Subgroups — #72341443

Order 2048.

At least 8873 conjugacy classes of subgroups; only the 988 normal subgroups are shown.

The subgroup lattice has 435 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72341438	C₂	1	4	yes	maximal, complemented
2	#72341436	C₂	1	4	yes	maximal, complemented
3	#72341320	C₂	1	2	yes	maximal, complemented
4	#72341312	C₂	1	2	yes	maximal, complemented
5	#72318630	C₂	1	4	yes	maximal, complemented
6	#72312153	C₂	1	1	yes	maximal, characteristic, complemented
7	#72306899	C₂	1	1	yes	maximal, characteristic, complemented
8	#72306419	C₂	1	2	yes	maximal, complemented
9	#72303064	C₂	1	1	yes	maximal, characteristic, complemented
10	#72284823	C₂	1	2	yes	maximal, complemented
11	#72260942	C₂	1	4	yes	maximal, complemented
12	#72236979	C₂	1	1	yes	maximal, characteristic, complemented
13	#72234146	C₂	1	1	yes	maximal, characteristic, complemented
14	#72233917	C₂	1	1	yes	maximal, characteristic, complemented
15	#72210524	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#60388	C₂²	1	1	yes	characteristic
17	C₂×#60388	C₂²	1	1	yes	characteristic, complemented
18	#8926850	C₂²	1	2	yes	complemented
19	#8926849	C₂²	1	2	yes	—
20	#8757069	C₂²	1	2	yes	complemented
21	#8195812	C₂²	1	2	yes	complemented
22	#8109945	C₂²	1	2	yes	complemented
23	#7743195	C₂²	1	2	yes	—
24	#7737652	C₂²	1	1	yes	characteristic
25	#7737411	C₂²	1	1	yes	characteristic
26	#7672751	C₂²	1	1	yes	characteristic
27	#6628901	C₂²	1	1	yes	characteristic, complemented
28	#6628897	C₂²	1	2	yes	complemented
29	#6628896	C₂²	1	2	yes	complemented
30	#499849	C₂²	1	8	yes	complemented
31	#499845	C₂²	1	4	yes	complemented
32	#499843	C₂²	1	4	yes	complemented
33	#499838	C₂²	1	8	yes	complemented
34	#499834	C₂²	1	4	yes	complemented
35	#499832	C₂²	1	4	yes	complemented
36	#494682	C₂²	1	2	yes	complemented
37	#494682	C₂²	1	2	yes	complemented
38	#494681	C₂²	1	2	yes	complemented
39	#494681	C₂²	1	2	yes	complemented
40	#493430	C₂²	1	1	yes	characteristic
41	#493430	C₂²	1	1	yes	characteristic
42	#493430	C₂²	1	2	yes	complemented
43	#449492	C₂²	1	2	yes	complemented
44	#417807	C₂²	1	2	yes	complemented
45	#417566	C₂²	1	2	yes	complemented
46	#417566	C₂²	1	2	yes	complemented
47	#374009	C₂²	1	1	yes	characteristic, complemented
48	#359605	C₂²	1	1	yes	characteristic
49	#359605	C₂²	1	1	yes	characteristic, complemented
50	#251844	C₂²	1	8	yes	complemented
51	#245255	C₂²	1	8	yes	complemented
52	#213860	C₂²	1	2	yes	complemented
53	#213855	C₂²	1	2	yes	complemented
54	#213854	C₂²	1	2	yes	complemented
55	#134009	C₂²	1	2	yes	complemented
56	#133905	C₂²	1	2	yes	complemented
57	#133905	C₂²	1	2	yes	complemented
58	#133835	C₂²	1	2	yes	complemented
