Group #33003025 — subgroups

Subgroups — #33003025

Order 18688.

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

normal subgroups only

This group has 496 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	C₂×#17988636	C₂	1	1	yes	maximal, characteristic
2	C₂×#17988403	C₂	1	2	yes	maximal, complemented
3	C₂×#17988369	C₂	1	1	yes	maximal, characteristic
4	#22608029	C₂	1	2	yes	maximal, complemented
5	C₂×#470×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×#11924012	—	2	1	no	—
7	C₂×#14556531	C₂²	1	2	yes	—
8	#17988636	—	2	4	no	—
9	C₂×#14556527	—	2	1	no	—
10	C₂×#14556527	C₂²	1	2	yes	—
11	#17988403	—	2	4	no	—
12	#17988369	—	2	2	no	—
13	C₂²×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic
14	C₂²×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
15	C₂×C₂²⋊Q₈×C₇₃	—	2	1	no	—
16	#470×C₇₃	—	2	2	no	—
17	#470×C₇₃	C₄	1	4	yes	—
18	C₂×#106×C₇₃	C₂²	1	1	yes	characteristic
19	C₂×#103×C₇₃	—	2	1	no	—
20	C₂×#11924012	—	2	4	no	—
21	C₂×#11924012	—	2	2	no	—
22	C₂×#11924012	—	4	1	no	—
23	C₂×#11924012	—	4	2	no	—
24	C₂²×#10596831	—	4	1	no	—
25	#14556531	—	2	2	no	—
26	#14556531	—	2	2	no	—
27	C₂×#11924003	—	2	2	no	—
28	#14556527	—	2	4	no	—
29	#14556527	—	2	2	no	—
30	#14556527	D₄	1	4	yes	—
31	C₂²×Q₈×C₇₃	—	2	1	no	—
32	C₂³×C₄×C₇₃	D₄	1	1	yes	characteristic
33	C₂×Q₁₆×C₇₃	—	2	2	no	—
34	C₂×Q₁₆×C₇₃	—	2	1	no	—
35	C₂×Q₁₆×C₇₃	—	2	2	no	—
36	C₂×Q₁₆×C₇₃	C₂×C₄	1	2	yes	—
37	C₂×M₁₆×C₇₃	—	2	2	no	—
38	C₂×M₁₆×C₇₃	—	2	2	no	—
39	C₂×M₁₆×C₇₃	C₂×C₄	1	2	yes	—
40	C₂×M₁₆×C₇₃	D₄	1	2	yes	—
41	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
42	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
43	C₂²⋊Q₈×C₇₃	—	2	4	no	—
44	C₂²⋊Q₈×C₇₃	—	4	2	no	—
45	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
46	C₂×C₄⋊C₄×C₇₃	—	4	1	no	—
47	C₂×C₂²⋊C₄×C₇₃	—	4	1	no	—
48	#106×C₇₃	—	2	1	no	—
49	#106×C₇₃	C₂×C₄	1	2	yes	—
50	#103×C₇₃	—	2	4	no	—
51	#11924012	—	2	4	no	—
52	#11924012	—	4	4	no	—
53	#11924012	—	4	2	no	—
54	C₂×#10596831	—	4	4	no	—
55	C₂×#10596831	—	4	2	no	—
56	#11924003	—	4	2	no	—
57	C₂⁴×C₇₃	SD₁₆	1	1	yes	characteristic
58	C₂×Q₈×C₇₃	—	2	2	no	—
59	C₂×Q₈×C₇₃	—	4	1	no	—
60	C₂×Q₈×C₇₃	—	4	1	no	—
