Group #33002912 — subgroups

Subgroups — #33002912

Order 18688.

470 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 135 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	#22618632	C₂	1	1	yes	maximal, characteristic
2	#22611552	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#17988368	C₂	1	2	yes	maximal, complemented
4	#22608018	C₂	1	2	yes	maximal, complemented
5	C₇₃×#3407	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#11924011	C₂²	1	1	yes	characteristic
7	#17989094	C₄	1	1	yes	characteristic
8	C₂×#14556531	C₂²	1	2	yes	—
9	#17988663	—	2	2	no	—
10	#17988658	—	2	2	no	—
11	#17988615	C₄	1	1	yes	characteristic
12	#17988554	C₄	1	1	yes	characteristic
13	#17988550	C₄	1	1	yes	characteristic
14	#17988542	C₂²	1	1	yes	characteristic
15	#17988369	—	2	2	no	—
16	#17988368	—	2	4	no	—
17	C₂×#131×C₇₃	C₂²	1	1	yes	characteristic
18	#504×C₇₃	—	2	4	no	—
19	C₂×M₃₂×C₇₃	—	2	2	no	—
20	C₂×M₃₂×C₇₃	C₂²	1	2	yes	—
21	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
22	C₂×#11924012	C₂×C₄	1	1	yes	characteristic
23	C₂×#11924011	—	2	2	no	—
24	C₂×#11924011	—	2	1	no	—
25	C₂×#11924011	—	2	1	no	—
26	C₂×#11924011	—	2	2	no	—
27	C₂²×#10596831	C₂×C₄	1	1	yes	characteristic
28	#14556572	C₈	1	2	yes	—
29	#14556567	—	2	1	no	—
30	#14556562	—	2	1	no	—
31	#14556559	C₈	1	2	yes	—
32	C₄×C₂²⋊D₇₃	—	2	2	no	—
33	#14556550	C₂×C₄	1	1	yes	characteristic
34	#14556531	—	2	2	no	—
35	#14556531	—	2	2	no	—
36	C₂×#11924003	—	2	2	no	—
37	#14556520	—	2	2	no	—
38	C₂²⋊#10596831	—	2	2	no	—
39	#14556503	—	2	2	no	—
40	#14556501	—	2	1	no	—
41	C₈×Dic₇₃	—	2	1	no	—
42	C₂×#41×C₇₃	C₂×C₄	1	1	yes	characteristic
43	#131×C₇₃	—	2	2	no	—
44	#131×C₇₃	—	2	2	no	—
45	C₂×M₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
46	C₂×M₁₆×C₇₃	D₄	1	2	yes	—
47	C₂²×C₈×C₇₃	D₄	1	2	yes	—
48	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
49	M₃₂×C₇₃	—	2	4	no	—
50	M₃₂×C₇₃	—	2	2	no	—
51	M₃₂×C₇₃	D₄	1	4	yes	complemented
52	C₂×C₁₆×C₇₃	—	2	4	no	—
53	C₂×C₁₆×C₇₃	—	2	2	no	—
54	C₂³×D₇₃	C₂×C₈	1	1	yes	characteristic
55	C₂×C₂²⋊D₇₃	—	2	2	no	—
56	C₂²×Dic₇₃	C₂×C₈	1	1	yes	characteristic
