Subgroups — C₁₀₇×#29110 #41055074

Order 27392.

1078 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₇×#2851	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#390×C₁₀₇	C₂	1	1	yes	maximal, characteristic
3	C₁₀₇×#2073	C₂	1	2	yes	maximal, complemented
4	C₁₀₇×#2025	C₂	1	2	yes	maximal, complemented
5	C₁₀₇×#1936	C₂	1	4	yes	maximal, complemented
6	C₁₀₇×#1823	C₂	1	2	yes	maximal, complemented
7	C₁₀₇×#1786	C₂	1	2	yes	maximal
8	C₁₀₇×#1749	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₁₀₇	C₂²	1	1	yes	characteristic
10	C₂×#125×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
11	C₂²×C₄⋊C₄×C₁₀₇	C₂²	1	1	yes	characteristic
12	C₂²×C₂²⋊C₄×C₁₀₇	—	2	2	no	—
13	C₂²×C₄²×C₁₀₇	C₂²	1	1	yes	characteristic
14	C₂×#102×C₁₀₇	C₂²	1	4	yes	—
15	C₂×#102×C₁₀₇	C₂²	1	4	yes	—
16	C₂×C₂²⋊C₈×C₁₀₇	C₂²	1	2	yes	—
17	C₂×#97×C₁₀₇	C₂²	1	2	yes	complemented
18	#390×C₁₀₇	—	2	2	no	—
19	#390×C₁₀₇	C₂²	1	2	yes	—
20	#390×C₁₀₇	C₂²	1	2	yes	—
21	#389×C₁₀₇	C₂²	1	2	yes	complemented
22	#387×C₁₀₇	—	2	2	no	—
23	#385×C₁₀₇	—	2	2	no	—
24	#382×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
25	#380×C₁₀₇	C₂²	1	2	yes	—
26	#340×C₁₀₇	C₂²	1	4	yes	complemented
27	#340×C₁₀₇	C₂²	1	4	yes	complemented
28	#336×C₁₀₇	C₂²	1	2	yes	complemented
29	C₂⁵×C₁₀₇	—	2	1	no	—
30	C₂²×D₄×C₁₀₇	—	2	4	no	—
31	C₂²×D₄×C₁₀₇	—	2	1	no	—
32	C₂²×D₄×C₁₀₇	—	2	4	no	—
33	C₂²×D₄×C₁₀₇	—	4	2	no	—
34	C₂²×D₄×C₁₀₇	C₂³	1	2	yes	—
35	C₂³×C₄×C₁₀₇	—	2	1	no	—
36	C₂³×C₄×C₁₀₇	D₄	1	2	yes	—
37	C₂³×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
38	C₂²×C₈×C₁₀₇	C₂³	1	4	yes	—
39	#125×C₁₀₇	—	4	2	no	—
40	C₂×C₄⋊C₄×C₁₀₇	—	2	4	no	—
41	C₂×C₄⋊C₄×C₁₀₇	—	2	2	no	—
42	C₂×C₄⋊C₄×C₁₀₇	—	2	2	no	—
43	C₂×C₄⋊C₄×C₁₀₇	—	2	1	no	—
44	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	2	yes	—
45	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	2	yes	—
46	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	2	yes	—
47	C₂×C₂²⋊C₄×C₁₀₇	—	2	2	no	—
48	C₂×C₂²⋊C₄×C₁₀₇	—	2	4	no	—
49	C₂×C₂²⋊C₄×C₁₀₇	—	2	4	no	—
