Subgroups — C₂×C₁₀₇×#1271 #41033523

Order 27392.

714 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#389×C₁₀₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#336×C₁₀₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#336×C₁₀₇	C₂	1	1	yes	maximal, characteristic
4	C₁₀₇×#1271	C₂	1	4	yes	maximal, direct product factor
5	C₂³×C₈×C₁₀₇	—	2	1	no	—
6	C₂³×C₈×C₁₀₇	—	2	1	no	—
7	C₂²×C₄⋊C₄×C₁₀₇	—	2	1	no	—
8	C₂²×C₄⋊C₄×C₁₀₇	C₄	1	1	yes	characteristic
9	C₂²×C₄⋊C₄×C₁₀₇	C₄	1	1	yes	characteristic
10	C₂²×C₄²×C₁₀₇	C₂²	1	1	yes	characteristic
11	#389×C₁₀₇	—	2	1	no	—
12	#389×C₁₀₇	—	2	1	no	—
13	#389×C₁₀₇	C₄	1	2	yes	—
14	#389×C₁₀₇	C₂²	1	2	yes	—
15	C₂×#95×C₁₀₇	—	2	1	no	—
16	#336×C₁₀₇	—	2	1	no	—
17	#336×C₁₀₇	—	2	1	no	—
18	#336×C₁₀₇	C₂²	1	2	yes	—
19	#336×C₁₀₇	C₂²	1	2	yes	—
20	C₂³×C₄×C₁₀₇	—	2	1	no	—
21	C₂³×C₄×C₁₀₇	—	2	1	no	—
22	C₂³×C₄×C₁₀₇	C₂×C₄	1	1	yes	characteristic
23	C₂³×C₄×C₁₀₇	D₄	1	1	yes	characteristic
24	C₂³×C₄×C₁₀₇	D₄	1	1	yes	characteristic
25	C₂²×C₈×C₁₀₇	—	2	4	no	—
26	C₂²×C₈×C₁₀₇	—	2	4	no	—
27	C₂²×C₈×C₁₀₇	—	2	2	no	—
28	C₂²×C₈×C₁₀₇	—	2	2	no	—
29	C₂²×C₈×C₁₀₇	—	4	2	no	—
30	C₂²×C₈×C₁₀₇	—	4	2	no	—
31	C₂²×C₈×C₁₀₇	—	4	2	no	—
32	C₂²×C₈×C₁₀₇	—	4	2	no	—
33	C₂×C₄⋊C₄×C₁₀₇	—	2	1	no	—
34	C₂×C₄⋊C₄×C₁₀₇	—	2	2	no	—
35	C₂×C₄⋊C₄×C₁₀₇	—	2	1	no	—
36	C₂×C₄⋊C₄×C₁₀₇	—	2	2	no	—
37	C₂×C₄⋊C₄×C₁₀₇	—	2	2	no	—
38	C₂×C₄⋊C₄×C₁₀₇	—	4	2	no	—
39	C₂×C₄⋊C₄×C₁₀₇	—	4	2	no	—
40	C₂×C₄⋊C₄×C₁₀₇	—	4	2	no	—
41	C₂×C₄⋊C₄×C₁₀₇	C₈	1	4	yes	complemented
42	C₂×C₄⋊C₄×C₁₀₇	C₂×C₄	1	2	yes	—
43	C₂×C₄⋊C₄×C₁₀₇	C₂×C₄	1	2	yes	—
44	C₂×C₄²×C₁₀₇	—	4	2	no	—
45	C₂×C₄²×C₁₀₇	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₁₀₇	D₄	1	1	yes	characteristic
47	C₂×C₄²×C₁₀₇	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₁₀₇	C₂³	1	1	yes	characteristic
49	#95×C₁₀₇	—	2	2	no	—
50	#95×C₁₀₇	—	2	2	no	—
51	C₂⁴×C₁₀₇	C₂²⋊C₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₀₇	—	2	2	no	—
53	C₂²×C₄×C₁₀₇	—	2	2	no	—
54	C₂²×C₄×C₁₀₇	—	2	2	no	—
55	C₂²×C₄×C₁₀₇	—	2	2	no	—
56	C₂²×C₄×C₁₀₇	—	2	2	no	—
