Subgroups — #31012623

Order 17152.

668 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22573348	C₂	1	2	yes	maximal, complemented
2	#22572009	C₂	1	1	yes	maximal, characteristic, complemented
3	#22562458	C₂	1	1	yes	maximal, characteristic, complemented
4	#22562327	C₂	1	2	yes	maximal, complemented
5	#22562285	C₂	1	1	yes	maximal, characteristic, complemented
6	#22562282	C₂	1	1	yes	maximal, characteristic, complemented
7	#22562166	C₂	1	2	yes	maximal, complemented
8	#22562164	C₂	1	2	yes	maximal, complemented
9	#22562088	C₂	1	1	yes	maximal, characteristic, complemented
10	#22562046	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3292	C₂	1	1	yes	maximal, characteristic, complemented
12	#16864201	C₂²	1	2	yes	complemented
13	#16864198	—	2	1	no	—
14	#16863832	—	2	2	no	—
15	#16863832	C₂²	1	2	yes	complemented
16	#16863831	—	2	2	no	—
17	#16863831	C₂²	1	2	yes	complemented
18	#16863826	—	2	2	no	—
19	#16863826	C₂²	1	1	yes	characteristic
20	C₂×#14523984	—	2	2	no	—
21	C₂×#14523984	C₂²	1	2	yes	complemented
22	C₂×#14523984	C₂²	1	2	yes	complemented
23	#16863813	C₂²	1	2	yes	complemented
24	#16863773	C₂²	1	1	yes	characteristic, complemented
25	#16863667	—	2	1	no	—
26	#16863666	C₂²	1	2	yes	complemented
27	#16863565	—	2	2	no	—
28	#16863514	C₂²	1	1	yes	characteristic, complemented
29	#16863225	C₂²	1	1	yes	characteristic, complemented
30	#16863217	C₂²	1	1	yes	characteristic, complemented
31	#16863209	C₂²	1	2	yes	complemented
32	#16863208	C₂²	1	2	yes	complemented
33	#16863203	C₂²	1	1	yes	characteristic, complemented
34	#16863202	C₂²	1	1	yes	characteristic, complemented
35	#16863180	C₂²	1	2	yes	complemented
36	C₄×C₆₇⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
37	#576×C₆₇	—	2	1	no	—
38	#576×C₆₇	C₂²	1	2	yes	complemented
39	#493×C₆₇	C₂²	1	1	yes	characteristic, complemented
40	#472×C₆₇	—	2	1	no	—
41	#472×C₆₇	C₂²	1	2	yes	complemented
42	#453×C₆₇	—	2	2	no	—
43	#443×C₆₇	C₂²	1	1	yes	characteristic
44	#443×C₆₇	C₂²	1	1	yes	characteristic, complemented
45	#14524089	—	2	2	no	—
46	#14524071	—	2	2	no	—
47	#14524071	—	4	2	no	—
48	#14524070	—	4	2	no	—
49	#14524068	—	2	2	no	—
50	#14524066	—	4	1	no	—
51	#14524065	—	2	2	no	—
52	#14524065	C₂³	1	1	yes	characteristic
53	C₂×D₅₃₆	—	2	2	no	—
54	C₂×D₅₃₆	—	2	1	no	—
55	C₂×D₅₃₆	C₂³	1	2	yes	—
56	D₈×D₆₇	—	4	1	no	—
57	#14524049	—	2	1	no	—
