Subgroups — C₂×#542×C₂₇₇ #47980843

Order 35456.

1132 conjugacy classes of subgroups.

The subgroup lattice has 296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#542×C₂₇₇	C₂	1	16	yes	maximal, direct product factor
2	C₂×C₄⋊Q₈×C₂₇₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#126×C₂₇₇	C₂	1	2	yes	maximal, complemented
4	C₂×#124×C₂₇₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#124×C₂₇₇	C₂	1	2	yes	maximal, complemented
6	C₂×#123×C₂₇₇	C₂	1	2	yes	maximal, complemented
7	C₂×C₂²⋊Q₈×C₂₇₇	C₂	1	2	yes	maximal, complemented
8	C₂×C₂²⋊Q₈×C₂₇₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#121×C₂₇₇	C₂	1	1	yes	maximal, characteristic
10	C₂×C₄×Q₈×C₂₇₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×D₄×C₂₇₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#117×C₂₇₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×Q₈×C₂₇₇	C₂²	1	1	yes	characteristic
14	C₂²×Q₈×C₂₇₇	C₂²	1	2	yes	—
15	C₂²×D₄×C₂₇₇	C₂²	1	1	yes	characteristic
16	C₂²×D₄×C₂₇₇	C₂²	1	2	yes	—
17	C₂³×C₄×C₂₇₇	C₂²	1	1	yes	characteristic
18	C₂³×C₄×C₂₇₇	C₂²	1	2	yes	—
19	C₄⋊Q₈×C₂₇₇	C₂²	1	8	yes	complemented
20	#126×C₂₇₇	C₂²	1	16	yes	complemented
21	#124×C₂₇₇	C₂²	1	8	yes	complemented
22	#124×C₂₇₇	C₂²	1	16	yes	complemented
23	#123×C₂₇₇	C₂²	1	16	yes	complemented
24	C₂²⋊Q₈×C₂₇₇	C₂²	1	16	yes	complemented
25	C₂²⋊Q₈×C₂₇₇	C₂²	1	8	yes	complemented
26	#121×C₂₇₇	C₂²	1	8	yes	—
27	C₄×Q₈×C₂₇₇	C₂²	1	8	yes	complemented
28	C₄×D₄×C₂₇₇	C₂²	1	8	yes	complemented
29	#117×C₂₇₇	C₂²	1	8	yes	complemented
30	C₂×C₄⋊C₄×C₂₇₇	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊C₄×C₂₇₇	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊C₄×C₂₇₇	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊C₄×C₂₇₇	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊C₄×C₂₇₇	C₂²	1	2	yes	—
35	C₂×C₄⋊C₄×C₂₇₇	C₂²	1	2	yes	—
36	C₂×C₄⋊C₄×C₂₇₇	C₂²	1	2	yes	—
37	C₂×C₂²⋊C₄×C₂₇₇	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊C₄×C₂₇₇	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊C₄×C₂₇₇	C₂²	1	2	yes	—
