Subgroups — #72340454

Order 4096.

At least 18517 conjugacy classes of subgroups; only the 833 normal subgroups are shown.

The subgroup lattice has 362 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×#72213808	C₂	1	1	yes	maximal, characteristic, complemented
2	#72340448	C₂	1	2	yes	maximal, complemented
3	#72340447	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#72213781	C₂	1	2	yes	maximal, complemented
5	#72340445	C₂	1	1	yes	maximal, characteristic, complemented
6	#72340442	C₂	1	1	yes	maximal, characteristic, complemented
7	#72340438	C₂	1	2	yes	maximal, complemented
8	#72340435	C₂²	1	1	yes	characteristic, complemented
9	#72340434	C₂	1	1	yes	maximal, characteristic, complemented
10	#72340431	C₂²	1	1	yes	characteristic
11	C₂×#418884	C₂²	1	2	yes	complemented
12	#72340428	C₂	1	2	yes	maximal, complemented
13	C₂×#485614	C₂²	1	2	yes	complemented
14	#72340425	C₂²	1	2	yes	complemented
15	#72340424	C₂²	1	1	yes	characteristic, complemented
16	#72340411	C₂²	1	2	yes	—
17	#72340397	C₂	1	1	yes	maximal, characteristic, complemented
18	#72340394	C₂²	1	2	yes	complemented
19	C₂×#72213791	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#94173	C₂²	1	2	yes	complemented
21	C₂×#94173	C₂²	1	2	yes	complemented
22	C₂×#130056	C₂²	1	2	yes	complemented
23	C₂×#251855	C₂²	1	1	yes	characteristic
24	C₂×#251855	C₂²	1	1	yes	characteristic, complemented
25	C₂×#150561	C₂²	1	2	yes	complemented
26	C₂×#150561	C₂²	1	2	yes	complemented
27	C₂×#149742	C₂²	1	1	yes	characteristic, complemented
28	C₂×#149742	C₂²	1	1	yes	characteristic, complemented
29	C₂×#149742	C₂²	1	2	yes	complemented
30	C₂×#356056	C₂²	1	1	yes	characteristic, complemented
31	#72340238	C₂	1	4	yes	maximal, complemented
32	#72340236	C₂²	1	4	yes	complemented
33	#72340231	C₂²	1	1	yes	characteristic
34	#72340231	C₂²	1	1	yes	characteristic, complemented
35	#72318369	C₂²	1	2	yes	complemented
36	C₂×#6437630	C₂²	1	1	yes	characteristic, complemented
37	#72310928	C₂	1	4	yes	maximal, complemented
38	#72310922	C₂²	1	4	yes	complemented
39	#72310920	C₂²	1	2	yes	complemented
40	#72310916	C₂²	1	4	yes	complemented
41	#72310908	C₂²	1	4	yes	complemented
42	#72284724	C₂²	1	2	yes	complemented
43	#72283994	C₂²	1	8	yes	complemented
44	#72283848	C₂	1	4	yes	maximal, complemented
45	#72283788	C₂²	1	4	yes	complemented
46	#72283765	C₂²	1	8	yes	complemented
47	#72283725	C₂²	1	2	yes	complemented
48	#72283702	C₂²	1	4	yes	complemented
