Subgroups — #20289280

Order 6784.

1032 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16811377	C₂	1	2	yes	maximal, complemented
2	#16811371	C₂	1	2	yes	maximal, complemented
3	#16811345	C₂	1	2	yes	maximal, complemented
4	#16811297	C₂	1	4	yes	maximal, complemented
5	#16811286	C₂	1	2	yes	maximal, complemented
6	#16811285	C₂	1	2	yes	maximal, complemented
7	#16811264	C₂	1	2	yes	maximal, complemented
8	#16811248	C₂	1	2	yes	maximal, complemented
9	#16811247	C₂	1	2	yes	maximal, complemented
10	#16811245	C₂	1	4	yes	maximal, complemented
11	#16811213	C₂	1	2	yes	maximal, complemented
12	#16811198	C₂	1	2	yes	maximal, complemented
13	#16811157	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#13133205	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#11719949	C₂²	1	2	yes	—
17	C₂²×Dic₁₀₆	C₂²	1	1	yes	characteristic
18	C₂×Q₈×D₅₃	C₂²	1	2	yes	complemented
19	C₂²×D₂₁₂	C₂²	1	1	yes	characteristic
20	#13133216	C₂²	1	4	yes	complemented
21	#13133215	C₂²	1	2	yes	complemented
22	#13133212	C₂²	1	4	yes	complemented
23	#13133212	C₂²	1	4	yes	complemented
24	#13133211	C₂²	1	4	yes	complemented
25	#13133211	C₂²	1	2	yes	complemented
26	#13133209	C₂²	1	1	yes	characteristic, complemented
27	#13133206	C₂²	1	2	yes	—
28	#13133206	C₂²	1	4	yes	complemented
29	#13133205	C₂²	1	2	yes	—
30	#13133205	C₂²	1	2	yes	—
31	#13133205	C₂²	1	2	yes	—
32	#13133205	C₂²	1	2	yes	—
33	#13133205	C₂²	1	4	yes	complemented
34	#13133205	C₂²	1	1	yes	characteristic, complemented
35	#13133202	C₂²	1	4	yes	—
36	#13133202	C₂²	1	4	yes	complemented
37	#13133202	C₂²	1	4	yes	complemented
38	#13133202	C₂²	1	4	yes	complemented
39	#13133200	C₂²	1	2	yes	—
40	#13133197	C₂²	1	2	yes	complemented
41	#13133197	C₂²	1	4	yes	complemented
42	#13133196	C₂²	1	1	yes	characteristic
43	#13133195	C₂²	1	4	yes	complemented
44	#13133195	C₂²	1	4	yes	complemented
45	#13133195	C₂²	1	4	yes	complemented
46	#13133195	C₂²	1	4	yes	complemented
47	#13133194	C₂²	1	4	yes	—
48	#13133193	C₂²	1	4	yes	complemented
49	#13133192	C₂²	1	2	yes	—
50	#13133192	C₂²	1	4	yes	—
51	#13133192	C₂²	1	4	yes	complemented
52	#13133191	C₂²	1	1	yes	characteristic
53	#13133187	C₂²	1	4	yes	—
54	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
55	#13133182	C₂²	1	2	yes	complemented
56	C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
57	C₄×D₂₁₂	C₂²	1	4	yes	complemented
58	#13133179	C₂²	1	2	yes	—
59	C₄×C₂²⋊D₅₃	C₂²	1	2	yes	—
