Subgroups — #72240215

Order 2048.

At least 9656 conjugacy classes of subgroups; only the 998 normal subgroups are shown.

The subgroup lattice has 510 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72240214	C₂	1	1	yes	maximal, characteristic, complemented
2	#72240213	C₂	1	1	yes	maximal, characteristic, complemented
3	#72240212	C₂	1	1	yes	maximal, characteristic, complemented
4	#72240211	C₂	1	1	yes	maximal, characteristic, complemented
5	#72240210	C₂	1	1	yes	maximal, characteristic, complemented
6	#72240207	C₂	1	1	yes	maximal, characteristic, complemented
7	#72240206	C₂	1	1	yes	maximal, characteristic, complemented
8	#72240205	C₂	1	1	yes	maximal, characteristic, complemented
9	#72240204	C₂	1	1	yes	maximal, characteristic, complemented
10	#72240203	C₂	1	1	yes	maximal, characteristic, complemented
11	#72240202	C₂	1	8	yes	maximal, complemented
12	#72240201	C₂	1	8	yes	maximal, complemented
13	C₂×#8058967	C₂	1	1	yes	maximal, characteristic, complemented
14	#72231069	C₂	1	1	yes	maximal, characteristic, complemented
15	#72231032	C₂	1	1	yes	maximal, characteristic, complemented
16	#72230994	C₂	1	1	yes	maximal, characteristic, complemented
17	#72213883	C₂	1	1	yes	maximal, characteristic, complemented
18	#10577301	C₂²	1	1	yes	characteristic, complemented
19	#8058967	C₂²	1	8	yes	—
20	C₂×#45693	C₂²	1	1	yes	characteristic
21	C₂×#47814	C₂²	1	1	yes	characteristic
22	C₂×#47182	C₂²	1	1	yes	characteristic
23	C₂×#45355	C₂²	1	1	yes	characteristic
24	C₂×#43893	C₂²	1	1	yes	characteristic
25	C₂×#36212	C₂²	1	1	yes	characteristic
26	C₂×#34468	C₂²	1	1	yes	characteristic
27	#6454047	C₂²	1	1	yes	characteristic, complemented
28	#6454041	C₂²	1	1	yes	characteristic, complemented
29	#6453841	C₂²	1	1	yes	characteristic
30	#6347310	C₂²	1	1	yes	characteristic, complemented
31	#6346631	C₂²	1	1	yes	characteristic, complemented
32	#6346600	C₂²	1	1	yes	characteristic, complemented
33	#512030	C₂²	1	4	yes	complemented
34	#511938	C₂²	1	4	yes	complemented
35	#493998	C₂²	1	1	yes	characteristic, complemented
36	#493995	C₂²	1	1	yes	characteristic, complemented
37	#493962	C₂²	1	1	yes	characteristic
38	#486600	C₂²	1	4	yes	complemented
39	#486582	C₂²	1	4	yes	complemented
40	#486520	C₂²	1	4	yes	complemented
41	#486502	C₂²	1	4	yes	complemented
42	#486483	C₂²	1	4	yes	complemented
43	#486435	C₂²	1	4	yes	complemented
44	#482444	C₂²	1	1	yes	characteristic, complemented
45	#482433	C₂²	1	1	yes	characteristic, complemented
46	#482423	C₂²	1	1	yes	characteristic, complemented
47	#482413	C₂²	1	1	yes	characteristic, complemented
48	#482360	C₂²	1	1	yes	characteristic, complemented
49	#482360	C₂²	1	1	yes	characteristic, complemented
50	#480400	C₂²	1	1	yes	characteristic
51	#480382	C₂²	1	1	yes	characteristic, complemented
52	#480376	C₂²	1	1	yes	characteristic, complemented
53	#248459	C₂²	1	4	yes	complemented
54	#248458	C₂²	1	4	yes	complemented
55	#245712	C₂²	1	4	yes	complemented
56	#245711	C₂²	1	4	yes	complemented
57	#245547	C₂²	1	4	yes	complemented
