Subgroups — C₄×#11719102 #16797406

Order 3328.

1326 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11719102	C₂	1	2	yes	maximal
2	C₄×D₄×#261	C₂	1	2	yes	maximal, complemented
3	#13130651	C₂	1	2	yes	maximal, complemented
4	C₄×#88101	C₂	1	1	yes	maximal, characteristic, complemented
5	#13130607	C₂	1	4	yes	maximal, complemented
6	C₄×#88115	C₂	1	2	yes	maximal, complemented
7	C₄×#88100	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×D₈×D₁₃	C₂	1	1	yes	maximal, characteristic
9	C₂×D₄×#261	C₂²	1	4	yes	—
10	C₂²×C₄×#261	—	2	2	no	—
11	C₂×D₈×D₁₃	C₂²	1	1	yes	characteristic
12	C₄×D₄×D₁₃	C₂²	1	2	yes	—
13	C₂×#88115	C₂²	1	4	yes	—
14	C₄×C₂²⋊#261	—	2	2	no	—
15	#11719102	C₄	1	16	yes	direct product factor
16	C₂×#88101	C₂²	1	2	yes	—
17	C₂×#88100	C₂²	1	2	yes	—
18	C₂×#88100	C₂²	1	2	yes	—
19	C₄⋊C₄×#261	C₂²	1	4	yes	—
20	C₂²⋊C₄×#261	—	2	4	no	—
21	C₄×C₄⋊#261	C₂²	1	2	yes	—
22	C₄²×#261	C₂²	1	1	yes	characteristic
23	C₄×D₁₃⋊C₈	C₂²	1	1	yes	characteristic
24	C₄×C₁₃×D₈	C₄	1	1	yes	characteristic, complemented
25	D₈×Dic₁₃	C₄	1	1	yes	characteristic, complemented
26	C₄×#6104	C₄	1	2	yes	complemented
27	D₁₃×#107	C₂²	1	1	yes	characteristic
28	#11718533	C₄	1	1	yes	characteristic, complemented
29	D₁₃×#102	C₂²	1	2	yes	—
30	#11718417	C₄	1	2	yes	complemented
31	C₄×D₁₀₄	C₄	1	1	yes	characteristic, complemented
32	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
33	#11718265	C₂²	1	2	yes	—
34	#11718246	C₂²	1	4	yes	—
35	C₂³×#261	—	2	4	no	—
36	C₂×D₄×D₁₃	C₂³	1	2	yes	—
37	C₂²×C₄×D₁₃	—	2	2	no	—
38	C₂×C₂²⋊#261	—	2	4	no	—
39	D₄×#261	—	2	8	no	—
40	D₄×#261	C₂×C₄	1	16	yes	complemented
41	C₂×C₄⋊#261	C₂³	1	4	yes	—
42	C₂×C₄×#261	—	2	4	no	—
43	C₂×C₄×#261	—	2	2	no	—
44	C₂×C₄×#261	—	4	8	no	—
45	C₂×C₄×#261	D₄	1	2	yes	—
46	C₂×C₄×#261	D₄	1	2	yes	—
47	C₂×C₄×#261	C₂³	1	2	yes	—
48	C₂×D₁₃⋊C₈	C₂³	1	2	yes	—
49	C₂×C₁₃×D₈	C₂×C₄	1	1	yes	characteristic
50	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	complemented
51	D₄×Dic₁₃	C₂×C₄	1	2	yes	complemented
52	C₂×#6104	C₂×C₄	1	2	yes	—
53	C₄×C₂²⋊D₁₃	—	2	2	no	—
54	D₈×D₁₃	C₂×C₄	1	8	yes	—
55	C₂×D₁₀₄	C₂×C₄	1	1	yes	characteristic
56	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
57	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
58	#88147	C₂×C₄	1	2	yes	complemented
59	C₄⋊C₄×D₁₃	C₂³	1	2	yes	—
60	#88135	—	2	2	no	—
61	C₂²⋊C₄×D₁₃	—	2	2	no	—
62	C₄×D₅₂	C₂×C₄	1	2	yes	complemented
63	C₄²×D₁₃	C₂³	1	1	yes	characteristic
