Subgroups — C₁₀₇×#18039 #41044003

Order 27392.

652 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₇×#2971	C₂	1	2	yes	maximal, complemented
2	C₄×#135×C₁₀₇	C₂	1	1	yes	maximal, characteristic
3	C₁₀₇×#1589	C₂	1	2	yes	maximal, complemented
4	C₁₀₇×#1583	C₂	1	4	yes	maximal, complemented
5	C₈×Q₁₆×C₁₀₇	C₂	1	2	yes	maximal, complemented
6	C₁₀₇×#1568	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₀₇×#1488	C₂	1	2	yes	maximal, complemented
8	C₈×M₁₆×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#135×C₁₀₇	C₄	1	1	yes	characteristic
10	C₄×#41×C₁₀₇	C₂²	1	2	yes	—
11	C₈×Q₈×C₁₀₇	C₂²	1	4	yes	—
12	C₄×Q₁₆×C₁₀₇	C₄	1	1	yes	characteristic
13	C₄×Q₁₆×C₁₀₇	C₂²	1	1	yes	characteristic
14	C₄×SD₁₆×C₁₀₇	C₄	1	2	yes	—
15	C₄×SD₁₆×C₁₀₇	C₂²	1	2	yes	—
16	C₄×D₈×C₁₀₇	C₄	1	1	yes	characteristic
17	C₄×D₈×C₁₀₇	C₂²	1	1	yes	characteristic
18	#436×C₁₀₇	—	2	4	no	—
19	#436×C₁₀₇	C₂²	1	4	yes	—
20	#432×C₁₀₇	—	2	2	no	—
21	#432×C₁₀₇	C₂²	1	2	yes	—
22	#431×C₁₀₇	C₂²	1	1	yes	characteristic
23	#427×C₁₀₇	C₄	1	1	yes	characteristic
24	#416×C₁₀₇	C₄	1	2	yes	—
25	C₄×M₁₆×C₁₀₇	—	2	2	no	—
26	C₄×M₁₆×C₁₀₇	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₀₇	C₂²	1	1	yes	characteristic
28	#335×C₁₀₇	C₂²	1	2	yes	—
29	#334×C₁₀₇	C₂²	1	2	yes	—
30	Q₈⋊C₈×C₁₀₇	C₂²	1	4	yes	—
31	D₄⋊C₈×C₁₀₇	C₂²	1	4	yes	—
32	#322×C₁₀₇	C₂²	1	2	yes	—
33	C₈²×C₁₀₇	C₂²	1	2	yes	—
34	C₂×#41×C₁₀₇	C₂×C₄	1	2	yes	—
35	#135×C₁₀₇	—	2	4	no	—
36	C₂×Q₁₆×C₁₀₇	C₂×C₄	1	1	yes	characteristic
37	C₂×SD₁₆×C₁₀₇	C₂×C₄	1	2	yes	—
38	C₂×D₈×C₁₀₇	C₂×C₄	1	1	yes	characteristic
39	C₂×M₁₆×C₁₀₇	—	2	4	no	—
40	C₂×M₁₆×C₁₀₇	D₄	1	2	yes	—
41	C₂²×C₈×C₁₀₇	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₈×C₁₀₇	C₂×C₄	1	1	yes	characteristic
43	C₄×Q₈×C₁₀₇	C₂×C₄	1	2	yes	—
44	C₄×Q₈×C₁₀₇	C₂³	1	2	yes	—
45	C₄×D₄×C₁₀₇	—	2	2	no	—
46	C₄×D₄×C₁₀₇	—	2	2	no	—
47	C₄×D₄×C₁₀₇	C₂×C₄	1	2	yes	—
48	C₄×D₄×C₁₀₇	C₂³	1	2	yes	—
49	#117×C₁₀₇	—	2	2	no	—
50	#117×C₁₀₇	C₂×C₄	1	2	yes	—
51	C₂×C₄²×C₁₀₇	—	2	2	no	—
52	C₂×C₄²×C₁₀₇	C₂³	1	1	yes	characteristic
53	#107×C₁₀₇	C₂×C₄	1	1	yes	characteristic
