Subgroups — #72238694

Order 2048.

At least 8096 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	#72238693	C₂	1	2	yes	maximal, complemented
2	#72238692	C₂	1	2	yes	maximal, complemented
3	#72238691	C₂	1	2	yes	maximal, complemented
4	#72238690	C₂	1	2	yes	maximal, complemented
5	#72238688	C₂	1	1	yes	maximal, characteristic, complemented
6	#72238687	C₂	1	1	yes	maximal, characteristic, complemented
7	#72238676	C₂	1	1	yes	maximal, characteristic, complemented
8	#72238673	C₂	1	1	yes	maximal, characteristic, complemented
9	#72237547	C₂	1	1	yes	maximal, characteristic, complemented
10	#72235087	C₂	1	1	yes	maximal, characteristic, complemented
11	#72232286	C₂	1	1	yes	maximal, characteristic
12	C₂×#47177	C₄	1	1	yes	characteristic, complemented
13	C₂×#35222	C₂²	1	1	yes	characteristic
14	#6374576	C₂²	1	1	yes	characteristic, complemented
15	#6342640	C₂²	1	1	yes	characteristic, complemented
16	#4933525	C₂²	1	1	yes	characteristic
17	#4932464	C₄	1	1	yes	characteristic, complemented
18	#4598732	C₂²	1	1	yes	characteristic
19	#4598429	C₄	1	1	yes	characteristic, complemented
20	#4320270	C₄	1	1	yes	characteristic, complemented
21	#4319989	C₄	1	1	yes	characteristic, complemented
22	#2812811	C₄	1	1	yes	characteristic, complemented
23	#2807924	C₂²	1	1	yes	characteristic
24	#1495845	C₄	1	1	yes	characteristic, complemented
25	#1494110	C₂²	1	1	yes	characteristic
26	#619125	C₂²	1	1	yes	characteristic
27	#619101	C₂²	1	1	yes	characteristic
28	#576588	C₄	1	1	yes	characteristic, complemented
29	#188029	C₂²	1	1	yes	characteristic, complemented
30	#188029	C₂²	1	1	yes	characteristic, complemented
31	#139851	C₂²	1	2	yes	complemented
32	#139795	C₂²	1	2	yes	complemented
33	#139794	C₂²	1	2	yes	complemented
34	#139794	C₂²	1	2	yes	complemented
35	#139474	C₂²	1	2	yes	complemented
36	#139472	C₂²	1	2	yes	complemented
37	#139472	C₂²	1	2	yes	complemented
38	#139434	C₂²	1	2	yes	complemented
39	#133828	C₂²	1	2	yes	—
40	#133828	C₂²	1	2	yes	complemented
41	#115640	C₂²	1	2	yes	—
42	#115640	C₂²	1	2	yes	complemented
43	C₂⁵×D₄	D₄	1	1	yes	characteristic
44	C₂²×#535	D₄	1	1	yes	characteristic
45	C₂²×#535	D₄	1	1	yes	characteristic
46	C₂²×#525	C₂³	1	1	yes	characteristic
47	C₂×#2784	C₂×C₄	1	1	yes	characteristic, complemented
48	C₂×#2679	C₂×C₄	1	1	yes	characteristic, complemented
49	C₂×#2828	C₂×C₄	1	1	yes	characteristic, complemented
50	C₂×#2544	D₄	1	1	yes	characteristic
51	C₂×#2535	D₄	1	1	yes	characteristic
52	C₂×#2610	C₂×C₄	1	1	yes	characteristic
53	C₂×#2598	C₂×C₄	1	1	yes	characteristic
54	C₂×#2555	C₂×C₄	1	1	yes	characteristic, complemented
55	C₂×#2435	C₂×C₄	1	1	yes	characteristic
56	C₂×#2435	C₂×C₄	1	1	yes	characteristic
57	C₂×#2435	D₄	1	1	yes	characteristic
58	C₂×#2435	D₄	1	1	yes	characteristic
59	C₂×#2433	D₄	1	1	yes	characteristic
60	C₂×#2433	D₄	1	1	yes	characteristic
61	C₂×#2433	C₂³	1	1	yes	characteristic
62	C₂×#2433	C₂³	1	1	yes	characteristic
63	C₂×#2631	D₄	1	1	yes	characteristic
64	C₂×#2328	D₄	1	1	yes	characteristic
65	C₂×#2309	C₂×C₄	1	1	yes	characteristic
66	C₂×#2309	C₂×C₄	1	1	yes	characteristic
67	C₂×#2280	D₄	1	1	yes	characteristic
68	#21793	C₂³	1	2	yes	—
69	#17396	C₂³	1	2	yes	—
70	#15820	C₂×C₄	1	1	yes	characteristic, complemented
71	#15820	C₂×C₄	1	1	yes	characteristic, complemented
72	#15674	C₂³	1	1	yes	characteristic
73	#15673	C₂³	1	1	yes	characteristic
74	#15671	C₂×C₄	1	1	yes	characteristic
75	#15670	C₂×C₄	1	1	yes	characteristic
76	#15669	D₄	1	1	yes	characteristic
77	#15668	D₄	1	1	yes	characteristic
78	#15662	C₂×C₄	1	1	yes	characteristic, complemented
79	#15662	C₂×C₄	1	1	yes	characteristic, complemented
80	#15630	C₂×C₄	1	1	yes	characteristic, complemented
81	#15630	C₂×C₄	1	1	yes	characteristic, complemented
