Subgroups — #72261358

Order 2048.

At least 6269 conjugacy classes of subgroups; only the 860 normal subgroups are shown.

The subgroup lattice has 379 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72261331	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#112857	C₂	1	1	yes	maximal, characteristic, complemented
3	#72260968	C₂	1	2	yes	maximal, complemented
4	C₂×#115179	C₂	1	2	yes	maximal, complemented
5	C₂×#4307937	C₂	1	1	yes	maximal, characteristic, complemented
6	#72235217	C₂	1	2	yes	maximal, complemented
7	C₂×#114565	C₂	1	2	yes	maximal, complemented
8	C₂×#115697	C₂	1	1	yes	maximal, characteristic, complemented
9	#72234304	C₂	1	1	yes	maximal, characteristic, complemented
10	#72231771	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#6628842	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂⁶×D₄	C₂²	1	1	yes	characteristic
13	C₂²×#3003	C₂²	1	2	yes	—
14	#7641875	C₂²	1	1	yes	characteristic, complemented
15	C₂×#36614	C₂²	1	1	yes	characteristic
16	C₂²×#2849	C₂²	1	1	yes	characteristic
17	C₂²×#2613	C₂²	1	2	yes	—
18	C₂×#21748	C₂²	1	1	yes	characteristic, complemented
19	C₂×#21747	C₂²	1	1	yes	characteristic, complemented
20	C₂×#20598	C₂²	1	2	yes	—
21	C₂×#20598	C₂²	1	2	yes	—
22	C₂×#20598	C₂²	1	2	yes	—
23	C₂×#20579	C₂²	1	1	yes	characteristic
24	C₂×#20579	C₂²	1	1	yes	characteristic
25	C₂×#17587	C₂²	1	2	yes	complemented
26	C₂×#17392	C₂²	1	2	yes	complemented
27	#607558	C₂²	1	1	yes	characteristic
28	C₂×#14681	C₂²	1	1	yes	characteristic
29	C₂×#14335	C₂²	1	2	yes	—
30	#355915	C₂²	1	1	yes	characteristic, complemented
31	#181740	C₂²	1	2	yes	complemented
32	C₂×#8114	C₂²	1	2	yes	complemented
33	C₂×#7943	C₂²	1	2	yes	complemented
34	C₂×#7943	C₂²	1	2	yes	complemented
35	C₂⁵×D₄	D₄	1	4	yes	complemented
36	C₂⁵×D₄	C₂³	1	2	yes	—
37	C₂⁶×C₄	C₂³	1	1	yes	characteristic
38	C₂²×#525	D₄	1	2	yes	complemented
39	C₂²×#525	C₂³	1	1	yes	characteristic
40	C₂³×#123	D₄	1	1	yes	characteristic
41	C₂³×#123	C₂³	1	1	yes	characteristic
42	C₂³×#120	D₄	1	1	yes	characteristic
43	C₂²×#450	D₄	1	4	yes	complemented
44	C₂²×#447	D₄	1	4	yes	complemented
45	C₂²×#407	C₂³	1	2	yes	—
46	C₂²×#407	C₂³	1	2	yes	—
47	C₂²×#394	D₄	1	4	yes	complemented
48	C₂²×#392	D₄	1	4	yes	complemented
49	C₂×#2280	D₄	1	2	yes	complemented
50	C₂×#2280	D₄	1	4	yes	complemented
51	C₂×#2280	C₂³	1	1	yes	characteristic
52	C₂×#2280	C₂³	1	1	yes	characteristic
