Subgroups — #72338240

Order 2048.

At least 7195 conjugacy classes of subgroups; only the 784 normal subgroups are shown.

The subgroup lattice has 593 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72338239	C₂	1	1	yes	maximal, characteristic, complemented
2	#72338238	C₂	1	1	yes	maximal, characteristic, complemented
3	#72338237	C₂	1	1	yes	maximal, characteristic, complemented
4	#72338236	C₂	1	1	yes	maximal, characteristic, complemented
5	#72338235	C₂	1	1	yes	maximal, characteristic, complemented
6	#72338234	C₂	1	1	yes	maximal, characteristic, complemented
7	#72338210	C₂	1	1	yes	maximal, characteristic, complemented
8	#72338207	C₂	1	1	yes	maximal, characteristic, complemented
9	#72310294	C₂	1	1	yes	maximal, characteristic, complemented
10	#72279493	C₂	1	1	yes	maximal, characteristic, complemented
11	#72279460	C₂	1	1	yes	maximal, characteristic, complemented
12	#72257768	C₂	1	1	yes	maximal, characteristic, complemented
13	#72257694	C₂	1	1	yes	maximal, characteristic, complemented
14	#72257575	C₂	1	1	yes	maximal, characteristic, complemented
15	#72226726	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×#60561	C₂²	1	1	yes	characteristic
20	C₂×#60561	C₂²	1	1	yes	characteristic, complemented
21	C₂²×#3038	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	#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	#6372358	C₂²	1	1	yes	characteristic, complemented
31	#6370997	C₂²	1	1	yes	characteristic, complemented
32	C₂×#17745	C₂²	1	1	yes	characteristic, complemented
33	C₂×#17741	C₂²	1	1	yes	characteristic
34	C₂×#17741	C₂²	1	1	yes	characteristic
35	#6343804	C₂²	1	1	yes	characteristic
36	#6343804	C₂²	1	1	yes	characteristic
37	#6343377	C₂²	1	1	yes	characteristic, complemented
38	#6343016	C₂²	1	1	yes	characteristic, complemented
39	#6342561	C₂²	1	1	yes	characteristic
40	#6342561	C₂²	1	1	yes	characteristic
41	#6342561	C₂²	1	1	yes	characteristic, complemented
42	#353804	C₂²	1	1	yes	characteristic, complemented
43	#181791	C₂²	1	1	yes	characteristic, complemented
44	#181433	C₂²	1	1	yes	characteristic, complemented
45	#181375	C₂²	1	1	yes	characteristic, complemented
46	#181222	C₂²	1	1	yes	characteristic, complemented
47	#181197	C₂²	1	1	yes	characteristic, complemented
48	#181175	C₂²	1	1	yes	characteristic, complemented
49	#181124	C₂²	1	1	yes	characteristic, complemented
50	#180880	C₂²	1	1	yes	characteristic, complemented
51	C₂²×#532	D₄	1	2	yes	—
52	C₂²×#532	C₂³	1	1	yes	characteristic
53	C₂²×#532	C₂³	1	1	yes	characteristic
54	C₂³×#127	D₄	1	2	yes	—
55	C₂³×#127	C₂³	1	1	yes	characteristic
56	C₂²×C₄×#41	C₂³	1	1	yes	characteristic
57	C₂²×C₄×#41	C₂³	1	1	yes	characteristic
58	C₂×#3214	D₄	1	4	yes	complemented
59	C₂²×#493	D₄	1	2	yes	complemented
60	C₂²×#492	D₄	1	2	yes	complemented
61	C₂×#3103	D₄	1	2	yes	complemented
62	C₂×#3100	D₄	1	2	yes	complemented
63	C₂²×#460	D₄	1	2	yes	complemented
64	C₂²×#459	D₄	1	2	yes	complemented
65	C₂×#2920	C₂³	1	1	yes	characteristic
