Subgroups — #16807149

Order 3328.

692 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11719162	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#88106	C₂	1	1	yes	maximal, characteristic, complemented
3	#13131220	C₂	1	2	yes	maximal, complemented
4	#13131216	C₂	1	2	yes	maximal, complemented
5	#13131216	C₂	1	2	yes	maximal, complemented
6	D₄×#6092	C₂	1	2	yes	maximal, complemented
7	#13131171	C₂	1	1	yes	maximal, characteristic, complemented
8	#13131066	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₂²⋊#6092	C₂	1	1	yes	maximal, characteristic, complemented
10	#13131045	C₂	1	1	yes	maximal, characteristic, complemented
11	#13123531	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#525	C₄	1	1	yes	characteristic
13	C₂×#88202	C₂²	1	1	yes	characteristic
14	C₂³×#1055	C₂²	1	1	yes	characteristic
15	#11719162	—	2	4	no	—
16	C₂×#88106	—	2	4	no	—
17	C₂×#88106	C₂²	1	1	yes	characteristic
18	C₂×#88106	C₂²	1	2	yes	—
19	C₂×#88106	C₂²	1	1	yes	characteristic
20	C₂×#88106	C₂²	1	2	yes	complemented
21	C₂²×#6092	C₂²	1	2	yes	—
22	C₂²×#6092	C₂²	1	1	yes	characteristic
23	C₂²×#6092	C₂²	1	1	yes	characteristic
24	C₂²×#6092	C₂²	1	2	yes	complemented
25	#11718895	C₄	1	1	yes	characteristic
26	#11718868	C₄	1	1	yes	characteristic
27	#11718672	C₄	1	2	yes	—
28	#11718672	C₄	1	2	yes	—
29	D₄×#1055	C₂²	1	2	yes	—
30	D₄×#1055	C₂²	1	2	yes	—
31	#11718660	C₄	1	1	yes	characteristic
32	#11718658	C₂²	1	1	yes	characteristic
33	C₂²⋊#6092	C₂²	1	1	yes	characteristic
34	C₂²⋊#6092	C₂²	1	1	yes	characteristic
35	C₂²⋊#6092	C₂²	1	1	yes	characteristic
36	C₂²⋊#6092	C₂²	1	1	yes	characteristic
37	C₂²⋊#6092	C₂²	1	2	yes	complemented
38	C₂²⋊#6092	C₂²	1	2	yes	complemented
39	#11718231	C₂²	1	2	yes	complemented
40	C₄⋊#6092	C₂²	1	2	yes	complemented
41	C₄⋊#6092	C₂²	1	2	yes	complemented
42	C₄×#6092	C₂²	1	2	yes	complemented
43	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
45	C₁₃×#123	C₈	1	2	yes	—
46	C₁₃×C₂²⋊Q₈	C₈	1	1	yes	characteristic
47	C₁₃×C₂²⋊Q₈	C₈	1	1	yes	characteristic
48	C₁₃×#121	C₈	1	1	yes	characteristic
49	C₁₃×#121	C₈	1	1	yes	characteristic
50	C₁₃×#120	C₈	1	2	yes	—
51	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
52	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
53	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
54	#88202	—	2	2	no	—
55	#88202	—	2	2	no	—
56	C₂×#6099	C₂×C₄	1	1	yes	characteristic
57	C₂×#6099	C₂×C₄	1	1	yes	characteristic
58	C₂×#6099	C₂×C₄	1	2	yes	—
59	C₂²×#1055	—	2	2	no	—
60	C₂²×#1055	—	2	2	no	—
61	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
62	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
63	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
64	C₂²×#1055	C₂³	1	1	yes	characteristic
65	C₂²×#1055	C₂³	1	1	yes	characteristic
