Subgroups — #72270632

Order 6144.

At least 13198 conjugacy classes of subgroups; only the 561 normal subgroups are shown.

The subgroup lattice has 332 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72270609	C₂	1	1	yes	maximal, characteristic, complemented
2	#72270550	C₂	1	2	yes	maximal, complemented
3	#72270467	C₂	1	2	yes	maximal, complemented
4	#72270339	C₂	1	1	yes	maximal, characteristic, complemented
5	#72270150	C₂	1	1	yes	maximal, characteristic, complemented
6	#72270134	C₂²	1	2	yes	—
7	#72255212	C₂	1	1	yes	maximal, characteristic, complemented
8	#72255106	C₂	1	2	yes	maximal, complemented
9	#72255084	C₂²	1	1	yes	characteristic, complemented
10	#72255069	C₂²	1	1	yes	characteristic
11	#72255063	C₂²	1	2	yes	complemented
12	C₃×#72210566	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₃×#52004	C₂²	1	1	yes	characteristic
14	C₃×#496225	C₂²	1	2	yes	complemented
15	#72253719	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#86330	C₂²	1	1	yes	characteristic
17	#72253541	C₂	1	1	yes	maximal, characteristic, complemented
18	#72253523	C₂²	1	2	yes	complemented
19	#72253522	C₂²	1	1	yes	characteristic, complemented
20	#72253519	C₂²	1	1	yes	characteristic
21	#72253514	C₂²	1	1	yes	characteristic
22	C₃×#493370	C₂²	1	1	yes	characteristic
23	C₃×#359509	C₂²	1	1	yes	characteristic
24	#72249307	C₂²	1	2	yes	complemented
25	#72249306	C₂²	1	2	yes	complemented
26	#72248860	C₂	1	2	yes	maximal, complemented
27	#72248848	C₂²	1	2	yes	complemented
28	#72248847	C₂²	1	2	yes	complemented
29	#72248674	C₂²	1	2	yes	complemented
30	#72248668	C₂²	1	2	yes	complemented
31	#72248596	C₂²	1	1	yes	characteristic, complemented
32	C₃×#201664	C₂²	1	2	yes	complemented
33	#72248352	C₂²	1	1	yes	characteristic, complemented
34	#72248257	C₂²	1	2	yes	—
35	#72210566	D₃	1	1	yes	characteristic, complemented
36	C₂³×#1009	D₄	1	1	yes	characteristic, complemented
37	C₂⁴×D₃×D₄	C₂³	1	1	yes	characteristic
38	C₂×#87239	C₂³	1	1	yes	characteristic
39	C₂²×#5805	C₂³	1	1	yes	characteristic
40	C₂²×#5524	D₄	1	1	yes	characteristic, complemented
41	C₂²×#5828	D₄	1	1	yes	characteristic, complemented
42	C₂³×#937	D₄	1	2	yes	complemented
43	C₂²×#5521	D₄	1	1	yes	characteristic, complemented
44	C₂×#83394	D₄	1	2	yes	complemented
45	C₂×#84052	D₄	1	2	yes	complemented
46	C₂×#71860	D₄	1	4	yes	complemented
47	#10796774	D₄	1	2	yes	complemented
48	C₂×#72129	C₂³	1	1	yes	characteristic
49	C₂×#72130	C₂³	1	2	yes	—
50	#10740381	D₄	1	2	yes	complemented
51	#10733628	D₄	1	2	yes	complemented
