Subgroups — #30652775

Order 16256.

1124 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22550598	C₂	1	1	yes	maximal, characteristic, complemented
2	#22550581	C₂	1	1	yes	maximal, characteristic, complemented
3	#22550558	C₂	1	2	yes	maximal, complemented
4	#22550555	C₂	1	2	yes	maximal, complemented
5	#22550553	C₂	1	2	yes	maximal, complemented
6	#22550541	C₂	1	1	yes	maximal, characteristic, complemented
7	#22550536	C₂	1	2	yes	maximal, complemented
8	#22550528	C₂	1	1	yes	maximal, characteristic, complemented
9	#22550527	C₂	1	1	yes	maximal, characteristic, complemented
10	#22550522	C₂	1	1	yes	maximal, characteristic, complemented
11	#22550517	C₂	1	1	yes	maximal, characteristic, complemented
12	#22550500	C₂	1	1	yes	maximal, characteristic, complemented
13	#22550499	C₂	1	1	yes	maximal, characteristic, complemented
14	#22550474	C₂	1	2	yes	maximal, complemented
15	#22550472	C₂	1	2	yes	maximal, complemented
16	#22550428	C₂	1	1	yes	maximal, characteristic, complemented
17	#22550406	C₂	1	1	yes	maximal, characteristic, complemented
18	#22550385	C₂	1	2	yes	maximal, complemented
19	C₂²⋊Q₈×D₁₂₇	C₂	1	2	yes	maximal, complemented
20	#22550358	C₂	1	1	yes	maximal, characteristic, complemented
21	#22550357	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#16861171	C₂	1	1	yes	maximal, characteristic, complemented
23	#554×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14523249	C₂²	1	1	yes	characteristic
25	C₂×#14523248	C₂²	1	1	yes	characteristic
26	C₂×#14523248	C₂²	1	2	yes	complemented
27	C₂×Q₈×D₁₂₇	C₂²	1	2	yes	complemented
28	C₂²×D₅₀₈	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₁₂₇	C₂²	1	2	yes	—
30	#16861208	C₂²	1	1	yes	characteristic, complemented
31	#16861208	C₂²	1	1	yes	characteristic, complemented
32	#16861207	C₂²	1	1	yes	characteristic, complemented
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	1	yes	characteristic, complemented
37	#16861203	C₂²	1	2	yes	complemented
38	#16861202	C₂²	1	1	yes	characteristic, complemented
39	#16861199	C₂²	1	1	yes	characteristic, complemented
40	#16861199	C₂²	1	2	yes	complemented
41	#16861199	C₂²	1	2	yes	complemented
42	#16861198	C₂²	1	1	yes	characteristic
43	#16861198	C₂²	1	2	yes	complemented
44	#16861197	C₂²	1	1	yes	characteristic
45	#16861195	C₂²	1	1	yes	characteristic, complemented
46	#16861195	C₂²	1	2	yes	complemented
47	#16861194	C₂²	1	2	yes	—
48	#16861194	C₂²	1	2	yes	—
49	#16861194	C₂²	1	2	yes	complemented
50	#16861194	C₂²	1	2	yes	complemented
51	#16861194	C₂²	1	2	yes	complemented
52	#16861193	C₂²	1	1	yes	characteristic
53	#16861192	C₂²	1	2	yes	complemented
54	#16861191	C₂²	1	2	yes	complemented
55	#16861191	C₂²	1	2	yes	complemented
56	#16861190	C₂²	1	1	yes	characteristic
57	#16861189	C₂²	1	1	yes	characteristic, complemented
58	#16861189	C₂²	1	2	yes	complemented
59	#16861188	C₂²	1	2	yes	—
60	#16861188	C₂²	1	1	yes	characteristic
61	#16861187	C₂²	1	2	yes	complemented
62	#16861187	C₂²	1	2	yes	complemented
63	#16861187	C₂²	1	2	yes	complemented
