Subgroups — #3265×C₂₂₇ #44397221

Order 29056.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×AGL(1,ℤ/8)×C₂₂₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×SD₁₆×C₂₂₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#548×C₂₂₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄²×C₂₂₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#496×C₂₂₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#468×C₂₂₇	C₂	1	1	yes	maximal, characteristic, complemented
7	#466×C₂₂₇	C₂	1	1	yes	maximal, characteristic, complemented
8	#463×C₂₂₇	C₂	1	1	yes	maximal, characteristic, complemented
9	#460×C₂₂₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#450×C₂₂₇	C₂	1	1	yes	maximal, characteristic, complemented
11	#449×C₂₂₇	C₂	1	1	yes	maximal, characteristic, complemented
12	#448×C₂₂₇	C₂	1	1	yes	maximal, characteristic, complemented
13	#447×C₂₂₇	C₂	1	1	yes	maximal, characteristic, complemented
14	#440×C₂₂₇	C₂	1	1	yes	maximal, characteristic, complemented
15	#435×C₂₂₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#41×C₂₂₇	C₂²	1	1	yes	characteristic, complemented
17	C₂²×Q₈×C₂₂₇	C₂²	1	1	yes	characteristic, complemented
18	C₂²×D₄×C₂₂₇	—	2	1	no	—
19	C₂²×D₄×C₂₂₇	C₂²	1	1	yes	characteristic
20	C₂²×D₄×C₂₂₇	C₂²	1	1	yes	characteristic
21	AGL(1,ℤ/8)×C₂₂₇	—	2	4	no	—
22	C₂×SD₁₆×C₂₂₇	—	2	4	no	—
23	C₂×SD₁₆×C₂₂₇	C₂²	1	1	yes	characteristic
24	C₂×SD₁₆×C₂₂₇	C₂²	1	1	yes	characteristic
25	C₂×SD₁₆×C₂₂₇	C₂²	1	1	yes	characteristic, complemented
26	C₂×SD₁₆×C₂₂₇	C₂²	1	1	yes	characteristic, complemented
27	C₂×SD₁₆×C₂₂₇	C₂²	1	1	yes	characteristic, complemented
28	C₂×SD₁₆×C₂₂₇	C₂²	1	1	yes	characteristic, complemented
29	C₂×D₈×C₂₂₇	C₂²	1	1	yes	characteristic
30	C₂×D₈×C₂₂₇	C₂²	1	1	yes	characteristic, complemented
31	C₂×D₈×C₂₂₇	C₂²	1	1	yes	characteristic, complemented
32	C₂×M₁₆×C₂₂₇	C₂²	1	1	yes	characteristic, complemented
33	C₂²×C₈×C₂₂₇	C₂²	1	1	yes	characteristic, complemented
34	#127×C₂₂₇	C₂²	1	1	yes	characteristic
35	#124×C₂₂₇	—	2	1	no	—
36	#124×C₂₂₇	C₂²	1	1	yes	characteristic, complemented
37	C₂²⋊Q₈×C₂₂₇	—	2	1	no	—
38	C₂²⋊Q₈×C₂₂₇	C₂²	1	1	yes	characteristic, complemented
39	#121×C₂₂₇	—	2	1	no	—
40	#121×C₂₂₇	—	2	1	no	—
41	#121×C₂₂₇	C₂²	1	1	yes	characteristic
