Subgroups — #225709

Order 512.

572 conjugacy classes of subgroups.

The subgroup lattice has 423 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22782	C₂	1	2	yes	maximal
2	C₈×#135	C₂	1	1	yes	maximal, characteristic
3	#17827	C₂	1	1	yes	maximal, characteristic, complemented
4	#17826	C₂	1	1	yes	maximal, characteristic, complemented
5	#9632	C₂	1	2	yes	maximal, complemented
6	#8903	C₂	1	2	yes	maximal, complemented
7	#8902	C₂	1	2	yes	maximal, complemented
8	#8824	C₂	1	1	yes	maximal, characteristic, complemented
9	#8666	C₂	1	1	yes	maximal, characteristic, complemented
10	#8666	C₂	1	1	yes	maximal, characteristic, complemented
11	#8283	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈×#41	C₂²	1	1	yes	characteristic
13	C₈×#41	C₂²	1	1	yes	characteristic
14	C₄×#135	C₂²	1	1	yes	characteristic
15	#2925	C₂²	1	2	yes	—
16	#2906	C₂²	1	2	yes	—
17	#1938	—	2	2	no	—
18	#1922	—	2	2	no	—
19	#1876	—	2	2	no	—
20	#1837	C₂²	1	2	yes	—
21	#1806	C₂²	1	2	yes	—
22	#1806	C₂²	1	2	yes	—
23	C₄×#106	C₂²	1	1	yes	characteristic
24	#1770	C₂²	1	2	yes	—
25	#1765	—	2	2	no	—
26	C₈×Q₁₆	C₄	1	1	yes	characteristic, complemented
27	C₈×Q₁₆	C₄	1	1	yes	characteristic, complemented
28	C₈×SD₁₆	C₄	1	1	yes	characteristic, complemented
29	C₈×SD₁₆	C₄	1	1	yes	characteristic, complemented
30	C₈×SD₁₆	C₄	1	1	yes	characteristic, complemented
31	C₈×SD₁₆	C₄	1	1	yes	characteristic, complemented
32	C₈×D₈	C₄	1	1	yes	characteristic, complemented
33	C₈×D₈	C₄	1	1	yes	characteristic, complemented
34	#1572	—	2	2	no	—
35	#1571	C₂²	1	2	yes	—
36	#1570	—	2	2	no	—
37	#1570	C₂²	1	2	yes	—
38	#1568	—	2	1	no	—
39	#1567	C₂²	1	2	yes	—
40	#1566	—	2	1	no	—
41	#1566	C₂²	1	1	yes	characteristic
42	#1566	C₂²	1	1	yes	characteristic
43	#1564	—	2	1	no	—
44	#1564	C₂²	1	1	yes	characteristic
45	C₂×#334	—	2	1	no	—
46	C₂×#334	C₂²	1	1	yes	characteristic
47	#1476	C₂²	1	1	yes	characteristic
48	#1476	C₂²	1	1	yes	characteristic
49	C₂×C₈²	C₂²	1	1	yes	characteristic
50	#1303	C₂²	1	2	yes	—
51	#1303	C₂²	1	2	yes	—
52	#1279	C₂²	1	2	yes	—
53	C₂×#135	D₄	1	1	yes	characteristic
54	C₂×#131	—	2	2	no	—
55	C₄×#41	C₂³	1	1	yes	characteristic
56	C₄×#41	C₂³	1	1	yes	characteristic
57	C₈×Q₈	C₂×C₄	1	1	yes	characteristic
58	C₈×Q₈	C₂×C₄	1	1	yes	characteristic
59	C₈×Q₈	C₂×C₄	1	1	yes	characteristic
60	C₈×Q₈	C₂×C₄	1	1	yes	characteristic
61	C₄×Q₁₆	C₂×C₄	1	1	yes	characteristic
62	C₄×Q₁₆	Q₈	1	1	yes	characteristic
63	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic
64	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic
65	C₄×SD₁₆	Q₈	1	1	yes	characteristic
66	C₄×SD₁₆	Q₈	1	1	yes	characteristic
67	C₄×D₈	C₂×C₄	1	1	yes	characteristic
68	C₄×D₈	Q₈	1	1	yes	characteristic
