Subgroups — #72239069

Order 2048.

At least 8012 conjugacy classes of subgroups; only the 780 normal subgroups are shown.

The subgroup lattice has 612 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72239067	C₂	1	1	yes	maximal, characteristic, complemented
2	#72239066	C₂	1	1	yes	maximal, characteristic, complemented
3	#72239064	C₂	1	1	yes	maximal, characteristic, complemented
4	#72239063	C₂	1	1	yes	maximal, characteristic, complemented
5	#72239062	C₂	1	1	yes	maximal, characteristic, complemented
6	#72239060	C₂	1	1	yes	maximal, characteristic, complemented
7	#72239030	C₂	1	1	yes	maximal, characteristic, complemented
8	#72239029	C₂	1	1	yes	maximal, characteristic, complemented
9	#72239021	C₂	1	1	yes	maximal, characteristic, complemented
10	#72238993	C₂	1	1	yes	maximal, characteristic, complemented
11	#72238987	C₂	1	1	yes	maximal, characteristic, complemented
12	#72238966	C₂	1	1	yes	maximal, characteristic, complemented
13	#72238775	C₂	1	1	yes	maximal, characteristic, complemented
14	#72237152	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#6453969	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×D₄×#41	C₂²	1	1	yes	characteristic
17	#10575872	C₂²	1	1	yes	characteristic
18	#10575094	C₂²	1	1	yes	characteristic
19	C₂×#60558	C₂²	1	1	yes	characteristic
20	C₂×#60558	C₂²	1	1	yes	characteristic, complemented
21	C₂²×#3109	C₂²	1	1	yes	characteristic
22	C₂³×#442	C₂²	1	1	yes	characteristic
23	C₂×#34963	C₂²	1	1	yes	characteristic
24	#6374710	C₂²	1	1	yes	characteristic, complemented
25	#6374239	C₂²	1	1	yes	characteristic, complemented
26	C₂×#21408	C₂²	1	1	yes	characteristic
27	#6372352	C₂²	1	1	yes	characteristic, complemented
28	C₂×#21379	C₂²	1	1	yes	characteristic
29	C₂×#20739	C₂²	1	1	yes	characteristic
30	C₂×#20726	C₂²	1	1	yes	characteristic
31	C₂×#20726	C₂²	1	1	yes	characteristic, complemented
32	#6344036	C₂²	1	1	yes	characteristic
33	#6343804	C₂²	1	1	yes	characteristic
34	#6343804	C₂²	1	1	yes	characteristic
35	#6343801	C₂²	1	1	yes	characteristic, complemented
36	#6342924	C₂²	1	1	yes	characteristic
37	#6342924	C₂²	1	1	yes	characteristic
38	#6342924	C₂²	1	1	yes	characteristic
39	C₂×#17448	C₂²	1	1	yes	characteristic
40	C₂×#17448	C₂²	1	1	yes	characteristic, complemented
41	C₂×#17364	C₂²	1	1	yes	characteristic
42	#353794	C₂²	1	1	yes	characteristic, complemented
43	#181798	C₂²	1	1	yes	characteristic, complemented
44	#181796	C₂²	1	1	yes	characteristic, complemented
45	#181265	C₂²	1	1	yes	characteristic, complemented
46	#181219	C₂²	1	1	yes	characteristic, complemented
47	#181194	C₂²	1	1	yes	characteristic, complemented
48	C₂×#7919	C₂²	1	1	yes	characteristic, complemented
49	C₂×#7861	C₂²	1	1	yes	characteristic, complemented
50	#180869	C₂²	1	1	yes	characteristic, complemented
51	C₂⁴×D₈	D₄	1	1	yes	characteristic
52	C₂²×#550	D₄	1	1	yes	characteristic
53	C₂²×#547	D₄	1	1	yes	characteristic
54	C₂²×D₄×Q₈	D₄	1	1	yes	characteristic
55	C₂²×D₄²	D₄	1	1	yes	characteristic
56	C₂×#3444	C₂³	1	1	yes	characteristic
57	C₂²×#532	C₂³	1	1	yes	characteristic
58	C₂²×C₄×#41	C₂³	1	1	yes	characteristic
59	C₂³×C₄×D₄	C₂³	1	1	yes	characteristic
