Subgroups — #72324156

Order 8192.

At least 38654 conjugacy classes of subgroups; only the 544 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	#72323954	C₂	1	2	yes	maximal, complemented
2	#72323927	C₂	1	2	yes	maximal, complemented
3	#72323874	C₂	1	2	yes	maximal, complemented
4	#72323858	C₂	1	2	yes	maximal, complemented
5	#72323220	C₂	1	1	yes	maximal, characteristic, complemented
6	#72323219	C₂²	1	2	yes	complemented
7	#72323217	C₂²	1	2	yes	complemented
8	#72315799	C₂	1	1	yes	maximal, characteristic
9	#72314925	C₄	1	2	yes	complemented
10	#72314621	C₂	1	1	yes	maximal, characteristic, complemented
11	#72314618	C₂²	1	2	yes	complemented
12	#72314610	C₂²	1	2	yes	complemented
13	#72302204	C₂	1	1	yes	maximal, characteristic, complemented
14	#72302137	C₂²	1	2	yes	—
15	#72302137	C₂²	1	2	yes	—
16	#72302130	D₄	1	4	yes	complemented
17	#72266446	C₂²	1	2	yes	—
18	#72266442	C₂²	1	2	yes	—
19	#72265785	C₂²	1	1	yes	characteristic
20	#72265766	C₂³	1	2	yes	—
21	#72260662	C₄	1	2	yes	complemented
22	#72256276	C₂	1	1	yes	maximal, characteristic, complemented
23	#72240489	C₄	1	1	yes	characteristic, complemented
24	#72240132	C₂×C₄	1	2	yes	complemented
25	#72240132	C₂×C₄	1	2	yes	complemented
26	#72238601	C₂²	1	2	yes	complemented
27	#72238353	C₂	1	1	yes	maximal, characteristic, complemented
28	#72237864	C₂²	1	2	yes	complemented
29	#72237628	C₂²	1	1	yes	characteristic
30	#72237618	C₂×C₄	1	1	yes	characteristic, complemented
31	#72237608	C₂×C₄	1	2	yes	complemented
32	#72237606	C₂²	1	1	yes	characteristic, complemented
33	#72237591	C₂²	1	1	yes	characteristic, complemented
34	#72237588	C₂²	1	1	yes	characteristic, complemented
35	#72237581	C₂²	1	1	yes	characteristic, complemented
36	#72235213	C₄	1	1	yes	characteristic, complemented
37	#72235186	C₂×C₄	1	2	yes	complemented
38	#72234688	C₂²	1	1	yes	characteristic
39	#72234688	C₂²	1	1	yes	characteristic
40	#72234668	C₂³	1	1	yes	characteristic
41	#72234641	D₄	1	4	yes	complemented
42	#72234625	C₂³	1	1	yes	characteristic
43	#72234592	D₄	1	2	yes	complemented
44	#72232592	C₂×C₄	1	1	yes	characteristic, complemented
45	#72231950	C₂×C₄	1	2	yes	complemented
46	#72226177	C₂	1	1	yes	maximal, characteristic, complemented
47	#72226102	C₂²	1	2	yes	—
48	#72226043	C₂²	1	2	yes	—
49	#72225883	C₂²	1	1	yes	characteristic
50	#72225870	C₂³	1	2	yes	—
51	#72225776	D₄	1	2	yes	complemented
52	#72225615	C₂²	1	1	yes	characteristic
53	#72219397	C₂²	1	1	yes	characteristic
54	#72219311	C₂³	1	1	yes	characteristic
55	#72219311	C₂³	1	1	yes	characteristic
56	#72219311	C₂³	1	1	yes	characteristic
57	#72219311	C₂³	1	2	yes	—
58	#72219310	C₂³	1	1	yes	characteristic
