Subgroups — C₄×#442×C₁₀₇ #41046464

Order 27392.

1326 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	C₂×#442×C₁₀₇	C₂	1	2	yes	maximal
2	C₂×C₄×D₈×C₁₀₇	C₂	1	1	yes	maximal, characteristic
3	C₄²×D₄×C₁₀₇	C₂	1	2	yes	maximal, complemented
4	C₁₀₇×#1776	C₂	1	2	yes	maximal, complemented
5	C₄×#106×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₀₇×#1762	C₂	1	4	yes	maximal, complemented
7	C₄×#102×C₁₀₇	C₂	1	2	yes	maximal, complemented
8	C₄×#97×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×D₈×C₁₀₇	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₄×C₁₀₇	C₂²	1	2	yes	—
11	C₂×C₄×D₄×C₁₀₇	C₂²	1	4	yes	—
12	C₂²×C₄²×C₁₀₇	—	2	2	no	—
13	#442×C₁₀₇	C₄	1	16	yes	direct product factor
14	C₄×D₈×C₁₀₇	C₄	1	8	yes	complemented
15	C₂×#107×C₁₀₇	C₂²	1	1	yes	characteristic
16	C₂×#106×C₁₀₇	C₂²	1	2	yes	—
17	C₂×#102×C₁₀₇	C₂²	1	2	yes	—
18	C₂×#102×C₁₀₇	C₂²	1	4	yes	—
19	C₂×#97×C₁₀₇	C₂²	1	2	yes	—
20	C₂×#97×C₁₀₇	C₂²	1	2	yes	—
21	C₂×C₄×C₈×C₁₀₇	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₈×C₁₀₇	C₂²	1	1	yes	characteristic
23	C₄×C₄⋊C₄×C₁₀₇	C₂²	1	2	yes	—
24	C₄×C₄⋊C₄×C₁₀₇	C₂²	1	4	yes	—
25	C₄×C₂²⋊C₄×C₁₀₇	—	2	4	no	—
26	C₄×C₂²⋊C₄×C₁₀₇	—	2	2	no	—
27	C₄³×C₁₀₇	C₂²	1	1	yes	characteristic
28	#340×C₁₀₇	C₂²	1	4	yes	—
29	#340×C₁₀₇	C₂²	1	2	yes	—
30	C₂²×D₄×C₁₀₇	C₂³	1	2	yes	—
31	C₂³×C₄×C₁₀₇	—	2	4	no	—
32	C₂³×C₄×C₁₀₇	—	2	2	no	—
33	C₂×D₈×C₁₀₇	C₂×C₄	1	4	yes	—
34	C₂×D₈×C₁₀₇	C₂×C₄	1	8	yes	—
35	C₂²×C₈×C₁₀₇	C₂³	1	2	yes	—
36	C₂²×C₈×C₁₀₇	C₂³	1	1	yes	characteristic
37	C₂²×C₈×C₁₀₇	C₂³	1	1	yes	characteristic
38	C₄×D₄×C₁₀₇	—	2	4	no	—
39	C₄×D₄×C₁₀₇	—	2	8	no	—
40	C₄×D₄×C₁₀₇	C₂×C₄	1	8	yes	complemented
41	C₄×D₄×C₁₀₇	C₂×C₄	1	16	yes	complemented
42	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	4	yes	—
43	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	2	yes	—
44	C₂×C₂²⋊C₄×C₁₀₇	—	2	2	no	—
45	C₂×C₂²⋊C₄×C₁₀₇	—	2	4	no	—
46	C₂×C₄²×C₁₀₇	—	2	4	no	—
47	C₂×C₄²×C₁₀₇	—	2	2	no	—
48	C₂×C₄²×C₁₀₇	—	4	8	no	—
49	C₂×C₄²×C₁₀₇	D₄	1	2	yes	—
50	C₂×C₄²×C₁₀₇	D₄	1	2	yes	—
51	C₂×C₄²×C₁₀₇	C₂³	1	2	yes	—
