Group #33004693 — subgroups

Subgroups — #33004693

Order 18688.

566 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 119 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×Dic₅₈₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#17988828	C₂	1	2	yes	maximal
3	C₂×#17988392	C₂	1	2	yes	maximal, complemented
4	#22608023	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂²⋊C₁₆×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₂₉₂	C₂²	1	2	yes	—
7	C₂×#14556570	—	2	2	no	—
8	C₂×Dic₅₈₄	—	2	4	no	—
9	C₂×Dic₅₈₄	—	2	2	no	—
10	#17988828	—	2	4	no	—
11	#17988828	—	2	4	no	—
12	C₂×#14556525	C₂²	1	2	yes	—
13	C₂×#14556516	—	2	2	no	—
14	#17988392	—	2	4	no	—
15	C₂³×C₈×C₇₃	C₂²	1	1	yes	characteristic
16	C₂²×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
17	C₂²×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
18	C₂²⋊C₁₆×C₇₃	—	2	2	no	—
19	C₂²×Dic₁₄₆	—	2	2	no	—
20	C₂×Dic₂₉₂	—	2	2	no	—
21	C₂×Dic₂₉₂	—	2	2	no	—
22	C₂×Dic₂₉₂	—	2	2	no	—
23	C₂×Dic₂₉₂	—	2	2	no	—
24	C₂×Dic₂₉₂	—	2	2	no	—
25	C₂×Dic₂₉₂	D₄	1	4	yes	—
26	#14556570	—	2	8	no	—
27	#14556570	—	4	4	no	—
28	C₂×C₄⋊Dic₇₃	—	2	2	no	—
29	C₂×#11924007	—	4	2	no	—
30	C₂×C₂²⋊Dic₇₃	—	4	2	no	—
31	Dic₅₈₄	—	2	8	no	—
32	#14556525	—	2	2	no	—
33	#14556525	D₄	1	4	yes	—
34	#14556516	—	2	8	no	—
35	C₂³×C₄×C₇₃	D₄	1	1	yes	characteristic
36	C₂²×C₈×C₇₃	—	2	2	no	—
37	C₂²×C₈×C₇₃	—	2	2	no	—
38	C₂²×C₈×C₇₃	—	2	1	no	—
39	C₂²×C₈×C₇₃	—	2	1	no	—
40	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
41	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
42	C₂×C₁₆×C₇₃	—	2	2	no	—
43	C₂×C₁₆×C₇₃	—	2	2	no	—
44	C₂×C₁₆×C₇₃	—	2	1	no	—
45	C₂×C₁₆×C₇₃	D₄	1	2	yes	—
46	C₂×Dic₁₄₆	—	2	4	no	—
47	C₂×Dic₁₄₆	—	4	2	no	—
48	C₂×Dic₁₄₆	—	4	2	no	—
49	C₂×Dic₁₄₆	—	4	2	no	—
50	C₂×Dic₁₄₆	—	4	2	no	—
51	C₂×Dic₁₄₆	—	4	2	no	—
52	C₂²×Dic₇₃	—	4	2	no	—
53	C₂²×Dic₇₃	—	4	2	no	—
54	Dic₂₉₂	—	2	4	no	—
55	Dic₂₉₂	—	2	4	no	—
56	Dic₂₉₂	—	4	2	no	—
57	Dic₂₉₂	—	4	2	no	—
58	C₄⋊Dic₇₃	—	2	4	no	—
59	C₄⋊Dic₇₃	—	4	2	no	—
60	#11924007	—	4	8	no	—
61	C₂²⋊Dic₇₃	—	4	8	no	—
62	C₂⁴×C₇₃	D₈	1	1	yes	characteristic
63	C₂²×C₄×C₇₃	—	2	2	no	—
64	C₂²×C₄×C₇₃	—	2	1	no	—
65	C₂²×C₄×C₇₃	—	2	1	no	—
66	C₂²×C₄×C₇₃	—	2	2	no	—
67	C₂²×C₄×C₇₃	D₈	1	1	yes	characteristic
68	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
69	C₂×C₈×C₇₃	—	2	2	no	—
70	C₂×C₈×C₇₃	—	2	1	no	—
71	C₂×C₈×C₇₃	—	4	1	no	—
72	C₂×C₈×C₇₃	—	4	2	no	—
73	C₂×C₈×C₇₃	—	4	1	no	—
74	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
75	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
76	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
77	C₂×C₈×C₇₃	#41	1	1	yes	characteristic