59	#133433	C₂²	1	8	yes	complemented
60	#133359	C₂²	1	8	yes	complemented
61	#133357	C₂²	1	4	yes	complemented
62	#133356	C₂²	1	4	yes	complemented
63	#133335	C₂²	1	8	yes	complemented
64	#133333	C₂²	1	4	yes	complemented
65	#133332	C₂²	1	4	yes	complemented
66	#133311	C₂²	1	8	yes	complemented
67	C₂×H(7,𝔽₂)	C₂³	1	1	yes	characteristic
68	C₂×#3498	D₄	1	1	yes	characteristic, complemented
69	C₂×#3498	D₄	1	1	yes	characteristic, complemented
70	C₂×#3498	C₂³	1	1	yes	characteristic
71	C₂×#3498	C₂³	1	1	yes	characteristic
72	C₂²×#559	D₄	1	1	yes	characteristic, complemented
73	C₂²×D₄²	D₄	1	1	yes	characteristic, complemented
74	C₂²×#560	D₄	1	2	yes	complemented
75	C₂×#3019	C₂³	1	2	yes	—
76	C₂×#3019	C₂³	1	2	yes	complemented
77	C₂²×#453	C₂³	1	2	yes	—
78	C₂²×#453	C₂³	1	2	yes	complemented
79	C₂×#2888	C₂³	1	1	yes	characteristic
80	C₂×#2888	C₂³	1	1	yes	characteristic
81	#59143	C₂³	1	2	yes	—
82	#59126	C₂³	1	2	yes	—
83	#59070	D₄	1	2	yes	complemented
84	#59041	D₄	1	2	yes	complemented
85	#52054	D₄	1	2	yes	complemented
86	#52054	C₂³	1	2	yes	—
87	#52013	D₄	1	4	yes	complemented
88	#52012	C₂³	1	4	yes	—
89	#52004	D₄	1	2	yes	complemented
90	#52004	C₂³	1	2	yes	—
91	#46389	C₂³	1	4	yes	—
92	#46386	D₄	1	4	yes	complemented
93	#46384	D₄	1	4	yes	complemented
94	#46324	C₂³	1	4	yes	—
95	#46276	D₄	1	4	yes	complemented
96	#37232	C₂³	1	4	yes	—
97	#36955	D₄	1	2	yes	complemented
98	#36955	D₄	1	2	yes	complemented
99	#36721	D₄	1	4	yes	complemented
100	#36714	D₄	1	4	yes	complemented
101	#36702	D₄	1	2	yes	complemented
102	#36702	D₄	1	2	yes	complemented
103	C₂×#2867	C₂³	1	1	yes	characteristic
104	#35527	D₄	1	1	yes	characteristic, complemented
105	#35527	D₄	1	1	yes	characteristic, complemented
106	#35527	C₂³	1	1	yes	characteristic
107	#35527	C₂³	1	1	yes	characteristic
108	#35527	C₂³	1	2	yes	complemented
109	#35446	C₂³	1	2	yes	—
110	#35346	C₂³	1	2	yes	—
111	#35272	D₄	1	1	yes	characteristic, complemented
112	#35272	D₄	1	1	yes	characteristic, complemented
113	#35272	C₂³	1	1	yes	characteristic
114	#35272	C₂³	1	1	yes	characteristic
115	#34364	D₄	1	1	yes	characteristic, complemented
116	#34364	D₄	1	1	yes	characteristic, complemented
117	#34364	D₄	1	2	yes	complemented
118	C₄×#532	D₄	1	1	yes	characteristic, complemented
119	C₄×#532	D₄	1	1	yes	characteristic, complemented
120	#32900	C₂³	1	8	yes	complemented
121	#32898	C₂³	1	8	yes	—
122	#20586	C₂³	1	1	yes	characteristic
123	#20586	C₂³	1	2	yes	complemented
124	#20585	C₂³	1	2	yes	—
125	#20585	C₂³	1	2	yes	—
126	#13082	C₂³	1	8	yes	—
127	#13082	C₂³	1	8	yes	—
128	#13080	C₂³	1	8	yes	complemented
129	#13080	C₂³	1	8	yes	complemented
130	#12696	C₂³	1	2	yes	—
131	#12696	C₂³	1	2	yes	—
