Subgroups — #72251774

Order 2048.

At least 6356 conjugacy classes of subgroups; only the 984 normal subgroups are shown.

The subgroup lattice has 338 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72251773	C₂	1	2	yes	maximal, complemented
2	#72251753	C₂	1	8	yes	maximal, complemented
3	#72251743	C₂	1	8	yes	maximal, complemented
4	#72237534	C₂	1	1	yes	maximal, characteristic, complemented
5	#72235082	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#8181078	C₂	1	1	yes	maximal, characteristic, complemented
7	#72231754	C₂	1	2	yes	maximal, complemented
8	#72231744	C₂	1	2	yes	maximal, complemented
9	#72219496	C₂	1	1	yes	maximal, characteristic, complemented
10	#72219495	C₂	1	1	yes	maximal, characteristic, complemented
11	#72215568	C₂	1	1	yes	maximal, characteristic, complemented
12	#72215536	C₂	1	1	yes	maximal, characteristic, complemented
13	#72210564	C₂	1	2	yes	maximal, complemented
14	#10575442	C₂²	1	1	yes	characteristic, complemented
15	#8181078	C₂²	1	8	yes	—
16	C₂×#52004	C₂²	1	1	yes	characteristic
17	C₂×#51902	C₂²	1	1	yes	characteristic
18	C₂×#46355	C₂²	1	2	yes	—
19	C₂×#59089	C₂²	1	2	yes	—
20	C₂×#35222	C₂²	1	1	yes	characteristic
21	#6470228	C₂²	1	2	yes	complemented
22	#6470025	C₂²	1	2	yes	complemented
23	#6437616	C₂²	1	1	yes	characteristic, complemented
24	#6437449	C₂²	1	1	yes	characteristic, complemented
25	#500221	C₂²	1	8	yes	complemented
26	#500203	C₂²	1	4	yes	complemented
27	#500179	C₂²	1	4	yes	complemented
28	#499855	C₂²	1	4	yes	complemented
29	#499831	C₂²	1	4	yes	complemented
30	#499788	C₂²	1	8	yes	complemented
31	#496228	C₂²	1	2	yes	complemented
32	#496228	C₂²	1	2	yes	complemented
33	#496208	C₂²	1	2	yes	complemented
34	#496190	C₂²	1	2	yes	complemented
35	#493385	C₂²	1	1	yes	characteristic, complemented
36	#493372	C₂²	1	1	yes	characteristic, complemented
37	#493352	C₂²	1	2	yes	complemented
38	#449562	C₂²	1	4	yes	complemented
39	#449496	C₂²	1	4	yes	complemented
40	#382419	C₂²	1	1	yes	characteristic, complemented
41	#359513	C₂²	1	1	yes	characteristic, complemented
42	#359507	C₂²	1	1	yes	characteristic, complemented
43	#246327	C₂²	1	8	yes	complemented
44	#246319	C₂²	1	8	yes	complemented
45	#201819	C₂²	1	2	yes	complemented
46	#201091	C₂²	1	2	yes	complemented
47	#187756	C₂²	1	2	yes	complemented
48	#133843	C₂²	1	8	yes	complemented
49	#133398	C₂²	1	16	yes	complemented
50	#133382	C₂²	1	16	yes	complemented
51	#133362	C₂²	1	8	yes	complemented
52	#133350	C₂²	1	8	yes	complemented
53	C₂⁵×D₄	D₄	1	1	yes	characteristic, complemented
54	#62811	C₂³	1	1	yes	characteristic, complemented
55	C₂²×D₄²	D₄	1	1	yes	characteristic, complemented