64	#16861187	C₂²	1	2	yes	complemented
65	#16861187	C₂²	1	2	yes	complemented
66	#16861186	C₂²	1	1	yes	characteristic
67	#16861186	C₂²	1	2	yes	—
68	#16861185	C₂²	1	2	yes	complemented
69	#16861185	C₂²	1	2	yes	complemented
70	#16861184	C₂²	1	2	yes	—
71	#16861184	C₂²	1	1	yes	characteristic
72	#16861183	C₂²	1	1	yes	characteristic
73	#16861182	C₂²	1	2	yes	—
74	#16861182	C₂²	1	2	yes	complemented
75	#16861181	C₂²	1	1	yes	characteristic
76	#16861179	C₂²	1	2	yes	—
77	#16861177	C₂²	1	2	yes	—
78	Q₈×Dic₁₂₇	C₂²	1	1	yes	characteristic, complemented
79	C₄×Dic₂₅₄	C₂²	1	1	yes	characteristic, complemented
80	#16861174	C₂²	1	2	yes	complemented
81	#16861174	C₂²	1	1	yes	characteristic, complemented
82	#16861174	C₂²	1	1	yes	characteristic, complemented
83	C₄×D₅₀₈	C₂²	1	1	yes	characteristic
84	C₄×D₅₀₈	C₂²	1	2	yes	complemented
85	#16861171	C₂²	1	1	yes	characteristic
86	#16861171	C₂²	1	2	yes	—
87	#16861171	C₂²	1	1	yes	characteristic
88	#16861171	C₂²	1	1	yes	characteristic
89	#16861171	C₂²	1	1	yes	characteristic
90	#16861171	C₂²	1	2	yes	—
91	#16861171	C₂²	1	1	yes	characteristic
92	#16861171	C₂²	1	2	yes	complemented
93	C₄×C₂²⋊D₁₂₇	C₂²	1	2	yes	—
94	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic
95	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic, complemented
96	C₄×C₂²⋊D₁₂₇	C₂²	1	2	yes	complemented
97	C₄×C₂²⋊D₁₂₇	C₂²	1	2	yes	complemented
98	#16861168	C₂²	1	1	yes	characteristic, complemented
99	#16861167	C₂²	1	2	yes	complemented
100	#16861166	C₂²	1	2	yes	complemented
101	#16861166	C₂²	1	2	yes	complemented
102	#16861166	C₂²	1	1	yes	characteristic, complemented
103	#16861165	C₂²	1	2	yes	—
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	C₄⋊C₄×D₁₂₇	C₂²	1	2	yes	complemented
108	C₂×(C₂×D₁₂₇)⋊C₄	C₂²	1	2	yes	—
109	C₂²⋊C₄×D₁₂₇	C₂²	1	2	yes	—
110	C₂²⋊C₄×D₁₂₇	C₂²	1	2	yes	—
111	C₂×C₄×Dic₁₂₇	C₂²	1	1	yes	characteristic
112	C₄⋊Q₈×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
113	#125×C₁₂₇	C₂²	1	2	yes	complemented
114	C₂²⋊Q₈×C₁₂₇	C₂²	1	2	yes	—
115	C₂²⋊Q₈×C₁₂₇	C₂²	1	1	yes	characteristic
116	C₂²⋊Q₈×C₁₂₇	C₂²	1	1	yes	characteristic, 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	2	yes	—
120	C₄×D₄×C₁₂₇	C₂²	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₁₂₇	C₂²	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₂₇	C₂³	1	2	yes	—
124	#14523249	—	2	4	no	—
125	#14523248	—	2	4	no	—
126	#14523248	—	4	4	no	—
127	C₂×Dic₂₅₄	C₂³	1	1	yes	characteristic
128	C₂×Dic₂₅₄	C₂³	1	2	yes	—
129	C₂×Dic₂₅₄	C₂³	1	1	yes	characteristic
130	C₂×Dic₂₅₄	C₂³	1	2	yes	—
131	Q₈×D₁₂₇	—	4	4	no	—
132	C₂×D₅₀₈	—	2	4	no	—
133	C₂×D₅₀₈	C₂³	1	2	yes	—
134	C₂×D₅₀₈	C₂³	1	2	yes	—
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×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
142	C₂²×Dic₁₂₇	C₂³	1	1	yes	characteristic
143	C₂²×Dic₁₂₇	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₁₂₇	—	4	4	no	—
145	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
147	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
