Subgroups — #28350791

Order 13696.

1260 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20293368	C₂	1	4	yes	maximal, complemented
2	#20293362	C₂	1	1	yes	maximal, characteristic, complemented
3	#20293299	C₂	1	1	yes	maximal, characteristic, complemented
4	#20293298	C₂	1	1	yes	maximal, characteristic, complemented
5	#20293273	C₂	1	2	yes	maximal, complemented
6	#20293268	C₂	1	2	yes	maximal, complemented
7	D₄×D₄₂₈	C₂	1	2	yes	maximal, complemented
8	D₄×D₄₂₈	C₂	1	1	yes	maximal, characteristic, complemented
9	#20293261	C₂	1	2	yes	maximal, complemented
10	#20293233	C₂	1	2	yes	maximal, complemented
11	#20293232	C₂	1	2	yes	maximal, complemented
12	#20293196	C₂	1	2	yes	maximal, complemented
13	#20293195	C₂	1	2	yes	maximal, complemented
14	#20293188	C₂	1	4	yes	maximal, complemented
15	C₂×#16812106	C₂	1	1	yes	maximal, characteristic, complemented
16	#20293161	C₂	1	1	yes	maximal, characteristic, complemented
17	#529×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#13133819	C₂²	1	2	yes	complemented
19	C₂×#13133818	C₂²	1	2	yes	complemented
20	C₂²×D₄₂₈	C₂²	1	2	yes	complemented
21	C₂²×D₄₂₈	C₂²	1	2	yes	complemented
22	C₂²×D₄₂₈	C₂²	1	2	yes	complemented
23	C₂²×D₄₂₈	C₂²	1	2	yes	complemented
24	C₂×D₄×D₁₀₇	C₂²	1	4	yes	complemented
25	C₂×D₄×D₁₀₇	C₂²	1	2	yes	complemented
26	#16812106	C₂²	1	1	yes	characteristic
27	#16812106	C₂²	1	2	yes	complemented
28	#16812106	C₂²	1	2	yes	complemented
29	#16812106	C₂²	1	1	yes	characteristic, complemented
30	#16812106	C₂²	1	2	yes	complemented
31	#16812106	C₂²	1	2	yes	complemented
32	#16812105	C₂²	1	2	yes	complemented
33	#16812103	C₂²	1	2	yes	complemented
34	#16812101	C₂²	1	1	yes	characteristic, complemented
35	#16812098	C₂²	1	2	yes	complemented
36	#16812097	C₂²	1	1	yes	characteristic, complemented
37	#16812097	C₂²	1	2	yes	complemented
38	#16812094	C₂²	1	4	yes	complemented
39	#16812094	C₂²	1	4	yes	complemented
40	#16812094	C₂²	1	4	yes	complemented
41	#16812094	C₂²	1	4	yes	complemented
42	#16812092	C₂²	1	2	yes	complemented
43	#16812088	C₂²	1	1	yes	characteristic, complemented
44	#16812084	C₂²	1	4	yes	complemented
45	#16812084	C₂²	1	4	yes	complemented
46	#16812084	C₂²	1	4	yes	complemented
47	#16812084	C₂²	1	2	yes	complemented
48	#16812084	C₂²	1	2	yes	complemented