56	C₂²×D₄²	D₄	1	2	yes	complemented
57	C₂²×H(3,𝔽₄)	D₄	1	1	yes	characteristic, complemented
58	C₂²×#535	C₂³	1	1	yes	characteristic
59	C₂²×#535	C₂³	1	1	yes	characteristic
60	C₂²×#534	D₄	1	2	yes	complemented
61	C₂²×#525	C₂³	1	1	yes	characteristic
62	#60518	C₂³	1	2	yes	complemented
63	C₂×#3025	C₂³	1	2	yes	complemented
64	C₂×#3021	C₂³	1	2	yes	complemented
65	#60369	C₂³	1	2	yes	complemented
66	#60064	C₂³	1	1	yes	characteristic, complemented
67	#59089	D₄	1	8	yes	complemented
68	#59089	C₂³	1	8	yes	—
69	C₂×#2733	D₄	1	2	yes	complemented
70	C₂×#2709	D₄	1	2	yes	complemented
71	C₂×#2697	D₄	1	2	yes	complemented
72	C₂×#2669	D₄	1	2	yes	complemented
73	#52004	D₄	1	4	yes	complemented
74	#52004	C₂³	1	4	yes	—
75	#51902	D₄	1	4	yes	complemented
76	#51902	C₂³	1	4	yes	—
77	#46355	D₄	1	8	yes	complemented
78	#46355	C₂³	1	8	yes	—
79	C₂×#2815	D₄	1	2	yes	complemented
80	#35222	D₄	1	4	yes	complemented
81	#35222	C₂³	1	4	yes	—
82	C₂×#2539	D₄	1	2	yes	complemented
83	C₂×#2404	C₂³	1	2	yes	—
84	C₂×#2431	C₂³	1	2	yes	—
85	C₂×#2380	D₄	1	1	yes	characteristic, complemented
86	C₂×#2372	D₄	1	1	yes	characteristic, complemented
87	C₂×#2358	D₄	1	2	yes	complemented
88	C₂×#2333	D₄	1	2	yes	complemented
89	C₂×#2309	D₄	1	1	yes	characteristic, complemented
90	C₂×#2309	D₄	1	1	yes	characteristic, complemented
91	C₂×#2280	D₄	1	1	yes	characteristic, complemented
92	#33021	C₂³	1	4	yes	complemented
93	#32992	C₂³	1	4	yes	complemented
94	#32899	C₂³	1	4	yes	complemented
95	#32890	C₂³	1	4	yes	complemented
96	#20959	C₂³	1	2	yes	complemented
97	#20956	C₂³	1	2	yes	complemented
98	#20591	C₂³	1	2	yes	complemented
99	#20591	C₂³	1	1	yes	characteristic, complemented
100	#20584	C₂³	1	2	yes	complemented
101	#20584	C₂³	1	1	yes	characteristic, complemented
102	#13093	C₂³	1	8	yes	complemented
103	#13089	C₂³	1	8	yes	complemented
104	#13087	C₂³	1	8	yes	complemented
105	#13083	C₂³	1	8	yes	complemented
106	#12703	C₂³	1	4	yes	complemented
107	#12697	C₂³	1	4	yes	complemented
108	#12689	C₂³	1	8	yes	complemented
109	#10993	C₂³	1	4	yes	complemented
110	#10987	C₂³	1	4	yes	complemented
111	#10984	C₂³	1	4	yes	complemented
112	#9511	C₂³	1	8	yes	complemented
113	#9445	C₂³	1	8	yes	complemented
114	#8516	C₂³	1	8	yes	complemented
115	C₂×#585	C₂⁴	1	1	yes	characteristic, complemented
116	C₂³×#41	C₂⁴	1	1	yes	characteristic
117	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
118	C₂⁴×D₄	C₂×D₄	1	4	yes	—
119	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
120	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
121	C₂×H(3,𝔽₄)	C₂×D₄	1	4	yes	—
122	C₂×D₄²	C₂×D₄	1	4	yes	—
123	C₂×D₄²	C₂×D₄	1	8	yes	—
124	C₂×#535	C₂×D₄	1	2	yes	—
