Subgroups — #79376

Order 384.

412 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#5524	C₂	1	1	yes	maximal, characteristic
2	C₃×#433	C₂	1	1	yes	maximal, characteristic, complemented
3	#5000	C₂	1	1	yes	maximal, characteristic, complemented
4	#4838	C₂	1	1	yes	maximal, characteristic, complemented
5	#4836	C₂	1	1	yes	maximal, characteristic, complemented
6	#4836	C₂	1	1	yes	maximal, characteristic, complemented
7	#4834	C₂	1	1	yes	maximal, characteristic, complemented
8	#4727	C₂	1	1	yes	maximal, characteristic, complemented
9	#4727	C₂	1	1	yes	maximal, characteristic, complemented
10	#4726	C₂	1	1	yes	maximal, characteristic, complemented
11	D₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	#4706	C₂	1	1	yes	maximal, characteristic, complemented
13	#4706	C₂	1	1	yes	maximal, characteristic, complemented
14	#4688	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
16	#2976	—	3	1	no	maximal, Sylow
17	C₂×#235	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₃	C₂²	1	1	yes	characteristic
19	C₃×#117	C₂²	1	1	yes	characteristic
20	C₂×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
21	C₂×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
22	C₂×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic, complemented
23	C₂×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic, complemented
24	C₂×D₃×C₈	C₂²	1	1	yes	characteristic
25	C₂×D₃×C₈	C₂²	1	1	yes	characteristic
26	C₂×D₃×C₈	C₂²	1	1	yes	characteristic, complemented
27	C₂×D₃×C₈	C₂²	1	1	yes	characteristic, complemented
28	#897	C₄	1	1	yes	characteristic
29	#897	C₄	1	1	yes	characteristic
30	#895	C₄	1	1	yes	characteristic
31	#895	C₄	1	1	yes	characteristic
32	#886	C₄	1	1	yes	characteristic
33	#886	C₄	1	1	yes	characteristic
34	#882	C₄	1	1	yes	characteristic
35	#882	C₄	1	1	yes	characteristic
36	C₄×D₁₂	C₂²	1	1	yes	characteristic
37	C₄×D₁₂	C₂²	1	1	yes	characteristic
38	C₄×D₁₂	C₂²	1	1	yes	characteristic
39	C₄×D₁₂	C₂²	1	1	yes	characteristic
40	C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
41	C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
42	C₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
43	C₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
44	C₃×#97	C₂²	1	1	yes	characteristic, complemented
45	C₃×C₄×C₈	C₂²	1	1	yes	characteristic, complemented
46	#830	C₂²	1	1	yes	characteristic
47	#830	C₂²	1	1	yes	characteristic
48	(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic
49	(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic
50	(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic
51	(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic
52	(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
53	(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
54	(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
55	(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
