Subgroups — #60217

Order 256.

957 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3475	C₂	1	1	yes	maximal, characteristic
2	#2971	C₂	1	2	yes	maximal, complemented
3	#2969	C₂	1	2	yes	maximal, complemented
4	#2969	C₂	1	4	yes	maximal, complemented
5	#2967	C₂	1	4	yes	maximal, complemented
6	#2966	C₂	1	2	yes	maximal, complemented
7	#2965	C₂	1	2	yes	maximal, complemented
8	#2962	C₂	1	1	yes	maximal, characteristic, complemented
9	#2960	C₂	1	1	yes	maximal, characteristic, complemented
10	D₄×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	#2933	C₂	1	2	yes	maximal, complemented
12	#2930	C₂	1	2	yes	maximal, complemented
13	C₂×#436	C₂	1	1	yes	maximal, characteristic, complemented
14	#2925	C₂	1	1	yes	maximal, characteristic, complemented
15	#2924	C₂	1	2	yes	maximal, complemented
16	C₄×#131	C₂	1	1	yes	maximal, characteristic, complemented
17	#2873	C₂	1	2	yes	maximal, complemented
18	C₂×#131	C₂²	1	1	yes	characteristic
19	C₂×#131	C₂²	1	1	yes	characteristic
20	C₂²×M₁₆	C₂²	1	2	yes	—
21	C₂²×M₁₆	C₂²	1	2	yes	—
22	#556	C₄	1	1	yes	characteristic
23	#555	C₄	1	1	yes	characteristic
24	#554	C₄	1	1	yes	characteristic
25	#553	C₄	1	2	yes	—
26	#552	C₄	1	2	yes	—
27	#552	C₄	1	2	yes	—
28	#551	C₄	1	4	yes	—
29	#547	C₄	1	1	yes	characteristic
30	#546	C₄	1	2	yes	—
31	#533	C₂²	1	1	yes	characteristic
32	#529	C₂²	1	2	yes	—
33	#529	C₂²	1	4	yes	—
34	#525	C₂²	1	2	yes	—
35	C₄×#41	C₂²	1	2	yes	—
36	C₄×#41	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
38	C₂×#117	C₂²	1	2	yes	—
39	#446	C₂²	1	2	yes	complemented
40	#446	C₂²	1	2	yes	complemented
41	#446	C₂²	1	2	yes	complemented
42	#446	C₂²	1	4	yes	complemented
43	C₈×Q₈	C₂²	1	2	yes	complemented
44	C₈×Q₈	C₂²	1	2	yes	complemented
45	C₈×Q₈	C₂²	1	2	yes	complemented
46	#436	C₂²	1	1	yes	characteristic
47	#436	C₂²	1	1	yes	characteristic
48	#436	C₂²	1	2	yes	—
49	#436	C₂²	1	1	yes	characteristic
50	#436	C₂²	1	2	yes	—
51	#436	C₂²	1	1	yes	characteristic
52	#436	C₂²	1	2	yes	—
53	#436	C₂²	1	4	yes	complemented
54	#436	C₂²	1	4	yes	complemented
55	#436	C₂²	1	4	yes	complemented
56	#435	C₂²	1	4	yes	—
57	#435	C₂²	1	4	yes	complemented
58	#435	C₂²	1	4	yes	complemented
59	#435	C₂²	1	4	yes	complemented
60	#435	C₂²	1	4	yes	complemented
61	C₈×D₄	C₂²	1	2	yes	—
