Subgroups — C₂×#72216611 #72251421

Order 4096.

At least 17355 conjugacy classes of subgroups; only the 4179 normal subgroups are shown.

The subgroup lattice has 686 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#72213519	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#72215721	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#72216601	C₂	1	8	yes	maximal, complemented
4	C₂×#152716	C₂²	1	4	yes	complemented
5	C₂×#7487871	C₂²	1	4	yes	complemented
6	C₂×#72213671	C₂	1	2	yes	maximal, complemented
7	C₂×#10576178	C₂²	1	1	yes	characteristic, complemented
8	C₂×#72216577	C₂	1	2	yes	maximal, complemented
9	C₂×#72216589	C₂	1	2	yes	maximal, complemented
10	C₂×#152017	C₂²	1	2	yes	complemented
11	C₂×#7504294	C₂²	1	1	yes	characteristic, complemented
12	C₂×#72216584	C₂	1	2	yes	maximal, complemented
13	C₂×#152323	C₂²	1	2	yes	complemented
14	C₂×#6407636	C₂²	1	1	yes	characteristic, complemented
15	C₂×#72216600	C₂	1	4	yes	maximal, complemented
16	C₂×#512862	C₂²	1	8	yes	complemented
17	C₂×#152602	C₂²	1	8	yes	complemented
18	C₂×#72216603	C₂	1	4	yes	maximal, complemented
19	C₂×#7487865	C₂²	1	4	yes	—
20	C₂×#152191	C₂²	1	8	yes	complemented
21	C₂×#153305	C₂²	1	8	yes	complemented
22	C₂×#153305	C₂²	1	8	yes	complemented
23	C₂×#152477	C₂²	1	8	yes	complemented
24	C₂×#72215568	C₂	1	1	yes	maximal, characteristic, complemented
25	C₂×#501096	C₂²	1	4	yes	complemented
26	C₂×#500179	C₂²	1	2	yes	complemented
27	C₂×#499831	C₂²	1	2	yes	—
28	C₂×#153189	C₂²	1	8	yes	complemented
29	C₂×#153189	C₂²	1	8	yes	complemented
30	C₂×#72213428	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂×#512663	C₂²	1	4	yes	complemented
32	C₂×#152069	C₂²	1	2	yes	complemented
33	C₂×#152049	C₂²	1	2	yes	complemented
34	C₂×#152103	C₂²	1	4	yes	complemented
35	C₂×#72216567	C₂	1	1	yes	maximal, characteristic, complemented
36	C₂×#152679	C₂²	1	4	yes	complemented
37	C₂×#152679	C₂²	1	4	yes	complemented
38	C₂×#152717	C₂²	1	4	yes	complemented
39	C₂×#152018	C₂²	1	2	yes	complemented
40	C₂×#152322	C₂²	1	2	yes	complemented
41	C₂×#7504292	C₂²	1	1	yes	characteristic, complemented
42	C₂×#72213685	C₂	1	1	yes	maximal, characteristic, complemented
43	C₂×#246930	C₂²	1	2	yes	complemented
44	C₂×#246957	C₂²	1	4	yes	complemented
45	C₂×#246927	C₂²	1	2	yes	—
46	C₂×#72210575	C₂	1	1	yes	maximal, characteristic, complemented
47	C₂×#512119	C₂²	1	2	yes	complemented
48	C₂×#512119	C₂²	1	2	yes	complemented
49	C₂×#501097	C₂²	1	4	yes	complemented
50	C₂×#500177	C₂²	1	2	yes	complemented
51	C₂×#493370	C₂²	1	1	yes	characteristic, complemented
52	C₂×#6437445	C₂²	1	1	yes	characteristic
53	C₂×#6437449	C₂²	1	1	yes	characteristic
54	C₂×#493372	C₂²	1	1	yes	characteristic, complemented
55	C₂×#200876	C₂²	1	2	yes	complemented
56	C₂×#499832	C₂²	1	2	yes	—
57	C₂×#6348967	C₂²	1	2	yes	complemented
58	C₂×#187811	C₂²	1	1	yes	characteristic, complemented
59	C₂×#10575547	C₂²	1	1	yes	characteristic
60	C₂²×#52004	C₂²	1	1	yes	characteristic, complemented
61	C₂×#511771	C₂²	1	2	yes	complemented
62	C₂×#511771	C₂²	1	2	yes	complemented
63	#72216611	C₂	1	32	yes	maximal, direct product factor
64	#72216603	C₂²	1	64	yes	complemented
65	#72216601	C₂²	1	128	yes	complemented
66	#72216600	C₂²	1	64	yes	complemented
67	#72216589	C₂²	1	32	yes	complemented
68	#72216584	C₂²	1	32	yes	complemented
69	#72216577	C₂²	1	32	yes	complemented
70	#72216567	C₂²	1	16	yes	complemented
71	#72215721	C₂²	1	16	yes	complemented
72	#72215568	C₂²	1	16	yes	complemented
73	#72213685	C₂²	1	16	yes	complemented
74	#72213671	C₂²	1	32	yes	complemented
75	#72213519	C₂²	1	16	yes	complemented
76	#72213428	C₂²	1	16	yes	complemented
77	#72210575	C₂²	1	16	yes	complemented
78	C₂×#62814	D₄	1	1	yes	characteristic, complemented
79	C₂×#62811	D₄	1	1	yes	characteristic, complemented
80	C₂²×#3484	D₄	1	1	yes	characteristic, complemented
81	C₂³×D₄²	C₂³	1	1	yes	characteristic, complemented
82	C₂³×#535	C₂³	1	1	yes	characteristic