50	C₂×C₂²⋊C₄×C₁₀₇	—	4	8	no	—
51	C₂×C₄²×C₁₀₇	—	4	2	no	—
52	C₂×C₄²×C₁₀₇	D₄	1	2	yes	—
53	C₂×C₄²×C₁₀₇	C₂³	1	1	yes	characteristic
54	C₂×C₄²×C₁₀₇	C₂³	1	1	yes	characteristic
55	#102×C₁₀₇	—	2	8	no	—
56	#102×C₁₀₇	—	4	4	no	—
57	C₂²⋊C₈×C₁₀₇	—	2	4	no	—
58	#97×C₁₀₇	—	4	2	no	—
59	#95×C₁₀₇	—	2	2	no	—
60	#95×C₁₀₇	—	2	2	no	—
61	#95×C₁₀₇	—	2	2	no	—
62	C₂⁴×C₁₀₇	—	2	4	no	—
63	C₂⁴×C₁₀₇	—	2	2	no	—
64	C₂⁴×C₁₀₇	—	4	2	no	—
65	C₂⁴×C₁₀₇	—	4	4	no	—
66	C₂⁴×C₁₀₇	—	4	2	no	—
67	C₂⁴×C₁₀₇	—	4	4	no	—
68	C₂⁴×C₁₀₇	C₂×D₄	1	1	yes	characteristic
69	C₂×D₄×C₁₀₇	—	2	4	no	—
70	C₂×D₄×C₁₀₇	—	2	4	no	—
71	C₂×D₄×C₁₀₇	—	2	2	no	—
72	C₂×D₄×C₁₀₇	—	2	4	no	—
73	C₂×D₄×C₁₀₇	—	4	16	no	—
74	C₂×D₄×C₁₀₇	—	4	2	no	—
75	C₂×D₄×C₁₀₇	—	4	2	no	—
76	C₂×D₄×C₁₀₇	#41	1	4	yes	—
77	C₂²×C₄×C₁₀₇	—	2	2	no	—
78	C₂²×C₄×C₁₀₇	—	2	2	no	—
79	C₂²×C₄×C₁₀₇	—	2	4	no	—
80	C₂²×C₄×C₁₀₇	—	2	2	no	—
81	C₂²×C₄×C₁₀₇	—	2	2	no	—
82	C₂²×C₄×C₁₀₇	—	2	2	no	—
83	C₂²×C₄×C₁₀₇	—	4	2	no	—
84	C₂²×C₄×C₁₀₇	—	4	2	no	—
85	C₂²×C₄×C₁₀₇	—	4	2	no	—
86	C₂²×C₄×C₁₀₇	—	4	4	no	—
87	C₂²×C₄×C₁₀₇	C₂×D₄	1	2	yes	—
88	C₂²×C₄×C₁₀₇	C₂×D₄	1	2	yes	—
89	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₀₇	#41	1	4	yes	—
91	C₂²×C₄×C₁₀₇	C₂⁴	1	1	yes	characteristic
92	C₂×C₈×C₁₀₇	—	2	4	no	—
93	C₂×C₈×C₁₀₇	—	2	4	no	—
94	C₂×C₈×C₁₀₇	—	2	4	no	—
95	C₄⋊C₄×C₁₀₇	—	2	4	no	—
96	C₄⋊C₄×C₁₀₇	—	2	4	no	—
97	C₄⋊C₄×C₁₀₇	—	2	4	no	—
98	C₄⋊C₄×C₁₀₇	—	4	4	no	—
99	C₄⋊C₄×C₁₀₇	—	4	4	no	—
100	C₄⋊C₄×C₁₀₇	—	4	2	no	—
101	C₂²⋊C₄×C₁₀₇	—	4	8	no	—
102	C₂²⋊C₄×C₁₀₇	—	4	8	no	—
103	C₂²⋊C₄×C₁₀₇	—	4	4	no	—
104	C₄²×C₁₀₇	—	2	2	no	—
105	C₄²×C₁₀₇	—	2	2	no	—
106	C₄²×C₁₀₇	—	4	2	no	—
107	C₂³×C₁₀₇	—	2	1	no	—
108	C₂³×C₁₀₇	—	2	1	no	—
109	C₂³×C₁₀₇	—	2	2	no	—
110	C₂³×C₁₀₇	—	2	4	no	—
111	C₂³×C₁₀₇	—	4	8	no	—
112	C₂³×C₁₀₇	—	4	16	no	—
113	C₂³×C₁₀₇	—	4	2	no	—
114	C₂³×C₁₀₇	—	4	2	no	—
115	C₂³×C₁₀₇	—	4	4	no	—
116	C₂³×C₁₀₇	—	4	4	no	—
117	C₂³×C₁₀₇	—	8	4	no	—
118	C₂³×C₁₀₇	—	8	8	no	—
119	C₂³×C₁₀₇	—	8	4	no	—
120	C₂³×C₁₀₇	#124	1	2	yes	—
121	C₂³×C₁₀₇	AGL(1,ℤ/8)	1	4	yes	—
122	C₂³×C₁₀₇	C₂²×D₄	1	1	yes	characteristic