54	#107×C₁₀₇	C₂×C₄	1	1	yes	characteristic
55	#106×C₁₀₇	C₂×C₄	1	2	yes	—
56	C₄⋊C₈×C₁₀₇	—	2	4	no	—
57	C₄⋊C₈×C₁₀₇	—	2	1	no	—
58	C₄⋊C₈×C₁₀₇	C₂³	1	4	yes	—
59	#103×C₁₀₇	C₂×C₄	1	2	yes	—
60	#103×C₁₀₇	C₂×C₄	1	2	yes	—
61	#102×C₁₀₇	C₂×C₄	1	2	yes	—
62	#102×C₁₀₇	C₂×C₄	1	2	yes	—
63	C₂²⋊C₈×C₁₀₇	—	2	2	no	—
64	C₂²⋊C₈×C₁₀₇	—	2	1	no	—
65	C₂²⋊C₈×C₁₀₇	—	2	4	no	—
66	#97×C₁₀₇	—	2	2	no	—
67	#97×C₁₀₇	D₄	1	1	yes	characteristic
68	#97×C₁₀₇	D₄	1	1	yes	characteristic
69	C₄×C₈×C₁₀₇	—	2	4	no	—
70	C₄×C₈×C₁₀₇	C₂×C₄	1	1	yes	characteristic
71	C₄×C₈×C₁₀₇	C₂×C₄	1	1	yes	characteristic
72	C₄×C₈×C₁₀₇	C₂³	1	2	yes	—
73	C₄×C₈×C₁₀₇	C₂³	1	1	yes	characteristic
74	C₄×C₈×C₁₀₇	C₂³	1	1	yes	characteristic
75	C₄×C₈×C₁₀₇	C₂³	1	2	yes	—
76	#41×C₁₀₇	—	2	4	no	—
77	#41×C₁₀₇	—	4	2	no	—
78	C₂×Q₈×C₁₀₇	C₂²×C₄	1	2	yes	—
79	C₂×D₄×C₁₀₇	—	2	2	no	—
80	C₂×D₄×C₁₀₇	C₂²×C₄	1	2	yes	—
81	C₂²×C₄×C₁₀₇	—	2	2	no	—
82	C₂²×C₄×C₁₀₇	—	2	2	no	—
83	C₂²×C₄×C₁₀₇	—	2	2	no	—
84	C₂²×C₄×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₀₇	#41	1	1	yes	characteristic
87	Q₁₆×C₁₀₇	M₁₆	1	4	yes	complemented
88	SD₁₆×C₁₀₇	—	2	4	no	—
89	D₈×C₁₀₇	—	2	2	no	—
90	M₁₆×C₁₀₇	—	2	4	no	—
91	M₁₆×C₁₀₇	—	4	8	no	—
92	C₂×C₈×C₁₀₇	—	2	2	no	—
93	C₂×C₈×C₁₀₇	—	2	4	no	—
94	C₂×C₈×C₁₀₇	—	2	2	no	—
95	C₂×C₈×C₁₀₇	—	4	1	no	—
96	C₂×C₈×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₈×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₈×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₈×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₈×C₁₀₇	C₂×D₄	1	2	yes	—
101	C₂×C₈×C₁₀₇	C₂×D₄	1	2	yes	—
102	C₄⋊C₄×C₁₀₇	—	2	2	no	—
103	C₄⋊C₄×C₁₀₇	—	2	2	no	—
104	C₄⋊C₄×C₁₀₇	C₂²×C₄	1	2	yes	—
105	C₄⋊C₄×C₁₀₇	C₂²×C₄	1	2	yes	—
106	C₂²⋊C₄×C₁₀₇	—	2	2	no	—
107	C₂²⋊C₄×C₁₀₇	—	2	2	no	—
108	C₂²⋊C₄×C₁₀₇	—	2	2	no	—
109	C₄²×C₁₀₇	—	2	2	no	—
110	C₄²×C₁₀₇	—	2	2	no	—
111	C₄²×C₁₀₇	—	2	2	no	—
112	C₄²×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
113	C₄²×C₁₀₇	C₂×D₄	1	1	yes	characteristic
114	C₄²×C₁₀₇	#41	1	1	yes	characteristic
115	C₄²×C₁₀₇	C₂⁴	1	1	yes	characteristic
116	C₂³×C₁₀₇	—	2	2	no	—
