Subgroups — #72310049

Order 2048.

At least 8236 conjugacy classes of subgroups; only the 840 normal subgroups are shown.

The subgroup lattice has 393 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72309377	C₂	1	2	yes	maximal, complemented
2	#72266028	C₂	1	1	yes	maximal, characteristic, complemented
3	#72237398	C₂	1	1	yes	maximal, characteristic, complemented
4	#72236453	C₂	1	2	yes	maximal, complemented
5	#72235847	C₂	1	1	yes	maximal, characteristic, complemented
6	#72234661	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#394058	C₂	1	1	yes	maximal, characteristic, complemented
8	#72218451	C₂	1	1	yes	maximal, characteristic, complemented
9	#72217875	C₂	1	1	yes	maximal, characteristic, complemented
10	#72217699	C₂	1	2	yes	maximal, complemented
11	C₂×#115690	C₂	1	2	yes	maximal, complemented
12	C₂²×#3484	C₂²	1	1	yes	characteristic
13	C₂⁴×#120	C₂²	1	1	yes	characteristic
14	#7641845	C₂²	1	2	yes	—
15	C₂²×#2846	C₂²	1	2	yes	—
16	C₂²×#2846	C₂²	1	1	yes	characteristic, complemented
17	C₂×#34980	C₂²	1	1	yes	characteristic
18	C₂×#21746	C₂²	1	2	yes	—
19	C₂×#21746	C₂²	1	2	yes	—
20	C₂×#21746	C₂²	1	2	yes	—
21	C₂×#21746	C₂²	1	2	yes	complemented
22	C₂²×#1898	C₂²	1	1	yes	characteristic, complemented
23	C₂²×#1781	C₂²	1	1	yes	characteristic
24	C₂²×#1781	C₂²	1	1	yes	characteristic
25	C₂×#14679	C₂²	1	1	yes	characteristic, complemented
26	C₂×#14679	C₂²	1	2	yes	complemented
27	#517411	C₂²	1	1	yes	characteristic
28	#517411	C₂²	1	1	yes	characteristic
29	#516383	C₂²	1	2	yes	—
30	#355913	C₂²	1	2	yes	complemented
31	C₂×#10735	C₂²	1	1	yes	characteristic, complemented
32	C₂×#10735	C₂²	1	2	yes	complemented
33	C₂×#8101	C₂²	1	2	yes	complemented
34	C₂×#8101	C₂²	1	2	yes	complemented
35	C₂⁸	C₂³	1	1	yes	characteristic
36	C₂³×H(5,𝔽₂)	D₄	1	1	yes	characteristic, complemented
37	C₂⁵×D₄	C₂³	1	1	yes	characteristic
38	C₂²×#534	D₄	1	2	yes	complemented
39	C₂²×#534	D₄	1	2	yes	complemented
40	C₂³×#120	D₄	1	2	yes	complemented
41	C₂³×#120	D₄	1	2	yes	complemented
42	C₂³×#120	D₄	1	4	yes	complemented
43	C₂³×#120	C₂³	1	1	yes	characteristic
44	C₂³×#120	C₂³	1	2	yes	—
45	C₂²×#518	D₄	1	1	yes	characteristic, complemented
46	C₂⁴×C₂²⋊C₄	C₂³	1	1	yes	characteristic
47	C₂³×#99	D₄	1	4	yes	complemented
48	#34992	D₄	1	4	yes	complemented
49	#34980	D₄	1	4	yes	complemented
50	C₂×#2308	D₄	1	2	yes	complemented
51	C₂²×#379	D₄	1	4	yes	complemented
