Subgroups — #72338694

Order 2048.

At least 7872 conjugacy classes of subgroups; only the 990 normal subgroups are shown.

The subgroup lattice has 468 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72338692	C₂	1	1	yes	maximal, characteristic, complemented
2	#72338689	C₂	1	1	yes	maximal, characteristic, complemented
3	#72338685	C₂	1	1	yes	maximal, characteristic, complemented
4	#72338682	C₂	1	8	yes	maximal, complemented
5	#72338680	C₂	1	8	yes	maximal, complemented
6	#72338679	C₂	1	1	yes	maximal, characteristic, complemented
7	#72338678	C₂	1	1	yes	maximal, characteristic, complemented
8	#72338676	C₂	1	1	yes	maximal, characteristic, complemented
9	#72338668	C₂	1	1	yes	maximal, characteristic, complemented
10	#72316511	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#8698894	C₂	1	1	yes	maximal, characteristic, complemented
12	#72240305	C₂	1	1	yes	maximal, characteristic, complemented
13	#72240303	C₂	1	1	yes	maximal, characteristic, complemented
14	#72231294	C₂	1	1	yes	maximal, characteristic, complemented
15	#72231282	C₂	1	1	yes	maximal, characteristic, complemented
16	#72231038	C₂	1	1	yes	maximal, characteristic, complemented
17	#72214295	C₂	1	1	yes	maximal, characteristic, complemented
18	#10577301	C₂²	1	1	yes	characteristic, complemented
19	#8698894	C₂²	1	8	yes	—
20	C₂×#45599	C₂²	1	1	yes	characteristic
21	C₂×#59945	C₂²	1	1	yes	characteristic
22	C₂×#58997	C₂²	1	1	yes	characteristic
23	C₂×#39361	C₂²	1	1	yes	characteristic
24	C₂×#38904	C₂²	1	1	yes	characteristic
25	C₂×#52301	C₂²	1	1	yes	characteristic
26	C₂×D₄×#120	C₂²	1	1	yes	characteristic
27	#6454041	C₂²	1	1	yes	characteristic, complemented
28	#6454041	C₂²	1	1	yes	characteristic, complemented
29	#6453830	C₂²	1	1	yes	characteristic, complemented
30	#6347316	C₂²	1	1	yes	characteristic, complemented
31	#6346608	C₂²	1	1	yes	characteristic, complemented
32	#6346599	C₂²	1	1	yes	characteristic
33	#508249	C₂²	1	4	yes	complemented
34	#508193	C₂²	1	4	yes	complemented
35	#493995	C₂²	1	1	yes	characteristic, complemented
36	#493995	C₂²	1	1	yes	characteristic, complemented
37	#493956	C₂²	1	1	yes	characteristic, complemented
38	#486613	C₂²	1	4	yes	complemented
39	#486593	C₂²	1	4	yes	complemented
40	#486533	C₂²	1	4	yes	complemented
41	#486513	C₂²	1	4	yes	complemented
42	#486347	C₂²	1	4	yes	complemented
43	#486243	C₂²	1	4	yes	complemented
44	#482443	C₂²	1	1	yes	characteristic, complemented
45	#482424	C₂²	1	1	yes	characteristic, complemented
46	#482377	C₂²	1	1	yes	characteristic
47	#482369	C₂²	1	1	yes	characteristic, complemented
48	#482369	C₂²	1	1	yes	characteristic, complemented
49	#482357	C₂²	1	1	yes	characteristic
50	#480390	C₂²	1	1	yes	characteristic, complemented
