Subgroups — C₁₀₇×#23119 #41049083

Order 27392.

980 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#435×C₁₀₇	C₂	1	2	yes	maximal, complemented
2	C₄×#121×C₁₀₇	C₂	1	1	yes	maximal, characteristic
3	C₁₀₇×#1924	C₂	1	2	yes	maximal, complemented
4	C₁₀₇×#1917	C₂	1	2	yes	maximal, complemented
5	C₁₀₇×#1870	C₂	1	2	yes	maximal, complemented
6	C₁₀₇×#1869	C₂	1	2	yes	maximal, complemented
7	C₁₀₇×#1752	C₂	1	2	yes	maximal, complemented
8	C₁₀₇×#1749	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₀₇×#1728	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×M₁₆×C₁₀₇	C₂²	1	2	yes	—
11	C₂³×C₈×C₁₀₇	C₂²	1	2	yes	—
12	C₂×#121×C₁₀₇	C₄	1	1	yes	characteristic
13	C₂×C₄×D₄×C₁₀₇	C₂²	1	2	yes	—
14	C₂×C₄×D₄×C₁₀₇	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₁₀₇	C₂²	1	1	yes	characteristic
16	#435×C₁₀₇	—	2	8	no	—
17	C₂×C₄⋊C₈×C₁₀₇	C₂²	1	2	yes	—
18	C₂×C₂²⋊C₈×C₁₀₇	C₂²	1	2	yes	—
19	C₂×C₂²⋊C₈×C₁₀₇	C₂²	1	2	yes	—
20	C₂×C₂²⋊C₈×C₁₀₇	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊C₈×C₁₀₇	C₂²	1	2	yes	—
22	C₂×C₂²⋊C₈×C₁₀₇	C₂²	1	1	yes	characteristic
23	C₂×#97×C₁₀₇	C₂²	1	2	yes	—
24	C₂×#97×C₁₀₇	C₂²	1	2	yes	—
25	#390×C₁₀₇	C₄	1	1	yes	characteristic
26	#389×C₁₀₇	C₄	1	1	yes	characteristic
27	#388×C₁₀₇	C₄	1	2	yes	—
28	#386×C₁₀₇	C₄	1	2	yes	—
29	#380×C₁₀₇	C₄	1	1	yes	characteristic
30	C₄×C₄⋊C₄×C₁₀₇	C₂²	1	1	yes	characteristic
31	C₄×C₂²⋊C₄×C₁₀₇	C₂²	1	2	yes	—
32	#336×C₁₀₇	C₂²	1	2	yes	—
33	#336×C₁₀₇	C₂²	1	2	yes	—
34	#336×C₁₀₇	C₂²	1	2	yes	—
35	#336×C₁₀₇	C₂²	1	2	yes	—
36	#336×C₁₀₇	C₂²	1	1	yes	characteristic
37	#336×C₁₀₇	C₂²	1	1	yes	characteristic
38	C₂²×D₄×C₁₀₇	C₂×C₄	1	2	yes	—
39	C₂²×D₄×C₁₀₇	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₀₇	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₄×C₁₀₇	C₂×C₄	1	1	yes	characteristic
42	C₂³×C₄×C₁₀₇	C₂³	1	2	yes	—
43	C₂³×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
44	C₂×M₁₆×C₁₀₇	—	2	4	no	—
45	C₂×M₁₆×C₁₀₇	—	2	4	no	—
46	C₂×M₁₆×C₁₀₇	—	4	2	no	—
