Subgroups — C₂×C₁₀₇×#2537 #41060886

Order 27392.

4782 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#121×C₁₀₇	C₂	1	4	yes	maximal, complemented
2	C₂²×C₄×D₄×C₁₀₇	C₂	1	2	yes	maximal, complemented
3	C₁₀₇×#2537	C₂	1	16	yes	maximal, direct product factor
4	C₂×#394×C₁₀₇	C₂	1	4	yes	maximal, complemented
5	C₂×#384×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#380×C₁₀₇	C₂	1	4	yes	maximal, complemented
7	C₂³×D₄×C₁₀₇	C₂²	1	4	yes	—
8	C₂³×D₄×C₁₀₇	C₂²	1	2	yes	—
9	C₂⁴×C₄×C₁₀₇	C₂²	1	4	yes	—
10	C₂×#121×C₁₀₇	—	2	32	no	—
11	C₂×#121×C₁₀₇	C₂²	1	32	yes	complemented
12	C₂×C₄×D₄×C₁₀₇	—	2	16	no	—
13	C₂×C₄×D₄×C₁₀₇	C₂²	1	16	yes	complemented
14	C₂²×C₄⋊C₄×C₁₀₇	C₂²	1	2	yes	—
15	C₂²×C₄⋊C₄×C₁₀₇	C₂²	1	4	yes	—
16	C₂²×C₄⋊C₄×C₁₀₇	C₂²	1	2	yes	—
17	C₂²×C₂²⋊C₄×C₁₀₇	C₂²	1	4	yes	—
18	C₂²×C₂²⋊C₄×C₁₀₇	C₂²	1	8	yes	—
19	C₂²×C₄²×C₁₀₇	C₂²	1	1	yes	characteristic
20	#394×C₁₀₇	C₂²	1	32	yes	complemented
21	#384×C₁₀₇	C₂²	1	8	yes	complemented
22	#380×C₁₀₇	C₂²	1	32	yes	complemented
23	C₂×#95×C₁₀₇	C₂²	1	4	yes	—
24	C₂⁵×C₁₀₇	C₂³	1	4	yes	—
25	C₂²×D₄×C₁₀₇	—	2	32	no	—
26	C₂²×D₄×C₁₀₇	—	2	8	no	—
27	C₂²×D₄×C₁₀₇	—	2	8	no	—
28	C₂²×D₄×C₁₀₇	—	4	8	no	—
29	C₂²×D₄×C₁₀₇	D₄	1	16	yes	complemented
30	C₂²×D₄×C₁₀₇	C₂³	1	16	yes	—
31	C₂²×D₄×C₁₀₇	C₂³	1	8	yes	—
32	C₂³×C₄×C₁₀₇	—	2	16	no	—
33	C₂³×C₄×C₁₀₇	—	2	16	no	—
34	C₂³×C₄×C₁₀₇	—	2	16	no	—
35	C₂³×C₄×C₁₀₇	C₂³	1	16	yes	—
36	C₂³×C₄×C₁₀₇	C₂³	1	4	yes	—
37	C₂³×C₄×C₁₀₇	C₂³	1	4	yes	—
38	C₂³×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
39	C₂³×C₄×C₁₀₇	C₂³	1	2	yes	—
40	#121×C₁₀₇	—	2	128	no	—
41	C₄×D₄×C₁₀₇	—	2	64	no	—
42	C₂×C₄⋊C₄×C₁₀₇	—	2	8	no	—
43	C₂×C₄⋊C₄×C₁₀₇	—	2	16	no	—
44	C₂×C₄⋊C₄×C₁₀₇	—	4	4	no	—
45	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	8	yes	—
46	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	16	yes	—
47	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	8	yes	—
48	C₂×C₂²⋊C₄×C₁₀₇	—	2	32	no	—
49	C₂×C₂²⋊C₄×C₁₀₇	—	2	16	no	—
50	C₂×C₂²⋊C₄×C₁₀₇	C₂³	1	32	yes	—
51	C₂×C₂²⋊C₄×C₁₀₇	C₂³	1	16	yes	—
