Subgroups — C₂×C₄×C₄⋊Q₈×C₁₃₉ #48028633

Order 35584.

3358 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×Q₈×C₁₃₉	C₂	1	2	yes	maximal
3	C₄×C₄⋊Q₈×C₁₃₉	C₂	1	16	yes	maximal, direct product factor
4	C₂×#391×C₁₃₉	C₂	1	2	yes	maximal
5	C₂×#389×C₁₃₉	C₂	1	4	yes	maximal
6	C₂×#384×C₁₃₉	C₂	1	1	yes	maximal, characteristic
7	C₂×C₄×C₄⋊C₄×C₁₃₉	C₂	1	4	yes	maximal
8	C₂×C₄³×C₁₃₉	C₂	1	1	yes	maximal, characteristic
9	C₂³×Q₈×C₁₃₉	C₂²	1	2	yes	—
10	C₂×C₄⋊Q₈×C₁₃₉	C₄	1	16	yes	direct product factor
11	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	8	yes	—
12	C₂×C₄×Q₈×C₁₃₉	—	2	16	no	—
13	C₂×C₄×Q₈×C₁₃₉	C₂²	1	16	yes	—
14	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
15	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
16	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
17	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
18	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
19	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
20	C₂²×C₄²×C₁₃₉	C₂²	1	4	yes	—
21	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
23	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
24	#391×C₁₃₉	C₂²	1	16	yes	—
25	#389×C₁₃₉	C₂²	1	32	yes	—
26	#384×C₁₃₉	C₂²	1	8	yes	—
27	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	32	yes	—
28	C₂×#95×C₁₃₉	C₂²	1	8	yes	—
29	C₄³×C₁₃₉	C₂²	1	8	yes	—
30	C₂²×Q₈×C₁₃₉	—	2	8	no	—
31	C₂²×Q₈×C₁₃₉	—	2	8	no	—
32	C₂²×Q₈×C₁₃₉	C₂×C₄	1	16	yes	—
33	C₂²×Q₈×C₁₃₉	C₂³	1	8	yes	—
34	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
35	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
36	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
37	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
38	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
39	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
40	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
41	C₄⋊Q₈×C₁₃₉	C₂×C₄	1	64	yes	direct product factor
42	C₄×Q₈×C₁₃₉	—	2	64	no	—
43	C₂×C₄⋊C₄×C₁₃₉	—	2	16	no	—
44	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
45	C₂×C₄⋊C₄×C₁₃₉	—	2	16	no	—
46	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	32	yes	—
47	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
48	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	16	yes	—
49	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	16	yes	—
50	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	16	yes	—
51	C₂×C₄²×C₁₃₉	—	2	16	no	—
52	C₂×C₄²×C₁₃₉	—	2	4	no	—
53	C₂×C₄²×C₁₃₉	—	2	8	no	—
54	C₂×C₄²×C₁₃₉	C₂×C₄	1	8	yes	—
55	C₂×C₄²×C₁₃₉	D₄	1	8	yes	—
56	C₂×C₄²×C₁₃₉	Q₈	1	16	yes	complemented
57	C₂×C₄²×C₁₃₉	C₂³	1	16	yes	—
58	C₂×C₄²×C₁₃₉	C₂³	1	8	yes	—
59	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
60	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
61	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
62	C₂×C₄²×C₁₃₉	C₂³	1	8	yes	—