69	C₈×D₄	—	2	1	no	—
70	C₈×D₄	—	2	1	no	—
71	C₈×D₄	—	2	1	no	—
72	C₈×D₄	—	2	1	no	—
73	C₈×D₄	C₂×C₄	1	1	yes	characteristic
74	C₈×D₄	C₂×C₄	1	1	yes	characteristic
75	C₈×D₄	C₂×C₄	1	1	yes	characteristic
76	C₈×D₄	C₂×C₄	1	1	yes	characteristic
77	#433	—	4	2	no	—
78	#432	—	2	2	no	—
79	#431	—	2	1	no	—
80	#431	—	2	1	no	—
81	#431	—	2	2	no	—
82	#431	C₂³	1	1	yes	characteristic
83	#431	C₂³	1	1	yes	characteristic
84	#427	D₄	1	1	yes	characteristic
85	C₂×#106	—	2	1	no	—
86	#424	—	2	2	no	—
87	#424	—	4	2	no	—
88	#423	—	2	2	no	—
89	#423	C₂³	1	2	yes	—
90	#423	C₂³	1	2	yes	—
91	C₂×C₄⋊C₈	—	2	2	no	—
92	C₂×C₄⋊C₈	C₂³	1	2	yes	—
93	C₂×#104	—	2	2	no	—
94	C₂×#104	—	2	2	no	—
95	#416	D₄	1	1	yes	characteristic
96	#416	D₄	1	1	yes	characteristic
97	#408	—	2	2	no	—
98	#405	—	2	2	no	—
99	C₂×#97	—	2	2	no	—
100	C₂×C₄×C₈	—	2	1	no	—
101	C₂×C₄×C₈	—	2	1	no	—
102	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
103	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
104	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
105	C₄×C₄⋊C₄	C₂³	1	2	yes	—
106	#341	—	2	2	no	—
107	#341	—	2	2	no	—
108	#340	—	2	1	no	—
109	#339	—	2	2	no	—
110	#339	—	2	2	no	—
111	#336	—	2	2	no	—
112	#335	—	2	2	no	—
113	#335	—	2	2	no	—
114	#335	—	4	2	no	—
115	#335	C₂×C₄	1	1	yes	characteristic
116	#335	C₂×C₄	1	1	yes	characteristic
117	#334	—	2	2	no	—
118	#334	—	2	2	no	—
119	#334	—	2	1	no	—
120	#334	—	2	1	no	—
121	#334	—	2	1	no	—
122	#334	—	2	1	no	—
123	#334	C₂×C₄	1	1	yes	characteristic
124	#334	C₂×C₄	1	1	yes	characteristic
125	#334	D₄	1	1	yes	characteristic
126	#334	D₄	1	1	yes	characteristic
127	#334	D₄	1	2	yes	—
128	Q₈⋊C₈	C₂×C₄	1	1	yes	characteristic
129	Q₈⋊C₈	C₂×C₄	1	1	yes	characteristic
130	Q₈⋊C₈	C₂×C₄	1	1	yes	characteristic
131	Q₈⋊C₈	C₂×C₄	1	1	yes	characteristic
132	D₄⋊C₈	C₂×C₄	1	1	yes	characteristic
133	D₄⋊C₈	C₂×C₄	1	1	yes	characteristic
134	D₄⋊C₈	C₂×C₄	1	1	yes	characteristic
135	D₄⋊C₈	C₂×C₄	1	1	yes	characteristic
136	C₈²	C₂×C₄	1	1	yes	characteristic
137	C₈²	C₂×C₄	1	1	yes	characteristic
138	C₈²	C₂×C₄	1	1	yes	characteristic
139	C₈²	C₂×C₄	1	1	yes	characteristic
140	C₂×#41	C₂×D₄	1	1	yes	characteristic
141	C₂×#41	C₂×D₄	1	1	yes	characteristic
142	#135	—	2	4	no	—
143	C₂×Q₁₆	C₄⋊C₄	1	1	yes	characteristic
144	C₂×SD₁₆	C₄⋊C₄	1	1	yes	characteristic
145	C₂×SD₁₆	C₄⋊C₄	1	1	yes	characteristic
146	C₂×D₈	C₄⋊C₄	1	1	yes	characteristic
147	#131	—	4	4	no	—
148	#131	—	8	2	no	—
149	C₂×M₁₆	—	2	2	no	—
150	C₂×M₁₆	—	2	2	no	—
151	C₂×M₁₆	—	4	2	no	—
152	C₂²×C₈	—	2	2	no	—
153	C₂²×C₈	—	2	1	no	—
154	C₂²×C₈	—	2	1	no	—
155	C₂²×C₈	—	2	1	no	—
156	C₂²×C₈	—	2	1	no	—
157	C₂²×C₈	—	2	1	no	—
158	C₂²×C₈	—	4	2	no	—
