Subgroups — #72219555

Order 2048.

At least 12332 conjugacy classes of subgroups; only the 1276 normal subgroups are shown.

The subgroup lattice has 571 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72214850	C₂	1	1	yes	maximal, characteristic, complemented
2	#72214821	C₂	1	2	yes	maximal, complemented
3	#72214788	C₂	1	2	yes	maximal, complemented
4	#72214761	C₂	1	2	yes	maximal, complemented
5	#72214750	C₂	1	1	yes	maximal, characteristic, complemented
6	#72214707	C₂	1	2	yes	maximal, complemented
7	#72214667	C₂	1	2	yes	maximal, complemented
8	#72214640	C₂	1	2	yes	maximal, complemented
9	#72214595	C₂	1	2	yes	maximal, complemented
10	#72214564	C₂	1	2	yes	maximal, complemented
11	#72214520	C₂	1	2	yes	maximal, complemented
12	#72214454	C₂	1	2	yes	maximal, complemented
13	#72214356	C₂	1	2	yes	maximal, complemented
14	#72214287	C₂	1	2	yes	maximal, complemented
15	#72214220	C₂	1	1	yes	maximal, characteristic, complemented
16	#72214049	C₂	1	1	yes	maximal, characteristic, complemented
17	#72213999	C₂	1	1	yes	maximal, characteristic, complemented
18	#72213738	C₂	1	1	yes	maximal, characteristic, complemented
19	#72213548	C₂	1	1	yes	maximal, characteristic, complemented
20	#10586169	C₂²	1	1	yes	characteristic, complemented
21	C₂²×#3484	C₂²	1	1	yes	characteristic
22	#10577303	C₂²	1	2	yes	—
23	#10577303	C₂²	1	2	yes	complemented
24	#10577301	C₂²	1	2	yes	—
25	#10577301	C₂²	1	2	yes	complemented
26	#10575547	C₂²	1	2	yes	complemented
27	#10575142	C₂²	1	2	yes	—
28	#10574294	C₂²	1	1	yes	characteristic, complemented
29	C₂×D₄×#127	C₂²	1	1	yes	characteristic, complemented
30	C₂×#35921	C₂²	1	1	yes	characteristic, complemented
31	C₂×#35691	C₂²	1	1	yes	characteristic, complemented
32	#6490931	C₂²	1	2	yes	complemented
33	#6453829	C₂²	1	2	yes	complemented
34	#6348967	C₂²	1	4	yes	complemented
35	#6347316	C₂²	1	2	yes	complemented
36	#6347262	C₂²	1	2	yes	complemented
37	#6346455	C₂²	1	2	yes	complemented
38	#6346450	C₂²	1	2	yes	complemented
39	#763819	C₂²	1	1	yes	characteristic, complemented
40	#719700	C₂²	1	1	yes	characteristic, complemented
41	#719145	C₂²	1	1	yes	characteristic, complemented
42	#674656	C₂²	1	1	yes	characteristic, complemented
43	#674175	C₂²	1	1	yes	characteristic, complemented
44	#625788	C₂²	1	1	yes	characteristic, complemented
45	#617364	C₂²	1	1	yes	characteristic
46	#609006	C₂²	1	1	yes	characteristic
47	#519050	C₂²	1	1	yes	characteristic, complemented
48	#518680	C₂²	1	1	yes	characteristic, complemented
49	#513736	C₂²	1	1	yes	characteristic, complemented
50	#237607	C₂²	1	4	yes	complemented
51	#237607	C₂²	1	4	yes	complemented
52	#236367	C₂²	1	4	yes	complemented
53	#235365	C₂²	1	4	yes	complemented
54	#235245	C₂²	1	4	yes	complemented
55	#234216	C₂²	1	4	yes	complemented
56	#201205	C₂²	1	2	yes	complemented
57	#200521	C₂²	1	2	yes	complemented
58	#199468	C₂²	1	4	yes	complemented
59	#198038	C₂²	1	4	yes	complemented
60	#197472	C₂²	1	2	yes	complemented
61	#197248	C₂²	1	4	yes	complemented
62	#195029	C₂²	1	2	yes	complemented
63	#194974	C₂²	1	2	yes	complemented
64	#193833	C₂²	1	2	yes	complemented
65	#188081	C₂²	1	1	yes	characteristic, complemented
66	#188081	C₂²	1	1	yes	characteristic, complemented
67	#187811	C₂²	1	2	yes	complemented
68	#186810	C₂²	1	2	yes	complemented
69	#186803	C₂²	1	2	yes	complemented
70	#185755	C₂²	1	2	yes	complemented
71	#185755	C₂²	1	2	yes	complemented
