Group #33004849 — subgroups

Subgroups — #33004849

Order 18688.

650 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 650 conjugacy classes of subgroups — too many to draw. Only its 105 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×#17989023	C₂	1	2	yes	maximal, complemented
2	C₂×#17988400	C₂	1	2	yes	maximal, complemented
3	#22610819	C₂	1	1	yes	maximal, characteristic, complemented
4	#22608013	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#493×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#14556613	C₂²	1	1	yes	characteristic
7	#17989023	—	2	4	no	—
8	#17989023	—	2	4	no	—
9	C₂×#14556535	—	2	2	no	—
10	C₂×#14556532	—	2	2	no	—
11	C₂×#14556531	C₂²	1	2	yes	—
12	C₂×#14556527	C₂²	1	1	yes	characteristic
13	C₂×#14556519	—	2	1	no	—
14	#17988553	—	2	1	no	—
15	#17988400	—	2	4	no	—
16	C₂²×D₈×C₇₃	—	2	1	no	—
17	C₂²×D₈×C₇₃	C₂²	1	2	yes	—
18	C₂×#127×C₇₃	—	2	1	no	—
19	#493×C₇₃	—	2	4	no	—
20	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
21	C₂×#11924028	—	2	1	no	—
22	#14556613	—	2	2	no	—
23	#14556613	—	2	2	no	—
24	C₂×Dic₂₉₂	D₄	1	1	yes	characteristic, complemented
25	C₂×#11924017	—	2	1	no	—
26	C₂×D₅₈₄	D₄	1	1	yes	characteristic, complemented
27	C₂×#11924012	—	2	1	no	—
28	#14556535	—	2	8	no	—
29	#14556532	—	2	8	no	—
30	#14556531	—	2	2	no	—
31	#14556531	D₄	1	4	yes	complemented
32	C₂×#11924003	—	2	2	no	—
33	#14556527	—	2	2	no	—
34	#14556519	—	4	2	no	—
35	#14556503	—	4	2	no	—
36	C₂²×D₄×C₇₃	—	2	2	no	—
37	C₂²×D₄×C₇₃	—	4	2	no	—
38	C₂×D₈×C₇₃	—	2	4	no	—
39	C₂×D₈×C₇₃	—	2	2	no	—
40	C₂×D₈×C₇₃	—	2	2	no	—
41	C₂×D₈×C₇₃	—	2	2	no	—
42	C₂×D₈×C₇₃	—	2	2	no	—
43	C₂×D₈×C₇₃	—	2	2	no	—
44	C₂×D₈×C₇₃	—	4	2	no	—
45	C₂×D₈×C₇₃	—	4	2	no	—
46	C₂×D₈×C₇₃	D₄	1	4	yes	—
47	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
48	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
49	#127×C₇₃	—	2	4	no	—
50	#127×C₇₃	—	4	2	no	—
51	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
52	C₄×C₈×C₇₃	—	2	2	no	—
53	#11924028	—	4	1	no	—
54	#11924028	—	4	1	no	—
55	#11924028	—	4	1	no	—
56	#11924028	—	4	1	no	—
57	C₂×Dic₁₄₆	—	2	1	no	—
58	C₂×D₂₉₂	—	2	1	no	—
59	C₂×C₂²⋊D₇₃	—	4	1	no	—
60	C₂×C₄×D₇₃	—	4	1	no	—
61	Dic₂₉₂	—	2	2	no	—
