Subgroups — #72281596

Order 2048.

At least 8113 conjugacy classes of subgroups; only the 760 normal subgroups are shown.

The subgroup lattice has 617 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72281567	C₂	1	1	yes	maximal, characteristic, complemented
2	#72281549	C₂	1	1	yes	maximal, characteristic, complemented
3	#72281521	C₂	1	4	yes	maximal, complemented
4	#72281407	C₂	1	1	yes	maximal, characteristic, complemented
5	#72281322	C₂	1	1	yes	maximal, characteristic, complemented
6	#72280561	C₂	1	1	yes	maximal, characteristic
7	#72257778	C₂	1	1	yes	maximal, characteristic, complemented
8	#72257610	C₂	1	1	yes	maximal, characteristic, complemented
9	#72251901	C₂	1	4	yes	maximal, complemented
10	C₂²×C₄×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
11	C₂×#34963	C₄	1	1	yes	characteristic, complemented
12	C₂×#34963	C₂²	1	1	yes	characteristic
13	C₂²×#2397	C₄	1	1	yes	characteristic, complemented
14	#6370950	C₂²	1	1	yes	characteristic
15	#6370937	C₂²	1	1	yes	characteristic
16	#6342561	C₂²	1	1	yes	characteristic
17	#6342561	C₂²	1	1	yes	characteristic
18	#4929027	C₄	1	2	yes	complemented
19	#4929027	C₂²	1	2	yes	—
20	#4929019	C₄	1	2	yes	complemented
21	#4929019	C₂²	1	2	yes	—
22	#515258	C₄	1	1	yes	characteristic, complemented
23	#514189	C₄	1	1	yes	characteristic, complemented
24	#514189	C₂²	1	1	yes	characteristic
25	#482574	C₂²	1	4	yes	complemented
26	#482550	C₂²	1	4	yes	complemented
27	#392259	C₂²	1	2	yes	complemented
28	#392257	C₂²	1	2	yes	complemented
29	#184981	C₂²	1	2	yes	complemented
30	#184979	C₂²	1	2	yes	complemented
31	#127223	C₂²	1	4	yes	complemented
32	#127216	C₂²	1	4	yes	complemented
33	C₂³×H(5,𝔽₂)	D₄	1	1	yes	characteristic
34	C₂²×#520	C₂×C₄	1	1	yes	characteristic
35	C₂²×#520	D₄	1	1	yes	characteristic
36	C₂²×#520	D₄	1	1	yes	characteristic
37	C₂²×#520	C₂³	1	1	yes	characteristic
38	C₂²×#518	C₂×C₄	1	1	yes	characteristic
39	C₂²×#518	D₄	1	1	yes	characteristic
40	C₂²×#518	C₂³	1	1	yes	characteristic
41	C₂²×C₄×#41	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₄×#41	D₄	1	1	yes	characteristic
43	C₂²×C₄×#41	D₄	1	1	yes	characteristic
44	C₂²×C₄×#41	C₂³	1	1	yes	characteristic
45	C₂³×C₄×D₄	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×D₄	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×D₄	D₄	1	1	yes	characteristic
48	C₂³×C₄×D₄	D₄	1	1	yes	characteristic
49	C₂×#2580	C₂×C₄	1	2	yes	—
50	C₂×#2535	C₂×C₄	1	2	yes	—
51	C₂×#2598	C₂×C₄	1	2	yes	—
52	C₂×#2598	C₂³	1	2	yes	—
53	C₂×#2487	D₄	1	1	yes	characteristic
54	C₂×#2487	D₄	1	1	yes	characteristic
55	C₂×#2408	D₄	1	1	yes	characteristic
56	C₂×#2408	D₄	1	1	yes	characteristic
57	C₂×#2398	D₄	1	2	yes	—
58	C₂×#2397	C₂×C₄	1	2	yes	—
59	C₂×#2397	C₂×C₄	1	2	yes	—
60	C₂×#2397	D₄	1	2	yes	—
61	C₂×#2283	C₂×C₄	1	1	yes	characteristic
62	C₂×#2283	C₂×C₄	1	1	yes	characteristic
63	C₂²×#376	C₂×C₄	1	1	yes	characteristic
64	#20694	C₂³	1	2	yes	—
65	#20688	C₂³	1	2	yes	—
66	#20637	D₄	1	2	yes	complemented
67	#20632	D₄	1	2	yes	complemented
68	C₄×#413	D₄	1	2	yes	complemented
69	C₄×#410	D₄	1	2	yes	complemented
70	#17361	D₄	1	2	yes	complemented
71	#17361	D₄	1	2	yes	complemented
72	#17357	C₂³	1	2	yes	—
73	#17357	C₂³	1	2	yes	—
74	#17349	D₄	1	2	yes	complemented
75	#17349	D₄	1	2	yes	complemented
76	#14345	C₂×C₄	1	2	yes	—
77	#14345	C₂×C₄	1	2	yes	—
78	#13961	C₂×C₄	1	2	yes	—
79	#13961	D₄	1	2	yes	—
80	#13959	C₂×C₄	1	2	yes	—
