Subgroups — C₂×C₁₀₇×SD₁₆⋊C₈ #41043810

Order 27392.

806 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×Q₈×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×SD₁₆×C₁₀₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×D₄×C₁₀₇	C₂	1	1	yes	maximal, characteristic
4	C₁₀₇×SD₁₆⋊C₈	C₂	1	8	yes	maximal, direct product factor
5	C₂×#335×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Q₈⋊C₈×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×D₄⋊C₈×C₁₀₇	C₂	1	1	yes	maximal, characteristic
8	C₂×#322×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×SD₁₆×C₁₀₇	C₄	1	1	yes	characteristic
10	C₂³×C₈×C₁₀₇	—	2	1	no	—
11	C₂×C₄×Q₈×C₁₀₇	C₂²	1	1	yes	characteristic
12	C₂×C₄×D₄×C₁₀₇	C₂²	1	1	yes	characteristic
13	C₈×Q₈×C₁₀₇	—	2	2	no	—
14	C₈×Q₈×C₁₀₇	C₂²	1	4	yes	complemented
15	C₄×SD₁₆×C₁₀₇	C₄	1	4	yes	—
16	C₄×SD₁₆×C₁₀₇	C₂²	1	4	yes	—
17	C₈×D₄×C₁₀₇	—	2	2	no	—
18	C₈×D₄×C₁₀₇	C₂²	1	4	yes	—
19	C₂×#106×C₁₀₇	C₄	1	1	yes	characteristic
20	C₂×C₄⋊C₈×C₁₀₇	—	2	1	no	—
21	C₂×C₄⋊C₈×C₁₀₇	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₁₀₇	C₂²	1	1	yes	characteristic
23	C₂×#103×C₁₀₇	C₄	1	1	yes	characteristic
24	C₂×#102×C₁₀₇	C₄	1	1	yes	characteristic
25	C₂×C₂²⋊C₈×C₁₀₇	—	2	1	no	—
26	C₂×C₄×C₈×C₁₀₇	—	2	1	no	—
27	C₂×C₄×C₈×C₁₀₇	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₁₀₇	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₁₀₇	C₂²	1	1	yes	characteristic
30	#335×C₁₀₇	C₂²	1	4	yes	complemented
31	Q₈⋊C₈×C₁₀₇	C₂²	1	4	yes	complemented
32	D₄⋊C₈×C₁₀₇	C₂²	1	4	yes	—
33	#322×C₁₀₇	C₂²	1	4	yes	complemented
34	C₂²×Q₈×C₁₀₇	C₂×C₄	1	1	yes	characteristic
35	C₂²×D₄×C₁₀₇	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₀₇	—	2	1	no	—
37	C₂×SD₁₆×C₁₀₇	C₈	1	8	yes	complemented
38	C₂×SD₁₆×C₁₀₇	C₂×C₄	1	4	yes	—
39	C₂²×C₈×C₁₀₇	—	2	1	no	—
40	C₂²×C₈×C₁₀₇	—	2	1	no	—
41	C₂²×C₈×C₁₀₇	—	2	1	no	—
42	C₂²×C₈×C₁₀₇	—	2	4	no	—
43	C₂²×C₈×C₁₀₇	—	4	4	no	—
44	C₂²×C₈×C₁₀₇	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₈×C₁₀₇	C₂×C₄	1	1	yes	characteristic
