Subgroups — C₂×C₁₀₇×#2190 #41059492

Order 27392.

1180 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#575×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#509×C₁₀₇	C₂	1	2	yes	maximal, complemented
3	C₂×#469×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₇×#2190	C₂	1	8	yes	maximal, direct product factor
5	C₂×#360×C₁₀₇	C₂	1	2	yes	maximal, complemented
6	C₂×#349×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#41×C₁₀₇	—	2	1	no	—
8	#575×C₁₀₇	—	2	4	no	—
9	#575×C₁₀₇	—	2	2	no	—
10	#575×C₁₀₇	C₂²	1	4	yes	complemented
11	C₂×#137×C₁₀₇	—	2	2	no	—
12	C₂×AGL(1,ℤ/8)×C₁₀₇	—	2	2	no	—
13	C₂×#135×C₁₀₇	—	2	1	no	—
14	C₂×#135×C₁₀₇	C₂²	1	2	yes	—
15	C₂²×D₈×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
16	C₂²×M₁₆×C₁₀₇	C₂²	1	1	yes	characteristic
17	C₂×#121×C₁₀₇	—	2	1	no	—
18	#509×C₁₀₇	—	2	4	no	—
19	#509×C₁₀₇	C₂²	1	8	yes	complemented
20	C₂×SD₃₂×C₁₀₇	—	2	2	no	—
21	C₂×D₁₆×C₁₀₇	—	2	2	no	—
22	C₂×M₃₂×C₁₀₇	C₂²	1	2	yes	complemented
23	#469×C₁₀₇	—	2	2	no	—
24	#469×C₁₀₇	C₂²	1	4	yes	complemented
25	C₂×#106×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
26	C₂×#102×C₁₀₇	—	2	1	no	—
27	#360×C₁₀₇	C₂²	1	8	yes	complemented
28	#349×C₁₀₇	C₂²	1	4	yes	complemented
29	C₂×#41×C₁₀₇	—	2	2	no	—
30	C₂×#41×C₁₀₇	—	2	4	no	—
31	C₂×#41×C₁₀₇	—	2	4	no	—
32	C₂×#41×C₁₀₇	—	2	2	no	—
33	C₂×#41×C₁₀₇	—	4	1	no	—
34	C₂×#41×C₁₀₇	—	4	2	no	—
35	C₂×#41×C₁₀₇	—	4	1	no	—
36	C₂×#41×C₁₀₇	—	4	2	no	—
37	C₂²×Q₈×C₁₀₇	—	2	1	no	—
38	C₂²×D₄×C₁₀₇	—	2	1	no	—
39	C₂²×D₄×C₁₀₇	—	2	1	no	—
40	C₂²×D₄×C₁₀₇	—	4	1	no	—
41	C₂²×D₄×C₁₀₇	—	4	1	no	—
42	C₂³×C₄×C₁₀₇	—	4	1	no	—
43	C₂³×C₄×C₁₀₇	D₄	1	1	yes	characteristic
44	#137×C₁₀₇	—	2	8	no	—
45	#137×C₁₀₇	—	2	8	no	—
46	AGL(1,ℤ/8)×C₁₀₇	—	2	8	no	—
47	AGL(1,ℤ/8)×C₁₀₇	—	2	8	no	—
48	#135×C₁₀₇	—	2	4	no	—
49	#135×C₁₀₇	—	2	4	no	—
50	#135×C₁₀₇	—	2	2	no	—
51	#135×C₁₀₇	—	2	2	no	—
52	#135×C₁₀₇	D₄	1	4	yes	complemented
53	#135×C₁₀₇	C₂³	1	4	yes	—
