Subgroups — C₂×#13070514 #14907214

Order 2816.

710 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10622806	C₂	1	1	yes	maximal, characteristic
2	C₂×#10622324	C₂	1	1	yes	maximal, characteristic, complemented
3	#13070514	C₂	1	8	yes	maximal, direct product factor
4	C₂×#10622132	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#10622133	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10622204	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#10622104	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₁×#444	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₁×#135	C₂²	1	1	yes	characteristic
10	C₂×C₁₁×#131	—	2	1	no	—
11	C₂²×D₈₈	C₂²	1	1	yes	characteristic
12	C₂×C₄×D₄₄	—	2	1	no	—
13	C₁₁×#444	—	2	2	no	—
14	C₁₁×#444	C₂²	1	4	yes	complemented
15	C₂×C₁₁×#108	C₂²	1	1	yes	characteristic
16	C₂×C₁₁×#104	—	2	1	no	—
17	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
18	#10622806	C₄	1	4	yes	complemented
19	#10622806	C₂²	1	4	yes	—
20	C₂×#66892	C₄	1	2	yes	complemented
21	C₂×#66890	C₄	1	2	yes	complemented
22	C₂×#66885	—	2	1	no	—
23	C₂×#66881	C₂²	1	1	yes	characteristic
24	C₂×#66876	C₂²	1	1	yes	characteristic
25	C₂×#66876	C₂²	1	1	yes	characteristic
26	#10622324	—	2	2	no	—
27	#10622324	C₂²	1	4	yes	complemented
28	#10622204	C₂²	1	4	yes	complemented
29	#10622133	C₂²	1	4	yes	complemented
30	#10622132	C₂²	1	4	yes	complemented
31	#10622104	C₂²	1	4	yes	complemented
32	C₂×C₁₁×#41	—	2	1	no	—
33	C₂²×D₄₄	—	2	1	no	—
34	C₂²×C₄×D₁₁	—	4	1	no	—
35	C₁₁×#135	—	2	1	no	—
36	C₁₁×#135	—	2	1	no	—
37	C₁₁×#135	C₂×C₄	1	2	yes	complemented
38	C₁₁×#135	C₂³	1	2	yes	—
39	C₂×C₁₁×Q₁₆	C₂×C₄	1	1	yes	characteristic, complemented
40	C₂×C₁₁×SD₁₆	—	2	1	no	—
41	C₂×C₁₁×D₈	C₂×C₄	1	1	yes	characteristic, complemented
42	C₁₁×#131	—	2	4	no	—
43	C₁₁×#131	—	4	2	no	—
44	C₂×C₁₁×M₁₆	—	2	1	no	—
45	C₂×C₁₁×M₁₆	—	4	1	no	—
46	C₂²×C₈×C₁₁	—	4	1	no	—
47	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
48	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
49	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
50	C₂×(C₂×D₁₁)⋊C₄	—	4	1	no	—
51	C₂×C₄⋊Dic₁₁	—	2	1	no	—
52	C₂×D₈₈	—	2	1	no	—
53	C₂×D₈₈	—	2	1	no	—
54	C₂×D₈₈	—	2	1	no	—
55	C₂×D₈₈	C₂×C₄	1	2	yes	—
56	C₂×D₈₈	C₂×C₄	1	2	yes	—
57	C₂×D₈₈	C₂³	1	2	yes	—
58	C₄×D₄₄	—	2	4	no	—
59	C₄×D₄₄	—	4	2	no	—
60	C₁₁×#108	—	2	1	no	—
61	C₁₁×#108	C₂³	1	2	yes	—
62	C₁₁×#104	—	2	4	no	—
63	C₁₁×#97	D₄	1	2	yes	—
64	C₁₁×#97	C₂³	1	2	yes	—
65	#66892	C₂×C₄	1	8	yes	complemented
66	#66890	C₂×C₄	1	8	yes	complemented
67	#66885	—	2	4	no	—
68	#66881	—	2	1	no	—
69	#66881	C₂³	1	2	yes	—
70	#66876	—	2	1	no	—
71	#66876	C₂×C₄	1	2	yes	complemented
