Subgroups — #34021340

Order 18688.

1070 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17989598	C₂	1	2	yes	maximal
2	C₂×#17989597	C₂	1	1	yes	maximal, characteristic
3	C₂²×#14556659	C₂	1	1	yes	maximal, characteristic
4	#22626412	C₂	1	2	yes	maximal
5	#22625869	C₂	1	4	yes	maximal, complemented
6	#22625868	C₂	1	2	yes	maximal, complemented
7	#22625866	C₂	1	2	yes	maximal, complemented
8	#405×D₇₃	C₂	1	1	yes	maximal, characteristic
9	C₂×#14556670	C₂²	1	2	yes	—
10	C₂²×C₄⋊#64408	C₂²	1	2	yes	—
11	#17989598	—	2	8	no	—
12	#17989597	—	2	4	no	—
13	C₂×#14556660	C₂²	1	2	yes	—
14	C₂×#14556660	C₂²	1	4	yes	—
15	C₂×#14556659	—	2	4	no	—
16	C₂×#14556659	C₂²	1	2	yes	—
17	C₂×#14556659	C₂²	1	2	yes	—
18	C₂×#14556659	C₂²	1	1	yes	characteristic
19	C₂×#14556659	C₂²	1	1	yes	characteristic
20	C₂×#14556659	C₂²	1	4	yes	—
21	#17989538	—	2	4	no	—
22	#17989534	—	2	4	no	—
23	#17989533	C₂²	1	4	yes	—
24	#17989531	C₂²	1	4	yes	—
25	C₂×M₁₆×D₇₃	C₂²	1	1	yes	characteristic
26	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
27	#117×D₇₃	C₂²	1	1	yes	characteristic
28	#17988545	C₄	1	1	yes	characteristic, complemented
29	#17988544	C₄	1	2	yes	complemented
30	#17988543	C₄	1	1	yes	characteristic, complemented
31	#17988542	C₄	1	1	yes	characteristic, complemented
32	#17988541	C₄	1	2	yes	complemented
33	#97×D₇₃	C₂²	1	2	yes	—
34	C₄×C₈×D₇₃	C₂²	1	2	yes	—
35	#405×C₇₃	C₄	1	1	yes	characteristic, complemented
36	C₂³×#64408	—	2	2	no	—
37	#14556670	—	2	4	no	—
38	#14556670	—	2	4	no	—
39	C₂×C₄⋊#64408	—	2	4	no	—
40	C₂×C₄⋊#64408	—	2	4	no	—
41	C₂×C₄⋊#64408	—	2	2	no	—
42	C₂×C₄⋊#64408	—	2	8	no	—
43	C₂×C₄⋊#64408	C₂³	1	4	yes	—
44	C₂×C₄⋊#64408	C₂³	1	2	yes	—
45	C₂×C₄⋊#64408	C₂³	1	2	yes	—
46	C₂×C₂²⋊#64408	—	2	2	no	—
47	C₂×C₄×#64408	—	2	2	no	—
48	#14556660	—	2	4	no	—
49	#14556660	—	2	8	no	—
50	#14556659	—	2	4	no	—
51	#14556659	—	2	4	no	—
52	#14556659	—	2	2	no	—
53	#14556659	—	2	2	no	—
54	#14556659	—	2	8	no	—
55	(C₂×#64408)⋊C₄	—	2	8	no	—
56	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
57	C₂×#11924012	C₂×C₄	1	1	yes	characteristic
58	C₂×#11924011	C₂×C₄	1	2	yes	—
59	M₁₆×D₇₃	D₄	1	4	yes	—
60	M₁₆×D₇₃	Q₈	1	4	yes	—
61	C₂²×#10596831	C₂×C₄	1	1	yes	characteristic
62	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
63	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
64	C₂×C₈×D₇₃	D₄	1	4	yes	—
65	C₂×C₈×D₇₃	Q₈	1	4	yes	—
66	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
