Group #33002017 — subgroups

Subgroups — #33002017

Order 18688.

420 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 115 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	#22611616	C₂	1	2	yes	maximal
2	#22609981	C₂	1	2	yes	maximal, complemented
3	#22608054	C₂	1	2	yes	maximal, complemented
4	C₇₃×#2931	C₂	1	1	yes	maximal, characteristic
5	C₂×#14556527	—	2	2	no	—
6	#17988571	C₂²	1	4	yes	—
7	#17988386	—	2	2	no	—
8	#17988384	—	2	2	no	—
9	#17988345	—	2	2	no	—
10	C₂×#131×C₇₃	C₄	1	1	yes	characteristic
11	C₂×#131×C₇₃	C₂²	1	1	yes	characteristic
12	#532×C₇₃	C₂²	1	1	yes	characteristic
13	#436×C₇₃	—	2	2	no	—
14	C₈×D₄×C₇₃	—	2	2	no	—
15	#423×C₇₃	C₄	1	1	yes	characteristic
16	#408×C₇₃	C₄	1	1	yes	characteristic
17	#408×C₇₃	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₈×C₇₃	C₄	1	1	yes	characteristic
19	C₂×#11924012	—	2	4	no	—
20	#14556527	—	4	4	no	—
21	#14556510	—	2	4	no	—
22	#14556508	—	2	4	no	—
23	C₂×#41×C₇₃	C₂×C₄	1	1	yes	characteristic
24	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
25	#131×C₇₃	—	4	2	no	—
26	#131×C₇₃	—	4	2	no	—
27	C₂×M₁₆×C₇₃	—	2	1	no	—
28	C₂×M₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
29	C₂×M₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
30	C₂×M₁₆×C₇₃	D₄	1	2	yes	—
31	C₂²×C₈×C₇₃	—	2	1	no	—
32	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₈×C₇₃	D₄	1	2	yes	—
35	C₄⋊Q₈×C₇₃	D₄	1	1	yes	characteristic
36	#127×C₇₃	Q₈	1	1	yes	characteristic
37	#124×C₇₃	D₄	1	1	yes	characteristic
38	#124×C₇₃	Q₈	1	1	yes	characteristic
39	#121×C₇₃	—	2	2	no	—
40	C₄×D₄×C₇₃	—	2	2	no	—
41	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
42	C₄⋊C₈×C₇₃	—	2	2	no	—
43	C₂²⋊C₈×C₇₃	—	2	2	no	—
44	C₂²⋊C₈×C₇₃	—	2	2	no	—
45	C₄×C₈×C₇₃	—	2	1	no	—
46	C₄×C₈×C₇₃	—	2	1	no	—
47	#11924012	—	4	4	no	—
48	#11924012	—	4	4	no	—
49	C₂×#10596831	—	4	4	no	—
50	#41×C₇₃	—	4	1	no	—
51	#41×C₇₃	—	4	1	no	—
52	#41×C₇₃	—	4	1	no	—
53	#41×C₇₃	—	4	1	no	—
54	C₂×Q₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
55	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
56	C₂×D₄×C₇₃	—	2	1	no	—
57	C₂×D₄×C₇₃	—	2	2	no	—
58	C₂×D₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
59	C₂×D₄×C₇₃	C₂×Q₈	1	1	yes	characteristic
60	C₂×D₄×C₇₃	#41	1	2	yes	—
61	C₂²×C₄×C₇₃	—	2	1	no	—
62	C₂²×C₄×C₇₃	—	2	1	no	—
63	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
64	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
65	M₁₆×C₇₃	—	4	1	no	—
66	M₁₆×C₇₃	—	4	2	no	—
67	M₁₆×C₇₃	—	4	2	no	—
68	M₁₆×C₇₃	—	4	1	no	—
69	C₂×C₈×C₇₃	—	2	2	no	—
70	C₂×C₈×C₇₃	—	2	4	no	—
71	C₂×C₈×C₇₃	—	2	1	no	—
72	C₂×C₈×C₇₃	—	2	1	no	—
73	C₂×C₈×C₇₃	—	4	2	no	—
74	C₂×C₈×C₇₃	—	4	1	no	—
