Subgroups — C₂×C₁₀₇×#2194 #41059499

Order 27392.

1130 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#576×C₁₀₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#510×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×SD₃₂×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#473×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₇×#2194	C₂	1	8	yes	maximal, direct product factor
6	C₂×#361×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#359×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#350×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×H(5,𝔽₂)×C₁₀₇	—	2	1	no	—
10	#576×C₁₀₇	—	2	2	no	—
11	#576×C₁₀₇	—	2	2	no	—
12	#576×C₁₀₇	—	2	2	no	—
13	#576×C₁₀₇	C₂²	1	4	yes	—
14	C₂×#137×C₁₀₇	—	2	1	no	—
15	C₂×AGL(1,ℤ/8)×C₁₀₇	—	2	2	no	—
16	C₂×AGL(1,ℤ/8)×C₁₀₇	—	2	1	no	—
17	C₂×#135×C₁₀₇	—	2	1	no	—
18	C₂×#135×C₁₀₇	C₂²	1	1	yes	characteristic
19	C₂²×Q₁₆×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
20	C₂²×D₈×C₁₀₇	—	2	1	no	—
21	C₂²×D₈×C₁₀₇	C₂²	1	1	yes	characteristic
22	C₂×#131×C₁₀₇	C₂²	1	1	yes	characteristic
23	#510×C₁₀₇	—	2	2	no	—
24	#510×C₁₀₇	C₂²	1	4	yes	complemented
25	C₂×Q₃₂×C₁₀₇	—	2	1	no	—
26	C₂×SD₃₂×C₁₀₇	—	2	2	no	—
27	C₂×SD₃₂×C₁₀₇	—	2	2	no	—
28	C₂×SD₃₂×C₁₀₇	—	2	1	no	—
29	C₂×SD₃₂×C₁₀₇	C₂²	1	4	yes	complemented
30	C₂×M₃₂×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
31	C₂²×C₁₆×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
32	#473×C₁₀₇	—	2	2	no	—
33	#473×C₁₀₇	C₂²	1	4	yes	complemented
34	C₂×#108×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
35	C₂×#101×C₁₀₇	—	2	1	no	—
36	#361×C₁₀₇	C₂²	1	4	yes	complemented
37	#359×C₁₀₇	C₂²	1	4	yes	complemented
38	#350×C₁₀₇	C₂²	1	4	yes	complemented
39	H(5,𝔽₂)×C₁₀₇	—	2	4	no	—
40	H(5,𝔽₂)×C₁₀₇	—	2	4	no	—
41	H(5,𝔽₂)×C₁₀₇	—	4	2	no	—
42	H(5,𝔽₂)×C₁₀₇	—	4	2	no	—
43	C₂×#41×C₁₀₇	—	2	2	no	—
44	C₂×#41×C₁₀₇	—	2	1	no	—
45	C₂×#41×C₁₀₇	—	4	1	no	—
46	C₂×#41×C₁₀₇	D₄	1	1	yes	characteristic
47	C₂²×Q₈×C₁₀₇	—	2	1	no	—
48	C₂²×D₄×C₁₀₇	—	2	2	no	—
49	C₂²×D₄×C₁₀₇	—	2	1	no	—
50	C₂²×D₄×C₁₀₇	—	4	2	no	—
51	C₂²×D₄×C₁₀₇	—	4	1	no	—
52	#137×C₁₀₇	—	2	4	no	—
53	#137×C₁₀₇	—	4	2	no	—
54	AGL(1,ℤ/8)×C₁₀₇	—	2	4	no	—
55	AGL(1,ℤ/8)×C₁₀₇	—	2	8	no	—
56	AGL(1,ℤ/8)×C₁₀₇	—	2	8	no	—
