Subgroups — #72340428

Order 2048.

At least 14434 conjugacy classes of subgroups; only the 1008 normal subgroups are shown.

The subgroup lattice has 563 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#485614	C₂	1	1	yes	maximal, characteristic, complemented
2	#72340425	C₂	1	1	yes	maximal, characteristic, complemented
3	#72340424	C₂	1	1	yes	maximal, characteristic, complemented
4	#72340422	C₂	1	4	yes	maximal, complemented
5	#72340421	C₂	1	4	yes	maximal, complemented
6	#72340419	C₂	1	2	yes	maximal, complemented
7	#72340418	C₂	1	2	yes	maximal, complemented
8	#72340417	C₂	1	2	yes	maximal, complemented
9	#72340416	C₂	1	2	yes	maximal, complemented
10	#72340411	C₂	1	1	yes	maximal, characteristic, complemented
11	#72340394	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#130056	C₂	1	1	yes	maximal, characteristic, complemented
13	#72340236	C₂	1	2	yes	maximal, complemented
14	#72318369	C₂	1	1	yes	maximal, characteristic, complemented
15	#72310908	C₂	1	2	yes	maximal, complemented
16	#72283702	C₂	1	2	yes	maximal, complemented
17	#72213362	C₂	1	2	yes	maximal, complemented
18	#10575251	C₂²	1	1	yes	characteristic, complemented
19	#8994068	C₂²	1	2	yes	complemented
20	#8983814	C₂²	1	2	yes	complemented
21	#8934620	C₂²	1	1	yes	characteristic, complemented
22	#8932887	C₂²	1	1	yes	characteristic, complemented
23	#8929993	C₂²	1	1	yes	characteristic, complemented
24	#8928621	C₂²	1	1	yes	characteristic, complemented
25	#7773976	C₂²	1	2	yes	—
26	#7726391	C₂²	1	2	yes	—
27	#7713426	C₂²	1	1	yes	characteristic
28	C₂×#47563	C₂²	1	1	yes	characteristic
29	#7630502	C₂²	1	1	yes	characteristic
30	C₂×#23445	C₂²	1	1	yes	characteristic, complemented
31	#6431733	C₂²	1	1	yes	characteristic, complemented
32	#6347124	C₂²	1	2	yes	complemented
33	C₂×#18332	C₂²	1	2	yes	complemented
34	#485667	C₂²	1	4	yes	complemented
35	#485666	C₂²	1	4	yes	complemented
36	#485648	C₂²	1	4	yes	complemented
37	#485646	C₂²	1	4	yes	complemented
38	#485634	C₂²	1	4	yes	complemented
39	#485615	C₂²	1	2	yes	complemented
40	#485614	C₂²	1	2	yes	complemented
41	#485614	C₂²	1	2	yes	complemented
42	#485614	C₂²	1	2	yes	complemented
43	#485614	C₂²	1	4	yes	complemented
44	#481702	C₂²	1	2	yes	complemented
45	C₂×#11765	C₂²	1	2	yes	complemented
46	#481680	C₂²	1	2	yes	complemented
47	C₂×#11758	C₂²	1	2	yes	complemented
48	#480264	C₂²	1	2	yes	complemented
49	C₂×#11503	C₂²	1	1	yes	characteristic, complemented
50	C₂×#11503	C₂²	1	1	yes	characteristic, complemented
51	#417800	C₂²	1	2	yes	complemented
52	#417800	C₂²	1	2	yes	complemented
53	#417798	C₂²	1	2	yes	complemented
54	#417798	C₂²	1	2	yes	complemented
55	#357493	C₂²	1	1	yes	characteristic, complemented
56	C₂×#10939	C₂²	1	1	yes	characteristic, complemented
57	#354051	C₂²	1	1	yes	characteristic, complemented
58	#246992	C₂²	1	4	yes	complemented
59	#246991	C₂²	1	4	yes	complemented
60	#246988	C₂²	1	4	yes	complemented
61	#246987	C₂²	1	4	yes	complemented
62	#200460	C₂²	1	2	yes	complemented
63	C₂×#9387	C₂²	1	2	yes	complemented
64	#187819	C₂²	1	2	yes	complemented
65	#134056	C₂²	1	2	yes	complemented
66	#134056	C₂²	1	2	yes	complemented
67	#134053	C₂²	1	2	yes	complemented
68	#134053	C₂²	1	2	yes	complemented
69	#132001	C₂²	1	4	yes	complemented
