Group #33004829 — subgroups

Subgroups — #33004829

Order 18688.

594 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 129 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×#14556536	C₂	1	2	yes	maximal
2	C₂×#17988967	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#17988392	C₂	1	2	yes	maximal, complemented
4	#22610797	C₂	1	1	yes	maximal, characteristic
5	C₇₃×#1374	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×Dic₂₉₂	—	2	1	no	—
7	C₂²×Dic₂₉₂	C₂²	1	2	yes	—
8	C₂²×D₅₈₄	C₂²	1	1	yes	characteristic
9	C₂×#14556591	—	2	1	no	—
10	C₂×#14556536	—	2	4	no	—
11	C₂×#14556536	—	2	4	no	—
12	C₂×#14556536	—	2	4	no	—
13	#17988967	—	2	4	no	—
14	C₂×#14556525	C₂²	1	1	yes	characteristic
15	C₂×#14556513	—	2	1	no	—
16	#17988489	—	2	1	no	—
17	#17988392	—	2	4	no	—
18	C₂²×C₁₆×C₇₃	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
20	C₂²×Dic₁₄₆	—	2	2	no	—
21	C₂²×D₂₉₂	—	2	1	no	—
22	C₂×Dic₂₉₂	—	2	4	no	—
23	C₂×Dic₂₉₂	—	2	2	no	—
24	C₂×Dic₂₉₂	—	2	2	no	—
25	C₂×Dic₂₉₂	—	2	2	no	—
26	C₂×Dic₂₉₂	—	2	2	no	—
27	C₂×Dic₂₉₂	—	2	2	no	—
28	C₂×Dic₂₉₂	—	4	2	no	—
29	C₂×Dic₂₉₂	—	4	2	no	—
30	C₂×Dic₂₉₂	D₄	1	4	yes	—
31	C₂×D₅₈₄	—	2	2	no	—
32	C₂×D₅₈₄	—	2	2	no	—
33	C₂×D₅₈₄	—	2	1	no	—
34	C₂×D₅₈₄	D₄	1	2	yes	—
35	#14556591	—	2	4	no	—
36	#14556591	—	4	2	no	—
37	C₂×C₄⋊Dic₇₃	—	2	1	no	—
38	C₂×C₄⋊Dic₇₃	—	4	2	no	—
39	C₂×#11924005	—	4	2	no	—
40	#14556536	—	2	16	no	—
41	#14556525	—	2	2	no	—
42	#14556513	—	4	2	no	—
43	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
44	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
45	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
46	C₂×C₁₆×C₇₃	—	2	2	no	—
47	C₂×C₁₆×C₇₃	—	2	2	no	—
48	C₂×C₁₆×C₇₃	D₄	1	4	yes	—
49	C₄×C₈×C₇₃	—	2	2	no	—
50	C₂³×D₇₃	—	4	1	no	—
51	C₂×Dic₁₄₆	—	2	4	no	—
52	C₂×Dic₁₄₆	—	4	2	no	—
53	C₂×Dic₁₄₆	—	4	2	no	—
54	C₂×Dic₁₄₆	—	4	2	no	—
55	C₂×Dic₁₄₆	—	4	2	no	—
56	C₂×Dic₁₄₆	—	4	2	no	—
57	C₂×D₂₉₂	—	2	2	no	—
58	C₂×D₂₉₂	—	4	1	no	—
59	C₂×D₂₉₂	—	4	1	no	—
60	C₂×D₂₉₂	—	4	1	no	—
61	C₂×D₂₉₂	—	4	1	no	—
62	C₂×D₂₉₂	—	4	1	no	—
63	C₂²×Dic₇₃	—	4	2	no	—
64	C₂²×Dic₇₃	—	4	1	no	—
65	Dic₂₉₂	—	2	4	no	—
66	Dic₂₉₂	—	2	4	no	—
