Subgroups — C₂⁴×#551 #72295505

Order 1024.

633253 conjugacy classes of subgroups.

The subgroup lattice has 345 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#551	C₂	1	240	yes	maximal, direct product factor
2	C₂⁴×#126	C₂	1	2	yes	maximal, complemented
3	C₂⁴×#124	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂⁴×#123	C₂	1	2	yes	maximal, complemented
5	C₂⁴×#123	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂⁴×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
7	C₂⁴×#120	C₂	1	1	yes	maximal, characteristic
8	C₂⁴×C₄×D₄	C₂	1	2	yes	maximal, complemented
9	C₂⁴×#117	C₂	1	2	yes	maximal, complemented
10	C₂⁵×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
11	C₂⁸	C₂²	1	1	yes	characteristic
12	C₂⁵×Q₈	C₂²	1	1	yes	characteristic, complemented
13	C₂⁵×D₄	C₂²	1	2	yes	—
14	C₂⁵×D₄	C₂²	1	1	yes	characteristic
15	C₂⁶×C₄	C₂²	1	2	yes	—
16	C₂⁶×C₄	C₂²	1	2	yes	—
17	C₂⁶×C₄	C₂²	1	1	yes	characteristic, complemented
18	C₂²×#551	C₂²	1	8960	yes	direct product factor
19	C₂³×#126	C₂²	1	240	yes	complemented
20	C₂³×#124	C₂²	1	120	yes	complemented
21	C₂³×#123	C₂²	1	240	yes	complemented
22	C₂³×#123	C₂²	1	120	yes	complemented
23	C₂³×C₂²⋊Q₈	C₂²	1	240	yes	complemented
24	C₂³×#120	C₂²	1	120	yes	—
25	C₂³×C₄×D₄	C₂²	1	240	yes	complemented
26	C₂³×#117	C₂²	1	240	yes	complemented
27	C₂⁴×C₄⋊C₄	C₂²	1	2	yes	complemented
28	C₂⁴×C₄⋊C₄	C₂²	1	2	yes	complemented
29	C₂⁴×C₄⋊C₄	C₂²	1	2	yes	complemented
30	C₂⁴×C₄⋊C₄	C₂²	1	2	yes	complemented
31	C₂⁴×C₂²⋊C₄	C₂²	1	2	yes	—
32	C₂⁴×C₂²⋊C₄	C₂²	1	2	yes	—
33	C₂⁴×C₂²⋊C₄	C₂²	1	2	yes	—
34	C₂⁴×C₂²⋊C₄	C₂²	1	2	yes	—
35	C₂⁴×C₂²⋊C₄	C₂²	1	2	yes	—
36	C₂⁴×C₂²⋊C₄	C₂²	1	1	yes	characteristic
37	C₂⁴×C₂²⋊C₄	C₂²	1	240	yes	complemented
38	C₂⁴×C₂²⋊C₄	C₂²	1	2	yes	complemented
39	C₂⁴×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
40	C₂⁴×C₄²	C₂²	1	1	yes	characteristic, complemented
41	C₂⁴×C₄²	C₂²	1	2	yes	complemented
42	C₂⁷	—	2	64	no	—
43	C₂⁷	—	4	16	no	—
44	C₂⁷	C₂³	1	1	yes	characteristic
45	C₂⁷	C₂³	1	1	yes	characteristic
