Subgroups — #72337509

Order 2048.

Only the 1408 normal subgroups are shown; non-normal subgroups are omitted.

The subgroup lattice has 402 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72337506	C₂	1	1	yes	maximal, characteristic, complemented
2	#72337433	C₂	1	8	yes	maximal, complemented
3	#72337426	C₂	1	8	yes	maximal, complemented
4	#72312834	C₂	1	2	yes	maximal, complemented
5	#72312697	C₂	1	2	yes	maximal, complemented
6	#72280972	C₂	1	1	yes	maximal, characteristic, complemented
7	#72280881	C₂	1	2	yes	maximal, complemented
8	#72280746	C₂	1	1	yes	maximal, characteristic, complemented
9	#72280610	C₂	1	2	yes	maximal, complemented
10	C₂×#6628885	C₂	1	2	yes	maximal, complemented
11	C₂²×#33553	C₂	1	2	yes	maximal, complemented
12	C₂×#63103	C₂²	1	1	yes	characteristic, complemented
13	C₂²×#3537	C₂²	1	1	yes	characteristic, complemented
14	C₂²×#3027	C₂²	1	2	yes	—
15	C₂²×#3025	C₂²	1	2	yes	—
16	C₂×#60369	C₂²	1	2	yes	—
17	C₂²×#3021	C₂²	1	2	yes	—
18	#7629120	C₂²	1	1	yes	characteristic
19	C₂×#33553	C₂²	1	16	yes	complemented
20	C₂²×#2128	C₂²	1	2	yes	complemented
21	C₂²×#2122	C₂²	1	2	yes	complemented
22	C₂²×#2120	C₂²	1	2	yes	complemented
23	#6628899	C₂²	1	4	yes	complemented
24	#6628898	C₂²	1	4	yes	complemented
25	C₂×#32895	C₂²	1	8	yes	complemented
26	C₂×#32894	C₂²	1	8	yes	complemented
27	#6499824	C₂²	1	4	yes	complemented
28	#6499823	C₂²	1	4	yes	complemented
29	#6374164	C₂²	1	2	yes	complemented
30	#6374112	C₂²	1	1	yes	characteristic, complemented
31	C₂×#20623	C₂²	1	2	yes	complemented
32	C₂×#20620	C₂²	1	2	yes	complemented
33	C₂×#20612	C₂²	1	2	yes	complemented
34	#6370734	C₂²	1	2	yes	complemented
35	#6370692	C₂²	1	1	yes	characteristic, complemented
36	C₂×#12589	C₂²	1	2	yes	complemented
37	#492906	C₂²	1	1	yes	characteristic, complemented
38	#492899	C₂²	1	1	yes	characteristic, complemented
39	C₂×#12577	C₂²	1	2	yes	complemented
40	#147764	C₂²	1	16	yes	complemented
41	#147755	C₂²	1	16	yes	complemented
42	#147751	C₂²	1	16	yes	complemented
43	#147586	C₂²	1	8	yes	complemented
44	#147585	C₂²	1	8	yes	complemented
45	#147574	C₂²	1	4	yes	complemented
46	#147573	C₂²	1	4	yes	complemented
47	C₂×2₋¹⁺⁶	C₂³	1	2	yes	complemented
48	C₂×H(7,𝔽₂)	C₂³	1	2	yes	complemented
49	C₂²×#585	C₂³	1	2	yes	—
50	C₂²×#585	C₂³	1	1	yes	characteristic
51	C₂³×AGL(1,ℤ/8)	D₄	1	2	yes	complemented
52	C₂³×AGL(1,ℤ/8)	D₄	1	2	yes	complemented
53	C₂×#3537	C₂³	1	4	yes	complemented
54	C₂²×#535	C₂³	1	2	yes	—
55	C₂²×#525	D₄	1	1	yes	characteristic, complemented
56	C₂²×#525	D₄	1	1	yes	characteristic, complemented