49	#72283562	C₂²	1	4	yes	complemented
50	#72213831	C₂	1	4	yes	maximal, complemented
51	#72213808	C₂²	1	4	yes	complemented
52	#72213808	C₂²	1	4	yes	complemented
53	#72213808	C₂²	1	4	yes	complemented
54	#72213791	C₂²	1	4	yes	complemented
55	#72213791	C₂²	1	4	yes	complemented
56	#72213791	C₂²	1	4	yes	complemented
57	#72213781	C₂²	1	8	yes	complemented
58	#72213781	C₂²	1	8	yes	complemented
59	#72213781	C₂²	1	8	yes	complemented
60	#72213758	C₂²	1	4	yes	complemented
61	#72213746	C₂²	1	8	yes	complemented
62	#72213423	C₂²	1	4	yes	complemented
63	#72213362	C₂²	1	4	yes	complemented
64	#72213228	C₂²	1	2	yes	complemented
65	C₂²×H(7,𝔽₂)	D₄	1	1	yes	characteristic
66	#10575251	D₄	1	2	yes	complemented
67	#8934620	C₂³	1	1	yes	characteristic, complemented
68	#8932887	C₂³	1	1	yes	characteristic, complemented
69	#8929993	C₂³	1	1	yes	characteristic, complemented
70	#8928621	C₂³	1	1	yes	characteristic, complemented
71	#7713426	C₂³	1	1	yes	characteristic
72	C₂×#47563	C₂³	1	1	yes	characteristic
73	#7630502	D₄	1	1	yes	characteristic
74	#7630502	D₄	1	1	yes	characteristic
75	#7630502	C₂³	1	1	yes	characteristic
76	#6628902	D₄	1	2	yes	—
77	#6628902	C₂³	1	2	yes	—
78	#6628901	D₄	1	2	yes	—
79	#6628901	C₂³	1	2	yes	—
80	#6437630	C₂³	1	4	yes	—
81	C₂×#23445	C₂³	1	2	yes	—
82	#6431733	D₄	1	2	yes	complemented
83	C₂×#20586	D₄	1	1	yes	characteristic
84	C₂×#20586	C₂³	1	1	yes	characteristic
85	C₂×#20586	C₂³	1	1	yes	characteristic
86	#485615	C₂³	1	4	yes	complemented
87	#485614	C₂³	1	4	yes	complemented
88	#485614	C₂³	1	4	yes	complemented
89	#485614	C₂³	1	4	yes	complemented
90	C₂×#11503	C₂³	1	2	yes	—
91	C₂×#11503	C₂³	1	2	yes	—
92	#418884	C₂³	1	8	yes	—
93	#417800	D₄	1	4	yes	complemented
94	#417800	C₂³	1	4	yes	—
95	#417798	D₄	1	4	yes	complemented
96	#417798	C₂³	1	4	yes	—
97	#357493	D₄	1	2	yes	complemented
98	#356056	C₂³	1	4	yes	—
99	C₂×#10939	C₂³	1	2	yes	—
100	#354051	D₄	1	2	yes	complemented
101	#251855	D₄	1	2	yes	—
102	#251855	D₄	1	2	yes	—
103	#251855	C₂³	1	2	yes	—
104	#251855	C₂³	1	2	yes	—
105	#251855	C₂³	1	2	yes	—
106	#251855	C₂³	1	2	yes	complemented
107	#251855	C₂³	1	2	yes	complemented
108	#251855	C₂³	1	2	yes	complemented
109	#251850	C₂³	1	2	yes	—
110	#251850	C₂³	1	2	yes	complemented
111	#251833	D₄	1	2	yes	—
112	#251828	D₄	1	2	yes	—
113	#238082	D₄	1	2	yes	—
114	C₂×#10390	D₄	1	2	yes	—
115	#233549	D₄	1	2	yes	—
116	C₂×#10336	D₄	1	2	yes	—
117	#213862	C₂³	1	2	yes	complemented
