Subgroups — C₂²×#11719432 #16769834

Order 3328.

11798 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×Q₈×D₁₃	C₂	1	2	yes	maximal, complemented
2	C₂×#11719432	C₂	1	48	yes	maximal, direct product factor
3	C₂²×#88142	C₂	1	2	yes	maximal, complemented
4	C₂²×#88150	C₂	1	4	yes	maximal, complemented
5	C₂²×#88200	C₂	1	2	yes	maximal, complemented
6	C₂²×C₄×Dic₂₆	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₄×D₅₂	C₂	1	1	yes	maximal, characteristic
8	C₂²×#88147	C₂	1	2	yes	maximal
9	C₂²×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×Q₈×C₁₃	C₂²	1	2	yes	—
11	C₂²×Q₈×D₁₃	—	2	32	no	—
12	C₂²×Q₈×D₁₃	C₂²	1	48	yes	complemented
13	C₂³×D₅₂	C₂²	1	1	yes	characteristic
14	C₂³×C₄×D₁₃	C₂²	1	4	yes	—
15	C₂³×C₄×D₁₃	C₂²	1	2	yes	—
16	C₂³×Dic₂₆	C₂²	1	4	yes	—
17	C₂³×Dic₂₆	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×C₄⋊Q₈	C₂²	1	24	yes	complemented
19	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
21	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×#88200	C₂²	1	48	yes	complemented
23	C₂²×#6103	C₂²	1	4	yes	—
24	C₂²×#6103	C₂²	1	2	yes	—
25	C₂²×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
26	C₂²×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
27	C₂²×#6101	C₂²	1	2	yes	—
28	C₂²×#6101	C₂²	1	4	yes	—
29	C₂²×C₄×Dic₁₃	C₂²	1	2	yes	—
30	#11719432	C₂²	1	256	yes	direct product factor
31	C₂×#88150	C₂²	1	96	yes	complemented
32	C₂×#88147	C₂²	1	48	yes	—
33	C₂×#88142	C₂²	1	48	yes	complemented
34	C₂×C₄×D₅₂	C₂²	1	24	yes	—
35	C₂×C₄×Dic₂₆	C₂²	1	24	yes	complemented
36	C₂⁴×D₁₃	C₂³	1	2	yes	—
37	C₂²×Q₈×C₁₃	—	2	16	no	—
38	C₂²×Q₈×C₁₃	C₂³	1	24	yes	—
39	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
40	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
41	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
43	C₂³×Dic₁₃	C₂³	1	2	yes	—
44	C₂³×Dic₁₃	C₂³	1	2	yes	—
45	C₂³×Dic₁₃	C₂³	1	2	yes	—
46	C₂×Q₈×D₁₃	—	2	384	no	—
47	C₂×Q₈×D₁₃	C₂³	1	128	yes	complemented
48	C₂²×D₅₂	Q₈	1	16	yes	complemented
49	C₂²×D₅₂	C₂³	1	12	yes	—
50	C₂²×C₄×D₁₃	—	2	16	no	—
51	C₂²×C₄×D₁₃	—	2	32	no	—
52	C₂²×C₄×D₁₃	C₂³	1	24	yes	—
53	C₂²×C₄×D₁₃	C₂³	1	48	yes	—
54	C₂²×Dic₂₆	—	2	32	no	—
55	C₂²×Dic₂₆	D₄	1	16	yes	complemented
56	C₂²×Dic₂₆	C₂³	1	48	yes	—
57	C₂²×Dic₂₆	C₂³	1	12	yes	—
58	C₁₃×C₄⋊Q₈	C₂³	1	64	yes	complemented
59	C₂×C₁₃×C₄⋊C₄	C₂³	1	24	yes	—
60	C₂×C₁₃×C₄⋊C₄	C₂³	1	24	yes	—
61	C₂×C₄²×C₁₃	C₂³	1	12	yes	—
62	#88200	C₂³	1	128	yes	complemented
63	C₂×#6103	C₂³	1	24	yes	—
64	C₂×#6103	C₂³	1	48	yes	—
65	C₂×C₄⋊Dic₁₃	C₂³	1	12	yes	—
66	C₂×C₄⋊Dic₁₃	C₂³	1	12	yes	—
67	C₂×#6101	C₂³	1	24	yes	—