123	D₄×C₁₀₇	—	2	8	no	—
124	D₄×C₁₀₇	—	4	8	no	—
125	D₄×C₁₀₇	—	4	4	no	—
126	C₂×C₄×C₁₀₇	—	2	1	no	—
127	C₂×C₄×C₁₀₇	—	2	1	no	—
128	C₂×C₄×C₁₀₇	—	2	8	no	—
129	C₂×C₄×C₁₀₇	—	2	2	no	—
130	C₂×C₄×C₁₀₇	—	2	2	no	—
131	C₂×C₄×C₁₀₇	—	2	2	no	—
132	C₂×C₄×C₁₀₇	—	2	2	no	—
133	C₂×C₄×C₁₀₇	—	2	2	no	—
134	C₂×C₄×C₁₀₇	—	2	2	no	—
135	C₂×C₄×C₁₀₇	—	4	8	no	—
136	C₂×C₄×C₁₀₇	—	4	2	no	—
137	C₂×C₄×C₁₀₇	—	4	2	no	—
138	C₂×C₄×C₁₀₇	—	4	2	no	—
139	C₂×C₄×C₁₀₇	—	4	4	no	—
140	C₂×C₄×C₁₀₇	—	4	2	no	—
141	C₂×C₄×C₁₀₇	—	4	2	no	—
142	C₂×C₄×C₁₀₇	—	4	2	no	—
143	C₂×C₄×C₁₀₇	—	4	2	no	—
144	C₂×C₄×C₁₀₇	—	8	4	no	—
145	C₂×C₄×C₁₀₇	#124	1	2	yes	—
146	C₂×C₄×C₁₀₇	C₂×#41	1	2	yes	—
147	C₂×C₄×C₁₀₇	C₂×#41	1	2	yes	—
148	C₂×C₄×C₁₀₇	H(5,𝔽₂)	1	2	yes	—
149	C₈×C₁₀₇	—	4	4	no	—
150	C₂²×C₁₀₇	—	2	2	no	—
151	C₂²×C₁₀₇	—	2	4	no	—
152	C₂²×C₁₀₇	—	2	2	no	—
153	C₂²×C₁₀₇	—	2	4	no	—
154	C₂²×C₁₀₇	—	4	4	no	—
155	C₂²×C₁₀₇	—	4	8	no	—
156	C₂²×C₁₀₇	—	8	16	no	—
157	C₂²×C₁₀₇	—	8	2	no	—
158	C₂²×C₁₀₇	—	8	2	no	—
159	C₂²×C₁₀₇	—	8	4	no	—
160	C₂²×C₁₀₇	#490	1	4	yes	—
161	C₂²×C₁₀₇	#525	1	1	yes	characteristic
162	C₂²×C₁₀₇	C₂×#124	1	1	yes	characteristic
163	C₂²×C₁₀₇	#534	1	1	yes	characteristic
164	C₂²×C₁₀₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
165	C₂²×C₁₀₇	#575	1	2	yes	—
166	C₄×C₁₀₇	—	2	2	no	—
167	C₄×C₁₀₇	—	4	2	no	—
168	C₄×C₁₀₇	—	4	2	no	—
169	C₄×C₁₀₇	—	8	2	no	—
170	C₄×C₁₀₇	—	8	2	no	—
171	C₄×C₁₀₇	—	8	2	no	—
172	C₄×C₁₀₇	#551	1	4	yes	—
173	#29110	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
174	C₂×C₁₀₇	—	2	4	no	—
175	C₂×C₁₀₇	—	8	4	no	—
176	C₂×C₁₀₇	#2561	1	1	yes	characteristic
177	C₂×C₁₀₇	#3114	1	2	yes	—
178	C₂×C₁₀₇	C₂×#490	1	1	yes	characteristic
179	C₂×C₁₀₇	#3140	1	1	yes	characteristic
180	C₂×C₁₀₇	#3194	1	2	yes	—
181	#2851	C₂×C₁₀₇	1	1	yes	characteristic, complemented
182	C₂×#390	C₂×C₁₀₇	1	1	yes	characteristic
183	#2073	C₂×C₁₀₇	1	2	yes	complemented
184	#2025	C₂×C₁₀₇	1	2	yes	complemented
185	#1936	C₂×C₁₀₇	1	4	yes	complemented
186	#1823	C₂×C₁₀₇	1	2	yes	complemented
187	#1786	C₂×C₁₀₇	1	2	yes	—
