Subgroups — C₂×#72216684 #72256446

Order 4096.

At least 30911 conjugacy classes of subgroups; only the 915 normal subgroups are shown.

The subgroup lattice has 664 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×#72213436	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#72216567	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#72215737	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#72213443	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#72213738	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#72210511	C₂	1	1	yes	maximal, characteristic
7	C₂×#392113	C₄	1	1	yes	characteristic, complemented
8	C₂×#6437445	C₄	1	1	yes	characteristic, complemented
9	C₂×#6437445	C₂²	1	1	yes	characteristic
10	C₂×#72214353	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#493372	C₂²	1	1	yes	characteristic
12	C₂×#493385	C₂²	1	1	yes	characteristic
13	C₂×#359509	C₄	1	1	yes	characteristic, complemented
14	C₂×#359509	C₂²	1	1	yes	characteristic
15	C₂×#187811	C₂²	1	1	yes	characteristic
16	C₂×#187811	C₂²	1	1	yes	characteristic
17	C₂³×#3484	C₂²	1	1	yes	characteristic
18	C₂×#7630939	C₄	1	1	yes	characteristic, complemented
19	#72216684	C₂	1	8	yes	maximal, direct product factor
20	#72216567	C₂²	1	4	yes	complemented
21	#72215737	C₂²	1	4	yes	complemented
22	#72214353	C₂²	1	4	yes	complemented
23	#72213738	C₂²	1	4	yes	complemented
24	#72213443	C₂²	1	4	yes	complemented
25	#72213436	C₂²	1	4	yes	complemented
26	#72210511	C₄	1	4	yes	complemented
27	#72210511	C₂²	1	4	yes	—
28	C₂⁴×H(5,𝔽₂)	D₄	1	1	yes	characteristic
29	C₂⁶×D₄	C₂×C₄	1	1	yes	characteristic
30	C₂²×#3484	C₂×C₄	1	1	yes	characteristic
31	C₂²×#3484	C₂×C₄	1	2	yes	—
32	C₂²×#3484	D₄	1	2	yes	—
33	C₂²×#3484	D₄	1	2	yes	—
34	C₂²×#3484	C₂³	1	2	yes	—
35	C₂³×#535	C₂×C₄	1	1	yes	characteristic
36	C₂³×#535	C₂³	1	1	yes	characteristic
37	C₂³×#525	D₄	1	1	yes	characteristic
38	C₂³×#525	D₄	1	1	yes	characteristic
39	C₂³×#518	D₄	1	1	yes	characteristic
40	C₂²×#3019	D₄	1	1	yes	characteristic
41	C₂²×#3019	D₄	1	1	yes	characteristic
42	#7630939	C₂×C₄	1	4	yes	complemented
43	C₂×#34171	C₂×C₄	1	1	yes	characteristic
44	C₂²×#2134	D₄	1	2	yes	complemented
45	C₂²×#2128	D₄	1	2	yes	complemented
46	#6437445	C₂×C₄	1	2	yes	—
47	#6437445	C₂×C₄	1	4	yes	complemented
48	#6437445	D₄	1	2	yes	—
49	#6437445	D₄	1	2	yes	—
50	#6437445	C₂³	1	2	yes	—
51	C₂×#20953	D₄	1	1	yes	characteristic
52	C₂×#20953	D₄	1	1	yes	characteristic
53	C₂²×#1783	C₂×C₄	1	1	yes	characteristic
54	C₂²×#1783	C₂×C₄	1	1	yes	characteristic
55	C₂×#17741	D₄	1	2	yes	complemented
56	C₂×#17666	D₄	1	2	yes	complemented
57	#493385	D₄	1	2	yes	complemented
58	#493385	C₂³	1	2	yes	—
59	#493372	D₄	1	2	yes	complemented
60	#493372	C₂³	1	2	yes	—
61	#392113	C₂×C₄	1	4	yes	complemented
62	#359509	C₂×C₄	1	2	yes	—
63	#359509	C₂×C₄	1	4	yes	complemented
64	#359509	D₄	1	2	yes	—
65	#359509	D₄	1	2	yes	—
66	#359509	C₂³	1	2	yes	—
67	C₂×#10989	D₄	1	2	yes	—
68	C₂×#10989	D₄	1	2	yes	—
69	#187811	D₄	1	2	yes	complemented
70	#187811	D₄	1	2	yes	complemented
71	#187811	C₂³	1	2	yes	—
72	#187811	C₂³	1	2	yes	—
73	C₂³×H(5,𝔽₂)	C₂²⋊C₄	1	2	yes	—
74	C₂³×H(5,𝔽₂)	C₂²⋊C₄	1	1	yes	characteristic
75	C₂³×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
76	C₂⁴×#41	C₂²⋊C₄	1	1	yes	characteristic
77	C₂⁴×#41	C₂×D₄	1	1	yes	characteristic
78	C₂⁵×D₄	C₂²⋊C₄	1	2	yes	—
79	C₂⁵×D₄	C₂²⋊C₄	1	1	yes	characteristic
80	C₂⁵×D₄	C₂²×C₄	1	2	yes	—
81	C₂⁵×D₄	C₂²×C₄	1	1	yes	characteristic
82	C₂⁶×C₄	C₂²⋊C₄	1	1	yes	characteristic
83	C₂×#3484	C₂²⋊C₄	1	2	yes	—
