Group #33004832 — subgroups

Subgroups — #33004832

Order 18688.

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

normal subgroups only

This group has 662 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×#14556535	C₂	1	2	yes	maximal, complemented
2	C₂×#17988388	C₂	1	2	yes	maximal, complemented
3	#22610792	C₂	1	1	yes	maximal, characteristic, complemented
4	#22608009	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#493×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₂₉₂	C₂²	1	1	yes	characteristic
7	C₂×#14556535	—	2	4	no	—
8	C₂×#14556535	—	2	4	no	—
9	C₂×#14556535	—	2	4	no	—
10	C₂²×#11924003	C₂²	1	2	yes	—
11	C₂×#14556525	C₂²	1	1	yes	characteristic
12	C₂×#14556516	—	2	1	no	—
13	#17988493	—	2	1	no	—
14	#17988388	—	2	4	no	—
15	C₂²×D₈×C₇₃	—	2	1	no	—
16	C₂²×D₈×C₇₃	C₂²	1	2	yes	—
17	C₂×#127×C₇₃	—	2	1	no	—
18	#493×C₇₃	—	2	4	no	—
19	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
20	C₂²×Dic₁₄₆	—	2	1	no	—
21	C₂×Dic₂₉₂	—	2	2	no	—
22	C₂×Dic₂₉₂	—	2	2	no	—
23	C₂×Dic₂₉₂	—	2	1	no	—
24	C₂×Dic₂₉₂	D₄	1	2	yes	complemented
25	C₂×C₄⋊Dic₇₃	—	2	1	no	—
26	#14556535	—	2	16	no	—
27	C₂×#11924003	—	2	2	no	—
28	C₂×#11924003	—	2	2	no	—
29	C₂×#11924003	D₄	1	4	yes	complemented
30	#14556525	—	2	2	no	—
31	#14556516	—	4	2	no	—
32	#14556498	—	4	2	no	—
33	C₂²×D₄×C₇₃	—	2	2	no	—
34	C₂²×D₄×C₇₃	—	4	2	no	—
35	C₂×D₈×C₇₃	—	2	4	no	—
36	C₂×D₈×C₇₃	—	2	2	no	—
37	C₂×D₈×C₇₃	—	2	2	no	—
38	C₂×D₈×C₇₃	—	2	2	no	—
39	C₂×D₈×C₇₃	—	2	2	no	—
40	C₂×D₈×C₇₃	—	2	2	no	—
41	C₂×D₈×C₇₃	—	4	2	no	—
42	C₂×D₈×C₇₃	—	4	2	no	—
43	C₂×D₈×C₇₃	D₄	1	4	yes	—
44	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
45	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
46	#127×C₇₃	—	2	4	no	—
47	#127×C₇₃	—	4	2	no	—
48	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
49	C₄×C₈×C₇₃	—	2	2	no	—
50	C₂×Dic₁₄₆	—	2	2	no	—
51	C₂×Dic₁₄₆	—	4	1	no	—
52	C₂×Dic₁₄₆	—	4	1	no	—
53	C₂×Dic₁₄₆	—	4	1	no	—
54	C₂×Dic₁₄₆	—	4	1	no	—
55	C₂×Dic₁₄₆	—	4	1	no	—
56	C₂²×Dic₇₃	—	4	1	no	—
57	C₂²×Dic₇₃	—	4	1	no	—
58	Dic₂₉₂	—	2	4	no	—
59	Dic₂₉₂	—	4	2	no	—
60	C₄⋊Dic₇₃	—	4	1	no	—
61	C₄⋊Dic₇₃	—	4	1	no	—
62	#11924003	—	2	4	no	—
63	C₂⁴×C₇₃	—	4	2	no	—