42	#121×C₂₂₇	C₂²	1	1	yes	characteristic
43	#121×C₂₂₇	C₂²	1	1	yes	characteristic, complemented
44	#120×C₂₂₇	—	2	1	no	—
45	#120×C₂₂₇	—	2	1	no	—
46	C₄×Q₈×C₂₂₇	C₂²	1	1	yes	characteristic, complemented
47	C₄×D₄×C₂₂₇	—	2	1	no	—
48	C₄×D₄×C₂₂₇	C₂²	1	1	yes	characteristic
49	C₄×D₄×C₂₂₇	C₂²	1	1	yes	characteristic
50	#107×C₂₂₇	C₂²	1	1	yes	characteristic, complemented
51	C₄⋊C₈×C₂₂₇	C₂²	1	1	yes	characteristic, complemented
52	#103×C₂₂₇	C₂²	1	1	yes	characteristic, complemented
53	#103×C₂₂₇	C₂²	1	1	yes	characteristic, complemented
54	#102×C₂₂₇	C₂²	1	1	yes	characteristic
55	#102×C₂₂₇	C₂²	1	1	yes	characteristic, complemented
56	#102×C₂₂₇	C₂²	1	1	yes	characteristic, complemented
57	#102×C₂₂₇	C₂²	1	1	yes	characteristic, complemented
58	C₂²⋊C₈×C₂₂₇	C₂²	1	1	yes	characteristic, complemented
59	C₂²⋊C₈×C₂₂₇	C₂²	1	1	yes	characteristic, complemented
60	#97×C₂₂₇	C₂²	1	1	yes	characteristic, complemented
61	C₂⁴×C₂₂₇	—	2	1	no	—
62	C₂⁴×C₂₂₇	—	2	1	no	—
63	#41×C₂₂₇	—	2	2	no	—
64	#41×C₂₂₇	—	4	1	no	—
65	C₂×Q₈×C₂₂₇	—	2	1	no	—
66	C₂×Q₈×C₂₂₇	—	2	2	no	—
67	C₂×Q₈×C₂₂₇	—	4	1	no	—
68	C₂×Q₈×C₂₂₇	C₂³	1	1	yes	characteristic
69	C₂×Q₈×C₂₂₇	C₂³	1	1	yes	characteristic
70	C₂×D₄×C₂₂₇	—	2	2	no	—
71	C₂×D₄×C₂₂₇	—	2	2	no	—
72	C₂×D₄×C₂₂₇	—	2	1	no	—
73	C₂×D₄×C₂₂₇	—	2	1	no	—
74	C₂×D₄×C₂₂₇	—	2	1	no	—
75	C₂×D₄×C₂₂₇	—	2	1	no	—
76	C₂×D₄×C₂₂₇	—	2	1	no	—
77	C₂×D₄×C₂₂₇	—	2	1	no	—
78	C₂×D₄×C₂₂₇	—	2	1	no	—
79	C₂×D₄×C₂₂₇	—	2	1	no	—
80	C₂×D₄×C₂₂₇	—	4	1	no	—
81	C₂×D₄×C₂₂₇	—	4	1	no	—
82	C₂×D₄×C₂₂₇	—	4	4	no	—
83	C₂×D₄×C₂₂₇	D₄	1	1	yes	characteristic
84	C₂×D₄×C₂₂₇	C₂³	1	1	yes	characteristic
85	C₂×D₄×C₂₂₇	C₂³	1	1	yes	characteristic
86	C₂×D₄×C₂₂₇	C₂³	1	1	yes	characteristic
87	C₂×D₄×C₂₂₇	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₂₂₇	—	2	1	no	—
89	C₂²×C₄×C₂₂₇	—	2	1	no	—
90	C₂²×C₄×C₂₂₇	—	2	1	no	—
91	C₂²×C₄×C₂₂₇	C₂³	1	1	yes	characteristic
92	C₂²×C₄×C₂₂₇	C₂³	1	1	yes	characteristic
93	SD₁₆×C₂₂₇	—	2	2	no	—
94	SD₁₆×C₂₂₇	—	2	2	no	—
95	SD₁₆×C₂₂₇	—	2	2	no	—
96	SD₁₆×C₂₂₇	—	2	2	no	—
97	SD₁₆×C₂₂₇	—	4	1	no	—
98	SD₁₆×C₂₂₇	D₄	1	4	yes	complemented
99	D₈×C₂₂₇	—	2	2	no	—
100	D₈×C₂₂₇	—	2	2	no	—
101	D₈×C₂₂₇	—	4	1	no	—
102	M₁₆×C₂₂₇	—	2	2	no	—
103	C₂×C₈×C₂₂₇	—	2	2	no	—
104	C₂×C₈×C₂₂₇	C₂³	1	1	yes	characteristic