67	C₂×C₈×D₇₃	C₂³	1	2	yes	—
68	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
69	#14556550	C₂×C₄	1	1	yes	characteristic
70	#14556549	Q₈	1	2	yes	—
71	#14556548	C₂×C₄	1	2	yes	—
72	#14556547	Q₈	1	2	yes	—
73	C₄⋊C₄×D₇₃	D₄	1	2	yes	—
74	C₂²⋊C₄×D₇₃	D₄	1	2	yes	—
75	C₄²×D₇₃	C₂³	1	2	yes	—
76	#14556502	C₂×C₄	1	2	yes	complemented
77	#14556501	C₂×C₄	1	2	yes	complemented
78	#14556501	C₂×C₄	1	2	yes	complemented
79	C₄×#10596831	C₂×C₄	1	2	yes	complemented
80	C₈×Dic₇₃	C₂×C₄	1	2	yes	complemented
81	C₈×Dic₇₃	C₂×C₄	1	2	yes	complemented
82	C₂×M₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
83	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
84	#117×C₇₃	C₂×C₄	1	1	yes	characteristic
85	#97×C₇₃	C₂×C₄	1	2	yes	complemented
86	C₄×C₈×C₇₃	C₂×C₄	1	2	yes	complemented
87	C₂²×#64408	—	2	4	no	—
88	C₂²×#64408	—	2	2	no	—
89	C₂²×#64408	—	2	2	no	—
90	C₂²×#64408	—	4	4	no	—
91	C₂²×#64408	—	8	4	no	—
92	C₄⋊#64408	—	2	4	no	—
93	C₄⋊#64408	—	2	2	no	—
94	C₄⋊#64408	—	2	4	no	—
95	C₄⋊#64408	—	2	2	no	—
96	C₄⋊#64408	—	2	2	no	—
97	C₄⋊#64408	—	2	2	no	—
98	C₄⋊#64408	—	4	4	no	—
99	C₄⋊#64408	—	8	8	no	—
100	C₂²⋊#64408	—	4	4	no	—
101	C₄×#64408	—	4	4	no	—
102	C₂³×D₇₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
104	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₄×D₇₃	C₂×D₄	1	4	yes	—
106	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
107	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
108	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
109	C₂×C₄×D₇₃	C₂×Q₈	1	2	yes	—
110	C₂×C₄×D₇₃	C₂×Q₈	1	2	yes	—
111	C₂×C₄×D₇₃	C₂×Q₈	1	1	yes	characteristic
112	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
113	#11924012	C₄⋊C₄	1	4	yes	complemented
114	#11924011	C₄⋊C₄	1	8	yes	complemented
115	C₂×#10596831	C₄⋊C₄	1	4	yes	complemented
116	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
117	C₂×#10596831	C₂²×C₄	1	2	yes	—
118	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
119	C₈×D₇₃	C₄⋊C₄	1	4	yes	complemented
120	C₈×D₇₃	C₄⋊C₄	1	4	yes	complemented
121	C₈×D₇₃	C₂×D₄	1	2	yes	—
122	C₈×D₇₃	C₂×D₄	1	2	yes	—
123	C₈×D₇₃	C₂×D₄	1	4	yes	—
124	C₈×D₇₃	C₂×Q₈	1	2	yes	—
125	C₈×D₇₃	C₂×Q₈	1	2	yes	—
126	C₈×D₇₃	C₂×Q₈	1	4	yes	—
127	C₄⋊Dic₇₃	C₄⋊C₄	1	2	yes	—
128	#11924007	C₄⋊C₄	1	4	yes	—
129	C₂²⋊Dic₇₃	C₄⋊C₄	1	2	yes	—
130	#11924005	C₄⋊C₄	1	4	yes	—
131	C₄×Dic₇₃	C₂²×C₄	1	2	yes	—
132	C₄×Dic₇₃	C₂×Q₈	1	4	yes	—
