Subgroups — C₈×#88166 #15832292

Order 3328.

750 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×#6129	C₂	1	2	yes	maximal, complemented
2	C₄×#88166	C₂	1	1	yes	maximal, characteristic
3	C₈×Dic₅₂	C₂	1	1	yes	maximal, characteristic, complemented
4	#13113642	C₂	1	1	yes	maximal, characteristic, complemented
5	#13113639	C₂	1	2	yes	maximal, complemented
6	C₈×#6105	C₂	1	2	yes	maximal, complemented
7	D₈×#1055	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113583	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113215	C₂	1	2	yes	maximal, complemented
10	C₈²×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#88166	C₄	1	1	yes	characteristic
13	C₄×#6129	C₂²	1	2	yes	—
14	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
15	C₈×D₄×C₁₃	C₂²	1	2	yes	—
16	D₈×Dic₁₃	C₄	1	1	yes	characteristic
17	C₈×C₂²⋊D₁₃	—	2	2	no	—
18	C₂×C₈×Dic₁₃	—	2	2	no	—
19	C₄×#6105	C₂²	1	2	yes	—
20	D₄×#1055	C₂²	1	2	yes	—
21	#11718541	C₄	1	1	yes	characteristic
22	#11718534	C₄	1	1	yes	characteristic
23	#11718494	C₂²	1	2	yes	—
24	#11718491	C₂²	1	2	yes	—
25	#11718433	C₄	1	2	yes	—
26	#11718419	C₄	1	2	yes	—
27	#11718386	—	2	2	no	—
28	#11718379	—	2	2	no	—
29	C₄×Dic₅₂	C₂²	1	1	yes	characteristic
30	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
31	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
32	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
33	C₈×Dic₂₆	C₂²	1	2	yes	—
34	C₁₃×#335	C₂²	1	1	yes	characteristic
35	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
36	C₈²×C₁₃	C₂²	1	1	yes	characteristic
37	D₄⋊#1055	C₂²	1	2	yes	—
38	#11718076	C₂²	1	2	yes	—
39	#11718072	C₂²	1	2	yes	—
40	#11718050	C₂²	1	1	yes	characteristic
41	#11718048	C₂²	1	2	yes	—
42	C₈×#1055	C₂²	1	1	yes	characteristic
43	C₈×#1055	C₂²	1	1	yes	characteristic
44	C₈×#1055	C₂²	1	1	yes	characteristic
45	C₂×#6129	C₂×C₄	1	2	yes	—
46	C₂×C₁₃×D₈	C₂×C₄	1	1	yes	characteristic
47	C₂²×C₈×C₁₃	—	2	2	no	—
48	C₄×D₄×C₁₃	C₂³	1	2	yes	—
49	D₄×Dic₁₃	C₂×C₄	1	2	yes	—
50	C₂×#6105	C₂×C₄	1	2	yes	—
51	C₄×C₂²⋊D₁₃	—	2	2	no	—
52	C₂×C₄×Dic₁₃	—	2	2	no	—
53	C₂²×#1055	—	2	2	no	—
54	#88166	C₈	1	8	yes	direct product factor
55	C₂×Dic₅₂	C₂×C₄	1	1	yes	characteristic
56	C₂×C₈×D₁₃	—	2	1	no	—
57	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
58	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
59	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
60	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
61	#88146	C₂×C₄	1	2	yes	—
62	#88141	C₂×C₄	1	2	yes	—
63	#88135	—	2	2	no	—
64	#88131	—	2	2	no	—
65	C₄²×D₁₃	C₂³	1	1	yes	characteristic
66	C₄×Dic₂₆	C₂³	1	2	yes	—
67	C₁₃×#107	C₂×C₄	1	1	yes	characteristic
68	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
69	C₁₃×#102	C₂×C₄	1	2	yes	—
