Subgroups — #72310536

Order 4096.

At least 13148 conjugacy classes of subgroups; only the 377 normal subgroups are shown.

The subgroup lattice has 343 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72310535	C₂	1	1	yes	maximal, characteristic, complemented
2	#72310532	C₂	1	1	yes	maximal, characteristic, complemented
3	#72310530	C₂	1	2	yes	maximal, complemented
4	#72310529	C₂	1	2	yes	maximal, complemented
5	#72310528	C₂	1	2	yes	maximal, complemented
6	#72310527	C₂²	1	2	yes	complemented
7	#72310526	C₂²	1	2	yes	complemented
8	#72310525	C₂	1	2	yes	maximal, complemented
9	#72310524	C₂²	1	2	yes	—
10	#72310523	C₂²	1	2	yes	—
11	#72310517	C₂	1	1	yes	maximal, characteristic, complemented
12	#72310516	C₂²	1	2	yes	—
13	#72310515	C₂²	1	2	yes	complemented
14	#72309392	C₂	1	1	yes	maximal, characteristic, complemented
15	#72309391	C₂²	1	2	yes	complemented
16	#72302062	C₂	1	1	yes	maximal, characteristic, complemented
17	#72302061	C₂²	1	2	yes	complemented
18	#72265929	C₂²	1	2	yes	—
19	#72237770	C₂	1	1	yes	maximal, characteristic, complemented
20	#72237769	C₂	1	1	yes	maximal, characteristic
21	#72237754	C₂²	1	1	yes	characteristic
22	#72237754	C₂²	1	1	yes	characteristic
23	#72237749	C₄	1	1	yes	characteristic, complemented
24	#72237746	C₄	1	1	yes	characteristic, complemented
25	#72237746	C₄	1	1	yes	characteristic, complemented
26	#72237743	C₄	1	1	yes	characteristic, complemented
27	#72237740	C₄	1	1	yes	characteristic, complemented
28	#72237734	C₂²	1	2	yes	complemented
29	#72237732	C₄	1	1	yes	characteristic, complemented
30	#72237732	C₄	1	1	yes	characteristic, complemented
31	#72237725	C₂²	1	2	yes	—
32	#72237724	C₄	1	1	yes	characteristic, complemented
33	C₂×#97550	C₂²	1	1	yes	characteristic, complemented
34	#72225873	C₂²	1	1	yes	characteristic, complemented
35	#72225777	C₂²	1	1	yes	characteristic, complemented
36	#72225776	C₂²	1	1	yes	characteristic, complemented
37	#72225733	C₂²	1	1	yes	characteristic
38	#72225733	C₂²	1	1	yes	characteristic
39	#72225655	C₂²	1	1	yes	characteristic
40	#72216697	C₂²	1	2	yes	—
41	#72210507	C₂²	1	1	yes	characteristic
42	#72210026	C₂²	1	1	yes	characteristic
43	#10586066	D₄	1	1	yes	characteristic
44	#7642273	D₄	1	1	yes	characteristic
45	#7642273	D₄	1	1	yes	characteristic
46	#7642244	D₄	1	1	yes	characteristic
47	#7642244	D₄	1	1	yes	characteristic
48	C₂×#35346	C₂³	1	1	yes	characteristic
49	#7513948	C₂×C₄	1	1	yes	characteristic, complemented
50	#7513948	C₂×C₄	1	1	yes	characteristic, complemented
51	#6631461	C₂×C₄	1	1	yes	characteristic, complemented
52	#6629262	D₄	1	1	yes	characteristic
53	#6629262	C₂³	1	1	yes	characteristic
54	#6628896	D₄	1	1	yes	characteristic
55	#6628896	C₂³	1	1	yes	characteristic
56	#6451874	C₂×C₄	1	1	yes	characteristic
57	#6451874	C₂×C₄	1	1	yes	characteristic
58	#6451874	D₄	1	1	yes	characteristic
59	#6451874	D₄	1	1	yes	characteristic
60	#6437629	C₂×C₄	1	1	yes	characteristic, complemented
61	#6432953	C₂×C₄	1	1	yes	characteristic
62	#6432953	C₂×C₄	1	1	yes	characteristic
63	#6432953	D₄	1	1	yes	characteristic