72	#185555	C₂²	1	2	yes	complemented
73	#185555	C₂²	1	2	yes	complemented
74	#185265	C₂²	1	2	yes	complemented
75	#185251	C₂²	1	2	yes	complemented
76	#185247	C₂²	1	2	yes	complemented
77	#185245	C₂²	1	2	yes	complemented
78	#184979	C₂²	1	2	yes	complemented
79	#115568	C₂²	1	4	yes	complemented
80	#113483	C₂²	1	4	yes	complemented
81	#113471	C₂²	1	4	yes	complemented
82	#113110	C₂²	1	4	yes	complemented
83	#113096	C₂²	1	4	yes	complemented
84	#111807	C₂²	1	4	yes	complemented
85	#107133	C₂²	1	2	yes	complemented
86	#106758	C₂²	1	2	yes	complemented
87	#106602	C₂²	1	2	yes	complemented
88	#106600	C₂²	1	2	yes	complemented
89	#106572	C₂²	1	2	yes	complemented
90	#106383	C₂²	1	2	yes	complemented
91	C₂³×H(5,𝔽₂)	D₄	1	1	yes	characteristic
92	C₂⁵×D₄	D₄	1	1	yes	characteristic
93	#62814	C₂³	1	2	yes	—
94	#62773	C₂³	1	2	yes	—
95	#62773	C₂³	1	2	yes	—
96	C₂²×#546	D₄	1	1	yes	characteristic
97	C₂²×#546	D₄	1	1	yes	characteristic
98	C₂²×#546	C₂³	1	1	yes	characteristic
99	C₂²×#546	C₂³	1	1	yes	characteristic
100	C₂²×D₄²	D₄	1	1	yes	characteristic
101	C₂²×D₄²	D₄	1	1	yes	characteristic
102	C₂²×D₄²	C₂³	1	1	yes	characteristic
103	C₂²×D₄²	C₂³	1	1	yes	characteristic
104	C₂²×D₄²	C₂³	1	1	yes	characteristic, complemented
105	C₂²×#535	D₄	1	1	yes	characteristic
106	C₂²×#535	C₂³	1	1	yes	characteristic
107	C₂²×#525	D₄	1	1	yes	characteristic
108	C₂²×#525	C₂³	1	1	yes	characteristic
109	C₂²×#518	C₂³	1	1	yes	characteristic
110	#61582	D₄	1	8	yes	complemented
111	#61576	D₄	1	8	yes	complemented
112	#61570	D₄	1	4	yes	complemented
113	#61569	D₄	1	4	yes	complemented
114	#61560	D₄	1	4	yes	complemented
115	#61559	D₄	1	4	yes	complemented
116	#60799	C₂³	1	4	yes	—
117	#60798	C₂³	1	4	yes	—
118	#60798	C₂³	1	4	yes	complemented
119	#60564	D₄	1	8	yes	complemented
120	#60558	C₂³	1	4	yes	—
121	#60558	C₂³	1	4	yes	—
122	#60558	C₂³	1	4	yes	complemented
123	#60490	D₄	1	4	yes	complemented
124	#60423	D₄	1	4	yes	complemented
125	#60230	C₂³	1	2	yes	—
126	#60230	C₂³	1	2	yes	—
127	#60124	C₂³	1	2	yes	—
128	C₂×#2867	C₂³	1	1	yes	characteristic, complemented
129	C₂×#2541	C₂³	1	1	yes	characteristic
130	C₂×#2541	C₂³	1	1	yes	characteristic
131	C₂×#2541	C₂³	1	1	yes	characteristic, complemented
132	C₂×#2541	C₂³	1	1	yes	characteristic, complemented
133	C₂×#2540	C₂³	1	1	yes	characteristic, complemented
134	C₂×#2535	C₂³	1	1	yes	characteristic, complemented
135	C₂×#2657	C₂³	1	1	yes	characteristic, complemented
136	C₂×#2619	C₂³	1	1	yes	characteristic
137	C₂×#2397	C₂³	1	1	yes	characteristic
138	C₂×#2392	C₂³	1	1	yes	characteristic
139	C₂×#2349	C₂³	1	1	yes	characteristic, complemented
140	C₂×C₄×#127	C₂³	1	1	yes	characteristic
141	C₂×#2275	C₂³	1	1	yes	characteristic, complemented
142	C₂×C₄²×D₄	C₂³	1	1	yes	characteristic, complemented
143	#21899	C₂³	1	4	yes	complemented
144	#21415	C₂³	1	4	yes	complemented
145	#20726	C₂³	1	2	yes	—
146	#20726	C₂³	1	2	yes	—
147	#17741	C₂³	1	4	yes	complemented
148	#17741	C₂³	1	4	yes	complemented
149	#17666	C₂³	1	4	yes	complemented
150	#17588	C₂³	1	4	yes	complemented
151	#17546	C₂³	1	4	yes	complemented
152	#17546	C₂³	1	4	yes	complemented
153	#17541	C₂³	1	4	yes	complemented
154	#17448	C₂³	1	4	yes	complemented
155	#17448	C₂³	1	4	yes	complemented
156	#17448	C₂³	1	4	yes	complemented
157	#17364	C₂³	1	2	yes	—
158	#17364	C₂³	1	2	yes	—
159	#17357	C₂³	1	2	yes	—
160	#17357	C₂³	1	2	yes	—
161	#15453	D₄	1	1	yes	characteristic
162	#15453	D₄	1	2	yes	—
