Group #18084848 — subgroups

Subgroups — #18084848

Order 4864.

676 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 676 conjugacy classes of subgroups — too many to draw. Only its 137 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	C₂×#11926744	C₂	1	2	yes	maximal
2	#14564440	C₂	1	1	yes	maximal, characteristic
3	C₂×Q₈⋊(C₁₉⋊C₈)	C₂	1	2	yes	maximal, complemented
4	#14561518	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2582	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#64527	—	2	2	no	—
7	C₂×#10597320	C₂²	1	1	yes	characteristic
8	#11926744	—	2	4	no	—
9	#11926744	—	2	4	no	—
10	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
11	C₂×#10597266	—	2	2	no	—
12	C₂×#10597266	—	2	2	no	—
13	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
14	Q₈⋊(C₁₉⋊C₈)	—	2	4	no	—
15	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
16	C₁₉×#398	—	2	2	no	—
17	C₁₉×#391	—	2	2	no	—
18	C₁₉×#389	—	2	2	no	—
19	C₁₉×#384	C₂²	1	1	yes	characteristic
20	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
21	C₂²×D₇₆	—	2	1	no	—
22	C₂²×D₇₆	—	2	2	no	—
23	C₄×Q₈×C₁₉	—	2	2	no	—
24	C₄×Q₈×C₁₉	—	2	2	no	—
25	C₄×Q₈×C₁₉	—	2	2	no	—
26	C₄×Q₈×C₁₉	—	2	2	no	—
27	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
28	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
29	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
30	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
31	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
32	C₂×C₄²×C₁₉	—	2	2	no	—
33	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
34	C₂×#64527	—	2	8	no	—
35	C₂×#64527	—	4	4	no	—
36	C₂×#64527	—	4	4	no	—
37	C₂²×C₁₉⋊C₈	—	2	1	no	—
38	C₂²×C₁₉⋊C₈	—	2	2	no	—
39	#10597320	—	2	2	no	—
40	#10597320	—	2	1	no	—
41	#10597320	D₄	1	2	yes	—
42	C₁₉×#95	—	2	4	no	—
43	C₁₉×#95	—	2	2	no	—
44	#10597266	—	2	8	no	—
45	#10597266	—	4	4	no	—
46	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
47	C₄⋊(C₁₉⋊C₈)	D₄	1	4	yes	—
48	C₄×C₁₉⋊C₈	—	2	2	no	—
49	C₂³×D₁₉	—	4	1	no	—
50	C₂×Q₈×C₁₉	—	2	2	no	—
51	C₂×Q₈×C₁₉	—	2	2	no	—
52	C₂×Q₈×C₁₉	—	2	2	no	—
53	C₂×Q₈×C₁₉	—	2	2	no	—
54	C₂×Q₈×C₁₉	—	2	2	no	—
55	C₂×Q₈×C₁₉	SD₁₆	1	4	yes	complemented
56	C₂²×C₄×C₁₉	—	2	2	no	—
57	C₂²×C₄×C₁₉	—	2	2	no	—