49	#16812084	C₂²	1	4	yes	complemented
50	#16812083	C₂²	1	1	yes	characteristic
51	#16812083	C₂²	1	2	yes	complemented
52	#16812083	C₂²	1	2	yes	complemented
53	#16812082	C₂²	1	4	yes	complemented
54	#16812082	C₂²	1	4	yes	complemented
55	#16812082	C₂²	1	4	yes	complemented
56	#16812082	C₂²	1	4	yes	complemented
57	#16812079	C₂²	1	4	yes	complemented
58	#16812079	C₂²	1	4	yes	complemented
59	#16812079	C₂²	1	4	yes	complemented
60	#16812079	C₂²	1	4	yes	complemented
61	#16812079	C₂²	1	4	yes	complemented
62	#16812077	C₂²	1	4	yes	complemented
63	C₄×Dic₂₁₄	C₂²	1	1	yes	characteristic, complemented
64	C₄×D₄₂₈	C₂²	1	1	yes	characteristic, complemented
65	C₄×D₄₂₈	C₂²	1	2	yes	complemented
66	C₄×D₄₂₈	C₂²	1	2	yes	complemented
67	#16812071	C₂²	1	2	yes	complemented
68	#16812071	C₂²	1	2	yes	complemented
69	C₄×C₂²⋊D₁₀₇	C₂²	1	2	yes	complemented
70	#16812066	C₂²	1	2	yes	complemented
71	C₂²⋊C₄×D₁₀₇	C₂²	1	4	yes	complemented
72	#126×C₁₀₇	C₂²	1	2	yes	complemented
73	#125×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
74	#124×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
75	#123×C₁₀₇	C₂²	1	2	yes	complemented
76	C₂²⋊Q₈×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
77	#121×C₁₀₇	C₂²	1	1	yes	characteristic
78	C₄×Q₈×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
79	C₄×D₄×C₁₀₇	C₂²	1	2	yes	complemented
80	C₄×D₄×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
81	#117×C₁₀₇	C₂²	1	2	yes	complemented
82	C₂×C₄²×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
83	C₂³×D₁₀₇	C₂³	1	4	yes	—
84	C₂³×D₁₀₇	C₂³	1	4	yes	—
85	#13133819	—	4	4	no	—
86	#13133818	—	4	4	no	—
87	C₂×Dic₂₁₄	C₂³	1	1	yes	characteristic
88	C₂×D₄₂₈	—	4	4	no	—
89	C₂×D₄₂₈	—	4	4	no	—
90	C₂×D₄₂₈	—	4	4	no	—
91	C₂×D₄₂₈	—	4	4	no	—
92	C₂×D₄₂₈	C₂³	1	2	yes	—
93	C₂×D₄₂₈	C₂³	1	2	yes	—
94	C₂×D₄₂₈	C₂³	1	1	yes	characteristic
95	C₂×D₄₂₈	C₂³	1	2	yes	—
96	C₂×D₄₂₈	C₂³	1	2	yes	—
97	C₂×D₄₂₈	C₂³	1	4	yes	—
98	C₂×D₄₂₈	C₂³	1	4	yes	—
99	C₂×D₄₂₈	C₂³	1	2	yes	—
100	C₂×D₄₂₈	C₂³	1	4	yes	—
101	C₂×D₄₂₈	C₂³	1	4	yes	—
102	C₂×D₄₂₈	C₂³	1	4	yes	—
103	C₂×D₄₂₈	C₂³	1	4	yes	—
104	C₂×D₄₂₈	C₂³	1	2	yes	—
105	C₂×C₂²⋊D₁₀₇	C₂³	1	2	yes	—
106	C₂×C₂²⋊D₁₀₇	C₂³	1	4	yes	—
107	C₂×C₂²⋊D₁₀₇	C₂³	1	4	yes	—
108	C₂×C₂²⋊D₁₀₇	C₂³	1	4	yes	—
109	D₄×D₁₀₇	—	4	4	no	—
110	D₄×D₁₀₇	—	4	8	no	—
111	C₂×C₄×D₁₀₇	C₂³	1	2	yes	—