125	C₂×#535	C₂×D₄	1	2	yes	—
126	C₂×#535	C₂×D₄	1	4	yes	—
127	C₂×#535	C₂×D₄	1	2	yes	—
128	C₂×#535	C₂×D₄	1	2	yes	—
129	C₂×#535	C₂⁴	1	2	yes	—
130	C₂×#535	C₂⁴	1	2	yes	—
131	C₂×#534	C₂×D₄	1	8	yes	—
132	C₂²×#127	C₂×D₄	1	1	yes	characteristic
133	C₂²×#127	C₂×D₄	1	1	yes	characteristic
134	C₂²×#127	C₂×D₄	1	2	yes	—
135	C₂²×#124	C₂×D₄	1	1	yes	characteristic
136	C₂²×#124	C₂×D₄	1	1	yes	characteristic
137	C₂²×#124	C₂×D₄	1	2	yes	—
138	C₂×#525	C₂×D₄	1	4	yes	—
139	C₂×#525	C₂×D₄	1	2	yes	—
140	C₂×#525	C₂⁴	1	2	yes	—
141	C₂²×#123	C₂×D₄	1	2	yes	—
142	C₂²×#121	C₂×D₄	1	2	yes	—
143	C₂²×#121	C₂×D₄	1	2	yes	—
144	C₂²×#121	C₂×D₄	1	2	yes	—
145	C₂²×#120	C₂×D₄	1	2	yes	—
146	C₂²×#120	C₂×D₄	1	2	yes	—
147	C₂²×#120	C₂×D₄	1	2	yes	—
148	#3428	C₂⁴	1	1	yes	characteristic, complemented
149	C₂²×#117	C₂×D₄	1	1	yes	characteristic
150	C₂²×#117	C₂×D₄	1	1	yes	characteristic
151	C₂²×#117	C₂×D₄	1	1	yes	characteristic
152	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
153	C₂×#413	C₂⁴	1	2	yes	complemented
154	C₂×#410	C₂⁴	1	2	yes	complemented
155	#2879	C₂⁴	1	2	yes	complemented
156	#2815	C₂×D₄	1	8	yes	—
157	#2733	C₂×D₄	1	8	yes	—
158	#2709	C₂×D₄	1	8	yes	—
159	#2697	C₂×D₄	1	8	yes	—
160	#2669	C₂×D₄	1	8	yes	—
161	#2539	C₂×D₄	1	8	yes	—
162	#2431	C₂×D₄	1	4	yes	—
163	#2431	C₂×D₄	1	4	yes	—
164	#2431	C₂×D₄	1	4	yes	—
165	#2431	C₂⁴	1	4	yes	—
166	#2404	C₂×D₄	1	4	yes	—
167	#2404	C₂×D₄	1	4	yes	—
168	#2404	C₂×D₄	1	4	yes	—
169	#2404	C₂⁴	1	4	yes	—
170	#2380	C₂×D₄	1	4	yes	—
171	#2372	C₂×D₄	1	4	yes	—
172	#2358	C₂×D₄	1	8	yes	—
173	#2333	C₂×D₄	1	8	yes	—
174	#2309	C₂×D₄	1	4	yes	—
175	#2309	C₂×D₄	1	4	yes	—
176	C₂×#391	C₂×D₄	1	2	yes	—
177	C₂×#390	C₂×D₄	1	2	yes	—
178	C₂×#386	C₂×D₄	1	2	yes	—
179	C₂×#386	C₂×D₄	1	2	yes	—
180	#2280	C₂×D₄	1	4	yes	—
181	C₂×#381	C₂×D₄	1	2	yes	—
182	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	2	yes	—
183	#1785	C₂⁴	1	4	yes	complemented
184	#1782	C₂⁴	1	4	yes	complemented
185	C₂⁶	#120	1	1	yes	characteristic
186	C₂⁶	#120	1	2	yes	—
187	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
188	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
189	C₂²×#41	C₂²×D₄	1	2	yes	—
190	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
191	C₂²×#41	C₂²×D₄	1	2	yes	—
192	C₂²×#41	C₂⁵	1	1	yes	characteristic
193	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
194	C₂³×D₄	#120	1	1	yes	characteristic
195	C₂³×D₄	#120	1	2	yes	—
196	C₂³×D₄	#120	1	2	yes	—
197	C₂³×D₄	#120	1	1	yes	characteristic
198	C₂³×D₄	#120	1	2	yes	—
199	C₂³×D₄	#120	1	1	yes	characteristic
200	C₂³×D₄	#120	1	1	yes	characteristic
201	C₂³×D₄	C₂²×D₄	1	2	yes	—
202	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
203	C₂³×D₄	C₂²×D₄	1	2	yes	—