66	C₂²×#1055	C₂³	1	2	yes	—
67	C₂²×#1055	C₂³	1	1	yes	characteristic
68	#88106	—	2	2	no	—
69	#88106	—	2	4	no	—
70	#88106	—	2	4	no	—
71	#88106	D₄	1	4	yes	complemented
72	C₂×#6092	—	2	2	no	—
73	C₂×#6092	—	2	2	no	—
74	C₂×#6092	—	2	4	no	—
75	C₂×#6092	—	2	4	no	—
76	C₂×#6092	C₂³	1	1	yes	characteristic
77	C₂×#6092	C₂³	1	1	yes	characteristic
78	C₂×#6092	C₂³	1	1	yes	characteristic
79	C₂×#6092	C₂³	1	2	yes	—
80	C₂×#6092	C₂³	1	1	yes	characteristic
81	C₂×#6092	C₂³	1	2	yes	—
82	C₂²⋊#1055	C₂×C₄	1	2	yes	—
83	C₂²⋊#1055	C₂×C₄	1	2	yes	—
84	C₂²⋊#1055	C₂×C₄	1	2	yes	—
85	C₂²⋊#1055	C₂×C₄	1	2	yes	—
86	C₄⋊#1055	C₂×C₄	1	2	yes	—
87	C₄⋊#1055	C₂×C₄	1	2	yes	—
88	#88043	C₂×C₄	1	2	yes	—
89	C₄×#1055	C₂³	1	2	yes	—
90	#33436	—	13	1	no	maximal, Sylow
91	C₂⁴×C₁₃	C₂×C₈	1	1	yes	characteristic
92	C₁₃×#41	—	2	2	no	—
93	C₁₃×#41	—	2	2	no	—
94	C₂×Q₈×C₁₃	C₂×C₈	1	1	yes	characteristic
95	C₂×D₄×C₁₃	C₂×C₈	1	2	yes	—
96	C₂×D₄×C₁₃	C₂×C₈	1	2	yes	—
97	C₂×D₄×C₁₃	C₂×C₈	1	1	yes	characteristic
98	C₂×D₄×C₁₃	C₂×C₈	1	2	yes	—
99	C₂²×C₄×C₁₃	—	2	2	no	—
100	C₂²×C₄×C₁₃	—	2	2	no	—
101	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
103	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
104	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
108	C₁₃×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
109	C₁₃×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
110	C₁₃×C₄⋊C₄	C₂×C₈	1	2	yes	—
111	C₁₃×C₄⋊C₄	C₂×C₈	1	2	yes	—
112	C₁₃×C₂²⋊C₄	C₂×C₈	1	2	yes	—
113	C₁₃×C₂²⋊C₄	C₂×C₈	1	2	yes	—
114	C₁₃×C₂²⋊C₄	C₂×C₈	1	2	yes	—
115	C₁₃×C₂²⋊C₄	C₂×C₈	1	2	yes	—
116	C₁₃×C₂²⋊C₄	C₂×C₈	1	2	yes	—
117	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
118	#6099	—	2	2	no	—
119	#6099	—	2	2	no	—
120	#6099	—	2	4	no	—
121	C₂×#1055	—	2	2	no	—
122	C₂×#1055	—	2	2	no	—
123	C₂×#1055	—	2	2	no	—
124	C₂×#1055	—	2	1	no	—
125	C₂×#1055	—	2	2	no	—
126	C₂×#1055	—	2	1	no	—
127	C₂×#1055	—	2	1	no	—
128	C₂×#1055	—	2	1	no	—
129	C₂×#1055	—	2	2	no	—
130	C₂×#1055	C₂²×C₄	1	2	yes	—
131	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
132	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
133	C₂×#1055	C₂²×C₄	1	2	yes	—
134	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
135	C₂×#1055	C₂×D₄	1	2	yes	—
136	C₂×#1055	#41	1	2	yes	—
137	C₂×#1055	C₂⁴	1	1	yes	characteristic
138	#6092	—	2	1	no	—
139	#6092	—	2	1	no	—
140	#6092	—	2	2	no	—
141	#6092	—	2	1	no	—
142	#6092	—	2	1	no	—
143	#6092	C₂×D₄	1	4	yes	—
144	C₂×#504	—	13	1	no	—
145	C₂²×M₃₂	—	13	1	no	—
146	#2929	—	13	1	no	—
147	#2169	—	13	2	no	—
148	#2168	—	13	2	no	—
149	#2168	—	13	2	no	—
150	D₄×C₁₆	—	13	2	no	—
151	#2151	—	13	1	no	—
152	#2113	—	13	1	no	—
153	C₂×C₂²⋊C₁₆	—	13	1	no	—
154	#2108	—	13	1	no	—
155	C₂³×C₁₃	—	2	2	no	—
156	C₂³×C₁₃	—	2	2	no	—
157	C₂³×C₁₃	—	4	1	no	—
