Subgroups — #72294269

Order 2048.

At least 6259 conjugacy classes of subgroups; only the 1336 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	#72294242	C₂	1	2	yes	maximal, complemented
2	#72294224	C₂	1	1	yes	maximal, characteristic, complemented
3	#72294214	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#245246	C₂	1	4	yes	maximal, complemented
5	#72261295	C₂	1	2	yes	maximal, complemented
6	#72258052	C₂	1	1	yes	maximal, characteristic, complemented
7	#72257508	C₂	1	2	yes	maximal, complemented
8	#72251570	C₂	1	4	yes	maximal, complemented
9	#72241188	C₂	1	4	yes	maximal, complemented
10	#72237453	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×#35346	C₂	1	1	yes	maximal, characteristic, complemented
12	#72225609	C₂	1	4	yes	maximal, complemented
13	#72219118	C₂	1	1	yes	maximal, characteristic, complemented
14	#72218518	C₂	1	1	yes	maximal, characteristic, complemented
15	#72214549	C₂	1	2	yes	maximal, complemented
16	C₂⁴×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
17	C₂⁴×#120	C₂²	1	1	yes	characteristic
18	C₂×#36714	C₂²	1	2	yes	complemented
19	C₂×#35346	C₂²	1	4	yes	—
20	C₂×#35346	C₂²	1	4	yes	—
21	C₂×#34980	C₂²	1	1	yes	characteristic, complemented
22	C₂²×#2403	C₂²	1	2	yes	—
23	C₂²×#2403	C₂²	1	2	yes	—
24	C₂²×#2308	C₂²	1	1	yes	characteristic
25	C₂×#32900	C₂²	1	4	yes	complemented
26	C₂×#32898	C₂²	1	4	yes	complemented
27	C₂×#29634	C₂²	1	4	yes	complemented
28	#617161	C₂²	1	2	yes	complemented
29	#616960	C₂²	1	2	yes	complemented
30	#612617	C₂²	1	1	yes	characteristic
31	#612617	C₂²	1	1	yes	characteristic, complemented
32	#612617	C₂²	1	2	yes	complemented
33	#612424	C₂²	1	1	yes	characteristic
34	#612424	C₂²	1	1	yes	characteristic, complemented
35	#612424	C₂²	1	2	yes	complemented
36	#555894	C₂²	1	2	yes	complemented
37	#517415	C₂²	1	1	yes	characteristic, complemented
38	#405104	C₂²	1	4	yes	complemented
39	#393929	C₂²	1	4	yes	complemented
40	#392125	C₂²	1	4	yes	complemented
41	#392125	C₂²	1	4	yes	complemented
42	#392109	C₂²	1	1	yes	characteristic
43	#392109	C₂²	1	1	yes	characteristic
44	#392109	C₂²	1	2	yes	complemented
45	#392109	C₂²	1	2	yes	complemented
46	#392109	C₂²	1	2	yes	complemented
47	#392109	C₂²	1	2	yes	complemented
48	#379754	C₂²	1	4	yes	complemented
49	#359799	C₂²	1	2	yes	complemented
50	#359428	C₂²	1	2	yes	complemented
51	C₂×#10337	C₂²	1	8	yes	complemented
52	C₂×#10336	C₂²	1	8	yes	complemented
53	C₂×#9497	C₂²	1	8	yes	complemented
54	C₂×#9499	C₂²	1	4	yes	complemented
55	C₂×#9495	C₂²	1	4	yes	complemented
56	C₂×#8541	C₂²	1	4	yes	complemented
57	C₂×#8541	C₂²	1	4	yes	complemented
58	#115133	C₂²	1	8	yes	complemented
59	#111458	C₂²	1	8	yes	complemented
60	#111458	C₂²	1	8	yes	complemented
61	#106542	C₂²	1	4	yes	complemented
