Subgroups — #72283035

Order 2048.

At least 7226 conjugacy classes of subgroups; only the 588 normal subgroups are shown.

The subgroup lattice has 398 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72283026	C₂	1	1	yes	maximal, characteristic, complemented
2	#72283013	C₂	1	1	yes	maximal, characteristic, complemented
3	#72283003	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×#2358	C₂	1	1	yes	maximal, characteristic, complemented
5	#72282917	C₂	1	1	yes	maximal, characteristic, complemented
6	#72282888	C₂	1	1	yes	maximal, characteristic, complemented
7	#72282872	C₂	1	1	yes	maximal, characteristic, complemented
8	#72282843	C₂	1	1	yes	maximal, characteristic, complemented
9	#72282765	C₂	1	1	yes	maximal, characteristic, complemented
10	#72282698	C₂	1	1	yes	maximal, characteristic, complemented
11	#72282624	C₂	1	1	yes	maximal, characteristic, complemented
12	#72282505	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#130740	C₂	1	1	yes	maximal, characteristic, complemented
14	#72264018	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#248455	C₂	1	1	yes	maximal, characteristic
16	C₂×#61559	C₂²	1	1	yes	characteristic
17	C₂×D₄×#120	C₂²	1	1	yes	characteristic
18	C₂×#24260	C₂²	1	1	yes	characteristic
19	C₂×#18194	C₂²	1	1	yes	characteristic
20	#533373	C₂²	1	1	yes	characteristic
21	#533069	C₂²	1	1	yes	characteristic
22	#531679	C₂²	1	1	yes	characteristic
23	D₄×#390	C₂²	1	1	yes	characteristic
24	D₄×#386	C₂²	1	1	yes	characteristic
25	C₄×#2358	C₂²	1	1	yes	characteristic
26	C₂×#12793	C₂²	1	1	yes	characteristic
27	C₂×#11880	C₂²	1	1	yes	characteristic
28	C₂×#11873	C₂²	1	1	yes	characteristic
29	C₂×#11471	C₂²	1	1	yes	characteristic
30	#361668	C₂²	1	1	yes	characteristic, complemented
31	#361664	C₂²	1	1	yes	characteristic, complemented
32	#248455	C₄	1	8	yes	complemented
33	C₂×#9468	C₂²	1	1	yes	characteristic
34	C₂×#8965	C₂²	1	1	yes	characteristic
35	#185958	C₂²	1	1	yes	characteristic, complemented
36	#185946	C₂²	1	1	yes	characteristic, complemented
37	C₂×#8383	C₂²	1	1	yes	characteristic
38	C₂×#8375	C₂²	1	1	yes	characteristic
39	C₂×#8375	C₂²	1	1	yes	characteristic
40	#147014	C₂²	1	1	yes	characteristic, complemented
41	#147008	C₂²	1	1	yes	characteristic, complemented
42	#127619	C₂²	1	1	yes	characteristic, complemented
43	#127618	C₂²	1	1	yes	characteristic, complemented
44	#127618	C₂²	1	1	yes	characteristic, complemented
45	#127615	C₂²	1	1	yes	characteristic, complemented
46	#126951	C₂²	1	1	yes	characteristic, complemented
47	#126947	C₂²	1	1	yes	characteristic, complemented
48	#108186	C₂²	1	1	yes	characteristic, complemented
49	#107082	C₂²	1	1	yes	characteristic, complemented
