Subgroups — #18078951

Order 4864.

534 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926744	C₂	1	1	yes	maximal, characteristic
2	#14564475	C₂	1	1	yes	maximal, characteristic
3	#14562304	C₂	1	1	yes	maximal, characteristic
4	#14562064	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561509	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561486	C₂	1	1	yes	maximal, characteristic, complemented
7	Q₈×M₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#64527	C₄	1	2	yes	—
9	C₂×#10597320	C₂²	1	1	yes	characteristic
10	#11926744	—	2	1	no	—
11	#11926744	—	2	1	no	—
12	#11926744	—	2	1	no	—
13	#11926744	—	2	1	no	—
14	#11926597	C₂²	1	1	yes	characteristic
15	#11926568	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×#10597266	C₄	1	2	yes	—
18	C₂×#10597280	—	2	1	no	—
19	C₂×#10597280	—	2	1	no	—
20	#11926287	—	2	2	no	—
21	Q₈⋊(C₁₉⋊C₈)	—	2	1	no	—
22	Q₈⋊(C₁₉⋊C₈)	—	2	1	no	—
23	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#446	—	2	2	no	—
25	C₁₉×#446	—	2	1	no	—
26	C₈×Q₈×C₁₉	—	2	1	no	—
27	C₁₉×#423	—	2	1	no	—
28	C₁₉×#423	C₂²	1	1	yes	characteristic
29	C₄×M₁₆×C₁₉	—	2	1	no	—
30	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
31	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
32	C₂²×D₇₆	—	2	1	no	—
33	C₂²×D₇₆	—	2	1	no	—
34	C₂²×D₇₆	C₂×C₄	1	2	yes	—
35	C₂×M₁₆×C₁₉	—	2	1	no	—
36	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
37	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
38	C₄×Q₈×C₁₉	—	2	1	no	—
39	C₄×Q₈×C₁₉	—	2	1	no	—
40	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
41	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
42	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
43	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
44	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
45	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₁₉	—	2	1	no	—
47	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
48	C₂×#64527	—	2	2	no	—
49	C₂×#64527	—	2	2	no	—
50	C₂×#64527	—	4	4	no	—
51	C₂×#64520	—	2	1	no	—
52	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
53	#10597320	—	2	1	no	—
54	#10597320	—	2	1	no	—
55	#10597320	—	2	1	no	—
56	#10597320	—	2	1	no	—
57	C₁₉×C₄⋊C₈	—	2	2	no	—
58	C₁₉×C₄⋊C₈	—	2	2	no	—
59	C₁₉×C₄⋊C₈	—	2	1	no	—
60	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
61	C₁₉×#97	—	2	2	no	—
62	C₁₉×#97	—	2	1	no	—
63	C₄×C₈×C₁₉	—	2	2	no	—
64	C₄×C₈×C₁₉	—	2	1	no	—
65	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
66	#10597280	—	4	2	no	—
67	#10597280	—	4	2	no	—
68	#10597266	—	2	2	no	—
69	#10597266	—	2	2	no	—
70	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
71	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
72	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
73	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
74	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
75	C₄×C₁₉⋊C₈	—	2	1	no	—
76	C₂³×D₁₉	—	2	2	no	—
77	C₂×Q₈×C₁₉	—	2	1	no	—
78	C₂×Q₈×C₁₉	—	2	2	no	—
79	C₂×Q₈×C₁₉	—	4	1	no	—
80	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
81	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₉	—	2	1	no	—
83	C₂²×C₄×C₁₉	—	2	1	no	—
84	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
87	C₂×D₇₆	—	2	2	no	—
88	C₂×D₇₆	—	2	2	no	—
89	C₂×D₇₆	—	4	2	no	—
