Subgroups — #496076

Order 512.

473 conjugacy classes of subgroups.

The subgroup lattice has 415 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21668	C₂	1	1	yes	maximal, characteristic
2	#13121	C₂	1	1	yes	maximal, characteristic
3	#13120	C₂	1	1	yes	maximal, characteristic
4	#13120	C₂	1	1	yes	maximal, characteristic
5	#13105	C₂	1	1	yes	maximal, characteristic, complemented
6	#13104	C₂	1	1	yes	maximal, characteristic, complemented
7	#13104	C₂	1	1	yes	maximal, characteristic, complemented
8	#12895	C₂	1	1	yes	maximal, characteristic, complemented
9	#12663	C₂	1	1	yes	maximal, characteristic, complemented
10	#12662	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₆×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	#12612	C₂	1	1	yes	maximal, characteristic
13	#12612	C₂	1	1	yes	maximal, characteristic
14	#12612	C₂	1	1	yes	maximal, characteristic
15	#12539	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×M₃₂	C₂²	1	1	yes	characteristic
17	#2401	C₄	1	1	yes	characteristic
18	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
24	C₂×#346	C₂²	1	1	yes	characteristic
25	C₂×#346	C₂²	1	1	yes	characteristic
26	C₂×#346	C₂²	1	1	yes	characteristic
27	C₂×#346	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₁₆	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₁₆	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₁₆	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₁₆	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₁₆	C₂²	1	1	yes	characteristic
33	#1924	C₄	1	1	yes	characteristic
34	#1924	C₄	1	1	yes	characteristic
35	#1924	C₄	1	1	yes	characteristic
36	#1917	C₄	1	1	yes	characteristic
37	#1917	C₄	1	1	yes	characteristic
38	#1917	C₄	1	1	yes	characteristic
39	#1840	C₄	1	1	yes	characteristic
40	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
41	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
42	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
43	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
44	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
45	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
46	#1726	C₂²	1	1	yes	characteristic
47	#1374	C₂²	1	1	yes	characteristic
48	#1374	C₂²	1	1	yes	characteristic
49	#1374	C₂²	1	1	yes	characteristic
50	#1374	C₂²	1	1	yes	characteristic
51	#1374	C₂²	1	1	yes	characteristic
52	#1374	C₂²	1	1	yes	characteristic
53	#1374	C₂²	1	1	yes	characteristic
54	#1374	C₂²	1	1	yes	characteristic
55	#1374	C₂²	1	1	yes	characteristic
56	#1374	C₂²	1	1	yes	characteristic
57	#1374	C₂²	1	1	yes	characteristic
58	#1374	C₂²	1	1	yes	characteristic
59	C₂³×C₈	C₂³	1	1	yes	characteristic
60	C₂×M₃₂	—	2	2	no	—
61	C₂×M₃₂	—	2	2	no	—
62	C₂×M₃₂	—	2	2	no	—
63	C₂²×C₁₆	C₂³	1	1	yes	characteristic
64	C₂²×C₁₆	C₂³	1	1	yes	characteristic
65	C₂²×C₁₆	C₂³	1	1	yes	characteristic
66	C₂²×C₁₆	C₂³	1	1	yes	characteristic
67	C₂²×C₁₆	C₂³	1	1	yes	characteristic
68	C₂²×C₁₆	C₂³	1	1	yes	characteristic
69	C₂²×C₁₆	C₂³	1	1	yes	characteristic
70	C₂²×C₁₆	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
74	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
75	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
76	C₂×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
