Subgroups — C₂²×D₄⋊C₈×C₁₀₇ #41043395

Order 27392.

1886 conjugacy classes of subgroups.

The subgroup lattice has 306 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₁₀₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄⋊C₈×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×C₈×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄⋊C₈×C₁₀₇	C₂	1	12	yes	maximal, direct product factor
5	C₂³×D₄×C₁₀₇	C₄	1	1	yes	characteristic
6	C₂⁴×C₄×C₁₀₇	—	2	1	no	—
7	C₂³×C₈×C₁₀₇	—	2	1	no	—
8	C₂³×C₈×C₁₀₇	—	2	1	no	—
9	C₂×C₄×D₄×C₁₀₇	—	2	3	no	—
10	C₂×C₄×D₄×C₁₀₇	—	2	3	no	—
11	C₂×C₄×D₄×C₁₀₇	C₄	1	6	yes	—
12	C₂×C₄×D₄×C₁₀₇	C₂²	1	6	yes	—
13	C₂²×C₄⋊C₄×C₁₀₇	C₄	1	1	yes	characteristic
14	C₂²×C₂²⋊C₄×C₁₀₇	—	2	1	no	—
15	C₂²×C₄²×C₁₀₇	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊C₈×C₁₀₇	—	2	3	no	—
17	C₂×C₄⋊C₈×C₁₀₇	C₂²	1	6	yes	complemented
18	C₂×C₄×C₈×C₁₀₇	—	2	3	no	—
19	C₂×C₄×C₈×C₁₀₇	C₂²	1	6	yes	complemented
20	D₄⋊C₈×C₁₀₇	C₂²	1	16	yes	direct product factor
21	C₂⁵×C₁₀₇	—	2	1	no	—
22	C₂²×D₄×C₁₀₇	—	2	3	no	—
23	C₂²×D₄×C₁₀₇	—	2	4	no	—
24	C₂²×D₄×C₁₀₇	C₈	1	8	yes	complemented
25	C₂²×D₄×C₁₀₇	C₂×C₄	1	6	yes	—
26	C₂³×C₄×C₁₀₇	—	2	1	no	—
27	C₂³×C₄×C₁₀₇	—	2	6	no	—
28	C₂³×C₄×C₁₀₇	—	2	6	no	—
29	C₂³×C₄×C₁₀₇	—	4	4	no	—
30	C₂³×C₄×C₁₀₇	—	4	4	no	—
31	C₂³×C₄×C₁₀₇	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₁₀₇	D₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₀₇	D₄	1	1	yes	characteristic
34	C₂²×C₈×C₁₀₇	—	2	8	no	—
35	C₂²×C₈×C₁₀₇	—	2	6	no	—
36	C₂²×C₈×C₁₀₇	—	2	6	no	—
37	C₂²×C₈×C₁₀₇	—	4	4	no	—
38	C₄×D₄×C₁₀₇	—	2	12	no	—
39	C₄×D₄×C₁₀₇	—	2	6	no	—
40	C₄×D₄×C₁₀₇	—	2	6	no	—
41	C₄×D₄×C₁₀₇	C₂×C₄	1	12	yes	—
42	C₄×D₄×C₁₀₇	C₂³	1	4	yes	—
43	C₂×C₄⋊C₄×C₁₀₇	—	2	3	no	—
44	C₂×C₄⋊C₄×C₁₀₇	C₂×C₄	1	6	yes	—
45	C₂×C₂²⋊C₄×C₁₀₇	—	2	6	no	—
46	C₂×C₂²⋊C₄×C₁₀₇	—	2	6	no	—
47	C₂×C₄²×C₁₀₇	C₂×C₄	1	3	yes	—
48	C₂×C₄²×C₁₀₇	D₄	1	3	yes	—
