Subgroups — #14578123

Order 2432.

910 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	#11927295	C₂	1	4	yes	maximal, complemented
2	Q₈×Dic₃₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#11927273	C₂	1	1	yes	maximal, characteristic, complemented
4	#11927272	C₂	1	2	yes	maximal, complemented
5	#11927267	C₂	1	1	yes	maximal, characteristic, complemented
6	#11927267	C₂	1	2	yes	maximal, complemented
7	#11927265	C₂	1	2	yes	maximal, complemented
8	#11927254	C₂	1	1	yes	maximal, characteristic, complemented
9	#11927228	C₂	1	2	yes	maximal, complemented
10	#11927171	C₂	1	2	yes	maximal, complemented
11	#11927165	C₂	1	2	yes	maximal
12	#11927156	C₂	1	2	yes	maximal, complemented
13	#11927155	C₂	1	2	yes	maximal, complemented
14	#11927153	C₂	1	4	yes	maximal, complemented
15	#11927101	C₂	1	1	yes	maximal, characteristic, complemented
16	#11927078	C₂	1	1	yes	maximal, characteristic
17	C₁₉×#533	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₁₉×#125	C₂²	1	2	yes	—
21	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
22	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
23	C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
24	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
25	C₄×Q₈×C₁₉	C₂²	1	2	yes	—
26	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
27	C₁₉×#117	C₂²	1	2	yes	—
28	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
29	#10597392	C₂²	1	2	yes	—
30	#10597392	C₂²	1	2	yes	—
31	#10597392	C₂²	1	4	yes	—
32	Q₈×Dic₁₉	C₂²	1	2	yes	—
33	Q₈×Dic₁₉	C₂²	1	2	yes	—
34	#10597390	C₂²	1	4	yes	—
35	#10597376	C₂²	1	1	yes	characteristic
36	#10597375	C₂²	1	2	yes	—
37	C₄×C₂²⋊D₁₉	C₂²	1	2	yes	—
38	#10597372	C₂²	1	2	yes	—
39	#10597370	C₂²	1	1	yes	characteristic
40	#10597370	C₂²	1	2	yes	—
41	#10597370	C₂²	1	2	yes	—
42	#10597344	C₂²	1	4	yes	—
43	#10597344	C₂²	1	4	yes	—
44	#10597344	C₂²	1	4	yes	—
45	#10597344	C₂²	1	4	yes	—
46	#10597342	C₂²	1	4	yes	—
47	#10597342	C₂²	1	4	yes	—
48	#10597338	C₂²	1	4	yes	—
49	#10597338	C₂²	1	2	yes	—
50	C₄⋊C₄×D₁₉	C₂²	1	2	yes	—
51	#10597336	C₂²	1	4	yes	—
52	#10597336	C₂²	1	2	yes	—
53	#10597335	C₂²	1	4	yes	—
54	#10597335	C₂²	1	4	yes	—
55	#10597335	C₂²	1	4	yes	—
56	#10597335	C₂²	1	4	yes	—
57	#10597334	C₂²	1	4	yes	—
58	#10597334	C₂²	1	2	yes	—
59	#10597333	C₂²	1	4	yes	—
60	#10597331	C₂²	1	4	yes	—
61	#10597329	C₂²	1	4	yes	—
62	#10597325	C₂²	1	4	yes	—
63	#10597325	C₂²	1	4	yes	—
64	#10597322	C₂²	1	2	yes	—
65	#10597321	C₂²	1	1	yes	characteristic
66	#10597321	C₂²	1	2	yes	—
67	C₄×D₇₆	C₂²	1	1	yes	characteristic
68	C₄×D₇₆	C₂²	1	2	yes	—
69	#10597318	C₂²	1	2	yes	—
70	#10597316	C₂²	1	1	yes	characteristic
71	#10597316	C₂²	1	2	yes	—
72	#10597316	C₂²	1	2	yes	—
73	#10597315	C₂²	1	1	yes	characteristic
74	#10597315	C₂²	1	1	yes	characteristic
75	#10597315	C₂²	1	2	yes	—
76	#10597315	C₂²	1	2	yes	—
77	C₄×Dic₃₈	C₂²	1	1	yes	characteristic
78	C₄×Dic₃₈	C₂²	1	2	yes	—
