Subgroups — C₂²×C₄×#6127 #16769493

Order 3328.

12878 conjugacy classes of subgroups.

The subgroup lattice has 342 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
2	C₂×C₄×#6127	C₂	1	48	yes	maximal, direct product factor
3	C₂²×C₄×Dic₂₆	C₂	1	2	yes	maximal, complemented
4	C₂²×C₄×D₅₂	C₂	1	2	yes	maximal, complemented
5	C₂²×C₄×C₂²⋊D₁₃	C₂	1	4	yes	maximal, complemented
6	C₂²×#88180	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#88126	C₂	1	2	yes	maximal, complemented
8	C₂²×C₄²×D₁₃	C₂	1	2	yes	maximal, complemented
9	C₂³×C₄²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
11	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
12	C₂³×C₂²⋊D₁₃	C₂²	1	2	yes	—
13	C₂²×#6127	C₄	1	32	yes	direct product factor
14	C₂²×#6127	C₂²	1	24	yes	—
15	C₂³×D₅₂	C₂²	1	1	yes	characteristic
16	C₂³×C₄×D₁₃	C₂²	1	4	yes	—
17	C₂³×C₄×D₁₃	C₂²	1	2	yes	—
18	C₂³×Dic₂₆	C₂²	1	1	yes	characteristic
19	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
20	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
21	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₁₃	C₂²	1	24	yes	complemented
23	C₂²×C₂²⋊Dic₁₃	C₂²	1	2	yes	—
24	C₂×C₄×C₂²⋊D₁₃	C₂²	1	96	yes	complemented
25	C₂²×#6103	C₂²	1	4	yes	—
26	C₂×#88180	C₂²	1	24	yes	complemented
27	C₂²×C₄⋊Dic₁₃	C₂²	1	2	yes	—
28	C₂²×#6101	C₂²	1	4	yes	—
29	C₂²×C₄×Dic₁₃	C₂²	1	2	yes	—
30	C₂²×C₄×Dic₁₃	C₂²	1	4	yes	—
31	C₄×#6127	C₂²	1	256	yes	direct product factor
32	C₂×C₄×D₅₂	C₂²	1	48	yes	complemented
33	C₂×#88126	C₂²	1	48	yes	complemented
34	C₂×C₄²×D₁₃	C₂²	1	48	yes	complemented
35	C₂×C₄×Dic₂₆	C₂²	1	48	yes	complemented
36	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
37	C₂⁴×D₁₃	C₂³	1	2	yes	—
38	C₂³×C₄×C₁₃	—	2	16	no	—
39	C₂³×C₄×C₁₃	C₂×C₄	1	16	yes	complemented
40	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
41	C₂³×C₄×C₁₃	C₂³	1	24	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	12	yes	—
45	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
46	C₂²×C₂²⋊D₁₃	C₂×C₄	1	32	yes	complemented
47	C₂²×C₂²⋊D₁₃	C₂³	1	24	yes	—
48	C₂³×Dic₁₃	C₂³	1	4	yes	—
49	C₂³×Dic₁₃	C₂³	1	2	yes	—
50	C₂×#6127	C₂×C₄	1	384	yes	direct product factor
51	C₂×#6127	C₂³	1	64	yes	—
52	C₂²×D₅₂	C₂×C₄	1	16	yes	complemented
53	C₂²×D₅₂	C₂³	1	12	yes	—
54	C₂²×C₄×D₁₃	—	2	32	no	—
55	C₂²×C₄×D₁₃	C₂×C₄	1	32	yes	complemented
56	C₂²×C₄×D₁₃	C₂³	1	48	yes	—
