Group #18085250 — subgroups

Subgroups — #18085250

Order 4864.

588 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 588 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14574786	C₂	1	1	yes	maximal, characteristic
2	#14574583	C₂	1	1	yes	maximal, characteristic
3	#14564612	C₂	1	1	yes	maximal, characteristic
4	#14562320	C₂	1	1	yes	maximal, characteristic
5	#14562316	C₂	1	1	yes	maximal, characteristic
6	#14561468	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#2868	C₂	1	1	yes	maximal, characteristic
8	#11927101	C₂²	1	1	yes	characteristic
9	#11926947	—	2	1	no	—
10	#11926923	—	2	1	no	—
11	#11926896	—	2	1	no	—
12	#11926894	—	2	1	no	—
13	#11926879	—	2	2	no	—
14	#11926836	—	2	2	no	—
15	#11926751	—	2	2	no	—
16	#11926700	—	2	2	no	—
17	#11926597	C₂²	1	1	yes	characteristic
18	#11926597	C₂²	1	1	yes	characteristic
19	#11926568	C₂²	1	1	yes	characteristic
20	#11926304	—	2	2	no	—
21	#11926293	—	2	2	no	—
22	#11926290	—	2	2	no	—
23	C₂×C₁₉×C₄⋊Q₈	—	2	2	no	—
24	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₁₉×#384	—	2	2	no	—
27	C₁₉×#384	—	2	2	no	—
28	C₄³×C₁₉	C₂²	1	1	yes	characteristic
29	C₂²×Q₈×C₁₉	—	2	1	no	—
30	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
31	C₁₉×C₄⋊Q₈	—	2	1	no	—
32	C₁₉×C₄⋊Q₈	—	2	1	no	—
33	C₁₉×C₄⋊Q₈	—	2	1	no	—
34	C₁₉×C₄⋊Q₈	—	2	1	no	—
35	C₁₉×C₄⋊Q₈	—	2	1	no	—
36	C₁₉×C₄⋊Q₈	—	2	1	no	—
37	C₁₉×C₄⋊Q₈	—	2	1	no	—
38	C₁₉×C₄⋊Q₈	—	2	1	no	—
39	C₁₉×C₄⋊Q₈	—	4	8	no	—
40	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
41	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
42	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
43	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
44	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
45	C₂×C₄²×C₁₉	—	2	1	no	—
46	C₂×C₄²×C₁₉	—	2	1	no	—
47	C₂×C₄²×C₁₉	D₄	1	2	yes	—
48	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
49	C₂×#64528	—	2	4	no	—
50	#10597372	—	2	1	no	—
51	#10597370	—	2	1	no	—
52	#10597370	—	2	1	no	—
53	C₂×#64520	—	2	1	no	—
54	#10597316	—	2	1	no	—
55	#10597315	D₄	1	1	yes	characteristic
56	#10597315	D₄	1	1	yes	characteristic
57	C₄×Dic₃₈	—	2	1	no	—
58	C₄×Dic₃₈	—	2	1	no	—
59	#10597292	—	2	4	no	—
60	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
61	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
62	#10597267	—	2	4	no	—
63	#10597264	—	2	4	no	—
64	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
65	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
