Subgroups — C₂×#22626048 #34022151

Order 18688.

918 conjugacy classes of subgroups.

The subgroup lattice has 448 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	C₂²×#14556659	C₂	1	1	yes	maximal, characteristic
3	C₂×#17989550	C₂	1	1	yes	maximal, characteristic
4	#22626048	C₂	1	8	yes	maximal, direct product factor
5	C₂×#17989466	C₂	1	2	yes	maximal
6	C₂×#108×D₇₃	C₂	1	1	yes	maximal, characteristic
7	C₂×D₇₃⋊M₁₆	C₂²	1	1	yes	characteristic
8	C₂×#14556670	C₂²	1	1	yes	characteristic
9	C₂²×C₄⋊#64408	C₂²	1	2	yes	—
10	#17989598	—	2	4	no	—
11	#17989598	C₂²	1	8	yes	—
12	C₂×#14556660	—	2	2	no	—
13	C₂×#14556659	—	2	2	no	—
14	C₂×#14556659	—	2	1	no	—
15	C₂×#14556659	—	2	1	no	—
16	C₂×#14556659	—	2	2	no	—
17	C₂×#14556659	C₂²	1	4	yes	—
18	#17989550	—	2	2	no	—
19	#17989550	C₂²	1	4	yes	—
20	C₂×#14556645	—	2	1	no	—
21	C₂×C₈×#64408	—	2	1	no	—
22	#17989466	C₂²	1	8	yes	—
23	C₂×M₁₆×D₇₃	C₂²	1	2	yes	—
24	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
25	C₂×#14556527	C₄	1	1	yes	characteristic, complemented
26	C₂×#14556526	C₄	1	2	yes	complemented
27	#108×D₇₃	C₄	1	4	yes	complemented
28	#108×D₇₃	C₂²	1	4	yes	—
29	C₂×#108×C₇₃	C₄	1	1	yes	characteristic, complemented
30	C₂³×#64408	—	2	2	no	—
31	C₂×#11924038	—	2	1	no	—
32	D₇₃⋊M₁₆	—	2	1	no	—
33	D₇₃⋊M₁₆	—	2	1	no	—
34	D₇₃⋊M₁₆	Q₈	1	2	yes	—
35	D₇₃⋊M₁₆	C₂³	1	2	yes	—
36	C₂×#11924037	Q₈	1	2	yes	—
37	C₂×#11924036	—	2	1	no	—
38	#14556670	—	2	1	no	—
39	#14556670	—	2	1	no	—
40	#14556670	D₄	1	2	yes	—
41	#14556670	C₂³	1	2	yes	—
42	C₂×C₄⋊#64408	—	2	2	no	—
43	C₂×C₄⋊#64408	—	2	2	no	—
44	C₂×C₄⋊#64408	—	2	2	no	—
45	C₂×C₄⋊#64408	—	2	2	no	—
46	C₂×C₄⋊#64408	—	2	2	no	—
47	C₂×C₄⋊#64408	D₄	1	2	yes	—
48	C₂×C₄⋊#64408	C₂³	1	4	yes	—
49	C₂×C₂²⋊#64408	—	2	1	no	—
50	C₂×C₄×#64408	—	2	1	no	—
51	#14556660	—	2	8	no	—
52	#14556659	—	2	8	no	—
53	#14556659	—	2	4	no	—
54	#14556659	—	2	4	no	—
55	#14556645	—	2	4	no	—
56	C₈×#64408	—	2	4	no	—
57	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
58	C₂×#11924012	C₂×C₄	1	2	yes	—
59	C₂×#11924011	—	2	2	no	—
60	M₁₆×D₇₃	—	2	2	no	—
61	M₁₆×D₇₃	—	2	2	no	—
62	M₁₆×D₇₃	C₂×C₄	1	4	yes	—
63	M₁₆×D₇₃	C₂³	1	4	yes	—
64	C₂²×#10596831	C₂×C₄	1	1	yes	characteristic
65	C₂×C₈×D₇₃	—	2	2	no	—
66	C₂×C₈×D₇₃	C₂×C₄	1	2	yes	—
67	C₂×C₈×D₇₃	D₄	1	1	yes	characteristic
68	C₂×C₈×D₇₃	D₄	1	1	yes	characteristic
69	C₂×C₈×D₇₃	D₄	1	2	yes	—
70	C₂×C₈×D₇₃	Q₈	1	1	yes	characteristic
71	C₂×C₈×D₇₃	Q₈	1	1	yes	characteristic
