Subgroups — C₁₀₇×#24243 #41050207

Order 27392.

1406 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Q₈×C₁₀₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#462×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#451×C₁₀₇	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×Q₁₆×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₇×#2538	C₂	1	1	yes	maximal, characteristic
6	C₁₀₇×#2036	C₂	1	2	yes	maximal, complemented
7	C₁₀₇×#2001	C₂	1	2	yes	maximal, complemented
8	C₁₀₇×#1956	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₀₇×#1954	C₂	1	1	yes	maximal, characteristic
10	C₁₀₇×#1803	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₀₇×#1787	C₂	1	2	yes	maximal, complemented
12	C₂³×Q₈×C₁₀₇	C₂²	1	2	yes	—
13	C₂²×Q₁₆×C₁₀₇	C₂²	1	2	yes	—
14	C₂²×Q₁₆×C₁₀₇	C₂²	1	1	yes	characteristic
15	D₄×Q₈×C₁₀₇	—	2	4	no	—
16	D₄×Q₈×C₁₀₇	—	2	4	no	—
17	C₂×C₄⋊Q₈×C₁₀₇	—	2	1	no	—
18	C₂×C₄⋊Q₈×C₁₀₇	C₂²	1	1	yes	characteristic
19	C₂×C₂²⋊Q₈×C₁₀₇	—	2	2	no	—
20	C₂×C₂²⋊Q₈×C₁₀₇	C₂²	1	2	yes	—
21	C₂×C₂²⋊Q₈×C₁₀₇	C₂²	1	2	yes	—
22	C₂×C₄×Q₈×C₁₀₇	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₁₀₇	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₁₀₇	—	2	1	no	—
25	C₂×C₄×D₄×C₁₀₇	C₂²	1	1	yes	characteristic
26	#462×C₁₀₇	—	2	4	no	—
27	#451×C₁₀₇	—	2	8	no	—
28	C₄×Q₁₆×C₁₀₇	—	2	4	no	—
29	C₂×#107×C₁₀₇	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊C₈×C₁₀₇	C₂²	1	1	yes	characteristic
31	C₂×#103×C₁₀₇	C₂²	1	1	yes	characteristic
32	C₂×#103×C₁₀₇	C₂²	1	1	yes	characteristic
33	C₂×#103×C₁₀₇	C₂²	1	2	yes	—
34	C₂×#103×C₁₀₇	C₂²	1	2	yes	—
35	C₂×#103×C₁₀₇	C₂²	1	2	yes	—
36	C₂×#103×C₁₀₇	C₂²	1	2	yes	—
37	C₂×C₂²⋊C₈×C₁₀₇	C₂²	1	2	yes	—
38	C₂×C₂²⋊C₈×C₁₀₇	C₂²	1	2	yes	—
39	C₂×C₄×C₈×C₁₀₇	C₂²	1	1	yes	characteristic
40	#396×C₁₀₇	—	2	2	no	—
41	#390×C₁₀₇	—	2	1	no	—
42	#389×C₁₀₇	—	2	1	no	—
43	#384×C₁₀₇	C₂²	1	1	yes	characteristic
44	#380×C₁₀₇	C₂²	1	2	yes	—
45	#340×C₁₀₇	C₂²	1	2	yes	—
46	C₂²×Q₈×C₁₀₇	—	2	4	no	—
47	C₂²×Q₈×C₁₀₇	—	2	4	no	—
48	C₂²×Q₈×C₁₀₇	—	2	2	no	—
49	C₂²×Q₈×C₁₀₇	—	2	4	no	—
50	C₂²×Q₈×C₁₀₇	—	2	4	no	—
51	C₂²×Q₈×C₁₀₇	—	4	2	no	—
52	C₂²×Q₈×C₁₀₇	—	4	2	no	—
53	C₂²×Q₈×C₁₀₇	C₂³	1	2	yes	—
54	C₂²×Q₈×C₁₀₇	C₂³	1	1	yes	characteristic
55	C₂²×Q₈×C₁₀₇	C₂³	1	1	yes	characteristic
56	C₂²×D₄×C₁₀₇	D₄	1	1	yes	characteristic
57	C₂³×C₄×C₁₀₇	—	2	2	no	—