66	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
67	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
68	C₄×C₁₉⋊C₈	—	2	1	no	—
69	C₄×C₁₉⋊C₈	—	2	1	no	—
70	C₂×Q₈×C₁₉	—	2	2	no	—
71	C₂×Q₈×C₁₉	—	2	2	no	—
72	C₂×Q₈×C₁₉	—	4	4	no	—
73	C₂×Q₈×C₁₉	—	4	4	no	—
74	C₂×Q₈×C₁₉	—	4	1	no	—
75	C₂×Q₈×C₁₉	—	4	1	no	—
76	C₂²×C₄×C₁₉	—	2	2	no	—
77	C₂²×C₄×C₁₉	—	2	2	no	—
78	C₂²×C₄×C₁₉	—	2	2	no	—
79	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
82	C₂×Dic₃₈	—	2	1	no	—
83	C₂×Dic₃₈	—	2	1	no	—
84	C₄⋊C₄×C₁₉	—	2	2	no	—
85	C₄⋊C₄×C₁₉	—	2	2	no	—
86	C₄⋊C₄×C₁₉	—	4	16	no	—
87	C₄⋊C₄×C₁₉	—	4	1	no	—
88	C₄⋊C₄×C₁₉	—	4	1	no	—
89	C₄⋊C₄×C₁₉	—	4	1	no	—
90	C₄⋊C₄×C₁₉	—	4	1	no	—
91	C₄⋊C₄×C₁₉	—	4	1	no	—
92	C₄⋊C₄×C₁₉	—	4	1	no	—
93	C₄²×C₁₉	—	2	4	no	—
94	C₄²×C₁₉	—	2	4	no	—
95	C₄²×C₁₉	—	2	2	no	—
96	C₄²×C₁₉	Q₁₆	1	4	yes	complemented
97	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
98	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
99	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
100	C₄²×C₁₉	#41	1	1	yes	characteristic
101	C₂²⋊Dic₁₉	—	4	1	no	—
102	#64528	—	8	4	no	—
103	C₄⋊Dic₁₉	—	2	1	no	—
104	C₄⋊Dic₁₉	—	2	1	no	—
105	C₄⋊Dic₁₉	—	2	1	no	—
106	C₄⋊Dic₁₉	—	2	1	no	—
107	Dic₁₉⋊C₄	—	4	1	no	—
108	Dic₁₉⋊C₄	—	4	1	no	—
109	C₄×Dic₁₉	—	4	1	no	—
110	#64520	—	4	2	no	—
111	C₂×C₁₉⋊C₈	—	2	2	no	—
112	C₂×C₁₉⋊C₈	—	2	2	no	—
113	C₂×C₁₉⋊C₈	—	4	1	no	—
114	#10293	—	19	1	no	maximal, Sylow
115	C₂³×C₁₉	#120	1	1	yes	characteristic
116	Q₈×C₁₉	—	4	4	no	—
117	Q₈×C₁₉	—	8	2	no	—
118	Q₈×C₁₉	—	8	2	no	—
119	Q₈×C₁₉	—	8	2	no	—
120	C₂×C₄×C₁₉	—	2	4	no	—
121	C₂×C₄×C₁₉	—	2	4	no	—
122	C₂×C₄×C₁₉	—	2	4	no	—
123	C₂×C₄×C₁₉	—	2	2	no	—
124	C₂×C₄×C₁₉	—	2	2	no	—
125	C₂×C₄×C₁₉	—	4	4	no	—
126	C₂×C₄×C₁₉	—	4	4	no	—
127	C₂×C₄×C₁₉	—	4	2	no	—
128	C₂×C₄×C₁₉	—	4	2	no	—
129	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
130	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
131	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
132	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
133	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
134	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
135	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
136	C₂×C₄×C₁₉	#137	1	2	yes	—
137	C₂×Dic₁₉	—	4	1	no	—
138	C₂×Dic₁₉	—	4	1	no	—
139	Dic₃₈	—	4	2	no	—
140	Dic₃₈	—	4	2	no	—
141	C₁₉⋊C₈	—	4	2	no	—
142	C₁₉⋊C₈	—	4	2	no	—
143	C₁₉⋊C₈	—	8	1	no	—
144	#3230	—	19	1	no	—
145	#3209	—	19	1	no	—
