Subgroups — C₂×C₁₀₇×#2024 #41049413

Order 27392.

1518 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊Q₈×C₁₀₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×#103×C₁₀₇	C₂	1	2	yes	maximal
3	C₂×#391×C₁₀₇	C₂	1	1	yes	maximal, characteristic
4	C₁₀₇×#2024	C₂	1	8	yes	maximal, direct product factor
5	C₂×#340×C₁₀₇	C₂	1	2	yes	maximal
6	C₂×#336×C₁₀₇	C₂	1	1	yes	maximal, characteristic
7	C₂³×Q₈×C₁₀₇	—	2	1	no	—
8	C₂³×Q₈×C₁₀₇	C₂²	1	1	yes	characteristic
9	C₂³×C₈×C₁₀₇	C₂²	1	2	yes	—
10	C₂×C₄⋊Q₈×C₁₀₇	—	2	8	no	—
11	C₂×C₄⋊Q₈×C₁₀₇	—	2	2	no	—
12	C₂×C₄⋊Q₈×C₁₀₇	C₂²	1	4	yes	—
13	C₂²×C₄⋊C₄×C₁₀₇	—	2	1	no	—
14	C₂²×C₄⋊C₄×C₁₀₇	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₁₀₇	C₂²	1	2	yes	—
16	C₂²×C₄²×C₁₀₇	C₂²	1	1	yes	characteristic
17	C₂×#103×C₁₀₇	—	2	8	no	—
18	C₂×#103×C₁₀₇	C₂²	1	8	yes	—
19	#391×C₁₀₇	—	2	2	no	—
20	#391×C₁₀₇	C₂²	1	4	yes	—
21	C₂×#95×C₁₀₇	—	2	1	no	—
22	C₂×#95×C₁₀₇	—	2	1	no	—
23	#340×C₁₀₇	C₂²	1	8	yes	—
24	#336×C₁₀₇	C₂²	1	4	yes	—
25	C₂²×Q₈×C₁₀₇	—	2	8	no	—
26	C₂²×Q₈×C₁₀₇	—	2	1	no	—
27	C₂²×Q₈×C₁₀₇	—	2	4	no	—
28	C₂²×Q₈×C₁₀₇	—	2	2	no	—
29	C₂²×Q₈×C₁₀₇	—	2	4	no	—
30	C₂²×Q₈×C₁₀₇	—	2	4	no	—
31	C₂²×Q₈×C₁₀₇	—	4	4	no	—
32	C₂²×Q₈×C₁₀₇	—	4	4	no	—
33	C₂²×Q₈×C₁₀₇	Q₈	1	4	yes	complemented
34	C₂²×Q₈×C₁₀₇	C₂³	1	2	yes	—
35	C₂³×C₄×C₁₀₇	—	2	1	no	—
36	C₂³×C₄×C₁₀₇	—	2	2	no	—
37	C₂³×C₄×C₁₀₇	—	2	1	no	—
38	C₂³×C₄×C₁₀₇	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₀₇	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
41	C₂²×C₈×C₁₀₇	—	2	4	no	—
42	C₂²×C₈×C₁₀₇	—	2	4	no	—
43	C₂²×C₈×C₁₀₇	—	2	4	no	—
44	C₂²×C₈×C₁₀₇	C₂³	1	4	yes	—
45	C₄⋊Q₈×C₁₀₇	—	2	16	no	—
46	C₄⋊Q₈×C₁₀₇	—	2	16	no	—
47	C₂×C₄⋊C₄×C₁₀₇	—	2	8	no	—
48	C₂×C₄⋊C₄×C₁₀₇	—	2	4	no	—
49	C₂×C₄⋊C₄×C₁₀₇	—	2	2	no	—
50	C₂×C₄⋊C₄×C₁₀₇	—	2	4	no	—
51	C₂×C₄⋊C₄×C₁₀₇	—	2	4	no	—
52	C₂×C₄⋊C₄×C₁₀₇	—	2	1	no	—
53	C₂×C₄⋊C₄×C₁₀₇	D₄	1	8	yes	—
54	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	2	yes	—
55	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	4	yes	—
56	C₂×C₄²×C₁₀₇	—	2	4	no	—
57	C₂×C₄²×C₁₀₇	D₄	1	2	yes	—
58	C₂×C₄²×C₁₀₇	C₂³	1	2	yes	—