57	AGL(1,ℤ/8)×C₁₀₇	—	2	4	no	—
58	#135×C₁₀₇	—	2	4	no	—
59	#135×C₁₀₇	—	2	4	no	—
60	#135×C₁₀₇	—	2	1	no	—
61	#135×C₁₀₇	—	2	1	no	—
62	#135×C₁₀₇	D₄	1	2	yes	—
63	#135×C₁₀₇	C₂³	1	2	yes	—
64	C₂×Q₁₆×C₁₀₇	—	2	1	no	—
65	C₂×Q₁₆×C₁₀₇	—	2	1	no	—
66	C₂×Q₁₆×C₁₀₇	—	2	1	no	—
67	C₂×Q₁₆×C₁₀₇	—	2	1	no	—
68	C₂×Q₁₆×C₁₀₇	—	2	1	no	—
69	C₂×Q₁₆×C₁₀₇	—	4	1	no	—
70	C₂×Q₁₆×C₁₀₇	D₄	1	1	yes	characteristic
71	C₂×Q₁₆×C₁₀₇	C₂³	1	2	yes	complemented
72	C₂×SD₁₆×C₁₀₇	—	2	2	no	—
73	C₂×SD₁₆×C₁₀₇	—	2	1	no	—
74	C₂×SD₁₆×C₁₀₇	—	4	1	no	—
75	C₂×D₈×C₁₀₇	—	2	2	no	—
76	C₂×D₈×C₁₀₇	—	2	4	no	—
77	C₂×D₈×C₁₀₇	—	2	4	no	—
78	C₂×D₈×C₁₀₇	—	2	1	no	—
79	C₂×D₈×C₁₀₇	—	2	1	no	—
80	C₂×D₈×C₁₀₇	—	2	1	no	—
81	C₂×D₈×C₁₀₇	D₄	1	1	yes	characteristic
82	C₂×D₈×C₁₀₇	D₄	1	2	yes	—
83	C₂×D₈×C₁₀₇	D₄	1	2	yes	—
84	C₂×D₈×C₁₀₇	C₂³	1	2	yes	—
85	#131×C₁₀₇	—	2	1	no	—
86	#131×C₁₀₇	—	2	1	no	—
87	#131×C₁₀₇	D₄	1	2	yes	—
88	#131×C₁₀₇	C₂³	1	2	yes	—
89	C₂×M₁₆×C₁₀₇	—	2	1	no	—
90	C₂×M₁₆×C₁₀₇	—	2	1	no	—
91	C₂×M₁₆×C₁₀₇	D₄	1	1	yes	characteristic
92	C₂²×C₈×C₁₀₇	—	2	1	no	—
93	C₂²×C₈×C₁₀₇	C₂³	1	1	yes	characteristic
94	Q₃₂×C₁₀₇	—	2	4	no	—
95	SD₃₂×C₁₀₇	—	2	8	no	—
96	SD₃₂×C₁₀₇	—	2	4	no	—
97	M₃₂×C₁₀₇	—	2	1	no	—
98	M₃₂×C₁₀₇	C₂³	1	2	yes	complemented
99	C₂×C₁₆×C₁₀₇	—	2	1	no	—
100	C₂×C₁₆×C₁₀₇	—	2	1	no	—
101	C₂×C₁₆×C₁₀₇	—	2	1	no	—
102	C₂×C₁₆×C₁₀₇	C₂³	1	2	yes	complemented
103	#108×C₁₀₇	—	2	1	no	—
104	#108×C₁₀₇	C₂³	1	2	yes	complemented
105	#101×C₁₀₇	—	2	4	no	—
106	C₂⁴×C₁₀₇	—	4	2	no	—
107	C₂⁴×C₁₀₇	—	4	1	no	—
108	#41×C₁₀₇	—	2	1	no	—
109	#41×C₁₀₇	—	2	1	no	—
110	#41×C₁₀₇	—	2	8	no	—
111	#41×C₁₀₇	—	2	2	no	—
112	#41×C₁₀₇	—	2	2	no	—
113	#41×C₁₀₇	—	4	4	no	—
114	#41×C₁₀₇	—	4	4	no	—
115	#41×C₁₀₇	—	4	4	no	—
116	#41×C₁₀₇	—	4	1	no	—
117	#41×C₁₀₇	—	4	1	no	—
118	#41×C₁₀₇	D₈	1	2	yes	—
119	#41×C₁₀₇	C₂×D₄	1	2	yes	—
120	C₂×Q₈×C₁₀₇	—	2	1	no	—
121	C₂×Q₈×C₁₀₇	—	2	2	no	—
122	C₂×Q₈×C₁₀₇	—	4	1	no	—
123	C₂×Q₈×C₁₀₇	—	4	1	no	—
124	C₂×Q₈×C₁₀₇	—	4	1	no	—
125	C₂×Q₈×C₁₀₇	—	4	1	no	—
126	C₂×Q₈×C₁₀₇	—	4	1	no	—
127	C₂×Q₈×C₁₀₇	D₈	1	1	yes	characteristic
128	C₂×D₄×C₁₀₇	—	2	1	no	—
129	C₂×D₄×C₁₀₇	—	2	8	no	—
130	C₂×D₄×C₁₀₇	—	2	1	no	—
131	C₂×D₄×C₁₀₇	—	2	2	no	—
132	C₂×D₄×C₁₀₇	—	2	2	no	—
133	C₂×D₄×C₁₀₇	—	2	2	no	—
134	C₂×D₄×C₁₀₇	—	4	2	no	—
135	C₂×D₄×C₁₀₇	—	4	4	no	—