61	C₂×Q₈×C₇₃	—	4	1	no	—
62	C₂×Q₈×C₇₃	—	4	1	no	—
63	C₂×Q₈×C₇₃	—	4	1	no	—
64	C₂²×C₄×C₇₃	—	2	1	no	—
65	C₂²×C₄×C₇₃	—	2	1	no	—
66	C₂²×C₄×C₇₃	—	2	1	no	—
67	C₂²×C₄×C₇₃	—	2	1	no	—
68	C₂²×C₄×C₇₃	—	4	1	no	—
69	C₂²×C₄×C₇₃	—	4	1	no	—
70	C₂²×C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
71	C₂²×C₄×C₇₃	D₈	1	2	yes	—
72	C₂²×C₄×C₇₃	SD₁₆	1	1	yes	characteristic
73	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
74	Q₁₆×C₇₃	—	2	4	no	—
75	Q₁₆×C₇₃	—	4	2	no	—
76	M₁₆×C₇₃	—	2	4	no	—
77	M₁₆×C₇₃	—	2	4	no	—
78	C₂×C₈×C₇₃	—	2	1	no	—
79	C₂×C₈×C₇₃	—	2	1	no	—
80	C₂×C₈×C₇₃	C₂²⋊C₄	1	2	yes	—
81	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
82	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
83	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
84	C₂×C₈×C₇₃	#41	1	2	yes	—
85	C₄⋊C₄×C₇₃	—	2	2	no	—
86	C₄⋊C₄×C₇₃	—	4	4	no	—
87	C₄⋊C₄×C₇₃	—	4	1	no	—
88	C₂²⋊C₄×C₇₃	—	4	4	no	—
89	C₂³×C₇₃	—	2	1	no	—
90	C₂³×C₇₃	—	2	1	no	—
91	C₂³×C₇₃	—	4	2	no	—
92	C₂³×C₇₃	#102	1	2	yes	—
93	C₂³×C₇₃	C₂×SD₁₆	1	1	yes	characteristic
94	Q₈×C₇₃	—	4	2	no	—
95	Q₈×C₇₃	—	4	2	no	—
96	Q₈×C₇₃	—	8	1	no	—
97	Q₈×C₇₃	—	8	1	no	—
98	C₂×C₄×C₇₃	—	2	1	no	—
99	C₂×C₄×C₇₃	—	2	1	no	—
100	C₂×C₄×C₇₃	—	2	2	no	—
101	C₂×C₄×C₇₃	—	2	2	no	—
102	C₂×C₄×C₇₃	—	2	2	no	—
103	C₂×C₄×C₇₃	—	2	2	no	—
104	C₂×C₄×C₇₃	—	4	2	no	—
105	C₂×C₄×C₇₃	—	4	2	no	—
106	C₂×C₄×C₇₃	—	8	2	no	—
107	C₂×C₄×C₇₃	—	8	1	no	—
108	C₂×C₄×C₇₃	—	8	1	no	—
109	C₂×C₄×C₇₃	#102	1	2	yes	—
110	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
111	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
112	C₂×C₄×C₇₃	#123	1	1	yes	characteristic
113	C₂×C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
114	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
115	C₂×C₄×C₇₃	#137	1	1	yes	characteristic
116	C₈×C₇₃	—	2	2	no	—
117	C₈×C₇₃	C₄×D₄	1	2	yes	—
118	C₈×C₇₃	#121	1	2	yes	—
119	#10596831	—	4	4	no	—
120	C₂²×C₇₃	—	2	2	no	—
121	C₂²×C₇₃	—	2	2	no	—
122	C₂²×C₇₃	—	4	2	no	—
123	C₂²×C₇₃	—	4	2	no	—
124	C₂²×C₇₃	—	8	1	no	—
125	C₂²×C₇₃	C₂×#102	1	1	yes	characteristic
126	C₂²×C₇₃	#448	1	1	yes	characteristic
127	C₂²×C₇₃	#481	1	1	yes	characteristic
128	C₄×C₇₃	—	2	2	no	—
