Subgroups — #14575343

Order 2432.

504 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10597396	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#64527	C₂	1	1	yes	maximal, characteristic, complemented
3	#11927190	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926926	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926775	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926771	C₂	1	1	yes	maximal, characteristic, complemented
7	#11926766	C₂	1	1	yes	maximal, characteristic, complemented
8	#11926756	C₂	1	1	yes	maximal, characteristic, complemented
9	#11926704	C₂	1	1	yes	maximal, characteristic, complemented
10	#11926700	C₂	1	1	yes	maximal, characteristic, complemented
11	#11926689	C₂	1	1	yes	maximal, characteristic, complemented
12	#11926677	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×#64527	C₂	1	1	yes	maximal, characteristic, complemented
14	D₄×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#548	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic, complemented
17	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×#64541	C₂²	1	1	yes	characteristic
19	C₂²×D₇₆	C₂²	1	1	yes	characteristic
20	C₁₉×#124	—	2	1	no	—
21	C₁₉×#124	C₂²	1	1	yes	characteristic, complemented
22	C₁₉×C₂²⋊Q₈	—	2	1	no	—
23	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
24	C₁₉×#121	—	2	1	no	—
25	C₁₉×#121	C₂²	1	1	yes	characteristic
26	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
27	C₄×D₄×C₁₉	—	2	1	no	—
28	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
29	#10597396	—	2	4	no	—
30	C₂×#64528	C₂²	1	1	yes	characteristic, complemented
31	C₂×#64528	C₂²	1	1	yes	characteristic, complemented
32	C₂×#64527	—	2	4	no	—
33	C₂×#64527	C₂²	1	1	yes	characteristic
34	C₂×#64527	C₂²	1	1	yes	characteristic
35	C₂×#64527	C₂²	1	1	yes	characteristic
36	C₂×#64527	C₂²	1	1	yes	characteristic
37	#10597383	—	2	1	no	—
38	C₂×#64526	C₂²	1	1	yes	characteristic, complemented
39	C₂×#64525	C₂²	1	1	yes	characteristic
40	C₂×#64525	C₂²	1	1	yes	characteristic
41	#10597376	C₂²	1	1	yes	characteristic
42	#10597370	C₂²	1	1	yes	characteristic
43	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
44	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
45	#10597340	—	2	1	no	—
46	#10597330	—	2	1	no	—
47	C₂²⋊C₄×D₁₉	—	2	1	no	—
48	#10597321	C₂²	1	1	yes	characteristic
49	C₄×D₇₆	C₂²	1	1	yes	characteristic
50	#10597292	C₂²	1	1	yes	characteristic, complemented
51	#10597292	C₂²	1	1	yes	characteristic, complemented
52	#10597289	C₂²	1	1	yes	characteristic, complemented
53	C₂²⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
54	C₂²⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic, complemented
55	#10597267	C₂²	1	1	yes	characteristic, complemented
56	#10597266	C₂²	1	1	yes	characteristic
57	#10597266	C₂²	1	1	yes	characteristic
58	#10597265	C₂²	1	1	yes	characteristic, complemented
