Subgroups — C₁₀₇×#8939 #41034903

Order 27392.

768 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊C₈×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#121×C₁₀₇	C₂	1	1	yes	maximal, characteristic
3	C₄×C₂²⋊C₈×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄⋊C₈×C₁₀₇	C₂	1	2	yes	maximal, complemented
5	C₁₀₇×#1279	C₂	1	2	yes	maximal, complemented
6	C₂³×C₈×C₁₀₇	—	2	1	no	—
7	C₂×#121×C₁₀₇	C₄	1	1	yes	characteristic
8	C₂×C₄×D₄×C₁₀₇	—	2	1	no	—
9	C₂×C₄×D₄×C₁₀₇	C₂²	1	1	yes	characteristic
10	C₂²×C₄²×C₁₀₇	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊C₈×C₁₀₇	—	2	1	no	—
12	C₂×C₄⋊C₈×C₁₀₇	—	2	4	no	—
13	C₂×C₄⋊C₈×C₁₀₇	C₂²	1	2	yes	—
14	C₂×C₂²⋊C₈×C₁₀₇	—	2	1	no	—
15	C₂×C₄×C₈×C₁₀₇	C₂²	1	2	yes	—
16	#390×C₁₀₇	C₄	1	1	yes	characteristic
17	#389×C₁₀₇	C₄	1	1	yes	characteristic
18	#388×C₁₀₇	—	2	1	no	—
19	#386×C₁₀₇	—	2	1	no	—
20	#380×C₁₀₇	C₄	1	1	yes	characteristic
21	C₄×C₄⋊C₄×C₁₀₇	C₂²	1	1	yes	characteristic
22	C₄×C₂²⋊C₄×C₁₀₇	—	2	1	no	—
23	#336×C₁₀₇	—	2	1	no	—
24	D₄⋊C₈×C₁₀₇	—	2	4	no	—
25	C₂²×D₄×C₁₀₇	—	2	1	no	—
26	C₂²×D₄×C₁₀₇	C₂×C₄	1	1	yes	characteristic
27	C₂³×C₄×C₁₀₇	—	2	1	no	—
28	C₂³×C₄×C₁₀₇	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₀₇	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₀₇	D₄	1	1	yes	characteristic
31	C₂²×C₈×C₁₀₇	—	2	4	no	—
32	C₂²×C₈×C₁₀₇	—	2	2	no	—
33	C₂²×C₈×C₁₀₇	—	2	2	no	—
34	C₂²×C₈×C₁₀₇	—	4	2	no	—
35	C₂²×C₈×C₁₀₇	—	4	2	no	—
36	#121×C₁₀₇	—	2	2	no	—
37	#121×C₁₀₇	C₈	1	4	yes	complemented
38	C₄×D₄×C₁₀₇	—	2	2	no	—
39	C₄×D₄×C₁₀₇	—	2	2	no	—
40	C₄×D₄×C₁₀₇	—	4	2	no	—
41	C₄×D₄×C₁₀₇	—	4	2	no	—
42	C₂×C₄⋊C₄×C₁₀₇	—	2	1	no	—
43	C₂×C₄⋊C₄×C₁₀₇	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄⋊C₄×C₁₀₇	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄⋊C₄×C₁₀₇	C₂×C₄	1	1	yes	characteristic
46	C₂×C₂²⋊C₄×C₁₀₇	—	2	1	no	—
47	C₂×C₂²⋊C₄×C₁₀₇	—	2	1	no	—
48	C₂×C₂²⋊C₄×C₁₀₇	—	2	1	no	—
49	C₂×C₂²⋊C₄×C₁₀₇	—	2	1	no	—
50	C₂×C₂²⋊C₄×C₁₀₇	—	2	1	no	—
51	C₂×C₄²×C₁₀₇	—	2	2	no	—
52	C₂×C₄²×C₁₀₇	—	2	2	no	—
53	C₂×C₄²×C₁₀₇	—	2	1	no	—
54	C₂×C₄²×C₁₀₇	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₁₀₇	D₄	1	1	yes	characteristic