51	#480376	C₂²	1	1	yes	characteristic, complemented
52	#480376	C₂²	1	1	yes	characteristic, complemented
53	#248507	C₂²	1	4	yes	complemented
54	#248506	C₂²	1	4	yes	complemented
55	#248456	C₂²	1	4	yes	complemented
56	#248455	C₂²	1	4	yes	complemented
57	#248000	C₂²	1	4	yes	complemented
58	#247999	C₂²	1	4	yes	complemented
59	#201388	C₂²	1	1	yes	characteristic, complemented
60	#201386	C₂²	1	1	yes	characteristic
61	#200521	C₂²	1	1	yes	characteristic, complemented
62	#193892	C₂²	1	1	yes	characteristic, complemented
63	#193892	C₂²	1	1	yes	characteristic, complemented
64	#193832	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	#130982	C₂²	1	8	yes	complemented
69	#130773	C₂²	1	8	yes	complemented
70	#130740	C₂²	1	8	yes	complemented
71	#130403	C₂²	1	8	yes	complemented
72	#130355	C₂²	1	8	yes	complemented
73	#130260	C₂²	1	8	yes	complemented
74	#129645	C₂²	1	8	yes	complemented
75	C₂⁵×D₄	D₄	1	1	yes	characteristic, complemented
76	#62773	C₂³	1	1	yes	characteristic
77	C₂²×#550	D₄	1	1	yes	characteristic, complemented
78	C₂²×D₄²	C₂³	1	1	yes	characteristic
79	C₂³×#121	D₄	1	1	yes	characteristic, complemented
80	#61560	C₂³	1	2	yes	complemented
81	#61559	C₂³	1	2	yes	complemented
82	#60230	C₂³	1	1	yes	characteristic
83	#59945	D₄	1	4	yes	complemented
84	#59945	C₂³	1	4	yes	—
85	#58997	D₄	1	4	yes	complemented
86	#58997	C₂³	1	4	yes	—
87	#52301	D₄	1	4	yes	—
88	#52301	C₂³	1	4	yes	—
89	C₂×#2804	D₄	1	1	yes	characteristic
90	C₂×#2782	D₄	1	2	yes	complemented
91	C₂×#2684	D₄	1	1	yes	characteristic
92	C₂×#2684	D₄	1	1	yes	characteristic
93	C₂×#2679	D₄	1	1	yes	characteristic
94	C₂×#2675	D₄	1	2	yes	complemented
95	C₂×#2668	D₄	1	2	yes	complemented
96	#45599	D₄	1	4	yes	complemented
97	#45599	C₂³	1	4	yes	—
98	#39361	D₄	1	4	yes	complemented
99	#39361	C₂³	1	4	yes	—
100	#38904	D₄	1	4	yes	complemented
101	#38904	C₂³	1	4	yes	—
102	C₂×#2826	D₄	1	2	yes	complemented
103	C₂×#2867	D₄	1	1	yes	characteristic, complemented
104	C₂×#2847	D₄	1	1	yes	characteristic, complemented
105	C₂×#2847	D₄	1	1	yes	characteristic, complemented
106	D₄×#120	D₄	1	4	yes	complemented
107	D₄×#120	C₂³	1	4	yes	—
108	C₂×#2548	D₄	1	1	yes	characteristic, complemented
109	C₂×#2541	C₂³	1	1	yes	characteristic
110	C₂×#2572	D₄	1	2	yes	complemented
111	C₂×#2504	D₄	1	1	yes	characteristic, complemented
112	C₂×#2487	C₂³	1	1	yes	characteristic
113	C₂×#2433	D₄	1	1	yes	characteristic, complemented
114	C₂×#2408	C₂³	1	1	yes	characteristic
115	C₂×#2403	D₄	1	2	yes	complemented
116	C₂×D₄×C₂²⋊C₄	D₄	1	1	yes	characteristic, complemented
117	C₂×D₄×C₂²⋊C₄	D₄	1	1	yes	characteristic, complemented
118	C₂×C₄×#124	C₂³	1	1	yes	characteristic
119	C₂×C₄×#120	C₂³	1	1	yes	characteristic
120	C₂×C₄×#120	C₂³	1	1	yes	characteristic