64	C₂×D₄×C₇₃	—	2	4	no	—
65	C₂×D₄×C₇₃	—	4	8	no	—
66	C₂×D₄×C₇₃	—	4	2	no	—
67	C₂×D₄×C₇₃	—	4	2	no	—
68	C₂×D₄×C₇₃	—	4	2	no	—
69	C₂×D₄×C₇₃	—	4	2	no	—
70	C₂×D₄×C₇₃	—	4	2	no	—
71	C₂×D₄×C₇₃	—	8	4	no	—
72	C₂×D₄×C₇₃	—	8	4	no	—
73	C₂²×C₄×C₇₃	D₈	1	2	yes	—
74	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
75	D₈×C₇₃	—	2	4	no	—
76	D₈×C₇₃	—	2	4	no	—
77	D₈×C₇₃	—	4	8	no	—
78	D₈×C₇₃	—	4	2	no	—
79	D₈×C₇₃	—	4	2	no	—
80	C₂×C₈×C₇₃	—	2	1	no	—
81	C₂×C₈×C₇₃	—	2	1	no	—
82	C₂×C₈×C₇₃	D₈	1	2	yes	—
83	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
84	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
85	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
86	C₂×C₈×C₇₃	#41	1	1	yes	characteristic
87	C₄²×C₇₃	—	2	1	no	—
88	C₄²×C₇₃	—	2	1	no	—
89	C₂³×C₇₃	—	4	4	no	—
90	C₂³×C₇₃	—	8	2	no	—
91	C₂³×C₇₃	—	8	2	no	—
92	C₂³×C₇₃	—	8	4	no	—
93	C₂³×C₇₃	—	8	4	no	—
94	C₂³×C₇₃	C₂×D₈	1	1	yes	characteristic
95	D₄×C₇₃	—	4	4	no	—
96	D₄×C₇₃	—	4	4	no	—
97	D₄×C₇₃	—	8	16	no	—
98	D₄×C₇₃	—	8	2	no	—
99	D₄×C₇₃	—	8	2	no	—
100	C₂×C₄×C₇₃	—	2	2	no	—
101	C₂×C₄×C₇₃	—	2	2	no	—
102	C₂×C₄×C₇₃	SD₃₂	1	4	yes	complemented
103	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
104	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
105	C₂×C₄×C₇₃	#127	1	1	yes	characteristic
106	C₂×C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
107	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
108	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
109	C₂×Dic₇₃	—	4	2	no	—
110	C₂×Dic₇₃	—	8	1	no	—
111	C₂×Dic₇₃	—	8	1	no	—
112	C₂×Dic₇₃	—	8	1	no	—
113	C₂×Dic₇₃	—	8	2	no	—
114	Dic₁₄₆	—	4	2	no	—
115	Dic₁₄₆	—	4	2	no	—
116	Dic₁₄₆	—	8	1	no	—
117	Dic₁₄₆	—	8	1	no	—
118	C₈×C₇₃	—	2	2	no	—
119	C₈×C₇₃	#120	1	2	yes	—
120	C₈×C₇₃	#121	1	2	yes	—
121	C₂²×C₇₃	—	8	8	no	—
122	C₂²×C₇₃	—	8	4	no	—
123	C₂²×C₇₃	—	16	4	no	—
124	C₂²×C₇₃	—	16	2	no	—
125	C₂²×C₇₃	—	16	2	no	—
126	C₂²×C₇₃	#447	1	1	yes	characteristic
127	C₂²×C₇₃	#459	1	1	yes	characteristic
128	C₂²×C₇₃	#493	1	1	yes	characteristic
129	C₂²×C₇₃	C₂×SD₃₂	1	2	yes	—
130	C₂²×C₇₃	#509	1	2	yes	—
131	C₄×C₇₃	—	2	4	no	—
132	C₄×C₇₃	#392	1	1	yes	characteristic
133	C₄×C₇₃	#447	1	1	yes	characteristic
