Subgroups — #72238669

Order 2048.

At least 7644 conjugacy classes of subgroups; only the 376 normal subgroups are shown.

The subgroup lattice has 341 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72238668	C₂	1	2	yes	maximal, complemented
2	#72238667	C₂	1	2	yes	maximal, complemented
3	#72238659	C₂	1	1	yes	maximal, characteristic, complemented
4	#72238650	C₂	1	1	yes	maximal, characteristic, complemented
5	#72238642	C₂	1	1	yes	maximal, characteristic, complemented
6	#72238640	C₂	1	1	yes	maximal, characteristic, complemented
7	#72237556	C₂	1	1	yes	maximal, characteristic, complemented
8	#72235094	C₂	1	1	yes	maximal, characteristic, complemented
9	#72233382	C₂	1	2	yes	maximal, complemented
10	#72232284	C₂	1	1	yes	maximal, characteristic
11	#72215671	C₂	1	2	yes	maximal, complemented
12	C₂×#59089	C₄	1	1	yes	characteristic, complemented
13	C₂×#36614	C₂²	1	1	yes	characteristic
14	#6374576	C₂²	1	1	yes	characteristic, complemented
15	#6374576	C₂²	1	1	yes	characteristic, complemented
16	#2039915	C₄	1	1	yes	characteristic, complemented
17	#2039810	C₄	1	1	yes	characteristic, complemented
18	#2039127	C₂²	1	1	yes	characteristic
19	#2038758	C₂²	1	1	yes	characteristic
20	#850465	C₄	1	1	yes	characteristic, complemented
21	#850278	C₄	1	1	yes	characteristic, complemented
22	#664428	C₄	1	1	yes	characteristic, complemented
23	#663621	C₄	1	1	yes	characteristic, complemented
24	#648750	C₂²	1	1	yes	characteristic
25	#647656	C₂²	1	1	yes	characteristic
26	#619512	C₂²	1	1	yes	characteristic
27	#619112	C₂²	1	1	yes	characteristic
28	#532097	C₄	1	1	yes	characteristic, complemented
29	#188081	C₂²	1	1	yes	characteristic, complemented
30	#188081	C₂²	1	1	yes	characteristic, complemented
31	#139828	C₂²	1	2	yes	complemented
32	#139716	C₂²	1	2	yes	—
33	#139716	C₂²	1	2	yes	—
34	#139714	C₂²	1	2	yes	complemented
35	#139506	C₂²	1	2	yes	complemented
36	#139504	C₂²	1	2	yes	—
37	#139504	C₂²	1	2	yes	—
38	#139484	C₂²	1	2	yes	complemented
39	#134034	C₂²	1	2	yes	complemented
40	#134033	C₂²	1	2	yes	—
41	#115692	C₂²	1	2	yes	complemented
42	#115690	C₂²	1	2	yes	—
43	C₂⁶×C₄	D₄	1	1	yes	characteristic
44	C₂²×D₄²	C₂×C₄	1	1	yes	characteristic
45	C₂²×#525	C₂×C₄	1	1	yes	characteristic
46	C₂²×#525	C₂×C₄	1	1	yes	characteristic
47	C₂²×#525	C₂³	1	1	yes	characteristic
48	C₂×#2709	C₂×C₄	1	1	yes	characteristic
49	C₂×#2697	C₂×C₄	1	1	yes	characteristic
50	C₂×#2849	C₂×C₄	1	1	yes	characteristic
51	C₂×#2849	C₂×C₄	1	1	yes	characteristic
52	C₂×#2849	D₄	1	1	yes	characteristic
53	C₂×#2849	D₄	1	1	yes	characteristic
54	C₂×#2849	D₄	1	1	yes	characteristic
55	C₂×#2849	C₂³	1	1	yes	characteristic
56	C₂×#2846	D₄	1	1	yes	characteristic
57	C₂×#2846	C₂³	1	1	yes	characteristic
58	C₂×#2543	D₄	1	1	yes	characteristic
59	C₂×#2534	D₄	1	1	yes	characteristic
60	C₂×#2404	C₂×C₄	1	1	yes	characteristic
61	C₂×#2431	C₂×C₄	1	1	yes	characteristic
62	C₂×#2635	D₄	1	1	yes	characteristic
63	C₂×#2358	C₂×C₄	1	1	yes	characteristic
64	C₂×#2321	D₄	1	1	yes	characteristic
65	C₂×#2280	D₄	1	1	yes	characteristic
66	C₂×#2280	D₄	1	1	yes	characteristic
67	C₂×#2280	D₄	1	1	yes	characteristic
68	#21746	C₂³	1	2	yes	—
69	#21746	C₂³	1	2	yes	—
70	#15984	D₄	1	1	yes	characteristic
71	#15983	C₂×C₄	1	1	yes	characteristic
72	#15982	C₂×C₄	1	1	yes	characteristic
73	#15948	C₂×C₄	1	1	yes	characteristic
74	#15948	C₂×C₄	1	1	yes	characteristic
75	#15948	C₂³	1	1	yes	characteristic
76	#15947	C₂×C₄	1	1	yes	characteristic
77	#15947	C₂³	1	1	yes	characteristic
78	#15466	D₄	1	1	yes	characteristic
79	#15465	D₄	1	1	yes	characteristic
80	#15464	C₂×C₄	1	1	yes	characteristic
