Subgroups — C₁₀₇×#10742 #41036706

Order 27392.

1226 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#568×C₁₀₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#410×C₁₀₇	C₂	1	1	yes	maximal, characteristic
3	C₁₀₇×#2311	C₂	1	1	yes	maximal, characteristic
4	C₁₀₇×#1736	C₂	1	2	yes	maximal, complemented
5	C₂×H(3,ℤ/4)×C₁₀₇	C₂	1	2	yes	maximal, complemented
6	C₂²×#41×C₁₀₇	C₂²	1	1	yes	characteristic
7	#568×C₁₀₇	—	2	2	no	—
8	#568×C₁₀₇	—	2	4	no	—
9	#568×C₁₀₇	C₄	1	4	yes	complemented
10	C₂×#131×C₁₀₇	—	2	4	no	—
11	C₂²×M₁₆×C₁₀₇	—	2	2	no	—
12	C₂²×M₁₆×C₁₀₇	C₂²	1	2	yes	—
13	C₂×#117×C₁₀₇	C₂²	1	2	yes	—
14	C₂×#117×C₁₀₇	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₁₀₇	C₂²	1	1	yes	characteristic
16	#410×C₁₀₇	—	2	2	no	—
17	#410×C₁₀₇	C₄	1	4	yes	complemented
18	C₂×#99×C₁₀₇	—	2	2	no	—
19	#391×C₁₀₇	C₄	1	2	yes	complemented
20	#390×C₁₀₇	C₄	1	2	yes	complemented
21	#386×C₁₀₇	—	2	2	no	—
22	#380×C₁₀₇	—	2	2	no	—
23	#340×C₁₀₇	—	2	4	no	—
24	H(3,ℤ/4)×C₁₀₇	—	2	4	no	—
25	C₂×#41×C₁₀₇	—	2	2	no	—
26	C₂×#41×C₁₀₇	—	2	2	no	—
27	C₂×#41×C₁₀₇	—	2	2	no	—
28	C₂×#41×C₁₀₇	—	2	2	no	—
29	C₂×#41×C₁₀₇	C₂×C₄	1	2	yes	—
30	C₂×#41×C₁₀₇	C₂×C₄	1	2	yes	—
31	C₂×#41×C₁₀₇	D₄	1	2	yes	—
32	C₂×#41×C₁₀₇	Q₈	1	2	yes	—
33	C₂²×Q₈×C₁₀₇	C₂×C₄	1	1	yes	characteristic
34	C₂²×D₄×C₁₀₇	C₂×C₄	1	1	yes	characteristic
35	C₂²×D₄×C₁₀₇	D₄	1	2	yes	—
36	C₂³×C₄×C₁₀₇	—	2	1	no	—
37	C₂³×C₄×C₁₀₇	D₄	1	2	yes	—
38	C₂³×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
39	#131×C₁₀₇	—	2	16	no	—
40	#131×C₁₀₇	—	2	16	no	—
41	C₂×M₁₆×C₁₀₇	—	2	4	no	—
42	C₂×M₁₆×C₁₀₇	—	2	8	no	—
43	C₂×M₁₆×C₁₀₇	—	2	8	no	—
44	C₂×M₁₆×C₁₀₇	—	2	2	no	—
45	C₂×M₁₆×C₁₀₇	—	2	2	no	—
46	C₂×M₁₆×C₁₀₇	—	2	2	no	—
47	C₂×M₁₆×C₁₀₇	—	2	2	no	—
48	C₂×M₁₆×C₁₀₇	C₂×C₄	1	4	yes	—
49	C₂×M₁₆×C₁₀₇	D₄	1	4	yes	—
50	C₂²×C₈×C₁₀₇	—	2	4	no	—
51	C₂²×C₈×C₁₀₇	D₄	1	4	yes	—
52	#117×C₁₀₇	—	2	2	no	—
53	#117×C₁₀₇	—	2	2	no	—
54	#117×C₁₀₇	—	2	2	no	—
55	#117×C₁₀₇	—	2	2	no	—
56	#117×C₁₀₇	—	2	2	no	—
57	#117×C₁₀₇	C₂×C₄	1	4	yes	—
58	C₂×C₄⋊C₄×C₁₀₇	—	2	2	no	—