50	#106350	C₂²	1	1	yes	characteristic, complemented
51	#106314	C₂²	1	1	yes	characteristic, complemented
52	C₂⁵×D₄	D₄	1	1	yes	characteristic
53	C₂×#3496	C₂³	1	1	yes	characteristic
54	C₂²×D₄²	C₂³	1	1	yes	characteristic
55	C₂³×C₄×D₄	D₄	1	1	yes	characteristic, complemented
56	#61559	C₂×C₄	1	4	yes	complemented
57	C₂×#2972	C₂³	1	1	yes	characteristic
58	C₂×#2847	D₄	1	1	yes	characteristic
59	D₄×#120	C₂×C₄	1	4	yes	—
60	D₄×#120	D₄	1	4	yes	—
61	C₂×#2433	D₄	1	1	yes	characteristic
62	C₂×#2408	C₂³	1	1	yes	characteristic
63	C₂×#2358	D₄	1	1	yes	characteristic
64	C₂×#2358	D₄	1	1	yes	characteristic
65	C₂×D₄×C₄⋊C₄	D₄	1	1	yes	characteristic, complemented
66	C₂×D₄×C₂²⋊C₄	D₄	1	1	yes	characteristic
67	C₂×D₄×C₂²⋊C₄	D₄	1	1	yes	characteristic, complemented
68	C₂×C₄×#120	C₂³	1	1	yes	characteristic
69	C₂×C₄²×D₄	D₄	1	1	yes	characteristic, complemented
70	#24260	C₂×C₄	1	4	yes	complemented
71	C₂×#1800	C₂³	1	1	yes	characteristic
72	C₂×#1799	C₂³	1	1	yes	characteristic
73	C₂×#1799	C₂³	1	1	yes	characteristic
74	#18194	C₂×C₄	1	4	yes	complemented
75	C₂×#1460	C₂³	1	1	yes	characteristic
76	C₂×#1459	C₂³	1	1	yes	characteristic
77	C₂×#1459	C₂³	1	1	yes	characteristic
78	#14713	D₄	1	1	yes	characteristic, complemented
79	#14698	D₄	1	1	yes	characteristic, complemented
80	#14572	D₄	1	2	yes	complemented
81	#14535	D₄	1	2	yes	complemented
82	#14402	D₄	1	2	yes	—
83	#14224	D₄	1	2	yes	complemented
84	#14171	D₄	1	2	yes	complemented
85	#14154	D₄	1	1	yes	characteristic, complemented
86	#14137	D₄	1	1	yes	characteristic, complemented
87	#14127	D₄	1	2	yes	—
88	#13906	C₂³	1	1	yes	characteristic
89	#13872	C₂³	1	1	yes	characteristic
90	#13824	D₄	1	1	yes	characteristic
91	#13824	D₄	1	1	yes	characteristic
92	C₄×#390	C₂³	1	1	yes	characteristic
93	C₄×#386	C₂³	1	1	yes	characteristic
94	#9468	C₂×C₄	1	4	yes	complemented
95	#8965	C₂×C₄	1	4	yes	complemented
96	#8375	C₂×C₄	1	4	yes	complemented
97	C₂⁴×D₄	C₂²⋊C₄	1	4	yes	complemented
98	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
99	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
100	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
101	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
102	#3496	C₂²×C₄	1	2	yes	complemented
103	C₂×D₄²	C₂²×C₄	1	2	yes	—
104	C₂×D₄²	C₂×D₄	1	2	yes	—
105	C₂×D₄²	#41	1	2	yes	—
106	C₂×D₄²	#41	1	2	yes	—
107	C₂²×#127	C₂×D₄	1	1	yes	characteristic
108	C₂²×#121	C₂×D₄	1	1	yes	characteristic
109	C₂²×#121	C₂×D₄	1	1	yes	characteristic
110	C₂²×#120	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×D₄	C₂⁴	1	1	yes	characteristic
113	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
114	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
115	#2972	C₂²×C₄	1	2	yes	complemented
