Group #33003359 — subgroups

Subgroups — #33003359

Order 18688.

506 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 143 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	C₂²×#14556531	C₂	1	1	yes	maximal, characteristic
2	C₂×#17988828	C₂	1	1	yes	maximal, characteristic
3	C₂×#17988390	C₂	1	2	yes	maximal, complemented
4	#22608022	C₂	1	2	yes	maximal, complemented
5	C₇₃×#1808	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₂₉₂	C₂²	1	1	yes	characteristic
7	C₂×#14556570	—	2	1	no	—
8	C₂×#14556531	—	2	4	no	—
9	C₂×#14556531	—	2	2	no	—
10	C₂²×#11924003	C₂²	1	2	yes	—
11	#17988828	—	2	2	no	—
12	#17988828	C₄	1	4	yes	complemented
13	C₂×#14556525	C₂²	1	1	yes	characteristic
14	C₂×#14556516	—	2	1	no	—
15	#17988390	—	2	4	no	—
16	C₂³×C₈×C₇₃	C₂²	1	1	yes	characteristic
17	C₂×#107×C₇₃	C₂²	1	2	yes	—
18	#380×C₇₃	—	2	1	no	—
19	#340×C₇₃	—	2	1	no	—
20	C₂²×Dic₁₄₆	—	2	1	no	—
21	C₂×Dic₂₉₂	—	2	2	no	—
22	C₂×Dic₂₉₂	—	2	1	no	—
23	C₂×Dic₂₉₂	—	2	2	no	—
24	C₂×Dic₂₉₂	C₂×C₄	1	2	yes	—
25	#14556570	—	2	4	no	—
26	#14556570	—	4	2	no	—
27	C₂×C₄⋊Dic₇₃	—	2	1	no	—
28	C₂×#11924007	—	4	1	no	—
29	C₂×C₂²⋊Dic₇₃	—	4	1	no	—
30	#14556531	—	2	8	no	—
31	C₂×#11924003	—	2	2	no	—
32	C₂×#11924003	—	2	2	no	—
33	C₂×#11924003	D₄	1	4	yes	—
34	#14556525	—	2	1	no	—
35	#14556525	C₂×C₄	1	2	yes	—
36	#14556516	—	2	4	no	—
37	C₂³×C₄×C₇₃	D₄	1	1	yes	characteristic
38	C₂²×C₈×C₇₃	—	2	2	no	—
39	C₂²×C₈×C₇₃	—	2	2	no	—
40	C₂²×C₈×C₇₃	C₂×C₄	1	2	yes	—
41	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
42	C₂²×C₈×C₇₃	D₄	1	2	yes	—
43	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
44	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
45	C₂×C₂²⋊C₄×C₇₃	—	4	1	no	—
46	#107×C₇₃	—	2	2	no	—
47	#107×C₇₃	—	2	2	no	—
48	#95×C₇₃	—	4	1	no	—
49	C₂×Dic₁₄₆	—	2	2	no	—
50	C₂×Dic₁₄₆	—	4	2	no	—
51	C₂×Dic₁₄₆	—	4	2	no	—
52	C₂×Dic₁₄₆	—	4	1	no	—
53	C₂²×Dic₇₃	—	4	1	no	—
54	C₂²×Dic₇₃	—	4	1	no	—
55	Dic₂₉₂	—	2	4	no	—
56	Dic₂₉₂	—	4	1	no	—
57	Dic₂₉₂	—	4	1	no	—
58	C₄⋊Dic₇₃	—	2	2	no	—
59	C₄⋊Dic₇₃	—	4	1	no	—
60	#11924007	—	4	4	no	—
61	C₂²⋊Dic₇₃	—	4	4	no	—
62	#11924003	—	2	4	no	—
63	C₂⁴×C₇₃	D₈	1	1	yes	characteristic
64	C₂²×C₄×C₇₃	—	2	2	no	—
65	C₂²×C₄×C₇₃	—	2	2	no	—
66	C₂²×C₄×C₇₃	—	4	2	no	—
67	C₂²×C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
68	C₂²×C₄×C₇₃	D₈	1	1	yes	characteristic
69	C₂²×C₄×C₇₃	SD₁₆	1	2	yes	—
70	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
71	C₂×C₈×C₇₃	—	2	2	no	—
72	C₂×C₈×C₇₃	—	2	4	no	—
73	C₂×C₈×C₇₃	—	2	2	no	—
74	C₂×C₈×C₇₃	—	2	2	no	—
75	C₂×C₈×C₇₃	C₂²⋊C₄	1	2	yes	—
76	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
77	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
78	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
79	C₂×C₈×C₇₃	#41	1	2	yes	—
