Subgroups — #72252030

Order 2048.

At least 9848 conjugacy classes of subgroups; only the 492 normal subgroups are shown.

The subgroup lattice has 387 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72251885	C₂	1	1	yes	maximal, characteristic, complemented
2	#72251879	C₂	1	1	yes	maximal, characteristic, complemented
3	#72251842	C₂	1	1	yes	maximal, characteristic, complemented
4	#72251773	C₂	1	2	yes	maximal, complemented
5	#72251725	C₂	1	2	yes	maximal, complemented
6	#72238416	C₂	1	1	yes	maximal, characteristic, complemented
7	#72235111	C₂	1	1	yes	maximal, characteristic, complemented
8	#72219498	C₂	1	2	yes	maximal, complemented
9	#72215559	C₂	1	2	yes	maximal, complemented
10	#72213729	C₂	1	1	yes	maximal, characteristic, complemented
11	#72210448	C₂	1	1	yes	maximal, characteristic
12	C₂²×#3484	C₂²	1	1	yes	characteristic
13	C₂×#47830	C₄	1	1	yes	characteristic, complemented
14	C₂×#46355	C₂²	1	1	yes	characteristic
15	C₂×#43001	C₄	1	1	yes	characteristic, complemented
16	#6374136	C₂²	1	1	yes	characteristic, complemented
17	#6374123	C₂²	1	1	yes	characteristic, complemented
18	#4930608	C₂²	1	1	yes	characteristic
19	#4928938	C₂²	1	1	yes	characteristic
20	#4420353	C₄	1	1	yes	characteristic, complemented
21	#4417886	C₄	1	1	yes	characteristic, complemented
22	#758216	C₄	1	1	yes	characteristic, complemented
23	#719140	C₄	1	1	yes	characteristic, complemented
24	#619512	C₂²	1	1	yes	characteristic
25	#619112	C₂²	1	1	yes	characteristic
26	#576038	C₂²	1	1	yes	characteristic
27	#574895	C₄	1	1	yes	characteristic, complemented
28	#539762	C₄	1	1	yes	characteristic, complemented
29	#496228	C₂²	1	2	yes	complemented
30	#496228	C₂²	1	2	yes	complemented
31	#496208	C₂²	1	2	yes	complemented
32	#496190	C₂²	1	2	yes	complemented
33	#392132	C₂²	1	2	yes	complemented
34	#392132	C₂²	1	2	yes	complemented
35	#382419	C₂²	1	2	yes	—
36	#188071	C₂²	1	1	yes	characteristic, complemented
37	#188029	C₂²	1	1	yes	characteristic, complemented
38	#187756	C₂²	1	2	yes	—
39	#128074	C₂²	1	2	yes	complemented
40	#128074	C₂²	1	2	yes	complemented
41	#128059	C₂²	1	2	yes	complemented
42	#128057	C₂²	1	2	yes	complemented
43	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
44	C₂⁵×D₄	D₄	1	1	yes	characteristic
45	C₂²×#546	C₂×C₄	1	1	yes	characteristic
46	C₂²×#546	C₂×C₄	1	1	yes	characteristic
47	C₂²×#546	D₄	1	1	yes	characteristic
48	C₂²×#546	D₄	1	1	yes	characteristic
49	C₂²×D₄²	C₂×C₄	1	1	yes	characteristic
50	C₂²×D₄²	C₂×C₄	1	1	yes	characteristic
51	C₂²×D₄²	D₄	1	1	yes	characteristic
52	C₂²×D₄²	D₄	1	1	yes	characteristic
53	C₂²×#535	D₄	1	1	yes	characteristic
54	C₂²×#535	C₂³	1	1	yes	characteristic
55	C₂²×#534	C₂×C₄	1	1	yes	characteristic, complemented
56	C₂²×#525	D₄	1	1	yes	characteristic
57	C₂²×#525	C₂³	1	1	yes	characteristic
58	C₂²×#518	D₄	1	1	yes	characteristic
59	C₂×#2815	C₂×C₄	1	1	yes	characteristic, complemented
60	C₂×#2539	C₂×C₄	1	1	yes	characteristic, complemented
61	C₂×#2543	C₂×C₄	1	1	yes	characteristic
62	C₂×#2534	C₂×C₄	1	1	yes	characteristic
63	C₂×#2404	C₂×C₄	1	1	yes	characteristic, complemented
64	C₂×#2404	C₂³	1	1	yes	characteristic
65	C₂×#2431	C₂³	1	1	yes	characteristic