58	C₂³×C₄×C₁₀₇	C₂³	1	2	yes	—
59	C₂×Q₁₆×C₁₀₇	—	2	2	no	—
60	C₂×Q₁₆×C₁₀₇	—	2	2	no	—
61	C₂×Q₁₆×C₁₀₇	—	2	4	no	—
62	C₂×Q₁₆×C₁₀₇	—	2	4	no	—
63	C₂×Q₁₆×C₁₀₇	—	4	2	no	—
64	C₂×Q₁₆×C₁₀₇	D₄	1	4	yes	complemented
65	C₂²×C₈×C₁₀₇	C₂³	1	2	yes	—
66	C₂²×C₈×C₁₀₇	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₁₀₇	C₂³	1	1	yes	characteristic
68	C₄⋊Q₈×C₁₀₇	—	2	8	no	—
69	C₄⋊Q₈×C₁₀₇	—	2	2	no	—
70	C₄⋊Q₈×C₁₀₇	D₄	1	4	yes	—
71	C₂²⋊Q₈×C₁₀₇	—	2	16	no	—
72	C₂²⋊Q₈×C₁₀₇	—	2	4	no	—
73	C₂²⋊Q₈×C₁₀₇	—	2	4	no	—
74	C₂²⋊Q₈×C₁₀₇	—	2	4	no	—
75	C₂²⋊Q₈×C₁₀₇	—	4	2	no	—
76	C₄×Q₈×C₁₀₇	—	2	2	no	—
77	C₄×Q₈×C₁₀₇	—	2	2	no	—
78	C₄×Q₈×C₁₀₇	—	2	2	no	—
79	C₄×Q₈×C₁₀₇	D₄	1	4	yes	—
80	C₄×D₄×C₁₀₇	—	2	8	no	—
81	C₄×D₄×C₁₀₇	—	2	2	no	—
82	C₄×D₄×C₁₀₇	—	2	2	no	—
83	C₂×C₄⋊C₄×C₁₀₇	—	2	1	no	—
84	C₂×C₄⋊C₄×C₁₀₇	—	2	1	no	—
85	C₂×C₄⋊C₄×C₁₀₇	—	2	1	no	—
86	C₂×C₄⋊C₄×C₁₀₇	—	2	2	no	—
87	C₂×C₄⋊C₄×C₁₀₇	—	2	1	no	—
88	C₂×C₄⋊C₄×C₁₀₇	—	2	2	no	—
89	C₂×C₄⋊C₄×C₁₀₇	—	2	1	no	—
90	C₂×C₄⋊C₄×C₁₀₇	—	2	1	no	—
91	C₂×C₄⋊C₄×C₁₀₇	D₄	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	2	yes	—
93	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
95	C₂×C₂²⋊C₄×C₁₀₇	—	2	2	no	—
96	C₂×C₂²⋊C₄×C₁₀₇	—	2	2	no	—
97	C₂×C₂²⋊C₄×C₁₀₇	—	2	2	no	—
98	C₂×C₂²⋊C₄×C₁₀₇	D₄	1	2	yes	—
99	C₂×C₄²×C₁₀₇	—	2	1	no	—
100	C₂×C₄²×C₁₀₇	—	2	1	no	—
101	C₂×C₄²×C₁₀₇	C₂³	1	1	yes	characteristic
102	#107×C₁₀₇	—	2	2	no	—
103	C₄⋊C₈×C₁₀₇	—	2	2	no	—
104	#103×C₁₀₇	—	2	2	no	—
105	#103×C₁₀₇	—	2	4	no	—
106	#103×C₁₀₇	—	2	4	no	—
107	#103×C₁₀₇	—	2	4	no	—
108	#103×C₁₀₇	—	2	2	no	—
109	#103×C₁₀₇	—	4	2	no	—
110	C₂²⋊C₈×C₁₀₇	—	2	4	no	—
111	C₂²⋊C₈×C₁₀₇	—	4	2	no	—
112	C₄×C₈×C₁₀₇	—	2	2	no	—
113	#95×C₁₀₇	—	2	2	no	—
114	C₂⁴×C₁₀₇	C₂×D₄	1	2	yes	—
115	C₂×Q₈×C₁₀₇	—	2	8	no	—
116	C₂×Q₈×C₁₀₇	—	2	1	no	—
117	C₂×Q₈×C₁₀₇	—	2	2	no	—
118	C₂×Q₈×C₁₀₇	—	2	1	no	—
119	C₂×Q₈×C₁₀₇	—	2	1	no	—
120	C₂×Q₈×C₁₀₇	—	2	1	no	—
121	C₂×Q₈×C₁₀₇	—	2	1	no	—
122	C₂×Q₈×C₁₀₇	—	2	2	no	—
123	C₂×Q₈×C₁₀₇	—	2	1	no	—
124	C₂×Q₈×C₁₀₇	—	2	1	no	—
125	C₂×Q₈×C₁₀₇	—	2	2	no	—
126	C₂×Q₈×C₁₀₇	—	2	2	no	—
127	C₂×Q₈×C₁₀₇	—	2	1	no	—
128	C₂×Q₈×C₁₀₇	—	2	2	no	—
129	C₂×Q₈×C₁₀₇	—	4	4	no	—
130	C₂×Q₈×C₁₀₇	—	4	4	no	—
131	C₂×Q₈×C₁₀₇	—	4	8	no	—
132	C₂×Q₈×C₁₀₇	—	4	8	no	—
133	C₂×Q₈×C₁₀₇	—	4	8	no	—
134	C₂×Q₈×C₁₀₇	—	4	8	no	—
135	C₂×Q₈×C₁₀₇	C₂×D₄	1	4	yes	—
136	C₂×Q₈×C₁₀₇	C₂×D₄	1	2	yes	—
