Subgroups — #72338252

Order 2048.

At least 6070 conjugacy classes of subgroups; only the 1108 normal subgroups are shown.

The subgroup lattice has 659 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72338238	C₂	1	1	yes	maximal, characteristic, complemented
2	#72338237	C₂	1	1	yes	maximal, characteristic, complemented
3	#72338232	C₂	1	1	yes	maximal, characteristic, complemented
4	#72338228	C₂	1	1	yes	maximal, characteristic, complemented
5	#72338226	C₂	1	1	yes	maximal, characteristic, complemented
6	#72338212	C₂	1	1	yes	maximal, characteristic, complemented
7	#72337486	C₂	1	1	yes	maximal, characteristic, complemented
8	#72316822	C₂	1	1	yes	maximal, characteristic, complemented
9	#72316741	C₂	1	1	yes	maximal, characteristic, complemented
10	#72282687	C₂	1	1	yes	maximal, characteristic, complemented
11	#72279460	C₂	1	1	yes	maximal, characteristic
12	#72257771	C₂	1	1	yes	maximal, characteristic, complemented
13	#72257440	C₂	1	1	yes	maximal, characteristic, complemented
14	#72240820	C₂	1	1	yes	maximal, characteristic, complemented
15	#72214607	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#3498	C₂²	1	1	yes	characteristic
17	C₂×#60803	C₂²	1	1	yes	characteristic
18	C₂²×#3151	C₂²	1	1	yes	characteristic
19	C₂×#60232	C₂²	1	1	yes	characteristic
20	#7628578	C₂²	1	1	yes	characteristic
21	#7625999	C₂²	1	1	yes	characteristic
22	#6516758	C₄	1	4	yes	complemented
23	#6516757	C₄	1	4	yes	complemented
24	#6374304	C₂²	1	1	yes	characteristic
25	#6374304	C₂²	1	1	yes	characteristic
26	#6374304	C₂²	1	1	yes	characteristic
27	#6374304	C₂²	1	1	yes	characteristic
28	#6372442	C₂²	1	1	yes	characteristic
29	#6372358	C₂²	1	1	yes	characteristic
30	#6370997	C₂²	1	1	yes	characteristic
31	#6370978	C₂²	1	1	yes	characteristic
32	#6370978	C₂²	1	1	yes	characteristic
33	#6344036	C₂²	1	1	yes	characteristic
34	C₂×#17741	C₂²	1	1	yes	characteristic
35	#6343377	C₂²	1	1	yes	characteristic
36	#6343377	C₂²	1	1	yes	characteristic, complemented
37	#6343377	C₂²	1	1	yes	characteristic, complemented
38	#6343377	C₂²	1	1	yes	characteristic, complemented
39	#6343016	C₂²	1	1	yes	characteristic, complemented
40	#6342924	C₂²	1	1	yes	characteristic
41	#353804	C₂²	1	1	yes	characteristic, complemented
42	#353776	C₂²	1	1	yes	characteristic, complemented
43	#181375	C₂²	1	1	yes	characteristic, complemented
44	#181339	C₂²	1	1	yes	characteristic, complemented
45	#181222	C₂²	1	1	yes	characteristic, complemented
46	#181220	C₂²	1	1	yes	characteristic, complemented
47	#181220	C₂²	1	1	yes	characteristic, complemented
48	#181197	C₂²	1	1	yes	characteristic, complemented
49	#181124	C₂²	1	1	yes	characteristic, complemented
50	#181055	C₂²	1	1	yes	characteristic, complemented
51	#180880	C₂²	1	1	yes	characteristic, complemented
52	#180871	C₂²	1	1	yes	characteristic, complemented
53	C₂×#3498	C₂×C₄	1	4	yes	—
54	C₂×#3498	D₄	1	4	yes	—
55	C₂²×#550	D₄	1	2	yes	—
56	C₂²×D₄²	D₄	1	2	yes	—
57	C₂²×#532	C₂³	1	1	yes	characteristic
58	C₂²×#532	C₂³	1	1	yes	characteristic
59	C₂³×#127	C₂³	1	1	yes	characteristic
60	C₂²×C₄×#41	C₂³	1	1	yes	characteristic
61	C₂×#3207	D₄	1	4	yes	—
62	C₂×#3206	C₂×C₄	1	2	yes	—
63	C₂×#3205	C₂×C₄	1	2	yes	—
64	C₂×#3151	D₄	1	2	yes	—
65	C₂²×#493	C₂×C₄	1	2	yes	complemented
66	C₂²×#492	C₂×C₄	1	2	yes	complemented
67	C₂×#3141	D₄	1	2	yes	—
68	C₂×#2981	D₄	1	4	yes	complemented
69	C₂×#2920	C₂³	1	1	yes	characteristic