148	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
149	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
150	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
151	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
152	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
153	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
154	C₂×C₄×D₁₂₇	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	2	yes	—
159	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
160	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
161	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
162	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
163	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
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	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
169	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
170	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
171	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
172	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
173	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
174	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic
175	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	—
177	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
178	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
179	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
180	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
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	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	1	yes	characteristic
192	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
193	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
194	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
195	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
196	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
197	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
198	C₄×Dic₁₂₇	C₂³	1	2	yes	—
199	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
200	C₄×Dic₁₂₇	C₂³	1	2	yes	—
201	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
202	C₄×Dic₁₂₇	C₂³	1	2	yes	—
203	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
204	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic
205	C₂×Q₈×C₁₂₇	C₂³	1	1	yes	characteristic
206	C₂×Q₈×C₁₂₇	C₂³	1	2	yes	—
207	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
208	C₂²×C₄×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	2	yes	—
212	C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	—
213	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
214	C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	—
215	C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	—
216	C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	—
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	1	yes	characteristic
221	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
222	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
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	C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
227	C₄²×C₁₂₇	C₂³	1	2	yes	—
228	C₂²×D₁₂₇	—	2	4	no	—
229	C₂²×D₁₂₇	—	2	4	no	—
230	C₂²×D₁₂₇	—	4	2	no	—
231	C₂²×D₁₂₇	C₂⁴	1	2	yes	—
232	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
233	C₂²×D₁₂₇	C₂⁴	1	2	yes	—
234	Dic₂₅₄	—	2	2	no	—
235	Dic₂₅₄	—	2	2	no	—
236	Dic₂₅₄	—	2	4	no	—
237	Dic₂₅₄	—	4	2	no	—
238	D₅₀₈	—	2	4	no	—
239	D₅₀₈	—	2	4	no	—
240	D₅₀₈	—	2	2	no	—
241	D₅₀₈	—	4	2	no	—
242	D₅₀₈	#41	1	4	yes	complemented
243	C₂²⋊D₁₂₇	—	2	2	no	—
244	C₂²⋊D₁₂₇	—	2	4	no	—
245	C₂²⋊D₁₂₇	—	2	2	no	—
246	C₂²⋊D₁₂₇	—	4	2	no	—
247	C₂×Dic₁₂₇	—	2	2	no	—
248	C₂×Dic₁₂₇	—	2	2	no	—
249	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
250	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
251	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
252	C₂×Dic₁₂₇	C₂⁴	1	2	yes	—
253	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
254	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
255	C₂×Dic₁₂₇	C₂⁴	1	2	yes	—
256	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
257	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
258	C₄×D₁₂₇	—	2	4	no	—
259	C₄×D₁₂₇	—	2	4	no	—
260	C₄×D₁₂₇	—	2	2	no	—
261	C₄×D₁₂₇	—	2	4	no	—
262	C₄×D₁₂₇	—	2	4	no	—
263	C₄×D₁₂₇	—	4	2	no	—
264	C₄×D₁₂₇	—	4	2	no	—
265	C₄×D₁₂₇	—	4	2	no	—
266	C₄×D₁₂₇	—	4	2	no	—
267	C₄×D₁₂₇	—	4	2	no	—
268	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
269	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
270	Q₈×C₁₂₇	—	2	2	no	—
271	Q₈×C₁₂₇	—	4	2	no	—
272	D₄×C₁₂₇	—	2	2	no	—
273	C₂×C₄×C₁₂₇	—	2	2	no	—
274	C₂×C₄×C₁₂₇	—	2	2	no	—
275	C₂×C₄×C₁₂₇	—	4	2	no	—
276	C₂×C₄×C₁₂₇	—	4	2	no	—
277	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
278	C₂×C₄×C₁₂₇	C₂⁴	1	2	yes	—
279	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
280	C₂×C₄×C₁₂₇	C₂⁴	1	2	yes	—
281	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
282	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
283	C₂×C₄×C₁₂₇	C₂⁴	1	2	yes	—
284	C₂×C₄×C₁₂₇	C₂⁴	1	2	yes	—
285	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
286	C₂²×C₁₂₇	—	2	1	no	—
287	C₂²×C₁₂₇	—	2	1	no	—
288	C₂²×C₁₂₇	—	2	1	no	—
289	C₂²×C₁₂₇	—	2	1	no	—
290	C₂²×C₁₂₇	—	2	1	no	—
291	C₂²×C₁₂₇	2₋¹⁺⁴	1	2	yes	—
292	C₂²×C₁₂₇	C₂⁵	1	1	yes	characteristic
293	C₂×D₁₂₇	—	2	2	no	—
294	C₂×D₁₂₇	—	2	2	no	—
295	C₂×D₁₂₇	—	2	1	no	—
296	C₂×D₁₂₇	—	2	2	no	—
297	C₂×D₁₂₇	—	2	2	no	—
298	C₂×D₁₂₇	—	2	1	no	—
299	C₂×D₁₂₇	—	2	1	no	—
300	C₂×D₁₂₇	—	2	2	no	—
301	C₂×D₁₂₇	—	4	8	no	—
302	C₂×D₁₂₇	C₂×#41	1	4	yes	—
303	C₄×C₁₂₇	—	2	1	no	—
304	C₄×C₁₂₇	—	2	1	no	—
305	C₄×C₁₂₇	—	2	2	no	—
306	C₄×C₁₂₇	—	2	2	no	—
307	C₄×C₁₂₇	—	2	2	no	—
308	C₄×C₁₂₇	—	2	2	no	—
309	C₄×C₁₂₇	—	2	1	no	—
310	C₄×C₁₂₇	—	2	1	no	—
311	C₄×C₁₂₇	C₂×#41	1	2	yes	—
312	Dic₁₂₇	—	2	1	no	—
313	Dic₁₂₇	—	2	2	no	—
314	Dic₁₂₇	—	2	1	no	—
315	Dic₁₂₇	—	2	2	no	—
316	Dic₁₂₇	—	2	1	no	—
317	Dic₁₂₇	—	2	1	no	—
318	Dic₁₂₇	—	2	1	no	—
319	Dic₁₂₇	—	2	1	no	—
320	Dic₁₂₇	H(5,𝔽₂)	1	2	yes	—
