Subgroups — #72338258

Order 2048.

At least 7983 conjugacy classes of subgroups; only the 784 normal subgroups are shown.

The subgroup lattice has 616 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72338236	C₂	1	1	yes	maximal, characteristic, complemented
2	#72338234	C₂	1	1	yes	maximal, characteristic, complemented
3	#72338230	C₂	1	1	yes	maximal, characteristic, complemented
4	#72338228	C₂	1	1	yes	maximal, characteristic, complemented
5	#72338217	C₂	1	1	yes	maximal, characteristic, complemented
6	#72337549	C₂	1	1	yes	maximal, characteristic, complemented
7	#72316822	C₂	1	1	yes	maximal, characteristic, complemented
8	#72316811	C₂	1	1	yes	maximal, characteristic, complemented
9	#72316807	C₂	1	1	yes	maximal, characteristic, complemented
10	#72280259	C₂	1	1	yes	maximal, characteristic, complemented
11	#72279737	C₂	1	1	yes	maximal, characteristic, complemented
12	#72257755	C₂	1	1	yes	maximal, characteristic, complemented
13	#72257555	C₂	1	1	yes	maximal, characteristic, complemented
14	#72257449	C₂	1	1	yes	maximal, characteristic, complemented
15	#72224743	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#3481	C₂²	1	1	yes	characteristic
17	C₂×#60803	C₂²	1	1	yes	characteristic
18	C₂×#60561	C₂²	1	1	yes	characteristic
19	C₂×#60561	C₂²	1	1	yes	characteristic, complemented
20	C₂×#60415	C₂²	1	1	yes	characteristic
21	C₂×C₄×#575	C₂²	1	1	yes	characteristic
22	#7628578	C₂²	1	1	yes	characteristic
23	#7628157	C₂²	1	1	yes	characteristic
24	#6374554	C₂²	1	1	yes	characteristic
25	#6374537	C₂²	1	1	yes	characteristic
26	#6374317	C₂²	1	1	yes	characteristic
27	#6372442	C₂²	1	1	yes	characteristic
28	#6372442	C₂²	1	1	yes	characteristic, complemented
29	#6372358	C₂²	1	1	yes	characteristic
30	#6370997	C₂²	1	1	yes	characteristic
31	#6370997	C₂²	1	1	yes	characteristic
32	#6370978	C₂²	1	1	yes	characteristic
33	#6370978	C₂²	1	1	yes	characteristic
34	#6370937	C₂²	1	1	yes	characteristic, complemented
35	#6343804	C₂²	1	1	yes	characteristic
36	#6343377	C₂²	1	1	yes	characteristic, complemented
37	#6343016	C₂²	1	1	yes	characteristic, complemented
38	#6342924	C₂²	1	1	yes	characteristic
39	#6342924	C₂²	1	1	yes	characteristic
40	C₂×#17451	C₂²	1	1	yes	characteristic, complemented
41	#6342561	C₂²	1	1	yes	characteristic, complemented
42	#353804	C₂²	1	1	yes	characteristic, complemented
43	#181433	C₂²	1	1	yes	characteristic, complemented
44	#181220	C₂²	1	1	yes	characteristic, complemented
45	#181197	C₂²	1	1	yes	characteristic, complemented
46	#181175	C₂²	1	1	yes	characteristic, complemented
47	#181175	C₂²	1	1	yes	characteristic, complemented
48	#181124	C₂²	1	1	yes	characteristic, complemented
49	#181122	C₂²	1	1	yes	characteristic, complemented
50	#181055	C₂²	1	1	yes	characteristic, complemented
51	C₂²×#575	D₄	1	1	yes	characteristic
52	C₂²×#559	D₄	1	1	yes	characteristic
53	C₂²×#554	D₄	1	1	yes	characteristic
54	C₂²×#554	D₄	1	1	yes	characteristic
55	C₂²×D₄²	D₄	1	1	yes	characteristic
56	C₂²×#532	C₂³	1	1	yes	characteristic
57	C₂²×#532	C₂³	1	1	yes	characteristic
58	C₂²×C₄×#41	C₂³	1	1	yes	characteristic
59	C₂²×C₄×#41	C₂³	1	1	yes	characteristic
60	C₂²×C₄×#41	C₂³	1	1	yes	characteristic
61	C₂×#3214	D₄	1	4	yes	complemented