70	C₂×#2920	C₂³	1	1	yes	characteristic
71	C₂×#2920	C₂³	1	1	yes	characteristic
72	C₂×#2920	C₂³	1	1	yes	characteristic
73	C₂×#2920	C₂³	1	1	yes	characteristic
74	C₂×#2920	C₂³	1	1	yes	characteristic
75	C₂²×C₄×M₁₆	C₂³	1	1	yes	characteristic
76	#35279	C₂×C₄	1	2	yes	complemented
77	#35272	C₂×C₄	1	2	yes	complemented
78	#34369	D₄	1	4	yes	complemented
79	#34012	C₂³	1	1	yes	characteristic
80	#34012	C₂³	1	1	yes	characteristic
81	#34012	C₂³	1	1	yes	characteristic
82	#34012	C₂³	1	1	yes	characteristic
83	#21803	C₂×C₄	1	4	yes	complemented
84	#21803	D₄	1	4	yes	complemented
85	#21803	D₄	1	4	yes	complemented
86	#21408	D₄	1	4	yes	—
87	#21401	C₂×C₄	1	4	yes	—
88	#21373	C₂×C₄	1	4	yes	complemented
89	#20973	D₄	1	4	yes	—
90	#20701	D₄	1	2	yes	—
91	#20600	D₄	1	2	yes	—
92	C₄×#419	D₄	1	2	yes	—
93	C₄×#418	D₄	1	2	yes	—
94	#17744	D₄	1	4	yes	complemented
95	#17544	D₄	1	4	yes	complemented
96	C₂³×#41	C₂×D₄	1	1	yes	characteristic
97	C₂³×M₁₆	C₂×D₄	1	2	yes	—
98	C₂×#550	C₂²⋊C₄	1	8	yes	—
99	C₂×D₄²	C₂²⋊C₄	1	8	yes	—
100	C₂×#532	C₂²×C₄	1	2	yes	—
101	C₂×#532	C₂×D₄	1	2	yes	—
102	C₂×#532	C₂×D₄	1	2	yes	—
103	C₂×#532	C₂×D₄	1	2	yes	—
104	C₂×#532	C₂×D₄	1	2	yes	—
105	C₂×#532	C₂×D₄	1	2	yes	—
106	C₂×#532	C₂×D₄	1	2	yes	—
107	C₂×#532	C₂×D₄	1	2	yes	—
108	C₂×#532	C₂×D₄	1	2	yes	—
109	C₂×#532	C₂×D₄	1	2	yes	—
110	C₂×#532	#41	1	2	yes	—
111	C₂×#532	#41	1	2	yes	—
112	C₂×#532	#41	1	2	yes	—
113	C₂×#532	#41	1	2	yes	—
114	C₂²×C₄⋊Q₈	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic
116	C₂²×#127	C₂²×C₄	1	1	yes	characteristic
117	C₂²×#127	C₂²×C₄	1	2	yes	—
118	C₂²×#127	C₂×D₄	1	2	yes	—
119	C₂²×#127	C₂×D₄	1	2	yes	—
120	C₂²×#127	C₂×D₄	1	2	yes	—
121	C₂²×#127	C₂×D₄	1	2	yes	—
122	C₂²×#127	C₂×D₄	1	1	yes	characteristic
123	C₂²×#127	#41	1	2	yes	—
124	C₂²×#127	#41	1	2	yes	—
125	C₂²×#121	C₂×D₄	1	2	yes	—
126	C₂×C₄×#41	C₂²×C₄	1	2	yes	—
127	C₂×C₄×#41	C₂×D₄	1	2	yes	—
128	C₂×C₄×#41	#41	1	2	yes	—
129	C₂×C₄×#41	#41	1	2	yes	—
130	C₂²×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
135	C₂²×#117	C₂×D₄	1	1	yes	characteristic
136	C₂³×C₄²	C₂⁴	1	1	yes	characteristic
137	C₂×#493	C₂²⋊C₄	1	4	yes	—
138	C₂×#492	C₂²⋊C₄	1	4	yes	—
139	C₂×#487	C₂²⋊C₄	1	4	yes	—
140	C₂×#486	C₂²⋊C₄	1	4	yes	—
141	#2920	C₂×D₄	1	2	yes	—
142	#2920	C₂×D₄	1	2	yes	—
143	C₂×#432	C₂×D₄	1	2	yes	—
144	C₂×#432	C₂×D₄	1	2	yes	—
145	C₂×#431	C₂²×C₄	1	2	yes	—
146	C₂×#431	C₂×D₄	1	2	yes	—
147	C₂×#431	C₂×D₄	1	2	yes	—
148	C₂×#431	C₂×D₄	1	2	yes	—
149	C₂×#431	C₂×D₄	1	2	yes	—
150	C₂×#407	C₂×D₄	1	2	yes	—
151	C₂×C₄×M₁₆	C₂×D₄	1	2	yes	—
152	C₂×C₄×M₁₆	C₂×D₄	1	2	yes	—
153	C₂²×#97	C₂×D₄	1	2	yes	—
154	C₂²×C₄×C₈	C₂²×C₄	1	2	yes	—
155	#2285	C₂²×C₄	1	2	yes	—
156	#2285	C₂×D₄	1	2	yes	—
157	#2285	C₂×D₄	1	2	yes	—
158	#2283	C₂×D₄	1	2	yes	—
159	#2283	C₂×D₄	1	2	yes	—
160	#2283	C₂×D₄	1	2	yes	—
161	#2280	C₂×D₄	1	2	yes	—
162	#2280	C₂×D₄	1	2	yes	—
163	C₄×#117	C₂×D₄	1	2	yes	—
164	C₄×#117	C₂×D₄	1	2	yes	—
165	#1893	C₂²⋊C₄	1	16	yes	—
166	C₂²×#41	C₄×D₄	1	2	yes	—
167	C₂²×#41	#121	1	2	yes	—
168	C₂³×Q₈	#120	1	1	yes	characteristic
169	C₂³×D₄	#120	1	1	yes	characteristic
170	C₂³×D₄	#120	1	2	yes	—
171	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
172	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
173	C₂⁴×C₄	H(5,𝔽₂)	1	1	yes	characteristic
174	C₂³×C₈	C₂×C₂²⋊C₄	1	4	yes	—
175	#532	C₄×D₄	1	4	yes	—
176	#532	C₄×D₄	1	4	yes	—
177	#532	C₄×D₄	1	4	yes	—
178	#532	C₄×D₄	1	4	yes	—
179	#532	#120	1	4	yes	—
180	#532	#120	1	4	yes	—
181	#532	#121	1	4	yes	—