62	#11924017	—	4	2	no	—
63	D₅₈₄	—	2	2	no	—
64	#11924012	—	4	1	no	—
65	#11924012	—	4	1	no	—
66	C₂×#10596831	—	4	1	no	—
67	#11924003	—	2	4	no	—
68	C₂⁴×C₇₃	—	4	2	no	—
69	C₂×D₄×C₇₃	—	2	4	no	—
70	C₂×D₄×C₇₃	—	4	8	no	—
71	C₂×D₄×C₇₃	—	4	2	no	—
72	C₂×D₄×C₇₃	—	4	2	no	—
73	C₂×D₄×C₇₃	—	4	2	no	—
74	C₂×D₄×C₇₃	—	4	2	no	—
75	C₂×D₄×C₇₃	—	4	2	no	—
76	C₂×D₄×C₇₃	—	8	8	no	—
77	C₂²×C₄×C₇₃	—	2	1	no	—
78	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
79	D₈×C₇₃	—	2	4	no	—
80	D₈×C₇₃	—	2	4	no	—
81	D₈×C₇₃	—	4	8	no	—
82	D₈×C₇₃	—	4	2	no	—
83	D₈×C₇₃	—	4	2	no	—
84	C₂×C₈×C₇₃	—	2	1	no	—
85	C₂×C₈×C₇₃	—	2	1	no	—
86	C₂×C₈×C₇₃	D₈	1	2	yes	—
87	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
88	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
89	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
90	C₂×C₈×C₇₃	#41	1	1	yes	characteristic
91	C₄²×C₇₃	—	2	1	no	—
92	C₄²×C₇₃	D₈	1	2	yes	—
93	C₂³×C₇₃	—	4	4	no	—
94	C₂³×C₇₃	—	8	8	no	—
95	C₂³×C₇₃	—	8	2	no	—
96	C₂³×C₇₃	—	8	2	no	—
97	C₂³×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
98	C₂²×D₇₃	—	4	1	no	—
99	D₄×C₇₃	—	4	4	no	—
100	D₄×C₇₃	—	4	4	no	—
101	D₄×C₇₃	—	8	16	no	—
102	D₄×C₇₃	—	8	2	no	—
103	D₄×C₇₃	—	8	2	no	—
104	C₂×C₄×C₇₃	—	2	4	no	—
105	C₂×C₄×C₇₃	—	2	2	no	—
106	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
107	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
108	C₂×C₄×C₇₃	#127	1	1	yes	characteristic
109	C₂×C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
110	C₂×C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
111	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
112	C₂²⋊D₇₃	—	8	1	no	—
113	C₂²⋊D₇₃	—	8	1	no	—
114	C₂×Dic₇₃	—	4	1	no	—
115	D₂₉₂	—	4	1	no	—
116	D₂₉₂	—	4	1	no	—
117	C₄×D₇₃	—	8	1	no	—
118	C₄×D₇₃	—	8	1	no	—
119	Dic₁₄₆	—	4	1	no	—
120	Dic₁₄₆	—	4	1	no	—
121	C₈×C₇₃	—	2	2	no	—
122	C₈×C₇₃	#120	1	2	yes	—
123	C₈×C₇₃	#121	1	2	yes	—
124	#10596831	—	8	1	no	—
125	C₂²×C₇₃	—	2	2	no	—
126	C₂²×C₇₃	—	8	8	no	—
127	C₂²×C₇₃	—	8	4	no	—
128	C₂²×C₇₃	—	16	4	no	—
129	C₂²×C₇₃	—	16	4	no	—
130	C₂²×C₇₃	#447	1	1	yes	characteristic
131	C₂²×C₇₃	#459	1	1	yes	characteristic
132	C₂²×C₇₃	#496	1	1	yes	characteristic
133	C₂×D₇₃	—	8	2	no	—