57	C₂²×C₄×D₁₃	C₂³	1	24	yes	—
58	C₂²×Dic₂₆	C₂×C₄	1	16	yes	complemented
59	C₂²×Dic₂₆	C₂³	1	12	yes	—
60	C₂×C₄²×C₁₃	C₂³	1	24	yes	—
61	C₂×C₄²×C₁₃	C₂³	1	12	yes	—
62	C₂×C₄²×C₁₃	C₂³	1	12	yes	—
63	C₂×C₄²×C₁₃	C₂³	1	64	yes	complemented
64	C₂×C₂²⋊Dic₁₃	C₂³	1	24	yes	—
65	C₄×C₂²⋊D₁₃	C₂³	1	256	yes	complemented
66	C₂×#6103	C₂³	1	48	yes	—
67	#88180	C₂³	1	64	yes	complemented
68	C₂×C₄⋊Dic₁₃	C₂³	1	24	yes	—
69	C₂×#6101	C₂³	1	48	yes	—
70	C₂×C₄×Dic₁₃	C₂³	1	48	yes	—
71	C₂×C₄×Dic₁₃	C₂³	1	24	yes	—
72	C₄×D₅₂	C₂³	1	128	yes	complemented
73	#88126	C₂³	1	128	yes	complemented
74	C₄²×D₁₃	C₂³	1	128	yes	complemented
75	C₄×Dic₂₆	C₂³	1	128	yes	complemented
76	C₂²×C₄×#41	—	13	1	no	maximal, Sylow
77	C₂⁴×C₁₃	—	2	8	no	—
78	C₂⁴×C₁₃	C₂²×C₄	1	8	yes	—
79	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
80	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
81	C₂³×D₁₃	—	2	16	no	—
82	C₂³×D₁₃	C₂²×C₄	1	16	yes	—
83	C₂³×D₁₃	C₂⁴	1	12	yes	—
84	C₂²×C₄×C₁₃	—	2	8	no	—
85	C₂²×C₄×C₁₃	—	2	96	no	—
86	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
87	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
88	C₂²×C₄×C₁₃	C₂²×C₄	1	96	yes	complemented
89	C₂²×C₄×C₁₃	#41	1	16	yes	complemented
90	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
91	C₂²×C₄×C₁₃	C₂⁴	1	32	yes	—
92	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
93	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
94	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
95	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
96	C₂×C₂²⋊D₁₃	C₂²×C₄	1	192	yes	complemented
97	C₂×C₂²⋊D₁₃	C₂⁴	1	32	yes	—
98	C₂²×Dic₁₃	—	2	16	no	—
99	C₂²×Dic₁₃	C₂²×C₄	1	16	yes	—
100	C₂²×Dic₁₃	C₂⁴	1	24	yes	—
101	C₂²×Dic₁₃	C₂⁴	1	12	yes	—
102	#6127	C₂²×C₄	1	512	yes	direct product factor
103	C₂×D₅₂	C₂²×C₄	1	96	yes	complemented
104	C₂×D₅₂	C₂⁴	1	16	yes	—
105	C₂×C₄×D₁₃	—	2	192	no	—
106	C₂×C₄×D₁₃	C₂²×C₄	1	192	yes	complemented
107	C₂×C₄×D₁₃	C₂⁴	1	64	yes	—
108	C₂×C₄×D₁₃	C₂⁴	1	32	yes	—
109	C₂×Dic₂₆	C₂²×C₄	1	96	yes	complemented
110	C₂×Dic₂₆	C₂⁴	1	16	yes	—
111	C₄²×C₁₃	C₂⁴	1	32	yes	—
112	C₄²×C₁₃	C₂⁴	1	16	yes	—
113	C₄²×C₁₃	C₂⁴	1	16	yes	—
114	C₂²⋊Dic₁₃	C₂⁴	1	32	yes	—
115	#6103	C₂⁴	1	64	yes	—
116	C₄⋊Dic₁₃	C₂⁴	1	32	yes	—
117	#6101	C₂⁴	1	64	yes	—
118	C₄×Dic₁₃	C₂⁴	1	64	yes	—
119	C₄×Dic₁₃	C₂⁴	1	32	yes	—
120	C₂³×#41	—	13	1	no	—
