Subgroups — C₁₀₇×#24065 #41050029

Order 27392.

1072 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#533×C₁₀₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#485×C₁₀₇	C₂	1	2	yes	maximal
3	C₁₀₇×#2296	C₂	1	1	yes	maximal, characteristic
4	C₁₀₇×#2058	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₇×#2057	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₀₇×#2043	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₀₇×#2043	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₀₇×#1873	C₂	1	2	yes	maximal
9	C₁₀₇×#1865	C₂	1	2	yes	maximal, complemented
10	C₁₀₇×#1863	C₂	1	2	yes	maximal, complemented
11	C₁₀₇×#1817	C₂	1	1	yes	maximal, characteristic
12	#533×C₁₀₇	—	2	8	no	—
13	C₂×C₄⋊Q₈×C₁₀₇	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Q₈×C₁₀₇	C₂²	1	1	yes	characteristic
15	C₂×#125×C₁₀₇	—	2	1	no	—
16	C₂×C₂²⋊Q₈×C₁₀₇	—	2	1	no	—
17	C₂×C₂²⋊Q₈×C₁₀₇	C₂²	1	2	yes	—
18	C₂×C₄×Q₈×C₁₀₇	—	2	1	no	—
19	C₂×C₄×Q₈×C₁₀₇	C₂²	1	2	yes	—
20	C₂×#117×C₁₀₇	—	2	1	no	—
21	C₂×#117×C₁₀₇	C₂²	1	1	yes	characteristic
22	C₂×#117×C₁₀₇	C₂²	1	1	yes	characteristic
23	C₂²×C₄²×C₁₀₇	C₂²	1	1	yes	characteristic
24	#485×C₁₀₇	—	2	8	no	—
25	C₂×#107×C₁₀₇	C₂²	1	2	yes	—
26	C₂×#106×C₁₀₇	C₂²	1	2	yes	—
27	C₂×#103×C₁₀₇	C₂²	1	2	yes	—
28	C₂×#103×C₁₀₇	C₂²	1	2	yes	—
29	C₂×#103×C₁₀₇	C₂²	1	2	yes	—
30	C₂×#103×C₁₀₇	C₂²	1	2	yes	—
31	C₂×C₂²⋊C₈×C₁₀₇	C₂²	1	2	yes	—
32	#389×C₁₀₇	C₂²	1	1	yes	characteristic
33	#389×C₁₀₇	C₂²	1	1	yes	characteristic
34	#389×C₁₀₇	C₂²	1	1	yes	characteristic
35	#389×C₁₀₇	C₂²	1	1	yes	characteristic
36	#385×C₁₀₇	—	2	1	no	—
37	#385×C₁₀₇	—	2	1	no	—
38	C₄×C₄⋊C₄×C₁₀₇	—	2	1	no	—
39	C₄×C₄⋊C₄×C₁₀₇	—	2	1	no	—
40	#340×C₁₀₇	C₂²	1	2	yes	—
41	#340×C₁₀₇	C₂²	1	2	yes	—
42	#336×C₁₀₇	C₂²	1	2	yes	—
43	#336×C₁₀₇	C₂²	1	1	yes	characteristic
44	#336×C₁₀₇	C₂²	1	1	yes	characteristic
45	C₂²×Q₈×C₁₀₇	—	2	1	no	—
46	C₂²×Q₈×C₁₀₇	C₂³	1	2	yes	—
47	C₂³×C₄×C₁₀₇	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₀₇	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₀₇	C₂³	1	2	yes	—
51	C₂²×C₈×C₁₀₇	C₂³	1	2	yes	—
52	C₄⋊Q₈×C₁₀₇	—	2	4	no	—
53	C₄⋊Q₈×C₁₀₇	—	2	4	no	—
54	#125×C₁₀₇	—	2	8	no	—
55	C₂²⋊Q₈×C₁₀₇	—	2	8	no	—
