Subgroups — #72237991

Order 2048.

At least 6438 conjugacy classes of subgroups; only the 824 normal subgroups are shown.

The subgroup lattice has 329 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72237990	C₂	1	4	yes	maximal, complemented
2	#72237989	C₂	1	2	yes	maximal, complemented
3	#72237988	C₂	1	2	yes	maximal, complemented
4	#72237987	C₂	1	4	yes	maximal, complemented
5	#72237982	C₂	1	2	yes	maximal, complemented
6	#72237980	C₂	1	2	yes	maximal, complemented
7	#72237978	C₂	1	2	yes	maximal, complemented
8	#72237976	C₂	1	2	yes	maximal, complemented
9	#72237938	C₂	1	2	yes	maximal, complemented
10	#72237868	C₂	1	2	yes	maximal, complemented
11	#72234716	C₂	1	1	yes	maximal, characteristic, complemented
12	#72231446	C₂	1	4	yes	maximal, complemented
13	#72224136	C₂	1	1	yes	maximal, characteristic, complemented
14	#72219310	C₂	1	1	yes	maximal, characteristic, complemented
15	#10586404	C₂²	1	1	yes	characteristic
16	C₂×#47031	C₂²	1	1	yes	characteristic, complemented
17	#7630939	C₂²	1	2	yes	—
18	C₂×#34980	C₂²	1	1	yes	characteristic
19	#6499871	C₂²	1	2	yes	—
20	#6499871	C₂²	1	2	yes	—
21	#6499869	C₂²	1	2	yes	—
22	#6499869	C₂²	1	2	yes	—
23	#6470019	C₂²	1	4	yes	—
24	#6374210	C₂²	1	2	yes	—
25	#6374128	C₂²	1	1	yes	characteristic
26	#6347398	C₂²	1	4	yes	complemented
27	#6347363	C₂²	1	4	yes	complemented
28	#5025772	C₂²	1	1	yes	characteristic, complemented
29	#5020747	C₂²	1	1	yes	characteristic, complemented
30	#4435227	C₂²	1	1	yes	characteristic, complemented
31	#4381972	C₂²	1	2	yes	complemented
32	#4379699	C₂²	1	2	yes	—
33	#686193	C₂²	1	1	yes	characteristic, complemented
34	#631841	C₂²	1	2	yes	complemented
35	#612801	C₂²	1	2	yes	complemented
36	#576189	C₂²	1	1	yes	characteristic, complemented
37	#392113	C₂²	1	2	yes	complemented
38	#238038	C₂²	1	4	yes	complemented
39	#234400	C₂²	1	8	yes	complemented
40	#234325	C₂²	1	8	yes	complemented
41	#232538	C₂²	1	4	yes	complemented
42	#202024	C₂²	1	8	yes	complemented
43	#201293	C₂²	1	4	yes	complemented
44	#190147	C₂²	1	2	yes	complemented
45	#188109	C₂²	1	2	yes	—
46	#186808	C₂²	1	4	yes	—
47	#185285	C₂²	1	4	yes	complemented
48	#185273	C₂²	1	4	yes	complemented
49	#119544	C₂²	1	4	yes	complemented
50	#119538	C₂²	1	4	yes	complemented
51	#116028	C₂²	1	8	yes	complemented
52	#115697	C₂²	1	2	yes	complemented
53	#115697	C₂²	1	2	yes	complemented
54	#115633	C₂²	1	2	yes	complemented
55	#115633	C₂²	1	2	yes	complemented
56	#112274	C₂²	1	4	yes	complemented
57	#111945	C₂²	1	8	yes	complemented
58	#111939	C₂²	1	4	yes	complemented
59	#111633	C₂²	1	8	yes	complemented
60	#110152	C₂²	1	4	yes	complemented