117	C₂³×C₁₀₇	C₄×D₄	1	1	yes	characteristic
118	Q₈×C₁₀₇	—	2	2	no	—
119	Q₈×C₁₀₇	C₂×M₁₆	1	4	yes	—
120	D₄×C₁₀₇	—	2	2	no	—
121	D₄×C₁₀₇	—	2	2	no	—
122	D₄×C₁₀₇	—	4	4	no	—
123	C₂×C₄×C₁₀₇	—	2	2	no	—
124	C₂×C₄×C₁₀₇	—	2	1	no	—
125	C₂×C₄×C₁₀₇	—	2	1	no	—
126	C₂×C₄×C₁₀₇	—	2	2	no	—
127	C₂×C₄×C₁₀₇	—	2	2	no	—
128	C₂×C₄×C₁₀₇	—	2	2	no	—
129	C₂×C₄×C₁₀₇	—	4	1	no	—
130	C₂×C₄×C₁₀₇	—	4	4	no	—
131	C₂×C₄×C₁₀₇	—	4	4	no	—
132	C₂×C₄×C₁₀₇	—	8	2	no	—
133	C₂×C₄×C₁₀₇	C₄×D₄	1	1	yes	characteristic
134	C₂×C₄×C₁₀₇	C₄×D₄	1	1	yes	characteristic
135	C₂×C₄×C₁₀₇	C₄×D₄	1	1	yes	characteristic
136	C₂×C₄×C₁₀₇	C₂³×C₄	1	1	yes	characteristic
137	C₂×C₄×C₁₀₇	C₂²×D₄	1	1	yes	characteristic
138	C₂×C₄×C₁₀₇	C₂×#41	1	1	yes	characteristic
139	C₈×C₁₀₇	—	2	1	no	—
140	C₈×C₁₀₇	—	2	1	no	—
141	C₈×C₁₀₇	—	2	1	no	—
142	C₈×C₁₀₇	—	2	2	no	—
143	C₈×C₁₀₇	—	4	2	no	—
144	C₈×C₁₀₇	—	4	4	no	—
145	C₈×C₁₀₇	C₂×M₁₆	1	2	yes	—
146	C₈×C₁₀₇	#135	1	4	yes	complemented
147	C₂²×C₁₀₇	—	2	1	no	—
148	C₂²×C₁₀₇	—	2	1	no	—
149	C₂²×C₁₀₇	—	2	1	no	—
150	C₂²×C₁₀₇	—	4	2	no	—
151	C₂²×C₁₀₇	—	4	2	no	—
152	C₂²×C₁₀₇	—	4	2	no	—
153	C₂²×C₁₀₇	C₂×C₄×D₄	1	1	yes	characteristic
154	C₄×C₁₀₇	—	2	1	no	—
155	C₄×C₁₀₇	—	2	4	no	—
156	C₄×C₁₀₇	—	2	1	no	—
157	C₄×C₁₀₇	—	2	1	no	—
158	C₄×C₁₀₇	—	2	1	no	—
159	C₄×C₁₀₇	—	4	2	no	—
160	C₄×C₁₀₇	—	4	2	no	—
161	C₄×C₁₀₇	C₂²×M₁₆	1	1	yes	characteristic
162	C₄×C₁₀₇	#568	1	1	yes	characteristic
163	C₄×C₁₀₇	C₂×#135	1	2	yes	—
164	#18039	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
165	C₂×C₁₀₇	—	4	1	no	—
166	C₂×C₁₀₇	—	8	2	no	—
167	C₂×C₁₀₇	D₄×M₁₆	1	1	yes	characteristic
168	C₂×C₁₀₇	C₄×#135	1	1	yes	characteristic
169	C₂×C₁₀₇	#2957	1	1	yes	characteristic
170	#2971	C₂×C₁₀₇	1	2	yes	complemented
171	C₄×#135	C₂×C₁₀₇	1	1	yes	characteristic
172	#1589	C₂×C₁₀₇	1	2	yes	complemented
173	#1583	C₂×C₁₀₇	1	4	yes	complemented
174	C₈×Q₁₆	C₂×C₁₀₇	1	2	yes	complemented
175	#1568	C₂×C₁₀₇	1	1	yes	characteristic, complemented
176	#1488	C₂×C₁₀₇	1	2	yes	complemented
177	C₈×M₁₆	C₂×C₁₀₇	1	1	yes	characteristic, complemented
178	C₁₀₇	#18039	1	1	yes	characteristic, direct product factor, Sylow
