Subgroups — #33056903

Order 18688.

670 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22619962	C₂	1	1	yes	maximal, characteristic
2	Q₈×#11924012	C₂	1	1	yes	maximal, characteristic, complemented
3	#22618674	C₂	1	1	yes	maximal, characteristic
4	#22608818	C₂	1	2	yes	maximal, complemented
5	#22608771	C₂	1	2	yes	maximal, complemented
6	#22608770	C₂	1	2	yes	maximal, complemented
7	#22608728	C₂	1	2	yes	maximal, complemented
8	#22608701	C₂	1	1	yes	maximal, characteristic, complemented
9	#22608383	C₂	1	1	yes	maximal, characteristic
10	C₈×#11924012	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×Q₈⋊C₈×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14556597	—	2	1	no	—
13	#17989137	C₂²	1	1	yes	characteristic
14	#17988905	C₄	1	2	yes	—
15	#17988872	C₄	1	1	yes	characteristic
16	#17988872	C₄	1	1	yes	characteristic
17	#17988787	C₄	1	1	yes	characteristic
18	#17988787	C₄	1	1	yes	characteristic
19	#17988726	C₄	1	2	yes	—
20	#17988718	—	2	2	no	—
21	#17988718	C₂²	1	2	yes	—
22	Q₈×#10596831	C₂²	1	2	yes	—
23	C₄×#11924015	C₂²	1	2	yes	—
24	C₄×#11924015	C₂²	1	2	yes	—
25	#17988664	C₂²	1	2	yes	—
26	#17988657	—	2	2	no	—
27	#17988652	C₂²	1	2	yes	—
28	#17988640	C₂²	1	1	yes	characteristic
29	#17988611	—	2	1	no	—
30	#17988611	C₂²	1	1	yes	characteristic
31	#17988553	—	2	1	no	—
32	C₄×#11924012	—	2	1	no	—
33	C₄×#11924012	C₂²	1	1	yes	characteristic
34	#17988337	C₂²	1	2	yes	—
35	#17988337	C₂²	1	2	yes	—
36	#17988316	C₂²	1	2	yes	—
37	#17988316	C₂²	1	2	yes	—
38	#17988309	C₂²	1	2	yes	—
39	C₈×#10596831	C₂²	1	2	yes	—
40	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
43	Q₈⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
44	Q₈⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
45	Q₈⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
46	Q₈⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
47	C₂×#11924028	—	2	1	no	—
48	C₂×#11924015	C₂×C₄	1	2	yes	—
49	C₂×#11924015	C₂×C₄	1	2	yes	—
50	#14556597	—	4	4	no	—
51	C₂×#11924012	—	2	1	no	—
52	C₂×#11924012	D₄	1	1	yes	characteristic
53	C₂×#11924012	D₄	1	1	yes	characteristic
54	C₂×#11924011	—	2	2	no	—
55	C₂×C₈×D₇₃	—	2	2	no	—
56	#14556591	C₂×C₄	1	1	yes	characteristic
57	#14556588	C₂×C₄	1	1	yes	characteristic
58	#14556579	—	2	1	no	—
59	#14556565	—	2	1	no	—
60	#14556565	C₂×C₄	1	2	yes	—
61	C₄×D₂₉₂	—	2	1	no	—
62	C₄×D₂₉₂	C₂³	1	2	yes	—
63	#14556522	C₂×C₄	1	2	yes	—
64	#14556522	C₂×C₄	1	2	yes	—
65	C₄⋊#10596831	—	2	2	no	—
66	C₄⋊#10596831	—	2	2	no	—
67	C₄⋊#10596831	—	2	1	no	—
68	C₄⋊#10596831	C₂×C₄	1	1	yes	characteristic
69	C₄⋊#10596831	C₂×C₄	1	1	yes	characteristic
70	C₄⋊#10596831	C₂³	1	2	yes	—
71	#14556515	C₂×C₄	1	2	yes	—
72	#14556515	C₂×C₄	1	2	yes	—
73	#14556511	C₂×C₄	1	2	yes	—
74	#14556511	C₂×C₄	1	2	yes	—
75	C₂²⋊#10596831	C₂×C₄	1	2	yes	—
76	#14556503	—	2	2	no	—
77	#14556503	—	2	2	no	—
78	#14556502	—	2	2	no	—
