Subgroups — #60323

Order 256.

970 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	#3481	C₂	1	1	yes	maximal, characteristic
2	#2994	C₂	1	2	yes	maximal, complemented
3	#2993	C₂	1	2	yes	maximal, complemented
4	#2991	C₂	1	1	yes	maximal, characteristic, complemented
5	#2990	C₂	1	1	yes	maximal, characteristic, complemented
6	#2979	C₂	1	1	yes	maximal, characteristic, complemented
7	#2976	C₂	1	4	yes	maximal, complemented
8	#2974	C₂	1	2	yes	maximal, complemented
9	#2972	C₂	1	2	yes	maximal, complemented
10	#2969	C₂	1	2	yes	maximal, complemented
11	#2966	C₂	1	2	yes	maximal, complemented
12	#2965	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈×#41	C₂	1	1	yes	maximal, characteristic, complemented
14	D₄×M₁₆	C₂	1	2	yes	maximal, complemented
15	#2933	C₂	1	4	yes	maximal, complemented
16	#2931	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#436	C₂	1	2	yes	maximal, complemented
18	C₂×#131	C₂²	1	2	yes	complemented
19	C₂²×M₁₆	C₂²	1	4	yes	complemented
20	#559	C₄	1	1	yes	characteristic
21	#554	C₄	1	1	yes	characteristic
22	#554	C₄	1	1	yes	characteristic
23	#553	C₄	1	2	yes	—
24	#553	C₄	1	2	yes	—
25	#551	C₄	1	4	yes	—
26	#546	C₄	1	2	yes	—
27	#546	C₄	1	2	yes	—
28	D₄²	C₄	1	1	yes	characteristic
29	#532	C₂²	1	1	yes	characteristic
30	#529	C₂²	1	2	yes	—
31	#529	C₂²	1	2	yes	—
32	#525	C₂²	1	4	yes	—
33	C₄×#41	C₂²	1	1	yes	characteristic
34	C₄×#41	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄	C₂²	1	2	yes	—
36	C₂×C₄×D₄	C₂²	1	2	yes	—
37	#446	C₂²	1	1	yes	characteristic, complemented
38	#446	C₂²	1	1	yes	characteristic, complemented
39	#446	C₂²	1	2	yes	complemented
40	C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
41	C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
42	C₈×Q₈	C₂²	1	2	yes	complemented
43	#436	C₂²	1	1	yes	characteristic
44	#436	C₂²	1	2	yes	—
45	#436	C₂²	1	1	yes	characteristic
46	#436	C₂²	1	2	yes	complemented
47	#436	C₂²	1	4	yes	complemented
48	#436	C₂²	1	4	yes	complemented
49	#436	C₂²	1	2	yes	complemented
50	#436	C₂²	1	2	yes	complemented
51	#436	C₂²	1	4	yes	complemented
52	#436	C₂²	1	2	yes	complemented
53	#435	C₂²	1	2	yes	complemented
54	#435	C₂²	1	4	yes	complemented
55	#435	C₂²	1	4	yes	complemented
56	#435	C₂²	1	4	yes	complemented