137	C₂×Q₈×C₁₀₇	C₂×D₄	1	2	yes	—
138	C₂×Q₈×C₁₀₇	C₂×D₄	1	2	yes	—
139	C₂×Q₈×C₁₀₇	#41	1	2	yes	—
140	C₂×D₄×C₁₀₇	—	2	2	no	—
141	C₂×D₄×C₁₀₇	—	2	2	no	—
142	C₂×D₄×C₁₀₇	Q₁₆	1	4	yes	complemented
143	C₂²×C₄×C₁₀₇	—	2	1	no	—
144	C₂²×C₄×C₁₀₇	—	2	8	no	—
145	C₂²×C₄×C₁₀₇	—	2	1	no	—
146	C₂²×C₄×C₁₀₇	—	2	1	no	—
147	C₂²×C₄×C₁₀₇	—	2	2	no	—
148	C₂²×C₄×C₁₀₇	—	2	2	no	—
149	C₂²×C₄×C₁₀₇	—	2	2	no	—
150	C₂²×C₄×C₁₀₇	—	2	2	no	—
151	C₂²×C₄×C₁₀₇	—	2	2	no	—
152	C₂²×C₄×C₁₀₇	—	2	2	no	—
153	C₂²×C₄×C₁₀₇	—	2	2	no	—
154	C₂²×C₄×C₁₀₇	—	2	1	no	—
155	C₂²×C₄×C₁₀₇	—	2	2	no	—
156	C₂²×C₄×C₁₀₇	—	4	4	no	—
157	C₂²×C₄×C₁₀₇	—	4	4	no	—
158	C₂²×C₄×C₁₀₇	C₂×D₄	1	2	yes	—
159	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₀₇	C₂⁴	1	1	yes	characteristic
162	Q₁₆×C₁₀₇	—	2	8	no	—
163	Q₁₆×C₁₀₇	—	4	8	no	—
164	C₂×C₈×C₁₀₇	—	2	1	no	—
165	C₂×C₈×C₁₀₇	—	2	1	no	—
166	C₂×C₈×C₁₀₇	—	2	1	no	—
167	C₂×C₈×C₁₀₇	—	2	2	no	—
168	C₂×C₈×C₁₀₇	—	2	2	no	—
169	C₂×C₈×C₁₀₇	—	2	1	no	—
170	C₂×C₈×C₁₀₇	—	2	2	no	—
171	C₂×C₈×C₁₀₇	—	2	1	no	—
172	C₂×C₈×C₁₀₇	C₂×D₄	1	2	yes	—
173	C₄⋊C₄×C₁₀₇	—	2	8	no	—
174	C₄⋊C₄×C₁₀₇	—	2	4	no	—
175	C₄⋊C₄×C₁₀₇	—	2	4	no	—
176	C₄⋊C₄×C₁₀₇	—	2	4	no	—
177	C₄⋊C₄×C₁₀₇	—	2	2	no	—
178	C₄⋊C₄×C₁₀₇	—	2	1	no	—
179	C₄⋊C₄×C₁₀₇	—	2	1	no	—
180	C₄⋊C₄×C₁₀₇	—	2	2	no	—
181	C₄⋊C₄×C₁₀₇	—	2	1	no	—
182	C₄⋊C₄×C₁₀₇	—	2	2	no	—
183	C₄⋊C₄×C₁₀₇	—	4	4	no	—
184	C₄⋊C₄×C₁₀₇	—	4	2	no	—
185	C₄⋊C₄×C₁₀₇	—	4	2	no	—
186	C₄⋊C₄×C₁₀₇	—	8	1	no	—
187	C₄⋊C₄×C₁₀₇	C₂×D₄	1	2	yes	—
188	C₂²⋊C₄×C₁₀₇	—	2	8	no	—
189	C₂²⋊C₄×C₁₀₇	—	2	4	no	—
190	C₂²⋊C₄×C₁₀₇	—	4	4	no	—
191	C₂²⋊C₄×C₁₀₇	—	8	2	no	—
192	C₄²×C₁₀₇	—	2	4	no	—
193	C₄²×C₁₀₇	—	4	2	no	—
194	C₄²×C₁₀₇	C₂×D₄	1	2	yes	—
195	C₄²×C₁₀₇	C₂×D₄	1	2	yes	—
196	C₂³×C₁₀₇	—	2	2	no	—
197	C₂³×C₁₀₇	—	2	2	no	—
198	C₂³×C₁₀₇	—	2	2	no	—
199	C₂³×C₁₀₇	—	2	2	no	—
200	C₂³×C₁₀₇	—	2	2	no	—
201	C₂³×C₁₀₇	—	2	2	no	—
202	C₂³×C₁₀₇	C₂×Q₁₆	1	4	yes	—
203	C₂³×C₁₀₇	C₂²×D₄	1	1	yes	characteristic
204	Q₈×C₁₀₇	—	2	2	no	—
205	Q₈×C₁₀₇	—	2	2	no	—
206	Q₈×C₁₀₇	—	2	2	no	—
207	Q₈×C₁₀₇	—	2	2	no	—
208	Q₈×C₁₀₇	—	2	2	no	—
209	Q₈×C₁₀₇	—	2	4	no	—
210	Q₈×C₁₀₇	—	2	4	no	—
211	Q₈×C₁₀₇	—	4	16	no	—
212	Q₈×C₁₀₇	—	4	2	no	—
213	Q₈×C₁₀₇	—	4	1	no	—
214	Q₈×C₁₀₇	—	4	2	no	—
215	Q₈×C₁₀₇	—	4	1	no	—
216	Q₈×C₁₀₇	#121	1	4	yes	—
217	D₄×C₁₀₇	—	2	8	no	—
218	C₂×C₄×C₁₀₇	—	2	2	no	—
219	C₂×C₄×C₁₀₇	—	2	2	no	—