61	#110118	C₂²	1	4	yes	complemented
62	#106744	C₂²	1	4	yes	complemented
63	C₂⁵×D₄	C₂³	1	1	yes	characteristic
64	#62820	C₂³	1	2	yes	—
65	#62820	C₂³	1	2	yes	—
66	C₂×#3484	C₂³	1	2	yes	—
67	C₂²×#534	D₄	1	1	yes	characteristic
68	C₂²×#534	C₂³	1	1	yes	characteristic
69	C₂³×#120	D₄	1	1	yes	characteristic
70	#60750	C₂³	1	8	yes	—
71	C₂×#2813	C₂³	1	2	yes	—
72	C₂×#2815	C₂³	1	1	yes	characteristic, complemented
73	#36614	C₂³	1	4	yes	—
74	C₂×#2849	C₂³	1	1	yes	characteristic
75	C₂×#2849	C₂³	1	1	yes	characteristic
76	C₂×#2847	C₂³	1	2	yes	complemented
77	C₂×#2846	D₄	1	1	yes	characteristic
78	C₂×#2846	D₄	1	1	yes	characteristic
79	#35222	C₂³	1	4	yes	—
80	C₂×#2607	C₂³	1	1	yes	characteristic, complemented
81	C₂×#2433	C₂³	1	2	yes	—
82	C₂×#2433	C₂³	1	2	yes	complemented
83	C₂×#2661	C₂³	1	2	yes	—
84	C₂×#2613	D₄	1	1	yes	characteristic
85	C₂×#2613	D₄	1	1	yes	characteristic
86	C₂×#2613	C₂³	1	1	yes	characteristic
87	C₂×#2613	C₂³	1	1	yes	characteristic
88	#34171	C₂³	1	2	yes	—
89	C₂×#2333	C₂³	1	2	yes	complemented
90	C₂×#2308	D₄	1	1	yes	characteristic
91	C₂×#2308	C₂³	1	1	yes	characteristic
92	C₂²×#379	D₄	1	1	yes	characteristic
93	#21773	C₂³	1	8	yes	—
94	#21750	D₄	1	8	yes	complemented
95	#21748	C₂³	1	4	yes	—
96	#21748	C₂³	1	4	yes	—
97	#21747	C₂³	1	2	yes	—
98	#21747	C₂³	1	2	yes	—
99	#20689	D₄	1	4	yes	complemented
100	C₂×#1783	C₂³	1	4	yes	—
101	C₂×#1783	C₂³	1	4	yes	complemented
102	#20585	D₄	1	4	yes	complemented
103	#20579	C₂³	1	4	yes	complemented
104	#17592	C₂³	1	8	yes	—
105	#17577	C₂³	1	8	yes	complemented
106	#17542	C₂³	1	8	yes	—
107	#17392	C₂³	1	4	yes	—
108	#17392	C₂³	1	4	yes	—
109	#15674	D₄	1	2	yes	complemented
110	#15464	D₄	1	2	yes	complemented
111	#15340	D₄	1	2	yes	complemented
112	#15310	D₄	1	2	yes	complemented
113	#15310	D₄	1	2	yes	complemented
114	#15283	D₄	1	2	yes	complemented
115	#15261	D₄	1	2	yes	complemented
116	#15258	D₄	1	2	yes	complemented
117	#14295	C₂³	1	2	yes	complemented
118	#14287	C₂³	1	2	yes	—
119	#14167	C₂³	1	2	yes	—
120	#13902	C₂³	1	2	yes	—
121	#13902	C₂³	1	2	yes	complemented
122	#13828	C₂³	1	1	yes	characteristic, complemented
123	#13807	C₂³	1	1	yes	characteristic, complemented
124	C₄×#379	C₂³	1	2	yes	complemented
125	#8114	C₂³	1	4	yes	complemented
126	#8114	C₂³	1	4	yes	complemented
127	#8051	C₂³	1	8	yes	complemented
128	#7983	C₂³	1	8	yes	complemented
129	#7942	C₂³	1	8	yes	complemented
130	C₂⁷	C₂×D₄	1	1	yes	characteristic
131	C₂⁷	C₂×D₄	1	1	yes	characteristic
132	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
133	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