133	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
134	M₁₆×C₇₃	C₄⋊C₄	1	4	yes	complemented
135	C₂×C₈×C₇₃	C₄⋊C₄	1	4	yes	complemented
136	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
138	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
139	C₄⋊C₄×C₇₃	C₄⋊C₄	1	2	yes	—
140	C₂²⋊C₄×C₇₃	C₄⋊C₄	1	2	yes	—
141	C₄²×C₇₃	C₂²×C₄	1	2	yes	—
142	C₂³×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂²×D₇₃	—	2	4	no	—
144	C₂²×D₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₂²×D₇₃	#127	1	2	yes	—
146	C₂²×D₇₃	C₄⋊Q₈	1	2	yes	—
147	C₂²×D₇₃	C₂²×D₄	1	1	yes	characteristic
148	C₂×#64408	—	4	2	no	—
149	C₂×#64408	—	4	2	no	—
150	C₂×#64408	—	4	4	no	—
151	C₂×#64408	—	4	4	no	—
152	C₂×#64408	—	4	8	no	—
153	C₂×#64408	—	4	4	no	—
154	C₂×#64408	—	8	8	no	—
155	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	4	yes	—
156	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
157	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
158	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
160	C₂×Dic₇₃	C₂×C₄⋊C₄	1	4	yes	—
161	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂×Dic₇₃	C₄⋊Q₈	1	2	yes	—
163	C₂×Dic₇₃	C₄⋊Q₈	1	2	yes	—
164	C₂×Dic₇₃	C₂²×Q₈	1	1	yes	characteristic
165	C₄×D₇₃	—	2	8	no	—
166	C₄×D₇₃	C₂×C₄⋊C₄	1	2	yes	—
167	C₄×D₇₃	C₂×C₄⋊C₄	1	2	yes	—
168	C₄×D₇₃	#127	1	2	yes	—
169	C₄×D₇₃	C₄⋊Q₈	1	2	yes	—
170	C₄×D₇₃	C₄⋊Q₈	1	2	yes	—
171	C₄×D₇₃	C₄⋊Q₈	1	2	yes	—
172	C₄×D₇₃	C₂²×D₄	1	1	yes	characteristic
173	C₄×D₇₃	C₂²×D₄	1	1	yes	characteristic
174	C₄×D₇₃	C₂²×Q₈	1	1	yes	characteristic
175	C₄×D₇₃	C₂²×Q₈	1	1	yes	characteristic
176	C₈×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
177	C₈×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
178	C₈×C₇₃	C₂×C₄⋊C₄	1	4	yes	—
179	#10596831	C₂×C₄⋊C₄	1	2	yes	—
180	#10596831	C₂×C₄⋊C₄	1	2	yes	—
181	#10596831	C₂×C₄⋊C₄	1	4	yes	—
182	C₂²×C₇₃	—	2	2	no	—
183	C₂²×C₇₃	#384	1	2	yes	—
184	C₂²×C₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
185	C₂×D₇₃	—	2	2	no	—
186	C₂×D₇₃	—	2	4	no	—
187	C₂×D₇₃	—	2	4	no	—
188	C₂×D₇₃	#384	1	2	yes	—
189	C₂×D₇₃	C₂×#127	1	1	yes	characteristic
190	C₂×D₇₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
191	C₂×D₇₃	#577	1	4	yes	—
192	#64408	—	8	2	no	—
193	#64408	—	8	2	no	—
194	#64408	—	8	4	no	—
195	C₄×C₇₃	—	2	4	no	—
196	C₄×C₇₃	#384	1	2	yes	—
197	C₄×C₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
198	C₄×C₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