121	C₂×#2293	D₄	1	1	yes	characteristic, complemented
122	#24350	C₂³	1	2	yes	complemented
123	#24350	C₂³	1	2	yes	complemented
124	#24314	C₂³	1	2	yes	complemented
125	#24260	C₂³	1	2	yes	complemented
126	#24260	C₂³	1	2	yes	complemented
127	#24224	C₂³	1	2	yes	complemented
128	#20726	C₂³	1	1	yes	characteristic
129	#20722	C₂³	1	1	yes	characteristic
130	#20722	C₂³	1	1	yes	characteristic
131	#18389	C₂³	1	2	yes	complemented
132	#18387	C₂³	1	2	yes	complemented
133	#18205	C₂³	1	2	yes	complemented
134	#18203	C₂³	1	2	yes	complemented
135	#18196	C₂³	1	2	yes	—
136	#18194	C₂³	1	2	yes	—
137	#17364	C₂³	1	1	yes	characteristic
138	#17362	C₂³	1	1	yes	characteristic
139	#17362	C₂³	1	1	yes	characteristic
140	#12798	C₂³	1	4	yes	complemented
141	#12793	C₂³	1	4	yes	complemented
142	#12793	C₂³	1	4	yes	complemented
143	#11903	C₂³	1	4	yes	complemented
144	#11899	C₂³	1	4	yes	complemented
145	#11880	C₂³	1	4	yes	—
146	#11877	C₂³	1	4	yes	complemented
147	#11877	C₂³	1	4	yes	complemented
148	#11873	C₂³	1	4	yes	—
149	#11477	C₂³	1	4	yes	complemented
150	#11471	C₂³	1	4	yes	complemented
151	#11471	C₂³	1	4	yes	complemented
152	#9469	C₂³	1	4	yes	complemented
153	#9468	C₂³	1	4	yes	—
154	#9397	C₂³	1	4	yes	complemented
155	#8965	C₂³	1	4	yes	complemented
156	#8965	C₂³	1	4	yes	complemented
157	#8957	C₂³	1	4	yes	complemented
158	#8383	C₂³	1	4	yes	complemented
159	#8375	C₂³	1	4	yes	complemented
160	#8375	C₂³	1	4	yes	complemented
161	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
162	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
163	C₂⁴×D₄	C₂×D₄	1	4	yes	—
164	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
165	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
166	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
167	#3501	C₂⁴	1	1	yes	characteristic
168	#3496	C₂⁴	1	1	yes	characteristic
169	C₂×#550	C₂×D₄	1	4	yes	—
170	C₂×D₄²	C₂×D₄	1	2	yes	—
171	C₂×D₄²	C₂×D₄	1	2	yes	—
172	C₂×D₄²	C₂×D₄	1	2	yes	—
173	C₂×D₄²	C₂⁴	1	2	yes	—
174	C₂²×#127	C₂×D₄	1	1	yes	characteristic
175	C₂²×#127	C₂×D₄	1	1	yes	characteristic
176	C₂²×#124	C₂×D₄	1	1	yes	characteristic
177	C₂²×#121	C₂×D₄	1	1	yes	characteristic
178	C₂²×#121	C₂×D₄	1	1	yes	characteristic
179	C₂²×#121	C₂×D₄	1	4	yes	—
180	C₂²×#120	C₂×D₄	1	1	yes	characteristic
181	C₂²×#120	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×D₄	C₂⁴	1	1	yes	characteristic
185	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
186	#2972	C₂⁴	1	2	yes	—
187	#2867	C₂×D₄	1	4	yes	—
188	#2847	C₂×D₄	1	4	yes	—
189	#2847	C₂×D₄	1	4	yes	—
190	#2826	C₂×D₄	1	8	yes	—
191	#2804	C₂×D₄	1	4	yes	—
192	#2782	C₂×D₄	1	8	yes	—
193	#2684	C₂×D₄	1	4	yes	—
194	#2684	C₂×D₄	1	4	yes	—
195	#2679	C₂×D₄	1	4	yes	—
196	#2675	C₂×D₄	1	8	yes	—
197	#2668	C₂×D₄	1	8	yes	—
