Subgroups — C₂²×#11719230 #16769677

Order 3328.

14414 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	C₂³×#6127	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁴×D₅₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#11719230	C₂	1	48	yes	maximal, direct product factor
4	C₂²×#88128	C₂	1	2	yes	maximal, complemented
5	C₂²×#88129	C₂	1	2	yes	maximal, complemented
6	C₂²×#88149	C₂	1	4	yes	maximal, complemented
7	C₂²×#88136	C₂	1	4	yes	maximal, complemented
8	C₂²×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂⁵×D₁₃	C₂²	1	2	yes	—
10	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
11	C₂³×C₂²⋊D₁₃	C₂²	1	2	yes	—
12	C₂²×#6127	—	2	16	no	—
13	C₂²×#6127	C₂²	1	24	yes	complemented
14	C₂³×D₅₂	—	2	16	no	—
15	C₂³×D₅₂	C₂²	1	2	yes	—
16	C₂³×D₅₂	C₂²	1	2	yes	—
17	C₂³×D₅₂	C₂²	1	24	yes	complemented
18	C₂³×D₅₂	C₂²	1	1	yes	characteristic, complemented
19	C₂³×D₅₂	C₂²	1	8	yes	complemented
20	C₂³×C₄×D₁₃	C₂²	1	2	yes	complemented
21	C₂³×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₁₃×#117	C₂²	1	24	yes	complemented
23	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
24	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₂²×C₄²×C₁₃	C₂²	1	2	yes	complemented
26	C₂²×#6103	C₂²	1	8	yes	complemented
27	#11719230	C₂²	1	256	yes	direct product factor
28	C₂×#88149	C₂²	1	96	yes	complemented
29	C₂×#88136	C₂²	1	96	yes	complemented
30	C₂×#88129	C₂²	1	48	yes	complemented
31	C₂×#88128	C₂²	1	48	yes	complemented
32	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
33	C₂⁴×D₁₃	—	2	16	no	—
34	C₂⁴×D₁₃	—	4	16	no	—
35	C₂⁴×D₁₃	C₂³	1	4	yes	—
36	C₂⁴×D₁₃	C₂³	1	2	yes	—
37	C₂⁴×D₁₃	C₂³	1	24	yes	—
38	C₂³×C₄×C₁₃	D₄	1	16	yes	complemented
39	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
40	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₁₃	C₂³	1	12	yes	—
43	C₂²×C₂²⋊D₁₃	—	2	16	no	—
44	C₂²×C₂²⋊D₁₃	C₂³	1	24	yes	—
45	C₂³×Dic₁₃	C₂³	1	2	yes	—
46	C₂×#6127	—	2	192	no	—
47	C₂×#6127	C₂³	1	64	yes	complemented
48	C₂²×D₅₂	—	2	16	no	—
49	C₂²×D₅₂	—	2	16	no	—
50	C₂²×D₅₂	—	2	8	no	—
51	C₂²×D₅₂	—	2	192	no	—
52	C₂²×D₅₂	—	4	32	no	—
53	C₂²×D₅₂	C₂³	1	24	yes	—
54	C₂²×D₅₂	C₂³	1	24	yes	—
55	C₂²×D₅₂	C₂³	1	64	yes	complemented
56	C₂²×D₅₂	C₂³	1	12	yes	complemented
