Subgroups — C₂×C₁₀₇×#2045 #41049481

Order 27392.

1586 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₈×C₁₀₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#424×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#418×C₁₀₇	C₂	1	2	yes	maximal, complemented
4	C₂²×#100×C₁₀₇	C₂	1	2	yes	maximal, complemented
5	C₁₀₇×#2045	C₂	1	8	yes	maximal, direct product factor
6	C₂×#341×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂³×D₄×C₁₀₇	C₂²	1	2	yes	—
8	C₂²×D₈×C₁₀₇	—	2	8	no	—
9	C₂²×D₈×C₁₀₇	—	2	2	no	—
10	C₂²×D₈×C₁₀₇	—	2	2	no	—
11	C₂²×D₈×C₁₀₇	C₂²	1	4	yes	—
12	C₂²×M₁₆×C₁₀₇	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₁₀₇	C₂²	1	2	yes	—
14	C₂³×C₈×C₁₀₇	C₂²	1	1	yes	characteristic
15	C₂×#117×C₁₀₇	C₂²	1	1	yes	characteristic
16	#424×C₁₀₇	—	2	2	no	—
17	#424×C₁₀₇	C₂²	1	4	yes	complemented
18	C₂×C₄⋊C₈×C₁₀₇	—	2	2	no	—
19	#418×C₁₀₇	—	2	4	no	—
20	#418×C₁₀₇	C₂²	1	8	yes	complemented
21	C₂×#102×C₁₀₇	—	2	4	no	—
22	C₂×#100×C₁₀₇	—	2	8	no	—
23	C₂×#100×C₁₀₇	C₂²	1	8	yes	complemented
24	#341×C₁₀₇	C₂²	1	4	yes	complemented
25	C₂⁵×C₁₀₇	—	2	2	no	—
26	C₂²×D₄×C₁₀₇	—	2	2	no	—
27	C₂²×D₄×C₁₀₇	—	2	2	no	—
28	C₂²×D₄×C₁₀₇	—	2	4	no	—
29	C₂²×D₄×C₁₀₇	—	2	2	no	—
30	C₂²×D₄×C₁₀₇	—	2	2	no	—
31	C₂²×D₄×C₁₀₇	—	2	4	no	—
32	C₂²×D₄×C₁₀₇	—	2	2	no	—
33	C₂²×D₄×C₁₀₇	—	2	4	no	—
34	C₂²×D₄×C₁₀₇	D₄	1	8	yes	—
35	C₂²×D₄×C₁₀₇	C₂³	1	4	yes	—
36	C₂³×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
37	C₂×D₈×C₁₀₇	—	2	16	no	—
38	C₂×D₈×C₁₀₇	—	2	16	no	—
39	C₂×D₈×C₁₀₇	—	2	16	no	—
40	C₂×D₈×C₁₀₇	—	2	8	no	—
41	C₂×M₁₆×C₁₀₇	—	2	2	no	—
42	C₂×M₁₆×C₁₀₇	—	2	1	no	—
43	C₂×M₁₆×C₁₀₇	—	2	4	no	—
44	C₂×M₁₆×C₁₀₇	—	2	4	no	—
45	C₂×M₁₆×C₁₀₇	—	2	4	no	—
46	C₂×M₁₆×C₁₀₇	C₂³	1	4	yes	—
47	C₂×M₁₆×C₁₀₇	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₀₇	—	2	4	no	—
49	C₂²×C₈×C₁₀₇	—	2	2	no	—
50	C₂²×C₈×C₁₀₇	—	2	1	no	—
51	C₂²×C₈×C₁₀₇	D₄	1	2	yes	—
52	C₂²×C₈×C₁₀₇	D₄	1	2	yes	—
53	C₂²×C₈×C₁₀₇	C₂³	1	2	yes	—
54	#117×C₁₀₇	—	2	1	no	—
55	#117×C₁₀₇	—	2	1	no	—
56	#117×C₁₀₇	D₄	1	2	yes	—