62	#106542	C₂²	1	4	yes	complemented
63	C₂²⋊#1304	C₂²	1	2	yes	complemented
64	C₂²⋊#1304	C₂²	1	2	yes	complemented
65	C₂⁸	D₄	1	1	yes	characteristic, complemented
66	C₂³×H(5,𝔽₂)	C₂³	1	4	yes	—
67	C₂⁵×D₄	C₂³	1	1	yes	characteristic
68	C₂⁵×D₄	C₂³	1	2	yes	—
69	C₂⁵×D₄	C₂³	1	1	yes	characteristic
70	C₂⁵×D₄	C₂³	1	1	yes	characteristic
71	C₂²×#534	C₂³	1	1	yes	characteristic, complemented
72	C₂²×#534	C₂³	1	1	yes	characteristic, complemented
73	C₂³×#120	D₄	1	4	yes	complemented
74	C₂³×#120	D₄	1	2	yes	complemented
75	C₂³×#120	D₄	1	2	yes	complemented
76	C₂³×#120	C₂³	1	1	yes	characteristic
77	C₂³×#120	C₂³	1	2	yes	—
78	C₂³×#120	C₂³	1	2	yes	—
79	C₂⁴×C₂²⋊C₄	D₄	1	1	yes	characteristic, complemented
80	C₂⁴×C₂²⋊C₄	D₄	1	1	yes	characteristic, complemented
81	C₂⁴×C₂²⋊C₄	D₄	1	1	yes	characteristic, complemented
82	#35346	D₄	1	32	yes	complemented
83	C₂×#2405	D₄	1	4	yes	complemented
84	C₂×#2405	C₂³	1	2	yes	—
85	C₂×#2405	C₂³	1	2	yes	complemented
86	C₂×#2405	C₂³	1	4	yes	complemented
87	C₂×#2403	D₄	1	8	yes	complemented
88	C₂×#2403	D₄	1	4	yes	complemented
89	C₂×#2403	C₂³	1	4	yes	—
90	C₂×#2403	C₂³	1	2	yes	—
91	C₂×#2403	C₂³	1	8	yes	—
92	C₂×#2403	C₂³	1	4	yes	—
93	C₂×#2403	C₂³	1	2	yes	complemented
94	C₂×#2403	C₂³	1	4	yes	complemented
95	C₂×#2309	C₂³	1	2	yes	complemented
96	C₂×#2308	C₂³	1	4	yes	—
97	C₂×#2308	C₂³	1	1	yes	characteristic, complemented
98	C₂×#2308	C₂³	1	1	yes	characteristic, complemented
99	C₂²×#386	D₄	1	4	yes	complemented
100	C₂²×#379	C₂³	1	2	yes	—
101	C₂²×#379	C₂³	1	1	yes	characteristic
102	C₂×#1819	C₂³	1	4	yes	complemented
103	C₂×#1781	C₂³	1	4	yes	—
104	C₂×#1781	C₂³	1	4	yes	—
105	C₂×#1781	C₂³	1	4	yes	complemented
106	C₂×#1781	C₂³	1	4	yes	complemented
107	C₂×#1781	C₂³	1	8	yes	complemented
108	C₂×#1781	C₂³	1	8	yes	complemented
109	C₂×#1781	C₂³	1	4	yes	complemented
110	C₂×#1781	C₂³	1	8	yes	complemented
111	#14679	C₂³	1	2	yes	—
112	#14679	C₂³	1	2	yes	—
113	#14679	C₂³	1	1	yes	characteristic
114	#14679	C₂³	1	1	yes	characteristic
115	#14335	C₂³	1	2	yes	complemented
116	#13867	D₄	1	4	yes	complemented
117	#13867	D₄	1	4	yes	complemented
118	#13867	C₂³	1	2	yes	—
119	#13867	C₂³	1	2	yes	—
120	#13867	C₂³	1	2	yes	complemented
121	#13867	C₂³	1	2	yes	complemented
122	#13867	C₂³	1	4	yes	complemented
123	#13867	C₂³	1	4	yes	complemented
124	#10725	C₂³	1	4	yes	complemented
125	#10725	C₂³	1	4	yes	complemented
126	C₂×#1304	C₂³	1	8	yes	complemented
127	C₂×#1304	C₂³	1	8	yes	complemented
128	C₂⁷	C₂×D₄	1	1	yes	characteristic
129	C₂⁷	C₂×D₄	1	1	yes	characteristic
130	C₂⁷	C₂×D₄	1	2	yes	—
131	C₂⁷	C₂×D₄	1	2	yes	—
132	C₂⁷	C₂×D₄	1	1	yes	characteristic
133	C₂⁷	C₂×D₄	1	2	yes	—
134	C₂⁷	C₂⁴	1	1	yes	characteristic
135	C₂²×H(5,𝔽₂)	C₂×D₄	1	16	yes	—
136	C₂⁴×D₄	C₂×D₄	1	4	yes	—
137	C₂⁴×D₄	C₂×D₄	1	4	yes	—
138	C₂⁴×D₄	C₂×D₄	1	4	yes	—