59	C₂×C₄⋊C₄×C₁₀₇	—	2	2	no	—
60	C₂×C₄⋊C₄×C₁₀₇	—	2	2	no	—
61	C₂×C₄⋊C₄×C₁₀₇	—	2	1	no	—
62	C₂×C₄⋊C₄×C₁₀₇	—	2	1	no	—
63	C₂×C₄⋊C₄×C₁₀₇	C₂×C₄	1	2	yes	—
64	C₂×C₂²⋊C₄×C₁₀₇	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₁₀₇	—	2	1	no	—
66	C₂×C₂²⋊C₄×C₁₀₇	—	2	4	no	—
67	C₂×C₄²×C₁₀₇	—	2	2	no	—
68	C₂×C₄²×C₁₀₇	C₂×C₄	1	2	yes	—
69	#99×C₁₀₇	—	2	8	no	—
70	#95×C₁₀₇	—	2	4	no	—
71	C₂⁴×C₁₀₇	C₂²⋊C₄	1	2	yes	—
72	C₂⁴×C₁₀₇	C₂×D₄	1	1	yes	characteristic
73	#41×C₁₀₇	—	2	4	no	—
74	#41×C₁₀₇	—	2	4	no	—
75	#41×C₁₀₇	—	2	4	no	—
76	#41×C₁₀₇	—	2	4	no	—
77	#41×C₁₀₇	—	2	4	no	—
78	#41×C₁₀₇	—	2	4	no	—
79	#41×C₁₀₇	—	2	4	no	—
80	#41×C₁₀₇	—	2	4	no	—
81	C₂×Q₈×C₁₀₇	—	2	2	no	—
82	C₂×Q₈×C₁₀₇	—	2	2	no	—
83	C₂×Q₈×C₁₀₇	C₄²	1	2	yes	—
84	C₂×Q₈×C₁₀₇	C₄⋊C₄	1	2	yes	—
85	C₂×D₄×C₁₀₇	—	2	4	no	—
86	C₂×D₄×C₁₀₇	—	2	4	no	—
87	C₂×D₄×C₁₀₇	—	2	2	no	—
88	C₂×D₄×C₁₀₇	—	2	2	no	—
89	C₂×D₄×C₁₀₇	C₄²	1	2	yes	—
90	C₂×D₄×C₁₀₇	C₂²⋊C₄	1	4	yes	—
91	C₂×D₄×C₁₀₇	C₄⋊C₄	1	4	yes	—
92	C₂×D₄×C₁₀₇	C₄⋊C₄	1	2	yes	—
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	—	4	2	no	—
100	C₂²×C₄×C₁₀₇	—	4	2	no	—
101	C₂²×C₄×C₁₀₇	—	8	2	no	—
102	C₂²×C₄×C₁₀₇	C₂²⋊C₄	1	2	yes	—
103	C₂²×C₄×C₁₀₇	C₂²⋊C₄	1	4	yes	—
104	C₂²×C₄×C₁₀₇	C₄⋊C₄	1	4	yes	—
105	C₂²×C₄×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₀₇	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₁₀₇	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₀₇	C₂×Q₈	1	1	yes	characteristic
113	C₂²×C₄×C₁₀₇	#41	1	2	yes	—
114	C₂²×C₄×C₁₀₇	#41	1	2	yes	—
115	M₁₆×C₁₀₇	—	2	16	no	—
116	M₁₆×C₁₀₇	—	2	4	no	—
117	M₁₆×C₁₀₇	—	2	4	no	—
118	M₁₆×C₁₀₇	—	2	4	no	—
119	M₁₆×C₁₀₇	—	2	4	no	—
120	C₂×C₈×C₁₀₇	—	2	16	no	—
121	C₂×C₈×C₁₀₇	—	2	4	no	—
122	C₂×C₈×C₁₀₇	—	2	4	no	—
123	C₂×C₈×C₁₀₇	C₂²⋊C₄	1	8	yes	complemented
124	C₄⋊C₄×C₁₀₇	—	2	4	no	—
125	C₄⋊C₄×C₁₀₇	—	2	4	no	—
126	C₄⋊C₄×C₁₀₇	—	4	1	no	—
127	C₄⋊C₄×C₁₀₇	—	4	1	no	—
128	C₄⋊C₄×C₁₀₇	—	4	2	no	—
129	C₄⋊C₄×C₁₀₇	—	4	1	no	—
130	C₄⋊C₄×C₁₀₇	—	4	1	no	—
131	C₂²⋊C₄×C₁₀₇	—	2	4	no	—
132	C₂²⋊C₄×C₁₀₇	—	4	2	no	—
133	C₂²⋊C₄×C₁₀₇	—	4	2	no	—
134	C₂²⋊C₄×C₁₀₇	—	8	4	no	—