70	#132000	C₂²	1	4	yes	complemented
71	#131999	C₂²	1	4	yes	complemented
72	#131997	C₂²	1	4	yes	complemented
73	#130078	C₂²	1	4	yes	complemented
74	#130077	C₂²	1	4	yes	complemented
75	#130076	C₂²	1	4	yes	complemented
76	#130074	C₂²	1	4	yes	complemented
77	#130059	C₂²	1	4	yes	complemented
78	#130057	C₂²	1	2	yes	complemented
79	#130056	C₂²	1	2	yes	complemented
80	#130056	C₂²	1	2	yes	complemented
81	#130056	C₂²	1	2	yes	complemented
82	#130056	C₂²	1	4	yes	complemented
83	C₂³×H(5,𝔽₂)	D₄	1	1	yes	characteristic
84	C₂×#3558	D₄	1	2	yes	complemented
85	C₂×#3449	D₄	1	1	yes	characteristic
86	C₂×#3449	C₂³	1	1	yes	characteristic
87	C₂×#3449	C₂³	1	1	yes	characteristic, complemented
88	C₂²×#535	D₄	1	1	yes	characteristic
89	#60645	C₂³	1	2	yes	complemented
90	#60644	C₂³	1	2	yes	complemented
91	C₂×#2873	C₂³	1	1	yes	characteristic, complemented
92	#60048	C₂³	1	2	yes	—
93	#59620	C₂³	1	2	yes	—
94	C₂×#2670	D₄	1	2	yes	—
95	#51903	D₄	1	2	yes	complemented
96	#51903	C₂³	1	2	yes	—
97	#51902	D₄	1	2	yes	complemented
98	#51902	C₂³	1	2	yes	—
99	#51749	D₄	1	2	yes	complemented
100	#51749	C₂³	1	2	yes	—
101	#51541	D₄	1	2	yes	complemented
102	#51541	C₂³	1	2	yes	—
103	#47664	D₄	1	2	yes	complemented
104	#47658	D₄	1	2	yes	complemented
105	#47563	D₄	1	2	yes	—
106	#47563	D₄	1	1	yes	characteristic
107	#47563	D₄	1	1	yes	characteristic
108	#47563	C₂³	1	2	yes	—
109	#47563	C₂³	1	1	yes	characteristic
110	#47563	C₂³	1	1	yes	characteristic
111	#47563	C₂³	1	1	yes	characteristic
112	#47195	C₂³	1	1	yes	characteristic
113	#47177	D₄	1	2	yes	complemented
114	#47174	D₄	1	2	yes	complemented
115	#47026	C₂³	1	2	yes	—
116	#46998	D₄	1	1	yes	characteristic
117	#46458	D₄	1	2	yes	—
118	#46384	D₄	1	1	yes	characteristic
119	#46287	C₂³	1	2	yes	—
120	#46274	C₂³	1	2	yes	—
121	#42023	D₄	1	2	yes	complemented
122	#42011	D₄	1	2	yes	complemented
123	#41997	D₄	1	2	yes	complemented
124	#41981	D₄	1	2	yes	complemented
125	#37536	D₄	1	2	yes	complemented
126	#37475	D₄	1	1	yes	characteristic
127	#37436	D₄	1	1	yes	characteristic
128	#36725	D₄	1	2	yes	—
129	C₂×#2840	D₄	1	1	yes	characteristic
130	#35616	D₄	1	1	yes	characteristic
131	#35616	D₄	1	1	yes	characteristic
132	#35616	C₂³	1	1	yes	characteristic
133	#35616	C₂³	1	1	yes	characteristic
134	#35527	D₄	1	1	yes	characteristic
135	#35527	D₄	1	1	yes	characteristic
136	#35527	C₂³	1	1	yes	characteristic
137	#35527	C₂³	1	1	yes	characteristic
138	#35303	D₄	1	2	yes	complemented
139	#35118	C₂³	1	2	yes	—
140	C₂×#2610	C₂³	1	2	yes	—
141	C₂×#2403	D₄	1	1	yes	characteristic
142	#34222	D₄	1	2	yes	complemented
143	#34044	D₄	1	1	yes	characteristic
144	#34044	C₂³	1	1	yes	characteristic
145	C₂×#2309	C₂³	1	1	yes	characteristic
146	#23445	C₂³	1	2	yes	—
147	#23445	C₂³	1	2	yes	complemented
148	#23406	C₂³	1	2	yes	complemented
149	#23406	C₂³	1	2	yes	complemented
150	C₂×#1742	C₂³	1	1	yes	characteristic, complemented
151	C₂×#1740	C₂³	1	1	yes	characteristic, complemented
152	#18339	C₂³	1	4	yes	complemented
153	#18332	C₂³	1	4	yes	complemented
154	#18332	C₂³	1	4	yes	complemented
155	#18332	C₂³	1	4	yes	complemented
156	C₂×#1464	C₂³	1	2	yes	complemented
157	C₂×#1464	C₂³	1	2	yes	complemented
158	#11767	C₂³	1	4	yes	complemented
159	#11765	C₂³	1	4	yes	complemented
160	#11765	C₂³	1	4	yes	complemented