57	C₂²×C₄×C₁₀₇	—	2	2	no	—
58	C₂²×C₄×C₁₀₇	—	2	4	no	—
59	C₂²×C₄×C₁₀₇	—	2	2	no	—
60	C₂²×C₄×C₁₀₇	—	2	2	no	—
61	C₂²×C₄×C₁₀₇	—	4	2	no	—
62	C₂²×C₄×C₁₀₇	—	4	2	no	—
63	C₂²×C₄×C₁₀₇	—	4	2	no	—
64	C₂²×C₄×C₁₀₇	—	4	2	no	—
65	C₂²×C₄×C₁₀₇	—	4	2	no	—
66	C₂²×C₄×C₁₀₇	C₂²⋊C₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₀₇	C₂²⋊C₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₀₇	C₂²⋊C₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₀₇	C₂×C₈	1	2	yes	—
70	C₂²×C₄×C₁₀₇	M₁₆	1	2	yes	—
71	C₂²×C₄×C₁₀₇	D₈	1	2	yes	—
72	C₂²×C₄×C₁₀₇	SD₁₆	1	2	yes	—
73	C₂²×C₄×C₁₀₇	SD₁₆	1	2	yes	—
74	C₂²×C₄×C₁₀₇	Q₁₆	1	2	yes	—
75	C₂²×C₄×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
78	C₂×C₈×C₁₀₇	—	2	4	no	—
79	C₂×C₈×C₁₀₇	—	2	4	no	—
80	C₂×C₈×C₁₀₇	—	4	8	no	—
81	C₂×C₈×C₁₀₇	—	4	8	no	—
82	C₂×C₈×C₁₀₇	—	4	2	no	—
83	C₂×C₈×C₁₀₇	—	4	2	no	—
84	C₂×C₈×C₁₀₇	—	4	2	no	—
85	C₂×C₈×C₁₀₇	—	4	2	no	—
86	C₄⋊C₄×C₁₀₇	—	2	4	no	—
87	C₄⋊C₄×C₁₀₇	—	2	2	no	—
88	C₄⋊C₄×C₁₀₇	—	4	2	no	—
89	C₄⋊C₄×C₁₀₇	—	4	2	no	—
90	C₄⋊C₄×C₁₀₇	—	4	4	no	—
91	C₄⋊C₄×C₁₀₇	—	4	2	no	—
92	C₄⋊C₄×C₁₀₇	—	4	2	no	—
93	C₄⋊C₄×C₁₀₇	C₂×C₈	1	4	yes	complemented
94	C₄²×C₁₀₇	—	4	1	no	—
95	C₄²×C₁₀₇	—	4	1	no	—
96	C₄²×C₁₀₇	—	4	1	no	—
97	C₄²×C₁₀₇	—	4	1	no	—
98	C₂³×C₁₀₇	C₂²⋊C₈	1	2	yes	—
99	C₂³×C₁₀₇	#99	1	2	yes	—
100	C₂³×C₁₀₇	#101	1	2	yes	—
101	C₂³×C₁₀₇	#102	1	2	yes	—
102	C₂³×C₁₀₇	#103	1	2	yes	—
103	C₂³×C₁₀₇	#104	1	2	yes	—
104	C₂³×C₁₀₇	#104	1	2	yes	—
105	C₂³×C₁₀₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
106	C₂×C₄×C₁₀₇	—	2	4	no	—
107	C₂×C₄×C₁₀₇	—	2	4	no	—
108	C₂×C₄×C₁₀₇	—	2	4	no	—
109	C₂×C₄×C₁₀₇	—	2	4	no	—
110	C₂×C₄×C₁₀₇	—	2	4	no	—
111	C₂×C₄×C₁₀₇	—	2	4	no	—
112	C₂×C₄×C₁₀₇	—	2	1	no	—
113	C₂×C₄×C₁₀₇	—	2	1	no	—
114	C₂×C₄×C₁₀₇	—	2	1	no	—
115	C₂×C₄×C₁₀₇	—	2	1	no	—
116	C₂×C₄×C₁₀₇	—	2	1	no	—
117	C₂×C₄×C₁₀₇	—	2	1	no	—
118	C₂×C₄×C₁₀₇	—	2	1	no	—
119	C₂×C₄×C₁₀₇	—	2	1	no	—
120	C₂×C₄×C₁₀₇	—	2	1	no	—
121	C₂×C₄×C₁₀₇	—	2	1	no	—
122	C₂×C₄×C₁₀₇	—	2	1	no	—
123	C₂×C₄×C₁₀₇	—	2	1	no	—
124	C₂×C₄×C₁₀₇	—	2	4	no	—