56	C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
57	C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
58	#803	C₂²	1	1	yes	characteristic, complemented
59	C₄×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
60	#525	—	3	1	no	—
61	#436	—	3	1	no	—
62	#436	—	3	1	no	—
63	#435	—	3	1	no	—
64	#435	—	3	1	no	—
65	#435	—	3	1	no	—
66	#435	—	3	1	no	—
67	C₈×D₄	—	3	1	no	—
68	C₈×D₄	—	3	1	no	—
69	#433	—	3	1	no	—
70	#433	D₃	1	1	yes	characteristic, complemented
71	#408	—	3	1	no	—
72	#408	—	3	1	no	—
73	#407	—	3	1	no	—
74	C₂×C₂²⋊C₈	—	3	1	no	—
75	C₂³×D₃	C₂×C₄	1	1	yes	characteristic
76	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
77	C₂×#67	C₂×C₄	1	1	yes	characteristic
78	C₂×#67	C₂×C₄	1	1	yes	characteristic
79	C₂²×Dic₃	C₂×C₄	1	1	yes	characteristic
80	#235	—	4	1	no	—
81	#235	—	4	1	no	—
82	C₂×D₁₂	C₂×C₄	1	1	yes	characteristic
83	C₂×D₁₂	C₂×C₄	1	1	yes	characteristic
84	C₂×D₁₂	C₂×C₄	1	1	yes	characteristic
85	C₂×D₁₂	C₂×C₄	1	1	yes	characteristic
86	C₂×D₁₂	C₂×C₄	1	1	yes	characteristic
87	C₂×C₄×D₃	—	4	1	no	—
88	C₂×C₄×D₃	—	4	1	no	—
89	C₂×C₄×D₃	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄×D₃	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
92	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
93	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
94	C₂×C₄×D₃	C₂³	1	1	yes	characteristic
95	C₂×Dic₆	C₂×C₄	1	1	yes	characteristic
96	C₂×C₃×C₈	C₂³	1	1	yes	characteristic
97	C₂×C₃×C₈	C₂³	1	1	yes	characteristic
98	C₂×C₃×C₈	C₂³	1	1	yes	characteristic
99	C₂×C₃×C₈	C₂³	1	1	yes	characteristic
100	C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
101	C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
102	C₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
103	C₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
104	C₃×C₄²	C₂³	1	1	yes	characteristic
105	C₃×C₄²	C₂³	1	1	yes	characteristic
106	(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
107	(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
108	(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
109	(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
110	(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
111	(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
112	(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
113	(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
114	C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
115	C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
116	C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
117	C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
118	C₂×C₃⋊C₈	C₂³	1	1	yes	characteristic
119	C₂×C₃⋊C₈	C₂³	1	1	yes	characteristic
120	C₂×C₃⋊C₈	C₂³	1	1	yes	characteristic
121	C₂×C₃⋊C₈	C₂³	1	1	yes	characteristic
122	ΓL(1,𝔽₂₅)	—	4	1	no	—
123	ΓL(1,𝔽₂₅)	—	4	1	no	—