47	C₂²×C₈×C₁₀₇	—	2	4	no	—
48	C₂²×C₈×C₁₀₇	—	2	4	no	—
49	C₂²×C₈×C₁₀₇	—	4	2	no	—
50	C₂²×C₈×C₁₀₇	C₂³	1	2	yes	—
51	C₂²×C₈×C₁₀₇	C₂³	1	2	yes	—
52	C₂²×C₈×C₁₀₇	C₂³	1	2	yes	—
53	C₂²×C₈×C₁₀₇	C₂³	1	2	yes	—
54	#121×C₁₀₇	—	2	4	no	—
55	C₄×D₄×C₁₀₇	—	2	4	no	—
56	C₄×D₄×C₁₀₇	—	2	4	no	—
57	C₄×D₄×C₁₀₇	—	4	2	no	—
58	C₂×C₄⋊C₄×C₁₀₇	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₁₀₇	C₂×C₄	1	2	yes	—
60	C₂×C₄⋊C₄×C₁₀₇	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₁₀₇	C₂×C₄	1	1	yes	characteristic
62	C₂×C₂²⋊C₄×C₁₀₇	C₂×C₄	1	2	yes	—
63	C₂×C₂²⋊C₄×C₁₀₇	C₂×C₄	1	2	yes	—
64	C₂×C₂²⋊C₄×C₁₀₇	C₂×C₄	1	2	yes	—
65	C₂×C₂²⋊C₄×C₁₀₇	C₂×C₄	1	2	yes	—
66	C₂×C₂²⋊C₄×C₁₀₇	C₂×C₄	1	2	yes	—
67	C₂×C₄²×C₁₀₇	—	4	2	no	—
68	C₂×C₄²×C₁₀₇	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄²×C₁₀₇	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄²×C₁₀₇	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₁₀₇	C₂³	1	2	yes	—
72	C₂×C₄²×C₁₀₇	C₂³	1	1	yes	characteristic
73	C₄⋊C₈×C₁₀₇	—	2	4	no	—
74	C₂²⋊C₈×C₁₀₇	—	2	2	no	—
75	C₂²⋊C₈×C₁₀₇	—	2	4	no	—
76	C₂²⋊C₈×C₁₀₇	—	2	4	no	—
77	C₂²⋊C₈×C₁₀₇	—	4	2	no	—
78	C₂²⋊C₈×C₁₀₇	D₄	1	4	yes	complemented
79	#97×C₁₀₇	—	2	4	no	—
80	#97×C₁₀₇	—	4	2	no	—
81	#95×C₁₀₇	C₂×C₄	1	2	yes	—
82	#95×C₁₀₇	C₂×C₄	1	2	yes	—
83	#95×C₁₀₇	C₂×C₄	1	2	yes	—
84	C₂⁴×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
85	C₂⁴×C₁₀₇	C₂²×C₄	1	2	yes	—
86	C₂×D₄×C₁₀₇	—	2	4	no	—
87	C₂×D₄×C₁₀₇	—	2	4	no	—
88	C₂×D₄×C₁₀₇	—	4	1	no	—
89	C₂×D₄×C₁₀₇	—	4	1	no	—
90	C₂×D₄×C₁₀₇	—	4	2	no	—
91	C₂×D₄×C₁₀₇	M₁₆	1	4	yes	complemented
92	C₂²×C₄×C₁₀₇	—	2	2	no	—
93	C₂²×C₄×C₁₀₇	—	2	2	no	—
94	C₂²×C₄×C₁₀₇	—	2	2	no	—
95	C₂²×C₄×C₁₀₇	—	2	2	no	—
96	C₂²×C₄×C₁₀₇	—	2	2	no	—
97	C₂²×C₄×C₁₀₇	—	2	2	no	—
98	C₂²×C₄×C₁₀₇	—	2	2	no	—
99	C₂²×C₄×C₁₀₇	—	2	2	no	—
100	C₂²×C₄×C₁₀₇	—	2	2	no	—
101	C₂²×C₄×C₁₀₇	—	4	1	no	—
102	C₂²×C₄×C₁₀₇	—	4	1	no	—
103	C₂²×C₄×C₁₀₇	—	4	1	no	—
104	C₂²×C₄×C₁₀₇	—	4	1	no	—
105	C₂²×C₄×C₁₀₇	—	4	1	no	—
106	C₂²×C₄×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