198	#2572	C₂×D₄	1	8	yes	—
199	#2548	C₂×D₄	1	4	yes	—
200	#2541	C₂×D₄	1	2	yes	—
201	#2541	C₂×D₄	1	2	yes	—
202	#2541	C₂×D₄	1	2	yes	—
203	#2541	C₂⁴	1	2	yes	—
204	#2504	C₂×D₄	1	4	yes	—
205	#2487	C₂×D₄	1	2	yes	—
206	#2487	C₂×D₄	1	2	yes	—
207	#2487	C₂×D₄	1	2	yes	—
208	#2487	C₂⁴	1	2	yes	—
209	#2433	C₂×D₄	1	4	yes	—
210	#2408	C₂×D₄	1	2	yes	—
211	#2408	C₂×D₄	1	2	yes	—
212	#2408	C₂×D₄	1	2	yes	—
213	#2408	C₂⁴	1	2	yes	—
214	#2403	C₂×D₄	1	8	yes	—
215	C₂×#400	C₂×D₄	1	2	yes	—
216	C₂×#399	C₂×D₄	1	2	yes	—
217	C₂×#394	C₂×D₄	1	2	yes	—
218	C₂×#392	C₂×D₄	1	2	yes	—
219	C₂×#392	C₂×D₄	1	2	yes	—
220	C₂×#392	C₂×D₄	1	2	yes	—
221	D₄×C₂²⋊C₄	C₂×D₄	1	4	yes	—
222	D₄×C₂²⋊C₄	C₂×D₄	1	4	yes	—
223	C₄×#124	C₂×D₄	1	2	yes	—
224	C₄×#124	C₂×D₄	1	2	yes	—
225	C₄×#124	C₂×D₄	1	2	yes	—
226	C₄×#124	C₂⁴	1	2	yes	—
227	C₄×#120	C₂×D₄	1	2	yes	—
228	C₄×#120	C₂×D₄	1	2	yes	—
229	C₄×#120	C₂×D₄	1	2	yes	—
230	C₄×#120	C₂×D₄	1	2	yes	—
231	C₄×#120	C₂×D₄	1	2	yes	—
232	C₄×#120	C₂×D₄	1	2	yes	—
233	C₄×#120	C₂⁴	1	2	yes	—
234	C₄×#120	C₂⁴	1	2	yes	—
235	C₂×#391	C₂×D₄	1	1	yes	characteristic
236	#2293	C₂×D₄	1	4	yes	—
237	C₂×#390	C₂×D₄	1	1	yes	characteristic
238	C₂×#386	C₂×D₄	1	1	yes	characteristic
239	C₂×#386	C₂×D₄	1	1	yes	characteristic
240	C₂×#385	C₂×D₄	1	1	yes	characteristic
241	C₂×#385	C₂×D₄	1	1	yes	characteristic
242	C₂×#382	C₂×D₄	1	1	yes	characteristic
243	C₂×#380	C₂×D₄	1	1	yes	characteristic
244	C₂×#380	C₂×D₄	1	1	yes	characteristic
245	C₂×#379	C₂×D₄	1	1	yes	characteristic
246	C₂×#379	C₂×D₄	1	1	yes	characteristic
247	C₂×C₄×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
248	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
249	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
250	C₂×C₄³	C₂×D₄	1	1	yes	characteristic
251	#1800	C₂⁴	1	2	yes	—
252	#1799	C₂⁴	1	2	yes	—
253	#1799	C₂⁴	1	2	yes	—
254	#1460	C₂⁴	1	2	yes	—
255	#1459	C₂⁴	1	2	yes	—
256	#1459	C₂⁴	1	2	yes	—
257	C₂⁶	#120	1	1	yes	characteristic
258	C₂⁶	#120	1	1	yes	characteristic
259	C₂³×Q₈	#120	1	1	yes	characteristic
260	C₂³×D₄	#120	1	2	yes	—
261	C₂³×D₄	#120	1	2	yes	—
262	C₂³×D₄	#120	1	2	yes	—
263	C₂³×D₄	#120	1	2	yes	—
264	C₂³×D₄	#120	1	2	yes	—
265	C₂³×D₄	#120	1	1	yes	characteristic
266	C₂³×D₄	#120	1	1	yes	characteristic
267	C₂³×D₄	#120	1	1	yes	characteristic
268	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
269	C₂³×D₄	C₂²×D₄	1	2	yes	—
270	C₂³×D₄	C₂²×D₄	1	2	yes	—
271	C₂³×D₄	C₂²×D₄	1	2	yes	—
272	C₂⁴×C₄	#120	1	2	yes	—
273	C₂⁴×C₄	#120	1	1	yes	characteristic
274	C₂⁴×C₄	#120	1	2	yes	—
275	C₂⁴×C₄	#120	1	1	yes	characteristic
276	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
277	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
278	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
279	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
