Subgroups — #20291449

Order 6784.

502 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13133304	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₅₃⋊M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#16811657	C₂	1	1	yes	maximal, characteristic, complemented
4	#16811656	C₂	1	1	yes	maximal, characteristic, complemented
5	#16811655	C₂	1	1	yes	maximal, characteristic, complemented
6	#16811653	C₂	1	1	yes	maximal, characteristic, complemented
7	#16811653	C₂	1	1	yes	maximal, characteristic, complemented
8	#16811652	C₂	1	1	yes	maximal, characteristic, complemented
9	#16811651	C₂	1	1	yes	maximal, characteristic, complemented
10	#16811650	C₂	1	1	yes	maximal, characteristic, complemented
11	#16811629	C₂	1	1	yes	maximal, characteristic, complemented
12	#16811596	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#13133274	C₂	1	1	yes	maximal, characteristic, complemented
14	#16811587	C₂	1	1	yes	maximal, characteristic, complemented
15	#16811131	C₂	1	1	yes	maximal, characteristic
16	#13133304	—	2	4	no	—
17	C₂×#11719936	C₂²	1	1	yes	characteristic
18	C₂×#11719936	C₂²	1	1	yes	characteristic
19	C₂×#11719936	C₂²	1	1	yes	characteristic, complemented
20	D₅₃⋊M₁₆	—	2	4	no	—
21	C₂×#11719940	C₂²	1	1	yes	characteristic
22	C₂×#11719940	C₂²	1	1	yes	characteristic
23	C₂×#11719940	C₂²	1	1	yes	characteristic, complemented
24	C₂×D₅₃⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×D₅₃⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×D₅₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
27	C₂²×#88324	C₂²	1	1	yes	characteristic
28	C₂²×#88324	C₂²	1	1	yes	characteristic
29	C₂²×#88324	C₂²	1	1	yes	characteristic, complemented
30	#13133284	C₂²	1	1	yes	characteristic, complemented
31	#13133284	C₂²	1	1	yes	characteristic, complemented
32	C₄⋊#88324	C₂²	1	1	yes	characteristic, complemented
33	C₄⋊#88324	C₂²	1	1	yes	characteristic, complemented
34	#13133274	C₂²	1	1	yes	characteristic
35	#13133274	C₂²	1	1	yes	characteristic
36	#13133274	C₂²	1	1	yes	characteristic
37	#13133274	C₂²	1	1	yes	characteristic
38	#13133274	C₂²	1	1	yes	characteristic, complemented
39	#13133274	C₂²	1	1	yes	characteristic, complemented
40	C₂²⋊#88324	C₂²	1	1	yes	characteristic, complemented
41	C₂²⋊#88324	C₂²	1	1	yes	characteristic, complemented
42	#13133272	C₂²	1	1	yes	characteristic, complemented
43	#13133272	C₂²	1	1	yes	characteristic, complemented
44	C₄×#88324	C₂²	1	1	yes	characteristic, complemented
45	C₄×#88324	C₂²	1	1	yes	characteristic, complemented
46	C₂×#11719947	C₂²	1	1	yes	characteristic
47	C₂²×C₄×D₅₃	C₂²	1	1	yes	characteristic
48	#13133200	C₄	1	1	yes	characteristic
49	#13133195	C₄	1	1	yes	characteristic
50	#13133195	C₄	1	1	yes	characteristic
51	#13133190	C₄	1	1	yes	characteristic
52	#13133190	C₄	1	1	yes	characteristic