116	#2847	C₂²⋊C₄	1	4	yes	complemented
117	#2433	C₂²⋊C₄	1	4	yes	complemented
118	#2408	C₂²×C₄	1	2	yes	—
119	#2408	C₂×D₄	1	2	yes	—
120	#2408	#41	1	2	yes	—
121	#2408	#41	1	2	yes	—
122	C₂×#394	C₂×D₄	1	2	yes	—
123	C₂×#392	C₂×D₄	1	2	yes	—
124	#2358	D₈	1	4	yes	complemented
125	D₄×C₂²⋊C₄	C₂²⋊C₄	1	4	yes	complemented
126	C₄×#120	C₂²×C₄	1	2	yes	—
127	C₄×#120	C₂×D₄	1	2	yes	—
128	C₄×#120	#41	1	2	yes	—
129	C₄×#120	#41	1	2	yes	—
130	C₂×#390	C₂×D₄	1	1	yes	characteristic
131	C₂×#390	C₂×D₄	1	1	yes	characteristic
132	C₂×#386	C₂×D₄	1	1	yes	characteristic
133	C₂×#386	C₂×D₄	1	1	yes	characteristic
134	C₂×#386	C₂×D₄	1	1	yes	characteristic
135	C₂×#385	C₂×D₄	1	1	yes	characteristic
136	C₂×#384	C₂×D₄	1	1	yes	characteristic
137	C₂×#380	C₂×D₄	1	1	yes	characteristic
138	C₂×#380	C₂×D₄	1	1	yes	characteristic
139	C₂×#379	C₂×D₄	1	1	yes	characteristic
140	C₂×C₄×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
141	C₂×C₄×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
142	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
143	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
144	C₂×C₄³	C₂×D₄	1	1	yes	characteristic
145	#1799	C₂²×C₄	1	2	yes	complemented
146	#1459	C₂²×C₄	1	2	yes	complemented
147	#1441	C₂×D₄	1	2	yes	—
148	#1439	C₂×D₄	1	2	yes	—
149	#1439	C₂×D₄	1	2	yes	—
150	#1439	C₂×D₄	1	2	yes	—
151	C₄⋊#95	C₂×D₄	1	1	yes	characteristic
152	C₄⋊#95	C₂×D₄	1	1	yes	characteristic
153	C₂²⋊#95	C₂×D₄	1	1	yes	characteristic
154	C₂²⋊#95	C₂×D₄	1	1	yes	characteristic
155	C₂⁶	#120	1	1	yes	characteristic
156	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
157	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
158	C₂³×D₄	C₄×D₄	1	2	yes	—
159	C₂³×D₄	#120	1	2	yes	—
160	C₂³×D₄	#120	1	1	yes	characteristic
161	C₂³×D₄	#120	1	1	yes	characteristic
162	C₂³×D₄	#120	1	1	yes	characteristic
163	C₂³×D₄	#121	1	2	yes	—
164	C₂³×D₄	#123	1	2	yes	—
165	C₂³×D₄	#123	1	2	yes	—
166	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
167	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
168	C₂⁴×C₄	#120	1	1	yes	characteristic
169	C₂⁴×C₄	#120	1	1	yes	characteristic
170	C₂⁴×C₄	#120	1	1	yes	characteristic
171	C₂⁴×C₄	#123	1	2	yes	—
172	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
173	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
174	C₂×#127	C₄×D₄	1	2	yes	—
175	C₂×#127	#121	1	2	yes	—
176	C₂×#121	C₂×C₂²⋊C₄	1	2	yes	—
177	C₂×#121	C₄×D₄	1	2	yes	—
178	C₂×#121	#121	1	2	yes	—
179	C₂×#121	#123	1	2	yes	—
180	C₂×#120	C₄×D₄	1	2	yes	—
181	C₂×#120	#121	1	2	yes	—
182	C₂×#120	C₂×D₈	1	2	yes	—
183	C₂×#120	#135	1	2	yes	—
184	C₂×#120	AGL(1,ℤ/8)	1	2	yes	—
185	C₂×#120	AGL(1,ℤ/8)	1	2	yes	—
186	C₂×C₄×D₄	C₄×D₄	1	2	yes	—