81	#13959	D₄	1	2	yes	—
82	#13957	C₂×C₄	1	2	yes	—
83	#13957	C₂³	1	2	yes	—
84	C₄×#386	D₄	1	2	yes	—
85	C₄×#386	D₄	1	2	yes	—
86	C₂³×#41	C₂²⋊C₄	1	1	yes	characteristic
87	C₂³×#41	C₂²⋊C₄	1	1	yes	characteristic
88	C₂³×#41	C₂×D₄	1	1	yes	characteristic
89	C₂³×#41	C₂×D₄	1	1	yes	characteristic
90	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
91	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
92	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
93	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
94	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
95	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
96	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
97	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
98	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
99	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
100	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
101	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
102	C₂×C₄×#41	#41	1	1	yes	characteristic
103	C₂×C₄×#41	#41	1	1	yes	characteristic
104	C₂×C₄×#41	#41	1	1	yes	characteristic
105	C₂×C₄×#41	#41	1	1	yes	characteristic
106	C₂×C₄×#41	#41	1	1	yes	characteristic
107	C₂×C₄×#41	#41	1	1	yes	characteristic
108	C₂×C₄×#41	#41	1	1	yes	characteristic
109	C₂×C₄×#41	#41	1	1	yes	characteristic
110	C₂²×C₄×Q₈	C₂²⋊C₄	1	1	yes	characteristic
111	C₂²×C₄×Q₈	C₂²⋊C₄	1	1	yes	characteristic
112	C₂²×C₄×Q₈	C₂²×C₄	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×Q₈	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
117	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
118	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
119	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
120	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
121	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
122	C₂²×C₄×D₄	C₂²⋊C₄	1	2	yes	—
123	C₂²×C₄×D₄	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×D₄	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×D₄	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×D₄	C₂²×C₄	1	2	yes	—
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×C₄×D₄	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	1	yes	characteristic
135	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
136	C₂²×#117	C₂²⋊C₄	1	1	yes	characteristic
137	C₂²×#117	C₂²⋊C₄	1	1	yes	characteristic
138	C₂²×#117	C₂²×C₄	1	1	yes	characteristic
139	C₂²×#117	C₂×D₄	1	1	yes	characteristic
140	C₂²×#117	C₂×D₄	1	1	yes	characteristic
141	C₂²×#117	C₂⁴	1	1	yes	characteristic
142	C₂³×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
143	C₂³×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
144	C₂³×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
145	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
146	C₂³×C₄²	C₂²⋊C₄	1	2	yes	—
147	C₂³×C₄²	C₂²×C₄	1	1	yes	characteristic
148	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
149	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
150	C₂×#400	C₂²⋊C₄	1	2	yes	—
151	C₂×#400	C₂×D₄	1	2	yes	—
152	C₂×#399	C₂²⋊C₄	1	2	yes	—
153	C₂×#399	C₂×D₄	1	2	yes	—
154	C₂×#394	C₂²⋊C₄	1	2	yes	—
155	C₂×#394	C₂×D₄	1	2	yes	—
156	C₂×#392	C₂²⋊C₄	1	2	yes	—
157	C₂×#392	C₂×D₄	1	2	yes	—
158	C₂×#383	C₂²⋊C₄	1	2	yes	—
159	C₂×#383	C₂²×C₄	1	2	yes	—
160	C₂×#382	C₂²×C₄	1	2	yes	—
161	C₂×#380	C₂²⋊C₄	1	1	yes	characteristic
162	C₂×#380	C₂²⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