204	C₂³×D₄	C₂²×D₄	1	2	yes	—
205	C₂⁴×C₄	#120	1	2	yes	—
206	C₂⁴×C₄	#120	1	1	yes	characteristic
207	C₂⁴×C₄	#120	1	2	yes	—
208	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
209	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
210	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
211	C₂×#127	#120	1	2	yes	—
212	C₂×#127	#120	1	2	yes	—
213	C₂×#127	#120	1	4	yes	—
214	C₂×#127	C₂²×D₄	1	2	yes	—
215	C₂×#127	C₂²×D₄	1	2	yes	—
216	C₂×#127	C₂²×D₄	1	4	yes	—
217	C₂×#124	#120	1	2	yes	—
218	C₂×#124	#120	1	2	yes	—
219	C₂×#124	#120	1	4	yes	—
220	C₂×#124	C₂²×D₄	1	2	yes	—
221	C₂×#124	C₂²×D₄	1	2	yes	—
222	C₂×#124	C₂²×D₄	1	4	yes	—
223	C₂×#123	#120	1	4	yes	—
224	C₂×#123	C₂²×D₄	1	4	yes	—
225	C₂×#121	#120	1	4	yes	—
226	C₂×#121	#120	1	4	yes	—
227	C₂×#121	#120	1	4	yes	—
228	C₂×#121	C₂²×D₄	1	4	yes	—
229	C₂×#121	C₂²×D₄	1	4	yes	—
230	C₂×#121	C₂²×D₄	1	4	yes	—
231	C₂×#120	#120	1	4	yes	—
232	C₂×#120	#120	1	4	yes	—
233	C₂×#120	#120	1	4	yes	—
234	C₂×#120	C₂²×D₄	1	4	yes	—
235	C₂×#120	C₂²×D₄	1	4	yes	—
236	C₂×#120	C₂²×D₄	1	4	yes	—
237	C₂×#117	#120	1	2	yes	—
238	C₂×#117	#120	1	2	yes	—
239	C₂×#117	#120	1	2	yes	—
240	C₂×#117	C₂²×D₄	1	2	yes	—
241	C₂×#117	C₂²×D₄	1	2	yes	—
242	C₂×#117	C₂²×D₄	1	2	yes	—
243	C₂²×C₄⋊C₄	#120	1	2	yes	—
244	C₂²×C₄⋊C₄	#120	1	2	yes	—
245	C₂²×C₂²⋊C₄	#120	1	4	yes	—
246	C₂²×C₂²⋊C₄	#120	1	2	yes	—
247	C₂²×C₂²⋊C₄	#120	1	2	yes	—
248	C₂²×C₂²⋊C₄	#120	1	2	yes	—
249	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
250	C₂²×C₄²	#120	1	1	yes	characteristic
251	C₂²×C₄²	#120	1	1	yes	characteristic
252	C₂²×C₄²	#120	1	2	yes	—
253	C₂²×C₄²	#120	1	2	yes	—
254	#391	#120	1	4	yes	—
255	#391	C₂²×D₄	1	4	yes	—
256	#390	#120	1	4	yes	—
257	#390	C₂²×D₄	1	4	yes	—
258	#386	#120	1	4	yes	—
259	#386	#120	1	4	yes	—
260	#386	C₂²×D₄	1	4	yes	—
261	#386	C₂²×D₄	1	4	yes	—
262	#381	#120	1	4	yes	—
263	#381	C₂²×D₄	1	4	yes	—
264	C₄×C₂²⋊C₄	#120	1	4	yes	—
265	C₄×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
266	C₂⁵	C₂×#120	1	1	yes	characteristic
267	C₂⁵	C₂×#120	1	2	yes	—
268	C₂⁵	C₂×#120	1	2	yes	—
269	C₂⁵	C₂×#120	1	4	yes	—
270	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
271	C₂²×Q₈	C₂×#120	1	2	yes	—
272	C₂²×Q₈	C₂³×D₄	1	1	yes	characteristic
273	C₂²×D₄	B(4,𝔽₂)	1	4	yes	—
274	C₂²×D₄	C₂×#120	1	2	yes	—
275	C₂²×D₄	C₂×#120	1	2	yes	—
276	C₂²×D₄	C₂×#120	1	2	yes	—
277	C₂²×D₄	C₂×#120	1	2	yes	—
278	C₂²×D₄	C₂×#120	1	2	yes	—
279	C₂²×D₄	C₂×#120	1	1	yes	characteristic
280	C₂²×D₄	C₂×#120	1	2	yes	—
281	C₂²×D₄	C₂×#120	1	2	yes	—
282	C₂²×D₄	C₂×#120	1	4	yes	—
283	C₂²×D₄	C₂×#120	1	2	yes	—
284	C₂²×D₄	C₂³×D₄	1	2	yes	—
285	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
