Subgroups — C₂×#22625736 #34020235

Order 18688.

1102 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17989597	C₂	1	1	yes	maximal, characteristic
2	C₂×#17989553	C₂	1	2	yes	maximal
3	C₂²×C₈×#64408	C₂	1	1	yes	maximal, characteristic
4	#22625736	C₂	1	8	yes	maximal, direct product factor
5	C₂×#17989459	C₂	1	2	yes	maximal
6	C₂×#108×D₇₃	C₂	1	1	yes	maximal, characteristic
7	C₂²×#11924036	C₂²	1	1	yes	characteristic
8	C₂×#14556670	C₂²	1	2	yes	—
9	C₂²×C₄×#64408	C₂²	1	1	yes	characteristic
10	#17989597	C₄	1	4	yes	complemented
11	#17989597	C₂²	1	4	yes	—
12	C₂×#14556660	C₄	1	2	yes	complemented
13	C₂×#14556659	C₄	1	2	yes	complemented
14	#17989553	—	2	4	no	—
15	#17989553	C₂²	1	8	yes	—
16	C₂×#14556645	—	2	2	no	—
17	C₂×C₈×#64408	—	2	2	no	—
18	C₂×C₈×#64408	C₄	1	2	yes	complemented
19	C₂×C₈×#64408	C₄	1	2	yes	complemented
20	C₂×C₈×#64408	C₄	1	4	yes	complemented
21	C₂×C₈×#64408	C₂²	1	4	yes	—
22	#17989459	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	1	no	—
31	C₂×#11924036	C₂×C₄	1	2	yes	—
32	C₂×#11924036	C₂×C₄	1	2	yes	—
33	C₂×#11924036	D₄	1	1	yes	characteristic
34	C₂×#11924036	D₄	1	1	yes	characteristic
35	C₂×#11924036	D₄	1	2	yes	—
36	C₂×#11924036	Q₈	1	2	yes	—
37	C₂×#11924036	C₂³	1	2	yes	—
38	C₂²×#10596833	Q₈	1	2	yes	—
39	#14556670	—	2	2	no	—
40	#14556670	—	2	2	no	—
41	#14556670	C₂×C₄	1	4	yes	—
42	#14556670	C₂³	1	4	yes	—
43	C₂×C₄⋊#64408	C₂×C₄	1	4	yes	—
44	C₂×C₂²⋊#64408	—	2	2	no	—
45	C₂×C₄×#64408	—	2	2	no	—
46	C₂×C₄×#64408	—	2	1	no	—
47	C₂×C₄×#64408	—	2	1	no	—
48	C₂×C₄×#64408	—	2	1	no	—
49	C₂×C₄×#64408	C₂×C₄	1	2	yes	—
50	C₂×C₄×#64408	C₂×C₄	1	2	yes	—
51	C₂×C₄×#64408	C₂³	1	2	yes	—
52	#14556660	C₂×C₄	1	8	yes	complemented
53	#14556659	C₂×C₄	1	8	yes	complemented
54	#14556645	—	2	8	no	—
55	C₈×#64408	—	2	8	no	—
56	C₈×#64408	C₂×C₄	1	8	yes	complemented
57	C₈×#64408	C₂×C₄	1	8	yes	complemented
58	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
59	C₂×#11924012	C₂×C₄	1	2	yes	—
60	C₂×#11924011	—	2	2	no	—
61	M₁₆×D₇₃	—	2	2	no	—
62	M₁₆×D₇₃	—	2	2	no	—
63	M₁₆×D₇₃	C₂×C₄	1	4	yes	—
64	M₁₆×D₇₃	C₂³	1	4	yes	—
65	C₂²×#10596831	C₂×C₄	1	1	yes	characteristic
66	C₂×C₈×D₇₃	—	2	2	no	—
67	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
68	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
69	C₂×C₈×D₇₃	C₂×C₄	1	2	yes	—
70	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
71	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
72	C₂×C₈×D₇₃	C₂×C₄	1	2	yes	—
73	C₂×C₈×D₇₃	C₂×C₄	1	2	yes	—