58	#14524040	—	2	1	no	—
59	#14523989	D₄	1	1	yes	characteristic, complemented
60	#14523987	—	2	2	no	—
61	#14523987	D₄	1	1	yes	characteristic, complemented
62	#14523986	—	2	2	no	—
63	#14523986	D₄	1	1	yes	characteristic, complemented
64	#14523984	—	2	2	no	—
65	#14523984	—	2	2	no	—
66	#14523984	—	2	2	no	—
67	#14523984	—	2	2	no	—
68	#14523984	—	4	2	no	—
69	#14523984	D₄	1	1	yes	characteristic, complemented
70	#14523983	—	2	2	no	—
71	#14523983	C₂³	1	2	yes	—
72	C₂×C₆₇⋊C₁₆	—	2	2	no	—
73	C₂×C₆₇⋊C₁₆	C₂³	1	1	yes	characteristic
74	C₂×C₆₇⋊C₁₆	C₂³	1	1	yes	characteristic
75	#14523979	C₂³	1	1	yes	characteristic
76	#14523971	—	2	1	no	—
77	#14523959	—	2	2	no	—
78	H(5,𝔽₂)×C₆₇	—	2	2	no	—
79	AGL(1,ℤ/8)×C₆₇	—	2	2	no	—
80	AGL(1,ℤ/8)×C₆₇	—	2	2	no	—
81	AGL(1,ℤ/8)×C₆₇	—	4	2	no	—
82	AGL(1,ℤ/8)×C₆₇	—	4	2	no	—
83	#135×C₆₇	—	2	2	no	—
84	#135×C₆₇	—	4	1	no	—
85	#135×C₆₇	D₄	1	1	yes	characteristic
86	#135×C₆₇	C₂³	1	1	yes	characteristic
87	C₂×D₈×C₆₇	—	2	2	no	—
88	C₂×D₈×C₆₇	—	2	1	no	—
89	C₂×D₈×C₆₇	—	4	1	no	—
90	C₂×D₈×C₆₇	C₂³	1	2	yes	—
91	#131×C₆₇	—	2	1	no	—
92	#131×C₆₇	C₂³	1	2	yes	—
93	#127×C₆₇	—	2	1	no	—
94	#108×C₆₇	D₄	1	1	yes	characteristic
95	#108×C₆₇	C₂³	1	1	yes	characteristic
96	#104×C₆₇	—	2	1	no	—
97	#104×C₆₇	D₄	1	2	yes	—
98	#100×C₆₇	—	2	2	no	—
99	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
100	#11761629	—	4	2	no	—
101	#11761628	—	2	1	no	—
102	#11761628	—	4	2	no	—
103	C₂×D₂₆₈	—	2	2	no	—
104	C₂×D₂₆₈	—	4	2	no	—
105	C₂×D₂₆₈	—	8	1	no	—
106	D₄×D₆₇	—	4	2	no	—
107	D₄×D₆₇	—	8	2	no	—
108	Dic₂₆₈	C₂×D₄	1	1	yes	characteristic
109	#11761617	—	2	1	no	—
110	#11761617	—	4	2	no	—
111	#11761615	—	4	2	no	—
112	D₅₃₆	—	2	2	no	—
113	D₅₃₆	—	2	2	no	—
114	D₅₃₆	—	4	2	no	—
115	D₅₃₆	—	4	1	no	—
116	D₅₃₆	—	4	1	no	—
117	D₅₃₆	C₂×D₄	1	1	yes	characteristic
118	#11761613	—	4	2	no	—
119	#11761612	—	2	1	no	—
120	#11761611	—	4	1	no	—
121	C₈×D₆₇	—	4	1	no	—
122	C₆₇⋊C₁₆	—	2	2	no	—
123	C₆₇⋊C₁₆	—	2	1	no	—
124	C₆₇⋊C₁₆	C₂×D₄	1	1	yes	characteristic
125	C₆₇⋊C₁₆	C₂×D₄	1	1	yes	characteristic
126	#41×C₆₇	—	2	1	no	—
127	#41×C₆₇	—	4	2	no	—
128	#41×C₆₇	—	4	2	no	—
129	#41×C₆₇	C₂×D₄	1	2	yes	—
130	C₂×D₄×C₆₇	—	2	2	no	—
131	C₂×D₄×C₆₇	—	4	2	no	—
132	C₂×D₄×C₆₇	—	4	2	no	—
133	C₂×D₄×C₆₇	—	8	1	no	—
134	C₂×D₄×C₆₇	—	8	2	no	—
135	Q₁₆×C₆₇	D₈	1	1	yes	characteristic
136	Q₁₆×C₆₇	C₂×D₄	1	1	yes	characteristic
137	SD₁₆×C₆₇	—	2	1	no	—
138	SD₁₆×C₆₇	—	4	2	no	—