58	#245546	C₂²	1	4	yes	complemented
59	#201549	C₂²	1	1	yes	characteristic, complemented
60	#201385	C₂²	1	1	yes	characteristic, complemented
61	#200404	C₂²	1	1	yes	characteristic, complemented
62	#196338	C₂²	1	1	yes	characteristic, complemented
63	#196279	C₂²	1	1	yes	characteristic
64	#193892	C₂²	1	1	yes	characteristic, complemented
65	#185755	C₂²	1	1	yes	characteristic, complemented
66	#185643	C₂²	1	1	yes	characteristic, complemented
67	#185643	C₂²	1	1	yes	characteristic, complemented
68	#130995	C₂²	1	8	yes	complemented
69	#130976	C₂²	1	8	yes	complemented
70	#130752	C₂²	1	8	yes	complemented
71	#130416	C₂²	1	8	yes	complemented
72	#130397	C₂²	1	8	yes	complemented
73	#130342	C₂²	1	8	yes	complemented
74	#129599	C₂²	1	8	yes	complemented
75	C₂⁴×#41	D₄	1	1	yes	characteristic, complemented
76	#62773	C₂³	1	1	yes	characteristic
77	C₂²×D₄²	D₄	1	1	yes	characteristic
78	C₂²×D₄²	D₄	1	1	yes	characteristic, complemented
79	C₂²×D₄²	C₂³	1	1	yes	characteristic
80	C₂²×#538	D₄	1	1	yes	characteristic, complemented
81	#61560	C₂³	1	2	yes	complemented
82	#61559	C₂³	1	2	yes	complemented
83	#60230	C₂³	1	1	yes	characteristic
84	C₂×#2784	D₄	1	1	yes	characteristic, complemented
85	C₂×#2736	D₄	1	1	yes	characteristic, complemented
86	C₂×#2735	D₄	1	1	yes	characteristic, complemented
87	C₂×#2683	D₄	1	1	yes	characteristic, complemented
88	C₂×#2670	D₄	1	1	yes	characteristic, complemented
89	C₂×#2670	D₄	1	1	yes	characteristic, complemented
90	#47814	D₄	1	4	yes	complemented
91	#47814	C₂³	1	4	yes	—
92	#47182	D₄	1	4	yes	complemented
93	#47182	C₂³	1	4	yes	—
94	#45693	D₄	1	4	yes	complemented
95	#45693	C₂³	1	4	yes	—
96	#45355	D₄	1	4	yes	complemented
97	#45355	C₂³	1	4	yes	—
98	#43893	D₄	1	4	yes	complemented
99	#43893	C₂³	1	4	yes	—
100	C₂×#2844	D₄	1	1	yes	characteristic, complemented
101	C₂×#2835	D₄	1	1	yes	characteristic, complemented
102	C₂×#2826	D₄	1	1	yes	characteristic, complemented
103	C₂×#2824	D₄	1	1	yes	characteristic, complemented
104	C₂×#2847	D₄	1	1	yes	characteristic, complemented
105	#36212	D₄	1	4	yes	complemented
106	#36212	C₂³	1	4	yes	—
107	C₂×#2535	D₄	1	1	yes	characteristic, complemented
108	C₂×#2535	C₂³	1	1	yes	characteristic
109	C₂×#2612	D₄	1	1	yes	characteristic, complemented
110	C₂×#2564	C₂³	1	1	yes	characteristic
111	C₂×#2523	D₄	1	1	yes	characteristic, complemented
112	C₂×#2436	D₄	1	1	yes	characteristic, complemented
113	C₂×#2435	D₄	1	1	yes	characteristic, complemented
114	C₂×#2409	C₂³	1	1	yes	characteristic
115	C₂×#2397	D₄	1	1	yes	characteristic, complemented
116	C₂²×#392	D₄	1	1	yes	characteristic, complemented
117	#34468	D₄	1	4	yes	—
118	#34468	C₂³	1	4	yes	—
119	C₂×#2380	D₄	1	1	yes	characteristic
120	C₂×#2375	D₄	1	1	yes	characteristic
121	C₂×#2364	D₄	1	1	yes	characteristic, complemented
122	C₂×#2358	D₄	1	1	yes	characteristic
123	C₂×D₄×C₂²⋊C₄	D₄	1	1	yes	characteristic, complemented
124	C₂×#2328	D₄	1	1	yes	characteristic, complemented
125	C₂×#2328	C₂³	1	1	yes	characteristic
126	C₂×#2321	C₂³	1	1	yes	characteristic
127	C₂×C₄×#120	C₂³	1	1	yes	characteristic
