Subgroups — #61329

Order 256.

948 conjugacy classes of subgroups.

The subgroup lattice has 439 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	#3503	C₂	1	1	yes	maximal, characteristic, complemented
3	#3375	C₂	1	2	yes	maximal, complemented
4	#3373	C₂	1	2	yes	maximal, complemented
5	#3368	C₂	1	2	yes	maximal, complemented
6	#3366	C₂	1	2	yes	maximal, complemented
7	#3365	C₂	1	2	yes	maximal, complemented
8	#3362	C₂	1	2	yes	maximal, complemented
9	#3361	C₂	1	2	yes	maximal, complemented
10	#3358	C₂	1	2	yes	maximal, complemented
11	#3136	C₂	1	2	yes	maximal, complemented
12	C₂×#486	C₂	1	1	yes	maximal, characteristic, complemented
13	#3081	C₂	1	2	yes	maximal, complemented
14	#3079	C₂	1	1	yes	maximal, characteristic, complemented
15	#3045	C₂	1	2	yes	maximal, complemented
16	#3038	C₂	1	1	yes	maximal, characteristic, complemented
17	#2960	C₂	1	1	yes	maximal, characteristic, complemented
18	#2946	C₂	1	2	yes	maximal, complemented
19	C₄×#135	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×AGL(1,ℤ/8)	C₂²	1	2	yes	—
21	C₂×#135	C₂²	1	1	yes	characteristic
22	#559	C₂²	1	2	yes	—
23	#559	C₂²	1	2	yes	—
24	Q₈²	C₂²	1	2	yes	complemented
25	#557	C₂²	1	2	yes	complemented
26	#554	—	2	2	no	—
27	#554	C₂²	1	2	yes	complemented
28	#550	C₂²	1	2	yes	—
29	#550	C₂²	1	2	yes	—
30	D₄×Q₈	—	2	2	no	—
31	D₄×Q₈	C₂²	1	2	yes	complemented
32	#546	—	2	2	no	—
33	#546	—	2	2	no	—
34	#544	—	2	2	no	—
35	#544	C₂²	1	2	yes	—
36	#540	—	2	2	no	—
37	#535	C₂²	1	2	yes	—
38	#533	—	2	1	no	—
39	#533	C₂²	1	1	yes	characteristic
40	#532	—	2	1	no	—
41	#532	—	2	1	no	—
42	C₂×C₄⋊Q₈	—	2	1	no	—
43	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic
44	C₂×#127	C₂²	1	1	yes	characteristic
45	#520	C₂²	1	2	yes	—
46	#518	C₂²	1	2	yes	—
47	C₄×#41	C₂²	1	1	yes	characteristic
48	C₄×#41	C₂²	1	1	yes	characteristic
49	#490	C₂²	1	4	yes	complemented
50	#489	C₂²	1	4	yes	complemented
51	#488	C₂²	1	4	yes	complemented
52	#486	C₂²	1	2	yes	—
53	#486	C₂²	1	2	yes	—
54	#486	C₂²	1	2	yes	—
55	#486	C₂²	1	2	yes	—
56	#486	C₂²	1	4	yes	complemented
57	#478	C₂²	1	4	yes	complemented
58	#478	C₂²	1	4	yes	complemented
59	#477	C₂²	1	2	yes	complemented
60	#476	C₂²	1	2	yes	complemented
61	#476	C₂²	1	4	yes	complemented
62	#475	C₂²	1	2	yes	complemented
63	#474	C₂²	1	2	yes	complemented
