Subgroups — #30652801

Order 16256.

1042 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22550600	C₂	1	1	yes	maximal, characteristic, complemented
2	#22550599	C₂	1	1	yes	maximal, characteristic, complemented
3	#22550579	C₂	1	1	yes	maximal, characteristic, complemented
4	#22550574	C₂	1	2	yes	maximal, complemented
5	#22550568	C₂	1	2	yes	maximal, complemented
6	#22550564	C₂	1	1	yes	maximal, characteristic, complemented
7	#22550553	C₂	1	2	yes	maximal, complemented
8	#22550553	C₂	1	2	yes	maximal, complemented
9	#22550530	C₂	1	1	yes	maximal, characteristic, complemented
10	#22550521	C₂	1	1	yes	maximal, characteristic, complemented
11	#22550521	C₂	1	1	yes	maximal, characteristic, complemented
12	#22550500	C₂	1	1	yes	maximal, characteristic, complemented
13	#22550489	C₂	1	1	yes	maximal, characteristic, complemented
14	#22550475	C₂	1	2	yes	maximal, complemented
15	#22550466	C₂	1	2	yes	maximal, complemented
16	#22550413	C₂	1	1	yes	maximal, characteristic, complemented
17	#22550412	C₂	1	2	yes	maximal, complemented
18	#22550411	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#16861204	C₂	1	2	yes	maximal, complemented
20	#22550355	C₂	1	1	yes	maximal, characteristic, complemented
21	#22550348	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#14523247	C₂	1	1	yes	maximal, characteristic, complemented
23	#554×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14523247	C₂²	1	1	yes	characteristic
25	C₂×#14523247	C₂²	1	1	yes	characteristic
26	C₂×D₄×D₁₂₇	C₂²	1	1	yes	characteristic
27	#16861209	C₂²	1	1	yes	characteristic, complemented
28	#16861204	C₂²	1	2	yes	—
29	#16861204	C₂²	1	2	yes	—
30	#16861204	C₂²	1	2	yes	—
31	#16861204	C₂²	1	1	yes	characteristic
32	#16861204	C₂²	1	2	yes	—
33	#16861204	C₂²	1	2	yes	complemented
34	#16861204	C₂²	1	2	yes	complemented
35	#16861204	C₂²	1	2	yes	complemented
36	#16861204	C₂²	1	2	yes	complemented
37	#16861204	C₂²	1	2	yes	complemented
38	#16861204	C₂²	1	2	yes	complemented
39	#16861204	C₂²	1	1	yes	characteristic, complemented
40	#16861200	C₂²	1	2	yes	complemented
41	#16861200	C₂²	1	1	yes	characteristic, complemented
42	#16861200	C₂²	1	2	yes	complemented
43	#16861200	C₂²	1	2	yes	complemented
44	#16861198	C₂²	1	1	yes	characteristic
45	#16861198	C₂²	1	2	yes	—
46	#16861198	C₂²	1	2	yes	complemented
47	#16861197	C₂²	1	1	yes	characteristic
48	#16861197	C₂²	1	1	yes	characteristic
49	#16861194	C₂²	1	1	yes	characteristic
50	#16861194	C₂²	1	2	yes	—
51	#16861194	C₂²	1	2	yes	complemented
52	#16861194	C₂²	1	2	yes	complemented
53	#16861194	C₂²	1	1	yes	characteristic, complemented
54	#16861194	C₂²	1	2	yes	complemented
55	#16861193	C₂²	1	2	yes	—
56	#16861193	C₂²	1	2	yes	—
57	#16861193	C₂²	1	2	yes	complemented
58	#16861193	C₂²	1	2	yes	complemented
59	#16861189	C₂²	1	1	yes	characteristic
60	#16861189	C₂²	1	1	yes	characteristic
61	#16861189	C₂²	1	1	yes	characteristic, complemented
62	#16861189	C₂²	1	1	yes	characteristic, complemented
63	#16861185	C₂²	1	2	yes	complemented
64	#16861185	C₂²	1	2	yes	complemented
65	#16861185	C₂²	1	1	yes	characteristic, complemented
66	#16861184	C₂²	1	1	yes	characteristic
67	#16861184	C₂²	1	1	yes	characteristic
68	#16861184	C₂²	1	1	yes	characteristic