54	C₂×Q₁₆×C₁₀₇	—	2	1	no	—
55	C₂×Q₁₆×C₁₀₇	D₄	1	2	yes	complemented
56	C₂×SD₁₆×C₁₀₇	—	2	2	no	—
57	C₂×SD₁₆×C₁₀₇	—	2	2	no	—
58	C₂×D₈×C₁₀₇	—	2	1	no	—
59	C₂×D₈×C₁₀₇	—	2	2	no	—
60	C₂×D₈×C₁₀₇	—	2	2	no	—
61	C₂×D₈×C₁₀₇	—	2	1	no	—
62	C₂×D₈×C₁₀₇	D₄	1	2	yes	complemented
63	C₂×D₈×C₁₀₇	C₂³	1	2	yes	complemented
64	C₂×M₁₆×C₁₀₇	—	2	2	no	—
65	C₂×M₁₆×C₁₀₇	—	2	2	no	—
66	C₂×M₁₆×C₁₀₇	D₄	1	2	yes	—
67	C₂×M₁₆×C₁₀₇	C₂³	1	2	yes	—
68	C₂²×C₈×C₁₀₇	D₄	1	1	yes	characteristic
69	C₂²×C₈×C₁₀₇	C₂³	1	1	yes	characteristic
70	#121×C₁₀₇	—	2	4	no	—
71	#121×C₁₀₇	—	4	2	no	—
72	C₂×C₄⋊C₄×C₁₀₇	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₁₀₇	—	4	1	no	—
74	SD₃₂×C₁₀₇	—	2	8	no	—
75	D₁₆×C₁₀₇	—	2	8	no	—
76	M₃₂×C₁₀₇	—	2	2	no	—
77	M₃₂×C₁₀₇	C₂³	1	4	yes	complemented
78	C₂×C₁₆×C₁₀₇	—	2	2	no	—
79	#106×C₁₀₇	—	2	1	no	—
80	#106×C₁₀₇	C₂³	1	2	yes	complemented
81	#102×C₁₀₇	—	2	4	no	—
82	C₂⁴×C₁₀₇	—	4	1	no	—
83	C₂⁴×C₁₀₇	—	4	1	no	—
84	C₂⁴×C₁₀₇	D₈	1	1	yes	characteristic
85	#41×C₁₀₇	—	2	8	no	—
86	#41×C₁₀₇	—	2	4	no	—
87	#41×C₁₀₇	—	2	4	no	—
88	#41×C₁₀₇	—	4	4	no	—
89	#41×C₁₀₇	—	4	4	no	—
90	#41×C₁₀₇	—	4	4	no	—
91	#41×C₁₀₇	—	4	4	no	—
92	#41×C₁₀₇	—	4	4	no	—
93	#41×C₁₀₇	—	4	2	no	—
94	#41×C₁₀₇	—	4	2	no	—
95	C₂×Q₈×C₁₀₇	—	2	4	no	—
96	C₂×Q₈×C₁₀₇	—	2	2	no	—
97	C₂×Q₈×C₁₀₇	—	4	1	no	—
98	C₂×Q₈×C₁₀₇	—	4	2	no	—
99	C₂×D₄×C₁₀₇	—	2	4	no	—
100	C₂×D₄×C₁₀₇	—	2	2	no	—
101	C₂×D₄×C₁₀₇	—	2	2	no	—
102	C₂×D₄×C₁₀₇	—	4	1	no	—
103	C₂×D₄×C₁₀₇	—	4	2	no	—
104	C₂×D₄×C₁₀₇	—	4	4	no	—
105	C₂×D₄×C₁₀₇	—	4	2	no	—
106	C₂×D₄×C₁₀₇	—	4	4	no	—
107	C₂×D₄×C₁₀₇	—	4	2	no	—
108	C₂×D₄×C₁₀₇	—	4	4	no	—
109	C₂×D₄×C₁₀₇	—	4	1	no	—
110	C₂×D₄×C₁₀₇	—	4	1	no	—
111	C₂×D₄×C₁₀₇	—	4	1	no	—
112	C₂×D₄×C₁₀₇	—	4	1	no	—
113	C₂×D₄×C₁₀₇	—	4	1	no	—
114	C₂×D₄×C₁₀₇	—	8	4	no	—
115	C₂²×C₄×C₁₀₇	—	2	1	no	—
116	C₂²×C₄×C₁₀₇	—	2	1	no	—
117	C₂²×C₄×C₁₀₇	—	2	1	no	—
118	C₂²×C₄×C₁₀₇	—	2	1	no	—
119	C₂²×C₄×C₁₀₇	—	4	2	no	—
120	C₂²×C₄×C₁₀₇	—	4	4	no	—
121	C₂²×C₄×C₁₀₇	—	4	4	no	—
