Subgroups — C₁₀₇×#20876 #41046840

Order 27392.

1598 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#518×C₁₀₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#428×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#418×C₁₀₇	C₂	1	1	yes	maximal, characteristic
4	C₂²×#102×C₁₀₇	C₂	1	1	yes	maximal, characteristic
5	C₁₀₇×#2317	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₀₇×#1864	C₂	1	4	yes	maximal, complemented
7	C₁₀₇×#1862	C₂	1	4	yes	maximal, complemented
8	C₁₀₇×#1735	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₀₇×#1729	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×D₄×C₁₀₇	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₁₀₇	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₁₀₇	C₂²	1	1	yes	characteristic
13	#518×C₁₀₇	—	2	4	no	—
14	#518×C₁₀₇	—	2	4	no	—
15	C₂×C₄×D₄×C₁₀₇	—	2	1	no	—
16	C₂×C₄×D₄×C₁₀₇	—	2	1	no	—
17	C₂×C₄×D₄×C₁₀₇	C₂²	1	2	yes	—
18	C₂×C₄×D₄×C₁₀₇	C₂²	1	2	yes	—
19	C₂×#117×C₁₀₇	C₂²	1	1	yes	characteristic
20	C₂×#117×C₁₀₇	C₂²	1	1	yes	characteristic
21	C₂×#117×C₁₀₇	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₁₀₇	C₂²	1	1	yes	characteristic
23	C₂²×C₂²⋊C₄×C₁₀₇	—	2	2	no	—
24	#428×C₁₀₇	—	2	4	no	—
25	C₂×#107×C₁₀₇	C₂²	1	2	yes	complemented
26	C₂×#106×C₁₀₇	C₂²	1	2	yes	complemented
27	#418×C₁₀₇	C₄	1	8	yes	complemented
28	C₂×#102×C₁₀₇	—	2	4	no	—
29	C₂×#102×C₁₀₇	C₂²	1	4	yes	—
30	C₂×#102×C₁₀₇	C₂²	1	4	yes	—
31	#389×C₁₀₇	C₂²	1	4	yes	complemented
32	#385×C₁₀₇	—	2	2	no	—
33	#384×C₁₀₇	—	2	1	no	—
34	#382×C₁₀₇	—	2	1	no	—
35	#340×C₁₀₇	C₂²	1	2	yes	complemented
36	#340×C₁₀₇	C₂²	1	2	yes	complemented
37	#336×C₁₀₇	C₂²	1	4	yes	complemented
38	C₂⁵×C₁₀₇	—	2	1	no	—
39	C₂²×D₄×C₁₀₇	—	2	1	no	—
40	C₂²×D₄×C₁₀₇	—	2	2	no	—
41	C₂²×D₄×C₁₀₇	—	2	2	no	—
42	C₂²×D₄×C₁₀₇	—	2	2	no	—
43	C₂²×D₄×C₁₀₇	C₂×C₄	1	4	yes	—
44	C₂²×D₄×C₁₀₇	D₄	1	4	yes	—
45	C₂²×D₄×C₁₀₇	Q₈	1	4	yes	—
46	C₂²×D₄×C₁₀₇	C₂³	1	2	yes	—
47	C₂³×C₄×C₁₀₇	—	2	2	no	—
48	C₂³×C₄×C₁₀₇	—	2	2	no	—
49	C₂³×C₄×C₁₀₇	—	2	1	no	—
50	C₂³×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
51	C₂×M₁₆×C₁₀₇	—	2	2	no	—
52	C₂×M₁₆×C₁₀₇	—	2	2	no	—