128	#24352	C₂³	1	2	yes	complemented
129	#24350	C₂³	1	2	yes	complemented
130	#24316	C₂³	1	2	yes	—
131	#24262	C₂³	1	2	yes	complemented
132	#24260	C₂³	1	2	yes	complemented
133	#24226	C₂³	1	2	yes	—
134	#20726	C₂³	1	1	yes	characteristic
135	#20722	C₂³	1	1	yes	characteristic
136	#20722	C₂³	1	1	yes	characteristic
137	#18383	C₂³	1	2	yes	complemented
138	#18381	C₂³	1	2	yes	complemented
139	#18212	C₂³	1	2	yes	complemented
140	#18210	C₂³	1	2	yes	complemented
141	#18197	C₂³	1	2	yes	complemented
142	#18195	C₂³	1	2	yes	complemented
143	#17364	C₂³	1	1	yes	characteristic
144	#17362	C₂³	1	1	yes	characteristic
145	#17362	C₂³	1	1	yes	characteristic
146	#12799	C₂³	1	4	yes	—
147	#12795	C₂³	1	4	yes	complemented
148	#12793	C₂³	1	4	yes	complemented
149	#11906	C₂³	1	4	yes	complemented
150	#11904	C₂³	1	4	yes	complemented
151	#11902	C₂³	1	4	yes	complemented
152	#11898	C₂³	1	4	yes	complemented
153	#11875	C₂³	1	4	yes	complemented
154	#11875	C₂³	1	4	yes	complemented
155	#11479	C₂³	1	4	yes	—
156	#11473	C₂³	1	4	yes	complemented
157	#11471	C₂³	1	4	yes	complemented
158	#9485	C₂³	1	4	yes	complemented
159	#9467	C₂³	1	4	yes	complemented
160	#9383	C₂³	1	4	yes	complemented
161	#9107	C₂³	1	4	yes	complemented
162	#9101	C₂³	1	4	yes	—
163	#8965	C₂³	1	4	yes	complemented
164	#8383	C₂³	1	4	yes	complemented
165	#8375	C₂³	1	4	yes	complemented
166	#8375	C₂³	1	4	yes	complemented
167	C₂³×#41	C₂×D₄	1	4	yes	—
168	C₂⁴×Q₈	C₂×D₄	1	1	yes	characteristic
169	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
170	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
171	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
172	#3501	C₂⁴	1	1	yes	characteristic
173	#3496	C₂⁴	1	1	yes	characteristic
174	C₂×D₄²	C₂×D₄	1	4	yes	—
175	C₂×D₄²	C₂×D₄	1	2	yes	—
176	C₂×D₄²	C₂×D₄	1	2	yes	—
177	C₂×D₄²	C₂×D₄	1	4	yes	—
178	C₂×D₄²	C₂×D₄	1	2	yes	—
179	C₂×D₄²	C₂⁴	1	2	yes	—
180	C₂×#538	C₂×D₄	1	4	yes	—
181	C₂²×#127	C₂×D₄	1	1	yes	characteristic
182	C₂²×#127	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₂²⋊Q₈	C₂×D₄	1	1	yes	characteristic
184	C₂²×#121	C₂×D₄	1	1	yes	characteristic
185	C₂²×#121	C₂×D₄	1	1	yes	characteristic
186	C₂²×#120	C₂×D₄	1	1	yes	characteristic
187	C₂²×#120	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
191	C₂²×C₄×D₄	C₂⁴	1	1	yes	characteristic
192	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
193	#2972	C₂⁴	1	2	yes	—
194	#2847	C₂×D₄	1	4	yes	—
195	#2844	C₂×D₄	1	4	yes	—
196	#2835	C₂×D₄	1	4	yes	—
197	#2826	C₂×D₄	1	4	yes	—
198	#2824	C₂×D₄	1	4	yes	—
199	#2784	C₂×D₄	1	4	yes	—
200	#2736	C₂×D₄	1	4	yes	—
201	#2735	C₂×D₄	1	4	yes	—
202	#2683	C₂×D₄	1	4	yes	—
203	#2670	C₂×D₄	1	4	yes	—
204	#2670	C₂×D₄	1	4	yes	—
205	#2612	C₂×D₄	1	4	yes	—
206	#2564	C₂×D₄	1	2	yes	—
207	#2564	C₂×D₄	1	2	yes	—
208	#2564	C₂×D₄	1	2	yes	—
209	#2564	C₂⁴	1	2	yes	—
210	#2535	C₂×D₄	1	2	yes	—
211	#2535	C₂×D₄	1	2	yes	—
212	#2535	C₂×D₄	1	4	yes	—
213	#2535	C₂×D₄	1	2	yes	—
214	#2535	C₂⁴	1	2	yes	—
215	#2523	C₂×D₄	1	4	yes	—
216	#2436	C₂×D₄	1	4	yes	—
217	#2435	C₂×D₄	1	4	yes	—
