474	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
475	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
476	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
477	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
478	C₂⁵	C₂×#120	1	1	yes	characteristic
479	C₂⁵	C₂×#120	1	1	yes	characteristic
480	C₂⁵	C₂×#120	1	1	yes	characteristic
481	C₂⁵	C₂×#120	1	1	yes	characteristic
482	C₂⁵	C₂×#120	1	1	yes	characteristic
483	C₂⁵	C₂×#120	1	1	yes	characteristic
484	C₂⁵	C₂×#120	1	1	yes	characteristic
485	C₂⁵	C₂×#120	1	1	yes	characteristic
486	C₂⁵	C₂×#120	1	1	yes	characteristic
487	C₂⁵	C₂×#120	1	1	yes	characteristic
488	C₂⁵	C₂×#120	1	1	yes	characteristic
489	C₂⁵	C₂×#120	1	1	yes	characteristic
490	C₂⁵	C₂×#120	1	1	yes	characteristic
491	C₂⁵	C₂×#120	1	1	yes	characteristic
492	C₂⁵	C₂×#120	1	1	yes	characteristic
493	C₂⁵	C₂×#121	1	1	yes	characteristic
494	C₂⁵	C₂×#121	1	1	yes	characteristic
495	C₂⁵	C₂×#121	1	1	yes	characteristic
496	C₂⁵	C₂×#121	1	1	yes	characteristic
497	C₂⁵	C₂×#121	1	1	yes	characteristic
498	C₂⁵	C₂×#121	1	1	yes	characteristic
499	C₂⁵	C₂×#121	1	1	yes	characteristic
500	C₂⁵	C₂×#121	1	1	yes	characteristic
501	C₂⁵	C₂×#121	1	1	yes	characteristic
502	C₂⁵	C₂×#121	1	1	yes	characteristic
503	C₂⁵	C₂×#121	1	1	yes	characteristic
504	C₂⁵	C₂×#121	1	1	yes	characteristic
505	C₂⁵	C₂×#127	1	1	yes	characteristic
506	C₂⁵	C₂×#127	1	1	yes	characteristic
507	C₂⁵	C₂×#127	1	1	yes	characteristic
508	C₂⁵	C₂×#127	1	1	yes	characteristic
509	C₂⁵	C₂×#127	1	1	yes	characteristic
510	C₂⁵	C₂×#127	1	1	yes	characteristic
511	C₂⁵	C₂³×D₄	1	1	yes	characteristic
512	C₂⁵	C₂³×D₄	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	#392	1	1	yes	characteristic
520	C₂²×D₄	#392	1	1	yes	characteristic
521	C₂²×D₄	#392	1	1	yes	characteristic
522	C₂²×D₄	#392	1	1	yes	characteristic
523	C₂²×D₄	#392	1	1	yes	characteristic
524	C₂²×D₄	#392	1	1	yes	characteristic
525	C₂²×D₄	#392	1	1	yes	characteristic
526	C₂²×D₄	#392	1	1	yes	characteristic
527	C₂²×D₄	#392	1	1	yes	characteristic
528	C₂²×D₄	#392	1	1	yes	characteristic
529	C₂²×D₄	#392	1	1	yes	characteristic
530	C₂²×D₄	#392	1	1	yes	characteristic
531	C₂²×D₄	#392	1	1	yes	characteristic
532	C₂²×D₄	#392	1	1	yes	characteristic
533	C₂²×D₄	#392	1	1	yes	characteristic
534	C₂²×D₄	#392	1	1	yes	characteristic
535	C₂²×D₄	#392	1	1	yes	characteristic
536	C₂²×D₄	#392	1	1	yes	characteristic
537	C₂²×D₄	C₂×#120	1	1	yes	characteristic
538	C₂²×D₄	C₂×#120	1	1	yes	characteristic
539	C₂²×D₄	C₂×#120	1	1	yes	characteristic
540	C₂²×D₄	C₂×#120	1	1	yes	characteristic
541	C₂²×D₄	C₂×#120	1	1	yes	characteristic
542	C₂²×D₄	C₂×#120	1	1	yes	characteristic
543	C₂²×D₄	C₂×#120	1	1	yes	characteristic
544	C₂²×D₄	C₂×#120	1	1	yes	characteristic
545	C₂²×D₄	C₂×#120	1	1	yes	characteristic
546	C₂²×D₄	C₂×#120	1	1	yes	characteristic
547	C₂²×D₄	C₂×#120	1	1	yes	characteristic
548	C₂²×D₄	C₂×#120	1	1	yes	characteristic
549	C₂²×D₄	C₂×#121	1	1	yes	characteristic
550	C₂²×D₄	C₂×#121	1	1	yes	characteristic
551	C₂²×D₄	C₂×#121	1	1	yes	characteristic
552	C₂²×D₄	C₂×#121	1	1	yes	characteristic
553	C₂²×D₄	C₂×#121	1	1	yes	characteristic
554	C₂²×D₄	C₂×#121	1	1	yes	characteristic
555	C₂²×D₄	C₂×#121	1	1	yes	characteristic
556	C₂²×D₄	C₂×#121	1	1	yes	characteristic