72	C₂×C₈×D₇₃	Q₈	1	2	yes	—
73	C₂×C₈×D₇₃	C₂³	1	2	yes	—
74	#14556527	C₂×C₄	1	4	yes	complemented
75	#14556526	C₂×C₄	1	8	yes	complemented
76	C₂×M₁₆×C₇₃	C₂×C₄	1	2	yes	—
77	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
78	#108×C₇₃	C₂×C₄	1	4	yes	complemented
79	C₂²×#64408	—	2	2	no	—
80	C₂²×#64408	—	2	4	no	—
81	C₂²×#64408	—	4	2	no	—
82	C₂²×#64408	—	4	2	no	—
83	C₂²×#64408	—	8	4	no	—
84	#11924038	—	2	2	no	—
85	#11924038	—	2	2	no	—
86	#11924037	—	2	2	no	—
87	#11924037	C₂×Q₈	1	4	yes	—
88	#11924036	—	2	2	no	—
89	#11924036	—	2	2	no	—
90	C₂×#10596833	—	2	2	no	—
91	C₄⋊#64408	—	2	2	no	—
92	C₄⋊#64408	—	2	4	no	—
93	C₄⋊#64408	—	2	4	no	—
94	C₄⋊#64408	—	4	2	no	—
95	C₄⋊#64408	—	4	2	no	—
96	C₄⋊#64408	C₂×D₄	1	4	yes	—
97	C₂²⋊#64408	—	2	2	no	—
98	C₂²⋊#64408	—	2	2	no	—
99	C₄×#64408	—	2	2	no	—
100	C₄×#64408	—	2	2	no	—
101	C₂³×D₇₃	#41	1	1	yes	characteristic
102	C₂²×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
103	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
105	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
106	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
107	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
108	C₂×C₄×D₇₃	C₂×Q₈	1	1	yes	characteristic
109	C₂×C₄×D₇₃	C₂×Q₈	1	1	yes	characteristic
110	C₂×C₄×D₇₃	C₂×Q₈	1	1	yes	characteristic
111	C₂×C₄×D₇₃	#41	1	1	yes	characteristic
112	C₂×C₄×D₇₃	#41	1	1	yes	characteristic
113	C₂×C₄×D₇₃	#41	1	1	yes	characteristic
114	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
115	#11924012	—	2	2	no	—
116	#11924012	C₂²×C₄	1	4	yes	—
117	#11924011	—	2	4	no	—
118	#11924011	—	2	4	no	—
119	C₂×#10596831	—	2	2	no	—
120	C₂×#10596831	C₄⋊C₄	1	1	yes	characteristic
121	C₂×#10596831	C₄⋊C₄	1	1	yes	characteristic
122	C₂×#10596831	C₄⋊C₄	1	2	yes	—
123	C₂×#10596831	C₂²×C₄	1	2	yes	—
124	C₈×D₇₃	—	2	4	no	—
125	C₈×D₇₃	—	2	4	no	—
126	C₈×D₇₃	C₄⋊C₄	1	2	yes	—
127	C₈×D₇₃	C₄⋊C₄	1	2	yes	—
128	C₈×D₇₃	C₄⋊C₄	1	2	yes	—
129	C₈×D₇₃	C₄⋊C₄	1	2	yes	—
130	C₈×D₇₃	C₂×D₄	1	2	yes	—
131	C₈×D₇₃	C₂×D₄	1	2	yes	—
132	C₈×D₇₃	C₂×Q₈	1	2	yes	—
133	C₈×D₇₃	C₂×Q₈	1	2	yes	—
134	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
135	M₁₆×C₇₃	—	2	2	no	—
136	M₁₆×C₇₃	C₂²×C₄	1	4	yes	—
137	C₂×C₈×C₇₃	—	2	2	no	—
138	C₂×C₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
139	C₂×C₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
140	C₂×C₈×C₇₃	C₄⋊C₄	1	2	yes	—
141	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