164	C₂×#376	C₂²⋊C₄	1	2	yes	—
165	C₂×#376	C₂²⋊C₄	1	2	yes	—
166	C₂×#376	C₂²×C₄	1	2	yes	—
167	#1742	C₂×D₄	1	4	yes	complemented
168	#1740	C₂×D₄	1	4	yes	complemented
169	#1458	C₂×D₄	1	4	yes	complemented
170	#1458	C₂×D₄	1	4	yes	complemented
171	#1437	C₂²⋊C₄	1	4	yes	—
172	#1437	C₂×D₄	1	4	yes	—
173	#1436	C₂²⋊C₄	1	4	yes	—
174	#1436	C₂×D₄	1	4	yes	—
175	C₂²×#41	#120	1	1	yes	characteristic
176	C₂²×#41	#120	1	1	yes	characteristic
177	C₂²×#41	#121	1	1	yes	characteristic
178	C₂²×#41	#121	1	1	yes	characteristic
179	C₂²×#41	#121	1	1	yes	characteristic
180	C₂²×#41	#121	1	1	yes	characteristic
181	C₂²×#41	#123	1	1	yes	characteristic
182	C₂²×#41	#123	1	1	yes	characteristic
183	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
184	C₂³×Q₈	#120	1	1	yes	characteristic
185	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
186	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
187	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
188	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
189	C₂³×D₄	#120	1	1	yes	characteristic
190	C₂³×D₄	#120	1	1	yes	characteristic
191	C₂³×D₄	#120	1	1	yes	characteristic
192	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
193	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
194	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
195	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
196	C₂⁴×C₄	#120	1	1	yes	characteristic
197	C₂⁴×C₄	#120	1	1	yes	characteristic
198	C₂⁴×C₄	#120	1	1	yes	characteristic
199	C₂⁴×C₄	#120	1	1	yes	characteristic
200	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×Q₈	#99	1	2	yes	—
202	C₂×C₄×Q₈	#99	1	2	yes	—
203	C₂×C₄×Q₈	#120	1	1	yes	characteristic
204	C₂×C₄×Q₈	#120	1	1	yes	characteristic
205	C₂×C₄×Q₈	#121	1	1	yes	characteristic
206	C₂×C₄×Q₈	#121	1	1	yes	characteristic
207	C₂×C₄×Q₈	#121	1	1	yes	characteristic
208	C₂×C₄×Q₈	#121	1	1	yes	characteristic
209	C₂×C₄×Q₈	#121	1	1	yes	characteristic
210	C₂×C₄×Q₈	#121	1	1	yes	characteristic
211	C₂×C₄×Q₈	#121	1	1	yes	characteristic
212	C₂×C₄×Q₈	#121	1	1	yes	characteristic
213	C₂×C₄×Q₈	#123	1	1	yes	characteristic
214	C₂×C₄×Q₈	#123	1	1	yes	characteristic
215	C₂×C₄×Q₈	#124	1	1	yes	characteristic
216	C₂×C₄×Q₈	#124	1	1	yes	characteristic
217	C₂×C₄×Q₈	#127	1	1	yes	characteristic
218	C₂×C₄×Q₈	#127	1	1	yes	characteristic
219	C₂×C₄×D₄	#99	1	2	yes	—
220	C₂×C₄×D₄	#99	1	2	yes	—
221	C₂×C₄×D₄	#99	1	2	yes	—
222	C₂×C₄×D₄	#99	1	2	yes	—
223	C₂×C₄×D₄	#99	1	2	yes	—
224	C₂×C₄×D₄	#99	1	2	yes	—
225	C₂×C₄×D₄	#120	1	1	yes	characteristic
226	C₂×C₄×D₄	#120	1	1	yes	characteristic
227	C₂×C₄×D₄	#120	1	1	yes	characteristic
228	C₂×C₄×D₄	#120	1	1	yes	characteristic
229	C₂×C₄×D₄	#120	1	1	yes	characteristic
230	C₂×C₄×D₄	#120	1	1	yes	characteristic
231	C₂×C₄×D₄	#121	1	1	yes	characteristic
232	C₂×C₄×D₄	#121	1	1	yes	characteristic
233	C₂×C₄×D₄	#121	1	1	yes	characteristic
234	C₂×C₄×D₄	#121	1	1	yes	characteristic
235	C₂×C₄×D₄	#121	1	1	yes	characteristic
236	C₂×C₄×D₄	#121	1	1	yes	characteristic
237	C₂×C₄×D₄	#121	1	1	yes	characteristic
238	C₂×C₄×D₄	#121	1	1	yes	characteristic
239	C₂×C₄×D₄	#121	1	1	yes	characteristic
240	C₂×C₄×D₄	#121	1	1	yes	characteristic
241	C₂×C₄×D₄	#121	1	1	yes	characteristic
242	C₂×C₄×D₄	#121	1	1	yes	characteristic
243	C₂×C₄×D₄	#121	1	1	yes	characteristic
244	C₂×C₄×D₄	#121	1	1	yes	characteristic
245	C₂×C₄×D₄	#121	1	1	yes	characteristic
