Subgroups — #34034995

Order 18688.

536 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22627158	C₂	1	2	yes	maximal, complemented
2	#22627142	C₂	1	2	yes	maximal, complemented
3	#22627141	C₂	1	2	yes	maximal, complemented
4	#22627139	C₂	1	2	yes	maximal, complemented
5	#22627135	C₂	1	1	yes	maximal, characteristic, complemented
6	#22627132	C₂	1	1	yes	maximal, characteristic, complemented
7	#22627130	C₂	1	1	yes	maximal, characteristic, complemented
8	#22627121	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#17989690	C₂	1	1	yes	maximal, characteristic, complemented
10	#22627117	C₂	1	1	yes	maximal, characteristic, complemented
11	#22626735	C₂	1	1	yes	maximal, characteristic
12	C₂×#14556688	C₂²	1	2	yes	—
13	C₂×#14556686	C₂²	1	2	yes	—
14	C₂²×#11924040	C₂²	1	2	yes	—
15	#17989690	C₂²	1	1	yes	characteristic
16	#17989690	C₂²	1	1	yes	characteristic
17	#17989690	C₂²	1	1	yes	characteristic
18	#17989690	C₂²	1	2	yes	—
19	#17989690	C₂²	1	2	yes	—
20	#17989690	C₂²	1	1	yes	characteristic
21	C₄⋊#11924040	C₂²	1	2	yes	—
22	#17989684	C₂²	1	2	yes	—
23	#17989684	C₂²	1	2	yes	—
24	C₂²⋊#11924040	C₂²	1	2	yes	—
25	#17989681	C₂²	1	2	yes	—
26	#17989681	C₂²	1	2	yes	—
27	C₄×#11924040	C₂²	1	2	yes	—
28	#17989636	C₄	1	1	yes	characteristic
29	#17989636	C₂²	1	1	yes	characteristic
30	#17989615	C₄	1	1	yes	characteristic
31	#17989615	C₂²	1	1	yes	characteristic
32	#17989614	C₄	1	1	yes	characteristic
33	#17989614	C₄	1	1	yes	characteristic
34	#17989614	C₂²	1	1	yes	characteristic
35	#17989614	C₂²	1	1	yes	characteristic
36	#17989605	C₄	1	1	yes	characteristic
37	#17989605	C₄	1	1	yes	characteristic
38	#17989603	C₄	1	1	yes	characteristic
39	C₄×#11924036	C₂²	1	1	yes	characteristic
40	C₄×#11924036	C₂²	1	1	yes	characteristic
41	C₂×C₄×#10596833	C₂²	1	1	yes	characteristic
42	#17989055	C₄	1	1	yes	characteristic
43	#14556688	—	4	2	no	—
44	#14556686	—	4	2	no	—
45	C₂×#11924040	—	4	2	no	—
46	C₂×#11924040	C₂³	1	2	yes	—
47	C₂×#11924040	C₂³	1	2	yes	—
48	C₂×#11924040	C₂³	1	2	yes	—
49	C₂×#11924040	C₂³	1	2	yes	—
50	C₂×#11924036	C₂×C₄	1	1	yes	characteristic
51	C₂×#11924036	C₂×C₄	1	1	yes	characteristic
52	C₂×#11924036	C₂³	1	1	yes	characteristic
53	C₂×#11924036	C₂³	1	1	yes	characteristic
54	C₂²×#10596833	C₂×C₄	1	1	yes	characteristic
55	C₂²×#10596833	C₂³	1	1	yes	characteristic
56	#14556658	C₂×C₄	1	1	yes	characteristic
57	#14556658	C₂×C₄	1	1	yes	characteristic
58	#14556658	C₂×C₄	1	1	yes	characteristic
59	#14556658	C₂×C₄	1	1	yes	characteristic