52	#10732891	D₄	1	2	yes	complemented
53	#10732883	D₄	1	2	yes	complemented
54	#10726342	D₄	1	2	yes	complemented
55	#10726229	D₄	1	1	yes	characteristic, complemented
56	#10723343	D₄	1	2	yes	complemented
57	#10720467	D₄	1	1	yes	characteristic, complemented
58	#10717058	D₄	1	2	yes	complemented
59	#10717057	C₂³	1	2	yes	—
60	C₂²×C₃×D₄²	D₄	1	1	yes	characteristic, complemented
61	C₂²×C₃×#535	C₂³	1	1	yes	characteristic
62	C₂×C₃×#2684	D₄	1	2	yes	complemented
63	C₂×C₃×#2403	C₂³	1	2	yes	—
64	C₂×C₃×#2380	D₄	1	1	yes	characteristic, complemented
65	C₃×#34171	C₂³	1	1	yes	characteristic
66	C₂×C₃×#1783	C₂³	1	1	yes	characteristic
67	C₂×C₃×#1781	C₂³	1	2	yes	—
68	C₃×#10989	D₄	1	4	yes	complemented
69	C₂×#52004	C₂×D₃	1	1	yes	characteristic
70	#496225	C₂×D₃	1	2	yes	complemented
71	#493370	C₂×D₃	1	1	yes	characteristic
72	#359509	C₂×D₃	1	1	yes	characteristic
73	#201664	C₂×D₃	1	2	yes	complemented
74	C₂⁶×D₃	C₂×D₄	1	2	yes	—
75	C₂³×C₃×#41	C₂×D₄	1	1	yes	characteristic
76	C₂⁴×C₃×D₄	C₂×D₄	1	2	yes	—
77	C₂⁴×C₃×D₄	C₂⁴	1	1	yes	characteristic
78	C₂⁴×#67	C₂×D₄	1	2	yes	—
79	C₂²×#1004	C₂×D₄	1	1	yes	characteristic, complemented
80	C₂³×#235	C₂×D₄	1	1	yes	characteristic
81	C₂⁴×D₁₂	C₂×D₄	1	1	yes	characteristic
82	C₂⁴×C₄×D₃	C₂×D₄	1	1	yes	characteristic
83	C₂×C₃×#535	C₂×D₄	1	2	yes	—
84	C₂×C₃×#535	C₂×D₄	1	2	yes	—
85	C₂×C₃×#535	C₂×D₄	1	2	yes	—
86	C₂×C₃×#535	#41	1	2	yes	—
87	C₂²×C₃×#127	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₃×#127	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₃×#124	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₃×#124	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₃×#120	C₂×D₄	1	2	yes	—
92	C₂²×C₃×#120	C₂×D₄	1	2	yes	—
93	C₂²×C₃×#117	C₂×D₄	1	1	yes	characteristic
94	C₂³×#217	C₂×D₄	1	2	yes	—
95	C₂²×#940	C₂×D₄	1	2	yes	—
96	C₂²×#936	C₂×D₄	1	2	yes	—
97	C₂×#5798	C₂×D₄	1	1	yes	characteristic, complemented
98	C₂²×#926	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₃×#100	C₂×D₄	1	2	yes	complemented
100	C₃×#2309	C₂×D₄	1	2	yes	complemented
101	C₂×C₃×#386	C₂×D₄	1	2	yes	—
102	C₂×C₃×#386	C₂×D₄	1	2	yes	—
103	C₂×C₃×#379	C₂×D₄	1	2	yes	—
104	C₂×#5247	C₂×D₄	1	2	yes	—
105	C₂²×#834	C₂×D₄	1	4	yes	complemented
106	C₂²×#833	C₂×D₄	1	2	yes	complemented
107	#72131	C₂×D₄	1	2	yes	—
108	#72131	C₂×D₄	1	2	yes	—
109	#72131	C₂×D₄	1	2	yes	—
110	#72131	C₂×D₄	1	2	yes	—
111	C₂²×D₄²	D₁₂	1	1	yes	characteristic, complemented
112	C₂²×#535	C₂²×D₃	1	1	yes	characteristic
113	C₂×#2684	D₁₂	1	2	yes	complemented
114	C₂×#2403	C₂²×D₃	1	2	yes	—
115	C₂×#2380	D₁₂	1	1	yes	characteristic, complemented
