Subgroups — #28350833

Order 13696.

1150 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20293365	C₂	1	4	yes	maximal, complemented
2	#20293347	C₂	1	1	yes	maximal, characteristic, complemented
3	#20293323	C₂	1	2	yes	maximal, complemented
4	#20293298	C₂	1	1	yes	maximal, characteristic, complemented
5	#20293295	C₂	1	2	yes	maximal, complemented
6	#20293281	C₂	1	1	yes	maximal, characteristic, complemented
7	#20293274	C₂	1	2	yes	maximal, complemented
8	#20293273	C₂	1	2	yes	maximal, complemented
9	D₄×D₄₂₈	C₂	1	1	yes	maximal, characteristic, complemented
10	#20293251	C₂	1	2	yes	maximal, complemented
11	#20293211	C₂	1	4	yes	maximal, complemented
12	#20293205	C₂	1	2	yes	maximal, complemented
13	#20293191	C₂	1	2	yes	maximal, complemented
14	#20293190	C₂	1	2	yes	maximal, complemented
15	#20293177	C₂	1	1	yes	maximal, characteristic, complemented
16	#20293161	C₂	1	1	yes	maximal, characteristic, complemented
17	#532×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#13133818	C₂²	1	2	yes	complemented
19	C₂×#13133818	C₂²	1	2	yes	complemented
20	C₂×#13133817	C₂²	1	2	yes	complemented
21	C₂²×D₄₂₈	C₂²	1	2	yes	—
22	C₂×D₄×D₁₀₇	C₂²	1	2	yes	—
23	#16812109	C₂²	1	1	yes	characteristic, complemented
24	#16812106	C₂²	1	1	yes	characteristic
25	#16812105	C₂²	1	2	yes	complemented
26	#16812105	C₂²	1	4	yes	complemented
27	#16812104	C₂²	1	4	yes	complemented
28	#16812103	C₂²	1	2	yes	complemented
29	#16812102	C₂²	1	4	yes	complemented
30	#16812101	C₂²	1	1	yes	characteristic, complemented
31	#16812098	C₂²	1	4	yes	complemented
32	#16812097	C₂²	1	1	yes	characteristic
33	#16812097	C₂²	1	2	yes	complemented
34	#16812096	C₂²	1	2	yes	—
35	#16812094	C₂²	1	4	yes	complemented
36	#16812093	C₂²	1	4	yes	complemented
37	#16812092	C₂²	1	2	yes	complemented
38	#16812091	C₂²	1	4	yes	complemented
39	#16812089	C₂²	1	2	yes	complemented
40	#16812088	C₂²	1	1	yes	characteristic, complemented
41	#16812088	C₂²	1	2	yes	complemented
42	#16812085	C₂²	1	4	yes	complemented
43	#16812084	C₂²	1	2	yes	—
44	#16812083	C₂²	1	1	yes	characteristic
45	#16812083	C₂²	1	2	yes	—
46	#16812083	C₂²	1	2	yes	—
47	#16812083	C₂²	1	2	yes	complemented