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	2	yes	—
110	C₂²×C₄×C₁₀₇	C₂²×C₄	1	2	yes	—
111	C₂²×C₄×C₁₀₇	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₀₇	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₁₀₇	#41	1	2	yes	—
116	C₂²×C₄×C₁₀₇	C₂⁴	1	1	yes	characteristic
117	M₁₆×C₁₀₇	—	4	8	no	—
118	C₂×C₈×C₁₀₇	—	2	2	no	—
119	C₂×C₈×C₁₀₇	—	2	2	no	—
120	C₂×C₈×C₁₀₇	—	2	2	no	—
121	C₂×C₈×C₁₀₇	—	2	2	no	—
122	C₂×C₈×C₁₀₇	—	2	2	no	—
123	C₂×C₈×C₁₀₇	—	2	2	no	—
124	C₂×C₈×C₁₀₇	—	2	2	no	—
125	C₂×C₈×C₁₀₇	—	2	2	no	—
126	C₂×C₈×C₁₀₇	—	2	2	no	—
127	C₂×C₈×C₁₀₇	—	2	2	no	—
128	C₂×C₈×C₁₀₇	—	4	8	no	—
129	C₂×C₈×C₁₀₇	C₂×D₄	1	4	yes	—
130	C₂×C₈×C₁₀₇	#41	1	4	yes	—
131	C₄⋊C₄×C₁₀₇	—	2	4	no	—
132	C₄⋊C₄×C₁₀₇	—	2	2	no	—
133	C₄⋊C₄×C₁₀₇	—	4	1	no	—
134	C₄⋊C₄×C₁₀₇	—	4	1	no	—
135	C₂²⋊C₄×C₁₀₇	—	2	4	no	—
136	C₂²⋊C₄×C₁₀₇	—	2	4	no	—
137	C₂²⋊C₄×C₁₀₇	—	2	4	no	—
138	C₂²⋊C₄×C₁₀₇	—	4	2	no	—
139	C₂²⋊C₄×C₁₀₇	—	4	2	no	—
140	C₄²×C₁₀₇	—	2	2	no	—
141	C₄²×C₁₀₇	—	2	2	no	—
142	C₄²×C₁₀₇	—	2	2	no	—
143	C₄²×C₁₀₇	—	2	2	no	—
144	C₄²×C₁₀₇	—	4	1	no	—
145	C₄²×C₁₀₇	—	4	1	no	—
146	C₂³×C₁₀₇	—	2	2	no	—
147	C₂³×C₁₀₇	—	2	1	no	—
148	C₂³×C₁₀₇	—	2	2	no	—
149	C₂³×C₁₀₇	—	2	2	no	—
150	C₂³×C₁₀₇	—	2	1	no	—
151	C₂³×C₁₀₇	—	2	1	no	—
152	C₂³×C₁₀₇	—	2	2	no	—
153	C₂³×C₁₀₇	—	2	1	no	—
154	C₂³×C₁₀₇	—	2	1	no	—
155	C₂³×C₁₀₇	—	2	1	no	—
156	C₂³×C₁₀₇	—	2	2	no	—
157	C₂³×C₁₀₇	—	2	2	no	—
158	C₂³×C₁₀₇	C₄×D₄	1	2	yes	—
159	C₂³×C₁₀₇	C₂×M₁₆	1	4	yes	—
160	C₂³×C₁₀₇	C₂³×C₄	1	1	yes	characteristic
161	D₄×C₁₀₇	—	4	4	no	—
162	D₄×C₁₀₇	—	4	8	no	—
163	C₂×C₄×C₁₀₇	—	2	1	no	—
164	C₂×C₄×C₁₀₇	—	2	1	no	—
165	C₂×C₄×C₁₀₇	—	2	1	no	—
166	C₂×C₄×C₁₀₇	—	2	1	no	—
167	C₂×C₄×C₁₀₇	—	2	4	no	—
168	C₂×C₄×C₁₀₇	—	2	4	no	—
169	C₂×C₄×C₁₀₇	—	2	2	no	—
170	C₂×C₄×C₁₀₇	—	2	2	no	—
171	C₂×C₄×C₁₀₇	—	2	2	no	—
172	C₂×C₄×C₁₀₇	—	2	2	no	—
173	C₂×C₄×C₁₀₇	—	2	1	no	—
174	C₂×C₄×C₁₀₇	—	2	1	no	—
175	C₂×C₄×C₁₀₇	—	2	1	no	—
176	C₂×C₄×C₁₀₇	—	2	2	no	—
177	C₂×C₄×C₁₀₇	—	2	1	no	—
178	C₂×C₄×C₁₀₇	—	2	2	no	—