246	C₂×C₄×D₄	#121	1	1	yes	characteristic
247	C₂×C₄×D₄	#121	1	1	yes	characteristic
248	C₂×C₄×D₄	#121	1	1	yes	characteristic
249	C₂×C₄×D₄	#121	1	1	yes	characteristic
250	C₂×C₄×D₄	#121	1	1	yes	characteristic
251	C₂×C₄×D₄	#121	1	1	yes	characteristic
252	C₂×C₄×D₄	#121	1	1	yes	characteristic
253	C₂×C₄×D₄	#121	1	1	yes	characteristic
254	C₂×C₄×D₄	#121	1	1	yes	characteristic
255	C₂×C₄×D₄	#123	1	1	yes	characteristic
256	C₂×C₄×D₄	#123	1	1	yes	characteristic
257	C₂×C₄×D₄	#123	1	1	yes	characteristic
258	C₂×C₄×D₄	#123	1	1	yes	characteristic
259	C₂×C₄×D₄	#123	1	1	yes	characteristic
260	C₂×C₄×D₄	#123	1	1	yes	characteristic
261	C₂×C₄×D₄	#124	1	1	yes	characteristic
262	C₂×C₄×D₄	#124	1	1	yes	characteristic
263	C₂×C₄×D₄	#124	1	1	yes	characteristic
264	C₂×C₄×D₄	#124	1	1	yes	characteristic
265	C₂×C₄×D₄	#124	1	1	yes	characteristic
266	C₂×C₄×D₄	#124	1	1	yes	characteristic
267	C₂×C₄×D₄	#127	1	1	yes	characteristic
268	C₂×C₄×D₄	#127	1	1	yes	characteristic
269	C₂×C₄×D₄	#127	1	1	yes	characteristic
270	C₂×C₄×D₄	#127	1	1	yes	characteristic
271	C₂×C₄×D₄	#127	1	1	yes	characteristic
272	C₂×C₄×D₄	#127	1	1	yes	characteristic
273	C₂×#117	C₄×D₄	1	1	yes	characteristic
274	C₂×#117	C₄×D₄	1	1	yes	characteristic
275	C₂×#117	C₄×D₄	1	1	yes	characteristic
276	C₂×#117	C₄×D₄	1	1	yes	characteristic
277	C₂×#117	C₄×D₄	1	1	yes	characteristic
278	C₂×#117	C₄×D₄	1	1	yes	characteristic
279	C₂×#117	C₄×D₄	1	1	yes	characteristic
280	C₂×#117	C₄×D₄	1	1	yes	characteristic
281	C₂×#117	#120	1	1	yes	characteristic
282	C₂×#117	#120	1	1	yes	characteristic
283	C₂×#117	#121	1	1	yes	characteristic
284	C₂×#117	#121	1	1	yes	characteristic
285	C₂×#117	#121	1	1	yes	characteristic
286	C₂×#117	#121	1	1	yes	characteristic
287	C₂×#117	#123	1	1	yes	characteristic
288	C₂×#117	#123	1	1	yes	characteristic
289	C₂×#117	C₂²×D₄	1	1	yes	characteristic
290	C₂×#117	C₂²×D₄	1	1	yes	characteristic
291	C₂×#117	C₂²×D₄	1	1	yes	characteristic
292	C₂×#117	C₂²×D₄	1	1	yes	characteristic
293	C₂×#117	C₂×#41	1	1	yes	characteristic
294	C₂×#117	C₂×#41	1	1	yes	characteristic
295	C₂×#117	C₂×#41	1	1	yes	characteristic
296	C₂×#117	C₂×#41	1	1	yes	characteristic
297	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
298	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
299	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
300	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
301	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
302	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
303	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
304	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
305	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
306	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
307	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
308	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
309	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
310	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
311	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
312	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
313	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
314	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
315	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
316	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
317	C₂²×C₄²	C₂×C₂²⋊C₄	1	4	yes	—
