Subgroups — C₂×C₁₀₇×#2187 #41059475

Order 27392.

1382 conjugacy classes of subgroups.

The subgroup lattice has 336 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	C₂²×SD₃₂×C₁₀₇	C₂	1	2	yes	maximal, complemented
3	C₂×#467×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₇×#2187	C₂	1	8	yes	maximal, direct product factor
5	C₂×#357×C₁₀₇	C₂	1	2	yes	maximal, complemented
6	C₂×C₂²⋊C₁₆×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂³×D₄×C₁₀₇	—	2	1	no	—
8	C₂²×Q₁₆×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
9	C₂²×D₈×C₁₀₇	—	2	8	no	—
10	C₂²×D₈×C₁₀₇	—	2	1	no	—
11	C₂²×D₈×C₁₀₇	—	2	2	no	—
12	C₂²×D₈×C₁₀₇	C₂²	1	4	yes	—
13	C₂²×D₈×C₁₀₇	C₂²	1	2	yes	—
14	C₂³×C₈×C₁₀₇	C₂²	1	1	yes	characteristic
15	C₂×C₂²⋊Q₈×C₁₀₇	—	2	1	no	—
16	C₂×SD₃₂×C₁₀₇	—	2	8	no	—
17	C₂×SD₃₂×C₁₀₇	C₂²	1	8	yes	complemented
18	C₂²×C₁₆×C₁₀₇	C₂²	1	2	yes	complemented
19	#467×C₁₀₇	—	2	2	no	—
20	#467×C₁₀₇	C₂²	1	4	yes	complemented
21	C₂×#107×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
22	C₂×#103×C₁₀₇	—	2	1	no	—
23	#357×C₁₀₇	C₂²	1	8	yes	complemented
24	C₂²⋊C₁₆×C₁₀₇	C₂²	1	4	yes	complemented
25	C₂⁵×C₁₀₇	—	4	1	no	—
26	C₂²×Q₈×C₁₀₇	—	2	1	no	—
27	C₂²×D₄×C₁₀₇	—	2	8	no	—
28	C₂²×D₄×C₁₀₇	—	2	4	no	—
29	C₂²×D₄×C₁₀₇	—	2	2	no	—
30	C₂²×D₄×C₁₀₇	—	4	4	no	—
31	C₂²×D₄×C₁₀₇	—	4	2	no	—
32	C₂²×D₄×C₁₀₇	—	4	1	no	—
33	C₂³×C₄×C₁₀₇	D₄	1	1	yes	characteristic
34	C₂×Q₁₆×C₁₀₇	—	2	4	no	—
35	C₂×Q₁₆×C₁₀₇	—	2	1	no	—
36	C₂×Q₁₆×C₁₀₇	C₂³	1	2	yes	complemented
37	C₂×D₈×C₁₀₇	—	2	8	no	—
38	C₂×D₈×C₁₀₇	—	2	16	no	—
39	C₂×D₈×C₁₀₇	—	2	16	no	—
40	C₂×D₈×C₁₀₇	—	2	4	no	—
41	C₂×D₈×C₁₀₇	—	2	2	no	—
42	C₂×D₈×C₁₀₇	—	2	4	no	—
43	C₂×D₈×C₁₀₇	D₄	1	8	yes	—
44	C₂×D₈×C₁₀₇	C₂³	1	4	yes	—
45	C₂²×C₈×C₁₀₇	—	2	4	no	—
46	C₂²×C₈×C₁₀₇	D₄	1	1	yes	characteristic
47	C₂²×C₈×C₁₀₇	D₄	1	2	yes	—
48	C₂²×C₈×C₁₀₇	C₂³	1	2	yes	—
49	C₂²×C₈×C₁₀₇	C₂³	1	1	yes	characteristic
50	C₂²⋊Q₈×C₁₀₇	—	2	4	no	—
51	C₂²⋊Q₈×C₁₀₇	—	4	2	no	—
52	C₂×C₄⋊C₄×C₁₀₇	—	2	1	no	—
53	C₂×C₄⋊C₄×C₁₀₇	—	4	1	no	—