60	C₄⋊#10596833	C₂×C₄	1	1	yes	characteristic
61	C₄⋊#10596833	C₂×C₄	1	1	yes	characteristic
62	#14556648	C₂×C₄	1	1	yes	characteristic
63	#14556648	C₂×C₄	1	1	yes	characteristic
64	#14556648	C₂×C₄	1	1	yes	characteristic
65	#14556648	C₂×C₄	1	1	yes	characteristic
66	C₂²⋊#10596833	C₂×C₄	1	1	yes	characteristic
67	C₂²⋊#10596833	C₂×C₄	1	1	yes	characteristic
68	C₄×#10596833	C₂×C₄	1	1	yes	characteristic
69	C₄×#10596833	C₂×C₄	1	1	yes	characteristic
70	C₄×#10596833	C₂×C₄	1	1	yes	characteristic
71	C₄×#10596833	C₂×C₄	1	1	yes	characteristic
72	C₄×#10596833	C₂×C₄	1	1	yes	characteristic
73	C₄×#10596833	C₂×C₄	1	1	yes	characteristic
74	C₄×#10596833	C₂³	1	1	yes	characteristic
75	C₄×#10596833	C₂³	1	1	yes	characteristic
76	C₄×#10596833	C₂³	1	1	yes	characteristic
77	C₄×#10596833	C₂³	1	1	yes	characteristic
78	C₂×#11924028	C₈	1	1	yes	characteristic
79	#14556556	C₈	1	1	yes	characteristic
80	#14556556	C₂×C₄	1	1	yes	characteristic
81	#14556553	C₈	1	1	yes	characteristic
82	#14556553	C₂×C₄	1	1	yes	characteristic
83	#14556551	C₈	1	1	yes	characteristic
84	#14556551	C₈	1	1	yes	characteristic
85	#14556551	C₂×C₄	1	1	yes	characteristic
86	#14556551	C₂×C₄	1	1	yes	characteristic
87	#14556548	C₈	1	1	yes	characteristic
88	#14556548	C₈	1	1	yes	characteristic
89	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
90	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
91	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
92	#117×C₇₃	C₈	1	1	yes	characteristic
93	#11924040	—	2	2	no	—
94	#11924040	—	2	2	no	—
95	#11924040	—	2	2	no	—
96	#11924040	—	2	2	no	—
97	#11924036	—	2	1	no	—
98	#11924036	—	2	1	no	—
99	#11924036	—	2	1	no	—
100	#11924036	—	2	1	no	—
101	#11924036	—	4	1	no	—
102	#11924036	—	4	1	no	—
103	C₂×#10596833	—	2	1	no	—
104	C₂×#10596833	—	2	1	no	—
105	C₂×#10596833	—	4	1	no	—
106	C₂×#10596833	C₂²×C₄	1	1	yes	characteristic
107	C₂×#10596833	C₂²×C₄	1	1	yes	characteristic
108	C₂×#10596833	C₂²×C₄	1	1	yes	characteristic
109	C₂×#10596833	C₂²×C₄	1	1	yes	characteristic
110	C₂×#10596833	C₂²×C₄	1	1	yes	characteristic
111	C₂×#10596833	C₂²×C₄	1	1	yes	characteristic
112	C₂×#10596833	C₂²×C₄	1	1	yes	characteristic
113	C₂×#10596833	C₂⁴	1	1	yes	characteristic
114	#11924028	—	2	4	no	—
115	C₂×Dic₁₄₆	C₂×C₈	1	1	yes	characteristic
116	C₂×D₂₉₂	C₂×C₈	1	1	yes	characteristic
117	C₂×C₂²⋊D₇₃	C₂×C₈	1	1	yes	characteristic
118	C₂×C₂²⋊D₇₃	C₂×C₈	1	1	yes	characteristic
119	C₂²×Dic₇₃	C₂×C₈	1	1	yes	characteristic
120	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