57	C₂×C₄×D₇₃	—	2	1	no	—
58	C₂×C₄×D₇₃	—	2	2	no	—
59	C₂×C₄×D₇₃	—	2	1	no	—
60	C₂×C₄×D₇₃	—	2	2	no	—
61	#11924012	—	2	2	no	—
62	#11924011	—	4	1	no	—
63	#11924011	—	4	2	no	—
64	#11924011	—	4	1	no	—
65	C₂×#10596831	—	2	1	no	—
66	C₂×#10596831	—	2	1	no	—
67	C₂×#10596831	—	2	2	no	—
68	C₄⋊Dic₇₃	—	2	1	no	—
69	#11924007	—	2	2	no	—
70	C₂²⋊Dic₇₃	—	2	2	no	—
71	C₂²⋊Dic₇₃	C₂×C₈	1	2	yes	—
72	#11924005	—	2	2	no	—
73	C₄×Dic₇₃	—	2	1	no	—
74	#11924003	—	4	2	no	—
75	#41×C₇₃	—	2	2	no	—
76	#41×C₇₃	—	2	2	no	—
77	C₂×Q₈×C₇₃	M₁₆	1	1	yes	characteristic
78	C₂×D₄×C₇₃	C₂×C₈	1	2	yes	—
79	C₂×D₄×C₇₃	M₁₆	1	1	yes	characteristic
80	C₂²×C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
81	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
82	M₁₆×C₇₃	—	2	2	no	—
83	M₁₆×C₇₃	—	2	4	no	—
84	C₂×C₈×C₇₃	—	2	2	no	—
85	C₂×C₈×C₇₃	—	2	2	no	—
86	C₂×C₈×C₇₃	C₂²⋊C₄	1	2	yes	—
87	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
88	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
89	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
90	C₂×C₈×C₇₃	#41	1	2	yes	—
91	C₁₆×C₇₃	—	2	4	no	—
92	C₂³×C₇₃	C₂²⋊C₈	1	2	yes	—
93	C₂³×C₇₃	C₂²×C₈	1	1	yes	characteristic
94	C₂²×D₇₃	—	2	1	no	—
95	C₂²×D₇₃	—	2	2	no	—
96	C₂²×D₇₃	—	8	1	no	—
97	Q₈×C₇₃	—	2	2	no	—
98	D₄×C₇₃	—	2	4	no	—
99	D₄×C₇₃	—	2	2	no	—
100	C₂×C₄×C₇₃	—	2	2	no	—
101	C₂×C₄×C₇₃	—	2	2	no	—
102	C₂×C₄×C₇₃	C₂²⋊C₈	1	2	yes	—
103	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
104	C₂×C₄×C₇₃	C₄×D₄	1	2	yes	—
105	C₂×C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
106	C₂×C₄×C₇₃	#131	1	2	yes	—
107	C₂²⋊D₇₃	—	8	2	no	—
108	C₂×Dic₇₃	—	2	2	no	—
109	C₂×Dic₇₃	—	2	1	no	—
110	C₂×Dic₇₃	—	2	2	no	—
111	C₄×D₇₃	—	4	1	no	—
112	C₄×D₇₃	—	4	1	no	—
113	C₄×D₇₃	—	4	2	no	—
114	C₈×C₇₃	—	2	2	no	—
115	C₈×C₇₃	#120	1	1	yes	characteristic
116	C₈×C₇₃	#121	1	2	yes	—
117	C₈×C₇₃	#123	1	1	yes	characteristic
118	#10596831	—	4	1	no	—
119	#10596831	—	4	1	no	—
120	C₂²×C₇₃	—	2	2	no	—
121	C₂²×C₇₃	—	4	1	no	—
122	C₂²×C₇₃	—	4	2	no	—
123	C₂²×C₇₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
124	C₂²×C₇₃	C₈×D₄	1	2	yes	—
