Subgroups — C₂×C₁₀₇×#1294 #41033975

Order 27392.

1454 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂²⋊C₈×C₁₀₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#380×C₁₀₇	C₂	1	1	yes	maximal, characteristic
3	C₂²×#95×C₁₀₇	C₂	1	1	yes	maximal, characteristic
4	C₁₀₇×#1294	C₂	1	4	yes	maximal, direct product factor
5	C₂⁴×C₄×C₁₀₇	—	2	1	no	—
6	C₂⁴×C₄×C₁₀₇	C₂²	1	1	yes	characteristic
7	C₂³×C₈×C₁₀₇	—	2	1	no	—
8	C₂²×C₄⋊C₄×C₁₀₇	C₄	1	2	yes	complemented
9	C₂²×C₂²⋊C₄×C₁₀₇	—	2	1	no	—
10	C₂×C₂²⋊C₈×C₁₀₇	—	2	1	no	—
11	C₂×C₂²⋊C₈×C₁₀₇	—	2	2	no	—
12	C₂×C₂²⋊C₈×C₁₀₇	C₄	1	4	yes	complemented
13	C₂×C₂²⋊C₈×C₁₀₇	C₂²	1	2	yes	—
14	#380×C₁₀₇	—	2	1	no	—
15	#380×C₁₀₇	—	2	1	no	—
16	#380×C₁₀₇	C₄	1	2	yes	complemented
17	#380×C₁₀₇	C₂²	1	2	yes	—
18	C₂×#95×C₁₀₇	—	2	1	no	—
19	C₂×#95×C₁₀₇	—	2	2	no	—
20	C₂×#95×C₁₀₇	—	2	1	no	—
21	C₂×#95×C₁₀₇	C₄	1	4	yes	complemented
22	C₂×#95×C₁₀₇	C₂²	1	2	yes	—
23	C₂⁵×C₁₀₇	D₄	1	1	yes	characteristic
24	C₂³×C₄×C₁₀₇	—	2	8	no	—
25	C₂³×C₄×C₁₀₇	—	2	4	no	—
26	C₂³×C₄×C₁₀₇	—	2	2	no	—
27	C₂³×C₄×C₁₀₇	—	2	2	no	—
28	C₂³×C₄×C₁₀₇	—	4	4	no	—
29	C₂³×C₄×C₁₀₇	—	4	4	no	—
30	C₂³×C₄×C₁₀₇	—	4	2	no	—
31	C₂³×C₄×C₁₀₇	—	4	2	no	—
32	C₂³×C₄×C₁₀₇	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₀₇	C₂×C₄	1	2	yes	—
34	C₂³×C₄×C₁₀₇	C₂×C₄	1	2	yes	—
35	C₂³×C₄×C₁₀₇	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₀₇	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₁₀₇	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₀₇	D₄	1	2	yes	—
39	C₂³×C₄×C₁₀₇	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₀₇	Q₈	1	2	yes	—
41	C₂³×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₁₀₇	—	2	4	no	—
43	C₂²×C₈×C₁₀₇	—	2	2	no	—
44	C₂²×C₈×C₁₀₇	—	4	4	no	—
45	C₂×C₄⋊C₄×C₁₀₇	—	2	2	no	—
46	C₂×C₄⋊C₄×C₁₀₇	—	4	4	no	—
47	C₂×C₄⋊C₄×C₁₀₇	C₂×C₄	1	4	yes	complemented
48	C₂×C₂²⋊C₄×C₁₀₇	—	2	2	no	—
49	C₂×C₂²⋊C₄×C₁₀₇	—	2	2	no	—
50	C₂×C₂²⋊C₄×C₁₀₇	—	4	2	no	—
51	C₂×C₂²⋊C₄×C₁₀₇	—	4	2	no	—
52	C₂²⋊C₈×C₁₀₇	—	2	4	no	—
53	C₂²⋊C₈×C₁₀₇	—	2	2	no	—
54	C₂²⋊C₈×C₁₀₇	C₂×C₄	1	4	yes	complemented
55	#95×C₁₀₇	—	2	4	no	—
56	#95×C₁₀₇	—	2	2	no	—
57	#95×C₁₀₇	—	2	2	no	—
58	#95×C₁₀₇	—	2	2	no	—
59	#95×C₁₀₇	C₂×C₄	1	4	yes	complemented
60	C₂⁴×C₁₀₇	—	2	4	no	—