53	C₂×#2280	C₂³	1	1	yes	characteristic
54	C₂²×#381	D₄	1	1	yes	characteristic
55	C₂²×#381	C₂³	1	2	yes	—
56	C₂²×#381	C₂³	1	1	yes	characteristic
57	C₂²×#379	D₄	1	1	yes	characteristic
58	#20598	D₄	1	8	yes	complemented
59	C₂×#1786	D₄	1	8	yes	complemented
60	#20579	D₄	1	4	yes	complemented
61	#14681	D₄	1	4	yes	complemented
62	#14335	D₄	1	8	yes	complemented
63	C₂⁷	C₂×D₄	1	1	yes	characteristic
64	C₂³×#41	C₂×D₄	1	1	yes	characteristic
65	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
66	C₂⁴×D₄	C₂×D₄	1	4	yes	—
67	C₂⁴×D₄	C₂×D₄	1	4	yes	—
68	C₂⁴×D₄	C₂×D₄	1	4	yes	—
69	C₂⁴×D₄	C₂×D₄	1	4	yes	—
70	C₂⁴×D₄	C₂×D₄	1	4	yes	—
71	C₂⁴×D₄	C₂×D₄	1	4	yes	—
72	C₂⁴×D₄	#41	1	4	yes	—
73	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
74	C₂⁵×C₄	C₂×D₄	1	2	yes	—
75	C₂⁵×C₄	C₂×D₄	1	2	yes	—
76	C₂⁵×C₄	C₂×D₄	1	2	yes	—
77	C₂⁵×C₄	C₂×D₄	1	2	yes	—
78	C₂⁵×C₄	C₂×D₄	1	2	yes	—
79	C₂⁵×C₄	#41	1	2	yes	—
80	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
81	C₂²×C₂²⋊Q₈	C₂×D₄	1	2	yes	—
82	C₂²×#121	C₂×D₄	1	2	yes	—
83	C₂²×#117	C₂×D₄	1	2	yes	—
84	C₂²×#117	C₂×D₄	1	2	yes	—
85	C₂²×#117	C₂×D₄	1	1	yes	characteristic
86	C₂²×#117	C₂×D₄	1	2	yes	—
87	C₂³×C₄⋊C₄	C₂×D₄	1	2	yes	—
88	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
89	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
90	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
91	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
92	C₂×#407	C₂×D₄	1	4	yes	—
93	C₂×#407	C₂×D₄	1	4	yes	—
94	C₂²×C₂²⋊C₈	C₂×D₄	1	4	yes	—
95	C₂²×C₂²⋊C₈	C₂×D₄	1	4	yes	—
96	#2280	C₂×D₄	1	4	yes	—
97	C₂×#381	C₂×D₄	1	4	yes	—
98	C₂×#381	C₂×D₄	1	4	yes	—
99	C₂×#381	C₂×D₄	1	4	yes	—
100	C₂×#380	C₂×D₄	1	4	yes	—
101	C₂²×#95	C₂×D₄	1	4	yes	—
102	C₂⁶	#120	1	2	yes	—
103	C₂⁶	#120	1	2	yes	—
104	C₂⁶	#120	1	1	yes	characteristic
105	C₂⁶	#121	1	2	yes	—
106	C₂⁶	C₂²×D₄	1	1	yes	characteristic
107	C₂³×Q₈	#120	1	1	yes	characteristic, complemented
108	C₂³×D₄	#120	1	8	yes	—
109	C₂³×D₄	#120	1	8	yes	—
110	C₂³×D₄	#120	1	8	yes	—
111	C₂³×D₄	#120	1	1	yes	characteristic, complemented
112	C₂³×D₄	#121	1	8	yes	—
113	C₂³×D₄	#121	1	8	yes	—
114	C₂³×D₄	#121	1	8	yes	—
115	C₂³×D₄	#127	1	8	yes	—
116	C₂⁴×C₄	#120	1	2	yes	—
117	C₂⁴×C₄	#120	1	4	yes	—
118	C₂⁴×C₄	#120	1	2	yes	—
119	C₂⁴×C₄	#120	1	1	yes	characteristic
120	C₂⁴×C₄	#120	1	2	yes	—
121	C₂⁴×C₄	#121	1	4	yes	—
122	C₂⁴×C₄	#121	1	4	yes	—
123	C₂⁴×C₄	#121	1	2	yes	—
124	C₂⁴×C₄	#127	1	4	yes	—
125	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
