Subgroups — #30914738

Order 17152.

674 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22570749	C₂	1	1	yes	maximal, characteristic, complemented
2	#22570073	C₂	1	2	yes	maximal
3	#22568806	C₂	1	1	yes	maximal, characteristic
4	#22561719	C₂	1	2	yes	maximal, complemented
5	#22561558	C₂	1	2	yes	maximal, complemented
6	#22560995	C₂	1	1	yes	maximal, characteristic, complemented
7	#22560443	C₂	1	2	yes	maximal
8	#22560373	C₂	1	1	yes	maximal, characteristic, complemented
9	#22560270	C₂	1	1	yes	maximal, characteristic
10	#22560046	C₂	1	1	yes	maximal, characteristic
11	C₆₇×#1945	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14524049	C₂²	1	1	yes	characteristic
13	#16864024	C₂²	1	2	yes	—
14	#16863876	C₂²	1	2	yes	—
15	#16863803	—	2	2	no	—
16	#16863800	—	2	1	no	—
17	#16863797	—	2	1	no	—
18	#16863704	—	2	2	no	—
19	#16863697	—	2	2	no	—
20	#16863687	—	2	2	no	—
21	#16863682	—	2	2	no	—
22	#16863439	C₂²	1	2	yes	—
23	#16863439	C₂²	1	2	yes	—
24	#16863438	C₂²	1	2	yes	—
25	#16863435	—	2	2	no	—
26	#16863433	—	2	1	no	—
27	C₂×#14523977	C₂²	1	1	yes	characteristic
28	C₂×#14523977	C₂²	1	1	yes	characteristic
29	#107×D₆₇	—	2	1	no	—
30	C₂×#14523975	C₂²	1	2	yes	—
31	C₂×#14523971	C₂²	1	1	yes	characteristic
32	#16863398	C₂²	1	2	yes	—
33	#16863393	C₂²	1	1	yes	characteristic
34	#16863351	C₂²	1	1	yes	characteristic
35	#16863262	C₂²	1	2	yes	—
36	#16863164	C₂²	1	2	yes	—
37	#16863164	C₂²	1	2	yes	—
38	#16863161	C₂²	1	1	yes	characteristic
39	#16863156	C₂²	1	1	yes	characteristic
40	C₂×#108×C₆₇	C₂²	1	1	yes	characteristic
41	#427×C₆₇	C₂²	1	1	yes	characteristic
42	#424×C₆₇	C₂²	1	2	yes	—
43	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
44	#339×C₆₇	C₂²	1	2	yes	—
45	C₂×#11761628	C₂³	1	1	yes	characteristic
46	#14524049	—	2	2	no	—
47	#14524049	Q₈	1	4	yes	complemented
48	C₂×#11761612	C₂³	1	1	yes	characteristic
49	C₂×#11761612	C₂³	1	1	yes	characteristic
50	C₂×#11761611	—	2	1	no	—
51	C₂×C₈×D₆₇	—	2	1	no	—
52	#14524043	—	2	2	no	—
53	#14524042	—	2	2	no	—
54	#14524035	—	2	2	no	—
55	#14524034	—	2	2	no	—
56	#14524020	—	4	2	no	—
57	C₄×Dic₁₃₄	—	2	2	no	—
58	C₄×D₂₆₈	—	2	2	no	—
59	(C₂²⋊D₆₇)⋊C₄	—	4	2	no	—
60	#14524002	C₂³	1	1	yes	characteristic
61	#14524001	—	2	2	no	—
62	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
63	C₂×C₄⋊Dic₆₇	C₂³	1	2	yes	—
64	C₄⋊C₄×D₆₇	—	2	2	no	—
65	#14523977	—	2	2	no	—
66	#14523977	—	2	1	no	—
67	#14523977	—	2	1	no	—
68	#14523977	—	2	1	no	—
69	#14523977	—	2	1	no	—
70	#14523976	—	2	2	no	—
71	#14523976	—	2	2	no	—
72	#14523975	—	2	2	no	—
73	#14523975	—	2	2	no	—
74	#14523975	—	2	2	no	—
75	#14523974	—	2	2	no	—
76	#14523974	—	2	2	no	—
77	#14523971	Q₈	1	4	yes	complemented
