Subgroups — C₁₀₇×#10777 #41036741

Order 27392.

1178 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#519×C₁₀₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#419×C₁₀₇	C₂	1	2	yes	maximal
3	C₁₀₇×#1742	C₂	1	1	yes	maximal, characteristic
4	C₁₀₇×#1740	C₂	1	1	yes	maximal, characteristic
5	C₁₀₇×#1733	C₂	1	2	yes	maximal
6	C₂³×Q₈×C₁₀₇	C₂²	1	1	yes	characteristic
7	C₂²×M₁₆×C₁₀₇	C₂²	1	2	yes	—
8	#519×C₁₀₇	—	2	4	no	—
9	#519×C₁₀₇	—	2	4	no	—
10	C₂×C₄×Q₈×C₁₀₇	—	2	2	no	—
11	C₂×C₄×Q₈×C₁₀₇	C₄	1	4	yes	complemented
12	C₂×#117×C₁₀₇	—	2	2	no	—
13	C₂×#117×C₁₀₇	C₂²	1	2	yes	—
14	C₂×#117×C₁₀₇	C₂²	1	1	yes	characteristic
15	C₂×#117×C₁₀₇	C₂²	1	1	yes	characteristic
16	#419×C₁₀₇	—	2	4	no	—
17	#419×C₁₀₇	C₄	1	8	yes	complemented
18	C₂×#103×C₁₀₇	—	2	4	no	—
19	#343×C₁₀₇	—	2	2	no	—
20	#342×C₁₀₇	—	2	2	no	—
21	#339×C₁₀₇	—	2	4	no	—
22	C₂²×Q₈×C₁₀₇	—	2	1	no	—
23	C₂²×Q₈×C₁₀₇	—	2	2	no	—
24	C₂²×Q₈×C₁₀₇	—	2	2	no	—
25	C₂²×Q₈×C₁₀₇	—	2	1	no	—
26	C₂²×Q₈×C₁₀₇	—	2	1	no	—
27	C₂²×Q₈×C₁₀₇	C₂×C₄	1	4	yes	—
28	C₂²×Q₈×C₁₀₇	C₂×C₄	1	2	yes	—
29	C₂²×Q₈×C₁₀₇	D₄	1	4	yes	—
30	C₂²×Q₈×C₁₀₇	D₄	1	2	yes	—
31	C₂²×Q₈×C₁₀₇	Q₈	1	2	yes	—
32	C₂³×C₄×C₁₀₇	—	2	1	no	—
33	C₂³×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
34	C₂×M₁₆×C₁₀₇	—	2	2	no	—
35	C₂×M₁₆×C₁₀₇	—	2	2	no	—
36	C₂×M₁₆×C₁₀₇	—	2	2	no	—
37	C₂×M₁₆×C₁₀₇	—	2	2	no	—
38	C₂×M₁₆×C₁₀₇	—	2	2	no	—
39	C₂×M₁₆×C₁₀₇	C₂×C₄	1	4	yes	—
40	C₂²×C₈×C₁₀₇	—	2	2	no	—
41	C₄×Q₈×C₁₀₇	—	2	16	no	—
42	C₄×Q₈×C₁₀₇	—	2	8	no	—
43	C₄×Q₈×C₁₀₇	—	2	8	no	—
44	#117×C₁₀₇	—	2	16	no	—
45	#117×C₁₀₇	—	2	2	no	—
46	#117×C₁₀₇	—	2	2	no	—
47	#117×C₁₀₇	—	2	2	no	—
48	#117×C₁₀₇	—	2	2	no	—
49	#117×C₁₀₇	—	2	2	no	—
50	#117×C₁₀₇	—	2	2	no	—
51	#117×C₁₀₇	C₂×C₄	1	4	yes	—
52	#117×C₁₀₇	D₄	1	4	yes	—
53	C₂×C₄⋊C₄×C₁₀₇	—	2	4	no	—
54	C₂×C₄⋊C₄×C₁₀₇	—	2	2	no	—
55	C₂×C₄⋊C₄×C₁₀₇	C₂×C₄	1	2	yes	—
56	C₂×C₄⋊C₄×C₁₀₇	D₄	1	2	yes	—
57	C₂×C₂²⋊C₄×C₁₀₇	—	2	1	no	—
58	C₂×C₂²⋊C₄×C₁₀₇	—	2	2	no	—
59	C₂×C₂²⋊C₄×C₁₀₇	D₄	1	2	yes	—
60	C₂×C₄²×C₁₀₇	—	2	4	no	—
61	C₂×C₄²×C₁₀₇	—	2	1	no	—
62	C₂×C₄²×C₁₀₇	—	2	2	no	—
63	C₂×C₄²×C₁₀₇	C₂×C₄	1	2	yes	—
64	#103×C₁₀₇	—	2	16	no	—