136	C₂×D₄×C₁₀₇	—	4	8	no	—
137	C₂×D₄×C₁₀₇	—	4	8	no	—
138	C₂×D₄×C₁₀₇	—	4	4	no	—
139	C₂×D₄×C₁₀₇	—	4	2	no	—
140	C₂×D₄×C₁₀₇	—	4	1	no	—
141	C₂×D₄×C₁₀₇	—	4	4	no	—
142	C₂×D₄×C₁₀₇	—	4	1	no	—
143	C₂×D₄×C₁₀₇	—	4	1	no	—
144	C₂×D₄×C₁₀₇	—	4	1	no	—
145	C₂×D₄×C₁₀₇	D₈	1	1	yes	characteristic
146	C₂²×C₄×C₁₀₇	—	2	1	no	—
147	C₂²×C₄×C₁₀₇	—	4	2	no	—
148	C₂²×C₄×C₁₀₇	—	4	1	no	—
149	C₂²×C₄×C₁₀₇	—	4	1	no	—
150	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
151	Q₁₆×C₁₀₇	—	2	1	no	—
152	Q₁₆×C₁₀₇	—	2	2	no	—
153	Q₁₆×C₁₀₇	—	2	2	no	—
154	Q₁₆×C₁₀₇	—	4	4	no	—
155	Q₁₆×C₁₀₇	—	4	1	no	—
156	Q₁₆×C₁₀₇	—	4	1	no	—
157	Q₁₆×C₁₀₇	C₂×D₄	1	2	yes	—
158	SD₁₆×C₁₀₇	—	2	8	no	—
159	SD₁₆×C₁₀₇	—	2	2	no	—
160	SD₁₆×C₁₀₇	—	2	2	no	—
161	SD₁₆×C₁₀₇	—	4	4	no	—
162	D₈×C₁₀₇	—	2	8	no	—
163	D₈×C₁₀₇	—	2	1	no	—
164	D₈×C₁₀₇	—	2	2	no	—
165	D₈×C₁₀₇	—	2	2	no	—
166	D₈×C₁₀₇	—	2	2	no	—
167	D₈×C₁₀₇	C₂×D₄	1	2	yes	—
168	D₈×C₁₀₇	C₂×D₄	1	4	yes	—
169	M₁₆×C₁₀₇	—	2	1	no	—
170	M₁₆×C₁₀₇	—	2	2	no	—
171	M₁₆×C₁₀₇	—	2	2	no	—
172	M₁₆×C₁₀₇	—	2	2	no	—
173	M₁₆×C₁₀₇	—	4	1	no	—
174	M₁₆×C₁₀₇	C₂×D₄	1	2	yes	—
175	C₂×C₈×C₁₀₇	—	2	1	no	—
176	C₂×C₈×C₁₀₇	—	2	2	no	—
177	C₂×C₈×C₁₀₇	—	2	2	no	—
178	C₂×C₈×C₁₀₇	—	4	1	no	—
179	C₂×C₈×C₁₀₇	C₂×D₄	1	1	yes	characteristic
180	C₂×C₈×C₁₀₇	C₂×D₄	1	1	yes	characteristic
181	C₂×C₈×C₁₀₇	C₂×D₄	1	1	yes	characteristic
182	C₂×C₈×C₁₀₇	C₂×D₄	1	1	yes	characteristic
183	C₂×C₈×C₁₀₇	C₂×D₄	1	1	yes	characteristic
184	C₂×C₈×C₁₀₇	C₂⁴	1	1	yes	characteristic
185	C₁₆×C₁₀₇	—	2	2	no	—
186	C₁₆×C₁₀₇	—	2	2	no	—
187	C₂³×C₁₀₇	—	2	1	no	—
188	C₂³×C₁₀₇	—	4	8	no	—
189	C₂³×C₁₀₇	—	4	2	no	—
190	C₂³×C₁₀₇	—	4	1	no	—
191	C₂³×C₁₀₇	—	4	2	no	—
192	C₂³×C₁₀₇	—	4	2	no	—
193	C₂³×C₁₀₇	—	16	2	no	—
194	C₂³×C₁₀₇	—	16	4	no	—
195	C₂³×C₁₀₇	AGL(1,ℤ/8)	1	1	yes	characteristic
196	Q₈×C₁₀₇	—	2	1	no	—
197	Q₈×C₁₀₇	—	2	2	no	—
198	Q₈×C₁₀₇	—	4	1	no	—
199	Q₈×C₁₀₇	—	4	2	no	—
200	Q₈×C₁₀₇	—	4	2	no	—
201	Q₈×C₁₀₇	—	8	1	no	—
202	Q₈×C₁₀₇	—	8	1	no	—
203	Q₈×C₁₀₇	C₂×D₈	1	2	yes	—
204	D₄×C₁₀₇	—	2	2	no	—
205	D₄×C₁₀₇	—	2	2	no	—
206	D₄×C₁₀₇	—	2	2	no	—
207	D₄×C₁₀₇	—	2	4	no	—
208	D₄×C₁₀₇	—	2	1	no	—
209	D₄×C₁₀₇	—	4	8	no	—
210	D₄×C₁₀₇	—	4	8	no	—
211	D₄×C₁₀₇	—	4	2	no	—
212	D₄×C₁₀₇	—	4	2	no	—
213	D₄×C₁₀₇	—	4	2	no	—
214	D₄×C₁₀₇	—	4	1	no	—
215	D₄×C₁₀₇	—	4	2	no	—