70	C₁₃×C₂²⋊C₈	—	2	2	no	—
71	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
72	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
73	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
74	#88072	C₂×C₄	1	2	yes	—
75	C₂²⋊#1055	—	2	2	no	—
76	#88060	—	2	2	no	—
77	#88058	C₂×C₄	1	1	yes	characteristic
78	#88056	C₂×C₄	1	2	yes	—
79	#88054	—	2	2	no	—
80	#88054	—	2	2	no	—
81	C₈×Dic₁₃	—	2	2	no	—
82	C₈×Dic₁₃	—	2	2	no	—
83	C₈×Dic₁₃	—	2	1	no	—
84	C₈×Dic₁₃	—	2	2	no	—
85	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
86	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
87	C₈×Dic₁₃	D₄	1	1	yes	characteristic
88	C₈×Dic₁₃	D₄	1	1	yes	characteristic
89	#88050	C₂×C₄	1	2	yes	—
90	#88048	C₂×C₄	1	2	yes	—
91	C₄⋊#1055	C₂³	1	2	yes	—
92	C₄×#1055	C₂³	1	1	yes	characteristic
93	C₄×#1055	C₂³	1	1	yes	characteristic
94	C₄×#1055	C₂³	1	1	yes	characteristic
95	C₈×#135	—	13	1	no	maximal, Sylow
96	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₁₃	—	2	2	no	—
98	C₂×C₂²⋊D₁₃	—	2	2	no	—
99	C₂²×Dic₁₃	—	2	2	no	—
100	C₂²×Dic₁₃	—	2	2	no	—
101	#6129	—	2	4	no	—
102	#6129	C₂×C₈	1	8	yes	complemented
103	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
105	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
106	C₂×Dic₂₆	C₂²×C₄	1	2	yes	—
107	C₁₃×D₈	C₂×C₈	1	4	yes	complemented
108	C₂×C₈×C₁₃	—	2	1	no	—
109	C₂×C₈×C₁₃	—	2	2	no	—
110	C₂×C₈×C₁₃	—	4	4	no	—
111	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
114	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
115	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
116	C₁₃×C₂²⋊C₄	—	2	2	no	—
117	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
118	C₂²⋊Dic₁₃	—	2	2	no	—
119	#6105	C₂×C₈	1	8	yes	complemented
120	#6103	—	2	2	no	—
121	C₄⋊Dic₁₃	C₂²×C₄	1	2	yes	—
122	#6101	—	2	2	no	—
123	#6101	—	2	2	no	—
124	C₄×Dic₁₃	—	2	2	no	—
125	C₄×Dic₁₃	—	2	2	no	—
126	C₄×Dic₁₃	—	2	2	no	—
127	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
128	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
129	C₄×Dic₁₃	#41	1	1	yes	characteristic
130	C₂×#1055	—	2	1	no	—
131	C₂×#1055	—	2	2	no	—
132	C₂×#1055	—	4	4	no	—
133	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
134	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
135	C₂×#1055	C₂×D₄	1	1	yes	characteristic
136	C₂×#1055	C₂×D₄	1	1	yes	characteristic
137	Dic₅₂	C₂×C₈	1	4	yes	complemented
138	C₈×D₁₃	—	2	4	no	—
139	C₈×D₁₃	—	2	2	no	—
140	C₈×D₁₃	—	2	2	no	—
141	C₈×D₁₃	—	2	2	no	—
142	C₈×D₁₃	C₂×C₈	1	4	yes	complemented
143	C₈×#41	—	13	2	no	—
144	C₄×#135	—	13	1	no	—
145	C₈×Q₁₆	—	13	1	no	—
146	C₈×Q₁₆	—	13	1	no	—
147	C₈×SD₁₆	—	13	2	no	—
148	C₈×SD₁₆	—	13	2	no	—
149	C₈×D₈	—	13	1	no	—
150	C₈×D₈	D₁₃	1	1	yes	characteristic, complemented