182	#532	#121	1	4	yes	—
183	#532	#121	1	4	yes	—
184	#532	#121	1	4	yes	—
185	#532	#121	1	4	yes	—
186	#532	#121	1	4	yes	—
187	#532	#123	1	4	yes	—
188	#532	#123	1	4	yes	—
189	#532	#124	1	4	yes	—
190	#532	#127	1	4	yes	—
191	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	2	yes	—
192	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	2	yes	—
193	C₂×C₄⋊Q₈	#120	1	2	yes	—
194	C₂×C₄⋊Q₈	#120	1	2	yes	—
195	C₂×C₄⋊Q₈	#121	1	2	yes	—
196	C₂×C₄⋊Q₈	#121	1	2	yes	—
197	C₂×C₄⋊Q₈	#123	1	2	yes	—
198	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
199	C₂×#127	C₂×C₂²⋊C₄	1	4	yes	—
200	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
201	C₂×#127	C₄×D₄	1	4	yes	—
202	C₂×#127	C₄×D₄	1	4	yes	—
203	C₂×#127	#120	1	4	yes	—
204	C₂×#127	#120	1	2	yes	—
205	C₂×#127	#120	1	2	yes	—
206	C₂×#127	#121	1	4	yes	—
207	C₂×#127	#121	1	4	yes	—
208	C₂×#127	#121	1	2	yes	—
209	C₂×#127	#121	1	2	yes	—
210	C₂×#127	#123	1	4	yes	—
211	C₂×#127	#123	1	2	yes	—
212	C₂×#121	C₂×C₂²⋊C₄	1	4	yes	—
213	C₂×#121	#120	1	4	yes	—
214	C₂×#121	#121	1	4	yes	—
215	C₂×#121	#121	1	4	yes	—
216	C₂×#121	#124	1	4	yes	—
217	C₂×#121	#127	1	4	yes	—
218	C₂×C₄×Q₈	C₂×C₂²⋊C₄	1	2	yes	—
219	C₂×C₄×Q₈	C₄×D₄	1	2	yes	—
220	C₂×C₄×Q₈	#121	1	2	yes	—
221	C₂×C₄×Q₈	#123	1	2	yes	—
222	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	4	yes	—
223	C₂×C₄×D₄	C₂×C₂²⋊C₄	1	2	yes	—
224	C₂×C₄×D₄	C₄×D₄	1	2	yes	—
225	C₂×C₄×D₄	#120	1	4	yes	—
226	C₂×C₄×D₄	#120	1	4	yes	—
227	C₂×C₄×D₄	#121	1	2	yes	—
228	C₂×C₄×D₄	#121	1	4	yes	—
229	C₂×C₄×D₄	#121	1	4	yes	—
230	C₂×C₄×D₄	#123	1	2	yes	—
231	C₂×C₄×D₄	#123	1	4	yes	—
232	C₂×#117	C₄×D₄	1	2	yes	—
233	C₂×#117	#121	1	2	yes	—
234	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
235	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
236	C₂²×C₄⋊C₄	#120	1	2	yes	—
237	C₂²×C₄²	C₂³×C₄	1	1	yes	characteristic
238	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
239	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
240	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
241	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
242	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
243	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
244	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
245	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
246	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
247	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
248	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
249	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
250	C₂²×C₄²	C₂×#41	1	1	yes	characteristic
251	C₂²×C₄²	C₂×#41	1	1	yes	characteristic
252	C₂²×C₄²	C₂×#41	1	1	yes	characteristic
253	C₂²×C₄²	C₂×#41	1	1	yes	characteristic
254	C₂²×C₄²	C₂×#41	1	1	yes	characteristic
255	C₂²×C₄²	C₂×#41	1	1	yes	characteristic
256	C₂²×C₄²	C₂×#41	1	1	yes	characteristic
257	C₂²×C₄²	C₂×#41	1	1	yes	characteristic
258	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
259	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
260	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
261	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
262	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
263	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
264	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
265	C₂×C₂²⋊C₈	#120	1	4	yes	—
266	C₂×C₄×C₈	C₂×C₂²⋊C₄	1	4	yes	—
267	C₂×C₄×C₈	#120	1	4	yes	—