62	C₂×#3103	D₄	1	2	yes	complemented
63	C₂×#3100	D₄	1	2	yes	complemented
64	C₂×#3037	D₄	1	2	yes	—
65	C₂×#3036	D₄	1	2	yes	—
66	C₂×#2920	C₂³	1	1	yes	characteristic
67	C₂×#2920	C₂³	1	1	yes	characteristic
68	C₂×#2920	C₂³	1	1	yes	characteristic
69	C₂×#2920	C₂³	1	1	yes	characteristic
70	C₂×#2920	C₂³	1	1	yes	characteristic
71	C₂×#2911	D₄	1	1	yes	characteristic
72	C₂²×#423	C₂³	1	1	yes	characteristic
73	C₂×#2896	D₄	1	1	yes	characteristic
74	C₂×#2896	D₄	1	1	yes	characteristic
75	C₂²×C₄×M₁₆	C₂³	1	1	yes	characteristic
76	#35279	D₄	1	2	yes	complemented
77	#35272	D₄	1	2	yes	complemented
78	#34952	D₄	1	2	yes	complemented
79	#34935	D₄	1	2	yes	complemented
80	#34012	C₂³	1	1	yes	characteristic
81	#34012	C₂³	1	1	yes	characteristic
82	#34012	C₂³	1	1	yes	characteristic
83	#21891	D₄	1	4	yes	complemented
84	#21847	D₄	1	4	yes	complemented
85	#21408	D₄	1	4	yes	complemented
86	#21373	D₄	1	4	yes	complemented
87	#20701	D₄	1	2	yes	—
88	#20600	D₄	1	2	yes	—
89	C₄×#419	D₄	1	2	yes	—
90	C₄×#418	D₄	1	2	yes	—
91	C₄×#421	D₄	1	4	yes	complemented
92	#17663	D₄	1	4	yes	complemented
93	#17450	D₄	1	4	yes	complemented
94	C₂³×#41	C₂×D₄	1	1	yes	characteristic
95	C₂³×#41	C₂×D₄	1	1	yes	characteristic
96	C₂³×#41	C₂×D₄	1	1	yes	characteristic
97	C₂³×M₁₆	C₂×D₄	1	1	yes	characteristic
98	C₂³×M₁₆	C₂×D₄	1	1	yes	characteristic
99	C₂×#532	C₂×D₄	1	2	yes	—
100	C₂×#532	C₂×D₄	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	#41	1	2	yes	—
107	C₂²×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic
109	C₂²×#127	C₂×D₄	1	1	yes	characteristic
110	C₂²×#127	C₂×D₄	1	1	yes	characteristic
111	C₂×C₄×#41	C₂×D₄	1	2	yes	—
112	C₂×C₄×#41	C₂×D₄	1	2	yes	—
113	C₂×C₄×#41	C₂×D₄	1	2	yes	—
114	C₂×C₄×#41	C₂×D₄	1	2	yes	—
115	C₂×C₄×#41	C₂×D₄	1	2	yes	—
116	C₂×C₄×#41	C₂×D₄	1	2	yes	—
117	C₂×C₄×#41	#41	1	2	yes	—
118	C₂×C₄×#41	#41	1	2	yes	—
119	C₂²×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
131	C₂²×#117	C₂×D₄	1	1	yes	characteristic
132	C₂²×#117	C₂×D₄	1	1	yes	characteristic
133	C₂²×#117	C₂×D₄	1	1	yes	characteristic
134	C₂³×C₄²	C₂⁴	1	1	yes	characteristic
135	#2920	C₂×D₄	1	2	yes	—
136	#2920	C₂×D₄	1	2	yes	—
137	#2920	C₂×D₄	1	2	yes	—
138	#2920	C₂×D₄	1	2	yes	—
139	C₂×#432	C₂×D₄	1	2	yes	—
140	C₂×#431	C₂×D₄	1	2	yes	—
141	C₂×#431	C₂×D₄	1	2	yes	—
142	C₂×#431	C₂×D₄	1	2	yes	—
143	C₂×#423	C₂×D₄	1	2	yes	—
144	C₂×#423	C₂×D₄	1	2	yes	—
145	C₂²×C₄⋊C₈	C₂×D₄	1	2	yes	—
146	C₂×#407	C₂×D₄	1	2	yes	—
147	C₂×C₄×M₁₆	C₂×D₄	1	2	yes	—
148	C₂×C₄×M₁₆	C₂×D₄	1	2	yes	—
149	C₂²×#97	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₈	C₂×D₄	1	2	yes	—
151	#2285	C₂×D₄	1	2	yes	—
152	#2285	C₂×D₄	1	2	yes	—
153	#2283	C₂×D₄	1	2	yes	—
154	#2283	C₂×D₄	1	2	yes	—
155	#2280	C₂×D₄	1	2	yes	—
156	C₄×#117	C₂×D₄	1	2	yes	—
157	C₄×#117	C₂×D₄	1	2	yes	—
158	C₂²×#41	#120	1	2	yes	—
159	C₂²×#41	#121	1	2	yes	—
160	C₂²×#41	#121	1	2	yes	—
161	C₂²×#41	#127	1	2	yes	—
162	C₂³×Q₈	#120	1	1	yes	characteristic
163	C₂³×Q₈	#120	1	1	yes	characteristic
164	C₂³×Q₈	#120	1	1	yes	characteristic
165	C₂³×D₄	#120	1	1	yes	characteristic
166	C₂³×D₄	#120	1	1	yes	characteristic
167	C₂³×D₄	#120	1	1	yes	characteristic
168	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
169	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
170	C₂⁴×C₄	H(5,𝔽₂)	1	1	yes	characteristic