161	#11765	C₂³	1	4	yes	complemented
162	#11760	C₂³	1	4	yes	complemented
163	#11758	C₂³	1	4	yes	complemented
164	#11758	C₂³	1	4	yes	complemented
165	#11758	C₂³	1	4	yes	complemented
166	#11507	C₂³	1	4	yes	complemented
167	#11507	C₂³	1	4	yes	complemented
168	#11503	C₂³	1	2	yes	—
169	#11503	C₂³	1	2	yes	—
170	#11503	C₂³	1	2	yes	complemented
171	#11503	C₂³	1	2	yes	complemented
172	#11007	C₂³	1	2	yes	complemented
173	#11006	C₂³	1	2	yes	complemented
174	#10959	C₂³	1	2	yes	complemented
175	#10959	C₂³	1	2	yes	complemented
176	#10939	C₂³	1	2	yes	—
177	#10939	C₂³	1	2	yes	complemented
178	#9388	C₂³	1	4	yes	complemented
179	#9387	C₂³	1	4	yes	complemented
180	#9387	C₂³	1	4	yes	complemented
181	#9387	C₂³	1	4	yes	complemented
182	#8524	C₂³	1	4	yes	complemented
183	#8522	C₂³	1	4	yes	complemented
184	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
185	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
186	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
187	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
188	C₂³×#41	C₂×D₄	1	1	yes	characteristic
189	C₂³×#41	C₂×D₄	1	1	yes	characteristic
190	C₂³×#41	C₂×D₄	1	1	yes	characteristic
191	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
192	C₂×#562	C₂×D₄	1	2	yes	complemented
193	C₂×#562	C₂×D₄	1	2	yes	complemented
194	C₂×H(3,𝔽₄)	C₂×D₄	1	2	yes	complemented
195	C₂×H(3,𝔽₄)	C₂×D₄	1	2	yes	complemented
196	#3449	C₂⁴	1	2	yes	—
197	C₂×#536	C₂×D₄	1	1	yes	characteristic
198	C₂×#536	C₂×D₄	1	1	yes	characteristic
199	C₂×#536	C₂×D₄	1	1	yes	characteristic
200	C₂×#536	C₂×D₄	1	2	yes	—
201	C₂×#536	C₂⁴	1	1	yes	characteristic
202	C₂×#535	C₂×D₄	1	1	yes	characteristic
203	C₂×#535	C₂×D₄	1	1	yes	characteristic
204	C₂×#535	C₂×D₄	1	1	yes	characteristic
205	C₂×#535	C₂×D₄	1	2	yes	—
206	C₂×#535	C₂⁴	1	1	yes	characteristic
207	C₂×#532	C₂×D₄	1	2	yes	—
208	C₂×#532	C₂×D₄	1	2	yes	—
209	C₂²×#127	C₂×D₄	1	1	yes	characteristic
210	C₂²×#127	C₂×D₄	1	1	yes	characteristic
211	C₂×#529	C₂×D₄	1	2	yes	—
212	C₂²×#124	C₂×D₄	1	1	yes	characteristic
213	C₂²×#124	C₂×D₄	1	1	yes	characteristic
214	C₂²×#124	C₂×D₄	1	2	yes	—
215	C₂²×#117	C₂×D₄	1	1	yes	characteristic
216	C₂²×#117	C₂×D₄	1	1	yes	characteristic
217	C₂²×#117	C₂⁴	1	1	yes	characteristic
218	#2873	C₂⁴	1	2	yes	—
219	#2842	C₂×D₄	1	1	yes	characteristic
220	#2840	C₂×D₄	1	1	yes	characteristic
221	#2840	C₂×D₄	1	1	yes	characteristic
222	#2840	C₂×D₄	1	1	yes	characteristic
223	#2840	C₂×D₄	1	2	yes	—
224	#2832	C₂×D₄	1	2	yes	complemented
225	#2832	C₂×D₄	1	2	yes	complemented
226	#2830	C₂×D₄	1	2	yes	complemented
227	#2828	C₂×D₄	1	2	yes	complemented
228	#2812	C₂×D₄	1	2	yes	—
229	#2811	C₂×D₄	1	2	yes	complemented
230	#2799	C₂×D₄	1	2	yes	complemented
231	#2784	C₂×D₄	1	2	yes	complemented
232	#2736	C₂×D₄	1	2	yes	—
233	#2735	C₂×D₄	1	2	yes	—
234	#2733	C₂×D₄	1	2	yes	complemented
235	#2728	C₂×D₄	1	2	yes	complemented
236	#2699	C₂×D₄	1	2	yes	complemented
237	#2683	C₂×D₄	1	2	yes	complemented
238	#2679	C₂×D₄	1	2	yes	complemented
239	#2670	C₂×D₄	1	2	yes	—
240	#2670	C₂×D₄	1	2	yes	—
241	#2670	C₂×D₄	1	2	yes	—
242	#2670	C₂×D₄	1	2	yes	—
243	#2670	C₂×D₄	1	2	yes	—
244	#2668	C₂×D₄	1	2	yes	—
245	#2660	C₂×D₄	1	2	yes	complemented
246	#2657	C₂×D₄	1	2	yes	complemented
247	#2657	C₂×D₄	1	2	yes	complemented
