Subgroups — C₄×#10597324 #14566166

Order 2432.

656 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10597324	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Dic₃₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×Dic₁₉	C₂	1	1	yes	maximal, characteristic
4	#11926448	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926441	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926431	C₂	1	1	yes	maximal, characteristic, complemented
7	#11926427	C₂	1	1	yes	maximal, characteristic, complemented
8	#11926419	C₂	1	1	yes	maximal, characteristic
9	#11926416	C₂	1	1	yes	maximal, characteristic
10	#11926402	C₂	1	1	yes	maximal, characteristic
11	C₄×Dic₁₉⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×Dic₁₉⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×C₄⋊Dic₁₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₂²⋊Dic₁₉	C₂	1	1	yes	maximal, characteristic
15	C₄×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
16	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₂³×Dic₁₉	C₂²	1	1	yes	characteristic
18	C₂³×Dic₁₉	C₂²	1	1	yes	characteristic
19	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
20	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
23	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
29	C₂×Dic₁₉⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×Dic₁₉⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×Dic₁₉⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×Dic₁₉⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×Dic₁₉⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×Dic₁₉⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×C₄×Dic₁₉	—	2	4	no	—
36	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
38	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
39	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
40	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
41	C₂×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
42	#10597324	C₄	1	8	yes	direct product factor
43	C₄×Dic₃₈	—	2	4	no	—
44	C₁₉×#95	C₂²	1	1	yes	characteristic
45	C₁₉×#95	C₂²	1	1	yes	characteristic
46	C₁₉⋊#95	C₂²	1	1	yes	characteristic
47	C₁₉⋊#95	C₂²	1	1	yes	characteristic
48	C₁₉⋊#95	C₂²	1	1	yes	characteristic
49	C₁₉⋊#95	C₂²	1	1	yes	characteristic
50	C₁₉⋊#95	C₂²	1	1	yes	characteristic
51	C₁₉⋊#95	C₂²	1	1	yes	characteristic
52	C₁₉⋊#95	C₂²	1	1	yes	characteristic
53	C₁₉⋊#95	C₂²	1	1	yes	characteristic
54	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
55	C₂²×C₄×C₁₉	—	2	2	no	—
56	C₂²×C₄×C₁₉	—	2	2	no	—
57	C₂²×C₄×C₁₉	Q₈	1	4	yes	complemented
58	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
59	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