53	#13133187	C₄	1	1	yes	characteristic
54	#13133185	C₄	1	1	yes	characteristic
55	#13133179	C₂²	1	1	yes	characteristic
56	#13133179	C₂²	1	1	yes	characteristic
57	#13133177	C₂²	1	1	yes	characteristic
58	#13133177	C₂²	1	1	yes	characteristic
59	#13133173	C₂²	1	1	yes	characteristic
60	#123×C₅₃	C₄	1	1	yes	characteristic
61	C₂³×D₅₃	C₂×C₄	1	1	yes	characteristic
62	C₂×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
64	C₂×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
65	C₂×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
66	C₂×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
67	C₂×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
68	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
69	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
70	#11719947	—	2	2	no	—
71	#11719947	—	2	2	no	—
72	C₂×D₂₁₂	C₂×C₄	1	1	yes	characteristic
73	C₂×D₂₁₂	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄×D₅₃	—	2	2	no	—
75	C₂×C₄×D₅₃	—	2	2	no	—
76	C₂×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
79	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
80	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
81	C₂×Dic₁₀₆	C₂×C₄	1	1	yes	characteristic
82	#11719940	—	2	2	no	—
83	#11719940	—	2	2	no	—
84	#11719940	D₄	1	4	yes	complemented
85	C₂×#88324	—	2	2	no	—
86	C₂×#88324	—	2	2	no	—
87	C₂×#88324	—	2	2	no	—
88	C₂×#88324	C₂³	1	1	yes	characteristic
89	C₂×#88324	C₂³	1	1	yes	characteristic
90	C₂×#88324	C₂³	1	1	yes	characteristic
91	C₂×#88324	C₂³	1	1	yes	characteristic
92	C₂×#88324	C₂³	1	1	yes	characteristic
93	C₂×#88324	C₂³	1	1	yes	characteristic
94	C₂×#88324	C₂³	1	1	yes	characteristic
95	C₂×#88324	C₂³	1	1	yes	characteristic
96	#11719936	—	2	2	no	—
97	#11719936	—	2	2	no	—
98	#11719936	—	2	2	no	—
99	D₅₃⋊C₈	—	2	2	no	—
100	D₅₃⋊C₈	—	2	2	no	—
101	D₅₃⋊C₈	—	2	2	no	—
102	C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
103	C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
104	C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
105	C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
106	C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
107	C₂²⋊Dic₅₃	C₂×C₄	1	1	yes	characteristic
108	#11719921	C₂×C₄	1	1	yes	characteristic
109	#11719921	C₂×C₄	1	1	yes	characteristic
110	#11719921	C₂×C₄	1	1	yes	characteristic
111	#11719921	C₂×C₄	1	1	yes	characteristic
112	#11719921	C₂×C₄	1	1	yes	characteristic
113	#11719921	C₂×C₄	1	1	yes	characteristic
114	#11719919	C₂×C₄	1	1	yes	characteristic
115	#11719919	C₂×C₄	1	1	yes	characteristic
116	#11719919	C₂×C₄	1	1	yes	characteristic
117	#11719919	C₂×C₄	1	1	yes	characteristic
118	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
119	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
120	C₂³×C₅₃	C₂²×C₄	1	1	yes	characteristic