132	#12696	C₂³	1	4	yes	complemented
133	#12693	C₂³	1	2	yes	—
134	#12693	C₂³	1	2	yes	—
135	#12693	C₂³	1	4	yes	complemented
136	#11167	C₂³	1	2	yes	complemented
137	#10989	C₂³	1	2	yes	—
138	#10989	C₂³	1	2	yes	complemented
139	#10981	C₂³	1	2	yes	complemented
140	#10975	C₂³	1	2	yes	—
141	#10975	C₂³	1	2	yes	complemented
142	#9501	C₂³	1	8	yes	complemented
143	#9497	C₂³	1	8	yes	—
144	#8748	C₂³	1	4	yes	complemented
145	#8546	C₂³	1	4	yes	complemented
146	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
147	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
148	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic, complemented
149	C₂²×H(5,𝔽₂)	C₂⁴	1	2	yes	—
150	C₂²×H(5,𝔽₂)	C₂⁴	1	1	yes	characteristic
151	C₂×#560	C₂×D₄	1	4	yes	complemented
152	C₂×#560	C₂×D₄	1	4	yes	complemented
153	C₂×#559	C₂×D₄	1	2	yes	complemented
154	C₂×#559	C₂×D₄	1	2	yes	complemented
155	C₂×D₄²	C₂×D₄	1	2	yes	—
156	C₂×D₄²	C₂×D₄	1	2	yes	—
157	C₂×#535	C₂×D₄	1	1	yes	characteristic
158	C₂×#535	C₂×D₄	1	2	yes	—
159	C₂×#535	C₂×D₄	1	1	yes	characteristic
160	C₂×#535	C₂×D₄	1	1	yes	characteristic
161	C₂×#535	C₂×D₄	1	2	yes	—
162	C₂×#535	C₂×D₄	1	1	yes	characteristic
163	C₂×#535	C₂×D₄	1	1	yes	characteristic
164	C₂×#535	C₂×D₄	1	1	yes	characteristic
165	C₂×#535	C₂×D₄	1	1	yes	characteristic
166	C₂×#535	C₂×D₄	1	1	yes	characteristic
167	C₂×#535	C₂×D₄	1	1	yes	characteristic, complemented
168	C₂×#535	C₂×D₄	1	1	yes	characteristic, complemented
169	C₂×#535	C₂⁴	1	1	yes	characteristic
170	C₂×#535	C₂⁴	1	1	yes	characteristic
171	C₂×#534	C₂×D₄	1	4	yes	complemented
172	C₂×#532	C₂×D₄	1	1	yes	characteristic
173	C₂×#532	C₂×D₄	1	1	yes	characteristic
174	C₂×#532	C₂×D₄	1	1	yes	characteristic
175	C₂×#532	C₂×D₄	1	1	yes	characteristic
176	C₂×#532	C₂×D₄	1	2	yes	—
177	C₂²×#127	C₂×D₄	1	1	yes	characteristic
178	C₂²×#127	C₂×D₄	1	2	yes	—
179	C₂²×#127	C₂×D₄	1	1	yes	characteristic
180	C₂²×#127	C₂×D₄	1	1	yes	characteristic, complemented
181	C₂²×#127	C₂×D₄	1	1	yes	characteristic, complemented
182	C₂²×#127	C₂×D₄	1	1	yes	characteristic, complemented
183	C₂²×#127	C₂⁴	1	1	yes	characteristic
184	C₂²×#127	C₂⁴	1	1	yes	characteristic
185	C₂²×#127	C₂⁴	1	1	yes	characteristic
186	C₂²×#123	C₂×D₄	1	2	yes	—
187	C₂²×#123	C₂×D₄	1	2	yes	—
188	C₂²×#123	C₂×D₄	1	2	yes	—
189	C₂²×#120	C₂×D₄	1	2	yes	—
190	C₂²×#120	C₂×D₄	1	2	yes	—
191	C₂²×#120	C₂×D₄	1	2	yes	—
192	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
193	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
194	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic, complemented
195	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic, complemented
196	C₂²×#100	C₂⁴	1	2	yes	—
197	C₂²×#100	C₂⁴	1	2	yes	—