125	C₂×D₇₃	—	4	1	no	—
126	C₂×D₇₃	—	4	1	no	—
127	C₂×D₇₃	—	4	1	no	—
128	C₂×D₇₃	—	8	2	no	—
129	C₄×C₇₃	—	2	2	no	—
130	C₄×C₇₃	#386	1	1	yes	characteristic
131	C₄×C₇₃	#408	1	1	yes	characteristic
132	C₄×C₇₃	#435	1	2	yes	—
133	Dic₇₃	—	4	2	no	—
134	Dic₇₃	—	4	1	no	—
135	#12989	—	73	1	no	maximal, Sylow
136	C₂×C₇₃	—	2	1	no	—
137	C₂×C₇₃	—	2	2	no	—
138	C₂×C₇₃	—	4	2	no	—
139	C₂×C₇₃	#1869	1	1	yes	characteristic
140	D₇₃	—	8	1	no	—
141	#3407	D₇₃	1	1	yes	characteristic, complemented
142	#2930	—	73	1	no	—
143	#2115	—	73	1	no	—
144	C₂×#349	—	73	2	no	—
145	#1378	—	73	2	no	—
146	C₇₃	#12989	1	1	yes	characteristic, complemented, Sylow
147	C₂×#131	C₂×D₇₃	1	1	yes	characteristic
148	C₂²×M₁₆	—	73	1	no	—
149	#525	—	73	1	no	—
150	#504	—	2	4	no	—
151	C₂×M₃₂	—	2	2	no	—
152	C₂×M₃₂	—	73	2	no	—
153	C₂×M₃₂	C₂×D₇₃	1	2	yes	—
154	#436	—	146	2	no	—
155	#435	—	146	2	no	—
156	#424	—	73	1	no	—
157	#408	—	73	1	no	—
158	#407	—	73	1	no	—
159	#405	—	73	1	no	—
160	#349	—	146	2	no	—
161	#349	—	146	4	no	—
162	C₂×#41	C₄×D₇₃	1	1	yes	characteristic
163	C₂³×C₄	—	73	1	no	—
164	#131	—	2	2	no	—
165	#131	—	2	2	no	—
166	C₂×M₁₆	—	73	1	no	—
167	C₂×M₁₆	—	146	2	no	—
168	C₂×M₁₆	—	146	1	no	—
169	C₂×M₁₆	—	146	1	no	—
170	C₂×M₁₆	—	146	2	no	—
171	C₂×M₁₆	C₄×D₇₃	1	1	yes	characteristic
172	C₂×M₁₆	D₂₉₂	1	2	yes	—
173	C₂²×C₈	—	73	1	no	—
174	C₂²×C₈	C₂²⋊D₇₃	1	2	yes	—
175	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
176	#123	—	73	2	no	—
177	C₂²⋊Q₈	—	146	1	no	—
178	#121	—	146	1	no	—
179	#120	—	73	2	no	—
180	C₄×D₄	—	146	2	no	—
181	#117	—	73	1	no	—
182	M₃₂	—	2	4	no	—
183	M₃₂	—	2	2	no	—
184	M₃₂	—	146	2	no	—
185	M₃₂	—	146	2	no	—
186	M₃₂	C₂²⋊D₇₃	1	4	yes	complemented
187	C₂×C₁₆	—	2	4	no	—
188	C₂×C₁₆	—	2	2	no	—
189	C₂×C₁₆	—	146	2	no	—
190	C₄⋊C₈	—	146	2	no	—
191	C₂²⋊C₈	—	146	2	no	—
192	C₂²⋊C₈	—	146	2	no	—
193	#97	—	146	1	no	—
194	C₄×C₈	—	146	1	no	—
195	C₂⁴	—	73	1	no	—
196	#41	—	2	2	no	—
197	#41	—	2	2	no	—
198	C₂×Q₈	#11924011	1	1	yes	characteristic
199	C₂×D₄	—	146	2	no	—
200	C₂×D₄	C₈×D₇₃	1	2	yes	—
201	C₂×D₄	#11924011	1	1	yes	characteristic
202	C₂²×C₄	—	73	1	no	—
203	C₂²×C₄	—	146	1	no	—