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	C₂²×#423	C₂³	1	1	yes	characteristic
72	C₂²×C₄×M₁₆	C₂³	1	1	yes	characteristic
73	#34955	D₄	1	2	yes	—
74	#34936	D₄	1	2	yes	—
75	#34809	D₄	1	2	yes	—
76	#34736	D₄	1	2	yes	—
77	#34012	C₂³	1	1	yes	characteristic
78	#34012	C₂³	1	1	yes	characteristic
79	#21891	D₄	1	4	yes	complemented
80	#21803	D₄	1	4	yes	complemented
81	#21803	D₄	1	4	yes	complemented
82	#21408	D₄	1	4	yes	complemented
83	#21303	D₄	1	2	yes	—
84	#21190	D₄	1	2	yes	—
85	#20898	D₄	1	4	yes	—
86	C₂×#1555	D₄	1	4	yes	complemented
87	#17663	D₄	1	4	yes	complemented
88	#17357	D₄	1	4	yes	—
89	C₂³×#41	C₂×D₄	1	1	yes	characteristic
90	C₂³×#41	#41	1	1	yes	characteristic
91	C₂³×M₁₆	C₂×D₄	1	2	yes	—
92	C₂×#532	C₂×D₄	1	2	yes	—
93	C₂×#532	C₂×D₄	1	2	yes	—
94	C₂×#532	C₂×D₄	1	2	yes	—
95	C₂×#532	C₂×D₄	1	2	yes	—
96	C₂×#532	C₂×D₄	1	2	yes	—
97	C₂×#532	C₂×D₄	1	2	yes	—
98	C₂×#532	C₂×D₄	1	2	yes	—
99	C₂×#532	#41	1	2	yes	—
100	C₂²×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic
102	C₂²×#127	C₂×D₄	1	1	yes	characteristic
103	C₂²×#127	C₂×D₄	1	1	yes	characteristic
104	C₂²×#127	C₂×D₄	1	2	yes	—
105	C₂²×#127	C₂×D₄	1	2	yes	—
106	C₂²×#127	C₂×D₄	1	2	yes	—
107	C₂²×#127	C₂×D₄	1	2	yes	—
108	C₂²×#127	C₂×D₄	1	2	yes	—
109	C₂²×#127	C₂×D₄	1	2	yes	—
110	C₂²×#127	#41	1	2	yes	—
111	C₂²×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×D₄	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	1	yes	characteristic
121	C₂²×#117	C₂×D₄	1	1	yes	characteristic
122	C₂²×#117	C₂×D₄	1	2	yes	—
123	C₂²×#117	#41	1	1	yes	characteristic
124	C₂³×C₄²	C₂×D₄	1	2	yes	—
125	C₂³×C₄²	C₂⁴	1	1	yes	characteristic
126	#2920	C₂×D₄	1	2	yes	—
127	#2920	C₂×D₄	1	2	yes	—
128	#2920	C₂×D₄	1	2	yes	—
129	#2920	C₂×D₄	1	2	yes	—
130	C₂×#432	C₂×D₄	1	2	yes	—
131	C₂×#432	C₂×D₄	1	2	yes	—
132	C₂×#432	C₂×D₄	1	2	yes	—
133	C₂×#431	C₂×D₄	1	2	yes	—
134	C₂×#431	C₂×D₄	1	2	yes	—
135	C₂×#431	C₂×D₄	1	2	yes	—
136	C₂×#423	C₂×D₄	1	2	yes	—
137	C₂×#423	C₂×D₄	1	2	yes	—
138	C₂²×C₄⋊C₈	C₂×D₄	1	2	yes	—
139	C₂×#407	C₂×D₄	1	2	yes	—
140	C₂×C₄×M₁₆	C₂×D₄	1	2	yes	—
141	C₂²×#97	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₈	C₂×D₄	1	2	yes	—
143	#2285	C₂×D₄	1	2	yes	—
144	#2285	C₂×D₄	1	2	yes	—
145	#2283	C₂×D₄	1	2	yes	—
146	#2283	C₂×D₄	1	2	yes	—
147	#2280	C₂×D₄	1	2	yes	—
148	C₄×#117	C₂×D₄	1	2	yes	—
149	C₂³×Q₈	#120	1	1	yes	characteristic
150	C₂³×Q₈	#121	1	1	yes	characteristic
151	C₂³×D₄	#120	1	1	yes	characteristic
152	C₂³×D₄	#121	1	1	yes	characteristic
153	C₂³×D₄	#121	1	2	yes	—
154	C₂⁴×C₄	#120	1	2	yes	—
155	C₂⁴×C₄	#120	1	2	yes	—
156	C₂⁴×C₄	#121	1	2	yes	—
157	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
158	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
159	C₂⁴×C₄	C₂×#41	1	1	yes	characteristic
160	C₂³×C₈	#120	1	4	yes	—
161	#532	#120	1	4	yes	—
162	#532	#121	1	4	yes	—
163	#532	#121	1	4	yes	—
164	#532	#127	1	4	yes	—
165	C₂×C₄⋊Q₈	#120	1	2	yes	—
166	C₂×C₄⋊Q₈	#120	1	2	yes	—
167	C₂×C₄⋊Q₈	#120	1	2	yes	—
168	C₂×C₄⋊Q₈	#121	1	2	yes	—