77	C₂×#97	C₂×C₄	1	1	yes	characteristic
78	C₂×#97	C₂×C₄	1	1	yes	characteristic
79	C₂×#97	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
81	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
82	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
83	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
84	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
85	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
86	#401	C₈	1	1	yes	characteristic
87	#400	C₈	1	1	yes	characteristic
88	#400	C₈	1	1	yes	characteristic
89	#400	C₈	1	1	yes	characteristic
90	#397	C₈	1	1	yes	characteristic
91	#397	C₈	1	1	yes	characteristic
92	#397	C₈	1	1	yes	characteristic
93	#396	C₈	1	1	yes	characteristic
94	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
95	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
96	C₄×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
97	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
98	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
99	C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
100	#376	C₂×C₄	1	1	yes	characteristic
101	C₄⋊C₁₆	—	2	2	no	—
102	C₄⋊C₁₆	—	2	2	no	—
103	C₄⋊C₁₆	—	2	2	no	—
104	C₂²⋊C₁₆	—	2	2	no	—
105	C₂²⋊C₁₆	—	2	2	no	—
106	C₂²⋊C₁₆	—	2	2	no	—
107	#346	—	2	2	no	—
108	#346	—	2	2	no	—
109	#346	—	2	2	no	—
110	#346	—	2	2	no	—
111	C₄×C₁₆	—	2	2	no	—
112	C₄×C₁₆	—	2	2	no	—
113	C₄×C₁₆	—	2	2	no	—
114	C₄×C₁₆	—	2	2	no	—
115	C₄×C₁₆	—	2	2	no	—
116	#336	C₂×C₄	1	1	yes	characteristic
117	#336	C₂×C₄	1	1	yes	characteristic
118	#336	C₂×C₄	1	1	yes	characteristic
119	#336	C₂×C₄	1	1	yes	characteristic
120	#336	C₂×C₄	1	1	yes	characteristic
121	#336	C₂×C₄	1	1	yes	characteristic
122	#336	C₂×C₄	1	1	yes	characteristic
123	#336	C₂×C₄	1	1	yes	characteristic
124	#336	C₂×C₄	1	1	yes	characteristic
125	#336	C₂×C₄	1	1	yes	characteristic
126	#336	C₂×C₄	1	1	yes	characteristic
127	#336	C₂×C₄	1	1	yes	characteristic
128	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₈	—	2	1	no	—
130	C₂²×C₈	—	2	1	no	—
131	C₂²×C₈	—	2	1	no	—
132	C₂²×C₈	—	2	1	no	—
133	C₂²×C₈	—	2	1	no	—
134	C₂²×C₈	—	2	1	no	—
135	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₈	C₂⁴	1	1	yes	characteristic
143	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
144	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
145	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
146	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
147	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
148	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
149	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
150	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
151	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
152	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
153	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
154	C₂×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
155	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
156	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
157	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
161	M₃₂	—	4	4	no	—
162	C₂×C₁₆	—	2	1	no	—
163	C₂×C₁₆	—	2	1	no	—
164	C₂×C₁₆	—	2	1	no	—
165	C₂×C₁₆	—	2	1	no	—
166	C₂×C₁₆	—	2	1	no	—
167	C₂×C₁₆	—	2	1	no	—