52	C₂×C₄²×C₁₀₇	C₂³	1	1	yes	characteristic
53	#107×C₁₀₇	C₂×C₄	1	4	yes	complemented
54	#106×C₁₀₇	C₂×C₄	1	8	yes	complemented
55	#102×C₁₀₇	C₂×C₄	1	8	yes	complemented
56	#102×C₁₀₇	C₂×C₄	1	16	yes	complemented
57	#97×C₁₀₇	—	2	4	no	—
58	#97×C₁₀₇	C₂×C₄	1	8	yes	complemented
59	C₄×C₈×C₁₀₇	—	2	2	no	—
60	C₄×C₈×C₁₀₇	C₂×C₄	1	4	yes	complemented
61	#95×C₁₀₇	—	2	2	no	—
62	#95×C₁₀₇	—	2	4	no	—
63	C₂⁴×C₁₀₇	—	2	2	no	—
64	C₂×D₄×C₁₀₇	—	2	2	no	—
65	C₂×D₄×C₁₀₇	—	2	4	no	—
66	C₂×D₄×C₁₀₇	C₂²×C₄	1	4	yes	—
67	C₂×D₄×C₁₀₇	C₂²×C₄	1	8	yes	—
68	C₂²×C₄×C₁₀₇	—	2	2	no	—
69	C₂²×C₄×C₁₀₇	—	2	4	no	—
70	C₂²×C₄×C₁₀₇	—	2	16	no	—
71	C₂²×C₄×C₁₀₇	—	2	8	no	—
72	C₂²×C₄×C₁₀₇	—	4	8	no	—
73	C₂²×C₄×C₁₀₇	—	4	8	no	—
74	C₂²×C₄×C₁₀₇	—	4	4	no	—
75	C₂²×C₄×C₁₀₇	—	4	4	no	—
76	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₀₇	C₂×D₄	1	4	yes	—
78	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₀₇	C₂⁴	1	1	yes	characteristic
80	D₈×C₁₀₇	C₄²	1	16	yes	complemented
81	C₂×C₈×C₁₀₇	—	2	2	no	—
82	C₂×C₈×C₁₀₇	—	2	2	no	—
83	C₂×C₈×C₁₀₇	—	2	2	no	—
84	C₂×C₈×C₁₀₇	C₂²×C₄	1	2	yes	—
85	C₂×C₈×C₁₀₇	C₂²×C₄	1	4	yes	—
86	C₂×C₈×C₁₀₇	C₂²×C₄	1	2	yes	—
87	C₂×C₈×C₁₀₇	C₂²×C₄	1	4	yes	—
88	C₄⋊C₄×C₁₀₇	—	2	4	no	—
89	C₄⋊C₄×C₁₀₇	—	2	2	no	—
90	C₄⋊C₄×C₁₀₇	C₂²×C₄	1	8	yes	—
91	C₄⋊C₄×C₁₀₇	C₂²×C₄	1	4	yes	—
92	C₂²⋊C₄×C₁₀₇	—	2	8	no	—
93	C₂²⋊C₄×C₁₀₇	—	2	16	no	—
94	C₄²×C₁₀₇	—	2	4	no	—
95	C₄²×C₁₀₇	—	4	2	no	—
96	C₄²×C₁₀₇	—	4	8	no	—
97	C₄²×C₁₀₇	—	4	4	no	—
98	C₄²×C₁₀₇	C₂²×C₄	1	2	yes	—
99	C₄²×C₁₀₇	C₂²×C₄	1	4	yes	—
100	C₄²×C₁₀₇	#41	1	2	yes	—
101	C₄²×C₁₀₇	#41	1	4	yes	—
102	C₂³×C₁₀₇	—	2	4	no	—
103	C₂³×C₁₀₇	—	2	8	no	—
104	C₂³×C₁₀₇	—	4	2	no	—
105	C₂³×C₁₀₇	—	4	2	no	—
106	C₂³×C₁₀₇	—	4	4	no	—
107	C₂³×C₁₀₇	C₂²×D₄	1	1	yes	characteristic
108	D₄×C₁₀₇	—	2	4	no	—
109	D₄×C₁₀₇	—	2	8	no	—
110	D₄×C₁₀₇	C₂×C₄²	1	8	yes	complemented
111	C₂×C₄×C₁₀₇	—	2	4	no	—
112	C₂×C₄×C₁₀₇	—	2	4	no	—
113	C₂×C₄×C₁₀₇	—	2	2	no	—
114	C₂×C₄×C₁₀₇	—	2	4	no	—
115	C₂×C₄×C₁₀₇	—	2	8	no	—
116	C₂×C₄×C₁₀₇	—	4	32	no	—
117	C₂×C₄×C₁₀₇	—	4	2	no	—
118	C₂×C₄×C₁₀₇	—	4	4	no	—