64	#6432953	D₄	1	1	yes	characteristic
65	#6374210	C₂×C₄	1	1	yes	characteristic
66	#6374210	C₂×C₄	1	1	yes	characteristic
67	#6370693	D₄	1	1	yes	characteristic
68	#449090	C₂×C₄	1	1	yes	characteristic, complemented
69	#449090	C₂×C₄	1	1	yes	characteristic, complemented
70	#436464	C₂×C₄	1	1	yes	characteristic, complemented
71	#436464	C₂×C₄	1	1	yes	characteristic, complemented
72	#432839	C₂×C₄	1	1	yes	characteristic, complemented
73	#432839	C₂×C₄	1	1	yes	characteristic, complemented
74	#418911	C₂×C₄	1	1	yes	characteristic, complemented
75	#418911	C₂×C₄	1	1	yes	characteristic, complemented
76	#417896	C₂×C₄	1	1	yes	characteristic
77	#417896	C₂×C₄	1	1	yes	characteristic
78	#417896	D₄	1	1	yes	characteristic
79	#417896	D₄	1	1	yes	characteristic
80	#417896	D₄	1	1	yes	characteristic
81	#417896	D₄	1	1	yes	characteristic
82	#417896	C₂³	1	1	yes	characteristic
83	#417896	C₂³	1	1	yes	characteristic
84	#417824	C₂×C₄	1	1	yes	characteristic
85	#417824	C₂×C₄	1	1	yes	characteristic
86	#417824	D₄	1	1	yes	characteristic
87	#417824	D₄	1	1	yes	characteristic
88	#417824	D₄	1	1	yes	characteristic
89	#417824	D₄	1	1	yes	characteristic
90	#417824	C₂³	1	1	yes	characteristic
91	#417824	C₂³	1	1	yes	characteristic
92	#388001	C₂×C₄	1	1	yes	characteristic, complemented
93	#388001	C₂×C₄	1	1	yes	characteristic, complemented
94	#382422	D₄	1	1	yes	characteristic
95	#382422	D₄	1	1	yes	characteristic
96	#359705	C₂×C₄	1	1	yes	characteristic
97	#359705	C₂×C₄	1	1	yes	characteristic
98	#359705	D₄	1	1	yes	characteristic
99	#359705	D₄	1	1	yes	characteristic
100	#357285	C₂×C₄	1	1	yes	characteristic, complemented
101	#356055	C₂×C₄	1	1	yes	characteristic, complemented
102	#213890	C₂³	1	2	yes	—
103	#213829	C₂³	1	2	yes	—
104	#134045	C₂³	1	2	yes	—
105	#97550	C₂³	1	2	yes	—
106	C₂×H(7,𝔽₂)	C₂×D₄	1	1	yes	characteristic
107	C₂³×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
108	#62842	C₂²⋊C₄	1	1	yes	characteristic
109	#62842	C₂²⋊C₄	1	1	yes	characteristic
110	C₂×#3490	C₂²⋊C₄	1	1	yes	characteristic
111	C₂×#3490	C₂²⋊C₄	1	1	yes	characteristic
112	C₂×#3484	C₂²⋊C₄	1	1	yes	characteristic
113	C₂×#3484	C₂²⋊C₄	1	1	yes	characteristic
114	C₂³×#120	C₂×D₄	1	1	yes	characteristic
115	C₂³×#120	C₂×D₄	1	1	yes	characteristic
116	C₂³×#120	C₂×D₄	1	1	yes	characteristic
117	#62652	C₂×D₄	1	1	yes	characteristic
118	#35390	C₂²⋊C₄	1	1	yes	characteristic
119	#35390	C₂²⋊C₄	1	1	yes	characteristic
120	#35390	C₂×D₄	1	1	yes	characteristic
121	#35390	C₂×D₄	1	1	yes	characteristic
122	#35367	C₂²⋊C₄	1	1	yes	characteristic
123	#35367	C₂²⋊C₄	1	1	yes	characteristic
124	#35367	C₂×D₄	1	1	yes	characteristic
125	#35367	C₂×D₄	1	1	yes	characteristic
126	#35350	C₂²⋊C₄	1	1	yes	characteristic
127	#35350	C₂²⋊C₄	1	1	yes	characteristic
128	#35350	C₂×D₄	1	1	yes	characteristic
129	#35350	C₂×D₄	1	1	yes	characteristic
130	#35346	C₂²⋊C₄	1	1	yes	characteristic
131	#35346	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	C₂×D₄	1	1	yes	characteristic
140	#35346	C₂×D₄	1	1	yes	characteristic
141	#35346	C₂⁴	1	1	yes	characteristic