74	C₂×C₈×D₇₃	C₂³	1	2	yes	—
75	#14556527	C₂×C₄	1	4	yes	complemented
76	#14556526	C₂×C₄	1	8	yes	complemented
77	C₂×M₁₆×C₇₃	C₂×C₄	1	2	yes	—
78	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
79	#108×C₇₃	C₂×C₄	1	4	yes	complemented
80	C₂²×#64408	—	2	8	no	—
81	C₂²×#64408	—	2	2	no	—
82	C₂²×#64408	—	2	2	no	—
83	C₂²×#64408	—	2	2	no	—
84	C₂²×#64408	—	2	4	no	—
85	#11924036	C₄⋊C₄	1	2	yes	—
86	#11924036	C₄⋊C₄	1	2	yes	—
87	#11924036	C₄⋊C₄	1	4	yes	—
88	#11924036	C₂²×C₄	1	4	yes	—
89	#11924036	C₂×D₄	1	2	yes	—
90	#11924036	C₂×D₄	1	2	yes	—
91	C₂×#10596833	C₄⋊C₄	1	2	yes	—
92	C₂×#10596833	C₄⋊C₄	1	2	yes	—
93	C₂×#10596833	C₄⋊C₄	1	4	yes	—
94	C₂×#10596833	C₂×Q₈	1	4	yes	—
95	C₄⋊#64408	—	2	4	no	—
96	C₄⋊#64408	C₂²×C₄	1	8	yes	—
97	C₂²⋊#64408	—	2	4	no	—
98	C₂²⋊#64408	—	2	4	no	—
99	C₄×#64408	—	2	2	no	—
100	C₄×#64408	—	2	2	no	—
101	C₄×#64408	—	2	4	no	—
102	C₄×#64408	—	2	4	no	—
103	C₄×#64408	—	2	2	no	—
104	C₄×#64408	C₂²×C₄	1	4	yes	—
105	C₂³×D₇₃	#41	1	1	yes	characteristic
106	C₂²×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
107	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
113	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
114	C₂×C₄×D₇₃	C₂×Q₈	1	1	yes	characteristic
115	C₂×C₄×D₇₃	#41	1	1	yes	characteristic
116	C₂×C₄×D₇₃	#41	1	1	yes	characteristic
117	C₂×C₄×D₇₃	#41	1	1	yes	characteristic
118	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
119	#11924012	—	2	2	no	—
120	#11924012	C₂²×C₄	1	4	yes	—
121	#11924011	—	2	4	no	—
122	#11924011	—	2	4	no	—
123	C₂×#10596831	—	2	2	no	—
124	C₂×#10596831	C₄²	1	1	yes	characteristic
125	C₂×#10596831	C₄²	1	1	yes	characteristic
126	C₂×#10596831	C₄²	1	2	yes	—
127	C₂×#10596831	C₂²×C₄	1	2	yes	—
128	C₈×D₇₃	—	2	4	no	—
129	C₈×D₇₃	—	2	4	no	—
130	C₈×D₇₃	C₄²	1	2	yes	—
131	C₈×D₇₃	C₄²	1	2	yes	—
132	C₈×D₇₃	C₄²	1	2	yes	—
133	C₈×D₇₃	C₄²	1	2	yes	—
134	C₈×D₇₃	C₂²×C₄	1	2	yes	—
135	C₈×D₇₃	C₂²×C₄	1	2	yes	—
136	C₈×D₇₃	C₂²×C₄	1	2	yes	—
137	C₈×D₇₃	C₂²×C₄	1	2	yes	—
138	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
139	M₁₆×C₇₃	—	2	2	no	—
140	M₁₆×C₇₃	C₂²×C₄	1	4	yes	—
141	C₂×C₈×C₇₃	—	2	2	no	—
142	C₂×C₈×C₇₃	C₄²	1	1	yes	characteristic
143	C₂×C₈×C₇₃	C₄²	1	1	yes	characteristic
144	C₂×C₈×C₇₃	C₄²	1	2	yes	—
145	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
146	C₂³×C₇₃	C₄×Q₈	1	1	yes	characteristic
147	C₂²×D₇₃	—	2	4	no	—
148	C₂²×D₇₃	#117	1	1	yes	characteristic
149	C₂²×D₇₃	#117	1	1	yes	characteristic
150	C₂²×D₇₃	C₄×D₄	1	1	yes	characteristic