198	#2842	C₂×D₄	1	4	yes	complemented
199	#2717	C₂×D₄	1	4	yes	complemented
200	#2717	C₂×D₄	1	4	yes	complemented
201	#2709	C₂×D₄	1	4	yes	complemented
202	#2709	C₂×D₄	1	4	yes	complemented
203	#2684	C₂×D₄	1	4	yes	—
204	#2684	C₂×D₄	1	4	yes	complemented
205	#2669	C₂×D₄	1	4	yes	—
206	#2669	C₂×D₄	1	4	yes	complemented
207	#2406	C₂×D₄	1	4	yes	—
208	#2406	C₂×D₄	1	4	yes	—
209	#2405	C₂×D₄	1	4	yes	—
210	#2405	C₂×D₄	1	4	yes	complemented
211	#2405	C₂×D₄	1	4	yes	complemented
212	#2405	C₂⁴	1	4	yes	—
213	#2404	C₂×D₄	1	4	yes	—
214	#2404	C₂×D₄	1	4	yes	—
215	#2403	C₂×D₄	1	4	yes	—
216	#2403	C₂×D₄	1	4	yes	—
217	#2403	C₂×D₄	1	4	yes	—
218	#2403	C₂×D₄	1	4	yes	complemented
219	#2403	C₂⁴	1	4	yes	—
220	#2380	C₂×D₄	1	2	yes	—
221	#2380	C₂×D₄	1	2	yes	complemented
222	#2380	C₂×D₄	1	4	yes	complemented
223	#2366	C₂×D₄	1	2	yes	—
224	#2366	C₂×D₄	1	2	yes	complemented
225	#2366	C₂×D₄	1	4	yes	complemented
226	#2312	C₂×D₄	1	4	yes	complemented
227	#2309	C₂×D₄	1	4	yes	complemented
228	#2309	C₂×D₄	1	1	yes	characteristic, complemented
229	#2309	C₂×D₄	1	1	yes	characteristic, complemented
230	#2309	C₂×D₄	1	1	yes	characteristic, complemented
231	#2309	C₂⁴	1	2	yes	—
232	#2309	C₂⁴	1	1	yes	characteristic
233	#2308	C₂×D₄	1	2	yes	—
234	#2308	C₂×D₄	1	2	yes	—
235	#2308	C₂×D₄	1	2	yes	—
236	#2308	C₂×D₄	1	2	yes	—
237	#2308	C₂×D₄	1	2	yes	—
238	#2308	C₂×D₄	1	2	yes	—
239	#2308	C₂×D₄	1	4	yes	complemented
240	#2297	C₂×D₄	1	1	yes	characteristic
241	#2297	C₂×D₄	1	1	yes	characteristic
242	#2297	C₂×D₄	1	1	yes	characteristic, complemented
243	#2297	C₂×D₄	1	1	yes	characteristic, complemented
244	#2285	C₂×D₄	1	1	yes	characteristic, complemented
245	#2285	C₂×D₄	1	1	yes	characteristic, complemented
246	C₂×C₄³	C₂×D₄	1	1	yes	characteristic, complemented
247	#1781	C₂⁴	1	4	yes	—
248	#1781	C₂⁴	1	4	yes	—
249	C₂⁶	#120	1	2	yes	—
250	C₂²×#41	#120	1	1	yes	characteristic
251	C₂²×#41	#120	1	1	yes	characteristic
252	C₂²×#41	#120	1	2	yes	—
253	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
254	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
255	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
256	C₂²×#41	C₂²×D₄	1	2	yes	—
257	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
258	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
259	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
260	C₂³×D₄	#120	1	1	yes	characteristic
261	C₂³×D₄	#120	1	1	yes	characteristic
262	C₂³×D₄	#120	1	2	yes	—
263	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
264	C₂³×D₄	C₂²×D₄	1	2	yes	—
265	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
266	C₂³×D₄	C₂²×D₄	1	4	yes	—
267	C₂³×D₄	C₂²×D₄	1	4	yes	—
268	C₂³×D₄	C₂²×D₄	1	2	yes	—
