Subgroups — C₂²×#11719433 #16769623

Order 3328.

8238 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11719433	C₂	1	48	yes	maximal, direct product factor
2	C₂²×#88123	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#88144	C₂	1	2	yes	maximal, complemented
4	C₂²×#88151	C₂	1	2	yes	maximal
5	C₂²×#88200	C₂	1	2	yes	maximal
6	C₂²×Q₈×Dic₁₃	C₂	1	2	yes	maximal, complemented
7	C₂²×#88141	C₂	1	2	yes	maximal, complemented
8	C₂²×#88146	C₂	1	2	yes	maximal
9	C₂²×C₄²×D₁₃	C₂	1	1	yes	maximal, characteristic
10	C₂²×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×Q₈×C₁₃	C₂²	1	2	yes	—
12	C₂³×C₄×D₁₃	C₂²	1	1	yes	characteristic
13	C₂³×C₄×D₁₃	C₂²	1	1	yes	characteristic
14	C₂³×C₄×D₁₃	C₂²	1	1	yes	characteristic
15	C₂³×Dic₂₆	C₂²	1	2	yes	—
16	C₂×C₁₃×C₄⋊Q₈	C₂²	1	24	yes	complemented
17	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
18	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
19	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×#88200	C₂²	1	48	yes	—
21	C₂×Q₈×Dic₁₃	C₂²	1	48	yes	complemented
22	C₂²×#6103	C₂²	1	4	yes	—
23	C₂²×C₄⋊Dic₁₃	C₂²	1	2	yes	—
24	C₂²×C₄⋊Dic₁₃	C₂²	1	2	yes	—
25	C₂²×C₄⋊Dic₁₃	C₂²	1	4	yes	—
26	C₂²×#6101	C₂²	1	4	yes	—
27	C₂²×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
28	C₂²×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
29	C₂²×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
30	C₂²×C₄×Dic₁₃	C₂²	1	4	yes	—
31	#11719433	C₂²	1	256	yes	direct product factor
32	C₂×#88151	C₂²	1	48	yes	—
33	C₂×#88146	C₂²	1	48	yes	—
34	C₂×#88144	C₂²	1	48	yes	complemented
35	C₂×#88141	C₂²	1	48	yes	complemented
36	C₂×C₄²×D₁₃	C₂²	1	24	yes	—
37	C₂×#88123	C₂²	1	24	yes	complemented
38	C₂⁴×D₁₃	C₂³	1	1	yes	characteristic
39	C₂²×Q₈×C₁₃	—	2	16	no	—
40	C₂²×Q₈×C₁₃	C₂³	1	24	yes	—
41	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
42	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
43	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
45	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
46	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
47	C₂³×Dic₁₃	C₂³	1	4	yes	—
48	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
49	C₂²×C₄×D₁₃	—	2	8	no	—
50	C₂²×C₄×D₁₃	—	2	8	no	—
51	C₂²×C₄×D₁₃	Q₈	1	16	yes	complemented
52	C₂²×C₄×D₁₃	C₂³	1	12	yes	—
53	C₂²×C₄×D₁₃	C₂³	1	12	yes	—
54	C₂²×C₄×D₁₃	C₂³	1	12	yes	—
55	C₂²×Dic₂₆	—	2	16	no	—
56	C₂²×Dic₂₆	C₂³	1	24	yes	—
57	C₁₃×C₄⋊Q₈	C₂³	1	64	yes	complemented
58	C₂×C₁₃×C₄⋊C₄	C₂³	1	24	yes	—
59	C₂×C₁₃×C₄⋊C₄	C₂³	1	24	yes	—
60	C₂×C₄²×C₁₃	C₂³	1	12	yes	—
61	#88200	C₂³	1	128	yes	—