57	C₂²×D₅₂	C₂³	1	96	yes	complemented
58	C₂²×C₄×D₁₃	—	2	16	no	—
59	C₂²×C₄×D₁₃	C₂³	1	24	yes	complemented
60	C₂²×Dic₂₆	—	2	8	no	—
61	C₂²×Dic₂₆	C₂³	1	12	yes	complemented
62	C₁₃×#117	C₂³	1	64	yes	complemented
63	C₂×C₁₃×C₄⋊C₄	C₂³	1	24	yes	complemented
64	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	—
65	C₂×C₄²×C₁₃	C₂³	1	24	yes	complemented
66	C₂×#6103	C₂³	1	96	yes	complemented
67	#88149	C₂³	1	256	yes	complemented
68	#88136	C₂³	1	256	yes	complemented
69	#88129	C₂³	1	128	yes	complemented
70	#88128	C₂³	1	128	yes	complemented
71	C₂²×#535	—	13	1	no	maximal, Sylow
72	C₂⁴×C₁₃	—	2	8	no	—
73	C₂⁴×C₁₃	C₂×D₄	1	8	yes	—
74	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
75	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
76	C₂³×D₁₃	—	2	8	no	—
77	C₂³×D₁₃	—	2	96	no	—
78	C₂³×D₁₃	—	2	16	no	—
79	C₂³×D₁₃	—	2	16	no	—
80	C₂³×D₁₃	—	2	32	no	—
81	C₂³×D₁₃	—	4	96	no	—
82	C₂³×D₁₃	—	4	128	no	—
83	C₂³×D₁₃	C₂⁴	1	24	yes	—
84	C₂³×D₁₃	C₂⁴	1	12	yes	—
85	C₂³×D₁₃	C₂⁴	1	32	yes	—
86	C₂²×C₄×C₁₃	—	2	16	no	—
87	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
88	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
89	C₂²×C₄×C₁₃	C₂×D₄	1	96	yes	complemented
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	16	yes	—
94	C₂×C₂²⋊D₁₃	—	2	96	no	—
95	C₂×C₂²⋊D₁₃	C₂⁴	1	32	yes	—
96	C₂²×Dic₁₃	—	2	8	no	—
97	C₂²×Dic₁₃	C₂⁴	1	12	yes	—
98	#6127	—	2	256	no	—
99	C₂×D₅₂	—	2	96	no	—
100	C₂×D₅₂	—	2	96	no	—
101	C₂×D₅₂	—	2	48	no	—
102	C₂×D₅₂	—	2	256	no	—
103	C₂×D₅₂	—	4	192	no	—
104	C₂×D₅₂	C₂⁴	1	32	yes	—
105	C₂×D₅₂	C₂⁴	1	32	yes	—
106	C₂×D₅₂	C₂⁴	1	16	yes	complemented
107	C₂×D₅₂	C₂⁴	1	128	yes	complemented
108	C₂×C₄×D₁₃	—	2	96	no	—
109	C₂×C₄×D₁₃	C₂⁴	1	32	yes	complemented
110	C₂×Dic₂₆	—	2	48	no	—
111	C₂×Dic₂₆	C₂⁴	1	16	yes	complemented
112	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	complemented
113	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
114	C₄²×C₁₃	C₂⁴	1	32	yes	complemented
115	#6103	C₂⁴	1	128	yes	complemented
116	C₂³×#41	—	13	1	no	—
117	C₂⁴×D₄	—	13	1	no	—
118	C₂×#535	—	13	48	no	—
119	C₂²×#127	—	13	2	no	—
120	C₂²×#124	—	13	2	no	—
121	C₂²×#121	—	13	4	no	—
122	C₂²×#120	—	13	4	no	—
123	C₂²×#117	D₁₃	1	1	yes	characteristic, complemented