122	C₂²×C₄×C₁₀₇	—	4	1	no	—
123	C₂²×C₄×C₁₀₇	—	4	2	no	—
124	C₂²×C₄×C₁₀₇	—	4	1	no	—
125	C₂²×C₄×C₁₀₇	D₈	1	1	yes	characteristic
126	C₂²×C₄×C₁₀₇	D₈	1	2	yes	—
127	C₂²×C₄×C₁₀₇	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
129	Q₁₆×C₁₀₇	—	2	4	no	—
130	Q₁₆×C₁₀₇	—	2	2	no	—
131	Q₁₆×C₁₀₇	C₂×D₄	1	4	yes	complemented
132	SD₁₆×C₁₀₇	—	2	8	no	—
133	SD₁₆×C₁₀₇	—	2	4	no	—
134	SD₁₆×C₁₀₇	—	2	4	no	—
135	D₈×C₁₀₇	—	2	4	no	—
136	D₈×C₁₀₇	—	2	2	no	—
137	D₈×C₁₀₇	—	2	4	no	—
138	D₈×C₁₀₇	—	4	2	no	—
139	D₈×C₁₀₇	C₂×D₄	1	4	yes	complemented
140	M₁₆×C₁₀₇	—	2	4	no	—
141	M₁₆×C₁₀₇	—	2	4	no	—
142	C₂×C₈×C₁₀₇	—	2	1	no	—
143	C₂×C₈×C₁₀₇	—	2	1	no	—
144	C₂×C₈×C₁₀₇	C₂×D₄	1	2	yes	—
145	C₂×C₈×C₁₀₇	C₂×D₄	1	1	yes	characteristic
146	C₂×C₈×C₁₀₇	C₂×D₄	1	2	yes	—
147	C₂×C₈×C₁₀₇	C₂×D₄	1	2	yes	—
148	C₂×C₈×C₁₀₇	C₂⁴	1	1	yes	characteristic
149	C₄⋊C₄×C₁₀₇	—	2	2	no	—
150	C₄⋊C₄×C₁₀₇	—	4	1	no	—
151	C₂²⋊C₄×C₁₀₇	—	4	4	no	—
152	C₁₆×C₁₀₇	—	2	4	no	—
153	C₂³×C₁₀₇	—	2	1	no	—
154	C₂³×C₁₀₇	—	2	1	no	—
155	C₂³×C₁₀₇	—	4	2	no	—
156	C₂³×C₁₀₇	—	4	4	no	—
157	C₂³×C₁₀₇	—	4	2	no	—
158	C₂³×C₁₀₇	—	4	2	no	—
159	C₂³×C₁₀₇	—	8	2	no	—
160	C₂³×C₁₀₇	—	8	2	no	—
161	C₂³×C₁₀₇	—	8	4	no	—
162	C₂³×C₁₀₇	—	8	1	no	—
163	C₂³×C₁₀₇	—	8	1	no	—
164	C₂³×C₁₀₇	C₂×D₈	1	1	yes	characteristic
165	C₂³×C₁₀₇	C₂×D₈	1	2	yes	—
166	Q₈×C₁₀₇	—	2	4	no	—
167	Q₈×C₁₀₇	—	4	4	no	—
168	Q₈×C₁₀₇	—	4	2	no	—
169	D₄×C₁₀₇	—	2	4	no	—
170	D₄×C₁₀₇	—	4	4	no	—
171	D₄×C₁₀₇	—	4	8	no	—
172	D₄×C₁₀₇	—	4	4	no	—
173	D₄×C₁₀₇	—	4	4	no	—
174	D₄×C₁₀₇	—	4	2	no	—
175	D₄×C₁₀₇	—	4	2	no	—
176	D₄×C₁₀₇	—	4	2	no	—
177	D₄×C₁₀₇	—	8	8	no	—
178	D₄×C₁₀₇	—	8	1	no	—
179	D₄×C₁₀₇	—	8	1	no	—
180	C₂×C₄×C₁₀₇	—	2	1	no	—
181	C₂×C₄×C₁₀₇	—	2	1	no	—
182	C₂×C₄×C₁₀₇	—	2	2	no	—
183	C₂×C₄×C₁₀₇	—	2	2	no	—
184	C₂×C₄×C₁₀₇	—	2	2	no	—
185	C₂×C₄×C₁₀₇	—	2	2	no	—
186	C₂×C₄×C₁₀₇	—	4	8	no	—
187	C₂×C₄×C₁₀₇	—	4	4	no	—
188	C₂×C₄×C₁₀₇	—	4	2	no	—
189	C₂×C₄×C₁₀₇	—	4	4	no	—
190	C₂×C₄×C₁₀₇	—	4	4	no	—
191	C₂×C₄×C₁₀₇	—	4	2	no	—