112	C₂×C₄×D₁₀₇	C₂³	1	4	yes	—
113	C₂×C₄×D₁₀₇	C₂³	1	4	yes	—
114	C₂×C₄×D₁₀₇	C₂³	1	4	yes	—
115	C₄⋊Dic₁₀₇	C₂³	1	1	yes	characteristic
116	C₄⋊Dic₁₀₇	C₂³	1	1	yes	characteristic
117	Dic₁₀₇⋊C₄	C₂³	1	2	yes	—
118	Dic₁₀₇⋊C₄	C₂³	1	2	yes	—
119	Dic₁₀₇⋊C₄	C₂³	1	2	yes	—
120	Dic₁₀₇⋊C₄	C₂³	1	2	yes	—
121	C₂²⋊Dic₁₀₇	C₂³	1	2	yes	—
122	(C₂×D₁₀₇)⋊C₄	C₂³	1	4	yes	—
123	(C₂×D₁₀₇)⋊C₄	C₂³	1	4	yes	—
124	(C₂×D₁₀₇)⋊C₄	C₂³	1	2	yes	—
125	(C₂×D₁₀₇)⋊C₄	C₂³	1	2	yes	—
126	(C₂×D₁₀₇)⋊C₄	C₂³	1	2	yes	—
127	(C₂×D₁₀₇)⋊C₄	C₂³	1	4	yes	—
128	(C₂×D₁₀₇)⋊C₄	C₂³	1	4	yes	—
129	(C₂×D₁₀₇)⋊C₄	C₂³	1	4	yes	—
130	(C₂×D₁₀₇)⋊C₄	C₂³	1	4	yes	—
131	(C₂×D₁₀₇)⋊C₄	C₂³	1	2	yes	—
132	C₄×Dic₁₀₇	C₂³	1	2	yes	—
133	C₂×Q₈×C₁₀₇	C₂³	1	1	yes	characteristic
134	C₂×D₄×C₁₀₇	C₂³	1	2	yes	—
135	C₂×D₄×C₁₀₇	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
137	C₂²×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
138	C₂²×C₄×C₁₀₇	C₂³	1	2	yes	—
139	C₂²×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
140	C₄⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
141	C₄⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
142	C₄⋊C₄×C₁₀₇	C₂³	1	2	yes	—
143	C₄⋊C₄×C₁₀₇	C₂³	1	2	yes	—
144	C₄⋊C₄×C₁₀₇	C₂³	1	2	yes	—
145	C₄⋊C₄×C₁₀₇	C₂³	1	2	yes	—
146	C₂²⋊C₄×C₁₀₇	C₂³	1	2	yes	—
147	C₂²⋊C₄×C₁₀₇	C₂³	1	2	yes	—
148	C₂²⋊C₄×C₁₀₇	C₂³	1	2	yes	—
149	C₂²⋊C₄×C₁₀₇	C₂³	1	2	yes	—
150	C₂²⋊C₄×C₁₀₇	C₂³	1	2	yes	—
151	C₄²×C₁₀₇	C₂³	1	1	yes	characteristic
152	C₄²×C₁₀₇	C₂³	1	2	yes	—
153	C₄²×C₁₀₇	C₂³	1	1	yes	characteristic
154	C₄²×C₁₀₇	C₂³	1	1	yes	characteristic
155	C₄²×C₁₀₇	C₂³	1	1	yes	characteristic
156	C₂³×C₁₀₇	C₂⁴	1	2	yes	—
157	C₂³×C₁₀₇	C₂⁴	1	1	yes	characteristic
158	C₂²×D₁₀₇	—	2	8	no	—
159	C₂²×D₁₀₇	—	4	4	no	—
160	C₂²×D₁₀₇	—	4	4	no	—
161	C₂²×D₁₀₇	—	4	4	no	—
162	C₂²×D₁₀₇	—	4	4	no	—
163	C₂²×D₁₀₇	—	4	4	no	—
164	C₂²×D₁₀₇	C₂⁴	1	2	yes	—
165	C₂²×D₁₀₇	C₂⁴	1	4	yes	—
166	C₂²×D₁₀₇	C₂⁴	1	4	yes	—
167	Q₈×C₁₀₇	—	2	2	no	—
168	D₄×C₁₀₇	—	2	4	no	—
169	D₄×C₁₀₇	—	2	2	no	—
170	C₂×C₄×C₁₀₇	—	2	2	no	—
171	C₂×C₄×C₁₀₇	—	2	2	no	—
172	C₂×C₄×C₁₀₇	—	2	2	no	—
173	C₂×C₄×C₁₀₇	—	2	4	no	—
174	C₂×C₄×C₁₀₇	C₂⁴	1	1	yes	characteristic
175	C₂×C₄×C₁₀₇	C₂⁴	1	1	yes	characteristic
176	C₂×C₄×C₁₀₇	C₂⁴	1	1	yes	characteristic
177	C₂×C₄×C₁₀₇	C₂⁴	1	1	yes	characteristic
178	C₂×C₄×C₁₀₇	C₂⁴	1	2	yes	—
179	C₂×C₄×C₁₀₇	C₂⁴	1	2	yes	—