66	C₂×#2433	C₂×C₄	1	1	yes	characteristic, complemented
67	C₂×#2615	C₂×C₄	1	1	yes	characteristic, complemented
68	C₂×#2635	C₂×C₄	1	1	yes	characteristic
69	C₂²×#392	C₂×C₄	1	1	yes	characteristic, complemented
70	C₂×#2377	C₂×C₄	1	1	yes	characteristic, complemented
71	C₂×#2364	C₂×C₄	1	1	yes	characteristic, complemented
72	C₂×#2333	C₂×C₄	1	1	yes	characteristic, complemented
73	C₂×#2321	C₂×C₄	1	1	yes	characteristic
74	#20591	C₂³	1	2	yes	—
75	#20591	C₂³	1	2	yes	—
76	#20584	C₂³	1	2	yes	—
77	#20584	C₂³	1	2	yes	—
78	#15984	D₄	1	1	yes	characteristic
79	#15982	D₄	1	1	yes	characteristic
80	#15948	D₄	1	1	yes	characteristic
81	#15948	D₄	1	1	yes	characteristic
82	#15947	D₄	1	1	yes	characteristic
83	#15466	D₄	1	1	yes	characteristic
84	#15465	D₄	1	1	yes	characteristic
85	#15464	D₄	1	1	yes	characteristic
86	#15283	D₄	1	1	yes	characteristic
87	#15264	D₄	1	1	yes	characteristic
88	#15264	D₄	1	1	yes	characteristic
89	#15261	D₄	1	1	yes	characteristic
90	#15260	D₄	1	1	yes	characteristic
91	#15258	D₄	1	1	yes	characteristic
92	#15257	D₄	1	1	yes	characteristic
93	#15257	D₄	1	1	yes	characteristic
94	#14344	C₂×C₄	1	1	yes	characteristic
95	#14335	C₂×C₄	1	1	yes	characteristic, complemented
96	#14290	C₂×C₄	1	1	yes	characteristic, complemented
97	#14271	C₂×C₄	1	1	yes	characteristic, complemented
98	#13956	C₂×C₄	1	1	yes	characteristic, complemented
99	#13956	C₂³	1	1	yes	characteristic
100	#13940	C₂×C₄	1	1	yes	characteristic
101	#13940	C₂×C₄	1	1	yes	characteristic
102	#13937	C₂³	1	1	yes	characteristic
103	#13902	C₂×C₄	1	1	yes	characteristic, complemented
104	#13851	C₂×C₄	1	1	yes	characteristic, complemented
105	#13784	C₂×C₄	1	1	yes	characteristic
106	#10984	D₄	1	8	yes	complemented
107	C₂³×#41	C₂²×C₄	1	1	yes	characteristic
108	C₂³×#41	C₂×D₄	1	1	yes	characteristic
109	C₂³×#41	C₂×D₄	1	1	yes	characteristic
110	C₂³×#41	C₂⁴	1	1	yes	characteristic
111	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
112	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
113	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
114	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
115	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
116	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
117	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
118	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
119	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
120	C₂×#535	C₂×D₄	1	4	yes	—
121	C₂×#535	#41	1	4	yes	—
122	C₂²×#127	C₂²⋊C₄	1	1	yes	characteristic
123	C₂²×#127	C₂²⋊C₄	1	1	yes	characteristic
124	C₂²×#127	C₂×D₄	1	1	yes	characteristic
125	C₂²×#124	C₂²⋊C₄	1	1	yes	characteristic
126	C₂²×#124	C₂²⋊C₄	1	1	yes	characteristic
127	C₂²×#124	C₂×D₄	1	1	yes	characteristic
128	C₂²×#123	C₂²⋊C₄	1	1	yes	characteristic
129	C₂²×#123	C₂×D₄	1	1	yes	characteristic
130	C₂²×#123	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₂²⋊Q₈	C₂²⋊C₄	1	1	yes	characteristic
132	C₂²×C₂²⋊Q₈	C₂²⋊C₄	1	1	yes	characteristic
133	C₂²×C₂²⋊Q₈	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₂²⋊Q₈	C₂×D₄	1	1	yes	characteristic
135	C₂²×#121	C₂²⋊C₄	1	1	yes	characteristic
136	C₂²×#121	C₂²⋊C₄	1	1	yes	characteristic
