Subgroups — #72234316

Order 2048.

886 conjugacy classes of subgroups.

The subgroup lattice has 595 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72231936	C₂	1	4	yes	maximal, complemented
2	#72231935	C₂	1	4	yes	maximal, complemented
3	#72231929	C₂	1	4	yes	maximal, complemented
4	#72231926	C₂	1	1	yes	maximal, characteristic
5	C₂²×#7099	C₂	1	1	yes	maximal, characteristic
6	#72231858	C₂	1	1	yes	maximal, characteristic
7	#512728	C₄	1	1	yes	characteristic
8	#512728	C₄	1	1	yes	characteristic
9	#483346	—	2	1	no	—
10	C₂²×#1367	—	2	1	no	—
11	C₂²×#1311	C₂²	1	1	yes	characteristic
12	#149513	C₄	1	2	yes	—
13	#149513	C₄	1	2	yes	—
14	#149513	C₂²	1	2	yes	—
15	#149513	C₂²	1	2	yes	—
16	#149502	C₄	1	2	yes	—
17	#149495	C₂²	1	2	yes	—
18	#122922	—	2	1	no	—
19	#122922	C₂²	1	2	yes	—
20	#122921	—	2	1	no	—
21	#122921	C₂²	1	2	yes	—
22	#122919	—	2	1	no	—
23	#122919	C₂²	1	2	yes	—
24	C₂×#7099	—	2	1	no	—
25	C₂×#7099	—	2	1	no	—
26	C₂×#7099	—	2	1	no	—
27	C₂×#7099	C₂²	1	2	yes	—
28	C₂×#7099	C₂²	1	2	yes	—
29	C₂×#7099	C₂²	1	2	yes	—
30	#93877	C₂²	1	16	yes	complemented
31	#33418	—	4	1	no	—
32	C₂²×C₄⋊C₁₆	—	4	1	no	—
33	C₂²×C₄×C₁₆	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₄×C₁₆	Q₈	1	1	yes	characteristic
35	C₂²×C₈²	D₄	1	1	yes	characteristic
36	#13640	C₂×C₄	1	2	yes	—
37	#13640	C₂×C₄	1	2	yes	—
38	#13640	C₂×C₄	1	2	yes	—
39	#13640	C₂×C₄	1	2	yes	—
40	#13639	—	2	1	no	—
41	#13639	—	2	1	no	—
42	#13639	C₈	1	2	yes	—
43	#13639	C₈	1	2	yes	—
44	#13627	—	2	1	no	—
45	#13627	C₈	1	2	yes	—
46	#13553	—	2	1	no	—
47	#13553	C₈	1	2	yes	—
48	C₄×M₆₄	C₂×C₄	1	2	yes	—
49	C₄×M₆₄	C₂×C₄	1	2	yes	—
50	#12013	—	2	2	no	—
51	#12013	—	4	1	no	—
52	#12012	—	2	2	no	—
53	#12012	—	4	1	no	—
54	#12004	—	4	1	no	—
55	#11996	—	2	2	no	—
56	C₂×#1367	—	2	2	no	—
57	C₂×#1367	—	2	2	no	—
58	C₂×#1367	—	2	2	no	—
59	C₂×#1367	—	4	1	no	—
60	C₂×#1367	—	4	1	no	—
61	C₂×#1367	—	4	1	no	—
62	C₂×#1311	C₂×C₄	1	1	yes	characteristic
63	C₂×#1311	C₂×C₄	1	1	yes	characteristic
64	C₂×#1311	C₂×C₄	1	1	yes	characteristic
65	C₂×#1311	D₄	1	1	yes	characteristic
66	C₂×#1311	D₄	1	1	yes	characteristic
67	C₂×#1311	D₄	1	1	yes	characteristic
68	C₂×#1311	Q₈	1	1	yes	characteristic
69	C₂×#1311	Q₈	1	1	yes	characteristic
70	C₂×#1311	Q₈	1	1	yes	characteristic
71	C₂×#1311	C₂³	1	1	yes	characteristic
72	C₂×#1311	C₂³	1	1	yes	characteristic
73	C₂×#1311	C₂³	1	1	yes	characteristic