204	C₂²×C₄	—	146	2	no	—
205	C₂²×C₄	—	146	1	no	—
206	C₂²×C₄	—	146	2	no	—
207	C₂²×C₄	#11924005	1	2	yes	—
208	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
209	M₁₆	—	2	2	no	—
210	M₁₆	—	2	4	no	—
211	M₁₆	—	292	1	no	—
212	M₁₆	—	292	2	no	—
213	M₁₆	—	292	1	no	—
214	M₁₆	—	146	2	no	—
215	C₂×C₈	—	2	2	no	—
216	C₂×C₈	—	2	2	no	—
217	C₂×C₈	—	146	1	no	—
218	C₂×C₈	—	146	1	no	—
219	C₂×C₈	—	146	2	no	—
220	C₂×C₈	#11924005	1	2	yes	—
221	C₂×C₈	C₂×C₂²⋊D₇₃	1	2	yes	—
222	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
223	C₂×C₈	C₂×D₂₉₂	1	1	yes	characteristic
224	C₂×C₈	#11924028	1	2	yes	—
225	C₄⋊C₄	—	146	2	no	—
226	C₄⋊C₄	—	146	1	no	—
227	C₂²⋊C₄	—	73	2	no	—
228	C₂²⋊C₄	—	146	2	no	—
229	C₂²⋊C₄	—	146	2	no	—
230	C₄²	—	146	1	no	—
231	C₁₆	—	2	4	no	—
232	C₁₆	—	292	2	no	—
233	C₂³	—	584	1	no	—
234	C₂³	—	146	1	no	—
235	C₂³	—	146	2	no	—
236	C₂³	#14556503	1	2	yes	—
237	C₂³	C₂×C₈×D₇₃	1	1	yes	characteristic
238	Q₈	—	2	2	no	—
239	D₄	—	2	4	no	—
240	D₄	—	2	2	no	—
241	D₄	—	584	2	no	—
242	C₂×C₄	—	2	2	no	—
243	C₂×C₄	—	2	2	no	—
244	C₂×C₄	—	292	2	no	—
245	C₂×C₄	—	292	1	no	—
246	C₂×C₄	—	292	1	no	—
247	C₂×C₄	—	146	2	no	—
248	C₂×C₄	—	146	2	no	—
249	C₂×C₄	—	146	1	no	—
250	C₂×C₄	#14556503	1	2	yes	—
251	C₂×C₄	C₂×#11924005	1	1	yes	characteristic
252	C₂×C₄	C₄×C₂²⋊D₇₃	1	2	yes	—
253	C₂×C₄	C₂×#11924011	1	1	yes	characteristic
254	C₂×C₄	#14556597	1	2	yes	—
255	C₈	—	2	2	no	—
256	C₈	—	292	1	no	—
257	C₈	—	292	1	no	—
258	C₈	#14556560	1	1	yes	characteristic
259	C₈	#14556565	1	2	yes	—
260	C₈	#14556574	1	1	yes	characteristic
261	C₂²	—	2	2	no	—
262	C₂²	—	4	1	no	—
263	C₂²	—	4	2	no	—
264	C₂²	—	292	1	no	—
265	C₂²	—	292	1	no	—
266	C₂²	—	292	1	no	—
267	C₂²	—	584	2	no	—
268	C₂²	C₂×#14556503	1	1	yes	characteristic
269	C₂²	C₈×C₂²⋊D₇₃	1	2	yes	—
270	C₄	—	2	2	no	—
271	C₄	—	292	2	no	—
272	C₄	—	292	1	no	—
273	C₄	#17988466	1	1	yes	characteristic
274	C₄	#17988553	1	1	yes	characteristic
275	C₄	#17988658	1	2	yes	—
276	C₂	—	2	1	no	—
277	C₂	—	2	2	no	—
278	C₂	—	4	2	no	—
279	C₂	—	584	1	no	—
280	C₂	#22610223	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22618632