135	C₄²×C₁₀₇	—	2	4	no	—
136	C₄²×C₁₀₇	—	2	4	no	—
137	C₄²×C₁₀₇	—	4	2	no	—
138	C₂³×C₁₀₇	—	2	2	no	—
139	C₂³×C₁₀₇	—	2	2	no	—
140	C₂³×C₁₀₇	—	4	1	no	—
141	C₂³×C₁₀₇	—	4	1	no	—
142	C₂³×C₁₀₇	—	4	2	no	—
143	C₂³×C₁₀₇	—	4	2	no	—
144	C₂³×C₁₀₇	#95	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	#121	1	2	yes	—
149	C₂³×C₁₀₇	#121	1	2	yes	—
150	Q₈×C₁₀₇	—	2	4	no	—
151	Q₈×C₁₀₇	—	2	4	no	—
152	D₄×C₁₀₇	—	2	8	no	—
153	D₄×C₁₀₇	—	2	8	no	—
154	D₄×C₁₀₇	—	2	4	no	—
155	D₄×C₁₀₇	—	2	4	no	—
156	C₂×C₄×C₁₀₇	—	2	2	no	—
157	C₂×C₄×C₁₀₇	—	2	2	no	—
158	C₂×C₄×C₁₀₇	—	2	4	no	—
159	C₂×C₄×C₁₀₇	—	2	4	no	—
160	C₂×C₄×C₁₀₇	—	2	4	no	—
161	C₂×C₄×C₁₀₇	—	2	4	no	—
162	C₂×C₄×C₁₀₇	—	4	2	no	—
163	C₂×C₄×C₁₀₇	—	4	4	no	—
164	C₂×C₄×C₁₀₇	—	4	2	no	—
165	C₂×C₄×C₁₀₇	—	4	2	no	—
166	C₂×C₄×C₁₀₇	—	4	4	no	—
167	C₂×C₄×C₁₀₇	—	4	2	no	—
168	C₂×C₄×C₁₀₇	—	8	2	no	—
169	C₂×C₄×C₁₀₇	—	8	2	no	—
170	C₂×C₄×C₁₀₇	—	8	4	no	—
171	C₂×C₄×C₁₀₇	#95	1	4	yes	—
172	C₂×C₄×C₁₀₇	C₂×C₄²	1	1	yes	characteristic
173	C₂×C₄×C₁₀₇	C₂×C₂²⋊C₄	1	2	yes	—
174	C₂×C₄×C₁₀₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
175	C₂×C₄×C₁₀₇	C₂×C₄⋊C₄	1	1	yes	characteristic
176	C₂×C₄×C₁₀₇	C₂×C₄⋊C₄	1	1	yes	characteristic
177	C₂×C₄×C₁₀₇	#117	1	2	yes	—
178	C₂×C₄×C₁₀₇	C₄×D₄	1	2	yes	—
179	C₂×C₄×C₁₀₇	C₄×D₄	1	2	yes	—
180	C₂×C₄×C₁₀₇	C₄×D₄	1	2	yes	—
181	C₂×C₄×C₁₀₇	C₄×D₄	1	2	yes	—
182	C₂×C₄×C₁₀₇	#120	1	2	yes	—
183	C₂×C₄×C₁₀₇	#120	1	1	yes	characteristic
184	C₂×C₄×C₁₀₇	#120	1	1	yes	characteristic
185	C₂×C₄×C₁₀₇	C₂²⋊Q₈	1	2	yes	—
186	C₂×C₄×C₁₀₇	C₂²⋊Q₈	1	2	yes	—
187	C₂×C₄×C₁₀₇	#123	1	2	yes	—
188	C₂×C₄×C₁₀₇	#123	1	1	yes	characteristic
189	C₂×C₄×C₁₀₇	#123	1	1	yes	characteristic
190	C₈×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	2	no	—
195	C₂²×C₁₀₇	—	2	4	no	—
196	C₂²×C₁₀₇	—	4	1	no	—
197	C₂²×C₁₀₇	—	4	1	no	—
198	C₂²×C₁₀₇	—	4	2	no	—
199	C₂²×C₁₀₇	—	4	4	no	—
200	C₂²×C₁₀₇	—	4	2	no	—
201	C₂²×C₁₀₇	—	4	2	no	—
202	C₂²×C₁₀₇	—	8	2	no	—
203	C₂²×C₁₀₇	C₂×#95	1	1	yes	characteristic
204	C₂²×C₁₀₇	#380	1	2	yes	—
205	C₂²×C₁₀₇	#386	1	1	yes	characteristic