137	C₂²×#121	C₂²×C₄	1	1	yes	characteristic
138	C₂²×#121	C₂²×C₄	1	1	yes	characteristic
139	C₂²×#121	C₂²×C₄	1	1	yes	characteristic
140	C₂²×#121	C₂×D₄	1	1	yes	characteristic
141	C₂²×#121	C₂×D₄	1	1	yes	characteristic
142	C₂²×#121	C₂×D₄	1	1	yes	characteristic
143	C₂²×#121	C₂×D₄	1	1	yes	characteristic
144	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
145	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic
146	C₂²×#120	C₂×D₄	1	1	yes	characteristic
147	C₂²×#120	C₂×D₄	1	1	yes	characteristic
148	C₂²×#120	C₂×D₄	1	1	yes	characteristic
149	C₂²×#120	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
151	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
152	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
153	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
154	C₂²×C₄×D₄	C₂²×C₄	1	1	yes	characteristic
155	C₂²×C₄×D₄	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
158	C₂²×#117	C₂×D₄	1	1	yes	characteristic
159	C₂²×#117	C₂×D₄	1	1	yes	characteristic
160	C₂³×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
161	C₂×#413	C₂×D₄	1	4	yes	complemented
162	C₂×#410	C₂×D₄	1	4	yes	complemented
163	C₂×#400	C₂²⋊C₄	1	1	yes	characteristic
164	C₂×#399	C₂²⋊C₄	1	1	yes	characteristic
165	C₂×#398	C₂²⋊C₄	1	1	yes	characteristic
166	C₂×#397	C₂²⋊C₄	1	1	yes	characteristic
167	C₂×#394	C₂²⋊C₄	1	1	yes	characteristic
168	C₂×#394	C₂²⋊C₄	1	1	yes	characteristic
169	C₂×#392	C₂²⋊C₄	1	1	yes	characteristic
170	C₂×#392	C₂²⋊C₄	1	1	yes	characteristic
171	C₂×#391	C₂×D₄	1	1	yes	characteristic
172	C₂×#390	C₂×D₄	1	1	yes	characteristic
173	C₂×#386	C₂²⋊C₄	1	1	yes	characteristic
174	C₂×#386	C₂×D₄	1	1	yes	characteristic
175	C₂×#386	C₂×D₄	1	1	yes	characteristic
176	C₂×#385	C₂²⋊C₄	1	1	yes	characteristic
177	C₂×#381	C₂²⋊C₄	1	1	yes	characteristic
178	C₂×#381	C₂²×C₄	1	1	yes	characteristic
179	C₂×#381	C₂²×C₄	1	1	yes	characteristic
180	C₂×#380	C₂²×C₄	1	1	yes	characteristic
181	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
182	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
183	C₂×C₄×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
184	C₂×C₄×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
185	C₂²×#95	C₂²×C₄	1	1	yes	characteristic
186	#1446	C₂×D₄	1	1	yes	characteristic
187	#1446	C₂×D₄	1	1	yes	characteristic
188	#1440	C₂²⋊C₄	1	1	yes	characteristic
189	#1440	C₂²⋊C₄	1	1	yes	characteristic
190	#1440	C₂²⋊C₄	1	1	yes	characteristic
191	#1440	C₂²⋊C₄	1	1	yes	characteristic
192	#1438	C₂²⋊C₄	1	1	yes	characteristic
193	#1438	C₂²⋊C₄	1	1	yes	characteristic
194	#1438	C₂²⋊C₄	1	1	yes	characteristic
195	#1438	C₂²⋊C₄	1	1	yes	characteristic
196	#1438	C₂×D₄	1	1	yes	characteristic
197	#1438	C₂×D₄	1	1	yes	characteristic
198	#1438	C₂×D₄	1	1	yes	characteristic
199	#1438	C₂×D₄	1	1	yes	characteristic
200	#1438	C₂×D₄	1	1	yes	characteristic
201	#1438	C₂×D₄	1	1	yes	characteristic
202	#1437	C₂²⋊C₄	1	1	yes	characteristic
203	#1437	C₂²⋊C₄	1	1	yes	characteristic
204	#1437	C₂²⋊C₄	1	1	yes	characteristic
205	#1437	C₂²⋊C₄	1	1	yes	characteristic
206	#1436	C₂²⋊C₄	1	1	yes	characteristic
207	#1436	C₂²⋊C₄	1	1	yes	characteristic
208	#1436	C₂²⋊C₄	1	1	yes	characteristic
