Subgroups — C₂²×D₄×Dic₁₀₆ #28291008

Order 13568.

11798 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×Dic₁₀₆	C₂	1	2	yes	maximal, complemented
2	C₂×D₄×Dic₁₀₆	C₂	1	48	yes	maximal, direct product factor
3	C₂²×#13133217	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#13133216	C₂	1	2	yes	maximal, complemented
5	C₂²×#13133196	C₂	1	2	yes	maximal, complemented
6	C₂²×#13133194	C₂	1	4	yes	maximal, complemented
7	C₂²×C₄×Dic₁₀₆	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×D₄×Dic₅₃	C₂	1	2	yes	maximal
9	C₂²×C₄×D₄×C₅₃	C₂	1	1	yes	maximal, characteristic
10	C₂³×Dic₁₀₆	—	2	32	no	—
11	C₂³×Dic₁₀₆	C₂²	1	4	yes	—
12	C₂³×Dic₁₀₆	C₂²	1	2	yes	—
13	C₂³×Dic₁₀₆	C₂²	1	1	yes	characteristic
14	C₂³×Dic₁₀₆	C₂²	1	48	yes	complemented
15	C₂⁴×Dic₅₃	C₂²	1	4	yes	—
16	D₄×Dic₁₀₆	C₂²	1	256	yes	direct product factor
17	C₂×#13133217	C₂²	1	24	yes	complemented
18	C₂×#13133216	C₂²	1	48	yes	complemented
19	C₂×#13133196	C₂²	1	48	yes	complemented
20	C₂×#13133194	C₂²	1	96	yes	complemented
21	C₂×C₄×Dic₁₀₆	C₂²	1	24	yes	complemented
22	C₂×D₄×Dic₅₃	C₂²	1	48	yes	—
23	C₂²×C₄⋊Dic₅₃	C₂²	1	2	yes	—
24	C₂²×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic
25	C₂²×C₄⋊Dic₅₃	C₂²	1	2	yes	—
26	C₂²×#11719919	C₂²	1	2	yes	—
27	C₂²×#11719919	C₂²	1	4	yes	—
28	C₂²×C₂²⋊Dic₅₃	C₂²	1	4	yes	—
29	C₂²×C₄×Dic₅₃	C₂²	1	2	yes	—
30	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
31	C₂⁴×C₄×C₅₃	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₅₃	C₂²	1	24	yes	—
33	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
34	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
35	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
36	C₂²×Dic₁₀₆	—	2	16	no	—
37	C₂²×Dic₁₀₆	—	2	32	no	—
38	C₂²×Dic₁₀₆	—	2	384	no	—
39	C₂²×Dic₁₀₆	D₄	1	16	yes	direct product factor
40	C₂²×Dic₁₀₆	C₂³	1	48	yes	—
41	C₂²×Dic₁₀₆	C₂³	1	24	yes	—
42	C₂²×Dic₁₀₆	C₂³	1	12	yes	—
43	C₂²×Dic₁₀₆	C₂³	1	128	yes	complemented
44	C₂³×Dic₅₃	—	2	32	no	—
45	C₂³×Dic₅₃	C₂³	1	2	yes	—
46	C₂³×Dic₅₃	C₂³	1	4	yes	—
47	C₂³×Dic₅₃	C₂³	1	48	yes	—
48	C₂³×Dic₅₃	C₂³	1	2	yes	—
49	#13133217	C₂³	1	64	yes	complemented
50	#13133216	C₂³	1	128	yes	complemented
51	#13133196	C₂³	1	128	yes	complemented
52	#13133194	C₂³	1	256	yes	complemented