67	Dic₂₉₂	—	4	8	no	—
68	Dic₂₉₂	—	4	2	no	—
69	Dic₂₉₂	—	4	2	no	—
70	D₅₈₄	—	2	4	no	—
71	D₅₈₄	—	4	2	no	—
72	C₄⋊Dic₇₃	—	4	8	no	—
73	C₄⋊Dic₇₃	—	4	1	no	—
74	C₄⋊Dic₇₃	—	4	1	no	—
75	#11924005	—	8	4	no	—
76	C₂²×C₄×C₇₃	D₈	1	2	yes	—
77	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
78	C₂×C₈×C₇₃	—	2	1	no	—
79	C₂×C₈×C₇₃	—	2	1	no	—
80	C₂×C₈×C₇₃	D₈	1	2	yes	—
81	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
82	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
83	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
84	C₂×C₈×C₇₃	#41	1	1	yes	characteristic
85	C₄²×C₇₃	—	2	1	no	—
86	C₄²×C₇₃	—	2	1	no	—
87	C₁₆×C₇₃	—	2	4	no	—
88	C₂³×C₇₃	C₂×D₈	1	1	yes	characteristic
89	C₂²×D₇₃	—	4	2	no	—
90	C₂²×D₇₃	—	8	1	no	—
91	C₂²×D₇₃	—	8	1	no	—
92	C₂²×D₇₃	—	8	2	no	—
93	C₂²×D₇₃	—	8	2	no	—
94	C₂×C₄×C₇₃	—	2	2	no	—
95	C₂×C₄×C₇₃	—	2	2	no	—
96	C₂×C₄×C₇₃	SD₃₂	1	4	yes	complemented
97	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
98	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
99	C₂×C₄×C₇₃	#127	1	1	yes	characteristic
100	C₂×C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
101	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
102	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
103	C₂×Dic₇₃	—	4	4	no	—
104	C₂×Dic₇₃	—	8	2	no	—
105	C₂×Dic₇₃	—	8	2	no	—
106	C₂×Dic₇₃	—	8	1	no	—
107	C₂×Dic₇₃	—	8	2	no	—
108	D₂₉₂	—	4	2	no	—
109	D₂₉₂	—	4	2	no	—
110	D₂₉₂	—	8	1	no	—
111	D₂₉₂	—	8	1	no	—
112	Dic₁₄₆	—	4	4	no	—
113	Dic₁₄₆	—	4	4	no	—
114	Dic₁₄₆	—	8	2	no	—
115	Dic₁₄₆	—	8	2	no	—
116	C₈×C₇₃	—	2	2	no	—
117	C₈×C₇₃	#120	1	2	yes	—
118	C₈×C₇₃	#121	1	2	yes	—
119	C₂²×C₇₃	#447	1	1	yes	characteristic
120	C₂²×C₇₃	#459	1	1	yes	characteristic
121	C₂²×C₇₃	#493	1	1	yes	characteristic
122	C₂²×C₇₃	C₂×SD₃₂	1	2	yes	—
123	C₂²×C₇₃	#510	1	2	yes	—
124	C₂×D₇₃	—	8	4	no	—
125	C₂×D₇₃	—	8	2	no	—
126	C₂×D₇₃	—	16	2	no	—
127	C₂×D₇₃	—	16	1	no	—
128	C₂×D₇₃	—	16	1	no	—
129	C₄×C₇₃	—	2	4	no	—
130	C₄×C₇₃	#392	1	1	yes	characteristic
131	C₄×C₇₃	#447	1	1	yes	characteristic
132	C₄×C₇₃	#459	1	1	yes	characteristic
133	C₄×C₇₃	#496	1	1	yes	characteristic
134	Dic₇₃	—	8	4	no	—