121	C₂×C₄×#41	—	13	48	no	—
122	C₂²×C₄×Q₈	—	13	2	no	—
123	C₂²×C₄×D₄	—	13	2	no	—
124	C₂²×C₄×D₄	—	13	4	no	—
125	C₂²×#117	—	13	2	no	—
126	C₂²×#117	—	13	1	no	—
127	C₂³×C₄²	—	13	2	no	—
128	C₂³×C₄²	D₁₃	1	1	yes	characteristic, complemented
129	C₂³×C₁₃	—	2	32	no	—
130	C₂³×C₁₃	—	2	24	no	—
131	C₂³×C₁₃	C₂³×C₄	1	24	yes	—
132	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
133	C₂³×C₁₃	C₂×#41	1	8	yes	—
134	C₂³×C₁₃	C₂⁵	1	4	yes	—
135	C₂³×C₁₃	C₂⁵	1	3	yes	—
136	C₂²×D₁₃	—	2	64	no	—
137	C₂²×D₁₃	—	2	48	no	—
138	C₂²×D₁₃	C₂³×C₄	1	48	yes	—
139	C₂²×D₁₃	C₂⁵	1	8	yes	—
140	C₂×C₄×C₁₃	—	2	24	no	—
141	C₂×C₄×C₁₃	—	2	64	no	—
142	C₂×C₄×C₁₃	C₂³×C₄	1	24	yes	—
143	C₂×C₄×C₁₃	C₂³×C₄	1	24	yes	—
144	C₂×C₄×C₁₃	C₂³×C₄	1	64	yes	complemented
145	C₂×C₄×C₁₃	C₂×#41	1	48	yes	complemented
146	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
147	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
148	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
149	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
150	C₂²⋊D₁₃	C₂³×C₄	1	128	yes	complemented
151	C₂×Dic₁₃	—	2	48	no	—
152	C₂×Dic₁₃	C₂³×C₄	1	48	yes	—
153	C₂×Dic₁₃	C₂⁵	1	16	yes	—
154	C₂×Dic₁₃	C₂⁵	1	8	yes	—
155	D₅₂	C₂³×C₄	1	64	yes	complemented
156	C₄×D₁₃	—	2	128	no	—
157	C₄×D₁₃	C₂³×C₄	1	128	yes	complemented
158	Dic₂₆	C₂³×C₄	1	64	yes	complemented
159	C₂²×#41	—	13	32	no	—
160	C₂²×#41	—	13	24	no	—
161	C₂³×Q₈	—	13	1	no	—
162	C₂³×D₄	—	13	2	no	—
163	C₂³×D₄	—	13	1	no	—
164	C₂⁴×C₄	—	13	2	no	—
165	C₂⁴×C₄	—	13	4	no	—
166	C₂⁴×C₄	C₂×D₁₃	1	2	yes	—
167	C₂⁴×C₄	C₂×D₁₃	1	1	yes	characteristic
168	C₄×#41	—	13	256	no	—
169	C₂×C₄×Q₈	—	13	48	no	—
170	C₂×C₄×D₄	—	13	96	no	—
171	C₂×C₄×D₄	—	13	48	no	—
172	C₂×#117	—	13	24	no	—
173	C₂×#117	—	13	48	no	—
174	C₂²×C₄⋊C₄	—	13	4	no	—
175	C₂²×C₄⋊C₄	—	13	2	no	—
176	C₂²×C₂²⋊C₄	—	13	2	no	—
177	C₂²×C₂²⋊C₄	—	13	4	no	—
178	C₂²×C₄²	—	13	2	no	—
179	C₂²×C₄²	—	13	4	no	—
180	C₂²×C₄²	—	13	48	no	—
181	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
182	C₂²×C₄²	C₂×D₁₃	1	2	yes	—
183	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
184	C₂²×C₄²	C₂×D₁₃	1	24	yes	complemented
185	C₂²×C₁₃	—	2	8	no	—
186	C₂²×C₁₃	—	2	48	no	—
187	C₂²×C₁₃	C₄×#41	1	16	yes	complemented
188	C₂²×C₁₃	C₂⁴×C₄	1	8	yes	—
189	C₂²×C₁₃	C₂⁴×C₄	1	6	yes	—
190	C₂²×C₁₃	C₂²×#41	1	12	yes	—
191	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