80	C₄⋊C₄×C₇₃	—	4	2	no	—
81	C₄⋊C₄×C₇₃	—	4	2	no	—
82	C₂²⋊C₄×C₇₃	—	8	2	no	—
83	C₂³×C₇₃	—	2	2	no	—
84	C₂³×C₇₃	—	2	1	no	—
85	C₂³×C₇₃	—	2	2	no	—
86	C₂³×C₇₃	—	2	1	no	—
87	C₂³×C₇₃	#102	1	2	yes	—
88	C₂³×C₇₃	C₂×D₈	1	1	yes	characteristic
89	C₂×C₄×C₇₃	—	2	2	no	—
90	C₂×C₄×C₇₃	—	2	2	no	—
91	C₂×C₄×C₇₃	—	2	2	no	—
92	C₂×C₄×C₇₃	—	2	4	no	—
93	C₂×C₄×C₇₃	—	8	2	no	—
94	C₂×C₄×C₇₃	—	8	2	no	—
95	C₂×C₄×C₇₃	—	8	2	no	—
96	C₂×C₄×C₇₃	#102	1	2	yes	—
97	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₄×C₇₃	#121	1	2	yes	—
99	C₂×C₄×C₇₃	C₂×SD₁₆	1	1	yes	characteristic
100	C₂×C₄×C₇₃	#135	1	2	yes	—
101	C₂×Dic₇₃	—	4	2	no	—
102	C₂×Dic₇₃	—	4	2	no	—
103	C₂×Dic₇₃	—	8	2	no	—
104	C₂×Dic₇₃	—	8	1	no	—
105	C₂×Dic₇₃	—	8	1	no	—
106	Dic₁₄₆	—	4	2	no	—
107	Dic₁₄₆	—	4	2	no	—
108	Dic₁₄₆	—	8	2	no	—
109	C₈×C₇₃	—	2	2	no	—
110	C₈×C₇₃	C₄×D₄	1	2	yes	—
111	C₈×C₇₃	#120	1	1	yes	characteristic
112	C₈×C₇₃	#123	1	1	yes	characteristic
113	C₂²×C₇₃	—	2	2	no	—
114	C₂²×C₇₃	—	2	2	no	—
115	C₂²×C₇₃	—	2	2	no	—
116	C₂²×C₇₃	—	4	2	no	—
117	C₂²×C₇₃	—	4	2	no	—
118	C₂²×C₇₃	C₂×#102	1	1	yes	characteristic
119	C₂²×C₇₃	#466	1	2	yes	—
120	C₂²×C₇₃	#509	1	1	yes	characteristic
121	C₂²×C₇₃	#510	1	2	yes	—
122	C₂²×C₇₃	#510	1	1	yes	characteristic
123	C₄×C₇₃	—	2	2	no	—
124	C₄×C₇₃	—	16	2	no	—
125	C₄×C₇₃	#386	1	1	yes	characteristic
126	C₄×C₇₃	#416	1	1	yes	characteristic
127	C₄×C₇₃	#465	1	2	yes	—
128	Dic₇₃	—	8	2	no	—
129	Dic₇₃	—	8	2	no	—
130	#13062	—	73	1	no	maximal, Sylow
131	C₂×C₇₃	—	4	2	no	—
132	C₂×C₇₃	#1893	1	1	yes	characteristic
133	C₂×C₇₃	#2139	1	1	yes	characteristic
134	C₂×C₇₃	#2141	1	1	yes	characteristic
135	C₂×C₇₃	#2219	1	2	yes	—
136	C₂×C₇₃	#2220	1	2	yes	—
137	C₂²×M₃₂	—	73	1	no	—
138	C₂×#467	—	73	1	no	—
139	C₂×#358	—	73	2	no	—
140	#1808	D₇₃	1	1	yes	characteristic
141	#1380	—	73	2	no	—
142	C₇₃	#13062	1	1	yes	characteristic, complemented, Sylow
143	C₂²×Q₁₆	—	73	1	no	—
144	C₂³×C₈	C₂×D₇₃	1	1	yes	characteristic
145	C₂×C₂²⋊Q₈	—	146	1	no	—
146	C₂×M₃₂	—	146	4	no	—
147	C₂×M₃₂	—	146	2	no	—
148	C₂²×C₁₆	—	73	2	no	—
149	#467	—	73	4	no	—
150	#467	—	146	2	no	—
151	C₂×#107	—	73	1	no	—
152	C₂×#107	C₂×D₇₃	1	2	yes	—
153	C₂×#103	—	146	1	no	—
154	#380	—	2	1	no	—
155	#358	—	146	4	no	—
156	#340	—	2	1	no	—
157	C₂²×Q₈	—	146	1	no	—
158	C₂³×C₄	C₂²⋊D₇₃	1	1	yes	characteristic
159	C₂×Q₁₆	—	73	2	no	—
160	C₂×Q₁₆	—	146	2	no	—
161	C₂×Q₁₆	—	146	1	no	—
162	C₂×Q₁₆	—	146	2	no	—
163	C₂²×C₈	—	2	2	no	—
164	C₂²×C₈	—	2	2	no	—
165	C₂²×C₈	C₄×D₇₃	1	2	yes	—
166	C₂²×C₈	D₂₉₂	1	2	yes	—
167	C₂²×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
168	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
169	C₂²⋊Q₈	—	292	2	no	—
170	C₂²⋊Q₈	—	146	4	no	—
171	C₂×C₄⋊C₄	—	2	2	no	—
172	C₂×C₄⋊C₄	—	292	1	no	—
173	C₂×C₄⋊C₄	—	146	1	no	—
174	C₂×C₂²⋊C₄	—	4	1	no	—