83	#10576178	C₂³	1	8	yes	complemented
84	C₂×#61110	C₂³	1	4	yes	—
85	#10575547	D₄	1	8	yes	complemented
86	#10575547	C₂³	1	8	yes	—
87	C₂×#60806	D₄	1	2	yes	complemented
88	C₂×#60806	C₂³	1	2	yes	—
89	C₂×#60799	D₄	1	2	yes	complemented
90	C₂×#60798	C₂³	1	2	yes	—
91	C₂×#60644	D₄	1	1	yes	characteristic, complemented
92	C₂×#60644	C₂³	1	1	yes	characteristic
93	C₂×#60619	D₄	1	1	yes	characteristic, complemented
94	C₂×#60619	C₂³	1	1	yes	characteristic
95	C₂²×#3021	D₄	1	1	yes	characteristic, complemented
96	C₂²×#3021	C₂³	1	1	yes	characteristic
97	C₂²×#3019	D₄	1	1	yes	characteristic, complemented
98	C₂²×#3019	C₂³	1	1	yes	characteristic
99	C₂×#60124	D₄	1	1	yes	characteristic, complemented
100	C₂×#52004	C₂³	1	2	yes	—
101	C₂×#52004	C₂³	1	8	yes	complemented
102	C₂×#52004	C₂³	1	2	yes	complemented
103	C₂²×#2380	C₂³	1	1	yes	characteristic, complemented
104	C₂²×#2196	C₂³	1	4	yes	—
105	C₂²×#2196	C₂³	1	4	yes	—
106	C₂²×#2128	C₂³	1	2	yes	complemented
107	C₂²×#2127	C₂³	1	2	yes	complemented
108	#7504294	C₂³	1	8	yes	complemented
109	#7504292	C₂³	1	8	yes	complemented
110	C₂×#31282	C₂³	1	4	yes	—
111	C₂×#31282	C₂³	1	4	yes	—
112	#7487871	C₂³	1	32	yes	complemented
113	#7487865	C₂³	1	32	yes	—
114	#6437449	D₄	1	8	yes	complemented
115	#6437449	C₂³	1	8	yes	—
116	#6437445	D₄	1	8	yes	complemented
117	#6437445	C₂³	1	8	yes	—
118	C₂×#23913	D₄	1	2	yes	complemented
119	C₂×#23913	C₂³	1	2	yes	—
120	C₂×#23912	D₄	1	2	yes	complemented
121	C₂×#23912	C₂³	1	2	yes	—
122	C₂×#23907	D₄	1	2	yes	complemented
123	C₂×#23906	D₄	1	2	yes	complemented
124	C₂×#23906	C₂³	1	2	yes	—
125	C₂×#23906	C₂³	1	2	yes	—
126	#6407636	C₂³	1	8	yes	complemented
127	C₂×#23361	C₂³	1	4	yes	—
128	C₂×#20956	D₄	1	1	yes	characteristic, complemented
129	C₂×#20956	C₂³	1	1	yes	characteristic
130	C₂×#20953	D₄	1	1	yes	characteristic, complemented
131	C₂×#20953	C₂³	1	1	yes	characteristic
132	C₂×#20591	D₄	1	1	yes	characteristic, complemented
133	C₂²×#1783	D₄	1	1	yes	characteristic, complemented
134	#6348967	C₂³	1	16	yes	complemented
135	C₂×#18529	C₂³	1	4	yes	complemented
136	C₂×#18524	C₂³	1	4	yes	—
137	C₂×#17741	C₂³	1	2	yes	complemented
138	#512862	C₂³	1	64	yes	complemented
139	#512663	C₂³	1	32	yes	complemented
140	C₂×#13595	C₂³	1	8	yes	complemented
141	C₂×#13584	C₂³	1	8	yes	—
142	C₂×#13561	C₂³	1	8	yes	—
143	C₂×#13561	C₂³	1	8	yes	—
144	#512119	C₂³	1	16	yes	complemented
145	#512119	C₂³	1	16	yes	complemented
146	#511771	C₂³	1	16	yes	complemented
147	#511771	C₂³	1	16	yes	complemented
148	#501097	C₂³	1	32	yes	complemented
149	#501096	C₂³	1	32	yes	complemented
150	#500179	C₂³	1	16	yes	complemented
151	#500177	C₂³	1	16	yes	complemented
152	#499832	C₂³	1	16	yes	—
153	#499831	C₂³	1	16	yes	—
154	C₂×#13049	C₂³	1	4	yes	—
155	C₂×#13049	C₂³	1	4	yes	—
156	C₂×#12966	C₂³	1	4	yes	complemented
157	C₂×#12966	C₂³	1	4	yes	complemented
158	C₂×#12759	C₂³	1	4	yes	complemented
159	C₂×#12759	C₂³	1	4	yes	complemented
160	#493372	C₂³	1	8	yes	complemented
161	#493370	C₂³	1	8	yes	complemented
162	C₂×#12697	C₂³	1	2	yes	—
163	C₂×#12696	C₂³	1	2	yes	—
164	C₂×#12693	C₂³	1	2	yes	complemented
165	C₂×#12693	C₂³	1	2	yes	complemented
166	#246957	C₂³	1	32	yes	complemented
167	#246930	C₂³	1	16	yes	complemented
168	#246927	C₂³	1	16	yes	—
169	#200876	C₂³	1	16	yes	complemented
170	C₂×#9428	C₂³	1	4	yes	—
171	C₂×#9425	C₂³	1	4	yes	complemented
172	#187811	C₂³	1	8	yes	complemented
173	C₂×#8522	C₂³	1	2	yes	—
174	C₂×#8522	C₂³	1	2	yes	complemented
175	#153305	C₂³	1	64	yes	complemented
176	#153305	C₂³	1	64	yes	complemented
177	#153189	C₂³	1	64	yes	complemented
178	#153189	C₂³	1	64	yes	complemented
179	#152717	C₂³	1	32	yes	complemented
180	#152716	C₂³	1	32	yes	complemented
181	#152679	C₂³	1	32	yes	complemented
182	#152679	C₂³	1	32	yes	complemented
183	#152602	C₂³	1	64	yes	complemented
184	#152477	C₂³	1	64	yes	complemented
185	#152323	C₂³	1	16	yes	complemented
186	#152322	C₂³	1	16	yes	complemented
187	#152191	C₂³	1	64	yes	complemented