192	C₂×D₁₃	—	2	16	no	—
193	C₂×D₁₃	—	2	96	no	—
194	C₂×D₁₃	C₂⁴×C₄	1	16	yes	—
195	C₄×C₁₃	—	2	8	no	—
196	C₄×C₁₃	C₂⁴×C₄	1	8	yes	—
197	C₄×C₁₃	C₂⁴×C₄	1	8	yes	—
198	C₄×C₁₃	C₂²×#41	1	16	yes	complemented
199	Dic₁₃	—	2	16	no	—
200	Dic₁₃	C₂⁴×C₄	1	16	yes	—
201	C₂⁵	—	13	2	no	—
202	C₂⁵	C₂²×D₁₃	1	1	yes	characteristic
203	C₂×#41	—	13	384	no	—
204	C₂×#41	—	13	64	no	—
205	C₂²×Q₈	—	13	16	no	—
206	C₂²×Q₈	—	13	12	no	—
207	C₂²×D₄	—	13	32	no	—
208	C₂²×D₄	—	13	24	no	—
209	C₂²×D₄	—	13	16	no	—
210	C₂²×D₄	—	13	12	no	—
211	C₂³×C₄	—	2	16	no	—
212	C₂³×C₄	—	13	2	no	—
213	C₂³×C₄	—	13	32	no	—
214	C₂³×C₄	—	13	24	no	—
215	C₂³×C₄	—	13	4	no	—
216	C₂³×C₄	—	13	48	no	—
217	C₂³×C₄	—	26	32	no	—
218	C₂³×C₄	C₄×D₁₃	1	16	yes	complemented
219	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
220	C₂³×C₄	C₂²×D₁₃	1	24	yes	—
221	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
222	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
223	C₂³×C₄	C₂²×D₁₃	1	12	yes	—
224	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
225	C₄×Q₈	—	13	128	no	—
226	C₄×D₄	—	13	256	no	—
227	C₄×D₄	—	13	128	no	—
228	#117	—	13	64	no	—
229	#117	—	13	128	no	—
230	C₂×C₄⋊C₄	—	13	48	no	—
231	C₂×C₄⋊C₄	—	13	24	no	—
232	C₂×C₂²⋊C₄	—	13	24	no	—
233	C₂×C₂²⋊C₄	—	13	48	no	—
234	C₂×C₄²	—	13	24	no	—
235	C₂×C₄²	—	13	48	no	—
236	C₂×C₄²	—	13	128	no	—
237	C₂×C₄²	C₂²×D₁₃	1	12	yes	—
238	C₂×C₄²	C₂²×D₁₃	1	24	yes	—
239	C₂×C₄²	C₂²×D₁₃	1	12	yes	—
240	C₂×C₄²	C₂²×D₁₃	1	64	yes	complemented
241	C₂×C₁₃	—	2	8	no	—
242	C₂×C₁₃	C₂×C₄×#41	1	12	yes	complemented
243	C₂×C₁₃	C₂⁵×C₄	1	1	yes	characteristic
244	C₂×C₁₃	C₂³×#41	1	2	yes	—
245	D₁₃	—	2	16	no	—
246	C₂⁴	—	2	8	no	—
247	C₂⁴	—	13	16	no	—
248	C₂⁴	—	13	12	no	—
249	C₂⁴	—	26	16	no	—
250	C₂⁴	C₂×C₄×D₁₃	1	8	yes	—
251	C₂⁴	C₂³×D₁₃	1	6	yes	—
252	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
253	#41	—	13	512	no	—
254	C₂×Q₈	—	13	96	no	—
255	C₂×Q₈	—	13	16	no	—
256	C₂×D₄	—	13	192	no	—
257	C₂×D₄	—	13	32	no	—
258	C₂×D₄	—	13	96	no	—
259	C₂×D₄	—	13	16	no	—
260	C₂²×C₄	—	2	8	no	—
261	C₂²×C₄	—	2	96	no	—
262	C₂²×C₄	—	13	16	no	—
263	C₂²×C₄	—	13	12	no	—
264	C₂²×C₄	—	13	192	no	—
265	C₂²×C₄	—	13	32	no	—
266	C₂²×C₄	—	13	24	no	—
267	C₂²×C₄	—	13	64	no	—
268	C₂²×C₄	—	26	16	no	—
269	C₂²×C₄	—	26	192	no	—
270	C₂²×C₄	C₂×C₄×D₁₃	1	8	yes	—
271	C₂²×C₄	C₂×C₄×D₁₃	1	8	yes	—