171	C₂³×C₈	#120	1	2	yes	—
172	C₂³×C₈	#120	1	2	yes	—
173	#532	#120	1	4	yes	—
174	#532	#121	1	4	yes	—
175	#532	#121	1	4	yes	—
176	#532	#127	1	4	yes	—
177	C₂×C₄⋊Q₈	#120	1	2	yes	—
178	C₂×C₄⋊Q₈	#120	1	2	yes	—
179	C₂×C₄⋊Q₈	#120	1	2	yes	—
180	C₂×C₄⋊Q₈	#121	1	2	yes	—
181	C₂×#127	#120	1	2	yes	—
182	C₂×#127	#120	1	2	yes	—
183	C₂×#127	#120	1	2	yes	—
184	C₂×#127	#121	1	2	yes	—
185	C₂×C₄×Q₈	#120	1	2	yes	—
186	C₂×C₄×Q₈	#120	1	2	yes	—
187	C₂×C₄×Q₈	#120	1	2	yes	—
188	C₂×C₄×Q₈	#121	1	2	yes	—
189	C₂×C₄×Q₈	#121	1	2	yes	—
190	C₂×C₄×Q₈	#121	1	2	yes	—
191	C₂×C₄×Q₈	#121	1	2	yes	—
192	C₂×C₄×Q₈	#127	1	2	yes	—
193	C₂×C₄×D₄	#120	1	2	yes	—
194	C₂×C₄×D₄	#120	1	2	yes	—
195	C₂×C₄×D₄	#120	1	2	yes	—
196	C₂×C₄×D₄	#121	1	2	yes	—
197	C₂×C₄×D₄	#121	1	2	yes	—
198	C₂×C₄×D₄	#121	1	2	yes	—
199	C₂×C₄×D₄	#121	1	2	yes	—
200	C₂×C₄×D₄	#127	1	2	yes	—
201	C₂×#117	#120	1	2	yes	—
202	C₂×#117	#121	1	2	yes	—
203	C₂×#117	#121	1	2	yes	—
204	C₂×#117	#127	1	2	yes	—
205	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
206	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
207	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
208	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
209	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
210	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
211	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
212	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
213	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
214	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
215	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
216	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
217	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
218	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
219	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
220	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
221	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
222	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
223	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
224	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
225	C₂²×C₄²	C₂×#41	1	1	yes	characteristic
226	C₂²×C₄²	C₂×#41	1	1	yes	characteristic
227	C₂²×C₄²	C₂×#41	1	1	yes	characteristic
228	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
229	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
230	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
231	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
232	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
233	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
234	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
235	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
236	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
237	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
238	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
239	C₂×C₄⋊C₈	#120	1	4	yes	—
240	C₂×C₂²⋊C₈	#120	1	4	yes	—
241	C₄×M₁₆	#120	1	4	yes	—
242	C₂×C₄×C₈	#120	1	4	yes	—
243	#380	#120	1	4	yes	—
244	C₄×C₄⋊C₄	#120	1	4	yes	—
245	C₂⁵	D₄²	1	1	yes	characteristic
246	C₂²×Q₈	#392	1	2	yes	—
247	C₂²×Q₈	#392	1	2	yes	—
248	C₂²×D₄	#392	1	2	yes	—