187	C₂×C₄×D₄	#121	1	2	yes	—
188	C₂×C₄×D₄	C₂³×C₄	1	1	yes	characteristic
189	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×D₄	C₂×#41	1	1	yes	characteristic
191	C₂×C₄×D₄	C₂×#41	1	1	yes	characteristic
192	C₂×C₄×D₄	C₂×#41	1	1	yes	characteristic
193	C₂×C₄×D₄	C₂×#41	1	1	yes	characteristic
194	C₂×C₄×D₄	C₂×#41	1	1	yes	characteristic
195	C₂×C₄×D₄	C₂×#41	1	1	yes	characteristic
196	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
197	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
198	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
199	C₂²×C₄⋊C₄	#120	1	2	yes	—
200	C₂²×C₄⋊C₄	#120	1	2	yes	—
201	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
202	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
203	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
204	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
205	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
206	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
207	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
208	C₂²×C₄²	#120	1	1	yes	characteristic
209	C₂²×C₄²	#120	1	1	yes	characteristic
210	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
211	#394	C₄×D₄	1	4	yes	—
212	#394	#121	1	4	yes	—
213	#392	C₄×D₄	1	4	yes	—
214	#392	#121	1	4	yes	—
215	#390	C₂×D₈	1	2	yes	—
216	#390	AGL(1,ℤ/8)	1	2	yes	—
217	#386	C₄×D₄	1	2	yes	—
218	#386	#121	1	2	yes	—
219	#386	C₂×D₈	1	2	yes	—
220	#386	AGL(1,ℤ/8)	1	2	yes	—
221	#385	C₄×D₄	1	2	yes	—
222	#385	#121	1	2	yes	—
223	#380	C₂×C₂²⋊C₄	1	2	yes	—
224	#380	#123	1	2	yes	—
225	#379	C₄×D₄	1	2	yes	—
226	#379	#121	1	2	yes	—
227	C₄×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
228	C₄×C₂²⋊C₄	#123	1	2	yes	—
229	C₂×#95	#120	1	2	yes	—
230	C₂×#95	#120	1	2	yes	—
231	C₂×#95	#120	1	2	yes	—
232	C₂⁵	#386	1	2	yes	—
233	C₂⁵	#447	1	2	yes	—
234	C₂⁵	#449	1	2	yes	—
235	C₂⁵	C₂×#120	1	1	yes	characteristic
236	C₂⁵	C₂×#120	1	1	yes	characteristic
237	C₂²×D₄	#386	1	2	yes	—
238	C₂²×D₄	#386	1	2	yes	—
239	C₂²×D₄	#386	1	2	yes	—
240	C₂²×D₄	#386	1	4	yes	—
241	C₂²×D₄	B(4,𝔽₂)	1	2	yes	—
242	C₂²×D₄	B(4,𝔽₂)	1	2	yes	—
243	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
244	C₂²×D₄	C₂×#121	1	1	yes	characteristic
245	C₂²×D₄	#525	1	1	yes	characteristic
246	C₂²×D₄	#525	1	1	yes	characteristic
247	C₂²×D₄	C₂²×D₈	1	1	yes	characteristic
248	C₂²×D₄	C₂×#135	1	1	yes	characteristic
249	C₂²×D₄	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
250	C₂²×D₄	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
251	C₂²×D₄	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
252	C₂²×D₄	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
253	C₂²×D₄	#575	1	1	yes	characteristic
254	C₂²×D₄	#575	1	1	yes	characteristic