82	#15630	C₂×C₄	1	1	yes	characteristic, complemented
83	#15630	C₂×C₄	1	1	yes	characteristic, complemented
84	#15453	C₂×C₄	1	1	yes	characteristic
85	#15453	C₂×C₄	1	1	yes	characteristic
86	#15412	D₄	1	1	yes	characteristic
87	#15412	D₄	1	1	yes	characteristic
88	#15310	C₂³	1	1	yes	characteristic
89	#15310	C₂³	1	1	yes	characteristic
90	#15283	D₄	1	1	yes	characteristic
91	#15259	D₄	1	1	yes	characteristic
92	#15258	D₄	1	1	yes	characteristic
93	#15258	D₄	1	1	yes	characteristic
94	#14503	C₂×C₄	1	1	yes	characteristic, complemented
95	#14445	C₂×C₄	1	1	yes	characteristic, complemented
96	#14345	D₄	1	1	yes	characteristic
97	#13959	D₄	1	1	yes	characteristic
98	#13959	D₄	1	1	yes	characteristic
99	#13957	C₂×C₄	1	1	yes	characteristic
100	#13938	C₂×C₄	1	1	yes	characteristic
101	#13832	C₂×C₄	1	1	yes	characteristic, complemented
102	#13824	C₂×C₄	1	1	yes	characteristic, complemented
103	#13785	D₄	1	1	yes	characteristic
104	#8542	C₂³	1	2	yes	—
105	#8542	C₂³	1	2	yes	—
106	C₂³×#41	C₂×D₄	1	1	yes	characteristic
107	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
108	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
109	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
110	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
111	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
112	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
113	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
114	C₂²×#127	C₂×D₄	1	1	yes	characteristic
115	C₂²×#127	C₂×D₄	1	1	yes	characteristic
116	C₂²×#127	C₂×D₄	1	1	yes	characteristic
117	C₂²×#127	C₂×D₄	1	1	yes	characteristic
118	C₂²×#127	C₂×D₄	1	1	yes	characteristic
119	C₂²×#127	C₂×D₄	1	1	yes	characteristic
120	C₂²×#124	C₂²⋊C₄	1	1	yes	characteristic
121	C₂²×#124	C₂²⋊C₄	1	1	yes	characteristic
122	C₂²×#124	C₂²⋊C₄	1	1	yes	characteristic
123	C₂²×#124	C₂²⋊C₄	1	1	yes	characteristic
124	C₂²×#124	C₂²⋊C₄	1	1	yes	characteristic
125	C₂²×#124	C₂×D₄	1	1	yes	characteristic
126	C₂²×#123	C₂×D₄	1	1	yes	characteristic
127	C₂²×#123	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₂²⋊Q₈	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₂²⋊Q₈	C₂×D₄	1	1	yes	characteristic
130	C₂²×#121	C₂×D₄	1	1	yes	characteristic
131	C₂²×#121	C₂⁴	1	1	yes	characteristic
132	C₂²×#120	C₂×D₄	1	1	yes	characteristic
133	C₂²×#120	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
135	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
139	C₂²×#117	C₂²⋊C₄	1	1	yes	characteristic
140	C₂²×#117	C₂²⋊C₄	1	1	yes	characteristic
141	C₂²×#117	C₂²×C₄	1	1	yes	characteristic
142	C₂×#400	C₂²×C₄	1	1	yes	characteristic
143	C₂×#399	C₂²⋊C₄	1	1	yes	characteristic
144	C₂×#397	C₂²⋊C₄	1	1	yes	characteristic
145	C₂×#397	C₂×D₄	1	1	yes	characteristic
146	C₂×#395	C₂²×C₄	1	1	yes	characteristic
147	C₂×#394	C₂²×C₄	1	1	yes	characteristic
148	C₂×#394	C₂²×C₄	1	1	yes	characteristic
149	C₂×#393	C₂²⋊C₄	1	1	yes	characteristic
150	C₂×#393	C₂²⋊C₄	1	1	yes	characteristic
151	C₂×#393	C₂×D₄	1	1	yes	characteristic
152	C₂×#392	C₂²⋊C₄	1	1	yes	characteristic
153	C₂×#392	C₂²⋊C₄	1	1	yes	characteristic
154	C₂×#392	C₂²⋊C₄	1	1	yes	characteristic
155	C₂×#392	C₂²⋊C₄	1	1	yes	characteristic
156	C₂×#392	C₂×D₄	1	1	yes	characteristic
157	C₂×#392	C₂×D₄	1	1	yes	characteristic
158	C₂×#391	C₂²⋊C₄	1	1	yes	characteristic
159	C₂×#390	C₂²⋊C₄	1	1	yes	characteristic
160	C₂×#390	C₂²⋊C₄	1	1	yes	characteristic
161	C₂×#390	C₂²⋊C₄	1	1	yes	characteristic
162	C₂×#390	C₂²⋊C₄	1	1	yes	characteristic
163	C₂×#390	C₂²⋊C₄	1	1	yes	characteristic
164	C₂×#390	C₂²⋊C₄	1	1	yes	characteristic
165	C₂×#390	C₂²×C₄	1	1	yes	characteristic
166	C₂×#390	C₂²×C₄	1	1	yes	characteristic
167	C₂×#390	C₂²×C₄	1	1	yes	characteristic
168	C₂×#390	C₂²×C₄	1	1	yes	characteristic
169	C₂×#390	C₂×D₄	1	1	yes	characteristic