65	C₂⁴×C₁₀₇	C₂×D₄	1	1	yes	characteristic
66	C₂×Q₈×C₁₀₇	—	2	2	no	—
67	C₂×Q₈×C₁₀₇	—	2	2	no	—
68	C₂×Q₈×C₁₀₇	—	2	2	no	—
69	C₂×Q₈×C₁₀₇	—	2	4	no	—
70	C₂×Q₈×C₁₀₇	—	2	4	no	—
71	C₂×Q₈×C₁₀₇	—	2	4	no	—
72	C₂×Q₈×C₁₀₇	—	2	4	no	—
73	C₂×Q₈×C₁₀₇	—	2	2	no	—
74	C₂×Q₈×C₁₀₇	—	2	4	no	—
75	C₂×Q₈×C₁₀₇	—	2	2	no	—
76	C₂×Q₈×C₁₀₇	—	2	4	no	—
77	C₂×Q₈×C₁₀₇	—	2	4	no	—
78	C₂×Q₈×C₁₀₇	—	2	4	no	—
79	C₂×Q₈×C₁₀₇	C₄²	1	4	yes	—
80	C₂×Q₈×C₁₀₇	C₂²⋊C₄	1	8	yes	—
81	C₂×Q₈×C₁₀₇	C₂²⋊C₄	1	4	yes	—
82	C₂×Q₈×C₁₀₇	C₄⋊C₄	1	4	yes	—
83	C₂×Q₈×C₁₀₇	C₄⋊C₄	1	8	yes	—
84	C₂²×C₄×C₁₀₇	—	2	2	no	—
85	C₂²×C₄×C₁₀₇	—	2	4	no	—
86	C₂²×C₄×C₁₀₇	—	2	4	no	—
87	C₂²×C₄×C₁₀₇	—	2	2	no	—
88	C₂²×C₄×C₁₀₇	—	2	2	no	—
89	C₂²×C₄×C₁₀₇	—	2	2	no	—
90	C₂²×C₄×C₁₀₇	—	4	2	no	—
91	C₂²×C₄×C₁₀₇	C₂²⋊C₄	1	4	yes	—
92	C₂²×C₄×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₀₇	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₁₀₇	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₀₇	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₀₇	C₂×Q₈	1	1	yes	characteristic
99	C₂²×C₄×C₁₀₇	#41	1	1	yes	characteristic
100	C₂²×C₄×C₁₀₇	#41	1	1	yes	characteristic
101	C₂²×C₄×C₁₀₇	#41	1	2	yes	—
102	M₁₆×C₁₀₇	—	2	4	no	—
103	M₁₆×C₁₀₇	—	2	4	no	—
104	M₁₆×C₁₀₇	—	4	2	no	—
105	M₁₆×C₁₀₇	—	4	2	no	—
106	C₂×C₈×C₁₀₇	—	2	4	no	—
107	C₂×C₈×C₁₀₇	—	4	2	no	—
108	C₂×C₈×C₁₀₇	—	4	2	no	—
109	C₄⋊C₄×C₁₀₇	—	2	16	no	—
110	C₄⋊C₄×C₁₀₇	—	2	2	no	—
111	C₄⋊C₄×C₁₀₇	—	2	4	no	—
112	C₄⋊C₄×C₁₀₇	—	2	4	no	—
113	C₄⋊C₄×C₁₀₇	—	4	2	no	—
114	C₄⋊C₄×C₁₀₇	C₂²⋊C₄	1	4	yes	—
115	C₂²⋊C₄×C₁₀₇	—	2	4	no	—
116	C₂²⋊C₄×C₁₀₇	—	2	4	no	—
117	C₂²⋊C₄×C₁₀₇	—	2	4	no	—
118	C₂²⋊C₄×C₁₀₇	—	4	2	no	—
119	C₄²×C₁₀₇	—	2	16	no	—
120	C₄²×C₁₀₇	—	2	2	no	—
121	C₄²×C₁₀₇	—	2	2	no	—
122	C₄²×C₁₀₇	—	2	4	no	—
123	C₄²×C₁₀₇	—	2	4	no	—
124	C₄²×C₁₀₇	—	4	2	no	—
125	C₂³×C₁₀₇	—	4	2	no	—
126	C₂³×C₁₀₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
127	C₂³×C₁₀₇	C₄×D₄	1	2	yes	—
128	C₂³×C₁₀₇	#120	1	2	yes	—
129	C₂³×C₁₀₇	#121	1	1	yes	characteristic
130	C₂³×C₁₀₇	C₂²⋊Q₈	1	1	yes	characteristic
131	Q₈×C₁₀₇	—	2	4	no	—
132	Q₈×C₁₀₇	—	2	4	no	—
133	Q₈×C₁₀₇	—	2	4	no	—
134	Q₈×C₁₀₇	—	2	8	no	—
135	Q₈×C₁₀₇	—	2	8	no	—
