Subgroups — C₈×#88238 #16792591

Order 3328.

922 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13131641	C₂	1	1	yes	maximal, characteristic
2	C₄×#88238	C₂	1	1	yes	maximal, characteristic
3	#13130042	C₂	1	1	yes	maximal, characteristic, complemented
4	#13130041	C₂	1	2	yes	maximal, complemented
5	#13130038	C₂	1	1	yes	maximal, characteristic, complemented
6	#13130037	C₂	1	2	yes	maximal, complemented
7	C₈×#6118	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈×#6122	C₂	1	2	yes	maximal, complemented
9	C₈×D₁₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₈×#1057	C₂	1	2	yes	maximal, complemented
11	C₈×#6129	C₂	1	1	yes	maximal, characteristic
12	C₂×#88238	C₄	1	2	yes	—
13	C₄×#6129	C₂²	1	1	yes	characteristic
14	D₄×#1057	C₄	1	2	yes	—
15	#11719125	C₂²	1	2	yes	—
16	C₄×#6122	C₂²	1	2	yes	—
17	C₂×C₄×#1057	C₂²	1	2	yes	—
18	C₂×C₄×#1057	C₂²	1	2	yes	—
19	#11719074	C₄	1	2	yes	—
20	#11719072	C₄	1	2	yes	—
21	#11719063	C₄	1	4	yes	—
22	#11719062	C₄	1	4	yes	—
23	#11719051	C₂²	1	1	yes	characteristic
24	C₄×#6118	C₂²	1	1	yes	characteristic
25	C₄×D₁₃⋊C₈	C₂²	1	1	yes	characteristic
26	C₄×D₁₃⋊C₈	C₂²	1	1	yes	characteristic
27	C₈×D₄×C₁₃	C₄	1	1	yes	characteristic
28	C₈×C₂²⋊D₁₃	C₄	1	2	yes	—
29	C₂×C₈×Dic₁₃	C₂²	1	2	yes	—
30	D₄×#1055	C₄	1	1	yes	characteristic
31	#11718494	C₂²	1	1	yes	characteristic
32	#11718491	C₄	1	1	yes	characteristic
33	#11718386	C₄	1	2	yes	—
34	#11718379	C₂²	1	2	yes	—
35	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
36	C₈×Dic₂₆	C₄	1	1	yes	characteristic
37	#1057⋊C₈	C₂²	1	2	yes	—
38	#1057⋊C₈	C₂²	1	2	yes	—
39	#1057⋊C₈	C₂²	1	2	yes	—
40	C₈×#1057	C₂²	1	1	yes	characteristic
41	C₈×#1057	C₂²	1	2	yes	—
42	C₈×#1057	C₂²	1	2	yes	—
43	C₈×#1057	C₂²	1	2	yes	—
44	C₈×#1057	C₂²	1	1	yes	characteristic
45	C₈×#1057	C₂²	1	1	yes	characteristic
46	C₈×#1057	C₂²	1	1	yes	characteristic
47	C₂×#6129	C₂×C₄	1	1	yes	characteristic
48	C₂×#6122	C₂×C₄	1	4	yes	—
49	C₂²×#1057	C₂×C₄	1	4	yes	—
50	C₂²×#1057	C₂×C₄	1	4	yes	—
51	#88238	C₈	1	16	yes	direct product factor
52	C₂×#6118	C₂×C₄	1	2	yes	—
53	C₂×D₁₃⋊C₈	C₂×C₄	1	2	yes	—
54	C₂×D₁₃⋊C₈	C₂×C₄	1	2	yes	—
55	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
56	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
57	D₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
58	C₄×C₂²⋊D₁₃	C₂×C₄	1	2	yes	—
59	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
60	C₂²×#1055	C₂×C₄	1	2	yes	—
61	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
62	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
63	#88146	C₂×C₄	1	1	yes	characteristic
64	#88141	C₂×C₄	1	1	yes	characteristic
65	#88135	C₂×C₄	1	2	yes	—
66	#88131	C₂×C₄	1	2	yes	—
67	C₄²×D₁₃	C₂³	1	1	yes	characteristic
68	C₄×Dic₂₆	C₂×C₄	1	1	yes	characteristic
69	C₂²⋊#1057	C₂×C₄	1	4	yes	—
70	#88112	C₂×C₄	1	4	yes	—
71	#88111	C₂×C₄	1	2	yes	—
72	#88110	C₂×C₄	1	2	yes	—
73	#88110	C₂×C₄	1	4	yes	—
74	C₄⋊#1057	C₂×C₄	1	2	yes	—
75	C₄×#1057	C₂×C₄	1	2	yes	—
76	C₄×#1057	C₂×C₄	1	2	yes	—
77	C₄×#1057	C₂×C₄	1	4	yes	—
78	C₄×#1057	C₂×C₄	1	4	yes	—
79	C₄×#1057	C₂³	1	1	yes	characteristic
80	C₄×#1057	C₂³	1	1	yes	characteristic
81	C₄×#1057	C₂³	1	1	yes	characteristic
82	C₄×#1057	C₂³	1	1	yes	characteristic
83	C₄×#1057	C₂³	1	2	yes	—
