Subgroups — #30652776

Order 16256.

1124 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22550594	C₂	1	1	yes	maximal, characteristic, complemented
2	#22550582	C₂	1	2	yes	maximal, complemented
3	#22550564	C₂	1	1	yes	maximal, characteristic, complemented
4	#22550551	C₂	1	2	yes	maximal, complemented
5	#22550550	C₂	1	2	yes	maximal, complemented
6	#22550539	C₂	1	1	yes	maximal, characteristic, complemented
7	#22550538	C₂	1	1	yes	maximal, characteristic, complemented
8	#22550535	C₂	1	1	yes	maximal, characteristic, complemented
9	#22550528	C₂	1	1	yes	maximal, characteristic, complemented
10	#22550527	C₂	1	1	yes	maximal, characteristic, complemented
11	#22550518	C₂	1	2	yes	maximal, complemented
12	#22550492	C₂	1	2	yes	maximal, complemented
13	#22550474	C₂	1	2	yes	maximal, complemented
14	#22550470	C₂	1	2	yes	maximal, complemented
15	#22550430	C₂	1	1	yes	maximal, characteristic, complemented
16	#22550411	C₂	1	1	yes	maximal, characteristic, complemented
17	#22550389	C₂	1	1	yes	maximal, characteristic, complemented
18	#22550388	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#16861189	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²⋊Q₈×D₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
21	#22550356	C₂	1	2	yes	maximal, complemented
22	C₄×D₄×D₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
23	#552×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14523249	C₂²	1	1	yes	characteristic, complemented
25	C₂×#14523248	C₂²	1	2	yes	—
26	C₂×#14523248	C₂²	1	1	yes	characteristic, complemented
27	C₂²×Dic₂₅₄	C₂²	1	1	yes	characteristic, complemented
28	C₂×Q₈×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
29	C₂×D₄×D₁₂₇	C₂²	1	1	yes	characteristic
30	C₂²×C₄×D₁₂₇	C₂²	1	1	yes	characteristic
31	C₂²×C₄×D₁₂₇	C₂²	1	1	yes	characteristic
32	#16861208	C₂²	1	2	yes	complemented
33	#16861208	C₂²	1	1	yes	characteristic, complemented
34	#16861207	C₂²	1	1	yes	characteristic, complemented
35	#16861204	C₂²	1	2	yes	complemented
36	#16861204	C₂²	1	2	yes	complemented
37	#16861203	C₂²	1	2	yes	complemented
38	#16861202	C₂²	1	2	yes	complemented
39	#16861200	C₂²	1	2	yes	complemented
40	#16861199	C₂²	1	2	yes	complemented
41	#16861197	C₂²	1	1	yes	characteristic, complemented
42	#16861197	C₂²	1	2	yes	complemented
43	#16861195	C₂²	1	2	yes	—
44	#16861195	C₂²	1	2	yes	complemented
45	#16861194	C₂²	1	2	yes	—
46	#16861194	C₂²	1	2	yes	—
47	#16861194	C₂²	1	2	yes	complemented
48	#16861194	C₂²	1	2	yes	complemented
49	#16861194	C₂²	1	2	yes	complemented
50	#16861193	C₂²	1	2	yes	complemented
51	#16861192	C₂²	1	2	yes	complemented
52	#16861191	C₂²	1	2	yes	complemented
53	#16861189	C₂²	1	2	yes	—
54	#16861189	C₂²	1	1	yes	characteristic
55	#16861189	C₂²	1	1	yes	characteristic
56	#16861189	C₂²	1	1	yes	characteristic, complemented
57	#16861189	C₂²	1	2	yes	complemented
58	#16861189	C₂²	1	1	yes	characteristic, complemented
59	#16861189	C₂²	1	1	yes	characteristic, complemented
60	#16861189	C₂²	1	2	yes	complemented
61	#16861188	C₂²	1	1	yes	characteristic, complemented
62	#16861187	C₂²	1	2	yes	—
63	#16861187	C₂²	1	2	yes	—
64	#16861187	C₂²	1	2	yes	complemented
65	#16861187	C₂²	1	2	yes	complemented
66	#16861187	C₂²	1	2	yes	complemented
67	#16861186	C₂²	1	2	yes	complemented
68	#16861186	C₂²	1	2	yes	complemented