59	#103×C₁₀₇	—	2	16	no	—
60	#95×C₁₀₇	—	2	4	no	—
61	#95×C₁₀₇	—	2	4	no	—
62	C₂⁴×C₁₀₇	C₂×D₄	1	1	yes	characteristic
63	C₂×Q₈×C₁₀₇	—	2	16	no	—
64	C₂×Q₈×C₁₀₇	—	2	4	no	—
65	C₂×Q₈×C₁₀₇	—	2	2	no	—
66	C₂×Q₈×C₁₀₇	—	2	16	no	—
67	C₂×Q₈×C₁₀₇	—	2	4	no	—
68	C₂×Q₈×C₁₀₇	—	2	4	no	—
69	C₂×Q₈×C₁₀₇	—	4	8	no	—
70	C₂×Q₈×C₁₀₇	—	4	32	no	—
71	C₂×Q₈×C₁₀₇	—	4	2	no	—
72	C₂×Q₈×C₁₀₇	—	4	2	no	—
73	C₂×Q₈×C₁₀₇	—	4	8	no	—
74	C₂×Q₈×C₁₀₇	—	4	8	no	—
75	C₂×Q₈×C₁₀₇	C₂×Q₈	1	4	yes	complemented
76	C₂²×C₄×C₁₀₇	—	2	2	no	—
77	C₂²×C₄×C₁₀₇	—	2	2	no	—
78	C₂²×C₄×C₁₀₇	—	2	2	no	—
79	C₂²×C₄×C₁₀₇	—	2	2	no	—
80	C₂²×C₄×C₁₀₇	—	2	8	no	—
81	C₂²×C₄×C₁₀₇	—	2	4	no	—
82	C₂²×C₄×C₁₀₇	—	2	2	no	—
83	C₂²×C₄×C₁₀₇	—	2	4	no	—
84	C₂²×C₄×C₁₀₇	—	2	2	no	—
85	C₂²×C₄×C₁₀₇	—	4	2	no	—
86	C₂²×C₄×C₁₀₇	—	4	2	no	—
87	C₂²×C₄×C₁₀₇	—	4	4	no	—
88	C₂²×C₄×C₁₀₇	—	4	4	no	—
89	C₂²×C₄×C₁₀₇	—	4	2	no	—
90	C₂²×C₄×C₁₀₇	—	4	2	no	—
91	C₂²×C₄×C₁₀₇	—	4	2	no	—
92	C₂²×C₄×C₁₀₇	SD₁₆	1	4	yes	—
93	C₂²×C₄×C₁₀₇	Q₁₆	1	4	yes	—
94	C₂²×C₄×C₁₀₇	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₁₀₇	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₀₇	C₂×D₄	1	4	yes	—
98	C₂²×C₄×C₁₀₇	C₂×Q₈	1	2	yes	—
99	C₂²×C₄×C₁₀₇	#41	1	4	yes	—
100	C₂²×C₄×C₁₀₇	#41	1	2	yes	—
101	C₂²×C₄×C₁₀₇	C₂⁴	1	1	yes	characteristic
102	C₂×C₈×C₁₀₇	—	2	4	no	—
103	C₂×C₈×C₁₀₇	—	2	4	no	—
104	C₂×C₈×C₁₀₇	—	2	4	no	—
105	C₂×C₈×C₁₀₇	—	4	8	no	—
106	C₄⋊C₄×C₁₀₇	—	2	16	no	—
107	C₄⋊C₄×C₁₀₇	—	2	8	no	—
108	C₄⋊C₄×C₁₀₇	—	2	4	no	—
109	C₄⋊C₄×C₁₀₇	—	2	4	no	—
110	C₄⋊C₄×C₁₀₇	—	4	2	no	—
111	C₄⋊C₄×C₁₀₇	C₂×D₄	1	8	yes	—
112	C₄²×C₁₀₇	—	2	4	no	—
113	C₄²×C₁₀₇	—	2	4	no	—
114	C₂³×C₁₀₇	#120	1	2	yes	—
115	C₂³×C₁₀₇	C₂²⋊Q₈	1	2	yes	—
116	C₂³×C₁₀₇	#124	1	2	yes	—
117	C₂³×C₁₀₇	C₂×SD₁₆	1	2	yes	—
118	C₂³×C₁₀₇	C₂×Q₁₆	1	2	yes	—
119	C₂³×C₁₀₇	AGL(1,ℤ/8)	1	2	yes	—
120	C₂³×C₁₀₇	#137	1	2	yes	—
121	C₂³×C₁₀₇	C₂²×D₄	1	1	yes	characteristic
122	Q₈×C₁₀₇	—	2	8	no	—
123	Q₈×C₁₀₇	—	4	32	no	—
124	Q₈×C₁₀₇	—	4	4	no	—
125	Q₈×C₁₀₇	—	4	8	no	—
126	C₂×C₄×C₁₀₇	—	2	2	no	—
127	C₂×C₄×C₁₀₇	—	2	2	no	—
128	C₂×C₄×C₁₀₇	—	2	2	no	—
129	C₂×C₄×C₁₀₇	—	2	2	no	—