268	#380	C₂×C₂²⋊C₄	1	4	yes	—
269	#380	#120	1	4	yes	—
270	C₄×C₄⋊C₄	#120	1	4	yes	—
271	C₂⁵	D₄²	1	1	yes	characteristic
272	C₂²×Q₈	#386	1	2	yes	—
273	C₂²×D₄	#379	1	4	yes	—
274	C₂²×D₄	#386	1	2	yes	—
275	C₂²×D₄	#392	1	4	yes	—
276	C₂²×D₄	#394	1	4	yes	—
277	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
278	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
279	C₂³×C₄	#518	1	1	yes	characteristic
280	C₂³×C₄	C₂×#120	1	1	yes	characteristic
281	C₂³×C₄	C₂×#120	1	1	yes	characteristic
282	C₂³×C₄	C₂×#120	1	1	yes	characteristic
283	C₂³×C₄	C₂×#120	1	1	yes	characteristic
284	C₂³×C₄	C₂×#120	1	1	yes	characteristic
285	C₂³×C₄	C₂×#121	1	1	yes	characteristic
286	C₂³×C₄	C₂×#121	1	1	yes	characteristic
287	C₂³×C₄	C₂×#121	1	1	yes	characteristic
288	C₂³×C₄	#525	1	1	yes	characteristic
289	C₂³×C₄	#525	1	1	yes	characteristic
290	C₂³×C₄	C₂×#124	1	1	yes	characteristic
291	C₂³×C₄	C₂×#127	1	1	yes	characteristic
292	C₂³×C₄	#534	1	1	yes	characteristic
293	C₂³×C₄	#534	1	1	yes	characteristic
294	C₂³×C₄	#534	1	1	yes	characteristic
295	C₂³×C₄	#535	1	1	yes	characteristic
296	C₂³×C₄	#538	1	1	yes	characteristic
297	C₂³×C₄	#538	1	1	yes	characteristic
298	C₂³×C₄	D₄²	1	1	yes	characteristic
299	C₂³×C₄	D₄²	1	1	yes	characteristic
300	C₂³×C₄	D₄²	1	1	yes	characteristic
301	C₂³×C₄	D₄²	1	1	yes	characteristic
302	C₂³×C₄	D₄²	1	1	yes	characteristic
303	C₂³×C₄	D₄²	1	1	yes	characteristic
304	C₂³×C₄	D₄²	1	1	yes	characteristic
305	C₂³×C₄	D₄²	1	1	yes	characteristic
306	C₂³×C₄	D₄²	1	1	yes	characteristic
307	C₂³×C₄	D₄²	1	1	yes	characteristic
308	C₂³×C₄	#546	1	1	yes	characteristic
309	C₂³×C₄	#546	1	1	yes	characteristic
310	C₂³×C₄	#546	1	1	yes	characteristic
311	C₂³×C₄	#546	1	1	yes	characteristic
312	C₂³×C₄	#546	1	1	yes	characteristic
313	C₂³×C₄	#546	1	1	yes	characteristic
314	C₂³×C₄	#546	1	1	yes	characteristic
315	C₂³×C₄	#546	1	1	yes	characteristic
316	C₂³×C₄	#546	1	1	yes	characteristic
317	C₂³×C₄	#546	1	1	yes	characteristic
318	C₂³×C₄	#551	1	1	yes	characteristic
319	C₄⋊Q₈	#386	1	4	yes	—
320	C₄⋊Q₈	#386	1	4	yes	—
321	C₄⋊Q₈	#392	1	4	yes	—
322	C₄⋊Q₈	#394	1	4	yes	—
323	#127	#386	1	8	yes	—
324	#127	#386	1	4	yes	—
325	#127	#386	1	4	yes	—
326	#127	#392	1	4	yes	—
327	#127	#394	1	4	yes	—
328	#121	#390	1	8	yes	—
329	#121	#390	1	8	yes	—
330	#121	#392	1	8	yes	—
331	#121	#394	1	8	yes	—
332	C₄×D₄	#386	1	8	yes	—
333	C₄×D₄	#386	1	8	yes	—
334	C₄×D₄	#392	1	8	yes	—
335	C₄×D₄	#394	1	8	yes	—
336	C₂×C₄⋊C₄	#379	1	4	yes	—
337	C₂×C₄⋊C₄	#386	1	2	yes	—
338	C₂×C₄⋊C₄	#386	1	2	yes	—
339	C₂×C₄⋊C₄	#392	1	4	yes	—
340	C₂×C₄⋊C₄	#394	1	4	yes	—
341	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
342	C₂×C₄²	C₂²×C₂²⋊C₄	1	1	yes	characteristic
343	C₂×C₄²	C₂×C₄×D₄	1	1	yes	characteristic
344	C₂×C₄²	C₂×C₄×D₄	1	1	yes	characteristic
345	C₂×C₄²	C₂×C₄×D₄	1	1	yes	characteristic
346	C₂×C₄²	C₂×C₄×D₄	1	1	yes	characteristic
347	C₂×C₄²	C₂×C₄×D₄	1	1	yes	characteristic
348	C₂×C₄²	C₂×C₄×D₄	1	1	yes	characteristic
349	C₂×C₄²	C₂×C₄×D₄	1	1	yes	characteristic
350	C₂×C₄²	#518	1	1	yes	characteristic
351	C₂×C₄²	#518	1	1	yes	characteristic
352	C₂×C₄²	#518	1	1	yes	characteristic
353	C₂×C₄²	C₂×#120	1	1	yes	characteristic
354	C₂×C₄²	C₂×#120	1	1	yes	characteristic
355	C₂×C₄²	C₂×#120	1	1	yes	characteristic
356	C₂×C₄²	C₂×#120	1	1	yes	characteristic
357	C₂×C₄²	C₂×#120	1	1	yes	characteristic
358	C₂×C₄²	C₂×#120	1	1	yes	characteristic
359	C₂×C₄²	C₂×#120	1	1	yes	characteristic