57	C₂²×#525	C₂³	1	1	yes	characteristic
58	C₂×#3027	D₄	1	16	yes	complemented
59	C₂×#3027	C₂³	1	8	yes	—
60	C₂×#3025	D₄	1	8	yes	complemented
61	C₂×#3025	C₂³	1	8	yes	—
62	C₂²×#458	D₄	1	4	yes	complemented
63	C₂²×B(4,𝔽₂)	D₄	1	4	yes	complemented
64	C₂×#3021	D₄	1	16	yes	complemented
65	C₂×#3021	C₂³	1	8	yes	—
66	C₂×#3010	D₄	1	4	yes	complemented
67	C₂×#3010	C₂³	1	4	yes	—
68	C₂×#3008	D₄	1	4	yes	complemented
69	C₂×#3008	C₂³	1	4	yes	—
70	C₂×#2896	D₄	1	2	yes	complemented
71	C₂×#2896	D₄	1	2	yes	complemented
72	C₂²×#413	C₂³	1	2	yes	—
73	C₂²×#410	C₂³	1	2	yes	—
74	C₂²×#410	C₂³	1	2	yes	—
75	C₂×#2879	C₂³	1	2	yes	—
76	#35659	D₄	1	2	yes	complemented
77	#35659	C₂³	1	2	yes	—
78	#35512	D₄	1	2	yes	complemented
79	#35512	C₂³	1	2	yes	—
80	#34044	D₄	1	1	yes	characteristic, complemented
81	#34044	D₄	1	1	yes	characteristic, complemented
82	#34044	C₂³	1	1	yes	characteristic
83	C₂×#2128	C₂³	1	8	yes	complemented
84	C₂×#2122	C₂³	1	8	yes	complemented
85	C₂×#2120	C₂³	1	8	yes	complemented
86	#21770	C₂³	1	8	yes	complemented
87	#21744	C₂³	1	4	yes	complemented
88	C₂×#1796	C₂³	1	4	yes	complemented
89	C₂×#1795	C₂³	1	4	yes	complemented
90	C₂×#1794	C₂³	1	8	yes	complemented
91	C₂×#1791	C₂³	1	8	yes	complemented
92	#20610	C₂³	1	8	yes	complemented
93	#20587	C₂³	1	2	yes	complemented
94	#20586	C₂³	1	2	yes	complemented
95	C₂×#1395	C₂³	1	8	yes	complemented
96	#12587	C₂³	1	4	yes	complemented
97	#12583	C₂³	1	4	yes	complemented
98	C₂×#1391	C₂³	1	8	yes	complemented
99	C₂×#585	C₂×D₄	1	8	yes	—
100	C₂×#585	C₂×D₄	1	8	yes	—
101	C₂×#585	C₂×D₄	1	4	yes	—
102	C₂×#585	C₂⁴	1	4	yes	—
103	C₂²×2₋¹⁺⁴	C₂×D₄	1	1	yes	characteristic
104	C₂²×2₋¹⁺⁴	C₂×D₄	1	2	yes	—
105	C₂²×2₋¹⁺⁴	C₂⁴	1	1	yes	characteristic
106	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
107	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
108	C₂²×H(5,𝔽₂)	C₂×D₄	1	4	yes	—
109	C₂²×H(5,𝔽₂)	C₂⁴	1	1	yes	characteristic
110	C₂³×#41	C₂×D₄	1	2	yes	—
111	C₂³×#41	C₂×D₄	1	1	yes	characteristic
112	C₂³×#41	C₂×D₄	1	2	yes	—
113	C₂³×#41	C₂×D₄	1	1	yes	characteristic
114	C₂³×#41	C₂⁴	1	1	yes	characteristic
115	C₂⁴×D₄	C₂×D₄	1	2	yes	—
116	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
117	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	4	yes	complemented
118	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	4	yes	complemented
119	C₂³×SD₁₆	C₂×D₄	1	4	yes	complemented
120	C₂³×D₈	C₂×D₄	1	4	yes	complemented
121	C₂³×M₁₆	C₂×D₄	1	2	yes	—
122	C₂³×M₁₆	C₂×D₄	1	2	yes	—
123	C₂×#535	C₂×D₄	1	8	yes	—
124	C₂×#535	C₂×D₄	1	8	yes	—