69	#16861185	C₂²	1	1	yes	characteristic
70	#16861184	C₂²	1	2	yes	—
71	#16861184	C₂²	1	1	yes	characteristic
72	#16861184	C₂²	1	1	yes	characteristic, complemented
73	#16861183	C₂²	1	1	yes	characteristic, complemented
74	#16861182	C₂²	1	2	yes	—
75	#16861181	C₂²	1	2	yes	—
76	#16861179	C₂²	1	2	yes	—
77	#16861179	C₂²	1	2	yes	—
78	C₄×Dic₂₅₄	C₂²	1	1	yes	characteristic, complemented
79	C₄×Dic₂₅₄	C₂²	1	2	yes	complemented
80	C₄×Dic₂₅₄	C₂²	1	2	yes	complemented
81	#16861174	C₂²	1	1	yes	characteristic, complemented
82	C₄×D₅₀₈	C₂²	1	1	yes	characteristic
83	C₄×D₅₀₈	C₂²	1	2	yes	—
84	C₄×D₅₀₈	C₂²	1	2	yes	complemented
85	C₄×D₅₀₈	C₂²	1	2	yes	complemented
86	D₄×Dic₁₂₇	C₂²	1	1	yes	characteristic
87	#16861171	C₂²	1	2	yes	—
88	#16861171	C₂²	1	2	yes	—
89	#16861171	C₂²	1	1	yes	characteristic
90	#16861171	C₂²	1	1	yes	characteristic, complemented
91	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic
92	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic
93	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	2	yes	—
94	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	1	yes	characteristic
95	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	1	yes	characteristic
96	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	2	yes	complemented
97	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	2	yes	complemented
98	#16861167	C₂²	1	2	yes	complemented
99	#16861167	C₂²	1	1	yes	characteristic, complemented
100	#16861167	C₂²	1	2	yes	complemented
101	#16861166	C₂²	1	2	yes	—
102	C₂×C₄⋊Dic₁₂₇	C₂²	1	2	yes	complemented
103	C₄⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic
104	C₄⋊C₄×D₁₂₇	C₂²	1	2	yes	complemented
105	C₄⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
106	C₄⋊C₄×D₁₂₇	C₂²	1	2	yes	complemented
107	C₂×(C₂×D₁₂₇)⋊C₄	C₂²	1	2	yes	—
108	C₂²⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic
109	C₂²⋊C₄×D₁₂₇	C₂²	1	1	yes	characteristic
110	C₂²⋊C₄×D₁₂₇	C₂²	1	2	yes	—
111	C₄²×D₁₂₇	C₂²	1	1	yes	characteristic
112	#126×C₁₂₇	C₂²	1	2	yes	complemented
113	#125×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
114	#125×C₁₂₇	C₂²	1	2	yes	complemented
115	#123×C₁₂₇	C₂²	1	2	yes	—
116	C₂²⋊Q₈×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
117	C₂²⋊Q₈×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
118	C₄×Q₈×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₄×C₁₂₇	C₂²	1	1	yes	characteristic
120	#117×C₁₂₇	C₂²	1	2	yes	complemented
121	#117×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₄⋊C₄×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₂₇	C₂³	1	1	yes	characteristic
124	C₂³×D₁₂₇	C₂³	1	1	yes	characteristic
125	#14523249	—	4	2	no	—
126	#14523248	—	2	8	no	—
127	#14523248	—	4	2	no	—
128	C₂×Dic₂₅₄	—	4	2	no	—
129	C₂×Dic₂₅₄	C₂³	1	2	yes	—
130	C₂×Dic₂₅₄	C₂³	1	1	yes	characteristic
131	C₂×Dic₂₅₄	C₂³	1	1	yes	characteristic
132	C₂×Dic₂₅₄	C₂³	1	2	yes	—
133	C₂×Dic₂₅₄	C₂³	1	2	yes	—
134	Q₈×D₁₂₇	—	4	2	no	—
135	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
136	C₂×D₅₀₈	C₂³	1	2	yes	—
137	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
138	C₂×D₅₀₈	C₂³	1	2	yes	—
139	C₂×D₅₀₈	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
142	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
144	D₄×D₁₂₇	—	2	4	no	—
145	C₂²×Dic₁₂₇	C₂³	1	1	yes	characteristic