146	#2868	D₁₉	1	1	yes	characteristic
147	#1994	—	19	1	no	—
148	#1549	—	19	1	no	—
149	#1548	—	19	1	no	—
150	#1276	—	19	1	no	—
151	C₂²×C₁₉	—	2	1	no	—
152	C₂²×C₁₉	—	2	1	no	—
153	C₂²×C₁₉	#392	1	1	yes	characteristic
154	C₂²×C₁₉	#451	1	2	yes	—
155	C₄×C₁₉	—	2	8	no	—
156	C₄×C₁₉	—	2	1	no	—
157	C₄×C₁₉	—	2	1	no	—
158	C₄×C₁₉	—	8	2	no	—
159	C₄×C₁₉	—	8	2	no	—
160	C₄×C₁₉	#453	1	2	yes	—
161	C₄×C₁₉	#456	1	2	yes	—
162	C₄×C₁₉	#462	1	2	yes	—
163	C₄×C₁₉	#494	1	1	yes	characteristic
164	C₄×C₁₉	#497	1	1	yes	characteristic
165	Dic₁₉	—	8	1	no	—
166	Dic₁₉	—	8	1	no	—
167	#533	—	19	1	no	—
168	C₂×C₄⋊Q₈	—	2	2	no	—
169	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
170	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
171	#500	—	38	1	no	—
172	#494	—	38	1	no	—
173	#487	—	38	1	no	—
174	#487	—	38	1	no	—
175	#484	—	38	2	no	—
176	#477	—	38	2	no	—
177	#462	—	38	2	no	—
178	#451	—	38	2	no	—
179	#431	—	19	1	no	—
180	#431	—	19	1	no	—
181	#423	—	19	1	no	—
182	#384	—	2	2	no	—
183	#384	—	2	2	no	—
184	C₄³	C₂×D₁₉	1	1	yes	characteristic
185	#339	—	38	2	no	—
186	#333	—	38	2	no	—
187	#332	—	38	2	no	—
188	C₂×C₁₉	—	2	2	no	—
189	C₂×C₁₉	#2002	1	1	yes	characteristic
190	C₂×C₁₉	#2005	1	1	yes	characteristic
191	C₂×C₁₉	#2016	1	1	yes	characteristic
192	C₂²×Q₈	—	2	1	no	—
193	C₂²×Q₈	C₂²⋊D₁₉	1	2	yes	—
194	C₂×Q₁₆	—	38	4	no	—
195	C₂×M₁₆	—	38	1	no	—
196	C₄⋊Q₈	—	2	1	no	—
197	C₄⋊Q₈	—	2	1	no	—
198	C₄⋊Q₈	—	2	1	no	—
199	C₄⋊Q₈	—	2	1	no	—
200	C₄⋊Q₈	—	2	1	no	—
201	C₄⋊Q₈	—	2	1	no	—
202	C₄⋊Q₈	—	2	1	no	—
203	C₄⋊Q₈	—	2	1	no	—
204	C₄⋊Q₈	—	4	8	no	—
205	C₄⋊Q₈	—	19	1	no	—
206	C₄⋊Q₈	—	19	1	no	—
207	#125	—	38	1	no	—
208	C₂²⋊Q₈	—	38	1	no	—
209	C₂²⋊Q₈	—	38	1	no	—
210	C₄×Q₈	—	38	1	no	—
211	C₄×Q₈	—	38	1	no	—
212	#117	—	38	1	no	—
213	C₂×C₄⋊C₄	—	2	8	no	—
214	C₂×C₄⋊C₄	—	2	1	no	—
215	C₂×C₄⋊C₄	—	2	1	no	—
216	C₂×C₄⋊C₄	—	2	1	no	—
217	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
218	C₂×C₄²	—	2	1	no	—
219	C₂×C₄²	—	2	1	no	—
220	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
221	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
222	#107	—	38	4	no	—
223	C₄⋊C₈	—	19	2	no	—
224	C₄⋊C₈	—	19	2	no	—
225	C₄⋊C₈	—	38	1	no	—
226	C₄⋊C₈	—	38	1	no	—
227	#103	—	38	4	no	—
228	#103	—	38	4	no	—
229	C₂²⋊C₈	—	38	1	no	—
230	C₂²⋊C₈	—	38	1	no	—
231	C₄×C₈	—	38	1	no	—
232	C₄×C₈	—	38	1	no	—
233	C₁₉	#10293	1	1	yes	characteristic, complemented, Sylow
234	C₂×Q₈	—	2	2	no	—
235	C₂×Q₈	—	2	2	no	—
236	C₂×Q₈	—	4	4	no	—
237	C₂×Q₈	—	4	4	no	—