57	#117×C₁₀₇	C₂³	1	2	yes	—
58	C₂×C₄⋊C₄×C₁₀₇	D₄	1	2	yes	—
59	C₂×C₂²⋊C₄×C₁₀₇	—	2	1	no	—
60	C₂×C₄²×C₁₀₇	—	2	1	no	—
61	C₄⋊C₈×C₁₀₇	—	2	8	no	—
62	#102×C₁₀₇	—	2	16	no	—
63	#100×C₁₀₇	—	2	16	no	—
64	C₂⁴×C₁₀₇	—	2	8	no	—
65	C₂⁴×C₁₀₇	—	2	4	no	—
66	C₂⁴×C₁₀₇	—	4	2	no	—
67	C₂⁴×C₁₀₇	—	4	2	no	—
68	C₂⁴×C₁₀₇	—	4	4	no	—
69	C₂⁴×C₁₀₇	—	8	8	no	—
70	C₂⁴×C₁₀₇	#41	1	1	yes	characteristic
71	C₂×D₄×C₁₀₇	—	2	8	no	—
72	C₂×D₄×C₁₀₇	—	2	8	no	—
73	C₂×D₄×C₁₀₇	—	2	8	no	—
74	C₂×D₄×C₁₀₇	—	2	8	no	—
75	C₂×D₄×C₁₀₇	—	2	8	no	—
76	C₂×D₄×C₁₀₇	—	2	4	no	—
77	C₂×D₄×C₁₀₇	—	2	4	no	—
78	C₂×D₄×C₁₀₇	—	2	4	no	—
79	C₂×D₄×C₁₀₇	—	2	4	no	—
80	C₂×D₄×C₁₀₇	—	2	4	no	—
81	C₂×D₄×C₁₀₇	—	4	4	no	—
82	C₂×D₄×C₁₀₇	—	4	4	no	—
83	C₂×D₄×C₁₀₇	—	4	2	no	—
84	C₂×D₄×C₁₀₇	—	4	2	no	—
85	C₂×D₄×C₁₀₇	—	4	4	no	—
86	C₂×D₄×C₁₀₇	—	4	4	no	—
87	C₂×D₄×C₁₀₇	—	4	4	no	—
88	C₂×D₄×C₁₀₇	C₂×D₄	1	8	yes	—
89	C₂²×C₄×C₁₀₇	—	2	2	no	—
90	C₂²×C₄×C₁₀₇	C₂×D₄	1	4	yes	—
91	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₀₇	#41	1	1	yes	characteristic
96	C₂²×C₄×C₁₀₇	#41	1	4	yes	—
97	C₂²×C₄×C₁₀₇	C₂⁴	1	1	yes	characteristic
98	D₈×C₁₀₇	—	2	32	no	—
99	M₁₆×C₁₀₇	—	2	4	no	—
100	M₁₆×C₁₀₇	—	2	4	no	—
101	M₁₆×C₁₀₇	—	2	4	no	—
102	M₁₆×C₁₀₇	—	4	2	no	—
103	M₁₆×C₁₀₇	—	4	4	no	—
104	C₂×C₈×C₁₀₇	—	2	4	no	—
105	C₂×C₈×C₁₀₇	—	2	4	no	—
106	C₂×C₈×C₁₀₇	—	2	4	no	—
107	C₂×C₈×C₁₀₇	—	2	4	no	—
108	C₂×C₈×C₁₀₇	—	2	2	no	—
109	C₂×C₈×C₁₀₇	—	4	2	no	—
110	C₂×C₈×C₁₀₇	—	4	4	no	—
111	C₂×C₈×C₁₀₇	C₂×D₄	1	4	yes	—
112	C₄⋊C₄×C₁₀₇	—	2	2	no	—
113	C₄⋊C₄×C₁₀₇	C₂×D₄	1	4	yes	—
114	C₂²⋊C₄×C₁₀₇	—	2	2	no	—
115	C₂²⋊C₄×C₁₀₇	—	2	2	no	—
116	C₄²×C₁₀₇	—	2	2	no	—
117	C₄²×C₁₀₇	—	2	2	no	—
118	C₂³×C₁₀₇	—	2	4	no	—
119	C₂³×C₁₀₇	—	2	8	no	—
120	C₂³×C₁₀₇	—	4	4	no	—
121	C₂³×C₁₀₇	—	4	4	no	—
122	C₂³×C₁₀₇	—	4	8	no	—
123	C₂³×C₁₀₇	—	4	8	no	—
124	C₂³×C₁₀₇	—	8	8	no	—
125	C₂³×C₁₀₇	—	8	16	no	—
126	C₂³×C₁₀₇	—	8	8	no	—
127	C₂³×C₁₀₇	—	8	16	no	—
128	C₂³×C₁₀₇	—	8	8	no	—
129	C₂³×C₁₀₇	#121	1	1	yes	characteristic
130	C₂³×C₁₀₇	#121	1	1	yes	characteristic
131	C₂³×C₁₀₇	#123	1	4	yes	—
132	C₂³×C₁₀₇	C₂×#41	1	1	yes	characteristic