180	C₂×C₄×C₁₀₇	C₂⁴	1	2	yes	—
181	C₂×C₄×C₁₀₇	C₂⁴	1	1	yes	characteristic
182	C₂×C₄×C₁₀₇	C₂⁴	1	1	yes	characteristic
183	C₂²⋊D₁₀₇	—	2	4	no	—
184	C₂²⋊D₁₀₇	—	4	4	no	—
185	C₂²⋊D₁₀₇	—	4	4	no	—
186	C₂²⋊D₁₀₇	—	4	4	no	—
187	C₂×Dic₁₀₇	C₂⁴	1	2	yes	—
188	C₂×Dic₁₀₇	C₂⁴	1	2	yes	—
189	C₂×Dic₁₀₇	C₂⁴	1	2	yes	—
190	D₄₂₈	—	2	4	no	—
191	D₄₂₈	—	2	2	no	—
192	D₄₂₈	—	2	4	no	—
193	D₄₂₈	—	2	4	no	—
194	D₄₂₈	—	2	4	no	—
195	D₄₂₈	—	4	4	no	—
196	D₄₂₈	—	4	4	no	—
197	D₄₂₈	—	4	4	no	—
198	D₄₂₈	—	4	4	no	—
199	D₄₂₈	—	4	2	no	—
200	D₄₂₈	—	4	4	no	—
201	D₄₂₈	—	4	2	no	—
202	D₄₂₈	—	4	4	no	—
203	C₄×D₁₀₇	—	2	4	no	—
204	C₄×D₁₀₇	—	4	4	no	—
205	C₄×D₁₀₇	—	4	4	no	—
206	C₄×D₁₀₇	—	4	4	no	—
207	Dic₂₁₄	—	2	2	no	—
208	C₂²×C₁₀₇	—	2	1	no	—
209	C₂²×C₁₀₇	—	2	1	no	—
210	C₂²×C₁₀₇	—	2	2	no	—
211	C₂²×C₁₀₇	—	2	2	no	—
212	C₂²×C₁₀₇	—	2	2	no	—
213	C₂²×C₁₀₇	H(5,𝔽₂)	1	2	yes	—
214	C₂²×C₁₀₇	C₂⁵	1	1	yes	characteristic
215	C₂×D₁₀₇	—	2	2	no	—
216	C₂×D₁₀₇	—	2	4	no	—
217	C₂×D₁₀₇	—	2	4	no	—
218	C₂×D₁₀₇	—	2	4	no	—
219	C₂×D₁₀₇	—	2	2	no	—
220	C₂×D₁₀₇	—	2	4	no	—
221	C₂×D₁₀₇	—	2	4	no	—
222	C₂×D₁₀₇	—	2	4	no	—
223	C₂×D₁₀₇	—	2	2	no	—
224	C₂×D₁₀₇	—	8	8	no	—
225	C₂×D₁₀₇	—	8	8	no	—
226	C₄×C₁₀₇	—	2	2	no	—
227	C₄×C₁₀₇	—	2	2	no	—
228	C₄×C₁₀₇	—	2	2	no	—
229	C₄×C₁₀₇	—	2	1	no	—
230	C₄×C₁₀₇	—	2	1	no	—
231	C₄×C₁₀₇	—	2	1	no	—
232	C₄×C₁₀₇	—	2	1	no	—
233	C₄×C₁₀₇	H(5,𝔽₂)	1	2	yes	—
234	C₄×C₁₀₇	H(5,𝔽₂)	1	2	yes	—
235	Dic₁₀₇	—	2	2	no	—
236	Dic₁₀₇	—	2	2	no	—
237	Dic₁₀₇	—	2	2	no	—
238	C₂×C₁₀₇	—	2	2	no	—
239	C₂×C₁₀₇	—	4	2	no	—
240	C₂×C₁₀₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
241	C₂×C₁₀₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
242	C₂×C₁₀₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
243	D₁₀₇	—	4	4	no	—
244	D₁₀₇	—	4	2	no	—
245	D₁₀₇	—	4	4	no	—
246	#3543	—	107	1	no	maximal, Sylow
247	C₁₀₇	#3543	1	1	yes	characteristic, complemented, Sylow
248	#560	—	107	4	no	—
249	#559	—	107	1	no	—
250	#550	—	107	1	no	—
251	#550	—	107	1	no	—
252	#546	—	107	2	no	—
253	#546	—	107	2	no	—
254	D₄²	—	107	2	no	—
255	D₄²	—	107	1	no	—
256	D₄²	—	107	2	no	—
257	#540	—	107	2	no	—
258	#540	—	107	2	no	—
259	#535	—	107	2	no	—
260	#535	—	107	2	no	—
261	#534	—	107	4	no	—
262	C₂×#127	—	107	1	no	—
263	#529	—	107	1	no	—
264	#529	D₁₀₇	1	1	yes	characteristic, complemented
265	C₂×#41	—	107	2	no	—