75	C₂×C₈×C₇₃	C₂²⋊C₄	1	2	yes	—
76	C₂×C₈×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
77	C₂×C₈×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
78	C₄⋊C₄×C₇₃	—	2	2	no	—
79	C₂²⋊C₄×C₇₃	—	2	2	no	—
80	C₂²⋊C₄×C₇₃	—	2	2	no	—
81	C₄²×C₇₃	—	2	1	no	—
82	C₄²×C₇₃	C₄⋊C₄	1	1	yes	characteristic
83	C₄²×C₇₃	C₄⋊C₄	1	1	yes	characteristic
84	C₂³×C₇₃	—	2	1	no	—
85	C₂³×C₇₃	#117	1	1	yes	characteristic
86	C₂³×C₇₃	C₂²⋊Q₈	1	2	yes	—
87	Q₈×C₇₃	—	4	1	no	—
88	Q₈×C₇₃	—	4	1	no	—
89	D₄×C₇₃	—	4	1	no	—
90	D₄×C₇₃	—	4	2	no	—
91	D₄×C₇₃	—	4	1	no	—
92	D₄×C₇₃	—	4	4	no	—
93	D₄×C₇₃	—	4	2	no	—
94	C₂×C₄×C₇₃	—	2	1	no	—
95	C₂×C₄×C₇₃	—	2	1	no	—
96	C₂×C₄×C₇₃	—	2	2	no	—
97	C₂×C₄×C₇₃	—	2	1	no	—
98	C₂×C₄×C₇₃	—	2	2	no	—
99	C₂×C₄×C₇₃	—	2	1	no	—
100	C₂×C₄×C₇₃	—	2	1	no	—
101	C₂×C₄×C₇₃	—	4	2	no	—
102	C₂×C₄×C₇₃	—	4	1	no	—
103	C₂×C₄×C₇₃	—	4	1	no	—
104	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
105	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
106	C₂×C₄×C₇₃	#121	1	2	yes	—
107	C₈×C₇₃	—	2	2	no	—
108	C₈×C₇₃	—	2	1	no	—
109	C₈×C₇₃	—	4	1	no	—
110	C₈×C₇₃	—	4	1	no	—
111	C₈×C₇₃	#99	1	2	yes	—
112	#10596831	—	8	4	no	—
113	C₂²×C₇₃	—	2	1	no	—
114	C₂²×C₇₃	—	2	2	no	—
115	C₂²×C₇₃	—	4	1	no	—
116	C₂²×C₇₃	—	4	2	no	—
117	C₂²×C₇₃	—	4	2	no	—
118	C₂²×C₇₃	—	4	1	no	—
119	C₂²×C₇₃	#380	1	1	yes	characteristic
120	C₄×C₇₃	—	2	2	no	—
121	C₄×C₇₃	—	2	2	no	—
122	C₄×C₇₃	—	2	1	no	—
123	C₄×C₇₃	—	4	1	no	—
124	C₄×C₇₃	—	4	1	no	—
125	C₄×C₇₃	C₂×#99	1	1	yes	characteristic
126	C₄×C₇₃	#410	1	1	yes	characteristic
127	#12809	—	73	1	no	maximal, Sylow
128	C₂×C₇₃	—	2	1	no	—
129	C₂×C₇₃	—	4	1	no	—
130	C₂×C₇₃	—	4	2	no	—
131	C₂×C₇₃	—	8	1	no	—
132	C₂×C₇₃	#1799	1	1	yes	characteristic
133	#2931	D₇₃	1	1	yes	characteristic
134	#2132	—	73	2	no	—
135	#1813	—	73	2	no	—
136	#1392	—	73	2	no	—
137	C₇₃	#12809	1	1	yes	characteristic, complemented, Sylow
138	C₂×#131	Dic₇₃	1	1	yes	characteristic
139	C₂×#131	C₂×D₇₃	1	1	yes	characteristic
140	#532	C₂×D₇₃	1	1	yes	characteristic
141	#436	—	2	2	no	—
142	C₈×D₄	—	2	2	no	—
143	C₂×#108	—	146	2	no	—
144	#423	Dic₇₃	1	1	yes	characteristic
145	#413	—	73	4	no	—
146	#408	Dic₇₃	1	1	yes	characteristic
147	#408	C₂×D₇₃	1	1	yes	characteristic
148	C₂×C₄×C₈	Dic₇₃	1	1	yes	characteristic
149	#356	—	146	2	no	—
150	#355	—	146	2	no	—
151	#338	—	146	2	no	—
152	C₂×#41	C₂×Dic₇₃	1	1	yes	characteristic
153	C₂×#41	C₂²×D₇₃	1	1	yes	characteristic
154	#131	—	4	2	no	—
155	#131	—	4	2	no	—
156	C₂×M₁₆	—	2	1	no	—
157	C₂×M₁₆	—	146	4	no	—
158	C₂×M₁₆	C₂×Dic₇₃	1	1	yes	characteristic
159	C₂×M₁₆	C₂×Dic₇₃	1	1	yes	characteristic
160	C₂×M₁₆	C₂²⋊D₇₃	1	2	yes	—
161	C₂²×C₈	—	2	1	no	—
162	C₂²×C₈	C₂×Dic₇₃	1	1	yes	characteristic
163	C₂²×C₈	C₂×Dic₇₃	1	1	yes	characteristic