192	C₂×C₄×C₁₀₇	—	8	2	no	—
193	C₂×C₄×C₁₀₇	#120	1	1	yes	characteristic
194	C₂×C₄×C₁₀₇	#120	1	1	yes	characteristic
195	C₂×C₄×C₁₀₇	C₂×D₈	1	2	yes	—
196	C₂×C₄×C₁₀₇	C₂×D₈	1	1	yes	characteristic
197	C₂×C₄×C₁₀₇	AGL(1,ℤ/8)	1	1	yes	characteristic
198	C₂×C₄×C₁₀₇	AGL(1,ℤ/8)	1	1	yes	characteristic
199	C₂×C₄×C₁₀₇	C₂²×D₄	1	1	yes	characteristic
200	C₈×C₁₀₇	—	2	2	no	—
201	C₈×C₁₀₇	#120	1	2	yes	—
202	C₈×C₁₀₇	C₂²×D₄	1	2	yes	—
203	C₂²×C₁₀₇	—	2	2	no	—
204	C₂²×C₁₀₇	—	2	2	no	—
205	C₂²×C₁₀₇	—	4	2	no	—
206	C₂²×C₁₀₇	—	4	2	no	—
207	C₂²×C₁₀₇	—	4	4	no	—
208	C₂²×C₁₀₇	—	8	1	no	—
209	C₂²×C₁₀₇	—	8	2	no	—
210	C₂²×C₁₀₇	—	8	2	no	—
211	C₂²×C₁₀₇	—	8	8	no	—
212	C₂²×C₁₀₇	—	8	4	no	—
213	C₂²×C₁₀₇	—	8	2	no	—
214	C₂²×C₁₀₇	—	16	2	no	—
215	C₂²×C₁₀₇	—	16	2	no	—
216	C₂²×C₁₀₇	#447	1	1	yes	characteristic
217	C₂²×C₁₀₇	#447	1	1	yes	characteristic
218	C₂²×C₁₀₇	C₂²×D₈	1	1	yes	characteristic
219	C₄×C₁₀₇	—	2	2	no	—
220	C₄×C₁₀₇	—	4	4	no	—
221	C₄×C₁₀₇	—	8	2	no	—
222	C₄×C₁₀₇	#447	1	1	yes	characteristic
223	C₄×C₁₀₇	#447	1	1	yes	characteristic
224	C₄×C₁₀₇	C₂×#120	1	1	yes	characteristic
225	C₄×C₁₀₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
226	C₂×#2190	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
227	C₂×C₁₀₇	—	2	1	no	—
228	C₂×C₁₀₇	—	2	1	no	—
229	C₂×C₁₀₇	—	4	2	no	—
230	C₂×C₁₀₇	—	8	4	no	—
231	C₂×C₁₀₇	—	16	2	no	—
232	C₂×C₁₀₇	#2190	1	2	yes	direct product factor
233	C₂×C₁₀₇	C₂×#447	1	1	yes	characteristic
234	C₂×#575	C₂×C₁₀₇	1	1	yes	characteristic, complemented
235	C₂×#509	C₂×C₁₀₇	1	2	yes	complemented
236	C₂×#469	C₂×C₁₀₇	1	1	yes	characteristic, complemented
237	#2190	C₂×C₁₀₇	1	8	yes	direct product factor
238	C₂×#360	C₂×C₁₀₇	1	2	yes	complemented
239	C₂×#349	C₂×C₁₀₇	1	1	yes	characteristic, complemented
240	C₁₀₇	C₂×#2190	1	1	yes	characteristic, direct product factor, Sylow
241	C₂²×#41	—	2	1	no	—
242	#575	—	2	4	no	—
243	#575	—	2	2	no	—
244	#575	C₂²×C₁₀₇	1	4	yes	complemented