119	C₂×C₄×C₁₀₇	—	4	2	no	—
120	C₂×C₄×C₁₀₇	—	4	4	no	—
121	C₂×C₄×C₁₀₇	—	4	16	no	—
122	C₂×C₄×C₁₀₇	C₄×D₄	1	2	yes	—
123	C₂×C₄×C₁₀₇	C₄×D₄	1	8	yes	—
124	C₂×C₄×C₁₀₇	C₄×D₄	1	2	yes	—
125	C₂×C₄×C₁₀₇	AGL(1,ℤ/8)	1	4	yes	—
126	C₂×C₄×C₁₀₇	C₂³×C₄	1	1	yes	characteristic
127	C₂×C₄×C₁₀₇	C₂³×C₄	1	2	yes	—
128	C₂×C₄×C₁₀₇	C₂×#41	1	1	yes	characteristic
129	C₂×C₄×C₁₀₇	C₂×#41	1	2	yes	—
130	C₈×C₁₀₇	—	2	4	no	—
131	C₈×C₁₀₇	—	2	2	no	—
132	C₈×C₁₀₇	C₂×C₄²	1	4	yes	complemented
133	C₂²×C₁₀₇	—	2	8	no	—
134	C₂²×C₁₀₇	—	4	4	no	—
135	C₂²×C₁₀₇	—	4	4	no	—
136	C₂²×C₁₀₇	—	4	8	no	—
137	C₂²×C₁₀₇	—	4	8	no	—
138	C₂²×C₁₀₇	C₂×C₄×D₄	1	1	yes	characteristic
139	C₂²×C₁₀₇	C₂×C₄×D₄	1	2	yes	—
140	C₂²×C₁₀₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
141	C₂²×C₁₀₇	#575	1	2	yes	—
142	C₄×C₁₀₇	—	2	2	no	—
143	C₄×C₁₀₇	—	2	8	no	—
144	C₄×C₁₀₇	—	4	4	no	—
145	C₄×C₁₀₇	—	4	8	no	—
146	C₄×C₁₀₇	#442	1	4	yes	direct product factor
147	C₄×C₁₀₇	C₂²×C₄²	1	1	yes	characteristic
148	C₄×C₁₀₇	C₄×#41	1	2	yes	—
149	C₄×C₁₀₇	C₄×#41	1	1	yes	characteristic
150	C₄×#442	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
151	C₂×C₁₀₇	—	4	8	no	—
152	C₂×C₁₀₇	C₄²×D₄	1	1	yes	characteristic
153	C₂×C₁₀₇	C₂×#442	1	1	yes	characteristic
154	C₂×C₁₀₇	#2943	1	1	yes	characteristic
155	C₂×C₁₀₇	C₄×AGL(1,ℤ/8)	1	4	yes	—
156	C₂×#442	C₂×C₁₀₇	1	2	yes	—
157	C₂×C₄×D₈	C₂×C₁₀₇	1	1	yes	characteristic
158	C₄²×D₄	C₂×C₁₀₇	1	2	yes	complemented
159	#1776	C₂×C₁₀₇	1	2	yes	complemented
160	C₄×#106	C₂×C₁₀₇	1	1	yes	characteristic, complemented
161	#1762	C₂×C₁₀₇	1	4	yes	complemented
162	C₄×#102	C₂×C₁₀₇	1	2	yes	complemented
163	C₄×#97	C₂×C₁₀₇	1	1	yes	characteristic, complemented
164	C₁₀₇	C₄×#442	1	1	yes	characteristic, direct product factor, Sylow
165	C₂²×D₈	C₂²×C₁₀₇	1	1	yes	characteristic
166	C₂×C₄×D₄	C₂²×C₁₀₇	1	2	yes	—
167	C₂×C₄×D₄	C₂²×C₁₀₇	1	4	yes	—
168	C₂²×C₄²	—	2	2	no	—
169	#442	C₄×C₁₀₇	1	16	yes	direct product factor
170	C₄×D₈	C₄×C₁₀₇	1	8	yes	complemented
171	C₂×#107	C₂²×C₁₀₇	1	1	yes	characteristic
172	C₂×#106	C₂²×C₁₀₇	1	2	yes	—