280	C₂×#127	#120	1	2	yes	—
281	C₂×#127	#120	1	2	yes	—
282	C₂×#127	C₂²×D₄	1	2	yes	—
283	C₂×#127	C₂²×D₄	1	2	yes	—
284	C₂×#124	#120	1	2	yes	—
285	C₂×#124	C₂²×D₄	1	2	yes	—
286	C₂×#121	#120	1	2	yes	—
287	C₂×#121	#120	1	2	yes	—
288	C₂×#121	C₂²×D₄	1	2	yes	—
289	C₂×#121	C₂²×D₄	1	2	yes	—
290	C₂×#120	#120	1	2	yes	—
291	C₂×#120	#120	1	2	yes	—
292	C₂×#120	C₂²×D₄	1	2	yes	—
293	C₂×#120	C₂²×D₄	1	2	yes	—
294	C₂×C₄×Q₈	#120	1	2	yes	—
295	C₂×C₄×Q₈	C₂²×D₄	1	2	yes	—
296	C₂×C₄×D₄	#120	1	2	yes	—
297	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
298	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
299	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
300	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
301	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
302	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
303	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
304	C₂×C₄×D₄	C₂²×D₄	1	1	yes	characteristic
305	C₂×C₄×D₄	C₂⁵	1	1	yes	characteristic
306	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
307	C₂²×C₄⋊C₄	#120	1	2	yes	—
308	C₂²×C₄⋊C₄	#120	1	2	yes	—
309	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
310	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
311	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
312	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
313	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
314	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
315	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
316	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
317	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
318	C₂²×C₄²	#120	1	1	yes	characteristic
319	C₂²×C₄²	#120	1	1	yes	characteristic
320	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
321	#400	#120	1	4	yes	—
322	#400	C₂²×D₄	1	4	yes	—
323	#399	#120	1	4	yes	—
324	#399	C₂²×D₄	1	4	yes	—
325	#394	#120	1	4	yes	—
326	#394	C₂²×D₄	1	4	yes	—
327	#392	#120	1	4	yes	—
328	#392	#120	1	4	yes	—
329	#392	#120	1	4	yes	—
330	#392	C₂²×D₄	1	4	yes	—
331	#392	C₂²×D₄	1	4	yes	—
332	#392	C₂²×D₄	1	4	yes	—
333	#391	#120	1	2	yes	—
334	#391	C₂²×D₄	1	2	yes	—
335	#390	#120	1	2	yes	—
336	#390	C₂²×D₄	1	2	yes	—
337	#386	#120	1	2	yes	—
338	#386	#120	1	2	yes	—
339	#386	C₂²×D₄	1	2	yes	—
340	#386	C₂²×D₄	1	2	yes	—
341	#385	#120	1	2	yes	—
342	#385	#120	1	2	yes	—
343	#385	C₂²×D₄	1	2	yes	—
344	#385	C₂²×D₄	1	2	yes	—
345	#382	#120	1	2	yes	—
346	#382	C₂²×D₄	1	2	yes	—
347	#380	#120	1	2	yes	—
348	#380	#120	1	2	yes	—
349	#380	C₂²×D₄	1	2	yes	—
350	#380	C₂²×D₄	1	2	yes	—
351	#379	#120	1	2	yes	—
352	#379	#120	1	2	yes	—
353	#379	C₂²×D₄	1	2	yes	—
354	#379	C₂²×D₄	1	2	yes	—
355	C₄×C₄⋊C₄	#120	1	2	yes	—
356	C₄×C₄⋊C₄	C₂²×D₄	1	2	yes	—