84	C₂×#3484	C₂²×C₄	1	2	yes	—
85	C₂²×#535	C₂²⋊C₄	1	2	yes	—
86	C₂²×#535	C₂²×C₄	1	2	yes	—
87	C₂²×#535	C₂²×C₄	1	1	yes	characteristic
88	C₂²×#535	C₂×D₄	1	1	yes	characteristic
89	C₂²×#535	C₂×D₄	1	1	yes	characteristic
90	C₂²×#535	C₂×D₄	1	1	yes	characteristic
91	C₂²×#535	C₂×D₄	1	1	yes	characteristic
92	C₂²×#535	C₂×D₄	1	1	yes	characteristic
93	C₂²×#535	C₂×D₄	1	1	yes	characteristic
94	C₂²×#535	C₂×D₄	1	1	yes	characteristic
95	C₂²×#535	C₂×D₄	1	1	yes	characteristic
96	C₂²×#535	C₂×D₄	1	1	yes	characteristic
97	C₂²×#535	C₂×D₄	1	1	yes	characteristic
98	C₂²×#535	C₂×D₄	1	1	yes	characteristic
99	C₂²×#535	C₂×D₄	1	1	yes	characteristic
100	C₂²×#535	C₂×D₄	1	1	yes	characteristic
101	C₂²×#535	C₂×D₄	1	1	yes	characteristic
102	C₂²×#535	C₂×D₄	1	1	yes	characteristic
103	C₂²×#535	C₂×D₄	1	1	yes	characteristic
104	C₂²×#535	#41	1	1	yes	characteristic
105	C₂²×#535	#41	1	1	yes	characteristic
106	C₂²×#535	#41	1	1	yes	characteristic
107	C₂²×#535	#41	1	1	yes	characteristic
108	C₂²×#535	#41	1	1	yes	characteristic
109	C₂²×#535	#41	1	1	yes	characteristic
110	C₂²×#535	C₂⁴	1	1	yes	characteristic
111	C₂³×#127	C₂×D₄	1	1	yes	characteristic
112	C₂³×#127	#41	1	1	yes	characteristic
113	C₂³×#124	C₂×D₄	1	1	yes	characteristic
114	C₂³×#124	#41	1	1	yes	characteristic
115	C₂²×#525	C₂²⋊C₄	1	2	yes	—
116	C₂²×#525	C₂²⋊C₄	1	2	yes	—
117	C₂²×#525	C₂×D₄	1	2	yes	—
118	C₂²×#525	C₂×D₄	1	2	yes	—
119	C₂²×#518	C₂²⋊C₄	1	1	yes	characteristic
120	C₂²×#518	C₂²⋊C₄	1	2	yes	—
121	C₂²×#518	C₂×D₄	1	2	yes	—
122	C₂³×#117	C₂²⋊C₄	1	1	yes	characteristic
123	C₂³×#117	C₂×D₄	1	1	yes	characteristic
124	C₂×#3019	C₂²⋊C₄	1	2	yes	—
125	C₂×#3019	C₂²⋊C₄	1	2	yes	—
126	C₂×#3019	C₂×D₄	1	2	yes	—
127	C₂×#3019	C₂×D₄	1	2	yes	—
128	C₂³×#100	C₂²⋊C₄	1	1	yes	characteristic
129	C₂³×#100	C₂²⋊C₄	1	1	yes	characteristic
130	C₂³×#100	C₂²⋊C₄	1	2	yes	—
131	#34171	C₂²⋊C₄	1	2	yes	—
132	#34171	C₂²×C₄	1	2	yes	—
133	C₂×#2309	C₂²⋊C₄	1	2	yes	—
134	C₂×#2134	C₂×D₄	1	4	yes	complemented
135	C₂×#2128	C₂×D₄	1	4	yes	complemented
136	#20953	C₂²⋊C₄	1	2	yes	—
137	#20953	C₂²⋊C₄	1	2	yes	—
138	#20953	C₂×D₄	1	2	yes	—
139	#20953	C₂×D₄	1	2	yes	—
140	C₂×#1783	C₂²⋊C₄	1	2	yes	—
141	C₂×#1783	C₂²⋊C₄	1	2	yes	—
142	C₂×#1783	C₂²×C₄	1	2	yes	—
143	C₂×#1783	C₂²×C₄	1	2	yes	—
144	#17741	C₂×D₄	1	4	yes	complemented
145	#17666	C₂×D₄	1	4	yes	complemented
146	#10989	C₂²⋊C₄	1	4	yes	—
147	#10989	C₂²⋊C₄	1	4	yes	—
148	#10989	C₂×D₄	1	4	yes	—
149	#10989	C₂×D₄	1	4	yes	—
150	C₂⁷	#99	1	1	yes	characteristic
151	C₂²×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	2	yes	—
152	C₂³×#41	#99	1	2	yes	—
153	C₂³×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
154	C₂³×#41	C₂×C₂²⋊C₄	1	2	yes	—
155	C₂³×#41	#120	1	1	yes	characteristic
156	C₂³×#41	#120	1	1	yes	characteristic
157	C₂³×#41	#120	1	1	yes	characteristic
158	C₂³×#41	#120	1	1	yes	characteristic
159	C₂³×#41	#120	1	1	yes	characteristic
160	C₂³×#41	#120	1	1	yes	characteristic
161	C₂³×#41	#121	1	1	yes	characteristic
162	C₂³×#41	#121	1	1	yes	characteristic
163	C₂³×#41	#123	1	1	yes	characteristic
164	C₂³×#41	#123	1	1	yes	characteristic
165	C₂³×#41	C₂²×D₄	1	1	yes	characteristic
166	C₂⁴×Q₈	#99	1	1	yes	characteristic
167	C₂⁴×Q₈	#121	1	1	yes	characteristic
168	C₂⁴×D₄	#99	1	2	yes	—
169	C₂⁴×D₄	#99	1	2	yes	—
170	C₂⁴×D₄	#99	1	1	yes	characteristic
171	C₂⁴×D₄	C₂×C₂²⋊C₄	1	2	yes	—
172	C₂⁴×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
173	C₂⁴×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
174	C₂⁴×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
