Subgroups — #72256444

Order 4096.

At least 17060 conjugacy classes of subgroups; only the 691 normal subgroups are shown.

The subgroup lattice has 585 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#72213436	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#72213428	C₂	1	1	yes	maximal, characteristic
3	C₂×#512663	C₄	1	4	yes	complemented
4	C₂×#72213396	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#72213445	C₂	1	1	yes	maximal, characteristic, complemented
6	#72250517	C₂	1	1	yes	maximal, characteristic
7	#72250477	C₄	1	1	yes	characteristic, complemented
8	#72250472	C₄	1	1	yes	characteristic, complemented
9	#72250462	C₄	1	1	yes	characteristic, complemented
10	#72250448	C₄	1	1	yes	characteristic, complemented
11	C₂×#72210462	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#493370	C₂²	1	1	yes	characteristic
13	C₂×#493372	C₂²	1	1	yes	characteristic
14	C₂×#359513	C₂²	1	1	yes	characteristic
15	C₂×#72213377	C₂	1	1	yes	maximal, characteristic
16	C₂×#359509	C₂²	1	1	yes	characteristic
17	C₂×#187811	C₂²	1	1	yes	characteristic
18	C₂×#112156	C₄	1	2	yes	complemented
19	C₂×#10575547	C₂²	1	1	yes	characteristic
20	C₂×#114858	C₄	1	2	yes	complemented
21	C₂×#581603	C₂²	1	1	yes	characteristic
22	C₂×#62814	D₄	1	1	yes	characteristic
23	C₂³×#535	C₂³	1	1	yes	characteristic
24	C₂×#60806	C₂×C₄	1	2	yes	—
25	C₂×#60806	Q₈	1	2	yes	—
26	C₂×#60799	C₂×C₄	1	2	yes	—
27	C₂×#60798	D₄	1	2	yes	—
28	C₂×#60644	C₂×C₄	1	1	yes	characteristic
29	C₂×#60644	D₄	1	1	yes	characteristic
30	C₂×#60619	C₂×C₄	1	1	yes	characteristic
31	C₂×#60619	D₄	1	1	yes	characteristic
32	C₂×#60124	D₄	1	1	yes	characteristic
33	C₂×#60064	D₄	1	1	yes	characteristic
34	C₂×#34171	D₄	1	1	yes	characteristic
35	C₂²×#2128	C₂×C₄	1	2	yes	—
36	C₂²×#2127	C₂×C₄	1	2	yes	—
37	C₂²×#1783	D₄	1	1	yes	characteristic
38	C₂×#20584	D₄	1	1	yes	characteristic
39	C₂×#17666	C₂×C₄	1	2	yes	—
40	#581603	D₄	1	2	yes	—
41	#581603	D₄	1	2	yes	—
42	C₂×#14662	C₂×C₄	1	1	yes	characteristic
43	C₂×#14169	C₂×C₄	1	1	yes	characteristic
44	#493372	D₄	1	2	yes	—
45	#493372	D₄	1	2	yes	—
46	#493370	D₄	1	2	yes	—
47	#493370	D₄	1	2	yes	—
48	C₂×#10989	C₂×C₄	1	1	yes	characteristic
49	C₂×#10989	C₂×C₄	1	1	yes	characteristic
50	C₂×#10989	D₄	1	1	yes	characteristic
51	C₂×#10989	D₄	1	1	yes	characteristic
52	C₂×#10987	C₂×C₄	1	1	yes	characteristic
53	C₂×#10987	C₂×C₄	1	1	yes	characteristic
54	C₂×#10987	D₄	1	1	yes	characteristic
55	C₂×#10987	D₄	1	1	yes	characteristic
56	#187811	D₄	1	2	yes	—
57	#187811	D₄	1	2	yes	—
58	C₂⁴×#41	C₂×D₄	1	1	yes	characteristic
59	C₂⁵×D₄	C₂×D₄	1	1	yes	characteristic
60	C₂×#3455	C₄⋊C₄	1	2	yes	—
61	C₂×#3458	C₂²⋊C₄	1	1	yes	characteristic
62	C₂×#3449	C₂²⋊C₄	1	1	yes	characteristic
63	C₂²×#535	C₂²×C₄	1	1	yes	characteristic
64	C₂²×#535	C₂²×C₄	1	1	yes	characteristic
65	C₂²×#535	C₂×D₄	1	1	yes	characteristic
66	C₂²×#535	C₂×D₄	1	1	yes	characteristic
67	C₂²×#535	C₂×D₄	1	1	yes	characteristic
68	C₂²×#535	C₂×D₄	1	1	yes	characteristic
69	C₂²×#535	C₂×D₄	1	1	yes	characteristic
70	C₂²×#535	C₂×D₄	1	1	yes	characteristic
71	C₂²×#535	C₂×D₄	1	1	yes	characteristic
72	C₂²×#535	C₂×D₄	1	1	yes	characteristic
