Subgroups — #72337729

Order 4096.

At least 13247 conjugacy classes of subgroups; only the 361 normal subgroups are shown.

The subgroup lattice has 335 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72337728	C₂	1	2	yes	maximal, complemented
2	#72337727	C₂	1	2	yes	maximal, complemented
3	#72337726	C₂	1	2	yes	maximal, complemented
4	#72337725	C₂	1	2	yes	maximal, complemented
5	#72337182	C₂	1	1	yes	maximal, characteristic
6	#72337181	C₄	1	1	yes	characteristic, complemented
7	#72337181	C₂²	1	1	yes	characteristic
8	#72337178	C₄	1	1	yes	characteristic, complemented
9	#72337171	C₄	1	1	yes	characteristic, complemented
10	#72337171	C₂²	1	1	yes	characteristic
11	#72321756	C₂	1	1	yes	maximal, characteristic, complemented
12	#72321737	C₂²	1	2	yes	complemented
13	#72321733	C₂²	1	2	yes	complemented
14	#72318802	C₄	1	1	yes	characteristic, complemented
15	#72318802	C₂²	1	1	yes	characteristic
16	#72309339	C₄	1	1	yes	characteristic, complemented
17	#72302685	C₂	1	1	yes	maximal, characteristic, complemented
18	#72265915	C₂²	1	2	yes	complemented
19	#72265915	C₂²	1	2	yes	complemented
20	#72240433	C₄	1	1	yes	characteristic, complemented
21	#72240433	C₂²	1	1	yes	characteristic
22	#72237770	C₂	1	1	yes	maximal, characteristic, complemented
23	#72237770	C₂	1	1	yes	maximal, characteristic, complemented
24	#72237756	C₂²	1	2	yes	complemented
25	#72237751	C₂²	1	2	yes	complemented
26	#72237734	C₂²	1	2	yes	complemented
27	#72237725	C₂²	1	2	yes	complemented
28	#72227421	C₄	1	1	yes	characteristic, complemented
29	#72226352	C₂	1	1	yes	maximal, characteristic, complemented
30	#72226352	C₂	1	1	yes	maximal, characteristic, complemented
31	#72226351	C₂²	1	2	yes	—
32	#72226351	C₂²	1	2	yes	—
33	#72225873	C₂²	1	1	yes	characteristic
34	#72225873	C₂²	1	1	yes	characteristic
35	#72225776	C₂²	1	1	yes	characteristic
36	#72225776	C₂²	1	1	yes	characteristic
37	#72225733	C₂²	1	1	yes	characteristic
38	#72225658	C₂²	1	1	yes	characteristic
39	#72217643	C₄	1	1	yes	characteristic, complemented
40	C₂×#449475	C₂²	1	1	yes	characteristic
41	#72216681	C₂²	1	2	yes	—
42	#72216681	C₂²	1	2	yes	—
43	#7642273	C₂×C₄	1	1	yes	characteristic
44	C₂²×#2846	C₂×C₄	1	1	yes	characteristic
45	C₂²×#2846	D₄	1	1	yes	characteristic
46	C₂²×#2846	D₄	1	1	yes	characteristic
47	C₂×#35346	C₂³	1	1	yes	characteristic
48	#6451874	D₄	1	1	yes	characteristic
49	#6451874	D₄	1	1	yes	characteristic
50	#6370693	D₄	1	1	yes	characteristic
51	#6370693	D₄	1	1	yes	characteristic
52	#479829	C₂×C₄	1	1	yes	characteristic, complemented
53	#479829	C₂×C₄	1	1	yes	characteristic, complemented
54	#478249	C₂×C₄	1	1	yes	characteristic, complemented
55	#478249	C₂×C₄	1	1	yes	characteristic, complemented
56	#449475	C₂×C₄	1	1	yes	characteristic