170	C₂×#383	C₂²⋊C₄	1	1	yes	characteristic
171	C₂×#383	C₂²⋊C₄	1	1	yes	characteristic
172	C₂×#382	C₂²⋊C₄	1	1	yes	characteristic
173	C₂×#382	C₂²⋊C₄	1	1	yes	characteristic
174	C₂×C₄×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
175	C₂×C₄×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
176	C₂×C₄×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
177	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
178	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
179	C₂×#376	C₂²⋊C₄	1	1	yes	characteristic
180	C₂×#376	C₂²⋊C₄	1	1	yes	characteristic
181	#1445	C₂²⋊C₄	1	1	yes	characteristic
182	#1445	C₂²⋊C₄	1	1	yes	characteristic
183	#1445	C₂²⋊C₄	1	1	yes	characteristic
184	#1445	C₂²⋊C₄	1	1	yes	characteristic
185	#1438	C₂×D₄	1	1	yes	characteristic
186	#1438	C₂×D₄	1	1	yes	characteristic
187	#1438	C₂×D₄	1	1	yes	characteristic
188	#1438	C₂×D₄	1	1	yes	characteristic
189	#1437	C₂²⋊C₄	1	1	yes	characteristic
190	#1437	C₂²⋊C₄	1	1	yes	characteristic
191	#1437	C₂²⋊C₄	1	1	yes	characteristic
192	#1437	C₂²⋊C₄	1	1	yes	characteristic
193	#1437	C₂²⋊C₄	1	1	yes	characteristic
194	#1437	C₂²⋊C₄	1	1	yes	characteristic
195	#1437	C₂²⋊C₄	1	1	yes	characteristic
196	#1437	C₂²⋊C₄	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
202	#1436	C₂²×C₄	1	1	yes	characteristic
203	#1436	C₂²×C₄	1	1	yes	characteristic
204	#1436	C₂²×C₄	1	1	yes	characteristic
205	C₂⁶	#120	1	1	yes	characteristic
206	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
207	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
208	C₂³×D₄	#99	1	2	yes	—
209	C₂³×D₄	#99	1	2	yes	—
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	C₂×C₂²⋊C₄	1	1	yes	characteristic
214	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
215	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
216	C₂³×D₄	#120	1	1	yes	characteristic
217	C₂³×D₄	#120	1	1	yes	characteristic
218	C₂³×D₄	#120	1	1	yes	characteristic
219	C₂³×D₄	#120	1	1	yes	characteristic
220	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
221	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
222	C₂³×D₄	C₂²×D₄	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	#120	1	1	yes	characteristic
226	C₂⁴×C₄	#120	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	C₂²×D₄	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	C₂×C₂²⋊C₄	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	C₂³×C₄	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	#120	1	1	yes	characteristic
245	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
246	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
247	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
248	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
249	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
250	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
251	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
252	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
253	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
254	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
255	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
256	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
257	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
258	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
259	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
260	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
261	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
262	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
263	C₂×#95	C₂×C₂²⋊C₄	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	#379	1	1	yes	characteristic
270	C₂⁵	C₂×#120	1	1	yes	characteristic
271	C₂⁵	C₂×#120	1	1	yes	characteristic
272	C₂⁵	C₂×#120	1	1	yes	characteristic