72	#66876	C₂³	1	2	yes	—
73	#66876	C₂³	1	2	yes	—
74	C₂×C₁₁⋊C₁₆	—	2	1	no	—
75	C₂×C₁₁⋊C₁₆	C₂×C₄	1	2	yes	complemented
76	C₂×AGL(1,ℤ/16)	—	11	1	no	maximal, Sylow
77	C₂³×D₁₁	—	4	1	no	—
78	C₁₁×#41	—	2	2	no	—
79	C₁₁×#41	—	2	2	no	—
80	C₁₁×#41	—	4	1	no	—
81	C₁₁×#41	—	4	1	no	—
82	C₂×Q₈×C₁₁	—	2	1	no	—
83	C₂×D₄×C₁₁	—	2	1	no	—
84	C₂×D₄×C₁₁	—	4	1	no	—
85	C₂²×C₄×C₁₁	—	2	1	no	—
86	C₂²×C₄×C₁₁	—	4	1	no	—
87	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
88	C₂²×Dic₁₁	—	4	1	no	—
89	C₂×D₄₄	—	2	2	no	—
90	C₂×D₄₄	—	2	2	no	—
91	C₂×D₄₄	—	2	2	no	—
92	C₂×D₄₄	—	4	1	no	—
93	C₂×D₄₄	—	4	1	no	—
94	C₂×D₄₄	—	4	1	no	—
95	C₂×C₄×D₁₁	—	4	4	no	—
96	C₂×C₄×D₁₁	—	8	4	no	—
97	C₁₁×Q₁₆	—	2	1	no	—
98	C₁₁×Q₁₆	C₂²×C₄	1	2	yes	complemented
99	C₁₁×SD₁₆	—	2	2	no	—
100	C₁₁×SD₁₆	—	2	2	no	—
101	C₁₁×D₈	—	2	1	no	—
102	C₁₁×D₈	C₂²×C₄	1	2	yes	complemented
103	C₁₁×M₁₆	—	2	2	no	—
104	C₁₁×M₁₆	—	4	4	no	—
105	C₁₁×M₁₆	—	4	1	no	—
106	C₂×C₈×C₁₁	—	2	1	no	—
107	C₂×C₈×C₁₁	—	2	1	no	—
108	C₂×C₈×C₁₁	—	4	4	no	—
109	C₂×C₈×C₁₁	—	4	1	no	—
110	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
113	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
114	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
115	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
116	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
117	C₄²×C₁₁	—	2	1	no	—
118	C₄²×C₁₁	C₂×D₄	1	2	yes	—
119	(C₂×D₁₁)⋊C₄	—	4	4	no	—
120	C₄⋊Dic₁₁	—	2	2	no	—
121	C₄⋊Dic₁₁	—	4	1	no	—
122	D₈₈	—	2	2	no	—
123	D₈₈	—	2	2	no	—
124	D₈₈	—	2	2	no	—
125	D₈₈	C₂²×C₄	1	4	yes	—
126	C₁₁⋊C₁₆	—	2	2	no	—
127	C₁₁⋊C₁₆	C₂²×C₄	1	4	yes	complemented
128	C₂×#509	—	11	1	no	—
129	C₂×#444	D₁₁	1	1	yes	characteristic, complemented
130	C₂×#442	—	11	1	no	—
131	AGL(1,ℤ/16)	—	11	8	no	—
132	C₂×#365	—	11	1	no	—
133	C₂×#361	—	11	1	no	—
134	C₂×#360	—	11	1	no	—
135	C₂×#347	—	11	1	no	—
136	C₂³×C₁₁	—	4	1	no	—
137	C₂³×C₁₁	AGL(1,ℤ/8)	1	1	yes	characteristic
138	C₂²×D₁₁	—	4	2	no	—
139	C₂²×D₁₁	—	4	2	no	—
140	C₂²×D₁₁	—	4	2	no	—
141	C₂²×D₁₁	—	8	2	no	—
142	C₂²×D₁₁	—	8	2	no	—
143	Q₈×C₁₁	—	2	2	no	—
144	Q₈×C₁₁	—	4	1	no	—
145	D₄×C₁₁	—	2	2	no	—
146	D₄×C₁₁	—	4	2	no	—
147	D₄×C₁₁	—	4	2	no	—
148	D₄×C₁₁	—	4	1	no	—
149	C₂×C₄×C₁₁	—	2	2	no	—
150	C₂×C₄×C₁₁	—	4	2	no	—
151	C₂×C₄×C₁₁	—	4	1	no	—
152	C₂×C₄×C₁₁	—	4	2	no	—
153	C₂×C₄×C₁₁	—	4	2	no	—
154	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
155	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
156	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	1	yes	characteristic
157	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	1	yes	characteristic
158	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	1	yes	characteristic