57	#449475	C₂×C₄	1	1	yes	characteristic
58	#449475	D₄	1	1	yes	characteristic
59	#449475	D₄	1	1	yes	characteristic
60	#449475	D₄	1	1	yes	characteristic
61	#449475	D₄	1	1	yes	characteristic
62	#449475	C₂³	1	1	yes	characteristic
63	#449475	C₂³	1	1	yes	characteristic
64	#417896	C₂×C₄	1	1	yes	characteristic
65	#417896	D₄	1	1	yes	characteristic
66	#417896	D₄	1	1	yes	characteristic
67	#417896	C₂³	1	1	yes	characteristic
68	#417890	C₂×C₄	1	1	yes	characteristic, complemented
69	#417890	C₂×C₄	1	1	yes	characteristic, complemented
70	#417824	C₂×C₄	1	1	yes	characteristic
71	#417824	D₄	1	1	yes	characteristic
72	#417824	D₄	1	1	yes	characteristic
73	#417824	C₂³	1	1	yes	characteristic
74	#417744	C₂×C₄	1	1	yes	characteristic, complemented
75	#417744	C₂×C₄	1	1	yes	characteristic, complemented
76	#391692	C₂×C₄	1	1	yes	characteristic, complemented
77	#391692	C₂×C₄	1	1	yes	characteristic, complemented
78	#387715	C₂×C₄	1	1	yes	characteristic, complemented
79	#387715	C₂×C₄	1	1	yes	characteristic, complemented
80	#386017	C₂×C₄	1	1	yes	characteristic, complemented
81	#386017	C₂×C₄	1	1	yes	characteristic, complemented
82	#382707	D₄	1	1	yes	characteristic
83	#382707	D₄	1	1	yes	characteristic
84	#382422	C₂×C₄	1	1	yes	characteristic
85	#382422	C₂×C₄	1	1	yes	characteristic
86	#382422	C₂×C₄	1	1	yes	characteristic
87	#379806	C₂×C₄	1	1	yes	characteristic
88	#379806	C₂×C₄	1	1	yes	characteristic
89	#379806	D₄	1	1	yes	characteristic
90	#379806	D₄	1	1	yes	characteristic
91	#379806	D₄	1	1	yes	characteristic
92	#379806	D₄	1	1	yes	characteristic
93	#379806	C₂³	1	1	yes	characteristic
94	#379806	C₂³	1	1	yes	characteristic
95	#374022	C₂×C₄	1	1	yes	characteristic, complemented
96	#374022	C₂×C₄	1	1	yes	characteristic, complemented
97	#359705	D₄	1	1	yes	characteristic
98	#359705	D₄	1	1	yes	characteristic
99	C₂×#10965	C₂×C₄	1	1	yes	characteristic
100	C₂×#10965	D₄	1	1	yes	characteristic
101	C₂×#10965	D₄	1	1	yes	characteristic
102	#213829	C₂³	1	2	yes	—
103	#213828	C₂³	1	2	yes	—
104	#134045	C₂³	1	2	yes	—
105	#134045	C₂³	1	2	yes	—
106	C₂⁸	C₂²⋊C₄	1	1	yes	characteristic
107	C₂³×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
108	C₂×#3490	C₂²⋊C₄	1	1	yes	characteristic
109	C₂³×#120	C₂²×C₄	1	1	yes	characteristic
110	C₂³×#120	C₂×D₄	1	1	yes	characteristic
111	C₂³×#120	C₂×D₄	1	1	yes	characteristic
112	C₂×#2883	C₂²⋊C₄	1	1	yes	characteristic
113	C₂×#2883	C₂²⋊C₄	1	1	yes	characteristic
114	C₂×#2883	C₂×D₄	1	1	yes	characteristic
115	C₂×#2883	C₂×D₄	1	1	yes	characteristic
116	C₂×#2846	C₂²⋊C₄	1	1	yes	characteristic
117	C₂×#2846	C₂²⋊C₄	1	1	yes	characteristic
118	C₂×#2846	C₂²⋊C₄	1	1	yes	characteristic
119	C₂×#2846	C₂²⋊C₄	1	1	yes	characteristic
120	C₂×#2846	C₂²⋊C₄	1	1	yes	characteristic
121	C₂×#2846	C₂²⋊C₄	1	1	yes	characteristic