74	#7332	C₂×C₄	1	4	yes	—
75	#7332	C₂×C₄	1	4	yes	—
76	#7330	C₂×C₄	1	4	yes	—
77	#7330	C₂³	1	4	yes	—
78	#7099	—	2	2	no	—
79	#7099	—	2	2	no	—
80	#7099	—	2	2	no	—
81	#7099	—	2	2	no	—
82	#7099	—	2	2	no	—
83	#7099	—	2	2	no	—
84	#7099	C₂³	1	4	yes	—
85	#7099	C₂³	1	4	yes	—
86	C₂³×C₁₆	—	2	1	no	—
87	C₂³×C₁₆	—	8	1	no	—
88	C₂³×C₁₆	C₂×C₈	1	1	yes	characteristic
89	C₂³×C₁₆	M₁₆	1	1	yes	characteristic
90	C₂²×C₄×C₈	C₄⋊C₄	1	1	yes	characteristic
91	C₂²×C₄×C₈	SD₁₆	1	1	yes	characteristic
92	C₂²×C₄×C₈	SD₁₆	1	1	yes	characteristic
93	C₂×M₆₄	—	2	2	no	—
94	C₂×M₆₄	C₂×C₈	1	4	yes	—
95	#2163	—	4	2	no	—
96	#2163	—	8	1	no	—
97	#2162	—	4	2	no	—
98	#2162	—	8	1	no	—
99	#2150	—	4	2	no	—
100	C₂×C₄⋊C₁₆	—	4	2	no	—
101	C₂×C₄⋊C₁₆	—	4	2	no	—
102	C₂×C₄⋊C₁₆	—	4	2	no	—
103	C₂×C₄⋊C₁₆	—	8	1	no	—
104	C₂×C₄⋊C₁₆	—	8	1	no	—
105	C₂×C₄⋊C₁₆	—	8	1	no	—
106	#2112	—	8	1	no	—
107	C₄×M₃₂	—	8	1	no	—
108	C₂×C₄×C₁₆	—	2	1	no	—
109	C₂×C₄×C₁₆	—	2	1	no	—
110	C₂×C₄×C₁₆	—	2	1	no	—
111	C₂×C₄×C₁₆	C₄⋊C₄	1	1	yes	characteristic
112	C₂×C₄×C₁₆	C₄⋊C₄	1	1	yes	characteristic
113	C₂×C₄×C₁₆	C₄⋊C₄	1	1	yes	characteristic
114	C₂×C₄×C₁₆	C₄⋊C₄	1	1	yes	characteristic
115	C₂×C₄×C₁₆	C₄⋊C₄	1	1	yes	characteristic
116	C₂×C₄×C₁₆	C₄⋊C₄	1	1	yes	characteristic
117	C₂×C₄×C₁₆	C₂×C₈	1	1	yes	characteristic
118	C₂×C₄×C₁₆	C₂×C₈	1	1	yes	characteristic
119	C₂×C₄×C₁₆	C₂×C₈	1	1	yes	characteristic
120	C₂×C₄×C₁₆	M₁₆	1	1	yes	characteristic
121	C₂×C₄×C₁₆	M₁₆	1	1	yes	characteristic
122	C₂×C₄×C₁₆	M₁₆	1	1	yes	characteristic
123	C₂×C₄×C₁₆	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₄×C₁₆	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₄×C₁₆	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₄×C₁₆	C₂×Q₈	1	1	yes	characteristic
127	C₂×C₄×C₁₆	C₂×Q₈	1	1	yes	characteristic
128	C₂×C₄×C₁₆	C₂×Q₈	1	1	yes	characteristic
129	C₂×C₈²	C₄⋊C₄	1	1	yes	characteristic
130	C₂×C₈²	C₄⋊C₄	1	1	yes	characteristic
131	C₂×C₈²	C₄⋊C₄	1	1	yes	characteristic
132	C₂×C₈²	SD₁₆	1	1	yes	characteristic
133	C₂×C₈²	SD₁₆	1	1	yes	characteristic
134	C₂×C₈²	SD₁₆	1	1	yes	characteristic
135	C₂×C₈²	SD₁₆	1	1	yes	characteristic
136	C₂×C₈²	SD₁₆	1	1	yes	characteristic
137	C₂×C₈²	SD₁₆	1	1	yes	characteristic
138	C₂×C₈²	C₂×D₄	1	1	yes	characteristic
139	C₂×C₈²	C₂×D₄	1	1	yes	characteristic
140	C₂×C₈²	C₂×D₄	1	1	yes	characteristic
141	C₄⋊C₃₂	—	2	2	no	—
142	C₄⋊C₃₂	—	2	2	no	—
143	C₄⋊C₃₂	C₂×C₈	1	4	yes	—