46	C₂²×C₈×C₁₀₇	D₄	1	1	yes	characteristic
47	C₂²×C₈×C₁₀₇	D₄	1	1	yes	characteristic
48	C₄×Q₈×C₁₀₇	—	2	1	no	—
49	C₄×Q₈×C₁₀₇	—	2	1	no	—
50	C₄×Q₈×C₁₀₇	C₂×C₄	1	2	yes	—
51	C₄×Q₈×C₁₀₇	C₂³	1	2	yes	—
52	C₄×D₄×C₁₀₇	—	2	1	no	—
53	C₄×D₄×C₁₀₇	—	2	1	no	—
54	C₄×D₄×C₁₀₇	C₂×C₄	1	2	yes	—
55	C₄×D₄×C₁₀₇	C₂³	1	2	yes	—
56	C₂×C₄⋊C₄×C₁₀₇	—	2	1	no	—
57	C₂×C₄⋊C₄×C₁₀₇	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₁₀₇	C₂×C₄	1	1	yes	characteristic
59	C₂×C₂²⋊C₄×C₁₀₇	—	2	1	no	—
60	C₂×C₄²×C₁₀₇	—	2	1	no	—
61	C₂×C₄²×C₁₀₇	C₂³	1	1	yes	characteristic
62	#106×C₁₀₇	C₂×C₄	1	4	yes	—
63	C₄⋊C₈×C₁₀₇	—	2	4	no	—
64	C₄⋊C₈×C₁₀₇	—	2	1	no	—
65	C₄⋊C₈×C₁₀₇	—	2	1	no	—
66	C₄⋊C₈×C₁₀₇	C₂³	1	2	yes	—
67	C₄⋊C₈×C₁₀₇	C₂³	1	2	yes	—
68	#103×C₁₀₇	C₂×C₄	1	4	yes	—
69	#102×C₁₀₇	C₂×C₄	1	4	yes	—
70	C₂²⋊C₈×C₁₀₇	—	2	4	no	—
71	C₄×C₈×C₁₀₇	—	2	4	no	—
72	C₄×C₈×C₁₀₇	—	2	1	no	—
73	C₄×C₈×C₁₀₇	C₂×C₄	1	2	yes	—
74	C₄×C₈×C₁₀₇	D₄	1	2	yes	—
75	C₄×C₈×C₁₀₇	C₂³	1	2	yes	—
76	C₄×C₈×C₁₀₇	C₂³	1	2	yes	—
77	C₄×C₈×C₁₀₇	C₂³	1	2	yes	—
78	C₂⁴×C₁₀₇	—	2	1	no	—
79	C₂×Q₈×C₁₀₇	—	2	1	no	—
80	C₂×Q₈×C₁₀₇	—	2	2	no	—
81	C₂×Q₈×C₁₀₇	C₂×C₈	1	4	yes	complemented
82	C₂×Q₈×C₁₀₇	C₂²×C₄	1	2	yes	—
83	C₂×D₄×C₁₀₇	—	2	1	no	—
84	C₂×D₄×C₁₀₇	—	2	2	no	—
85	C₂×D₄×C₁₀₇	C₂×C₈	1	4	yes	—
86	C₂×D₄×C₁₀₇	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₁₀₇	—	2	1	no	—
88	C₂²×C₄×C₁₀₇	—	2	1	no	—
89	C₂²×C₄×C₁₀₇	—	2	1	no	—
90	C₂²×C₄×C₁₀₇	—	2	2	no	—
91	C₂²×C₄×C₁₀₇	—	2	2	no	—
92	C₂²×C₄×C₁₀₇	—	4	2	no	—
93	C₂²×C₄×C₁₀₇	—	4	2	no	—
94	C₂²×C₄×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₀₇	#41	1	1	yes	characteristic
97	SD₁₆×C₁₀₇	C₂×C₈	1	16	yes	complemented
98	C₂×C₈×C₁₀₇	—	2	2	no	—
99	C₂×C₈×C₁₀₇	—	2	2	no	—
100	C₂×C₈×C₁₀₇	—	2	2	no	—
101	C₂×C₈×C₁₀₇	—	2	2	no	—
102	C₂×C₈×C₁₀₇	—	2	2	no	—
103	C₂×C₈×C₁₀₇	—	2	2	no	—
104	C₂×C₈×C₁₀₇	—	4	8	no	—
105	C₂×C₈×C₁₀₇	—	4	2	no	—
106	C₂×C₈×C₁₀₇	—	4	2	no	—
107	C₂×C₈×C₁₀₇	—	4	2	no	—
108	C₂×C₈×C₁₀₇	C₂×C₈	1	4	yes	complemented
109	C₂×C₈×C₁₀₇	C₂²×C₄	1	2	yes	—
110	C₂×C₈×C₁₀₇	C₂²×C₄	1	2	yes	—
111	C₂×C₈×C₁₀₇	C₂×D₄	1	2	yes	—
112	C₂×C₈×C₁₀₇	C₂×D₄	1	2	yes	—