73	C₂²×#535	C₂×D₄	1	1	yes	characteristic
74	C₂²×#535	C₂×D₄	1	1	yes	characteristic
75	C₂²×#535	C₂×D₄	1	1	yes	characteristic
76	C₂²×#535	C₂×Q₈	1	1	yes	characteristic
77	C₂²×#535	#41	1	1	yes	characteristic
78	C₂²×#535	#41	1	1	yes	characteristic
79	C₂²×#535	#41	1	1	yes	characteristic
80	C₂²×#535	#41	1	1	yes	characteristic
81	C₂²×#535	#41	1	1	yes	characteristic
82	C₂²×#535	#41	1	1	yes	characteristic
83	C₂²×#535	#41	1	1	yes	characteristic
84	C₂²×#535	#41	1	1	yes	characteristic
85	C₂²×#535	#41	1	1	yes	characteristic
86	C₂²×#535	#41	1	1	yes	characteristic
87	C₂×#3444	C₂²⋊C₄	1	2	yes	—
88	C₂³×#127	C₂×D₄	1	1	yes	characteristic
89	C₂³×#127	#41	1	1	yes	characteristic
90	C₂³×#124	C₂²×C₄	1	1	yes	characteristic
91	C₂³×#124	#41	1	1	yes	characteristic
92	C₂³×#117	C₂×D₄	1	1	yes	characteristic
93	C₂×#3153	C₄²	1	2	yes	—
94	C₂×#3153	C₄⋊C₄	1	2	yes	—
95	C₂×#3151	C₂²⋊C₄	1	2	yes	—
96	C₂×#3151	C₄⋊C₄	1	2	yes	—
97	C₂×#3140	C₄²	1	2	yes	—
98	C₂×#3140	C₄⋊C₄	1	2	yes	—
99	C₂×#3138	C₂²⋊C₄	1	2	yes	—
100	C₂×#3138	C₄⋊C₄	1	2	yes	—
101	C₂×#2921	C₄⋊C₄	1	2	yes	—
102	C₂×#2920	C₂²⋊C₄	1	2	yes	—
103	C₂³×#100	C₂²⋊C₄	1	1	yes	characteristic
104	C₂³×#100	C₂²⋊C₄	1	1	yes	characteristic
105	C₂²×#410	C₂²⋊C₄	1	1	yes	characteristic
106	C₂²×#410	C₂²⋊C₄	1	1	yes	characteristic
107	C₂×#2879	C₂²⋊C₄	1	1	yes	characteristic
108	C₂×#2879	C₂²⋊C₄	1	1	yes	characteristic
109	C₂×#2873	C₂²⋊C₄	1	1	yes	characteristic
110	C₂×#2873	C₂²⋊C₄	1	1	yes	characteristic
111	C₂×#2309	C₂²⋊C₄	1	1	yes	characteristic
112	C₂×#2309	C₂²⋊C₄	1	1	yes	characteristic
113	C₂×#2128	C₂²⋊C₄	1	4	yes	complemented
114	C₂×#2127	C₂²⋊C₄	1	4	yes	complemented
115	#17666	C₂²⋊C₄	1	4	yes	complemented
116	#14662	C₂²⋊C₄	1	2	yes	complemented
117	#14169	C₂²⋊C₄	1	2	yes	complemented
118	C₂³×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
119	C₂³×#41	C₄×D₄	1	1	yes	characteristic
120	C₂³×#41	#120	1	1	yes	characteristic
121	C₂³×#41	#120	1	1	yes	characteristic
122	C₂³×#41	#121	1	1	yes	characteristic
123	C₂³×#41	#121	1	1	yes	characteristic
124	C₂³×#41	#121	1	1	yes	characteristic
125	C₂³×#41	#121	1	1	yes	characteristic
126	C₂³×#41	C₂²⋊Q₈	1	1	yes	characteristic
127	C₂³×#41	#123	1	1	yes	characteristic
128	C₂³×#41	#124	1	1	yes	characteristic
129	C₂³×#41	#127	1	1	yes	characteristic
130	C₂⁴×Q₈	C₄×D₄	1	1	yes	characteristic
131	C₂⁴×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
132	C₂⁴×D₄	C₄×D₄	1	1	yes	characteristic
133	C₂⁴×D₄	C₄×D₄	1	1	yes	characteristic
134	C₂⁴×D₄	#120	1	1	yes	characteristic
135	C₂⁴×D₄	#120	1	1	yes	characteristic
136	C₂⁴×D₄	#121	1	1	yes	characteristic
137	C₂⁴×D₄	#121	1	1	yes	characteristic
138	C₂⁴×D₄	#121	1	1	yes	characteristic
139	C₂⁴×D₄	#121	1	1	yes	characteristic
140	C₂⁴×D₄	#121	1	1	yes	characteristic
141	C₂⁴×D₄	#121	1	1	yes	characteristic
142	C₂⁴×D₄	C₂²⋊Q₈	1	1	yes	characteristic
143	C₂⁴×D₄	#123	1	1	yes	characteristic
144	C₂⁴×D₄	#124	1	1	yes	characteristic
145	C₂⁴×D₄	#127	1	1	yes	characteristic
146	C₂⁵×C₄	#120	1	1	yes	characteristic
147	C₂×#535	C₂×C₂²⋊C₄	1	1	yes	characteristic
148	C₂×#535	C₂×C₂²⋊C₄	1	1	yes	characteristic
149	C₂×#535	#117	1	1	yes	characteristic