144	C₄⋊C₃₂	C₂×C₈	1	4	yes	—
145	C₂²⋊C₃₂	—	2	2	no	—
146	C₂²⋊C₃₂	—	2	2	no	—
147	C₂²⋊C₃₂	C₂×C₈	1	4	yes	—
148	C₂²⋊C₃₂	C₂×C₈	1	4	yes	—
149	#1397	C₂²×C₄	1	4	yes	—
150	#1397	C₂²×C₄	1	4	yes	—
151	C₄×C₃₂	—	2	2	no	—
152	C₄×C₃₂	C₂×C₈	1	4	yes	—
153	#1370	—	4	2	no	—
154	#1370	—	4	2	no	—
155	#1367	—	2	4	no	—
156	#1367	—	2	4	no	—
157	#1367	—	4	2	no	—
158	#1367	—	4	2	no	—
159	#1367	—	4	2	no	—
160	#1367	—	4	2	no	—
161	#1311	C₄⋊C₄	1	1	yes	characteristic
162	#1311	C₄⋊C₄	1	1	yes	characteristic
163	#1311	C₄⋊C₄	1	1	yes	characteristic
164	#1311	C₄⋊C₄	1	1	yes	characteristic
165	#1311	C₄⋊C₄	1	1	yes	characteristic
166	#1311	C₄⋊C₄	1	1	yes	characteristic
167	#1311	C₂²×C₄	1	1	yes	characteristic
168	#1311	C₂²×C₄	1	1	yes	characteristic
169	#1311	C₂²×C₄	1	1	yes	characteristic
170	#1311	C₂×D₄	1	1	yes	characteristic
171	#1311	C₂×D₄	1	1	yes	characteristic
172	#1311	C₂×D₄	1	1	yes	characteristic
173	#1311	C₂×Q₈	1	1	yes	characteristic
174	#1311	C₂×Q₈	1	1	yes	characteristic
175	#1311	C₂×Q₈	1	1	yes	characteristic
176	#1311	C₂⁴	1	1	yes	characteristic
177	C₂³×C₈	—	2	1	no	—
178	C₂³×C₈	—	2	1	no	—
179	C₂³×C₈	C₄⋊C₈	1	1	yes	characteristic
180	C₂³×C₈	#108	1	1	yes	characteristic
181	C₂²×C₄²	#106	1	1	yes	characteristic
182	C₂×M₃₂	—	8	2	no	—
183	C₂²×C₁₆	—	2	1	no	—
184	C₂²×C₁₆	—	2	4	no	—
185	C₂²×C₁₆	—	2	1	no	—
186	C₂²×C₁₆	—	2	1	no	—
187	C₂²×C₁₆	—	2	1	no	—
188	C₂²×C₁₆	—	2	1	no	—
189	C₂²×C₁₆	—	2	1	no	—
190	C₂²×C₁₆	—	4	2	no	—
191	C₂²×C₁₆	—	4	4	no	—
192	C₂²×C₁₆	—	8	2	no	—
193	C₂²×C₁₆	—	8	2	no	—
194	C₂²×C₁₆	—	8	2	no	—
195	C₂²×C₁₆	—	16	4	no	—
196	C₂²×C₁₆	C₄⋊C₈	1	1	yes	characteristic
197	C₂²×C₁₆	C₄⋊C₈	1	1	yes	characteristic
198	C₂²×C₁₆	C₄⋊C₈	1	1	yes	characteristic
199	C₂²×C₁₆	C₄⋊C₈	1	1	yes	characteristic
200	C₂²×C₁₆	C₄⋊C₈	1	1	yes	characteristic
201	C₂²×C₁₆	C₄⋊C₈	1	1	yes	characteristic
202	C₂²×C₁₆	C₂²×C₈	1	1	yes	characteristic
203	C₂²×C₁₆	C₂²×C₈	1	1	yes	characteristic
204	C₂²×C₁₆	C₂²×C₈	1	1	yes	characteristic
205	C₂²×C₁₆	C₂×M₁₆	1	1	yes	characteristic
206	C₂²×C₁₆	C₂×M₁₆	1	1	yes	characteristic
207	C₂²×C₁₆	C₂×M₁₆	1	1	yes	characteristic
208	C₂×C₄×C₈	—	2	1	no	—
209	C₂×C₄×C₈	—	2	1	no	—
210	C₂×C₄×C₈	—	2	1	no	—
211	C₂×C₄×C₈	—	2	1	no	—
212	C₂×C₄×C₈	—	2	1	no	—
213	C₂×C₄×C₈	—	2	1	no	—
214	C₂×C₄×C₈	C₄⋊C₈	1	1	yes	characteristic
215	C₂×C₄×C₈	C₄⋊C₈	1	1	yes	characteristic
216	C₂×C₄×C₈	C₄⋊C₈	1	1	yes	characteristic
217	C₂×C₄×C₈	#106	1	1	yes	characteristic
