Subgroups — #18085919

Order 4864.

572 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14568634	C₂	1	1	yes	maximal, characteristic
2	#14564441	C₂	1	1	yes	maximal, characteristic
3	#14564394	C₂	1	1	yes	maximal, characteristic, complemented
4	#14563640	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11926287	C₂	1	1	yes	maximal, characteristic
6	#14561475	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10597320	C₂²	1	1	yes	characteristic
9	C₂×#10597393	—	2	1	no	—
10	C₂×#10597275	—	2	1	no	—
11	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
12	C₂×#10597292	—	2	1	no	—
13	C₂×#10597278	—	2	2	no	—
14	#11926461	—	2	2	no	—
15	#11926446	—	2	1	no	—
16	#11926446	—	2	1	no	—
17	#11926445	—	2	1	no	—
18	#11926414	C₂²	1	1	yes	characteristic
19	C₄×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
20	#11926307	—	2	1	no	—
21	#11926306	—	2	1	no	—
22	#11926287	—	2	2	no	—
23	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×Q₈⋊C₈	—	2	2	no	—
27	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
28	C₂²×D₇₆	—	2	1	no	—
29	C₂²×D₇₆	—	2	1	no	—
30	C₂²×D₇₆	D₄	1	2	yes	—
31	C₂²×C₈×C₁₉	—	2	1	no	—
32	C₂²×C₈×C₁₉	—	2	1	no	—
33	C₄×Q₈×C₁₉	—	2	1	no	—
34	C₄×Q₈×C₁₉	—	2	1	no	—
35	C₄×Q₈×C₁₉	—	2	1	no	—
36	C₄×Q₈×C₁₉	—	2	1	no	—
37	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
38	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₉	—	2	1	no	—
40	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
41	#10597393	—	4	2	no	—
42	#10597393	—	4	2	no	—
43	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
44	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
45	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
46	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
47	C₂×C₄⋊Dic₁₉	—	2	1	no	—
48	C₂×C₄⋊Dic₁₉	—	2	1	no	—
49	C₂×C₄⋊Dic₁₉	—	2	1	no	—
50	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
51	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
52	C₂×C₄×Dic₁₉	—	2	1	no	—
53	C₂²×C₁₉⋊C₈	—	2	1	no	—
54	#10597320	—	2	1	no	—
55	#10597320	—	2	1	no	—
56	#10597320	—	2	1	no	—
57	#10597320	—	2	1	no	—
58	C₁₉×C₄⋊C₈	—	2	1	no	—
59	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
60	C₄×C₈×C₁₉	—	2	1	no	—
61	C₄×C₈×C₁₉	—	2	1	no	—
62	#10597292	—	4	2	no	—
63	C₁₉⋊#95	—	2	1	no	—
64	#10597278	—	4	4	no	—
65	#10597275	—	4	2	no	—
66	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
67	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
68	C₂³×D₁₉	—	2	2	no	—
69	C₂×Q₈×C₁₉	—	2	1	no	—
70	C₂×Q₈×C₁₉	—	2	1	no	—
71	C₂×Q₈×C₁₉	—	2	1	no	—
72	C₂×Q₈×C₁₉	—	2	1	no	—
73	C₂×Q₈×C₁₉	—	2	1	no	—
74	C₂×Q₈×C₁₉	D₈	1	2	yes	—
75	C₂²×C₄×C₁₉	—	2	1	no	—
76	C₂²×C₄×C₁₉	—	2	1	no	—
77	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
80	C₂²×Dic₁₉	—	2	1	no	—
81	C₂²×Dic₁₉	—	2	1	no	—