134	C₄×C₇₃	#459	1	1	yes	characteristic
135	C₄×C₇₃	#496	1	1	yes	characteristic
136	Dic₇₃	—	8	2	no	—
137	Dic₇₃	—	16	1	no	—
138	#13328	—	73	1	no	maximal, Sylow
139	C₂×C₇₃	—	16	4	no	—
140	C₂×C₇₃	#2011	1	1	yes	characteristic
141	C₂×C₇₃	#2187	1	2	yes	—
142	C₂×C₇₃	#2207	1	2	yes	—
143	C₂×C₇₃	#2248	1	1	yes	characteristic
144	C₂×C₇₃	#2250	1	1	yes	characteristic
145	C₂²×SD₃₂	—	73	2	no	—
146	C₂×#493	D₇₃	1	1	yes	characteristic
147	C₂×#357	—	73	2	no	—
148	#1969	—	73	1	no	—
149	#1374	—	73	1	no	—
150	C₇₃	#13328	1	1	yes	characteristic, complemented, Sylow
151	C₂²×Q₁₆	—	73	1	no	—
152	C₂²×D₈	—	2	1	no	—
153	C₂²×D₈	C₂×D₇₃	1	2	yes	—
154	C₂×#127	—	2	1	no	—
155	C₂×SD₃₂	—	146	4	no	—
156	C₂×SD₃₂	—	146	4	no	—
157	C₂×SD₃₂	—	146	4	no	—
158	C₂²×C₁₆	—	73	2	no	—
159	#493	—	2	4	no	—
160	C₂×#107	—	73	1	no	—
161	C₂×#103	—	146	1	no	—
162	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
163	#391	—	146	1	no	—
164	#357	—	146	4	no	—
165	C₂²×Q₈	—	146	1	no	—
166	C₂²×D₄	—	2	2	no	—
167	C₂²×D₄	—	4	2	no	—
168	C₂×Q₁₆	—	73	2	no	—
169	C₂×Q₁₆	—	146	2	no	—
170	C₂×Q₁₆	—	146	2	no	—
171	C₂×Q₁₆	—	146	1	no	—
172	C₂×D₈	—	2	4	no	—
173	C₂×D₈	—	2	2	no	—
174	C₂×D₈	—	2	2	no	—
175	C₂×D₈	—	2	2	no	—
176	C₂×D₈	—	2	2	no	—
177	C₂×D₈	—	2	2	no	—
178	C₂×D₈	—	4	2	no	—
179	C₂×D₈	—	4	2	no	—
180	C₂×D₈	C₂²⋊D₇₃	1	4	yes	—
181	C₂²×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
182	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
183	#127	—	2	4	no	—
184	#127	—	4	2	no	—
185	C₂×C₄⋊C₄	—	146	1	no	—
186	C₂×C₄²	C₂²⋊D₇₃	1	1	yes	characteristic
187	SD₃₂	—	146	16	no	—
188	C₂×C₁₆	—	73	4	no	—
189	C₂×C₁₆	—	146	2	no	—
190	C₂×C₁₆	—	146	2	no	—
191	#107	—	146	2	no	—
192	#103	—	292	2	no	—
193	C₄×C₈	—	2	2	no	—
194	#95	—	292	2	no	—
195	C₂⁴	—	4	2	no	—
196	C₂×Q₈	—	292	1	no	—
197	C₂×Q₈	—	292	1	no	—
198	C₂×Q₈	—	292	1	no	—
199	C₂×Q₈	—	292	1	no	—
200	C₂×Q₈	—	292	1	no	—
201	C₂×Q₈	—	146	2	no	—
202	C₂×D₄	—	2	4	no	—
203	C₂×D₄	—	4	8	no	—
204	C₂×D₄	—	4	2	no	—
205	C₂×D₄	—	4	2	no	—
206	C₂×D₄	—	4	2	no	—
207	C₂×D₄	—	4	2	no	—
208	C₂×D₄	—	4	2	no	—
209	C₂×D₄	—	8	4	no	—
210	C₂×D₄	—	8	4	no	—
211	C₂²×C₄	—	292	1	no	—
212	C₂²×C₄	—	292	1	no	—
213	C₂²×C₄	#11924013	1	2	yes	—