175	C₂×C₂²⋊C₄	—	292	1	no	—
176	M₃₂	—	146	8	no	—
177	C₂×C₁₆	—	73	4	no	—
178	C₂×C₁₆	—	146	2	no	—
179	C₂×C₁₆	—	146	2	no	—
180	#107	—	2	2	no	—
181	#107	—	2	2	no	—
182	#107	—	73	2	no	—
183	#107	—	146	1	no	—
184	#103	—	146	4	no	—
185	#95	—	4	1	no	—
186	C₂⁴	#11924013	1	1	yes	characteristic
187	C₂×Q₈	—	292	1	no	—
188	C₂×Q₈	—	292	2	no	—
189	C₂×Q₈	—	292	2	no	—
190	C₂×Q₈	—	146	2	no	—
191	C₂²×C₄	—	2	2	no	—
192	C₂²×C₄	—	2	2	no	—
193	C₂²×C₄	—	4	2	no	—
194	C₂²×C₄	—	292	1	no	—
195	C₂²×C₄	—	292	1	no	—
196	C₂²×C₄	#11924005	1	2	yes	—
197	C₂²×C₄	#11924013	1	1	yes	characteristic
198	C₂²×C₄	#11924015	1	2	yes	—
199	C₂²×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
200	Q₁₆	—	292	1	no	—
201	Q₁₆	—	292	1	no	—
202	Q₁₆	—	146	4	no	—
203	C₂×C₈	—	2	2	no	—
204	C₂×C₈	—	2	4	no	—
205	C₂×C₈	—	2	2	no	—
206	C₂×C₈	—	2	2	no	—
207	C₂×C₈	#11924005	1	2	yes	—
208	C₂×C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
209	C₂×C₈	D₄×D₇₃	1	2	yes	—
210	C₂×C₈	C₂×D₂₉₂	1	1	yes	characteristic
211	C₂×C₈	#11924027	1	2	yes	—
212	C₄⋊C₄	—	4	2	no	—
213	C₄⋊C₄	—	4	2	no	—
214	C₄⋊C₄	—	292	4	no	—
215	C₄⋊C₄	—	292	1	no	—
216	C₄⋊C₄	—	146	2	no	—
217	C₂²⋊C₄	—	8	2	no	—
218	C₂²⋊C₄	—	292	4	no	—
219	C₁₆	—	146	4	no	—
220	C₂³	—	2	1	no	—
221	C₂³	—	2	2	no	—
222	C₂³	—	2	1	no	—
223	C₂³	—	2	2	no	—
224	C₂³	#14556511	1	2	yes	—
225	C₂³	C₂×#11924013	1	1	yes	characteristic
226	Q₈	—	292	2	no	—
227	Q₈	—	292	2	no	—
228	Q₈	—	584	2	no	—
229	C₂×C₄	—	2	2	no	—
230	C₂×C₄	—	2	2	no	—
231	C₂×C₄	—	2	4	no	—
232	C₂×C₄	—	2	2	no	—
233	C₂×C₄	—	8	2	no	—
234	C₂×C₄	—	8	2	no	—
235	C₂×C₄	—	8	2	no	—
236	C₂×C₄	—	292	2	no	—
237	C₂×C₄	—	292	2	no	—
238	C₂×C₄	—	584	1	no	—
239	C₂×C₄	—	584	1	no	—
240	C₂×C₄	—	584	2	no	—
241	C₂×C₄	#14556511	1	2	yes	—
242	C₂×C₄	C₂×#11924005	1	1	yes	characteristic
243	C₂×C₄	#14556563	1	2	yes	—
244	C₂×C₄	C₂×#11924015	1	1	yes	characteristic
245	C₂×C₄	#14556611	1	2	yes	—
246	C₈	—	2	2	no	—
247	C₈	#14556551	1	2	yes	—
248	C₈	#14556561	1	1	yes	characteristic
249	C₈	#14556575	1	1	yes	characteristic
250	C₂²	—	2	2	no	—
251	C₂²	—	2	2	no	—
252	C₂²	—	2	2	no	—
253	C₂²	—	4	2	no	—
254	C₂²	—	4	2	no	—
255	C₂²	C₂×#14556511	1	1	yes	characteristic
256	C₂²	#17988821	1	2	yes	—
257	C₂²	#17989023	1	1	yes	characteristic
258	C₂²	#17989027	1	2	yes	—
259	C₂²	#17989028	1	1	yes	characteristic
260	C₄	—	2	2	no	—
261	C₄	—	16	2	no	—
262	C₄	—	584	2	no	—
263	C₄	—	584	2	no	—
264	C₄	#17988464	1	1	yes	characteristic
265	C₄	#17988581	1	1	yes	characteristic
266	C₄	#17988818	1	2	yes	—
267	C₂	—	4	2	no	—
268	C₂	#22610357	1	1	yes	characteristic
269	C₂	#22611641	1	1	yes	characteristic
270	C₂	#22611650	1	1	yes	characteristic
271	C₂	#22612037	1	2	yes	—
272	C₂	#22612042	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#14556531