125	C₂×C₄×C₁₀₇	—	4	8	no	—
126	C₂×C₄×C₁₀₇	—	4	2	no	—
127	C₂×C₄×C₁₀₇	—	4	2	no	—
128	C₂×C₄×C₁₀₇	—	4	2	no	—
129	C₂×C₄×C₁₀₇	—	4	2	no	—
130	C₂×C₄×C₁₀₇	—	4	2	no	—
131	C₂×C₄×C₁₀₇	—	8	4	no	—
132	C₂×C₄×C₁₀₇	C₂²⋊C₈	1	2	yes	—
133	C₂×C₄×C₁₀₇	#102	1	2	yes	—
134	C₂×C₄×C₁₀₇	#103	1	2	yes	—
135	C₂×C₄×C₁₀₇	C₂²×C₈	1	1	yes	characteristic
136	C₂×C₄×C₁₀₇	C₂×M₁₆	1	1	yes	characteristic
137	C₂×C₄×C₁₀₇	C₂×D₈	1	1	yes	characteristic
138	C₂×C₄×C₁₀₇	C₂×SD₁₆	1	1	yes	characteristic
139	C₂×C₄×C₁₀₇	C₂×SD₁₆	1	1	yes	characteristic
140	C₂×C₄×C₁₀₇	C₂×Q₁₆	1	1	yes	characteristic
141	C₈×C₁₀₇	—	4	4	no	—
142	C₈×C₁₀₇	—	4	4	no	—
143	C₂²×C₁₀₇	#324	1	4	yes	—
144	C₂²×C₁₀₇	D₄⋊C₈	1	4	yes	—
145	C₂²×C₁₀₇	Q₈⋊C₈	1	4	yes	—
146	C₂²×C₁₀₇	#327	1	4	yes	—
147	C₂²×C₁₀₇	#328	1	4	yes	—
148	C₂²×C₁₀₇	#330	1	4	yes	—
149	C₂²×C₁₀₇	#332	1	4	yes	—
150	C₂²×C₁₀₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
151	C₂²×C₁₀₇	C₂×#99	1	1	yes	characteristic
152	C₂²×C₁₀₇	C₂×#101	1	1	yes	characteristic
153	C₂²×C₁₀₇	C₂×#102	1	1	yes	characteristic
154	C₂²×C₁₀₇	C₂×#103	1	1	yes	characteristic
155	C₂²×C₁₀₇	C₂×#104	1	1	yes	characteristic
156	C₂²×C₁₀₇	C₂×#104	1	1	yes	characteristic
157	C₄×C₁₀₇	—	2	2	no	—
158	C₄×C₁₀₇	—	2	1	no	—
159	C₄×C₁₀₇	—	2	1	no	—
160	C₄×C₁₀₇	—	2	1	no	—
161	C₄×C₁₀₇	—	2	2	no	—
162	C₄×C₁₀₇	—	2	1	no	—
163	C₄×C₁₀₇	—	2	1	no	—
164	C₄×C₁₀₇	—	2	2	no	—
165	C₄×C₁₀₇	—	2	1	no	—
166	C₄×C₁₀₇	—	4	4	no	—
167	C₄×C₁₀₇	—	8	2	no	—
168	C₂×#1271	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
169	C₂×C₁₀₇	#1271	1	8	yes	direct product factor
170	C₂×C₁₀₇	C₂×#324	1	1	yes	characteristic
171	C₂×C₁₀₇	C₂×D₄⋊C₈	1	1	yes	characteristic
172	C₂×C₁₀₇	C₂×Q₈⋊C₈	1	1	yes	characteristic
173	C₂×C₁₀₇	C₂×#327	1	1	yes	characteristic
174	C₂×C₁₀₇	C₂×#328	1	1	yes	characteristic
175	C₂×C₁₀₇	C₂×#330	1	1	yes	characteristic
176	C₂×C₁₀₇	C₂×#332	1	1	yes	characteristic
177	C₂×#389	C₂×C₁₀₇	1	1	yes	characteristic
178	C₂×#336	C₂×C₁₀₇	1	1	yes	characteristic
179	C₂×#336	C₂×C₁₀₇	1	1	yes	characteristic
