Group #33002876 — subgroups

Subgroups — #33002876

Order 18688.

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

normal subgroups only

This group has 508 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	C₂³×#11924003	C₂	1	1	yes	maximal, characteristic, complemented
2	#22618625	C₂	1	1	yes	maximal, characteristic
3	C₂×#17988372	C₂	1	2	yes	maximal, complemented
4	#22608021	C₂	1	2	yes	maximal, complemented
5	C₇₃×#2112	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#14556597	C₂²	1	1	yes	characteristic
7	#17989098	C₄	1	1	yes	characteristic
8	C₂²×#11924003	—	2	4	no	—
9	C₂²×#11924003	—	2	2	no	—
10	C₂²×#11924003	C₂²	1	2	yes	—
11	#17988658	—	2	2	no	—
12	C₈×C₂²⋊D₇₃	—	2	2	no	—
13	#17988613	C₄	1	1	yes	characteristic
14	#17988553	C₄	1	1	yes	characteristic
15	#17988551	C₄	1	1	yes	characteristic
16	#17988542	C₂²	1	1	yes	characteristic
17	#17988372	—	2	4	no	—
18	C₂³×C₈×C₇₃	C₂²	1	1	yes	characteristic
19	C₂×M₃₂×C₇₃	C₂²	1	2	yes	—
20	C₂²⋊C₁₆×C₇₃	—	2	2	no	—
21	C₂×#11924028	C₂×C₄	1	1	yes	characteristic
22	#14556597	—	2	2	no	—
23	#14556597	—	2	2	no	—
24	C₂×#11924012	C₂×C₄	1	1	yes	characteristic
25	C₂×#11924012	C₂×C₄	1	1	yes	characteristic
26	C₂×#11924011	—	2	1	no	—
27	C₂×C₈×D₇₃	—	2	1	no	—
28	#14556574	—	2	1	no	—
29	#14556570	C₈	1	2	yes	—
30	#14556565	C₈	1	2	yes	—
31	#14556560	—	2	1	no	—
32	C₄×C₂²⋊D₇₃	—	2	2	no	—
33	#14556550	C₂×C₄	1	1	yes	characteristic
34	C₂×#11924003	—	2	8	no	—
35	C₂×#11924003	—	2	2	no	—
36	C₂×#11924003	—	2	2	no	—
37	C₂×#11924003	D₄	1	4	yes	complemented
38	#14556520	—	2	2	no	—
39	C₂²⋊#10596831	—	2	2	no	—
40	#14556503	—	2	2	no	—
41	#14556501	—	2	1	no	—
42	C₈×Dic₇₃	—	2	1	no	—
43	C₂³×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₈×C₇₃	—	2	2	no	—
45	C₂²×C₈×C₇₃	—	2	2	no	—
46	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
47	C₂²×C₈×C₇₃	D₄	1	2	yes	—
48	C₂²×C₈×C₇₃	D₄	1	2	yes	—
49	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
50	M₃₂×C₇₃	—	2	2	no	—
51	M₃₂×C₇₃	—	2	2	no	—
52	C₂×C₁₆×C₇₃	—	2	2	no	—
53	#11924028	—	2	2	no	—
54	#11924028	—	2	2	no	—
55	C₂×Dic₁₄₆	C₂×C₈	1	1	yes	characteristic