79	C₄×Dic₃₈	C₂²	1	2	yes	—
80	C₄×Dic₃₈	C₂²	1	2	yes	—
81	C₄×Dic₃₈	C₂²	1	2	yes	—
82	C₄×Dic₃₈	C₂²	1	2	yes	—
83	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
84	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
85	C₂×Q₈×C₁₉	C₂³	1	2	yes	—
86	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
89	C₂×C₂²⋊D₁₉	C₂³	1	2	yes	—
90	C₂×D₇₆	C₂³	1	1	yes	characteristic
91	C₂×C₄×D₁₉	C₂³	1	2	yes	—
92	C₂×C₄×D₁₉	C₂³	1	4	yes	—
93	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
94	C₂×Dic₃₈	C₂³	1	2	yes	—
95	C₂×Dic₃₈	C₂³	1	4	yes	—
96	C₂×Dic₃₈	C₂³	1	2	yes	—
97	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
98	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
99	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
100	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
101	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
102	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
103	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
104	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
105	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
106	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
107	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
108	C₄²×C₁₉	C₂³	1	1	yes	characteristic
109	C₄²×C₁₉	C₂³	1	1	yes	characteristic
110	C₄²×C₁₉	C₂³	1	1	yes	characteristic
111	C₄²×C₁₉	C₂³	1	1	yes	characteristic
112	C₄²×C₁₉	C₂³	1	2	yes	—
113	C₄²×C₁₉	C₂³	1	2	yes	—
114	C₂²⋊Dic₁₉	C₂³	1	2	yes	—
115	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
116	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
117	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
118	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
119	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
120	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
121	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
122	(C₂×D₁₉)⋊C₄	C₂³	1	2	yes	—
123	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
124	C₄⋊Dic₁₉	C₂³	1	2	yes	—
125	C₄⋊Dic₁₉	C₂³	1	2	yes	—
126	C₄⋊Dic₁₉	C₂³	1	4	yes	—
127	C₄⋊Dic₁₉	C₂³	1	4	yes	—
128	C₄⋊Dic₁₉	C₂³	1	4	yes	—
129	C₄⋊Dic₁₉	C₂³	1	2	yes	—
130	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
131	C₄⋊Dic₁₉	C₂³	1	2	yes	—
132	Dic₁₉⋊C₄	C₂³	1	2	yes	—
133	Dic₁₉⋊C₄	C₂³	1	4	yes	—
134	Dic₁₉⋊C₄	C₂³	1	4	yes	—
135	Dic₁₉⋊C₄	C₂³	1	4	yes	—
136	Dic₁₉⋊C₄	C₂³	1	4	yes	—
137	Dic₁₉⋊C₄	C₂³	1	4	yes	—
138	Dic₁₉⋊C₄	C₂³	1	4	yes	—
139	Dic₁₉⋊C₄	C₂³	1	4	yes	—
140	Dic₁₉⋊C₄	C₂³	1	2	yes	—
141	Dic₁₉⋊C₄	C₂³	1	2	yes	—
142	Dic₁₉⋊C₄	C₂³	1	2	yes	—
143	C₄×Dic₁₉	C₂³	1	4	yes	—
144	C₄×Dic₁₉	C₂³	1	2	yes	—
145	C₄×Dic₁₉	C₂³	1	4	yes	—
146	C₄×Dic₁₉	C₂³	1	4	yes	—
147	C₄×Dic₁₉	C₂³	1	4	yes	—
148	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
149	C₂²×D₁₉	C₂⁴	1	2	yes	—
150	Q₈×C₁₉	—	2	2	no	—
151	Q₈×C₁₉	—	2	2	no	—
152	Q₈×C₁₉	—	4	2	no	—
153	C₂×C₄×C₁₉	—	2	2	no	—
154	C₂×C₄×C₁₉	—	2	2	no	—
155	C₂×C₄×C₁₉	—	4	1	no	—