142	C₂³×C₇₃	C₄×Q₈	1	1	yes	characteristic
143	C₂²×D₇₃	—	2	4	no	—
144	C₂²×D₇₃	C₄×Q₈	1	1	yes	characteristic
145	C₂²×D₇₃	#121	1	1	yes	characteristic
146	C₂²×D₇₃	#121	1	1	yes	characteristic
147	C₂²×D₇₃	#125	1	1	yes	characteristic
148	C₂²×D₇₃	#125	1	1	yes	characteristic
149	C₂²×D₇₃	C₂×#41	1	1	yes	characteristic
150	C₂×#64408	—	2	4	no	—
151	C₂×#64408	—	4	4	no	—
152	C₂×#64408	—	4	4	no	—
153	C₂×#64408	—	8	4	no	—
154	C₂×#64408	—	8	4	no	—
155	C₂×#64408	—	8	4	no	—
156	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
159	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
160	C₂×C₄×C₇₃	C₄×Q₈	1	1	yes	characteristic
161	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
162	C₂×Dic₇₃	C₄×Q₈	1	1	yes	characteristic
163	C₂×Dic₇₃	C₂²⋊Q₈	1	1	yes	characteristic
164	C₂×Dic₇₃	C₂²⋊Q₈	1	1	yes	characteristic
165	C₂×Dic₇₃	C₄⋊Q₈	1	1	yes	characteristic
166	C₂×Dic₇₃	C₄⋊Q₈	1	1	yes	characteristic
167	C₂×Dic₇₃	C₂²×Q₈	1	1	yes	characteristic
168	C₄×D₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₄×D₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₄×D₇₃	C₄×D₄	1	1	yes	characteristic
171	C₄×D₇₃	C₄×D₄	1	1	yes	characteristic
172	C₄×D₇₃	#121	1	1	yes	characteristic
173	C₄×D₇₃	#121	1	1	yes	characteristic
174	C₄×D₇₃	C₂²⋊Q₈	1	1	yes	characteristic
175	C₄×D₇₃	C₂²⋊Q₈	1	1	yes	characteristic
176	C₄×D₇₃	#125	1	1	yes	characteristic
177	C₄×D₇₃	#125	1	1	yes	characteristic
178	C₄×D₇₃	C₄⋊Q₈	1	1	yes	characteristic
179	C₄×D₇₃	C₄⋊Q₈	1	1	yes	characteristic
180	C₄×D₇₃	C₂²×D₄	1	1	yes	characteristic
181	C₄×D₇₃	C₂²×D₄	1	1	yes	characteristic
182	C₄×D₇₃	C₂²×Q₈	1	1	yes	characteristic
183	C₄×D₇₃	C₂×#41	1	1	yes	characteristic
184	#10596833	—	2	4	no	—
185	C₈×C₇₃	—	2	4	no	—
186	C₈×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
187	C₈×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
188	#10596831	—	2	4	no	—
189	#10596831	C₂×C₄⋊C₄	1	2	yes	—
190	#10596831	C₂×C₄⋊C₄	1	2	yes	—
191	C₂²×C₇₃	—	2	2	no	—
192	C₂²×C₇₃	#389	1	1	yes	characteristic
193	C₂²×C₇₃	#389	1	1	yes	characteristic
194	C₂²×C₇₃	C₂×C₄×Q₈	1	1	yes	characteristic
195	C₂×D₇₃	—	2	2	no	—
196	C₂×D₇₃	—	2	2	no	—
197	C₂×D₇₃	—	2	2	no	—
198	C₂×D₇₃	—	2	2	no	—
199	C₂×D₇₃	—	2	2	no	—
200	C₂×D₇₃	#389	1	1	yes	characteristic
201	C₂×D₇₃	#389	1	1	yes	characteristic
202	C₂×D₇₃	#471	1	4	yes	—
203	C₂×D₇₃	C₂×#121	1	1	yes	characteristic
204	C₂×D₇₃	C₂×#125	1	1	yes	characteristic
205	#64408	—	4	4	no	—
206	#64408	—	8	4	no	—