151	#1564	—	13	1	no	—
152	#1476	—	13	2	no	—
153	C₂×C₈²	—	13	1	no	—
154	C₂³×C₁₃	—	2	2	no	—
155	C₂²×D₁₃	C₄×D₄	1	1	yes	characteristic
156	D₄×C₁₃	—	2	2	no	—
157	D₄×C₁₃	C₂²×C₈	1	4	yes	—
158	C₂×C₄×C₁₃	—	2	2	no	—
159	C₂×C₄×C₁₃	—	4	2	no	—
160	C₂×C₄×C₁₃	—	4	2	no	—
161	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
162	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
164	C₂²⋊D₁₃	—	2	8	no	—
165	C₂×Dic₁₃	—	2	2	no	—
166	C₂×Dic₁₃	—	2	8	no	—
167	C₂×Dic₁₃	—	2	2	no	—
168	C₂×Dic₁₃	—	4	4	no	—
169	C₂×Dic₁₃	C₄×D₄	1	1	yes	characteristic
170	C₂×Dic₁₃	C₄×D₄	1	1	yes	characteristic
171	C₂×Dic₁₃	C₄×D₄	1	1	yes	characteristic
172	C₄×D₁₃	—	2	1	no	—
173	C₄×D₁₃	—	2	1	no	—
174	C₄×D₁₃	—	2	2	no	—
175	C₄×D₁₃	C₂²×C₈	1	2	yes	—
176	C₄×D₁₃	#131	1	2	yes	—
177	Dic₂₆	—	2	2	no	—
178	Dic₂₆	C₂²×C₈	1	4	yes	—
179	C₈×C₁₃	—	2	2	no	—
180	C₈×C₁₃	—	2	1	no	—
181	C₈×C₁₃	—	2	1	no	—
182	C₈×C₁₃	—	4	2	no	—
183	C₈×C₁₃	C₂²×C₈	1	2	yes	—
184	C₈×C₁₃	#135	1	2	yes	complemented
185	#1055	—	2	2	no	—
186	#1055	—	2	1	no	—
187	#1055	—	2	1	no	—
188	#1055	—	4	2	no	—
189	#1055	C₂²×C₈	1	2	yes	—
190	#1055	#135	1	2	yes	complemented
191	C₂×#135	—	13	1	no	—
192	C₄×#41	—	13	2	no	—
193	C₈×Q₈	—	13	2	no	—
194	C₈×Q₈	—	13	2	no	—
195	C₄×Q₁₆	—	13	1	no	—
196	C₄×Q₁₆	—	13	1	no	—
197	C₄×SD₁₆	—	13	2	no	—
198	C₄×SD₁₆	—	13	2	no	—
199	C₄×D₈	—	13	1	no	—
200	C₄×D₈	C₂×D₁₃	1	1	yes	characteristic
201	C₈×D₄	—	13	2	no	—
202	C₈×D₄	—	26	2	no	—
203	C₈×D₄	—	26	2	no	—
204	C₈×D₄	C₂×D₁₃	1	2	yes	—
205	#431	—	13	2	no	—
206	#431	—	26	2	no	—
207	#427	—	13	1	no	—
208	#416	—	13	2	no	—
209	C₂×C₄×C₈	—	13	1	no	—
210	C₂×C₄×C₈	—	13	1	no	—
211	C₂×C₄×C₈	—	13	1	no	—
212	C₂×C₄×C₈	—	26	2	no	—
213	#335	—	13	1	no	—
214	#335	C₂×D₁₃	1	1	yes	characteristic
215	#334	—	13	2	no	—
216	Q₈⋊C₈	—	13	2	no	—
217	Q₈⋊C₈	—	13	2	no	—
218	D₄⋊C₈	—	13	2	no	—
219	D₄⋊C₈	C₂×D₁₃	1	2	yes	—
220	C₈²	—	13	1	no	—
221	C₈²	—	13	1	no	—
222	C₈²	—	13	1	no	—
223	C₈²	C₂×D₁₃	1	1	yes	characteristic
224	C₂²×C₁₃	—	2	4	no	—
225	C₂²×C₁₃	—	4	2	no	—
226	C₂²×C₁₃	—	4	2	no	—
227	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
228	C₂×D₁₃	—	2	1	no	—
229	C₂×D₁₃	—	2	1	no	—
230	C₂×D₁₃	C₈×D₄	1	2	yes	—
231	C₄×C₁₃	—	2	1	no	—
232	C₄×C₁₃	—	4	2	no	—
233	C₄×C₁₃	C₂³×C₈	1	1	yes	characteristic
234	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
235	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
236	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
237	Dic₁₃	—	2	4	no	—
238	Dic₁₃	—	2	1	no	—
239	Dic₁₃	—	4	2	no	—
240	Dic₁₃	C₈×D₄	1	2	yes	—
241	Dic₁₃	#443	1	2	yes	—
242	C₂×#41	—	13	2	no	—
243	#135	—	13	8	no	—
244	C₂×Q₁₆	—	13	1	no	—
245	C₂×SD₁₆	—	13	2	no	—
246	C₂×D₈	C₄×D₁₃	1	1	yes	characteristic
247	C₂²×C₈	—	2	2	no	—
248	C₂²×C₈	—	13	1	no	—
249	C₂²×C₈	—	13	1	no	—