52	C₂²×#379	C₂³	1	1	yes	characteristic
53	C₂²×#379	C₂³	1	1	yes	characteristic
54	C₂²×#379	C₂³	1	2	yes	—
55	C₂²×#379	C₂³	1	2	yes	—
56	C₂²×#379	C₂³	1	2	yes	—
57	C₂²×#379	C₂³	1	1	yes	characteristic
58	#21746	D₄	1	8	yes	complemented
59	C₂×#1898	D₄	1	8	yes	complemented
60	C₂×#1781	D₄	1	4	yes	complemented
61	#14681	D₄	1	2	yes	complemented
62	#14679	D₄	1	2	yes	complemented
63	#13869	D₄	1	4	yes	complemented
64	#13867	D₄	1	4	yes	complemented
65	C₂⁷	C₂×D₄	1	4	yes	—
66	C₂⁷	C₂×D₄	1	2	yes	—
67	C₂⁷	C₂×D₄	1	1	yes	characteristic
68	C₂⁷	C₂⁴	1	1	yes	characteristic
69	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
70	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
71	C₂⁴×D₄	C₂×D₄	1	2	yes	—
72	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
73	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
74	C₂⁴×D₄	C₂×D₄	1	2	yes	—
75	C₂⁴×D₄	C₂×D₄	1	2	yes	—
76	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
77	C₂⁴×D₄	C₂×D₄	1	2	yes	—
78	C₂⁴×D₄	C₂×D₄	1	2	yes	—
79	C₂⁴×D₄	C₂×D₄	1	2	yes	—
80	C₂⁴×D₄	C₂×D₄	1	2	yes	—
81	C₂⁴×D₄	#41	1	2	yes	—
82	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
83	C₂²×#120	C₂×D₄	1	4	yes	—
84	C₂²×#120	C₂×D₄	1	4	yes	—
85	C₂²×#120	C₂×D₄	1	4	yes	—
86	C₂²×#120	#41	1	4	yes	—
87	C₂³×C₂²⋊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	2	yes	—
91	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
92	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
93	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
94	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
95	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
96	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
97	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
98	C₂×#379	C₂×D₄	1	2	yes	—
99	C₂×#379	C₂×D₄	1	4	yes	—
100	C₂×#379	C₂×D₄	1	2	yes	—
101	C₂×#379	C₂×D₄	1	4	yes	—
102	C₂×#379	C₂×D₄	1	4	yes	—
103	C₂×#379	C₂×D₄	1	4	yes	—
104	C₂×#379	C₂×D₄	1	4	yes	—
105	C₂×#379	C₂×D₄	1	4	yes	—
106	C₂⁶	#120	1	1	yes	characteristic
107	C₂⁶	#120	1	4	yes	—
108	C₂⁶	#120	1	2	yes	—
109	C₂⁶	#120	1	1	yes	characteristic
110	C₂⁶	#120	1	1	yes	characteristic, complemented
111	C₂⁶	#121	1	2	yes	—
112	C₂⁶	#127	1	2	yes	—
113	C₂⁶	C₂²×D₄	1	1	yes	characteristic
114	C₂⁶	C₂²×D₄	1	1	yes	characteristic
115	C₂⁶	C₂²×D₄	1	1	yes	characteristic
116	C₂⁶	C₂²×D₄	1	1	yes	characteristic
117	C₂⁶	C₂²×D₄	1	2	yes	—