357	C₄×C₂²⋊C₄	#120	1	2	yes	—
358	C₄×C₂²⋊C₄	#120	1	2	yes	—
359	C₄×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
360	C₄×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
361	C₂×#95	#120	1	2	yes	—
362	C₂×#95	#120	1	2	yes	—
363	C₂×#95	#120	1	2	yes	—
364	C₄³	#120	1	2	yes	—
365	C₄³	C₂²×D₄	1	2	yes	—
366	C₂⁵	C₂×#120	1	1	yes	characteristic
367	C₂⁵	C₂×#120	1	1	yes	characteristic
368	C₂⁵	C₂×#120	1	2	yes	—
369	C₂⁵	C₂×#120	1	2	yes	—
370	C₂²×Q₈	C₂×#120	1	2	yes	—
371	C₂²×D₄	B(4,𝔽₂)	1	2	yes	—
372	C₂²×D₄	B(4,𝔽₂)	1	2	yes	—
373	C₂²×D₄	C₂×#120	1	1	yes	characteristic
374	C₂²×D₄	C₂×#120	1	1	yes	characteristic
375	C₂²×D₄	C₂×#120	1	2	yes	—
376	C₂²×D₄	C₂×#120	1	2	yes	—
377	C₂²×D₄	C₂×#120	1	1	yes	characteristic
378	C₂²×D₄	C₂×#120	1	2	yes	—
379	C₂²×D₄	C₂×#120	1	4	yes	—
380	C₂²×D₄	C₂×#120	1	4	yes	—
381	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
382	C₂³×C₄	C₂×#120	1	1	yes	characteristic
383	C₂³×C₄	C₂×#120	1	1	yes	characteristic
384	C₂³×C₄	C₂×#120	1	1	yes	characteristic
385	C₂³×C₄	C₂×#120	1	1	yes	characteristic
386	C₂³×C₄	C₂×#120	1	1	yes	characteristic
387	C₂³×C₄	C₂×#120	1	1	yes	characteristic
388	C₂³×C₄	C₂×#120	1	1	yes	characteristic
389	C₂³×C₄	C₂×#120	1	1	yes	characteristic
390	C₂³×C₄	C₂×#120	1	1	yes	characteristic
391	C₂³×C₄	C₂×#120	1	1	yes	characteristic
392	C₂³×C₄	C₂×#120	1	2	yes	—
393	C₂³×C₄	C₂×#120	1	2	yes	—
394	C₂³×C₄	C₂×#120	1	1	yes	characteristic
395	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
396	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
397	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
398	C₂×C₄⋊C₄	C₂×#120	1	4	yes	—
399	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
400	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
401	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
402	C₂×C₄⋊C₄	C₂×#120	1	1	yes	characteristic
403	C₂×C₄⋊C₄	C₂³×D₄	1	1	yes	characteristic
404	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
405	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
406	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
407	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
408	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
409	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
410	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
411	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
412	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
413	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
414	C₂×C₂²⋊C₄	C₂³×D₄	1	1	yes	characteristic
415	C₂×C₂²⋊C₄	C₂³×D₄	1	1	yes	characteristic
416	C₂×C₄²	C₂×#120	1	2	yes	—
417	C₂×C₄²	C₂×#120	1	1	yes	characteristic
418	C₂×C₄²	C₂×#120	1	1	yes	characteristic
419	C₂×C₄²	C₂×#120	1	1	yes	characteristic