142	#34176	C₂²⋊C₄	1	1	yes	characteristic
143	#34176	C₂²⋊C₄	1	1	yes	characteristic
144	#34171	C₂²⋊C₄	1	1	yes	characteristic
145	#34171	C₂²⋊C₄	1	1	yes	characteristic
146	C₂×#2308	C₂²×C₄	1	1	yes	characteristic
147	C₂×#2308	C₂×D₄	1	1	yes	characteristic
148	C₂×#2308	C₂×D₄	1	1	yes	characteristic
149	#23468	C₂²⋊C₄	1	1	yes	characteristic
150	#23468	C₂²⋊C₄	1	1	yes	characteristic
151	#23468	C₂²⋊C₄	1	1	yes	characteristic
152	#23468	C₂²⋊C₄	1	1	yes	characteristic
153	#23468	C₂²×C₄	1	1	yes	characteristic
154	#23468	C₂²×C₄	1	1	yes	characteristic
155	#23468	C₂×D₄	1	1	yes	characteristic
156	#23468	C₂×D₄	1	1	yes	characteristic
157	#23444	C₂²⋊C₄	1	1	yes	characteristic
158	#23444	C₂²⋊C₄	1	1	yes	characteristic
159	#23444	C₂²⋊C₄	1	1	yes	characteristic
160	#23444	C₂²⋊C₄	1	1	yes	characteristic
161	#23444	C₂²×C₄	1	1	yes	characteristic
162	#23444	C₂²×C₄	1	1	yes	characteristic
163	#23444	C₂×D₄	1	1	yes	characteristic
164	#23444	C₂×D₄	1	1	yes	characteristic
165	#20689	C₂²⋊C₄	1	1	yes	characteristic
166	#20689	C₂²⋊C₄	1	1	yes	characteristic
167	#20689	C₂²×C₄	1	1	yes	characteristic
168	#20689	C₂²×C₄	1	1	yes	characteristic
169	C₂×#1819	C₂²⋊C₄	1	1	yes	characteristic
170	C₂×#1819	C₂²⋊C₄	1	1	yes	characteristic
171	C₂×#1819	C₂²⋊C₄	1	1	yes	characteristic
172	C₂×#1819	C₂²⋊C₄	1	1	yes	characteristic
173	#20585	C₂²⋊C₄	1	1	yes	characteristic
174	#20585	C₂²⋊C₄	1	1	yes	characteristic
175	#20585	C₂²⋊C₄	1	1	yes	characteristic
176	#20585	C₂²⋊C₄	1	1	yes	characteristic
177	#20585	C₂²×C₄	1	1	yes	characteristic
178	#20585	C₂²×C₄	1	1	yes	characteristic
179	#20585	C₂×D₄	1	1	yes	characteristic
180	#20585	C₂×D₄	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	C₂×D₄	1	1	yes	characteristic
186	#10965	C₂×D₄	1	1	yes	characteristic
187	#10965	C₂×D₄	1	1	yes	characteristic
188	#10965	C₂×D₄	1	1	yes	characteristic
189	#10938	C₂²⋊C₄	1	1	yes	characteristic
190	#10938	C₂²⋊C₄	1	1	yes	characteristic
191	#10938	C₂²⋊C₄	1	1	yes	characteristic
192	#10938	C₂²⋊C₄	1	1	yes	characteristic
193	#10938	C₂²⋊C₄	1	1	yes	characteristic
194	#10938	C₂²⋊C₄	1	1	yes	characteristic
195	#10938	C₂²⋊C₄	1	1	yes	characteristic
196	#10938	C₂²⋊C₄	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	#120	1	1	yes	characteristic
206	C₂²×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	1	yes	characteristic
207	C₂²×H(5,𝔽₂)	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×#543	C₂×C₂²⋊C₄	1	1	yes	characteristic
217	C₂×#535	#99	1	2	yes	—
218	C₂×#534	C₂×C₂²⋊C₄	1	1	yes	characteristic
219	C₂×#534	C₂×C₂²⋊C₄	1	1	yes	characteristic
220	C₂×#525	#99	1	2	yes	—
221	C₂²×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
222	C₂²×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
223	C₂²×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
224	C₂²×#120	#120	1	1	yes	characteristic
225	C₂²×#120	#120	1	1	yes	characteristic
226	C₂²×#120	#120	1	1	yes	characteristic
227	C₂²×#120	#120	1	1	yes	characteristic
228	C₂²×#120	#120	1	1	yes	characteristic
229	C₂²×#120	#120	1	1	yes	characteristic
230	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