56	C₂×D₂₉₂	C₂×C₈	1	1	yes	characteristic
57	C₂×C₂²⋊D₇₃	—	2	2	no	—
58	C₂×C₂²⋊D₇₃	—	2	1	no	—
59	C₂×C₄×D₇₃	—	2	1	no	—
60	#11924012	—	2	2	no	—
61	#11924012	—	2	2	no	—
62	#11924011	—	4	1	no	—
63	#11924011	—	4	1	no	—
64	C₂×#10596831	—	2	1	no	—
65	C₂×#10596831	—	2	1	no	—
66	C₈×D₇₃	—	4	2	no	—
67	C₄⋊Dic₇₃	C₂×C₈	1	2	yes	—
68	#11924007	—	2	2	no	—
69	C₂²⋊Dic₇₃	—	2	2	no	—
70	C₂²⋊Dic₇₃	—	2	1	no	—
71	#11924005	—	2	2	no	—
72	C₄×Dic₇₃	—	2	1	no	—
73	#11924003	—	2	4	no	—
74	C₂⁴×C₇₃	M₁₆	1	1	yes	characteristic
75	C₂²×C₄×C₇₃	—	2	2	no	—
76	C₂²×C₄×C₇₃	—	2	2	no	—
77	C₂²×C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
78	C₂²×C₄×C₇₃	C₂×C₈	1	2	yes	—
79	C₂²×C₄×C₇₃	M₁₆	1	1	yes	characteristic
80	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
81	C₂×C₈×C₇₃	—	2	2	no	—
82	C₂×C₈×C₇₃	—	2	2	no	—
83	C₂×C₈×C₇₃	—	2	4	no	—
84	C₂×C₈×C₇₃	—	2	2	no	—
85	C₂×C₈×C₇₃	C₂²⋊C₄	1	2	yes	—
86	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
87	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
88	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
89	C₂×C₈×C₇₃	#41	1	2	yes	—
90	C₁₆×C₇₃	—	4	2	no	—
91	C₂³×C₇₃	—	2	4	no	—
92	C₂³×C₇₃	—	2	2	no	—
93	C₂³×C₇₃	C₂²⋊C₈	1	2	yes	—
94	C₂³×C₇₃	C₂×M₁₆	1	1	yes	characteristic
95	C₂²×D₇₃	—	2	1	no	—
96	C₂×C₄×C₇₃	—	2	2	no	—
97	C₂×C₄×C₇₃	—	2	2	no	—
98	C₂×C₄×C₇₃	—	2	2	no	—
99	C₂×C₄×C₇₃	—	2	4	no	—
100	C₂×C₄×C₇₃	C₂²⋊C₈	1	2	yes	—
101	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
102	C₂×C₄×C₇₃	C₄×D₄	1	2	yes	—
103	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
104	C₂×C₄×C₇₃	#131	1	2	yes	—
105	C₂²⋊D₇₃	—	4	4	no	—
106	C₂²⋊D₇₃	—	4	2	no	—
107	C₂×Dic₇₃	—	2	2	no	—
108	C₂×Dic₇₃	—	2	1	no	—
109	D₂₉₂	—	2	2	no	—
110	C₄×D₇₃	—	4	1	no	—
111	C₄×D₇₃	—	4	1	no	—
112	Dic₁₄₆	—	2	2	no	—
113	C₈×C₇₃	—	2	2	no	—
114	C₈×C₇₃	#120	1	1	yes	characteristic
115	C₈×C₇₃	#121	1	2	yes	—
116	C₈×C₇₃	#123	1	1	yes	characteristic
117	#10596831	—	4	1	no	—
118	#10596831	—	4	1	no	—
119	C₂²×C₇₃	—	2	8	no	—
120	C₂²×C₇₃	—	2	2	no	—
121	C₂²×C₇₃	—	2	2	no	—
122	C₂²×C₇₃	—	2	2	no	—
123	C₂²×C₇₃	#350	1	4	yes	complemented
124	C₂²×C₇₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
