Subgroups — #28350684

Order 13696.

1134 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20293374	C₂	1	2	yes	maximal, complemented
2	#20293373	C₂	1	2	yes	maximal, complemented
3	#20293338	C₂	1	1	yes	maximal, characteristic, complemented
4	#20293332	C₂	1	1	yes	maximal, characteristic, complemented
5	#20293286	C₂	1	1	yes	maximal, characteristic, complemented
6	#20293283	C₂	1	1	yes	maximal, characteristic, complemented
7	#20293278	C₂	1	1	yes	maximal, characteristic, complemented
8	#20293274	C₂	1	1	yes	maximal, characteristic, complemented
9	#20293272	C₂	1	1	yes	maximal, characteristic, complemented
10	#20293269	C₂	1	2	yes	maximal, complemented
11	#20293265	C₂	1	2	yes	maximal, complemented
12	#20293252	C₂	1	2	yes	maximal, complemented
13	#20293251	C₂	1	1	yes	maximal, characteristic, complemented
14	#20293242	C₂	1	1	yes	maximal, characteristic, complemented
15	#20293221	C₂	1	2	yes	maximal, complemented
16	#20293213	C₂	1	2	yes	maximal, complemented
17	#20293208	C₂	1	1	yes	maximal, characteristic, complemented
18	#20293206	C₂	1	1	yes	maximal, characteristic, complemented
19	#20293205	C₂	1	2	yes	maximal, complemented
20	#20293136	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#16812089	C₂	1	1	yes	maximal, characteristic, complemented
22	#121×D₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
23	#547×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13133818	C₂²	1	1	yes	characteristic, complemented
25	C₂×#13133818	C₂²	1	2	yes	complemented
26	C₂×#13133818	C₂²	1	1	yes	characteristic, complemented
27	C₂×#13133817	C₂²	1	1	yes	characteristic, complemented
28	C₂²×Dic₂₁₄	C₂²	1	1	yes	characteristic, complemented
29	C₂×D₄×D₁₀₇	C₂²	1	2	yes	—
30	C₂×D₄×D₁₀₇	C₂²	1	1	yes	characteristic
31	C₂²×C₄×D₁₀₇	C₂²	1	1	yes	characteristic
32	#16812108	C₂²	1	1	yes	characteristic, complemented
33	#16812104	C₂²	1	2	yes	complemented
34	#16812102	C₂²	1	2	yes	complemented
35	#16812100	C₂²	1	2	yes	complemented
36	#16812099	C₂²	1	2	yes	complemented
37	#16812098	C₂²	1	2	yes	complemented
38	#16812097	C₂²	1	1	yes	characteristic, complemented
39	#16812096	C₂²	1	1	yes	characteristic, complemented
40	#16812095	C₂²	1	2	yes	complemented
41	#16812095	C₂²	1	2	yes	complemented
42	#16812095	C₂²	1	2	yes	complemented
43	#16812094	C₂²	1	1	yes	characteristic, complemented
44	#16812094	C₂²	1	2	yes	complemented
45	#16812094	C₂²	1	2	yes	complemented
46	#16812093	C₂²	1	2	yes	complemented
47	#16812092	C₂²	1	2	yes	complemented
48	#16812092	C₂²	1	2	yes	complemented
49	#16812091	C₂²	1	1	yes	characteristic, complemented
50	#16812091	C₂²	1	2	yes	complemented
51	#16812089	C₂²	1	2	yes	—
52	#16812089	C₂²	1	1	yes	characteristic
53	#16812089	C₂²	1	1	yes	characteristic
54	#16812089	C₂²	1	1	yes	characteristic, complemented
55	#16812089	C₂²	1	1	yes	characteristic, complemented
56	#16812089	C₂²	1	2	yes	complemented
57	#16812089	C₂²	1	2	yes	complemented
58	#16812089	C₂²	1	1	yes	characteristic, complemented
59	#16812088	C₂²	1	2	yes	complemented
60	#16812088	C₂²	1	2	yes	complemented
61	#16812088	C₂²	1	1	yes	characteristic, complemented
62	#16812087	C₂²	1	1	yes	characteristic
63	#16812087	C₂²	1	2	yes	—
64	#16812087	C₂²	1	2	yes	complemented
65	#16812087	C₂²	1	2	yes	complemented