179	C₂×#135	C₄×C₁₀₇	1	1	yes	characteristic
180	C₄×#41	C₂²×C₁₀₇	1	2	yes	—
181	C₈×Q₈	C₂²×C₁₀₇	1	4	yes	—
182	C₄×Q₁₆	C₄×C₁₀₇	1	1	yes	characteristic
183	C₄×Q₁₆	C₂²×C₁₀₇	1	1	yes	characteristic
184	C₄×SD₁₆	C₄×C₁₀₇	1	2	yes	—
185	C₄×SD₁₆	C₂²×C₁₀₇	1	2	yes	—
186	C₄×D₈	C₄×C₁₀₇	1	1	yes	characteristic
187	C₄×D₈	C₂²×C₁₀₇	1	1	yes	characteristic
188	#436	—	2	4	no	—
189	#436	C₂²×C₁₀₇	1	4	yes	—
190	#432	—	2	2	no	—
191	#432	C₂²×C₁₀₇	1	2	yes	—
192	#431	C₂²×C₁₀₇	1	1	yes	characteristic
193	#427	C₄×C₁₀₇	1	1	yes	characteristic
194	#416	C₄×C₁₀₇	1	2	yes	—
195	C₄×M₁₆	—	2	2	no	—
196	C₄×M₁₆	C₂²×C₁₀₇	1	1	yes	characteristic
197	C₂×C₄×C₈	C₂²×C₁₀₇	1	1	yes	characteristic
198	#335	C₂²×C₁₀₇	1	2	yes	—
199	#334	C₂²×C₁₀₇	1	2	yes	—
200	Q₈⋊C₈	C₂²×C₁₀₇	1	4	yes	—
201	D₄⋊C₈	C₂²×C₁₀₇	1	4	yes	—
202	#322	C₂²×C₁₀₇	1	2	yes	—
203	C₈²	C₂²×C₁₀₇	1	2	yes	—
204	C₂×#41	C₂×C₄×C₁₀₇	1	2	yes	—
205	#135	—	2	4	no	—
206	C₂×Q₁₆	C₂×C₄×C₁₀₇	1	1	yes	characteristic
207	C₂×SD₁₆	C₂×C₄×C₁₀₇	1	2	yes	—
208	C₂×D₈	C₂×C₄×C₁₀₇	1	1	yes	characteristic
209	C₂×M₁₆	—	2	4	no	—
210	C₂×M₁₆	D₄×C₁₀₇	1	2	yes	—
211	C₂²×C₈	C₂×C₄×C₁₀₇	1	1	yes	characteristic
212	C₂²×C₈	C₂×C₄×C₁₀₇	1	1	yes	characteristic
213	C₄×Q₈	C₂×C₄×C₁₀₇	1	2	yes	—
214	C₄×Q₈	C₂³×C₁₀₇	1	2	yes	—
215	C₄×D₄	—	2	2	no	—
216	C₄×D₄	—	2	2	no	—
217	C₄×D₄	C₂×C₄×C₁₀₇	1	2	yes	—
218	C₄×D₄	C₂³×C₁₀₇	1	2	yes	—
219	#117	—	2	2	no	—
220	#117	C₂×C₄×C₁₀₇	1	2	yes	—
221	C₂×C₄²	—	2	2	no	—
222	C₂×C₄²	C₂³×C₁₀₇	1	1	yes	characteristic
223	#107	C₂×C₄×C₁₀₇	1	1	yes	characteristic
224	#107	C₂×C₄×C₁₀₇	1	1	yes	characteristic
225	#106	C₂×C₄×C₁₀₇	1	2	yes	—
226	C₄⋊C₈	—	2	4	no	—
227	C₄⋊C₈	—	2	1	no	—
228	C₄⋊C₈	C₂³×C₁₀₇	1	4	yes	—
229	#103	C₂×C₄×C₁₀₇	1	2	yes	—
230	#103	C₂×C₄×C₁₀₇	1	2	yes	—
231	#102	C₂×C₄×C₁₀₇	1	2	yes	—
232	#102	C₂×C₄×C₁₀₇	1	2	yes	—
233	C₂²⋊C₈	—	2	2	no	—
234	C₂²⋊C₈	—	2	1	no	—
235	C₂²⋊C₈	—	2	4	no	—
236	#97	—	2	2	no	—
237	#97	D₄×C₁₀₇	1	1	yes	characteristic
238	#97	D₄×C₁₀₇	1	1	yes	characteristic
239	C₄×C₈	—	2	4	no	—
240	C₄×C₈	C₂×C₄×C₁₀₇	1	1	yes	characteristic
241	C₄×C₈	C₂×C₄×C₁₀₇	1	1	yes	characteristic
