Subgroups — C₁₀₇×#7870 #41033834

Order 27392.

684 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₇×#2920	C₂	1	1	yes	maximal, characteristic
2	C₂×#431×C₁₀₇	C₂	1	1	yes	maximal, characteristic
3	C₄×#117×C₁₀₇	C₂	1	1	yes	maximal, characteristic
4	C₁₀₇×#1276	C₂	1	4	yes	maximal, complemented
5	C₂×#117×C₁₀₇	—	2	1	no	—
6	C₂²×C₄²×C₁₀₇	C₂²	1	1	yes	characteristic
7	#432×C₁₀₇	—	2	1	no	—
8	#432×C₁₀₇	C₄	1	2	yes	complemented
9	#431×C₁₀₇	—	2	1	no	—
10	#431×C₁₀₇	—	2	1	no	—
11	#431×C₁₀₇	—	2	1	no	—
12	#431×C₁₀₇	C₄	1	2	yes	complemented
13	#431×C₁₀₇	C₂²	1	2	yes	—
14	#431×C₁₀₇	C₂²	1	2	yes	—
15	#423×C₁₀₇	C₄	1	2	yes	complemented
16	C₂×C₄⋊C₈×C₁₀₇	C₄	1	2	yes	complemented
17	#407×C₁₀₇	—	2	1	no	—
18	C₂×C₂²⋊C₈×C₁₀₇	—	2	1	no	—
19	C₄×M₁₆×C₁₀₇	—	2	1	no	—
20	C₂×C₄×C₈×C₁₀₇	—	2	1	no	—
21	C₄×C₄⋊C₄×C₁₀₇	—	2	1	no	—
22	C₄×C₄⋊C₄×C₁₀₇	C₄	1	2	yes	—
23	C₄×C₂²⋊C₄×C₁₀₇	—	2	1	no	—
24	C₄×C₂²⋊C₄×C₁₀₇	C₄	1	2	yes	—
25	#376×C₁₀₇	—	2	1	no	—
26	C₄³×C₁₀₇	C₂²	1	2	yes	—
27	C₂³×C₄×C₁₀₇	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₀₇	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₀₇	D₄	1	1	yes	characteristic
30	C₂×M₁₆×C₁₀₇	—	2	2	no	—
31	C₂²×C₈×C₁₀₇	—	2	2	no	—
32	#117×C₁₀₇	—	2	8	no	—
33	C₂×C₄⋊C₄×C₁₀₇	—	2	2	no	—
34	C₂×C₂²⋊C₄×C₁₀₇	—	2	2	no	—
35	C₂×C₄²×C₁₀₇	—	2	2	no	—
36	C₂×C₄²×C₁₀₇	—	2	2	no	—
37	C₂×C₄²×C₁₀₇	C₂×C₄	1	4	yes	—
38	C₂×C₄²×C₁₀₇	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₀₇	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₀₇	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₀₇	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₁₀₇	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄²×C₁₀₇	D₄	1	1	yes	characteristic
44	C₂×C₄²×C₁₀₇	D₄	1	1	yes	characteristic
45	C₂×C₄²×C₁₀₇	D₄	1	1	yes	characteristic
46	C₂×C₄²×C₁₀₇	D₄	1	1	yes	characteristic
47	C₂×C₄²×C₁₀₇	Q₈	1	1	yes	characteristic
48	C₂×C₄²×C₁₀₇	Q₈	1	1	yes	characteristic
49	C₂×C₄²×C₁₀₇	C₂³	1	1	yes	characteristic
50	C₄⋊C₈×C₁₀₇	—	2	2	no	—
51	C₄⋊C₈×C₁₀₇	—	2	2	no	—
52	C₄⋊C₈×C₁₀₇	C₂×C₄	1	4	yes	—
53	C₄⋊C₈×C₁₀₇	C₂×C₄	1	4	yes	—
54	C₂²⋊C₈×C₁₀₇	—	2	2	no	—
55	C₂²⋊C₈×C₁₀₇	—	2	2	no	—
56	C₂²⋊C₈×C₁₀₇	—	2	2	no	—
57	C₂²⋊C₈×C₁₀₇	—	2	2	no	—
58	#97×C₁₀₇	—	2	2	no	—
59	C₄×C₈×C₁₀₇	—	2	2	no	—