216	D₄×C₁₀₇	—	4	2	no	—
217	D₄×C₁₀₇	C₂×D₈	1	2	yes	—
218	C₂×C₄×C₁₀₇	—	2	1	no	—
219	C₂×C₄×C₁₀₇	—	2	2	no	—
220	C₂×C₄×C₁₀₇	—	2	2	no	—
221	C₂×C₄×C₁₀₇	—	4	8	no	—
222	C₂×C₄×C₁₀₇	—	4	1	no	—
223	C₂×C₄×C₁₀₇	—	4	2	no	—
224	C₂×C₄×C₁₀₇	—	4	2	no	—
225	C₂×C₄×C₁₀₇	—	4	2	no	—
226	C₂×C₄×C₁₀₇	—	8	1	no	—
227	C₂×C₄×C₁₀₇	—	8	1	no	—
228	C₂×C₄×C₁₀₇	#120	1	1	yes	characteristic
229	C₂×C₄×C₁₀₇	#120	1	1	yes	characteristic
230	C₂×C₄×C₁₀₇	C₂×D₈	1	1	yes	characteristic
231	C₂×C₄×C₁₀₇	C₂×D₈	1	1	yes	characteristic
232	C₂×C₄×C₁₀₇	AGL(1,ℤ/8)	1	1	yes	characteristic
233	C₂×C₄×C₁₀₇	C₂²×D₄	1	1	yes	characteristic
234	C₈×C₁₀₇	—	2	2	no	—
235	C₈×C₁₀₇	—	4	2	no	—
236	C₈×C₁₀₇	#120	1	1	yes	characteristic
237	C₈×C₁₀₇	#120	1	1	yes	characteristic
238	C₈×C₁₀₇	C₂²×D₄	1	1	yes	characteristic
239	C₈×C₁₀₇	C₂²×D₄	1	1	yes	characteristic
240	C₂²×C₁₀₇	—	2	2	no	—
241	C₂²×C₁₀₇	—	2	2	no	—
242	C₂²×C₁₀₇	—	4	2	no	—
243	C₂²×C₁₀₇	—	4	4	no	—
244	C₂²×C₁₀₇	—	4	2	no	—
245	C₂²×C₁₀₇	—	8	4	no	—
246	C₂²×C₁₀₇	—	8	2	no	—
247	C₂²×C₁₀₇	—	16	2	no	—
248	C₂²×C₁₀₇	—	16	2	no	—
249	C₂²×C₁₀₇	—	16	8	no	—
250	C₂²×C₁₀₇	#447	1	1	yes	characteristic
251	C₂²×C₁₀₇	#447	1	1	yes	characteristic
252	C₂²×C₁₀₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
253	C₄×C₁₀₇	—	2	2	no	—
254	C₄×C₁₀₇	—	4	2	no	—
255	C₄×C₁₀₇	—	8	2	no	—
256	C₄×C₁₀₇	#447	1	1	yes	characteristic
257	C₄×C₁₀₇	#447	1	1	yes	characteristic
258	C₄×C₁₀₇	C₂×#120	1	1	yes	characteristic
259	C₄×C₁₀₇	C₂²×D₈	1	1	yes	characteristic
260	C₂×#2194	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
261	C₂×C₁₀₇	—	2	1	no	—
262	C₂×C₁₀₇	—	2	1	no	—
263	C₂×C₁₀₇	—	4	2	no	—
264	C₂×C₁₀₇	—	8	4	no	—
265	C₂×C₁₀₇	—	8	2	no	—
266	C₂×C₁₀₇	#2194	1	2	yes	direct product factor
267	C₂×C₁₀₇	C₂×#447	1	1	yes	characteristic
268	C₂×#576	C₂×C₁₀₇	1	1	yes	characteristic
269	C₂×#510	C₂×C₁₀₇	1	1	yes	characteristic, complemented
270	C₂²×SD₃₂	C₂×C₁₀₇	1	1	yes	characteristic, complemented
271	C₂×#473	C₂×C₁₀₇	1	1	yes	characteristic, complemented
272	#2194	C₂×C₁₀₇	1	8	yes	direct product factor
273	C₂×#361	C₂×C₁₀₇	1	1	yes	characteristic, complemented
274	C₂×#359	C₂×C₁₀₇	1	1	yes	characteristic, complemented
275	C₂×#350	C₂×C₁₀₇	1	1	yes	characteristic, complemented
276	C₁₀₇	C₂×#2194	1	1	yes	characteristic, direct product factor, Sylow
