Subgroups — SD₁₆²×C₁₀₇ #41045941

Order 27392.

716 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×SD₁₆×C₁₀₇	C₂	1	2	yes	maximal, complemented
2	D₄×SD₁₆×C₁₀₇	C₂	1	2	yes	maximal
3	C₁₀₇×#1705	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₇×#1671	C₂	1	2	yes	maximal, complemented
5	C₁₀₇×#1666	C₂	1	2	yes	maximal, complemented
6	C₁₀₇×#1651	C₂	1	2	yes	maximal, complemented
7	C₁₀₇×#1629	C₂	1	1	yes	maximal, characteristic
8	C₁₀₇×#1623	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×SD₁₆×C₁₀₇	C₂	1	2	yes	maximal, complemented
10	C₂²×SD₁₆×C₁₀₇	—	2	2	no	—
11	Q₈²×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
12	D₄×Q₈×C₁₀₇	C₂²	1	2	yes	—
13	D₄²×C₁₀₇	C₂²	1	1	yes	characteristic
14	#498×C₁₀₇	—	2	2	no	—
15	#498×C₁₀₇	C₂²	1	2	yes	complemented
16	#498×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
17	#492×C₁₀₇	C₂²	1	2	yes	—
18	#492×C₁₀₇	C₂²	1	1	yes	characteristic
19	#476×C₁₀₇	—	2	2	no	—
20	#476×C₁₀₇	C₂²	1	2	yes	—
21	#475×C₁₀₇	—	2	2	no	—
22	#475×C₁₀₇	C₂²	1	2	yes	complemented
23	#465×C₁₀₇	—	2	2	no	—
24	#461×C₁₀₇	C₂²	1	2	yes	—
25	#460×C₁₀₇	C₂²	1	2	yes	—
26	#450×C₁₀₇	—	2	2	no	—
27	#448×C₁₀₇	—	2	2	no	—
28	C₈×Q₈×C₁₀₇	C₂²	1	2	yes	complemented
29	C₄×SD₁₆×C₁₀₇	—	2	2	no	—
30	C₄×SD₁₆×C₁₀₇	C₂²	1	2	yes	—
31	C₈×D₄×C₁₀₇	C₂²	1	2	yes	—
32	#334×C₁₀₇	C₂²	1	2	yes	complemented
33	#333×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
34	#332×C₁₀₇	C₂²	1	2	yes	complemented
35	#331×C₁₀₇	C₂²	1	1	yes	characteristic
36	Q₈⋊C₈×C₁₀₇	C₂²	1	2	yes	complemented
37	D₄⋊C₈×C₁₀₇	C₂²	1	2	yes	—
38	C₈²×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
39	C₂²×Q₈×C₁₀₇	—	2	2	no	—
40	C₂²×D₄×C₁₀₇	—	2	2	no	—
41	C₂×SD₁₆×C₁₀₇	—	2	2	no	—
42	C₂×SD₁₆×C₁₀₇	—	2	2	no	—
43	C₂×SD₁₆×C₁₀₇	—	2	2	no	—
44	C₂×SD₁₆×C₁₀₇	—	2	2	no	—
45	C₂×SD₁₆×C₁₀₇	—	4	1	no	—
46	C₂×SD₁₆×C₁₀₇	—	4	8	no	—
47	C₂×SD₁₆×C₁₀₇	D₄	1	2	yes	—
48	C₂²×C₈×C₁₀₇	—	2	2	no	—
49	C₄⋊Q₈×C₁₀₇	—	2	2	no	—
50	C₄⋊Q₈×C₁₀₇	—	2	2	no	—
51	C₄⋊Q₈×C₁₀₇	—	4	1	no	—
52	C₄⋊Q₈×C₁₀₇	C₂³	1	2	yes	—
53	C₄⋊Q₈×C₁₀₇	C₂³	1	1	yes	characteristic