46	C₂⁷	C₂³	1	60	yes	—
47	C₂⁷	C₂³	1	2	yes	—
48	C₂⁴×Q₈	—	4	16	no	—
49	C₂⁴×Q₈	C₂³	1	60	yes	complemented
50	C₂⁴×D₄	—	2	64	no	—
51	C₂⁴×D₄	—	4	16	no	—
52	C₂⁴×D₄	C₂³	1	120	yes	—
53	C₂⁴×D₄	C₂³	1	60	yes	—
54	C₂⁵×C₄	—	2	64	no	—
55	C₂⁵×C₄	—	4	32	no	—
56	C₂⁵×C₄	—	4	16	no	—
57	C₂⁵×C₄	C₂³	1	120	yes	—
58	C₂⁵×C₄	C₂³	1	2	yes	—
59	C₂⁵×C₄	C₂³	1	2	yes	—
60	C₂⁵×C₄	C₂³	1	2	yes	—
61	C₂⁵×C₄	C₂³	1	2	yes	—
62	C₂⁵×C₄	C₂³	1	1	yes	characteristic
63	C₂⁵×C₄	C₂³	1	2	yes	—
64	C₂⁵×C₄	C₂³	1	120	yes	—
65	C₂⁵×C₄	C₂³	1	60	yes	complemented
66	C₂×#551	C₂³	1	61440	yes	direct product factor
67	C₂²×#126	C₂³	1	4480	yes	complemented
68	C₂²×#124	C₂³	1	2240	yes	complemented
69	C₂²×#123	C₂³	1	2240	yes	complemented
70	C₂²×#123	C₂³	1	4480	yes	complemented
71	C₂²×C₂²⋊Q₈	C₂³	1	4480	yes	complemented
72	C₂²×#120	C₂³	1	2240	yes	—
73	C₂²×C₄×D₄	C₂³	1	4480	yes	complemented
74	C₂²×#117	C₂³	1	4480	yes	complemented
75	C₂³×C₄⋊C₄	C₂³	1	120	yes	complemented
76	C₂³×C₄⋊C₄	C₂³	1	120	yes	complemented
77	C₂³×C₄⋊C₄	C₂³	1	120	yes	complemented
78	C₂³×C₄⋊C₄	C₂³	1	120	yes	complemented
79	C₂³×C₂²⋊C₄	C₂³	1	120	yes	—
80	C₂³×C₂²⋊C₄	C₂³	1	120	yes	—
81	C₂³×C₂²⋊C₄	C₂³	1	120	yes	—
82	C₂³×C₂²⋊C₄	C₂³	1	120	yes	—
83	C₂³×C₂²⋊C₄	C₂³	1	120	yes	—
84	C₂³×C₂²⋊C₄	C₂³	1	60	yes	—
85	C₂³×C₂²⋊C₄	C₂³	1	4480	yes	complemented
86	C₂³×C₂²⋊C₄	C₂³	1	120	yes	complemented
87	C₂³×C₂²⋊C₄	C₂³	1	60	yes	complemented
88	C₂³×C₄²	C₂³	1	60	yes	complemented
89	C₂³×C₄²	C₂³	1	120	yes	complemented
90	C₂⁶	—	2	32	no	—
91	C₂⁶	—	2	32	no	—
92	C₂⁶	—	2	32	no	—
93	C₂⁶	—	2	1920	no	—
94	C₂⁶	—	2	32	no	—
95	C₂⁶	—	2	16	no	—
96	C₂⁶	—	2	16	no	—
97	C₂⁶	—	4	480	no	—
98	C₂⁶	—	4	1024	no	—
99	C₂⁶	#41	1	64	yes	—
100	C₂⁶	C₂⁴	1	30	yes	—
101	C₂⁶	C₂⁴	1	30	yes	—
102	C₂⁶	C₂⁴	1	560	yes	—
103	C₂⁶	C₂⁴	1	60	yes	—
104	C₂⁶	C₂⁴	1	1	yes	characteristic
105	C₂³×Q₈	—	4	480	no	—
106	C₂³×Q₈	C₂⁴	1	560	yes	complemented
107	C₂³×D₄	—	2	1920	no	—
108	C₂³×D₄	—	4	480	no	—
109	C₂³×D₄	C₂⁴	1	1120	yes	—
110	C₂³×D₄	C₂⁴	1	560	yes	—
111	C₂⁴×C₄	—	2	1920	no	—