249	C₂²×D₄	#392	1	2	yes	—
250	C₂³×C₄	C₂×#120	1	1	yes	characteristic
251	C₂³×C₄	C₂×#120	1	1	yes	characteristic
252	C₂³×C₄	C₂×#120	1	1	yes	characteristic
253	C₂³×C₄	C₂×#120	1	1	yes	characteristic
254	C₂³×C₄	C₂×#120	1	1	yes	characteristic
255	C₂³×C₄	C₂×#120	1	1	yes	characteristic
256	C₂³×C₄	C₂×#120	1	1	yes	characteristic
257	C₂³×C₄	C₂×#121	1	1	yes	characteristic
258	C₂³×C₄	C₂×#121	1	1	yes	characteristic
259	C₂³×C₄	C₂×#127	1	1	yes	characteristic
260	C₂³×C₄	#534	1	1	yes	characteristic
261	C₂³×C₄	#534	1	1	yes	characteristic
262	C₂³×C₄	#534	1	1	yes	characteristic
263	C₂³×C₄	#534	1	1	yes	characteristic
264	C₂³×C₄	#534	1	1	yes	characteristic
265	C₂³×C₄	#535	1	1	yes	characteristic
266	C₂³×C₄	#535	1	1	yes	characteristic
267	C₂³×C₄	#535	1	1	yes	characteristic
268	C₂³×C₄	#535	1	1	yes	characteristic
269	C₂³×C₄	#535	1	1	yes	characteristic
270	C₂³×C₄	#538	1	1	yes	characteristic
271	C₂³×C₄	D₄²	1	1	yes	characteristic
272	C₂³×C₄	D₄²	1	1	yes	characteristic
273	C₂³×C₄	D₄²	1	1	yes	characteristic
274	C₂³×C₄	D₄²	1	1	yes	characteristic
275	C₂³×C₄	D₄²	1	1	yes	characteristic
276	C₂³×C₄	D₄²	1	1	yes	characteristic
277	C₂³×C₄	D₄²	1	1	yes	characteristic
278	C₂³×C₄	D₄²	1	1	yes	characteristic
279	C₂³×C₄	D₄²	1	1	yes	characteristic
280	C₂³×C₄	D₄²	1	1	yes	characteristic
281	C₂³×C₄	D₄²	1	1	yes	characteristic
282	C₂³×C₄	D₄²	1	1	yes	characteristic
283	C₂³×C₄	D₄²	1	1	yes	characteristic
284	C₂³×C₄	#546	1	1	yes	characteristic
285	C₂³×C₄	#546	1	1	yes	characteristic
286	C₂³×C₄	#546	1	1	yes	characteristic
287	C₂³×C₄	#546	1	1	yes	characteristic
288	C₂³×C₄	#546	1	1	yes	characteristic
289	C₂³×C₄	#546	1	1	yes	characteristic
290	C₂³×C₄	#560	1	1	yes	characteristic
291	C₂³×C₄	#560	1	1	yes	characteristic
292	C₄⋊Q₈	#392	1	4	yes	—
293	#127	#392	1	4	yes	—
294	C₂×C₄⋊C₄	#392	1	2	yes	—
295	C₂×C₄⋊C₄	#392	1	2	yes	—
296	C₂×C₄⋊C₄	#392	1	2	yes	—
297	C₂×C₄⋊C₄	#392	1	2	yes	—
298	C₂×C₄²	C₂×#120	1	1	yes	characteristic
299	C₂×C₄²	C₂×#120	1	1	yes	characteristic
300	C₂×C₄²	C₂×#120	1	1	yes	characteristic
301	C₂×C₄²	C₂×#120	1	1	yes	characteristic
302	C₂×C₄²	C₂×#120	1	1	yes	characteristic
303	C₂×C₄²	C₂×#120	1	1	yes	characteristic
304	C₂×C₄²	C₂×#120	1	1	yes	characteristic
305	C₂×C₄²	C₂×#120	1	1	yes	characteristic
306	C₂×C₄²	C₂×#120	1	1	yes	characteristic
307	C₂×C₄²	C₂×#120	1	1	yes	characteristic
308	C₂×C₄²	C₂×#120	1	1	yes	characteristic
309	C₂×C₄²	C₂×#121	1	1	yes	characteristic
310	C₂×C₄²	C₂×#121	1	1	yes	characteristic
311	C₂×C₄²	C₂×#121	1	1	yes	characteristic
312	C₂×C₄²	C₂×#121	1	1	yes	characteristic
313	C₂×C₄²	C₂×#121	1	1	yes	characteristic
314	C₂×C₄²	C₂×#121	1	1	yes	characteristic
315	C₂×C₄²	C₂×#121	1	1	yes	characteristic
316	C₂×C₄²	#525	1	1	yes	characteristic
317	C₂×C₄²	#525	1	1	yes	characteristic
318	C₂×C₄²	#525	1	1	yes	characteristic
319	C₂×C₄²	C₂×#127	1	1	yes	characteristic
320	C₂×C₄²	C₂×#127	1	1	yes	characteristic
321	C₂×C₄²	#534	1	1	yes	characteristic
322	C₂×C₄²	#534	1	1	yes	characteristic
323	C₂×C₄²	#534	1	1	yes	characteristic
324	C₂×C₄²	#534	1	1	yes	characteristic
325	C₂×C₄²	#534	1	1	yes	characteristic
326	C₂×C₄²	#534	1	1	yes	characteristic
327	C₂×C₄²	#534	1	1	yes	characteristic
328	C₂×C₄²	#534	1	1	yes	characteristic
329	C₂×C₄²	#534	1	1	yes	characteristic