49	C₂×C₄²×C₁₀₇	D₄	1	3	yes	—
50	C₂×C₄²×C₁₀₇	C₂³	1	3	yes	—
51	C₄⋊C₈×C₁₀₇	—	2	6	no	—
52	C₄⋊C₈×C₁₀₇	C₂³	1	4	yes	complemented
53	C₄×C₈×C₁₀₇	—	2	6	no	—
54	C₄×C₈×C₁₀₇	C₂³	1	4	yes	complemented
55	C₂⁴×C₁₀₇	—	2	8	no	—
56	C₂⁴×C₁₀₇	—	2	6	no	—
57	C₂⁴×C₁₀₇	—	4	4	no	—
58	C₂⁴×C₁₀₇	—	4	4	no	—
59	C₂⁴×C₁₀₇	C₂²⋊C₄	1	1	yes	characteristic
60	C₂×D₄×C₁₀₇	—	2	24	no	—
61	C₂×D₄×C₁₀₇	—	2	6	no	—
62	C₂×D₄×C₁₀₇	—	2	12	no	—
63	C₂×D₄×C₁₀₇	C₂×C₈	1	24	yes	complemented
64	C₂×D₄×C₁₀₇	C₂²×C₄	1	4	yes	—
65	C₂²×C₄×C₁₀₇	—	2	4	no	—
66	C₂²×C₄×C₁₀₇	—	2	6	no	—
67	C₂²×C₄×C₁₀₇	—	2	12	no	—
68	C₂²×C₄×C₁₀₇	—	2	4	no	—
69	C₂²×C₄×C₁₀₇	—	4	4	no	—
70	C₂²×C₄×C₁₀₇	—	4	24	no	—
71	C₂²×C₄×C₁₀₇	—	4	12	no	—
72	C₂²×C₄×C₁₀₇	—	4	12	no	—
73	C₂²×C₄×C₁₀₇	C₂²⋊C₄	1	3	yes	—
74	C₂²×C₄×C₁₀₇	C₂²⋊C₄	1	3	yes	—
75	C₂²×C₄×C₁₀₇	C₂²⋊C₄	1	3	yes	—
76	C₂²×C₄×C₁₀₇	C₂×C₈	1	4	yes	—
77	C₂²×C₄×C₁₀₇	M₁₆	1	4	yes	—
78	C₂²×C₄×C₁₀₇	D₈	1	4	yes	—
79	C₂²×C₄×C₁₀₇	SD₁₆	1	4	yes	—
80	C₂²×C₄×C₁₀₇	C₂²×C₄	1	3	yes	—
81	C₂²×C₄×C₁₀₇	C₂×D₄	1	3	yes	—
82	C₂²×C₄×C₁₀₇	C₂×D₄	1	3	yes	—
83	C₂×C₈×C₁₀₇	—	2	24	no	—
84	C₂×C₈×C₁₀₇	—	2	4	no	—
85	C₂×C₈×C₁₀₇	—	2	4	no	—
86	C₂×C₈×C₁₀₇	—	4	12	no	—
87	C₄⋊C₄×C₁₀₇	—	2	6	no	—
88	C₄⋊C₄×C₁₀₇	C₂²×C₄	1	4	yes	—
89	C₂²⋊C₄×C₁₀₇	—	2	12	no	—
90	C₂²⋊C₄×C₁₀₇	—	2	4	no	—
91	C₄²×C₁₀₇	C₂²⋊C₄	1	6	yes	—
92	C₄²×C₁₀₇	C₂²×C₄	1	3	yes	—
93	C₄²×C₁₀₇	C₂×D₄	1	3	yes	—
94	C₄²×C₁₀₇	C₂×D₄	1	3	yes	—
95	C₄²×C₁₀₇	C₂⁴	1	1	yes	characteristic
96	C₂³×C₁₀₇	—	2	4	no	—
97	C₂³×C₁₀₇	—	2	24	no	—
98	C₂³×C₁₀₇	—	4	32	no	—
99	C₂³×C₁₀₇	—	4	12	no	—
100	C₂³×C₁₀₇	—	4	12	no	—
101	C₂³×C₁₀₇	C₂²⋊C₈	1	4	yes	—
102	C₂³×C₁₀₇	#102	1	4	yes	—
103	C₂³×C₁₀₇	#104	1	4	yes	—
104	C₂³×C₁₀₇	C₂×C₂²⋊C₄	1	3	yes	—
105	D₄×C₁₀₇	—	2	4	no	—
106	D₄×C₁₀₇	—	2	24	no	—
107	D₄×C₁₀₇	C₂²×C₈	1	8	yes	complemented
108	C₂×C₄×C₁₀₇	—	2	6	no	—
109	C₂×C₄×C₁₀₇	—	2	6	no	—
110	C₂×C₄×C₁₀₇	—	2	4	no	—
111	C₂×C₄×C₁₀₇	—	4	12	no	—
112	C₂×C₄×C₁₀₇	—	4	4	no	—