58	C₂²×C₄×C₁₉	—	2	2	no	—
59	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
61	C₂×D₇₆	—	2	4	no	—
62	C₂×D₇₆	—	2	2	no	—
63	C₂×D₇₆	—	4	2	no	—
64	C₂×D₇₆	—	4	2	no	—
65	C₂×D₇₆	—	4	2	no	—
66	C₂×D₇₆	—	4	2	no	—
67	C₂×D₇₆	—	4	2	no	—
68	C₂×D₇₆	—	4	2	no	—
69	C₂×D₇₆	—	4	2	no	—
70	C₂×D₇₆	—	4	1	no	—
71	C₄⋊C₄×C₁₉	—	2	2	no	—
72	C₄⋊C₄×C₁₉	—	2	2	no	—
73	C₄⋊C₄×C₁₉	—	4	2	no	—
74	C₄⋊C₄×C₁₉	—	4	2	no	—
75	C₄⋊C₄×C₁₉	—	4	2	no	—
76	C₄⋊C₄×C₁₉	—	4	2	no	—
77	C₄⋊C₄×C₁₉	—	4	2	no	—
78	C₄⋊C₄×C₁₉	—	8	2	no	—
79	C₄²×C₁₉	—	4	2	no	—
80	C₄²×C₁₉	—	4	2	no	—
81	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
82	C₄²×C₁₉	C₂×D₄	1	2	yes	—
83	C₄²×C₁₉	#41	1	1	yes	characteristic
84	#64527	—	4	16	no	—
85	C₂×C₁₉⋊C₈	—	2	2	no	—
86	C₂×C₁₉⋊C₈	—	2	4	no	—
87	C₂×C₁₉⋊C₈	—	4	1	no	—
88	C₂×C₁₉⋊C₈	—	4	1	no	—
89	C₂×C₁₉⋊C₈	—	4	2	no	—
90	C₂×C₁₉⋊C₈	—	4	2	no	—
91	#10230	—	19	1	no	maximal, Sylow
92	C₂³×C₁₉	#120	1	1	yes	characteristic
93	C₂²×D₁₉	—	4	2	no	—
94	C₂²×D₁₉	—	8	2	no	—
95	C₂²×D₁₉	—	8	2	no	—
96	C₂²×D₁₉	—	8	1	no	—
97	C₂²×D₁₉	—	8	1	no	—
98	Q₈×C₁₉	—	2	4	no	—
99	Q₈×C₁₉	—	2	4	no	—
100	Q₈×C₁₉	—	4	2	no	—
101	Q₈×C₁₉	—	4	2	no	—
102	C₂×C₄×C₁₉	—	2	1	no	—
103	C₂×C₄×C₁₉	—	2	1	no	—
104	C₂×C₄×C₁₉	—	2	4	no	—
105	C₂×C₄×C₁₉	—	4	2	no	—
106	C₂×C₄×C₁₉	—	4	2	no	—
107	C₂×C₄×C₁₉	—	4	2	no	—
108	C₂×C₄×C₁₉	—	4	4	no	—
109	C₂×C₄×C₁₉	—	4	2	no	—
110	C₂×C₄×C₁₉	—	4	2	no	—
111	C₂×C₄×C₁₉	—	4	2	no	—
112	C₂×C₄×C₁₉	#120	1	2	yes	—
113	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
114	C₂×C₄×C₁₉	#121	1	2	yes	—
115	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
116	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
117	C₂×C₄×C₁₉	#135	1	2	yes	—
118	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
119	C₂×C₄×C₁₉	#137	1	2	yes	—
120	D₇₆	—	4	4	no	—
121	D₇₆	—	4	4	no	—
122	D₇₆	—	4	4	no	—
123	D₇₆	—	8	2	no	—
124	D₇₆	—	8	2	no	—
125	D₇₆	—	8	2	no	—
126	C₁₉⋊C₈	—	4	2	no	—
127	C₁₉⋊C₈	—	4	4	no	—
128	C₂×#460	—	19	2	no	—
129	#2582	D₁₉	1	1	yes	characteristic, complemented
130	#1957	—	19	1	no	—
131	C₂×Q₈⋊C₈	—	19	2	no	—
132	#1296	—	19	1	no	—
133	C₂²×C₁₉	#392	1	1	yes	characteristic
134	C₂²×C₁₉	#448	1	2	yes	—
135	C₂²×C₁₉	#449	1	2	yes	—
136	C₂²×C₁₉	#453	1	1	yes	characteristic