255	C₂³×C₄	#386	1	2	yes	—
256	C₂³×C₄	#447	1	2	yes	complemented
257	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
258	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
259	C₂³×C₄	C₂×#120	1	1	yes	characteristic
260	C₂³×C₄	C₂×#120	1	1	yes	characteristic
261	C₂³×C₄	C₂×#120	1	1	yes	characteristic
262	C₂³×C₄	C₂×#120	1	1	yes	characteristic
263	C₂³×C₄	C₂×#120	1	1	yes	characteristic
264	C₂³×C₄	C₂×#121	1	1	yes	characteristic
265	C₂³×C₄	C₂×#123	1	1	yes	characteristic
266	C₂³×C₄	C₂×#123	1	1	yes	characteristic
267	C₂³×C₄	C₂×#123	1	1	yes	characteristic
268	C₂³×C₄	#525	1	1	yes	characteristic
269	C₂³×C₄	#525	1	1	yes	characteristic
270	#120	C₄×D₈	1	4	yes	—
271	#120	#442	1	4	yes	—
272	#120	#459	1	4	yes	—
273	#120	#463	1	4	yes	—
274	C₂×C₄⋊C₄	#386	1	2	yes	—
275	C₂×C₄⋊C₄	#447	1	2	yes	complemented
276	C₂×C₄⋊C₄	C₂×C₄×D₄	1	1	yes	characteristic
277	C₂×C₄⋊C₄	C₂×#121	1	1	yes	characteristic
278	C₂×C₄⋊C₄	#525	1	1	yes	characteristic
279	C₂×C₄⋊C₄	#525	1	1	yes	characteristic
280	C₂×C₂²⋊C₄	#386	1	2	yes	—
281	C₂×C₂²⋊C₄	#386	1	2	yes	—
282	C₂×C₂²⋊C₄	#447	1	2	yes	—
283	C₂×C₂²⋊C₄	#447	1	2	yes	complemented
284	C₂×C₂²⋊C₄	#449	1	2	yes	—
285	C₂×C₂²⋊C₄	C₂×C₄×D₄	1	1	yes	characteristic
286	C₂×C₂²⋊C₄	C₂×C₄×D₄	1	1	yes	characteristic
287	C₂×C₂²⋊C₄	C₂×#121	1	1	yes	characteristic
288	C₂×C₂²⋊C₄	C₂×#121	1	1	yes	characteristic
289	C₂×C₂²⋊C₄	#525	1	1	yes	characteristic
290	C₂×C₂²⋊C₄	#525	1	1	yes	characteristic
291	C₂×C₂²⋊C₄	#525	1	1	yes	characteristic
292	C₂×C₂²⋊C₄	#525	1	1	yes	characteristic
293	C₂×C₄²	#447	1	2	yes	complemented
294	C₂×C₄²	C₂×C₄×D₄	1	1	yes	characteristic
295	C₂×C₄²	C₂×#121	1	1	yes	characteristic
296	C₂×C₄²	#525	1	1	yes	characteristic
297	C₂×C₄²	#525	1	1	yes	characteristic
298	#95	#386	1	4	yes	—
299	C₂⁴	#1879	1	4	yes	complemented
300	C₂⁴	C₂×#386	1	1	yes	characteristic
301	C₂⁴	C₄×#120	1	1	yes	characteristic
302	C₂⁴	#2846	1	1	yes	characteristic
303	C₂⁴	#2847	1	1	yes	characteristic
304	C₂⁴	#2849	1	1	yes	characteristic
305	C₂⁴	C₂×#447	1	1	yes	characteristic
306	C₂⁴	C₂×#447	1	1	yes	characteristic
307	C₂⁴	C₂×#449	1	1	yes	characteristic
308	C₂⁴	#3002	1	1	yes	characteristic
309	C₂⁴	#3003	1	1	yes	characteristic
310	C₂⁴	#3003	1	1	yes	characteristic
311	C₂⁴	#3005	1	1	yes	characteristic
312	C₂⁴	#3006	1	1	yes	characteristic
313	C₂×D₄	#1889	1	4	yes	—
314	C₂×D₄	#2196	1	4	yes	—
315	C₂×D₄	#2197	1	4	yes	—
316	C₂×D₄	C₂×C₄×D₈	1	1	yes	characteristic
317	C₂×D₄	C₂×#442	1	1	yes	characteristic
318	C₂×D₄	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
319	C₂×D₄	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
320	C₂×D₄	C₂×#459	1	1	yes	characteristic
321	C₂×D₄	C₂×#463	1	1	yes	characteristic
322	C₂×D₄	#3036	1	1	yes	characteristic