56	C₂×C₄²×C₁₀₇	D₄	1	1	yes	characteristic
57	C₂×C₄²×C₁₀₇	C₂³	1	1	yes	characteristic
58	C₄⋊C₈×C₁₀₇	—	2	4	no	—
59	C₄⋊C₈×C₁₀₇	—	2	2	no	—
60	C₄⋊C₈×C₁₀₇	D₄	1	4	yes	complemented
61	C₂²⋊C₈×C₁₀₇	—	2	4	no	—
62	C₄×C₈×C₁₀₇	—	2	2	no	—
63	C₄×C₈×C₁₀₇	—	2	2	no	—
64	#95×C₁₀₇	—	2	1	no	—
65	#95×C₁₀₇	—	2	1	no	—
66	#95×C₁₀₇	—	2	1	no	—
67	C₂⁴×C₁₀₇	—	2	1	no	—
68	C₂⁴×C₁₀₇	C₂²⋊C₄	1	1	yes	characteristic
69	C₂×D₄×C₁₀₇	—	2	4	no	—
70	C₂×D₄×C₁₀₇	—	2	2	no	—
71	C₂×D₄×C₁₀₇	—	2	1	no	—
72	C₂×D₄×C₁₀₇	—	2	2	no	—
73	C₂×D₄×C₁₀₇	—	4	2	no	—
74	C₂×D₄×C₁₀₇	—	4	2	no	—
75	C₂×D₄×C₁₀₇	C₂×C₈	1	2	yes	complemented
76	C₂²×C₄×C₁₀₇	—	2	2	no	—
77	C₂²×C₄×C₁₀₇	—	2	1	no	—
78	C₂²×C₄×C₁₀₇	—	2	1	no	—
79	C₂²×C₄×C₁₀₇	—	2	2	no	—
80	C₂²×C₄×C₁₀₇	—	2	1	no	—
81	C₂²×C₄×C₁₀₇	—	2	1	no	—
82	C₂²×C₄×C₁₀₇	—	2	2	no	—
83	C₂²×C₄×C₁₀₇	—	2	1	no	—
84	C₂²×C₄×C₁₀₇	—	2	2	no	—
85	C₂²×C₄×C₁₀₇	—	2	1	no	—
86	C₂²×C₄×C₁₀₇	—	2	1	no	—
87	C₂²×C₄×C₁₀₇	—	4	1	no	—
88	C₂²×C₄×C₁₀₇	—	4	1	no	—
89	C₂²×C₄×C₁₀₇	—	4	1	no	—
90	C₂²×C₄×C₁₀₇	—	4	1	no	—
91	C₂²×C₄×C₁₀₇	—	4	1	no	—
92	C₂²×C₄×C₁₀₇	—	4	1	no	—
93	C₂²×C₄×C₁₀₇	—	4	1	no	—
94	C₂²×C₄×C₁₀₇	C₂²⋊C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₀₇	C₂²⋊C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₀₇	C₂²⋊C₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₀₇	C₂×C₈	1	2	yes	—
98	C₂²×C₄×C₁₀₇	M₁₆	1	2	yes	—
99	C₂²×C₄×C₁₀₇	D₈	1	2	yes	—
100	C₂²×C₄×C₁₀₇	SD₁₆	1	2	yes	—
101	C₂²×C₄×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
104	C₂×C₈×C₁₀₇	—	2	4	no	—
105	C₂×C₈×C₁₀₇	—	2	4	no	—
106	C₂×C₈×C₁₀₇	—	4	2	no	—
107	C₂×C₈×C₁₀₇	—	4	8	no	—
108	C₂×C₈×C₁₀₇	—	4	2	no	—
109	C₂×C₈×C₁₀₇	—	4	2	no	—
110	C₂×C₈×C₁₀₇	—	4	2	no	—
111	C₄⋊C₄×C₁₀₇	—	2	1	no	—
112	C₄⋊C₄×C₁₀₇	—	2	2	no	—
113	C₄⋊C₄×C₁₀₇	—	2	2	no	—
114	C₄⋊C₄×C₁₀₇	—	4	2	no	—
115	C₄⋊C₄×C₁₀₇	C₂×C₈	1	2	yes	complemented
116	C₂²⋊C₄×C₁₀₇	—	2	4	no	—
117	C₂²⋊C₄×C₁₀₇	—	4	2	no	—
118	C₂²⋊C₄×C₁₀₇	—	4	2	no	—
119	C₂²⋊C₄×C₁₀₇	—	4	2	no	—
120	C₂²⋊C₄×C₁₀₇	—	4	2	no	—
121	C₄²×C₁₀₇	—	2	2	no	—
122	C₄²×C₁₀₇	—	2	1	no	—
123	C₄²×C₁₀₇	—	2	2	no	—
124	C₄²×C₁₀₇	—	2	1	no	—
125	C₄²×C₁₀₇	—	4	1	no	—
126	C₄²×C₁₀₇	—	4	1	no	—
127	C₄²×C₁₀₇	C₂×D₄	1	2	yes	—
128	C₄²×C₁₀₇	#41	1	2	yes	—