52	C₂×C₄²×C₁₀₇	D₄	1	8	yes	complemented
53	C₂×C₄²×C₁₀₇	C₂³	1	4	yes	—
54	#95×C₁₀₇	C₂³	1	16	yes	—
55	C₂⁴×C₁₀₇	—	2	8	no	—
56	C₂⁴×C₁₀₇	—	2	8	no	—
57	C₂⁴×C₁₀₇	—	2	8	no	—
58	C₂⁴×C₁₀₇	—	2	8	no	—
59	C₂⁴×C₁₀₇	—	2	8	no	—
60	C₂⁴×C₁₀₇	—	2	8	no	—
61	C₂⁴×C₁₀₇	C₂×D₄	1	16	yes	—
62	C₂⁴×C₁₀₇	C₂⁴	1	8	yes	—
63	C₂⁴×C₁₀₇	C₂⁴	1	1	yes	characteristic
64	C₂×D₄×C₁₀₇	—	2	64	no	—
65	C₂×D₄×C₁₀₇	—	2	64	no	—
66	C₂×D₄×C₁₀₇	—	2	16	no	—
67	C₂×D₄×C₁₀₇	—	2	16	no	—
68	C₂×D₄×C₁₀₇	—	4	16	no	—
69	C₂×D₄×C₁₀₇	—	4	64	no	—
70	C₂×D₄×C₁₀₇	C₂×D₄	1	32	yes	complemented
71	C₂²×C₄×C₁₀₇	—	2	2	no	—
72	C₂²×C₄×C₁₀₇	—	2	2	no	—
73	C₂²×C₄×C₁₀₇	—	2	8	no	—
74	C₂²×C₄×C₁₀₇	—	2	8	no	—
75	C₂²×C₄×C₁₀₇	—	2	16	no	—
76	C₂²×C₄×C₁₀₇	—	2	8	no	—
77	C₂²×C₄×C₁₀₇	—	2	8	no	—
78	C₂²×C₄×C₁₀₇	—	2	32	no	—
79	C₂²×C₄×C₁₀₇	—	2	32	no	—
80	C₂²×C₄×C₁₀₇	—	2	32	no	—
81	C₂²×C₄×C₁₀₇	—	4	64	no	—
82	C₂²×C₄×C₁₀₇	C₂×D₄	1	4	yes	—
83	C₂²×C₄×C₁₀₇	C₂×D₄	1	8	yes	—
84	C₂²×C₄×C₁₀₇	C₂×D₄	1	8	yes	—
85	C₂²×C₄×C₁₀₇	#41	1	8	yes	—
86	C₂²×C₄×C₁₀₇	C₂⁴	1	8	yes	—
87	C₂²×C₄×C₁₀₇	C₂⁴	1	8	yes	—
88	C₂²×C₄×C₁₀₇	C₂⁴	1	2	yes	—
89	C₂²×C₄×C₁₀₇	C₂⁴	1	4	yes	—
90	C₄⋊C₄×C₁₀₇	—	2	16	no	—
91	C₄⋊C₄×C₁₀₇	—	2	32	no	—
92	C₄⋊C₄×C₁₀₇	—	4	8	no	—
93	C₂²⋊C₄×C₁₀₇	—	2	64	no	—
94	C₂²⋊C₄×C₁₀₇	—	2	32	no	—
95	C₄²×C₁₀₇	C₂×D₄	1	16	yes	complemented
96	C₂³×C₁₀₇	—	2	32	no	—
97	C₂³×C₁₀₇	—	2	32	no	—
98	C₂³×C₁₀₇	—	2	32	no	—
99	C₂³×C₁₀₇	—	2	8	no	—
100	C₂³×C₁₀₇	—	2	8	no	—
101	C₂³×C₁₀₇	—	2	8	no	—
102	C₂³×C₁₀₇	—	2	8	no	—
103	C₂³×C₁₀₇	—	2	8	no	—
104	C₂³×C₁₀₇	—	2	8	no	—
105	C₂³×C₁₀₇	—	4	16	no	—
106	C₂³×C₁₀₇	—	4	16	no	—
107	C₂³×C₁₀₇	—	4	16	no	—
108	C₂³×C₁₀₇	—	4	16	no	—
109	C₂³×C₁₀₇	C₂²×D₄	1	16	yes	—
110	C₂³×C₁₀₇	C₂²×D₄	1	2	yes	—
111	C₂³×C₁₀₇	C₂²×D₄	1	4	yes	—
112	C₂³×C₁₀₇	C₂×#41	1	4	yes	—
113	C₂³×C₁₀₇	H(5,𝔽₂)	1	2	yes	—
114	C₂³×C₁₀₇	2₋¹⁺⁴	1	2	yes	—
115	C₂³×C₁₀₇	C₂⁵	1	1	yes	characteristic
116	D₄×C₁₀₇	—	2	64	no	—
117	D₄×C₁₀₇	—	4	64	no	—
118	C₂×C₄×C₁₀₇	—	2	8	no	—
119	C₂×C₄×C₁₀₇	—	2	2	no	—
120	C₂×C₄×C₁₀₇	—	2	2	no	—
121	C₂×C₄×C₁₀₇	—	2	8	no	—