169	C₂×#127	#120	1	2	yes	—
170	C₂×#127	#120	1	4	yes	—
171	C₂×#127	#120	1	4	yes	—
172	C₂×#127	#120	1	2	yes	—
173	C₂×#127	#120	1	2	yes	—
174	C₂×#127	#120	1	4	yes	—
175	C₂×#127	#121	1	4	yes	—
176	C₂×#127	#121	1	2	yes	—
177	C₂×#127	#121	1	4	yes	—
178	C₂×#127	#121	1	4	yes	—
179	C₂×#127	#127	1	4	yes	—
180	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
181	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
182	C₂²×C₄⋊C₄	#120	1	2	yes	—
183	C₂²×C₄⋊C₄	#121	1	1	yes	characteristic
184	C₂²×C₄⋊C₄	#121	1	1	yes	characteristic
185	C₂²×C₄⋊C₄	#127	1	2	yes	—
186	C₂²×C₂²⋊C₄	#120	1	2	yes	—
187	C₂²×C₂²⋊C₄	#121	1	2	yes	—
188	C₂²×C₂²⋊C₄	#127	1	2	yes	—
189	C₂²×C₄²	#120	1	2	yes	—
190	C₂²×C₄²	#120	1	2	yes	—
191	C₂²×C₄²	#121	1	2	yes	—
192	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
193	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
194	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
195	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
196	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
197	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
198	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
199	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
200	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
201	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
202	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
203	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
204	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
205	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
206	C₂²×C₄²	C₂×#41	1	1	yes	characteristic
207	C₂²×C₄²	C₂×#41	1	1	yes	characteristic
208	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
209	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
210	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
211	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
212	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
213	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
214	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
215	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
216	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
217	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
218	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
219	C₂²×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
220	#432	#120	1	4	yes	—
221	C₂×C₄⋊C₈	#120	1	4	yes	—
222	C₂×C₂²⋊C₈	#120	1	4	yes	—
223	C₂×C₄×C₈	#120	1	4	yes	—
224	#380	#120	1	4	yes	—
225	C₄×C₄⋊C₄	#120	1	4	yes	—
226	C₂⁵	#392	1	2	yes	—
227	C₂⁵	C₂×#121	1	1	yes	characteristic
228	C₂³×C₄	#392	1	2	yes	—
229	C₂³×C₄	#392	1	2	yes	—
230	C₂³×C₄	#392	1	2	yes	—
231	C₂³×C₄	C₂×#120	1	1	yes	characteristic
232	C₂³×C₄	C₂×#120	1	1	yes	characteristic
233	C₂³×C₄	C₂×#120	1	1	yes	characteristic
234	C₂³×C₄	C₂×#120	1	1	yes	characteristic
235	C₂³×C₄	C₂×#120	1	1	yes	characteristic
236	C₂³×C₄	C₂×#120	1	1	yes	characteristic
237	C₂³×C₄	C₂×#120	1	1	yes	characteristic