116	#34171	C₂²×D₃	1	1	yes	characteristic
117	C₂×#1783	C₂²×D₃	1	1	yes	characteristic
118	C₂×#1781	C₂²×D₃	1	2	yes	—
119	#10989	#67	1	4	yes	complemented
120	C₂⁶×C₃	#120	1	2	yes	—
121	C₂⁶×C₃	C₂²×D₄	1	2	yes	—
122	C₂⁵×D₃	#120	1	1	yes	characteristic
123	C₂⁵×D₃	#120	1	2	yes	—
124	C₂²×C₃×#41	#120	1	2	yes	—
125	C₂²×C₃×#41	#121	1	2	yes	—
126	C₂³×C₃×Q₈	#120	1	1	yes	characteristic
127	C₂³×C₃×D₄	#120	1	1	yes	characteristic
128	C₂³×C₃×D₄	C₂²×D₄	1	1	yes	characteristic
129	C₂³×C₃×D₄	C₂²×D₄	1	2	yes	—
130	C₂³×C₃×D₄	C₂²×D₄	1	1	yes	characteristic
131	C₂³×C₃×D₄	C₂²×D₄	1	1	yes	characteristic
132	C₂³×C₃×D₄	C₂²×D₄	1	1	yes	characteristic
133	C₂³×C₃×D₄	C₂²×D₄	1	1	yes	characteristic
134	C₂³×C₃×D₄	C₂×#41	1	1	yes	characteristic
135	C₂³×C₃×D₄	H(5,𝔽₂)	1	2	yes	—
136	C₂³×C₃×D₄	H(5,𝔽₂)	1	2	yes	—
137	C₂⁴×C₃×C₄	#120	1	2	yes	—
138	C₂⁴×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
139	C₂⁴×Dic₃	#120	1	1	yes	characteristic
140	C₂³×D₁₂	#120	1	1	yes	characteristic
141	C₂³×Dic₆	#120	1	1	yes	characteristic
142	C₂×C₃×#127	#120	1	2	yes	—
143	C₂×C₃×#127	#121	1	2	yes	—
144	C₂×C₃×#127	#121	1	2	yes	—
145	C₂×C₃×#127	#127	1	2	yes	—
146	C₂×C₃×#124	#120	1	2	yes	—
147	C₂×C₃×#124	#121	1	2	yes	—
148	C₂×C₃×#124	#121	1	2	yes	—
149	C₂×C₃×#124	#127	1	2	yes	—
150	C₂×C₃×#117	#120	1	2	yes	—
151	C₂×C₃×#117	#121	1	2	yes	—
152	C₂²×C₃×C₂²⋊C₄	#120	1	2	yes	—
153	C₂²×C₃×C₂²⋊C₄	#120	1	2	yes	—
154	C₂²×C₃×C₄²	#120	1	1	yes	characteristic
155	C₂²×C₃×C₄²	#120	1	1	yes	characteristic
156	C₂²×#217	#120	1	2	yes	—
157	C₂²×#217	#120	1	2	yes	—
158	C₂²×#217	#120	1	2	yes	—
159	C₂²×#217	#120	1	2	yes	—
160	C₂²×C₄×Dic₃	#120	1	2	yes	—
161	C₂³×#41	D₃×D₄	1	1	yes	characteristic
162	C₂⁴×D₄	D₃×D₄	1	2	yes	—
163	C₂⁴×D₄	C₂³×D₃	1	1	yes	characteristic
164	C₂×#535	#235	1	2	yes	—
165	C₂×#535	D₃×D₄	1	2	yes	—
166	C₂×#535	D₃×D₄	1	2	yes	—
167	C₂×#535	C₂×#67	1	2	yes	—
168	C₂²×#127	C₂×D₁₂	1	1	yes	characteristic
169	C₂²×#127	D₃×D₄	1	1	yes	characteristic
170	C₂²×#124	C₂×D₁₂	1	1	yes	characteristic
171	C₂²×#124	D₃×D₄	1	1	yes	characteristic
172	C₂²×#120	C₂×D₁₂	1	2	yes	—
173	C₂²×#120	D₃×D₄	1	2	yes	—
174	C₂²×#117	D₃×D₄	1	1	yes	characteristic
175	C₂²×#100	C₂×#67	1	2	yes	complemented
176	#2309	C₂×#67	1	2	yes	complemented
177	C₂×#386	C₂×D₁₂	1	2	yes	—
178	C₂×#386	D₃×D₄	1	2	yes	—
179	C₂×#379	D₃×D₄	1	2	yes	—
180	C₂⁵×C₃	C₂×#120	1	2	yes	—
181	C₂⁵×C₃	C₂×#120	1	2	yes	—
182	C₂⁵×C₃	C₂×#120	1	1	yes	characteristic
183	C₂⁵×C₃	D₄²	1	2	yes	—
184	C₂⁵×C₃	D₄²	1	2	yes	—
185	C₂⁵×C₃	D₄²	1	2	yes	—
186	C₂⁵×C₃	#546	1	2	yes	—
187	C₂⁴×D₃	B(4,𝔽₂)	1	4	yes	—