188	#152103	C₂³	1	32	yes	complemented
189	#152069	C₂³	1	16	yes	complemented
190	#152049	C₂³	1	16	yes	complemented
191	#152018	C₂³	1	16	yes	complemented
192	#152017	C₂³	1	16	yes	complemented
193	C₂×#7493	C₂³	1	8	yes	complemented
194	C₂×#7493	C₂³	1	8	yes	complemented
195	C₂²×#585	C₂×D₄	1	1	yes	characteristic
196	C₂³×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
197	C₂⁴×#41	C₂×D₄	1	1	yes	characteristic
198	C₂⁵×D₄	C₂×D₄	1	1	yes	characteristic
199	#62814	C₂×D₄	1	8	yes	complemented
200	#62811	C₂×D₄	1	8	yes	complemented
201	C₂×#3485	C₂×D₄	1	2	yes	—
202	C₂×#3484	C₂×D₄	1	2	yes	—
203	C₂×#3484	C₂×D₄	1	2	yes	—
204	C₂×#3484	C₂×D₄	1	2	yes	—
205	C₂×#3484	C₂×D₄	1	8	yes	complemented
206	C₂²×D₄²	C₂⁴	1	2	yes	—
207	C₂²×D₄²	C₂⁴	1	4	yes	complemented
208	C₂×#3455	C₂×D₄	1	2	yes	—
209	C₂×#3458	C₂×D₄	1	1	yes	characteristic
210	C₂×#3449	C₂×D₄	1	1	yes	characteristic
211	C₂²×#535	C₂×D₄	1	1	yes	characteristic
212	C₂²×#535	C₂×D₄	1	4	yes	—
213	C₂²×#535	C₂×D₄	1	1	yes	characteristic
214	C₂²×#535	C₂×D₄	1	1	yes	characteristic
215	C₂²×#535	C₂×D₄	1	1	yes	characteristic
216	C₂²×#535	C₂×D₄	1	4	yes	—
217	C₂²×#535	C₂×D₄	1	1	yes	characteristic
218	C₂²×#535	C₂×D₄	1	1	yes	characteristic
219	C₂²×#535	C₂×D₄	1	4	yes	—
220	C₂²×#535	C₂⁴	1	1	yes	characteristic
221	C₂²×#535	C₂⁴	1	1	yes	characteristic
222	C₂²×#535	C₂⁴	1	4	yes	—
223	C₂×#3444	C₂×D₄	1	2	yes	—
224	C₂³×#127	C₂×D₄	1	1	yes	characteristic
225	C₂³×#127	C₂⁴	1	1	yes	characteristic
226	C₂³×#124	C₂×D₄	1	1	yes	characteristic
227	C₂³×#124	C₂×D₄	1	1	yes	characteristic
228	C₂×#3428	C₂×D₄	1	1	yes	characteristic
229	C₂²×#518	C₂×D₄	1	1	yes	characteristic
230	C₂³×#117	C₂×D₄	1	1	yes	characteristic
231	#61110	C₂⁴	1	16	yes	—
232	#60806	C₂×D₄	1	8	yes	—
233	#60806	C₂×D₄	1	16	yes	complemented
234	#60806	C₂⁴	1	8	yes	—
235	#60799	C₂×D₄	1	16	yes	complemented
236	#60798	C₂×D₄	1	8	yes	—
237	#60798	C₂⁴	1	8	yes	—
238	#60644	C₂×D₄	1	4	yes	—
239	#60644	C₂×D₄	1	8	yes	complemented
240	#60644	C₂⁴	1	4	yes	—
241	C₂×#3153	C₂×D₄	1	2	yes	—
242	C₂×#3153	C₂×D₄	1	2	yes	—
243	C₂×#3151	C₂×D₄	1	2	yes	—
244	C₂×#3151	C₂⁴	1	2	yes	—
245	#60619	C₂×D₄	1	4	yes	—
246	#60619	C₂×D₄	1	8	yes	complemented
247	#60619	C₂⁴	1	4	yes	—
248	C₂×#3140	C₂×D₄	1	2	yes	—
249	C₂×#3140	C₂×D₄	1	2	yes	—
250	C₂×#3138	C₂×D₄	1	2	yes	—
251	C₂×#3138	C₂⁴	1	2	yes	—
252	C₂×#3021	C₂×D₄	1	4	yes	—
253	C₂×#3021	C₂×D₄	1	8	yes	complemented
254	C₂×#3021	C₂⁴	1	4	yes	—
255	C₂×#3019	C₂×D₄	1	4	yes	—
256	C₂×#3019	C₂×D₄	1	8	yes	complemented
257	C₂×#3019	C₂⁴	1	4	yes	—
258	C₂²×#455	C₂×D₄	1	2	yes	—
259	C₂²×#455	C₂×D₄	1	2	yes	—
260	C₂²×#453	C₂×D₄	1	2	yes	—
261	C₂²×#453	C₂×D₄	1	2	yes	—
262	C₂²×#453	C₂×D₄	1	2	yes	—
263	C₂²×#453	C₂×D₄	1	2	yes	—
264	C₂²×#453	C₂⁴	1	2	yes	—
265	C₂²×#453	C₂⁴	1	2	yes	—
266	#60124	C₂×D₄	1	8	yes	complemented
267	C₂×#2921	C₂×D₄	1	2	yes	—
268	C₂×#2920	C₂×D₄	1	2	yes	—
269	C₂²×#413	C₂×D₄	1	1	yes	characteristic
270	C₂²×#413	C₂×D₄	1	1	yes	characteristic
271	C₂³×#100	C₂×D₄	1	1	yes	characteristic
272	C₂³×#100	C₂×D₄	1	1	yes	characteristic
273	C₂×#2873	C₂×D₄	1	1	yes	characteristic
274	C₂×#2873	C₂×D₄	1	1	yes	characteristic
275	#52004	C₂⁴	1	8	yes	—
276	#52004	C₂⁴	1	8	yes	complemented
277	C₂×#2380	C₂⁴	1	2	yes	—
278	C₂×#2380	C₂⁴	1	4	yes	complemented
279	C₂×#2196	C₂⁴	1	16	yes	—
280	C₂×#2196	C₂⁴	1	16	yes	—
281	C₂×#2128	C₂⁴	1	8	yes	complemented
282	C₂×#2127	C₂⁴	1	8	yes	complemented
283	C₂²×#353	C₂⁴	1	4	yes	—
284	C₂²×#353	C₂⁴	1	4	yes	—
285	#31282	C₂⁴	1	16	yes	—
286	#31282	C₂⁴	1	16	yes	—
287	#23913	C₂×D₄	1	8	yes	—
288	#23913	C₂×D₄	1	16	yes	complemented
289	#23913	C₂⁴	1	8	yes	—
290	#23912	C₂×D₄	1	8	yes	—
291	#23912	C₂×D₄	1	16	yes	complemented
292	#23912	C₂⁴	1	8	yes	—
293	#23907	C₂×D₄	1	16	yes	complemented
294	#23906	C₂×D₄	1	8	yes	—
295	#23906	C₂×D₄	1	8	yes	—
296	#23906	C₂×D₄	1	16	yes	complemented
297	#23906	C₂⁴	1	8	yes	—
298	#23906	C₂⁴	1	8	yes	—
299	#23361	C₂⁴	1	16	yes	—
300	#20956	C₂×D₄	1	4	yes	—
301	#20956	C₂×D₄	1	8	yes	complemented
302	#20956	C₂⁴	1	4	yes	—