60	C₂³×C₄×D₄	C₂³	1	1	yes	characteristic
61	#60941	D₄	1	2	yes	complemented
62	#60940	D₄	1	2	yes	complemented
63	#60562	D₄	1	2	yes	—
64	#60561	D₄	1	2	yes	—
65	C₂×#3109	D₄	1	4	yes	—
66	C₂×#3077	D₄	1	2	yes	complemented
67	C₂×#3036	D₄	1	2	yes	complemented
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×#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×#432	C₂³	1	1	yes	characteristic
76	C₂³×#106	D₄	1	1	yes	characteristic
77	C₂³×#102	D₄	1	1	yes	characteristic
78	C₂³×#102	D₄	1	1	yes	characteristic
79	C₂³×#97	C₂³	1	1	yes	characteristic
80	#34963	D₄	1	4	yes	—
81	C₂×#2283	C₂³	1	1	yes	characteristic
82	#21408	D₄	1	4	yes	—
83	#21379	D₄	1	4	yes	—
84	C₂×#1762	D₄	1	2	yes	—
85	C₂×#1762	D₄	1	2	yes	—
86	C₂×C₄×#100	D₄	1	4	yes	complemented
87	#17743	D₄	1	4	yes	complemented
88	#17671	D₄	1	4	yes	complemented
89	#17449	D₄	1	2	yes	—
90	#17448	D₄	1	2	yes	—
91	#17447	D₄	1	4	yes	—
92	C₂×#1478	D₄	1	4	yes	complemented
93	C₂³×#41	#41	1	1	yes	characteristic
94	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
95	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
96	C₂⁴×C₈	C₂×D₄	1	1	yes	characteristic
97	C₂⁴×C₈	C₂×D₄	1	1	yes	characteristic
98	C₂×#533	C₂×D₄	1	1	yes	characteristic
99	C₂×#533	C₂×D₄	1	1	yes	characteristic
100	C₂×#533	C₂×D₄	1	1	yes	characteristic
101	C₂×#532	C₂×D₄	1	1	yes	characteristic
102	C₂×#532	C₂×D₄	1	1	yes	characteristic
103	C₂×#532	C₂×D₄	1	1	yes	characteristic
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	#41	1	2	yes	—
110	C₂²×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic
111	C₂²×#127	C₂×D₄	1	1	yes	characteristic
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	C₂²×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
119	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
120	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
121	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
126	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
128	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×D₄	#41	1	2	yes	—
130	C₂²×#117	#41	1	1	yes	characteristic
131	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
132	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
133	C₂³×C₄²	C₂⁴	1	1	yes	characteristic
134	#2920	C₂×D₄	1	2	yes	—
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	#2920	C₂×D₄	1	2	yes	—
140	#2920	C₂×D₄	1	2	yes	—
141	C₂×#432	C₂×D₄	1	2	yes	—
142	C₂×#432	C₂×D₄	1	2	yes	—
143	C₂×#432	C₂×D₄	1	2	yes	—
144	C₂×#431	C₂×D₄	1	2	yes	—
145	C₂×#431	C₂×D₄	1	2	yes	—
146	C₂×#431	C₂×D₄	1	2	yes	—
147	C₂×#423	C₂×D₄	1	2	yes	—
148	C₂×C₄×M₁₆	C₂×D₄	1	2	yes	—
149	C₂×C₄×M₁₆	C₂×D₄	1	2	yes	—
150	C₂×C₄×M₁₆	C₂×D₄	1	2	yes	—
151	C₂²×#97	C₂×D₄	1	2	yes	—
152	C₂²×#97	C₂×D₄	1	2	yes	—
153	C₂²×#97	C₂×D₄	1	2	yes	—
154	#2283	C₂×D₄	1	2	yes	—
155	#2283	C₂×D₄	1	2	yes	—
156	C₂×C₄×C₄⋊C₄	C₂×D₄	1	2	yes	—
157	C₂²×#41	#121	1	2	yes	—
158	C₂²×#41	#121	1	2	yes	—
159	C₂³×Q₈	#121	1	1	yes	characteristic
160	C₂³×D₄	#120	1	1	yes	characteristic
161	C₂³×D₄	#120	1	2	yes	—
162	C₂³×D₄	#120	1	2	yes	—
163	C₂³×D₄	#120	1	1	yes	characteristic
164	C₂³×D₄	#121	1	2	yes	—
165	C₂³×D₄	#121	1	1	yes	characteristic