134	C₂×D₇₃	—	8	1	no	—
135	C₄×C₇₃	—	2	4	no	—
136	C₄×C₇₃	#392	1	1	yes	characteristic
137	C₄×C₇₃	#447	1	1	yes	characteristic
138	C₄×C₇₃	#459	1	1	yes	characteristic
139	C₄×C₇₃	#493	1	1	yes	characteristic
140	Dic₇₃	—	8	1	no	—
141	#13331	—	73	1	no	maximal, Sylow
142	C₂×C₇₃	—	2	1	no	—
143	C₂×C₇₃	—	2	1	no	—
144	C₂×C₇₃	—	16	4	no	—
145	C₂×C₇₃	#2011	1	1	yes	characteristic
146	C₂×C₇₃	#2213	1	2	yes	—
147	D₇₃	—	16	1	no	—
148	C₂×#509	—	73	2	no	—
149	C₂×#493	D₇₃	1	1	yes	characteristic, complemented
150	C₂×#361	—	73	2	no	—
151	#1974	—	73	1	no	—
152	#1376	—	73	1	no	—
153	C₇₃	#13331	1	1	yes	characteristic, complemented, Sylow
154	C₂×#135	—	73	1	no	—
155	C₂²×D₈	—	2	1	no	—
156	C₂²×D₈	C₂×D₇₃	1	2	yes	—
157	C₂×#127	—	2	1	no	—
158	#509	—	146	4	no	—
159	#509	—	146	4	no	—
160	C₂×SD₃₂	—	146	2	no	—
161	C₂×D₁₆	—	146	2	no	—
162	C₂×M₃₂	—	73	2	no	—
163	#493	—	2	4	no	—
164	C₂×#108	—	73	1	no	—
165	C₂×#104	—	146	1	no	—
166	#408	—	146	1	no	—
167	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
168	#361	—	146	4	no	—
169	C₂×#41	—	146	1	no	—
170	C₂²×D₄	—	2	2	no	—
171	C₂²×D₄	—	4	2	no	—
172	#135	—	146	2	no	—
173	#135	—	146	2	no	—
174	C₂×Q₁₆	—	73	1	no	—
175	C₂×SD₁₆	—	146	1	no	—
176	C₂×D₈	—	2	4	no	—
177	C₂×D₈	—	2	2	no	—
178	C₂×D₈	—	2	2	no	—
179	C₂×D₈	—	2	2	no	—
180	C₂×D₈	—	2	2	no	—
181	C₂×D₈	—	2	2	no	—
182	C₂×D₈	—	4	2	no	—
183	C₂×D₈	—	4	2	no	—
184	C₂×D₈	—	73	1	no	—
185	C₂×D₈	C₂²⋊D₇₃	1	4	yes	—
186	C₂×M₁₆	—	146	1	no	—
187	C₂²×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
188	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
189	#127	—	2	4	no	—
190	#127	—	4	2	no	—
191	C₂×C₄²	C₂²⋊D₇₃	1	1	yes	characteristic
192	SD₃₂	—	146	8	no	—
193	D₁₆	—	146	8	no	—
194	M₃₂	—	73	4	no	—
195	M₃₂	—	146	2	no	—
196	C₂×C₁₆	—	146	2	no	—
197	#108	—	146	2	no	—
198	#104	—	292	2	no	—
199	C₂²⋊C₈	—	292	2	no	—
200	C₄×C₈	—	2	2	no	—
201	C₂⁴	—	4	2	no	—
202	#41	—	292	1	no	—
203	#41	—	292	1	no	—
204	#41	—	292	1	no	—
205	#41	—	292	1	no	—
206	C₂×Q₈	—	146	1	no	—
207	C₂×D₄	—	2	4	no	—
208	C₂×D₄	—	4	8	no	—
209	C₂×D₄	—	4	2	no	—
210	C₂×D₄	—	4	2	no	—
211	C₂×D₄	—	4	2	no	—
212	C₂×D₄	—	4	2	no	—
213	C₂×D₄	—	4	2	no	—
214	C₂×D₄	—	8	8	no	—
215	C₂×D₄	—	292	1	no	—