82	C₂²×Dic₁₉	—	4	1	no	—
83	C₂×D₇₆	—	2	2	no	—
84	C₂×D₇₆	—	2	2	no	—
85	C₂×D₇₆	—	4	2	no	—
86	C₂×D₇₆	—	4	2	no	—
87	C₂×D₇₆	—	4	1	no	—
88	C₂×D₇₆	—	4	1	no	—
89	C₂×D₇₆	—	4	1	no	—
90	C₂×D₇₆	—	4	1	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×C₈×C₁₉	—	2	2	no	—
100	C₂×C₈×C₁₉	—	2	2	no	—
101	C₂×C₈×C₁₉	—	4	1	no	—
102	C₂×C₈×C₁₉	—	4	1	no	—
103	C₂×C₈×C₁₉	—	4	1	no	—
104	C₂×C₈×C₁₉	—	4	1	no	—
105	C₄⋊C₄×C₁₉	—	2	1	no	—
106	C₄⋊C₄×C₁₉	—	2	1	no	—
107	C₄⋊C₄×C₁₉	—	4	1	no	—
108	C₄⋊C₄×C₁₉	—	4	1	no	—
109	C₄²×C₁₉	—	4	1	no	—
110	C₄²×C₁₉	—	4	1	no	—
111	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
112	C₄²×C₁₉	#41	1	1	yes	characteristic
113	C₄²×C₁₉	#41	1	1	yes	characteristic
114	C₄²×C₁₉	#41	1	1	yes	characteristic
115	(C₂×D₁₉)⋊C₄	—	4	4	no	—
116	(C₂×D₁₉)⋊C₄	—	4	4	no	—
117	(C₂×D₁₉)⋊C₄	—	8	2	no	—
118	(C₂×D₁₉)⋊C₄	—	8	2	no	—
119	C₄⋊Dic₁₉	—	2	1	no	—
120	C₄⋊Dic₁₉	—	2	1	no	—
121	C₄⋊Dic₁₉	—	2	1	no	—
122	C₄⋊Dic₁₉	—	2	1	no	—
123	C₄⋊Dic₁₉	—	4	2	no	—
124	C₄⋊Dic₁₉	—	4	1	no	—
125	C₄⋊Dic₁₉	—	4	1	no	—
126	C₄⋊Dic₁₉	—	4	1	no	—
127	C₄⋊Dic₁₉	—	4	1	no	—
128	C₄×Dic₁₉	—	4	1	no	—
129	C₄×Dic₁₉	—	4	1	no	—
130	C₂×C₁₉⋊C₈	—	4	1	no	—
131	C₂×C₁₉⋊C₈	—	4	1	no	—
132	C₂×C₁₉⋊C₈	—	4	1	no	—
133	#10411	—	19	1	no	maximal, Sylow
134	C₂³×C₁₉	#120	1	1	yes	characteristic
135	C₂²×D₁₉	—	4	2	no	—
136	C₂²×D₁₉	—	4	2	no	—
137	C₂²×D₁₉	—	4	2	no	—
138	C₂²×D₁₉	—	4	2	no	—
139	C₂²×D₁₉	—	4	2	no	—
140	C₂²×D₁₉	—	4	2	no	—
141	C₂²×D₁₉	—	4	2	no	—
142	Q₈×C₁₉	—	2	2	no	—
143	Q₈×C₁₉	—	2	2	no	—
144	Q₈×C₁₉	—	4	1	no	—
145	Q₈×C₁₉	—	4	1	no	—
146	C₂×C₄×C₁₉	—	2	1	no	—
147	C₂×C₄×C₁₉	—	2	1	no	—
148	C₂×C₄×C₁₉	—	2	2	no	—
149	C₂×C₄×C₁₉	—	4	1	no	—
150	C₂×C₄×C₁₉	—	4	1	no	—
151	C₂×C₄×C₁₉	—	4	1	no	—
152	C₂×C₄×C₁₉	—	4	1	no	—
153	C₂×C₄×C₁₉	—	4	1	no	—
154	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
155	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
156	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
157	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
158	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
159	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
160	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
161	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
162	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
163	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
164	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
165	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
166	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
167	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
168	C₂×Dic₁₉	—	4	1	no	—
169	C₂×Dic₁₉	—	4	1	no	—
170	C₂×Dic₁₉	—	4	1	no	—
171	C₂×Dic₁₉	—	4	1	no	—
172	C₂×Dic₁₉	—	4	1	no	—
173	C₂×Dic₁₉	—	4	1	no	—
174	C₂×Dic₁₉	—	8	1	no	—
175	C₂×Dic₁₉	—	8	1	no	—