54	#127×C₁₀₇	C₂³	1	1	yes	characteristic
55	C₂²⋊Q₈×C₁₀₇	—	2	2	no	—
56	C₂²⋊Q₈×C₁₀₇	—	4	2	no	—
57	#121×C₁₀₇	—	2	2	no	—
58	#120×C₁₀₇	—	4	1	no	—
59	C₄×Q₈×C₁₀₇	—	2	2	no	—
60	C₄×Q₈×C₁₀₇	C₂³	1	2	yes	—
61	C₄×D₄×C₁₀₇	—	2	2	no	—
62	C₄×D₄×C₁₀₇	C₂³	1	2	yes	—
63	#106×C₁₀₇	—	2	2	no	—
64	#106×C₁₀₇	—	2	2	no	—
65	#106×C₁₀₇	—	2	2	no	—
66	#106×C₁₀₇	—	2	2	no	—
67	#106×C₁₀₇	—	4	1	no	—
68	#106×C₁₀₇	D₄	1	2	yes	—
69	C₄⋊C₈×C₁₀₇	—	2	2	no	—
70	C₄⋊C₈×C₁₀₇	C₂³	1	2	yes	—
71	C₄⋊C₈×C₁₀₇	C₂³	1	2	yes	—
72	#103×C₁₀₇	—	2	2	no	—
73	#103×C₁₀₇	—	2	2	no	—
74	#103×C₁₀₇	D₄	1	2	yes	—
75	#102×C₁₀₇	—	2	2	no	—
76	#102×C₁₀₇	—	2	2	no	—
77	#102×C₁₀₇	D₄	1	2	yes	—
78	C₂²⋊C₈×C₁₀₇	—	2	2	no	—
79	C₄×C₈×C₁₀₇	—	2	2	no	—
80	C₄×C₈×C₁₀₇	C₂³	1	1	yes	characteristic
81	C₄×C₈×C₁₀₇	C₂³	1	2	yes	—
82	C₂⁴×C₁₀₇	—	4	1	no	—
83	C₂×Q₈×C₁₀₇	—	2	2	no	—
84	C₂×Q₈×C₁₀₇	—	2	1	no	—
85	C₂×Q₈×C₁₀₇	—	4	2	no	—
86	C₂×Q₈×C₁₀₇	—	4	1	no	—
87	C₂×Q₈×C₁₀₇	—	4	4	no	—
88	C₂×Q₈×C₁₀₇	—	8	2	no	—
89	C₂×Q₈×C₁₀₇	C₂×D₄	1	2	yes	—
90	C₂×D₄×C₁₀₇	—	2	2	no	—
91	C₂×D₄×C₁₀₇	—	2	1	no	—
92	C₂×D₄×C₁₀₇	—	4	2	no	—
93	C₂×D₄×C₁₀₇	—	4	4	no	—
94	C₂×D₄×C₁₀₇	—	8	2	no	—
95	C₂×D₄×C₁₀₇	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₁₀₇	—	2	2	no	—
97	C₂²×C₄×C₁₀₇	—	4	2	no	—
98	SD₁₆×C₁₀₇	—	4	4	no	—
99	SD₁₆×C₁₀₇	—	4	4	no	—
100	SD₁₆×C₁₀₇	—	4	4	no	—
101	SD₁₆×C₁₀₇	—	8	2	no	—
102	SD₁₆×C₁₀₇	—	8	2	no	—
103	SD₁₆×C₁₀₇	SD₁₆	1	8	yes	direct product factor
104	C₂×C₈×C₁₀₇	—	2	1	no	—
105	C₂×C₈×C₁₀₇	—	2	2	no	—
106	C₂×C₈×C₁₀₇	—	2	2	no	—
107	C₂×C₈×C₁₀₇	—	4	4	no	—
108	C₂×C₈×C₁₀₇	C₂×D₄	1	2	yes	—
109	C₂×C₈×C₁₀₇	C₂×D₄	1	2	yes	—
110	C₄⋊C₄×C₁₀₇	—	2	2	no	—
111	C₄⋊C₄×C₁₀₇	—	2	2	no	—
112	C₄⋊C₄×C₁₀₇	—	2	2	no	—
113	C₄⋊C₄×C₁₀₇	—	2	2	no	—
114	C₄⋊C₄×C₁₀₇	—	4	2	no	—
115	C₄⋊C₄×C₁₀₇	—	4	2	no	—
116	C₄⋊C₄×C₁₀₇	C₂×D₄	1	2	yes	—
117	C₄⋊C₄×C₁₀₇	C₂×D₄	1	2	yes	—
118	C₂²⋊C₄×C₁₀₇	—	2	2	no	—
119	C₂²⋊C₄×C₁₀₇	—	4	1	no	—
120	C₂²⋊C₄×C₁₀₇	—	4	2	no	—
121	C₄²×C₁₀₇	—	2	2	no	—
122	C₄²×C₁₀₇	—	4	1	no	—
123	C₄²×C₁₀₇	C₂⁴	1	1	yes	characteristic
124	C₂³×C₁₀₇	—	2	2	no	—