48	#16812083	C₂²	1	2	yes	complemented
49	#16812083	C₂²	1	2	yes	complemented
50	#16812082	C₂²	1	4	yes	complemented
51	#16812082	C₂²	1	4	yes	complemented
52	#16812081	C₂²	1	4	yes	complemented
53	#16812081	C₂²	1	4	yes	complemented
54	#16812081	C₂²	1	4	yes	complemented
55	#16812080	C₂²	1	4	yes	complemented
56	#16812079	C₂²	1	4	yes	—
57	#16812077	C₂²	1	4	yes	complemented
58	#16812077	C₂²	1	4	yes	complemented
59	#16812077	C₂²	1	4	yes	complemented
60	C₄×Dic₂₁₄	C₂²	1	1	yes	characteristic, complemented
61	#16812074	C₂²	1	2	yes	complemented
62	C₄×D₄₂₈	C₂²	1	1	yes	characteristic
63	C₄×D₄₂₈	C₂²	1	2	yes	complemented
64	C₄×D₄₂₈	C₂²	1	2	yes	complemented
65	#16812071	C₂²	1	2	yes	complemented
66	C₄×C₂²⋊D₁₀₇	C₂²	1	2	yes	complemented
67	(C₂²⋊D₁₀₇)⋊C₄	C₂²	1	4	yes	complemented
68	#16812068	C₂²	1	2	yes	complemented
69	#16812066	C₂²	1	2	yes	complemented
70	C₂×C₄⋊Dic₁₀₇	C₂²	1	2	yes	complemented
71	C₂²⋊C₄×D₁₀₇	C₂²	1	4	yes	complemented
72	C₂×#41×C₁₀₇	C₂²	1	2	yes	complemented
73	C₄⋊Q₈×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
74	#127×C₁₀₇	C₂²	1	1	yes	characteristic
75	#124×C₁₀₇	C₂²	1	2	yes	complemented
76	#121×C₁₀₇	C₂²	1	1	yes	characteristic
77	#121×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
78	#121×C₁₀₇	C₂²	1	2	yes	complemented
79	C₄×D₄×C₁₀₇	C₂²	1	1	yes	characteristic
80	C₄×D₄×C₁₀₇	C₂²	1	2	yes	complemented
81	C₄×D₄×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
82	C₂×C₄²×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
83	C₂³×D₁₀₇	C₂³	1	4	yes	—
84	#13133818	—	4	4	no	—
85	#13133818	—	4	4	no	—
86	#13133817	—	4	4	no	—
87	C₂×Dic₂₁₄	C₂³	1	2	yes	—
88	C₂×Dic₂₁₄	C₂³	1	1	yes	characteristic
89	C₂×D₄₂₈	—	4	4	no	—
90	C₂×D₄₂₈	C₂³	1	2	yes	—
91	C₂×D₄₂₈	C₂³	1	1	yes	characteristic
92	C₂×D₄₂₈	C₂³	1	2	yes	—
93	C₂×D₄₂₈	C₂³	1	2	yes	—
94	C₂×D₄₂₈	C₂³	1	4	yes	—
95	C₂×C₂²⋊D₁₀₇	C₂³	1	4	yes	—
96	C₂×C₂²⋊D₁₀₇	C₂³	1	2	yes	—
97	C₂×C₂²⋊D₁₀₇	C₂³	1	4	yes	—
98	C₂×C₂²⋊D₁₀₇	C₂³	1	4	yes	—
99	C₂×C₂²⋊D₁₀₇	C₂³	1	4	yes	—
100	C₂×C₂²⋊D₁₀₇	C₂³	1	4	yes	—
101	D₄×D₁₀₇	—	4	4	no	—
102	C₂²×Dic₁₀₇	C₂³	1	4	yes	—
103	C₂×C₄×D₁₀₇	C₂³	1	2	yes	—
104	C₂×C₄×D₁₀₇	C₂³	1	4	yes	—
105	C₂×C₄×D₁₀₇	C₂³	1	4	yes	—