66	#16812086	C₂²	1	1	yes	characteristic, complemented
67	#16812086	C₂²	1	2	yes	complemented
68	#16812086	C₂²	1	2	yes	complemented
69	#16812085	C₂²	1	2	yes	—
70	#16812085	C₂²	1	2	yes	complemented
71	#16812085	C₂²	1	2	yes	complemented
72	#16812084	C₂²	1	1	yes	characteristic
73	#16812084	C₂²	1	2	yes	complemented
74	#16812084	C₂²	1	1	yes	characteristic, complemented
75	#16812083	C₂²	1	1	yes	characteristic
76	#16812083	C₂²	1	2	yes	complemented
77	#16812083	C₂²	1	2	yes	complemented
78	#16812083	C₂²	1	2	yes	complemented
79	#16812082	C₂²	1	1	yes	characteristic
80	#16812082	C₂²	1	2	yes	—
81	#16812082	C₂²	1	2	yes	complemented
82	#16812081	C₂²	1	2	yes	—
83	#16812081	C₂²	1	1	yes	characteristic, complemented
84	#16812081	C₂²	1	2	yes	complemented
85	#16812081	C₂²	1	2	yes	complemented
86	#16812081	C₂²	1	2	yes	complemented
87	#16812080	C₂²	1	1	yes	characteristic
88	#16812080	C₂²	1	2	yes	complemented
89	#16812080	C₂²	1	2	yes	complemented
90	#16812079	C₂²	1	1	yes	characteristic
91	#16812079	C₂²	1	2	yes	—
92	#16812077	C₂²	1	1	yes	characteristic
93	#16812077	C₂²	1	2	yes	—
94	C₄×Dic₂₁₄	C₂²	1	1	yes	characteristic, complemented
95	#16812074	C₂²	1	1	yes	characteristic, complemented
96	C₄×D₄₂₈	C₂²	1	1	yes	characteristic
97	D₄×Dic₁₀₇	C₂²	1	2	yes	complemented
98	#16812071	C₂²	1	2	yes	—
99	#16812071	C₂²	1	1	yes	characteristic, complemented
100	C₄×C₂²⋊D₁₀₇	C₂²	1	1	yes	characteristic
101	C₄×C₂²⋊D₁₀₇	C₂²	1	2	yes	—
102	C₄×C₂²⋊D₁₀₇	C₂²	1	1	yes	characteristic, complemented
103	(C₂²⋊D₁₀₇)⋊C₄	C₂²	1	2	yes	complemented
104	#16812066	C₂²	1	1	yes	characteristic, complemented
105	C₂×C₄⋊Dic₁₀₇	C₂²	1	2	yes	complemented
106	C₄⋊C₄×D₁₀₇	C₂²	1	1	yes	characteristic
107	C₄⋊C₄×D₁₀₇	C₂²	1	1	yes	characteristic, complemented
108	C₂×(C₂×D₁₀₇)⋊C₄	C₂²	1	2	yes	—
109	C₂×(C₂×D₁₀₇)⋊C₄	C₂²	1	2	yes	—
110	C₂²⋊C₄×D₁₀₇	C₂²	1	2	yes	—
111	C₂²⋊C₄×D₁₀₇	C₂²	1	2	yes	—
112	C₂×#41×C₁₀₇	C₂²	1	2	yes	complemented
113	C₄⋊Q₈×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
114	#123×C₁₀₇	C₂²	1	2	yes	complemented
115	#123×C₁₀₇	C₂²	1	2	yes	complemented
116	C₂²⋊Q₈×C₁₀₇	C₂²	1	2	yes	complemented
117	#121×C₁₀₇	C₂²	1	1	yes	characteristic
118	#121×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₄×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₄×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
121	C₂×C₄⋊C₄×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₄⋊C₄×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₀₇	C₂³	1	1	yes	characteristic
124	C₂³×D₁₀₇	C₂³	1	2	yes	—
125	#13133818	—	4	2	no	—
126	#13133818	—	4	2	no	—
127	#13133818	—	4	4	no	—
128	#13133817	—	4	2	no	—
129	C₂×Dic₂₁₄	—	4	2	no	—
130	C₂×Dic₂₁₄	C₂³	1	1	yes	characteristic
131	C₂×Dic₂₁₄	C₂³	1	1	yes	characteristic
132	C₂×Dic₂₁₄	C₂³	1	1	yes	characteristic
133	C₂×Dic₂₁₄	C₂³	1	2	yes	—
134	C₂×Dic₂₁₄	C₂³	1	2	yes	—
135	C₂×D₄₂₈	C₂³	1	1	yes	characteristic
136	C₂×D₄₂₈	C₂³	1	1	yes	characteristic
137	C₂×D₄₂₈	C₂³	1	1	yes	characteristic
138	C₂×D₄₂₈	C₂³	1	2	yes	—
139	C₂×D₄₂₈	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₁₀₇	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₁₀₇	C₂³	1	1	yes	characteristic
142	C₂×C₂²⋊D₁₀₇	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊D₁₀₇	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₁₀₇	C₂³	1	1	yes	characteristic