C₂

yes

maximal, characteristic

#22611552

C₂

yes

maximal, characteristic, complemented

C₂×#17988368

C₂

yes

maximal, complemented

#22608018

C₂

yes

maximal, complemented

C₇₃×#3407

C₂

yes

maximal, characteristic, complemented

C₂²×#11924011

C₂²

yes

characteristic

#17989094

C₄

yes

characteristic

C₂×#14556531

C₂²

yes

—

#17988663

—

#17988658

—

#17988615

C₄

yes

characteristic

#17988554

C₄

yes

characteristic

#17988550

C₄

yes

characteristic

#17988542

C₂²

yes

characteristic

#17988369

—

#17988368

—

C₂×#131×C₇₃

C₂²

yes

characteristic

#504×C₇₃

—

C₂×M₃₂×C₇₃

—

C₂×M₃₂×C₇₃

C₂²

yes

—

C₂²×C₄×D₇₃

C₂×C₄

yes

characteristic

C₂×#11924012

C₂×C₄

yes

—

—

—

—

C₂×C₄

yes

characteristic

#14556572

C₈

yes

—

#14556567

—

#14556562

—

#14556559

C₈

yes

—

C₄×C₂²⋊D₇₃

—

#14556550

C₂×C₄

yes

—

—

—

—

—

—

—

C₈×Dic₇₃

—

C₂×#41×C₇₃

C₂×C₄

yes

characteristic

#131×C₇₃

—

#131×C₇₃

—

C₂×M₁₆×C₇₃

C₂×C₄

yes

characteristic

C₂×M₁₆×C₇₃

D₄

yes

—

C₂²×C₈×C₇₃

D₄

yes

—

C₂²×C₈×C₇₃

C₂³

yes

characteristic

M₃₂×C₇₃

—

M₃₂×C₇₃

—

M₃₂×C₇₃

D₄

yes

complemented

C₂×C₁₆×C₇₃

—

C₂×C₁₆×C₇₃

—

C₂³×D₇₃

C₂×C₈

yes

characteristic

C₂×C₂²⋊D₇₃

—

C₂²×Dic₇₃

C₂×C₈

yes

characteristic

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

—

—

—

—

—

—

—

—

C₄⋊Dic₇₃

—

#11924007

—

C₂²⋊Dic₇₃

—

C₂²⋊Dic₇₃

C₂×C₈

yes

—

#11924005

—

C₄×Dic₇₃

—

#11924003

—

#41×C₇₃

—

#41×C₇₃

—

C₂×Q₈×C₇₃

M₁₆

yes

characteristic

C₂×D₄×C₇₃

C₂×C₈

yes

—

C₂×D₄×C₇₃

M₁₆

yes

characteristic

C₂²×C₄×C₇₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₇₃

C₂²×C₄

yes

characteristic

M₁₆×C₇₃

—

M₁₆×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

C₂²⋊C₈

yes

—

C₂³×C₇₃

C₂²×C₈

yes

characteristic

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

—

Q₈×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

100

C₂×C₄×C₇₃

—

101

C₂×C₄×C₇₃

—

102

C₂×C₄×C₇₃

C₂²⋊C₈

yes

—

103

C₂×C₄×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

104

C₂×C₄×C₇₃

C₄×D₄

yes

—

105

C₂×C₄×C₇₃

C₂×M₁₆

yes

characteristic

106

C₂×C₄×C₇₃

#131

yes

—

107

C₂²⋊D₇₃

—

108

C₂×Dic₇₃

—

109

C₂×Dic₇₃

—

110

C₂×Dic₇₃

—

111

C₄×D₇₃

—

112

C₄×D₇₃

—

113

C₄×D₇₃

—

114

C₈×C₇₃

—

115

C₈×C₇₃

#120

yes

characteristic

116

C₈×C₇₃

#121

yes

—

117

C₈×C₇₃

#123

yes

characteristic

118

#10596831

—

119

#10596831

—

120

C₂²×C₇₃

—

121

C₂²×C₇₃

—

122

C₂²×C₇₃

—

123

C₂²×C₇₃