360	C₂×C₄²	C₂×#120	1	1	yes	characteristic
361	C₂×C₄²	C₂×#120	1	1	yes	characteristic
362	C₂×C₄²	C₂×#121	1	1	yes	characteristic
363	C₂×C₄²	C₂×#121	1	1	yes	characteristic
364	C₂×C₄²	C₂×#121	1	1	yes	characteristic
365	C₂×C₄²	C₂×#121	1	1	yes	characteristic
366	C₂×C₄²	C₂×#121	1	1	yes	characteristic
367	C₂×C₄²	C₂×#121	1	1	yes	characteristic
368	C₂×C₄²	C₂×#121	1	1	yes	characteristic
369	C₂×C₄²	C₂×#121	1	1	yes	characteristic
370	C₂×C₄²	C₂×#121	1	1	yes	characteristic
371	C₂×C₄²	C₂×#121	1	1	yes	characteristic
372	C₂×C₄²	C₂×#121	1	1	yes	characteristic
373	C₂×C₄²	C₂×#121	1	1	yes	characteristic
374	C₂×C₄²	C₂×#121	1	1	yes	characteristic
375	C₂×C₄²	C₂×#123	1	1	yes	characteristic
376	C₂×C₄²	C₂×#123	1	1	yes	characteristic
377	C₂×C₄²	C₂×#123	1	1	yes	characteristic
378	C₂×C₄²	C₂×#123	1	1	yes	characteristic
379	C₂×C₄²	C₂×#123	1	1	yes	characteristic
380	C₂×C₄²	C₂×#123	1	1	yes	characteristic
381	C₂×C₄²	#525	1	1	yes	characteristic
382	C₂×C₄²	#525	1	1	yes	characteristic
383	C₂×C₄²	#525	1	1	yes	characteristic
384	C₂×C₄²	#525	1	1	yes	characteristic
385	C₂×C₄²	#525	1	1	yes	characteristic
386	C₂×C₄²	#525	1	1	yes	characteristic
387	C₂×C₄²	#525	1	1	yes	characteristic
388	C₂×C₄²	#525	1	1	yes	characteristic
389	C₂×C₄²	#525	1	1	yes	characteristic
390	C₂×C₄²	#525	1	1	yes	characteristic
391	C₂×C₄²	C₂×#124	1	1	yes	characteristic
392	C₂×C₄²	C₂×#127	1	1	yes	characteristic
393	C₂×C₄²	#534	1	1	yes	characteristic
394	C₂×C₄²	#534	1	1	yes	characteristic
395	C₂×C₄²	#534	1	1	yes	characteristic
396	C₂×C₄²	#534	1	1	yes	characteristic
397	C₂×C₄²	#534	1	1	yes	characteristic
398	C₂×C₄²	#534	1	1	yes	characteristic
399	C₂×C₄²	#534	1	1	yes	characteristic
400	C₂×C₄²	#534	1	1	yes	characteristic
401	C₂×C₄²	#534	1	1	yes	characteristic
402	C₂×C₄²	#535	1	1	yes	characteristic
403	C₂×C₄²	#535	1	1	yes	characteristic
404	C₂×C₄²	#535	1	1	yes	characteristic
405	C₂×C₄²	#538	1	1	yes	characteristic
406	C₂×C₄²	#538	1	1	yes	characteristic
407	C₂×C₄²	#538	1	1	yes	characteristic
408	C₂×C₄²	#538	1	1	yes	characteristic
409	C₂×C₄²	#538	1	1	yes	characteristic
410	C₂×C₄²	#538	1	1	yes	characteristic
411	C₂×C₄²	D₄²	1	1	yes	characteristic
412	C₂×C₄²	D₄²	1	1	yes	characteristic
413	C₂×C₄²	D₄²	1	1	yes	characteristic
414	C₂×C₄²	D₄²	1	1	yes	characteristic
415	C₂×C₄²	D₄²	1	1	yes	characteristic
416	C₂×C₄²	D₄²	1	1	yes	characteristic
417	C₂×C₄²	D₄²	1	1	yes	characteristic
418	C₂×C₄²	D₄²	1	1	yes	characteristic
419	C₂×C₄²	D₄²	1	1	yes	characteristic
420	C₂×C₄²	D₄²	1	1	yes	characteristic
421	C₂×C₄²	D₄²	1	1	yes	characteristic
422	C₂×C₄²	D₄²	1	1	yes	characteristic
423	C₂×C₄²	D₄²	1	1	yes	characteristic
424	C₂×C₄²	#546	1	1	yes	characteristic
425	C₂×C₄²	#546	1	1	yes	characteristic
426	C₂×C₄²	#546	1	1	yes	characteristic
427	C₂×C₄²	#546	1	1	yes	characteristic
428	C₂×C₄²	#546	1	1	yes	characteristic
429	C₂×C₄²	#546	1	1	yes	characteristic
430	C₂×C₄²	#546	1	1	yes	characteristic
431	C₂×C₄²	#546	1	1	yes	characteristic
432	C₂×C₄²	#546	1	1	yes	characteristic
433	C₂×C₄²	#546	1	1	yes	characteristic
434	C₂×C₄²	#546	1	1	yes	characteristic
435	C₂×C₄²	#546	1	1	yes	characteristic
436	C₂×C₄²	#546	1	1	yes	characteristic
437	C₂×C₄²	#546	1	1	yes	characteristic
438	C₂×C₄²	#546	1	1	yes	characteristic
439	C₂×C₄²	#546	1	1	yes	characteristic
440	C₂×C₄²	#546	1	1	yes	characteristic
441	C₂×C₄²	#546	1	1	yes	characteristic
442	C₂×C₄²	#546	1	1	yes	characteristic
443	C₂×C₄²	#546	1	1	yes	characteristic