209	#1436	C₂²⋊C₄	1	1	yes	characteristic
210	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
211	C₂⁶	#120	1	1	yes	characteristic
212	C₂²×#41	C₂²×D₄	1	2	yes	—
213	C₂²×#41	C₂×#41	1	2	yes	—
214	C₂²×#41	H(5,𝔽₂)	1	2	yes	—
215	C₂²×#41	H(5,𝔽₂)	1	2	yes	—
216	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
217	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
218	C₂³×D₄	#99	1	2	yes	—
219	C₂³×D₄	#99	1	2	yes	—
220	C₂³×D₄	#99	1	2	yes	—
221	C₂³×D₄	#99	1	2	yes	—
222	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
223	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
224	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
225	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
226	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
227	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
228	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
229	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
230	C₂³×D₄	#120	1	2	yes	—
231	C₂³×D₄	#120	1	1	yes	characteristic
232	C₂³×D₄	#120	1	1	yes	characteristic
233	C₂³×D₄	#123	1	2	yes	—
234	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
235	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
236	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
237	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
238	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
239	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
240	C₂⁴×C₄	#120	1	1	yes	characteristic
241	C₂⁴×C₄	#120	1	1	yes	characteristic
242	C₂⁴×C₄	#120	1	1	yes	characteristic
243	C₂⁴×C₄	C₂³×C₄	1	1	yes	characteristic
244	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
245	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₂²⋊Q₈	#99	1	2	yes	—
247	C₂×C₂²⋊Q₈	#99	1	2	yes	—
248	C₂×#121	#99	1	2	yes	—
249	C₂×#121	#99	1	2	yes	—
250	C₂×#121	C₄×D₄	1	4	yes	—
251	C₂×#121	C₄×D₄	1	4	yes	—
252	C₂×#121	#121	1	4	yes	—
253	C₂×#121	#121	1	4	yes	—
254	C₂×#117	#120	1	2	yes	—
255	C₂×#117	#123	1	2	yes	—
256	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
257	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
258	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
259	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
260	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
261	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
262	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
263	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
264	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
265	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
266	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
267	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
268	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
269	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
270	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
271	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
272	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
273	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
274	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
275	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