173	C₂×#102	C₂²×C₁₀₇	1	2	yes	—
174	C₂×#102	C₂²×C₁₀₇	1	4	yes	—
175	C₂×#97	C₂²×C₁₀₇	1	2	yes	—
176	C₂×#97	C₂²×C₁₀₇	1	2	yes	—
177	C₂×C₄×C₈	C₂²×C₁₀₇	1	1	yes	characteristic
178	C₂×C₄×C₈	C₂²×C₁₀₇	1	1	yes	characteristic
179	C₄×C₄⋊C₄	C₂²×C₁₀₇	1	2	yes	—
180	C₄×C₄⋊C₄	C₂²×C₁₀₇	1	4	yes	—
181	C₄×C₂²⋊C₄	—	2	2	no	—
182	C₄×C₂²⋊C₄	—	2	4	no	—
183	C₄³	C₂²×C₁₀₇	1	1	yes	characteristic
184	#340	C₂²×C₁₀₇	1	4	yes	—
185	#340	C₂²×C₁₀₇	1	2	yes	—
186	C₂²×D₄	C₂³×C₁₀₇	1	2	yes	—
187	C₂³×C₄	—	2	4	no	—
188	C₂³×C₄	—	2	2	no	—
189	C₂×D₈	C₂×C₄×C₁₀₇	1	4	yes	—
190	C₂×D₈	C₂×C₄×C₁₀₇	1	8	yes	—
191	C₂²×C₈	C₂³×C₁₀₇	1	2	yes	—
192	C₂²×C₈	C₂³×C₁₀₇	1	1	yes	characteristic
193	C₂²×C₈	C₂³×C₁₀₇	1	1	yes	characteristic
194	C₄×D₄	—	2	4	no	—
195	C₄×D₄	—	2	8	no	—
196	C₄×D₄	C₂×C₄×C₁₀₇	1	8	yes	complemented
197	C₄×D₄	C₂×C₄×C₁₀₇	1	16	yes	complemented
198	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	4	yes	—
199	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	2	yes	—
200	C₂×C₂²⋊C₄	—	2	2	no	—
201	C₂×C₂²⋊C₄	—	2	4	no	—
202	C₂×C₄²	—	2	4	no	—
203	C₂×C₄²	—	2	2	no	—
204	C₂×C₄²	—	4	8	no	—
205	C₂×C₄²	D₄×C₁₀₇	1	2	yes	—
206	C₂×C₄²	D₄×C₁₀₇	1	2	yes	—
207	C₂×C₄²	C₂³×C₁₀₇	1	1	yes	characteristic
208	C₂×C₄²	C₂³×C₁₀₇	1	2	yes	—
209	#107	C₂×C₄×C₁₀₇	1	4	yes	complemented
210	#106	C₂×C₄×C₁₀₇	1	8	yes	complemented
211	#102	C₂×C₄×C₁₀₇	1	8	yes	complemented
212	#102	C₂×C₄×C₁₀₇	1	16	yes	complemented
213	#97	—	2	4	no	—
214	#97	C₂×C₄×C₁₀₇	1	8	yes	complemented
215	C₄×C₈	—	2	2	no	—
216	C₄×C₈	C₂×C₄×C₁₀₇	1	4	yes	complemented
217	#95	—	2	2	no	—
218	#95	—	2	4	no	—
219	C₂⁴	—	2	2	no	—
220	C₂×D₄	—	2	2	no	—
221	C₂×D₄	—	2	4	no	—
222	C₂×D₄	C₂²×C₄×C₁₀₇	1	4	yes	—
223	C₂×D₄	C₂²×C₄×C₁₀₇	1	8	yes	—
224	C₂²×C₄	—	2	2	no	—
225	C₂²×C₄	—	2	4	no	—
226	C₂²×C₄	—	2	16	no	—
227	C₂²×C₄	—	2	8	no	—
228	C₂²×C₄	—	4	8	no	—
229	C₂²×C₄	—	4	8	no	—
230	C₂²×C₄	—	4	4	no	—
231	C₂²×C₄	—	4	4	no	—
232	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
233	C₂²×C₄	C₂×D₄×C₁₀₇	1	4	yes	—
234	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