330	C₂×C₄²	#534	1	1	yes	characteristic
331	C₂×C₄²	#534	1	1	yes	characteristic
332	C₂×C₄²	#534	1	1	yes	characteristic
333	C₂×C₄²	#534	1	1	yes	characteristic
334	C₂×C₄²	#534	1	1	yes	characteristic
335	C₂×C₄²	#534	1	1	yes	characteristic
336	C₂×C₄²	#534	1	1	yes	characteristic
337	C₂×C₄²	#535	1	1	yes	characteristic
338	C₂×C₄²	#535	1	1	yes	characteristic
339	C₂×C₄²	#535	1	1	yes	characteristic
340	C₂×C₄²	#535	1	1	yes	characteristic
341	C₂×C₄²	#535	1	1	yes	characteristic
342	C₂×C₄²	#535	1	1	yes	characteristic
343	C₂×C₄²	#535	1	1	yes	characteristic
344	C₂×C₄²	#535	1	1	yes	characteristic
345	C₂×C₄²	#535	1	1	yes	characteristic
346	C₂×C₄²	#535	1	1	yes	characteristic
347	C₂×C₄²	#538	1	1	yes	characteristic
348	C₂×C₄²	#538	1	1	yes	characteristic
349	C₂×C₄²	#538	1	1	yes	characteristic
350	C₂×C₄²	#538	1	1	yes	characteristic
351	C₂×C₄²	#538	1	1	yes	characteristic
352	C₂×C₄²	D₄²	1	1	yes	characteristic
353	C₂×C₄²	D₄²	1	1	yes	characteristic
354	C₂×C₄²	D₄²	1	1	yes	characteristic
355	C₂×C₄²	D₄²	1	1	yes	characteristic
356	C₂×C₄²	D₄²	1	1	yes	characteristic
357	C₂×C₄²	D₄²	1	1	yes	characteristic
358	C₂×C₄²	D₄²	1	1	yes	characteristic
359	C₂×C₄²	D₄²	1	1	yes	characteristic
360	C₂×C₄²	D₄²	1	1	yes	characteristic
361	C₂×C₄²	D₄²	1	1	yes	characteristic
362	C₂×C₄²	D₄²	1	1	yes	characteristic
363	C₂×C₄²	D₄²	1	1	yes	characteristic
364	C₂×C₄²	D₄²	1	1	yes	characteristic
365	C₂×C₄²	D₄²	1	1	yes	characteristic
366	C₂×C₄²	D₄²	1	1	yes	characteristic
367	C₂×C₄²	D₄²	1	1	yes	characteristic
368	C₂×C₄²	D₄²	1	1	yes	characteristic
369	C₂×C₄²	D₄²	1	1	yes	characteristic
370	C₂×C₄²	D₄²	1	1	yes	characteristic
371	C₂×C₄²	D₄²	1	1	yes	characteristic
372	C₂×C₄²	D₄²	1	1	yes	characteristic
373	C₂×C₄²	D₄²	1	1	yes	characteristic
374	C₂×C₄²	D₄²	1	1	yes	characteristic
375	C₂×C₄²	D₄²	1	1	yes	characteristic
376	C₂×C₄²	D₄²	1	1	yes	characteristic
377	C₂×C₄²	D₄²	1	1	yes	characteristic
378	C₂×C₄²	D₄²	1	1	yes	characteristic
379	C₂×C₄²	D₄²	1	1	yes	characteristic
380	C₂×C₄²	D₄²	1	1	yes	characteristic
381	C₂×C₄²	D₄²	1	1	yes	characteristic
382	C₂×C₄²	D₄²	1	1	yes	characteristic
383	C₂×C₄²	D₄²	1	1	yes	characteristic
384	C₂×C₄²	D₄²	1	1	yes	characteristic
385	C₂×C₄²	D₄²	1	1	yes	characteristic
386	C₂×C₄²	#546	1	1	yes	characteristic
387	C₂×C₄²	#546	1	1	yes	characteristic
388	C₂×C₄²	#546	1	1	yes	characteristic
389	C₂×C₄²	#546	1	1	yes	characteristic
390	C₂×C₄²	#546	1	1	yes	characteristic
391	C₂×C₄²	#546	1	1	yes	characteristic
392	C₂×C₄²	#546	1	1	yes	characteristic
393	C₂×C₄²	#546	1	1	yes	characteristic
394	C₂×C₄²	#546	1	1	yes	characteristic
395	C₂×C₄²	#546	1	1	yes	characteristic
396	C₂×C₄²	#546	1	1	yes	characteristic
397	C₂×C₄²	#546	1	1	yes	characteristic
398	C₂×C₄²	#546	1	1	yes	characteristic
399	C₂×C₄²	#546	1	1	yes	characteristic
400	C₂×C₄²	#546	1	1	yes	characteristic
401	C₂×C₄²	#546	1	1	yes	characteristic
402	C₂×C₄²	#546	1	1	yes	characteristic
403	C₂×C₄²	#546	1	1	yes	characteristic
404	C₂×C₄²	#560	1	1	yes	characteristic
405	C₂×C₄²	#560	1	1	yes	characteristic
406	C₂×C₄²	#560	1	1	yes	characteristic
407	C₂×C₄²	#560	1	1	yes	characteristic
408	C₂×C₄²	H(3,𝔽₄)	1	1	yes	characteristic
409	C₂×C₄²	H(3,𝔽₄)	1	1	yes	characteristic
410	C₂⁴	#2403	1	1	yes	characteristic