150	C₂×#535	#117	1	1	yes	characteristic
151	C₂×#535	C₄×D₄	1	1	yes	characteristic
152	C₂×#535	C₄×D₄	1	1	yes	characteristic
153	C₂×#535	C₄×D₄	1	1	yes	characteristic
154	C₂×#535	C₄×D₄	1	1	yes	characteristic
155	C₂×#535	C₄×D₄	1	1	yes	characteristic
156	C₂×#535	C₄×D₄	1	1	yes	characteristic
157	C₂×#535	C₄×D₄	1	1	yes	characteristic
158	C₂×#535	C₄×D₄	1	1	yes	characteristic
159	C₂×#535	C₄×D₄	1	1	yes	characteristic
160	C₂×#535	C₄×D₄	1	1	yes	characteristic
161	C₂×#535	C₄×D₄	1	1	yes	characteristic
162	C₂×#535	C₄×D₄	1	1	yes	characteristic
163	C₂×#535	#120	1	1	yes	characteristic
164	C₂×#535	#120	1	1	yes	characteristic
165	C₂×#535	#120	1	1	yes	characteristic
166	C₂×#535	#120	1	1	yes	characteristic
167	C₂×#535	#121	1	1	yes	characteristic
168	C₂×#535	#121	1	1	yes	characteristic
169	C₂×#535	#121	1	1	yes	characteristic
170	C₂×#535	#121	1	1	yes	characteristic
171	C₂×#535	#121	1	1	yes	characteristic
172	C₂×#535	#121	1	1	yes	characteristic
173	C₂×#535	#121	1	1	yes	characteristic
174	C₂×#535	#121	1	1	yes	characteristic
175	C₂×#535	#121	1	1	yes	characteristic
176	C₂×#535	#121	1	1	yes	characteristic
177	C₂×#535	#121	1	1	yes	characteristic
178	C₂×#535	#121	1	1	yes	characteristic
179	C₂×#535	#121	1	1	yes	characteristic
180	C₂×#535	#121	1	1	yes	characteristic
181	C₂×#535	#121	1	1	yes	characteristic
182	C₂×#535	#121	1	1	yes	characteristic
183	C₂×#535	C₂²⋊Q₈	1	1	yes	characteristic
184	C₂×#535	C₂²⋊Q₈	1	1	yes	characteristic
185	C₂×#535	C₂²⋊Q₈	1	1	yes	characteristic
186	C₂×#535	C₂²⋊Q₈	1	1	yes	characteristic
187	C₂×#535	C₂²⋊Q₈	1	1	yes	characteristic
188	C₂×#535	C₂²⋊Q₈	1	1	yes	characteristic
189	C₂×#535	C₂²⋊Q₈	1	1	yes	characteristic
190	C₂×#535	C₂²⋊Q₈	1	1	yes	characteristic
191	C₂×#535	#123	1	1	yes	characteristic
192	C₂×#535	#123	1	1	yes	characteristic
193	C₂×#535	#123	1	1	yes	characteristic
194	C₂×#535	#123	1	1	yes	characteristic
195	C₂×#535	#123	1	1	yes	characteristic
196	C₂×#535	#123	1	1	yes	characteristic
197	C₂×#535	#123	1	1	yes	characteristic
198	C₂×#535	#123	1	1	yes	characteristic
199	C₂×#535	#124	1	1	yes	characteristic
200	C₂×#535	#124	1	1	yes	characteristic
201	C₂×#535	#124	1	1	yes	characteristic
202	C₂×#535	#124	1	1	yes	characteristic
203	C₂×#535	#124	1	1	yes	characteristic
204	C₂×#535	#124	1	1	yes	characteristic
205	C₂×#535	#126	1	1	yes	characteristic
206	C₂×#535	#126	1	1	yes	characteristic
207	C₂×#535	#126	1	1	yes	characteristic
208	C₂×#535	#126	1	1	yes	characteristic
209	C₂×#535	#127	1	1	yes	characteristic
210	C₂×#535	#127	1	1	yes	characteristic
211	C₂×#533	#95	1	2	yes	—
212	C₂×#532	#95	1	2	yes	—
213	C₂²×#127	C₂×C₂²⋊C₄	1	1	yes	characteristic
214	C₂²×#127	C₂×C₄⋊C₄	1	1	yes	characteristic
215	C₂²×#127	#117	1	1	yes	characteristic
216	C₂²×#127	C₄×D₄	1	1	yes	characteristic
217	C₂²×#127	#120	1	1	yes	characteristic
218	C₂²×#127	#120	1	1	yes	characteristic
219	C₂²×#127	#120	1	1	yes	characteristic
220	C₂²×#127	#120	1	1	yes	characteristic
221	C₂²×#127	#121	1	1	yes	characteristic
222	C₂²×#127	#121	1	1	yes	characteristic
223	C₂²×#127	#121	1	1	yes	characteristic
224	C₂²×#127	#121	1	1	yes	characteristic