63	#95×C₁₃₉	C₂³	1	32	yes	—
64	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
65	C₂×Q₈×C₁₃₉	—	2	64	no	—
66	C₂×Q₈×C₁₃₉	—	2	16	no	—
67	C₂×Q₈×C₁₃₉	—	2	16	no	—
68	C₂×Q₈×C₁₃₉	C₂²×C₄	1	32	yes	—
69	C₂²×C₄×C₁₃₉	—	2	8	no	—
70	C₂²×C₄×C₁₃₉	—	2	4	no	—
71	C₂²×C₄×C₁₃₉	—	2	4	no	—
72	C₂²×C₄×C₁₃₉	—	2	4	no	—
73	C₂²×C₄×C₁₃₉	—	2	8	no	—
74	C₂²×C₄×C₁₃₉	—	2	8	no	—
75	C₂²×C₄×C₁₃₉	—	2	16	no	—
76	C₂²×C₄×C₁₃₉	C₂²×C₄	1	16	yes	—
77	C₂²×C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
78	C₂²×C₄×C₁₃₉	C₂²×C₄	1	8	yes	—
79	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
80	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
81	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
82	C₂²×C₄×C₁₃₉	C₂×Q₈	1	8	yes	—
83	C₂²×C₄×C₁₃₉	C₂×Q₈	1	8	yes	—
84	C₂²×C₄×C₁₃₉	C₂×Q₈	1	8	yes	—
85	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
86	C₂²×C₄×C₁₃₉	#41	1	8	yes	—
87	C₂²×C₄×C₁₃₉	C₂⁴	1	8	yes	—
88	C₂²×C₄×C₁₃₉	C₂⁴	1	8	yes	—
89	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
90	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
91	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
92	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
93	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
94	C₄⋊C₄×C₁₃₉	—	2	32	no	—
95	C₄⋊C₄×C₁₃₉	—	2	16	no	—
96	C₄⋊C₄×C₁₃₉	—	2	32	no	—
97	C₄⋊C₄×C₁₃₉	C₂²×C₄	1	64	yes	—
98	C₄²×C₁₃₉	—	2	32	no	—
99	C₄²×C₁₃₉	—	2	8	no	—
100	C₄²×C₁₃₉	—	2	16	no	—
101	C₄²×C₁₃₉	C₂²×C₄	1	16	yes	—
102	C₄²×C₁₃₉	C₂×D₄	1	16	yes	—
103	C₄²×C₁₃₉	C₂×Q₈	1	32	yes	complemented
104	C₂³×C₁₃₉	C₂³×C₄	1	2	yes	—
105	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
106	C₂³×C₁₃₉	C₂²×Q₈	1	4	yes	—
107	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
108	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
109	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
110	Q₈×C₁₃₉	—	2	64	no	—
111	C₂×C₄×C₁₃₉	—	2	32	no	—
112	C₂×C₄×C₁₃₉	—	2	8	no	—
113	C₂×C₄×C₁₃₉	—	2	16	no	—
114	C₂×C₄×C₁₃₉	—	2	8	no	—
115	C₂×C₄×C₁₃₉	—	2	4	no	—
116	C₂×C₄×C₁₃₉	—	2	4	no	—
117	C₂×C₄×C₁₃₉	—	2	4	no	—
118	C₂×C₄×C₁₃₉	—	2	8	no	—
119	C₂×C₄×C₁₃₉	—	2	8	no	—
120	C₂×C₄×C₁₃₉	—	2	16	no	—
121	C₂×C₄×C₁₃₉	—	4	16	no	—
122	C₂×C₄×C₁₃₉	C₄×D₄	1	16	yes	—
123	C₂×C₄×C₁₃₉	C₄×Q₈	1	32	yes	complemented
124	C₂×C₄×C₁₃₉	C₄⋊Q₈	1	16	yes	direct product factor
125	C₂×C₄×C₁₃₉	C₂³×C₄	1	16	yes	—
126	C₂×C₄×C₁₃₉	C₂³×C₄	1	4	yes	—
127	C₂×C₄×C₁₃₉	C₂³×C₄	1	8	yes	—
128	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
129	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
130	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
131	C₂×C₄×C₁₃₉	C₂²×Q₈	1	8	yes	—
132	C₂×C₄×C₁₃₉	C₂²×Q₈	1	8	yes	—
133	C₂×C₄×C₁₃₉	C₂²×Q₈	1	8	yes	—
134	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
135	C₂×C₄×C₁₃₉	C₂×#41	1	8	yes	—
136	C₂²×C₁₃₉	C₂×C₄×D₄	1	4	yes	—
137	C₂²×C₁₃₉	C₂×C₄×Q₈	1	8	yes	—
138	C₂²×C₁₃₉	C₂×C₄⋊Q₈	1	4	yes	—