62	Q₈×Dic₁₃	C₂³	1	128	yes	complemented
63	C₂×#6103	C₂³	1	48	yes	—
64	C₂×C₄⋊Dic₁₃	C₂³	1	24	yes	—
65	C₂×C₄⋊Dic₁₃	C₂³	1	24	yes	—
66	C₂×C₄⋊Dic₁₃	C₂³	1	48	yes	—
67	C₂×#6101	C₂³	1	48	yes	—
68	C₂×C₄×Dic₁₃	C₂³	1	12	yes	—
69	C₂×C₄×Dic₁₃	C₂³	1	12	yes	—
70	C₂×C₄×Dic₁₃	C₂³	1	12	yes	—
71	C₂×C₄×Dic₁₃	C₂³	1	48	yes	—
72	#88151	C₂³	1	128	yes	—
73	#88146	C₂³	1	128	yes	—
74	#88144	C₂³	1	128	yes	complemented
75	#88141	C₂³	1	128	yes	complemented
76	C₄²×D₁₃	C₂³	1	64	yes	—
77	#88123	C₂³	1	64	yes	complemented
78	C₂²×#533	—	13	1	no	maximal, Sylow
79	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
80	C₂³×D₁₃	—	2	4	no	—
81	C₂³×D₁₃	—	2	4	no	—
82	C₂³×D₁₃	C₂×Q₈	1	8	yes	—
83	C₂³×D₁₃	C₂⁴	1	6	yes	—
84	C₂×Q₈×C₁₃	—	2	96	no	—
85	C₂×Q₈×C₁₃	C₂⁴	1	32	yes	—
86	C₂²×C₄×C₁₃	—	2	16	no	—
87	C₂²×C₄×C₁₃	C₂×Q₈	1	8	yes	—
88	C₂²×C₄×C₁₃	#41	1	8	yes	—
89	C₂²×C₄×C₁₃	#41	1	8	yes	—
90	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
91	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
92	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
93	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
94	C₂²×Dic₁₃	—	2	16	no	—
95	C₂²×Dic₁₃	—	2	4	no	—
96	C₂²×Dic₁₃	—	2	4	no	—
97	C₂²×Dic₁₃	C₂×Q₈	1	8	yes	—
98	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
99	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
100	C₂²×Dic₁₃	C₂⁴	1	24	yes	—
101	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
102	C₂×C₄×D₁₃	—	2	48	no	—
103	C₂×C₄×D₁₃	—	2	48	no	—
104	C₂×C₄×D₁₃	C₂×Q₈	1	96	yes	complemented
105	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
106	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
107	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
108	C₂×Dic₂₆	—	2	96	no	—
109	C₂×Dic₂₆	C₂⁴	1	32	yes	—
110	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
111	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
112	C₄²×C₁₃	C₂⁴	1	16	yes	—
113	#6103	C₂⁴	1	64	yes	—
114	C₄⋊Dic₁₃	C₂⁴	1	32	yes	—
115	C₄⋊Dic₁₃	C₂⁴	1	32	yes	—
116	C₄⋊Dic₁₃	C₂⁴	1	64	yes	—
117	#6101	C₂⁴	1	64	yes	—
118	C₄×Dic₁₃	C₂⁴	1	16	yes	—
119	C₄×Dic₁₃	C₂⁴	1	16	yes	—
120	C₄×Dic₁₃	C₂⁴	1	16	yes	—
121	C₄×Dic₁₃	C₂⁴	1	64	yes	—
122	C₂×#533	—	13	48	no	—
123	C₂²×C₄⋊Q₈	—	13	1	no	—
124	C₂²×C₄⋊Q₈	D₁₃	1	1	yes	characteristic, complemented
125	C₂²×#125	—	13	2	no	—
126	C₂²×C₂²⋊Q₈	—	13	2	no	—
127	C₂²×C₂²⋊Q₈	—	13	2	no	—
128	C₂²×C₄×Q₈	—	13	2	no	—
129	C₂²×C₄×Q₈	—	13	2	no	—
130	C₂²×#117	—	13	2	no	—
131	C₂³×C₄²	—	13	1	no	—
132	C₂³×C₁₃	C₂²×Q₈	1	4	yes	—
133	C₂³×C₁₃	C₂×#41	1	4	yes	—
134	C₂³×C₁₃	C₂×#41	1	4	yes	—