220	C₂×C₄×C₁₀₇	—	2	2	no	—
221	C₂×C₄×C₁₀₇	—	2	1	no	—
222	C₂×C₄×C₁₀₇	—	2	1	no	—
223	C₂×C₄×C₁₀₇	—	2	2	no	—
224	C₂×C₄×C₁₀₇	—	2	4	no	—
225	C₂×C₄×C₁₀₇	—	2	2	no	—
226	C₂×C₄×C₁₀₇	—	2	2	no	—
227	C₂×C₄×C₁₀₇	—	2	2	no	—
228	C₂×C₄×C₁₀₇	—	2	2	no	—
229	C₂×C₄×C₁₀₇	—	4	16	no	—
230	C₂×C₄×C₁₀₇	—	4	1	no	—
231	C₂×C₄×C₁₀₇	—	4	2	no	—
232	C₂×C₄×C₁₀₇	—	4	2	no	—
233	C₂×C₄×C₁₀₇	—	4	1	no	—
234	C₂×C₄×C₁₀₇	—	4	1	no	—
235	C₂×C₄×C₁₀₇	—	4	1	no	—
236	C₂×C₄×C₁₀₇	—	4	2	no	—
237	C₂×C₄×C₁₀₇	—	4	2	no	—
238	C₂×C₄×C₁₀₇	—	4	2	no	—
239	C₂×C₄×C₁₀₇	—	4	2	no	—
240	C₂×C₄×C₁₀₇	—	4	1	no	—
241	C₂×C₄×C₁₀₇	—	4	2	no	—
242	C₂×C₄×C₁₀₇	—	4	2	no	—
243	C₂×C₄×C₁₀₇	—	4	1	no	—
244	C₂×C₄×C₁₀₇	—	4	2	no	—
245	C₂×C₄×C₁₀₇	—	4	1	no	—
246	C₂×C₄×C₁₀₇	#120	1	2	yes	—
247	C₂×C₄×C₁₀₇	#120	1	2	yes	—
248	C₂×C₄×C₁₀₇	C₂×Q₁₆	1	2	yes	—
249	C₂×C₄×C₁₀₇	#137	1	2	yes	—
250	C₂×C₄×C₁₀₇	C₂²×D₄	1	1	yes	characteristic
251	C₂×C₄×C₁₀₇	C₂²×D₄	1	1	yes	characteristic
252	C₂×C₄×C₁₀₇	C₂²×D₄	1	1	yes	characteristic
253	C₂×C₄×C₁₀₇	C₂×#41	1	1	yes	characteristic
254	C₂×C₄×C₁₀₇	H(5,𝔽₂)	1	1	yes	characteristic
255	C₂×C₄×C₁₀₇	H(5,𝔽₂)	1	1	yes	characteristic
256	C₈×C₁₀₇	—	2	2	no	—
257	C₈×C₁₀₇	—	4	1	no	—
258	C₈×C₁₀₇	—	4	2	no	—
259	C₂²×C₁₀₇	—	2	4	no	—
260	C₂²×C₁₀₇	—	2	4	no	—
261	C₂²×C₁₀₇	—	2	4	no	—
262	C₂²×C₁₀₇	—	4	2	no	—
263	C₂²×C₁₀₇	—	4	2	no	—
264	C₂²×C₁₀₇	—	4	2	no	—
265	C₂²×C₁₀₇	—	4	2	no	—
266	C₂²×C₁₀₇	C₂×#120	1	1	yes	characteristic
267	C₂²×C₁₀₇	D₄²	1	1	yes	characteristic
268	C₂²×C₁₀₇	#546	1	1	yes	characteristic
269	C₂²×C₁₀₇	C₂²×Q₁₆	1	1	yes	characteristic
270	C₂²×C₁₀₇	C₂×#137	1	1	yes	characteristic
271	C₂²×C₁₀₇	#577	1	1	yes	characteristic
272	C₂²×C₁₀₇	#578	1	1	yes	characteristic
273	C₄×C₁₀₇	—	2	4	no	—
274	C₄×C₁₀₇	—	2	2	no	—
275	C₄×C₁₀₇	—	4	2	no	—
276	C₄×C₁₀₇	—	4	4	no	—
277	C₄×C₁₀₇	—	4	2	no	—
278	C₄×C₁₀₇	—	4	2	no	—
279	C₄×C₁₀₇	—	8	1	no	—
280	C₄×C₁₀₇	—	8	2	no	—
281	C₄×C₁₀₇	#451	1	4	yes	complemented
282	C₄×C₁₀₇	C₂×#121	1	1	yes	characteristic
283	C₄×C₁₀₇	#535	1	1	yes	characteristic
284	C₄×C₁₀₇	D₄²	1	1	yes	characteristic
285	C₄×C₁₀₇	#546	1	1	yes	characteristic
286	#24243	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
287	C₂×C₁₀₇	—	4	4	no	—
288	C₂×C₁₀₇	#2408	1	1	yes	characteristic
289	C₂×C₁₀₇	C₂×#451	1	1	yes	characteristic
290	C₂×C₁₀₇	#3013	1	1	yes	characteristic
291	C₂×C₁₀₇	#3278	1	1	yes	characteristic