57	#435	C₂²	1	4	yes	complemented
58	#435	C₂²	1	2	yes	complemented
59	#435	C₂²	1	4	yes	complemented
60	C₈×D₄	C₂²	1	1	yes	characteristic
61	C₈×D₄	C₂²	1	2	yes	—
62	C₈×D₄	C₂²	1	1	yes	characteristic
63	C₈×D₄	C₂²	1	2	yes	complemented
64	C₈×D₄	C₂²	1	2	yes	complemented
65	C₈×D₄	C₂²	1	2	yes	complemented
66	C₈×D₄	C₂²	1	4	yes	complemented
67	C₈×D₄	C₂²	1	2	yes	complemented
68	C₈×D₄	C₂²	1	4	yes	complemented
69	C₈×D₄	C₂²	1	2	yes	complemented
70	C₈×D₄	C₂²	1	2	yes	complemented
71	#433	C₂²	1	4	yes	complemented
72	#433	C₂²	1	4	yes	complemented
73	#432	C₂²	1	2	yes	complemented
74	#431	C₂²	1	2	yes	complemented
75	#431	C₂²	1	1	yes	characteristic, complemented
76	#431	C₂²	1	2	yes	complemented
77	#431	C₂²	1	1	yes	characteristic, complemented
78	#431	C₂²	1	2	yes	complemented
79	#424	C₂²	1	4	yes	complemented
80	#423	C₂²	1	1	yes	characteristic, complemented
81	#423	C₂²	1	2	yes	complemented
82	C₂×C₄⋊C₈	C₂²	1	2	yes	complemented
83	#408	C₂²	1	2	yes	complemented
84	#408	C₂²	1	4	yes	complemented
85	#407	C₂²	1	4	yes	complemented
86	C₂×C₂²⋊C₈	C₂²	1	4	yes	complemented
87	C₂×C₂²⋊C₈	C₂²	1	4	yes	complemented
88	#405	C₂²	1	4	yes	complemented
89	C₄×M₁₆	C₂²	1	2	yes	complemented
90	C₂×C₄×C₈	C₂²	1	2	yes	complemented
91	C₂×C₄×C₈	C₂²	1	1	yes	characteristic, complemented
92	C₂×#41	C₂×C₄	1	1	yes	characteristic
93	C₂×#41	C₂×C₄	1	1	yes	characteristic
94	C₂×#41	C₂³	1	2	yes	—
95	C₂²×D₄	C₂×C₄	1	2	yes	—
96	C₂²×D₄	C₂×C₄	1	2	yes	—
97	C₂³×C₄	C₂³	1	4	yes	—
98	#131	—	4	4	no	—
99	C₂×M₁₆	—	4	8	no	—
100	C₂×M₁₆	C₂³	1	2	yes	—
101	C₂×M₁₆	C₂³	1	4	yes	—
102	C₂×M₁₆	C₂³	1	4	yes	—
103	C₂×M₁₆	C₂³	1	4	yes	—
104	C₂×M₁₆	C₂³	1	2	yes	—
105	C₂×M₁₆	C₂³	1	2	yes	—
106	C₂²×C₈	C₂³	1	2	yes	—
107	C₂²×C₈	C₂³	1	1	yes	characteristic
108	C₂²×C₈	C₂³	1	4	yes	—
109	C₂²×C₈	C₂³	1	4	yes	—
110	C₂²×C₈	C₂³	1	2	yes	—
111	C₂²×C₈	C₂³	1	1	yes	characteristic
112	C₂²×C₈	C₂³	1	4	yes	—
113	C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
114	#127	C₂×C₄	1	1	yes	characteristic
115	#126	C₂×C₄	1	4	yes	—
116	#126	C₂×C₄	1	4	yes	—
117	#125	C₂×C₄	1	2	yes	—
118	#125	C₂×C₄	1	2	yes	—
119	#124	C₂×C₄	1	2	yes	—
120	#124	C₂×C₄	1	2	yes	—
121	#124	C₂×C₄	1	2	yes	—
122	#123	C₂×C₄	1	4	yes	—
123	#123	C₂×C₄	1	4	yes	—
124	#123	C₂×C₄	1	4	yes	—
125	#123	C₂×C₄	1	4	yes	—
126	C₂²⋊Q₈	C₂×C₄	1	4	yes	—