199	Dic₇₃	—	2	4	no	—
200	Dic₇₃	#384	1	2	yes	—
201	Dic₇₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
202	Dic₇₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
203	#20802	—	73	1	no	maximal, Sylow
204	C₂×C₇₃	—	2	2	no	—
205	C₂×C₇₃	C₂×#384	1	1	yes	characteristic
206	C₂×C₇₃	#2912	1	2	yes	—
207	D₇₃	—	2	2	no	—
208	D₇₃	#3154	1	2	yes	—
209	D₇₃	#3163	1	2	yes	—
210	C₂×#428	—	73	2	no	—
211	C₂×#427	—	73	1	no	—
212	C₂²×#106	—	73	1	no	—
213	C₂×#405	—	73	1	no	—
214	#2317	—	73	2	no	—
215	#1847	—	73	4	no	—
216	#1846	—	73	2	no	—
217	#1844	—	73	2	no	—
218	C₇₃	#20802	1	1	yes	characteristic, complemented, Sylow
219	C₂²×M₁₆	—	73	1	no	—
220	C₂³×C₈	—	73	1	no	—
221	C₂×#117	—	73	1	no	—
222	C₂×#117	—	73	2	no	—
223	C₂²×C₄⋊C₄	—	73	2	no	—
224	#428	—	146	8	no	—
225	#427	—	146	4	no	—
226	C₂×#107	—	73	4	no	—
227	C₂×#107	—	73	2	no	—
228	C₂×#106	—	73	1	no	—
229	C₂×#106	—	73	2	no	—
230	C₂×#106	—	73	4	no	—
231	C₂×#106	—	73	1	no	—
232	C₂×#106	—	73	2	no	—
233	C₂×#106	—	146	4	no	—
234	#405	—	73	1	no	—
235	#405	—	73	1	no	—
236	#405	—	73	1	no	—
237	#405	—	73	2	no	—
238	#405	—	73	2	no	—
239	#405	#64408	1	1	yes	characteristic, complemented
240	C₂×#97	—	73	2	no	—
241	C₂×C₄×C₈	—	73	2	no	—
242	#389	—	146	4	no	—
243	#385	—	146	4	no	—
244	#384	—	73	4	no	—
245	#382	—	73	4	no	—
246	C₂³×C₄	—	73	1	no	—
247	C₂³×C₄	—	146	2	no	—
248	C₂×M₁₆	—	73	1	no	—
249	C₂×M₁₆	—	73	4	no	—
250	C₂×M₁₆	—	73	4	no	—
251	C₂×M₁₆	—	73	2	no	—
252	C₂×M₁₆	C₂×#64408	1	1	yes	characteristic
253	C₂²×C₈	—	73	1	no	—
254	C₂²×C₈	—	73	4	no	—
255	C₂²×C₈	—	73	4	no	—
256	C₂²×C₈	—	73	1	no	—
257	C₂²×C₈	—	73	1	no	—
258	C₂²×C₈	—	73	1	no	—
259	C₂²×C₈	—	73	1	no	—
260	C₂²×C₈	—	73	2	no	—
261	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
262	#117	—	73	1	no	—
263	#117	—	73	2	no	—
264	#117	—	73	2	no	—
265	#117	—	73	2	no	—
266	#117	—	146	4	no	—
267	#117	—	146	4	no	—
268	#117	C₂×#64408	1	1	yes	characteristic
269	C₂×C₄⋊C₄	—	73	2	no	—
270	C₂×C₄⋊C₄	—	73	4	no	—
271	C₂×C₄⋊C₄	—	73	2	no	—
272	C₂×C₄⋊C₄	—	73	2	no	—
273	C₂×C₄⋊C₄	—	146	2	no	—
274	C₂×C₄⋊C₄	—	146	4	no	—
275	C₂×C₄⋊C₄	—	146	4	no	—
276	C₂×C₄⋊C₄	—	146	8	no	—
277	C₂×C₂²⋊C₄	—	73	2	no	—
278	C₂×C₂²⋊C₄	—	146	2	no	—
279	C₂×C₄²	—	73	2	no	—
280	C₂×C₄²	—	146	2	no	—
281	#107	—	146	4	no	—
282	#107	—	146	8	no	—
283	#106	—	146	4	no	—
284	#106	—	146	4	no	—
285	#106	—	146	2	no	—
286	#106	—	146	2	no	—
287	#106	—	146	8	no	—
288	#97	—	73	2	no	—
289	#97	—	73	2	no	—