269	C₂³×D₄	C₂²×D₄	1	2	yes	—
270	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
271	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
272	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
273	C₂³×D₄	C₂⁵	1	1	yes	characteristic
274	C₂⁴×C₄	#120	1	2	yes	—
275	C₂×C₄⋊Q₈	#120	1	1	yes	characteristic
276	C₂×C₄⋊Q₈	#120	1	1	yes	characteristic
277	C₂×#127	#120	1	2	yes	—
278	C₂×#127	#120	1	1	yes	characteristic
279	C₂×#127	#120	1	1	yes	characteristic
280	C₂×#127	#120	1	1	yes	characteristic
281	C₂×#127	#120	1	1	yes	characteristic
282	C₂×#127	C₂²×D₄	1	2	yes	—
283	C₂×#127	C₂²×D₄	1	1	yes	characteristic
284	C₂×#127	C₂²×D₄	1	1	yes	characteristic
285	C₂×#127	C₂²×D₄	1	2	yes	—
286	C₂×#127	C₂²×D₄	1	1	yes	characteristic
287	C₂×#127	C₂²×D₄	1	1	yes	characteristic
288	C₂×#127	C₂²×D₄	1	1	yes	characteristic
289	C₂×#127	C₂²×D₄	1	1	yes	characteristic
290	C₂×#127	C₂²×D₄	1	2	yes	—
291	C₂×#124	#120	1	1	yes	characteristic
292	C₂×#124	#120	1	1	yes	characteristic
293	C₂×#124	#120	1	1	yes	characteristic
294	C₂×#124	#120	1	1	yes	characteristic
295	C₂×#124	#120	1	1	yes	characteristic
296	C₂×#124	#120	1	1	yes	characteristic
297	C₂×#124	#120	1	2	yes	—
298	C₂×#124	C₂²×D₄	1	1	yes	characteristic
299	C₂×#124	C₂²×D₄	1	1	yes	characteristic
300	C₂×#124	C₂²×D₄	1	2	yes	—
301	C₂×#123	#120	1	4	yes	—
302	C₂×#123	#120	1	4	yes	—
303	C₂×#123	C₂²×D₄	1	4	yes	—
304	C₂×#123	C₂²×D₄	1	4	yes	—
305	C₂×#120	#120	1	4	yes	—
306	C₂×#120	#120	1	2	yes	—
307	C₂×#120	#120	1	4	yes	—
308	C₂×#120	#120	1	2	yes	—
309	C₂×#120	#120	1	4	yes	—
310	C₂×#120	C₂²×D₄	1	4	yes	—
311	C₂×#120	C₂²×D₄	1	4	yes	—
312	C₂×#117	#120	1	1	yes	characteristic
313	C₂×#117	#120	1	1	yes	characteristic
314	C₂×#117	#120	1	2	yes	—
315	C₂×#117	C₂²×D₄	1	1	yes	characteristic
316	C₂×#117	C₂²×D₄	1	1	yes	characteristic
317	C₂×#117	C₂²×D₄	1	1	yes	characteristic
318	C₂×#117	C₂²×D₄	1	1	yes	characteristic
319	C₂²×C₄⋊C₄	#120	1	4	yes	—
320	C₂²×C₂²⋊C₄	#120	1	2	yes	—
321	C₂²×C₂²⋊C₄	#120	1	2	yes	—
322	C₂²×C₂²⋊C₄	#120	1	4	yes	—
323	C₂²×C₂²⋊C₄	#120	1	2	yes	—
324	C₂²×C₂²⋊C₄	#120	1	2	yes	—
325	C₂²×C₂²⋊C₄	#120	1	2	yes	—
326	C₂²×C₂²⋊C₄	#120	1	2	yes	—
327	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
328	C₂²×C₄²	#120	1	2	yes	—
329	C₂²×C₄²	#120	1	1	yes	characteristic
330	C₂²×C₄²	#120	1	1	yes	characteristic
331	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
332	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
333	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
334	#386	#120	1	4	yes	—
335	#386	#120	1	4	yes	—
336	#386	#120	1	4	yes	—
337	#386	#120	1	4	yes	—
338	#386	#120	1	2	yes	—
339	#386	#120	1	4	yes	—
340	#386	#120	1	2	yes	—
341	#386	C₂²×D₄	1	4	yes	—
342	#386	C₂²×D₄	1	4	yes	—