125	C₂×#535	C₂×D₄	1	4	yes	—
126	C₂×#535	C₂⁴	1	4	yes	—
127	C₂×#525	C₂×D₄	1	4	yes	—
128	C₂×#525	C₂×D₄	1	2	yes	—
129	C₂×#525	C₂×D₄	1	2	yes	complemented
130	C₂×#525	C₂×D₄	1	2	yes	complemented
131	C₂×#525	C₂⁴	1	2	yes	—
132	C₂²×#123	C₂×D₄	1	2	yes	—
133	C₂²×C₂²⋊Q₈	C₂×D₄	1	2	yes	complemented
134	C₂²×#121	C₂×D₄	1	2	yes	complemented
135	C₂²×#120	C₂×D₄	1	2	yes	—
136	C₂²×#117	C₂×D₄	1	1	yes	characteristic
137	C₂²×#117	C₂×D₄	1	1	yes	characteristic
138	C₂²×#117	C₂×D₄	1	2	yes	—
139	C₂²×#117	C₂×D₄	1	1	yes	characteristic
140	#3027	C₂×D₄	1	32	yes	complemented
141	C₂×#458	C₂×D₄	1	16	yes	complemented
142	C₂×B(4,𝔽₂)	C₂×D₄	1	16	yes	complemented
143	#3021	C₂×D₄	1	32	yes	complemented
144	C₂×#419	C₂×D₄	1	4	yes	complemented
145	C₂×#418	C₂×D₄	1	4	yes	complemented
146	C₂×#416	C₂×D₄	1	4	yes	complemented
147	C₂×#416	C₂×D₄	1	4	yes	complemented
148	C₂×#413	C₂×D₄	1	8	yes	—
149	C₂×#413	C₂⁴	1	4	yes	—
150	C₂×#410	C₂×D₄	1	4	yes	—
151	C₂×#410	C₂×D₄	1	8	yes	—
152	C₂×#410	C₂⁴	1	4	yes	—
153	C₂×#410	C₂⁴	1	4	yes	—
154	C₂²×#99	C₂×D₄	1	4	yes	—
155	C₂×#408	C₂×D₄	1	4	yes	—
156	C₂×#408	C₂⁴	1	4	yes	—
157	#2311	C₂×D₄	1	2	yes	—
158	#2311	C₂×D₄	1	2	yes	complemented
159	#2311	C₂×D₄	1	2	yes	complemented
160	#2311	C₂⁴	1	2	yes	—
161	#2310	C₂×D₄	1	2	yes	complemented
162	#2309	C₂×D₄	1	2	yes	complemented
163	C₂⁶	#120	1	1	yes	characteristic
164	#585	#120	1	16	yes	—
165	#585	C₂²×D₄	1	8	yes	—
166	#585	C₂²×D₄	1	8	yes	—
167	C₂×H(5,𝔽₂)	#120	1	16	yes	—
168	C₂×H(5,𝔽₂)	C₂²×D₄	1	8	yes	—
169	C₂²×#41	#120	1	2	yes	—
170	C₂²×#41	#120	1	2	yes	—
171	C₂²×#41	#120	1	2	yes	—
172	C₂²×#41	#120	1	1	yes	characteristic
173	C₂²×#41	#120	1	2	yes	—
174	C₂²×#41	#120	1	1	yes	characteristic
175	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
176	C₂²×#41	C₂²×D₄	1	2	yes	—
177	C₂²×#41	C₂²×D₄	1	4	yes	—
178	C₂²×#41	C₂²×D₄	1	4	yes	—
179	C₂²×#41	C₂²×D₄	1	2	yes	—
180	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
181	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
182	C₂²×#41	C₂²×D₄	1	2	yes	—
183	C₂²×#41	C₂²×D₄	1	2	yes	—
184	C₂²×#41	H(5,𝔽₂)	1	4	yes	—
185	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
186	C₂²×#41	H(5,𝔽₂)	1	4	yes	—
187	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
188	C₂²×#41	C₂⁵	1	1	yes	characteristic
189	C₂³×Q₈	#120	1	2	yes	—
190	C₂³×Q₈	#120	1	1	yes	characteristic
191	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
192	C₂³×Q₈	C₂²×D₄	1	2	yes	—
193	C₂³×Q₈	H(5,𝔽₂)	1	1	yes	characteristic
194	C₂³×D₄	#120	1	2	yes	—
195	C₂³×D₄	#120	1	1	yes	characteristic