78	#14523968	—	2	2	no	—
79	#14523968	D₄	1	1	yes	characteristic
80	#14523968	D₄	1	1	yes	characteristic
81	#14523965	—	2	2	no	—
82	#14523965	D₄	1	1	yes	characteristic
83	#14523965	D₄	1	1	yes	characteristic
84	#14523953	—	2	1	no	—
85	C₈×Dic₆₇	—	2	1	no	—
86	C₆₇⋊#95	—	4	2	no	—
87	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
88	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
90	#117×C₆₇	C₂³	1	2	yes	—
91	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
92	#108×C₆₇	—	2	2	no	—
93	#107×C₆₇	D₄	1	1	yes	characteristic
94	#107×C₆₇	D₄	1	1	yes	characteristic
95	#106×C₆₇	D₄	1	2	yes	—
96	C₄⋊C₈×C₆₇	—	2	2	no	—
97	C₄⋊C₈×C₆₇	—	2	2	no	—
98	C₄×C₈×C₆₇	—	2	2	no	—
99	#11761628	—	2	1	no	—
100	#11761628	—	2	1	no	—
101	#11761628	C₂×Q₈	1	2	yes	—
102	#11761628	C₂×Q₈	1	2	yes	—
103	C₂×Dic₁₃₄	—	4	2	no	—
104	C₂×Dic₁₃₄	C₂×D₄	1	1	yes	characteristic
105	C₂×D₂₆₈	C₂×D₄	1	1	yes	characteristic
106	C₂×C₂²⋊D₆₇	—	2	1	no	—
107	C₂²×Dic₆₇	—	2	2	no	—
108	C₂²×Dic₆₇	—	2	2	no	—
109	C₂×C₄×D₆₇	—	2	1	no	—
110	C₂×C₄×D₆₇	—	4	2	no	—
111	#11761612	—	2	1	no	—
112	#11761612	—	2	1	no	—
113	#11761612	C₂×Q₈	1	2	yes	—
114	#11761612	C₂×Q₈	1	2	yes	—
115	#11761611	—	2	4	no	—
116	C₂×C₆₇⋊C₈	—	2	1	no	—
117	C₂×C₆₇⋊C₈	—	2	1	no	—
118	C₈×D₆₇	—	2	4	no	—
119	C₄⋊Dic₆₇	—	2	2	no	—
120	C₄⋊Dic₆₇	—	2	2	no	—
121	C₄⋊Dic₆₇	—	2	2	no	—
122	C₄⋊Dic₆₇	—	2	2	no	—
123	C₄⋊Dic₆₇	—	4	2	no	—
124	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
125	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
126	Dic₆₇⋊C₄	—	4	2	no	—
127	Dic₆₇⋊C₄	—	4	2	no	—
128	Dic₆₇⋊C₄	—	4	2	no	—
129	C₂²⋊Dic₆₇	—	2	1	no	—
130	(C₂×D₆₇)⋊C₄	—	4	2	no	—
131	C₄×Dic₆₇	—	2	1	no	—
132	C₄×Dic₆₇	—	4	2	no	—
133	C₂²×C₄×C₆₇	—	2	1	no	—
134	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
135	M₁₆×C₆₇	—	2	2	no	—
136	M₁₆×C₆₇	—	2	2	no	—
137	C₂×C₈×C₆₇	—	2	1	no	—
138	C₂×C₈×C₆₇	—	2	1	no	—
139	C₂×C₈×C₆₇	—	2	2	no	—
140	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
141	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
142	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₆₇	C₂×Q₈	1	2	yes	—
145	C₂×C₈×C₆₇	#41	1	2	yes	—
146	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
147	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
148	C₂²⋊C₄×C₆₇	—	2	2	no	—
149	C₄²×C₆₇	—	2	2	no	—
150	C₄²×C₆₇	—	2	1	no	—
151	C₄²×C₆₇	C₂×Q₈	1	2	yes	—
152	C₂³×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
153	C₂²×D₆₇	—	2	1	no	—
154	C₂×C₄×C₆₇	—	2	2	no	—
155	C₂×C₄×C₆₇	—	2	2	no	—
156	C₂×C₄×C₆₇	—	2	2	no	—
157	C₂×C₄×C₆₇	—	4	1	no	—
158	C₂×C₄×C₆₇	—	4	1	no	—
159	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₆₇	C₂²×Q₈	1	1	yes	characteristic
162	C₂×C₄×C₆₇	C₂²×Q₈	1	1	yes	characteristic