129	C₂³×C₁₀₇	—	2	1	no	—
130	C₂³×C₁₀₇	—	2	1	no	—
131	C₂³×C₁₀₇	—	2	1	no	—
132	C₂³×C₁₀₇	—	2	1	no	—
133	C₂³×C₁₀₇	—	2	2	no	—
134	C₂³×C₁₀₇	—	4	1	no	—
135	C₂³×C₁₀₇	—	4	1	no	—
136	C₂³×C₁₀₇	—	4	1	no	—
137	C₂³×C₁₀₇	—	4	1	no	—
138	C₂³×C₁₀₇	—	4	1	no	—
139	C₂³×C₁₀₇	—	4	1	no	—
140	C₂³×C₁₀₇	C₂²⋊C₈	1	2	yes	—
141	C₂³×C₁₀₇	#102	1	2	yes	—
142	C₂³×C₁₀₇	#104	1	2	yes	—
143	C₂³×C₁₀₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
144	D₄×C₁₀₇	—	2	4	no	—
145	D₄×C₁₀₇	—	4	8	no	—
146	D₄×C₁₀₇	—	4	2	no	—
147	C₂×C₄×C₁₀₇	—	2	1	no	—
148	C₂×C₄×C₁₀₇	—	2	1	no	—
149	C₂×C₄×C₁₀₇	—	2	1	no	—
150	C₂×C₄×C₁₀₇	—	2	1	no	—
151	C₂×C₄×C₁₀₇	—	2	1	no	—
152	C₂×C₄×C₁₀₇	—	2	1	no	—
153	C₂×C₄×C₁₀₇	—	2	4	no	—
154	C₂×C₄×C₁₀₇	—	2	4	no	—
155	C₂×C₄×C₁₀₇	—	2	2	no	—
156	C₂×C₄×C₁₀₇	—	2	2	no	—
157	C₂×C₄×C₁₀₇	—	2	2	no	—
158	C₂×C₄×C₁₀₇	—	2	2	no	—
159	C₂×C₄×C₁₀₇	—	2	1	no	—
160	C₂×C₄×C₁₀₇	—	2	2	no	—
161	C₂×C₄×C₁₀₇	—	2	1	no	—
162	C₂×C₄×C₁₀₇	—	2	1	no	—
163	C₂×C₄×C₁₀₇	—	4	4	no	—
164	C₂×C₄×C₁₀₇	—	4	1	no	—
165	C₂×C₄×C₁₀₇	—	4	1	no	—
166	C₂×C₄×C₁₀₇	—	4	1	no	—
167	C₂×C₄×C₁₀₇	—	4	1	no	—
168	C₂×C₄×C₁₀₇	—	4	1	no	—
169	C₂×C₄×C₁₀₇	—	4	1	no	—
170	C₂×C₄×C₁₀₇	—	4	1	no	—
171	C₂×C₄×C₁₀₇	—	4	1	no	—
172	C₂×C₄×C₁₀₇	—	8	1	no	—
173	C₂×C₄×C₁₀₇	—	8	1	no	—
174	C₂×C₄×C₁₀₇	—	8	1	no	—
175	C₂×C₄×C₁₀₇	—	8	1	no	—
176	C₂×C₄×C₁₀₇	C₂²⋊C₈	1	2	yes	—
177	C₂×C₄×C₁₀₇	#102	1	2	yes	—
178	C₂×C₄×C₁₀₇	C₄×D₄	1	2	yes	—
179	C₂×C₄×C₁₀₇	#120	1	1	yes	characteristic
180	C₂×C₄×C₁₀₇	#121	1	2	yes	—
181	C₂×C₄×C₁₀₇	#123	1	1	yes	characteristic
182	C₂×C₄×C₁₀₇	C₂²×C₈	1	1	yes	characteristic
183	C₂×C₄×C₁₀₇	C₂×M₁₆	1	1	yes	characteristic
184	C₂×C₄×C₁₀₇	#131	1	2	yes	—
185	C₂×C₄×C₁₀₇	C₂×D₈	1	1	yes	characteristic
186	C₂×C₄×C₁₀₇	C₂×SD₁₆	1	1	yes	characteristic
187	C₂×C₄×C₁₀₇	AGL(1,ℤ/8)	1	1	yes	characteristic
188	C₂×C₄×C₁₀₇	#137	1	1	yes	characteristic
189	C₈×C₁₀₇	—	4	4	no	—
190	C₈×C₁₀₇	—	4	4	no	—
191	C₂²×C₁₀₇	—	2	2	no	—
192	C₂²×C₁₀₇	—	2	2	no	—
193	C₂²×C₁₀₇	—	2	2	no	—
194	C₂²×C₁₀₇	—	2	2	no	—
195	C₂²×C₁₀₇	—	2	2	no	—
196	C₂²×C₁₀₇	—	2	2	no	—
197	C₂²×C₁₀₇	—	4	2	no	—
198	C₂²×C₁₀₇	—	4	2	no	—
199	C₂²×C₁₀₇	—	4	2	no	—
200	C₂²×C₁₀₇	—	8	1	no	—
201	C₂²×C₁₀₇	—	8	1	no	—