245	C₂×#137	—	2	2	no	—
246	C₂×AGL(1,ℤ/8)	—	2	2	no	—
247	C₂×#135	—	2	1	no	—
248	C₂×#135	C₂²×C₁₀₇	1	2	yes	—
249	C₂²×D₈	C₂²×C₁₀₇	1	1	yes	characteristic, complemented
250	C₂²×M₁₆	C₂²×C₁₀₇	1	1	yes	characteristic
251	C₂×#121	—	2	1	no	—
252	#509	—	2	4	no	—
253	#509	C₂²×C₁₀₇	1	8	yes	complemented
254	C₂×SD₃₂	—	2	2	no	—
255	C₂×D₁₆	—	2	2	no	—
256	C₂×M₃₂	C₂²×C₁₀₇	1	2	yes	complemented
257	#469	—	2	2	no	—
258	#469	C₂²×C₁₀₇	1	4	yes	complemented
259	C₂×#106	C₂²×C₁₀₇	1	1	yes	characteristic, complemented
260	C₂×#102	—	2	1	no	—
261	#360	C₂²×C₁₀₇	1	8	yes	complemented
262	#349	C₂²×C₁₀₇	1	4	yes	complemented
263	C₂×#41	—	2	2	no	—
264	C₂×#41	—	2	4	no	—
265	C₂×#41	—	2	2	no	—
266	C₂×#41	—	2	4	no	—
267	C₂×#41	—	4	1	no	—
268	C₂×#41	—	4	2	no	—
269	C₂×#41	—	4	1	no	—
270	C₂×#41	—	4	2	no	—
271	C₂²×Q₈	—	2	1	no	—
272	C₂²×D₄	—	2	1	no	—
273	C₂²×D₄	—	2	1	no	—
274	C₂²×D₄	—	4	1	no	—
275	C₂²×D₄	—	4	1	no	—
276	C₂³×C₄	—	4	1	no	—
277	C₂³×C₄	D₄×C₁₀₇	1	1	yes	characteristic
278	#137	—	2	8	no	—
279	#137	—	2	8	no	—
280	AGL(1,ℤ/8)	—	2	8	no	—
281	AGL(1,ℤ/8)	—	2	8	no	—
282	#135	—	2	4	no	—
283	#135	—	2	4	no	—
284	#135	—	2	2	no	—
285	#135	—	2	2	no	—
286	#135	D₄×C₁₀₇	1	4	yes	complemented
287	#135	C₂³×C₁₀₇	1	4	yes	—
288	C₂×Q₁₆	—	2	1	no	—
289	C₂×Q₁₆	D₄×C₁₀₇	1	2	yes	complemented
290	C₂×SD₁₆	—	2	2	no	—
291	C₂×SD₁₆	—	2	2	no	—
292	C₂×D₈	—	2	1	no	—
293	C₂×D₈	—	2	2	no	—
294	C₂×D₈	—	2	2	no	—
295	C₂×D₈	—	2	1	no	—
296	C₂×D₈	D₄×C₁₀₇	1	2	yes	complemented
297	C₂×D₈	C₂³×C₁₀₇	1	2	yes	complemented
298	C₂×M₁₆	—	2	2	no	—
299	C₂×M₁₆	—	2	2	no	—
300	C₂×M₁₆	D₄×C₁₀₇	1	2	yes	—
301	C₂×M₁₆	C₂³×C₁₀₇	1	2	yes	—
302	C₂²×C₈	D₄×C₁₀₇	1	1	yes	characteristic
303	C₂²×C₈	C₂³×C₁₀₇	1	1	yes	characteristic
304	#121	—	2	4	no	—
305	#121	—	4	2	no	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₂²⋊C₄	—	4	1	no	—
308	SD₃₂	—	2	8	no	—
309	D₁₆	—	2	8	no	—
310	M₃₂	—	2	2	no	—
311	M₃₂	C₂³×C₁₀₇	1	4	yes	complemented
312	C₂×C₁₆	—	2	2	no	—