129	C₄×C₇₃	—	8	2	no	—
130	C₄×C₇₃	—	8	2	no	—
131	C₄×C₇₃	#386	1	1	yes	characteristic
132	C₄×C₇₃	#417	1	1	yes	characteristic
133	C₄×C₇₃	#447	1	1	yes	characteristic
134	C₄×C₇₃	#480	1	1	yes	characteristic
135	#13009	—	73	1	no	maximal, Sylow
136	C₂×C₇₃	—	2	1	no	—
137	C₂×C₇₃	—	2	1	no	—
138	C₂×C₇₃	—	4	2	no	—
139	C₂×C₇₃	#1874	1	1	yes	characteristic
140	C₂×C₇₃	#2239	1	2	yes	—
141	C₂×#470	D₇₃	1	1	yes	characteristic
142	C₂×#430	—	73	1	no	—
143	C₂×#362	—	73	2	no	—
144	C₂×#349	—	73	1	no	—
145	#1383	—	73	2	no	—
146	C₇₃	#13009	1	1	yes	characteristic, complemented, Sylow
147	C₂²×Q₁₆	C₂×D₇₃	1	1	yes	characteristic
148	C₂²×M₁₆	—	146	1	no	—
149	C₂²×M₁₆	C₂×D₇₃	1	1	yes	characteristic
150	C₂×C₂²⋊Q₈	—	2	1	no	—
151	C₂×M₃₂	—	73	2	no	—
152	#470	—	2	2	no	—
153	#470	Dic₇₃	1	4	yes	—
154	#430	—	146	4	no	—
155	C₂×#108	—	73	2	no	—
156	C₂×#108	—	146	1	no	—
157	C₂×#106	C₂×D₇₃	1	1	yes	characteristic
158	C₂×#103	—	2	1	no	—
159	#362	—	146	4	no	—
160	#349	—	146	2	no	—
161	C₂²×Q₈	—	2	1	no	—
162	C₂³×C₄	C₂²⋊D₇₃	1	1	yes	characteristic
163	C₂×Q₁₆	—	2	2	no	—
164	C₂×Q₁₆	—	2	1	no	—
165	C₂×Q₁₆	—	2	2	no	—
166	C₂×Q₁₆	C₂×Dic₇₃	1	2	yes	—
167	C₂×M₁₆	—	2	2	no	—
168	C₂×M₁₆	—	2	2	no	—
169	C₂×M₁₆	—	292	1	no	—
170	C₂×M₁₆	—	292	2	no	—
171	C₂×M₁₆	—	146	4	no	—
172	C₂×M₁₆	—	146	2	no	—
173	C₂×M₁₆	C₂×Dic₇₃	1	2	yes	—
174	C₂×M₁₆	C₂²⋊D₇₃	1	2	yes	—
175	C₂²×C₈	—	292	1	no	—
176	C₂²×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
177	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
178	C₂²⋊Q₈	—	2	4	no	—
179	C₂²⋊Q₈	—	4	2	no	—
180	C₂×C₄⋊C₄	—	2	1	no	—
181	C₂×C₄⋊C₄	—	4	1	no	—
182	C₂×C₂²⋊C₄	—	4	1	no	—
183	M₃₂	—	146	2	no	—
184	M₃₂	—	146	2	no	—
185	C₂×C₁₆	—	146	2	no	—
186	#108	—	73	4	no	—
187	#108	—	146	4	no	—
188	#108	—	146	2	no	—
189	#106	—	2	1	no	—
190	#106	C₂×Dic₇₃	1	2	yes	—
191	#103	—	2	4	no	—
192	C₂⁴	#11924016	1	1	yes	characteristic
193	C₂×Q₈	—	2	2	no	—
194	C₂×Q₈	—	4	1	no	—
195	C₂×Q₈	—	4	1	no	—
196	C₂×Q₈	—	4	1	no	—
197	C₂×Q₈	—	4	1	no	—
198	C₂×Q₈	—	4	1	no	—
199	C₂²×C₄	—	2	1	no	—
200	C₂²×C₄	—	2	1	no	—
201	C₂²×C₄	—	2	1	no	—
202	C₂²×C₄	—	2	1	no	—
203	C₂²×C₄	—	4	1	no	—
204	C₂²×C₄	—	4	1	no	—
205	C₂²×C₄	C₂²⋊Dic₇₃	1	2	yes	—
