Subgroups — C₁₀₇×#33504 #41059468

Order 27392.

536 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×#41×C₁₀₇	C₂	1	1	yes	maximal, characteristic
2	C₁₀₇×#2183	C₂	1	2	yes	maximal, complemented
3	C₁₀₇×#2168	C₂	1	4	yes	maximal, complemented
4	D₄×C₁₆×C₁₀₇	C₂	1	2	yes	maximal, complemented
5	C₁₀₇×#2163	C₂	1	2	yes	maximal, complemented
6	C₁₀₇×#2162	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₀₇×#2150	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄⋊C₁₆×C₁₀₇	C₂	1	2	yes	maximal, complemented
9	C₄×#41×C₁₀₇	C₄	1	1	yes	characteristic
10	C₂×M₃₂×C₁₀₇	C₂²	1	2	yes	—
11	C₂²×C₁₆×C₁₀₇	C₂²	1	4	yes	—
12	C₈×Q₈×C₁₀₇	C₄	1	1	yes	characteristic
13	C₈×Q₈×C₁₀₇	C₂²	1	1	yes	characteristic
14	C₈×D₄×C₁₀₇	C₄	1	2	yes	—
15	C₈×D₄×C₁₀₇	C₄	1	1	yes	characteristic
16	C₈×D₄×C₁₀₇	C₂²	1	1	yes	characteristic
17	C₈×D₄×C₁₀₇	C₂²	1	2	yes	—
18	#431×C₁₀₇	C₄	1	1	yes	characteristic
19	#431×C₁₀₇	C₄	1	2	yes	—
20	C₂×C₄×C₈×C₁₀₇	C₂²	1	2	yes	—
21	C₂×C₄×C₈×C₁₀₇	C₂²	1	1	yes	characteristic
22	C₄⋊C₁₆×C₁₀₇	C₂²	1	1	yes	characteristic
23	C₄⋊C₁₆×C₁₀₇	C₂²	1	2	yes	—
24	C₄⋊C₁₆×C₁₀₇	C₂²	1	4	yes	—
25	C₄⋊C₁₆×C₁₀₇	C₂²	1	2	yes	—
26	C₄⋊C₁₆×C₁₀₇	C₂²	1	1	yes	characteristic
27	C₂²⋊C₁₆×C₁₀₇	C₂²	1	2	yes	—
28	C₂²⋊C₁₆×C₁₀₇	C₂²	1	4	yes	—
29	#346×C₁₀₇	C₂²	1	4	yes	—
30	C₄×C₁₆×C₁₀₇	C₂²	1	2	yes	—
31	C₂×#41×C₁₀₇	C₈	1	1	yes	characteristic
32	C₂²×C₈×C₁₀₇	C₂×C₄	1	2	yes	—
33	C₂²×C₈×C₁₀₇	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₈×C₁₀₇	C₂³	1	2	yes	—
35	C₂²×C₈×C₁₀₇	C₂³	1	1	yes	characteristic
36	C₄×Q₈×C₁₀₇	C₈	1	1	yes	characteristic
37	C₄×Q₈×C₁₀₇	C₂×C₄	1	1	yes	characteristic
38	C₄×D₄×C₁₀₇	C₈	1	2	yes	—
39	C₄×D₄×C₁₀₇	C₈	1	1	yes	characteristic
40	C₄×D₄×C₁₀₇	C₂×C₄	1	2	yes	—
41	C₄×D₄×C₁₀₇	C₂×C₄	1	1	yes	characteristic
42	#117×C₁₀₇	C₈	1	1	yes	characteristic
43	#117×C₁₀₇	C₈	1	2	yes	—
44	C₂×C₄²×C₁₀₇	C₂×C₄	1	2	yes	—
45	C₂×C₄²×C₁₀₇	C₂×C₄	1	1	yes	characteristic
46	M₃₂×C₁₀₇	—	4	2	no	—
47	C₂×C₁₆×C₁₀₇	—	4	4	no	—
48	C₂×C₁₆×C₁₀₇	C₂³	1	2	yes	—
49	C₂×C₁₆×C₁₀₇	C₂³	1	2	yes	—
50	C₂×C₁₆×C₁₀₇	C₂³	1	4	yes	—
51	C₄⋊C₈×C₁₀₇	C₂×C₄	1	2	yes	—