238	C₂×Q₈	—	4	1	no	—
239	C₂×Q₈	—	4	1	no	—
240	C₂×Q₈	—	38	1	no	—
241	C₂×Q₈	—	38	1	no	—
242	C₂²×C₄	—	2	2	no	—
243	C₂²×C₄	—	2	2	no	—
244	C₂²×C₄	—	2	2	no	—
245	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
246	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
247	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
248	Q₁₆	—	152	4	no	—
249	M₁₆	—	76	2	no	—
250	C₂×C₈	—	38	2	no	—
251	C₂×C₈	—	38	2	no	—
252	C₂×C₈	—	76	1	no	—
253	C₄⋊C₄	—	2	2	no	—
254	C₄⋊C₄	—	2	2	no	—
255	C₄⋊C₄	—	4	16	no	—
256	C₄⋊C₄	—	4	1	no	—
257	C₄⋊C₄	—	4	1	no	—
258	C₄⋊C₄	—	4	1	no	—
259	C₄⋊C₄	—	4	1	no	—
260	C₄⋊C₄	—	4	1	no	—
261	C₄⋊C₄	—	4	1	no	—
262	C₄⋊C₄	—	38	1	no	—
263	C₄⋊C₄	—	38	1	no	—
264	C₄⋊C₄	—	38	1	no	—
265	C₄⋊C₄	—	38	1	no	—
266	C₄⋊C₄	—	76	1	no	—
267	C₄⋊C₄	—	76	1	no	—
268	C₂²⋊C₄	—	76	1	no	—
269	C₄²	—	2	4	no	—
270	C₄²	—	2	4	no	—
271	C₄²	—	2	2	no	—
272	C₄²	—	76	1	no	—
273	C₄²	#64528	1	4	yes	complemented
274	C₄²	D₄×D₁₉	1	1	yes	characteristic
275	C₄²	D₄×D₁₉	1	1	yes	characteristic
276	C₄²	D₄×D₁₉	1	1	yes	characteristic
277	C₄²	#64543	1	1	yes	characteristic
278	C₂³	#10597399	1	1	yes	characteristic
279	Q₈	—	4	4	no	—
280	Q₈	—	8	2	no	—
281	Q₈	—	8	2	no	—
282	Q₈	—	8	2	no	—
283	Q₈	—	76	2	no	—
284	Q₈	—	76	2	no	—
285	C₂×C₄	—	2	4	no	—
286	C₂×C₄	—	2	4	no	—
287	C₂×C₄	—	2	4	no	—
288	C₂×C₄	—	2	2	no	—
289	C₂×C₄	—	2	2	no	—
290	C₂×C₄	—	4	4	no	—
291	C₂×C₄	—	4	4	no	—
292	C₂×C₄	—	4	2	no	—
293	C₂×C₄	—	4	2	no	—
294	C₂×C₄	—	76	1	no	—
295	C₂×C₄	—	76	1	no	—
296	C₂×C₄	#10597383	1	1	yes	characteristic
297	C₂×C₄	#10597383	1	1	yes	characteristic
298	C₂×C₄	#10597384	1	1	yes	characteristic
299	C₂×C₄	#10597385	1	1	yes	characteristic
300	C₂×C₄	#10597385	1	1	yes	characteristic
301	C₂×C₄	#10597386	1	1	yes	characteristic
302	C₂×C₄	#10597388	1	2	yes	—
303	C₂×C₄	C₂×#64528	1	2	yes	—
304	C₈	—	76	2	no	—
305	C₈	—	76	2	no	—
306	C₈	—	152	1	no	—
307	C₂²	—	2	1	no	—
308	C₂²	—	2	1	no	—
309	C₂²	#11926452	1	1	yes	characteristic
310	C₂²	#11926700	1	2	yes	—
311	C₄	—	2	8	no	—
312	C₄	—	2	1	no	—
313	C₄	—	2	1	no	—
314	C₄	—	8	2	no	—
315	C₄	—	8	2	no	—
316	C₄	—	152	1	no	—
317	C₄	—	152	1	no	—
318	C₄	#11926711	1	2	yes	—
319	C₄	#11926726	1	2	yes	—
320	C₄	#11926751	1	2	yes	—
321	C₄	#11926923	1	1	yes	characteristic
322	C₄	#11926936	1	1	yes	characteristic
323	C₂	—	2	2	no	—
324	C₂	#14564650	1	1	yes	characteristic
325	C₂	#14564671	1	1	yes	characteristic
326	C₂	#14564735	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14574786