62	C₈×D₄	C₂²	1	4	yes	complemented
63	#433	C₂²	1	4	yes	complemented
64	#433	C₂²	1	4	yes	complemented
65	#433	C₂²	1	4	yes	complemented
66	#432	C₂²	1	4	yes	complemented
67	#432	C₂²	1	2	yes	complemented
68	#431	C₂²	1	4	yes	complemented
69	#431	C₂²	1	2	yes	complemented
70	#424	C₂²	1	2	yes	—
71	#424	C₂²	1	2	yes	—
72	#423	C₂²	1	1	yes	characteristic
73	C₂×C₄⋊C₈	C₂²	1	1	yes	characteristic
74	#408	C₂²	1	2	yes	—
75	#407	C₂²	1	2	yes	—
76	C₂×C₂²⋊C₈	C₂²	1	2	yes	—
77	#405	C₂²	1	1	yes	characteristic
78	#405	C₂²	1	2	yes	—
79	#405	C₂²	1	2	yes	—
80	#405	C₂²	1	2	yes	—
81	#405	C₂²	1	1	yes	characteristic
82	#405	C₂²	1	4	yes	complemented
83	#405	C₂²	1	4	yes	complemented
84	#405	C₂²	1	2	yes	complemented
85	#405	C₂²	1	2	yes	complemented
86	C₄×M₁₆	C₂²	1	1	yes	characteristic
87	C₄×M₁₆	C₂²	1	4	yes	complemented
88	C₄×M₁₆	C₂²	1	4	yes	complemented
89	C₄×M₁₆	C₂²	1	2	yes	complemented
90	C₂×C₄×C₈	C₂²	1	1	yes	characteristic
91	C₂×C₄×C₈	C₂²	1	2	yes	complemented
92	C₂×#41	C₂×C₄	1	2	yes	—
93	C₂×#41	C₂³	1	1	yes	characteristic
94	C₂²×D₄	C₂×C₄	1	1	yes	characteristic
95	C₂³×C₄	C₂³	1	2	yes	—
96	#131	—	2	4	no	—
97	#131	—	2	4	no	—
98	C₂×M₁₆	—	2	8	no	—
99	C₂×M₁₆	—	2	8	no	—
100	C₂×M₁₆	C₂³	1	4	yes	—
101	C₂×M₁₆	C₂³	1	2	yes	—
102	C₂×M₁₆	C₂³	1	2	yes	—
103	C₂×M₁₆	C₂³	1	2	yes	—
104	C₂×M₁₆	C₂³	1	2	yes	—
105	C₂×M₁₆	C₂³	1	2	yes	—
106	C₂×M₁₆	C₂³	1	1	yes	characteristic
107	C₂×M₁₆	C₂³	1	2	yes	—
108	C₂×M₁₆	C₂³	1	2	yes	—
109	C₂×M₁₆	C₂³	1	1	yes	characteristic
110	C₂²×C₈	C₂³	1	2	yes	—
111	C₂²×C₈	C₂³	1	4	yes	—
112	C₂²×C₈	C₂³	1	1	yes	characteristic
113	C₂²×C₈	C₂³	1	2	yes	—
114	C₂²×C₈	C₂³	1	2	yes	—
115	C₂²×C₈	C₂³	1	1	yes	characteristic
116	C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
117	C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
118	#126	C₂×C₄	1	4	yes	—
119	#126	C₂×C₄	1	4	yes	—
120	#126	C₂×C₄	1	4	yes	—
121	#125	C₂×C₄	1	4	yes	—
122	#125	C₂×C₄	1	2	yes	—
123	#125	C₂×C₄	1	2	yes	—
124	#124	C₂×C₄	1	2	yes	—
125	#124	C₂×C₄	1	4	yes	—
126	#123	C₂×C₄	1	4	yes	—
127	#123	C₂×C₄	1	4	yes	—
128	#123	C₂×C₄	1	4	yes	—
129	#123	C₂×C₄	1	4	yes	—
130	C₂²⋊Q₈	C₂×C₄	1	2	yes	—
131	C₂²⋊Q₈	C₂×C₄	1	2	yes	—
132	C₂²⋊Q₈	C₂×C₄	1	2	yes	—
133	C₂²⋊Q₈	C₂×C₄	1	4	yes	—
134	C₂²⋊Q₈	C₂×C₄	1	2	yes	—
135	C₂²⋊Q₈	C₂×C₄	1	2	yes	—
136	#121	C₂×C₄	1	2	yes	—