146	C₂²×Dic₁₂₇	C₂³	1	2	yes	—
147	C₂²×Dic₁₂₇	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₁₂₇	—	4	2	no	—
149	C₂×C₄×D₁₂₇	—	4	2	no	—
150	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
154	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
157	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
158	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
160	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
161	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
162	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
163	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
164	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
165	C₄⋊Dic₁₂₇	C₂³	1	2	yes	—
166	C₄⋊Dic₁₂₇	C₂³	1	2	yes	—
167	C₄⋊Dic₁₂₇	C₂³	1	2	yes	—
168	C₄⋊Dic₁₂₇	C₂³	1	2	yes	—
169	C₄⋊Dic₁₂₇	C₂³	1	2	yes	—
170	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
171	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
172	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
173	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
174	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
175	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
176	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
177	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
178	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
179	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
180	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
181	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	—
183	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
184	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
185	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
186	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
189	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
190	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
191	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
192	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
193	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
194	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
195	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
196	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
197	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
198	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
199	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
200	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
201	C₄×Dic₁₂₇	C₂³	1	2	yes	—
202	C₄×Dic₁₂₇	C₂³	1	2	yes	—
203	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
204	C₄×Dic₁₂₇	C₂³	1	2	yes	—
205	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
206	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
207	C₂×Q₈×C₁₂₇	C₂³	1	1	yes	characteristic
208	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
209	C₂²×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
210	C₂²×C₄×C₁₂₇	C₂³	1	2	yes	—
211	C₂²×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
212	C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	—
213	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
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	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
220	C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	—