64	#474	C₂²	1	4	yes	complemented
65	#464	C₂²	1	4	yes	complemented
66	#463	C₂²	1	4	yes	complemented
67	#460	C₂²	1	2	yes	—
68	#460	C₂²	1	2	yes	—
69	#460	C₂²	1	4	yes	complemented
70	#459	C₂²	1	2	yes	—
71	#459	C₂²	1	2	yes	—
72	#459	C₂²	1	4	yes	complemented
73	#446	C₂²	1	2	yes	complemented
74	#446	C₂²	1	2	yes	complemented
75	C₈×Q₈	C₂²	1	2	yes	complemented
76	C₈×Q₈	C₂²	1	2	yes	complemented
77	#442	C₂²	1	4	yes	complemented
78	#440	C₂²	1	4	yes	complemented
79	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
80	C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
81	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
82	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
83	C₄×SD₁₆	C₂²	1	4	yes	complemented
84	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
85	C₄×SD₁₆	C₂²	1	1	yes	characteristic, complemented
86	C₄×D₈	C₂²	1	1	yes	characteristic, complemented
87	C₄×D₈	C₂²	1	4	yes	complemented
88	C₄×D₈	C₂²	1	1	yes	characteristic, complemented
89	#428	C₂²	1	2	yes	—
90	#427	C₂²	1	1	yes	characteristic
91	#424	C₂²	1	2	yes	—
92	#423	C₂²	1	1	yes	characteristic
93	#418	C₂²	1	2	yes	—
94	#417	C₂²	1	2	yes	—
95	#416	C₂²	1	1	yes	characteristic
96	#416	C₂²	1	1	yes	characteristic
97	C₂×#102	C₂²	1	2	yes	—
98	C₂×#102	C₂²	1	2	yes	—
99	#405	C₂²	1	2	yes	—
100	C₂×C₄×C₈	C₂²	1	1	yes	characteristic
101	C₂×#41	—	2	2	no	—
102	C₂×#41	—	2	2	no	—
103	C₂×#41	C₂³	1	1	yes	characteristic
104	C₂×#41	C₂³	1	1	yes	characteristic
105	C₂²×Q₈	—	2	2	no	—
106	C₂²×Q₈	—	2	1	no	—
107	C₂²×D₄	—	2	1	no	—
108	C₂²×D₄	—	2	1	no	—
109	C₂²×D₄	C₂³	1	2	yes	—
110	AGL(1,ℤ/8)	—	2	8	no	—
111	#135	—	2	4	no	—
112	C₂×Q₁₆	C₂³	1	1	yes	characteristic
113	C₂×SD₁₆	C₂³	1	1	yes	characteristic
114	C₂×SD₁₆	C₂³	1	1	yes	characteristic
115	C₂×SD₁₆	C₂³	1	4	yes	—
116	C₂×D₈	C₂³	1	1	yes	characteristic
117	C₂×D₈	C₂³	1	4	yes	—
118	C₂×M₁₆	C₂³	1	2	yes	—
119	C₂²×C₈	C₂³	1	1	yes	characteristic
120	C₂²×C₈	C₂³	1	1	yes	characteristic
121	C₄⋊Q₈	—	2	2	no	—
122	C₄⋊Q₈	—	2	2	no	—
123	C₄⋊Q₈	—	2	2	no	—
124	C₄⋊Q₈	—	2	4	no	—
125	C₄⋊Q₈	—	2	1	no	—
126	C₄⋊Q₈	—	2	1	no	—
127	C₄⋊Q₈	D₄	1	1	yes	characteristic
128	C₄⋊Q₈	D₄	1	1	yes	characteristic
129	C₄⋊Q₈	C₂³	1	2	yes	—
130	C₄⋊Q₈	C₂³	1	2	yes	—
131	C₄⋊Q₈	C₂³	1	4	yes	—
132	#127	—	2	1	no	—
133	#127	—	2	1	no	—
134	#127	C₂³	1	2	yes	—