106	C₄⋊Dic₁₀₇	C₂³	1	1	yes	characteristic
107	C₄⋊Dic₁₀₇	C₂³	1	2	yes	—
108	C₄⋊Dic₁₀₇	C₂³	1	4	yes	—
109	C₄⋊Dic₁₀₇	C₂³	1	1	yes	characteristic
110	C₄⋊Dic₁₀₇	C₂³	1	2	yes	—
111	Dic₁₀₇⋊C₄	C₂³	1	2	yes	—
112	Dic₁₀₇⋊C₄	C₂³	1	2	yes	—
113	Dic₁₀₇⋊C₄	C₂³	1	2	yes	—
114	Dic₁₀₇⋊C₄	C₂³	1	4	yes	—
115	Dic₁₀₇⋊C₄	C₂³	1	2	yes	—
116	C₂²⋊Dic₁₀₇	C₂³	1	4	yes	—
117	C₂²⋊Dic₁₀₇	C₂³	1	4	yes	—
118	C₂²⋊Dic₁₀₇	C₂³	1	2	yes	—
119	(C₂×D₁₀₇)⋊C₄	C₂³	1	2	yes	—
120	(C₂×D₁₀₇)⋊C₄	C₂³	1	4	yes	—
121	(C₂×D₁₀₇)⋊C₄	C₂³	1	2	yes	—
122	(C₂×D₁₀₇)⋊C₄	C₂³	1	2	yes	—
123	(C₂×D₁₀₇)⋊C₄	C₂³	1	4	yes	—
124	(C₂×D₁₀₇)⋊C₄	C₂³	1	4	yes	—
125	(C₂×D₁₀₇)⋊C₄	C₂³	1	2	yes	—
126	(C₂×D₁₀₇)⋊C₄	C₂³	1	4	yes	—
127	(C₂×D₁₀₇)⋊C₄	C₂³	1	4	yes	—
128	C₄×Dic₁₀₇	C₂³	1	2	yes	—
129	C₄×Dic₁₀₇	C₂³	1	4	yes	—
130	#41×C₁₀₇	—	4	4	no	—
131	C₂×Q₈×C₁₀₇	C₂³	1	2	yes	—
132	C₂×D₄×C₁₀₇	C₂³	1	1	yes	characteristic
133	C₂×D₄×C₁₀₇	C₂³	1	1	yes	characteristic
134	C₂×D₄×C₁₀₇	C₂³	1	2	yes	—
135	C₂×D₄×C₁₀₇	C₂³	1	2	yes	—
136	C₂×D₄×C₁₀₇	C₂³	1	2	yes	—
137	C₂×D₄×C₁₀₇	C₂³	1	2	yes	—
138	C₂²×C₄×C₁₀₇	C₂³	1	2	yes	—
139	C₂²×C₄×C₁₀₇	C₂³	1	2	yes	—
140	C₂²×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
141	C₂²×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
142	C₂²×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
143	C₄⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
144	C₄⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
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	C₄²×C₁₀₇	C₂³	1	1	yes	characteristic
151	C₄²×C₁₀₇	C₂³	1	1	yes	characteristic
152	C₄²×C₁₀₇	C₂³	1	1	yes	characteristic
153	C₄²×C₁₀₇	C₂³	1	1	yes	characteristic
154	C₂³×C₁₀₇	C₂⁴	1	2	yes	—
155	C₂³×C₁₀₇	C₂⁴	1	2	yes	—
156	C₂³×C₁₀₇	C₂⁴	1	1	yes	characteristic
157	C₂²×D₁₀₇	—	4	4	no	—
158	C₂²×D₁₀₇	—	4	4	no	—
159	C₂²×D₁₀₇	—	4	4	no	—
160	C₂²×D₁₀₇	C₂⁴	1	2	yes	—
161	C₂²×D₁₀₇	C₂⁴	1	4	yes	—
162	Q₈×C₁₀₇	—	4	2	no	—
163	D₄×C₁₀₇	—	2	2	no	—
164	D₄×C₁₀₇	—	2	2	no	—
165	D₄×C₁₀₇	—	4	2	no	—
166	D₄×C₁₀₇	—	4	2	no	—
167	D₄×C₁₀₇	—	4	2	no	—
168	D₄×C₁₀₇	—	4	2	no	—
169	C₂×C₄×C₁₀₇	—	2	2	no	—
170	C₂×C₄×C₁₀₇	—	2	4	no	—
171	C₂×C₄×C₁₀₇	—	2	4	no	—
172	C₂×C₄×C₁₀₇	—	2	2	no	—
