Subgroups — C₂×#11927348 #14578387

Order 2432.

1512 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×#10597435	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#10597430	C₂	1	1	yes	maximal, characteristic, complemented
3	#11927348	C₂	1	16	yes	maximal, direct product factor
4	C₂×#10597354	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#10597360	C₂	1	2	yes	maximal, complemented
6	C₂×#10597357	C₂	1	2	yes	maximal, complemented
7	C₂×#10597362	C₂	1	2	yes	maximal, complemented
8	C₂×#10597396	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#64525	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×D₈×D₁₉	C₂	1	2	yes	maximal, complemented
11	C₂×#10597353	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic, complemented
14	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
15	C₂²×C₂²⋊D₁₉	—	2	2	no	—
16	#10597435	—	2	4	no	—
17	#10597435	C₂²	1	8	yes	complemented
18	C₂×#64545	C₂²	1	2	yes	complemented
19	#10597430	—	2	4	no	—
20	#10597430	C₂²	1	8	yes	complemented
21	C₂×#64543	—	2	1	no	—
22	C₂×#64543	C₂²	1	2	yes	complemented
23	C₂×D₄×D₁₉	—	2	2	no	—
24	C₂×D₄×D₁₉	—	2	1	no	—
25	C₂×D₄×D₁₉	C₂²	1	2	yes	complemented
26	C₂×D₄×D₁₉	C₂²	1	2	yes	complemented
27	C₂×#64541	—	2	1	no	—
28	C₂×#64541	C₂²	1	1	yes	characteristic
29	C₂×#64541	C₂²	1	1	yes	characteristic, complemented
30	C₂²×D₇₆	—	2	1	no	—
31	C₂²×D₇₆	C₂²	1	1	yes	characteristic, complemented
32	C₁₉×AGL(1,ℤ/8)	C₂²	1	8	yes	complemented
33	C₂×SD₁₆×C₁₉	C₂²	1	2	yes	complemented
34	C₂×D₈×C₁₉	C₂²	1	2	yes	complemented
35	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
36	#10597396	C₂²	1	8	yes	complemented
37	C₂×#64528	C₂²	1	1	yes	characteristic, complemented
38	C₂×#64527	C₂²	1	1	yes	characteristic, complemented
39	C₂×#64526	C₂²	1	1	yes	characteristic, complemented
40	C₂×#64525	C₂²	1	1	yes	characteristic, complemented
41	C₂×#64525	C₂²	1	2	yes	complemented
42	C₂×#64525	C₂²	1	2	yes	complemented
43	C₂×#64525	C₂²	1	8	yes	complemented
44	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
45	#10597362	C₂²	1	16	yes	complemented
46	#10597360	C₂²	1	16	yes	complemented
47	#10597357	C₂²	1	16	yes	complemented
48	D₈×D₁₉	C₂²	1	16	yes	complemented