124	ΓL(1,𝔽₂₅)	—	4	1	no	—
125	ΓL(1,𝔽₂₅)	—	4	1	no	—
126	D₃×C₈	—	4	1	no	—
127	D₃×C₈	—	4	1	no	—
128	D₃×C₈	—	4	1	no	—
129	D₃×C₈	—	4	1	no	—
130	C₂×#41	—	3	1	no	—
131	C₂³×C₄	—	3	1	no	—
132	C₂×M₁₆	—	3	1	no	—
133	C₂×M₁₆	—	3	1	no	—
134	C₂×M₁₆	—	3	1	no	—
135	C₂×M₁₆	—	3	1	no	—
136	C₂²×C₈	—	3	1	no	—
137	C₂²×C₈	—	3	1	no	—
138	C₂²×C₈	—	3	1	no	—
139	C₂²×C₈	—	3	1	no	—
140	#123	—	3	1	no	—
141	#123	—	3	1	no	—
142	C₂²⋊Q₈	—	3	1	no	—
143	C₂²⋊Q₈	—	3	1	no	—
144	#121	—	3	1	no	—
145	#121	—	3	1	no	—
146	#120	—	3	1	no	—
147	#120	—	3	1	no	—
148	C₄×D₄	—	3	1	no	—
149	C₄×D₄	—	3	1	no	—
150	C₄×D₄	—	3	1	no	—
151	C₄×D₄	—	3	1	no	—
152	#117	C₂×D₃	1	1	yes	characteristic
153	C₄⋊C₈	—	3	1	no	—
154	C₄⋊C₈	—	3	1	no	—
155	C₄⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
156	C₄⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
157	C₂²⋊C₈	—	3	1	no	—
158	C₂²⋊C₈	—	3	1	no	—
159	C₂²⋊C₈	—	3	1	no	—
160	C₂²⋊C₈	—	3	1	no	—
161	C₂²⋊C₈	—	3	1	no	—
162	C₂²⋊C₈	—	3	1	no	—
163	C₂²⋊C₈	—	3	1	no	—
164	C₂²⋊C₈	—	3	1	no	—
165	C₂²⋊C₈	—	3	1	no	—
166	C₂²⋊C₈	—	3	1	no	—
167	C₂²⋊C₈	C₂×D₃	1	1	yes	characteristic
168	C₂²⋊C₈	C₂×D₃	1	1	yes	characteristic
169	#97	—	3	1	no	—
170	#97	C₂×D₃	1	1	yes	characteristic, complemented
171	C₄×C₈	—	3	1	no	—
172	C₄×C₈	C₂×D₃	1	1	yes	characteristic, complemented
173	C₂³×C₃	C₂²×C₄	1	1	yes	characteristic
174	C₂²×D₃	—	2	2	no	—
175	C₂²×D₃	—	4	1	no	—
176	C₂²×D₃	—	4	1	no	—
177	C₂²×D₃	C₂²×C₄	1	1	yes	characteristic
178	C₂²×D₃	C₂²×C₄	1	1	yes	characteristic
179	C₂²×D₃	C₂²×C₄	1	1	yes	characteristic
180	C₂²×D₃	C₂²×C₄	1	1	yes	characteristic
181	C₂×C₃×C₄	—	2	1	no	—
182	C₂×C₃×C₄	—	2	1	no	—
183	C₂×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
184	C₂×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
185	C₂×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
186	C₂×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
187	C₂×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
188	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
189	#67	—	4	1	no	—
190	#67	—	4	1	no	—
191	C₂×Dic₃	—	4	1	no	—
192	C₂×Dic₃	C₂²×C₄	1	1	yes	characteristic
193	C₂×Dic₃	C₂²×C₄	1	1	yes	characteristic
194	C₂×Dic₃	C₂²×C₄	1	1	yes	characteristic
195	C₂×Dic₃	C₂²×C₄	1	1	yes	characteristic
196	D₁₂	—	2	2	no	—
197	D₁₂	—	2	2	no	—
198	D₁₂	—	4	1	no	—
199	D₁₂	—	4	1	no	—
200	D₁₂	—	4	1	no	—
201	C₄×D₃	—	2	1	no	—
202	C₄×D₃	—	2	1	no	—
203	C₄×D₃	—	2	1	no	—
204	C₄×D₃	—	2	1	no	—
205	C₄×D₃	—	2	1	no	—
206	C₄×D₃	—	2	1	no	—
207	C₄×D₃	—	2	1	no	—
208	C₄×D₃	—	2	1	no	—
209	C₄×D₃	—	4	1	no	—
210	C₄×D₃	—	4	1	no	—
211	Dic₆	—	4	1	no	—
212	C₃×C₈	—	2	1	no	—
213	C₃×C₈	—	2	1	no	—
214	C₃×C₈	—	2	1	no	—
215	C₃×C₈	—	2	1	no	—
216	C₃⋊C₈	—	2	1	no	—
217	C₃⋊C₈	—	2	1	no	—
218	C₃⋊C₈	—	2	1	no	—
219	C₃⋊C₈	—	2	1	no	—
220	C₂⁴	—	3	1	no	—
221	#41	—	12	1	no	—
222	#41	—	12	1	no	—
223	C₂×Q₈	—	3	1	no	—
224	C₂×D₄	—	3	1	no	—
225	C₂×D₄	—	3	1	no	—