166	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
167	C₂⁴×C₄	C₂×#41	1	1	yes	characteristic
168	C₂⁴×C₄	H(5,𝔽₂)	1	1	yes	characteristic
169	C₂³×C₈	#120	1	2	yes	—
170	C₂³×C₈	#120	1	2	yes	—
171	#532	#120	1	4	yes	—
172	#532	#121	1	4	yes	—
173	#532	#121	1	4	yes	—
174	#532	#127	1	4	yes	—
175	C₂×C₄⋊Q₈	#120	1	1	yes	characteristic
176	C₂×C₄⋊Q₈	#120	1	1	yes	characteristic
177	C₂×C₄⋊Q₈	#120	1	1	yes	characteristic
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	1	yes	characteristic
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	#127	1	2	yes	—
189	C₂×C₄×D₄	#120	1	2	yes	—
190	C₂×C₄×D₄	#120	1	2	yes	—
191	C₂×C₄×D₄	#120	1	2	yes	—
192	C₂×C₄×D₄	#120	1	2	yes	—
193	C₂×C₄×D₄	#120	1	2	yes	—
194	C₂×C₄×D₄	#121	1	2	yes	—
195	C₂×C₄×D₄	#121	1	2	yes	—
196	C₂×C₄×D₄	#121	1	2	yes	—
197	C₂×C₄×D₄	#121	1	2	yes	—
198	C₂×C₄×D₄	#127	1	2	yes	—
199	C₂×C₄×D₄	#127	1	2	yes	—
200	C₂×C₄×D₄	#127	1	2	yes	—
201	C₂×#117	#121	1	2	yes	—
202	C₂×#117	#121	1	2	yes	—
203	C₂²×C₄⋊C₄	#120	1	2	yes	—
204	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
205	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
206	C₂²×C₄⋊C₄	#120	1	2	yes	—
207	C₂²×C₄⋊C₄	#121	1	2	yes	—
208	C₂²×C₄⋊C₄	#121	1	1	yes	characteristic
209	C₂²×C₄⋊C₄	#121	1	1	yes	characteristic
210	C₂²×C₄²	C₂²×D₄	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	H(5,𝔽₂)	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	#431	#120	1	4	yes	—
239	#423	#120	1	4	yes	—
240	C₄×M₁₆	#120	1	4	yes	—
241	C₂×#97	#120	1	4	yes	—
242	C₂×C₄×C₈	#120	1	4	yes	—
243	C₄×C₄⋊C₄	#120	1	4	yes	—
244	C₂⁵	#546	1	1	yes	characteristic
245	C₂²×Q₈	#392	1	2	yes	—
246	C₂²×D₄	#392	1	2	yes	—
247	C₂²×D₄	#392	1	2	yes	—
248	C₂²×D₄	#392	1	2	yes	—
249	C₂³×C₄	C₂×#120	1	1	yes	characteristic
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×#121	1	1	yes	characteristic
254	C₂³×C₄	C₂×#121	1	1	yes	characteristic
255	C₂³×C₄	C₂×#121	1	1	yes	characteristic
256	C₂³×C₄	C₂×#121	1	1	yes	characteristic
257	C₂³×C₄	#525	1	1	yes	characteristic
258	C₂³×C₄	#525	1	1	yes	characteristic
259	C₂³×C₄	#534	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	#535	1	1	yes	characteristic
265	C₂³×C₄	#535	1	1	yes	characteristic
266	C₂³×C₄	#535	1	1	yes	characteristic
267	C₂³×C₄	#538	1	1	yes	characteristic
268	C₂³×C₄	#538	1	1	yes	characteristic
269	C₂³×C₄	#538	1	1	yes	characteristic
270	C₂³×C₄	D₄²	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	#546	1	1	yes	characteristic
281	C₂³×C₄	#546	1	1	yes	characteristic
282	C₂³×C₄	#546	1	1	yes	characteristic
283	C₂³×C₄	#546	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	#560	1	1	yes	characteristic
290	C₂³×C₄	#560	1	1	yes	characteristic
291	C₄⋊Q₈	#392	1	4	yes	—
292	#127	#392	1	4	yes	—
293	C₂×C₄⋊C₄	#392	1	2	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×C₄²	C₂×#120	1	1	yes	characteristic
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×#120	1	1	yes	characteristic
310	C₂×C₄²	C₂×#120	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	C₂×#127	1	1	yes	characteristic
318	C₂×C₄²	C₂×#127	1	1	yes	characteristic
319	C₂×C₄²	C₂×#127	1	1	yes	characteristic