130	C₂×C₄×C₁₀₇	—	2	8	no	—
131	C₂×C₄×C₁₀₇	—	2	8	no	—
132	C₂×C₄×C₁₀₇	—	2	8	no	—
133	C₂×C₄×C₁₀₇	—	2	4	no	—
134	C₂×C₄×C₁₀₇	—	4	2	no	—
135	C₂×C₄×C₁₀₇	—	4	2	no	—
136	C₂×C₄×C₁₀₇	—	4	4	no	—
137	C₂×C₄×C₁₀₇	—	4	4	no	—
138	C₂×C₄×C₁₀₇	—	4	8	no	—
139	C₂×C₄×C₁₀₇	—	4	16	no	—
140	C₂×C₄×C₁₀₇	—	4	2	no	—
141	C₂×C₄×C₁₀₇	—	4	2	no	—
142	C₂×C₄×C₁₀₇	—	4	2	no	—
143	C₂×C₄×C₁₀₇	—	8	4	no	—
144	C₂×C₄×C₁₀₇	#120	1	2	yes	—
145	C₂×C₄×C₁₀₇	C₂²⋊Q₈	1	8	yes	—
146	C₂×C₄×C₁₀₇	C₂²⋊Q₈	1	2	yes	—
147	C₂×C₄×C₁₀₇	#124	1	8	yes	—
148	C₂×C₄×C₁₀₇	#124	1	2	yes	—
149	C₂×C₄×C₁₀₇	C₂×SD₁₆	1	4	yes	—
150	C₂×C₄×C₁₀₇	C₂×Q₁₆	1	4	yes	—
151	C₂×C₄×C₁₀₇	C₂²×D₄	1	2	yes	—
152	C₂×C₄×C₁₀₇	C₂²×Q₈	1	1	yes	characteristic
153	C₂×C₄×C₁₀₇	C₂×#41	1	2	yes	—
154	C₂×C₄×C₁₀₇	C₂×#41	1	1	yes	characteristic
155	C₈×C₁₀₇	—	4	4	no	—
156	C₂²×C₁₀₇	#393	1	4	yes	—
157	C₂²×C₁₀₇	#450	1	4	yes	—
158	C₂²×C₁₀₇	#451	1	4	yes	—
159	C₂²×C₁₀₇	#475	1	4	yes	—
160	C₂²×C₁₀₇	#477	1	4	yes	—
161	C₂²×C₁₀₇	#487	1	4	yes	—
162	C₂²×C₁₀₇	#489	1	4	yes	—
163	C₂²×C₁₀₇	C₂×#120	1	1	yes	characteristic
164	C₂²×C₁₀₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
165	C₂²×C₁₀₇	C₂×#124	1	1	yes	characteristic
166	C₂²×C₁₀₇	C₂²×SD₁₆	1	1	yes	characteristic
167	C₂²×C₁₀₇	C₂²×Q₁₆	1	1	yes	characteristic
168	C₂²×C₁₀₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
169	C₂²×C₁₀₇	C₂×#137	1	1	yes	characteristic
170	C₄×C₁₀₇	—	2	4	no	—
171	C₄×C₁₀₇	—	2	4	no	—
172	C₄×C₁₀₇	—	4	4	no	—
173	C₄×C₁₀₇	—	4	8	no	—
174	C₄×C₁₀₇	—	8	2	no	—
175	C₄×C₁₀₇	#393	1	4	yes	—
176	C₄×C₁₀₇	C₂×C₂²⋊Q₈	1	2	yes	—
177	C₄×C₁₀₇	C₂×#124	1	2	yes	—
178	C₂×#2024	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
179	C₂×C₁₀₇	#2024	1	8	yes	direct product factor
180	C₂×C₁₀₇	C₂×#393	1	1	yes	characteristic
181	C₂×C₁₀₇	C₂×#450	1	1	yes	characteristic
182	C₂×C₁₀₇	C₂×#451	1	1	yes	characteristic
183	C₂×C₁₀₇	C₂×#475	1	1	yes	characteristic
184	C₂×C₁₀₇	C₂×#477	1	1	yes	characteristic
185	C₂×C₁₀₇	C₂×#487	1	1	yes	characteristic
186	C₂×C₁₀₇	C₂×#489	1	1	yes	characteristic
187	C₂²×C₄⋊Q₈	C₂×C₁₀₇	1	1	yes	characteristic