179	C₂×C₄×C₁₀₇	—	2	1	no	—
180	C₂×C₄×C₁₀₇	—	2	2	no	—
181	C₂×C₄×C₁₀₇	—	2	2	no	—
182	C₂×C₄×C₁₀₇	—	2	1	no	—
183	C₂×C₄×C₁₀₇	—	2	1	no	—
184	C₂×C₄×C₁₀₇	—	2	1	no	—
185	C₂×C₄×C₁₀₇	—	2	1	no	—
186	C₂×C₄×C₁₀₇	—	2	2	no	—
187	C₂×C₄×C₁₀₇	—	4	4	no	—
188	C₂×C₄×C₁₀₇	—	4	4	no	—
189	C₂×C₄×C₁₀₇	—	4	2	no	—
190	C₂×C₄×C₁₀₇	—	4	2	no	—
191	C₂×C₄×C₁₀₇	—	4	2	no	—
192	C₂×C₄×C₁₀₇	—	4	2	no	—
193	C₂×C₄×C₁₀₇	C₄×D₄	1	2	yes	—
194	C₂×C₄×C₁₀₇	C₂×M₁₆	1	2	yes	—
195	C₂×C₄×C₁₀₇	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₁₀₇	C₂×#41	1	2	yes	—
197	C₂×C₄×C₁₀₇	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₁₀₇	H(5,𝔽₂)	1	2	yes	—
199	C₈×C₁₀₇	—	2	4	no	—
200	C₈×C₁₀₇	—	2	4	no	—
201	C₈×C₁₀₇	—	4	2	no	—
202	C₈×C₁₀₇	—	4	2	no	—
203	C₂²×C₁₀₇	—	2	2	no	—
204	C₂²×C₁₀₇	—	2	2	no	—
205	C₂²×C₁₀₇	—	2	2	no	—
206	C₂²×C₁₀₇	—	2	4	no	—
207	C₂²×C₁₀₇	—	2	4	no	—
208	C₂²×C₁₀₇	—	2	4	no	—
209	C₂²×C₁₀₇	—	4	2	no	—
210	C₂²×C₁₀₇	—	4	2	no	—
211	C₂²×C₁₀₇	—	4	1	no	—
212	C₂²×C₁₀₇	—	4	2	no	—
213	C₂²×C₁₀₇	—	4	1	no	—
214	C₂²×C₁₀₇	—	4	1	no	—
215	C₂²×C₁₀₇	—	4	1	no	—
216	C₂²×C₁₀₇	—	4	2	no	—
217	C₂²×C₁₀₇	C₂×C₄×D₄	1	1	yes	characteristic
218	C₂²×C₁₀₇	C₄×#41	1	1	yes	characteristic
219	C₂²×C₁₀₇	#518	1	1	yes	characteristic
220	C₂²×C₁₀₇	C₂²×M₁₆	1	1	yes	characteristic
221	C₂²×C₁₀₇	#568	1	1	yes	characteristic
222	C₂²×C₁₀₇	#568	1	1	yes	characteristic
223	C₂²×C₁₀₇	#568	1	1	yes	characteristic
224	C₄×C₁₀₇	—	2	2	no	—
225	C₄×C₁₀₇	—	2	2	no	—
226	C₄×C₁₀₇	—	4	2	no	—
227	C₄×C₁₀₇	—	4	2	no	—
228	C₄×C₁₀₇	—	4	2	no	—
229	C₄×C₁₀₇	—	4	1	no	—
230	C₄×C₁₀₇	—	4	1	no	—
231	C₄×C₁₀₇	—	4	1	no	—
232	C₄×C₁₀₇	#546	1	2	yes	—
233	C₄×C₁₀₇	#553	1	2	yes	—
234	#23119	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
235	C₂×C₁₀₇	—	4	2	no	—
236	C₂×C₁₀₇	—	4	4	no	—
237	C₂×C₁₀₇	#2364	1	1	yes	characteristic
238	C₂×C₁₀₇	#2932	1	1	yes	characteristic
239	C₂×C₁₀₇	D₄×M₁₆	1	1	yes	characteristic
240	C₂×C₁₀₇	#2967	1	1	yes	characteristic
241	C₂×C₁₀₇	#2970	1	1	yes	characteristic
242	C₂×C₁₀₇	#2973	1	1	yes	characteristic