C₂

yes

maximal, characteristic

C₂×#17988828

C₂

yes

maximal, characteristic

C₂×#17988390

C₂

yes

maximal, complemented

#22608022

C₂

yes

maximal, complemented

C₇₃×#1808

C₂

yes

maximal, characteristic

C₂²×Dic₂₉₂

C₂²

yes

—

—

—

C₂²

yes

—

#17988828

—

#17988828

C₄

yes

complemented

C₂×#14556525

C₂²

yes

characteristic

C₂×#14556516

—

#17988390

—

C₂³×C₈×C₇₃

C₂²

yes

characteristic

C₂×#107×C₇₃

C₂²

yes

—

#380×C₇₃

—

#340×C₇₃

—

C₂²×Dic₁₄₆

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

C₂×C₄

yes

—

#14556570

—

#14556570

—

C₂×C₄⋊Dic₇₃

—

C₂×#11924007

—

C₂×C₂²⋊Dic₇₃

—

—

—

—

D₄

yes

—

#14556525

—

#14556525

C₂×C₄

yes

—

#14556516

—

C₂³×C₄×C₇₃

D₄

yes

characteristic

C₂²×C₈×C₇₃

—

C₂²×C₈×C₇₃

—

C₂²×C₈×C₇₃

C₂×C₄

yes

—

C₂²×C₈×C₇₃

D₄

yes

characteristic

C₂²×C₈×C₇₃

D₄

yes

—

C₂²×C₈×C₇₃

C₂³

yes

characteristic

C₂×C₄⋊C₄×C₇₃

—

C₂×C₂²⋊C₄×C₇₃

—

#107×C₇₃

—

#107×C₇₃

—

#95×C₇₃

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

—

Dic₂₉₂

—

Dic₂₉₂

—

Dic₂₉₂

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

#11924007

—

C₂²⋊Dic₇₃

—

#11924003

—

C₂⁴×C₇₃

D₈

yes

characteristic

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₇₃

D₈

yes

characteristic

C₂²×C₄×C₇₃

SD₁₆

yes

—

C₂²×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₂²⋊C₄

yes

—

C₂×C₈×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₇₃

C₂×D₄

yes

—

C₂×C₈×C₇₃

C₂×D₄

yes

characteristic

C₂×C₈×C₇₃

#41

yes

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

#102

yes

—

C₂³×C₇₃

C₂×D₈

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

#102

yes

—

C₂×C₄×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

#121

yes

—

C₂×C₄×C₇₃

C₂×SD₁₆

yes

characteristic

100

C₂×C₄×C₇₃

#135

yes

—

101

C₂×Dic₇₃

—

102

C₂×Dic₇₃

—

103

C₂×Dic₇₃

—

104

C₂×Dic₇₃

—

105

C₂×Dic₇₃

—

106

Dic₁₄₆

—

107

Dic₁₄₆

—

108

Dic₁₄₆

—

109

C₈×C₇₃

—

110

C₈×C₇₃

C₄×D₄

yes

—

111

C₈×C₇₃

#120

yes

characteristic

112

C₈×C₇₃

#123

yes

characteristic

113

C₂²×C₇₃

—

114

C₂²×C₇₃

—

115

C₂²×C₇₃

—

116

C₂²×C₇₃

—

117

C₂²×C₇₃

—

118

C₂²×C₇₃

C₂×#102

yes

characteristic

119

C₂²×C₇₃

#466

yes

—

120

C₂²×C₇₃

#509

yes

characteristic

121

C₂²×C₇₃

#510

yes

—

122

C₂²×C₇₃

#510

yes

characteristic

123

C₄×C₇₃

—

124

C₄×C₇₃

—

125

C₄×C₇₃