168	C₂×C₁₆	—	2	1	no	—
169	C₂×C₁₆	—	2	1	no	—
170	C₂×C₁₆	—	2	1	no	—
171	C₂×C₁₆	—	2	1	no	—
172	C₂×C₁₆	—	2	1	no	—
173	C₂×C₁₆	—	2	1	no	—
174	C₂×C₁₆	—	2	1	no	—
175	C₂×C₁₆	—	2	1	no	—
176	C₂×C₁₆	—	2	1	no	—
177	C₂×C₁₆	—	2	1	no	—
178	C₂×C₁₆	—	2	1	no	—
179	C₂×C₁₆	—	2	1	no	—
180	C₂×C₁₆	#41	1	2	yes	—
181	C₂×C₁₆	#41	1	2	yes	—
182	C₂×C₁₆	#41	1	2	yes	—
183	C₂×C₁₆	#41	1	2	yes	—
184	C₂×C₁₆	#41	1	2	yes	—
185	C₂×C₁₆	#41	1	2	yes	—
186	C₄⋊C₈	—	2	2	no	—
187	C₄⋊C₈	—	2	2	no	—
188	C₄⋊C₈	—	2	2	no	—
189	C₂²⋊C₈	—	2	2	no	—
190	C₂²⋊C₈	—	2	2	no	—
191	C₂²⋊C₈	—	2	2	no	—
192	#97	—	2	2	no	—
193	#97	—	2	2	no	—
194	#97	—	2	2	no	—
195	C₄×C₈	—	2	1	no	—
196	C₄×C₈	—	2	1	no	—
197	C₄×C₈	—	2	1	no	—
198	C₄×C₈	—	2	1	no	—
199	C₄×C₈	—	2	1	no	—
200	C₄×C₈	—	2	1	no	—
201	C₄×C₈	—	2	1	no	—
202	C₄×C₈	—	2	1	no	—
203	C₄×C₈	—	2	1	no	—
204	C₄×C₈	—	2	1	no	—
205	C₄×C₈	—	2	1	no	—
206	C₄×C₈	—	2	1	no	—
207	#95	C₂×C₈	1	1	yes	characteristic
208	#95	C₂×C₈	1	1	yes	characteristic
209	#95	C₂×C₈	1	1	yes	characteristic
210	#95	C₂×C₈	1	1	yes	characteristic
211	#95	C₂×C₈	1	1	yes	characteristic
212	#95	C₂×C₈	1	1	yes	characteristic
213	#95	C₂×C₈	1	1	yes	characteristic
214	#95	C₂×C₈	1	1	yes	characteristic
215	#95	C₂×C₈	1	1	yes	characteristic
216	#95	C₂×C₈	1	1	yes	characteristic
217	#95	C₂×C₈	1	1	yes	characteristic
218	#95	C₂×C₈	1	1	yes	characteristic
219	#95	C₂×C₈	1	1	yes	characteristic
220	#95	C₂×C₈	1	1	yes	characteristic
221	#95	C₂×C₈	1	1	yes	characteristic
222	#95	C₂×C₈	1	1	yes	characteristic
223	C₂⁴	C₂²×C₈	1	1	yes	characteristic
224	C₂²×C₄	—	2	1	no	—
225	C₂²×C₄	—	2	1	no	—
226	C₂²×C₄	—	2	1	no	—
227	C₂²×C₄	—	2	1	no	—
228	C₂²×C₄	—	2	1	no	—
229	C₂²×C₄	—	2	1	no	—
230	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
231	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
232	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
233	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
234	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
235	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
236	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
237	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
238	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
239	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
240	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
241	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
242	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
243	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
244	C₂×C₈	—	2	1	no	—
245	C₂×C₈	—	2	1	no	—
246	C₂×C₈	—	2	1	no	—
247	C₂×C₈	—	2	1	no	—
248	C₂×C₈	—	2	1	no	—
249	C₂×C₈	—	2	1	no	—
250	C₂×C₈	—	2	1	no	—
251	C₂×C₈	—	2	1	no	—
252	C₂×C₈	—	2	1	no	—
253	C₂×C₈	—	2	1	no	—
254	C₂×C₈	—	2	1	no	—
255	C₂×C₈	—	2	1	no	—
256	C₂×C₈	—	2	1	no	—
257	C₂×C₈	—	2	1	no	—
258	C₂×C₈	—	2	1	no	—
259	C₂×C₈	—	2	1	no	—
260	C₂×C₈	—	2	1	no	—
261	C₂×C₈	—	2	1	no	—
262	C₂×C₈	—	4	1	no	—
263	C₂×C₈	—	4	1	no	—
264	C₂×C₈	—	4	1	no	—
265	C₂×C₈	—	4	1	no	—
266	C₂×C₈	#131	1	2	yes	—
267	C₂×C₈	#131	1	2	yes	—
268	C₂×C₈	#131	1	2	yes	—
269	C₂×C₈	C₂×#41	1	1	yes	characteristic
270	C₂×C₈	C₂×#41	1	1	yes	characteristic
271	C₂×C₈	C₂×#41	1	1	yes	characteristic
272	C₂×C₈	C₂×#41	1	1	yes	characteristic