122	C₂×C₄×C₁₀₇	—	2	8	no	—
123	C₂×C₄×C₁₀₇	—	2	16	no	—
124	C₂×C₄×C₁₀₇	—	2	8	no	—
125	C₂×C₄×C₁₀₇	—	2	8	no	—
126	C₂×C₄×C₁₀₇	—	4	16	no	—
127	C₂×C₄×C₁₀₇	—	4	16	no	—
128	C₂×C₄×C₁₀₇	—	4	64	no	—
129	C₂×C₄×C₁₀₇	#121	1	32	yes	complemented
130	C₂×C₄×C₁₀₇	C₂²×D₄	1	4	yes	—
131	C₂×C₄×C₁₀₇	C₂²×D₄	1	8	yes	—
132	C₂×C₄×C₁₀₇	C₂²×D₄	1	8	yes	—
133	C₂×C₄×C₁₀₇	C₂×#41	1	8	yes	—
134	C₂²×C₁₀₇	—	2	16	no	—
135	C₂²×C₁₀₇	—	2	16	no	—
136	C₂²×C₁₀₇	—	2	16	no	—
137	C₂²×C₁₀₇	—	4	8	no	—
138	C₂²×C₁₀₇	—	4	8	no	—
139	C₂²×C₁₀₇	—	4	8	no	—
140	C₂²×C₁₀₇	—	4	8	no	—
141	C₂²×C₁₀₇	—	4	64	no	—
142	C₂²×C₁₀₇	C₂×#121	1	8	yes	—
143	C₂²×C₁₀₇	#537	1	4	yes	—
144	C₂²×C₁₀₇	D₄²	1	4	yes	—
145	C₂²×C₁₀₇	#547	1	8	yes	—
146	C₂²×C₁₀₇	#555	1	4	yes	—
147	C₂²×C₁₀₇	C₂³×D₄	1	1	yes	characteristic
148	C₂²×C₁₀₇	C₂³×D₄	1	2	yes	—
149	C₂²×C₁₀₇	C₂²×#41	1	2	yes	—
150	C₂²×C₁₀₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
151	C₂²×C₁₀₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
152	C₄×C₁₀₇	—	2	4	no	—
153	C₄×C₁₀₇	—	4	8	no	—
154	C₄×C₁₀₇	—	4	8	no	—
155	C₄×C₁₀₇	C₂×#121	1	16	yes	complemented
156	C₂×#2537	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
157	C₂×C₁₀₇	—	4	16	no	—
158	C₂×C₁₀₇	#2537	1	8	yes	direct product factor
159	C₂×C₁₀₇	C₂²×#121	1	2	yes	—
160	C₂×C₁₀₇	C₂×#537	1	1	yes	characteristic
161	C₂×C₁₀₇	C₂×D₄²	1	1	yes	characteristic
162	C₂×C₁₀₇	C₂×#547	1	2	yes	—
163	C₂×C₁₀₇	C₂×#555	1	1	yes	characteristic
164	C₂²×#121	C₂×C₁₀₇	1	4	yes	complemented
165	C₂²×C₄×D₄	C₂×C₁₀₇	1	2	yes	complemented
166	#2537	C₂×C₁₀₇	1	16	yes	direct product factor
167	C₂×#394	C₂×C₁₀₇	1	4	yes	complemented
168	C₂×#384	C₂×C₁₀₇	1	1	yes	characteristic, complemented
169	C₂×#380	C₂×C₁₀₇	1	4	yes	complemented
170	C₁₀₇	C₂×#2537	1	1	yes	characteristic, direct product factor, Sylow
171	C₂³×D₄	C₂²×C₁₀₇	1	4	yes	—
172	C₂³×D₄	C₂²×C₁₀₇	1	2	yes	—
173	C₂⁴×C₄	C₂²×C₁₀₇	1	4	yes	—
174	C₂×#121	—	2	32	no	—
175	C₂×#121	C₂²×C₁₀₇	1	32	yes	complemented
176	C₂×C₄×D₄	—	2	16	no	—
177	C₂×C₄×D₄	C₂²×C₁₀₇	1	16	yes	complemented