273	C₂²×D₄	C₂×#99	1	2	yes	—
274	C₂²×D₄	C₂×#99	1	2	yes	—
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	1	yes	characteristic
285	C₂³×C₄	B(4,𝔽₂)	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	#458	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	C₂²×C₂²⋊C₄	1	1	yes	characteristic
294	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
295	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
296	C₂³×C₄	C₂×#120	1	1	yes	characteristic
297	C₂×C₄²	C₂×#99	1	2	yes	—
298	C₂×C₄²	C₂×#99	1	2	yes	—
299	C₂⁴	#1781	1	1	yes	characteristic
300	C₂⁴	#1781	1	1	yes	characteristic
301	C₂⁴	#1790	1	1	yes	characteristic
302	C₂⁴	#1790	1	1	yes	characteristic
303	C₂⁴	C₂×#379	1	1	yes	characteristic
304	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
305	C₂⁴	C₂×#458	1	1	yes	characteristic
306	C₂×D₄	#2127	1	4	yes	—
307	C₂²×C₄	#1781	1	1	yes	characteristic
308	C₂²×C₄	#1781	1	1	yes	characteristic
309	C₂²×C₄	#1790	1	1	yes	characteristic
310	C₂²×C₄	#1790	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	C₂²×#99	1	1	yes	characteristic
316	C₂²×C₄	C₂²×#99	1	1	yes	characteristic
317	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
318	C₂²×C₄	C₂×#458	1	1	yes	characteristic
319	C₂³	#12707	1	2	yes	—
320	C₂³	#12778	1	2	yes	—
321	C₂³	C₂×#1781	1	1	yes	characteristic
322	C₂³	C₂×#1790	1	1	yes	characteristic
323	C₂³	C₂×#1790	1	1	yes	characteristic
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	C₂×#2127	1	2	yes	—
330	C₂²	C₂×#8534	1	1	yes	characteristic
331	C₂²	#493370	1	1	yes	characteristic
332	C₂²	C₂×#12707	1	1	yes	characteristic
333	C₂²	#493584	1	1	yes	characteristic
334	C₂²	#493595	1	1	yes	characteristic
335	C₂²	C₂×#12778	1	1	yes	characteristic
336	C₂²	#493621	1	1	yes	characteristic
337	C₂	#72219022	1	1	yes	characteristic
338	C₂	#72238618	1	1	yes	characteristic
339	C₂	#72238622	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×#8534
commutator	C₂²×C₄⋊C₄	C₂³×C₄
Frattini, cosocle	C₂²×#121	C₂⁴
prime radical	#72232286	C₂
LCS	G ▷ C₂²×C₄⋊C₄ ▷ C₂⁴ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂²×#525 ◁ G
LECS	G ▷ C₂²×#121 ▷ C₂⁴ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72238693	C₂	semidirect
2. #72238692	C₂	semidirect
3. #72238691	C₂	semidirect
4. #72238690	C₂	semidirect
5. #72238688	C₂	semidirect
6. #72238687	C₂	semidirect
7. #72238676	C₂	semidirect
8. #72238673	C₂	semidirect
9. #72237547	C₂	semidirect
10. #72235087	C₂	semidirect
12. C₂×#47177	C₄	semidirect
14. #6374576	C₂²	semidirect
15. #6342640	C₂²	semidirect
17. #4932464	C₄	semidirect
19. #4598429	C₄	semidirect
20. #4320270	C₄	semidirect
21. #4319989	C₄	semidirect
22. #2812811	C₄	semidirect
24. #1495845	C₄	semidirect
28. #576588	C₄	semidirect
29. #188029	C₂²	semidirect
30. #188029	C₂²	semidirect
31. #139851	C₂²	semidirect
32. #139795	C₂²	semidirect
33. #139794	C₂²	semidirect
34. #139794	C₂²	semidirect
35. #139474	C₂²	semidirect
36. #139472	C₂²	semidirect
37. #139472	C₂²	semidirect
38. #139434	C₂²	semidirect
40. #133828	C₂²	semidirect
42. #115640	C₂²	semidirect
47. C₂×#2784	C₂×C₄	semidirect
48. C₂×#2679	C₂×C₄	semidirect
49. C₂×#2828	C₂×C₄	semidirect
54. C₂×#2555	C₂×C₄	semidirect
70. #15820	C₂×C₄	semidirect
71. #15820	C₂×C₄	semidirect
78. #15662	C₂×C₄	semidirect
79. #15662	C₂×C₄	semidirect
80. #15630	C₂×C₄	semidirect
81. #15630	C₂×C₄	semidirect
82. #15630	C₂×C₄	semidirect
83. #15630	C₂×C₄	semidirect
94. #14503	C₂×C₄	semidirect
95. #14445	C₂×C₄	semidirect
101. #13832	C₂×C₄	semidirect
102. #13824	C₂×C₄	semidirect

Maximal subgroups

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

subgroup	index
#72238693	2
#72238692	2
#72238691	2
#72238690	2
#72238688	2
#72238687	2
#72238676	2
#72238673	2
#72237547	2
#72235087	2
#72232286	2