135	#127	C₂³	1	2	yes	—
136	#127	C₂³	1	4	yes	—
137	#125	—	2	2	no	—
138	#125	—	2	4	no	—
139	#125	D₄	1	2	yes	—
140	#125	C₂³	1	4	yes	—
141	#124	—	2	2	no	—
142	#124	—	2	2	no	—
143	#124	C₂³	1	4	yes	—
144	#123	—	2	4	no	—
145	#123	—	2	4	no	—
146	C₂²⋊Q₈	—	2	2	no	—
147	C₂²⋊Q₈	—	2	2	no	—
148	C₂²⋊Q₈	—	2	4	no	—
149	C₂²⋊Q₈	—	2	4	no	—
150	C₂²⋊Q₈	—	2	4	no	—
151	C₂²⋊Q₈	D₄	1	2	yes	—
152	C₂²⋊Q₈	D₄	1	2	yes	—
153	#121	—	2	2	no	—
154	#121	—	2	2	no	—
155	#121	—	2	2	no	—
156	#121	—	2	2	no	—
157	#121	—	2	4	no	—
158	#121	—	2	4	no	—
159	#120	—	2	4	no	—
160	C₄×Q₈	—	2	2	no	—
161	C₄×Q₈	—	2	2	no	—
162	C₄×Q₈	C₂³	1	1	yes	characteristic
163	C₄×Q₈	C₂³	1	1	yes	characteristic
164	C₄×Q₈	C₂³	1	1	yes	characteristic
165	C₄×Q₈	C₂³	1	1	yes	characteristic
166	C₄×Q₈	C₂³	1	4	yes	—
167	C₄×Q₈	C₂³	1	2	yes	—
168	C₄×Q₈	C₂³	1	2	yes	—
169	C₄×D₄	—	2	1	no	—
170	C₄×D₄	—	2	1	no	—
171	C₄×D₄	—	2	1	no	—
172	C₄×D₄	—	2	1	no	—
173	C₄×D₄	—	2	2	no	—
174	C₄×D₄	—	2	2	no	—
175	C₄×D₄	—	2	2	no	—
176	C₄×D₄	—	2	2	no	—
177	C₄×D₄	—	2	4	no	—
178	C₄×D₄	C₂³	1	1	yes	characteristic
179	C₄×D₄	C₂³	1	1	yes	characteristic
180	C₄×D₄	C₂³	1	1	yes	characteristic
181	C₄×D₄	C₂³	1	1	yes	characteristic
182	C₄×D₄	C₂³	1	4	yes	—
183	C₄×D₄	C₂³	1	4	yes	—
184	C₄×D₄	C₂³	1	4	yes	—
185	#117	—	2	2	no	—
186	#117	—	2	1	no	—
187	#117	—	2	1	no	—
188	#117	C₂³	1	1	yes	characteristic
189	#117	C₂³	1	1	yes	characteristic
190	#117	C₂³	1	2	yes	—
191	C₂×C₄⋊C₄	—	2	1	no	—
192	C₂×C₄⋊C₄	—	2	2	no	—
193	C₂×C₄⋊C₄	—	2	2	no	—
194	C₂×C₄⋊C₄	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄	—	2	4	no	—
196	C₂×C₄²	—	2	1	no	—
197	C₂×C₄²	—	2	1	no	—
198	C₂×C₄²	C₂³	1	1	yes	characteristic
199	#107	C₂³	1	1	yes	characteristic
200	#107	C₂³	1	1	yes	characteristic
201	#107	C₂³	1	4	yes	—
202	#106	C₂³	1	1	yes	characteristic
203	#106	C₂³	1	1	yes	characteristic
204	#106	C₂³	1	4	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	#103	C₂³	1	1	yes	characteristic
210	#103	C₂³	1	1	yes	characteristic
211	#103	C₂³	1	1	yes	characteristic
212	#103	C₂³	1	1	yes	characteristic
213	#103	C₂³	1	4	yes	—
214	#102	C₂³	1	4	yes	—
215	#102	C₂³	1	4	yes	—
216	#102	C₂³	1	4	yes	—
217	#102	C₂³	1	4	yes	—
218	#102	C₂³	1	1	yes	characteristic
219	#102	C₂³	1	1	yes	characteristic
220	#102	C₂³	1	1	yes	characteristic
221	#102	C₂³	1	1	yes	characteristic