124	C₂³×C₁₃	—	2	32	no	—
125	C₂³×C₁₃	—	2	24	no	—
126	C₂³×C₁₃	C₂²×D₄	1	24	yes	—
127	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
128	C₂³×C₁₃	H(5,𝔽₂)	1	8	yes	—
129	C₂³×C₁₃	C₂⁵	1	4	yes	—
130	C₂³×C₁₃	C₂⁵	1	3	yes	—
131	C₂²×D₁₃	—	2	24	no	—
132	C₂²×D₁₃	—	2	64	no	—
133	C₂²×D₁₃	—	2	48	no	—
134	C₂²×D₁₃	—	2	48	no	—
135	C₂²×D₁₃	—	2	96	no	—
136	C₂²×D₁₃	—	4	64	no	—
137	C₂²×D₁₃	—	4	384	no	—
138	C₂²×D₁₃	—	4	32	no	—
139	C₂²×D₁₃	—	4	64	no	—
140	C₂²×D₁₃	C₂⁵	1	16	yes	—
141	C₂²×D₁₃	C₂⁵	1	8	yes	—
142	C₂×C₄×C₁₃	—	2	48	no	—
143	C₂×C₄×C₁₃	C₂²×D₄	1	24	yes	—
144	C₂×C₄×C₁₃	C₂²×D₄	1	24	yes	—
145	C₂×C₄×C₁₃	C₂²×D₄	1	64	yes	complemented
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	C₂²⋊D₁₃	—	2	64	no	—
150	C₂×Dic₁₃	—	2	24	no	—
151	C₂×Dic₁₃	C₂⁵	1	8	yes	—
152	D₅₂	—	2	64	no	—
153	D₅₂	—	2	64	no	—
154	D₅₂	—	2	32	no	—
155	D₅₂	—	4	128	no	—
156	C₄×D₁₃	—	2	64	no	—
157	Dic₂₆	—	2	32	no	—
158	C₂⁶	—	13	2	no	—
159	C₂²×#41	—	13	24	no	—
160	C₂²×#41	—	26	16	no	—
161	C₂³×Q₈	—	13	1	no	—
162	C₂³×D₄	—	13	2	no	—
163	C₂³×D₄	—	13	2	no	—
164	C₂³×D₄	—	13	2	no	—
165	C₂³×D₄	—	13	24	no	—
166	C₂³×D₄	—	13	1	no	—
167	C₂³×D₄	—	13	8	no	—
168	C₂³×D₄	—	26	16	no	—
169	C₂⁴×C₄	—	13	2	no	—
170	C₂⁴×C₄	C₂×D₁₃	1	1	yes	characteristic
171	#535	—	13	256	no	—
172	C₂×#127	—	13	48	no	—
173	C₂×#124	—	13	48	no	—
174	C₂×#121	—	13	96	no	—
175	C₂×#120	—	13	96	no	—
176	C₂×#117	C₂×D₁₃	1	24	yes	complemented
177	C₂²×C₄⋊C₄	C₂×D₁₃	1	2	yes	complemented
178	C₂²×C₂²⋊C₄	—	13	8	no	—
179	C₂²×C₂²⋊C₄	C₂×D₁₃	1	2	yes	—
180	C₂²×C₄²	C₂×D₁₃	1	2	yes	complemented
181	C₂²×C₁₃	—	2	8	no	—
182	C₂²×C₁₃	—	2	48	no	—
183	C₂²×C₁₃	#535	1	16	yes	complemented
184	C₂²×C₁₃	C₂³×D₄	1	8	yes	—
185	C₂²×C₁₃	C₂³×D₄	1	6	yes	—
186	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	12	yes	—
187	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
188	C₂×D₁₃	—	2	8	no	—
189	C₂×D₁₃	—	2	16	no	—
190	C₂×D₁₃	—	2	16	no	—
191	C₂×D₁₃	—	2	32	no	—
192	C₂×D₁₃	—	4	128	no	—
193	C₂×D₁₃	—	4	48	no	—
194	C₂×D₁₃	—	4	96	no	—
195	C₄×C₁₃	—	2	16	no	—
196	C₄×C₁₃	C₂³×D₄	1	8	yes	—
197	C₄×C₁₃	C₂³×D₄	1	8	yes	—
198	Dic₁₃	—	2	8	no	—
199	C₂⁵	—	13	4	no	—
200	C₂⁵	—	13	2	no	—
201	C₂⁵	—	13	24	no	—
202	C₂⁵	—	26	16	no	—
203	C₂⁵	—	52	16	no	—