79	#14556502	D₄	1	2	yes	—
80	C₄×#10596831	—	2	2	no	—
81	C₄×#10596831	C₂³	1	2	yes	—
82	C₄×#10596831	C₂³	1	2	yes	—
83	C₂²×Q₈×C₇₃	C₂×C₄	1	1	yes	characteristic
84	C₂²×C₈×C₇₃	—	2	1	no	—
85	C₂²×C₈×C₇₃	—	2	1	no	—
86	C₄×Q₈×C₇₃	—	2	1	no	—
87	C₄×Q₈×C₇₃	—	2	1	no	—
88	C₄×Q₈×C₇₃	C₂×C₄	1	1	yes	characteristic
89	C₄×Q₈×C₇₃	C₂×C₄	1	1	yes	characteristic
90	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
91	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
93	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄²×C₇₃	—	2	1	no	—
95	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
96	C₄⋊C₈×C₇₃	—	2	1	no	—
97	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
99	C₄×C₈×C₇₃	—	2	1	no	—
100	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
102	#11924028	—	4	2	no	—
103	#11924028	—	4	2	no	—
104	C₂×Dic₁₄₆	—	2	1	no	—
105	C₂×D₂₉₂	—	2	1	no	—
106	C₂×D₂₉₂	—	2	1	no	—
107	C₂×D₂₉₂	C₂²×C₄	1	2	yes	—
108	C₂×C₂²⋊D₇₃	—	2	2	no	—
109	C₂×C₄×D₇₃	—	2	2	no	—
110	#11924015	—	2	4	no	—
111	#11924015	—	4	2	no	—
112	#11924012	—	2	2	no	—
113	#11924012	—	4	2	no	—
114	#11924012	SD₁₆	1	4	yes	complemented
115	#11924011	—	4	4	no	—
116	C₂×#10596831	—	2	2	no	—
117	C₂×#10596831	C₂²×C₄	1	2	yes	—
118	C₂×#10596831	C₂²×C₄	1	2	yes	—
119	C₂×#10596831	C₂×D₄	1	2	yes	—
120	C₂×#10596831	C₂×D₄	1	2	yes	—
121	C₈×D₇₃	—	4	4	no	—
122	C₄⋊Dic₇₃	—	2	1	no	—
123	C₄⋊Dic₇₃	C₂²×C₄	1	2	yes	—
124	#11924005	—	2	2	no	—
125	#11924005	—	2	2	no	—
126	C₂×Q₈×C₇₃	—	2	1	no	—
127	C₂×Q₈×C₇₃	—	2	2	no	—
128	C₂×Q₈×C₇₃	—	4	1	no	—
129	C₂×Q₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
130	C₂×Q₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₇₃	—	2	1	no	—
132	C₂²×C₄×C₇₃	—	2	1	no	—
133	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
136	C₂×C₈×C₇₃	—	2	1	no	—
137	C₂×C₈×C₇₃	—	2	1	no	—
138	C₂×C₈×C₇₃	—	2	1	no	—
139	C₂×C₈×C₇₃	—	2	1	no	—
140	C₂×C₈×C₇₃	—	4	2	no	—
141	C₂×C₈×C₇₃	—	4	2	no	—
142	C₄⋊C₄×C₇₃	—	2	1	no	—
143	C₄⋊C₄×C₇₃	—	2	1	no	—
144	C₄⋊C₄×C₇₃	—	2	1	no	—
145	C₄⋊C₄×C₇₃	—	2	1	no	—
146	C₄⋊C₄×C₇₃	—	2	1	no	—
147	C₄⋊C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
148	C₄⋊C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
149	C₄²×C₇₃	—	2	1	no	—
150	C₄²×C₇₃	—	2	1	no	—
151	C₄²×C₇₃	—	2	1	no	—
152	C₄²×C₇₃	—	2	1	no	—
153	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
154	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₇₃	#41	1	1	yes	characteristic
156	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
157	C₂³×C₇₃	C₄×D₄	1	1	yes	characteristic
158	C₂²×D₇₃	—	2	2	no	—
159	Q₈×C₇₃	—	2	1	no	—
160	Q₈×C₇₃	—	2	1	no	—
161	Q₈×C₇₃	—	2	1	no	—
162	Q₈×C₇₃	—	4	2	no	—
163	Q₈×C₇₃	#131	1	2	yes	complemented
164	C₂×C₄×C₇₃	—	2	1	no	—
165	C₂×C₄×C₇₃	—	2	1	no	—
166	C₂×C₄×C₇₃	—	2	1	no	—
167	C₂×C₄×C₇₃	—	2	1	no	—
168	C₂×C₄×C₇₃	—	2	1	no	—
169	C₂×C₄×C₇₃	—	2	1	no	—
170	C₂×C₄×C₇₃	—	4	1	no	—
171	C₂×C₄×C₇₃	—	4	2	no	—