54	C₂×C₂²⋊C₄×C₁₀₇	—	4	1	no	—
55	SD₃₂×C₁₀₇	—	2	16	no	—
56	C₂×C₁₆×C₁₀₇	—	2	4	no	—
57	C₂×C₁₆×C₁₀₇	C₂³	1	4	yes	complemented
58	#107×C₁₀₇	—	2	1	no	—
59	#107×C₁₀₇	C₂³	1	2	yes	complemented
60	#103×C₁₀₇	—	2	4	no	—
61	C₂⁴×C₁₀₇	—	4	8	no	—
62	C₂⁴×C₁₀₇	—	4	4	no	—
63	C₂⁴×C₁₀₇	—	4	2	no	—
64	C₂⁴×C₁₀₇	—	8	4	no	—
65	C₂⁴×C₁₀₇	—	8	4	no	—
66	C₂⁴×C₁₀₇	D₈	1	1	yes	characteristic
67	C₂×Q₈×C₁₀₇	—	2	2	no	—
68	C₂×Q₈×C₁₀₇	—	4	1	no	—
69	C₂×Q₈×C₁₀₇	—	4	2	no	—
70	C₂×Q₈×C₁₀₇	—	4	2	no	—
71	C₂×D₄×C₁₀₇	—	2	16	no	—
72	C₂×D₄×C₁₀₇	—	2	8	no	—
73	C₂×D₄×C₁₀₇	—	2	4	no	—
74	C₂×D₄×C₁₀₇	—	4	8	no	—
75	C₂×D₄×C₁₀₇	—	4	8	no	—
76	C₂×D₄×C₁₀₇	—	4	16	no	—
77	C₂×D₄×C₁₀₇	—	4	4	no	—
78	C₂×D₄×C₁₀₇	—	4	2	no	—
79	C₂×D₄×C₁₀₇	—	4	4	no	—
80	C₂²×C₄×C₁₀₇	—	2	2	no	—
81	C₂²×C₄×C₁₀₇	—	2	2	no	—
82	C₂²×C₄×C₁₀₇	—	4	1	no	—
83	C₂²×C₄×C₁₀₇	—	4	1	no	—
84	C₂²×C₄×C₁₀₇	D₈	1	2	yes	—
85	C₂²×C₄×C₁₀₇	D₈	1	1	yes	characteristic
86	C₂²×C₄×C₁₀₇	C₂×D₄	1	2	yes	—
87	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
88	Q₁₆×C₁₀₇	—	2	4	no	—
89	Q₁₆×C₁₀₇	—	4	2	no	—
90	D₈×C₁₀₇	—	2	16	no	—
91	D₈×C₁₀₇	—	2	8	no	—
92	D₈×C₁₀₇	—	2	4	no	—
93	D₈×C₁₀₇	C₂×D₄	1	8	yes	—
94	C₂×C₈×C₁₀₇	—	2	2	no	—
95	C₂×C₈×C₁₀₇	—	2	4	no	—
96	C₂×C₈×C₁₀₇	—	2	4	no	—
97	C₂×C₈×C₁₀₇	C₂×D₄	1	2	yes	—
98	C₂×C₈×C₁₀₇	C₂×D₄	1	1	yes	characteristic
99	C₂×C₈×C₁₀₇	C₂×D₄	1	4	yes	—
100	C₂×C₈×C₁₀₇	C₂⁴	1	1	yes	characteristic
101	C₄⋊C₄×C₁₀₇	—	2	2	no	—
102	C₄⋊C₄×C₁₀₇	—	4	1	no	—
103	C₄⋊C₄×C₁₀₇	—	4	4	no	—
104	C₂²⋊C₄×C₁₀₇	—	4	4	no	—
105	C₁₆×C₁₀₇	—	2	4	no	—
106	C₂³×C₁₀₇	—	2	2	no	—
107	C₂³×C₁₀₇	—	2	2	no	—
108	C₂³×C₁₀₇	—	4	16	no	—
109	C₂³×C₁₀₇	—	4	4	no	—
110	C₂³×C₁₀₇	—	4	8	no	—
111	C₂³×C₁₀₇	—	8	8	no	—
112	C₂³×C₁₀₇	—	8	32	no	—
113	C₂³×C₁₀₇	—	8	4	no	—
114	C₂³×C₁₀₇	—	8	8	no	—
115	C₂³×C₁₀₇	—	8	4	no	—
116	C₂³×C₁₀₇	SD₃₂	1	4	yes	complemented
117	C₂³×C₁₀₇	C₂×D₈	1	2	yes	—
118	C₂³×C₁₀₇	C₂×D₈	1	1	yes	characteristic
119	Q₈×C₁₀₇	—	4	2	no	—
120	Q₈×C₁₀₇	—	4	2	no	—
121	Q₈×C₁₀₇	—	8	2	no	—
122	D₄×C₁₀₇	—	2	8	no	—
123	D₄×C₁₀₇	—	4	16	no	—