81	#15463	C₂×C₄	1	1	yes	characteristic
82	#15283	C₂³	1	1	yes	characteristic
83	#15281	C₂×C₄	1	1	yes	characteristic
84	#15266	C₂×C₄	1	1	yes	characteristic
85	#15264	D₄	1	1	yes	characteristic
86	#15264	D₄	1	1	yes	characteristic
87	#15261	C₂×C₄	1	1	yes	characteristic
88	#15261	C₂×C₄	1	1	yes	characteristic
89	#15260	D₄	1	1	yes	characteristic
90	#15258	C₂×C₄	1	1	yes	characteristic
91	#15258	C₂³	1	1	yes	characteristic
92	#15257	D₄	1	1	yes	characteristic
93	#15257	D₄	1	1	yes	characteristic
94	#14506	C₂×C₄	1	1	yes	characteristic
95	#14506	C₂×C₄	1	1	yes	characteristic
96	#14344	D₄	1	1	yes	characteristic
97	#14134	C₂×C₄	1	1	yes	characteristic
98	#14134	C₂×C₄	1	1	yes	characteristic
99	#13956	C₂×C₄	1	1	yes	characteristic
100	#13940	D₄	1	1	yes	characteristic
101	#13940	D₄	1	1	yes	characteristic
102	#13937	C₂×C₄	1	1	yes	characteristic
103	#13784	D₄	1	1	yes	characteristic
104	#8547	C₂³	1	2	yes	—
105	#8547	C₂³	1	2	yes	—
106	C₂⁷	C₂×D₄	1	1	yes	characteristic
107	C₂³×#41	C₂²×C₄	1	1	yes	characteristic
108	C₂⁵×C₄	C₂²⋊C₄	1	1	yes	characteristic
109	C₂⁵×C₄	C₂²⋊C₄	1	1	yes	characteristic
110	C₂⁵×C₄	C₂²⋊C₄	1	1	yes	characteristic
111	C₂⁵×C₄	C₂²⋊C₄	1	1	yes	characteristic
112	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
113	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
114	C₂²×#127	C₂²×C₄	1	1	yes	characteristic
115	C₂²×#124	C₂²⋊C₄	1	1	yes	characteristic, complemented
116	C₂²×#123	C₂²⋊C₄	1	1	yes	characteristic
117	C₂²×#123	C₂²⋊C₄	1	1	yes	characteristic
118	C₂²×#123	C₂²×C₄	1	1	yes	characteristic
119	C₂²×#123	C₂²×C₄	1	1	yes	characteristic
120	C₂²×#123	C₂²×C₄	1	1	yes	characteristic
121	C₂²×#123	C₂×D₄	1	1	yes	characteristic
122	C₂²×#123	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₂²⋊Q₈	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₂²⋊Q₈	C₂×D₄	1	1	yes	characteristic
125	C₂²×#121	C₂²⋊C₄	1	1	yes	characteristic, complemented
126	C₂²×#121	C₂×D₄	1	1	yes	characteristic
127	C₂²×#121	C₂×D₄	1	1	yes	characteristic
128	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
129	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
130	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic, complemented
131	C₂²×#120	C₂²×C₄	1	1	yes	characteristic
132	C₂²×#120	C₂²×C₄	1	1	yes	characteristic
133	C₂²×#120	C₂²×C₄	1	1	yes	characteristic
134	C₂²×#120	C₂×D₄	1	1	yes	characteristic
135	C₂²×#120	C₂×D₄	1	1	yes	characteristic
136	C₂²×#120	C₂×D₄	1	1	yes	characteristic
137	C₂²×#120	C₂⁴	1	1	yes	characteristic
138	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
142	C₂²×#117	C₂²⋊C₄	1	1	yes	characteristic
143	C₂²×#117	C₂²⋊C₄	1	1	yes	characteristic
144	C₂²×#117	C₂×D₄	1	1	yes	characteristic
145	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
146	C₂×#400	C₂²⋊C₄	1	1	yes	characteristic, complemented
147	C₂×#399	C₂×D₄	1	1	yes	characteristic
148	C₂×#398	C₂²⋊C₄	1	1	yes	characteristic, complemented
149	C₂×#397	C₂×D₄	1	1	yes	characteristic
150	C₂×#394	C₂²⋊C₄	1	1	yes	characteristic, complemented
151	C₂×#394	C₂²⋊C₄	1	1	yes	characteristic, complemented
152	C₂×#392	C₂×D₄	1	1	yes	characteristic
153	C₂×#392	C₂×D₄	1	1	yes	characteristic
154	C₂×#391	C₂²⋊C₄	1	1	yes	characteristic, complemented
155	C₂×#390	C₂²×C₄	1	1	yes	characteristic
156	C₂×#386	C₂²⋊C₄	1	1	yes	characteristic, complemented
157	C₂×#386	C₂²×C₄	1	1	yes	characteristic
158	C₂×#386	C₂×D₄	1	1	yes	characteristic
159	C₂×#385	C₂²⋊C₄	1	1	yes	characteristic, complemented
160	C₂×#381	C₂²⋊C₄	1	1	yes	characteristic
161	C₂×#381	C₂²⋊C₄	1	1	yes	characteristic
162	C₂×#381	C₂²⋊C₄	1	1	yes	characteristic