53	C₄×Dic₁₀₆	C₂³	1	64	yes	complemented
54	D₄×Dic₅₃	C₂³	1	128	yes	—
55	C₂×C₄⋊Dic₅₃	C₂³	1	24	yes	—
56	C₂×C₄⋊Dic₅₃	C₂³	1	12	yes	—
57	C₂×C₄⋊Dic₅₃	C₂³	1	24	yes	—
58	C₂×#11719919	C₂³	1	24	yes	—
59	C₂×#11719919	C₂³	1	48	yes	—
60	C₂×C₂²⋊Dic₅₃	C₂³	1	48	yes	—
61	C₂×C₄×Dic₅₃	C₂³	1	24	yes	—
62	C₂⁵×C₅₃	C₂³	1	2	yes	—
63	C₂²×D₄×C₅₃	Q₈	1	16	yes	complemented
64	C₂²×D₄×C₅₃	C₂³	1	12	yes	—
65	C₂³×C₄×C₅₃	—	2	16	no	—
66	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
68	C₂³×C₄×C₅₃	C₂³	1	24	yes	—
69	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
71	C₄×D₄×C₅₃	C₂³	1	64	yes	—
72	C₂×C₄⋊C₄×C₅₃	C₂³	1	12	yes	—
73	C₂×C₂²⋊C₄×C₅₃	C₂³	1	24	yes	—
74	C₂×C₄²×C₅₃	C₂³	1	12	yes	—
75	C₂⁴×C₅₃	—	2	8	no	—
76	C₂⁴×C₅₃	—	2	8	no	—
77	C₂⁴×C₅₃	C₂×Q₈	1	16	yes	complemented
78	C₂⁴×C₅₃	C₂⁴	1	12	yes	—
79	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
80	C₂×D₄×C₅₃	C₂×Q₈	1	96	yes	complemented
81	C₂×D₄×C₅₃	C₂⁴	1	16	yes	—
82	C₂²×C₄×C₅₃	—	2	8	no	—
83	C₂²×C₄×C₅₃	—	2	4	no	—
84	C₂²×C₄×C₅₃	—	2	96	no	—
85	C₂²×C₄×C₅₃	C₂×D₄	1	8	yes	—
86	C₂²×C₄×C₅₃	C₂×Q₈	1	8	yes	complemented
87	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
88	C₂²×C₄×C₅₃	C₂⁴	1	12	yes	—
89	C₂²×C₄×C₅₃	C₂⁴	1	32	yes	—
90	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
91	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
92	C₂²×Dic₅₃	—	2	16	no	—
93	C₂²×Dic₅₃	—	2	8	no	—
94	C₂²×Dic₅₃	—	2	192	no	—
95	C₂²×Dic₅₃	C₂×D₄	1	16	yes	—
96	C₂²×Dic₅₃	C₂⁴	1	12	yes	—
97	C₂²×Dic₅₃	C₂⁴	1	24	yes	—
98	C₂²×Dic₅₃	C₂⁴	1	64	yes	—
99	C₂²×Dic₅₃	C₂⁴	1	12	yes	—
100	C₂×Dic₁₀₆	—	2	96	no	—
101	C₂×Dic₁₀₆	—	2	192	no	—
102	C₂×Dic₁₀₆	—	2	512	no	—
103	C₂×Dic₁₀₆	C₂×D₄	1	96	yes	direct product factor
104	C₂×Dic₁₀₆	C₂⁴	1	64	yes	—
105	C₂×Dic₁₀₆	C₂⁴	1	32	yes	—
106	C₂×Dic₁₀₆	C₂⁴	1	16	yes	—
107	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	—
108	C₂²⋊C₄×C₅₃	C₂⁴	1	32	yes	—
109	C₄²×C₅₃	C₂⁴	1	16	yes	—
110	C₂²⋊Dic₅₃	C₂⁴	1	64	yes	—
111	C₄⋊Dic₅₃	C₂⁴	1	32	yes	—
112	C₄⋊Dic₅₃	C₂⁴	1	16	yes	—
113	C₄⋊Dic₅₃	C₂⁴	1	32	yes	—
114	#11719919	C₂⁴	1	32	yes	—
115	#11719919	C₂⁴	1	64	yes	—
116	C₄×Dic₅₃	C₂⁴	1	32	yes	—
117	C₂³×C₅₃	—	2	64	no	—
118	C₂³×C₅₃	—	2	24	no	—
119	C₂³×C₅₃	—	2	24	no	—
120	C₂³×C₅₃	C₂²×D₄	1	4	yes	—