134	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
135	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
136	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
137	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
138	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
139	C₂×#535	C₂×D₄	1	4	yes	—
140	C₂²×#127	C₂×D₄	1	2	yes	—
141	C₂²×#127	C₂×D₄	1	2	yes	—
142	C₂×#525	C₂⁴	1	4	yes	—
143	C₂²×#123	C₂×D₄	1	1	yes	characteristic
144	C₂²×#123	C₂×D₄	1	1	yes	characteristic
145	C₂²×#123	C₂×D₄	1	2	yes	—
146	C₂²×#123	C₂⁴	1	1	yes	characteristic
147	C₂²×#123	C₂⁴	1	1	yes	characteristic
148	C₂²×#121	C₂×D₄	1	2	yes	—
149	C₂²×#121	C₂×D₄	1	2	yes	—
150	C₂²×#121	C₂⁴	1	2	yes	—
151	C₂²×#120	C₂×D₄	1	1	yes	characteristic
152	C₂²×#120	C₂×D₄	1	1	yes	characteristic
153	C₂²×#120	C₂×D₄	1	1	yes	characteristic
154	C₂²×#120	C₂×D₄	1	1	yes	characteristic
155	C₂²×#120	C₂×D₄	1	1	yes	characteristic
156	C₂²×#120	C₂×D₄	1	1	yes	characteristic
157	C₂²×#120	C₂×D₄	1	1	yes	characteristic
158	C₂²×#120	C₂×D₄	1	1	yes	characteristic
159	C₂²×#120	C₂×D₄	1	2	yes	—
160	C₂×#518	C₂×D₄	1	2	yes	—
161	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
162	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
163	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
164	C₂×#407	C₂⁴	1	8	yes	—
165	C₂×#400	C₂×D₄	1	2	yes	complemented
166	C₂×#399	C₂×D₄	1	2	yes	complemented
167	C₂×#398	C₂×D₄	1	2	yes	complemented
168	C₂×#397	C₂×D₄	1	2	yes	complemented
169	C₂×#394	C₂×D₄	1	2	yes	complemented
170	C₂×#394	C₂×D₄	1	2	yes	complemented
171	C₂×#392	C₂×D₄	1	2	yes	complemented
172	C₂×#392	C₂×D₄	1	2	yes	complemented
173	#2308	C₂×D₄	1	4	yes	—
174	#2308	C₂×D₄	1	4	yes	—
175	#2308	C₂×D₄	1	4	yes	—
176	#2308	C₂×D₄	1	4	yes	—
177	C₂×#390	C₂×D₄	1	2	yes	—
178	C₂×#390	C₂×D₄	1	2	yes	—
179	#2280	C₂⁴	1	4	yes	—
180	C₂×#381	C₂×D₄	1	1	yes	characteristic
181	C₂×#381	C₂×D₄	1	1	yes	characteristic
182	C₂×#381	C₂⁴	1	1	yes	characteristic
183	C₂×#381	C₂⁴	1	1	yes	characteristic
184	C₂×#380	C₂⁴	1	2	yes	—
185	C₂×#379	C₂×D₄	1	1	yes	characteristic
186	C₂×#379	C₂×D₄	1	1	yes	characteristic
187	C₂×#379	C₂×D₄	1	1	yes	characteristic
188	C₂×#379	C₂×D₄	1	1	yes	characteristic
189	C₂×#379	C₂×D₄	1	1	yes	characteristic
190	C₂×#379	C₂×D₄	1	1	yes	characteristic
191	C₂×#379	C₂×D₄	1	1	yes	characteristic
192	C₂×#379	C₂×D₄	1	1	yes	characteristic
193	C₂×C₄×C₂²⋊C₄	C₂⁴	1	2	yes	—
194	C₂×C₄×C₂²⋊C₄	C₂⁴	1	2	yes	—
195	#1820	C₂×D₄	1	8	yes	—
196	#1820	C₂×D₄	1	8	yes	—
197	#1782	C₂×D₄	1	8	yes	—
198	#1782	C₂×D₄	1	8	yes	—
199	#1438	C₂×D₄	1	2	yes	—
200	#1438	C₂×D₄	1	2	yes	—
201	#1438	C₂×D₄	1	2	yes	—
202	#1438	C₂×D₄	1	2	yes	—