125	C₂²×C₇₃	#435	1	2	yes	—
126	C₂×D₇₃	—	4	2	no	—
127	C₂×D₇₃	—	4	1	no	—
128	C₄×C₇₃	—	2	2	no	—
129	C₄×C₇₃	#386	1	1	yes	characteristic
130	C₄×C₇₃	#408	1	1	yes	characteristic
131	C₄×C₇₃	C₈×D₄	1	2	yes	—
132	Dic₇₃	—	4	2	no	—
133	Dic₇₃	—	4	1	no	—
134	#12983	—	73	1	no	maximal, Sylow
135	C₂×C₇₃	—	2	4	no	—
136	C₂×C₇₃	—	2	2	no	—
137	C₂×C₇₃	#1869	1	1	yes	characteristic
138	C₂×C₇₃	C₂×#350	1	2	yes	—
139	D₇₃	—	8	1	no	—
140	C₂³×C₁₆	—	73	1	no	—
141	#2929	—	73	1	no	—
142	C₂×#350	—	73	2	no	—
143	#2112	D₇₃	1	1	yes	characteristic, complemented
144	#1379	—	73	2	no	—
145	C₇₃	#12983	1	1	yes	characteristic, complemented, Sylow
146	C₂×#131	—	73	1	no	—
147	C₂³×C₈	C₂×D₇₃	1	1	yes	characteristic
148	#525	—	73	1	no	—
149	C₂×M₃₂	C₂×D₇₃	1	2	yes	—
150	C₂²×C₁₆	—	73	2	no	—
151	C₂²×C₁₆	—	146	4	no	—
152	C₂²×C₁₆	—	146	2	no	—
153	#435	—	146	2	no	—
154	C₈×D₄	—	146	2	no	—
155	#424	—	73	1	no	—
156	#408	—	73	1	no	—
157	#407	—	73	1	no	—
158	#405	—	73	1	no	—
159	#350	—	146	4	no	—
160	C₂²⋊C₁₆	—	2	2	no	—
161	C₂×#41	—	73	1	no	—
162	C₂³×C₄	C₄×D₇₃	1	1	yes	characteristic
163	#131	—	146	2	no	—
164	#131	—	146	2	no	—
165	C₂×M₁₆	—	73	1	no	—
166	C₂×M₁₆	—	73	1	no	—
167	C₂×M₁₆	—	146	1	no	—
168	C₂²×C₈	—	2	2	no	—
169	C₂²×C₈	—	2	2	no	—
170	C₂²×C₈	—	146	1	no	—
171	C₂²×C₈	C₄×D₇₃	1	1	yes	characteristic
172	C₂²×C₈	D₂₉₂	1	2	yes	—
173	C₂²×C₈	C₂²⋊D₇₃	1	2	yes	—
174	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
175	#123	—	146	1	no	—
176	C₂²⋊Q₈	—	73	2	no	—
177	#121	—	73	2	no	—
178	#120	—	146	1	no	—
179	C₄×D₄	—	146	2	no	—
180	#117	—	73	1	no	—
181	M₃₂	—	2	2	no	—
182	M₃₂	—	2	2	no	—
183	C₂×C₁₆	—	2	2	no	—
184	C₂×C₁₆	—	73	4	no	—
185	C₂×C₁₆	—	146	8	no	—
186	C₂×C₁₆	—	146	2	no	—
187	C₂×C₁₆	—	146	2	no	—
188	C₄⋊C₈	—	146	2	no	—
189	C₂²⋊C₈	—	146	2	no	—
190	C₂²⋊C₈	—	146	2	no	—
191	#97	—	146	1	no	—
192	C₄×C₈	—	146	1	no	—
193	C₂⁴	#11924011	1	1	yes	characteristic
194	#41	—	146	2	no	—
195	#41	—	146	2	no	—
196	C₂×Q₈	—	73	1	no	—
197	C₂×D₄	—	73	1	no	—
198	C₂×D₄	—	146	2	no	—
199	C₂×D₄	—	146	1	no	—
200	C₂²×C₄	—	2	2	no	—
201	C₂²×C₄	—	2	2	no	—
202	C₂²×C₄	—	146	1	no	—
203	C₂²×C₄	#11924005	1	2	yes	—