59	#72219301	D₄	1	2	yes	complemented
60	#72219295	C₄	1	1	yes	characteristic, complemented
61	C₂×#139716	C₂×C₄	1	2	yes	complemented
62	C₂×#139716	C₂×C₄	1	2	yes	complemented
63	#72219268	D₄	1	2	yes	—
64	#72219267	D₄	1	2	yes	—
65	#72219266	C₂×C₄	1	2	yes	—
66	#72219264	C₂³	1	2	yes	—
67	#72219257	D₄	1	1	yes	characteristic
68	#72219254	D₄	1	1	yes	characteristic
69	#72219242	C₄	1	1	yes	characteristic, complemented
70	#72219241	C₂×C₄	1	2	yes	complemented
71	#72219225	D₄	1	1	yes	characteristic
72	C₂²×#15947	C₂×C₄	1	1	yes	characteristic
73	C₂×#7670203	C₂³	1	1	yes	characteristic
74	C₂²×#62817	D₄	1	1	yes	characteristic
75	#72218518	C₂×C₄	1	1	yes	characteristic, complemented
76	#72218518	D₄	1	2	yes	complemented
77	#72218291	C₂×C₄	1	1	yes	characteristic, complemented
78	#72217875	C₂×C₄	1	1	yes	characteristic
79	#72217789	C₂×C₄	1	1	yes	characteristic, complemented
80	#72217511	C₂×C₄	1	1	yes	characteristic, complemented
81	#72216481	D₄	1	4	yes	complemented
82	C₂×#347042	C₂×C₄	1	2	yes	complemented
83	#72211163	D₄	1	4	yes	complemented
84	C₂×#62817	C₂²×C₄	1	1	yes	characteristic, complemented
85	C₂²×#3532	C₂²⋊C₄	1	2	yes	—
86	C₂²×#3532	C₂×D₄	1	2	yes	—
87	C₂²×#3484	C₂²⋊C₄	1	1	yes	characteristic
88	C₂²×#3484	C₂×D₄	1	1	yes	characteristic
89	C₂²×#3484	C₂×D₄	1	1	yes	characteristic
90	C₂⁴×#120	C₂²⋊C₄	1	1	yes	characteristic
91	C₂⁴×#120	C₂²×C₄	1	1	yes	characteristic
92	C₂⁴×#120	C₂×D₄	1	1	yes	characteristic
93	C₂²×#2846	#41	1	1	yes	characteristic
94	C₂×#35390	C₂×D₄	1	1	yes	characteristic
95	C₂×#35348	C₂×D₄	1	1	yes	characteristic
96	C₂×#35348	#41	1	1	yes	characteristic
97	C₂×#35346	C₂×D₄	1	1	yes	characteristic
98	C₂×#34981	C₂²×C₄	1	1	yes	characteristic
99	C₂×#34981	#41	1	1	yes	characteristic
100	C₂×#34980	C₂×D₄	1	1	yes	characteristic
101	C₂×#34980	C₂⁴	1	1	yes	characteristic
102	#7626202	C₂²×C₄	1	1	yes	characteristic, complemented
103	C₂×#34198	C₂×D₄	1	1	yes	characteristic
104	C₂×#34198	#41	1	1	yes	characteristic
105	C₂×#21746	C₂²×C₄	1	1	yes	characteristic, complemented
106	C₂×#21746	C₂²×C₄	1	1	yes	characteristic, complemented
107	#5025789	#41	1	2	yes	—
108	#5025782	C₂×D₄	1	2	yes	—
109	#5021140	#41	1	2	yes	—
110	#5021138	C₂×D₄	1	2	yes	—
111	#4422949	#41	1	2	yes	—
112	#4420586	C₂×D₄	1	2	yes	—
113	#763514	C₂²⋊C₄	1	2	yes	—
114	#763333	C₂×D₄	1	2	yes	—
115	#686187	#41	1	2	yes	—
116	#647656	C₂×D₄	1	2	yes	—
117	#617161	C₂²⋊C₄	1	2	yes	—
118	#616961	C₂²⋊C₄	1	2	yes	—
119	#616961	C₂²×C₄	1	2	yes	—
120	#616960	C₂×D₄	1	2	yes	—
121	C₂×#15947	C₂²⋊C₄	1	2	yes	—
122	C₂×#15947	C₂²×C₄	1	2	yes	—
123	#552677	C₂²⋊C₄	1	2	yes	—
124	#552670	C₂×D₄	1	2	yes	—