411	C₂⁴	#2403	1	1	yes	characteristic
412	C₂⁴	#2408	1	1	yes	characteristic
413	C₂⁴	#2410	1	1	yes	characteristic
414	C₂⁴	#2433	1	1	yes	characteristic
415	C₂⁴	#2669	1	1	yes	characteristic
416	C₂⁴	#2678	1	1	yes	characteristic
417	C₂×D₄	#2008	1	4	yes	complemented
418	C₂×D₄	#2010	1	4	yes	—
419	C₂²×C₄	C₂×#392	1	1	yes	characteristic
420	C₂²×C₄	C₂×#392	1	1	yes	characteristic
421	C₂²×C₄	#2403	1	1	yes	characteristic
422	C₂²×C₄	#2403	1	1	yes	characteristic
423	C₂²×C₄	#2403	1	1	yes	characteristic
424	C₂²×C₄	#2403	1	1	yes	characteristic
425	C₂²×C₄	#2403	1	1	yes	characteristic
426	C₂²×C₄	#2403	1	1	yes	characteristic
427	C₂²×C₄	#2403	1	1	yes	characteristic
428	C₂²×C₄	#2403	1	1	yes	characteristic
429	C₂²×C₄	#2403	1	1	yes	characteristic
430	C₂²×C₄	#2403	1	1	yes	characteristic
431	C₂²×C₄	#2404	1	1	yes	characteristic
432	C₂²×C₄	#2404	1	1	yes	characteristic
433	C₂²×C₄	#2408	1	1	yes	characteristic
434	C₂²×C₄	#2408	1	1	yes	characteristic
435	C₂²×C₄	#2408	1	1	yes	characteristic
436	C₂²×C₄	#2408	1	1	yes	characteristic
437	C₂²×C₄	#2408	1	1	yes	characteristic
438	C₂²×C₄	#2408	1	1	yes	characteristic
439	C₂²×C₄	#2408	1	1	yes	characteristic
440	C₂²×C₄	#2410	1	1	yes	characteristic
441	C₂²×C₄	#2410	1	1	yes	characteristic
442	C₂²×C₄	#2410	1	1	yes	characteristic
443	C₂²×C₄	#2410	1	1	yes	characteristic
444	C₂²×C₄	#2410	1	1	yes	characteristic
445	C₂²×C₄	#2410	1	1	yes	characteristic
446	C₂²×C₄	#2410	1	1	yes	characteristic
447	C₂²×C₄	#2410	1	1	yes	characteristic
448	C₂²×C₄	#2410	1	1	yes	characteristic
449	C₂²×C₄	#2410	1	1	yes	characteristic
450	C₂²×C₄	#2410	1	1	yes	characteristic
451	C₂²×C₄	#2410	1	1	yes	characteristic
452	C₂²×C₄	#2410	1	1	yes	characteristic
453	C₂²×C₄	#2424	1	1	yes	characteristic
454	C₂²×C₄	#2424	1	1	yes	characteristic
455	C₂²×C₄	#2424	1	1	yes	characteristic
456	C₂²×C₄	#2424	1	1	yes	characteristic
457	C₂²×C₄	#2424	1	1	yes	characteristic
458	C₂²×C₄	#2424	1	1	yes	characteristic
459	C₂²×C₄	#2433	1	1	yes	characteristic
460	C₂²×C₄	#2433	1	1	yes	characteristic
461	C₂²×C₄	#2433	1	1	yes	characteristic
462	C₂²×C₄	#2433	1	1	yes	characteristic
463	C₂²×C₄	#2433	1	1	yes	characteristic
464	C₂²×C₄	#2433	1	1	yes	characteristic
465	C₂²×C₄	#2433	1	1	yes	characteristic
466	C₂²×C₄	#2433	1	1	yes	characteristic
467	C₂²×C₄	#2433	1	1	yes	characteristic
468	C₂²×C₄	#2539	1	1	yes	characteristic
469	C₂²×C₄	#2613	1	1	yes	characteristic
470	C₂²×C₄	#2613	1	1	yes	characteristic
471	C₂²×C₄	#2613	1	1	yes	characteristic
472	C₂²×C₄	#2613	1	1	yes	characteristic
473	C₂²×C₄	#2617	1	1	yes	characteristic
474	C₂²×C₄	#2668	1	1	yes	characteristic
475	C₂²×C₄	#2668	1	1	yes	characteristic
476	C₂²×C₄	#2668	1	1	yes	characteristic
477	C₂²×C₄	#2668	1	1	yes	characteristic
478	C₂²×C₄	#2668	1	1	yes	characteristic
479	C₂²×C₄	#2669	1	1	yes	characteristic
480	C₂²×C₄	#2669	1	1	yes	characteristic
481	C₂²×C₄	#2669	1	1	yes	characteristic
482	C₂²×C₄	#2669	1	1	yes	characteristic
483	C₂²×C₄	#2669	1	1	yes	characteristic
484	C₂²×C₄	#2669	1	1	yes	characteristic
485	C₂²×C₄	#2669	1	1	yes	characteristic
486	C₂²×C₄	#2669	1	1	yes	characteristic
487	C₂²×C₄	#2669	1	1	yes	characteristic
488	C₂²×C₄	#2669	1	1	yes	characteristic
489	C₂²×C₄	#2669	1	1	yes	characteristic
490	C₂²×C₄	#2670	1	1	yes	characteristic