225	C₂²×#127	C₂²⋊Q₈	1	1	yes	characteristic
226	C₂²×#127	#123	1	1	yes	characteristic
227	C₂²×#127	#123	1	1	yes	characteristic
228	C₂²×#127	#123	1	1	yes	characteristic
229	C₂²×#127	#123	1	1	yes	characteristic
230	C₂²×#127	#123	1	1	yes	characteristic
231	C₂²×#127	#123	1	1	yes	characteristic
232	C₂²×#127	#123	1	1	yes	characteristic
233	C₂²×#127	#124	1	1	yes	characteristic
234	C₂²×#127	#124	1	1	yes	characteristic
235	C₂²×#127	#126	1	1	yes	characteristic
236	C₂²×#127	#126	1	1	yes	characteristic
237	C₂²×#124	C₂×C₄²	1	1	yes	characteristic
238	C₂²×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
239	C₂²×#124	C₂×C₂²⋊C₄	1	1	yes	characteristic
240	C₂²×#124	C₂×C₄⋊C₄	1	1	yes	characteristic
241	C₂²×#124	#117	1	1	yes	characteristic
242	C₂²×#124	#117	1	1	yes	characteristic
243	C₂²×#124	#117	1	1	yes	characteristic
244	C₂²×#124	C₄×D₄	1	1	yes	characteristic
245	C₂²×#124	C₄×D₄	1	1	yes	characteristic
246	C₂²×#124	C₄×D₄	1	1	yes	characteristic
247	C₂²×#124	C₄×D₄	1	1	yes	characteristic
248	C₂²×#124	C₄×D₄	1	1	yes	characteristic
249	C₂²×#124	C₄×D₄	1	1	yes	characteristic
250	C₂²×#124	C₄×D₄	1	1	yes	characteristic
251	C₂²×#124	#121	1	1	yes	characteristic
252	C₂²×#124	#121	1	1	yes	characteristic
253	C₂²×#124	C₂²⋊Q₈	1	1	yes	characteristic
254	C₂²×#124	#123	1	1	yes	characteristic
255	C₂²×#124	#123	1	1	yes	characteristic
256	C₂²×#124	#123	1	1	yes	characteristic
257	C₂²×#124	#124	1	1	yes	characteristic
258	C₂²×#124	#124	1	1	yes	characteristic
259	C₂²×#124	#126	1	1	yes	characteristic
260	C₂²×#124	#126	1	1	yes	characteristic
261	C₂²×#117	C₂×C₂²⋊C₄	1	1	yes	characteristic
262	C₂²×#117	C₂×C₄⋊C₄	1	1	yes	characteristic
263	C₂²×#117	#120	1	1	yes	characteristic
264	C₂²×#117	#120	1	1	yes	characteristic
265	C₂²×#117	#120	1	1	yes	characteristic
266	C₂²×#117	#121	1	1	yes	characteristic
267	C₂²×#117	#121	1	1	yes	characteristic
268	C₂²×#117	#121	1	1	yes	characteristic
269	C₂²×#117	#121	1	1	yes	characteristic
270	C₂²×#117	#123	1	1	yes	characteristic
271	C₂²×#117	#123	1	1	yes	characteristic
272	C₂²×#117	#123	1	1	yes	characteristic
273	C₂³×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
274	C₂³×C₄²	#123	1	1	yes	characteristic
275	C₂×#493	#99	1	4	yes	—
276	C₂×#492	#99	1	4	yes	—
277	#3138	#99	1	8	yes	—
278	C₂×C₄×M₁₆	#95	1	2	yes	—
279	C₂×C₄×M₁₆	#95	1	2	yes	—
280	C₂⁶	B(4,𝔽₂)	1	1	yes	characteristic
281	C₂²×#41	#386	1	1	yes	characteristic
282	C₂²×#41	#386	1	1	yes	characteristic
283	C₂²×#41	#386	1	1	yes	characteristic
284	C₂²×#41	#388	1	1	yes	characteristic
285	C₂²×#41	#388	1	1	yes	characteristic
286	C₂²×#41	#390	1	1	yes	characteristic
287	C₂²×#41	#390	1	1	yes	characteristic
288	C₂²×#41	#390	1	1	yes	characteristic
289	C₂²×#41	#392	1	1	yes	characteristic
290	C₂²×#41	#392	1	1	yes	characteristic
291	C₂²×#41	#393	1	1	yes	characteristic
292	C₂²×#41	#394	1	1	yes	characteristic
293	C₂²×#41	#394	1	1	yes	characteristic
294	C₂²×#41	#396	1	1	yes	characteristic
295	C₂²×#41	#396	1	1	yes	characteristic
296	C₂²×#41	#399	1	1	yes	characteristic
297	C₂³×Q₈	C₄×C₂²⋊C₄	1	1	yes	characteristic
298	C₂³×Q₈	#385	1	1	yes	characteristic