105	C₂×C₈×C₂₂₇	C₂³	1	1	yes	characteristic
106	C₂×C₈×C₂₂₇	C₂³	1	1	yes	characteristic
107	C₂×C₈×C₂₂₇	C₂³	1	1	yes	characteristic
108	C₄⋊C₄×C₂₂₇	—	2	1	no	—
109	C₄⋊C₄×C₂₂₇	—	2	1	no	—
110	C₄⋊C₄×C₂₂₇	D₄	1	1	yes	characteristic
111	C₄⋊C₄×C₂₂₇	C₂³	1	1	yes	characteristic
112	C₄⋊C₄×C₂₂₇	C₂³	1	1	yes	characteristic
113	C₂²⋊C₄×C₂₂₇	—	2	1	no	—
114	C₂²⋊C₄×C₂₂₇	—	2	1	no	—
115	C₂²⋊C₄×C₂₂₇	—	2	1	no	—
116	C₂²⋊C₄×C₂₂₇	—	2	1	no	—
117	C₂²⋊C₄×C₂₂₇	—	2	1	no	—
118	C₂²⋊C₄×C₂₂₇	—	2	1	no	—
119	C₂²⋊C₄×C₂₂₇	—	2	1	no	—
120	C₂²⋊C₄×C₂₂₇	D₄	1	1	yes	characteristic
121	C₂²⋊C₄×C₂₂₇	D₄	1	1	yes	characteristic
122	C₄²×C₂₂₇	—	2	1	no	—
123	C₄²×C₂₂₇	C₂³	1	1	yes	characteristic
124	C₂³×C₂₂₇	—	2	1	no	—
125	C₂³×C₂₂₇	—	2	1	no	—
126	C₂³×C₂₂₇	—	2	1	no	—
127	C₂³×C₂₂₇	—	2	1	no	—
128	C₂³×C₂₂₇	—	4	2	no	—
129	C₂³×C₂₂₇	—	4	2	no	—
130	C₂³×C₂₂₇	—	4	2	no	—
131	C₂³×C₂₂₇	—	4	2	no	—
132	C₂³×C₂₂₇	—	8	1	no	—
133	C₂³×C₂₂₇	—	8	1	no	—
134	C₂³×C₂₂₇	C₂×D₄	1	1	yes	characteristic
135	C₂³×C₂₂₇	C₂×D₄	1	1	yes	characteristic
136	Q₈×C₂₂₇	—	2	1	no	—
137	Q₈×C₂₂₇	—	2	1	no	—
138	Q₈×C₂₂₇	—	2	1	no	—
139	Q₈×C₂₂₇	—	4	2	no	—
140	Q₈×C₂₂₇	C₂×D₄	1	2	yes	complemented
141	D₄×C₂₂₇	—	2	2	no	—
142	D₄×C₂₂₇	—	2	1	no	—
143	D₄×C₂₂₇	—	2	1	no	—
144	D₄×C₂₂₇	—	2	1	no	—
145	D₄×C₂₂₇	—	2	1	no	—
146	D₄×C₂₂₇	—	2	1	no	—
147	D₄×C₂₂₇	—	2	1	no	—
148	D₄×C₂₂₇	—	2	1	no	—
149	D₄×C₂₂₇	—	4	2	no	—
150	D₄×C₂₂₇	—	4	2	no	—
151	D₄×C₂₂₇	—	4	2	no	—
152	D₄×C₂₂₇	—	4	2	no	—
153	D₄×C₂₂₇	—	4	2	no	—
154	D₄×C₂₂₇	—	4	2	no	—
155	D₄×C₂₂₇	—	4	2	no	—
156	D₄×C₂₂₇	—	8	1	no	—
157	D₄×C₂₂₇	C₂×D₄	1	2	yes	—
158	C₂×C₄×C₂₂₇	—	2	1	no	—
159	C₂×C₄×C₂₂₇	—	2	1	no	—
160	C₂×C₄×C₂₂₇	—	2	1	no	—
161	C₂×C₄×C₂₂₇	—	2	1	no	—
162	C₂×C₄×C₂₂₇	—	2	1	no	—
163	C₂×C₄×C₂₂₇	—	2	1	no	—
164	C₂×C₄×C₂₂₇	—	2	1	no	—
165	C₂×C₄×C₂₂₇	—	2	1	no	—
166	C₂×C₄×C₂₂₇	—	4	2	no	—
167	C₂×C₄×C₂₂₇	—	4	2	no	—
168	C₂×C₄×C₂₂₇	—	4	2	no	—
169	C₂×C₄×C₂₂₇	C₂×D₄	1	1	yes	characteristic
170	C₂×C₄×C₂₂₇	C₂×D₄	1	1	yes	characteristic
171	C₂×C₄×C₂₂₇	C₂×D₄	1	1	yes	characteristic
172	C₂×C₄×C₂₂₇	C₂×D₄	1	1	yes	characteristic
173	C₂×C₄×C₂₂₇	C₂⁴	1	1	yes	characteristic
174	C₈×C₂₂₇	—	2	1	no	—
175	C₈×C₂₂₇	—	2	1	no	—
176	C₈×C₂₂₇	—	2	1	no	—
177	C₈×C₂₂₇	C₂×D₄	1	2	yes	complemented
178	C₂²×C₂₂₇	—	2	1	no	—
179	C₂²×C₂₂₇	—	2	1	no	—
180	C₂²×C₂₂₇	—	2	1	no	—