159	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
160	C₂×Dic₁₁	—	4	2	no	—
161	C₂×Dic₁₁	—	8	2	no	—
162	D₄₄	—	2	4	no	—
163	D₄₄	—	4	2	no	—
164	D₄₄	—	4	2	no	—
165	D₄₄	—	4	2	no	—
166	C₄×D₁₁	—	8	8	no	—
167	C₈×C₁₁	—	2	2	no	—
168	C₈×C₁₁	—	4	2	no	—
169	C₈×C₁₁	C₄×D₄	1	1	yes	characteristic
170	C₈×C₁₁	C₄×D₄	1	1	yes	characteristic
171	C₈×C₁₁	C₂³×C₄	1	1	yes	characteristic
172	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
173	C₂×#135	C₂×D₁₁	1	1	yes	characteristic
174	C₂²×D₈	—	11	1	no	—
175	C₂×#131	—	2	1	no	—
176	C₂×C₄×D₄	—	22	1	no	—
177	#509	—	11	4	no	—
178	#509	—	11	4	no	—
179	C₂×SD₃₂	—	11	2	no	—
180	C₂×D₁₆	—	11	2	no	—
181	C₂×M₃₂	—	11	1	no	—
182	C₂×M₃₂	—	11	1	no	—
183	#444	—	2	2	no	—
184	#444	C₂×D₁₁	1	4	yes	complemented
185	#442	—	11	4	no	—
186	#442	—	22	2	no	—
187	C₂×#108	C₂×D₁₁	1	1	yes	characteristic
188	C₂×#106	—	11	1	no	—
189	C₂×#104	—	2	1	no	—
190	C₂×#102	—	22	1	no	—
191	C₂×#97	C₂×D₁₁	1	1	yes	characteristic
192	#365	—	11	4	no	—
193	#361	—	11	4	no	—
194	#360	—	11	4	no	—
195	#347	—	11	4	no	—
196	C₂²×C₁₁	—	2	2	no	—
197	C₂²×C₁₁	—	4	2	no	—
198	C₂²×C₁₁	—	8	2	no	—
199	C₂²×C₁₁	#442	1	1	yes	characteristic
200	C₂²×C₁₁	#442	1	1	yes	characteristic
201	C₂²×C₁₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
202	C₂×D₁₁	—	4	4	no	—
203	C₂×D₁₁	—	8	2	no	—
204	C₂×D₁₁	—	8	4	no	—
205	C₂×D₁₁	—	8	2	no	—
206	C₂×D₁₁	—	8	4	no	—
207	C₄×C₁₁	—	4	2	no	—
208	C₄×C₁₁	—	4	2	no	—
209	C₄×C₁₁	#442	1	1	yes	characteristic
210	C₄×C₁₁	#442	1	1	yes	characteristic
211	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
212	C₄×C₁₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
213	Dic₁₁	—	8	2	no	—
214	C₂×#41	—	2	1	no	—
215	C₂²×D₄	—	22	1	no	—
216	C₂³×C₄	—	44	1	no	—
217	#135	—	2	1	no	—
218	#135	—	2	1	no	—
219	#135	C₄×D₁₁	1	2	yes	complemented
220	#135	C₂²×D₁₁	1	2	yes	—
221	C₂×Q₁₆	C₄×D₁₁	1	1	yes	characteristic, complemented
222	C₂×SD₁₆	—	2	1	no	—
223	C₂×D₈	—	11	2	no	—
224	C₂×D₈	—	11	2	no	—
225	C₂×D₈	—	11	2	no	—
226	C₂×D₈	—	22	1	no	—
227	C₂×D₈	—	22	1	no	—
228	C₂×D₈	—	22	1	no	—
229	C₂×D₈	C₄×D₁₁	1	1	yes	characteristic, complemented
230	#131	—	2	4	no	—
231	#131	—	4	2	no	—
232	C₂×M₁₆	—	2	1	no	—
233	C₂×M₁₆	—	4	1	no	—
234	C₂²×C₈	—	4	1	no	—
235	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
236	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
237	C₄×D₄	—	22	4	no	—
238	C₄×D₄	—	44	2	no	—
239	C₂×C₄⋊C₄	—	22	1	no	—
240	C₂×C₂²⋊C₄	—	44	1	no	—
241	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
242	SD₃₂	—	11	8	no	—
243	D₁₆	—	11	8	no	—
244	M₃₂	—	11	2	no	—
245	M₃₂	—	11	2	no	—
246	M₃₂	—	11	2	no	—
247	M₃₂	—	22	1	no	—
248	C₂×C₁₆	—	11	2	no	—