49	#10597354	C₂²	1	8	yes	complemented
50	#10597353	C₂²	1	8	yes	complemented
51	C₂×D₁₅₂	C₂²	1	2	yes	complemented
52	C₂×#64516	C₂²	1	2	yes	complemented
53	C₂×#64515	C₂²	1	2	yes	complemented
54	C₂×C₈×D₁₉	C₂²	1	2	yes	complemented
55	C₂⁴×C₁₉	—	2	1	no	—
56	C₂³×D₁₉	—	2	1	no	—
57	C₂³×D₁₉	—	2	2	no	—
58	C₂³×D₁₉	—	2	2	no	—
59	#41×C₁₉	—	2	2	no	—
60	#41×C₁₉	C₂³	1	4	yes	complemented
61	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
62	C₂×D₄×C₁₉	—	2	1	no	—
63	C₂×D₄×C₁₉	—	2	1	no	—
64	C₂×D₄×C₁₉	—	2	2	no	—
65	C₂×D₄×C₁₉	C₂³	1	2	yes	—
66	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
67	C₂×D₄×C₁₉	C₂³	1	4	yes	complemented
68	C₂²×C₄×C₁₉	—	2	1	no	—
69	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
70	C₂×C₂²⋊D₁₉	—	2	1	no	—
71	C₂×C₂²⋊D₁₉	—	2	2	no	—
72	C₂×C₂²⋊D₁₉	—	2	16	no	—
73	C₂×C₂²⋊D₁₉	—	2	2	no	—
74	C₂×C₂²⋊D₁₉	—	2	2	no	—
75	C₂×C₂²⋊D₁₉	D₄	1	2	yes	—
76	C₂²×Dic₁₉	—	2	2	no	—
77	#64545	—	2	4	no	—
78	#64545	C₂³	1	8	yes	complemented
79	#64543	—	2	4	no	—
80	#64543	—	2	8	no	—
81	#64543	C₂³	1	8	yes	complemented
82	D₄×D₁₉	—	2	16	no	—
83	D₄×D₁₉	—	2	8	no	—
84	D₄×D₁₉	—	2	4	no	—
85	D₄×D₁₉	—	2	4	no	—
86	D₄×D₁₉	C₂³	1	8	yes	complemented
87	D₄×D₁₉	C₂³	1	8	yes	complemented
88	#64541	—	2	2	no	—
89	#64541	—	2	8	no	—
90	#64541	D₄	1	4	yes	—
91	#64541	C₂³	1	4	yes	—
92	#64541	C₂³	1	4	yes	complemented
93	C₂×D₇₆	—	2	2	no	—
94	C₂×D₇₆	—	2	1	no	—
95	C₂×D₇₆	—	2	2	no	—
96	C₂×D₇₆	—	2	8	no	—
97	C₂×D₇₆	D₄	1	1	yes	characteristic
98	C₂×D₇₆	C₂³	1	2	yes	—
99	C₂×D₇₆	C₂³	1	1	yes	characteristic
100	C₂×D₇₆	C₂³	1	4	yes	complemented
101	C₂×C₄×D₁₉	—	2	1	no	—
102	C₂×C₄×D₁₉	—	2	2	no	—
103	C₂×C₄×D₁₉	C₂³	1	2	yes	—
104	C₂×Dic₃₈	D₄	1	1	yes	characteristic
105	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
106	SD₁₆×C₁₉	C₂³	1	8	yes	complemented
107	D₈×C₁₉	C₂³	1	8	yes	complemented
108	M₁₆×C₁₉	C₂³	1	4	yes	complemented
109	C₂×C₈×C₁₉	C₂³	1	2	yes	—
110	#64528	C₂³	1	4	yes	complemented
111	#64527	C₂³	1	4	yes	complemented
112	#64526	C₂³	1	4	yes	complemented
113	#64525	C₂³	1	8	yes	complemented
114	#64525	C₂³	1	8	yes	complemented
115	#64525	C₂³	1	4	yes	complemented
116	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
117	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
