Subgroups — C₂×#13115555 #15866185

Order 3328.

1246 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	C₂²×C₄⋊#1055	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄⋊#1055	C₂	1	2	yes	maximal
3	C₂²×C₄×#1055	C₂	1	1	yes	maximal, characteristic
4	#13115555	C₂	1	8	yes	maximal, direct product factor
5	C₂×#11718116	C₂	1	2	yes	maximal
6	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₁₃×C₄⋊C₄	C₄	1	1	yes	characteristic
8	C₂²×C₁₃×C₄⋊C₄	C₄	1	1	yes	characteristic
9	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
10	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
11	C₂³×#1055	C₂²	1	2	yes	—
12	C₂³×#1055	C₂²	1	1	yes	characteristic
13	C₂³×#1055	C₂²	1	1	yes	characteristic
14	C₄×C₁₃×C₄⋊C₄	C₄	1	4	yes	—
15	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
16	C₂×C₁₃×#95	C₄	1	2	yes	—
17	C₂×C₄⋊#1055	—	2	4	no	—
18	C₂×C₄⋊#1055	—	2	8	no	—
19	C₂×C₄⋊#1055	C₂²	1	4	yes	—
20	C₂×C₄⋊#1055	C₂²	1	8	yes	—
21	C₂×C₄×#1055	—	2	4	no	—
22	C₂×C₄×#1055	C₂²	1	4	yes	—
23	#11718116	C₂²	1	8	yes	—
24	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
25	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
27	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
29	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
30	C₂×C₁₃×C₄⋊C₄	C₈	1	8	yes	complemented
31	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
32	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
33	C₂×C₄²×C₁₃	—	2	4	no	—
34	C₂×C₄²×C₁₃	—	2	4	no	—
35	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
36	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
37	C₂×C₄²×C₁₃	D₄	1	4	yes	—
38	C₂×C₄²×C₁₃	Q₈	1	4	yes	—
39	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
40	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
41	C₂²×#1055	—	2	2	no	—
42	C₂²×#1055	—	2	2	no	—
43	C₂²×#1055	—	2	2	no	—
44	C₂²×#1055	—	2	2	no	—
45	C₂²×#1055	—	2	4	no	—
46	C₂²×#1055	—	2	4	no	—
47	C₂²×#1055	—	2	4	no	—
48	C₂²×#1055	D₄	1	4	yes	—
49	C₂²×#1055	Q₈	1	4	yes	—
50	C₂²×#1055	C₂³	1	4	yes	—
51	C₂²×#1055	C₂³	1	2	yes	—
52	C₂²×#1055	C₂³	1	2	yes	—
53	C₁₃×#95	C₂×C₄	1	8	yes	—
54	C₄⋊#1055	—	2	8	no	—
55	C₄⋊#1055	—	2	16	no	—
56	C₄×#1055	—	2	8	no	—
57	C₂×#1939	—	13	1	no	maximal, Sylow
58	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₃	—	2	4	no	—
60	C₂²×C₄×C₁₃	—	2	2	no	—
61	C₂²×C₄×C₁₃	—	2	2	no	—
62	C₂²×C₄×C₁₃	—	2	4	no	—
63	C₂²×C₄×C₁₃	—	2	4	no	—
64	C₂²×C₄×C₁₃	—	2	4	no	—
65	C₂²×C₄×C₁₃	—	2	4	no	—
66	C₂²×C₄×C₁₃	C₄⋊C₄	1	4	yes	—
67	C₂²×C₄×C₁₃	C₄⋊C₄	1	4	yes	—
68	C₂²×C₄×C₁₃	C₂×C₈	1	8	yes	—
69	C₂²×C₄×C₁₃	C₂×C₈	1	4	yes	—
70	C₂²×C₄×C₁₃	M₁₆	1	4	yes	—