64	#88115	C₂×C₄	1	16	yes	complemented
65	(C₂×#261)⋊C₄	—	2	4	no	—
66	(C₂×#261)⋊C₄	—	2	2	no	—
67	C₄×#1057	—	2	1	no	—
68	C₄×#1057	—	2	1	no	—
69	#88101	C₂×C₄	1	8	yes	complemented
70	#88100	—	2	4	no	—
71	#88100	C₂×C₄	1	8	yes	complemented
72	C₁₃×#107	C₂×C₄	1	1	yes	characteristic, complemented
73	C₁₃×#102	C₂×C₄	1	2	yes	complemented
74	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic, complemented
75	#88072	C₂×C₄	1	2	yes	complemented
76	#88061	C₂×C₄	1	2	yes	complemented
77	#88058	C₂×C₄	1	1	yes	characteristic, complemented
78	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic, complemented
79	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic, complemented
80	#88049	C₂×C₄	1	2	yes	complemented
81	#88047	C₂×C₄	1	2	yes	complemented
82	C₄×#1055	C₂×C₄	1	1	yes	characteristic, complemented
83	C₄×#442	—	13	1	no	maximal, Sylow
84	C₂³×D₁₃	—	2	2	no	—
85	C₂²×#261	—	2	4	no	—
86	C₂²×#261	—	2	16	no	—
87	C₂²×#261	—	4	8	no	—
88	C₂²×#261	—	4	8	no	—
89	C₂²×#261	C₂×D₄	1	4	yes	—
90	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₁₃	—	2	2	no	—
92	C₂×C₂²⋊D₁₃	—	2	2	no	—
93	C₂²×Dic₁₃	—	2	2	no	—
94	D₄×D₁₃	—	2	4	no	—
95	D₄×D₁₃	C₂²×C₄	1	8	yes	—
96	C₂×D₅₂	C₂²×C₄	1	2	yes	—
97	C₂×C₄×D₁₃	—	2	2	no	—
98	C₂×C₄×D₁₃	—	2	2	no	—
99	C₂×C₄×D₁₃	—	2	2	no	—
100	C₂×C₄×D₁₃	—	4	4	no	—
101	C₂×C₄×D₁₃	—	4	4	no	—
102	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
103	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
104	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
105	C₂²⋊#261	—	2	16	no	—
106	C₂×#1057	—	2	2	no	—
107	C₄⋊#261	—	2	4	no	—
108	C₄⋊#261	C₂²×C₄	1	8	yes	—
109	C₄×#261	—	2	4	no	—
110	C₄×#261	—	4	2	no	—
111	C₄×#261	—	4	8	no	—
112	C₄×#261	—	4	4	no	—
113	C₄×#261	C₂²×C₄	1	4	yes	—
114	C₄×#261	#41	1	4	yes	—
115	D₁₃⋊C₈	—	2	2	no	—
116	D₁₃⋊C₈	C₂²×C₄	1	4	yes	—
117	C₁₃×D₈	C₄²	1	4	yes	complemented
118	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
120	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
121	C₁₃×C₂²⋊C₄	—	2	2	no	—
122	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
123	C₂²⋊Dic₁₃	—	2	2	no	—
124	#6104	C₄²	1	8	yes	complemented
125	#6103	—	2	2	no	—
126	#6103	—	2	2	no	—
127	C₄⋊Dic₁₃	C₂²×C₄	1	2	yes	—
128	#6101	—	2	2	no	—
129	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
130	C₄×Dic₁₃	#41	1	1	yes	characteristic
131	C₄×Dic₁₃	#41	1	1	yes	characteristic
132	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