118	C₂×C₁₉⋊C₈	C₂³	1	4	yes	complemented
119	D₁₅₂	C₂³	1	8	yes	complemented
120	#64516	C₂³	1	8	yes	complemented
121	#64515	C₂³	1	8	yes	complemented
122	C₈×D₁₉	C₂³	1	8	yes	complemented
123	C₂³×C₁₉	—	2	2	no	—
124	C₂³×C₁₉	—	2	1	no	—
125	C₂³×C₁₉	—	2	4	no	—
126	C₂³×C₁₉	—	8	2	no	—
127	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
128	C₂²×D₁₉	—	2	2	no	—
129	C₂²×D₁₉	—	2	1	no	—
130	C₂²×D₁₉	—	2	4	no	—
131	C₂²×D₁₉	—	2	8	no	—
132	C₂²×D₁₉	—	2	8	no	—
133	C₂²×D₁₉	—	8	4	no	—
134	C₂²×D₁₉	—	8	4	no	—
135	C₂²×D₁₉	—	8	2	no	—
136	C₂²×D₁₉	C₂×D₄	1	2	yes	—
137	Q₈×C₁₉	—	2	1	no	—
138	Q₈×C₁₉	C₂⁴	1	2	yes	—
139	D₄×C₁₉	—	2	4	no	—
140	D₄×C₁₉	—	2	1	no	—
141	D₄×C₁₉	—	2	2	no	—
142	D₄×C₁₉	—	2	4	no	—
143	D₄×C₁₉	C₂⁴	1	4	yes	—
144	D₄×C₁₉	C₂⁴	1	2	yes	—
145	C₂×C₄×C₁₉	—	2	1	no	—
146	C₂×C₄×C₁₉	—	2	4	no	—
147	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
148	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
149	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
150	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
151	C₂²⋊D₁₉	—	2	4	no	—
152	C₂²⋊D₁₉	—	2	8	no	—
153	C₂²⋊D₁₉	—	2	8	no	—
154	C₂²⋊D₁₉	—	2	8	no	—
155	C₂²⋊D₁₉	C₂×D₄	1	8	yes	—
156	C₂×Dic₁₉	—	2	1	no	—
157	C₂×Dic₁₉	—	2	8	no	—
158	C₂×Dic₁₉	C₂×D₄	1	2	yes	—
159	D₇₆	—	2	8	no	—
160	D₇₆	—	2	4	no	—
161	D₇₆	—	2	2	no	—
162	D₇₆	—	2	1	no	—
163	D₇₆	C₂×D₄	1	4	yes	—
164	D₇₆	C₂⁴	1	4	yes	—
165	D₇₆	C₂⁴	1	2	yes	—
166	C₄×D₁₉	—	2	4	no	—
167	C₄×D₁₉	—	2	8	no	—
168	C₄×D₁₉	C₂×D₄	1	4	yes	—
169	C₄×D₁₉	C₂⁴	1	4	yes	—
170	Dic₃₈	—	2	1	no	—
171	Dic₃₈	C₂×D₄	1	4	yes	—
172	Dic₃₈	C₂⁴	1	2	yes	—
173	C₈×C₁₉	C₂⁴	1	4	yes	—
174	C₁₉⋊C₈	C₂⁴	1	2	yes	—
175	C₁₉⋊C₈	C₂⁴	1	2	yes	—
176	C₂×#576	—	19	1	no	maximal, Sylow
177	C₂²×C₁₉	—	2	2	no	—
178	C₂²×C₁₉	—	2	4	no	—
179	C₂²×C₁₉	—	2	2	no	—
180	C₂²×C₁₉	—	4	2	no	—
181	C₂²×C₁₉	—	4	4	no	—
182	C₂²×C₁₉	—	8	4	no	—
183	C₂²×C₁₉	C₂²×D₄	1	2	yes	—
184	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
185	C₂×D₁₉	—	2	4	no	—
186	C₂×D₁₉	—	2	4	no	—
187	C₂×D₁₉	—	2	2	no	—
188	C₂×D₁₉	—	4	4	no	—
189	C₂×D₁₉	—	4	2	no	—
190	C₂×D₁₉	—	8	8	no	—
191	C₂×D₁₉	—	8	8	no	—
192	C₂×D₁₉	—	8	4	no	—
193	C₂×D₁₉	C₂²×D₄	1	4	yes	—
194	C₄×C₁₉	—	2	2	no	—
195	C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