321	C₂×C₁₂₇	—	2	2	no	—
322	C₂×C₁₂₇	—	4	1	no	—
323	C₂×C₁₂₇	C₂²×#41	1	1	yes	characteristic
324	C₂×C₁₂₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
325	C₂×C₁₂₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
326	D₁₂₇	—	2	4	no	—
327	D₁₂₇	—	4	1	no	—
328	D₁₂₇	—	4	2	no	—
329	#3520	—	127	1	no	maximal, Sylow
330	C₁₂₇	#3520	1	1	yes	characteristic, complemented, Sylow
331	#556	—	127	1	no	—
332	#554	—	127	1	no	—
333	#554	D₁₂₇	1	1	yes	characteristic, complemented
334	#552	—	127	2	no	—
335	#551	—	127	2	no	—
336	#551	—	127	2	no	—
337	D₄×Q₈	—	127	1	no	—
338	#548	—	127	2	no	—
339	#547	—	127	1	no	—
340	#547	—	127	1	no	—
341	#546	—	127	1	no	—
342	#546	—	127	1	no	—
343	#542	—	127	1	no	—
344	#542	—	127	1	no	—
345	#539	—	127	2	no	—
346	#539	—	127	2	no	—
347	#533	—	127	1	no	—
348	#529	—	127	1	no	—
349	#525	—	127	2	no	—
350	C₂×C₂²⋊Q₈	—	127	2	no	—
351	#520	—	127	1	no	—
352	#520	—	127	1	no	—
353	C₂×C₄×D₄	—	127	1	no	—
354	C₂×#41	—	127	1	no	—
355	C₂×#41	—	127	2	no	—
356	C₂×#41	—	127	1	no	—
357	C₂²×Q₈	—	127	2	no	—
358	C₂²×D₄	—	127	1	no	—
359	C₂³×C₄	—	127	2	no	—
360	C₄⋊Q₈	—	127	1	no	—
361	C₄⋊Q₈	—	127	1	no	—
362	C₄⋊Q₈	—	127	1	no	—
363	C₄⋊Q₈	C₂×D₁₂₇	1	1	yes	characteristic, complemented
364	#126	—	127	1	no	—
365	#126	—	127	2	no	—
366	#126	—	127	2	no	—
367	#126	—	127	2	no	—
368	#126	—	127	1	no	—
369	#126	—	127	2	no	—
370	#125	—	127	1	no	—
371	#125	—	127	2	no	—
372	#125	—	127	2	no	—
373	#125	C₂×D₁₂₇	1	2	yes	complemented
374	#124	—	127	1	no	—
375	#124	—	127	2	no	—
376	#124	—	127	1	no	—
377	#124	—	127	2	no	—
378	#124	—	127	1	no	—
379	#123	—	127	1	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	#123	—	127	2	no	—
386	#123	—	127	2	no	—
387	#123	—	127	2	no	—
388	#123	—	127	1	no	—
389	C₂²⋊Q₈	—	127	2	no	—
390	C₂²⋊Q₈	—	127	2	no	—
391	C₂²⋊Q₈	—	127	2	no	—
392	C₂²⋊Q₈	—	127	1	no	—
393	C₂²⋊Q₈	—	127	2	no	—
394	C₂²⋊Q₈	—	127	2	no	—
395	C₂²⋊Q₈	—	127	2	no	—
396	C₂²⋊Q₈	—	127	2	no	—
397	C₂²⋊Q₈	—	127	2	no	—
398	C₂²⋊Q₈	—	127	2	no	—
399	C₂²⋊Q₈	—	127	1	no	—
400	C₂²⋊Q₈	—	127	1	no	—
401	C₂²⋊Q₈	—	127	2	no	—
402	C₂²⋊Q₈	C₂×D₁₂₇	1	2	yes	—
403	C₂²⋊Q₈	C₂×D₁₂₇	1	1	yes	characteristic
404	C₂²⋊Q₈	C₂×D₁₂₇	1	2	yes	complemented
405	C₂²⋊Q₈	C₂×D₁₂₇	1	1	yes	characteristic, complemented
406	#121	—	127	1	no	—
407	#121	—	127	1	no	—
408	#121	—	127	2	no	—
409	#121	—	127	1	no	—
410	#121	—	127	2	no	—
411	#121	—	127	2	no	—
412	#120	—	127	2	no	—
413	#120	—	127	2	no	—
414	C₄×Q₈	—	127	1	no	—
415	C₄×Q₈	—	127	1	no	—
416	C₄×Q₈	—	127	1	no	—
417	C₄×Q₈	—	127	2	no	—
418	C₄×Q₈	—	127	1	no	—
419	C₄×Q₈	C₂×D₁₂₇	1	1	yes	characteristic, complemented
420	C₄×D₄	—	127	2	no	—
421	C₄×D₄	—	127	2	no	—
422	C₄×D₄	—	127	2	no	—
423	C₄×D₄	—	127	1	no	—
424	C₄×D₄	—	127	1	no	—
425	C₄×D₄	—	127	1	no	—
426	C₄×D₄	—	127	2	no	—
427	C₄×D₄	—	127	1	no	—
428	C₄×D₄	—	127	1	no	—
429	C₄×D₄	—	127	1	no	—
430	C₄×D₄	—	127	2	no	—
431	C₄×D₄	—	127	1	no	—
432	C₄×D₄	—	127	2	no	—
433	C₄×D₄	—	127	2	no	—
434	C₄×D₄	—	127	1	no	—
435	C₄×D₄	C₂×D₁₂₇	1	2	yes	—
436	C₄×D₄	C₂×D₁₂₇	1	1	yes	characteristic
437	#117	—	127	1	no	—