137	#121	C₂×C₄	1	2	yes	—
138	#121	C₂×C₄	1	4	yes	—
139	#121	C₂×C₄	1	2	yes	—
140	#120	C₂×C₄	1	4	yes	—
141	C₄×Q₈	C₂×C₄	1	1	yes	characteristic
142	C₄×Q₈	C₂×C₄	1	2	yes	—
143	C₄×Q₈	C₂×C₄	1	1	yes	characteristic
144	C₄×Q₈	C₂³	1	2	yes	—
145	C₄×Q₈	C₂³	1	2	yes	—
146	C₄×D₄	C₂×C₄	1	1	yes	characteristic
147	C₄×D₄	C₂×C₄	1	2	yes	—
148	C₄×D₄	C₂×C₄	1	1	yes	characteristic
149	C₄×D₄	C₂×C₄	1	2	yes	—
150	C₄×D₄	C₂×C₄	1	2	yes	—
151	C₄×D₄	C₂×C₄	1	1	yes	characteristic
152	C₄×D₄	C₂×C₄	1	2	yes	—
153	C₄×D₄	C₂×C₄	1	4	yes	—
154	C₄×D₄	C₂×C₄	1	1	yes	characteristic
155	C₄×D₄	C₂³	1	1	yes	characteristic
156	C₄×D₄	C₂³	1	1	yes	characteristic
157	C₄×D₄	C₂³	1	2	yes	—
158	C₄×D₄	C₂³	1	4	yes	—
159	C₄×D₄	C₂³	1	4	yes	—
160	#117	C₂×C₄	1	4	yes	—
161	#117	C₂×C₄	1	2	yes	—
162	#117	C₂×C₄	1	2	yes	—
163	#117	C₂×C₄	1	4	yes	—
164	#117	C₂×C₄	1	2	yes	—
165	#117	C₂³	1	1	yes	characteristic
166	#117	C₂³	1	2	yes	—
167	#117	C₂³	1	4	yes	—
168	#117	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄	C₂×C₄	1	2	yes	—
170	C₂×C₄⋊C₄	C₂×C₄	1	2	yes	—
171	C₂×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
172	C₂×C₂²⋊C₄	C₂×C₄	1	4	yes	—
173	C₂×C₂²⋊C₄	C₂×C₄	1	2	yes	—
174	C₂×C₄²	C₂³	1	4	yes	—
175	C₂×C₄²	C₂³	1	1	yes	characteristic
176	C₂×C₄²	C₂³	1	2	yes	—
177	C₄⋊C₈	C₂³	1	1	yes	characteristic
178	C₄⋊C₈	C₂³	1	1	yes	characteristic
179	C₄⋊C₈	C₂³	1	2	yes	—
180	C₄⋊C₈	C₂³	1	2	yes	—
181	C₄⋊C₈	C₂³	1	2	yes	—
182	C₄⋊C₈	C₂³	1	4	yes	—
183	C₄⋊C₈	C₂³	1	4	yes	—
184	C₄⋊C₈	C₂³	1	4	yes	—
185	C₄⋊C₈	C₂³	1	4	yes	—
186	C₂²⋊C₈	C₂³	1	2	yes	—
187	C₂²⋊C₈	C₂³	1	2	yes	—
188	C₂²⋊C₈	C₂³	1	2	yes	—
189	C₂²⋊C₈	C₂³	1	2	yes	—
190	C₂²⋊C₈	C₂³	1	4	yes	—
191	C₂²⋊C₈	C₂³	1	4	yes	—
192	C₂²⋊C₈	C₂³	1	4	yes	—
193	C₂²⋊C₈	C₂³	1	4	yes	—
194	#97	C₂³	1	2	yes	—
195	#97	C₂³	1	2	yes	—
196	#97	C₂³	1	4	yes	—
197	#97	C₂³	1	2	yes	—
198	#97	C₂³	1	4	yes	—
199	#97	C₂³	1	4	yes	—
200	C₄×C₈	C₂³	1	1	yes	characteristic
201	C₄×C₈	C₂³	1	1	yes	characteristic
202	C₄×C₈	C₂³	1	1	yes	characteristic
203	C₄×C₈	C₂³	1	1	yes	characteristic
204	C₄×C₈	C₂³	1	2	yes	—
205	C₄×C₈	C₂³	1	2	yes	—
206	C₄×C₈	C₂³	1	2	yes	—
207	C₄×C₈	C₂³	1	4	yes	—
208	C₄×C₈	C₂³	1	4	yes	—
209	C₄×C₈	C₂³	1	4	yes	—
210	C₂⁴	C₂²×C₄	1	2	yes	—
211	#41	—	2	2	no	—
212	#41	—	2	2	no	—
213	#41	—	4	4	no	—
214	C₂×Q₈	C₂²×C₄	1	1	yes	characteristic