557	C₂²×D₄	C₂×#121	1	1	yes	characteristic
558	C₂²×D₄	C₂×#121	1	1	yes	characteristic
559	C₂²×D₄	C₂×#121	1	1	yes	characteristic
560	C₂²×D₄	C₂×#121	1	1	yes	characteristic
561	C₂²×D₄	C₂×#121	1	1	yes	characteristic
562	C₂²×D₄	C₂×#121	1	1	yes	characteristic
563	C₂²×D₄	C₂×#121	1	1	yes	characteristic
564	C₂²×D₄	C₂×#121	1	1	yes	characteristic
565	C₂²×D₄	C₂×#121	1	1	yes	characteristic
566	C₂²×D₄	C₂×#121	1	1	yes	characteristic
567	C₂²×D₄	C₂×#127	1	1	yes	characteristic
568	C₂²×D₄	C₂×#127	1	1	yes	characteristic
569	C₂²×D₄	C₂×#127	1	1	yes	characteristic
570	C₂²×D₄	C₂×#127	1	1	yes	characteristic
571	C₂²×D₄	C₂×#127	1	1	yes	characteristic
572	C₂²×D₄	C₂×#127	1	1	yes	characteristic
573	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
574	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
575	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
576	C₂²×D₄	C₂²×#41	1	1	yes	characteristic
577	C₂³×C₄	#392	1	1	yes	characteristic
578	C₂³×C₄	#392	1	1	yes	characteristic
579	C₂³×C₄	#392	1	1	yes	characteristic
580	C₂³×C₄	#392	1	1	yes	characteristic
581	C₂³×C₄	#392	1	1	yes	characteristic
582	C₂³×C₄	#392	1	1	yes	characteristic
583	C₂³×C₄	#392	1	1	yes	characteristic
584	C₂³×C₄	#392	1	1	yes	characteristic
585	C₂³×C₄	#392	1	1	yes	characteristic
586	C₂³×C₄	#392	1	1	yes	characteristic
587	C₂³×C₄	#392	1	1	yes	characteristic
588	C₂³×C₄	#392	1	1	yes	characteristic
589	C₂³×C₄	C₂×#120	1	1	yes	characteristic
590	C₂³×C₄	C₂×#120	1	1	yes	characteristic
591	C₂³×C₄	C₂×#120	1	1	yes	characteristic
592	C₂³×C₄	C₂×#120	1	1	yes	characteristic
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×#120	1	1	yes	characteristic
597	C₂³×C₄	C₂×#120	1	1	yes	characteristic
598	C₂³×C₄	C₂×#121	1	1	yes	characteristic
599	C₂³×C₄	C₂×#121	1	1	yes	characteristic
600	C₂³×C₄	C₂×#121	1	1	yes	characteristic
601	C₂³×C₄	C₂×#121	1	1	yes	characteristic
602	C₂³×C₄	C₂×#121	1	1	yes	characteristic
603	C₂³×C₄	C₂×#121	1	1	yes	characteristic
604	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
605	C₂⁴	#2021	1	1	yes	characteristic
606	C₂⁴	#2021	1	1	yes	characteristic
607	C₂⁴	#2021	1	1	yes	characteristic
608	C₂⁴	#2021	1	1	yes	characteristic
609	C₂⁴	#2021	1	1	yes	characteristic
610	C₂⁴	#2021	1	1	yes	characteristic
611	C₂⁴	#2021	1	1	yes	characteristic
612	C₂⁴	#2021	1	1	yes	characteristic
613	C₂⁴	#2021	1	1	yes	characteristic
614	C₂⁴	#2021	1	1	yes	characteristic
615	C₂⁴	#2021	1	1	yes	characteristic
616	C₂⁴	#2021	1	1	yes	characteristic
617	C₂⁴	#2021	1	1	yes	characteristic
618	C₂⁴	#2021	1	1	yes	characteristic
619	C₂⁴	#2021	1	1	yes	characteristic
620	C₂⁴	#2021	1	1	yes	characteristic
621	C₂⁴	C₂×#392	1	1	yes	characteristic
622	C₂⁴	C₂×#392	1	1	yes	characteristic
623	C₂⁴	C₂×#392	1	1	yes	characteristic
624	C₂⁴	C₂×#392	1	1	yes	characteristic
625	C₂⁴	C₂×#392	1	1	yes	characteristic
626	C₂⁴	C₂×#392	1	1	yes	characteristic
627	C₂⁴	C₂×#392	1	1	yes	characteristic
628	C₂⁴	C₂×#392	1	1	yes	characteristic
629	C₂⁴	C₂×#392	1	1	yes	characteristic
630	C₂⁴	C₂×#392	1	1	yes	characteristic
631	C₂⁴	C₂×#392	1	1	yes	characteristic
632	C₂⁴	C₂×#392	1	1	yes	characteristic
633	C₂⁴	C₂×#392	1	1	yes	characteristic
634	C₂⁴	C₂×#392	1	1	yes	characteristic
635	C₂⁴	C₂×#392	1	1	yes	characteristic
636	C₂⁴	C₂×#392	1	1	yes	characteristic