125	C₂³×C₁₀₇	—	4	1	no	—
126	C₂³×C₁₀₇	—	8	4	no	—
127	C₂³×C₁₀₇	—	16	1	no	—
128	Q₈×C₁₀₇	—	2	2	no	—
129	Q₈×C₁₀₇	—	4	2	no	—
130	Q₈×C₁₀₇	—	4	2	no	—
131	Q₈×C₁₀₇	—	8	4	no	—
132	Q₈×C₁₀₇	—	8	1	no	—
133	Q₈×C₁₀₇	—	16	1	no	—
134	Q₈×C₁₀₇	C₂×SD₁₆	1	4	yes	complemented
135	D₄×C₁₀₇	—	2	2	no	—
136	D₄×C₁₀₇	—	4	2	no	—
137	D₄×C₁₀₇	—	4	2	no	—
138	D₄×C₁₀₇	—	8	1	no	—
139	D₄×C₁₀₇	—	8	4	no	—
140	D₄×C₁₀₇	C₂×SD₁₆	1	4	yes	—
141	C₂×C₄×C₁₀₇	—	2	2	no	—
142	C₂×C₄×C₁₀₇	—	2	2	no	—
143	C₂×C₄×C₁₀₇	—	2	2	no	—
144	C₂×C₄×C₁₀₇	—	4	2	no	—
145	C₂×C₄×C₁₀₇	—	4	2	no	—
146	C₂×C₄×C₁₀₇	—	4	1	no	—
147	C₂×C₄×C₁₀₇	—	4	2	no	—
148	C₂×C₄×C₁₀₇	—	8	4	no	—
149	C₂×C₄×C₁₀₇	C₂²×D₄	1	2	yes	—
150	C₂×C₄×C₁₀₇	H(5,𝔽₂)	1	1	yes	characteristic
151	C₈×C₁₀₇	—	2	2	no	—
152	C₈×C₁₀₇	—	2	2	no	—
153	C₈×C₁₀₇	—	4	2	no	—
154	C₈×C₁₀₇	—	4	2	no	—
155	C₈×C₁₀₇	C₂×SD₁₆	1	4	yes	complemented
156	C₂²×C₁₀₇	—	2	4	no	—
157	C₂²×C₁₀₇	—	4	2	no	—
158	C₂²×C₁₀₇	—	4	2	no	—
159	C₂²×C₁₀₇	—	8	2	no	—
160	C₂²×C₁₀₇	—	8	1	no	—
161	C₂²×C₁₀₇	—	16	4	no	—
162	C₂²×C₁₀₇	D₄²	1	1	yes	characteristic
163	C₄×C₁₀₇	—	2	4	no	—
164	C₄×C₁₀₇	—	2	1	no	—
165	C₄×C₁₀₇	—	4	2	no	—
166	C₄×C₁₀₇	—	4	2	no	—
167	C₄×C₁₀₇	—	8	2	no	—
168	C₄×C₁₀₇	—	8	1	no	—
169	C₄×C₁₀₇	C₂²×SD₁₆	1	2	yes	—
170	C₄×C₁₀₇	#577	1	2	yes	—
171	SD₁₆²	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
172	C₂×C₁₀₇	—	4	4	no	—
173	C₂×C₁₀₇	—	16	1	no	—
174	C₂×C₁₀₇	D₄×SD₁₆	1	2	yes	—
175	C₂×C₁₀₇	#3291	1	1	yes	characteristic
176	Q₈×SD₁₆	C₂×C₁₀₇	1	2	yes	complemented
177	D₄×SD₁₆	C₂×C₁₀₇	1	2	yes	—
178	#1705	C₂×C₁₀₇	1	1	yes	characteristic, complemented
179	#1671	C₂×C₁₀₇	1	2	yes	complemented
180	#1666	C₂×C₁₀₇	1	2	yes	complemented
181	#1651	C₂×C₁₀₇	1	2	yes	complemented
182	#1629	C₂×C₁₀₇	1	1	yes	characteristic
183	#1623	C₂×C₁₀₇	1	1	yes	characteristic, complemented
184	C₈×SD₁₆	C₂×C₁₀₇	1	2	yes	complemented
185	C₁₀₇	SD₁₆²	1	1	yes	characteristic, direct product factor, Sylow
186	C₂²×SD₁₆	—	2	2	no	—
187	Q₈²	C₂²×C₁₀₇	1	1	yes	characteristic, complemented
188	D₄×Q₈	C₂²×C₁₀₇	1	2	yes	—
189	D₄²	C₂²×C₁₀₇	1	1	yes	characteristic