222	#102	C₂³	1	4	yes	—
223	#102	C₂³	1	4	yes	—
224	#102	C₂³	1	4	yes	—
225	#97	C₂³	1	4	yes	—
226	C₄×C₈	C₂³	1	1	yes	characteristic
227	C₄×C₈	C₂³	1	1	yes	characteristic
228	C₄×C₈	C₂³	1	1	yes	characteristic
229	C₄×C₈	C₂³	1	1	yes	characteristic
230	C₄×C₈	C₂³	1	4	yes	—
231	C₂⁴	—	2	2	no	—
232	#41	—	2	2	no	—
233	#41	—	2	2	no	—
234	#41	—	2	2	no	—
235	#41	—	8	4	no	—
236	#41	—	8	4	no	—
237	#41	#41	1	4	yes	complemented
238	C₂×Q₈	—	2	2	no	—
239	C₂×Q₈	—	2	4	no	—
240	C₂×Q₈	—	2	2	no	—
241	C₂×Q₈	—	8	2	no	—
242	C₂×Q₈	—	8	4	no	—
243	C₂×Q₈	C₂×D₄	1	2	yes	—
244	C₂×Q₈	C₂×D₄	1	2	yes	—
245	C₂×Q₈	C₂⁴	1	1	yes	characteristic
246	C₂×Q₈	C₂⁴	1	1	yes	characteristic
247	C₂×D₄	—	2	1	no	—
248	C₂×D₄	—	2	1	no	—
249	C₂×D₄	—	2	2	no	—
250	C₂×D₄	—	2	2	no	—
251	C₂×D₄	—	2	2	no	—
252	C₂×D₄	—	2	4	no	—
253	C₂×D₄	—	2	4	no	—
254	C₂×D₄	—	2	2	no	—
255	C₂×D₄	—	2	2	no	—
256	C₂×D₄	—	2	4	no	—
257	C₂×D₄	—	2	4	no	—
258	C₂×D₄	—	8	2	no	—
259	C₂×D₄	—	8	2	no	—
260	C₂×D₄	C₂⁴	1	4	yes	—
261	C₂×D₄	C₂⁴	1	1	yes	characteristic
262	C₂×D₄	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄	—	2	1	no	—
264	C₂²×C₄	—	2	2	no	—
265	C₂²×C₄	—	2	1	no	—
266	C₂²×C₄	—	2	1	no	—
267	C₂²×C₄	—	2	1	no	—
268	C₂²×C₄	—	2	1	no	—
269	C₂²×C₄	—	2	1	no	—
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
274	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
275	C₂²×C₄	C₂⁴	1	1	yes	characteristic
276	Q₁₆	—	2	2	no	—
277	SD₁₆	—	2	2	no	—
278	SD₁₆	—	2	8	no	—
279	SD₁₆	—	2	2	no	—
280	D₈	—	2	2	no	—
281	D₈	—	2	8	no	—
282	M₁₆	—	2	4	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	C₂⁴	1	1	yes	characteristic
286	C₂×C₈	C₂⁴	1	1	yes	characteristic
287	C₂×C₈	C₂⁴	1	1	yes	characteristic
288	C₂×C₈	C₂⁴	1	1	yes	characteristic
289	C₂×C₈	C₂⁴	1	4	yes	—
290	C₄⋊C₄	—	2	2	no	—
291	C₄⋊C₄	—	2	2	no	—
292	C₄⋊C₄	—	2	4	no	—
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	—	2	4	no	—
295	C₄⋊C₄	—	2	1	no	—
296	C₄⋊C₄	—	2	1	no	—
297	C₄⋊C₄	—	2	1	no	—
298	C₄⋊C₄	—	2	1	no	—
299	C₄⋊C₄	—	2	4	no	—
300	C₄⋊C₄	—	2	4	no	—
301	C₄⋊C₄	C₂×D₄	1	2	yes	—
302	C₄⋊C₄	C₂×D₄	1	2	yes	—
303	C₄⋊C₄	C₂×D₄	1	2	yes	—
304	C₄⋊C₄	C₂×D₄	1	2	yes	—
305	C₄⋊C₄	C₂×D₄	1	4	yes	—
306	C₄⋊C₄	C₂×D₄	1	4	yes	—
307	C₄⋊C₄	C₂⁴	1	4	yes	—
308	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
309	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