290	#97	—	73	2	no	—
291	#97	C₂×#64408	1	2	yes	complemented
292	C₄×C₈	—	73	2	no	—
293	C₄×C₈	—	73	2	no	—
294	C₄×C₈	—	73	2	no	—
295	C₄×C₈	C₂×#64408	1	2	yes	complemented
296	#95	—	146	8	no	—
297	C₂⁴	—	73	1	no	—
298	C₂²×C₄	—	292	4	no	—
299	C₂²×C₄	—	584	4	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	2	no	—
305	C₂²×C₄	—	73	2	no	—
306	C₂²×C₄	—	73	1	no	—
307	C₂²×C₄	—	73	2	no	—
308	C₂²×C₄	—	73	2	no	—
309	C₂²×C₄	—	73	4	no	—
310	C₂²×C₄	—	146	2	no	—
311	C₂²×C₄	—	146	4	no	—
312	C₂²×C₄	—	146	2	no	—
313	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
314	M₁₆	—	73	4	no	—
315	M₁₆	—	73	8	no	—
316	M₁₆	C₄⋊#64408	1	4	yes	complemented
317	C₂×C₈	—	73	1	no	—
318	C₂×C₈	—	73	2	no	—
319	C₂×C₈	—	73	1	no	—
320	C₂×C₈	—	73	4	no	—
321	C₂×C₈	—	73	4	no	—
322	C₂×C₈	—	73	4	no	—
323	C₂×C₈	—	73	2	no	—
324	C₂×C₈	—	73	2	no	—
325	C₂×C₈	—	73	4	no	—
326	C₂×C₈	—	73	2	no	—
327	C₂×C₈	—	73	2	no	—
328	C₂×C₈	—	73	4	no	—
329	C₂×C₈	C₄⋊#64408	1	4	yes	complemented
330	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
331	C₂×C₈	C₂²×#64408	1	2	yes	—
332	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
333	C₄⋊C₄	—	292	4	no	—
334	C₄⋊C₄	—	584	8	no	—
335	C₄⋊C₄	—	73	4	no	—
336	C₄⋊C₄	—	73	2	no	—
337	C₄⋊C₄	—	146	4	no	—
338	C₄⋊C₄	—	146	2	no	—
339	C₄⋊C₄	—	146	4	no	—
340	C₄⋊C₄	—	146	2	no	—
341	C₄⋊C₄	—	146	2	no	—
342	C₄⋊C₄	—	146	2	no	—
343	C₄⋊C₄	C₄⋊#64408	1	2	yes	—
344	C₂²⋊C₄	—	292	4	no	—
345	C₂²⋊C₄	—	73	2	no	—
346	C₂²⋊C₄	—	73	4	no	—
347	C₂²⋊C₄	C₄⋊#64408	1	2	yes	—
348	C₄²	—	292	4	no	—
349	C₄²	—	73	2	no	—
350	C₄²	—	73	4	no	—
351	C₄²	C₂²×#64408	1	2	yes	—
352	C₂³	—	73	1	no	—
353	C₂³	—	73	1	no	—
354	C₂³	—	73	2	no	—
355	C₂³	—	73	2	no	—
356	C₂³	—	146	4	no	—
357	C₂³	C₂×C₄⋊#64408	1	1	yes	characteristic
358	C₂×C₄	—	292	2	no	—
359	C₂×C₄	—	292	2	no	—
360	C₂×C₄	—	292	4	no	—
361	C₂×C₄	—	292	4	no	—
362	C₂×C₄	—	292	8	no	—
363	C₂×C₄	—	292	4	no	—
364	C₂×C₄	—	584	8	no	—
365	C₂×C₄	—	73	1	no	—
366	C₂×C₄	—	73	1	no	—
367	C₂×C₄	—	73	2	no	—
368	C₂×C₄	—	73	2	no	—
369	C₂×C₄	—	73	1	no	—
370	C₂×C₄	—	73	1	no	—
371	C₂×C₄	—	73	2	no	—
372	C₂×C₄	—	73	1	no	—
373	C₂×C₄	—	73	1	no	—
374	C₂×C₄	—	73	2	no	—
375	C₂×C₄	—	73	2	no	—
376	C₂×C₄	—	73	2	no	—
377	C₂×C₄	—	73	2	no	—
378	C₂×C₄	—	73	2	no	—
379	C₂×C₄	—	73	4	no	—
380	C₂×C₄	—	146	8	no	—
381	C₂×C₄	C₂×C₄⋊#64408	1	4	yes	—
382	C₂×C₄	C₂×C₄⋊#64408	1	2	yes	—
383	C₂×C₄	C₂×C₄⋊#64408	1	2	yes	—
384	C₂×C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