135	Dic₇₃	—	16	1	no	—
136	#13327	—	73	1	no	maximal, Sylow
137	C₂×C₇₃	#2011	1	1	yes	characteristic
138	C₂×C₇₃	#2185	1	2	yes	—
139	C₂×C₇₃	#2208	1	2	yes	—
140	C₂×C₇₃	#2248	1	1	yes	characteristic
141	C₂×C₇₃	#2251	1	1	yes	characteristic
142	D₇₃	—	16	2	no	—
143	C₂²×SD₃₂	—	73	2	no	—
144	C₂×#494	—	73	1	no	—
145	C₂×#358	—	73	2	no	—
146	#1970	—	73	1	no	—
147	#1374	D₇₃	1	1	yes	characteristic, complemented
148	C₇₃	#13327	1	1	yes	characteristic, complemented, Sylow
149	C₂²×Q₁₆	—	73	2	no	—
150	C₂²×Q₁₆	—	146	1	no	—
151	C₂²×D₈	—	73	1	no	—
152	C₂×C₄⋊Q₈	—	146	1	no	—
153	C₂×SD₃₂	—	146	4	no	—
154	C₂×SD₃₂	—	146	4	no	—
155	C₂×SD₃₂	—	146	4	no	—
156	C₂²×C₁₆	C₂×D₇₃	1	2	yes	—
157	#494	—	146	4	no	—
158	C₂×#107	—	73	1	no	—
159	C₂×#102	—	146	1	no	—
160	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
161	#390	—	146	1	no	—
162	#358	—	146	4	no	—
163	C₂²×Q₈	—	146	2	no	—
164	C₂²×D₄	—	146	1	no	—
165	C₂×Q₁₆	—	292	2	no	—
166	C₂×Q₁₆	—	292	2	no	—
167	C₂×Q₁₆	—	73	4	no	—
168	C₂×Q₁₆	—	146	4	no	—
169	C₂×Q₁₆	—	146	2	no	—
170	C₂×Q₁₆	—	146	2	no	—
171	C₂×Q₁₆	—	146	2	no	—
172	C₂×Q₁₆	—	146	2	no	—
173	C₂×Q₁₆	—	146	2	no	—
174	C₂×D₈	—	73	2	no	—
175	C₂×D₈	—	146	2	no	—
176	C₂×D₈	—	146	2	no	—
177	C₂×D₈	—	146	1	no	—
178	C₂²×C₈	D₂₉₂	1	1	yes	characteristic
179	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
180	C₄⋊Q₈	—	292	2	no	—
181	C₄⋊Q₈	—	146	4	no	—
182	C₂×C₄⋊C₄	—	292	2	no	—
183	C₂×C₄⋊C₄	—	146	1	no	—
184	C₂×C₂²⋊C₄	—	292	2	no	—
185	C₂×C₄²	D₂₉₂	1	1	yes	characteristic
186	SD₃₂	—	146	16	no	—
187	C₂×C₁₆	—	2	2	no	—
188	C₂×C₁₆	—	2	2	no	—
189	C₂×C₁₆	D₂₉₂	1	4	yes	—
190	#107	—	146	2	no	—
191	#102	—	292	2	no	—
192	C₄×C₈	—	2	2	no	—
193	C₂⁴	—	292	1	no	—
194	C₂×Q₈	—	292	2	no	—
195	C₂×Q₈	—	292	2	no	—
196	C₂×Q₈	—	292	2	no	—
197	C₂×Q₈	—	292	2	no	—
198	C₂×Q₈	—	292	2	no	—
199	C₂×Q₈	—	146	4	no	—
200	C₂×D₄	—	292	1	no	—
201	C₂×D₄	—	292	1	no	—
202	C₂×D₄	—	292	1	no	—
203	C₂×D₄	—	292	1	no	—
204	C₂×D₄	—	292	1	no	—
205	C₂×D₄	—	146	2	no	—
206	C₂²×C₄	—	292	2	no	—
207	C₂²×C₄	—	292	1	no	—
208	C₂²×C₄	D₅₈₄	1	2	yes	—
209	C₂²×C₄	C₂×D₂₉₂	1	1	yes	characteristic
210	Q₁₆	—	292	8	no	—
211	Q₁₆	—	292	2	no	—