491	C₂²×C₄	#2670	1	1	yes	characteristic
492	C₂²×C₄	#2670	1	1	yes	characteristic
493	C₂²×C₄	#2678	1	1	yes	characteristic
494	C₂²×C₄	#2678	1	1	yes	characteristic
495	C₂²×C₄	#2678	1	1	yes	characteristic
496	C₂²×C₄	#2678	1	1	yes	characteristic
497	C₂²×C₄	#2678	1	1	yes	characteristic
498	C₂²×C₄	#2679	1	1	yes	characteristic
499	C₂²×C₄	#2679	1	1	yes	characteristic
500	C₂²×C₄	#2812	1	1	yes	characteristic
501	C₂²×C₄	#2846	1	1	yes	characteristic
502	C₂²×C₄	#2846	1	1	yes	characteristic
503	C₄²	C₂×#392	1	1	yes	characteristic
504	C₄²	#2403	1	1	yes	characteristic
505	C₄²	#2403	1	1	yes	characteristic
506	C₄²	#2403	1	1	yes	characteristic
507	C₄²	#2403	1	1	yes	characteristic
508	C₄²	#2403	1	1	yes	characteristic
509	C₄²	#2403	1	1	yes	characteristic
510	C₄²	#2403	1	1	yes	characteristic
511	C₄²	#2403	1	1	yes	characteristic
512	C₄²	#2403	1	1	yes	characteristic
513	C₄²	#2404	1	1	yes	characteristic
514	C₄²	#2408	1	1	yes	characteristic
515	C₄²	#2408	1	1	yes	characteristic
516	C₄²	#2408	1	1	yes	characteristic
517	C₄²	#2408	1	1	yes	characteristic
518	C₄²	#2410	1	1	yes	characteristic
519	C₄²	#2410	1	1	yes	characteristic
520	C₄²	#2410	1	1	yes	characteristic
521	C₄²	#2410	1	1	yes	characteristic
522	C₄²	#2410	1	1	yes	characteristic
523	C₄²	#2410	1	1	yes	characteristic
524	C₄²	#2410	1	1	yes	characteristic
525	C₄²	#2410	1	1	yes	characteristic
526	C₄²	#2410	1	1	yes	characteristic
527	C₄²	#2410	1	1	yes	characteristic
528	C₄²	#2424	1	1	yes	characteristic
529	C₄²	#2424	1	1	yes	characteristic
530	C₄²	#2424	1	1	yes	characteristic
531	C₄²	#2424	1	1	yes	characteristic
532	C₄²	#2424	1	1	yes	characteristic
533	C₄²	#2424	1	1	yes	characteristic
534	C₄²	#2433	1	1	yes	characteristic
535	C₄²	#2433	1	1	yes	characteristic
536	C₄²	#2433	1	1	yes	characteristic
537	C₄²	#2433	1	1	yes	characteristic
538	C₄²	#2433	1	1	yes	characteristic
539	C₄²	#2539	1	1	yes	characteristic
540	C₄²	#2539	1	1	yes	characteristic
541	C₄²	#2613	1	1	yes	characteristic
542	C₄²	#2613	1	1	yes	characteristic
543	C₄²	#2617	1	1	yes	characteristic
544	C₄²	#2617	1	1	yes	characteristic
545	C₄²	#2668	1	1	yes	characteristic
546	C₄²	#2669	1	1	yes	characteristic
547	C₄²	#2669	1	1	yes	characteristic
548	C₄²	#2669	1	1	yes	characteristic
549	C₄²	#2669	1	1	yes	characteristic
550	C₄²	#2669	1	1	yes	characteristic
551	C₄²	#2669	1	1	yes	characteristic
552	C₄²	#2670	1	1	yes	characteristic
553	C₄²	#2670	1	1	yes	characteristic
554	C₄²	#2670	1	1	yes	characteristic
555	C₄²	#2678	1	1	yes	characteristic
556	C₄²	#2678	1	1	yes	characteristic
557	C₄²	#2678	1	1	yes	characteristic
558	C₄²	#2678	1	1	yes	characteristic
559	C₄²	#2678	1	1	yes	characteristic
560	C₄²	#2678	1	1	yes	characteristic
561	C₄²	#2679	1	1	yes	characteristic
562	C₄²	#2679	1	1	yes	characteristic
563	C₄²	#2679	1	1	yes	characteristic
564	C₄²	#2679	1	1	yes	characteristic
565	C₄²	#2812	1	1	yes	characteristic
566	C₄²	#2847	1	1	yes	characteristic
567	C₂³	#14715	1	1	yes	characteristic
568	C₂³	#14715	1	1	yes	characteristic
569	C₂³	#15257	1	1	yes	characteristic
570	C₂³	#15257	1	1	yes	characteristic
571	C₂³	#15258	1	1	yes	characteristic
572	C₂³	#15267	1	1	yes	characteristic
573	C₂³	#16249	1	1	yes	characteristic