163	#15430	D₄	1	1	yes	characteristic
164	#15412	D₄	1	2	yes	—
165	#15412	D₄	1	1	yes	characteristic
166	#15384	D₄	1	1	yes	characteristic
167	#15340	D₄	1	1	yes	characteristic
168	#15310	D₄	1	1	yes	characteristic
169	#15310	D₄	1	2	yes	—
170	#15283	D₄	1	1	yes	characteristic
171	#15258	D₄	1	1	yes	characteristic
172	#15258	D₄	1	2	yes	—
173	#14708	C₂³	1	1	yes	characteristic, complemented
174	#14272	C₂³	1	1	yes	characteristic, complemented
175	#14154	C₂³	1	1	yes	characteristic, complemented
176	#14153	C₂³	1	1	yes	characteristic, complemented
177	#13905	C₂³	1	1	yes	characteristic
178	#13905	C₂³	1	1	yes	characteristic
179	#13847	C₂³	1	1	yes	characteristic
180	#13785	C₂³	1	1	yes	characteristic, complemented
181	#13777	C₂³	1	1	yes	characteristic
182	C₄×#390	C₂³	1	1	yes	characteristic
183	C₄×#390	C₂³	1	1	yes	characteristic, complemented
184	#13761	C₂³	1	1	yes	characteristic
185	#8098	C₂³	1	4	yes	complemented
186	#8098	C₂³	1	4	yes	complemented
187	#8072	C₂³	1	4	yes	complemented
188	#7959	C₂³	1	4	yes	complemented
189	#7950	C₂³	1	4	yes	complemented
190	#7867	C₂³	1	4	yes	complemented
191	C₂³×#41	C₂×D₄	1	1	yes	characteristic
192	C₂³×#41	C₂×D₄	1	1	yes	characteristic
193	C₂³×#41	C₂×D₄	1	1	yes	characteristic
194	C₂³×#41	C₂×D₄	1	1	yes	characteristic
195	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
196	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
197	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
198	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
199	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
200	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
201	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
202	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
203	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
204	#3506	C₂×D₄	1	4	yes	complemented
205	#3506	C₂×D₄	1	4	yes	complemented
206	#3501	C₂×D₄	1	2	yes	complemented
207	#3501	C₂×D₄	1	2	yes	complemented
208	#3496	C₂×D₄	1	2	yes	complemented
209	#3496	C₂×D₄	1	2	yes	complemented
210	C₂×#546	C₂×D₄	1	4	yes	—
211	C₂×#546	C₂×D₄	1	4	yes	—
212	C₂×D₄²	C₂×D₄	1	4	yes	—
213	C₂×D₄²	C₂×D₄	1	4	yes	—
214	#3458	C₂×D₄	1	2	yes	complemented
215	#3455	C₂×D₄	1	4	yes	complemented
216	#3449	C₂×D₄	1	2	yes	complemented
217	#3444	C₂⁴	1	4	yes	—
218	C₂²×#127	C₂×D₄	1	1	yes	characteristic
219	C₂²×#127	C₂×D₄	1	1	yes	characteristic
220	C₂²×#127	C₂×D₄	1	2	yes	—
221	C₂²×#127	C₂⁴	1	1	yes	characteristic
222	C₂²×#127	C₂⁴	1	1	yes	characteristic
223	C₂²×#124	C₂×D₄	1	1	yes	characteristic
224	C₂²×#124	C₂⁴	1	1	yes	characteristic
225	C₂²×#123	C₂×D₄	1	1	yes	characteristic
226	C₂²×#123	C₂×D₄	1	1	yes	characteristic
227	C₂²×C₂²⋊Q₈	C₂×D₄	1	1	yes	characteristic
228	C₂²×C₂²⋊Q₈	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₂²⋊Q₈	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₂²⋊Q₈	C₂×D₄	1	1	yes	characteristic
231	C₂²×#121	C₂×D₄	1	1	yes	characteristic
232	C₂²×#121	C₂×D₄	1	1	yes	characteristic
233	C₂²×#121	C₂×D₄	1	1	yes	characteristic
234	C₂²×#121	C₂×D₄	1	1	yes	characteristic
235	C₂²×#121	C₂×D₄	1	1	yes	characteristic
236	C₂²×#121	C₂×D₄	1	1	yes	characteristic
237	C₂²×#121	C₂×D₄	1	1	yes	characteristic
238	C₂²×#121	C₂×D₄	1	1	yes	characteristic
239	C₂²×#120	C₂×D₄	1	1	yes	characteristic
240	C₂²×#120	C₂×D₄	1	1	yes	characteristic
241	C₂×#518	C₂×D₄	1	4	yes	—
242	C₂×#518	C₂×D₄	1	4	yes	—
243	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×D₄	C₂⁴	1	1	yes	characteristic