206	C₂²×C₁₀₇	#386	1	2	yes	—
207	C₂²×C₁₀₇	#386	1	1	yes	characteristic
208	C₄×C₁₀₇	—	2	4	no	—
209	C₄×C₁₀₇	—	8	2	no	—
210	C₄×C₁₀₇	—	8	4	no	—
211	C₄×C₁₀₇	—	8	2	no	—
212	C₄×C₁₀₇	C₄×C₂²⋊C₄	1	2	yes	—
213	C₄×C₁₀₇	#379	1	1	yes	characteristic
214	C₄×C₁₀₇	#381	1	1	yes	characteristic
215	C₄×C₁₀₇	#385	1	1	yes	characteristic
216	C₄×C₁₀₇	#385	1	1	yes	characteristic
217	C₄×C₁₀₇	#385	1	2	yes	—
218	#10742	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
219	C₂×C₁₀₇	—	2	1	no	—
220	C₂×C₁₀₇	—	2	2	no	—
221	C₂×C₁₀₇	—	2	1	no	—
222	C₂×C₁₀₇	—	2	2	no	—
223	C₂×C₁₀₇	—	4	4	no	—
224	C₂×C₁₀₇	C₂²⋊#95	1	1	yes	characteristic
225	C₂×C₁₀₇	#1909	1	1	yes	characteristic
226	C₂×C₁₀₇	#1910	1	1	yes	characteristic
227	C₂×#568	C₂×C₁₀₇	1	1	yes	characteristic
228	C₂×#410	C₂×C₁₀₇	1	1	yes	characteristic
229	#2311	C₂×C₁₀₇	1	1	yes	characteristic
230	#1736	C₂×C₁₀₇	1	2	yes	complemented
231	C₂×H(3,ℤ/4)	C₂×C₁₀₇	1	2	yes	complemented
232	C₁₀₇	#10742	1	1	yes	characteristic, direct product factor, Sylow
233	C₂²×#41	C₂²×C₁₀₇	1	1	yes	characteristic
234	#568	—	2	2	no	—
235	#568	—	2	4	no	—
236	#568	C₄×C₁₀₇	1	4	yes	complemented
237	C₂×#131	—	2	4	no	—
238	C₂²×M₁₆	—	2	2	no	—
239	C₂²×M₁₆	C₂²×C₁₀₇	1	2	yes	—
240	C₂×#117	C₂²×C₁₀₇	1	2	yes	—
241	C₂×#117	C₂²×C₁₀₇	1	1	yes	characteristic
242	C₂²×C₄⋊C₄	C₂²×C₁₀₇	1	1	yes	characteristic
243	#410	—	2	2	no	—
244	#410	C₄×C₁₀₇	1	4	yes	complemented
245	C₂×#99	—	2	2	no	—
246	#391	C₄×C₁₀₇	1	2	yes	complemented
247	#390	C₄×C₁₀₇	1	2	yes	complemented
248	#386	—	2	2	no	—
249	#380	—	2	2	no	—
250	#340	—	2	4	no	—
251	H(3,ℤ/4)	—	2	4	no	—
252	C₂×#41	—	2	2	no	—
253	C₂×#41	—	2	2	no	—
254	C₂×#41	—	2	2	no	—
255	C₂×#41	—	2	2	no	—
256	C₂×#41	C₂×C₄×C₁₀₇	1	2	yes	—
257	C₂×#41	C₂×C₄×C₁₀₇	1	2	yes	—
258	C₂×#41	D₄×C₁₀₇	1	2	yes	—
259	C₂×#41	Q₈×C₁₀₇	1	2	yes	—
260	C₂²×Q₈	C₂×C₄×C₁₀₇	1	1	yes	characteristic
261	C₂²×D₄	C₂×C₄×C₁₀₇	1	1	yes	characteristic
262	C₂²×D₄	D₄×C₁₀₇	1	2	yes	—
263	C₂³×C₄	—	2	1	no	—
264	C₂³×C₄	D₄×C₁₀₇	1	2	yes	—
265	C₂³×C₄	C₂³×C₁₀₇	1	1	yes	characteristic