156	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
157	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
158	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
159	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
160	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
161	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
162	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
163	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
164	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
165	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
166	C₂²⋊D₁₉	—	4	2	no	—
167	C₂×Dic₁₉	C₂⁴	1	2	yes	—
168	C₂×Dic₁₉	C₂⁴	1	4	yes	—
169	C₂×Dic₁₉	C₂⁴	1	2	yes	—
170	C₂×Dic₁₉	C₂⁴	1	2	yes	—
171	C₂×Dic₁₉	C₂⁴	1	4	yes	—
172	D₇₆	—	2	2	no	—
173	C₄×D₁₉	—	2	4	no	—
174	C₄×D₁₉	—	4	4	no	—
175	Dic₃₈	—	2	2	no	—
176	Dic₃₈	—	2	4	no	—
177	Dic₃₈	—	4	2	no	—
178	Dic₃₈	—	4	4	no	—
179	#3555	—	19	1	no	maximal, Sylow
180	C₂²×C₁₉	—	2	1	no	—
181	C₂²×C₁₉	—	2	1	no	—
182	C₂²×C₁₉	—	2	1	no	—
183	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
184	C₂×D₁₉	—	2	2	no	—
185	C₂×D₁₉	—	2	2	no	—
186	C₂×D₁₉	—	2	2	no	—
187	C₄×C₁₉	—	2	1	no	—
188	C₄×C₁₉	—	2	1	no	—
189	C₄×C₁₉	—	2	2	no	—
190	C₄×C₁₉	—	2	2	no	—
191	C₄×C₁₉	—	2	1	no	—
192	C₄×C₁₉	—	2	2	no	—
193	C₄×C₁₉	—	2	2	no	—
194	C₄×C₁₉	—	2	1	no	—
195	C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
196	C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
197	Dic₁₉	—	2	4	no	—
198	Dic₁₉	—	2	2	no	—
199	Dic₁₉	—	2	2	no	—
200	Dic₁₉	—	2	4	no	—
201	Dic₁₉	—	2	2	no	—
202	#563	—	19	4	no	—
203	Q₈²	—	19	1	no	—
204	#557	—	19	2	no	—
205	#557	—	19	1	no	—
206	#556	—	19	2	no	—
207	#556	—	19	2	no	—
208	#556	—	19	1	no	—
209	#554	—	19	1	no	—
210	#552	—	19	2	no	—
211	#544	—	19	2	no	—
212	#542	—	19	2	no	—
213	#541	—	19	2	no	—
214	#541	—	19	4	no	—
215	#541	—	19	2	no	—
216	#533	—	19	1	no	—
217	#533	D₁₉	1	1	yes	characteristic, complemented
218	#529	—	19	1	no	—
219	C₂×C₁₉	—	4	1	no	—
220	C₂×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
221	C₂×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
222	C₂×C₁₉	#585	1	1	yes	characteristic
223	D₁₉	—	4	2	no	—
224	C₄⋊Q₈	—	19	4	no	—
225	C₄⋊Q₈	—	19	4	no	—
226	C₄⋊Q₈	—	19	2	no	—
227	C₄⋊Q₈	—	19	1	no	—
228	C₄⋊Q₈	—	19	1	no	—
229	C₄⋊Q₈	—	19	2	no	—
230	C₄⋊Q₈	—	19	2	no	—
231	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
232	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
233	#126	—	19	4	no	—
234	#126	—	19	4	no	—
235	#126	—	19	4	no	—
236	#126	—	19	4	no	—
237	#126	—	19	4	no	—
238	#126	—	19	4	no	—
239	#126	—	19	2	no	—
240	#125	—	19	4	no	—
241	#125	—	19	4	no	—
242	#125	—	19	4	no	—
243	#125	—	19	4	no	—
244	#125	—	19	4	no	—
245	#125	—	19	2	no	—
246	#125	—	19	1	no	—
247	#125	—	19	2	no	—
248	#125	—	19	2	no	—
249	#125	C₂×D₁₉	1	2	yes	—
250	#124	—	19	4	no	—
251	#124	—	19	1	no	—
252	#124	—	19	2	no	—
253	#123	—	19	2	no	—
