Subgroups — #34008801

Order 18688.

774 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14556659	C₂	1	1	yes	maximal, characteristic
2	C₂×#17989550	C₂	1	1	yes	maximal, characteristic
3	C₂×#17989466	C₂	1	2	yes	maximal
4	#22625619	C₂	1	2	yes	maximal
5	C₂×#108×D₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂×D₇₃⋊M₁₆	C₂²	1	1	yes	characteristic
7	C₂×#14556670	C₂²	1	1	yes	characteristic
8	C₂²×C₄⋊#64408	C₂²	1	2	yes	—
9	C₂×#14556659	—	2	2	no	—
10	C₂×#14556659	—	2	1	no	—
11	C₂×#14556659	—	2	1	no	—
12	C₂×#14556659	C₄	1	4	yes	complemented
13	#17989550	—	2	2	no	—
14	#17989550	C₄	1	4	yes	complemented
15	C₂×#14556645	—	2	1	no	—
16	C₂×C₈×#64408	—	2	1	no	—
17	#17989466	—	2	4	no	—
18	#17989461	—	2	4	no	—
19	C₂×M₁₆×D₇₃	C₂²	1	2	yes	—
20	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
21	C₂×#14556527	C₄	1	1	yes	characteristic, complemented
22	C₂×#14556526	C₄	1	2	yes	complemented
23	#108×D₇₃	—	2	2	no	—
24	#108×D₇₃	—	2	2	no	—
25	C₂×#108×C₇₃	C₄	1	1	yes	characteristic, complemented
26	C₂³×#64408	—	2	2	no	—
27	C₂×#11924038	—	2	1	no	—
28	D₇₃⋊M₁₆	—	2	1	no	—
29	D₇₃⋊M₁₆	—	2	1	no	—
30	D₇₃⋊M₁₆	C₂×C₄	1	2	yes	—
31	D₇₃⋊M₁₆	D₄	1	2	yes	—
32	C₂×#11924037	Q₈	1	2	yes	—
33	C₂×#11924036	—	2	1	no	—
34	#14556670	—	2	1	no	—
35	#14556670	—	2	1	no	—
36	#14556670	C₂×C₄	1	2	yes	—
37	#14556670	Q₈	1	2	yes	—
38	C₂×C₄⋊#64408	—	2	2	no	—
39	C₂×C₄⋊#64408	—	2	2	no	—
40	C₂×C₄⋊#64408	—	2	2	no	—
41	C₂×C₄⋊#64408	—	2	2	no	—
42	C₂×C₄⋊#64408	—	2	2	no	—
43	C₂×C₄⋊#64408	C₂×C₄	1	4	yes	—
44	C₂×C₄⋊#64408	D₄	1	2	yes	—
45	C₂×C₂²⋊#64408	—	2	1	no	—
46	C₂×C₄×#64408	—	2	1	no	—
47	#14556659	—	2	4	no	—
48	#14556659	—	2	4	no	—
49	#14556645	—	2	4	no	—
50	C₈×#64408	—	2	4	no	—
51	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
52	C₂×#11924012	C₂×C₄	1	2	yes	—
53	C₂×#11924011	—	2	2	no	—
54	M₁₆×D₇₃	—	2	2	no	—
55	M₁₆×D₇₃	—	2	2	no	—
56	M₁₆×D₇₃	—	2	2	no	—
57	M₁₆×D₇₃	—	2	2	no	—
58	C₂²×#10596831	C₂×C₄	1	1	yes	characteristic
59	C₂×C₈×D₇₃	—	2	2	no	—
60	C₂×C₈×D₇₃	C₂×C₄	1	2	yes	—
61	C₂×C₈×D₇₃	C₂×C₄	1	2	yes	—
62	C₂×C₈×D₇₃	D₄	1	2	yes	—
63	C₂×C₈×D₇₃	D₄	1	2	yes	—
64	C₂×C₈×D₇₃	D₄	1	1	yes	characteristic
65	C₂×C₈×D₇₃	D₄	1	1	yes	characteristic
66	C₂×C₈×D₇₃	Q₈	1	1	yes	characteristic
67	C₂×C₈×D₇₃	Q₈	1	1	yes	characteristic
68	#14556527	—	2	2	no	—