139	C₂⁴×D₄	C₂×D₄	1	4	yes	—
140	C₂⁴×D₄	C₂×D₄	1	2	yes	—
141	C₂⁴×D₄	C₂×D₄	1	4	yes	—
142	C₂⁴×D₄	C₂×D₄	1	2	yes	—
143	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
144	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
145	C₂⁴×D₄	C₂×D₄	1	2	yes	complemented
146	C₂⁴×D₄	C₂⁴	1	4	yes	—
147	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
148	C₂⁴×D₄	C₂⁴	1	2	yes	—
149	C₂⁴×D₄	C₂⁴	1	2	yes	—
150	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
151	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
152	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
153	C₂⁵×C₄	C₂×D₄	1	2	yes	—
154	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
155	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
156	C₂²×#123	C₂×D₄	1	4	yes	complemented
157	C₂²×#120	C₂×D₄	1	8	yes	—
158	C₂²×#120	C₂×D₄	1	8	yes	—
159	C₂²×#120	C₂×D₄	1	16	yes	—
160	C₂²×#120	C₂×D₄	1	4	yes	complemented
161	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
162	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
163	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
164	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
165	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
166	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
167	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
168	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
169	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
170	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
171	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
172	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
173	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
174	#2403	C₂×D₄	1	32	yes	—
175	#2403	C₂×D₄	1	32	yes	—
176	#2308	C₂×D₄	1	16	yes	—
177	C₂×#386	C₂×D₄	1	8	yes	—
178	C₂×#386	C₂×D₄	1	8	yes	—
179	C₂×#386	C₂×D₄	1	4	yes	complemented
180	C₂×#386	C₂×D₄	1	4	yes	complemented
181	C₂×#386	C₂×D₄	1	8	yes	complemented
182	C₂×#386	C₂×D₄	1	8	yes	complemented
183	C₂×#379	C₂×D₄	1	4	yes	—
184	C₂×#379	C₂×D₄	1	4	yes	complemented
185	C₂×#379	C₂×D₄	1	4	yes	complemented
186	C₂×#379	C₂⁴	1	4	yes	—
187	C₂×#379	C₂⁴	1	4	yes	—
188	C₂×#379	C₂⁴	1	4	yes	—
189	C₂×#379	C₂⁴	1	2	yes	—
190	C₂×#379	C₂⁴	1	2	yes	—
191	C₂⁶	#120	1	4	yes	—
192	C₂⁶	#120	1	2	yes	—
193	C₂⁶	#120	1	2	yes	—
194	C₂⁶	#120	1	8	yes	complemented
195	C₂⁶	C₂²×D₄	1	1	yes	characteristic
196	C₂⁶	C₂²×D₄	1	2	yes	—
197	C₂⁶	C₂²×D₄	1	1	yes	characteristic
198	C₂⁶	C₂²×D₄	1	2	yes	—
199	C₂⁶	C₂²×D₄	1	2	yes	—
200	C₂⁶	C₂²×D₄	1	2	yes	—
201	C₂⁶	C₂²×D₄	1	2	yes	—
202	C₂⁶	C₂²×D₄	1	4	yes	—
203	C₂⁶	C₂²×D₄	1	1	yes	characteristic
204	C₂⁶	C₂²×D₄	1	1	yes	characteristic
205	C₂⁶	C₂²×D₄	1	2	yes	—
206	C₂⁶	C₂²×D₄	1	1	yes	characteristic, complemented
207	C₂⁶	H(5,𝔽₂)	1	4	yes	—
208	C₂⁶	C₂⁵	1	1	yes	characteristic