206	C₂²×C₄	#11924013	1	2	yes	—
207	C₂²×C₄	#11924016	1	1	yes	characteristic
208	C₂²×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
209	Q₁₆	—	2	4	no	—
210	Q₁₆	—	4	2	no	—
211	M₁₆	—	2	4	no	—
212	M₁₆	—	2	4	no	—
213	M₁₆	—	292	4	no	—
214	M₁₆	—	292	2	no	—
215	M₁₆	—	146	4	no	—
216	C₂×C₈	—	2	1	no	—
217	C₂×C₈	—	2	1	no	—
218	C₂×C₈	—	292	4	no	—
219	C₂×C₈	—	292	2	no	—
220	C₂×C₈	C₂²⋊Dic₇₃	1	2	yes	—
221	C₂×C₈	C₂²×Dic₇₃	1	1	yes	characteristic
222	C₂×C₈	D₄×D₇₃	1	2	yes	—
223	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
224	C₂×C₈	#11924027	1	2	yes	—
225	C₄⋊C₄	—	2	2	no	—
226	C₄⋊C₄	—	4	4	no	—
227	C₄⋊C₄	—	4	1	no	—
228	C₂²⋊C₄	—	4	4	no	—
229	C₁₆	—	292	2	no	—
230	C₂³	—	2	1	no	—
231	C₂³	—	2	1	no	—
232	C₂³	—	4	2	no	—
233	C₂³	#14556512	1	2	yes	—
234	C₂³	C₂×#11924016	1	1	yes	characteristic
235	Q₈	—	4	2	no	—
236	Q₈	—	4	2	no	—
237	Q₈	—	8	1	no	—
238	Q₈	—	8	1	no	—
239	C₂×C₄	—	2	1	no	—
240	C₂×C₄	—	2	1	no	—
241	C₂×C₄	—	2	2	no	—
242	C₂×C₄	—	2	2	no	—
243	C₂×C₄	—	2	2	no	—
244	C₂×C₄	—	2	2	no	—
245	C₂×C₄	—	4	2	no	—
246	C₂×C₄	—	4	2	no	—
247	C₂×C₄	—	8	2	no	—
248	C₂×C₄	—	8	1	no	—
249	C₂×C₄	—	8	1	no	—
250	C₂×C₄	#14556512	1	2	yes	—
251	C₂×C₄	C₂×C₂²⋊Dic₇₃	1	1	yes	characteristic
252	C₂×C₄	#14556559	1	1	yes	characteristic
253	C₂×C₄	#14556572	1	1	yes	characteristic
254	C₂×C₄	C₂×#11924013	1	1	yes	characteristic
255	C₂×C₄	#14556616	1	1	yes	characteristic
256	C₂×C₄	#14556621	1	1	yes	characteristic
257	C₈	—	2	2	no	—
258	C₈	—	292	4	no	—
259	C₈	D₄×Dic₇₃	1	2	yes	—
260	C₈	#14556563	1	2	yes	—
261	C₂²	—	2	2	no	—
262	C₂²	—	2	2	no	—
263	C₂²	—	4	2	no	—
264	C₂²	—	4	2	no	—
265	C₂²	—	8	1	no	—
266	C₂²	C₂×#14556512	1	1	yes	characteristic
267	C₂²	#17988725	1	1	yes	characteristic
268	C₂²	#17988903	1	1	yes	characteristic
269	C₄	—	2	2	no	—
270	C₄	—	8	2	no	—
271	C₄	—	8	2	no	—
272	C₄	#17988467	1	1	yes	characteristic
273	C₄	#17988588	1	1	yes	characteristic
274	C₄	#17988720	1	1	yes	characteristic
275	C₄	#17988898	1	1	yes	characteristic
276	C₂	—	2	1	no	—
277	C₂	—	2	1	no	—
278	C₂	—	4	2	no	—
279	C₂	#22610249	1	1	yes	characteristic
280	C₂	#22612148	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#17988636