218	#2409	C₂×D₄	1	2	yes	—
219	#2409	C₂×D₄	1	2	yes	—
220	#2409	C₂×D₄	1	2	yes	—
221	#2409	C₂⁴	1	2	yes	—
222	#2397	C₂×D₄	1	4	yes	—
223	C₂×#400	C₂×D₄	1	1	yes	characteristic
224	C₂×#399	C₂×D₄	1	1	yes	characteristic
225	C₂×#397	C₂×D₄	1	1	yes	characteristic
226	C₂×#397	C₂×D₄	1	1	yes	characteristic
227	C₂×#395	C₂×D₄	1	1	yes	characteristic
228	C₂×#395	C₂×D₄	1	1	yes	characteristic
229	C₂×#395	C₂×D₄	1	1	yes	characteristic
230	C₂×#393	C₂×D₄	1	1	yes	characteristic
231	C₂×#393	C₂×D₄	1	1	yes	characteristic
232	C₂×#393	C₂×D₄	1	1	yes	characteristic
233	C₂×#392	C₂×D₄	1	1	yes	characteristic
234	C₂×#392	C₂×D₄	1	1	yes	characteristic
235	C₂×#392	C₂×D₄	1	4	yes	—
236	#2380	C₂×D₄	1	4	yes	—
237	#2375	C₂×D₄	1	4	yes	—
238	#2364	C₂×D₄	1	4	yes	—
239	#2358	C₂×D₄	1	4	yes	—
240	D₄×C₂²⋊C₄	C₂×D₄	1	4	yes	—
241	#2328	C₂×D₄	1	4	yes	—
242	#2328	C₂×D₄	1	2	yes	—
243	#2328	C₂×D₄	1	2	yes	—
244	#2328	C₂×D₄	1	2	yes	—
245	#2328	C₂⁴	1	2	yes	—
246	#2321	C₂×D₄	1	2	yes	—
247	#2321	C₂×D₄	1	2	yes	—
248	#2321	C₂×D₄	1	2	yes	—
249	#2321	C₂⁴	1	2	yes	—
250	C₄×#120	C₂×D₄	1	2	yes	—
251	C₄×#120	C₂×D₄	1	2	yes	—
252	C₄×#120	C₂×D₄	1	2	yes	—
253	C₄×#120	C₂⁴	1	2	yes	—
254	C₂×#390	C₂×D₄	1	1	yes	characteristic
255	C₂×#390	C₂×D₄	1	1	yes	characteristic
256	C₂×#386	C₂×D₄	1	1	yes	characteristic
257	C₂×#386	C₂×D₄	1	1	yes	characteristic
258	C₂×#385	C₂×D₄	1	1	yes	characteristic
259	C₂×#385	C₂×D₄	1	1	yes	characteristic
260	C₂×#382	C₂×D₄	1	1	yes	characteristic
261	C₂×#382	C₂×D₄	1	1	yes	characteristic
262	C₂×#380	C₂×D₄	1	1	yes	characteristic
263	C₂×#379	C₂×D₄	1	1	yes	characteristic
264	C₂×#379	C₂×D₄	1	1	yes	characteristic
265	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
266	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
267	C₂×#376	C₂×D₄	1	1	yes	characteristic
268	C₂²×#95	C₂×D₄	1	1	yes	characteristic
269	#1800	C₂⁴	1	2	yes	—
270	#1799	C₂⁴	1	2	yes	—
271	#1799	C₂⁴	1	2	yes	—
272	#1460	C₂⁴	1	2	yes	—
273	#1459	C₂⁴	1	2	yes	—
274	#1459	C₂⁴	1	2	yes	—
275	C₂⁶	#120	1	1	yes	characteristic
276	C₂⁶	#120	1	1	yes	characteristic
277	C₂³×Q₈	#120	1	1	yes	characteristic
278	C₂³×Q₈	#120	1	1	yes	characteristic
279	C₂³×Q₈	#120	1	2	yes	—
280	C₂³×Q₈	#120	1	1	yes	characteristic
281	C₂³×Q₈	C₂²×D₄	1	2	yes	—
282	C₂³×D₄	#120	1	1	yes	characteristic
283	C₂³×D₄	#120	1	2	yes	—
284	C₂³×D₄	#120	1	1	yes	characteristic
285	C₂³×D₄	#120	1	2	yes	—
286	C₂³×D₄	#120	1	1	yes	characteristic
287	C₂³×D₄	#120	1	1	yes	characteristic
288	C₂³×D₄	#120	1	1	yes	characteristic
289	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
290	C₂³×D₄	C₂²×D₄	1	2	yes	—
291	C₂³×D₄	C₂²×D₄	1	2	yes	—
292	C₂⁴×C₄	#120	1	1	yes	characteristic
293	C₂⁴×C₄	#120	1	2	yes	—
294	C₂⁴×C₄	#120	1	1	yes	characteristic
295	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
296	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
297	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
298	C₂×#127	#120	1	2	yes	—
299	C₂×#127	#120	1	2	yes	—
300	C₂×#127	C₂²×D₄	1	2	yes	—
301	C₂×#127	C₂²×D₄	1	2	yes	—
302	C₂×C₂²⋊Q₈	#120	1	2	yes	—
303	C₂×C₂²⋊Q₈	C₂²×D₄	1	2	yes	—