#386

yes

characteristic

126

C₄×C₇₃

#416

yes

characteristic

127

C₄×C₇₃

#465

yes

—

128

Dic₇₃

—

129

Dic₇₃

—

130

#13062

—

maximal, Sylow

131

C₂×C₇₃

—

132

C₂×C₇₃

#1893

yes

characteristic

133

C₂×C₇₃

#2139

yes

characteristic

134

C₂×C₇₃

#2141

yes

characteristic

135

C₂×C₇₃

#2219

yes

—

136

C₂×C₇₃

#2220

yes

—

137

C₂²×M₃₂

—

138

C₂×#467

—

139

C₂×#358

—

140

#1808

D₇₃

yes

characteristic

141

#1380

—

142

C₇₃

#13062

yes

characteristic, complemented, Sylow

143

C₂²×Q₁₆

—

144

C₂³×C₈

C₂×D₇₃

yes

characteristic

145

C₂×C₂²⋊Q₈

—

146

—

146

C₂×M₃₂

—

146

—

147

C₂×M₃₂

—

146

—

148

C₂²×C₁₆

—

149

#467

—

150

#467

—

146

—

151

C₂×#107

—

152

C₂×#107

C₂×D₇₃

yes

—

153

C₂×#103

—

146

—

154

#380

—

155

#358

—

146

—

156

#340

—

157

C₂²×Q₈

—

146

—

158

C₂³×C₄

C₂²⋊D₇₃

yes

characteristic

159

C₂×Q₁₆

—

160

C₂×Q₁₆

—

146

—

161

C₂×Q₁₆

—

146

—

162

C₂×Q₁₆

—

146

—

163

C₂²×C₈

—

164

C₂²×C₈

—

165

C₂²×C₈

C₄×D₇₃

yes

—

166

C₂²×C₈

D₂₉₂

yes

—

167

C₂²×C₈

C₂²⋊D₇₃

yes

characteristic

168

C₂²×C₈

C₂²×D₇₃

yes

characteristic

169

C₂²⋊Q₈

—

292

—

170

C₂²⋊Q₈

—

146

—

171

C₂×C₄⋊C₄

—

172

C₂×C₄⋊C₄

—

292

—

173

C₂×C₄⋊C₄

—

146

—

174

C₂×C₂²⋊C₄

—

175

C₂×C₂²⋊C₄

—

292

—

176

M₃₂

—

146

—

177

C₂×C₁₆

—

178

C₂×C₁₆

—

146

—

179

C₂×C₁₆

—

146

—

180

#107

—

181

#107

—

182

#107

—

183

#107

—

146

—

184

#103

—

146

—

185

#95

—

186

C₂⁴

#11924013

yes

characteristic

187

C₂×Q₈

—

292

—

188

C₂×Q₈

—

292

—

189

C₂×Q₈

—

292

—

190

C₂×Q₈

—

146

—

191

C₂²×C₄

—

192

C₂²×C₄

—

193

C₂²×C₄

—

194

C₂²×C₄

—

292

—

195

C₂²×C₄

—

292

—

196

C₂²×C₄

#11924005

yes

—

197

C₂²×C₄

#11924013

yes

characteristic

198

C₂²×C₄

#11924015

yes

—

199

C₂²×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

200

Q₁₆

—

292

—

201

Q₁₆

—

292

—

202

Q₁₆

—

146

—

203

C₂×C₈

—

204

C₂×C₈

—

205

C₂×C₈

—

206

C₂×C₈

—

207

C₂×C₈

#11924005

yes

—

208

C₂×C₈

C₂×C₄×D₇₃

yes

characteristic

209

C₂×C₈

D₄×D₇₃

yes

—

210

C₂×C₈

C₂×D₂₉₂

yes

characteristic

211

C₂×C₈

#11924027

yes

—

212

C₄⋊C₄

—

213

C₄⋊C₄

—

214

C₄⋊C₄

—

292

—

215

C₄⋊C₄

—

292

—

216

C₄⋊C₄

—

146

—

217

C₂²⋊C₄

—

218

C₂²⋊C₄

—

292

—

219

C₁₆

—

146

—

220

C₂³

—

221