218	C₂×C₄×C₈	#106	1	1	yes	characteristic
219	C₂×C₄×C₈	#106	1	1	yes	characteristic
220	C₂×C₄×C₈	#106	1	1	yes	characteristic
221	C₂×C₄×C₈	#106	1	1	yes	characteristic
222	C₂×C₄×C₈	#106	1	1	yes	characteristic
223	C₂×C₄×C₈	#106	1	1	yes	characteristic
224	C₂×C₄×C₈	#106	1	1	yes	characteristic
225	C₂×C₄×C₈	#106	1	1	yes	characteristic
226	C₂×C₄×C₈	#108	1	1	yes	characteristic
227	C₂×C₄×C₈	#108	1	1	yes	characteristic
228	C₂×C₄×C₈	#108	1	1	yes	characteristic
229	C₂×C₄×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
230	C₂×C₄×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
231	C₂×C₄×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
232	C₂×C₄×C₈	C₂×SD₁₆	1	1	yes	characteristic
233	C₂×C₄×C₈	C₂×SD₁₆	1	1	yes	characteristic
234	C₂×C₄×C₈	C₂×SD₁₆	1	1	yes	characteristic
235	C₂×C₄×C₈	C₂×SD₁₆	1	1	yes	characteristic
236	C₂×C₄×C₈	C₂×SD₁₆	1	1	yes	characteristic
237	C₂×C₄×C₈	C₂×SD₁₆	1	1	yes	characteristic
238	M₆₄	—	2	8	no	—
239	M₆₄	—	4	4	no	—
240	C₂×C₃₂	—	2	4	no	—
241	C₂×C₃₂	C₂²×C₈	1	8	yes	—
242	C₄⋊C₁₆	—	4	4	no	—
243	C₄⋊C₁₆	—	4	4	no	—
244	C₄⋊C₁₆	—	8	2	no	—
245	C₄⋊C₁₆	—	8	2	no	—
246	C₄⋊C₁₆	—	8	2	no	—
247	C₄⋊C₁₆	—	8	2	no	—
248	C₂²⋊C₁₆	—	8	2	no	—
249	C₂²⋊C₁₆	—	8	2	no	—
250	#346	—	8	2	no	—
251	C₄×C₁₆	—	2	1	no	—
252	C₄×C₁₆	—	2	1	no	—
253	C₄×C₁₆	—	2	1	no	—
254	C₄×C₁₆	—	2	1	no	—
255	C₄×C₁₆	—	2	1	no	—
256	C₄×C₁₆	—	2	1	no	—
257	C₄×C₁₆	—	8	2	no	—
258	C₄×C₁₆	C₄⋊C₈	1	1	yes	characteristic
259	C₄×C₁₆	C₄⋊C₈	1	1	yes	characteristic
260	C₄×C₁₆	C₄⋊C₈	1	1	yes	characteristic
261	C₄×C₁₆	C₄⋊C₈	1	1	yes	characteristic
262	C₄×C₁₆	C₄⋊C₈	1	1	yes	characteristic
263	C₄×C₁₆	C₄⋊C₈	1	1	yes	characteristic
264	C₄×C₁₆	C₂×C₄⋊C₄	1	1	yes	characteristic
265	C₄×C₁₆	C₂×C₄⋊C₄	1	1	yes	characteristic
266	C₄×C₁₆	C₂×C₄⋊C₄	1	1	yes	characteristic
267	C₄×C₁₆	C₂×C₄⋊C₄	1	1	yes	characteristic
268	C₄×C₁₆	C₂×C₄⋊C₄	1	1	yes	characteristic
269	C₄×C₁₆	C₂×C₄⋊C₄	1	1	yes	characteristic
270	C₄×C₁₆	C₂²×C₈	1	1	yes	characteristic
271	C₄×C₁₆	C₂²×C₈	1	1	yes	characteristic
272	C₄×C₁₆	C₂²×C₈	1	1	yes	characteristic
273	C₄×C₁₆	C₂×M₁₆	1	1	yes	characteristic
274	C₄×C₁₆	C₂×M₁₆	1	1	yes	characteristic
275	C₄×C₁₆	C₂×M₁₆	1	1	yes	characteristic
276	C₄×C₁₆	C₂³×C₄	1	1	yes	characteristic
277	C₄×C₁₆	C₂²×Q₈	1	1	yes	characteristic
278	C₈²	#106	1	1	yes	characteristic
279	C₈²	#106	1	1	yes	characteristic
280	C₈²	#106	1	1	yes	characteristic