136	Q₈×C₁₀₇	#95	1	8	yes	—
137	C₂×C₄×C₁₀₇	—	2	4	no	—
138	C₂×C₄×C₁₀₇	—	2	4	no	—
139	C₂×C₄×C₁₀₇	—	2	4	no	—
140	C₂×C₄×C₁₀₇	—	2	8	no	—
141	C₂×C₄×C₁₀₇	—	2	8	no	—
142	C₂×C₄×C₁₀₇	—	2	4	no	—
143	C₂×C₄×C₁₀₇	—	2	4	no	—
144	C₂×C₄×C₁₀₇	—	4	4	no	—
145	C₂×C₄×C₁₀₇	—	4	4	no	—
146	C₂×C₄×C₁₀₇	—	4	4	no	—
147	C₂×C₄×C₁₀₇	—	8	4	no	—
148	C₂×C₄×C₁₀₇	C₂×C₄²	1	1	yes	characteristic
149	C₂×C₄×C₁₀₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₁₀₇	C₂×C₂²⋊C₄	1	2	yes	—
151	C₂×C₄×C₁₀₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₁₀₇	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₁₀₇	C₂×C₄⋊C₄	1	2	yes	—
154	C₂×C₄×C₁₀₇	#117	1	1	yes	characteristic
155	C₂×C₄×C₁₀₇	#117	1	1	yes	characteristic
156	C₂×C₄×C₁₀₇	C₄×D₄	1	2	yes	—
157	C₂×C₄×C₁₀₇	C₄×D₄	1	2	yes	—
158	C₂×C₄×C₁₀₇	C₄×D₄	1	2	yes	—
159	C₂×C₄×C₁₀₇	#120	1	2	yes	—
160	C₂×C₄×C₁₀₇	#121	1	2	yes	—
161	C₂×C₄×C₁₀₇	#121	1	1	yes	characteristic
162	C₂×C₄×C₁₀₇	C₂²⋊Q₈	1	2	yes	—
163	C₂×C₄×C₁₀₇	C₂²⋊Q₈	1	1	yes	characteristic
164	C₂×C₄×C₁₀₇	#123	1	2	yes	—
165	C₂×C₄×C₁₀₇	#123	1	2	yes	—
166	C₈×C₁₀₇	—	4	4	no	—
167	C₂²×C₁₀₇	—	2	2	no	—
168	C₂²×C₁₀₇	—	2	4	no	—
169	C₂²×C₁₀₇	—	4	2	no	—
170	C₂²×C₁₀₇	—	4	1	no	—
171	C₂²×C₁₀₇	—	4	1	no	—
172	C₂²×C₁₀₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
173	C₂²×C₁₀₇	#379	1	1	yes	characteristic
174	C₂²×C₁₀₇	#380	1	1	yes	characteristic
175	C₂²×C₁₀₇	#385	1	2	yes	—
176	C₂²×C₁₀₇	#386	1	2	yes	—
177	C₄×C₁₀₇	—	2	8	no	—
178	C₄×C₁₀₇	—	4	4	no	—
179	C₄×C₁₀₇	—	4	4	no	—
180	C₄×C₁₀₇	—	8	4	no	—
181	C₄×C₁₀₇	C₂×#95	1	1	yes	characteristic
182	C₄×C₁₀₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
183	C₄×C₁₀₇	#380	1	1	yes	characteristic
184	C₄×C₁₀₇	#381	1	1	yes	characteristic
185	C₄×C₁₀₇	#385	1	2	yes	—
186	C₄×C₁₀₇	#386	1	2	yes	—
187	#10777	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
188	C₂×C₁₀₇	—	2	2	no	—
189	C₂×C₁₀₇	—	2	1	no	—
190	C₂×C₁₀₇	—	2	1	no	—
191	C₂×C₁₀₇	—	2	2	no	—
192	C₂×C₁₀₇	C₂²⋊#95	1	1	yes	characteristic
193	C₂×C₁₀₇	#1796	1	2	yes	—
194	C₂×#519	C₂×C₁₀₇	1	1	yes	characteristic
195	C₂×#419	C₂×C₁₀₇	1	2	yes	—