59	C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic, complemented
60	C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₁₉	—	2	1	no	—
62	#41×C₁₉	—	2	2	no	—
63	#41×C₁₉	—	4	1	no	—
64	C₂×Q₈×C₁₉	—	2	1	no	—
65	C₂×Q₈×C₁₉	—	2	2	no	—
66	C₂×Q₈×C₁₉	—	4	1	no	—
67	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
68	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
69	C₂×D₄×C₁₉	—	2	1	no	—
70	C₂×D₄×C₁₉	—	2	1	no	—
71	C₂×D₄×C₁₉	D₄	1	1	yes	characteristic
72	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
73	C₂²×C₄×C₁₉	—	2	1	no	—
74	C₂²×C₄×C₁₉	—	2	1	no	—
75	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
76	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
77	C₂×C₂²⋊D₁₉	—	2	1	no	—
78	C₂×C₂²⋊D₁₉	—	2	1	no	—
79	#64541	—	2	2	no	—
80	#64541	—	4	1	no	—
81	C₂×D₇₆	—	2	2	no	—
82	C₂×D₇₆	—	2	1	no	—
83	C₂×D₇₆	—	4	1	no	—
84	C₂×D₇₆	C₂³	1	1	yes	characteristic
85	C₂×D₇₆	C₂³	1	1	yes	characteristic
86	C₂×C₄×D₁₉	—	2	1	no	—
87	C₂×C₄×D₁₉	—	2	1	no	—
88	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
89	C₄⋊C₄×C₁₉	—	2	1	no	—
90	C₄⋊C₄×C₁₉	—	2	1	no	—
91	C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
92	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
93	C₂²⋊C₄×C₁₉	—	2	1	no	—
94	C₂²⋊C₄×C₁₉	—	2	1	no	—
95	C₂²⋊C₄×C₁₉	—	2	1	no	—
96	C₂²⋊C₄×C₁₉	—	2	1	no	—
97	C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
98	C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
99	C₄²×C₁₉	—	2	1	no	—
100	C₄²×C₁₉	C₂³	1	1	yes	characteristic
101	C₂²⋊Dic₁₉	—	2	1	no	—
102	#64528	—	2	2	no	—
103	#64528	—	4	1	no	—
104	#64527	—	2	2	no	—
105	#64527	—	2	2	no	—
106	#64527	—	2	2	no	—
107	#64527	D₄	1	4	yes	complemented
108	#64526	—	2	2	no	—
109	#64525	—	2	2	no	—
110	#64525	—	4	1	no	—
111	(C₂×D₁₉)⋊C₄	—	2	1	no	—
112	(C₂×D₁₉)⋊C₄	—	2	1	no	—
113	(C₂×D₁₉)⋊C₄	—	2	1	no	—
114	(C₂×D₁₉)⋊C₄	—	2	1	no	—
115	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
116	Dic₁₉⋊C₄	—	2	1	no	—
117	C₂×C₁₉⋊C₈	—	2	2	no	—
118	C₂×C₁₉⋊C₈	—	2	2	no	—
119	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
120	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
121	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
122	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
123	C₂³×C₁₉	—	2	1	no	—
124	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
125	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
126	C₂²×D₁₉	—	2	1	no	—
127	C₂²×D₁₉	—	2	1	no	—
128	C₂²×D₁₉	—	4	2	no	—
129	C₂²×D₁₉	—	4	2	no	—
130	C₂²×D₁₉	—	8	1	no	—
131	Q₈×C₁₉	—	2	1	no	—
132	Q₈×C₁₉	—	2	1	no	—
133	Q₈×C₁₉	—	2	1	no	—
134	Q₈×C₁₉	—	4	2	no	—
135	Q₈×C₁₉	C₂×D₄	1	2	yes	—
136	D₄×C₁₉	—	2	2	no	—
137	D₄×C₁₉	—	2	1	no	—
138	D₄×C₁₉	—	2	1	no	—
139	D₄×C₁₉	—	4	2	no	—
140	D₄×C₁₉	—	4	2	no	—
141	C₂×C₄×C₁₉	—	2	1	no	—
142	C₂×C₄×C₁₉	—	2	1	no	—
143	C₂×C₄×C₁₉	—	2	1	no	—
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	—	4	2	no	—
149	C₂×C₄×C₁₉	—	4	2	no	—