113	C₄⋊C₄×C₁₀₇	—	2	2	no	—
114	C₄⋊C₄×C₁₀₇	—	2	1	no	—
115	C₄⋊C₄×C₁₀₇	—	2	1	no	—
116	C₄⋊C₄×C₁₀₇	—	2	2	no	—
117	C₄⋊C₄×C₁₀₇	C₂²×C₄	1	2	yes	—
118	C₄⋊C₄×C₁₀₇	C₂²×C₄	1	2	yes	—
119	C₂²⋊C₄×C₁₀₇	—	2	2	no	—
120	C₂²⋊C₄×C₁₀₇	—	2	2	no	—
121	C₄²×C₁₀₇	—	2	2	no	—
122	C₄²×C₁₀₇	—	2	2	no	—
123	C₄²×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
124	C₄²×C₁₀₇	C₂×D₄	1	1	yes	characteristic
125	C₄²×C₁₀₇	#41	1	1	yes	characteristic
126	C₄²×C₁₀₇	C₂⁴	1	1	yes	characteristic
127	C₂³×C₁₀₇	—	2	2	no	—
128	C₂³×C₁₀₇	—	2	4	no	—
129	C₂³×C₁₀₇	—	4	2	no	—
130	C₂³×C₁₀₇	—	4	2	no	—
131	C₂³×C₁₀₇	C₄×D₄	1	1	yes	characteristic
132	Q₈×C₁₀₇	—	2	2	no	—
133	Q₈×C₁₀₇	—	2	4	no	—
134	Q₈×C₁₀₇	C₂²×C₈	1	4	yes	complemented
135	D₄×C₁₀₇	—	2	2	no	—
136	D₄×C₁₀₇	—	2	4	no	—
137	D₄×C₁₀₇	C₂²×C₈	1	4	yes	—
138	C₂×C₄×C₁₀₇	—	2	2	no	—
139	C₂×C₄×C₁₀₇	—	2	4	no	—
140	C₂×C₄×C₁₀₇	—	2	2	no	—
141	C₂×C₄×C₁₀₇	—	2	2	no	—
142	C₂×C₄×C₁₀₇	—	2	2	no	—
143	C₂×C₄×C₁₀₇	—	4	2	no	—
144	C₂×C₄×C₁₀₇	—	4	2	no	—
145	C₂×C₄×C₁₀₇	—	4	2	no	—
146	C₂×C₄×C₁₀₇	—	4	2	no	—
147	C₂×C₄×C₁₀₇	—	4	4	no	—
148	C₂×C₄×C₁₀₇	C₄×D₄	1	1	yes	characteristic
149	C₂×C₄×C₁₀₇	C₄×D₄	1	1	yes	characteristic
150	C₂×C₄×C₁₀₇	C₄×D₄	1	1	yes	characteristic
151	C₂×C₄×C₁₀₇	C₂²×C₈	1	2	yes	—
152	C₂×C₄×C₁₀₇	#131	1	2	yes	—
153	C₂×C₄×C₁₀₇	AGL(1,ℤ/8)	1	2	yes	—
154	C₂×C₄×C₁₀₇	#137	1	2	yes	—
155	C₂×C₄×C₁₀₇	C₂³×C₄	1	1	yes	characteristic
156	C₂×C₄×C₁₀₇	C₂²×D₄	1	1	yes	characteristic
157	C₂×C₄×C₁₀₇	C₂×#41	1	1	yes	characteristic
158	C₈×C₁₀₇	—	2	2	no	—
159	C₈×C₁₀₇	—	2	2	no	—
160	C₈×C₁₀₇	—	2	2	no	—
161	C₈×C₁₀₇	—	4	2	no	—
162	C₈×C₁₀₇	—	4	2	no	—
163	C₈×C₁₀₇	—	4	2	no	—
164	C₈×C₁₀₇	C₂²×C₈	1	4	yes	complemented
165	C₂²×C₁₀₇	—	2	4	no	—
166	C₂²×C₁₀₇	—	4	8	no	—
167	C₂²×C₁₀₇	—	4	2	no	—
168	C₂²×C₁₀₇	—	4	2	no	—
169	C₂²×C₁₀₇	C₈×D₄	1	2	yes	—
170	C₂²×C₁₀₇	#440	1	2	yes	—
171	C₂²×C₁₀₇	#444	1	2	yes	—
172	C₂²×C₁₀₇	C₂×C₄×D₄	1	1	yes	characteristic
173	C₄×C₁₀₇	—	2	4	no	—
174	C₄×C₁₀₇	—	2	1	no	—
175	C₄×C₁₀₇	—	2	1	no	—
176	C₄×C₁₀₇	—	4	2	no	—
177	C₄×C₁₀₇	—	4	2	no	—
178	C₄×C₁₀₇	C₈×D₄	1	2	yes	—