221	C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	—
222	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	—
223	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	—
224	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	—
225	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
226	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
227	C₄²×C₁₂₇	C₂³	1	2	yes	—
228	C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
229	C₄²×C₁₂₇	C₂³	1	2	yes	—
230	C₂²×D₁₂₇	—	2	2	no	—
231	C₂²×D₁₂₇	—	2	2	no	—
232	C₂²×D₁₂₇	—	2	2	no	—
233	C₂²×D₁₂₇	—	2	2	no	—
234	C₂²×D₁₂₇	—	4	1	no	—
235	C₂²×D₁₂₇	—	4	1	no	—
236	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
237	C₂²×D₁₂₇	C₂⁴	1	2	yes	—
238	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
239	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
240	Dic₂₅₄	—	2	2	no	—
241	Dic₂₅₄	—	2	2	no	—
242	Dic₂₅₄	—	2	4	no	—
243	Dic₂₅₄	—	4	2	no	—
244	Dic₂₅₄	—	4	2	no	—
245	D₅₀₈	—	2	2	no	—
246	D₅₀₈	—	2	4	no	—
247	D₅₀₈	—	2	4	no	—
248	D₅₀₈	—	2	2	no	—
249	D₅₀₈	—	4	2	no	—
250	C₂²⋊D₁₂₇	—	2	4	no	—
251	C₂²⋊D₁₂₇	—	2	2	no	—
252	C₂²⋊D₁₂₇	—	4	2	no	—
253	C₂²⋊D₁₂₇	#41	1	4	yes	complemented
254	C₂×Dic₁₂₇	—	4	1	no	—
255	C₂×Dic₁₂₇	—	4	1	no	—
256	C₂×Dic₁₂₇	—	4	2	no	—
257	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
258	C₂×Dic₁₂₇	C₂⁴	1	2	yes	—
259	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
260	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
261	C₂×Dic₁₂₇	C₂⁴	1	2	yes	—
262	C₂×Dic₁₂₇	C₂⁴	1	2	yes	—
263	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
264	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
265	C₄×D₁₂₇	—	2	4	no	—
266	C₄×D₁₂₇	—	2	2	no	—
267	C₄×D₁₂₇	—	2	2	no	—
268	C₄×D₁₂₇	—	2	2	no	—
269	C₄×D₁₂₇	—	2	2	no	—
270	C₄×D₁₂₇	—	2	2	no	—
271	C₄×D₁₂₇	—	2	4	no	—
272	C₄×D₁₂₇	—	4	1	no	—
273	C₄×D₁₂₇	—	4	1	no	—
274	C₄×D₁₂₇	—	4	1	no	—
275	C₄×D₁₂₇	—	4	1	no	—
276	C₄×D₁₂₇	—	4	2	no	—
277	C₄×D₁₂₇	—	4	2	no	—
278	C₄×D₁₂₇	—	4	2	no	—
279	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
280	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
281	Q₈×C₁₂₇	—	2	2	no	—
282	D₄×C₁₂₇	—	2	2	no	—
283	C₂×C₄×C₁₂₇	—	2	4	no	—
284	C₂×C₄×C₁₂₇	—	2	2	no	—
285	C₂×C₄×C₁₂₇	—	2	2	no	—
286	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
287	C₂×C₄×C₁₂₇	C₂⁴	1	2	yes	—
288	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
289	C₂×C₄×C₁₂₇	C₂⁴	1	2	yes	—
290	C₂×C₄×C₁₂₇	C₂⁴	1	2	yes	—
291	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
292	C₂×C₄×C₁₂₇	C₂⁴	1	2	yes	—
293	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
294	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
295	C₂²×C₁₂₇	—	2	1	no	—
296	C₂²×C₁₂₇	—	2	1	no	—
297	C₂²×C₁₂₇	—	2	1	no	—
298	C₂²×C₁₂₇	—	2	1	no	—
299	C₂²×C₁₂₇	—	2	1	no	—
300	C₂²×C₁₂₇	C₂×#41	1	2	yes	—
301	C₂²×C₁₂₇	C₂⁵	1	1	yes	characteristic
302	C₂×D₁₂₇	—	2	1	no	—
303	C₂×D₁₂₇	—	2	1	no	—
304	C₂×D₁₂₇	—	2	1	no	—
305	C₂×D₁₂₇	—	2	1	no	—
306	C₂×D₁₂₇	—	2	2	no	—
307	C₂×D₁₂₇	—	2	1	no	—
308	C₂×D₁₂₇	—	2	1	no	—
309	C₂×D₁₂₇	—	2	2	no	—
310	C₂×D₁₂₇	—	2	2	no	—
311	C₂×D₁₂₇	—	2	1	no	—
312	C₂×D₁₂₇	—	4	4	no	—
313	C₂×D₁₂₇	—	4	4	no	—
314	C₂×D₁₂₇	C₂×#41	1	2	yes	—
315	C₂×D₁₂₇	2₋¹⁺⁴	1	2	yes	—
316	C₄×C₁₂₇	—	2	2	no	—
317	C₄×C₁₂₇	—	2	2	no	—
318	C₄×C₁₂₇	—	2	1	no	—
319	C₄×C₁₂₇	—	2	1	no	—
320	C₄×C₁₂₇	—	2	1	no	—
321	C₄×C₁₂₇	—	2	2	no	—
322	C₄×C₁₂₇	—	2	1	no	—