60	#13133177	C₂²	1	4	yes	—
61	#13133174	C₂²	1	4	yes	complemented
62	#13133174	C₂²	1	2	yes	complemented
63	C₂×#11719921	C₂²	1	2	yes	—
64	C₂×#11719921	C₂²	1	2	yes	—
65	C₂²⋊C₄×D₅₃	C₂²	1	4	yes	—
66	C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
67	C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
68	#125×C₅₃	C₂²	1	2	yes	complemented
69	C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
70	C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	—
71	C₄×Q₈×C₅₃	C₂²	1	2	yes	complemented
72	C₄×Q₈×C₅₃	C₂²	1	2	yes	complemented
73	#117×C₅₃	C₂²	1	2	yes	—
74	C₂×C₄²×C₅₃	C₂²	1	1	yes	characteristic
75	C₂³×D₅₃	C₂³	1	2	yes	—
76	C₂×Q₈×C₅₃	C₂³	1	2	yes	—
77	C₂×Q₈×C₅₃	C₂³	1	2	yes	—
78	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
79	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
80	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
81	C₂×C₂²⋊D₅₃	C₂³	1	2	yes	—
82	C₂²×Dic₅₃	C₂³	1	2	yes	—
83	#11719949	—	4	4	no	—
84	Q₈×D₅₃	—	4	4	no	—
85	C₂×D₂₁₂	—	4	2	no	—
86	C₂×D₂₁₂	C₂³	1	2	yes	—
87	C₂×D₂₁₂	C₂³	1	4	yes	—
88	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
89	C₂×D₂₁₂	C₂³	1	4	yes	—
90	C₂×D₂₁₂	C₂³	1	2	yes	—
91	C₂×C₄×D₅₃	C₂³	1	2	yes	—
92	C₂×C₄×D₅₃	C₂³	1	4	yes	—
93	C₂×C₄×D₅₃	C₂³	1	4	yes	—
94	C₂×C₄×D₅₃	C₂³	1	4	yes	—
95	C₂×Dic₁₀₆	—	4	2	no	—
96	C₂×Dic₁₀₆	C₂³	1	2	yes	—
97	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
98	C₂×Dic₁₀₆	C₂³	1	4	yes	—
99	C₂×Dic₁₀₆	C₂³	1	2	yes	—
100	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
101	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
102	C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
103	C₄⋊C₄×C₅₃	C₂³	1	4	yes	—
104	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
105	C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
106	C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
107	C₄²×C₅₃	C₂³	1	1	yes	characteristic
108	C₄²×C₅₃	C₂³	1	1	yes	characteristic
109	C₄²×C₅₃	C₂³	1	1	yes	characteristic
110	C₄²×C₅₃	C₂³	1	1	yes	characteristic
111	C₄²×C₅₃	C₂³	1	4	yes	—
112	C₂²⋊Dic₅₃	C₂³	1	2	yes	—
113	#11719921	C₂³	1	4	yes	—
114	#11719921	C₂³	1	4	yes	—
115	#11719921	C₂³	1	4	yes	—
116	#11719921	C₂³	1	4	yes	—
117	#11719921	C₂³	1	4	yes	—
118	#11719921	C₂³	1	4	yes	—
119	#11719921	C₂³	1	4	yes	—
120	#11719921	C₂³	1	2	yes	—
121	#11719921	C₂³	1	2	yes	—
122	#11719921	C₂³	1	4	yes	—
123	#11719921	C₂³	1	2	yes	—
124	#11719921	C₂³	1	4	yes	—
125	#11719921	C₂³	1	2	yes	—