84	C₄×#1057	C₂³	1	2	yes	—
85	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
86	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
87	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
88	C₂²⋊#1055	C₂×C₄	1	2	yes	—
89	#88060	C₂×C₄	1	2	yes	—
90	#88054	C₂×C₄	1	2	yes	—
91	#88054	C₂×C₄	1	2	yes	—
92	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
93	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
94	C₈×Dic₁₃	C₂³	1	2	yes	—
95	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
96	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
97	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
98	C₄×#1055	C₂×C₄	1	1	yes	characteristic
99	C₈×#131	—	13	1	no	maximal, Sylow
100	C₂×D₄×C₁₃	C₄²	1	1	yes	characteristic
101	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
102	C₂×C₂²⋊D₁₃	C₄²	1	2	yes	—
103	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
104	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
105	#6129	C₂×C₈	1	8	yes	—
106	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
109	C₂×Dic₂₆	C₄²	1	1	yes	characteristic
110	#6122	C₂×C₈	1	16	yes	complemented
111	C₂×#1057	—	2	8	no	—
112	C₂×#1057	C₂×C₈	1	16	yes	complemented
113	C₂×#1057	C₂²×C₄	1	4	yes	—
114	C₂×#1057	C₂²×C₄	1	2	yes	—
115	C₂×#1057	C₂²×C₄	1	2	yes	—
116	C₂×#1057	C₂²×C₄	1	2	yes	—
117	C₂×#1057	C₂²×C₄	1	4	yes	—
118	C₂×#1057	C₂²×C₄	1	2	yes	—
119	#6118	C₂×C₈	1	8	yes	complemented
120	D₁₃⋊C₈	—	2	4	no	—
121	D₁₃⋊C₈	C₂×C₈	1	8	yes	complemented
122	C₂×C₈×C₁₃	—	2	4	no	—
123	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
125	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
126	C₁₃×C₄⋊C₄	C₄²	1	1	yes	characteristic
127	C₁₃×C₂²⋊C₄	C₄²	1	2	yes	—
128	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
129	C₂²⋊Dic₁₃	C₄²	1	2	yes	—
130	#6103	C₄²	1	2	yes	—
131	C₄⋊Dic₁₃	C₄²	1	1	yes	characteristic
132	#6101	C₄²	1	2	yes	—
133	#6101	C₄²	1	2	yes	—
134	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
135	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
136	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
137	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
138	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
139	C₄×Dic₁₃	C₂⁴	1	1	yes	characteristic
140	C₂×#1055	—	2	4	no	—
141	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
142	C₂×#1055	C₂²×C₄	1	2	yes	—
143	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
144	C₈×D₁₃	—	2	2	no	—
145	C₈×D₁₃	—	2	2	no	—
146	C₈×#41	—	13	1	no	—
147	C₈×#41	—	13	1	no	—
148	C₄×#131	—	13	1	no	—
149	#1450	—	13	2	no	—
150	#1450	—	13	1	no	—
151	C₈×M₁₆	—	13	2	no	—
152	C₈×M₁₆	—	13	1	no	—
153	C₈×M₁₆	—	13	2	no	—
154	C₈×M₁₆	—	13	1	no	—
155	C₂×C₈²	—	13	2	no	—
156	C₂×C₈²	—	13	1	no	—
157	C₂³×C₁₃	C₂×C₄²	1	2	yes	—
158	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
159	D₄×C₁₃	C₄×C₈	1	4	yes	—
160	C₂×C₄×C₁₃	—	2	2	no	—
161	C₂×C₄×C₁₃	—	2	2	no	—
162	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
163	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
164	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
165	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
166	C₂²⋊D₁₃	C₄×C₈	1	8	yes	—
167	C₂×Dic₁₃	—	2	4	no	—
168	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