163	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
164	C₂×C₄×C₆₇	2₋¹⁺⁴	1	1	yes	characteristic
165	C₂²⋊D₆₇	—	2	2	no	—
166	C₂²⋊D₆₇	—	2	2	no	—
167	C₂×Dic₆₇	—	2	1	no	—
168	C₂×Dic₆₇	—	2	1	no	—
169	C₂×Dic₆₇	—	2	1	no	—
170	C₂×Dic₆₇	—	4	2	no	—
171	C₂×Dic₆₇	—	4	2	no	—
172	C₂×Dic₆₇	—	8	2	no	—
173	C₂×Dic₆₇	—	8	2	no	—
174	D₂₆₈	—	2	1	no	—
175	D₂₆₈	C₄⋊Q₈	1	2	yes	—
176	C₄×D₆₇	—	2	2	no	—
177	C₄×D₆₇	—	2	2	no	—
178	C₄×D₆₇	—	16	2	no	—
179	Dic₁₃₄	—	2	1	no	—
180	Dic₁₃₄	—	16	2	no	—
181	Dic₁₃₄	C₄⋊Q₈	1	2	yes	—
182	C₈×C₆₇	—	2	1	no	—
183	C₈×C₆₇	—	2	1	no	—
184	C₈×C₆₇	—	4	2	no	—
185	C₈×C₆₇	C₂²⋊Q₈	1	2	yes	—
186	C₈×C₆₇	C₂²⋊Q₈	1	2	yes	—
187	C₆₇⋊C₈	—	2	2	no	—
188	C₆₇⋊C₈	—	2	2	no	—
189	C₂²×C₆₇	—	2	1	no	—
190	C₂²×C₆₇	—	2	1	no	—
191	C₂²×C₆₇	#544	1	1	yes	characteristic
192	C₂²×C₆₇	D₄²	1	1	yes	characteristic
193	C₂²×C₆₇	#554	1	1	yes	characteristic
194	C₂×D₆₇	—	2	2	no	—
195	C₂×D₆₇	—	4	1	no	—
196	C₂×D₆₇	—	4	1	no	—
197	C₄×C₆₇	—	4	2	no	—
198	C₄×C₆₇	—	4	2	no	—
199	C₄×C₆₇	—	4	2	no	—
200	C₄×C₆₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
201	C₄×C₆₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
202	C₄×C₆₇	#547	1	1	yes	characteristic
203	C₄×C₆₇	D₄×Q₈	1	1	yes	characteristic
204	Dic₆₇	—	2	2	no	—
205	Dic₆₇	—	4	1	no	—
206	Dic₆₇	—	4	1	no	—
207	Dic₆₇	—	8	2	no	—
208	Dic₆₇	—	8	2	no	—
209	#26082	—	67	1	no	maximal, Sylow
210	C₂×C₆₇	—	2	1	no	—
211	C₂×C₆₇	—	2	1	no	—
212	C₂×C₆₇	#2440	1	1	yes	characteristic
213	C₂×C₆₇	#3290	1	1	yes	characteristic
214	C₂×C₆₇	#3290	1	1	yes	characteristic
215	D₆₇	—	4	2	no	—
216	#3164	—	67	1	no	—
217	#3084	—	67	2	no	—
218	#2913	—	67	1	no	—
219	#2090	—	67	2	no	—
220	#2061	—	67	2	no	—
221	#1952	—	67	1	no	—
222	#1945	D₆₇	1	1	yes	characteristic, complemented
223	#1860	—	67	2	no	—
224	#1846	—	67	1	no	—
225	#1816	—	67	1	no	—
226	#1764	—	67	1	no	—
227	C₆₇	#26082	1	1	yes	characteristic, complemented, Sylow
228	C₂×#131	—	67	1	no	—
229	#544	—	67	2	no	—
230	#520	—	67	2	no	—
231	#501	—	134	2	no	—
232	#500	—	134	1	no	—
233	#499	—	134	1	no	—
234	#479	—	134	2	no	—
235	#478	—	134	2	no	—
236	#476	—	134	2	no	—
237	#475	—	134	2	no	—
238	C₂×#108	C₂×D₆₇	1	1	yes	characteristic
239	#428	—	67	2	no	—
240	#428	—	67	2	no	—
241	#428	—	67	2	no	—
242	#428	—	134	2	no	—
243	#427	—	134	1	no	—
244	#427	C₂×D₆₇	1	1	yes	characteristic
245	C₂×#107	—	67	1	no	—
246	C₂×#107	—	67	1	no	—
247	C₂×#107	—	134	1	no	—
248	C₂×#106	—	67	2	no	—
249	#424	C₂×D₆₇	1	2	yes	—
250	C₂×#104	—	67	1	no	—
251	#417	—	67	2	no	—
252	#416	—	67	1	no	—
253	#405	—	67	1	no	—
254	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
255	#382	—	67	2	no	—
256	#343	—	67	2	no	—
257	#343	—	67	2	no	—
258	#341	—	67	1	no	—
259	#339	—	67	1	no	—