C₂

yes

maximal, characteristic

#14574583

C₂

yes

maximal, characteristic

#14564612

C₂

yes

maximal, characteristic

#14562320

C₂

yes

maximal, characteristic

#14562316

C₂

yes

maximal, characteristic

#14561468

C₂

yes

maximal, characteristic

C₁₉×#2868

C₂

yes

maximal, characteristic

#11927101

C₂²

yes

—

—

—

—

—

—

—

—

C₂²

yes

characteristic

#11926597

C₂²

yes

characteristic

#11926568

C₂²

yes

—

—

—

C₂×C₁₉×C₄⋊Q₈

—

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₁₉×#384

—

C₁₉×#384

—

C₄³×C₁₉

C₂²

yes

characteristic

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

D₄

yes

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

—

—

—

—

—

—

D₄

yes

characteristic

#10597315

D₄

yes

characteristic

C₄×Dic₃₈

—

C₄×Dic₃₈

—

#10597292

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

#10597267

—

#10597264

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

Q₁₆

yes

complemented

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

100

C₄²×C₁₉

#41

yes

characteristic

101

C₂²⋊Dic₁₉

—

102

#64528

—

103

C₄⋊Dic₁₉

—

104

C₄⋊Dic₁₉

—

105

C₄⋊Dic₁₉

—

106

C₄⋊Dic₁₉

—

107

Dic₁₉⋊C₄

—

108

Dic₁₉⋊C₄

—

109

C₄×Dic₁₉

—

110

#64520

—

111

C₂×C₁₉⋊C₈

—

112

C₂×C₁₉⋊C₈

—

113

C₂×C₁₉⋊C₈

—

114

#10293

—

maximal, Sylow

115

C₂³×C₁₉

#120

yes

characteristic

116

Q₈×C₁₉

—

117

Q₈×C₁₉

—

118

Q₈×C₁₉

—

119

Q₈×C₁₉

—

120

C₂×C₄×C₁₉

—

121

C₂×C₄×C₁₉

—

122

C₂×C₄×C₁₉

—

123

C₂×C₄×C₁₉

—

124

C₂×C₄×C₁₉

—

125

C₂×C₄×C₁₉

—

126

C₂×C₄×C₁₉

—

127

C₂×C₄×C₁₉

—

128

C₂×C₄×C₁₉

—

129

C₂×C₄×C₁₉

#120

yes

characteristic

130

C₂×C₄×C₁₉

#120

yes

characteristic

131

C₂×C₄×C₁₉

#121

yes

characteristic

132

C₂×C₄×C₁₉

#121

yes

characteristic

133

C₂×C₄×C₁₉

#121

yes

characteristic

134

C₂×C₄×C₁₉

#127

yes

characteristic

135

C₂×C₄×C₁₉

C₂×Q₁₆

yes

—

136

C₂×C₄×C₁₉

#137

yes

—

137

C₂×Dic₁₉

—

138

C₂×Dic₁₉

—

139

Dic₃₈

—

140

Dic₃₈

—

141

C₁₉⋊C₈

—

142

C₁₉⋊C₈

—

143

C₁₉⋊C₈

—

144

#3230

—

145

#3209

—

146

#2868

D₁₉

yes

characteristic

147

#1994

—

148

#1549

—

149

#1548

—

150

#1276

—

151

C₂²×C₁₉

—

152

C₂²×C₁₉

—

153

C₂²×C₁₉

#392

yes

characteristic

154

C₂²×C₁₉

#451

yes

—

155