163	C₂×#381	C₂²⋊C₄	1	1	yes	characteristic
164	C₂×#381	C₂²⋊C₄	1	1	yes	characteristic, complemented
165	C₂×#381	C₂²⋊C₄	1	1	yes	characteristic, complemented
166	C₂×#381	C₂²⋊C₄	1	1	yes	characteristic, complemented
167	C₂×#381	C₂×D₄	1	1	yes	characteristic
168	C₂×#381	C₂×D₄	1	1	yes	characteristic
169	C₂×#380	C₂²⋊C₄	1	1	yes	characteristic, complemented
170	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
171	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
172	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic, complemented
173	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic, complemented
174	C₂×#379	C₂×D₄	1	1	yes	characteristic
175	C₂×#379	C₂×D₄	1	1	yes	characteristic
176	C₂×#379	C₂×D₄	1	1	yes	characteristic
177	C₂×#379	C₂×D₄	1	1	yes	characteristic
178	C₂×C₄×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
179	C₂×C₄×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
180	C₂²×#95	C₂²⋊C₄	1	1	yes	characteristic, complemented
181	#1446	C₂²⋊C₄	1	1	yes	characteristic, complemented
182	#1446	C₂²⋊C₄	1	1	yes	characteristic, complemented
183	#1440	C₂²⋊C₄	1	1	yes	characteristic, complemented
184	#1440	C₂²⋊C₄	1	1	yes	characteristic, complemented
185	#1440	C₂²⋊C₄	1	1	yes	characteristic, complemented
186	#1440	C₂²⋊C₄	1	1	yes	characteristic, complemented
187	#1438	C₂²⋊C₄	1	1	yes	characteristic, complemented
188	#1438	C₂²⋊C₄	1	1	yes	characteristic, complemented
189	#1438	C₂²×C₄	1	1	yes	characteristic
190	#1438	C₂²×C₄	1	1	yes	characteristic
191	#1438	C₂²×C₄	1	1	yes	characteristic
192	#1438	C₂²×C₄	1	1	yes	characteristic
193	#1438	C₂×D₄	1	1	yes	characteristic
194	#1438	C₂×D₄	1	1	yes	characteristic
195	#1438	C₂×D₄	1	1	yes	characteristic
196	#1438	C₂×D₄	1	1	yes	characteristic
197	#1437	C₂×D₄	1	1	yes	characteristic
198	#1437	C₂×D₄	1	1	yes	characteristic
199	#1437	C₂×D₄	1	1	yes	characteristic
200	#1437	C₂×D₄	1	1	yes	characteristic
201	#1436	C₂²⋊C₄	1	1	yes	characteristic, complemented
202	#1436	C₂²⋊C₄	1	1	yes	characteristic, complemented
203	#1436	C₂²⋊C₄	1	1	yes	characteristic, complemented
204	#1436	C₂²⋊C₄	1	1	yes	characteristic, complemented
205	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
206	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
207	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
208	C₂⁶	C₂²×D₄	1	1	yes	characteristic
209	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
210	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
211	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
212	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
213	C₂³×D₄	#120	1	1	yes	characteristic
214	C₂³×D₄	#120	1	1	yes	characteristic
215	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
216	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
217	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
218	C₂⁴×C₄	#99	1	2	yes	—
219	C₂⁴×C₄	#99	1	2	yes	—
220	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
221	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
222	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
223	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
224	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
225	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
226	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
227	C₂⁴×C₄	#120	1	1	yes	characteristic
228	C₂⁴×C₄	#120	1	1	yes	characteristic
229	C₂⁴×C₄	#120	1	1	yes	characteristic
230	C₂⁴×C₄	#120	1	1	yes	characteristic
231	C₂×#117	#99	1	2	yes	—
232	C₂×#117	#99	1	2	yes	—
233	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