172	C₂×C₄×C₇₃	—	8	1	no	—
173	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
174	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
175	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
176	C₂×C₄×C₇₃	C₂×SD₁₆	1	2	yes	—
177	C₂×C₄×C₇₃	#135	1	2	yes	—
178	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
179	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
181	C₂²⋊D₇₃	—	4	4	no	—
182	C₂×Dic₇₃	—	2	2	no	—
183	D₂₉₂	—	2	2	no	—
184	D₂₉₂	—	2	2	no	—
185	D₂₉₂	—	4	2	no	—
186	D₂₉₂	—	8	1	no	—
187	C₄×D₇₃	—	4	2	no	—
188	C₄×D₇₃	—	4	2	no	—
189	Dic₁₄₆	—	4	2	no	—
190	C₈×C₇₃	—	2	2	no	—
191	C₈×C₇₃	—	4	1	no	—
192	C₈×C₇₃	—	4	1	no	—
193	C₈×C₇₃	—	4	1	no	—
194	#10596831	—	2	2	no	—
195	#10596831	—	2	2	no	—
196	#10596831	—	2	2	no	—
197	#10596831	—	4	2	no	—
198	#10596831	C₂×SD₁₆	1	4	yes	—
199	C₂²×C₇₃	—	2	1	no	—
200	C₂²×C₇₃	—	2	1	no	—
201	C₂²×C₇₃	C₄×SD₁₆	1	2	yes	—
202	C₂²×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
203	C₂×D₇₃	—	4	2	no	—
204	C₂×D₇₃	—	4	2	no	—
205	C₂×D₇₃	—	4	2	no	—
206	C₄×C₇₃	—	2	1	no	—
207	C₄×C₇₃	—	2	2	no	—
208	C₄×C₇₃	—	2	1	no	—
209	C₄×C₇₃	—	2	1	no	—
210	C₄×C₇₃	—	4	1	no	—
211	C₄×C₇₃	—	4	1	no	—
212	C₄×C₇₃	—	4	1	no	—
213	C₄×C₇₃	C₄×SD₁₆	1	2	yes	—
214	C₄×C₇₃	C₂×#131	1	1	yes	characteristic
215	C₄×C₇₃	#568	1	1	yes	characteristic
216	C₄×C₇₃	C₂²×SD₁₆	1	1	yes	characteristic
217	C₄×C₇₃	C₂×#135	1	1	yes	characteristic
218	Dic₇₃	—	4	2	no	—
219	#17997	—	73	1	no	maximal, Sylow
220	C₂×C₇₃	—	2	2	no	—
221	C₂×C₇₃	#2933	1	1	yes	characteristic
222	C₂×C₇₃	C₂×C₄×SD₁₆	1	1	yes	characteristic
223	C₂×C₇₃	#2956	1	1	yes	characteristic
224	D₇₃	—	8	2	no	—
225	#3103	—	73	1	no	—
226	Q₈×M₁₆	—	73	1	no	—
227	#2935	—	73	1	no	—
228	#1590	—	73	2	no	—
229	#1583	—	73	2	no	—
230	#1582	—	73	2	no	—
231	C₈×SD₁₆	—	73	2	no	—
232	#1570	—	73	1	no	—
233	#1492	—	73	1	no	—
234	C₂×Q₈⋊C₈	D₇₃	1	1	yes	characteristic, complemented
235	C₈×M₁₆	—	73	1	no	—
236	C₇₃	#17997	1	1	yes	characteristic, complemented, Sylow
237	C₂×#131	—	146	1	no	—
238	#532	—	73	1	no	—
239	C₂×C₄×Q₈	C₂×D₇₃	1	1	yes	characteristic
240	#481	—	73	2	no	—
241	#475	—	73	1	no	—
242	#475	—	73	1	no	—
243	#460	—	73	1	no	—
244	#460	—	73	1	no	—
245	#448	—	73	2	no	—
246	#446	—	73	2	no	—
247	#446	—	146	2	no	—
248	C₈×Q₈	—	73	2	no	—
249	C₄×SD₁₆	—	73	2	no	—
250	C₄×SD₁₆	—	73	2	no	—
251	#436	—	73	2	no	—
252	#435	—	146	2	no	—
253	C₈×D₄	—	73	2	no	—
254	#431	—	73	1	no	—
255	#423	—	73	1	no	—
256	#423	—	146	1	no	—
257	C₂×C₄⋊C₈	C₂×D₇₃	1	1	yes	characteristic
258	#408	—	146	1	no	—
259	C₄×M₁₆	—	73	1	no	—
260	C₄×M₁₆	—	146	1	no	—
261	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
262	#334	—	73	2	no	—
263	#334	—	73	2	no	—
264	Q₈⋊C₈	C₂×D₇₃	1	1	yes	characteristic
265	Q₈⋊C₈	C₂×D₇₃	1	1	yes	characteristic
266	Q₈⋊C₈	C₂×D₇₃	1	1	yes	characteristic
267	Q₈⋊C₈	C₂×D₇₃	1	1	yes	characteristic
268	D₄⋊C₈	—	73	2	no	—
269	D₄⋊C₈	—	73	2	no	—
270	#322	—	73	2	no	—