69	#14556526	—	2	4	no	—
70	C₂×M₁₆×C₇₃	C₂×C₄	1	2	yes	—
71	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
72	#108×C₇₃	—	2	2	no	—
73	C₂²×#64408	—	2	2	no	—
74	C₂²×#64408	—	2	4	no	—
75	C₂²×#64408	—	4	2	no	—
76	C₂²×#64408	—	4	2	no	—
77	C₂²×#64408	—	8	4	no	—
78	#11924038	—	2	2	no	—
79	#11924038	—	2	2	no	—
80	#11924037	—	2	2	no	—
81	#11924037	C₄⋊C₄	1	4	yes	—
82	#11924036	—	2	2	no	—
83	#11924036	—	2	2	no	—
84	C₂×#10596833	—	2	2	no	—
85	C₄⋊#64408	—	2	4	no	—
86	C₄⋊#64408	—	2	4	no	—
87	C₄⋊#64408	—	2	2	no	—
88	C₄⋊#64408	—	4	2	no	—
89	C₄⋊#64408	—	4	2	no	—
90	C₄⋊#64408	C₄⋊C₄	1	4	yes	—
91	C₂²⋊#64408	—	2	2	no	—
92	C₂²⋊#64408	—	2	2	no	—
93	C₄×#64408	—	2	2	no	—
94	C₄×#64408	—	2	2	no	—
95	C₂³×D₇₃	#41	1	1	yes	characteristic
96	C₂²×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
97	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
100	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
101	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
102	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
103	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
104	C₂×C₄×D₇₃	C₂×Q₈	1	1	yes	characteristic
105	C₂×C₄×D₇₃	C₂×Q₈	1	1	yes	characteristic
106	C₂×C₄×D₇₃	#41	1	1	yes	characteristic
107	C₂×C₄×D₇₃	#41	1	1	yes	characteristic
108	C₂×C₄×D₇₃	#41	1	1	yes	characteristic
109	#11924012	—	2	2	no	—
110	#11924012	—	2	2	no	—
111	#11924011	—	4	2	no	—
112	#11924011	—	4	2	no	—
113	C₂×#10596831	—	2	2	no	—
114	C₂×#10596831	C₄²	1	2	yes	—
115	C₂×#10596831	C₂²⋊C₄	1	2	yes	—
116	C₂×#10596831	C₄⋊C₄	1	1	yes	characteristic
117	C₂×#10596831	C₄⋊C₄	1	1	yes	characteristic
118	C₈×D₇₃	—	4	2	no	—
119	C₈×D₇₃	—	4	2	no	—
120	C₈×D₇₃	C₂²⋊C₄	1	2	yes	—
121	C₈×D₇₃	C₂²⋊C₄	1	2	yes	—
122	C₈×D₇₃	C₂²⋊C₄	1	2	yes	—
123	C₈×D₇₃	C₂²⋊C₄	1	2	yes	—
124	C₈×D₇₃	C₄⋊C₄	1	2	yes	—
125	C₈×D₇₃	C₄⋊C₄	1	2	yes	—
126	C₈×D₇₃	C₄⋊C₄	1	2	yes	—
127	C₈×D₇₃	C₄⋊C₄	1	2	yes	—
128	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
129	M₁₆×C₇₃	—	2	2	no	—
130	M₁₆×C₇₃	—	2	2	no	—
131	C₂×C₈×C₇₃	—	2	2	no	—
132	C₂×C₈×C₇₃	C₄²	1	2	yes	—
133	C₂×C₈×C₇₃	C₂²⋊C₄	1	2	yes	—
134	C₂×C₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
135	C₂×C₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
136	C₂³×C₇₃	C₄×Q₈	1	1	yes	characteristic
137	C₂²×D₇₃	—	2	4	no	—