179	C₄×C₁₀₇	#440	1	2	yes	—
180	C₄×C₁₀₇	C₂³×C₈	1	1	yes	characteristic
181	C₄×C₁₀₇	C₂×#131	1	1	yes	characteristic
182	C₄×C₁₀₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
183	C₄×C₁₀₇	C₂×#137	1	1	yes	characteristic
184	C₂×SD₁₆⋊C₈	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
185	C₂×C₁₀₇	—	4	4	no	—
186	C₂×C₁₀₇	SD₁₆⋊C₈	1	4	yes	direct product factor
187	C₂×C₁₀₇	C₂×C₈×D₄	1	1	yes	characteristic
188	C₂×C₁₀₇	C₂×#440	1	1	yes	characteristic
189	C₂×C₁₀₇	C₂×#444	1	1	yes	characteristic
190	C₂×C₈×Q₈	C₂×C₁₀₇	1	1	yes	characteristic, complemented
191	C₂×C₄×SD₁₆	C₂×C₁₀₇	1	1	yes	characteristic
192	C₂×C₈×D₄	C₂×C₁₀₇	1	1	yes	characteristic
193	SD₁₆⋊C₈	C₂×C₁₀₇	1	8	yes	direct product factor
194	C₂×#335	C₂×C₁₀₇	1	1	yes	characteristic, complemented
195	C₂×Q₈⋊C₈	C₂×C₁₀₇	1	1	yes	characteristic, complemented
196	C₂×D₄⋊C₈	C₂×C₁₀₇	1	1	yes	characteristic
197	C₂×#322	C₂×C₁₀₇	1	1	yes	characteristic, complemented
198	C₁₀₇	C₂×SD₁₆⋊C₈	1	1	yes	characteristic, direct product factor, Sylow
199	C₂²×SD₁₆	C₄×C₁₀₇	1	1	yes	characteristic
200	C₂³×C₈	—	2	1	no	—
201	C₂×C₄×Q₈	C₂²×C₁₀₇	1	1	yes	characteristic
202	C₂×C₄×D₄	C₂²×C₁₀₇	1	1	yes	characteristic
203	C₈×Q₈	—	2	2	no	—
204	C₈×Q₈	C₂²×C₁₀₇	1	4	yes	complemented
205	C₄×SD₁₆	C₄×C₁₀₇	1	4	yes	—
206	C₄×SD₁₆	C₂²×C₁₀₇	1	4	yes	—
207	C₈×D₄	—	2	2	no	—
208	C₈×D₄	C₂²×C₁₀₇	1	4	yes	—
209	C₂×#106	C₄×C₁₀₇	1	1	yes	characteristic
210	C₂×C₄⋊C₈	—	2	1	no	—
211	C₂×C₄⋊C₈	C₂²×C₁₀₇	1	1	yes	characteristic
212	C₂×C₄⋊C₈	C₂²×C₁₀₇	1	1	yes	characteristic
213	C₂×#103	C₄×C₁₀₇	1	1	yes	characteristic
214	C₂×#102	C₄×C₁₀₇	1	1	yes	characteristic
215	C₂×C₂²⋊C₈	—	2	1	no	—
216	C₂×C₄×C₈	—	2	1	no	—
217	C₂×C₄×C₈	C₂²×C₁₀₇	1	1	yes	characteristic
218	C₂×C₄×C₈	C₂²×C₁₀₇	1	1	yes	characteristic
219	C₂×C₄×C₈	C₂²×C₁₀₇	1	1	yes	characteristic
220	#335	C₂²×C₁₀₇	1	4	yes	complemented
221	Q₈⋊C₈	C₂²×C₁₀₇	1	4	yes	complemented
222	D₄⋊C₈	C₂²×C₁₀₇	1	4	yes	—
223	#322	C₂²×C₁₀₇	1	4	yes	complemented
224	C₂²×Q₈	C₂×C₄×C₁₀₇	1	1	yes	characteristic