150	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
151	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
153	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
155	C₂²⋊D₁₉	—	4	2	no	—
156	C₂²⋊D₁₉	—	8	1	no	—
157	C₂×Dic₁₉	—	2	1	no	—
158	C₂×Dic₁₉	—	2	1	no	—
159	D₇₆	—	2	1	no	—
160	D₇₆	—	2	1	no	—
161	D₇₆	—	2	1	no	—
162	D₇₆	—	4	2	no	—
163	D₇₆	C₂×D₄	1	2	yes	—
164	C₄×D₁₉	—	4	2	no	—
165	C₄×D₁₉	—	8	1	no	—
166	Dic₃₈	—	2	1	no	—
167	Dic₃₈	—	2	1	no	—
168	C₁₉⋊C₈	—	2	1	no	—
169	C₁₉⋊C₈	—	2	1	no	—
170	C₁₉⋊C₈	—	2	1	no	—
171	C₁₉⋊C₈	C₂×D₄	1	2	yes	—
172	#3282	—	19	1	no	maximal, Sylow
173	C₂²×C₁₉	—	2	1	no	—
174	C₂²×C₁₉	—	2	1	no	—
175	C₂²×C₁₉	—	2	1	no	—
176	C₂²×C₁₉	—	2	1	no	—
177	C₂²×C₁₉	—	2	1	no	—
178	C₂²×C₁₉	—	4	1	no	—
179	C₂²×C₁₉	—	4	1	no	—
180	C₂²×C₁₉	—	4	1	no	—
181	C₂²×C₁₉	#135	1	2	yes	complemented
182	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
183	C₂×D₁₉	—	2	2	no	—
184	C₂×D₁₉	—	4	1	no	—
185	C₂×D₁₉	—	4	1	no	—
186	C₂×D₁₉	—	4	1	no	—
187	C₂×D₁₉	—	4	1	no	—
188	C₂×D₁₉	—	4	1	no	—
189	C₂×D₁₉	—	8	4	no	—
190	C₄×C₁₉	—	2	1	no	—
191	C₄×C₁₉	—	2	1	no	—
192	C₄×C₁₉	—	2	2	no	—
193	C₄×C₁₉	—	2	1	no	—
194	C₄×C₁₉	—	2	1	no	—
195	C₄×C₁₉	—	4	1	no	—
196	C₄×C₁₉	—	4	1	no	—
197	C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
198	C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
199	Dic₁₉	—	4	1	no	—
200	Dic₁₉	—	4	1	no	—
201	C₂×#135	—	19	1	no	—
202	C₂²×SD₁₆	—	19	1	no	—
203	#548	D₁₉	1	1	yes	characteristic, complemented
204	#546	—	19	1	no	—
205	#495	—	19	1	no	—
206	#465	—	19	1	no	—
207	#465	—	19	1	no	—
208	#464	—	19	1	no	—
209	#463	—	19	1	no	—
210	#452	—	19	1	no	—
211	#451	—	19	1	no	—
212	#449	—	19	1	no	—
213	#447	—	19	1	no	—
214	C₄×SD₁₆	—	19	1	no	—
215	C₈×D₄	—	19	1	no	—
216	C₂×C₁₉	—	2	2	no	—
217	C₂×C₁₉	—	4	1	no	—
218	C₂×C₁₉	—	8	1	no	—
219	C₂×C₁₉	D₄²	1	1	yes	characteristic
220	C₂×C₁₉	C₂×#135	1	1	yes	characteristic
221	C₂×C₁₉	#577	1	1	yes	characteristic
222	D₁₉	—	4	2	no	—
223	D₁₉	—	8	1	no	—
224	C₂×#41	—	19	1	no	—
225	C₂×#41	C₂×D₁₉	1	1	yes	characteristic, complemented
226	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic
227	C₂²×D₄	—	19	1	no	—
228	#135	—	38	4	no	—
229	C₂×Q₁₆	—	19	1	no	—
230	C₂×Q₁₆	—	19	1	no	—
231	C₂×SD₁₆	—	19	1	no	—
232	C₂×SD₁₆	—	19	1	no	—
233	C₂×SD₁₆	—	19	1	no	—
234	C₂×SD₁₆	—	19	1	no	—
235	C₂×SD₁₆	—	19	1	no	—
236	C₂×SD₁₆	—	38	4	no	—
237	C₂×D₈	—	19	1	no	—
238	C₂×D₈	—	19	1	no	—
239	C₂²×C₈	—	19	1	no	—
240	C₂²×C₈	—	19	1	no	—
241	#124	—	2	1	no	—
242	#124	—	19	1	no	—
243	#124	C₂×D₁₉	1	1	yes	characteristic, complemented
244	#123	—	38	1	no	—
245	C₂²⋊Q₈	—	2	1	no	—
246	C₂²⋊Q₈	—	19	1	no	—
247	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
248	#121	—	2	1	no	—
249	#121	—	19	1	no	—
250	#121	—	38	1	no	—
251	#121	C₂×D₁₉	1	1	yes	characteristic
252	#120	—	38	1	no	—
253	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
254	C₄×D₄	—	2	1	no	—