139	C₂²×C₁₃₉	#532	1	4	yes	—
140	C₂²×C₁₃₉	#533	1	8	yes	—
141	C₂²×C₁₃₉	C₂⁴×C₄	1	1	yes	characteristic
142	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
143	C₂²×C₁₃₉	C₂³×Q₈	1	2	yes	—
144	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
145	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
146	C₄×C₁₃₉	—	2	16	no	—
147	C₄×C₁₃₉	—	2	4	no	—
148	C₄×C₁₃₉	—	2	8	no	—
149	C₄×C₁₃₉	—	4	8	no	—
150	C₄×C₁₃₉	C₂×C₄×D₄	1	8	yes	—
151	C₄×C₁₃₉	C₂×C₄×Q₈	1	16	yes	complemented
152	C₄×C₁₃₉	C₂×C₄⋊Q₈	1	8	yes	direct product factor
153	C₂×C₁₃₉	C₄×C₄⋊Q₈	1	8	yes	direct product factor
154	C₂×C₁₃₉	C₂²×C₄×D₄	1	1	yes	characteristic
155	C₂×C₁₃₉	C₂²×C₄×Q₈	1	2	yes	—
156	C₂×C₁₃₉	C₂²×C₄⋊Q₈	1	1	yes	characteristic
157	C₂×C₁₃₉	C₂×#532	1	1	yes	characteristic
158	C₂×C₁₃₉	C₂×#533	1	2	yes	—
159	C₂×C₄×C₄⋊Q₈	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
160	C₁₃₉	C₂×C₄×C₄⋊Q₈	1	1	yes	characteristic, direct product factor, Sylow
161	C₂²×C₄⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic
162	C₂²×C₄×Q₈	C₂×C₁₃₉	1	2	yes	—
163	C₄×C₄⋊Q₈	C₂×C₁₃₉	1	16	yes	direct product factor
164	C₂×#391	C₂×C₁₃₉	1	2	yes	—
165	C₂×#389	C₂×C₁₃₉	1	4	yes	—
166	C₂×#384	C₂×C₁₃₉	1	1	yes	characteristic
167	C₂×C₄×C₄⋊C₄	C₂×C₁₃₉	1	4	yes	—
168	C₂×C₄³	C₂×C₁₃₉	1	1	yes	characteristic
169	C₂³×Q₈	C₂²×C₁₃₉	1	2	yes	—
170	C₂×C₄⋊Q₈	C₄×C₁₃₉	1	16	yes	direct product factor
171	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	8	yes	—
172	C₂×C₄×Q₈	—	2	16	no	—
173	C₂×C₄×Q₈	C₂²×C₁₃₉	1	16	yes	—
174	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
175	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
176	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
177	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
178	C₂²×C₄²	C₂²×C₁₃₉	1	4	yes	—
179	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
180	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
181	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
182	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
183	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
184	#391	C₂²×C₁₃₉	1	16	yes	—
185	#389	C₂²×C₁₃₉	1	32	yes	—
186	#384	C₂²×C₁₃₉	1	8	yes	—
187	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	32	yes	—
188	C₂×#95	C₂²×C₁₃₉	1	8	yes	—
189	C₄³	C₂²×C₁₃₉	1	8	yes	—
190	C₂²×Q₈	—	2	8	no	—
191	C₂²×Q₈	—	2	8	no	—
192	C₂²×Q₈	C₂×C₄×C₁₃₉	1	16	yes	—
193	C₂²×Q₈	C₂³×C₁₃₉	1	8	yes	—
194	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
195	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
196	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
197	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
198	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
199	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
200	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
201	C₄⋊Q₈	C₂×C₄×C₁₃₉	1	64	yes	direct product factor