135	C₂³×C₁₃	C₂⁵	1	3	yes	—
136	C₂²×D₁₃	—	2	32	no	—
137	C₂²×D₁₃	—	2	12	no	—
138	C₂²×D₁₃	—	2	12	no	—
139	C₂²×D₁₃	C₂²×Q₈	1	24	yes	—
140	C₂²×D₁₃	C₂⁵	1	4	yes	—
141	Q₈×C₁₃	—	2	64	no	—
142	C₂×C₄×C₁₃	—	2	48	no	—
143	C₂×C₄×C₁₃	C₂²×Q₈	1	24	yes	—
144	C₂×C₄×C₁₃	C₂×#41	1	24	yes	—
145	C₂×C₄×C₁₃	C₂×#41	1	24	yes	—
146	C₂×C₄×C₁₃	C₂⁵	1	16	yes	—
147	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
148	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
149	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
150	C₂×Dic₁₃	—	2	48	no	—
151	C₂×Dic₁₃	—	2	12	no	—
152	C₂×Dic₁₃	—	2	12	no	—
153	C₂×Dic₁₃	C₂²×Q₈	1	24	yes	—
154	C₂×Dic₁₃	C₂⁵	1	4	yes	—
155	C₂×Dic₁₃	C₂⁵	1	4	yes	—
156	C₂×Dic₁₃	C₂⁵	1	16	yes	—
157	C₂×Dic₁₃	C₂⁵	1	4	yes	—
158	C₄×D₁₃	—	2	32	no	—
159	C₄×D₁₃	—	2	32	no	—
160	C₄×D₁₃	C₂²×Q₈	1	64	yes	complemented
161	Dic₂₆	—	2	64	no	—
162	C₂³×Q₈	—	13	2	no	—
163	C₂³×Q₈	C₂×D₁₃	1	2	yes	—
164	C₂⁴×C₄	—	13	1	no	—
165	C₂⁴×C₄	—	13	1	no	—
166	C₂⁴×C₄	—	13	1	no	—
167	#533	—	13	256	no	—
168	C₂×C₄⋊Q₈	—	13	24	no	—
169	C₂×C₄⋊Q₈	C₂×D₁₃	1	24	yes	complemented
170	C₂×#125	—	13	48	no	—
171	C₂×C₂²⋊Q₈	—	13	48	no	—
172	C₂×C₂²⋊Q₈	—	13	48	no	—
173	C₂×C₄×Q₈	—	13	48	no	—
174	C₂×C₄×Q₈	—	13	48	no	—
175	C₂×#117	—	13	48	no	—
176	C₂²×C₄⋊C₄	—	13	4	no	—
177	C₂²×C₄⋊C₄	—	13	2	no	—
178	C₂²×C₄⋊C₄	—	13	4	no	—
179	C₂²×C₄⋊C₄	—	13	2	no	—
180	C₂²×C₄⋊C₄	C₂×D₁₃	1	2	yes	—
181	C₂²×C₄⋊C₄	C₂×D₁₃	1	2	yes	—
182	C₂²×C₂²⋊C₄	—	13	4	no	—
183	C₂²×C₄²	—	13	1	no	—
184	C₂²×C₄²	—	13	1	no	—
185	C₂²×C₄²	—	13	1	no	—
186	C₂²×C₄²	—	13	4	no	—
187	C₂²×C₄²	—	13	24	no	—
188	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
189	C₂²×C₁₃	#533	1	16	yes	complemented
190	C₂²×C₁₃	C₂³×Q₈	1	6	yes	—
191	C₂²×C₁₃	C₂²×#41	1	6	yes	—
192	C₂²×C₁₃	C₂²×#41	1	6	yes	—
193	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
194	C₂×D₁₃	—	2	4	no	—
195	C₂×D₁₃	—	2	4	no	—
196	C₂×D₁₃	—	2	48	no	—
197	C₂×D₁₃	C₂³×Q₈	1	8	yes	—
198	C₄×C₁₃	—	2	16	no	—
199	C₄×C₁₃	C₂³×Q₈	1	8	yes	—
200	C₄×C₁₃	C₂²×#41	1	8	yes	—
201	C₄×C₁₃	C₂²×#41	1	8	yes	—
202	Dic₁₃	—	2	16	no	—
203	Dic₁₃	—	2	4	no	—
204	Dic₁₃	—	2	4	no	—
205	Dic₁₃	C₂³×Q₈	1	8	yes	—
206	C₂⁵	—	13	1	no	—
207	C₂²×Q₈	—	2	16	no	—
208	C₂²×Q₈	—	13	24	no	—
209	C₂²×Q₈	—	26	16	no	—
210	C₂²×Q₈	C₂²×D₁₃	1	24	yes	—
211	C₂³×C₄	—	13	1	no	—
212	C₂³×C₄	—	13	16	no	—
213	C₂³×C₄	—	13	12	no	—
214	C₂³×C₄	—	13	4	no	—
215	C₂³×C₄	—	13	1	no	—
216	C₂³×C₄	—	13	1	no	—
217	C₂³×C₄	—	13	12	no	—
218	C₂³×C₄	—	13	12	no	—
219	C₂³×C₄	—	26	8	no	—
220	C₂³×C₄	—	26	8	no	—
221	C₂³×C₄	C₂²×D₁₃	1	4	yes	—