318	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
319	C₂²×C₄²	C₄×D₄	1	1	yes	characteristic
320	C₂²×C₄²	C₄×D₄	1	1	yes	characteristic
321	C₂²×C₄²	C₄×D₄	1	1	yes	characteristic
322	C₂²×C₄²	C₄×D₄	1	1	yes	characteristic
323	C₂²×C₄²	C₄×D₄	1	1	yes	characteristic
324	C₂²×C₄²	C₄×D₄	1	1	yes	characteristic
325	C₂²×C₄²	C₄×D₄	1	1	yes	characteristic
326	C₂²×C₄²	C₄×D₄	1	1	yes	characteristic
327	C₂²×C₄²	#120	1	1	yes	characteristic
328	C₂²×C₄²	#120	1	1	yes	characteristic
329	C₂²×C₄²	#120	1	1	yes	characteristic
330	C₂²×C₄²	#120	1	1	yes	characteristic
331	C₂²×C₄²	#120	1	1	yes	characteristic
332	C₂²×C₄²	#120	1	1	yes	characteristic
333	C₂²×C₄²	#120	1	1	yes	characteristic
334	C₂²×C₄²	#120	1	1	yes	characteristic
335	C₂²×C₄²	#121	1	1	yes	characteristic
336	C₂²×C₄²	#121	1	1	yes	characteristic
337	C₂²×C₄²	#121	1	1	yes	characteristic
338	C₂²×C₄²	#121	1	1	yes	characteristic
339	C₂²×C₄²	#121	1	1	yes	characteristic
340	C₂²×C₄²	#121	1	1	yes	characteristic
341	C₂²×C₄²	#121	1	1	yes	characteristic
342	C₂²×C₄²	#121	1	1	yes	characteristic
343	C₂²×C₄²	#123	1	1	yes	characteristic
344	C₂²×C₄²	#123	1	1	yes	characteristic
345	C₂²×C₄²	#123	1	1	yes	characteristic
346	C₂²×C₄²	#123	1	1	yes	characteristic
347	C₂²×C₄²	C₂³×C₄	1	1	yes	characteristic
348	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
349	C₂×#95	C₂×C₂²⋊C₄	1	2	yes	—
350	C₂×#95	C₂×C₂²⋊C₄	1	2	yes	—
351	C₂×#95	C₂×C₂²⋊C₄	1	4	yes	—
352	C₂⁵	#379	1	1	yes	characteristic
353	C₂⁵	#379	1	1	yes	characteristic
354	C₂⁵	C₂×#120	1	1	yes	characteristic
355	C₂²×Q₈	#392	1	1	yes	characteristic
356	C₂²×Q₈	#392	1	1	yes	characteristic
357	C₂²×Q₈	#394	1	1	yes	characteristic
358	C₂²×Q₈	#394	1	1	yes	characteristic
359	C₂²×Q₈	C₂×#99	1	2	yes	—
360	C₂²×D₄	#392	1	1	yes	characteristic
361	C₂²×D₄	#392	1	1	yes	characteristic
362	C₂²×D₄	#392	1	1	yes	characteristic
363	C₂²×D₄	#392	1	1	yes	characteristic
364	C₂²×D₄	#392	1	1	yes	characteristic
365	C₂²×D₄	#392	1	1	yes	characteristic
366	C₂²×D₄	#394	1	1	yes	characteristic
367	C₂²×D₄	#394	1	1	yes	characteristic
368	C₂²×D₄	#394	1	1	yes	characteristic
369	C₂²×D₄	#394	1	1	yes	characteristic
370	C₂²×D₄	#394	1	1	yes	characteristic
371	C₂²×D₄	#394	1	1	yes	characteristic
372	C₂²×D₄	C₂×#99	1	2	yes	—
373	C₂²×D₄	C₂×#99	1	2	yes	—
374	C₂²×D₄	C₂×#99	1	2	yes	—
375	C₂³×C₄	#379	1	1	yes	characteristic
376	C₂³×C₄	#379	1	1	yes	characteristic
377	C₂³×C₄	#379	1	1	yes	characteristic
378	C₂³×C₄	#379	1	1	yes	characteristic
379	C₂³×C₄	#379	1	1	yes	characteristic
380	C₂³×C₄	#379	1	1	yes	characteristic
381	C₂³×C₄	#386	1	1	yes	characteristic
382	C₂³×C₄	#386	1	1	yes	characteristic
383	C₂³×C₄	#386	1	1	yes	characteristic
384	C₂³×C₄	#386	1	1	yes	characteristic
385	C₂³×C₄	#386	1	1	yes	characteristic
386	C₂³×C₄	#386	1	1	yes	characteristic
387	C₂³×C₄	#386	1	1	yes	characteristic
388	C₂³×C₄	#386	1	1	yes	characteristic
389	C₂³×C₄	#386	1	1	yes	characteristic
390	C₂³×C₄	#386	1	1	yes	characteristic
391	C₂³×C₄	#386	1	1	yes	characteristic
392	C₂³×C₄	#386	1	1	yes	characteristic
393	C₂³×C₄	#390	1	1	yes	characteristic
394	C₂³×C₄	#390	1	1	yes	characteristic
395	C₂³×C₄	#390	1	1	yes	characteristic
396	C₂³×C₄	#390	1	1	yes	characteristic
397	C₂³×C₄	#392	1	1	yes	characteristic
398	C₂³×C₄	#392	1	1	yes	characteristic
399	C₂³×C₄	#392	1	1	yes	characteristic
400	C₂³×C₄	#392	1	1	yes	characteristic
401	C₂³×C₄	#392	1	1	yes	characteristic
402	C₂³×C₄	#392	1	1	yes	characteristic