175	C₂⁴×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
176	C₂⁴×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
177	C₂⁴×D₄	C₄×D₄	1	1	yes	characteristic
178	C₂⁴×D₄	C₄×D₄	1	1	yes	characteristic
179	C₂⁴×D₄	C₄×D₄	1	1	yes	characteristic
180	C₂⁴×D₄	C₄×D₄	1	1	yes	characteristic
181	C₂⁴×D₄	C₄×D₄	1	1	yes	characteristic
182	C₂⁴×D₄	C₄×D₄	1	1	yes	characteristic
183	C₂⁴×D₄	C₄×D₄	1	1	yes	characteristic
184	C₂⁴×D₄	C₄×D₄	1	1	yes	characteristic
185	C₂⁴×D₄	#121	1	1	yes	characteristic
186	C₂⁴×D₄	C₂³×C₄	1	1	yes	characteristic
187	C₂⁵×C₄	#99	1	1	yes	characteristic
188	C₂⁵×C₄	#99	1	2	yes	—
189	C₂⁵×C₄	C₂×C₂²⋊C₄	1	2	yes	—
190	C₂⁵×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
191	C₂×#535	C₂×C₂²⋊C₄	1	1	yes	characteristic
192	C₂×#535	C₂×C₂²⋊C₄	1	1	yes	characteristic
193	C₂×#535	C₂×C₂²⋊C₄	1	1	yes	characteristic
194	C₂×#535	C₂×C₂²⋊C₄	1	1	yes	characteristic
195	C₂×#535	C₄×D₄	1	1	yes	characteristic
196	C₂×#535	C₄×D₄	1	1	yes	characteristic
197	C₂×#535	C₄×D₄	1	1	yes	characteristic
198	C₂×#535	C₄×D₄	1	1	yes	characteristic
199	C₂×#535	#120	1	1	yes	characteristic
200	C₂×#535	#120	1	1	yes	characteristic
201	C₂×#535	#120	1	1	yes	characteristic
202	C₂×#535	#120	1	1	yes	characteristic
203	C₂×#535	#120	1	1	yes	characteristic
204	C₂×#535	#120	1	1	yes	characteristic
205	C₂×#535	#120	1	1	yes	characteristic
206	C₂×#535	#120	1	1	yes	characteristic
207	C₂×#535	#120	1	1	yes	characteristic
208	C₂×#535	#120	1	1	yes	characteristic
209	C₂×#535	#120	1	1	yes	characteristic
210	C₂×#535	#120	1	1	yes	characteristic
211	C₂×#535	#120	1	1	yes	characteristic
212	C₂×#535	#120	1	1	yes	characteristic
213	C₂×#535	#121	1	1	yes	characteristic
214	C₂×#535	#121	1	1	yes	characteristic
215	C₂×#535	#121	1	1	yes	characteristic
216	C₂×#535	#121	1	1	yes	characteristic
217	C₂×#535	#121	1	1	yes	characteristic
218	C₂×#535	#121	1	1	yes	characteristic
219	C₂×#535	#121	1	1	yes	characteristic
220	C₂×#535	#121	1	1	yes	characteristic
221	C₂×#535	#121	1	1	yes	characteristic
222	C₂×#535	#121	1	1	yes	characteristic
223	C₂×#535	#121	1	1	yes	characteristic
224	C₂×#535	#121	1	1	yes	characteristic
225	C₂×#535	#121	1	1	yes	characteristic
226	C₂×#535	#121	1	1	yes	characteristic
227	C₂×#535	#121	1	1	yes	characteristic
228	C₂×#535	#121	1	1	yes	characteristic
229	C₂×#535	#121	1	1	yes	characteristic
230	C₂×#535	#121	1	1	yes	characteristic
231	C₂×#535	#121	1	1	yes	characteristic
232	C₂×#535	#121	1	1	yes	characteristic
233	C₂×#535	#123	1	1	yes	characteristic
234	C₂×#535	#123	1	1	yes	characteristic
235	C₂×#535	#123	1	1	yes	characteristic
236	C₂×#535	#123	1	1	yes	characteristic
237	C₂×#535	#123	1	1	yes	characteristic
238	C₂×#535	#123	1	1	yes	characteristic
239	C₂×#535	#124	1	1	yes	characteristic
240	C₂×#535	#124	1	1	yes	characteristic
241	C₂×#535	#124	1	1	yes	characteristic
242	C₂×#535	#124	1	1	yes	characteristic
243	C₂×#535	#127	1	1	yes	characteristic
244	C₂×#535	#127	1	1	yes	characteristic
245	C₂×#535	#127	1	1	yes	characteristic
246	C₂×#535	#127	1	1	yes	characteristic
247	C₂×#535	C₂²×D₄	1	1	yes	characteristic
248	C₂×#535	C₂²×D₄	1	1	yes	characteristic
249	C₂×#535	C₂²×D₄	1	1	yes	characteristic
250	C₂×#535	C₂²×D₄	1	1	yes	characteristic
251	C₂×#535	C₂²×D₄	1	1	yes	characteristic
252	C₂×#535	C₂²×D₄	1	1	yes	characteristic
253	C₂×#535	C₂×#41	1	1	yes	characteristic
254	C₂×#535	C₂×#41	1	1	yes	characteristic
255	C₂²×#127	C₄×D₄	1	1	yes	characteristic
256	C₂²×#127	C₄×D₄	1	1	yes	characteristic
257	C₂²×#127	#120	1	1	yes	characteristic
258	C₂²×#127	#120	1	1	yes	characteristic