C₂×C₂²⋊C₈

yes

characteristic

124

C₂²×C₇₃

C₈×D₄

yes

—

125

C₂×D₇₃

—

126

C₂×D₇₃

—

127

C₂×D₇₃

—

128

C₂×D₇₃

—

129

C₄×C₇₃

—

130

C₄×C₇₃

#386

yes

characteristic

131

C₄×C₇₃

#408

yes

characteristic

132

C₄×C₇₃

#435

yes

—

133

Dic₇₃

—

134

Dic₇₃

—

135

#12989

—

maximal, Sylow

136

C₂×C₇₃

—

137

C₂×C₇₃

—

138

C₂×C₇₃

—

139

C₂×C₇₃

#1869

yes

characteristic

140

D₇₃

—

141

#3407

D₇₃

yes

characteristic, complemented

142

#2930

—

143

#2115

—

144

C₂×#349

—

145

#1378

—

146

C₇₃

#12989

yes

characteristic, complemented, Sylow

147

C₂×#131

C₂×D₇₃

yes

characteristic

148

C₂²×M₁₆

—

149

#525

—

150

#504

—

151

C₂×M₃₂

—

152

C₂×M₃₂

—

153

C₂×M₃₂

C₂×D₇₃

yes

—

154

#436

—

146

—

155

#435

—

146

—

156

#424

—

157

#408

—

158

#407

—

159

#405

—

160

#349

—

146

—

161

#349

—

146

—

162

C₂×#41

C₄×D₇₃

yes

characteristic

163

C₂³×C₄

—

164

#131

—

165

#131

—

166

C₂×M₁₆

—

167

C₂×M₁₆

—

146

—

168

C₂×M₁₆

—

146

—

169

C₂×M₁₆

—

146

—

170

C₂×M₁₆

—

146

—

171

C₂×M₁₆

C₄×D₇₃

yes

characteristic

172

C₂×M₁₆

D₂₉₂

yes

—

173

C₂²×C₈

—

174

C₂²×C₈

C₂²⋊D₇₃

yes

—

175

C₂²×C₈

C₂²×D₇₃

yes

characteristic

176

#123

—

177

C₂²⋊Q₈

—

146

—

178

#121

—

146

—

179

#120

—

180

C₄×D₄

—

146

—

181

#117

—

182

M₃₂

—

183

M₃₂

—

184

M₃₂

—

146

—

185

M₃₂

—

146

—

186

M₃₂

C₂²⋊D₇₃

yes

complemented

187

C₂×C₁₆

—

188

C₂×C₁₆

—

189

C₂×C₁₆

—

146

—

190

C₄⋊C₈

—

146

—

191

C₂²⋊C₈

—

146

—

192

C₂²⋊C₈

—

146

—

193

#97

—

146

—

194

C₄×C₈

—

146

—

195

C₂⁴

—

196

#41

—

197

#41

—

198

C₂×Q₈

#11924011

yes

characteristic

199

C₂×D₄

—

146

—

200

C₂×D₄

C₈×D₇₃

yes

—

201

C₂×D₄

#11924011

yes

characteristic

202

C₂²×C₄

—

203

C₂²×C₄

—

146

—

204

C₂²×C₄

—

146

—

205

C₂²×C₄

—

146

—

206

C₂²×C₄

—

146

—

207

C₂²×C₄

#11924005

yes

—

208

C₂²×C₄

C₂×C₄×D₇₃

yes

characteristic

209

M₁₆

—

210

M₁₆

—

211

M₁₆

—

292

—

212

M₁₆

—

292

—

213

M₁₆

—

292

—

214

M₁₆

—

146

—

215

C₂×C₈

—

216

C₂×C₈

—

217

C₂×C₈

—

146

—

218

C₂×C₈

—

146

—

219

C₂×C₈

—

146

—

220

C₂×C₈

#11924005

yes

—

221

C₂×C₈

C₂×C₂²⋊D₇₃

yes

—

222

C₂×C₈

C₂×C₂²⋊D₇₃

yes

characteristic

223

C₂×C₈

C₂×D₂₉₂

yes

characteristic

224

C₂×C₈

#11924028

yes

—

225

C₄⋊C₄

—

146

—

226

C₄⋊C₄

—

146

—

227

C₂²⋊C₄

—

228

C₂²⋊C₄

—

146

—

229

C₂²⋊C₄

—

146

—

230