60	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
61	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
62	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
63	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
64	C₂²×Dic₁₉	—	2	2	no	—
65	C₂²×Dic₁₉	—	2	2	no	—
66	C₂²×Dic₁₉	—	2	2	no	—
67	C₂²×Dic₁₉	—	2	2	no	—
68	C₂²×Dic₁₉	—	2	2	no	—
69	C₂²×Dic₁₉	C₂×C₄	1	4	yes	—
70	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
71	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
72	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
73	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
74	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
75	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
76	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
77	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
78	C₂×Dic₃₈	—	2	2	no	—
79	C₂×Dic₃₈	—	2	2	no	—
80	C₂×Dic₃₈	C₂×C₄	1	4	yes	complemented
81	C₂²⋊C₄×C₁₉	—	2	2	no	—
82	C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
83	C₄²×C₁₉	—	2	2	no	—
84	C₄²×C₁₉	—	2	2	no	—
85	C₂²⋊Dic₁₉	—	2	2	no	—
86	C₂²⋊Dic₁₉	C₂×C₄	1	4	yes	—
87	C₄⋊Dic₁₉	—	2	2	no	—
88	C₄⋊Dic₁₉	—	2	2	no	—
89	C₄⋊Dic₁₉	C₂×C₄	1	4	yes	complemented
90	Dic₁₉⋊C₄	—	2	2	no	—
91	Dic₁₉⋊C₄	—	2	2	no	—
92	Dic₁₉⋊C₄	—	2	2	no	—
93	Dic₁₉⋊C₄	—	2	2	no	—
94	Dic₁₉⋊C₄	C₂×C₄	1	4	yes	complemented
95	Dic₁₉⋊C₄	C₂×C₄	1	4	yes	complemented
96	C₄×Dic₁₉	—	2	2	no	—
97	C₄×Dic₁₉	—	2	2	no	—
98	C₄×Dic₁₉	—	2	2	no	—
99	C₄×Dic₁₉	—	2	2	no	—
100	C₄×Dic₁₉	—	2	2	no	—
101	C₄×Dic₁₉	D₄	1	4	yes	—
102	C₂³×C₁₉	—	2	1	no	—
103	C₂³×C₁₉	—	2	1	no	—
104	C₂³×C₁₉	—	2	1	no	—
105	C₂³×C₁₉	—	2	1	no	—
106	C₂³×C₁₉	C₂²×C₄	1	2	yes	—
107	C₂³×C₁₉	C₂×Q₈	1	2	yes	—
108	C₂³×C₁₉	#41	1	2	yes	—
109	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
110	C₂×C₄×C₁₉	—	2	1	no	—
111	C₂×C₄×C₁₉	—	2	1	no	—
112	C₂×C₄×C₁₉	—	2	1	no	—
113	C₂×C₄×C₁₉	—	2	1	no	—
114	C₂×C₄×C₁₉	—	2	1	no	—
115	C₂×C₄×C₁₉	—	2	1	no	—
116	C₂×C₄×C₁₉	—	2	8	no	—
117	C₂×C₄×C₁₉	—	2	1	no	—
118	C₂×C₄×C₁₉	—	2	1	no	—
119	C₂×C₄×C₁₉	—	2	1	no	—
120	C₂×C₄×C₁₉	—	2	1	no	—
121	C₂×C₄×C₁₉	—	2	1	no	—
122	C₂×C₄×C₁₉	—	2	1	no	—
123	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
124	C₂×C₄×C₁₉	C₂²×C₄	1	2	yes	—
125	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
126	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
127	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
128	C₂×C₄×C₁₉	#41	1	2	yes	—
129	C₂×Dic₁₉	—	2	8	no	—
130	C₂×Dic₁₉	—	2	1	no	—
131	C₂×Dic₁₉	—	2	1	no	—
132	C₂×Dic₁₉	—	2	1	no	—
133	C₂×Dic₁₉	—	2	1	no	—
134	C₂×Dic₁₉	—	2	1	no	—
135	C₂×Dic₁₉	—	2	1	no	—
136	C₂×Dic₁₉	—	2	1	no	—
137	C₂×Dic₁₉	—	2	1	no	—
138	C₂×Dic₁₉	—	2	1	no	—
139	C₂×Dic₁₉	—	2	1	no	—
140	C₂×Dic₁₉	—	2	8	no	—