176	C₂×Dic₁₉	—	8	1	no	—
177	D₇₆	—	4	4	no	—
178	D₇₆	—	8	2	no	—
179	D₇₆	—	8	1	no	—
180	D₇₆	—	8	1	no	—
181	D₇₆	—	8	1	no	—
182	D₇₆	—	8	1	no	—
183	D₇₆	—	8	1	no	—
184	D₇₆	—	8	1	no	—
185	D₇₆	—	8	1	no	—
186	D₇₆	—	8	1	no	—
187	C₈×C₁₉	—	4	2	no	—
188	C₈×C₁₉	—	4	2	no	—
189	C₁₉⋊C₈	—	8	1	no	—
190	#2548	—	19	1	no	—
191	#1957	—	19	1	no	—
192	#1947	—	19	1	no	—
193	#1803	—	19	1	no	—
194	C₂×#331	—	19	1	no	—
195	C₂×Q₈⋊C₈	D₁₉	1	1	yes	characteristic, complemented
196	#1279	—	19	1	no	—
197	C₂²×C₁₉	#394	1	1	yes	characteristic
198	C₂²×C₁₉	#447	1	1	yes	characteristic
199	C₂²×C₁₉	#449	1	1	yes	characteristic
200	C₂²×C₁₉	#452	1	1	yes	characteristic
201	C₂²×C₁₉	#452	1	1	yes	characteristic
202	C₂²×C₁₉	#453	1	1	yes	characteristic
203	C₂²×C₁₉	#455	1	1	yes	characteristic
204	C₂×D₁₉	—	8	2	no	—
205	C₂×D₁₉	—	8	2	no	—
206	C₂×D₁₉	—	8	2	no	—
207	C₂×D₁₉	—	8	2	no	—
208	C₂×D₁₉	—	8	2	no	—
209	C₂×D₁₉	—	8	2	no	—
210	C₂×D₁₉	—	8	2	no	—
211	C₄×C₁₉	—	2	1	no	—
212	C₄×C₁₉	—	2	1	no	—
213	C₄×C₁₉	—	4	2	no	—
214	C₄×C₁₉	—	8	1	no	—
215	C₄×C₁₉	#463	1	1	yes	characteristic
216	C₄×C₁₉	#464	1	1	yes	characteristic
217	C₄×C₁₉	#466	1	1	yes	characteristic
218	C₄×C₁₉	#468	1	1	yes	characteristic
219	C₄×C₁₉	#480	1	1	yes	characteristic
220	C₄×C₁₉	#482	1	1	yes	characteristic
221	C₄×C₁₉	#488	1	1	yes	characteristic
222	C₄×C₁₉	#489	1	1	yes	characteristic
223	Dic₁₉	—	8	1	no	—
224	Dic₁₉	—	8	1	no	—
225	Dic₁₉	—	16	1	no	—
226	C₂×#127	—	19	1	no	—
227	C₂×#124	—	38	1	no	—
228	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
229	C₂×#107	—	38	1	no	—
230	C₂×C₄⋊C₈	—	19	1	no	—
231	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
232	C₂×#103	—	38	1	no	—
233	C₂×#102	—	38	2	no	—
234	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
235	#394	—	38	2	no	—
236	#390	—	38	1	no	—
237	#390	—	38	1	no	—
238	#390	—	38	1	no	—
239	#384	—	19	1	no	—
240	C₄×C₄⋊C₄	—	19	1	no	—
241	#340	—	38	1	no	—
242	#340	—	38	1	no	—
243	#331	—	38	2	no	—
244	Q₈⋊C₈	—	2	2	no	—
245	C₂×C₁₉	#1621	1	1	yes	characteristic
246	C₂×C₁₉	#1630	1	1	yes	characteristic
247	C₂×C₁₉	#1640	1	1	yes	characteristic
248	C₂×C₁₉	#1641	1	1	yes	characteristic
249	C₂×C₁₉	#2033	1	1	yes	characteristic
250	C₂×C₁₉	#2037	1	1	yes	characteristic
251	C₂×C₁₉	#2042	1	1	yes	characteristic
252	D₁₉	—	16	2	no	—
253	C₂²×Q₈	D₇₆	1	1	yes	characteristic
254	C₂²×D₄	—	19	2	no	—
255	C₂²×D₄	—	38	1	no	—
256	C₂²×D₄	—	38	1	no	—
257	C₂²×C₈	—	2	1	no	—
258	C₂²×C₈	—	2	1	no	—
259	C₂²×C₈	—	38	1	no	—
260	#127	—	38	1	no	—
261	#127	—	38	1	no	—
262	#127	—	38	1	no	—
263	#127	—	38	1	no	—
264	#124	—	76	2	no	—
265	#124	—	76	2	no	—
266	C₄×Q₈	—	2	1	no	—
267	C₄×Q₈	—	2	1	no	—
268	C₄×Q₈	—	2	1	no	—
269	C₄×Q₈	—	2	1	no	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	—	19	1	no	—
272	C₂×C₄⋊C₄	—	19	1	no	—