203	#1437	C₂×D₄	1	2	yes	complemented
204	#1437	C₂×D₄	1	2	yes	complemented
205	#1437	C₂×D₄	1	2	yes	complemented
206	#1437	C₂×D₄	1	2	yes	complemented
207	#1436	C₂×D₄	1	2	yes	complemented
208	#1436	C₂×D₄	1	2	yes	complemented
209	#1436	C₂×D₄	1	2	yes	complemented
210	#1436	C₂×D₄	1	2	yes	complemented
211	C₂⁶	#120	1	1	yes	characteristic
212	C₂⁶	C₂²×D₄	1	1	yes	characteristic
213	C₂⁶	C₂²×D₄	1	1	yes	characteristic
214	C₂⁶	C₂²×D₄	1	1	yes	characteristic
215	C₂⁶	C₂²×D₄	1	1	yes	characteristic
216	C₂⁶	C₂²×D₄	1	1	yes	characteristic
217	C₂²×#41	C₂²×D₄	1	4	yes	—
218	C₂³×D₄	#120	1	1	yes	characteristic
219	C₂³×D₄	#120	1	1	yes	characteristic
220	C₂³×D₄	#120	1	2	yes	—
221	C₂³×D₄	#120	1	2	yes	—
222	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
223	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
224	C₂³×D₄	C₂²×D₄	1	2	yes	—
225	C₂³×D₄	C₂²×D₄	1	2	yes	—
226	C₂³×D₄	C₂²×D₄	1	2	yes	—
227	C₂³×D₄	C₂²×D₄	1	2	yes	—
228	C₂³×D₄	C₂²×D₄	1	2	yes	—
229	C₂³×D₄	H(5,𝔽₂)	1	2	yes	—
230	C₂³×D₄	H(5,𝔽₂)	1	2	yes	—
231	C₂⁴×C₄	#120	1	1	yes	characteristic
232	C₂⁴×C₄	#120	1	2	yes	—
233	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
234	C₂⁴×C₄	C₂⁵	1	1	yes	characteristic
235	C₂×C₂²⋊Q₈	H(5,𝔽₂)	1	8	yes	—
236	C₂×#121	H(5,𝔽₂)	1	8	yes	—
237	C₂×#117	C₂²×D₄	1	4	yes	—
238	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
239	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
240	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
241	C₂²×C₂²⋊C₄	#120	1	2	yes	—
242	C₂²×C₂²⋊C₄	#120	1	2	yes	—
243	C₂²×C₂²⋊C₄	#120	1	2	yes	—
244	C₂²×C₂²⋊C₄	#120	1	2	yes	—
245	C₂²×C₂²⋊C₄	#120	1	2	yes	—
246	C₂²×C₂²⋊C₄	#120	1	2	yes	—
247	C₂²×C₂²⋊C₄	#120	1	2	yes	—
248	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
249	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
250	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
251	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
252	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
253	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
254	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
255	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
256	C₂²×C₄²	C₂²×D₄	1	2	yes	—
257	C₂²×C₄²	C₂²×D₄	1	2	yes	—
258	#381	C₂²×D₄	1	8	yes	—
259	#381	C₂²×D₄	1	4	yes	—
260	#381	C₂²×D₄	1	4	yes	—
261	#379	#120	1	4	yes	—
262	#379	#120	1	4	yes	—
263	C₂×#95	C₂²×D₄	1	2	yes	—
264	C₂×#95	C₂²×D₄	1	2	yes	—
265	C₂×#95	C₂²×D₄	1	2	yes	—
266	C₂×#95	C₂²×D₄	1	2	yes	—
267	C₂⁵	C₂×#120	1	1	yes	characteristic
268	C₂⁵	C₂×#120	1	1	yes	characteristic
269	C₂⁵	C₂×#120	1	1	yes	characteristic
270	C₂⁵	C₂×#120	1	1	yes	characteristic