248	#2657	C₂×D₄	1	2	yes	complemented
249	#2641	C₂×D₄	1	2	yes	complemented
250	#2640	C₂×D₄	1	2	yes	complemented
251	#2640	C₂×D₄	1	2	yes	complemented
252	#2640	C₂×D₄	1	2	yes	complemented
253	#2627	C₂×D₄	1	2	yes	—
254	#2626	C₂×D₄	1	2	yes	—
255	#2618	C₂×D₄	1	2	yes	—
256	#2617	C₂×D₄	1	2	yes	—
257	#2611	C₂×D₄	1	2	yes	—
258	#2611	C₂⁴	1	2	yes	—
259	#2610	C₂×D₄	1	2	yes	—
260	#2610	C₂×D₄	1	2	yes	—
261	#2610	C₂×D₄	1	2	yes	—
262	#2610	C₂×D₄	1	2	yes	—
263	#2610	C₂×D₄	1	2	yes	—
264	#2610	C₂×D₄	1	2	yes	—
265	#2610	C₂×D₄	1	2	yes	—
266	#2610	C₂⁴	1	2	yes	—
267	#2610	C₂⁴	1	2	yes	—
268	#2610	C₂⁴	1	2	yes	—
269	#2599	C₂×D₄	1	2	yes	—
270	#2599	C₂×D₄	1	2	yes	—
271	#2598	C₂×D₄	1	2	yes	—
272	#2598	C₂×D₄	1	2	yes	—
273	#2586	C₂×D₄	1	2	yes	complemented
274	#2572	C₂×D₄	1	2	yes	complemented
275	#2555	C₂×D₄	1	2	yes	complemented
276	#2555	C₂×D₄	1	2	yes	complemented
277	#2483	C₂×D₄	1	1	yes	characteristic
278	#2437	C₂×D₄	1	2	yes	—
279	#2403	C₂×D₄	1	1	yes	characteristic
280	#2403	C₂×D₄	1	1	yes	characteristic
281	#2403	C₂×D₄	1	2	yes	—
282	#2403	C₂×D₄	1	1	yes	characteristic
283	C₂×#395	C₂×D₄	1	2	yes	—
284	C₂×#394	C₂×D₄	1	2	yes	—
285	C₂×#393	C₂×D₄	1	2	yes	—
286	C₂×#392	C₂×D₄	1	2	yes	—
287	#2372	C₂×D₄	1	2	yes	complemented
288	#2372	C₂×D₄	1	2	yes	complemented
289	#2372	C₂×D₄	1	2	yes	complemented
290	#2372	C₂×D₄	1	2	yes	complemented
291	#2311	C₂×D₄	1	2	yes	—
292	#2311	C₂×D₄	1	2	yes	—
293	#2310	C₂×D₄	1	2	yes	—
294	#2309	C₂×D₄	1	2	yes	—
295	#2309	C₂×D₄	1	1	yes	characteristic
296	#2309	C₂×D₄	1	1	yes	characteristic
297	#2309	C₂×D₄	1	1	yes	characteristic
298	#2309	C₂×D₄	1	1	yes	characteristic
299	#2309	C₂×D₄	1	1	yes	characteristic
300	#2309	C₂×D₄	1	1	yes	characteristic
301	#2309	C₂⁴	1	1	yes	characteristic
302	#2309	C₂⁴	1	1	yes	characteristic
303	#2297	C₂×D₄	1	1	yes	characteristic
304	#2297	C₂×D₄	1	1	yes	characteristic
305	#2297	C₂×D₄	1	1	yes	characteristic
306	#2297	C₂×D₄	1	1	yes	characteristic
307	#2297	C₂×D₄	1	1	yes	characteristic
308	#2297	C₂×D₄	1	1	yes	characteristic
309	#2297	C₂⁴	1	1	yes	characteristic
310	#2297	C₂⁴	1	1	yes	characteristic
311	#2283	C₂×D₄	1	2	yes	—
312	C₂×#379	C₂×D₄	1	1	yes	characteristic
313	C₂×#379	C₂×D₄	1	1	yes	characteristic
314	C₂×#379	C₂×D₄	1	1	yes	characteristic
315	C₂×#379	C₂×D₄	1	1	yes	characteristic
316	C₂×#376	C₂×D₄	1	2	yes	—
317	#1742	C₂⁴	1	2	yes	—
318	#1740	C₂⁴	1	2	yes	—
319	#1464	C₂⁴	1	4	yes	—
320	#1464	C₂⁴	1	4	yes	—
321	C₂⁶	#120	1	1	yes	characteristic
322	C₂⁶	#120	1	1	yes	characteristic
323	C₂²×#41	#120	1	1	yes	characteristic
324	C₂²×#41	#120	1	1	yes	characteristic
325	C₂²×#41	#120	1	2	yes	—
326	C₂²×#41	#120	1	1	yes	characteristic
327	C₂²×#41	#120	1	2	yes	—
328	C₂²×#41	#120	1	1	yes	characteristic
329	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
330	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
331	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
332	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
333	C₂³×Q₈	#120	1	1	yes	characteristic
334	C₂³×Q₈	#120	1	1	yes	characteristic
335	C₂³×Q₈	#120	1	2	yes	—
336	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
337	C₂³×D₄	#120	1	1	yes	characteristic
338	C₂³×D₄	#120	1	1	yes	characteristic
339	C₂³×D₄	#120	1	1	yes	characteristic
340	C₂³×D₄	#120	1	1	yes	characteristic
341	C₂³×D₄	#120	1	2	yes	—