138	C₂²×D₇₃	#117	1	1	yes	characteristic
139	C₂²×D₇₃	C₄×D₄	1	1	yes	characteristic
140	C₂²×D₇₃	#121	1	1	yes	characteristic
141	C₂²×D₇₃	C₂²⋊Q₈	1	1	yes	characteristic
142	C₂²×D₇₃	#124	1	1	yes	characteristic
143	C₂²×D₇₃	#125	1	1	yes	characteristic
144	C₂×#64408	—	2	4	no	—
145	C₂×#64408	—	4	4	no	—
146	C₂×#64408	—	4	4	no	—
147	C₂×#64408	—	8	4	no	—
148	C₂×#64408	—	8	4	no	—
149	C₂×#64408	—	8	4	no	—
150	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
151	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
154	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
155	C₂×C₄×C₇₃	C₄×Q₈	1	1	yes	characteristic
156	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
157	C₂×Dic₇₃	C₄×Q₈	1	1	yes	characteristic
158	C₂×Dic₇₃	C₂²⋊Q₈	1	1	yes	characteristic
159	C₂×Dic₇₃	C₂²⋊Q₈	1	1	yes	characteristic
160	C₂×Dic₇₃	C₄⋊Q₈	1	1	yes	characteristic
161	C₂×Dic₇₃	C₄⋊Q₈	1	1	yes	characteristic
162	C₄×D₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
163	C₄×D₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
164	C₄×D₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₄×D₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
166	C₄×D₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₄×D₇₃	#117	1	1	yes	characteristic
168	C₄×D₇₃	C₄×D₄	1	1	yes	characteristic
169	C₄×D₇₃	C₄×Q₈	1	1	yes	characteristic
170	C₄×D₇₃	#121	1	1	yes	characteristic
171	C₄×D₇₃	#121	1	1	yes	characteristic
172	C₄×D₇₃	#121	1	1	yes	characteristic
173	C₄×D₇₃	C₂²⋊Q₈	1	1	yes	characteristic
174	C₄×D₇₃	#124	1	1	yes	characteristic
175	C₄×D₇₃	#125	1	1	yes	characteristic
176	C₄×D₇₃	#127	1	1	yes	characteristic
177	C₄×D₇₃	C₄⋊Q₈	1	1	yes	characteristic
178	#10596833	—	2	4	no	—
179	C₈×C₇₃	—	4	2	no	—
180	C₈×C₇₃	#95	1	2	yes	—
181	C₈×C₇₃	#95	1	2	yes	—
182	#10596831	—	4	2	no	—
183	#10596831	#95	1	2	yes	—
184	#10596831	#95	1	2	yes	—
185	C₂²×C₇₃	—	2	2	no	—
186	C₂²×C₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
187	C₂²×C₇₃	#389	1	1	yes	characteristic
188	C₂²×C₇₃	#391	1	1	yes	characteristic
189	C₂×D₇₃	—	2	2	no	—
190	C₂×D₇₃	—	2	2	no	—
191	C₂×D₇₃	—	2	2	no	—
192	C₂×D₇₃	—	2	2	no	—
193	C₂×D₇₃	—	2	2	no	—
194	C₂×D₇₃	#380	1	1	yes	characteristic
195	C₂×D₇₃	#382	1	1	yes	characteristic
196	C₂×D₇₃	#389	1	1	yes	characteristic
197	C₂×D₇₃	#390	1	1	yes	characteristic