281	C₈²	#106	1	1	yes	characteristic
282	C₈²	#106	1	1	yes	characteristic
283	C₈²	#106	1	1	yes	characteristic
284	C₈²	C₂×C₄⋊C₄	1	1	yes	characteristic
285	C₈²	C₂×C₄⋊C₄	1	1	yes	characteristic
286	C₈²	C₂×C₄⋊C₄	1	1	yes	characteristic
287	C₈²	C₂×SD₁₆	1	1	yes	characteristic
288	C₈²	C₂×SD₁₆	1	1	yes	characteristic
289	C₈²	C₂×SD₁₆	1	1	yes	characteristic
290	C₈²	C₂×SD₁₆	1	1	yes	characteristic
291	C₈²	C₂×SD₁₆	1	1	yes	characteristic
292	C₈²	C₂×SD₁₆	1	1	yes	characteristic
293	C₈²	C₂²×D₄	1	1	yes	characteristic
294	C₂³×C₄	#334	1	1	yes	characteristic
295	C₂³×C₄	#365	1	1	yes	characteristic
296	C₂³×C₄	#365	1	1	yes	characteristic
297	C₂²×C₈	—	2	2	no	—
298	C₂²×C₈	—	2	2	no	—
299	C₂²×C₈	—	2	1	no	—
300	C₂²×C₈	—	2	1	no	—
301	C₂²×C₈	—	2	1	no	—
302	C₂²×C₈	—	2	1	no	—
303	C₂²×C₈	—	2	1	no	—
304	C₂²×C₈	—	2	1	no	—
305	C₂²×C₈	—	2	1	no	—
306	C₂²×C₈	—	2	1	no	—
307	C₂²×C₈	—	2	1	no	—
308	C₂²×C₈	—	2	1	no	—
309	C₂²×C₈	—	2	1	no	—
310	C₂²×C₈	—	2	1	no	—
311	C₂²×C₈	—	4	2	no	—
312	C₂²×C₈	—	4	4	no	—
313	C₂²×C₈	—	8	2	no	—
314	C₂²×C₈	#334	1	1	yes	characteristic
315	C₂²×C₈	#334	1	1	yes	characteristic
316	C₂²×C₈	#334	1	1	yes	characteristic
317	C₂²×C₈	#334	1	1	yes	characteristic
318	C₂²×C₈	#334	1	1	yes	characteristic
319	C₂²×C₈	#334	1	1	yes	characteristic
320	C₂²×C₈	C₂×C₄⋊C₈	1	1	yes	characteristic
321	C₂²×C₈	C₂×C₄⋊C₈	1	1	yes	characteristic
322	C₂²×C₈	C₂×C₄⋊C₈	1	1	yes	characteristic
323	C₂²×C₈	C₂×#108	1	1	yes	characteristic
324	C₂²×C₈	C₂×#108	1	1	yes	characteristic
325	C₂²×C₈	C₂×#108	1	1	yes	characteristic
326	C₂×C₄²	#334	1	1	yes	characteristic
327	C₂×C₄²	#334	1	1	yes	characteristic
328	C₂×C₄²	#334	1	1	yes	characteristic
329	C₂×C₄²	#365	1	1	yes	characteristic
330	C₂×C₄²	#365	1	1	yes	characteristic
331	C₂×C₄²	#365	1	1	yes	characteristic
332	C₂×C₄²	#365	1	1	yes	characteristic
333	C₂×C₄²	#365	1	1	yes	characteristic
334	C₂×C₄²	#365	1	1	yes	characteristic
335	C₂×C₄²	C₂×#106	1	1	yes	characteristic
336	C₂×C₄²	C₂×#106	1	1	yes	characteristic
337	C₂×C₄²	C₂×#106	1	1	yes	characteristic
338	M₃₂	—	16	4	no	—
339	C₂×C₁₆	—	2	4	no	—
340	C₂×C₁₆	—	2	1	no	—
341	C₂×C₁₆	—	2	1	no	—
342	C₂×C₁₆	—	2	2	no	—
343	C₂×C₁₆	—	2	2	no	—
344	C₂×C₁₆	—	2	2	no	—
345	C₂×C₁₆	—	2	2	no	—
346	C₂×C₁₆	—	2	2	no	—
347	C₂×C₁₆	—	2	2	no	—
348	C₂×C₁₆	—	2	2	no	—
349	C₂×C₁₆	—	2	1	no	—
350	C₂×C₁₆	—	2	1	no	—
351	C₂×C₁₆	—	4	1	no	—
352	C₂×C₁₆	—	4	1	no	—
353	C₂×C₁₆	—	4	1	no	—