53	C₂×M₁₆×C₁₀₇	C₂×C₄	1	4	yes	complemented
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	C₂³	1	2	yes	—
58	C₂²×C₈×C₁₀₇	C₂³	1	2	yes	—
59	C₄×D₄×C₁₀₇	—	2	8	no	—
60	C₄×D₄×C₁₀₇	—	2	8	no	—
61	C₄×D₄×C₁₀₇	—	2	4	no	—
62	C₄×D₄×C₁₀₇	—	2	4	no	—
63	C₄×D₄×C₁₀₇	—	2	4	no	—
64	C₄×D₄×C₁₀₇	—	2	4	no	—
65	#117×C₁₀₇	—	2	2	no	—
66	#117×C₁₀₇	—	2	2	no	—
67	#117×C₁₀₇	—	2	2	no	—
68	#117×C₁₀₇	—	2	2	no	—
69	#117×C₁₀₇	C₂×C₄	1	4	yes	complemented
70	#117×C₁₀₇	D₄	1	4	yes	—
71	C₂×C₄⋊C₄×C₁₀₇	—	2	2	no	—
72	C₂×C₄⋊C₄×C₁₀₇	—	2	2	no	—
73	C₂×C₄⋊C₄×C₁₀₇	—	2	1	no	—
74	C₂×C₄⋊C₄×C₁₀₇	—	2	4	no	—
75	C₂×C₄⋊C₄×C₁₀₇	D₄	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₁₀₇	D₄	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	2	yes	—
78	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	2	yes	—
79	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
81	C₂×C₂²⋊C₄×C₁₀₇	—	2	16	no	—
82	C₂×C₂²⋊C₄×C₁₀₇	—	2	1	no	—
83	C₂×C₂²⋊C₄×C₁₀₇	—	2	1	no	—
84	C₂×C₂²⋊C₄×C₁₀₇	—	2	2	no	—
85	C₂×C₂²⋊C₄×C₁₀₇	—	2	2	no	—
86	C₂×C₂²⋊C₄×C₁₀₇	D₄	1	2	yes	—
87	C₂×C₄²×C₁₀₇	—	2	1	no	—
88	C₂×C₄²×C₁₀₇	—	2	1	no	—
89	C₂×C₄²×C₁₀₇	C₂³	1	2	yes	—
90	#107×C₁₀₇	—	2	4	no	—
91	#106×C₁₀₇	—	2	4	no	—
92	#102×C₁₀₇	—	2	8	no	—
93	#102×C₁₀₇	C₂×C₄	1	16	yes	complemented
94	#95×C₁₀₇	—	2	4	no	—
95	C₂⁴×C₁₀₇	—	2	2	no	—
96	C₂⁴×C₁₀₇	—	2	4	no	—
97	C₂⁴×C₁₀₇	—	2	4	no	—
98	C₂⁴×C₁₀₇	—	2	4	no	—
99	C₂⁴×C₁₀₇	—	8	2	no	—
100	C₂⁴×C₁₀₇	—	8	2	no	—
101	C₂⁴×C₁₀₇	C₂×D₄	1	1	yes	characteristic
102	C₂×D₄×C₁₀₇	—	2	8	no	—
103	C₂×D₄×C₁₀₇	—	2	4	no	—
104	C₂×D₄×C₁₀₇	—	2	4	no	—
105	C₂×D₄×C₁₀₇	—	2	8	no	—
106	C₂×D₄×C₁₀₇	—	2	4	no	—
107	C₂×D₄×C₁₀₇	—	2	8	no	—
108	C₂×D₄×C₁₀₇	—	2	2	no	—
109	C₂×D₄×C₁₀₇	—	2	2	no	—
110	C₂×D₄×C₁₀₇	—	2	2	no	—
111	C₂×D₄×C₁₀₇	C₄⋊C₄	1	16	yes	complemented
112	C₂×D₄×C₁₀₇	C₂²×C₄	1	4	yes	—
113	C₂×D₄×C₁₀₇	C₂×D₄	1	4	yes	—
114	C₂×D₄×C₁₀₇	C₂×Q₈	1	4	yes	—
115	C₂²×C₄×C₁₀₇	—	2	2	no	—
116	C₂²×C₄×C₁₀₇	—	2	1	no	—
117	C₂²×C₄×C₁₀₇	—	2	1	no	—
118	C₂²×C₄×C₁₀₇	—	2	8	no	—
119	C₂²×C₄×C₁₀₇	—	2	8	no	—
120	C₂²×C₄×C₁₀₇	—	2	2	no	—
121	C₂²×C₄×C₁₀₇	—	4	2	no	—
122	C₂²×C₄×C₁₀₇	—	8	4	no	—
123	C₂²×C₄×C₁₀₇	—	8	4	no	—