60	C₄×C₈×C₁₀₇	—	2	2	no	—
61	C₄×C₈×C₁₀₇	—	2	2	no	—
62	#95×C₁₀₇	—	2	2	no	—
63	#95×C₁₀₇	—	2	2	no	—
64	C₂⁴×C₁₀₇	C₂²⋊C₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₀₇	—	2	4	no	—
66	C₂²×C₄×C₁₀₇	—	2	4	no	—
67	C₂²×C₄×C₁₀₇	—	2	4	no	—
68	C₂²×C₄×C₁₀₇	—	4	2	no	—
69	C₂²×C₄×C₁₀₇	C₄²	1	1	yes	characteristic
70	C₂²×C₄×C₁₀₇	C₄²	1	1	yes	characteristic
71	C₂²×C₄×C₁₀₇	C₂²⋊C₄	1	1	yes	characteristic
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	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₀₇	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₀₇	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₀₇	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₀₇	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₀₇	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₀₇	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
87	M₁₆×C₁₀₇	—	4	4	no	—
88	C₂×C₈×C₁₀₇	—	2	4	no	—
89	C₂×C₈×C₁₀₇	—	2	4	no	—
90	C₂×C₈×C₁₀₇	—	4	4	no	—
91	C₄⋊C₄×C₁₀₇	—	2	8	no	—
92	C₂²⋊C₄×C₁₀₇	—	2	8	no	—
93	C₄²×C₁₀₇	—	2	8	no	—
94	C₄²×C₁₀₇	—	2	8	no	—
95	C₄²×C₁₀₇	—	4	4	no	—
96	C₄²×C₁₀₇	C₄²	1	1	yes	characteristic
97	C₄²×C₁₀₇	C₄²	1	1	yes	characteristic
98	C₄²×C₁₀₇	C₂²⋊C₄	1	1	yes	characteristic
99	C₄²×C₁₀₇	C₂²⋊C₄	1	1	yes	characteristic
100	C₄²×C₁₀₇	C₂²⋊C₄	1	1	yes	characteristic
101	C₄²×C₁₀₇	C₂²⋊C₄	1	1	yes	characteristic
102	C₄²×C₁₀₇	C₄⋊C₄	1	1	yes	characteristic
103	C₄²×C₁₀₇	C₄⋊C₄	1	1	yes	characteristic
104	C₄²×C₁₀₇	C₄⋊C₄	1	1	yes	characteristic
105	C₄²×C₁₀₇	C₄⋊C₄	1	1	yes	characteristic
106	C₄²×C₁₀₇	C₄⋊C₄	1	1	yes	characteristic
107	C₄²×C₁₀₇	C₄⋊C₄	1	1	yes	characteristic
108	C₄²×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
109	C₄²×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
110	C₄²×C₁₀₇	C₂×D₄	1	1	yes	characteristic
111	C₄²×C₁₀₇	C₂×Q₈	1	1	yes	characteristic
112	C₂³×C₁₀₇	—	2	2	no	—
113	C₂³×C₁₀₇	—	2	2	no	—
114	C₂³×C₁₀₇	—	4	1	no	—
115	C₂³×C₁₀₇	#95	1	1	yes	characteristic
116	C₂³×C₁₀₇	#95	1	1	yes	characteristic
117	C₂³×C₁₀₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
118	C₂×C₄×C₁₀₇	—	2	2	no	—
119	C₂×C₄×C₁₀₇	—	2	2	no	—
120	C₂×C₄×C₁₀₇	—	2	2	no	—
121	C₂×C₄×C₁₀₇	—	2	2	no	—
122	C₂×C₄×C₁₀₇	—	2	2	no	—
123	C₂×C₄×C₁₀₇	—	2	2	no	—