151	C₂²×D₇₃	C₄×D₄	1	1	yes	characteristic
152	C₂²×D₇₃	C₄×Q₈	1	1	yes	characteristic
153	C₂²×D₇₃	C₂×#41	1	1	yes	characteristic
154	C₂×#64408	—	2	8	no	—
155	C₂×#64408	—	2	8	no	—
156	C₂×#64408	—	2	8	no	—
157	C₂×#64408	—	2	4	no	—
158	C₂×#64408	—	2	8	no	—
159	C₂×#64408	—	4	8	no	—
160	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
161	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
162	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
164	C₂×C₄×C₇₃	C₄×Q₈	1	1	yes	characteristic
165	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
166	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
168	C₂×Dic₇₃	C₄×Q₈	1	1	yes	characteristic
169	C₂×Dic₇₃	C₄×Q₈	1	1	yes	characteristic
170	C₂×Dic₇₃	C₄×Q₈	1	1	yes	characteristic
171	C₂×Dic₇₃	C₂²×Q₈	1	1	yes	characteristic
172	C₄×D₇₃	C₂×C₄²	1	1	yes	characteristic
173	C₄×D₇₃	C₂×C₄²	1	1	yes	characteristic
174	C₄×D₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₄×D₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
176	C₄×D₇₃	#117	1	1	yes	characteristic
177	C₄×D₇₃	#117	1	1	yes	characteristic
178	C₄×D₇₃	C₄×D₄	1	1	yes	characteristic
179	C₄×D₇₃	C₄×D₄	1	1	yes	characteristic
180	C₄×D₇₃	C₄×D₄	1	1	yes	characteristic
181	C₄×D₇₃	C₄×D₄	1	1	yes	characteristic
182	C₄×D₇₃	C₄×Q₈	1	1	yes	characteristic
183	C₄×D₇₃	C₄×Q₈	1	1	yes	characteristic
184	C₄×D₇₃	C₂³×C₄	1	1	yes	characteristic
185	C₄×D₇₃	C₂³×C₄	1	1	yes	characteristic
186	C₄×D₇₃	C₂²×D₄	1	1	yes	characteristic
187	C₄×D₇₃	C₂×#41	1	1	yes	characteristic
188	#10596833	C₂×C₄⋊C₄	1	4	yes	—
189	#10596833	C₂×C₄⋊C₄	1	4	yes	—
190	C₈×C₇₃	—	2	4	no	—
191	C₈×C₇₃	C₂×C₄²	1	2	yes	—
192	C₈×C₇₃	C₂×C₄²	1	2	yes	—
193	#10596831	—	2	4	no	—
194	#10596831	C₂×C₄²	1	2	yes	—
195	#10596831	C₂×C₄²	1	2	yes	—
196	C₂²×C₇₃	—	2	2	no	—
197	C₂²×C₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
198	C₂²×C₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
199	C₂²×C₇₃	C₂×C₄×Q₈	1	1	yes	characteristic
200	C₂×D₇₃	—	2	2	no	—
201	C₂×D₇₃	—	2	2	no	—
202	C₂×D₇₃	—	2	2	no	—
203	C₂×D₇₃	—	2	2	no	—
204	C₂×D₇₃	—	2	2	no	—
205	C₂×D₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
206	C₂×D₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
207	C₂×D₇₃	#443	1	4	yes	—
208	C₂×D₇₃	C₂×#117	1	1	yes	characteristic
209	C₂×D₇₃	C₂×C₄×D₄	1	1	yes	characteristic
210	#64408	—	2	8	no	—
211	#64408	—	4	8	no	—
212	C₄×C₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
213	C₄×C₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