214	C₂²×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
215	Q₁₆	—	292	2	no	—
216	Q₁₆	—	146	4	no	—
217	D₈	—	2	4	no	—
218	D₈	—	2	4	no	—
219	D₈	—	4	8	no	—
220	D₈	—	4	2	no	—
221	D₈	—	4	2	no	—
222	C₂×C₈	—	2	1	no	—
223	C₂×C₈	—	2	1	no	—
224	C₂×C₈	#11924013	1	2	yes	—
225	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
226	C₂×C₈	D₄×D₇₃	1	2	yes	—
227	C₂×C₈	C₂×C₂²⋊D₇₃	1	2	yes	—
228	C₂×C₈	#11924027	1	1	yes	characteristic
229	C₄⋊C₄	—	292	1	no	—
230	C₄⋊C₄	—	292	1	no	—
231	C₄²	—	2	1	no	—
232	C₄²	—	2	1	no	—
233	C₁₆	—	146	4	no	—
234	C₂³	—	4	4	no	—
235	C₂³	—	8	2	no	—
236	C₂³	—	8	4	no	—
237	C₂³	—	8	4	no	—
238	C₂³	—	8	2	no	—
239	C₂³	C₂×#11924013	1	1	yes	characteristic
240	Q₈	—	292	2	no	—
241	Q₈	—	292	2	no	—
242	Q₈	—	584	1	no	—
243	Q₈	—	584	1	no	—
244	D₄	—	4	4	no	—
245	D₄	—	4	4	no	—
246	D₄	—	8	16	no	—
247	D₄	—	8	2	no	—
248	D₄	—	8	2	no	—
249	C₂×C₄	—	2	2	no	—
250	C₂×C₄	—	2	2	no	—
251	C₂×C₄	—	292	2	no	—
252	C₂×C₄	—	584	1	no	—
253	C₂×C₄	—	584	1	no	—
254	C₂×C₄	—	584	1	no	—
255	C₂×C₄	—	584	2	no	—
256	C₂×C₄	#14556535	1	4	yes	complemented
257	C₂×C₄	#14556560	1	1	yes	characteristic
258	C₂×C₄	#14556562	1	1	yes	characteristic
259	C₂×C₄	#14556587	1	1	yes	characteristic
260	C₂×C₄	C₂×#11924013	1	1	yes	characteristic
261	C₂×C₄	#14556617	1	1	yes	characteristic
262	C₂×C₄	#14556617	1	1	yes	characteristic
263	C₈	—	2	2	no	—
264	C₈	#14556559	1	2	yes	—
265	C₈	#14556563	1	2	yes	—
266	C₂²	—	8	4	no	—
267	C₂²	—	8	8	no	—
268	C₂²	—	16	4	no	—
269	C₂²	—	16	2	no	—
270	C₂²	—	16	2	no	—
271	C₂²	#17988721	1	1	yes	characteristic
272	C₂²	#17988779	1	1	yes	characteristic
273	C₂²	#17988963	1	1	yes	characteristic
274	C₂²	C₂×#14556535	1	2	yes	—
275	C₂²	#17989023	1	2	yes	—
276	C₄	—	2	4	no	—
277	C₄	—	584	2	no	—
278	C₄	—	1168	1	no	—
279	C₄	#17988495	1	1	yes	characteristic
280	C₄	#17988721	1	1	yes	characteristic
281	C₄	#17988779	1	1	yes	characteristic
282	C₄	#17988974	1	1	yes	characteristic
283	C₂	—	16	4	no	—
284	C₂	#22611002	1	1	yes	characteristic
285	C₂	#22611860	1	2	yes	—
286	C₂	#22611968	1	2	yes	—
287	C₂	#22612186	1	1	yes	characteristic
288	C₂	#22612195	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#14556535