169	C₂×Dic₁₃	C₂×C₄²	1	2	yes	—
170	C₂×Dic₁₃	C₂×C₄²	1	2	yes	—
171	C₂×Dic₁₃	C₂²×C₈	1	8	yes	—
172	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
173	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
174	C₄×D₁₃	—	2	1	no	—
175	C₄×D₁₃	—	2	1	no	—
176	C₄×D₁₃	—	2	2	no	—
177	C₄×D₁₃	C₂²×C₈	1	4	yes	—
178	Dic₂₆	C₄×C₈	1	4	yes	—
179	#1057	—	2	2	no	—
180	#1057	—	2	4	no	—
181	#1057	C₂²×C₈	1	4	yes	—
182	#1057	C₂²×C₈	1	4	yes	—
183	#1057	C₂²×C₈	1	8	yes	—
184	#1057	#131	1	4	yes	complemented
185	C₈×C₁₃	—	2	1	no	—
186	C₈×C₁₃	—	2	2	no	—
187	C₈×C₁₃	#131	1	2	yes	complemented
188	#1055	—	2	1	no	—
189	#1055	—	2	2	no	—
190	#1055	#131	1	2	yes	complemented
191	C₂×#131	—	13	2	no	—
192	C₄×#41	—	13	1	no	—
193	C₈×Q₈	—	13	2	no	—
194	C₈×Q₈	—	13	1	no	—
195	C₈×Q₈	—	13	1	no	—
196	C₈×D₄	—	13	4	no	—
197	C₈×D₄	—	13	2	no	—
198	C₈×D₄	—	13	2	no	—
199	C₈×D₄	—	13	1	no	—
200	C₈×D₄	—	13	2	no	—
201	C₈×D₄	#261	1	1	yes	characteristic
202	#431	—	13	1	no	—
203	#431	—	13	2	no	—
204	#431	—	13	1	no	—
205	#431	—	13	2	no	—
206	#405	—	13	4	no	—
207	#405	—	13	2	no	—
208	C₄×M₁₆	—	13	1	no	—
209	C₄×M₁₆	—	13	2	no	—
210	C₂×C₄×C₈	—	13	1	no	—
211	C₂×C₄×C₈	—	13	2	no	—
212	C₂×C₄×C₈	—	13	1	no	—
213	C₂×C₄×C₈	—	13	2	no	—
214	C₂×C₄×C₈	—	13	2	no	—
215	C₂×C₄×C₈	—	13	1	no	—
216	#322	—	13	2	no	—
217	#322	—	13	2	no	—
218	#322	—	13	2	no	—
219	C₈²	—	13	1	no	—
220	C₈²	—	13	2	no	—
221	C₈²	—	13	1	no	—
222	C₈²	—	13	2	no	—
223	C₈²	—	13	1	no	—
224	C₈²	—	13	2	no	—
225	C₈²	—	13	1	no	—
226	C₂²×C₁₃	—	2	2	no	—
227	C₂²×C₁₃	—	2	2	no	—
228	C₂²×C₁₃	C₂×C₄×C₈	1	4	yes	—
229	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
230	C₂×D₁₃	—	2	1	no	—
231	C₂×D₁₃	—	2	1	no	—
232	C₂×D₁₃	C₂×C₄×C₈	1	2	yes	—
233	C₄×C₁₃	—	2	1	no	—
234	C₄×C₁₃	—	2	2	no	—
235	C₄×C₁₃	C₂×C₄×C₈	1	2	yes	—
236	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
237	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
238	Dic₁₃	—	2	1	no	—
239	Dic₁₃	—	2	2	no	—
240	Dic₁₃	C₂×C₄×C₈	1	4	yes	—
241	Dic₁₃	C₂³×C₈	1	2	yes	—
242	Dic₁₃	C₂×#131	1	2	yes	—
243	C₂×#41	—	13	1	no	—
244	#131	—	13	16	no	—
245	C₂×M₁₆	—	13	2	no	—
246	C₂×M₁₆	—	13	4	no	—
247	C₂²×C₈	—	13	2	no	—
248	C₂²×C₈	—	13	4	no	—
249	C₂²×C₈	—	13	2	no	—
250	C₂²×C₈	—	13	4	no	—
251	C₂²×C₈	—	13	2	no	—
252	C₂²×C₈	—	13	1	no	—
253	C₂²×C₈	—	13	1	no	—
254	C₂²×C₈	C₂×#261	1	2	yes	—
255	C₄×Q₈	—	13	1	no	—
256	C₄×Q₈	—	13	1	no	—
257	C₄×D₄	—	13	1	no	—
258	C₄×D₄	—	13	2	no	—
259	C₄×D₄	—	13	2	no	—
260	C₄×D₄	C₂×#261	1	1	yes	characteristic
261	#117	—	13	1	no	—
262	#117	—	13	2	no	—
263	C₂×C₄²	—	13	2	no	—
264	C₂×C₄²	—	13	1	no	—
265	C₄⋊C₈	—	13	2	no	—
266	C₄⋊C₈	—	13	4	no	—
267	C₄⋊C₈	—	13	2	no	—
268	C₄⋊C₈	—	13	2	no	—
269	C₄⋊C₈	—	13	1	no	—
270	C₄⋊C₈	C₂×#261	1	1	yes	characteristic
271	C₂²⋊C₈	—	13	2	no	—
272	C₂²⋊C₈	—	13	4	no	—
273	C₂²⋊C₈	—	13	2	no	—
274	C₂²⋊C₈	—	13	2	no	—
275	C₂²⋊C₈	C₂×#261	1	2	yes	—
276	#97	—	13	2	no	—
277	#97	—	13	4	no	—
278	C₄×C₈	—	13	2	no	—
279	C₄×C₈	—	13	4	no	—
280	C₄×C₈	—	13	2	no	—
281	C₄×C₈	—	13	4	no	—
282	C₄×C₈	—	13	1	no	—
283	C₄×C₈	—	13	1	no	—
284	C₄×C₈	—	13	1	no	—
285	C₄×C₈	—	13	2	no	—
286	C₄×C₈	—	13	1	no	—
287	C₄×C₈	—	13	2	no	—
288	C₄×C₈	—	13	2	no	—
289	C₄×C₈	—	13	1	no	—
290	C₄×C₈	—	13	2	no	—
291	C₄×C₈	—	13	1	no	—
292	C₄×C₈	—	13	2	no	—