216	C₂×D₄	—	146	1	no	—
217	C₂²×C₄	—	2	1	no	—
218	C₂²×C₄	—	292	1	no	—
219	C₂²×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
220	Q₁₆	—	146	2	no	—
221	SD₁₆	—	292	2	no	—
222	D₈	—	2	4	no	—
223	D₈	—	2	4	no	—
224	D₈	—	4	8	no	—
225	D₈	—	4	2	no	—
226	D₈	—	4	2	no	—
227	D₈	—	146	2	no	—
228	M₁₆	—	292	1	no	—
229	M₁₆	—	292	1	no	—
230	C₂×C₈	—	2	1	no	—
231	C₂×C₈	—	2	1	no	—
232	C₂×C₈	—	292	1	no	—
233	C₂×C₈	#11924013	1	2	yes	—
234	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
235	C₂×C₈	D₄×D₇₃	1	2	yes	—
236	C₂×C₈	C₂×C₂²⋊D₇₃	1	2	yes	—
237	C₂×C₈	#11924027	1	1	yes	characteristic
238	C₄²	—	2	1	no	—
239	C₄²	#11924013	1	2	yes	—
240	C₁₆	—	146	4	no	—
241	C₂³	—	4	4	no	—
242	C₂³	—	8	8	no	—
243	C₂³	—	8	2	no	—
244	C₂³	—	8	2	no	—
245	C₂³	—	292	1	no	—
246	C₂³	#14556617	1	1	yes	characteristic
247	Q₈	—	292	1	no	—
248	Q₈	—	292	1	no	—
249	D₄	—	4	4	no	—
250	D₄	—	4	4	no	—
251	D₄	—	8	16	no	—
252	D₄	—	8	2	no	—
253	D₄	—	8	2	no	—
254	D₄	—	292	1	no	—
255	D₄	—	292	1	no	—
256	D₄	—	584	1	no	—
257	D₄	—	584	1	no	—
258	C₂×C₄	—	2	4	no	—
259	C₂×C₄	—	2	2	no	—
260	C₂×C₄	—	292	1	no	—
261	C₂×C₄	—	584	1	no	—
262	C₂×C₄	—	584	1	no	—
263	C₂×C₄	#14556560	1	1	yes	characteristic
264	C₂×C₄	#14556562	1	1	yes	characteristic
265	C₂×C₄	#14556587	1	1	yes	characteristic
266	C₂×C₄	C₂×#11924013	1	1	yes	characteristic
267	C₂×C₄	C₂×#11924013	1	1	yes	characteristic
268	C₂×C₄	#14556617	1	1	yes	characteristic
269	C₈	—	2	2	no	—
270	C₈	—	584	1	no	—
271	C₈	#14556559	1	2	yes	—
272	C₈	#14556563	1	2	yes	—
273	C₂²	—	2	2	no	—
274	C₂²	—	8	8	no	—
275	C₂²	—	8	4	no	—
276	C₂²	—	16	4	no	—
277	C₂²	—	16	4	no	—
278	C₂²	—	584	2	no	—
279	C₂²	—	584	1	no	—
280	C₂²	#17988721	1	1	yes	characteristic
281	C₂²	#17988779	1	1	yes	characteristic
282	C₂²	#17988974	1	1	yes	characteristic
283	C₄	—	2	4	no	—
284	C₄	—	584	1	no	—
285	C₄	#17988495	1	1	yes	characteristic
286	C₄	#17988721	1	1	yes	characteristic
287	C₄	#17988779	1	1	yes	characteristic
288	C₄	#17988963	1	1	yes	characteristic
289	C₂	—	2	1	no	—
290	C₂	—	2	1	no	—
291	C₂	—	16	4	no	—
292	C₂	—	1168	1	no	—
293	C₂	#22611002	1	1	yes	characteristic
294	C₂	#22612004	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#17989023