125	#517411	C₂²⋊C₄	1	1	yes	characteristic
126	C₂²×#1438	C₂²⋊C₄	1	1	yes	characteristic
127	#392109	C₂×D₄	1	2	yes	—
128	#392109	C₂×D₄	1	2	yes	—
129	#190116	C₂×D₄	1	4	yes	—
130	C₂×#8547	C₂²×C₄	1	2	yes	complemented
131	C₂×#8541	C₂²×C₄	1	2	yes	complemented
132	#115690	C₂×D₄	1	4	yes	—
133	#115690	C₂×D₄	1	4	yes	—
134	#115631	C₂×D₄	1	4	yes	—
135	#115631	C₂×D₄	1	4	yes	—
136	C₂⁸	#99	1	1	yes	characteristic, complemented
137	C₂⁸	C₄×D₄	1	1	yes	characteristic
138	C₂³×H(5,𝔽₂)	#99	1	1	yes	characteristic, complemented
139	C₂³×H(5,𝔽₂)	#120	1	1	yes	characteristic
140	C₂⁵×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
141	C₂⁵×D₄	C₂²×D₄	1	1	yes	characteristic
142	C₂²×#551	#99	1	2	yes	complemented
143	C₂²×#551	#123	1	2	yes	—
144	C₂²×D₄²	#99	1	2	yes	complemented
145	C₂²×D₄²	#120	1	2	yes	—
146	C₂²×H(3,𝔽₄)	#99	1	2	yes	complemented
147	C₂²×H(3,𝔽₄)	#120	1	2	yes	—
148	C₂²×#560	#99	1	2	yes	complemented
149	C₂²×#560	#123	1	2	yes	—
150	C₂²×#535	C₂×C₂²⋊C₄	1	2	yes	—
151	C₂²×#534	C₂×C₂²⋊C₄	1	1	yes	characteristic
152	C₂²×#534	#121	1	1	yes	characteristic
153	C₂²×#534	#121	1	1	yes	characteristic
154	C₂²×#534	C₂²×D₄	1	1	yes	characteristic
155	C₂²×#534	C₂²×D₄	1	1	yes	characteristic
156	C₂²×#525	#99	1	2	yes	complemented
157	C₂³×#120	#99	1	2	yes	complemented
158	C₂³×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
159	C₂³×#120	C₂×C₂²⋊C₄	1	2	yes	—
160	C₂³×#120	C₄×D₄	1	1	yes	characteristic
161	C₂³×#120	C₄×D₄	1	1	yes	characteristic
162	C₂³×#120	C₄×D₄	1	1	yes	characteristic
163	C₂³×#120	#120	1	1	yes	characteristic
164	C₂³×#120	#120	1	1	yes	characteristic
165	C₂³×#120	#121	1	1	yes	characteristic
166	C₂³×#120	#121	1	1	yes	characteristic
167	C₂³×#120	#121	1	1	yes	characteristic
168	C₂³×#120	#123	1	1	yes	characteristic
169	C₂³×#120	C₂³×C₄	1	1	yes	characteristic
170	C₂²×#518	#99	1	1	yes	characteristic, complemented
171	C₂²×#518	#120	1	1	yes	characteristic
172	C₂²×#518	#123	1	1	yes	characteristic
173	C₂⁴×C₂²⋊C₄	#99	1	1	yes	characteristic, complemented
174	C₂⁴×C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic
175	C₂⁴×C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic
176	C₂×#2849	C₂×#41	1	2	yes	—
177	C₂×#2846	C₂²×D₄	1	2	yes	—
178	C₂×#2613	C₂²×D₄	1	2	yes	—
179	C₂×#2613	C₂×#41	1	2	yes	—
180	C₂×#2315	C₄×D₄	1	1	yes	characteristic
181	C₂×#2315	#123	1	1	yes	characteristic
182	C₂×#2308	C₂×C₂²⋊C₄	1	1	yes	characteristic
183	C₂×#2308	C₄×D₄	1	1	yes	characteristic
184	C₂×#2308	#121	1	1	yes	characteristic
185	C₂×#2308	C₂²×D₄	1	1	yes	characteristic
186	C₂×#2308	C₂×#41	1	1	yes	characteristic
187	C₂²×#379	#121	1	1	yes	characteristic
188	C₂²×#379	#123	1	1	yes	characteristic