145	C₂×C₂²⋊D₁₀₇	C₂³	1	2	yes	—
146	C₂×C₂²⋊D₁₀₇	C₂³	1	2	yes	—
147	C₂×C₂²⋊D₁₀₇	C₂³	1	1	yes	characteristic
148	C₂×C₂²⋊D₁₀₇	C₂³	1	2	yes	—
149	D₄×D₁₀₇	—	4	2	no	—
150	D₄×D₁₀₇	—	4	4	no	—
151	C₂²×Dic₁₀₇	C₂³	1	2	yes	—
152	C₂²×Dic₁₀₇	C₂³	1	2	yes	—
153	C₂²×Dic₁₀₇	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₁₀₇	—	4	2	no	—
155	C₂×C₄×D₁₀₇	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₁₀₇	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₁₀₇	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₁₀₇	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₁₀₇	C₂³	1	2	yes	—
160	C₂×C₄×D₁₀₇	C₂³	1	2	yes	—
161	C₂×C₄×D₁₀₇	C₂³	1	2	yes	—
162	C₂×C₄×D₁₀₇	C₂³	1	2	yes	—
163	C₂×C₄×D₁₀₇	C₂³	1	1	yes	characteristic
164	C₄⋊Dic₁₀₇	C₂³	1	1	yes	characteristic
165	C₄⋊Dic₁₀₇	C₂³	1	2	yes	—
166	C₄⋊Dic₁₀₇	C₂³	1	2	yes	—
167	C₄⋊Dic₁₀₇	C₂³	1	2	yes	—
168	C₄⋊Dic₁₀₇	C₂³	1	2	yes	—
169	C₄⋊Dic₁₀₇	C₂³	1	2	yes	—
170	C₄⋊Dic₁₀₇	C₂³	1	1	yes	characteristic
171	Dic₁₀₇⋊C₄	C₂³	1	2	yes	—
172	Dic₁₀₇⋊C₄	C₂³	1	2	yes	—
173	Dic₁₀₇⋊C₄	C₂³	1	1	yes	characteristic
174	Dic₁₀₇⋊C₄	C₂³	1	1	yes	characteristic
175	Dic₁₀₇⋊C₄	C₂³	1	2	yes	—
176	Dic₁₀₇⋊C₄	C₂³	1	1	yes	characteristic
177	Dic₁₀₇⋊C₄	C₂³	1	2	yes	—
178	Dic₁₀₇⋊C₄	C₂³	1	1	yes	characteristic
179	Dic₁₀₇⋊C₄	C₂³	1	2	yes	—
180	Dic₁₀₇⋊C₄	C₂³	1	2	yes	—
181	C₂²⋊Dic₁₀₇	C₂³	1	2	yes	—
182	C₂²⋊Dic₁₀₇	C₂³	1	2	yes	—
183	C₂²⋊Dic₁₀₇	C₂³	1	1	yes	characteristic
184	C₂²⋊Dic₁₀₇	C₂³	1	2	yes	—
185	C₂²⋊Dic₁₀₇	C₂³	1	1	yes	characteristic
186	C₂²⋊Dic₁₀₇	C₂³	1	2	yes	—
187	(C₂×D₁₀₇)⋊C₄	C₂³	1	1	yes	characteristic
188	(C₂×D₁₀₇)⋊C₄	C₂³	1	2	yes	—
189	(C₂×D₁₀₇)⋊C₄	C₂³	1	2	yes	—
190	(C₂×D₁₀₇)⋊C₄	C₂³	1	2	yes	—
191	(C₂×D₁₀₇)⋊C₄	C₂³	1	2	yes	—
192	(C₂×D₁₀₇)⋊C₄	C₂³	1	1	yes	characteristic
193	(C₂×D₁₀₇)⋊C₄	C₂³	1	2	yes	—
194	(C₂×D₁₀₇)⋊C₄	C₂³	1	2	yes	—
195	(C₂×D₁₀₇)⋊C₄	C₂³	1	2	yes	—
196	(C₂×D₁₀₇)⋊C₄	C₂³	1	2	yes	—
197	(C₂×D₁₀₇)⋊C₄	C₂³	1	1	yes	characteristic
198	(C₂×D₁₀₇)⋊C₄	C₂³	1	1	yes	characteristic
199	(C₂×D₁₀₇)⋊C₄	C₂³	1	2	yes	—
200	(C₂×D₁₀₇)⋊C₄	C₂³	1	1	yes	characteristic
201	(C₂×D₁₀₇)⋊C₄	C₂³	1	2	yes	—
202	(C₂×D₁₀₇)⋊C₄	C₂³	1	2	yes	—
203	(C₂×D₁₀₇)⋊C₄	C₂³	1	1	yes	characteristic
204	C₄×Dic₁₀₇	C₂³	1	1	yes	characteristic
205	C₄×Dic₁₀₇	C₂³	1	2	yes	—
206	C₄×Dic₁₀₇	C₂³	1	2	yes	—
207	#41×C₁₀₇	—	4	4	no	—
208	C₂×Q₈×C₁₀₇	C₂³	1	2	yes	—
209	C₂×D₄×C₁₀₇	C₂³	1	2	yes	—
210	C₂×D₄×C₁₀₇	C₂³	1	1	yes	characteristic
211	C₂×D₄×C₁₀₇	C₂³	1	1	yes	characteristic
212	C₂×D₄×C₁₀₇	C₂³	1	2	yes	—
213	C₂²×C₄×C₁₀₇	C₂³	1	2	yes	—
214	C₂²×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
215	C₂²×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
216	C₂²×C₄×C₁₀₇	C₂³	1	2	yes	—
217	C₂²×C₄×C₁₀₇	C₂³	1	2	yes	—
218	C₄⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
219	C₄⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
220	C₄⋊C₄×C₁₀₇	C₂³	1	2	yes	—
221	C₄⋊C₄×C₁₀₇	C₂³	1	2	yes	—
222	C₄⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
223	C₄⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
224	C₄⋊C₄×C₁₀₇	C₂³	1	2	yes	—
225	C₂²⋊C₄×C₁₀₇	C₂³	1	2	yes	—
226	C₂²⋊C₄×C₁₀₇	C₂³	1	2	yes	—
227	C₂²⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
228	C₂²⋊C₄×C₁₀₇	C₂³	1	2	yes	—
229	C₂²⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