133	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
134	D₁₀₄	C₄²	1	4	yes	complemented
135	C₈×D₁₃	—	2	2	no	—
136	C₈×D₁₃	C₂²×C₄	1	4	yes	—
137	C₂×#442	—	13	2	no	—
138	C₂×C₄×D₈	—	13	1	no	—
139	C₄²×D₄	—	13	2	no	—
140	#1776	—	13	2	no	—
141	C₄×#106	—	13	1	no	—
142	#1762	—	13	4	no	—
143	C₄×#102	—	13	2	no	—
144	C₄×#97	—	13	1	no	—
145	C₂³×C₁₃	—	2	2	no	—
146	C₂²×D₁₃	—	2	2	no	—
147	C₂²×D₁₃	—	2	8	no	—
148	C₂²×D₁₃	—	4	2	no	—
149	C₂²×D₁₃	—	4	2	no	—
150	C₂²×D₁₃	—	4	4	no	—
151	C₂²×D₁₃	C₂²×D₄	1	1	yes	characteristic
152	C₂×#261	—	2	4	no	—
153	C₂×#261	—	2	4	no	—
154	C₂×#261	—	2	8	no	—
155	C₂×#261	—	4	32	no	—
156	C₂×#261	—	4	4	no	—
157	C₂×#261	—	4	4	no	—
158	C₂×#261	C₄×D₄	1	8	yes	—
159	D₄×C₁₃	—	2	2	no	—
160	D₄×C₁₃	C₂×C₄²	1	4	yes	complemented
161	C₂×C₄×C₁₃	—	2	2	no	—
162	C₂×C₄×C₁₃	—	4	4	no	—
163	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
164	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
165	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
166	C₂²⋊D₁₃	—	2	8	no	—
167	C₂×Dic₁₃	—	2	2	no	—
168	C₂×Dic₁₃	—	4	4	no	—
169	C₂×Dic₁₃	C₄×D₄	1	1	yes	characteristic
170	C₂×Dic₁₃	C₄×D₄	1	1	yes	characteristic
171	C₂×Dic₁₃	C₂×#41	1	1	yes	characteristic
172	D₅₂	—	2	2	no	—
173	D₅₂	C₂×C₄²	1	4	yes	complemented
174	C₄×D₁₃	—	2	2	no	—
175	C₄×D₁₃	—	4	2	no	—
176	C₄×D₁₃	—	4	2	no	—
177	C₄×D₁₃	—	4	4	no	—
178	C₄×D₁₃	—	4	4	no	—
179	C₄×D₁₃	AGL(1,ℤ/8)	1	4	yes	—
180	C₄×D₁₃	C₂³×C₄	1	2	yes	—
181	C₄×D₁₃	C₂×#41	1	2	yes	—
182	#1057	—	2	4	no	—
183	C₈×C₁₃	—	2	1	no	—
184	C₈×C₁₃	C₂×C₄²	1	2	yes	complemented
185	#1055	—	2	1	no	—
186	#1055	C₂×C₄²	1	2	yes	complemented
187	C₂²×D₈	—	13	1	no	—
188	C₂×C₄×D₄	—	13	4	no	—
189	C₂×C₄×D₄	—	13	2	no	—
190	C₂²×C₄²	—	26	2	no	—
191	#442	—	13	16	no	—
192	C₄×D₈	—	13	1	no	—
193	C₄×D₈	—	13	2	no	—
194	C₄×D₈	—	13	1	no	—
195	C₄×D₈	—	13	2	no	—
196	C₄×D₈	—	13	1	no	—
197	C₄×D₈	#261	1	1	yes	characteristic, complemented
198	C₂×#107	—	13	1	no	—
199	C₂×#106	—	13	2	no	—
200	C₂×#102	—	13	4	no	—
201	C₂×#102	—	13	2	no	—
202	C₂×#97	—	13	2	no	—
203	C₂×#97	—	13	2	no	—
204	C₂×C₄×C₈	—	13	1	no	—
205	C₂×C₄×C₈	—	13	1	no	—
206	C₄×C₄⋊C₄	—	13	2	no	—
207	C₄×C₄⋊C₄	—	13	4	no	—
208	C₄×C₂²⋊C₄	—	26	4	no	—
209	C₄×C₂²⋊C₄	—	26	2	no	—
210	C₄³	—	13	1	no	—
211	#340	—	13	4	no	—
212	#340	—	13	2	no	—
213	C₂²×C₁₃	—	2	4	no	—
214	C₂²×C₁₃	—	4	2	no	—
215	C₂²×C₁₃	—	4	2	no	—
216	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
217	C₂×D₁₃	—	2	4	no	—
218	C₂×D₁₃	—	4	2	no	—