189	C₂²×#379	C₂×#41	1	1	yes	characteristic
190	C₂×#2273	#121	1	1	yes	characteristic
191	C₂×#1781	#120	1	4	yes	complemented
192	#15948	#121	1	2	yes	—
193	#15948	#121	1	2	yes	—
194	#15947	C₄×D₄	1	2	yes	—
195	#15947	C₄×D₄	1	2	yes	—
196	#15947	C₄×D₄	1	2	yes	—
197	#15947	C₄×D₄	1	2	yes	—
198	#15947	#121	1	2	yes	—
199	#15947	#121	1	2	yes	—
200	#15262	#121	1	2	yes	—
201	#15261	#121	1	2	yes	—
202	#15259	C₄×D₄	1	2	yes	—
203	#15259	C₄×D₄	1	2	yes	—
204	#15259	#121	1	2	yes	—
205	#15258	C₄×D₄	1	2	yes	—
206	#15258	C₄×D₄	1	2	yes	—
207	#15258	#121	1	2	yes	—
208	#14679	#120	1	4	yes	complemented
209	#14658	#123	1	2	yes	—
210	#14657	#120	1	2	yes	—
211	#14335	C₂×C₂²⋊C₄	1	2	yes	—
212	#14167	#123	1	2	yes	—
213	#14134	#120	1	2	yes	—
214	C₂×#1438	C₂×C₂²⋊C₄	1	2	yes	—
215	#8101	#120	1	8	yes	complemented
216	C₂⁷	#386	1	1	yes	characteristic
217	C₂⁷	#386	1	1	yes	characteristic
218	C₂⁷	C₂×#99	1	1	yes	characteristic
219	C₂⁷	C₂×#99	1	2	yes	—
220	C₂⁷	C₂×C₄×D₄	1	1	yes	characteristic
221	C₂⁷	C₂×#120	1	1	yes	characteristic
222	C₂²×H(5,𝔽₂)	B(4,𝔽₂)	1	2	yes	—
223	C₂²×H(5,𝔽₂)	B(4,𝔽₂)	1	2	yes	—
224	C₂³×#41	C₂×#99	1	2	yes	—
225	C₂⁴×D₄	#386	1	1	yes	characteristic
226	C₂⁴×D₄	#386	1	1	yes	characteristic
227	C₂⁴×D₄	C₂×#99	1	1	yes	characteristic
228	C₂⁴×D₄	C₂×#99	1	1	yes	characteristic
229	C₂⁴×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
230	C₂⁴×D₄	C₂×#120	1	1	yes	characteristic
231	C₂⁴×D₄	C₂×#120	1	1	yes	characteristic
232	C₂⁴×D₄	C₂×#121	1	1	yes	characteristic
233	C₂⁴×D₄	#525	1	1	yes	characteristic
234	C₂⁵×C₄	C₂×#99	1	1	yes	characteristic
235	C₂⁵×C₄	#525	1	1	yes	characteristic
236	C₂²×#127	#386	1	2	yes	—
237	C₂²×#127	C₂×#99	1	2	yes	—
238	C₂²×#124	#386	1	2	yes	—
239	C₂²×#124	C₂×#99	1	2	yes	—
240	C₂²×#123	C₂×#99	1	2	yes	—
241	C₂²×#123	C₂×#121	1	2	yes	—
242	C₂²×#123	C₂×#123	1	2	yes	—
243	C₂²×#120	#386	1	2	yes	—
244	C₂²×#120	#386	1	2	yes	—
245	C₂²×#120	C₂×#99	1	2	yes	—
246	C₂²×#120	C₂×#99	1	2	yes	—
247	C₂²×#120	C₂×#99	1	2	yes	—
248	C₂²×#120	C₂×C₄×D₄	1	2	yes	—
249	C₂²×#120	C₂×C₄×D₄	1	2	yes	—
250	C₂²×#120	C₂×#120	1	2	yes	—
251	C₂²×#120	C₂×#121	1	2	yes	—
252	C₂²×#117	C₂×#99	1	2	yes	—
253	C₂³×C₂²⋊C₄	#386	1	1	yes	characteristic
254	C₂³×C₂²⋊C₄	#386	1	1	yes	characteristic
255	C₂³×C₂²⋊C₄	#386	1	1	yes	characteristic
256	C₂³×C₂²⋊C₄	#386	1	1	yes	characteristic
257	C₂³×C₂²⋊C₄	C₂×#99	1	2	yes	—
258	C₂³×C₂²⋊C₄	C₂×C₄×D₄	1	1	yes	characteristic
259	C₂³×C₂²⋊C₄	C₂×#121	1	1	yes	characteristic
260	C₂³×C₂²⋊C₄	C₂×#123	1	1	yes	characteristic
261	C₂×#381	#525	1	2	yes	—
262	C₂×#381	#525	1	2	yes	—
263	C₂×#379	C₂×#120	1	2	yes	—
264	C₂×#379	#525	1	2	yes	—
265	C₂×#379	#525	1	2	yes	—
266	C₂×#379	#525	1	2	yes	—