299	C₂³×Q₈	#386	1	1	yes	characteristic
300	C₂³×Q₈	#388	1	1	yes	characteristic
301	C₂³×Q₈	#388	1	1	yes	characteristic
302	C₂³×Q₈	#390	1	1	yes	characteristic
303	C₂³×D₄	C₄×C₂²⋊C₄	1	1	yes	characteristic
304	C₂³×D₄	#380	1	1	yes	characteristic
305	C₂³×D₄	#380	1	1	yes	characteristic
306	C₂³×D₄	#385	1	1	yes	characteristic
307	C₂³×D₄	#386	1	1	yes	characteristic
308	C₂³×D₄	#386	1	1	yes	characteristic
309	C₂³×D₄	#386	1	1	yes	characteristic
310	C₂³×D₄	#386	1	1	yes	characteristic
311	C₂³×D₄	#386	1	1	yes	characteristic
312	C₂³×D₄	#386	1	1	yes	characteristic
313	C₂³×D₄	#388	1	1	yes	characteristic
314	C₂³×D₄	#388	1	1	yes	characteristic
315	C₂³×D₄	#388	1	1	yes	characteristic
316	C₂³×D₄	#388	1	1	yes	characteristic
317	C₂³×D₄	#390	1	1	yes	characteristic
318	C₂³×D₄	#390	1	1	yes	characteristic
319	C₂³×D₄	#390	1	1	yes	characteristic
320	C₂³×D₄	#390	1	1	yes	characteristic
321	C₂³×D₄	#392	1	1	yes	characteristic
322	C₂³×D₄	#392	1	1	yes	characteristic
323	C₂³×D₄	#392	1	1	yes	characteristic
324	C₂³×D₄	#392	1	1	yes	characteristic
325	C₂³×D₄	#393	1	1	yes	characteristic
326	C₂³×D₄	#394	1	1	yes	characteristic
327	C₂³×D₄	#394	1	1	yes	characteristic
328	C₂³×D₄	#394	1	1	yes	characteristic
329	C₂³×D₄	#394	1	1	yes	characteristic
330	C₂³×D₄	#394	1	1	yes	characteristic
331	C₂³×D₄	#394	1	1	yes	characteristic
332	C₂³×D₄	#396	1	1	yes	characteristic
333	C₂³×D₄	#396	1	1	yes	characteristic
334	C₂³×D₄	#397	1	1	yes	characteristic
335	C₂³×D₄	#397	1	1	yes	characteristic
336	C₂³×D₄	#399	1	1	yes	characteristic
337	C₂⁴×C₄	#379	1	1	yes	characteristic
338	C₂⁴×C₄	#385	1	1	yes	characteristic
339	C₂⁴×C₄	#386	1	1	yes	characteristic
340	C₂⁴×C₄	#392	1	1	yes	characteristic
341	C₂⁴×C₄	#392	1	1	yes	characteristic
342	C₂⁴×C₄	#394	1	1	yes	characteristic
343	C₂⁴×C₄	#394	1	1	yes	characteristic
344	C₂⁴×C₄	B(4,𝔽₂)	1	1	yes	characteristic
345	C₂⁴×C₄	B(4,𝔽₂)	1	1	yes	characteristic
346	C₂⁴×C₄	B(4,𝔽₂)	1	1	yes	characteristic
347	C₂⁴×C₄	#458	1	1	yes	characteristic
348	C₂⁴×C₄	#458	1	1	yes	characteristic
349	C₂⁴×C₄	#458	1	1	yes	characteristic
350	C₂⁴×C₄	#458	1	1	yes	characteristic
351	#533	#342	1	4	yes	complemented
352	C₂×C₄⋊Q₈	#342	1	2	yes	complemented
353	C₂×#127	#342	1	2	yes	complemented
354	C₂×#127	#379	1	1	yes	characteristic
355	C₂×#127	#381	1	1	yes	characteristic
356	C₂×#127	#385	1	1	yes	characteristic
357	C₂×#127	#385	1	1	yes	characteristic
358	C₂×#127	#385	1	1	yes	characteristic
359	C₂×#127	#385	1	1	yes	characteristic
360	C₂×#127	#386	1	1	yes	characteristic
361	C₂×#127	#386	1	1	yes	characteristic
362	C₂×#127	#386	1	1	yes	characteristic
363	C₂×#127	#388	1	1	yes	characteristic
364	C₂×#127	#388	1	1	yes	characteristic
365	C₂×#127	#388	1	1	yes	characteristic
366	C₂×#127	#388	1	1	yes	characteristic
367	C₂×#127	#388	1	1	yes	characteristic
368	C₂×#127	#388	1	1	yes	characteristic
369	C₂×#127	#390	1	1	yes	characteristic
370	C₂×#127	#392	1	1	yes	characteristic
371	C₂×#127	#392	1	1	yes	characteristic
372	C₂×#127	#393	1	1	yes	characteristic
373	C₂×#127	#394	1	1	yes	characteristic
374	C₂×#127	#394	1	1	yes	characteristic
375	C₂×#127	#394	1	1	yes	characteristic