112	C₂⁴×C₄	—	2	32	no	—
113	C₂⁴×C₄	—	2	32	no	—
114	C₂⁴×C₄	—	2	32	no	—
115	C₂⁴×C₄	—	2	32	no	—
116	C₂⁴×C₄	—	2	32	no	—
117	C₂⁴×C₄	—	2	16	no	—
118	C₂⁴×C₄	—	4	960	no	—
119	C₂⁴×C₄	—	4	480	no	—
120	C₂⁴×C₄	C₂⁴	1	60	yes	—
121	C₂⁴×C₄	C₂⁴	1	60	yes	—
122	C₂⁴×C₄	C₂⁴	1	60	yes	—
123	C₂⁴×C₄	C₂⁴	1	60	yes	—
124	C₂⁴×C₄	C₂⁴	1	1120	yes	—
125	C₂⁴×C₄	C₂⁴	1	30	yes	—
126	C₂⁴×C₄	C₂⁴	1	60	yes	—
127	C₂⁴×C₄	C₂⁴	1	1120	yes	—
128	C₂⁴×C₄	C₂⁴	1	560	yes	complemented
129	#551	C₂⁴	1	65536	yes	direct product factor
130	C₂×#126	C₂⁴	1	15360	yes	complemented
131	C₂×#124	C₂⁴	1	7680	yes	complemented
132	C₂×#123	C₂⁴	1	7680	yes	complemented
133	C₂×#123	C₂⁴	1	15360	yes	complemented
134	C₂×C₂²⋊Q₈	C₂⁴	1	15360	yes	complemented
135	C₂×#120	C₂⁴	1	7680	yes	—
136	C₂×C₄×D₄	C₂⁴	1	15360	yes	complemented
137	C₂×#117	C₂⁴	1	15360	yes	complemented
138	C₂²×C₄⋊C₄	C₂⁴	1	1120	yes	complemented
139	C₂²×C₄⋊C₄	C₂⁴	1	1120	yes	complemented
140	C₂²×C₄⋊C₄	C₂⁴	1	1120	yes	complemented
141	C₂²×C₄⋊C₄	C₂⁴	1	1120	yes	complemented
142	C₂²×C₂²⋊C₄	C₂⁴	1	1120	yes	—
143	C₂²×C₂²⋊C₄	C₂⁴	1	1120	yes	—
144	C₂²×C₂²⋊C₄	C₂⁴	1	1120	yes	—
145	C₂²×C₂²⋊C₄	C₂⁴	1	1120	yes	—
146	C₂²×C₂²⋊C₄	C₂⁴	1	1120	yes	—
147	C₂²×C₂²⋊C₄	C₂⁴	1	560	yes	—
148	C₂²×C₂²⋊C₄	C₂⁴	1	15360	yes	complemented
149	C₂²×C₂²⋊C₄	C₂⁴	1	1120	yes	complemented
150	C₂²×C₂²⋊C₄	C₂⁴	1	560	yes	complemented
151	C₂²×C₄²	C₂⁴	1	560	yes	complemented
152	C₂²×C₄²	C₂⁴	1	1120	yes	complemented
153	C₂⁵	—	2	1024	no	—
154	C₂⁵	—	2	480	no	—
155	C₂⁵	—	2	480	no	—
156	C₂⁵	—	2	480	no	—
157	C₂⁵	—	2	8960	no	—
158	C₂⁵	—	2	480	no	—
159	C₂⁵	—	2	240	no	—
160	C₂⁵	—	2	240	no	—
161	C₂⁵	—	4	2240	no	—
162	C₂⁵	—	4	15360	no	—
163	C₂⁵	—	4	256	no	—
164	C₂⁵	—	4	256	no	—
165	C₂⁵	C₂×#41	1	960	yes	—
166	C₂⁵	C₂×#41	1	32	yes	—
167	C₂⁵	H(5,𝔽₂)	1	16	yes	—
168	C₂⁵	C₂⁵	1	140	yes	—
169	C₂⁵	C₂⁵	1	140	yes	—
170	C₂⁵	C₂⁵	1	960	yes	—
171	C₂⁵	C₂⁵	1	280	yes	—
172	C₂⁵	C₂⁵	1	15	yes	—
173	C₂²×Q₈	—	4	2240	no	—
174	C₂²×Q₈	C₂⁵	1	960	yes	complemented
175	C₂²×D₄	—	2	8960	no	—
176	C₂²×D₄	—	4	2240	no	—