231	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
232	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
233	C₂×#518	C₂×C₂²⋊C₄	1	1	yes	characteristic
234	C₂×#518	C₂×C₂²⋊C₄	1	1	yes	characteristic
235	C₂³×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
236	C₂³×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
237	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
238	#2309	#99	1	2	yes	—
239	#2308	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	C₂×C₂²⋊C₄	1	1	yes	characteristic
244	#2308	C₂×C₂²⋊C₄	1	1	yes	characteristic
245	#2308	C₂×C₂²⋊C₄	1	1	yes	characteristic
246	#2308	C₂×C₂²⋊C₄	1	1	yes	characteristic
247	#2308	C₂×C₂²⋊C₄	1	1	yes	characteristic
248	#2308	#120	1	1	yes	characteristic
249	#2308	#120	1	1	yes	characteristic
250	#2308	#120	1	1	yes	characteristic
251	#2308	#120	1	1	yes	characteristic
252	#2308	C₂³×C₄	1	1	yes	characteristic
253	#2308	C₂²×D₄	1	1	yes	characteristic
254	#2308	C₂²×D₄	1	1	yes	characteristic
255	C₂×#379	#99	1	2	yes	—
256	#2273	C₂×C₂²⋊C₄	1	1	yes	characteristic
257	#2273	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	C₂×#342	C₂×C₂²⋊C₄	1	1	yes	characteristic
265	C₂×#342	C₂×C₂²⋊C₄	1	1	yes	characteristic
266	C₂×#342	C₂×C₂²⋊C₄	1	1	yes	characteristic
267	C₂×#342	C₂×C₂²⋊C₄	1	1	yes	characteristic
268	C₂⁶	#379	1	1	yes	characteristic
269	C₂⁶	#379	1	1	yes	characteristic
270	C₂⁶	C₂×#99	1	1	yes	characteristic
271	C₂⁶	B(4,𝔽₂)	1	1	yes	characteristic
272	C₂⁶	#458	1	1	yes	characteristic
273	C₂⁶	C₂×#120	1	1	yes	characteristic
274	C₂²×#41	C₂×#99	1	2	yes	—
275	C₂³×D₄	#379	1	1	yes	characteristic
276	C₂³×D₄	#379	1	1	yes	characteristic
277	C₂³×D₄	#379	1	1	yes	characteristic
278	C₂³×D₄	C₂×#99	1	1	yes	characteristic
279	C₂³×D₄	C₂×#99	1	1	yes	characteristic
280	C₂³×D₄	B(4,𝔽₂)	1	1	yes	characteristic
281	C₂³×D₄	B(4,𝔽₂)	1	1	yes	characteristic
282	C₂³×D₄	#458	1	1	yes	characteristic
283	C₂³×D₄	#458	1	1	yes	characteristic
284	C₂³×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
285	C₂³×D₄	C₂×#120	1	1	yes	characteristic
286	C₂³×D₄	C₂×#120	1	1	yes	characteristic
287	C₂⁴×C₄	C₂×#99	1	1	yes	characteristic
288	C₂⁴×C₄	B(4,𝔽₂)	1	1	yes	characteristic
289	C₂⁴×C₄	#458	1	1	yes	characteristic
290	C₂×#117	C₂×#99	1	2	yes	—
291	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
292	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
293	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
294	C₂²×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
295	C₂²×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
296	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
297	#379	C₂×#99	1	2	yes	—
298	#379	C₂×#99	1	2	yes	—
299	C₂⁵	#1781	1	1	yes	characteristic
300	C₂⁵	#1781	1	1	yes	characteristic
301	C₂⁵	#1781	1	1	yes	characteristic
302	C₂⁵	#1790	1	1	yes	characteristic
303	C₂⁵	#1790	1	1	yes	characteristic
304	C₂⁵	#1790	1	1	yes	characteristic
305	C₂⁵	#1790	1	1	yes	characteristic
306	C₂⁵	#1790	1	1	yes	characteristic
307	C₂⁵	#1790	1	1	yes	characteristic
308	C₂⁵	C₂×#379	1	1	yes	characteristic