118	#213861	C₂³	1	2	yes	complemented
119	C₂×#8748	C₂³	1	1	yes	characteristic
120	C₂×#8748	C₂³	1	1	yes	characteristic
121	#150561	C₂³	1	8	yes	complemented
122	#150561	C₂³	1	8	yes	complemented
123	#149742	C₂³	1	4	yes	—
124	#149742	C₂³	1	4	yes	—
125	#149742	C₂³	1	8	yes	complemented
126	#134056	C₂³	1	4	yes	complemented
127	#134053	C₂³	1	4	yes	complemented
128	#130057	C₂³	1	4	yes	complemented
129	#130056	C₂³	1	4	yes	complemented
130	#130056	C₂³	1	4	yes	complemented
131	#130056	C₂³	1	4	yes	complemented
132	#94173	C₂³	1	8	yes	complemented
133	#94173	C₂³	1	8	yes	complemented
134	C₂×H(7,𝔽₂)	C₂×D₄	1	2	yes	—
135	C₂×H(7,𝔽₂)	C₂×D₄	1	2	yes	—
136	C₂³×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
137	C₂³×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
138	C₂³×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
139	C₂×#3449	C₂×D₄	1	2	yes	—
140	C₂×#3449	C₂×D₄	1	2	yes	complemented
141	C₂²×#535	C₂×D₄	1	1	yes	characteristic
142	#60645	C₂×D₄	1	4	yes	complemented
143	#60644	C₂×D₄	1	4	yes	complemented
144	C₂×#2873	C₂×D₄	1	2	yes	complemented
145	#47563	C₂×D₄	1	1	yes	characteristic
146	#47563	C₂×D₄	1	1	yes	characteristic
147	#47563	C₂⁴	1	1	yes	characteristic
148	#47563	C₂⁴	1	1	yes	characteristic
149	#47563	C₂⁴	1	1	yes	characteristic
150	#47195	C₂⁴	1	1	yes	characteristic
151	#46998	C₂×D₄	1	1	yes	characteristic
152	#46384	C₂×D₄	1	1	yes	characteristic
153	#37475	C₂×D₄	1	1	yes	characteristic
154	#37436	C₂×D₄	1	1	yes	characteristic
155	C₂×#2840	C₂×D₄	1	1	yes	characteristic
156	#35616	C₂×D₄	1	2	yes	—
157	#35616	C₂×D₄	1	1	yes	characteristic
158	#35616	C₂×D₄	1	2	yes	—
159	#35616	C₂×D₄	1	2	yes	—
160	#35616	C₂⁴	1	1	yes	characteristic
161	#35527	C₂×D₄	1	2	yes	—
162	#35527	C₂×D₄	1	1	yes	characteristic
163	#35527	C₂×D₄	1	2	yes	—
164	#35527	C₂×D₄	1	2	yes	—
165	#35527	C₂⁴	1	1	yes	characteristic
166	C₂×#2403	C₂×D₄	1	1	yes	characteristic
167	#34044	C₂×D₄	1	2	yes	—
168	C₂×#2309	C₂×D₄	1	1	yes	characteristic
169	C₂×#2309	C₂×D₄	1	1	yes	characteristic
170	C₂×#2309	C₂⁴	1	1	yes	characteristic
171	#23445	C₂×D₄	1	4	yes	complemented
172	#23445	C₂⁴	1	4	yes	—
173	#23406	C₂×D₄	1	4	yes	complemented
174	#23406	C₂×D₄	1	4	yes	complemented
175	#20586	C₂×D₄	1	2	yes	—
176	#20586	C₂×D₄	1	2	yes	—
177	#20586	C₂×D₄	1	2	yes	—
178	#20586	C₂×D₄	1	2	yes	—
179	#20586	C₂×D₄	1	2	yes	—
180	#20586	C₂×D₄	1	2	yes	—
181	#20586	C₂⁴	1	2	yes	—
182	#20586	C₂⁴	1	2	yes	—
183	C₂×#1781	C₂×D₄	1	2	yes	—
184	C₂×#1781	C₂×D₄	1	2	yes	—