259	C₂²×#127	#120	1	1	yes	characteristic
260	C₂²×#127	#121	1	1	yes	characteristic
261	C₂²×#127	#121	1	1	yes	characteristic
262	C₂²×#127	#121	1	1	yes	characteristic
263	C₂²×#127	#121	1	1	yes	characteristic
264	C₂²×#127	#121	1	1	yes	characteristic
265	C₂²×#127	#121	1	1	yes	characteristic
266	C₂²×#127	#121	1	1	yes	characteristic
267	C₂²×#127	#121	1	1	yes	characteristic
268	C₂²×#127	#121	1	1	yes	characteristic
269	C₂²×#127	#121	1	1	yes	characteristic
270	C₂²×#127	#123	1	1	yes	characteristic
271	C₂²×#127	#123	1	1	yes	characteristic
272	C₂²×#127	#123	1	1	yes	characteristic
273	C₂²×#127	#124	1	1	yes	characteristic
274	C₂²×#127	#124	1	1	yes	characteristic
275	C₂²×#127	#127	1	1	yes	characteristic
276	C₂²×#127	#127	1	1	yes	characteristic
277	C₂²×#127	C₂²×D₄	1	1	yes	characteristic
278	C₂²×#127	C₂×#41	1	1	yes	characteristic
279	C₂²×#124	C₄×D₄	1	1	yes	characteristic
280	C₂²×#124	C₄×D₄	1	1	yes	characteristic
281	C₂²×#124	#120	1	1	yes	characteristic
282	C₂²×#124	#120	1	1	yes	characteristic
283	C₂²×#124	#120	1	1	yes	characteristic
284	C₂²×#124	#121	1	1	yes	characteristic
285	C₂²×#124	#121	1	1	yes	characteristic
286	C₂²×#124	#121	1	1	yes	characteristic
287	C₂²×#124	#121	1	1	yes	characteristic
288	C₂²×#124	#121	1	1	yes	characteristic
289	C₂²×#124	#121	1	1	yes	characteristic
290	C₂²×#124	#121	1	1	yes	characteristic
291	C₂²×#124	#121	1	1	yes	characteristic
292	C₂²×#124	#121	1	1	yes	characteristic
293	C₂²×#124	#121	1	1	yes	characteristic
294	C₂²×#124	#123	1	1	yes	characteristic
295	C₂²×#124	#123	1	1	yes	characteristic
296	C₂²×#124	#123	1	1	yes	characteristic
297	C₂²×#124	#124	1	1	yes	characteristic
298	C₂²×#124	#124	1	1	yes	characteristic
299	C₂²×#124	#127	1	1	yes	characteristic
300	C₂²×#124	#127	1	1	yes	characteristic
301	C₂²×#124	C₂²×D₄	1	1	yes	characteristic
302	C₂²×#124	C₂×#41	1	1	yes	characteristic
303	C₂×#518	C₂×C₂²⋊C₄	1	2	yes	—
304	C₂²×#117	#99	1	2	yes	—
305	C₂²×#117	#99	1	2	yes	—
306	C₂²×#117	C₂×C₂²⋊C₄	1	2	yes	—
307	C₂²×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
308	C₂²×#117	#120	1	1	yes	characteristic
309	C₂²×#117	#120	1	1	yes	characteristic
310	C₂²×#117	#120	1	1	yes	characteristic
311	C₂²×#117	#120	1	1	yes	characteristic
312	C₂²×#117	#120	1	1	yes	characteristic
313	C₂²×#117	#121	1	1	yes	characteristic
314	C₂²×#117	#121	1	1	yes	characteristic
315	C₂²×#117	#121	1	1	yes	characteristic
316	C₂²×#117	#121	1	1	yes	characteristic
317	C₂²×#117	#123	1	1	yes	characteristic
318	C₂²×#117	C₂²×D₄	1	1	yes	characteristic
319	C₂³×C₄²	#120	1	1	yes	characteristic
320	C₂³×C₄²	#123	1	1	yes	characteristic
321	C₂²×#100	C₂×C₂²⋊C₄	1	2	yes	—
322	C₂²×#100	C₂×C₂²⋊C₄	1	2	yes	—
323	C₂²×#100	C₂×C₂²⋊C₄	1	4	yes	—
324	#2309	C₂×C₂²⋊C₄	1	4	yes	—
325	C₂⁶	C₂×#99	1	1	yes	characteristic
326	C₂⁶	C₂×#99	1	2	yes	—
327	C₂²×#41	#379	1	1	yes	characteristic
328	C₂²×#41	#379	1	1	yes	characteristic
329	C₂²×#41	#386	1	1	yes	characteristic
330	C₂²×#41	#386	1	1	yes	characteristic
331	C₂²×#41	#392	1	1	yes	characteristic
332	C₂²×#41	#392	1	1	yes	characteristic
333	C₂²×#41	#392	1	1	yes	characteristic
334	C₂²×#41	#392	1	1	yes	characteristic
335	C₂²×#41	#394	1	1	yes	characteristic
336	C₂²×#41	#394	1	1	yes	characteristic
337	C₂²×#41	#394	1	1	yes	characteristic
338	C₂²×#41	#394	1	1	yes	characteristic
339	C₂²×#41	C₂×#120	1	1	yes	characteristic
340	C₂²×#41	C₂×#120	1	1	yes	characteristic
341	C₂²×#41	C₂×#120	1	1	yes	characteristic
342	C₂²×#41	C₂×#123	1	1	yes	characteristic
343	C₂³×Q₈	#386	1	1	yes	characteristic