277	C₂×H(5,𝔽₂)	—	2	1	no	—
278	#576	—	2	2	no	—
279	#576	—	2	2	no	—
280	#576	—	2	2	no	—
281	#576	C₂²×C₁₀₇	1	4	yes	—
282	C₂×#137	—	2	1	no	—
283	C₂×AGL(1,ℤ/8)	—	2	2	no	—
284	C₂×AGL(1,ℤ/8)	—	2	1	no	—
285	C₂×#135	—	2	1	no	—
286	C₂×#135	C₂²×C₁₀₇	1	1	yes	characteristic
287	C₂²×Q₁₆	C₂²×C₁₀₇	1	1	yes	characteristic, complemented
288	C₂²×D₈	—	2	1	no	—
289	C₂²×D₈	C₂²×C₁₀₇	1	1	yes	characteristic
290	C₂×#131	C₂²×C₁₀₇	1	1	yes	characteristic
291	#510	—	2	2	no	—
292	#510	C₂²×C₁₀₇	1	4	yes	complemented
293	C₂×Q₃₂	—	2	1	no	—
294	C₂×SD₃₂	—	2	2	no	—
295	C₂×SD₃₂	—	2	2	no	—
296	C₂×SD₃₂	—	2	1	no	—
297	C₂×SD₃₂	C₂²×C₁₀₇	1	4	yes	complemented
298	C₂×M₃₂	C₂²×C₁₀₇	1	1	yes	characteristic, complemented
299	C₂²×C₁₆	C₂²×C₁₀₇	1	1	yes	characteristic, complemented
300	#473	—	2	2	no	—
301	#473	C₂²×C₁₀₇	1	4	yes	complemented
302	C₂×#108	C₂²×C₁₀₇	1	1	yes	characteristic, complemented
303	C₂×#101	—	2	1	no	—
304	#361	C₂²×C₁₀₇	1	4	yes	complemented
305	#359	C₂²×C₁₀₇	1	4	yes	complemented
306	#350	C₂²×C₁₀₇	1	4	yes	complemented
307	H(5,𝔽₂)	—	2	4	no	—
308	H(5,𝔽₂)	—	2	4	no	—
309	H(5,𝔽₂)	—	4	2	no	—
310	H(5,𝔽₂)	—	4	2	no	—
311	C₂×#41	—	2	2	no	—
312	C₂×#41	—	2	1	no	—
313	C₂×#41	—	4	1	no	—
314	C₂×#41	D₄×C₁₀₇	1	1	yes	characteristic
315	C₂²×Q₈	—	2	1	no	—
316	C₂²×D₄	—	2	2	no	—
317	C₂²×D₄	—	2	1	no	—
318	C₂²×D₄	—	4	2	no	—
319	C₂²×D₄	—	4	1	no	—
320	#137	—	2	4	no	—
321	#137	—	4	2	no	—
322	AGL(1,ℤ/8)	—	2	4	no	—
323	AGL(1,ℤ/8)	—	2	8	no	—
324	AGL(1,ℤ/8)	—	2	8	no	—
325	AGL(1,ℤ/8)	—	2	4	no	—
326	#135	—	2	4	no	—
327	#135	—	2	4	no	—
328	#135	—	2	1	no	—
329	#135	—	2	1	no	—
330	#135	D₄×C₁₀₇	1	2	yes	—
331	#135	C₂³×C₁₀₇	1	2	yes	—
332	C₂×Q₁₆	—	2	1	no	—
333	C₂×Q₁₆	—	2	1	no	—
334	C₂×Q₁₆	—	2	1	no	—
335	C₂×Q₁₆	—	2	1	no	—
336	C₂×Q₁₆	—	2	1	no	—
337	C₂×Q₁₆	—	4	1	no	—
338	C₂×Q₁₆	D₄×C₁₀₇	1	1	yes	characteristic
339	C₂×Q₁₆	C₂³×C₁₀₇	1	2	yes	complemented
340	C₂×SD₁₆	—	2	2	no	—
341	C₂×SD₁₆	—	2	1	no	—
342	C₂×SD₁₆	—	4	1	no	—
343	C₂×D₈	—	2	2	no	—
344	C₂×D₈	—	2	4	no	—
345	C₂×D₈	—	2	4	no	—
346	C₂×D₈	—	2	1	no	—
347	C₂×D₈	—	2	1	no	—
348	C₂×D₈	—	2	1	no	—
349	C₂×D₈	D₄×C₁₀₇	1	1	yes	characteristic
350	C₂×D₈	D₄×C₁₀₇	1	2	yes	—
351	C₂×D₈	D₄×C₁₀₇	1	2	yes	—
352	C₂×D₈	C₂³×C₁₀₇	1	2	yes	—