185	C₂×#1742	C₂×D₄	1	2	yes	complemented
186	C₂×#1740	C₂×D₄	1	2	yes	complemented
187	#11503	C₂⁴	1	4	yes	—
188	#11503	C₂⁴	1	4	yes	—
189	#11007	C₂×D₄	1	4	yes	complemented
190	#11006	C₂×D₄	1	4	yes	complemented
191	#10959	C₂×D₄	1	4	yes	complemented
192	#10959	C₂×D₄	1	4	yes	complemented
193	#10939	C₂×D₄	1	4	yes	complemented
194	#10939	C₂⁴	1	4	yes	—
195	#10392	C₂×D₄	1	4	yes	—
196	#10390	C₂×D₄	1	4	yes	—
197	#10390	C₂×D₄	1	4	yes	—
198	#10390	C₂×D₄	1	4	yes	—
199	#10338	C₂×D₄	1	4	yes	—
200	#10336	C₂×D₄	1	4	yes	—
201	#10336	C₂×D₄	1	4	yes	—
202	#10336	C₂×D₄	1	4	yes	—
203	#8748	C₂×D₄	1	2	yes	—
204	#8748	C₂×D₄	1	2	yes	—
205	#8748	C₂⁴	1	2	yes	—
206	#8748	C₂⁴	1	2	yes	—
207	C₂×#1304	C₂×D₄	1	2	yes	—
208	C₂×#1304	C₂×D₄	1	2	yes	—
209	C₂²×H(5,𝔽₂)	#120	1	2	yes	—
210	C₂²×H(5,𝔽₂)	#120	1	2	yes	—
211	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
212	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
213	C₂²×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
214	C₂²×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
215	C₂³×#41	#120	1	1	yes	characteristic
216	C₂³×#41	#120	1	2	yes	—
217	C₂⁴×D₄	#120	1	2	yes	—
218	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
219	#3449	C₂²×D₄	1	4	yes	—
220	C₂×#536	#120	1	2	yes	—
221	C₂×#536	C₂²×D₄	1	2	yes	—
222	C₂×#535	#120	1	2	yes	—
223	C₂×#535	C₂²×D₄	1	2	yes	—
224	C₂²×#127	#120	1	1	yes	characteristic
225	C₂²×#127	C₂²×D₄	1	1	yes	characteristic
226	C₂²×#124	#120	1	1	yes	characteristic
227	C₂²×#124	C₂²×D₄	1	1	yes	characteristic
228	C₂²×#117	#120	1	1	yes	characteristic
229	C₂²×#117	C₂²×D₄	1	2	yes	—
230	#2873	C₂²×D₄	1	4	yes	—
231	#2842	C₂²×D₄	1	1	yes	characteristic
232	#2840	C₂²×D₄	1	1	yes	characteristic
233	#2840	C₂²×D₄	1	1	yes	characteristic
234	#2840	C₂²×D₄	1	1	yes	characteristic
235	#2483	C₂²×D₄	1	1	yes	characteristic
236	#2403	C₂²×D₄	1	1	yes	characteristic
237	#2403	C₂²×D₄	1	1	yes	characteristic
238	#2403	C₂²×D₄	1	1	yes	characteristic
239	#2309	#120	1	2	yes	—
240	#2309	C₂²×D₄	1	2	yes	—
241	#2309	C₂²×D₄	1	2	yes	—
242	#2309	C₂²×D₄	1	1	yes	characteristic
243	#2309	C₂²×D₄	1	2	yes	—
244	#2309	C₂²×D₄	1	1	yes	characteristic
245	#2309	C₂²×D₄	1	1	yes	characteristic
246	#2309	H(5,𝔽₂)	1	2	yes	—
247	#2309	C₂⁵	1	1	yes	characteristic
248	#2297	#120	1	2	yes	—
249	#2297	#120	1	2	yes	—
250	#2297	C₂²×D₄	1	2	yes	—
251	#2297	C₂²×D₄	1	2	yes	—
252	C₂×#379	#120	1	2	yes	—
253	C₂×#379	C₂²×D₄	1	1	yes	characteristic
