Subgroups — #13128245

Order 1664.

1160 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×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719509	C₂	1	2	yes	maximal, complemented
3	#11719496	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×C₂²⋊D₁₃	C₂	1	2	yes	maximal, complemented
5	#11719269	C₂	1	4	yes	maximal, complemented
6	#11719265	C₂	1	4	yes	maximal, complemented
7	#11719252	C₂	1	4	yes	maximal, complemented
8	#11719243	C₂	1	4	yes	maximal, complemented
9	#11719220	C₂	1	2	yes	maximal, complemented
10	#11719199	C₂	1	2	yes	maximal, complemented
11	#11719198	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719188	C₂	1	1	yes	maximal, characteristic, complemented
13	#11719184	C₂	1	2	yes	maximal, complemented
14	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂³×C₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₂³×C₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
17	C₂²×C₂²⋊D₁₃	C₂²	1	2	yes	—
18	C₂×#6127	C₂²	1	2	yes	complemented
19	C₂²×C₄×D₁₃	C₂²	1	2	yes	complemented
20	C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
21	C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
22	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
26	#88207	C₂²	1	4	yes	complemented
27	C₂×C₂²⋊Dic₁₃	C₂²	1	2	yes	—
28	#88193	C₂²	1	4	yes	—
29	#88193	C₂²	1	4	yes	—
30	#88191	C₂²	1	4	yes	complemented
31	#88189	C₂²	1	4	yes	complemented
32	#88184	C₂²	1	2	yes	—
33	#88184	C₂²	1	2	yes	—
34	#88184	C₂²	1	2	yes	complemented
35	#88183	C₂²	1	4	yes	complemented
36	#88183	C₂²	1	4	yes	complemented
37	C₄×C₂²⋊D₁₃	C₂²	1	4	yes	complemented
38	C₄×C₂²⋊D₁₃	C₂²	1	4	yes	complemented
39	C₄×C₂²⋊D₁₃	C₂²	1	4	yes	complemented
40	C₄×C₂²⋊D₁₃	C₂²	1	4	yes	complemented
41	C₄×C₂²⋊D₁₃	C₂²	1	4	yes	complemented
42	C₂×#6103	C₂²	1	2	yes	complemented
43	#88180	C₂²	1	2	yes	complemented
44	#88178	C₂²	1	2	yes	complemented
45	#88178	C₂²	1	2	yes	complemented
46	#88178	C₂²	1	2	yes	complemented
47	C₂×#6101	C₂²	1	2	yes	complemented
48	C₂×C₄×Dic₁₃	C₂²	1	2	yes	complemented
49	#88152	C₂²	1	4	yes	complemented
50	#88150	C₂²	1	4	yes	complemented
51	#88148	C₂²	1	4	yes	complemented
52	#88143	C₂²	1	4	yes	complemented
53	#88140	C₂²	1	4	yes	complemented
54	#88139	C₂²	1	4	yes	complemented
55	#88138	C₂²	1	4	yes	complemented
56	#88137	C₂²	1	4	yes	complemented
57	#88136	C₂²	1	4	yes	complemented
58	#88133	C₂²	1	4	yes	complemented
59	#88132	C₂²	1	4	yes	complemented
60	#88132	C₂²	1	4	yes	complemented