124	C₂×C₄×C₁₀₇	—	2	2	no	—
125	C₂×C₄×C₁₀₇	—	2	2	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	2	no	—
130	C₂×C₄×C₁₀₇	—	2	2	no	—
131	C₂×C₄×C₁₀₇	—	2	8	no	—
132	C₂×C₄×C₁₀₇	—	4	1	no	—
133	C₂×C₄×C₁₀₇	—	4	1	no	—
134	C₂×C₄×C₁₀₇	—	4	1	no	—
135	C₂×C₄×C₁₀₇	—	4	4	no	—
136	C₂×C₄×C₁₀₇	—	4	4	no	—
137	C₂×C₄×C₁₀₇	#95	1	1	yes	characteristic
138	C₂×C₄×C₁₀₇	#95	1	1	yes	characteristic
139	C₂×C₄×C₁₀₇	#95	1	1	yes	characteristic
140	C₂×C₄×C₁₀₇	#95	1	1	yes	characteristic
141	C₂×C₄×C₁₀₇	#95	1	1	yes	characteristic
142	C₂×C₄×C₁₀₇	#95	1	1	yes	characteristic
143	C₂×C₄×C₁₀₇	#104	1	4	yes	—
144	C₂×C₄×C₁₀₇	C₂×C₄²	1	1	yes	characteristic
145	C₂×C₄×C₁₀₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₁₀₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₁₀₇	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₁₀₇	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₁₀₇	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₁₀₇	#131	1	4	yes	—
151	C₈×C₁₀₇	—	4	4	no	—
152	C₈×C₁₀₇	—	4	4	no	—
153	C₂²×C₁₀₇	—	2	1	no	—
154	C₂²×C₁₀₇	—	2	1	no	—
155	C₂²×C₁₀₇	—	2	1	no	—
156	C₂²×C₁₀₇	—	2	1	no	—
157	C₂²×C₁₀₇	—	2	1	no	—
158	C₂²×C₁₀₇	—	2	1	no	—
159	C₂²×C₁₀₇	—	2	1	no	—
160	C₂²×C₁₀₇	—	4	4	no	—
161	C₂²×C₁₀₇	#339	1	2	yes	—
162	C₂²×C₁₀₇	C₂×#95	1	1	yes	characteristic
163	C₂²×C₁₀₇	#408	1	2	yes	—
164	C₄×C₁₀₇	—	2	1	no	—
165	C₄×C₁₀₇	—	2	1	no	—
166	C₄×C₁₀₇	—	2	1	no	—
167	C₄×C₁₀₇	—	2	1	no	—
168	C₄×C₁₀₇	—	2	1	no	—
169	C₄×C₁₀₇	—	2	1	no	—
170	C₄×C₁₀₇	—	2	1	no	—
171	C₄×C₁₀₇	—	4	8	no	—
172	C₄×C₁₀₇	#339	1	2	yes	—
173	C₄×C₁₀₇	#405	1	2	yes	—
174	C₄×C₁₀₇	C₂×#104	1	2	yes	—
175	C₄×C₁₀₇	#421	1	2	yes	—
176	C₄×C₁₀₇	#424	1	2	yes	—
177	#7870	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
178	C₂×C₁₀₇	—	2	2	no	—
179	C₂×C₁₀₇	—	2	2	no	—
180	C₂×C₁₀₇	—	4	1	no	—
181	C₂×C₁₀₇	#1729	1	1	yes	characteristic
182	C₂×C₁₀₇	C₂×#339	1	1	yes	characteristic
183	C₂×C₁₀₇	#1733	1	1	yes	characteristic
184	#2920	C₂×C₁₀₇	1	1	yes	characteristic
185	C₂×#431	C₂×C₁₀₇	1	1	yes	characteristic
186	C₄×#117	C₂×C₁₀₇	1	1	yes	characteristic
187	#1276	C₂×C₁₀₇	1	4	yes	complemented
188	C₁₀₇	#7870	1	1	yes	characteristic, direct product factor, Sylow
189	C₂×#117	—	2	1	no	—
190	C₂²×C₄²	C₂²×C₁₀₇	1	1	yes	characteristic