225	C₂²×D₄	C₂×C₄×C₁₀₇	1	1	yes	characteristic
226	C₂³×C₄	—	2	1	no	—
227	C₂×SD₁₆	C₈×C₁₀₇	1	8	yes	complemented
228	C₂×SD₁₆	C₂×C₄×C₁₀₇	1	4	yes	—
229	C₂²×C₈	—	2	1	no	—
230	C₂²×C₈	—	2	1	no	—
231	C₂²×C₈	—	2	1	no	—
232	C₂²×C₈	—	2	4	no	—
233	C₂²×C₈	—	4	4	no	—
234	C₂²×C₈	C₂×C₄×C₁₀₇	1	1	yes	characteristic
235	C₂²×C₈	C₂×C₄×C₁₀₇	1	1	yes	characteristic
236	C₂²×C₈	D₄×C₁₀₇	1	1	yes	characteristic
237	C₂²×C₈	D₄×C₁₀₇	1	1	yes	characteristic
238	C₄×Q₈	—	2	1	no	—
239	C₄×Q₈	—	2	1	no	—
240	C₄×Q₈	C₂×C₄×C₁₀₇	1	2	yes	—
241	C₄×Q₈	C₂³×C₁₀₇	1	2	yes	—
242	C₄×D₄	—	2	1	no	—
243	C₄×D₄	—	2	1	no	—
244	C₄×D₄	C₂×C₄×C₁₀₇	1	2	yes	—
245	C₄×D₄	C₂³×C₁₀₇	1	2	yes	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	C₂×C₄×C₁₀₇	1	1	yes	characteristic
248	C₂×C₄⋊C₄	C₂×C₄×C₁₀₇	1	1	yes	characteristic
249	C₂×C₂²⋊C₄	—	2	1	no	—
250	C₂×C₄²	—	2	1	no	—
251	C₂×C₄²	C₂³×C₁₀₇	1	1	yes	characteristic
252	#106	C₂×C₄×C₁₀₇	1	4	yes	—
253	C₄⋊C₈	—	2	4	no	—
254	C₄⋊C₈	—	2	1	no	—
255	C₄⋊C₈	—	2	1	no	—
256	C₄⋊C₈	C₂³×C₁₀₇	1	2	yes	—
257	C₄⋊C₈	C₂³×C₁₀₇	1	2	yes	—
258	#103	C₂×C₄×C₁₀₇	1	4	yes	—
259	#102	C₂×C₄×C₁₀₇	1	4	yes	—
260	C₂²⋊C₈	—	2	4	no	—
261	C₄×C₈	—	2	4	no	—
262	C₄×C₈	—	2	1	no	—
263	C₄×C₈	C₂×C₄×C₁₀₇	1	2	yes	—
264	C₄×C₈	D₄×C₁₀₇	1	2	yes	—
265	C₄×C₈	C₂³×C₁₀₇	1	2	yes	—
266	C₄×C₈	C₂³×C₁₀₇	1	2	yes	—
267	C₄×C₈	C₂³×C₁₀₇	1	2	yes	—
268	C₂⁴	—	2	1	no	—
269	C₂×Q₈	—	2	1	no	—
270	C₂×Q₈	—	2	2	no	—
271	C₂×Q₈	C₂×C₈×C₁₀₇	1	4	yes	complemented
272	C₂×Q₈	C₂²×C₄×C₁₀₇	1	2	yes	—
273	C₂×D₄	—	2	1	no	—
274	C₂×D₄	—	2	2	no	—
275	C₂×D₄	C₂×C₈×C₁₀₇	1	4	yes	—
276	C₂×D₄	C₂²×C₄×C₁₀₇	1	2	yes	—
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	—	2	1	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	4	2	no	—
283	C₂²×C₄	—	4	2	no	—
284	C₂²×C₄	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
285	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
286	C₂²×C₄	#41×C₁₀₇	1	1	yes	characteristic
287	SD₁₆	C₂×C₈×C₁₀₇	1	16	yes	complemented
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	4	8	no	—
295	C₂×C₈	—	4	2	no	—
296	C₂×C₈	—	4	2	no	—