40	C₂×C₂²⋊C₄×C₂₇₇	C₂²	1	2	yes	—
41	C₂×C₂²⋊C₄×C₂₇₇	C₂²	1	2	yes	—
42	C₂×C₂²⋊C₄×C₂₇₇	C₂²	1	2	yes	—
43	C₂×C₂²⋊C₄×C₂₇₇	C₂²	1	2	yes	—
44	C₂×C₄²×C₂₇₇	C₂²	1	1	yes	characteristic
45	C₂×C₄²×C₂₇₇	C₂²	1	1	yes	characteristic
46	C₂×C₄²×C₂₇₇	C₂²	1	2	yes	—
47	C₂⁴×C₂₇₇	C₂³	1	1	yes	characteristic
48	C₂⁴×C₂₇₇	C₂³	1	2	yes	—
49	C₂×Q₈×C₂₇₇	—	2	4	no	—
50	C₂×Q₈×C₂₇₇	—	4	4	no	—
51	C₂×Q₈×C₂₇₇	C₂³	1	4	yes	—
52	C₂×Q₈×C₂₇₇	C₂³	1	8	yes	—
53	C₂×D₄×C₂₇₇	—	2	4	no	—
54	C₂×D₄×C₂₇₇	—	4	4	no	—
55	C₂×D₄×C₂₇₇	C₂³	1	4	yes	—
56	C₂×D₄×C₂₇₇	C₂³	1	8	yes	—
57	C₂²×C₄×C₂₇₇	—	2	4	no	—
58	C₂²×C₄×C₂₇₇	—	4	4	no	—
59	C₂²×C₄×C₂₇₇	C₂³	1	4	yes	—
60	C₂²×C₄×C₂₇₇	C₂³	1	1	yes	characteristic
61	C₂²×C₄×C₂₇₇	C₂³	1	1	yes	characteristic
62	C₂²×C₄×C₂₇₇	C₂³	1	2	yes	—
63	C₂²×C₄×C₂₇₇	C₂³	1	1	yes	characteristic
64	C₂²×C₄×C₂₇₇	C₂³	1	1	yes	characteristic
65	C₂²×C₄×C₂₇₇	C₂³	1	2	yes	—
66	C₂²×C₄×C₂₇₇	C₂³	1	1	yes	characteristic
67	C₂²×C₄×C₂₇₇	C₂³	1	2	yes	—
68	C₂²×C₄×C₂₇₇	C₂³	1	8	yes	—
69	C₂²×C₄×C₂₇₇	C₂³	1	1	yes	characteristic
70	C₄⋊C₄×C₂₇₇	C₂³	1	4	yes	—
71	C₄⋊C₄×C₂₇₇	C₂³	1	4	yes	—
72	C₄⋊C₄×C₂₇₇	C₂³	1	4	yes	—
73	C₄⋊C₄×C₂₇₇	C₂³	1	4	yes	—
74	C₄⋊C₄×C₂₇₇	C₂³	1	8	yes	—
75	C₄⋊C₄×C₂₇₇	C₂³	1	8	yes	—
76	C₄⋊C₄×C₂₇₇	C₂³	1	8	yes	—
77	C₂²⋊C₄×C₂₇₇	C₂³	1	4	yes	—
78	C₂²⋊C₄×C₂₇₇	C₂³	1	4	yes	—
79	C₂²⋊C₄×C₂₇₇	C₂³	1	8	yes	—
80	C₂²⋊C₄×C₂₇₇	C₂³	1	8	yes	—
81	C₂²⋊C₄×C₂₇₇	C₂³	1	8	yes	—
82	C₂²⋊C₄×C₂₇₇	C₂³	1	8	yes	—
83	C₂²⋊C₄×C₂₇₇	C₂³	1	8	yes	—
84	C₄²×C₂₇₇	C₂³	1	4	yes	—
85	C₄²×C₂₇₇	C₂³	1	4	yes	—
86	C₄²×C₂₇₇	C₂³	1	8	yes	—
87	C₂³×C₂₇₇	—	2	2	no	—
88	C₂³×C₂₇₇	—	2	4	no	—
89	C₂³×C₂₇₇	—	2	4	no	—
90	C₂³×C₂₇₇	—	2	2	no	—
91	C₂³×C₂₇₇	—	2	2	no	—
92	C₂³×C₂₇₇	—	2	4	no	—
93	C₂³×C₂₇₇	C₂⁴	1	2	yes	—
94	C₂³×C₂₇₇	C₂⁴	1	4	yes	—
95	C₂³×C₂₇₇	C₂⁴	1	1	yes	characteristic
96	Q₈×C₂₇₇	—	2	8	no	—
97	Q₈×C₂₇₇	—	4	8	no	—
98	D₄×C₂₇₇	—	2	8	no	—
99	D₄×C₂₇₇	—	4	8	no	—
100	C₂×C₄×C₂₇₇	—	2	2	no	—
101	C₂×C₄×C₂₇₇	—	2	4	no	—
102	C₂×C₄×C₂₇₇	—	2	2	no	—
103	C₂×C₄×C₂₇₇	—	2	4	no	—
104	C₂×C₄×C₂₇₇	—	2	4	no	—
105	C₂×C₄×C₂₇₇	—	2	2	no	—
106	C₂×C₄×C₂₇₇	—	2	2	no	—
107	C₂×C₄×C₂₇₇	—	2	2	no	—