353	#131	—	2	1	no	—
354	#131	—	2	1	no	—
355	#131	D₄×C₁₀₇	1	2	yes	—
356	#131	C₂³×C₁₀₇	1	2	yes	—
357	C₂×M₁₆	—	2	1	no	—
358	C₂×M₁₆	—	2	1	no	—
359	C₂×M₁₆	D₄×C₁₀₇	1	1	yes	characteristic
360	C₂²×C₈	—	2	1	no	—
361	C₂²×C₈	C₂³×C₁₀₇	1	1	yes	characteristic
362	Q₃₂	—	2	4	no	—
363	SD₃₂	—	2	8	no	—
364	SD₃₂	—	2	4	no	—
365	M₃₂	—	2	1	no	—
366	M₃₂	C₂³×C₁₀₇	1	2	yes	complemented
367	C₂×C₁₆	—	2	1	no	—
368	C₂×C₁₆	—	2	1	no	—
369	C₂×C₁₆	—	2	1	no	—
370	C₂×C₁₆	C₂³×C₁₀₇	1	2	yes	complemented
371	#108	—	2	1	no	—
372	#108	C₂³×C₁₀₇	1	2	yes	complemented
373	#101	—	2	4	no	—
374	C₂⁴	—	4	2	no	—
375	C₂⁴	—	4	1	no	—
376	#41	—	2	1	no	—
377	#41	—	2	1	no	—
378	#41	—	2	8	no	—
379	#41	—	2	2	no	—
380	#41	—	2	2	no	—
381	#41	—	4	4	no	—
382	#41	—	4	4	no	—
383	#41	—	4	4	no	—
384	#41	—	4	1	no	—
385	#41	—	4	1	no	—
386	#41	D₈×C₁₀₇	1	2	yes	—
387	#41	C₂×D₄×C₁₀₇	1	2	yes	—
388	C₂×Q₈	—	2	1	no	—
389	C₂×Q₈	—	2	2	no	—
390	C₂×Q₈	—	4	1	no	—
391	C₂×Q₈	—	4	1	no	—
392	C₂×Q₈	—	4	1	no	—
393	C₂×Q₈	—	4	1	no	—
394	C₂×Q₈	—	4	1	no	—
395	C₂×Q₈	D₈×C₁₀₇	1	1	yes	characteristic
396	C₂×D₄	—	2	1	no	—
397	C₂×D₄	—	2	8	no	—
398	C₂×D₄	—	2	1	no	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	2	2	no	—
402	C₂×D₄	—	4	2	no	—
403	C₂×D₄	—	4	4	no	—
404	C₂×D₄	—	4	8	no	—
405	C₂×D₄	—	4	8	no	—
406	C₂×D₄	—	4	4	no	—
407	C₂×D₄	—	4	2	no	—
408	C₂×D₄	—	4	1	no	—
409	C₂×D₄	—	4	4	no	—
410	C₂×D₄	—	4	1	no	—
411	C₂×D₄	—	4	1	no	—
412	C₂×D₄	—	4	1	no	—
413	C₂×D₄	D₈×C₁₀₇	1	1	yes	characteristic
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	4	2	no	—
416	C₂²×C₄	—	4	1	no	—
417	C₂²×C₄	—	4	1	no	—
418	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
419	Q₁₆	—	2	1	no	—
420	Q₁₆	—	2	2	no	—
421	Q₁₆	—	2	2	no	—
422	Q₁₆	—	4	4	no	—
423	Q₁₆	—	4	1	no	—
424	Q₁₆	—	4	1	no	—
425	Q₁₆	C₂×D₄×C₁₀₇	1	2	yes	—
426	SD₁₆	—	2	8	no	—
427	SD₁₆	—	2	2	no	—
428	SD₁₆	—	2	2	no	—
429	SD₁₆	—	4	4	no	—
430	D₈	—	2	8	no	—
431	D₈	—	2	1	no	—
432	D₈	—	2	2	no	—
433	D₈	—	2	2	no	—
434	D₈	—	2	2	no	—
435	D₈	C₂×D₄×C₁₀₇	1	2	yes	—
436	D₈	C₂×D₄×C₁₀₇	1	4	yes	—
437	M₁₆	—	2	1	no	—
438	M₁₆	—	2	2	no	—
439	M₁₆	—	2	2	no	—
440	M₁₆	—	2	2	no	—
441	M₁₆	—	4	1	no	—
442	M₁₆	C₂×D₄×C₁₀₇	1	2	yes	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	2	no	—
445	C₂×C₈	—	2	2	no	—