272	C₂²×C₄	C₂×C₄×D₁₃	1	96	yes	complemented
273	C₂²×C₄	#6127	1	16	yes	direct product factor
274	C₂²×C₄	C₂³×D₁₃	1	12	yes	—
275	C₂²×C₄	C₂³×D₁₃	1	32	yes	—
276	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
277	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
278	C₂²×C₄	C₂³×D₁₃	1	16	yes	—
279	C₂²×C₄	C₂³×D₁₃	1	12	yes	—
280	C₄⋊C₄	—	13	64	no	—
281	C₄⋊C₄	—	13	32	no	—
282	C₂²⋊C₄	—	13	32	no	—
283	C₂²⋊C₄	—	13	64	no	—
284	C₄²	—	13	32	no	—
285	C₄²	—	13	64	no	—
286	C₄²	C₂³×D₁₃	1	16	yes	—
287	C₄²	C₂³×D₁₃	1	16	yes	—
288	C₄²	C₂³×D₁₃	1	32	yes	—
289	C₁₃	C₂²×C₄×#41	1	1	yes	characteristic, complemented, Sylow
290	C₂³	—	2	32	no	—
291	C₂³	—	2	24	no	—
292	C₂³	—	13	48	no	—
293	C₂³	—	13	8	no	—
294	C₂³	—	26	64	no	—
295	C₂³	—	26	48	no	—
296	C₂³	C₂²×C₄×D₁₃	1	24	yes	—
297	C₂³	C₂²×C₄×D₁₃	1	4	yes	—
298	C₂³	C₂×#6127	1	8	yes	—
299	C₂³	C₂⁴×D₁₃	1	4	yes	—
300	C₂³	C₂⁴×D₁₃	1	3	yes	—
301	Q₈	—	13	64	no	—
302	D₄	—	13	128	no	—
303	D₄	—	13	64	no	—
304	C₂×C₄	—	2	24	no	—
305	C₂×C₄	—	2	64	no	—
306	C₂×C₄	—	13	48	no	—
307	C₂×C₄	—	13	8	no	—
308	C₂×C₄	—	13	128	no	—
309	C₂×C₄	—	13	16	no	—
310	C₂×C₄	—	26	48	no	—
311	C₂×C₄	—	26	128	no	—
312	C₂×C₄	C₂²×C₄×D₁₃	1	24	yes	—
313	C₂×C₄	C₂²×C₄×D₁₃	1	24	yes	—
314	C₂×C₄	C₂²×C₄×D₁₃	1	64	yes	complemented
315	C₂×C₄	C₂×#6127	1	48	yes	direct product factor
316	C₂×C₄	C₂⁴×D₁₃	1	8	yes	—
317	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
318	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
319	C₂×C₄	C₂⁴×D₁₃	1	8	yes	—
320	C₂²	—	2	48	no	—
321	C₂²	—	2	8	no	—
322	C₂²	—	13	16	no	—
323	C₂²	—	26	96	no	—
324	C₂²	—	26	16	no	—
325	C₂²	C₄×#6127	1	16	yes	direct product factor
326	C₂²	C₂³×C₄×D₁₃	1	8	yes	—
327	C₂²	C₂³×C₄×D₁₃	1	6	yes	—
328	C₂²	C₂²×#6127	1	12	yes	—
329	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
330	C₄	—	2	8	no	—
331	C₄	—	13	16	no	—
332	C₄	—	26	16	no	—
333	C₄	C₂³×C₄×D₁₃	1	8	yes	—
334	C₄	C₂³×C₄×D₁₃	1	8	yes	—
335	C₄	C₂²×#6127	1	16	yes	direct product factor
336	C₂	—	2	8	no	—
337	C₂	—	26	16	no	—
338	C₂	C₂×C₄×#6127	1	12	yes	direct product factor
339	C₂	C₂⁴×C₄×D₁₃	1	1	yes	characteristic
340	C₂	C₂³×#6127	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄²	C₂×D₁₃
commutator	C₂×C₁₃	C₂⁵×C₄
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂³×C₄²×C₁₃	C₂
socle	C₂⁴×C₁₃	C₂⁴
prime radical	C₂³×#6127	C₂
cosocle	C₂²×C₁₃	C₂⁶