344	C₂³×Q₈	#392	1	1	yes	characteristic
345	C₂³×Q₈	#392	1	1	yes	characteristic
346	C₂³×Q₈	#394	1	1	yes	characteristic
347	C₂³×Q₈	#394	1	1	yes	characteristic
348	C₂³×Q₈	C₂×#99	1	2	yes	—
349	C₂³×Q₈	C₂×#121	1	1	yes	characteristic
350	C₂³×D₄	AΣL(1,𝔽₁₆)	1	4	yes	—
351	C₂³×D₄	AΣL(1,𝔽₁₆)	1	4	yes	—
352	C₂³×D₄	#379	1	1	yes	characteristic
353	C₂³×D₄	#379	1	1	yes	characteristic
354	C₂³×D₄	#386	1	1	yes	characteristic
355	C₂³×D₄	#386	1	1	yes	characteristic
356	C₂³×D₄	#386	1	1	yes	characteristic
357	C₂³×D₄	#386	1	1	yes	characteristic
358	C₂³×D₄	#386	1	1	yes	characteristic
359	C₂³×D₄	#386	1	1	yes	characteristic
360	C₂³×D₄	#386	1	1	yes	characteristic
361	C₂³×D₄	#386	1	1	yes	characteristic
362	C₂³×D₄	#386	1	1	yes	characteristic
363	C₂³×D₄	#386	1	1	yes	characteristic
364	C₂³×D₄	#386	1	1	yes	characteristic
365	C₂³×D₄	#386	1	1	yes	characteristic
366	C₂³×D₄	#386	1	1	yes	characteristic
367	C₂³×D₄	#390	1	1	yes	characteristic
368	C₂³×D₄	#390	1	1	yes	characteristic
369	C₂³×D₄	#390	1	1	yes	characteristic
370	C₂³×D₄	#390	1	1	yes	characteristic
371	C₂³×D₄	#390	1	1	yes	characteristic
372	C₂³×D₄	#390	1	1	yes	characteristic
373	C₂³×D₄	#390	1	1	yes	characteristic
374	C₂³×D₄	#390	1	1	yes	characteristic
375	C₂³×D₄	#392	1	1	yes	characteristic
376	C₂³×D₄	#392	1	1	yes	characteristic
377	C₂³×D₄	#394	1	1	yes	characteristic
378	C₂³×D₄	#394	1	1	yes	characteristic
379	C₂³×D₄	C₂×#99	1	4	yes	—
380	C₂³×D₄	C₂×#99	1	2	yes	—
381	C₂³×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
382	C₂³×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
383	C₂³×D₄	C₂×C₄×D₄	1	1	yes	characteristic
384	C₂³×D₄	C₂×C₄×D₄	1	1	yes	characteristic
385	C₂³×D₄	C₂×C₄×D₄	1	1	yes	characteristic
386	C₂³×D₄	C₂×C₄×D₄	1	1	yes	characteristic
387	C₂³×D₄	C₂×#121	1	1	yes	characteristic
388	C₂⁴×C₄	#379	1	1	yes	characteristic
389	C₂⁴×C₄	#379	1	1	yes	characteristic
390	C₂⁴×C₄	#386	1	1	yes	characteristic
391	C₂⁴×C₄	#386	1	1	yes	characteristic
392	C₂⁴×C₄	#386	1	1	yes	characteristic
393	C₂⁴×C₄	#386	1	1	yes	characteristic
394	C₂⁴×C₄	C₂×#99	1	1	yes	characteristic
395	C₂⁴×C₄	C₂×#99	1	1	yes	characteristic
396	C₂⁴×C₄	C₂×#99	1	1	yes	characteristic
397	C₂⁴×C₄	C₂×#99	1	1	yes	characteristic
398	C₂⁴×C₄	C₂×#99	1	1	yes	characteristic
399	C₂⁴×C₄	C₂×#99	1	1	yes	characteristic
400	C₂⁴×C₄	C₂×#99	1	2	yes	—
401	C₂⁴×C₄	C₂×#99	1	1	yes	characteristic
402	C₂⁴×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
403	C₂×#127	#386	1	1	yes	characteristic
404	C₂×#127	#386	1	1	yes	characteristic
405	C₂×#127	#386	1	1	yes	characteristic
406	C₂×#127	#386	1	1	yes	characteristic
407	C₂×#127	#390	1	1	yes	characteristic
408	C₂×#127	#390	1	1	yes	characteristic
409	C₂×#127	#390	1	1	yes	characteristic
410	C₂×#127	#390	1	1	yes	characteristic
411	C₂×#127	#392	1	1	yes	characteristic
412	C₂×#127	#392	1	1	yes	characteristic
413	C₂×#127	#392	1	1	yes	characteristic
414	C₂×#127	#392	1	1	yes	characteristic
415	C₂×#127	#392	1	1	yes	characteristic
416	C₂×#127	#392	1	1	yes	characteristic
417	C₂×#127	#392	1	1	yes	characteristic
418	C₂×#127	#392	1	1	yes	characteristic
419	C₂×#127	#394	1	1	yes	characteristic
420	C₂×#127	#394	1	1	yes	characteristic
421	C₂×#127	#394	1	1	yes	characteristic
422	C₂×#127	#394	1	1	yes	characteristic
423	C₂×#127	#394	1	1	yes	characteristic
424	C₂×#127	#394	1	1	yes	characteristic
425	C₂×#127	#394	1	1	yes	characteristic
426	C₂×#127	#394	1	1	yes	characteristic
427	C₂×#127	B(4,𝔽₂)	1	4	yes	—
428	C₂×#127	B(4,𝔽₂)	1	4	yes	—
429	C₂×#127	C₂×#120	1	1	yes	characteristic
430	C₂×#127	C₂×#121	1	1	yes	characteristic