446	C₂×C₈	—	4	1	no	—
447	C₂×C₈	C₂×D₄×C₁₀₇	1	1	yes	characteristic
448	C₂×C₈	C₂×D₄×C₁₀₇	1	1	yes	characteristic
449	C₂×C₈	C₂×D₄×C₁₀₇	1	1	yes	characteristic
450	C₂×C₈	C₂×D₄×C₁₀₇	1	1	yes	characteristic
451	C₂×C₈	C₂×D₄×C₁₀₇	1	1	yes	characteristic
452	C₂×C₈	C₂⁴×C₁₀₇	1	1	yes	characteristic
453	C₁₆	—	2	2	no	—
454	C₁₆	—	2	2	no	—
455	C₂³	—	2	1	no	—
456	C₂³	—	4	8	no	—
457	C₂³	—	4	2	no	—
458	C₂³	—	4	1	no	—
459	C₂³	—	4	2	no	—
460	C₂³	—	4	2	no	—
461	C₂³	—	16	2	no	—
462	C₂³	—	16	4	no	—
463	C₂³	AGL(1,ℤ/8)×C₁₀₇	1	1	yes	characteristic
464	Q₈	—	2	1	no	—
465	Q₈	—	2	2	no	—
466	Q₈	—	4	1	no	—
467	Q₈	—	4	2	no	—
468	Q₈	—	4	2	no	—
469	Q₈	—	8	1	no	—
470	Q₈	—	8	1	no	—
471	Q₈	C₂×D₈×C₁₀₇	1	2	yes	—
472	D₄	—	2	2	no	—
473	D₄	—	2	2	no	—
474	D₄	—	2	1	no	—
475	D₄	—	2	2	no	—
476	D₄	—	2	4	no	—
477	D₄	—	4	8	no	—
478	D₄	—	4	8	no	—
479	D₄	—	4	2	no	—
480	D₄	—	4	2	no	—
481	D₄	—	4	1	no	—
482	D₄	—	4	2	no	—
483	D₄	—	4	2	no	—
484	D₄	—	4	2	no	—
485	D₄	C₂×D₈×C₁₀₇	1	2	yes	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	4	8	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	2	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	8	1	no	—
495	C₂×C₄	—	8	1	no	—
496	C₂×C₄	#120×C₁₀₇	1	1	yes	characteristic
497	C₂×C₄	#120×C₁₀₇	1	1	yes	characteristic
498	C₂×C₄	C₂×D₈×C₁₀₇	1	1	yes	characteristic
499	C₂×C₄	C₂×D₈×C₁₀₇	1	1	yes	characteristic
500	C₂×C₄	AGL(1,ℤ/8)×C₁₀₇	1	1	yes	characteristic
501	C₂×C₄	C₂²×D₄×C₁₀₇	1	1	yes	characteristic
502	C₈	—	2	2	no	—
503	C₈	—	4	2	no	—
504	C₈	#120×C₁₀₇	1	1	yes	characteristic
505	C₈	#120×C₁₀₇	1	1	yes	characteristic
506	C₈	C₂²×D₄×C₁₀₇	1	1	yes	characteristic
507	C₈	C₂²×D₄×C₁₀₇	1	1	yes	characteristic
508	C₂²	—	2	2	no	—
509	C₂²	—	2	2	no	—
510	C₂²	—	4	2	no	—
511	C₂²	—	4	4	no	—
512	C₂²	—	4	2	no	—
513	C₂²	—	8	4	no	—
514	C₂²	—	8	2	no	—
515	C₂²	—	16	2	no	—
516	C₂²	—	16	2	no	—
517	C₂²	—	16	8	no	—
518	C₂²	#447×C₁₀₇	1	1	yes	characteristic
519	C₂²	#447×C₁₀₇	1	1	yes	characteristic
520	C₂²	C₂×AGL(1,ℤ/8)×C₁₀₇	1	1	yes	characteristic
521	C₄	—	2	2	no	—
522	C₄	—	4	2	no	—
523	C₄	—	8	2	no	—
524	C₄	#447×C₁₀₇	1	1	yes	characteristic
525	C₄	#447×C₁₀₇	1	1	yes	characteristic
526	C₄	C₂×#120×C₁₀₇	1	1	yes	characteristic
527	C₄	C₂²×D₈×C₁₀₇	1	1	yes	characteristic