238	C₂³×C₄	C₂×#121	1	1	yes	characteristic
239	C₂³×C₄	C₂×#121	1	1	yes	characteristic
240	C₂³×C₄	#525	1	1	yes	characteristic
241	C₂³×C₄	#525	1	1	yes	characteristic
242	C₂³×C₄	C₂×#127	1	1	yes	characteristic
243	C₂³×C₄	#534	1	1	yes	characteristic
244	C₂³×C₄	#534	1	1	yes	characteristic
245	C₂³×C₄	#535	1	1	yes	characteristic
246	C₂³×C₄	#535	1	1	yes	characteristic
247	C₂³×C₄	#538	1	1	yes	characteristic
248	C₂³×C₄	#538	1	1	yes	characteristic
249	C₂³×C₄	D₄²	1	1	yes	characteristic
250	C₂³×C₄	D₄²	1	1	yes	characteristic
251	C₂³×C₄	D₄²	1	1	yes	characteristic
252	C₂³×C₄	D₄²	1	1	yes	characteristic
253	C₂³×C₄	D₄²	1	1	yes	characteristic
254	C₂³×C₄	D₄²	1	1	yes	characteristic
255	C₂³×C₄	D₄²	1	1	yes	characteristic
256	C₂³×C₄	D₄²	1	1	yes	characteristic
257	C₂³×C₄	D₄²	1	1	yes	characteristic
258	C₂³×C₄	D₄²	1	1	yes	characteristic
259	C₂³×C₄	D₄²	1	1	yes	characteristic
260	C₂³×C₄	D₄²	1	1	yes	characteristic
261	C₂³×C₄	#546	1	1	yes	characteristic
262	C₂³×C₄	#546	1	1	yes	characteristic
263	C₂³×C₄	#546	1	1	yes	characteristic
264	C₂³×C₄	#546	1	1	yes	characteristic
265	C₂³×C₄	#546	1	1	yes	characteristic
266	C₂³×C₄	#546	1	1	yes	characteristic
267	C₂³×C₄	#546	1	1	yes	characteristic
268	C₂³×C₄	#546	1	1	yes	characteristic
269	C₂³×C₄	#546	1	1	yes	characteristic
270	C₂³×C₄	#546	1	1	yes	characteristic
271	C₂³×C₄	#546	1	1	yes	characteristic
272	C₂³×C₄	#546	1	1	yes	characteristic
273	C₄⋊Q₈	#392	1	4	yes	—
274	#127	#392	1	4	yes	—
275	#127	#392	1	8	yes	—
276	C₂×C₄²	C₂×#120	1	1	yes	characteristic
277	C₂×C₄²	C₂×#120	1	1	yes	characteristic
278	C₂×C₄²	C₂×#120	1	1	yes	characteristic
279	C₂×C₄²	C₂×#120	1	1	yes	characteristic
280	C₂×C₄²	C₂×#120	1	1	yes	characteristic
281	C₂×C₄²	C₂×#120	1	1	yes	characteristic
282	C₂×C₄²	C₂×#120	1	1	yes	characteristic
283	C₂×C₄²	C₂×#120	1	1	yes	characteristic
284	C₂×C₄²	C₂×#120	1	1	yes	characteristic
285	C₂×C₄²	C₂×#120	1	1	yes	characteristic
286	C₂×C₄²	C₂×#120	1	1	yes	characteristic
287	C₂×C₄²	C₂×#121	1	1	yes	characteristic
288	C₂×C₄²	C₂×#121	1	1	yes	characteristic
289	C₂×C₄²	C₂×#121	1	1	yes	characteristic
290	C₂×C₄²	C₂×#121	1	1	yes	characteristic
291	C₂×C₄²	C₂×#121	1	1	yes	characteristic
292	C₂×C₄²	C₂×#121	1	1	yes	characteristic
293	C₂×C₄²	#525	1	1	yes	characteristic
294	C₂×C₄²	C₂×#127	1	1	yes	characteristic
295	C₂×C₄²	C₂×#127	1	1	yes	characteristic
296	C₂×C₄²	#534	1	1	yes	characteristic
297	C₂×C₄²	#534	1	1	yes	characteristic
298	C₂×C₄²	#534	1	1	yes	characteristic
299	C₂×C₄²	#534	1	1	yes	characteristic
300	C₂×C₄²	#534	1	1	yes	characteristic
301	C₂×C₄²	#534	1	1	yes	characteristic
302	C₂×C₄²	#534	1	1	yes	characteristic
303	C₂×C₄²	#534	1	1	yes	characteristic
304	C₂×C₄²	#534	1	1	yes	characteristic
305	C₂×C₄²	#534	1	1	yes	characteristic
306	C₂×C₄²	#534	1	1	yes	characteristic
307	C₂×C₄²	#534	1	1	yes	characteristic
308	C₂×C₄²	#534	1	1	yes	characteristic
309	C₂×C₄²	#534	1	1	yes	characteristic
310	C₂×C₄²	#534	1	1	yes	characteristic
311	C₂×C₄²	#534	1	1	yes	characteristic