127	C₂²⋊Q₈	C₂×C₄	1	4	yes	—
128	C₂²⋊Q₈	C₂×C₄	1	2	yes	—
129	C₂²⋊Q₈	C₂×C₄	1	2	yes	—
130	#121	C₂×C₄	1	4	yes	—
131	#121	C₂×C₄	1	4	yes	—
132	#121	C₂×C₄	1	2	yes	—
133	#121	C₂×C₄	1	2	yes	—
134	#121	C₂×C₄	1	2	yes	—
135	#121	C₂×C₄	1	2	yes	—
136	#120	C₂×C₄	1	4	yes	—
137	#120	C₂×C₄	1	4	yes	—
138	C₄×Q₈	C₂×C₄	1	1	yes	characteristic
139	C₄×Q₈	C₂×C₄	1	1	yes	characteristic
140	C₄×Q₈	C₂³	1	1	yes	characteristic
141	C₄×Q₈	C₂³	1	1	yes	characteristic
142	C₄×D₄	C₂×C₄	1	2	yes	—
143	C₄×D₄	C₂×C₄	1	2	yes	—
144	C₄×D₄	C₂×C₄	1	4	yes	—
145	C₄×D₄	C₂×C₄	1	4	yes	—
146	C₄×D₄	C₂×C₄	1	2	yes	—
147	C₄×D₄	C₂×C₄	1	2	yes	—
148	C₄×D₄	C₂×C₄	1	1	yes	characteristic
149	C₄×D₄	C₂×C₄	1	1	yes	characteristic
150	C₄×D₄	C₂×C₄	1	2	yes	—
151	C₄×D₄	C₂×C₄	1	2	yes	—
152	C₄×D₄	C₂³	1	1	yes	characteristic
153	C₄×D₄	C₂³	1	1	yes	characteristic
154	C₄×D₄	C₂³	1	4	yes	—
155	C₄×D₄	C₂³	1	4	yes	—
156	C₄×D₄	C₂³	1	2	yes	—
157	C₄×D₄	C₂³	1	2	yes	—
158	C₄×D₄	C₂³	1	2	yes	—
159	C₄×D₄	C₂³	1	2	yes	—
160	#117	C₂×C₄	1	2	yes	—
161	#117	C₂×C₄	1	2	yes	—
162	#117	C₂×C₄	1	1	yes	characteristic
163	#117	C₂×C₄	1	1	yes	characteristic
164	#117	C₂³	1	4	yes	—
165	C₂×C₄⋊C₄	C₂×C₄	1	2	yes	—
166	C₂×C₄⋊C₄	C₂×C₄	1	2	yes	—
167	C₂×C₂²⋊C₄	C₂×C₄	1	4	yes	—
168	C₂×C₂²⋊C₄	C₂×C₄	1	4	yes	—
169	C₂×C₄²	C₂³	1	2	yes	—
170	C₂×C₄²	C₂³	1	2	yes	—
171	C₂×C₄²	C₂³	1	1	yes	characteristic
172	C₄⋊C₈	C₂³	1	1	yes	characteristic
173	C₄⋊C₈	C₂³	1	2	yes	—
174	C₄⋊C₈	C₂³	1	4	yes	—
175	C₄⋊C₈	C₂³	1	2	yes	—
176	C₄⋊C₈	C₂³	1	1	yes	characteristic
177	C₄⋊C₈	C₂³	1	4	yes	—
178	C₄⋊C₈	C₂³	1	2	yes	—
179	C₄⋊C₈	C₂³	1	2	yes	—
180	C₄⋊C₈	C₂³	1	1	yes	characteristic
181	C₄⋊C₈	C₂³	1	1	yes	characteristic
182	C₄⋊C₈	C₂³	1	2	yes	—
183	C₄⋊C₈	C₂³	1	2	yes	—
184	C₂²⋊C₈	C₂³	1	2	yes	—
185	C₂²⋊C₈	C₂³	1	2	yes	—
186	C₂²⋊C₈	C₂³	1	2	yes	—
187	C₂²⋊C₈	C₂³	1	4	yes	—
188	C₂²⋊C₈	C₂³	1	4	yes	—
189	C₂²⋊C₈	C₂³	1	4	yes	—
190	C₂²⋊C₈	C₂³	1	4	yes	—
191	C₂²⋊C₈	C₂³	1	2	yes	—
192	C₂²⋊C₈	C₂³	1	4	yes	—
193	C₂²⋊C₈	C₂³	1	4	yes	—
194	C₂²⋊C₈	C₂³	1	2	yes	—
195	C₂²⋊C₈	C₂³	1	2	yes	—
196	#97	C₂³	1	2	yes	—
197	#97	C₂³	1	2	yes	—
198	#97	C₂³	1	4	yes	—
199	C₄×C₈	C₂³	1	1	yes	characteristic
200	C₄×C₈	C₂³	1	1	yes	characteristic
201	C₄×C₈	C₂³	1	2	yes	—
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	C₂⁴	C₂²×C₄	1	4	yes	—
209	#41	—	2	4	no	—