113	C₂×C₄×C₁₀₇	—	4	4	no	—
114	C₂×C₄×C₁₀₇	—	4	24	no	—
115	C₂×C₄×C₁₀₇	C₂²⋊C₈	1	12	yes	—
116	C₂×C₄×C₁₀₇	#102	1	12	yes	—
117	C₂×C₄×C₁₀₇	C₂×C₂²⋊C₄	1	3	yes	—
118	C₂×C₄×C₁₀₇	C₂×C₂²⋊C₄	1	3	yes	—
119	C₂×C₄×C₁₀₇	C₂×C₂²⋊C₄	1	3	yes	—
120	C₂×C₄×C₁₀₇	C₂²×C₈	1	6	yes	—
121	C₂×C₄×C₁₀₇	C₂×M₁₆	1	6	yes	—
122	C₂×C₄×C₁₀₇	C₂×D₈	1	6	yes	—
123	C₂×C₄×C₁₀₇	C₂×SD₁₆	1	6	yes	—
124	C₂×C₄×C₁₀₇	C₂³×C₄	1	1	yes	characteristic
125	C₂×C₄×C₁₀₇	C₂²×D₄	1	1	yes	characteristic
126	C₂×C₄×C₁₀₇	C₂²×D₄	1	1	yes	characteristic
127	C₈×C₁₀₇	—	2	8	no	—
128	C₈×C₁₀₇	—	4	4	no	—
129	C₂²×C₁₀₇	—	2	8	no	—
130	C₂²×C₁₀₇	—	4	4	no	—
131	C₂²×C₁₀₇	—	4	4	no	—
132	C₂²×C₁₀₇	—	4	48	no	—
133	C₂²×C₁₀₇	D₄⋊C₈	1	16	yes	direct product factor
134	C₂²×C₁₀₇	C₂×C₂²⋊C₈	1	6	yes	—
135	C₂²×C₁₀₇	C₂×#102	1	6	yes	—
136	C₂²×C₁₀₇	C₂×#104	1	6	yes	—
137	C₂²×C₁₀₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
138	C₄×C₁₀₇	—	2	1	no	—
139	C₄×C₁₀₇	—	2	3	no	—
140	C₄×C₁₀₇	—	4	4	no	—
141	C₄×C₁₀₇	C₂×C₂²⋊C₈	1	6	yes	—
142	C₄×C₁₀₇	C₂×#102	1	6	yes	—
143	C₄×C₁₀₇	C₂³×C₈	1	1	yes	characteristic
144	C₄×C₁₀₇	C₂²×M₁₆	1	1	yes	characteristic
145	C₄×C₁₀₇	C₂²×D₈	1	1	yes	characteristic
146	C₄×C₁₀₇	C₂²×SD₁₆	1	1	yes	characteristic
147	C₂²×D₄⋊C₈	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
148	C₂×C₁₀₇	—	4	8	no	—
149	C₂×C₁₀₇	C₂×D₄⋊C₈	1	12	yes	direct product factor
150	C₂×C₁₀₇	C₂²×C₂²⋊C₈	1	1	yes	characteristic
151	C₂×C₁₀₇	C₂²×#102	1	1	yes	characteristic
152	C₂×C₁₀₇	C₂²×#104	1	1	yes	characteristic
153	C₂²×C₄×D₄	C₂×C₁₀₇	1	1	yes	characteristic
154	C₂²×C₄⋊C₈	C₂×C₁₀₇	1	1	yes	characteristic, complemented
155	C₂²×C₄×C₈	C₂×C₁₀₇	1	1	yes	characteristic, complemented
156	C₂×D₄⋊C₈	C₂×C₁₀₇	1	12	yes	direct product factor
157	C₁₀₇	C₂²×D₄⋊C₈	1	1	yes	characteristic, direct product factor, Sylow
158	C₂³×D₄	C₄×C₁₀₇	1	1	yes	characteristic
159	C₂⁴×C₄	—	2	1	no	—
160	C₂³×C₈	—	2	1	no	—
161	C₂³×C₈	—	2	1	no	—