141	C₂×Dic₁₉	—	2	1	no	—
142	C₂×Dic₁₉	—	2	1	no	—
143	C₂×Dic₁₉	—	2	1	no	—
144	C₂×Dic₁₉	—	2	1	no	—
145	C₂×Dic₁₉	—	2	1	no	—
146	C₂×Dic₁₉	—	2	1	no	—
147	C₂×Dic₁₉	C₂²×C₄	1	2	yes	—
148	C₂×Dic₁₉	C₂²×C₄	1	2	yes	—
149	C₂×Dic₁₉	C₂²×C₄	1	2	yes	—
150	C₂×Dic₁₉	C₂²×C₄	1	2	yes	—
151	C₂×Dic₁₉	C₂×D₄	1	2	yes	—
152	C₂×Dic₁₉	C₂×D₄	1	2	yes	—
153	C₂×Dic₁₉	#41	1	2	yes	—
154	C₂×Dic₁₉	#41	1	2	yes	—
155	Dic₃₈	—	2	8	no	—
156	C₄×C₂²⋊Q₈	—	19	1	no	maximal, Sylow
157	C₂²×C₁₉	—	2	2	no	—
158	C₂²×C₁₉	—	2	2	no	—
159	C₂²×C₁₉	—	2	2	no	—
160	C₂²×C₁₉	—	2	2	no	—
161	C₂²×C₁₉	—	2	2	no	—
162	C₂²×C₁₉	—	2	2	no	—
163	C₂²×C₁₉	C₄×Q₈	1	4	yes	complemented
164	C₂²×C₁₉	C₂³×C₄	1	1	yes	characteristic
165	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
166	C₂²×C₁₉	C₂²×Q₈	1	1	yes	characteristic
167	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
168	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
169	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
170	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
171	C₄×C₁₉	—	2	2	no	—
172	C₄×C₁₉	—	2	2	no	—
173	C₄×C₁₉	—	2	2	no	—
174	C₄×C₁₉	—	4	1	no	—
175	C₄×C₁₉	—	4	1	no	—
176	C₄×C₁₉	C₂²⋊Q₈	1	4	yes	complemented
177	Dic₁₉	—	2	2	no	—
178	Dic₁₉	—	2	2	no	—
179	Dic₁₉	—	2	2	no	—
180	Dic₁₉	—	2	2	no	—
181	Dic₁₉	—	2	2	no	—
182	Dic₁₉	—	4	1	no	—
183	Dic₁₉	—	4	1	no	—
184	Dic₁₉	C₄×D₄	1	4	yes	—
185	C₂×C₂²⋊Q₈	—	19	1	no	—
186	C₂×C₄×Q₈	—	19	1	no	—
187	C₂²×C₄²	—	19	1	no	—
188	#391	—	19	1	no	—
189	#389	—	19	1	no	—
190	#387	—	19	1	no	—
191	#387	—	19	1	no	—
192	#385	—	19	1	no	—
193	#385	—	19	1	no	—
194	#380	—	19	1	no	—
195	C₄×C₄⋊C₄	—	19	1	no	—
196	C₄×C₄⋊C₄	—	19	1	no	—
197	C₄×C₄⋊C₄	—	19	1	no	—
198	C₄×C₂²⋊C₄	—	19	1	no	—
199	C₄×C₂²⋊C₄	D₁₉	1	1	yes	characteristic
200	C₂×C₁₉	—	2	4	no	—
201	C₂×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
202	C₂×C₁₉	C₂×C₄×Q₈	1	1	yes	characteristic
203	C₂×C₁₉	C₄×#41	1	1	yes	characteristic
204	C₂×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
205	C₂×C₁₉	#525	1	1	yes	characteristic
206	C₂×C₁₉	#529	1	1	yes	characteristic
207	C₂×C₁₉	#533	1	1	yes	characteristic
208	C₂²×Q₈	—	19	1	no	—
209	C₂³×C₄	—	19	1	no	—
210	C₂³×C₄	—	19	1	no	—
211	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
212	C₂²⋊Q₈	—	19	8	no	—
213	C₄×Q₈	—	38	4	no	—
214	C₂×C₄⋊C₄	—	19	1	no	—
215	C₂×C₄⋊C₄	—	19	1	no	—
216	C₂×C₄⋊C₄	—	19	1	no	—
217	C₂×C₄⋊C₄	—	19	1	no	—
218	C₂×C₄⋊C₄	—	19	1	no	—
219	C₂×C₄⋊C₄	—	19	1	no	—
220	C₂×C₄⋊C₄	—	19	1	no	—
221	C₂×C₄⋊C₄	—	19	1	no	—
222	C₂×C₄⋊C₄	—	19	1	no	—
223	C₂×C₂²⋊C₄	—	19	1	no	—
224	C₂×C₂²⋊C₄	—	19	1	no	—
225	C₂×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic
226	C₂×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic
227	C₂×C₄²	—	19	1	no	—