C₂

yes

maximal, characteristic

C₂×#17988403

C₂

yes

maximal, complemented

C₂×#17988369

C₂

yes

maximal, characteristic

#22608029

C₂

yes

maximal, complemented

C₂×#470×C₇₃

C₂

yes

maximal, characteristic

C₂²×#11924012

—

C₂×#14556531

C₂²

yes

—

#17988636

—

C₂×#14556527

—

C₂×#14556527

C₂²

yes

—

#17988403

—

#17988369

—

C₂²×Q₁₆×C₇₃

C₂²

yes

characteristic

C₂²×M₁₆×C₇₃

C₂²

yes

characteristic

C₂×C₂²⋊Q₈×C₇₃

—

#470×C₇₃

—

#470×C₇₃

C₄

yes

—

C₂×#106×C₇₃

C₂²

yes

characteristic

C₂×#103×C₇₃

—

—

—

—

—

—

—

—

—

—

—

D₄

yes

—

C₂²×Q₈×C₇₃

—

C₂³×C₄×C₇₃

D₄

yes

characteristic

C₂×Q₁₆×C₇₃

—

C₂×Q₁₆×C₇₃

—

C₂×Q₁₆×C₇₃

—

C₂×Q₁₆×C₇₃

C₂×C₄

yes

—

C₂×M₁₆×C₇₃

—

C₂×M₁₆×C₇₃

—

C₂×M₁₆×C₇₃

C₂×C₄

yes

—

C₂×M₁₆×C₇₃

D₄

yes

—

C₂²×C₈×C₇₃

D₄

yes

characteristic

C₂²×C₈×C₇₃

C₂³

yes

characteristic

C₂²⋊Q₈×C₇₃

—

C₂²⋊Q₈×C₇₃

—

C₂×C₄⋊C₄×C₇₃

—

C₂×C₄⋊C₄×C₇₃

—

C₂×C₂²⋊C₄×C₇₃

—

#106×C₇₃

—

#106×C₇₃

C₂×C₄

yes

—

#103×C₇₃

—

—

—

—

—

—

—

C₂⁴×C₇₃

SD₁₆

yes

characteristic

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₇₃

D₈

yes

—

C₂²×C₄×C₇₃

SD₁₆

yes

characteristic

C₂²×C₄×C₇₃

C₂×D₄

yes

characteristic

Q₁₆×C₇₃

—

Q₁₆×C₇₃

—

M₁₆×C₇₃

—

M₁₆×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₂²⋊C₄

yes

—

C₂×C₈×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₇₃

C₂×D₄

yes

—

C₂×C₈×C₇₃

C₂×D₄

yes

characteristic

C₂×C₈×C₇₃

#41

yes

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

#102

yes

—

C₂³×C₇₃

C₂×SD₁₆

yes

characteristic

Q₈×C₇₃

—

Q₈×C₇₃

—

Q₈×C₇₃

—

Q₈×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

100

C₂×C₄×C₇₃

—

101

C₂×C₄×C₇₃

—

102

C₂×C₄×C₇₃

—

103

C₂×C₄×C₇₃

—

104

C₂×C₄×C₇₃

—

105

C₂×C₄×C₇₃

—

106

C₂×C₄×C₇₃

—

107

C₂×C₄×C₇₃

—

108

C₂×C₄×C₇₃

—

109

C₂×C₄×C₇₃

#102

yes

—

110

C₂×C₄×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

111

C₂×C₄×C₇₃

#120

yes

characteristic

112

C₂×C₄×C₇₃

#123

yes

characteristic

113

C₂×C₄×C₇₃

C₂×D₈

yes

characteristic

114

C₂×C₄×C₇₃

AGL(1,ℤ/8)