243	C₂×C₁₀₇	#2978	1	1	yes	characteristic
244	C₂×#435	C₂×C₁₀₇	1	2	yes	complemented
245	C₄×#121	C₂×C₁₀₇	1	1	yes	characteristic
246	#1924	C₂×C₁₀₇	1	2	yes	complemented
247	#1917	C₂×C₁₀₇	1	2	yes	complemented
248	#1870	C₂×C₁₀₇	1	2	yes	complemented
249	#1869	C₂×C₁₀₇	1	2	yes	complemented
250	#1752	C₂×C₁₀₇	1	2	yes	complemented
251	#1749	C₂×C₁₀₇	1	1	yes	characteristic, complemented
252	#1728	C₂×C₁₀₇	1	1	yes	characteristic, complemented
253	C₁₀₇	#23119	1	1	yes	characteristic, direct product factor, Sylow
254	C₂²×M₁₆	C₂²×C₁₀₇	1	2	yes	—
255	C₂³×C₈	C₂²×C₁₀₇	1	2	yes	—
256	C₂×#121	C₄×C₁₀₇	1	1	yes	characteristic
257	C₂×C₄×D₄	C₂²×C₁₀₇	1	2	yes	—
258	C₂×C₄×D₄	C₂²×C₁₀₇	1	1	yes	characteristic
259	C₂²×C₄²	C₂²×C₁₀₇	1	1	yes	characteristic
260	#435	—	2	8	no	—
261	C₂×C₄⋊C₈	C₂²×C₁₀₇	1	2	yes	—
262	C₂×C₂²⋊C₈	C₂²×C₁₀₇	1	2	yes	—
263	C₂×C₂²⋊C₈	C₂²×C₁₀₇	1	2	yes	—
264	C₂×C₂²⋊C₈	C₂²×C₁₀₇	1	1	yes	characteristic
265	C₂×C₂²⋊C₈	C₂²×C₁₀₇	1	2	yes	—
266	C₂×C₂²⋊C₈	C₂²×C₁₀₇	1	1	yes	characteristic
267	C₂×#97	C₂²×C₁₀₇	1	2	yes	—
268	C₂×#97	C₂²×C₁₀₇	1	2	yes	—
269	#390	C₄×C₁₀₇	1	1	yes	characteristic
270	#389	C₄×C₁₀₇	1	1	yes	characteristic
271	#388	C₄×C₁₀₇	1	2	yes	—
272	#386	C₄×C₁₀₇	1	2	yes	—
273	#380	C₄×C₁₀₇	1	1	yes	characteristic
274	C₄×C₄⋊C₄	C₂²×C₁₀₇	1	1	yes	characteristic
275	C₄×C₂²⋊C₄	C₂²×C₁₀₇	1	2	yes	—
276	#336	C₂²×C₁₀₇	1	2	yes	—
277	#336	C₂²×C₁₀₇	1	2	yes	—
278	#336	C₂²×C₁₀₇	1	2	yes	—
279	#336	C₂²×C₁₀₇	1	2	yes	—
280	#336	C₂²×C₁₀₇	1	1	yes	characteristic
281	#336	C₂²×C₁₀₇	1	1	yes	characteristic
282	C₂²×D₄	C₂×C₄×C₁₀₇	1	2	yes	—
283	C₂²×D₄	C₂×C₄×C₁₀₇	1	1	yes	characteristic
284	C₂³×C₄	C₂×C₄×C₁₀₇	1	1	yes	characteristic
285	C₂³×C₄	C₂×C₄×C₁₀₇	1	1	yes	characteristic
286	C₂³×C₄	C₂³×C₁₀₇	1	2	yes	—
287	C₂³×C₄	C₂³×C₁₀₇	1	1	yes	characteristic
288	C₂×M₁₆	—	2	4	no	—
289	C₂×M₁₆	—	2	4	no	—
290	C₂×M₁₆	—	4	2	no	—
291	C₂²×C₈	—	2	4	no	—
292	C₂²×C₈	—	2	4	no	—
293	C₂²×C₈	—	4	2	no	—
294	C₂²×C₈	C₂³×C₁₀₇	1	2	yes	—