250	C₂²×C₈	—	13	1	no	—
251	C₂²×C₈	—	13	1	no	—
252	C₂²×C₈	—	26	1	no	—
253	C₂²×C₈	—	26	2	no	—
254	C₄×Q₈	—	13	2	no	—
255	C₄×Q₈	—	13	2	no	—
256	C₄×D₄	—	13	2	no	—
257	C₄×D₄	—	26	2	no	—
258	C₄×D₄	—	26	2	no	—
259	C₄×D₄	C₂²×D₁₃	1	2	yes	—
260	#117	—	13	2	no	—
261	#117	—	26	2	no	—
262	C₂×C₄²	—	13	1	no	—
263	C₂×C₄²	—	26	2	no	—
264	#107	—	13	1	no	—
265	#107	C₄×D₁₃	1	1	yes	characteristic
266	#106	—	13	2	no	—
267	C₄⋊C₈	—	13	2	no	—
268	C₄⋊C₈	—	26	2	no	—
269	C₄⋊C₈	—	26	2	no	—
270	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
271	#103	—	13	2	no	—
272	#103	—	13	2	no	—
273	#102	—	13	2	no	—
274	#102	C₄×D₁₃	1	2	yes	—
275	C₂²⋊C₈	—	2	2	no	—
276	C₂²⋊C₈	—	26	2	no	—
277	C₂²⋊C₈	—	26	2	no	—
278	C₄×C₈	—	13	1	no	—
279	C₄×C₈	—	13	1	no	—
280	C₄×C₈	—	13	1	no	—
281	C₄×C₈	—	13	1	no	—
282	C₄×C₈	—	13	1	no	—
283	C₄×C₈	—	13	1	no	—
284	C₄×C₈	—	13	1	no	—
285	C₄×C₈	—	26	1	no	—
286	C₄×C₈	—	26	2	no	—
287	C₄×C₈	—	26	2	no	—
288	C₄×C₈	—	26	2	no	—
289	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
290	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
291	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
292	C₂×C₁₃	—	4	4	no	—
293	C₂×C₁₃	C₂×C₈×D₄	1	1	yes	characteristic
294	C₂×C₁₃	C₄×#135	1	1	yes	characteristic
295	C₂×C₁₃	C₂×#443	1	1	yes	characteristic
296	D₁₃	—	2	2	no	—
297	#41	—	13	8	no	—
298	#41	—	26	4	no	—
299	C₂×Q₈	—	13	2	no	—
300	C₂×D₄	—	26	2	no	—
301	C₂×D₄	C₂×C₄×D₁₃	1	2	yes	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	13	1	no	—
304	C₂²×C₄	—	13	1	no	—
305	C₂²×C₄	—	13	1	no	—
306	C₂²×C₄	—	26	2	no	—
307	C₂²×C₄	—	26	2	no	—
308	Q₁₆	—	13	4	no	—
309	SD₁₆	—	13	8	no	—
310	D₈	C₈×D₁₃	1	4	yes	complemented
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	4	4	no	—
314	C₂×C₈	—	13	1	no	—
315	C₂×C₈	—	13	1	no	—
316	C₂×C₈	—	13	4	no	—
317	C₂×C₈	—	13	1	no	—
318	C₂×C₈	—	13	1	no	—
319	C₂×C₈	—	26	2	no	—
320	C₂×C₈	—	26	2	no	—
321	C₂×C₈	—	26	4	no	—
322	C₂×C₈	—	26	1	no	—
323	C₂×C₈	—	26	2	no	—
324	C₂×C₈	—	26	2	no	—
325	C₂×C₈	—	52	4	no	—
326	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
327	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
328	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
329	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
330	C₄⋊C₄	—	13	2	no	—
331	C₄⋊C₄	—	26	2	no	—
332	C₄⋊C₄	—	26	2	no	—
333	C₄⋊C₄	C₂×C₄×D₁₃	1	2	yes	—
334	C₂²⋊C₄	—	2	2	no	—
335	C₂²⋊C₄	—	26	2	no	—
336	C₂²⋊C₄	—	26	2	no	—
337	C₄²	—	13	1	no	—
338	C₄²	—	13	1	no	—
339	C₄²	—	13	1	no	—
340	C₄²	—	26	2	no	—
341	C₄²	—	26	2	no	—
342	C₄²	—	26	2	no	—
343	C₄²	C₂³×D₁₃	1	1	yes	characteristic
344	C₁₃	C₈×#135	1	1	yes	characteristic, complemented, Sylow
345	C₂³	—	2	2	no	—
346	C₂³	—	13	1	no	—
347	Q₈	—	13	4	no	—
348	Q₈	—	26	2	no	—
349	D₄	—	2	2	no	—
350	D₄	—	26	8	no	—