124	D₄×C₁₀₇	—	4	4	no	—
125	D₄×C₁₀₇	—	4	8	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	—	2	4	no	—
130	C₂×C₄×C₁₀₇	—	4	2	no	—
131	C₂×C₄×C₁₀₇	—	4	2	no	—
132	C₂×C₄×C₁₀₇	—	8	2	no	—
133	C₂×C₄×C₁₀₇	—	8	2	no	—
134	C₂×C₄×C₁₀₇	#120	1	2	yes	—
135	C₂×C₄×C₁₀₇	C₂×D₈	1	2	yes	—
136	C₂×C₄×C₁₀₇	C₂×D₈	1	1	yes	characteristic
137	C₂×C₄×C₁₀₇	AGL(1,ℤ/8)	1	2	yes	—
138	C₂×C₄×C₁₀₇	C₂²×D₄	1	1	yes	characteristic
139	C₈×C₁₀₇	—	2	2	no	—
140	C₈×C₁₀₇	#120	1	2	yes	—
141	C₈×C₁₀₇	C₂²×D₄	1	2	yes	—
142	C₂²×C₁₀₇	—	2	2	no	—
143	C₂²×C₁₀₇	—	2	8	no	—
144	C₂²×C₁₀₇	—	2	2	no	—
145	C₂²×C₁₀₇	—	4	8	no	—
146	C₂²×C₁₀₇	—	8	32	no	—
147	C₂²×C₁₀₇	—	8	4	no	—
148	C₂²×C₁₀₇	—	8	4	no	—
149	C₂²×C₁₀₇	—	8	16	no	—
150	C₂²×C₁₀₇	#447	1	2	yes	—
151	C₂²×C₁₀₇	C₂×SD₃₂	1	2	yes	—
152	C₂²×C₁₀₇	C₂×SD₃₂	1	4	yes	complemented
153	C₂²×C₁₀₇	#509	1	2	yes	—
154	C₂²×C₁₀₇	C₂²×D₈	1	1	yes	characteristic
155	C₄×C₁₀₇	—	2	2	no	—
156	C₄×C₁₀₇	—	8	2	no	—
157	C₄×C₁₀₇	—	8	2	no	—
158	C₄×C₁₀₇	#447	1	2	yes	—
159	C₄×C₁₀₇	C₂×#120	1	1	yes	characteristic
160	C₄×C₁₀₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
161	C₂×#2187	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
162	C₂×C₁₀₇	—	2	4	no	—
163	C₂×C₁₀₇	—	8	8	no	—
164	C₂×C₁₀₇	#2187	1	4	yes	direct product factor
165	C₂×C₁₀₇	C₂×#447	1	1	yes	characteristic
166	C₂×C₁₀₇	C₂²×SD₃₂	1	1	yes	characteristic
167	C₂×C₁₀₇	C₂×#509	1	1	yes	characteristic
168	C₂³×D₈	C₂×C₁₀₇	1	1	yes	characteristic
169	C₂²×SD₃₂	C₂×C₁₀₇	1	2	yes	complemented
170	C₂×#467	C₂×C₁₀₇	1	1	yes	characteristic, complemented
171	#2187	C₂×C₁₀₇	1	8	yes	direct product factor
172	C₂×#357	C₂×C₁₀₇	1	2	yes	complemented
173	C₂×C₂²⋊C₁₆	C₂×C₁₀₇	1	1	yes	characteristic, complemented
174	C₁₀₇	C₂×#2187	1	1	yes	characteristic, direct product factor, Sylow
175	C₂³×D₄	—	2	1	no	—
176	C₂²×Q₁₆	C₂²×C₁₀₇	1	1	yes	characteristic, complemented
177	C₂²×D₈	—	2	8	no	—
178	C₂²×D₈	—	2	1	no	—
179	C₂²×D₈	—	2	2	no	—
180	C₂²×D₈	C₂²×C₁₀₇	1	4	yes	—
181	C₂²×D₈	C₂²×C₁₀₇	1	2	yes	—