C₂

yes

maximal, complemented

C₂×#17988400

C₂

yes

maximal, complemented

#22610819

C₂

yes

maximal, characteristic, complemented

#22608013

C₂

yes

maximal, characteristic, complemented

C₂×#493×C₇₃

C₂

yes

maximal, characteristic, complemented

C₂×#14556613

C₂²

yes

—

—

—

—

C₂²

yes

—

C₂×#14556527

C₂²

yes

—

—

—

C₂²×D₈×C₇₃

—

C₂²×D₈×C₇₃

C₂²

yes

—

C₂×#127×C₇₃

—

#493×C₇₃

—

C₂×C₄×C₈×C₇₃

C₂²

yes

—

—

—

C₂×Dic₂₉₂

D₄

yes

characteristic, complemented

C₂×#11924017

—

C₂×D₅₈₄

D₄

yes

characteristic, complemented

—

—

—

—

D₄

yes

—

—

—

—

C₂²×D₄×C₇₃

—

C₂²×D₄×C₇₃

—

C₂×D₈×C₇₃

—

C₂×D₈×C₇₃

—

C₂×D₈×C₇₃

—

C₂×D₈×C₇₃

—

C₂×D₈×C₇₃

—

C₂×D₈×C₇₃

—

C₂×D₈×C₇₃

—

C₂×D₈×C₇₃

—

C₂×D₈×C₇₃

D₄

yes

—

C₂²×C₈×C₇₃

D₄

yes

characteristic

C₂²×C₈×C₇₃

C₂³

yes

characteristic

#127×C₇₃

—

#127×C₇₃

—

C₂×C₄²×C₇₃

D₄

yes

characteristic

C₄×C₈×C₇₃

—

—

—

—

—

C₂×Dic₁₄₆

—

C₂×D₂₉₂

—

C₂×C₂²⋊D₇₃

—

C₂×C₄×D₇₃

—

Dic₂₉₂

—

#11924017

—

D₅₈₄

—

—

—

—

—

C₂⁴×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂×D₄

yes

characteristic

D₈×C₇₃

—

D₈×C₇₃

—

D₈×C₇₃

—

D₈×C₇₃

—

D₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

D₈

yes

—

C₂×C₈×C₇₃

C₂×D₄

yes

characteristic

C₂×C₈×C₇₃

C₂×D₄

yes

—

C₂×C₈×C₇₃

C₂×D₄

yes

—

C₂×C₈×C₇₃

#41

yes

characteristic

C₄²×C₇₃

—

C₄²×C₇₃

D₈

yes

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

AGL(1,ℤ/8)

yes

characteristic

C₂²×D₇₃

—

D₄×C₇₃

—

100

D₄×C₇₃

—

101

D₄×C₇₃

—

102

D₄×C₇₃

—

103

D₄×C₇₃

—

104

C₂×C₄×C₇₃

—

105

C₂×C₄×C₇₃

—

106

C₂×C₄×C₇₃

#120

yes

characteristic

107

C₂×C₄×C₇₃

#121

yes

characteristic

108

C₂×C₄×C₇₃

#127

yes

characteristic

109

C₂×C₄×C₇₃

C₂×D₈

yes

characteristic

110

C₂×C₄×C₇₃

C₂×D₈

yes

characteristic

111

C₂×C₄×C₇₃

AGL(1,ℤ/8)