56	C₂²⋊Q₈×C₁₀₇	—	2	4	no	—
57	C₂²⋊Q₈×C₁₀₇	D₄	1	8	yes	—
58	C₄×Q₈×C₁₀₇	—	2	8	no	—
59	C₄×Q₈×C₁₀₇	—	2	4	no	—
60	C₄×Q₈×C₁₀₇	—	2	4	no	—
61	#117×C₁₀₇	—	2	8	no	—
62	#117×C₁₀₇	—	2	2	no	—
63	#117×C₁₀₇	—	2	2	no	—
64	#117×C₁₀₇	—	2	4	no	—
65	C₂×C₄⋊C₄×C₁₀₇	—	2	1	no	—
66	C₂×C₄⋊C₄×C₁₀₇	—	2	1	no	—
67	C₂×C₄⋊C₄×C₁₀₇	—	2	1	no	—
68	C₂×C₄⋊C₄×C₁₀₇	—	2	2	no	—
69	C₂×C₄⋊C₄×C₁₀₇	—	2	2	no	—
70	C₂×C₄⋊C₄×C₁₀₇	—	2	1	no	—
71	C₂×C₄⋊C₄×C₁₀₇	—	2	1	no	—
72	C₂×C₄⋊C₄×C₁₀₇	—	2	1	no	—
73	C₂×C₄⋊C₄×C₁₀₇	—	2	1	no	—
74	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	2	yes	—
77	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
79	C₂×C₂²⋊C₄×C₁₀₇	—	2	1	no	—
80	C₂×C₂²⋊C₄×C₁₀₇	—	2	2	no	—
81	C₂×C₂²⋊C₄×C₁₀₇	—	2	1	no	—
82	C₂×C₄²×C₁₀₇	—	2	1	no	—
83	C₂×C₄²×C₁₀₇	—	2	4	no	—
84	C₂×C₄²×C₁₀₇	—	2	2	no	—
85	C₂×C₄²×C₁₀₇	—	2	1	no	—
86	C₂×C₄²×C₁₀₇	D₄	1	1	yes	characteristic
87	C₂×C₄²×C₁₀₇	D₄	1	1	yes	characteristic
88	C₂×C₄²×C₁₀₇	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₁₀₇	C₂³	1	1	yes	characteristic
90	#107×C₁₀₇	—	2	4	no	—
91	#106×C₁₀₇	—	2	4	no	—
92	#103×C₁₀₇	—	2	4	no	—
93	#103×C₁₀₇	—	2	4	no	—
94	#103×C₁₀₇	—	2	4	no	—
95	#103×C₁₀₇	—	2	4	no	—
96	C₂²⋊C₈×C₁₀₇	—	2	4	no	—
97	#95×C₁₀₇	—	2	1	no	—
98	#95×C₁₀₇	—	2	1	no	—
99	#95×C₁₀₇	—	2	1	no	—
100	#95×C₁₀₇	—	2	1	no	—
101	C₂⁴×C₁₀₇	C₂×D₄	1	1	yes	characteristic
102	C₂×Q₈×C₁₀₇	—	2	4	no	—
103	C₂×Q₈×C₁₀₇	—	2	2	no	—
104	C₂×Q₈×C₁₀₇	—	2	2	no	—
105	C₂×Q₈×C₁₀₇	—	2	2	no	—
106	C₂×Q₈×C₁₀₇	—	2	2	no	—
107	C₂×Q₈×C₁₀₇	—	2	2	no	—
108	C₂×Q₈×C₁₀₇	—	4	2	no	—
109	C₂×Q₈×C₁₀₇	—	4	2	no	—
110	C₂×Q₈×C₁₀₇	C₂×D₄	1	4	yes	—
111	C₂²×C₄×C₁₀₇	—	2	2	no	—
112	C₂²×C₄×C₁₀₇	—	2	2	no	—
113	C₂²×C₄×C₁₀₇	—	2	2	no	—
114	C₂²×C₄×C₁₀₇	—	2	1	no	—
115	C₂²×C₄×C₁₀₇	—	2	1	no	—
116	C₂²×C₄×C₁₀₇	—	2	2	no	—
117	C₂²×C₄×C₁₀₇	—	2	2	no	—
118	C₂²×C₄×C₁₀₇	—	2	1	no	—
119	C₂²×C₄×C₁₀₇	—	2	1	no	—
120	C₂²×C₄×C₁₀₇	—	2	2	no	—
121	C₂²×C₄×C₁₀₇	—	2	2	no	—
122	C₂²×C₄×C₁₀₇	—	2	2	no	—
123	C₂²×C₄×C₁₀₇	—	2	1	no	—
124	C₂²×C₄×C₁₀₇	—	2	1	no	—
125	C₂²×C₄×C₁₀₇	—	4	1	no	—
126	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₀₇	C₂×D₄	1	4	yes	—
129	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₀₇	C₂⁴	1	1	yes	characteristic