309	C₂⁵	C₂²×#99	1	1	yes	characteristic
310	C₂⁵	C₂×B(4,𝔽₂)	1	1	yes	characteristic
311	C₂⁵	C₂×#458	1	1	yes	characteristic
312	C₂²×Q₈	#2127	1	2	yes	complemented
313	C₂²×D₄	#2127	1	2	yes	complemented
314	C₂³×C₄	#1781	1	1	yes	characteristic
315	C₂³×C₄	#1790	1	1	yes	characteristic
316	C₂³×C₄	#1790	1	1	yes	characteristic
317	C₂³×C₄	C₂²×#99	1	1	yes	characteristic
318	C₂³×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
319	C₂³×C₄	C₂×#458	1	1	yes	characteristic
320	C₂⁴	#8534	1	1	yes	characteristic
321	C₂⁴	#8534	1	1	yes	characteristic
322	C₂⁴	#8534	1	1	yes	characteristic
323	C₂⁴	#8534	1	1	yes	characteristic
324	C₂⁴	#12707	1	2	yes	—
325	C₂⁴	C₂×#1781	1	1	yes	characteristic
326	C₂⁴	C₂×#1790	1	1	yes	characteristic
327	C₂⁴	C₂×#1790	1	1	yes	characteristic
328	C₂⁴	#33551	1	2	yes	—
329	C₂²×C₄	C₂×#2127	1	2	yes	—
330	C₂²×C₄	#33551	1	2	yes	—
331	C₂³	C₂×#8534	1	1	yes	characteristic
332	C₂³	#493370	1	1	yes	characteristic
333	C₂³	C₂×#12707	1	1	yes	characteristic
334	C₂³	#493562	1	1	yes	characteristic
335	C₂³	#493562	1	1	yes	characteristic
336	C₂³	#493582	1	1	yes	characteristic
337	C₂³	#493582	1	1	yes	characteristic
338	C₂²	#72219022	1	1	yes	characteristic
339	C₂²	#72258238	1	1	yes	characteristic
340	C₂²	#72258238	1	1	yes	characteristic
341	C₂	#72266163	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	#72266163
commutator	#2308	C₂³×C₄
Frattini, cosocle	#35346	C₂⁴
prime radical	#72237769	C₂
LCS	G ▷ #2308 ▷ 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. #72310535	C₂	semidirect
2. #72310532	C₂	semidirect
3. #72310530	C₂	semidirect
4. #72310529	C₂	semidirect
5. #72310528	C₂	semidirect
6. #72310527	C₂²	semidirect
7. #72310526	C₂²	semidirect
8. #72310525	C₂	semidirect
11. #72310517	C₂	semidirect
13. #72310515	C₂²	semidirect
14. #72309392	C₂	semidirect
15. #72309391	C₂²	semidirect
16. #72302062	C₂	semidirect
17. #72302061	C₂²	semidirect
19. #72237770	C₂	semidirect
23. #72237749	C₄	semidirect
24. #72237746	C₄	semidirect
25. #72237746	C₄	semidirect
26. #72237743	C₄	semidirect
27. #72237740	C₄	semidirect
28. #72237734	C₂²	semidirect
29. #72237732	C₄	semidirect
30. #72237732	C₄	semidirect
32. #72237724	C₄	semidirect
33. C₂×#97550	C₂²	semidirect
34. #72225873	C₂²	semidirect
35. #72225777	C₂²	semidirect
36. #72225776	C₂²	semidirect
49. #7513948	C₂×C₄	semidirect
50. #7513948	C₂×C₄	semidirect
51. #6631461	C₂×C₄	semidirect
60. #6437629	C₂×C₄	semidirect
68. #449090	C₂×C₄	semidirect
69. #449090	C₂×C₄	semidirect
70. #436464	C₂×C₄	semidirect
71. #436464	C₂×C₄	semidirect
72. #432839	C₂×C₄	semidirect
73. #432839	C₂×C₄	semidirect
74. #418911	C₂×C₄	semidirect
75. #418911	C₂×C₄	semidirect
92. #388001	C₂×C₄	semidirect
93. #388001	C₂×C₄	semidirect
100. #357285	C₂×C₄	semidirect
101. #356055	C₂×C₄	semidirect
312. C₂²×Q₈	#2127	semidirect
313. C₂²×D₄	#2127	semidirect

Maximal subgroups

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

subgroup	index
#72310535	2
#72310532	2
#72310530	2
#72310529	2
#72310528	2
#72310525	2
#72310517	2
#72309392	2
#72302062	2
#72237770	2
#72237769	2