188	C₂²×#103	C₂×C₁₀₇	1	2	yes	—
189	C₂×#391	C₂×C₁₀₇	1	1	yes	characteristic
190	#2024	C₂×C₁₀₇	1	8	yes	direct product factor
191	C₂×#340	C₂×C₁₀₇	1	2	yes	—
192	C₂×#336	C₂×C₁₀₇	1	1	yes	characteristic
193	C₁₀₇	C₂×#2024	1	1	yes	characteristic, direct product factor, Sylow
194	C₂³×Q₈	—	2	1	no	—
195	C₂³×Q₈	C₂²×C₁₀₇	1	1	yes	characteristic
196	C₂³×C₈	C₂²×C₁₀₇	1	2	yes	—
197	C₂×C₄⋊Q₈	—	2	8	no	—
198	C₂×C₄⋊Q₈	—	2	2	no	—
199	C₂×C₄⋊Q₈	C₂²×C₁₀₇	1	4	yes	—
200	C₂²×C₄⋊C₄	—	2	1	no	—
201	C₂²×C₄⋊C₄	C₂²×C₁₀₇	1	1	yes	characteristic
202	C₂²×C₄⋊C₄	C₂²×C₁₀₇	1	2	yes	—
203	C₂²×C₄²	C₂²×C₁₀₇	1	1	yes	characteristic
204	C₂×#103	—	2	8	no	—
205	C₂×#103	C₂²×C₁₀₇	1	8	yes	—
206	#391	—	2	2	no	—
207	#391	C₂²×C₁₀₇	1	4	yes	—
208	C₂×#95	—	2	1	no	—
209	C₂×#95	—	2	1	no	—
210	#340	C₂²×C₁₀₇	1	8	yes	—
211	#336	C₂²×C₁₀₇	1	4	yes	—
212	C₂²×Q₈	—	2	8	no	—
213	C₂²×Q₈	—	2	4	no	—
214	C₂²×Q₈	—	2	1	no	—
215	C₂²×Q₈	—	2	2	no	—
216	C₂²×Q₈	—	2	4	no	—
217	C₂²×Q₈	—	2	4	no	—
218	C₂²×Q₈	—	4	4	no	—
219	C₂²×Q₈	—	4	4	no	—
220	C₂²×Q₈	Q₈×C₁₀₇	1	4	yes	complemented
221	C₂²×Q₈	C₂³×C₁₀₇	1	2	yes	—
222	C₂³×C₄	—	2	2	no	—
223	C₂³×C₄	—	2	1	no	—
224	C₂³×C₄	—	2	1	no	—
225	C₂³×C₄	D₄×C₁₀₇	1	1	yes	characteristic
226	C₂³×C₄	D₄×C₁₀₇	1	1	yes	characteristic
227	C₂³×C₄	C₂³×C₁₀₇	1	1	yes	characteristic
228	C₂²×C₈	—	2	4	no	—
229	C₂²×C₈	—	2	4	no	—
230	C₂²×C₈	—	2	4	no	—
231	C₂²×C₈	C₂³×C₁₀₇	1	4	yes	—
232	C₄⋊Q₈	—	2	16	no	—
233	C₄⋊Q₈	—	2	16	no	—
234	C₂×C₄⋊C₄	—	2	8	no	—
235	C₂×C₄⋊C₄	—	2	4	no	—
236	C₂×C₄⋊C₄	—	2	2	no	—
237	C₂×C₄⋊C₄	—	2	4	no	—
238	C₂×C₄⋊C₄	—	2	4	no	—
239	C₂×C₄⋊C₄	—	2	1	no	—
240	C₂×C₄⋊C₄	D₄×C₁₀₇	1	8	yes	—
241	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	2	yes	—
242	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	4	yes	—
243	C₂×C₄²	—	2	4	no	—
244	C₂×C₄²	D₄×C₁₀₇	1	2	yes	—
245	C₂×C₄²	C₂³×C₁₀₇	1	2	yes	—
246	#103	—	2	16	no	—
247	#95	—	2	4	no	—
248	#95	—	2	4	no	—
249	C₂⁴	C₂×D₄×C₁₀₇	1	1	yes	characteristic
250	C₂×Q₈	—	2	16	no	—
251	C₂×Q₈	—	2	4	no	—
252	C₂×Q₈	—	2	2	no	—
253	C₂×Q₈	—	2	16	no	—
254	C₂×Q₈	—	2	4	no	—
255	C₂×Q₈	—	2	4	no	—