52	C₄⋊C₈×C₁₀₇	C₂×C₄	1	1	yes	characteristic
53	C₄⋊C₈×C₁₀₇	C₂×C₄	1	1	yes	characteristic
54	C₄⋊C₈×C₁₀₇	C₂×C₄	1	2	yes	—
55	C₂²⋊C₈×C₁₀₇	C₂×C₄	1	2	yes	—
56	C₂²⋊C₈×C₁₀₇	C₂×C₄	1	2	yes	—
57	C₂²⋊C₈×C₁₀₇	C₂×C₄	1	2	yes	—
58	C₄×C₈×C₁₀₇	C₂×C₄	1	2	yes	—
59	C₄×C₈×C₁₀₇	C₂×C₄	1	1	yes	characteristic
60	C₄×C₈×C₁₀₇	C₂×C₄	1	2	yes	—
61	C₄×C₈×C₁₀₇	C₂×C₄	1	1	yes	characteristic
62	C₄×C₈×C₁₀₇	C₂³	1	1	yes	characteristic
63	C₄×C₈×C₁₀₇	C₂³	1	2	yes	—
64	C₄×C₈×C₁₀₇	C₂³	1	1	yes	characteristic
65	#41×C₁₀₇	—	2	4	no	—
66	C₂×Q₈×C₁₀₇	C₂×C₈	1	1	yes	characteristic
67	C₂×D₄×C₁₀₇	C₂×C₈	1	2	yes	—
68	C₂×D₄×C₁₀₇	C₂×C₈	1	1	yes	characteristic
69	C₂²×C₄×C₁₀₇	C₂×C₈	1	2	yes	—
70	C₂²×C₄×C₁₀₇	C₂×C₈	1	1	yes	characteristic
71	C₂²×C₄×C₁₀₇	C₂×C₈	1	1	yes	characteristic
72	C₂²×C₄×C₁₀₇	C₂×C₈	1	2	yes	—
73	C₂²×C₄×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₀₇	C₂²×C₄	1	2	yes	—
75	C₂×C₈×C₁₀₇	—	2	2	no	—
76	C₂×C₈×C₁₀₇	—	2	1	no	—
77	C₂×C₈×C₁₀₇	—	2	2	no	—
78	C₂×C₈×C₁₀₇	—	2	1	no	—
79	C₂×C₈×C₁₀₇	—	4	2	no	—
80	C₂×C₈×C₁₀₇	—	4	1	no	—
81	C₂×C₈×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
82	C₂×C₈×C₁₀₇	C₂²×C₄	1	2	yes	—
83	C₂×C₈×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
84	C₂×C₈×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
85	C₂×C₈×C₁₀₇	C₂²×C₄	1	2	yes	—
86	C₂×C₈×C₁₀₇	C₂⁴	1	1	yes	characteristic
87	C₄⋊C₄×C₁₀₇	C₂×C₈	1	2	yes	—
88	C₄⋊C₄×C₁₀₇	C₂×C₈	1	1	yes	characteristic
89	C₄⋊C₄×C₁₀₇	C₂×C₈	1	2	yes	—
90	C₄⋊C₄×C₁₀₇	C₂×C₈	1	1	yes	characteristic
91	C₂²⋊C₄×C₁₀₇	C₂×C₈	1	2	yes	—
92	C₂²⋊C₄×C₁₀₇	C₂×C₈	1	2	yes	—
93	C₂²⋊C₄×C₁₀₇	C₂×C₈	1	2	yes	—
94	C₄²×C₁₀₇	C₂×C₈	1	2	yes	—
95	C₄²×C₁₀₇	C₂×C₈	1	1	yes	characteristic
96	C₄²×C₁₀₇	C₂×C₈	1	2	yes	—
97	C₄²×C₁₀₇	C₂×C₈	1	1	yes	characteristic
98	C₄²×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
99	C₄²×C₁₀₇	C₂²×C₄	1	2	yes	—
100	C₄²×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
101	C₁₆×C₁₀₇	—	2	2	no	—
102	C₁₆×C₁₀₇	—	2	4	no	—
103	C₁₆×C₁₀₇	—	2	2	no	—
104	C₂³×C₁₀₇	C₂²×C₈	1	1	yes	characteristic
105	C₂³×C₁₀₇	C₂²×C₈	1	2	yes	—