207	C₄×C₇₃	#389	1	1	yes	characteristic
208	C₄×C₇₃	#389	1	1	yes	characteristic
209	C₄×C₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
210	C₄×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
211	Dic₇₃	#389	1	1	yes	characteristic
212	Dic₇₃	#389	1	1	yes	characteristic
213	Dic₇₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
214	Dic₇₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
215	C₂×#1951	—	73	1	no	maximal, Sylow
216	C₂×C₇₃	—	2	1	no	—
217	C₂×C₇₃	—	2	1	no	—
218	C₂×C₇₃	#1951	1	2	yes	complemented
219	C₂×C₇₃	C₂×#389	1	1	yes	characteristic
220	D₇₃	—	2	1	no	—
221	D₇₃	—	2	1	no	—
222	D₇₃	#1951	1	2	yes	complemented
223	D₇₃	C₂×#471	1	2	yes	—
224	C₂²×#108	—	73	1	no	—
225	C₂×#428	—	73	2	no	—
226	C₂²×#106	—	73	1	no	—
227	C₂×#405	—	73	1	no	—
228	#1951	—	73	8	no	—
229	C₂×#343	—	73	2	no	—
230	C₇₃	C₂×#1951	1	1	yes	characteristic, complemented, Sylow
231	C₂²×M₁₆	—	73	1	no	—
232	C₂²×M₁₆	—	73	2	no	—
233	C₂³×C₈	—	73	1	no	—
234	C₂×#117	—	73	1	no	—
235	C₂²×C₄⋊C₄	—	73	2	no	—
236	C₂×#108	—	73	2	no	—
237	C₂×#108	—	73	1	no	—
238	C₂×#108	—	73	4	no	—
239	C₂×#108	—	73	4	no	—
240	C₂×#108	#64408	1	1	yes	characteristic, complemented
241	#428	—	73	8	no	—
242	#428	—	146	4	no	—
243	C₂×#107	—	146	2	no	—
244	C₂×#106	—	73	4	no	—
245	C₂×#106	—	146	2	no	—
246	C₂×#106	—	146	1	no	—
247	C₂×#106	—	146	1	no	—
248	C₂×#106	—	146	2	no	—
249	#405	—	73	4	no	—
250	#405	—	146	2	no	—
251	C₂×#97	—	146	1	no	—
252	C₂×C₄×C₈	—	146	1	no	—
253	#343	—	73	8	no	—
254	C₂³×C₄	—	73	1	no	—
255	C₂³×C₄	—	146	2	no	—
256	C₂×M₁₆	—	73	2	no	—
257	C₂×M₁₆	—	73	2	no	—
258	C₂×M₁₆	—	73	2	no	—
259	C₂×M₁₆	—	73	2	no	—
260	C₂×M₁₆	—	73	4	no	—
261	C₂×M₁₆	—	73	4	no	—
262	C₂×M₁₆	—	146	2	no	—
263	C₂×M₁₆	—	146	2	no	—
264	C₂×M₁₆	—	146	2	no	—
265	C₂×M₁₆	—	146	1	no	—
266	C₂×M₁₆	—	146	1	no	—
267	C₂×M₁₆	—	146	1	no	—
268	C₂×M₁₆	C₂×#64408	1	2	yes	—
269	C₂²×C₈	—	73	1	no	—
270	C₂²×C₈	—	73	1	no	—
271	C₂²×C₈	—	73	1	no	—
272	C₂²×C₈	—	73	2	no	—
273	C₂²×C₈	—	73	2	no	—
274	C₂²×C₈	—	73	1	no	—
275	C₂²×C₈	—	73	1	no	—
276	C₂²×C₈	—	73	2	no	—
277	C₂²×C₈	—	73	2	no	—
278	C₂²×C₈	—	146	2	no	—
279	C₂²×C₈	—	146	1	no	—
280	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
281	#117	—	73	2	no	—
282	#117	—	73	2	no	—
283	#117	—	146	1	no	—
284	#117	—	146	1	no	—
285	C₂×C₄⋊C₄	—	73	2	no	—
286	C₂×C₄⋊C₄	—	73	4	no	—
287	C₂×C₄⋊C₄	—	146	2	no	—
288	C₂×C₄⋊C₄	—	146	2	no	—
289	C₂×C₄⋊C₄	—	146	2	no	—
290	C₂×C₄⋊C₄	—	146	2	no	—