210	#41	—	4	2	no	—
211	#41	—	4	2	no	—
212	#41	—	4	2	no	—
213	C₂×Q₈	C₂²×C₄	1	1	yes	characteristic
214	C₂×Q₈	C₂²×C₄	1	1	yes	characteristic
215	C₂×Q₈	C₂²×C₄	1	2	yes	—
216	C₂×D₄	—	2	8	no	—
217	C₂×D₄	—	4	4	no	—
218	C₂×D₄	C₂²×C₄	1	1	yes	characteristic
219	C₂×D₄	C₂²×C₄	1	2	yes	—
220	C₂×D₄	C₂²×C₄	1	4	yes	—
221	C₂×D₄	C₂²×C₄	1	2	yes	—
222	C₂×D₄	C₂²×C₄	1	2	yes	—
223	C₂×D₄	C₂²×C₄	1	2	yes	—
224	C₂×D₄	C₂²×C₄	1	4	yes	—
225	C₂×D₄	C₂²×C₄	1	2	yes	—
226	C₂×D₄	C₂²×C₄	1	4	yes	—
227	C₂×D₄	C₂²×C₄	1	1	yes	characteristic
228	C₂²×C₄	—	4	4	no	—
229	C₂²×C₄	—	4	4	no	—
230	C₂²×C₄	C₂²×C₄	1	2	yes	—
231	C₂²×C₄	C₂²×C₄	1	2	yes	—
232	C₂²×C₄	C₂²×C₄	1	2	yes	—
233	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
234	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
235	C₂²×C₄	C₂²×C₄	1	2	yes	—
236	C₂²×C₄	C₂²×C₄	1	4	yes	—
237	C₂²×C₄	C₂²×C₄	1	4	yes	—
238	C₂²×C₄	C₂²×C₄	1	4	yes	—
239	C₂²×C₄	C₂⁴	1	2	yes	—
240	C₂²×C₄	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄	C₂⁴	1	2	yes	—
242	C₂²×C₄	C₂⁴	1	4	yes	—
243	M₁₆	—	2	4	no	—
244	M₁₆	—	2	8	no	—
245	M₁₆	—	4	4	no	—
246	M₁₆	—	4	4	no	—
247	M₁₆	—	4	2	no	—
248	M₁₆	—	4	2	no	—
249	C₂×C₈	—	2	4	no	—
250	C₂×C₈	—	2	2	no	—
251	C₂×C₈	—	4	2	no	—
252	C₂×C₈	—	4	4	no	—
253	C₂×C₈	—	4	1	no	—
254	C₂×C₈	—	4	4	no	—
255	C₂×C₈	—	4	4	no	—
256	C₂×C₈	C₂⁴	1	1	yes	characteristic
257	C₂×C₈	C₂⁴	1	2	yes	—
258	C₂×C₈	C₂⁴	1	1	yes	characteristic
259	C₂×C₈	C₂⁴	1	1	yes	characteristic
260	C₂×C₈	C₂⁴	1	2	yes	—
261	C₂×C₈	C₂⁴	1	2	yes	—
262	C₂×C₈	C₂⁴	1	2	yes	—
263	C₂×C₈	C₂⁴	1	4	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	2	yes	—
268	C₄⋊C₄	C₂²×C₄	1	2	yes	—
269	C₄⋊C₄	C₂²×C₄	1	4	yes	—
270	C₄⋊C₄	C₂²×C₄	1	4	yes	—
271	C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
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	2	yes	—
276	C₄⋊C₄	C₂²×C₄	1	2	yes	—
277	C₄⋊C₄	C₂²×C₄	1	4	yes	—
278	C₄⋊C₄	C₂²×C₄	1	4	yes	—
279	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
280	C₂²⋊C₄	C₂²×C₄	1	2	yes	—
281	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
282	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
283	C₂²⋊C₄	C₂²×C₄	1	4	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	2	yes	—
291	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
292	C₂²⋊C₄	C₂²×C₄	1	4	yes	—