78	C₁₆×C₇₃	—	2	2	no	—
79	C₁₆×C₇₃	—	4	1	no	—
80	C₂³×C₇₃	—	2	2	no	—
81	C₂³×C₇₃	—	2	1	no	—
82	C₂³×C₇₃	—	2	1	no	—
83	C₂³×C₇₃	—	2	2	no	—
84	C₂³×C₇₃	Q₃₂	1	2	yes	complemented
85	C₂³×C₇₃	C₂×D₈	1	1	yes	characteristic
86	C₂×C₄×C₇₃	—	2	2	no	—
87	C₂×C₄×C₇₃	—	2	1	no	—
88	C₂×C₄×C₇₃	—	4	1	no	—
89	C₂×C₄×C₇₃	—	4	2	no	—
90	C₂×C₄×C₇₃	—	4	1	no	—
91	C₂×C₄×C₇₃	#120	1	2	yes	—
92	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
93	C₂×C₄×C₇₃	#135	1	1	yes	characteristic
94	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
95	C₂×Dic₇₃	—	4	4	no	—
96	C₂×Dic₇₃	—	4	4	no	—
97	C₂×Dic₇₃	—	8	2	no	—
98	C₂×Dic₇₃	—	8	2	no	—
99	C₂×Dic₇₃	—	8	2	no	—
100	C₂×Dic₇₃	—	8	2	no	—
101	Dic₁₄₆	—	4	4	no	—
102	Dic₁₄₆	—	4	4	no	—
103	Dic₁₄₆	—	8	2	no	—
104	Dic₁₄₆	—	8	2	no	—
105	C₈×C₇₃	—	4	1	no	—
106	C₈×C₇₃	#120	1	1	yes	characteristic
107	C₈×C₇₃	#121	1	2	yes	—
108	C₈×C₇₃	#127	1	1	yes	characteristic
109	C₂²×C₇₃	—	2	4	no	—
110	C₂²×C₇₃	—	2	2	no	—
111	C₂²×C₇₃	—	4	2	no	—
112	C₂²×C₇₃	—	4	1	no	—
113	C₂²×C₇₃	—	4	1	no	—
114	C₂²×C₇₃	#447	1	2	yes	—
115	C₂²×C₇₃	#466	1	1	yes	characteristic
116	C₂²×C₇₃	C₂×Q₃₂	1	1	yes	characteristic
117	C₂²×C₇₃	#508	1	1	yes	characteristic
118	C₂²×C₇₃	#510	1	2	yes	—
119	C₄×C₇₃	—	4	1	no	—
120	C₄×C₇₃	#392	1	1	yes	characteristic
121	C₄×C₇₃	#449	1	2	yes	—
122	C₄×C₇₃	#469	1	1	yes	characteristic
123	Dic₇₃	—	8	4	no	—
124	Dic₇₃	—	8	4	no	—
125	#13306	—	73	1	no	maximal, Sylow
126	C₂×C₇₃	—	4	2	no	—
127	C₂×C₇₃	#1999	1	1	yes	characteristic
128	C₂×C₇₃	#2188	1	2	yes	—
129	C₂×C₇₃	#2189	1	2	yes	—
130	C₂×C₇₃	#2216	1	1	yes	characteristic
131	C₂×C₇₃	#2219	1	1	yes	characteristic
132	C₂²×Q₃₂	—	73	1	no	—
133	C₂×#467	—	73	2	no	—
134	C₂×#358	—	73	2	no	—
135	C₂×C₂²⋊C₁₆	D₇₃	1	1	yes	characteristic
136	#1380	—	73	1	no	—
137	C₇₃	#13306	1	1	yes	characteristic, complemented, Sylow
138	C₂²×Q₁₆	—	73	2	no	—
139	C₂³×C₈	C₂×D₇₃	1	1	yes	characteristic
140	C₂×C₂²⋊Q₈	—	146	2	no	—
141	C₂×Q₃₂	—	146	4	no	—
142	C₂×Q₃₂	—	146	2	no	—
143	C₂²×C₁₆	C₂×D₇₃	1	1	yes	characteristic
144	C₂²×C₁₆	C₂×D₇₃	1	1	yes	characteristic
145	#467	—	146	4	no	—
146	#467	—	146	4	no	—
147	C₂×#107	—	73	2	no	—
148	C₂×#103	—	146	2	no	—
149	#358	—	146	4	no	—
150	C₂²⋊C₁₆	—	2	2	no	—
151	C₂²×Q₈	—	146	2	no	—
152	C₂³×C₄	D₂₉₂	1	1	yes	characteristic
153	C₂×Q₁₆	—	73	4	no	—
154	C₂×Q₁₆	—	146	2	no	—
155	C₂×Q₁₆	—	146	2	no	—
156	C₂×Q₁₆	—	146	2	no	—
157	C₂×Q₁₆	—	146	2	no	—
158	C₂×Q₁₆	—	146	2	no	—
159	C₂²×C₈	—	2	2	no	—
160	C₂²×C₈	—	2	2	no	—
161	C₂²×C₈	—	2	1	no	—
162	C₂²×C₈	—	2	1	no	—
163	C₂²×C₈	D₂₉₂	1	1	yes	characteristic
164	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
165	C₂²⋊Q₈	—	292	4	no	—
166	C₂²⋊Q₈	—	146	8	no	—