403	C₂³×C₄	#392	1	1	yes	characteristic
404	C₂³×C₄	#392	1	1	yes	characteristic
405	C₂³×C₄	#394	1	1	yes	characteristic
406	C₂³×C₄	#394	1	1	yes	characteristic
407	C₂³×C₄	#394	1	1	yes	characteristic
408	C₂³×C₄	#394	1	1	yes	characteristic
409	C₂³×C₄	#394	1	1	yes	characteristic
410	C₂³×C₄	#394	1	1	yes	characteristic
411	C₂³×C₄	#394	1	1	yes	characteristic
412	C₂³×C₄	#394	1	1	yes	characteristic
413	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
414	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
415	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
416	C₂³×C₄	C₂×#120	1	1	yes	characteristic
417	C₂³×C₄	C₂×#120	1	1	yes	characteristic
418	C₂³×C₄	C₂×#120	1	1	yes	characteristic
419	C₂³×C₄	C₂×#120	1	1	yes	characteristic
420	C₂³×C₄	C₂×#121	1	1	yes	characteristic
421	C₂³×C₄	C₂×#121	1	1	yes	characteristic
422	C₂³×C₄	C₂×#123	1	1	yes	characteristic
423	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
424	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
425	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
426	C₂×C₄⋊C₄	#386	1	1	yes	characteristic
427	C₂×C₄⋊C₄	#390	1	1	yes	characteristic
428	C₂×C₄⋊C₄	#390	1	1	yes	characteristic
429	C₂×C₄⋊C₄	#390	1	1	yes	characteristic
430	C₂×C₄⋊C₄	#390	1	1	yes	characteristic
431	C₂×C₄⋊C₄	#392	1	1	yes	characteristic
432	C₂×C₄⋊C₄	#392	1	1	yes	characteristic
433	C₂×C₄⋊C₄	#392	1	1	yes	characteristic
434	C₂×C₄⋊C₄	#392	1	1	yes	characteristic
435	C₂×C₄⋊C₄	#394	1	1	yes	characteristic
436	C₂×C₄⋊C₄	#394	1	1	yes	characteristic
437	C₂×C₄⋊C₄	#394	1	1	yes	characteristic
438	C₂×C₄⋊C₄	#394	1	1	yes	characteristic
439	C₂×C₄⋊C₄	C₂×#99	1	2	yes	—
440	C₂×C₄⋊C₄	C₂×#99	1	2	yes	—
441	C₂×C₄⋊C₄	C₂×#99	1	2	yes	—
442	C₂×C₄⋊C₄	C₂×#99	1	2	yes	—
443	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
444	C₂×C₄⋊C₄	C₂×#121	1	1	yes	characteristic
445	C₂×C₄⋊C₄	C₂×#121	1	1	yes	characteristic
446	C₂×C₄⋊C₄	C₂×#121	1	1	yes	characteristic
447	C₂×C₄⋊C₄	C₂×#121	1	1	yes	characteristic
448	C₂×C₄⋊C₄	C₂×#123	1	1	yes	characteristic
449	C₂×C₄⋊C₄	C₂×#124	1	1	yes	characteristic
450	C₂×C₄⋊C₄	C₂×#127	1	1	yes	characteristic
451	C₂×C₂²⋊C₄	#386	1	1	yes	characteristic
452	C₂×C₂²⋊C₄	#386	1	1	yes	characteristic
453	C₂×C₂²⋊C₄	#386	1	1	yes	characteristic
454	C₂×C₂²⋊C₄	#386	1	1	yes	characteristic
455	C₂×C₂²⋊C₄	#390	1	1	yes	characteristic
456	C₂×C₂²⋊C₄	#390	1	1	yes	characteristic
457	C₂×C₂²⋊C₄	#390	1	1	yes	characteristic
458	C₂×C₂²⋊C₄	#390	1	1	yes	characteristic
459	C₂×C₂²⋊C₄	#392	1	1	yes	characteristic
460	C₂×C₂²⋊C₄	#392	1	1	yes	characteristic
461	C₂×C₂²⋊C₄	#392	1	1	yes	characteristic
462	C₂×C₂²⋊C₄	#392	1	1	yes	characteristic
463	C₂×C₂²⋊C₄	#394	1	1	yes	characteristic
464	C₂×C₂²⋊C₄	#394	1	1	yes	characteristic
465	C₂×C₂²⋊C₄	#394	1	1	yes	characteristic
466	C₂×C₂²⋊C₄	#394	1	1	yes	characteristic
467	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
468	C₂×C₂²⋊C₄	C₂×#121	1	1	yes	characteristic
469	C₂×C₂²⋊C₄	C₂×#121	1	1	yes	characteristic
470	C₂×C₂²⋊C₄	C₂×#121	1	1	yes	characteristic
471	C₂×C₂²⋊C₄	C₂×#121	1	1	yes	characteristic
472	C₂×C₂²⋊C₄	C₂×#123	1	1	yes	characteristic
473	C₂×C₂²⋊C₄	C₂×#124	1	1	yes	characteristic
474	C₂×C₂²⋊C₄	C₂×#127	1	1	yes	characteristic
475	C₂×C₄²	#386	1	1	yes	characteristic
476	C₂×C₄²	#386	1	1	yes	characteristic
477	C₂×C₄²	#386	1	1	yes	characteristic
478	C₂×C₄²	#386	1	1	yes	characteristic
479	C₂×C₄²	#386	1	1	yes	characteristic
480	C₂×C₄²	#386	1	1	yes	characteristic