212	Q₁₆	—	292	2	no	—
213	Q₁₆	—	146	4	no	—
214	Q₁₆	—	146	4	no	—
215	D₈	—	292	2	no	—
216	D₈	—	146	4	no	—
217	C₂×C₈	—	2	1	no	—
218	C₂×C₈	—	2	1	no	—
219	C₂×C₈	D₅₈₄	1	2	yes	—
220	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
221	C₂×C₈	D₄×D₇₃	1	2	yes	—
222	C₂×C₈	C₂×D₂₉₂	1	2	yes	—
223	C₂×C₈	#11924029	1	1	yes	characteristic
224	C₄⋊C₄	—	292	8	no	—
225	C₄⋊C₄	—	292	1	no	—
226	C₄⋊C₄	—	292	1	no	—
227	C₂²⋊C₄	—	584	4	no	—
228	C₄²	—	2	1	no	—
229	C₄²	—	2	1	no	—
230	C₁₆	—	2	4	no	—
231	C₂³	—	292	2	no	—
232	C₂³	—	584	1	no	—
233	C₂³	—	584	1	no	—
234	C₂³	—	584	2	no	—
235	C₂³	—	584	2	no	—
236	C₂³	C₂×D₅₈₄	1	1	yes	characteristic
237	Q₈	—	292	4	no	—
238	Q₈	—	292	4	no	—
239	Q₈	—	584	2	no	—
240	Q₈	—	584	2	no	—
241	D₄	—	292	2	no	—
242	D₄	—	292	2	no	—
243	D₄	—	584	1	no	—
244	D₄	—	584	1	no	—
245	C₂×C₄	—	2	2	no	—
246	C₂×C₄	—	2	2	no	—
247	C₂×C₄	—	292	4	no	—
248	C₂×C₄	—	584	2	no	—
249	C₂×C₄	—	584	2	no	—
250	C₂×C₄	—	584	1	no	—
251	C₂×C₄	—	584	2	no	—
252	C₂×C₄	#14556536	1	4	yes	complemented
253	C₂×C₄	#14556561	1	1	yes	characteristic
254	C₂×C₄	#14556566	1	1	yes	characteristic
255	C₂×C₄	#14556588	1	1	yes	characteristic
256	C₂×C₄	C₂×D₅₈₄	1	1	yes	characteristic
257	C₂×C₄	#14556619	1	1	yes	characteristic
258	C₂×C₄	#14556619	1	1	yes	characteristic
259	C₈	—	2	2	no	—
260	C₈	#14556561	1	2	yes	—
261	C₈	#14556566	1	2	yes	—
262	C₂²	—	584	4	no	—
263	C₂²	—	584	2	no	—
264	C₂²	—	1168	2	no	—
265	C₂²	—	1168	1	no	—
266	C₂²	—	1168	1	no	—
267	C₂²	#17988723	1	1	yes	characteristic
268	C₂²	#17988783	1	1	yes	characteristic
269	C₂²	#17988964	1	1	yes	characteristic
270	C₂²	C₂×#14556536	1	2	yes	—
271	C₂²	#17989030	1	2	yes	—
272	C₄	—	2	4	no	—
273	C₄	—	584	4	no	—
274	C₄	—	1168	1	no	—
275	C₄	#17988497	1	1	yes	characteristic
276	C₄	#17988723	1	1	yes	characteristic
277	C₄	#17988783	1	1	yes	characteristic
278	C₄	#17988976	1	1	yes	characteristic
279	C₂	—	1168	2	no	—
280	C₂	#22611004	1	1	yes	characteristic
281	C₂	#22611850	1	2	yes	—
282	C₂	#22611977	1	2	yes	—
283	C₂	#22612187	1	1	yes	characteristic
284	C₂	#22612202	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#14556536