126	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
127	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
128	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
129	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
130	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
131	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
132	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
133	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
134	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
135	C₂⁴×C₄	C₂×#41	1	2	yes	—
136	C₂⁴×C₄	C₂×#41	1	1	yes	characteristic
137	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
138	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
139	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
140	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
141	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
142	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
143	C₂×#117	#120	1	4	yes	complemented
144	C₂²×C₄⋊C₄	#120	1	2	yes	complemented
145	C₂²×C₄⋊C₄	#120	1	4	yes	complemented
146	C₂²×C₂²⋊C₄	#120	1	2	yes	—
147	C₂²×C₂²⋊C₄	#120	1	2	yes	—
148	C₂×C₂²⋊C₈	#120	1	8	yes	complemented
149	C₂×#95	#120	1	8	yes	—
150	C₂⁵	#392	1	4	yes	—
151	C₂⁵	B(4,𝔽₂)	1	8	yes	—
152	C₂⁵	C₂×#120	1	1	yes	characteristic
153	C₂⁵	C₂×#120	1	1	yes	characteristic
154	C₂⁵	C₂×#120	1	1	yes	characteristic
155	C₂⁵	C₂×#120	1	1	yes	characteristic
156	C₂⁵	C₂×#121	1	1	yes	characteristic
157	C₂⁵	#534	1	1	yes	characteristic
158	C₂⁵	#534	1	1	yes	characteristic
159	C₂⁵	D₄²	1	2	yes	—
160	C₂⁵	D₄²	1	2	yes	—
161	C₂⁵	D₄²	1	2	yes	—
162	C₂⁵	#546	1	2	yes	—
163	C₂²×D₄	#392	1	16	yes	—
164	C₂³×C₄	#392	1	4	yes	—
165	C₂³×C₄	B(4,𝔽₂)	1	8	yes	—
166	C₂³×C₄	C₂×#120	1	1	yes	characteristic
167	C₂³×C₄	C₂×#120	1	1	yes	characteristic
168	C₂³×C₄	C₂×#120	1	1	yes	characteristic
169	C₂³×C₄	C₂×#120	1	1	yes	characteristic
170	C₂³×C₄	C₂×#120	1	2	yes	—
171	C₂³×C₄	C₂×#120	1	2	yes	—
172	C₂³×C₄	C₂×#120	1	2	yes	—
173	C₂³×C₄	C₂×#120	1	2	yes	—
174	C₂³×C₄	C₂×#120	1	2	yes	—
175	C₂³×C₄	C₂×#121	1	1	yes	characteristic
176	C₂³×C₄	C₂×#121	1	1	yes	characteristic
177	C₂³×C₄	C₂×#121	1	2	yes	—
178	C₂³×C₄	C₂×#121	1	2	yes	—
179	C₂³×C₄	C₂×#121	1	2	yes	—
180	C₂³×C₄	#525	1	1	yes	characteristic
181	C₂³×C₄	#525	1	2	yes	—
182	C₂³×C₄	C₂×#127	1	1	yes	characteristic
183	C₂³×C₄	C₂×#127	1	2	yes	—
184	C₂³×C₄	#534	1	1	yes	characteristic