133	D₄×C₁₀₇	—	2	8	no	—
134	D₄×C₁₀₇	—	2	8	no	—
135	D₄×C₁₀₇	—	4	4	no	—
136	D₄×C₁₀₇	—	4	4	no	—
137	D₄×C₁₀₇	—	4	8	no	—
138	D₄×C₁₀₇	—	4	8	no	—
139	C₂×C₄×C₁₀₇	—	2	4	no	—
140	C₂×C₄×C₁₀₇	—	4	4	no	—
141	C₂×C₄×C₁₀₇	#120	1	2	yes	—
142	C₂×C₄×C₁₀₇	#120	1	2	yes	—
143	C₂×C₄×C₁₀₇	#121	1	4	yes	—
144	C₂×C₄×C₁₀₇	#121	1	4	yes	—
145	C₂×C₄×C₁₀₇	#121	1	1	yes	characteristic
146	C₂×C₄×C₁₀₇	#121	1	1	yes	characteristic
147	C₂×C₄×C₁₀₇	#123	1	4	yes	—
148	C₂×C₄×C₁₀₇	#124	1	2	yes	—
149	C₂×C₄×C₁₀₇	#124	1	2	yes	—
150	C₂×C₄×C₁₀₇	C₂²×D₄	1	2	yes	—
151	C₂×C₄×C₁₀₇	C₂²×D₄	1	1	yes	characteristic
152	C₂×C₄×C₁₀₇	C₂²×D₄	1	1	yes	characteristic
153	C₂×C₄×C₁₀₇	C₂×#41	1	2	yes	—
154	C₈×C₁₀₇	—	2	4	no	—
155	C₈×C₁₀₇	—	4	2	no	—
156	C₈×C₁₀₇	—	4	4	no	—
157	C₂²×C₁₀₇	—	2	2	no	—
158	C₂²×C₁₀₇	—	2	2	no	—
159	C₂²×C₁₀₇	—	2	8	no	—
160	C₂²×C₁₀₇	—	4	8	no	—
161	C₂²×C₁₀₇	—	8	8	no	—
162	C₂²×C₁₀₇	—	8	8	no	—
163	C₂²×C₁₀₇	—	8	16	no	—
164	C₂²×C₁₀₇	—	8	8	no	—
165	C₂²×C₁₀₇	—	8	16	no	—
166	C₂²×C₁₀₇	#394	1	2	yes	—
167	C₂²×C₁₀₇	#394	1	2	yes	—
168	C₂²×C₁₀₇	#472	1	4	yes	—
169	C₂²×C₁₀₇	C₂×#121	1	1	yes	characteristic
170	C₂²×C₁₀₇	C₂×#123	1	2	yes	—
171	C₄×C₁₀₇	—	4	4	no	—
172	C₄×C₁₀₇	#394	1	2	yes	—
173	C₄×C₁₀₇	#394	1	2	yes	—
174	C₄×C₁₀₇	C₂×#120	1	1	yes	characteristic
175	C₄×C₁₀₇	C₂×#121	1	2	yes	—
176	C₄×C₁₀₇	C₂×#124	1	1	yes	characteristic
177	C₂×#2045	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
178	C₂×C₁₀₇	—	2	2	no	—
179	C₂×C₁₀₇	—	2	2	no	—
180	C₂×C₁₀₇	—	8	8	no	—
181	C₂×C₁₀₇	#2045	1	4	yes	direct product factor
182	C₂×C₁₀₇	C₂×#394	1	1	yes	characteristic
183	C₂×C₁₀₇	C₂×#472	1	2	yes	—
184	C₂³×D₈	C₂×C₁₀₇	1	1	yes	characteristic
185	C₂×#424	C₂×C₁₀₇	1	1	yes	characteristic, complemented
186	C₂×#418	C₂×C₁₀₇	1	2	yes	complemented
187	C₂²×#100	C₂×C₁₀₇	1	2	yes	complemented
188	#2045	C₂×C₁₀₇	1	8	yes	direct product factor
189	C₂×#341	C₂×C₁₀₇	1	1	yes	characteristic, complemented
190	C₁₀₇	C₂×#2045	1	1	yes	characteristic, direct product factor, Sylow
191	C₂³×D₄	C₂²×C₁₀₇	1	2	yes	—