255	C₄×D₄	—	19	1	no	—
256	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
257	C₂×C₂²⋊C₄	—	38	1	no	—
258	#106	—	19	1	no	—
259	C₄⋊C₈	—	19	1	no	—
260	#103	—	19	1	no	—
261	#103	—	19	1	no	—
262	#103	—	19	1	no	—
263	#102	—	19	1	no	—
264	#102	—	19	1	no	—
265	#102	—	19	1	no	—
266	C₂²⋊C₈	—	19	1	no	—
267	C₂²⋊C₈	—	19	1	no	—
268	C₄×C₈	—	19	1	no	—
269	C₁₉	#3282	1	1	yes	characteristic, complemented, Sylow
270	C₂⁴	—	38	1	no	—
271	#41	—	2	2	no	—
272	#41	—	4	1	no	—
273	#41	—	38	2	no	—
274	#41	—	76	1	no	—
275	C₂×Q₈	—	2	1	no	—
276	C₂×Q₈	—	2	2	no	—
277	C₂×Q₈	—	4	1	no	—
278	C₂×Q₈	—	19	1	no	—
279	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
280	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
281	C₂×D₄	—	2	1	no	—
282	C₂×D₄	—	2	1	no	—
283	C₂×D₄	—	19	1	no	—
284	C₂×D₄	—	19	1	no	—
285	C₂×D₄	—	38	2	no	—
286	C₂×D₄	—	38	1	no	—
287	C₂×D₄	—	38	1	no	—
288	C₂×D₄	—	38	1	no	—
289	C₂×D₄	—	76	1	no	—
290	C₂×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
291	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	38	1	no	—
295	C₂²×C₄	—	38	1	no	—
296	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
297	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
298	Q₁₆	—	38	2	no	—
299	Q₁₆	—	76	1	no	—
300	SD₁₆	—	19	4	no	—
301	SD₁₆	—	38	2	no	—
302	SD₁₆	—	38	2	no	—
303	SD₁₆	—	38	2	no	—
304	SD₁₆	—	38	2	no	—
305	D₈	—	38	2	no	—
306	D₈	—	76	1	no	—
307	C₂×C₈	—	19	1	no	—
308	C₂×C₈	—	19	1	no	—
309	C₂×C₈	—	19	1	no	—
310	C₂×C₈	—	19	1	no	—
311	C₂×C₈	—	38	2	no	—
312	C₂×C₈	—	38	2	no	—
313	C₄⋊C₄	—	2	1	no	—
314	C₄⋊C₄	—	2	1	no	—
315	C₄⋊C₄	—	19	1	no	—
316	C₄⋊C₄	—	38	1	no	—
317	C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
318	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
319	C₂²⋊C₄	—	2	1	no	—
320	C₂²⋊C₄	—	2	1	no	—
321	C₂²⋊C₄	—	2	1	no	—
322	C₂²⋊C₄	—	2	1	no	—
323	C₂²⋊C₄	—	38	1	no	—
324	C₂²⋊C₄	—	38	1	no	—
325	C₂²⋊C₄	—	38	1	no	—
326	C₂²⋊C₄	—	38	1	no	—
327	C₂²⋊C₄	—	38	1	no	—
328	C₂²⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
329	C₂²⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
330	C₄²	—	2	1	no	—
331	C₄²	C₂²×D₁₉	1	1	yes	characteristic
332	C₂³	—	2	1	no	—
333	C₂³	—	38	1	no	—
334	C₂³	—	38	1	no	—
335	C₂³	—	76	2	no	—
336	C₂³	—	76	2	no	—
337	C₂³	—	152	1	no	—
338	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
339	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
340	Q₈	—	2	1	no	—
341	Q₈	—	2	1	no	—
342	Q₈	—	2	1	no	—
343	Q₈	—	4	2	no	—
344	Q₈	—	38	1	no	—
345	Q₈	—	38	1	no	—
346	Q₈	D₄×D₁₉	1	2	yes	—
347	D₄	—	2	2	no	—
348	D₄	—	2	1	no	—
349	D₄	—	2	1	no	—
350	D₄	—	4	2	no	—
351	D₄	—	4	2	no	—
352	D₄	—	19	2	no	—
353	D₄	—	38	1	no	—
354	D₄	—	38	1	no	—
355	D₄	—	38	1	no	—
356	D₄	—	76	2	no	—
357	D₄	—	76	2	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	—	2	1	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	38	1	no	—
369	C₂×C₄	—	38	1	no	—
370	C₂×C₄	—	76	2	no	—