108	C₂×C₄×C₂₇₇	—	2	8	no	—
109	C₂×C₄×C₂₇₇	—	4	8	no	—
110	C₂×C₄×C₂₇₇	#41	1	4	yes	—
111	C₂×C₄×C₂₇₇	C₂⁴	1	2	yes	—
112	C₂×C₄×C₂₇₇	C₂⁴	1	2	yes	—
113	C₂×C₄×C₂₇₇	C₂⁴	1	4	yes	—
114	C₂×C₄×C₂₇₇	C₂⁴	1	2	yes	—
115	C₂×C₄×C₂₇₇	C₂⁴	1	2	yes	—
116	C₂×C₄×C₂₇₇	C₂⁴	1	4	yes	—
117	C₂×C₄×C₂₇₇	C₂⁴	1	2	yes	—
118	C₂×C₄×C₂₇₇	C₂⁴	1	4	yes	—
119	C₂×C₄×C₂₇₇	C₂⁴	1	2	yes	—
120	C₂²×C₂₇₇	—	2	2	no	—
121	C₂²×C₂₇₇	—	2	4	no	—
122	C₂²×C₂₇₇	—	2	4	no	—
123	C₂²×C₂₇₇	—	2	2	no	—
124	C₂²×C₂₇₇	—	2	2	no	—
125	C₂²×C₂₇₇	—	2	4	no	—
126	C₂²×C₂₇₇	—	4	4	no	—
127	C₂²×C₂₇₇	—	4	8	no	—
128	C₂²×C₂₇₇	C₂×#41	1	2	yes	—
129	C₂²×C₂₇₇	H(5,𝔽₂)	1	2	yes	—
130	C₂²×C₂₇₇	2₋¹⁺⁴	1	2	yes	—
131	C₂²×C₂₇₇	C₂⁵	1	1	yes	characteristic
132	C₄×C₂₇₇	—	2	2	no	—
133	C₄×C₂₇₇	—	2	4	no	—
134	C₄×C₂₇₇	—	2	2	no	—
135	C₄×C₂₇₇	—	2	4	no	—
136	C₄×C₂₇₇	—	2	4	no	—
137	C₄×C₂₇₇	—	2	2	no	—
138	C₄×C₂₇₇	—	2	2	no	—
139	C₄×C₂₇₇	—	2	2	no	—
140	C₄×C₂₇₇	C₂×#41	1	4	yes	—
141	C₂×C₂₇₇	—	4	2	no	—
142	C₂×C₂₇₇	—	4	4	no	—
143	C₂×C₂₇₇	#542	1	4	yes	direct product factor
144	C₂×C₂₇₇	C₂²×#41	1	1	yes	characteristic
145	C₂×C₂₇₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
146	C₂×C₂₇₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
147	C₂₇₇	C₂×#542	1	1	yes	characteristic, direct product factor, Sylow
148	C₂×#542	C₂₇₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
149	#542	C₂×C₂₇₇	1	16	yes	direct product factor
150	C₂×C₄⋊Q₈	C₂×C₂₇₇	1	1	yes	characteristic, complemented
151	C₂×#126	C₂×C₂₇₇	1	2	yes	complemented
152	C₂×#124	C₂×C₂₇₇	1	1	yes	characteristic, complemented
153	C₂×#124	C₂×C₂₇₇	1	2	yes	complemented
154	C₂×#123	C₂×C₂₇₇	1	2	yes	complemented
155	C₂×C₂²⋊Q₈	C₂×C₂₇₇	1	2	yes	complemented
156	C₂×C₂²⋊Q₈	C₂×C₂₇₇	1	1	yes	characteristic, complemented
157	C₂×#121	C₂×C₂₇₇	1	1	yes	characteristic
158	C₂×C₄×Q₈	C₂×C₂₇₇	1	1	yes	characteristic, complemented
159	C₂×C₄×D₄	C₂×C₂₇₇	1	1	yes	characteristic, complemented
160	C₂×#117	C₂×C₂₇₇	1	1	yes	characteristic, complemented
161	C₂²×Q₈	C₂²×C₂₇₇	1	1	yes	characteristic
162	C₂²×Q₈	C₂²×C₂₇₇	1	2	yes	—