266	#131	—	2	16	no	—
267	#131	—	2	16	no	—
268	C₂×M₁₆	—	2	4	no	—
269	C₂×M₁₆	—	2	8	no	—
270	C₂×M₁₆	—	2	8	no	—
271	C₂×M₁₆	—	2	2	no	—
272	C₂×M₁₆	—	2	2	no	—
273	C₂×M₁₆	—	2	2	no	—
274	C₂×M₁₆	—	2	2	no	—
275	C₂×M₁₆	C₂×C₄×C₁₀₇	1	4	yes	—
276	C₂×M₁₆	D₄×C₁₀₇	1	4	yes	—
277	C₂²×C₈	—	2	4	no	—
278	C₂²×C₈	D₄×C₁₀₇	1	4	yes	—
279	#117	—	2	2	no	—
280	#117	—	2	2	no	—
281	#117	—	2	2	no	—
282	#117	—	2	2	no	—
283	#117	—	2	2	no	—
284	#117	C₂×C₄×C₁₀₇	1	4	yes	—
285	C₂×C₄⋊C₄	—	2	2	no	—
286	C₂×C₄⋊C₄	—	2	2	no	—
287	C₂×C₄⋊C₄	—	2	2	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₄⋊C₄	C₂×C₄×C₁₀₇	1	2	yes	—
291	C₂×C₂²⋊C₄	—	2	2	no	—
292	C₂×C₂²⋊C₄	—	2	1	no	—
293	C₂×C₂²⋊C₄	—	2	4	no	—
294	C₂×C₄²	—	2	2	no	—
295	C₂×C₄²	C₂×C₄×C₁₀₇	1	2	yes	—
296	#99	—	2	8	no	—
297	#95	—	2	4	no	—
298	C₂⁴	C₂²⋊C₄×C₁₀₇	1	2	yes	—
299	C₂⁴	C₂×D₄×C₁₀₇	1	1	yes	characteristic
300	#41	—	2	4	no	—
301	#41	—	2	4	no	—
302	#41	—	2	4	no	—
303	#41	—	2	4	no	—
304	#41	—	2	4	no	—
305	#41	—	2	4	no	—
306	#41	—	2	4	no	—
307	#41	—	2	4	no	—
308	C₂×Q₈	—	2	2	no	—
309	C₂×Q₈	—	2	2	no	—
310	C₂×Q₈	C₄²×C₁₀₇	1	2	yes	—
311	C₂×Q₈	C₄⋊C₄×C₁₀₇	1	2	yes	—
312	C₂×D₄	—	2	4	no	—
313	C₂×D₄	—	2	4	no	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	C₄²×C₁₀₇	1	2	yes	—
317	C₂×D₄	C₂²⋊C₄×C₁₀₇	1	4	yes	—
318	C₂×D₄	C₄⋊C₄×C₁₀₇	1	4	yes	—
319	C₂×D₄	C₄⋊C₄×C₁₀₇	1	2	yes	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	4	2	no	—
327	C₂²×C₄	—	4	2	no	—
328	C₂²×C₄	—	8	2	no	—
329	C₂²×C₄	C₂²⋊C₄×C₁₀₇	1	2	yes	—
330	C₂²×C₄	C₂²⋊C₄×C₁₀₇	1	4	yes	—
331	C₂²×C₄	C₄⋊C₄×C₁₀₇	1	4	yes	—
332	C₂²×C₄	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
333	C₂²×C₄	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
334	C₂²×C₄	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
335	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
336	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
337	C₂²×C₄	C₂×D₄×C₁₀₇	1	2	yes	—
338	C₂²×C₄	C₂×D₄×C₁₀₇	1	2	yes	—
339	C₂²×C₄	C₂×Q₈×C₁₀₇	1	1	yes	characteristic
340	C₂²×C₄	#41×C₁₀₇	1	2	yes	—