190	#498	—	2	2	no	—
191	#498	C₂²×C₁₀₇	1	2	yes	complemented
192	#498	C₂²×C₁₀₇	1	1	yes	characteristic, complemented
193	#492	C₂²×C₁₀₇	1	2	yes	—
194	#492	C₂²×C₁₀₇	1	1	yes	characteristic
195	#476	—	2	2	no	—
196	#476	C₂²×C₁₀₇	1	2	yes	—
197	#475	—	2	2	no	—
198	#475	C₂²×C₁₀₇	1	2	yes	complemented
199	#465	—	2	2	no	—
200	#461	C₂²×C₁₀₇	1	2	yes	—
201	#460	C₂²×C₁₀₇	1	2	yes	—
202	#450	—	2	2	no	—
203	#448	—	2	2	no	—
204	C₈×Q₈	C₂²×C₁₀₇	1	2	yes	complemented
205	C₄×SD₁₆	—	2	2	no	—
206	C₄×SD₁₆	C₂²×C₁₀₇	1	2	yes	—
207	C₈×D₄	C₂²×C₁₀₇	1	2	yes	—
208	#334	C₂²×C₁₀₇	1	2	yes	complemented
209	#333	C₂²×C₁₀₇	1	1	yes	characteristic, complemented
210	#332	C₂²×C₁₀₇	1	2	yes	complemented
211	#331	C₂²×C₁₀₇	1	1	yes	characteristic
212	Q₈⋊C₈	C₂²×C₁₀₇	1	2	yes	complemented
213	D₄⋊C₈	C₂²×C₁₀₇	1	2	yes	—
214	C₈²	C₂²×C₁₀₇	1	1	yes	characteristic, complemented
215	C₂²×Q₈	—	2	2	no	—
216	C₂²×D₄	—	2	2	no	—
217	C₂×SD₁₆	—	2	2	no	—
218	C₂×SD₁₆	—	2	2	no	—
219	C₂×SD₁₆	—	2	2	no	—
220	C₂×SD₁₆	—	2	2	no	—
221	C₂×SD₁₆	—	4	1	no	—
222	C₂×SD₁₆	—	4	8	no	—
223	C₂×SD₁₆	D₄×C₁₀₇	1	2	yes	—
224	C₂²×C₈	—	2	2	no	—
225	C₄⋊Q₈	—	2	2	no	—
226	C₄⋊Q₈	—	2	2	no	—
227	C₄⋊Q₈	—	4	1	no	—
228	C₄⋊Q₈	C₂³×C₁₀₇	1	2	yes	—
229	C₄⋊Q₈	C₂³×C₁₀₇	1	1	yes	characteristic
230	#127	C₂³×C₁₀₇	1	1	yes	characteristic
231	C₂²⋊Q₈	—	2	2	no	—
232	C₂²⋊Q₈	—	4	2	no	—
233	#121	—	2	2	no	—
234	#120	—	4	1	no	—
235	C₄×Q₈	—	2	2	no	—
236	C₄×Q₈	C₂³×C₁₀₇	1	2	yes	—
237	C₄×D₄	—	2	2	no	—
238	C₄×D₄	C₂³×C₁₀₇	1	2	yes	—
239	#106	—	2	2	no	—
240	#106	—	2	2	no	—
241	#106	—	2	2	no	—
242	#106	—	2	2	no	—
243	#106	—	4	1	no	—
244	#106	D₄×C₁₀₇	1	2	yes	—
245	C₄⋊C₈	—	2	2	no	—
246	C₄⋊C₈	C₂³×C₁₀₇	1	2	yes	—
247	C₄⋊C₈	C₂³×C₁₀₇	1	2	yes	—
248	#103	—	2	2	no	—
249	#103	—	2	2	no	—
250	#103	D₄×C₁₀₇	1	2	yes	—
251	#102	—	2	2	no	—
252	#102	—	2	2	no	—
253	#102	D₄×C₁₀₇	1	2	yes	—
254	C₂²⋊C₈	—	2	2	no	—
255	C₄×C₈	—	2	2	no	—
256	C₄×C₈	C₂³×C₁₀₇	1	1	yes	characteristic
257	C₄×C₈	C₂³×C₁₀₇	1	2	yes	—
258	C₂⁴	—	4	1	no	—
259	C₂×Q₈	—	2	2	no	—
260	C₂×Q₈	—	2	1	no	—