286	C₂³×C₄	C₂×#120	1	1	yes	characteristic
287	C₂³×C₄	C₂×#120	1	1	yes	characteristic
288	C₂³×C₄	C₂×#120	1	1	yes	characteristic
289	C₂³×C₄	C₂×#120	1	2	yes	—
290	C₂³×C₄	C₂×#120	1	2	yes	—
291	C₂³×C₄	C₂×#120	1	2	yes	—
292	C₂³×C₄	C₂×#120	1	2	yes	—
293	C₂³×C₄	C₂×#120	1	2	yes	—
294	C₂³×C₄	C₂×#120	1	1	yes	characteristic
295	C₂³×C₄	C₂×#120	1	4	yes	—
296	C₂³×C₄	C₂×#120	1	1	yes	characteristic
297	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
298	C₂³×C₄	C₂³×D₄	1	2	yes	—
299	C₂×C₄⋊C₄	C₂×#120	1	4	yes	—
300	C₂×C₄⋊C₄	C₂×#120	1	4	yes	—
301	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
302	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
303	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
304	C₂×C₄²	C₂×#120	1	2	yes	—
305	C₂×C₄²	C₂×#120	1	2	yes	—
306	C₂×C₄²	C₂×#120	1	4	yes	—
307	C₂×C₄²	C₂×#120	1	4	yes	—
308	C₂⁴	#2846	1	1	yes	characteristic
309	C₂⁴	#2846	1	1	yes	characteristic
310	C₂⁴	#2846	1	2	yes	—
311	C₂⁴	#3026	1	4	yes	—
312	C₂⁴	C₂²×#120	1	2	yes	—
313	C₂⁴	C₂²×#120	1	1	yes	characteristic
314	C₂×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
315	C₂×D₄	#3026	1	4	yes	—
316	C₂²×C₄	#2846	1	1	yes	characteristic
317	C₂²×C₄	#2846	1	2	yes	—
318	C₂²×C₄	#2846	1	1	yes	characteristic
319	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
320	C₂²×C₄	#3026	1	2	yes	—
321	C₂²×C₄	C₂²×#120	1	2	yes	—
322	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
323	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
324	C₂³	#32898	1	2	yes	—
325	C₂³	C₂×#2846	1	1	yes	characteristic
326	C₂³	C₂×#3026	1	2	yes	—
327	C₂×C₄	#32898	1	2	yes	—
328	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
329	C₂×C₄	C₂×#3026	1	1	yes	characteristic
330	C₂×C₄	C₂×#3026	1	2	yes	—
331	C₂²	#511819	1	4	yes	—
332	C₂²	C₂×#32898	1	1	yes	characteristic
333	C₂²	#6628892	1	1	yes	characteristic
334	C₂²	#6628892	1	1	yes	characteristic
335	C₂	C₂×#511819	1	2	yes	—
336	C₂	#72233581	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×#32898
commutator, Frattini, cosocle	C₂²×#41	C₂⁵
LCS	G ▷ C₂²×#41 ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂²×#535 ◁ G
LECS	G ▷ C₂²×#41 ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72251773	C₂	semidirect
2. #72251753	C₂	semidirect
3. #72251743	C₂	semidirect
4. #72237534	C₂	semidirect
5. #72235082	C₂	semidirect
6. C₂×#8181078	C₂	semidirect
7. #72231754	C₂	semidirect
8. #72231744	C₂	semidirect
9. #72219496	C₂	semidirect
10. #72219495	C₂	semidirect
11. #72215568	C₂	semidirect
12. #72215536	C₂	semidirect
13. #72210564	C₂	semidirect
14. #10575442	C₂²	semidirect
21. #6470228	C₂²	semidirect
22. #6470025	C₂²	semidirect
23. #6437616	C₂²	semidirect