637	C₂⁴	C₂×#392	1	1	yes	characteristic
638	C₂⁴	C₂×#392	1	1	yes	characteristic
639	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
640	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
641	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
642	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
643	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
644	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
645	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
646	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
647	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
648	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
649	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
650	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
651	C₂⁴	C₂²×#120	1	1	yes	characteristic
652	C₂⁴	C₂²×#120	1	1	yes	characteristic
653	C₂⁴	C₂²×#121	1	1	yes	characteristic
654	C₂⁴	C₂²×#121	1	1	yes	characteristic
655	C₂⁴	C₂²×#127	1	1	yes	characteristic
656	C₂×D₄	#3026	1	4	yes	—
657	C₂×D₄	#3026	1	4	yes	—
658	C₂²×C₄	C₂×#392	1	1	yes	characteristic
659	C₂²×C₄	C₂×#392	1	1	yes	characteristic
660	C₂²×C₄	C₂×#392	1	1	yes	characteristic
661	C₂²×C₄	C₂×#392	1	1	yes	characteristic
662	C₂²×C₄	C₂×#392	1	1	yes	characteristic
663	C₂²×C₄	C₂×#392	1	1	yes	characteristic
664	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
665	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
666	C₂³	C₂×#2021	1	1	yes	characteristic
667	C₂³	C₂×#2021	1	1	yes	characteristic
668	C₂³	C₂×#2021	1	1	yes	characteristic
669	C₂³	C₂×#2021	1	1	yes	characteristic
670	C₂³	C₂×#2021	1	1	yes	characteristic
671	C₂³	C₂×#2021	1	1	yes	characteristic
672	C₂³	C₂×#2021	1	1	yes	characteristic
673	C₂³	C₂×#2021	1	1	yes	characteristic
674	C₂³	C₂×#2021	1	1	yes	characteristic
675	C₂³	C₂×#2021	1	1	yes	characteristic
676	C₂³	C₂×#2021	1	1	yes	characteristic
677	C₂³	C₂×#2021	1	1	yes	characteristic
678	C₂³	#23444	1	2	yes	—
679	C₂³	#23444	1	2	yes	—
680	C₂³	#23444	1	2	yes	—
681	C₂³	#33551	1	2	yes	—
682	C₂³	#33551	1	2	yes	—
683	C₂³	C₂²×#392	1	1	yes	characteristic
684	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
685	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
686	C₂³	C₂×#3026	1	2	yes	—
687	C₂×C₄	#23444	1	2	yes	—
688	C₂×C₄	C₂×#3026	1	2	yes	—
689	C₂²	#498927	1	2	yes	—
690	C₂²	#498927	1	2	yes	—
691	C₂²	C₂²×#2021	1	1	yes	characteristic
692	C₂²	C₂×#23444	1	1	yes	characteristic
693	C₂²	C₂×#23444	1	1	yes	characteristic
694	C₂²	C₂×#33551	1	1	yes	characteristic
695	C₂²	C₂×#33551	1	1	yes	characteristic
696	C₂²	#7622875	1	2	yes	—
697	C₂	C₂×#498927	1	1	yes	characteristic
698	C₂	#72236431	1	1	yes	characteristic
699	C₂	#72256607	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 ◁ C₂⁶ ◁ C₂⁵×D₄ ◁ 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. #72263558	C₂	semidirect
2. #72263557	C₂	semidirect
3. #72263556	C₂	semidirect
4. #72263555	C₂	semidirect
5. #72263547	C₂	semidirect
6. #72237398	C₂	semidirect
7. #72236704	C₂	semidirect
8. #72236701	C₂	semidirect
9. #72236670	C₂	semidirect
10. C₂×#496225	C₂	semidirect
11. #72236527	C₂	semidirect
12. C₂×#6470225	C₂	semidirect
13. #72234544	C₂	semidirect
14. #72231479	C₂	semidirect