303	#20953	C₂×D₄	1	4	yes	—
304	#20953	C₂×D₄	1	8	yes	complemented
305	#20953	C₂⁴	1	4	yes	—
306	C₂×#1887	C₂×D₄	1	2	yes	—
307	C₂×#1887	C₂×D₄	1	2	yes	—
308	C₂×#1887	C₂×D₄	1	2	yes	—
309	C₂×#1887	C₂×D₄	1	2	yes	—
310	C₂×#1887	C₂⁴	1	2	yes	—
311	C₂×#1887	C₂⁴	1	2	yes	—
312	C₂×#1885	C₂×D₄	1	2	yes	—
313	C₂×#1885	C₂×D₄	1	2	yes	—
314	#20591	C₂×D₄	1	8	yes	complemented
315	C₂×#1785	C₂×D₄	1	2	yes	—
316	C₂×#1783	C₂×D₄	1	2	yes	—
317	C₂×#1783	C₂×D₄	1	2	yes	—
318	C₂×#1783	C₂×D₄	1	2	yes	—
319	C₂×#1783	C₂×D₄	1	8	yes	complemented
320	#18529	C₂⁴	1	16	yes	complemented
321	#18524	C₂⁴	1	16	yes	—
322	#17741	C₂⁴	1	8	yes	complemented
323	C₂×#1555	C₂⁴	1	4	yes	—
324	#13595	C₂⁴	1	32	yes	complemented
325	#13584	C₂⁴	1	32	yes	—
326	#13561	C₂⁴	1	32	yes	—
327	#13561	C₂⁴	1	32	yes	—
328	#13049	C₂⁴	1	16	yes	—
329	#13049	C₂⁴	1	16	yes	—
330	#12966	C₂⁴	1	16	yes	complemented
331	#12966	C₂⁴	1	16	yes	complemented
332	#12759	C₂⁴	1	16	yes	complemented
333	#12759	C₂⁴	1	16	yes	complemented
334	#12697	C₂⁴	1	8	yes	—
335	#12696	C₂⁴	1	8	yes	—
336	#12693	C₂⁴	1	8	yes	complemented
337	#12693	C₂⁴	1	8	yes	complemented
338	#9428	C₂⁴	1	16	yes	—
339	#9425	C₂⁴	1	16	yes	complemented
340	#8522	C₂⁴	1	8	yes	—
341	#8522	C₂⁴	1	8	yes	complemented
342	#7493	C₂⁴	1	32	yes	complemented
343	#7493	C₂⁴	1	32	yes	complemented
344	C₂×#585	C₂²×D₄	1	4	yes	—
345	C₂²×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
346	C₂²×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
347	C₂²×H(5,𝔽₂)	C₂²×D₄	1	4	yes	—
348	C₂³×#41	#120	1	1	yes	characteristic
349	C₂³×#41	#120	1	1	yes	characteristic
350	C₂³×#41	#120	1	4	yes	—
351	C₂³×#41	C₂²×D₄	1	1	yes	characteristic
352	C₂³×#41	C₂²×D₄	1	1	yes	characteristic
353	C₂³×#41	C₂²×D₄	1	4	yes	—
354	C₂⁴×Q₈	#120	1	1	yes	characteristic
355	C₂⁴×D₄	#120	1	1	yes	characteristic
356	C₂⁴×D₄	#120	1	1	yes	characteristic
357	C₂⁴×D₄	#120	1	1	yes	characteristic
358	C₂⁴×D₄	#120	1	4	yes	—
359	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
360	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
361	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
362	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
363	C₂⁴×D₄	C₂²×D₄	1	4	yes	—
364	C₂⁵×C₄	#120	1	1	yes	characteristic
365	#3485	C₂²×D₄	1	8	yes	—
366	#3484	C₂²×D₄	1	8	yes	—
367	#3484	C₂²×D₄	1	8	yes	—
368	#3484	C₂²×D₄	1	8	yes	—
369	C₂×D₄²	C₂⁵	1	4	yes	—
370	#3458	C₂²×D₄	1	4	yes	—
371	#3455	C₂²×D₄	1	8	yes	—
372	#3449	C₂²×D₄	1	4	yes	—
373	C₂×#535	#120	1	4	yes	—
374	C₂×#535	#120	1	4	yes	—
375	C₂×#535	#120	1	4	yes	—
376	C₂×#535	#120	1	4	yes	—
377	C₂×#535	#120	1	4	yes	—
378	C₂×#535	#120	1	4	yes	—
379	C₂×#535	C₂²×D₄	1	2	yes	—
380	C₂×#535	C₂²×D₄	1	2	yes	—
381	C₂×#535	C₂²×D₄	1	4	yes	—
382	C₂×#535	C₂²×D₄	1	4	yes	—
383	C₂×#535	C₂²×D₄	1	2	yes	—
384	C₂×#535	C₂²×D₄	1	2	yes	—
385	C₂×#535	C₂²×D₄	1	4	yes	—
386	C₂×#535	C₂²×D₄	1	4	yes	—
387	C₂×#535	C₂²×D₄	1	2	yes	—
388	C₂×#535	C₂²×D₄	1	2	yes	—
389	C₂×#535	C₂²×D₄	1	4	yes	—
390	C₂×#535	C₂²×D₄	1	4	yes	—
391	C₂×#535	C₂⁵	1	2	yes	—
392	C₂×#535	C₂⁵	1	2	yes	—
393	#3444	C₂²×D₄	1	8	yes	—
394	C₂×#533	C₂²×D₄	1	2	yes	—
395	C₂×#532	C₂²×D₄	1	2	yes	—
396	C₂²×#127	#120	1	1	yes	characteristic
397	C₂²×#127	#120	1	1	yes	characteristic
398	C₂²×#127	#120	1	4	yes	—
399	C₂²×#127	C₂²×D₄	1	1	yes	characteristic
400	C₂²×#127	C₂²×D₄	1	1	yes	characteristic
401	C₂²×#127	C₂²×D₄	1	1	yes	characteristic
402	C₂²×#127	C₂²×D₄	1	2	yes	—
403	C₂²×#127	C₂²×D₄	1	2	yes	—
404	C₂²×#127	C₂²×D₄	1	2	yes	—
405	C₂²×#127	C₂²×D₄	1	1	yes	characteristic
406	C₂²×#127	C₂²×D₄	1	1	yes	characteristic
407	C₂²×#127	C₂²×D₄	1	4	yes	—
408	C₂²×#127	C₂⁵	1	2	yes	—
409	C₂²×#127	C₂⁵	1	1	yes	characteristic
410	C₂²×#124	#120	1	1	yes	characteristic
411	C₂²×#124	#120	1	1	yes	characteristic
412	C₂²×#124	#120	1	4	yes	—
413	C₂²×#124	#120	1	1	yes	characteristic
414	C₂²×#124	#120	1	1	yes	characteristic
415	C₂²×#124	#120	1	4	yes	—
416	C₂²×#124	C₂²×D₄	1	1	yes	characteristic
417	C₂²×#124	C₂²×D₄	1	1	yes	characteristic