191	#432	—	2	1	no	—
192	#432	C₄×C₁₀₇	1	2	yes	complemented
193	#431	—	2	1	no	—
194	#431	—	2	1	no	—
195	#431	—	2	1	no	—
196	#431	C₄×C₁₀₇	1	2	yes	complemented
197	#431	C₂²×C₁₀₇	1	2	yes	—
198	#431	C₂²×C₁₀₇	1	2	yes	—
199	#423	C₄×C₁₀₇	1	2	yes	complemented
200	C₂×C₄⋊C₈	C₄×C₁₀₇	1	2	yes	complemented
201	#407	—	2	1	no	—
202	C₂×C₂²⋊C₈	—	2	1	no	—
203	C₄×M₁₆	—	2	1	no	—
204	C₂×C₄×C₈	—	2	1	no	—
205	C₄×C₄⋊C₄	—	2	1	no	—
206	C₄×C₄⋊C₄	C₄×C₁₀₇	1	2	yes	—
207	C₄×C₂²⋊C₄	—	2	1	no	—
208	C₄×C₂²⋊C₄	C₄×C₁₀₇	1	2	yes	—
209	#376	—	2	1	no	—
210	C₄³	C₂²×C₁₀₇	1	2	yes	—
211	C₂³×C₄	C₂×C₄×C₁₀₇	1	1	yes	characteristic
212	C₂³×C₄	D₄×C₁₀₇	1	1	yes	characteristic
213	C₂³×C₄	D₄×C₁₀₇	1	1	yes	characteristic
214	C₂×M₁₆	—	2	2	no	—
215	C₂²×C₈	—	2	2	no	—
216	#117	—	2	8	no	—
217	C₂×C₄⋊C₄	—	2	2	no	—
218	C₂×C₂²⋊C₄	—	2	2	no	—
219	C₂×C₄²	—	2	2	no	—
220	C₂×C₄²	—	2	2	no	—
221	C₂×C₄²	C₂×C₄×C₁₀₇	1	4	yes	—
222	C₂×C₄²	C₂×C₄×C₁₀₇	1	1	yes	characteristic
223	C₂×C₄²	C₂×C₄×C₁₀₇	1	1	yes	characteristic
224	C₂×C₄²	C₂×C₄×C₁₀₇	1	1	yes	characteristic
225	C₂×C₄²	C₂×C₄×C₁₀₇	1	1	yes	characteristic
226	C₂×C₄²	C₂×C₄×C₁₀₇	1	1	yes	characteristic
227	C₂×C₄²	D₄×C₁₀₇	1	1	yes	characteristic
228	C₂×C₄²	D₄×C₁₀₇	1	1	yes	characteristic
229	C₂×C₄²	D₄×C₁₀₇	1	1	yes	characteristic
230	C₂×C₄²	D₄×C₁₀₇	1	1	yes	characteristic
231	C₂×C₄²	Q₈×C₁₀₇	1	1	yes	characteristic
232	C₂×C₄²	Q₈×C₁₀₇	1	1	yes	characteristic
233	C₂×C₄²	C₂³×C₁₀₇	1	1	yes	characteristic
234	C₄⋊C₈	—	2	2	no	—
235	C₄⋊C₈	—	2	2	no	—
236	C₄⋊C₈	C₂×C₄×C₁₀₇	1	4	yes	—
237	C₄⋊C₈	C₂×C₄×C₁₀₇	1	4	yes	—
238	C₂²⋊C₈	—	2	2	no	—
239	C₂²⋊C₈	—	2	2	no	—
240	C₂²⋊C₈	—	2	2	no	—
241	C₂²⋊C₈	—	2	2	no	—
242	#97	—	2	2	no	—
243	C₄×C₈	—	2	2	no	—
244	C₄×C₈	—	2	2	no	—
245	C₄×C₈	—	2	2	no	—
246	#95	—	2	2	no	—
247	#95	—	2	2	no	—
248	C₂⁴	C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
249	C₂²×C₄	—	2	4	no	—
250	C₂²×C₄	—	2	4	no	—
251	C₂²×C₄	—	2	4	no	—
252	C₂²×C₄	—	4	2	no	—
253	C₂²×C₄	C₄²×C₁₀₇	1	1	yes	characteristic
254	C₂²×C₄	C₄²×C₁₀₇	1	1	yes	characteristic
255	C₂²×C₄	C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
256	C₂²×C₄	C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
257	C₂²×C₄	C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