343	#386	C₂²×D₄	1	4	yes	—
344	#386	C₂²×D₄	1	4	yes	—
345	#381	#120	1	4	yes	—
346	#381	#120	1	4	yes	—
347	#379	C₂²×D₄	1	4	yes	—
348	#379	C₂²×D₄	1	4	yes	—
349	#379	C₂²×D₄	1	4	yes	—
350	C₂⁵	C₂×#120	1	2	yes	—
351	C₂⁵	C₂×#120	1	2	yes	—
352	C₂⁵	C₂×#120	1	2	yes	—
353	C₂⁵	C₂×#120	1	4	yes	—
354	C₂⁵	C₂³×D₄	1	2	yes	—
355	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
356	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
357	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
358	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
359	C₂²×D₄	C₂×#120	1	1	yes	characteristic
360	C₂²×D₄	C₂×#120	1	2	yes	—
361	C₂²×D₄	C₂×#120	1	1	yes	characteristic
362	C₂²×D₄	C₂×#120	1	2	yes	—
363	C₂²×D₄	C₂×#120	1	2	yes	—
364	C₂²×D₄	C₂×#120	1	2	yes	—
365	C₂²×D₄	C₂×#120	1	2	yes	—
366	C₂²×D₄	C₂×#120	1	1	yes	characteristic
367	C₂²×D₄	C₂×#120	1	2	yes	—
368	C₂²×D₄	C₂×#120	1	1	yes	characteristic
369	C₂²×D₄	C₂×#120	1	1	yes	characteristic
370	C₂²×D₄	C₂×#120	1	1	yes	characteristic
371	C₂²×D₄	C₂×#120	1	1	yes	characteristic
372	C₂²×D₄	C₂×#120	1	1	yes	characteristic
373	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
374	C₂²×D₄	C₂³×D₄	1	2	yes	—
375	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
376	C₂³×C₄	C₂×#120	1	1	yes	characteristic
377	C₂³×C₄	C₂×#120	1	2	yes	—
378	C₂³×C₄	C₂×#120	1	1	yes	characteristic
379	C₂³×C₄	C₂×#120	1	2	yes	—
380	C₂³×C₄	C₂×#120	1	4	yes	—
381	C₂³×C₄	C₂×#120	1	4	yes	—
382	C₂³×C₄	C₂×#120	1	4	yes	—
383	C₂³×C₄	C₂×#120	1	2	yes	—
384	C₂³×C₄	C₂×#120	1	2	yes	—
385	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
386	#127	B(4,𝔽₂)	1	4	yes	—
387	#127	B(4,𝔽₂)	1	4	yes	—
388	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
389	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
390	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
391	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
392	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
393	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
394	C₂×C₄²	C₂×#120	1	1	yes	characteristic
395	C₂×C₄²	C₂×#120	1	1	yes	characteristic
396	C₂×C₄²	C₂×#120	1	1	yes	characteristic
397	C₂×C₄²	C₂×#120	1	1	yes	characteristic
398	C₂×C₄²	C₂×#120	1	2	yes	—
399	C₂×C₄²	C₂×#120	1	1	yes	characteristic
400	C₂×C₄²	C₂×#120	1	1	yes	characteristic
401	C₂⁴	#2846	1	1	yes	characteristic
402	C₂⁴	#2846	1	2	yes	—
403	C₂⁴	#2846	1	1	yes	characteristic
404	C₂⁴	C₂²×#120	1	2	yes	—
405	C₂⁴	C₂²×#120	1	2	yes	—
406	C₂⁴	C₂²×#120	1	1	yes	characteristic
407	C₂×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
408	C₂×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
409	C₂×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