124	C₂²×C₄×C₁₀₇	—	8	2	no	—
125	C₂²×C₄×C₁₀₇	C₂²×C₄	1	2	yes	—
126	C₂²×C₄×C₁₀₇	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₁₀₇	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₁₀₇	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₀₇	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₁₀₇	C₂×Q₈	1	2	yes	—
132	C₂²×C₄×C₁₀₇	#41	1	2	yes	—
133	C₂²×C₄×C₁₀₇	#41	1	2	yes	—
134	C₂²×C₄×C₁₀₇	C₂⁴	1	1	yes	characteristic
135	M₁₆×C₁₀₇	—	2	8	no	—
136	C₂×C₈×C₁₀₇	—	2	2	no	—
137	C₂×C₈×C₁₀₇	—	2	2	no	—
138	C₂×C₈×C₁₀₇	—	2	2	no	—
139	C₂×C₈×C₁₀₇	—	2	2	no	—
140	C₂×C₈×C₁₀₇	—	2	2	no	—
141	C₂×C₈×C₁₀₇	—	4	4	no	—
142	C₂×C₈×C₁₀₇	C₂²×C₄	1	4	yes	—
143	C₄⋊C₄×C₁₀₇	—	2	2	no	—
144	C₄⋊C₄×C₁₀₇	—	2	2	no	—
145	C₄⋊C₄×C₁₀₇	—	2	1	no	—
146	C₄⋊C₄×C₁₀₇	—	2	1	no	—
147	C₄⋊C₄×C₁₀₇	—	2	2	no	—
148	C₄⋊C₄×C₁₀₇	—	2	2	no	—
149	C₄⋊C₄×C₁₀₇	—	2	2	no	—
150	C₄⋊C₄×C₁₀₇	—	4	2	no	—
151	C₄⋊C₄×C₁₀₇	—	8	4	no	—
152	C₄⋊C₄×C₁₀₇	C₂²×C₄	1	4	yes	—
153	C₄⋊C₄×C₁₀₇	C₂×D₄	1	2	yes	—
154	C₄⋊C₄×C₁₀₇	C₂×D₄	1	2	yes	—
155	C₂²⋊C₄×C₁₀₇	—	2	8	no	—
156	C₂²⋊C₄×C₁₀₇	—	2	8	no	—
157	C₂²⋊C₄×C₁₀₇	—	2	4	no	—
158	C₂²⋊C₄×C₁₀₇	—	2	4	no	—
159	C₂²⋊C₄×C₁₀₇	—	2	4	no	—
160	C₄²×C₁₀₇	—	2	4	no	—
161	C₄²×C₁₀₇	—	2	4	no	—
162	C₄²×C₁₀₇	—	2	2	no	—
163	C₄²×C₁₀₇	—	2	2	no	—
164	C₂³×C₁₀₇	—	2	2	no	—
165	C₂³×C₁₀₇	—	2	2	no	—
166	C₂³×C₁₀₇	—	2	4	no	—
167	C₂³×C₁₀₇	—	2	4	no	—
168	C₂³×C₁₀₇	—	2	4	no	—
169	C₂³×C₁₀₇	—	2	16	no	—
170	C₂³×C₁₀₇	—	4	4	no	—
171	C₂³×C₁₀₇	—	4	4	no	—
172	C₂³×C₁₀₇	—	8	8	no	—
173	C₂³×C₁₀₇	—	8	8	no	—
174	C₂³×C₁₀₇	—	8	4	no	—
175	C₂³×C₁₀₇	—	8	4	no	—
176	C₂³×C₁₀₇	C₄×D₄	1	2	yes	—
177	C₂³×C₁₀₇	#120	1	2	yes	—
178	C₂³×C₁₀₇	C₂²⋊Q₈	1	2	yes	—
179	C₂³×C₁₀₇	C₂²×D₄	1	1	yes	characteristic
180	D₄×C₁₀₇	—	2	4	no	—
181	D₄×C₁₀₇	—	2	4	no	—
182	D₄×C₁₀₇	—	2	4	no	—
183	D₄×C₁₀₇	—	2	16	no	—
184	D₄×C₁₀₇	C₂×C₄⋊C₄	1	8	yes	—
185	C₂×C₄×C₁₀₇	—	2	4	no	—
186	C₂×C₄×C₁₀₇	—	2	2	no	—
187	C₂×C₄×C₁₀₇	—	2	2	no	—
188	C₂×C₄×C₁₀₇	—	2	2	no	—
189	C₂×C₄×C₁₀₇	—	2	2	no	—
190	C₂×C₄×C₁₀₇	—	2	4	no	—
191	C₂×C₄×C₁₀₇	—	2	4	no	—
192	C₂×C₄×C₁₀₇	—	4	2	no	—
193	C₂×C₄×C₁₀₇	—	4	2	no	—
194	C₂×C₄×C₁₀₇	—	4	2	no	—
195	C₂×C₄×C₁₀₇	—	4	2	no	—