121	C₂³×C₅₃	C₂²×Q₈	1	4	yes	—
122	C₂³×C₅₃	C₂²×Q₈	1	48	yes	complemented
123	C₂³×C₅₃	2₋¹⁺⁴	1	4	yes	—
124	C₂³×C₅₃	C₂⁵	1	8	yes	—
125	C₂³×C₅₃	C₂⁵	1	3	yes	—
126	D₄×C₅₃	C₂²×Q₈	1	64	yes	complemented
127	C₂×C₄×C₅₃	—	2	24	no	—
128	C₂×C₄×C₅₃	—	2	12	no	—
129	C₂×C₄×C₅₃	—	2	64	no	—
130	C₂×C₄×C₅₃	C₂²×D₄	1	24	yes	—
131	C₂×C₄×C₅₃	C₂²×Q₈	1	24	yes	complemented
132	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
133	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
134	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
135	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
136	C₂×Dic₅₃	—	2	48	no	—
137	C₂×Dic₅₃	—	2	24	no	—
138	C₂×Dic₅₃	—	2	128	no	—
139	C₂×Dic₅₃	C₂²×D₄	1	48	yes	—
140	C₂×Dic₅₃	C₂⁵	1	16	yes	—
141	C₂×Dic₅₃	C₂⁵	1	8	yes	—
142	C₂×Dic₅₃	C₂⁵	1	8	yes	—
143	Dic₁₀₆	—	2	64	no	—
144	Dic₁₀₆	—	2	128	no	—
145	Dic₁₀₆	C₂²×D₄	1	64	yes	direct product factor
146	C₂²×D₄×Q₈	—	53	1	no	maximal, Sylow
147	C₂²×C₅₃	—	2	8	no	—
148	C₂²×C₅₃	—	2	8	no	—
149	C₂²×C₅₃	—	2	96	no	—
150	C₂²×C₅₃	D₄×Q₈	1	16	yes	complemented
151	C₂²×C₅₃	C₂³×D₄	1	6	yes	—
152	C₂²×C₅₃	C₂³×Q₈	1	6	yes	—
153	C₂²×C₅₃	C₂³×Q₈	1	16	yes	complemented
154	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	6	yes	—
155	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
156	C₄×C₅₃	—	2	8	no	—
157	C₄×C₅₃	—	2	4	no	—
158	C₄×C₅₃	C₂³×D₄	1	8	yes	—
159	C₄×C₅₃	C₂³×Q₈	1	8	yes	complemented
160	Dic₅₃	—	2	16	no	—
161	Dic₅₃	—	2	8	no	—
162	Dic₅₃	C₂³×D₄	1	16	yes	—
163	C₂⁴×Q₈	—	53	2	no	—
164	C₂×D₄×Q₈	—	53	48	no	—
165	C₂²×C₄⋊Q₈	—	53	1	no	—
166	C₂²×C₄⋊Q₈	—	53	2	no	—
167	C₂²×C₂²⋊Q₈	—	53	2	no	—
168	C₂²×C₂²⋊Q₈	—	53	4	no	—
169	C₂²×C₄×Q₈	—	53	1	no	—
170	C₂²×C₄×D₄	—	53	2	no	—
171	C₂²×C₄×D₄	D₅₃	1	1	yes	characteristic
172	C₂×C₅₃	—	2	16	no	—
173	C₂×C₅₃	C₂×D₄×Q₈	1	12	yes	complemented
174	C₂×C₅₃	C₂⁴×D₄	1	1	yes	characteristic
175	C₂×C₅₃	C₂⁴×Q₈	1	1	yes	characteristic
176	C₂×C₅₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
177	C₂³×Q₈	—	53	1	no	—
178	C₂³×Q₈	—	53	4	no	—
179	C₂³×Q₈	—	53	2	no	—
180	C₂³×Q₈	—	53	48	no	—
181	C₂³×Q₈	—	106	32	no	—
182	C₂³×D₄	C₂×D₅₃	1	1	yes	characteristic
183	C₂⁴×C₄	—	53	4	no	—
184	C₂⁴×C₄	C₂×D₅₃	1	2	yes	—
185	D₄×Q₈	—	53	256	no	—
186	C₂×C₄⋊Q₈	—	53	48	no	—