291	C₂×C₄⋊C₄	—	146	2	no	—
292	C₂×C₂²⋊C₄	—	146	1	no	—
293	C₂×C₄²	—	146	1	no	—
294	#108	—	73	8	no	—
295	#108	—	73	4	no	—
296	#108	C₂×#64408	1	4	yes	complemented
297	#107	—	146	8	no	—
298	#106	—	146	8	no	—
299	#106	—	146	4	no	—
300	#106	—	146	4	no	—
301	#97	—	146	4	no	—
302	C₄×C₈	—	146	4	no	—
303	C₂⁴	—	73	1	no	—
304	C₂²×C₄	—	292	2	no	—
305	C₂²×C₄	—	292	2	no	—
306	C₂²×C₄	—	584	4	no	—
307	C₂²×C₄	—	73	1	no	—
308	C₂²×C₄	—	73	1	no	—
309	C₂²×C₄	—	73	1	no	—
310	C₂²×C₄	—	73	1	no	—
311	C₂²×C₄	—	73	1	no	—
312	C₂²×C₄	—	73	1	no	—
313	C₂²×C₄	—	73	1	no	—
314	C₂²×C₄	—	73	1	no	—
315	C₂²×C₄	—	73	1	no	—
316	C₂²×C₄	—	73	1	no	—
317	C₂²×C₄	—	73	1	no	—
318	C₂²×C₄	—	73	1	no	—
319	C₂²×C₄	—	73	1	no	—
320	C₂²×C₄	—	146	2	no	—
321	C₂²×C₄	—	146	4	no	—
322	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
323	M₁₆	—	2	2	no	—
324	M₁₆	—	73	4	no	—
325	M₁₆	—	73	4	no	—
326	M₁₆	—	146	4	no	—
327	M₁₆	—	146	4	no	—
328	M₁₆	—	146	2	no	—
329	M₁₆	—	146	2	no	—
330	M₁₆	—	146	2	no	—
331	M₁₆	—	146	2	no	—
332	M₁₆	C₂²×#64408	1	4	yes	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	73	2	no	—
335	C₂×C₈	—	73	2	no	—
336	C₂×C₈	—	73	1	no	—
337	C₂×C₈	—	73	1	no	—
338	C₂×C₈	—	73	2	no	—
339	C₂×C₈	—	73	2	no	—
340	C₂×C₈	—	73	2	no	—
341	C₂×C₈	—	73	2	no	—
342	C₂×C₈	—	73	2	no	—
343	C₂×C₈	—	73	2	no	—
344	C₂×C₈	—	73	2	no	—
345	C₂×C₈	—	73	2	no	—
346	C₂×C₈	—	146	4	no	—
347	C₂×C₈	—	146	4	no	—
348	C₂×C₈	—	146	2	no	—
349	C₂×C₈	—	146	2	no	—
350	C₂×C₈	—	146	2	no	—
351	C₂×C₈	—	146	2	no	—
352	C₂×C₈	C₄⋊#64408	1	2	yes	—
353	C₂×C₈	C₄⋊#64408	1	1	yes	characteristic
354	C₂×C₈	C₄⋊#64408	1	1	yes	characteristic
355	C₂×C₈	C₂²×#64408	1	2	yes	—
356	C₄⋊C₄	—	292	2	no	—
357	C₄⋊C₄	—	292	2	no	—
358	C₄⋊C₄	—	73	4	no	—
359	C₄⋊C₄	—	146	4	no	—
360	C₄⋊C₄	—	146	4	no	—
361	C₄⋊C₄	—	146	2	no	—
362	C₂²⋊C₄	—	146	2	no	—
363	C₂²⋊C₄	—	146	2	no	—
364	C₄²	—	146	2	no	—
365	C₄²	—	146	2	no	—
366	C₂³	—	73	1	no	—
367	C₂³	—	73	1	no	—
368	C₂³	—	73	1	no	—
369	C₂³	—	73	1	no	—
370	C₂³	—	73	1	no	—
371	C₂³	—	73	1	no	—
372	C₂³	—	146	4	no	—
373	C₂³	Q₈×#64408	1	1	yes	characteristic
374	C₂×C₄	—	292	4	no	—
375	C₂×C₄	—	292	4	no	—
376	C₂×C₄	—	584	4	no	—
377	C₂×C₄	—	584	4	no	—
378	C₂×C₄	—	584	4	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	—	73	1	no	—
390	C₂×C₄	—	73	1	no	—
391	C₂×C₄	—	73	1	no	—
392	C₂×C₄	—	73	1	no	—
393	C₂×C₄	—	73	1	no	—
394	C₂×C₄	—	73	1	no	—
395	C₂×C₄	—	73	1	no	—
396	C₂×C₄	—	73	1	no	—
397	C₂×C₄	—	73	1	no	—
398	C₂×C₄	—	73	1	no	—