106	Q₈×C₁₀₇	—	2	2	no	—
107	D₄×C₁₀₇	—	2	4	no	—
108	D₄×C₁₀₇	M₃₂	1	4	yes	complemented
109	C₂×C₄×C₁₀₇	—	2	4	no	—
110	C₂×C₄×C₁₀₇	—	2	2	no	—
111	C₂×C₄×C₁₀₇	—	2	1	no	—
112	C₂×C₄×C₁₀₇	—	2	2	no	—
113	C₂×C₄×C₁₀₇	—	2	1	no	—
114	C₂×C₄×C₁₀₇	—	2	2	no	—
115	C₂×C₄×C₁₀₇	—	2	4	no	—
116	C₂×C₄×C₁₀₇	—	2	2	no	—
117	C₂×C₄×C₁₀₇	C₂²×C₈	1	1	yes	characteristic
118	C₂×C₄×C₁₀₇	C₂²×C₈	1	2	yes	—
119	C₂×C₄×C₁₀₇	C₂²×C₈	1	1	yes	characteristic
120	C₂×C₄×C₁₀₇	C₂²×C₈	1	2	yes	—
121	C₂×C₄×C₁₀₇	C₂²×C₈	1	1	yes	characteristic
122	C₂×C₄×C₁₀₇	C₂²×C₈	1	2	yes	—
123	C₂×C₄×C₁₀₇	C₂²×C₈	1	1	yes	characteristic
124	C₂×C₄×C₁₀₇	C₂²×C₈	1	1	yes	characteristic
125	C₂×C₄×C₁₀₇	C₂³×C₄	1	1	yes	characteristic
126	C₈×C₁₀₇	—	2	2	no	—
127	C₈×C₁₀₇	—	2	1	no	—
128	C₈×C₁₀₇	—	2	1	no	—
129	C₈×C₁₀₇	—	2	1	no	—
130	C₈×C₁₀₇	—	2	2	no	—
131	C₈×C₁₀₇	H(5,𝔽₂)	1	1	yes	characteristic
132	C₈×C₁₀₇	2₋¹⁺⁴	1	1	yes	characteristic
133	C₂²×C₁₀₇	—	2	2	no	—
134	C₂²×C₁₀₇	—	2	2	no	—
135	C₂²×C₁₀₇	—	2	1	no	—
136	C₂²×C₁₀₇	—	2	1	no	—
137	C₂²×C₁₀₇	—	2	1	no	—
138	C₂²×C₁₀₇	C₂×M₃₂	1	4	yes	—
139	C₂²×C₁₀₇	C₂³×C₈	1	1	yes	characteristic
140	C₄×C₁₀₇	—	2	1	no	—
141	C₄×C₁₀₇	—	2	2	no	—
142	C₄×C₁₀₇	—	2	2	no	—
143	C₄×C₁₀₇	—	2	1	no	—
144	C₄×C₁₀₇	—	2	2	no	—
145	C₄×C₁₀₇	—	2	1	no	—
146	C₄×C₁₀₇	C₂×M₃₂	1	2	yes	—
147	C₄×C₁₀₇	#504	1	2	yes	—
148	C₄×C₁₀₇	#520	1	1	yes	characteristic
149	C₄×C₁₀₇	#568	1	1	yes	characteristic
150	#33504	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
151	C₂×C₁₀₇	—	2	4	no	—
152	C₂×C₁₀₇	—	4	1	no	—
153	C₂×C₁₀₇	#2988	1	1	yes	characteristic
154	C₂×C₁₀₇	C₂²×M₃₂	1	1	yes	characteristic
155	C₂×C₁₀₇	C₂×#504	1	1	yes	characteristic
156	C₈×#41	C₂×C₁₀₇	1	1	yes	characteristic
157	#2183	C₂×C₁₀₇	1	2	yes	complemented
158	#2168	C₂×C₁₀₇	1	4	yes	complemented
159	D₄×C₁₆	C₂×C₁₀₇	1	2	yes	complemented
160	#2163	C₂×C₁₀₇	1	2	yes	complemented
161	#2162	C₂×C₁₀₇	1	1	yes	characteristic, complemented
162	#2150	C₂×C₁₀₇	1	1	yes	characteristic, complemented
163	C₂×C₄⋊C₁₆	C₂×C₁₀₇	1	2	yes	complemented
164	C₁₀₇	#33504	1	1	yes	characteristic, direct product factor, Sylow