351	D₄	C₂×C₈×D₁₃	1	4	yes	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	13	1	no	—
356	C₂×C₄	—	13	1	no	—
357	C₂×C₄	—	13	2	no	—
358	C₂×C₄	—	13	2	no	—
359	C₂×C₄	—	13	1	no	—
360	C₂×C₄	—	26	2	no	—
361	C₂×C₄	—	26	8	no	—
362	C₂×C₄	—	26	2	no	—
363	C₂×C₄	—	26	1	no	—
364	C₂×C₄	—	26	1	no	—
365	C₂×C₄	—	26	2	no	—
366	C₂×C₄	—	52	4	no	—
367	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
368	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
369	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
370	C₈	—	2	2	no	—
371	C₈	—	2	1	no	—
372	C₈	—	2	1	no	—
373	C₈	—	4	2	no	—
374	C₈	—	13	2	no	—
375	C₈	—	13	2	no	—
376	C₈	—	26	2	no	—
377	C₈	—	26	1	no	—
378	C₈	—	26	1	no	—
379	C₈	—	52	2	no	—
380	C₈	C₂×C₈×D₁₃	1	2	yes	—
381	C₈	#88166	1	2	yes	direct product factor
382	C₂²	—	2	4	no	—
383	C₂²	—	4	2	no	—
384	C₂²	—	4	2	no	—
385	C₂²	—	13	2	no	—
386	C₂²	—	26	1	no	—
387	C₂²	—	26	1	no	—
388	C₂²	C₄×D₄×D₁₃	1	1	yes	characteristic
389	C₄	—	2	1	no	—
390	C₄	—	4	2	no	—
391	C₄	—	13	2	no	—
392	C₄	—	13	2	no	—
393	C₄	—	26	1	no	—
394	C₄	—	26	4	no	—
395	C₄	—	52	2	no	—
396	C₄	C₂²×C₈×D₁₃	1	1	yes	characteristic
397	C₄	D₁₃×#131	1	1	yes	characteristic
398	C₄	C₂×#88166	1	1	yes	characteristic
399	C₄	D₁₃×#135	1	1	yes	characteristic
400	C₂	—	4	4	no	—
401	C₂	—	26	2	no	—
402	C₂	C₈×D₄×D₁₃	1	1	yes	characteristic
403	C₂	C₄×#88166	1	1	yes	characteristic
404	C₂	D₁₃×#443	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	D₄×D₁₃
commutator	C₄×C₁₃	C₂³×C₈
Frattini	C₄²	C₂³×D₁₃
Fitting	C₈×C₁₃×D₈	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂×#88166	C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	C₈×D₈	D₁₃
hypocenter	C₁₃	C₈×#135
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₈×D₈

Complements

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

N	H ≅ G/N	type
1. C₈×#6129	C₂	semidirect
3. C₈×Dic₅₂	C₂	semidirect
4. #13113642	C₂	semidirect
5. #13113639	C₂	semidirect
6. C₈×#6105	C₂	semidirect
7. D₈×#1055	C₂	semidirect
8. #13113583	C₂	semidirect
9. #13113215	C₂	semidirect
10. C₈²×D₁₃	C₂	semidirect
11. C₈×C₁₃×D₈	C₂	semidirect
54. #88166	C₈	direct (N × H)
102. #6129	C₂×C₈	semidirect
107. C₁₃×D₈	C₂×C₈	semidirect
119. #6105	C₂×C₈	semidirect
137. Dic₅₂	C₂×C₈	semidirect
142. C₈×D₁₃	C₂×C₈	semidirect
150. C₈×D₈	D₁₃	semidirect
184. C₈×C₁₃	#135	semidirect
190. #1055	#135	semidirect
310. D₈	C₈×D₁₃	semidirect
344. C₁₃	C₈×#135	semidirect
381. C₈	#88166	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈×#6129	2
C₄×#88166	2
C₈×Dic₅₂	2
#13113642	2
#13113639	2
C₈×#6105	2
D₈×#1055	2
#13113583	2
#13113215	2
C₈²×D₁₃	2
C₈×C₁₃×D₈	2
C₈×#135	13

Subgroups — C8×#88166 #15832292

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×#88166 #15832292