230	C₄²×C₁₀₇	C₂³	1	1	yes	characteristic
231	C₂³×C₁₀₇	C₂⁴	1	2	yes	—
232	C₂³×C₁₀₇	C₂⁴	1	1	yes	characteristic
233	C₂³×C₁₀₇	C₂⁴	1	1	yes	characteristic
234	C₂²×D₁₀₇	—	2	2	no	—
235	C₂²×D₁₀₇	—	2	2	no	—
236	C₂²×D₁₀₇	—	2	4	no	—
237	C₂²×D₁₀₇	—	4	1	no	—
238	C₂²×D₁₀₇	—	4	2	no	—
239	C₂²×D₁₀₇	—	4	2	no	—
240	C₂²×D₁₀₇	C₂⁴	1	1	yes	characteristic
241	C₂²×D₁₀₇	C₂⁴	1	2	yes	—
242	C₂²×D₁₀₇	C₂⁴	1	1	yes	characteristic
243	C₂²×D₁₀₇	C₂⁴	1	1	yes	characteristic
244	Q₈×C₁₀₇	—	4	2	no	—
245	D₄×C₁₀₇	—	2	2	no	—
246	D₄×C₁₀₇	—	2	4	no	—
247	D₄×C₁₀₇	—	2	2	no	—
248	D₄×C₁₀₇	—	4	2	no	—
249	C₂×C₄×C₁₀₇	—	2	4	no	—
250	C₂×C₄×C₁₀₇	—	2	2	no	—
251	C₂×C₄×C₁₀₇	—	2	2	no	—
252	C₂×C₄×C₁₀₇	—	4	2	no	—
253	C₂×C₄×C₁₀₇	—	4	2	no	—
254	C₂×C₄×C₁₀₇	C₂⁴	1	1	yes	characteristic
255	C₂×C₄×C₁₀₇	C₂⁴	1	1	yes	characteristic
256	C₂×C₄×C₁₀₇	C₂⁴	1	1	yes	characteristic
257	C₂×C₄×C₁₀₇	C₂⁴	1	1	yes	characteristic
258	C₂×C₄×C₁₀₇	C₂⁴	1	2	yes	—
259	C₂×C₄×C₁₀₇	C₂⁴	1	2	yes	—
260	C₂×C₄×C₁₀₇	C₂⁴	1	2	yes	—
261	C₂×C₄×C₁₀₇	C₂⁴	1	1	yes	characteristic
262	C₂²⋊D₁₀₇	—	2	4	no	—
263	C₂²⋊D₁₀₇	—	2	2	no	—
264	C₂²⋊D₁₀₇	—	2	2	no	—
265	C₂²⋊D₁₀₇	—	4	2	no	—
266	C₂²⋊D₁₀₇	—	4	2	no	—
267	C₂²⋊D₁₀₇	—	4	2	no	—
268	C₂²⋊D₁₀₇	—	4	2	no	—
269	C₂²⋊D₁₀₇	—	4	1	no	—
270	C₂²⋊D₁₀₇	—	4	1	no	—
271	C₂×Dic₁₀₇	—	4	1	no	—
272	C₂×Dic₁₀₇	—	4	2	no	—
273	C₂×Dic₁₀₇	—	4	2	no	—
274	C₂×Dic₁₀₇	C₂⁴	1	1	yes	characteristic
275	C₂×Dic₁₀₇	C₂⁴	1	2	yes	—
276	C₂×Dic₁₀₇	C₂⁴	1	2	yes	—
277	C₂×Dic₁₀₇	C₂⁴	1	1	yes	characteristic
278	C₂×Dic₁₀₇	C₂⁴	1	2	yes	—
279	C₂×Dic₁₀₇	C₂⁴	1	1	yes	characteristic
280	C₂×Dic₁₀₇	C₂⁴	1	1	yes	characteristic
281	C₂×Dic₁₀₇	C₂⁴	1	1	yes	characteristic
282	D₄₂₈	—	2	2	no	—
283	D₄₂₈	—	2	2	no	—
284	D₄₂₈	—	4	2	no	—
285	D₄₂₈	—	4	1	no	—
286	D₄₂₈	—	4	2	no	—
287	C₄×D₁₀₇	—	2	2	no	—
288	C₄×D₁₀₇	—	2	2	no	—
289	C₄×D₁₀₇	—	2	2	no	—
290	C₄×D₁₀₇	—	4	1	no	—
291	C₄×D₁₀₇	—	4	1	no	—
292	C₄×D₁₀₇	—	4	2	no	—
293	C₄×D₁₀₇	—	4	2	no	—
294	C₄×D₁₀₇	—	4	2	no	—
295	C₄×D₁₀₇	—	4	2	no	—
296	Dic₂₁₄	—	2	2	no	—
297	Dic₂₁₄	—	2	2	no	—
298	Dic₂₁₄	—	4	2	no	—
299	Dic₂₁₄	—	4	2	no	—
300	Dic₂₁₄	—	4	1	no	—
301	C₂²×C₁₀₇	—	2	1	no	—
302	C₂²×C₁₀₇	—	2	1	no	—
303	C₂²×C₁₀₇	—	2	2	no	—
304	C₂²×C₁₀₇	—	2	1	no	—
305	C₂²×C₁₀₇	—	2	2	no	—
306	C₂²×C₁₀₇	—	2	1	no	—
307	C₂²×C₁₀₇	—	2	1	no	—
308	C₂²×C₁₀₇	—	2	2	no	—
309	C₂²×C₁₀₇	H(5,𝔽₂)	1	2	yes	—
310	C₂²×C₁₀₇	C₂⁵	1	1	yes	characteristic
311	C₂×D₁₀₇	—	2	1	no	—
312	C₂×D₁₀₇	—	2	1	no	—
313	C₂×D₁₀₇	—	2	1	no	—
314	C₂×D₁₀₇	—	2	1	no	—
315	C₂×D₁₀₇	—	2	1	no	—
316	C₂×D₁₀₇	—	2	2	no	—
317	C₂×D₁₀₇	—	2	2	no	—
318	C₂×D₁₀₇	—	2	1	no	—
319	C₂×D₁₀₇	—	2	1	no	—
320	C₂×D₁₀₇	—	2	1	no	—
321	C₂×D₁₀₇	—	2	2	no	—
322	C₂×D₁₀₇	—	4	4	no	—
323	C₂×D₁₀₇	—	8	4	no	—
324	C₂×D₁₀₇	2₋¹⁺⁴	1	2	yes	—
325	C₄×C₁₀₇	—	2	1	no	—
326	C₄×C₁₀₇	—	2	1	no	—
327	C₄×C₁₀₇	—	2	2	no	—
328	C₄×C₁₀₇	—	2	2	no	—
329	C₄×C₁₀₇	—	2	2	no	—
330	C₄×C₁₀₇	—	2	1	no	—
331	C₄×C₁₀₇	—	2	1	no	—
332	C₄×C₁₀₇	H(5,𝔽₂)	1	2	yes	—
333	Dic₁₀₇	—	2	2	no	—
334	Dic₁₀₇	—	2	2	no	—
335	Dic₁₀₇	—	2	1	no	—
336	Dic₁₀₇	—	2	1	no	—
337	Dic₁₀₇	—	2	1	no	—
338	Dic₁₀₇	—	2	2	no	—
339	Dic₁₀₇	—	2	1	no	—
340	Dic₁₀₇	—	2	1	no	—
341	C₂×C₁₀₇	—	2	2	no	—
342	C₂×C₁₀₇	—	4	2	no	—
343	C₂×C₁₀₇	—	4	1	no	—
344	C₂×C₁₀₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
345	C₂×C₁₀₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
346	C₂×C₁₀₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