196	C₂×C₄×C₁₀₇	—	4	2	no	—
197	C₂×C₄×C₁₀₇	—	4	4	no	—
198	C₂×C₄×C₁₀₇	—	8	8	no	—
199	C₂×C₄×C₁₀₇	—	8	8	no	—
200	C₂×C₄×C₁₀₇	—	8	4	no	—
201	C₂×C₄×C₁₀₇	C₂×C₄⋊C₄	1	4	yes	—
202	C₂×C₄×C₁₀₇	C₄×D₄	1	4	yes	—
203	C₂×C₄×C₁₀₇	C₄×D₄	1	2	yes	—
204	C₂×C₄×C₁₀₇	#120	1	2	yes	—
205	C₂×C₄×C₁₀₇	C₂²⋊Q₈	1	4	yes	—
206	C₂×C₄×C₁₀₇	C₂²⋊Q₈	1	2	yes	—
207	C₂×C₄×C₁₀₇	#123	1	4	yes	—
208	C₂×C₄×C₁₀₇	C₂³×C₄	1	1	yes	characteristic
209	C₂×C₄×C₁₀₇	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₁₀₇	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₁₀₇	C₂²×Q₈	1	1	yes	characteristic
212	C₂×C₄×C₁₀₇	C₂×#41	1	1	yes	characteristic
213	C₂×C₄×C₁₀₇	C₂×#41	1	1	yes	characteristic
214	C₈×C₁₀₇	—	2	4	no	—
215	C₈×C₁₀₇	—	4	2	no	—
216	C₂²×C₁₀₇	—	2	4	no	—
217	C₂²×C₁₀₇	—	2	4	no	—
218	C₂²×C₁₀₇	—	2	2	no	—
219	C₂²×C₁₀₇	—	2	2	no	—
220	C₂²×C₁₀₇	—	2	8	no	—
221	C₂²×C₁₀₇	—	4	8	no	—
222	C₂²×C₁₀₇	—	4	8	no	—
223	C₂²×C₁₀₇	—	4	4	no	—
224	C₂²×C₁₀₇	—	4	4	no	—
225	C₂²×C₁₀₇	—	8	16	no	—
226	C₂²×C₁₀₇	#385	1	4	yes	—
227	C₂²×C₁₀₇	C₂×C₄×D₄	1	1	yes	characteristic
228	C₂²×C₁₀₇	C₂×#120	1	1	yes	characteristic
229	C₂²×C₁₀₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
230	C₂²×C₁₀₇	#576	1	2	yes	—
231	C₂²×C₁₀₇	#577	1	2	yes	—
232	C₄×C₁₀₇	—	4	4	no	—
233	C₄×C₁₀₇	—	4	2	no	—
234	C₄×C₁₀₇	—	4	2	no	—
235	C₄×C₁₀₇	—	4	2	no	—
236	C₄×C₁₀₇	—	4	2	no	—
237	C₄×C₁₀₇	—	8	2	no	—
238	C₄×C₁₀₇	#385	1	4	yes	—
239	C₄×C₁₀₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
240	C₄×C₁₀₇	C₂×C₄×D₄	1	1	yes	characteristic
241	C₄×C₁₀₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
242	C₄×C₁₀₇	C₂×#123	1	1	yes	characteristic
243	#20876	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
244	C₂×C₁₀₇	—	2	4	no	—
245	C₂×C₁₀₇	—	4	8	no	—
246	C₂×C₁₀₇	C₂×#385	1	1	yes	characteristic
247	C₂×C₁₀₇	#2946	1	2	yes	—
248	C₂×C₁₀₇	#3008	1	1	yes	characteristic
249	C₂×C₁₀₇	#3009	1	1	yes	characteristic
250	C₂×C₁₀₇	#3081	1	2	yes	—
251	C₂×#518	C₂×C₁₀₇	1	1	yes	characteristic
252	C₂×#428	C₂×C₁₀₇	1	1	yes	characteristic, complemented
253	C₂×#418	C₂×C₁₀₇	1	1	yes	characteristic
254	C₂²×#102	C₂×C₁₀₇	1	1	yes	characteristic