271	C₂⁵	C₂×#120	1	1	yes	characteristic
272	C₂⁵	C₂×#120	1	2	yes	—
273	C₂⁵	C₂×#120	1	2	yes	—
274	C₂⁵	C₂×#120	1	1	yes	characteristic
275	C₂⁵	#534	1	1	yes	characteristic
276	C₂⁵	#534	1	1	yes	characteristic
277	C₂⁵	#534	1	2	yes	—
278	C₂⁵	C₂³×D₄	1	1	yes	characteristic
279	C₂²×Q₈	#535	1	4	yes	complemented
280	C₂²×D₄	#535	1	4	yes	complemented
281	C₂²×D₄	D₄²	1	4	yes	—
282	C₂²×D₄	D₄²	1	4	yes	—
283	C₂²×D₄	D₄²	1	4	yes	—
284	C₂²×D₄	D₄²	1	4	yes	—
285	C₂³×C₄	C₂×#120	1	2	yes	—
286	C₂³×C₄	C₂×#120	1	2	yes	—
287	C₂³×C₄	C₂×#120	1	1	yes	characteristic
288	C₂³×C₄	C₂×#120	1	1	yes	characteristic
289	C₂³×C₄	C₂³×D₄	1	2	yes	—
290	C₂³×C₄	C₂³×D₄	1	2	yes	—
291	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
292	C₂³×C₄	C₂×H(5,𝔽₂)	1	8	yes	—
293	C₂×C₄⋊C₄	#535	1	8	yes	complemented
294	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
295	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
296	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
297	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
298	C₂⁴	#2403	1	4	yes	—
299	C₂⁴	#2403	1	1	yes	characteristic
300	C₂⁴	#2403	1	1	yes	characteristic
301	C₂⁴	#2403	1	1	yes	characteristic
302	C₂⁴	#2403	1	1	yes	characteristic
303	C₂⁴	C₂²×#120	1	1	yes	characteristic
304	C₂⁴	C₂²×#120	1	1	yes	characteristic
305	C₂⁴	C₂×#534	1	1	yes	characteristic
306	C₂⁴	#3484	1	4	yes	—
307	C₂²×C₄	C₂×#535	1	4	yes	—
308	C₂²×C₄	C₂×D₄²	1	4	yes	—
309	C₂²×C₄	#3484	1	4	yes	—
310	C₂²×C₄	#3484	1	4	yes	—
311	C₂²×C₄	#3484	1	4	yes	—
312	C₂²×C₄	#3532	1	4	yes	—
313	C₂²×C₄	#3532	1	4	yes	—
314	C₂³	#23895	1	2	yes	—
315	C₂³	#23895	1	2	yes	—
316	C₂³	C₂×#2403	1	1	yes	characteristic
317	C₂³	#35222	1	2	yes	—
318	C₂³	#35346	1	2	yes	—
319	C₂³	#36702	1	2	yes	—
320	C₂×C₄	#37645	1	8	yes	—
321	C₂²	#616961	1	1	yes	characteristic
322	C₂²	C₂×#23895	1	1	yes	characteristic
323	C₂²	C₂×#23895	1	1	yes	characteristic
324	C₂²	#6499855	1	2	yes	—
325	C₂²	#6499861	1	2	yes	—
326	C₂	#72225733	1	1	yes	characteristic
327	C₂	#72237986	1	2	yes	—

	subgroup	G/H
center, socle	C₂²	#616961
commutator, Frattini, cosocle	C₂⁴×C₄	C₂⁵
LCS	G ▷ C₂⁴×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁴×C₄ ◁ G
LECS	G ▷ C₂⁴×C₄ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72237990	C₂	semidirect
2. #72237989	C₂	semidirect
3. #72237988	C₂	semidirect
4. #72237987	C₂	semidirect
5. #72237982	C₂	semidirect
6. #72237980	C₂	semidirect
7. #72237978	C₂	semidirect
8. #72237976	C₂	semidirect
9. #72237938	C₂	semidirect
10. #72237868	C₂	semidirect
11. #72234716	C₂	semidirect
12. #72231446	C₂	semidirect
13. #72224136	C₂	semidirect
14. #72219310	C₂	semidirect