242	C₄×C₈	C₂³×C₁₀₇	1	2	yes	—
243	C₄×C₈	C₂³×C₁₀₇	1	1	yes	characteristic
244	C₄×C₈	C₂³×C₁₀₇	1	1	yes	characteristic
245	C₄×C₈	C₂³×C₁₀₇	1	2	yes	—
246	#41	—	2	4	no	—
247	#41	—	4	2	no	—
248	C₂×Q₈	C₂²×C₄×C₁₀₇	1	2	yes	—
249	C₂×D₄	—	2	2	no	—
250	C₂×D₄	C₂²×C₄×C₁₀₇	1	2	yes	—
251	C₂²×C₄	—	2	2	no	—
252	C₂²×C₄	—	2	2	no	—
253	C₂²×C₄	—	2	2	no	—
254	C₂²×C₄	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
255	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
256	C₂²×C₄	#41×C₁₀₇	1	1	yes	characteristic
257	Q₁₆	M₁₆×C₁₀₇	1	4	yes	complemented
258	SD₁₆	—	2	4	no	—
259	D₈	—	2	2	no	—
260	M₁₆	—	2	4	no	—
261	M₁₆	—	4	8	no	—
262	C₂×C₈	—	2	2	no	—
263	C₂×C₈	—	2	4	no	—
264	C₂×C₈	—	2	2	no	—
265	C₂×C₈	—	4	1	no	—
266	C₂×C₈	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
267	C₂×C₈	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
268	C₂×C₈	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
269	C₂×C₈	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
270	C₂×C₈	C₂×D₄×C₁₀₇	1	2	yes	—
271	C₂×C₈	C₂×D₄×C₁₀₇	1	2	yes	—
272	C₄⋊C₄	—	2	2	no	—
273	C₄⋊C₄	—	2	2	no	—
274	C₄⋊C₄	C₂²×C₄×C₁₀₇	1	2	yes	—
275	C₄⋊C₄	C₂²×C₄×C₁₀₇	1	2	yes	—
276	C₂²⋊C₄	—	2	2	no	—
277	C₂²⋊C₄	—	2	2	no	—
278	C₂²⋊C₄	—	2	2	no	—
279	C₄²	—	2	2	no	—
280	C₄²	—	2	2	no	—
281	C₄²	—	2	2	no	—
282	C₄²	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
283	C₄²	C₂×D₄×C₁₀₇	1	1	yes	characteristic
284	C₄²	#41×C₁₀₇	1	1	yes	characteristic
285	C₄²	C₂⁴×C₁₀₇	1	1	yes	characteristic
286	C₂³	—	2	2	no	—
287	C₂³	C₄×D₄×C₁₀₇	1	1	yes	characteristic
288	Q₈	—	2	2	no	—
289	Q₈	C₂×M₁₆×C₁₀₇	1	4	yes	—
290	D₄	—	2	2	no	—
291	D₄	—	2	2	no	—
292	D₄	—	4	4	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	2	1	no	—
295	C₂×C₄	—	2	1	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	4	1	no	—
300	C₂×C₄	—	4	4	no	—
301	C₂×C₄	—	4	4	no	—
302	C₂×C₄	—	8	2	no	—
303	C₂×C₄	C₄×D₄×C₁₀₇	1	1	yes	characteristic
304	C₂×C₄	C₄×D₄×C₁₀₇	1	1	yes	characteristic
305	C₂×C₄	C₄×D₄×C₁₀₇	1	1	yes	characteristic
306	C₂×C₄	C₂³×C₄×C₁₀₇	1	1	yes	characteristic