354	C₂×C₁₆	—	4	1	no	—
355	C₂×C₁₆	—	4	2	no	—
356	C₂×C₁₆	—	4	2	no	—
357	C₂×C₁₆	—	4	2	no	—
358	C₂×C₁₆	—	4	2	no	—
359	C₂×C₁₆	—	4	2	no	—
360	C₂×C₁₆	—	8	4	no	—
361	C₂×C₁₆	—	8	4	no	—
362	C₂×C₁₆	—	16	4	no	—
363	C₂×C₁₆	—	16	4	no	—
364	C₂×C₁₆	—	16	4	no	—
365	C₂×C₁₆	C₂×C₄⋊C₈	1	1	yes	characteristic
366	C₂×C₁₆	C₂×C₄⋊C₈	1	1	yes	characteristic
367	C₂×C₁₆	C₂×C₄⋊C₈	1	1	yes	characteristic
368	C₂×C₁₆	C₂×C₄⋊C₈	1	1	yes	characteristic
369	C₂×C₁₆	C₂×C₄⋊C₈	1	1	yes	characteristic
370	C₂×C₁₆	C₂×C₄⋊C₈	1	1	yes	characteristic
371	C₂×C₁₆	#504	1	4	yes	—
372	C₂×C₁₆	C₂³×C₈	1	1	yes	characteristic
373	C₂×C₁₆	C₂²×M₁₆	1	1	yes	characteristic
374	C₄×C₈	—	2	1	no	—
375	C₄×C₈	—	2	1	no	—
376	C₄×C₈	—	2	1	no	—
377	C₄×C₈	—	2	1	no	—
378	C₄×C₈	—	2	1	no	—
379	C₄×C₈	—	2	1	no	—
380	C₄×C₈	—	2	1	no	—
381	C₄×C₈	—	2	1	no	—
382	C₄×C₈	—	2	1	no	—
383	C₄×C₈	—	2	1	no	—
384	C₄×C₈	—	2	1	no	—
385	C₄×C₈	—	2	1	no	—
386	C₄×C₈	#334	1	1	yes	characteristic
387	C₄×C₈	#334	1	1	yes	characteristic
388	C₄×C₈	#334	1	1	yes	characteristic
389	C₄×C₈	#334	1	1	yes	characteristic
390	C₄×C₈	#334	1	1	yes	characteristic
391	C₄×C₈	#334	1	1	yes	characteristic
392	C₄×C₈	C₂×C₄⋊C₈	1	1	yes	characteristic
393	C₄×C₈	C₂×C₄⋊C₈	1	1	yes	characteristic
394	C₄×C₈	C₂×C₄⋊C₈	1	1	yes	characteristic
395	C₄×C₈	C₂×#106	1	1	yes	characteristic
396	C₄×C₈	C₂×#106	1	1	yes	characteristic
397	C₄×C₈	C₂×#106	1	1	yes	characteristic
398	C₄×C₈	C₂×#106	1	1	yes	characteristic
399	C₄×C₈	C₂×#106	1	1	yes	characteristic
400	C₄×C₈	C₂×#106	1	1	yes	characteristic
401	C₄×C₈	C₂×#106	1	1	yes	characteristic
402	C₄×C₈	C₂×#106	1	1	yes	characteristic
403	C₄×C₈	C₂×#106	1	1	yes	characteristic
404	C₄×C₈	C₂×#108	1	1	yes	characteristic
405	C₄×C₈	C₂×#108	1	1	yes	characteristic
406	C₄×C₈	C₂×#108	1	1	yes	characteristic
407	C₄×C₈	C₂²×C₄⋊C₄	1	1	yes	characteristic
408	C₄×C₈	C₂²×SD₁₆	1	1	yes	characteristic
409	C₄×C₈	C₂²×SD₁₆	1	1	yes	characteristic
410	C₃₂	—	2	8	no	—
411	C₃₂	—	4	4	no	—
412	C₂⁴	#1368	1	1	yes	characteristic
413	C₂²×C₄	—	2	4	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	4	2	no	—
417	C₂²×C₄	#1368	1	1	yes	characteristic
418	C₂²×C₄	#1368	1	1	yes	characteristic
419	C₂²×C₄	#1368	1	1	yes	characteristic
420	C₂²×C₄	#1368	1	1	yes	characteristic
421	C₂²×C₄	#1368	1	1	yes	characteristic
422	C₂²×C₄	#1368	1	1	yes	characteristic
423	C₂²×C₄	#1368	1	1	yes	characteristic
424	C₂²×C₄	#1368	1	1	yes	characteristic