313	#106	—	2	1	no	—
314	#106	C₂³×C₁₀₇	1	2	yes	complemented
315	#102	—	2	4	no	—
316	C₂⁴	—	4	1	no	—
317	C₂⁴	—	4	1	no	—
318	C₂⁴	D₈×C₁₀₇	1	1	yes	characteristic
319	#41	—	2	8	no	—
320	#41	—	2	4	no	—
321	#41	—	2	4	no	—
322	#41	—	4	4	no	—
323	#41	—	4	4	no	—
324	#41	—	4	4	no	—
325	#41	—	4	4	no	—
326	#41	—	4	4	no	—
327	#41	—	4	2	no	—
328	#41	—	4	2	no	—
329	C₂×Q₈	—	2	4	no	—
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	—	4	1	no	—
332	C₂×Q₈	—	4	2	no	—
333	C₂×D₄	—	2	4	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	4	1	no	—
337	C₂×D₄	—	4	2	no	—
338	C₂×D₄	—	4	4	no	—
339	C₂×D₄	—	4	2	no	—
340	C₂×D₄	—	4	4	no	—
341	C₂×D₄	—	4	2	no	—
342	C₂×D₄	—	4	4	no	—
343	C₂×D₄	—	4	1	no	—
344	C₂×D₄	—	4	1	no	—
345	C₂×D₄	—	4	1	no	—
346	C₂×D₄	—	4	1	no	—
347	C₂×D₄	—	4	1	no	—
348	C₂×D₄	—	8	4	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	4	2	no	—
354	C₂²×C₄	—	4	4	no	—
355	C₂²×C₄	—	4	4	no	—
356	C₂²×C₄	—	4	1	no	—
357	C₂²×C₄	—	4	2	no	—
358	C₂²×C₄	—	4	1	no	—
359	C₂²×C₄	D₈×C₁₀₇	1	1	yes	characteristic
360	C₂²×C₄	D₈×C₁₀₇	1	2	yes	—
361	C₂²×C₄	C₂×D₄×C₁₀₇	1	2	yes	—
362	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
363	Q₁₆	—	2	4	no	—
364	Q₁₆	—	2	2	no	—
365	Q₁₆	C₂×D₄×C₁₀₇	1	4	yes	complemented
366	SD₁₆	—	2	8	no	—
367	SD₁₆	—	2	4	no	—
368	SD₁₆	—	2	4	no	—
369	D₈	—	2	4	no	—
370	D₈	—	2	2	no	—
371	D₈	—	2	4	no	—
372	D₈	—	4	2	no	—
373	D₈	C₂×D₄×C₁₀₇	1	4	yes	complemented
374	M₁₆	—	2	4	no	—
375	M₁₆	—	2	4	no	—
376	C₂×C₈	—	2	1	no	—
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	C₂×D₄×C₁₀₇	1	2	yes	—
379	C₂×C₈	C₂×D₄×C₁₀₇	1	1	yes	characteristic
380	C₂×C₈	C₂×D₄×C₁₀₇	1	2	yes	—
381	C₂×C₈	C₂×D₄×C₁₀₇	1	2	yes	—
382	C₂×C₈	C₂⁴×C₁₀₇	1	1	yes	characteristic
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	4	1	no	—
385	C₂²⋊C₄	—	4	4	no	—
386	C₁₆	—	2	4	no	—
387	C₂³	—	2	1	no	—
388	C₂³	—	2	1	no	—
389	C₂³	—	4	2	no	—
390	C₂³	—	4	4	no	—
391	C₂³	—	4	2	no	—
392	C₂³	—	4	2	no	—