187	C₂×C₄⋊Q₈	—	53	24	no	—
188	C₂×C₂²⋊Q₈	—	53	48	no	—
189	C₂×C₂²⋊Q₈	—	53	96	no	—
190	C₂×C₄×Q₈	—	53	24	no	—
191	C₂×C₄×D₄	—	53	48	no	—
192	C₂×C₄×D₄	C₂×D₅₃	1	24	yes	—
193	C₂²×C₄⋊C₄	—	53	2	no	—
194	C₂²×C₄⋊C₄	—	53	4	no	—
195	C₂²×C₄⋊C₄	—	53	2	no	—
196	C₂²×C₄⋊C₄	—	53	1	no	—
197	C₂²×C₄⋊C₄	—	53	2	no	—
198	C₂²×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic
199	C₂²×C₂²⋊C₄	—	53	4	no	—
200	C₂²×C₂²⋊C₄	C₂×D₅₃	1	2	yes	—
201	C₂²×C₄²	—	53	2	no	—
202	C₂²×C₄²	C₂×D₅₃	1	1	yes	characteristic
203	C₅₃	C₂²×D₄×Q₈	1	1	yes	characteristic, complemented, Sylow
204	C₂⁵	C₂²×D₅₃	1	2	yes	—
205	C₂²×Q₈	—	53	16	no	—
206	C₂²×Q₈	—	53	12	no	—
207	C₂²×Q₈	—	53	48	no	—
208	C₂²×Q₈	—	53	24	no	—
209	C₂²×Q₈	—	53	128	no	—
210	C₂²×Q₈	—	106	32	no	—
211	C₂²×Q₈	—	106	384	no	—
212	C₂²×Q₈	—	106	16	no	—
213	C₂²×D₄	Dic₁₀₆	1	16	yes	direct product factor
214	C₂²×D₄	C₂²×D₅₃	1	12	yes	—
215	C₂³×C₄	—	2	16	no	—
216	C₂³×C₄	—	53	2	no	—
217	C₂³×C₄	—	53	48	no	—
218	C₂³×C₄	—	53	2	no	—
219	C₂³×C₄	—	53	4	no	—
220	C₂³×C₄	—	106	32	no	—
221	C₂³×C₄	C₂²×D₅₃	1	24	yes	—
222	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
223	C₂³×C₄	C₂²×D₅₃	1	2	yes	—
224	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
225	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
226	C₄⋊Q₈	—	53	128	no	—
227	C₄⋊Q₈	—	53	64	no	—
228	C₂²⋊Q₈	—	53	128	no	—
229	C₂²⋊Q₈	—	53	256	no	—
230	C₄×Q₈	—	53	64	no	—
231	C₄×D₄	—	53	128	no	—
232	C₄×D₄	C₂²×D₅₃	1	64	yes	—
233	C₂×C₄⋊C₄	—	53	24	no	—
234	C₂×C₄⋊C₄	—	53	24	no	—
235	C₂×C₄⋊C₄	—	53	12	no	—
236	C₂×C₄⋊C₄	—	53	48	no	—
237	C₂×C₄⋊C₄	—	53	24	no	—
238	C₂×C₄⋊C₄	C₂²×D₅₃	1	12	yes	—
239	C₂×C₂²⋊C₄	—	53	48	no	—
240	C₂×C₂²⋊C₄	C₂²×D₅₃	1	24	yes	—
241	C₂×C₄²	—	53	24	no	—
242	C₂×C₄²	C₂²×D₅₃	1	12	yes	—
243	C₂⁴	—	2	8	no	—
244	C₂⁴	—	2	8	no	—
245	C₂⁴	C₂×Dic₁₀₆	1	16	yes	complemented
246	C₂⁴	C₂³×D₅₃	1	12	yes	—
247	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
248	C₂×Q₈	—	53	96	no	—
249	C₂×Q₈	—	53	16	no	—
250	C₂×Q₈	—	53	64	no	—
251	C₂×Q₈	—	53	32	no	—
252	C₂×Q₈	—	106	192	no	—
253	C₂×Q₈	—	106	512	no	—
254	C₂×Q₈	—	106	96	no	—
255	C₂×D₄	C₂×Dic₁₀₆	1	96	yes	direct product factor
256	C₂×D₄	C₂³×D₅₃	1	16	yes	—
257	C₂²×C₄	—	2	8	no	—
258	C₂²×C₄	—	2	4	no	—
259	C₂²×C₄	—	2	96	no	—