165	C₄×#41	C₄×C₁₀₇	1	1	yes	characteristic
166	C₂×M₃₂	C₂²×C₁₀₇	1	2	yes	—
167	C₂²×C₁₆	C₂²×C₁₀₇	1	4	yes	—
168	C₈×Q₈	C₄×C₁₀₇	1	1	yes	characteristic
169	C₈×Q₈	C₂²×C₁₀₇	1	1	yes	characteristic
170	C₈×D₄	C₄×C₁₀₇	1	2	yes	—
171	C₈×D₄	C₄×C₁₀₇	1	1	yes	characteristic
172	C₈×D₄	C₂²×C₁₀₇	1	1	yes	characteristic
173	C₈×D₄	C₂²×C₁₀₇	1	2	yes	—
174	#431	C₄×C₁₀₇	1	1	yes	characteristic
175	#431	C₄×C₁₀₇	1	2	yes	—
176	C₂×C₄×C₈	C₂²×C₁₀₇	1	2	yes	—
177	C₂×C₄×C₈	C₂²×C₁₀₇	1	1	yes	characteristic
178	C₄⋊C₁₆	C₂²×C₁₀₇	1	1	yes	characteristic
179	C₄⋊C₁₆	C₂²×C₁₀₇	1	2	yes	—
180	C₄⋊C₁₆	C₂²×C₁₀₇	1	4	yes	—
181	C₄⋊C₁₆	C₂²×C₁₀₇	1	2	yes	—
182	C₄⋊C₁₆	C₂²×C₁₀₇	1	1	yes	characteristic
183	C₂²⋊C₁₆	C₂²×C₁₀₇	1	2	yes	—
184	C₂²⋊C₁₆	C₂²×C₁₀₇	1	4	yes	—
185	#346	C₂²×C₁₀₇	1	4	yes	—
186	C₄×C₁₆	C₂²×C₁₀₇	1	2	yes	—
187	C₂×#41	C₈×C₁₀₇	1	1	yes	characteristic
188	C₂²×C₈	C₂×C₄×C₁₀₇	1	2	yes	—
189	C₂²×C₈	C₂×C₄×C₁₀₇	1	1	yes	characteristic
190	C₂²×C₈	C₂³×C₁₀₇	1	2	yes	—
191	C₂²×C₈	C₂³×C₁₀₇	1	1	yes	characteristic
192	C₄×Q₈	C₈×C₁₀₇	1	1	yes	characteristic
193	C₄×Q₈	C₂×C₄×C₁₀₇	1	1	yes	characteristic
194	C₄×D₄	C₈×C₁₀₇	1	2	yes	—
195	C₄×D₄	C₈×C₁₀₇	1	1	yes	characteristic
196	C₄×D₄	C₂×C₄×C₁₀₇	1	2	yes	—
197	C₄×D₄	C₂×C₄×C₁₀₇	1	1	yes	characteristic
198	#117	C₈×C₁₀₇	1	1	yes	characteristic
199	#117	C₈×C₁₀₇	1	2	yes	—
200	C₂×C₄²	C₂×C₄×C₁₀₇	1	2	yes	—
201	C₂×C₄²	C₂×C₄×C₁₀₇	1	1	yes	characteristic
202	M₃₂	—	4	2	no	—
203	C₂×C₁₆	—	4	4	no	—
204	C₂×C₁₆	C₂³×C₁₀₇	1	2	yes	—
205	C₂×C₁₆	C₂³×C₁₀₇	1	2	yes	—
206	C₂×C₁₆	C₂³×C₁₀₇	1	4	yes	—
207	C₄⋊C₈	C₂×C₄×C₁₀₇	1	2	yes	—
208	C₄⋊C₈	C₂×C₄×C₁₀₇	1	1	yes	characteristic
209	C₄⋊C₈	C₂×C₄×C₁₀₇	1	1	yes	characteristic
210	C₄⋊C₈	C₂×C₄×C₁₀₇	1	2	yes	—
211	C₂²⋊C₈	C₂×C₄×C₁₀₇	1	2	yes	—
212	C₂²⋊C₈	C₂×C₄×C₁₀₇	1	2	yes	—
213	C₂²⋊C₈	C₂×C₄×C₁₀₇	1	2	yes	—
214	C₄×C₈	C₂×C₄×C₁₀₇	1	2	yes	—
215	C₄×C₈	C₂×C₄×C₁₀₇	1	1	yes	characteristic
216	C₄×C₈	C₂×C₄×C₁₀₇	1	2	yes	—
217	C₄×C₈	C₂×C₄×C₁₀₇	1	1	yes	characteristic
218	C₄×C₈	C₂³×C₁₀₇	1	1	yes	characteristic
219	C₄×C₈	C₂³×C₁₀₇	1	2	yes	—
220	C₄×C₈	C₂³×C₁₀₇	1	1	yes	characteristic