234	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
235	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
236	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
237	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
238	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
239	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
240	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
241	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
242	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
243	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
244	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
245	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
246	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
247	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
248	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
249	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
250	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
251	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
252	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
253	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
254	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
255	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
256	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
257	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
258	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
259	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
260	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
261	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
262	C₂²×C₄²	#120	1	1	yes	characteristic
263	C₂²×C₄²	#120	1	1	yes	characteristic
264	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
265	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
266	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
267	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
268	C₂⁵	#379	1	1	yes	characteristic
269	C₂⁵	C₂×#99	1	2	yes	—
270	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
271	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
272	C₂⁵	C₂×#120	1	1	yes	characteristic
273	C₂⁵	C₂×#120	1	1	yes	characteristic
274	C₂³×C₄	#379	1	1	yes	characteristic
275	C₂³×C₄	#379	1	1	yes	characteristic
276	C₂³×C₄	#379	1	1	yes	characteristic
277	C₂³×C₄	#379	1	1	yes	characteristic
278	C₂³×C₄	#379	1	1	yes	characteristic
279	C₂³×C₄	#379	1	1	yes	characteristic
280	C₂³×C₄	#379	1	1	yes	characteristic
281	C₂³×C₄	C₂×#99	1	1	yes	characteristic
282	C₂³×C₄	C₂×#99	1	1	yes	characteristic
283	C₂³×C₄	C₂×#99	1	1	yes	characteristic
284	C₂³×C₄	C₂×#99	1	2	yes	—
285	C₂³×C₄	C₂×#99	1	1	yes	characteristic
286	C₂³×C₄	B(4,𝔽₂)	1	1	yes	characteristic
287	C₂³×C₄	B(4,𝔽₂)	1	1	yes	characteristic
288	C₂³×C₄	B(4,𝔽₂)	1	1	yes	characteristic
289	C₂³×C₄	B(4,𝔽₂)	1	1	yes	characteristic
290	C₂³×C₄	#458	1	1	yes	characteristic
291	C₂³×C₄	#458	1	1	yes	characteristic
292	C₂³×C₄	#458	1	1	yes	characteristic
293	C₂³×C₄	#458	1	1	yes	characteristic
294	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
295	C₂³×C₄	C₂×#120	1	1	yes	characteristic
296	C₂³×C₄	C₂×#120	1	1	yes	characteristic
297	C₂×C₂²⋊C₄	C₂×#99	1	2	yes	—
298	C₂×C₂²⋊C₄	C₂×#99	1	2	yes	—
299	C₂⁴	#2121	1	4	yes	—
300	C₂⁴	C₂×#379	1	1	yes	characteristic
301	C₂⁴	C₂²×#99	1	1	yes	characteristic
302	C₂⁴	C₂²×#99	1	1	yes	characteristic
303	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
304	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
305	C₂⁴	C₂×#458	1	1	yes	characteristic