295	C₂²×C₈	C₂³×C₁₀₇	1	2	yes	—
296	C₂²×C₈	C₂³×C₁₀₇	1	2	yes	—
297	C₂²×C₈	C₂³×C₁₀₇	1	2	yes	—
298	#121	—	2	4	no	—
299	C₄×D₄	—	2	4	no	—
300	C₄×D₄	—	2	4	no	—
301	C₄×D₄	—	4	2	no	—
302	C₂×C₄⋊C₄	C₂×C₄×C₁₀₇	1	2	yes	—
303	C₂×C₄⋊C₄	C₂×C₄×C₁₀₇	1	1	yes	characteristic
304	C₂×C₄⋊C₄	C₂×C₄×C₁₀₇	1	1	yes	characteristic
305	C₂×C₄⋊C₄	C₂×C₄×C₁₀₇	1	1	yes	characteristic
306	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₇	1	2	yes	—
307	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₇	1	2	yes	—
308	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₇	1	2	yes	—
309	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₇	1	2	yes	—
310	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₇	1	2	yes	—
311	C₂×C₄²	—	4	2	no	—
312	C₂×C₄²	C₂×C₄×C₁₀₇	1	1	yes	characteristic
313	C₂×C₄²	C₂×C₄×C₁₀₇	1	1	yes	characteristic
314	C₂×C₄²	C₂³×C₁₀₇	1	1	yes	characteristic
315	C₂×C₄²	C₂³×C₁₀₇	1	2	yes	—
316	C₂×C₄²	C₂³×C₁₀₇	1	1	yes	characteristic
317	C₄⋊C₈	—	2	4	no	—
318	C₂²⋊C₈	—	2	2	no	—
319	C₂²⋊C₈	—	2	4	no	—
320	C₂²⋊C₈	—	2	4	no	—
321	C₂²⋊C₈	—	4	2	no	—
322	C₂²⋊C₈	D₄×C₁₀₇	1	4	yes	complemented
323	#97	—	2	4	no	—
324	#97	—	4	2	no	—
325	#95	C₂×C₄×C₁₀₇	1	2	yes	—
326	#95	C₂×C₄×C₁₀₇	1	2	yes	—
327	#95	C₂×C₄×C₁₀₇	1	2	yes	—
328	C₂⁴	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
329	C₂⁴	C₂²×C₄×C₁₀₇	1	2	yes	—
330	C₂×D₄	—	2	4	no	—
331	C₂×D₄	—	2	4	no	—
332	C₂×D₄	—	4	1	no	—
333	C₂×D₄	—	4	1	no	—
334	C₂×D₄	—	4	2	no	—
335	C₂×D₄	M₁₆×C₁₀₇	1	4	yes	complemented
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	4	1	no	—
346	C₂²×C₄	—	4	1	no	—
347	C₂²×C₄	—	4	1	no	—
348	C₂²×C₄	—	4	1	no	—
349	C₂²×C₄	—	4	1	no	—
350	C₂²×C₄	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
351	C₂²×C₄	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
352	C₂²×C₄	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
353	C₂²×C₄	C₂²×C₄×C₁₀₇	1	2	yes	—
354	C₂²×C₄	C₂²×C₄×C₁₀₇	1	2	yes	—
355	C₂²×C₄	C₂²×C₄×C₁₀₇	1	2	yes	—
356	C₂²×C₄	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