181	C₂²×C₂₂₇	—	2	2	no	—
182	C₂²×C₂₂₇	—	2	1	no	—
183	C₂²×C₂₂₇	—	2	1	no	—
184	C₂²×C₂₂₇	—	4	1	no	—
185	C₂²×C₂₂₇	—	4	1	no	—
186	C₂²×C₂₂₇	—	4	1	no	—
187	C₂²×C₂₂₇	—	4	1	no	—
188	C₂²×C₂₂₇	—	4	1	no	—
189	C₂²×C₂₂₇	—	4	1	no	—
190	C₂²×C₂₂₇	—	4	1	no	—
191	C₂²×C₂₂₇	—	4	1	no	—
192	C₂²×C₂₂₇	—	4	1	no	—
193	C₂²×C₂₂₇	—	4	1	no	—
194	C₂²×C₂₂₇	—	4	1	no	—
195	C₂²×C₂₂₇	—	8	4	no	—
196	C₂²×C₂₂₇	—	8	4	no	—
197	C₂²×C₂₂₇	AGL(1,ℤ/8)	1	2	yes	complemented
198	C₂²×C₂₂₇	C₂²×D₄	1	1	yes	characteristic
199	C₄×C₂₂₇	—	2	1	no	—
200	C₄×C₂₂₇	—	2	1	no	—
201	C₄×C₂₂₇	—	2	2	no	—
202	C₄×C₂₂₇	—	2	1	no	—
203	C₄×C₂₂₇	—	2	1	no	—
204	C₄×C₂₂₇	—	4	1	no	—
205	C₄×C₂₂₇	—	4	1	no	—
206	C₄×C₂₂₇	—	4	1	no	—
207	C₄×C₂₂₇	C₂²×D₄	1	1	yes	characteristic
208	C₄×C₂₂₇	H(5,𝔽₂)	1	1	yes	characteristic
209	C₂×C₂₂₇	—	2	2	no	—
210	C₂×C₂₂₇	—	4	1	no	—
211	C₂×C₂₂₇	—	4	2	no	—
212	C₂×C₂₂₇	—	8	1	no	—
213	C₂×C₂₂₇	—	8	1	no	—
214	C₂×C₂₂₇	—	8	1	no	—
215	C₂×C₂₂₇	D₄²	1	1	yes	characteristic
216	C₂×C₂₂₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
217	C₂×C₂₂₇	#577	1	1	yes	characteristic
218	C₂₂₇	#3265	1	1	yes	characteristic, direct product factor, Sylow
219	#3265	C₂₂₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
220	C₂×AGL(1,ℤ/8)	C₂×C₂₂₇	1	1	yes	characteristic, complemented
221	C₂²×SD₁₆	C₂×C₂₂₇	1	1	yes	characteristic, complemented
222	#548	C₂×C₂₂₇	1	1	yes	characteristic, complemented
223	D₄²	C₂×C₂₂₇	1	1	yes	characteristic, complemented
224	#496	C₂×C₂₂₇	1	1	yes	characteristic, complemented
225	#468	C₂×C₂₂₇	1	1	yes	characteristic, complemented
226	#466	C₂×C₂₂₇	1	1	yes	characteristic, complemented
227	#463	C₂×C₂₂₇	1	1	yes	characteristic, complemented
228	#460	C₂×C₂₂₇	1	1	yes	characteristic, complemented
229	#450	C₂×C₂₂₇	1	1	yes	characteristic, complemented
230	#449	C₂×C₂₂₇	1	1	yes	characteristic, complemented
231	#448	C₂×C₂₂₇	1	1	yes	characteristic, complemented
232	#447	C₂×C₂₂₇	1	1	yes	characteristic, complemented
233	#440	C₂×C₂₂₇	1	1	yes	characteristic, complemented
234	#435	C₂×C₂₂₇	1	1	yes	characteristic, complemented
235	C₂×#41	C₂²×C₂₂₇	1	1	yes	characteristic, complemented
236	C₂²×Q₈	C₂²×C₂₂₇	1	1	yes	characteristic, complemented
237	C₂²×D₄	—	2	1	no	—
238	C₂²×D₄	C₂²×C₂₂₇	1	1	yes	characteristic