198	C₂×D₇₃	#471	1	4	yes	—
199	#64408	—	4	4	no	—
200	#64408	—	8	4	no	—
201	C₄×C₇₃	C₂×#95	1	1	yes	characteristic
202	C₄×C₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
203	C₄×C₇₃	#389	1	1	yes	characteristic
204	C₄×C₇₃	#390	1	1	yes	characteristic
205	Dic₇₃	#380	1	1	yes	characteristic
206	Dic₇₃	#384	1	1	yes	characteristic
207	Dic₇₃	#389	1	1	yes	characteristic
208	Dic₇₃	#391	1	1	yes	characteristic
209	#10869	—	73	1	no	maximal, Sylow
210	C₂×C₇₃	—	2	1	no	—
211	C₂×C₇₃	—	2	1	no	—
212	C₂×C₇₃	C₄⋊#95	1	1	yes	characteristic
213	C₂×C₇₃	#1951	1	2	yes	—
214	D₇₃	—	2	1	no	—
215	D₇₃	—	2	1	no	—
216	D₇₃	#1815	1	2	yes	—
217	D₇₃	#1977	1	2	yes	—
218	C₂²×#108	—	73	1	no	—
219	C₂²×#106	—	73	1	no	—
220	C₂×#405	—	73	1	no	—
221	C₂×#343	—	73	2	no	—
222	#1736	—	73	2	no	—
223	C₇₃	#10869	1	1	yes	characteristic, complemented, Sylow
224	C₂²×M₁₆	—	73	1	no	—
225	C₂²×M₁₆	—	73	2	no	—
226	C₂³×C₈	—	73	1	no	—
227	C₂×#117	—	73	1	no	—
228	C₂²×C₄⋊C₄	—	73	2	no	—
229	C₂×#108	—	73	2	no	—
230	C₂×#108	—	73	1	no	—
231	C₂×#108	—	146	2	no	—
232	C₂×#108	—	146	2	no	—
233	C₂×#108	#64408	1	1	yes	characteristic, complemented
234	C₂×#106	—	73	4	no	—
235	C₂×#106	—	146	2	no	—
236	C₂×#106	—	146	1	no	—
237	C₂×#106	—	146	1	no	—
238	#405	—	73	4	no	—
239	#405	—	146	2	no	—
240	C₂×#97	—	146	1	no	—
241	C₂×C₄×C₈	—	146	1	no	—
242	#343	—	146	4	no	—
243	#340	—	146	4	no	—
244	C₂³×C₄	—	73	1	no	—
245	C₂³×C₄	—	146	2	no	—
246	C₂×M₁₆	—	73	2	no	—
247	C₂×M₁₆	—	73	2	no	—
248	C₂×M₁₆	—	73	2	no	—
249	C₂×M₁₆	—	73	2	no	—
250	C₂×M₁₆	—	146	2	no	—
251	C₂×M₁₆	—	146	2	no	—
252	C₂×M₁₆	—	146	2	no	—
253	C₂×M₁₆	—	146	2	no	—
254	C₂×M₁₆	—	146	2	no	—
255	C₂×M₁₆	—	146	1	no	—
256	C₂×M₁₆	—	146	1	no	—
257	C₂×M₁₆	—	146	1	no	—
258	C₂×M₁₆	C₂×#64408	1	2	yes	—
259	C₂²×C₈	—	73	1	no	—
260	C₂²×C₈	—	73	2	no	—
261	C₂²×C₈	—	73	2	no	—
262	C₂²×C₈	—	73	2	no	—
263	C₂²×C₈	—	73	2	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	—	146	2	no	—
269	C₂²×C₈	—	146	1	no	—
270	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
271	#117	—	73	2	no	—
272	#117	—	73	2	no	—
273	#117	—	146	1	no	—
274	#117	—	146	1	no	—
275	C₂×C₄⋊C₄	—	73	2	no	—
276	C₂×C₄⋊C₄	—	73	4	no	—
277	C₂×C₄⋊C₄	—	146	2	no	—
278	C₂×C₄⋊C₄	—	146	2	no	—
279	C₂×C₄⋊C₄	—	146	2	no	—
280	C₂×C₄⋊C₄	—	146	2	no	—