248	C₂²×C₄×D₄	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×D₄	C₂⁴	1	1	yes	characteristic
250	C₂²×C₄×D₄	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×D₄	C₂⁴	1	1	yes	characteristic
252	C₂²×#117	C₂×D₄	1	1	yes	characteristic
253	C₂²×#117	C₂⁴	1	1	yes	characteristic
254	#3215	C₂×D₄	1	8	yes	complemented
255	#3213	C₂×D₄	1	8	yes	complemented
256	#3208	C₂×D₄	1	8	yes	complemented
257	#3205	C₂×D₄	1	8	yes	complemented
258	#3110	C₂×D₄	1	8	yes	—
259	#3109	C₂×D₄	1	8	yes	—
260	#3101	C₂×D₄	1	8	yes	—
261	#3100	C₂×D₄	1	8	yes	—
262	#3077	C₂×D₄	1	8	yes	—
263	#3077	C₂×D₄	1	8	yes	complemented
264	#3036	C₂×D₄	1	8	yes	—
265	#3036	C₂×D₄	1	8	yes	complemented
266	#2975	C₂×D₄	1	4	yes	complemented
267	#2973	C₂×D₄	1	4	yes	complemented
268	#2973	C₂×D₄	1	4	yes	complemented
269	#2972	C₂×D₄	1	4	yes	complemented
270	#2921	C₂×D₄	1	4	yes	complemented
271	#2920	C₂⁴	1	4	yes	—
272	#2920	C₂⁴	1	4	yes	—
273	#2920	C₂⁴	1	4	yes	—
274	#2905	C₂×D₄	1	4	yes	complemented
275	C₂×#399	C₂×D₄	1	1	yes	characteristic
276	C₂×#399	C₂×D₄	1	1	yes	characteristic
277	C₂×#398	C₂×D₄	1	1	yes	characteristic
278	C₂×#397	C₂×D₄	1	1	yes	characteristic
279	C₂×#394	C₂×D₄	1	2	yes	—
280	C₂×#394	C₂×D₄	1	1	yes	characteristic
281	C₂×#392	C₂×D₄	1	2	yes	—
282	C₂×#392	C₂×D₄	1	2	yes	—
283	C₂×#392	C₂×D₄	1	1	yes	characteristic
284	C₂×#392	C₂×D₄	1	1	yes	characteristic
285	C₂×#392	C₂×D₄	1	2	yes	—
286	C₂×#392	C₂×D₄	1	1	yes	characteristic
287	C₂×#390	C₂×D₄	1	2	yes	—
288	C₂×#390	C₂×D₄	1	1	yes	characteristic
289	C₂×#390	C₂×D₄	1	1	yes	characteristic
290	C₂×#384	C₂×D₄	1	1	yes	characteristic
291	C₂×#382	C₂⁴	1	1	yes	characteristic
292	C₂×C₄×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
293	C₂×C₄×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
294	C₂×C₄×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
295	C₂×#376	C₂⁴	1	1	yes	characteristic
296	C₂×C₄³	C₂⁴	1	1	yes	characteristic
297	#1445	C₂×D₄	1	1	yes	characteristic
298	#1445	C₂×D₄	1	1	yes	characteristic
299	#1445	C₂×D₄	1	2	yes	—
300	#1438	C₂×D₄	1	1	yes	characteristic
301	#1438	C₂×D₄	1	1	yes	characteristic
302	#1438	C₂×D₄	1	2	yes	—
303	#1437	C₂×D₄	1	1	yes	characteristic
304	#1437	C₂×D₄	1	1	yes	characteristic
305	#1437	C₂×D₄	1	1	yes	characteristic
306	#1437	C₂×D₄	1	2	yes	—
307	#1437	C₂×D₄	1	1	yes	characteristic
308	#1437	C₂×D₄	1	2	yes	—
309	#1437	C₂×D₄	1	1	yes	characteristic
310	#1437	C₂×D₄	1	1	yes	characteristic
311	#1437	C₂×D₄	1	2	yes	—
312	#1436	C₂×D₄	1	1	yes	characteristic
313	#1436	C₂×D₄	1	1	yes	characteristic
314	#1436	C₂×D₄	1	2	yes	—
315	C₂⁶	#120	1	1	yes	characteristic
316	C₂²×#41	#120	1	4	yes	—
317	C₂³×Q₈	#120	1	1	yes	characteristic
318	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
319	C₂³×D₄	#120	1	2	yes	—
320	C₂³×D₄	#120	1	2	yes	—
321	C₂³×D₄	#120	1	1	yes	characteristic
322	C₂³×D₄	#120	1	1	yes	characteristic
323	C₂³×D₄	#120	1	1	yes	characteristic
324	C₂³×D₄	#120	1	1	yes	characteristic
325	C₂³×D₄	#120	1	1	yes	characteristic
326	C₂³×D₄	#120	1	2	yes	—
327	C₂³×D₄	#120	1	2	yes	—
328	C₂³×D₄	#120	1	2	yes	—
329	C₂³×D₄	#120	1	2	yes	—
330	C₂³×D₄	#120	1	4	yes	—
331	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
332	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
333	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
334	C₂³×D₄	C₂²×D₄	1	2	yes	—
335	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