158	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
159	C₂³×C₁₃	C₂²×C₈	1	2	yes	—
160	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
161	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
162	Q₈×C₁₃	—	2	2	no	—
163	D₄×C₁₃	—	2	4	no	—
164	D₄×C₁₃	—	2	4	no	—
165	D₄×C₁₃	—	2	2	no	—
166	D₄×C₁₃	—	4	2	no	—
167	C₂×C₄×C₁₃	—	2	2	no	—
168	C₂×C₄×C₁₃	—	2	1	no	—
169	C₂×C₄×C₁₃	—	2	1	no	—
170	C₂×C₄×C₁₃	—	2	2	no	—
171	C₂×C₄×C₁₃	—	2	1	no	—
172	C₂×C₄×C₁₃	—	2	1	no	—
173	C₂×C₄×C₁₃	—	2	2	no	—
174	C₂×C₄×C₁₃	—	2	2	no	—
175	C₂×C₄×C₁₃	—	2	2	no	—
176	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
177	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
178	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
179	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
181	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
182	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
183	C₂×C₄×C₁₃	#131	1	2	yes	—
184	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
185	#1055	—	2	1	no	—
186	#1055	—	2	1	no	—
187	#1055	—	2	2	no	—
188	#1055	—	2	2	no	—
189	#1055	C₄×D₄	1	2	yes	—
190	#1055	C₂²×D₄	1	1	yes	characteristic
191	#1055	C₂×#41	1	1	yes	characteristic
192	C₂×#131	—	13	1	no	—
193	C₂³×C₈	—	13	1	no	—
194	#525	#261	1	1	yes	characteristic
195	#504	—	26	4	no	—
196	C₂×M₃₂	—	13	1	no	—
197	C₂×M₃₂	—	13	1	no	—
198	C₂×M₃₂	—	13	2	no	—
199	C₂×M₃₂	—	13	2	no	—
200	C₂×M₃₂	—	26	4	no	—
201	C₂²×C₁₆	—	13	1	no	—
202	C₂²×C₁₆	—	13	1	no	—
203	C₂²×C₁₆	—	13	2	no	—
204	C₂²×C₁₆	—	13	2	no	—
205	#435	—	13	2	no	—
206	#435	—	13	2	no	—
207	C₈×D₄	—	13	2	no	—
208	C₈×D₄	—	13	2	no	—
209	#424	—	13	1	no	—
210	#408	—	13	1	no	—
211	#407	—	13	1	no	—
212	#405	—	13	1	no	—
213	C₄⋊C₁₆	—	13	2	no	—
214	C₄⋊C₁₆	—	13	2	no	—
215	C₂²⋊C₁₆	—	13	1	no	—
216	C₂²⋊C₁₆	—	13	1	no	—
217	C₂²⋊C₁₆	—	13	1	no	—
218	C₂²⋊C₁₆	—	13	1	no	—
219	C₂²⋊C₁₆	—	13	2	no	—
220	C₂²⋊C₁₆	—	13	2	no	—
221	#346	—	13	2	no	—
222	C₄×C₁₆	—	13	2	no	—
223	C₂²×C₁₃	—	2	1	no	—
224	C₂²×C₁₃	—	2	1	no	—
225	C₂²×C₁₃	—	2	1	no	—
226	C₂²×C₁₃	—	2	1	no	—
227	C₂²×C₁₃	—	2	2	no	—
228	C₂²×C₁₃	—	2	1	no	—
229	C₂²×C₁₃	—	2	1	no	—
230	C₂²×C₁₃	—	2	2	no	—
231	C₂²×C₁₃	—	2	1	no	—
232	C₂²×C₁₃	—	2	2	no	—
233	C₂²×C₁₃	—	4	4	no	—
234	C₂²×C₁₃	C₈×D₄	1	2	yes	—
235	C₂²×C₁₃	#504	1	2	yes	complemented
236	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
237	C₄×C₁₃	—	2	2	no	—
238	C₄×C₁₃	—	2	2	no	—
239	C₄×C₁₃	—	2	1	no	—
240	C₄×C₁₃	—	2	1	no	—
241	C₄×C₁₃	—	2	2	no	—
242	C₄×C₁₃	C₈×D₄	1	2	yes	—
243	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
244	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
245	C₂×#41	C₂×#261	1	1	yes	characteristic
246	C₂³×C₄	C₂×#261	1	1	yes	characteristic
247	#131	—	26	2	no	—
248	#131	—	26	2	no	—
249	C₂×M₁₆	—	13	1	no	—
250	C₂×M₁₆	—	13	2	no	—
251	C₂×M₁₆	—	13	1	no	—