255	#2317	C₂×C₁₀₇	1	1	yes	characteristic, complemented
256	#1864	C₂×C₁₀₇	1	4	yes	complemented
257	#1862	C₂×C₁₀₇	1	4	yes	complemented
258	#1735	C₂×C₁₀₇	1	1	yes	characteristic, complemented
259	#1729	C₂×C₁₀₇	1	1	yes	characteristic, complemented
260	C₁₀₇	#20876	1	1	yes	characteristic, direct product factor, Sylow
261	C₂³×D₄	C₂²×C₁₀₇	1	1	yes	characteristic
262	C₂²×M₁₆	C₂²×C₁₀₇	1	1	yes	characteristic
263	C₂³×C₈	C₂²×C₁₀₇	1	1	yes	characteristic
264	#518	—	2	4	no	—
265	#518	—	2	4	no	—
266	C₂×C₄×D₄	—	2	1	no	—
267	C₂×C₄×D₄	—	2	1	no	—
268	C₂×C₄×D₄	C₂²×C₁₀₇	1	2	yes	—
269	C₂×C₄×D₄	C₂²×C₁₀₇	1	2	yes	—
270	C₂×#117	C₂²×C₁₀₇	1	1	yes	characteristic
271	C₂×#117	C₂²×C₁₀₇	1	1	yes	characteristic
272	C₂×#117	C₂²×C₁₀₇	1	1	yes	characteristic
273	C₂²×C₄⋊C₄	C₂²×C₁₀₇	1	1	yes	characteristic
274	C₂²×C₂²⋊C₄	—	2	2	no	—
275	#428	—	2	4	no	—
276	C₂×#107	C₂²×C₁₀₇	1	2	yes	complemented
277	C₂×#106	C₂²×C₁₀₇	1	2	yes	complemented
278	#418	C₄×C₁₀₇	1	8	yes	complemented
279	C₂×#102	—	2	4	no	—
280	C₂×#102	C₂²×C₁₀₇	1	4	yes	—
281	C₂×#102	C₂²×C₁₀₇	1	4	yes	—
282	#389	C₂²×C₁₀₇	1	4	yes	complemented
283	#385	—	2	2	no	—
284	#384	—	2	1	no	—
285	#382	—	2	1	no	—
286	#340	C₂²×C₁₀₇	1	2	yes	complemented
287	#340	C₂²×C₁₀₇	1	2	yes	complemented
288	#336	C₂²×C₁₀₇	1	4	yes	complemented
289	C₂⁵	—	2	1	no	—
290	C₂²×D₄	—	2	1	no	—
291	C₂²×D₄	—	2	2	no	—
292	C₂²×D₄	—	2	2	no	—
293	C₂²×D₄	—	2	2	no	—
294	C₂²×D₄	C₂×C₄×C₁₀₇	1	4	yes	—
295	C₂²×D₄	D₄×C₁₀₇	1	4	yes	—
296	C₂²×D₄	Q₈×C₁₀₇	1	4	yes	—
297	C₂²×D₄	C₂³×C₁₀₇	1	2	yes	—
298	C₂³×C₄	—	2	2	no	—
299	C₂³×C₄	—	2	2	no	—
300	C₂³×C₄	—	2	1	no	—
301	C₂³×C₄	C₂³×C₁₀₇	1	1	yes	characteristic
302	C₂×M₁₆	—	2	2	no	—
303	C₂×M₁₆	—	2	2	no	—
304	C₂×M₁₆	C₂×C₄×C₁₀₇	1	4	yes	complemented
305	C₂²×C₈	—	2	2	no	—
306	C₂²×C₈	—	2	2	no	—
307	C₂²×C₈	—	2	2	no	—
308	C₂²×C₈	C₂³×C₁₀₇	1	2	yes	—
309	C₂²×C₈	C₂³×C₁₀₇	1	2	yes	—
310	C₄×D₄	—	2	8	no	—
311	C₄×D₄	—	2	8	no	—
312	C₄×D₄	—	2	4	no	—
313	C₄×D₄	—	2	4	no	—
314	C₄×D₄	—	2	4	no	—
315	C₄×D₄	—	2	4	no	—
316	#117	—	2	2	no	—
317	#117	—	2	2	no	—
318	#117	—	2	2	no	—
319	#117	—	2	2	no	—
320	#117	C₂×C₄×C₁₀₇	1	4	yes	complemented