204	C₂⁵	C₂²×D₁₃	1	1	yes	characteristic
205	C₂×#41	—	13	64	no	—
206	C₂×#41	—	26	192	no	—
207	C₂²×Q₈	—	13	12	no	—
208	C₂²×Q₈	—	26	8	no	—
209	C₂²×D₄	—	13	24	no	—
210	C₂²×D₄	—	13	24	no	—
211	C₂²×D₄	—	13	24	no	—
212	C₂²×D₄	—	13	12	no	—
213	C₂²×D₄	—	13	64	no	—
214	C₂²×D₄	—	13	96	no	—
215	C₂²×D₄	—	26	16	no	—
216	C₂²×D₄	—	26	16	no	—
217	C₂²×D₄	—	26	16	no	—
218	C₂²×D₄	—	26	8	no	—
219	C₂²×D₄	—	26	192	no	—
220	C₂²×D₄	—	52	32	no	—
221	C₂³×C₄	—	13	2	no	—
222	C₂³×C₄	—	13	24	no	—
223	C₂³×C₄	—	26	16	no	—
224	C₂³×C₄	D₅₂	1	16	yes	complemented
225	C₂³×C₄	C₂²×D₁₃	1	4	yes	—
226	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
227	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
228	C₂³×C₄	C₂²×D₁₃	1	12	yes	—
229	#127	—	13	128	no	—
230	#124	—	13	128	no	—
231	#121	—	13	256	no	—
232	#120	—	13	256	no	—
233	#117	C₂²×D₁₃	1	64	yes	complemented
234	C₂×C₄⋊C₄	C₂²×D₁₃	1	24	yes	complemented
235	C₂×C₂²⋊C₄	—	13	96	no	—
236	C₂×C₂²⋊C₄	C₂²×D₁₃	1	24	yes	—
237	C₂×C₄²	C₂²×D₁₃	1	24	yes	complemented
238	C₂×C₁₃	—	2	8	no	—
239	C₂×C₁₃	C₂×#535	1	12	yes	complemented
240	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
241	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	2	yes	—
242	D₁₃	—	4	8	no	—
243	D₁₃	—	4	16	no	—
244	C₂⁴	—	2	8	no	—
245	C₂⁴	—	13	24	no	—
246	C₂⁴	—	13	12	no	—
247	C₂⁴	—	13	32	no	—
248	C₂⁴	—	26	8	no	—
249	C₂⁴	—	26	96	no	—
250	C₂⁴	—	26	16	no	—
251	C₂⁴	—	26	16	no	—
252	C₂⁴	—	26	32	no	—
253	C₂⁴	—	52	96	no	—
254	C₂⁴	—	52	128	no	—
255	C₂⁴	C₂×D₅₂	1	8	yes	—
256	C₂⁴	C₂³×D₁₃	1	6	yes	—
257	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
258	#41	—	26	256	no	—
259	C₂×Q₈	—	13	16	no	—
260	C₂×Q₈	—	26	48	no	—
261	C₂×D₄	—	13	32	no	—
262	C₂×D₄	—	13	32	no	—
263	C₂×D₄	—	13	32	no	—
264	C₂×D₄	—	13	16	no	—
265	C₂×D₄	—	13	128	no	—
266	C₂×D₄	—	26	96	no	—
267	C₂×D₄	—	26	96	no	—
268	C₂×D₄	—	26	96	no	—
269	C₂×D₄	—	26	48	no	—
270	C₂×D₄	—	26	256	no	—
271	C₂×D₄	—	52	192	no	—
272	C₂²×C₄	—	2	16	no	—
273	C₂²×C₄	—	13	12	no	—
274	C₂²×C₄	—	13	32	no	—
275	C₂²×C₄	—	26	8	no	—
276	C₂²×C₄	—	26	96	no	—
277	C₂²×C₄	C₂×D₅₂	1	8	yes	—
278	C₂²×C₄	C₂×D₅₂	1	8	yes	—
279	C₂²×C₄	C₂×D₅₂	1	96	yes	complemented
280	C₂²×C₄	C₂³×D₁₃	1	24	yes	—
281	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