yes

characteristic

112

C₂²⋊D₇₃

—

113

C₂²⋊D₇₃

—

114

C₂×Dic₇₃

—

115

D₂₉₂

—

116

D₂₉₂

—

117

C₄×D₇₃

—

118

C₄×D₇₃

—

119

Dic₁₄₆

—

120

Dic₁₄₆

—

121

C₈×C₇₃

—

122

C₈×C₇₃

#120

yes

—

123

C₈×C₇₃

#121

yes

—

124

#10596831

—

125

C₂²×C₇₃

—

126

C₂²×C₇₃

—

127

C₂²×C₇₃

—

128

C₂²×C₇₃

—

129

C₂²×C₇₃

—

130

C₂²×C₇₃

#447

yes

characteristic

131

C₂²×C₇₃

#459

yes

characteristic

132

C₂²×C₇₃

#496

yes

characteristic

133

C₂×D₇₃

—

134

C₂×D₇₃

—

135

C₄×C₇₃

—

136

C₄×C₇₃

#392

yes

characteristic

137

C₄×C₇₃

#447

yes

characteristic

138

C₄×C₇₃

#459

yes

characteristic

139

C₄×C₇₃

#493

yes

characteristic

140

Dic₇₃

—

141

#13331

—

maximal, Sylow

142

C₂×C₇₃

—

143

C₂×C₇₃

—

144

C₂×C₇₃

—

145

C₂×C₇₃

#2011

yes

characteristic

146

C₂×C₇₃

#2213

yes

—

147

D₇₃

—

148

C₂×#509

—

149

C₂×#493

D₇₃

yes

characteristic, complemented

150

C₂×#361

—

151

#1974

—

152

#1376

—

153

C₇₃

#13331

yes

characteristic, complemented, Sylow

154

C₂×#135

—

155

C₂²×D₈

—

156

C₂²×D₈

C₂×D₇₃

yes

—

157

C₂×#127

—

158

#509

—

146

—

159

#509

—

146

—

160

C₂×SD₃₂

—

146

—

161

C₂×D₁₆

—

146

—

162

C₂×M₃₂

—

163

#493

—

164

C₂×#108

—

165

C₂×#104

—

146

—

166

#408

—

146

—

167

C₂×C₄×C₈

C₂×D₇₃

yes

characteristic

168

#361

—

146

—

169

C₂×#41

—

146

—

170

C₂²×D₄

—

171

C₂²×D₄

—

172

#135

—

146

—

173

#135

—

146

—

174

C₂×Q₁₆

—

175

C₂×SD₁₆

—

146

—

176

C₂×D₈

—

177

C₂×D₈

—

178

C₂×D₈

—

179

C₂×D₈

—

180

C₂×D₈

—

181

C₂×D₈

—

182

C₂×D₈

—

183

C₂×D₈

—

184

C₂×D₈

—

185

C₂×D₈

C₂²⋊D₇₃

yes

—

186

C₂×M₁₆

—

146

—

187

C₂²×C₈

C₂²⋊D₇₃

yes

characteristic

188

C₂²×C₈

C₂²×D₇₃

yes

characteristic

189

#127

—

190

#127

—

191

C₂×C₄²

C₂²⋊D₇₃

yes

characteristic

192

SD₃₂

—

146

—

193

D₁₆

—

146

—

194

M₃₂

—

195

M₃₂

—

146

—

196

C₂×C₁₆

—

146

—

197

#108

—

146

—

198

#104

—

292

—

199

C₂²⋊C₈

—

292

—

200

C₄×C₈

—

201

C₂⁴

—

202

#41

—

292

—

203

#41

—

292

—

204

#41

—

292

—

205

#41

—

292

—

206

C₂×Q₈

—

146

—

207

C₂×D₄

—

208

C₂×D₄

—

209

C₂×D₄

—

210

C₂×D₄

—

211

C₂×D₄

—

212

C₂×D₄

—

213

C₂×D₄

—

214

C₂×D₄

—

215

C₂×D₄

—

292

—

216

C₂×D₄

—

146

—

217

C₂²×C₄

—

218

C₂²×C₄

—

292

—

219

C₂²×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

220

Q₁₆

—

146

—

221

SD₁₆

—

292

—

222

D₈

—

223

D₈

—

224

D₈

—

225

D₈

—

226

D₈

—

227

D₈

—

146

—

228

M₁₆

—

292

—

229

M₁₆

—

292

—

230

C₂×C₈

—

231

C₂×C₈

—

232

C₂×C₈

—

292

—

233

C₂×C₈

#11924013

yes

—

234

C₂×C₈

D₄×D₇₃

yes

characteristic

235

C₂×C₈

D₄×D₇₃

yes

—

236

C₂×C₈

C₂×C₂²⋊D₇₃

yes

—

237