185	C₂³×C₄	#534	1	1	yes	characteristic
186	C₂³×C₄	#534	1	1	yes	characteristic
187	C₂³×C₄	#534	1	2	yes	—
188	C₂³×C₄	#534	1	2	yes	—
189	C₂³×C₄	#534	1	2	yes	—
190	C₂³×C₄	#534	1	2	yes	—
191	C₂³×C₄	#534	1	2	yes	—
192	C₂³×C₄	#534	1	2	yes	—
193	C₂³×C₄	#534	1	2	yes	—
194	C₂³×C₄	#534	1	2	yes	—
195	C₂³×C₄	#535	1	1	yes	characteristic
196	C₂³×C₄	#535	1	2	yes	—
197	C₂³×C₄	#535	1	2	yes	—
198	C₂³×C₄	#535	1	2	yes	—
199	C₂³×C₄	#535	1	2	yes	—
200	C₂³×C₄	#535	1	2	yes	—
201	C₂³×C₄	#535	1	2	yes	—
202	C₂³×C₄	#535	1	2	yes	—
203	C₂³×C₄	#538	1	2	yes	—
204	C₂³×C₄	#538	1	2	yes	—
205	C₂³×C₄	#538	1	2	yes	—
206	C₂³×C₄	D₄²	1	2	yes	—
207	C₂³×C₄	D₄²	1	2	yes	—
208	C₂³×C₄	D₄²	1	2	yes	—
209	C₂³×C₄	D₄²	1	2	yes	—
210	C₂³×C₄	D₄²	1	2	yes	—
211	C₂³×C₄	D₄²	1	2	yes	—
212	C₂³×C₄	D₄²	1	2	yes	—
213	C₂³×C₄	D₄²	1	2	yes	—
214	C₂³×C₄	D₄²	1	2	yes	—
215	C₂³×C₄	D₄²	1	2	yes	—
216	C₂³×C₄	D₄²	1	2	yes	—
217	C₂³×C₄	D₄²	1	2	yes	—
218	C₂³×C₄	D₄²	1	2	yes	—
219	C₂³×C₄	D₄²	1	2	yes	—
220	C₂³×C₄	D₄²	1	2	yes	—
221	C₂³×C₄	D₄²	1	2	yes	—
222	C₂³×C₄	D₄²	1	2	yes	—
223	C₂³×C₄	D₄²	1	2	yes	—
224	C₂³×C₄	D₄²	1	2	yes	—
225	C₂³×C₄	D₄²	1	2	yes	—
226	C₂³×C₄	D₄²	1	2	yes	—
227	C₂³×C₄	#546	1	2	yes	—
228	C₂³×C₄	#546	1	2	yes	—
229	C₂³×C₄	#546	1	2	yes	—
230	C₂³×C₄	#546	1	2	yes	—
231	C₂³×C₄	#546	1	2	yes	—
232	C₂³×C₄	#546	1	2	yes	—
233	C₂³×C₄	#546	1	2	yes	—
234	C₂³×C₄	#546	1	2	yes	—
235	C₂³×C₄	#546	1	2	yes	—
236	C₂³×C₄	#546	1	2	yes	—
237	C₂³×C₄	#546	1	2	yes	—
238	C₂³×C₄	#560	1	2	yes	—
239	C₂³×C₄	#560	1	2	yes	—
240	C₂³×C₄	#560	1	2	yes	—
241	C₂³×C₄	H(3,𝔽₄)	1	2	yes	—
242	C₂⁴	#2021	1	8	yes	—
243	C₂⁴	C₂×#392	1	1	yes	characteristic
244	C₂⁴	#2403	1	2	yes	—
245	C₂⁴	#2403	1	2	yes	—
246	C₂⁴	#2403	1	1	yes	characteristic
247	C₂⁴	#2403	1	1	yes	characteristic
248	C₂⁴	#2403	1	1	yes	characteristic
249	C₂⁴	#2403	1	1	yes	characteristic
250	C₂⁴	#2403	1	1	yes	characteristic
251	C₂⁴	#2404	1	1	yes	characteristic
252	C₂⁴	#2408	1	2	yes	—
253	C₂⁴	#2408	1	2	yes	—
254	C₂⁴	#2410	1	1	yes	characteristic
255	C₂⁴	#2410	1	2	yes	—
256	C₂⁴	#2410	1	2	yes	—
257	C₂⁴	#2410	1	1	yes	characteristic
258	C₂⁴	#2424	1	2	yes	—
259	C₂⁴	#2433	1	2	yes	—
260	C₂⁴	#2613	1	1	yes	characteristic
261	C₂⁴	#2668	1	2	yes	—
262	C₂⁴	#2669	1	2	yes	—
263	C₂⁴	#2678	1	2	yes	—
264	C₂⁴	#2679	1	2	yes	—
265	C₂⁴	#2846	1	1	yes	characteristic
266	C₂⁴	C₂×B(4,𝔽₂)	1	4	yes	—
267	C₂⁴	C₂×B(4,𝔽₂)	1	4	yes	—
268	C₂²×C₄	#2021	1	8	yes	—
269	C₂²×C₄	C₂×#392	1	2	yes	—