24. #6437449	C₂²	semidirect
25. #500221	C₂²	semidirect
26. #500203	C₂²	semidirect
27. #500179	C₂²	semidirect
28. #499855	C₂²	semidirect
29. #499831	C₂²	semidirect
30. #499788	C₂²	semidirect
31. #496228	C₂²	semidirect
32. #496228	C₂²	semidirect
33. #496208	C₂²	semidirect
34. #496190	C₂²	semidirect
35. #493385	C₂²	semidirect
36. #493372	C₂²	semidirect
37. #493352	C₂²	semidirect
38. #449562	C₂²	semidirect
39. #449496	C₂²	semidirect
40. #382419	C₂²	semidirect
41. #359513	C₂²	semidirect
42. #359507	C₂²	semidirect
43. #246327	C₂²	semidirect
44. #246319	C₂²	semidirect
45. #201819	C₂²	semidirect
46. #201091	C₂²	semidirect
47. #187756	C₂²	semidirect
48. #133843	C₂²	semidirect
49. #133398	C₂²	semidirect
50. #133382	C₂²	semidirect
51. #133362	C₂²	semidirect
52. #133350	C₂²	semidirect
53. C₂⁵×D₄	D₄	semidirect
54. #62811	C₂³	semidirect
55. C₂²×D₄²	D₄	semidirect
56. C₂²×D₄²	D₄	semidirect
57. C₂²×H(3,𝔽₄)	D₄	semidirect
60. C₂²×#534	D₄	semidirect
62. #60518	C₂³	semidirect
63. C₂×#3025	C₂³	semidirect
64. C₂×#3021	C₂³	semidirect
65. #60369	C₂³	semidirect
66. #60064	C₂³	semidirect
67. #59089	D₄	semidirect
69. C₂×#2733	D₄	semidirect
70. C₂×#2709	D₄	semidirect
71. C₂×#2697	D₄	semidirect
72. C₂×#2669	D₄	semidirect
73. #52004	D₄	semidirect
75. #51902	D₄	semidirect
77. #46355	D₄	semidirect
79. C₂×#2815	D₄	semidirect
80. #35222	D₄	semidirect
82. C₂×#2539	D₄	semidirect
85. C₂×#2380	D₄	semidirect
86. C₂×#2372	D₄	semidirect
87. C₂×#2358	D₄	semidirect
88. C₂×#2333	D₄	semidirect
89. C₂×#2309	D₄	semidirect
90. C₂×#2309	D₄	semidirect
91. C₂×#2280	D₄	semidirect
92. #33021	C₂³	semidirect
93. #32992	C₂³	semidirect
94. #32899	C₂³	semidirect
95. #32890	C₂³	semidirect
96. #20959	C₂³	semidirect
97. #20956	C₂³	semidirect
98. #20591	C₂³	semidirect
99. #20591	C₂³	semidirect
100. #20584	C₂³	semidirect
101. #20584	C₂³	semidirect
102. #13093	C₂³	semidirect
103. #13089	C₂³	semidirect
104. #13087	C₂³	semidirect
105. #13083	C₂³	semidirect
106. #12703	C₂³	semidirect
107. #12697	C₂³	semidirect
108. #12689	C₂³	semidirect
109. #10993	C₂³	semidirect
110. #10987	C₂³	semidirect
111. #10984	C₂³	semidirect
112. #9511	C₂³	semidirect
113. #9445	C₂³	semidirect
114. #8516	C₂³	semidirect
115. C₂×#585	C₂⁴	semidirect
148. #3428	C₂⁴	semidirect
153. C₂×#413	C₂⁴	semidirect
154. C₂×#410	C₂⁴	semidirect
155. #2879	C₂⁴	semidirect
183. #1785	C₂⁴	semidirect
184. #1782	C₂⁴	semidirect

Maximal subgroups

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

subgroup	index
#72251773	2
#72251753	2
#72251743	2
#72237534	2
#72235082	2
C₂×#8181078	2
#72231754	2
#72231744	2
#72219496	2
#72219495	2
#72215568	2
#72215536	2
#72210564	2