126	C₄⋊Dic₅₃	C₂³	1	4	yes	—
127	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
128	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
129	#11719919	C₂³	1	2	yes	—
130	#11719919	C₂³	1	2	yes	—
131	#11719919	C₂³	1	4	yes	—
132	#11719919	C₂³	1	2	yes	—
133	#11719919	C₂³	1	4	yes	—
134	#11719919	C₂³	1	2	yes	—
135	#11719919	C₂³	1	4	yes	—
136	C₄×Dic₅₃	C₂³	1	4	yes	—
137	C₄×Dic₅₃	C₂³	1	2	yes	—
138	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
139	C₂²×D₅₃	—	2	4	no	—
140	C₂²×D₅₃	—	4	2	no	—
141	C₂²×D₅₃	—	4	2	no	—
142	C₂²×D₅₃	C₂⁴	1	2	yes	—
143	C₂²×D₅₃	C₂⁴	1	4	yes	—
144	Q₈×C₅₃	—	2	4	no	—
145	Q₈×C₅₃	—	4	2	no	—
146	C₂×C₄×C₅₃	—	2	2	no	—
147	C₂×C₄×C₅₃	—	2	2	no	—
148	C₂×C₄×C₅₃	—	4	1	no	—
149	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
150	C₂×C₄×C₅₃	C₂⁴	1	4	yes	—
151	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
152	C₂×C₄×C₅₃	C₂⁴	1	4	yes	—
153	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
154	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
155	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
156	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
157	C₂²⋊D₅₃	—	2	4	no	—
158	C₂×Dic₅₃	—	4	2	no	—
159	C₂×Dic₅₃	C₂⁴	1	4	yes	—
160	C₂×Dic₅₃	C₂⁴	1	2	yes	—
161	C₂×Dic₅₃	C₂⁴	1	2	yes	—
162	C₂×Dic₅₃	C₂⁴	1	2	yes	—
163	D₂₁₂	—	2	4	no	—
164	D₂₁₂	—	4	2	no	—
165	D₂₁₂	—	4	1	no	—
166	D₂₁₂	—	4	4	no	—
167	D₂₁₂	—	4	4	no	—
168	C₄×D₅₃	—	2	4	no	—
169	C₄×D₅₃	—	4	4	no	—
170	C₄×D₅₃	—	4	4	no	—
171	C₄×D₅₃	—	4	4	no	—
172	Dic₁₀₆	—	2	4	no	—
173	Dic₁₀₆	—	4	2	no	—
174	Dic₁₀₆	—	4	1	no	—
175	Dic₁₀₆	—	4	4	no	—
176	C₂²×C₅₃	—	2	1	no	—
177	C₂²×C₅₃	—	2	1	no	—
178	C₂²×C₅₃	2₋¹⁺⁴	1	2	yes	—
179	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
180	C₂×D₅₃	—	2	2	no	—
181	C₂×D₅₃	—	2	4	no	—
182	C₂×D₅₃	—	2	2	no	—
183	C₂×D₅₃	—	2	4	no	—
184	C₂×D₅₃	—	2	4	no	—
185	C₂×D₅₃	—	2	2	no	—
186	C₂×D₅₃	—	8	4	no	—
187	C₄×C₅₃	—	2	1	no	—
188	C₄×C₅₃	—	2	4	no	—
189	C₄×C₅₃	—	2	1	no	—
190	C₄×C₅₃	—	2	1	no	—
191	C₄×C₅₃	—	2	1	no	—
192	C₄×C₅₃	—	2	4	no	—
193	C₄×C₅₃	—	2	1	no	—
194	C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
195	Dic₅₃	—	2	4	no	—
196	Dic₅₃	—	2	2	no	—
197	Dic₅₃	—	2	2	no	—
198	Dic₅₃	—	2	2	no	—
199	#3561	—	53	1	no	maximal, Sylow
200	C₂×C₅₃	—	2	2	no	—
201	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
202	C₂×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
203	C₂×C₅₃	#585	1	1	yes	characteristic
204	D₅₃	—	4	2	no	—
205	D₅₃	—	4	4	no	—