167	C₂×C₄⋊C₄	—	292	2	no	—
168	C₂×C₄⋊C₄	—	146	2	no	—
169	C₂×C₂²⋊C₄	—	292	2	no	—
170	Q₃₂	—	146	8	no	—
171	C₂×C₁₆	—	2	2	no	—
172	C₂×C₁₆	—	2	2	no	—
173	C₂×C₁₆	—	2	1	no	—
174	C₂×C₁₆	C₂²⋊D₇₃	1	2	yes	—
175	#107	—	73	4	no	—
176	#107	—	146	2	no	—
177	#103	—	146	8	no	—
178	C₂⁴	D₅₈₄	1	1	yes	characteristic
179	C₂×Q₈	—	292	2	no	—
180	C₂×Q₈	—	292	2	no	—
181	C₂×Q₈	—	292	2	no	—
182	C₂×Q₈	—	292	2	no	—
183	C₂×Q₈	—	292	2	no	—
184	C₂×Q₈	—	146	4	no	—
185	C₂²×C₄	—	2	2	no	—
186	C₂²×C₄	—	2	1	no	—
187	C₂²×C₄	—	2	1	no	—
188	C₂²×C₄	—	2	2	no	—
189	C₂²×C₄	—	292	2	no	—
190	C₂²×C₄	—	292	2	no	—
191	C₂²×C₄	D₅₈₄	1	1	yes	characteristic
192	C₂²×C₄	C₂×D₂₉₂	1	1	yes	characteristic
193	Q₁₆	—	292	2	no	—
194	Q₁₆	—	292	2	no	—
195	Q₁₆	—	146	4	no	—
196	Q₁₆	—	146	4	no	—
197	C₂×C₈	—	2	2	no	—
198	C₂×C₈	—	2	1	no	—
199	C₂×C₈	—	4	1	no	—
200	C₂×C₈	—	4	2	no	—
201	C₂×C₈	—	4	1	no	—
202	C₂×C₈	D₄×D₇₃	1	2	yes	—
203	C₂×C₈	D₄×D₇₃	1	2	yes	—
204	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
205	C₂×C₈	#11924028	1	1	yes	characteristic
206	C₄⋊C₄	—	292	8	no	—
207	C₄⋊C₄	—	292	2	no	—
208	C₄⋊C₄	—	146	4	no	—
209	C₂²⋊C₄	—	292	8	no	—
210	C₁₆	—	2	2	no	—
211	C₁₆	—	4	1	no	—
212	C₂³	—	2	2	no	—
213	C₂³	—	2	1	no	—
214	C₂³	—	2	2	no	—
215	C₂³	—	2	1	no	—
216	C₂³	Dic₅₈₄	1	2	yes	complemented
217	C₂³	C₂×D₅₈₄	1	1	yes	characteristic
218	Q₈	—	292	4	no	—
219	Q₈	—	292	4	no	—
220	Q₈	—	584	2	no	—
221	Q₈	—	584	2	no	—
222	C₂×C₄	—	2	2	no	—
223	C₂×C₄	—	2	1	no	—
224	C₂×C₄	—	4	2	no	—
225	C₂×C₄	—	4	1	no	—
226	C₂×C₄	—	4	1	no	—
227	C₂×C₄	—	292	4	no	—
228	C₂×C₄	—	292	4	no	—
229	C₂×C₄	—	584	2	no	—
230	C₂×C₄	—	584	2	no	—
231	C₂×C₄	—	584	2	no	—
232	C₂×C₄	—	584	2	no	—
233	C₂×C₄	#14556561	1	2	yes	—
234	C₂×C₄	#14556565	1	1	yes	characteristic
235	C₂×C₄	#14556613	1	1	yes	characteristic
236	C₂×C₄	#14556619	1	2	yes	—
237	C₈	—	4	1	no	—
238	C₈	#14556559	1	1	yes	characteristic
239	C₈	#14556564	1	2	yes	—
240	C₈	#14556587	1	1	yes	characteristic
241	C₂²	—	2	2	no	—
242	C₂²	—	2	4	no	—
243	C₂²	—	4	1	no	—
244	C₂²	—	4	2	no	—
245	C₂²	—	4	1	no	—
246	C₂²	#17988723	1	2	yes	—
247	C₂²	#17988823	1	1	yes	characteristic
248	C₂²	C₂×Dic₅₈₄	1	1	yes	characteristic
249	C₂²	#17989019	1	1	yes	characteristic
250	C₂²	#17989030	1	2	yes	—
251	C₄	—	4	1	no	—
252	C₄	—	584	4	no	—
253	C₄	—	584	4	no	—
254	C₄	#17988496	1	1	yes	characteristic
255	C₄	#17988734	1	2	yes	—
256	C₄	#17988840	1	1	yes	characteristic
257	C₂	—	4	2	no	—
258	C₂	#22610929	1	1	yes	characteristic
259	C₂	#22611867	1	2	yes	—
260	C₂	#22611873	1	2	yes	—
261	C₂	#22612022	1	1	yes	characteristic
262	C₂	#22612039	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Dic₅₈₄