61	C₂⁴×C₁₀₇	—	2	4	no	—
62	C₂⁴×C₁₀₇	C₂²⋊C₄	1	1	yes	characteristic
63	C₂⁴×C₁₀₇	C₂²⋊C₄	1	2	yes	—
64	C₂⁴×C₁₀₇	C₂²⋊C₄	1	1	yes	characteristic
65	C₂⁴×C₁₀₇	C₄⋊C₄	1	2	yes	—
66	C₂⁴×C₁₀₇	D₈	1	2	yes	—
67	C₂⁴×C₁₀₇	SD₁₆	1	2	yes	—
68	C₂⁴×C₁₀₇	SD₁₆	1	2	yes	—
69	C₂⁴×C₁₀₇	Q₁₆	1	2	yes	—
70	C₂⁴×C₁₀₇	C₂×D₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₀₇	—	2	4	no	—
72	C₂²×C₄×C₁₀₇	—	2	4	no	—
73	C₂²×C₄×C₁₀₇	—	2	16	no	—
74	C₂²×C₄×C₁₀₇	—	2	8	no	—
75	C₂²×C₄×C₁₀₇	—	2	4	no	—
76	C₂²×C₄×C₁₀₇	—	2	4	no	—
77	C₂²×C₄×C₁₀₇	—	4	4	no	—
78	C₂²×C₄×C₁₀₇	—	4	4	no	—
79	C₂²×C₄×C₁₀₇	—	4	2	no	—
80	C₂²×C₄×C₁₀₇	—	4	4	no	—
81	C₂²×C₄×C₁₀₇	—	4	2	no	—
82	C₂²×C₄×C₁₀₇	—	4	2	no	—
83	C₂²×C₄×C₁₀₇	—	4	4	no	—
84	C₂²×C₄×C₁₀₇	—	4	2	no	—
85	C₂²×C₄×C₁₀₇	—	4	16	no	—
86	C₂²×C₄×C₁₀₇	—	4	16	no	—
87	C₂²×C₄×C₁₀₇	—	4	8	no	—
88	C₂²×C₄×C₁₀₇	—	4	4	no	—
89	C₂²×C₄×C₁₀₇	—	4	8	no	—
90	C₂²×C₄×C₁₀₇	—	4	2	no	—
91	C₂²×C₄×C₁₀₇	—	4	2	no	—
92	C₂²×C₄×C₁₀₇	—	4	4	no	—
93	C₂²×C₄×C₁₀₇	—	4	4	no	—
94	C₂²×C₄×C₁₀₇	—	4	4	no	—
95	C₂²×C₄×C₁₀₇	C₄²	1	2	yes	—
96	C₂²×C₄×C₁₀₇	C₄²	1	2	yes	—
97	C₂²×C₄×C₁₀₇	C₂²⋊C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₀₇	C₂²⋊C₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₀₇	C₂²⋊C₄	1	2	yes	—
100	C₂²×C₄×C₁₀₇	C₂²⋊C₄	1	2	yes	—
101	C₂²×C₄×C₁₀₇	C₂²⋊C₄	1	2	yes	—
102	C₂²×C₄×C₁₀₇	C₄⋊C₄	1	2	yes	—
103	C₂²×C₄×C₁₀₇	C₄⋊C₄	1	2	yes	—
104	C₂²×C₄×C₁₀₇	C₄⋊C₄	1	2	yes	—
105	C₂²×C₄×C₁₀₇	C₄⋊C₄	1	2	yes	—
106	C₂²×C₄×C₁₀₇	C₄⋊C₄	1	2	yes	—
107	C₂²×C₄×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₀₇	C₂×Q₈	1	1	yes	characteristic
113	C₂×C₈×C₁₀₇	—	2	4	no	—
114	C₂×C₈×C₁₀₇	—	4	8	no	—
115	C₂×C₈×C₁₀₇	—	4	4	no	—
116	C₄⋊C₄×C₁₀₇	—	4	4	no	—
117	C₄⋊C₄×C₁₀₇	—	4	4	no	—
118	C₂²⋊C₄×C₁₀₇	—	4	4	no	—
119	C₂²⋊C₄×C₁₀₇	—	4	2	no	—
120	C₂²⋊C₄×C₁₀₇	—	4	2	no	—
121	C₂³×C₁₀₇	—	2	8	no	—
122	C₂³×C₁₀₇	—	2	8	no	—
123	C₂³×C₁₀₇	—	2	8	no	—
124	C₂³×C₁₀₇	—	2	8	no	—
125	C₂³×C₁₀₇	—	2	4	no	—
126	C₂³×C₁₀₇	—	2	4	no	—
127	C₂³×C₁₀₇	—	2	4	no	—
128	C₂³×C₁₀₇	—	2	4	no	—
129	C₂³×C₁₀₇	—	2	2	no	—
130	C₂³×C₁₀₇	—	2	2	no	—
131	C₂³×C₁₀₇	—	2	2	no	—
132	C₂³×C₁₀₇	—	2	2	no	—
133	C₂³×C₁₀₇	#95	1	2	yes	—
134	C₂³×C₁₀₇	#95	1	2	yes	—
135	C₂³×C₁₀₇	#99	1	4	yes	—
136	C₂³×C₁₀₇	#102	1	2	yes	—