239	C₂²×D₄	C₂²×C₂₂₇	1	1	yes	characteristic
240	AGL(1,ℤ/8)	—	2	4	no	—
241	C₂×SD₁₆	—	2	4	no	—
242	C₂×SD₁₆	C₂²×C₂₂₇	1	1	yes	characteristic
243	C₂×SD₁₆	C₂²×C₂₂₇	1	1	yes	characteristic
244	C₂×SD₁₆	C₂²×C₂₂₇	1	1	yes	characteristic, complemented
245	C₂×SD₁₆	C₂²×C₂₂₇	1	1	yes	characteristic, complemented
246	C₂×SD₁₆	C₂²×C₂₂₇	1	1	yes	characteristic, complemented
247	C₂×SD₁₆	C₂²×C₂₂₇	1	1	yes	characteristic, complemented
248	C₂×D₈	C₂²×C₂₂₇	1	1	yes	characteristic
249	C₂×D₈	C₂²×C₂₂₇	1	1	yes	characteristic, complemented
250	C₂×D₈	C₂²×C₂₂₇	1	1	yes	characteristic, complemented
251	C₂×M₁₆	C₂²×C₂₂₇	1	1	yes	characteristic, complemented
252	C₂²×C₈	C₂²×C₂₂₇	1	1	yes	characteristic, complemented
253	#127	C₂²×C₂₂₇	1	1	yes	characteristic
254	#124	—	2	1	no	—
255	#124	C₂²×C₂₂₇	1	1	yes	characteristic, complemented
256	C₂²⋊Q₈	—	2	1	no	—
257	C₂²⋊Q₈	C₂²×C₂₂₇	1	1	yes	characteristic, complemented
258	#121	—	2	1	no	—
259	#121	—	2	1	no	—
260	#121	C₂²×C₂₂₇	1	1	yes	characteristic
261	#121	C₂²×C₂₂₇	1	1	yes	characteristic
262	#121	C₂²×C₂₂₇	1	1	yes	characteristic, complemented
263	#120	—	2	1	no	—
264	#120	—	2	1	no	—
265	C₄×Q₈	C₂²×C₂₂₇	1	1	yes	characteristic, complemented
266	C₄×D₄	—	2	1	no	—
267	C₄×D₄	C₂²×C₂₂₇	1	1	yes	characteristic
268	C₄×D₄	C₂²×C₂₂₇	1	1	yes	characteristic
269	#107	C₂²×C₂₂₇	1	1	yes	characteristic, complemented
270	C₄⋊C₈	C₂²×C₂₂₇	1	1	yes	characteristic, complemented
271	#103	C₂²×C₂₂₇	1	1	yes	characteristic, complemented
272	#103	C₂²×C₂₂₇	1	1	yes	characteristic, complemented
273	#102	C₂²×C₂₂₇	1	1	yes	characteristic
274	#102	C₂²×C₂₂₇	1	1	yes	characteristic, complemented
275	#102	C₂²×C₂₂₇	1	1	yes	characteristic, complemented
276	#102	C₂²×C₂₂₇	1	1	yes	characteristic, complemented
277	C₂²⋊C₈	C₂²×C₂₂₇	1	1	yes	characteristic, complemented
278	C₂²⋊C₈	C₂²×C₂₂₇	1	1	yes	characteristic, complemented
279	#97	C₂²×C₂₂₇	1	1	yes	characteristic, complemented
280	C₂⁴	—	2	1	no	—
281	C₂⁴	—	2	1	no	—
282	#41	—	2	2	no	—
283	#41	—	4	1	no	—
284	C₂×Q₈	—	2	1	no	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	4	1	no	—
287	C₂×Q₈	C₂³×C₂₂₇	1	1	yes	characteristic
288	C₂×Q₈	C₂³×C₂₂₇	1	1	yes	characteristic
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	1	no	—
292	C₂×D₄	—	2	1	no	—
293	C₂×D₄	—	2	1	no	—