C₂

yes

maximal

C₂×#17988967

C₂

yes

maximal, characteristic, complemented

C₂×#17988392

C₂

yes

maximal, complemented

#22610797

C₂

yes

maximal, characteristic

C₇₃×#1374

C₂

yes

maximal, characteristic, complemented

C₂²×Dic₂₉₂

—

C₂²×Dic₂₉₂

C₂²

yes

—

C₂²×D₅₈₄

C₂²

yes

—

—

—

—

—

C₂²

yes

—

—

—

C₂²×C₁₆×C₇₃

C₂²

yes

—

C₂×C₄×C₈×C₇₃

C₂²

yes

characteristic

C₂²×Dic₁₄₆

—

C₂²×D₂₉₂

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

D₄

yes

—

C₂×D₅₈₄

—

C₂×D₅₈₄

—

C₂×D₅₈₄

—

C₂×D₅₈₄

D₄

yes

—

#14556591

—

#14556591

—

C₂×C₄⋊Dic₇₃

—

C₂×C₄⋊Dic₇₃

—

—

—

—

—

C₂²×C₈×C₇₃

D₄

yes

characteristic

C₂²×C₈×C₇₃

C₂³

yes

characteristic

C₂×C₄²×C₇₃

D₄

yes

characteristic

C₂×C₁₆×C₇₃

—

C₂×C₁₆×C₇₃

—

C₂×C₁₆×C₇₃

D₄

yes

—

C₄×C₈×C₇₃

—

C₂³×D₇₃

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

—

Dic₂₉₂

—

Dic₂₉₂

—

Dic₂₉₂

—

Dic₂₉₂

—

Dic₂₉₂

—

D₅₈₄

—

D₅₈₄

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

#11924005

—

C₂²×C₄×C₇₃

D₈

yes

—

C₂²×C₄×C₇₃

C₂×D₄

yes

characteristic

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

—

C₁₆×C₇₃

—

C₂³×C₇₃

C₂×D₈

yes

characteristic

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

SD₃₂

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

100

C₂×C₄×C₇₃

C₂×D₈

yes

characteristic

101

C₂×C₄×C₇₃

AGL(1,ℤ/8)

yes

characteristic

102

C₂×C₄×C₇₃

AGL(1,ℤ/8)