341	C₂²×C₄	#41×C₁₀₇	1	2	yes	—
342	M₁₆	—	2	16	no	—
343	M₁₆	—	2	4	no	—
344	M₁₆	—	2	4	no	—
345	M₁₆	—	2	4	no	—
346	M₁₆	—	2	4	no	—
347	C₂×C₈	—	2	16	no	—
348	C₂×C₈	—	2	4	no	—
349	C₂×C₈	—	2	4	no	—
350	C₂×C₈	C₂²⋊C₄×C₁₀₇	1	8	yes	complemented
351	C₄⋊C₄	—	2	4	no	—
352	C₄⋊C₄	—	2	4	no	—
353	C₄⋊C₄	—	4	1	no	—
354	C₄⋊C₄	—	4	1	no	—
355	C₄⋊C₄	—	4	2	no	—
356	C₄⋊C₄	—	4	1	no	—
357	C₄⋊C₄	—	4	1	no	—
358	C₂²⋊C₄	—	2	4	no	—
359	C₂²⋊C₄	—	4	2	no	—
360	C₂²⋊C₄	—	4	2	no	—
361	C₂²⋊C₄	—	8	4	no	—
362	C₄²	—	2	4	no	—
363	C₄²	—	2	4	no	—
364	C₄²	—	4	2	no	—
365	C₂³	—	2	2	no	—
366	C₂³	—	2	2	no	—
367	C₂³	—	4	1	no	—
368	C₂³	—	4	1	no	—
369	C₂³	—	4	2	no	—
370	C₂³	—	4	2	no	—
371	C₂³	#95×C₁₀₇	1	4	yes	—
372	C₂³	C₂×C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
373	C₂³	C₂×C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
374	C₂³	C₂×C₄⋊C₄×C₁₀₇	1	1	yes	characteristic
375	C₂³	#121×C₁₀₇	1	2	yes	—
376	C₂³	#121×C₁₀₇	1	2	yes	—
377	Q₈	—	2	4	no	—
378	Q₈	—	2	4	no	—
379	D₄	—	2	8	no	—
380	D₄	—	2	8	no	—
381	D₄	—	2	4	no	—
382	D₄	—	2	4	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	4	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	4	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	8	4	no	—
396	C₂×C₄	—	8	2	no	—
397	C₂×C₄	—	8	2	no	—
398	C₂×C₄	#95×C₁₀₇	1	4	yes	—
399	C₂×C₄	C₂×C₄²×C₁₀₇	1	1	yes	characteristic
400	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₇	1	2	yes	—
401	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
402	C₂×C₄	C₂×C₄⋊C₄×C₁₀₇	1	1	yes	characteristic
403	C₂×C₄	C₂×C₄⋊C₄×C₁₀₇	1	1	yes	characteristic
404	C₂×C₄	#117×C₁₀₇	1	2	yes	—
405	C₂×C₄	C₄×D₄×C₁₀₇	1	2	yes	—
406	C₂×C₄	C₄×D₄×C₁₀₇	1	2	yes	—
407	C₂×C₄	C₄×D₄×C₁₀₇	1	2	yes	—
408	C₂×C₄	C₄×D₄×C₁₀₇	1	2	yes	—
409	C₂×C₄	#120×C₁₀₇	1	1	yes	characteristic
410	C₂×C₄	#120×C₁₀₇	1	2	yes	—
411	C₂×C₄	#120×C₁₀₇	1	1	yes	characteristic
412	C₂×C₄	C₂²⋊Q₈×C₁₀₇	1	2	yes	—
413	C₂×C₄	C₂²⋊Q₈×C₁₀₇	1	2	yes	—
414	C₂×C₄	#123×C₁₀₇	1	2	yes	—
415	C₂×C₄	#123×C₁₀₇	1	1	yes	characteristic
416	C₂×C₄	#123×C₁₀₇	1	1	yes	characteristic