209	C₂³×D₄	#120	1	8	yes	—
210	C₂³×D₄	#120	1	4	yes	—
211	C₂³×D₄	#120	1	4	yes	—
212	C₂³×D₄	C₂²×D₄	1	4	yes	—
213	C₂³×D₄	C₂²×D₄	1	4	yes	—
214	C₂³×D₄	C₂²×D₄	1	4	yes	—
215	C₂³×D₄	C₂²×D₄	1	16	yes	—
216	C₂³×D₄	C₂²×D₄	1	8	yes	—
217	C₂³×D₄	C₂²×D₄	1	4	yes	—
218	C₂³×D₄	C₂²×D₄	1	8	yes	—
219	C₂³×D₄	C₂²×D₄	1	8	yes	—
220	C₂³×D₄	H(5,𝔽₂)	1	8	yes	—
221	C₂⁴×C₄	#120	1	4	yes	—
222	C₂⁴×C₄	#120	1	2	yes	—
223	C₂⁴×C₄	#120	1	2	yes	—
224	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
225	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
226	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
227	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
228	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
229	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic, complemented
230	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic, complemented
231	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic, complemented
232	C₂⁴×C₄	C₂²×D₄	1	2	yes	complemented
233	C₂⁴×C₄	C₂²×D₄	1	2	yes	complemented
234	C₂×#120	#120	1	32	yes	complemented
235	C₂²×C₂²⋊C₄	#120	1	8	yes	complemented
236	C₂²×C₂²⋊C₄	#120	1	8	yes	complemented
237	C₂²×C₂²⋊C₄	#120	1	8	yes	complemented
238	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
239	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	complemented
240	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	complemented
241	#386	#120	1	32	yes	complemented
242	#379	C₂²×D₄	1	16	yes	—
243	C₂⁵	B(4,𝔽₂)	1	16	yes	—
244	C₂⁵	C₂×#120	1	1	yes	characteristic
245	C₂⁵	C₂×#120	1	1	yes	characteristic
246	C₂⁵	C₂×#120	1	2	yes	—
247	C₂⁵	C₂×#120	1	2	yes	—
248	C₂⁵	C₂×#120	1	2	yes	—
249	C₂⁵	C₂×#120	1	2	yes	—
250	C₂⁵	C₂×#120	1	2	yes	—
251	C₂⁵	C₂×#120	1	4	yes	—
252	C₂⁵	C₂×#120	1	4	yes	—
253	C₂⁵	C₂×#120	1	4	yes	—
254	C₂⁵	C₂×#120	1	8	yes	—
255	C₂⁵	C₂×#120	1	4	yes	—
256	C₂⁵	#534	1	2	yes	—
257	C₂⁵	#534	1	4	yes	—
258	C₂⁵	#534	1	2	yes	—
259	C₂⁵	D₄²	1	4	yes	—
260	C₂⁵	D₄²	1	4	yes	—
261	C₂⁵	D₄²	1	4	yes	—
262	C₂⁵	D₄²	1	4	yes	—
263	C₂⁵	C₂³×D₄	1	1	yes	characteristic
264	C₂⁵	C₂³×D₄	1	2	yes	—
265	C₂⁵	C₂³×D₄	1	1	yes	characteristic
266	C₂⁵	C₂³×D₄	1	1	yes	characteristic
267	C₂⁵	C₂³×D₄	1	4	yes	—
268	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
269	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
270	C₂²×D₄	C₂×#120	1	16	yes	—
271	C₂²×D₄	D₄²	1	16	yes	—
272	C₂²×D₄	D₄²	1	16	yes	—
273	C₂³×C₄	C₂×#120	1	2	yes	—
274	C₂³×C₄	C₂×#120	1	2	yes	—
275	C₂³×C₄	C₂×#120	1	4	yes	—
276	C₂³×C₄	C₂×#120	1	8	yes	—
277	C₂³×C₄	C₂×#120	1	4	yes	—
278	C₂³×C₄	C₂×#120	1	4	yes	—
279	C₂³×C₄	C₂×#120	1	4	yes	—
280	C₂³×C₄	#534	1	4	yes	—
281	C₂×C₂²⋊C₄	C₂×#120	1	16	yes	—
282	C₂⁴	#2403	1	4	yes	—
283	C₂⁴	#2403	1	2	yes	—
284	C₂⁴	#2403	1	2	yes	—
285	C₂⁴	#2403	1	8	yes	—