173	C₂×C₄×C₁₀₇	—	4	1	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	1	yes	characteristic
181	C₂×C₄×C₁₀₇	C₂⁴	1	1	yes	characteristic
182	C₂²⋊D₁₀₇	—	4	4	no	—
183	C₂²⋊D₁₀₇	—	4	4	no	—
184	C₂²⋊D₁₀₇	—	4	2	no	—
185	C₂²⋊D₁₀₇	—	4	4	no	—
186	C₂²⋊D₁₀₇	—	4	4	no	—
187	C₂²⋊D₁₀₇	—	4	4	no	—
188	C₂×Dic₁₀₇	—	4	4	no	—
189	C₂×Dic₁₀₇	C₂⁴	1	2	yes	—
190	C₂×Dic₁₀₇	C₂⁴	1	4	yes	—
191	C₂×Dic₁₀₇	C₂⁴	1	2	yes	—
192	C₂×Dic₁₀₇	C₂⁴	1	2	yes	—
193	D₄₂₈	—	2	4	no	—
194	D₄₂₈	—	2	2	no	—
195	D₄₂₈	—	2	4	no	—
196	D₄₂₈	—	4	4	no	—
197	D₄₂₈	—	4	2	no	—
198	C₄×D₁₀₇	—	2	4	no	—
199	C₄×D₁₀₇	—	4	4	no	—
200	C₄×D₁₀₇	—	4	4	no	—
201	Dic₂₁₄	—	2	4	no	—
202	Dic₂₁₄	—	2	2	no	—
203	C₂²×C₁₀₇	—	2	2	no	—
204	C₂²×C₁₀₇	—	2	1	no	—
205	C₂²×C₁₀₇	—	2	2	no	—
206	C₂²×C₁₀₇	—	2	2	no	—
207	C₂²×C₁₀₇	—	2	1	no	—
208	C₂²×C₁₀₇	—	2	2	no	—
209	C₂²×C₁₀₇	—	2	1	no	—
210	C₂²×C₁₀₇	—	2	2	no	—
211	C₂²×C₁₀₇	—	2	2	no	—
212	C₂²×C₁₀₇	C₂⁵	1	1	yes	characteristic
213	C₂×D₁₀₇	—	2	2	no	—
214	C₂×D₁₀₇	—	2	4	no	—
215	C₂×D₁₀₇	—	2	4	no	—
216	C₂×D₁₀₇	—	2	2	no	—
217	C₂×D₁₀₇	—	2	4	no	—
218	C₂×D₁₀₇	—	2	2	no	—
219	C₂×D₁₀₇	—	8	8	no	—
220	C₄×C₁₀₇	—	2	1	no	—
221	C₄×C₁₀₇	—	2	2	no	—
222	C₄×C₁₀₇	—	2	2	no	—
223	C₄×C₁₀₇	—	2	1	no	—
224	C₄×C₁₀₇	—	2	1	no	—
225	C₄×C₁₀₇	—	2	1	no	—
226	C₄×C₁₀₇	H(5,𝔽₂)	1	2	yes	—
227	C₄×C₁₀₇	H(5,𝔽₂)	1	2	yes	—
228	Dic₁₀₇	—	2	2	no	—
229	Dic₁₀₇	—	2	4	no	—
230	Dic₁₀₇	—	2	2	no	—
231	Dic₁₀₇	—	2	2	no	—
232	C₂×C₁₀₇	—	4	2	no	—
233	C₂×C₁₀₇	—	4	2	no	—
234	C₂×C₁₀₇	—	4	1	no	—
235	C₂×C₁₀₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
236	C₂×C₁₀₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
237	C₂×C₁₀₇	#585	1	1	yes	characteristic
238	D₁₀₇	—	4	4	no	—
239	D₁₀₇	—	4	2	no	—
240	#3546	—	107	1	no	maximal, Sylow
241	C₁₀₇	#3546	1	1	yes	characteristic, complemented, Sylow
242	#560	—	107	4	no	—
243	#556	—	107	1	no	—
244	#553	—	107	2	no	—
245	#550	—	107	2	no	—
246	#550	—	107	1	no	—
247	#547	—	107	1	no	—
248	#546	—	107	2	no	—
249	#546	—	107	2	no	—
250	D₄²	—	107	1	no	—
251	#542	—	107	2	no	—
252	#538	—	107	4	no	—
253	#537	—	107	2	no	—
254	#535	—	107	2	no	—
255	#535	—	107	2	no	—
256	#532	—	107	1	no	—
257	#532	D₁₀₇	1	1	yes	characteristic, complemented
258	#529	—	107	1	no	—
259	C₂×#41	—	107	2	no	—