336	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
337	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
338	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
339	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
340	C₂⁴×C₄	#120	1	1	yes	characteristic
341	C₂⁴×C₄	#120	1	1	yes	characteristic
342	C₂⁴×C₄	#120	1	1	yes	characteristic
343	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
344	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
345	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
346	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
347	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
348	#533	C₂²×D₄	1	4	yes	—
349	#533	C₂²×D₄	1	4	yes	—
350	#533	C₂²×D₄	1	4	yes	—
351	#532	C₂²×D₄	1	4	yes	—
352	#532	C₂²×D₄	1	4	yes	—
353	#532	C₂²×D₄	1	4	yes	—
354	C₂×#127	C₂²×D₄	1	4	yes	—
355	C₂×#124	C₂²×D₄	1	4	yes	—
356	C₂×C₂²⋊Q₈	#120	1	2	yes	—
357	C₂×C₂²⋊Q₈	#120	1	2	yes	—
358	C₂×#121	#120	1	2	yes	—
359	C₂×#121	#120	1	2	yes	—
360	C₂×#121	#120	1	4	yes	—
361	C₂×#121	#120	1	4	yes	—
362	C₂×C₄×D₄	#120	1	4	yes	—
363	C₂×C₄×D₄	#120	1	4	yes	—
364	C₂×C₄×D₄	C₂²×D₄	1	4	yes	—
365	C₂×C₄×D₄	C₂²×D₄	1	4	yes	—
366	C₂×C₄×D₄	C₂²×D₄	1	4	yes	—
367	C₂×C₄×D₄	C₂²×D₄	1	4	yes	—
368	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
369	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
370	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
371	C₂×C₄×D₄	C₂²×D₄	1	2	yes	—
372	C₂×C₄×D₄	H(5,𝔽₂)	1	2	yes	—
373	C₂×C₄×D₄	H(5,𝔽₂)	1	2	yes	—
374	C₂×C₄×D₄	H(5,𝔽₂)	1	2	yes	—
375	C₂×C₄×D₄	H(5,𝔽₂)	1	2	yes	—
376	C₂×#117	#120	1	2	yes	—
377	C₂×#117	#120	1	2	yes	—
378	C₂×#117	C₂²×D₄	1	2	yes	—
379	C₂×#117	C₂²×D₄	1	2	yes	—
380	C₂×#117	H(5,𝔽₂)	1	2	yes	—
381	C₂×#117	H(5,𝔽₂)	1	2	yes	—
382	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
383	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
384	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
385	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
386	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
387	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
388	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
389	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
390	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
391	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
392	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
393	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
394	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
395	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
396	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
397	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
398	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
399	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
400	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
401	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
402	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
403	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
404	C₂²×C₄²	C₂²×D₄	1	2	yes	—
405	C₂²×C₄²	C₂⁵	1	1	yes	characteristic
406	#476	#120	1	16	yes	complemented
407	#474	#120	1	16	yes	complemented
408	#461	#120	1	16	yes	complemented
409	#459	#120	1	16	yes	complemented
410	#432	C₂²×D₄	1	8	yes	—
411	#431	C₂²×D₄	1	8	yes	—
412	#423	C₂²×D₄	1	8	yes	—
413	C₂×#95	C₂²×D₄	1	2	yes	—
414	C₂×#95	C₂²×D₄	1	1	yes	characteristic