410	C₂×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
411	C₂×D₄	#3026	1	2	yes	—
412	C₂×D₄	#3026	1	2	yes	—
413	C₂²×C₄	#2846	1	1	yes	characteristic
414	C₂²×C₄	#2846	1	2	yes	—
415	C₂²×C₄	#2846	1	1	yes	characteristic
416	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
417	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
418	C₄²	C₂×B(4,𝔽₂)	1	2	yes	—
419	C₄²	C₂×B(4,𝔽₂)	1	2	yes	—
420	C₂³	#32898	1	2	yes	—
421	C₂³	#32898	1	4	yes	—
422	C₂³	#32898	1	2	yes	—
423	C₂³	C₂×#2846	1	1	yes	characteristic
424	C₂³	#60399	1	2	yes	—
425	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
426	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
427	C₂×C₄	C₂×#3026	1	1	yes	characteristic
428	C₂×C₄	C₂×#3026	1	1	yes	characteristic
429	C₂²	C₂×#32898	1	1	yes	characteristic
430	C₂²	C₂×#32898	1	1	yes	characteristic
431	C₂²	#6628896	1	1	yes	characteristic
432	C₂	#72216323	1	1	yes	characteristic
433	C₂	#72249650	1	2	yes	—

	subgroup	G/H
center, socle	C₂²	#6628896
commutator, Frattini, cosocle	C₂³×D₄	C₂⁵
LCS	G ▷ C₂³×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ #35527 ◁ G
LECS	G ▷ C₂³×D₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72341438	C₂	semidirect
2. #72341436	C₂	semidirect
3. #72341320	C₂	semidirect
4. #72341312	C₂	semidirect
5. #72318630	C₂	semidirect
6. #72312153	C₂	semidirect
7. #72306899	C₂	semidirect
8. #72306419	C₂	semidirect
9. #72303064	C₂	semidirect
10. #72284823	C₂	semidirect
11. #72260942	C₂	semidirect
12. #72236979	C₂	semidirect
13. #72234146	C₂	semidirect
14. #72233917	C₂	semidirect
15. #72210524	C₂	semidirect
17. C₂×#60388	C₂²	semidirect
18. #8926850	C₂²	semidirect
20. #8757069	C₂²	semidirect
21. #8195812	C₂²	semidirect
22. #8109945	C₂²	semidirect
27. #6628901	C₂²	semidirect
28. #6628897	C₂²	semidirect
29. #6628896	C₂²	semidirect
30. #499849	C₂²	semidirect
31. #499845	C₂²	semidirect
32. #499843	C₂²	semidirect
33. #499838	C₂²	semidirect
34. #499834	C₂²	semidirect
35. #499832	C₂²	semidirect
36. #494682	C₂²	semidirect
37. #494682	C₂²	semidirect
38. #494681	C₂²	semidirect
39. #494681	C₂²	semidirect
42. #493430	C₂²	semidirect
43. #449492	C₂²	semidirect
44. #417807	C₂²	semidirect
45. #417566	C₂²	semidirect
46. #417566	C₂²	semidirect
47. #374009	C₂²	semidirect
49. #359605	C₂²	semidirect
50. #251844	C₂²	semidirect
51. #245255	C₂²	semidirect
52. #213860	C₂²	semidirect
53. #213855	C₂²	semidirect
54. #213854	C₂²	semidirect
55. #134009	C₂²	semidirect
56. #133905	C₂²	semidirect
57. #133905	C₂²	semidirect
58. #133835	C₂²	semidirect
59. #133433	C₂²	semidirect
60. #133359	C₂²	semidirect
61. #133357	C₂²	semidirect
62. #133356	C₂²	semidirect
63. #133335	C₂²	semidirect