196	C₂³×D₄	#120	1	8	yes	complemented
197	C₂³×D₄	C₂²×D₄	1	2	yes	—
198	C₂³×D₄	C₂²×D₄	1	4	yes	—
199	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
200	C₂³×D₄	C₂²×D₄	1	2	yes	—
201	C₂³×D₄	H(5,𝔽₂)	1	1	yes	characteristic
202	C₂⁴×C₄	#120	1	1	yes	characteristic
203	C₂⁴×C₄	#120	1	2	yes	—
204	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
205	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
206	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
207	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
208	C₂³×C₈	C₂²×D₄	1	4	yes	—
209	#535	#120	1	16	yes	complemented
210	#535	C₂²×D₄	1	8	yes	—
211	#535	C₂²×D₄	1	8	yes	—
212	C₂×#123	#120	1	4	yes	—
213	C₂×#123	C₂²×D₄	1	4	yes	—
214	C₂×#120	#120	1	4	yes	—
215	C₂×#120	C₂²×D₄	1	4	yes	—
216	C₂×#117	#120	1	2	yes	—
217	C₂×#117	#120	1	8	yes	complemented
218	C₂×#117	C₂²×D₄	1	2	yes	—
219	C₂×#117	C₂²×D₄	1	4	yes	—
220	C₂×#117	C₂²×D₄	1	2	yes	—
221	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
222	C₂²×C₂²⋊C₄	#120	1	2	yes	—
223	#413	C₂²×D₄	1	8	yes	—
224	#410	C₂²×D₄	1	8	yes	—
225	C₂×#99	C₂²×D₄	1	8	yes	—
226	C₂⁵	C₂×#120	1	1	yes	characteristic
227	C₂⁵	C₂×#120	1	2	yes	—
228	C₂⁵	D₄²	1	2	yes	—
229	H(5,𝔽₂)	C₂×#120	1	16	yes	—
230	C₂×#41	B(4,𝔽₂)	1	4	yes	—
231	C₂×#41	B(4,𝔽₂)	1	4	yes	—
232	C₂×#41	B(4,𝔽₂)	1	8	yes	—
233	C₂×#41	C₂×#120	1	4	yes	—
234	C₂×#41	C₂×#120	1	4	yes	—
235	C₂×#41	#534	1	4	yes	—
236	C₂×#41	#534	1	4	yes	—
237	C₂×#41	#534	1	4	yes	—
238	C₂×#41	#534	1	4	yes	—
239	C₂×#41	D₄²	1	2	yes	—
240	C₂×#41	D₄²	1	4	yes	—
241	C₂×#41	D₄²	1	2	yes	—
242	C₂×#41	D₄²	1	4	yes	—
243	C₂×#41	D₄²	1	4	yes	—
244	C₂×#41	D₄²	1	4	yes	—
245	C₂×#41	D₄²	1	4	yes	—
246	C₂×#41	D₄²	1	4	yes	—
247	C₂×#41	H(3,𝔽₄)	1	2	yes	—
248	C₂×#41	H(3,𝔽₄)	1	2	yes	—
249	C₂×#41	C₂³×D₄	1	2	yes	—
250	C₂×#41	C₂³×D₄	1	2	yes	—
251	C₂×#41	C₂×H(5,𝔽₂)	1	2	yes	—
252	C₂×#41	C₂×H(5,𝔽₂)	1	2	yes	—
253	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
254	C₂²×Q₈	C₂×#120	1	2	yes	—
255	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
256	C₂²×Q₈	#534	1	1	yes	characteristic
257	C₂²×Q₈	#534	1	4	yes	—
258	C₂²×Q₈	D₄²	1	2	yes	—
259	C₂²×Q₈	D₄²	1	2	yes	—
260	C₂²×Q₈	H(3,𝔽₄)	1	2	yes	—
261	C₂²×Q₈	C₂×H(5,𝔽₂)	1	1	yes	characteristic
262	C₂²×D₄	C₂×#120	1	2	yes	—
263	C₂²×D₄	C₂×#120	1	4	yes	—
264	C₂²×D₄	C₂×#120	1	8	yes	—
265	C₂²×D₄	C₂×#120	1	1	yes	characteristic
266	C₂²×D₄	C₂×#120	1	2	yes	—
267	C₂²×D₄	C₂×#120	1	1	yes	characteristic
268	C₂²×D₄	#534	1	1	yes	characteristic
269	C₂²×D₄	#534	1	4	yes	—
270	C₂²×D₄	#534	1	4	yes	—
271	C₂²×D₄	D₄²	1	2	yes	—