249	C₂×C₁₆	—	22	1	no	—
250	#108	—	2	1	no	—
251	#108	C₂²×D₁₁	1	2	yes	—
252	#106	—	11	2	no	—
253	#106	—	22	1	no	—
254	#104	—	2	4	no	—
255	#102	—	22	4	no	—
256	#97	C₂²⋊D₁₁	1	2	yes	—
257	#97	C₂²×D₁₁	1	2	yes	—
258	C₂×C₁₁	—	2	1	no	—
259	C₂×C₁₁	—	2	1	no	—
260	C₂×C₁₁	—	8	2	no	—
261	C₂×C₁₁	AGL(1,ℤ/16)	1	2	yes	complemented
262	C₂×C₁₁	C₂×#442	1	1	yes	characteristic
263	D₁₁	—	8	4	no	—
264	C₂⁴	—	44	1	no	—
265	#41	—	2	2	no	—
266	#41	—	2	2	no	—
267	#41	—	4	1	no	—
268	#41	—	4	1	no	—
269	C₂×Q₈	—	2	1	no	—
270	C₂×D₄	—	2	1	no	—
271	C₂×D₄	—	4	1	no	—
272	C₂×D₄	—	22	2	no	—
273	C₂×D₄	—	22	2	no	—
274	C₂×D₄	—	22	2	no	—
275	C₂×D₄	—	44	1	no	—
276	C₂×D₄	—	44	1	no	—
277	C₂×D₄	—	44	1	no	—
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	—	4	1	no	—
280	C₂²×C₄	—	44	4	no	—
281	C₂²×C₄	—	44	1	no	—
282	C₂²×C₄	—	88	4	no	—
283	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
284	Q₁₆	—	2	1	no	—
285	Q₁₆	C₂×C₄×D₁₁	1	2	yes	complemented
286	SD₁₆	—	2	2	no	—
287	SD₁₆	—	2	2	no	—
288	D₈	—	2	1	no	—
289	D₈	—	11	4	no	—
290	D₈	—	22	2	no	—
291	D₈	—	22	2	no	—
292	D₈	—	22	2	no	—
293	D₈	C₂×C₄×D₁₁	1	2	yes	complemented
294	M₁₆	—	2	2	no	—
295	M₁₆	—	4	4	no	—
296	M₁₆	—	4	1	no	—
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	4	4	no	—
300	C₂×C₈	—	4	1	no	—
301	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
302	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
303	C₂×C₈	#4339	1	1	yes	characteristic
304	C₂×C₈	#4339	1	1	yes	characteristic
305	C₂×C₈	C₂×C₂²⋊D₁₁	1	2	yes	—
306	C₂×C₈	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
307	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
308	C₄⋊C₄	—	22	2	no	—
309	C₄⋊C₄	—	44	1	no	—
310	C₂²⋊C₄	—	44	4	no	—
311	C₄²	—	2	1	no	—
312	C₄²	C₂×C₂²⋊D₁₁	1	2	yes	—
313	C₁₆	—	11	4	no	—
314	C₁₆	—	22	2	no	—
315	C₁₁	C₂×AGL(1,ℤ/16)	1	1	yes	characteristic, complemented, Sylow
316	C₂³	—	4	1	no	—
317	C₂³	—	44	2	no	—
318	C₂³	—	44	2	no	—
319	C₂³	—	44	2	no	—
320	C₂³	—	88	2	no	—
321	C₂³	—	88	2	no	—
322	C₂³	#67002	1	1	yes	characteristic
323	Q₈	—	2	2	no	—
324	Q₈	—	4	1	no	—
325	D₄	—	2	2	no	—
326	D₄	—	4	2	no	—
327	D₄	—	4	2	no	—
328	D₄	—	4	1	no	—
329	D₄	—	22	4	no	—
330	D₄	—	44	2	no	—
331	D₄	—	44	2	no	—
332	D₄	—	44	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	44	2	no	—
339	C₂×C₄	—	88	8	no	—
340	C₂×C₄	—	88	2	no	—
341	C₂×C₄	C₄×C₂²⋊D₁₁	1	1	yes	characteristic
342	C₂×C₄	C₄×C₂²⋊D₁₁	1	1	yes	characteristic
343	C₂×C₄	#66985	1	1	yes	characteristic
344	C₂×C₄	#66985	1	1	yes	characteristic
345	C₂×C₄	#67002	1	1	yes	characteristic
346	C₂×C₄	C₂²×C₂²⋊D₁₁	1	1	yes	characteristic
347	C₈	—	2	2	no	—
348	C₈	—	4	2	no	—
349	C₈	C₄×C₂²⋊D₁₁	1	1	yes	characteristic