69	#16861184	C₂²	1	2	yes	complemented
70	#16861183	C₂²	1	2	yes	—
71	#16861183	C₂²	1	2	yes	—
72	#16861183	C₂²	1	2	yes	complemented
73	#16861179	C₂²	1	2	yes	—
74	#16861179	C₂²	1	2	yes	—
75	Q₈×Dic₁₂₇	C₂²	1	2	yes	complemented
76	C₄×Dic₂₅₄	C₂²	1	1	yes	characteristic, complemented
77	C₄×Dic₂₅₄	C₂²	1	1	yes	characteristic, complemented
78	#16861174	C₂²	1	1	yes	characteristic, complemented
79	#16861174	C₂²	1	1	yes	characteristic, complemented
80	C₄×D₅₀₈	C₂²	1	1	yes	characteristic
81	C₄×D₅₀₈	C₂²	1	1	yes	characteristic
82	C₄×D₅₀₈	C₂²	1	1	yes	characteristic
83	C₄×D₅₀₈	C₂²	1	1	yes	characteristic, complemented
84	D₄×Dic₁₂₇	C₂²	1	1	yes	characteristic
85	#16861171	C₂²	1	1	yes	characteristic
86	#16861171	C₂²	1	2	yes	complemented
87	#16861171	C₂²	1	2	yes	complemented
88	C₄×C₂²⋊D₁₂₇	C₂²	1	2	yes	—
89	C₄×C₂²⋊D₁₂₇	C₂²	1	2	yes	complemented
90	C₄×C₂²⋊D₁₂₇	C₂²	1	2	yes	complemented
91	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	2	yes	—
92	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	2	yes	complemented
93	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	2	yes	complemented
94	#16861167	C₂²	1	1	yes	characteristic
95	#16861167	C₂²	1	2	yes	complemented
96	#16861167	C₂²	1	2	yes	complemented
97	#16861167	C₂²	1	2	yes	complemented
98	#16861167	C₂²	1	1	yes	characteristic, complemented
99	#16861166	C₂²	1	1	yes	characteristic
100	#16861166	C₂²	1	1	yes	characteristic, complemented
101	#16861165	C₂²	1	2	yes	complemented
102	#16861165	C₂²	1	2	yes	complemented
103	C₂×C₄⋊Dic₁₂₇	C₂²	1	2	yes	complemented
104	C₂×Dic₁₂₇⋊C₄	C₂²	1	2	yes	complemented
105	C₄⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
106	C₂×(C₂×D₁₂₇)⋊C₄	C₂²	1	2	yes	—
107	C₂×(C₂×D₁₂₇)⋊C₄	C₂²	1	2	yes	—
108	C₂×(C₂×D₁₂₇)⋊C₄	C₂²	1	2	yes	—
109	C₂²⋊C₄×D₁₂₇	C₂²	1	2	yes	—
110	C₂×C₄×Dic₁₂₇	C₂²	1	2	yes	complemented
111	C₄²×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
112	C₄⋊Q₈×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
113	#125×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
114	#125×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
115	C₂²⋊Q₈×C₁₂₇	C₂²	1	2	yes	complemented
116	C₂²⋊Q₈×C₁₂₇	C₂²	1	2	yes	complemented
117	C₂²⋊Q₈×C₁₂₇	C₂²	1	2	yes	complemented
118	C₄×Q₈×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₄×C₁₂₇	C₂²	1	1	yes	characteristic
120	C₄×D₄×C₁₂₇	C₂²	1	1	yes	characteristic
121	C₄×D₄×C₁₂₇	C₂²	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₁₂₇	C₂²	1	2	yes	complemented
123	C₂³×D₁₂₇	C₂³	1	2	yes	—
124	#14523247	—	2	4	no	—
125	#14523247	—	2	4	no	—
126	C₂×Dic₂₅₄	C₂³	1	1	yes	characteristic
127	C₂×Dic₂₅₄	C₂³	1	1	yes	characteristic
128	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
129	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
130	C₂×D₅₀₈	C₂³	1	2	yes	—
131	C₂×D₅₀₈	C₂³	1	2	yes	—
132	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
133	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
137	D₄×D₁₂₇	—	2	4	no	—
138	C₂²×Dic₁₂₇	C₂³	1	2	yes	—
139	C₂²×Dic₁₂₇	C₂³	1	2	yes	—
140	C₂²×Dic₁₂₇	C₂³	1	2	yes	—
141	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
142	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
143	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