312	C₂×C₄²	#534	1	1	yes	characteristic
313	C₂×C₄²	#534	1	1	yes	characteristic
314	C₂×C₄²	#534	1	1	yes	characteristic
315	C₂×C₄²	#535	1	1	yes	characteristic
316	C₂×C₄²	#535	1	1	yes	characteristic
317	C₂×C₄²	#535	1	1	yes	characteristic
318	C₂×C₄²	#535	1	1	yes	characteristic
319	C₂×C₄²	#535	1	1	yes	characteristic
320	C₂×C₄²	#535	1	1	yes	characteristic
321	C₂×C₄²	#535	1	1	yes	characteristic
322	C₂×C₄²	#535	1	1	yes	characteristic
323	C₂×C₄²	#535	1	1	yes	characteristic
324	C₂×C₄²	#535	1	1	yes	characteristic
325	C₂×C₄²	#535	1	1	yes	characteristic
326	C₂×C₄²	#535	1	1	yes	characteristic
327	C₂×C₄²	#535	1	1	yes	characteristic
328	C₂×C₄²	#538	1	1	yes	characteristic
329	C₂×C₄²	#538	1	1	yes	characteristic
330	C₂×C₄²	#538	1	1	yes	characteristic
331	C₂×C₄²	#538	1	1	yes	characteristic
332	C₂×C₄²	D₄²	1	1	yes	characteristic
333	C₂×C₄²	D₄²	1	1	yes	characteristic
334	C₂×C₄²	D₄²	1	1	yes	characteristic
335	C₂×C₄²	D₄²	1	1	yes	characteristic
336	C₂×C₄²	D₄²	1	1	yes	characteristic
337	C₂×C₄²	D₄²	1	1	yes	characteristic
338	C₂×C₄²	D₄²	1	1	yes	characteristic
339	C₂×C₄²	D₄²	1	1	yes	characteristic
340	C₂×C₄²	D₄²	1	1	yes	characteristic
341	C₂×C₄²	D₄²	1	1	yes	characteristic
342	C₂×C₄²	D₄²	1	1	yes	characteristic
343	C₂×C₄²	D₄²	1	1	yes	characteristic
344	C₂×C₄²	D₄²	1	1	yes	characteristic
345	C₂×C₄²	D₄²	1	1	yes	characteristic
346	C₂×C₄²	D₄²	1	1	yes	characteristic
347	C₂×C₄²	D₄²	1	1	yes	characteristic
348	C₂×C₄²	D₄²	1	1	yes	characteristic
349	C₂×C₄²	D₄²	1	1	yes	characteristic
350	C₂×C₄²	D₄²	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	#546	1	1	yes	characteristic
369	C₂×C₄²	#546	1	1	yes	characteristic
370	C₂×C₄²	#546	1	1	yes	characteristic
371	C₂×C₄²	#546	1	1	yes	characteristic
372	C₂×C₄²	#546	1	1	yes	characteristic
373	C₂×C₄²	#546	1	1	yes	characteristic
374	C₂×C₄²	#546	1	1	yes	characteristic
375	C₂×C₄²	#546	1	1	yes	characteristic
376	C₂×C₄²	#546	1	1	yes	characteristic
377	C₂×C₄²	#546	1	1	yes	characteristic
378	C₂×C₄²	#546	1	1	yes	characteristic
379	C₂×C₄²	#546	1	1	yes	characteristic
380	C₂×C₄²	#560	1	1	yes	characteristic
381	C₂×C₄²	#560	1	1	yes	characteristic
382	C₂×C₄²	#560	1	1	yes	characteristic
383	C₂×C₄²	#560	1	1	yes	characteristic
384	C₂×C₄²	#560	1	1	yes	characteristic
385	C₂×C₄²	#560	1	1	yes	characteristic
386	C₂×C₄²	H(3,𝔽₄)	1	1	yes	characteristic
387	C₂×C₄²	H(3,𝔽₄)	1	1	yes	characteristic
388	C₂⁴	C₂×#392	1	1	yes	characteristic
389	C₂⁴	#2408	1	1	yes	characteristic
390	C₂⁴	#2408	1	1	yes	characteristic
391	C₂⁴	#2410	1	1	yes	characteristic
392	C₂⁴	#2410	1	1	yes	characteristic
393	C₂⁴	#2424	1	1	yes	characteristic
394	C₂⁴	#2424	1	1	yes	characteristic
395	C₂²×C₄	#2403	1	1	yes	characteristic
396	C₂²×C₄	#2403	1	1	yes	characteristic
397	C₂²×C₄	#2403	1	1	yes	characteristic
398	C₂²×C₄	#2403	1	1	yes	characteristic
399	C₂²×C₄	#2403	1	1	yes	characteristic
400	C₂²×C₄	#2403	1	1	yes	characteristic
401	C₂²×C₄	#2403	1	1	yes	characteristic
402	C₂²×C₄	#2403	1	1	yes	characteristic