206	#563	—	53	2	no	—
207	#562	—	53	2	no	—
208	#556	—	53	2	no	—
209	#551	—	53	4	no	—
210	D₄×Q₈	—	53	2	no	—
211	#548	—	53	2	no	—
212	#546	—	53	2	no	—
213	#543	—	53	2	no	—
214	#542	—	53	2	no	—
215	#542	—	53	4	no	—
216	#538	—	53	2	no	—
217	#536	—	53	2	no	—
218	#533	D₅₃	1	1	yes	characteristic, complemented
219	#529	—	53	1	no	—
220	C₂×#124	—	53	1	no	—
221	C₅₃	#3561	1	1	yes	characteristic, complemented, Sylow
222	C₂×#41	—	53	2	no	—
223	C₂²×Q₈	—	53	2	no	—
224	C₂²×Q₈	—	53	1	no	—
225	C₂²×D₄	—	53	1	no	—
226	C₄⋊Q₈	—	53	2	no	—
227	C₄⋊Q₈	—	53	4	no	—
228	C₄⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
229	C₄⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
230	#126	—	53	4	no	—
231	#126	—	53	4	no	—
232	#126	—	53	2	no	—
233	#126	—	53	4	no	—
234	#125	—	53	1	no	—
235	#125	C₂×D₅₃	1	2	yes	complemented
236	#124	—	53	2	no	—
237	#124	—	53	4	no	—
238	#124	—	53	2	no	—
239	#124	—	53	2	no	—
240	#124	—	53	2	no	—
241	#124	—	53	2	no	—
242	#124	—	53	1	no	—
243	#124	—	53	4	no	—
244	#123	—	53	2	no	—
245	#123	—	53	4	no	—
246	#123	—	53	4	no	—
247	#123	—	53	4	no	—
248	#123	—	53	4	no	—
249	C₂²⋊Q₈	—	53	4	no	—
250	C₂²⋊Q₈	—	53	1	no	—
251	C₂²⋊Q₈	—	53	4	no	—
252	C₂²⋊Q₈	—	53	4	no	—
253	C₂²⋊Q₈	—	53	2	no	—
254	C₂²⋊Q₈	—	53	4	no	—
255	C₂²⋊Q₈	—	53	4	no	—
256	C₂²⋊Q₈	—	53	4	no	—
257	C₂²⋊Q₈	—	53	4	no	—
258	C₂²⋊Q₈	C₂×D₅₃	1	2	yes	—
259	C₂²⋊Q₈	C₂×D₅₃	1	2	yes	—
260	#121	—	53	1	no	—
261	#121	—	53	4	no	—
262	#121	—	53	2	no	—
263	#121	—	53	4	no	—
264	#120	—	53	4	no	—
265	C₄×Q₈	—	53	2	no	—
266	C₄×Q₈	—	53	1	no	—
267	C₄×Q₈	C₂×D₅₃	1	2	yes	complemented
268	C₄×Q₈	C₂×D₅₃	1	2	yes	complemented
269	C₄×D₄	—	53	2	no	—
270	C₄×D₄	—	53	2	no	—
271	C₄×D₄	—	53	4	no	—
272	C₄×D₄	—	53	1	no	—
273	C₄×D₄	—	53	4	no	—
274	#117	—	53	2	no	—
275	#117	—	53	4	no	—
276	#117	C₂×D₅₃	1	2	yes	—
277	C₂×C₂²⋊C₄	—	53	2	no	—
278	C₂×C₂²⋊C₄	—	53	2	no	—
279	C₂×C₂²⋊C₄	—	53	4	no	—
280	C₂×C₄²	C₂×D₅₃	1	1	yes	characteristic
281	C₂⁴	—	53	2	no	—
282	#41	—	212	4	no	—
283	C₂×Q₈	—	53	2	no	—
284	C₂×Q₈	—	53	1	no	—
285	C₂×Q₈	—	53	4	no	—
286	C₂×Q₈	—	53	2	no	—
287	C₂×Q₈	—	212	2	no	—
288	C₂×Q₈	—	212	4	no	—
289	C₂×Q₈	C₂²×D₅₃	1	2	yes	—
290	C₂×Q₈	C₂²×D₅₃	1	2	yes	—
291	C₂×D₄	—	53	2	no	—
292	C₂×D₄	—	53	2	no	—
293	C₂×D₄	—	53	4	no	—
294	C₂×D₄	—	53	1	no	—
295	C₂×D₄	—	53	4	no	—
296	C₂×D₄	—	53	2	no	—
297	C₂×D₄	—	212	2	no	—
298	C₂²×C₄	—	53	2	no	—
299	C₂²×C₄	—	53	2	no	—
300	C₂²×C₄	—	53	4	no	—
301	C₂²×C₄	—	53	4	no	—
302	C₂²×C₄	—	53	4	no	—