162	C₂×C₄×D₄	—	2	3	no	—
163	C₂×C₄×D₄	—	2	3	no	—
164	C₂×C₄×D₄	C₄×C₁₀₇	1	6	yes	—
165	C₂×C₄×D₄	C₂²×C₁₀₇	1	6	yes	—
166	C₂²×C₄⋊C₄	C₄×C₁₀₇	1	1	yes	characteristic
167	C₂²×C₂²⋊C₄	—	2	1	no	—
168	C₂²×C₄²	C₂²×C₁₀₇	1	1	yes	characteristic
169	C₂×C₄⋊C₈	—	2	3	no	—
170	C₂×C₄⋊C₈	C₂²×C₁₀₇	1	6	yes	complemented
171	C₂×C₄×C₈	—	2	3	no	—
172	C₂×C₄×C₈	C₂²×C₁₀₇	1	6	yes	complemented
173	D₄⋊C₈	C₂²×C₁₀₇	1	16	yes	direct product factor
174	C₂⁵	—	2	1	no	—
175	C₂²×D₄	—	2	3	no	—
176	C₂²×D₄	—	2	4	no	—
177	C₂²×D₄	C₈×C₁₀₇	1	8	yes	complemented
178	C₂²×D₄	C₂×C₄×C₁₀₇	1	6	yes	—
179	C₂³×C₄	—	2	1	no	—
180	C₂³×C₄	—	2	6	no	—
181	C₂³×C₄	—	2	6	no	—
182	C₂³×C₄	—	4	4	no	—
183	C₂³×C₄	—	4	4	no	—
184	C₂³×C₄	C₂×C₄×C₁₀₇	1	1	yes	characteristic
185	C₂³×C₄	D₄×C₁₀₇	1	1	yes	characteristic
186	C₂³×C₄	D₄×C₁₀₇	1	1	yes	characteristic
187	C₂²×C₈	—	2	8	no	—
188	C₂²×C₈	—	2	6	no	—
189	C₂²×C₈	—	2	6	no	—
190	C₂²×C₈	—	4	4	no	—
191	C₄×D₄	—	2	12	no	—
192	C₄×D₄	—	2	6	no	—
193	C₄×D₄	—	2	6	no	—
194	C₄×D₄	C₂×C₄×C₁₀₇	1	12	yes	—
195	C₄×D₄	C₂³×C₁₀₇	1	4	yes	—
196	C₂×C₄⋊C₄	—	2	3	no	—
197	C₂×C₄⋊C₄	C₂×C₄×C₁₀₇	1	6	yes	—
198	C₂×C₂²⋊C₄	—	2	6	no	—
199	C₂×C₂²⋊C₄	—	2	6	no	—
200	C₂×C₄²	C₂×C₄×C₁₀₇	1	3	yes	—
201	C₂×C₄²	D₄×C₁₀₇	1	3	yes	—
202	C₂×C₄²	D₄×C₁₀₇	1	3	yes	—
203	C₂×C₄²	C₂³×C₁₀₇	1	3	yes	—
204	C₄⋊C₈	—	2	6	no	—
205	C₄⋊C₈	C₂³×C₁₀₇	1	4	yes	complemented
206	C₄×C₈	—	2	6	no	—
207	C₄×C₈	C₂³×C₁₀₇	1	4	yes	complemented
208	C₂⁴	—	2	8	no	—
209	C₂⁴	—	2	6	no	—
210	C₂⁴	—	4	4	no	—
211	C₂⁴	—	4	4	no	—
212	C₂⁴	C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
213	C₂×D₄	—	2	24	no	—
214	C₂×D₄	—	2	6	no	—
215	C₂×D₄	—	2	12	no	—
216	C₂×D₄	C₂×C₈×C₁₀₇	1	24	yes	complemented
217	C₂×D₄	C₂²×C₄×C₁₀₇	1	4	yes	—
218	C₂²×C₄	—	2	4	no	—
219	C₂²×C₄	—	2	6	no	—
220	C₂²×C₄	—	2	12	no	—
221	C₂²×C₄	—	2	4	no	—
222	C₂²×C₄	—	4	4	no	—
223	C₂²×C₄	—	4	24	no	—
224	C₂²×C₄	—	4	12	no	—
225	C₂²×C₄	—	4	12	no	—