215	C₂×Q₈	C₂²×C₄	1	2	yes	—
216	C₂×Q₈	C₂²×C₄	1	2	yes	—
217	C₂×D₄	—	4	2	no	—
218	C₂×D₄	C₂²×C₄	1	1	yes	characteristic
219	C₂×D₄	C₂²×C₄	1	2	yes	—
220	C₂×D₄	C₂²×C₄	1	1	yes	characteristic
221	C₂×D₄	C₂²×C₄	1	1	yes	characteristic
222	C₂×D₄	C₂²×C₄	1	4	yes	—
223	C₂×D₄	C₂²×C₄	1	2	yes	—
224	C₂×D₄	C₂²×C₄	1	4	yes	—
225	C₂²×C₄	—	2	4	no	—
226	C₂²×C₄	—	2	4	no	—
227	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
228	C₂²×C₄	C₂²×C₄	1	2	yes	—
229	C₂²×C₄	C₂²×C₄	1	2	yes	—
230	C₂²×C₄	C₂²×C₄	1	2	yes	—
231	C₂²×C₄	C₂²×C₄	1	2	yes	—
232	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
233	C₂²×C₄	C₂²×C₄	1	4	yes	—
234	C₂²×C₄	C₂²×C₄	1	4	yes	—
235	C₂²×C₄	C₂²×C₄	1	2	yes	—
236	C₂²×C₄	C₂⁴	1	2	yes	—
237	C₂²×C₄	C₂⁴	1	2	yes	—
238	C₂²×C₄	C₂⁴	1	2	yes	—
239	C₂²×C₄	C₂⁴	1	1	yes	characteristic
240	M₁₆	—	2	4	no	—
241	M₁₆	—	2	2	no	—
242	M₁₆	—	2	8	no	—
243	M₁₆	—	2	4	no	—
244	M₁₆	—	2	4	no	—
245	M₁₆	—	2	4	no	—
246	M₁₆	—	2	4	no	—
247	M₁₆	—	2	4	no	—
248	M₁₆	—	2	4	no	—
249	M₁₆	#41	1	4	yes	complemented
250	C₂×C₈	—	2	4	no	—
251	C₂×C₈	—	2	2	no	—
252	C₂×C₈	—	2	8	no	—
253	C₂×C₈	—	2	4	no	—
254	C₂×C₈	—	2	4	no	—
255	C₂×C₈	#41	1	4	yes	complemented
256	C₂×C₈	C₂⁴	1	1	yes	characteristic
257	C₂×C₈	C₂⁴	1	1	yes	characteristic
258	C₂×C₈	C₂⁴	1	2	yes	—
259	C₂×C₈	C₂⁴	1	2	yes	—
260	C₂×C₈	C₂⁴	1	4	yes	—
261	C₂×C₈	C₂⁴	1	2	yes	—
262	C₂×C₈	C₂⁴	1	1	yes	characteristic
263	C₂×C₈	C₂⁴	1	2	yes	—
264	C₂×C₈	C₂⁴	1	1	yes	characteristic
265	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
266	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
267	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
268	C₄⋊C₄	C₂²×C₄	1	2	yes	—
269	C₄⋊C₄	C₂²×C₄	1	2	yes	—
270	C₄⋊C₄	C₂²×C₄	1	4	yes	—
271	C₄⋊C₄	C₂²×C₄	1	4	yes	—
272	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
273	C₄⋊C₄	C₂²×C₄	1	2	yes	—
274	C₄⋊C₄	C₂²×C₄	1	2	yes	—
275	C₄⋊C₄	C₂²×C₄	1	4	yes	—
276	C₄⋊C₄	C₂²×C₄	1	4	yes	—
277	C₄⋊C₄	C₂²×C₄	1	2	yes	—
278	C₄⋊C₄	C₂²×C₄	1	2	yes	—
279	C₄⋊C₄	C₂²×C₄	1	4	yes	—
280	C₄⋊C₄	C₂²×C₄	1	4	yes	—
281	C₄⋊C₄	C₂²×C₄	1	2	yes	—
282	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
283	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
284	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
285	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