260	C₂×#41	—	107	2	no	—
261	C₂×#41	—	107	2	no	—
262	C₂×#41	C₂×D₁₀₇	1	2	yes	complemented
263	C₂²×D₄	—	107	2	no	—
264	C₂²×D₄	—	107	2	no	—
265	C₄⋊Q₈	—	107	1	no	—
266	C₄⋊Q₈	C₂×D₁₀₇	1	1	yes	characteristic, complemented
267	#127	—	107	2	no	—
268	#127	—	107	4	no	—
269	#127	—	107	1	no	—
270	#127	C₂×D₁₀₇	1	1	yes	characteristic
271	#126	—	107	4	no	—
272	#126	—	107	4	no	—
273	#126	—	107	2	no	—
274	#125	—	107	1	no	—
275	#124	—	107	4	no	—
276	#124	—	107	2	no	—
277	#124	—	107	1	no	—
278	#124	—	107	2	no	—
279	#124	C₂×D₁₀₇	1	2	yes	complemented
280	#123	—	107	2	no	—
281	#123	—	107	4	no	—
282	#123	—	107	4	no	—
283	#123	—	107	4	no	—
284	C₂²⋊Q₈	—	107	4	no	—
285	C₂²⋊Q₈	—	107	1	no	—
286	C₂²⋊Q₈	—	107	2	no	—
287	C₂²⋊Q₈	—	107	2	no	—
288	#121	—	107	4	no	—
289	#121	—	107	4	no	—
290	#121	—	107	4	no	—
291	#121	—	107	4	no	—
292	#121	—	107	1	no	—
293	#121	—	107	2	no	—
294	#121	—	107	2	no	—
295	#121	—	107	2	no	—
296	#121	—	107	2	no	—
297	#121	—	107	2	no	—
298	#121	—	107	2	no	—
299	#121	—	107	4	no	—
300	#121	—	107	4	no	—
301	#121	C₂×D₁₀₇	1	1	yes	characteristic
302	#121	C₂×D₁₀₇	1	1	yes	characteristic, complemented
303	#121	C₂×D₁₀₇	1	2	yes	complemented
304	#120	—	107	4	no	—
305	#120	—	107	4	no	—
306	#120	—	107	4	no	—
307	#120	—	107	4	no	—
308	C₄×Q₈	—	107	2	no	—
309	C₄×Q₈	—	107	1	no	—
310	C₄×D₄	—	107	2	no	—
311	C₄×D₄	—	107	2	no	—
312	C₄×D₄	—	107	4	no	—
313	C₄×D₄	—	107	1	no	—
314	C₄×D₄	—	107	2	no	—
315	C₄×D₄	—	107	2	no	—
316	C₄×D₄	C₂×D₁₀₇	1	1	yes	characteristic
317	C₄×D₄	C₂×D₁₀₇	1	2	yes	complemented
318	C₄×D₄	C₂×D₁₀₇	1	1	yes	characteristic, complemented
319	#117	—	107	2	no	—
320	#117	—	107	2	no	—
321	C₂×C₄⋊C₄	—	107	2	no	—
322	C₂×C₂²⋊C₄	—	107	4	no	—
323	C₂×C₄²	C₂×D₁₀₇	1	1	yes	characteristic, complemented
324	C₂⁴	—	107	4	no	—
325	#41	—	4	4	no	—
326	#41	—	428	4	no	—
327	#41	—	428	4	no	—
328	#41	—	428	4	no	—
329	C₂×Q₈	—	107	1	no	—
330	C₂×Q₈	—	107	2	no	—
331	C₂×Q₈	C₂²×D₁₀₇	1	2	yes	—
332	C₂×D₄	—	107	2	no	—
333	C₂×D₄	—	107	4	no	—
334	C₂×D₄	—	107	4	no	—
335	C₂×D₄	—	107	4	no	—
336	C₂×D₄	—	107	4	no	—
337	C₂×D₄	—	107	4	no	—
338	C₂×D₄	—	107	2	no	—
339	C₂×D₄	—	107	4	no	—
340	C₂×D₄	—	107	1	no	—