C₄²

—

146

—

231

C₁₆

—

232

C₁₆

—

292

—

233

C₂³

—

584

—

234

C₂³

—

146

—

235

C₂³

—

146

—

236

C₂³

#14556503

yes

—

237

C₂³

C₂×C₈×D₇₃

yes

characteristic

238

Q₈

—

239

D₄

—

240

D₄

—

241

D₄

—

584

—

242

C₂×C₄

—

243

C₂×C₄

—

244

C₂×C₄

—

292

—

245

C₂×C₄

—

292

—

246

C₂×C₄

—

292

—

247

C₂×C₄

—

146

—

248

C₂×C₄

—

146

—

249

C₂×C₄

—

146

—

250

C₂×C₄

#14556503

yes

—

251

C₂×C₄

C₂×#11924005

yes

characteristic

252

C₂×C₄

C₄×C₂²⋊D₇₃

yes

—

253

C₂×C₄

C₂×#11924011

yes

characteristic

254

C₂×C₄

#14556597

yes

—

255

C₈

—

256

C₈

—

292

—

257

C₈

—

292

—

258

C₈

#14556560

yes

characteristic

259

C₈

#14556565

yes

—

260

C₈

#14556574

yes

characteristic

261

C₂²

—

262

C₂²

—

263

C₂²

—

264

C₂²

—

292

—

265

C₂²

—

292

—

266

C₂²

—

292

—

267

C₂²

—

584

—

268

C₂²

C₂×#14556503

yes

characteristic

269

C₂²

C₈×C₂²⋊D₇₃

yes

—

270

C₄

—

271

C₄

—

292

—

272

C₄

—

292

—

273

C₄

#17988466

yes

characteristic

274

C₄

#17988553

yes

characteristic

275

C₄

#17988658

yes

—

276

C₂

—

277

C₂

—

278

C₂

—

279

C₂

—

584

—

280

C₂

#22610223

yes

characteristic

	subgroup	G/H
center	C₄	#17988466
commutator	C₂³×C₇₃	C₂²×C₈
Frattini	C₂²×C₈	C₂²×D₇₃
Fitting	C₇₃×#3407	C₂
socle	C₂×C₇₃	#1869
prime radical	#17989094	C₄
cosocle	C₂²×C₈×C₇₃	C₂³
hypercenter	#3407	D₇₃
hypocenter	C₇₃	#12989
LCS	G ▷ C₂³×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₈ ◁ #3407

subgroup

G/H

center

C₄

#17988466

commutator

C₂³×C₇₃

C₂²×C₈

Frattini

C₂²×C₈

C₂²×D₇₃

Fitting

C₇₃×#3407

C₂

C₂×C₇₃

C₄

C₂²×C₈×C₇₃

C₂³

D₇₃

C₇₃

G ▷ C₂³×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₄ ◁ C₂²×C₈ ◁ #3407

N	H ≅ G/N	type
2. #22611552	C₂	semidirect
3. C₂×#17988368	C₂	semidirect
4. #22608018	C₂	semidirect
5. C₇₃×#3407	C₂	semidirect
51. M₃₂×C₇₃	D₄	semidirect
141. #3407	D₇₃	semidirect
146. C₇₃	#12989	semidirect
186. M₃₂	C₂²⋊D₇₃	semidirect

H ≅ G/N

type

2. #22611552

C₂

semidirect

3. C₂×#17988368

C₂

semidirect

4. #22608018

C₂

semidirect

5. C₇₃×#3407

C₂

semidirect

51. M₃₂×C₇₃

D₄

semidirect

141. #3407

D₇₃

semidirect

146. C₇₃

#12989

semidirect

186. M₃₂

C₂²⋊D₇₃

semidirect

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

subgroup	index
#22618632	2
#22611552	2
C₂×#17988368	2
#22608018	2
C₇₃×#3407	2
#12989	73

subgroup

index

C₇₃×#3407

Subgroups — #33002912

Conjugacy classes of subgroups

Complements

Maximal subgroups