320	C₂×C₄²	#534	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	#535	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	#535	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	D₄²	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	D₄²	1	1	yes	characteristic
387	C₂×C₄²	D₄²	1	1	yes	characteristic
388	C₂×C₄²	D₄²	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	#560	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	H(3,𝔽₄)	1	1	yes	characteristic
408	C₂×C₄²	H(3,𝔽₄)	1	1	yes	characteristic
409	C₂⁴	#2404	1	1	yes	characteristic
410	C₂⁴	#2408	1	1	yes	characteristic
411	C₂⁴	#2410	1	1	yes	characteristic
412	C₂⁴	#2410	1	1	yes	characteristic
413	C₂⁴	#2424	1	1	yes	characteristic
414	C₂⁴	#2668	1	1	yes	characteristic
415	C₂⁴	#2678	1	1	yes	characteristic
416	C₂×D₄	#2010	1	4	yes	—
417	C₂²×C₄	C₂×#392	1	1	yes	characteristic
418	C₂²×C₄	C₂×#392	1	1	yes	characteristic
419	C₂²×C₄	#2403	1	1	yes	characteristic
420	C₂²×C₄	#2403	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	#2408	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	#2410	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	#2424	1	1	yes	characteristic
452	C₂²×C₄	#2424	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	#2424	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	#2539	1	1	yes	characteristic
466	C₂²×C₄	#2539	1	1	yes	characteristic
467	C₂²×C₄	#2613	1	1	yes	characteristic
468	C₂²×C₄	#2613	1	1	yes	characteristic
469	C₂²×C₄	#2613	1	1	yes	characteristic
470	C₂²×C₄	#2617	1	1	yes	characteristic
471	C₂²×C₄	#2617	1	1	yes	characteristic
472	C₂²×C₄	#2668	1	1	yes	characteristic
473	C₂²×C₄	#2668	1	1	yes	characteristic
474	C₂²×C₄	#2668	1	1	yes	characteristic
475	C₂²×C₄	#2668	1	1	yes	characteristic
476	C₂²×C₄	#2669	1	1	yes	characteristic
477	C₂²×C₄	#2669	1	1	yes	characteristic
478	C₂²×C₄	#2669	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	#2670	1	1	yes	characteristic
487	C₂²×C₄	#2670	1	1	yes	characteristic
488	C₂²×C₄	#2670	1	1	yes	characteristic
489	C₂²×C₄	#2678	1	1	yes	characteristic
490	C₂²×C₄	#2678	1	1	yes	characteristic
491	C₂²×C₄	#2678	1	1	yes	characteristic
492	C₂²×C₄	#2678	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	#2679	1	1	yes	characteristic
497	C₂²×C₄	#2679	1	1	yes	characteristic
498	C₂²×C₄	#2812	1	1	yes	characteristic
499	C₂²×C₄	#2846	1	1	yes	characteristic
500	C₂²×C₄	#2847	1	1	yes	characteristic
501	C₄²	C₂×#392	1	1	yes	characteristic
502	C₄²	#2403	1	1	yes	characteristic
503	C₄²	#2403	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	#2404	1	1	yes	characteristic
512	C₄²	#2408	1	1	yes	characteristic
513	C₄²	#2408	1	1	yes	characteristic
514	C₄²	#2408	1	1	yes	characteristic
515	C₄²	#2408	1	1	yes	characteristic
516	C₄²	#2410	1	1	yes	characteristic
517	C₄²	#2410	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	#2424	1	1	yes	characteristic
527	C₄²	#2424	1	1	yes	characteristic
528	C₄²	#2433	1	1	yes	characteristic
529	C₄²	#2433	1	1	yes	characteristic
530	C₄²	#2433	1	1	yes	characteristic
531	C₄²	#2433	1	1	yes	characteristic
532	C₄²	#2433	1	1	yes	characteristic
533	C₄²	#2433	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	#2539	1	1	yes	characteristic