321	#117	D₄×C₁₀₇	1	4	yes	—
322	C₂×C₄⋊C₄	—	2	2	no	—
323	C₂×C₄⋊C₄	—	2	2	no	—
324	C₂×C₄⋊C₄	—	2	1	no	—
325	C₂×C₄⋊C₄	—	2	4	no	—
326	C₂×C₄⋊C₄	D₄×C₁₀₇	1	1	yes	characteristic
327	C₂×C₄⋊C₄	D₄×C₁₀₇	1	1	yes	characteristic
328	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	2	yes	—
329	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	2	yes	—
330	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	1	yes	characteristic
331	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	1	yes	characteristic
332	C₂×C₂²⋊C₄	—	2	16	no	—
333	C₂×C₂²⋊C₄	—	2	1	no	—
334	C₂×C₂²⋊C₄	—	2	1	no	—
335	C₂×C₂²⋊C₄	—	2	2	no	—
336	C₂×C₂²⋊C₄	—	2	2	no	—
337	C₂×C₂²⋊C₄	D₄×C₁₀₇	1	2	yes	—
338	C₂×C₄²	—	2	1	no	—
339	C₂×C₄²	—	2	1	no	—
340	C₂×C₄²	C₂³×C₁₀₇	1	2	yes	—
341	#107	—	2	4	no	—
342	#106	—	2	4	no	—
343	#102	—	2	8	no	—
344	#102	C₂×C₄×C₁₀₇	1	16	yes	complemented
345	#95	—	2	4	no	—
346	C₂⁴	—	2	2	no	—
347	C₂⁴	—	2	4	no	—
348	C₂⁴	—	2	4	no	—
349	C₂⁴	—	2	4	no	—
350	C₂⁴	—	8	2	no	—
351	C₂⁴	—	8	2	no	—
352	C₂⁴	C₂×D₄×C₁₀₇	1	1	yes	characteristic
353	C₂×D₄	—	2	4	no	—
354	C₂×D₄	—	2	8	no	—
355	C₂×D₄	—	2	4	no	—
356	C₂×D₄	—	2	4	no	—
357	C₂×D₄	—	2	8	no	—
358	C₂×D₄	—	2	8	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	C₄⋊C₄×C₁₀₇	1	16	yes	complemented
363	C₂×D₄	C₂²×C₄×C₁₀₇	1	4	yes	—
364	C₂×D₄	C₂×D₄×C₁₀₇	1	4	yes	—
365	C₂×D₄	C₂×Q₈×C₁₀₇	1	4	yes	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	8	no	—
370	C₂²×C₄	—	2	8	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	4	2	no	—
373	C₂²×C₄	—	8	4	no	—
374	C₂²×C₄	—	8	4	no	—
375	C₂²×C₄	—	8	2	no	—
376	C₂²×C₄	C₂²×C₄×C₁₀₇	1	2	yes	—
377	C₂²×C₄	C₂×D₄×C₁₀₇	1	2	yes	—
378	C₂²×C₄	C₂×D₄×C₁₀₇	1	2	yes	—
379	C₂²×C₄	C₂×D₄×C₁₀₇	1	2	yes	—
380	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
381	C₂²×C₄	C₂×D₄×C₁₀₇	1	2	yes	—
382	C₂²×C₄	C₂×Q₈×C₁₀₇	1	2	yes	—
383	C₂²×C₄	#41×C₁₀₇	1	2	yes	—
384	C₂²×C₄	#41×C₁₀₇	1	2	yes	—
385	C₂²×C₄	C₂⁴×C₁₀₇	1	1	yes	characteristic
386	M₁₆	—	2	8	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	4	4	no	—
393	C₂×C₈	C₂²×C₄×C₁₀₇	1	4	yes	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	4	2	no	—