122	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
123	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
124	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
125	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
127	#11924007	C₂×C₈	1	1	yes	characteristic
128	#11924007	C₂×C₈	1	1	yes	characteristic
129	#11924007	C₂×C₈	1	1	yes	characteristic
130	#11924007	C₂×C₈	1	1	yes	characteristic
131	#11924005	C₂×C₈	1	1	yes	characteristic
132	#11924005	C₂×C₈	1	1	yes	characteristic
133	#11924005	C₂×C₈	1	1	yes	characteristic
134	#11924005	C₂×C₈	1	1	yes	characteristic
135	C₄×Dic₇₃	C₂×C₈	1	1	yes	characteristic
136	C₄×Dic₇₃	C₂×C₈	1	1	yes	characteristic
137	C₄×Dic₇₃	C₂×C₈	1	1	yes	characteristic
138	C₄×Dic₇₃	C₂×C₈	1	1	yes	characteristic
139	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
140	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
141	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
142	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
144	C₄⋊C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
145	C₄⋊C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
146	C₂²⋊C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
147	C₂²⋊C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
148	C₄²×C₇₃	C₂×C₈	1	1	yes	characteristic
149	C₄²×C₇₃	C₂×C₈	1	1	yes	characteristic
150	C₂³×C₇₃	C₂²×C₈	1	1	yes	characteristic
151	C₂²×D₇₃	C₂²×C₈	1	1	yes	characteristic
152	C₂²×D₇₃	C₂²×C₈	1	1	yes	characteristic
153	C₂×C₄×C₇₃	—	2	2	no	—
154	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
155	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
156	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
157	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
158	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
159	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
160	C₂²⋊D₇₃	—	2	2	no	—
161	C₂²⋊D₇₃	M₃₂	1	4	yes	complemented
162	C₂×Dic₇₃	—	2	1	no	—
163	C₂×Dic₇₃	—	2	1	no	—
164	C₂×Dic₇₃	—	2	2	no	—
165	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
166	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
167	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
168	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
169	C₂×Dic₇₃	C₂²×C₈	1	1	yes	characteristic
170	C₂×Dic₇₃	C₂³×C₄	1	1	yes	characteristic
171	D₂₉₂	—	2	2	no	—
172	C₄×D₇₃	—	2	2	no	—
173	C₄×D₇₃	—	2	1	no	—
174	C₄×D₇₃	—	2	1	no	—
175	C₄×D₇₃	—	2	1	no	—
176	C₄×D₇₃	—	2	1	no	—
177	C₄×D₇₃	—	2	2	no	—