347	D₁₀₇	—	2	2	no	—
348	D₁₀₇	—	4	1	no	—
349	D₁₀₇	—	4	1	no	—
350	D₁₀₇	—	4	2	no	—
351	#3536	—	107	1	no	maximal, Sylow
352	C₁₀₇	#3536	1	1	yes	characteristic, complemented, Sylow
353	#562	—	107	2	no	—
354	#562	—	107	2	no	—
355	#554	—	107	1	no	—
356	#554	—	107	1	no	—
357	#548	—	107	1	no	—
358	#548	—	107	1	no	—
359	#547	—	107	1	no	—
360	#547	D₁₀₇	1	1	yes	characteristic, complemented
361	#546	—	107	2	no	—
362	#546	—	107	2	no	—
363	#546	—	107	1	no	—
364	#546	—	107	1	no	—
365	#543	—	107	2	no	—
366	#542	—	107	1	no	—
367	#542	—	107	1	no	—
368	#539	—	107	2	no	—
369	#538	—	107	2	no	—
370	#537	—	107	2	no	—
371	#537	—	107	1	no	—
372	#537	—	107	1	no	—
373	#525	—	107	1	no	—
374	C₂×C₂²⋊Q₈	—	107	1	no	—
375	C₂×#121	—	107	1	no	—
376	C₂×#41	—	107	1	no	—
377	C₂×#41	—	107	1	no	—
378	C₂×#41	—	107	2	no	—
379	C₂×#41	—	107	1	no	—
380	C₂×#41	C₂×D₁₀₇	1	2	yes	complemented
381	C₂²×Q₈	—	107	1	no	—
382	C₂²×D₄	—	107	2	no	—
383	C₂²×D₄	—	107	1	no	—
384	C₂³×C₄	—	107	1	no	—
385	C₄⋊Q₈	—	107	1	no	—
386	C₄⋊Q₈	C₂×D₁₀₇	1	1	yes	characteristic, complemented
387	#126	—	107	2	no	—
388	#126	—	107	2	no	—
389	#125	—	107	2	no	—
390	#125	—	107	2	no	—
391	#124	—	107	2	no	—
392	#124	—	107	1	no	—
393	#124	—	107	2	no	—
394	#124	—	107	2	no	—
395	#124	—	107	2	no	—
396	#124	—	107	1	no	—
397	#123	—	107	2	no	—
398	#123	—	107	2	no	—
399	#123	—	107	1	no	—
400	#123	—	107	2	no	—
401	#123	—	107	2	no	—
402	#123	—	107	1	no	—
403	#123	—	107	2	no	—
404	#123	—	107	2	no	—
405	#123	C₂×D₁₀₇	1	2	yes	complemented
406	#123	C₂×D₁₀₇	1	2	yes	complemented
407	C₂²⋊Q₈	—	107	2	no	—
408	C₂²⋊Q₈	—	107	2	no	—
409	C₂²⋊Q₈	—	107	2	no	—
410	C₂²⋊Q₈	—	107	2	no	—
411	C₂²⋊Q₈	—	107	1	no	—
412	C₂²⋊Q₈	—	107	2	no	—
413	C₂²⋊Q₈	—	107	1	no	—
414	C₂²⋊Q₈	—	107	1	no	—
415	C₂²⋊Q₈	—	107	2	no	—
416	C₂²⋊Q₈	—	107	1	no	—
417	C₂²⋊Q₈	—	107	1	no	—
418	C₂²⋊Q₈	—	107	2	no	—
419	C₂²⋊Q₈	—	107	1	no	—
420	C₂²⋊Q₈	—	107	2	no	—
421	C₂²⋊Q₈	—	107	1	no	—
422	C₂²⋊Q₈	—	107	2	no	—
423	C₂²⋊Q₈	—	107	2	no	—
424	C₂²⋊Q₈	—	107	2	no	—
425	C₂²⋊Q₈	—	107	1	no	—
426	C₂²⋊Q₈	—	107	2	no	—
427	C₂²⋊Q₈	—	107	2	no	—
428	C₂²⋊Q₈	C₂×D₁₀₇	1	2	yes	complemented
429	#121	—	107	2	no	—
430	#121	—	107	1	no	—
431	#121	—	107	1	no	—
432	#121	—	107	2	no	—
433	#121	—	107	2	no	—
434	#121	—	107	2	no	—
435	#121	—	107	2	no	—
436	#121	—	107	2	no	—
437	#121	—	107	1	no	—
438	#121	—	107	2	no	—
439	#121	—	107	2	no	—
440	#121	—	107	2	no	—
441	#121	—	107	1	no	—
442	#121	—	107	1	no	—
443	#121	—	107	2	no	—
444	#121	—	107	2	no	—
445	#121	—	107	1	no	—
446	#121	—	107	2	no	—
447	#121	C₂×D₁₀₇	1	1	yes	characteristic
448	#121	C₂×D₁₀₇	1	1	yes	characteristic, complemented
449	#120	—	107	1	no	—
450	#120	—	107	2	no	—
451	#120	—	107	1	no	—
452	#120	—	107	2	no	—
453	C₄×Q₈	—	107	1	no	—
454	C₄×Q₈	—	107	1	no	—
455	C₄×D₄	—	107	2	no	—
456	C₄×D₄	—	107	1	no	—
457	C₄×D₄	—	107	1	no	—
458	C₄×D₄	—	107	2	no	—
459	C₄×D₄	—	107	2	no	—
460	C₄×D₄	—	107	1	no	—
461	C₄×D₄	—	107	2	no	—
462	C₄×D₄	—	107	1	no	—
463	C₄×D₄	C₂×D₁₀₇	1	1	yes	characteristic, complemented
464	C₄×D₄	C₂×D₁₀₇	1	1	yes	characteristic, complemented
465	#117	—	107	1	no	—
466	C₂×C₄⋊C₄	—	107	2	no	—
467	C₂×C₄⋊C₄	—	107	1	no	—
468	C₂×C₄⋊C₄	—	107	1	no	—
469	C₂×C₄⋊C₄	C₂×D₁₀₇	1	1	yes	characteristic, complemented