145	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
146	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
147	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
148	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
149	C₄⋊Dic₁₂₇	C₂³	1	2	yes	—
150	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
151	C₄⋊Dic₁₂₇	C₂³	1	2	yes	—
152	C₄⋊Dic₁₂₇	C₂³	1	2	yes	—
153	C₄⋊Dic₁₂₇	C₂³	1	2	yes	—
154	C₄⋊Dic₁₂₇	C₂³	1	2	yes	—
155	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
156	C₄⋊Dic₁₂₇	C₂³	1	2	yes	—
157	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
158	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
159	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
160	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
161	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
162	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
163	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
164	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
165	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
166	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
167	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
168	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	—
169	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
170	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
171	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
172	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
173	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
174	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
175	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
176	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
177	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
178	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
179	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
180	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
181	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
182	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
183	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
184	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
185	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
186	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
188	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
189	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
190	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
191	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
192	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
193	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
194	C₄×Dic₁₂₇	C₂³	1	2	yes	—
195	C₄×Dic₁₂₇	C₂³	1	2	yes	—
196	C₄×Dic₁₂₇	C₂³	1	2	yes	—
197	C₄×Dic₁₂₇	C₂³	1	2	yes	—
198	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
199	C₄×Dic₁₂₇	C₂³	1	2	yes	—
200	C₄×Dic₁₂₇	C₂³	1	2	yes	—
201	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
202	C₂×Q₈×C₁₂₇	C₂³	1	1	yes	characteristic
203	C₂×Q₈×C₁₂₇	C₂³	1	2	yes	—
204	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
205	C₂²×C₄×C₁₂₇	C₂³	1	2	yes	—
206	C₂²×C₄×C₁₂₇	C₂³	1	2	yes	—
207	C₂²×C₄×C₁₂₇	C₂³	1	2	yes	—
208	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