133	C₂×C₈×C₁₀₇	—	2	2	no	—
134	C₂×C₈×C₁₀₇	—	2	2	no	—
135	C₂×C₈×C₁₀₇	—	2	2	no	—
136	C₂×C₈×C₁₀₇	—	2	2	no	—
137	C₂×C₈×C₁₀₇	—	2	2	no	—
138	C₂×C₈×C₁₀₇	—	2	2	no	—
139	C₄⋊C₄×C₁₀₇	—	2	4	no	—
140	C₄⋊C₄×C₁₀₇	—	2	4	no	—
141	C₄⋊C₄×C₁₀₇	—	2	8	no	—
142	C₄⋊C₄×C₁₀₇	—	2	4	no	—
143	C₄⋊C₄×C₁₀₇	—	2	8	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	—	4	2	no	—
150	C₄⋊C₄×C₁₀₇	—	4	2	no	—
151	C₄⋊C₄×C₁₀₇	—	4	2	no	—
152	C₄⋊C₄×C₁₀₇	—	4	2	no	—
153	C₄⋊C₄×C₁₀₇	C₂×D₄	1	4	yes	—
154	C₄⋊C₄×C₁₀₇	#41	1	2	yes	—
155	C₄⋊C₄×C₁₀₇	#41	1	2	yes	—
156	C₂²⋊C₄×C₁₀₇	—	2	4	no	—
157	C₂²⋊C₄×C₁₀₇	—	2	8	no	—
158	C₂²⋊C₄×C₁₀₇	—	4	2	no	—
159	C₄²×C₁₀₇	—	2	4	no	—
160	C₄²×C₁₀₇	—	2	8	no	—
161	C₄²×C₁₀₇	—	2	2	no	—
162	C₄²×C₁₀₇	—	2	2	no	—
163	C₄²×C₁₀₇	—	2	2	no	—
164	C₄²×C₁₀₇	—	2	2	no	—
165	C₄²×C₁₀₇	—	4	2	no	—
166	C₂³×C₁₀₇	—	2	1	no	—
167	C₂³×C₁₀₇	—	2	1	no	—
168	C₂³×C₁₀₇	—	2	1	no	—
169	C₂³×C₁₀₇	—	2	1	no	—
170	C₂³×C₁₀₇	—	2	1	no	—
171	C₂³×C₁₀₇	—	2	1	no	—
172	C₂³×C₁₀₇	#120	1	2	yes	—
173	C₂³×C₁₀₇	C₂²×D₄	1	1	yes	characteristic
174	Q₈×C₁₀₇	—	2	4	no	—
175	Q₈×C₁₀₇	—	2	4	no	—
176	Q₈×C₁₀₇	—	4	8	no	—
177	Q₈×C₁₀₇	—	4	2	no	—
178	Q₈×C₁₀₇	—	4	2	no	—
179	C₂×C₄×C₁₀₇	—	2	8	no	—
180	C₂×C₄×C₁₀₇	—	2	1	no	—
181	C₂×C₄×C₁₀₇	—	2	1	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	1	no	—
187	C₂×C₄×C₁₀₇	—	2	1	no	—
188	C₂×C₄×C₁₀₇	—	2	4	no	—
189	C₂×C₄×C₁₀₇	—	2	4	no	—
190	C₂×C₄×C₁₀₇	—	2	1	no	—
191	C₂×C₄×C₁₀₇	—	2	4	no	—
192	C₂×C₄×C₁₀₇	—	2	4	no	—
193	C₂×C₄×C₁₀₇	—	2	2	no	—
194	C₂×C₄×C₁₀₇	—	2	2	no	—
195	C₂×C₄×C₁₀₇	—	2	1	no	—
196	C₂×C₄×C₁₀₇	—	2	1	no	—
197	C₂×C₄×C₁₀₇	—	4	4	no	—
198	C₂×C₄×C₁₀₇	—	4	2	no	—
199	C₂×C₄×C₁₀₇	—	4	2	no	—
200	C₂×C₄×C₁₀₇	—	4	1	no	—
201	C₂×C₄×C₁₀₇	—	4	2	no	—
202	C₂×C₄×C₁₀₇	—	4	1	no	—
203	C₂×C₄×C₁₀₇	—	4	1	no	—
204	C₂×C₄×C₁₀₇	—	4	1	no	—
205	C₂×C₄×C₁₀₇	—	4	2	no	—
206	C₂×C₄×C₁₀₇	—	4	1	no	—
207	C₂×C₄×C₁₀₇	—	4	1	no	—
208	C₂×C₄×C₁₀₇	—	4	1	no	—
209	C₂×C₄×C₁₀₇	—	4	1	no	—
210	C₂×C₄×C₁₀₇	—	4	1	no	—
211	C₂×C₄×C₁₀₇	—	4	1	no	—
212	C₂×C₄×C₁₀₇	#120	1	2	yes	—
213	C₂×C₄×C₁₀₇	#135	1	2	yes	—
214	C₂×C₄×C₁₀₇	#137	1	2	yes	—
215	C₂×C₄×C₁₀₇	#137	1	2	yes	—
216	C₂×C₄×C₁₀₇	C₂²×D₄	1	2	yes	—