286	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
287	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
288	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
289	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
290	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
291	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
292	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
293	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
294	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
295	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
296	C₄²	C₂²×C₄	1	4	yes	—
297	C₄²	C₂²×C₄	1	4	yes	—
298	C₄²	C₂²×C₄	1	2	yes	—
299	C₄²	C₂²×C₄	1	1	yes	characteristic
300	C₄²	C₂²×C₄	1	1	yes	characteristic
301	C₄²	C₂²×C₄	1	2	yes	—
302	C₄²	C₂⁴	1	2	yes	—
303	C₄²	C₂⁴	1	1	yes	characteristic
304	C₄²	C₂⁴	1	1	yes	characteristic
305	C₄²	C₂⁴	1	4	yes	—
306	C₂³	—	2	4	no	—
307	C₂³	—	4	2	no	—
308	C₂³	—	4	2	no	—
309	C₂³	C₂³×C₄	1	2	yes	—
310	C₂³	C₂³×C₄	1	2	yes	—
311	C₂³	C₂³×C₄	1	2	yes	—
312	C₂³	C₂³×C₄	1	1	yes	characteristic
313	Q₈	—	2	2	no	—
314	Q₈	—	2	4	no	—
315	Q₈	—	4	2	no	—
316	D₄	—	2	4	no	—
317	D₄	—	2	2	no	—
318	D₄	—	2	2	no	—
319	D₄	—	2	2	no	—
320	D₄	—	4	2	no	—
321	D₄	—	4	4	no	—
322	D₄	—	4	4	no	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	4	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	4	no	—
338	C₂×C₄	C₂³×C₄	1	2	yes	—
339	C₂×C₄	C₂³×C₄	1	2	yes	—
340	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
341	C₂×C₄	C₂³×C₄	1	2	yes	—
342	C₂×C₄	C₂³×C₄	1	2	yes	—
343	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
344	C₂×C₄	C₂³×C₄	1	4	yes	—
345	C₂×C₄	C₂³×C₄	1	4	yes	—
346	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
347	C₂×C₄	C₂³×C₄	1	2	yes	—
348	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
349	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
350	C₂×C₄	C₂×#41	1	2	yes	—
351	C₂×C₄	C₂×#41	1	2	yes	—
352	C₂×C₄	C₂⁵	1	1	yes	characteristic
353	C₈	—	2	1	no	—
354	C₈	—	2	2	no	—
355	C₈	—	2	2	no	—
356	C₈	—	2	1	no	—
357	C₈	—	2	4	no	—
358	C₈	—	2	2	no	—
359	C₈	C₂×#41	1	4	yes	—
360	C₈	C₂×#41	1	2	yes	—
361	C₈	C₂×#41	1	2	yes	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	2	2	no	—
367	C₂²	—	2	2	no	—