393	C₂³	—	8	2	no	—
394	C₂³	—	8	2	no	—
395	C₂³	—	8	4	no	—
396	C₂³	—	8	1	no	—
397	C₂³	—	8	1	no	—
398	C₂³	C₂×D₈×C₁₀₇	1	1	yes	characteristic
399	C₂³	C₂×D₈×C₁₀₇	1	2	yes	—
400	Q₈	—	2	4	no	—
401	Q₈	—	4	4	no	—
402	Q₈	—	4	2	no	—
403	D₄	—	2	4	no	—
404	D₄	—	4	4	no	—
405	D₄	—	4	8	no	—
406	D₄	—	4	4	no	—
407	D₄	—	4	4	no	—
408	D₄	—	4	2	no	—
409	D₄	—	4	2	no	—
410	D₄	—	4	2	no	—
411	D₄	—	8	8	no	—
412	D₄	—	8	1	no	—
413	D₄	—	8	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	4	8	no	—
421	C₂×C₄	—	4	4	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	4	no	—
424	C₂×C₄	—	4	4	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	8	2	no	—
427	C₂×C₄	#120×C₁₀₇	1	1	yes	characteristic
428	C₂×C₄	#120×C₁₀₇	1	1	yes	characteristic
429	C₂×C₄	C₂×D₈×C₁₀₇	1	2	yes	—
430	C₂×C₄	C₂×D₈×C₁₀₇	1	1	yes	characteristic
431	C₂×C₄	AGL(1,ℤ/8)×C₁₀₇	1	1	yes	characteristic
432	C₂×C₄	AGL(1,ℤ/8)×C₁₀₇	1	1	yes	characteristic
433	C₂×C₄	C₂²×D₄×C₁₀₇	1	1	yes	characteristic
434	C₈	—	2	2	no	—
435	C₈	#120×C₁₀₇	1	2	yes	—
436	C₈	C₂²×D₄×C₁₀₇	1	2	yes	—
437	C₂²	—	2	2	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	4	no	—
442	C₂²	—	8	1	no	—
443	C₂²	—	8	2	no	—
444	C₂²	—	8	2	no	—
445	C₂²	—	8	8	no	—
446	C₂²	—	8	4	no	—
447	C₂²	—	8	2	no	—
448	C₂²	—	16	2	no	—
449	C₂²	—	16	2	no	—
450	C₂²	#447×C₁₀₇	1	1	yes	characteristic
451	C₂²	#447×C₁₀₇	1	1	yes	characteristic
452	C₂²	C₂²×D₈×C₁₀₇	1	1	yes	characteristic
453	C₄	—	2	2	no	—
454	C₄	—	4	4	no	—
455	C₄	—	8	2	no	—
456	C₄	#447×C₁₀₇	1	1	yes	characteristic
457	C₄	#447×C₁₀₇	1	1	yes	characteristic
458	C₄	C₂×#120×C₁₀₇	1	1	yes	characteristic
459	C₄	C₂×AGL(1,ℤ/8)×C₁₀₇	1	1	yes	characteristic
460	C₂	—	2	1	no	—
461	C₂	—	2	1	no	—
462	C₂	—	4	2	no	—
463	C₂	—	8	4	no	—
464	C₂	—	16	2	no	—
465	C₂	C₁₀₇×#2190	1	2	yes	direct product factor
466	C₂	C₂×#447×C₁₀₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₀₇	#447
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₀₇
