Subgroups — C₂²×C₄×#6105 #16726925

Order 3328.

3262 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#6105	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×Dic₂₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×#6105	C₂	1	24	yes	maximal, direct product factor
4	C₂²×#88048	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#88050	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#88072	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₄×#1055	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
9	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
10	C₂⁴×C₄×C₁₃	—	2	1	no	—
11	C₂³×Dic₂₆	C₂²	1	1	yes	characteristic
12	C₂×C₄×D₄×C₁₃	—	2	6	no	—
13	C₂×C₄×D₄×C₁₃	C₂²	1	12	yes	—
14	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂²×C₁₃×C₂²⋊C₄	—	2	1	no	—
16	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
17	C₂²×#6105	C₄	1	16	yes	direct product factor
18	C₂²×#6105	C₂²	1	12	yes	—
19	C₂²×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
20	C₂²×#6101	—	2	1	no	—
21	C₂²×C₄×Dic₁₃	—	2	1	no	—
22	C₂³×#1055	C₂²	1	1	yes	characteristic
23	C₂³×#1055	C₂²	1	1	yes	characteristic
24	C₂×C₄×Dic₂₆	—	2	6	no	—
25	C₂×C₄×Dic₂₆	C₂²	1	12	yes	complemented
26	C₂×#88072	C₂²	1	12	yes	—
27	C₄×#6105	C₂²	1	64	yes	direct product factor
28	C₂×#88050	C₂²	1	12	yes	complemented
29	C₂×#88048	C₂²	1	12	yes	complemented
30	C₂×C₄×#1055	C₂²	1	12	yes	complemented
31	C₂⁵×C₁₃	—	2	1	no	—
32	C₂²×D₄×C₁₃	—	2	3	no	—
33	C₂²×D₄×C₁₃	—	2	4	no	—
34	C₂²×D₄×C₁₃	C₂×C₄	1	8	yes	—
35	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
36	C₂³×C₄×C₁₃	—	2	1	no	—
37	C₂³×C₄×C₁₃	—	2	12	no	—
38	C₂³×C₄×C₁₃	—	4	8	no	—
39	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
42	C₂³×Dic₁₃	—	2	1	no	—
43	C₂³×Dic₁₃	—	2	1	no	—
44	C₂²×Dic₂₆	—	2	3	no	—
45	C₂²×Dic₂₆	—	2	4	no	—
46	C₂²×Dic₂₆	C₂×C₄	1	8	yes	complemented
47	C₂²×Dic₂₆	C₂³	1	6	yes	—
48	C₄×D₄×C₁₃	—	2	24	no	—
49	C₄×D₄×C₁₃	C₂³	1	16	yes	—
50	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
51	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
52	C₂×C₁₃×C₂²⋊C₄	—	2	12	no	—
53	C₂×C₄²×C₁₃	D₄	1	6	yes	—
54	C₂×C₄²×C₁₃	C₂³	1	6	yes	—
55	C₂×#6105	C₂×C₄	1	96	yes	direct product factor
56	C₂×#6105	C₂³	1	16	yes	—
57	C₂×C₄⋊Dic₁₃	—	2	3	no	—
58	C₂×C₄⋊Dic₁₃	C₂³	1	6	yes	—
59	C₂×#6101	—	2	12	no	—
60	C₂×C₄×Dic₁₃	—	2	12	no	—
61	C₂²×#1055	—	2	4	no	—
62	C₂²×#1055	C₂×C₄	1	8	yes	complemented
63	C₂²×#1055	C₂³	1	6	yes	—
64	C₂²×#1055	C₂³	1	6	yes	—
65	C₄×Dic₂₆	—	2	24	no	—
66	C₄×Dic₂₆	C₂³	1	16	yes	complemented