118	C₂⁶	C₂²×D₄	1	2	yes	—
119	C₂⁶	C₂²×D₄	1	2	yes	—
120	C₂⁶	C₂²×D₄	1	2	yes	—
121	C₂⁶	C₂²×D₄	1	1	yes	characteristic
122	C₂⁶	C₂²×D₄	1	2	yes	—
123	C₂⁶	C₂²×D₄	1	1	yes	characteristic
124	C₂⁶	C₂×#41	1	2	yes	—
125	C₂⁶	C₂×#41	1	1	yes	characteristic
126	C₂⁶	H(5,𝔽₂)	1	2	yes	—
127	C₂⁶	H(5,𝔽₂)	1	2	yes	—
128	C₂⁶	H(5,𝔽₂)	1	2	yes	—
129	C₂⁶	H(5,𝔽₂)	1	2	yes	—
130	C₂⁶	H(5,𝔽₂)	1	2	yes	—
131	C₂⁶	H(5,𝔽₂)	1	2	yes	—
132	C₂³×D₄	#120	1	2	yes	—
133	C₂³×D₄	#120	1	2	yes	—
134	C₂³×D₄	#120	1	2	yes	—
135	C₂³×D₄	#120	1	2	yes	—
136	C₂³×D₄	#120	1	4	yes	—
137	C₂³×D₄	#120	1	4	yes	—
138	C₂³×D₄	#121	1	2	yes	—
139	C₂³×D₄	#121	1	2	yes	—
140	C₂³×D₄	#121	1	2	yes	—
141	C₂³×D₄	#121	1	2	yes	—
142	C₂³×D₄	#121	1	4	yes	—
143	C₂³×D₄	#121	1	4	yes	—
144	C₂³×D₄	#121	1	4	yes	—
145	C₂³×D₄	#127	1	4	yes	—
146	C₂⁴×C₄	#120	1	1	yes	characteristic
147	C₂⁴×C₄	#120	1	1	yes	characteristic
148	C₂⁴×C₄	#120	1	2	yes	—
149	C₂⁴×C₄	#120	1	2	yes	—
150	C₂⁴×C₄	#120	1	2	yes	—
151	C₂⁴×C₄	#120	1	1	yes	characteristic, complemented
152	C₂⁴×C₄	#120	1	2	yes	complemented
153	C₂⁴×C₄	#121	1	2	yes	—
154	C₂⁴×C₄	#127	1	2	yes	—
155	C₂²×C₂²⋊C₄	#120	1	4	yes	—
156	C₂²×C₂²⋊C₄	#120	1	4	yes	—
157	C₂²×C₂²⋊C₄	#120	1	4	yes	—
158	C₂²×C₂²⋊C₄	#120	1	8	yes	—
159	C₂²×C₂²⋊C₄	#120	1	4	yes	complemented
160	C₂²×C₂²⋊C₄	#120	1	8	yes	complemented
161	C₂²×C₂²⋊C₄	#121	1	4	yes	—
162	C₂²×C₂²⋊C₄	#121	1	4	yes	—
163	C₂²×C₂²⋊C₄	#121	1	4	yes	—
164	C₂²×C₂²⋊C₄	#127	1	4	yes	—
165	#379	#120	1	4	yes	complemented
166	C₂⁵	#392	1	2	yes	—
167	C₂⁵	#392	1	2	yes	—
168	C₂⁵	#392	1	4	yes	—
169	C₂⁵	C₂×#120	1	1	yes	characteristic
170	C₂⁵	C₂×#120	1	2	yes	—
171	C₂⁵	C₂×#120	1	1	yes	characteristic
172	C₂⁵	C₂×#120	1	2	yes	—
173	C₂⁵	C₂×#120	1	2	yes	—
174	C₂⁵	C₂×#120	1	2	yes	—
175	C₂⁵	C₂×#120	1	2	yes	—
176	C₂⁵	C₂×#120	1	1	yes	characteristic
177	C₂⁵	C₂×#120	1	1	yes	characteristic
178	C₂⁵	C₂×#120	1	1	yes	characteristic
179	C₂⁵	C₂×#120	1	1	yes	characteristic
180	C₂⁵	C₂×#120	1	1	yes	characteristic
181	C₂⁵	C₂×#120	1	1	yes	characteristic
182	C₂⁵	C₂×#121	1	1	yes	characteristic
183	C₂⁵	C₂×#121	1	2	yes	—
184	C₂⁵	C₂×#121	1	1	yes	characteristic
185	C₂⁵	C₂×#121	1	1	yes	characteristic
186	C₂⁵	C₂×#121	1	2	yes	—
187	C₂⁵	C₂×#121	1	2	yes	—
188	C₂⁵	#525	1	2	yes	—
189	C₂⁵	#525	1	1	yes	characteristic
190	C₂⁵	C₂×#127	1	1	yes	characteristic
191	C₂⁵	C₂×#127	1	2	yes	—
192	C₂⁵	#534	1	1	yes	characteristic
193	C₂⁵	#534	1	2	yes	—
194	C₂⁵	#534	1	2	yes	—