188	#1749	C₂×C₁₀₇	1	1	yes	characteristic, complemented
189	C₁₀₇	#29110	1	1	yes	characteristic, direct product factor, Sylow
190	C₂³×D₄	C₂²×C₁₀₇	1	1	yes	characteristic
191	C₂×#125	C₂²×C₁₀₇	1	1	yes	characteristic, complemented
192	C₂²×C₄⋊C₄	C₂²×C₁₀₇	1	1	yes	characteristic
193	C₂²×C₂²⋊C₄	—	2	2	no	—
194	C₂²×C₄²	C₂²×C₁₀₇	1	1	yes	characteristic
195	C₂×#102	C₂²×C₁₀₇	1	4	yes	—
196	C₂×#102	C₂²×C₁₀₇	1	4	yes	—
197	C₂×C₂²⋊C₈	C₂²×C₁₀₇	1	2	yes	—
198	C₂×#97	C₂²×C₁₀₇	1	2	yes	complemented
199	#390	—	2	2	no	—
200	#390	C₂²×C₁₀₇	1	2	yes	—
201	#390	C₂²×C₁₀₇	1	2	yes	—
202	#389	C₂²×C₁₀₇	1	2	yes	complemented
203	#387	—	2	2	no	—
204	#385	—	2	2	no	—
205	#382	C₂²×C₁₀₇	1	1	yes	characteristic, complemented
206	#380	C₂²×C₁₀₇	1	2	yes	—
207	#340	C₂²×C₁₀₇	1	4	yes	complemented
208	#340	C₂²×C₁₀₇	1	4	yes	complemented
209	#336	C₂²×C₁₀₇	1	2	yes	complemented
210	C₂⁵	—	2	1	no	—
211	C₂²×D₄	—	2	4	no	—
212	C₂²×D₄	—	2	1	no	—
213	C₂²×D₄	—	2	4	no	—
214	C₂²×D₄	—	4	2	no	—
215	C₂²×D₄	C₂³×C₁₀₇	1	2	yes	—
216	C₂³×C₄	—	2	1	no	—
217	C₂³×C₄	D₄×C₁₀₇	1	2	yes	—
218	C₂³×C₄	C₂³×C₁₀₇	1	1	yes	characteristic
219	C₂²×C₈	C₂³×C₁₀₇	1	4	yes	—
220	#125	—	4	2	no	—
221	C₂×C₄⋊C₄	—	2	4	no	—
222	C₂×C₄⋊C₄	—	2	1	no	—
223	C₂×C₄⋊C₄	—	2	2	no	—
224	C₂×C₄⋊C₄	—	2	2	no	—
225	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	2	yes	—
226	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	2	yes	—
227	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	2	yes	—
228	C₂×C₂²⋊C₄	—	2	2	no	—
229	C₂×C₂²⋊C₄	—	2	4	no	—
230	C₂×C₂²⋊C₄	—	2	4	no	—
231	C₂×C₂²⋊C₄	—	4	8	no	—
232	C₂×C₄²	—	4	2	no	—
233	C₂×C₄²	D₄×C₁₀₇	1	2	yes	—
234	C₂×C₄²	C₂³×C₁₀₇	1	1	yes	characteristic
235	C₂×C₄²	C₂³×C₁₀₇	1	1	yes	characteristic
236	#102	—	2	8	no	—
237	#102	—	4	4	no	—
238	C₂²⋊C₈	—	2	4	no	—
239	#97	—	4	2	no	—
240	#95	—	2	2	no	—
241	#95	—	2	2	no	—
242	#95	—	2	2	no	—
243	C₂⁴	—	2	4	no	—
244	C₂⁴	—	2	2	no	—
245	C₂⁴	—	4	2	no	—
246	C₂⁴	—	4	4	no	—
247	C₂⁴	—	4	2	no	—
248	C₂⁴	—	4	4	no	—
249	C₂⁴	C₂×D₄×C₁₀₇	1	1	yes	characteristic