137	C₂³×C₁₀₇	#102	1	4	yes	—
138	C₂³×C₁₀₇	#102	1	2	yes	—
139	C₂³×C₁₀₇	#103	1	4	yes	—
140	C₂³×C₁₀₇	#103	1	2	yes	—
141	C₂³×C₁₀₇	#103	1	2	yes	—
142	C₂³×C₁₀₇	#104	1	4	yes	—
143	C₂³×C₁₀₇	#106	1	4	yes	—
144	C₂³×C₁₀₇	#107	1	4	yes	—
145	C₂³×C₁₀₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂³×C₁₀₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	C₂³×C₁₀₇	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂³×C₁₀₇	C₂×D₈	1	1	yes	characteristic
149	C₂³×C₁₀₇	C₂×SD₁₆	1	1	yes	characteristic
150	C₂³×C₁₀₇	C₂×SD₁₆	1	1	yes	characteristic
151	C₂³×C₁₀₇	C₂×Q₁₆	1	1	yes	characteristic
152	C₂×C₄×C₁₀₇	—	2	4	no	—
153	C₂×C₄×C₁₀₇	—	2	4	no	—
154	C₂×C₄×C₁₀₇	—	2	4	no	—
155	C₂×C₄×C₁₀₇	—	2	4	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	2	no	—
160	C₂×C₄×C₁₀₇	—	2	8	no	—
161	C₂×C₄×C₁₀₇	—	4	2	no	—
162	C₂×C₄×C₁₀₇	—	4	2	no	—
163	C₂×C₄×C₁₀₇	—	4	2	no	—
164	C₂×C₄×C₁₀₇	—	4	2	no	—
165	C₂×C₄×C₁₀₇	—	4	2	no	—
166	C₂×C₄×C₁₀₇	—	4	2	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	32	no	—
172	C₂×C₄×C₁₀₇	—	4	4	no	—
173	C₂×C₄×C₁₀₇	—	4	8	no	—
174	C₂×C₄×C₁₀₇	—	4	8	no	—
175	C₂×C₄×C₁₀₇	—	4	4	no	—
176	C₂×C₄×C₁₀₇	—	4	4	no	—
177	C₂×C₄×C₁₀₇	—	4	4	no	—
178	C₂×C₄×C₁₀₇	—	4	4	no	—
179	C₂×C₄×C₁₀₇	—	8	8	no	—
180	C₂×C₄×C₁₀₇	#95	1	2	yes	—
181	C₂×C₄×C₁₀₇	#95	1	2	yes	—
182	C₂×C₄×C₁₀₇	C₂×C₄²	1	1	yes	characteristic
183	C₂×C₄×C₁₀₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
184	C₂×C₄×C₁₀₇	C₂×C₄⋊C₄	1	1	yes	characteristic
185	C₂×C₄×C₁₀₇	C₂×C₄⋊C₄	1	1	yes	characteristic
186	C₈×C₁₀₇	—	4	4	no	—
187	C₂²×C₁₀₇	—	2	8	no	—
188	C₂²×C₁₀₇	—	2	8	no	—
189	C₂²×C₁₀₇	—	2	8	no	—
190	C₂²×C₁₀₇	—	2	8	no	—
191	C₂²×C₁₀₇	—	2	1	no	—
192	C₂²×C₁₀₇	—	2	2	no	—
193	C₂²×C₁₀₇	—	2	1	no	—
194	C₂²×C₁₀₇	—	2	1	no	—
195	C₂²×C₁₀₇	—	2	2	no	—
196	C₂²×C₁₀₇	—	2	1	no	—
197	C₂²×C₁₀₇	—	2	2	no	—
198	C₂²×C₁₀₇	—	2	4	no	—
199	C₂²×C₁₀₇	—	2	2	no	—
200	C₂²×C₁₀₇	—	2	2	no	—
201	C₂²×C₁₀₇	—	2	4	no	—
202	C₂²×C₁₀₇	—	2	2	no	—
203	C₂²×C₁₀₇	#327	1	8	yes	—
204	C₂²×C₁₀₇	#328	1	8	yes	—
205	C₂²×C₁₀₇	#339	1	4	yes	—
206	C₂²×C₁₀₇	#340	1	4	yes	—
207	C₂²×C₁₀₇	#340	1	4	yes	—
208	C₂²×C₁₀₇	#342	1	4	yes	—
209	C₂²×C₁₀₇	C₂×#95	1	1	yes	characteristic
210	C₂²×C₁₀₇	C₂×#99	1	2	yes	—
211	C₂²×C₁₀₇	C₂×#102	1	1	yes	characteristic