217	C₂×C₄×C₁₀₇	C₂×#41	1	1	yes	characteristic
218	C₂×C₄×C₁₀₇	C₂×#41	1	1	yes	characteristic
219	C₂×C₄×C₁₀₇	2₋¹⁺⁴	1	2	yes	—
220	C₈×C₁₀₇	—	4	2	no	—
221	C₈×C₁₀₇	—	4	2	no	—
222	C₂²×C₁₀₇	—	2	2	no	—
223	C₂²×C₁₀₇	—	2	2	no	—
224	C₂²×C₁₀₇	—	2	2	no	—
225	C₂²×C₁₀₇	—	4	1	no	—
226	C₂²×C₁₀₇	—	4	1	no	—
227	C₂²×C₁₀₇	—	4	1	no	—
228	C₂²×C₁₀₇	—	4	1	no	—
229	C₂²×C₁₀₇	C₂×#120	1	1	yes	characteristic
230	C₂²×C₁₀₇	#525	1	1	yes	characteristic
231	C₂²×C₁₀₇	#536	1	1	yes	characteristic
232	C₂²×C₁₀₇	C₂×#135	1	1	yes	characteristic
233	C₂²×C₁₀₇	C₂×#137	1	1	yes	characteristic
234	C₂²×C₁₀₇	C₂×#137	1	1	yes	characteristic
235	C₂²×C₁₀₇	#575	1	1	yes	characteristic
236	C₄×C₁₀₇	—	2	2	no	—
237	C₄×C₁₀₇	—	2	2	no	—
238	C₄×C₁₀₇	—	2	2	no	—
239	C₄×C₁₀₇	—	2	2	no	—
240	C₄×C₁₀₇	—	4	2	no	—
241	C₄×C₁₀₇	—	4	2	no	—
242	C₄×C₁₀₇	—	4	4	no	—
243	C₄×C₁₀₇	—	4	1	no	—
244	C₄×C₁₀₇	—	4	4	no	—
245	C₄×C₁₀₇	—	8	1	no	—
246	C₄×C₁₀₇	—	8	1	no	—
247	C₄×C₁₀₇	#547	1	2	yes	—
248	C₄×C₁₀₇	#547	1	2	yes	—
249	#24065	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
250	C₂×C₁₀₇	—	4	2	no	—
251	C₂×C₁₀₇	#2406	1	1	yes	characteristic
252	C₂×C₁₀₇	#3002	1	1	yes	characteristic
253	C₂×C₁₀₇	#3004	1	1	yes	characteristic
254	C₂×C₁₀₇	#3107	1	1	yes	characteristic
255	C₂×C₁₀₇	#3116	1	1	yes	characteristic
256	C₂×C₁₀₇	#3231	1	1	yes	characteristic
257	C₂×C₁₀₇	#3237	1	1	yes	characteristic
258	C₂×#533	C₂×C₁₀₇	1	1	yes	characteristic
259	C₂×#485	C₂×C₁₀₇	1	2	yes	—
260	#2296	C₂×C₁₀₇	1	1	yes	characteristic
261	#2058	C₂×C₁₀₇	1	1	yes	characteristic, complemented
262	#2057	C₂×C₁₀₇	1	1	yes	characteristic, complemented
263	#2043	C₂×C₁₀₇	1	1	yes	characteristic, complemented
264	#2043	C₂×C₁₀₇	1	1	yes	characteristic, complemented
265	#1873	C₂×C₁₀₇	1	2	yes	—
266	#1865	C₂×C₁₀₇	1	2	yes	complemented
267	#1863	C₂×C₁₀₇	1	2	yes	complemented
268	#1817	C₂×C₁₀₇	1	1	yes	characteristic
269	C₁₀₇	#24065	1	1	yes	characteristic, direct product factor, Sylow
270	#533	—	2	8	no	—
271	C₂×C₄⋊Q₈	C₂²×C₁₀₇	1	1	yes	characteristic
272	C₂×C₄⋊Q₈	C₂²×C₁₀₇	1	1	yes	characteristic
273	C₂×#125	—	2	1	no	—
274	C₂×C₂²⋊Q₈	—	2	1	no	—
275	C₂×C₂²⋊Q₈	C₂²×C₁₀₇	1	2	yes	—
276	C₂×C₄×Q₈	—	2	1	no	—