209	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
210	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
211	C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	—
212	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
213	C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	—
214	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
215	C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	—
216	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
217	C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	—
218	C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	—
219	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	—
220	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	—
221	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	—
222	C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
223	C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
224	C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
225	C₂²×D₁₂₇	—	2	4	no	—
226	C₂²×D₁₂₇	—	4	2	no	—
227	C₂²×D₁₂₇	—	4	2	no	—
228	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
229	C₂²×D₁₂₇	C₂⁴	1	2	yes	—
230	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
231	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
232	Dic₂₅₄	—	2	2	no	—
233	Dic₂₅₄	—	2	2	no	—
234	D₅₀₈	—	2	2	no	—
235	D₅₀₈	—	4	1	no	—
236	D₅₀₈	—	4	2	no	—
237	D₅₀₈	—	4	2	no	—
238	D₅₀₈	—	4	1	no	—
239	D₅₀₈	—	4	1	no	—
240	C₂²⋊D₁₂₇	—	2	4	no	—
241	C₂²⋊D₁₂₇	—	2	4	no	—
242	C₂²⋊D₁₂₇	—	2	4	no	—
243	C₂×Dic₁₂₇	—	2	4	no	—
244	C₂×Dic₁₂₇	—	2	4	no	—
245	C₂×Dic₁₂₇	—	4	2	no	—
246	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
247	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
248	C₂×Dic₁₂₇	C₂⁴	1	2	yes	—
249	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
250	C₂×Dic₁₂₇	C₂⁴	1	2	yes	—
251	C₂×Dic₁₂₇	C₂⁴	1	2	yes	—
252	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
253	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
254	C₄×D₁₂₇	—	2	2	no	—
255	C₄×D₁₂₇	—	2	2	no	—
256	C₄×D₁₂₇	—	2	2	no	—
257	C₄×D₁₂₇	—	4	1	no	—
258	C₄×D₁₂₇	—	4	2	no	—
259	C₄×D₁₂₇	—	4	2	no	—
260	C₄×D₁₂₇	—	4	2	no	—
261	C₄×D₁₂₇	—	4	1	no	—
262	C₂³×C₁₂₇	C₂⁴	1	2	yes	—
263	Q₈×C₁₂₇	—	4	1	no	—
264	Q₈×C₁₂₇	—	4	2	no	—
265	D₄×C₁₂₇	#41	1	4	yes	—
266	C₂×C₄×C₁₂₇	—	4	2	no	—
267	C₂×C₄×C₁₂₇	—	4	2	no	—
268	C₂×C₄×C₁₂₇	—	4	2	no	—
269	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
270	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
271	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
272	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
273	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
274	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
275	C₂×C₄×C₁₂₇	C₂⁴	1	2	yes	—
276	C₂×C₄×C₁₂₇	C₂⁴	1	2	yes	—
277	C₂×C₄×C₁₂₇	C₂⁴	1	2	yes	—
278	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
279	C₂²×C₁₂₇	—	2	2	no	—
280	C₂²×C₁₂₇	—	2	2	no	—
281	C₂²×C₁₂₇	C₂×#41	1	4	yes	—
282	C₂²×C₁₂₇	C₂⁵	1	1	yes	characteristic
283	C₂×D₁₂₇	—	2	1	no	—
284	C₂×D₁₂₇	—	2	1	no	—
285	C₂×D₁₂₇	—	2	1	no	—
286	C₂×D₁₂₇	—	2	2	no	—
287	C₂×D₁₂₇	—	2	1	no	—
288	C₂×D₁₂₇	—	2	1	no	—
289	C₂×D₁₂₇	—	2	1	no	—
290	C₂×D₁₂₇	—	2	2	no	—
291	C₂×D₁₂₇	—	2	2	no	—
292	C₂×D₁₂₇	—	2	1	no	—