323	C₄×C₁₂₇	—	2	2	no	—
324	C₄×C₁₂₇	H(5,𝔽₂)	1	2	yes	—
325	Dic₁₂₇	—	2	2	no	—
326	Dic₁₂₇	—	2	1	no	—
327	Dic₁₂₇	—	2	1	no	—
328	Dic₁₂₇	—	2	1	no	—
329	Dic₁₂₇	—	2	2	no	—
330	Dic₁₂₇	—	2	2	no	—
331	Dic₁₂₇	—	2	1	no	—
332	Dic₁₂₇	C₂×#41	1	2	yes	—
333	C₂×C₁₂₇	—	2	2	no	—
334	C₂×C₁₂₇	—	4	1	no	—
335	C₂×C₁₂₇	C₂²×#41	1	1	yes	characteristic
336	C₂×C₁₂₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
337	C₂×C₁₂₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
338	D₁₂₇	—	2	2	no	—
339	D₁₂₇	—	2	2	no	—
340	D₁₂₇	—	4	2	no	—
341	D₁₂₇	—	4	1	no	—
342	#3520	—	127	1	no	maximal, Sylow
343	C₁₂₇	#3520	1	1	yes	characteristic, complemented, Sylow
344	#556	—	127	1	no	—
345	#554	—	127	2	no	—
346	#552	—	127	1	no	—
347	#552	D₁₂₇	1	1	yes	characteristic, complemented
348	#551	—	127	2	no	—
349	#551	—	127	2	no	—
350	D₄×Q₈	—	127	1	no	—
351	#548	—	127	1	no	—
352	#548	—	127	1	no	—
353	#547	—	127	1	no	—
354	#547	—	127	1	no	—
355	#546	—	127	2	no	—
356	#542	—	127	2	no	—
357	#539	—	127	2	no	—
358	#539	—	127	2	no	—
359	#533	—	127	1	no	—
360	#529	—	127	1	no	—
361	#525	—	127	1	no	—
362	#525	—	127	1	no	—
363	C₂×C₂²⋊Q₈	—	127	1	no	—
364	C₂×C₂²⋊Q₈	—	127	1	no	—
365	#520	—	127	2	no	—
366	C₂×C₄×D₄	—	127	1	no	—
367	C₂×#41	—	127	1	no	—
368	C₂×#41	—	127	1	no	—
369	C₂×#41	—	127	2	no	—
370	C₂²×Q₈	—	127	1	no	—
371	C₂²×Q₈	—	127	1	no	—
372	C₂²×D₄	—	127	1	no	—
373	C₂³×C₄	—	127	1	no	—
374	C₂³×C₄	—	127	1	no	—
375	C₄⋊Q₈	—	127	1	no	—
376	C₄⋊Q₈	—	127	1	no	—
377	C₄⋊Q₈	—	127	2	no	—
378	#126	—	127	2	no	—
379	#126	—	127	2	no	—
380	#126	—	127	2	no	—
381	#126	—	127	2	no	—
382	#126	C₂×D₁₂₇	1	2	yes	complemented
383	#125	—	127	2	no	—
384	#125	—	127	2	no	—
385	#125	C₂×D₁₂₇	1	1	yes	characteristic, complemented
386	#125	C₂×D₁₂₇	1	2	yes	complemented
387	#124	—	127	2	no	—
388	#124	—	127	2	no	—
389	#124	—	127	1	no	—
390	#124	—	127	2	no	—
391	#123	—	127	2	no	—
392	#123	—	127	2	no	—
393	#123	—	127	2	no	—
394	#123	—	127	2	no	—
395	#123	—	127	2	no	—
396	#123	—	127	2	no	—
397	#123	—	127	2	no	—
398	#123	—	127	2	no	—
399	#123	C₂×D₁₂₇	1	2	yes	—
400	C₂²⋊Q₈	—	127	1	no	—
401	C₂²⋊Q₈	—	127	1	no	—
402	C₂²⋊Q₈	—	127	2	no	—
403	C₂²⋊Q₈	—	127	2	no	—
404	C₂²⋊Q₈	—	127	2	no	—
405	C₂²⋊Q₈	—	127	2	no	—
406	C₂²⋊Q₈	—	127	2	no	—
407	C₂²⋊Q₈	—	127	1	no	—
408	C₂²⋊Q₈	—	127	1	no	—
409	C₂²⋊Q₈	—	127	2	no	—
410	C₂²⋊Q₈	—	127	2	no	—
411	C₂²⋊Q₈	—	127	1	no	—
412	C₂²⋊Q₈	—	127	1	no	—
413	C₂²⋊Q₈	—	127	1	no	—
414	C₂²⋊Q₈	—	127	2	no	—
415	C₂²⋊Q₈	—	127	2	no	—
416	C₂²⋊Q₈	—	127	2	no	—
417	C₂²⋊Q₈	C₂×D₁₂₇	1	1	yes	characteristic, complemented
418	C₂²⋊Q₈	C₂×D₁₂₇	1	1	yes	characteristic, complemented
419	#121	—	127	2	no	—
420	#121	—	127	1	no	—
421	#121	—	127	1	no	—
422	#121	—	127	2	no	—
423	#121	—	127	1	no	—
424	#121	—	127	2	no	—
425	#120	—	127	2	no	—
426	#120	—	127	2	no	—
427	C₄×Q₈	—	127	1	no	—
428	C₄×Q₈	—	127	2	no	—
429	C₄×Q₈	—	127	2	no	—
430	C₄×Q₈	—	127	1	no	—
431	C₄×Q₈	C₂×D₁₂₇	1	1	yes	characteristic, complemented
432	C₄×D₄	—	127	1	no	—
433	C₄×D₄	—	127	1	no	—
434	C₄×D₄	—	127	1	no	—
435	C₄×D₄	—	127	1	no	—
436	C₄×D₄	—	127	2	no	—
437	C₄×D₄	—	127	2	no	—
438	C₄×D₄	—	127	1	no	—
439	C₄×D₄	—	127	1	no	—
440	C₄×D₄	—	127	1	no	—
441	C₄×D₄	—	127	2	no	—
442	C₄×D₄	—	127	2	no	—
443	C₄×D₄	—	127	2	no	—
444	C₄×D₄	—	127	1	no	—
445	C₄×D₄	—	127	2	no	—
446	C₄×D₄	—	127	2	no	—
447	C₄×D₄	—	127	2	no	—