61	#88130	C₂²	1	4	yes	complemented
62	#88129	C₂²	1	2	yes	complemented
63	C₄×D₅₂	C₂²	1	2	yes	complemented
64	#88126	C₂²	1	4	yes	complemented
65	#88124	C₂²	1	2	yes	complemented
66	C₄×Dic₂₆	C₂²	1	2	yes	complemented
67	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
68	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
69	C₂³×D₁₃	C₂³	1	2	yes	—
70	C₂×D₄×C₁₃	—	2	4	no	—
71	C₂×D₄×C₁₃	C₂³	1	4	yes	—
72	C₂²×C₄×C₁₃	—	4	2	no	—
73	C₂²×C₄×C₁₃	—	4	2	no	—
74	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
75	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
76	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
77	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
78	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
79	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
80	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
81	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
82	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
83	C₂×C₂²⋊D₁₃	—	2	8	no	—
84	C₂×C₂²⋊D₁₃	C₂³	1	4	yes	—
85	C₂×C₂²⋊D₁₃	C₂³	1	4	yes	—
86	C₂×C₂²⋊D₁₃	C₂³	1	4	yes	—
87	C₂×C₂²⋊D₁₃	C₂³	1	4	yes	—
88	C₂²×Dic₁₃	C₂³	1	2	yes	—
89	C₂²×Dic₁₃	C₂³	1	2	yes	—
90	C₂²×Dic₁₃	C₂³	1	2	yes	—
91	#6127	—	4	4	no	—
92	C₂×D₅₂	C₂³	1	2	yes	—
93	C₂×D₅₂	C₂³	1	2	yes	—
94	C₂×C₄×D₁₃	—	4	4	no	—
95	C₂×C₄×D₁₃	C₂³	1	4	yes	—
96	C₂×C₄×D₁₃	C₂³	1	4	yes	—
97	C₂×Dic₂₆	C₂³	1	2	yes	—
98	C₂×Dic₂₆	C₂³	1	2	yes	—
99	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
100	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
101	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
102	C₄²×C₁₃	C₂³	1	2	yes	—
103	C₄²×C₁₃	C₂³	1	2	yes	—
104	C₂²⋊Dic₁₃	C₂³	1	4	yes	—
105	C₂²⋊Dic₁₃	C₂³	1	4	yes	—
106	C₂²⋊Dic₁₃	C₂³	1	4	yes	—
107	C₂²⋊Dic₁₃	C₂³	1	4	yes	—
108	#6103	C₂³	1	4	yes	—
109	#6103	C₂³	1	4	yes	—
110	#6103	C₂³	1	4	yes	—
111	#6103	C₂³	1	4	yes	—
112	#6103	C₂³	1	4	yes	—
113	#6103	C₂³	1	4	yes	—
114	C₄⋊Dic₁₃	C₂³	1	2	yes	—
115	C₄⋊Dic₁₃	C₂³	1	2	yes	—
116	C₄⋊Dic₁₃	C₂³	1	2	yes	—
117	C₄⋊Dic₁₃	C₂³	1	2	yes	—
118	#6101	C₂³	1	4	yes	—
119	#6101	C₂³	1	4	yes	—
120	#6101	C₂³	1	4	yes	—
121	#6101	C₂³	1	4	yes	—
122	#6101	C₂³	1	4	yes	—
123	#6101	C₂³	1	4	yes	—
124	C₄×Dic₁₃	C₂³	1	4	yes	—
125	C₄×Dic₁₃	C₂³	1	4	yes	—
126	#3459	—	13	1	no	maximal, Sylow
127	C₂³×C₁₃	—	2	2	no	—
128	C₂³×C₁₃	—	4	1	no	—
129	C₂³×C₁₃	—	4	1	no	—
130	C₂³×C₁₃	—	4	1	no	—
131	C₂³×C₁₃	—	4	1	no	—
132	C₂³×C₁₃	#41	1	4	yes	complemented