196	C₄×C₁₉	C₂²×D₄	1	2	yes	—
197	C₄×C₁₉	C₂⁵	1	1	yes	characteristic
198	Dic₁₉	—	2	2	no	—
199	Dic₁₉	C₂²×D₄	1	4	yes	—
200	C₂×H(5,𝔽₂)	—	19	1	no	—
201	C₂×H(5,𝔽₂)	—	19	1	no	—
202	#576	—	19	16	no	—
203	C₂×AGL(1,ℤ/8)	—	19	2	no	—
204	C₂×AGL(1,ℤ/8)	—	19	2	no	—
205	C₂×AGL(1,ℤ/8)	—	19	1	no	—
206	C₂×AGL(1,ℤ/8)	D₁₉	1	1	yes	characteristic, complemented
207	C₂×#135	—	19	1	no	—
208	C₂×#135	—	19	2	no	—
209	C₂²×D₈	—	19	1	no	—
210	C₂²×D₈	—	19	2	no	—
211	C₂×#131	—	19	1	no	—
212	C₂×C₁₉	—	2	2	no	—
213	C₂×C₁₉	—	4	2	no	—
214	C₂×C₁₉	—	4	4	no	—
215	C₂×C₁₉	#576	1	2	yes	complemented
216	C₂×C₁₉	C₂³×D₄	1	1	yes	characteristic
217	D₁₉	—	2	4	no	—
218	D₁₉	—	4	4	no	—
219	D₁₉	—	4	2	no	—
220	H(5,𝔽₂)	—	19	8	no	—
221	H(5,𝔽₂)	—	19	8	no	—
222	H(5,𝔽₂)	—	38	4	no	—
223	H(5,𝔽₂)	—	38	4	no	—
224	C₂×#41	—	19	1	no	—
225	C₂×#41	—	19	2	no	—
226	C₂×#41	—	19	2	no	—
227	C₂×#41	—	19	1	no	—
228	C₂×#41	—	38	1	no	—
229	C₂×#41	—	38	1	no	—
230	C₂×#41	C₂×D₁₉	1	1	yes	characteristic, complemented
231	C₂²×D₄	—	19	2	no	—
232	C₂²×D₄	—	19	2	no	—
233	C₂²×D₄	—	19	1	no	—
234	C₂²×D₄	—	38	1	no	—
235	C₂²×D₄	—	38	2	no	—
236	C₂²×D₄	—	38	1	no	—
237	C₂²×D₄	—	38	2	no	—
238	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic, complemented
239	AGL(1,ℤ/8)	—	19	16	no	—
240	AGL(1,ℤ/8)	—	19	16	no	—
241	AGL(1,ℤ/8)	—	19	8	no	—
242	AGL(1,ℤ/8)	C₂×D₁₉	1	8	yes	complemented
243	#135	—	19	8	no	—
244	#135	—	19	16	no	—
245	C₂×Q₁₆	—	19	1	no	—
246	C₂×SD₁₆	—	19	1	no	—
247	C₂×SD₁₆	—	19	1	no	—
248	C₂×SD₁₆	—	19	2	no	—
249	C₂×SD₁₆	C₂×D₁₉	1	2	yes	complemented
250	C₂×D₈	—	19	2	no	—
251	C₂×D₈	—	19	1	no	—
252	C₂×D₈	—	19	2	no	—
253	C₂×D₈	—	19	8	no	—
254	C₂×D₈	—	19	16	no	—
255	C₂×D₈	—	19	2	no	—
256	C₂×D₈	C₂×D₁₉	1	2	yes	complemented
257	#131	—	19	8	no	—
258	C₂×M₁₆	—	19	2	no	—
259	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic, complemented
260	C₂²×C₈	—	19	1	no	—
261	C₂²×C₈	—	19	2	no	—
262	C₁₉	C₂×#576	1	1	yes	characteristic, complemented, Sylow
263	C₂⁴	—	2	1	no	—
264	C₂⁴	—	38	2	no	—
265	C₂⁴	—	38	2	no	—
266	C₂⁴	—	38	1	no	—
267	#41	—	2	2	no	—
268	#41	—	19	4	no	—
269	#41	—	19	4	no	—
270	#41	—	19	8	no	—
271	#41	—	19	8	no	—
272	#41	—	19	4	no	—
273	#41	—	38	8	no	—
274	#41	—	38	4	no	—
275	#41	—	38	4	no	—