293	C₄²	C₂²×C₄	1	1	yes	characteristic
294	C₄²	C₂²×C₄	1	2	yes	—
295	C₄²	C₂²×C₄	1	2	yes	—
296	C₄²	C₂²×C₄	1	2	yes	—
297	C₄²	C₂²×C₄	1	2	yes	—
298	C₄²	C₂²×C₄	1	1	yes	characteristic
299	C₄²	C₂⁴	1	1	yes	characteristic
300	C₄²	C₂⁴	1	1	yes	characteristic
301	C₄²	C₂⁴	1	2	yes	—
302	C₄²	C₂⁴	1	2	yes	—
303	C₂³	—	2	8	no	—
304	C₂³	—	4	4	no	—
305	C₂³	—	4	4	no	—
306	C₂³	C₂³×C₄	1	4	yes	—
307	C₂³	C₂³×C₄	1	2	yes	—
308	C₂³	C₂³×C₄	1	1	yes	characteristic
309	C₂³	C₂³×C₄	1	2	yes	—
310	Q₈	—	2	2	no	—
311	Q₈	—	2	2	no	—
312	Q₈	—	4	2	no	—
313	D₄	—	2	8	no	—
314	D₄	—	2	4	no	—
315	D₄	—	2	4	no	—
316	D₄	—	2	2	no	—
317	D₄	—	2	4	no	—
318	D₄	—	4	4	no	—
319	D₄	—	4	4	no	—
320	D₄	—	4	2	no	—
321	D₄	—	4	2	no	—
322	D₄	#131	1	4	yes	complemented
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	4	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	4	4	no	—
337	C₂×C₄	—	4	4	no	—
338	C₂×C₄	—	4	4	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
341	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
342	C₂×C₄	C₂³×C₄	1	2	yes	—
343	C₂×C₄	C₂³×C₄	1	2	yes	—
344	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
345	C₂×C₄	C₂³×C₄	1	2	yes	—
346	C₂×C₄	C₂³×C₄	1	2	yes	—
347	C₂×C₄	C₂³×C₄	1	2	yes	—
348	C₂×C₄	C₂³×C₄	1	2	yes	—
349	C₂×C₄	C₂³×C₄	1	4	yes	—
350	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
351	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
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	4	no	—
357	C₈	—	2	1	no	—
358	C₈	—	2	2	no	—
359	C₈	—	2	2	no	—
360	C₈	—	2	1	no	—
361	C₈	H(5,𝔽₂)	1	2	yes	—
362	C₂²	—	2	2	no	—
363	C₂²	—	2	2	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	2	4	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	2	2	no	—
369	C₂²	—	2	4	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	2	no	—
372	C₂²	—	2	4	no	—
373	C₂²	—	8	8	no	—
374	C₂²	C₂×#131	1	4	yes	—
375	C₂²	C₂⁴×C₄	1	1	yes	characteristic
376	C₄	—	2	2	no	—
377	C₄	—	2	2	no	—
378	C₄	—	2	4	no	—
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	2	2	no	—
382	C₄	—	2	2	no	—
383	C₄	—	2	1	no	—
384	C₄	—	2	2	no	—
385	C₄	—	2	2	no	—
386	C₄	C₂×#131	1	2	yes	—
387	C₄	#568	1	2	yes	—
388	C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
389	C₄	#585	1	1	yes	characteristic
390	C₂	—	2	4	no	—
391	C₂	—	4	1	no	—