222	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
223	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
224	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
225	C₄⋊Q₈	—	13	64	no	—
226	C₄⋊Q₈	C₂²×D₁₃	1	64	yes	complemented
227	#125	—	13	128	no	—
228	C₂²⋊Q₈	—	13	128	no	—
229	C₂²⋊Q₈	—	13	128	no	—
230	C₄×Q₈	—	13	128	no	—
231	C₄×Q₈	—	13	128	no	—
232	#117	—	13	128	no	—
233	C₂×C₄⋊C₄	—	13	24	no	—
234	C₂×C₄⋊C₄	—	13	48	no	—
235	C₂×C₄⋊C₄	—	13	48	no	—
236	C₂×C₄⋊C₄	—	13	24	no	—
237	C₂×C₄⋊C₄	C₂²×D₁₃	1	24	yes	—
238	C₂×C₄⋊C₄	C₂²×D₁₃	1	24	yes	—
239	C₂×C₂²⋊C₄	—	13	48	no	—
240	C₂×C₄²	—	13	48	no	—
241	C₂×C₄²	—	13	12	no	—
242	C₂×C₄²	—	13	12	no	—
243	C₂×C₄²	—	13	12	no	—
244	C₂×C₄²	—	13	64	no	—
245	C₂×C₄²	C₂²×D₁₃	1	12	yes	—
246	C₂×C₁₃	C₂×#533	1	12	yes	complemented
247	C₂×C₁₃	C₂⁴×Q₈	1	1	yes	characteristic
248	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
249	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
250	D₁₃	—	2	8	no	—
251	C₂⁴	—	13	8	no	—
252	C₂⁴	—	13	6	no	—
253	C₂⁴	—	26	4	no	—
254	C₂⁴	—	26	4	no	—
255	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
256	C₂×Q₈	—	2	96	no	—
257	C₂×Q₈	—	13	32	no	—
258	C₂×Q₈	—	26	96	no	—
259	C₂×Q₈	C₂³×D₁₃	1	32	yes	—
260	C₂²×C₄	—	2	16	no	—
261	C₂²×C₄	—	13	8	no	—
262	C₂²×C₄	—	13	6	no	—
263	C₂²×C₄	—	13	96	no	—
264	C₂²×C₄	—	13	16	no	—
265	C₂²×C₄	—	13	6	no	—
266	C₂²×C₄	—	13	6	no	—
267	C₂²×C₄	—	13	24	no	—
268	C₂²×C₄	—	13	16	no	—
269	C₂²×C₄	—	13	16	no	—
270	C₂²×C₄	—	26	4	no	—
271	C₂²×C₄	—	26	4	no	—
272	C₂²×C₄	—	26	16	no	—
273	C₂²×C₄	—	26	48	no	—
274	C₂²×C₄	—	26	48	no	—
275	C₂²×C₄	#6129	1	8	yes	—
276	C₂²×C₄	Q₈×D₁₃	1	8	yes	—
277	C₂²×C₄	#6131	1	8	yes	—
278	C₂²×C₄	C₂³×D₁₃	1	24	yes	—
279	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
280	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
281	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
282	C₄⋊C₄	—	13	32	no	—
283	C₄⋊C₄	—	13	64	no	—
284	C₄⋊C₄	—	13	64	no	—
285	C₄⋊C₄	—	13	32	no	—
286	C₄⋊C₄	C₂³×D₁₃	1	32	yes	—
287	C₄⋊C₄	C₂³×D₁₃	1	32	yes	—
288	C₂²⋊C₄	—	13	64	no	—
289	C₄²	—	13	16	no	—
290	C₄²	—	13	16	no	—
291	C₄²	—	13	16	no	—
292	C₄²	—	13	64	no	—
293	C₄²	C₂³×D₁₃	1	16	yes	—
294	C₁₃	C₂²×#533	1	1	yes	characteristic, complemented, Sylow
295	C₂³	—	13	24	no	—
296	C₂³	—	13	4	no	—
297	C₂³	—	26	32	no	—
298	C₂³	—	26	12	no	—
299	C₂³	—	26	12	no	—
300	C₂³	C₂×#6129	1	4	yes	—
301	C₂³	C₂×Q₈×D₁₃	1	4	yes	—
302	C₂³	C₂×#6131	1	4	yes	—
303	C₂³	C₂⁴×D₁₃	1	3	yes	—
304	Q₈	—	2	64	no	—
305	Q₈	—	26	64	no	—
306	C₂×C₄	—	2	48	no	—
307	C₂×C₄	—	13	24	no	—
308	C₂×C₄	—	13	4	no	—