260	C₂²×C₄	—	53	16	no	—
261	C₂²×C₄	—	53	12	no	—
262	C₂²×C₄	—	53	12	no	—
263	C₂²×C₄	—	53	24	no	—
264	C₂²×C₄	—	53	64	no	—
265	C₂²×C₄	—	106	192	no	—
266	C₂²×C₄	—	106	16	no	—
267	C₂²×C₄	—	106	8	no	—
268	C₂²×C₄	C₂×Dic₁₀₆	1	8	yes	complemented
269	C₂²×C₄	D₄×D₅₃	1	8	yes	—
270	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
271	C₂²×C₄	C₂³×D₅₃	1	12	yes	—
272	C₂²×C₄	C₂³×D₅₃	1	32	yes	—
273	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
274	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
275	C₄⋊C₄	—	53	32	no	—
276	C₄⋊C₄	—	53	32	no	—
277	C₄⋊C₄	—	53	16	no	—
278	C₄⋊C₄	—	53	64	no	—
279	C₄⋊C₄	—	53	32	no	—
280	C₄⋊C₄	C₂³×D₅₃	1	16	yes	—
281	C₂²⋊C₄	—	53	64	no	—
282	C₂²⋊C₄	C₂³×D₅₃	1	32	yes	—
283	C₄²	—	53	32	no	—
284	C₄²	C₂³×D₅₃	1	16	yes	—
285	C₂³	—	2	64	no	—
286	C₂³	—	2	24	no	—
287	C₂³	—	2	24	no	—
288	C₂³	C₂×D₄×D₅₃	1	4	yes	—
289	C₂³	C₂²×Dic₁₀₆	1	4	yes	—
290	C₂³	C₂²×Dic₁₀₆	1	48	yes	complemented
291	C₂³	#13133264	1	4	yes	—
292	C₂³	C₂⁴×D₅₃	1	8	yes	—
293	C₂³	C₂⁴×D₅₃	1	3	yes	—
294	Q₈	—	53	64	no	—
295	Q₈	—	106	128	no	—
296	Q₈	—	106	64	no	—
297	D₄	C₂²×Dic₁₀₆	1	64	yes	direct product factor
298	C₂×C₄	—	2	24	no	—
299	C₂×C₄	—	2	12	no	—
300	C₂×C₄	—	2	64	no	—
301	C₂×C₄	—	53	48	no	—
302	C₂×C₄	—	53	8	no	—
303	C₂×C₄	—	53	8	no	—
304	C₂×C₄	—	53	16	no	—
305	C₂×C₄	—	106	128	no	—
306	C₂×C₄	—	106	48	no	—
307	C₂×C₄	—	106	24	no	—
308	C₂×C₄	C₂×D₄×D₅₃	1	24	yes	—
309	C₂×C₄	C₂²×Dic₁₀₆	1	24	yes	complemented
310	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
311	C₂×C₄	C₂⁴×D₅₃	1	8	yes	—
312	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
313	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
314	C₂²	—	2	96	no	—
315	C₂²	—	2	8	no	—
316	C₂²	—	2	8	no	—
317	C₂²	D₄×Dic₁₀₆	1	16	yes	direct product factor
318	C₂²	C₂²×D₄×D₅₃	1	6	yes	—
319	C₂²	C₂³×Dic₁₀₆	1	6	yes	—
320	C₂²	C₂³×Dic₁₀₆	1	16	yes	complemented
321	C₂²	C₂×#13133264	1	6	yes	—
322	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
323	C₄	—	2	8	no	—
324	C₄	—	2	4	no	—
325	C₄	—	53	16	no	—
326	C₄	—	106	16	no	—
327	C₄	—	106	8	no	—
328	C₄	C₂²×D₄×D₅₃	1	8	yes	—
329	C₄	C₂³×Dic₁₀₆	1	8	yes	complemented
330	C₂	—	2	16	no	—
331	C₂	C₂×D₄×Dic₁₀₆	1	12	yes	direct product factor