272	C₂²×D₄	D₄²	1	2	yes	—
273	C₂²×D₄	D₄²	1	4	yes	—
274	C₂²×D₄	D₄²	1	4	yes	—
275	C₂²×D₄	D₄²	1	2	yes	—
276	C₂²×D₄	D₄²	1	2	yes	—
277	C₂²×D₄	H(3,𝔽₄)	1	2	yes	—
278	C₂²×D₄	C₂³×D₄	1	2	yes	—
279	C₂²×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
280	C₂³×C₄	C₂×#120	1	1	yes	characteristic
281	C₂³×C₄	C₂×#120	1	4	yes	—
282	C₂³×C₄	C₂×#120	1	1	yes	characteristic
283	C₂³×C₄	C₂×#120	1	2	yes	—
284	C₂³×C₄	C₂×#120	1	2	yes	—
285	C₂³×C₄	C₂×#120	1	1	yes	characteristic
286	C₂³×C₄	#534	1	4	yes	—
287	C₂³×C₄	#534	1	1	yes	characteristic
288	C₂³×C₄	#534	1	1	yes	characteristic
289	C₂³×C₄	D₄²	1	2	yes	—
290	C₂³×C₄	D₄²	1	4	yes	—
291	C₂³×C₄	D₄²	1	2	yes	—
292	C₂³×C₄	D₄²	1	2	yes	—
293	C₂³×C₄	D₄²	1	4	yes	—
294	C₂³×C₄	D₄²	1	4	yes	—
295	C₂³×C₄	D₄²	1	4	yes	—
296	C₂³×C₄	C₂³×D₄	1	2	yes	—
297	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
298	#117	C₂×#120	1	8	yes	—
299	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
300	C₂⁴	#2403	1	1	yes	characteristic
301	C₂⁴	#2403	1	2	yes	—
302	C₂⁴	#2403	1	4	yes	—
303	C₂⁴	#2403	1	4	yes	—
304	C₂⁴	#2403	1	1	yes	characteristic
305	C₂⁴	#2679	1	4	yes	—
306	C₂⁴	C₂²×#120	1	1	yes	characteristic
307	C₂⁴	C₂×D₄²	1	2	yes	—
308	C₂×Q₈	#2403	1	4	yes	—
309	C₂×Q₈	#2679	1	2	yes	—
310	C₂×Q₈	#2679	1	2	yes	—
311	C₂×Q₈	#2679	1	4	yes	—
312	C₂×Q₈	C₂×B(4,𝔽₂)	1	2	yes	—
313	C₂×Q₈	C₂×B(4,𝔽₂)	1	2	yes	—
314	C₂×Q₈	C₂×B(4,𝔽₂)	1	4	yes	—
315	C₂×Q₈	C₂×#534	1	2	yes	—
316	C₂×Q₈	C₂×D₄²	1	1	yes	characteristic
317	C₂×Q₈	C₂×H(3,𝔽₄)	1	1	yes	characteristic
318	C₂×D₄	#2403	1	4	yes	—
319	C₂×D₄	#2403	1	4	yes	—
320	C₂×D₄	#2403	1	4	yes	—
321	C₂×D₄	#2403	1	4	yes	—
322	C₂×D₄	#2403	1	4	yes	—
323	C₂×D₄	#2679	1	4	yes	—
324	C₂×D₄	#2679	1	4	yes	—
325	C₂×D₄	#2679	1	2	yes	—
326	C₂×D₄	#2679	1	4	yes	—
327	C₂×D₄	#2679	1	2	yes	—
328	C₂×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
329	C₂×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
330	C₂×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
331	C₂×D₄	C₂²×#120	1	2	yes	—
332	C₂×D₄	C₂×#534	1	2	yes	—
333	C₂×D₄	C₂×#534	1	2	yes	—
334	C₂×D₄	C₂×D₄²	1	2	yes	—
335	C₂×D₄	C₂×D₄²	1	2	yes	—
336	C₂×D₄	C₂×D₄²	1	1	yes	characteristic
337	C₂×D₄	C₂×H(3,𝔽₄)	1	1	yes	characteristic
338	C₂²×C₄	#2403	1	1	yes	characteristic
339	C₂²×C₄	#2403	1	1	yes	characteristic
340	C₂²×C₄	#2403	1	2	yes	—
341	C₂²×C₄	#2403	1	4	yes	—
342	C₂²×C₄	#2403	1	4	yes	—
343	C₂²×C₄	#2403	1	4	yes	—
344	C₂²×C₄	#2403	1	4	yes	—
345	C₂²×C₄	#2403	1	4	yes	—
346	C₂²×C₄	#2403	1	4	yes	—
347	C₂²×C₄	#2403	1	4	yes	—
348	C₂²×C₄	#2403	1	4	yes	—
349	C₂²×C₄	#2679	1	4	yes	—