539	C₄²	#2613	1	1	yes	characteristic
540	C₄²	#2613	1	1	yes	characteristic
541	C₄²	#2613	1	1	yes	characteristic
542	C₄²	#2617	1	1	yes	characteristic
543	C₄²	#2668	1	1	yes	characteristic
544	C₄²	#2669	1	1	yes	characteristic
545	C₄²	#2669	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	#2679	1	1	yes	characteristic
560	C₄²	#2679	1	1	yes	characteristic
561	C₄²	#2679	1	1	yes	characteristic
562	C₄²	#2679	1	1	yes	characteristic
563	C₄²	#2812	1	1	yes	characteristic
564	C₄²	#2846	1	1	yes	characteristic
565	C₂³	#14715	1	1	yes	characteristic
566	C₂³	#14716	1	1	yes	characteristic
567	C₂³	#15257	1	1	yes	characteristic
568	C₂³	#15257	1	1	yes	characteristic
569	C₂³	#15257	1	1	yes	characteristic
570	C₂³	#15267	1	1	yes	characteristic
571	C₂³	#16249	1	1	yes	characteristic
572	C₂³	#30434	1	4	yes	—
573	C₂×C₄	#14715	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	#15257	1	1	yes	characteristic
581	C₂×C₄	#15257	1	1	yes	characteristic
582	C₂×C₄	#15257	1	1	yes	characteristic
583	C₂×C₄	#15258	1	1	yes	characteristic
584	C₂×C₄	#15258	1	1	yes	characteristic
585	C₂×C₄	#15258	1	1	yes	characteristic
586	C₂×C₄	#15267	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	#15947	1	1	yes	characteristic
592	C₂×C₄	#16249	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	C₂×#2010	1	2	yes	—
598	C₂×C₄	#23414	1	2	yes	—
599	C₂²	#156684	1	1	yes	characteristic
600	C₂²	#394133	1	2	yes	—
601	C₂²	#394261	1	2	yes	—
602	C₂²	#417674	1	2	yes	—
603	C₂²	#417674	1	2	yes	—
604	C₂²	#454002	1	2	yes	—
605	C₄	#393936	1	2	yes	—
606	C₄	#393988	1	1	yes	characteristic
607	C₄	#393989	1	1	yes	characteristic
608	C₂	#72237177	1	1	yes	characteristic
609	C₂	#72237252	1	1	yes	characteristic
610	C₂	#72238744	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. #72239067	C₂	semidirect
2. #72239066	C₂	semidirect
3. #72239064	C₂	semidirect
4. #72239063	C₂	semidirect
5. #72239062	C₂	semidirect
6. #72239060	C₂	semidirect
7. #72239030	C₂	semidirect
8. #72239029	C₂	semidirect
9. #72239021	C₂	semidirect
10. #72238993	C₂	semidirect
11. #72238987	C₂	semidirect
12. #72238966	C₂	semidirect
13. #72238775	C₂	semidirect
14. #72237152	C₂	semidirect
15. C₂×#6453969	C₂	semidirect
20. C₂×#60558	C₂²	semidirect
24. #6374710	C₂²	semidirect
25. #6374239	C₂²	semidirect
27. #6372352	C₂²	semidirect
31. C₂×#20726	C₂²	semidirect
35. #6343801	C₂²	semidirect
40. C₂×#17448	C₂²	semidirect
42. #353794	C₂²	semidirect
43. #181798	C₂²	semidirect
44. #181796	C₂²	semidirect
45. #181265	C₂²	semidirect
46. #181219	C₂²	semidirect
47. #181194	C₂²	semidirect
48. C₂×#7919	C₂²	semidirect
49. C₂×#7861	C₂²	semidirect
50. #180869	C₂²	semidirect
61. #60941	D₄	semidirect
62. #60940	D₄	semidirect
66. C₂×#3077	D₄	semidirect
67. C₂×#3036	D₄	semidirect
86. C₂×C₄×#100	D₄	semidirect
87. #17743	D₄	semidirect
88. #17671	D₄	semidirect
92. C₂×#1478	D₄	semidirect

Maximal subgroups

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

subgroup	index
#72239067	2
#72239066	2
#72239064	2
#72239063	2
#72239062	2
#72239060	2
#72239030	2
#72239029	2
#72239021	2
#72238993	2
#72238987	2
#72238966	2
#72238775	2
#72237152	2
C₂×#6453969	2