309	C₂×C₄	—	13	64	no	—
310	C₂×C₄	—	13	4	no	—
311	C₂×C₄	—	13	4	no	—
312	C₂×C₄	—	13	16	no	—
313	C₂×C₄	—	26	12	no	—
314	C₂×C₄	—	26	12	no	—
315	C₂×C₄	—	26	48	no	—
316	C₂×C₄	—	26	32	no	—
317	C₂×C₄	—	26	32	no	—
318	C₂×C₄	C₂×#6129	1	24	yes	—
319	C₂×C₄	C₂×Q₈×D₁₃	1	24	yes	—
320	C₂×C₄	C₂×#6131	1	24	yes	—
321	C₂×C₄	C₂⁴×D₁₃	1	16	yes	—
322	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
323	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
324	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
325	C₂²	—	13	8	no	—
326	C₂²	—	26	4	no	—
327	C₂²	—	26	4	no	—
328	C₂²	—	26	48	no	—
329	C₂²	#11719433	1	16	yes	direct product factor
330	C₂²	C₂²×#6129	1	6	yes	—
331	C₂²	C₂²×Q₈×D₁₃	1	6	yes	—
332	C₂²	C₂²×#6131	1	6	yes	—
333	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
334	C₄	—	2	16	no	—
335	C₄	—	13	8	no	—
336	C₄	—	26	4	no	—
337	C₄	—	26	4	no	—
338	C₄	—	26	16	no	—
339	C₄	C₂²×#6129	1	8	yes	—
340	C₄	C₂²×Q₈×D₁₃	1	8	yes	—
341	C₄	C₂²×#6131	1	8	yes	—
342	C₂	—	26	8	no	—
343	C₂	C₂×#11719433	1	12	yes	direct product factor
344	C₂	C₂³×Q₈×D₁₃	1	1	yes	characteristic
345	C₂	C₂³×#6129	1	1	yes	characteristic
346	C₂	C₂³×#6131	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	C₂⁴×D₁₃	C₂³
hypercenter	C₂²×C₄⋊Q₈	D₁₃
hypocenter	C₁₃	C₂²×#533
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. C₂×#11719433	C₂	direct (N × H)
2. C₂²×#88123	C₂	semidirect
3. C₂²×#88144	C₂	semidirect
6. C₂²×Q₈×Dic₁₃	C₂	semidirect
7. C₂²×#88141	C₂	semidirect
10. C₂²×C₁₃×C₄⋊Q₈	C₂	semidirect
16. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
21. C₂×Q₈×Dic₁₃	C₂²	semidirect
31. #11719433	C₂²	direct (N × H)
34. C₂×#88144	C₂²	semidirect
35. C₂×#88141	C₂²	semidirect
37. C₂×#88123	C₂²	semidirect
51. C₂²×C₄×D₁₃	Q₈	semidirect
57. C₁₃×C₄⋊Q₈	C₂³	semidirect
62. Q₈×Dic₁₃	C₂³	semidirect
74. #88144	C₂³	semidirect
75. #88141	C₂³	semidirect
77. #88123	C₂³	semidirect
104. C₂×C₄×D₁₃	C₂×Q₈	semidirect
124. C₂²×C₄⋊Q₈	D₁₃	semidirect
160. C₄×D₁₃	C₂²×Q₈	semidirect
169. C₂×C₄⋊Q₈	C₂×D₁₃	semidirect
189. C₂²×C₁₃	#533	semidirect
226. C₄⋊Q₈	C₂²×D₁₃	semidirect
246. C₂×C₁₃	C₂×#533	semidirect
294. C₁₃	C₂²×#533	semidirect
329. C₂²	#11719433	direct (N × H)
343. C₂	C₂×#11719433	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×#11719433	2
C₂²×#88123	2
C₂²×#88144	2
C₂²×#88151	2
C₂²×#88200	2
C₂²×Q₈×Dic₁₃	2
C₂²×#88141	2
C₂²×#88146	2
C₂²×C₄²×D₁₃	2
C₂²×C₁₃×C₄⋊Q₈	2
C₂²×#533	13

Subgroups — C22×#11719433 #16769623

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#11719433 #16769623