342	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
343	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
344	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
345	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
346	C₂×C₄⋊Q₈	#120	1	2	yes	—
347	C₂×C₄⋊Q₈	C₂²×D₄	1	2	yes	—
348	C₂×#127	#120	1	2	yes	—
349	C₂×#127	C₂²×D₄	1	2	yes	—
350	C₂×#125	C₂²×D₄	1	2	yes	—
351	C₂×#124	#120	1	2	yes	—
352	C₂×#124	#120	1	2	yes	—
353	C₂×#124	#120	1	2	yes	—
354	C₂×#124	#120	1	2	yes	—
355	C₂×#124	C₂²×D₄	1	2	yes	—
356	C₂×#124	C₂²×D₄	1	2	yes	—
357	C₂×#124	C₂²×D₄	1	2	yes	—
358	C₂×#124	C₂²×D₄	1	2	yes	—
359	C₂×#124	C₂²×D₄	1	2	yes	—
360	C₂×C₂²⋊Q₈	#120	1	2	yes	—
361	C₂×#121	#120	1	2	yes	—
362	C₂×C₄×Q₈	#120	1	2	yes	—
363	C₂×C₄×D₄	#120	1	2	yes	—
364	C₂×#117	#120	1	1	yes	characteristic
365	C₂×#117	#120	1	1	yes	characteristic
366	C₂×#117	#120	1	2	yes	—
367	C₂×#117	#120	1	2	yes	—
368	C₂×#117	C₂²×D₄	1	1	yes	characteristic
369	C₂×#117	C₂²×D₄	1	1	yes	characteristic
370	C₂×#117	C₂²×D₄	1	1	yes	characteristic
371	C₂×#117	C₂²×D₄	1	2	yes	—
372	C₂×#117	C₂²×D₄	1	1	yes	characteristic
373	C₂×#117	C₂²×D₄	1	1	yes	characteristic
374	C₂×#117	C₂²×D₄	1	2	yes	—
375	C₂×#117	C₂⁵	1	1	yes	characteristic
376	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
377	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
378	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
379	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
380	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
381	C₂²×C₄²	C₂²×D₄	1	2	yes	—
382	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
383	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
384	#400	#120	1	2	yes	—
385	#400	C₂²×D₄	1	2	yes	—
386	#399	#120	1	2	yes	—
387	#399	C₂²×D₄	1	2	yes	—
388	#398	#120	1	2	yes	—
389	#398	C₂²×D₄	1	2	yes	—
390	#397	#120	1	2	yes	—
391	#397	C₂²×D₄	1	2	yes	—
392	#395	#120	1	2	yes	—
393	#395	#120	1	2	yes	—
394	#395	#120	1	2	yes	—
395	#395	C₂²×D₄	1	2	yes	—
396	#395	C₂²×D₄	1	2	yes	—
397	#395	C₂²×D₄	1	2	yes	—
398	#394	#120	1	2	yes	—
399	#394	#120	1	2	yes	—
400	#394	#120	1	2	yes	—
401	#394	C₂²×D₄	1	2	yes	—
402	#394	C₂²×D₄	1	2	yes	—
403	#394	C₂²×D₄	1	2	yes	—
404	#393	#120	1	2	yes	—
405	#393	#120	1	2	yes	—
406	#393	#120	1	2	yes	—
407	#393	C₂²×D₄	1	2	yes	—
408	#393	C₂²×D₄	1	2	yes	—
409	#393	C₂²×D₄	1	2	yes	—
410	#392	#120	1	2	yes	—
411	#392	#120	1	2	yes	—
412	#392	#120	1	2	yes	—
413	#392	C₂²×D₄	1	2	yes	—
414	#392	C₂²×D₄	1	2	yes	—
415	#392	C₂²×D₄	1	2	yes	—
416	#391	#120	1	2	yes	—
417	#391	#120	1	2	yes	—
418	#391	C₂²×D₄	1	2	yes	—
419	#391	C₂²×D₄	1	2	yes	—
420	#390	#120	1	2	yes	—
421	#390	#120	1	2	yes	—
422	#390	C₂²×D₄	1	2	yes	—
423	#390	C₂²×D₄	1	2	yes	—
424	#383	#120	1	2	yes	—
425	#383	#120	1	2	yes	—
426	#380	#120	1	2	yes	—
427	#380	#120	1	2	yes	—
428	#379	#120	1	1	yes	characteristic
429	#379	#120	1	1	yes	characteristic
430	#379	#120	1	1	yes	characteristic
431	#379	#120	1	1	yes	characteristic
432	#379	#120	1	1	yes	characteristic
433	#379	#120	1	1	yes	characteristic
434	#379	#120	1	1	yes	characteristic
435	#379	#120	1	1	yes	characteristic
436	#379	C₂²×D₄	1	1	yes	characteristic
437	#379	C₂²×D₄	1	1	yes	characteristic
438	#379	C₂²×D₄	1	1	yes	characteristic
439	#379	C₂²×D₄	1	1	yes	characteristic