182	C₂³×C₈	C₂²×C₁₀₇	1	1	yes	characteristic
183	C₂×C₂²⋊Q₈	—	2	1	no	—
184	C₂×SD₃₂	—	2	8	no	—
185	C₂×SD₃₂	C₂²×C₁₀₇	1	8	yes	complemented
186	C₂²×C₁₆	C₂²×C₁₀₇	1	2	yes	complemented
187	#467	—	2	2	no	—
188	#467	C₂²×C₁₀₇	1	4	yes	complemented
189	C₂×#107	C₂²×C₁₀₇	1	1	yes	characteristic, complemented
190	C₂×#103	—	2	1	no	—
191	#357	C₂²×C₁₀₇	1	8	yes	complemented
192	C₂²⋊C₁₆	C₂²×C₁₀₇	1	4	yes	complemented
193	C₂⁵	—	4	1	no	—
194	C₂²×Q₈	—	2	1	no	—
195	C₂²×D₄	—	2	8	no	—
196	C₂²×D₄	—	2	4	no	—
197	C₂²×D₄	—	2	2	no	—
198	C₂²×D₄	—	4	4	no	—
199	C₂²×D₄	—	4	1	no	—
200	C₂²×D₄	—	4	2	no	—
201	C₂³×C₄	D₄×C₁₀₇	1	1	yes	characteristic
202	C₂×Q₁₆	—	2	4	no	—
203	C₂×Q₁₆	—	2	1	no	—
204	C₂×Q₁₆	C₂³×C₁₀₇	1	2	yes	complemented
205	C₂×D₈	—	2	8	no	—
206	C₂×D₈	—	2	16	no	—
207	C₂×D₈	—	2	16	no	—
208	C₂×D₈	—	2	4	no	—
209	C₂×D₈	—	2	2	no	—
210	C₂×D₈	—	2	4	no	—
211	C₂×D₈	D₄×C₁₀₇	1	8	yes	—
212	C₂×D₈	C₂³×C₁₀₇	1	4	yes	—
213	C₂²×C₈	—	2	4	no	—
214	C₂²×C₈	D₄×C₁₀₇	1	1	yes	characteristic
215	C₂²×C₈	D₄×C₁₀₇	1	2	yes	—
216	C₂²×C₈	C₂³×C₁₀₇	1	2	yes	—
217	C₂²×C₈	C₂³×C₁₀₇	1	1	yes	characteristic
218	C₂²⋊Q₈	—	2	4	no	—
219	C₂²⋊Q₈	—	4	2	no	—
220	C₂×C₄⋊C₄	—	2	1	no	—
221	C₂×C₄⋊C₄	—	4	1	no	—
222	C₂×C₂²⋊C₄	—	4	1	no	—
223	SD₃₂	—	2	16	no	—
224	C₂×C₁₆	—	2	4	no	—
225	C₂×C₁₆	C₂³×C₁₀₇	1	4	yes	complemented
226	#107	—	2	1	no	—
227	#107	C₂³×C₁₀₇	1	2	yes	complemented
228	#103	—	2	4	no	—
229	C₂⁴	—	4	8	no	—
230	C₂⁴	—	4	4	no	—
231	C₂⁴	—	4	2	no	—
232	C₂⁴	—	8	4	no	—
233	C₂⁴	—	8	4	no	—
234	C₂⁴	D₈×C₁₀₇	1	1	yes	characteristic
235	C₂×Q₈	—	2	2	no	—
236	C₂×Q₈	—	4	1	no	—
237	C₂×Q₈	—	4	2	no	—
238	C₂×Q₈	—	4	2	no	—
239	C₂×D₄	—	2	16	no	—
240	C₂×D₄	—	2	8	no	—
241	C₂×D₄	—	2	4	no	—
242	C₂×D₄	—	4	8	no	—
243	C₂×D₄	—	4	16	no	—
244	C₂×D₄	—	4	8	no	—
245	C₂×D₄	—	4	4	no	—
246	C₂×D₄	—	4	2	no	—
247	C₂×D₄	—	4	4	no	—
248	C₂²×C₄	—	2	2	no	—
249	C₂²×C₄	—	2	2	no	—
250	C₂²×C₄	—	4	1	no	—
251	C₂²×C₄	—	4	1	no	—
252	C₂²×C₄	D₈×C₁₀₇	1	1	yes	characteristic
253	C₂²×C₄	D₈×C₁₀₇	1	2	yes	—
