Subgroups — C₁₀₇×#8566 #41034530

Order 27392.

568 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×Q₈×C₁₀₇	C₂	1	1	yes	maximal, characteristic
2	C₁₀₇×#1831	C₂	1	1	yes	maximal, characteristic
3	C₄×C₄⋊C₈×C₁₀₇	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₈⋊C₈×C₁₀₇	C₂	1	2	yes	maximal
5	C₁₀₇×#1279	C₂	1	2	yes	maximal
6	C₂×C₄×Q₈×C₁₀₇	C₄	1	1	yes	characteristic
7	C₂×C₄×Q₈×C₁₀₇	C₄	1	1	yes	characteristic
8	C₂×C₄×Q₈×C₁₀₇	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊C₈×C₁₀₇	—	2	1	no	—
10	C₂×C₄⋊C₈×C₁₀₇	C₂²	1	2	yes	—
11	C₂×C₄×C₈×C₁₀₇	C₂²	1	2	yes	—
12	C₄×C₄⋊C₄×C₁₀₇	—	2	1	no	—
13	C₄×C₄⋊C₄×C₁₀₇	—	2	1	no	—
14	C₄×C₄⋊C₄×C₁₀₇	—	2	1	no	—
15	C₄×C₄⋊C₄×C₁₀₇	C₄	1	1	yes	characteristic
16	C₄×C₄⋊C₄×C₁₀₇	C₄	1	1	yes	characteristic
17	C₄×C₄⋊C₄×C₁₀₇	C₂²	1	1	yes	characteristic
18	C₄³×C₁₀₇	—	2	1	no	—
19	C₄³×C₁₀₇	C₂²	1	1	yes	characteristic
20	#336×C₁₀₇	—	2	1	no	—
21	#336×C₁₀₇	—	2	1	no	—
22	#336×C₁₀₇	—	2	1	no	—
23	Q₈⋊C₈×C₁₀₇	—	2	4	no	—
24	C₂²×Q₈×C₁₀₇	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₈×C₁₀₇	—	2	2	no	—
26	C₂²×C₈×C₁₀₇	—	2	2	no	—
27	C₄×Q₈×C₁₀₇	—	2	2	no	—
28	C₄×Q₈×C₁₀₇	—	2	2	no	—
29	C₄×Q₈×C₁₀₇	—	2	2	no	—
30	C₄×Q₈×C₁₀₇	—	2	1	no	—
31	C₄×Q₈×C₁₀₇	—	2	1	no	—
32	C₄×Q₈×C₁₀₇	C₈	1	4	yes	complemented
33	C₄×Q₈×C₁₀₇	D₄	1	2	yes	—
34	C₄×Q₈×C₁₀₇	Q₈	1	2	yes	—
35	C₂×C₄⋊C₄×C₁₀₇	—	2	1	no	—
36	C₂×C₄⋊C₄×C₁₀₇	—	2	1	no	—
37	C₂×C₄⋊C₄×C₁₀₇	—	2	1	no	—
38	C₂×C₄⋊C₄×C₁₀₇	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄⋊C₄×C₁₀₇	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄⋊C₄×C₁₀₇	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₀₇	—	2	1	no	—
42	C₂×C₄²×C₁₀₇	—	2	1	no	—
43	C₂×C₄²×C₁₀₇	—	2	1	no	—
44	C₂×C₄²×C₁₀₇	—	2	1	no	—
45	C₂×C₄²×C₁₀₇	—	2	1	no	—
46	C₂×C₄²×C₁₀₇	—	2	1	no	—
47	C₂×C₄²×C₁₀₇	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₁₀₇	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₁₀₇	D₄	1	1	yes	characteristic
50	C₂×C₄²×C₁₀₇	D₄	1	1	yes	characteristic
51	C₂×C₄²×C₁₀₇	D₄	1	1	yes	characteristic
52	C₂×C₄²×C₁₀₇	D₄	1	1	yes	characteristic
53	C₂×C₄²×C₁₀₇	C₂³	1	1	yes	characteristic
54	C₄⋊C₈×C₁₀₇	—	2	4	no	—