178	C₂²×C₄⋊C₄	C₂²×C₁₀₇	1	2	yes	—
179	C₂²×C₄⋊C₄	C₂²×C₁₀₇	1	4	yes	—
180	C₂²×C₄⋊C₄	C₂²×C₁₀₇	1	2	yes	—
181	C₂²×C₂²⋊C₄	C₂²×C₁₀₇	1	4	yes	—
182	C₂²×C₂²⋊C₄	C₂²×C₁₀₇	1	8	yes	—
183	C₂²×C₄²	C₂²×C₁₀₇	1	1	yes	characteristic
184	#394	C₂²×C₁₀₇	1	32	yes	complemented
185	#384	C₂²×C₁₀₇	1	8	yes	complemented
186	#380	C₂²×C₁₀₇	1	32	yes	complemented
187	C₂×#95	C₂²×C₁₀₇	1	4	yes	—
188	C₂⁵	C₂³×C₁₀₇	1	4	yes	—
189	C₂²×D₄	—	2	32	no	—
190	C₂²×D₄	—	2	8	no	—
191	C₂²×D₄	—	2	8	no	—
192	C₂²×D₄	—	4	8	no	—
193	C₂²×D₄	D₄×C₁₀₇	1	16	yes	complemented
194	C₂²×D₄	C₂³×C₁₀₇	1	16	yes	—
195	C₂²×D₄	C₂³×C₁₀₇	1	8	yes	—
196	C₂³×C₄	—	2	16	no	—
197	C₂³×C₄	—	2	16	no	—
198	C₂³×C₄	—	2	16	no	—
199	C₂³×C₄	C₂³×C₁₀₇	1	4	yes	—
200	C₂³×C₄	C₂³×C₁₀₇	1	4	yes	—
201	C₂³×C₄	C₂³×C₁₀₇	1	16	yes	—
202	C₂³×C₄	C₂³×C₁₀₇	1	1	yes	characteristic
203	C₂³×C₄	C₂³×C₁₀₇	1	2	yes	—
204	#121	—	2	128	no	—
205	C₄×D₄	—	2	64	no	—
206	C₂×C₄⋊C₄	—	2	8	no	—
207	C₂×C₄⋊C₄	—	2	16	no	—
208	C₂×C₄⋊C₄	—	4	4	no	—
209	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	8	yes	—
210	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	16	yes	—
211	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	8	yes	—
212	C₂×C₂²⋊C₄	—	2	32	no	—
213	C₂×C₂²⋊C₄	—	2	16	no	—
214	C₂×C₂²⋊C₄	C₂³×C₁₀₇	1	16	yes	—
215	C₂×C₂²⋊C₄	C₂³×C₁₀₇	1	32	yes	—
216	C₂×C₄²	D₄×C₁₀₇	1	8	yes	complemented
217	C₂×C₄²	C₂³×C₁₀₇	1	4	yes	—
218	#95	C₂³×C₁₀₇	1	16	yes	—
219	C₂⁴	—	2	8	no	—
220	C₂⁴	—	2	8	no	—
221	C₂⁴	—	2	8	no	—
222	C₂⁴	—	2	8	no	—
223	C₂⁴	—	2	8	no	—
224	C₂⁴	—	2	8	no	—
225	C₂⁴	C₂×D₄×C₁₀₇	1	16	yes	—
226	C₂⁴	C₂⁴×C₁₀₇	1	8	yes	—
227	C₂⁴	C₂⁴×C₁₀₇	1	1	yes	characteristic
228	C₂×D₄	—	2	64	no	—
229	C₂×D₄	—	2	64	no	—
230	C₂×D₄	—	2	16	no	—
231	C₂×D₄	—	2	16	no	—
232	C₂×D₄	—	4	16	no	—
233	C₂×D₄	—	4	64	no	—
234	C₂×D₄	C₂×D₄×C₁₀₇	1	32	yes	complemented
235	C₂²×C₄	—	2	2	no	—
236	C₂²×C₄	—	2	2	no	—
237	C₂²×C₄	—	2	8	no	—
238	C₂²×C₄	—	2	8	no	—
239	C₂²×C₄	—	2	16	no	—
240	C₂²×C₄	—	2	8	no	—
241	C₂²×C₄	—	2	8	no	—
242	C₂²×C₄	—	2	32	no	—
243	C₂²×C₄	—	2	32	no	—