228	C₂×C₄²	—	19	1	no	—
229	C₂×C₄²	—	19	1	no	—
230	C₂×C₄²	—	19	1	no	—
231	C₂×C₄²	—	19	1	no	—
232	C₂×C₄²	—	19	1	no	—
233	C₂×C₄²	—	38	4	no	—
234	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
235	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
236	#95	—	19	1	no	—
237	#95	—	19	1	no	—
238	#95	—	19	1	no	—
239	#95	—	19	1	no	—
240	#95	—	19	1	no	—
241	#95	—	19	1	no	—
242	#95	—	19	1	no	—
243	#95	—	19	1	no	—
244	#95	C₂×D₁₉	1	1	yes	characteristic
245	#95	C₂×D₁₉	1	1	yes	characteristic
246	C₁₉	C₄×C₂²⋊Q₈	1	1	yes	characteristic, complemented, Sylow
247	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
248	C₂×Q₈	—	19	4	no	—
249	C₂×Q₈	—	38	2	no	—
250	C₂×Q₈	—	38	2	no	—
251	C₂²×C₄	—	2	2	no	—
252	C₂²×C₄	—	2	2	no	—
253	C₂²×C₄	—	19	1	no	—
254	C₂²×C₄	—	19	4	no	—
255	C₂²×C₄	—	19	1	no	—
256	C₂²×C₄	—	19	1	no	—
257	C₂²×C₄	—	19	1	no	—
258	C₂²×C₄	—	19	1	no	—
259	C₂²×C₄	—	19	1	no	—
260	C₂²×C₄	—	19	1	no	—
261	C₂²×C₄	—	19	1	no	—
262	C₂²×C₄	—	38	2	no	—
263	C₂²×C₄	—	38	2	no	—
264	C₂²×C₄	—	38	2	no	—
265	C₂²×C₄	—	38	2	no	—
266	C₂²×C₄	—	38	2	no	—
267	C₂²×C₄	Dic₃₈	1	4	yes	complemented
268	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
269	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
270	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
271	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
272	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
273	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
274	C₄⋊C₄	—	19	4	no	—
275	C₄⋊C₄	—	19	4	no	—
276	C₄⋊C₄	—	19	4	no	—
277	C₄⋊C₄	—	38	2	no	—
278	C₄⋊C₄	—	38	2	no	—
279	C₄⋊C₄	—	38	2	no	—
280	C₄⋊C₄	—	38	2	no	—
281	C₄⋊C₄	—	38	2	no	—
282	C₄⋊C₄	—	38	2	no	—
283	C₂²⋊C₄	—	2	2	no	—
284	C₂²⋊C₄	—	19	4	no	—
285	C₂²⋊C₄	—	38	2	no	—
286	C₂²⋊C₄	C₄×D₁₉	1	4	yes	—
287	C₄²	—	2	2	no	—
288	C₄²	—	2	2	no	—
289	C₄²	—	19	4	no	—
290	C₄²	—	38	2	no	—
291	C₄²	—	38	2	no	—
292	C₄²	—	38	2	no	—
293	C₄²	—	38	2	no	—
294	C₄²	—	38	2	no	—
295	C₂³	—	2	1	no	—
296	C₂³	—	2	1	no	—
297	C₂³	—	2	1	no	—
298	C₂³	—	2	1	no	—
299	C₂³	C₂×Dic₃₈	1	2	yes	—
300	C₂³	C₂×C₄×D₁₉	1	2	yes	—
301	C₂³	#64541	1	2	yes	—
302	C₂³	C₂³×D₁₉	1	1	yes	characteristic
303	Q₈	—	38	8	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	1	no	—
306	C₂×C₄	—	2	1	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	1	no	—
310	C₂×C₄	—	2	8	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	19	2	no	—
318	C₂×C₄	—	19	2	no	—
319	C₂×C₄	—	19	2	no	—
320	C₂×C₄	—	19	2	no	—
321	C₂×C₄	—	19	2	no	—
322	C₂×C₄	—	19	2	no	—
323	C₂×C₄	—	19	2	no	—
324	C₂×C₄	—	19	2	no	—
325	C₂×C₄	—	38	8	no	—
326	C₂×C₄	—	38	8	no	—
327	C₂×C₄	—	38	1	no	—
328	C₂×C₄	—	38	1	no	—
329	C₂×C₄	—	38	1	no	—
330	C₂×C₄	—	38	1	no	—
331	C₂×C₄	—	38	1	no	—
332	C₂×C₄	—	38	1	no	—