438	#117	—	127	2	no	—
439	#117	—	127	2	no	—
440	#117	—	127	1	no	—
441	#117	—	127	2	no	—
442	#117	—	127	2	no	—
443	C₂×C₄⋊C₄	—	127	2	no	—
444	C₂×C₄⋊C₄	—	127	2	no	—
445	C₂×C₄⋊C₄	—	127	1	no	—
446	C₂×C₄⋊C₄	—	127	2	no	—
447	C₂×C₄⋊C₄	C₂×D₁₂₇	1	1	yes	characteristic
448	C₂×C₄⋊C₄	C₂×D₁₂₇	1	1	yes	characteristic, complemented
449	C₂×C₂²⋊C₄	—	127	2	no	—
450	C₂×C₂²⋊C₄	—	127	2	no	—
451	C₂×C₂²⋊C₄	—	127	2	no	—
452	C₂×C₄²	—	127	1	no	—
453	C₂⁴	—	127	2	no	—
454	#41	—	508	4	no	—
455	#41	—	254	4	no	—
456	#41	—	254	4	no	—
457	C₂×Q₈	—	127	2	no	—
458	C₂×Q₈	—	127	1	no	—
459	C₂×Q₈	—	127	1	no	—
460	C₂×Q₈	—	127	2	no	—
461	C₂×Q₈	—	508	4	no	—
462	C₂×Q₈	C₂²×D₁₂₇	1	1	yes	characteristic
463	C₂×Q₈	C₂²×D₁₂₇	1	2	yes	—
464	C₂×D₄	—	127	2	no	—
465	C₂×D₄	—	127	1	no	—
466	C₂×D₄	—	127	2	no	—
467	C₂×D₄	—	127	1	no	—
468	C₂×D₄	—	127	1	no	—
469	C₂×D₄	—	127	2	no	—
470	C₂×D₄	—	127	2	no	—
471	C₂×D₄	—	127	2	no	—
472	C₂×D₄	—	127	1	no	—
473	C₂×D₄	—	254	4	no	—
474	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
475	C₂²×C₄	—	127	1	no	—
476	C₂²×C₄	—	127	1	no	—
477	C₂²×C₄	—	127	2	no	—
478	C₂²×C₄	—	127	2	no	—
479	C₂²×C₄	—	127	2	no	—
480	C₂²×C₄	—	127	2	no	—
481	C₂²×C₄	—	127	2	no	—
482	C₂²×C₄	—	127	2	no	—
483	C₂²×C₄	—	127	2	no	—
484	C₂²×C₄	—	127	1	no	—
485	C₂²×C₄	—	127	2	no	—
486	C₂²×C₄	—	127	2	no	—
487	C₂²×C₄	—	508	4	no	—
488	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
489	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
490	C₂²×C₄	C₂²×D₁₂₇	1	2	yes	—
491	C₂²×C₄	C₂²×D₁₂₇	1	2	yes	—
492	C₄⋊C₄	—	127	1	no	—
493	C₄⋊C₄	—	127	2	no	—
494	C₄⋊C₄	—	127	1	no	—
495	C₄⋊C₄	—	127	2	no	—
496	C₄⋊C₄	—	127	2	no	—
497	C₄⋊C₄	—	127	2	no	—
498	C₄⋊C₄	—	127	1	no	—
499	C₄⋊C₄	—	127	1	no	—
500	C₄⋊C₄	—	127	2	no	—
501	C₄⋊C₄	—	127	2	no	—
502	C₄⋊C₄	—	127	2	no	—
503	C₄⋊C₄	—	127	1	no	—
504	C₄⋊C₄	—	127	2	no	—
505	C₄⋊C₄	—	127	1	no	—
506	C₄⋊C₄	—	127	1	no	—
507	C₄⋊C₄	—	127	1	no	—
508	C₄⋊C₄	—	127	2	no	—
509	C₄⋊C₄	—	127	2	no	—
510	C₄⋊C₄	—	127	1	no	—
511	C₄⋊C₄	—	127	1	no	—
512	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
513	C₄⋊C₄	C₂²×D₁₂₇	1	2	yes	—
514	C₄⋊C₄	C₂²×D₁₂₇	1	2	yes	—
515	C₄⋊C₄	C₂²×D₁₂₇	1	2	yes	—
516	C₄⋊C₄	C₂²×D₁₂₇	1	2	yes	—
517	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
518	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
519	C₄⋊C₄	C₂²×D₁₂₇	1	2	yes	—
520	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
521	C₄⋊C₄	C₂²×D₁₂₇	1	2	yes	—
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	1	no	—
527	C₂²⋊C₄	—	127	2	no	—
528	C₂²⋊C₄	—	127	2	no	—
529	C₂²⋊C₄	—	127	2	no	—
530	C₂²⋊C₄	—	127	2	no	—
531	C₂²⋊C₄	—	127	2	no	—
532	C₂²⋊C₄	—	127	2	no	—
533	C₂²⋊C₄	—	127	2	no	—
534	C₂²⋊C₄	—	127	2	no	—
535	C₂²⋊C₄	—	127	2	no	—
536	C₂²⋊C₄	—	127	2	no	—
537	C₂²⋊C₄	—	127	1	no	—
538	C₂²⋊C₄	—	127	1	no	—
539	C₂²⋊C₄	—	127	2	no	—
540	C₂²⋊C₄	—	127	2	no	—
541	C₂²⋊C₄	—	127	1	no	—
542	C₂²⋊C₄	—	127	2	no	—
543	C₂²⋊C₄	—	127	1	no	—
544	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
545	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	—