137	C₂²×C₁₉	#454	1	1	yes	characteristic
138	C₂×D₁₉	—	8	4	no	—
139	C₂×D₁₉	—	8	2	no	—
140	C₂×D₁₉	—	16	1	no	—
141	C₂×D₁₉	—	16	1	no	—
142	C₂×D₁₉	—	16	2	no	—
143	C₄×C₁₉	—	2	1	no	—
144	C₄×C₁₉	—	2	1	no	—
145	C₄×C₁₉	—	4	4	no	—
146	C₄×C₁₉	—	8	2	no	—
147	C₄×C₁₉	—	8	2	no	—
148	C₄×C₁₉	#450	1	2	yes	—
149	C₄×C₁₉	#452	1	2	yes	—
150	C₄×C₁₉	#465	1	2	yes	—
151	C₄×C₁₉	#468	1	2	yes	—
152	C₂²×SD₁₆	—	38	2	no	—
153	C₂×#127	—	19	1	no	—
154	C₂×C₄×Q₈	C₂×D₁₉	1	2	yes	—
155	#460	—	38	4	no	—
156	#460	—	38	4	no	—
157	C₂×C₄⋊C₈	—	19	2	no	—
158	C₂×#102	—	38	2	no	—
159	C₂×#102	—	38	2	no	—
160	C₂×C₄×C₈	—	19	1	no	—
161	#398	—	2	2	no	—
162	#391	—	2	2	no	—
163	#389	—	2	2	no	—
164	#384	C₂×D₁₉	1	1	yes	characteristic
165	Q₈⋊C₈	—	38	4	no	—
166	C₂×C₁₉	#1620	1	1	yes	characteristic
167	C₂×C₁₉	#1623	1	1	yes	characteristic
168	C₂×C₁₉	#1626	1	2	yes	—
169	C₂×C₁₉	#2000	1	2	yes	—
170	C₂×C₁₉	#2006	1	1	yes	characteristic
171	D₁₉	—	16	2	no	—
172	C₂²×Q₈	C₂²⋊D₁₉	1	2	yes	—
173	C₂²×D₄	—	38	2	no	—
174	C₂²×D₄	—	38	1	no	—
175	C₂×SD₁₆	—	38	8	no	—
176	C₂×SD₁₆	—	76	4	no	—
177	C₂×SD₁₆	—	76	4	no	—
178	C₂²×C₈	—	38	2	no	—
179	C₂²×C₈	—	38	1	no	—
180	#127	—	19	2	no	—
181	#127	—	38	2	no	—
182	#127	—	38	1	no	—
183	C₄×Q₈	—	2	2	no	—
184	C₄×Q₈	—	2	2	no	—
185	C₄×Q₈	—	2	2	no	—
186	C₄×Q₈	—	2	2	no	—
187	C₂×C₄⋊C₄	—	2	2	no	—
188	C₂×C₄⋊C₄	—	2	2	no	—
189	C₂×C₄⋊C₄	—	2	2	no	—
190	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
191	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
192	C₂×C₄²	—	2	2	no	—
193	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
194	C₄⋊C₈	—	19	4	no	—
195	C₄⋊C₈	—	38	2	no	—
196	#102	—	38	8	no	—
197	#102	—	76	4	no	—
198	C₄×C₈	—	38	2	no	—
199	#95	—	2	4	no	—
200	#95	—	2	2	no	—
201	C₁₉	#10230	1	1	yes	characteristic, complemented, Sylow
202	C₂⁴	—	76	1	no	—
203	C₂×Q₈	—	2	2	no	—
204	C₂×Q₈	—	2	2	no	—
205	C₂×Q₈	—	2	2	no	—
206	C₂×Q₈	—	2	2	no	—
207	C₂×Q₈	—	2	2	no	—
208	C₂×Q₈	#64527	1	4	yes	complemented
209	C₂×D₄	—	38	4	no	—
210	C₂×D₄	—	38	2	no	—
211	C₂×D₄	—	76	2	no	—
212	C₂×D₄	—	76	2	no	—
213	C₂×D₄	—	76	2	no	—
214	C₂×D₄	—	76	1	no	—
215	C₂×D₄	—	76	2	no	—
216	C₂×D₄	—	76	2	no	—
217	C₂×D₄	—	76	2	no	—
218	C₂×D₄	—	76	2	no	—
219	C₂²×C₄	—	2	2	no	—
220	C₂²×C₄	—	2	2	no	—
221	C₂²×C₄	—	2	2	no	—