415	C₂×#95	C₂²×D₄	1	1	yes	characteristic
416	C₂×#95	C₂²×D₄	1	1	yes	characteristic
417	C₂×#95	C₂²×D₄	1	1	yes	characteristic
418	C₂×#95	C₂²×D₄	1	2	yes	—
419	C₂⁵	C₂×#120	1	1	yes	characteristic
420	C₂⁵	C₂×#120	1	1	yes	characteristic
421	C₂⁵	C₂×#120	1	1	yes	characteristic
422	C₂⁵	C₂×#120	1	1	yes	characteristic
423	C₂⁵	C₂×#120	1	1	yes	characteristic
424	C₂²×Q₈	C₂×#120	1	2	yes	—
425	C₂²×D₄	#453	1	8	yes	complemented
426	C₂²×D₄	C₂×#120	1	2	yes	—
427	C₂²×D₄	C₂×#120	1	2	yes	—
428	C₂²×D₄	C₂×#120	1	2	yes	—
429	C₂²×D₄	C₂×#120	1	2	yes	—
430	C₂²×D₄	C₂×#120	1	2	yes	—
431	C₂²×D₄	C₂×#120	1	2	yes	—
432	C₂²×D₄	C₂×#120	1	2	yes	—
433	C₂²×D₄	D₄²	1	2	yes	—
434	C₂²×D₄	D₄²	1	2	yes	—
435	C₂²×D₄	D₄²	1	2	yes	—
436	C₂²×D₄	D₄²	1	2	yes	—
437	C₂³×C₄	C₂×#120	1	1	yes	characteristic
438	C₂³×C₄	C₂×#120	1	1	yes	characteristic
439	C₂³×C₄	C₂×#120	1	1	yes	characteristic
440	C₂³×C₄	C₂×#120	1	1	yes	characteristic
441	C₂³×C₄	C₂×#120	1	1	yes	characteristic
442	C₂³×C₄	C₂×#120	1	1	yes	characteristic
443	C₂³×C₄	C₂×#120	1	1	yes	characteristic
444	C₂³×C₄	C₂×#120	1	1	yes	characteristic
445	C₂³×C₄	C₂×#120	1	1	yes	characteristic
446	C₂³×C₄	C₂×#120	1	1	yes	characteristic
447	C₂³×C₄	C₂×#120	1	1	yes	characteristic
448	C₂³×C₄	C₂×#120	1	2	yes	—
449	C₂³×C₄	C₂×#120	1	2	yes	—
450	C₂³×C₄	C₂×#120	1	1	yes	characteristic
451	C₂³×C₄	C₂×#120	1	1	yes	characteristic
452	C₂³×C₄	#534	1	1	yes	characteristic
453	C₂³×C₄	#534	1	1	yes	characteristic
454	C₂³×C₄	#534	1	1	yes	characteristic
455	C₂³×C₄	#534	1	1	yes	characteristic
456	C₂³×C₄	#534	1	2	yes	—
457	C₂³×C₄	#534	1	2	yes	—
458	C₂³×C₄	#534	1	1	yes	characteristic
459	C₂³×C₄	#534	1	1	yes	characteristic
460	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
461	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
462	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
463	C₄⋊Q₈	C₂×#120	1	4	yes	complemented
464	C₄⋊Q₈	C₂×#120	1	4	yes	complemented
465	C₄⋊Q₈	C₂×#120	1	4	yes	complemented
466	#127	C₂×#120	1	4	yes	complemented
467	C₄×D₄	C₂×#120	1	16	yes	—
468	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
469	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
470	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
471	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
472	C₂×C₄⋊C₄	D₄²	1	2	yes	—
473	C₂×C₄⋊C₄	D₄²	1	2	yes	—
474	C₂×C₄⋊C₄	D₄²	1	2	yes	—
475	C₂×C₄⋊C₄	D₄²	1	2	yes	—
476	C₂×C₄⋊C₄	D₄²	1	2	yes	—
477	C₂×C₄⋊C₄	D₄²	1	2	yes	—
478	C₂×C₄⋊C₄	D₄²	1	2	yes	—
479	C₂×C₄⋊C₄	D₄²	1	2	yes	—
480	C₂×C₂²⋊C₄	D₄²	1	2	yes	—
481	C₂×C₂²⋊C₄	D₄²	1	2	yes	—
482	C₂×C₂²⋊C₄	D₄²	1	2	yes	—
483	C₂×C₂²⋊C₄	D₄²	1	2	yes	—
484	C₂×C₂²⋊C₄	D₄²	1	2	yes	—
485	C₂×C₂²⋊C₄	D₄²	1	2	yes	—
486	C₂×C₂²⋊C₄	D₄²	1	2	yes	—
487	C₂×C₂²⋊C₄	D₄²	1	2	yes	—
488	C₂×C₂²⋊C₄	D₄²	1	2	yes	—
489	C₂×C₂²⋊C₄	D₄²	1	2	yes	—
490	C₂×C₂²⋊C₄	D₄²	1	2	yes	—
491	C₂×C₂²⋊C₄	D₄²	1	2	yes	—
492	C₂×C₄²	C₂×#120	1	2	yes	—
493	C₂×C₄²	#534	1	2	yes	—
494	C₂×C₄²	C₂³×D₄	1	2	yes	—
495	C₂×C₄²	C₂³×D₄	1	2	yes	—
496	C₂×C₄²	C₂³×D₄	1	2	yes	—
497	C₂×C₄²	C₂×H(5,𝔽₂)	1	2	yes	—
498	C₂×C₄²	C₂×H(5,𝔽₂)	1	2	yes	—
499	C₂×C₄²	C₂×H(5,𝔽₂)	1	2	yes	—
500	C₄⋊C₈	C₂×#120	1	16	yes	complemented
501	C₂⁴	#2403	1	1	yes	characteristic
502	C₂⁴	#2403	1	1	yes	characteristic
503	C₂⁴	#2403	1	1	yes	characteristic
504	C₂⁴	#2403	1	2	yes	—
505	C₂⁴	#2403	1	2	yes	—
506	C₂⁴	#2403	1	1	yes	characteristic
507	C₂⁴	#2403	1	1	yes	characteristic
508	C₂⁴	#2403	1	1	yes	characteristic
509	C₂⁴	C₂²×#120	1	1	yes	characteristic
510	C₂×D₄	#2846	1	4	yes	—