402	C₄⋊C₄	—	8	4	no	—
403	C₄⋊C₄	C₂²×C₄×C₁₀₇	1	4	yes	—
404	C₄⋊C₄	C₂×D₄×C₁₀₇	1	2	yes	—
405	C₄⋊C₄	C₂×D₄×C₁₀₇	1	2	yes	—
406	C₂²⋊C₄	—	2	8	no	—
407	C₂²⋊C₄	—	2	8	no	—
408	C₂²⋊C₄	—	2	4	no	—
409	C₂²⋊C₄	—	2	4	no	—
410	C₂²⋊C₄	—	2	4	no	—
411	C₄²	—	2	4	no	—
412	C₄²	—	2	4	no	—
413	C₄²	—	2	2	no	—
414	C₄²	—	2	2	no	—
415	C₂³	—	2	2	no	—
416	C₂³	—	2	2	no	—
417	C₂³	—	2	4	no	—
418	C₂³	—	2	4	no	—
419	C₂³	—	2	4	no	—
420	C₂³	—	2	16	no	—
421	C₂³	—	4	4	no	—
422	C₂³	—	4	4	no	—
423	C₂³	—	8	8	no	—
424	C₂³	—	8	4	no	—
425	C₂³	—	8	4	no	—
426	C₂³	—	8	8	no	—
427	C₂³	C₄×D₄×C₁₀₇	1	2	yes	—
428	C₂³	#120×C₁₀₇	1	2	yes	—
429	C₂³	C₂²⋊Q₈×C₁₀₇	1	2	yes	—
430	C₂³	C₂²×D₄×C₁₀₇	1	1	yes	characteristic
431	D₄	—	2	16	no	—
432	D₄	—	2	4	no	—
433	D₄	—	2	4	no	—
434	D₄	—	2	4	no	—
435	D₄	C₂×C₄⋊C₄×C₁₀₇	1	8	yes	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	4	no	—
449	C₂×C₄	—	8	8	no	—
450	C₂×C₄	—	8	8	no	—
451	C₂×C₄	—	8	4	no	—
452	C₂×C₄	C₂×C₄⋊C₄×C₁₀₇	1	4	yes	—
453	C₂×C₄	C₄×D₄×C₁₀₇	1	2	yes	—
454	C₂×C₄	C₄×D₄×C₁₀₇	1	4	yes	—
455	C₂×C₄	#120×C₁₀₇	1	2	yes	—
456	C₂×C₄	C₂²⋊Q₈×C₁₀₇	1	2	yes	—
457	C₂×C₄	C₂²⋊Q₈×C₁₀₇	1	4	yes	—
458	C₂×C₄	#123×C₁₀₇	1	4	yes	—
459	C₂×C₄	C₂³×C₄×C₁₀₇	1	1	yes	characteristic
460	C₂×C₄	C₂²×D₄×C₁₀₇	1	1	yes	characteristic
461	C₂×C₄	C₂²×D₄×C₁₀₇	1	1	yes	characteristic
462	C₂×C₄	C₂²×Q₈×C₁₀₇	1	1	yes	characteristic
463	C₂×C₄	C₂×#41×C₁₀₇	1	1	yes	characteristic
464	C₂×C₄	C₂×#41×C₁₀₇	1	1	yes	characteristic
465	C₈	—	2	4	no	—
466	C₈	—	4	2	no	—
467	C₂²	—	2	4	no	—
468	C₂²	—	2	2	no	—
469	C₂²	—	2	2	no	—
470	C₂²	—	2	4	no	—
471	C₂²	—	2	8	no	—
472	C₂²	—	4	8	no	—
473	C₂²	—	4	4	no	—
474	C₂²	—	4	4	no	—
475	C₂²	—	4	8	no	—
476	C₂²	—	8	16	no	—
477	C₂²	#385×C₁₀₇	1	4	yes	—
478	C₂²	C₂×C₄×D₄×C₁₀₇	1	1	yes	characteristic
479	C₂²	C₂×#120×C₁₀₇	1	1	yes	characteristic
480	C₂²	C₂×C₂²⋊Q₈×C₁₀₇	1	1	yes	characteristic
481	C₂²	#576×C₁₀₇	1	2	yes	—
482	C₂²	#577×C₁₀₇	1	2	yes	—
483	C₄	—	4	4	no	—
484	C₄	—	4	2	no	—
485	C₄	—	4	2	no	—
486	C₄	—	4	2	no	—
487	C₄	—	4	2	no	—
488	C₄	—	8	2	no	—
489	C₄	#385×C₁₀₇	1	4	yes	—
490	C₄	C₂²×C₄⋊C₄×C₁₀₇	1	1	yes	characteristic