C₂

yes

maximal, characteristic, complemented

C₂×#17988828

C₂

yes

maximal

C₂×#17988392

C₂

yes

maximal, complemented

#22608023

C₂

yes

maximal, characteristic, complemented

C₂×C₂²⋊C₁₆×C₇₃

C₂

yes

maximal, characteristic

C₂²×Dic₂₉₂

C₂²

yes

—

C₂×#14556570

—

C₂×Dic₅₈₄

—

C₂×Dic₅₈₄

—

#17988828

—

#17988828

—

C₂×#14556525

C₂²

yes

—

C₂×#14556516

—

#17988392

—

C₂³×C₈×C₇₃

C₂²

yes

characteristic

C₂²×C₁₆×C₇₃

C₂²

yes

characteristic

C₂²×C₁₆×C₇₃

C₂²

yes

characteristic

C₂²⋊C₁₆×C₇₃

—

C₂²×Dic₁₄₆

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

D₄

yes

—

#14556570

—

#14556570

—

C₂×C₄⋊Dic₇₃

—

C₂×#11924007

—

C₂×C₂²⋊Dic₇₃

—

Dic₅₈₄

—

#14556525

—

#14556525

D₄

yes

—

#14556516

—

C₂³×C₄×C₇₃

D₄

yes

characteristic

C₂²×C₈×C₇₃

—

C₂²×C₈×C₇₃

—

C₂²×C₈×C₇₃

—

C₂²×C₈×C₇₃

—

C₂²×C₈×C₇₃

D₄

yes

characteristic

C₂²×C₈×C₇₃

C₂³

yes

characteristic

C₂×C₁₆×C₇₃

—

C₂×C₁₆×C₇₃

—

C₂×C₁₆×C₇₃

—

C₂×C₁₆×C₇₃

D₄

yes

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

—

Dic₂₉₂

—

Dic₂₉₂

—

Dic₂₉₂

—

Dic₂₉₂

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

#11924007

—

C₂²⋊Dic₇₃

—

C₂⁴×C₇₃

D₈

yes

characteristic

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

D₈

yes

characteristic

C₂²×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₂×D₄

yes

—

C₂×C₈×C₇₃

C₂×D₄

yes

—

C₂×C₈×C₇₃

C₂×D₄

yes

characteristic

C₂×C₈×C₇₃

#41

yes

characteristic

C₁₆×C₇₃

—

C₁₆×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

Q₃₂

yes

complemented

C₂³×C₇₃

C₂×D₈

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

#120

yes

—

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

100

C₂×Dic₇₃

—

101

Dic₁₄₆

—

102

Dic₁₄₆

—

103

Dic₁₄₆

—

104

Dic₁₄₆

—

105

C₈×C₇₃

—

106

C₈×C₇₃

#120

yes

characteristic

107

C₈×C₇₃

#121

yes

—

108

C₈×C₇₃

#127

yes

characteristic

109

C₂²×C₇₃

—

110

C₂²×C₇₃

—

111

C₂²×C₇₃

—

112

C₂²×C₇₃

—

113

C₂²×C₇₃

—

114

C₂²×C₇₃

#447

yes

—

115

C₂²×C₇₃

#466

yes

characteristic

116

C₂²×C₇₃

C₂×Q₃₂

yes

characteristic

117

C₂²×C₇₃

#508

yes

characteristic

118

C₂²×C₇₃

#510

yes

—

119

C₄×C₇₃

—

120

C₄×C₇₃

#392

yes

characteristic

121

C₄×C₇₃

#449

yes

—

122

C₄×C₇₃

#469

yes

characteristic

123

Dic₇₃

—

124

Dic₇₃

—

125

#13306

—

maximal, Sylow

126

C₂×C₇₃