212	C₂²×C₁₀₇	C₂×#102	1	1	yes	characteristic
213	C₂²×C₁₀₇	C₂×#103	1	1	yes	characteristic
214	C₂²×C₁₀₇	C₂×#103	1	1	yes	characteristic
215	C₂²×C₁₀₇	C₂×#104	1	2	yes	—
216	C₂²×C₁₀₇	C₂×#106	1	1	yes	characteristic
217	C₂²×C₁₀₇	C₂×#107	1	1	yes	characteristic
218	C₄×C₁₀₇	—	2	1	no	—
219	C₄×C₁₀₇	—	2	2	no	—
220	C₄×C₁₀₇	—	2	2	no	—
221	C₄×C₁₀₇	—	2	1	no	—
222	C₄×C₁₀₇	—	2	1	no	—
223	C₄×C₁₀₇	—	2	1	no	—
224	C₄×C₁₀₇	—	4	8	no	—
225	C₄×C₁₀₇	—	8	4	no	—
226	C₂×#1294	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
227	C₂×C₁₀₇	—	2	1	no	—
228	C₂×C₁₀₇	—	2	4	no	—
229	C₂×C₁₀₇	—	2	1	no	—
230	C₂×C₁₀₇	—	2	1	no	—
231	C₂×C₁₀₇	—	2	1	no	—
232	C₂×C₁₀₇	#1294	1	8	yes	direct product factor
233	C₂×C₁₀₇	C₂×#327	1	2	yes	—
234	C₂×C₁₀₇	C₂×#328	1	2	yes	—
235	C₂×C₁₀₇	C₂×#339	1	1	yes	characteristic
236	C₂×C₁₀₇	C₂×#340	1	1	yes	characteristic
237	C₂×C₁₀₇	C₂×#342	1	1	yes	characteristic
238	C₂²×C₂²⋊C₈	C₂×C₁₀₇	1	1	yes	characteristic
239	C₂×#380	C₂×C₁₀₇	1	1	yes	characteristic
240	C₂²×#95	C₂×C₁₀₇	1	1	yes	characteristic
241	#1294	C₂×C₁₀₇	1	4	yes	direct product factor
242	C₁₀₇	C₂×#1294	1	1	yes	characteristic, direct product factor, Sylow
243	C₂⁴×C₄	—	2	1	no	—
244	C₂⁴×C₄	C₂²×C₁₀₇	1	1	yes	characteristic
245	C₂³×C₈	—	2	1	no	—
246	C₂²×C₄⋊C₄	C₄×C₁₀₇	1	2	yes	complemented
247	C₂²×C₂²⋊C₄	—	2	1	no	—
248	C₂×C₂²⋊C₈	—	2	1	no	—
249	C₂×C₂²⋊C₈	—	2	2	no	—
250	C₂×C₂²⋊C₈	C₄×C₁₀₇	1	4	yes	complemented
251	C₂×C₂²⋊C₈	C₂²×C₁₀₇	1	2	yes	—
252	#380	—	2	1	no	—
253	#380	—	2	1	no	—
254	#380	C₄×C₁₀₇	1	2	yes	complemented
255	#380	C₂²×C₁₀₇	1	2	yes	—
256	C₂×#95	—	2	1	no	—
257	C₂×#95	—	2	2	no	—
258	C₂×#95	—	2	1	no	—
259	C₂×#95	C₄×C₁₀₇	1	4	yes	complemented
260	C₂×#95	C₂²×C₁₀₇	1	2	yes	—
261	C₂⁵	D₄×C₁₀₇	1	1	yes	characteristic
262	C₂³×C₄	—	2	8	no	—
263	C₂³×C₄	—	2	4	no	—
264	C₂³×C₄	—	2	2	no	—
265	C₂³×C₄	—	2	2	no	—
266	C₂³×C₄	—	4	4	no	—
267	C₂³×C₄	—	4	4	no	—
268	C₂³×C₄	—	4	2	no	—
269	C₂³×C₄	—	4	2	no	—
270	C₂³×C₄	C₂×C₄×C₁₀₇	1	1	yes	characteristic
271	C₂³×C₄	C₂×C₄×C₁₀₇	1	2	yes	—
272	C₂³×C₄	C₂×C₄×C₁₀₇	1	2	yes	—
273	C₂³×C₄	C₂×C₄×C₁₀₇	1	1	yes	characteristic
274	C₂³×C₄	D₄×C₁₀₇	1	1	yes	characteristic
275	C₂³×C₄	D₄×C₁₀₇	1	1	yes	characteristic