68	C₂×#6101	C₂³	1	48	yes	—
69	C₂×C₄×Dic₁₃	C₂³	1	24	yes	—
70	#88150	C₂³	1	256	yes	complemented
71	#88147	C₂³	1	128	yes	—
72	#88142	C₂³	1	128	yes	complemented
73	C₄×D₅₂	C₂³	1	64	yes	—
74	C₄×Dic₂₆	C₂³	1	64	yes	complemented
75	C₂²×D₄×Q₈	—	13	1	no	maximal, Sylow
76	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
77	C₂³×D₁₃	—	2	8	no	—
78	C₂³×D₁₃	—	2	8	no	—
79	C₂³×D₁₃	C₂×Q₈	1	16	yes	complemented
80	C₂³×D₁₃	C₂⁴	1	12	yes	—
81	C₂×Q₈×C₁₃	—	2	96	no	—
82	C₂×Q₈×C₁₃	C₂⁴	1	32	yes	—
83	C₂²×C₄×C₁₃	—	2	16	no	—
84	C₂²×C₄×C₁₃	—	2	4	no	—
85	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
86	C₂²×C₄×C₁₃	C₂×Q₈	1	8	yes	complemented
87	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
88	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
89	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
90	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
91	C₂²×Dic₁₃	—	2	8	no	—
92	C₂²×Dic₁₃	—	2	8	no	—
93	C₂²×Dic₁₃	C₂×D₄	1	16	yes	—
94	C₂²×Dic₁₃	C₂⁴	1	12	yes	—
95	C₂²×Dic₁₃	C₂⁴	1	12	yes	—
96	C₂²×Dic₁₃	C₂⁴	1	12	yes	—
97	Q₈×D₁₃	—	2	512	no	—
98	C₂×D₅₂	C₂×Q₈	1	96	yes	complemented
99	C₂×D₅₂	C₂⁴	1	16	yes	—
100	C₂×C₄×D₁₃	—	2	96	no	—
101	C₂×C₄×D₁₃	—	2	192	no	—
102	C₂×C₄×D₁₃	C₂⁴	1	32	yes	—
103	C₂×C₄×D₁₃	C₂⁴	1	64	yes	—
104	C₂×Dic₂₆	—	2	192	no	—
105	C₂×Dic₂₆	C₂×D₄	1	96	yes	complemented
106	C₂×Dic₂₆	C₂⁴	1	64	yes	—
107	C₂×Dic₂₆	C₂⁴	1	16	yes	—
108	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
109	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
110	C₄²×C₁₃	C₂⁴	1	16	yes	—
111	#6103	C₂⁴	1	32	yes	—
112	#6103	C₂⁴	1	64	yes	—
113	C₄⋊Dic₁₃	C₂⁴	1	16	yes	—
114	C₄⋊Dic₁₃	C₂⁴	1	16	yes	—
115	#6101	C₂⁴	1	32	yes	—
116	#6101	C₂⁴	1	64	yes	—
117	C₄×Dic₁₃	C₂⁴	1	32	yes	—
118	C₂⁴×Q₈	—	13	2	no	—
119	C₂×D₄×Q₈	—	13	48	no	—
120	C₂²×C₄⋊Q₈	—	13	2	no	—
121	C₂²×C₄⋊Q₈	D₁₃	1	1	yes	characteristic, complemented
122	C₂²×C₂²⋊Q₈	—	13	2	no	—
123	C₂²×C₂²⋊Q₈	—	13	4	no	—
124	C₂²×C₄×Q₈	—	13	1	no	—
125	C₂²×C₄×D₄	—	13	1	no	—
126	C₂²×C₄×D₄	—	13	2	no	—
127	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
128	C₂³×C₁₃	C₂²×Q₈	1	4	yes	—
129	C₂³×C₁₃	2₋¹⁺⁴	1	4	yes	—
130	C₂³×C₁₃	C₂⁵	1	3	yes	—
131	C₂²×D₁₃	—	2	64	no	—
132	C₂²×D₁₃	—	2	24	no	—
133	C₂²×D₁₃	—	2	24	no	—
134	C₂²×D₁₃	C₂²×Q₈	1	48	yes	complemented
135	C₂²×D₁₃	C₂⁵	1	8	yes	—
136	Q₈×C₁₃	—	2	64	no	—
137	C₂×C₄×C₁₃	—	2	48	no	—
138	C₂×C₄×C₁₃	—	2	12	no	—
139	C₂×C₄×C₁₃	C₂²×D₄	1	24	yes	—
140	C₂×C₄×C₁₃	C₂²×Q₈	1	24	yes	complemented
141	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
142	C₂×C₄×C₁₃	C₂⁵	1	16	yes	—