271	C₈²	—	73	2	no	—
272	C₂×#41	—	146	1	no	—
273	C₂²×Q₈	C₄×D₇₃	1	1	yes	characteristic
274	C₂×SD₁₆	—	73	2	no	—
275	C₂×SD₁₆	—	73	2	no	—
276	#131	—	292	4	no	—
277	C₂×M₁₆	—	73	1	no	—
278	C₂×M₁₆	—	73	1	no	—
279	C₂×M₁₆	—	146	2	no	—
280	C₂×M₁₆	—	146	1	no	—
281	C₂²×C₈	—	2	1	no	—
282	C₂²×C₈	—	2	1	no	—
283	C₂²×C₈	—	146	2	no	—
284	C₄⋊Q₈	—	73	1	no	—
285	#127	—	73	1	no	—
286	#124	—	146	1	no	—
287	#121	—	73	2	no	—
288	#121	—	146	1	no	—
289	C₄×Q₈	—	2	1	no	—
290	C₄×Q₈	—	2	1	no	—
291	C₄×Q₈	C₄×D₇₃	1	1	yes	characteristic
292	C₄×Q₈	C₄×D₇₃	1	1	yes	characteristic
293	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
294	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
295	C₄×D₄	—	73	2	no	—
296	C₄×D₄	—	146	1	no	—
297	C₂×C₄⋊C₄	—	2	1	no	—
298	C₂×C₄⋊C₄	C₄×D₇₃	1	1	yes	characteristic
299	C₂×C₄²	—	2	1	no	—
300	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
301	#106	—	73	2	no	—
302	#106	—	73	2	no	—
303	C₄⋊C₈	—	2	1	no	—
304	C₄⋊C₈	—	73	1	no	—
305	C₄⋊C₈	—	73	1	no	—
306	C₄⋊C₈	—	73	2	no	—
307	C₄⋊C₈	—	146	2	no	—
308	C₄⋊C₈	—	146	2	no	—
309	C₄⋊C₈	—	146	1	no	—
310	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
311	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
312	#103	—	73	2	no	—
313	#103	—	73	2	no	—
314	#102	—	73	2	no	—
315	#102	—	73	2	no	—
316	C₂²⋊C₈	—	73	2	no	—
317	C₂²⋊C₈	—	146	2	no	—
318	C₂²⋊C₈	—	146	2	no	—
319	#97	—	73	2	no	—
320	#97	—	146	2	no	—
321	C₄×C₈	—	2	1	no	—
322	C₄×C₈	—	73	2	no	—
323	C₄×C₈	—	73	2	no	—
324	C₄×C₈	—	146	2	no	—
325	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
326	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
327	#41	—	292	2	no	—
328	#41	—	292	2	no	—
329	C₂×Q₈	—	2	1	no	—
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	—	4	1	no	—
332	C₂×Q₈	—	146	1	no	—
333	C₂×Q₈	C₂×C₄×D₇₃	1	1	yes	characteristic
334	C₂×Q₈	C₂×C₄×D₇₃	1	1	yes	characteristic
335	C₂×D₄	—	73	2	no	—
336	C₂×D₄	—	146	2	no	—
337	C₂×D₄	—	146	1	no	—
338	C₂×D₄	—	146	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	146	2	no	—
342	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
343	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
344	C₂²×C₄	#11924027	1	1	yes	characteristic
345	SD₁₆	—	292	2	no	—
346	SD₁₆	—	146	4	no	—
347	M₁₆	—	292	4	no	—
348	M₁₆	—	292	2	no	—
349	M₁₆	—	73	4	no	—
350	M₁₆	—	146	2	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	4	2	no	—
356	C₂×C₈	—	4	2	no	—
357	C₂×C₈	—	292	4	no	—
358	C₂×C₈	—	73	2	no	—
359	C₂×C₈	—	73	2	no	—
360	C₂×C₈	—	73	2	no	—
361	C₂×C₈	—	73	2	no	—
362	C₂×C₈	—	146	2	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	73	2	no	—
369	C₄⋊C₄	—	146	1	no	—
370	C₄⋊C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
371	C₄⋊C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
372	C₂²⋊C₄	—	146	2	no	—
373	C₂²⋊C₄	—	146	2	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	2	1	no	—
376	C₄²	—	2	1	no	—