222	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
223	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
224	SD₁₆	—	76	16	no	—
225	C₂×C₈	—	38	2	no	—
226	C₂×C₈	—	38	4	no	—
227	C₂×C₈	—	76	1	no	—
228	C₂×C₈	—	76	1	no	—
229	C₂×C₈	—	76	2	no	—
230	C₂×C₈	—	76	2	no	—
231	C₄⋊C₄	—	2	2	no	—
232	C₄⋊C₄	—	2	2	no	—
233	C₄⋊C₄	—	4	2	no	—
234	C₄⋊C₄	—	4	2	no	—
235	C₄⋊C₄	—	4	2	no	—
236	C₄⋊C₄	—	4	2	no	—
237	C₄⋊C₄	—	4	2	no	—
238	C₄⋊C₄	—	8	2	no	—
239	C₄²	—	4	2	no	—
240	C₄²	—	4	2	no	—
241	C₄²	D₄×D₁₉	1	1	yes	characteristic
242	C₄²	D₄×D₁₉	1	2	yes	—
243	C₄²	#64543	1	1	yes	characteristic
244	C₂³	—	76	2	no	—
245	C₂³	—	152	2	no	—
246	C₂³	—	152	2	no	—
247	C₂³	—	152	1	no	—
248	C₂³	—	152	1	no	—
249	C₂³	#10597399	1	1	yes	characteristic
250	Q₈	—	2	4	no	—
251	Q₈	—	2	4	no	—
252	Q₈	—	4	2	no	—
253	Q₈	—	4	2	no	—
254	D₄	—	76	4	no	—
255	D₄	—	76	4	no	—
256	D₄	—	76	4	no	—
257	D₄	—	152	2	no	—
258	D₄	—	152	2	no	—
259	D₄	—	152	2	no	—
260	C₂×C₄	—	2	1	no	—
261	C₂×C₄	—	2	1	no	—
262	C₂×C₄	—	2	4	no	—
263	C₂×C₄	—	4	2	no	—
264	C₂×C₄	—	4	2	no	—
265	C₂×C₄	—	4	4	no	—
266	C₂×C₄	—	4	2	no	—
267	C₂×C₄	—	4	2	no	—
268	C₂×C₄	—	4	2	no	—
269	C₂×C₄	—	4	2	no	—
270	C₂×C₄	#10597383	1	2	yes	—
271	C₂×C₄	#10597384	1	1	yes	characteristic
272	C₂×C₄	#10597385	1	2	yes	—
273	C₂×C₄	#10597386	1	1	yes	characteristic
274	C₂×C₄	C₂×#64527	1	2	yes	—
275	C₂×C₄	#10597388	1	2	yes	—
276	C₂×C₄	#10597395	1	2	yes	—
277	C₂×C₄	#10597396	1	2	yes	—
278	C₈	—	76	2	no	—
279	C₈	—	76	4	no	—
280	C₂²	—	304	1	no	—
281	C₂²	—	304	1	no	—
282	C₂²	—	304	2	no	—
283	C₂²	—	152	4	no	—
284	C₂²	—	152	2	no	—
285	C₂²	#11926452	1	1	yes	characteristic
286	C₂²	#11926683	1	2	yes	—
287	C₂²	#11926689	1	2	yes	—
288	C₂²	#11926712	1	1	yes	characteristic
289	C₂²	#11926717	1	1	yes	characteristic
290	C₄	—	2	1	no	—
291	C₄	—	2	1	no	—
292	C₄	—	4	4	no	—
293	C₄	—	8	2	no	—
294	C₄	—	8	2	no	—
295	C₄	#11926694	1	2	yes	—
296	C₄	#11926704	1	2	yes	—
297	C₄	#11926775	1	2	yes	—
298	C₄	#11926792	1	2	yes	—
299	C₂	—	304	2	no	—
300	C₂	#14562694	1	1	yes	characteristic
301	C₂	#14562713	1	1	yes	characteristic
302	C₂	#14562731	1	2	yes	—
303	C₂	#14564636	1	2	yes	—
304	C₂	#14564677	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11926744