250	C₂×D₄	—	2	4	no	—
251	C₂×D₄	—	2	4	no	—
252	C₂×D₄	—	2	2	no	—
253	C₂×D₄	—	2	4	no	—
254	C₂×D₄	—	4	16	no	—
255	C₂×D₄	—	4	2	no	—
256	C₂×D₄	—	4	2	no	—
257	C₂×D₄	#41×C₁₀₇	1	4	yes	—
258	C₂²×C₄	—	2	2	no	—
259	C₂²×C₄	—	2	2	no	—
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	4	2	no	—
265	C₂²×C₄	—	4	2	no	—
266	C₂²×C₄	—	4	2	no	—
267	C₂²×C₄	—	4	4	no	—
268	C₂²×C₄	C₂×D₄×C₁₀₇	1	2	yes	—
269	C₂²×C₄	C₂×D₄×C₁₀₇	1	2	yes	—
270	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
271	C₂²×C₄	#41×C₁₀₇	1	4	yes	—
272	C₂²×C₄	C₂⁴×C₁₀₇	1	1	yes	characteristic
273	C₂×C₈	—	2	4	no	—
274	C₂×C₈	—	2	4	no	—
275	C₂×C₈	—	2	4	no	—
276	C₄⋊C₄	—	2	4	no	—
277	C₄⋊C₄	—	2	4	no	—
278	C₄⋊C₄	—	2	4	no	—
279	C₄⋊C₄	—	4	4	no	—
280	C₄⋊C₄	—	4	4	no	—
281	C₄⋊C₄	—	4	2	no	—
282	C₂²⋊C₄	—	4	8	no	—
283	C₂²⋊C₄	—	4	8	no	—
284	C₂²⋊C₄	—	4	4	no	—
285	C₄²	—	2	2	no	—
286	C₄²	—	2	2	no	—
287	C₄²	—	4	2	no	—
288	C₂³	—	2	1	no	—
289	C₂³	—	2	1	no	—
290	C₂³	—	2	2	no	—
291	C₂³	—	2	4	no	—
292	C₂³	—	4	8	no	—
293	C₂³	—	4	16	no	—
294	C₂³	—	4	2	no	—
295	C₂³	—	4	2	no	—
296	C₂³	—	4	4	no	—
297	C₂³	—	4	4	no	—
298	C₂³	—	8	8	no	—
299	C₂³	—	8	4	no	—
300	C₂³	—	8	4	no	—
301	C₂³	#124×C₁₀₇	1	2	yes	—
302	C₂³	AGL(1,ℤ/8)×C₁₀₇	1	4	yes	—
303	C₂³	C₂²×D₄×C₁₀₇	1	1	yes	characteristic
304	D₄	—	2	8	no	—
305	D₄	—	4	8	no	—
306	D₄	—	4	4	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	8	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	4	8	no	—
317	C₂×C₄	—	4	2	no	—
318	C₂×C₄	—	4	2	no	—
319	C₂×C₄	—	4	2	no	—
320	C₂×C₄	—	4	4	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	—	4	2	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	—	8	4	no	—
326	C₂×C₄	#124×C₁₀₇	1	2	yes	—
327	C₂×C₄	C₂×#41×C₁₀₇	1	2	yes	—
328	C₂×C₄	C₂×#41×C₁₀₇	1	2	yes	—
329	C₂×C₄	H(5,𝔽₂)×C₁₀₇	1	2	yes	—
330	C₈	—	4	4	no	—
331	C₂²	—	2	4	no	—
332	C₂²	—	2	2	no	—
333	C₂²	—	2	4	no	—
334	C₂²	—	2	2	no	—
335	C₂²	—	4	4	no	—
336	C₂²	—	4	8	no	—
337	C₂²	—	8	16	no	—
338	C₂²	—	8	4	no	—
339	C₂²	—	8	2	no	—
340	C₂²	—	8	2	no	—
341	C₂²	#490×C₁₀₇	1	4	yes	—