448	C₄×D₄	C₂×D₁₂₇	1	1	yes	characteristic
449	#117	—	127	2	no	—
450	#117	—	127	2	no	—
451	#117	—	127	1	no	—
452	#117	—	127	2	no	—
453	#117	C₂×D₁₂₇	1	2	yes	complemented
454	#117	C₂×D₁₂₇	1	1	yes	characteristic, complemented
455	C₂×C₄⋊C₄	—	127	2	no	—
456	C₂×C₄⋊C₄	—	127	1	no	—
457	C₂×C₄⋊C₄	—	127	2	no	—
458	C₂×C₄⋊C₄	—	127	2	no	—
459	C₂×C₄⋊C₄	—	127	1	no	—
460	C₂×C₄⋊C₄	C₂×D₁₂₇	1	1	yes	characteristic, complemented
461	C₂×C₂²⋊C₄	—	127	2	no	—
462	C₂×C₂²⋊C₄	—	127	1	no	—
463	C₂×C₂²⋊C₄	—	127	1	no	—
464	C₂×C₂²⋊C₄	—	127	2	no	—
465	C₂×C₄²	—	127	1	no	—
466	C₂⁴	—	127	1	no	—
467	C₂⁴	—	127	1	no	—
468	#41	—	508	2	no	—
469	#41	—	508	2	no	—
470	#41	—	254	8	no	—
471	C₂×Q₈	—	127	2	no	—
472	C₂×Q₈	—	127	2	no	—
473	C₂×Q₈	—	127	2	no	—
474	C₂×Q₈	—	127	1	no	—
475	C₂×Q₈	—	127	1	no	—
476	C₂×Q₈	—	508	2	no	—
477	C₂×Q₈	—	508	2	no	—
478	C₂×Q₈	C₂²×D₁₂₇	1	1	yes	characteristic
479	C₂×D₄	—	127	1	no	—
480	C₂×D₄	—	127	2	no	—
481	C₂×D₄	—	127	2	no	—
482	C₂×D₄	—	127	1	no	—
483	C₂×D₄	—	127	2	no	—
484	C₂×D₄	—	127	2	no	—
485	C₂×D₄	—	127	2	no	—
486	C₂×D₄	—	127	1	no	—
487	C₂×D₄	—	127	1	no	—
488	C₂×D₄	—	254	4	no	—
489	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
490	C₂²×C₄	—	127	2	no	—
491	C₂²×C₄	—	127	1	no	—
492	C₂²×C₄	—	127	1	no	—
493	C₂²×C₄	—	127	2	no	—
494	C₂²×C₄	—	127	1	no	—
495	C₂²×C₄	—	127	1	no	—
496	C₂²×C₄	—	127	1	no	—
497	C₂²×C₄	—	127	2	no	—
498	C₂²×C₄	—	127	2	no	—
499	C₂²×C₄	—	127	1	no	—
500	C₂²×C₄	—	127	1	no	—
501	C₂²×C₄	—	127	1	no	—
502	C₂²×C₄	—	127	1	no	—
503	C₂²×C₄	—	127	2	no	—
504	C₂²×C₄	—	127	2	no	—
505	C₂²×C₄	—	127	1	no	—
506	C₂²×C₄	—	127	1	no	—
507	C₂²×C₄	—	508	2	no	—
508	C₂²×C₄	—	508	2	no	—
509	C₂²×C₄	C₂²×D₁₂₇	1	2	yes	—
510	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
511	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
512	C₄⋊C₄	—	127	1	no	—
513	C₄⋊C₄	—	127	1	no	—
514	C₄⋊C₄	—	127	2	no	—
515	C₄⋊C₄	—	127	2	no	—
516	C₄⋊C₄	—	127	2	no	—
517	C₄⋊C₄	—	127	2	no	—
518	C₄⋊C₄	—	127	2	no	—
519	C₄⋊C₄	—	127	2	no	—
520	C₄⋊C₄	—	127	2	no	—
521	C₄⋊C₄	—	127	2	no	—
522	C₄⋊C₄	—	127	2	no	—
523	C₄⋊C₄	—	127	2	no	—
524	C₄⋊C₄	—	127	1	no	—
525	C₄⋊C₄	—	127	1	no	—
526	C₄⋊C₄	—	127	2	no	—
527	C₄⋊C₄	—	127	2	no	—
528	C₄⋊C₄	—	127	2	no	—
529	C₄⋊C₄	C₂²×D₁₂₇	1	2	yes	—
530	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
531	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
532	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
533	C₄⋊C₄	C₂²×D₁₂₇	1	2	yes	—
534	C₄⋊C₄	C₂²×D₁₂₇	1	2	yes	—
535	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
536	C₄⋊C₄	C₂²×D₁₂₇	1	2	yes	—
537	C₄⋊C₄	C₂²×D₁₂₇	1	2	yes	—
538	C₄⋊C₄	C₂²×D₁₂₇	1	2	yes	—
539	C₂²⋊C₄	—	127	1	no	—
540	C₂²⋊C₄	—	127	1	no	—
541	C₂²⋊C₄	—	127	2	no	—
542	C₂²⋊C₄	—	127	2	no	—
543	C₂²⋊C₄	—	127	1	no	—
544	C₂²⋊C₄	—	127	2	no	—
545	C₂²⋊C₄	—	127	2	no	—
546	C₂²⋊C₄	—	127	1	no	—
547	C₂²⋊C₄	—	127	1	no	—
548	C₂²⋊C₄	—	127	1	no	—
549	C₂²⋊C₄	—	127	2	no	—
550	C₂²⋊C₄	—	127	2	no	—
551	C₂²⋊C₄	—	127	2	no	—
552	C₂²⋊C₄	—	127	2	no	—
553	C₂²⋊C₄	—	127	2	no	—
554	C₂²⋊C₄	—	127	2	no	—
555	C₂²⋊C₄	—	127	2	no	—
556	C₂²⋊C₄	—	127	2	no	—
557	C₂²⋊C₄	—	127	2	no	—
558	C₂²⋊C₄	—	127	2	no	—
559	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
560	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
561	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	—
562	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	—