226	C₂²×C₄	C₂²⋊C₄×C₁₀₇	1	3	yes	—
227	C₂²×C₄	C₂²⋊C₄×C₁₀₇	1	3	yes	—
228	C₂²×C₄	C₂²⋊C₄×C₁₀₇	1	3	yes	—
229	C₂²×C₄	C₂×C₈×C₁₀₇	1	4	yes	—
230	C₂²×C₄	M₁₆×C₁₀₇	1	4	yes	—
231	C₂²×C₄	D₈×C₁₀₇	1	4	yes	—
232	C₂²×C₄	SD₁₆×C₁₀₇	1	4	yes	—
233	C₂²×C₄	C₂²×C₄×C₁₀₇	1	3	yes	—
234	C₂²×C₄	C₂×D₄×C₁₀₇	1	3	yes	—
235	C₂²×C₄	C₂×D₄×C₁₀₇	1	3	yes	—
236	C₂×C₈	—	2	24	no	—
237	C₂×C₈	—	2	4	no	—
238	C₂×C₈	—	2	4	no	—
239	C₂×C₈	—	4	12	no	—
240	C₄⋊C₄	—	2	6	no	—
241	C₄⋊C₄	C₂²×C₄×C₁₀₇	1	4	yes	—
242	C₂²⋊C₄	—	2	12	no	—
243	C₂²⋊C₄	—	2	4	no	—
244	C₄²	C₂²⋊C₄×C₁₀₇	1	6	yes	—
245	C₄²	C₂²×C₄×C₁₀₇	1	3	yes	—
246	C₄²	C₂×D₄×C₁₀₇	1	3	yes	—
247	C₄²	C₂×D₄×C₁₀₇	1	3	yes	—
248	C₄²	C₂⁴×C₁₀₇	1	1	yes	characteristic
249	C₂³	—	2	24	no	—
250	C₂³	—	2	4	no	—
251	C₂³	—	4	12	no	—
252	C₂³	—	4	12	no	—
253	C₂³	—	4	32	no	—
254	C₂³	C₂²⋊C₈×C₁₀₇	1	4	yes	—
255	C₂³	#102×C₁₀₇	1	4	yes	—
256	C₂³	#104×C₁₀₇	1	4	yes	—
257	C₂³	C₂×C₂²⋊C₄×C₁₀₇	1	3	yes	—
258	D₄	—	2	24	no	—
259	D₄	—	2	4	no	—
260	D₄	C₂²×C₈×C₁₀₇	1	8	yes	complemented
261	C₂×C₄	—	2	6	no	—
262	C₂×C₄	—	2	6	no	—
263	C₂×C₄	—	2	4	no	—
264	C₂×C₄	—	4	12	no	—
265	C₂×C₄	—	4	24	no	—
266	C₂×C₄	—	4	4	no	—
267	C₂×C₄	—	4	4	no	—
268	C₂×C₄	C₂²⋊C₈×C₁₀₇	1	12	yes	—
269	C₂×C₄	#102×C₁₀₇	1	12	yes	—
270	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₇	1	3	yes	—
271	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₇	1	3	yes	—
272	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₇	1	3	yes	—
273	C₂×C₄	C₂²×C₈×C₁₀₇	1	6	yes	—
274	C₂×C₄	C₂×M₁₆×C₁₀₇	1	6	yes	—
275	C₂×C₄	C₂×D₈×C₁₀₇	1	6	yes	—
276	C₂×C₄	C₂×SD₁₆×C₁₀₇	1	6	yes	—
277	C₂×C₄	C₂³×C₄×C₁₀₇	1	1	yes	characteristic
278	C₂×C₄	C₂²×D₄×C₁₀₇	1	1	yes	characteristic
279	C₂×C₄	C₂²×D₄×C₁₀₇	1	1	yes	characteristic
280	C₈	—	2	8	no	—
281	C₈	—	4	4	no	—
282	C₂²	—	2	8	no	—
283	C₂²	—	4	4	no	—
284	C₂²	—	4	4	no	—
285	C₂²	—	4	48	no	—
286	C₂²	D₄⋊C₈×C₁₀₇	1	16	yes	direct product factor
287	C₂²	C₂×C₂²⋊C₈×C₁₀₇	1	6	yes	—