323	C₂×D₄	#3036	1	1	yes	characteristic
324	C₂×D₄	#3100	1	1	yes	characteristic
325	C₂×D₄	#3100	1	1	yes	characteristic
326	C₂×D₄	#3105	1	1	yes	characteristic
327	C₂×D₄	#3105	1	1	yes	characteristic
328	C₂×D₄	#3109	1	1	yes	characteristic
329	C₂×D₄	#3109	1	1	yes	characteristic
330	C₂×D₄	#3114	1	1	yes	characteristic
331	C₂×D₄	#3114	1	1	yes	characteristic
332	C₂²×C₄	C₂×#386	1	1	yes	characteristic
333	C₂²×C₄	C₂×#386	1	1	yes	characteristic
334	C₂²×C₄	C₄×#120	1	1	yes	characteristic
335	C₂²×C₄	C₄×#120	1	1	yes	characteristic
336	C₂²×C₄	C₄×#120	1	1	yes	characteristic
337	C₂²×C₄	#2847	1	1	yes	characteristic
338	C₂²×C₄	#2847	1	1	yes	characteristic
339	C₂²×C₄	#2847	1	1	yes	characteristic
340	C₂²×C₄	#2849	1	1	yes	characteristic
341	C₂²×C₄	#2849	1	1	yes	characteristic
342	C₂²×C₄	C₂×#447	1	1	yes	characteristic
343	C₂²×C₄	#3002	1	1	yes	characteristic
344	C₂²×C₄	#3003	1	1	yes	characteristic
345	C₂²×C₄	#3006	1	1	yes	characteristic
346	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
347	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
348	C₂²×C₄	#3026	1	1	yes	characteristic
349	C₂²×C₄	#3026	1	1	yes	characteristic
350	C₂²⋊C₄	#1879	1	4	yes	complemented
351	C₂³	#14694	1	1	yes	characteristic
352	C₂³	C₂×#1879	1	1	yes	characteristic
353	C₂³	#20925	1	1	yes	characteristic
354	C₂³	C₄×#447	1	1	yes	characteristic
355	C₂³	#21452	1	1	yes	characteristic
356	C₂³	#32878	1	1	yes	characteristic
357	C₂³	#32880	1	1	yes	characteristic
358	C₂³	#32894	1	1	yes	characteristic
359	C₂³	#32894	1	1	yes	characteristic
360	C₂³	#32898	1	1	yes	characteristic
361	C₂³	#32898	1	1	yes	characteristic
362	C₂³	#32902	1	1	yes	characteristic
363	C₂³	#32908	1	1	yes	characteristic
364	C₂³	#33002	1	1	yes	characteristic
365	C₂³	#33004	1	1	yes	characteristic
366	D₄	#13041	1	8	yes	complemented
367	C₂×C₄	C₂×#1889	1	1	yes	characteristic
368	C₂×C₄	#20960	1	1	yes	characteristic
369	C₂×C₄	C₄×#447	1	1	yes	characteristic
370	C₂×C₄	#21452	1	1	yes	characteristic
371	C₂×C₄	#32902	1	1	yes	characteristic
372	C₂×C₄	#32908	1	1	yes	characteristic
373	C₂×C₄	#33020	1	1	yes	characteristic
374	C₂×C₄	#33020	1	1	yes	characteristic
375	C₂×C₄	C₂×#2196	1	2	yes	—
376	C₂×C₄	C₂×#2197	1	2	yes	—
377	C₂²	#346518	1	1	yes	characteristic
378	C₂²	#346518	1	1	yes	characteristic
379	C₂²	#346519	1	1	yes	characteristic
380	C₂²	#346519	1	1	yes	characteristic
381	C₂²	#392632	1	1	yes	characteristic
382	C₂²	#392658	1	1	yes	characteristic
383	C₂²	#392725	1	1	yes	characteristic
384	C₂²	#511771	1	1	yes	characteristic
385	C₂²	#511772	1	1	yes	characteristic
386	C₂²	#511819	1	1	yes	characteristic
387	C₂²	#511821	1	1	yes	characteristic
388	C₄	C₂×#13041	1	2	yes	—