282	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
283	C₂²×C₄	C₂³×D₁₃	1	16	yes	—
284	C₄⋊C₄	C₂³×D₁₃	1	32	yes	complemented
285	C₂²⋊C₄	—	13	128	no	—
286	C₂²⋊C₄	C₂³×D₁₃	1	32	yes	—
287	C₄²	C₂³×D₁₃	1	32	yes	complemented
288	C₁₃	C₂²×#535	1	1	yes	characteristic, complemented, Sylow
289	C₂³	—	2	32	no	—
290	C₂³	—	2	24	no	—
291	C₂³	—	13	16	no	—
292	C₂³	—	13	8	no	—
293	C₂³	—	26	24	no	—
294	C₂³	—	26	64	no	—
295	C₂³	—	26	48	no	—
296	C₂³	—	26	48	no	—
297	C₂³	—	26	96	no	—
298	C₂³	—	52	64	no	—
299	C₂³	—	52	384	no	—
300	C₂³	—	52	64	no	—
301	C₂³	—	52	32	no	—
302	C₂³	C₂²×D₅₂	1	24	yes	—
303	C₂³	C₂²×D₅₂	1	4	yes	—
304	C₂³	#88256	1	8	yes	—
305	C₂³	C₂⁴×D₁₃	1	4	yes	—
306	C₂³	C₂⁴×D₁₃	1	3	yes	—
307	Q₈	—	26	32	no	—
308	D₄	—	26	64	no	—
309	D₄	—	26	64	no	—
310	D₄	—	26	64	no	—
311	D₄	—	26	32	no	—
312	D₄	—	52	128	no	—
313	C₂×C₄	—	2	48	no	—
314	C₂×C₄	—	13	8	no	—
315	C₂×C₄	—	26	24	no	—
316	C₂×C₄	—	26	64	no	—
317	C₂×C₄	C₂²×D₅₂	1	24	yes	—
318	C₂×C₄	C₂²×D₅₂	1	24	yes	—
319	C₂×C₄	C₂²×D₅₂	1	64	yes	complemented
320	C₂×C₄	C₂⁴×D₁₃	1	16	yes	—
321	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
322	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
323	C₂²	—	2	8	no	—
324	C₂²	—	2	48	no	—
325	C₂²	—	26	8	no	—
326	C₂²	—	26	16	no	—
327	C₂²	—	26	16	no	—
328	C₂²	—	26	32	no	—
329	C₂²	—	52	128	no	—
330	C₂²	—	52	48	no	—
331	C₂²	—	52	96	no	—
332	C₂²	#11719230	1	16	yes	direct product factor
333	C₂²	C₂³×D₅₂	1	8	yes	—
334	C₂²	C₂³×D₅₂	1	6	yes	—
335	C₂²	C₂×#88256	1	12	yes	—
336	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
337	C₄	—	2	16	no	—
338	C₄	—	26	8	no	—
339	C₄	C₂³×D₅₂	1	8	yes	—
340	C₄	C₂³×D₅₂	1	8	yes	—
341	C₂	—	2	8	no	—
342	C₂	—	52	16	no	—
343	C₂	—	52	8	no	—
344	C₂	C₂×#11719230	1	12	yes	direct product factor
345	C₂	C₂⁴×D₅₂	1	1	yes	characteristic
346	C₂	C₂²×#88256	1	2	yes	—

	subgroup	G/H
center	C₂⁴	C₂³×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂²×C₁₃×#117	C₂
socle	C₂⁴×C₁₃	C₂⁴
hypercenter	C₂²×#117	D₁₃
hypocenter	C₁₃	C₂²×#535
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂⁴ ◁ C₂²×#117

Complements

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

N	H ≅ G/N	type
1. C₂³×#6127	C₂	semidirect