254	#123	—	19	4	no	—
255	C₂²⋊Q₈	—	19	2	no	—
256	C₂²⋊Q₈	—	19	2	no	—
257	C₂²⋊Q₈	—	19	4	no	—
258	C₂²⋊Q₈	—	19	1	no	—
259	C₂²⋊Q₈	—	19	2	no	—
260	C₂²⋊Q₈	—	19	2	no	—
261	C₂²⋊Q₈	—	19	4	no	—
262	C₂²⋊Q₈	—	19	4	no	—
263	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
264	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
265	C₂²⋊Q₈	C₂×D₁₉	1	2	yes	—
266	#121	—	19	1	no	—
267	C₄×Q₈	—	19	2	no	—
268	C₄×Q₈	—	19	2	no	—
269	C₄×Q₈	—	19	4	no	—
270	C₄×Q₈	—	19	1	no	—
271	C₄×Q₈	—	19	2	no	—
272	C₄×Q₈	—	19	2	no	—
273	C₄×Q₈	—	19	2	no	—
274	C₄×Q₈	—	19	2	no	—
275	C₄×Q₈	—	19	2	no	—
276	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
277	C₄×Q₈	C₂×D₁₉	1	2	yes	—
278	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
279	C₄×D₄	—	19	2	no	—
280	C₄×D₄	—	19	1	no	—
281	C₄×D₄	—	19	2	no	—
282	#117	—	19	2	no	—
283	#117	—	19	4	no	—
284	#117	—	19	2	no	—
285	#117	—	19	2	no	—
286	#117	C₂×D₁₉	1	2	yes	—
287	C₂×C₄⋊C₄	—	19	2	no	—
288	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
289	C₁₉	#3555	1	1	yes	characteristic, complemented, Sylow
290	C₂×Q₈	—	19	1	no	—
291	C₂×Q₈	—	19	2	no	—
292	C₂×Q₈	—	19	2	no	—
293	C₂×Q₈	—	19	4	no	—
294	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
295	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
296	C₂×Q₈	C₂²×D₁₉	1	2	yes	—
297	C₂×D₄	—	19	2	no	—
298	C₂×D₄	—	19	1	no	—
299	C₂²×C₄	—	19	2	no	—
300	C₂²×C₄	—	19	4	no	—
301	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
302	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
303	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
304	C₄⋊C₄	—	19	4	no	—
305	C₄⋊C₄	—	19	2	no	—
306	C₄⋊C₄	—	19	2	no	—
307	C₄⋊C₄	—	19	2	no	—
308	C₄⋊C₄	—	19	4	no	—
309	C₄⋊C₄	—	19	4	no	—
310	C₄⋊C₄	—	19	4	no	—
311	C₄⋊C₄	—	19	4	no	—
312	C₄⋊C₄	—	19	4	no	—
313	C₄⋊C₄	—	19	4	no	—
314	C₄⋊C₄	—	19	2	no	—
315	C₄⋊C₄	—	19	2	no	—
316	C₄⋊C₄	—	19	2	no	—
317	C₄⋊C₄	—	19	4	no	—
318	C₄⋊C₄	—	19	1	no	—
319	C₄⋊C₄	—	19	2	no	—
320	C₄⋊C₄	—	19	1	no	—
321	C₄⋊C₄	—	19	2	no	—
322	C₄⋊C₄	—	19	4	no	—
323	C₄⋊C₄	—	19	4	no	—
324	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
325	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
326	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
327	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
328	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
329	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
330	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
331	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
332	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
333	C₂²⋊C₄	—	19	4	no	—
334	C₂²⋊C₄	—	19	2	no	—
335	C₂²⋊C₄	—	19	2	no	—
336	C₂²⋊C₄	—	19	2	no	—
337	C₂²⋊C₄	—	19	2	no	—
338	C₂²⋊C₄	—	19	4	no	—
339	C₂²⋊C₄	—	19	4	no	—
340	C₂²⋊C₄	—	19	2	no	—
341	C₂²⋊C₄	—	19	4	no	—
342	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
343	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
344	C₄²	—	19	4	no	—