67	#88072	C₂³	1	16	yes	—
68	#88050	C₂³	1	16	yes	complemented
69	#88048	C₂³	1	16	yes	complemented
70	C₄×#1055	C₂³	1	16	yes	complemented
71	C₂²×C₄×SD₁₆	—	13	1	no	maximal, Sylow
72	C₂⁴×C₁₃	—	2	8	no	—
73	C₂⁴×C₁₃	—	2	6	no	—
74	C₂⁴×C₁₃	—	4	4	no	—
75	C₂⁴×C₁₃	—	4	4	no	—
76	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
77	C₂×D₄×C₁₃	—	2	24	no	—
78	C₂×D₄×C₁₃	—	2	6	no	—
79	C₂×D₄×C₁₃	—	2	12	no	—
80	C₂×D₄×C₁₃	C₂²×C₄	1	24	yes	—
81	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
82	C₂²×C₄×C₁₃	—	2	4	no	—
83	C₂²×C₄×C₁₃	—	2	6	no	—
84	C₂²×C₄×C₁₃	—	2	16	no	—
85	C₂²×C₄×C₁₃	—	4	4	no	—
86	C₂²×C₄×C₁₃	—	4	48	no	—
87	C₂²×C₄×C₁₃	SD₁₆	1	8	yes	complemented
88	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
89	C₂²×C₄×C₁₃	C₂×D₄	1	6	yes	—
90	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
91	C₂²×C₄×C₁₃	C₂×D₄	1	6	yes	—
92	C₂²×C₄×C₁₃	#41	1	4	yes	—
93	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
94	C₂²×Dic₁₃	—	2	8	no	—
95	C₂²×Dic₁₃	—	2	6	no	—
96	C₂²×Dic₁₃	—	2	6	no	—
97	C₂²×Dic₁₃	—	4	4	no	—
98	C₂×Dic₂₆	—	2	24	no	—
99	C₂×Dic₂₆	—	2	6	no	—
100	C₂×Dic₂₆	—	2	12	no	—
101	C₂×Dic₂₆	C₂²×C₄	1	24	yes	complemented
102	C₂×Dic₂₆	C₂⁴	1	4	yes	—
103	C₁₃×C₄⋊C₄	—	2	6	no	—
104	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
105	C₁₃×C₂²⋊C₄	—	2	16	no	—
106	C₄²×C₁₃	C₂×D₄	1	12	yes	—
107	C₄²×C₁₃	C₂⁴	1	4	yes	—
108	#6105	C₂²×C₄	1	64	yes	direct product factor
109	C₄⋊Dic₁₃	—	2	6	no	—
110	C₄⋊Dic₁₃	C₂⁴	1	4	yes	—
111	#6101	—	2	16	no	—
112	C₄×Dic₁₃	—	2	16	no	—
113	C₂×#1055	—	2	12	no	—
114	C₂×#1055	C₂²×C₄	1	24	yes	complemented
115	C₂×#1055	C₂⁴	1	4	yes	—
116	C₂×#1055	C₂⁴	1	4	yes	—
117	C₂³×SD₁₆	—	13	1	no	—
118	C₂²×C₄×Q₈	—	13	1	no	—
119	C₂²×C₄×D₄	D₁₃	1	1	yes	characteristic
120	C₂×C₄×SD₁₆	—	13	24	no	—
121	C₂²×#106	—	13	1	no	—
122	C₂²×#103	—	13	1	no	—
123	C₂²×#102	—	13	1	no	—
124	C₂²×C₄×C₈	—	13	1	no	—
125	C₂³×C₁₃	—	2	24	no	—
126	C₂³×C₁₃	—	2	4	no	—
127	C₂³×C₁₃	—	4	12	no	—
128	C₂³×C₁₃	—	4	12	no	—
129	C₂³×C₁₃	—	4	32	no	—
130	C₂³×C₁₃	C₄×D₄	1	4	yes	—
131	C₂³×C₁₃	C₂×SD₁₆	1	4	yes	—
132	C₂³×C₁₃	#135	1	4	yes	—
133	C₂³×C₁₃	C₂²×D₄	1	3	yes	—
134	D₄×C₁₃	—	2	24	no	—
135	D₄×C₁₃	—	2	4	no	—
136	D₄×C₁₃	C₂³×C₄	1	8	yes	—
137	C₂×C₄×C₁₃	—	2	12	no	—
138	C₂×C₄×C₁₃	—	2	4	no	—
139	C₂×C₄×C₁₃	—	4	12	no	—
140	C₂×C₄×C₁₃	—	4	32	no	—
141	C₂×C₄×C₁₃	C₄×D₄	1	12	yes	—
142	C₂×C₄×C₁₃	C₂×SD₁₆	1	24	yes	complemented
143	C₂×C₄×C₁₃	C₂³×C₄	1	6	yes	—
144	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
145	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