357	C₂²×C₄	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
358	C₂²×C₄	C₂×D₄×C₁₀₇	1	2	yes	—
359	C₂²×C₄	#41×C₁₀₇	1	2	yes	—
360	C₂²×C₄	C₂⁴×C₁₀₇	1	1	yes	characteristic
361	M₁₆	—	4	8	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	4	8	no	—
373	C₂×C₈	C₂×D₄×C₁₀₇	1	4	yes	—
374	C₂×C₈	#41×C₁₀₇	1	4	yes	—
375	C₄⋊C₄	—	2	4	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	4	1	no	—
378	C₄⋊C₄	—	4	1	no	—
379	C₂²⋊C₄	—	2	4	no	—
380	C₂²⋊C₄	—	2	4	no	—
381	C₂²⋊C₄	—	2	4	no	—
382	C₂²⋊C₄	—	4	2	no	—
383	C₂²⋊C₄	—	4	2	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	2	2	no	—
386	C₄²	—	2	2	no	—
387	C₄²	—	2	2	no	—
388	C₄²	—	4	1	no	—
389	C₄²	—	4	1	no	—
390	C₂³	—	2	2	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	2	1	no	—
393	C₂³	—	2	2	no	—
394	C₂³	—	2	1	no	—
395	C₂³	—	2	1	no	—
396	C₂³	—	2	2	no	—
397	C₂³	—	2	1	no	—
398	C₂³	—	2	1	no	—
399	C₂³	—	2	1	no	—
400	C₂³	—	2	2	no	—
401	C₂³	—	2	2	no	—
402	C₂³	C₄×D₄×C₁₀₇	1	2	yes	—
403	C₂³	C₂×M₁₆×C₁₀₇	1	4	yes	—
404	C₂³	C₂³×C₄×C₁₀₇	1	1	yes	characteristic
405	D₄	—	4	4	no	—
406	D₄	—	4	8	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	4	4	no	—
432	C₂×C₄	—	4	4	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	C₄×D₄×C₁₀₇	1	2	yes	—
438	C₂×C₄	C₂×M₁₆×C₁₀₇	1	2	yes	—
439	C₂×C₄	C₂²×D₄×C₁₀₇	1	1	yes	characteristic
440	C₂×C₄	C₂×#41×C₁₀₇	1	2	yes	—
441	C₂×C₄	C₂×#41×C₁₀₇	1	1	yes	characteristic
442	C₂×C₄	H(5,𝔽₂)×C₁₀₇	1	2	yes	—
443	C₈	—	2	4	no	—
444	C₈	—	2	4	no	—
445	C₈	—	4	2	no	—
446	C₈	—	4	2	no	—
447	C₂²	—	2	2	no	—
448	C₂²	—	2	2	no	—
449	C₂²	—	2	4	no	—
450	C₂²	—	2	4	no	—
451	C₂²	—	2	4	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	4	2	no	—
454	C₂²	—	4	1	no	—
455	C₂²	—	4	2	no	—
456	C₂²	—	4	1	no	—
457	C₂²	—	4	1	no	—
458	C₂²	—	4	1	no	—
459	C₂²	—	4	2	no	—
460	C₂²	—	4	2	no	—
461	C₂²	C₂×C₄×D₄×C₁₀₇	1	1	yes	characteristic
462	C₂²	C₄×#41×C₁₀₇	1	1	yes	characteristic
463	C₂²	#518×C₁₀₇	1	1	yes	characteristic