276	C₂³×C₄	D₄×C₁₀₇	1	2	yes	—
277	C₂³×C₄	D₄×C₁₀₇	1	1	yes	characteristic
278	C₂³×C₄	Q₈×C₁₀₇	1	2	yes	—
279	C₂³×C₄	C₂³×C₁₀₇	1	1	yes	characteristic
280	C₂²×C₈	—	2	4	no	—
281	C₂²×C₈	—	2	2	no	—
282	C₂²×C₈	—	4	4	no	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	—	4	4	no	—
285	C₂×C₄⋊C₄	C₂×C₄×C₁₀₇	1	4	yes	complemented
286	C₂×C₂²⋊C₄	—	2	2	no	—
287	C₂×C₂²⋊C₄	—	2	2	no	—
288	C₂×C₂²⋊C₄	—	4	2	no	—
289	C₂×C₂²⋊C₄	—	4	2	no	—
290	C₂²⋊C₈	—	2	4	no	—
291	C₂²⋊C₈	—	2	2	no	—
292	C₂²⋊C₈	C₂×C₄×C₁₀₇	1	4	yes	complemented
293	#95	—	2	4	no	—
294	#95	—	2	2	no	—
295	#95	—	2	2	no	—
296	#95	—	2	2	no	—
297	#95	C₂×C₄×C₁₀₇	1	4	yes	complemented
298	C₂⁴	—	2	4	no	—
299	C₂⁴	—	2	4	no	—
300	C₂⁴	C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
301	C₂⁴	C₂²⋊C₄×C₁₀₇	1	2	yes	—
302	C₂⁴	C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
303	C₂⁴	C₄⋊C₄×C₁₀₇	1	2	yes	—
304	C₂⁴	D₈×C₁₀₇	1	2	yes	—
305	C₂⁴	SD₁₆×C₁₀₇	1	2	yes	—
306	C₂⁴	SD₁₆×C₁₀₇	1	2	yes	—
307	C₂⁴	Q₁₆×C₁₀₇	1	2	yes	—
308	C₂⁴	C₂×D₄×C₁₀₇	1	1	yes	characteristic
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	2	16	no	—
312	C₂²×C₄	—	2	8	no	—
313	C₂²×C₄	—	2	4	no	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	4	4	no	—
316	C₂²×C₄	—	4	4	no	—
317	C₂²×C₄	—	4	2	no	—
318	C₂²×C₄	—	4	4	no	—
319	C₂²×C₄	—	4	2	no	—
320	C₂²×C₄	—	4	2	no	—
321	C₂²×C₄	—	4	4	no	—
322	C₂²×C₄	—	4	2	no	—
323	C₂²×C₄	—	4	8	no	—
324	C₂²×C₄	—	4	4	no	—
325	C₂²×C₄	—	4	16	no	—
326	C₂²×C₄	—	4	16	no	—
327	C₂²×C₄	—	4	8	no	—
328	C₂²×C₄	—	4	2	no	—
329	C₂²×C₄	—	4	2	no	—
330	C₂²×C₄	—	4	4	no	—
331	C₂²×C₄	—	4	4	no	—
332	C₂²×C₄	—	4	4	no	—
333	C₂²×C₄	C₄²×C₁₀₇	1	2	yes	—
334	C₂²×C₄	C₄²×C₁₀₇	1	2	yes	—
335	C₂²×C₄	C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
336	C₂²×C₄	C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
337	C₂²×C₄	C₂²⋊C₄×C₁₀₇	1	2	yes	—
338	C₂²×C₄	C₂²⋊C₄×C₁₀₇	1	2	yes	—
339	C₂²×C₄	C₂²⋊C₄×C₁₀₇	1	2	yes	—
340	C₂²×C₄	C₄⋊C₄×C₁₀₇	1	2	yes	—
341	C₂²×C₄	C₄⋊C₄×C₁₀₇	1	2	yes	—
342	C₂²×C₄	C₄⋊C₄×C₁₀₇	1	2	yes	—
343	C₂²×C₄	C₄⋊C₄×C₁₀₇	1	2	yes	—
344	C₂²×C₄	C₄⋊C₄×C₁₀₇	1	2	yes	—
345	C₂²×C₄	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
346	C₂²×C₄	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