333	C₂×C₄	—	38	1	no	—
334	C₂×C₄	—	38	1	no	—
335	C₂×C₄	—	38	1	no	—
336	C₂×C₄	—	38	1	no	—
337	C₂×C₄	—	38	1	no	—
338	C₂×C₄	—	38	1	no	—
339	C₂×C₄	—	38	1	no	—
340	C₂×C₄	—	38	1	no	—
341	C₂×C₄	—	38	1	no	—
342	C₂×C₄	—	38	1	no	—
343	C₂×C₄	C₂×Dic₃₈	1	2	yes	—
344	C₂×C₄	C₂×Dic₃₈	1	2	yes	—
345	C₂×C₄	C₂×C₄×D₁₉	1	2	yes	—
346	C₂×C₄	C₂×C₄×D₁₉	1	2	yes	—
347	C₂×C₄	D₄×D₁₉	1	2	yes	—
348	C₂×C₄	#64543	1	2	yes	—
349	C₂²	—	2	2	no	—
350	C₂²	—	2	2	no	—
351	C₂²	—	2	2	no	—
352	C₂²	—	2	2	no	—
353	C₂²	—	2	2	no	—
354	C₂²	—	2	2	no	—
355	C₂²	C₄×Dic₃₈	1	4	yes	complemented
356	C₂²	C₂²×Dic₃₈	1	1	yes	characteristic
357	C₂²	C₂²×C₄×D₁₉	1	1	yes	characteristic
358	C₂²	C₂×#64541	1	1	yes	characteristic
359	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
360	C₂²	C₂×#64543	1	1	yes	characteristic
361	C₂²	#41×D₁₉	1	1	yes	characteristic
362	C₂²	#41×D₁₉	1	1	yes	characteristic
363	C₄	—	2	2	no	—
364	C₄	—	2	2	no	—
365	C₄	—	2	2	no	—
366	C₄	—	4	1	no	—
367	C₄	—	4	1	no	—
368	C₄	—	19	4	no	—
369	C₄	—	38	2	no	—
370	C₄	—	38	2	no	—
371	C₄	—	38	2	no	—
372	C₄	—	38	2	no	—
373	C₄	—	38	2	no	—
374	C₄	—	76	1	no	—
375	C₄	—	76	1	no	—
376	C₄	#10597324	1	4	yes	direct product factor
377	C₂	—	2	4	no	—
378	C₂	C₄×D₄×D₁₉	1	1	yes	characteristic
379	C₂	C₂×C₄×Dic₃₈	1	1	yes	characteristic
380	C₂	C₄×#64543	1	1	yes	characteristic
381	C₂	C₂×#10597324	1	1	yes	characteristic
382	C₂	#11927053	1	1	yes	characteristic
383	C₂	#11927074	1	1	yes	characteristic
384	C₂	#11927097	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²×D₁₉
commutator	C₂²×C₁₉	C₂³×C₄
Frattini	C₂³	C₂³×D₁₉
Fitting	C₄×C₂²⋊C₄×C₁₉	C₂
socle, cosocle	C₂³×C₁₉	C₂⁴
prime radical	C₂⁴×C₁₉	C₂³
hypercenter	C₄×C₂²⋊C₄	D₁₉
hypocenter	C₁₉	C₄×C₂²⋊Q₈
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×Dic₃₈	C₂	semidirect
4. #11926448	C₂	semidirect
5. #11926441	C₂	semidirect
6. #11926431	C₂	semidirect
7. #11926427	C₂	semidirect
11. C₄×Dic₁₉⋊C₄	C₂	semidirect
12. C₄×Dic₁₉⋊C₄	C₂	semidirect
13. C₄×C₄⋊Dic₁₉	C₂	semidirect
42. #10597324	C₄	direct (N × H)
57. C₂²×C₄×C₁₉	Q₈	semidirect
80. C₂×Dic₃₈	C₂×C₄	semidirect
89. C₄⋊Dic₁₉	C₂×C₄	semidirect
94. Dic₁₉⋊C₄	C₂×C₄	semidirect
95. Dic₁₉⋊C₄	C₂×C₄	semidirect
163. C₂²×C₁₉	C₄×Q₈	semidirect
176. C₄×C₁₉	C₂²⋊Q₈	semidirect
246. C₁₉	C₄×C₂²⋊Q₈	semidirect
267. C₂²×C₄	Dic₃₈	semidirect
355. C₂²	C₄×Dic₃₈	semidirect
376. C₄	#10597324	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×#10597324	2
C₂×C₄×Dic₃₈	2
C₂²×C₄×Dic₁₉	2
#11926448	2
#11926441	2
#11926431	2
#11926427	2
#11926419	2
#11926416	2
#11926402	2
C₄×Dic₁₉⋊C₄	2
C₄×C₄⋊Dic₁₉	2
C₄×C₂²⋊Dic₁₉	2
C₄×C₂²⋊C₄×C₁₉	2
C₄×C₂²⋊Q₈	19

Subgroups — C4×#10597324 #14566166

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#10597324 #14566166