90	C₂×D₇₆	—	4	2	no	—
91	C₂×D₇₆	—	4	1	no	—
92	C₂×D₇₆	—	4	1	no	—
93	C₂×D₇₆	—	4	1	no	—
94	C₂×D₇₆	—	4	1	no	—
95	C₂×D₇₆	—	4	1	no	—
96	C₂×D₇₆	—	4	1	no	—
97	C₂×D₇₆	—	4	1	no	—
98	C₂×D₇₆	—	4	1	no	—
99	C₂×D₇₆	—	8	2	no	—
100	M₁₆×C₁₉	—	2	1	no	—
101	M₁₆×C₁₉	—	2	1	no	—
102	M₁₆×C₁₉	—	2	1	no	—
103	M₁₆×C₁₉	—	4	1	no	—
104	M₁₆×C₁₉	—	4	1	no	—
105	M₁₆×C₁₉	SD₁₆	1	2	yes	complemented
106	C₂×C₈×C₁₉	—	2	1	no	—
107	C₂×C₈×C₁₉	—	2	2	no	—
108	C₂×C₈×C₁₉	—	2	1	no	—
109	C₄⋊C₄×C₁₉	—	2	1	no	—
110	C₄⋊C₄×C₁₉	—	2	1	no	—
111	C₄⋊C₄×C₁₉	—	2	1	no	—
112	C₄⋊C₄×C₁₉	—	2	1	no	—
113	C₄⋊C₄×C₁₉	—	2	1	no	—
114	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
115	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
116	C₄²×C₁₉	—	2	1	no	—
117	C₄²×C₁₉	—	2	1	no	—
118	C₄²×C₁₉	—	2	1	no	—
119	C₄²×C₁₉	—	2	1	no	—
120	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
121	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
123	C₄²×C₁₉	#41	1	1	yes	characteristic
124	#64527	—	4	4	no	—
125	#64527	—	4	4	no	—
126	#64520	—	4	1	no	—
127	#64520	—	4	1	no	—
128	C₂×C₁₉⋊C₈	—	2	2	no	—
129	C₂×C₁₉⋊C₈	—	4	2	no	—
130	C₂×C₁₉⋊C₈	—	4	1	no	—
131	C₂×C₁₉⋊C₈	—	4	1	no	—
132	#9254	—	19	1	no	maximal, Sylow
133	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
134	C₂²×D₁₉	—	4	2	no	—
135	C₂²×D₁₉	—	4	2	no	—
136	C₂²×D₁₉	—	4	2	no	—
137	C₂²×D₁₉	—	8	2	no	—
138	C₂²×D₁₉	—	8	2	no	—
139	Q₈×C₁₉	—	2	1	no	—
140	Q₈×C₁₉	—	2	1	no	—
141	Q₈×C₁₉	—	2	1	no	—
142	Q₈×C₁₉	—	4	2	no	—
143	Q₈×C₁₉	#100	1	2	yes	complemented
144	C₂×C₄×C₁₉	—	2	1	no	—
145	C₂×C₄×C₁₉	—	2	1	no	—
146	C₂×C₄×C₁₉	—	2	1	no	—
147	C₂×C₄×C₁₉	—	2	1	no	—
148	C₂×C₄×C₁₉	—	2	1	no	—
149	C₂×C₄×C₁₉	—	2	1	no	—
150	C₂×C₄×C₁₉	—	4	1	no	—
151	C₂×C₄×C₁₉	—	4	2	no	—
152	C₂×C₄×C₁₉	—	8	1	no	—
153	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
155	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
156	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
157	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
158	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
159	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
160	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
161	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
162	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
163	D₇₆	—	4	2	no	—
164	D₇₆	—	4	2	no	—
165	D₇₆	—	8	2	no	—
166	D₇₆	—	8	2	no	—
167	D₇₆	—	8	2	no	—
168	D₇₆	—	8	1	no	—
169	D₇₆	—	8	1	no	—
170	D₇₆	—	8	1	no	—
171	D₇₆	—	8	1	no	—
172	C₈×C₁₉	—	2	2	no	—
173	C₈×C₁₉	—	4	1	no	—
174	C₈×C₁₉	—	4	2	no	—
175	C₁₉⋊C₈	—	4	2	no	—
176	C₁₉⋊C₈	—	8	1	no	—
177	C₁₉⋊C₈	—	8	1	no	—
178	C₂×#460	—	19	1	no	—
179	Q₈×M₁₆	D₁₉	1	1	yes	characteristic, complemented
180	#1965	—	19	1	no	—
181	#1545	—	19	1	no	—
182	#1487	—	19	1	no	—
183	#1292	—	19	1	no	—
184	#1283	—	19	1	no	—
185	C₂²×C₁₉	—	2	1	no	—
186	C₂²×C₁₉	—	2	1	no	—
187	C₂²×C₁₉	#386	1	1	yes	characteristic
188	C₂²×C₁₉	C₄×SD₁₆	1	1	yes	characteristic
189	C₂²×C₁₉	#440	1	1	yes	characteristic
190	C₂×D₁₉	—	8	2	no	—
191	C₂×D₁₉	—	8	2	no	—
192	C₂×D₁₉	—	8	2	no	—
193	C₂×D₁₉	—	16	2	no	—
194	C₂×D₁₉	—	16	2	no	—
195	C₄×C₁₉	—	2	1	no	—
196	C₄×C₁₉	—	2	2	no	—
197	C₄×C₁₉	—	2	1	no	—
198	C₄×C₁₉	—	2	1	no	—
199	C₄×C₁₉	—	4	1	no	—
200	C₄×C₁₉	—	4	1	no	—
201	C₄×C₁₉	—	4	1	no	—
202	C₄×C₁₉	C₂×#100	1	1	yes	characteristic