121	C₂³×C₅₃	C₂²×C₄	1	1	yes	characteristic
122	C₂²×D₅₃	—	2	2	no	—
123	C₂²×D₅₃	—	2	2	no	—
124	C₂²×D₅₃	—	4	1	no	—
125	C₂²×D₅₃	C₂²×C₄	1	1	yes	characteristic
126	C₂²×D₅₃	C₂²×C₄	1	1	yes	characteristic
127	C₂²×D₅₃	C₂²×C₄	1	1	yes	characteristic
128	D₄×C₅₃	—	2	2	no	—
129	C₂×C₄×C₅₃	—	2	2	no	—
130	C₂×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
135	C₂²⋊D₅₃	—	2	2	no	—
136	C₂²⋊D₅₃	—	2	2	no	—
137	C₂²⋊D₅₃	—	2	2	no	—
138	C₂²⋊D₅₃	—	4	1	no	—
139	C₂×Dic₅₃	—	2	1	no	—
140	C₂×Dic₅₃	—	2	1	no	—
141	C₂×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
142	C₂×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
143	C₂×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
144	C₂×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
145	C₂×Dic₅₃	C₂×D₄	1	2	yes	—
146	C₂×Dic₅₃	#41	1	2	yes	—
147	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
148	D₂₁₂	—	2	2	no	—
149	D₂₁₂	—	4	1	no	—
150	C₄×D₅₃	—	2	2	no	—
151	C₄×D₅₃	—	2	2	no	—
152	C₄×D₅₃	—	2	1	no	—
153	C₄×D₅₃	—	2	1	no	—
154	C₄×D₅₃	—	2	1	no	—
155	C₄×D₅₃	—	2	1	no	—
156	C₄×D₅₃	—	2	1	no	—
157	C₄×D₅₃	—	2	1	no	—
158	Dic₁₀₆	—	2	2	no	—
159	#88324	—	2	1	no	—
160	#88324	—	2	1	no	—
161	#88324	—	2	1	no	—
162	#88324	—	2	1	no	—
163	#88324	—	2	1	no	—
164	#88324	—	2	1	no	—
165	#88324	C₂×D₄	1	2	yes	—
166	#88324	C₂×D₄	1	2	yes	—
167	C₂²×C₅₃	—	2	1	no	—
168	C₂²×C₅₃	—	2	1	no	—
169	C₂²×C₅₃	—	2	1	no	—
170	C₂²×C₅₃	—	2	1	no	—
171	C₂²×C₅₃	—	2	1	no	—
172	C₂²×C₅₃	C₄×D₄	1	2	yes	—
173	C₂²×C₅₃	C₂³×C₄	1	1	yes	characteristic
174	C₂×D₅₃	—	2	1	no	—
175	C₂×D₅₃	—	2	1	no	—
176	C₂×D₅₃	—	2	1	no	—
177	C₂×D₅₃	—	2	1	no	—
178	C₂×D₅₃	—	2	1	no	—
179	C₂×D₅₃	—	2	1	no	—
180	C₂×D₅₃	—	2	1	no	—
181	C₂×D₅₃	—	2	1	no	—
182	C₂×D₅₃	—	4	4	no	—
183	C₂×D₅₃	#131	1	2	yes	complemented
184	C₄×C₅₃	—	2	1	no	—
185	C₄×C₅₃	—	2	1	no	—
186	C₄×C₅₃	—	2	1	no	—
187	C₄×C₅₃	—	2	1	no	—
188	C₄×C₅₃	—	2	1	no	—
189	Dic₅₃	—	2	1	no	—
190	Dic₅₃	—	2	1	no	—
191	Dic₅₃	—	2	1	no	—
192	Dic₅₃	C₄×D₄	1	2	yes	—
193	Dic₅₃	C₂²×D₄	1	1	yes	characteristic
194	Dic₅₃	C₂×#41	1	1	yes	characteristic
195	#2933	—	53	1	no	maximal, Sylow
196	C₂×C₅₃	—	2	2	no	—
197	C₂×C₅₃	—	4	1	no	—
198	C₂×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
199	C₂×C₅₃	C₂×#131	1	1	yes	characteristic
200	C₂×C₅₃	#568	1	1	yes	characteristic
201	D₅₃	—	2	2	no	—
202	D₅₃	—	4	1	no	—
203	D₅₃	—	4	1	no	—
204	C₂×#131	—	53	1	no	—
205	C₂²×M₁₆	—	53	1	no	—
206	#525	—	53	1	no	—
207	#436	—	53	1	no	—
208	#436	—	53	1	no	—
209	#435	—	53	1	no	—
210	#435	—	53	1	no	—
211	#435	—	53	1	no	—
212	#435	—	53	1	no	—
213	C₈×D₄	—	53	1	no	—
214	C₈×D₄	—	53	1	no	—
215	#424	—	53	1	no	—
216	#408	—	53	1	no	—
217	C₂×C₂²⋊C₈	—	53	1	no	—
218	#405	—	53	1	no	—
219	C₅₃	#2933	1	1	yes	characteristic, complemented, Sylow
220	C₂×#41	—	53	1	no	—
221	C₂³×C₄	—	53	1	no	—
222	#131	—	106	4	no	—
223	C₂×M₁₆	—	53	1	no	—
224	C₂×M₁₆	—	53	1	no	—