192	C₂²×D₈	—	2	8	no	—
193	C₂²×D₈	—	2	2	no	—
194	C₂²×D₈	—	2	2	no	—
195	C₂²×D₈	C₂²×C₁₀₇	1	4	yes	—
196	C₂²×M₁₆	C₂²×C₁₀₇	1	1	yes	characteristic
197	C₂²×M₁₆	C₂²×C₁₀₇	1	2	yes	—
198	C₂³×C₈	C₂²×C₁₀₇	1	1	yes	characteristic
199	C₂×#117	C₂²×C₁₀₇	1	1	yes	characteristic
200	#424	—	2	2	no	—
201	#424	C₂²×C₁₀₇	1	4	yes	complemented
202	C₂×C₄⋊C₈	—	2	2	no	—
203	#418	—	2	4	no	—
204	#418	C₂²×C₁₀₇	1	8	yes	complemented
205	C₂×#102	—	2	4	no	—
206	C₂×#100	—	2	8	no	—
207	C₂×#100	C₂²×C₁₀₇	1	8	yes	complemented
208	#341	C₂²×C₁₀₇	1	4	yes	complemented
209	C₂⁵	—	2	2	no	—
210	C₂²×D₄	—	2	4	no	—
211	C₂²×D₄	—	2	2	no	—
212	C₂²×D₄	—	2	2	no	—
213	C₂²×D₄	—	2	2	no	—
214	C₂²×D₄	—	2	2	no	—
215	C₂²×D₄	—	2	4	no	—
216	C₂²×D₄	—	2	2	no	—
217	C₂²×D₄	—	2	4	no	—
218	C₂²×D₄	D₄×C₁₀₇	1	8	yes	—
219	C₂²×D₄	C₂³×C₁₀₇	1	4	yes	—
220	C₂³×C₄	C₂³×C₁₀₇	1	1	yes	characteristic
221	C₂×D₈	—	2	16	no	—
222	C₂×D₈	—	2	16	no	—
223	C₂×D₈	—	2	16	no	—
224	C₂×D₈	—	2	8	no	—
225	C₂×M₁₆	—	2	2	no	—
226	C₂×M₁₆	—	2	1	no	—
227	C₂×M₁₆	—	2	4	no	—
228	C₂×M₁₆	—	2	4	no	—
229	C₂×M₁₆	—	2	4	no	—
230	C₂×M₁₆	C₂³×C₁₀₇	1	4	yes	—
231	C₂×M₁₆	C₂³×C₁₀₇	1	2	yes	—
232	C₂²×C₈	—	2	4	no	—
233	C₂²×C₈	—	2	2	no	—
234	C₂²×C₈	—	2	1	no	—
235	C₂²×C₈	D₄×C₁₀₇	1	2	yes	—
236	C₂²×C₈	D₄×C₁₀₇	1	2	yes	—
237	C₂²×C₈	C₂³×C₁₀₇	1	2	yes	—
238	#117	—	2	1	no	—
239	#117	—	2	1	no	—
240	#117	D₄×C₁₀₇	1	2	yes	—
241	#117	C₂³×C₁₀₇	1	2	yes	—
242	C₂×C₄⋊C₄	D₄×C₁₀₇	1	2	yes	—
243	C₂×C₂²⋊C₄	—	2	1	no	—
244	C₂×C₄²	—	2	1	no	—
245	C₄⋊C₈	—	2	8	no	—
246	#102	—	2	16	no	—
247	#100	—	2	16	no	—
248	C₂⁴	—	2	8	no	—
249	C₂⁴	—	2	4	no	—
250	C₂⁴	—	4	2	no	—
251	C₂⁴	—	4	2	no	—
252	C₂⁴	—	4	4	no	—
253	C₂⁴	—	8	8	no	—
254	C₂⁴	#41×C₁₀₇	1	1	yes	characteristic
255	C₂×D₄	—	2	8	no	—
256	C₂×D₄	—	2	8	no	—
257	C₂×D₄	—	2	8	no	—
258	C₂×D₄	—	2	8	no	—
259	C₂×D₄	—	2	8	no	—
260	C₂×D₄	—	2	4	no	—
261	C₂×D₄	—	2	4	no	—
262	C₂×D₄	—	2	4	no	—
263	C₂×D₄	—	2	4	no	—
264	C₂×D₄	—	2	4	no	—
265	C₂×D₄	—	4	2	no	—
266	C₂×D₄	—	4	2	no	—
267	C₂×D₄	—	4	4	no	—
268	C₂×D₄	—	4	4	no	—
269	C₂×D₄	—	4	4	no	—