71	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
72	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
73	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
74	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
76	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
77	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
78	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
79	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
80	C₂²×C₄×C₁₃	#41	1	2	yes	—
81	C₂²×C₄×C₁₃	#41	1	2	yes	—
82	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
83	C₁₃×C₄⋊C₄	—	2	8	no	—
84	C₁₃×C₄⋊C₄	C₂×C₈	1	16	yes	complemented
85	C₄²×C₁₃	—	2	8	no	—
86	C₄²×C₁₃	—	2	4	no	—
87	C₄²×C₁₃	—	2	4	no	—
88	C₄²×C₁₃	C₄⋊C₄	1	8	yes	—
89	C₄²×C₁₃	C₂×D₄	1	4	yes	—
90	C₄²×C₁₃	C₂×Q₈	1	4	yes	—
91	C₂×#1055	—	2	8	no	—
92	C₂×#1055	—	2	8	no	—
93	C₂×#1055	—	2	2	no	—
94	C₂×#1055	—	2	2	no	—
95	C₂×#1055	—	2	2	no	—
96	C₂×#1055	—	2	2	no	—
97	C₂×#1055	—	2	4	no	—
98	C₂×#1055	—	2	4	no	—
99	C₂×#1055	—	2	4	no	—
100	C₂×#1055	—	4	8	no	—
101	C₂×#1055	C₂×D₄	1	4	yes	—
102	C₂×#1055	C₂×Q₈	1	4	yes	—
103	C₂²×C₄⋊C₈	—	13	2	no	—
104	C₂²×C₄⋊C₈	—	13	1	no	—
105	C₂²×C₄×C₈	—	13	1	no	—
106	C₂×C₄×C₄⋊C₄	D₁₃	1	1	yes	characteristic
107	#1939	—	13	8	no	—
108	C₂×#336	—	13	2	no	—
109	C₂³×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
110	C₂³×C₁₃	C₄×D₄	1	2	yes	—
111	C₂³×C₁₃	C₄×Q₈	1	2	yes	—
112	C₂³×C₁₃	C₂²×C₈	1	2	yes	—
113	C₂³×C₁₃	C₂×M₁₆	1	2	yes	—
114	C₂³×C₁₃	#131	1	2	yes	—
115	C₂³×C₁₃	#131	1	2	yes	—
116	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
117	C₂×C₄×C₁₃	—	2	4	no	—
118	C₂×C₄×C₁₃	—	2	2	no	—
119	C₂×C₄×C₁₃	—	2	2	no	—
120	C₂×C₄×C₁₃	—	2	4	no	—
121	C₂×C₄×C₁₃	—	2	8	no	—
122	C₂×C₄×C₁₃	—	2	16	no	—
123	C₂×C₄×C₁₃	—	2	4	no	—
124	C₂×C₄×C₁₃	—	2	4	no	—
125	C₂×C₄×C₁₃	—	2	4	no	—
126	C₂×C₄×C₁₃	—	4	8	no	—
127	C₂×C₄×C₁₃	C₄⋊C₈	1	16	yes	complemented
128	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
129	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
130	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
131	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
132	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
133	C₂×C₄×C₁₃	#121	1	4	yes	—
134	C₂×C₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
135	C₂×C₄×C₁₃	#125	1	4	yes	—
136	C₂×C₄×C₁₃	C₄⋊Q₈	1	4	yes	—
137	C₂×C₄×C₁₃	C₂²×C₈	1	8	yes	—
138	C₂×C₄×C₁₃	C₂²×C₈	1	4	yes	—
139	C₂×C₄×C₁₃	C₂×M₁₆	1	4	yes	—
140	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
141	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
142	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