292	C₂×C₁₀₇	D₄×Q₁₆	1	1	yes	characteristic
293	C₂×C₁₀₇	#3299	1	1	yes	characteristic
294	C₂×C₁₀₇	#3328	1	1	yes	characteristic
295	C₂×D₄×Q₈	C₂×C₁₀₇	1	1	yes	characteristic
296	C₂×#462	C₂×C₁₀₇	1	1	yes	characteristic, complemented
297	C₂×#451	C₂×C₁₀₇	1	2	yes	complemented
298	C₂×C₄×Q₁₆	C₂×C₁₀₇	1	1	yes	characteristic, complemented
299	#2538	C₂×C₁₀₇	1	1	yes	characteristic
300	#2036	C₂×C₁₀₇	1	2	yes	complemented
301	#2001	C₂×C₁₀₇	1	2	yes	complemented
302	#1956	C₂×C₁₀₇	1	1	yes	characteristic, complemented
303	#1954	C₂×C₁₀₇	1	1	yes	characteristic
304	#1803	C₂×C₁₀₇	1	1	yes	characteristic, complemented
305	#1787	C₂×C₁₀₇	1	2	yes	complemented
306	C₁₀₇	#24243	1	1	yes	characteristic, direct product factor, Sylow
307	C₂³×Q₈	C₂²×C₁₀₇	1	2	yes	—
308	C₂²×Q₁₆	C₂²×C₁₀₇	1	2	yes	—
309	C₂²×Q₁₆	C₂²×C₁₀₇	1	1	yes	characteristic
310	D₄×Q₈	—	2	4	no	—
311	D₄×Q₈	—	2	4	no	—
312	C₂×C₄⋊Q₈	—	2	1	no	—
313	C₂×C₄⋊Q₈	C₂²×C₁₀₇	1	1	yes	characteristic
314	C₂×C₂²⋊Q₈	—	2	2	no	—
315	C₂×C₂²⋊Q₈	C₂²×C₁₀₇	1	2	yes	—
316	C₂×C₂²⋊Q₈	C₂²×C₁₀₇	1	2	yes	—
317	C₂×C₄×Q₈	C₂²×C₁₀₇	1	1	yes	characteristic
318	C₂×C₄×Q₈	C₂²×C₁₀₇	1	1	yes	characteristic
319	C₂×C₄×D₄	—	2	1	no	—
320	C₂×C₄×D₄	C₂²×C₁₀₇	1	1	yes	characteristic
321	#462	—	2	4	no	—
322	#451	—	2	8	no	—
323	C₄×Q₁₆	—	2	4	no	—
324	C₂×#107	C₂²×C₁₀₇	1	1	yes	characteristic
325	C₂×C₄⋊C₈	C₂²×C₁₀₇	1	1	yes	characteristic
326	C₂×#103	C₂²×C₁₀₇	1	2	yes	—
327	C₂×#103	C₂²×C₁₀₇	1	1	yes	characteristic
328	C₂×#103	C₂²×C₁₀₇	1	1	yes	characteristic
329	C₂×#103	C₂²×C₁₀₇	1	2	yes	—
330	C₂×#103	C₂²×C₁₀₇	1	2	yes	—
331	C₂×#103	C₂²×C₁₀₇	1	2	yes	—
332	C₂×C₂²⋊C₈	C₂²×C₁₀₇	1	2	yes	—
333	C₂×C₂²⋊C₈	C₂²×C₁₀₇	1	2	yes	—
334	C₂×C₄×C₈	C₂²×C₁₀₇	1	1	yes	characteristic
335	#396	—	2	2	no	—
336	#390	—	2	1	no	—
337	#389	—	2	1	no	—
338	#384	C₂²×C₁₀₇	1	1	yes	characteristic
339	#380	C₂²×C₁₀₇	1	2	yes	—
340	#340	C₂²×C₁₀₇	1	2	yes	—
341	C₂²×Q₈	—	2	4	no	—
342	C₂²×Q₈	—	2	4	no	—
343	C₂²×Q₈	—	2	2	no	—
344	C₂²×Q₈	—	2	4	no	—
345	C₂²×Q₈	—	2	4	no	—
346	C₂²×Q₈	—	4	2	no	—
347	C₂²×Q₈	—	4	2	no	—
348	C₂²×Q₈	C₂³×C₁₀₇	1	1	yes	characteristic
349	C₂²×Q₈	C₂³×C₁₀₇	1	2	yes	—
350	C₂²×Q₈	C₂³×C₁₀₇	1	1	yes	characteristic
351	C₂²×D₄	D₄×C₁₀₇	1	1	yes	characteristic
352	C₂³×C₄	—	2	2	no	—
353	C₂³×C₄	C₂³×C₁₀₇	1	2	yes	—
354	C₂×Q₁₆	—	2	2	no	—