15. #72213293	C₂	semidirect
22. #6470020	C₂²	semidirect
24. #6470019	C₂²	semidirect
26. #6440354	C₂²	semidirect
28. #6437445	C₂²	semidirect
32. #4866529	C₂²	semidirect
33. #4866528	C₂²	semidirect
34. #4327960	C₂²	semidirect
35. #4312024	C₂²	semidirect
36. #846393	C₂²	semidirect
37. #846389	C₂²	semidirect
38. #846061	C₂²	semidirect
39. #846057	C₂²	semidirect
41. #496225	C₂²	semidirect
42. #496225	C₂²	semidirect
43. #496191	C₂²	semidirect
44. #496191	C₂²	semidirect
45. #496189	C₂²	semidirect
46. #496189	C₂²	semidirect
47. #493883	C₂²	semidirect
48. C₂×#12852	C₂²	semidirect
49. #493370	C₂²	semidirect
50. C₂×#12687	C₂²	semidirect
51. #187944	C₂²	semidirect
54. #187928	C₂²	semidirect
55. #144429	C₂²	semidirect
56. #144428	C₂²	semidirect
57. #144415	C₂²	semidirect
58. #144414	C₂²	semidirect
59. #144404	C₂²	semidirect
60. #144404	C₂²	semidirect
61. #144388	C₂²	semidirect
62. #144386	C₂²	semidirect
63. #128073	C₂²	semidirect
64. #128073	C₂²	semidirect
65. #128073	C₂²	semidirect
66. #128033	C₂²	semidirect
67. C₂³×H(5,𝔽₂)	D₄	semidirect
70. C₂×#3484	D₄	semidirect
71. C₂×#3484	D₄	semidirect
72. C₂×#3484	D₄	semidirect
76. C₂²×#535	D₄	semidirect
78. C₂²×#525	D₄	semidirect
81. C₂²×#518	D₄	semidirect
82. C₂³×#100	D₄	semidirect
83. C₂³×#99	D₄	semidirect
84. C₂×#2435	D₄	semidirect
85. C₂×#2435	D₄	semidirect
88. C₂×#2433	D₄	semidirect
89. C₂×#2433	D₄	semidirect
96. C₂×#2309	D₄	semidirect
100. C₂×#2280	D₄	semidirect
102. C₂²×#379	D₄	semidirect
103. C₂²×#379	D₄	semidirect
110. C₂×#1783	D₄	semidirect
111. C₂×#1783	D₄	semidirect
112. C₂×#1783	D₄	semidirect
116. C₂×#1781	D₄	semidirect
117. C₂×#1781	D₄	semidirect
118. C₂×#1781	D₄	semidirect
125. #16074	C₂³	semidirect
126. #15784	C₂³	semidirect
127. #15342	C₂³	semidirect
128. #15313	C₂³	semidirect
129. #15281	C₂³	semidirect
130. #15281	C₂³	semidirect
131. #15259	C₂³	semidirect
132. #15258	C₂³	semidirect
133. #14335	D₄	semidirect
135. #13867	D₄	semidirect
136. #13867	D₄	semidirect
137. #13867	D₄	semidirect
141. #12856	C₂³	semidirect
142. #12856	C₂³	semidirect
143. #12852	C₂³	semidirect
144. #12694	C₂³	semidirect
145. #12693	C₂³	semidirect
146. #12687	C₂³	semidirect
149. #7304	C₂³	semidirect
150. #7304	C₂³	semidirect
157. C₂³×#41	C₂×D₄	semidirect
195. C₂²×#127	C₂×D₄	semidirect
196. C₂²×#127	C₂×D₄	semidirect
199. C₂²×#124	C₂×D₄	semidirect
200. C₂²×#124	C₂×D₄	semidirect
203. C₂²×C₂²⋊Q₈	C₂×D₄	semidirect
205. C₂²×#121	C₂×D₄	semidirect
213. C₂²×#117	C₂×D₄	semidirect
214. C₂²×#117	C₂×D₄	semidirect
215. C₂²×#117	C₂×D₄	semidirect
220. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
222. C₂²×#100	C₂×D₄	semidirect
223. C₂²×#100	C₂×D₄	semidirect
229. C₂×#390	C₂×D₄	semidirect
230. C₂×#390	C₂×D₄	semidirect
231. C₂×#390	C₂×D₄	semidirect
232. C₂×#390	C₂×D₄	semidirect
243. C₂×#379	C₂×D₄	semidirect
244. C₂×#379	C₂×D₄	semidirect
245. C₂×#379	C₂×D₄	semidirect
248. C₂×C₄×C₂²⋊C₄	C₂×D₄	semidirect
249. C₂×C₄×C₂²⋊C₄	C₂×D₄	semidirect
251. #1783	C₂×D₄	semidirect
252. #1783	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
#72263558	2
#72263557	2
#72263556	2
#72263555	2
#72263547	2
#72237398	2
#72236704	2
#72236701	2
#72236670	2
C₂×#496225	2
#72236527	2
C₂×#6470225	2
#72234544	2
#72231479	2
#72213293	2