195	C₂⁵	#534	1	2	yes	—
196	C₂⁵	#534	1	2	yes	—
197	C₂⁵	#534	1	1	yes	characteristic
198	C₂⁵	#534	1	2	yes	—
199	C₂⁵	#534	1	2	yes	—
200	C₂⁵	#534	1	2	yes	—
201	C₂⁵	#534	1	2	yes	—
202	C₂⁵	#534	1	1	yes	characteristic
203	C₂⁵	#534	1	1	yes	characteristic
204	C₂⁵	#534	1	1	yes	characteristic
205	C₂⁵	#535	1	2	yes	—
206	C₂⁵	#535	1	2	yes	—
207	C₂⁵	#535	1	2	yes	—
208	C₂⁵	#535	1	2	yes	—
209	C₂⁵	#535	1	1	yes	characteristic
210	C₂⁵	#535	1	2	yes	—
211	C₂⁵	#535	1	2	yes	—
212	C₂⁵	#535	1	2	yes	—
213	C₂⁵	#538	1	2	yes	—
214	C₂⁵	#538	1	2	yes	—
215	C₂⁵	#538	1	2	yes	—
216	C₂⁵	D₄²	1	2	yes	—
217	C₂⁵	D₄²	1	2	yes	—
218	C₂⁵	D₄²	1	2	yes	—
219	C₂⁵	D₄²	1	2	yes	—
220	C₂⁵	D₄²	1	2	yes	—
221	C₂⁵	D₄²	1	2	yes	—
222	C₂⁵	D₄²	1	2	yes	—
223	C₂⁵	D₄²	1	2	yes	—
224	C₂⁵	D₄²	1	2	yes	—
225	C₂⁵	D₄²	1	2	yes	—
226	C₂⁵	D₄²	1	2	yes	—
227	C₂⁵	D₄²	1	2	yes	—
228	C₂⁵	D₄²	1	2	yes	—
229	C₂⁵	D₄²	1	2	yes	—
230	C₂⁵	D₄²	1	2	yes	—
231	C₂⁵	D₄²	1	2	yes	—
232	C₂⁵	D₄²	1	2	yes	—
233	C₂⁵	D₄²	1	2	yes	—
234	C₂⁵	D₄²	1	2	yes	—
235	C₂⁵	D₄²	1	2	yes	—
236	C₂⁵	D₄²	1	2	yes	—
237	C₂⁵	D₄²	1	2	yes	—
238	C₂⁵	D₄²	1	2	yes	—
239	C₂⁵	D₄²	1	2	yes	—
240	C₂⁵	#546	1	2	yes	—
241	C₂⁵	#546	1	2	yes	—
242	C₂⁵	#546	1	2	yes	—
243	C₂⁵	#546	1	2	yes	—
244	C₂⁵	#546	1	2	yes	—
245	C₂⁵	#546	1	2	yes	—
246	C₂⁵	#546	1	2	yes	—
247	C₂⁵	#546	1	2	yes	—
248	C₂⁵	#546	1	2	yes	—
249	C₂⁵	#546	1	2	yes	—
250	C₂⁵	#546	1	2	yes	—
251	C₂⁵	#546	1	2	yes	—
252	C₂⁵	#560	1	2	yes	—
253	C₂⁵	#560	1	2	yes	—
254	C₂⁵	#560	1	2	yes	—
255	C₂⁵	H(3,𝔽₄)	1	2	yes	—
256	C₂²×D₄	B(4,𝔽₂)	1	8	yes	—
257	C₂³×C₄	#392	1	2	yes	—
258	C₂³×C₄	#392	1	2	yes	—
259	C₂³×C₄	#392	1	4	yes	—
260	C₂³×C₄	#392	1	4	yes	—
261	C₂³×C₄	#392	1	4	yes	—
262	C₂⁴	#2021	1	4	yes	complemented
263	C₂⁴	C₂×#392	1	2	yes	—
264	C₂⁴	C₂×#392	1	1	yes	characteristic
265	C₂⁴	#2403	1	2	yes	—
266	C₂⁴	#2403	1	2	yes	—
267	C₂⁴	#2403	1	2	yes	—
268	C₂⁴	#2403	1	2	yes	—
269	C₂⁴	#2403	1	2	yes	—
270	C₂⁴	#2403	1	1	yes	characteristic
271	C₂⁴	#2403	1	1	yes	characteristic
272	C₂⁴	#2403	1	2	yes	—
273	C₂⁴	#2403	1	1	yes	characteristic
274	C₂⁴	#2403	1	1	yes	characteristic
275	C₂⁴	#2403	1	1	yes	characteristic
276	C₂⁴	#2403	1	2	yes	—
277	C₂⁴	#2403	1	2	yes	—
278	C₂⁴	#2404	1	2	yes	—
279	C₂⁴	#2404	1	1	yes	characteristic
280	C₂⁴	#2408	1	2	yes	—
281	C₂⁴	#2408	1	2	yes	—
282	C₂⁴	#2408	1	2	yes	—
283	C₂⁴	#2408	1	2	yes	—
284	C₂⁴	#2408	1	2	yes	—
285	C₂⁴	#2408	1	2	yes	—
286	C₂⁴	#2410	1	1	yes	characteristic