273	C₂×C₄⋊C₄	—	38	1	no	—
274	C₂×C₄⋊C₄	—	38	1	no	—
275	C₂×C₄⋊C₄	—	38	1	no	—
276	C₂×C₄⋊C₄	D₇₆	1	1	yes	characteristic
277	C₂×C₂²⋊C₄	—	38	2	no	—
278	C₂×C₂²⋊C₄	—	38	2	no	—
279	C₂×C₂²⋊C₄	—	38	2	no	—
280	C₂×C₂²⋊C₄	—	38	2	no	—
281	C₂×C₄²	—	2	1	no	—
282	C₂×C₄²	—	38	1	no	—
283	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
284	#107	—	76	2	no	—
285	C₄⋊C₈	—	2	1	no	—
286	C₄⋊C₈	—	38	1	no	—
287	C₄⋊C₈	—	38	1	no	—
288	C₄⋊C₈	C₂²⋊D₁₉	1	2	yes	—
289	#103	—	76	2	no	—
290	#102	—	76	4	no	—
291	C₄×C₈	—	2	1	no	—
292	C₄×C₈	—	2	1	no	—
293	#95	—	38	1	no	—
294	C₁₉	#10411	1	1	yes	characteristic, complemented, Sylow
295	C₂⁴	—	38	2	no	—
296	C₂×Q₈	—	2	1	no	—
297	C₂×Q₈	—	2	1	no	—
298	C₂×Q₈	—	2	1	no	—
299	C₂×Q₈	—	2	1	no	—
300	C₂×Q₈	—	2	1	no	—
301	C₂×Q₈	D₁₅₂	1	2	yes	—
302	C₂×D₄	—	38	2	no	—
303	C₂×D₄	—	38	2	no	—
304	C₂×D₄	—	76	2	no	—
305	C₂×D₄	—	76	2	no	—
306	C₂×D₄	—	76	1	no	—
307	C₂×D₄	—	76	1	no	—
308	C₂×D₄	—	76	1	no	—
309	C₂×D₄	—	76	1	no	—
310	C₂×D₄	—	76	1	no	—
311	C₂×D₄	—	76	1	no	—
312	C₂×D₄	—	76	1	no	—
313	C₂×D₄	—	76	1	no	—
314	C₂×D₄	—	76	1	no	—
315	C₂×D₄	—	76	1	no	—
316	C₂×D₄	—	76	1	no	—
317	C₂×D₄	—	76	1	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	38	1	no	—
321	C₂²×C₄	—	38	1	no	—
322	C₂²×C₄	—	76	1	no	—
323	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
324	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
325	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	4	1	no	—
329	C₂×C₈	—	4	1	no	—
330	C₂×C₈	—	4	1	no	—
331	C₂×C₈	—	4	1	no	—
332	C₂×C₈	—	76	1	no	—
333	C₂×C₈	—	76	1	no	—
334	C₂×C₈	—	76	1	no	—
335	C₄⋊C₄	—	2	1	no	—
336	C₄⋊C₄	—	2	1	no	—
337	C₄⋊C₄	—	4	1	no	—
338	C₄⋊C₄	—	4	1	no	—
339	C₄⋊C₄	—	38	1	no	—
340	C₄⋊C₄	—	38	1	no	—
341	C₄⋊C₄	—	38	1	no	—
342	C₄⋊C₄	—	38	1	no	—
343	C₄⋊C₄	—	76	2	no	—
344	C₄⋊C₄	—	76	1	no	—
345	C₄⋊C₄	—	76	1	no	—
346	C₄⋊C₄	—	76	1	no	—
347	C₄⋊C₄	—	76	1	no	—
348	C₂²⋊C₄	—	76	4	no	—
349	C₂²⋊C₄	—	76	4	no	—
350	C₂²⋊C₄	—	152	2	no	—
351	C₂²⋊C₄	—	152	2	no	—
352	C₄²	—	4	1	no	—
353	C₄²	—	4	1	no	—
354	C₄²	—	76	1	no	—
355	C₄²	—	76	1	no	—
356	C₄²	#64541	1	1	yes	characteristic
357	C₄²	#64543	1	1	yes	characteristic
358	C₄²	#64543	1	1	yes	characteristic
359	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
360	C₂³	—	76	2	no	—
361	C₂³	—	76	2	no	—
362	C₂³	—	76	2	no	—
363	C₂³	—	76	2	no	—
364	C₂³	—	76	2	no	—
365	C₂³	—	76	2	no	—
366	C₂³	—	76	2	no	—
367	C₂³	#10597328	1	1	yes	characteristic
368	Q₈	—	2	2	no	—
369	Q₈	—	2	2	no	—
370	Q₈	—	4	1	no	—
371	Q₈	—	4	1	no	—
372	D₄	—	76	4	no	—
373	D₄	—	152	2	no	—
374	D₄	—	152	1	no	—
375	D₄	—	152	1	no	—
376	D₄	—	152	1	no	—
377	D₄	—	152	1	no	—
378	D₄	—	152	1	no	—
379	D₄	—	152	1	no	—
380	D₄	—	152	1	no	—
381	D₄	—	152	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	76	1	no	—
391	C₂×C₄	—	76	1	no	—
392	C₂×C₄	—	76	1	no	—