281	C₂×C₄⋊C₄	—	146	2	no	—
282	C₂×C₂²⋊C₄	—	146	1	no	—
283	C₂×C₄²	—	146	1	no	—
284	#108	—	2	2	no	—
285	#108	—	146	4	no	—
286	#108	—	146	2	no	—
287	#106	—	146	4	no	—
288	#106	—	146	4	no	—
289	#97	—	146	4	no	—
290	C₄×C₈	—	146	4	no	—
291	C₂⁴	—	73	1	no	—
292	C₂²×C₄	—	292	2	no	—
293	C₂²×C₄	—	292	2	no	—
294	C₂²×C₄	—	584	4	no	—
295	C₂²×C₄	—	73	1	no	—
296	C₂²×C₄	—	73	1	no	—
297	C₂²×C₄	—	73	1	no	—
298	C₂²×C₄	—	73	1	no	—
299	C₂²×C₄	—	73	1	no	—
300	C₂²×C₄	—	73	1	no	—
301	C₂²×C₄	—	73	1	no	—
302	C₂²×C₄	—	73	1	no	—
303	C₂²×C₄	—	73	1	no	—
304	C₂²×C₄	—	73	1	no	—
305	C₂²×C₄	—	73	1	no	—
306	C₂²×C₄	—	73	1	no	—
307	C₂²×C₄	—	73	1	no	—
308	C₂²×C₄	—	146	2	no	—
309	C₂²×C₄	—	146	4	no	—
310	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
311	M₁₆	—	2	2	no	—
312	M₁₆	—	2	2	no	—
313	M₁₆	—	292	2	no	—
314	M₁₆	—	292	2	no	—
315	M₁₆	—	73	4	no	—
316	M₁₆	—	146	2	no	—
317	M₁₆	—	146	2	no	—
318	M₁₆	—	146	2	no	—
319	M₁₆	—	146	2	no	—
320	M₁₆	—	146	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	292	2	no	—
323	C₂×C₈	—	292	2	no	—
324	C₂×C₈	—	73	2	no	—
325	C₂×C₈	—	73	2	no	—
326	C₂×C₈	—	73	1	no	—
327	C₂×C₈	—	73	1	no	—
328	C₂×C₈	—	73	2	no	—
329	C₂×C₈	—	73	2	no	—
330	C₂×C₈	—	73	2	no	—
331	C₂×C₈	—	73	2	no	—
332	C₂×C₈	—	73	2	no	—
333	C₂×C₈	—	73	2	no	—
334	C₂×C₈	—	73	2	no	—
335	C₂×C₈	—	73	2	no	—
336	C₂×C₈	—	146	2	no	—
337	C₂×C₈	—	146	2	no	—
338	C₂×C₈	—	146	2	no	—
339	C₂×C₈	—	146	2	no	—
340	C₂×C₈	C₄×#64408	1	2	yes	—
341	C₂×C₈	C₂²⋊#64408	1	2	yes	—
342	C₂×C₈	C₄⋊#64408	1	1	yes	characteristic
343	C₂×C₈	C₄⋊#64408	1	1	yes	characteristic
344	C₄⋊C₄	—	292	2	no	—
345	C₄⋊C₄	—	292	2	no	—
346	C₄⋊C₄	—	73	4	no	—
347	C₄⋊C₄	—	146	4	no	—
348	C₄⋊C₄	—	146	4	no	—
349	C₄⋊C₄	—	146	2	no	—
350	C₂²⋊C₄	—	146	2	no	—
351	C₂²⋊C₄	—	146	2	no	—
352	C₄²	—	146	2	no	—
353	C₄²	—	146	2	no	—
354	C₂³	—	73	1	no	—
355	C₂³	—	73	1	no	—
356	C₂³	—	73	1	no	—
357	C₂³	—	73	1	no	—
358	C₂³	—	73	1	no	—
359	C₂³	—	73	1	no	—
360	C₂³	—	146	4	no	—
361	C₂³	Q₈×#64408	1	1	yes	characteristic
362	C₂×C₄	—	292	4	no	—
363	C₂×C₄	—	292	4	no	—
364	C₂×C₄	—	584	4	no	—
365	C₂×C₄	—	584	4	no	—
366	C₂×C₄	—	584	4	no	—
367	C₂×C₄	—	73	1	no	—
368	C₂×C₄	—	73	1	no	—
369	C₂×C₄	—	73	1	no	—
370	C₂×C₄	—	73	1	no	—
371	C₂×C₄	—	73	1	no	—
372	C₂×C₄	—	73	1	no	—
373	C₂×C₄	—	73	1	no	—
374	C₂×C₄	—	73	1	no	—