303	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
304	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
305	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
306	C₄⋊C₄	—	53	2	no	—
307	C₄⋊C₄	—	53	2	no	—
308	C₄⋊C₄	—	53	4	no	—
309	C₄⋊C₄	—	53	2	no	—
310	C₄⋊C₄	—	53	1	no	—
311	C₄⋊C₄	—	53	4	no	—
312	C₄⋊C₄	—	53	4	no	—
313	C₄⋊C₄	—	53	2	no	—
314	C₄⋊C₄	—	53	1	no	—
315	C₄⋊C₄	—	53	4	no	—
316	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
317	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
318	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
319	C₄⋊C₄	C₂²×D₅₃	1	4	yes	—
320	C₄⋊C₄	C₂²×D₅₃	1	4	yes	—
321	C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
322	C₂²⋊C₄	—	53	2	no	—
323	C₂²⋊C₄	—	53	4	no	—
324	C₂²⋊C₄	—	53	4	no	—
325	C₂²⋊C₄	—	53	4	no	—
326	C₂²⋊C₄	—	53	4	no	—
327	C₂²⋊C₄	—	53	4	no	—
328	C₂²⋊C₄	—	53	4	no	—
329	C₂²⋊C₄	—	53	4	no	—
330	C₂²⋊C₄	—	53	2	no	—
331	C₂²⋊C₄	—	53	2	no	—
332	C₂²⋊C₄	—	53	2	no	—
333	C₂²⋊C₄	—	53	4	no	—
334	C₂²⋊C₄	—	53	2	no	—
335	C₂²⋊C₄	—	53	4	no	—
336	C₂²⋊C₄	C₂²×D₅₃	1	4	yes	—
337	C₄²	—	53	2	no	—
338	C₄²	—	53	4	no	—
339	C₄²	C₂²×D₅₃	1	1	yes	characteristic
340	C₄²	C₂²×D₅₃	1	1	yes	characteristic
341	C₄²	C₂²×D₅₃	1	1	yes	characteristic
342	C₄²	C₂²×D₅₃	1	1	yes	characteristic
343	C₄²	C₂²×D₅₃	1	4	yes	—
344	C₂³	—	53	4	no	—
345	C₂³	—	53	2	no	—
346	C₂³	—	106	4	no	—
347	C₂³	—	212	2	no	—
348	C₂³	—	212	2	no	—
349	C₂³	C₂³×D₅₃	1	1	yes	characteristic
350	Q₈	—	2	4	no	—
351	Q₈	—	4	2	no	—
352	Q₈	—	106	4	no	—
353	Q₈	—	212	1	no	—
354	Q₈	—	212	2	no	—
355	Q₈	—	212	4	no	—
356	D₄	—	106	4	no	—
357	D₄	—	106	4	no	—
358	D₄	—	212	1	no	—
359	D₄	—	212	4	no	—
360	D₄	—	212	2	no	—
361	D₄	—	212	4	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	53	2	no	—
366	C₂×C₄	—	53	2	no	—
367	C₂×C₄	—	53	4	no	—
368	C₂×C₄	—	53	2	no	—
369	C₂×C₄	—	106	4	no	—
370	C₂×C₄	—	212	4	no	—
371	C₂×C₄	—	212	4	no	—
372	C₂×C₄	—	212	4	no	—
373	C₂×C₄	—	212	2	no	—
374	C₂×C₄	C₂³×D₅₃	1	4	yes	—
375	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
376	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
377	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
378	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
379	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
380	C₂×C₄	C₂³×D₅₃	1	4	yes	—
381	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	106	2	no	—
385	C₂²	—	106	4	no	—
386	C₂²	—	106	2	no	—
387	C₂²	—	106	4	no	—