146	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
147	C₂×C₄×C₁₃	C₂×#41	1	6	yes	—
148	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
149	C₂×Dic₁₃	—	2	24	no	—
150	C₂×Dic₁₃	—	2	4	no	—
151	C₂×Dic₁₃	—	2	4	no	—
152	C₂×Dic₁₃	—	4	12	no	—
153	Dic₂₆	—	2	24	no	—
154	Dic₂₆	—	2	4	no	—
155	Dic₂₆	C₂³×C₄	1	8	yes	complemented
156	#1055	—	2	4	no	—
157	#1055	C₂³×C₄	1	8	yes	complemented
158	C₂³×Q₈	—	13	1	no	—
159	C₂³×D₄	C₂×D₁₃	1	1	yes	characteristic
160	C₂⁴×C₄	—	2	1	no	—
161	C₂²×SD₁₆	—	13	16	no	—
162	C₂²×SD₁₆	—	13	12	no	—
163	C₂³×C₈	—	13	1	no	—
164	C₂³×C₈	—	13	1	no	—
165	C₂×C₄×Q₈	—	13	12	no	—
166	C₂×C₄×Q₈	—	26	6	no	—
167	C₂×C₄×D₄	—	2	6	no	—
168	C₂×C₄×D₄	C₂×D₁₃	1	12	yes	—
169	C₂²×C₄⋊C₄	—	13	1	no	—
170	C₂²×C₄⋊C₄	—	26	1	no	—
171	C₂²×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
172	C₂²×C₂²⋊C₄	—	2	1	no	—
173	C₂²×C₄²	—	26	1	no	—
174	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
175	C₄×SD₁₆	—	13	64	no	—
176	C₂×#106	—	13	12	no	—
177	C₂×#103	—	13	12	no	—
178	C₂×#102	—	13	12	no	—
179	C₂×C₄×C₈	—	13	12	no	—
180	C₂²×C₁₃	—	2	8	no	—
181	C₂²×C₁₃	—	4	48	no	—
182	C₂²×C₁₃	—	4	4	no	—
183	C₂²×C₁₃	—	4	4	no	—
184	C₂²×C₁₃	C₄×SD₁₆	1	16	yes	complemented
185	C₂²×C₁₃	C₂×C₄×D₄	1	6	yes	—
186	C₂²×C₁₃	C₂²×SD₁₆	1	6	yes	—
187	C₂²×C₁₃	C₂×#135	1	6	yes	—
188	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
189	C₄×C₁₃	—	2	4	no	—
190	C₄×C₁₃	—	4	4	no	—
191	C₄×C₁₃	C₂×C₄×D₄	1	6	yes	—
192	C₄×C₁₃	C₂²×SD₁₆	1	8	yes	complemented
193	C₄×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
194	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
195	Dic₁₃	—	2	8	no	—
196	Dic₁₃	—	4	4	no	—
197	C₂⁵	—	2	1	no	—
198	C₂²×Q₈	—	13	8	no	—
199	C₂²×Q₈	—	13	6	no	—
200	C₂²×Q₈	—	26	4	no	—
201	C₂²×Q₈	—	26	3	no	—
202	C₂²×D₄	—	2	4	no	—
203	C₂²×D₄	—	2	3	no	—
204	C₂²×D₄	C₄×D₁₃	1	8	yes	—
205	C₂²×D₄	C₂²×D₁₃	1	6	yes	—
206	C₂³×C₄	—	2	1	no	—
207	C₂³×C₄	—	2	12	no	—
208	C₂³×C₄	—	4	8	no	—
209	C₂³×C₄	—	26	1	no	—
210	C₂³×C₄	—	26	1	no	—
211	C₂³×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
212	C₂³×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
213	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
214	C₂×SD₁₆	—	13	96	no	—
215	C₂×SD₁₆	—	13	16	no	—
216	C₂²×C₈	—	13	8	no	—
217	C₂²×C₈	—	13	6	no	—
218	C₂²×C₈	—	13	6	no	—
219	C₂²×C₈	—	26	4	no	—
220	C₄×Q₈	—	13	16	no	—
221	C₄×Q₈	—	26	24	no	—
222	C₄×D₄	—	2	24	no	—
223	C₄×D₄	C₂²×D₁₃	1	16	yes	—
224	C₂×C₄⋊C₄	—	2	3	no	—
225	C₂×C₄⋊C₄	—	13	6	no	—
226	C₂×C₄⋊C₄	—	26	3	no	—
227	C₂×C₄⋊C₄	—	26	12	no	—
228	C₂×C₄⋊C₄	C₂²×D₁₃	1	6	yes	—