277	C₂×C₄×Q₈	C₂²×C₁₀₇	1	2	yes	—
278	C₂×#117	—	2	1	no	—
279	C₂×#117	C₂²×C₁₀₇	1	1	yes	characteristic
280	C₂×#117	C₂²×C₁₀₇	1	1	yes	characteristic
281	C₂²×C₄²	C₂²×C₁₀₇	1	1	yes	characteristic
282	#485	—	2	8	no	—
283	C₂×#107	C₂²×C₁₀₇	1	2	yes	—
284	C₂×#106	C₂²×C₁₀₇	1	2	yes	—
285	C₂×#103	C₂²×C₁₀₇	1	2	yes	—
286	C₂×#103	C₂²×C₁₀₇	1	2	yes	—
287	C₂×#103	C₂²×C₁₀₇	1	2	yes	—
288	C₂×#103	C₂²×C₁₀₇	1	2	yes	—
289	C₂×C₂²⋊C₈	C₂²×C₁₀₇	1	2	yes	—
290	#389	C₂²×C₁₀₇	1	1	yes	characteristic
291	#389	C₂²×C₁₀₇	1	1	yes	characteristic
292	#389	C₂²×C₁₀₇	1	1	yes	characteristic
293	#389	C₂²×C₁₀₇	1	1	yes	characteristic
294	#385	—	2	1	no	—
295	#385	—	2	1	no	—
296	C₄×C₄⋊C₄	—	2	1	no	—
297	C₄×C₄⋊C₄	—	2	1	no	—
298	#340	C₂²×C₁₀₇	1	2	yes	—
299	#340	C₂²×C₁₀₇	1	2	yes	—
300	#336	C₂²×C₁₀₇	1	1	yes	characteristic
301	#336	C₂²×C₁₀₇	1	1	yes	characteristic
302	#336	C₂²×C₁₀₇	1	2	yes	—
303	C₂²×Q₈	—	2	1	no	—
304	C₂²×Q₈	C₂³×C₁₀₇	1	2	yes	—
305	C₂³×C₄	D₄×C₁₀₇	1	1	yes	characteristic
306	C₂³×C₄	D₄×C₁₀₇	1	1	yes	characteristic
307	C₂³×C₄	C₂³×C₁₀₇	1	1	yes	characteristic
308	C₂²×C₈	C₂³×C₁₀₇	1	2	yes	—
309	C₂²×C₈	C₂³×C₁₀₇	1	2	yes	—
310	C₄⋊Q₈	—	2	4	no	—
311	C₄⋊Q₈	—	2	4	no	—
312	#125	—	2	8	no	—
313	C₂²⋊Q₈	—	2	8	no	—
314	C₂²⋊Q₈	—	2	4	no	—
315	C₂²⋊Q₈	D₄×C₁₀₇	1	8	yes	—
316	C₄×Q₈	—	2	8	no	—
317	C₄×Q₈	—	2	4	no	—
318	C₄×Q₈	—	2	4	no	—
319	#117	—	2	8	no	—
320	#117	—	2	2	no	—
321	#117	—	2	2	no	—
322	#117	—	2	4	no	—
323	C₂×C₄⋊C₄	—	2	1	no	—
324	C₂×C₄⋊C₄	—	2	1	no	—
325	C₂×C₄⋊C₄	—	2	1	no	—
326	C₂×C₄⋊C₄	—	2	2	no	—
327	C₂×C₄⋊C₄	—	2	2	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	—	2	1	no	—
330	C₂×C₄⋊C₄	—	2	1	no	—
331	C₂×C₄⋊C₄	—	2	1	no	—
332	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	1	yes	characteristic
333	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	1	yes	characteristic
334	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	2	yes	—
335	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	1	yes	characteristic
336	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	1	yes	characteristic
337	C₂×C₂²⋊C₄	—	2	2	no	—
338	C₂×C₂²⋊C₄	—	2	1	no	—
339	C₂×C₂²⋊C₄	—	2	1	no	—
340	C₂×C₄²	—	2	2	no	—
341	C₂×C₄²	—	2	1	no	—