258	C₂²×C₄	C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
259	C₂²×C₄	C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
260	C₂²×C₄	C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
261	C₂²×C₄	C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
262	C₂²×C₄	C₄⋊C₄×C₁₀₇	1	1	yes	characteristic
263	C₂²×C₄	C₄⋊C₄×C₁₀₇	1	1	yes	characteristic
264	C₂²×C₄	C₄⋊C₄×C₁₀₇	1	1	yes	characteristic
265	C₂²×C₄	C₄⋊C₄×C₁₀₇	1	1	yes	characteristic
266	C₂²×C₄	C₄⋊C₄×C₁₀₇	1	1	yes	characteristic
267	C₂²×C₄	C₄⋊C₄×C₁₀₇	1	1	yes	characteristic
268	C₂²×C₄	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
269	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
270	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
271	M₁₆	—	4	4	no	—
272	C₂×C₈	—	2	4	no	—
273	C₂×C₈	—	2	4	no	—
274	C₂×C₈	—	4	4	no	—
275	C₄⋊C₄	—	2	8	no	—
276	C₂²⋊C₄	—	2	8	no	—
277	C₄²	—	2	8	no	—
278	C₄²	—	2	8	no	—
279	C₄²	—	4	4	no	—
280	C₄²	C₄²×C₁₀₇	1	1	yes	characteristic
281	C₄²	C₄²×C₁₀₇	1	1	yes	characteristic
282	C₄²	C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
283	C₄²	C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
284	C₄²	C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
285	C₄²	C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
286	C₄²	C₄⋊C₄×C₁₀₇	1	1	yes	characteristic
287	C₄²	C₄⋊C₄×C₁₀₇	1	1	yes	characteristic
288	C₄²	C₄⋊C₄×C₁₀₇	1	1	yes	characteristic
289	C₄²	C₄⋊C₄×C₁₀₇	1	1	yes	characteristic
290	C₄²	C₄⋊C₄×C₁₀₇	1	1	yes	characteristic
291	C₄²	C₄⋊C₄×C₁₀₇	1	1	yes	characteristic
292	C₄²	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
293	C₄²	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
294	C₄²	C₂×D₄×C₁₀₇	1	1	yes	characteristic
295	C₄²	C₂×Q₈×C₁₀₇	1	1	yes	characteristic
296	C₂³	—	2	2	no	—
297	C₂³	—	2	2	no	—
298	C₂³	—	4	1	no	—
299	C₂³	#95×C₁₀₇	1	1	yes	characteristic
300	C₂³	#95×C₁₀₇	1	1	yes	characteristic
301	C₂³	C₂×C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	8	no	—
316	C₂×C₄	—	4	1	no	—
317	C₂×C₄	—	4	1	no	—
318	C₂×C₄	—	4	1	no	—
319	C₂×C₄	—	4	4	no	—
320	C₂×C₄	—	4	4	no	—
321	C₂×C₄	#95×C₁₀₇	1	1	yes	characteristic
322	C₂×C₄	#95×C₁₀₇	1	1	yes	characteristic
323	C₂×C₄	#95×C₁₀₇	1	1	yes	characteristic