304	C₂×#121	#120	1	2	yes	—
305	C₂×#121	#120	1	2	yes	—
306	C₂×#121	C₂²×D₄	1	2	yes	—
307	C₂×#121	C₂²×D₄	1	2	yes	—
308	C₂×#120	#120	1	2	yes	—
309	C₂×#120	#120	1	2	yes	—
310	C₂×#120	C₂²×D₄	1	2	yes	—
311	C₂×#120	C₂²×D₄	1	2	yes	—
312	C₂×C₄×D₄	#120	1	2	yes	—
313	C₂×C₄×D₄	#120	1	2	yes	—
314	C₂×C₄×D₄	#120	1	2	yes	—
315	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
316	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
317	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
318	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
319	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
320	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
321	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
322	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
323	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
324	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
325	C₂×C₄×D₄	C₂⁵	1	1	yes	characteristic
326	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
327	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
328	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
329	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
330	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
331	C₂²×C₂²⋊C₄	#120	1	2	yes	—
332	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
333	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
334	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
335	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
336	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
337	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
338	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
339	C₂²×C₄²	#120	1	1	yes	characteristic
340	C₂²×C₄²	#120	1	1	yes	characteristic
341	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
342	#400	#120	1	2	yes	—
343	#400	C₂²×D₄	1	2	yes	—
344	#399	#120	1	2	yes	—
345	#399	C₂²×D₄	1	2	yes	—
346	#397	#120	1	2	yes	—
347	#397	#120	1	2	yes	—
348	#397	C₂²×D₄	1	2	yes	—
349	#397	C₂²×D₄	1	2	yes	—
350	#395	#120	1	2	yes	—
351	#395	#120	1	2	yes	—
352	#395	#120	1	2	yes	—
353	#395	C₂²×D₄	1	2	yes	—
354	#395	C₂²×D₄	1	2	yes	—
355	#395	C₂²×D₄	1	2	yes	—
356	#393	#120	1	2	yes	—
357	#393	#120	1	2	yes	—
358	#393	#120	1	2	yes	—
359	#393	C₂²×D₄	1	2	yes	—
360	#393	C₂²×D₄	1	2	yes	—
361	#393	C₂²×D₄	1	2	yes	—
362	#392	#120	1	2	yes	—
363	#392	#120	1	2	yes	—
364	#392	C₂²×D₄	1	2	yes	—
365	#392	C₂²×D₄	1	2	yes	—
366	#390	#120	1	2	yes	—
367	#390	#120	1	2	yes	—
368	#390	C₂²×D₄	1	2	yes	—
369	#390	C₂²×D₄	1	2	yes	—
370	#386	#120	1	2	yes	—
371	#386	#120	1	2	yes	—
372	#386	C₂²×D₄	1	2	yes	—
373	#386	C₂²×D₄	1	2	yes	—
374	#385	#120	1	2	yes	—
375	#385	#120	1	2	yes	—
376	#385	C₂²×D₄	1	2	yes	—
377	#385	C₂²×D₄	1	2	yes	—
378	#382	#120	1	2	yes	—
379	#382	#120	1	2	yes	—
380	#382	C₂²×D₄	1	2	yes	—
381	#382	C₂²×D₄	1	2	yes	—
382	#380	#120	1	2	yes	—
383	#380	C₂²×D₄	1	2	yes	—
384	#379	#120	1	2	yes	—
385	#379	#120	1	2	yes	—
386	#379	C₂²×D₄	1	2	yes	—
387	#379	C₂²×D₄	1	2	yes	—