163	C₂²×D₄	C₂²×C₂₇₇	1	1	yes	characteristic
164	C₂²×D₄	C₂²×C₂₇₇	1	2	yes	—
165	C₂³×C₄	C₂²×C₂₇₇	1	1	yes	characteristic
166	C₂³×C₄	C₂²×C₂₇₇	1	2	yes	—
167	C₄⋊Q₈	C₂²×C₂₇₇	1	8	yes	complemented
168	#126	C₂²×C₂₇₇	1	16	yes	complemented
169	#124	C₂²×C₂₇₇	1	8	yes	complemented
170	#124	C₂²×C₂₇₇	1	16	yes	complemented
171	#123	C₂²×C₂₇₇	1	16	yes	complemented
172	C₂²⋊Q₈	C₂²×C₂₇₇	1	16	yes	complemented
173	C₂²⋊Q₈	C₂²×C₂₇₇	1	8	yes	complemented
174	#121	C₂²×C₂₇₇	1	8	yes	—
175	C₄×Q₈	C₂²×C₂₇₇	1	8	yes	complemented
176	C₄×D₄	C₂²×C₂₇₇	1	8	yes	complemented
177	#117	C₂²×C₂₇₇	1	8	yes	complemented
178	C₂×C₄⋊C₄	C₂²×C₂₇₇	1	1	yes	characteristic
179	C₂×C₄⋊C₄	C₂²×C₂₇₇	1	1	yes	characteristic
180	C₂×C₄⋊C₄	C₂²×C₂₇₇	1	1	yes	characteristic
181	C₂×C₄⋊C₄	C₂²×C₂₇₇	1	1	yes	characteristic
182	C₂×C₄⋊C₄	C₂²×C₂₇₇	1	2	yes	—
183	C₂×C₄⋊C₄	C₂²×C₂₇₇	1	2	yes	—
184	C₂×C₄⋊C₄	C₂²×C₂₇₇	1	2	yes	—
185	C₂×C₂²⋊C₄	C₂²×C₂₇₇	1	1	yes	characteristic
186	C₂×C₂²⋊C₄	C₂²×C₂₇₇	1	1	yes	characteristic
187	C₂×C₂²⋊C₄	C₂²×C₂₇₇	1	2	yes	—
188	C₂×C₂²⋊C₄	C₂²×C₂₇₇	1	2	yes	—
189	C₂×C₂²⋊C₄	C₂²×C₂₇₇	1	2	yes	—
190	C₂×C₂²⋊C₄	C₂²×C₂₇₇	1	2	yes	—
191	C₂×C₂²⋊C₄	C₂²×C₂₇₇	1	2	yes	—
192	C₂×C₄²	C₂²×C₂₇₇	1	1	yes	characteristic
193	C₂×C₄²	C₂²×C₂₇₇	1	1	yes	characteristic
194	C₂×C₄²	C₂²×C₂₇₇	1	2	yes	—
195	C₂⁴	C₂³×C₂₇₇	1	1	yes	characteristic
196	C₂⁴	C₂³×C₂₇₇	1	2	yes	—
197	C₂×Q₈	—	2	4	no	—
198	C₂×Q₈	—	4	4	no	—
199	C₂×Q₈	C₂³×C₂₇₇	1	4	yes	—
200	C₂×Q₈	C₂³×C₂₇₇	1	8	yes	—
201	C₂×D₄	—	2	4	no	—
202	C₂×D₄	—	4	4	no	—
203	C₂×D₄	C₂³×C₂₇₇	1	4	yes	—
204	C₂×D₄	C₂³×C₂₇₇	1	8	yes	—
205	C₂²×C₄	—	2	4	no	—
206	C₂²×C₄	—	4	4	no	—
207	C₂²×C₄	C₂³×C₂₇₇	1	1	yes	characteristic
208	C₂²×C₄	C₂³×C₂₇₇	1	1	yes	characteristic
209	C₂²×C₄	C₂³×C₂₇₇	1	2	yes	—
210	C₂²×C₄	C₂³×C₂₇₇	1	1	yes	characteristic
211	C₂²×C₄	C₂³×C₂₇₇	1	1	yes	characteristic
212	C₂²×C₄	C₂³×C₂₇₇	1	2	yes	—
213	C₂²×C₄	C₂³×C₂₇₇	1	1	yes	characteristic
214	C₂²×C₄	C₂³×C₂₇₇	1	2	yes	—
215	C₂²×C₄	C₂³×C₂₇₇	1	4	yes	—
216	C₂²×C₄	C₂³×C₂₇₇	1	8	yes	—
217	C₂²×C₄	C₂³×C₂₇₇	1	1	yes	characteristic
218	C₄⋊C₄	C₂³×C₂₇₇	1	4	yes	—