226	C₂×D₄	—	3	1	no	—
227	C₂×D₄	—	3	1	no	—
228	C₂×D₄	—	3	1	no	—
229	C₂×D₄	—	3	1	no	—
230	C₂×D₄	—	3	1	no	—
231	C₂²×C₄	—	3	1	no	—
232	C₂²×C₄	—	3	1	no	—
233	C₂²×C₄	—	3	1	no	—
234	C₂²×C₄	—	3	1	no	—
235	C₂²×C₄	—	3	1	no	—
236	C₂²×C₄	—	3	1	no	—
237	C₂²×C₄	—	3	1	no	—
238	C₂²×C₄	—	12	1	no	—
239	C₂²×C₄	—	12	1	no	—
240	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
241	M₁₆	—	12	1	no	—
242	M₁₆	—	12	1	no	—
243	M₁₆	—	12	1	no	—
244	M₁₆	—	12	1	no	—
245	C₂×C₈	—	3	1	no	—
246	C₂×C₈	—	3	1	no	—
247	C₂×C₈	—	3	1	no	—
248	C₂×C₈	—	3	1	no	—
249	C₂×C₈	—	12	1	no	—
250	C₂×C₈	—	12	1	no	—
251	C₂×C₈	—	12	1	no	—
252	C₂×C₈	—	12	1	no	—
253	C₂×C₈	C₂²×D₃	1	1	yes	characteristic
254	C₂×C₈	C₂²×D₃	1	1	yes	characteristic
255	C₂×C₈	C₂²×D₃	1	1	yes	characteristic
256	C₂×C₈	C₂²×D₃	1	1	yes	characteristic
257	C₄⋊C₄	—	3	1	no	—
258	C₄⋊C₄	—	3	1	no	—
259	C₄⋊C₄	—	3	1	no	—
260	C₄⋊C₄	—	3	1	no	—
261	C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
262	C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
263	C₂²⋊C₄	—	3	1	no	—
264	C₂²⋊C₄	—	3	1	no	—
265	C₂²⋊C₄	—	3	1	no	—
266	C₂²⋊C₄	—	3	1	no	—
267	C₂²⋊C₄	—	3	1	no	—
268	C₂²⋊C₄	—	3	1	no	—
269	C₂²⋊C₄	—	3	1	no	—
270	C₂²⋊C₄	—	3	1	no	—
271	C₂²⋊C₄	C₄×D₃	1	1	yes	characteristic
272	C₂²⋊C₄	C₄×D₃	1	1	yes	characteristic
273	C₄²	C₂²×D₃	1	1	yes	characteristic
274	C₄²	C₂²×D₃	1	1	yes	characteristic
275	C₂²×C₃	—	2	1	no	—
276	C₂²×C₃	—	2	1	no	—
277	C₂²×C₃	—	2	1	no	—
278	C₂²×C₃	C₂³×C₄	1	1	yes	characteristic
279	C₂×D₃	—	2	1	no	—
280	C₂×D₃	—	2	1	no	—
281	C₂×D₃	—	2	1	no	—
282	C₂×D₃	—	2	1	no	—
283	C₂×D₃	—	2	1	no	—
284	C₂×D₃	—	2	1	no	—
285	C₂×D₃	—	2	1	no	—
286	C₂×D₃	—	2	1	no	—
287	C₂×D₃	—	2	1	no	—
288	C₂×D₃	—	2	1	no	—
289	C₂×D₃	—	2	1	no	—
290	C₂×D₃	—	4	4	no	—
291	C₂×D₃	#131	1	2	yes	—
292	C₃×C₄	—	2	1	no	—
293	C₃×C₄	—	2	1	no	—
294	C₃×C₄	—	2	1	no	—
295	C₃×C₄	—	2	1	no	—
296	C₃×C₄	—	2	1	no	—
297	C₃×C₄	H(5,𝔽₂)	1	1	yes	characteristic
298	C₃×C₄	H(5,𝔽₂)	1	1	yes	characteristic
299	Dic₃	—	2	1	no	—
300	Dic₃	—	2	1	no	—
301	Dic₃	—	2	1	no	—
302	Dic₃	—	2	1	no	—
303	C₂³	—	3	1	no	—
304	C₂³	—	3	1	no	—
305	C₂³	—	3	1	no	—
306	C₂³	—	3	1	no	—
307	C₂³	—	6	2	no	—
308	C₂³	—	12	1	no	—
309	C₂³	—	12	1	no	—
310	C₂³	C₂×C₄×D₃	1	1	yes	characteristic
311	Q₈	—	12	1	no	—
312	D₄	—	6	2	no	—
313	D₄	—	6	2	no	—
314	D₄	—	12	1	no	—
315	D₄	—	12	1	no	—
316	D₄	—	12	1	no	—
317	D₄	—	12	1	no	—
318	D₄	—	12	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	3	1	no	—
322	C₂×C₄	—	3	1	no	—
323	C₂×C₄	—	3	1	no	—
324	C₂×C₄	—	3	1	no	—
325	C₂×C₄	—	6	1	no	—
326	C₂×C₄	—	6	1	no	—
327	C₂×C₄	—	6	1	no	—
328	C₂×C₄	—	6	1	no	—
329	C₂×C₄	—	6	1	no	—
330	C₂×C₄	—	6	1	no	—
331	C₂×C₄	—	6	1	no	—
332	C₂×C₄	—	6	1	no	—
333	C₂×C₄	—	12	1	no	—
334	C₂×C₄	—	12	1	no	—
335	C₂×C₄	—	12	1	no	—
336	C₂×C₄	C₂×C₄×D₃	1	1	yes	characteristic
337	C₂×C₄	C₂×C₄×D₃	1	1	yes	characteristic
338	C₂×C₄	C₂×C₄×D₃	1	1	yes	characteristic