yes

characteristic

103

C₂×Dic₇₃

—

104

C₂×Dic₇₃

—

105

C₂×Dic₇₃

—

106

C₂×Dic₇₃

—

107

C₂×Dic₇₃

—

108

D₂₉₂

—

109

D₂₉₂

—

110

D₂₉₂

—

111

D₂₉₂

—

112

Dic₁₄₆

—

113

Dic₁₄₆

—

114

Dic₁₄₆

—

115

Dic₁₄₆

—

116

C₈×C₇₃

—

117

C₈×C₇₃

#120

yes

—

118

C₈×C₇₃

#121

yes

—

119

C₂²×C₇₃

#447

yes

characteristic

120

C₂²×C₇₃

#459

yes

characteristic

121

C₂²×C₇₃

#493

yes

characteristic

122

C₂²×C₇₃

C₂×SD₃₂

yes

—

123

C₂²×C₇₃

#510

yes

—

124

C₂×D₇₃

—

125

C₂×D₇₃

—

126

C₂×D₇₃

—

127

C₂×D₇₃

—

128

C₂×D₇₃

—

129

C₄×C₇₃

—

130

C₄×C₇₃

#392

yes

characteristic

131

C₄×C₇₃

#447

yes

characteristic

132

C₄×C₇₃

#459

yes

characteristic

133

C₄×C₇₃

#496

yes

characteristic

134

Dic₇₃

—

135

Dic₇₃

—

136

#13327

—

maximal, Sylow

137

C₂×C₇₃

#2011

yes

characteristic

138

C₂×C₇₃

#2185

yes

—

139

C₂×C₇₃

#2208

yes

—

140

C₂×C₇₃

#2248

yes

characteristic

141

C₂×C₇₃

#2251

yes

characteristic

142

D₇₃

—

143

C₂²×SD₃₂

—

144

C₂×#494

—

145

C₂×#358

—

146

#1970

—

147

#1374

D₇₃

yes

characteristic, complemented

148

C₇₃

#13327

yes

characteristic, complemented, Sylow

149

C₂²×Q₁₆

—

150

C₂²×Q₁₆

—

146

—

151

C₂²×D₈

—

152

C₂×C₄⋊Q₈

—

146

—

153

C₂×SD₃₂

—

146

—

154

C₂×SD₃₂

—

146

—

155

C₂×SD₃₂

—

146

—

156

C₂²×C₁₆

C₂×D₇₃

yes

—

157

#494

—

146

—

158

C₂×#107

—

159

C₂×#102

—

146

—

160

C₂×C₄×C₈

C₂×D₇₃

yes

characteristic

161

#390

—

146

—

162

#358

—

146

—

163

C₂²×Q₈

—

146

—

164

C₂²×D₄

—

146

—

165

C₂×Q₁₆

—

292

—

166

C₂×Q₁₆

—

292

—

167

C₂×Q₁₆

—

168

C₂×Q₁₆

—

146

—

169

C₂×Q₁₆

—

146

—

170

C₂×Q₁₆

—

146

—

171

C₂×Q₁₆

—

146

—

172

C₂×Q₁₆

—

146

—

173

C₂×Q₁₆

—

146

—

174

C₂×D₈

—

175

C₂×D₈

—

146

—

176

C₂×D₈

—

146

—

177

C₂×D₈

—

146

—

178

C₂²×C₈

D₂₉₂

yes

characteristic

179

C₂²×C₈

C₂²×D₇₃

yes

characteristic

180

C₄⋊Q₈

—

292

—

181

C₄⋊Q₈

—

146

—

182

C₂×C₄⋊C₄

—

292

—

183

C₂×C₄⋊C₄

—

146

—

184

C₂×C₂²⋊C₄

—

292

—

185

C₂×C₄²

D₂₉₂

yes

characteristic

186

SD₃₂

—

146

—

187

C₂×C₁₆

—

188

C₂×C₁₆

—

189

C₂×C₁₆

D₂₉₂

yes

—

190

#107

—

146

—

191

#102

—

292

—

192

C₄×C₈

—

193

C₂⁴

—

292

—

194

C₂×Q₈

—

292

—

195

C₂×Q₈

—

292

—

196

C₂×Q₈

—

292

—

197

C₂×Q₈

—

292

—

198

C₂×Q₈

—

292

—

199

C₂×Q₈

—

146

—

200

C₂×D₄

—

292

—

201

C₂×D₄

—

292

—

202

C₂×D₄

—

292

—

203

C₂×D₄

—

292

—

204

C₂×D₄

—

292

—

205

C₂×D₄

—

146

—

206

C₂²×C₄

—

292

—

207

C₂²×C₄

—

292

—

208

C₂²×C₄

D₅₈₄

yes

—

209

C₂²×C₄

C₂×D₂₉₂

yes

characteristic

210

Q₁₆

—

292

—

211

Q₁₆

—

292

—

212

Q₁₆

—

292

—

213

Q₁₆

—

146

—

214

Q₁₆

—

146

—

215

D₈

—

292

—

216

D₈

—

146

—

217

C₂×C₈

—

218

C₂×C₈

—

219

C₂×C₈

D₅₈₄

yes

—

220

C₂×C₈

D₄×D₇₃

yes

characteristic

221

C₂×C₈

D₄×D₇₃

yes

—

222

C₂×C₈

C₂×D₂₉₂

yes

—

223

C₂×C₈

#11924029

yes