219	C₄⋊C₄	C₂³×C₂₇₇	1	4	yes	—
220	C₄⋊C₄	C₂³×C₂₇₇	1	4	yes	—
221	C₄⋊C₄	C₂³×C₂₇₇	1	4	yes	—
222	C₄⋊C₄	C₂³×C₂₇₇	1	8	yes	—
223	C₄⋊C₄	C₂³×C₂₇₇	1	8	yes	—
224	C₄⋊C₄	C₂³×C₂₇₇	1	8	yes	—
225	C₂²⋊C₄	C₂³×C₂₇₇	1	4	yes	—
226	C₂²⋊C₄	C₂³×C₂₇₇	1	4	yes	—
227	C₂²⋊C₄	C₂³×C₂₇₇	1	8	yes	—
228	C₂²⋊C₄	C₂³×C₂₇₇	1	8	yes	—
229	C₂²⋊C₄	C₂³×C₂₇₇	1	8	yes	—
230	C₂²⋊C₄	C₂³×C₂₇₇	1	8	yes	—
231	C₂²⋊C₄	C₂³×C₂₇₇	1	8	yes	—
232	C₄²	C₂³×C₂₇₇	1	4	yes	—
233	C₄²	C₂³×C₂₇₇	1	4	yes	—
234	C₄²	C₂³×C₂₇₇	1	8	yes	—
235	C₂³	—	2	2	no	—
236	C₂³	—	2	4	no	—
237	C₂³	—	2	4	no	—
238	C₂³	—	2	2	no	—
239	C₂³	—	2	2	no	—
240	C₂³	—	2	4	no	—
241	C₂³	C₂⁴×C₂₇₇	1	2	yes	—
242	C₂³	C₂⁴×C₂₇₇	1	4	yes	—
243	C₂³	C₂⁴×C₂₇₇	1	1	yes	characteristic
244	Q₈	—	2	8	no	—
245	Q₈	—	4	8	no	—
246	D₄	—	2	8	no	—
247	D₄	—	4	8	no	—
248	C₂×C₄	—	2	2	no	—
249	C₂×C₄	—	2	4	no	—
250	C₂×C₄	—	2	2	no	—
251	C₂×C₄	—	2	4	no	—
252	C₂×C₄	—	2	4	no	—
253	C₂×C₄	—	2	2	no	—
254	C₂×C₄	—	2	2	no	—
255	C₂×C₄	—	2	2	no	—
256	C₂×C₄	—	2	8	no	—
257	C₂×C₄	—	4	8	no	—
258	C₂×C₄	#41×C₂₇₇	1	4	yes	—
259	C₂×C₄	C₂⁴×C₂₇₇	1	2	yes	—
260	C₂×C₄	C₂⁴×C₂₇₇	1	2	yes	—
261	C₂×C₄	C₂⁴×C₂₇₇	1	4	yes	—
262	C₂×C₄	C₂⁴×C₂₇₇	1	2	yes	—
263	C₂×C₄	C₂⁴×C₂₇₇	1	2	yes	—
264	C₂×C₄	C₂⁴×C₂₇₇	1	4	yes	—
265	C₂×C₄	C₂⁴×C₂₇₇	1	2	yes	—
266	C₂×C₄	C₂⁴×C₂₇₇	1	4	yes	—
267	C₂×C₄	C₂⁴×C₂₇₇	1	2	yes	—
268	C₂²	—	2	2	no	—
269	C₂²	—	2	4	no	—
270	C₂²	—	2	4	no	—
271	C₂²	—	2	2	no	—
272	C₂²	—	2	2	no	—
273	C₂²	—	2	4	no	—
274	C₂²	—	4	4	no	—
275	C₂²	—	4	8	no	—
276	C₂²	C₂×#41×C₂₇₇	1	2	yes	—
277	C₂²	H(5,𝔽₂)×C₂₇₇	1	2	yes	—
278	C₂²	2₋¹⁺⁴×C₂₇₇	1	2	yes	—
279	C₂²	C₂⁵×C₂₇₇	1	1	yes	characteristic
280	C₄	—	2	2	no	—
281	C₄	—	2	4	no	—
282	C₄	—	2	2	no	—
283	C₄	—	2	4	no	—
284	C₄	—	2	4	no	—
285	C₄	—	2	2	no	—
286	C₄	—	2	2	no	—
287	C₄	—	2	2	no	—
288	C₄	C₂×#41×C₂₇₇	1	4	yes	—
289	C₂	—	4	2	no	—
290	C₂	—	4	4	no	—
291	C₂	#542×C₂₇₇	1	4	yes	direct product factor
292	C₂	C₂²×#41×C₂₇₇	1	1	yes	characteristic
293	C₂	C₂×H(5,𝔽₂)×C₂₇₇	1	1	yes	characteristic
294	C₂	C₂×2₋¹⁺⁴×C₂₇₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₇₇	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁵×C₂₇₇