345	C₄²	—	19	2	no	—
346	C₄²	—	19	4	no	—
347	C₄²	—	19	4	no	—
348	C₄²	—	19	4	no	—
349	C₄²	C₂²×D₁₉	1	1	yes	characteristic
350	C₄²	C₂²×D₁₉	1	1	yes	characteristic
351	C₄²	C₂²×D₁₉	1	1	yes	characteristic
352	C₄²	C₂²×D₁₉	1	1	yes	characteristic
353	C₄²	C₂²×D₁₉	1	2	yes	—
354	C₄²	C₂²×D₁₉	1	2	yes	—
355	C₂³	—	19	2	no	—
356	C₂³	C₂³×D₁₉	1	1	yes	characteristic
357	Q₈	—	2	2	no	—
358	Q₈	—	2	2	no	—
359	Q₈	—	4	2	no	—
360	Q₈	—	38	2	no	—
361	Q₈	—	38	4	no	—
362	Q₈	—	76	2	no	—
363	Q₈	—	76	4	no	—
364	D₄	—	38	2	no	—
365	D₄	—	76	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	19	4	no	—
370	C₂×C₄	—	19	2	no	—
371	C₂×C₄	—	19	2	no	—
372	C₂×C₄	—	19	2	no	—
373	C₂×C₄	—	19	4	no	—
374	C₂×C₄	—	38	4	no	—
375	C₂×C₄	—	76	4	no	—
376	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
377	C₂×C₄	C₂³×D₁₉	1	2	yes	—
378	C₂×C₄	C₂³×D₁₉	1	2	yes	—
379	C₂×C₄	C₂³×D₁₉	1	2	yes	—
380	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
381	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
382	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
383	C₂×C₄	C₂³×D₁₉	1	2	yes	—
384	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
385	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
386	C₂²	—	2	1	no	—
387	C₂²	—	2	1	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	38	2	no	—
390	C₂²	—	38	2	no	—
391	C₂²	—	38	2	no	—
392	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
393	C₄	—	2	1	no	—
394	C₄	—	2	2	no	—
395	C₄	—	2	2	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	2	1	no	—
399	C₄	—	2	2	no	—
400	C₄	—	2	2	no	—
401	C₄	—	38	2	no	—
402	C₄	—	38	4	no	—
403	C₄	—	38	2	no	—
404	C₄	—	38	4	no	—
405	C₄	—	38	2	no	—
406	C₄	#10597433	1	2	yes	—
407	C₄	#10597436	1	2	yes	—
408	C₂	—	4	1	no	—
409	C₂	—	76	2	no	—
410	C₂	C₂×#10597436	1	1	yes	characteristic
411	C₂	C₂×#10597433	1	1	yes	characteristic
412	C₂	#11927380	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₁₉×#533	C₂
prime radical	#10597376	C₂²
hypercenter	#533	D₁₉
hypocenter	C₁₉	#3555
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ #533

Complements

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

N	H ≅ G/N	type
1. #11927295	C₂	semidirect
2. Q₈×Dic₃₈	C₂	semidirect
3. #11927273	C₂	semidirect
4. #11927272	C₂	semidirect
5. #11927267	C₂	semidirect
6. #11927267	C₂	semidirect
7. #11927265	C₂	semidirect
8. #11927254	C₂	semidirect
9. #11927228	C₂	semidirect
10. #11927171	C₂	semidirect
12. #11927156	C₂	semidirect
13. #11927155	C₂	semidirect
14. #11927153	C₂	semidirect
15. #11927101	C₂	semidirect
17. C₁₉×#533	C₂	semidirect
217. #533	D₁₉	semidirect
289. C₁₉	#3555	semidirect

Maximal subgroups

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

subgroup	index
#11927295	2
Q₈×Dic₃₈	2
#11927273	2
#11927272	2
#11927267	2
#11927265	2
#11927254	2
#11927228	2
#11927171	2
#11927165	2
#11927156	2
#11927155	2
#11927153	2
#11927101	2
#11927078	2
C₁₉×#533	2
#3555	19