276	#41	—	38	8	no	—
277	#41	—	38	2	no	—
278	#41	C₂²×D₁₉	1	4	yes	complemented
279	C₂×Q₈	—	19	1	no	—
280	C₂×Q₈	—	19	1	no	—
281	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
282	C₂×D₄	—	2	1	no	—
283	C₂×D₄	—	2	1	no	—
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	—	19	2	no	—
286	C₂×D₄	—	19	8	no	—
287	C₂×D₄	—	19	8	no	—
288	C₂×D₄	—	19	1	no	—
289	C₂×D₄	—	19	2	no	—
290	C₂×D₄	—	19	1	no	—
291	C₂×D₄	—	19	4	no	—
292	C₂×D₄	—	38	8	no	—
293	C₂×D₄	—	38	2	no	—
294	C₂×D₄	—	38	4	no	—
295	C₂×D₄	—	38	4	no	—
296	C₂×D₄	—	38	2	no	—
297	C₂×D₄	—	38	2	no	—
298	C₂×D₄	—	38	16	no	—
299	C₂×D₄	—	38	8	no	—
300	C₂×D₄	—	38	16	no	—
301	C₂×D₄	—	38	2	no	—
302	C₂×D₄	—	38	1	no	—
303	C₂×D₄	—	38	1	no	—
304	C₂×D₄	—	38	2	no	—
305	C₂×D₄	C₂²×D₁₉	1	2	yes	—
306	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
307	C₂×D₄	C₂²×D₁₉	1	4	yes	complemented
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	19	2	no	—
310	C₂²×C₄	—	38	2	no	—
311	C₂²×C₄	—	38	2	no	—
312	C₂²×C₄	—	38	1	no	—
313	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
314	Q₁₆	—	19	4	no	—
315	SD₁₆	—	19	4	no	—
316	SD₁₆	—	19	4	no	—
317	SD₁₆	—	19	8	no	—
318	SD₁₆	C₂²×D₁₉	1	8	yes	complemented
319	D₈	—	19	8	no	—
320	D₈	—	19	4	no	—
321	D₈	—	19	8	no	—
322	D₈	—	19	8	no	—
323	D₈	C₂²×D₁₉	1	8	yes	complemented
324	M₁₆	—	19	8	no	—
325	M₁₆	C₂²×D₁₉	1	4	yes	complemented
326	C₂×C₈	—	19	1	no	—
327	C₂×C₈	—	19	1	no	—
328	C₂×C₈	—	19	4	no	—
329	C₂×C₈	—	19	8	no	—
330	C₂×C₈	C₂²×D₁₉	1	2	yes	—
331	C₂³	—	2	1	no	—
332	C₂³	—	2	2	no	—
333	C₂³	—	2	4	no	—
334	C₂³	—	8	2	no	—
335	C₂³	—	19	2	no	—
336	C₂³	—	38	8	no	—
337	C₂³	—	38	8	no	—
338	C₂³	—	38	2	no	—
339	C₂³	—	38	1	no	—
340	C₂³	—	38	4	no	—
341	C₂³	—	152	2	no	—
342	C₂³	—	152	4	no	—
343	C₂³	—	152	4	no	—
344	C₂³	D₄×D₁₉	1	1	yes	characteristic
345	Q₈	—	2	1	no	—
346	Q₈	—	19	4	no	—
347	Q₈	—	19	2	no	—
348	Q₈	—	38	1	no	—
349	Q₈	C₂³×D₁₉	1	2	yes	—
350	D₄	—	2	4	no	—
351	D₄	—	2	2	no	—
352	D₄	—	2	4	no	—
353	D₄	—	2	1	no	—
354	D₄	—	19	8	no	—
355	D₄	—	19	4	no	—
356	D₄	—	19	4	no	—
357	D₄	—	19	2	no	—
358	D₄	—	38	8	no	—
359	D₄	—	38	8	no	—
360	D₄	—	38	8	no	—
361	D₄	—	38	8	no	—
362	D₄	—	38	4	no	—
363	D₄	—	38	4	no	—
364	D₄	—	38	1	no	—
365	D₄	—	38	2	no	—