143	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
144	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
145	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
146	#1055	—	2	4	no	—
147	#1055	—	2	4	no	—
148	#1055	—	4	4	no	—
149	C₂³×C₈	—	13	1	no	—
150	C₂³×C₈	—	13	1	no	—
151	C₂³×C₈	—	13	2	no	—
152	C₂²×C₄⋊C₄	Dic₁₃	1	1	yes	characteristic
153	C₂²×C₄⋊C₄	Dic₁₃	1	1	yes	characteristic
154	C₂²×C₄²	C₂×D₁₃	1	2	yes	—
155	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
156	C₂×C₄⋊C₈	—	13	8	no	—
157	C₂×C₄⋊C₈	—	13	4	no	—
158	C₂×C₄⋊C₈	—	26	8	no	—
159	C₂×C₄⋊C₈	—	26	4	no	—
160	C₂×C₄×C₈	—	13	4	no	—
161	C₂×C₄×C₈	—	26	4	no	—
162	C₄×C₄⋊C₄	Dic₁₃	1	4	yes	—
163	C₄×C₄⋊C₄	C₂×D₁₃	1	4	yes	—
164	C₂×#95	Dic₁₃	1	2	yes	—
165	#336	—	13	8	no	—
166	C₂²×C₁₃	#389	1	4	yes	—
167	C₂²×C₁₃	C₂×C₄⋊C₈	1	4	yes	—
168	C₂²×C₁₃	#424	1	4	yes	—
169	C₂²×C₁₃	C₈×D₄	1	4	yes	—
170	C₂²×C₁₃	#436	1	4	yes	—
171	C₂²×C₁₃	C₈×Q₈	1	4	yes	—
172	C₂²×C₁₃	#446	1	4	yes	—
173	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
174	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
175	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
176	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
177	C₂²×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
178	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
179	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
180	C₄×C₁₃	—	2	4	no	—
181	C₄×C₁₃	—	2	8	no	—
182	C₄×C₁₃	—	4	4	no	—
183	C₄×C₁₃	#389	1	4	yes	—
184	C₄×C₁₃	C₂×C₄⋊C₈	1	8	yes	complemented
185	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
186	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
187	C₄×C₁₃	C₂×#125	1	1	yes	characteristic
188	C₄×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
189	C₂³×C₄	C₂×Dic₁₃	1	2	yes	—
190	C₂³×C₄	C₂×Dic₁₃	1	2	yes	—
191	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
192	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
193	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
194	C₂²×C₈	—	13	4	no	—
195	C₂²×C₈	—	13	4	no	—
196	C₂²×C₈	—	13	2	no	—
197	C₂²×C₈	—	13	2	no	—
198	C₂²×C₈	—	13	4	no	—
199	C₂²×C₈	—	26	2	no	—
200	C₂²×C₈	—	26	2	no	—
201	C₂²×C₈	—	26	2	no	—
202	C₂²×C₈	—	26	2	no	—
203	C₂²×C₈	—	26	4	no	—
204	C₂²×C₈	—	26	4	no	—
205	C₂²×C₈	—	26	4	no	—
206	C₂×C₄⋊C₄	—	2	4	no	—
207	C₂×C₄⋊C₄	#1055	1	8	yes	complemented
208	C₂×C₄⋊C₄	C₂×Dic₁₃	1	4	yes	—
209	C₂×C₄⋊C₄	C₂×Dic₁₃	1	4	yes	—
210	C₂×C₄²	—	2	4	no	—
211	C₂×C₄²	—	2	4	no	—
212	C₂×C₄²	Dic₂₆	1	4	yes	—
213	C₂×C₄²	D₅₂	1	4	yes	—
214	C₂×C₄²	C₂×Dic₁₃	1	4	yes	—
215	C₂×C₄²	C₂×Dic₁₃	1	2	yes	—
216	C₂×C₄²	C₂²×D₁₃	1	4	yes	—
217	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