180	#1271	C₂×C₁₀₇	1	4	yes	direct product factor
181	C₁₀₇	C₂×#1271	1	1	yes	characteristic, direct product factor, Sylow
182	C₂³×C₈	—	2	1	no	—
183	C₂³×C₈	—	2	1	no	—
184	C₂²×C₄⋊C₄	—	2	1	no	—
185	C₂²×C₄⋊C₄	C₄×C₁₀₇	1	1	yes	characteristic
186	C₂²×C₄⋊C₄	C₄×C₁₀₇	1	1	yes	characteristic
187	C₂²×C₄²	C₂²×C₁₀₇	1	1	yes	characteristic
188	#389	—	2	1	no	—
189	#389	—	2	1	no	—
190	#389	C₄×C₁₀₇	1	2	yes	—
191	#389	C₂²×C₁₀₇	1	2	yes	—
192	C₂×#95	—	2	1	no	—
193	#336	—	2	1	no	—
194	#336	—	2	1	no	—
195	#336	C₂²×C₁₀₇	1	2	yes	—
196	#336	C₂²×C₁₀₇	1	2	yes	—
197	C₂³×C₄	—	2	1	no	—
198	C₂³×C₄	—	2	1	no	—
199	C₂³×C₄	C₂×C₄×C₁₀₇	1	1	yes	characteristic
200	C₂³×C₄	D₄×C₁₀₇	1	1	yes	characteristic
201	C₂³×C₄	D₄×C₁₀₇	1	1	yes	characteristic
202	C₂²×C₈	—	2	4	no	—
203	C₂²×C₈	—	2	4	no	—
204	C₂²×C₈	—	2	2	no	—
205	C₂²×C₈	—	2	2	no	—
206	C₂²×C₈	—	4	2	no	—
207	C₂²×C₈	—	4	2	no	—
208	C₂²×C₈	—	4	2	no	—
209	C₂²×C₈	—	4	2	no	—
210	C₂×C₄⋊C₄	—	2	1	no	—
211	C₂×C₄⋊C₄	—	2	2	no	—
212	C₂×C₄⋊C₄	—	2	2	no	—
213	C₂×C₄⋊C₄	—	2	1	no	—
214	C₂×C₄⋊C₄	—	2	2	no	—
215	C₂×C₄⋊C₄	—	4	2	no	—
216	C₂×C₄⋊C₄	—	4	2	no	—
217	C₂×C₄⋊C₄	—	4	2	no	—
218	C₂×C₄⋊C₄	C₈×C₁₀₇	1	4	yes	complemented
219	C₂×C₄⋊C₄	C₂×C₄×C₁₀₇	1	2	yes	—
220	C₂×C₄⋊C₄	C₂×C₄×C₁₀₇	1	2	yes	—
221	C₂×C₄²	—	4	2	no	—
222	C₂×C₄²	C₂×C₄×C₁₀₇	1	1	yes	characteristic
223	C₂×C₄²	D₄×C₁₀₇	1	1	yes	characteristic
224	C₂×C₄²	D₄×C₁₀₇	1	1	yes	characteristic
225	C₂×C₄²	C₂³×C₁₀₇	1	1	yes	characteristic
226	#95	—	2	2	no	—
227	#95	—	2	2	no	—
228	C₂⁴	C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
229	C₂²×C₄	—	2	2	no	—
230	C₂²×C₄	—	2	2	no	—
231	C₂²×C₄	—	2	2	no	—
232	C₂²×C₄	—	2	2	no	—
233	C₂²×C₄	—	2	2	no	—
234	C₂²×C₄	—	2	2	no	—
235	C₂²×C₄	—	2	4	no	—
236	C₂²×C₄	—	2	2	no	—
237	C₂²×C₄	—	2	2	no	—
238	C₂²×C₄	—	4	2	no	—
239	C₂²×C₄	—	4	2	no	—
240	C₂²×C₄	—	4	2	no	—
241	C₂²×C₄	—	4	2	no	—
242	C₂²×C₄	—	4	2	no	—
243	C₂²×C₄	C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
244	C₂²×C₄	C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