256	C₂×Q₈	—	4	32	no	—
257	C₂×Q₈	—	4	8	no	—
258	C₂×Q₈	—	4	2	no	—
259	C₂×Q₈	—	4	8	no	—
260	C₂×Q₈	—	4	2	no	—
261	C₂×Q₈	—	4	8	no	—
262	C₂×Q₈	C₂×Q₈×C₁₀₇	1	4	yes	complemented
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	2	no	—
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	8	no	—
268	C₂²×C₄	—	2	4	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	4	2	no	—
273	C₂²×C₄	—	4	2	no	—
274	C₂²×C₄	—	4	4	no	—
275	C₂²×C₄	—	4	4	no	—
276	C₂²×C₄	—	4	2	no	—
277	C₂²×C₄	—	4	2	no	—
278	C₂²×C₄	—	4	2	no	—
279	C₂²×C₄	SD₁₆×C₁₀₇	1	4	yes	—
280	C₂²×C₄	Q₁₆×C₁₀₇	1	4	yes	—
281	C₂²×C₄	C₂×D₄×C₁₀₇	1	2	yes	—
282	C₂²×C₄	C₂×D₄×C₁₀₇	1	2	yes	—
283	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
284	C₂²×C₄	C₂×D₄×C₁₀₇	1	4	yes	—
285	C₂²×C₄	C₂×Q₈×C₁₀₇	1	2	yes	—
286	C₂²×C₄	#41×C₁₀₇	1	4	yes	—
287	C₂²×C₄	#41×C₁₀₇	1	2	yes	—
288	C₂²×C₄	C₂⁴×C₁₀₇	1	1	yes	characteristic
289	C₂×C₈	—	2	4	no	—
290	C₂×C₈	—	2	4	no	—
291	C₂×C₈	—	2	4	no	—
292	C₂×C₈	—	4	8	no	—
293	C₄⋊C₄	—	2	16	no	—
294	C₄⋊C₄	—	2	8	no	—
295	C₄⋊C₄	—	2	4	no	—
296	C₄⋊C₄	—	2	4	no	—
297	C₄⋊C₄	—	4	2	no	—
298	C₄⋊C₄	C₂×D₄×C₁₀₇	1	8	yes	—
299	C₄²	—	2	4	no	—
300	C₄²	—	2	4	no	—
301	C₂³	#120×C₁₀₇	1	2	yes	—
302	C₂³	C₂²⋊Q₈×C₁₀₇	1	2	yes	—
303	C₂³	#124×C₁₀₇	1	2	yes	—
304	C₂³	C₂×SD₁₆×C₁₀₇	1	2	yes	—
305	C₂³	C₂×Q₁₆×C₁₀₇	1	2	yes	—
306	C₂³	AGL(1,ℤ/8)×C₁₀₇	1	2	yes	—
307	C₂³	#137×C₁₀₇	1	2	yes	—
308	C₂³	C₂²×D₄×C₁₀₇	1	1	yes	characteristic
309	Q₈	—	2	8	no	—
310	Q₈	—	4	32	no	—
311	Q₈	—	4	8	no	—
312	Q₈	—	4	4	no	—
313	C₂×C₄	—	2	8	no	—
314	C₂×C₄	—	2	8	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	8	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	4	8	no	—
322	C₂×C₄	—	4	16	no	—
323	C₂×C₄	—	4	2	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	—	4	4	no	—
326	C₂×C₄	—	4	4	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	8	4	no	—
331	C₂×C₄	#120×C₁₀₇	1	2	yes	—
332	C₂×C₄	C₂²⋊Q₈×C₁₀₇	1	2	yes	—
333	C₂×C₄	C₂²⋊Q₈×C₁₀₇	1	8	yes	—
334	C₂×C₄	#124×C₁₀₇	1	2	yes	—
335	C₂×C₄	#124×C₁₀₇	1	8	yes	—
336	C₂×C₄	C₂×SD₁₆×C₁₀₇	1	4	yes	—
337	C₂×C₄	C₂×Q₁₆×C₁₀₇	1	4	yes	—