122	C₂×#2846	C₂²×C₄	1	1	yes	characteristic
123	C₂×#2846	C₂²×C₄	1	1	yes	characteristic
124	C₂×#2846	C₂×D₄	1	1	yes	characteristic
125	C₂×#2846	C₂×D₄	1	1	yes	characteristic
126	C₂×#2846	C₂×D₄	1	1	yes	characteristic
127	C₂×#2846	C₂×D₄	1	1	yes	characteristic
128	#35390	C₂²⋊C₄	1	1	yes	characteristic
129	#35390	C₂²×C₄	1	1	yes	characteristic
130	#35367	C₂²⋊C₄	1	1	yes	characteristic
131	#35367	C₂²×C₄	1	1	yes	characteristic
132	#35346	C₂²×C₄	1	1	yes	characteristic
133	#35346	C₂×D₄	1	1	yes	characteristic
134	#35346	C₂×D₄	1	1	yes	characteristic
135	#35346	C₂×D₄	1	1	yes	characteristic
136	#35346	C₂×D₄	1	1	yes	characteristic
137	#35346	C₂×D₄	1	1	yes	characteristic
138	#35346	C₂×D₄	1	1	yes	characteristic
139	#35346	C₂⁴	1	1	yes	characteristic
140	#34176	C₂²⋊C₄	1	1	yes	characteristic
141	C₂×#2308	C₂×D₄	1	1	yes	characteristic
142	C₂×#2308	C₂×D₄	1	1	yes	characteristic
143	C₂×#2308	C₂×D₄	1	1	yes	characteristic
144	C₂²×#379	C₂²⋊C₄	1	1	yes	characteristic
145	C₂²×#379	C₂²⋊C₄	1	1	yes	characteristic
146	C₂²×#379	C₂²⋊C₄	1	1	yes	characteristic
147	#23468	C₂²⋊C₄	1	1	yes	characteristic
148	#23468	C₂²⋊C₄	1	1	yes	characteristic
149	#23468	C₂×D₄	1	1	yes	characteristic
150	#23468	C₂×D₄	1	1	yes	characteristic
151	#23444	C₂²⋊C₄	1	1	yes	characteristic
152	#23444	C₂²⋊C₄	1	1	yes	characteristic
153	#23444	C₂×D₄	1	1	yes	characteristic
154	#23444	C₂×D₄	1	1	yes	characteristic
155	C₂×#1819	C₂²⋊C₄	1	1	yes	characteristic
156	C₂×#1819	C₂²⋊C₄	1	1	yes	characteristic
157	#20585	C₂²⋊C₄	1	1	yes	characteristic
158	#20585	C₂²⋊C₄	1	1	yes	characteristic
159	#20585	C₂×D₄	1	1	yes	characteristic
160	#20585	C₂×D₄	1	1	yes	characteristic
161	C₂×#1781	C₂²⋊C₄	1	1	yes	characteristic
162	C₂×#1781	C₂²⋊C₄	1	1	yes	characteristic
163	C₂×#1781	C₂²⋊C₄	1	1	yes	characteristic
164	C₂×#1781	C₂²⋊C₄	1	1	yes	characteristic
165	#11166	C₂²⋊C₄	1	1	yes	characteristic
166	#11166	C₂²⋊C₄	1	1	yes	characteristic
167	#11166	C₂²⋊C₄	1	1	yes	characteristic
168	#11166	C₂²⋊C₄	1	1	yes	characteristic
169	#11166	C₂×D₄	1	1	yes	characteristic
170	#11166	C₂×D₄	1	1	yes	characteristic
171	#11166	C₂×D₄	1	1	yes	characteristic
172	#11166	C₂×D₄	1	1	yes	characteristic
173	#10965	C₂²⋊C₄	1	1	yes	characteristic
174	#10965	C₂²⋊C₄	1	1	yes	characteristic
175	#10965	C₂²⋊C₄	1	1	yes	characteristic
176	#10965	C₂²⋊C₄	1	1	yes	characteristic
177	#10965	C₂²⋊C₄	1	1	yes	characteristic
178	#10965	C₂²⋊C₄	1	1	yes	characteristic
179	#10965	C₂²⋊C₄	1	1	yes	characteristic
180	#10965	C₂²⋊C₄	1	1	yes	characteristic
181	#10965	C₂²⋊C₄	1	1	yes	characteristic
182	#10965	C₂²⋊C₄	1	1	yes	characteristic
183	#10965	C₂²⋊C₄	1	1	yes	characteristic
184	#10965	C₂²⋊C₄	1	1	yes	characteristic
185	#10965	C₂²×C₄	1	1	yes	characteristic
186	#10965	C₂²×C₄	1	1	yes	characteristic