287	C₂⁴	#2410	1	2	yes	—
288	C₂⁴	#2410	1	2	yes	—
289	C₂⁴	#2410	1	2	yes	—
290	C₂⁴	#2410	1	2	yes	—
291	C₂⁴	#2410	1	2	yes	—
292	C₂⁴	#2410	1	2	yes	—
293	C₂⁴	#2410	1	2	yes	—
294	C₂⁴	#2410	1	1	yes	characteristic
295	C₂⁴	#2410	1	2	yes	—
296	C₂⁴	#2410	1	2	yes	—
297	C₂⁴	#2410	1	1	yes	characteristic
298	C₂⁴	#2410	1	1	yes	characteristic
299	C₂⁴	#2410	1	2	yes	—
300	C₂⁴	#2424	1	2	yes	—
301	C₂⁴	#2424	1	2	yes	—
302	C₂⁴	#2424	1	2	yes	—
303	C₂⁴	#2424	1	2	yes	—
304	C₂⁴	#2424	1	2	yes	—
305	C₂⁴	#2424	1	2	yes	—
306	C₂⁴	#2433	1	1	yes	characteristic
307	C₂⁴	#2433	1	2	yes	—
308	C₂⁴	#2433	1	2	yes	—
309	C₂⁴	#2433	1	2	yes	—
310	C₂⁴	#2433	1	2	yes	—
311	C₂⁴	#2433	1	2	yes	—
312	C₂⁴	#2433	1	2	yes	—
313	C₂⁴	#2433	1	2	yes	—
314	C₂⁴	#2539	1	1	yes	characteristic
315	C₂⁴	#2539	1	2	yes	—
316	C₂⁴	#2613	1	2	yes	—
317	C₂⁴	#2613	1	2	yes	—
318	C₂⁴	#2613	1	1	yes	characteristic
319	C₂⁴	#2613	1	1	yes	characteristic
320	C₂⁴	#2617	1	2	yes	—
321	C₂⁴	#2617	1	1	yes	characteristic
322	C₂⁴	#2668	1	2	yes	—
323	C₂⁴	#2668	1	2	yes	—
324	C₂⁴	#2668	1	2	yes	—
325	C₂⁴	#2669	1	2	yes	—
326	C₂⁴	#2669	1	2	yes	—
327	C₂⁴	#2669	1	2	yes	—
328	C₂⁴	#2669	1	2	yes	—
329	C₂⁴	#2669	1	2	yes	—
330	C₂⁴	#2669	1	2	yes	—
331	C₂⁴	#2669	1	2	yes	—
332	C₂⁴	#2669	1	2	yes	—
333	C₂⁴	#2669	1	2	yes	—
334	C₂⁴	#2670	1	2	yes	—
335	C₂⁴	#2670	1	2	yes	—
336	C₂⁴	#2670	1	2	yes	—
337	C₂⁴	#2678	1	2	yes	—
338	C₂⁴	#2678	1	2	yes	—
339	C₂⁴	#2678	1	2	yes	—
340	C₂⁴	#2678	1	2	yes	—
341	C₂⁴	#2678	1	2	yes	—
342	C₂⁴	#2678	1	2	yes	—
343	C₂⁴	#2679	1	2	yes	—
344	C₂⁴	#2679	1	2	yes	—
345	C₂⁴	#2679	1	2	yes	—
346	C₂⁴	#2812	1	2	yes	—
347	C₂⁴	#2846	1	1	yes	characteristic
348	C₂⁴	#2846	1	1	yes	characteristic
349	C₂⁴	#2847	1	1	yes	characteristic
350	C₂⁴	C₂×B(4,𝔽₂)	1	4	yes	—
351	C₂⁴	#3026	1	4	yes	—
352	C₂²×C₄	#2021	1	4	yes	complemented
353	C₂³	#14715	1	1	yes	characteristic
354	C₂³	#14715	1	2	yes	—
355	C₂³	#14715	1	2	yes	—
356	C₂³	#14715	1	1	yes	characteristic
357	C₂³	#14716	1	2	yes	—
358	C₂³	#14716	1	1	yes	characteristic
359	C₂³	#15257	1	1	yes	characteristic
360	C₂³	#15257	1	2	yes	—
361	C₂³	#15257	1	1	yes	characteristic
362	C₂³	#15257	1	2	yes	—
363	C₂³	#15258	1	1	yes	characteristic
364	C₂³	#15258	1	2	yes	—
365	C₂³	#15267	1	2	yes	—
366	C₂³	#15267	1	2	yes	—
367	C₂³	#15267	1	2	yes	—
368	C₂³	#15947	1	1	yes	characteristic
369	C₂³	#16249	1	2	yes	—
370	C₂³	#16249	1	2	yes	—
371	C₂³	#16249	1	2	yes	—