355	C₂×Q₁₆	—	2	2	no	—
356	C₂×Q₁₆	—	2	4	no	—
357	C₂×Q₁₆	—	2	4	no	—
358	C₂×Q₁₆	—	4	2	no	—
359	C₂×Q₁₆	D₄×C₁₀₇	1	4	yes	complemented
360	C₂²×C₈	C₂³×C₁₀₇	1	2	yes	—
361	C₂²×C₈	C₂³×C₁₀₇	1	1	yes	characteristic
362	C₂²×C₈	C₂³×C₁₀₇	1	1	yes	characteristic
363	C₄⋊Q₈	—	2	8	no	—
364	C₄⋊Q₈	—	2	2	no	—
365	C₄⋊Q₈	D₄×C₁₀₇	1	4	yes	—
366	C₂²⋊Q₈	—	2	16	no	—
367	C₂²⋊Q₈	—	2	4	no	—
368	C₂²⋊Q₈	—	2	4	no	—
369	C₂²⋊Q₈	—	2	4	no	—
370	C₂²⋊Q₈	—	4	2	no	—
371	C₄×Q₈	—	2	2	no	—
372	C₄×Q₈	—	2	2	no	—
373	C₄×Q₈	—	2	2	no	—
374	C₄×Q₈	D₄×C₁₀₇	1	4	yes	—
375	C₄×D₄	—	2	8	no	—
376	C₄×D₄	—	2	2	no	—
377	C₄×D₄	—	2	2	no	—
378	C₂×C₄⋊C₄	—	2	1	no	—
379	C₂×C₄⋊C₄	—	2	1	no	—
380	C₂×C₄⋊C₄	—	2	1	no	—
381	C₂×C₄⋊C₄	—	2	2	no	—
382	C₂×C₄⋊C₄	—	2	1	no	—
383	C₂×C₄⋊C₄	—	2	2	no	—
384	C₂×C₄⋊C₄	—	2	1	no	—
385	C₂×C₄⋊C₄	—	2	1	no	—
386	C₂×C₄⋊C₄	D₄×C₁₀₇	1	1	yes	characteristic
387	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	1	yes	characteristic
388	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	2	yes	—
389	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	1	yes	characteristic
390	C₂×C₂²⋊C₄	—	2	2	no	—
391	C₂×C₂²⋊C₄	—	2	2	no	—
392	C₂×C₂²⋊C₄	—	2	2	no	—
393	C₂×C₂²⋊C₄	D₄×C₁₀₇	1	2	yes	—
394	C₂×C₄²	—	2	1	no	—
395	C₂×C₄²	—	2	1	no	—
396	C₂×C₄²	C₂³×C₁₀₇	1	1	yes	characteristic
397	#107	—	2	2	no	—
398	C₄⋊C₈	—	2	2	no	—
399	#103	—	2	2	no	—
400	#103	—	2	4	no	—
401	#103	—	2	4	no	—
402	#103	—	2	4	no	—
403	#103	—	2	2	no	—
404	#103	—	4	2	no	—
405	C₂²⋊C₈	—	2	4	no	—
406	C₂²⋊C₈	—	4	2	no	—
407	C₄×C₈	—	2	2	no	—
408	#95	—	2	2	no	—
409	C₂⁴	C₂×D₄×C₁₀₇	1	2	yes	—
410	C₂×Q₈	—	2	8	no	—
411	C₂×Q₈	—	2	1	no	—
412	C₂×Q₈	—	2	2	no	—
413	C₂×Q₈	—	2	1	no	—
414	C₂×Q₈	—	2	1	no	—
415	C₂×Q₈	—	2	1	no	—
416	C₂×Q₈	—	2	1	no	—
417	C₂×Q₈	—	2	2	no	—
418	C₂×Q₈	—	2	1	no	—
419	C₂×Q₈	—	2	1	no	—
420	C₂×Q₈	—	2	2	no	—
421	C₂×Q₈	—	2	2	no	—
422	C₂×Q₈	—	2	1	no	—
423	C₂×Q₈	—	2	2	no	—
424	C₂×Q₈	—	4	4	no	—
425	C₂×Q₈	—	4	4	no	—
426	C₂×Q₈	—	4	8	no	—
427	C₂×Q₈	—	4	8	no	—
428	C₂×Q₈	—	4	8	no	—
429	C₂×Q₈	—	4	8	no	—
430	C₂×Q₈	C₂×D₄×C₁₀₇	1	4	yes	—
431	C₂×Q₈	C₂×D₄×C₁₀₇	1	2	yes	—
432	C₂×Q₈	C₂×D₄×C₁₀₇	1	2	yes	—
433	C₂×Q₈	C₂×D₄×C₁₀₇	1	2	yes	—
434	C₂×Q₈	#41×C₁₀₇	1	2	yes	—
435	C₂×D₄	—	2	2	no	—
436	C₂×D₄	—	2	2	no	—
437	C₂×D₄	Q₁₆×C₁₀₇	1	4	yes	complemented