377	C₄²	—	2	1	no	—
378	C₄²	C₂×C₄×D₇₃	1	1	yes	characteristic
379	C₄²	D₄×D₇₃	1	1	yes	characteristic
380	C₄²	#11924027	1	1	yes	characteristic
381	C₄²	C₂³×D₇₃	1	1	yes	characteristic
382	C₂³	—	146	2	no	—
383	C₂³	#14556551	1	1	yes	characteristic
384	Q₈	—	2	1	no	—
385	Q₈	—	2	1	no	—
386	Q₈	—	2	1	no	—
387	Q₈	—	4	2	no	—
388	Q₈	—	292	2	no	—
389	Q₈	#14556597	1	2	yes	complemented
390	D₄	—	292	4	no	—
391	D₄	—	292	2	no	—
392	D₄	—	584	1	no	—
393	D₄	—	146	2	no	—
394	D₄	—	146	2	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	8	1	no	—
404	C₂×C₄	—	292	2	no	—
405	C₂×C₄	—	292	2	no	—
406	C₂×C₄	—	146	2	no	—
407	C₂×C₄	#14556551	1	1	yes	characteristic
408	C₂×C₄	#14556551	1	1	yes	characteristic
409	C₂×C₄	#14556551	1	1	yes	characteristic
410	C₂×C₄	SD₁₆×D₇₃	1	2	yes	—
411	C₂×C₄	#14556614	1	2	yes	—
412	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
413	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
414	C₂×C₄	C₂×#11924027	1	1	yes	characteristic
415	C₈	—	2	2	no	—
416	C₈	—	4	1	no	—
417	C₈	—	4	1	no	—
418	C₈	—	4	1	no	—
419	C₈	—	292	2	no	—
420	C₈	—	73	4	no	—
421	C₈	—	146	2	no	—
422	C₈	—	146	2	no	—
423	C₈	—	146	2	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	292	2	no	—
427	C₂²	—	292	2	no	—
428	C₂²	—	292	2	no	—
429	C₂²	#17988672	1	2	yes	—
430	C₂²	C₂×#14556551	1	1	yes	characteristic
431	C₄	—	2	1	no	—
432	C₄	—	2	2	no	—
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	4	1	no	—
436	C₄	—	4	1	no	—
437	C₄	—	4	1	no	—
438	C₄	—	292	2	no	—
439	C₄	#17988672	1	2	yes	—
440	C₄	C₂×#14556597	1	1	yes	characteristic
441	C₄	#17989353	1	1	yes	characteristic
442	C₄	C₂×SD₁₆×D₇₃	1	1	yes	characteristic
443	C₄	C₂×#14556614	1	1	yes	characteristic
444	C₂	—	2	2	no	—
445	C₂	—	584	2	no	—
446	C₂	#22618652	1	1	yes	characteristic
447	C₂	C₂×#17988672	1	1	yes	characteristic
448	C₂	#22618837	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇₃
commutator	C₂×C₄×C₇₃	C₂³×C₄
Frattini	C₄²	C₂³×D₇₃
Fitting	C₂×Q₈⋊C₈×C₇₃	C₂
socle	C₂²×C₇₃	C₂×C₄×D₄
prime radical	#17989137	C₂²
cosocle	C₄²×C₇₃	C₂⁴
hypercenter	C₂×Q₈⋊C₈	D₇₃
hypocenter	C₇₃	#17997
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×Q₈⋊C₈

Complements

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

N	H ≅ G/N	type
2. Q₈×#11924012	C₂	semidirect
4. #22608818	C₂	semidirect
5. #22608771	C₂	semidirect
6. #22608770	C₂	semidirect
7. #22608728	C₂	semidirect
8. #22608701	C₂	semidirect
10. C₈×#11924012	C₂	semidirect
11. C₂×Q₈⋊C₈×C₇₃	C₂	semidirect
114. #11924012	SD₁₆	semidirect
163. Q₈×C₇₃	#131	semidirect
234. C₂×Q₈⋊C₈	D₇₃	semidirect
236. C₇₃	#17997	semidirect
389. Q₈	#14556597	semidirect

Maximal subgroups

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

subgroup	index
#22619962	2
Q₈×#11924012	2
#22618674	2
#22608818	2
#22608771	2
#22608770	2
#22608728	2
#22608701	2
#22608383	2
C₈×#11924012	2
C₂×Q₈⋊C₈×C₇₃	2
#17997	73