219	C₂×D₁₃	—	4	2	no	—
220	C₂×D₁₃	—	4	8	no	—
221	C₂×D₁₃	—	4	8	no	—
222	C₂×D₁₃	C₂×C₄×D₄	1	2	yes	—
223	C₂×D₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
224	C₂×D₁₃	#575	1	2	yes	—
225	#261	—	2	8	no	—
226	#261	—	4	8	no	—
227	C₄×C₁₃	—	2	1	no	—
228	C₄×C₁₃	—	4	2	no	—
229	C₄×C₁₃	#442	1	2	yes	complemented
230	C₄×C₁₃	C₂²×C₄²	1	1	yes	characteristic
231	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
232	Dic₁₃	—	2	1	no	—
233	Dic₁₃	—	4	2	no	—
234	Dic₁₃	#442	1	2	yes	complemented
235	Dic₁₃	C₄×#41	1	2	yes	—
236	C₂²×D₄	—	13	2	no	—
237	C₂³×C₄	—	26	2	no	—
238	C₂³×C₄	—	26	4	no	—
239	C₂×D₈	—	13	2	no	—
240	C₂×D₈	—	13	8	no	—
241	C₂×D₈	—	13	1	no	—
242	C₂×D₈	C₂×#261	1	1	yes	characteristic
243	C₂²×C₈	—	13	1	no	—
244	C₂²×C₈	—	13	2	no	—
245	C₂²×C₈	—	13	1	no	—
246	C₄×D₄	—	13	16	no	—
247	C₄×D₄	—	13	2	no	—
248	C₄×D₄	—	13	2	no	—
249	C₄×D₄	—	13	2	no	—
250	C₄×D₄	—	26	2	no	—
251	C₄×D₄	—	26	2	no	—
252	C₄×D₄	—	26	8	no	—
253	C₄×D₄	C₂×#261	1	2	yes	complemented
254	C₂×C₄⋊C₄	—	13	4	no	—
255	C₂×C₄⋊C₄	—	13	2	no	—
256	C₂×C₂²⋊C₄	—	26	2	no	—
257	C₂×C₂²⋊C₄	—	26	4	no	—
258	C₂×C₄²	—	13	2	no	—
259	C₂×C₄²	—	13	1	no	—
260	C₂×C₄²	—	13	2	no	—
261	C₂×C₄²	—	13	2	no	—
262	C₂×C₄²	—	26	2	no	—
263	C₂×C₄²	—	26	4	no	—
264	C₂×C₄²	—	52	8	no	—
265	#107	—	13	1	no	—
266	#107	—	13	2	no	—
267	#107	C₂×#261	1	1	yes	characteristic, complemented
268	#106	—	13	8	no	—
269	#102	—	13	16	no	—
270	#102	—	13	2	no	—
271	#102	—	13	2	no	—
272	#102	—	13	2	no	—
273	#102	C₂×#261	1	2	yes	complemented
274	#97	—	13	8	no	—
275	#97	—	26	4	no	—
276	C₄×C₈	—	13	1	no	—
277	C₄×C₈	—	13	1	no	—
278	C₄×C₈	—	13	1	no	—
279	C₄×C₈	—	26	1	no	—
280	C₄×C₈	—	26	1	no	—
281	C₄×C₈	C₂×#261	1	1	yes	characteristic, complemented
282	#95	—	26	4	no	—
283	#95	—	26	2	no	—
284	C₂×C₁₃	—	4	4	no	—
285	C₂×C₁₃	C₄²×D₄	1	1	yes	characteristic
286	C₂×C₁₃	C₂×#442	1	1	yes	characteristic
287	C₂×C₁₃	#2943	1	1	yes	characteristic
288	D₁₃	—	4	4	no	—
289	D₁₃	C₄×AGL(1,ℤ/8)	1	4	yes	—
290	C₂⁴	—	26	2	no	—
291	C₂×D₄	—	13	8	no	—
292	C₂×D₄	—	13	2	no	—
293	C₂×D₄	—	26	4	no	—
294	C₂×D₄	—	26	2	no	—
295	C₂×D₄	C₂²×#261	1	2	yes	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	13	1	no	—
298	C₂²×C₄	—	13	1	no	—
299	C₂²×C₄	—	13	4	no	—
300	C₂²×C₄	—	13	1	no	—
301	C₂²×C₄	—	26	2	no	—
302	C₂²×C₄	—	26	2	no	—
303	C₂²×C₄	—	26	2	no	—
304	C₂²×C₄	—	26	16	no	—
305	C₂²×C₄	—	26	4	no	—
306	C₂²×C₄	—	26	2	no	—
307	C₂²×C₄	—	52	4	no	—
308	C₂²×C₄	—	52	4	no	—