hypercenter	C₂³×C₄²	D₁₃
hypocenter	C₁₃	C₂²×C₄×#41
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄² ◁ C₂³×C₄²

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×#6127	C₂	direct (N × H)
3. C₂²×C₄×Dic₂₆	C₂	semidirect
4. C₂²×C₄×D₅₂	C₂	semidirect
5. C₂²×C₄×C₂²⋊D₁₃	C₂	semidirect
6. C₂²×#88180	C₂	semidirect
7. C₂²×#88126	C₂	semidirect
8. C₂²×C₄²×D₁₃	C₂	semidirect
9. C₂³×C₄²×C₁₃	C₂	semidirect
13. C₂²×#6127	C₄	direct (N × H)
22. C₂²×C₄²×C₁₃	C₂²	semidirect
24. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
26. C₂×#88180	C₂²	semidirect
31. C₄×#6127	C₂²	direct (N × H)
32. C₂×C₄×D₅₂	C₂²	semidirect
33. C₂×#88126	C₂²	semidirect
34. C₂×C₄²×D₁₃	C₂²	semidirect
35. C₂×C₄×Dic₂₆	C₂²	semidirect
39. C₂³×C₄×C₁₃	C₂×C₄	semidirect
46. C₂²×C₂²⋊D₁₃	C₂×C₄	semidirect
50. C₂×#6127	C₂×C₄	direct (N × H)
52. C₂²×D₅₂	C₂×C₄	semidirect
55. C₂²×C₄×D₁₃	C₂×C₄	semidirect
58. C₂²×Dic₂₆	C₂×C₄	semidirect
63. C₂×C₄²×C₁₃	C₂³	semidirect
65. C₄×C₂²⋊D₁₃	C₂³	semidirect
67. #88180	C₂³	semidirect
72. C₄×D₅₂	C₂³	semidirect
73. #88126	C₂³	semidirect
74. C₄²×D₁₃	C₂³	semidirect
75. C₄×Dic₂₆	C₂³	semidirect
88. C₂²×C₄×C₁₃	C₂²×C₄	semidirect
89. C₂²×C₄×C₁₃	#41	semidirect
96. C₂×C₂²⋊D₁₃	C₂²×C₄	semidirect
102. #6127	C₂²×C₄	direct (N × H)
103. C₂×D₅₂	C₂²×C₄	semidirect
106. C₂×C₄×D₁₃	C₂²×C₄	semidirect
109. C₂×Dic₂₆	C₂²×C₄	semidirect
128. C₂³×C₄²	D₁₃	semidirect
144. C₂×C₄×C₁₃	C₂³×C₄	semidirect
145. C₂×C₄×C₁₃	C₂×#41	semidirect
150. C₂²⋊D₁₃	C₂³×C₄	semidirect
155. D₅₂	C₂³×C₄	semidirect
157. C₄×D₁₃	C₂³×C₄	semidirect
158. Dic₂₆	C₂³×C₄	semidirect
184. C₂²×C₄²	C₂×D₁₃	semidirect
187. C₂²×C₁₃	C₄×#41	semidirect
198. C₄×C₁₃	C₂²×#41	semidirect
218. C₂³×C₄	C₄×D₁₃	semidirect
240. C₂×C₄²	C₂²×D₁₃	semidirect
242. C₂×C₁₃	C₂×C₄×#41	semidirect
272. C₂²×C₄	C₂×C₄×D₁₃	semidirect
273. C₂²×C₄	#6127	direct (N × H)
289. C₁₃	C₂²×C₄×#41	semidirect
314. C₂×C₄	C₂²×C₄×D₁₃	semidirect
315. C₂×C₄	C₂×#6127	direct (N × H)
325. C₂²	C₄×#6127	direct (N × H)
335. C₄	C₂²×#6127	direct (N × H)
338. C₂	C₂×C₄×#6127	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
C₂×C₄×#6127	2
C₂²×C₄×Dic₂₆	2
C₂²×C₄×D₅₂	2
C₂²×C₄×C₂²⋊D₁₃	2
C₂²×#88180	2
C₂²×#88126	2
C₂²×C₄²×D₁₃	2
C₂³×C₄²×C₁₃	2
C₂²×C₄×#41	13

Subgroups — C22×C4×#6127 #16769493

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄×#6127 #16769493