470	C₂×C₄⋊C₄	C₂×D₁₀₇	1	1	yes	characteristic, complemented
471	C₂×C₂²⋊C₄	—	107	2	no	—
472	C₂×C₂²⋊C₄	—	107	2	no	—
473	C₂×C₂²⋊C₄	—	107	2	no	—
474	C₂×C₂²⋊C₄	—	107	2	no	—
475	C₂⁴	—	107	2	no	—
476	C₂⁴	—	107	1	no	—
477	#41	—	4	4	no	—
478	#41	—	428	2	no	—
479	#41	—	428	4	no	—
480	#41	—	428	2	no	—
481	#41	—	428	2	no	—
482	C₂×Q₈	—	107	1	no	—
483	C₂×Q₈	—	107	2	no	—
484	C₂×Q₈	—	107	2	no	—
485	C₂×Q₈	—	107	1	no	—
486	C₂×Q₈	—	107	1	no	—
487	C₂×Q₈	—	428	2	no	—
488	C₂×Q₈	C₂²×D₁₀₇	1	2	yes	—
489	C₂×D₄	—	107	1	no	—
490	C₂×D₄	—	107	2	no	—
491	C₂×D₄	—	107	2	no	—
492	C₂×D₄	—	107	1	no	—
493	C₂×D₄	—	107	2	no	—
494	C₂×D₄	—	107	2	no	—
495	C₂×D₄	—	107	1	no	—
496	C₂×D₄	—	107	1	no	—
497	C₂×D₄	—	107	2	no	—
498	C₂×D₄	—	107	2	no	—
499	C₂×D₄	—	107	1	no	—
500	C₂×D₄	—	107	2	no	—
501	C₂×D₄	—	107	1	no	—
502	C₂×D₄	—	107	1	no	—
503	C₂×D₄	—	428	4	no	—
504	C₂×D₄	—	428	2	no	—
505	C₂×D₄	C₂²×D₁₀₇	1	2	yes	—
506	C₂×D₄	C₂²×D₁₀₇	1	1	yes	characteristic
507	C₂×D₄	C₂²×D₁₀₇	1	1	yes	characteristic
508	C₂×D₄	C₂²×D₁₀₇	1	2	yes	—
509	C₂²×C₄	—	107	2	no	—
510	C₂²×C₄	—	107	2	no	—
511	C₂²×C₄	—	107	1	no	—
512	C₂²×C₄	—	107	1	no	—
513	C₂²×C₄	—	107	2	no	—
514	C₂²×C₄	—	107	2	no	—
515	C₂²×C₄	—	107	2	no	—
516	C₂²×C₄	—	107	2	no	—
517	C₂²×C₄	—	107	1	no	—
518	C₂²×C₄	—	107	1	no	—
519	C₂²×C₄	—	107	1	no	—
520	C₂²×C₄	—	107	1	no	—
521	C₂²×C₄	—	428	2	no	—
522	C₂²×C₄	C₂²×D₁₀₇	1	2	yes	—
523	C₂²×C₄	C₂²×D₁₀₇	1	1	yes	characteristic
524	C₂²×C₄	C₂²×D₁₀₇	1	1	yes	characteristic
525	C₂²×C₄	C₂²×D₁₀₇	1	2	yes	—
526	C₂²×C₄	C₂²×D₁₀₇	1	2	yes	—
527	C₄⋊C₄	—	107	1	no	—
528	C₄⋊C₄	—	107	2	no	—
529	C₄⋊C₄	—	107	2	no	—
530	C₄⋊C₄	—	107	2	no	—
531	C₄⋊C₄	—	107	2	no	—
532	C₄⋊C₄	—	107	2	no	—
533	C₄⋊C₄	—	107	2	no	—
534	C₄⋊C₄	—	107	1	no	—
535	C₄⋊C₄	—	107	1	no	—
536	C₄⋊C₄	—	107	2	no	—
537	C₄⋊C₄	—	107	2	no	—
538	C₄⋊C₄	—	107	1	no	—
539	C₄⋊C₄	—	107	1	no	—
540	C₄⋊C₄	—	107	1	no	—
541	C₄⋊C₄	—	107	2	no	—
542	C₄⋊C₄	—	107	2	no	—
543	C₄⋊C₄	—	107	2	no	—
544	C₄⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
545	C₄⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
546	C₄⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
547	C₄⋊C₄	C₂²×D₁₀₇	1	2	yes	—
548	C₄⋊C₄	C₂²×D₁₀₇	1	2	yes	—
549	C₄⋊C₄	C₂²×D₁₀₇	1	2	yes	—
550	C₄⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
551	C₂²⋊C₄	—	107	2	no	—
552	C₂²⋊C₄	—	107	2	no	—
553	C₂²⋊C₄	—	107	1	no	—
554	C₂²⋊C₄	—	107	2	no	—
555	C₂²⋊C₄	—	107	1	no	—
556	C₂²⋊C₄	—	107	2	no	—
557	C₂²⋊C₄	—	107	2	no	—
558	C₂²⋊C₄	—	107	2	no	—
559	C₂²⋊C₄	—	107	1	no	—
560	C₂²⋊C₄	—	107	1	no	—
561	C₂²⋊C₄	—	107	2	no	—
562	C₂²⋊C₄	—	107	2	no	—
563	C₂²⋊C₄	—	107	2	no	—
564	C₂²⋊C₄	—	107	2	no	—
565	C₂²⋊C₄	—	107	2	no	—
566	C₂²⋊C₄	—	107	2	no	—
567	C₂²⋊C₄	—	107	1	no	—
568	C₂²⋊C₄	—	107	1	no	—
569	C₂²⋊C₄	—	107	2	no	—
570	C₂²⋊C₄	—	107	2	no	—
571	C₂²⋊C₄	—	107	1	no	—
572	C₂²⋊C₄	—	107	2	no	—
573	C₂²⋊C₄	—	107	1	no	—
574	C₂²⋊C₄	C₂²×D₁₀₇	1	2	yes	—
575	C₂²⋊C₄	C₂²×D₁₀₇	1	2	yes	—
576	C₂²⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
577	C₂²⋊C₄	C₂²×D₁₀₇	1	2	yes	—
578	C₂²⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
579	C₄²	—	107	1	no	—
580	C₄²	—	107	2	no	—
581	C₄²	—	107	2	no	—
582	C₄²	C₂²×D₁₀₇	1	1	yes	characteristic
583	C₂³	—	107	1	no	—
584	C₂³	—	107	2	no	—
585	C₂³	—	107	1	no	—
586	C₂³	—	107	1	no	—
587	C₂³	—	428	2	no	—
588	C₂³	—	428	2	no	—