376	C₂×#127	#394	1	1	yes	characteristic
377	C₂×#127	#394	1	1	yes	characteristic
378	C₂×#127	#394	1	1	yes	characteristic
379	C₂×#127	#396	1	1	yes	characteristic
380	C₂×#127	#396	1	1	yes	characteristic
381	C₂×#127	#397	1	1	yes	characteristic
382	C₂×#127	#397	1	1	yes	characteristic
383	C₂×#127	#397	1	1	yes	characteristic
384	C₂×#127	#397	1	1	yes	characteristic
385	C₂×#127	#399	1	1	yes	characteristic
386	C₂×#127	C₂×#99	1	4	yes	—
387	C₂×#127	C₂×#99	1	4	yes	—
388	C₂×#124	C₄×C₂²⋊C₄	1	1	yes	characteristic
389	C₂×#124	C₄×C₂²⋊C₄	1	1	yes	characteristic
390	C₂×#124	C₄×C₂²⋊C₄	1	1	yes	characteristic
391	C₂×#124	C₄×C₂²⋊C₄	1	1	yes	characteristic
392	C₂×#124	#380	1	1	yes	characteristic
393	C₂×#124	#380	1	1	yes	characteristic
394	C₂×#124	#385	1	1	yes	characteristic
395	C₂×#124	#385	1	1	yes	characteristic
396	C₂×#124	#386	1	1	yes	characteristic
397	C₂×#124	#386	1	1	yes	characteristic
398	C₂×#124	#386	1	1	yes	characteristic
399	C₂×#124	#388	1	1	yes	characteristic
400	C₂×#124	#388	1	1	yes	characteristic
401	C₂×#124	#388	1	1	yes	characteristic
402	C₂×#124	#388	1	1	yes	characteristic
403	C₂×#124	#388	1	1	yes	characteristic
404	C₂×#124	#388	1	1	yes	characteristic
405	C₂×#124	#388	1	1	yes	characteristic
406	C₂×#124	#388	1	1	yes	characteristic
407	C₂×#124	#388	1	1	yes	characteristic
408	C₂×#124	#388	1	1	yes	characteristic
409	C₂×#124	#390	1	1	yes	characteristic
410	C₂×#124	#390	1	1	yes	characteristic
411	C₂×#124	#390	1	1	yes	characteristic
412	C₂×#124	#393	1	1	yes	characteristic
413	C₂×#124	#394	1	1	yes	characteristic
414	C₂×#124	#394	1	1	yes	characteristic
415	C₂×#124	#396	1	1	yes	characteristic
416	C₂×#124	#396	1	1	yes	characteristic
417	C₂×#124	#397	1	1	yes	characteristic
418	C₂×#124	#397	1	1	yes	characteristic
419	C₂×#124	#399	1	1	yes	characteristic
420	C₂×#117	#380	1	1	yes	characteristic
421	C₂×#117	#380	1	1	yes	characteristic
422	C₂×#117	#385	1	1	yes	characteristic
423	C₂×#117	#385	1	1	yes	characteristic
424	C₂×#117	#386	1	1	yes	characteristic
425	C₂×#117	#386	1	1	yes	characteristic
426	C₂×#117	#386	1	1	yes	characteristic
427	C₂×#117	#386	1	1	yes	characteristic
428	C₂×#117	#392	1	1	yes	characteristic
429	C₂×#117	#392	1	1	yes	characteristic
430	C₂×#117	#394	1	1	yes	characteristic
431	C₂×#117	#394	1	1	yes	characteristic
432	C₂×#117	#394	1	1	yes	characteristic
433	C₂×#117	#394	1	1	yes	characteristic
434	C₂×#117	#397	1	1	yes	characteristic
435	C₂×#117	#397	1	1	yes	characteristic
436	C₂²×C₄²	C₂×#95	1	1	yes	characteristic
437	C₂²×C₄²	#379	1	1	yes	characteristic
438	C₂²×C₄²	#381	1	1	yes	characteristic
439	C₂²×C₄²	#381	1	1	yes	characteristic
440	C₂²×C₄²	#385	1	1	yes	characteristic
441	C₂²×C₄²	#386	1	1	yes	characteristic
442	C₂²×C₄²	#386	1	1	yes	characteristic
443	C₂²×C₄²	#386	1	1	yes	characteristic
444	C₂²×C₄²	#394	1	1	yes	characteristic
445	C₂²×C₄²	#394	1	1	yes	characteristic
446	C₂²×C₄²	#397	1	1	yes	characteristic
447	C₂²×C₄²	#397	1	1	yes	characteristic
448	C₄×M₁₆	#342	1	4	yes	complemented
449	C₂×C₄×C₈	#342	1	4	yes	complemented
450	C₂⁵	#1790	1	1	yes	characteristic
451	C₂⁵	#1867	1	1	yes	characteristic