276	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
277	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
278	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
279	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
280	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
281	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
282	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
283	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
284	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
285	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
286	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
287	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
288	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
289	C₂⁵	#379	1	1	yes	characteristic
290	C₂⁵	#379	1	1	yes	characteristic
291	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
292	C₂⁵	C₂×#120	1	1	yes	characteristic
293	C₂⁵	C₂×#120	1	1	yes	characteristic
294	C₂²×Q₈	C₂×#99	1	2	yes	—
295	C₂²×Q₈	D₄²	1	2	yes	—
296	C₂²×Q₈	#546	1	2	yes	—
297	C₂²×D₄	#386	1	2	yes	—
298	C₂²×D₄	#386	1	2	yes	—
299	C₂²×D₄	C₂×#99	1	2	yes	—
300	C₂²×D₄	C₂×#99	1	2	yes	—
301	C₂²×D₄	C₂×#99	1	2	yes	—
302	C₂²×D₄	C₂×#99	1	2	yes	—
303	C₂²×D₄	C₂×#99	1	2	yes	—
304	C₂²×D₄	D₄²	1	2	yes	—
305	C₂²×D₄	D₄²	1	2	yes	—
306	C₂²×D₄	D₄²	1	2	yes	—
307	C₂²×D₄	#546	1	2	yes	—
308	C₂²×D₄	#546	1	2	yes	—
309	C₂²×D₄	#546	1	2	yes	—
310	C₂³×C₄	#379	1	1	yes	characteristic
311	C₂³×C₄	#379	1	1	yes	characteristic
312	C₂³×C₄	#379	1	1	yes	characteristic
313	C₂³×C₄	#379	1	1	yes	characteristic
314	C₂³×C₄	#379	1	1	yes	characteristic
315	C₂³×C₄	#379	1	1	yes	characteristic
316	C₂³×C₄	C₂×#99	1	1	yes	characteristic
317	C₂³×C₄	C₂×#99	1	1	yes	characteristic
318	C₂³×C₄	C₂×#99	1	1	yes	characteristic
319	C₂³×C₄	C₂×#99	1	1	yes	characteristic
320	C₂³×C₄	C₂×#99	1	1	yes	characteristic
321	C₂³×C₄	C₂×#99	1	1	yes	characteristic
322	C₂³×C₄	C₂×#99	1	1	yes	characteristic
323	C₂³×C₄	C₂×#99	1	1	yes	characteristic
324	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
325	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
326	C₂³×C₄	C₂×C₄×D₄	1	2	yes	—
327	C₂³×C₄	#518	1	2	yes	—
328	C₂³×C₄	C₂×#120	1	1	yes	characteristic
329	C₂³×C₄	C₂×#120	1	1	yes	characteristic
330	C₂³×C₄	C₂×#120	1	1	yes	characteristic
331	C₂³×C₄	C₂×#121	1	2	yes	—
332	C₂³×C₄	C₂×#123	1	1	yes	characteristic
333	C₂³×C₄	#534	1	1	yes	characteristic
334	C₂³×C₄	#534	1	1	yes	characteristic
335	C₂³×C₄	#534	1	2	yes	—
336	C₂×C₄⋊C₄	#386	1	2	yes	—
337	C₂×C₄⋊C₄	#386	1	2	yes	—
338	C₂×C₄⋊C₄	C₂×#99	1	2	yes	—
339	C₂×C₄⋊C₄	C₂×#99	1	2	yes	—
340	C₂⁴	#1781	1	1	yes	characteristic
341	C₂⁴	#1781	1	1	yes	characteristic
342	C₂⁴	#1781	1	1	yes	characteristic
343	C₂⁴	#1781	1	1	yes	characteristic
344	C₂⁴	C₂×#379	1	1	yes	characteristic
345	C₂⁴	D₄×C₂²⋊C₄	1	2	yes	—
346	C₂⁴	#2403	1	1	yes	characteristic
347	C₂⁴	#2405	1	1	yes	characteristic
348	C₂⁴	#2410	1	2	yes	—
349	C₂×D₄	#1898	1	4	yes	—
350	C₂²×C₄	#1781	1	1	yes	characteristic
351	C₂²×C₄	#1781	1	1	yes	characteristic
352	C₂²×C₄	#1781	1	1	yes	characteristic
353	C₂²×C₄	#1781	1	1	yes	characteristic
354	C₂²×C₄	C₂×#386	1	1	yes	characteristic