C₂

yes

maximal, complemented

C₂×#17988388

C₂

yes

maximal, complemented

#22610792

C₂

yes

maximal, characteristic, complemented

#22608009

C₂

yes

maximal, characteristic, complemented

C₂×#493×C₇₃

C₂

yes

maximal, characteristic

C₂²×Dic₂₉₂

C₂²

yes

—

—

—

C₂²

yes

—

C₂×#14556525

C₂²

yes

—

—

—

C₂²×D₈×C₇₃

—

C₂²×D₈×C₇₃

C₂²

yes

—

C₂×#127×C₇₃

—

#493×C₇₃

—

C₂×C₄×C₈×C₇₃

C₂²

yes

characteristic

C₂²×Dic₁₄₆

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

D₄

yes

complemented

C₂×C₄⋊Dic₇₃

—

—

—

—

D₄

yes

—

—

—

C₂²×D₄×C₇₃

—

C₂²×D₄×C₇₃

—

C₂×D₈×C₇₃

—

C₂×D₈×C₇₃

—

C₂×D₈×C₇₃

—

C₂×D₈×C₇₃

—

C₂×D₈×C₇₃

—

C₂×D₈×C₇₃

—

C₂×D₈×C₇₃

—

C₂×D₈×C₇₃

—

C₂×D₈×C₇₃

D₄

yes

—

C₂²×C₈×C₇₃

D₄

yes

characteristic

C₂²×C₈×C₇₃

C₂³

yes

characteristic

#127×C₇₃

—

#127×C₇₃

—

C₂×C₄²×C₇₃

D₄

yes

characteristic

C₄×C₈×C₇₃

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

—

Dic₂₉₂

—

Dic₂₉₂

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

#11924003

—

C₂⁴×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂²×C₄×C₇₃

D₈

yes

—

C₂²×C₄×C₇₃

C₂×D₄

yes

characteristic

D₈×C₇₃

—

D₈×C₇₃

—

D₈×C₇₃

—

D₈×C₇₃

—

D₈×C₇₃

—

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

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

C₂×D₈

yes

characteristic

D₄×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

100

C₂×C₄×C₇₃

—

101

C₂×C₄×C₇₃

—

102

C₂×C₄×C₇₃

SD₃₂

yes

complemented

103

C₂×C₄×C₇₃

#120

yes

characteristic

104

C₂×C₄×C₇₃

#121

yes

characteristic

105

C₂×C₄×C₇₃

#127

yes

characteristic

106

C₂×C₄×C₇₃

C₂×D₈

yes

characteristic

107

C₂×C₄×C₇₃

AGL(1,ℤ/8)

yes

characteristic

108

C₂×C₄×C₇₃

AGL(1,ℤ/8)