372	C₂³	C₂×#2021	1	2	yes	—
373	C₂³	#23444	1	2	yes	—
374	C₂³	#23895	1	8	yes	—
375	C₂³	#23900	1	4	yes	—
376	C₂³	#23903	1	4	yes	—
377	C₂³	#24404	1	8	yes	—
378	C₂³	#29634	1	4	yes	—
379	C₂³	#32898	1	4	yes	—
380	C₂²	#156684	1	1	yes	characteristic
381	C₂²	#393929	1	2	yes	—
382	C₂²	#394058	1	1	yes	characteristic
383	C₂²	#394061	1	1	yes	characteristic
384	C₂²	#394064	1	4	yes	—
385	C₂²	#394066	1	4	yes	—
386	C₂²	#394267	1	2	yes	—
387	C₂²	#417532	1	4	yes	—
388	C₂²	#417824	1	4	yes	—
389	C₂²	#454045	1	4	yes	—
390	C₂	#72225643	1	1	yes	characteristic
391	C₂	#72240549	1	2	yes	—

	subgroup	G/H
center, socle	C₂²	#156684
commutator, Frattini, cosocle	C₂⁷	C₂⁴
LCS	G ▷ C₂⁷ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁷ ◁ G
LECS	G ▷ C₂⁷ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72309377	C₂	semidirect
2. #72266028	C₂	semidirect
3. #72237398	C₂	semidirect
4. #72236453	C₂	semidirect
5. #72235847	C₂	semidirect
6. #72234661	C₂	semidirect
7. C₂×#394058	C₂	semidirect
8. #72218451	C₂	semidirect
9. #72217875	C₂	semidirect
10. #72217699	C₂	semidirect
11. C₂×#115690	C₂	semidirect
16. C₂²×#2846	C₂²	semidirect
21. C₂×#21746	C₂²	semidirect
22. C₂²×#1898	C₂²	semidirect
25. C₂×#14679	C₂²	semidirect
26. C₂×#14679	C₂²	semidirect
30. #355913	C₂²	semidirect
31. C₂×#10735	C₂²	semidirect
32. C₂×#10735	C₂²	semidirect
33. C₂×#8101	C₂²	semidirect
34. C₂×#8101	C₂²	semidirect
36. C₂³×H(5,𝔽₂)	D₄	semidirect
38. C₂²×#534	D₄	semidirect
39. C₂²×#534	D₄	semidirect
40. C₂³×#120	D₄	semidirect
41. C₂³×#120	D₄	semidirect
42. C₂³×#120	D₄	semidirect
45. C₂²×#518	D₄	semidirect
47. C₂³×#99	D₄	semidirect
48. #34992	D₄	semidirect
49. #34980	D₄	semidirect
50. C₂×#2308	D₄	semidirect
51. C₂²×#379	D₄	semidirect
58. #21746	D₄	semidirect
59. C₂×#1898	D₄	semidirect
60. C₂×#1781	D₄	semidirect
61. #14681	D₄	semidirect
62. #14679	D₄	semidirect
63. #13869	D₄	semidirect
64. #13867	D₄	semidirect
110. C₂⁶	#120	semidirect
151. C₂⁴×C₄	#120	semidirect
152. C₂⁴×C₄	#120	semidirect
159. C₂²×C₂²⋊C₄	#120	semidirect
160. C₂²×C₂²⋊C₄	#120	semidirect
165. #379	#120	semidirect
262. C₂⁴	#2021	semidirect
352. C₂²×C₄	#2021	semidirect

Maximal subgroups

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

subgroup	index
#72309377	2
#72266028	2
#72237398	2
#72236453	2
#72235847	2
#72234661	2
C₂×#394058	2
#72218451	2
#72217875	2
#72217699	2
C₂×#115690	2