293	C₂×D₁₂₇	—	2	1	no	—
294	C₂×D₁₂₇	—	2	1	no	—
295	C₂×D₁₂₇	—	8	4	no	—
296	C₄×C₁₂₇	—	2	1	no	—
297	C₄×C₁₂₇	—	2	1	no	—
298	C₄×C₁₂₇	—	2	1	no	—
299	C₄×C₁₂₇	—	2	2	no	—
300	C₄×C₁₂₇	—	2	2	no	—
301	C₄×C₁₂₇	—	2	2	no	—
302	C₄×C₁₂₇	—	2	1	no	—
303	C₄×C₁₂₇	—	2	1	no	—
304	C₄×C₁₂₇	—	2	1	no	—
305	C₄×C₁₂₇	C₂×#41	1	2	yes	—
306	Dic₁₂₇	—	2	1	no	—
307	Dic₁₂₇	—	2	1	no	—
308	Dic₁₂₇	—	2	1	no	—
309	Dic₁₂₇	—	2	2	no	—
310	Dic₁₂₇	—	2	2	no	—
311	Dic₁₂₇	—	2	1	no	—
312	Dic₁₂₇	—	2	2	no	—
313	Dic₁₂₇	—	2	1	no	—
314	C₂×C₁₂₇	—	2	4	no	—
315	C₂×C₁₂₇	C₂²×#41	1	1	yes	characteristic
316	C₂×C₁₂₇	#585	1	1	yes	characteristic
317	C₂×C₁₂₇	#585	1	1	yes	characteristic
318	D₁₂₇	—	4	1	no	—
319	D₁₂₇	—	4	1	no	—
320	D₁₂₇	—	4	2	no	—
321	D₁₂₇	—	4	1	no	—
322	#3521	—	127	1	no	maximal, Sylow
323	C₁₂₇	#3521	1	1	yes	characteristic, complemented, Sylow
324	#556	—	127	1	no	—
325	#556	—	127	1	no	—
326	#554	D₁₂₇	1	1	yes	characteristic, complemented
327	#553	—	127	1	no	—
328	#553	—	127	2	no	—
329	#552	—	127	1	no	—
330	#552	—	127	2	no	—
331	#551	—	127	2	no	—
332	#551	—	127	2	no	—
333	#547	—	127	1	no	—
334	#546	—	127	1	no	—
335	#546	—	127	1	no	—
336	#542	—	127	1	no	—
337	#541	—	127	1	no	—
338	#539	—	127	2	no	—
339	#538	—	127	2	no	—
340	#529	—	127	1	no	—
341	#529	—	127	2	no	—
342	#529	—	127	1	no	—
343	C₂×#126	—	127	2	no	—
344	#520	—	127	1	no	—
345	#518	—	127	1	no	—
346	C₄×#41	—	127	1	no	—
347	C₂×#41	—	127	1	no	—
348	C₂×#41	—	127	1	no	—
349	C₂²×D₄	—	127	1	no	—
350	C₄⋊Q₈	—	127	1	no	—
351	C₄⋊Q₈	C₂×D₁₂₇	1	1	yes	characteristic, complemented
352	#126	—	127	1	no	—
353	#126	—	127	2	no	—
354	#126	—	127	2	no	—
355	#126	—	127	2	no	—
356	#126	—	127	2	no	—
357	#126	—	127	2	no	—
358	#126	—	127	2	no	—
359	#126	—	127	2	no	—
360	#126	—	127	1	no	—
361	#126	—	127	2	no	—
362	#126	—	127	2	no	—
363	#126	—	127	2	no	—
364	#125	—	127	2	no	—
365	#125	—	127	1	no	—
366	#125	—	127	2	no	—
367	#125	—	127	2	no	—
368	#125	C₂×D₁₂₇	1	1	yes	characteristic, complemented
369	#125	C₂×D₁₂₇	1	1	yes	characteristic, complemented
370	#124	—	127	1	no	—
371	#124	—	127	2	no	—
372	#124	—	127	2	no	—
373	#124	—	127	1	no	—
374	#124	—	127	1	no	—
375	#123	—	127	1	no	—
376	#123	—	127	2	no	—
377	#123	—	127	2	no	—
378	#123	—	127	1	no	—
379	#123	—	127	2	no	—
380	#123	—	127	2	no	—
381	#123	—	127	2	no	—
382	#123	—	127	2	no	—
383	#123	—	127	2	no	—
384	#123	—	127	2	no	—
385	C₂²⋊Q₈	—	127	1	no	—
386	C₂²⋊Q₈	—	127	2	no	—
387	C₂²⋊Q₈	—	127	2	no	—
388	C₂²⋊Q₈	—	127	1	no	—
389	C₂²⋊Q₈	—	127	1	no	—
390	C₂²⋊Q₈	—	127	1	no	—
391	C₂²⋊Q₈	—	127	1	no	—
392	C₂²⋊Q₈	C₂×D₁₂₇	1	2	yes	complemented
393	C₂²⋊Q₈	C₂×D₁₂₇	1	2	yes	complemented
394	C₂²⋊Q₈	C₂×D₁₂₇	1	2	yes	complemented
395	#121	—	127	2	no	—
396	#121	—	127	2	no	—
397	#121	—	127	2	no	—
398	#121	—	127	1	no	—
399	#121	—	127	1	no	—
400	#121	—	127	1	no	—
401	#121	—	127	2	no	—
402	#120	—	127	2	no	—
403	#120	—	127	2	no	—
404	C₄×Q₈	—	127	2	no	—
405	C₄×Q₈	—	127	1	no	—
406	C₄×Q₈	—	127	1	no	—
407	C₄×Q₈	—	127	1	no	—
408	C₄×Q₈	—	127	1	no	—
409	C₄×Q₈	C₂×D₁₂₇	1	1	yes	characteristic, complemented
410	C₄×D₄	—	127	1	no	—
411	C₄×D₄	—	127	2	no	—
412	C₄×D₄	—	127	2	no	—
413	C₄×D₄	—	127	2	no	—
414	C₄×D₄	—	127	1	no	—
415	C₄×D₄	—	127	2	no	—
416	C₄×D₄	—	127	2	no	—
417	C₄×D₄	—	127	2	no	—
418	C₄×D₄	—	127	2	no	—