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₇ ◁ C₂²×C₄×C₁₀₇ ◁ C₂²×M₁₆×C₁₀₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#575×C₁₀₇	C₂	semidirect
2. C₂×#509×C₁₀₇	C₂	semidirect
3. C₂×#469×C₁₀₇	C₂	semidirect
4. C₁₀₇×#2190	C₂	direct (N × H)
5. C₂×#360×C₁₀₇	C₂	semidirect
6. C₂×#349×C₁₀₇	C₂	semidirect
10. #575×C₁₀₇	C₂²	semidirect
15. C₂²×D₈×C₁₀₇	C₂²	semidirect
19. #509×C₁₀₇	C₂²	semidirect
22. C₂×M₃₂×C₁₀₇	C₂²	semidirect
24. #469×C₁₀₇	C₂²	semidirect
25. C₂×#106×C₁₀₇	C₂²	semidirect
27. #360×C₁₀₇	C₂²	semidirect
28. #349×C₁₀₇	C₂²	semidirect
52. #135×C₁₀₇	D₄	semidirect
55. C₂×Q₁₆×C₁₀₇	D₄	semidirect
62. C₂×D₈×C₁₀₇	D₄	semidirect
63. C₂×D₈×C₁₀₇	C₂³	semidirect
77. M₃₂×C₁₀₇	C₂³	semidirect
80. #106×C₁₀₇	C₂³	semidirect
131. Q₁₆×C₁₀₇	C₂×D₄	semidirect
139. D₈×C₁₀₇	C₂×D₄	semidirect
226. C₂×#2190	C₁₀₇	direct (N × H)
232. C₂×C₁₀₇	#2190	direct (N × H)
234. C₂×#575	C₂×C₁₀₇	semidirect
235. C₂×#509	C₂×C₁₀₇	semidirect
236. C₂×#469	C₂×C₁₀₇	semidirect
237. #2190	C₂×C₁₀₇	direct (N × H)
238. C₂×#360	C₂×C₁₀₇	semidirect
239. C₂×#349	C₂×C₁₀₇	semidirect
240. C₁₀₇	C₂×#2190	direct (N × H)
244. #575	C₂²×C₁₀₇	semidirect
249. C₂²×D₈	C₂²×C₁₀₇	semidirect
253. #509	C₂²×C₁₀₇	semidirect
256. C₂×M₃₂	C₂²×C₁₀₇	semidirect
258. #469	C₂²×C₁₀₇	semidirect
259. C₂×#106	C₂²×C₁₀₇	semidirect
261. #360	C₂²×C₁₀₇	semidirect
262. #349	C₂²×C₁₀₇	semidirect
286. #135	D₄×C₁₀₇	semidirect
289. C₂×Q₁₆	D₄×C₁₀₇	semidirect
296. C₂×D₈	D₄×C₁₀₇	semidirect
297. C₂×D₈	C₂³×C₁₀₇	semidirect
311. M₃₂	C₂³×C₁₀₇	semidirect
314. #106	C₂³×C₁₀₇	semidirect
365. Q₁₆	C₂×D₄×C₁₀₇	semidirect
373. D₈	C₂×D₄×C₁₀₇	semidirect
465. C₂	C₁₀₇×#2190	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×#575×C₁₀₇	2
C₂×#509×C₁₀₇	2
C₂×#469×C₁₀₇	2
C₁₀₇×#2190	2
C₂×#360×C₁₀₇	2
C₂×#349×C₁₀₇	2
C₂×#2190	107

Subgroups — C2×C107×#2190 #41059492

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₀₇×#2190 #41059492