270	C₂²×C₄	#2403	1	2	yes	—
271	C₂²×C₄	#2403	1	2	yes	—
272	C₂²×C₄	#2403	1	2	yes	—
273	C₂²×C₄	#2403	1	2	yes	—
274	C₂²×C₄	#2403	1	2	yes	—
275	C₂²×C₄	#2403	1	2	yes	—
276	C₂²×C₄	#2404	1	2	yes	—
277	C₂²×C₄	#2408	1	2	yes	—
278	C₂²×C₄	#2408	1	2	yes	—
279	C₂²×C₄	#2408	1	2	yes	—
280	C₂²×C₄	#2408	1	2	yes	—
281	C₂²×C₄	#2410	1	2	yes	—
282	C₂²×C₄	#2410	1	2	yes	—
283	C₂²×C₄	#2410	1	2	yes	—
284	C₂²×C₄	#2410	1	2	yes	—
285	C₂²×C₄	#2410	1	1	yes	characteristic
286	C₂²×C₄	#2410	1	1	yes	characteristic
287	C₂²×C₄	#2410	1	2	yes	—
288	C₂²×C₄	#2410	1	2	yes	—
289	C₂²×C₄	#2410	1	2	yes	—
290	C₂²×C₄	#2410	1	2	yes	—
291	C₂²×C₄	#2424	1	2	yes	—
292	C₂²×C₄	#2424	1	2	yes	—
293	C₂²×C₄	#2424	1	2	yes	—
294	C₂²×C₄	#2424	1	2	yes	—
295	C₂²×C₄	#2424	1	2	yes	—
296	C₂²×C₄	#2433	1	2	yes	—
297	C₂²×C₄	#2433	1	2	yes	—
298	C₂²×C₄	#2433	1	1	yes	characteristic
299	C₂²×C₄	#2433	1	2	yes	—
300	C₂²×C₄	#2433	1	2	yes	—
301	C₂²×C₄	#2433	1	2	yes	—
302	C₂²×C₄	#2433	1	2	yes	—
303	C₂²×C₄	#2539	1	1	yes	characteristic
304	C₂²×C₄	#2539	1	2	yes	—
305	C₂²×C₄	#2613	1	1	yes	characteristic
306	C₂²×C₄	#2613	1	2	yes	—
307	C₂²×C₄	#2613	1	2	yes	—
308	C₂²×C₄	#2617	1	1	yes	characteristic
309	C₂²×C₄	#2617	1	2	yes	—
310	C₂²×C₄	#2668	1	2	yes	—
311	C₂²×C₄	#2668	1	2	yes	—
312	C₂²×C₄	#2669	1	2	yes	—
313	C₂²×C₄	#2669	1	2	yes	—
314	C₂²×C₄	#2669	1	2	yes	—
315	C₂²×C₄	#2669	1	2	yes	—
316	C₂²×C₄	#2669	1	2	yes	—
317	C₂²×C₄	#2669	1	2	yes	—
318	C₂²×C₄	#2669	1	2	yes	—
319	C₂²×C₄	#2669	1	2	yes	—
320	C₂²×C₄	#2670	1	2	yes	—
321	C₂²×C₄	#2670	1	2	yes	—
322	C₂²×C₄	#2670	1	2	yes	—
323	C₂²×C₄	#2678	1	2	yes	—
324	C₂²×C₄	#2678	1	2	yes	—
325	C₂²×C₄	#2678	1	2	yes	—
326	C₂²×C₄	#2678	1	2	yes	—
327	C₂²×C₄	#2678	1	2	yes	—
328	C₂²×C₄	#2679	1	2	yes	—
329	C₂²×C₄	#2679	1	2	yes	—
330	C₂²×C₄	#2812	1	2	yes	—
331	C₂²×C₄	#2846	1	1	yes	characteristic
332	C₂²×C₄	#2847	1	1	yes	characteristic
333	C₂³	#14715	1	1	yes	characteristic
334	C₂³	#14715	1	1	yes	characteristic
335	C₂³	#14715	1	2	yes	—
336	C₂³	#14716	1	1	yes	characteristic
337	C₂³	#15257	1	2	yes	—
338	C₂³	#15257	1	1	yes	characteristic
339	C₂³	#15257	1	1	yes	characteristic
340	C₂³	#15258	1	1	yes	characteristic
341	C₂³	#15267	1	2	yes	—
342	C₂³	#15947	1	1	yes	characteristic
343	C₂³	#16249	1	2	yes	—
344	C₂³	C₂×#2021	1	2	yes	—
345	C₂³	C₂×#2021	1	2	yes	—
346	C₂³	#23882	1	8	yes	—
347	C₂³	#23900	1	2	yes	—
348	C₂³	#23900	1	4	yes	—
349	C₂³	#23900	1	2	yes	—