341	C₂×D₄	—	107	2	no	—
342	C₂×D₄	—	107	2	no	—
343	C₂×D₄	—	428	4	no	—
344	C₂×D₄	—	428	4	no	—
345	C₂×D₄	C₂²×D₁₀₇	1	1	yes	characteristic
346	C₂×D₄	C₂²×D₁₀₇	1	1	yes	characteristic
347	C₂×D₄	C₂²×D₁₀₇	1	2	yes	—
348	C₂×D₄	C₂²×D₁₀₇	1	2	yes	—
349	C₂×D₄	C₂²×D₁₀₇	1	2	yes	—
350	C₂×D₄	C₂²×D₁₀₇	1	2	yes	—
351	C₂²×C₄	—	107	4	no	—
352	C₂²×C₄	—	107	4	no	—
353	C₂²×C₄	—	107	4	no	—
354	C₂²×C₄	—	107	2	no	—
355	C₂²×C₄	C₂²×D₁₀₇	1	1	yes	characteristic
356	C₂²×C₄	C₂²×D₁₀₇	1	1	yes	characteristic
357	C₂²×C₄	C₂²×D₁₀₇	1	2	yes	—
358	C₂²×C₄	C₂²×D₁₀₇	1	2	yes	—
359	C₂²×C₄	C₂²×D₁₀₇	1	1	yes	characteristic
360	C₄⋊C₄	—	107	1	no	—
361	C₄⋊C₄	—	107	2	no	—
362	C₄⋊C₄	—	107	4	no	—
363	C₄⋊C₄	—	107	1	no	—
364	C₄⋊C₄	—	107	2	no	—
365	C₄⋊C₄	—	107	2	no	—
366	C₄⋊C₄	—	107	2	no	—
367	C₄⋊C₄	—	107	2	no	—
368	C₄⋊C₄	—	107	4	no	—
369	C₄⋊C₄	—	107	2	no	—
370	C₄⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
371	C₄⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
372	C₄⋊C₄	C₂²×D₁₀₇	1	2	yes	—
373	C₂²⋊C₄	—	107	4	no	—
374	C₂²⋊C₄	—	107	4	no	—
375	C₂²⋊C₄	—	107	2	no	—
376	C₂²⋊C₄	—	107	2	no	—
377	C₂²⋊C₄	—	107	4	no	—
378	C₂²⋊C₄	—	107	2	no	—
379	C₂²⋊C₄	—	107	2	no	—
380	C₂²⋊C₄	—	107	2	no	—
381	C₂²⋊C₄	—	107	4	no	—
382	C₂²⋊C₄	—	107	4	no	—
383	C₂²⋊C₄	—	107	4	no	—
384	C₂²⋊C₄	—	107	4	no	—
385	C₂²⋊C₄	C₂²×D₁₀₇	1	2	yes	—
386	C₂²⋊C₄	C₂²×D₁₀₇	1	2	yes	—
387	C₂²⋊C₄	C₂²×D₁₀₇	1	2	yes	—
388	C₂²⋊C₄	C₂²×D₁₀₇	1	2	yes	—
389	C₄²	—	107	2	no	—
390	C₄²	—	107	4	no	—
391	C₄²	C₂²×D₁₀₇	1	1	yes	characteristic
392	C₄²	C₂²×D₁₀₇	1	1	yes	characteristic
393	C₄²	C₂²×D₁₀₇	1	1	yes	characteristic
394	C₄²	C₂²×D₁₀₇	1	1	yes	characteristic
395	C₂³	—	107	2	no	—
396	C₂³	—	107	4	no	—
397	C₂³	—	428	4	no	—
398	C₂³	—	428	4	no	—
399	C₂³	—	428	4	no	—
400	C₂³	C₂³×D₁₀₇	1	2	yes	—
401	C₂³	C₂³×D₁₀₇	1	1	yes	characteristic
402	C₂³	C₂³×D₁₀₇	1	2	yes	—
403	Q₈	—	4	2	no	—
404	Q₈	—	214	2	no	—
405	Q₈	—	214	4	no	—
406	D₄	—	2	2	no	—
407	D₄	—	2	2	no	—
408	D₄	—	4	2	no	—
409	D₄	—	4	2	no	—
410	D₄	—	4	2	no	—
411	D₄	—	4	2	no	—
412	D₄	—	428	4	no	—
413	D₄	—	428	2	no	—
414	D₄	—	428	4	no	—
415	D₄	—	428	4	no	—
416	D₄	—	428	4	no	—
417	D₄	—	428	4	no	—
418	D₄	—	428	2	no	—
419	D₄	—	428	4	no	—