187	#10965	C₂²×C₄	1	1	yes	characteristic
188	#10965	C₂²×C₄	1	1	yes	characteristic
189	#10965	C₂²×C₄	1	1	yes	characteristic
190	#10965	C₂²×C₄	1	1	yes	characteristic
191	#10965	C₂²×C₄	1	1	yes	characteristic
192	#10965	C₂²×C₄	1	1	yes	characteristic
193	#10965	C₂×D₄	1	1	yes	characteristic
194	#10965	C₂×D₄	1	1	yes	characteristic
195	#10965	C₂×D₄	1	1	yes	characteristic
196	#10965	C₂×D₄	1	1	yes	characteristic
197	#10938	C₂²⋊C₄	1	1	yes	characteristic
198	#10938	C₂²⋊C₄	1	1	yes	characteristic
199	#10938	C₂²⋊C₄	1	1	yes	characteristic
200	#10938	C₂²⋊C₄	1	1	yes	characteristic
201	#10938	C₂×D₄	1	1	yes	characteristic
202	#10938	C₂×D₄	1	1	yes	characteristic
203	#10938	C₂×D₄	1	1	yes	characteristic
204	#10938	C₂×D₄	1	1	yes	characteristic
205	C₂⁷	C₂×C₂²⋊C₄	1	1	yes	characteristic
206	C₂⁷	C₂×C₂²⋊C₄	1	1	yes	characteristic
207	C₂⁷	C₂×C₂²⋊C₄	1	1	yes	characteristic
208	C₂²×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	1	yes	characteristic
209	C₂²×H(5,𝔽₂)	#120	1	1	yes	characteristic
210	C₂²×H(5,𝔽₂)	#120	1	1	yes	characteristic
211	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
212	C₂⁴×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
213	C₂⁴×D₄	#120	1	1	yes	characteristic
214	C₂⁴×D₄	#120	1	1	yes	characteristic
215	C₂×#543	C₂×C₂²⋊C₄	1	1	yes	characteristic
216	C₂×#534	C₂×C₂²⋊C₄	1	1	yes	characteristic
217	C₂²×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
218	C₂²×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
219	C₂²×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
220	C₂²×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
221	C₂²×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
222	C₂²×#120	#120	1	1	yes	characteristic
223	C₂²×#120	#120	1	1	yes	characteristic
224	C₂²×#120	#120	1	1	yes	characteristic
225	C₂²×#120	#120	1	1	yes	characteristic
226	C₂²×#120	C₂³×C₄	1	1	yes	characteristic
227	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
228	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
229	C₂³×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
230	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
231	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
232	C₂²×#99	C₂×C₂²⋊C₄	1	1	yes	characteristic
233	C₂²×#99	C₂×C₂²⋊C₄	1	1	yes	characteristic
234	C₂²×#99	C₂×C₂²⋊C₄	1	1	yes	characteristic
235	C₂²×#99	C₂×C₂²⋊C₄	1	1	yes	characteristic
236	C₂²×#99	C₂×C₂²⋊C₄	1	1	yes	characteristic
237	C₂²×#99	C₂×C₂²⋊C₄	1	1	yes	characteristic
238	C₂²×#99	C₂×C₂²⋊C₄	1	1	yes	characteristic
239	C₂²×#99	C₂×C₂²⋊C₄	1	1	yes	characteristic
240	#2308	C₂×C₂²⋊C₄	1	1	yes	characteristic
241	#2308	C₂×C₂²⋊C₄	1	1	yes	characteristic
242	#2308	C₂×C₂²⋊C₄	1	1	yes	characteristic
243	#2308	#120	1	1	yes	characteristic
244	#2308	#120	1	1	yes	characteristic