418	C₂²×#124	C₂²×D₄	1	1	yes	characteristic
419	C₂²×#124	C₂²×D₄	1	1	yes	characteristic
420	C₂²×#124	C₂²×D₄	1	4	yes	—
421	C₂²×#124	C₂²×D₄	1	4	yes	—
422	#3428	C₂²×D₄	1	4	yes	—
423	C₂×#518	C₂²×D₄	1	2	yes	—
424	C₂×#518	C₂²×D₄	1	2	yes	—
425	C₂×#518	C₂²×D₄	1	4	yes	—
426	C₂²×#117	#120	1	1	yes	characteristic
427	C₂²×#117	#120	1	1	yes	characteristic
428	C₂²×#117	#120	1	4	yes	—
429	C₂²×#117	C₂²×D₄	1	1	yes	characteristic
430	C₂²×#117	C₂²×D₄	1	1	yes	characteristic
431	C₂²×#117	C₂²×D₄	1	4	yes	—
432	C₂³×C₄²	#120	1	1	yes	characteristic
433	C₂³×C₄²	C₂²×D₄	1	1	yes	characteristic
434	#3153	C₂²×D₄	1	8	yes	—
435	#3153	C₂²×D₄	1	8	yes	—
436	#3151	C₂²×D₄	1	8	yes	—
437	#3151	C₂²×D₄	1	4	yes	—
438	#3151	H(5,𝔽₂)	1	8	yes	—
439	#3151	C₂⁵	1	4	yes	—
440	C₂×#493	H(5,𝔽₂)	1	4	yes	—
441	C₂×#492	H(5,𝔽₂)	1	4	yes	—
442	#3140	C₂²×D₄	1	8	yes	—
443	#3140	C₂²×D₄	1	8	yes	—
444	#3138	C₂²×D₄	1	4	yes	—
445	#3138	C₂²×D₄	1	8	yes	—
446	#3138	C₂⁵	1	4	yes	—
447	C₂×#455	C₂²×D₄	1	8	yes	—
448	C₂×#455	C₂²×D₄	1	8	yes	—
449	C₂×#453	C₂²×D₄	1	4	yes	—
450	C₂×#453	C₂²×D₄	1	4	yes	—
451	C₂×#453	C₂²×D₄	1	8	yes	—
452	C₂×#453	C₂²×D₄	1	8	yes	—
453	C₂×#453	C₂²×D₄	1	8	yes	—
454	C₂×#453	C₂²×D₄	1	8	yes	—
455	C₂×#453	C₂⁵	1	4	yes	—
456	C₂×#453	C₂⁵	1	4	yes	—
457	#2921	C₂²×D₄	1	8	yes	—
458	#2920	C₂²×D₄	1	8	yes	—
459	C₂×#413	C₂²×D₄	1	4	yes	—
460	C₂×#413	C₂²×D₄	1	4	yes	—
461	C₂²×#100	C₂²×D₄	1	2	yes	—
462	C₂²×#100	C₂²×D₄	1	2	yes	—
463	C₂²×#100	C₂²×D₄	1	2	yes	—
464	C₂²×#100	C₂²×D₄	1	2	yes	—
465	C₂²×#100	C₂²×D₄	1	4	yes	—
466	C₂²×#100	C₂²×D₄	1	4	yes	—
467	#2873	C₂²×D₄	1	4	yes	—
468	#2873	C₂²×D₄	1	4	yes	—
469	C₂×C₄×M₁₆	C₂²×D₄	1	2	yes	—
470	C₂×C₄×M₁₆	C₂²×D₄	1	2	yes	—
471	#2380	C₂⁵	1	4	yes	—
472	C₂×#353	C₂⁵	1	8	yes	—
473	C₂×#353	C₂⁵	1	8	yes	—
474	#1887	C₂²×D₄	1	4	yes	—
475	#1887	C₂²×D₄	1	4	yes	—
476	#1887	C₂²×D₄	1	8	yes	—
477	#1887	C₂²×D₄	1	8	yes	—
478	#1887	C₂²×D₄	1	8	yes	—
479	#1887	C₂²×D₄	1	8	yes	—
480	#1887	C₂⁵	1	4	yes	—
481	#1887	C₂⁵	1	4	yes	—
482	#1885	C₂²×D₄	1	8	yes	—
483	#1885	C₂²×D₄	1	8	yes	—
484	#1785	C₂²×D₄	1	8	yes	—
485	#1783	C₂²×D₄	1	8	yes	—
486	#1783	C₂²×D₄	1	8	yes	—
487	#1783	C₂²×D₄	1	8	yes	—
488	#1555	C₂⁵	1	8	yes	—
489	C₂⁶	B(4,𝔽₂)	1	1	yes	characteristic
490	C₂×H(5,𝔽₂)	C₂³×D₄	1	4	yes	—
491	C₂×H(5,𝔽₂)	C₂³×D₄	1	4	yes	—
492	C₂²×#41	C₂×#120	1	2	yes	—
493	C₂²×#41	C₂×#120	1	2	yes	—
494	C₂²×#41	C₂×#120	1	4	yes	—
495	C₂²×#41	C₂×#120	1	4	yes	—
496	C₂²×#41	C₂³×D₄	1	2	yes	—
497	C₂²×#41	C₂³×D₄	1	2	yes	—
498	C₂³×Q₈	C₂×#120	1	1	yes	characteristic
499	C₂³×Q₈	C₂×#120	1	1	yes	characteristic
500	C₂³×Q₈	C₂×#120	1	4	yes	—
501	C₂³×D₄	C₂×#120	1	1	yes	characteristic
502	C₂³×D₄	C₂×#120	1	1	yes	characteristic
503	C₂³×D₄	C₂×#120	1	1	yes	characteristic
504	C₂³×D₄	C₂×#120	1	1	yes	characteristic
505	C₂³×D₄	C₂×#120	1	2	yes	—
506	C₂³×D₄	C₂×#120	1	2	yes	—
507	C₂³×D₄	C₂×#120	1	2	yes	—
508	C₂³×D₄	C₂×#120	1	2	yes	—
509	C₂³×D₄	C₂×#120	1	4	yes	—
510	C₂³×D₄	C₂×#120	1	4	yes	—
511	C₂³×D₄	C₂×#120	1	4	yes	—
512	C₂³×D₄	C₂³×D₄	1	2	yes	—
513	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
514	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
515	C₂³×D₄	C₂³×D₄	1	2	yes	—
516	C₂³×D₄	C₂³×D₄	1	2	yes	—
517	C₂³×D₄	C₂³×D₄	1	2	yes	—
518	C₂⁴×C₄	B(4,𝔽₂)	1	1	yes	characteristic
519	C₂⁴×C₄	B(4,𝔽₂)	1	1	yes	characteristic
520	C₂⁴×C₄	B(4,𝔽₂)	1	1	yes	characteristic
521	C₂⁴×C₄	B(4,𝔽₂)	1	4	yes	—
522	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
523	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
524	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
525	C₂⁴×C₄	C₂×#120	1	4	yes	—
526	#533	C₂³×D₄	1	4	yes	—
527	#532	#534	1	4	yes	complemented
528	#532	C₂³×D₄	1	4	yes	—
529	C₂×C₄⋊Q₈	#534	1	2	yes	complemented
530	C₂×#127	C₂×#120	1	2	yes	—
531	C₂×#127	C₂×#120	1	2	yes	—
532	C₂×#127	C₂×#120	1	2	yes	—
533	C₂×#127	C₂×#120	1	2	yes	—
534	C₂×#127	C₂×#120	1	2	yes	—
535	C₂×#127	C₂×#120	1	4	yes	—
536	C₂×#127	C₂×#120	1	4	yes	—
537	C₂×#127	#534	1	2	yes	complemented
538	C₂×#127	C₂³×D₄	1	2	yes	—