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	8	no	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	2	2	no	—
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	4	4	no	—
452	C₂²×C₄	—	4	4	no	—
453	C₂²×C₄	C₂×D₄×C₁₀₇	1	2	yes	—
454	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
455	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
456	C₂²×C₄	C₂⁴×C₁₀₇	1	1	yes	characteristic
457	Q₁₆	—	2	8	no	—
458	Q₁₆	—	4	8	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	2	no	—
463	C₂×C₈	—	2	2	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	2	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	C₂×D₄×C₁₀₇	1	2	yes	—
468	C₄⋊C₄	—	2	8	no	—
469	C₄⋊C₄	—	2	4	no	—
470	C₄⋊C₄	—	2	4	no	—
471	C₄⋊C₄	—	2	4	no	—
472	C₄⋊C₄	—	2	2	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	2	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	2	no	—
478	C₄⋊C₄	—	4	4	no	—
479	C₄⋊C₄	—	4	2	no	—
480	C₄⋊C₄	—	4	2	no	—
481	C₄⋊C₄	—	8	1	no	—
482	C₄⋊C₄	C₂×D₄×C₁₀₇	1	2	yes	—
483	C₂²⋊C₄	—	2	8	no	—
484	C₂²⋊C₄	—	2	4	no	—
485	C₂²⋊C₄	—	4	4	no	—
486	C₂²⋊C₄	—	8	2	no	—
487	C₄²	—	2	4	no	—
488	C₄²	—	4	2	no	—
489	C₄²	C₂×D₄×C₁₀₇	1	2	yes	—
490	C₄²	C₂×D₄×C₁₀₇	1	2	yes	—
491	C₂³	—	2	2	no	—
492	C₂³	—	2	2	no	—
493	C₂³	—	2	2	no	—
494	C₂³	—	2	2	no	—
495	C₂³	—	2	2	no	—
496	C₂³	—	2	2	no	—
497	C₂³	C₂×Q₁₆×C₁₀₇	1	4	yes	—
498	C₂³	C₂²×D₄×C₁₀₇	1	1	yes	characteristic
499	Q₈	—	2	2	no	—
500	Q₈	—	2	2	no	—
501	Q₈	—	2	2	no	—
502	Q₈	—	2	2	no	—
503	Q₈	—	2	2	no	—
504	Q₈	—	2	4	no	—
505	Q₈	—	2	4	no	—
506	Q₈	—	4	16	no	—
507	Q₈	—	4	2	no	—
508	Q₈	—	4	2	no	—
509	Q₈	—	4	1	no	—
510	Q₈	—	4	1	no	—
511	Q₈	#121×C₁₀₇	1	4	yes	—
512	D₄	—	2	8	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	4	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	4	16	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	2	no	—
537	C₂×C₄	—	4	2	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	2	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	#120×C₁₀₇	1	2	yes	—
542	C₂×C₄	#120×C₁₀₇	1	2	yes	—
543	C₂×C₄	C₂×Q₁₆×C₁₀₇	1	2	yes	—
544	C₂×C₄	#137×C₁₀₇	1	2	yes	—
545	C₂×C₄	C₂²×D₄×C₁₀₇	1	1	yes	characteristic
546	C₂×C₄	C₂²×D₄×C₁₀₇	1	1	yes	characteristic
547	C₂×C₄	C₂²×D₄×C₁₀₇	1	1	yes	characteristic
548	C₂×C₄	C₂×#41×C₁₀₇	1	1	yes	characteristic
549	C₂×C₄	H(5,𝔽₂)×C₁₀₇	1	1	yes	characteristic
550	C₂×C₄	H(5,𝔽₂)×C₁₀₇	1	1	yes	characteristic