589	C₂³	—	428	1	no	—
590	C₂³	—	214	4	no	—
591	C₂³	—	214	2	no	—
592	C₂³	—	214	2	no	—
593	C₂³	C₂³×D₁₀₇	1	2	yes	—
594	C₂³	C₂³×D₁₀₇	1	1	yes	characteristic
595	C₂³	C₂³×D₁₀₇	1	1	yes	characteristic
596	Q₈	—	4	2	no	—
597	Q₈	—	428	2	no	—
598	Q₈	—	428	2	no	—
599	Q₈	—	428	1	no	—
600	Q₈	—	214	2	no	—
601	Q₈	—	214	2	no	—
602	D₄	—	2	4	no	—
603	D₄	—	2	2	no	—
604	D₄	—	2	2	no	—
605	D₄	—	4	2	no	—
606	D₄	—	428	2	no	—
607	D₄	—	428	2	no	—
608	D₄	—	428	1	no	—
609	D₄	—	428	2	no	—
610	D₄	—	428	2	no	—
611	D₄	—	428	1	no	—
612	D₄	—	428	1	no	—
613	D₄	—	428	2	no	—
614	D₄	—	428	2	no	—
615	D₄	—	214	2	no	—
616	D₄	—	214	2	no	—
617	D₄	—	214	4	no	—
618	D₄	—	214	2	no	—
619	D₄	—	214	2	no	—
620	C₂×C₄	—	2	4	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	4	2	no	—
624	C₂×C₄	—	4	2	no	—
625	C₂×C₄	—	107	1	no	—
626	C₂×C₄	—	107	1	no	—
627	C₂×C₄	—	107	2	no	—
628	C₂×C₄	—	107	2	no	—
629	C₂×C₄	—	107	2	no	—
630	C₂×C₄	—	107	1	no	—
631	C₂×C₄	—	107	1	no	—
632	C₂×C₄	—	107	1	no	—
633	C₂×C₄	—	428	1	no	—
634	C₂×C₄	—	428	1	no	—
635	C₂×C₄	—	428	2	no	—
636	C₂×C₄	—	428	2	no	—
637	C₂×C₄	—	428	2	no	—
638	C₂×C₄	—	428	2	no	—
639	C₂×C₄	—	428	1	no	—
640	C₂×C₄	—	428	2	no	—
641	C₂×C₄	—	428	2	no	—
642	C₂×C₄	—	214	2	no	—
643	C₂×C₄	—	214	2	no	—
644	C₂×C₄	—	214	2	no	—
645	C₂×C₄	C₂³×D₁₀₇	1	1	yes	characteristic
646	C₂×C₄	C₂³×D₁₀₇	1	2	yes	—
647	C₂×C₄	C₂³×D₁₀₇	1	1	yes	characteristic
648	C₂×C₄	C₂³×D₁₀₇	1	1	yes	characteristic
649	C₂×C₄	C₂³×D₁₀₇	1	2	yes	—
650	C₂×C₄	C₂³×D₁₀₇	1	2	yes	—
651	C₂×C₄	C₂³×D₁₀₇	1	1	yes	characteristic
652	C₂×C₄	C₂³×D₁₀₇	1	1	yes	characteristic
653	C₂²	—	2	1	no	—
654	C₂²	—	2	1	no	—
655	C₂²	—	2	1	no	—
656	C₂²	—	2	2	no	—
657	C₂²	—	2	1	no	—
658	C₂²	—	2	2	no	—
659	C₂²	—	2	1	no	—
660	C₂²	—	2	2	no	—
661	C₂²	—	856	4	no	—
662	C₂²	—	107	2	no	—
663	C₂²	—	428	4	no	—
664	C₂²	—	214	1	no	—
665	C₂²	—	214	2	no	—
666	C₂²	—	214	1	no	—
667	C₂²	—	214	1	no	—
668	C₂²	—	214	2	no	—
669	C₂²	—	214	1	no	—
670	C₂²	—	214	1	no	—
671	C₂²	—	214	2	no	—
672	C₂²	—	214	1	no	—
673	C₂²	—	214	1	no	—
674	C₂²	—	214	1	no	—
675	C₂²	#16812154	1	2	yes	—
676	C₂²	C₂⁴×D₁₀₇	1	1	yes	characteristic
677	C₄	—	2	2	no	—
678	C₄	—	2	2	no	—
679	C₄	—	2	1	no	—
680	C₄	—	2	2	no	—
681	C₄	—	2	1	no	—
682	C₄	—	2	1	no	—
683	C₄	—	2	1	no	—
684	C₄	—	214	2	no	—
685	C₄	—	214	1	no	—
686	C₄	—	214	1	no	—
687	C₄	—	214	1	no	—
688	C₄	—	214	1	no	—
689	C₄	—	214	2	no	—
690	C₄	—	214	2	no	—
691	C₄	—	214	1	no	—
692	C₄	#16812155	1	2	yes	—
693	C₂	—	2	2	no	—
694	C₂	—	4	2	no	—
695	C₂	—	4	1	no	—
696	C₂	—	428	2	no	—
697	C₂	—	428	1	no	—
698	C₂	—	428	1	no	—
699	C₂	—	214	2	no	—
700	C₂	C₂×#16812154	1	1	yes	characteristic
701	C₂	C₂×#16812155	1	1	yes	characteristic
702	C₂	2₋¹⁺⁴×D₁₀₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₀₇
commutator, socle, cosocle	C₂²×C₁₀₇	C₂⁵
Fitting	#547×C₁₀₇	C₂
hypercenter	#547	D₁₀₇
hypocenter	C₁₀₇	#3536
LCS	G ▷ C₂²×C₁₀₇ ▷ C₁₀₇
UCS	C₁ ◁ C₂² ◁ #547

Complements

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

N	H ≅ G/N	type
1. #20293374	C₂	semidirect
2. #20293373	C₂	semidirect
3. #20293338	C₂	semidirect
4. #20293332	C₂	semidirect
5. #20293286	C₂	semidirect
6. #20293283	C₂	semidirect
7. #20293278	C₂	semidirect
8. #20293274	C₂	semidirect
9. #20293272	C₂	semidirect
10. #20293269	C₂	semidirect
11. #20293265	C₂	semidirect