260	#339	C₂×D₆₇	1	2	yes	—
261	C₂×#41	—	67	1	no	—
262	#131	—	67	4	no	—
263	#131	—	134	2	no	—
264	C₂×M₁₆	—	67	1	no	—
265	C₂×M₁₆	—	67	1	no	—
266	C₂×M₁₆	—	134	1	no	—
267	C₂×M₁₆	C₂²×D₆₇	1	2	yes	—
268	C₂²×C₈	—	134	1	no	—
269	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
270	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
271	C₄⋊Q₈	—	134	2	no	—
272	C₄⋊Q₈	—	134	2	no	—
273	#125	—	134	2	no	—
274	#125	—	134	2	no	—
275	C₂²⋊Q₈	—	268	2	no	—
276	C₄×Q₈	—	134	2	no	—
277	C₄×D₄	—	268	2	no	—
278	C₄×D₄	—	134	2	no	—
279	#117	—	67	1	no	—
280	#117	—	134	2	no	—
281	#117	C₂²×D₆₇	1	2	yes	—
282	C₂×C₄⋊C₄	—	67	2	no	—
283	C₂×C₄⋊C₄	—	67	2	no	—
284	C₂×C₄⋊C₄	—	134	2	no	—
285	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
286	#108	—	2	2	no	—
287	#107	—	134	2	no	—
288	#107	—	134	1	no	—
289	#107	—	134	1	no	—
290	#107	—	134	1	no	—
291	#107	—	134	1	no	—
292	#107	—	134	2	no	—
293	#107	—	134	2	no	—
294	#107	D₂₆₈	1	1	yes	characteristic
295	#107	D₂₆₈	1	1	yes	characteristic
296	#106	—	134	2	no	—
297	#106	—	134	2	no	—
298	#106	—	134	2	no	—
299	#106	—	134	2	no	—
300	#106	—	134	2	no	—
301	#106	D₂₆₈	1	2	yes	—
302	C₄⋊C₈	—	2	2	no	—
303	C₄⋊C₈	—	2	2	no	—
304	#104	—	67	4	no	—
305	#103	—	67	1	no	—
306	#103	—	67	1	no	—
307	#103	—	134	2	no	—
308	#102	—	67	1	no	—
309	#102	—	67	1	no	—
310	#102	—	134	2	no	—
311	#97	—	134	1	no	—
312	C₄×C₈	—	2	2	no	—
313	C₄×C₈	—	134	1	no	—
314	#95	—	268	2	no	—
315	#41	—	67	2	no	—
316	#41	—	67	2	no	—
317	#41	—	134	1	no	—
318	#41	—	134	1	no	—
319	C₂×Q₈	—	268	2	no	—
320	C₂×Q₈	—	67	1	no	—
321	C₂×D₄	—	67	1	no	—
322	C₂×D₄	—	134	1	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	268	2	no	—
325	C₂²×C₄	—	134	2	no	—
326	C₂²×C₄	—	134	2	no	—
327	C₂²×C₄	—	134	1	no	—
328	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
329	M₁₆	—	2	2	no	—
330	M₁₆	—	2	2	no	—
331	M₁₆	—	67	2	no	—
332	M₁₆	—	67	2	no	—
333	M₁₆	—	134	1	no	—
334	M₁₆	—	134	1	no	—
335	M₁₆	—	134	4	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	134	1	no	—
340	C₂×C₈	—	134	1	no	—
341	C₂×C₈	—	134	4	no	—
342	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
343	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
344	C₂×C₈	C₂×D₂₆₈	1	1	yes	characteristic
345	C₂×C₈	C₂×D₂₆₈	1	1	yes	characteristic
346	C₂×C₈	Q₈×D₆₇	1	2	yes	—
347	C₂×C₈	#11761627	1	2	yes	—
348	C₄⋊C₄	—	268	2	no	—
349	C₄⋊C₄	—	268	2	no	—
350	C₄⋊C₄	—	268	2	no	—
351	C₄⋊C₄	—	268	2	no	—
352	C₄⋊C₄	—	67	1	no	—
353	C₄⋊C₄	—	67	1	no	—
354	C₄⋊C₄	—	134	2	no	—
355	C₄⋊C₄	—	134	2	no	—
356	C₄⋊C₄	—	134	2	no	—
357	C₄⋊C₄	—	134	2	no	—
358	C₄⋊C₄	C₂×D₂₆₈	1	2	yes	—
359	C₄⋊C₄	C₂×D₂₆₈	1	2	yes	—
360	C₂²⋊C₄	—	2	2	no	—
361	C₂²⋊C₄	—	268	2	no	—
362	C₂²⋊C₄	—	134	1	no	—