393	C₂×C₄	—	76	1	no	—
394	C₂×C₄	—	76	1	no	—
395	C₂×C₄	—	76	1	no	—
396	C₂×C₄	—	152	1	no	—
397	C₂×C₄	—	152	1	no	—
398	C₂×C₄	—	152	1	no	—
399	C₂×C₄	#10597329	1	1	yes	characteristic
400	C₂×C₄	#10597331	1	1	yes	characteristic
401	C₂×C₄	#10597332	1	1	yes	characteristic
402	C₂×C₄	C₂×D₁₅₂	1	1	yes	characteristic
403	C₂×C₄	#10597350	1	1	yes	characteristic
404	C₂×C₄	#10597354	1	1	yes	characteristic
405	C₂×C₄	#10597355	1	1	yes	characteristic
406	C₂×C₄	#10597360	1	1	yes	characteristic
407	C₂×C₄	#10597362	1	1	yes	characteristic
408	C₂×C₄	#10597364	1	1	yes	characteristic
409	C₂×C₄	#10597365	1	1	yes	characteristic
410	C₂×C₄	#10597376	1	1	yes	characteristic
411	C₂×C₄	#10597384	1	1	yes	characteristic
412	C₂×C₄	#10597385	1	1	yes	characteristic
413	C₈	—	4	2	no	—
414	C₈	—	4	2	no	—
415	C₈	—	152	1	no	—
416	C₂²	—	152	2	no	—
417	C₂²	—	152	2	no	—
418	C₂²	—	152	2	no	—
419	C₂²	—	152	2	no	—
420	C₂²	—	152	2	no	—
421	C₂²	—	152	2	no	—
422	C₂²	—	152	2	no	—
423	C₂²	#11926460	1	1	yes	characteristic
424	C₂²	#11926680	1	1	yes	characteristic
425	C₂²	#11926692	1	1	yes	characteristic
426	C₂²	#11926708	1	1	yes	characteristic
427	C₂²	#11926709	1	1	yes	characteristic
428	C₂²	#11926713	1	1	yes	characteristic
429	C₂²	#11926723	1	1	yes	characteristic
430	C₄	—	2	1	no	—
431	C₄	—	2	1	no	—
432	C₄	—	4	2	no	—
433	C₄	—	8	1	no	—
434	C₄	—	304	1	no	—
435	C₄	—	152	1	no	—
436	C₄	—	152	1	no	—
437	C₄	#11926761	1	1	yes	characteristic
438	C₄	#11926768	1	1	yes	characteristic
439	C₄	#11926780	1	1	yes	characteristic
440	C₄	#11926790	1	1	yes	characteristic
441	C₄	#11926858	1	1	yes	characteristic
442	C₄	#11926869	1	1	yes	characteristic
443	C₄	#11926900	1	1	yes	characteristic
444	C₄	#11926905	1	1	yes	characteristic
445	C₂	—	304	2	no	—
446	C₂	#14562702	1	1	yes	characteristic
447	C₂	#14562758	1	1	yes	characteristic
448	C₂	#14562824	1	1	yes	characteristic
449	C₂	#14562830	1	1	yes	characteristic
450	C₂	#14564818	1	1	yes	characteristic
451	C₂	#14564844	1	1	yes	characteristic
452	C₂	#14564873	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597328
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×Q₈⋊C₈	C₂
socle	C₂³×C₁₉	#120
prime radical	C₂×#10597320	C₂²
hypercenter	C₂×Q₈⋊C₈	D₁₉
hypocenter	C₁₉	#10411
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×Q₈⋊C₈

Complements

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

N	H ≅ G/N	type
3. #14564394	C₂	semidirect
4. #14563640	C₂	semidirect
6. #14561475	C₂	semidirect
7. C₂×C₁₉×Q₈⋊C₈	C₂	semidirect
195. C₂×Q₈⋊C₈	D₁₉	semidirect
294. C₁₉	#10411	semidirect

Maximal subgroups

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

subgroup	index
#14568634	2
#14564441	2
#14564394	2
#14563640	2
C₂×#11926287	2
#14561475	2
C₂×C₁₉×Q₈⋊C₈	2
#10411	19