539	C₂×#127	C₂³×D₄	1	1	yes	characteristic
540	C₂×#127	C₂³×D₄	1	2	yes	—
541	C₂×#127	C₂³×D₄	1	2	yes	—
542	C₂×#127	C₂³×D₄	1	2	yes	—
543	C₂×#127	C₂³×D₄	1	2	yes	—
544	C₂×#127	C₂³×D₄	1	1	yes	characteristic
545	C₂×#127	C₂³×D₄	1	1	yes	characteristic
546	C₂×#127	C₂×H(5,𝔽₂)	1	4	yes	—
547	C₂×#127	C₂×H(5,𝔽₂)	1	4	yes	—
548	C₂×#127	C₂⁶	1	1	yes	characteristic
549	C₂×#124	C₂×#120	1	2	yes	—
550	C₂×#124	C₂×#120	1	2	yes	—
551	C₂×#124	C₂×#120	1	2	yes	—
552	C₂×#124	C₂×#120	1	4	yes	—
553	C₂×#124	C₂×#120	1	4	yes	—
554	C₂×#124	C₂×#120	1	2	yes	—
555	C₂×#124	C₂×#120	1	4	yes	—
556	C₂×#124	C₂×#120	1	4	yes	—
557	C₂×#124	C₂³×D₄	1	2	yes	—
558	C₂×#124	C₂³×D₄	1	2	yes	—
559	C₂×#124	C₂³×D₄	1	2	yes	—
560	C₂×#124	C₂³×D₄	1	2	yes	—
561	#518	C₂³×D₄	1	4	yes	—
562	#518	C₂³×D₄	1	4	yes	—
563	C₂×#117	C₂×#120	1	2	yes	—
564	C₂×#117	C₂×#120	1	4	yes	—
565	C₂×#117	C₂×#120	1	2	yes	—
566	C₂×#117	C₂×#120	1	4	yes	—
567	C₂×#117	C₂³×D₄	1	2	yes	—
568	C₂×#117	C₂³×D₄	1	2	yes	—
569	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
570	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
571	C₂²×C₄²	C₂×#120	1	2	yes	—
572	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
573	C₂²×C₄²	C₂×#120	1	4	yes	—
574	C₂²×C₄²	C₂³×D₄	1	2	yes	—
575	C₂²×C₄²	C₂³×D₄	1	1	yes	characteristic
576	#493	#534	1	8	yes	complemented
577	#493	C₂×H(5,𝔽₂)	1	8	yes	—
578	#492	#534	1	8	yes	complemented
579	#492	C₂×H(5,𝔽₂)	1	8	yes	—
580	C₂×#100	C₂³×D₄	1	4	yes	—
581	C₂×#100	C₂³×D₄	1	4	yes	—
582	C₂×#100	C₂³×D₄	1	4	yes	—
583	C₂×#100	C₂³×D₄	1	4	yes	—
584	C₄×M₁₆	#534	1	4	yes	complemented
585	C₄×M₁₆	C₂³×D₄	1	4	yes	—
586	C₄×M₁₆	C₂³×D₄	1	4	yes	—
587	C₂×C₄×C₈	#534	1	4	yes	complemented
588	C₂⁵	C₂×B(4,𝔽₂)	1	1	yes	characteristic
589	C₂⁵	C₂×B(4,𝔽₂)	1	1	yes	characteristic
590	C₂⁵	C₂×B(4,𝔽₂)	1	1	yes	characteristic
591	C₂⁵	C₂×B(4,𝔽₂)	1	4	yes	—
592	C₂²×Q₈	C₂²×#120	1	2	yes	—
593	C₂²×Q₈	C₂²×#120	1	2	yes	—
594	C₂²×D₄	C₂²×#120	1	2	yes	—
595	C₂²×D₄	C₂²×#120	1	2	yes	—
596	C₂²×D₄	C₂²×#120	1	2	yes	—
597	C₂²×D₄	C₂²×#120	1	2	yes	—
598	C₂²×D₄	C₂²×#120	1	1	yes	characteristic
599	C₂²×D₄	C₂²×#120	1	1	yes	characteristic
600	C₂²×D₄	#3484	1	2	yes	—
601	C₂²×D₄	#3484	1	2	yes	—
602	C₂²×D₄	#3484	1	2	yes	—
603	C₂²×D₄	#3484	1	2	yes	—
604	C₂²×D₄	C₂⁴×D₄	1	1	yes	characteristic
605	C₂²×D₄	C₂⁴×D₄	1	1	yes	characteristic
606	C₂³×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
607	C₂³×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
608	C₂³×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
609	C₂³×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
610	C₂³×C₄	C₂×B(4,𝔽₂)	1	4	yes	—
611	C₂³×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
612	C₂³×C₄	C₂×B(4,𝔽₂)	1	4	yes	—
613	C₂³×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
614	C₂³×C₄	C₂×B(4,𝔽₂)	1	4	yes	—
615	C₂³×C₄	C₂²×#120	1	2	yes	—
616	C₂³×C₄	C₂²×#120	1	1	yes	characteristic
617	C₂³×C₄	C₂²×#120	1	2	yes	—
618	C₂³×C₄	C₂²×#120	1	2	yes	—
619	C₄⋊Q₈	C₂×#534	1	4	yes	complemented
620	#127	C₂×#534	1	4	yes	—
621	#127	C₂×#534	1	4	yes	complemented
622	#127	#3484	1	4	yes	—
623	#127	#3484	1	4	yes	—
624	#127	C₂²×H(5,𝔽₂)	1	4	yes	—
625	C₂×C₄²	#3026	1	2	yes	—
626	C₂×C₄²	#3026	1	2	yes	—
627	C₂×C₄²	C₂²×#120	1	2	yes	—
628	C₂×C₄²	C₂²×#120	1	2	yes	—
629	C₂×C₄²	C₂²×#120	1	1	yes	characteristic
630	C₂×C₄²	C₂²×#120	1	2	yes	—
631	C₂×C₄²	C₂×#534	1	2	yes	—
632	C₂×C₄²	C₂×#534	1	2	yes	—
633	C₂×C₄²	C₂⁴×D₄	1	1	yes	characteristic
634	C₄×C₈	C₂×#534	1	8	yes	complemented
635	C₂⁴	#33551	1	1	yes	characteristic
636	C₂⁴	#33551	1	1	yes	characteristic
637	C₂⁴	#33551	1	2	yes	—
638	C₂⁴	C₂²×B(4,𝔽₂)	1	2	yes	—
639	C₂⁴	C₂²×B(4,𝔽₂)	1	2	yes	—
640	C₂⁴	C₂²×B(4,𝔽₂)	1	2	yes	—
641	C₂⁴	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
642	C₂×D₄	#34980	1	2	yes	—
643	C₂×D₄	#34980	1	2	yes	—
644	C₂×D₄	C₂×#3484	1	2	yes	—
645	C₂×D₄	C₂×#3484	1	2	yes	—
646	C₂²×C₄	#33551	1	1	yes	characteristic
647	C₂²×C₄	#33551	1	1	yes	characteristic
648	C₂²×C₄	#33551	1	2	yes	—
649	C₂²×C₄	#34980	1	1	yes	characteristic