133	C₂³×C₁₃	C₂⁴	1	2	yes	—
134	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
135	C₂³×C₁₃	C₂⁴	1	2	yes	—
136	C₂²×D₁₃	—	2	4	no	—
137	C₂²×D₁₃	—	4	2	no	—
138	C₂²×D₁₃	—	4	2	no	—
139	C₂²×D₁₃	C₂⁴	1	4	yes	—
140	D₄×C₁₃	—	2	8	no	—
141	C₂×C₄×C₁₃	—	2	2	no	—
142	C₂×C₄×C₁₃	—	2	4	no	—
143	C₂×C₄×C₁₃	—	2	4	no	—
144	C₂×C₄×C₁₃	—	2	2	no	—
145	C₂×C₄×C₁₃	—	4	1	no	—
146	C₂×C₄×C₁₃	—	4	2	no	—
147	C₂×C₄×C₁₃	—	4	1	no	—
148	C₂×C₄×C₁₃	—	4	2	no	—
149	C₂×C₄×C₁₃	—	4	1	no	—
150	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
151	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
152	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
153	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
154	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
155	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
156	C₂²⋊D₁₃	—	2	8	no	—
157	C₂²⋊D₁₃	—	2	8	no	—
158	C₂²⋊D₁₃	—	4	4	no	—
159	C₂²⋊D₁₃	—	4	4	no	—
160	C₂×Dic₁₃	—	2	4	no	—
161	C₂×Dic₁₃	—	4	2	no	—
162	C₂×Dic₁₃	—	4	2	no	—
163	C₂×Dic₁₃	C₂⁴	1	4	yes	—
164	C₂×Dic₁₃	C₂⁴	1	4	yes	—
165	C₂×Dic₁₃	C₂⁴	1	4	yes	—
166	D₅₂	—	4	2	no	—
167	D₅₂	—	4	2	no	—
168	C₄×D₁₃	—	2	8	no	—
169	C₄×D₁₃	—	4	4	no	—
170	Dic₂₆	—	4	2	no	—
171	Dic₂₆	—	4	2	no	—
172	#543	—	13	1	no	—
173	#539	—	13	4	no	—
174	#539	—	13	2	no	—
175	#538	—	13	4	no	—
176	#538	—	13	2	no	—
177	#534	—	13	2	no	—
178	#534	—	13	1	no	—
179	#529	—	13	4	no	—
180	#529	—	13	2	no	—
181	#525	—	13	2	no	—
182	#525	—	13	4	no	—
183	C₂×C₄×D₄	—	13	2	no	—
184	C₂×C₄×D₄	D₁₃	1	1	yes	characteristic, complemented
185	C₂²×C₁₃	—	2	2	no	—
186	C₂²×C₁₃	—	2	1	no	—
187	C₂²×C₁₃	—	2	2	no	—
188	C₂²×C₁₃	—	2	1	no	—
189	C₂²×C₁₃	—	2	2	no	—
190	C₂²×C₁₃	—	2	2	no	—
191	C₂²×C₁₃	—	2	2	no	—
192	C₂²×C₁₃	—	4	4	no	—
193	C₂²×C₁₃	—	4	4	no	—
194	C₂²×C₁₃	C₂×#41	1	4	yes	—
195	C₂²×C₁₃	C₂×#41	1	2	yes	—
196	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
197	C₂×D₁₃	—	2	4	no	—
198	C₂×D₁₃	—	2	4	no	—
199	C₂×D₁₃	—	2	4	no	—
200	C₂×D₁₃	—	4	8	no	—
201	C₄×C₁₃	—	2	2	no	—
202	C₄×C₁₃	—	2	2	no	—
203	C₄×C₁₃	—	2	2	no	—
204	C₄×C₁₃	—	2	1	no	—
205	C₄×C₁₃	—	2	2	no	—
206	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
207	Dic₁₃	—	2	4	no	—
208	Dic₁₃	—	2	4	no	—
209	Dic₁₃	—	2	4	no	—
210	C₂×#41	—	13	2	no	—
211	C₂²×D₄	—	13	2	no	—
212	C₂²×D₄	C₂×D₁₃	1	1	yes	characteristic
213	C₂³×C₄	—	13	2	no	—
214	C₂³×C₄	C₂×D₁₃	1	1	yes	characteristic
215	C₂³×C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
216	#126	—	13	4	no	—
217	#126	—	13	4	no	—
218	#126	—	13	4	no	—