324	C₂×C₄	#95×C₁₀₇	1	1	yes	characteristic
325	C₂×C₄	#95×C₁₀₇	1	1	yes	characteristic
326	C₂×C₄	#95×C₁₀₇	1	1	yes	characteristic
327	C₂×C₄	#104×C₁₀₇	1	4	yes	—
328	C₂×C₄	C₂×C₄²×C₁₀₇	1	1	yes	characteristic
329	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
330	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
331	C₂×C₄	C₂×C₄⋊C₄×C₁₀₇	1	1	yes	characteristic
332	C₂×C₄	C₂×C₄⋊C₄×C₁₀₇	1	1	yes	characteristic
333	C₂×C₄	C₂×C₄⋊C₄×C₁₀₇	1	1	yes	characteristic
334	C₂×C₄	#131×C₁₀₇	1	4	yes	—
335	C₈	—	4	4	no	—
336	C₈	—	4	4	no	—
337	C₂²	—	2	1	no	—
338	C₂²	—	2	1	no	—
339	C₂²	—	2	1	no	—
340	C₂²	—	2	1	no	—
341	C₂²	—	2	1	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	4	4	no	—
345	C₂²	#339×C₁₀₇	1	2	yes	—
346	C₂²	C₂×#95×C₁₀₇	1	1	yes	characteristic
347	C₂²	#408×C₁₀₇	1	2	yes	—
348	C₄	—	2	1	no	—
349	C₄	—	2	1	no	—
350	C₄	—	2	1	no	—
351	C₄	—	2	1	no	—
352	C₄	—	2	1	no	—
353	C₄	—	2	1	no	—
354	C₄	—	2	1	no	—
355	C₄	—	4	8	no	—
356	C₄	#339×C₁₀₇	1	2	yes	—
357	C₄	#405×C₁₀₇	1	2	yes	—
358	C₄	C₂×#104×C₁₀₇	1	2	yes	—
359	C₄	#421×C₁₀₇	1	2	yes	—
360	C₄	#424×C₁₀₇	1	2	yes	—
361	C₂	—	2	2	no	—
362	C₂	—	2	2	no	—
363	C₂	—	4	1	no	—
364	C₂	C₁₀₇×#1729	1	1	yes	characteristic
365	C₂	C₂×#339×C₁₀₇	1	1	yes	characteristic
366	C₂	C₁₀₇×#1733	1	1	yes	characteristic

	subgroup	G/H
center	C₄²×C₁₀₇	C₂×D₄
commutator	C₂×C₄	C₂×C₄²×C₁₀₇
Frattini, cosocle	C₂×C₄²	C₂³×C₁₀₇
socle	C₂²×C₁₀₇	C₂×#95
prime radical	C₂⁴×C₁₀₇	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄²×C₁₀₇ ◁ C₂²×C₄²×C₁₀₇ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₀₇×#1276	C₂	semidirect
8. #432×C₁₀₇	C₄	semidirect
12. #431×C₁₀₇	C₄	semidirect
15. #423×C₁₀₇	C₄	semidirect
16. C₂×C₄⋊C₈×C₁₀₇	C₄	semidirect
177. #7870	C₁₀₇	direct (N × H)
187. #1276	C₂×C₁₀₇	semidirect
188. C₁₀₇	#7870	direct (N × H)
192. #432	C₄×C₁₀₇	semidirect
196. #431	C₄×C₁₀₇	semidirect
199. #423	C₄×C₁₀₇	semidirect
200. C₂×C₄⋊C₈	C₄×C₁₀₇	semidirect

Maximal subgroups

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

subgroup	index
C₁₀₇×#2920	2
C₂×#431×C₁₀₇	2
C₄×#117×C₁₀₇	2
C₁₀₇×#1276	2
#7870	107

Subgroups — C107×#7870 #41033834

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₇×#7870 #41033834