254	C₂²×C₄	C₂×D₄×C₁₀₇	1	2	yes	—
255	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
256	Q₁₆	—	2	4	no	—
257	Q₁₆	—	4	2	no	—
258	D₈	—	2	16	no	—
259	D₈	—	2	8	no	—
260	D₈	—	2	4	no	—
261	D₈	C₂×D₄×C₁₀₇	1	8	yes	—
262	C₂×C₈	—	2	2	no	—
263	C₂×C₈	—	2	4	no	—
264	C₂×C₈	—	2	4	no	—
265	C₂×C₈	C₂×D₄×C₁₀₇	1	2	yes	—
266	C₂×C₈	C₂×D₄×C₁₀₇	1	1	yes	characteristic
267	C₂×C₈	C₂×D₄×C₁₀₇	1	4	yes	—
268	C₂×C₈	C₂⁴×C₁₀₇	1	1	yes	characteristic
269	C₄⋊C₄	—	2	2	no	—
270	C₄⋊C₄	—	4	1	no	—
271	C₄⋊C₄	—	4	4	no	—
272	C₂²⋊C₄	—	4	4	no	—
273	C₁₆	—	2	4	no	—
274	C₂³	—	2	2	no	—
275	C₂³	—	2	2	no	—
276	C₂³	—	4	16	no	—
277	C₂³	—	4	8	no	—
278	C₂³	—	4	4	no	—
279	C₂³	—	8	8	no	—
280	C₂³	—	8	32	no	—
281	C₂³	—	8	4	no	—
282	C₂³	—	8	8	no	—
283	C₂³	—	8	4	no	—
284	C₂³	SD₃₂×C₁₀₇	1	4	yes	complemented
285	C₂³	C₂×D₈×C₁₀₇	1	2	yes	—
286	C₂³	C₂×D₈×C₁₀₇	1	1	yes	characteristic
287	Q₈	—	4	2	no	—
288	Q₈	—	4	2	no	—
289	Q₈	—	8	2	no	—
290	D₄	—	2	8	no	—
291	D₄	—	4	16	no	—
292	D₄	—	4	8	no	—
293	D₄	—	4	4	no	—
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	2	4	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	4	2	no	—
299	C₂×C₄	—	4	2	no	—
300	C₂×C₄	—	8	2	no	—
301	C₂×C₄	—	8	2	no	—
302	C₂×C₄	#120×C₁₀₇	1	2	yes	—
303	C₂×C₄	C₂×D₈×C₁₀₇	1	2	yes	—
304	C₂×C₄	C₂×D₈×C₁₀₇	1	1	yes	characteristic
305	C₂×C₄	AGL(1,ℤ/8)×C₁₀₇	1	2	yes	—
306	C₂×C₄	C₂²×D₄×C₁₀₇	1	1	yes	characteristic
307	C₈	—	2	2	no	—
308	C₈	#120×C₁₀₇	1	2	yes	—
309	C₈	C₂²×D₄×C₁₀₇	1	2	yes	—
310	C₂²	—	2	2	no	—
311	C₂²	—	2	8	no	—
312	C₂²	—	2	2	no	—
313	C₂²	—	4	8	no	—
314	C₂²	—	8	32	no	—
315	C₂²	—	8	4	no	—
316	C₂²	—	8	4	no	—
317	C₂²	—	8	16	no	—
318	C₂²	#447×C₁₀₇	1	2	yes	—
319	C₂²	C₂×SD₃₂×C₁₀₇	1	2	yes	—
320	C₂²	C₂×SD₃₂×C₁₀₇	1	4	yes	complemented
321	C₂²	#509×C₁₀₇	1	2	yes	—
322	C₂²	C₂²×D₈×C₁₀₇	1	1	yes	characteristic
323	C₄	—	2	2	no	—
324	C₄	—	8	2	no	—
325	C₄	—	8	2	no	—
326	C₄	#447×C₁₀₇	1	2	yes	—
327	C₄	C₂×#120×C₁₀₇	1	1	yes	characteristic
328	C₄	C₂×AGL(1,ℤ/8)×C₁₀₇	1	1	yes	characteristic