293	C₄×C₈	—	13	1	no	—
294	C₄×C₈	C₂×#261	1	1	yes	characteristic
295	C₂×C₁₃	—	2	4	no	—
296	C₂×C₁₃	C₂²×C₄×C₈	1	1	yes	characteristic
297	C₂×C₁₃	C₄×#131	1	1	yes	characteristic
298	C₂×C₁₃	C₄×#131	1	1	yes	characteristic
299	D₁₃	—	2	2	no	—
300	#41	—	13	8	no	—
301	C₂×Q₈	—	13	1	no	—
302	C₂×D₄	—	13	2	no	—
303	C₂×D₄	C₄×#261	1	1	yes	characteristic
304	C₂²×C₄	—	13	2	no	—
305	C₂²×C₄	—	13	1	no	—
306	C₂²×C₄	—	13	2	no	—
307	C₂²×C₄	—	13	1	no	—
308	C₂²×C₄	—	13	1	no	—
309	C₂²×C₄	C₂²×#261	1	2	yes	—
310	M₁₆	—	13	8	no	—
311	M₁₆	—	13	16	no	—
312	C₂×C₈	—	2	4	no	—
313	C₂×C₈	—	13	2	no	—
314	C₂×C₈	—	13	2	no	—
315	C₂×C₈	—	13	2	no	—
316	C₂×C₈	—	13	4	no	—
317	C₂×C₈	—	13	8	no	—
318	C₂×C₈	—	13	16	no	—
319	C₂×C₈	—	13	1	no	—
320	C₂×C₈	—	13	4	no	—
321	C₂×C₈	—	13	2	no	—
322	C₂×C₈	—	13	1	no	—
323	C₂×C₈	—	13	2	no	—
324	C₂×C₈	—	26	2	no	—
325	C₂×C₈	—	26	4	no	—
326	C₂×C₈	—	26	4	no	—
327	C₂×C₈	—	26	8	no	—
328	C₂×C₈	—	26	2	no	—
329	C₂×C₈	C₂²×#261	1	2	yes	—
330	C₂×C₈	C₂²×#261	1	1	yes	characteristic
331	C₂×C₈	C₂²×#261	1	1	yes	characteristic
332	C₄⋊C₄	—	13	2	no	—
333	C₄⋊C₄	—	13	2	no	—
334	C₄⋊C₄	—	13	1	no	—
335	C₄⋊C₄	C₄×#261	1	1	yes	characteristic
336	C₂²⋊C₄	—	13	2	no	—
337	C₂²⋊C₄	—	13	2	no	—
338	C₂²⋊C₄	C₄×#261	1	2	yes	—
339	C₄²	—	13	2	no	—
340	C₄²	—	13	1	no	—
341	C₄²	—	13	2	no	—
342	C₄²	—	13	1	no	—
343	C₄²	—	13	1	no	—
344	C₄²	—	13	2	no	—
345	C₄²	C₂²×#261	1	1	yes	characteristic
346	C₁₃	C₈×#131	1	1	yes	characteristic, complemented, Sylow
347	C₂³	—	13	1	no	—
348	C₂³	C₂×C₄×#261	1	2	yes	—
349	Q₈	—	13	4	no	—
350	D₄	—	13	8	no	—
351	D₄	C₈×#261	1	4	yes	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	13	8	no	—
355	C₂×C₄	—	13	1	no	—
356	C₂×C₄	—	13	1	no	—
357	C₂×C₄	—	13	2	no	—
358	C₂×C₄	—	13	4	no	—
359	C₂×C₄	—	13	2	no	—
360	C₂×C₄	—	13	1	no	—
361	C₂×C₄	—	26	2	no	—
362	C₂×C₄	—	26	4	no	—
363	C₂×C₄	—	26	1	no	—
364	C₂×C₄	—	26	1	no	—
365	C₂×C₄	C₂×C₄×#261	1	2	yes	—
366	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
367	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
368	C₂×C₄	C₂³×#261	1	1	yes	characteristic
369	C₈	—	2	2	no	—
370	C₈	—	2	1	no	—
371	C₈	—	13	4	no	—
372	C₈	—	13	4	no	—
373	C₈	—	13	8	no	—
374	C₈	—	13	4	no	—
375	C₈	—	13	2	no	—
376	C₈	—	26	2	no	—
377	C₈	—	26	4	no	—
378	C₈	—	26	1	no	—
379	C₈	—	26	2	no	—
380	C₈	#88238	1	2	yes	direct product factor
381	C₂²	—	2	2	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	13	2	no	—
384	C₂²	—	26	1	no	—
385	C₂²	—	26	1	no	—
386	C₂²	C₂×C₈×#261	1	4	yes	—
387	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
388	C₄	—	2	1	no	—
389	C₄	—	2	2	no	—
390	C₄	—	13	2	no	—
391	C₄	—	13	4	no	—
392	C₄	—	13	2	no	—
393	C₄	—	26	2	no	—
394	C₄	—	26	1	no	—
395	C₄	C₂×C₈×#261	1	2	yes	—
396	C₄	C₂×#88238	1	1	yes	characteristic
397	C₄	D₁₃⋊#131	1	1	yes	characteristic
398	C₂	—	2	4	no	—
399	C₂	—	26	2	no	—
400	C₂	C₂²×C₈×#261	1	1	yes	characteristic
401	C₂	#131×#261	1	1	yes	characteristic
402	C₂	C₄×#88238	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²×#261
commutator	C₂×C₁₃	C₂²×C₄×C₈
Frattini	C₂×C₄	C₂³×#261
Fitting	C₈×D₄×C₁₃	C₄
socle	C₂²×C₁₃	C₂²×C₄²
prime radical	C₂×#6129	C₂×C₄
cosocle	C₄×Dic₁₃	C₂⁴
hypercenter	C₈×D₄	#261
hypocenter	C₁₃	C₈×#131
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₈×D₄