270	C₂×D₄	—	4	4	no	—
271	C₂×D₄	—	4	4	no	—
272	C₂×D₄	C₂×D₄×C₁₀₇	1	8	yes	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	C₂×D₄×C₁₀₇	1	4	yes	—
275	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
276	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
277	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
278	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
279	C₂²×C₄	#41×C₁₀₇	1	1	yes	characteristic
280	C₂²×C₄	#41×C₁₀₇	1	4	yes	—
281	C₂²×C₄	C₂⁴×C₁₀₇	1	1	yes	characteristic
282	D₈	—	2	32	no	—
283	M₁₆	—	2	4	no	—
284	M₁₆	—	2	4	no	—
285	M₁₆	—	2	4	no	—
286	M₁₆	—	4	2	no	—
287	M₁₆	—	4	4	no	—
288	C₂×C₈	—	2	4	no	—
289	C₂×C₈	—	2	4	no	—
290	C₂×C₈	—	2	4	no	—
291	C₂×C₈	—	2	4	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	4	2	no	—
294	C₂×C₈	—	4	4	no	—
295	C₂×C₈	C₂×D₄×C₁₀₇	1	4	yes	—
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	C₂×D₄×C₁₀₇	1	4	yes	—
298	C₂²⋊C₄	—	2	2	no	—
299	C₂²⋊C₄	—	2	2	no	—
300	C₄²	—	2	2	no	—
301	C₄²	—	2	2	no	—
302	C₂³	—	2	4	no	—
303	C₂³	—	2	8	no	—
304	C₂³	—	4	8	no	—
305	C₂³	—	4	8	no	—
306	C₂³	—	4	4	no	—
307	C₂³	—	4	4	no	—
308	C₂³	—	8	8	no	—
309	C₂³	—	8	16	no	—
310	C₂³	—	8	8	no	—
311	C₂³	—	8	16	no	—
312	C₂³	—	8	8	no	—
313	C₂³	#121×C₁₀₇	1	1	yes	characteristic
314	C₂³	#121×C₁₀₇	1	1	yes	characteristic
315	C₂³	#123×C₁₀₇	1	4	yes	—
316	C₂³	C₂×#41×C₁₀₇	1	1	yes	characteristic
317	D₄	—	2	8	no	—
318	D₄	—	2	8	no	—
319	D₄	—	4	8	no	—
320	D₄	—	4	8	no	—
321	D₄	—	4	4	no	—
322	D₄	—	4	4	no	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	4	4	no	—
325	C₂×C₄	#120×C₁₀₇	1	2	yes	—
326	C₂×C₄	#120×C₁₀₇	1	2	yes	—
327	C₂×C₄	#121×C₁₀₇	1	1	yes	characteristic
328	C₂×C₄	#121×C₁₀₇	1	1	yes	characteristic
329	C₂×C₄	#121×C₁₀₇	1	4	yes	—
330	C₂×C₄	#121×C₁₀₇	1	4	yes	—
331	C₂×C₄	#123×C₁₀₇	1	4	yes	—
332	C₂×C₄	#124×C₁₀₇	1	2	yes	—
333	C₂×C₄	#124×C₁₀₇	1	2	yes	—
334	C₂×C₄	C₂²×D₄×C₁₀₇	1	2	yes	—
335	C₂×C₄	C₂²×D₄×C₁₀₇	1	1	yes	characteristic
336	C₂×C₄	C₂²×D₄×C₁₀₇	1	1	yes	characteristic
337	C₂×C₄	C₂×#41×C₁₀₇	1	2	yes	—