229	C₂×C₂²⋊C₄	—	2	12	no	—
230	C₂×C₄²	—	26	12	no	—
231	C₂×C₄²	C₂²⋊D₁₃	1	6	yes	—
232	C₂×C₄²	C₂²×D₁₃	1	6	yes	—
233	#106	—	13	16	no	—
234	#103	—	13	16	no	—
235	#102	—	13	16	no	—
236	C₄×C₈	—	13	16	no	—
237	C₂×C₁₃	—	4	8	no	—
238	C₂×C₁₃	C₂×C₄×SD₁₆	1	12	yes	complemented
239	C₂×C₁₃	C₂²×C₄×D₄	1	1	yes	characteristic
240	C₂×C₁₃	C₂³×SD₁₆	1	1	yes	characteristic
241	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
242	C₂⁴	—	2	8	no	—
243	C₂⁴	—	2	6	no	—
244	C₂⁴	—	4	4	no	—
245	C₂⁴	—	4	4	no	—
246	C₂⁴	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
247	C₂×Q₈	—	13	24	no	—
248	C₂×Q₈	—	13	4	no	—
249	C₂×Q₈	—	26	24	no	—
250	C₂×Q₈	—	26	12	no	—
251	C₂×Q₈	—	26	6	no	—
252	C₂×D₄	—	2	24	no	—
253	C₂×D₄	—	2	12	no	—
254	C₂×D₄	—	2	6	no	—
255	C₂×D₄	C₂×C₄×D₁₃	1	24	yes	—
256	C₂×D₄	C₂³×D₁₃	1	4	yes	—
257	C₂²×C₄	—	2	4	no	—
258	C₂²×C₄	—	2	6	no	—
259	C₂²×C₄	—	2	16	no	—
260	C₂²×C₄	—	4	4	no	—
261	C₂²×C₄	—	4	48	no	—
262	C₂²×C₄	—	26	8	no	—
263	C₂²×C₄	—	26	6	no	—
264	C₂²×C₄	—	26	6	no	—
265	C₂²×C₄	—	52	4	no	—
266	C₂²×C₄	#6105	1	8	yes	direct product factor
267	C₂²×C₄	C₂×C₄×D₁₃	1	4	yes	—
268	C₂²×C₄	#6127	1	4	yes	—
269	C₂²×C₄	C₂×C₂²⋊D₁₃	1	6	yes	—
270	C₂²×C₄	C₂×C₂²⋊D₁₃	1	3	yes	—
271	C₂²×C₄	C₂×C₂²⋊D₁₃	1	6	yes	—
272	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
273	SD₁₆	—	13	64	no	—
274	C₂×C₈	—	13	24	no	—
275	C₂×C₈	—	13	4	no	—
276	C₂×C₈	—	13	4	no	—
277	C₂×C₈	—	26	12	no	—
278	C₄⋊C₄	—	2	6	no	—
279	C₄⋊C₄	—	13	4	no	—
280	C₄⋊C₄	—	26	6	no	—
281	C₄⋊C₄	—	26	16	no	—
282	C₄⋊C₄	C₂³×D₁₃	1	4	yes	—
283	C₂²⋊C₄	—	2	16	no	—
284	C₄²	—	26	16	no	—
285	C₄²	C₂×C₂²⋊D₁₃	1	12	yes	—
286	C₄²	C₂³×D₁₃	1	4	yes	—
287	C₁₃	C₂²×C₄×SD₁₆	1	1	yes	characteristic, complemented, Sylow
288	C₂³	—	2	24	no	—
289	C₂³	—	2	4	no	—
290	C₂³	—	4	32	no	—
291	C₂³	—	4	12	no	—
292	C₂³	—	4	12	no	—
293	C₂³	C₄×C₂²⋊D₁₃	1	4	yes	—
294	C₂³	C₂×#6105	1	4	yes	—
295	C₂³	#88204	1	4	yes	—
296	C₂³	C₂²×C₂²⋊D₁₃	1	3	yes	—
297	Q₈	—	13	8	no	—
298	Q₈	—	26	24	no	—
299	Q₈	—	26	4	no	—
300	D₄	—	2	24	no	—
301	D₄	—	2	4	no	—
302	D₄	C₂²×C₄×D₁₃	1	8	yes	—
303	C₂×C₄	—	2	12	no	—
304	C₂×C₄	—	2	4	no	—
305	C₂×C₄	—	4	12	no	—
306	C₂×C₄	—	4	32	no	—
307	C₂×C₄	—	26	24	no	—
308	C₂×C₄	—	26	4	no	—
309	C₂×C₄	—	26	4	no	—
310	C₂×C₄	—	52	12	no	—
311	C₂×C₄	C₄×C₂²⋊D₁₃	1	12	yes	—
312	C₂×C₄	C₂×#6105	1	24	yes	direct product factor
313	C₂×C₄	C₂²×C₄×D₁₃	1	6	yes	—
314	C₂×C₄	C₂×#6127	1	6	yes	—
315	C₂×C₄	C₂²×C₂²⋊D₁₃	1	4	yes	—
316	C₂×C₄	C₂²×C₂²⋊D₁₃	1	3	yes	—
317	C₂×C₄	C₂²×C₂²⋊D₁₃	1	4	yes	—
318	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