204	C₂²×C₄	C₈×D₇₃	1	2	yes	—
205	C₂²×C₄	#11924011	1	1	yes	characteristic
206	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
207	M₁₆	—	292	1	no	—
208	M₁₆	—	292	1	no	—
209	M₁₆	—	146	2	no	—
210	M₁₆	—	146	2	no	—
211	C₂×C₈	—	2	2	no	—
212	C₂×C₈	—	2	2	no	—
213	C₂×C₈	—	2	4	no	—
214	C₂×C₈	—	2	2	no	—
215	C₂×C₈	—	292	2	no	—
216	C₂×C₈	—	146	1	no	—
217	C₂×C₈	—	146	1	no	—
218	C₂×C₈	#11924005	1	2	yes	—
219	C₂×C₈	D₄×D₇₃	1	2	yes	—
220	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
221	C₂×C₈	C₂×D₂₉₂	1	1	yes	characteristic
222	C₂×C₈	#11924027	1	2	yes	—
223	C₄⋊C₄	—	73	2	no	—
224	C₄⋊C₄	—	146	2	no	—
225	C₂²⋊C₄	—	146	2	no	—
226	C₂²⋊C₄	—	146	1	no	—
227	C₂²⋊C₄	—	146	2	no	—
228	C₄²	—	146	1	no	—
229	C₁₆	—	4	2	no	—
230	C₁₆	—	146	4	no	—
231	C₂³	—	2	4	no	—
232	C₂³	—	2	2	no	—
233	C₂³	—	146	1	no	—
234	C₂³	#14556503	1	2	yes	—
235	C₂³	C₂×#11924011	1	1	yes	characteristic
236	Q₈	—	146	2	no	—
237	D₄	—	292	4	no	—
238	D₄	—	292	2	no	—
239	D₄	—	146	2	no	—
240	C₂×C₄	—	2	2	no	—
241	C₂×C₄	—	2	4	no	—
242	C₂×C₄	—	2	2	no	—
243	C₂×C₄	—	2	2	no	—
244	C₂×C₄	—	292	1	no	—
245	C₂×C₄	—	292	1	no	—
246	C₂×C₄	—	146	2	no	—
247	C₂×C₄	—	146	1	no	—
248	C₂×C₄	#14556503	1	2	yes	—
249	C₂×C₄	C₂×#11924005	1	1	yes	characteristic
250	C₂×C₄	#14556551	1	2	yes	—
251	C₂×C₄	C₂×C₈×D₇₃	1	1	yes	characteristic
252	C₂×C₄	#14556599	1	2	yes	—
253	C₈	—	2	2	no	—
254	C₈	—	292	1	no	—
255	C₈	—	292	1	no	—
256	C₈	#14556561	1	1	yes	characteristic
257	C₈	#14556563	1	2	yes	—
258	C₈	#14556575	1	1	yes	characteristic
259	C₂²	—	2	8	no	—
260	C₂²	—	2	2	no	—
261	C₂²	—	2	2	no	—
262	C₂²	—	2	2	no	—
263	C₂²	—	292	1	no	—
264	C₂²	—	292	2	no	—
265	C₂²	#17988372	1	4	yes	complemented
266	C₂²	C₂×#14556503	1	1	yes	characteristic
267	C₂²	#17988655	1	2	yes	—
268	C₄	—	2	2	no	—
269	C₄	—	292	1	no	—
270	C₄	—	292	2	no	—
271	C₄	#17988464	1	1	yes	characteristic
272	C₄	#17988555	1	1	yes	characteristic
273	C₄	#17988650	1	2	yes	—
274	C₂	—	2	4	no	—
275	C₂	—	2	2	no	—
276	C₂	—	584	1	no	—
277	C₂	#22610221	1	1	yes	characteristic
278	C₂	C₂×#17988372	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂³×#11924003