164	C₂²×C₈	C₂²⋊D₇₃	1	2	yes	—
165	C₄⋊Q₈	D₂₉₂	1	1	yes	characteristic
166	#127	Dic₁₄₆	1	1	yes	characteristic
167	#124	Dic₁₄₆	1	1	yes	characteristic
168	#124	D₂₉₂	1	1	yes	characteristic
169	#121	—	2	2	no	—
170	C₄×D₄	—	2	2	no	—
171	C₂×C₄²	C₂×Dic₇₃	1	1	yes	characteristic
172	#108	—	292	4	no	—
173	C₄⋊C₈	—	2	2	no	—
174	#101	—	146	4	no	—
175	#100	—	146	4	no	—
176	C₂²⋊C₈	—	2	2	no	—
177	C₂²⋊C₈	—	2	2	no	—
178	C₄×C₈	—	2	1	no	—
179	C₄×C₈	—	2	1	no	—
180	#41	—	4	1	no	—
181	#41	—	4	1	no	—
182	#41	—	4	1	no	—
183	#41	—	4	1	no	—
184	C₂×Q₈	C₄⋊Dic₇₃	1	1	yes	characteristic
185	C₂×Q₈	C₂×D₂₉₂	1	1	yes	characteristic
186	C₂×D₄	—	2	1	no	—
187	C₂×D₄	—	2	2	no	—
188	C₂×D₄	C₄⋊Dic₇₃	1	1	yes	characteristic
189	C₂×D₄	C₂×Dic₁₄₆	1	1	yes	characteristic
190	C₂×D₄	#11924028	1	2	yes	—
191	C₂²×C₄	—	2	1	no	—
192	C₂²×C₄	—	2	1	no	—
193	C₂²×C₄	C₂²×Dic₇₃	1	1	yes	characteristic
194	C₂²×C₄	C₂×C₂²⋊D₇₃	1	2	yes	—
195	M₁₆	—	4	1	no	—
196	M₁₆	—	4	2	no	—
197	M₁₆	—	4	2	no	—
198	M₁₆	—	4	1	no	—
199	M₁₆	—	292	4	no	—
200	M₁₆	—	292	4	no	—
201	C₂×C₈	—	2	4	no	—
202	C₂×C₈	—	2	2	no	—
203	C₂×C₈	—	2	1	no	—
204	C₂×C₈	—	2	1	no	—
205	C₂×C₈	—	4	2	no	—
206	C₂×C₈	—	4	1	no	—
207	C₂×C₈	—	292	4	no	—
208	C₂×C₈	C₂²⋊Dic₇₃	1	2	yes	—
209	C₂×C₈	C₂²⋊Dic₇₃	1	1	yes	characteristic
210	C₂×C₈	C₂²⋊Dic₇₃	1	1	yes	characteristic
211	C₄⋊C₄	—	2	2	no	—
212	C₂²⋊C₄	—	2	2	no	—
213	C₂²⋊C₄	—	2	2	no	—
214	C₄²	—	2	1	no	—
215	C₄²	C₄⋊Dic₇₃	1	1	yes	characteristic
216	C₄²	C₄⋊Dic₇₃	1	1	yes	characteristic
217	C₂³	—	2	1	no	—
218	C₂³	#14556550	1	1	yes	characteristic
219	C₂³	#14556570	1	2	yes	—
220	Q₈	—	4	1	no	—
221	Q₈	—	4	1	no	—
222	D₄	—	4	1	no	—
223	D₄	—	4	2	no	—
224	D₄	—	4	1	no	—
225	D₄	—	4	4	no	—
226	D₄	—	4	2	no	—
227	C₂×C₄	—	2	1	no	—
228	C₂×C₄	—	2	1	no	—
229	C₂×C₄	—	2	2	no	—
230	C₂×C₄	—	2	1	no	—
231	C₂×C₄	—	2	2	no	—
232	C₂×C₄	—	2	1	no	—
233	C₂×C₄	—	2	1	no	—
234	C₂×C₄	—	4	2	no	—
235	C₂×C₄	—	4	1	no	—
236	C₂×C₄	—	4	1	no	—
237	C₂×C₄	C₂×C₂²⋊Dic₇₃	1	1	yes	characteristic
238	C₂×C₄	C₂×C₄⋊Dic₇₃	1	1	yes	characteristic
239	C₂×C₄	#14556565	1	2	yes	—
240	C₈	—	2	2	no	—
241	C₈	—	2	1	no	—
242	C₈	—	4	1	no	—
243	C₈	—	4	1	no	—
244	C₈	—	584	4	no	—
245	C₈	#14556506	1	2	yes	—
246	C₂²	—	2	1	no	—
247	C₂²	—	2	2	no	—
248	C₂²	—	4	1	no	—
249	C₂²	—	4	2	no	—
250	C₂²	—	4	2	no	—
251	C₂²	—	4	1	no	—
252	C₂²	#17988447	1	1	yes	characteristic
253	C₄	—	2	2	no	—
254	C₄	—	2	2	no	—
255	C₄	—	2	1	no	—
256	C₄	—	4	1	no	—
257	C₄	—	4	1	no	—
258	C₄	C₂×#14556506	1	1	yes	characteristic
259	C₄	#17988561	1	1	yes	characteristic
260	C₂	—	2	1	no	—
261	C₂	—	4	1	no	—
262	C₂	—	4	2	no	—
263	C₂	—	8	1	no	—
264	C₂	#22609919	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22611616