254	C₂×#379	C₂²×D₄	1	1	yes	characteristic
255	C₂×#379	H(5,𝔽₂)	1	2	yes	—
256	#1781	#120	1	4	yes	—
257	#1781	#120	1	4	yes	—
258	#1781	C₂²×D₄	1	4	yes	—
259	#1781	C₂²×D₄	1	4	yes	—
260	#1742	C₂²×D₄	1	4	yes	—
261	#1740	C₂²×D₄	1	4	yes	—
262	#1304	C₂²×D₄	1	4	yes	—
263	#1304	C₂²×D₄	1	4	yes	—
264	C₂⁶	#453	1	2	yes	—
265	C₂⁶	C₂×#120	1	1	yes	characteristic
266	C₂⁶	#534	1	1	yes	characteristic
267	C₂²×#41	B(4,𝔽₂)	1	2	yes	—
268	C₂²×#41	B(4,𝔽₂)	1	2	yes	—
269	C₂²×#41	C₂×#120	1	2	yes	—
270	C₂²×#41	C₂×#120	1	2	yes	—
271	C₂³×Q₈	B(4,𝔽₂)	1	2	yes	—
272	C₂³×Q₈	C₂×#120	1	1	yes	characteristic
273	C₂³×D₄	#453	1	4	yes	—
274	C₂³×D₄	B(4,𝔽₂)	1	2	yes	—
275	C₂³×D₄	C₂×#120	1	1	yes	characteristic
276	C₂³×D₄	C₂×#120	1	1	yes	characteristic
277	C₂³×D₄	C₂×#120	1	1	yes	characteristic
278	C₂³×D₄	C₂×#120	1	4	yes	—
279	C₂³×D₄	#534	1	1	yes	characteristic
280	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
281	C₂⁴×C₄	#453	1	2	yes	—
282	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
283	C₂×#117	C₂×#120	1	2	yes	—
284	C₂×#117	D₄²	1	2	yes	—
285	C₂×#117	D₄²	1	2	yes	—
286	C₂×#117	C₂³×D₄	1	2	yes	—
287	C₂²×C₂²⋊C₄	D₄²	1	2	yes	—
288	C₂²×C₂²⋊C₄	D₄²	1	2	yes	—
289	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
290	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
291	#379	C₂×#120	1	4	yes	—
292	#379	C₂×#120	1	1	yes	characteristic
293	#379	C₂×#120	1	1	yes	characteristic
294	#379	#534	1	2	yes	—
295	#379	D₄²	1	2	yes	—
296	#379	D₄²	1	2	yes	—
297	#379	D₄²	1	2	yes	—
298	#379	D₄²	1	2	yes	—
299	#379	C₂³×D₄	1	1	yes	characteristic
300	#379	C₂³×D₄	1	1	yes	characteristic
301	#379	C₂×H(5,𝔽₂)	1	2	yes	—
302	C₂⁵	#2403	1	1	yes	characteristic
303	C₂⁵	#2403	1	1	yes	characteristic
304	C₂⁵	#2403	1	1	yes	characteristic
305	C₂⁵	C₂×#453	1	2	yes	—
306	C₂⁵	C₂×#453	1	2	yes	—
307	C₂⁵	C₂×#453	1	4	yes	—
308	C₂⁵	C₂²×#120	1	1	yes	characteristic
309	C₂⁵	C₂×#534	1	1	yes	characteristic
310	C₂×#41	#2196	1	4	yes	—
311	C₂×#41	#2196	1	4	yes	—
312	C₂²×Q₈	C₂×B(4,𝔽₂)	1	2	yes	—
313	C₂²×Q₈	C₂×B(4,𝔽₂)	1	2	yes	—
314	C₂²×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
315	C₂²×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
316	C₂³×C₄	#2403	1	1	yes	characteristic
317	C₂³×C₄	C₂×#453	1	4	yes	—
318	C₂³×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
319	C₂³×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
320	C₂³×C₄	C₂²×#120	1	1	yes	characteristic
321	C₂×C₂²⋊C₄	#2403	1	2	yes	—
322	C₂×C₂²⋊C₄	#2403	1	2	yes	—