307	C₂×C₄	C₂²×D₄×C₁₀₇	1	1	yes	characteristic
308	C₂×C₄	C₂×#41×C₁₀₇	1	1	yes	characteristic
309	C₈	—	2	1	no	—
310	C₈	—	2	1	no	—
311	C₈	—	2	1	no	—
312	C₈	—	2	2	no	—
313	C₈	—	4	2	no	—
314	C₈	—	4	4	no	—
315	C₈	C₂×M₁₆×C₁₀₇	1	2	yes	—
316	C₈	#135×C₁₀₇	1	4	yes	complemented
317	C₂²	—	2	1	no	—
318	C₂²	—	2	1	no	—
319	C₂²	—	2	1	no	—
320	C₂²	—	4	2	no	—
321	C₂²	—	4	2	no	—
322	C₂²	—	4	2	no	—
323	C₂²	C₂×C₄×D₄×C₁₀₇	1	1	yes	characteristic
324	C₄	—	2	1	no	—
325	C₄	—	2	4	no	—
326	C₄	—	2	1	no	—
327	C₄	—	2	1	no	—
328	C₄	—	2	1	no	—
329	C₄	—	4	2	no	—
330	C₄	—	4	2	no	—
331	C₄	C₂²×M₁₆×C₁₀₇	1	1	yes	characteristic
332	C₄	#568×C₁₀₇	1	1	yes	characteristic
333	C₄	C₂×#135×C₁₀₇	1	2	yes	—
334	C₂	—	4	1	no	—
335	C₂	—	8	2	no	—
336	C₂	D₄×M₁₆×C₁₀₇	1	1	yes	characteristic
337	C₂	C₄×#135×C₁₀₇	1	1	yes	characteristic
338	C₂	C₁₀₇×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₀₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₀₇
Frattini, cosocle	C₄²	C₂⁴×C₁₀₇
socle	C₂²×C₁₀₇	C₂×C₄×D₄
prime radical	C₂×#135×C₁₀₇	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₀₇ ◁ C₄×M₁₆×C₁₀₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₀₇×#2971	C₂	semidirect
3. C₁₀₇×#1589	C₂	semidirect
4. C₁₀₇×#1583	C₂	semidirect
5. C₈×Q₁₆×C₁₀₇	C₂	semidirect
6. C₁₀₇×#1568	C₂	semidirect
7. C₁₀₇×#1488	C₂	semidirect
8. C₈×M₁₆×C₁₀₇	C₂	semidirect
87. Q₁₆×C₁₀₇	M₁₆	semidirect
146. C₈×C₁₀₇	#135	semidirect
164. #18039	C₁₀₇	direct (N × H)
170. #2971	C₂×C₁₀₇	semidirect
172. #1589	C₂×C₁₀₇	semidirect
173. #1583	C₂×C₁₀₇	semidirect
174. C₈×Q₁₆	C₂×C₁₀₇	semidirect
175. #1568	C₂×C₁₀₇	semidirect
176. #1488	C₂×C₁₀₇	semidirect
177. C₈×M₁₆	C₂×C₁₀₇	semidirect
178. C₁₀₇	#18039	direct (N × H)
257. Q₁₆	M₁₆×C₁₀₇	semidirect
316. C₈	#135×C₁₀₇	semidirect

Maximal subgroups

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

subgroup	index
C₁₀₇×#2971	2
C₄×#135×C₁₀₇	2
C₁₀₇×#1589	2
C₁₀₇×#1583	2
C₈×Q₁₆×C₁₀₇	2
C₁₀₇×#1568	2
C₁₀₇×#1488	2
C₈×M₁₆×C₁₀₇	2
#18039	107

Subgroups — C107×#18039 #41044003

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₇×#18039 #41044003