366	D₄	C₂³×D₁₉	1	4	yes	—
367	D₄	C₂³×D₁₉	1	2	yes	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	19	2	no	—
371	C₂×C₄	—	19	4	no	—
372	C₂×C₄	—	19	4	no	—
373	C₂×C₄	—	38	8	no	—
374	C₂×C₄	—	38	8	no	—
375	C₂×C₄	—	38	1	no	—
376	C₂×C₄	—	38	4	no	—
377	C₂×C₄	D₄×D₁₉	1	2	yes	—
378	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
379	C₂×C₄	C₂³×D₁₉	1	2	yes	—
380	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
381	C₈	—	19	2	no	—
382	C₈	—	19	2	no	—
383	C₈	C₂³×D₁₉	1	4	yes	—
384	C₂²	—	2	2	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	2	4	no	—
387	C₂²	—	4	4	no	—
388	C₂²	—	4	2	no	—
389	C₂²	—	8	4	no	—
390	C₂²	—	19	4	no	—
391	C₂²	—	38	4	no	—
392	C₂²	—	38	4	no	—
393	C₂²	—	38	2	no	—
394	C₂²	—	76	4	no	—
395	C₂²	—	76	2	no	—
396	C₂²	—	152	4	no	—
397	C₂²	—	152	8	no	—
398	C₂²	—	152	8	no	—
399	C₂²	C₂×D₄×D₁₉	1	2	yes	—
400	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
401	C₄	—	2	2	no	—
402	C₄	—	19	4	no	—
403	C₄	—	38	2	no	—
404	C₄	C₂×D₄×D₁₉	1	2	yes	—
405	C₄	C₂×D₄×D₁₉	1	1	yes	characteristic
406	C₄	C₂⁴×D₁₉	1	1	yes	characteristic
407	C₂	—	2	2	no	—
408	C₂	—	4	4	no	—
409	C₂	—	4	2	no	—
410	C₂	—	38	4	no	—
411	C₂	—	76	4	no	—
412	C₂	—	76	2	no	—
413	C₂	#11927348	1	2	yes	direct product factor
414	C₂	C₂²×D₄×D₁₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₉
commutator, cosocle	C₄×C₁₉	C₂⁵
Frattini	C₄	C₂⁴×D₁₉
Fitting	C₂×C₁₉×AGL(1,ℤ/8)	C₂
socle	C₂²×C₁₉	C₂²×D₄
hypercenter	C₂×AGL(1,ℤ/8)	D₁₉
hypocenter	C₁₉	C₂×#576
LCS	G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×AGL(1,ℤ/8)

Complements

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

N	H ≅ G/N	type
1. C₂×#10597435	C₂	semidirect
2. C₂×#10597430	C₂	semidirect
3. #11927348	C₂	direct (N × H)
4. C₂×#10597354	C₂	semidirect
5. C₂×#10597360	C₂	semidirect
6. C₂×#10597357	C₂	semidirect
7. C₂×#10597362	C₂	semidirect
8. C₂×#10597396	C₂	semidirect
9. C₂²×#64525	C₂	semidirect
10. C₂×D₈×D₁₉	C₂	semidirect
11. C₂×#10597353	C₂	semidirect
12. C₂×C₁₉×AGL(1,ℤ/8)	C₂	semidirect
13. C₂×#41×C₁₉	C₂²	semidirect
14. C₂²×D₄×C₁₉	C₂²	semidirect
17. #10597435	C₂²	semidirect
18. C₂×#64545	C₂²	semidirect
20. #10597430	C₂²	semidirect
22. C₂×#64543	C₂²	semidirect
25. C₂×D₄×D₁₉	C₂²	semidirect