C₄×C₁₉

—

156

C₄×C₁₉

—

157

C₄×C₁₉

—

158

C₄×C₁₉

—

159

C₄×C₁₉

—

160

C₄×C₁₉

#453

yes

—

161

C₄×C₁₉

#456

yes

—

162

C₄×C₁₉

#462

yes

—

163

C₄×C₁₉

#494

yes

characteristic

164

C₄×C₁₉

#497

yes

characteristic

165

Dic₁₉

—

166

Dic₁₉

—

167

#533

—

168

C₂×C₄⋊Q₈

—

169

C₂×C₄⋊Q₈

C₂×D₁₉

yes

characteristic

170

C₂×C₄⋊Q₈

C₂×D₁₉

yes

characteristic

171

#500

—

172

#494

—

173

#487

—

174

#487

—

175

#484

—

176

#477

—

177

#462

—

178

#451

—

179

#431

—

180

#431

—

181

#423

—

182

#384

—

183

#384

—

184

C₄³

C₂×D₁₉

yes

characteristic

185

#339

—

186

#333

—

187

#332

—

188

C₂×C₁₉

—

189

C₂×C₁₉

#2002

yes

characteristic

190

C₂×C₁₉

#2005

yes

characteristic

191

C₂×C₁₉

#2016

yes

characteristic

192

C₂²×Q₈

—

193

C₂²×Q₈

C₂²⋊D₁₉

yes

—

194

C₂×Q₁₆

—

195

C₂×M₁₆

—

196

C₄⋊Q₈

—

197

C₄⋊Q₈

—

198

C₄⋊Q₈

—

199

C₄⋊Q₈

—

200

C₄⋊Q₈

—

201

C₄⋊Q₈

—

202

C₄⋊Q₈

—

203

C₄⋊Q₈

—

204

C₄⋊Q₈

—

205

C₄⋊Q₈

—

206

C₄⋊Q₈

—

207

#125

—

208

C₂²⋊Q₈

—

209

C₂²⋊Q₈

—

210

C₄×Q₈

—

211

C₄×Q₈

—

212

#117

—

213

C₂×C₄⋊C₄

—

214

C₂×C₄⋊C₄

—

215

C₂×C₄⋊C₄

—

216

C₂×C₄⋊C₄

—

217

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

—

218

C₂×C₄²

—

219

C₂×C₄²

—

220

C₂×C₄²

C₂²⋊D₁₉

yes

—

221

C₂×C₄²

C₂²×D₁₉

yes

characteristic

222

#107

—

223

C₄⋊C₈

—

224

C₄⋊C₈

—

225

C₄⋊C₈

—

226

C₄⋊C₈

—

227

#103

—

228

#103

—

229

C₂²⋊C₈

—

230

C₂²⋊C₈

—

231

C₄×C₈

—

232

C₄×C₈

—

233

C₁₉

#10293

yes

characteristic, complemented, Sylow

234

C₂×Q₈

—

235

C₂×Q₈

—

236

C₂×Q₈

—

237

C₂×Q₈

—

238

C₂×Q₈

—

239

C₂×Q₈

—

240

C₂×Q₈

—

241

C₂×Q₈

—

242

C₂²×C₄

—

243

C₂²×C₄

—

244

C₂²×C₄

—

245

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

246

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

247

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

248

Q₁₆

—

152

—

249

M₁₆

—

250

C₂×C₈

—

251

C₂×C₈

—

252

C₂×C₈

—

253

C₄⋊C₄

—

254

C₄⋊C₄

—

255

C₄⋊C₄

—

256

C₄⋊C₄

—

257

C₄⋊C₄

—

258

C₄⋊C₄

—

259

C₄⋊C₄

—

260

C₄⋊C₄

—

261

C₄⋊C₄

—

262

C₄⋊C₄

—

263

C₄⋊C₄

—

264

C₄⋊C₄

—

265

C₄⋊C₄

—

266

C₄⋊C₄

—

267

C₄⋊C₄

—

268

C₂²⋊C₄

—

269

C₄²

—

270