202	C₂²×C₁₀₇	—	8	1	no	—
203	C₂²×C₁₀₇	—	8	1	no	—
204	C₂²×C₁₀₇	D₄⋊C₈	1	4	yes	complemented
205	C₂²×C₁₀₇	#386	1	1	yes	characteristic
206	C₂²×C₁₀₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
207	C₂²×C₁₀₇	#408	1	1	yes	characteristic
208	C₂²×C₁₀₇	C₂×#102	1	1	yes	characteristic
209	C₂²×C₁₀₇	#417	1	1	yes	characteristic
210	C₂²×C₁₀₇	C₂×#104	1	1	yes	characteristic
211	C₂²×C₁₀₇	#421	1	1	yes	characteristic
212	C₄×C₁₀₇	—	2	2	no	—
213	C₄×C₁₀₇	—	2	2	no	—
214	C₄×C₁₀₇	—	2	2	no	—
215	C₄×C₁₀₇	—	4	1	no	—
216	C₄×C₁₀₇	—	4	2	no	—
217	C₄×C₁₀₇	—	8	1	no	—
218	C₄×C₁₀₇	—	8	1	no	—
219	C₄×C₁₀₇	C₈×D₄	1	2	yes	—
220	C₄×C₁₀₇	#435	1	2	yes	—
221	C₄×C₁₀₇	#447	1	1	yes	characteristic
222	C₄×C₁₀₇	#448	1	1	yes	characteristic
223	C₄×C₁₀₇	#480	1	1	yes	characteristic
224	C₄×C₁₀₇	#481	1	1	yes	characteristic
225	#8939	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
226	C₂×C₁₀₇	—	2	4	no	—
227	C₂×C₁₀₇	—	8	2	no	—
228	C₂×C₁₀₇	C₂×D₄⋊C₈	1	1	yes	characteristic
229	C₂×C₁₀₇	#1477	1	1	yes	characteristic
230	C₂×C₁₀₇	#1480	1	1	yes	characteristic
231	C₂×C₁₀₇	#1483	1	1	yes	characteristic
232	C₂×C₁₀₇	#1869	1	1	yes	characteristic
233	C₂×C₁₀₇	#1871	1	1	yes	characteristic
234	C₂×C₁₀₇	#1874	1	1	yes	characteristic
235	C₂²×C₄⋊C₈	C₂×C₁₀₇	1	1	yes	characteristic, complemented
236	C₄×#121	C₂×C₁₀₇	1	1	yes	characteristic
237	C₄×C₂²⋊C₈	C₂×C₁₀₇	1	1	yes	characteristic, complemented
238	C₂×D₄⋊C₈	C₂×C₁₀₇	1	2	yes	complemented
239	#1279	C₂×C₁₀₇	1	2	yes	complemented
240	C₁₀₇	#8939	1	1	yes	characteristic, direct product factor, Sylow
241	C₂³×C₈	—	2	1	no	—
242	C₂×#121	C₄×C₁₀₇	1	1	yes	characteristic
243	C₂×C₄×D₄	—	2	1	no	—
244	C₂×C₄×D₄	C₂²×C₁₀₇	1	1	yes	characteristic
245	C₂²×C₄²	C₂²×C₁₀₇	1	1	yes	characteristic
246	C₂×C₄⋊C₈	—	2	1	no	—
247	C₂×C₄⋊C₈	—	2	4	no	—
248	C₂×C₄⋊C₈	C₂²×C₁₀₇	1	2	yes	—
249	C₂×C₂²⋊C₈	—	2	1	no	—
250	C₂×C₄×C₈	C₂²×C₁₀₇	1	2	yes	—
251	#390	C₄×C₁₀₇	1	1	yes	characteristic
252	#389	C₄×C₁₀₇	1	1	yes	characteristic
253	#388	—	2	1	no	—
254	#386	—	2	1	no	—
255	#380	C₄×C₁₀₇	1	1	yes	characteristic
256	C₄×C₄⋊C₄	C₂²×C₁₀₇	1	1	yes	characteristic
257	C₄×C₂²⋊C₄	—	2	1	no	—