425	C₂²×C₄	#1368	1	1	yes	characteristic
426	C₂²×C₄	C₂×#334	1	1	yes	characteristic
427	C₂²×C₄	C₂×#334	1	1	yes	characteristic
428	C₂²×C₄	C₂×#334	1	1	yes	characteristic
429	C₂²×C₄	C₂×#365	1	1	yes	characteristic
430	C₂²×C₄	C₂×#365	1	1	yes	characteristic
431	C₂²×C₄	C₂×#365	1	1	yes	characteristic
432	C₂²×C₄	C₂×#365	1	1	yes	characteristic
433	C₂²×C₄	C₂×#365	1	1	yes	characteristic
434	C₂²×C₄	C₂×#365	1	1	yes	characteristic
435	C₂×C₈	—	2	2	no	—
436	C₂×C₈	—	2	2	no	—
437	C₂×C₈	—	2	2	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	2	no	—
443	C₂×C₈	—	2	2	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	4	1	no	—
453	C₂×C₈	—	4	1	no	—
454	C₂×C₈	—	4	1	no	—
455	C₂×C₈	—	4	1	no	—
456	C₂×C₈	—	4	2	no	—
457	C₂×C₈	—	4	2	no	—
458	C₂×C₈	—	4	2	no	—
459	C₂×C₈	—	4	2	no	—
460	C₂×C₈	—	4	2	no	—
461	C₂×C₈	—	4	2	no	—
462	C₂×C₈	—	4	2	no	—
463	C₂×C₈	—	4	2	no	—
464	C₂×C₈	—	8	1	no	—
465	C₂×C₈	—	8	1	no	—
466	C₂×C₈	—	8	1	no	—
467	C₂×C₈	—	8	1	no	—
468	C₂×C₈	C₂×#334	1	1	yes	characteristic
469	C₂×C₈	C₂×#334	1	1	yes	characteristic
470	C₂×C₈	C₂×#334	1	1	yes	characteristic
471	C₂×C₈	C₂×#334	1	1	yes	characteristic
472	C₂×C₈	C₂×#334	1	1	yes	characteristic
473	C₂×C₈	C₂×#334	1	1	yes	characteristic
474	C₂×C₈	#2151	1	2	yes	—
475	C₂×C₈	#2153	1	2	yes	—
476	C₂×C₈	C₂²×C₄⋊C₈	1	1	yes	characteristic
477	C₂×C₈	C₂²×#108	1	1	yes	characteristic
478	C₄²	#1368	1	1	yes	characteristic
479	C₄²	#1368	1	1	yes	characteristic
480	C₄²	#1368	1	1	yes	characteristic
481	C₄²	#1368	1	1	yes	characteristic
482	C₄²	#1368	1	1	yes	characteristic
483	C₄²	#1368	1	1	yes	characteristic
484	C₄²	C₂×#334	1	1	yes	characteristic
485	C₄²	C₂×#334	1	1	yes	characteristic
486	C₄²	C₂×#334	1	1	yes	characteristic
487	C₄²	C₂×#365	1	1	yes	characteristic
488	C₄²	C₂×#365	1	1	yes	characteristic
489	C₄²	C₂×#365	1	1	yes	characteristic
490	C₄²	C₂×#365	1	1	yes	characteristic
491	C₄²	C₂×#365	1	1	yes	characteristic
492	C₄²	C₂×#365	1	1	yes	characteristic
493	C₄²	C₂²×#106	1	1	yes	characteristic
494	C₁₆	—	2	2	no	—
495	C₁₆	—	2	2	no	—
496	C₁₆	—	2	1	no	—
497	C₁₆	—	2	1	no	—
498	C₁₆	—	2	1	no	—
499	C₁₆	—	2	1	no	—
500	C₁₆	—	2	1	no	—
501	C₁₆	—	2	1	no	—
502	C₁₆	—	4	1	no	—
503	C₁₆	—	4	1	no	—
504	C₁₆	—	16	4	no	—
505	C₁₆	—	16	4	no	—
506	C₁₆	#2151	1	2	yes	—
507	C₁₆	C₂×#504	1	2	yes	—
508	C₂³	—	2	2	no	—
509	C₂³	—	2	2	no	—
510	C₂³	—	2	2	no	—
511	C₂³	C₂×#1368	1	1	yes	characteristic