417	C₈	—	2	8	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	2	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	2	2	no	—
422	C₂²	—	2	4	no	—
423	C₂²	—	4	1	no	—
424	C₂²	—	4	1	no	—
425	C₂²	—	4	2	no	—
426	C₂²	—	4	4	no	—
427	C₂²	—	4	2	no	—
428	C₂²	—	4	2	no	—
429	C₂²	—	8	2	no	—
430	C₂²	C₂×#95×C₁₀₇	1	1	yes	characteristic
431	C₂²	#380×C₁₀₇	1	2	yes	—
432	C₂²	#386×C₁₀₇	1	1	yes	characteristic
433	C₂²	#386×C₁₀₇	1	2	yes	—
434	C₂²	#386×C₁₀₇	1	1	yes	characteristic
435	C₄	—	2	4	no	—
436	C₄	—	8	2	no	—
437	C₄	—	8	4	no	—
438	C₄	—	8	2	no	—
439	C₄	C₄×C₂²⋊C₄×C₁₀₇	1	2	yes	—
440	C₄	#379×C₁₀₇	1	1	yes	characteristic
441	C₄	#381×C₁₀₇	1	1	yes	characteristic
442	C₄	#385×C₁₀₇	1	1	yes	characteristic
443	C₄	#385×C₁₀₇	1	1	yes	characteristic
444	C₄	#385×C₁₀₇	1	2	yes	—
445	C₂	—	2	1	no	—
446	C₂	—	2	2	no	—
447	C₂	—	2	1	no	—
448	C₂	—	2	2	no	—
449	C₂	—	4	4	no	—
450	C₂	C₁₀₇×C₂²⋊#95	1	1	yes	characteristic
451	C₂	C₁₀₇×#1909	1	1	yes	characteristic
452	C₂	C₁₀₇×#1910	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₀₇	#386
commutator	C₂×C₄	C₂×C₄²×C₁₀₇
Frattini, cosocle	C₂³×C₄	C₂³×C₁₀₇
prime radical	C₂²×#41×C₁₀₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₇ ◁ C₂³×C₄×C₁₀₇ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₀₇×#1736	C₂	semidirect
5. C₂×H(3,ℤ/4)×C₁₀₇	C₂	semidirect
9. #568×C₁₀₇	C₄	semidirect
17. #410×C₁₀₇	C₄	semidirect
19. #391×C₁₀₇	C₄	semidirect
20. #390×C₁₀₇	C₄	semidirect
123. C₂×C₈×C₁₀₇	C₂²⋊C₄	semidirect
218. #10742	C₁₀₇	direct (N × H)
230. #1736	C₂×C₁₀₇	semidirect
231. C₂×H(3,ℤ/4)	C₂×C₁₀₇	semidirect
232. C₁₀₇	#10742	direct (N × H)
236. #568	C₄×C₁₀₇	semidirect
244. #410	C₄×C₁₀₇	semidirect
246. #391	C₄×C₁₀₇	semidirect
247. #390	C₄×C₁₀₇	semidirect
350. C₂×C₈	C₂²⋊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×#568×C₁₀₇	2
C₂×#410×C₁₀₇	2
C₁₀₇×#2311	2
C₁₀₇×#1736	2
C₂×H(3,ℤ/4)×C₁₀₇	2
#10742	107

Subgroups — C107×#10742 #41036706

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₇×#10742 #41036706