452	C₂⁵	#1889	1	1	yes	characteristic
453	C₂⁵	#2021	1	1	yes	characteristic
454	C₂⁵	#2021	1	1	yes	characteristic
455	C₂⁵	#2044	1	1	yes	characteristic
456	C₂⁵	#2044	1	1	yes	characteristic
457	C₂²×Q₈	#1437	1	1	yes	characteristic
458	C₂²×Q₈	#1437	1	1	yes	characteristic
459	C₂²×Q₈	#1439	1	1	yes	characteristic
460	C₂²×Q₈	#1439	1	1	yes	characteristic
461	C₂²×D₄	#1437	1	1	yes	characteristic
462	C₂²×D₄	#1437	1	1	yes	characteristic
463	C₂²×D₄	#1438	1	1	yes	characteristic
464	C₂²×D₄	#1438	1	1	yes	characteristic
465	C₂²×D₄	#1439	1	1	yes	characteristic
466	C₂²×D₄	#1439	1	1	yes	characteristic
467	C₂²×D₄	#1439	1	1	yes	characteristic
468	C₂²×D₄	#1439	1	1	yes	characteristic
469	C₂²×D₄	#1439	1	1	yes	characteristic
470	C₂²×D₄	#1439	1	1	yes	characteristic
471	C₂²×D₄	#1440	1	1	yes	characteristic
472	C₂²×D₄	#1440	1	1	yes	characteristic
473	C₂²×D₄	#1898	1	2	yes	—
474	C₂²×D₄	#1898	1	2	yes	—
475	C₂²×D₄	#1898	1	2	yes	—
476	C₂²×D₄	#1898	1	2	yes	—
477	C₂³×C₄	C₂²⋊#95	1	1	yes	characteristic
478	C₂³×C₄	#1438	1	1	yes	characteristic
479	C₂³×C₄	#1438	1	1	yes	characteristic
480	C₂³×C₄	#1438	1	1	yes	characteristic
481	C₂³×C₄	#1439	1	1	yes	characteristic
482	C₂³×C₄	#1439	1	1	yes	characteristic
483	C₂³×C₄	#1440	1	1	yes	characteristic
484	C₂³×C₄	#1790	1	1	yes	characteristic
485	C₂³×C₄	#1790	1	1	yes	characteristic
486	C₂³×C₄	#1790	1	1	yes	characteristic
487	C₂³×C₄	#1867	1	1	yes	characteristic
488	C₂³×C₄	#1867	1	1	yes	characteristic
489	C₂³×C₄	#1867	1	1	yes	characteristic
490	C₂³×C₄	#1889	1	1	yes	characteristic
491	C₂³×C₄	#1890	1	1	yes	characteristic
492	C₂³×C₄	#1890	1	1	yes	characteristic
493	C₂³×C₄	#2021	1	1	yes	characteristic
494	C₂³×C₄	#2021	1	1	yes	characteristic
495	C₂³×C₄	#2022	1	1	yes	characteristic
496	C₂³×C₄	#2022	1	1	yes	characteristic
497	C₂³×C₄	#2022	1	1	yes	characteristic
498	C₂³×C₄	#2022	1	1	yes	characteristic
499	C₂³×C₄	#2044	1	1	yes	characteristic
500	C₂³×C₄	#2044	1	1	yes	characteristic
501	C₂³×C₄	#2044	1	1	yes	characteristic
502	C₂³×C₄	#2044	1	1	yes	characteristic
503	C₂³×C₄	#2044	1	1	yes	characteristic
504	C₂³×C₄	#2044	1	1	yes	characteristic
505	#127	#1781	1	4	yes	—
506	#127	#1819	1	4	yes	—
507	#127	#1898	1	4	yes	—
508	#127	#1898	1	4	yes	—
509	C₂×C₄²	C₂²⋊#95	1	1	yes	characteristic
510	C₂×C₄²	C₂²⋊#95	1	1	yes	characteristic
511	C₂×C₄²	#1438	1	1	yes	characteristic
512	C₂×C₄²	#1439	1	1	yes	characteristic
513	C₂×C₄²	#1439	1	1	yes	characteristic
514	C₂×C₄²	#1440	1	1	yes	characteristic
515	C₂×C₄²	#1440	1	1	yes	characteristic
516	C₂×C₄²	#1440	1	1	yes	characteristic
517	C₂×C₄²	C₂×#342	1	2	yes	—
518	C₂×C₄²	C₂×#342	1	2	yes	—
519	C₂×C₄²	#1913	1	2	yes	—
520	C₂×C₄²	#1913	1	2	yes	—
521	C₂⁴	#10745	1	1	yes	characteristic
522	C₂⁴	#10991	1	1	yes	characteristic
523	C₂⁴	#10995	1	1	yes	characteristic
524	C₂⁴	#10995	1	1	yes	characteristic
525	C₂⁴	#11087	1	1	yes	characteristic
526	C₂⁴	#11087	1	1	yes	characteristic
527	C₂⁴	#11174	1	1	yes	characteristic
528	C₂⁴	#12753	1	1	yes	characteristic
529	C₂⁴	#12753	1	1	yes	characteristic
530	C₂⁴	#12754	1	1	yes	characteristic
531	C₂⁴	#12754	1	1	yes	characteristic
532	C₂×D₄	#10965	1	2	yes	—