178	C₄×D₇₃	—	2	2	no	—
179	C₄×D₇₃	—	2	2	no	—
180	Dic₁₄₆	—	2	2	no	—
181	#10596833	—	2	1	no	—
182	#10596833	—	2	1	no	—
183	#10596833	—	2	1	no	—
184	#10596833	—	2	1	no	—
185	#10596833	—	2	1	no	—
186	#10596833	—	2	1	no	—
187	#10596833	—	2	1	no	—
188	#10596833	H(5,𝔽₂)	1	1	yes	characteristic
189	#10596833	2₋¹⁺⁴	1	1	yes	characteristic
190	C₂²×C₇₃	—	2	1	no	—
191	C₂²×C₇₃	—	2	1	no	—
192	C₂²×C₇₃	C₂×M₃₂	1	2	yes	—
193	C₂²×C₇₃	C₂³×C₈	1	1	yes	characteristic
194	C₂×D₇₃	—	2	1	no	—
195	C₂×D₇₃	—	2	1	no	—
196	C₂×D₇₃	—	2	1	no	—
197	C₂×D₇₃	—	2	1	no	—
198	C₂×D₇₃	—	2	1	no	—
199	C₂×D₇₃	C₂×M₃₂	1	2	yes	—
200	C₄×C₇₃	—	2	1	no	—
201	C₄×C₇₃	—	2	1	no	—
202	C₄×C₇₃	—	2	1	no	—
203	C₄×C₇₃	—	2	1	no	—
204	C₄×C₇₃	—	2	1	no	—
205	C₄×C₇₃	—	2	1	no	—
206	Dic₇₃	—	2	1	no	—
207	Dic₇₃	—	2	1	no	—
208	Dic₇₃	—	2	1	no	—
209	Dic₇₃	C₂×M₃₂	1	2	yes	—
210	Dic₇₃	#504	1	2	yes	—
211	Dic₇₃	#520	1	1	yes	characteristic
212	Dic₇₃	#568	1	1	yes	characteristic
213	#33504	—	73	1	no	maximal, Sylow
214	C₂×C₇₃	—	2	2	no	—
215	C₂×C₇₃	#2988	1	1	yes	characteristic
216	C₂×C₇₃	C₂²×M₃₂	1	1	yes	characteristic
217	C₂×C₇₃	C₂×#504	1	1	yes	characteristic
218	D₇₃	—	2	2	no	—
219	D₇₃	—	4	1	no	—
220	C₈×#41	—	73	1	no	—
221	#2183	—	73	2	no	—
222	#2168	—	73	2	no	—
223	#2168	—	73	2	no	—
224	D₄×C₁₆	—	73	2	no	—
225	#2163	—	73	1	no	—
226	#2163	—	73	1	no	—
227	#2162	—	73	1	no	—
228	#2150	—	73	1	no	—
229	C₂×C₄⋊C₁₆	—	73	1	no	—
230	C₂×C₄⋊C₁₆	—	73	1	no	—
231	C₇₃	#33504	1	1	yes	characteristic, complemented, Sylow
232	C₄×#41	—	73	1	no	—
233	C₂×M₃₂	—	73	2	no	—
234	C₂²×C₁₆	—	73	2	no	—
235	C₂²×C₁₆	—	73	2	no	—
236	C₈×Q₈	—	73	1	no	—
237	C₈×Q₈	—	73	1	no	—
238	C₈×D₄	—	73	1	no	—
239	C₈×D₄	—	73	1	no	—
240	C₈×D₄	—	73	1	no	—
241	C₈×D₄	—	73	1	no	—
242	C₈×D₄	—	73	1	no	—
243	C₈×D₄	—	73	1	no	—
244	#431	—	73	1	no	—
245	#431	—	73	1	no	—
246	#431	—	73	1	no	—
247	C₂×C₄×C₈	—	73	1	no	—
248	C₂×C₄×C₈	—	73	1	no	—
249	C₂×C₄×C₈	—	73	1	no	—
250	C₄⋊C₁₆	—	73	2	no	—
251	C₄⋊C₁₆	—	73	1	no	—
252	C₄⋊C₁₆	—	73	1	no	—
253	C₄⋊C₁₆	—	73	1	no	—
254	C₄⋊C₁₆	—	73	2	no	—
255	C₄⋊C₁₆	—	73	2	no	—
256	C₄⋊C₁₆	—	73	1	no	—
257	C₂²⋊C₁₆	—	73	2	no	—
258	C₂²⋊C₁₆	—	73	2	no	—
259	C₂²⋊C₁₆	—	73	2	no	—
260	#346	—	73	2	no	—
261	#346	—	73	2	no	—
262	C₄×C₁₆	—	73	2	no	—
263	C₂×#41	—	73	1	no	—
264	C₂²×C₈	—	73	1	no	—
265	C₂²×C₈	—	73	1	no	—
266	C₂²×C₈	—	73	1	no	—
267	C₂²×C₈	—	73	1	no	—
268	C₂²×C₈	—	73	1	no	—
269	C₂²×C₈	—	73	1	no	—
270	C₄×Q₈	—	73	1	no	—
271	C₄×Q₈	—	73	1	no	—
272	C₄×D₄	—	73	1	no	—
273	C₄×D₄	—	73	1	no	—
274	C₄×D₄	—	73	1	no	—
275	C₄×D₄	—	73	1	no	—