342	C₂²	#525×C₁₀₇	1	1	yes	characteristic
343	C₂²	C₂×#124×C₁₀₇	1	1	yes	characteristic
344	C₂²	#534×C₁₀₇	1	1	yes	characteristic
345	C₂²	C₂×AGL(1,ℤ/8)×C₁₀₇	1	2	yes	—
346	C₂²	#575×C₁₀₇	1	2	yes	—
347	C₄	—	2	2	no	—
348	C₄	—	4	2	no	—
349	C₄	—	4	2	no	—
350	C₄	—	8	2	no	—
351	C₄	—	8	2	no	—
352	C₄	—	8	2	no	—
353	C₄	#551×C₁₀₇	1	4	yes	—
354	C₂	—	2	4	no	—
355	C₂	—	8	4	no	—
356	C₂	C₁₀₇×#2561	1	1	yes	characteristic
357	C₂	C₁₀₇×#3114	1	2	yes	—
358	C₂	C₂×#490×C₁₀₇	1	1	yes	characteristic
359	C₂	C₁₀₇×#3140	1	1	yes	characteristic
360	C₂	C₁₀₇×#3194	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₀₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₇
prime radical	C₂³×D₄×C₁₀₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₇ ◁ C₂²×C₄²×C₁₀₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₀₇×#2851	C₂	semidirect
3. C₁₀₇×#2073	C₂	semidirect
4. C₁₀₇×#2025	C₂	semidirect
5. C₁₀₇×#1936	C₂	semidirect
6. C₁₀₇×#1823	C₂	semidirect
8. C₁₀₇×#1749	C₂	semidirect
10. C₂×#125×C₁₀₇	C₂²	semidirect
17. C₂×#97×C₁₀₇	C₂²	semidirect
21. #389×C₁₀₇	C₂²	semidirect
24. #382×C₁₀₇	C₂²	semidirect
26. #340×C₁₀₇	C₂²	semidirect
27. #340×C₁₀₇	C₂²	semidirect
28. #336×C₁₀₇	C₂²	semidirect
173. #29110	C₁₀₇	direct (N × H)
181. #2851	C₂×C₁₀₇	semidirect
183. #2073	C₂×C₁₀₇	semidirect
184. #2025	C₂×C₁₀₇	semidirect
185. #1936	C₂×C₁₀₇	semidirect
186. #1823	C₂×C₁₀₇	semidirect
188. #1749	C₂×C₁₀₇	semidirect
189. C₁₀₇	#29110	direct (N × H)
191. C₂×#125	C₂²×C₁₀₇	semidirect
198. C₂×#97	C₂²×C₁₀₇	semidirect
202. #389	C₂²×C₁₀₇	semidirect
205. #382	C₂²×C₁₀₇	semidirect
207. #340	C₂²×C₁₀₇	semidirect
208. #340	C₂²×C₁₀₇	semidirect
209. #336	C₂²×C₁₀₇	semidirect

Maximal subgroups

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

subgroup	index
C₁₀₇×#2851	2
C₂×#390×C₁₀₇	2
C₁₀₇×#2073	2
C₁₀₇×#2025	2
C₁₀₇×#1936	2
C₁₀₇×#1823	2
C₁₀₇×#1786	2
C₁₀₇×#1749	2
#29110	107

Subgroups — C107×#29110 #41055074

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₇×#29110 #41055074