350	C₈	C₄×C₂²⋊D₁₁	1	1	yes	characteristic
351	C₈	C₂²×C₄×D₁₁	1	1	yes	characteristic
352	C₈	C₂×#4339	1	1	yes	characteristic
353	C₂²	—	2	2	no	—
354	C₂²	—	4	2	no	—
355	C₂²	—	8	2	no	—
356	C₂²	—	44	4	no	—
357	C₂²	—	88	2	no	—
358	C₂²	—	88	2	no	—
359	C₂²	—	88	4	no	—
360	C₂²	—	88	4	no	—
361	C₂²	#10622627	1	1	yes	characteristic
362	C₂²	#10622627	1	1	yes	characteristic
363	C₂²	C₂×#67002	1	1	yes	characteristic
364	C₄	—	4	2	no	—
365	C₄	—	4	2	no	—
366	C₄	—	88	2	no	—
367	C₄	#10622627	1	1	yes	characteristic
368	C₄	#10622627	1	1	yes	characteristic
369	C₄	C₂×C₄×C₂²⋊D₁₁	1	1	yes	characteristic
370	C₄	C₂×#66985	1	1	yes	characteristic
371	C₂	—	2	1	no	—
372	C₂	—	2	1	no	—
373	C₂	—	8	2	no	—
374	C₂	—	88	4	no	—
375	C₂	#13070514	1	2	yes	direct product factor
376	C₂	C₂×#10622627	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#10622627
commutator	C₈×C₁₁	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₁₁
Fitting	C₂×C₁₁×#444	C₂
socle	C₂²×C₁₁	#442
prime radical	C₂×#10622806	C₂
cosocle	C₂×C₈×C₁₁	C₂⁴
hypercenter	C₂×#444	D₁₁
hypocenter	C₁₁	C₂×AGL(1,ℤ/16)
LCS	G ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#97 ◁ C₂×#444

Complements

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

N	H ≅ G/N	type
2. C₂×#10622324	C₂	semidirect
3. #13070514	C₂	direct (N × H)
4. C₂×#10622132	C₂	semidirect
5. C₂×#10622133	C₂	semidirect
6. C₂×#10622204	C₂	semidirect
7. C₂×#10622104	C₂	semidirect
8. C₂×C₁₁×#444	C₂	semidirect
14. C₁₁×#444	C₂²	semidirect
18. #10622806	C₄	semidirect
20. C₂×#66892	C₄	semidirect
21. C₂×#66890	C₄	semidirect
27. #10622324	C₂²	semidirect
28. #10622204	C₂²	semidirect
29. #10622133	C₂²	semidirect
30. #10622132	C₂²	semidirect
31. #10622104	C₂²	semidirect
37. C₁₁×#135	C₂×C₄	semidirect
39. C₂×C₁₁×Q₁₆	C₂×C₄	semidirect
41. C₂×C₁₁×D₈	C₂×C₄	semidirect
65. #66892	C₂×C₄	semidirect
66. #66890	C₂×C₄	semidirect
71. #66876	C₂×C₄	semidirect
75. C₂×C₁₁⋊C₁₆	C₂×C₄	semidirect
98. C₁₁×Q₁₆	C₂²×C₄	semidirect
102. C₁₁×D₈	C₂²×C₄	semidirect
127. C₁₁⋊C₁₆	C₂²×C₄	semidirect
129. C₂×#444	D₁₁	semidirect
184. #444	C₂×D₁₁	semidirect
219. #135	C₄×D₁₁	semidirect
221. C₂×Q₁₆	C₄×D₁₁	semidirect
229. C₂×D₈	C₄×D₁₁	semidirect
261. C₂×C₁₁	AGL(1,ℤ/16)	semidirect
285. Q₁₆	C₂×C₄×D₁₁	semidirect
293. D₈	C₂×C₄×D₁₁	semidirect
315. C₁₁	C₂×AGL(1,ℤ/16)	semidirect
375. C₂	#13070514	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#10622806	2
C₂×#10622324	2
#13070514	2
C₂×#10622132	2
C₂×#10622133	2
C₂×#10622204	2
C₂×#10622104	2
C₂×C₁₁×#444	2
C₂×AGL(1,ℤ/16)	11

Subgroups — C2×#13070514 #14907214

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13070514 #14907214