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	2	1	no	—
296	C₂×D₄	—	2	1	no	—
297	C₂×D₄	—	2	1	no	—
298	C₂×D₄	—	2	1	no	—
299	C₂×D₄	—	4	1	no	—
300	C₂×D₄	—	4	1	no	—
301	C₂×D₄	—	4	4	no	—
302	C₂×D₄	D₄×C₂₂₇	1	1	yes	characteristic
303	C₂×D₄	C₂³×C₂₂₇	1	1	yes	characteristic
304	C₂×D₄	C₂³×C₂₂₇	1	1	yes	characteristic
305	C₂×D₄	C₂³×C₂₂₇	1	1	yes	characteristic
306	C₂×D₄	C₂³×C₂₂₇	1	1	yes	characteristic
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	C₂³×C₂₂₇	1	1	yes	characteristic
311	C₂²×C₄	C₂³×C₂₂₇	1	1	yes	characteristic
312	SD₁₆	—	2	2	no	—
313	SD₁₆	—	2	2	no	—
314	SD₁₆	—	2	2	no	—
315	SD₁₆	—	2	2	no	—
316	SD₁₆	—	4	1	no	—
317	SD₁₆	D₄×C₂₂₇	1	4	yes	complemented
318	D₈	—	2	2	no	—
319	D₈	—	2	2	no	—
320	D₈	—	4	1	no	—
321	M₁₆	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	C₂³×C₂₂₇	1	1	yes	characteristic
324	C₂×C₈	C₂³×C₂₂₇	1	1	yes	characteristic
325	C₂×C₈	C₂³×C₂₂₇	1	1	yes	characteristic
326	C₂×C₈	C₂³×C₂₂₇	1	1	yes	characteristic
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	D₄×C₂₂₇	1	1	yes	characteristic
330	C₄⋊C₄	C₂³×C₂₂₇	1	1	yes	characteristic
331	C₄⋊C₄	C₂³×C₂₂₇	1	1	yes	characteristic
332	C₂²⋊C₄	—	2	1	no	—
333	C₂²⋊C₄	—	2	1	no	—
334	C₂²⋊C₄	—	2	1	no	—
335	C₂²⋊C₄	—	2	1	no	—
336	C₂²⋊C₄	—	2	1	no	—
337	C₂²⋊C₄	—	2	1	no	—
338	C₂²⋊C₄	—	2	1	no	—
339	C₂²⋊C₄	D₄×C₂₂₇	1	1	yes	characteristic
340	C₂²⋊C₄	D₄×C₂₂₇	1	1	yes	characteristic
341	C₄²	—	2	1	no	—
342	C₄²	C₂³×C₂₂₇	1	1	yes	characteristic
343	C₂³	—	2	1	no	—
344	C₂³	—	2	1	no	—
345	C₂³	—	2	1	no	—
346	C₂³	—	2	1	no	—
347	C₂³	—	4	2	no	—
348	C₂³	—	4	2	no	—
349	C₂³	—	4	2	no	—
350	C₂³	—	4	2	no	—
351	C₂³	—	8	1	no	—
352	C₂³	—	8	1	no	—
353	C₂³	C₂×D₄×C₂₂₇	1	1	yes	characteristic
354	C₂³	C₂×D₄×C₂₂₇	1	1	yes	characteristic
355	Q₈	—	2	1	no	—
356	Q₈	—	2	1	no	—
357	Q₈	—	2	1	no	—
358	Q₈	—	4	2	no	—
359	Q₈	C₂×D₄×C₂₂₇	1	2	yes	complemented
360	D₄	—	2	2	no	—
361	D₄	—	2	1	no	—
362	D₄	—	2	1	no	—
363	D₄	—	2	1	no	—
364	D₄	—	2	1	no	—
365	D₄	—	2	1	no	—
366	D₄	—	2	1	no	—
367	D₄	—	2	1	no	—
368	D₄	—	4	2	no	—
369	D₄	—	4	2	no	—
370	D₄	—	4	2	no	—
371	D₄	—	4	2	no	—
372	D₄	—	4	2	no	—
373	D₄	—	4	2	no	—
374	D₄	—	4	2	no	—
375	D₄	—	8	1	no	—
376	D₄	C₂×D₄×C₂₂₇	1	2	yes	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	C₂×D₄×C₂₂₇	1	1	yes	characteristic