309	C₂²×C₄	—	52	8	no	—
310	C₂²×C₄	—	52	8	no	—
311	D₈	—	13	8	no	—
312	D₈	—	13	4	no	—
313	D₈	C₄×#261	1	4	yes	complemented
314	C₂×C₈	—	13	1	no	—
315	C₂×C₈	—	13	4	no	—
316	C₂×C₈	—	13	4	no	—
317	C₂×C₈	—	13	1	no	—
318	C₂×C₈	—	26	2	no	—
319	C₂×C₈	—	26	2	no	—
320	C₂×C₈	—	26	2	no	—
321	C₂×C₈	C₂²×#261	1	1	yes	characteristic
322	C₂×C₈	C₂²×#261	1	1	yes	characteristic
323	C₄⋊C₄	—	13	8	no	—
324	C₄⋊C₄	—	13	2	no	—
325	C₄⋊C₄	—	26	2	no	—
326	C₄⋊C₄	—	26	4	no	—
327	C₄⋊C₄	C₂²×#261	1	2	yes	—
328	C₂²⋊C₄	—	2	2	no	—
329	C₂²⋊C₄	—	26	2	no	—
330	C₂²⋊C₄	—	26	2	no	—
331	C₂²⋊C₄	—	26	16	no	—
332	C₂²⋊C₄	—	26	2	no	—
333	C₄²	—	13	4	no	—
334	C₄²	—	13	4	no	—
335	C₄²	—	13	1	no	—
336	C₄²	—	13	1	no	—
337	C₄²	—	13	1	no	—
338	C₄²	—	26	4	no	—
339	C₄²	—	52	4	no	—
340	C₄²	—	52	2	no	—
341	C₄²	—	52	8	no	—
342	C₄²	C₂²×#261	1	1	yes	characteristic
343	C₁₃	C₄×#442	1	1	yes	characteristic, complemented, Sylow
344	C₂³	—	2	2	no	—
345	C₂³	—	13	1	no	—
346	C₂³	—	26	8	no	—
347	C₂³	—	26	2	no	—
348	C₂³	—	52	2	no	—
349	C₂³	—	52	2	no	—
350	C₂³	—	52	4	no	—
351	D₄	—	2	2	no	—
352	D₄	—	13	4	no	—
353	D₄	—	26	8	no	—
354	D₄	—	26	2	no	—
355	D₄	C₂×C₄×#261	1	4	yes	complemented
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	4	4	no	—
358	C₂×C₄	—	13	1	no	—
359	C₂×C₄	—	13	1	no	—
360	C₂×C₄	—	13	4	no	—
361	C₂×C₄	—	13	2	no	—
362	C₂×C₄	—	13	2	no	—
363	C₂×C₄	—	13	8	no	—
364	C₂×C₄	—	13	1	no	—
365	C₂×C₄	—	26	2	no	—
366	C₂×C₄	—	26	4	no	—
367	C₂×C₄	—	26	4	no	—
368	C₂×C₄	—	26	8	no	—
369	C₂×C₄	—	26	2	no	—
370	C₂×C₄	—	52	4	no	—
371	C₂×C₄	—	52	2	no	—
372	C₂×C₄	—	52	2	no	—
373	C₂×C₄	—	52	4	no	—
374	C₂×C₄	—	52	32	no	—
375	C₂×C₄	—	52	4	no	—
376	C₂×C₄	—	52	4	no	—
377	C₂×C₄	—	52	4	no	—
378	C₂×C₄	D₄×#261	1	1	yes	characteristic
379	C₂×C₄	D₄×#261	1	1	yes	characteristic
380	C₂×C₄	C₂³×#261	1	1	yes	characteristic
381	C₈	—	2	1	no	—
382	C₈	—	13	2	no	—
383	C₈	—	26	4	no	—
384	C₈	—	26	1	no	—
385	C₈	C₂×C₄×#261	1	2	yes	complemented
386	C₂²	—	2	4	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	4	2	no	—
389	C₂²	—	13	2	no	—
390	C₂²	—	13	2	no	—
391	C₂²	—	13	2	no	—
392	C₂²	—	26	4	no	—
393	C₂²	—	52	8	no	—
394	C₂²	—	52	8	no	—
395	C₂²	—	52	2	no	—
396	C₂²	—	52	2	no	—
397	C₂²	C₂×D₄×#261	1	1	yes	characteristic
398	C₄	—	2	1	no	—
399	C₄	—	4	2	no	—
400	C₄	—	13	2	no	—
401	C₄	—	13	2	no	—
402	C₄	—	26	8	no	—
403	C₄	—	26	1	no	—
404	C₄	—	52	8	no	—
405	C₄	—	52	2	no	—
406	C₄	#11719102	1	2	yes	direct product factor
407	C₄	C₂²×C₄×#261	1	1	yes	characteristic