388	C₄×C₂²⋊C₄	#120	1	2	yes	—
389	C₄×C₂²⋊C₄	#120	1	2	yes	—
390	C₄×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
391	C₄×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
392	#376	#120	1	2	yes	—
393	#376	C₂²×D₄	1	2	yes	—
394	C₂×#95	#120	1	2	yes	—
395	C₂×#95	#120	1	1	yes	characteristic
396	C₂×#95	#120	1	1	yes	characteristic
397	C₂×#95	#120	1	1	yes	characteristic
398	C₂×#95	#120	1	1	yes	characteristic
399	C₂×#95	#120	1	1	yes	characteristic
400	C₂×#95	#120	1	1	yes	characteristic
401	C₂×#95	C₂²×D₄	1	2	yes	—
402	C₂⁵	C₂×#120	1	1	yes	characteristic
403	C₂⁵	C₂×#120	1	1	yes	characteristic
404	C₂⁵	C₂×#120	1	2	yes	—
405	C₂⁵	C₂×#120	1	2	yes	—
406	C₂²×Q₈	C₂×#120	1	2	yes	—
407	C₂²×Q₈	C₂×#120	1	2	yes	—
408	C₂²×Q₈	C₂×#120	1	2	yes	—
409	C₂²×D₄	B(4,𝔽₂)	1	2	yes	—
410	C₂²×D₄	B(4,𝔽₂)	1	2	yes	—
411	C₂²×D₄	C₂×#120	1	1	yes	characteristic
412	C₂²×D₄	C₂×#120	1	1	yes	characteristic
413	C₂²×D₄	C₂×#120	1	2	yes	—
414	C₂²×D₄	C₂×#120	1	1	yes	characteristic
415	C₂²×D₄	C₂×#120	1	2	yes	—
416	C₂²×D₄	C₂×#120	1	2	yes	—
417	C₂²×D₄	C₂×#120	1	2	yes	—
418	C₂²×D₄	C₂×#120	1	2	yes	—
419	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
420	C₂³×C₄	C₂×#120	1	1	yes	characteristic
421	C₂³×C₄	C₂×#120	1	1	yes	characteristic
422	C₂³×C₄	C₂×#120	1	1	yes	characteristic
423	C₂³×C₄	C₂×#120	1	1	yes	characteristic
424	C₂³×C₄	C₂×#120	1	1	yes	characteristic
425	C₂³×C₄	C₂×#120	1	1	yes	characteristic
426	C₂³×C₄	C₂×#120	1	1	yes	characteristic
427	C₂³×C₄	C₂×#120	1	1	yes	characteristic
428	C₂³×C₄	C₂×#120	1	1	yes	characteristic
429	C₂³×C₄	C₂×#120	1	1	yes	characteristic
430	C₂³×C₄	C₂×#120	1	2	yes	—
431	C₂³×C₄	C₂×#120	1	2	yes	—
432	C₂³×C₄	C₂×#120	1	1	yes	characteristic
433	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
434	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
435	#127	#575	1	8	yes	—
436	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
437	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
438	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
439	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
440	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
441	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
442	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
443	C₂×C₄⋊C₄	C₂³×D₄	1	1	yes	characteristic
444	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
445	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
446	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
447	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
448	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
449	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
450	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
451	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
452	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
453	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
454	C₂×C₂²⋊C₄	C₂³×D₄	1	1	yes	characteristic
455	C₂×C₂²⋊C₄	C₂³×D₄	1	1	yes	characteristic
456	C₂×C₄²	C₂×#120	1	1	yes	characteristic
457	C₂×C₄²	C₂×#120	1	1	yes	characteristic