C₂

yes

maximal

#14564440

C₂

yes

maximal, characteristic

C₂×Q₈⋊(C₁₉⋊C₈)

C₂

yes

maximal, complemented

#14561518

C₂

yes

maximal, characteristic, complemented

C₁₉×#2582

C₂

yes

maximal, characteristic, complemented

C₂²×#64527

—

C₂×#10597320

C₂²

yes

characteristic

#11926744

—

#11926744

—

C₂×C₄⋊(C₁₉⋊C₈)

C₂²

yes

—

C₂×#10597266

—

C₂×#10597266

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

characteristic

Q₈⋊(C₁₉⋊C₈)

—

C₂×C₄×Q₈×C₁₉

C₂²

yes

—

C₁₉×#398

—

C₁₉×#391

—

C₁₉×#389

—

C₁₉×#384

C₂²

yes

characteristic

C₂²×Q₈×C₁₉

D₄

yes

—

C₂²×D₇₆

—

C₂²×D₇₆

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

—

—

—

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

—

#10597320

—

#10597320

—

#10597320

D₄

yes

—

C₁₉×#95

—

C₁₉×#95

—

#10597266

—

#10597266

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

C₄×C₁₉⋊C₈

—

C₂³×D₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

SD₁₆

yes

complemented

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

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

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

characteristic

#64527

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

100

Q₈×C₁₉

—

101

Q₈×C₁₉

—

102

C₂×C₄×C₁₉

—

103

C₂×C₄×C₁₉

—

104

C₂×C₄×C₁₉

—

105

C₂×C₄×C₁₉

—

106

C₂×C₄×C₁₉

—

107

C₂×C₄×C₁₉

—

108

C₂×C₄×C₁₉

—

109

C₂×C₄×C₁₉

—

110

C₂×C₄×C₁₉

—

111

C₂×C₄×C₁₉

—

112

C₂×C₄×C₁₉

#120

yes

—

113

C₂×C₄×C₁₉

#121

yes

characteristic

114

C₂×C₄×C₁₉

#121

yes

—

115

C₂×C₄×C₁₉

#127

yes

characteristic

116

C₂×C₄×C₁₉

C₂×SD₁₆

yes

—

117

C₂×C₄×C₁₉

#135

yes

—

118

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

119

C₂×C₄×C₁₉

#137

yes

—

120

D₇₆

—

121

D₇₆

—

122

D₇₆

—

123

D₇₆

—

124

D₇₆

—

125

D₇₆

—

126

C₁₉⋊C₈

—

127

C₁₉⋊C₈

—

128

C₂×#460

—

129

#2582

D₁₉

yes

characteristic, complemented

130

#1957

—

131

C₂×Q₈⋊C₈

—

132

#1296

—

133

C₂²×C₁₉

#392

yes

characteristic

134

C₂²×C₁₉

#448

yes

—

135

C₂²×C₁₉

#449

yes

—

136

C₂²×C₁₉

#453

yes

characteristic

137

C₂²×C₁₉

#454

yes

characteristic

138

C₂×D₁₉

—

139

C₂×D₁₉

—

140

C₂×D₁₉

—

141

C₂×D₁₉

—

142

C₂×D₁₉

—

143

C₄×C₁₉

—

144

C₄×C₁₉

—

145

C₄×C₁₉

—

146

C₄×C₁₉

—

147

C₄×C₁₉

—

148

C₄×C₁₉

#450

yes

—

149

C₄×C₁₉

#452

yes

—

150

C₄×C₁₉

#465

yes

—

151

C₄×C₁₉

#468

yes

—

152

C₂²×SD₁₆

—

153

C₂×#127

—

154

C₂×C₄×Q₈

C₂×D₁₉

yes

—

155

#460

—

156

#460

—

157

C₂×C₄⋊C₈

—

158

C₂×#102

—

159

C₂×#102

—

160

C₂×C₄×C₈

—

161

#398

—

162

#391

—

163

#389

—

164

#384

C₂×D₁₉

yes

characteristic

165

Q₈⋊C₈

—

166

C₂×C₁₉

#1620

yes

characteristic

167

C₂×C₁₉

#1623

yes

characteristic

168

C₂×C₁₉

#1626

yes

—

169

C₂×C₁₉

#2000

yes

—

170

C₂×C₁₉

#2006

yes

characteristic

171

D₁₉

—

172

C₂²×Q₈

C₂²⋊D₁₉

yes

—

173

C₂²×D₄

—

174

C₂²×D₄

—

175

C₂×SD₁₆

—

176

C₂×SD₁₆

—

177

C₂×SD₁₆

—

178

C₂²×C₈

—

179

C₂²×C₈

—

180

#127

—

181

#127

—

182

#127

—

183

C₄×Q₈

—

184

C₄×Q₈

—

185

C₄×Q₈

—

186

C₄×Q₈

—

187

C₂×C₄⋊C₄

—

188

C₂×C₄⋊C₄

—

189

C₂×C₄⋊C₄

—

190

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

—

191

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

—

192

C₂×C₄²

—

193

C₂×C₄²

C₂²×D₁₉

yes

characteristic

194

C₄⋊C₈

—

195

C₄⋊C₈

—

196

#102

—

197

#102

—

198