139	SD₁₆×C₆₇	—	4	2	no	—
140	SD₁₆×C₆₇	D₈	1	2	yes	—
141	D₈×C₆₇	—	2	2	no	—
142	D₈×C₆₇	—	2	2	no	—
143	D₈×C₆₇	—	4	2	no	—
144	D₈×C₆₇	—	4	2	no	—
145	D₈×C₆₇	—	4	1	no	—
146	D₈×C₆₇	—	4	1	no	—
147	D₈×C₆₇	D₈	1	1	yes	characteristic
148	D₈×C₆₇	C₂×D₄	1	1	yes	characteristic
149	M₁₆×C₆₇	—	2	2	no	—
150	M₁₆×C₆₇	—	2	1	no	—
151	M₁₆×C₆₇	—	4	1	no	—
152	M₁₆×C₆₇	C₂×D₄	1	2	yes	—
153	C₂×C₈×C₆₇	—	2	2	no	—
154	C₂×C₈×C₆₇	—	4	1	no	—
155	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
156	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
157	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
158	C₂³×C₆₇	—	4	2	no	—
159	C₂³×C₆₇	—	8	2	no	—
160	C₂²×D₆₇	—	4	2	no	—
161	C₂²×D₆₇	—	8	2	no	—
162	Q₈×C₆₇	—	2	1	no	—
163	Q₈×C₆₇	C₂×D₈	1	2	yes	—
164	D₄×C₆₇	—	2	2	no	—
165	D₄×C₆₇	—	2	1	no	—
166	D₄×C₆₇	—	4	1	no	—
167	D₄×C₆₇	—	4	2	no	—
168	D₄×C₆₇	—	4	2	no	—
169	D₄×C₆₇	—	8	2	no	—
170	D₄×C₆₇	—	8	2	no	—
171	D₄×C₆₇	—	16	2	no	—
172	D₄×C₆₇	C₂×D₈	1	2	yes	—
173	C₂×C₄×C₆₇	—	2	1	no	—
174	C₂×C₄×C₆₇	—	2	2	no	—
175	C₂×C₄×C₆₇	—	4	1	no	—
176	C₂×C₄×C₆₇	—	8	2	no	—
177	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
178	C₂²⋊D₆₇	—	4	1	no	—
179	C₂²⋊D₆₇	—	8	2	no	—
180	D₂₆₈	—	2	1	no	—
181	D₂₆₈	—	4	2	no	—
182	D₂₆₈	—	4	2	no	—
183	D₂₆₈	—	8	2	no	—
184	D₂₆₈	—	16	2	no	—
185	C₄×D₆₇	—	4	1	no	—
186	C₄×D₆₇	—	8	2	no	—
187	Dic₁₃₄	—	2	1	no	—
188	C₈×C₆₇	—	2	2	no	—
189	C₈×C₆₇	—	4	1	no	—
190	C₈×C₆₇	C₂×D₈	1	1	yes	characteristic
191	C₈×C₆₇	C₂×D₈	1	1	yes	characteristic
192	C₈×C₆₇	C₂²×D₄	1	1	yes	characteristic
193	C₈×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
194	C₆₇⋊C₈	—	4	1	no	—
195	C₂²×C₆₇	—	2	2	no	—
196	C₂²×C₆₇	—	4	1	no	—
197	C₂²×C₆₇	—	8	2	no	—
198	C₂²×C₆₇	—	16	2	no	—
199	C₂²×C₆₇	—	32	2	no	—
200	C₂²×C₆₇	#576	1	1	yes	characteristic
201	C₂×D₆₇	—	4	1	no	—
202	C₂×D₆₇	—	8	2	no	—
203	C₂×D₆₇	—	16	2	no	—
204	C₂×D₆₇	—	32	2	no	—
205	C₄×C₆₇	—	2	2	no	—
206	C₄×C₆₇	—	2	2	no	—
207	C₄×C₆₇	—	4	1	no	—
208	C₄×C₆₇	D₄²	1	1	yes	characteristic
209	C₄×C₆₇	C₂²×D₈	1	1	yes	characteristic
210	Dic₆₇	—	4	1	no	—
211	#33858	—	67	1	no	maximal, Sylow
212	C₂×C₆₇	—	2	1	no	—
213	C₂×C₆₇	—	4	2	no	—
214	C₂×C₆₇	—	8	1	no	—
215	C₂×C₆₇	—	16	2	no	—
216	C₂×C₆₇	D₄×D₈	1	1	yes	characteristic
217	D₆₇	—	8	1	no	—
218	D₆₇	—	16	2	no	—
219	#3415	—	67	2	no	—
220	#3292	—	67	1	no	—
221	#3292	D₆₇	1	1	yes	characteristic, complemented
222	#2246	—	67	1	no	—
223	#2221	—	67	2	no	—