444	C₂×C₄²	#546	1	1	yes	characteristic
445	C₂×C₄²	#546	1	1	yes	characteristic
446	C₂×C₄²	#551	1	1	yes	characteristic
447	C₂×C₄²	#551	1	1	yes	characteristic
448	C₂×C₄²	#551	1	1	yes	characteristic
449	C₂×C₄²	#551	1	1	yes	characteristic
450	C₂×C₄²	#551	1	1	yes	characteristic
451	C₂×C₄²	#551	1	1	yes	characteristic
452	C₂×C₄²	#551	1	1	yes	characteristic
453	C₂⁴	D₄×C₂²⋊C₄	1	1	yes	characteristic
454	C₂⁴	#2403	1	1	yes	characteristic
455	C₂⁴	#2410	1	1	yes	characteristic
456	C₂⁴	#2410	1	1	yes	characteristic
457	C₂⁴	#2424	1	1	yes	characteristic
458	C₂⁴	#2433	1	1	yes	characteristic
459	C₂⁴	#2472	1	1	yes	characteristic
460	C₂×Q₈	#1904	1	4	yes	—
461	C₂×D₄	#1438	1	8	yes	—
462	C₂×D₄	#1904	1	4	yes	—
463	C₂²×C₄	C₂×#379	1	1	yes	characteristic
464	C₂²×C₄	C₂×#386	1	1	yes	characteristic
465	C₂²×C₄	C₂×#390	1	1	yes	characteristic
466	C₂²×C₄	C₂×#390	1	1	yes	characteristic
467	C₂²×C₄	C₄×#120	1	1	yes	characteristic
468	C₂²×C₄	C₄×#120	1	1	yes	characteristic
469	C₂²×C₄	#2308	1	1	yes	characteristic
470	C₂²×C₄	#2321	1	1	yes	characteristic
471	C₂²×C₄	#2321	1	1	yes	characteristic
472	C₂²×C₄	D₄×C₂²⋊C₄	1	1	yes	characteristic
473	C₂²×C₄	D₄×C₂²⋊C₄	1	1	yes	characteristic
474	C₂²×C₄	D₄×C₂²⋊C₄	1	1	yes	characteristic
475	C₂²×C₄	D₄×C₂²⋊C₄	1	1	yes	characteristic
476	C₂²×C₄	D₄×C₂²⋊C₄	1	1	yes	characteristic
477	C₂²×C₄	#2358	1	1	yes	characteristic
478	C₂²×C₄	#2358	1	1	yes	characteristic
479	C₂²×C₄	#2358	1	1	yes	characteristic
480	C₂²×C₄	#2358	1	1	yes	characteristic
481	C₂²×C₄	C₂×#392	1	1	yes	characteristic
482	C₂²×C₄	C₂×#392	1	1	yes	characteristic
483	C₂²×C₄	C₂×#394	1	1	yes	characteristic
484	C₂²×C₄	C₂×#394	1	1	yes	characteristic
485	C₂²×C₄	#2403	1	1	yes	characteristic
486	C₂²×C₄	#2403	1	1	yes	characteristic
487	C₂²×C₄	#2403	1	1	yes	characteristic
488	C₂²×C₄	#2403	1	1	yes	characteristic
489	C₂²×C₄	#2403	1	1	yes	characteristic
490	C₂²×C₄	#2404	1	1	yes	characteristic
491	C₂²×C₄	#2405	1	1	yes	characteristic
492	C₂²×C₄	#2405	1	1	yes	characteristic
493	C₂²×C₄	#2405	1	1	yes	characteristic
494	C₂²×C₄	#2408	1	1	yes	characteristic
495	C₂²×C₄	#2408	1	1	yes	characteristic
496	C₂²×C₄	#2408	1	1	yes	characteristic
497	C₂²×C₄	#2410	1	1	yes	characteristic
498	C₂²×C₄	#2410	1	1	yes	characteristic
499	C₂²×C₄	#2410	1	1	yes	characteristic
500	C₂²×C₄	#2410	1	1	yes	characteristic
501	C₂²×C₄	#2410	1	1	yes	characteristic
502	C₂²×C₄	#2410	1	1	yes	characteristic
503	C₂²×C₄	#2410	1	1	yes	characteristic
504	C₂²×C₄	#2410	1	1	yes	characteristic
505	C₂²×C₄	#2410	1	1	yes	characteristic
506	C₂²×C₄	#2410	1	1	yes	characteristic
507	C₂²×C₄	#2410	1	1	yes	characteristic
508	C₂²×C₄	#2410	1	1	yes	characteristic
509	C₂²×C₄	#2411	1	1	yes	characteristic
510	C₂²×C₄	#2411	1	1	yes	characteristic
511	C₂²×C₄	#2411	1	1	yes	characteristic
512	C₂²×C₄	#2412	1	1	yes	characteristic
513	C₂²×C₄	#2412	1	1	yes	characteristic
514	C₂²×C₄	#2412	1	1	yes	characteristic
515	C₂²×C₄	#2418	1	1	yes	characteristic
516	C₂²×C₄	#2418	1	1	yes	characteristic
517	C₂²×C₄	#2418	1	1	yes	characteristic
518	C₂²×C₄	#2418	1	1	yes	characteristic
519	C₂²×C₄	#2424	1	1	yes	characteristic
520	C₂²×C₄	#2424	1	1	yes	characteristic
521	C₂²×C₄	#2424	1	1	yes	characteristic
522	C₂²×C₄	#2424	1	1	yes	characteristic
523	C₂²×C₄	#2424	1	1	yes	characteristic
524	C₂²×C₄	#2424	1	1	yes	characteristic
525	C₂²×C₄	#2424	1	1	yes	characteristic
526	C₂²×C₄	#2424	1	1	yes	characteristic