55	C₄⋊C₈×C₁₀₇	—	2	2	no	—
56	C₄⋊C₈×C₁₀₇	—	2	2	no	—
57	C₄×C₈×C₁₀₇	—	2	2	no	—
58	C₄×C₈×C₁₀₇	—	2	2	no	—
59	#95×C₁₀₇	—	2	1	no	—
60	#95×C₁₀₇	—	2	1	no	—
61	#95×C₁₀₇	—	2	1	no	—
62	C₂×Q₈×C₁₀₇	—	2	1	no	—
63	C₂×Q₈×C₁₀₇	—	2	1	no	—
64	C₂×Q₈×C₁₀₇	—	2	1	no	—
65	C₂×Q₈×C₁₀₇	C₄⋊C₄	1	2	yes	—
66	C₂×Q₈×C₁₀₇	C₂×C₈	1	2	yes	—
67	C₂×Q₈×C₁₀₇	M₁₆	1	2	yes	—
68	C₂²×C₄×C₁₀₇	—	2	1	no	—
69	C₂²×C₄×C₁₀₇	—	2	1	no	—
70	C₂²×C₄×C₁₀₇	—	2	1	no	—
71	C₂²×C₄×C₁₀₇	—	2	1	no	—
72	C₂²×C₄×C₁₀₇	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₀₇	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₀₇	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₀₇	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
79	C₂×C₈×C₁₀₇	—	2	4	no	—
80	C₂×C₈×C₁₀₇	—	4	2	no	—
81	C₂×C₈×C₁₀₇	—	4	2	no	—
82	C₂×C₈×C₁₀₇	—	4	2	no	—
83	C₂×C₈×C₁₀₇	—	4	2	no	—
84	C₂×C₈×C₁₀₇	—	4	2	no	—
85	C₄⋊C₄×C₁₀₇	—	2	4	no	—
86	C₄⋊C₄×C₁₀₇	—	2	4	no	—
87	C₄⋊C₄×C₁₀₇	—	2	1	no	—
88	C₄⋊C₄×C₁₀₇	—	2	2	no	—
89	C₄⋊C₄×C₁₀₇	—	2	2	no	—
90	C₄⋊C₄×C₁₀₇	—	2	1	no	—
91	C₄⋊C₄×C₁₀₇	—	2	1	no	—
92	C₄⋊C₄×C₁₀₇	C₄⋊C₄	1	2	yes	—
93	C₄⋊C₄×C₁₀₇	C₂×C₈	1	2	yes	—
94	C₄⋊C₄×C₁₀₇	M₁₆	1	2	yes	—
95	C₄²×C₁₀₇	—	2	4	no	—
96	C₄²×C₁₀₇	—	2	4	no	—
97	C₄²×C₁₀₇	—	2	2	no	—
98	C₄²×C₁₀₇	—	2	2	no	—
99	C₄²×C₁₀₇	—	2	2	no	—
100	C₄²×C₁₀₇	—	2	1	no	—
101	C₄²×C₁₀₇	—	2	1	no	—
102	C₄²×C₁₀₇	—	2	2	no	—
103	C₄²×C₁₀₇	—	2	2	no	—
104	C₄²×C₁₀₇	—	4	1	no	—
105	C₄²×C₁₀₇	—	4	2	no	—
106	C₄²×C₁₀₇	—	4	2	no	—
107	C₄²×C₁₀₇	—	4	2	no	—
108	C₄²×C₁₀₇	C₂×C₈	1	2	yes	—
109	C₄²×C₁₀₇	M₁₆	1	2	yes	—
110	C₄²×C₁₀₇	C₂×D₄	1	1	yes	characteristic
111	C₄²×C₁₀₇	C₂×Q₈	1	1	yes	characteristic
112	C₄²×C₁₀₇	#41	1	1	yes	characteristic
113	C₄²×C₁₀₇	#41	1	1	yes	characteristic
114	C₂³×C₁₀₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
115	Q₈×C₁₀₇	—	2	2	no	—
116	Q₈×C₁₀₇	—	2	2	no	—
117	Q₈×C₁₀₇	—	2	2	no	—
118	Q₈×C₁₀₇	C₄⋊C₈	1	4	yes	complemented
119	C₂×C₄×C₁₀₇	—	2	2	no	—
120	C₂×C₄×C₁₀₇	—	2	2	no	—
121	C₂×C₄×C₁₀₇	—	2	1	no	—
122	C₂×C₄×C₁₀₇	—	2	2	no	—
123	C₂×C₄×C₁₀₇	—	2	1	no	—
124	C₂×C₄×C₁₀₇	—	2	1	no	—
125	C₂×C₄×C₁₀₇	—	2	1	no	—
126	C₂×C₄×C₁₀₇	—	2	1	no	—
127	C₂×C₄×C₁₀₇	—	2	1	no	—
128	C₂×C₄×C₁₀₇	—	2	1	no	—