224	#2213	—	67	1	no	—
225	#2213	—	67	1	no	—
226	#2192	—	67	2	no	—
227	#2192	—	67	2	no	—
228	#2178	—	67	1	no	—
229	#2170	—	67	1	no	—
230	C₆₇	#33858	1	1	yes	characteristic, complemented, Sylow
231	#576	—	2	1	no	—
232	#576	—	67	2	no	—
233	#576	—	134	1	no	—
234	#576	C₂×D₆₇	1	2	yes	complemented
235	#509	—	67	2	no	—
236	#509	—	67	2	no	—
237	#509	—	134	2	no	—
238	#509	—	134	2	no	—
239	#508	—	67	1	no	—
240	#508	—	134	2	no	—
241	C₂×D₁₆	—	67	2	no	—
242	C₂×D₁₆	—	67	2	no	—
243	C₂×D₁₆	—	134	2	no	—
244	#504	—	67	2	no	—
245	#493	—	67	1	no	—
246	#493	C₂×D₆₇	1	1	yes	characteristic, complemented
247	#472	—	2	1	no	—
248	#472	—	67	2	no	—
249	#472	—	134	1	no	—
250	#472	C₂×D₆₇	1	2	yes	complemented
251	#453	—	2	2	no	—
252	#453	—	134	2	no	—
253	#443	—	67	1	no	—
254	#443	C₂×D₆₇	1	1	yes	characteristic
255	#443	C₂×D₆₇	1	1	yes	characteristic, complemented
256	#368	—	67	1	no	—
257	#364	—	67	1	no	—
258	#361	—	67	2	no	—
259	#361	—	67	2	no	—
260	#359	—	67	1	no	—
261	#359	—	67	1	no	—
262	#350	—	67	2	no	—
263	C₄×C₁₆	—	67	1	no	—
264	H(5,𝔽₂)	—	2	2	no	—
265	H(5,𝔽₂)	—	134	2	no	—
266	AGL(1,ℤ/8)	—	2	2	no	—
267	AGL(1,ℤ/8)	—	2	2	no	—
268	AGL(1,ℤ/8)	—	4	2	no	—
269	AGL(1,ℤ/8)	—	4	2	no	—
270	AGL(1,ℤ/8)	—	268	2	no	—
271	AGL(1,ℤ/8)	—	268	2	no	—
272	AGL(1,ℤ/8)	—	134	2	no	—
273	AGL(1,ℤ/8)	—	134	2	no	—
274	#135	—	2	2	no	—
275	#135	—	4	1	no	—
276	#135	—	268	1	no	—
277	#135	—	67	1	no	—
278	#135	—	134	2	no	—
279	#135	C₂²⋊D₆₇	1	1	yes	characteristic
280	#135	C₂²×D₆₇	1	1	yes	characteristic
281	C₂×D₈	—	2	2	no	—
282	C₂×D₈	—	2	1	no	—
283	C₂×D₈	—	4	1	no	—
284	C₂×D₈	—	268	1	no	—
285	C₂×D₈	—	67	2	no	—
286	C₂×D₈	—	134	2	no	—
287	C₂×D₈	—	134	1	no	—
288	C₂×D₈	C₂²×D₆₇	1	2	yes	—
289	#131	—	2	1	no	—
290	#131	—	134	1	no	—
291	#131	C₂²×D₆₇	1	2	yes	—
292	#127	—	2	1	no	—
293	#127	—	134	1	no	—
294	Q₃₂	—	67	1	no	—
295	SD₃₂	—	67	1	no	—
296	SD₃₂	—	67	1	no	—
297	SD₃₂	—	134	2	no	—
298	SD₃₂	—	134	2	no	—
299	D₁₆	—	268	2	no	—
300	D₁₆	—	67	1	no	—
301	D₁₆	—	134	2	no	—
302	D₁₆	—	134	2	no	—
303	D₁₆	—	134	2	no	—
304	D₁₆	—	134	2	no	—
305	M₃₂	—	67	2	no	—
306	M₃₂	—	134	2	no	—
307	C₂×C₁₆	—	67	1	no	—
308	C₂×C₁₆	—	67	1	no	—
309	C₂×C₁₆	—	134	2	no	—
310	#108	—	67	1	no	—
311	#108	C₂²⋊D₆₇	1	1	yes	characteristic
312	#108	C₂²×D₆₇	1	1	yes	characteristic
313	#104	—	2	1	no	—
314	#104	—	134	1	no	—
315	#104	C₂²⋊D₆₇	1	2	yes	—
316	#100	—	2	2	no	—
317	#100	—	134	2	no	—