491	C₄	C₂×C₄×D₄×C₁₀₇	1	1	yes	characteristic
492	C₄	C₂×C₂²⋊Q₈×C₁₀₇	1	1	yes	characteristic
493	C₄	C₂×#123×C₁₀₇	1	1	yes	characteristic
494	C₂	—	2	4	no	—
495	C₂	—	4	8	no	—
496	C₂	C₂×#385×C₁₀₇	1	1	yes	characteristic
497	C₂	C₁₀₇×#2946	1	2	yes	—
498	C₂	C₁₀₇×#3008	1	1	yes	characteristic
499	C₂	C₁₀₇×#3009	1	1	yes	characteristic
500	C₂	C₁₀₇×#3081	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₀₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₀₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₇
prime radical	C₂³×D₄×C₁₀₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₇ ◁ C₂×#117×C₁₀₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#428×C₁₀₇	C₂	semidirect
5. C₁₀₇×#2317	C₂	semidirect
6. C₁₀₇×#1864	C₂	semidirect
7. C₁₀₇×#1862	C₂	semidirect
8. C₁₀₇×#1735	C₂	semidirect
9. C₁₀₇×#1729	C₂	semidirect
25. C₂×#107×C₁₀₇	C₂²	semidirect
26. C₂×#106×C₁₀₇	C₂²	semidirect
27. #418×C₁₀₇	C₄	semidirect
31. #389×C₁₀₇	C₂²	semidirect
35. #340×C₁₀₇	C₂²	semidirect
36. #340×C₁₀₇	C₂²	semidirect
37. #336×C₁₀₇	C₂²	semidirect
53. C₂×M₁₆×C₁₀₇	C₂×C₄	semidirect
69. #117×C₁₀₇	C₂×C₄	semidirect
93. #102×C₁₀₇	C₂×C₄	semidirect
111. C₂×D₄×C₁₀₇	C₄⋊C₄	semidirect
243. #20876	C₁₀₇	direct (N × H)
252. C₂×#428	C₂×C₁₀₇	semidirect
255. #2317	C₂×C₁₀₇	semidirect
256. #1864	C₂×C₁₀₇	semidirect
257. #1862	C₂×C₁₀₇	semidirect
258. #1735	C₂×C₁₀₇	semidirect
259. #1729	C₂×C₁₀₇	semidirect
260. C₁₀₇	#20876	direct (N × H)
276. C₂×#107	C₂²×C₁₀₇	semidirect
277. C₂×#106	C₂²×C₁₀₇	semidirect
278. #418	C₄×C₁₀₇	semidirect
282. #389	C₂²×C₁₀₇	semidirect
286. #340	C₂²×C₁₀₇	semidirect
287. #340	C₂²×C₁₀₇	semidirect
288. #336	C₂²×C₁₀₇	semidirect
304. C₂×M₁₆	C₂×C₄×C₁₀₇	semidirect
320. #117	C₂×C₄×C₁₀₇	semidirect
344. #102	C₂×C₄×C₁₀₇	semidirect
362. C₂×D₄	C₄⋊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×#518×C₁₀₇	2
C₂×#428×C₁₀₇	2
C₂×#418×C₁₀₇	2
C₂²×#102×C₁₀₇	2
C₁₀₇×#2317	2
C₁₀₇×#1864	2
C₁₀₇×#1862	2
C₁₀₇×#1735	2
C₁₀₇×#1729	2
#20876	107

Subgroups — C107×#20876 #41046840

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₇×#20876 #41046840