563	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	—
564	C₄²	—	127	1	no	—
565	C₄²	—	127	1	no	—
566	C₄²	—	127	1	no	—
567	C₄²	—	127	2	no	—
568	C₄²	—	127	2	no	—
569	C₄²	—	127	2	no	—
570	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic
571	C₄²	C₂²×D₁₂₇	1	2	yes	—
572	C₄²	C₂²×D₁₂₇	1	2	yes	—
573	C₂³	—	127	1	no	—
574	C₂³	—	127	1	no	—
575	C₂³	—	127	1	no	—
576	C₂³	—	127	2	no	—
577	C₂³	—	508	1	no	—
578	C₂³	—	508	1	no	—
579	C₂³	—	254	2	no	—
580	C₂³	—	254	2	no	—
581	C₂³	—	254	2	no	—
582	C₂³	—	254	2	no	—
583	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
584	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
585	Q₈	—	2	2	no	—
586	Q₈	—	508	2	no	—
587	Q₈	—	508	2	no	—
588	Q₈	—	254	4	no	—
589	Q₈	—	254	2	no	—
590	Q₈	—	254	2	no	—
591	D₄	—	2	2	no	—
592	D₄	—	127	4	no	—
593	D₄	—	508	2	no	—
594	D₄	—	508	2	no	—
595	D₄	—	254	2	no	—
596	D₄	—	254	4	no	—
597	D₄	—	254	4	no	—
598	D₄	—	254	2	no	—
599	D₄	—	254	4	no	—
600	D₄	—	254	2	no	—
601	C₂×C₄	—	2	4	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	127	1	no	—
605	C₂×C₄	—	127	1	no	—
606	C₂×C₄	—	127	2	no	—
607	C₂×C₄	—	127	1	no	—
608	C₂×C₄	—	127	1	no	—
609	C₂×C₄	—	127	2	no	—
610	C₂×C₄	—	127	2	no	—
611	C₂×C₄	—	127	1	no	—
612	C₂×C₄	—	508	1	no	—
613	C₂×C₄	—	508	1	no	—
614	C₂×C₄	—	508	1	no	—
615	C₂×C₄	—	508	1	no	—
616	C₂×C₄	—	508	2	no	—
617	C₂×C₄	—	508	2	no	—
618	C₂×C₄	—	508	2	no	—
619	C₂×C₄	—	508	1	no	—
620	C₂×C₄	—	508	1	no	—
621	C₂×C₄	—	508	2	no	—
622	C₂×C₄	—	254	2	no	—
623	C₂×C₄	—	254	4	no	—
624	C₂×C₄	—	254	4	no	—
625	C₂×C₄	—	254	2	no	—
626	C₂×C₄	—	254	2	no	—
627	C₂×C₄	—	254	2	no	—
628	C₂×C₄	—	254	2	no	—
629	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
630	C₂×C₄	C₂³×D₁₂₇	1	2	yes	—
631	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
632	C₂×C₄	C₂³×D₁₂₇	1	2	yes	—
633	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
634	C₂×C₄	C₂³×D₁₂₇	1	2	yes	—
635	C₂×C₄	C₂³×D₁₂₇	1	2	yes	—
636	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
637	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
638	C₂²	—	2	1	no	—
639	C₂²	—	2	1	no	—
640	C₂²	—	2	1	no	—
641	C₂²	—	2	1	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	127	2	no	—
644	C₂²	—	127	2	no	—
645	C₂²	—	508	4	no	—
646	C₂²	—	508	4	no	—
647	C₂²	—	254	2	no	—
648	C₂²	—	254	1	no	—
649	C₂²	—	254	2	no	—
650	C₂²	—	254	1	no	—
651	C₂²	—	254	2	no	—
652	C₂²	—	254	1	no	—
653	C₂²	—	254	1	no	—
654	C₂²	—	254	1	no	—
655	C₂²	—	254	1	no	—
656	C₂²	—	254	1	no	—
657	C₂²	#41×D₁₂₇	1	2	yes	—
658	C₂²	C₂⁴×D₁₂₇	1	1	yes	characteristic
659	C₄	—	2	2	no	—
660	C₄	—	2	2	no	—
661	C₄	—	2	1	no	—
662	C₄	—	2	1	no	—
663	C₄	—	2	1	no	—
664	C₄	—	2	2	no	—
665	C₄	—	2	1	no	—
666	C₄	—	2	2	no	—
667	C₄	—	127	2	no	—
668	C₄	—	254	2	no	—
669	C₄	—	254	1	no	—
670	C₄	—	254	1	no	—
671	C₄	—	254	1	no	—
672	C₄	—	254	2	no	—
673	C₄	—	254	2	no	—
674	C₄	—	254	1	no	—
675	C₄	#16861255	1	2	yes	—
676	C₂	—	2	2	no	—
677	C₂	—	4	1	no	—
678	C₂	—	508	1	no	—
679	C₂	—	508	2	no	—
680	C₂	—	254	2	no	—
681	C₂	—	254	2	no	—
682	C₂	C₂×#41×D₁₂₇	1	1	yes	characteristic
683	C₂	C₂×#16861255	1	1	yes	characteristic
684	C₂	2₋¹⁺⁴×D₁₂₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₂₇
commutator, socle, cosocle	C₂²×C₁₂₇	C₂⁵
Fitting	#552×C₁₂₇	C₂
hypercenter	#552	D₁₂₇
hypocenter	C₁₂₇	#3520