214	C₄×C₇₃	C₂²×C₄²	1	1	yes	characteristic
215	C₄×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
216	Dic₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
217	Dic₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
218	Dic₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
219	Dic₇₃	C₂×C₄×Q₈	1	1	yes	characteristic
220	C₂×#1772	—	73	1	no	maximal, Sylow
221	C₂×C₇₃	—	2	1	no	—
222	C₂×C₇₃	—	2	1	no	—
223	C₂×C₇₃	#1772	1	2	yes	complemented
224	C₂×C₇₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
225	D₇₃	—	2	1	no	—
226	D₇₃	—	2	1	no	—
227	D₇₃	#1772	1	2	yes	complemented
228	D₇₃	C₂×#443	1	2	yes	—
229	C₂²×#108	—	73	1	no	—
230	C₂×#427	—	73	1	no	—
231	C₂×#405	—	73	2	no	—
232	C₂²×C₄×C₈	—	73	1	no	—
233	#1772	—	73	8	no	—
234	C₂×#339	—	73	2	no	—
235	C₇₃	C₂×#1772	1	1	yes	characteristic, complemented, Sylow
236	C₂²×M₁₆	—	73	2	no	—
237	C₂³×C₈	—	73	1	no	—
238	C₂³×C₈	—	73	1	no	—
239	C₂×#117	—	73	2	no	—
240	C₂²×C₄²	—	73	1	no	—
241	C₂×#108	—	73	2	no	—
242	C₂×#108	—	73	1	no	—
243	C₂×#108	—	73	4	no	—
244	C₂×#108	—	73	4	no	—
245	C₂×#108	#64408	1	1	yes	characteristic, complemented
246	#427	—	73	4	no	—
247	#427	—	73	4	no	—
248	C₂×#107	—	73	2	no	—
249	C₂×#106	—	73	2	no	—
250	#405	—	73	8	no	—
251	#405	—	146	4	no	—
252	C₂×#97	—	146	2	no	—
253	C₂×C₄×C₈	—	73	2	no	—
254	C₂×C₄×C₈	—	73	2	no	—
255	C₂×C₄×C₈	—	73	4	no	—
256	C₂×C₄×C₈	—	73	4	no	—
257	C₂×C₄×C₈	—	146	2	no	—
258	#339	—	73	8	no	—
259	C₂³×C₄	—	73	1	no	—
260	C₂³×C₄	—	146	1	no	—
261	C₂×M₁₆	—	73	2	no	—
262	C₂×M₁₆	—	73	4	no	—
263	C₂×M₁₆	—	73	4	no	—
264	C₂×M₁₆	—	146	2	no	—
265	C₂×M₁₆	—	146	2	no	—
266	C₂×M₁₆	—	146	2	no	—
267	C₂×M₁₆	C₂×#64408	1	2	yes	—
268	C₂²×C₈	—	73	2	no	—
269	C₂²×C₈	—	73	2	no	—
270	C₂²×C₈	—	73	2	no	—
271	C₂²×C₈	—	73	1	no	—
272	C₂²×C₈	—	73	1	no	—
273	C₂²×C₈	—	73	2	no	—
274	C₂²×C₈	—	73	2	no	—
275	C₂²×C₈	—	73	2	no	—
276	C₂²×C₈	—	73	1	no	—
277	C₂²×C₈	—	73	1	no	—
278	C₂²×C₈	—	73	1	no	—
279	C₂²×C₈	—	73	2	no	—
280	C₂²×C₈	—	73	1	no	—
281	C₂²×C₈	—	73	1	no	—
282	C₂²×C₈	—	73	2	no	—
283	C₂²×C₈	—	73	2	no	—
284	C₂²×C₈	—	73	2	no	—
285	C₂²×C₈	—	146	2	no	—
286	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
287	#117	—	73	4	no	—
288	#117	—	73	4	no	—
289	#117	—	146	2	no	—
290	#117	—	146	2	no	—
291	C₂×C₄⋊C₄	—	73	4	no	—
292	C₂×C₂²⋊C₄	—	146	2	no	—
293	C₂×C₄²	—	73	2	no	—
294	C₂×C₄²	—	73	2	no	—
295	C₂×C₄²	—	73	2	no	—
296	C₂×C₄²	—	146	2	no	—
297	C₂×C₄²	—	146	1	no	—
298	C₂×C₄²	—	146	1	no	—
299	C₂×C₄²	—	146	1	no	—