420	C₂×C₄²	C₂×#120	1	2	yes	—
421	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
422	#95	C₂×#120	1	4	yes	—
423	#95	C₂×#120	1	4	yes	—
424	#95	C₂×#120	1	4	yes	—
425	C₂⁴	#2846	1	1	yes	characteristic
426	C₂⁴	#2846	1	1	yes	characteristic
427	C₂⁴	#2846	1	1	yes	characteristic
428	C₂⁴	C₂²×#120	1	1	yes	characteristic
429	C₂⁴	C₂²×#120	1	1	yes	characteristic
430	C₂×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
431	C₂×D₄	#3585	1	4	yes	—
432	C₂²×C₄	#2846	1	1	yes	characteristic
433	C₂²×C₄	#2846	1	1	yes	characteristic
434	C₂²×C₄	#2846	1	1	yes	characteristic
435	C₂²×C₄	#2846	1	1	yes	characteristic
436	C₂²×C₄	#2846	1	1	yes	characteristic
437	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
438	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
439	C₂²×C₄	#3026	1	1	yes	characteristic
440	C₂²×C₄	#3026	1	1	yes	characteristic
441	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
442	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
443	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
444	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
445	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
446	C₂³	#32898	1	1	yes	characteristic
447	C₂³	#32898	1	1	yes	characteristic
448	C₂³	C₂×#2846	1	1	yes	characteristic
449	C₂³	#60367	1	2	yes	—
450	C₂³	#60367	1	2	yes	—
451	C₂×C₄	#32898	1	1	yes	characteristic
452	C₂×C₄	#32898	1	1	yes	characteristic
453	C₂×C₄	#33551	1	4	yes	—
454	C₂×C₄	#60367	1	2	yes	—
455	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
456	C₂×C₄	C₂×#3026	1	1	yes	characteristic
457	C₂²	#511779	1	2	yes	—
458	C₂²	#511819	1	2	yes	—
459	C₂²	#6628847	1	1	yes	characteristic
460	C₂²	#6628883	1	1	yes	characteristic
461	C₂²	C₂×#32898	1	1	yes	characteristic
462	C₄	#511779	1	2	yes	—
463	C₄	C₂×#33551	1	2	yes	—
464	C₂	C₂×#511819	1	1	yes	characteristic
465	C₂	#72238197	1	1	yes	characteristic
466	C₂	C₂×#511779	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. #72338692	C₂	semidirect
2. #72338689	C₂	semidirect
3. #72338685	C₂	semidirect
4. #72338682	C₂	semidirect
5. #72338680	C₂	semidirect
6. #72338679	C₂	semidirect
7. #72338678	C₂	semidirect
8. #72338676	C₂	semidirect
9. #72338668	C₂	semidirect
10. #72316511	C₂	semidirect
11. C₂×#8698894	C₂	semidirect
12. #72240305	C₂	semidirect
13. #72240303	C₂	semidirect
14. #72231294	C₂	semidirect
15. #72231282	C₂	semidirect
16. #72231038	C₂	semidirect
17. #72214295	C₂	semidirect
18. #10577301	C₂²	semidirect
27. #6454041	C₂²	semidirect
28. #6454041	C₂²	semidirect
29. #6453830	C₂²	semidirect
30. #6347316	C₂²	semidirect
31. #6346608	C₂²	semidirect
33. #508249	C₂²	semidirect
34. #508193	C₂²	semidirect
35. #493995	C₂²	semidirect
36. #493995	C₂²	semidirect
37. #493956	C₂²	semidirect