yes

characteristic

115

C₂×C₄×C₇₃

#137

yes

characteristic

116

C₈×C₇₃

—

117

C₈×C₇₃

C₄×D₄

yes

—

118

C₈×C₇₃

#121

yes

—

119

#10596831

—

120

C₂²×C₇₃

—

121

C₂²×C₇₃

—

122

C₂²×C₇₃

—

123

C₂²×C₇₃

—

124

C₂²×C₇₃

—

125

C₂²×C₇₃

C₂×#102

yes

characteristic

126

C₂²×C₇₃

#448

yes

characteristic

127

C₂²×C₇₃

#481

yes

characteristic

128

C₄×C₇₃

—

129

C₄×C₇₃

—

130

C₄×C₇₃

—

131

C₄×C₇₃

#386

yes

characteristic

132

C₄×C₇₃

#417

yes

characteristic

133

C₄×C₇₃

#447

yes

characteristic

134

C₄×C₇₃

yes

135

—

136

C₂×C₇₃

—

137

C₂×C₇₃

—

138

C₂×C₇₃

—

139

C₂×C₇₃

#1874

yes

characteristic

140

C₂×C₇₃

#2239

yes

—

141

C₂×#470

D₇₃

yes

characteristic

142

C₂×#430

—

143

C₂×#362

—

144

C₂×#349

—

145

#1383

—

146

C₇₃

#13009

yes

characteristic, complemented, Sylow

147

C₂²×Q₁₆

C₂×D₇₃

yes

characteristic

148

C₂²×M₁₆

—

146

—

149

C₂²×M₁₆

C₂×D₇₃

yes

characteristic

150

C₂×C₂²⋊Q₈

—

151

C₂×M₃₂

—

152

#470

—

153

#470

Dic₇₃

yes

—

154

#430

—

146

—

155

C₂×#108

—

156

C₂×#108

—

146

—

157

C₂×#106

C₂×D₇₃

yes

characteristic

158

C₂×#103

—

159

#362

—

146

—

160

#349

—

146

—

161

C₂²×Q₈

—

162

C₂³×C₄

C₂²⋊D₇₃

yes

characteristic

163

C₂×Q₁₆

—

164

C₂×Q₁₆

—

165

C₂×Q₁₆

—

166

C₂×Q₁₆

C₂×Dic₇₃

yes

—

167

C₂×M₁₆

—

168

C₂×M₁₆

—

169

C₂×M₁₆

—

292

—

170

C₂×M₁₆

—

292

—

171

C₂×M₁₆

—

146

—

172

C₂×M₁₆

—

146

—

173

C₂×M₁₆

C₂×Dic₇₃

yes

—

174

C₂×M₁₆

C₂²⋊D₇₃

yes

—

175

C₂²×C₈

—

292

—

176

C₂²×C₈

C₂²⋊D₇₃

yes

characteristic

177

C₂²×C₈

C₂²×D₇₃

yes

characteristic

178

C₂²⋊Q₈

—

179

C₂²⋊Q₈

—

180

C₂×C₄⋊C₄

—

181

C₂×C₄⋊C₄

—

182

C₂×C₂²⋊C₄

—

183

M₃₂

—

146

—

184

M₃₂

—

146

—

185

C₂×C₁₆

—

146

—

186

#108

—

187

#108

—

146

—

188

#108

—

146

—

189

#106

—

190

#106

C₂×Dic₇₃

yes

—

191

#103

—

192

C₂⁴

#11924016

yes

characteristic

193

C₂×Q₈

—

194

C₂×Q₈

—

195

C₂×Q₈

—

196

C₂×Q₈

—

197

C₂×Q₈

—

198

C₂×Q₈

—

199

C₂²×C₄

—

200

C₂²×C₄

—

201

C₂²×C₄

—

202

C₂²×C₄

—

203

C₂²×C₄

—

204

C₂²×C₄

—

205

C₂²×C₄

C₂²⋊Dic₇₃

yes

—

206

C₂²×C₄

#11924013

yes

—

207

C₂²×C₄

#11924016

yes

characteristic

208

C₂²×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

209

Q₁₆

—

210

Q₁₆

—

211

M₁₆

—

212

M₁₆

—

213

M₁₆

—

292

—

214

M₁₆

—

292

—

215

M₁₆

—

146

—

216

C₂×C₈

—

217

C₂×C₈

—

218

C₂×C₈

—

292

—

219

C₂×C₈

—

292

—

220

C₂×C₈

C₂²⋊Dic₇₃

yes

—

221