235	C₂²×C₄	C₂⁴×C₁₀₇	1	1	yes	characteristic
236	D₈	C₄²×C₁₀₇	1	16	yes	complemented
237	C₂×C₈	—	2	2	no	—
238	C₂×C₈	—	2	2	no	—
239	C₂×C₈	—	2	2	no	—
240	C₂×C₈	C₂²×C₄×C₁₀₇	1	2	yes	—
241	C₂×C₈	C₂²×C₄×C₁₀₇	1	4	yes	—
242	C₂×C₈	C₂²×C₄×C₁₀₇	1	2	yes	—
243	C₂×C₈	C₂²×C₄×C₁₀₇	1	4	yes	—
244	C₄⋊C₄	—	2	4	no	—
245	C₄⋊C₄	—	2	2	no	—
246	C₄⋊C₄	C₂²×C₄×C₁₀₇	1	8	yes	—
247	C₄⋊C₄	C₂²×C₄×C₁₀₇	1	4	yes	—
248	C₂²⋊C₄	—	2	8	no	—
249	C₂²⋊C₄	—	2	16	no	—
250	C₄²	—	2	4	no	—
251	C₄²	—	4	2	no	—
252	C₄²	—	4	8	no	—
253	C₄²	—	4	4	no	—
254	C₄²	C₂²×C₄×C₁₀₇	1	2	yes	—
255	C₄²	C₂²×C₄×C₁₀₇	1	4	yes	—
256	C₄²	#41×C₁₀₇	1	2	yes	—
257	C₄²	#41×C₁₀₇	1	4	yes	—
258	C₂³	—	2	4	no	—
259	C₂³	—	2	8	no	—
260	C₂³	—	4	2	no	—
261	C₂³	—	4	2	no	—
262	C₂³	—	4	4	no	—
263	C₂³	C₂²×D₄×C₁₀₇	1	1	yes	characteristic
264	D₄	—	2	4	no	—
265	D₄	—	2	8	no	—
266	D₄	C₂×C₄²×C₁₀₇	1	8	yes	complemented
267	C₂×C₄	—	2	4	no	—
268	C₂×C₄	—	2	4	no	—
269	C₂×C₄	—	2	2	no	—
270	C₂×C₄	—	2	4	no	—
271	C₂×C₄	—	2	8	no	—
272	C₂×C₄	—	4	32	no	—
273	C₂×C₄	—	4	2	no	—
274	C₂×C₄	—	4	4	no	—
275	C₂×C₄	—	4	2	no	—
276	C₂×C₄	—	4	4	no	—
277	C₂×C₄	—	4	16	no	—
278	C₂×C₄	C₄×D₄×C₁₀₇	1	2	yes	—
279	C₂×C₄	C₄×D₄×C₁₀₇	1	8	yes	—
280	C₂×C₄	C₄×D₄×C₁₀₇	1	2	yes	—
281	C₂×C₄	AGL(1,ℤ/8)×C₁₀₇	1	4	yes	—
282	C₂×C₄	C₂³×C₄×C₁₀₇	1	1	yes	characteristic
283	C₂×C₄	C₂³×C₄×C₁₀₇	1	2	yes	—
284	C₂×C₄	C₂×#41×C₁₀₇	1	1	yes	characteristic
285	C₂×C₄	C₂×#41×C₁₀₇	1	2	yes	—
286	C₈	—	2	4	no	—
287	C₈	—	2	2	no	—
288	C₈	C₂×C₄²×C₁₀₇	1	4	yes	complemented
289	C₂²	—	2	8	no	—
290	C₂²	—	4	4	no	—
291	C₂²	—	4	4	no	—
292	C₂²	—	4	8	no	—
293	C₂²	—	4	8	no	—
294	C₂²	C₂×C₄×D₄×C₁₀₇	1	1	yes	characteristic
295	C₂²	C₂×C₄×D₄×C₁₀₇	1	2	yes	—
296	C₂²	C₂×AGL(1,ℤ/8)×C₁₀₇	1	2	yes	—
297	C₂²	#575×C₁₀₇	1	2	yes	—
298	C₄	—	2	2	no	—
299	C₄	—	2	8	no	—
300	C₄	—	4	4	no	—
301	C₄	—	4	8	no	—
302	C₄	#442×C₁₀₇	1	4	yes	direct product factor
303	C₄	C₂²×C₄²×C₁₀₇	1	1	yes	characteristic
304	C₄	C₄×#41×C₁₀₇	1	2	yes	—
305	C₄	C₄×#41×C₁₀₇	1	1	yes	characteristic
306	C₂	—	4	8	no	—
307	C₂	C₄²×D₄×C₁₀₇	1	1	yes	characteristic
308	C₂	C₂×#442×C₁₀₇	1	1	yes	characteristic