310	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
311	C₄⋊C₄	C₂⁴	1	1	yes	characteristic
312	C₂²⋊C₄	—	2	1	no	—
313	C₂²⋊C₄	—	2	1	no	—
314	C₂²⋊C₄	—	2	4	no	—
315	C₂²⋊C₄	—	2	4	no	—
316	C₂²⋊C₄	—	2	1	no	—
317	C₂²⋊C₄	—	2	1	no	—
318	C₂²⋊C₄	—	2	1	no	—
319	C₂²⋊C₄	—	2	1	no	—
320	C₂²⋊C₄	—	2	4	no	—
321	C₂²⋊C₄	—	2	4	no	—
322	C₂²⋊C₄	—	2	4	no	—
323	C₂²⋊C₄	C₂×D₄	1	4	yes	—
324	C₄²	—	2	1	no	—
325	C₄²	—	2	1	no	—
326	C₄²	—	2	1	no	—
327	C₄²	—	2	1	no	—
328	C₄²	—	2	1	no	—
329	C₄²	—	2	1	no	—
330	C₄²	—	2	4	no	—
331	C₄²	C₂×D₄	1	1	yes	characteristic
332	C₄²	C₂×D₄	1	1	yes	characteristic
333	C₄²	C₂⁴	1	1	yes	characteristic
334	C₄²	C₂⁴	1	1	yes	characteristic
335	C₄²	C₂⁴	1	4	yes	—
336	C₂³	—	2	1	no	—
337	C₂³	—	2	4	no	—
338	C₂³	—	2	1	no	—
339	C₂³	—	4	4	no	—
340	C₂³	—	8	2	no	—
341	C₂³	—	8	2	no	—
342	C₂³	C₂²×D₄	1	1	yes	characteristic
343	Q₈	—	2	4	no	—
344	Q₈	—	2	4	no	—
345	Q₈	—	2	1	no	—
346	Q₈	—	2	1	no	—
347	Q₈	—	2	1	no	—
348	Q₈	—	4	4	no	—
349	Q₈	—	8	2	no	—
350	Q₈	—	8	4	no	—
351	Q₈	C₂×#41	1	2	yes	—
352	D₄	—	2	4	no	—
353	D₄	—	2	4	no	—
354	D₄	—	2	1	no	—
355	D₄	—	2	1	no	—
356	D₄	—	2	4	no	—
357	D₄	—	2	1	no	—
358	D₄	—	4	2	no	—
359	D₄	—	4	4	no	—
360	D₄	—	4	4	no	—
361	D₄	—	4	4	no	—
362	D₄	—	8	2	no	—
363	D₄	—	8	2	no	—
364	D₄	—	8	4	no	—
365	D₄	—	8	4	no	—
366	D₄	C₂×#41	1	2	yes	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	8	4	no	—
383	C₂×C₄	—	8	4	no	—
384	C₂×C₄	—	8	4	no	—
385	C₂×C₄	—	8	2	no	—
386	C₂×C₄	C₂²×D₄	1	4	yes	—
387	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
388	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄	C₂²×D₄	1	4	yes	—
390	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
391	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
392	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
393	C₂×C₄	C₂×#41	1	2	yes	—
394	C₂×C₄	2₋¹⁺⁴	1	2	yes	—
395	C₂×C₄	C₂⁵	1	1	yes	characteristic
396	C₈	—	2	1	no	—
397	C₈	—	2	1	no	—
398	C₈	—	2	4	no	—
399	C₈	—	2	1	no	—
400	C₈	—	2	1	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	2	2	no	—
404	C₂²	—	4	1	no	—
405	C₂²	—	4	1	no	—
406	C₂²	—	4	1	no	—
407	C₂²	—	4	4	no	—
408	C₂²	—	4	1	no	—
409	C₂²	—	4	4	no	—
410	C₂²	—	4	1	no	—
411	C₂²	—	4	4	no	—
412	C₂²	—	16	4	no	—
413	C₂²	#548	1	2	yes	—
414	C₂²	C₂³×D₄	1	1	yes	characteristic
415	C₄	—	2	2	no	—