481	C₂×C₄²	#386	1	1	yes	characteristic
482	C₂×C₄²	#386	1	1	yes	characteristic
483	C₂×C₄²	#386	1	1	yes	characteristic
484	C₂×C₄²	#386	1	1	yes	characteristic
485	C₂×C₄²	#386	1	1	yes	characteristic
486	C₂×C₄²	#386	1	1	yes	characteristic
487	C₂×C₄²	#390	1	1	yes	characteristic
488	C₂×C₄²	#390	1	1	yes	characteristic
489	C₂×C₄²	#390	1	1	yes	characteristic
490	C₂×C₄²	#390	1	1	yes	characteristic
491	C₂×C₄²	#392	1	1	yes	characteristic
492	C₂×C₄²	#392	1	1	yes	characteristic
493	C₂×C₄²	#392	1	1	yes	characteristic
494	C₂×C₄²	#392	1	1	yes	characteristic
495	C₂×C₄²	#392	1	1	yes	characteristic
496	C₂×C₄²	#392	1	1	yes	characteristic
497	C₂×C₄²	#392	1	1	yes	characteristic
498	C₂×C₄²	#392	1	1	yes	characteristic
499	C₂×C₄²	#394	1	1	yes	characteristic
500	C₂×C₄²	#394	1	1	yes	characteristic
501	C₂×C₄²	#394	1	1	yes	characteristic
502	C₂×C₄²	#394	1	1	yes	characteristic
503	C₂×C₄²	#394	1	1	yes	characteristic
504	C₂×C₄²	#394	1	1	yes	characteristic
505	C₂×C₄²	#394	1	1	yes	characteristic
506	C₂×C₄²	#394	1	1	yes	characteristic
507	C₂×C₄²	C₂×#99	1	1	yes	characteristic
508	C₂×C₄²	C₂×#99	1	1	yes	characteristic
509	C₂×C₄²	C₂×#99	1	1	yes	characteristic
510	C₂×C₄²	C₂×#99	1	1	yes	characteristic
511	C₂×C₄²	C₂×#99	1	1	yes	characteristic
512	C₂×C₄²	C₂×#99	1	1	yes	characteristic
513	C₂×C₄²	C₂×#99	1	1	yes	characteristic
514	C₂×C₄²	C₂×#99	1	1	yes	characteristic
515	C₂×C₄²	C₂×C₄×D₄	1	1	yes	characteristic
516	C₂×C₄²	C₂×C₄×D₄	1	1	yes	characteristic
517	C₂×C₄²	C₂×C₄×D₄	1	1	yes	characteristic
518	C₂×C₄²	C₂×C₄×D₄	1	1	yes	characteristic
519	C₂×C₄²	C₂×#120	1	1	yes	characteristic
520	C₂×C₄²	C₂×#121	1	1	yes	characteristic
521	C₂×C₄²	C₂×#121	1	1	yes	characteristic
522	C₂×C₄²	C₂×#123	1	1	yes	characteristic
523	C₂⁴	#1438	1	1	yes	characteristic
524	C₂⁴	#1438	1	1	yes	characteristic
525	C₂⁴	#1438	1	1	yes	characteristic
526	C₂⁴	#1438	1	1	yes	characteristic
527	C₂⁴	C₂×#379	1	1	yes	characteristic
528	C₂⁴	C₂×#392	1	1	yes	characteristic
529	C₂⁴	C₂×#394	1	1	yes	characteristic
530	C₂×D₄	#2010	1	4	yes	—
531	C₂×D₄	#2010	1	4	yes	—
532	C₂²×C₄	#1438	1	1	yes	characteristic
533	C₂²×C₄	#1438	1	1	yes	characteristic
534	C₂²×C₄	#1438	1	1	yes	characteristic
535	C₂²×C₄	#1438	1	1	yes	characteristic
536	C₂²×C₄	#1438	1	1	yes	characteristic
537	C₂²×C₄	#1438	1	1	yes	characteristic
538	C₂²×C₄	#1438	1	1	yes	characteristic
539	C₂²×C₄	#1438	1	1	yes	characteristic
540	C₂²×C₄	#1438	1	1	yes	characteristic
541	C₂²×C₄	#1438	1	1	yes	characteristic
542	C₂²×C₄	#1438	1	1	yes	characteristic
543	C₂²×C₄	#1438	1	1	yes	characteristic
544	C₂²×C₄	#1781	1	1	yes	characteristic
545	C₂²×C₄	#1781	1	1	yes	characteristic
546	C₂²×C₄	#1781	1	1	yes	characteristic
547	C₂²×C₄	#1781	1	1	yes	characteristic
548	C₂²×C₄	#1781	1	1	yes	characteristic
549	C₂²×C₄	#1781	1	1	yes	characteristic
550	C₂²×C₄	#1781	1	1	yes	characteristic
551	C₂²×C₄	#1781	1	1	yes	characteristic
552	C₂²×C₄	C₂×#386	1	1	yes	characteristic
553	C₂²×C₄	C₂×#386	1	1	yes	characteristic
554	C₂²×C₄	C₂×#386	1	1	yes	characteristic
555	C₂²×C₄	C₂×#386	1	1	yes	characteristic
556	C₂²×C₄	C₂×#390	1	1	yes	characteristic
557	C₂²×C₄	C₂×#390	1	1	yes	characteristic
558	C₂²×C₄	C₂×#392	1	1	yes	characteristic
559	C₂²×C₄	C₂×#392	1	1	yes	characteristic
560	C₂²×C₄	C₂×#392	1	1	yes	characteristic
561	C₂²×C₄	C₂×#394	1	1	yes	characteristic
562	C₂²×C₄	C₂×#394	1	1	yes	characteristic
563	C₂²×C₄	C₂×#394	1	1	yes	characteristic