266	C₂×#41	—	107	2	no	—
267	C₂²×D₄	—	107	4	no	—
268	C₂²×D₄	—	107	2	no	—
269	C₂²×D₄	—	107	2	no	—
270	C₂²×D₄	—	107	2	no	—
271	C₂²×D₄	—	107	2	no	—
272	C₂²×D₄	—	107	2	no	—
273	#127	—	107	2	no	—
274	#127	—	107	2	no	—
275	#127	—	107	2	no	—
276	#127	—	107	1	no	—
277	#127	—	107	1	no	—
278	#127	—	107	2	no	—
279	#127	—	107	2	no	—
280	#126	—	107	2	no	—
281	#126	C₂×D₁₀₇	1	2	yes	complemented
282	#125	—	107	1	no	—
283	#125	C₂×D₁₀₇	1	1	yes	characteristic, complemented
284	#124	—	107	2	no	—
285	#124	—	107	1	no	—
286	#124	—	107	2	no	—
287	#124	C₂×D₁₀₇	1	1	yes	characteristic, complemented
288	#123	—	107	2	no	—
289	#123	—	107	4	no	—
290	#123	—	107	4	no	—
291	#123	—	107	4	no	—
292	#123	—	107	4	no	—
293	#123	C₂×D₁₀₇	1	2	yes	complemented
294	C₂²⋊Q₈	—	107	1	no	—
295	C₂²⋊Q₈	C₂×D₁₀₇	1	1	yes	characteristic, complemented
296	#121	—	107	1	no	—
297	#121	—	107	2	no	—
298	#121	—	107	2	no	—
299	#121	—	107	4	no	—
300	#121	—	107	4	no	—
301	#121	—	107	4	no	—
302	#121	—	107	2	no	—
303	#121	—	107	2	no	—
304	#121	—	107	4	no	—
305	#121	—	107	4	no	—
306	#121	—	107	4	no	—
307	#121	—	107	4	no	—
308	#121	—	107	4	no	—
309	#121	C₂×D₁₀₇	1	1	yes	characteristic
310	#120	—	107	4	no	—
311	#120	—	107	4	no	—
312	#120	—	107	4	no	—
313	#120	—	107	4	no	—
314	#120	—	107	4	no	—
315	#120	—	107	4	no	—
316	C₄×Q₈	—	107	1	no	—
317	C₄×Q₈	C₂×D₁₀₇	1	1	yes	characteristic, complemented
318	C₄×D₄	—	107	2	no	—
319	C₄×D₄	—	107	2	no	—
320	C₄×D₄	—	107	2	no	—
321	C₄×D₄	—	107	1	no	—
322	C₄×D₄	—	107	2	no	—
323	C₄×D₄	—	107	2	no	—
324	C₄×D₄	C₂×D₁₀₇	1	2	yes	complemented
325	C₄×D₄	C₂×D₁₀₇	1	1	yes	characteristic, complemented
326	#117	—	107	2	no	—
327	#117	C₂×D₁₀₇	1	2	yes	complemented
328	C₂×C₂²⋊C₄	—	107	4	no	—
329	C₂×C₄²	C₂×D₁₀₇	1	1	yes	characteristic, complemented
330	C₂⁴	—	107	4	no	—
331	C₂⁴	—	107	4	no	—
332	#41	—	428	4	no	—
333	#41	—	428	4	no	—
334	C₂×Q₈	—	107	1	no	—
335	C₂×Q₈	C₂²×D₁₀₇	1	1	yes	characteristic
336	C₂×D₄	—	107	4	no	—
337	C₂×D₄	—	107	4	no	—
338	C₂×D₄	—	107	4	no	—
339	C₂×D₄	—	107	2	no	—
340	C₂×D₄	—	107	4	no	—
341	C₂×D₄	—	107	4	no	—
342	C₂×D₄	—	107	2	no	—
343	C₂×D₄	—	107	4	no	—
344	C₂×D₄	—	107	4	no	—
345	C₂×D₄	—	107	4	no	—
346	C₂×D₄	—	107	4	no	—
347	C₂×D₄	—	107	2	no	—
348	C₂×D₄	—	107	2	no	—
349	C₂×D₄	—	107	1	no	—
350	C₂×D₄	—	107	2	no	—
351	C₂×D₄	—	107	2	no	—