C₄×C₈

—

199

#95

—

200

#95

—

201

C₁₉

#10230

yes

characteristic, complemented, Sylow

202

C₂⁴

—

203

C₂×Q₈

—

204

C₂×Q₈

—

205

C₂×Q₈

—

206

C₂×Q₈

—

207

C₂×Q₈

—

208

C₂×Q₈

#64527

yes

complemented

209

C₂×D₄

—

210

C₂×D₄

—

211

C₂×D₄

—

212

C₂×D₄

—

213

C₂×D₄

—

214

C₂×D₄

—

215

C₂×D₄

—

216

C₂×D₄

—

217

C₂×D₄

—

218

C₂×D₄

—

219

C₂²×C₄

—

220

C₂²×C₄

—

221

C₂²×C₄

—

222

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

223

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

224

SD₁₆

—

225

C₂×C₈

—

226

C₂×C₈

—

227

C₂×C₈

—

228

C₂×C₈

—

229

C₂×C₈

—

230

C₂×C₈

—

231

C₄⋊C₄

—

232

C₄⋊C₄

—

233

C₄⋊C₄

—

234

C₄⋊C₄

—

235

C₄⋊C₄

—

236

C₄⋊C₄

—

237

C₄⋊C₄

—

238

C₄⋊C₄

—

239

C₄²

—

240

C₄²

—

241

C₄²

D₄×D₁₉

yes

characteristic

242

C₄²

D₄×D₁₉

yes

—

243

C₄²

#64543

yes

characteristic

244

C₂³

—

245

C₂³

—

152

—

246

C₂³

—

152

—

247

C₂³

—

152

—

248

C₂³

—

152

—

249

C₂³

#10597399

yes

characteristic

250

Q₈

—

251

Q₈

—

252

Q₈

—

253

Q₈

—

254

D₄

—

255

D₄

—

256

D₄

—

257

D₄

—

152

—

258

D₄

—

152

—

259

D₄

—

152

—

260

C₂×C₄

—

261

C₂×C₄

—

262

C₂×C₄

—

263

C₂×C₄

—

264

C₂×C₄

—

265

C₂×C₄

—

266

C₂×C₄

—

267

C₂×C₄

—

268

C₂×C₄

—

269

C₂×C₄

—

270

C₂×C₄

#10597383

yes

—

271

C₂×C₄

#10597384

yes

characteristic

272

C₂×C₄

#10597385

yes

—

273

C₂×C₄

#10597386

yes

characteristic

274

C₂×C₄

C₂×#64527

yes

—

275

C₂×C₄

#10597388

yes

—

276

C₂×C₄

#10597395

yes

—

277

C₂×C₄

#10597396

yes

—

278

C₈

—

279

C₈

—

280

C₂²

—

304

—

281

C₂²

—

304

—

282

C₂²

—

304

—

283

C₂²

—

152

—

284

C₂²

—

152

—

285

C₂²

#11926452

yes

characteristic

286

C₂²

#11926683

yes

—

287

C₂²

#11926689

yes

—

288

C₂²

#11926712

yes

characteristic

289

C₂²

#11926717

yes

characteristic

290

C₄

—

291

C₄

—

292

C₄

—

293

C₄

—

294

C₄

—

295

C₄

#11926694

yes

—

296

C₄

#11926704

yes

—

297

C₄

#11926775

yes

—

298

C₄

#11926792

yes

—

299

C₂

—

304

—

300

C₂

#14562694

yes

characteristic

301

C₂

#14562713

yes

characteristic

302

C₂

#14562731

yes

—

303

C₂

#14564636

yes

—

304

C₂

#14564677

yes

characteristic

	subgroup	G/H
center	C₂³	#10597399
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2582	C₂
socle	C₂³×C₁₉	#120
prime radical	C₂×#10597320	C₂²
hypercenter	#2582	D₁₉
hypocenter	C₁₉	#10230
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2582

subgroup

G/H

center

C₂³

#10597399

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#2582

C₂

C₂³×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2582

N	H ≅ G/N	type
3. C₂×Q₈⋊(C₁₉⋊C₈)	C₂	semidirect
4. #14561518	C₂	semidirect
5. C₁₉×#2582	C₂	semidirect
55. C₂×Q₈×C₁₉	SD₁₆	semidirect
129. #2582	D₁₉	semidirect
201. C₁₉	#10230	semidirect
208. C₂×Q₈	#64527	semidirect

H ≅ G/N

type

3. C₂×Q₈⋊(C₁₉⋊C₈)

C₂

semidirect

4. #14561518

C₂

semidirect

5. C₁₉×#2582

C₂

semidirect

55. C₂×Q₈×C₁₉

SD₁₆

semidirect

129. #2582

D₁₉

semidirect

201. C₁₉

#10230

semidirect

208. C₂×Q₈

#64527

semidirect

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

subgroup	index
C₂×#11926744	2
#14564440	2
C₂×Q₈⋊(C₁₉⋊C₈)	2
#14561518	2
C₁₉×#2582	2
#10230	19

subgroup

index

C₂×Q₈⋊(C₁₉⋊C₈)

C₁₉×#2582

Subgroups — #18084848

Conjugacy classes of subgroups

Complements

Maximal subgroups