551	C₈	—	2	2	no	—
552	C₈	—	4	1	no	—
553	C₈	—	4	2	no	—
554	C₂²	—	2	4	no	—
555	C₂²	—	2	4	no	—
556	C₂²	—	2	4	no	—
557	C₂²	—	4	2	no	—
558	C₂²	—	4	2	no	—
559	C₂²	—	4	2	no	—
560	C₂²	—	4	2	no	—
561	C₂²	C₂×#120×C₁₀₇	1	1	yes	characteristic
562	C₂²	D₄²×C₁₀₇	1	1	yes	characteristic
563	C₂²	#546×C₁₀₇	1	1	yes	characteristic
564	C₂²	C₂²×Q₁₆×C₁₀₇	1	1	yes	characteristic
565	C₂²	C₂×#137×C₁₀₇	1	1	yes	characteristic
566	C₂²	#577×C₁₀₇	1	1	yes	characteristic
567	C₂²	#578×C₁₀₇	1	1	yes	characteristic
568	C₄	—	2	4	no	—
569	C₄	—	2	2	no	—
570	C₄	—	4	2	no	—
571	C₄	—	4	4	no	—
572	C₄	—	4	2	no	—
573	C₄	—	4	2	no	—
574	C₄	—	8	1	no	—
575	C₄	—	8	2	no	—
576	C₄	#451×C₁₀₇	1	4	yes	complemented
577	C₄	C₂×#121×C₁₀₇	1	1	yes	characteristic
578	C₄	#535×C₁₀₇	1	1	yes	characteristic
579	C₄	D₄²×C₁₀₇	1	1	yes	characteristic
580	C₄	#546×C₁₀₇	1	1	yes	characteristic
581	C₂	—	4	4	no	—
582	C₂	C₁₀₇×#2408	1	1	yes	characteristic
583	C₂	C₂×#451×C₁₀₇	1	1	yes	characteristic
584	C₂	C₁₀₇×#3013	1	1	yes	characteristic
585	C₂	C₁₀₇×#3278	1	1	yes	characteristic
586	C₂	D₄×Q₁₆×C₁₀₇	1	1	yes	characteristic
587	C₂	C₁₀₇×#3299	1	1	yes	characteristic
588	C₂	C₁₀₇×#3328	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂×#462×C₁₀₇	C₂	semidirect
3. C₂×#451×C₁₀₇	C₂	semidirect
4. C₂×C₄×Q₁₆×C₁₀₇	C₂	semidirect
6. C₁₀₇×#2036	C₂	semidirect
7. C₁₀₇×#2001	C₂	semidirect
8. C₁₀₇×#1956	C₂	semidirect
10. C₁₀₇×#1803	C₂	semidirect
11. C₁₀₇×#1787	C₂	semidirect
64. C₂×Q₁₆×C₁₀₇	D₄	semidirect
142. C₂×D₄×C₁₀₇	Q₁₆	semidirect
281. C₄×C₁₀₇	#451	semidirect
286. #24243	C₁₀₇	direct (N × H)
296. C₂×#462	C₂×C₁₀₇	semidirect
297. C₂×#451	C₂×C₁₀₇	semidirect
298. C₂×C₄×Q₁₆	C₂×C₁₀₇	semidirect
300. #2036	C₂×C₁₀₇	semidirect
301. #2001	C₂×C₁₀₇	semidirect
302. #1956	C₂×C₁₀₇	semidirect
304. #1803	C₂×C₁₀₇	semidirect
305. #1787	C₂×C₁₀₇	semidirect
306. C₁₀₇	#24243	direct (N × H)
359. C₂×Q₁₆	D₄×C₁₀₇	semidirect
437. C₂×D₄	Q₁₆×C₁₀₇	semidirect
576. C₄	#451×C₁₀₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×Q₈×C₁₀₇	2
C₂×#462×C₁₀₇	2
C₂×#451×C₁₀₇	2
C₂×C₄×Q₁₆×C₁₀₇	2
C₁₀₇×#2538	2
C₁₀₇×#2036	2
C₁₀₇×#2001	2
C₁₀₇×#1956	2
C₁₀₇×#1954	2
C₁₀₇×#1803	2
C₁₀₇×#1787	2
#24243	107

Subgroups — C107×#24243 #41050207

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₇×#24243 #41050207