528	C₂	—	2	1	no	—
529	C₂	—	2	1	no	—
530	C₂	—	4	2	no	—
531	C₂	—	8	4	no	—
532	C₂	—	8	2	no	—
533	C₂	C₁₀₇×#2194	1	2	yes	direct product factor
534	C₂	C₂×#447×C₁₀₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₀₇	#447
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₀₇
prime radical	C₂×#576×C₁₀₇	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₇ ◁ C₂²×C₄×C₁₀₇ ◁ C₂×#131×C₁₀₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#510×C₁₀₇	C₂	semidirect
3. C₂²×SD₃₂×C₁₀₇	C₂	semidirect
4. C₂×#473×C₁₀₇	C₂	semidirect
5. C₁₀₇×#2194	C₂	direct (N × H)
6. C₂×#361×C₁₀₇	C₂	semidirect
7. C₂×#359×C₁₀₇	C₂	semidirect
8. C₂×#350×C₁₀₇	C₂	semidirect
19. C₂²×Q₁₆×C₁₀₇	C₂²	semidirect
24. #510×C₁₀₇	C₂²	semidirect
29. C₂×SD₃₂×C₁₀₇	C₂²	semidirect
30. C₂×M₃₂×C₁₀₇	C₂²	semidirect
31. C₂²×C₁₆×C₁₀₇	C₂²	semidirect
33. #473×C₁₀₇	C₂²	semidirect
34. C₂×#108×C₁₀₇	C₂²	semidirect
36. #361×C₁₀₇	C₂²	semidirect
37. #359×C₁₀₇	C₂²	semidirect
38. #350×C₁₀₇	C₂²	semidirect
71. C₂×Q₁₆×C₁₀₇	C₂³	semidirect
98. M₃₂×C₁₀₇	C₂³	semidirect
102. C₂×C₁₆×C₁₀₇	C₂³	semidirect
104. #108×C₁₀₇	C₂³	semidirect
260. C₂×#2194	C₁₀₇	direct (N × H)
266. C₂×C₁₀₇	#2194	direct (N × H)
269. C₂×#510	C₂×C₁₀₇	semidirect
270. C₂²×SD₃₂	C₂×C₁₀₇	semidirect
271. C₂×#473	C₂×C₁₀₇	semidirect
272. #2194	C₂×C₁₀₇	direct (N × H)
273. C₂×#361	C₂×C₁₀₇	semidirect
274. C₂×#359	C₂×C₁₀₇	semidirect
275. C₂×#350	C₂×C₁₀₇	semidirect
276. C₁₀₇	C₂×#2194	direct (N × H)
287. C₂²×Q₁₆	C₂²×C₁₀₇	semidirect
292. #510	C₂²×C₁₀₇	semidirect
297. C₂×SD₃₂	C₂²×C₁₀₇	semidirect
298. C₂×M₃₂	C₂²×C₁₀₇	semidirect
299. C₂²×C₁₆	C₂²×C₁₀₇	semidirect
301. #473	C₂²×C₁₀₇	semidirect
302. C₂×#108	C₂²×C₁₀₇	semidirect
304. #361	C₂²×C₁₀₇	semidirect
305. #359	C₂²×C₁₀₇	semidirect
306. #350	C₂²×C₁₀₇	semidirect
339. C₂×Q₁₆	C₂³×C₁₀₇	semidirect
366. M₃₂	C₂³×C₁₀₇	semidirect
370. C₂×C₁₆	C₂³×C₁₀₇	semidirect
372. #108	C₂³×C₁₀₇	semidirect
533. C₂	C₁₀₇×#2194	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×#576×C₁₀₇	2
C₂×#510×C₁₀₇	2
C₂²×SD₃₂×C₁₀₇	2
C₂×#473×C₁₀₇	2
C₁₀₇×#2194	2
C₂×#361×C₁₀₇	2
C₂×#359×C₁₀₇	2
C₂×#350×C₁₀₇	2
C₂×#2194	107

Subgroups — C2×C107×#2194 #41059499

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₀₇×#2194 #41059499