533	C₂×D₄	#10965	1	2	yes	—
534	C₂×D₄	#11196	1	2	yes	—
535	C₂×D₄	#11196	1	2	yes	—
536	C₂²×C₄	#7555	1	1	yes	characteristic
537	C₂²×C₄	#10735	1	1	yes	characteristic
538	C₂²×C₄	#10735	1	1	yes	characteristic
539	C₂²×C₄	#10745	1	1	yes	characteristic
540	C₂²×C₄	#10754	1	1	yes	characteristic
541	C₂²×C₄	#10754	1	1	yes	characteristic
542	C₂²×C₄	#10992	1	1	yes	characteristic
543	C₂²×C₄	#10995	1	1	yes	characteristic
544	C₂²×C₄	#10995	1	1	yes	characteristic
545	C₂²×C₄	#11087	1	1	yes	characteristic
546	C₂²×C₄	#11087	1	1	yes	characteristic
547	C₂²×C₄	#11174	1	1	yes	characteristic
548	C₂²×C₄	#12753	1	1	yes	characteristic
549	C₂²×C₄	#12753	1	1	yes	characteristic
550	C₂²×C₄	#12754	1	1	yes	characteristic
551	C₂²×C₄	#12754	1	1	yes	characteristic
552	C₄²	#10725	1	2	yes	—
553	C₄²	#10735	1	2	yes	—
554	C₄²	#10972	1	2	yes	—
555	C₄²	#11172	1	2	yes	—
556	C₂³	#106766	1	1	yes	characteristic
557	C₂³	#106766	1	1	yes	characteristic
558	C₂³	#123590	1	1	yes	characteristic
559	C₂³	#146654	1	1	yes	characteristic
560	C₂³	#146654	1	1	yes	characteristic
561	C₂³	#146654	1	1	yes	characteristic
562	C₂³	#146654	1	1	yes	characteristic
563	C₂³	#147811	1	1	yes	characteristic
564	C₂³	#147812	1	1	yes	characteristic
565	C₂³	#147819	1	1	yes	characteristic
566	C₂³	#147819	1	1	yes	characteristic
567	C₂×C₄	#106766	1	1	yes	characteristic
568	C₂×C₄	#106766	1	1	yes	characteristic
569	C₂×C₄	#123513	1	1	yes	characteristic
570	C₂×C₄	#123581	1	1	yes	characteristic
571	C₂×C₄	#147811	1	1	yes	characteristic
572	C₂×C₄	#147812	1	1	yes	characteristic
573	C₂×C₄	#147819	1	1	yes	characteristic
574	C₂×C₄	#147819	1	1	yes	characteristic
575	C₂²	#72210462	1	1	yes	characteristic
576	C₂²	#72210462	1	1	yes	characteristic
577	C₂²	#72210473	1	1	yes	characteristic
578	C₂²	#72210473	1	1	yes	characteristic
579	C₂²	#72250028	1	1	yes	characteristic
580	C₂²	#72250028	1	1	yes	characteristic
581	C₂²	#72250064	1	1	yes	characteristic
582	C₂	#72213457	1	2	yes	—
583	C₂	#72250222	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#72210462
commutator	C₂²×#124	C₂×C₄²
Frattini, cosocle	C₂³×#535	C₂³
prime radical	C₂×#10575547	C₂²
LCS	G ▷ C₂²×#124 ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ C₂⁵×C₄ ◁ C₂³×#535 ◁ G
LECS	G ▷ C₂³×#535 ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂×#72213436	C₂	semidirect
3. C₂×#512663	C₄	semidirect
4. C₂×#72213396	C₂	semidirect
5. C₂×#72213445	C₂	semidirect
7. #72250477	C₄	semidirect
8. #72250472	C₄	semidirect
9. #72250462	C₄	semidirect
10. #72250448	C₄	semidirect
11. C₂×#72210462	C₂	semidirect
18. C₂×#112156	C₄	semidirect
20. C₂×#114858	C₄	semidirect
113. C₂×#2128	C₂²⋊C₄	semidirect
114. C₂×#2127	C₂²⋊C₄	semidirect
115. #17666	C₂²⋊C₄	semidirect
116. #14662	C₂²⋊C₄	semidirect
117. #14169	C₂²⋊C₄	semidirect
351. #533	#342	semidirect
352. C₂×C₄⋊Q₈	#342	semidirect
353. C₂×#127	#342	semidirect
448. C₄×M₁₆	#342	semidirect
449. C₂×C₄×C₈	#342	semidirect

Maximal subgroups

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

subgroup	index
C₂×#72213436	2
C₂×#72213428	2
C₂×#72213396	2
C₂×#72213445	2
#72250517	2
C₂×#72210462	2
C₂×#72213377	2