261	C₂×Q₈	—	4	2	no	—
262	C₂×Q₈	—	4	1	no	—
263	C₂×Q₈	—	4	4	no	—
264	C₂×Q₈	—	8	2	no	—
265	C₂×Q₈	C₂×D₄×C₁₀₇	1	2	yes	—
266	C₂×D₄	—	2	2	no	—
267	C₂×D₄	—	2	1	no	—
268	C₂×D₄	—	4	2	no	—
269	C₂×D₄	—	4	4	no	—
270	C₂×D₄	—	8	2	no	—
271	C₂×D₄	C₂×D₄×C₁₀₇	1	2	yes	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	4	2	no	—
274	SD₁₆	—	4	4	no	—
275	SD₁₆	—	4	4	no	—
276	SD₁₆	—	4	4	no	—
277	SD₁₆	—	8	2	no	—
278	SD₁₆	—	8	2	no	—
279	SD₁₆	SD₁₆×C₁₀₇	1	8	yes	direct product factor
280	C₂×C₈	—	2	1	no	—
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	—	2	2	no	—
283	C₂×C₈	—	4	4	no	—
284	C₂×C₈	C₂×D₄×C₁₀₇	1	2	yes	—
285	C₂×C₈	C₂×D₄×C₁₀₇	1	2	yes	—
286	C₄⋊C₄	—	2	2	no	—
287	C₄⋊C₄	—	2	2	no	—
288	C₄⋊C₄	—	2	2	no	—
289	C₄⋊C₄	—	2	2	no	—
290	C₄⋊C₄	—	4	2	no	—
291	C₄⋊C₄	—	4	2	no	—
292	C₄⋊C₄	C₂×D₄×C₁₀₇	1	2	yes	—
293	C₄⋊C₄	C₂×D₄×C₁₀₇	1	2	yes	—
294	C₂²⋊C₄	—	2	2	no	—
295	C₂²⋊C₄	—	4	1	no	—
296	C₂²⋊C₄	—	4	2	no	—
297	C₄²	—	2	2	no	—
298	C₄²	—	4	1	no	—
299	C₄²	C₂⁴×C₁₀₇	1	1	yes	characteristic
300	C₂³	—	2	2	no	—
301	C₂³	—	4	1	no	—
302	C₂³	—	8	4	no	—
303	C₂³	—	16	1	no	—
304	Q₈	—	2	2	no	—
305	Q₈	—	4	2	no	—
306	Q₈	—	4	2	no	—
307	Q₈	—	8	4	no	—
308	Q₈	—	8	1	no	—
309	Q₈	—	16	1	no	—
310	Q₈	C₂×SD₁₆×C₁₀₇	1	4	yes	complemented
311	D₄	—	2	2	no	—
312	D₄	—	4	2	no	—
313	D₄	—	4	2	no	—
314	D₄	—	8	1	no	—
315	D₄	—	8	4	no	—
316	D₄	C₂×SD₁₆×C₁₀₇	1	4	yes	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	4	2	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	4	1	no	—
323	C₂×C₄	—	4	2	no	—
324	C₂×C₄	—	8	4	no	—
325	C₂×C₄	C₂²×D₄×C₁₀₇	1	2	yes	—
326	C₂×C₄	H(5,𝔽₂)×C₁₀₇	1	1	yes	characteristic
327	C₈	—	2	2	no	—
328	C₈	—	2	2	no	—
329	C₈	—	4	2	no	—
330	C₈	—	4	2	no	—
331	C₈	C₂×SD₁₆×C₁₀₇	1	4	yes	complemented
332	C₂²	—	2	4	no	—
333	C₂²	—	4	2	no	—
334	C₂²	—	4	2	no	—
335	C₂²	—	8	2	no	—
336	C₂²	—	8	1	no	—
337	C₂²	—	16	4	no	—
338	C₂²	D₄²×C₁₀₇	1	1	yes	characteristic
339	C₄	—	2	4	no	—
340	C₄	—	2	1	no	—
341	C₄	—	4	2	no	—
342	C₄	—	4	2	no	—
343	C₄	—	8	2	no	—
344	C₄	—	8	1	no	—
345	C₄	C₂²×SD₁₆×C₁₀₇	1	2	yes	—