159	C₂²×C₈	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₈	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₈	#41	1	1	yes	characteristic
162	C₂²×C₈	#41	1	1	yes	characteristic
163	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
164	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
165	C₄×Q₈	C₂×Q₈	1	1	yes	characteristic
166	C₄×Q₈	C₂×Q₈	1	1	yes	characteristic
167	C₄×D₄	—	2	1	no	—
168	C₄×D₄	—	2	1	no	—
169	C₄×D₄	—	2	1	no	—
170	C₄×D₄	—	2	1	no	—
171	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
172	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
173	C₄×D₄	C₂×Q₈	1	1	yes	characteristic
174	C₄×D₄	C₂×Q₈	1	1	yes	characteristic
175	#117	—	2	1	no	—
176	#117	—	2	1	no	—
177	#117	C₂×D₄	1	1	yes	characteristic
178	#117	C₂×D₄	1	1	yes	characteristic
179	C₂×C₄⋊C₄	—	2	2	no	—
180	C₂×C₄²	—	2	1	no	—
181	C₂×C₄²	—	2	1	no	—
182	C₂×C₄²	—	2	2	no	—
183	C₂×C₄²	C₂⁴	1	1	yes	characteristic
184	#107	C₄⋊C₄	1	1	yes	characteristic
185	#107	C₄⋊C₄	1	1	yes	characteristic
186	#106	—	4	2	no	—
187	#106	C₄⋊C₄	1	1	yes	characteristic
188	#106	C₄⋊C₄	1	1	yes	characteristic
189	C₄⋊C₈	—	2	1	no	—
190	C₄⋊C₈	—	2	1	no	—
191	C₄⋊C₈	—	2	1	no	—
192	C₄⋊C₈	—	2	1	no	—
193	C₄⋊C₈	—	2	2	no	—
194	C₄⋊C₈	—	2	2	no	—
195	C₄⋊C₈	—	2	2	no	—
196	C₄⋊C₈	—	2	2	no	—
197	C₄⋊C₈	—	2	2	no	—
198	C₄⋊C₈	—	4	2	no	—
199	C₄⋊C₈	—	4	2	no	—
200	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
201	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
202	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
203	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
204	C₄⋊C₈	C₂×D₄	1	2	yes	—
205	C₄⋊C₈	C₂×D₄	1	2	yes	—
206	#104	—	4	4	no	—
207	#104	—	8	2	no	—
208	#103	C₄⋊C₄	1	1	yes	characteristic
209	#103	C₄⋊C₄	1	1	yes	characteristic
210	#103	C₄⋊C₄	1	1	yes	characteristic
211	#103	C₄⋊C₄	1	1	yes	characteristic
212	#102	C₄⋊C₄	1	1	yes	characteristic
213	#102	C₄⋊C₄	1	1	yes	characteristic
214	#102	C₄⋊C₄	1	1	yes	characteristic
215	#102	C₄⋊C₄	1	1	yes	characteristic
216	C₂²⋊C₈	—	2	1	no	—
217	C₂²⋊C₈	—	2	1	no	—
218	C₂²⋊C₈	—	2	1	no	—
219	C₂²⋊C₈	—	2	1	no	—
220	C₂²⋊C₈	—	2	1	no	—
221	C₂²⋊C₈	—	2	1	no	—
222	C₂²⋊C₈	—	4	2	no	—
223	C₂²⋊C₈	—	4	2	no	—
224	#97	—	4	2	no	—
225	#97	—	8	2	no	—
226	C₄×C₈	—	2	1	no	—
227	C₄×C₈	—	2	1	no	—
228	C₄×C₈	—	2	1	no	—
229	C₄×C₈	—	2	1	no	—
230	C₄×C₈	—	2	1	no	—
231	C₄×C₈	—	2	1	no	—
232	C₄×C₈	—	2	1	no	—
233	C₄×C₈	—	4	2	no	—
234	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
235	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
236	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
237	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
238	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
239	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