258	#336	—	2	1	no	—
259	D₄⋊C₈	—	2	4	no	—
260	C₂²×D₄	—	2	1	no	—
261	C₂²×D₄	C₂×C₄×C₁₀₇	1	1	yes	characteristic
262	C₂³×C₄	—	2	1	no	—
263	C₂³×C₄	C₂×C₄×C₁₀₇	1	1	yes	characteristic
264	C₂³×C₄	D₄×C₁₀₇	1	1	yes	characteristic
265	C₂³×C₄	D₄×C₁₀₇	1	1	yes	characteristic
266	C₂²×C₈	—	2	4	no	—
267	C₂²×C₈	—	2	2	no	—
268	C₂²×C₈	—	2	2	no	—
269	C₂²×C₈	—	4	2	no	—
270	C₂²×C₈	—	4	2	no	—
271	#121	—	2	2	no	—
272	#121	C₈×C₁₀₇	1	4	yes	complemented
273	C₄×D₄	—	2	2	no	—
274	C₄×D₄	—	2	2	no	—
275	C₄×D₄	—	4	2	no	—
276	C₄×D₄	—	4	2	no	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	C₂×C₄×C₁₀₇	1	1	yes	characteristic
279	C₂×C₄⋊C₄	C₂×C₄×C₁₀₇	1	1	yes	characteristic
280	C₂×C₄⋊C₄	C₂×C₄×C₁₀₇	1	1	yes	characteristic
281	C₂×C₂²⋊C₄	—	2	1	no	—
282	C₂×C₂²⋊C₄	—	2	1	no	—
283	C₂×C₂²⋊C₄	—	2	1	no	—
284	C₂×C₂²⋊C₄	—	2	1	no	—
285	C₂×C₂²⋊C₄	—	2	1	no	—
286	C₂×C₄²	—	2	2	no	—
287	C₂×C₄²	—	2	2	no	—
288	C₂×C₄²	—	2	1	no	—
289	C₂×C₄²	C₂×C₄×C₁₀₇	1	1	yes	characteristic
290	C₂×C₄²	D₄×C₁₀₇	1	1	yes	characteristic
291	C₂×C₄²	D₄×C₁₀₇	1	1	yes	characteristic
292	C₂×C₄²	C₂³×C₁₀₇	1	1	yes	characteristic
293	C₄⋊C₈	—	2	4	no	—
294	C₄⋊C₈	—	2	2	no	—
295	C₄⋊C₈	D₄×C₁₀₇	1	4	yes	complemented
296	C₂²⋊C₈	—	2	4	no	—
297	C₄×C₈	—	2	2	no	—
298	C₄×C₈	—	2	2	no	—
299	#95	—	2	1	no	—
300	#95	—	2	1	no	—
301	#95	—	2	1	no	—
302	C₂⁴	—	2	1	no	—
303	C₂⁴	C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
304	C₂×D₄	—	2	4	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	2	1	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	4	2	no	—
309	C₂×D₄	—	4	2	no	—
310	C₂×D₄	C₂×C₈×C₁₀₇	1	2	yes	complemented
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	4	1	no	—
323	C₂²×C₄	—	4	1	no	—
324	C₂²×C₄	—	4	1	no	—
325	C₂²×C₄	—	4	1	no	—
326	C₂²×C₄	—	4	1	no	—
327	C₂²×C₄	—	4	1	no	—
328	C₂²×C₄	—	4	1	no	—
329	C₂²×C₄	C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
330	C₂²×C₄	C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
331	C₂²×C₄	C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
332	C₂²×C₄	C₂×C₈×C₁₀₇	1	2	yes	—
333	C₂²×C₄	M₁₆×C₁₀₇	1	2	yes	—
334	C₂²×C₄	D₈×C₁₀₇	1	2	yes	—
335	C₂²×C₄	SD₁₆×C₁₀₇	1	2	yes	—