177	C₂²×D₄	C₂⁵	1	1920	yes	—
178	C₂²×D₄	C₂⁵	1	960	yes	—
179	C₂³×C₄	—	2	8960	no	—
180	C₂³×C₄	—	2	480	no	—
181	C₂³×C₄	—	2	480	no	—
182	C₂³×C₄	—	2	480	no	—
183	C₂³×C₄	—	2	480	no	—
184	C₂³×C₄	—	2	480	no	—
185	C₂³×C₄	—	2	240	no	—
186	C₂³×C₄	—	4	4480	no	—
187	C₂³×C₄	—	4	2240	no	—
188	C₂³×C₄	C₂⁵	1	280	yes	—
189	C₂³×C₄	C₂⁵	1	280	yes	—
190	C₂³×C₄	C₂⁵	1	280	yes	—
191	C₂³×C₄	C₂⁵	1	280	yes	—
192	C₂³×C₄	C₂⁵	1	280	yes	—
193	C₂³×C₄	C₂⁵	1	140	yes	—
194	C₂³×C₄	C₂⁵	1	1920	yes	—
195	C₂³×C₄	C₂⁵	1	1920	yes	—
196	C₂³×C₄	C₂⁵	1	960	yes	complemented
197	#126	C₂⁵	1	8192	yes	complemented
198	#124	C₂⁵	1	4096	yes	complemented
199	#123	C₂⁵	1	4096	yes	complemented
200	#123	C₂⁵	1	8192	yes	complemented
201	C₂²⋊Q₈	C₂⁵	1	8192	yes	complemented
202	#120	C₂⁵	1	4096	yes	—
203	C₄×D₄	C₂⁵	1	8192	yes	complemented
204	#117	C₂⁵	1	8192	yes	complemented
205	C₂×C₄⋊C₄	C₂⁵	1	1920	yes	complemented
206	C₂×C₄⋊C₄	C₂⁵	1	1920	yes	complemented
207	C₂×C₄⋊C₄	C₂⁵	1	1920	yes	complemented
208	C₂×C₄⋊C₄	C₂⁵	1	1920	yes	complemented
209	C₂×C₂²⋊C₄	C₂⁵	1	1920	yes	—
210	C₂×C₂²⋊C₄	C₂⁵	1	1920	yes	—
211	C₂×C₂²⋊C₄	C₂⁵	1	1920	yes	—
212	C₂×C₂²⋊C₄	C₂⁵	1	1920	yes	—
213	C₂×C₂²⋊C₄	C₂⁵	1	1920	yes	—
214	C₂×C₂²⋊C₄	C₂⁵	1	960	yes	—
215	C₂×C₂²⋊C₄	C₂⁵	1	8192	yes	complemented
216	C₂×C₂²⋊C₄	C₂⁵	1	1920	yes	complemented
217	C₂×C₂²⋊C₄	C₂⁵	1	960	yes	complemented
218	C₂×C₄²	C₂⁵	1	960	yes	complemented
219	C₂×C₄²	C₂⁵	1	1920	yes	complemented
220	C₂⁴	—	2	1120	no	—
221	C₂⁴	—	2	1120	no	—
222	C₂⁴	—	2	7680	no	—
223	C₂⁴	—	2	1120	no	—
224	C₂⁴	—	2	7680	no	—
225	C₂⁴	—	2	1120	no	—
226	C₂⁴	—	2	560	no	—
227	C₂⁴	—	2	560	no	—
228	C₂⁴	—	4	1920	no	—
229	C₂⁴	—	4	35840	no	—
230	C₂⁴	—	4	1920	no	—
231	C₂⁴	—	4	1920	no	—
232	C₂⁴	#551	1	256	yes	direct product factor
233	C₂⁴	C₂²×#41	1	2240	yes	—
234	C₂⁴	C₂²×#41	1	240	yes	—
235	C₂⁴	C₂×H(5,𝔽₂)	1	120	yes	—
236	C₂⁴	C₂⁶	1	120	yes	—
237	C₂⁴	C₂⁶	1	120	yes	—
238	C₂⁴	C₂⁶	1	256	yes	—
239	C₂⁴	C₂⁶	1	240	yes	—
240	C₂⁴	C₂⁶	1	35	yes	—
241	C₂×Q₈	—	4	1920	no	—
242	C₂×Q₈	C₂⁶	1	256	yes	complemented