339	C₂×C₄	C₂×C₄×D₃	1	1	yes	characteristic
340	C₂×C₄	C₂×C₄×D₃	1	1	yes	characteristic
341	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
342	C₈	—	2	1	no	—
343	C₈	—	2	1	no	—
344	C₈	—	2	1	no	—
345	C₈	—	2	1	no	—
346	C₈	—	6	1	no	—
347	C₈	—	6	1	no	—
348	C₈	—	6	1	no	—
349	C₈	—	6	1	no	—
350	C₂×C₃	—	4	1	no	—
351	C₂×C₃	#518	1	1	yes	characteristic
352	C₂×C₃	C₂×#131	1	1	yes	characteristic
353	C₂×C₃	#568	1	1	yes	characteristic
354	D₃	—	2	2	no	—
355	D₃	—	4	1	no	—
356	D₃	—	4	1	no	—
357	D₃	—	4	1	no	—
358	C₂²	—	2	1	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	3	2	no	—
362	C₂²	—	6	1	no	—
363	C₂²	—	6	1	no	—
364	C₂²	—	6	1	no	—
365	C₂²	—	6	1	no	—
366	C₂²	—	6	1	no	—
367	C₂²	—	6	1	no	—
368	C₂²	—	6	1	no	—
369	C₂²	—	6	1	no	—
370	C₂²	—	6	1	no	—
371	C₂²	—	6	1	no	—
372	C₂²	—	6	1	no	—
373	C₂²	—	12	4	no	—
374	C₂²	C₂²×C₄×D₃	1	1	yes	characteristic
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	2	1	no	—
379	C₄	—	2	1	no	—
380	C₄	—	6	1	no	—
381	C₄	—	6	1	no	—
382	C₄	—	6	1	no	—
383	C₄	—	6	1	no	—
384	C₄	#1009	1	1	yes	characteristic
385	C₄	#1009	1	1	yes	characteristic
386	C₃	#2976	1	1	yes	characteristic, complemented, Sylow
387	C₂	—	4	1	no	—
388	C₂	—	6	2	no	—
389	C₂	—	12	1	no	—
390	C₂	—	12	1	no	—
391	C₂	—	12	1	no	—
392	C₂	#5521	1	1	yes	characteristic
393	C₂	D₃×#131	1	1	yes	characteristic
394	C₂	#5750	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₃
commutator, socle	C₂²×C₃	C₂³×C₄
Fitting	C₃×#433	C₂
prime radical	#5524	C₂
cosocle	C₂×C₃×C₄	C₂⁴
hypercenter	#433	D₃
hypocenter	C₃	#2976
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄ ◁ #433

Complements

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

N	H ≅ G/N	type
2. C₃×#433	C₂	semidirect
3. #5000	C₂	semidirect
4. #4838	C₂	semidirect
5. #4836	C₂	semidirect
6. #4836	C₂	semidirect
7. #4834	C₂	semidirect
8. #4727	C₂	semidirect
9. #4727	C₂	semidirect
10. #4726	C₂	semidirect
11. D₃×C₂²⋊C₈	C₂	semidirect
12. #4706	C₂	semidirect
13. #4706	C₂	semidirect
14. #4688	C₂	semidirect
15. C₈×D₁₂	C₂	semidirect
22. C₂×ΓL(1,𝔽₂₅)	C₂²	semidirect
23. C₂×ΓL(1,𝔽₂₅)	C₂²	semidirect
26. C₂×D₃×C₈	C₂²	semidirect
27. C₂×D₃×C₈	C₂²	semidirect
40. C₃×C₄⋊C₈	C₂²	semidirect
41. C₃×C₄⋊C₈	C₂²	semidirect
44. C₃×#97	C₂²	semidirect
45. C₃×C₄×C₈	C₂²	semidirect
52. (C₂×D₃)⋊C₈	C₂²	semidirect
53. (C₂×D₃)⋊C₈	C₂²	semidirect
54. (C₂×D₃)⋊C₈	C₂²	semidirect
55. (C₂×D₃)⋊C₈	C₂²	semidirect
56. C₄⋊(C₃⋊C₈)	C₂²	semidirect
57. C₄⋊(C₃⋊C₈)	C₂²	semidirect
58. #803	C₂²	semidirect
59. C₄×C₃⋊C₈	C₂²	semidirect
70. #433	D₃	semidirect
155. C₄⋊C₈	C₂×D₃	semidirect
156. C₄⋊C₈	C₂×D₃	semidirect
170. #97	C₂×D₃	semidirect
172. C₄×C₈	C₂×D₃	semidirect
386. C₃	#2976	semidirect

Maximal subgroups

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

subgroup	index
#5524	2
C₃×#433	2
#5000	2
#4838	2
#4836	2
#4834	2
#4727	2
#4726	2
D₃×C₂²⋊C₈	2
#4706	2
#4688	2
C₈×D₁₂	2
#2976	3