346	C₄	#577×C₁₀₇	1	2	yes	—
347	C₂	—	4	4	no	—
348	C₂	—	16	1	no	—
349	C₂	D₄×SD₁₆×C₁₀₇	1	2	yes	—
350	C₂	C₁₀₇×#3291	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₀₇	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₀₇
prime radical	D₄²×C₁₀₇	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₇ ◁ C₄²×C₁₀₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. Q₈×SD₁₆×C₁₀₇	C₂	semidirect
3. C₁₀₇×#1705	C₂	semidirect
4. C₁₀₇×#1671	C₂	semidirect
5. C₁₀₇×#1666	C₂	semidirect
6. C₁₀₇×#1651	C₂	semidirect
8. C₁₀₇×#1623	C₂	semidirect
9. C₈×SD₁₆×C₁₀₇	C₂	semidirect
11. Q₈²×C₁₀₇	C₂²	semidirect
15. #498×C₁₀₇	C₂²	semidirect
16. #498×C₁₀₇	C₂²	semidirect
22. #475×C₁₀₇	C₂²	semidirect
28. C₈×Q₈×C₁₀₇	C₂²	semidirect
32. #334×C₁₀₇	C₂²	semidirect
33. #333×C₁₀₇	C₂²	semidirect
34. #332×C₁₀₇	C₂²	semidirect
36. Q₈⋊C₈×C₁₀₇	C₂²	semidirect
38. C₈²×C₁₀₇	C₂²	semidirect
103. SD₁₆×C₁₀₇	SD₁₆	direct (N × H)
134. Q₈×C₁₀₇	C₂×SD₁₆	semidirect
155. C₈×C₁₀₇	C₂×SD₁₆	semidirect
171. SD₁₆²	C₁₀₇	direct (N × H)
176. Q₈×SD₁₆	C₂×C₁₀₇	semidirect
178. #1705	C₂×C₁₀₇	semidirect
179. #1671	C₂×C₁₀₇	semidirect
180. #1666	C₂×C₁₀₇	semidirect
181. #1651	C₂×C₁₀₇	semidirect
183. #1623	C₂×C₁₀₇	semidirect
184. C₈×SD₁₆	C₂×C₁₀₇	semidirect
185. C₁₀₇	SD₁₆²	direct (N × H)
187. Q₈²	C₂²×C₁₀₇	semidirect
191. #498	C₂²×C₁₀₇	semidirect
192. #498	C₂²×C₁₀₇	semidirect
198. #475	C₂²×C₁₀₇	semidirect
204. C₈×Q₈	C₂²×C₁₀₇	semidirect
208. #334	C₂²×C₁₀₇	semidirect
209. #333	C₂²×C₁₀₇	semidirect
210. #332	C₂²×C₁₀₇	semidirect
212. Q₈⋊C₈	C₂²×C₁₀₇	semidirect
214. C₈²	C₂²×C₁₀₇	semidirect
279. SD₁₆	SD₁₆×C₁₀₇	direct (N × H)
310. Q₈	C₂×SD₁₆×C₁₀₇	semidirect
331. C₈	C₂×SD₁₆×C₁₀₇	semidirect

Maximal subgroups

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

subgroup	index
Q₈×SD₁₆×C₁₀₇	2
D₄×SD₁₆×C₁₀₇	2
C₁₀₇×#1705	2
C₁₀₇×#1671	2
C₁₀₇×#1666	2
C₁₀₇×#1651	2
C₁₀₇×#1629	2
C₁₀₇×#1623	2
C₈×SD₁₆×C₁₀₇	2
SD₁₆²	107

Subgroups — SD162×C107 #41045941

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — SD₁₆²×C₁₀₇ #41045941