431	C₂×#127	C₂×#121	1	1	yes	characteristic
432	C₂×#127	C₂×#121	1	1	yes	characteristic
433	C₂×#127	C₂×#121	1	1	yes	characteristic
434	C₂×#127	C₂×#123	1	1	yes	characteristic
435	C₂×#127	C₂×#124	1	1	yes	characteristic
436	C₂×#127	C₂×#127	1	1	yes	characteristic
437	C₂×#124	#386	1	1	yes	characteristic
438	C₂×#124	#386	1	1	yes	characteristic
439	C₂×#124	#386	1	1	yes	characteristic
440	C₂×#124	#386	1	1	yes	characteristic
441	C₂×#124	#390	1	1	yes	characteristic
442	C₂×#124	#390	1	1	yes	characteristic
443	C₂×#124	#390	1	1	yes	characteristic
444	C₂×#124	#390	1	1	yes	characteristic
445	C₂×#124	#392	1	1	yes	characteristic
446	C₂×#124	#392	1	1	yes	characteristic
447	C₂×#124	#392	1	1	yes	characteristic
448	C₂×#124	#392	1	1	yes	characteristic
449	C₂×#124	#392	1	1	yes	characteristic
450	C₂×#124	#392	1	1	yes	characteristic
451	C₂×#124	#392	1	1	yes	characteristic
452	C₂×#124	#392	1	1	yes	characteristic
453	C₂×#124	#394	1	1	yes	characteristic
454	C₂×#124	#394	1	1	yes	characteristic
455	C₂×#124	#394	1	1	yes	characteristic
456	C₂×#124	#394	1	1	yes	characteristic
457	C₂×#124	#394	1	1	yes	characteristic
458	C₂×#124	#394	1	1	yes	characteristic
459	C₂×#124	#394	1	1	yes	characteristic
460	C₂×#124	#394	1	1	yes	characteristic
461	C₂×#124	B(4,𝔽₂)	1	4	yes	—
462	C₂×#124	B(4,𝔽₂)	1	4	yes	—
463	C₂×#124	C₂×#120	1	1	yes	characteristic
464	C₂×#124	C₂×#121	1	1	yes	characteristic
465	C₂×#124	C₂×#121	1	1	yes	characteristic
466	C₂×#124	C₂×#121	1	1	yes	characteristic
467	C₂×#124	C₂×#121	1	1	yes	characteristic
468	C₂×#124	C₂×#123	1	1	yes	characteristic
469	C₂×#124	C₂×#124	1	1	yes	characteristic
470	C₂×#124	C₂×#127	1	1	yes	characteristic
471	C₂×#117	#379	1	1	yes	characteristic
472	C₂×#117	#379	1	1	yes	characteristic
473	C₂×#117	#386	1	1	yes	characteristic
474	C₂×#117	#386	1	1	yes	characteristic
475	C₂×#117	#392	1	1	yes	characteristic
476	C₂×#117	#392	1	1	yes	characteristic
477	C₂×#117	#392	1	1	yes	characteristic
478	C₂×#117	#392	1	1	yes	characteristic
479	C₂×#117	#394	1	1	yes	characteristic
480	C₂×#117	#394	1	1	yes	characteristic
481	C₂×#117	#394	1	1	yes	characteristic
482	C₂×#117	#394	1	1	yes	characteristic
483	C₂×#117	C₂×#99	1	4	yes	—
484	C₂×#117	C₂×#120	1	1	yes	characteristic
485	C₂×#117	C₂×#120	1	1	yes	characteristic
486	C₂×#117	C₂×#121	1	1	yes	characteristic
487	C₂×#117	C₂×#121	1	1	yes	characteristic
488	C₂²×C₄²	#386	1	1	yes	characteristic
489	C₂²×C₄²	#386	1	1	yes	characteristic
490	C₂²×C₄²	#392	1	1	yes	characteristic
491	C₂²×C₄²	#392	1	1	yes	characteristic
492	C₂²×C₄²	#392	1	1	yes	characteristic
493	C₂²×C₄²	#392	1	1	yes	characteristic
494	C₂²×C₄²	#394	1	1	yes	characteristic
495	C₂²×C₄²	#394	1	1	yes	characteristic
496	C₂²×C₄²	#394	1	1	yes	characteristic
497	C₂²×C₄²	#394	1	1	yes	characteristic
498	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
499	C₂²×C₄²	C₂×#123	1	1	yes	characteristic
500	C₂⁵	#1781	1	1	yes	characteristic
501	C₂⁵	#1781	1	1	yes	characteristic
502	C₂⁵	#1898	1	1	yes	characteristic
503	C₂⁵	#1898	1	1	yes	characteristic
504	C₂⁵	#1898	1	1	yes	characteristic
505	C₂⁵	#1898	1	1	yes	characteristic
506	C₂⁵	C₂²×#99	1	1	yes	characteristic
507	C₂²×Q₈	#1438	1	1	yes	characteristic
508	C₂²×Q₈	#1438	1	1	yes	characteristic
509	C₂²×Q₈	#2021	1	2	yes	—
510	C₂²×Q₈	#2021	1	2	yes	—
511	C₂²×Q₈	C₂×#392	1	1	yes	characteristic
512	C₂²×Q₈	C₂×#394	1	1	yes	characteristic
513	C₂²×D₄	#1438	1	1	yes	characteristic
514	C₂²×D₄	#1438	1	1	yes	characteristic
515	C₂²×D₄	#1438	1	1	yes	characteristic