564	C₂²×C₄	C₂²×#99	1	1	yes	characteristic
565	C₂²×C₄	C₂²×#99	1	1	yes	characteristic
566	C₂²×C₄	C₂²×#99	1	1	yes	characteristic
567	C₂²×C₄	C₂²×#99	1	1	yes	characteristic
568	C₄²	#1898	1	1	yes	characteristic
569	C₄²	#1898	1	1	yes	characteristic
570	C₄²	#1898	1	1	yes	characteristic
571	C₄²	#1898	1	1	yes	characteristic
572	C₄²	#1898	1	1	yes	characteristic
573	C₄²	#1898	1	1	yes	characteristic
574	C₄²	#1898	1	1	yes	characteristic
575	C₄²	#1898	1	1	yes	characteristic
576	C₄²	#1898	1	1	yes	characteristic
577	C₄²	#1898	1	1	yes	characteristic
578	C₄²	#1898	1	1	yes	characteristic
579	C₄²	#1898	1	1	yes	characteristic
580	C₄²	#1898	1	1	yes	characteristic
581	C₄²	#1898	1	1	yes	characteristic
582	C₄²	#1898	1	1	yes	characteristic
583	C₄²	#1898	1	1	yes	characteristic
584	C₂³	#10994	1	2	yes	—
585	C₂³	#10994	1	2	yes	—
586	C₂³	#10994	1	2	yes	—
587	C₂³	C₂×#1438	1	1	yes	characteristic
588	C₂³	C₂×#1781	1	1	yes	characteristic
589	C₂³	C₂×#1781	1	1	yes	characteristic
590	C₂³	C₂×#2010	1	2	yes	—
591	C₂×C₄	#10965	1	1	yes	characteristic
592	C₂×C₄	#10965	1	1	yes	characteristic
593	C₂×C₄	#10965	1	1	yes	characteristic
594	C₂×C₄	#10965	1	1	yes	characteristic
595	C₂×C₄	#10965	1	1	yes	characteristic
596	C₂×C₄	#10965	1	1	yes	characteristic
597	C₂×C₄	#10965	1	1	yes	characteristic
598	C₂×C₄	#10965	1	1	yes	characteristic
599	C₂×C₄	#10994	1	2	yes	—
600	C₂×C₄	#12711	1	4	yes	—
601	C₂×C₄	C₂×#1898	1	1	yes	characteristic
602	C₂×C₄	C₂×#1898	1	1	yes	characteristic
603	C₂×C₄	C₂×#1898	1	1	yes	characteristic
604	C₂×C₄	C₂×#1898	1	1	yes	characteristic
605	C₂×C₄	C₂×#2010	1	2	yes	—
606	C₂²	C₂×#10965	1	1	yes	characteristic
607	C₂²	C₂×#10994	1	1	yes	characteristic
608	C₂²	C₂×#10994	1	1	yes	characteristic
609	C₂²	C₂×#12711	1	2	yes	—
610	C₂²	#493410	1	2	yes	—
611	C₄	#147582	1	2	yes	—
612	C₄	#147582	1	2	yes	—
613	C₂	#72235096	1	1	yes	characteristic
614	C₂	C₂×#147582	1	1	yes	characteristic
615	C₂	#72280746	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#10965
commutator	C₂²×C₄²	C₂³×C₄
Frattini, cosocle	C₂²×#117	C₂⁴
socle	C₂²	C₂×#10965
prime radical	#72280561	C₂
LCS	G ▷ C₂²×C₄² ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ C₂²×C₄×H(5,𝔽₂) ◁ G
LECS	G ▷ C₂²×#117 ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72281567	C₂	semidirect
2. #72281549	C₂	semidirect
3. #72281521	C₂	semidirect
4. #72281407	C₂	semidirect
5. #72281322	C₂	semidirect
7. #72257778	C₂	semidirect
8. #72257610	C₂	semidirect
9. #72251901	C₂	semidirect
11. C₂×#34963	C₄	semidirect
13. C₂²×#2397	C₄	semidirect
18. #4929027	C₄	semidirect
20. #4929019	C₄	semidirect
22. #515258	C₄	semidirect
23. #514189	C₄	semidirect
25. #482574	C₂²	semidirect
26. #482550	C₂²	semidirect
27. #392259	C₂²	semidirect
28. #392257	C₂²	semidirect
29. #184981	C₂²	semidirect
30. #184979	C₂²	semidirect
31. #127223	C₂²	semidirect
32. #127216	C₂²	semidirect
66. #20637	D₄	semidirect
67. #20632	D₄	semidirect
68. C₄×#413	D₄	semidirect
69. C₄×#410	D₄	semidirect
70. #17361	D₄	semidirect
71. #17361	D₄	semidirect
74. #17349	D₄	semidirect
75. #17349	D₄	semidirect
167. #1742	C₂×D₄	semidirect
168. #1740	C₂×D₄	semidirect
169. #1458	C₂×D₄	semidirect
170. #1458	C₂×D₄	semidirect

Maximal subgroups

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

subgroup	index
#72281567	2
#72281549	2
#72281521	2
#72281407	2
#72281322	2
#72280561	2
#72257778	2
#72257610	2
#72251901	2