403	C₂²×C₄	#2403	1	1	yes	characteristic
404	C₂²×C₄	#2403	1	1	yes	characteristic
405	C₂²×C₄	#2403	1	1	yes	characteristic
406	C₂²×C₄	#2403	1	1	yes	characteristic
407	C₂²×C₄	#2403	1	1	yes	characteristic
408	C₂²×C₄	#2404	1	1	yes	characteristic
409	C₂²×C₄	#2404	1	1	yes	characteristic
410	C₂²×C₄	#2404	1	1	yes	characteristic
411	C₂²×C₄	#2408	1	1	yes	characteristic
412	C₂²×C₄	#2408	1	1	yes	characteristic
413	C₂²×C₄	#2408	1	1	yes	characteristic
414	C₂²×C₄	#2408	1	1	yes	characteristic
415	C₂²×C₄	#2408	1	1	yes	characteristic
416	C₂²×C₄	#2408	1	1	yes	characteristic
417	C₂²×C₄	#2410	1	1	yes	characteristic
418	C₂²×C₄	#2410	1	1	yes	characteristic
419	C₂²×C₄	#2410	1	1	yes	characteristic
420	C₂²×C₄	#2410	1	1	yes	characteristic
421	C₂²×C₄	#2410	1	1	yes	characteristic
422	C₂²×C₄	#2410	1	1	yes	characteristic
423	C₂²×C₄	#2410	1	1	yes	characteristic
424	C₂²×C₄	#2410	1	1	yes	characteristic
425	C₂²×C₄	#2410	1	1	yes	characteristic
426	C₂²×C₄	#2410	1	1	yes	characteristic
427	C₂²×C₄	#2410	1	1	yes	characteristic
428	C₂²×C₄	#2410	1	1	yes	characteristic
429	C₂²×C₄	#2410	1	1	yes	characteristic
430	C₂²×C₄	#2410	1	1	yes	characteristic
431	C₂²×C₄	#2424	1	1	yes	characteristic
432	C₂²×C₄	#2424	1	1	yes	characteristic
433	C₂²×C₄	#2424	1	1	yes	characteristic
434	C₂²×C₄	#2424	1	1	yes	characteristic
435	C₂²×C₄	#2424	1	1	yes	characteristic
436	C₂²×C₄	#2424	1	1	yes	characteristic
437	C₂²×C₄	#2433	1	1	yes	characteristic
438	C₂²×C₄	#2433	1	1	yes	characteristic
439	C₂²×C₄	#2433	1	1	yes	characteristic
440	C₂²×C₄	#2433	1	1	yes	characteristic
441	C₂²×C₄	#2433	1	1	yes	characteristic
442	C₂²×C₄	#2433	1	1	yes	characteristic
443	C₂²×C₄	#2433	1	1	yes	characteristic
444	C₂²×C₄	#2433	1	1	yes	characteristic
445	C₂²×C₄	#2433	1	1	yes	characteristic
446	C₂²×C₄	#2539	1	1	yes	characteristic
447	C₂²×C₄	#2539	1	1	yes	characteristic
448	C₂²×C₄	#2539	1	1	yes	characteristic
449	C₂²×C₄	#2613	1	1	yes	characteristic
450	C₂²×C₄	#2613	1	1	yes	characteristic
451	C₂²×C₄	#2617	1	1	yes	characteristic
452	C₂²×C₄	#2668	1	1	yes	characteristic
453	C₂²×C₄	#2668	1	1	yes	characteristic
454	C₂²×C₄	#2668	1	1	yes	characteristic
455	C₂²×C₄	#2668	1	1	yes	characteristic
456	C₂²×C₄	#2669	1	1	yes	characteristic
457	C₂²×C₄	#2669	1	1	yes	characteristic
458	C₂²×C₄	#2669	1	1	yes	characteristic
459	C₂²×C₄	#2669	1	1	yes	characteristic
460	C₂²×C₄	#2669	1	1	yes	characteristic
461	C₂²×C₄	#2669	1	1	yes	characteristic
462	C₂²×C₄	#2670	1	1	yes	characteristic
463	C₂²×C₄	#2670	1	1	yes	characteristic
464	C₂²×C₄	#2670	1	1	yes	characteristic
465	C₂²×C₄	#2670	1	1	yes	characteristic
466	C₂²×C₄	#2678	1	1	yes	characteristic
467	C₂²×C₄	#2678	1	1	yes	characteristic
468	C₂²×C₄	#2678	1	1	yes	characteristic
469	C₂²×C₄	#2678	1	1	yes	characteristic
470	C₂²×C₄	#2678	1	1	yes	characteristic
471	C₂²×C₄	#2678	1	1	yes	characteristic
472	C₂²×C₄	#2678	1	1	yes	characteristic
473	C₂²×C₄	#2678	1	1	yes	characteristic
474	C₂²×C₄	#2679	1	1	yes	characteristic