516	C₂²×D₄	#1438	1	1	yes	characteristic
517	C₂²×D₄	#1438	1	1	yes	characteristic
518	C₂²×D₄	#1438	1	1	yes	characteristic
519	C₂²×D₄	#1889	1	2	yes	—
520	C₂²×D₄	#1889	1	2	yes	—
521	C₂²×D₄	#1889	1	2	yes	—
522	C₂²×D₄	#1889	1	2	yes	—
523	C₂²×D₄	#2021	1	2	yes	—
524	C₂²×D₄	#2021	1	2	yes	—
525	C₂²×D₄	C₂×AΣL(1,𝔽₁₆)	1	8	yes	—
526	C₂²×D₄	C₂×#386	1	1	yes	characteristic
527	C₂²×D₄	C₂×#386	1	1	yes	characteristic
528	C₂²×D₄	C₂×#390	1	1	yes	characteristic
529	C₂²×D₄	C₂×#390	1	1	yes	characteristic
530	C₂²×D₄	C₂×#392	1	1	yes	characteristic
531	C₂²×D₄	C₂×#394	1	1	yes	characteristic
532	C₂³×C₄	#1438	1	1	yes	characteristic
533	C₂³×C₄	#1438	1	1	yes	characteristic
534	C₂³×C₄	#1438	1	1	yes	characteristic
535	C₂³×C₄	#1438	1	1	yes	characteristic
536	C₂³×C₄	#1781	1	1	yes	characteristic
537	C₂³×C₄	#1781	1	1	yes	characteristic
538	C₂³×C₄	#1781	1	1	yes	characteristic
539	C₂³×C₄	#1781	1	1	yes	characteristic
540	C₂³×C₄	#1781	1	1	yes	characteristic
541	C₂³×C₄	#1781	1	1	yes	characteristic
542	C₂³×C₄	#1898	1	1	yes	characteristic
543	C₂³×C₄	#1898	1	1	yes	characteristic
544	C₂³×C₄	#1898	1	1	yes	characteristic
545	C₂³×C₄	#1898	1	1	yes	characteristic
546	C₂³×C₄	#1898	1	1	yes	characteristic
547	C₂³×C₄	#1898	1	1	yes	characteristic
548	C₂³×C₄	#1898	1	1	yes	characteristic
549	C₂³×C₄	#1898	1	1	yes	characteristic
550	C₂³×C₄	#1898	1	1	yes	characteristic
551	C₂³×C₄	#1898	1	1	yes	characteristic
552	C₂³×C₄	#1898	1	1	yes	characteristic
553	C₂³×C₄	#1898	1	1	yes	characteristic
554	C₂³×C₄	C₂×AΣL(1,𝔽₁₆)	1	2	yes	—
555	C₂³×C₄	C₂×AΣL(1,𝔽₁₆)	1	2	yes	—
556	C₂³×C₄	#2121	1	2	yes	—
557	C₂³×C₄	#2121	1	2	yes	—
558	C₂³×C₄	C₂×#379	1	1	yes	characteristic
559	C₂³×C₄	C₂×#386	1	1	yes	characteristic
560	C₂³×C₄	C₂×#386	1	1	yes	characteristic
561	C₂³×C₄	C₂²×#99	1	1	yes	characteristic
562	C₂³×C₄	C₂²×#99	1	1	yes	characteristic
563	C₂³×C₄	C₂²×#99	1	1	yes	characteristic
564	#127	#1889	1	4	yes	—
565	#127	#2021	1	4	yes	—
566	#127	#2021	1	4	yes	—
567	#127	C₂×B(4,𝔽₂)	1	4	yes	—
568	#124	#1889	1	4	yes	—
569	#124	#2021	1	4	yes	—
570	#124	#2021	1	4	yes	—
571	#124	C₂×B(4,𝔽₂)	1	4	yes	—
572	C₂×C₄²	#1438	1	1	yes	characteristic
573	C₂×C₄²	#1438	1	1	yes	characteristic
574	C₂×C₄²	#1438	1	1	yes	characteristic
575	C₂×C₄²	#1438	1	1	yes	characteristic
576	C₂×C₄²	#2021	1	2	yes	—
577	C₂×C₄²	#2021	1	2	yes	—
578	C₂×C₄²	#2021	1	2	yes	—
579	C₂×C₄²	#2021	1	2	yes	—
580	C₂×C₄²	C₂×#392	1	1	yes	characteristic
581	C₂×C₄²	C₂×#392	1	1	yes	characteristic
582	C₂×C₄²	C₂×#394	1	1	yes	characteristic
583	C₂×C₄²	C₂×#394	1	1	yes	characteristic
584	C₂⁴	#10965	1	1	yes	characteristic
585	C₂⁴	#10965	1	1	yes	characteristic
586	C₂⁴	#10965	1	1	yes	characteristic
587	C₂⁴	#10965	1	1	yes	characteristic
588	C₂⁴	#12687	1	1	yes	characteristic
589	C₂⁴	#12687	1	1	yes	characteristic
590	C₂⁴	#12690	1	1	yes	characteristic
591	C₂⁴	#12690	1	1	yes	characteristic
592	C₂⁴	C₂×#1781	1	1	yes	characteristic
593	C₂⁴	C₂×#1898	1	1	yes	characteristic
594	C₂⁴	C₂×#1898	1	1	yes	characteristic
595	C₂×Q₈	#10991	1	2	yes	—
596	C₂×Q₈	C₂×#2021	1	2	yes	—
597	C₂×D₄	#10991	1	2	yes	—
598	C₂×D₄	#10991	1	2	yes	—
599	C₂×D₄	#10991	1	2	yes	—
600	C₂×D₄	C₂×#1889	1	2	yes	—
601	C₂×D₄	C₂×#1889	1	2	yes	—
602	C₂×D₄	C₂×#2021	1	2	yes	—
603	C₂²×C₄	#10965	1	1	yes	characteristic
604	C₂²×C₄	#10965	1	1	yes	characteristic
605	C₂²×C₄	#10965	1	1	yes	characteristic
606	C₂²×C₄	#10965	1	1	yes	characteristic
607	C₂²×C₄	#10991	1	1	yes	characteristic
608	C₂²×C₄	#10991	1	1	yes	characteristic
609	C₂²×C₄	#10991	1	1	yes	characteristic