245	C₂²×C₄	C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
246	C₂²×C₄	C₂×C₈×C₁₀₇	1	2	yes	—
247	C₂²×C₄	M₁₆×C₁₀₇	1	2	yes	—
248	C₂²×C₄	D₈×C₁₀₇	1	2	yes	—
249	C₂²×C₄	SD₁₆×C₁₀₇	1	2	yes	—
250	C₂²×C₄	SD₁₆×C₁₀₇	1	2	yes	—
251	C₂²×C₄	Q₁₆×C₁₀₇	1	2	yes	—
252	C₂²×C₄	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
253	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
254	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
255	C₂×C₈	—	2	4	no	—
256	C₂×C₈	—	2	4	no	—
257	C₂×C₈	—	4	2	no	—
258	C₂×C₈	—	4	2	no	—
259	C₂×C₈	—	4	8	no	—
260	C₂×C₈	—	4	8	no	—
261	C₂×C₈	—	4	2	no	—
262	C₂×C₈	—	4	2	no	—
263	C₄⋊C₄	—	2	4	no	—
264	C₄⋊C₄	—	2	2	no	—
265	C₄⋊C₄	—	4	2	no	—
266	C₄⋊C₄	—	4	2	no	—
267	C₄⋊C₄	—	4	4	no	—
268	C₄⋊C₄	—	4	2	no	—
269	C₄⋊C₄	—	4	2	no	—
270	C₄⋊C₄	C₂×C₈×C₁₀₇	1	4	yes	complemented
271	C₄²	—	4	1	no	—
272	C₄²	—	4	1	no	—
273	C₄²	—	4	1	no	—
274	C₄²	—	4	1	no	—
275	C₂³	C₂²⋊C₈×C₁₀₇	1	2	yes	—
276	C₂³	#99×C₁₀₇	1	2	yes	—
277	C₂³	#101×C₁₀₇	1	2	yes	—
278	C₂³	#102×C₁₀₇	1	2	yes	—
279	C₂³	#103×C₁₀₇	1	2	yes	—
280	C₂³	#104×C₁₀₇	1	2	yes	—
281	C₂³	#104×C₁₀₇	1	2	yes	—
282	C₂³	C₂×C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
283	C₂×C₄	—	2	1	no	—
284	C₂×C₄	—	2	1	no	—
285	C₂×C₄	—	2	1	no	—
286	C₂×C₄	—	2	1	no	—
287	C₂×C₄	—	2	1	no	—
288	C₂×C₄	—	2	1	no	—
289	C₂×C₄	—	2	1	no	—
290	C₂×C₄	—	2	1	no	—
291	C₂×C₄	—	2	1	no	—
292	C₂×C₄	—	2	1	no	—
293	C₂×C₄	—	2	1	no	—
294	C₂×C₄	—	2	1	no	—
295	C₂×C₄	—	2	4	no	—
296	C₂×C₄	—	2	4	no	—
297	C₂×C₄	—	2	4	no	—
298	C₂×C₄	—	2	4	no	—
299	C₂×C₄	—	2	4	no	—
300	C₂×C₄	—	2	4	no	—
301	C₂×C₄	—	2	4	no	—
302	C₂×C₄	—	4	2	no	—
303	C₂×C₄	—	4	2	no	—
304	C₂×C₄	—	4	8	no	—
305	C₂×C₄	—	4	2	no	—
306	C₂×C₄	—	4	2	no	—
307	C₂×C₄	—	4	2	no	—
308	C₂×C₄	—	8	4	no	—
309	C₂×C₄	C₂²⋊C₈×C₁₀₇	1	2	yes	—
310	C₂×C₄	#102×C₁₀₇	1	2	yes	—
311	C₂×C₄	#103×C₁₀₇	1	2	yes	—
312	C₂×C₄	C₂²×C₈×C₁₀₇	1	1	yes	characteristic
313	C₂×C₄	C₂×M₁₆×C₁₀₇	1	1	yes	characteristic
314	C₂×C₄	C₂×D₈×C₁₀₇	1	1	yes	characteristic
315	C₂×C₄	C₂×SD₁₆×C₁₀₇	1	1	yes	characteristic