C₂×C₈

#11924027

yes

characteristic

238

C₄²

—

239

C₄²

#11924013

yes

—

240

C₁₆

—

146

—

241

C₂³

—

242

C₂³

—

243

C₂³

—

244

C₂³

—

245

C₂³

—

292

—

246

C₂³

#14556617

yes

characteristic

247

Q₈

—

292

—

248

Q₈

—

292

—

249

D₄

—

250

D₄

—

251

D₄

—

252

D₄

—

253

D₄

—

254

D₄

—

292

—

255

D₄

—

292

—

256

D₄

—

584

—

257

D₄

—

584

—

258

C₂×C₄

—

259

C₂×C₄

—

260

C₂×C₄

—

292

—

261

C₂×C₄

—

584

—

262

C₂×C₄

—

584

—

263

C₂×C₄

#14556560

yes

characteristic

264

C₂×C₄

#14556562

yes

characteristic

265

C₂×C₄

#14556587

yes

characteristic

266

C₂×C₄

C₂×#11924013

yes

characteristic

267

C₂×C₄

C₂×#11924013

yes

characteristic

268

C₂×C₄

#14556617

yes

characteristic

269

C₈

—

270

C₈

—

584

—

271

C₈

#14556559

yes

—

272

C₈

#14556563

yes

—

273

C₂²

—

274

C₂²

—

275

C₂²

—

276

C₂²

—

277

C₂²

—

278

C₂²

—

584

—

279

C₂²

—

584

—

280

C₂²

#17988721

yes

characteristic

281

C₂²

#17988779

yes

characteristic

282

C₂²

#17988974

yes

characteristic

283

C₄

—

284

C₄

—

584

—

285

C₄

#17988495

yes

characteristic

286

C₄

#17988721

yes

characteristic

287

C₄

#17988779

yes

characteristic

288

C₄

#17988963

yes

characteristic

289

C₂

—

290

C₂

—

291

C₂

—

292

C₂

—

1168

—

293

C₂

#22611002

yes

characteristic

294

C₂

#22612004

yes

—

	subgroup	G/H
center	C₂²	#17988779
commutator, cosocle	C₂²×C₈×C₇₃	C₂³
Frattini	C₂²×C₈	C₂²×D₇₃
Fitting	C₂×#493×C₇₃	C₂
socle	C₂²×C₇₃	#459
hypercenter	C₂×#493	D₇₃
hypocenter	C₇₃	#13331
LCS	G ▷ C₂²×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ C₂×#493

subgroup

G/H

center

C₂²

#17988779

commutator, cosocle

C₂²×C₈×C₇₃

C₂³

Frattini

C₂²×C₈

C₂²×D₇₃

Fitting

C₂×#493×C₇₃

C₂

C₂²×C₇₃

D₇₃

C₇₃

G ▷ C₂²×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ C₂×#493

N	H ≅ G/N	type
1. C₂×#17989023	C₂	semidirect
2. C₂×#17988400	C₂	semidirect
3. #22610819	C₂	semidirect
4. #22608013	C₂	semidirect
5. C₂×#493×C₇₃	C₂	semidirect
24. C₂×Dic₂₉₂	D₄	semidirect
26. C₂×D₅₈₄	D₄	semidirect
31. #14556531	D₄	semidirect
149. C₂×#493	D₇₃	semidirect
153. C₇₃	#13331	semidirect

H ≅ G/N

type

1. C₂×#17989023

C₂

semidirect

2. C₂×#17988400

C₂

semidirect

3. #22610819

C₂

semidirect

4. #22608013

C₂

semidirect

5. C₂×#493×C₇₃

C₂

semidirect

24. C₂×Dic₂₉₂

D₄

semidirect

26. C₂×D₅₈₄

D₄

semidirect

31. #14556531

D₄

semidirect

149. C₂×#493

D₇₃

semidirect

153. C₇₃

#13331

semidirect

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

subgroup	index
C₂×#17989023	2
C₂×#17988400	2
#22610819	2
#22608013	2
C₂×#493×C₇₃	2
#13331	73

subgroup

index

C₂×#493×C₇₃

Subgroups — #33004849

Conjugacy classes of subgroups

Complements

Maximal subgroups