252	C₂²×C₈	—	13	1	no	—
253	C₂²×C₈	—	13	1	no	—
254	C₂²×C₈	—	13	1	no	—
255	C₂²×C₈	—	13	1	no	—
256	C₂²×C₈	—	13	1	no	—
257	C₂²×C₈	—	13	1	no	—
258	C₂²×C₈	—	13	2	no	—
259	C₂²×C₈	—	26	2	no	—
260	C₂²×C₈	—	26	2	no	—
261	#123	#1057	1	2	yes	—
262	C₂²⋊Q₈	#1057	1	1	yes	characteristic
263	C₂²⋊Q₈	#1057	1	1	yes	characteristic
264	#121	#1057	1	1	yes	characteristic
265	#121	#1057	1	1	yes	characteristic
266	#120	#1057	1	2	yes	—
267	C₄×D₄	C₂×#261	1	2	yes	—
268	C₄×D₄	C₂×#261	1	2	yes	—
269	#117	C₂×#261	1	1	yes	characteristic
270	M₃₂	—	13	4	no	—
271	M₃₂	—	26	4	no	—
272	M₃₂	—	26	4	no	—
273	M₃₂	—	26	2	no	—
274	C₂×C₁₆	—	13	2	no	—
275	C₂×C₁₆	—	13	1	no	—
276	C₂×C₁₆	—	13	1	no	—
277	C₂×C₁₆	—	13	1	no	—
278	C₂×C₁₆	—	13	1	no	—
279	C₂×C₁₆	—	13	2	no	—
280	C₂×C₁₆	—	26	4	no	—
281	C₂×C₁₆	—	26	4	no	—
282	C₂×C₁₆	—	26	2	no	—
283	C₂×C₁₆	—	26	2	no	—
284	C₄⋊C₈	—	13	2	no	—
285	C₄⋊C₈	—	13	2	no	—
286	C₂²⋊C₈	—	13	2	no	—
287	C₂²⋊C₈	—	13	2	no	—
288	C₂²⋊C₈	—	13	2	no	—
289	C₂²⋊C₈	—	13	2	no	—
290	#97	—	13	2	no	—
291	C₄×C₈	—	13	2	no	—
292	C₂×C₁₃	—	2	2	no	—
293	C₂×C₁₃	—	2	2	no	—
294	C₂×C₁₃	—	4	2	no	—
295	C₂×C₁₃	—	4	1	no	—
296	C₂×C₁₃	C₂×C₈×D₄	1	1	yes	characteristic
297	C₂×C₁₃	C₂×#504	1	1	yes	characteristic
298	C₂×C₁₃	#3407	1	1	yes	characteristic
299	C₂⁴	C₂×#1057	1	1	yes	characteristic
300	#41	—	2	2	no	—
301	#41	—	2	2	no	—
302	C₂×Q₈	C₂×#1057	1	1	yes	characteristic
303	C₂×D₄	C₂×#1057	1	2	yes	—
304	C₂×D₄	C₂×#1057	1	2	yes	—
305	C₂×D₄	C₂×#1057	1	1	yes	characteristic
306	C₂×D₄	C₂×#1057	1	2	yes	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	C₂×#1057	1	1	yes	characteristic
310	C₂²×C₄	C₂×#1057	1	1	yes	characteristic
311	C₂²×C₄	C₂×#1057	1	1	yes	characteristic
312	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
313	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
314	C₂²×C₄	C₂²×#261	1	2	yes	—
315	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
316	M₁₆	—	26	4	no	—
317	M₁₆	—	26	2	no	—
318	M₁₆	—	26	2	no	—
319	C₂×C₈	—	13	2	no	—
320	C₂×C₈	—	13	2	no	—
321	C₂×C₈	—	13	1	no	—
322	C₂×C₈	—	13	1	no	—
323	C₂×C₈	—	13	2	no	—
324	C₂×C₈	—	13	1	no	—
325	C₂×C₈	—	13	1	no	—
326	C₂×C₈	—	13	2	no	—
327	C₂×C₈	—	26	1	no	—
328	C₂×C₈	—	26	2	no	—
329	C₂×C₈	—	26	1	no	—
330	C₂×C₈	—	26	1	no	—
331	C₂×C₈	—	26	1	no	—
332	C₂×C₈	—	26	2	no	—
333	C₂×C₈	—	26	2	no	—
334	C₂×C₈	—	26	2	no	—
335	C₂×C₈	—	26	2	no	—
336	C₄⋊C₄	C₂×#1057	1	1	yes	characteristic
337	C₄⋊C₄	C₂×#1057	1	1	yes	characteristic
338	C₄⋊C₄	C₂×#1057	1	2	yes	—
339	C₄⋊C₄	C₂×#1057	1	2	yes	—
340	C₂²⋊C₄	C₂×#1057	1	2	yes	—
341	C₂²⋊C₄	C₂×#1057	1	2	yes	—
342	C₂²⋊C₄	C₂×#1057	1	2	yes	—
343	C₂²⋊C₄	C₂×#1057	1	2	yes	—
344	C₂²⋊C₄	C₂×#1057	1	2	yes	—
345	C₄²	C₂²×#261	1	2	yes	—
346	C₁₆	—	13	4	no	—
347	C₁₆	—	26	1	no	—
348	C₁₆	—	26	2	no	—
349	C₁₆	—	26	1	no	—