385	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
386	C₈	—	73	2	no	—
387	C₈	—	73	2	no	—
388	C₈	—	73	4	no	—
389	C₈	C₂×C₄⋊#64408	1	2	yes	—
390	C₈	C₂×C₄⋊#64408	1	2	yes	—
391	C₈	C₂×C₄⋊#64408	1	4	yes	—
392	C₂²	—	2	2	no	—
393	C₂²	—	73	4	no	—
394	C₂²	—	73	1	no	—
395	C₂²	—	73	1	no	—
396	C₂²	—	73	2	no	—
397	C₂²	—	146	4	no	—
398	C₂²	—	146	4	no	—
399	C₂²	—	146	2	no	—
400	C₂²	#17989533	1	2	yes	—
401	C₂²	C₂²×C₄⋊#64408	1	1	yes	characteristic
402	C₄	—	2	4	no	—
403	C₄	—	584	4	no	—
404	C₄	—	584	2	no	—
405	C₄	—	584	2	no	—
406	C₄	—	73	1	no	—
407	C₄	—	73	1	no	—
408	C₄	—	73	2	no	—
409	C₄	—	146	4	no	—
410	C₄	#17989533	1	2	yes	—
411	C₄	C₂²×C₄⋊#64408	1	1	yes	characteristic
412	C₄	C₂²×C₄⋊#64408	1	1	yes	characteristic
413	C₂	—	2	2	no	—
414	C₂	—	73	2	no	—
415	C₂	—	73	2	no	—
416	C₂	—	146	2	no	—
417	C₂	C₂×#17989533	1	1	yes	characteristic
418	C₂	#22626585	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂²×C₄⋊#64408
commutator	C₂×C₄×C₇₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×#64408
Fitting	#405×C₇₃	C₄
socle	C₂²×C₇₃	C₂²×C₄⋊C₄
prime radical	C₂³×D₇₃	C₂×D₄
cosocle	C₂×C₄×D₇₃	C₂⁴
hypercenter	#405	#64408
hypocenter	C₇₃	#20802
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ #117 ◁ #405

Complements

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

N	H ≅ G/N	type
5. #22625869	C₂	semidirect
6. #22625868	C₂	semidirect
7. #22625866	C₂	semidirect
28. #17988545	C₄	semidirect
29. #17988544	C₄	semidirect
30. #17988543	C₄	semidirect
31. #17988542	C₄	semidirect
32. #17988541	C₄	semidirect
35. #405×C₇₃	C₄	semidirect
76. #14556502	C₂×C₄	semidirect
77. #14556501	C₂×C₄	semidirect
78. #14556501	C₂×C₄	semidirect
79. C₄×#10596831	C₂×C₄	semidirect
80. C₈×Dic₇₃	C₂×C₄	semidirect
81. C₈×Dic₇₃	C₂×C₄	semidirect
85. #97×C₇₃	C₂×C₄	semidirect
86. C₄×C₈×C₇₃	C₂×C₄	semidirect
113. #11924012	C₄⋊C₄	semidirect
114. #11924011	C₄⋊C₄	semidirect
115. C₂×#10596831	C₄⋊C₄	semidirect
119. C₈×D₇₃	C₄⋊C₄	semidirect
120. C₈×D₇₃	C₄⋊C₄	semidirect
134. M₁₆×C₇₃	C₄⋊C₄	semidirect
135. C₂×C₈×C₇₃	C₄⋊C₄	semidirect
218. C₇₃	#20802	semidirect
239. #405	#64408	semidirect
291. #97	C₂×#64408	semidirect
295. C₄×C₈	C₂×#64408	semidirect
316. M₁₆	C₄⋊#64408	semidirect
329. C₂×C₈	C₄⋊#64408	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17989598	2
C₂×#17989597	2
C₂²×#14556659	2
#22626412	2
#22625869	2
#22625868	2
#22625866	2
#405×D₇₃	2
#20802	73