245	#2308	#120	1	1	yes	characteristic
246	#2308	#120	1	1	yes	characteristic
247	#2308	#120	1	1	yes	characteristic
248	#2308	#120	1	1	yes	characteristic
249	#2308	C₂²×D₄	1	1	yes	characteristic
250	#2308	C₂²×D₄	1	1	yes	characteristic
251	#2308	C₂²×D₄	1	1	yes	characteristic
252	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
253	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
254	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
255	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
256	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
257	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
258	#2273	C₂×C₂²⋊C₄	1	1	yes	characteristic
259	#2273	C₂×C₂²⋊C₄	1	1	yes	characteristic
260	C₂×#342	C₂×C₂²⋊C₄	1	1	yes	characteristic
261	C₂×#342	C₂×C₂²⋊C₄	1	1	yes	characteristic
262	C₂×#342	C₂×C₂²⋊C₄	1	1	yes	characteristic
263	C₂×#342	C₂×C₂²⋊C₄	1	1	yes	characteristic
264	C₂⁶	#379	1	1	yes	characteristic
265	C₂⁶	#379	1	1	yes	characteristic
266	C₂⁶	#410	1	1	yes	characteristic
267	C₂⁶	B(4,𝔽₂)	1	1	yes	characteristic
268	C₂⁶	B(4,𝔽₂)	1	1	yes	characteristic
269	C₂⁶	C₂²×C₂²⋊C₄	1	1	yes	characteristic
270	C₂³×D₄	#379	1	1	yes	characteristic
271	C₂³×D₄	#379	1	1	yes	characteristic
272	C₂³×D₄	#379	1	1	yes	characteristic
273	C₂³×D₄	#410	1	1	yes	characteristic
274	C₂³×D₄	#410	1	1	yes	characteristic
275	C₂³×D₄	B(4,𝔽₂)	1	1	yes	characteristic
276	C₂³×D₄	B(4,𝔽₂)	1	1	yes	characteristic
277	C₂³×D₄	#458	1	1	yes	characteristic
278	C₂³×D₄	#458	1	1	yes	characteristic
279	C₂³×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
280	C₂³×D₄	C₂×#120	1	1	yes	characteristic
281	C₂³×D₄	C₂×#120	1	1	yes	characteristic
282	C₂⁴×C₄	#410	1	1	yes	characteristic
283	C₂⁴×C₄	#458	1	1	yes	characteristic
284	C₂⁴×C₄	#458	1	1	yes	characteristic
285	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
286	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
287	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
288	C₂²×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
289	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
290	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
291	C₂⁵	#1782	1	1	yes	characteristic
292	C₂⁵	#1782	1	1	yes	characteristic
293	C₂⁵	#1782	1	1	yes	characteristic
294	C₂⁵	#1790	1	1	yes	characteristic
295	C₂⁵	#1790	1	1	yes	characteristic
296	C₂⁵	#1790	1	1	yes	characteristic
297	C₂⁵	#1790	1	1	yes	characteristic
298	C₂⁵	#1790	1	1	yes	characteristic
299	C₂⁵	#1790	1	1	yes	characteristic
300	C₂⁵	C₂×#379	1	1	yes	characteristic
301	C₂⁵	C₂×#410	1	1	yes	characteristic
302	C₂⁵	C₂×B(4,𝔽₂)	1	1	yes	characteristic
303	C₂⁵	C₂×B(4,𝔽₂)	1	1	yes	characteristic
304	C₂³×C₄	#1782	1	1	yes	characteristic
305	C₂³×C₄	#1790	1	1	yes	characteristic
306	C₂³×C₄	#1790	1	1	yes	characteristic