574	C₂×C₄	#14715	1	1	yes	characteristic
575	C₂×C₄	#14715	1	1	yes	characteristic
576	C₂×C₄	#14715	1	1	yes	characteristic
577	C₂×C₄	#14715	1	1	yes	characteristic
578	C₂×C₄	#14716	1	1	yes	characteristic
579	C₂×C₄	#14716	1	1	yes	characteristic
580	C₂×C₄	#14716	1	1	yes	characteristic
581	C₂×C₄	#15257	1	1	yes	characteristic
582	C₂×C₄	#15257	1	1	yes	characteristic
583	C₂×C₄	#15257	1	1	yes	characteristic
584	C₂×C₄	#15257	1	1	yes	characteristic
585	C₂×C₄	#15258	1	1	yes	characteristic
586	C₂×C₄	#15258	1	1	yes	characteristic
587	C₂×C₄	#15267	1	1	yes	characteristic
588	C₂×C₄	#15267	1	1	yes	characteristic
589	C₂×C₄	#15267	1	1	yes	characteristic
590	C₂×C₄	#15267	1	1	yes	characteristic
591	C₂×C₄	#15267	1	1	yes	characteristic
592	C₂×C₄	#15947	1	1	yes	characteristic
593	C₂×C₄	#16249	1	1	yes	characteristic
594	C₂×C₄	#16249	1	1	yes	characteristic
595	C₂×C₄	#16249	1	1	yes	characteristic
596	C₂×C₄	#16249	1	1	yes	characteristic
597	C₂×C₄	#16249	1	1	yes	characteristic
598	C₂×C₄	C₂×#2008	1	2	yes	—
599	C₂×C₄	#23412	1	2	yes	—
600	C₂×C₄	C₂×#2010	1	2	yes	—
601	C₂×C₄	#23414	1	2	yes	—
602	C₂²	#156684	1	1	yes	characteristic
603	C₂²	#393936	1	2	yes	—
604	C₂²	#394038	1	2	yes	—
605	C₄	#393979	1	1	yes	characteristic
606	C₄	#393981	1	1	yes	characteristic
607	C₄	#393988	1	1	yes	characteristic
608	C₄	#393989	1	1	yes	characteristic
609	C₄	#394261	1	2	yes	—
610	C₄	#394284	1	2	yes	—
611	C₄	#417736	1	2	yes	—
612	C₂	#72237252	1	1	yes	characteristic
613	C₂	#72237511	1	1	yes	characteristic
614	C₂	#72338199	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#156684
commutator, Frattini, cosocle	C₂³×C₄²	C₂⁴
LCS	G ▷ C₂³×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. #72338236	C₂	semidirect
2. #72338234	C₂	semidirect
3. #72338230	C₂	semidirect
4. #72338228	C₂	semidirect
5. #72338217	C₂	semidirect
6. #72337549	C₂	semidirect
7. #72316822	C₂	semidirect
8. #72316811	C₂	semidirect
9. #72316807	C₂	semidirect
10. #72280259	C₂	semidirect
11. #72279737	C₂	semidirect
12. #72257755	C₂	semidirect
13. #72257555	C₂	semidirect
14. #72257449	C₂	semidirect
15. #72224743	C₂	semidirect
19. C₂×#60561	C₂²	semidirect
28. #6372442	C₂²	semidirect
34. #6370937	C₂²	semidirect
36. #6343377	C₂²	semidirect
37. #6343016	C₂²	semidirect
40. C₂×#17451	C₂²	semidirect
41. #6342561	C₂²	semidirect
42. #353804	C₂²	semidirect
43. #181433	C₂²	semidirect
44. #181220	C₂²	semidirect
45. #181197	C₂²	semidirect
46. #181175	C₂²	semidirect
47. #181175	C₂²	semidirect
48. #181124	C₂²	semidirect
49. #181122	C₂²	semidirect
50. #181055	C₂²	semidirect
61. C₂×#3214	D₄	semidirect
62. C₂×#3103	D₄	semidirect
63. C₂×#3100	D₄	semidirect
76. #35279	D₄	semidirect
77. #35272	D₄	semidirect
78. #34952	D₄	semidirect
79. #34935	D₄	semidirect
83. #21891	D₄	semidirect
84. #21847	D₄	semidirect
85. #21408	D₄	semidirect
86. #21373	D₄	semidirect
91. C₄×#421	D₄	semidirect
92. #17663	D₄	semidirect
93. #17450	D₄	semidirect
417. C₂×D₄	#2008	semidirect

Maximal subgroups

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

subgroup	index
#72338236	2
#72338234	2
#72338230	2
#72338228	2
#72338217	2
#72337549	2
#72316822	2
#72316811	2
#72316807	2
#72280259	2
#72279737	2
#72257755	2
#72257555	2
#72257449	2
#72224743	2