196	#1742	C₂×C₁₀₇	1	1	yes	characteristic
197	#1740	C₂×C₁₀₇	1	1	yes	characteristic
198	#1733	C₂×C₁₀₇	1	2	yes	—
199	C₁₀₇	#10777	1	1	yes	characteristic, direct product factor, Sylow
200	C₂³×Q₈	C₂²×C₁₀₇	1	1	yes	characteristic
201	C₂²×M₁₆	C₂²×C₁₀₇	1	2	yes	—
202	#519	—	2	4	no	—
203	#519	—	2	4	no	—
204	C₂×C₄×Q₈	—	2	2	no	—
205	C₂×C₄×Q₈	C₄×C₁₀₇	1	4	yes	complemented
206	C₂×#117	—	2	2	no	—
207	C₂×#117	C₂²×C₁₀₇	1	2	yes	—
208	C₂×#117	C₂²×C₁₀₇	1	1	yes	characteristic
209	C₂×#117	C₂²×C₁₀₇	1	1	yes	characteristic
210	#419	—	2	4	no	—
211	#419	C₄×C₁₀₇	1	8	yes	complemented
212	C₂×#103	—	2	4	no	—
213	#343	—	2	2	no	—
214	#342	—	2	2	no	—
215	#339	—	2	4	no	—
216	C₂²×Q₈	—	2	1	no	—
217	C₂²×Q₈	—	2	2	no	—
218	C₂²×Q₈	—	2	2	no	—
219	C₂²×Q₈	—	2	1	no	—
220	C₂²×Q₈	—	2	1	no	—
221	C₂²×Q₈	C₂×C₄×C₁₀₇	1	2	yes	—
222	C₂²×Q₈	C₂×C₄×C₁₀₇	1	4	yes	—
223	C₂²×Q₈	D₄×C₁₀₇	1	4	yes	—
224	C₂²×Q₈	D₄×C₁₀₇	1	2	yes	—
225	C₂²×Q₈	Q₈×C₁₀₇	1	2	yes	—
226	C₂³×C₄	—	2	1	no	—
227	C₂³×C₄	C₂³×C₁₀₇	1	1	yes	characteristic
228	C₂×M₁₆	—	2	2	no	—
229	C₂×M₁₆	—	2	2	no	—
230	C₂×M₁₆	—	2	2	no	—
231	C₂×M₁₆	—	2	2	no	—
232	C₂×M₁₆	—	2	2	no	—
233	C₂×M₁₆	C₂×C₄×C₁₀₇	1	4	yes	—
234	C₂²×C₈	—	2	2	no	—
235	C₄×Q₈	—	2	16	no	—
236	C₄×Q₈	—	2	8	no	—
237	C₄×Q₈	—	2	8	no	—
238	#117	—	2	16	no	—
239	#117	—	2	2	no	—
240	#117	—	2	2	no	—
241	#117	—	2	2	no	—
242	#117	—	2	2	no	—
243	#117	—	2	2	no	—
244	#117	—	2	2	no	—
245	#117	C₂×C₄×C₁₀₇	1	4	yes	—
246	#117	D₄×C₁₀₇	1	4	yes	—
247	C₂×C₄⋊C₄	—	2	4	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	C₂×C₄×C₁₀₇	1	2	yes	—
250	C₂×C₄⋊C₄	D₄×C₁₀₇	1	2	yes	—
251	C₂×C₂²⋊C₄	—	2	1	no	—
252	C₂×C₂²⋊C₄	—	2	2	no	—
253	C₂×C₂²⋊C₄	D₄×C₁₀₇	1	2	yes	—
254	C₂×C₄²	—	2	4	no	—
255	C₂×C₄²	—	2	1	no	—
256	C₂×C₄²	—	2	2	no	—
257	C₂×C₄²	C₂×C₄×C₁₀₇	1	2	yes	—
258	#103	—	2	16	no	—
259	C₂⁴	C₂×D₄×C₁₀₇	1	1	yes	characteristic
260	C₂×Q₈	—	2	2	no	—
261	C₂×Q₈	—	2	2	no	—
262	C₂×Q₈	—	2	2	no	—
263	C₂×Q₈	—	2	4	no	—
264	C₂×Q₈	—	2	4	no	—
265	C₂×Q₈	—	2	4	no	—
266	C₂×Q₈	—	2	4	no	—
267	C₂×Q₈	—	2	2	no	—
268	C₂×Q₈	—	2	4	no	—
269	C₂×Q₈	—	2	2	no	—
270	C₂×Q₈	—	2	4	no	—
271	C₂×Q₈	—	2	4	no	—
272	C₂×Q₈	—	2	4	no	—