—

127

C₂×C₇₃

#1999

yes

characteristic

128

C₂×C₇₃

#2188

yes

—

129

C₂×C₇₃

#2189

yes

—

130

C₂×C₇₃

#2216

yes

characteristic

131

C₂×C₇₃

#2219

yes

characteristic

132

C₂²×Q₃₂

—

133

C₂×#467

—

134

C₂×#358

—

135

C₂×C₂²⋊C₁₆

D₇₃

yes

characteristic

136

#1380

—

137

C₇₃

#13306

yes

characteristic, complemented, Sylow

138

C₂²×Q₁₆

—

139

C₂³×C₈

C₂×D₇₃

yes

characteristic

140

C₂×C₂²⋊Q₈

—

146

—

141

C₂×Q₃₂

—

146

—

142

C₂×Q₃₂

—

146

—

143

C₂²×C₁₆

C₂×D₇₃

yes

characteristic

144

C₂²×C₁₆

C₂×D₇₃

yes

characteristic

145

#467

—

146

—

146

#467

—

146

—

147

C₂×#107

—

148

C₂×#103

—

146

—

149

#358

—

146

—

150

C₂²⋊C₁₆

—

151

C₂²×Q₈

—

146

—

152

C₂³×C₄

D₂₉₂

yes

characteristic

153

C₂×Q₁₆

—

154

C₂×Q₁₆

—

146

—

155

C₂×Q₁₆

—

146

—

156

C₂×Q₁₆

—

146

—

157

C₂×Q₁₆

—

146

—

158

C₂×Q₁₆

—

146

—

159

C₂²×C₈

—

160

C₂²×C₈

—

161

C₂²×C₈

—

162

C₂²×C₈

—

163

C₂²×C₈

D₂₉₂

yes

characteristic

164

C₂²×C₈

C₂²×D₇₃

yes

characteristic

165

C₂²⋊Q₈

—

292

—

166

C₂²⋊Q₈

—

146

—

167

C₂×C₄⋊C₄

—

292

—

168

C₂×C₄⋊C₄

—

146

—

169

C₂×C₂²⋊C₄

—

292

—

170

Q₃₂

—

146

—

171

C₂×C₁₆

—

172

C₂×C₁₆

—

173

C₂×C₁₆

—

174

C₂×C₁₆

C₂²⋊D₇₃

yes

—

175

#107

—

176

#107

—

146

—

177

#103

—

146

—

178

C₂⁴

D₅₈₄

yes

characteristic

179

C₂×Q₈

—

292

—

180

C₂×Q₈

—

292

—

181

C₂×Q₈

—

292

—

182

C₂×Q₈

—

292

—

183

C₂×Q₈

—

292

—

184

C₂×Q₈

—

146

—

185

C₂²×C₄

—

186

C₂²×C₄

—

187

C₂²×C₄

—

188

C₂²×C₄

—

189

C₂²×C₄

—

292

—

190

C₂²×C₄

—

292

—

191

C₂²×C₄

D₅₈₄

yes

characteristic

192

C₂²×C₄

C₂×D₂₉₂

yes

characteristic

193

Q₁₆

—

292

—

194

Q₁₆

—

292

—

195

Q₁₆

—

146

—

196

Q₁₆

—

146

—

197

C₂×C₈

—

198

C₂×C₈

—

199

C₂×C₈

—

200

C₂×C₈

—

201

C₂×C₈

—

202

C₂×C₈

D₄×D₇₃

yes

—

203

C₂×C₈

D₄×D₇₃

yes

—

204

C₂×C₈

C₂×C₂²⋊D₇₃

yes

characteristic

205

C₂×C₈

#11924028

yes

characteristic

206

C₄⋊C₄

—

292

—

207

C₄⋊C₄

—

292

—

208

C₄⋊C₄

—

146

—

209

C₂²⋊C₄

—

292

—

210

C₁₆

—

211

C₁₆

—

212

C₂³

—

213

C₂³

—

214

C₂³

—

215

C₂³

—

216

C₂³

Dic₅₈₄

yes

complemented

217

C₂³

C₂×D₅₈₄

yes

characteristic

218

Q₈

—

292

—

219

Q₈

—

292

—

220

Q₈

—

584

—

221

Q₈

—

584