yes

characteristic

109

C₂×Dic₇₃

—

110

C₂×Dic₇₃

—

111

C₂×Dic₇₃

—

112

C₂×Dic₇₃

—

113

C₂×Dic₇₃

—

114

Dic₁₄₆

—

115

Dic₁₄₆

—

116

Dic₁₄₆

—

117

Dic₁₄₆

—

118

C₈×C₇₃

—

119

C₈×C₇₃

#120

yes

—

120

C₈×C₇₃

#121

yes

—

121

C₂²×C₇₃

—

122

C₂²×C₇₃

—

123

C₂²×C₇₃

—

124

C₂²×C₇₃

—

125

C₂²×C₇₃

—

126

C₂²×C₇₃

#447

yes

characteristic

127

C₂²×C₇₃

#459

yes

characteristic

128

C₂²×C₇₃

#493

yes

characteristic

129

C₂²×C₇₃

C₂×SD₃₂

yes

—

130

C₂²×C₇₃

#509

yes

—

131

C₄×C₇₃

—

132

C₄×C₇₃

#392

yes

characteristic

133

C₄×C₇₃

#447

yes

characteristic

134

C₄×C₇₃

#459

yes

characteristic

135

C₄×C₇₃

#496

yes

characteristic

136

Dic₇₃

—

137

Dic₇₃

—

138

#13328

—

maximal, Sylow

139

C₂×C₇₃

—

140

C₂×C₇₃

#2011

yes

characteristic

141

C₂×C₇₃

#2187

yes

—

142

C₂×C₇₃

#2207

yes

—

143

C₂×C₇₃

#2248

yes

characteristic

144

C₂×C₇₃

#2250

yes

characteristic

145

C₂²×SD₃₂

—

146

C₂×#493

D₇₃

yes

characteristic

147

C₂×#357

—

148

#1969

—

149

#1374

—

150

C₇₃

#13328

yes

characteristic, complemented, Sylow

151

C₂²×Q₁₆

—

152

C₂²×D₈

—

153

C₂²×D₈

C₂×D₇₃

yes

—

154

C₂×#127

—

155

C₂×SD₃₂

—

146

—

156

C₂×SD₃₂

—

146

—

157

C₂×SD₃₂

—

146

—

158

C₂²×C₁₆

—

159

#493

—

160

C₂×#107

—

161

C₂×#103

—

146

—

162

C₂×C₄×C₈

C₂×D₇₃

yes

characteristic

163

#391

—

146

—

164

#357

—

146

—

165

C₂²×Q₈

—

146

—

166

C₂²×D₄

—

167

C₂²×D₄

—

168

C₂×Q₁₆

—

169

C₂×Q₁₆

—

146

—

170

C₂×Q₁₆

—

146

—

171

C₂×Q₁₆

—

146

—

172

C₂×D₈

—

173

C₂×D₈

—

174

C₂×D₈

—

175

C₂×D₈

—

176

C₂×D₈

—

177

C₂×D₈

—

178

C₂×D₈

—

179

C₂×D₈

—

180

C₂×D₈

C₂²⋊D₇₃

yes

—

181

C₂²×C₈

C₂²⋊D₇₃

yes

characteristic

182

C₂²×C₈

C₂²×D₇₃

yes

characteristic

183

#127

—

184

#127

—

185

C₂×C₄⋊C₄

—

146

—

186

C₂×C₄²

C₂²⋊D₇₃

yes

characteristic

187

SD₃₂

—

146

—

188

C₂×C₁₆

—

189

C₂×C₁₆

—

146

—

190

C₂×C₁₆

—

146

—

191

#107

—

146

—

192

#103

—

292

—

193

C₄×C₈

—

194

#95

—

292

—

195

C₂⁴

—

196

C₂×Q₈

—

292

—

197

C₂×Q₈

—

292

—

198

C₂×Q₈

—

292

—

199

C₂×Q₈

—

292

—

200

C₂×Q₈

—

292

—

201

C₂×Q₈

—

146

—

202

C₂×D₄

—

203

C₂×D₄

—

204

C₂×D₄

—

205

C₂×D₄

—

206

C₂×D₄

—

207

C₂×D₄

—

208

C₂×D₄

—

209

C₂×D₄

—

210

C₂×D₄

—

211

C₂²×C₄

—

292

—

212

C₂²×C₄

—

292

—

213

C₂²×C₄

#11924013

yes

—

214

C₂²×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

215

Q₁₆

—

292

—

216

Q₁₆

—

146

—

217

D₈

—

218

D₈

—

219

D₈

—

220

D₈

—

221

D₈

—

222

C₂×C₈

—

223

C₂×C₈

—

224

C₂×C₈

#11924013

yes

—

225

C₂×C₈

D₄×D₇₃

yes

characteristic

226

C₂×C₈

D₄×D₇₃

yes

—

227

C₂×C₈

C₂×C₂²⋊D₇₃

yes

—

228

C₂×C₈

#11924027

yes

characteristic

229

C₄⋊C₄

—

292

—

230

C₄⋊C₄

—

292

—

231

C₄²

—

232

C₄²

—