420	D₄	—	214	2	no	—
421	D₄	—	214	4	no	—
422	D₄	—	214	4	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	107	2	no	—
429	C₂×C₄	—	107	2	no	—
430	C₂×C₄	—	107	4	no	—
431	C₂×C₄	—	107	2	no	—
432	C₂×C₄	—	428	4	no	—
433	C₂×C₄	—	428	4	no	—
434	C₂×C₄	—	428	4	no	—
435	C₂×C₄	—	214	4	no	—
436	C₂×C₄	C₂³×D₁₀₇	1	2	yes	—
437	C₂×C₄	C₂³×D₁₀₇	1	1	yes	characteristic
438	C₂×C₄	C₂³×D₁₀₇	1	1	yes	characteristic
439	C₂×C₄	C₂³×D₁₀₇	1	1	yes	characteristic
440	C₂×C₄	C₂³×D₁₀₇	1	1	yes	characteristic
441	C₂×C₄	C₂³×D₁₀₇	1	2	yes	—
442	C₂×C₄	C₂³×D₁₀₇	1	1	yes	characteristic
443	C₂×C₄	C₂³×D₁₀₇	1	1	yes	characteristic
444	C₂²	—	2	1	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	2	1	no	—
448	C₂²	—	2	2	no	—
449	C₂²	—	2	2	no	—
450	C₂²	—	2	1	no	—
451	C₂²	—	2	2	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	856	8	no	—
454	C₂²	—	214	4	no	—
455	C₂²	—	214	2	no	—
456	C₂²	—	214	4	no	—
457	C₂²	—	214	2	no	—
458	C₂²	—	214	4	no	—
459	C₂²	—	214	2	no	—
460	C₂²	C₂⁴×D₁₀₇	1	1	yes	characteristic
461	C₄	—	2	2	no	—
462	C₄	—	2	1	no	—
463	C₄	—	2	2	no	—
464	C₄	—	2	1	no	—
465	C₄	—	2	1	no	—
466	C₄	—	2	1	no	—
467	C₄	—	214	2	no	—
468	C₄	—	214	2	no	—
469	C₄	—	214	4	no	—
470	C₄	—	214	2	no	—
471	C₄	#16812154	1	2	yes	—
472	C₄	#16812155	1	2	yes	—
473	C₂	—	4	2	no	—
474	C₂	—	4	1	no	—
475	C₂	—	4	2	no	—
476	C₂	—	428	2	no	—
477	C₂	—	428	4	no	—
478	C₂	C₂×#16812154	1	1	yes	characteristic
479	C₂	C₂×#16812155	1	1	yes	characteristic
480	C₂	#20293463	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₀₇
commutator, socle, cosocle	C₂²×C₁₀₇	C₂⁵
Fitting	#532×C₁₀₇	C₂
hypercenter	#532	D₁₀₇
hypocenter	C₁₀₇	#3546
LCS	G ▷ C₂²×C₁₀₇ ▷ C₁₀₇
UCS	C₁ ◁ C₂² ◁ #532

Complements

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

N	H ≅ G/N	type
1. #20293365	C₂	semidirect
2. #20293347	C₂	semidirect
3. #20293323	C₂	semidirect
4. #20293298	C₂	semidirect
5. #20293295	C₂	semidirect
6. #20293281	C₂	semidirect
7. #20293274	C₂	semidirect
8. #20293273	C₂	semidirect
9. D₄×D₄₂₈	C₂	semidirect
10. #20293251	C₂	semidirect
11. #20293211	C₂	semidirect
12. #20293205	C₂	semidirect
13. #20293191	C₂	semidirect
14. #20293190	C₂	semidirect
15. #20293177	C₂	semidirect