352	C₂×D₄	—	107	2	no	—
353	C₂×D₄	—	428	4	no	—
354	C₂×D₄	—	428	4	no	—
355	C₂×D₄	—	428	4	no	—
356	C₂×D₄	—	428	4	no	—
357	C₂×D₄	—	428	8	no	—
358	C₂×D₄	—	428	4	no	—
359	C₂×D₄	C₂²×D₁₀₇	1	2	yes	—
360	C₂×D₄	C₂²×D₁₀₇	1	1	yes	characteristic
361	C₂²×C₄	—	107	4	no	—
362	C₂²×C₄	—	107	4	no	—
363	C₂²×C₄	—	107	4	no	—
364	C₂²×C₄	—	107	2	no	—
365	C₂²×C₄	C₂²×D₁₀₇	1	1	yes	characteristic
366	C₂²×C₄	C₂²×D₁₀₇	1	1	yes	characteristic
367	C₂²×C₄	C₂²×D₁₀₇	1	1	yes	characteristic
368	C₂²×C₄	C₂²×D₁₀₇	1	2	yes	—
369	C₄⋊C₄	—	107	2	no	—
370	C₄⋊C₄	—	107	2	no	—
371	C₄⋊C₄	—	107	1	no	—
372	C₄⋊C₄	—	107	1	no	—
373	C₄⋊C₄	—	107	2	no	—
374	C₄⋊C₄	—	107	2	no	—
375	C₄⋊C₄	C₂²×D₁₀₇	1	2	yes	—
376	C₄⋊C₄	C₂²×D₁₀₇	1	2	yes	—
377	C₄⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
378	C₄⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
379	C₄⋊C₄	C₂²×D₁₀₇	1	2	yes	—
380	C₄⋊C₄	C₂²×D₁₀₇	1	2	yes	—
381	C₂²⋊C₄	—	107	2	no	—
382	C₂²⋊C₄	—	107	4	no	—
383	C₂²⋊C₄	—	107	4	no	—
384	C₂²⋊C₄	—	107	2	no	—
385	C₂²⋊C₄	—	107	2	no	—
386	C₂²⋊C₄	—	107	2	no	—
387	C₂²⋊C₄	—	107	2	no	—
388	C₂²⋊C₄	—	107	4	no	—
389	C₂²⋊C₄	—	107	4	no	—
390	C₂²⋊C₄	—	107	4	no	—
391	C₂²⋊C₄	—	107	4	no	—
392	C₂²⋊C₄	C₂²×D₁₀₇	1	2	yes	—
393	C₂²⋊C₄	C₂²×D₁₀₇	1	2	yes	—
394	C₂²⋊C₄	C₂²×D₁₀₇	1	2	yes	—
395	C₂²⋊C₄	C₂²×D₁₀₇	1	2	yes	—
396	C₂²⋊C₄	C₂²×D₁₀₇	1	2	yes	—
397	C₄²	—	107	2	no	—
398	C₄²	C₂²×D₁₀₇	1	1	yes	characteristic
399	C₄²	C₂²×D₁₀₇	1	1	yes	characteristic
400	C₄²	C₂²×D₁₀₇	1	1	yes	characteristic
401	C₄²	C₂²×D₁₀₇	1	1	yes	characteristic
402	C₄²	C₂²×D₁₀₇	1	2	yes	—
403	C₂³	—	107	4	no	—
404	C₂³	—	107	2	no	—
405	C₂³	—	107	4	no	—
406	C₂³	—	428	4	no	—
407	C₂³	—	428	4	no	—
408	C₂³	—	428	4	no	—
409	C₂³	—	428	4	no	—
410	C₂³	—	428	4	no	—
411	C₂³	—	214	8	no	—
412	C₂³	C₂³×D₁₀₇	1	2	yes	—
413	C₂³	C₂³×D₁₀₇	1	1	yes	characteristic
414	Q₈	—	2	2	no	—
415	Q₈	—	214	2	no	—
416	D₄	—	2	4	no	—
417	D₄	—	2	2	no	—
418	D₄	—	428	4	no	—
419	D₄	—	428	4	no	—
420	D₄	—	428	4	no	—
421	D₄	—	428	2	no	—
422	D₄	—	428	4	no	—
423	D₄	—	428	2	no	—
424	D₄	—	428	4	no	—
425	D₄	—	428	4	no	—
426	D₄	—	428	4	no	—
427	D₄	—	428	4	no	—
428	D₄	—	428	4	no	—
429	D₄	—	214	4	no	—
430	D₄	—	214	2	no	—
431	D₄	—	214	4	no	—
432	D₄	—	214	4	no	—
433	D₄	—	214	4	no	—
434	D₄	—	214	4	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	107	2	no	—