267	#1438	#386	1	2	yes	—
268	#1438	#386	1	2	yes	—
269	#1438	#386	1	2	yes	—
270	#1438	#386	1	2	yes	—
271	C₂⁶	#1898	1	1	yes	characteristic
272	C₂⁶	#1898	1	1	yes	characteristic
273	C₂⁶	#1898	1	1	yes	characteristic
274	C₂⁶	#1898	1	1	yes	characteristic
275	C₂⁶	#1898	1	2	yes	—
276	C₂⁶	#1898	1	2	yes	—
277	C₂⁶	C₂×#386	1	1	yes	characteristic
278	C₂⁶	C₄×#120	1	1	yes	characteristic
279	C₂⁶	C₄×#120	1	1	yes	characteristic
280	C₂⁶	#2846	1	1	yes	characteristic
281	C₂⁶	#2847	1	1	yes	characteristic
282	C₂⁶	C₂²×#99	1	1	yes	characteristic
283	C₂³×Q₈	#1898	1	2	yes	—
284	C₂³×D₄	#1889	1	1	yes	characteristic
285	C₂³×D₄	#1889	1	1	yes	characteristic
286	C₂³×D₄	#1889	1	2	yes	—
287	C₂³×D₄	#1898	1	2	yes	—
288	C₂³×D₄	#1913	1	1	yes	characteristic
289	C₂³×D₄	#1913	1	1	yes	characteristic
290	C₂³×D₄	#1913	1	2	yes	—
291	C₂³×D₄	C₂×#386	1	2	yes	—
292	C₂³×D₄	C₂²×#99	1	2	yes	—
293	C₂³×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
294	C₂³×D₄	#3026	1	2	yes	—
295	C₂⁴×C₄	#1898	1	1	yes	characteristic
296	C₂⁴×C₄	#1898	1	1	yes	characteristic
297	C₂⁴×C₄	#2847	1	1	yes	characteristic
298	C₂⁴×C₄	#2849	1	1	yes	characteristic
299	C₂⁴×C₄	C₂²×#99	1	1	yes	characteristic
300	C₂²×C₂²⋊C₄	#1898	1	2	yes	—
301	C₂²×C₂²⋊C₄	#1898	1	2	yes	—
302	C₂²×C₂²⋊C₄	#1898	1	2	yes	—
303	C₂²×C₂²⋊C₄	C₄×#120	1	2	yes	—
304	C₂²×C₂²⋊C₄	#2847	1	2	yes	—
305	C₂²×C₂²⋊C₄	#2849	1	2	yes	—
306	C₂²×C₄²	#1898	1	2	yes	—
307	C₂²×C₄²	#1898	1	2	yes	—
308	C₂⁵	#9495	1	1	yes	characteristic
309	C₂⁵	#9495	1	1	yes	characteristic
310	C₂⁵	#9495	1	2	yes	—
311	C₂⁵	#14694	1	1	yes	characteristic
312	C₂⁵	C₂×#1889	1	1	yes	characteristic
313	C₂⁵	#20960	1	1	yes	characteristic
314	C₂⁵	C₂×#1898	1	1	yes	characteristic
315	C₂⁵	C₂×#1898	1	2	yes	—
316	C₂⁵	C₂×#1898	1	1	yes	characteristic
317	C₂⁵	C₂×#1913	1	1	yes	characteristic
318	C₂⁵	C₂×#1913	1	1	yes	characteristic
319	C₂⁵	#32898	1	2	yes	—
320	C₂³×C₄	#9495	1	1	yes	characteristic
321	C₂³×C₄	#9495	1	1	yes	characteristic
322	C₂³×C₄	#9495	1	2	yes	—
323	C₂³×C₄	C₂×#1898	1	2	yes	—
324	C₂³×C₄	#33020	1	2	yes	—
325	C₂⁴	#139750	1	2	yes	—
326	C₂⁴	C₂×#9495	1	1	yes	characteristic
327	C₂⁴	C₂×#9495	1	1	yes	characteristic
328	C₂⁴	#201687	1	1	yes	characteristic
329	C₂⁴	#201687	1	1	yes	characteristic
330	C₂⁴	#392658	1	1	yes	characteristic
331	C₂⁴	#392675	1	1	yes	characteristic
332	C₂⁴	#392699	1	1	yes	characteristic
333	C₂⁴	#511790	1	4	yes	—
334	C₂³	C₂×#139750	1	1	yes	characteristic
335	C₂³	#72218104	1	2	yes	—
336	C₂³	#72238349	1	1	yes	characteristic
337	C₂³	#72258052	1	1	yes	characteristic
338	C₂²	#72258739	1	1	yes	characteristic
339	C₂²	#72265802	1	1	yes	characteristic
340	C₂²	#72265896	1	1	yes	characteristic