440	#379	C₂²×D₄	1	1	yes	characteristic
441	#379	C₂²×D₄	1	1	yes	characteristic
442	#379	C₂²×D₄	1	1	yes	characteristic
443	#379	C₂²×D₄	1	1	yes	characteristic
444	#376	#120	1	2	yes	—
445	#376	#120	1	2	yes	—
446	#376	C₂²×D₄	1	2	yes	—
447	#376	C₂²×D₄	1	2	yes	—
448	#376	C₂²×D₄	1	2	yes	—
449	#376	C₂²×D₄	1	2	yes	—
450	C₂×#95	#120	1	2	yes	—
451	C₂×#95	#120	1	2	yes	—
452	C₂⁵	#453	1	4	yes	—
453	C₂⁵	C₂×#120	1	1	yes	characteristic
454	C₂⁵	C₂×#120	1	1	yes	characteristic
455	C₂⁵	C₂×#120	1	1	yes	characteristic
456	C₂⁵	C₂×#120	1	1	yes	characteristic
457	C₂⁵	C₂×#120	1	1	yes	characteristic
458	C₂×#41	#453	1	4	yes	—
459	C₂×#41	B(4,𝔽₂)	1	2	yes	—
460	C₂×#41	B(4,𝔽₂)	1	2	yes	—
461	C₂²×Q₈	C₂×#120	1	2	yes	—
462	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
463	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
464	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
465	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
466	C₂²×Q₈	C₂×#120	1	2	yes	—
467	C₂²×Q₈	C₂×#120	1	2	yes	—
468	C₂²×Q₈	C₂×#120	1	2	yes	—
469	C₂²×D₄	C₂×#120	1	2	yes	—
470	C₂²×D₄	C₂×#120	1	1	yes	characteristic
471	C₂²×D₄	C₂×#120	1	1	yes	characteristic
472	C₂²×D₄	C₂×#120	1	1	yes	characteristic
473	C₂²×D₄	C₂×#120	1	1	yes	characteristic
474	C₂²×D₄	C₂×#120	1	2	yes	—
475	C₂²×D₄	C₂×#120	1	2	yes	—
476	C₂²×D₄	C₂×#120	1	2	yes	—
477	C₂³×C₄	C₂×#120	1	1	yes	characteristic
478	C₂³×C₄	C₂×#120	1	1	yes	characteristic
479	C₂³×C₄	C₂×#120	1	1	yes	characteristic
480	C₂³×C₄	C₂×#120	1	1	yes	characteristic
481	C₂³×C₄	C₂×#120	1	2	yes	—
482	C₂³×C₄	C₂×#120	1	2	yes	—
483	C₂³×C₄	C₂×#120	1	1	yes	characteristic
484	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
485	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
486	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
487	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
488	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
489	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
490	C₂×C₄⋊C₄	C₂³×D₄	1	2	yes	—
491	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
492	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
493	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
494	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
495	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
496	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
497	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
498	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
499	C₂×C₂²⋊C₄	C₂³×D₄	1	1	yes	characteristic
500	C₂×C₂²⋊C₄	C₂³×D₄	1	1	yes	characteristic
501	C₂×C₄²	C₂×#120	1	2	yes	—
502	C₂×C₄²	C₂×#120	1	2	yes	—
503	C₂×C₄²	C₂×#120	1	2	yes	—
504	C₂×C₄²	C₂×#120	1	2	yes	—
505	C₂×C₄²	C₂×#120	1	2	yes	—
506	C₂×C₄²	C₂³×D₄	1	2	yes	—
507	#95	C₂×#120	1	2	yes	—
508	#95	C₂×#120	1	2	yes	—
509	#95	C₂×#120	1	2	yes	—
510	#95	C₂×#120	1	2	yes	—
511	#95	C₂×#120	1	2	yes	—
512	#95	C₂×#120	1	2	yes	—
513	#95	C₂×#120	1	2	yes	—
514	#95	C₂×#120	1	2	yes	—
515	C₂⁴	#2846	1	1	yes	characteristic
516	C₂⁴	#2846	1	1	yes	characteristic
517	C₂⁴	C₂×#453	1	2	yes	—
518	C₂⁴	C₂×#453	1	2	yes	—
519	C₂⁴	C₂×#453	1	2	yes	—
520	C₂⁴	#3019	1	2	yes	—
521	C₂⁴	C₂²×#120	1	1	yes	characteristic
522	C₂×Q₈	C₂×#453	1	2	yes	—
523	C₂×Q₈	C₂×B(4,𝔽₂)	1	2	yes	—
524	C₂×D₄	C₂×#453	1	2	yes	—