286	C₂⁴	#2846	1	4	yes	—
287	C₂⁴	C₂×B(4,𝔽₂)	1	8	yes	—
288	C₂⁴	C₂×B(4,𝔽₂)	1	16	yes	—
289	C₂⁴	#3026	1	4	yes	—
290	C₂⁴	#3026	1	4	yes	—
291	C₂⁴	C₂²×#120	1	2	yes	—
292	C₂⁴	C₂²×#120	1	1	yes	characteristic
293	C₂⁴	C₂²×#120	1	1	yes	characteristic
294	C₂⁴	C₂²×#120	1	4	yes	—
295	C₂⁴	C₂×#534	1	1	yes	characteristic
296	C₂⁴	C₂×#534	1	2	yes	—
297	C₂⁴	C₂×D₄²	1	2	yes	—
298	C₂⁴	C₂×D₄²	1	2	yes	—
299	C₂⁴	C₂×D₄²	1	4	yes	—
300	C₂⁴	C₂×D₄²	1	4	yes	—
301	C₂⁴	#3484	1	4	yes	—
302	C₂⁴	#3484	1	8	yes	—
303	C₂²×C₄	#2403	1	8	yes	—
304	C₂²×C₄	#2846	1	4	yes	—
305	C₂³	#23895	1	4	yes	—
306	C₂³	#23900	1	4	yes	—
307	C₂³	#23900	1	4	yes	—
308	C₂³	#23900	1	16	yes	—
309	C₂³	#23903	1	4	yes	—
310	C₂³	C₂×#2403	1	2	yes	—
311	C₂³	C₂×#2403	1	1	yes	characteristic
312	C₂³	#34980	1	2	yes	—
313	C₂³	#34980	1	1	yes	characteristic
314	C₂³	D₄×#120	1	4	yes	—
315	C₂³	D₄×#120	1	4	yes	—
316	C₂³	C₂×#2846	1	1	yes	characteristic
317	C₂³	C₂²×B(4,𝔽₂)	1	4	yes	—
318	C₂³	C₂×#3026	1	2	yes	—
319	C₂³	C₂×#3026	1	2	yes	—
320	C₂²	#245246	1	8	yes	complemented
321	C₂²	#612424	1	1	yes	characteristic
322	C₂²	C₂×#23900	1	4	yes	—
323	C₂²	C₂×#23900	1	2	yes	—
324	C₂²	C₂×#23903	1	1	yes	characteristic
325	C₂²	#6437621	1	1	yes	characteristic
326	C₂²	C₂×#23895	1	2	yes	—
327	C₂²	#6470237	1	2	yes	—
328	C₂²	#6628892	1	2	yes	—
329	C₂	#72213862	1	1	yes	characteristic
330	C₂	#72215858	1	1	yes	characteristic
331	C₂	#72233065	1	2	yes	—
332	C₂	#72240108	1	1	yes	characteristic
333	C₂	C₂×#245246	1	2	yes	—

	subgroup	G/H
center, socle	C₂³	C₂×#2403
commutator, Frattini, cosocle	C₂⁶	C₂⁵
LCS	G ▷ C₂⁶ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂⁷ ◁ G
LECS	G ▷ C₂⁶ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72294242	C₂	semidirect
2. #72294224	C₂	semidirect
3. #72294214	C₂	semidirect
4. C₂×#245246	C₂	semidirect
5. #72261295	C₂	semidirect
6. #72258052	C₂	semidirect
7. #72257508	C₂	semidirect
8. #72251570	C₂	semidirect
9. #72241188	C₂	semidirect
10. #72237453	C₂	semidirect
11. C₂²×#35346	C₂	semidirect
12. #72225609	C₂	semidirect
13. #72219118	C₂	semidirect
14. #72218518	C₂	semidirect
15. #72214549	C₂	semidirect
18. C₂×#36714	C₂²	semidirect
21. C₂×#34980	C₂²	semidirect
25. C₂×#32900	C₂²	semidirect
26. C₂×#32898	C₂²	semidirect
27. C₂×#29634	C₂²	semidirect
28. #617161	C₂²	semidirect
29. #616960	C₂²	semidirect
31. #612617	C₂²	semidirect
32. #612617	C₂²	semidirect
34. #612424	C₂²	semidirect
35. #612424	C₂²	semidirect
36. #555894	C₂²	semidirect
37. #517415	C₂²	semidirect
38. #405104	C₂²	semidirect
39. #393929	C₂²	semidirect
40. #392125	C₂²	semidirect
41. #392125	C₂²	semidirect
44. #392109	C₂²	semidirect
45. #392109	C₂²	semidirect
46. #392109	C₂²	semidirect
47. #392109	C₂²	semidirect
48. #379754	C₂²	semidirect
49. #359799	C₂²	semidirect
50. #359428	C₂²	semidirect