16. #20293161	C₂	semidirect
17. #532×C₁₀₇	C₂	semidirect
18. C₂×#13133818	C₂²	semidirect
19. C₂×#13133818	C₂²	semidirect
20. C₂×#13133817	C₂²	semidirect
23. #16812109	C₂²	semidirect
25. #16812105	C₂²	semidirect
26. #16812105	C₂²	semidirect
27. #16812104	C₂²	semidirect
28. #16812103	C₂²	semidirect
29. #16812102	C₂²	semidirect
30. #16812101	C₂²	semidirect
31. #16812098	C₂²	semidirect
33. #16812097	C₂²	semidirect
35. #16812094	C₂²	semidirect
36. #16812093	C₂²	semidirect
37. #16812092	C₂²	semidirect
38. #16812091	C₂²	semidirect
39. #16812089	C₂²	semidirect
40. #16812088	C₂²	semidirect
41. #16812088	C₂²	semidirect
42. #16812085	C₂²	semidirect
47. #16812083	C₂²	semidirect
48. #16812083	C₂²	semidirect
49. #16812083	C₂²	semidirect
50. #16812082	C₂²	semidirect
51. #16812082	C₂²	semidirect
52. #16812081	C₂²	semidirect
53. #16812081	C₂²	semidirect
54. #16812081	C₂²	semidirect
55. #16812080	C₂²	semidirect
57. #16812077	C₂²	semidirect
58. #16812077	C₂²	semidirect
59. #16812077	C₂²	semidirect
60. C₄×Dic₂₁₄	C₂²	semidirect
61. #16812074	C₂²	semidirect
63. C₄×D₄₂₈	C₂²	semidirect
64. C₄×D₄₂₈	C₂²	semidirect
65. #16812071	C₂²	semidirect
66. C₄×C₂²⋊D₁₀₇	C₂²	semidirect
67. (C₂²⋊D₁₀₇)⋊C₄	C₂²	semidirect
68. #16812068	C₂²	semidirect
69. #16812066	C₂²	semidirect
70. C₂×C₄⋊Dic₁₀₇	C₂²	semidirect
71. C₂²⋊C₄×D₁₀₇	C₂²	semidirect
72. C₂×#41×C₁₀₇	C₂²	semidirect
73. C₄⋊Q₈×C₁₀₇	C₂²	semidirect
75. #124×C₁₀₇	C₂²	semidirect
77. #121×C₁₀₇	C₂²	semidirect
78. #121×C₁₀₇	C₂²	semidirect
80. C₄×D₄×C₁₀₇	C₂²	semidirect
81. C₄×D₄×C₁₀₇	C₂²	semidirect
82. C₂×C₄²×C₁₀₇	C₂²	semidirect
241. C₁₀₇	#3546	semidirect
257. #532	D₁₀₇	semidirect
262. C₂×#41	C₂×D₁₀₇	semidirect
266. C₄⋊Q₈	C₂×D₁₀₇	semidirect
279. #124	C₂×D₁₀₇	semidirect
302. #121	C₂×D₁₀₇	semidirect
303. #121	C₂×D₁₀₇	semidirect
317. C₄×D₄	C₂×D₁₀₇	semidirect
318. C₄×D₄	C₂×D₁₀₇	semidirect
323. 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
#20293365	2
#20293347	2
#20293323	2
#20293298	2
#20293295	2
#20293281	2
#20293274	2
#20293273	2
D₄×D₄₂₈	2
#20293251	2
#20293211	2
#20293205	2
#20293191	2
#20293190	2
#20293177	2
#20293161	2
#532×C₁₀₇	2
#3546	107