389	C₂×C₄	C₂×D₄×C₂₂₇	1	1	yes	characteristic
390	C₂×C₄	C₂×D₄×C₂₂₇	1	1	yes	characteristic
391	C₂×C₄	C₂×D₄×C₂₂₇	1	1	yes	characteristic
392	C₂×C₄	C₂⁴×C₂₂₇	1	1	yes	characteristic
393	C₈	—	2	1	no	—
394	C₈	—	2	1	no	—
395	C₈	—	2	1	no	—
396	C₈	C₂×D₄×C₂₂₇	1	2	yes	complemented
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	4	1	no	—
404	C₂²	—	4	1	no	—
405	C₂²	—	4	1	no	—
406	C₂²	—	4	1	no	—
407	C₂²	—	4	1	no	—
408	C₂²	—	4	1	no	—
409	C₂²	—	4	1	no	—
410	C₂²	—	4	1	no	—
411	C₂²	—	4	1	no	—
412	C₂²	—	4	1	no	—
413	C₂²	—	4	1	no	—
414	C₂²	—	8	4	no	—
415	C₂²	—	8	4	no	—
416	C₂²	AGL(1,ℤ/8)×C₂₂₇	1	2	yes	complemented
417	C₂²	C₂²×D₄×C₂₂₇	1	1	yes	characteristic
418	C₄	—	2	1	no	—
419	C₄	—	2	1	no	—
420	C₄	—	2	2	no	—
421	C₄	—	2	1	no	—
422	C₄	—	2	1	no	—
423	C₄	—	4	1	no	—
424	C₄	—	4	1	no	—
425	C₄	—	4	1	no	—
426	C₄	C₂²×D₄×C₂₂₇	1	1	yes	characteristic
427	C₄	H(5,𝔽₂)×C₂₂₇	1	1	yes	characteristic
428	C₂	—	2	2	no	—
429	C₂	—	4	1	no	—
430	C₂	—	4	2	no	—
431	C₂	—	8	1	no	—
432	C₂	—	8	1	no	—
433	C₂	—	8	1	no	—
434	C₂	D₄²×C₂₂₇	1	1	yes	characteristic
435	C₂	C₂×AGL(1,ℤ/8)×C₂₂₇	1	1	yes	characteristic
436	C₂	#577×C₂₂₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₂₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₂₂₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₂₇ ◁ C₄×D₄×C₂₂₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×AGL(1,ℤ/8)×C₂₂₇	C₂	semidirect
2. C₂²×SD₁₆×C₂₂₇	C₂	semidirect
3. #548×C₂₂₇	C₂	semidirect
4. D₄²×C₂₂₇	C₂	semidirect
5. #496×C₂₂₇	C₂	semidirect
6. #468×C₂₂₇	C₂	semidirect
7. #466×C₂₂₇	C₂	semidirect
8. #463×C₂₂₇	C₂	semidirect
9. #460×C₂₂₇	C₂	semidirect
10. #450×C₂₂₇	C₂	semidirect
11. #449×C₂₂₇	C₂	semidirect
12. #448×C₂₂₇	C₂	semidirect
13. #447×C₂₂₇	C₂	semidirect
14. #440×C₂₂₇	C₂	semidirect
15. #435×C₂₂₇	C₂	semidirect
16. C₂×#41×C₂₂₇	C₂²	semidirect
17. C₂²×Q₈×C₂₂₇	C₂²	semidirect
25. C₂×SD₁₆×C₂₂₇	C₂²	semidirect
26. C₂×SD₁₆×C₂₂₇	C₂²	semidirect
27. C₂×SD₁₆×C₂₂₇	C₂²	semidirect
28. C₂×SD₁₆×C₂₂₇	C₂²	semidirect
30. C₂×D₈×C₂₂₇	C₂²	semidirect
31. C₂×D₈×C₂₂₇	C₂²	semidirect
32. C₂×M₁₆×C₂₂₇	C₂²	semidirect
33. C₂²×C₈×C₂₂₇	C₂²	semidirect
36. #124×C₂₂₇	C₂²	semidirect
38. C₂²⋊Q₈×C₂₂₇	C₂²	semidirect
43. #121×C₂₂₇	C₂²	semidirect