336	C₂²×C₄	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
337	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
338	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
339	C₂×C₈	—	2	4	no	—
340	C₂×C₈	—	2	4	no	—
341	C₂×C₈	—	4	8	no	—
342	C₂×C₈	—	4	2	no	—
343	C₂×C₈	—	4	2	no	—
344	C₂×C₈	—	4	2	no	—
345	C₂×C₈	—	4	2	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	4	2	no	—
350	C₄⋊C₄	C₂×C₈×C₁₀₇	1	2	yes	complemented
351	C₂²⋊C₄	—	2	4	no	—
352	C₂²⋊C₄	—	4	2	no	—
353	C₂²⋊C₄	—	4	2	no	—
354	C₂²⋊C₄	—	4	2	no	—
355	C₂²⋊C₄	—	4	2	no	—
356	C₄²	—	2	2	no	—
357	C₄²	—	2	1	no	—
358	C₄²	—	2	2	no	—
359	C₄²	—	2	1	no	—
360	C₄²	—	4	1	no	—
361	C₄²	—	4	1	no	—
362	C₄²	C₂×D₄×C₁₀₇	1	2	yes	—
363	C₄²	#41×C₁₀₇	1	2	yes	—
364	C₂³	—	2	1	no	—
365	C₂³	—	2	1	no	—
366	C₂³	—	2	1	no	—
367	C₂³	—	2	1	no	—
368	C₂³	—	2	2	no	—
369	C₂³	—	4	1	no	—
370	C₂³	—	4	1	no	—
371	C₂³	—	4	1	no	—
372	C₂³	—	4	1	no	—
373	C₂³	—	4	1	no	—
374	C₂³	—	4	1	no	—
375	C₂³	C₂²⋊C₈×C₁₀₇	1	2	yes	—
376	C₂³	#102×C₁₀₇	1	2	yes	—
377	C₂³	#104×C₁₀₇	1	2	yes	—
378	C₂³	C₂×C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
379	D₄	—	2	4	no	—
380	D₄	—	4	8	no	—
381	D₄	—	4	2	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	4	4	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	8	1	no	—
408	C₂×C₄	—	8	1	no	—
409	C₂×C₄	—	8	1	no	—
410	C₂×C₄	—	8	1	no	—
411	C₂×C₄	C₂²⋊C₈×C₁₀₇	1	2	yes	—
412	C₂×C₄	#102×C₁₀₇	1	2	yes	—
413	C₂×C₄	C₄×D₄×C₁₀₇	1	2	yes	—
414	C₂×C₄	#120×C₁₀₇	1	1	yes	characteristic
415	C₂×C₄	#121×C₁₀₇	1	2	yes	—
416	C₂×C₄	#123×C₁₀₇	1	1	yes	characteristic
417	C₂×C₄	C₂²×C₈×C₁₀₇	1	1	yes	characteristic
418	C₂×C₄	C₂×M₁₆×C₁₀₇	1	1	yes	characteristic
419	C₂×C₄	#131×C₁₀₇	1	2	yes	—
420	C₂×C₄	C₂×D₈×C₁₀₇	1	1	yes	characteristic
421	C₂×C₄	C₂×SD₁₆×C₁₀₇	1	1	yes	characteristic
422	C₂×C₄	AGL(1,ℤ/8)×C₁₀₇	1	1	yes	characteristic
423	C₂×C₄	#137×C₁₀₇	1	1	yes	characteristic
424	C₈	—	4	4	no	—
425	C₈	—	4	4	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	2	2	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	4	2	no	—
433	C₂²	—	4	2	no	—
434	C₂²	—	4	2	no	—
435	C₂²	—	8	1	no	—
436	C₂²	—	8	1	no	—
437	C₂²	—	8	1	no	—
438	C₂²	—	8	1	no	—