225	C₂×M₁₆	—	53	1	no	—
226	C₂×M₁₆	—	53	1	no	—
227	C₂×M₁₆	—	53	1	no	—
228	C₂×M₁₆	—	53	1	no	—
229	C₂×M₁₆	—	106	4	no	—
230	C₂²×C₈	—	53	1	no	—
231	C₂²×C₈	—	53	1	no	—
232	C₂²×C₈	—	53	1	no	—
233	C₂²×C₈	—	53	1	no	—
234	C₂²×C₈	—	53	1	no	—
235	C₂²×C₈	—	53	1	no	—
236	#123	—	53	1	no	—
237	#123	#6157	1	1	yes	characteristic
238	C₂²⋊Q₈	—	53	1	no	—
239	C₂²⋊Q₈	—	53	1	no	—
240	#121	—	53	1	no	—
241	#121	—	53	1	no	—
242	#120	—	53	1	no	—
243	#120	—	53	1	no	—
244	C₄×D₄	—	53	1	no	—
245	C₄×D₄	—	53	1	no	—
246	C₄×D₄	—	53	1	no	—
247	C₄×D₄	—	53	1	no	—
248	#117	—	53	1	no	—
249	C₄⋊C₈	—	53	1	no	—
250	C₄⋊C₈	—	53	1	no	—
251	C₄⋊C₈	—	53	1	no	—
252	C₄⋊C₈	—	53	1	no	—
253	C₂²⋊C₈	—	53	1	no	—
254	C₂²⋊C₈	—	53	1	no	—
255	C₂²⋊C₈	—	53	1	no	—
256	C₂²⋊C₈	—	53	1	no	—
257	C₂²⋊C₈	—	53	1	no	—
258	C₂²⋊C₈	—	53	1	no	—
259	C₂²⋊C₈	—	53	1	no	—
260	C₂²⋊C₈	—	53	1	no	—
261	#97	—	53	1	no	—
262	#97	—	53	1	no	—
263	C₄×C₈	—	53	1	no	—
264	C₄×C₈	—	53	1	no	—
265	C₂⁴	—	53	1	no	—
266	#41	—	106	2	no	—
267	#41	—	106	2	no	—
268	C₂×Q₈	—	53	1	no	—
269	C₂×D₄	—	53	1	no	—
270	C₂×D₄	—	53	1	no	—
271	C₂×D₄	—	53	1	no	—
272	C₂×D₄	—	53	1	no	—
273	C₂×D₄	—	53	1	no	—
274	C₂×D₄	—	53	1	no	—
275	C₂×D₄	C₂×#6157	1	1	yes	characteristic
276	C₂²×C₄	—	53	1	no	—
277	C₂²×C₄	—	53	1	no	—
278	C₂²×C₄	—	53	1	no	—
279	C₂²×C₄	—	53	1	no	—
280	C₂²×C₄	—	53	1	no	—
281	C₂²×C₄	—	53	1	no	—
282	C₂²×C₄	—	53	1	no	—
283	C₂²×C₄	—	106	2	no	—
284	C₂²×C₄	—	106	2	no	—
285	C₂²×C₄	C₂×#6157	1	1	yes	characteristic
286	M₁₆	—	53	4	no	—
287	M₁₆	—	106	2	no	—
288	M₁₆	—	106	2	no	—
289	M₁₆	—	106	2	no	—
290	M₁₆	—	106	2	no	—
291	M₁₆	—	106	2	no	—
292	C₂×C₈	—	53	1	no	—
293	C₂×C₈	—	53	1	no	—
294	C₂×C₈	—	53	1	no	—
295	C₂×C₈	—	53	1	no	—
296	C₂×C₈	—	53	1	no	—
297	C₂×C₈	—	53	1	no	—
298	C₂×C₈	—	53	1	no	—
299	C₂×C₈	—	53	1	no	—
300	C₂×C₈	—	106	2	no	—
301	C₂×C₈	—	106	2	no	—
302	C₂×C₈	—	106	2	no	—
303	C₂×C₈	—	106	2	no	—
304	C₂×C₈	—	106	2	no	—
305	C₂×C₈	—	106	2	no	—
306	C₄⋊C₄	—	53	1	no	—
307	C₄⋊C₄	—	53	1	no	—
308	C₄⋊C₄	—	53	1	no	—
309	C₄⋊C₄	—	53	1	no	—
310	C₄⋊C₄	C₂×#6157	1	1	yes	characteristic
311	C₄⋊C₄	C₂×#6157	1	1	yes	characteristic
312	C₂²⋊C₄	—	53	1	no	—
313	C₂²⋊C₄	—	53	1	no	—
314	C₂²⋊C₄	—	53	1	no	—
315	C₂²⋊C₄	—	53	1	no	—
316	C₂²⋊C₄	—	53	1	no	—
317	C₂²⋊C₄	—	53	1	no	—
318	C₂²⋊C₄	—	53	1	no	—
319	C₂²⋊C₄	C₂×#6157	1	1	yes	characteristic
320	C₂²⋊C₄	C₂×#6157	1	1	yes	characteristic
321	C₂²⋊C₄	C₂×#6157	1	1	yes	characteristic
322	C₄²	—	53	1	no	—
323	C₄²	—	53	1	no	—
324	C₂³	—	53	1	no	—
325	C₂³	—	53	1	no	—
326	C₂³	—	53	1	no	—
327	C₂³	—	106	2	no	—
328	C₂³	—	106	2	no	—
329	C₂³	—	212	1	no	—
330	C₂³	C₂²×#6157	1	1	yes	characteristic
331	C₂³	C₂²×#6157	1	1	yes	characteristic
332	Q₈	—	106	2	no	—
333	D₄	—	2	2	no	—
334	D₄	—	106	2	no	—
335	D₄	—	106	2	no	—
336	D₄	—	106	2	no	—
337	D₄	—	106	2	no	—
338	D₄	—	212	1	no	—