650	C₂²×C₄	#34980	1	1	yes	characteristic
651	C₂²×C₄	C₂²×B(4,𝔽₂)	1	2	yes	—
652	C₂²×C₄	C₂²×B(4,𝔽₂)	1	2	yes	—
653	C₂²×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
654	C₂²×C₄	C₂²×B(4,𝔽₂)	1	2	yes	—
655	C₂²×C₄	C₂×#3026	1	1	yes	characteristic
656	C₂²×C₄	C₂×#3026	1	1	yes	characteristic
657	C₂²×C₄	C₂³×#120	1	1	yes	characteristic
658	C₄²	#34980	1	2	yes	—
659	C₄²	C₂×#3026	1	4	yes	—
660	C₄²	C₂²×#534	1	2	yes	—
661	C₂³	#6470225	1	1	yes	characteristic
662	C₂³	#6470225	1	1	yes	characteristic
663	C₂³	C₂×#33551	1	1	yes	characteristic
664	C₂³	C₂×#33551	1	1	yes	characteristic
665	C₂³	C₂×#33551	1	2	yes	—
666	C₂³	C₂×#33551	1	2	yes	—
667	C₂³	C₂×#33551	1	1	yes	characteristic
668	C₂³	C₂×#33551	1	1	yes	characteristic
669	C₂³	C₂³×B(4,𝔽₂)	1	1	yes	characteristic
670	C₂×C₄	#6470225	1	1	yes	characteristic
671	C₂×C₄	#6470225	1	1	yes	characteristic
672	C₂×C₄	C₂×#33551	1	2	yes	—
673	C₂×C₄	C₂×#33551	1	2	yes	—
674	C₂×C₄	C₂×#34980	1	1	yes	characteristic
675	C₂×C₄	C₂²×#3026	1	1	yes	characteristic
676	C₂²	#72210575	1	1	yes	characteristic
677	C₂²	#72210575	1	1	yes	characteristic
678	C₂²	#72210575	1	1	yes	characteristic
679	C₂²	#72210575	1	1	yes	characteristic
680	C₂²	C₂²×#33551	1	1	yes	characteristic
681	C₂²	C₂²×#33551	1	1	yes	characteristic
682	C₂²	C₂×#6470225	1	1	yes	characteristic
683	C₂	#72216611	1	2	yes	direct product factor
684	C₂	C₂×#72210575	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#72210575
commutator, Frattini, cosocle	C₂×#127	C₂⁶
LCS	G ▷ C₂×#127 ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ C₂⁵×C₄ ◁ C₂³×#535 ◁ G
LECS	G ▷ C₂×#127 ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂×#72213519	C₂	semidirect
2. C₂×#72215721	C₂	semidirect
3. C₂×#72216601	C₂	semidirect
4. C₂×#152716	C₂²	semidirect
5. C₂×#7487871	C₂²	semidirect
6. C₂×#72213671	C₂	semidirect
7. C₂×#10576178	C₂²	semidirect
8. C₂×#72216577	C₂	semidirect
9. C₂×#72216589	C₂	semidirect
10. C₂×#152017	C₂²	semidirect
11. C₂×#7504294	C₂²	semidirect
12. C₂×#72216584	C₂	semidirect
13. C₂×#152323	C₂²	semidirect
14. C₂×#6407636	C₂²	semidirect
15. C₂×#72216600	C₂	semidirect
16. C₂×#512862	C₂²	semidirect
17. C₂×#152602	C₂²	semidirect
18. C₂×#72216603	C₂	semidirect
20. C₂×#152191	C₂²	semidirect
21. C₂×#153305	C₂²	semidirect
22. C₂×#153305	C₂²	semidirect
23. C₂×#152477	C₂²	semidirect
24. C₂×#72215568	C₂	semidirect
25. C₂×#501096	C₂²	semidirect
26. C₂×#500179	C₂²	semidirect
28. C₂×#153189	C₂²	semidirect
29. C₂×#153189	C₂²	semidirect
30. C₂×#72213428	C₂	semidirect
31. C₂×#512663	C₂²	semidirect
32. C₂×#152069	C₂²	semidirect
33. C₂×#152049	C₂²	semidirect
34. C₂×#152103	C₂²	semidirect
35. C₂×#72216567	C₂	semidirect
36. C₂×#152679	C₂²	semidirect
37. C₂×#152679	C₂²	semidirect
38. C₂×#152717	C₂²	semidirect
39. C₂×#152018	C₂²	semidirect
40. C₂×#152322	C₂²	semidirect
41. C₂×#7504292	C₂²	semidirect
42. C₂×#72213685	C₂	semidirect
43. C₂×#246930	C₂²	semidirect
44. C₂×#246957	C₂²	semidirect
46. C₂×#72210575	C₂	semidirect
47. C₂×#512119	C₂²	semidirect
48. C₂×#512119	C₂²	semidirect
49. C₂×#501097	C₂²	semidirect
50. C₂×#500177	C₂²	semidirect
51. C₂×#493370	C₂²	semidirect
54. C₂×#493372	C₂²	semidirect
55. C₂×#200876	C₂²	semidirect
57. C₂×#6348967	C₂²	semidirect
58. C₂×#187811	C₂²	semidirect
60. C₂²×#52004	C₂²	semidirect
61. C₂×#511771	C₂²	semidirect
62. C₂×#511771	C₂²	semidirect
63. #72216611	C₂	direct (N × H)
64. #72216603	C₂²	semidirect
65. #72216601	C₂²	semidirect
66. #72216600	C₂²	semidirect
67. #72216589	C₂²	semidirect
68. #72216584	C₂²	semidirect
69. #72216577	C₂²	semidirect
70. #72216567	C₂²	semidirect
71. #72215721	C₂²	semidirect
72. #72215568	C₂²	semidirect
73. #72213685	C₂²	semidirect
74. #72213671	C₂²	semidirect
75. #72213519	C₂²	semidirect
76. #72213428	C₂²	semidirect
77. #72210575	C₂²	semidirect
78. C₂×#62814	D₄	semidirect
79. C₂×#62811	D₄	semidirect
80. C₂²×#3484	D₄	semidirect
81. C₂³×D₄²	C₂³	semidirect
83. #10576178	C₂³	semidirect