26. C₂×D₄×D₁₉	C₂²	semidirect
29. C₂×#64541	C₂²	semidirect
31. C₂²×D₇₆	C₂²	semidirect
32. C₁₉×AGL(1,ℤ/8)	C₂²	semidirect
33. C₂×SD₁₆×C₁₉	C₂²	semidirect
34. C₂×D₈×C₁₉	C₂²	semidirect
35. C₂×M₁₆×C₁₉	C₂²	semidirect
36. #10597396	C₂²	semidirect
37. C₂×#64528	C₂²	semidirect
38. C₂×#64527	C₂²	semidirect
39. C₂×#64526	C₂²	semidirect
40. C₂×#64525	C₂²	semidirect
41. C₂×#64525	C₂²	semidirect
42. C₂×#64525	C₂²	semidirect
43. C₂×#64525	C₂²	semidirect
44. C₂²×C₁₉⋊C₈	C₂²	semidirect
45. #10597362	C₂²	semidirect
46. #10597360	C₂²	semidirect
47. #10597357	C₂²	semidirect
48. D₈×D₁₉	C₂²	semidirect
49. #10597354	C₂²	semidirect
50. #10597353	C₂²	semidirect
51. C₂×D₁₅₂	C₂²	semidirect
52. C₂×#64516	C₂²	semidirect
53. C₂×#64515	C₂²	semidirect
54. C₂×C₈×D₁₉	C₂²	semidirect
60. #41×C₁₉	C₂³	semidirect
67. C₂×D₄×C₁₉	C₂³	semidirect
78. #64545	C₂³	semidirect
81. #64543	C₂³	semidirect
86. D₄×D₁₉	C₂³	semidirect
87. D₄×D₁₉	C₂³	semidirect
92. #64541	C₂³	semidirect
100. C₂×D₇₆	C₂³	semidirect
106. SD₁₆×C₁₉	C₂³	semidirect
107. D₈×C₁₉	C₂³	semidirect
108. M₁₆×C₁₉	C₂³	semidirect
110. #64528	C₂³	semidirect
111. #64527	C₂³	semidirect
112. #64526	C₂³	semidirect
113. #64525	C₂³	semidirect
114. #64525	C₂³	semidirect
115. #64525	C₂³	semidirect
118. C₂×C₁₉⋊C₈	C₂³	semidirect
119. D₁₅₂	C₂³	semidirect
120. #64516	C₂³	semidirect
121. #64515	C₂³	semidirect
122. C₈×D₁₉	C₂³	semidirect
206. C₂×AGL(1,ℤ/8)	D₁₉	semidirect
215. C₂×C₁₉	#576	semidirect
230. C₂×#41	C₂×D₁₉	semidirect
238. C₂²×D₄	C₂×D₁₉	semidirect
242. AGL(1,ℤ/8)	C₂×D₁₉	semidirect
249. C₂×SD₁₆	C₂×D₁₉	semidirect
256. C₂×D₈	C₂×D₁₉	semidirect
259. C₂×M₁₆	C₂×D₁₉	semidirect
262. C₁₉	C₂×#576	semidirect
278. #41	C₂²×D₁₉	semidirect
307. C₂×D₄	C₂²×D₁₉	semidirect
318. SD₁₆	C₂²×D₁₉	semidirect
323. D₈	C₂²×D₁₉	semidirect
325. M₁₆	C₂²×D₁₉	semidirect
413. C₂	#11927348	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×#10597435	2
C₂×#10597430	2
#11927348	2
C₂×#10597354	2
C₂×#10597360	2
C₂×#10597357	2
C₂×#10597362	2
C₂×#10597396	2
C₂²×#64525	2
C₂×D₈×D₁₉	2
C₂×#10597353	2
C₂×C₁₉×AGL(1,ℤ/8)	2
C₂×#576	19

Subgroups — C2×#11927348 #14578387

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11927348 #14578387