419	C₄×D₄	—	127	2	no	—
420	C₄×D₄	—	127	1	no	—
421	C₄×D₄	—	127	1	no	—
422	C₄×D₄	—	127	1	no	—
423	C₄×D₄	—	127	1	no	—
424	C₄×D₄	C₂×D₁₂₇	1	1	yes	characteristic
425	C₄×D₄	C₂×D₁₂₇	1	1	yes	characteristic
426	C₄×D₄	C₂×D₁₂₇	1	1	yes	characteristic
427	#117	—	127	1	no	—
428	#117	—	127	1	no	—
429	#117	—	127	2	no	—
430	#117	—	127	2	no	—
431	#117	—	127	2	no	—
432	#117	—	127	2	no	—
433	#117	—	127	2	no	—
434	#117	—	127	1	no	—
435	#117	—	127	1	no	—
436	C₂×C₄⋊C₄	—	127	2	no	—
437	C₂×C₄⋊C₄	—	127	2	no	—
438	C₂×C₄⋊C₄	—	127	1	no	—
439	C₂×C₄⋊C₄	C₂×D₁₂₇	1	2	yes	complemented
440	C₂×C₂²⋊C₄	—	127	2	no	—
441	C₂×C₂²⋊C₄	—	127	2	no	—
442	C₂×C₂²⋊C₄	—	127	2	no	—
443	C₂×C₂²⋊C₄	—	127	2	no	—
444	C₂×C₄²	—	127	2	no	—
445	C₂×C₄²	—	127	1	no	—
446	C₂⁴	—	127	2	no	—
447	#41	—	254	4	no	—
448	#41	—	254	4	no	—
449	C₂×Q₈	—	127	1	no	—
450	C₂×Q₈	—	127	1	no	—
451	C₂×Q₈	C₂²×D₁₂₇	1	2	yes	—
452	C₂×Q₈	C₂²×D₁₂₇	1	1	yes	characteristic
453	C₂×D₄	—	127	2	no	—
454	C₂×D₄	—	127	2	no	—
455	C₂×D₄	—	127	2	no	—
456	C₂×D₄	—	127	1	no	—
457	C₂×D₄	—	127	1	no	—
458	C₂×D₄	—	127	2	no	—
459	C₂×D₄	—	127	2	no	—
460	C₂×D₄	—	127	1	no	—
461	C₂×D₄	—	127	1	no	—
462	C₂×D₄	—	254	4	no	—
463	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
464	C₂²×C₄	—	127	2	no	—
465	C₂²×C₄	—	127	2	no	—
466	C₂²×C₄	—	127	2	no	—
467	C₂²×C₄	—	127	1	no	—
468	C₂²×C₄	—	127	1	no	—
469	C₂²×C₄	—	127	2	no	—
470	C₂²×C₄	—	127	2	no	—
471	C₂²×C₄	—	127	2	no	—
472	C₂²×C₄	—	127	1	no	—
473	C₂²×C₄	—	127	1	no	—
474	C₂²×C₄	—	127	1	no	—
475	C₂²×C₄	C₂²×D₁₂₇	1	2	yes	—
476	C₂²×C₄	C₂²×D₁₂₇	1	2	yes	—
477	C₂²×C₄	C₂²×D₁₂₇	1	2	yes	—
478	C₄⋊C₄	—	127	1	no	—
479	C₄⋊C₄	—	127	2	no	—
480	C₄⋊C₄	—	127	2	no	—
481	C₄⋊C₄	—	127	2	no	—
482	C₄⋊C₄	—	127	1	no	—
483	C₄⋊C₄	—	127	1	no	—
484	C₄⋊C₄	—	127	1	no	—
485	C₄⋊C₄	—	127	2	no	—
486	C₄⋊C₄	—	127	2	no	—
487	C₄⋊C₄	—	127	1	no	—
488	C₄⋊C₄	—	127	1	no	—
489	C₄⋊C₄	—	127	2	no	—
490	C₄⋊C₄	—	127	2	no	—
491	C₄⋊C₄	—	127	2	no	—
492	C₄⋊C₄	—	127	2	no	—
493	C₄⋊C₄	—	127	2	no	—
494	C₄⋊C₄	—	127	1	no	—
495	C₄⋊C₄	—	127	1	no	—
496	C₄⋊C₄	—	127	2	no	—
497	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
498	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
499	C₄⋊C₄	C₂²×D₁₂₇	1	2	yes	—
500	C₄⋊C₄	C₂²×D₁₂₇	1	2	yes	—
501	C₄⋊C₄	C₂²×D₁₂₇	1	2	yes	—
502	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
503	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
504	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
505	C₄⋊C₄	C₂²×D₁₂₇	1	2	yes	—
506	C₄⋊C₄	C₂²×D₁₂₇	1	2	yes	—
507	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
508	C₂²⋊C₄	—	127	2	no	—
509	C₂²⋊C₄	—	127	1	no	—
510	C₂²⋊C₄	—	127	2	no	—
511	C₂²⋊C₄	—	127	1	no	—
512	C₂²⋊C₄	—	127	1	no	—
513	C₂²⋊C₄	—	127	1	no	—
514	C₂²⋊C₄	—	127	2	no	—
515	C₂²⋊C₄	—	127	2	no	—
516	C₂²⋊C₄	—	127	2	no	—
517	C₂²⋊C₄	—	127	2	no	—
518	C₂²⋊C₄	—	127	2	no	—
519	C₂²⋊C₄	—	127	2	no	—
520	C₂²⋊C₄	—	127	2	no	—
521	C₂²⋊C₄	—	127	2	no	—
522	C₂²⋊C₄	—	127	1	no	—
523	C₂²⋊C₄	—	127	2	no	—
524	C₂²⋊C₄	—	127	1	no	—
525	C₂²⋊C₄	—	127	1	no	—
526	C₂²⋊C₄	—	127	2	no	—
527	C₂²⋊C₄	—	127	2	no	—
528	C₂²⋊C₄	—	127	2	no	—
529	C₂²⋊C₄	—	127	1	no	—
530	C₂²⋊C₄	—	127	1	no	—
531	C₂²⋊C₄	—	127	2	no	—
532	C₂²⋊C₄	—	127	1	no	—
533	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	—