12. #20293252	C₂	semidirect
13. #20293251	C₂	semidirect
14. #20293242	C₂	semidirect
15. #20293221	C₂	semidirect
16. #20293213	C₂	semidirect
17. #20293208	C₂	semidirect
18. #20293206	C₂	semidirect
19. #20293205	C₂	semidirect
20. #20293136	C₂	semidirect
21. C₂×#16812089	C₂	semidirect
22. #121×D₁₀₇	C₂	semidirect
23. #547×C₁₀₇	C₂	semidirect
24. C₂×#13133818	C₂²	semidirect
25. C₂×#13133818	C₂²	semidirect
26. C₂×#13133818	C₂²	semidirect
27. C₂×#13133817	C₂²	semidirect
28. C₂²×Dic₂₁₄	C₂²	semidirect
32. #16812108	C₂²	semidirect
33. #16812104	C₂²	semidirect
34. #16812102	C₂²	semidirect
35. #16812100	C₂²	semidirect
36. #16812099	C₂²	semidirect
37. #16812098	C₂²	semidirect
38. #16812097	C₂²	semidirect
39. #16812096	C₂²	semidirect
40. #16812095	C₂²	semidirect
41. #16812095	C₂²	semidirect
42. #16812095	C₂²	semidirect
43. #16812094	C₂²	semidirect
44. #16812094	C₂²	semidirect
45. #16812094	C₂²	semidirect
46. #16812093	C₂²	semidirect
47. #16812092	C₂²	semidirect
48. #16812092	C₂²	semidirect
49. #16812091	C₂²	semidirect
50. #16812091	C₂²	semidirect
54. #16812089	C₂²	semidirect
55. #16812089	C₂²	semidirect
56. #16812089	C₂²	semidirect
57. #16812089	C₂²	semidirect
58. #16812089	C₂²	semidirect
59. #16812088	C₂²	semidirect
60. #16812088	C₂²	semidirect
61. #16812088	C₂²	semidirect
64. #16812087	C₂²	semidirect
65. #16812087	C₂²	semidirect
66. #16812086	C₂²	semidirect
67. #16812086	C₂²	semidirect
68. #16812086	C₂²	semidirect
70. #16812085	C₂²	semidirect
71. #16812085	C₂²	semidirect
73. #16812084	C₂²	semidirect
74. #16812084	C₂²	semidirect
76. #16812083	C₂²	semidirect
77. #16812083	C₂²	semidirect
78. #16812083	C₂²	semidirect
81. #16812082	C₂²	semidirect
83. #16812081	C₂²	semidirect
84. #16812081	C₂²	semidirect
85. #16812081	C₂²	semidirect
86. #16812081	C₂²	semidirect
88. #16812080	C₂²	semidirect
89. #16812080	C₂²	semidirect
94. C₄×Dic₂₁₄	C₂²	semidirect
95. #16812074	C₂²	semidirect
97. D₄×Dic₁₀₇	C₂²	semidirect
99. #16812071	C₂²	semidirect
102. C₄×C₂²⋊D₁₀₇	C₂²	semidirect
103. (C₂²⋊D₁₀₇)⋊C₄	C₂²	semidirect
104. #16812066	C₂²	semidirect
105. C₂×C₄⋊Dic₁₀₇	C₂²	semidirect
107. C₄⋊C₄×D₁₀₇	C₂²	semidirect
112. C₂×#41×C₁₀₇	C₂²	semidirect
113. C₄⋊Q₈×C₁₀₇	C₂²	semidirect
114. #123×C₁₀₇	C₂²	semidirect
115. #123×C₁₀₇	C₂²	semidirect
116. C₂²⋊Q₈×C₁₀₇	C₂²	semidirect
118. #121×C₁₀₇	C₂²	semidirect
119. C₄×D₄×C₁₀₇	C₂²	semidirect
120. C₄×D₄×C₁₀₇	C₂²	semidirect
121. C₂×C₄⋊C₄×C₁₀₇	C₂²	semidirect
122. C₂×C₄⋊C₄×C₁₀₇	C₂²	semidirect
352. C₁₀₇	#3536	semidirect
360. #547	D₁₀₇	semidirect
380. C₂×#41	C₂×D₁₀₇	semidirect
386. C₄⋊Q₈	C₂×D₁₀₇	semidirect
405. #123	C₂×D₁₀₇	semidirect
406. #123	C₂×D₁₀₇	semidirect
428. C₂²⋊Q₈	C₂×D₁₀₇	semidirect
448. #121	C₂×D₁₀₇	semidirect
463. C₄×D₄	C₂×D₁₀₇	semidirect
464. C₄×D₄	C₂×D₁₀₇	semidirect
469. C₂×C₄⋊C₄	C₂×D₁₀₇	semidirect
470. C₂×C₄⋊C₄	C₂×D₁₀₇	semidirect

Maximal subgroups

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

subgroup	index
#20293374	2
#20293373	2
#20293338	2
#20293332	2
#20293286	2
#20293283	2
#20293278	2
#20293274	2
#20293272	2
#20293269	2
#20293265	2
#20293252	2
#20293251	2
#20293242	2
#20293221	2
#20293213	2
#20293208	2
#20293206	2
#20293205	2
#20293136	2
C₂×#16812089	2
#121×D₁₀₇	2
#547×C₁₀₇	2
#3536	107