475	C₂²×C₄	#2679	1	1	yes	characteristic
476	C₂²×C₄	#2846	1	1	yes	characteristic
477	C₂²×C₄	#2846	1	1	yes	characteristic
478	C₂²×C₄	#2847	1	1	yes	characteristic
479	C₄²	C₂×#392	1	1	yes	characteristic
480	C₄²	C₂×#392	1	1	yes	characteristic
481	C₄²	#2403	1	1	yes	characteristic
482	C₄²	#2403	1	1	yes	characteristic
483	C₄²	#2403	1	1	yes	characteristic
484	C₄²	#2403	1	1	yes	characteristic
485	C₄²	#2403	1	1	yes	characteristic
486	C₄²	#2403	1	1	yes	characteristic
487	C₄²	#2403	1	1	yes	characteristic
488	C₄²	#2403	1	1	yes	characteristic
489	C₄²	#2408	1	1	yes	characteristic
490	C₄²	#2408	1	1	yes	characteristic
491	C₄²	#2408	1	1	yes	characteristic
492	C₄²	#2408	1	1	yes	characteristic
493	C₄²	#2410	1	1	yes	characteristic
494	C₄²	#2410	1	1	yes	characteristic
495	C₄²	#2410	1	1	yes	characteristic
496	C₄²	#2410	1	1	yes	characteristic
497	C₄²	#2410	1	1	yes	characteristic
498	C₄²	#2410	1	1	yes	characteristic
499	C₄²	#2410	1	1	yes	characteristic
500	C₄²	#2410	1	1	yes	characteristic
501	C₄²	#2424	1	1	yes	characteristic
502	C₄²	#2424	1	1	yes	characteristic
503	C₄²	#2424	1	1	yes	characteristic
504	C₄²	#2424	1	1	yes	characteristic
505	C₄²	#2433	1	1	yes	characteristic
506	C₄²	#2433	1	1	yes	characteristic
507	C₄²	#2433	1	1	yes	characteristic
508	C₄²	#2433	1	1	yes	characteristic
509	C₄²	#2433	1	1	yes	characteristic
510	C₄²	#2433	1	1	yes	characteristic
511	C₄²	#2613	1	1	yes	characteristic
512	C₄²	#2613	1	1	yes	characteristic
513	C₄²	#2613	1	1	yes	characteristic
514	C₄²	#2613	1	1	yes	characteristic
515	C₄²	#2617	1	1	yes	characteristic
516	C₄²	#2617	1	1	yes	characteristic
517	C₄²	#2668	1	1	yes	characteristic
518	C₄²	#2668	1	1	yes	characteristic
519	C₄²	#2669	1	1	yes	characteristic
520	C₄²	#2669	1	1	yes	characteristic
521	C₄²	#2669	1	1	yes	characteristic
522	C₄²	#2669	1	1	yes	characteristic
523	C₄²	#2669	1	1	yes	characteristic
524	C₄²	#2669	1	1	yes	characteristic
525	C₄²	#2669	1	1	yes	characteristic
526	C₄²	#2669	1	1	yes	characteristic
527	C₄²	#2669	1	1	yes	characteristic
528	C₄²	#2669	1	1	yes	characteristic
529	C₄²	#2669	1	1	yes	characteristic
530	C₄²	#2669	1	1	yes	characteristic
531	C₄²	#2670	1	1	yes	characteristic
532	C₄²	#2670	1	1	yes	characteristic
533	C₄²	#2678	1	1	yes	characteristic
534	C₄²	#2678	1	1	yes	characteristic
535	C₄²	#2678	1	1	yes	characteristic
536	C₄²	#2678	1	1	yes	characteristic
537	C₄²	#2679	1	1	yes	characteristic
538	C₄²	#2679	1	1	yes	characteristic
539	C₄²	#2679	1	1	yes	characteristic
540	C₄²	#2679	1	1	yes	characteristic
541	C₄²	#2812	1	1	yes	characteristic
542	C₄²	#2812	1	1	yes	characteristic
543	C₂³	#14715	1	1	yes	characteristic
544	C₂³	#14715	1	1	yes	characteristic
545	C₂³	#14716	1	1	yes	characteristic
546	C₂³	#15257	1	1	yes	characteristic
547	C₂³	#15257	1	1	yes	characteristic
548	C₂³	#15267	1	1	yes	characteristic
549	C₂³	#15267	1	1	yes	characteristic
550	C₂×C₄	#14715	1	1	yes	characteristic
551	C₂×C₄	#14715	1	1	yes	characteristic
552	C₂×C₄	#14715	1	1	yes	characteristic