534	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	—
535	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	—
536	C₄²	—	127	1	no	—
537	C₄²	—	127	1	no	—
538	C₄²	—	127	1	no	—
539	C₄²	—	127	2	no	—
540	C₄²	—	127	2	no	—
541	C₄²	—	127	2	no	—
542	C₄²	—	127	2	no	—
543	C₄²	—	127	2	no	—
544	C₄²	—	127	2	no	—
545	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic
546	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic
547	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic
548	C₂³	—	127	1	no	—
549	C₂³	—	127	2	no	—
550	C₂³	—	127	1	no	—
551	C₂³	—	127	1	no	—
552	C₂³	—	508	2	no	—
553	C₂³	—	508	2	no	—
554	C₂³	—	254	4	no	—
555	C₂³	C₂³×D₁₂₇	1	2	yes	—
556	Q₈	—	4	2	no	—
557	Q₈	—	4	1	no	—
558	Q₈	—	254	2	no	—
559	Q₈	—	254	2	no	—
560	D₄	—	508	1	no	—
561	D₄	—	508	2	no	—
562	D₄	—	508	1	no	—
563	D₄	—	508	2	no	—
564	D₄	—	508	1	no	—
565	D₄	—	254	4	no	—
566	D₄	—	254	4	no	—
567	D₄	—	254	4	no	—
568	D₄	—	254	2	no	—
569	D₄	#14523249	1	4	yes	—
570	C₂×C₄	—	4	2	no	—
571	C₂×C₄	—	4	2	no	—
572	C₂×C₄	—	4	2	no	—
573	C₂×C₄	—	127	1	no	—
574	C₂×C₄	—	127	1	no	—
575	C₂×C₄	—	127	1	no	—
576	C₂×C₄	—	127	2	no	—
577	C₂×C₄	—	127	2	no	—
578	C₂×C₄	—	127	2	no	—
579	C₂×C₄	—	127	1	no	—
580	C₂×C₄	—	127	1	no	—
581	C₂×C₄	—	508	1	no	—
582	C₂×C₄	—	508	2	no	—
583	C₂×C₄	—	508	2	no	—
584	C₂×C₄	—	508	2	no	—
585	C₂×C₄	—	508	1	no	—
586	C₂×C₄	—	508	2	no	—
587	C₂×C₄	—	254	4	no	—
588	C₂×C₄	—	254	4	no	—
589	C₂×C₄	—	254	2	no	—
590	C₂×C₄	—	254	2	no	—
591	C₂×C₄	—	254	2	no	—
592	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
593	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
594	C₂×C₄	C₂³×D₁₂₇	1	2	yes	—
595	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
596	C₂×C₄	C₂³×D₁₂₇	1	2	yes	—
597	C₂×C₄	C₂³×D₁₂₇	1	2	yes	—
598	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
599	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
600	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
601	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
602	C₂²	—	2	2	no	—
603	C₂²	—	2	2	no	—
604	C₂²	—	1016	4	no	—
605	C₂²	—	254	1	no	—
606	C₂²	—	254	1	no	—
607	C₂²	—	254	1	no	—
608	C₂²	—	254	2	no	—
609	C₂²	—	254	1	no	—
610	C₂²	—	254	2	no	—
611	C₂²	—	254	1	no	—
612	C₂²	—	254	1	no	—
613	C₂²	—	254	1	no	—
614	C₂²	—	254	1	no	—
615	C₂²	—	254	2	no	—
616	C₂²	—	254	1	no	—
617	C₂²	C₂×#14523249	1	4	yes	—
618	C₂²	C₂⁴×D₁₂₇	1	1	yes	characteristic
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	2	2	no	—
622	C₄	—	2	2	no	—
623	C₄	—	2	1	no	—
624	C₄	—	2	1	no	—
625	C₄	—	2	2	no	—
626	C₄	—	2	1	no	—
627	C₄	—	2	1	no	—
628	C₄	—	254	1	no	—
629	C₄	—	254	1	no	—
630	C₄	—	254	1	no	—
631	C₄	—	254	2	no	—
632	C₄	—	254	2	no	—
633	C₄	—	254	1	no	—
634	C₄	—	254	2	no	—
635	C₄	—	254	1	no	—
636	C₄	C₂×#14523249	1	2	yes	—
637	C₂	—	2	4	no	—
638	C₂	—	508	1	no	—
639	C₂	—	508	2	no	—
640	C₂	—	508	1	no	—
641	C₂	—	508	1	no	—
642	C₂	C₂²×#14523249	1	1	yes	characteristic
643	C₂	#22550711	1	1	yes	characteristic
644	C₂	#22550712	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₂₇
commutator, socle, cosocle	C₂²×C₁₂₇	C₂⁵
Fitting	#554×C₁₂₇	C₂
hypercenter	#554	D₁₂₇
hypocenter	C₁₂₇	#3521
LCS	G ▷ C₂²×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₂² ◁ #554

Complements