244	C₂²×C₄	—	2	32	no	—
245	C₂²×C₄	—	4	64	no	—
246	C₂²×C₄	C₂×D₄×C₁₀₇	1	4	yes	—
247	C₂²×C₄	C₂×D₄×C₁₀₇	1	8	yes	—
248	C₂²×C₄	C₂×D₄×C₁₀₇	1	8	yes	—
249	C₂²×C₄	#41×C₁₀₇	1	8	yes	—
250	C₂²×C₄	C₂⁴×C₁₀₇	1	8	yes	—
251	C₂²×C₄	C₂⁴×C₁₀₇	1	8	yes	—
252	C₂²×C₄	C₂⁴×C₁₀₇	1	2	yes	—
253	C₂²×C₄	C₂⁴×C₁₀₇	1	4	yes	—
254	C₄⋊C₄	—	2	16	no	—
255	C₄⋊C₄	—	2	32	no	—
256	C₄⋊C₄	—	4	8	no	—
257	C₂²⋊C₄	—	2	64	no	—
258	C₂²⋊C₄	—	2	32	no	—
259	C₄²	C₂×D₄×C₁₀₇	1	16	yes	complemented
260	C₂³	—	2	32	no	—
261	C₂³	—	2	32	no	—
262	C₂³	—	2	32	no	—
263	C₂³	—	2	8	no	—
264	C₂³	—	2	8	no	—
265	C₂³	—	2	8	no	—
266	C₂³	—	2	8	no	—
267	C₂³	—	2	8	no	—
268	C₂³	—	2	8	no	—
269	C₂³	—	4	16	no	—
270	C₂³	—	4	16	no	—
271	C₂³	—	4	16	no	—
272	C₂³	—	4	16	no	—
273	C₂³	C₂²×D₄×C₁₀₇	1	16	yes	—
274	C₂³	C₂²×D₄×C₁₀₇	1	2	yes	—
275	C₂³	C₂²×D₄×C₁₀₇	1	4	yes	—
276	C₂³	C₂×#41×C₁₀₇	1	4	yes	—
277	C₂³	H(5,𝔽₂)×C₁₀₇	1	2	yes	—
278	C₂³	2₋¹⁺⁴×C₁₀₇	1	2	yes	—
279	C₂³	C₂⁵×C₁₀₇	1	1	yes	characteristic
280	D₄	—	2	64	no	—
281	D₄	—	4	64	no	—
282	C₂×C₄	—	2	8	no	—
283	C₂×C₄	—	2	2	no	—
284	C₂×C₄	—	2	2	no	—
285	C₂×C₄	—	2	8	no	—
286	C₂×C₄	—	2	8	no	—
287	C₂×C₄	—	2	16	no	—
288	C₂×C₄	—	2	8	no	—
289	C₂×C₄	—	2	8	no	—
290	C₂×C₄	—	4	16	no	—
291	C₂×C₄	—	4	16	no	—
292	C₂×C₄	—	4	64	no	—
293	C₂×C₄	#121×C₁₀₇	1	32	yes	complemented
294	C₂×C₄	C₂²×D₄×C₁₀₇	1	4	yes	—
295	C₂×C₄	C₂²×D₄×C₁₀₇	1	8	yes	—
296	C₂×C₄	C₂²×D₄×C₁₀₇	1	8	yes	—
297	C₂×C₄	C₂×#41×C₁₀₇	1	8	yes	—
298	C₂²	—	2	16	no	—
299	C₂²	—	2	16	no	—
300	C₂²	—	2	16	no	—
301	C₂²	—	4	8	no	—
302	C₂²	—	4	8	no	—
303	C₂²	—	4	8	no	—
304	C₂²	—	4	8	no	—
305	C₂²	—	4	64	no	—
306	C₂²	C₂×#121×C₁₀₇	1	8	yes	—
307	C₂²	#537×C₁₀₇	1	4	yes	—
308	C₂²	D₄²×C₁₀₇	1	4	yes	—
309	C₂²	#547×C₁₀₇	1	8	yes	—
310	C₂²	#555×C₁₀₇	1	4	yes	—
311	C₂²	C₂³×D₄×C₁₀₇	1	1	yes	characteristic
312	C₂²	C₂³×D₄×C₁₀₇	1	2	yes	—
313	C₂²	C₂²×#41×C₁₀₇	1	2	yes	—
314	C₂²	C₂×H(5,𝔽₂)×C₁₀₇	1	1	yes	characteristic
315	C₂²	C₂×2₋¹⁺⁴×C₁₀₇	1	1	yes	characteristic
316	C₄	—	2	4	no	—
317	C₄	—	4	8	no	—
318	C₄	—	4	8	no	—