511	C₂×D₄	C₂×#453	1	4	yes	—
512	C₂×D₄	C₂×#453	1	4	yes	—
513	C₂×D₄	#3019	1	4	yes	—
514	C₂²×C₄	#2403	1	1	yes	characteristic
515	C₂²×C₄	#2403	1	1	yes	characteristic
516	C₂²×C₄	#2403	1	2	yes	—
517	C₂²×C₄	#2403	1	2	yes	—
518	C₂²×C₄	#2403	1	2	yes	—
519	C₂²×C₄	#2403	1	2	yes	—
520	C₂²×C₄	#2403	1	1	yes	characteristic
521	C₂²×C₄	#2403	1	1	yes	characteristic
522	C₂²×C₄	#2403	1	1	yes	characteristic
523	C₂²×C₄	#2403	1	1	yes	characteristic
524	C₂²×C₄	C₂×#453	1	4	yes	—
525	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
526	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
527	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
528	C₂²×C₄	C₂×#534	1	1	yes	characteristic
529	C₂²×C₄	C₂×#534	1	1	yes	characteristic
530	C₂²×C₄	C₂×#534	1	1	yes	characteristic
531	C₂²×C₄	C₂×D₄²	1	2	yes	—
532	C₂²×C₄	C₂×D₄²	1	2	yes	—
533	C₂²×C₄	C₂×D₄²	1	2	yes	—
534	C₂²×C₄	C₂×D₄²	1	2	yes	—
535	C₂²×C₄	C₂×D₄²	1	2	yes	—
536	C₂²×C₄	C₂×D₄²	1	2	yes	—
537	C₄⋊C₄	#2846	1	4	yes	—
538	C₄²	C₂²×#120	1	4	yes	—
539	C₄²	#3484	1	4	yes	—
540	C₄²	#3484	1	4	yes	—
541	C₄²	#3484	1	4	yes	—
542	C₂³	#23872	1	2	yes	—
543	C₂³	#23882	1	2	yes	—
544	C₂³	#23906	1	2	yes	—
545	C₂³	C₂×#2403	1	1	yes	characteristic
546	C₂³	C₂×#2403	1	1	yes	characteristic
547	C₂³	C₂×#2403	1	1	yes	characteristic
548	D₄	#32888	1	8	yes	—
549	C₂×C₄	#23906	1	2	yes	—
550	C₂×C₄	#34980	1	1	yes	characteristic
551	C₂×C₄	#34980	1	1	yes	characteristic
552	C₂×C₄	#34980	1	1	yes	characteristic
553	C₂×C₄	D₄×#120	1	4	yes	—
554	C₂×C₄	D₄×#120	1	4	yes	—
555	C₂×C₄	C₂×#2846	1	1	yes	characteristic
556	C₂×C₄	C₂²×#453	1	2	yes	—
557	C₂×C₄	C₂×#3019	1	2	yes	—
558	C₂²	#612424	1	1	yes	characteristic
559	C₂²	C₂×#23906	1	1	yes	characteristic
560	C₂²	#6437445	1	1	yes	characteristic
561	C₂²	C₂×#23882	1	1	yes	characteristic
562	C₂²	#6437576	1	1	yes	characteristic
563	C₂²	C₂×#23872	1	1	yes	characteristic
564	C₂²	#6437585	1	1	yes	characteristic
565	C₄	#6470019	1	2	yes	—
566	C₄	C₂×#32888	1	2	yes	—
567	C₂	#72214896	1	1	yes	characteristic
568	C₂	#72219483	1	1	yes	characteristic
569	C₂	#72219554	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#612424
commutator, Frattini, cosocle	C₂²×C₄²	C₂⁵
LCS	G ▷ C₂²×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄² ◁ G
LECS	G ▷ C₂²×C₄² ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72214850	C₂	semidirect
2. #72214821	C₂	semidirect
3. #72214788	C₂	semidirect
4. #72214761	C₂	semidirect
5. #72214750	C₂	semidirect
6. #72214707	C₂	semidirect
7. #72214667	C₂	semidirect
8. #72214640	C₂	semidirect
9. #72214595	C₂	semidirect
10. #72214564	C₂	semidirect
11. #72214520	C₂	semidirect
12. #72214454	C₂	semidirect
13. #72214356	C₂	semidirect
14. #72214287	C₂	semidirect
15. #72214220	C₂	semidirect
16. #72214049	C₂	semidirect
17. #72213999	C₂	semidirect
18. #72213738	C₂	semidirect
19. #72213548	C₂	semidirect
20. #10586169	C₂²	semidirect
23. #10577303	C₂²	semidirect
25. #10577301	C₂²	semidirect
26. #10575547	C₂²	semidirect
28. #10574294	C₂²	semidirect
29. C₂×D₄×#127	C₂²	semidirect
30. C₂×#35921	C₂²	semidirect
31. C₂×#35691	C₂²	semidirect
32. #6490931	C₂²	semidirect
33. #6453829	C₂²	semidirect
34. #6348967	C₂²	semidirect
35. #6347316	C₂²	semidirect
36. #6347262	C₂²	semidirect
37. #6346455	C₂²	semidirect
38. #6346450	C₂²	semidirect
39. #763819	C₂²	semidirect
40. #719700	C₂²	semidirect
41. #719145	C₂²	semidirect
42. #674656	C₂²	semidirect