363	C₄²	—	2	2	no	—
364	C₄²	—	2	1	no	—
365	C₄²	—	268	2	no	—
366	C₄²	—	134	1	no	—
367	C₄²	Q₈×D₆₇	1	2	yes	—
368	C₂³	—	134	1	no	—
369	C₂³	#14524089	1	1	yes	characteristic
370	Q₈	—	1072	2	no	—
371	Q₈	—	67	2	no	—
372	Q₈	—	134	1	no	—
373	D₄	—	67	2	no	—
374	D₄	—	134	2	no	—
375	D₄	—	134	2	no	—
376	D₄	—	134	1	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	268	2	no	—
383	C₂×C₄	—	268	2	no	—
384	C₂×C₄	—	536	2	no	—
385	C₂×C₄	—	536	2	no	—
386	C₂×C₄	—	1072	2	no	—
387	C₂×C₄	—	134	1	no	—
388	C₂×C₄	—	134	1	no	—
389	C₂×C₄	—	134	1	no	—
390	C₂×C₄	—	134	2	no	—
391	C₂×C₄	—	134	2	no	—
392	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
393	C₂×C₄	C₂²×D₂₆₈	1	1	yes	characteristic
394	C₂×C₄	C₂×Q₈×D₆₇	1	1	yes	characteristic
395	C₂×C₄	C₂×Q₈×D₆₇	1	1	yes	characteristic
396	C₂×C₄	C₂×#11761627	1	1	yes	characteristic
397	C₂×C₄	#14524090	1	1	yes	characteristic
398	C₈	—	2	1	no	—
399	C₈	—	2	1	no	—
400	C₈	—	4	2	no	—
401	C₈	—	134	2	no	—
402	C₈	—	134	2	no	—
403	C₈	#14524023	1	2	yes	—
404	C₈	#14524023	1	2	yes	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	268	1	no	—
408	C₂²	—	268	1	no	—
409	C₂²	—	134	2	no	—
410	C₂²	#16864026	1	1	yes	characteristic
411	C₂²	D₄×D₂₆₈	1	1	yes	characteristic
412	C₂²	#16864104	1	1	yes	characteristic
413	C₄	—	4	2	no	—
414	C₄	—	4	2	no	—
415	C₄	—	4	2	no	—
416	C₄	—	268	1	no	—
417	C₄	—	268	1	no	—
418	C₄	—	536	2	no	—
419	C₄	—	536	2	no	—
420	C₄	—	134	2	no	—
421	C₄	C₂×#14524023	1	1	yes	characteristic
422	C₄	C₄⋊Q₈×D₆₇	1	1	yes	characteristic
423	C₄	#16864046	1	1	yes	characteristic
424	C₄	Q₈×D₂₆₈	1	1	yes	characteristic
425	C₂	—	2	1	no	—
426	C₂	—	2	1	no	—
427	C₂	—	268	2	no	—
428	C₂	#22563909	1	1	yes	characteristic
429	C₂	#22571997	1	1	yes	characteristic
430	C₂	#22571997	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₂₆₈
commutator, cosocle	C₂²×C₄×C₆₇	C₂⁴
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting	C₆₇×#1945	C₂
socle	C₂²×C₆₇	D₄²
prime radical	C₂×#11761628	C₂³
hypercenter	#1945	D₆₇
hypocenter	C₆₇	#26082
LCS	G ▷ C₂²×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #1945

Complements

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

N	H ≅ G/N	type
1. #22570749	C₂	semidirect
4. #22561719	C₂	semidirect
5. #22561558	C₂	semidirect
6. #22560995	C₂	semidirect
8. #22560373	C₂	semidirect
11. C₆₇×#1945	C₂	semidirect
47. #14524049	Q₈	semidirect
77. #14523971	Q₈	semidirect
222. #1945	D₆₇	semidirect
227. C₆₇	#26082	semidirect

Maximal subgroups

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

subgroup	index
#22570749	2
#22570073	2
#22568806	2
#22561719	2
#22561558	2
#22560995	2
#22560443	2
#22560373	2
#22560270	2
#22560046	2
C₆₇×#1945	2
#26082	67