85. #10575547	D₄	semidirect
87. C₂×#60806	D₄	semidirect
89. C₂×#60799	D₄	semidirect
91. C₂×#60644	D₄	semidirect
93. C₂×#60619	D₄	semidirect
95. C₂²×#3021	D₄	semidirect
97. C₂²×#3019	D₄	semidirect
99. C₂×#60124	D₄	semidirect
101. C₂×#52004	C₂³	semidirect
102. C₂×#52004	C₂³	semidirect
103. C₂²×#2380	C₂³	semidirect
106. C₂²×#2128	C₂³	semidirect
107. C₂²×#2127	C₂³	semidirect
108. #7504294	C₂³	semidirect
109. #7504292	C₂³	semidirect
112. #7487871	C₂³	semidirect
114. #6437449	D₄	semidirect
116. #6437445	D₄	semidirect
118. C₂×#23913	D₄	semidirect
120. C₂×#23912	D₄	semidirect
122. C₂×#23907	D₄	semidirect
123. C₂×#23906	D₄	semidirect
126. #6407636	C₂³	semidirect
128. C₂×#20956	D₄	semidirect
130. C₂×#20953	D₄	semidirect
132. C₂×#20591	D₄	semidirect
133. C₂²×#1783	D₄	semidirect
134. #6348967	C₂³	semidirect
135. C₂×#18529	C₂³	semidirect
137. C₂×#17741	C₂³	semidirect
138. #512862	C₂³	semidirect
139. #512663	C₂³	semidirect
140. C₂×#13595	C₂³	semidirect
144. #512119	C₂³	semidirect
145. #512119	C₂³	semidirect
146. #511771	C₂³	semidirect
147. #511771	C₂³	semidirect
148. #501097	C₂³	semidirect
149. #501096	C₂³	semidirect
150. #500179	C₂³	semidirect
151. #500177	C₂³	semidirect
156. C₂×#12966	C₂³	semidirect
157. C₂×#12966	C₂³	semidirect
158. C₂×#12759	C₂³	semidirect
159. C₂×#12759	C₂³	semidirect
160. #493372	C₂³	semidirect
161. #493370	C₂³	semidirect
164. C₂×#12693	C₂³	semidirect
165. C₂×#12693	C₂³	semidirect
166. #246957	C₂³	semidirect
167. #246930	C₂³	semidirect
169. #200876	C₂³	semidirect
171. C₂×#9425	C₂³	semidirect
172. #187811	C₂³	semidirect
174. C₂×#8522	C₂³	semidirect
175. #153305	C₂³	semidirect
176. #153305	C₂³	semidirect
177. #153189	C₂³	semidirect
178. #153189	C₂³	semidirect
179. #152717	C₂³	semidirect
180. #152716	C₂³	semidirect
181. #152679	C₂³	semidirect
182. #152679	C₂³	semidirect
183. #152602	C₂³	semidirect
184. #152477	C₂³	semidirect
185. #152323	C₂³	semidirect
186. #152322	C₂³	semidirect
187. #152191	C₂³	semidirect
188. #152103	C₂³	semidirect
189. #152069	C₂³	semidirect
190. #152049	C₂³	semidirect
191. #152018	C₂³	semidirect
192. #152017	C₂³	semidirect
193. C₂×#7493	C₂³	semidirect
194. C₂×#7493	C₂³	semidirect
199. #62814	C₂×D₄	semidirect
200. #62811	C₂×D₄	semidirect
205. C₂×#3484	C₂×D₄	semidirect
207. C₂²×D₄²	C₂⁴	semidirect
233. #60806	C₂×D₄	semidirect
235. #60799	C₂×D₄	semidirect
239. #60644	C₂×D₄	semidirect
246. #60619	C₂×D₄	semidirect
253. C₂×#3021	C₂×D₄	semidirect
256. C₂×#3019	C₂×D₄	semidirect
266. #60124	C₂×D₄	semidirect
276. #52004	C₂⁴	semidirect
278. C₂×#2380	C₂⁴	semidirect
281. C₂×#2128	C₂⁴	semidirect
282. C₂×#2127	C₂⁴	semidirect
288. #23913	C₂×D₄	semidirect
291. #23912	C₂×D₄	semidirect
293. #23907	C₂×D₄	semidirect
296. #23906	C₂×D₄	semidirect
301. #20956	C₂×D₄	semidirect
304. #20953	C₂×D₄	semidirect
314. #20591	C₂×D₄	semidirect
319. C₂×#1783	C₂×D₄	semidirect
320. #18529	C₂⁴	semidirect
322. #17741	C₂⁴	semidirect
324. #13595	C₂⁴	semidirect
330. #12966	C₂⁴	semidirect
331. #12966	C₂⁴	semidirect
332. #12759	C₂⁴	semidirect
333. #12759	C₂⁴	semidirect
336. #12693	C₂⁴	semidirect
337. #12693	C₂⁴	semidirect
339. #9425	C₂⁴	semidirect
341. #8522	C₂⁴	semidirect
342. #7493	C₂⁴	semidirect
343. #7493	C₂⁴	semidirect
527. #532	#534	semidirect
529. C₂×C₄⋊Q₈	#534	semidirect
537. C₂×#127	#534	semidirect
576. #493	#534	semidirect
578. #492	#534	semidirect
584. C₄×M₁₆	#534	semidirect
587. C₂×C₄×C₈	#534	semidirect
619. C₄⋊Q₈	C₂×#534	semidirect
621. #127	C₂×#534	semidirect
634. C₄×C₈	C₂×#534	semidirect
683. C₂	#72216611	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#72213519	2
C₂×#72215721	2
C₂×#72216601	2
C₂×#72213671	2
C₂×#72216577	2
C₂×#72216589	2
C₂×#72216584	2
C₂×#72216600	2
C₂×#72216603	2
C₂×#72215568	2
C₂×#72213428	2
C₂×#72216567	2
C₂×#72213685	2
C₂×#72210575	2
#72216611	2

Subgroups — C2×#72216611 #72251421

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#72216611 #72251421