458	C₂×C₄²	C₂×#120	1	1	yes	characteristic
459	C₂×C₄²	C₂×#120	1	2	yes	—
460	C₂×C₄²	C₂×#120	1	2	yes	—
461	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
462	#95	C₂×#120	1	2	yes	—
463	#95	C₂×#120	1	2	yes	—
464	#95	C₂×#120	1	2	yes	—
465	#95	C₂×#120	1	2	yes	—
466	#95	C₂×#120	1	2	yes	—
467	#95	C₂×#120	1	2	yes	—
468	C₂⁴	#2846	1	1	yes	characteristic
469	C₂⁴	#2846	1	1	yes	characteristic
470	C₂⁴	#2846	1	1	yes	characteristic
471	C₂⁴	C₂²×#120	1	1	yes	characteristic
472	C₂⁴	C₂²×#120	1	1	yes	characteristic
473	C₂×D₄	#3005	1	4	yes	complemented
474	C₂×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
475	C₂×D₄	C₂×#575	1	4	yes	—
476	C₂²×C₄	#2846	1	1	yes	characteristic
477	C₂²×C₄	#2846	1	1	yes	characteristic
478	C₂²×C₄	#2846	1	1	yes	characteristic
479	C₂²×C₄	#2846	1	1	yes	characteristic
480	C₂²×C₄	#2846	1	1	yes	characteristic
481	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
482	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
483	C₂²×C₄	#3026	1	1	yes	characteristic
484	C₂²×C₄	#3026	1	1	yes	characteristic
485	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
486	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
487	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
488	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
489	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
490	C₄²	#3005	1	4	yes	complemented
491	C₂³	#32898	1	1	yes	characteristic
492	C₂³	#32898	1	1	yes	characteristic
493	C₂³	C₂×#2846	1	1	yes	characteristic
494	C₂³	#60359	1	2	yes	—
495	C₂³	#60359	1	2	yes	—
496	C₂×C₄	#32898	1	1	yes	characteristic
497	C₂×C₄	#32898	1	1	yes	characteristic
498	C₂×C₄	C₂×#3005	1	2	yes	—
499	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
500	C₂×C₄	C₂×#3026	1	1	yes	characteristic
501	C₂²	#511790	1	2	yes	—
502	C₂²	#511827	1	2	yes	—
503	C₂²	#6628844	1	1	yes	characteristic
504	C₂²	#6628883	1	1	yes	characteristic
505	C₂²	C₂×#32898	1	1	yes	characteristic
506	C₂	C₂×#511790	1	1	yes	characteristic
507	C₂	#72238188	1	1	yes	characteristic
508	C₂	C₂×#511827	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×#32898
commutator, Frattini, cosocle	C₂×C₄×D₄	C₂⁵
LCS	G ▷ C₂×C₄×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂²×D₄² ◁ G
LECS	G ▷ C₂×C₄×D₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72240214	C₂	semidirect
2. #72240213	C₂	semidirect
3. #72240212	C₂	semidirect
4. #72240211	C₂	semidirect
5. #72240210	C₂	semidirect
6. #72240207	C₂	semidirect
7. #72240206	C₂	semidirect
8. #72240205	C₂	semidirect
9. #72240204	C₂	semidirect
10. #72240203	C₂	semidirect
11. #72240202	C₂	semidirect
12. #72240201	C₂	semidirect
13. C₂×#8058967	C₂	semidirect
14. #72231069	C₂	semidirect
15. #72231032	C₂	semidirect
16. #72230994	C₂	semidirect
17. #72213883	C₂	semidirect
18. #10577301	C₂²	semidirect
27. #6454047	C₂²	semidirect
28. #6454041	C₂²	semidirect
30. #6347310	C₂²	semidirect
31. #6346631	C₂²	semidirect
32. #6346600	C₂²	semidirect
33. #512030	C₂²	semidirect
34. #511938	C₂²	semidirect