C₂³

—

222

C₂³

—

223

C₂³

—

224

C₂³

#14556511

yes

—

225

C₂³

C₂×#11924013

yes

characteristic

226

Q₈

—

292

—

227

Q₈

—

292

—

228

Q₈

—

584

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

—

292

—

237

C₂×C₄

—

292

—

238

C₂×C₄

—

584

—

239

C₂×C₄

—

584

—

240

C₂×C₄

—

584

—

241

C₂×C₄

#14556511

yes

—

242

C₂×C₄

C₂×#11924005

yes

characteristic

243

C₂×C₄

#14556563

yes

—

244

C₂×C₄

C₂×#11924015

yes

characteristic

245

C₂×C₄

#14556611

yes

—

246

C₈

—

247

C₈

#14556551

yes

—

248

C₈

#14556561

yes

characteristic

249

C₈

#14556575

yes

characteristic

250

C₂²

—

251

C₂²

—

252

C₂²

—

253

C₂²

—

254

C₂²

—

255

C₂²

C₂×#14556511

yes

characteristic

256

C₂²

#17988821

yes

—

257

C₂²

#17989023

yes

characteristic

258

C₂²

#17989027

yes

—

259

C₂²

#17989028

yes

characteristic

260

C₄

—

261

C₄

—

262

C₄

—

584

—

263

C₄

—

584

—

264

C₄

#17988464

yes

characteristic

265

C₄

#17988581

yes

characteristic

266

C₄

#17988818

yes

—

267

C₂

—

268

C₂

#22610357

yes

characteristic

269

C₂

#22611641

yes

characteristic

270

C₂

#22611650

yes

characteristic

271

C₂

#22612037

yes

—

272

C₂

#22612042

yes

—

	subgroup	G/H
center	C₂³	C₂×#11924013
commutator	C₂×C₈×C₇₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₇₃
Fitting	C₇₃×#1808	C₂
socle	C₂³×C₇₃	C₂×D₈
prime radical	C₂⁴×C₇₃	D₈
cosocle	C₂²×C₈×C₇₃	C₂³
hypercenter	#1808	D₇₃
hypocenter	C₇₃	#13062
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ #1808

subgroup

G/H

center

C₂³

C₂×#11924013

commutator

C₂×C₈×C₇₃

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₇₃

Fitting

C₇₃×#1808

C₂

socle

C₂³×C₇₃

C₂×D₈

prime radical

C₂⁴×C₇₃

D₈

cosocle

C₂²×C₈×C₇₃

C₂³

D₇₃

C₇₃

G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ #1808

N	H ≅ G/N	type
3. C₂×#17988390	C₂	semidirect
4. #22608022	C₂	semidirect
12. #17988828	C₄	semidirect
142. C₇₃	#13062	semidirect

H ≅ G/N

type

3. C₂×#17988390

C₂

semidirect

4. #22608022

C₂

semidirect

12. #17988828

C₄

semidirect

142. C₇₃

#13062

semidirect

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

subgroup	index
C₂²×#14556531	2
C₂×#17988828	2
C₂×#17988390	2
#22608022	2
C₇₃×#1808	2
#13062	73

subgroup

index

C₇₃×#1808

Subgroups — #33003359

Conjugacy classes of subgroups

Complements

Maximal subgroups