143	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
144	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
145	C₂×Dic₁₃	—	2	24	no	—
146	C₂×Dic₁₃	—	2	24	no	—
147	C₂×Dic₁₃	C₂²×D₄	1	48	yes	—
148	C₂×Dic₁₃	C₂⁵	1	8	yes	—
149	C₂×Dic₁₃	C₂⁵	1	8	yes	—
150	C₂×Dic₁₃	C₂⁵	1	8	yes	—
151	D₅₂	C₂²×Q₈	1	64	yes	complemented
152	C₄×D₁₃	—	2	64	no	—
153	C₄×D₁₃	—	2	128	no	—
154	Dic₂₆	—	2	128	no	—
155	Dic₂₆	C₂²×D₄	1	64	yes	complemented
156	C₂³×Q₈	—	13	48	no	—
157	C₂³×Q₈	—	13	1	no	—
158	C₂³×Q₈	—	13	4	no	—
159	C₂³×Q₈	—	26	32	no	—
160	C₂³×Q₈	C₂×D₁₃	1	2	yes	—
161	C₂³×D₄	—	13	1	no	—
162	C₂⁴×C₄	—	13	4	no	—
163	C₂⁴×C₄	—	13	2	no	—
164	D₄×Q₈	—	13	256	no	—
165	C₂×C₄⋊Q₈	—	13	48	no	—
166	C₂×C₄⋊Q₈	C₂×D₁₃	1	24	yes	complemented
167	C₂×C₂²⋊Q₈	—	13	48	no	—
168	C₂×C₂²⋊Q₈	—	13	96	no	—
169	C₂×C₄×Q₈	—	13	24	no	—
170	C₂×C₄×D₄	—	13	48	no	—
171	C₂×C₄×D₄	—	13	24	no	—
172	C₂²×C₄⋊C₄	—	13	2	no	—
173	C₂²×C₄⋊C₄	—	13	4	no	—
174	C₂²×C₄⋊C₄	—	13	1	no	—
175	C₂²×C₄⋊C₄	—	13	1	no	—
176	C₂²×C₄⋊C₄	C₂×D₁₃	1	2	yes	—
177	C₂²×C₄⋊C₄	C₂×D₁₃	1	2	yes	—
178	C₂²×C₂²⋊C₄	—	13	4	no	—
179	C₂²×C₂²⋊C₄	—	13	2	no	—
180	C₂²×C₄²	—	13	2	no	—
181	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
182	C₂²×C₁₃	D₄×Q₈	1	16	yes	complemented
183	C₂²×C₁₃	C₂³×D₄	1	6	yes	—
184	C₂²×C₁₃	C₂³×Q₈	1	6	yes	—
185	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	6	yes	—
186	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
187	C₂×D₁₃	—	2	8	no	—
188	C₂×D₁₃	—	2	8	no	—
189	C₂×D₁₃	—	2	96	no	—
190	C₂×D₁₃	C₂³×Q₈	1	16	yes	complemented
191	C₄×C₁₃	—	2	16	no	—
192	C₄×C₁₃	—	2	4	no	—
193	C₄×C₁₃	C₂³×D₄	1	8	yes	—
194	C₄×C₁₃	C₂³×Q₈	1	8	yes	complemented
195	Dic₁₃	—	2	8	no	—
196	Dic₁₃	—	2	8	no	—
197	Dic₁₃	C₂³×D₄	1	16	yes	—
198	C₂⁵	—	13	2	no	—
199	C₂²×Q₈	—	2	16	no	—
200	C₂²×Q₈	—	13	128	no	—
201	C₂²×Q₈	—	13	16	no	—
202	C₂²×Q₈	—	13	12	no	—
203	C₂²×Q₈	—	13	48	no	—
204	C₂²×Q₈	—	26	32	no	—
205	C₂²×Q₈	—	26	384	no	—
206	C₂²×Q₈	C₂²×D₁₃	1	24	yes	—
207	C₂²×D₄	—	13	16	no	—
208	C₂²×D₄	—	13	12	no	—
209	C₂³×C₄	—	13	2	no	—
210	C₂³×C₄	—	13	2	no	—
211	C₂³×C₄	—	13	2	no	—
212	C₂³×C₄	—	13	48	no	—
213	C₂³×C₄	—	13	24	no	—
214	C₂³×C₄	—	26	32	no	—
215	C₂³×C₄	—	26	16	no	—
216	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
217	C₂³×C₄	C₂²×D₁₃	1	4	yes	—
218	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
219	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
220	C₄⋊Q₈	—	13	128	no	—
221	C₄⋊Q₈	C₂²×D₁₃	1	64	yes	complemented
222	C₂²⋊Q₈	—	13	128	no	—
223	C₂²⋊Q₈	—	13	256	no	—
224	C₄×Q₈	—	13	64	no	—
225	C₄×D₄	—	13	128	no	—
226	C₄×D₄	—	13	64	no	—
227	C₂×C₄⋊C₄	—	13	12	no	—