202	C₄×Q₈	—	2	64	no	—
203	C₂×C₄⋊C₄	—	2	16	no	—
204	C₂×C₄⋊C₄	—	2	8	no	—
205	C₂×C₄⋊C₄	—	2	16	no	—
206	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	32	yes	—
207	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
208	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	16	yes	—
209	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	16	yes	—
210	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	16	yes	—
211	C₂×C₄²	—	2	16	no	—
212	C₂×C₄²	—	2	4	no	—
213	C₂×C₄²	—	2	8	no	—
214	C₂×C₄²	C₂×C₄×C₁₃₉	1	8	yes	—
215	C₂×C₄²	D₄×C₁₃₉	1	8	yes	—
216	C₂×C₄²	Q₈×C₁₃₉	1	16	yes	complemented
217	C₂×C₄²	C₂³×C₁₃₉	1	16	yes	—
218	C₂×C₄²	C₂³×C₁₃₉	1	8	yes	—
219	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
220	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
221	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
222	C₂×C₄²	C₂³×C₁₃₉	1	8	yes	—
223	#95	C₂³×C₁₃₉	1	32	yes	—
224	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
225	C₂×Q₈	—	2	64	no	—
226	C₂×Q₈	—	2	16	no	—
227	C₂×Q₈	—	2	16	no	—
228	C₂×Q₈	C₂²×C₄×C₁₃₉	1	32	yes	—
229	C₂²×C₄	—	2	8	no	—
230	C₂²×C₄	—	2	4	no	—
231	C₂²×C₄	—	2	4	no	—
232	C₂²×C₄	—	2	4	no	—
233	C₂²×C₄	—	2	8	no	—
234	C₂²×C₄	—	2	8	no	—
235	C₂²×C₄	—	2	16	no	—
236	C₂²×C₄	C₂²×C₄×C₁₃₉	1	16	yes	—
237	C₂²×C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
238	C₂²×C₄	C₂²×C₄×C₁₃₉	1	8	yes	—
239	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
240	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
241	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
242	C₂²×C₄	C₂×Q₈×C₁₃₉	1	8	yes	—
243	C₂²×C₄	C₂×Q₈×C₁₃₉	1	8	yes	—
244	C₂²×C₄	C₂×Q₈×C₁₃₉	1	8	yes	—
245	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
246	C₂²×C₄	#41×C₁₃₉	1	8	yes	—
247	C₂²×C₄	C₂⁴×C₁₃₉	1	8	yes	—
248	C₂²×C₄	C₂⁴×C₁₃₉	1	8	yes	—
249	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
250	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
251	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
252	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
253	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
254	C₄⋊C₄	—	2	32	no	—
255	C₄⋊C₄	—	2	16	no	—
256	C₄⋊C₄	—	2	32	no	—
257	C₄⋊C₄	C₂²×C₄×C₁₃₉	1	64	yes	—
258	C₄²	—	2	32	no	—
259	C₄²	—	2	8	no	—
260	C₄²	—	2	16	no	—
261	C₄²	C₂²×C₄×C₁₃₉	1	16	yes	—
262	C₄²	C₂×D₄×C₁₃₉	1	16	yes	—
263	C₄²	C₂×Q₈×C₁₃₉	1	32	yes	complemented
264	C₂³	C₂³×C₄×C₁₃₉	1	2	yes	—
265	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
266	C₂³	C₂²×Q₈×C₁₃₉	1	4	yes	—
267	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
268	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
269	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
270	Q₈	—	2	64	no	—
271	C₂×C₄	—	2	32	no	—
272	C₂×C₄	—	2	8	no	—
273	C₂×C₄	—	2	16	no	—
274	C₂×C₄	—	2	8	no	—
275	C₂×C₄	—	2	4	no	—
276	C₂×C₄	—	2	4	no	—
277	C₂×C₄	—	2	4	no	—
278	C₂×C₄	—	2	8	no	—