323	C₂×C₂²⋊C₄	C₂×D₄²	1	2	yes	—
324	C₂×C₂²⋊C₄	C₂×D₄²	1	2	yes	—
325	C₂⁴	#23897	1	1	yes	characteristic
326	C₂⁴	#23897	1	1	yes	characteristic
327	C₂⁴	#23900	1	1	yes	characteristic
328	C₂⁴	#23900	1	1	yes	characteristic
329	C₂⁴	#23906	1	1	yes	characteristic
330	C₂⁴	#23906	1	1	yes	characteristic
331	C₂⁴	#23906	1	2	yes	—
332	C₂⁴	C₂×#2403	1	1	yes	characteristic
333	C₂⁴	C₂²×#453	1	2	yes	—
334	C₂×Q₈	C₂×#2196	1	4	yes	—
335	C₂×D₄	C₂×#2196	1	4	yes	—
336	C₂²×C₄	#23900	1	2	yes	—
337	C₂²×C₄	C₂×#2196	1	2	yes	—
338	C₂²×C₄	C₂×#2196	1	2	yes	—
339	C₂²×C₄	#33551	1	2	yes	—
340	C₂²×C₄	#33551	1	2	yes	—
341	C₂²×C₄	C₂²×B(4,𝔽₂)	1	2	yes	—
342	C₂³	#249319	1	1	yes	characteristic
343	C₂³	#249319	1	1	yes	characteristic
344	C₂³	#249319	1	1	yes	characteristic
345	C₂³	#249319	1	1	yes	characteristic
346	C₂³	#499787	1	2	yes	—
347	C₂³	#499787	1	2	yes	—
348	C₂³	C₂×#23906	1	1	yes	characteristic
349	C₂³	C₂×#23897	1	1	yes	characteristic
350	C₂³	C₂×#23900	1	1	yes	characteristic
351	C₂×C₄	#499787	1	2	yes	—
352	C₂×C₄	#499787	1	2	yes	—
353	C₂×C₄	C₂²×#2196	1	2	yes	—
354	C₂×C₄	C₂×#33551	1	2	yes	—
355	C₂²	#72213827	1	1	yes	characteristic
356	C₂²	#72213827	1	1	yes	characteristic
357	C₂²	#72213827	1	2	yes	—
358	C₂²	C₂×#499787	1	2	yes	—
359	C₂²	C₂×#249319	1	1	yes	characteristic
360	C₂	C₂×#72213827	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	C₂×#72213827
commutator, Frattini, cosocle	#2309	C₂⁵
LCS	G ▷ #2309 ▷ C₂⁴ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂⁴ ◁ C₂⁴×C₄ ◁ #7630502 ◁ G
LECS	G ▷ #2309 ▷ C₂⁴ ▷ C₂² ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂×#72213808	C₂	semidirect
2. #72340448	C₂	semidirect
3. #72340447	C₂	semidirect
4. C₂×#72213781	C₂	semidirect
5. #72340445	C₂	semidirect
6. #72340442	C₂	semidirect
7. #72340438	C₂	semidirect
8. #72340435	C₂²	semidirect
9. #72340434	C₂	semidirect
11. C₂×#418884	C₂²	semidirect
12. #72340428	C₂	semidirect
13. C₂×#485614	C₂²	semidirect
14. #72340425	C₂²	semidirect
15. #72340424	C₂²	semidirect
17. #72340397	C₂	semidirect
18. #72340394	C₂²	semidirect
19. C₂×#72213791	C₂	semidirect
20. C₂×#94173	C₂²	semidirect
21. C₂×#94173	C₂²	semidirect
22. C₂×#130056	C₂²	semidirect
24. C₂×#251855	C₂²	semidirect
25. C₂×#150561	C₂²	semidirect
26. C₂×#150561	C₂²	semidirect
27. C₂×#149742	C₂²	semidirect
28. C₂×#149742	C₂²	semidirect
29. C₂×#149742	C₂²	semidirect
30. C₂×#356056	C₂²	semidirect
31. #72340238	C₂	semidirect
32. #72340236	C₂²	semidirect