342	C₂×C₄²	—	2	4	no	—
343	C₂×C₄²	—	2	1	no	—
344	C₂×C₄²	D₄×C₁₀₇	1	1	yes	characteristic
345	C₂×C₄²	D₄×C₁₀₇	1	1	yes	characteristic
346	C₂×C₄²	C₂³×C₁₀₇	1	1	yes	characteristic
347	C₂×C₄²	C₂³×C₁₀₇	1	1	yes	characteristic
348	#107	—	2	4	no	—
349	#106	—	2	4	no	—
350	#103	—	2	4	no	—
351	#103	—	2	4	no	—
352	#103	—	2	4	no	—
353	#103	—	2	4	no	—
354	C₂²⋊C₈	—	2	4	no	—
355	#95	—	2	1	no	—
356	#95	—	2	1	no	—
357	#95	—	2	1	no	—
358	#95	—	2	1	no	—
359	C₂⁴	C₂×D₄×C₁₀₇	1	1	yes	characteristic
360	C₂×Q₈	—	2	4	no	—
361	C₂×Q₈	—	2	2	no	—
362	C₂×Q₈	—	2	2	no	—
363	C₂×Q₈	—	2	2	no	—
364	C₂×Q₈	—	2	2	no	—
365	C₂×Q₈	—	2	2	no	—
366	C₂×Q₈	—	4	2	no	—
367	C₂×Q₈	—	4	2	no	—
368	C₂×Q₈	C₂×D₄×C₁₀₇	1	4	yes	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	4	1	no	—
384	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
385	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
386	C₂²×C₄	C₂×D₄×C₁₀₇	1	4	yes	—
387	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
388	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
389	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
390	C₂²×C₄	C₂⁴×C₁₀₇	1	1	yes	characteristic
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₄⋊C₄	—	2	4	no	—
398	C₄⋊C₄	—	2	4	no	—
399	C₄⋊C₄	—	2	8	no	—
400	C₄⋊C₄	—	2	4	no	—
401	C₄⋊C₄	—	2	8	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	4	2	no	—
408	C₄⋊C₄	—	4	2	no	—
409	C₄⋊C₄	—	4	2	no	—
410	C₄⋊C₄	—	4	2	no	—
411	C₄⋊C₄	C₂×D₄×C₁₀₇	1	4	yes	—
412	C₄⋊C₄	#41×C₁₀₇	1	2	yes	—
413	C₄⋊C₄	#41×C₁₀₇	1	2	yes	—
414	C₂²⋊C₄	—	2	4	no	—
415	C₂²⋊C₄	—	2	8	no	—
416	C₂²⋊C₄	—	4	2	no	—
417	C₄²	—	2	8	no	—
418	C₄²	—	2	4	no	—
419	C₄²	—	2	2	no	—
420	C₄²	—	2	2	no	—
421	C₄²	—	2	2	no	—
422	C₄²	—	2	2	no	—
423	C₄²	—	4	2	no	—
424	C₂³	—	2	1	no	—
425	C₂³	—	2	1	no	—
426	C₂³	—	2	1	no	—
427	C₂³	—	2	1	no	—
428	C₂³	—	2	1	no	—
429	C₂³	—	2	1	no	—
430	C₂³	#120×C₁₀₇	1	2	yes	—
431	C₂³	C₂²×D₄×C₁₀₇	1	1	yes	characteristic
432	Q₈	—	2	4	no	—
433	Q₈	—	2	4	no	—
434	Q₈	—	4	8	no	—
435	Q₈	—	4	2	no	—
436	Q₈	—	4	2	no	—
437	C₂×C₄	—	2	8	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	4	4	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	—	4	1	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	#120×C₁₀₇	1	2	yes	—