221	#41	—	2	4	no	—
222	C₂×Q₈	C₂×C₈×C₁₀₇	1	1	yes	characteristic
223	C₂×D₄	C₂×C₈×C₁₀₇	1	2	yes	—
224	C₂×D₄	C₂×C₈×C₁₀₇	1	1	yes	characteristic
225	C₂²×C₄	C₂×C₈×C₁₀₇	1	2	yes	—
226	C₂²×C₄	C₂×C₈×C₁₀₇	1	1	yes	characteristic
227	C₂²×C₄	C₂×C₈×C₁₀₇	1	1	yes	characteristic
228	C₂²×C₄	C₂×C₈×C₁₀₇	1	2	yes	—
229	C₂²×C₄	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
230	C₂²×C₄	C₂²×C₄×C₁₀₇	1	2	yes	—
231	C₂×C₈	—	2	2	no	—
232	C₂×C₈	—	2	1	no	—
233	C₂×C₈	—	2	2	no	—
234	C₂×C₈	—	2	1	no	—
235	C₂×C₈	—	4	2	no	—
236	C₂×C₈	—	4	1	no	—
237	C₂×C₈	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
238	C₂×C₈	C₂²×C₄×C₁₀₇	1	2	yes	—
239	C₂×C₈	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
240	C₂×C₈	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
241	C₂×C₈	C₂²×C₄×C₁₀₇	1	2	yes	—
242	C₂×C₈	C₂⁴×C₁₀₇	1	1	yes	characteristic
243	C₄⋊C₄	C₂×C₈×C₁₀₇	1	2	yes	—
244	C₄⋊C₄	C₂×C₈×C₁₀₇	1	1	yes	characteristic
245	C₄⋊C₄	C₂×C₈×C₁₀₇	1	2	yes	—
246	C₄⋊C₄	C₂×C₈×C₁₀₇	1	1	yes	characteristic
247	C₂²⋊C₄	C₂×C₈×C₁₀₇	1	2	yes	—
248	C₂²⋊C₄	C₂×C₈×C₁₀₇	1	2	yes	—
249	C₂²⋊C₄	C₂×C₈×C₁₀₇	1	2	yes	—
250	C₄²	C₂×C₈×C₁₀₇	1	2	yes	—
251	C₄²	C₂×C₈×C₁₀₇	1	1	yes	characteristic
252	C₄²	C₂×C₈×C₁₀₇	1	2	yes	—
253	C₄²	C₂×C₈×C₁₀₇	1	1	yes	characteristic
254	C₄²	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
255	C₄²	C₂²×C₄×C₁₀₇	1	2	yes	—
256	C₄²	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
257	C₁₆	—	2	2	no	—
258	C₁₆	—	2	4	no	—
259	C₁₆	—	2	2	no	—
260	C₂³	C₂²×C₈×C₁₀₇	1	1	yes	characteristic
261	C₂³	C₂²×C₈×C₁₀₇	1	2	yes	—
262	Q₈	—	2	2	no	—
263	D₄	—	2	4	no	—
264	D₄	M₃₂×C₁₀₇	1	4	yes	complemented
265	C₂×C₄	—	2	4	no	—
266	C₂×C₄	—	2	2	no	—
267	C₂×C₄	—	2	4	no	—
268	C₂×C₄	—	2	2	no	—
269	C₂×C₄	—	2	2	no	—
270	C₂×C₄	—	2	1	no	—
271	C₂×C₄	—	2	2	no	—
272	C₂×C₄	—	2	1	no	—
273	C₂×C₄	C₂²×C₈×C₁₀₇	1	1	yes	characteristic
274	C₂×C₄	C₂²×C₈×C₁₀₇	1	2	yes	—
275	C₂×C₄	C₂²×C₈×C₁₀₇	1	1	yes	characteristic
276	C₂×C₄	C₂²×C₈×C₁₀₇	1	2	yes	—
277	C₂×C₄	C₂²×C₈×C₁₀₇	1	1	yes	characteristic
278	C₂×C₄	C₂²×C₈×C₁₀₇	1	2	yes	—