368	C₂²	—	2	2	no	—
369	C₂²	—	2	2	no	—
370	C₂²	—	2	2	no	—
371	C₂²	—	2	2	no	—
372	C₂²	—	2	2	no	—
373	C₂²	—	8	4	no	—
374	C₂²	C₄×#41	1	2	yes	—
375	C₂²	C₂⁴×C₄	1	1	yes	characteristic
376	C₄	—	2	2	no	—
377	C₄	—	2	2	no	—
378	C₄	—	2	2	no	—
379	C₄	—	2	2	no	—
380	C₄	—	2	1	no	—
381	C₄	—	2	4	no	—
382	C₄	—	2	1	no	—
383	C₄	—	2	2	no	—
384	C₄	—	2	4	no	—
385	C₄	—	2	1	no	—
386	C₄	C₄×#41	1	2	yes	—
387	C₄	#568	1	2	yes	—
388	C₄	C₂²×#41	1	1	yes	characteristic
389	C₄	C₂²×#41	1	1	yes	characteristic
390	C₂	—	2	2	no	—
391	C₂	—	4	2	no	—
392	C₂	—	4	2	no	—
393	C₂	—	4	2	no	—
394	C₂	C₂×C₄×#41	1	1	yes	characteristic
395	C₂	C₂×#568	1	1	yes	characteristic
396	C₂	#3573	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, cosocle	C₂×C₄	C₂⁵
commutator, socle	C₂²	C₂⁴×C₄
prime radical	#3475	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #2971	C₂	semidirect
3. #2969	C₂	semidirect
4. #2969	C₂	semidirect
5. #2967	C₂	semidirect
6. #2966	C₂	semidirect
7. #2965	C₂	semidirect
8. #2962	C₂	semidirect
9. #2960	C₂	semidirect
10. D₄×M₁₆	C₂	semidirect
11. #2933	C₂	semidirect
12. #2930	C₂	semidirect
13. C₂×#436	C₂	semidirect
14. #2925	C₂	semidirect
15. #2924	C₂	semidirect
16. C₄×#131	C₂	semidirect
17. #2873	C₂	semidirect
39. #446	C₂²	semidirect
40. #446	C₂²	semidirect
41. #446	C₂²	semidirect
42. #446	C₂²	semidirect
43. C₈×Q₈	C₂²	semidirect
44. C₈×Q₈	C₂²	semidirect
45. C₈×Q₈	C₂²	semidirect
53. #436	C₂²	semidirect
54. #436	C₂²	semidirect
55. #436	C₂²	semidirect
57. #435	C₂²	semidirect
58. #435	C₂²	semidirect
59. #435	C₂²	semidirect
60. #435	C₂²	semidirect
62. C₈×D₄	C₂²	semidirect
63. #433	C₂²	semidirect
64. #433	C₂²	semidirect
65. #433	C₂²	semidirect
66. #432	C₂²	semidirect
67. #432	C₂²	semidirect
68. #431	C₂²	semidirect
69. #431	C₂²	semidirect
82. #405	C₂²	semidirect
83. #405	C₂²	semidirect
84. #405	C₂²	semidirect
85. #405	C₂²	semidirect
87. C₄×M₁₆	C₂²	semidirect
88. C₄×M₁₆	C₂²	semidirect
89. C₄×M₁₆	C₂²	semidirect
91. C₂×C₄×C₈	C₂²	semidirect
249. M₁₆	#41	semidirect
255. C₂×C₈	#41	semidirect

Maximal subgroups

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

subgroup	index
#3475	2
#2971	2
#2969	2
#2967	2
#2966	2
#2965	2
#2962	2
#2960	2
D₄×M₁₆	2
#2933	2
#2930	2
C₂×#436	2
#2925	2
#2924	2
C₄×#131	2
#2873	2