273	C₂×Q₈	C₄²×C₁₀₇	1	4	yes	—
274	C₂×Q₈	C₂²⋊C₄×C₁₀₇	1	8	yes	—
275	C₂×Q₈	C₂²⋊C₄×C₁₀₇	1	4	yes	—
276	C₂×Q₈	C₄⋊C₄×C₁₀₇	1	4	yes	—
277	C₂×Q₈	C₄⋊C₄×C₁₀₇	1	8	yes	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	4	no	—
280	C₂²×C₄	—	2	4	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	4	2	no	—
285	C₂²×C₄	C₂²⋊C₄×C₁₀₇	1	4	yes	—
286	C₂²×C₄	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
287	C₂²×C₄	C₂²×C₄×C₁₀₇	1	2	yes	—
288	C₂²×C₄	C₂×D₄×C₁₀₇	1	2	yes	—
289	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
290	C₂²×C₄	C₂×D₄×C₁₀₇	1	2	yes	—
291	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
292	C₂²×C₄	C₂×Q₈×C₁₀₇	1	1	yes	characteristic
293	C₂²×C₄	#41×C₁₀₇	1	1	yes	characteristic
294	C₂²×C₄	#41×C₁₀₇	1	1	yes	characteristic
295	C₂²×C₄	#41×C₁₀₇	1	2	yes	—
296	M₁₆	—	2	4	no	—
297	M₁₆	—	2	4	no	—
298	M₁₆	—	4	2	no	—
299	M₁₆	—	4	2	no	—
300	C₂×C₈	—	2	4	no	—
301	C₂×C₈	—	4	2	no	—
302	C₂×C₈	—	4	2	no	—
303	C₄⋊C₄	—	2	16	no	—
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	2	4	no	—
306	C₄⋊C₄	—	2	4	no	—
307	C₄⋊C₄	—	4	2	no	—
308	C₄⋊C₄	C₂²⋊C₄×C₁₀₇	1	4	yes	—
309	C₂²⋊C₄	—	2	4	no	—
310	C₂²⋊C₄	—	2	4	no	—
311	C₂²⋊C₄	—	2	4	no	—
312	C₂²⋊C₄	—	4	2	no	—
313	C₄²	—	2	16	no	—
314	C₄²	—	2	2	no	—
315	C₄²	—	2	2	no	—
316	C₄²	—	2	4	no	—
317	C₄²	—	2	4	no	—
318	C₄²	—	4	2	no	—
319	C₂³	—	4	2	no	—
320	C₂³	C₂×C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
321	C₂³	C₄×D₄×C₁₀₇	1	2	yes	—
322	C₂³	#120×C₁₀₇	1	2	yes	—
323	C₂³	#121×C₁₀₇	1	1	yes	characteristic
324	C₂³	C₂²⋊Q₈×C₁₀₇	1	1	yes	characteristic
325	Q₈	—	2	4	no	—
326	Q₈	—	2	4	no	—
327	Q₈	—	2	4	no	—
328	Q₈	—	2	8	no	—
329	Q₈	—	2	8	no	—
330	Q₈	#95×C₁₀₇	1	8	yes	—
331	C₂×C₄	—	2	4	no	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	8	no	—
335	C₂×C₄	—	2	8	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	4	4	no	—
339	C₂×C₄	—	4	4	no	—
340	C₂×C₄	—	4	4	no	—
341	C₂×C₄	—	8	4	no	—
342	C₂×C₄	C₂×C₄²×C₁₀₇	1	1	yes	characteristic
343	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
344	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₇	1	2	yes	—