464	C₂²	C₂²×M₁₆×C₁₀₇	1	1	yes	characteristic
465	C₂²	#568×C₁₀₇	1	1	yes	characteristic
466	C₂²	#568×C₁₀₇	1	1	yes	characteristic
467	C₂²	#568×C₁₀₇	1	1	yes	characteristic
468	C₄	—	2	2	no	—
469	C₄	—	2	2	no	—
470	C₄	—	4	2	no	—
471	C₄	—	4	2	no	—
472	C₄	—	4	1	no	—
473	C₄	—	4	1	no	—
474	C₄	—	4	1	no	—
475	C₄	—	4	2	no	—
476	C₄	#546×C₁₀₇	1	2	yes	—
477	C₄	#553×C₁₀₇	1	2	yes	—
478	C₂	—	4	2	no	—
479	C₂	—	4	4	no	—
480	C₂	C₁₀₇×#2364	1	1	yes	characteristic
481	C₂	C₁₀₇×#2932	1	1	yes	characteristic
482	C₂	D₄×M₁₆×C₁₀₇	1	1	yes	characteristic
483	C₂	C₁₀₇×#2967	1	1	yes	characteristic
484	C₂	C₁₀₇×#2970	1	1	yes	characteristic
485	C₂	C₁₀₇×#2973	1	1	yes	characteristic
486	C₂	C₁₀₇×#2978	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₀₇	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₀₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₇
socle	C₂³×C₁₀₇	C₂³×C₄
prime radical	C₂×#121×C₁₀₇	C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₀₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#435×C₁₀₇	C₂	semidirect
3. C₁₀₇×#1924	C₂	semidirect
4. C₁₀₇×#1917	C₂	semidirect
5. C₁₀₇×#1870	C₂	semidirect
6. C₁₀₇×#1869	C₂	semidirect
7. C₁₀₇×#1752	C₂	semidirect
8. C₁₀₇×#1749	C₂	semidirect
9. C₁₀₇×#1728	C₂	semidirect
78. C₂²⋊C₈×C₁₀₇	D₄	semidirect
91. C₂×D₄×C₁₀₇	M₁₆	semidirect
234. #23119	C₁₀₇	direct (N × H)
244. C₂×#435	C₂×C₁₀₇	semidirect
246. #1924	C₂×C₁₀₇	semidirect
247. #1917	C₂×C₁₀₇	semidirect
248. #1870	C₂×C₁₀₇	semidirect
249. #1869	C₂×C₁₀₇	semidirect
250. #1752	C₂×C₁₀₇	semidirect
251. #1749	C₂×C₁₀₇	semidirect
252. #1728	C₂×C₁₀₇	semidirect
253. C₁₀₇	#23119	direct (N × H)
322. C₂²⋊C₈	D₄×C₁₀₇	semidirect
335. C₂×D₄	M₁₆×C₁₀₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#435×C₁₀₇	2
C₄×#121×C₁₀₇	2
C₁₀₇×#1924	2
C₁₀₇×#1917	2
C₁₀₇×#1870	2
C₁₀₇×#1869	2
C₁₀₇×#1752	2
C₁₀₇×#1749	2
C₁₀₇×#1728	2
#23119	107

Subgroups — C107×#23119 #41049083

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₇×#23119 #41049083