440	C₂×C₄	—	107	2	no	—
441	C₂×C₄	—	107	2	no	—
442	C₂×C₄	—	428	4	no	—
443	C₂×C₄	—	428	4	no	—
444	C₂×C₄	—	428	4	no	—
445	C₂×C₄	—	214	4	no	—
446	C₂×C₄	C₂³×D₁₀₇	1	1	yes	characteristic
447	C₂×C₄	C₂³×D₁₀₇	1	1	yes	characteristic
448	C₂×C₄	C₂³×D₁₀₇	1	1	yes	characteristic
449	C₂×C₄	C₂³×D₁₀₇	1	1	yes	characteristic
450	C₂×C₄	C₂³×D₁₀₇	1	2	yes	—
451	C₂×C₄	C₂³×D₁₀₇	1	2	yes	—
452	C₂×C₄	C₂³×D₁₀₇	1	2	yes	—
453	C₂×C₄	C₂³×D₁₀₇	1	1	yes	characteristic
454	C₂×C₄	C₂³×D₁₀₇	1	1	yes	characteristic
455	C₂²	—	2	1	no	—
456	C₂²	—	2	1	no	—
457	C₂²	—	2	2	no	—
458	C₂²	—	2	2	no	—
459	C₂²	—	2	2	no	—
460	C₂²	—	856	8	no	—
461	C₂²	—	856	8	no	—
462	C₂²	—	214	4	no	—
463	C₂²	—	214	4	no	—
464	C₂²	—	214	4	no	—
465	C₂²	—	214	2	no	—
466	C₂²	—	214	4	no	—
467	C₂²	—	214	2	no	—
468	C₂²	—	214	4	no	—
469	C₂²	—	214	2	no	—
470	C₂²	—	214	4	no	—
471	C₂²	#16812155	1	2	yes	—
472	C₂²	C₂⁴×D₁₀₇	1	1	yes	characteristic
473	C₄	—	2	2	no	—
474	C₄	—	2	1	no	—
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	2	2	no	—
479	C₄	—	2	2	no	—
480	C₄	—	214	2	no	—
481	C₄	—	214	2	no	—
482	C₄	—	214	2	no	—
483	C₄	#16812155	1	2	yes	—
484	C₄	#16812155	1	2	yes	—
485	C₂	—	2	2	no	—
486	C₂	—	4	2	no	—
487	C₂	—	428	4	no	—
488	C₂	—	428	2	no	—
489	C₂	—	428	4	no	—
490	C₂	C₂×#16812155	1	1	yes	characteristic
491	C₂	C₂×#16812155	1	1	yes	characteristic
492	C₂	C₂×#16812155	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₀₇
commutator, socle, cosocle	C₂²×C₁₀₇	C₂⁵
Fitting	#529×C₁₀₇	C₂
hypercenter	#529	D₁₀₇
hypocenter	C₁₀₇	#3543
LCS	G ▷ C₂²×C₁₀₇ ▷ C₁₀₇
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. #20293368	C₂	semidirect
2. #20293362	C₂	semidirect
3. #20293299	C₂	semidirect
4. #20293298	C₂	semidirect
5. #20293273	C₂	semidirect
6. #20293268	C₂	semidirect
7. D₄×D₄₂₈	C₂	semidirect
8. D₄×D₄₂₈	C₂	semidirect
9. #20293261	C₂	semidirect
10. #20293233	C₂	semidirect
11. #20293232	C₂	semidirect
12. #20293196	C₂	semidirect
13. #20293195	C₂	semidirect
14. #20293188	C₂	semidirect
15. C₂×#16812106	C₂	semidirect
16. #20293161	C₂	semidirect
17. #529×C₁₀₇	C₂	semidirect
18. C₂×#13133819	C₂²	semidirect
19. C₂×#13133818	C₂²	semidirect
20. C₂²×D₄₂₈	C₂²	semidirect
21. C₂²×D₄₂₈	C₂²	semidirect
22. C₂²×D₄₂₈	C₂²	semidirect
23. C₂²×D₄₂₈	C₂²	semidirect
24. C₂×D₄×D₁₀₇	C₂²	semidirect
25. C₂×D₄×D₁₀₇	C₂²	semidirect