219	#125	—	13	4	no	—
220	#125	—	13	2	no	—
221	#124	—	13	4	no	—
222	#124	—	13	2	no	—
223	#123	—	13	4	no	—
224	#123	—	13	4	no	—
225	#123	—	13	4	no	—
226	#123	—	13	4	no	—
227	#123	—	13	4	no	—
228	#123	—	13	4	no	—
229	C₂²⋊Q₈	—	13	2	no	—
230	C₂²⋊Q₈	—	13	2	no	—
231	C₂²⋊Q₈	—	13	2	no	—
232	C₂²⋊Q₈	—	13	4	no	—
233	C₂²⋊Q₈	—	13	4	no	—
234	C₂²⋊Q₈	—	13	4	no	—
235	#121	—	13	4	no	—
236	#121	—	13	4	no	—
237	#121	—	13	2	no	—
238	#121	—	13	2	no	—
239	#121	—	13	2	no	—
240	#121	—	13	4	no	—
241	#120	—	13	4	no	—
242	#120	—	13	4	no	—
243	#120	—	13	4	no	—
244	C₄×Q₈	—	13	2	no	—
245	C₄×D₄	—	13	4	no	—
246	C₄×D₄	—	13	4	no	—
247	C₄×D₄	—	13	4	no	—
248	C₄×D₄	—	13	4	no	—
249	C₄×D₄	—	13	4	no	—
250	C₄×D₄	—	13	2	no	—
251	C₄×D₄	C₂×D₁₃	1	4	yes	complemented
252	C₄×D₄	C₂×D₁₃	1	4	yes	complemented
253	#117	—	13	2	no	—
254	#117	—	13	4	no	—
255	C₂×C₄⋊C₄	—	13	2	no	—
256	C₂×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
257	C₂×C₂²⋊C₄	—	13	2	no	—
258	C₂×C₂²⋊C₄	—	13	2	no	—
259	C₂×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
260	C₂×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
261	C₂×C₄²	—	13	2	no	—
262	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic, complemented
263	C₂×C₁₃	—	2	4	no	—
264	C₂×C₁₃	—	2	2	no	—
265	C₂×C₁₃	—	4	2	no	—
266	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
267	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
268	C₂×C₁₃	#585	1	1	yes	characteristic
269	D₁₃	—	4	4	no	—
270	C₂⁴	—	13	2	no	—
271	C₂⁴	C₂²×D₁₃	1	1	yes	characteristic
272	C₂⁴	C₂²×D₁₃	1	1	yes	characteristic
273	#41	—	52	4	no	—
274	C₂×Q₈	—	13	2	no	—
275	C₂×Q₈	—	13	2	no	—
276	C₂×D₄	—	2	4	no	—
277	C₂×D₄	—	13	4	no	—
278	C₂×D₄	—	13	4	no	—
279	C₂×D₄	—	13	4	no	—
280	C₂×D₄	—	13	4	no	—
281	C₂×D₄	—	13	2	no	—
282	C₂×D₄	—	13	2	no	—
283	C₂×D₄	—	26	8	no	—
284	C₂×D₄	C₂²×D₁₃	1	4	yes	—
285	C₂²×C₄	—	4	2	no	—
286	C₂²×C₄	—	4	2	no	—
287	C₂²×C₄	—	13	2	no	—
288	C₂²×C₄	—	13	2	no	—
289	C₂²×C₄	—	13	2	no	—
290	C₂²×C₄	—	13	4	no	—
291	C₂²×C₄	—	13	4	no	—
292	C₂²×C₄	—	52	4	no	—
293	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
294	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
295	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
296	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
297	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
298	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
299	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