characteristic

224

C₄⋊C₄

—

292

—

225

C₄⋊C₄

—

292

—

226

C₄⋊C₄

—

292

—

227

C₂²⋊C₄

—

584

—

228

C₄²

—

229

C₄²

—

230

C₁₆

—

231

C₂³

—

292

—

232

C₂³

—

584

—

233

C₂³

—

584

—

234

C₂³

—

584

—

235

C₂³

—

584

—

236

C₂³

C₂×D₅₈₄

yes

characteristic

237

Q₈

—

292

—

238

Q₈

—

292

—

239

Q₈

—

584

—

240

Q₈

—

584

—

241

D₄

—

292

—

242

D₄

—

292

—

243

D₄

—

584

—

244

D₄

—

584

—

245

C₂×C₄

—

246

C₂×C₄

—

247

C₂×C₄

—

292

—

248

C₂×C₄

—

584

—

249

C₂×C₄

—

584

—

250

C₂×C₄

—

584

—

251

C₂×C₄

—

584

—

252

C₂×C₄

#14556536

yes

complemented

253

C₂×C₄

#14556561

yes

characteristic

254

C₂×C₄

#14556566

yes

characteristic

255

C₂×C₄

#14556588

yes

characteristic

256

C₂×C₄

C₂×D₅₈₄

yes

characteristic

257

C₂×C₄

#14556619

yes

characteristic

258

C₂×C₄

#14556619

yes

characteristic

259

C₈

—

260

C₈

#14556561

yes

—

261

C₈

#14556566

yes

—

262

C₂²

—

584

—

263

C₂²

—

584

—

264

C₂²

—

1168

—

265

C₂²

—

1168

—

266

C₂²

—

1168

—

267

C₂²

#17988723

yes

characteristic

268

C₂²

#17988783

yes

characteristic

269

C₂²

#17988964

yes

characteristic

270

C₂²

C₂×#14556536

yes

—

271

C₂²

#17989030

yes

—

272

C₄

—

273

C₄

—

584

—

274

C₄

—

1168

—

275

C₄

#17988497

yes

characteristic

276

C₄

#17988723

yes

characteristic

277

C₄

#17988783

yes

characteristic

278

C₄

#17988976

yes

characteristic

279

C₂

—

1168

—

280

C₂

#22611004

yes

characteristic

281

C₂

#22611850

yes

—

282

C₂

#22611977

yes

—

283

C₂

#22612187

yes

characteristic

284

C₂

#22612202

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×D₅₈₄
commutator, cosocle	C₂²×C₈×C₇₃	C₂³
Frattini	C₂²×C₈	C₂²×D₇₃
Fitting	C₇₃×#1374	C₂
socle	C₂³×C₇₃	C₂×D₈
prime radical	C₂²×D₅₈₄	C₂²
hypercenter	#1374	D₇₃
hypocenter	C₇₃	#13327
LCS	G ▷ C₂²×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #1374

subgroup

G/H

center

C₂³

C₂×D₅₈₄

commutator, cosocle

C₂²×C₈×C₇₃

C₂³

Frattini

C₂²×C₈

C₂²×D₇₃

Fitting

C₇₃×#1374

C₂

socle

C₂³×C₇₃

C₂×D₈

prime radical

C₂²×D₅₈₄

C₂²

D₇₃

C₇₃

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

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #1374

N	H ≅ G/N	type
2. C₂×#17988967	C₂	semidirect
3. C₂×#17988392	C₂	semidirect
5. C₇₃×#1374	C₂	semidirect
96. C₂×C₄×C₇₃	SD₃₂	semidirect
147. #1374	D₇₃	semidirect
148. C₇₃	#13327	semidirect
252. C₂×C₄	#14556536	semidirect

H ≅ G/N

type

2. C₂×#17988967

C₂

semidirect

3. C₂×#17988392

C₂

semidirect

5. C₇₃×#1374

C₂

semidirect

96. C₂×C₄×C₇₃

SD₃₂

semidirect

147. #1374

D₇₃

semidirect

148. C₇₃

#13327

semidirect

252. C₂×C₄

#14556536

semidirect

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

subgroup	index
C₂²×#14556536	2
C₂×#17988967	2
C₂×#17988392	2
#22610797	2
C₇₃×#1374	2
#13327	73

subgroup

index

C₇₃×#1374

Subgroups — #33004829

Conjugacy classes of subgroups

Complements

Maximal subgroups