188	C₂²×C₃×Q₈	#392	1	2	yes	—
189	C₂²×C₃×D₄	#392	1	2	yes	—
190	C₂²×C₃×D₄	C₂×#120	1	1	yes	characteristic
191	C₂²×C₃×D₄	C₂×#121	1	1	yes	characteristic
192	C₂²×C₃×D₄	C₂×#121	1	1	yes	characteristic
193	C₂²×C₃×D₄	C₂×#127	1	1	yes	characteristic
194	C₂²×C₃×D₄	#534	1	2	yes	—
195	C₂²×C₃×D₄	#535	1	2	yes	—
196	C₂²×C₃×D₄	D₄²	1	2	yes	—
197	C₂²×C₃×D₄	D₄²	1	2	yes	—
198	C₂²×C₃×D₄	D₄²	1	2	yes	—
199	C₂²×C₃×D₄	#546	1	2	yes	—
200	C₂³×C₃×C₄	C₂×#120	1	1	yes	characteristic
201	C₂³×C₃×C₄	C₂×#120	1	1	yes	characteristic
202	C₂³×C₃×C₄	C₂×#120	1	1	yes	characteristic
203	C₂³×C₃×C₄	C₂×#121	1	1	yes	characteristic
204	C₂³×C₃×C₄	#534	1	1	yes	characteristic
205	C₂³×C₃×C₄	#534	1	1	yes	characteristic
206	C₃×#127	B(4,𝔽₂)	1	8	yes	—
207	C₂×C₃×C₄²	#392	1	2	yes	—
208	C₂×C₃×C₄²	#392	1	2	yes	—
209	C₂⁶	#882	1	2	yes	—
210	C₂⁶	C₂×D₃×D₄	1	2	yes	—
211	C₂²×#41	#884	1	2	yes	—
212	C₂²×#41	#937	1	2	yes	—
213	C₂³×Q₈	#882	1	1	yes	characteristic
214	C₂³×D₄	#882	1	1	yes	characteristic
215	C₂³×D₄	C₂²×D₁₂	1	1	yes	characteristic
216	C₂³×D₄	C₂×#235	1	1	yes	characteristic
217	C₂³×D₄	C₂×D₃×D₄	1	1	yes	characteristic
218	C₂³×D₄	C₂×D₃×D₄	1	1	yes	characteristic
219	C₂³×D₄	C₂×D₃×D₄	1	1	yes	characteristic
220	C₂³×D₄	C₂×D₃×D₄	1	2	yes	—
221	C₂³×D₄	#1004	1	2	yes	—
222	C₂³×D₄	#1004	1	2	yes	—
223	C₂³×D₄	C₂²×#67	1	1	yes	characteristic
224	C₂⁴×C₄	#882	1	2	yes	—
225	C₂⁴×C₄	C₂×D₃×D₄	1	1	yes	characteristic
226	C₂×#127	#882	1	2	yes	—
227	C₂×#127	#884	1	2	yes	—
228	C₂×#127	#930	1	2	yes	—
229	C₂×#127	#940	1	2	yes	—
230	C₂×#124	#882	1	2	yes	—
231	C₂×#124	#884	1	2	yes	—
232	C₂×#124	#930	1	2	yes	—
233	C₂×#124	#940	1	2	yes	—
234	C₂×#117	#884	1	2	yes	—
235	C₂×#117	#937	1	2	yes	—
236	C₂²×C₂²⋊C₄	#882	1	2	yes	—
237	C₂²×C₂²⋊C₄	#882	1	2	yes	—
238	C₂²×C₄²	#882	1	1	yes	characteristic
239	C₂²×C₄²	#882	1	1	yes	characteristic
240	C₂⁴×C₃	#2403	1	2	yes	—
241	C₂⁴×C₃	#2403	1	1	yes	characteristic
242	C₂⁴×C₃	#2408	1	2	yes	—
243	C₂⁴×C₃	#2410	1	1	yes	characteristic
244	C₂⁴×C₃	#2410	1	2	yes	—
245	C₂⁴×C₃	#2433	1	2	yes	—
246	C₂⁴×C₃	#2846	1	1	yes	characteristic
247	C₂⁴×C₃	C₂×B(4,𝔽₂)	1	2	yes	—
248	C₂⁴×C₃	#3026	1	2	yes	—
249	C₂×C₃×D₄	#2021	1	4	yes	complemented
250	C₂×C₃×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
251	C₂²×C₃×C₄	C₂×#392	1	1	yes	characteristic
252	C₂²×C₃×C₄	#2403	1	1	yes	characteristic
253	C₂²×C₃×C₄	#2410	1	1	yes	characteristic
254	C₂²×C₃×C₄	#2613	1	1	yes	characteristic
255	C₃×C₄²	#2021	1	4	yes	complemented
256	C₂⁵	C₂×#882	1	2	yes	—
257	C₂⁵	#5490	1	2	yes	—
258	C₂⁵	D₃×#120	1	2	yes	—
259	C₂⁵	D₃×#120	1	1	yes	characteristic