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

N	H ≅ G/N	type
1. #22550600	C₂	semidirect
2. #22550599	C₂	semidirect
3. #22550579	C₂	semidirect
4. #22550574	C₂	semidirect
5. #22550568	C₂	semidirect
6. #22550564	C₂	semidirect
7. #22550553	C₂	semidirect
8. #22550553	C₂	semidirect
9. #22550530	C₂	semidirect
10. #22550521	C₂	semidirect
11. #22550521	C₂	semidirect
12. #22550500	C₂	semidirect
13. #22550489	C₂	semidirect
14. #22550475	C₂	semidirect
15. #22550466	C₂	semidirect
16. #22550413	C₂	semidirect
17. #22550412	C₂	semidirect
18. #22550411	C₂	semidirect
19. C₂×#16861204	C₂	semidirect
20. #22550355	C₂	semidirect
21. #22550348	C₂	semidirect
22. C₄×#14523247	C₂	semidirect
23. #554×C₁₂₇	C₂	semidirect
27. #16861209	C₂²	semidirect
33. #16861204	C₂²	semidirect
34. #16861204	C₂²	semidirect
35. #16861204	C₂²	semidirect
36. #16861204	C₂²	semidirect
37. #16861204	C₂²	semidirect
38. #16861204	C₂²	semidirect
39. #16861204	C₂²	semidirect
40. #16861200	C₂²	semidirect
41. #16861200	C₂²	semidirect
42. #16861200	C₂²	semidirect
43. #16861200	C₂²	semidirect
46. #16861198	C₂²	semidirect
51. #16861194	C₂²	semidirect
52. #16861194	C₂²	semidirect
53. #16861194	C₂²	semidirect
54. #16861194	C₂²	semidirect
57. #16861193	C₂²	semidirect
58. #16861193	C₂²	semidirect
61. #16861189	C₂²	semidirect
62. #16861189	C₂²	semidirect
63. #16861185	C₂²	semidirect
64. #16861185	C₂²	semidirect
65. #16861185	C₂²	semidirect
69. #16861184	C₂²	semidirect
72. #16861183	C₂²	semidirect
75. Q₈×Dic₁₂₇	C₂²	semidirect
76. C₄×Dic₂₅₄	C₂²	semidirect
77. C₄×Dic₂₅₄	C₂²	semidirect
78. #16861174	C₂²	semidirect
79. #16861174	C₂²	semidirect
83. C₄×D₅₀₈	C₂²	semidirect
86. #16861171	C₂²	semidirect
87. #16861171	C₂²	semidirect
89. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
90. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
92. (C₂²⋊D₁₂₇)⋊C₄	C₂²	semidirect
93. (C₂²⋊D₁₂₇)⋊C₄	C₂²	semidirect
95. #16861167	C₂²	semidirect
96. #16861167	C₂²	semidirect
97. #16861167	C₂²	semidirect
98. #16861167	C₂²	semidirect
100. #16861166	C₂²	semidirect
101. #16861165	C₂²	semidirect
102. #16861165	C₂²	semidirect
103. C₂×C₄⋊Dic₁₂₇	C₂²	semidirect
104. C₂×Dic₁₂₇⋊C₄	C₂²	semidirect
105. C₄⋊C₄×D₁₂₇	C₂²	semidirect
110. C₂×C₄×Dic₁₂₇	C₂²	semidirect
111. C₄²×D₁₂₇	C₂²	semidirect
112. C₄⋊Q₈×C₁₂₇	C₂²	semidirect
113. #125×C₁₂₇	C₂²	semidirect
114. #125×C₁₂₇	C₂²	semidirect
115. C₂²⋊Q₈×C₁₂₇	C₂²	semidirect
116. C₂²⋊Q₈×C₁₂₇	C₂²	semidirect
117. C₂²⋊Q₈×C₁₂₇	C₂²	semidirect
118. C₄×Q₈×C₁₂₇	C₂²	semidirect
122. C₂×C₄⋊C₄×C₁₂₇	C₂²	semidirect
323. C₁₂₇	#3521	semidirect
326. #554	D₁₂₇	semidirect
351. C₄⋊Q₈	C₂×D₁₂₇	semidirect
368. #125	C₂×D₁₂₇	semidirect
369. #125	C₂×D₁₂₇	semidirect
392. C₂²⋊Q₈	C₂×D₁₂₇	semidirect
393. C₂²⋊Q₈	C₂×D₁₂₇	semidirect
394. C₂²⋊Q₈	C₂×D₁₂₇	semidirect
409. C₄×Q₈	C₂×D₁₂₇	semidirect
439. C₂×C₄⋊C₄	C₂×D₁₂₇	semidirect

Maximal subgroups

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

subgroup	index
#22550600	2
#22550599	2
#22550579	2
#22550574	2
#22550568	2
#22550564	2
#22550553	2
#22550530	2
#22550521	2
#22550500	2
#22550489	2
#22550475	2
#22550466	2
#22550413	2
#22550412	2
#22550411	2
C₂×#16861204	2
#22550355	2
#22550348	2
C₄×#14523247	2
#554×C₁₂₇	2
#3521	127