546	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
547	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	—
548	C₄²	—	127	1	no	—
549	C₄²	—	127	1	no	—
550	C₄²	—	127	1	no	—
551	C₄²	—	127	1	no	—
552	C₄²	—	127	2	no	—
553	C₄²	—	127	2	no	—
554	C₄²	—	127	2	no	—
555	C₄²	—	127	1	no	—
556	C₄²	C₂²×D₁₂₇	1	2	yes	—
557	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic
558	C₂³	—	127	2	no	—
559	C₂³	—	127	2	no	—
560	C₂³	—	127	1	no	—
561	C₂³	—	508	2	no	—
562	C₂³	—	254	4	no	—
563	C₂³	—	254	4	no	—
564	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
565	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
566	Q₈	—	2	2	no	—
567	Q₈	—	4	2	no	—
568	Q₈	—	508	2	no	—
569	Q₈	—	254	2	no	—
570	Q₈	—	254	4	no	—
571	Q₈	—	254	2	no	—
572	D₄	—	2	2	no	—
573	D₄	—	127	4	no	—
574	D₄	—	508	2	no	—
575	D₄	—	508	2	no	—
576	D₄	—	254	4	no	—
577	D₄	—	254	4	no	—
578	D₄	—	254	2	no	—
579	D₄	—	254	4	no	—
580	D₄	—	254	2	no	—
581	D₄	—	254	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	4	2	no	—
585	C₂×C₄	—	4	2	no	—
586	C₂×C₄	—	127	1	no	—
587	C₂×C₄	—	127	1	no	—
588	C₂×C₄	—	127	1	no	—
589	C₂×C₄	—	127	1	no	—
590	C₂×C₄	—	127	2	no	—
591	C₂×C₄	—	127	1	no	—
592	C₂×C₄	—	127	1	no	—
593	C₂×C₄	—	127	2	no	—
594	C₂×C₄	—	127	1	no	—
595	C₂×C₄	—	508	2	no	—
596	C₂×C₄	—	508	2	no	—
597	C₂×C₄	—	508	2	no	—
598	C₂×C₄	—	508	2	no	—
599	C₂×C₄	—	508	2	no	—
600	C₂×C₄	—	254	4	no	—
601	C₂×C₄	—	254	4	no	—
602	C₂×C₄	—	254	4	no	—
603	C₂×C₄	—	254	4	no	—
604	C₂×C₄	—	254	2	no	—
605	C₂×C₄	—	254	2	no	—
606	C₂×C₄	—	254	2	no	—
607	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
608	C₂×C₄	C₂³×D₁₂₇	1	2	yes	—
609	C₂×C₄	C₂³×D₁₂₇	1	2	yes	—
610	C₂×C₄	C₂³×D₁₂₇	1	2	yes	—
611	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
612	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
613	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
614	C₂×C₄	C₂³×D₁₂₇	1	2	yes	—
615	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
616	C₂²	—	2	1	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	2	1	no	—
619	C₂²	—	2	1	no	—
620	C₂²	—	2	1	no	—
621	C₂²	—	127	4	no	—
622	C₂²	—	508	8	no	—
623	C₂²	—	254	1	no	—
624	C₂²	—	254	2	no	—
625	C₂²	—	254	1	no	—
626	C₂²	—	254	2	no	—
627	C₂²	—	254	1	no	—
628	C₂²	—	254	2	no	—
629	C₂²	—	254	2	no	—
630	C₂²	—	254	2	no	—
631	C₂²	#16861257	1	2	yes	—
632	C₂²	C₂⁴×D₁₂₇	1	1	yes	characteristic
633	C₄	—	2	1	no	—
634	C₄	—	2	1	no	—
635	C₄	—	2	2	no	—
636	C₄	—	2	2	no	—
637	C₄	—	2	2	no	—
638	C₄	—	2	2	no	—
639	C₄	—	2	1	no	—
640	C₄	—	2	1	no	—
641	C₄	—	127	2	no	—
642	C₄	—	254	1	no	—
643	C₄	—	254	2	no	—
644	C₄	—	254	1	no	—
645	C₄	—	254	2	no	—
646	C₄	—	254	1	no	—
647	C₄	—	254	1	no	—
648	C₄	—	254	1	no	—
649	C₄	—	254	1	no	—
650	C₄	#41×D₁₂₇	1	2	yes	—
651	C₂	—	2	2	no	—
652	C₂	—	4	1	no	—
653	C₂	—	508	2	no	—
654	C₂	—	508	1	no	—
655	C₂	—	254	4	no	—
656	C₂	C₂×#41×D₁₂₇	1	1	yes	characteristic
657	C₂	H(5,𝔽₂)×D₁₂₇	1	1	yes	characteristic
658	C₂	C₂×#16861257	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	#3520