338	C₂×C₄	C₂²×D₄×C₁₀₇	1	2	yes	—
339	C₂×C₄	C₂²×Q₈×C₁₀₇	1	1	yes	characteristic
340	C₂×C₄	C₂×#41×C₁₀₇	1	2	yes	—
341	C₂×C₄	C₂×#41×C₁₀₇	1	1	yes	characteristic
342	C₈	—	4	4	no	—
343	C₂²	#393×C₁₀₇	1	4	yes	—
344	C₂²	#450×C₁₀₇	1	4	yes	—
345	C₂²	#451×C₁₀₇	1	4	yes	—
346	C₂²	#475×C₁₀₇	1	4	yes	—
347	C₂²	#477×C₁₀₇	1	4	yes	—
348	C₂²	#487×C₁₀₇	1	4	yes	—
349	C₂²	#489×C₁₀₇	1	4	yes	—
350	C₂²	C₂×#120×C₁₀₇	1	1	yes	characteristic
351	C₂²	C₂×C₂²⋊Q₈×C₁₀₇	1	1	yes	characteristic
352	C₂²	C₂×#124×C₁₀₇	1	1	yes	characteristic
353	C₂²	C₂²×SD₁₆×C₁₀₇	1	1	yes	characteristic
354	C₂²	C₂²×Q₁₆×C₁₀₇	1	1	yes	characteristic
355	C₂²	C₂×AGL(1,ℤ/8)×C₁₀₇	1	1	yes	characteristic
356	C₂²	C₂×#137×C₁₀₇	1	1	yes	characteristic
357	C₄	—	2	4	no	—
358	C₄	—	2	4	no	—
359	C₄	—	4	4	no	—
360	C₄	—	4	8	no	—
361	C₄	—	8	2	no	—
362	C₄	#393×C₁₀₇	1	4	yes	—
363	C₄	C₂×C₂²⋊Q₈×C₁₀₇	1	2	yes	—
364	C₄	C₂×#124×C₁₀₇	1	2	yes	—
365	C₂	C₁₀₇×#2024	1	8	yes	direct product factor
366	C₂	C₂×#393×C₁₀₇	1	1	yes	characteristic
367	C₂	C₂×#450×C₁₀₇	1	1	yes	characteristic
368	C₂	C₂×#451×C₁₀₇	1	1	yes	characteristic
369	C₂	C₂×#475×C₁₀₇	1	1	yes	characteristic
370	C₂	C₂×#477×C₁₀₇	1	1	yes	characteristic
371	C₂	C₂×#487×C₁₀₇	1	1	yes	characteristic
372	C₂	C₂×#489×C₁₀₇	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₀₇	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₇
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ 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×#2024	C₂	direct (N × H)
33. C₂²×Q₈×C₁₀₇	Q₈	semidirect
75. C₂×Q₈×C₁₀₇	C₂×Q₈	semidirect
178. C₂×#2024	C₁₀₇	direct (N × H)
179. C₂×C₁₀₇	#2024	direct (N × H)
190. #2024	C₂×C₁₀₇	direct (N × H)
193. C₁₀₇	C₂×#2024	direct (N × H)
220. C₂²×Q₈	Q₈×C₁₀₇	semidirect
262. C₂×Q₈	C₂×Q₈×C₁₀₇	semidirect
365. C₂	C₁₀₇×#2024	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₄⋊Q₈×C₁₀₇	2
C₂²×#103×C₁₀₇	2
C₂×#391×C₁₀₇	2
C₁₀₇×#2024	2
C₂×#340×C₁₀₇	2
C₂×#336×C₁₀₇	2
C₂×#2024	107

Subgroups — C2×C107×#2024 #41049413

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₀₇×#2024 #41049413