46. C₄×Q₈×C₂₂₇	C₂²	semidirect
50. #107×C₂₂₇	C₂²	semidirect
51. C₄⋊C₈×C₂₂₇	C₂²	semidirect
52. #103×C₂₂₇	C₂²	semidirect
53. #103×C₂₂₇	C₂²	semidirect
55. #102×C₂₂₇	C₂²	semidirect
56. #102×C₂₂₇	C₂²	semidirect
57. #102×C₂₂₇	C₂²	semidirect
58. C₂²⋊C₈×C₂₂₇	C₂²	semidirect
59. C₂²⋊C₈×C₂₂₇	C₂²	semidirect
60. #97×C₂₂₇	C₂²	semidirect
98. SD₁₆×C₂₂₇	D₄	semidirect
140. Q₈×C₂₂₇	C₂×D₄	semidirect
177. C₈×C₂₂₇	C₂×D₄	semidirect
197. C₂²×C₂₂₇	AGL(1,ℤ/8)	semidirect
218. C₂₂₇	#3265	direct (N × H)
219. #3265	C₂₂₇	direct (N × H)
220. C₂×AGL(1,ℤ/8)	C₂×C₂₂₇	semidirect
221. C₂²×SD₁₆	C₂×C₂₂₇	semidirect
222. #548	C₂×C₂₂₇	semidirect
223. D₄²	C₂×C₂₂₇	semidirect
224. #496	C₂×C₂₂₇	semidirect
225. #468	C₂×C₂₂₇	semidirect
226. #466	C₂×C₂₂₇	semidirect
227. #463	C₂×C₂₂₇	semidirect
228. #460	C₂×C₂₂₇	semidirect
229. #450	C₂×C₂₂₇	semidirect
230. #449	C₂×C₂₂₇	semidirect
231. #448	C₂×C₂₂₇	semidirect
232. #447	C₂×C₂₂₇	semidirect
233. #440	C₂×C₂₂₇	semidirect
234. #435	C₂×C₂₂₇	semidirect
235. C₂×#41	C₂²×C₂₂₇	semidirect
236. C₂²×Q₈	C₂²×C₂₂₇	semidirect
244. C₂×SD₁₆	C₂²×C₂₂₇	semidirect
245. C₂×SD₁₆	C₂²×C₂₂₇	semidirect
246. C₂×SD₁₆	C₂²×C₂₂₇	semidirect
247. C₂×SD₁₆	C₂²×C₂₂₇	semidirect
249. C₂×D₈	C₂²×C₂₂₇	semidirect
250. C₂×D₈	C₂²×C₂₂₇	semidirect
251. C₂×M₁₆	C₂²×C₂₂₇	semidirect
252. C₂²×C₈	C₂²×C₂₂₇	semidirect
255. #124	C₂²×C₂₂₇	semidirect
257. C₂²⋊Q₈	C₂²×C₂₂₇	semidirect
262. #121	C₂²×C₂₂₇	semidirect
265. C₄×Q₈	C₂²×C₂₂₇	semidirect
269. #107	C₂²×C₂₂₇	semidirect
270. C₄⋊C₈	C₂²×C₂₂₇	semidirect
271. #103	C₂²×C₂₂₇	semidirect
272. #103	C₂²×C₂₂₇	semidirect
274. #102	C₂²×C₂₂₇	semidirect
275. #102	C₂²×C₂₂₇	semidirect
276. #102	C₂²×C₂₂₇	semidirect
277. C₂²⋊C₈	C₂²×C₂₂₇	semidirect
278. C₂²⋊C₈	C₂²×C₂₂₇	semidirect
279. #97	C₂²×C₂₂₇	semidirect
317. SD₁₆	D₄×C₂₂₇	semidirect
359. Q₈	C₂×D₄×C₂₂₇	semidirect
396. C₈	C₂×D₄×C₂₂₇	semidirect
416. C₂²	AGL(1,ℤ/8)×C₂₂₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×AGL(1,ℤ/8)×C₂₂₇	2
C₂²×SD₁₆×C₂₂₇	2
#548×C₂₂₇	2
D₄²×C₂₂₇	2
#496×C₂₂₇	2
#468×C₂₂₇	2
#466×C₂₂₇	2
#463×C₂₂₇	2
#460×C₂₂₇	2
#450×C₂₂₇	2
#449×C₂₂₇	2
#448×C₂₂₇	2
#447×C₂₂₇	2
#440×C₂₂₇	2
#435×C₂₂₇	2
#3265	227

Subgroups — #3265×C227 #44397221

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3265×C₂₂₇ #44397221