347	C₂²×C₄	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
348	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
349	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
350	C₂²×C₄	C₂×Q₈×C₁₀₇	1	1	yes	characteristic
351	C₂×C₈	—	2	4	no	—
352	C₂×C₈	—	4	8	no	—
353	C₂×C₈	—	4	4	no	—
354	C₄⋊C₄	—	4	4	no	—
355	C₄⋊C₄	—	4	4	no	—
356	C₂²⋊C₄	—	4	4	no	—
357	C₂²⋊C₄	—	4	2	no	—
358	C₂²⋊C₄	—	4	2	no	—
359	C₂³	—	2	4	no	—
360	C₂³	—	2	4	no	—
361	C₂³	—	2	4	no	—
362	C₂³	—	2	4	no	—
363	C₂³	—	2	2	no	—
364	C₂³	—	2	2	no	—
365	C₂³	—	2	2	no	—
366	C₂³	—	2	2	no	—
367	C₂³	—	2	8	no	—
368	C₂³	—	2	8	no	—
369	C₂³	—	2	8	no	—
370	C₂³	—	2	8	no	—
371	C₂³	#95×C₁₀₇	1	2	yes	—
372	C₂³	#95×C₁₀₇	1	2	yes	—
373	C₂³	#99×C₁₀₇	1	4	yes	—
374	C₂³	#102×C₁₀₇	1	2	yes	—
375	C₂³	#102×C₁₀₇	1	4	yes	—
376	C₂³	#102×C₁₀₇	1	2	yes	—
377	C₂³	#103×C₁₀₇	1	2	yes	—
378	C₂³	#103×C₁₀₇	1	4	yes	—
379	C₂³	#103×C₁₀₇	1	2	yes	—
380	C₂³	#104×C₁₀₇	1	4	yes	—
381	C₂³	#106×C₁₀₇	1	4	yes	—
382	C₂³	#107×C₁₀₇	1	4	yes	—
383	C₂³	C₂×C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
384	C₂³	C₂×C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
385	C₂³	C₂×C₄⋊C₄×C₁₀₇	1	1	yes	characteristic
386	C₂³	C₂×D₈×C₁₀₇	1	1	yes	characteristic
387	C₂³	C₂×SD₁₆×C₁₀₇	1	1	yes	characteristic
388	C₂³	C₂×SD₁₆×C₁₀₇	1	1	yes	characteristic
389	C₂³	C₂×Q₁₆×C₁₀₇	1	1	yes	characteristic
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	8	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	4	no	—
410	C₂×C₄	—	4	8	no	—
411	C₂×C₄	—	4	8	no	—
412	C₂×C₄	—	4	32	no	—
413	C₂×C₄	—	4	4	no	—
414	C₂×C₄	—	4	4	no	—
415	C₂×C₄	—	4	4	no	—
416	C₂×C₄	—	4	4	no	—
417	C₂×C₄	—	8	8	no	—
418	C₂×C₄	#95×C₁₀₇	1	2	yes	—
419	C₂×C₄	#95×C₁₀₇	1	2	yes	—
420	C₂×C₄	C₂×C₄²×C₁₀₇	1	1	yes	characteristic
421	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
422	C₂×C₄	C₂×C₄⋊C₄×C₁₀₇	1	1	yes	characteristic
423	C₂×C₄	C₂×C₄⋊C₄×C₁₀₇	1	1	yes	characteristic
424	C₈	—	4	4	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	4	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	2	4	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	2	8	no	—
438	C₂²	—	2	8	no	—
439	C₂²	—	2	8	no	—
440	C₂²	—	2	8	no	—