316	C₂×C₄	C₂×SD₁₆×C₁₀₇	1	1	yes	characteristic
317	C₂×C₄	C₂×Q₁₆×C₁₀₇	1	1	yes	characteristic
318	C₈	—	4	4	no	—
319	C₈	—	4	4	no	—
320	C₂²	#324×C₁₀₇	1	4	yes	—
321	C₂²	D₄⋊C₈×C₁₀₇	1	4	yes	—
322	C₂²	Q₈⋊C₈×C₁₀₇	1	4	yes	—
323	C₂²	#327×C₁₀₇	1	4	yes	—
324	C₂²	#328×C₁₀₇	1	4	yes	—
325	C₂²	#330×C₁₀₇	1	4	yes	—
326	C₂²	#332×C₁₀₇	1	4	yes	—
327	C₂²	C₂×C₂²⋊C₈×C₁₀₇	1	1	yes	characteristic
328	C₂²	C₂×#99×C₁₀₇	1	1	yes	characteristic
329	C₂²	C₂×#101×C₁₀₇	1	1	yes	characteristic
330	C₂²	C₂×#102×C₁₀₇	1	1	yes	characteristic
331	C₂²	C₂×#103×C₁₀₇	1	1	yes	characteristic
332	C₂²	C₂×#104×C₁₀₇	1	1	yes	characteristic
333	C₂²	C₂×#104×C₁₀₇	1	1	yes	characteristic
334	C₄	—	2	2	no	—
335	C₄	—	2	1	no	—
336	C₄	—	2	1	no	—
337	C₄	—	2	1	no	—
338	C₄	—	2	2	no	—
339	C₄	—	2	1	no	—
340	C₄	—	2	1	no	—
341	C₄	—	2	2	no	—
342	C₄	—	2	1	no	—
343	C₄	—	4	4	no	—
344	C₄	—	8	2	no	—
345	C₂	C₁₀₇×#1271	1	8	yes	direct product factor
346	C₂	C₂×#324×C₁₀₇	1	1	yes	characteristic
347	C₂	C₂×D₄⋊C₈×C₁₀₇	1	1	yes	characteristic
348	C₂	C₂×Q₈⋊C₈×C₁₀₇	1	1	yes	characteristic
349	C₂	C₂×#327×C₁₀₇	1	1	yes	characteristic
350	C₂	C₂×#328×C₁₀₇	1	1	yes	characteristic
351	C₂	C₂×#330×C₁₀₇	1	1	yes	characteristic
352	C₂	C₂×#332×C₁₀₇	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₀₇	C₂²⋊C₄
commutator	C₂×C₄	C₂²×C₈×C₁₀₇
Frattini, cosocle	C₂×C₄²	C₂³×C₁₀₇
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₀₇ ◁ C₂²×C₄²×C₁₀₇ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₀₇×#1271	C₂	direct (N × H)
41. C₂×C₄⋊C₄×C₁₀₇	C₈	semidirect
93. C₄⋊C₄×C₁₀₇	C₂×C₈	semidirect
168. C₂×#1271	C₁₀₇	direct (N × H)
169. C₂×C₁₀₇	#1271	direct (N × H)
180. #1271	C₂×C₁₀₇	direct (N × H)
181. C₁₀₇	C₂×#1271	direct (N × H)
218. C₂×C₄⋊C₄	C₈×C₁₀₇	semidirect
270. C₄⋊C₄	C₂×C₈×C₁₀₇	semidirect
345. C₂	C₁₀₇×#1271	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×#389×C₁₀₇	2
C₂×#336×C₁₀₇	2
C₁₀₇×#1271	2
C₂×#1271	107

Subgroups — C2×C107×#1271 #41033523

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₀₇×#1271 #41033523