C₂

yes

maximal

#22609981

C₂

yes

maximal, complemented

#22608054

C₂

yes

maximal, complemented

C₇₃×#2931

C₂

yes

maximal, characteristic

C₂×#14556527

—

#17988571

C₂²

yes

—

#17988386

—

#17988384

—

#17988345

—

C₂×#131×C₇₃

C₄

yes

characteristic

C₂×#131×C₇₃

C₂²

yes

characteristic

#532×C₇₃

C₂²

yes

characteristic

#436×C₇₃

—

C₈×D₄×C₇₃

—

#423×C₇₃

C₄

yes

characteristic

#408×C₇₃

C₄

yes

characteristic

#408×C₇₃

C₂²

yes

characteristic

C₂×C₄×C₈×C₇₃

C₄

yes

—

—

—

—

C₂×#41×C₇₃

C₂×C₄

yes

characteristic

C₂×#41×C₇₃

C₂³

yes

characteristic

#131×C₇₃

—

#131×C₇₃

—

C₂×M₁₆×C₇₃

—

C₂×M₁₆×C₇₃

C₂×C₄

yes

characteristic

C₂×M₁₆×C₇₃

C₂×C₄

yes

characteristic

C₂×M₁₆×C₇₃

D₄

yes

—

C₂²×C₈×C₇₃

—

C₂²×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂²×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂²×C₈×C₇₃