279	C₂×C₄	C₂²×C₈×C₁₀₇	1	1	yes	characteristic
280	C₂×C₄	C₂²×C₈×C₁₀₇	1	1	yes	characteristic
281	C₂×C₄	C₂³×C₄×C₁₀₇	1	1	yes	characteristic
282	C₈	—	2	2	no	—
283	C₈	—	2	1	no	—
284	C₈	—	2	1	no	—
285	C₈	—	2	1	no	—
286	C₈	—	2	2	no	—
287	C₈	H(5,𝔽₂)×C₁₀₇	1	1	yes	characteristic
288	C₈	2₋¹⁺⁴×C₁₀₇	1	1	yes	characteristic
289	C₂²	—	2	2	no	—
290	C₂²	—	2	2	no	—
291	C₂²	—	2	1	no	—
292	C₂²	—	2	1	no	—
293	C₂²	—	2	1	no	—
294	C₂²	C₂×M₃₂×C₁₀₇	1	4	yes	—
295	C₂²	C₂³×C₈×C₁₀₇	1	1	yes	characteristic
296	C₄	—	2	1	no	—
297	C₄	—	2	2	no	—
298	C₄	—	2	2	no	—
299	C₄	—	2	1	no	—
300	C₄	—	2	2	no	—
301	C₄	—	2	1	no	—
302	C₄	C₂×M₃₂×C₁₀₇	1	2	yes	—
303	C₄	#504×C₁₀₇	1	2	yes	—
304	C₄	#520×C₁₀₇	1	1	yes	characteristic
305	C₄	#568×C₁₀₇	1	1	yes	characteristic
306	C₂	—	2	4	no	—
307	C₂	—	4	1	no	—
308	C₂	C₁₀₇×#2988	1	1	yes	characteristic
309	C₂	C₂²×M₃₂×C₁₀₇	1	1	yes	characteristic
310	C₂	C₂×#504×C₁₀₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₁₀₇	C₂⁴
commutator	C₂²	C₂³×C₈×C₁₀₇
Frattini, cosocle	C₂×C₈	C₂⁴×C₁₀₇
socle	C₂²×C₁₀₇	C₂³×C₈
prime radical	C₂×#41×C₁₀₇	C₈
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₀₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₀₇×#2183	C₂	semidirect
3. C₁₀₇×#2168	C₂	semidirect
4. D₄×C₁₆×C₁₀₇	C₂	semidirect
5. C₁₀₇×#2163	C₂	semidirect
6. C₁₀₇×#2162	C₂	semidirect
7. C₁₀₇×#2150	C₂	semidirect
8. C₂×C₄⋊C₁₆×C₁₀₇	C₂	semidirect
108. D₄×C₁₀₇	M₃₂	semidirect
150. #33504	C₁₀₇	direct (N × H)
157. #2183	C₂×C₁₀₇	semidirect
158. #2168	C₂×C₁₀₇	semidirect
159. D₄×C₁₆	C₂×C₁₀₇	semidirect
160. #2163	C₂×C₁₀₇	semidirect
161. #2162	C₂×C₁₀₇	semidirect
162. #2150	C₂×C₁₀₇	semidirect
163. C₂×C₄⋊C₁₆	C₂×C₁₀₇	semidirect
164. C₁₀₇	#33504	direct (N × H)
264. D₄	M₃₂×C₁₀₇	semidirect

Maximal subgroups

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

subgroup	index
C₈×#41×C₁₀₇	2
C₁₀₇×#2183	2
C₁₀₇×#2168	2
D₄×C₁₆×C₁₀₇	2
C₁₀₇×#2163	2
C₁₀₇×#2162	2
C₁₀₇×#2150	2
C₂×C₄⋊C₁₆×C₁₀₇	2
#33504	107

Subgroups — C107×#33504 #41059468

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₇×#33504 #41059468