319	C₄	C₂×#121×C₁₀₇	1	16	yes	complemented
320	C₂	—	4	16	no	—
321	C₂	C₁₀₇×#2537	1	8	yes	direct product factor
322	C₂	C₂²×#121×C₁₀₇	1	2	yes	—
323	C₂	C₂×#537×C₁₀₇	1	1	yes	characteristic
324	C₂	C₂×D₄²×C₁₀₇	1	1	yes	characteristic
325	C₂	C₂×#547×C₁₀₇	1	2	yes	—
326	C₂	C₂×#555×C₁₀₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₀₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₀₇
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₀₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#121×C₁₀₇	C₂	semidirect
2. C₂²×C₄×D₄×C₁₀₇	C₂	semidirect
3. C₁₀₇×#2537	C₂	direct (N × H)
4. C₂×#394×C₁₀₇	C₂	semidirect
5. C₂×#384×C₁₀₇	C₂	semidirect
6. C₂×#380×C₁₀₇	C₂	semidirect
11. C₂×#121×C₁₀₇	C₂²	semidirect
13. C₂×C₄×D₄×C₁₀₇	C₂²	semidirect
20. #394×C₁₀₇	C₂²	semidirect
21. #384×C₁₀₇	C₂²	semidirect
22. #380×C₁₀₇	C₂²	semidirect
29. C₂²×D₄×C₁₀₇	D₄	semidirect
52. C₂×C₄²×C₁₀₇	D₄	semidirect
70. C₂×D₄×C₁₀₇	C₂×D₄	semidirect
95. C₄²×C₁₀₇	C₂×D₄	semidirect
129. C₂×C₄×C₁₀₇	#121	semidirect
155. C₄×C₁₀₇	C₂×#121	semidirect
156. C₂×#2537	C₁₀₇	direct (N × H)
158. C₂×C₁₀₇	#2537	direct (N × H)
164. C₂²×#121	C₂×C₁₀₇	semidirect
165. C₂²×C₄×D₄	C₂×C₁₀₇	semidirect
166. #2537	C₂×C₁₀₇	direct (N × H)
167. C₂×#394	C₂×C₁₀₇	semidirect
168. C₂×#384	C₂×C₁₀₇	semidirect
169. C₂×#380	C₂×C₁₀₇	semidirect
170. C₁₀₇	C₂×#2537	direct (N × H)
175. C₂×#121	C₂²×C₁₀₇	semidirect
177. C₂×C₄×D₄	C₂²×C₁₀₇	semidirect
184. #394	C₂²×C₁₀₇	semidirect
185. #384	C₂²×C₁₀₇	semidirect
186. #380	C₂²×C₁₀₇	semidirect
193. C₂²×D₄	D₄×C₁₀₇	semidirect
216. C₂×C₄²	D₄×C₁₀₇	semidirect
234. C₂×D₄	C₂×D₄×C₁₀₇	semidirect
259. C₄²	C₂×D₄×C₁₀₇	semidirect
293. C₂×C₄	#121×C₁₀₇	semidirect
319. C₄	C₂×#121×C₁₀₇	semidirect
321. C₂	C₁₀₇×#2537	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×#121×C₁₀₇	2
C₂²×C₄×D₄×C₁₀₇	2
C₁₀₇×#2537	2
C₂×#394×C₁₀₇	2
C₂×#384×C₁₀₇	2
C₂×#380×C₁₀₇	2
C₂×#2537	107

Subgroups — C2×C107×#2537 #41060886

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₀₇×#2537 #41060886