297	C₂×C₈	—	4	2	no	—
298	C₂×C₈	C₂×C₈×C₁₀₇	1	4	yes	complemented
299	C₂×C₈	C₂²×C₄×C₁₀₇	1	2	yes	—
300	C₂×C₈	C₂²×C₄×C₁₀₇	1	2	yes	—
301	C₂×C₈	C₂×D₄×C₁₀₇	1	2	yes	—
302	C₂×C₈	C₂×D₄×C₁₀₇	1	2	yes	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	—	2	1	no	—
305	C₄⋊C₄	—	2	1	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	C₂²×C₄×C₁₀₇	1	2	yes	—
308	C₄⋊C₄	C₂²×C₄×C₁₀₇	1	2	yes	—
309	C₂²⋊C₄	—	2	2	no	—
310	C₂²⋊C₄	—	2	2	no	—
311	C₄²	—	2	2	no	—
312	C₄²	—	2	2	no	—
313	C₄²	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
314	C₄²	C₂×D₄×C₁₀₇	1	1	yes	characteristic
315	C₄²	#41×C₁₀₇	1	1	yes	characteristic
316	C₄²	C₂⁴×C₁₀₇	1	1	yes	characteristic
317	C₂³	—	2	4	no	—
318	C₂³	—	2	2	no	—
319	C₂³	—	4	2	no	—
320	C₂³	—	4	2	no	—
321	C₂³	C₄×D₄×C₁₀₇	1	1	yes	characteristic
322	Q₈	—	2	4	no	—
323	Q₈	—	2	2	no	—
324	Q₈	C₂²×C₈×C₁₀₇	1	4	yes	complemented
325	D₄	—	2	4	no	—
326	D₄	—	2	2	no	—
327	D₄	C₂²×C₈×C₁₀₇	1	4	yes	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	4	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	C₄×D₄×C₁₀₇	1	1	yes	characteristic
339	C₂×C₄	C₄×D₄×C₁₀₇	1	1	yes	characteristic
340	C₂×C₄	C₄×D₄×C₁₀₇	1	1	yes	characteristic
341	C₂×C₄	C₂²×C₈×C₁₀₇	1	2	yes	—
342	C₂×C₄	#131×C₁₀₇	1	2	yes	—
343	C₂×C₄	AGL(1,ℤ/8)×C₁₀₇	1	2	yes	—
344	C₂×C₄	#137×C₁₀₇	1	2	yes	—
345	C₂×C₄	C₂³×C₄×C₁₀₇	1	1	yes	characteristic
346	C₂×C₄	C₂²×D₄×C₁₀₇	1	1	yes	characteristic
347	C₂×C₄	C₂×#41×C₁₀₇	1	1	yes	characteristic
348	C₈	—	2	2	no	—
349	C₈	—	2	2	no	—
350	C₈	—	2	2	no	—
351	C₈	—	4	2	no	—
352	C₈	—	4	2	no	—
353	C₈	—	4	2	no	—
354	C₈	C₂²×C₈×C₁₀₇	1	4	yes	complemented
355	C₂²	—	2	4	no	—
356	C₂²	—	4	2	no	—
357	C₂²	—	4	2	no	—
358	C₂²	—	4	8	no	—
359	C₂²	C₈×D₄×C₁₀₇	1	2	yes	—
360	C₂²	#440×C₁₀₇	1	2	yes	—
361	C₂²	#444×C₁₀₇	1	2	yes	—
362	C₂²	C₂×C₄×D₄×C₁₀₇	1	1	yes	characteristic
363	C₄	—	2	4	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	4	2	no	—
367	C₄	—	4	2	no	—
368	C₄	C₈×D₄×C₁₀₇	1	2	yes	—
369	C₄	#440×C₁₀₇	1	2	yes	—
370	C₄	C₂³×C₈×C₁₀₇	1	1	yes	characteristic