240	C₄×C₈	C₂×D₄	1	1	yes	characteristic
241	C₄×C₈	C₂×D₄	1	1	yes	characteristic
242	C₄×C₈	C₂×Q₈	1	1	yes	characteristic
243	C₄×C₈	C₂×Q₈	1	1	yes	characteristic
244	#95	—	2	2	no	—
245	#41	—	2	2	no	—
246	#41	—	2	2	no	—
247	#41	—	2	2	no	—
248	#41	#135	1	4	yes	—
249	C₂×Q₈	C₂×C₄⋊C₄	1	1	yes	characteristic
250	C₂×Q₈	C₂×C₄⋊C₄	1	1	yes	characteristic
251	C₂×D₄	—	2	1	no	—
252	C₂×D₄	—	2	1	no	—
253	C₂×D₄	C₂×C₄⋊C₄	1	1	yes	characteristic
254	C₂×D₄	C₂×C₄⋊C₄	1	1	yes	characteristic
255	C₂²×C₄	—	2	1	no	—
256	C₂²×C₄	—	2	1	no	—
257	C₂²×C₄	—	2	1	no	—
258	C₂²×C₄	—	2	1	no	—
259	C₂²×C₄	—	2	1	no	—
260	C₂²×C₄	—	2	1	no	—
261	C₂²×C₄	—	4	2	no	—
262	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
263	C₂²×C₄	C₂×#41	1	1	yes	characteristic
264	C₂²×C₄	2₋¹⁺⁴	1	1	yes	characteristic
265	Q₁₆	—	2	2	no	—
266	SD₁₆	—	2	2	no	—
267	SD₁₆	—	2	2	no	—
268	D₈	—	2	2	no	—
269	M₁₆	—	4	2	no	—
270	M₁₆	—	4	2	no	—
271	M₁₆	—	4	2	no	—
272	M₁₆	—	4	2	no	—
273	M₁₆	—	8	4	no	—
274	C₂×C₈	—	2	1	no	—
275	C₂×C₈	—	2	2	no	—
276	C₂×C₈	—	2	2	no	—
277	C₂×C₈	—	2	2	no	—
278	C₂×C₈	—	2	1	no	—
279	C₂×C₈	—	2	1	no	—
280	C₂×C₈	—	2	1	no	—
281	C₂×C₈	—	2	1	no	—
282	C₂×C₈	—	2	1	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	4	1	no	—
286	C₂×C₈	—	4	2	no	—
287	C₂×C₈	—	4	2	no	—
288	C₂×C₈	—	4	2	no	—
289	C₂×C₈	—	4	2	no	—
290	C₂×C₈	—	4	2	no	—
291	C₂×C₈	—	4	2	no	—
292	C₂×C₈	—	4	2	no	—
293	C₂×C₈	—	8	1	no	—
294	C₂×C₈	—	8	1	no	—
295	C₂×C₈	—	8	4	no	—
296	C₂×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
297	C₂×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
298	C₂×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
299	C₂×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
300	C₂×C₈	C₄×D₄	1	1	yes	characteristic
301	C₂×C₈	C₄×D₄	1	1	yes	characteristic
302	C₂×C₈	C₄×D₄	1	1	yes	characteristic
303	C₂×C₈	C₄×D₄	1	1	yes	characteristic
304	C₄⋊C₄	—	2	1	no	—
305	C₄⋊C₄	—	2	1	no	—
306	C₄⋊C₄	—	2	1	no	—
307	C₄⋊C₄	—	2	1	no	—
308	C₄⋊C₄	—	4	2	no	—
309	C₄⋊C₄	—	4	2	no	—
310	C₄⋊C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
311	C₄⋊C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
312	C₄⋊C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
313	C₄⋊C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
314	C₂²⋊C₄	—	2	1	no	—
315	C₂²⋊C₄	—	2	1	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	C₄²	—	2	1	no	—
321	C₄²	—	2	1	no	—
322	C₄²	—	2	1	no	—
323	C₄²	—	2	1	no	—
324	C₄²	—	2	1	no	—
325	C₄²	—	2	1	no	—
326	C₄²	—	4	2	no	—
327	C₄²	—	4	2	no	—
328	C₄²	C₂³×C₄	1	1	yes	characteristic
329	C₄²	C₂²×D₄	1	1	yes	characteristic
330	C₄²	C₂²×Q₈	1	1	yes	characteristic
331	C₄²	H(5,𝔽₂)	1	1	yes	characteristic
332	C₂³	—	2	1	no	—