243	C₂×D₄	—	2	7680	no	—
244	C₂×D₄	—	4	1920	no	—
245	C₂×D₄	C₂⁶	1	512	yes	—
246	C₂×D₄	C₂⁶	1	256	yes	—
247	C₂²×C₄	—	2	7680	no	—
248	C₂²×C₄	—	2	1120	no	—
249	C₂²×C₄	—	2	1120	no	—
250	C₂²×C₄	—	2	1120	no	—
251	C₂²×C₄	—	2	1120	no	—
252	C₂²×C₄	—	2	1120	no	—
253	C₂²×C₄	—	2	560	no	—
254	C₂²×C₄	—	4	3840	no	—
255	C₂²×C₄	—	4	1920	no	—
256	C₂²×C₄	C₂⁶	1	240	yes	—
257	C₂²×C₄	C₂⁶	1	240	yes	—
258	C₂²×C₄	C₂⁶	1	240	yes	—
259	C₂²×C₄	C₂⁶	1	120	yes	—
260	C₂²×C₄	C₂⁶	1	240	yes	—
261	C₂²×C₄	C₂⁶	1	240	yes	—
262	C₂²×C₄	C₂⁶	1	512	yes	—
263	C₂²×C₄	C₂⁶	1	512	yes	—
264	C₂²×C₄	C₂⁶	1	256	yes	complemented
265	C₄⋊C₄	C₂⁶	1	512	yes	complemented
266	C₄⋊C₄	C₂⁶	1	512	yes	complemented
267	C₄⋊C₄	C₂⁶	1	512	yes	complemented
268	C₄⋊C₄	C₂⁶	1	512	yes	complemented
269	C₂²⋊C₄	C₂⁶	1	512	yes	—
270	C₂²⋊C₄	C₂⁶	1	512	yes	—
271	C₂²⋊C₄	C₂⁶	1	512	yes	—
272	C₂²⋊C₄	C₂⁶	1	512	yes	—
273	C₂²⋊C₄	C₂⁶	1	512	yes	—
274	C₂²⋊C₄	C₂⁶	1	256	yes	—
275	C₂²⋊C₄	C₂⁶	1	512	yes	complemented
276	C₂²⋊C₄	C₂⁶	1	256	yes	complemented
277	C₄²	C₂⁶	1	256	yes	complemented
278	C₄²	C₂⁶	1	512	yes	complemented
279	C₂³	—	2	480	no	—
280	C₂³	—	2	480	no	—
281	C₂³	—	2	8960	no	—
282	C₂³	—	2	480	no	—
283	C₂³	—	2	1024	no	—
284	C₂³	—	2	480	no	—
285	C₂³	—	2	240	no	—
286	C₂³	—	2	240	no	—
287	C₂³	—	4	256	no	—
288	C₂³	—	4	15360	no	—
289	C₂³	—	4	2240	no	—
290	C₂³	—	4	2240	no	—
291	C₂³	C₂×#551	1	960	yes	direct product factor
292	C₂³	C₂³×#41	1	960	yes	—
293	C₂³	C₂³×#41	1	280	yes	—
294	C₂³	C₂²×H(5,𝔽₂)	1	140	yes	—
295	C₂³	C₂⁷	1	16	yes	—
296	C₂³	C₂⁷	1	16	yes	—
297	C₂³	C₂⁷	1	32	yes	—
298	C₂³	C₂⁷	1	15	yes	—
299	Q₈	—	4	256	no	—
300	D₄	—	2	1024	no	—
301	D₄	—	4	256	no	—
302	C₂×C₄	—	2	1024	no	—
303	C₂×C₄	—	2	480	no	—
304	C₂×C₄	—	2	480	no	—
305	C₂×C₄	—	2	480	no	—
306	C₂×C₄	—	2	480	no	—
307	C₂×C₄	—	2	480	no	—
308	C₂×C₄	—	2	240	no	—
309	C₂×C₄	—	4	512	no	—
310	C₂×C₄	—	4	256	no	—
311	C₂×C₄	C₂⁷	1	32	yes	—
312	C₂×C₄	C₂⁷	1	32	yes	—
313	C₂×C₄	C₂⁷	1	32	yes	—
314	C₂×C₄	C₂⁷	1	16	yes	—
315	C₂×C₄	C₂⁷	1	32	yes	—
316	C₂×C₄	C₂⁷	1	32	yes	—