300	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
301	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
302	C₄⋊C₄	—	13	4	no	—
303	C₄⋊C₄	—	13	4	no	—
304	C₄⋊C₄	—	13	4	no	—
305	C₄⋊C₄	—	13	2	no	—
306	C₄⋊C₄	—	13	4	no	—
307	C₄⋊C₄	—	13	2	no	—
308	C₄⋊C₄	—	13	4	no	—
309	C₄⋊C₄	—	13	2	no	—
310	C₄⋊C₄	—	13	4	no	—
311	C₄⋊C₄	—	13	2	no	—
312	C₄⋊C₄	C₂²×D₁₃	1	4	yes	—
313	C₂²⋊C₄	—	13	4	no	—
314	C₂²⋊C₄	—	13	4	no	—
315	C₂²⋊C₄	—	13	4	no	—
316	C₂²⋊C₄	—	13	4	no	—
317	C₂²⋊C₄	—	13	4	no	—
318	C₂²⋊C₄	—	13	4	no	—
319	C₂²⋊C₄	—	13	4	no	—
320	C₂²⋊C₄	—	13	4	no	—
321	C₂²⋊C₄	—	13	4	no	—
322	C₂²⋊C₄	—	13	4	no	—
323	C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
324	C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
325	C₄²	—	13	4	no	—
326	C₄²	—	13	4	no	—
327	C₄²	C₂²×D₁₃	1	2	yes	—
328	C₄²	C₂²×D₁₃	1	2	yes	—
329	C₁₃	#3459	1	1	yes	characteristic, complemented, Sylow
330	C₂³	—	2	2	no	—
331	C₂³	—	4	1	no	—
332	C₂³	—	4	1	no	—
333	C₂³	—	4	1	no	—
334	C₂³	—	4	1	no	—
335	C₂³	—	13	4	no	—
336	C₂³	—	26	4	no	—
337	C₂³	—	52	2	no	—
338	C₂³	—	52	2	no	—
339	C₂³	#6127	1	4	yes	complemented
340	C₂³	C₂³×D₁₃	1	2	yes	—
341	C₂³	C₂³×D₁₃	1	1	yes	characteristic
342	C₂³	C₂³×D₁₃	1	2	yes	—
343	Q₈	—	52	2	no	—
344	Q₈	—	52	2	no	—
345	D₄	—	2	8	no	—
346	D₄	—	26	8	no	—
347	D₄	—	26	8	no	—
348	D₄	—	52	2	no	—
349	D₄	—	52	2	no	—
350	D₄	—	52	4	no	—
351	D₄	—	52	4	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	13	4	no	—
362	C₂×C₄	—	13	4	no	—
363	C₂×C₄	—	13	4	no	—
364	C₂×C₄	—	26	4	no	—
365	C₂×C₄	—	26	8	no	—
366	C₂×C₄	—	52	4	no	—
367	C₂×C₄	—	52	2	no	—
368	C₂×C₄	—	52	2	no	—
369	C₂×C₄	C₂³×D₁₃	1	2	yes	—
370	C₂×C₄	C₂³×D₁₃	1	2	yes	—
371	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
372	C₂×C₄	C₂³×D₁₃	1	2	yes	—
373	C₂×C₄	C₂³×D₁₃	1	2	yes	—
374	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
375	C₂²	—	2	1	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	2	2	no	—
379	C₂²	—	2	2	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	4	4	no	—
383	C₂²	—	4	4	no	—
384	C₂²	—	26	4	no	—
385	C₂²	—	26	4	no	—
386	C₂²	—	26	4	no	—
387	C₂²	—	52	8	no	—
388	C₂²	C₂×#6127	1	2	yes	—
389	C₂²	C₂×#6127	1	4	yes	—
390	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
391	C₄	—	2	2	no	—
392	C₄	—	2	1	no	—
393	C₄	—	2	2	no	—
394	C₄	—	2	2	no	—
395	C₄	—	2	2	no	—
396	C₄	—	26	4	no	—
397	C₄	—	26	4	no	—
398	C₄	—	26	4	no	—
399	C₄	#88251	1	2	yes	—
400	C₂	—	2	2	no	—
401	C₂	—	2	4	no	—
402	C₂	—	4	2	no	—
403	C₂	—	52	4	no	—