371	C₄	C₂×#131×C₁₀₇	1	1	yes	characteristic
372	C₄	C₂×AGL(1,ℤ/8)×C₁₀₇	1	1	yes	characteristic
373	C₄	C₂×#137×C₁₀₇	1	1	yes	characteristic
374	C₂	—	4	4	no	—
375	C₂	C₁₀₇×SD₁₆⋊C₈	1	4	yes	direct product factor
376	C₂	C₂×C₈×D₄×C₁₀₇	1	1	yes	characteristic
377	C₂	C₂×#440×C₁₀₇	1	1	yes	characteristic
378	C₂	C₂×#444×C₁₀₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₀₇	C₂×D₄
commutator	C₄	C₂³×C₈×C₁₀₇
Frattini, cosocle	C₄²	C₂⁴×C₁₀₇
socle	C₂³×C₁₀₇	C₄×D₄
prime radical	C₂²×D₄×C₁₀₇	C₂×C₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₀₇ ◁ C₂×C₄×C₈×C₁₀₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₈×Q₈×C₁₀₇	C₂	semidirect
4. C₁₀₇×SD₁₆⋊C₈	C₂	direct (N × H)
5. C₂×#335×C₁₀₇	C₂	semidirect
6. C₂×Q₈⋊C₈×C₁₀₇	C₂	semidirect
8. C₂×#322×C₁₀₇	C₂	semidirect
14. C₈×Q₈×C₁₀₇	C₂²	semidirect
30. #335×C₁₀₇	C₂²	semidirect
31. Q₈⋊C₈×C₁₀₇	C₂²	semidirect
33. #322×C₁₀₇	C₂²	semidirect
37. C₂×SD₁₆×C₁₀₇	C₈	semidirect
81. C₂×Q₈×C₁₀₇	C₂×C₈	semidirect
97. SD₁₆×C₁₀₇	C₂×C₈	semidirect
108. C₂×C₈×C₁₀₇	C₂×C₈	semidirect
134. Q₈×C₁₀₇	C₂²×C₈	semidirect
164. C₈×C₁₀₇	C₂²×C₈	semidirect
184. C₂×SD₁₆⋊C₈	C₁₀₇	direct (N × H)
186. C₂×C₁₀₇	SD₁₆⋊C₈	direct (N × H)
190. C₂×C₈×Q₈	C₂×C₁₀₇	semidirect
193. SD₁₆⋊C₈	C₂×C₁₀₇	direct (N × H)
194. C₂×#335	C₂×C₁₀₇	semidirect
195. C₂×Q₈⋊C₈	C₂×C₁₀₇	semidirect
197. C₂×#322	C₂×C₁₀₇	semidirect
198. C₁₀₇	C₂×SD₁₆⋊C₈	direct (N × H)
204. C₈×Q₈	C₂²×C₁₀₇	semidirect
220. #335	C₂²×C₁₀₇	semidirect
221. Q₈⋊C₈	C₂²×C₁₀₇	semidirect
223. #322	C₂²×C₁₀₇	semidirect
227. C₂×SD₁₆	C₈×C₁₀₇	semidirect
271. C₂×Q₈	C₂×C₈×C₁₀₇	semidirect
287. SD₁₆	C₂×C₈×C₁₀₇	semidirect
298. C₂×C₈	C₂×C₈×C₁₀₇	semidirect
324. Q₈	C₂²×C₈×C₁₀₇	semidirect
354. C₈	C₂²×C₈×C₁₀₇	semidirect
375. C₂	C₁₀₇×SD₁₆⋊C₈	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×C₈×Q₈×C₁₀₇	2
C₂×C₄×SD₁₆×C₁₀₇	2
C₂×C₈×D₄×C₁₀₇	2
C₁₀₇×SD₁₆⋊C₈	2
C₂×#335×C₁₀₇	2
C₂×Q₈⋊C₈×C₁₀₇	2
C₂×D₄⋊C₈×C₁₀₇	2
C₂×#322×C₁₀₇	2
C₂×SD₁₆⋊C₈	107

Subgroups — C2×C107×SD16⋊C8 #41043810

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₀₇×SD₁₆⋊C₈ #41043810