399	C₂×C₄	—	73	1	no	—
400	C₂×C₄	—	73	1	no	—
401	C₂×C₄	—	146	4	no	—
402	C₂×C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
403	C₂×C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
404	C₂×C₄	D₄×#64408	1	1	yes	characteristic
405	C₂×C₄	D₄×#64408	1	1	yes	characteristic
406	C₂×C₄	Q₈×#64408	1	1	yes	characteristic
407	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
408	C₈	—	2	4	no	—
409	C₈	—	73	2	no	—
410	C₈	—	73	2	no	—
411	C₈	—	146	4	no	—
412	C₈	—	146	4	no	—
413	C₈	C₂×C₄⋊#64408	1	2	yes	—
414	C₈	C₂×C₄⋊#64408	1	2	yes	—
415	C₂²	—	2	2	no	—
416	C₂²	—	73	4	no	—
417	C₂²	—	73	1	no	—
418	C₂²	—	73	1	no	—
419	C₂²	—	73	1	no	—
420	C₂²	—	73	1	no	—
421	C₂²	—	146	2	no	—
422	C₂²	—	146	2	no	—
423	C₂²	—	146	2	no	—
424	C₂²	—	146	2	no	—
425	C₂²	—	146	2	no	—
426	C₂²	#17989538	1	1	yes	characteristic
427	C₂²	#17989538	1	1	yes	characteristic
428	C₂²	C₂×Q₈×#64408	1	1	yes	characteristic
429	C₄	—	292	4	no	—
430	C₄	—	584	4	no	—
431	C₄	—	73	1	no	—
432	C₄	—	73	1	no	—
433	C₄	—	73	1	no	—
434	C₄	—	73	1	no	—
435	C₄	#17989538	1	1	yes	characteristic
436	C₄	#17989538	1	1	yes	characteristic
437	C₄	C₂²×C₄⋊#64408	1	1	yes	characteristic
438	C₄	C₂×D₄×#64408	1	1	yes	characteristic
439	C₂	—	2	1	no	—
440	C₂	—	2	1	no	—
441	C₂	—	73	2	no	—
442	C₂	—	73	2	no	—
443	C₂	—	146	1	no	—
444	C₂	—	146	1	no	—
445	C₂	#22626048	1	2	yes	direct product factor
446	C₂	C₂×#17989538	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#17989538
commutator	C₂×C₄×C₇₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×#64408
Fitting	C₂×#108×C₇₃	C₄
socle	C₂²×C₇₃	#389
prime radical	C₂³×D₇₃	#41
cosocle	C₂×C₄×D₇₃	C₂⁴
hypercenter	C₂×#108	#64408
hypocenter	C₇₃	C₂×#1951
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
4. #22626048	C₂	direct (N × H)
25. C₂×#14556527	C₄	semidirect
26. C₂×#14556526	C₄	semidirect
27. #108×D₇₃	C₄	semidirect
29. C₂×#108×C₇₃	C₄	semidirect
74. #14556527	C₂×C₄	semidirect
75. #14556526	C₂×C₄	semidirect
78. #108×C₇₃	C₂×C₄	semidirect
218. C₂×C₇₃	#1951	semidirect
222. D₇₃	#1951	semidirect
230. C₇₃	C₂×#1951	semidirect
240. C₂×#108	#64408	semidirect
296. #108	C₂×#64408	semidirect
445. C₂	#22626048	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#17989598	2
C₂²×#14556659	2
C₂×#17989550	2
#22626048	2
C₂×#17989466	2
C₂×#108×D₇₃	2
C₂×#1951	73

Subgroups — C2×#22626048 #34022151

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22626048 #34022151