306	C₂⁴	C₂×#458	1	1	yes	characteristic
307	C₂²×C₄	#1781	1	1	yes	characteristic
308	C₂²×C₄	#1781	1	1	yes	characteristic
309	C₂²×C₄	#1781	1	1	yes	characteristic
310	C₂²×C₄	#1781	1	1	yes	characteristic
311	C₂²×C₄	#1790	1	1	yes	characteristic
312	C₂²×C₄	#1790	1	1	yes	characteristic
313	C₂²×C₄	#1790	1	1	yes	characteristic
314	C₂²×C₄	#1790	1	1	yes	characteristic
315	C₂²×C₄	#1790	1	1	yes	characteristic
316	C₂²×C₄	#1790	1	1	yes	characteristic
317	C₂²×C₄	#1790	1	1	yes	characteristic
318	C₂²×C₄	#1790	1	1	yes	characteristic
319	C₂³	C₂×#1781	1	1	yes	characteristic
320	C₂³	C₂×#1790	1	1	yes	characteristic
321	C₂³	C₂×#1790	1	1	yes	characteristic
322	C₂³	C₂×#2121	1	2	yes	—
323	C₂³	#33546	1	2	yes	—
324	C₂³	#33553	1	2	yes	—
325	C₂×C₄	#8534	1	1	yes	characteristic
326	C₂×C₄	#8534	1	1	yes	characteristic
327	C₂×C₄	#8534	1	1	yes	characteristic
328	C₂×C₄	#8534	1	1	yes	characteristic
329	C₂×C₄	#12705	1	2	yes	—
330	C₂²	C₂×#8534	1	1	yes	characteristic
331	C₂²	#493357	1	1	yes	characteristic
332	C₂²	C₂×#12705	1	1	yes	characteristic
333	C₂²	#493561	1	1	yes	characteristic
334	C₂²	#493561	1	1	yes	characteristic
335	C₂²	#493577	1	1	yes	characteristic
336	C₂²	#493584	1	1	yes	characteristic
337	C₂	#72219035	1	1	yes	characteristic
338	C₂	#72238628	1	1	yes	characteristic
339	C₂	#72238630	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×#8534
commutator	C₂³×D₄	C₂³×C₄
Frattini, cosocle	C₂²×#120	C₂⁴
prime radical	#72232284	C₂
LCS	G ▷ C₂³×D₄ ▷ C₂⁴ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂²×#525 ◁ G
LECS	G ▷ C₂²×#120 ▷ C₂⁴ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72238668	C₂	semidirect
2. #72238667	C₂	semidirect
3. #72238659	C₂	semidirect
4. #72238650	C₂	semidirect
5. #72238642	C₂	semidirect
6. #72238640	C₂	semidirect
7. #72237556	C₂	semidirect
8. #72235094	C₂	semidirect
9. #72233382	C₂	semidirect
11. #72215671	C₂	semidirect
12. C₂×#59089	C₄	semidirect
14. #6374576	C₂²	semidirect
15. #6374576	C₂²	semidirect
16. #2039915	C₄	semidirect
17. #2039810	C₄	semidirect
20. #850465	C₄	semidirect
21. #850278	C₄	semidirect
22. #664428	C₄	semidirect
23. #663621	C₄	semidirect
28. #532097	C₄	semidirect
29. #188081	C₂²	semidirect
30. #188081	C₂²	semidirect
31. #139828	C₂²	semidirect
34. #139714	C₂²	semidirect
35. #139506	C₂²	semidirect
38. #139484	C₂²	semidirect
39. #134034	C₂²	semidirect
41. #115692	C₂²	semidirect
115. C₂²×#124	C₂²⋊C₄	semidirect
125. C₂²×#121	C₂²⋊C₄	semidirect
130. C₂²×#120	C₂²⋊C₄	semidirect
145. C₂³×C₂²⋊C₄	C₂²⋊C₄	semidirect
146. C₂×#400	C₂²⋊C₄	semidirect
148. C₂×#398	C₂²⋊C₄	semidirect
150. C₂×#394	C₂²⋊C₄	semidirect
151. C₂×#394	C₂²⋊C₄	semidirect
154. C₂×#391	C₂²⋊C₄	semidirect
156. C₂×#386	C₂²⋊C₄	semidirect
159. C₂×#385	C₂²⋊C₄	semidirect
164. C₂×#381	C₂²⋊C₄	semidirect
165. C₂×#381	C₂²⋊C₄	semidirect
166. C₂×#381	C₂²⋊C₄	semidirect
169. C₂×#380	C₂²⋊C₄	semidirect
172. C₂×#379	C₂²⋊C₄	semidirect
173. C₂×#379	C₂²⋊C₄	semidirect
178. C₂×C₄×C₂²⋊C₄	C₂²⋊C₄	semidirect
179. C₂×C₄×C₂²⋊C₄	C₂²⋊C₄	semidirect
180. C₂²×#95	C₂²⋊C₄	semidirect
181. #1446	C₂²⋊C₄	semidirect
182. #1446	C₂²⋊C₄	semidirect
183. #1440	C₂²⋊C₄	semidirect
184. #1440	C₂²⋊C₄	semidirect
185. #1440	C₂²⋊C₄	semidirect
186. #1440	C₂²⋊C₄	semidirect
187. #1438	C₂²⋊C₄	semidirect
188. #1438	C₂²⋊C₄	semidirect
201. #1436	C₂²⋊C₄	semidirect
202. #1436	C₂²⋊C₄	semidirect
203. #1436	C₂²⋊C₄	semidirect
204. #1436	C₂²⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
#72238668	2
#72238667	2
#72238659	2
#72238650	2
#72238642	2
#72238640	2
#72237556	2
#72235094	2
#72233382	2
#72232284	2
#72215671	2