350	C₂³	#23900	1	4	yes	—
351	C₂³	#23900	1	2	yes	—
352	C₂³	#23900	1	4	yes	—
353	C₂³	#23900	1	2	yes	—
354	C₂³	#23984	1	4	yes	—
355	C₂×C₄	#14715	1	2	yes	—
356	C₂×C₄	#14716	1	2	yes	—
357	C₂×C₄	#15257	1	2	yes	—
358	C₂×C₄	#15258	1	2	yes	—
359	C₂×C₄	#15267	1	2	yes	—
360	C₂×C₄	#15267	1	2	yes	—
361	C₂×C₄	#16249	1	2	yes	—
362	C₂×C₄	#16249	1	2	yes	—
363	C₂²	#156684	1	1	yes	characteristic
364	C₂²	#394058	1	1	yes	characteristic
365	C₂²	#394058	1	2	yes	—
366	C₂²	#394058	1	1	yes	characteristic
367	C₂²	#394102	1	4	yes	—
368	C₂²	#394167	1	2	yes	—
369	C₂²	#417493	1	2	yes	—
370	C₂²	#417493	1	2	yes	—
371	C₂²	#417597	1	4	yes	—
372	C₂²	#417744	1	2	yes	—
373	C₂²	#449475	1	2	yes	—
374	C₂²	#449496	1	4	yes	—
375	C₂	#72218776	1	1	yes	characteristic
376	C₂	#72236737	1	2	yes	—
377	C₂	#72260429	1	4	yes	—

	subgroup	G/H
center, socle	C₂³	#15947
commutator, Frattini, cosocle	C₂⁵×C₄	C₂⁴
LCS	G ▷ C₂⁵×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂⁵×C₄ ◁ G
LECS	G ▷ C₂⁵×C₄ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72261331	C₂	semidirect
2. C₂×#112857	C₂	semidirect
3. #72260968	C₂	semidirect
4. C₂×#115179	C₂	semidirect
5. C₂×#4307937	C₂	semidirect
6. #72235217	C₂	semidirect
7. C₂×#114565	C₂	semidirect
8. C₂×#115697	C₂	semidirect
9. #72234304	C₂	semidirect
10. #72231771	C₂	semidirect
11. C₂×#6628842	C₂	semidirect
14. #7641875	C₂²	semidirect
18. C₂×#21748	C₂²	semidirect
19. C₂×#21747	C₂²	semidirect
25. C₂×#17587	C₂²	semidirect
26. C₂×#17392	C₂²	semidirect
30. #355915	C₂²	semidirect
31. #181740	C₂²	semidirect
32. C₂×#8114	C₂²	semidirect
33. C₂×#7943	C₂²	semidirect
34. C₂×#7943	C₂²	semidirect
35. C₂⁵×D₄	D₄	semidirect
38. C₂²×#525	D₄	semidirect
43. C₂²×#450	D₄	semidirect
44. C₂²×#447	D₄	semidirect
47. C₂²×#394	D₄	semidirect
48. C₂²×#392	D₄	semidirect
49. C₂×#2280	D₄	semidirect
50. C₂×#2280	D₄	semidirect
58. #20598	D₄	semidirect
59. C₂×#1786	D₄	semidirect
60. #20579	D₄	semidirect
61. #14681	D₄	semidirect
62. #14335	D₄	semidirect
107. C₂³×Q₈	#120	semidirect
111. C₂³×D₄	#120	semidirect
143. C₂×#117	#120	semidirect
144. C₂²×C₄⋊C₄	#120	semidirect
145. C₂²×C₄⋊C₄	#120	semidirect
148. C₂×C₂²⋊C₈	#120	semidirect

Maximal subgroups

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

subgroup	index
#72261331	2
C₂×#112857	2
#72260968	2
C₂×#115179	2
C₂×#4307937	2
#72235217	2
C₂×#114565	2
C₂×#115697	2
#72234304	2
#72231771	2
C₂×#6628842	2