332	C₂	C₂³×D₄×D₅₃	1	1	yes	characteristic
333	C₂	C₂⁴×Dic₁₀₆	1	1	yes	characteristic
334	C₂	C₂²×#13133264	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂³×D₅₃
commutator, cosocle	C₂²×C₅₃	C₂⁶
Frattini	C₂²	C₂⁵×D₅₃
Fitting	C₂²×C₄×D₄×C₅₃	C₂
socle	C₂⁴×C₅₃	C₂⁴
prime radical	C₂³×D₄×C₅₃	C₂²
hypercenter	C₂²×C₄×D₄	D₅₃
hypocenter	C₅₃	C₂²×D₄×Q₈
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂⁴×Dic₁₀₆	C₂	semidirect
2. C₂×D₄×Dic₁₀₆	C₂	direct (N × H)
3. C₂²×#13133217	C₂	semidirect
4. C₂²×#13133216	C₂	semidirect
5. C₂²×#13133196	C₂	semidirect
6. C₂²×#13133194	C₂	semidirect
7. C₂²×C₄×Dic₁₀₆	C₂	semidirect
14. C₂³×Dic₁₀₆	C₂²	semidirect
16. D₄×Dic₁₀₆	C₂²	direct (N × H)
17. C₂×#13133217	C₂²	semidirect
18. C₂×#13133216	C₂²	semidirect
19. C₂×#13133196	C₂²	semidirect
20. C₂×#13133194	C₂²	semidirect
21. C₂×C₄×Dic₁₀₆	C₂²	semidirect
39. C₂²×Dic₁₀₆	D₄	direct (N × H)
43. C₂²×Dic₁₀₆	C₂³	semidirect
49. #13133217	C₂³	semidirect
50. #13133216	C₂³	semidirect
51. #13133196	C₂³	semidirect
52. #13133194	C₂³	semidirect
53. C₄×Dic₁₀₆	C₂³	semidirect
63. C₂²×D₄×C₅₃	Q₈	semidirect
77. C₂⁴×C₅₃	C₂×Q₈	semidirect
80. C₂×D₄×C₅₃	C₂×Q₈	semidirect
86. C₂²×C₄×C₅₃	C₂×Q₈	semidirect
103. C₂×Dic₁₀₆	C₂×D₄	direct (N × H)
122. C₂³×C₅₃	C₂²×Q₈	semidirect
126. D₄×C₅₃	C₂²×Q₈	semidirect
131. C₂×C₄×C₅₃	C₂²×Q₈	semidirect
145. Dic₁₀₆	C₂²×D₄	direct (N × H)
150. C₂²×C₅₃	D₄×Q₈	semidirect
153. C₂²×C₅₃	C₂³×Q₈	semidirect
159. C₄×C₅₃	C₂³×Q₈	semidirect
173. C₂×C₅₃	C₂×D₄×Q₈	semidirect
203. C₅₃	C₂²×D₄×Q₈	semidirect
213. C₂²×D₄	Dic₁₀₆	direct (N × H)
245. C₂⁴	C₂×Dic₁₀₆	semidirect
255. C₂×D₄	C₂×Dic₁₀₆	direct (N × H)
268. C₂²×C₄	C₂×Dic₁₀₆	semidirect
290. C₂³	C₂²×Dic₁₀₆	semidirect
297. D₄	C₂²×Dic₁₀₆	direct (N × H)
309. C₂×C₄	C₂²×Dic₁₀₆	semidirect
317. C₂²	D₄×Dic₁₀₆	direct (N × H)
320. C₂²	C₂³×Dic₁₀₆	semidirect
329. C₄	C₂³×Dic₁₀₆	semidirect
331. C₂	C₂×D₄×Dic₁₀₆	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×Dic₁₀₆	2
C₂×D₄×Dic₁₀₆	2
C₂²×#13133217	2
C₂²×#13133216	2
C₂²×#13133196	2
C₂²×#13133194	2
C₂²×C₄×Dic₁₀₆	2
C₂²×D₄×Dic₅₃	2
C₂²×C₄×D₄×C₅₃	2
C₂²×D₄×Q₈	53

Subgroups — C22×D4×Dic106 #28291008

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×D₄×Dic₁₀₆ #28291008