233

C₁₆

—

146

—

234

C₂³

—

235

C₂³

—

236

C₂³

—

237

C₂³

—

238

C₂³

—

239

C₂³

C₂×#11924013

yes

characteristic

240

Q₈

—

292

—

241

Q₈

—

292

—

242

Q₈

—

584

—

243

Q₈

—

584

—

244

D₄

—

245

D₄

—

246

D₄

—

247

D₄

—

248

D₄

—

249

C₂×C₄

—

250

C₂×C₄

—

251

C₂×C₄

—

292

—

252

C₂×C₄

—

584

—

253

C₂×C₄

—

584

—

254

C₂×C₄

—

584

—

255

C₂×C₄

—

584

—

256

C₂×C₄

#14556535

yes

complemented

257

C₂×C₄

#14556560

yes

characteristic

258

C₂×C₄

#14556562

yes

characteristic

259

C₂×C₄

#14556587

yes

characteristic

260

C₂×C₄

C₂×#11924013

yes

characteristic

261

C₂×C₄

#14556617

yes

characteristic

262

C₂×C₄

#14556617

yes

characteristic

263

C₈

—

264

C₈

#14556559

yes

—

265

C₈

#14556563

yes

—

266

C₂²

—

267

C₂²

—

268

C₂²

—

269

C₂²

—

270

C₂²

—

271

C₂²

#17988721

yes

characteristic

272

C₂²

#17988779

yes

characteristic

273

C₂²

#17988963

yes

characteristic

274

C₂²

C₂×#14556535

yes

—

275

C₂²

#17989023

yes

—

276

C₄

—

277

C₄

—

584

—

278

C₄

—

1168

—

279

C₄

#17988495

yes

characteristic

280

C₄

#17988721

yes

characteristic

281

C₄

#17988779

yes

characteristic

282

C₄

#17988974

yes

characteristic

283

C₂

—

284

C₂

#22611002

yes

characteristic

285

C₂

#22611860

yes

—

286

C₂

#22611968

yes

—

287

C₂

#22612186

yes

characteristic

288

C₂

#22612195

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×#11924013
commutator, cosocle	C₂²×C₈×C₇₃	C₂³
Frattini	C₂²×C₈	C₂²×D₇₃
Fitting, prime radical	C₂×#493×C₇₃	C₂
socle	C₂³×C₇₃	C₂×D₈
hypercenter	C₂×#493	D₇₃
hypocenter	C₇₃	#13328
LCS	G ▷ C₂²×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#493

subgroup

G/H

center

C₂³

C₂×#11924013

commutator, cosocle

C₂²×C₈×C₇₃

C₂³

Frattini

C₂²×C₈

C₂²×D₇₃

Fitting, prime radical

C₂×#493×C₇₃

C₂

socle

C₂³×C₇₃

C₂×D₈

D₇₃

C₇₃

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

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#493

N	H ≅ G/N	type
1. C₂²×#14556535	C₂	semidirect
2. C₂×#17988388	C₂	semidirect
3. #22610792	C₂	semidirect
4. #22608009	C₂	semidirect
24. C₂×Dic₂₉₂	D₄	semidirect
29. C₂×#11924003	D₄	semidirect
102. C₂×C₄×C₇₃	SD₃₂	semidirect
150. C₇₃	#13328	semidirect
256. C₂×C₄	#14556535	semidirect

H ≅ G/N

type

1. C₂²×#14556535

C₂

semidirect

2. C₂×#17988388

C₂

semidirect

3. #22610792

C₂

semidirect

4. #22608009

C₂

semidirect

24. C₂×Dic₂₉₂

D₄

semidirect

29. C₂×#11924003

D₄

semidirect

102. C₂×C₄×C₇₃

SD₃₂

semidirect

150. C₇₃

#13328

semidirect

256. C₂×C₄

#14556535

semidirect

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

subgroup	index
C₂²×#14556535	2
C₂×#17988388	2
#22610792	2
#22608009	2
C₂×#493×C₇₃	2
#13328	73

subgroup

index

C₂×#493×C₇₃

Subgroups — #33004832

Conjugacy classes of subgroups

Complements

Maximal subgroups