276	C₄×D₄	—	73	1	no	—
277	C₄×D₄	—	73	1	no	—
278	#117	—	73	1	no	—
279	#117	—	73	1	no	—
280	#117	#10596842	1	1	yes	characteristic
281	C₂×C₄²	—	73	1	no	—
282	C₂×C₄²	—	73	1	no	—
283	C₂×C₄²	—	73	1	no	—
284	M₃₂	—	292	2	no	—
285	C₂×C₁₆	—	292	2	no	—
286	C₂×C₁₆	—	292	2	no	—
287	C₂×C₁₆	—	73	2	no	—
288	C₂×C₁₆	—	73	2	no	—
289	C₂×C₁₆	—	73	2	no	—
290	C₂×C₁₆	—	73	2	no	—
291	C₄⋊C₈	—	73	1	no	—
292	C₄⋊C₈	—	73	1	no	—
293	C₄⋊C₈	—	73	1	no	—
294	C₄⋊C₈	—	73	1	no	—
295	C₄⋊C₈	—	73	1	no	—
296	C₄⋊C₈	—	73	1	no	—
297	C₂²⋊C₈	—	73	1	no	—
298	C₂²⋊C₈	—	73	1	no	—
299	C₂²⋊C₈	—	73	1	no	—
300	C₂²⋊C₈	—	73	1	no	—
301	C₂²⋊C₈	—	73	1	no	—
302	C₂²⋊C₈	—	73	1	no	—
303	C₄×C₈	—	73	1	no	—
304	C₄×C₈	—	73	1	no	—
305	C₄×C₈	—	73	1	no	—
306	C₄×C₈	—	73	1	no	—
307	C₄×C₈	—	73	1	no	—
308	C₄×C₈	—	73	1	no	—
309	C₄×C₈	—	73	1	no	—
310	C₄×C₈	—	73	1	no	—
311	C₄×C₈	—	73	1	no	—
312	C₄×C₈	—	73	1	no	—
313	#41	—	146	4	no	—
314	C₂×Q₈	—	73	1	no	—
315	C₂×D₄	—	73	1	no	—
316	C₂×D₄	—	73	1	no	—
317	C₂×D₄	—	73	1	no	—
318	C₂²×C₄	—	73	1	no	—
319	C₂²×C₄	—	73	1	no	—
320	C₂²×C₄	—	73	1	no	—
321	C₂²×C₄	—	73	1	no	—
322	C₂²×C₄	—	73	1	no	—
323	C₂²×C₄	—	73	1	no	—
324	C₂²×C₄	—	73	1	no	—
325	C₂²×C₄	—	73	1	no	—
326	C₂²×C₄	C₂×#10596842	1	1	yes	characteristic
327	C₂×C₈	—	292	1	no	—
328	C₂×C₈	—	292	1	no	—
329	C₂×C₈	—	292	1	no	—
330	C₂×C₈	—	73	1	no	—
331	C₂×C₈	—	73	1	no	—
332	C₂×C₈	—	73	1	no	—
333	C₂×C₈	—	73	1	no	—
334	C₂×C₈	—	73	1	no	—
335	C₂×C₈	—	73	1	no	—
336	C₂×C₈	—	73	1	no	—
337	C₂×C₈	—	73	1	no	—
338	C₂×C₈	—	146	1	no	—
339	C₂×C₈	—	146	1	no	—
340	C₂×C₈	—	146	1	no	—
341	C₂×C₈	—	146	1	no	—
342	C₂×C₈	—	146	1	no	—
343	C₂×C₈	—	146	1	no	—
344	C₄⋊C₄	—	73	1	no	—
345	C₄⋊C₄	—	73	1	no	—
346	C₄⋊C₄	—	73	1	no	—
347	C₄⋊C₄	—	73	1	no	—
348	C₄⋊C₄	C₂×#10596842	1	1	yes	characteristic
349	C₄⋊C₄	C₂×#10596842	1	1	yes	characteristic
350	C₂²⋊C₄	—	73	1	no	—
351	C₂²⋊C₄	—	73	1	no	—
352	C₂²⋊C₄	—	73	1	no	—
353	C₂²⋊C₄	—	73	1	no	—
354	C₂²⋊C₄	C₂×#10596842	1	1	yes	characteristic
355	C₂²⋊C₄	C₂×#10596842	1	1	yes	characteristic
356	C₄²	—	73	1	no	—
357	C₄²	—	73	1	no	—
358	C₄²	—	73	1	no	—
359	C₄²	—	73	1	no	—
360	C₄²	—	73	1	no	—
361	C₄²	—	73	1	no	—
362	C₄²	—	73	1	no	—
363	C₄²	—	73	1	no	—
364	C₄²	C₂×#10596842	1	1	yes	characteristic
365	C₄²	C₂×#10596842	1	1	yes	characteristic
366	C₁₆	—	146	2	no	—
367	C₁₆	—	146	2	no	—
368	C₁₆	—	146	2	no	—
369	C₁₆	—	146	2	no	—
370	C₂³	—	73	1	no	—
371	C₂³	—	73	1	no	—
372	C₂³	C₂²×#10596842	1	1	yes	characteristic
373	Q₈	—	146	2	no	—
374	D₄	—	73	4	no	—
375	D₄	—	146	2	no	—