C₂

yes

maximal, characteristic, complemented

#22618625

C₂

yes

maximal, characteristic

C₂×#17988372

C₂

yes

maximal, complemented

#22608021

C₂

yes

maximal, complemented

C₇₃×#2112

C₂

yes

maximal, characteristic, complemented

C₂×#14556597

C₂²

yes

characteristic

#17989098

C₄

yes

—

—

C₂²

yes

—

#17988658

—

C₈×C₂²⋊D₇₃

—

#17988613

C₄

yes

characteristic

#17988553

C₄

yes

characteristic

#17988551

C₄

yes

characteristic

#17988542

C₂²

yes

characteristic

#17988372

—

C₂³×C₈×C₇₃

C₂²

yes

characteristic

C₂×M₃₂×C₇₃

C₂²

yes

—

C₂²⋊C₁₆×C₇₃

—

C₂×#11924028

C₂×C₄

yes

—

—

C₂×C₄

yes

characteristic

C₂×#11924012

C₂×C₄

yes

characteristic

C₂×#11924011

—

C₂×C₈×D₇₃

—

#14556574

—

#14556570

C₈

yes

—

#14556565

C₈

yes

—

#14556560

—

C₄×C₂²⋊D₇₃

—

#14556550

C₂×C₄

yes

—

—

—

D₄

yes

—

—

—

—

C₈×Dic₇₃

—

C₂³×C₄×C₇₃

C₂×C₄

yes

characteristic

C₂²×C₈×C₇₃

—

C₂²×C₈×C₇₃

—

C₂²×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂²×C₈×C₇₃

D₄

yes

—

C₂²×C₈×C₇₃

D₄

yes

—

C₂²×C₈×C₇₃

C₂³

yes

characteristic

M₃₂×C₇₃

—

M₃₂×C₇₃

—

C₂×C₁₆×C₇₃

—

#11924028

—

#11924028

—

C₂×Dic₁₄₆

C₂×C₈

yes

characteristic

C₂×D₂₉₂

C₂×C₈

yes

characteristic

C₂×C₂²⋊D₇₃

—

C₂×C₂²⋊D₇₃

—

C₂×C₄×D₇₃

—

—

—

—

—

—

—

C₈×D₇₃

—

C₄⋊Dic₇₃

C₂×C₈

yes

—

#11924007

—

C₂²⋊Dic₇₃

—

C₂²⋊Dic₇₃

—

#11924005

—

C₄×Dic₇₃

—

#11924003

—

C₂⁴×C₇₃

M₁₆

yes

characteristic

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₇₃

C₂×C₈

yes

—

C₂²×C₄×C₇₃

M₁₆

yes

characteristic

C₂²×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₂²⋊C₄

yes

—

C₂×C₈×C₇₃

C₂×D₄

yes

—

C₂×C₈×C₇₃

C₂×D₄

yes

characteristic

C₂×C₈×C₇₃

C₂×D₄

yes

characteristic

C₂×C₈×C₇₃

#41

yes

—

C₁₆×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

C₂²⋊C₈

yes

—

C₂³×C₇₃

C₂×M₁₆

yes

characteristic

C₂²×D₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

100

C₂×C₄×C₇₃

C₂²⋊C₈

yes

—

101

C₂×C₄×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

102

C₂×C₄×C₇₃

C₄×D₄

yes

—

103

C₂×C₄×C₇₃

C₂²×C₈

yes

characteristic

104

C₂×C₄×C₇₃

#131

yes

—

105

C₂²⋊D₇₃

—

106

C₂²⋊D₇₃

—

107

C₂×Dic₇₃

—

108

C₂×Dic₇₃

—

109

D₂₉₂

—

110

C₄×D₇₃

—

111

C₄×D₇₃

—

112

Dic₁₄₆

—

113

C₈×C₇₃

—

114

C₈×C₇₃

#120

yes

characteristic

115

C₈×C₇₃

#121

yes

—

116

C₈×C₇₃

#123

yes

characteristic

117

#10596831

—

118

#10596831

—

119

C₂²×C₇₃

—

120

C₂²×C₇₃

—

121

C₂²×C₇₃

—

122

C₂²×C₇₃

—

123

C₂²×C₇₃

#350

yes

complemented

124

C₂²×C₇₃

C₂×C₂²⋊C₈