43. #674175	C₂²	semidirect
44. #625788	C₂²	semidirect
47. #519050	C₂²	semidirect
48. #518680	C₂²	semidirect
49. #513736	C₂²	semidirect
50. #237607	C₂²	semidirect
51. #237607	C₂²	semidirect
52. #236367	C₂²	semidirect
53. #235365	C₂²	semidirect
54. #235245	C₂²	semidirect
55. #234216	C₂²	semidirect
56. #201205	C₂²	semidirect
57. #200521	C₂²	semidirect
58. #199468	C₂²	semidirect
59. #198038	C₂²	semidirect
60. #197472	C₂²	semidirect
61. #197248	C₂²	semidirect
62. #195029	C₂²	semidirect
63. #194974	C₂²	semidirect
64. #193833	C₂²	semidirect
65. #188081	C₂²	semidirect
66. #188081	C₂²	semidirect
67. #187811	C₂²	semidirect
68. #186810	C₂²	semidirect
69. #186803	C₂²	semidirect
70. #185755	C₂²	semidirect
71. #185755	C₂²	semidirect
72. #185555	C₂²	semidirect
73. #185555	C₂²	semidirect
74. #185265	C₂²	semidirect
75. #185251	C₂²	semidirect
76. #185247	C₂²	semidirect
77. #185245	C₂²	semidirect
78. #184979	C₂²	semidirect
79. #115568	C₂²	semidirect
80. #113483	C₂²	semidirect
81. #113471	C₂²	semidirect
82. #113110	C₂²	semidirect
83. #113096	C₂²	semidirect
84. #111807	C₂²	semidirect
85. #107133	C₂²	semidirect
86. #106758	C₂²	semidirect
87. #106602	C₂²	semidirect
88. #106600	C₂²	semidirect
89. #106572	C₂²	semidirect
90. #106383	C₂²	semidirect
104. C₂²×D₄²	C₂³	semidirect
110. #61582	D₄	semidirect
111. #61576	D₄	semidirect
112. #61570	D₄	semidirect
113. #61569	D₄	semidirect
114. #61560	D₄	semidirect
115. #61559	D₄	semidirect
118. #60798	C₂³	semidirect
119. #60564	D₄	semidirect
122. #60558	C₂³	semidirect
123. #60490	D₄	semidirect
124. #60423	D₄	semidirect
128. C₂×#2867	C₂³	semidirect
131. C₂×#2541	C₂³	semidirect
132. C₂×#2541	C₂³	semidirect
133. C₂×#2540	C₂³	semidirect
134. C₂×#2535	C₂³	semidirect
135. C₂×#2657	C₂³	semidirect
139. C₂×#2349	C₂³	semidirect
141. C₂×#2275	C₂³	semidirect
142. C₂×C₄²×D₄	C₂³	semidirect
143. #21899	C₂³	semidirect
144. #21415	C₂³	semidirect
147. #17741	C₂³	semidirect
148. #17741	C₂³	semidirect
149. #17666	C₂³	semidirect
150. #17588	C₂³	semidirect
151. #17546	C₂³	semidirect
152. #17546	C₂³	semidirect
153. #17541	C₂³	semidirect
154. #17448	C₂³	semidirect
155. #17448	C₂³	semidirect
156. #17448	C₂³	semidirect
173. #14708	C₂³	semidirect
174. #14272	C₂³	semidirect
175. #14154	C₂³	semidirect
176. #14153	C₂³	semidirect
180. #13785	C₂³	semidirect
183. C₄×#390	C₂³	semidirect
185. #8098	C₂³	semidirect
186. #8098	C₂³	semidirect
187. #8072	C₂³	semidirect
188. #7959	C₂³	semidirect
189. #7950	C₂³	semidirect
190. #7867	C₂³	semidirect
204. #3506	C₂×D₄	semidirect
205. #3506	C₂×D₄	semidirect
206. #3501	C₂×D₄	semidirect
207. #3501	C₂×D₄	semidirect
208. #3496	C₂×D₄	semidirect
209. #3496	C₂×D₄	semidirect
214. #3458	C₂×D₄	semidirect
215. #3455	C₂×D₄	semidirect
216. #3449	C₂×D₄	semidirect
254. #3215	C₂×D₄	semidirect
255. #3213	C₂×D₄	semidirect
256. #3208	C₂×D₄	semidirect
257. #3205	C₂×D₄	semidirect
263. #3077	C₂×D₄	semidirect
265. #3036	C₂×D₄	semidirect
266. #2975	C₂×D₄	semidirect
267. #2973	C₂×D₄	semidirect
268. #2973	C₂×D₄	semidirect
269. #2972	C₂×D₄	semidirect
270. #2921	C₂×D₄	semidirect
274. #2905	C₂×D₄	semidirect
406. #476	#120	semidirect
407. #474	#120	semidirect
408. #461	#120	semidirect
409. #459	#120	semidirect
425. C₂²×D₄	#453	semidirect
463. C₄⋊Q₈	C₂×#120	semidirect
464. C₄⋊Q₈	C₂×#120	semidirect
465. C₄⋊Q₈	C₂×#120	semidirect
466. #127	C₂×#120	semidirect
500. C₄⋊C₈	C₂×#120	semidirect