228	C₂×C₄⋊C₄	—	13	24	no	—
229	C₂×C₄⋊C₄	—	13	12	no	—
230	C₂×C₄⋊C₄	—	13	48	no	—
231	C₂×C₄⋊C₄	C₂²×D₁₃	1	24	yes	—
232	C₂×C₄⋊C₄	C₂²×D₁₃	1	24	yes	—
233	C₂×C₂²⋊C₄	—	13	48	no	—
234	C₂×C₂²⋊C₄	—	13	24	no	—
235	C₂×C₄²	—	13	24	no	—
236	C₂×C₄²	C₂²×D₁₃	1	12	yes	—
237	C₂×C₁₃	C₂×D₄×Q₈	1	12	yes	complemented
238	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
239	C₂×C₁₃	C₂⁴×Q₈	1	1	yes	characteristic
240	C₂×C₁₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
241	D₁₃	—	2	16	no	—
242	C₂⁴	—	13	16	no	—
243	C₂⁴	—	13	12	no	—
244	C₂⁴	—	26	8	no	—
245	C₂⁴	—	26	8	no	—
246	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
247	C₂×Q₈	—	2	96	no	—
248	C₂×Q₈	—	13	96	no	—
249	C₂×Q₈	—	13	16	no	—
250	C₂×Q₈	—	13	64	no	—
251	C₂×Q₈	—	26	192	no	—
252	C₂×Q₈	—	26	512	no	—
253	C₂×Q₈	C₂³×D₁₃	1	32	yes	—
254	C₂×D₄	—	13	96	no	—
255	C₂×D₄	—	13	16	no	—
256	C₂²×C₄	—	2	16	no	—
257	C₂²×C₄	—	2	4	no	—
258	C₂²×C₄	—	13	16	no	—
259	C₂²×C₄	—	13	12	no	—
260	C₂²×C₄	—	13	12	no	—
261	C₂²×C₄	—	13	12	no	—
262	C₂²×C₄	—	13	64	no	—
263	C₂²×C₄	—	13	32	no	—
264	C₂²×C₄	—	26	192	no	—
265	C₂²×C₄	—	26	8	no	—
266	C₂²×C₄	—	26	8	no	—
267	C₂²×C₄	—	26	96	no	—
268	C₂²×C₄	D₄×D₁₃	1	8	yes	—
269	C₂²×C₄	Q₈×D₁₃	1	8	yes	complemented
270	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
271	C₂²×C₄	C₂³×D₁₃	1	24	yes	—
272	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
273	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
274	C₄⋊C₄	—	13	16	no	—
275	C₄⋊C₄	—	13	32	no	—
276	C₄⋊C₄	—	13	16	no	—
277	C₄⋊C₄	—	13	64	no	—
278	C₄⋊C₄	C₂³×D₁₃	1	32	yes	—
279	C₄⋊C₄	C₂³×D₁₃	1	32	yes	—
280	C₂²⋊C₄	—	13	64	no	—
281	C₂²⋊C₄	—	13	32	no	—
282	C₄²	—	13	32	no	—
283	C₄²	C₂³×D₁₃	1	16	yes	—
284	C₁₃	C₂²×D₄×Q₈	1	1	yes	characteristic, complemented, Sylow
285	C₂³	—	13	48	no	—
286	C₂³	—	13	8	no	—
287	C₂³	—	26	64	no	—
288	C₂³	—	26	24	no	—
289	C₂³	—	26	24	no	—
290	C₂³	C₂×D₄×D₁₃	1	4	yes	—
291	C₂³	C₂×Q₈×D₁₃	1	4	yes	—
292	C₂³	#88254	1	4	yes	—
293	C₂³	C₂⁴×D₁₃	1	3	yes	—
294	Q₈	—	2	64	no	—
295	Q₈	—	13	64	no	—
296	Q₈	—	26	128	no	—
297	D₄	—	13	64	no	—
298	C₂×C₄	—	2	48	no	—
299	C₂×C₄	—	2	12	no	—
300	C₂×C₄	—	13	48	no	—
301	C₂×C₄	—	13	8	no	—
302	C₂×C₄	—	13	8	no	—
303	C₂×C₄	—	13	8	no	—
304	C₂×C₄	—	26	128	no	—
305	C₂×C₄	—	26	24	no	—
306	C₂×C₄	—	26	24	no	—
307	C₂×C₄	—	26	64	no	—
308	C₂×C₄	C₂×D₄×D₁₃	1	24	yes	—
309	C₂×C₄	C₂×Q₈×D₁₃	1	24	yes	complemented
310	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
311	C₂×C₄	C₂⁴×D₁₃	1	16	yes	—
312	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
313	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