512	C₂³	C₂×#1368	1	1	yes	characteristic
513	C₂³	C₂×#1368	1	1	yes	characteristic
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	#7457	1	4	yes	—
533	C₂×C₄	#11997	1	2	yes	—
534	C₂×C₄	C₂×#1368	1	1	yes	characteristic
535	C₂×C₄	C₂×#1368	1	1	yes	characteristic
536	C₂×C₄	C₂×#1368	1	1	yes	characteristic
537	C₂×C₄	C₂×#1368	1	1	yes	characteristic
538	C₂×C₄	C₂×#1368	1	1	yes	characteristic
539	C₂×C₄	C₂×#1368	1	1	yes	characteristic
540	C₂×C₄	C₂×#1368	1	1	yes	characteristic
541	C₂×C₄	C₂×#1368	1	1	yes	characteristic
542	C₂×C₄	C₂×#1368	1	1	yes	characteristic
543	C₂×C₄	#12002	1	2	yes	—
544	C₂×C₄	C₂²×#334	1	1	yes	characteristic
545	C₂×C₄	C₂²×#365	1	1	yes	characteristic
546	C₂×C₄	C₂²×#365	1	1	yes	characteristic
547	C₈	—	2	1	no	—
548	C₈	—	2	1	no	—
549	C₈	—	2	1	no	—
550	C₈	—	2	1	no	—
551	C₈	—	2	1	no	—
552	C₈	—	2	1	no	—
553	C₈	—	4	1	no	—
554	C₈	—	4	1	no	—
555	C₈	—	4	1	no	—
556	C₈	—	4	1	no	—
557	C₈	—	4	1	no	—
558	C₈	—	4	1	no	—
559	C₈	—	4	1	no	—
560	C₈	—	4	1	no	—
561	C₈	#11997	1	2	yes	—
562	C₈	C₂×#2151	1	1	yes	characteristic
563	C₈	C₂×#2153	1	1	yes	characteristic
564	C₂²	—	2	8	no	—
565	C₂²	—	2	1	no	—
566	C₂²	—	2	1	no	—
567	C₂²	—	2	1	no	—
568	C₂²	—	2	1	no	—
569	C₂²	—	2	1	no	—
570	C₂²	—	2	1	no	—
571	C₂²	#122924	1	2	yes	—
572	C₂²	C₂×#7457	1	2	yes	—
573	C₂²	#151024	1	2	yes	—
574	C₂²	C₂²×#1368	1	1	yes	characteristic
575	C₄	—	2	1	no	—
576	C₄	—	2	1	no	—
577	C₄	—	2	1	no	—
578	C₄	—	2	1	no	—
579	C₄	—	2	1	no	—
580	C₄	—	2	1	no	—
581	C₄	—	2	1	no	—
582	C₄	—	2	1	no	—
583	C₄	#122924	1	2	yes	—
584	C₄	C₂×#7457	1	2	yes	—
585	C₄	C₂×#7457	1	2	yes	—
586	C₄	C₂×#11997	1	1	yes	characteristic
587	C₄	C₂×#12002	1	1	yes	characteristic
588	C₂	—	2	2	no	—
589	C₂	—	2	2	no	—
590	C₂	—	2	2	no	—
591	C₂	C₂²×#7457	1	1	yes	characteristic
592	C₂	C₂×#151024	1	1	yes	characteristic
593	C₂	C₂×#122924	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#1368
commutator	C₂×C₁₆	C₂³×C₈
Frattini, cosocle	#1311	C₂⁴
socle	C₂²	C₂²×#1368
prime radical	C₂⁴	#1368
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ C₂²×C₈² ◁ C₂²×#1311 ◁ G
LECS	G ▷ #1311 ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72231936	C₂	semidirect
2. #72231935	C₂	semidirect
3. #72231929	C₂	semidirect
30. #93877	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#72231936	2
#72231935	2
#72231929	2
#72231926	2
C₂²×#7099	2
#72231858	2