yes

characteristic

125

C₂²×C₇₃

#435

yes

—

126

C₂×D₇₃

—

127

C₂×D₇₃

—

128

C₄×C₇₃

—

129

C₄×C₇₃

#386

yes

characteristic

130

C₄×C₇₃

#408

yes

characteristic

131

C₄×C₇₃

C₈×D₄

yes

—

132

Dic₇₃

—

133

Dic₇₃

—

134

#12983

—

maximal, Sylow

135

C₂×C₇₃

—

136

C₂×C₇₃

—

137

C₂×C₇₃

#1869

yes

characteristic

138

C₂×C₇₃

C₂×#350

yes

—

139

D₇₃

—

140

C₂³×C₁₆

—

141

#2929

—

142

C₂×#350

—

143

#2112

D₇₃

yes

characteristic, complemented

144

#1379

—

145

C₇₃

#12983

yes

characteristic, complemented, Sylow

146

C₂×#131

—

147

C₂³×C₈

C₂×D₇₃

yes

characteristic

148

#525

—

149

C₂×M₃₂

C₂×D₇₃

yes

—

150

C₂²×C₁₆

—

151

C₂²×C₁₆

—

146

—

152

C₂²×C₁₆

—

146

—

153

#435

—

146

—

154

C₈×D₄

—

146

—

155

#424

—

156

#408

—

157

#407

—

158

#405

—

159

#350

—

146

—

160

C₂²⋊C₁₆

—

161

C₂×#41

—

162

C₂³×C₄

C₄×D₇₃

yes

characteristic

163

#131

—

146

—

164

#131

—

146

—

165

C₂×M₁₆

—

166

C₂×M₁₆

—

167

C₂×M₁₆

—

146

—

168

C₂²×C₈

—

169

C₂²×C₈

—

170

C₂²×C₈

—

146

—

171

C₂²×C₈

C₄×D₇₃

yes

characteristic

172

C₂²×C₈

D₂₉₂

yes

—

173

C₂²×C₈

C₂²⋊D₇₃

yes

—

174

C₂²×C₈

C₂²×D₇₃

yes

characteristic

175

#123

—

146

—

176

C₂²⋊Q₈

—

177

#121

—

178

#120

—

146

—

179

C₄×D₄

—

146

—

180

#117

—

181

M₃₂

—

182

M₃₂

—

183

C₂×C₁₆

—

184

C₂×C₁₆

—

185

C₂×C₁₆

—

146

—

186

C₂×C₁₆

—

146

—

187

C₂×C₁₆

—

146

—

188

C₄⋊C₈

—

146

—

189

C₂²⋊C₈

—

146

—

190

C₂²⋊C₈

—

146

—

191

#97

—

146

—

192

C₄×C₈

—

146

—

193

C₂⁴

#11924011

yes

characteristic

194

#41

—

146

—

195

#41

—

146

—

196

C₂×Q₈

—

197

C₂×D₄

—

198

C₂×D₄

—

146

—

199

C₂×D₄

—

146

—

200

C₂²×C₄

—

201

C₂²×C₄

—

202

C₂²×C₄

—

146

—

203

C₂²×C₄

#11924005

yes

—

204

C₂²×C₄

C₈×D₇₃

yes

—

205

C₂²×C₄

#11924011

yes

characteristic

206

C₂²×C₄

C₂×C₄×D₇₃

yes

characteristic

207

M₁₆

—

292

—

208

M₁₆

—

292

—

209

M₁₆

—

146

—

210

M₁₆

—

146

—

211

C₂×C₈

—

212

C₂×C₈

—

213

C₂×C₈

—

214

C₂×C₈

—

215

C₂×C₈

—

292

—

216

C₂×C₈

—

146

—

217

C₂×C₈

—

146

—

218

C₂×C₈

#11924005

yes

—

219

C₂×C₈

D₄×D₇₃

yes

—

220

C₂×C₈

C₂×C₂²⋊D₇₃

yes

characteristic

221

C₂×C₈

C₂×D₂₉₂

yes

characteristic

222

C₂×C₈

#11924027

yes

—

223

C₄⋊C₄

—

224

C₄⋊C₄

—

146

—

225

C₂²⋊C₄

—

146

—

226

C₂²⋊C₄

—

146

—

227

C₂²⋊C₄

—

146

—

228

C₄²

—

146

—

229

C₁₆

—

230

C₁₆

—

146

—

231

C₂³

—

232

C₂³

—

233

C₂³

—

146

—

234