314	C₂²	—	13	16	no	—
315	C₂²	—	26	96	no	—
316	C₂²	—	26	8	no	—
317	C₂²	—	26	8	no	—
318	C₂²	#11719432	1	16	yes	direct product factor
319	C₂²	C₂²×D₄×D₁₃	1	6	yes	—
320	C₂²	C₂²×Q₈×D₁₃	1	6	yes	—
321	C₂²	C₂×#88254	1	6	yes	—
322	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
323	C₄	—	2	16	no	—
324	C₄	—	2	4	no	—
325	C₄	—	13	16	no	—
326	C₄	—	26	8	no	—
327	C₄	—	26	8	no	—
328	C₄	C₂²×D₄×D₁₃	1	8	yes	—
329	C₄	C₂²×Q₈×D₁₃	1	8	yes	complemented
330	C₂	—	26	16	no	—
331	C₂	C₂×#11719432	1	12	yes	direct product factor
332	C₂	C₂³×D₄×D₁₃	1	1	yes	characteristic
333	C₂	C₂³×Q₈×D₁₃	1	1	yes	characteristic
334	C₂	C₂²×#88254	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂³×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂²×C₁₃×C₄⋊Q₈	C₂
socle	C₂⁴×C₁₃	C₂⁴
prime radical	C₂³×D₅₂	C₂²
hypercenter	C₂²×C₄⋊Q₈	D₁₃
hypocenter	C₁₃	C₂²×D₄×Q₈
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₂³×Q₈×D₁₃	C₂	semidirect
2. C₂×#11719432	C₂	direct (N × H)
3. C₂²×#88142	C₂	semidirect
4. C₂²×#88150	C₂	semidirect
5. C₂²×#88200	C₂	semidirect
6. C₂²×C₄×Dic₂₆	C₂	semidirect
9. C₂²×C₁₃×C₄⋊Q₈	C₂	semidirect
12. C₂²×Q₈×D₁₃	C₂²	semidirect
18. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
22. C₂×#88200	C₂²	semidirect
30. #11719432	C₂²	direct (N × H)
31. C₂×#88150	C₂²	semidirect
33. C₂×#88142	C₂²	semidirect
35. C₂×C₄×Dic₂₆	C₂²	semidirect
47. C₂×Q₈×D₁₃	C₂³	semidirect
48. C₂²×D₅₂	Q₈	semidirect
55. C₂²×Dic₂₆	D₄	semidirect
58. C₁₃×C₄⋊Q₈	C₂³	semidirect
62. #88200	C₂³	semidirect
70. #88150	C₂³	semidirect
72. #88142	C₂³	semidirect
74. C₄×Dic₂₆	C₂³	semidirect
79. C₂³×D₁₃	C₂×Q₈	semidirect
86. C₂²×C₄×C₁₃	C₂×Q₈	semidirect
98. C₂×D₅₂	C₂×Q₈	semidirect
105. C₂×Dic₂₆	C₂×D₄	semidirect
121. C₂²×C₄⋊Q₈	D₁₃	semidirect
134. C₂²×D₁₃	C₂²×Q₈	semidirect
140. C₂×C₄×C₁₃	C₂²×Q₈	semidirect
151. D₅₂	C₂²×Q₈	semidirect
155. Dic₂₆	C₂²×D₄	semidirect
166. C₂×C₄⋊Q₈	C₂×D₁₃	semidirect
182. C₂²×C₁₃	D₄×Q₈	semidirect
190. C₂×D₁₃	C₂³×Q₈	semidirect
194. C₄×C₁₃	C₂³×Q₈	semidirect
221. C₄⋊Q₈	C₂²×D₁₃	semidirect
237. C₂×C₁₃	C₂×D₄×Q₈	semidirect
269. C₂²×C₄	Q₈×D₁₃	semidirect
284. C₁₃	C₂²×D₄×Q₈	semidirect
309. C₂×C₄	C₂×Q₈×D₁₃	semidirect
318. C₂²	#11719432	direct (N × H)
329. C₄	C₂²×Q₈×D₁₃	semidirect
331. C₂	C₂×#11719432	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×Q₈×D₁₃	2
C₂×#11719432	2
C₂²×#88142	2
C₂²×#88150	2
C₂²×#88200	2
C₂²×C₄×Dic₂₆	2
C₂²×C₄×D₅₂	2
C₂²×#88147	2
C₂²×C₁₃×C₄⋊Q₈	2
C₂²×D₄×Q₈	13

Subgroups — C22×#11719432 #16769834

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#11719432 #16769834