553	C₂×C₄	#14715	1	1	yes	characteristic
554	C₂×C₄	#14716	1	1	yes	characteristic
555	C₂×C₄	#14716	1	1	yes	characteristic
556	C₂×C₄	#15257	1	1	yes	characteristic
557	C₂×C₄	#15257	1	1	yes	characteristic
558	C₂×C₄	#15257	1	1	yes	characteristic
559	C₂×C₄	#15257	1	1	yes	characteristic
560	C₂×C₄	#15258	1	1	yes	characteristic
561	C₂×C₄	#15258	1	1	yes	characteristic
562	C₂×C₄	#15258	1	1	yes	characteristic
563	C₂×C₄	#15267	1	1	yes	characteristic
564	C₂×C₄	#15267	1	1	yes	characteristic
565	C₂×C₄	#15267	1	1	yes	characteristic
566	C₂×C₄	#15267	1	1	yes	characteristic
567	C₂×C₄	#15947	1	1	yes	characteristic
568	C₂×C₄	#16249	1	1	yes	characteristic
569	C₂×C₄	#16249	1	1	yes	characteristic
570	C₂×C₄	#16249	1	1	yes	characteristic
571	C₂×C₄	#16249	1	1	yes	characteristic
572	C₂×C₄	#16249	1	1	yes	characteristic
573	C₂×C₄	#16249	1	1	yes	characteristic
574	C₂×C₄	#23882	1	4	yes	—
575	C₂×C₄	#23882	1	2	yes	—
576	C₂×C₄	#23883	1	2	yes	—
577	C₂×C₄	#30434	1	4	yes	—
578	C₂²	#156684	1	1	yes	characteristic
579	C₂²	#394022	1	2	yes	—
580	C₂²	#394080	1	2	yes	—
581	C₂²	#417674	1	2	yes	—
582	C₄	#394102	1	2	yes	—
583	C₄	#394102	1	1	yes	characteristic
584	C₄	#394104	1	1	yes	characteristic
585	C₄	#417674	1	2	yes	—
586	C₄	#454002	1	2	yes	—
587	C₄	#454029	1	2	yes	—
588	C₄	#454049	1	2	yes	—
589	C₂	#72238744	1	1	yes	characteristic
590	C₂	#72338198	1	1	yes	characteristic
591	C₂	#72338200	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. #72338239	C₂	semidirect
2. #72338238	C₂	semidirect
3. #72338237	C₂	semidirect
4. #72338236	C₂	semidirect
5. #72338235	C₂	semidirect
6. #72338234	C₂	semidirect
7. #72338210	C₂	semidirect
8. #72338207	C₂	semidirect
9. #72310294	C₂	semidirect
10. #72279493	C₂	semidirect
11. #72279460	C₂	semidirect
12. #72257768	C₂	semidirect
13. #72257694	C₂	semidirect
14. #72257575	C₂	semidirect
15. #72226726	C₂	semidirect
20. C₂×#60561	C₂²	semidirect
30. #6372358	C₂²	semidirect
31. #6370997	C₂²	semidirect
32. C₂×#17745	C₂²	semidirect
37. #6343377	C₂²	semidirect
38. #6343016	C₂²	semidirect
41. #6342561	C₂²	semidirect
42. #353804	C₂²	semidirect
43. #181791	C₂²	semidirect
44. #181433	C₂²	semidirect
45. #181375	C₂²	semidirect
46. #181222	C₂²	semidirect
47. #181197	C₂²	semidirect
48. #181175	C₂²	semidirect
49. #181124	C₂²	semidirect
50. #180880	C₂²	semidirect
58. C₂×#3214	D₄	semidirect
59. C₂²×#493	D₄	semidirect
60. C₂²×#492	D₄	semidirect
61. C₂×#3103	D₄	semidirect
62. C₂×#3100	D₄	semidirect
63. C₂²×#460	D₄	semidirect
64. C₂²×#459	D₄	semidirect
79. #21891	D₄	semidirect
80. #21803	D₄	semidirect
81. #21803	D₄	semidirect
82. #21408	D₄	semidirect
86. C₂×#1555	D₄	semidirect
87. #17663	D₄	semidirect

Maximal subgroups

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

subgroup	index
#72338239	2
#72338238	2
#72338237	2
#72338236	2
#72338235	2
#72338234	2
#72338210	2
#72338207	2
#72310294	2
#72279493	2
#72279460	2
#72257768	2
#72257694	2
#72257575	2
#72226726	2