Complements

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

N	H ≅ G/N	type
3. #13130042	C₂	semidirect
4. #13130041	C₂	semidirect
5. #13130038	C₂	semidirect
6. #13130037	C₂	semidirect
7. C₈×#6118	C₂	semidirect
8. C₈×#6122	C₂	semidirect
9. C₈×D₁₃⋊C₈	C₂	semidirect
10. C₂×C₈×#1057	C₂	semidirect
51. #88238	C₈	direct (N × H)
110. #6122	C₂×C₈	semidirect
112. C₂×#1057	C₂×C₈	semidirect
119. #6118	C₂×C₈	semidirect
121. D₁₃⋊C₈	C₂×C₈	semidirect
184. #1057	#131	semidirect
187. C₈×C₁₃	#131	semidirect
190. #1055	#131	semidirect
346. C₁₃	C₈×#131	semidirect
380. C₈	#88238	direct (N × H)

Maximal subgroups

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

subgroup	index
#13131641	2
C₄×#88238	2
#13130042	2
#13130041	2
#13130038	2
#13130037	2
C₈×#6118	2
C₈×#6122	2
C₈×D₁₃⋊C₈	2
C₂×C₈×#1057	2
C₈×#6129	2
C₈×#131	13

Subgroups — C8×#88238 #16792591

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×#88238 #16792591