C₂³

#14556503

yes

—

235

C₂³

C₂×#11924011

yes

characteristic

236

Q₈

—

146

—

237

D₄

—

292

—

238

D₄

—

292

—

239

D₄

—

146

—

240

C₂×C₄

—

241

C₂×C₄

—

242

C₂×C₄

—

243

C₂×C₄

—

244

C₂×C₄

—

292

—

245

C₂×C₄

—

292

—

246

C₂×C₄

—

146

—

247

C₂×C₄

—

146

—

248

C₂×C₄

#14556503

yes

—

249

C₂×C₄

C₂×#11924005

yes

characteristic

250

C₂×C₄

#14556551

yes

—

251

C₂×C₄

C₂×C₈×D₇₃

yes

characteristic

252

C₂×C₄

#14556599

yes

—

253

C₈

—

254

C₈

—

292

—

255

C₈

—

292

—

256

C₈

#14556561

yes

characteristic

257

C₈

#14556563

yes

—

258

C₈

#14556575

yes

characteristic

259

C₂²

—

260

C₂²

—

261

C₂²

—

262

C₂²

—

263

C₂²

—

292

—

264

C₂²

—

292

—

265

C₂²

#17988372

yes

complemented

266

C₂²

C₂×#14556503

yes

characteristic

267

C₂²

#17988655

yes

—

268

C₄

—

269

C₄

—

292

—

270

C₄

—

292

—

271

C₄

#17988464

yes

characteristic

272

C₄

#17988555

yes

characteristic

273

C₄

#17988650

yes

—

274

C₂

—

275

C₂

—

276

C₂

—

584

—

277

C₂

#22610221

yes

characteristic

278

C₂

C₂×#17988372

yes

—

	subgroup	G/H
center	C₂×C₈	C₂×C₂²⋊D₇₃
commutator	C₂×C₄×C₇₃	C₂²×C₈
Frattini	C₂²×C₈	C₂²×D₇₃
Fitting	C₇₃×#2112	C₂
socle	C₂²×C₇₃	C₂×C₂²⋊C₈
prime radical	#17989098	C₄
cosocle	C₂²×C₈×C₇₃	C₂³
hypercenter	#2112	D₇₃
hypocenter	C₇₃	#12983
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂³×C₈ ◁ #2112

subgroup

G/H

center

C₂×C₈

C₂×C₂²⋊D₇₃

commutator

C₂×C₄×C₇₃

C₂²×C₈

Frattini

C₂²×C₈

C₂²×D₇₃

Fitting

C₇₃×#2112

C₂

socle

C₂²×C₇₃

C₂×C₂²⋊C₈

prime radical

#17989098

C₄

cosocle

C₂²×C₈×C₇₃

C₂³

D₇₃

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂×C₈ ◁ C₂³×C₈ ◁ #2112

N	H ≅ G/N	type
1. C₂³×#11924003	C₂	semidirect
3. C₂×#17988372	C₂	semidirect
4. #22608021	C₂	semidirect
5. C₇₃×#2112	C₂	semidirect
37. C₂×#11924003	D₄	semidirect
123. C₂²×C₇₃	#350	semidirect
143. #2112	D₇₃	semidirect
145. C₇₃	#12983	semidirect
265. C₂²	#17988372	semidirect

H ≅ G/N

type

1. C₂³×#11924003

C₂

semidirect

3. C₂×#17988372

C₂

semidirect

4. #22608021

C₂

semidirect

5. C₇₃×#2112

C₂

semidirect

37. C₂×#11924003

D₄

semidirect

123. C₂²×C₇₃

#350

semidirect

143. #2112

D₇₃

semidirect

145. C₇₃

#12983

semidirect

265. C₂²

#17988372

semidirect

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

subgroup	index
C₂³×#11924003	2
#22618625	2
C₂×#17988372	2
#22608021	2
C₇₃×#2112	2
#12983	73

subgroup

index

C₇₃×#2112

Subgroups — #33002876

Conjugacy classes of subgroups

Complements

Maximal subgroups