350	C₂²×C₄	#2679	1	2	yes	—
351	C₂²×C₄	#2679	1	4	yes	—
352	C₂²×C₄	#2679	1	2	yes	—
353	C₂²×C₄	#2679	1	2	yes	—
354	C₂²×C₄	#2679	1	4	yes	—
355	C₂²×C₄	#2679	1	2	yes	—
356	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
357	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
358	C₂²×C₄	C₂×B(4,𝔽₂)	1	4	yes	—
359	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
360	C₂²×C₄	C₂²×#120	1	2	yes	—
361	C₂²×C₄	C₂×#534	1	2	yes	—
362	C₂²×C₄	C₂×#534	1	1	yes	characteristic
363	C₂²×C₄	C₂×D₄²	1	2	yes	—
364	C₂²×C₄	C₂×D₄²	1	2	yes	—
365	C₂²×C₄	C₂×D₄²	1	2	yes	—
366	C₂²×C₄	C₂×D₄²	1	2	yes	—
367	C₂²×C₄	C₂×D₄²	1	2	yes	—
368	C₂³	#15947	1	4	yes	—
369	C₂³	#15947	1	2	yes	—
370	C₂³	#15947	1	2	yes	—
371	C₂³	#23900	1	2	yes	—
372	C₂³	#23900	1	2	yes	—
373	C₂³	C₂×#2403	1	2	yes	—
374	C₂³	C₂×#2403	1	2	yes	—
375	C₂³	C₂×#2403	1	1	yes	characteristic
376	C₂³	C₂×#2679	1	2	yes	—
377	C₂×C₄	#15947	1	2	yes	—
378	C₂×C₄	#15947	1	4	yes	—
379	C₂×C₄	#15947	1	2	yes	—
380	C₂×C₄	#23900	1	2	yes	—
381	C₂×C₄	#23900	1	2	yes	—
382	C₂×C₄	#23900	1	8	yes	—
383	C₂×C₄	#23900	1	8	yes	—
384	C₂×C₄	C₂×#2403	1	2	yes	—
385	C₂×C₄	C₂×#2403	1	2	yes	—
386	C₂×C₄	C₂×#2679	1	1	yes	characteristic
387	C₂×C₄	C₂×#2679	1	2	yes	—
388	C₂×C₄	C₂×#2679	1	1	yes	characteristic
389	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
390	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
391	C₂×C₄	C₂²×B(4,𝔽₂)	1	2	yes	—
392	C₂²	#449475	1	4	yes	—
393	C₂²	C₂×#15947	1	1	yes	characteristic
394	C₂²	C₂×#23900	1	1	yes	characteristic
395	C₂²	C₂×#23900	1	1	yes	characteristic
396	C₄	#449475	1	4	yes	—
397	C₄	C₂×#23900	1	2	yes	—
398	C₄	C₂×#23900	1	2	yes	—
399	C₂	C₂×#449475	1	1	yes	characteristic
400	C₂	#72237529	1	2	yes	—

	subgroup	G/H
center, socle	C₂²	C₂×#23900
commutator, Frattini, cosocle	C₂²×#41	C₂⁵
LCS	G ▷ C₂²×#41 ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂²×#585 ◁ G
LECS	G ▷ C₂²×#41 ▷ C₂² ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72337506	C₂	semidirect
2. #72337433	C₂	semidirect
3. #72337426	C₂	semidirect
4. #72312834	C₂	semidirect
5. #72312697	C₂	semidirect
6. #72280972	C₂	semidirect
7. #72280881	C₂	semidirect
8. #72280746	C₂	semidirect
9. #72280610	C₂	semidirect
10. C₂×#6628885	C₂	semidirect
11. C₂²×#33553	C₂	semidirect
12. C₂×#63103	C₂²	semidirect
13. C₂²×#3537	C₂²	semidirect
19. C₂×#33553	C₂²	semidirect
20. C₂²×#2128	C₂²	semidirect
21. C₂²×#2122	C₂²	semidirect
22. C₂²×#2120	C₂²	semidirect
23. #6628899	C₂²	semidirect
24. #6628898	C₂²	semidirect
25. C₂×#32895	C₂²	semidirect
26. C₂×#32894	C₂²	semidirect