317	C₂²	—	2	1920	no	—
318	C₂²	—	2	32	no	—
319	C₂²	—	2	32	no	—
320	C₂²	—	2	32	no	—
321	C₂²	—	2	32	no	—
322	C₂²	—	2	16	no	—
323	C₂²	—	2	16	no	—
324	C₂²	—	4	1024	no	—
325	C₂²	—	4	480	no	—
326	C₂²	—	4	480	no	—
327	C₂²	C₂²×#551	1	560	yes	direct product factor
328	C₂²	C₂⁴×#41	1	64	yes	—
329	C₂²	C₂⁴×#41	1	60	yes	—
330	C₂²	C₂³×H(5,𝔽₂)	1	30	yes	—
331	C₂²	C₂⁸	1	1	yes	characteristic
332	C₄	—	2	32	no	—
333	C₄	—	2	32	no	—
334	C₄	—	2	32	no	—
335	C₄	—	2	32	no	—
336	C₄	—	2	32	no	—
337	C₄	—	2	16	no	—
338	C₂	—	2	64	no	—
339	C₂	—	4	16	no	—
340	C₂	—	4	16	no	—
341	C₂	C₂³×#551	1	60	yes	direct product factor
342	C₂	C₂⁵×#41	1	2	yes	—
343	C₂	C₂⁴×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁶	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁸
prime radical	C₂⁴×#120	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁶ ◁ G
LECS	G ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂³×#551	C₂	direct (N × H)
2. C₂⁴×#126	C₂	semidirect
3. C₂⁴×#124	C₂	semidirect
4. C₂⁴×#123	C₂	semidirect
5. C₂⁴×#123	C₂	semidirect
6. C₂⁴×C₂²⋊Q₈	C₂	semidirect
8. C₂⁴×C₄×D₄	C₂	semidirect
9. C₂⁴×#117	C₂	semidirect
10. C₂⁵×C₂²⋊C₄	C₂	semidirect
12. C₂⁵×Q₈	C₂²	semidirect
17. C₂⁶×C₄	C₂²	semidirect
18. C₂²×#551	C₂²	direct (N × H)
19. C₂³×#126	C₂²	semidirect
20. C₂³×#124	C₂²	semidirect
21. C₂³×#123	C₂²	semidirect
22. C₂³×#123	C₂²	semidirect
23. C₂³×C₂²⋊Q₈	C₂²	semidirect
25. C₂³×C₄×D₄	C₂²	semidirect
26. C₂³×#117	C₂²	semidirect
27. C₂⁴×C₄⋊C₄	C₂²	semidirect
28. C₂⁴×C₄⋊C₄	C₂²	semidirect
29. C₂⁴×C₄⋊C₄	C₂²	semidirect
30. C₂⁴×C₄⋊C₄	C₂²	semidirect
37. C₂⁴×C₂²⋊C₄	C₂²	semidirect
38. C₂⁴×C₂²⋊C₄	C₂²	semidirect
39. C₂⁴×C₂²⋊C₄	C₂²	semidirect
40. C₂⁴×C₄²	C₂²	semidirect
41. C₂⁴×C₄²	C₂²	semidirect
49. C₂⁴×Q₈	C₂³	semidirect
65. C₂⁵×C₄	C₂³	semidirect
66. C₂×#551	C₂³	direct (N × H)
67. C₂²×#126	C₂³	semidirect
68. C₂²×#124	C₂³	semidirect
69. C₂²×#123	C₂³	semidirect
70. C₂²×#123	C₂³	semidirect
71. C₂²×C₂²⋊Q₈	C₂³	semidirect
73. C₂²×C₄×D₄	C₂³	semidirect
74. C₂²×#117	C₂³	semidirect