389	C₄	#512142	1	2	yes	—
390	C₂	#72231273	1	1	yes	characteristic
391	C₂	#72251717	1	1	yes	characteristic
392	C₂	#72281116	1	1	yes	characteristic
393	C₂	#72281302	1	1	yes	characteristic
394	C₂	#72281619	1	1	yes	characteristic
395	C₂	#72281850	1	1	yes	characteristic
396	C₂	#72282337	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	#32898
commutator	C₂×C₄×D₄	C₂³×C₄
Frattini, cosocle	C₂²×C₄×D₄	C₂⁴
prime radical	C₂×#248455	C₂
LCS	G ▷ C₂×C₄×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂²×D₄² ◁ G
LECS	G ▷ C₂²×C₄×D₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72283026	C₂	semidirect
2. #72283013	C₂	semidirect
3. #72283003	C₂	semidirect
4. D₄×#2358	C₂	semidirect
5. #72282917	C₂	semidirect
6. #72282888	C₂	semidirect
7. #72282872	C₂	semidirect
8. #72282843	C₂	semidirect
9. #72282765	C₂	semidirect
10. #72282698	C₂	semidirect
11. #72282624	C₂	semidirect
12. #72282505	C₂	semidirect
13. C₂×#130740	C₂	semidirect
14. #72264018	C₂	semidirect
30. #361668	C₂²	semidirect
31. #361664	C₂²	semidirect
32. #248455	C₄	semidirect
35. #185958	C₂²	semidirect
36. #185946	C₂²	semidirect
40. #147014	C₂²	semidirect
41. #147008	C₂²	semidirect
42. #127619	C₂²	semidirect
43. #127618	C₂²	semidirect
44. #127618	C₂²	semidirect
45. #127615	C₂²	semidirect
46. #126951	C₂²	semidirect
47. #126947	C₂²	semidirect
48. #108186	C₂²	semidirect
49. #107082	C₂²	semidirect
50. #106350	C₂²	semidirect
51. #106314	C₂²	semidirect
55. C₂³×C₄×D₄	D₄	semidirect
56. #61559	C₂×C₄	semidirect
65. C₂×D₄×C₄⋊C₄	D₄	semidirect
67. C₂×D₄×C₂²⋊C₄	D₄	semidirect
69. C₂×C₄²×D₄	D₄	semidirect
70. #24260	C₂×C₄	semidirect
74. #18194	C₂×C₄	semidirect
78. #14713	D₄	semidirect
79. #14698	D₄	semidirect
80. #14572	D₄	semidirect
81. #14535	D₄	semidirect
83. #14224	D₄	semidirect
84. #14171	D₄	semidirect
85. #14154	D₄	semidirect
86. #14137	D₄	semidirect
94. #9468	C₂×C₄	semidirect
95. #8965	C₂×C₄	semidirect
96. #8375	C₂×C₄	semidirect
97. C₂⁴×D₄	C₂²⋊C₄	semidirect
102. #3496	C₂²×C₄	semidirect
115. #2972	C₂²×C₄	semidirect
116. #2847	C₂²⋊C₄	semidirect
117. #2433	C₂²⋊C₄	semidirect
124. #2358	D₈	semidirect
125. D₄×C₂²⋊C₄	C₂²⋊C₄	semidirect
145. #1799	C₂²×C₄	semidirect
146. #1459	C₂²×C₄	semidirect
256. C₂³×C₄	#447	semidirect
275. C₂×C₄⋊C₄	#447	semidirect
283. C₂×C₂²⋊C₄	#447	semidirect
293. C₂×C₄²	#447	semidirect
299. C₂⁴	#1879	semidirect
350. C₂²⋊C₄	#1879	semidirect
366. D₄	#13041	semidirect

Maximal subgroups

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

subgroup	index
#72283026	2
#72283013	2
#72283003	2
D₄×#2358	2
#72282917	2
#72282888	2
#72282872	2
#72282843	2
#72282765	2
#72282698	2
#72282624	2
#72282505	2
C₂×#130740	2
#72264018	2
C₂×#248455	2