471	C₂×C₄	#135×C₁₀₇	1	2	yes	—
472	C₂×C₄	#137×C₁₀₇	1	2	yes	—
473	C₂×C₄	#137×C₁₀₇	1	2	yes	—
474	C₂×C₄	C₂²×D₄×C₁₀₇	1	2	yes	—
475	C₂×C₄	C₂×#41×C₁₀₇	1	1	yes	characteristic
476	C₂×C₄	C₂×#41×C₁₀₇	1	1	yes	characteristic
477	C₂×C₄	2₋¹⁺⁴×C₁₀₇	1	2	yes	—
478	C₈	—	4	2	no	—
479	C₈	—	4	2	no	—
480	C₂²	—	2	2	no	—
481	C₂²	—	2	2	no	—
482	C₂²	—	2	2	no	—
483	C₂²	—	4	1	no	—
484	C₂²	—	4	1	no	—
485	C₂²	—	4	1	no	—
486	C₂²	—	4	1	no	—
487	C₂²	C₂×#120×C₁₀₇	1	1	yes	characteristic
488	C₂²	#525×C₁₀₇	1	1	yes	characteristic
489	C₂²	#536×C₁₀₇	1	1	yes	characteristic
490	C₂²	C₂×#135×C₁₀₇	1	1	yes	characteristic
491	C₂²	C₂×#137×C₁₀₇	1	1	yes	characteristic
492	C₂²	C₂×#137×C₁₀₇	1	1	yes	characteristic
493	C₂²	#575×C₁₀₇	1	1	yes	characteristic
494	C₄	—	2	2	no	—
495	C₄	—	2	2	no	—
496	C₄	—	2	2	no	—
497	C₄	—	2	2	no	—
498	C₄	—	4	4	no	—
499	C₄	—	4	1	no	—
500	C₄	—	4	4	no	—
501	C₄	—	4	2	no	—
502	C₄	—	4	2	no	—
503	C₄	—	8	1	no	—
504	C₄	—	8	1	no	—
505	C₄	#547×C₁₀₇	1	2	yes	—
506	C₄	#547×C₁₀₇	1	2	yes	—
507	C₂	—	4	2	no	—
508	C₂	C₁₀₇×#2406	1	1	yes	characteristic
509	C₂	C₁₀₇×#3002	1	1	yes	characteristic
510	C₂	C₁₀₇×#3004	1	1	yes	characteristic
511	C₂	C₁₀₇×#3107	1	1	yes	characteristic
512	C₂	C₁₀₇×#3116	1	1	yes	characteristic
513	C₂	C₁₀₇×#3231	1	1	yes	characteristic
514	C₂	C₁₀₇×#3237	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. C₁₀₇×#2058	C₂	semidirect
5. C₁₀₇×#2057	C₂	semidirect
6. C₁₀₇×#2043	C₂	semidirect
7. C₁₀₇×#2043	C₂	semidirect
9. C₁₀₇×#1865	C₂	semidirect
10. C₁₀₇×#1863	C₂	semidirect
249. #24065	C₁₀₇	direct (N × H)
261. #2058	C₂×C₁₀₇	semidirect
262. #2057	C₂×C₁₀₇	semidirect
263. #2043	C₂×C₁₀₇	semidirect
264. #2043	C₂×C₁₀₇	semidirect
266. #1865	C₂×C₁₀₇	semidirect
267. #1863	C₂×C₁₀₇	semidirect
269. C₁₀₇	#24065	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#533×C₁₀₇	2
C₂×#485×C₁₀₇	2
C₁₀₇×#2296	2
C₁₀₇×#2058	2
C₁₀₇×#2057	2
C₁₀₇×#2043	2
C₁₀₇×#1873	2
C₁₀₇×#1865	2
C₁₀₇×#1863	2
C₁₀₇×#1817	2
#24065	107

Subgroups — C107×#24065 #41050029

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₇×#24065 #41050029