273	C₂×C₈	C₂×#41	1	1	yes	characteristic
274	C₂×C₈	C₂×#41	1	1	yes	characteristic
275	C₄⋊C₄	—	2	2	no	—
276	C₄⋊C₄	—	2	2	no	—
277	C₄⋊C₄	—	2	2	no	—
278	C₄⋊C₄	—	2	2	no	—
279	C₄⋊C₄	—	4	1	no	—
280	C₄⋊C₄	—	4	1	no	—
281	C₂²⋊C₄	—	2	2	no	—
282	C₂²⋊C₄	—	2	2	no	—
283	C₂²⋊C₄	—	4	1	no	—
284	C₂²⋊C₄	—	4	1	no	—
285	C₂²⋊C₄	—	4	1	no	—
286	C₂²⋊C₄	—	4	1	no	—
287	C₄²	—	2	1	no	—
288	C₄²	—	2	1	no	—
289	C₄²	—	2	1	no	—
290	C₄²	—	2	1	no	—
291	C₄²	—	2	1	no	—
292	C₄²	—	2	1	no	—
293	C₄²	—	2	1	no	—
294	C₄²	—	2	1	no	—
295	C₄²	—	2	1	no	—
296	C₄²	—	2	1	no	—
297	C₄²	—	2	1	no	—
298	C₄²	—	2	1	no	—
299	C₁₆	—	2	2	no	—
300	C₁₆	—	2	2	no	—
301	C₁₆	—	2	2	no	—
302	C₁₆	—	4	1	no	—
303	C₁₆	—	4	1	no	—
304	C₁₆	—	4	1	no	—
305	C₁₆	—	4	1	no	—
306	C₁₆	#126	1	4	yes	—
307	C₂³	—	2	1	no	—
308	C₂³	—	2	1	no	—
309	C₂³	—	2	1	no	—
310	C₂³	—	2	1	no	—
311	C₂³	—	2	1	no	—
312	C₂³	—	2	1	no	—
313	C₂³	—	2	1	no	—
314	C₂³	C₂³×C₈	1	1	yes	characteristic
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	#504	1	2	yes	—
357	C₂×C₄	#504	1	2	yes	—
358	C₂×C₄	C₄×#41	1	1	yes	characteristic
359	C₂×C₄	C₄×#41	1	1	yes	characteristic
360	C₂×C₄	C₄×#41	1	1	yes	characteristic
361	C₂×C₄	C₂×#131	1	1	yes	characteristic
362	C₂×C₄	C₂×#131	1	1	yes	characteristic
363	C₂×C₄	C₂×#131	1	1	yes	characteristic
364	C₈	—	2	2	no	—
365	C₈	—	2	2	no	—
366	C₈	—	2	2	no	—
367	C₈	—	4	1	no	—
368	C₈	—	4	1	no	—
369	C₈	—	4	1	no	—
370	C₈	—	4	1	no	—
371	C₈	C₂×#126	1	1	yes	characteristic
372	C₈	#529	1	1	yes	characteristic
373	C₈	#529	1	1	yes	characteristic
374	C₈	#529	1	1	yes	characteristic
375	C₂²	—	4	1	no	—
376	C₂²	—	4	1	no	—
377	C₂²	—	4	1	no	—
378	C₂²	—	4	1	no	—
379	C₂²	—	4	1	no	—
380	C₂²	—	4	1	no	—
381	C₂²	—	4	1	no	—
382	C₂²	C₈×#41	1	1	yes	characteristic
383	C₂²	C₈×#41	1	1	yes	characteristic
384	C₂²	C₈×#41	1	1	yes	characteristic
385	C₂²	C₂×#504	1	1	yes	characteristic
386	C₂²	C₂×#504	1	1	yes	characteristic
387	C₂²	#3407	1	1	yes	characteristic
388	C₂²	#3407	1	1	yes	characteristic
389	C₄	—	2	2	no	—
390	C₄	—	2	2	no	—
391	C₄	—	4	1	no	—
392	C₄	—	4	1	no	—
393	C₄	—	4	1	no	—
394	C₄	—	4	1	no	—
395	C₄	—	4	1	no	—
396	C₄	—	4	1	no	—
397	C₄	—	4	1	no	—
398	C₄	—	4	1	no	—
399	C₄	—	4	1	no	—
400	C₄	—	4	1	no	—
401	C₄	—	4	1	no	—
402	C₄	C₄×#126	1	1	yes	characteristic
403	C₄	#2966	1	1	yes	characteristic
404	C₄	#2966	1	1	yes	characteristic
405	C₄	#2966	1	1	yes	characteristic
406	C₂	—	8	1	no	—
407	C₂	C₈×#126	1	1	yes	characteristic
408	C₂	#33480	1	1	yes	characteristic
409	C₂	#33481	1	1	yes	characteristic
410	C₂	#33482	1	1	yes	characteristic
411	C₂	#33483	1	1	yes	characteristic
412	C₂	#33483	1	1	yes	characteristic
413	C₂	#33483	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, cosocle	C₂²×C₈	C₂⁴
commutator, socle	C₂³	C₂³×C₈
prime radical	C₂⁴	C₂²×C₈
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₈ ◁ G
LECS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
5. #13105	C₂	semidirect
6. #13104	C₂	semidirect
7. #13104	C₂	semidirect
8. #12895	C₂	semidirect
9. #12663	C₂	semidirect
10. #12662	C₂	semidirect
11. C₁₆×C₄⋊C₄	C₂	semidirect
15. #12539	C₂	semidirect

Maximal subgroups

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

subgroup	index
#21668	2
#13121	2
#13120	2
#13105	2
#13104	2
#12895	2
#12663	2
#12662	2
C₁₆×C₄⋊C₄	2
#12612	2
#12539	2