D₄

yes

—

C₄⋊Q₈×C₇₃

D₄

yes

characteristic

#127×C₇₃

Q₈

yes

characteristic

#124×C₇₃

D₄

yes

characteristic

#124×C₇₃

Q₈

yes

characteristic

#121×C₇₃

—

C₄×D₄×C₇₃

—

C₂×C₄²×C₇₃

C₂×C₄

yes

characteristic

C₄⋊C₈×C₇₃

—

C₂²⋊C₈×C₇₃

—

C₂²⋊C₈×C₇₃

—

C₄×C₈×C₇₃

—

C₄×C₈×C₇₃

—

#11924012

—

#11924012

—

C₂×#10596831

—

#41×C₇₃

—

#41×C₇₃

—

#41×C₇₃

—

#41×C₇₃

—

C₂×Q₈×C₇₃

C₄⋊C₄

yes

characteristic

C₂×Q₈×C₇₃

C₂×D₄

yes

characteristic

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

C₄⋊C₄

yes

characteristic

C₂×D₄×C₇₃

C₂×Q₈

yes

characteristic

C₂×D₄×C₇₃

#41

yes

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₇₃

C₂×D₄

yes

—

M₁₆×C₇₃

—

M₁₆×C₇₃

—

M₁₆×C₇₃

—

M₁₆×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

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

C₂²⋊C₄

yes

characteristic

C₄⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

—

C₄²×C₇₃

—

C₄²×C₇₃

C₄⋊C₄

yes

characteristic

C₄²×C₇₃

C₄⋊C₄

yes

characteristic

C₂³×C₇₃

—

C₂³×C₇₃

#117

yes

characteristic

C₂³×C₇₃

C₂²⋊Q₈

yes

—

Q₈×C₇₃

—

Q₈×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

100

C₂×C₄×C₇₃

—

101

C₂×C₄×C₇₃

—

102

C₂×C₄×C₇₃

—

103

C₂×C₄×C₇₃

—

104

C₂×C₄×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

105

C₂×C₄×C₇₃

C₂×C₄⋊C₄

yes

characteristic

106

C₂×C₄×C₇₃

#121

yes

—

107

C₈×C₇₃

—

108

C₈×C₇₃

—

109

C₈×C₇₃

—

110

C₈×C₇₃

—

111

C₈×C₇₃

#99

yes

—

112

#10596831

—

113

C₂²×C₇₃

—

114

C₂²×C₇₃

—

115

C₂²×C₇₃

—

116

C₂²×C₇₃

—

117

C₂²×C₇₃

—

118

C₂²×C₇₃

—

119

C₂²×C₇₃

#380

yes

characteristic

120

C₄×C₇₃

—

121

C₄×C₇₃

—

122

C₄×C₇₃

—

123

C₄×C₇₃

—

124

C₄×C₇₃

—

125

C₄×C₇₃

C₂×#99

yes

characteristic

126

C₄×C₇₃

yes

127

—

128

C₂×C₇₃

—

129

C₂×C₇₃

—

130

C₂×C₇₃

—

131

C₂×C₇₃

—

132

C₂×C₇₃

#1799

yes

characteristic

133

#2931

D₇₃

yes

characteristic

134

#2132

—

135

#1813

—

136

#1392

—

137

C₇₃

#12809

yes

characteristic, complemented, Sylow

138

C₂×#131

Dic₇₃

yes

characteristic

139

C₂×#131

C₂×D₇₃

yes

characteristic

140

#532

C₂×D₇₃

yes

characteristic

141

#436

—

142

C₈×D₄

—

143

C₂×#108

—

146

—

144

#423

Dic₇₃

yes

characteristic

145

#413

—

146

#408

Dic₇₃

yes

characteristic

147

#408

C₂×D₇₃

yes

characteristic

148

C₂×C₄×C₈

Dic₇₃

yes

characteristic

149

#356

—

146

—

150

#355

—

146

—

151

#338

—

146

—

152

C₂×#41

C₂×Dic₇₃

yes

characteristic

153

C₂×#41

C₂²×D₇₃

yes

characteristic

154

#131

—

155

#131

—

156

C₂×M₁₆

—

157

C₂×M₁₆

—

146

—

158

C₂×M₁₆

C₂×Dic₇₃

yes

characteristic

159

C₂×M₁₆

C₂×Dic₇₃

yes

characteristic

160

C₂×M₁₆

C₂²⋊D₇₃

yes

—

161

C₂²×C₈

—

162

C₂²×C₈

C₂×Dic₇₃

yes

characteristic

163

C₂²×C₈

C₂×Dic₇₃

yes

characteristic

164

C₂²×C₈

C₂²⋊D₇₃

yes

—

165

C₄⋊Q₈

D₂₉₂

yes

characteristic

166

#127

Dic₁₄₆

yes

characteristic

167

#124

Dic₁₄₆

yes

characteristic

168

#124

D₂₉₂