2. C₂⁴×D₅₂	C₂	semidirect
3. C₂×#11719230	C₂	direct (N × H)
4. C₂²×#88128	C₂	semidirect
5. C₂²×#88129	C₂	semidirect
6. C₂²×#88149	C₂	semidirect
7. C₂²×#88136	C₂	semidirect
8. C₂²×C₁₃×#117	C₂	semidirect
13. C₂²×#6127	C₂²	semidirect
17. C₂³×D₅₂	C₂²	semidirect
18. C₂³×D₅₂	C₂²	semidirect
19. C₂³×D₅₂	C₂²	semidirect
20. C₂³×C₄×D₁₃	C₂²	semidirect
21. C₂³×Dic₂₆	C₂²	semidirect
22. C₂×C₁₃×#117	C₂²	semidirect
23. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
25. C₂²×C₄²×C₁₃	C₂²	semidirect
26. C₂²×#6103	C₂²	semidirect
27. #11719230	C₂²	direct (N × H)
28. C₂×#88149	C₂²	semidirect
29. C₂×#88136	C₂²	semidirect
30. C₂×#88129	C₂²	semidirect
31. C₂×#88128	C₂²	semidirect
38. C₂³×C₄×C₁₃	D₄	semidirect
47. C₂×#6127	C₂³	semidirect
55. C₂²×D₅₂	C₂³	semidirect
56. C₂²×D₅₂	C₂³	semidirect
57. C₂²×D₅₂	C₂³	semidirect
59. C₂²×C₄×D₁₃	C₂³	semidirect
61. C₂²×Dic₂₆	C₂³	semidirect
62. C₁₃×#117	C₂³	semidirect
63. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
65. C₂×C₄²×C₁₃	C₂³	semidirect
66. C₂×#6103	C₂³	semidirect
67. #88149	C₂³	semidirect
68. #88136	C₂³	semidirect
69. #88129	C₂³	semidirect
70. #88128	C₂³	semidirect
89. C₂²×C₄×C₁₃	C₂×D₄	semidirect
106. C₂×D₅₂	C₂⁴	semidirect
107. C₂×D₅₂	C₂⁴	semidirect
109. C₂×C₄×D₁₃	C₂⁴	semidirect
111. C₂×Dic₂₆	C₂⁴	semidirect
112. C₁₃×C₄⋊C₄	C₂⁴	semidirect
114. C₄²×C₁₃	C₂⁴	semidirect
115. #6103	C₂⁴	semidirect
123. C₂²×#117	D₁₃	semidirect
145. C₂×C₄×C₁₃	C₂²×D₄	semidirect
176. C₂×#117	C₂×D₁₃	semidirect
177. C₂²×C₄⋊C₄	C₂×D₁₃	semidirect
180. C₂²×C₄²	C₂×D₁₃	semidirect
183. C₂²×C₁₃	#535	semidirect
224. C₂³×C₄	D₅₂	semidirect
233. #117	C₂²×D₁₃	semidirect
234. C₂×C₄⋊C₄	C₂²×D₁₃	semidirect
237. C₂×C₄²	C₂²×D₁₃	semidirect
239. C₂×C₁₃	C₂×#535	semidirect
279. C₂²×C₄	C₂×D₅₂	semidirect
284. C₄⋊C₄	C₂³×D₁₃	semidirect
287. C₄²	C₂³×D₁₃	semidirect
288. C₁₃	C₂²×#535	semidirect
319. C₂×C₄	C₂²×D₅₂	semidirect
332. C₂²	#11719230	direct (N × H)
344. C₂	C₂×#11719230	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×#6127	2
C₂⁴×D₅₂	2
C₂×#11719230	2
C₂²×#88128	2
C₂²×#88129	2
C₂²×#88149	2
C₂²×#88136	2
C₂²×C₁₃×#117	2
C₂²×#535	13

Subgroups — C22×#11719230 #16769677

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#11719230 #16769677