329	C₂	—	2	4	no	—
330	C₂	—	8	8	no	—
331	C₂	C₁₀₇×#2187	1	4	yes	direct product factor
332	C₂	C₂×#447×C₁₀₇	1	1	yes	characteristic
333	C₂	C₂²×SD₃₂×C₁₀₇	1	1	yes	characteristic
334	C₂	C₂×#509×C₁₀₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₀₇	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₀₇
prime radical	C₂³×D₈×C₁₀₇	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₇ ◁ C₂³×C₄×C₁₀₇ ◁ C₂³×C₈×C₁₀₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×SD₃₂×C₁₀₇	C₂	semidirect
3. C₂×#467×C₁₀₇	C₂	semidirect
4. C₁₀₇×#2187	C₂	direct (N × H)
5. C₂×#357×C₁₀₇	C₂	semidirect
6. C₂×C₂²⋊C₁₆×C₁₀₇	C₂	semidirect
8. C₂²×Q₁₆×C₁₀₇	C₂²	semidirect
17. C₂×SD₃₂×C₁₀₇	C₂²	semidirect
18. C₂²×C₁₆×C₁₀₇	C₂²	semidirect
20. #467×C₁₀₇	C₂²	semidirect
21. C₂×#107×C₁₀₇	C₂²	semidirect
23. #357×C₁₀₇	C₂²	semidirect
24. C₂²⋊C₁₆×C₁₀₇	C₂²	semidirect
36. C₂×Q₁₆×C₁₀₇	C₂³	semidirect
57. C₂×C₁₆×C₁₀₇	C₂³	semidirect
59. #107×C₁₀₇	C₂³	semidirect
116. C₂³×C₁₀₇	SD₃₂	semidirect
152. C₂²×C₁₀₇	C₂×SD₃₂	semidirect
161. C₂×#2187	C₁₀₇	direct (N × H)
164. C₂×C₁₀₇	#2187	direct (N × H)
169. C₂²×SD₃₂	C₂×C₁₀₇	semidirect
170. C₂×#467	C₂×C₁₀₇	semidirect
171. #2187	C₂×C₁₀₇	direct (N × H)
172. C₂×#357	C₂×C₁₀₇	semidirect
173. C₂×C₂²⋊C₁₆	C₂×C₁₀₇	semidirect
174. C₁₀₇	C₂×#2187	direct (N × H)
176. C₂²×Q₁₆	C₂²×C₁₀₇	semidirect
185. C₂×SD₃₂	C₂²×C₁₀₇	semidirect
186. C₂²×C₁₆	C₂²×C₁₀₇	semidirect
188. #467	C₂²×C₁₀₇	semidirect
189. C₂×#107	C₂²×C₁₀₇	semidirect
191. #357	C₂²×C₁₀₇	semidirect
192. C₂²⋊C₁₆	C₂²×C₁₀₇	semidirect
204. C₂×Q₁₆	C₂³×C₁₀₇	semidirect
225. C₂×C₁₆	C₂³×C₁₀₇	semidirect
227. #107	C₂³×C₁₀₇	semidirect
284. C₂³	SD₃₂×C₁₀₇	semidirect
320. C₂²	C₂×SD₃₂×C₁₀₇	semidirect
331. C₂	C₁₀₇×#2187	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
C₂²×SD₃₂×C₁₀₇	2
C₂×#467×C₁₀₇	2
C₁₀₇×#2187	2
C₂×#357×C₁₀₇	2
C₂×C₂²⋊C₁₆×C₁₀₇	2
C₂×#2187	107

Subgroups — C2×C107×#2187 #41059475

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₀₇×#2187 #41059475