375	C₂×C₄	—	73	1	no	—
376	C₂×C₄	—	73	1	no	—
377	C₂×C₄	—	73	1	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	—	73	1	no	—
385	C₂×C₄	—	73	1	no	—
386	C₂×C₄	—	73	1	no	—
387	C₂×C₄	—	73	1	no	—
388	C₂×C₄	—	73	1	no	—
389	C₂×C₄	—	146	4	no	—
390	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
391	C₂×C₄	C₂×C₂²⋊#64408	1	1	yes	characteristic
392	C₂×C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
393	C₂×C₄	D₄×#64408	1	1	yes	characteristic
394	C₂×C₄	D₄×#64408	1	1	yes	characteristic
395	C₂×C₄	Q₈×#64408	1	1	yes	characteristic
396	C₈	—	4	2	no	—
397	C₈	—	292	2	no	—
398	C₈	—	73	2	no	—
399	C₈	—	73	2	no	—
400	C₈	—	146	4	no	—
401	C₈	(C₂×#64408)⋊C₄	1	2	yes	—
402	C₈	(C₂×#64408)⋊C₄	1	2	yes	—
403	C₂²	—	2	2	no	—
404	C₂²	—	73	4	no	—
405	C₂²	—	73	1	no	—
406	C₂²	—	73	1	no	—
407	C₂²	—	73	1	no	—
408	C₂²	—	73	1	no	—
409	C₂²	—	146	2	no	—
410	C₂²	—	146	2	no	—
411	C₂²	—	146	2	no	—
412	C₂²	—	146	2	no	—
413	C₂²	—	146	2	no	—
414	C₂²	C₄⋊C₄×#64408	1	1	yes	characteristic
415	C₂²	#17989538	1	1	yes	characteristic
416	C₂²	(C₂×#64408)⋊Q₈	1	1	yes	characteristic
417	C₄	—	292	4	no	—
418	C₄	—	584	4	no	—
419	C₄	—	73	1	no	—
420	C₄	—	73	1	no	—
421	C₄	—	73	1	no	—
422	C₄	—	73	1	no	—
423	C₄	C₂×(C₂×#64408)⋊C₄	1	1	yes	characteristic
424	C₄	C₄⋊C₄×#64408	1	1	yes	characteristic
425	C₄	#17989538	1	1	yes	characteristic
426	C₄	#17989539	1	1	yes	characteristic
427	C₂	—	2	1	no	—
428	C₂	—	2	1	no	—
429	C₂	—	73	2	no	—
430	C₂	—	73	2	no	—
431	C₂	—	146	1	no	—
432	C₂	—	146	1	no	—
433	C₂	#22625108	1	1	yes	characteristic
434	C₂	#22626048	1	2	yes	—

	subgroup	G/H
center	C₂²	#17989538
commutator	C₂×C₄×C₇₃	C₂×C₄²
Frattini	C₂²×C₄	C₂²×#64408
Fitting	C₂×#108×C₇₃	C₄
socle	C₂²×C₇₃	#389
prime radical	C₂³×D₇₃	#41
cosocle	C₂²×C₄×D₇₃	C₂³
hypercenter	C₂×#108	#64408
hypocenter	C₇₃	#10869
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#108

Complements

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

N	H ≅ G/N	type
12. C₂×#14556659	C₄	semidirect
14. #17989550	C₄	semidirect
21. C₂×#14556527	C₄	semidirect
22. C₂×#14556526	C₄	semidirect
25. C₂×#108×C₇₃	C₄	semidirect
223. C₇₃	#10869	semidirect
233. C₂×#108	#64408	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#14556659	2
C₂×#17989550	2
C₂×#17989466	2
#22625619	2
C₂×#108×D₇₃	2
#10869	73