288	C₂²	C₂×#102×C₁₀₇	1	6	yes	—
289	C₂²	C₂×#104×C₁₀₇	1	6	yes	—
290	C₂²	C₂²×C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
291	C₄	—	2	1	no	—
292	C₄	—	2	3	no	—
293	C₄	—	4	4	no	—
294	C₄	C₂×C₂²⋊C₈×C₁₀₇	1	6	yes	—
295	C₄	C₂×#102×C₁₀₇	1	6	yes	—
296	C₄	C₂³×C₈×C₁₀₇	1	1	yes	characteristic
297	C₄	C₂²×M₁₆×C₁₀₇	1	1	yes	characteristic
298	C₄	C₂²×D₈×C₁₀₇	1	1	yes	characteristic
299	C₄	C₂²×SD₁₆×C₁₀₇	1	1	yes	characteristic
300	C₂	—	4	8	no	—
301	C₂	C₂×D₄⋊C₈×C₁₀₇	1	12	yes	direct product factor
302	C₂	C₂²×C₂²⋊C₈×C₁₀₇	1	1	yes	characteristic
303	C₂	C₂²×#102×C₁₀₇	1	1	yes	characteristic
304	C₂	C₂²×#104×C₁₀₇	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄⋊C₈×C₁₀₇	C₂	semidirect
3. C₂²×C₄×C₈×C₁₀₇	C₂	semidirect
4. C₂×D₄⋊C₈×C₁₀₇	C₂	direct (N × H)
17. C₂×C₄⋊C₈×C₁₀₇	C₂²	semidirect
19. C₂×C₄×C₈×C₁₀₇	C₂²	semidirect
20. D₄⋊C₈×C₁₀₇	C₂²	direct (N × H)
24. C₂²×D₄×C₁₀₇	C₈	semidirect
52. C₄⋊C₈×C₁₀₇	C₂³	semidirect
54. C₄×C₈×C₁₀₇	C₂³	semidirect
63. C₂×D₄×C₁₀₇	C₂×C₈	semidirect
107. D₄×C₁₀₇	C₂²×C₈	semidirect
133. C₂²×C₁₀₇	D₄⋊C₈	direct (N × H)
147. C₂²×D₄⋊C₈	C₁₀₇	direct (N × H)
149. C₂×C₁₀₇	C₂×D₄⋊C₈	direct (N × H)
154. C₂²×C₄⋊C₈	C₂×C₁₀₇	semidirect
155. C₂²×C₄×C₈	C₂×C₁₀₇	semidirect
156. C₂×D₄⋊C₈	C₂×C₁₀₇	direct (N × H)
157. C₁₀₇	C₂²×D₄⋊C₈	direct (N × H)
170. C₂×C₄⋊C₈	C₂²×C₁₀₇	semidirect
172. C₂×C₄×C₈	C₂²×C₁₀₇	semidirect
173. D₄⋊C₈	C₂²×C₁₀₇	direct (N × H)
177. C₂²×D₄	C₈×C₁₀₇	semidirect
205. C₄⋊C₈	C₂³×C₁₀₇	semidirect
207. C₄×C₈	C₂³×C₁₀₇	semidirect
216. C₂×D₄	C₂×C₈×C₁₀₇	semidirect
260. D₄	C₂²×C₈×C₁₀₇	semidirect
286. C₂²	D₄⋊C₈×C₁₀₇	direct (N × H)
301. C₂	C₂×D₄⋊C₈×C₁₀₇	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×D₄×C₁₀₇	2
C₂²×C₄⋊C₈×C₁₀₇	2
C₂²×C₄×C₈×C₁₀₇	2
C₂×D₄⋊C₈×C₁₀₇	2
C₂²×D₄⋊C₈	107

Subgroups — C22×D4⋊C8×C107 #41043395

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×D₄⋊C₈×C₁₀₇ #41043395