129	C₂×C₄×C₁₀₇	—	2	1	no	—
130	C₂×C₄×C₁₀₇	—	2	2	no	—
131	C₂×C₄×C₁₀₇	—	2	2	no	—
132	C₂×C₄×C₁₀₇	—	2	1	no	—
133	C₂×C₄×C₁₀₇	—	2	2	no	—
134	C₂×C₄×C₁₀₇	—	2	1	no	—
135	C₂×C₄×C₁₀₇	—	2	1	no	—
136	C₂×C₄×C₁₀₇	—	4	1	no	—
137	C₂×C₄×C₁₀₇	—	4	1	no	—
138	C₂×C₄×C₁₀₇	—	4	1	no	—
139	C₂×C₄×C₁₀₇	—	4	1	no	—
140	C₂×C₄×C₁₀₇	—	4	1	no	—
141	C₂×C₄×C₁₀₇	—	4	1	no	—
142	C₂×C₄×C₁₀₇	C₂²⋊C₈	1	2	yes	—
143	C₂×C₄×C₁₀₇	C₂²⋊C₈	1	2	yes	—
144	C₂×C₄×C₁₀₇	#104	1	2	yes	—
145	C₂×C₄×C₁₀₇	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₁₀₇	#117	1	1	yes	characteristic
147	C₂×C₄×C₁₀₇	#121	1	1	yes	characteristic
148	C₂×C₄×C₁₀₇	#121	1	1	yes	characteristic
149	C₂×C₄×C₁₀₇	C₂²⋊Q₈	1	1	yes	characteristic
150	C₂×C₄×C₁₀₇	C₂²⋊Q₈	1	1	yes	characteristic
151	C₂×C₄×C₁₀₇	C₂²×C₈	1	1	yes	characteristic
152	C₂×C₄×C₁₀₇	C₂×M₁₆	1	1	yes	characteristic
153	C₂×C₄×C₁₀₇	C₂×M₁₆	1	1	yes	characteristic
154	C₂×C₄×C₁₀₇	C₂×M₁₆	1	1	yes	characteristic
155	C₂×C₄×C₁₀₇	#135	1	2	yes	—
156	C₂×C₄×C₁₀₇	#137	1	2	yes	—
157	C₈×C₁₀₇	—	4	4	no	—
158	C₈×C₁₀₇	—	8	2	no	—
159	C₂²×C₁₀₇	#380	1	1	yes	characteristic
160	C₂²×C₁₀₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
161	C₂²×C₁₀₇	#407	1	1	yes	characteristic
162	C₂²×C₁₀₇	#416	1	1	yes	characteristic
163	C₂²×C₁₀₇	#419	1	1	yes	characteristic
164	C₂²×C₁₀₇	C₂×#104	1	1	yes	characteristic
165	C₂²×C₁₀₇	#421	1	1	yes	characteristic
166	C₄×C₁₀₇	—	2	4	no	—
167	C₄×C₁₀₇	—	2	1	no	—
168	C₄×C₁₀₇	—	2	1	no	—
169	C₄×C₁₀₇	—	2	2	no	—
170	C₄×C₁₀₇	—	2	2	no	—
171	C₄×C₁₀₇	—	2	2	no	—
172	C₄×C₁₀₇	—	4	2	no	—
173	C₄×C₁₀₇	—	4	2	no	—
174	C₄×C₁₀₇	—	4	1	no	—
175	C₄×C₁₀₇	—	4	2	no	—
176	C₄×C₁₀₇	C₂×C₄⋊C₈	1	1	yes	characteristic
177	C₄×C₁₀₇	#423	1	1	yes	characteristic
178	C₄×C₁₀₇	#431	1	1	yes	characteristic
179	C₄×C₁₀₇	#432	1	1	yes	characteristic
180	C₄×C₁₀₇	#464	1	2	yes	—
181	C₄×C₁₀₇	#479	1	2	yes	—
182	#8566	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
183	C₂×C₁₀₇	#1476	1	1	yes	characteristic
184	C₂×C₁₀₇	#1479	1	1	yes	characteristic
185	C₂×C₁₀₇	#1488	1	1	yes	characteristic
186	C₂×C₁₀₇	#1491	1	1	yes	characteristic
187	C₂×C₁₀₇	#1797	1	1	yes	characteristic