35. #493998	C₂²	semidirect
36. #493995	C₂²	semidirect
38. #486600	C₂²	semidirect
39. #486582	C₂²	semidirect
40. #486520	C₂²	semidirect
41. #486502	C₂²	semidirect
42. #486483	C₂²	semidirect
43. #486435	C₂²	semidirect
44. #482444	C₂²	semidirect
45. #482433	C₂²	semidirect
46. #482423	C₂²	semidirect
47. #482413	C₂²	semidirect
48. #482360	C₂²	semidirect
49. #482360	C₂²	semidirect
51. #480382	C₂²	semidirect
52. #480376	C₂²	semidirect
53. #248459	C₂²	semidirect
54. #248458	C₂²	semidirect
55. #245712	C₂²	semidirect
56. #245711	C₂²	semidirect
57. #245547	C₂²	semidirect
58. #245546	C₂²	semidirect
59. #201549	C₂²	semidirect
60. #201385	C₂²	semidirect
61. #200404	C₂²	semidirect
62. #196338	C₂²	semidirect
64. #193892	C₂²	semidirect
65. #185755	C₂²	semidirect
66. #185643	C₂²	semidirect
67. #185643	C₂²	semidirect
68. #130995	C₂²	semidirect
69. #130976	C₂²	semidirect
70. #130752	C₂²	semidirect
71. #130416	C₂²	semidirect
72. #130397	C₂²	semidirect
73. #130342	C₂²	semidirect
74. #129599	C₂²	semidirect
75. C₂⁴×#41	D₄	semidirect
78. C₂²×D₄²	D₄	semidirect
80. C₂²×#538	D₄	semidirect
81. #61560	C₂³	semidirect
82. #61559	C₂³	semidirect
84. C₂×#2784	D₄	semidirect
85. C₂×#2736	D₄	semidirect
86. C₂×#2735	D₄	semidirect
87. C₂×#2683	D₄	semidirect
88. C₂×#2670	D₄	semidirect
89. C₂×#2670	D₄	semidirect
90. #47814	D₄	semidirect
92. #47182	D₄	semidirect
94. #45693	D₄	semidirect
96. #45355	D₄	semidirect
98. #43893	D₄	semidirect
100. C₂×#2844	D₄	semidirect
101. C₂×#2835	D₄	semidirect
102. C₂×#2826	D₄	semidirect
103. C₂×#2824	D₄	semidirect
104. C₂×#2847	D₄	semidirect
105. #36212	D₄	semidirect
107. C₂×#2535	D₄	semidirect
109. C₂×#2612	D₄	semidirect
111. C₂×#2523	D₄	semidirect
112. C₂×#2436	D₄	semidirect
113. C₂×#2435	D₄	semidirect
115. C₂×#2397	D₄	semidirect
116. C₂²×#392	D₄	semidirect
121. C₂×#2364	D₄	semidirect
123. C₂×D₄×C₂²⋊C₄	D₄	semidirect
124. C₂×#2328	D₄	semidirect
128. #24352	C₂³	semidirect
129. #24350	C₂³	semidirect
131. #24262	C₂³	semidirect
132. #24260	C₂³	semidirect
137. #18383	C₂³	semidirect
138. #18381	C₂³	semidirect
139. #18212	C₂³	semidirect
140. #18210	C₂³	semidirect
141. #18197	C₂³	semidirect
142. #18195	C₂³	semidirect
147. #12795	C₂³	semidirect
148. #12793	C₂³	semidirect
149. #11906	C₂³	semidirect
150. #11904	C₂³	semidirect
151. #11902	C₂³	semidirect
152. #11898	C₂³	semidirect
153. #11875	C₂³	semidirect
154. #11875	C₂³	semidirect
156. #11473	C₂³	semidirect
157. #11471	C₂³	semidirect
158. #9485	C₂³	semidirect
159. #9467	C₂³	semidirect
160. #9383	C₂³	semidirect
161. #9107	C₂³	semidirect
163. #8965	C₂³	semidirect
164. #8383	C₂³	semidirect
165. #8375	C₂³	semidirect
166. #8375	C₂³	semidirect
473. C₂×D₄	#3005	semidirect
490. C₄²	#3005	semidirect

Maximal subgroups

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

subgroup	index
#72240214	2
#72240213	2
#72240212	2
#72240211	2
#72240210	2
#72240207	2
#72240206	2
#72240205	2
#72240204	2
#72240203	2
#72240202	2
#72240201	2
C₂×#8058967	2
#72231069	2
#72231032	2
#72230994	2
#72213883	2