279	C₂×C₄	—	2	8	no	—
280	C₂×C₄	—	2	16	no	—
281	C₂×C₄	—	4	16	no	—
282	C₂×C₄	C₄×D₄×C₁₃₉	1	16	yes	—
283	C₂×C₄	C₄×Q₈×C₁₃₉	1	32	yes	complemented
284	C₂×C₄	C₄⋊Q₈×C₁₃₉	1	16	yes	direct product factor
285	C₂×C₄	C₂³×C₄×C₁₃₉	1	16	yes	—
286	C₂×C₄	C₂³×C₄×C₁₃₉	1	4	yes	—
287	C₂×C₄	C₂³×C₄×C₁₃₉	1	8	yes	—
288	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
289	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
290	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
291	C₂×C₄	C₂²×Q₈×C₁₃₉	1	8	yes	—
292	C₂×C₄	C₂²×Q₈×C₁₃₉	1	8	yes	—
293	C₂×C₄	C₂²×Q₈×C₁₃₉	1	8	yes	—
294	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
295	C₂×C₄	C₂×#41×C₁₃₉	1	8	yes	—
296	C₂²	C₂×C₄×D₄×C₁₃₉	1	4	yes	—
297	C₂²	C₂×C₄×Q₈×C₁₃₉	1	8	yes	—
298	C₂²	C₂×C₄⋊Q₈×C₁₃₉	1	4	yes	—
299	C₂²	#532×C₁₃₉	1	4	yes	—
300	C₂²	#533×C₁₃₉	1	8	yes	—
301	C₂²	C₂⁴×C₄×C₁₃₉	1	1	yes	characteristic
302	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
303	C₂²	C₂³×Q₈×C₁₃₉	1	2	yes	—
304	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
305	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
306	C₄	—	2	16	no	—
307	C₄	—	2	4	no	—
308	C₄	—	2	8	no	—
309	C₄	—	4	8	no	—
310	C₄	C₂×C₄×D₄×C₁₃₉	1	8	yes	—
311	C₄	C₂×C₄×Q₈×C₁₃₉	1	16	yes	complemented
312	C₄	C₂×C₄⋊Q₈×C₁₃₉	1	8	yes	direct product factor
313	C₂	C₄×C₄⋊Q₈×C₁₃₉	1	8	yes	direct product factor
314	C₂	C₂²×C₄×D₄×C₁₃₉	1	1	yes	characteristic
315	C₂	C₂²×C₄×Q₈×C₁₃₉	1	2	yes	—
316	C₂	C₂²×C₄⋊Q₈×C₁₃₉	1	1	yes	characteristic
317	C₂	C₂×#532×C₁₃₉	1	1	yes	characteristic
318	C₂	C₂×#533×C₁₃₉	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄×C₁₃₉	C₂³
commutator	C₂²	C₂⁴×C₄×C₁₃₉
Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
socle, prime radical	C₂⁴×C₁₃₉	C₂⁴
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₄×C₄⋊Q₈×C₁₃₉	C₂	direct (N × H)
10. C₂×C₄⋊Q₈×C₁₃₉	C₄	direct (N × H)
41. C₄⋊Q₈×C₁₃₉	C₂×C₄	direct (N × H)
56. C₂×C₄²×C₁₃₉	Q₈	semidirect
103. C₄²×C₁₃₉	C₂×Q₈	semidirect
123. C₂×C₄×C₁₃₉	C₄×Q₈	semidirect
124. C₂×C₄×C₁₃₉	C₄⋊Q₈	direct (N × H)
151. C₄×C₁₃₉	C₂×C₄×Q₈	semidirect
152. C₄×C₁₃₉	C₂×C₄⋊Q₈	direct (N × H)
153. C₂×C₁₃₉	C₄×C₄⋊Q₈	direct (N × H)
159. C₂×C₄×C₄⋊Q₈	C₁₃₉	direct (N × H)
160. C₁₃₉	C₂×C₄×C₄⋊Q₈	direct (N × H)
163. C₄×C₄⋊Q₈	C₂×C₁₃₉	direct (N × H)
170. C₂×C₄⋊Q₈	C₄×C₁₃₉	direct (N × H)
201. C₄⋊Q₈	C₂×C₄×C₁₃₉	direct (N × H)
216. C₂×C₄²	Q₈×C₁₃₉	semidirect
263. C₄²	C₂×Q₈×C₁₃₉	semidirect
283. C₂×C₄	C₄×Q₈×C₁₃₉	semidirect
284. C₂×C₄	C₄⋊Q₈×C₁₃₉	direct (N × H)
311. C₄	C₂×C₄×Q₈×C₁₃₉	semidirect
312. C₄	C₂×C₄⋊Q₈×C₁₃₉	direct (N × H)
313. C₂	C₄×C₄⋊Q₈×C₁₃₉	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×C₁₃₉	2
C₂²×C₄×Q₈×C₁₃₉	2
C₄×C₄⋊Q₈×C₁₃₉	2
C₂×#391×C₁₃₉	2
C₂×#389×C₁₃₉	2
C₂×#384×C₁₃₉	2
C₂×C₄×C₄⋊C₄×C₁₃₉	2
C₂×C₄³×C₁₃₉	2
C₂×C₄×C₄⋊Q₈	139

Subgroups — C2×C4×C4⋊Q8×C139 #48028633

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×C₄⋊Q₈×C₁₃₉ #48028633