188	C₂×C₁₀₇	#1805	1	1	yes	characteristic
189	C₂×C₁₀₇	#1806	1	1	yes	characteristic
190	C₄²×Q₈	C₂×C₁₀₇	1	1	yes	characteristic
191	#1831	C₂×C₁₀₇	1	1	yes	characteristic
192	C₄×C₄⋊C₈	C₂×C₁₀₇	1	1	yes	characteristic
193	C₂×Q₈⋊C₈	C₂×C₁₀₇	1	2	yes	—
194	#1279	C₂×C₁₀₇	1	2	yes	—
195	C₁₀₇	#8566	1	1	yes	characteristic, direct product factor, Sylow
196	C₂×C₄×Q₈	C₄×C₁₀₇	1	1	yes	characteristic
197	C₂×C₄×Q₈	C₄×C₁₀₇	1	1	yes	characteristic
198	C₂×C₄×Q₈	C₂²×C₁₀₇	1	1	yes	characteristic
199	C₂×C₄⋊C₈	—	2	1	no	—
200	C₂×C₄⋊C₈	C₂²×C₁₀₇	1	2	yes	—
201	C₂×C₄×C₈	C₂²×C₁₀₇	1	2	yes	—
202	C₄×C₄⋊C₄	—	2	1	no	—
203	C₄×C₄⋊C₄	—	2	1	no	—
204	C₄×C₄⋊C₄	—	2	1	no	—
205	C₄×C₄⋊C₄	C₄×C₁₀₇	1	1	yes	characteristic
206	C₄×C₄⋊C₄	C₄×C₁₀₇	1	1	yes	characteristic
207	C₄×C₄⋊C₄	C₂²×C₁₀₇	1	1	yes	characteristic
208	C₄³	—	2	1	no	—
209	C₄³	C₂²×C₁₀₇	1	1	yes	characteristic
210	#336	—	2	1	no	—
211	#336	—	2	1	no	—
212	#336	—	2	1	no	—
213	Q₈⋊C₈	—	2	4	no	—
214	C₂²×Q₈	C₂×C₄×C₁₀₇	1	1	yes	characteristic
215	C₂²×C₈	—	2	2	no	—
216	C₂²×C₈	—	2	2	no	—
217	C₄×Q₈	—	2	2	no	—
218	C₄×Q₈	—	2	2	no	—
219	C₄×Q₈	—	2	2	no	—
220	C₄×Q₈	—	2	1	no	—
221	C₄×Q₈	—	2	1	no	—
222	C₄×Q₈	C₈×C₁₀₇	1	4	yes	complemented
223	C₄×Q₈	D₄×C₁₀₇	1	2	yes	—
224	C₄×Q₈	Q₈×C₁₀₇	1	2	yes	—
225	C₂×C₄⋊C₄	—	2	1	no	—
226	C₂×C₄⋊C₄	—	2	1	no	—
227	C₂×C₄⋊C₄	—	2	1	no	—
228	C₂×C₄⋊C₄	C₂×C₄×C₁₀₇	1	1	yes	characteristic
229	C₂×C₄⋊C₄	C₂×C₄×C₁₀₇	1	1	yes	characteristic
230	C₂×C₄⋊C₄	C₂×C₄×C₁₀₇	1	1	yes	characteristic
231	C₂×C₄²	—	2	1	no	—
232	C₂×C₄²	—	2	1	no	—
233	C₂×C₄²	—	2	1	no	—
234	C₂×C₄²	—	2	1	no	—
235	C₂×C₄²	—	2	1	no	—
236	C₂×C₄²	—	2	1	no	—
237	C₂×C₄²	C₂×C₄×C₁₀₇	1	1	yes	characteristic
238	C₂×C₄²	C₂×C₄×C₁₀₇	1	1	yes	characteristic
239	C₂×C₄²	D₄×C₁₀₇	1	1	yes	characteristic
240	C₂×C₄²	D₄×C₁₀₇	1	1	yes	characteristic
241	C₂×C₄²	D₄×C₁₀₇	1	1	yes	characteristic
242	C₂×C₄²	D₄×C₁₀₇	1	1	yes	characteristic
243	C₂×C₄²	C₂³×C₁₀₇	1	1	yes	characteristic
244	C₄⋊C₈	—	2	4	no	—
245	C₄⋊C₈	—	2	2	no	—
246	C₄⋊C₈	—	2	2	no	—
247	C₄×C₈	—	2	2	no	—
248	C₄×C₈	—	2	2	no	—
249	#95	—	2	1	no	—
250	#95	—	2	1	no	—
251	#95	—	2	1	no	—
252	C₂×Q₈	—	2	1	no	—
253	C₂×Q₈	—	2	1	no	—
254	C₂×Q₈	—	2	1	no	—