416	C₄	—	2	1	no	—
417	C₄	—	2	4	no	—
418	C₄	—	2	1	no	—
419	C₄	—	2	4	no	—
420	C₄	—	4	1	no	—
421	C₄	—	4	1	no	—
422	C₄	—	4	1	no	—
423	C₄	—	4	4	no	—
424	C₄	—	4	1	no	—
425	C₄	—	4	1	no	—
426	C₄	#548	1	2	yes	—
427	C₄	#576	1	2	yes	—
428	C₄	#577	1	2	yes	—
429	C₄	C₂²×#41	1	1	yes	characteristic
430	C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
431	C₂	—	2	2	no	—
432	C₂	—	4	2	no	—
433	C₂	—	8	1	no	—
434	C₂	—	8	4	no	—
435	C₂	C₂×#548	1	1	yes	characteristic
436	C₂	C₂×#576	1	1	yes	characteristic
437	C₂	C₂×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ #533 ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #3508	C₂	semidirect
2. #3503	C₂	semidirect
3. #3375	C₂	semidirect
4. #3373	C₂	semidirect
5. #3368	C₂	semidirect
6. #3366	C₂	semidirect
7. #3365	C₂	semidirect
8. #3362	C₂	semidirect
9. #3361	C₂	semidirect
10. #3358	C₂	semidirect
11. #3136	C₂	semidirect
12. C₂×#486	C₂	semidirect
13. #3081	C₂	semidirect
14. #3079	C₂	semidirect
15. #3045	C₂	semidirect
16. #3038	C₂	semidirect
17. #2960	C₂	semidirect
18. #2946	C₂	semidirect
19. C₄×#135	C₂	semidirect
24. Q₈²	C₂²	semidirect
25. #557	C₂²	semidirect
27. #554	C₂²	semidirect
31. D₄×Q₈	C₂²	semidirect
49. #490	C₂²	semidirect
50. #489	C₂²	semidirect
51. #488	C₂²	semidirect
56. #486	C₂²	semidirect
57. #478	C₂²	semidirect
58. #478	C₂²	semidirect
59. #477	C₂²	semidirect
60. #476	C₂²	semidirect
61. #476	C₂²	semidirect
62. #475	C₂²	semidirect
63. #474	C₂²	semidirect
64. #474	C₂²	semidirect
65. #464	C₂²	semidirect
66. #463	C₂²	semidirect
69. #460	C₂²	semidirect
72. #459	C₂²	semidirect
73. #446	C₂²	semidirect
74. #446	C₂²	semidirect
75. C₈×Q₈	C₂²	semidirect
76. C₈×Q₈	C₂²	semidirect
77. #442	C₂²	semidirect
78. #440	C₂²	semidirect
79. C₄×Q₁₆	C₂²	semidirect
80. C₄×Q₁₆	C₂²	semidirect
81. C₄×SD₁₆	C₂²	semidirect
82. C₄×SD₁₆	C₂²	semidirect
83. C₄×SD₁₆	C₂²	semidirect
84. C₄×SD₁₆	C₂²	semidirect
85. C₄×SD₁₆	C₂²	semidirect
86. C₄×D₈	C₂²	semidirect
87. C₄×D₈	C₂²	semidirect
88. C₄×D₈	C₂²	semidirect
237. #41	#41	semidirect

Maximal subgroups

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

subgroup	index
#3508	2
#3503	2
#3375	2
#3373	2
#3368	2
#3366	2
#3365	2
#3362	2
#3361	2
#3358	2
#3136	2
C₂×#486	2
#3081	2
#3079	2
#3045	2
#3038	2
#2960	2
#2946	2
C₄×#135	2