376	D₄	—	146	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	73	1	no	—
379	C₂×C₄	—	73	1	no	—
380	C₂×C₄	—	73	1	no	—
381	C₂×C₄	—	73	1	no	—
382	C₂×C₄	—	73	1	no	—
383	C₂×C₄	—	73	1	no	—
384	C₂×C₄	—	146	1	no	—
385	C₂×C₄	—	146	1	no	—
386	C₂×C₄	—	146	1	no	—
387	C₂×C₄	—	146	1	no	—
388	C₂×C₄	—	146	2	no	—
389	C₂×C₄	—	146	2	no	—
390	C₂×C₄	—	146	2	no	—
391	C₂×C₄	—	146	2	no	—
392	C₂×C₄	—	146	1	no	—
393	C₂×C₄	—	146	1	no	—
394	C₂×C₄	—	146	2	no	—
395	C₂×C₄	C₂²×#10596842	1	1	yes	characteristic
396	C₂×C₄	C₂²×#10596842	1	1	yes	characteristic
397	C₂×C₄	C₂²×#10596842	1	1	yes	characteristic
398	C₂×C₄	C₂²×#10596842	1	1	yes	characteristic
399	C₂×C₄	C₂²×#10596842	1	1	yes	characteristic
400	C₂×C₄	C₂²×#10596842	1	1	yes	characteristic
401	C₈	—	73	1	no	—
402	C₈	—	73	1	no	—
403	C₈	—	146	1	no	—
404	C₈	—	146	1	no	—
405	C₈	—	146	1	no	—
406	C₈	—	146	1	no	—
407	C₈	—	146	1	no	—
408	C₈	—	146	1	no	—
409	C₈	—	146	1	no	—
410	C₂²	—	2	1	no	—
411	C₂²	—	2	1	no	—
412	C₂²	—	73	2	no	—
413	C₂²	—	146	1	no	—
414	C₂²	—	146	1	no	—
415	C₂²	—	146	1	no	—
416	C₂²	—	146	1	no	—
417	C₂²	—	146	1	no	—
418	C₂²	#17989706	1	2	yes	—
419	C₂²	C₂³×#10596842	1	1	yes	characteristic
420	C₄	—	2	1	no	—
421	C₄	—	2	1	no	—
422	C₄	—	2	1	no	—
423	C₄	—	2	1	no	—
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	73	1	no	—
427	C₄	—	73	1	no	—
428	C₄	—	73	2	no	—
429	C₄	—	73	2	no	—
430	C₄	—	146	1	no	—
431	C₄	—	146	1	no	—
432	C₄	—	146	1	no	—
433	C₂	—	2	2	no	—
434	C₂	—	292	1	no	—
435	C₂	—	146	2	no	—
436	C₂	#22627175	1	1	yes	characteristic
437	C₂	C₂×#17989706	1	1	yes	characteristic
438	C₂	#22627182	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×#10596842
commutator, socle	C₂²×C₇₃	C₂³×C₈
Fitting	#117×C₇₃	C₈
prime radical	C₂×#11924028	C₈
cosocle	C₂×#10596833	C₂⁴
hypercenter	#117	#10596842
hypocenter	C₇₃	#33504
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ #117

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #22627158	C₂	semidirect
2. #22627142	C₂	semidirect
3. #22627141	C₂	semidirect
4. #22627139	C₂	semidirect
5. #22627135	C₂	semidirect
6. #22627132	C₂	semidirect
7. #22627130	C₂	semidirect
8. #22627121	C₂	semidirect
9. C₂×#17989690	C₂	semidirect
10. #22627117	C₂	semidirect
161. C₂²⋊D₇₃	M₃₂	semidirect
231. C₇₃	#33504	semidirect

Maximal subgroups

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

subgroup	index
#22627158	2
#22627142	2
#22627141	2
#22627139	2
#22627135	2
#22627132	2
#22627130	2
#22627121	2
C₂×#17989690	2
#22627117	2
#22626735	2
#33504	73