319	C₈	—	13	8	no	—
320	C₈	—	26	4	no	—
321	C₂²	—	2	8	no	—
322	C₂²	—	4	48	no	—
323	C₂²	—	4	4	no	—
324	C₂²	—	4	4	no	—
325	C₂²	C₄×#6105	1	16	yes	direct product factor
326	C₂²	C₂×C₄×C₂²⋊D₁₃	1	6	yes	—
327	C₂²	C₂²×#6105	1	6	yes	—
328	C₂²	C₂×#88204	1	6	yes	—
329	C₂²	C₂³×C₂²⋊D₁₃	1	1	yes	characteristic
330	C₄	—	2	4	no	—
331	C₄	—	4	4	no	—
332	C₄	—	26	8	no	—
333	C₄	—	52	4	no	—
334	C₄	C₂×C₄×C₂²⋊D₁₃	1	6	yes	—
335	C₄	C₂²×#6105	1	8	yes	direct product factor
336	C₄	C₂³×C₄×D₁₃	1	1	yes	characteristic
337	C₄	C₂²×#6127	1	1	yes	characteristic
338	C₂	—	4	8	no	—
339	C₂	C₂×C₄×#6105	1	12	yes	direct product factor
340	C₂	C₂²×C₄×C₂²⋊D₁₃	1	1	yes	characteristic
341	C₂	C₂³×#6105	1	1	yes	characteristic
342	C₂	C₂²×#88204	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄	C₂²⋊D₁₃
commutator	C₄×C₁₃	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₁₃
Fitting	C₂²×C₄×D₄×C₁₃	C₂
socle	C₂⁴×C₁₃	C₂×D₄
prime radical	C₂³×D₄×C₁₃	C₂²
cosocle	C₂×C₄×C₁₃	C₂⁵
hypercenter	C₂²×C₄×D₄	D₁₃
hypocenter	C₁₃	C₂²×C₄×SD₁₆
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×C₄² ◁ C₂²×C₄×D₄

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×Dic₂₆	C₂	semidirect
3. C₂×C₄×#6105	C₂	direct (N × H)
4. C₂²×#88048	C₂	semidirect
5. C₂²×#88050	C₂	semidirect
7. C₂²×C₄×#1055	C₂	semidirect
17. C₂²×#6105	C₄	direct (N × H)
25. C₂×C₄×Dic₂₆	C₂²	semidirect
27. C₄×#6105	C₂²	direct (N × H)
28. C₂×#88050	C₂²	semidirect
29. C₂×#88048	C₂²	semidirect
30. C₂×C₄×#1055	C₂²	semidirect
46. C₂²×Dic₂₆	C₂×C₄	semidirect
55. C₂×#6105	C₂×C₄	direct (N × H)
62. C₂²×#1055	C₂×C₄	semidirect
66. C₄×Dic₂₆	C₂³	semidirect
68. #88050	C₂³	semidirect
69. #88048	C₂³	semidirect
70. C₄×#1055	C₂³	semidirect
87. C₂²×C₄×C₁₃	SD₁₆	semidirect
101. C₂×Dic₂₆	C₂²×C₄	semidirect
108. #6105	C₂²×C₄	direct (N × H)
114. C₂×#1055	C₂²×C₄	semidirect
142. C₂×C₄×C₁₃	C₂×SD₁₆	semidirect
155. Dic₂₆	C₂³×C₄	semidirect
157. #1055	C₂³×C₄	semidirect
184. C₂²×C₁₃	C₄×SD₁₆	semidirect
192. C₄×C₁₃	C₂²×SD₁₆	semidirect
238. C₂×C₁₃	C₂×C₄×SD₁₆	semidirect
266. C₂²×C₄	#6105	direct (N × H)
287. C₁₃	C₂²×C₄×SD₁₆	semidirect
312. C₂×C₄	C₂×#6105	direct (N × H)
325. C₂²	C₄×#6105	direct (N × H)
335. C₄	C₂²×#6105	direct (N × H)
339. C₂	C₂×C₄×#6105	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×#6105	2
C₂²×C₄×Dic₂₆	2
C₂×C₄×#6105	2
C₂²×#88048	2
C₂²×#88050	2
C₂²×#88072	2
C₂²×C₄×#1055	2
C₂²×C₄×D₄×C₁₃	2
C₂²×C₄×SD₁₆	13

Subgroups — C22×C4×#6105 #16726925

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄×#6105 #16726925