388	C₂²	—	106	4	no	—
389	C₂²	—	106	2	no	—
390	C₂²	—	424	4	no	—
391	C₂²	#13133265	1	2	yes	—
392	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
393	C₄	—	2	1	no	—
394	C₄	—	2	4	no	—
395	C₄	—	2	1	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	2	1	no	—
399	C₄	—	2	4	no	—
400	C₄	—	106	2	no	—
401	C₄	—	106	4	no	—
402	C₄	—	106	2	no	—
403	C₄	—	106	2	no	—
404	C₄	#13133263	1	2	yes	—
405	C₂	—	2	2	no	—
406	C₂	—	212	4	no	—
407	C₂	—	212	2	no	—
408	C₂	C₂×#13133263	1	1	yes	characteristic
409	C₂	C₂×#13133265	1	1	yes	characteristic
410	C₂	#16811459	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁵
Fitting	C₅₃×#533	C₂
hypercenter	#533	D₅₃
hypocenter	C₅₃	#3561
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #533

Complements

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

N	H ≅ G/N	type
1. #16811377	C₂	semidirect
2. #16811371	C₂	semidirect
3. #16811345	C₂	semidirect
4. #16811297	C₂	semidirect
5. #16811286	C₂	semidirect
6. #16811285	C₂	semidirect
7. #16811264	C₂	semidirect
8. #16811248	C₂	semidirect
9. #16811247	C₂	semidirect
10. #16811245	C₂	semidirect
11. #16811213	C₂	semidirect
12. #16811198	C₂	semidirect
13. #16811157	C₂	semidirect
14. C₂×#13133205	C₂	semidirect
15. C₅₃×#533	C₂	semidirect
18. C₂×Q₈×D₅₃	C₂²	semidirect
20. #13133216	C₂²	semidirect
21. #13133215	C₂²	semidirect
22. #13133212	C₂²	semidirect
23. #13133212	C₂²	semidirect
24. #13133211	C₂²	semidirect
25. #13133211	C₂²	semidirect
26. #13133209	C₂²	semidirect
28. #13133206	C₂²	semidirect
33. #13133205	C₂²	semidirect
34. #13133205	C₂²	semidirect
36. #13133202	C₂²	semidirect
37. #13133202	C₂²	semidirect
38. #13133202	C₂²	semidirect
40. #13133197	C₂²	semidirect
41. #13133197	C₂²	semidirect
43. #13133195	C₂²	semidirect
44. #13133195	C₂²	semidirect
45. #13133195	C₂²	semidirect
46. #13133195	C₂²	semidirect
48. #13133193	C₂²	semidirect
51. #13133192	C₂²	semidirect
54. C₄×Dic₁₀₆	C₂²	semidirect
55. #13133182	C₂²	semidirect
56. C₄×D₂₁₂	C₂²	semidirect
57. C₄×D₂₁₂	C₂²	semidirect
61. #13133174	C₂²	semidirect
62. #13133174	C₂²	semidirect
66. C₄⋊Q₈×C₅₃	C₂²	semidirect
67. C₄⋊Q₈×C₅₃	C₂²	semidirect
68. #125×C₅₃	C₂²	semidirect
71. C₄×Q₈×C₅₃	C₂²	semidirect
72. C₄×Q₈×C₅₃	C₂²	semidirect
218. #533	D₅₃	semidirect
221. C₅₃	#3561	semidirect
228. C₄⋊Q₈	C₂×D₅₃	semidirect
229. C₄⋊Q₈	C₂×D₅₃	semidirect
235. #125	C₂×D₅₃	semidirect
267. C₄×Q₈	C₂×D₅₃	semidirect
268. C₄×Q₈	C₂×D₅₃	semidirect