75. C₂³×C₄⋊C₄	C₂³	semidirect
76. C₂³×C₄⋊C₄	C₂³	semidirect
77. C₂³×C₄⋊C₄	C₂³	semidirect
78. C₂³×C₄⋊C₄	C₂³	semidirect
85. C₂³×C₂²⋊C₄	C₂³	semidirect
86. C₂³×C₂²⋊C₄	C₂³	semidirect
87. C₂³×C₂²⋊C₄	C₂³	semidirect
88. C₂³×C₄²	C₂³	semidirect
89. C₂³×C₄²	C₂³	semidirect
106. C₂³×Q₈	C₂⁴	semidirect
128. C₂⁴×C₄	C₂⁴	semidirect
129. #551	C₂⁴	direct (N × H)
130. C₂×#126	C₂⁴	semidirect
131. C₂×#124	C₂⁴	semidirect
132. C₂×#123	C₂⁴	semidirect
133. C₂×#123	C₂⁴	semidirect
134. C₂×C₂²⋊Q₈	C₂⁴	semidirect
136. C₂×C₄×D₄	C₂⁴	semidirect
137. C₂×#117	C₂⁴	semidirect
138. C₂²×C₄⋊C₄	C₂⁴	semidirect
139. C₂²×C₄⋊C₄	C₂⁴	semidirect
140. C₂²×C₄⋊C₄	C₂⁴	semidirect
141. C₂²×C₄⋊C₄	C₂⁴	semidirect
148. C₂²×C₂²⋊C₄	C₂⁴	semidirect
149. C₂²×C₂²⋊C₄	C₂⁴	semidirect
150. C₂²×C₂²⋊C₄	C₂⁴	semidirect
151. C₂²×C₄²	C₂⁴	semidirect
152. C₂²×C₄²	C₂⁴	semidirect
174. C₂²×Q₈	C₂⁵	semidirect
196. C₂³×C₄	C₂⁵	semidirect
197. #126	C₂⁵	semidirect
198. #124	C₂⁵	semidirect
199. #123	C₂⁵	semidirect
200. #123	C₂⁵	semidirect
201. C₂²⋊Q₈	C₂⁵	semidirect
203. C₄×D₄	C₂⁵	semidirect
204. #117	C₂⁵	semidirect
205. C₂×C₄⋊C₄	C₂⁵	semidirect
206. C₂×C₄⋊C₄	C₂⁵	semidirect
207. C₂×C₄⋊C₄	C₂⁵	semidirect
208. C₂×C₄⋊C₄	C₂⁵	semidirect
215. C₂×C₂²⋊C₄	C₂⁵	semidirect
216. C₂×C₂²⋊C₄	C₂⁵	semidirect
217. C₂×C₂²⋊C₄	C₂⁵	semidirect
218. C₂×C₄²	C₂⁵	semidirect
219. C₂×C₄²	C₂⁵	semidirect
232. C₂⁴	#551	direct (N × H)
242. C₂×Q₈	C₂⁶	semidirect
264. C₂²×C₄	C₂⁶	semidirect
265. C₄⋊C₄	C₂⁶	semidirect
266. C₄⋊C₄	C₂⁶	semidirect
267. C₄⋊C₄	C₂⁶	semidirect
268. C₄⋊C₄	C₂⁶	semidirect
275. C₂²⋊C₄	C₂⁶	semidirect
276. C₂²⋊C₄	C₂⁶	semidirect
277. C₄²	C₂⁶	semidirect
278. C₄²	C₂⁶	semidirect
291. C₂³	C₂×#551	direct (N × H)
327. C₂²	C₂²×#551	direct (N × H)
341. C₂	C₂³×#551	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#551	2
C₂⁴×#126	2
C₂⁴×#124	2
C₂⁴×#123	2
C₂⁴×C₂²⋊Q₈	2
C₂⁴×#120	2
C₂⁴×C₄×D₄	2
C₂⁴×#117	2
C₂⁵×C₂²⋊C₄	2

Subgroups — C24×#551 #72295505

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×#551 #72295505