318	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
319	#41	—	2	1	no	—
320	#41	—	4	2	no	—
321	#41	—	4	2	no	—
322	#41	—	268	2	no	—
323	#41	—	268	2	no	—
324	#41	—	134	1	no	—
325	#41	C₂×C₂²⋊D₆₇	1	2	yes	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	4	2	no	—
328	C₂×D₄	—	4	2	no	—
329	C₂×D₄	—	8	1	no	—
330	C₂×D₄	—	8	2	no	—
331	C₂×D₄	—	268	2	no	—
332	C₂×D₄	—	268	2	no	—
333	C₂×D₄	—	536	1	no	—
334	C₂×D₄	—	536	2	no	—
335	C₂×D₄	—	134	2	no	—
336	Q₁₆	—	67	1	no	—
337	Q₁₆	#11761613	1	1	yes	characteristic
338	Q₁₆	D₄×D₆₇	1	1	yes	characteristic
339	SD₁₆	—	2	1	no	—
340	SD₁₆	—	4	2	no	—
341	SD₁₆	—	4	2	no	—
342	SD₁₆	—	268	2	no	—
343	SD₁₆	—	268	2	no	—
344	SD₁₆	—	134	1	no	—
345	SD₁₆	#11761613	1	2	yes	—
346	D₈	—	2	2	no	—
347	D₈	—	2	2	no	—
348	D₈	—	4	2	no	—
349	D₈	—	4	2	no	—
350	D₈	—	4	1	no	—
351	D₈	—	4	1	no	—
352	D₈	—	268	2	no	—
353	D₈	—	268	2	no	—
354	D₈	—	268	1	no	—
355	D₈	—	268	1	no	—
356	D₈	—	67	1	no	—
357	D₈	—	134	2	no	—
358	D₈	—	134	2	no	—
359	D₈	#11761613	1	1	yes	characteristic
360	D₈	D₄×D₆₇	1	1	yes	characteristic
361	M₁₆	—	2	2	no	—
362	M₁₆	—	2	1	no	—
363	M₁₆	—	4	1	no	—
364	M₁₆	—	268	1	no	—
365	M₁₆	—	134	1	no	—
366	M₁₆	C₂×C₂²⋊D₆₇	1	2	yes	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	4	1	no	—
369	C₂×C₈	—	268	1	no	—
370	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
371	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
372	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
373	C₁₆	—	67	1	no	—
374	C₁₆	—	67	1	no	—
375	C₁₆	—	134	2	no	—
376	C₁₆	—	134	1	no	—
377	C₂³	—	4	2	no	—
378	C₂³	—	8	2	no	—
379	C₂³	—	268	2	no	—
380	C₂³	—	536	2	no	—
381	Q₈	—	2	1	no	—
382	Q₈	—	134	1	no	—
383	Q₈	C₂×#11761613	1	2	yes	—
384	D₄	—	2	2	no	—
385	D₄	—	2	1	no	—
386	D₄	—	4	1	no	—
387	D₄	—	4	2	no	—
388	D₄	—	4	2	no	—
389	D₄	—	8	2	no	—
390	D₄	—	8	2	no	—
391	D₄	—	268	1	no	—
392	D₄	—	268	2	no	—
393	D₄	—	268	2	no	—
394	D₄	—	16	2	no	—
395	D₄	—	536	2	no	—
396	D₄	—	536	2	no	—
397	D₄	—	1072	2	no	—
398	D₄	—	134	1	no	—
399	D₄	C₂×#11761613	1	2	yes	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	8	2	no	—
404	C₂×C₄	—	268	1	no	—
405	C₂×C₄	—	536	2	no	—
406	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
407	C₈	—	2	2	no	—
408	C₈	—	4	1	no	—
409	C₈	—	268	1	no	—
410	C₈	C₂×#11761613	1	1	yes	characteristic
411	C₈	C₂×#11761613	1	1	yes	characteristic
412	C₈	C₂×D₄×D₆₇	1	1	yes	characteristic