355	C₂²×C₄	#2308	1	1	yes	characteristic
356	C₂²×C₄	D₄×C₂²⋊C₄	1	2	yes	—
357	C₂²×C₄	#2403	1	1	yes	characteristic
358	C₂²×C₄	#2405	1	1	yes	characteristic
359	C₂²×C₄	#2410	1	2	yes	—
360	C₂²×C₄	C₂²×#99	1	1	yes	characteristic
361	C₂²×C₄	C₂²×#99	1	1	yes	characteristic
362	C₂²×C₄	C₂²×#99	1	1	yes	characteristic
363	C₂²×C₄	C₂²×#99	1	1	yes	characteristic
364	C₄⋊C₄	#1898	1	4	yes	—
365	C₂³	#12711	1	2	yes	—
366	C₂³	#12718	1	2	yes	—
367	C₂³	#13867	1	1	yes	characteristic
368	C₂³	C₂×#1781	1	1	yes	characteristic
369	C₂³	C₂×#1781	1	1	yes	characteristic
370	C₂³	#23895	1	2	yes	—
371	C₂×C₄	C₂×#1898	1	1	yes	characteristic
372	C₂×C₄	C₂×#1898	1	1	yes	characteristic
373	C₂×C₄	#21746	1	1	yes	characteristic
374	C₂×C₄	#21746	1	1	yes	characteristic
375	C₂×C₄	#23895	1	2	yes	—
376	C₂²	#359428	1	1	yes	characteristic
377	C₂²	#359549	1	1	yes	characteristic
378	C₂²	#359549	1	1	yes	characteristic
379	C₂²	C₂×#12711	1	1	yes	characteristic
380	C₂²	#493411	1	1	yes	characteristic
381	C₂²	C₂×#12718	1	1	yes	characteristic
382	C₂²	#493421	1	1	yes	characteristic
383	C₂	#72218180	1	1	yes	characteristic
384	C₂	#72238620	1	1	yes	characteristic
385	C₂	#72238623	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#359428
commutator	C₂⁴×C₄	C₂³×C₄
Frattini, cosocle	C₂³×#41	C₂⁴
prime radical	#72210448	C₂
LCS	G ▷ C₂⁴×C₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂²×#3484 ◁ G
LECS	G ▷ C₂³×#41 ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72251885	C₂	semidirect
2. #72251879	C₂	semidirect
3. #72251842	C₂	semidirect
4. #72251773	C₂	semidirect
5. #72251725	C₂	semidirect
6. #72238416	C₂	semidirect
7. #72235111	C₂	semidirect
8. #72219498	C₂	semidirect
9. #72215559	C₂	semidirect
10. #72213729	C₂	semidirect
13. C₂×#47830	C₄	semidirect
15. C₂×#43001	C₄	semidirect
16. #6374136	C₂²	semidirect
17. #6374123	C₂²	semidirect
20. #4420353	C₄	semidirect
21. #4417886	C₄	semidirect
22. #758216	C₄	semidirect
23. #719140	C₄	semidirect
27. #574895	C₄	semidirect
28. #539762	C₄	semidirect
29. #496228	C₂²	semidirect
30. #496228	C₂²	semidirect
31. #496208	C₂²	semidirect
32. #496190	C₂²	semidirect
33. #392132	C₂²	semidirect
34. #392132	C₂²	semidirect
36. #188071	C₂²	semidirect
37. #188029	C₂²	semidirect
39. #128074	C₂²	semidirect
40. #128074	C₂²	semidirect
41. #128059	C₂²	semidirect
42. #128057	C₂²	semidirect
55. C₂²×#534	C₂×C₄	semidirect
59. C₂×#2815	C₂×C₄	semidirect
60. C₂×#2539	C₂×C₄	semidirect
63. C₂×#2404	C₂×C₄	semidirect
66. C₂×#2433	C₂×C₄	semidirect
67. C₂×#2615	C₂×C₄	semidirect
69. C₂²×#392	C₂×C₄	semidirect
70. C₂×#2377	C₂×C₄	semidirect
71. C₂×#2364	C₂×C₄	semidirect
72. C₂×#2333	C₂×C₄	semidirect
95. #14335	C₂×C₄	semidirect
96. #14290	C₂×C₄	semidirect
97. #14271	C₂×C₄	semidirect
98. #13956	C₂×C₄	semidirect
103. #13902	C₂×C₄	semidirect
104. #13851	C₂×C₄	semidirect
106. #10984	D₄	semidirect
161. C₂×#413	C₂×D₄	semidirect
162. C₂×#410	C₂×D₄	semidirect

Maximal subgroups

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

subgroup	index
#72251885	2
#72251879	2
#72251842	2
#72251773	2
#72251725	2
#72238416	2
#72235111	2
#72219498	2
#72215559	2
#72213729	2
#72210448	2