yes

characteristic

169

#121

—

170

C₄×D₄

—

171

C₂×C₄²

C₂×Dic₇₃

yes

characteristic

172

#108

—

292

—

173

C₄⋊C₈

—

174

#101

—

146

—

175

#100

—

146

—

176

C₂²⋊C₈

—

177

C₂²⋊C₈

—

178

C₄×C₈

—

179

C₄×C₈

—

180

#41

—

181

#41

—

182

#41

—

183

#41

—

184

C₂×Q₈

C₄⋊Dic₇₃

yes

characteristic

185

C₂×Q₈

C₂×D₂₉₂

yes

characteristic

186

C₂×D₄

—

187

C₂×D₄

—

188

C₂×D₄

C₄⋊Dic₇₃

yes

characteristic

189

C₂×D₄

C₂×Dic₁₄₆

yes

characteristic

190

C₂×D₄

#11924028

yes

—

191

C₂²×C₄

—

192

C₂²×C₄

—

193

C₂²×C₄

C₂²×Dic₇₃

yes

characteristic

194

C₂²×C₄

C₂×C₂²⋊D₇₃

yes

—

195

M₁₆

—

196

M₁₆

—

197

M₁₆

—

198

M₁₆

—

199

M₁₆

—

292

—

200

M₁₆

—

292

—

201

C₂×C₈

—

202

C₂×C₈

—

203

C₂×C₈

—

204

C₂×C₈

—

205

C₂×C₈

—

206

C₂×C₈

—

207

C₂×C₈

—

292

—

208

C₂×C₈

C₂²⋊Dic₇₃

yes

—

209

C₂×C₈

C₂²⋊Dic₇₃

yes

characteristic

210

C₂×C₈

C₂²⋊Dic₇₃

yes

characteristic

211

C₄⋊C₄

—

212

C₂²⋊C₄

—

213

C₂²⋊C₄

—

214

C₄²

—

215

C₄²

C₄⋊Dic₇₃

yes

characteristic

216

C₄²

C₄⋊Dic₇₃

yes

characteristic

217

C₂³

—

218

C₂³

#14556550

yes

characteristic

219

C₂³

#14556570

yes

—

220

Q₈

—

221

Q₈

—

222

D₄

—

223

D₄

—

224

D₄

—

225

D₄

—

226

D₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

—

237

C₂×C₄

C₂×C₂²⋊Dic₇₃

yes

characteristic

238

C₂×C₄

C₂×C₄⋊Dic₇₃

yes

characteristic

239

C₂×C₄

#14556565

yes

—

240

C₈

—

241

C₈

—

242

C₈

—

243

C₈

—

244

C₈

—

584

—

245

C₈

#14556506

yes

—

246

C₂²

—

247

C₂²

—

248

C₂²

—

249

C₂²

—

250

C₂²

—

251

C₂²

—

252

C₂²

#17988447

yes

characteristic

253

C₄

—

254

C₄

—

255

C₄

—

256

C₄

—

257

C₄

—

258

C₄

C₂×#14556506

yes

characteristic

259

C₄

#17988561

yes

characteristic

260

C₂

—

261

C₂

—

262

C₂

—

263

C₂

—

264

C₂

#22609919

yes

characteristic

	subgroup	G/H
center	C₄	#17988561
commutator	C₂²×C₄×C₇₃	C₂²×C₄
Frattini	C₂×#41	C₂²×D₇₃
Fitting	C₇₃×#2931	C₂
socle	C₂×C₇₃	#1799
prime radical	#532×C₇₃	C₂²
cosocle	C₂×#41×C₇₃	C₂³
hypercenter	#2931	D₇₃
hypocenter	C₇₃	#12809
LCS	G ▷ C₂²×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₂×#131 ◁ #2931

subgroup

G/H

center

C₄

#17988561

commutator

C₂²×C₄×C₇₃

C₂²×C₄

Frattini

C₂×#41

C₂²×D₇₃

Fitting

C₇₃×#2931

C₂

socle

C₂×C₇₃

#1799

prime radical

#532×C₇₃

C₂²

cosocle

C₂×#41×C₇₃

C₂³

D₇₃

C₇₃

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

UCS

C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₂×#131 ◁ #2931

N	H ≅ G/N	type
2. #22609981	C₂	semidirect
3. #22608054	C₂	semidirect
137. C₇₃	#12809	semidirect

H ≅ G/N

type

2. #22609981

C₂

semidirect

3. #22608054

C₂

semidirect

137. C₇₃

#12809

semidirect

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

subgroup	index
#22611616	2
#22609981	2
#22608054	2
C₇₃×#2931	2
#12809	73

subgroup

index

C₇₃×#2931

Subgroups — #33002017

Conjugacy classes of subgroups

Complements

Maximal subgroups