218	C₄⋊C₈	—	26	16	no	—
219	C₄⋊C₈	—	26	8	no	—
220	C₄×C₈	—	26	8	no	—
221	#95	C₂×Dic₁₃	1	8	yes	—
222	C₂×C₁₃	#1939	1	8	yes	complemented
223	C₂×C₁₃	C₂×#389	1	1	yes	characteristic
224	C₂×C₁₃	C₂²×C₄⋊C₈	1	1	yes	characteristic
225	C₂×C₁₃	C₂×#424	1	1	yes	characteristic
226	C₂×C₁₃	C₂×C₈×D₄	1	1	yes	characteristic
227	C₂×C₁₃	C₂×#436	1	1	yes	characteristic
228	C₂×C₁₃	C₂×C₈×Q₈	1	1	yes	characteristic
229	C₂×C₁₃	C₂×#446	1	1	yes	characteristic
230	C₂⁴	C₂²×Dic₁₃	1	1	yes	characteristic
231	C₂²×C₄	—	2	4	no	—
232	C₂²×C₄	—	2	2	no	—
233	C₂²×C₄	—	2	2	no	—
234	C₂²×C₄	—	2	4	no	—
235	C₂²×C₄	—	2	4	no	—
236	C₂²×C₄	—	2	4	no	—
237	C₂²×C₄	—	2	4	no	—
238	C₂²×C₄	C₂×#1055	1	8	yes	—
239	C₂²×C₄	C₂×#1055	1	4	yes	—
240	C₂²×C₄	#6099	1	4	yes	—
241	C₂²×C₄	C₄⋊Dic₁₃	1	4	yes	—
242	C₂²×C₄	C₄⋊Dic₁₃	1	4	yes	—
243	C₂²×C₄	C₂×Dic₂₆	1	2	yes	—
244	C₂²×C₄	C₂×D₅₂	1	2	yes	—
245	C₂²×C₄	D₄×D₁₃	1	2	yes	—
246	C₂²×C₄	#6129	1	2	yes	—
247	C₂²×C₄	Q₈×D₁₃	1	2	yes	—
248	C₂²×C₄	#6131	1	2	yes	—
249	C₂²×C₄	C₂²×Dic₁₃	1	4	yes	—
250	C₂²×C₄	C₂²×Dic₁₃	1	4	yes	—
251	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
252	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
253	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
254	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
255	C₂×C₈	—	13	4	no	—
256	C₂×C₈	—	13	4	no	—
257	C₂×C₈	—	26	8	no	—
258	C₂×C₈	—	26	8	no	—
259	C₂×C₈	—	26	2	no	—
260	C₂×C₈	—	26	2	no	—
261	C₂×C₈	—	26	2	no	—
262	C₂×C₈	—	26	2	no	—
263	C₂×C₈	—	26	4	no	—
264	C₂×C₈	—	26	4	no	—
265	C₂×C₈	—	26	4	no	—
266	C₂×C₈	—	52	8	no	—
267	C₄⋊C₄	—	2	8	no	—
268	C₄⋊C₄	C₂×#1055	1	16	yes	complemented
269	C₄²	—	2	8	no	—
270	C₄²	—	2	4	no	—
271	C₄²	—	2	4	no	—
272	C₄²	C₄⋊Dic₁₃	1	8	yes	—
273	C₄²	C₂×Dic₂₆	1	4	yes	—
274	C₄²	C₂×D₅₂	1	4	yes	—
275	C₁₃	C₂×#1939	1	1	yes	characteristic, complemented, Sylow
276	C₂³	C₂²×#1055	1	2	yes	—
277	C₂³	C₂×#6099	1	2	yes	—
278	C₂³	C₂×C₄⋊Dic₁₃	1	2	yes	—
279	C₂³	D₄×Dic₁₃	1	2	yes	—
280	C₂³	Q₈×Dic₁₃	1	2	yes	—
281	C₂³	#88202	1	2	yes	—
282	C₂³	#88202	1	2	yes	—
283	C₂³	C₂³×Dic₁₃	1	1	yes	characteristic
284	C₂×C₄	—	2	8	no	—
285	C₂×C₄	—	2	16	no	—
286	C₂×C₄	—	2	4	no	—
287	C₂×C₄	—	2	2	no	—
288	C₂×C₄	—	2	2	no	—
289	C₂×C₄	—	2	4	no	—
290	C₂×C₄	—	2	4	no	—
291	C₂×C₄	—	2	4	no	—
292	C₂×C₄	—	2	4	no	—
293	C₂×C₄	—	4	8	no	—
294	C₂×C₄	C₄⋊#1055	1	16	yes	complemented
295	C₂×C₄	#88142	1	4	yes	—
296	C₂×C₄	#88144	1	4	yes	—
297	C₂×C₄	#88149	1	4	yes	—
298	C₂×C₄	#88151	1	4	yes	—
299	C₂×C₄	C₂²×#1055	1	8	yes	—
300	C₂×C₄	C₂²×#1055	1	4	yes	—
301	C₂×C₄	C₂×#6099	1	4	yes	—
302	C₂×C₄	C₂×C₄⋊Dic₁₃	1	4	yes	—
303	C₂×C₄	C₂×C₄⋊Dic₁₃	1	4	yes	—