34. #72340231	C₂²	semidirect
35. #72318369	C₂²	semidirect
36. C₂×#6437630	C₂²	semidirect
37. #72310928	C₂	semidirect
38. #72310922	C₂²	semidirect
39. #72310920	C₂²	semidirect
40. #72310916	C₂²	semidirect
41. #72310908	C₂²	semidirect
42. #72284724	C₂²	semidirect
43. #72283994	C₂²	semidirect
44. #72283848	C₂	semidirect
45. #72283788	C₂²	semidirect
46. #72283765	C₂²	semidirect
47. #72283725	C₂²	semidirect
48. #72283702	C₂²	semidirect
49. #72283562	C₂²	semidirect
50. #72213831	C₂	semidirect
51. #72213808	C₂²	semidirect
52. #72213808	C₂²	semidirect
53. #72213808	C₂²	semidirect
54. #72213791	C₂²	semidirect
55. #72213791	C₂²	semidirect
56. #72213791	C₂²	semidirect
57. #72213781	C₂²	semidirect
58. #72213781	C₂²	semidirect
59. #72213781	C₂²	semidirect
60. #72213758	C₂²	semidirect
61. #72213746	C₂²	semidirect
62. #72213423	C₂²	semidirect
63. #72213362	C₂²	semidirect
64. #72213228	C₂²	semidirect
66. #10575251	D₄	semidirect
67. #8934620	C₂³	semidirect
68. #8932887	C₂³	semidirect
69. #8929993	C₂³	semidirect
70. #8928621	C₂³	semidirect
82. #6431733	D₄	semidirect
86. #485615	C₂³	semidirect
87. #485614	C₂³	semidirect
88. #485614	C₂³	semidirect
89. #485614	C₂³	semidirect
93. #417800	D₄	semidirect
95. #417798	D₄	semidirect
97. #357493	D₄	semidirect
100. #354051	D₄	semidirect
106. #251855	C₂³	semidirect
107. #251855	C₂³	semidirect
108. #251855	C₂³	semidirect
110. #251850	C₂³	semidirect
117. #213862	C₂³	semidirect
118. #213861	C₂³	semidirect
121. #150561	C₂³	semidirect
122. #150561	C₂³	semidirect
125. #149742	C₂³	semidirect
126. #134056	C₂³	semidirect
127. #134053	C₂³	semidirect
128. #130057	C₂³	semidirect
129. #130056	C₂³	semidirect
130. #130056	C₂³	semidirect
131. #130056	C₂³	semidirect
132. #94173	C₂³	semidirect
133. #94173	C₂³	semidirect
140. C₂×#3449	C₂×D₄	semidirect
142. #60645	C₂×D₄	semidirect
143. #60644	C₂×D₄	semidirect
144. C₂×#2873	C₂×D₄	semidirect
171. #23445	C₂×D₄	semidirect
173. #23406	C₂×D₄	semidirect
174. #23406	C₂×D₄	semidirect
185. C₂×#1742	C₂×D₄	semidirect
186. C₂×#1740	C₂×D₄	semidirect
189. #11007	C₂×D₄	semidirect
190. #11006	C₂×D₄	semidirect
191. #10959	C₂×D₄	semidirect
192. #10959	C₂×D₄	semidirect
193. #10939	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×#72213808	2
#72340448	2
#72340447	2
C₂×#72213781	2
#72340445	2
#72340442	2
#72340438	2
#72340434	2
#72340428	2
#72340397	2
C₂×#72213791	2
#72340238	2
#72310928	2
#72283848	2
#72213831	2