345	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
346	C₂×C₄	C₂×C₄⋊C₄×C₁₀₇	1	1	yes	characteristic
347	C₂×C₄	C₂×C₄⋊C₄×C₁₀₇	1	2	yes	—
348	C₂×C₄	#117×C₁₀₇	1	1	yes	characteristic
349	C₂×C₄	#117×C₁₀₇	1	1	yes	characteristic
350	C₂×C₄	C₄×D₄×C₁₀₇	1	2	yes	—
351	C₂×C₄	C₄×D₄×C₁₀₇	1	2	yes	—
352	C₂×C₄	C₄×D₄×C₁₀₇	1	2	yes	—
353	C₂×C₄	#120×C₁₀₇	1	2	yes	—
354	C₂×C₄	#121×C₁₀₇	1	2	yes	—
355	C₂×C₄	#121×C₁₀₇	1	1	yes	characteristic
356	C₂×C₄	C₂²⋊Q₈×C₁₀₇	1	2	yes	—
357	C₂×C₄	C₂²⋊Q₈×C₁₀₇	1	1	yes	characteristic
358	C₂×C₄	#123×C₁₀₇	1	2	yes	—
359	C₂×C₄	#123×C₁₀₇	1	2	yes	—
360	C₈	—	4	4	no	—
361	C₂²	—	2	2	no	—
362	C₂²	—	2	4	no	—
363	C₂²	—	4	2	no	—
364	C₂²	—	4	1	no	—
365	C₂²	—	4	1	no	—
366	C₂²	C₄×C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
367	C₂²	#379×C₁₀₇	1	1	yes	characteristic
368	C₂²	#380×C₁₀₇	1	1	yes	characteristic
369	C₂²	#385×C₁₀₇	1	2	yes	—
370	C₂²	#386×C₁₀₇	1	2	yes	—
371	C₄	—	2	8	no	—
372	C₄	—	4	4	no	—
373	C₄	—	4	4	no	—
374	C₄	—	8	4	no	—
375	C₄	C₂×#95×C₁₀₇	1	1	yes	characteristic
376	C₄	C₄×C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
377	C₄	#380×C₁₀₇	1	1	yes	characteristic
378	C₄	#381×C₁₀₇	1	1	yes	characteristic
379	C₄	#385×C₁₀₇	1	2	yes	—
380	C₄	#386×C₁₀₇	1	2	yes	—
381	C₂	—	2	2	no	—
382	C₂	—	2	1	no	—
383	C₂	—	2	1	no	—
384	C₂	—	2	2	no	—
385	C₂	C₁₀₇×C₂²⋊#95	1	1	yes	characteristic
386	C₂	C₁₀₇×#1796	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₀₇	#379
commutator	C₂×C₄	C₂×C₄²×C₁₀₇
Frattini, cosocle	C₂³×C₄	C₂³×C₁₀₇
prime radical	C₂⁴×C₁₀₇	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₇ ◁ C₂³×C₄×C₁₀₇ ◁ G

Complements

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

N	H ≅ G/N	type
11. C₂×C₄×Q₈×C₁₀₇	C₄	semidirect
17. #419×C₁₀₇	C₄	semidirect
187. #10777	C₁₀₇	direct (N × H)
199. C₁₀₇	#10777	direct (N × H)
205. C₂×C₄×Q₈	C₄×C₁₀₇	semidirect
211. #419	C₄×C₁₀₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#519×C₁₀₇	2
C₂×#419×C₁₀₇	2
C₁₀₇×#1742	2
C₁₀₇×#1740	2
C₁₀₇×#1733	2
#10777	107

Subgroups — C107×#10777 #41036741

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₇×#10777 #41036741