527	C₂²×C₄	#2424	1	1	yes	characteristic
528	C₂²×C₄	#2433	1	1	yes	characteristic
529	C₂²×C₄	#2433	1	1	yes	characteristic
530	C₂²×C₄	#2472	1	1	yes	characteristic
531	C₂²×C₄	#2472	1	1	yes	characteristic
532	C₂²×C₄	#2472	1	1	yes	characteristic
533	C₂²×C₄	#2472	1	1	yes	characteristic
534	C₂²×C₄	#2472	1	1	yes	characteristic
535	C₂²×C₄	#2534	1	1	yes	characteristic
536	C₂²×C₄	#2539	1	1	yes	characteristic
537	C₂²×C₄	#2539	1	1	yes	characteristic
538	C₂²×C₄	#2539	1	1	yes	characteristic
539	C₂²×C₄	#2613	1	1	yes	characteristic
540	C₂²×C₄	#2617	1	1	yes	characteristic
541	C₂²×C₄	#2617	1	1	yes	characteristic
542	C₂²×C₄	#2622	1	1	yes	characteristic
543	C₂²×C₄	#2846	1	1	yes	characteristic
544	C₂²×C₄	#2847	1	1	yes	characteristic
545	C₂²×C₄	#2847	1	1	yes	characteristic
546	C₂²×C₄	#2849	1	1	yes	characteristic
547	C₄⋊C₄	#1438	1	8	yes	—
548	C₄²	C₂×#386	1	1	yes	characteristic
549	C₄²	C₂×#386	1	1	yes	characteristic
550	C₄²	C₂×#386	1	1	yes	characteristic
551	C₄²	C₂×#386	1	1	yes	characteristic
552	C₄²	C₂×#386	1	1	yes	characteristic
553	C₄²	C₄×#120	1	1	yes	characteristic
554	C₄²	C₄×#120	1	1	yes	characteristic
555	C₄²	#2308	1	1	yes	characteristic
556	C₄²	#2321	1	1	yes	characteristic
557	C₄²	#2321	1	1	yes	characteristic
558	C₄²	D₄×C₂²⋊C₄	1	1	yes	characteristic
559	C₄²	D₄×C₂²⋊C₄	1	1	yes	characteristic
560	C₄²	#2358	1	1	yes	characteristic
561	C₄²	#2358	1	1	yes	characteristic
562	C₄²	#2358	1	1	yes	characteristic
563	C₄²	#2358	1	1	yes	characteristic
564	C₄²	C₂×#392	1	1	yes	characteristic
565	C₄²	C₂×#392	1	1	yes	characteristic
566	C₄²	C₂×#394	1	1	yes	characteristic
567	C₄²	C₂×#394	1	1	yes	characteristic
568	C₄²	#2403	1	1	yes	characteristic
569	C₄²	#2403	1	1	yes	characteristic
570	C₄²	#2404	1	1	yes	characteristic
571	C₄²	#2404	1	1	yes	characteristic
572	C₄²	#2404	1	1	yes	characteristic
573	C₄²	#2405	1	1	yes	characteristic
574	C₄²	#2408	1	1	yes	characteristic
575	C₄²	#2410	1	1	yes	characteristic
576	C₄²	#2410	1	1	yes	characteristic
577	C₄²	#2410	1	1	yes	characteristic
578	C₄²	#2410	1	1	yes	characteristic
579	C₄²	#2410	1	1	yes	characteristic
580	C₄²	#2410	1	1	yes	characteristic
581	C₄²	#2411	1	1	yes	characteristic
582	C₄²	#2412	1	1	yes	characteristic
583	C₄²	#2412	1	1	yes	characteristic
584	C₄²	#2412	1	1	yes	characteristic
585	C₄²	#2412	1	1	yes	characteristic
586	C₄²	#2412	1	1	yes	characteristic
587	C₄²	#2418	1	1	yes	characteristic
588	C₄²	#2418	1	1	yes	characteristic
589	C₄²	#2418	1	1	yes	characteristic
590	C₄²	#2418	1	1	yes	characteristic
591	C₄²	#2424	1	1	yes	characteristic
592	C₄²	#2424	1	1	yes	characteristic
593	C₄²	#2424	1	1	yes	characteristic
594	C₄²	#2424	1	1	yes	characteristic
595	C₄²	#2424	1	1	yes	characteristic
596	C₄²	#2424	1	1	yes	characteristic
597	C₄²	#2433	1	1	yes	characteristic
598	C₄²	#2472	1	1	yes	characteristic
599	C₄²	#2472	1	1	yes	characteristic
600	C₄²	#2534	1	1	yes	characteristic
601	C₄²	#2534	1	1	yes	characteristic
602	C₄²	#2534	1	1	yes	characteristic
603	C₄²	#2539	1	1	yes	characteristic
604	C₄²	#2613	1	1	yes	characteristic
605	C₄²	#2617	1	1	yes	characteristic
606	C₄²	#2617	1	1	yes	characteristic
607	C₄²	#2622	1	1	yes	characteristic
608	C₄²	#2847	1	1	yes	characteristic
609	C₄²	#2847	1	1	yes	characteristic
610	C₄²	#2849	1	1	yes	characteristic
611	C₄²	#2849	1	1	yes	characteristic
612	C₂³	#13867	1	1	yes	characteristic
613	C₂³	#13995	1	1	yes	characteristic
614	C₂³	#13995	1	1	yes	characteristic