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

292

—

228

C₂×C₄

—

292

—

229

C₂×C₄

—

584

—

230

C₂×C₄

—

584

—

231

C₂×C₄

—

584

—

232

C₂×C₄

—

584

—

233

C₂×C₄

#14556561

yes

—

234

C₂×C₄

#14556565

yes

characteristic

235

C₂×C₄

#14556613

yes

characteristic

236

C₂×C₄

#14556619

yes

—

237

C₈

—

238

C₈

#14556559

yes

characteristic

239

C₈

#14556564

yes

—

240

C₈

#14556587

yes

characteristic

241

C₂²

—

242

C₂²

—

243

C₂²

—

244

C₂²

—

245

C₂²

—

246

C₂²

#17988723

yes

—

247

C₂²

#17988823

yes

characteristic

248

C₂²

C₂×Dic₅₈₄

yes

characteristic

249

C₂²

#17989019

yes

characteristic

250

C₂²

#17989030

yes

—

251

C₄

—

252

C₄

—

584

—

253

C₄

—

584

—

254

C₄

#17988496

yes

characteristic

255

C₄

#17988734

yes

—

256

C₄

#17988840

yes

characteristic

257

C₂

—

258

C₂

#22610929

yes

characteristic

259

C₂

#22611867

yes

—

260

C₂

#22611873

yes

—

261

C₂

#22612022

yes

characteristic

262

C₂

#22612039

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×D₅₈₄
commutator, cosocle	C₂²×C₈×C₇₃	C₂³
Frattini	C₂²×C₈	C₂²×D₇₃
Fitting	C₂×C₂²⋊C₁₆×C₇₃	C₂
socle	C₂³×C₇₃	C₂×D₈
prime radical	C₂⁴×C₇₃	D₈
hypercenter	C₂×C₂²⋊C₁₆	D₇₃
hypocenter	C₇₃	#13306
LCS	G ▷ C₂²×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ C₂×C₂²⋊C₁₆

subgroup

G/H

center

C₂³

C₂×D₅₈₄

commutator, cosocle

C₂²×C₈×C₇₃

C₂³

Frattini

C₂²×C₈

C₂²×D₇₃

Fitting

C₂×C₂²⋊C₁₆×C₇₃

C₂

socle

C₂³×C₇₃

C₂×D₈

prime radical

C₂⁴×C₇₃

D₈

hypercenter

C₂×C₂²⋊C₁₆

D₇₃

hypocenter

C₇₃

#13306

LCS

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

UCS

C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ C₂×C₂²⋊C₁₆

N	H ≅ G/N	type
1. C₂²×Dic₅₈₄	C₂	semidirect
3. C₂×#17988392	C₂	semidirect
4. #22608023	C₂	semidirect
84. C₂³×C₇₃	Q₃₂	semidirect
137. C₇₃	#13306	semidirect
216. C₂³	Dic₅₈₄	semidirect

H ≅ G/N

type

1. C₂²×Dic₅₈₄

C₂

semidirect

3. C₂×#17988392

C₂

semidirect

4. #22608023

C₂

semidirect

84. C₂³×C₇₃

Q₃₂

semidirect

137. C₇₃

#13306

semidirect

216. C₂³

Dic₅₈₄

semidirect

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

subgroup	index
C₂²×Dic₅₈₄	2
C₂×#17988828	2
C₂×#17988392	2
#22608023	2
C₂×C₂²⋊C₁₆×C₇₃	2
#13306	73

subgroup

index

C₂²×Dic₅₈₄

C₂×C₂²⋊C₁₆×C₇₃

Subgroups — #33004693

Conjugacy classes of subgroups

Complements

Maximal subgroups