27. #16812106	C₂²	semidirect
28. #16812106	C₂²	semidirect
29. #16812106	C₂²	semidirect
30. #16812106	C₂²	semidirect
31. #16812106	C₂²	semidirect
32. #16812105	C₂²	semidirect
33. #16812103	C₂²	semidirect
34. #16812101	C₂²	semidirect
35. #16812098	C₂²	semidirect
36. #16812097	C₂²	semidirect
37. #16812097	C₂²	semidirect
38. #16812094	C₂²	semidirect
39. #16812094	C₂²	semidirect
40. #16812094	C₂²	semidirect
41. #16812094	C₂²	semidirect
42. #16812092	C₂²	semidirect
43. #16812088	C₂²	semidirect
44. #16812084	C₂²	semidirect
45. #16812084	C₂²	semidirect
46. #16812084	C₂²	semidirect
47. #16812084	C₂²	semidirect
48. #16812084	C₂²	semidirect
49. #16812084	C₂²	semidirect
51. #16812083	C₂²	semidirect
52. #16812083	C₂²	semidirect
53. #16812082	C₂²	semidirect
54. #16812082	C₂²	semidirect
55. #16812082	C₂²	semidirect
56. #16812082	C₂²	semidirect
57. #16812079	C₂²	semidirect
58. #16812079	C₂²	semidirect
59. #16812079	C₂²	semidirect
60. #16812079	C₂²	semidirect
61. #16812079	C₂²	semidirect
62. #16812077	C₂²	semidirect
63. C₄×Dic₂₁₄	C₂²	semidirect
64. C₄×D₄₂₈	C₂²	semidirect
65. C₄×D₄₂₈	C₂²	semidirect
66. C₄×D₄₂₈	C₂²	semidirect
67. #16812071	C₂²	semidirect
68. #16812071	C₂²	semidirect
69. C₄×C₂²⋊D₁₀₇	C₂²	semidirect
70. #16812066	C₂²	semidirect
71. C₂²⋊C₄×D₁₀₇	C₂²	semidirect
72. #126×C₁₀₇	C₂²	semidirect
73. #125×C₁₀₇	C₂²	semidirect
74. #124×C₁₀₇	C₂²	semidirect
75. #123×C₁₀₇	C₂²	semidirect
76. C₂²⋊Q₈×C₁₀₇	C₂²	semidirect
78. C₄×Q₈×C₁₀₇	C₂²	semidirect
79. C₄×D₄×C₁₀₇	C₂²	semidirect
80. C₄×D₄×C₁₀₇	C₂²	semidirect
81. #117×C₁₀₇	C₂²	semidirect
82. C₂×C₄²×C₁₀₇	C₂²	semidirect
247. C₁₀₇	#3543	semidirect
264. #529	D₁₀₇	semidirect
281. #126	C₂×D₁₀₇	semidirect
283. #125	C₂×D₁₀₇	semidirect
287. #124	C₂×D₁₀₇	semidirect
293. #123	C₂×D₁₀₇	semidirect
295. C₂²⋊Q₈	C₂×D₁₀₇	semidirect
317. C₄×Q₈	C₂×D₁₀₇	semidirect
324. C₄×D₄	C₂×D₁₀₇	semidirect
325. C₄×D₄	C₂×D₁₀₇	semidirect
327. #117	C₂×D₁₀₇	semidirect
329. C₂×C₄²	C₂×D₁₀₇	semidirect

Maximal subgroups

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

subgroup	index
#20293368	2
#20293362	2
#20293299	2
#20293298	2
#20293273	2
#20293268	2
D₄×D₄₂₈	2
#20293261	2
#20293233	2
#20293232	2
#20293196	2
#20293195	2
#20293188	2
C₂×#16812106	2
#20293161	2
#529×C₁₀₇	2
#3543	107