525	C₂×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
526	C₂²×C₄	#2846	1	1	yes	characteristic
527	C₂²×C₄	#2846	1	1	yes	characteristic
528	C₂²×C₄	#2846	1	2	yes	—
529	C₂²×C₄	#2846	1	2	yes	—
530	C₂²×C₄	C₂×#453	1	2	yes	—
531	C₂²×C₄	#3019	1	2	yes	—
532	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
533	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
534	C₂²×C₄	#3026	1	1	yes	characteristic
535	C₂²×C₄	#3026	1	1	yes	characteristic
536	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
537	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
538	C₂²×C₄	C₂²×#120	1	2	yes	—
539	C₂²×C₄	C₂²×#120	1	2	yes	—
540	C₂³	#32888	1	2	yes	—
541	C₂³	#32888	1	2	yes	—
542	C₂³	#32888	1	2	yes	—
543	C₂³	#32898	1	1	yes	characteristic
544	C₂³	#32898	1	1	yes	characteristic
545	C₂³	C₂×#2846	1	1	yes	characteristic
546	C₂³	C₂²×#453	1	1	yes	characteristic
547	C₂³	C₂×#3019	1	1	yes	characteristic
548	C₂×C₄	#32888	1	2	yes	—
549	C₂×C₄	#32898	1	1	yes	characteristic
550	C₂×C₄	#32898	1	1	yes	characteristic
551	C₂×C₄	C₂²×#453	1	1	yes	characteristic
552	C₂×C₄	C₂×#3019	1	1	yes	characteristic
553	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
554	C₂×C₄	C₂×#3026	1	1	yes	characteristic
555	C₂²	#346446	1	2	yes	—
556	C₂²	#346446	1	2	yes	—
557	C₂²	C₂×#32888	1	1	yes	characteristic
558	C₂²	C₂×#32888	1	1	yes	characteristic
559	C₂²	C₂×#32898	1	1	yes	characteristic
560	C₂	C₂×#346446	1	1	yes	characteristic
561	C₂	#72340414	1	2	yes	—

	subgroup	G/H
center, socle	C₂²	C₂×#32898
commutator, Frattini, cosocle	C₂×#117	C₂⁵
LCS	G ▷ C₂×#117 ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×#3449 ◁ G
LECS	G ▷ C₂×#117 ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂×#485614	C₂	semidirect
2. #72340425	C₂	semidirect
3. #72340424	C₂	semidirect
4. #72340422	C₂	semidirect
5. #72340421	C₂	semidirect
6. #72340419	C₂	semidirect
7. #72340418	C₂	semidirect
8. #72340417	C₂	semidirect
9. #72340416	C₂	semidirect
10. #72340411	C₂	semidirect
11. #72340394	C₂	semidirect
12. C₂×#130056	C₂	semidirect
13. #72340236	C₂	semidirect
14. #72318369	C₂	semidirect
15. #72310908	C₂	semidirect
16. #72283702	C₂	semidirect
17. #72213362	C₂	semidirect
18. #10575251	C₂²	semidirect
19. #8994068	C₂²	semidirect
20. #8983814	C₂²	semidirect
21. #8934620	C₂²	semidirect
22. #8932887	C₂²	semidirect
23. #8929993	C₂²	semidirect
24. #8928621	C₂²	semidirect
30. C₂×#23445	C₂²	semidirect
31. #6431733	C₂²	semidirect
32. #6347124	C₂²	semidirect
33. C₂×#18332	C₂²	semidirect
34. #485667	C₂²	semidirect
35. #485666	C₂²	semidirect
36. #485648	C₂²	semidirect
37. #485646	C₂²	semidirect
38. #485634	C₂²	semidirect
39. #485615	C₂²	semidirect
40. #485614	C₂²	semidirect
41. #485614	C₂²	semidirect
42. #485614	C₂²	semidirect
43. #485614	C₂²	semidirect
44. #481702	C₂²	semidirect
45. C₂×#11765	C₂²	semidirect
46. #481680	C₂²	semidirect
47. C₂×#11758	C₂²	semidirect
48. #480264	C₂²	semidirect
49. C₂×#11503	C₂²	semidirect
50. C₂×#11503	C₂²	semidirect
51. #417800	C₂²	semidirect
52. #417800	C₂²	semidirect
53. #417798	C₂²	semidirect
54. #417798	C₂²	semidirect
55. #357493	C₂²	semidirect
56. C₂×#10939	C₂²	semidirect
57. #354051	C₂²	semidirect
58. #246992	C₂²	semidirect
59. #246991	C₂²	semidirect
60. #246988	C₂²	semidirect