304	C₂×C₄	C₂×C₄⋊Dic₁₃	1	2	yes	—
305	C₂×C₄	D₄×Dic₁₃	1	2	yes	—
306	C₂×C₄	Q₈×Dic₁₃	1	2	yes	—
307	C₂×C₄	C₂²×Dic₂₆	1	1	yes	characteristic
308	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
309	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
310	C₂×C₄	C₂×#6129	1	1	yes	characteristic
311	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
312	C₂×C₄	C₂×#6131	1	1	yes	characteristic
313	C₈	—	26	4	no	—
314	C₈	—	26	4	no	—
315	C₈	—	52	4	no	—
316	C₂²	C₂×C₄⋊#1055	1	4	yes	—
317	C₂²	#11718646	1	4	yes	—
318	C₂²	#11718660	1	4	yes	—
319	C₂²	D₄×#1055	1	4	yes	—
320	C₂²	#11718673	1	4	yes	—
321	C₂²	Q₈×#1055	1	4	yes	—
322	C₂²	#11718685	1	4	yes	—
323	C₂²	C₂³×#1055	1	1	yes	characteristic
324	C₂²	C₂²×#6099	1	1	yes	characteristic
325	C₂²	C₂²×C₄⋊Dic₁₃	1	1	yes	characteristic
326	C₂²	C₂×D₄×Dic₁₃	1	1	yes	characteristic
327	C₂²	C₂×Q₈×Dic₁₃	1	1	yes	characteristic
328	C₂²	C₂×#88202	1	1	yes	characteristic
329	C₂²	C₂×#88202	1	1	yes	characteristic
330	C₄	—	2	4	no	—
331	C₄	—	2	8	no	—
332	C₄	—	4	4	no	—
333	C₄	C₂×C₄⋊#1055	1	8	yes	complemented
334	C₄	#11718646	1	4	yes	—
335	C₄	C₂×#88142	1	1	yes	characteristic
336	C₄	C₂×#88144	1	1	yes	characteristic
337	C₄	C₂×#88149	1	1	yes	characteristic
338	C₄	C₂×#88151	1	1	yes	characteristic
339	C₂	#13115555	1	8	yes	direct product factor
340	C₂	C₂×#11718646	1	1	yes	characteristic
341	C₂	C₂²×C₄⋊#1055	1	1	yes	characteristic
342	C₂	C₂×#11718660	1	1	yes	characteristic
343	C₂	C₂×D₄×#1055	1	1	yes	characteristic
344	C₂	C₂×#11718673	1	1	yes	characteristic
345	C₂	C₂×Q₈×#1055	1	1	yes	characteristic
346	C₂	C₂×#11718685	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄	C₂²×D₁₃
commutator	C₂²×C₁₃	C₂³×C₈
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₂×C₄×C₁₃×C₄⋊C₄	C₂
socle, prime radical	C₂⁴×C₁₃	C₂²×C₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₂×C₄×C₄⋊C₄	D₁₃
hypocenter	C₁₃	C₂×#1939
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³×C₄ ◁ C₂×C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
4. #13115555	C₂	direct (N × H)
30. C₂×C₁₃×C₄⋊C₄	C₈	semidirect
84. C₁₃×C₄⋊C₄	C₂×C₈	semidirect
127. C₂×C₄×C₁₃	C₄⋊C₈	semidirect
184. C₄×C₁₃	C₂×C₄⋊C₈	semidirect
207. C₂×C₄⋊C₄	#1055	semidirect
222. C₂×C₁₃	#1939	semidirect
268. C₄⋊C₄	C₂×#1055	semidirect
275. C₁₃	C₂×#1939	semidirect
294. C₂×C₄	C₄⋊#1055	semidirect
333. C₄	C₂×C₄⋊#1055	semidirect
339. C₂	#13115555	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊#1055	2
C₂²×C₄×#1055	2
#13115555	2
C₂×#11718116	2
C₂×C₄×C₁₃×C₄⋊C₄	2
C₂×#1939	13

Subgroups — C2×#13115555 #15866185

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13115555 #15866185