300	#108	—	73	8	no	—
301	#108	—	73	4	no	—
302	#108	C₂×#64408	1	4	yes	complemented
303	#107	—	73	8	no	—
304	#106	—	73	8	no	—
305	#97	—	146	8	no	—
306	C₄×C₈	—	73	8	no	—
307	C₄×C₈	—	73	8	no	—
308	C₄×C₈	—	146	8	no	—
309	C₂⁴	—	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	—	73	1	no	—
321	C₂²×C₄	—	73	1	no	—
322	C₂²×C₄	—	73	1	no	—
323	C₂²×C₄	—	146	4	no	—
324	C₂²×C₄	—	146	2	no	—
325	C₂²×C₄	—	146	2	no	—
326	C₂²×C₄	—	146	2	no	—
327	C₂²×C₄	—	146	8	no	—
328	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
329	M₁₆	—	2	2	no	—
330	M₁₆	—	73	4	no	—
331	M₁₆	—	146	4	no	—
332	M₁₆	—	146	4	no	—
333	M₁₆	—	146	2	no	—
334	M₁₆	C₂²×#64408	1	4	yes	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	73	2	no	—
337	C₂×C₈	—	73	2	no	—
338	C₂×C₈	—	73	4	no	—
339	C₂×C₈	—	73	4	no	—
340	C₂×C₈	—	73	2	no	—
341	C₂×C₈	—	73	2	no	—
342	C₂×C₈	—	73	4	no	—
343	C₂×C₈	—	73	4	no	—
344	C₂×C₈	—	73	2	no	—
345	C₂×C₈	—	73	2	no	—
346	C₂×C₈	—	73	2	no	—
347	C₂×C₈	—	73	1	no	—
348	C₂×C₈	—	73	1	no	—
349	C₂×C₈	—	73	2	no	—
350	C₂×C₈	—	73	2	no	—
351	C₂×C₈	—	73	2	no	—
352	C₂×C₈	—	73	2	no	—
353	C₂×C₈	—	73	2	no	—
354	C₂×C₈	—	73	2	no	—
355	C₂×C₈	—	73	2	no	—
356	C₂×C₈	—	73	2	no	—
357	C₂×C₈	—	73	2	no	—
358	C₂×C₈	—	146	4	no	—
359	C₂×C₈	—	146	4	no	—
360	C₂×C₈	—	146	2	no	—
361	C₂×C₈	C₄×#64408	1	1	yes	characteristic
362	C₂×C₈	C₄×#64408	1	1	yes	characteristic
363	C₂×C₈	C₄×#64408	1	2	yes	—
364	C₂×C₈	C₂²×#64408	1	2	yes	—
365	C₄⋊C₄	—	73	8	no	—
366	C₄⋊C₄	—	146	4	no	—
367	C₂²⋊C₄	—	146	4	no	—
368	C₂²⋊C₄	—	146	4	no	—
369	C₄²	—	73	4	no	—
370	C₄²	—	146	4	no	—
371	C₄²	—	146	2	no	—
372	C₄²	—	146	2	no	—
373	C₄²	—	146	2	no	—
374	C₄²	—	146	4	no	—
375	C₂³	—	73	1	no	—
376	C₂³	—	73	1	no	—
377	C₂³	—	73	1	no	—
378	C₂³	—	73	1	no	—
379	C₂³	—	73	1	no	—
380	C₂³	—	73	1	no	—
381	C₂³	—	146	4	no	—
382	C₂³	Q₈×#64408	1	1	yes	characteristic
383	C₂×C₄	—	292	8	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	—	73	1	no	—
402	C₂×C₄	—	73	1	no	—
403	C₂×C₄	—	73	1	no	—
404	C₂×C₄	—	73	1	no	—
405	C₂×C₄	—	73	1	no	—
406	C₂×C₄	—	146	8	no	—
407	C₂×C₄	—	146	4	no	—
408	C₂×C₄	—	146	8	no	—
409	C₂×C₄	—	146	8	no	—
410	C₂×C₄	—	146	8	no	—
411	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
412	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
413	C₂×C₄	D₄×#64408	1	1	yes	characteristic
414	C₂×C₄	D₄×#64408	1	1	yes	characteristic
415	C₂×C₄	Q₈×#64408	1	1	yes	characteristic
416	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