C₂×C₈

C₂²×Dic₇₃

yes

characteristic

222

C₂×C₈

D₄×D₇₃

yes

—

223

C₂×C₈

C₂×C₂²⋊D₇₃

yes

characteristic

224

C₂×C₈

#11924027

yes

—

225

C₄⋊C₄

—

226

C₄⋊C₄

—

227

C₄⋊C₄

—

228

C₂²⋊C₄

—

229

C₁₆

—

292

—

230

C₂³

—

231

C₂³

—

232

C₂³

—

233

C₂³

#14556512

yes

—

234

C₂³

C₂×#11924016

yes

characteristic

235

Q₈

—

236

Q₈

—

237

Q₈

—

238

Q₈

—

239

C₂×C₄

—

240

C₂×C₄

—

241

C₂×C₄

—

242

C₂×C₄

—

243

C₂×C₄

—

244

C₂×C₄

—

245

C₂×C₄

—

246

C₂×C₄

—

247

C₂×C₄

—

248

C₂×C₄

—

249

C₂×C₄

—

250

C₂×C₄

#14556512

yes

—

251

C₂×C₄

C₂×C₂²⋊Dic₇₃

yes

characteristic

252

C₂×C₄

#14556559

yes

characteristic

253

C₂×C₄

#14556572

yes

characteristic

254

C₂×C₄

C₂×#11924013

yes

characteristic

255

C₂×C₄

#14556616

yes

characteristic

256

C₂×C₄

#14556621

yes

characteristic

257

C₈

—

258

C₈

—

292

—

259

C₈

D₄×Dic₇₃

yes

—

260

C₈

#14556563

yes

—

261

C₂²

—

262

C₂²

—

263

C₂²

—

264

C₂²

—

265

C₂²

—

266

C₂²

C₂×#14556512

yes

characteristic

267

C₂²

#17988725

yes

characteristic

268

C₂²

#17988903

yes

characteristic

269

C₄

—

270

C₄

—

271

C₄

—

272

C₄

#17988467

yes

characteristic

273

C₄

#17988588

yes

characteristic

274

C₄

#17988720

yes

characteristic

275

C₄

#17988898

yes

characteristic

276

C₂

—

277

C₂

—

278

C₂

—

279

C₂

#22610249

yes

characteristic

280

C₂

#22612148

yes

—

	subgroup	G/H
center	C₂²	#17988903
commutator	C₂×C₈×C₇₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₇₃
Fitting	C₂×#470×C₇₃	C₂
socle	C₂²×C₇₃	#481
prime radical	C₂⁴×C₇₃	SD₁₆
cosocle	C₂²×C₈×C₇₃	C₂³
hypercenter	C₂×#470	D₇₃
hypocenter	C₇₃	#13009
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×M₁₆ ◁ C₂×#470

subgroup

G/H

center

C₂²

#17988903

commutator

C₂×C₈×C₇₃

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₇₃

Fitting

C₂×#470×C₇₃

C₂

socle

C₂²×C₇₃

#481

prime radical

C₂⁴×C₇₃

SD₁₆

cosocle

C₂²×C₈×C₇₃

C₂³

D₇₃

C₇₃

G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×M₁₆ ◁ C₂×#470

N	H ≅ G/N	type
2. C₂×#17988403	C₂	semidirect
4. #22608029	C₂	semidirect
146. C₇₃	#13009	semidirect

H ≅ G/N

type

2. C₂×#17988403

C₂

semidirect

4. #22608029

C₂

semidirect

146. C₇₃

#13009

semidirect

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

subgroup	index
C₂×#17988636	2
C₂×#17988403	2
C₂×#17988369	2
#22608029	2
C₂×#470×C₇₃	2
#13009	73

subgroup

index

C₂×#470×C₇₃

Subgroups — #33003025

Conjugacy classes of subgroups

Complements

Maximal subgroups