371	C₂×C₄	—	152	1	no	—
372	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
373	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
374	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
375	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
376	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
377	C₈	—	19	2	no	—
378	C₈	—	38	1	no	—
379	C₈	—	38	1	no	—
380	C₈	—	38	1	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	4	1	no	—
387	C₂²	—	4	1	no	—
388	C₂²	—	4	1	no	—
389	C₂²	—	38	2	no	—
390	C₂²	—	76	1	no	—
391	C₂²	—	76	1	no	—
392	C₂²	—	76	1	no	—
393	C₂²	—	76	1	no	—
394	C₂²	—	76	1	no	—
395	C₂²	—	152	4	no	—
396	C₂²	#10597396	1	2	yes	complemented
397	C₂²	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
398	C₄	—	2	1	no	—
399	C₄	—	2	1	no	—
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	2	2	no	—
403	C₄	—	4	1	no	—
404	C₄	—	4	1	no	—
405	C₄	—	76	1	no	—
406	C₄	—	76	1	no	—
407	C₄	C₂×D₄×D₁₉	1	1	yes	characteristic
408	C₄	#10597430	1	1	yes	characteristic
409	C₂	—	2	2	no	—
410	C₂	—	4	1	no	—
411	C₂	—	8	1	no	—
412	C₂	—	76	2	no	—
413	C₂	—	152	1	no	—
414	C₂	D₄×C₂²⋊D₁₉	1	1	yes	characteristic
415	C₂	C₂×#10597396	1	1	yes	characteristic
416	C₂	#11927352	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₁₉×#548	C₂
socle	C₂²×C₁₉	C₂²×D₄
hypercenter	#548	D₁₉
hypocenter	C₁₉	#3282
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄×D₄ ◁ #548

Complements

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

N	H ≅ G/N	type
1. C₂×#10597396	C₂	semidirect
2. C₂²×#64527	C₂	semidirect
3. #11927190	C₂	semidirect
4. #11926926	C₂	semidirect
5. #11926775	C₂	semidirect
6. #11926771	C₂	semidirect
7. #11926766	C₂	semidirect
8. #11926756	C₂	semidirect
9. #11926704	C₂	semidirect
10. #11926700	C₂	semidirect
11. #11926689	C₂	semidirect
12. #11926677	C₂	semidirect
13. C₄×#64527	C₂	semidirect
14. D₄×C₁₉⋊C₈	C₂	semidirect
15. C₁₉×#548	C₂	semidirect
16. C₂×#41×C₁₉	C₂²	semidirect
21. C₁₉×#124	C₂²	semidirect
23. C₁₉×C₂²⋊Q₈	C₂²	semidirect
26. C₄×Q₈×C₁₉	C₂²	semidirect
30. C₂×#64528	C₂²	semidirect
31. C₂×#64528	C₂²	semidirect
38. C₂×#64526	C₂²	semidirect
44. C₂²×C₁₉⋊C₈	C₂²	semidirect
50. #10597292	C₂²	semidirect
51. #10597292	C₂²	semidirect
52. #10597289	C₂²	semidirect
54. C₂²⋊(C₁₉⋊C₈)	C₂²	semidirect
55. #10597267	C₂²	semidirect
58. #10597265	C₂²	semidirect
59. C₄⋊(C₁₉⋊C₈)	C₂²	semidirect
60. C₄×C₁₉⋊C₈	C₂²	semidirect
107. #64527	D₄	semidirect
181. C₂²×C₁₉	#135	semidirect
203. #548	D₁₉	semidirect
225. C₂×#41	C₂×D₁₉	semidirect
243. #124	C₂×D₁₉	semidirect
247. C₂²⋊Q₈	C₂×D₁₉	semidirect
253. C₄×Q₈	C₂×D₁₉	semidirect
269. C₁₉	#3282	semidirect
396. C₂²	#10597396	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10597396	2
C₂²×#64527	2
#11927190	2
#11926926	2
#11926775	2
#11926771	2
#11926766	2
#11926756	2
#11926704	2
#11926700	2
#11926689	2
#11926677	2
C₄×#64527	2
D₄×C₁₉⋊C₈	2
C₁₉×#548	2
#3282	19