16. C₂×#47031	C₂²	semidirect
26. #6347398	C₂²	semidirect
27. #6347363	C₂²	semidirect
28. #5025772	C₂²	semidirect
29. #5020747	C₂²	semidirect
30. #4435227	C₂²	semidirect
31. #4381972	C₂²	semidirect
33. #686193	C₂²	semidirect
34. #631841	C₂²	semidirect
35. #612801	C₂²	semidirect
36. #576189	C₂²	semidirect
37. #392113	C₂²	semidirect
38. #238038	C₂²	semidirect
39. #234400	C₂²	semidirect
40. #234325	C₂²	semidirect
41. #232538	C₂²	semidirect
42. #202024	C₂²	semidirect
43. #201293	C₂²	semidirect
44. #190147	C₂²	semidirect
47. #185285	C₂²	semidirect
48. #185273	C₂²	semidirect
49. #119544	C₂²	semidirect
50. #119538	C₂²	semidirect
51. #116028	C₂²	semidirect
52. #115697	C₂²	semidirect
53. #115697	C₂²	semidirect
54. #115633	C₂²	semidirect
55. #115633	C₂²	semidirect
56. #112274	C₂²	semidirect
57. #111945	C₂²	semidirect
58. #111939	C₂²	semidirect
59. #111633	C₂²	semidirect
60. #110152	C₂²	semidirect
61. #110118	C₂²	semidirect
62. #106744	C₂²	semidirect
72. C₂×#2815	C₂³	semidirect
76. C₂×#2847	C₂³	semidirect
80. C₂×#2607	C₂³	semidirect
82. C₂×#2433	C₂³	semidirect
89. C₂×#2333	C₂³	semidirect
94. #21750	D₄	semidirect
99. #20689	D₄	semidirect
101. C₂×#1783	C₂³	semidirect
102. #20585	D₄	semidirect
103. #20579	C₂³	semidirect
105. #17577	C₂³	semidirect
109. #15674	D₄	semidirect
110. #15464	D₄	semidirect
111. #15340	D₄	semidirect
112. #15310	D₄	semidirect
113. #15310	D₄	semidirect
114. #15283	D₄	semidirect
115. #15261	D₄	semidirect
116. #15258	D₄	semidirect
117. #14295	C₂³	semidirect
121. #13902	C₂³	semidirect
122. #13828	C₂³	semidirect
123. #13807	C₂³	semidirect
124. C₄×#379	C₂³	semidirect
125. #8114	C₂³	semidirect
126. #8114	C₂³	semidirect
127. #8051	C₂³	semidirect
128. #7983	C₂³	semidirect
129. #7942	C₂³	semidirect
165. C₂×#400	C₂×D₄	semidirect
166. C₂×#399	C₂×D₄	semidirect
167. C₂×#398	C₂×D₄	semidirect
168. C₂×#397	C₂×D₄	semidirect
169. C₂×#394	C₂×D₄	semidirect
170. C₂×#394	C₂×D₄	semidirect
171. C₂×#392	C₂×D₄	semidirect
172. C₂×#392	C₂×D₄	semidirect
203. #1437	C₂×D₄	semidirect
204. #1437	C₂×D₄	semidirect
205. #1437	C₂×D₄	semidirect
206. #1437	C₂×D₄	semidirect
207. #1436	C₂×D₄	semidirect
208. #1436	C₂×D₄	semidirect
209. #1436	C₂×D₄	semidirect
210. #1436	C₂×D₄	semidirect
279. C₂²×Q₈	#535	semidirect
280. C₂²×D₄	#535	semidirect
293. C₂×C₄⋊C₄	#535	semidirect

Maximal subgroups

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

subgroup	index
#72237990	2
#72237989	2
#72237988	2
#72237987	2
#72237982	2
#72237980	2
#72237978	2
#72237976	2
#72237938	2
#72237868	2
#72234716	2
#72231446	2
#72224136	2
#72219310	2