404	C₂	C₂²×#6127	1	1	yes	characteristic
405	C₂	C₂×#88251	1	1	yes	characteristic
406	C₂	#11719648	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Frattini	C₂²	C₂⁴×D₁₃
Fitting	C₂×C₄×D₄×C₁₃	C₂
hypercenter	C₂×C₄×D₄	D₁₃
hypocenter	C₁₃	#3459
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×C₄×D₄×C₁₃	C₂	semidirect
2. #11719509	C₂	semidirect
3. #11719496	C₂	semidirect
4. C₂×C₄×C₂²⋊D₁₃	C₂	semidirect
5. #11719269	C₂	semidirect
6. #11719265	C₂	semidirect
7. #11719252	C₂	semidirect
8. #11719243	C₂	semidirect
9. #11719220	C₂	semidirect
10. #11719199	C₂	semidirect
11. #11719198	C₂	semidirect
12. #11719188	C₂	semidirect
13. #11719184	C₂	semidirect
16. C₂³×C₄×C₁₃	C₂²	semidirect
18. C₂×#6127	C₂²	semidirect
19. C₂²×C₄×D₁₃	C₂²	semidirect
20. C₄×D₄×C₁₃	C₂²	semidirect
21. C₄×D₄×C₁₃	C₂²	semidirect
22. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
24. C₂×C₁₃×C₂²⋊C₄	C₂²	semidirect
25. C₂×C₄²×C₁₃	C₂²	semidirect
26. #88207	C₂²	semidirect
30. #88191	C₂²	semidirect
31. #88189	C₂²	semidirect
34. #88184	C₂²	semidirect
35. #88183	C₂²	semidirect
36. #88183	C₂²	semidirect
37. C₄×C₂²⋊D₁₃	C₂²	semidirect
38. C₄×C₂²⋊D₁₃	C₂²	semidirect
39. C₄×C₂²⋊D₁₃	C₂²	semidirect
40. C₄×C₂²⋊D₁₃	C₂²	semidirect
41. C₄×C₂²⋊D₁₃	C₂²	semidirect
42. C₂×#6103	C₂²	semidirect
43. #88180	C₂²	semidirect
44. #88178	C₂²	semidirect
45. #88178	C₂²	semidirect
46. #88178	C₂²	semidirect
47. C₂×#6101	C₂²	semidirect
48. C₂×C₄×Dic₁₃	C₂²	semidirect
49. #88152	C₂²	semidirect
50. #88150	C₂²	semidirect
51. #88148	C₂²	semidirect
52. #88143	C₂²	semidirect
53. #88140	C₂²	semidirect
54. #88139	C₂²	semidirect
55. #88138	C₂²	semidirect
56. #88137	C₂²	semidirect
57. #88136	C₂²	semidirect
58. #88133	C₂²	semidirect
59. #88132	C₂²	semidirect
60. #88132	C₂²	semidirect
61. #88130	C₂²	semidirect
62. #88129	C₂²	semidirect
63. C₄×D₅₂	C₂²	semidirect
64. #88126	C₂²	semidirect
65. #88124	C₂²	semidirect
66. C₄×Dic₂₆	C₂²	semidirect
132. C₂³×C₁₃	#41	semidirect
184. C₂×C₄×D₄	D₁₃	semidirect
215. C₂³×C₄	C₂×D₁₃	semidirect
251. C₄×D₄	C₂×D₁₃	semidirect
252. C₄×D₄	C₂×D₁₃	semidirect
256. C₂×C₄⋊C₄	C₂×D₁₃	semidirect
260. C₂×C₂²⋊C₄	C₂×D₁₃	semidirect
262. C₂×C₄²	C₂×D₁₃	semidirect
329. C₁₃	#3459	semidirect
339. C₂³	#6127	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×D₄×C₁₃	2
#11719509	2
#11719496	2
C₂×C₄×C₂²⋊D₁₃	2
#11719269	2
#11719265	2
#11719252	2
#11719243	2
#11719220	2
#11719199	2
#11719198	2
#11719188	2
#11719184	2
#3459	13