203	C₄×C₁₉	#413	1	1	yes	characteristic
204	C₄×C₁₉	#448	1	1	yes	characteristic
205	C₄×C₁₉	#449	1	1	yes	characteristic
206	C₄×C₁₉	#460	1	1	yes	characteristic
207	C₄×C₁₉	#464	1	1	yes	characteristic
208	C₂²×SD₁₆	—	19	2	no	—
209	C₂×#127	—	19	1	no	—
210	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
211	#460	—	38	1	no	—
212	#460	—	38	1	no	—
213	#460	—	38	1	no	—
214	#460	—	38	1	no	—
215	#446	—	2	1	no	—
216	#446	—	2	2	no	—
217	C₈×Q₈	—	2	1	no	—
218	#431	—	19	1	no	—
219	#423	—	2	1	no	—
220	#423	—	19	1	no	—
221	#423	C₂×D₁₉	1	1	yes	characteristic
222	C₂×C₄⋊C₈	—	19	1	no	—
223	C₂×#102	—	19	2	no	—
224	C₂×#100	—	38	1	no	—
225	C₂×#100	—	38	1	no	—
226	C₄×M₁₆	—	2	1	no	—
227	C₄×M₁₆	C₂×D₁₉	1	1	yes	characteristic
228	#331	—	38	2	no	—
229	Q₈⋊C₈	—	38	1	no	—
230	Q₈⋊C₈	—	38	1	no	—
231	C₂×C₁₉	—	2	1	no	—
232	C₂×C₁₉	—	2	1	no	—
233	C₂×C₁₉	#1880	1	1	yes	characteristic
234	C₂×C₁₉	#1900	1	1	yes	characteristic
235	C₂×C₁₉	#1903	1	1	yes	characteristic
236	D₁₉	—	16	2	no	—
237	C₂²×Q₈	C₄×D₁₉	1	1	yes	characteristic
238	C₂²×D₄	—	19	2	no	—
239	C₂²×D₄	—	38	1	no	—
240	C₂²×D₄	—	38	1	no	—
241	C₂×SD₁₆	—	38	2	no	—
242	C₂×SD₁₆	—	38	2	no	—
243	C₂×SD₁₆	—	76	4	no	—
244	C₂×M₁₆	—	2	1	no	—
245	C₂×M₁₆	—	38	1	no	—
246	C₂×M₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
247	C₂×M₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
248	C₂²×C₈	—	19	2	no	—
249	#127	—	38	1	no	—
250	#127	—	38	1	no	—
251	#127	—	38	1	no	—
252	#127	—	38	1	no	—
253	C₄×Q₈	—	2	1	no	—
254	C₄×Q₈	—	2	1	no	—
255	C₄×Q₈	D₇₆	1	1	yes	characteristic
256	C₄×Q₈	D₇₆	1	1	yes	characteristic
257	C₄×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
258	C₄×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	C₄×D₁₉	1	1	yes	characteristic
261	C₂×C₄²	—	2	1	no	—
262	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
263	C₄⋊C₈	—	2	2	no	—
264	C₄⋊C₈	—	2	2	no	—
265	C₄⋊C₈	—	2	1	no	—
266	C₄⋊C₈	—	38	1	no	—
267	C₄⋊C₈	—	38	1	no	—
268	C₄⋊C₈	—	38	1	no	—
269	C₄⋊C₈	—	38	1	no	—
270	C₄⋊C₈	—	38	1	no	—
271	C₄⋊C₈	C₂²⋊D₁₉	1	2	yes	—
272	#102	—	38	2	no	—
273	#102	—	38	2	no	—
274	#100	—	76	2	no	—
275	#100	—	76	2	no	—
276	C₂²⋊C₈	—	38	1	no	—
277	#97	—	2	2	no	—
278	#97	—	2	1	no	—
279	C₄×C₈	—	2	2	no	—
280	C₄×C₈	—	2	1	no	—
281	C₄×C₈	—	38	1	no	—
282	C₁₉	#9254	1	1	yes	characteristic, complemented, Sylow
283	C₂⁴	—	38	2	no	—
284	C₂×Q₈	—	2	1	no	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	4	1	no	—
287	C₂×Q₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
288	C₂×Q₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
289	C₂×D₄	—	38	2	no	—
290	C₂×D₄	—	38	2	no	—
291	C₂×D₄	—	76	2	no	—
292	C₂×D₄	—	76	2	no	—
293	C₂×D₄	—	76	1	no	—
294	C₂×D₄	—	76	1	no	—
295	C₂×D₄	—	76	1	no	—
296	C₂×D₄	—	76	1	no	—
297	C₂×D₄	—	76	1	no	—
298	C₂×D₄	—	76	1	no	—
299	C₂×D₄	—	76	1	no	—
300	C₂×D₄	—	76	1	no	—
301	C₂×D₄	—	152	2	no	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
305	C₂²×C₄	#64541	1	1	yes	characteristic
306	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
307	SD₁₆	—	76	4	no	—
308	SD₁₆	—	76	4	no	—
309	M₁₆	—	2	1	no	—
310	M₁₆	—	2	1	no	—
311	M₁₆	—	2	1	no	—
312	M₁₆	—	4	1	no	—
313	M₁₆	—	4	1	no	—
314	M₁₆	—	76	1	no	—
315	M₁₆	—	76	1	no	—
316	M₁₆	#64527	1	2	yes	complemented
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	38	2	no	—