339	D₄	—	212	1	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	53	2	no	—
342	C₂×C₄	—	53	2	no	—
343	C₂×C₄	—	53	1	no	—
344	C₂×C₄	—	53	1	no	—
345	C₂×C₄	—	53	1	no	—
346	C₂×C₄	—	53	1	no	—
347	C₂×C₄	—	53	1	no	—
348	C₂×C₄	—	106	1	no	—
349	C₂×C₄	—	106	1	no	—
350	C₂×C₄	—	106	1	no	—
351	C₂×C₄	—	106	1	no	—
352	C₂×C₄	—	106	1	no	—
353	C₂×C₄	—	106	2	no	—
354	C₂×C₄	—	106	2	no	—
355	C₂×C₄	—	106	1	no	—
356	C₂×C₄	—	106	1	no	—
357	C₂×C₄	—	106	1	no	—
358	C₂×C₄	C₂²×#6157	1	1	yes	characteristic
359	C₂×C₄	C₂²×#6157	1	1	yes	characteristic
360	C₂×C₄	C₂²×#6157	1	1	yes	characteristic
361	C₂×C₄	C₂²×#6157	1	1	yes	characteristic
362	C₂×C₄	C₂²×#6157	1	1	yes	characteristic
363	C₈	—	53	2	no	—
364	C₈	—	53	2	no	—
365	C₈	—	106	1	no	—
366	C₈	—	106	1	no	—
367	C₈	—	106	1	no	—
368	C₈	—	106	1	no	—
369	C₈	—	106	1	no	—
370	C₈	—	106	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	53	2	no	—
377	C₂²	—	106	1	no	—
378	C₂²	—	106	1	no	—
379	C₂²	—	106	1	no	—
380	C₂²	—	106	1	no	—
381	C₂²	—	106	1	no	—
382	C₂²	—	106	1	no	—
383	C₂²	—	106	1	no	—
384	C₂²	—	106	1	no	—
385	C₂²	—	212	4	no	—
386	C₂²	D₄×#6157	1	2	yes	—
387	C₂²	C₂³×#6157	1	1	yes	characteristic
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	2	1	no	—
393	C₄	—	53	1	no	—
394	C₄	—	53	1	no	—
395	C₄	—	53	2	no	—
396	C₄	—	106	1	no	—
397	C₄	—	106	1	no	—
398	C₄	—	106	1	no	—
399	C₂	—	2	2	no	—
400	C₂	—	4	1	no	—
401	C₂	—	106	2	no	—
402	C₂	—	212	1	no	—
403	C₂	—	212	1	no	—
404	C₂	C₂×D₄×#6157	1	1	yes	characteristic
405	C₂	D₅₃⋊#131	1	1	yes	characteristic
406	C₂	#16811702	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×#6157
commutator, socle	C₂²×C₅₃	C₂³×C₄
Fitting	#123×C₅₃	C₄
hypercenter	#123	#6157
hypocenter	C₅₃	#2933
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #123

Complements

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

N	H ≅ G/N	type
1. C₂×#13133304	C₂	semidirect
2. C₂×D₅₃⋊M₁₆	C₂	semidirect
3. #16811657	C₂	semidirect
4. #16811656	C₂	semidirect
5. #16811655	C₂	semidirect
6. #16811653	C₂	semidirect
7. #16811653	C₂	semidirect
8. #16811652	C₂	semidirect
9. #16811651	C₂	semidirect
10. #16811650	C₂	semidirect
11. #16811629	C₂	semidirect
12. #16811596	C₂	semidirect
13. C₂×#13133274	C₂	semidirect
14. #16811587	C₂	semidirect
19. C₂×#11719936	C₂²	semidirect
23. C₂×#11719940	C₂²	semidirect
26. C₂×D₅₃⋊C₈	C₂²	semidirect
29. C₂²×#88324	C₂²	semidirect
30. #13133284	C₂²	semidirect
31. #13133284	C₂²	semidirect
32. C₄⋊#88324	C₂²	semidirect
33. C₄⋊#88324	C₂²	semidirect
38. #13133274	C₂²	semidirect
39. #13133274	C₂²	semidirect
40. C₂²⋊#88324	C₂²	semidirect
41. C₂²⋊#88324	C₂²	semidirect
42. #13133272	C₂²	semidirect
43. #13133272	C₂²	semidirect
44. C₄×#88324	C₂²	semidirect
45. C₄×#88324	C₂²	semidirect
84. #11719940	D₄	semidirect
183. C₂×D₅₃	#131	semidirect
219. C₅₃	#2933	semidirect