LCS	G ▷ C₂²×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₂² ◁ #552

Complements

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

N	H ≅ G/N	type
1. #22550594	C₂	semidirect
2. #22550582	C₂	semidirect
3. #22550564	C₂	semidirect
4. #22550551	C₂	semidirect
5. #22550550	C₂	semidirect
6. #22550539	C₂	semidirect
7. #22550538	C₂	semidirect
8. #22550535	C₂	semidirect
9. #22550528	C₂	semidirect
10. #22550527	C₂	semidirect
11. #22550518	C₂	semidirect
12. #22550492	C₂	semidirect
13. #22550474	C₂	semidirect
14. #22550470	C₂	semidirect
15. #22550430	C₂	semidirect
16. #22550411	C₂	semidirect
17. #22550389	C₂	semidirect
18. #22550388	C₂	semidirect
19. C₂×#16861189	C₂	semidirect
20. C₂²⋊Q₈×D₁₂₇	C₂	semidirect
21. #22550356	C₂	semidirect
22. C₄×D₄×D₁₂₇	C₂	semidirect
23. #552×C₁₂₇	C₂	semidirect
24. C₂×#14523249	C₂²	semidirect
26. C₂×#14523248	C₂²	semidirect
27. C₂²×Dic₂₅₄	C₂²	semidirect
28. C₂×Q₈×D₁₂₇	C₂²	semidirect
32. #16861208	C₂²	semidirect
33. #16861208	C₂²	semidirect
34. #16861207	C₂²	semidirect
35. #16861204	C₂²	semidirect
36. #16861204	C₂²	semidirect
37. #16861203	C₂²	semidirect
38. #16861202	C₂²	semidirect
39. #16861200	C₂²	semidirect
40. #16861199	C₂²	semidirect
41. #16861197	C₂²	semidirect
42. #16861197	C₂²	semidirect
44. #16861195	C₂²	semidirect
47. #16861194	C₂²	semidirect
48. #16861194	C₂²	semidirect
49. #16861194	C₂²	semidirect
50. #16861193	C₂²	semidirect
51. #16861192	C₂²	semidirect
52. #16861191	C₂²	semidirect
56. #16861189	C₂²	semidirect
57. #16861189	C₂²	semidirect
58. #16861189	C₂²	semidirect
59. #16861189	C₂²	semidirect
60. #16861189	C₂²	semidirect
61. #16861188	C₂²	semidirect
64. #16861187	C₂²	semidirect
65. #16861187	C₂²	semidirect
66. #16861187	C₂²	semidirect
67. #16861186	C₂²	semidirect
68. #16861186	C₂²	semidirect
72. #16861184	C₂²	semidirect
73. #16861183	C₂²	semidirect
78. C₄×Dic₂₅₄	C₂²	semidirect
79. C₄×Dic₂₅₄	C₂²	semidirect
80. C₄×Dic₂₅₄	C₂²	semidirect
81. #16861174	C₂²	semidirect
84. C₄×D₅₀₈	C₂²	semidirect
85. C₄×D₅₀₈	C₂²	semidirect
90. #16861171	C₂²	semidirect
96. (C₂²⋊D₁₂₇)⋊C₄	C₂²	semidirect
97. (C₂²⋊D₁₂₇)⋊C₄	C₂²	semidirect
98. #16861167	C₂²	semidirect
99. #16861167	C₂²	semidirect
100. #16861167	C₂²	semidirect
102. C₂×C₄⋊Dic₁₂₇	C₂²	semidirect
104. C₄⋊C₄×D₁₂₇	C₂²	semidirect
105. C₄⋊C₄×D₁₂₇	C₂²	semidirect
106. C₄⋊C₄×D₁₂₇	C₂²	semidirect
112. #126×C₁₂₇	C₂²	semidirect
113. #125×C₁₂₇	C₂²	semidirect
114. #125×C₁₂₇	C₂²	semidirect
116. C₂²⋊Q₈×C₁₂₇	C₂²	semidirect
117. C₂²⋊Q₈×C₁₂₇	C₂²	semidirect
118. C₄×Q₈×C₁₂₇	C₂²	semidirect
120. #117×C₁₂₇	C₂²	semidirect
121. #117×C₁₂₇	C₂²	semidirect
122. C₂×C₄⋊C₄×C₁₂₇	C₂²	semidirect
253. C₂²⋊D₁₂₇	#41	semidirect
343. C₁₂₇	#3520	semidirect
347. #552	D₁₂₇	semidirect
382. #126	C₂×D₁₂₇	semidirect
385. #125	C₂×D₁₂₇	semidirect
386. #125	C₂×D₁₂₇	semidirect
417. C₂²⋊Q₈	C₂×D₁₂₇	semidirect
418. C₂²⋊Q₈	C₂×D₁₂₇	semidirect
431. C₄×Q₈	C₂×D₁₂₇	semidirect
453. #117	C₂×D₁₂₇	semidirect
454. #117	C₂×D₁₂₇	semidirect
460. 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
#22550594	2
#22550582	2
#22550564	2
#22550551	2
#22550550	2
#22550539	2
#22550538	2
#22550535	2
#22550528	2
#22550527	2
#22550518	2
#22550492	2
#22550474	2
#22550470	2
#22550430	2
#22550411	2
#22550389	2
#22550388	2
C₂×#16861189	2
C₂²⋊Q₈×D₁₂₇	2
#22550356	2
C₄×D₄×D₁₂₇	2
#552×C₁₂₇	2
#3520	127