408	C₄	#41×#261	1	1	yes	characteristic
409	C₂	—	4	4	no	—
410	C₂	—	13	4	no	—
411	C₂	—	52	4	no	—
412	C₂	C₄×D₄×#261	1	1	yes	characteristic
413	C₂	C₂×#11719102	1	1	yes	characteristic
414	C₂	#13131590	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₄×#261
commutator	C₄×C₁₃	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#261
Fitting	C₄×C₁₃×D₈	C₄
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂×D₈×D₁₃	C₂²
cosocle	C₂×C₄×D₁₃	C₂⁴
hypercenter	C₄×D₈	#261
hypocenter	C₁₃	C₄×#442
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×D₈

Complements

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

N	H ≅ G/N	type
2. C₄×D₄×#261	C₂	semidirect
3. #13130651	C₂	semidirect
4. C₄×#88101	C₂	semidirect
5. #13130607	C₂	semidirect
6. C₄×#88115	C₂	semidirect
7. C₄×#88100	C₂	semidirect
15. #11719102	C₄	direct (N × H)
24. C₄×C₁₃×D₈	C₄	semidirect
25. D₈×Dic₁₃	C₄	semidirect
26. C₄×#6104	C₄	semidirect
28. #11718533	C₄	semidirect
30. #11718417	C₄	semidirect
31. C₄×D₁₀₄	C₄	semidirect
40. D₄×#261	C₂×C₄	semidirect
50. C₄×D₄×C₁₃	C₂×C₄	semidirect
51. D₄×Dic₁₃	C₂×C₄	semidirect
58. #88147	C₂×C₄	semidirect
62. C₄×D₅₂	C₂×C₄	semidirect
64. #88115	C₂×C₄	semidirect
69. #88101	C₂×C₄	semidirect
71. #88100	C₂×C₄	semidirect
72. C₁₃×#107	C₂×C₄	semidirect
73. C₁₃×#102	C₂×C₄	semidirect
74. C₄×C₈×C₁₃	C₂×C₄	semidirect
75. #88072	C₂×C₄	semidirect
76. #88061	C₂×C₄	semidirect
77. #88058	C₂×C₄	semidirect
78. C₈×Dic₁₃	C₂×C₄	semidirect
79. C₈×Dic₁₃	C₂×C₄	semidirect
80. #88049	C₂×C₄	semidirect
81. #88047	C₂×C₄	semidirect
82. C₄×#1055	C₂×C₄	semidirect
117. C₁₃×D₈	C₄²	semidirect
124. #6104	C₄²	semidirect
134. D₁₀₄	C₄²	semidirect
160. D₄×C₁₃	C₂×C₄²	semidirect
173. D₅₂	C₂×C₄²	semidirect
184. C₈×C₁₃	C₂×C₄²	semidirect
186. #1055	C₂×C₄²	semidirect
197. C₄×D₈	#261	semidirect
229. C₄×C₁₃	#442	semidirect
234. Dic₁₃	#442	semidirect
253. C₄×D₄	C₂×#261	semidirect
267. #107	C₂×#261	semidirect
273. #102	C₂×#261	semidirect
281. C₄×C₈	C₂×#261	semidirect
313. D₈	C₄×#261	semidirect
343. C₁₃	C₄×#442	semidirect
355. D₄	C₂×C₄×#261	semidirect
385. C₈	C₂×C₄×#261	semidirect
406. C₄	#11719102	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#11719102	2
C₄×D₄×#261	2
#13130651	2
C₄×#88101	2
#13130607	2
C₄×#88115	2
C₄×#88100	2
C₄×D₈×D₁₃	2
C₄×#442	13

Subgroups — C4×#11719102 #16797406

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11719102 #16797406