C₄²

—

271

C₄²

—

272

C₄²

—

273

C₄²

#64528

yes

complemented

274

C₄²

D₄×D₁₉

yes

characteristic

275

C₄²

D₄×D₁₉

yes

characteristic

276

C₄²

D₄×D₁₉

yes

characteristic

277

C₄²

#64543

yes

characteristic

278

C₂³

#10597399

yes

characteristic

279

Q₈

—

280

Q₈

—

281

Q₈

—

282

Q₈

—

283

Q₈

—

284

Q₈

—

285

C₂×C₄

—

286

C₂×C₄

—

287

C₂×C₄

—

288

C₂×C₄

—

289

C₂×C₄

—

290

C₂×C₄

—

291

C₂×C₄

—

292

C₂×C₄

—

293

C₂×C₄

—

294

C₂×C₄

—

295

C₂×C₄

—

296

C₂×C₄

#10597383

yes

characteristic

297

C₂×C₄

#10597383

yes

characteristic

298

C₂×C₄

#10597384

yes

characteristic

299

C₂×C₄

#10597385

yes

characteristic

300

C₂×C₄

#10597385

yes

characteristic

301

C₂×C₄

#10597386

yes

characteristic

302

C₂×C₄

#10597388

yes

—

303

C₂×C₄

C₂×#64528

yes

—

304

C₈

—

305

C₈

—

306

C₈

—

152

—

307

C₂²

—

308

C₂²

—

309

C₂²

#11926452

yes

characteristic

310

C₂²

#11926700

yes

—

311

C₄

—

312

C₄

—

313

C₄

—

314

C₄

—

315

C₄

—

316

C₄

—

152

—

317

C₄

—

152

—

318

C₄

#11926711

yes

—

319

C₄

#11926726

yes

—

320

C₄

#11926751

yes

—

321

C₄

#11926923

yes

characteristic

322

C₄

#11926936

yes

characteristic

323

C₂

—

324

C₂

#14564650

yes

characteristic

325

C₂

#14564671

yes

characteristic

326

C₂

#14564735

yes

characteristic

	subgroup	G/H
center	C₂²	#11926452
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2868	C₂
socle	C₂²×C₁₉	#392
prime radical	C₂³×C₁₉	#120
hypercenter	#2868	D₁₉
hypocenter	C₁₉	#10293
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2868

subgroup

G/H

center

C₂²

#11926452

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#2868

C₂

C₂²×C₁₉

C₂³×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2868

N	H ≅ G/N	type
96. C₄²×C₁₉	Q₁₆	semidirect
233. C₁₉	#10293	semidirect
273. C₄²	#64528	semidirect

H ≅ G/N

type

96. C₄²×C₁₉

Q₁₆

semidirect

233. C₁₉

#10293

semidirect

273. C₄²

#64528

semidirect

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

subgroup	index
#14574786	2
#14574583	2
#14564612	2
#14562320	2
#14562316	2
#14561468	2
C₁₉×#2868	2
#10293	19

subgroup

index

C₁₉×#2868

Subgroups — #18085250

Conjugacy classes of subgroups

Complements

Maximal subgroups