255	C₂×Q₈	C₄⋊C₄×C₁₀₇	1	2	yes	—
256	C₂×Q₈	C₂×C₈×C₁₀₇	1	2	yes	—
257	C₂×Q₈	M₁₆×C₁₀₇	1	2	yes	—
258	C₂²×C₄	—	2	1	no	—
259	C₂²×C₄	—	2	1	no	—
260	C₂²×C₄	—	2	1	no	—
261	C₂²×C₄	—	2	1	no	—
262	C₂²×C₄	C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
263	C₂²×C₄	C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
264	C₂²×C₄	C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
265	C₂²×C₄	C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
266	C₂²×C₄	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
267	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
268	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
269	C₂×C₈	—	2	4	no	—
270	C₂×C₈	—	4	2	no	—
271	C₂×C₈	—	4	2	no	—
272	C₂×C₈	—	4	2	no	—
273	C₂×C₈	—	4	2	no	—
274	C₂×C₈	—	4	2	no	—
275	C₄⋊C₄	—	2	4	no	—
276	C₄⋊C₄	—	2	4	no	—
277	C₄⋊C₄	—	2	1	no	—
278	C₄⋊C₄	—	2	2	no	—
279	C₄⋊C₄	—	2	2	no	—
280	C₄⋊C₄	—	2	1	no	—
281	C₄⋊C₄	—	2	1	no	—
282	C₄⋊C₄	C₄⋊C₄×C₁₀₇	1	2	yes	—
283	C₄⋊C₄	C₂×C₈×C₁₀₇	1	2	yes	—
284	C₄⋊C₄	M₁₆×C₁₀₇	1	2	yes	—
285	C₄²	—	2	4	no	—
286	C₄²	—	2	4	no	—
287	C₄²	—	2	2	no	—
288	C₄²	—	2	2	no	—
289	C₄²	—	2	2	no	—
290	C₄²	—	2	1	no	—
291	C₄²	—	2	1	no	—
292	C₄²	—	2	2	no	—
293	C₄²	—	2	2	no	—
294	C₄²	—	4	1	no	—
295	C₄²	—	4	2	no	—
296	C₄²	—	4	2	no	—
297	C₄²	—	4	2	no	—
298	C₄²	C₂×C₈×C₁₀₇	1	2	yes	—
299	C₄²	M₁₆×C₁₀₇	1	2	yes	—
300	C₄²	C₂×D₄×C₁₀₇	1	1	yes	characteristic
301	C₄²	C₂×Q₈×C₁₀₇	1	1	yes	characteristic
302	C₄²	#41×C₁₀₇	1	1	yes	characteristic
303	C₄²	#41×C₁₀₇	1	1	yes	characteristic
304	C₂³	C₂×C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
305	Q₈	—	2	2	no	—
306	Q₈	—	2	2	no	—
307	Q₈	—	2	2	no	—
308	Q₈	C₄⋊C₈×C₁₀₇	1	4	yes	complemented
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	4	1	no	—
327	C₂×C₄	—	4	1	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	—	4	1	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	C₂²⋊C₈×C₁₀₇	1	2	yes	—
333	C₂×C₄	C₂²⋊C₈×C₁₀₇	1	2	yes	—
334	C₂×C₄	#104×C₁₀₇	1	2	yes	—
335	C₂×C₄	C₂×C₄⋊C₄×C₁₀₇	1	1	yes	characteristic
336	C₂×C₄	#117×C₁₀₇	1	1	yes	characteristic
337	C₂×C₄	#121×C₁₀₇	1	1	yes	characteristic