260	C₂⁵	#5590	1	2	yes	—
261	C₂⁵	#5590	1	2	yes	—
262	C₂⁵	D₄×#67	1	2	yes	—
263	C₂²×Q₈	#4960	1	2	yes	—
264	C₂²×D₄	#4960	1	2	yes	—
265	C₂²×D₄	C₂×#882	1	1	yes	characteristic
266	C₂²×D₄	C₂×#884	1	1	yes	characteristic
267	C₂²×D₄	#5490	1	2	yes	—
268	C₂²×D₄	#5493	1	2	yes	—
269	C₂²×D₄	#5590	1	2	yes	—
270	C₂²×D₄	#5590	1	2	yes	—
271	C₂²×D₄	#5592	1	2	yes	—
272	C₂²×D₄	C₂×#930	1	1	yes	characteristic
273	C₂²×D₄	D₄×#67	1	2	yes	—
274	C₂²×D₄	C₂×#940	1	1	yes	characteristic
275	C₂³×C₄	C₂×#882	1	1	yes	characteristic
276	C₂³×C₄	C₂×#884	1	1	yes	characteristic
277	C₂³×C₄	D₃×#120	1	1	yes	characteristic
278	C₂³×C₄	#5589	1	1	yes	characteristic
279	C₂³×C₄	#5589	1	1	yes	characteristic
280	C₂³×C₄	C₂×#937	1	1	yes	characteristic
281	#127	#4741	1	8	yes	—
282	C₂×C₄²	#4960	1	2	yes	—
283	C₂×C₄²	#4960	1	2	yes	—
284	C₂³×C₃	#14715	1	1	yes	characteristic
285	C₂³×C₃	#23900	1	1	yes	characteristic
286	C₂³×C₃	#23900	1	4	yes	—
287	C₂³×C₃	#23903	1	1	yes	characteristic
288	C₂³×C₃	#24404	1	2	yes	—
289	C₂³×C₃	#32898	1	2	yes	—
290	C₂×C₃×C₄	C₂×#2021	1	2	yes	—
291	C₂×C₃×C₄	#23895	1	2	yes	—
292	C₂⁴	#73824	1	2	yes	—
293	C₂⁴	#73852	1	2	yes	—
294	C₂⁴	#73854	1	1	yes	characteristic
295	C₂⁴	#73861	1	1	yes	characteristic
296	C₂⁴	D₃×B(4,𝔽₂)	1	2	yes	—
297	C₂⁴	#80311	1	2	yes	—
298	C₂⁴	#82127	1	2	yes	—
299	C₂⁴	#82588	1	2	yes	—
300	C₂⁴	#82604	1	1	yes	characteristic
301	C₂×D₄	#70037	1	4	yes	complemented
302	C₂×D₄	C₂×#4741	1	4	yes	—
303	C₂²×C₄	#73854	1	1	yes	characteristic
304	C₂²×C₄	#73855	1	1	yes	characteristic
305	C₂²×C₄	C₂×#4960	1	1	yes	characteristic
306	C₂²×C₄	#82604	1	1	yes	characteristic
307	C₄²	#70037	1	4	yes	complemented
308	C₂²×C₃	#394058	1	1	yes	characteristic
309	C₂²×C₃	#394064	1	1	yes	characteristic
310	C₂²×C₃	#394066	1	1	yes	characteristic
311	C₂²×C₃	#511790	1	2	yes	—
312	C₂²×C₃	#511793	1	2	yes	—
313	C₂³	#10726565	1	1	yes	characteristic
314	C₂³	#10826765	1	1	yes	characteristic
315	C₂³	#10826769	1	4	yes	—
316	C₂³	#10826798	1	1	yes	characteristic
317	C₂³	#10832530	1	2	yes	—
318	C₂³	#10943959	1	2	yes	—
319	C₂×C₄	C₂×#70037	1	2	yes	—
320	C₂×C₄	#10826737	1	2	yes	—
321	C₂×C₃	#72210600	1	1	yes	characteristic
322	C₂×C₃	#72213329	1	2	yes	—
323	C₂²	#72219819	1	2	yes	—
324	C₂²	#72245186	1	1	yes	characteristic
325	C₂²	#72247581	1	1	yes	characteristic
326	C₂²	#72248284	1	2	yes	—
327	C₂²	#72248360	1	1	yes	characteristic
328	C₃	#72213344	1	1	yes	characteristic, complemented, Sylow
329	C₂	#72248538	1	2	yes	—
330	C₂	#72249047	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#72247581