413	C₈	#14524088	1	1	yes	characteristic
414	C₂²	—	2	2	no	—
415	C₂²	—	4	1	no	—
416	C₂²	—	8	2	no	—
417	C₂²	—	268	1	no	—
418	C₂²	—	16	2	no	—
419	C₂²	—	536	2	no	—
420	C₂²	—	32	2	no	—
421	C₂²	—	1072	2	no	—
422	C₂²	—	2144	2	no	—
423	C₂²	#16864199	1	1	yes	characteristic
424	C₄	—	2	2	no	—
425	C₄	—	2	2	no	—
426	C₄	—	4	1	no	—
427	C₄	—	268	1	no	—
428	C₄	D₄×C₂²⋊D₆₇	1	1	yes	characteristic
429	C₄	C₂²×#11761613	1	1	yes	characteristic
430	C₂	—	2	1	no	—
431	C₂	—	4	2	no	—
432	C₂	—	8	1	no	—
433	C₂	—	16	2	no	—
434	C₂	—	536	1	no	—
435	C₂	—	1072	2	no	—
436	C₂	D₄×#11761613	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×#11761613
commutator, cosocle	C₂×C₈×C₆₇	C₂⁴
Frattini	C₂×C₈	C₂³×D₆₇
Fitting	C₆₇×#3292	C₂
socle	C₂×C₆₇	D₄×D₈
hypercenter	#3292	D₆₇
hypocenter	C₆₇	#33858
LCS	G ▷ C₂×C₈×C₆₇ ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #443 ◁ #3292

Complements

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

N	H ≅ G/N	type
1. #22573348	C₂	semidirect
2. #22572009	C₂	semidirect
3. #22562458	C₂	semidirect
4. #22562327	C₂	semidirect
5. #22562285	C₂	semidirect
6. #22562282	C₂	semidirect
7. #22562166	C₂	semidirect
8. #22562164	C₂	semidirect
9. #22562088	C₂	semidirect
10. #22562046	C₂	semidirect
11. C₆₇×#3292	C₂	semidirect
12. #16864201	C₂²	semidirect
15. #16863832	C₂²	semidirect
17. #16863831	C₂²	semidirect
21. C₂×#14523984	C₂²	semidirect
22. C₂×#14523984	C₂²	semidirect
23. #16863813	C₂²	semidirect
24. #16863773	C₂²	semidirect
26. #16863666	C₂²	semidirect
28. #16863514	C₂²	semidirect
29. #16863225	C₂²	semidirect
30. #16863217	C₂²	semidirect
31. #16863209	C₂²	semidirect
32. #16863208	C₂²	semidirect
33. #16863203	C₂²	semidirect
34. #16863202	C₂²	semidirect
35. #16863180	C₂²	semidirect
36. C₄×C₆₇⋊C₁₆	C₂²	semidirect
38. #576×C₆₇	C₂²	semidirect
39. #493×C₆₇	C₂²	semidirect
41. #472×C₆₇	C₂²	semidirect
44. #443×C₆₇	C₂²	semidirect
59. #14523989	D₄	semidirect
61. #14523987	D₄	semidirect
63. #14523986	D₄	semidirect
69. #14523984	D₄	semidirect
221. #3292	D₆₇	semidirect
230. C₆₇	#33858	semidirect
234. #576	C₂×D₆₇	semidirect
246. #493	C₂×D₆₇	semidirect
250. #472	C₂×D₆₇	semidirect
255. #443	C₂×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
#22573348	2
#22572009	2
#22562458	2
#22562327	2
#22562285	2
#22562282	2
#22562166	2
#22562164	2
#22562088	2
#22562046	2
C₆₇×#3292	2
#33858	67