338	C₈	—	2	4	no	—
339	C₈	—	4	2	no	—
340	C₈	—	4	4	no	—
341	C₂²	—	2	2	no	—
342	C₂²	—	2	2	no	—
343	C₂²	—	2	8	no	—
344	C₂²	—	4	8	no	—
345	C₂²	—	8	8	no	—
346	C₂²	—	8	16	no	—
347	C₂²	—	8	8	no	—
348	C₂²	—	8	8	no	—
349	C₂²	—	8	16	no	—
350	C₂²	#394×C₁₀₇	1	2	yes	—
351	C₂²	#394×C₁₀₇	1	2	yes	—
352	C₂²	#472×C₁₀₇	1	4	yes	—
353	C₂²	C₂×#121×C₁₀₇	1	1	yes	characteristic
354	C₂²	C₂×#123×C₁₀₇	1	2	yes	—
355	C₄	—	4	4	no	—
356	C₄	#394×C₁₀₇	1	2	yes	—
357	C₄	#394×C₁₀₇	1	2	yes	—
358	C₄	C₂×#120×C₁₀₇	1	1	yes	characteristic
359	C₄	C₂×#121×C₁₀₇	1	2	yes	—
360	C₄	C₂×#124×C₁₀₇	1	1	yes	characteristic
361	C₂	—	2	2	no	—
362	C₂	—	2	2	no	—
363	C₂	—	8	8	no	—
364	C₂	C₁₀₇×#2045	1	4	yes	direct product factor
365	C₂	C₂×#394×C₁₀₇	1	1	yes	characteristic
366	C₂	C₂×#472×C₁₀₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₀₇	#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₇
prime radical	C₂³×D₈×C₁₀₇	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₇ ◁ C₂³×C₄×C₁₀₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#424×C₁₀₇	C₂	semidirect
3. C₂×#418×C₁₀₇	C₂	semidirect
4. C₂²×#100×C₁₀₇	C₂	semidirect
5. C₁₀₇×#2045	C₂	direct (N × H)
6. C₂×#341×C₁₀₇	C₂	semidirect
17. #424×C₁₀₇	C₂²	semidirect
20. #418×C₁₀₇	C₂²	semidirect
23. C₂×#100×C₁₀₇	C₂²	semidirect
24. #341×C₁₀₇	C₂²	semidirect
177. C₂×#2045	C₁₀₇	direct (N × H)
181. C₂×C₁₀₇	#2045	direct (N × H)
185. C₂×#424	C₂×C₁₀₇	semidirect
186. C₂×#418	C₂×C₁₀₇	semidirect
187. C₂²×#100	C₂×C₁₀₇	semidirect
188. #2045	C₂×C₁₀₇	direct (N × H)
189. C₂×#341	C₂×C₁₀₇	semidirect
190. C₁₀₇	C₂×#2045	direct (N × H)
201. #424	C₂²×C₁₀₇	semidirect
204. #418	C₂²×C₁₀₇	semidirect
207. C₂×#100	C₂²×C₁₀₇	semidirect
208. #341	C₂²×C₁₀₇	semidirect
364. C₂	C₁₀₇×#2045	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×D₈×C₁₀₇	2
C₂×#424×C₁₀₇	2
C₂×#418×C₁₀₇	2
C₂²×#100×C₁₀₇	2
C₁₀₇×#2045	2
C₂×#341×C₁₀₇	2
C₂×#2045	107

Subgroups — C2×C107×#2045 #41049481

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₀₇×#2045 #41049481