307	C₂³×C₄	C₂×#410	1	1	yes	characteristic
308	C₂³×C₄	C₂×#458	1	1	yes	characteristic
309	C₂³×C₄	C₂×#458	1	1	yes	characteristic
310	C₂⁴	#8535	1	1	yes	characteristic
311	C₂⁴	#8535	1	1	yes	characteristic
312	C₂⁴	#8535	1	1	yes	characteristic
313	C₂⁴	#8535	1	1	yes	characteristic
314	C₂⁴	#12725	1	2	yes	—
315	C₂⁴	#12725	1	2	yes	—
316	C₂⁴	#12753	1	2	yes	—
317	C₂⁴	C₂×#1782	1	1	yes	characteristic
318	C₂⁴	C₂×#1790	1	1	yes	characteristic
319	C₂⁴	C₂×#1790	1	1	yes	characteristic
320	C₂⁴	#33551	1	2	yes	—
321	C₂³	#133422	1	2	yes	—
322	C₂³	#133422	1	2	yes	—
323	C₂³	C₂×#8535	1	1	yes	characteristic
324	C₂³	C₂×#12725	1	1	yes	characteristic
325	C₂³	C₂×#12725	1	1	yes	characteristic
326	C₂³	C₂×#12753	1	1	yes	characteristic
327	C₂³	#493562	1	1	yes	characteristic
328	C₂³	#493582	1	1	yes	characteristic
329	C₂³	#493594	1	1	yes	characteristic
330	C₂²	#72265770	1	1	yes	characteristic
331	C₂²	#72265773	1	1	yes	characteristic
332	C₂²	C₂×#133422	1	1	yes	characteristic
333	C₂	#72266700	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	#72266700
commutator	C₂²×#120	C₂³×C₄
Frattini, cosocle	#35346	C₂⁴
prime radical	#72337182	C₂
LCS	G ▷ C₂²×#120 ▷ C₂⁵ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂³ ◁ C₂⁶ ◁ C₂×#35346 ◁ G
LECS	G ▷ #35346 ▷ C₂⁵ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72337728	C₂	semidirect
2. #72337727	C₂	semidirect
3. #72337726	C₂	semidirect
4. #72337725	C₂	semidirect
6. #72337181	C₄	semidirect
8. #72337178	C₄	semidirect
9. #72337171	C₄	semidirect
11. #72321756	C₂	semidirect
12. #72321737	C₂²	semidirect
13. #72321733	C₂²	semidirect
14. #72318802	C₄	semidirect
16. #72309339	C₄	semidirect
17. #72302685	C₂	semidirect
18. #72265915	C₂²	semidirect
19. #72265915	C₂²	semidirect
20. #72240433	C₄	semidirect
22. #72237770	C₂	semidirect
23. #72237770	C₂	semidirect
24. #72237756	C₂²	semidirect
25. #72237751	C₂²	semidirect
26. #72237734	C₂²	semidirect
27. #72237725	C₂²	semidirect
28. #72227421	C₄	semidirect
29. #72226352	C₂	semidirect
30. #72226352	C₂	semidirect
39. #72217643	C₄	semidirect
52. #479829	C₂×C₄	semidirect
53. #479829	C₂×C₄	semidirect
54. #478249	C₂×C₄	semidirect
55. #478249	C₂×C₄	semidirect
68. #417890	C₂×C₄	semidirect
69. #417890	C₂×C₄	semidirect
74. #417744	C₂×C₄	semidirect
75. #417744	C₂×C₄	semidirect
76. #391692	C₂×C₄	semidirect
77. #391692	C₂×C₄	semidirect
78. #387715	C₂×C₄	semidirect
79. #387715	C₂×C₄	semidirect
80. #386017	C₂×C₄	semidirect
81. #386017	C₂×C₄	semidirect
95. #374022	C₂×C₄	semidirect
96. #374022	C₂×C₄	semidirect

Maximal subgroups

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

subgroup	index
#72337728	2
#72337727	2
#72337726	2
#72337725	2
#72337182	2
#72321756	2
#72302685	2
#72237770	2
#72226352	2