615	C₂³	#14715	1	1	yes	characteristic
616	C₂³	#14716	1	1	yes	characteristic
617	C₂³	#14718	1	1	yes	characteristic
618	C₂³	#14725	1	1	yes	characteristic
619	C₂×C₄	C₂×#1438	1	1	yes	characteristic
620	C₂×C₄	#13867	1	1	yes	characteristic
621	C₂×C₄	#13967	1	1	yes	characteristic
622	C₂×C₄	#13967	1	1	yes	characteristic
623	C₂×C₄	#13967	1	1	yes	characteristic
624	C₂×C₄	#13967	1	1	yes	characteristic
625	C₂×C₄	#13995	1	1	yes	characteristic
626	C₂×C₄	#13995	1	1	yes	characteristic
627	C₂×C₄	#14134	1	1	yes	characteristic
628	C₂×C₄	#14134	1	1	yes	characteristic
629	C₂×C₄	#14255	1	1	yes	characteristic
630	C₂×C₄	#14694	1	1	yes	characteristic
631	C₂×C₄	#14715	1	1	yes	characteristic
632	C₂×C₄	#14716	1	1	yes	characteristic
633	C₂×C₄	#14716	1	1	yes	characteristic
634	C₂×C₄	#14716	1	1	yes	characteristic
635	C₂×C₄	#14718	1	1	yes	characteristic
636	C₂×C₄	#14718	1	1	yes	characteristic
637	C₂×C₄	#14718	1	1	yes	characteristic
638	C₂×C₄	#14725	1	1	yes	characteristic
639	C₂×C₄	#14725	1	1	yes	characteristic
640	C₂×C₄	#14725	1	1	yes	characteristic
641	C₂×C₄	#14911	1	1	yes	characteristic
642	C₂×C₄	#14911	1	1	yes	characteristic
643	C₂×C₄	C₂×#1904	1	2	yes	—
644	C₂×C₄	C₂×#1904	1	2	yes	—
645	C₂×C₄	#23882	1	4	yes	—
646	C₂²	#154195	1	1	yes	characteristic
647	C₂²	#359472	1	2	yes	—
648	C₂²	#394022	1	2	yes	—
649	C₄	#359645	1	2	yes	—
650	C₄	#364602	1	2	yes	—
651	C₄	#374114	1	2	yes	—
652	C₄	#392685	1	1	yes	characteristic
653	C₄	#392685	1	1	yes	characteristic
654	C₄	#394539	1	2	yes	—
655	C₂	#72237507	1	1	yes	characteristic
656	C₂	#72239583	1	1	yes	characteristic
657	C₂	#72280584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#154195
commutator	C₂²×C₄²	C₂³×C₄
Frattini, cosocle	C₂³×C₄²	C₂⁴
prime radical	#72279460	C₂
LCS	G ▷ C₂²×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂³×C₄² ◁ G
LECS	G ▷ C₂³×C₄² ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72338238	C₂	semidirect
2. #72338237	C₂	semidirect
3. #72338232	C₂	semidirect
4. #72338228	C₂	semidirect
5. #72338226	C₂	semidirect
6. #72338212	C₂	semidirect
7. #72337486	C₂	semidirect
8. #72316822	C₂	semidirect
9. #72316741	C₂	semidirect
10. #72282687	C₂	semidirect
12. #72257771	C₂	semidirect
13. #72257440	C₂	semidirect
14. #72240820	C₂	semidirect
15. #72214607	C₂	semidirect
22. #6516758	C₄	semidirect
23. #6516757	C₄	semidirect
36. #6343377	C₂²	semidirect
37. #6343377	C₂²	semidirect
38. #6343377	C₂²	semidirect
39. #6343016	C₂²	semidirect
41. #353804	C₂²	semidirect
42. #353776	C₂²	semidirect
43. #181375	C₂²	semidirect
44. #181339	C₂²	semidirect
45. #181222	C₂²	semidirect
46. #181220	C₂²	semidirect
47. #181220	C₂²	semidirect
48. #181197	C₂²	semidirect
49. #181124	C₂²	semidirect
50. #181055	C₂²	semidirect
51. #180880	C₂²	semidirect
52. #180871	C₂²	semidirect
65. C₂²×#493	C₂×C₄	semidirect
66. C₂²×#492	C₂×C₄	semidirect
68. C₂×#2981	D₄	semidirect
76. #35279	C₂×C₄	semidirect
77. #35272	C₂×C₄	semidirect
78. #34369	D₄	semidirect
83. #21803	C₂×C₄	semidirect
84. #21803	D₄	semidirect
85. #21803	D₄	semidirect
88. #21373	C₂×C₄	semidirect
94. #17744	D₄	semidirect
95. #17544	D₄	semidirect

Maximal subgroups

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

subgroup	index
#72338238	2
#72338237	2
#72338232	2
#72338228	2
#72338226	2
#72338212	2
#72337486	2
#72316822	2
#72316741	2
#72282687	2
#72279460	2
#72257771	2
#72257440	2
#72240820	2
#72214607	2