392	C₂	—	4	4	no	—
393	C₂	—	4	2	no	—
394	C₂	C₄×H(5,𝔽₂)	1	1	yes	characteristic
395	C₂	C₂²×#131	1	1	yes	characteristic
396	C₂	C₂×#568	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, cosocle	C₂×C₄	C₂⁵
commutator, socle	C₂²	C₂⁴×C₄
prime radical	#3481	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. #2994	C₂	semidirect
3. #2993	C₂	semidirect
4. #2991	C₂	semidirect
5. #2990	C₂	semidirect
6. #2979	C₂	semidirect
7. #2976	C₂	semidirect
8. #2974	C₂	semidirect
9. #2972	C₂	semidirect
10. #2969	C₂	semidirect
11. #2966	C₂	semidirect
12. #2965	C₂	semidirect
13. C₈×#41	C₂	semidirect
14. D₄×M₁₆	C₂	semidirect
15. #2933	C₂	semidirect
16. #2931	C₂	semidirect
17. C₂×#436	C₂	semidirect
18. C₂×#131	C₂²	semidirect
19. C₂²×M₁₆	C₂²	semidirect
37. #446	C₂²	semidirect
38. #446	C₂²	semidirect
39. #446	C₂²	semidirect
40. C₈×Q₈	C₂²	semidirect
41. C₈×Q₈	C₂²	semidirect
42. C₈×Q₈	C₂²	semidirect
46. #436	C₂²	semidirect
47. #436	C₂²	semidirect
48. #436	C₂²	semidirect
49. #436	C₂²	semidirect
50. #436	C₂²	semidirect
51. #436	C₂²	semidirect
52. #436	C₂²	semidirect
53. #435	C₂²	semidirect
54. #435	C₂²	semidirect
55. #435	C₂²	semidirect
56. #435	C₂²	semidirect
57. #435	C₂²	semidirect
58. #435	C₂²	semidirect
59. #435	C₂²	semidirect
63. C₈×D₄	C₂²	semidirect
64. C₈×D₄	C₂²	semidirect
65. C₈×D₄	C₂²	semidirect
66. C₈×D₄	C₂²	semidirect
67. C₈×D₄	C₂²	semidirect
68. C₈×D₄	C₂²	semidirect
69. C₈×D₄	C₂²	semidirect
70. C₈×D₄	C₂²	semidirect
71. #433	C₂²	semidirect
72. #433	C₂²	semidirect
73. #432	C₂²	semidirect
74. #431	C₂²	semidirect
75. #431	C₂²	semidirect
76. #431	C₂²	semidirect
77. #431	C₂²	semidirect
78. #431	C₂²	semidirect
79. #424	C₂²	semidirect
80. #423	C₂²	semidirect
81. #423	C₂²	semidirect
82. C₂×C₄⋊C₈	C₂²	semidirect
83. #408	C₂²	semidirect
84. #408	C₂²	semidirect
85. #407	C₂²	semidirect
86. C₂×C₂²⋊C₈	C₂²	semidirect
87. C₂×C₂²⋊C₈	C₂²	semidirect
88. #405	C₂²	semidirect
89. C₄×M₁₆	C₂²	semidirect
90. C₂×C₄×C₈	C₂²	semidirect
91. C₂×C₄×C₈	C₂²	semidirect
322. D₄	#131	semidirect

Maximal subgroups

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

subgroup	index
#3481	2
#2994	2
#2993	2
#2991	2
#2990	2
#2979	2
#2976	2
#2974	2
#2972	2
#2969	2
#2966	2
#2965	2
C₈×#41	2
D₄×M₁₆	2
#2933	2
#2931	2
C₂×#436	2