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. #22550598	C₂	semidirect
2. #22550581	C₂	semidirect
3. #22550558	C₂	semidirect
4. #22550555	C₂	semidirect
5. #22550553	C₂	semidirect
6. #22550541	C₂	semidirect
7. #22550536	C₂	semidirect
8. #22550528	C₂	semidirect
9. #22550527	C₂	semidirect
10. #22550522	C₂	semidirect
11. #22550517	C₂	semidirect
12. #22550500	C₂	semidirect
13. #22550499	C₂	semidirect
14. #22550474	C₂	semidirect
15. #22550472	C₂	semidirect
16. #22550428	C₂	semidirect
17. #22550406	C₂	semidirect
18. #22550385	C₂	semidirect
19. C₂²⋊Q₈×D₁₂₇	C₂	semidirect
20. #22550358	C₂	semidirect
21. #22550357	C₂	semidirect
22. C₂×#16861171	C₂	semidirect
23. #554×C₁₂₇	C₂	semidirect
26. C₂×#14523248	C₂²	semidirect
27. C₂×Q₈×D₁₂₇	C₂²	semidirect
30. #16861208	C₂²	semidirect
31. #16861208	C₂²	semidirect
32. #16861207	C₂²	semidirect
33. #16861204	C₂²	semidirect
34. #16861204	C₂²	semidirect
35. #16861204	C₂²	semidirect
36. #16861204	C₂²	semidirect
37. #16861203	C₂²	semidirect
38. #16861202	C₂²	semidirect
39. #16861199	C₂²	semidirect
40. #16861199	C₂²	semidirect
41. #16861199	C₂²	semidirect
43. #16861198	C₂²	semidirect
45. #16861195	C₂²	semidirect
46. #16861195	C₂²	semidirect
49. #16861194	C₂²	semidirect
50. #16861194	C₂²	semidirect
51. #16861194	C₂²	semidirect
53. #16861192	C₂²	semidirect
54. #16861191	C₂²	semidirect
55. #16861191	C₂²	semidirect
57. #16861189	C₂²	semidirect
58. #16861189	C₂²	semidirect
61. #16861187	C₂²	semidirect
62. #16861187	C₂²	semidirect
63. #16861187	C₂²	semidirect
64. #16861187	C₂²	semidirect
65. #16861187	C₂²	semidirect
68. #16861185	C₂²	semidirect
69. #16861185	C₂²	semidirect
74. #16861182	C₂²	semidirect
78. Q₈×Dic₁₂₇	C₂²	semidirect
79. C₄×Dic₂₅₄	C₂²	semidirect
80. #16861174	C₂²	semidirect
81. #16861174	C₂²	semidirect
82. #16861174	C₂²	semidirect
84. C₄×D₅₀₈	C₂²	semidirect
92. #16861171	C₂²	semidirect
95. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
96. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
97. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
98. #16861168	C₂²	semidirect
99. #16861167	C₂²	semidirect
100. #16861166	C₂²	semidirect
101. #16861166	C₂²	semidirect
102. #16861166	C₂²	semidirect
104. C₄⋊C₄×D₁₂₇	C₂²	semidirect
105. C₄⋊C₄×D₁₂₇	C₂²	semidirect
106. C₄⋊C₄×D₁₂₇	C₂²	semidirect
107. C₄⋊C₄×D₁₂₇	C₂²	semidirect
112. C₄⋊Q₈×C₁₂₇	C₂²	semidirect
113. #125×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
242. D₅₀₈	#41	semidirect
330. C₁₂₇	#3520	semidirect
333. #554	D₁₂₇	semidirect
363. C₄⋊Q₈	C₂×D₁₂₇	semidirect
373. #125	C₂×D₁₂₇	semidirect
404. C₂²⋊Q₈	C₂×D₁₂₇	semidirect
405. C₂²⋊Q₈	C₂×D₁₂₇	semidirect
419. C₄×Q₈	C₂×D₁₂₇	semidirect
448. 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
#22550598	2
#22550581	2
#22550558	2
#22550555	2
#22550553	2
#22550541	2
#22550536	2
#22550528	2
#22550527	2
#22550522	2
#22550517	2
#22550500	2
#22550499	2
#22550474	2
#22550472	2
#22550428	2
#22550406	2
#22550385	2
C₂²⋊Q₈×D₁₂₇	2
#22550358	2
#22550357	2
C₂×#16861171	2
#554×C₁₂₇	2
#3520	127