prime radical	C₂×#121×C₂₇₇	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₇₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. #542×C₂₇₇	C₂	direct (N × H)
2. C₂×C₄⋊Q₈×C₂₇₇	C₂	semidirect
3. C₂×#126×C₂₇₇	C₂	semidirect
4. C₂×#124×C₂₇₇	C₂	semidirect
5. C₂×#124×C₂₇₇	C₂	semidirect
6. C₂×#123×C₂₇₇	C₂	semidirect
7. C₂×C₂²⋊Q₈×C₂₇₇	C₂	semidirect
8. C₂×C₂²⋊Q₈×C₂₇₇	C₂	semidirect
10. C₂×C₄×Q₈×C₂₇₇	C₂	semidirect
11. C₂×C₄×D₄×C₂₇₇	C₂	semidirect
12. C₂×#117×C₂₇₇	C₂	semidirect
19. C₄⋊Q₈×C₂₇₇	C₂²	semidirect
20. #126×C₂₇₇	C₂²	semidirect
21. #124×C₂₇₇	C₂²	semidirect
22. #124×C₂₇₇	C₂²	semidirect
23. #123×C₂₇₇	C₂²	semidirect
24. C₂²⋊Q₈×C₂₇₇	C₂²	semidirect
25. C₂²⋊Q₈×C₂₇₇	C₂²	semidirect
27. C₄×Q₈×C₂₇₇	C₂²	semidirect
28. C₄×D₄×C₂₇₇	C₂²	semidirect
29. #117×C₂₇₇	C₂²	semidirect
143. C₂×C₂₇₇	#542	direct (N × H)
147. C₂₇₇	C₂×#542	direct (N × H)
148. C₂×#542	C₂₇₇	direct (N × H)
149. #542	C₂×C₂₇₇	direct (N × H)
150. C₂×C₄⋊Q₈	C₂×C₂₇₇	semidirect
151. C₂×#126	C₂×C₂₇₇	semidirect
152. C₂×#124	C₂×C₂₇₇	semidirect
153. C₂×#124	C₂×C₂₇₇	semidirect
154. C₂×#123	C₂×C₂₇₇	semidirect
155. C₂×C₂²⋊Q₈	C₂×C₂₇₇	semidirect
156. C₂×C₂²⋊Q₈	C₂×C₂₇₇	semidirect
158. C₂×C₄×Q₈	C₂×C₂₇₇	semidirect
159. C₂×C₄×D₄	C₂×C₂₇₇	semidirect
160. C₂×#117	C₂×C₂₇₇	semidirect
167. C₄⋊Q₈	C₂²×C₂₇₇	semidirect
168. #126	C₂²×C₂₇₇	semidirect
169. #124	C₂²×C₂₇₇	semidirect
170. #124	C₂²×C₂₇₇	semidirect
171. #123	C₂²×C₂₇₇	semidirect
172. C₂²⋊Q₈	C₂²×C₂₇₇	semidirect
173. C₂²⋊Q₈	C₂²×C₂₇₇	semidirect
175. C₄×Q₈	C₂²×C₂₇₇	semidirect
176. C₄×D₄	C₂²×C₂₇₇	semidirect
177. #117	C₂²×C₂₇₇	semidirect
291. C₂	#542×C₂₇₇	direct (N × H)

Maximal subgroups

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

subgroup	index
#542×C₂₇₇	2
C₂×C₄⋊Q₈×C₂₇₇	2
C₂×#126×C₂₇₇	2
C₂×#124×C₂₇₇	2
C₂×#123×C₂₇₇	2
C₂×C₂²⋊Q₈×C₂₇₇	2
C₂×#121×C₂₇₇	2
C₂×C₄×Q₈×C₂₇₇	2
C₂×C₄×D₄×C₂₇₇	2
C₂×#117×C₂₇₇	2
C₂×#542	277

Subgroups — C2×#542×C277 #47980843

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#542×C₂₇₇ #47980843