321	C₂×C₈	—	76	2	no	—
322	C₂×C₈	—	76	1	no	—
323	C₂×C₈	—	76	1	no	—
324	C₄⋊C₄	—	2	1	no	—
325	C₄⋊C₄	—	2	1	no	—
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
330	C₄⋊C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
331	C₄²	—	2	1	no	—
332	C₄²	—	2	1	no	—
333	C₄²	—	2	1	no	—
334	C₄²	—	2	1	no	—
335	C₄²	C₂×D₇₆	1	1	yes	characteristic
336	C₄²	#64541	1	1	yes	characteristic
337	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
338	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
339	C₂³	—	76	2	no	—
340	C₂³	—	76	2	no	—
341	C₂³	—	76	2	no	—
342	C₂³	—	152	2	no	—
343	C₂³	—	152	2	no	—
344	C₂³	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
345	Q₈	—	2	1	no	—
346	Q₈	—	2	1	no	—
347	Q₈	—	2	1	no	—
348	Q₈	—	4	2	no	—
349	Q₈	#10597280	1	2	yes	complemented
350	D₄	—	76	2	no	—
351	D₄	—	76	2	no	—
352	D₄	—	152	2	no	—
353	D₄	—	152	2	no	—
354	D₄	—	152	2	no	—
355	D₄	—	152	1	no	—
356	D₄	—	152	1	no	—
357	D₄	—	152	1	no	—
358	D₄	—	152	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	8	1	no	—
368	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
369	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
370	C₂×C₄	#10597375	1	1	yes	characteristic
371	C₂×C₄	#10597376	1	1	yes	characteristic
372	C₂×C₄	#10597376	1	1	yes	characteristic
373	C₂×C₄	C₂×#64527	1	1	yes	characteristic
374	C₂×C₄	#10597388	1	1	yes	characteristic
375	C₂×C₄	#10597395	1	1	yes	characteristic
376	C₂×C₄	#10597396	1	1	yes	characteristic
377	C₂×C₄	#10597399	1	1	yes	characteristic
378	C₈	—	2	2	no	—
379	C₈	—	4	1	no	—
380	C₈	—	4	2	no	—
381	C₈	—	76	2	no	—
382	C₈	—	152	1	no	—
383	C₈	—	152	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	304	2	no	—
387	C₂²	—	304	2	no	—
388	C₂²	—	152	2	no	—
389	C₂²	—	152	2	no	—
390	C₂²	—	152	2	no	—
391	C₂²	#11926423	1	1	yes	characteristic
392	C₂²	C₄×#64527	1	1	yes	characteristic
393	C₂²	#11926642	1	1	yes	characteristic
394	C₄	—	2	1	no	—
395	C₄	—	2	2	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	4	1	no	—
399	C₄	—	4	1	no	—
400	C₄	—	4	1	no	—
401	C₄	C₂×#10597280	1	1	yes	characteristic
402	C₄	#11926526	1	1	yes	characteristic
403	C₄	#11926683	1	1	yes	characteristic
404	C₄	#11926689	1	1	yes	characteristic
405	C₄	#11926744	1	1	yes	characteristic
406	C₄	#11926766	1	1	yes	characteristic
407	C₂	—	2	1	no	—
408	C₂	—	2	1	no	—
409	C₂	—	304	2	no	—
410	C₂	#14563990	1	1	yes	characteristic
411	C₂	#14564098	1	1	yes	characteristic
412	C₂	#14564115	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926423
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	Q₈×M₁₆×C₁₉	C₂
socle	C₂²×C₁₉	#386
prime radical	C₂×#10597320	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	Q₈×M₁₆	D₁₉
hypocenter	C₁₉	#9254
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ Q₈×M₁₆

Complements

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

N	H ≅ G/N	type
4. #14562064	C₂	semidirect
5. #14561509	C₂	semidirect
6. #14561486	C₂	semidirect
7. Q₈×M₁₆×C₁₉	C₂	semidirect
105. M₁₆×C₁₉	SD₁₆	semidirect
143. Q₈×C₁₉	#100	semidirect
179. Q₈×M₁₆	D₁₉	semidirect
282. C₁₉	#9254	semidirect
316. M₁₆	#64527	semidirect
349. Q₈	#10597280	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926744	2
#14564475	2
#14562304	2
#14562064	2
#14561509	2
#14561486	2
Q₈×M₁₆×C₁₉	2
#9254	19