441	C₂²	#327×C₁₀₇	1	8	yes	—
442	C₂²	#328×C₁₀₇	1	8	yes	—
443	C₂²	#339×C₁₀₇	1	4	yes	—
444	C₂²	#340×C₁₀₇	1	4	yes	—
445	C₂²	#340×C₁₀₇	1	4	yes	—
446	C₂²	#342×C₁₀₇	1	4	yes	—
447	C₂²	C₂×#95×C₁₀₇	1	1	yes	characteristic
448	C₂²	C₂×#99×C₁₀₇	1	2	yes	—
449	C₂²	C₂×#102×C₁₀₇	1	1	yes	characteristic
450	C₂²	C₂×#102×C₁₀₇	1	1	yes	characteristic
451	C₂²	C₂×#103×C₁₀₇	1	1	yes	characteristic
452	C₂²	C₂×#103×C₁₀₇	1	1	yes	characteristic
453	C₂²	C₂×#104×C₁₀₇	1	2	yes	—
454	C₂²	C₂×#106×C₁₀₇	1	1	yes	characteristic
455	C₂²	C₂×#107×C₁₀₇	1	1	yes	characteristic
456	C₄	—	2	1	no	—
457	C₄	—	2	2	no	—
458	C₄	—	2	2	no	—
459	C₄	—	2	1	no	—
460	C₄	—	2	1	no	—
461	C₄	—	2	1	no	—
462	C₄	—	4	8	no	—
463	C₄	—	8	4	no	—
464	C₂	—	2	1	no	—
465	C₂	—	2	4	no	—
466	C₂	—	2	1	no	—
467	C₂	—	2	1	no	—
468	C₂	—	2	1	no	—
469	C₂	C₁₀₇×#1294	1	8	yes	direct product factor
470	C₂	C₂×#327×C₁₀₇	1	2	yes	—
471	C₂	C₂×#328×C₁₀₇	1	2	yes	—
472	C₂	C₂×#339×C₁₀₇	1	1	yes	characteristic
473	C₂	C₂×#340×C₁₀₇	1	1	yes	characteristic
474	C₂	C₂×#342×C₁₀₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₀₇	C₂²⋊C₄
commutator	C₂×C₄	C₂×C₄²×C₁₀₇
Frattini, cosocle	C₂³×C₄	C₂³×C₁₀₇
prime radical	C₂⁵×C₁₀₇	D₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₀₇ ◁ C₂⁴×C₄×C₁₀₇ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₀₇×#1294	C₂	direct (N × H)
8. C₂²×C₄⋊C₄×C₁₀₇	C₄	semidirect
12. C₂×C₂²⋊C₈×C₁₀₇	C₄	semidirect
16. #380×C₁₀₇	C₄	semidirect
21. C₂×#95×C₁₀₇	C₄	semidirect
47. C₂×C₄⋊C₄×C₁₀₇	C₂×C₄	semidirect
54. C₂²⋊C₈×C₁₀₇	C₂×C₄	semidirect
59. #95×C₁₀₇	C₂×C₄	semidirect
226. C₂×#1294	C₁₀₇	direct (N × H)
232. C₂×C₁₀₇	#1294	direct (N × H)
241. #1294	C₂×C₁₀₇	direct (N × H)
242. C₁₀₇	C₂×#1294	direct (N × H)
246. C₂²×C₄⋊C₄	C₄×C₁₀₇	semidirect
250. C₂×C₂²⋊C₈	C₄×C₁₀₇	semidirect
254. #380	C₄×C₁₀₇	semidirect
259. C₂×#95	C₄×C₁₀₇	semidirect
285. C₂×C₄⋊C₄	C₂×C₄×C₁₀₇	semidirect
292. C₂²⋊C₈	C₂×C₄×C₁₀₇	semidirect
297. #95	C₂×C₄×C₁₀₇	semidirect
469. C₂	C₁₀₇×#1294	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₂²⋊C₈×C₁₀₇	2
C₂×#380×C₁₀₇	2
C₂²×#95×C₁₀₇	2
C₁₀₇×#1294	2
C₂×#1294	107

Subgroups — C2×C107×#1294 #41033975

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₀₇×#1294 #41033975