341	C₂	#72266321	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	#72266321
commutator	C₂³×#120	C₂³×C₄
Frattini, cosocle	C₂×#34980	C₂⁴
prime radical	#72315799	C₂
LCS	G ▷ C₂³×#120 ▷ C₂⁵ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂³ ◁ C₂⁶ ◁ C₂×#7670203 ◁ G
LECS	G ▷ C₂×#34980 ▷ C₂⁵ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72323954	C₂	semidirect
2. #72323927	C₂	semidirect
3. #72323874	C₂	semidirect
4. #72323858	C₂	semidirect
5. #72323220	C₂	semidirect
6. #72323219	C₂²	semidirect
7. #72323217	C₂²	semidirect
9. #72314925	C₄	semidirect
10. #72314621	C₂	semidirect
11. #72314618	C₂²	semidirect
12. #72314610	C₂²	semidirect
13. #72302204	C₂	semidirect
16. #72302130	D₄	semidirect
21. #72260662	C₄	semidirect
22. #72256276	C₂	semidirect
23. #72240489	C₄	semidirect
24. #72240132	C₂×C₄	semidirect
25. #72240132	C₂×C₄	semidirect
26. #72238601	C₂²	semidirect
27. #72238353	C₂	semidirect
28. #72237864	C₂²	semidirect
30. #72237618	C₂×C₄	semidirect
31. #72237608	C₂×C₄	semidirect
32. #72237606	C₂²	semidirect
33. #72237591	C₂²	semidirect
34. #72237588	C₂²	semidirect
35. #72237581	C₂²	semidirect
36. #72235213	C₄	semidirect
37. #72235186	C₂×C₄	semidirect
41. #72234641	D₄	semidirect
43. #72234592	D₄	semidirect
44. #72232592	C₂×C₄	semidirect
45. #72231950	C₂×C₄	semidirect
46. #72226177	C₂	semidirect
51. #72225776	D₄	semidirect
59. #72219301	D₄	semidirect
60. #72219295	C₄	semidirect
61. C₂×#139716	C₂×C₄	semidirect
62. C₂×#139716	C₂×C₄	semidirect
69. #72219242	C₄	semidirect
70. #72219241	C₂×C₄	semidirect
75. #72218518	C₂×C₄	semidirect
76. #72218518	D₄	semidirect
77. #72218291	C₂×C₄	semidirect
79. #72217789	C₂×C₄	semidirect
80. #72217511	C₂×C₄	semidirect
81. #72216481	D₄	semidirect
82. C₂×#347042	C₂×C₄	semidirect
83. #72211163	D₄	semidirect
84. C₂×#62817	C₂²×C₄	semidirect
102. #7626202	C₂²×C₄	semidirect
105. C₂×#21746	C₂²×C₄	semidirect
106. C₂×#21746	C₂²×C₄	semidirect
130. C₂×#8547	C₂²×C₄	semidirect
131. C₂×#8541	C₂²×C₄	semidirect
136. C₂⁸	#99	semidirect
138. C₂³×H(5,𝔽₂)	#99	semidirect
142. C₂²×#551	#99	semidirect
144. C₂²×D₄²	#99	semidirect
146. C₂²×H(3,𝔽₄)	#99	semidirect
148. C₂²×#560	#99	semidirect
156. C₂²×#525	#99	semidirect
157. C₂³×#120	#99	semidirect
170. C₂²×#518	#99	semidirect
173. C₂⁴×C₂²⋊C₄	#99	semidirect
191. C₂×#1781	#120	semidirect
208. #14679	#120	semidirect
215. #8101	#120	semidirect

Maximal subgroups

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

subgroup	index
#72323954	2
#72323927	2
#72323874	2
#72323858	2
#72323220	2
#72315799	2
#72314621	2
#72302204	2
#72256276	2
#72238353	2
#72226177	2