64. #133333	C₂²	semidirect
65. #133332	C₂²	semidirect
66. #133311	C₂²	semidirect
68. C₂×#3498	D₄	semidirect
69. C₂×#3498	D₄	semidirect
72. C₂²×#559	D₄	semidirect
73. C₂²×D₄²	D₄	semidirect
74. C₂²×#560	D₄	semidirect
76. C₂×#3019	C₂³	semidirect
78. C₂²×#453	C₂³	semidirect
83. #59070	D₄	semidirect
84. #59041	D₄	semidirect
85. #52054	D₄	semidirect
87. #52013	D₄	semidirect
89. #52004	D₄	semidirect
92. #46386	D₄	semidirect
93. #46384	D₄	semidirect
95. #46276	D₄	semidirect
97. #36955	D₄	semidirect
98. #36955	D₄	semidirect
99. #36721	D₄	semidirect
100. #36714	D₄	semidirect
101. #36702	D₄	semidirect
102. #36702	D₄	semidirect
104. #35527	D₄	semidirect
105. #35527	D₄	semidirect
108. #35527	C₂³	semidirect
111. #35272	D₄	semidirect
112. #35272	D₄	semidirect
115. #34364	D₄	semidirect
116. #34364	D₄	semidirect
117. #34364	D₄	semidirect
118. C₄×#532	D₄	semidirect
119. C₄×#532	D₄	semidirect
120. #32900	C₂³	semidirect
123. #20586	C₂³	semidirect
128. #13080	C₂³	semidirect
129. #13080	C₂³	semidirect
132. #12696	C₂³	semidirect
135. #12693	C₂³	semidirect
136. #11167	C₂³	semidirect
138. #10989	C₂³	semidirect
139. #10981	C₂³	semidirect
141. #10975	C₂³	semidirect
142. #9501	C₂³	semidirect
144. #8748	C₂³	semidirect
145. #8546	C₂³	semidirect
148. C₂²×H(5,𝔽₂)	C₂×D₄	semidirect
151. C₂×#560	C₂×D₄	semidirect
152. C₂×#560	C₂×D₄	semidirect
153. C₂×#559	C₂×D₄	semidirect
154. C₂×#559	C₂×D₄	semidirect
167. C₂×#535	C₂×D₄	semidirect
168. C₂×#535	C₂×D₄	semidirect
171. C₂×#534	C₂×D₄	semidirect
180. C₂²×#127	C₂×D₄	semidirect
181. C₂²×#127	C₂×D₄	semidirect
182. C₂²×#127	C₂×D₄	semidirect
194. C₂×C₄×#41	C₂×D₄	semidirect
195. C₂×C₄×#41	C₂×D₄	semidirect
198. #2842	C₂×D₄	semidirect
199. #2717	C₂×D₄	semidirect
200. #2717	C₂×D₄	semidirect
201. #2709	C₂×D₄	semidirect
202. #2709	C₂×D₄	semidirect
204. #2684	C₂×D₄	semidirect
206. #2669	C₂×D₄	semidirect
210. #2405	C₂×D₄	semidirect
211. #2405	C₂×D₄	semidirect
218. #2403	C₂×D₄	semidirect
221. #2380	C₂×D₄	semidirect
222. #2380	C₂×D₄	semidirect
224. #2366	C₂×D₄	semidirect
225. #2366	C₂×D₄	semidirect
226. #2312	C₂×D₄	semidirect
227. #2309	C₂×D₄	semidirect
228. #2309	C₂×D₄	semidirect
229. #2309	C₂×D₄	semidirect
230. #2309	C₂×D₄	semidirect
239. #2308	C₂×D₄	semidirect
242. #2297	C₂×D₄	semidirect
243. #2297	C₂×D₄	semidirect
244. #2285	C₂×D₄	semidirect
245. #2285	C₂×D₄	semidirect
246. C₂×C₄³	C₂×D₄	semidirect

Maximal subgroups

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

subgroup	index
#72341438	2
#72341436	2
#72341320	2
#72341312	2
#72318630	2
#72312153	2
#72306899	2
#72306419	2
#72303064	2
#72284823	2
#72260942	2
#72236979	2
#72234146	2
#72233917	2
#72210524	2