350	C₁₆	—	26	1	no	—
351	C₁₆	—	26	1	no	—
352	C₁₃	#33436	1	1	yes	characteristic, complemented, Sylow
353	C₂³	—	2	2	no	—
354	C₂³	—	2	2	no	—
355	C₂³	—	4	1	no	—
356	C₂³	C₂²×#1057	1	1	yes	characteristic
357	C₂³	C₂²×#1057	1	2	yes	—
358	C₂³	C₂²×#1057	1	1	yes	characteristic
359	C₂³	C₂²×#1057	1	1	yes	characteristic
360	Q₈	—	2	2	no	—
361	D₄	—	2	4	no	—
362	D₄	—	2	4	no	—
363	D₄	—	2	2	no	—
364	D₄	—	4	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	#88238	1	2	yes	—
375	C₂×C₄	D₄×#261	1	2	yes	—
376	C₂×C₄	C₂²×#1057	1	2	yes	—
377	C₂×C₄	C₂²×#1057	1	2	yes	—
378	C₂×C₄	C₂²×#1057	1	1	yes	characteristic
379	C₂×C₄	C₂²×#1057	1	1	yes	characteristic
380	C₂×C₄	C₂²×#1057	1	2	yes	—
381	C₂×C₄	C₂²×#1057	1	1	yes	characteristic
382	C₂×C₄	C₂³×#261	1	1	yes	characteristic
383	C₈	—	13	1	no	—
384	C₈	—	13	1	no	—
385	C₈	—	13	2	no	—
386	C₈	—	26	2	no	—
387	C₈	—	26	1	no	—
388	C₈	—	26	1	no	—
389	C₈	—	26	2	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	2	1	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	2	2	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	2	no	—
400	C₂²	—	4	4	no	—
401	C₂²	D₄×#1057	1	2	yes	—
402	C₂²	#11719162	1	2	yes	complemented
403	C₂²	C₂³×#1057	1	1	yes	characteristic
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	2	2	no	—
407	C₄	—	2	2	no	—
408	C₄	—	2	2	no	—
409	C₄	D₄×#1057	1	2	yes	—
410	C₄	C₂×#88238	1	1	yes	characteristic
411	C₄	C₂×D₄×#261	1	1	yes	characteristic
412	C₂	—	2	2	no	—
413	C₂	—	2	2	no	—
414	C₂	—	4	1	no	—
415	C₂	—	4	2	no	—
416	C₂	C₂×D₄×#1057	1	1	yes	characteristic
417	C₂	C₂×#11719162	1	1	yes	characteristic
418	C₂	#13131803	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#261
commutator, socle	C₂²×C₁₃	C₂³×C₈
Fitting, prime radical	C₁₃×#525	C₄
cosocle	C₂×#1055	C₂⁴
hypercenter	#525	#261
hypocenter	C₁₃	#33436
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #525

Complements

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

N	H ≅ G/N	type
1. C₂×#11719162	C₂	semidirect
2. C₂²×#88106	C₂	semidirect
3. #13131220	C₂	semidirect
4. #13131216	C₂	semidirect
5. #13131216	C₂	semidirect
6. D₄×#6092	C₂	semidirect
7. #13131171	C₂	semidirect
8. #13131066	C₂	semidirect
9. C₂×C₂²⋊#6092	C₂	semidirect
10. #13131045	C₂	semidirect
20. C₂×#88106	C₂²	semidirect
24. C₂²×#6092	C₂²	semidirect
37. C₂²⋊#6092	C₂²	semidirect
38. C₂²⋊#6092	C₂²	semidirect
39. #11718231	C₂²	semidirect
40. C₄⋊#6092	C₂²	semidirect
41. C₄⋊#6092	C₂²	semidirect
42. C₄×#6092	C₂²	semidirect
71. #88106	D₄	semidirect
235. C₂²×C₁₃	#504	semidirect
352. C₁₃	#33436	semidirect
402. C₂²	#11719162	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11719162	2
C₂²×#88106	2
#13131220	2
#13131216	2
D₄×#6092	2
#13131171	2
#13131066	2
C₂×C₂²⋊#6092	2
#13131045	2
#13123531	2
#33436	13