610	C₂²×C₄	#10991	1	1	yes	characteristic
611	C₂²×C₄	#12687	1	2	yes	—
612	C₂²×C₄	#12690	1	2	yes	—
613	C₂²×C₄	#12705	1	2	yes	—
614	C₂²×C₄	#12705	1	2	yes	—
615	C₂²×C₄	#13082	1	2	yes	—
616	C₂²×C₄	#13082	1	2	yes	—
617	C₂²×C₄	#13082	1	2	yes	—
618	C₂²×C₄	#13082	1	2	yes	—
619	C₂²×C₄	#13086	1	2	yes	—
620	C₂²×C₄	#13086	1	2	yes	—
621	C₂²×C₄	#13086	1	2	yes	—
622	C₂²×C₄	#13086	1	2	yes	—
623	C₂²×C₄	C₂×#1438	1	1	yes	characteristic
624	C₂²×C₄	C₂×#1781	1	1	yes	characteristic
625	C₂²×C₄	C₂×#1898	1	1	yes	characteristic
626	C₂²×C₄	C₂×#1898	1	1	yes	characteristic
627	C₂²×C₄	C₂²×AΣL(1,𝔽₁₆)	1	2	yes	—
628	C₂²×C₄	C₂×#2121	1	2	yes	—
629	C₄²	#10991	1	2	yes	—
630	C₄²	#10991	1	2	yes	—
631	C₄²	C₂×#2021	1	2	yes	—
632	C₄²	C₂×#2021	1	2	yes	—
633	C₂³	#115690	1	1	yes	characteristic
634	C₂³	#115690	1	1	yes	characteristic
635	C₂³	#147555	1	1	yes	characteristic
636	C₂³	#147555	1	1	yes	characteristic
637	C₂³	#147555	1	1	yes	characteristic
638	C₂³	#147555	1	1	yes	characteristic
639	C₂³	#147567	1	1	yes	characteristic
640	C₂³	#147567	1	1	yes	characteristic
641	C₂³	C₂×#10965	1	1	yes	characteristic
642	C₂³	C₂×#12687	1	1	yes	characteristic
643	C₂³	C₂×#12690	1	1	yes	characteristic
644	C₂×C₄	#115690	1	1	yes	characteristic
645	C₂×C₄	#115690	1	1	yes	characteristic
646	C₂×C₄	#147555	1	2	yes	—
647	C₂×C₄	#147555	1	2	yes	—
648	C₂×C₄	#147567	1	2	yes	—
649	C₂×C₄	C₂×#10991	1	1	yes	characteristic
650	C₂×C₄	C₂×#10991	1	1	yes	characteristic
651	C₂×C₄	C₂×#12705	1	2	yes	—
652	C₂×C₄	C₂×#13082	1	2	yes	—
653	C₂×C₄	C₂×#13086	1	2	yes	—
654	C₂²	#72213256	1	1	yes	characteristic
655	C₂²	#72213256	1	1	yes	characteristic
656	C₂²	#72213256	1	1	yes	characteristic
657	C₂²	#72213256	1	1	yes	characteristic
658	C₂²	C₂×#115690	1	1	yes	characteristic
659	C₂²	C₂×#147555	1	1	yes	characteristic
660	C₂²	C₂×#147567	1	1	yes	characteristic
661	C₂	#72216684	1	2	yes	direct product factor
662	C₂	C₂×#72213256	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#72213256
commutator	C₂⁴×D₄	C₂³×C₄
Frattini, cosocle	C₂²×#535	C₂⁴
prime radical	C₂×#72210511	C₂
LCS	G ▷ C₂⁴×D₄ ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ C₂⁵×C₄ ◁ C₂³×#3484 ◁ G
LECS	G ▷ C₂²×#535 ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂×#72213436	C₂	semidirect
2. C₂×#72216567	C₂	semidirect
3. C₂×#72215737	C₂	semidirect
4. C₂×#72213443	C₂	semidirect
5. C₂×#72213738	C₂	semidirect
7. C₂×#392113	C₄	semidirect
8. C₂×#6437445	C₄	semidirect
10. C₂×#72214353	C₂	semidirect
13. C₂×#359509	C₄	semidirect
18. C₂×#7630939	C₄	semidirect
19. #72216684	C₂	direct (N × H)
20. #72216567	C₂²	semidirect
21. #72215737	C₂²	semidirect
22. #72214353	C₂²	semidirect
23. #72213738	C₂²	semidirect
24. #72213443	C₂²	semidirect
25. #72213436	C₂²	semidirect
26. #72210511	C₄	semidirect
42. #7630939	C₂×C₄	semidirect
44. C₂²×#2134	D₄	semidirect
45. C₂²×#2128	D₄	semidirect
47. #6437445	C₂×C₄	semidirect
55. C₂×#17741	D₄	semidirect
56. C₂×#17666	D₄	semidirect
57. #493385	D₄	semidirect
59. #493372	D₄	semidirect
61. #392113	C₂×C₄	semidirect
63. #359509	C₂×C₄	semidirect
69. #187811	D₄	semidirect
70. #187811	D₄	semidirect
134. C₂×#2134	C₂×D₄	semidirect
135. C₂×#2128	C₂×D₄	semidirect
144. #17741	C₂×D₄	semidirect
145. #17666	C₂×D₄	semidirect
661. C₂	#72216684	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×#72213436	2
C₂×#72216567	2
C₂×#72215737	2
C₂×#72213443	2
C₂×#72213738	2
C₂×#72210511	2
C₂×#72214353	2
#72216684	2

Subgroups — C2×#72216684 #72256446

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#72216684 #72256446