38. #486613	C₂²	semidirect
39. #486593	C₂²	semidirect
40. #486533	C₂²	semidirect
41. #486513	C₂²	semidirect
42. #486347	C₂²	semidirect
43. #486243	C₂²	semidirect
44. #482443	C₂²	semidirect
45. #482424	C₂²	semidirect
47. #482369	C₂²	semidirect
48. #482369	C₂²	semidirect
50. #480390	C₂²	semidirect
51. #480376	C₂²	semidirect
52. #480376	C₂²	semidirect
53. #248507	C₂²	semidirect
54. #248506	C₂²	semidirect
55. #248456	C₂²	semidirect
56. #248455	C₂²	semidirect
57. #248000	C₂²	semidirect
58. #247999	C₂²	semidirect
59. #201388	C₂²	semidirect
61. #200521	C₂²	semidirect
62. #193892	C₂²	semidirect
63. #193892	C₂²	semidirect
64. #193832	C₂²	semidirect
65. #185755	C₂²	semidirect
66. #185643	C₂²	semidirect
67. #185643	C₂²	semidirect
68. #130982	C₂²	semidirect
69. #130773	C₂²	semidirect
70. #130740	C₂²	semidirect
71. #130403	C₂²	semidirect
72. #130355	C₂²	semidirect
73. #130260	C₂²	semidirect
74. #129645	C₂²	semidirect
75. C₂⁵×D₄	D₄	semidirect
77. C₂²×#550	D₄	semidirect
79. C₂³×#121	D₄	semidirect
80. #61560	C₂³	semidirect
81. #61559	C₂³	semidirect
83. #59945	D₄	semidirect
85. #58997	D₄	semidirect
90. C₂×#2782	D₄	semidirect
94. C₂×#2675	D₄	semidirect
95. C₂×#2668	D₄	semidirect
96. #45599	D₄	semidirect
98. #39361	D₄	semidirect
100. #38904	D₄	semidirect
102. C₂×#2826	D₄	semidirect
103. C₂×#2867	D₄	semidirect
104. C₂×#2847	D₄	semidirect
105. C₂×#2847	D₄	semidirect
106. D₄×#120	D₄	semidirect
108. C₂×#2548	D₄	semidirect
110. C₂×#2572	D₄	semidirect
111. C₂×#2504	D₄	semidirect
113. C₂×#2433	D₄	semidirect
115. C₂×#2403	D₄	semidirect
116. C₂×D₄×C₂²⋊C₄	D₄	semidirect
117. C₂×D₄×C₂²⋊C₄	D₄	semidirect
121. C₂×#2293	D₄	semidirect
122. #24350	C₂³	semidirect
123. #24350	C₂³	semidirect
124. #24314	C₂³	semidirect
125. #24260	C₂³	semidirect
126. #24260	C₂³	semidirect
127. #24224	C₂³	semidirect
131. #18389	C₂³	semidirect
132. #18387	C₂³	semidirect
133. #18205	C₂³	semidirect
134. #18203	C₂³	semidirect
140. #12798	C₂³	semidirect
141. #12793	C₂³	semidirect
142. #12793	C₂³	semidirect
143. #11903	C₂³	semidirect
144. #11899	C₂³	semidirect
146. #11877	C₂³	semidirect
147. #11877	C₂³	semidirect
149. #11477	C₂³	semidirect
150. #11471	C₂³	semidirect
151. #11471	C₂³	semidirect
152. #9469	C₂³	semidirect
154. #9397	C₂³	semidirect
155. #8965	C₂³	semidirect
156. #8965	C₂³	semidirect
157. #8957	C₂³	semidirect
158. #8383	C₂³	semidirect
159. #8375	C₂³	semidirect
160. #8375	C₂³	semidirect

Maximal subgroups

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

subgroup	index
#72338692	2
#72338689	2
#72338685	2
#72338682	2
#72338680	2
#72338679	2
#72338678	2
#72338676	2
#72338668	2
#72316511	2
C₂×#8698894	2
#72240305	2
#72240303	2
#72231294	2
#72231282	2
#72231038	2
#72214295	2