338	C₂×C₄	#121×C₁₀₇	1	1	yes	characteristic
339	C₂×C₄	C₂²⋊Q₈×C₁₀₇	1	1	yes	characteristic
340	C₂×C₄	C₂²⋊Q₈×C₁₀₇	1	1	yes	characteristic
341	C₂×C₄	C₂²×C₈×C₁₀₇	1	1	yes	characteristic
342	C₂×C₄	C₂×M₁₆×C₁₀₇	1	1	yes	characteristic
343	C₂×C₄	C₂×M₁₆×C₁₀₇	1	1	yes	characteristic
344	C₂×C₄	C₂×M₁₆×C₁₀₇	1	1	yes	characteristic
345	C₂×C₄	#135×C₁₀₇	1	2	yes	—
346	C₂×C₄	#137×C₁₀₇	1	2	yes	—
347	C₈	—	4	4	no	—
348	C₈	—	8	2	no	—
349	C₂²	#380×C₁₀₇	1	1	yes	characteristic
350	C₂²	C₂×C₂²⋊C₈×C₁₀₇	1	1	yes	characteristic
351	C₂²	#407×C₁₀₇	1	1	yes	characteristic
352	C₂²	#416×C₁₀₇	1	1	yes	characteristic
353	C₂²	#419×C₁₀₇	1	1	yes	characteristic
354	C₂²	C₂×#104×C₁₀₇	1	1	yes	characteristic
355	C₂²	#421×C₁₀₇	1	1	yes	characteristic
356	C₄	—	2	2	no	—
357	C₄	—	2	2	no	—
358	C₄	—	2	2	no	—
359	C₄	—	2	4	no	—
360	C₄	—	2	1	no	—
361	C₄	—	2	1	no	—
362	C₄	—	4	2	no	—
363	C₄	—	4	1	no	—
364	C₄	—	4	2	no	—
365	C₄	—	4	2	no	—
366	C₄	C₂×C₄⋊C₈×C₁₀₇	1	1	yes	characteristic
367	C₄	#423×C₁₀₇	1	1	yes	characteristic
368	C₄	#431×C₁₀₇	1	1	yes	characteristic
369	C₄	#432×C₁₀₇	1	1	yes	characteristic
370	C₄	#464×C₁₀₇	1	2	yes	—
371	C₄	#479×C₁₀₇	1	2	yes	—
372	C₂	C₁₀₇×#1476	1	1	yes	characteristic
373	C₂	C₁₀₇×#1479	1	1	yes	characteristic
374	C₂	C₁₀₇×#1488	1	1	yes	characteristic
375	C₂	C₁₀₇×#1491	1	1	yes	characteristic
376	C₂	C₁₀₇×#1797	1	1	yes	characteristic
377	C₂	C₁₀₇×#1805	1	1	yes	characteristic
378	C₂	C₁₀₇×#1806	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₀₇	C₂×D₄
commutator	C₂×C₄	C₂²×C₈×C₁₀₇
Frattini, cosocle	C₂×C₄²	C₂³×C₁₀₇
socle, prime radical	C₂³×C₁₀₇	C₂×C₂²⋊C₄
LCS	G ▷ C₂×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
32. C₄×Q₈×C₁₀₇	C₈	semidirect
118. Q₈×C₁₀₇	C₄⋊C₈	semidirect
182. #8566	C₁₀₇	direct (N × H)
195. C₁₀₇	#8566	direct (N × H)
222. C₄×Q₈	C₈×C₁₀₇	semidirect
308. Q₈	C₄⋊C₈×C₁₀₇	semidirect

Maximal subgroups

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

subgroup	index
C₄²×Q₈×C₁₀₇	2
C₁₀₇×#1831	2
C₄×C₄⋊C₈×C₁₀₇	2
C₂×Q₈⋊C₈×C₁₀₇	2
C₁₀₇×#1279	2
#8566	107

Subgroups — C107×#8566 #41034530

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₇×#8566 #41034530