333	C₂³	—	2	1	no	—
334	C₂³	#547	1	1	yes	characteristic
335	Q₈	—	2	1	no	—
336	Q₈	—	2	1	no	—
337	Q₈	—	2	1	no	—
338	Q₈	#427	1	2	yes	—
339	D₄	—	2	4	no	—
340	D₄	—	2	1	no	—
341	D₄	—	2	1	no	—
342	D₄	—	2	1	no	—
343	D₄	—	4	2	no	—
344	D₄	#427	1	2	yes	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	8	1	no	—
361	C₂×C₄	—	8	1	no	—
362	C₂×C₄	—	8	2	no	—
363	C₂×C₄	—	8	2	no	—
364	C₂×C₄	—	8	2	no	—
365	C₂×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
366	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
367	C₂×C₄	#520	1	1	yes	characteristic
368	C₂×C₄	D₄²	1	1	yes	characteristic
369	C₂×C₄	D₄×Q₈	1	1	yes	characteristic
370	C₂×C₄	#554	1	1	yes	characteristic
371	C₂×C₄	C₂×#135	1	2	yes	—
372	C₂×C₄	#577	1	2	yes	—
373	C₈	—	2	2	no	—
374	C₈	—	2	1	no	—
375	C₈	—	2	1	no	—
376	C₈	—	2	1	no	—
377	C₈	—	2	1	no	—
378	C₈	—	2	1	no	—
379	C₈	—	2	1	no	—
380	C₈	—	2	1	no	—
381	C₈	—	4	1	no	—
382	C₈	—	4	1	no	—
383	C₈	—	4	1	no	—
384	C₈	—	4	1	no	—
385	C₈	—	4	1	no	—
386	C₈	—	4	2	no	—
387	C₈	—	4	2	no	—
388	C₈	—	8	2	no	—
389	C₈	—	8	2	no	—
390	C₈	#444	1	2	yes	—
391	C₂²	—	2	1	no	—
392	C₂²	—	2	1	no	—
393	C₂²	—	2	2	no	—
394	C₂²	—	4	1	no	—
395	C₂²	—	4	1	no	—
396	C₂²	—	4	1	no	—
397	C₂²	—	4	1	no	—
398	C₂²	—	4	1	no	—
399	C₂²	D₄×C₄⋊C₄	1	1	yes	characteristic
400	C₂²	#3337	1	2	yes	—
401	C₄	—	2	2	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	2	1	no	—
405	C₄	—	4	1	no	—
406	C₄	—	4	1	no	—
407	C₄	—	4	1	no	—
408	C₄	—	4	1	no	—
409	C₄	—	4	1	no	—
410	C₄	—	16	2	no	—
411	C₄	C₂×#427	1	1	yes	characteristic
412	C₄	#2912	1	1	yes	characteristic
413	C₄	C₂×#444	1	1	yes	characteristic
414	C₄	#2957	1	1	yes	characteristic
415	C₄	#3282	1	2	yes	—
416	C₂	—	2	2	no	—
417	C₂	—	4	2	no	—
418	C₂	—	8	1	no	—
419	C₂	#22654	1	1	yes	characteristic
420	C₂	#22686	1	1	yes	characteristic
421	C₂	#22694	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₄²
commutator	C₄²	C₂³×C₄
Frattini, cosocle	C₂×C₄²	C₂⁴
socle	C₂²	D₄×C₄⋊C₄
prime radical	C₂×#135	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ G
LECS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
3. #17827	C₂	semidirect
4. #17826	C₂	semidirect
5. #9632	C₂	semidirect
6. #8903	C₂	semidirect
7. #8902	C₂	semidirect
8. #8824	C₂	semidirect
9. #8666	C₂	semidirect
10. #8666	C₂	semidirect
11. #8283	C₂	semidirect
26. C₈×Q₁₆	C₄	semidirect
27. C₈×Q₁₆	C₄	semidirect
28. C₈×SD₁₆	C₄	semidirect
29. C₈×SD₁₆	C₄	semidirect
30. C₈×SD₁₆	C₄	semidirect
31. C₈×SD₁₆	C₄	semidirect
32. C₈×D₈	C₄	semidirect
33. C₈×D₈	C₄	semidirect

Maximal subgroups

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

subgroup	index
#22782	2
C₈×#135	2
#17827	2
#17826	2
#9632	2
#8903	2
#8902	2
#8824	2
#8666	2
#8283	2