309	C₂	C₁₀₇×#2943	1	1	yes	characteristic
310	C₂	C₄×AGL(1,ℤ/8)×C₁₀₇	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₀₇	C₂×D₄
commutator	C₄	C₂²×C₄²×C₁₀₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₇
socle	C₂³×C₁₀₇	C₂²×D₄
prime radical	C₂²×D₈×C₁₀₇	C₂²
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₀₇ ◁ C₄³×C₁₀₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₄²×D₄×C₁₀₇	C₂	semidirect
4. C₁₀₇×#1776	C₂	semidirect
5. C₄×#106×C₁₀₇	C₂	semidirect
6. C₁₀₇×#1762	C₂	semidirect
7. C₄×#102×C₁₀₇	C₂	semidirect
8. C₄×#97×C₁₀₇	C₂	semidirect
13. #442×C₁₀₇	C₄	direct (N × H)
14. C₄×D₈×C₁₀₇	C₄	semidirect
40. C₄×D₄×C₁₀₇	C₂×C₄	semidirect
41. C₄×D₄×C₁₀₇	C₂×C₄	semidirect
53. #107×C₁₀₇	C₂×C₄	semidirect
54. #106×C₁₀₇	C₂×C₄	semidirect
55. #102×C₁₀₇	C₂×C₄	semidirect
56. #102×C₁₀₇	C₂×C₄	semidirect
58. #97×C₁₀₇	C₂×C₄	semidirect
60. C₄×C₈×C₁₀₇	C₂×C₄	semidirect
80. D₈×C₁₀₇	C₄²	semidirect
110. D₄×C₁₀₇	C₂×C₄²	semidirect
132. C₈×C₁₀₇	C₂×C₄²	semidirect
146. C₄×C₁₀₇	#442	direct (N × H)
150. C₄×#442	C₁₀₇	direct (N × H)
158. C₄²×D₄	C₂×C₁₀₇	semidirect
159. #1776	C₂×C₁₀₇	semidirect
160. C₄×#106	C₂×C₁₀₇	semidirect
161. #1762	C₂×C₁₀₇	semidirect
162. C₄×#102	C₂×C₁₀₇	semidirect
163. C₄×#97	C₂×C₁₀₇	semidirect
164. C₁₀₇	C₄×#442	direct (N × H)
169. #442	C₄×C₁₀₇	direct (N × H)
170. C₄×D₈	C₄×C₁₀₇	semidirect
196. C₄×D₄	C₂×C₄×C₁₀₇	semidirect
197. C₄×D₄	C₂×C₄×C₁₀₇	semidirect
209. #107	C₂×C₄×C₁₀₇	semidirect
210. #106	C₂×C₄×C₁₀₇	semidirect
211. #102	C₂×C₄×C₁₀₇	semidirect
212. #102	C₂×C₄×C₁₀₇	semidirect
214. #97	C₂×C₄×C₁₀₇	semidirect
216. C₄×C₈	C₂×C₄×C₁₀₇	semidirect
236. D₈	C₄²×C₁₀₇	semidirect
266. D₄	C₂×C₄²×C₁₀₇	semidirect
288. C₈	C₂×C₄²×C₁₀₇	semidirect
302. C₄	#442×C₁₀₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#442×C₁₀₇	2
C₂×C₄×D₈×C₁₀₇	2
C₄²×D₄×C₁₀₇	2
C₁₀₇×#1776	2
C₄×#106×C₁₀₇	2
C₁₀₇×#1762	2
C₄×#102×C₁₀₇	2
C₄×#97×C₁₀₇	2
C₄×#442	107

Subgroups — C4×#442×C107 #41046464

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#442×C₁₀₇ #41046464