61. #246987	C₂²	semidirect
62. #200460	C₂²	semidirect
63. C₂×#9387	C₂²	semidirect
64. #187819	C₂²	semidirect
65. #134056	C₂²	semidirect
66. #134056	C₂²	semidirect
67. #134053	C₂²	semidirect
68. #134053	C₂²	semidirect
69. #132001	C₂²	semidirect
70. #132000	C₂²	semidirect
71. #131999	C₂²	semidirect
72. #131997	C₂²	semidirect
73. #130078	C₂²	semidirect
74. #130077	C₂²	semidirect
75. #130076	C₂²	semidirect
76. #130074	C₂²	semidirect
77. #130059	C₂²	semidirect
78. #130057	C₂²	semidirect
79. #130056	C₂²	semidirect
80. #130056	C₂²	semidirect
81. #130056	C₂²	semidirect
82. #130056	C₂²	semidirect
84. C₂×#3558	D₄	semidirect
87. C₂×#3449	C₂³	semidirect
89. #60645	C₂³	semidirect
90. #60644	C₂³	semidirect
91. C₂×#2873	C₂³	semidirect
95. #51903	D₄	semidirect
97. #51902	D₄	semidirect
99. #51749	D₄	semidirect
101. #51541	D₄	semidirect
103. #47664	D₄	semidirect
104. #47658	D₄	semidirect
113. #47177	D₄	semidirect
114. #47174	D₄	semidirect
121. #42023	D₄	semidirect
122. #42011	D₄	semidirect
123. #41997	D₄	semidirect
124. #41981	D₄	semidirect
125. #37536	D₄	semidirect
138. #35303	D₄	semidirect
142. #34222	D₄	semidirect
147. #23445	C₂³	semidirect
148. #23406	C₂³	semidirect
149. #23406	C₂³	semidirect
150. C₂×#1742	C₂³	semidirect
151. C₂×#1740	C₂³	semidirect
152. #18339	C₂³	semidirect
153. #18332	C₂³	semidirect
154. #18332	C₂³	semidirect
155. #18332	C₂³	semidirect
156. C₂×#1464	C₂³	semidirect
157. C₂×#1464	C₂³	semidirect
158. #11767	C₂³	semidirect
159. #11765	C₂³	semidirect
160. #11765	C₂³	semidirect
161. #11765	C₂³	semidirect
162. #11760	C₂³	semidirect
163. #11758	C₂³	semidirect
164. #11758	C₂³	semidirect
165. #11758	C₂³	semidirect
166. #11507	C₂³	semidirect
167. #11507	C₂³	semidirect
170. #11503	C₂³	semidirect
171. #11503	C₂³	semidirect
172. #11007	C₂³	semidirect
173. #11006	C₂³	semidirect
174. #10959	C₂³	semidirect
175. #10959	C₂³	semidirect
177. #10939	C₂³	semidirect
178. #9388	C₂³	semidirect
179. #9387	C₂³	semidirect
180. #9387	C₂³	semidirect
181. #9387	C₂³	semidirect
182. #8524	C₂³	semidirect
183. #8522	C₂³	semidirect
192. C₂×#562	C₂×D₄	semidirect
193. C₂×#562	C₂×D₄	semidirect
194. C₂×H(3,𝔽₄)	C₂×D₄	semidirect
195. C₂×H(3,𝔽₄)	C₂×D₄	semidirect
224. #2832	C₂×D₄	semidirect
225. #2832	C₂×D₄	semidirect
226. #2830	C₂×D₄	semidirect
227. #2828	C₂×D₄	semidirect
229. #2811	C₂×D₄	semidirect
230. #2799	C₂×D₄	semidirect
231. #2784	C₂×D₄	semidirect
234. #2733	C₂×D₄	semidirect
235. #2728	C₂×D₄	semidirect
236. #2699	C₂×D₄	semidirect
237. #2683	C₂×D₄	semidirect
238. #2679	C₂×D₄	semidirect
245. #2660	C₂×D₄	semidirect
246. #2657	C₂×D₄	semidirect
247. #2657	C₂×D₄	semidirect
248. #2657	C₂×D₄	semidirect
249. #2641	C₂×D₄	semidirect
250. #2640	C₂×D₄	semidirect
251. #2640	C₂×D₄	semidirect
252. #2640	C₂×D₄	semidirect
273. #2586	C₂×D₄	semidirect
274. #2572	C₂×D₄	semidirect
275. #2555	C₂×D₄	semidirect
276. #2555	C₂×D₄	semidirect
287. #2372	C₂×D₄	semidirect
288. #2372	C₂×D₄	semidirect
289. #2372	C₂×D₄	semidirect
290. #2372	C₂×D₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×#485614	2
#72340425	2
#72340424	2
#72340422	2
#72340421	2
#72340419	2
#72340418	2
#72340417	2
#72340416	2
#72340411	2
#72340394	2
C₂×#130056	2
#72340236	2
#72318369	2
#72310908	2
#72283702	2
#72213362	2