commutator, cosocle	C₂⁴×C₃×D₄	C₂⁴
Frattini	C₂⁴×D₄	C₂³×D₃
Fitting	C₃×#72210566	C₂
socle	C₂²×C₃	#394066
hypercenter	#72210566	D₃
hypocenter	C₃	#72213344
LCS	G ▷ C₂⁴×C₃×D₄ ▷ C₂³×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ C₂⁴×D₄ ◁ #72210566

Complements

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

N	H ≅ G/N	type
1. #72270609	C₂	semidirect
2. #72270550	C₂	semidirect
3. #72270467	C₂	semidirect
4. #72270339	C₂	semidirect
5. #72270150	C₂	semidirect
7. #72255212	C₂	semidirect
8. #72255106	C₂	semidirect
9. #72255084	C₂²	semidirect
11. #72255063	C₂²	semidirect
12. C₃×#72210566	C₂	semidirect
14. C₃×#496225	C₂²	semidirect
15. #72253719	C₂	semidirect
17. #72253541	C₂	semidirect
18. #72253523	C₂²	semidirect
19. #72253522	C₂²	semidirect
24. #72249307	C₂²	semidirect
25. #72249306	C₂²	semidirect
26. #72248860	C₂	semidirect
27. #72248848	C₂²	semidirect
28. #72248847	C₂²	semidirect
29. #72248674	C₂²	semidirect
30. #72248668	C₂²	semidirect
31. #72248596	C₂²	semidirect
32. C₃×#201664	C₂²	semidirect
33. #72248352	C₂²	semidirect
35. #72210566	D₃	semidirect
36. C₂³×#1009	D₄	semidirect
40. C₂²×#5524	D₄	semidirect
41. C₂²×#5828	D₄	semidirect
42. C₂³×#937	D₄	semidirect
43. C₂²×#5521	D₄	semidirect
44. C₂×#83394	D₄	semidirect
45. C₂×#84052	D₄	semidirect
46. C₂×#71860	D₄	semidirect
47. #10796774	D₄	semidirect
50. #10740381	D₄	semidirect
51. #10733628	D₄	semidirect
52. #10732891	D₄	semidirect
53. #10732883	D₄	semidirect
54. #10726342	D₄	semidirect
55. #10726229	D₄	semidirect
56. #10723343	D₄	semidirect
57. #10720467	D₄	semidirect
58. #10717058	D₄	semidirect
60. C₂²×C₃×D₄²	D₄	semidirect
62. C₂×C₃×#2684	D₄	semidirect
64. C₂×C₃×#2380	D₄	semidirect
68. C₃×#10989	D₄	semidirect
70. #496225	C₂×D₃	semidirect
73. #201664	C₂×D₃	semidirect
79. C₂²×#1004	C₂×D₄	semidirect
97. C₂×#5798	C₂×D₄	semidirect
99. C₂²×C₃×#100	C₂×D₄	semidirect
100. C₃×#2309	C₂×D₄	semidirect
105. C₂²×#834	C₂×D₄	semidirect
106. C₂²×#833	C₂×D₄	semidirect
111. C₂²×D₄²	D₁₂	semidirect
113. C₂×#2684	D₁₂	semidirect
115. C₂×#2380	D₁₂	semidirect
119. #10989	#67	semidirect
175. C₂²×#100	C₂×#67	semidirect
176. #2309	C₂×#67	semidirect
249. C₂×C₃×D₄	#2021	semidirect
255. C₃×C₄²	#2021	semidirect
301. C₂×D₄	#70037	semidirect
307. C₄²	#70037	semidirect
328. C₃	#72213344	semidirect

Maximal subgroups

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

subgroup	index
#72270609	2
#72270550	2
#72270467	2
#72270339	2
#72270150	2
#72255212	2
#72255106	2
C₃×#72210566	2
#72253719	2
#72253541	2
#72248860	2
#72213344	3