417	C₈	—	2	4	no	—
418	C₈	—	73	4	no	—
419	C₈	—	73	4	no	—
420	C₈	—	73	2	no	—
421	C₈	—	73	2	no	—
422	C₈	—	146	4	no	—
423	C₈	C₂×C₄×#64408	1	2	yes	—
424	C₈	C₂×C₄×#64408	1	2	yes	—
425	C₂²	—	2	2	no	—
426	C₂²	—	73	1	no	—
427	C₂²	—	73	1	no	—
428	C₂²	—	73	4	no	—
429	C₂²	—	73	1	no	—
430	C₂²	—	73	1	no	—
431	C₂²	—	146	2	no	—
432	C₂²	—	146	2	no	—
433	C₂²	—	146	2	no	—
434	C₂²	—	146	2	no	—
435	C₂²	—	146	2	no	—
436	C₂²	C₄⋊C₄×#64408	1	1	yes	characteristic
437	C₂²	C₄⋊C₄×#64408	1	1	yes	characteristic
438	C₂²	C₂×Q₈×#64408	1	1	yes	characteristic
439	C₄	—	292	8	no	—
440	C₄	—	73	1	no	—
441	C₄	—	73	1	no	—
442	C₄	—	73	1	no	—
443	C₄	—	73	1	no	—
444	C₄	—	146	8	no	—
445	C₄	C₄⋊C₄×#64408	1	1	yes	characteristic
446	C₄	C₄⋊C₄×#64408	1	1	yes	characteristic
447	C₄	C₂²×C₄×#64408	1	1	yes	characteristic
448	C₄	C₂×D₄×#64408	1	1	yes	characteristic
449	C₂	—	2	1	no	—
450	C₂	—	2	1	no	—
451	C₂	—	73	2	no	—
452	C₂	—	73	2	no	—
453	C₂	—	146	1	no	—
454	C₂	—	146	1	no	—
455	C₂	#22625736	1	2	yes	direct product factor
456	C₂	C₂×C₄⋊C₄×#64408	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₄×#64408
commutator	C₄×C₇₃	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#64408
Fitting	C₂×#108×C₇₃	C₄
socle	C₂²×C₇₃	C₄×C₄⋊C₄
prime radical	C₂³×D₇₃	#41
cosocle	C₂×C₄×D₇₃	C₂⁴
hypercenter	C₂×#108	#64408
hypocenter	C₇₃	C₂×#1772
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#108

Complements

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

N	H ≅ G/N	type
4. #22625736	C₂	direct (N × H)
10. #17989597	C₄	semidirect
12. C₂×#14556660	C₄	semidirect
13. C₂×#14556659	C₄	semidirect
18. C₂×C₈×#64408	C₄	semidirect
19. C₂×C₈×#64408	C₄	semidirect
20. C₂×C₈×#64408	C₄	semidirect
25. C₂×#14556527	C₄	semidirect
26. C₂×#14556526	C₄	semidirect
27. #108×D₇₃	C₄	semidirect
29. C₂×#108×C₇₃	C₄	semidirect
52. #14556660	C₂×C₄	semidirect
53. #14556659	C₂×C₄	semidirect
56. C₈×#64408	C₂×C₄	semidirect
57. C₈×#64408	C₂×C₄	semidirect
75. #14556527	C₂×C₄	semidirect
76. #14556526	C₂×C₄	semidirect
79. #108×C₇₃	C₂×C₄	semidirect
223. C₂×C₇₃	#1772	semidirect
227. D₇₃	#1772	semidirect
235. C₇₃	C₂×#1772	semidirect
245. C₂×#108	#64408	semidirect
302. #108	C₂×#64408	semidirect
455. C₂	#22625736	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×#17989597	2
C₂×#17989553	2
C₂²×C₈×#64408	2
#22625736	2
C₂×#17989459	2
C₂×#108×D₇₃	2
C₂×#1772	73

Subgroups — C2×#22625736 #34020235

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22625736 #34020235