27. #6499824	C₂²	semidirect
28. #6499823	C₂²	semidirect
29. #6374164	C₂²	semidirect
30. #6374112	C₂²	semidirect
31. C₂×#20623	C₂²	semidirect
32. C₂×#20620	C₂²	semidirect
33. C₂×#20612	C₂²	semidirect
34. #6370734	C₂²	semidirect
35. #6370692	C₂²	semidirect
36. C₂×#12589	C₂²	semidirect
37. #492906	C₂²	semidirect
38. #492899	C₂²	semidirect
39. C₂×#12577	C₂²	semidirect
40. #147764	C₂²	semidirect
41. #147755	C₂²	semidirect
42. #147751	C₂²	semidirect
43. #147586	C₂²	semidirect
44. #147585	C₂²	semidirect
45. #147574	C₂²	semidirect
46. #147573	C₂²	semidirect
47. C₂×2₋¹⁺⁶	C₂³	semidirect
48. C₂×H(7,𝔽₂)	C₂³	semidirect
51. C₂³×AGL(1,ℤ/8)	D₄	semidirect
52. C₂³×AGL(1,ℤ/8)	D₄	semidirect
53. C₂×#3537	C₂³	semidirect
55. C₂²×#525	D₄	semidirect
56. C₂²×#525	D₄	semidirect
58. C₂×#3027	D₄	semidirect
60. C₂×#3025	D₄	semidirect
62. C₂²×#458	D₄	semidirect
63. C₂²×B(4,𝔽₂)	D₄	semidirect
64. C₂×#3021	D₄	semidirect
66. C₂×#3010	D₄	semidirect
68. C₂×#3008	D₄	semidirect
70. C₂×#2896	D₄	semidirect
71. C₂×#2896	D₄	semidirect
76. #35659	D₄	semidirect
78. #35512	D₄	semidirect
80. #34044	D₄	semidirect
81. #34044	D₄	semidirect
83. C₂×#2128	C₂³	semidirect
84. C₂×#2122	C₂³	semidirect
85. C₂×#2120	C₂³	semidirect
86. #21770	C₂³	semidirect
87. #21744	C₂³	semidirect
88. C₂×#1796	C₂³	semidirect
89. C₂×#1795	C₂³	semidirect
90. C₂×#1794	C₂³	semidirect
91. C₂×#1791	C₂³	semidirect
92. #20610	C₂³	semidirect
93. #20587	C₂³	semidirect
94. #20586	C₂³	semidirect
95. C₂×#1395	C₂³	semidirect
96. #12587	C₂³	semidirect
97. #12583	C₂³	semidirect
98. C₂×#1391	C₂³	semidirect
117. C₂²×AGL(1,ℤ/8)	C₂×D₄	semidirect
118. C₂²×AGL(1,ℤ/8)	C₂×D₄	semidirect
119. C₂³×SD₁₆	C₂×D₄	semidirect
120. C₂³×D₈	C₂×D₄	semidirect
129. C₂×#525	C₂×D₄	semidirect
130. C₂×#525	C₂×D₄	semidirect
133. C₂²×C₂²⋊Q₈	C₂×D₄	semidirect
134. C₂²×#121	C₂×D₄	semidirect
140. #3027	C₂×D₄	semidirect
141. C₂×#458	C₂×D₄	semidirect
142. C₂×B(4,𝔽₂)	C₂×D₄	semidirect
143. #3021	C₂×D₄	semidirect
144. C₂×#419	C₂×D₄	semidirect
145. C₂×#418	C₂×D₄	semidirect
146. C₂×#416	C₂×D₄	semidirect
147. C₂×#416	C₂×D₄	semidirect
158. #2311	C₂×D₄	semidirect
159. #2311	C₂×D₄	semidirect
161. #2310	C₂×D₄	semidirect
162. #2309	C₂×D₄	semidirect
196. C₂³×D₄	#120	semidirect
209. #535	#120	semidirect
217. C₂×#117	#120	semidirect

Maximal subgroups

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

subgroup	index
#72337506	2
#72337433	2
#72337426	2
#72312834	2
#72312697	2
#72280972	2
#72280881	2
#72280746	2
#72280610	2
C₂×#6628885	2
C₂²×#33553	2