439	C₂²	D₄⋊C₈×C₁₀₇	1	4	yes	complemented
440	C₂²	#386×C₁₀₇	1	1	yes	characteristic
441	C₂²	C₂×C₂²⋊C₈×C₁₀₇	1	1	yes	characteristic
442	C₂²	#408×C₁₀₇	1	1	yes	characteristic
443	C₂²	C₂×#102×C₁₀₇	1	1	yes	characteristic
444	C₂²	#417×C₁₀₇	1	1	yes	characteristic
445	C₂²	C₂×#104×C₁₀₇	1	1	yes	characteristic
446	C₂²	#421×C₁₀₇	1	1	yes	characteristic
447	C₄	—	2	2	no	—
448	C₄	—	2	2	no	—
449	C₄	—	2	2	no	—
450	C₄	—	4	1	no	—
451	C₄	—	4	2	no	—
452	C₄	—	8	1	no	—
453	C₄	—	8	1	no	—
454	C₄	C₈×D₄×C₁₀₇	1	2	yes	—
455	C₄	#435×C₁₀₇	1	2	yes	—
456	C₄	#447×C₁₀₇	1	1	yes	characteristic
457	C₄	#448×C₁₀₇	1	1	yes	characteristic
458	C₄	#480×C₁₀₇	1	1	yes	characteristic
459	C₄	#481×C₁₀₇	1	1	yes	characteristic
460	C₂	—	2	4	no	—
461	C₂	—	8	2	no	—
462	C₂	C₂×D₄⋊C₈×C₁₀₇	1	1	yes	characteristic
463	C₂	C₁₀₇×#1477	1	1	yes	characteristic
464	C₂	C₁₀₇×#1480	1	1	yes	characteristic
465	C₂	C₁₀₇×#1483	1	1	yes	characteristic
466	C₂	C₁₀₇×#1869	1	1	yes	characteristic
467	C₂	C₁₀₇×#1871	1	1	yes	characteristic
468	C₂	C₁₀₇×#1874	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	C₂³×C₁₀₇	C₂×C₂²⋊C₄
prime radical	C₂×#121×C₁₀₇	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₀₇ ◁ C₂²×C₄²×C₁₀₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₄⋊C₈×C₁₀₇	C₂	semidirect
3. C₄×C₂²⋊C₈×C₁₀₇	C₂	semidirect
4. C₂×D₄⋊C₈×C₁₀₇	C₂	semidirect
5. C₁₀₇×#1279	C₂	semidirect
37. #121×C₁₀₇	C₈	semidirect
60. C₄⋊C₈×C₁₀₇	D₄	semidirect
75. C₂×D₄×C₁₀₇	C₂×C₈	semidirect
115. C₄⋊C₄×C₁₀₇	C₂×C₈	semidirect
204. C₂²×C₁₀₇	D₄⋊C₈	semidirect
225. #8939	C₁₀₇	direct (N × H)
235. C₂²×C₄⋊C₈	C₂×C₁₀₇	semidirect
237. C₄×C₂²⋊C₈	C₂×C₁₀₇	semidirect
238. C₂×D₄⋊C₈	C₂×C₁₀₇	semidirect
239. #1279	C₂×C₁₀₇	semidirect
240. C₁₀₇	#8939	direct (N × H)
272. #121	C₈×C₁₀₇	semidirect
295. C₄⋊C₈	D₄×C₁₀₇	semidirect
310. C₂×D₄	C₂×C₈×C₁₀₇	semidirect
350. C₄⋊C₄	C₂×C₈×C₁₀₇	semidirect
439. C₂²	D₄⋊C₈×C₁₀₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊C₈×C₁₀₇	2
C₄×#121×C₁₀₇	2
C₄×C₂²⋊C₈×C₁₀₇	2
C₂×D₄⋊C₈×C₁₀₇	2
C₁₀₇×#1279	2
#8939	107

Subgroups — C107×#8939 #41034903

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₇×#8939 #41034903