51. C₂×#10337	C₂²	semidirect
52. C₂×#10336	C₂²	semidirect
53. C₂×#9497	C₂²	semidirect
54. C₂×#9499	C₂²	semidirect
55. C₂×#9495	C₂²	semidirect
56. C₂×#8541	C₂²	semidirect
57. C₂×#8541	C₂²	semidirect
58. #115133	C₂²	semidirect
59. #111458	C₂²	semidirect
60. #111458	C₂²	semidirect
61. #106542	C₂²	semidirect
62. #106542	C₂²	semidirect
63. C₂²⋊#1304	C₂²	semidirect
64. C₂²⋊#1304	C₂²	semidirect
65. C₂⁸	D₄	semidirect
71. C₂²×#534	C₂³	semidirect
72. C₂²×#534	C₂³	semidirect
73. C₂³×#120	D₄	semidirect
74. C₂³×#120	D₄	semidirect
75. C₂³×#120	D₄	semidirect
79. C₂⁴×C₂²⋊C₄	D₄	semidirect
80. C₂⁴×C₂²⋊C₄	D₄	semidirect
81. C₂⁴×C₂²⋊C₄	D₄	semidirect
82. #35346	D₄	semidirect
83. C₂×#2405	D₄	semidirect
85. C₂×#2405	C₂³	semidirect
86. C₂×#2405	C₂³	semidirect
87. C₂×#2403	D₄	semidirect
88. C₂×#2403	D₄	semidirect
93. C₂×#2403	C₂³	semidirect
94. C₂×#2403	C₂³	semidirect
95. C₂×#2309	C₂³	semidirect
97. C₂×#2308	C₂³	semidirect
98. C₂×#2308	C₂³	semidirect
99. C₂²×#386	D₄	semidirect
102. C₂×#1819	C₂³	semidirect
105. C₂×#1781	C₂³	semidirect
106. C₂×#1781	C₂³	semidirect
107. C₂×#1781	C₂³	semidirect
108. C₂×#1781	C₂³	semidirect
109. C₂×#1781	C₂³	semidirect
110. C₂×#1781	C₂³	semidirect
115. #14335	C₂³	semidirect
116. #13867	D₄	semidirect
117. #13867	D₄	semidirect
120. #13867	C₂³	semidirect
121. #13867	C₂³	semidirect
122. #13867	C₂³	semidirect
123. #13867	C₂³	semidirect
124. #10725	C₂³	semidirect
125. #10725	C₂³	semidirect
126. C₂×#1304	C₂³	semidirect
127. C₂×#1304	C₂³	semidirect
145. C₂⁴×D₄	C₂×D₄	semidirect
156. C₂²×#123	C₂×D₄	semidirect
160. C₂²×#120	C₂×D₄	semidirect
168. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
169. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
170. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
179. C₂×#386	C₂×D₄	semidirect
180. C₂×#386	C₂×D₄	semidirect
181. C₂×#386	C₂×D₄	semidirect
182. C₂×#386	C₂×D₄	semidirect
184. C₂×#379	C₂×D₄	semidirect
185. C₂×#379	C₂×D₄	semidirect
194. C₂⁶	#120	semidirect
206. C₂⁶	C₂²×D₄	semidirect
229. C₂⁴×C₄	C₂²×D₄	semidirect
230. C₂⁴×C₄	C₂²×D₄	semidirect
231. C₂⁴×C₄	C₂²×D₄	semidirect
232. C₂⁴×C₄	C₂²×D₄	semidirect
233. C₂⁴×C₄	C₂²×D₄	semidirect
234. C₂×#120	#120	semidirect
235. C₂²×C₂²⋊C₄	#120	semidirect
236. C₂²×C₂²⋊C₄	#120	semidirect
237. C₂²×C₂²⋊C₄	#120	semidirect
239. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
240. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
241. #386	#120	semidirect
320. C₂²	#245246	semidirect

Maximal subgroups

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

subgroup	index
#72294242	2
#72294224	2
#72294214	2
C₂×#245246	2
#72261295	2
#72258052	2
#72257508	2
#72251570	2
#72241188	2
#72237453	2
C₂²×#35346	2
#72225609	2
#72219118	2
#72218518	2
#72214549	2