Subgroups — #30838971

Order 17152.

714 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22571334	C₂	1	1	yes	maximal, characteristic, complemented
2	#22571124	C₂	1	1	yes	maximal, characteristic
3	C₂×#16863743	C₂	1	1	yes	maximal, characteristic, complemented
4	#22559742	C₂	1	4	yes	maximal, complemented
5	#22559618	C₂	1	4	yes	maximal, complemented
6	#22558957	C₂	1	1	yes	maximal, characteristic, complemented
7	#22558891	C₂	1	1	yes	maximal, characteristic, complemented
8	#22558878	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2931	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#14524043	C₂²	1	1	yes	characteristic
11	C₂×#14524040	C₂²	1	1	yes	characteristic
12	#16863792	—	2	1	no	—
13	#16863772	—	2	1	no	—
14	#16863744	—	2	1	no	—
15	#16863743	—	2	1	no	—
16	#16863743	—	2	1	no	—
17	#16863743	C₂²	1	2	yes	—
18	#16863743	C₂²	1	2	yes	—
19	#16863742	—	2	1	no	—
20	#16863712	—	2	2	no	—
21	#16863686	C₂²	1	4	yes	complemented
22	#16863591	C₂²	1	4	yes	—
23	#16863529	—	2	2	no	—
24	#16863449	C₂²	1	1	yes	characteristic
25	#16863449	C₂²	1	1	yes	characteristic
26	C₂×#14523965	—	2	1	no	—
27	C₂×#14523965	—	2	1	no	—
28	#16863149	C₂²	1	2	yes	complemented
29	#16863147	C₂²	1	2	yes	complemented
30	#16863144	C₂²	1	4	yes	complemented
31	#16863139	C₂²	1	4	yes	—
32	C₂×#131×C₆₇	—	2	1	no	—
33	#532×C₆₇	C₂²	1	1	yes	characteristic
34	#436×C₆₇	—	2	1	no	—
35	#436×C₆₇	C₂²	1	2	yes	complemented
36	C₈×D₄×C₆₇	—	2	1	no	—
37	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
38	#423×C₆₇	C₂²	1	1	yes	characteristic
39	#408×C₆₇	—	2	1	no	—
40	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
41	C₂²×Dic₁₃₄	—	2	1	no	—
42	C₂²×D₂₆₈	—	2	1	no	—
43	C₂²×D₂₆₈	—	2	1	no	—
44	C₂²×D₂₆₈	—	2	1	no	—
45	C₂×#11761613	—	2	4	no	—
46	#14524043	—	2	1	no	—
47	#14524043	—	2	1	no	—
48	#14524043	—	2	1	no	—
49	#14524043	C₂³	1	2	yes	—
50	#14524040	—	2	1	no	—
51	#14524040	—	2	1	no	—
52	#14524040	—	2	1	no	—
53	#14524040	C₂³	1	2	yes	—
54	C₂×C₄⋊Dic₆₇	—	2	1	no	—
55	C₂×C₄⋊Dic₆₇	—	2	1	no	—
56	#14523974	—	2	4	no	—
57	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
58	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
59	#14523965	—	2	2	no	—
60	#14523965	—	2	2	no	—
61	#14523965	—	2	2	no	—
62	#14523965	—	2	2	no	—
63	#14523964	—	2	4	no	—
64	#14523963	—	2	4	no	—
65	C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
66	C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
67	C₄×C₆₇⋊C₈	—	2	1	no	—
68	C₄×C₆₇⋊C₈	—	2	1	no	—
69	C₂×#41×C₆₇	—	2	1	no	—
70	#131×C₆₇	—	4	4	no	—
71	C₂×M₁₆×C₆₇	—	2	1	no	—
72	C₂×M₁₆×C₆₇	—	2	2	no	—
73	C₂²×C₈×C₆₇	—	2	2	no	—
74	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
75	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
76	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
77	#127×C₆₇	D₄	1	1	yes	characteristic
78	#124×C₆₇	—	2	1	no	—
79	#121×C₆₇	—	2	1	no	—
80	#121×C₆₇	D₄	1	2	yes	—
81	C₄×D₄×C₆₇	—	2	1	no	—
82	C₄×D₄×C₆₇	C₂³	1	2	yes	—
83	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
84	C₄⋊C₈×C₆₇	—	2	1	no	—
85	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
86	C₂²⋊C₈×C₆₇	—	2	2	no	—
87	C₂²⋊C₈×C₆₇	—	2	2	no	—
88	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
89	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
90	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
91	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
92	C₂³×D₆₇	—	4	1	no	—
93	C₂×Dic₁₃₄	—	2	2	no	—
94	C₂×Dic₁₃₄	—	4	1	no	—
95	C₂×Dic₁₃₄	—	8	2	no	—
96	C₂×D₂₆₈	—	2	2	no	—
97	C₂×D₂₆₈	—	2	2	no	—
98	C₂×D₂₆₈	—	2	2	no	—
99	C₂×D₂₆₈	—	4	2	no	—
100	C₂×D₂₆₈	—	4	2	no	—
101	C₂×D₂₆₈	—	4	1	no	—
102	C₂×D₂₆₈	—	4	1	no	—
103	C₂×D₂₆₈	—	4	1	no	—
104	C₂×D₂₆₈	—	8	2	no	—
105	C₂×D₂₆₈	—	8	2	no	—
106	C₂²×Dic₆₇	—	4	1	no	—
107	#11761613	—	8	4	no	—
108	C₂×C₆₇⋊C₈	—	2	2	no	—
109	C₂×C₆₇⋊C₈	—	2	2	no	—
110	C₄⋊Dic₆₇	—	2	2	no	—
111	C₄⋊Dic₆₇	—	2	2	no	—
112	C₄⋊Dic₆₇	—	4	1	no	—
113	C₄⋊Dic₆₇	—	4	1	no	—
114	#41×C₆₇	—	4	2	no	—
115	#41×C₆₇	—	4	2	no	—
116	C₂×Q₈×C₆₇	—	2	1	no	—
117	C₂×D₄×C₆₇	—	2	2	no	—
118	C₂×D₄×C₆₇	—	2	1	no	—
119	C₂×D₄×C₆₇	—	2	1	no	—
120	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₆₇	—	2	2	no	—
122	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
125	M₁₆×C₆₇	—	4	4	no	—
126	M₁₆×C₆₇	—	4	2	no	—
127	C₂×C₈×C₆₇	—	2	2	no	—
128	C₂×C₈×C₆₇	—	2	2	no	—
129	C₂×C₈×C₆₇	—	2	2	no	—
130	C₂×C₈×C₆₇	—	4	4	no	—
131	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
134	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
135	C₄⋊C₄×C₆₇	—	2	1	no	—
136	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
137	C₂²⋊C₄×C₆₇	—	2	2	no	—
138	C₂²⋊C₄×C₆₇	—	2	2	no	—
139	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₆₇	#41	1	1	yes	characteristic
142	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
143	C₂³×C₆₇	—	2	2	no	—
144	C₂³×C₆₇	#121	1	1	yes	characteristic
145	C₂²×D₆₇	—	4	2	no	—
146	C₂²×D₆₇	—	8	2	no	—
147	C₂²×D₆₇	—	8	2	no	—
148	C₂²×D₆₇	—	8	2	no	—
149	Q₈×C₆₇	—	4	2	no	—
150	D₄×C₆₇	—	2	4	no	—
151	D₄×C₆₇	—	4	4	no	—
152	D₄×C₆₇	—	4	2	no	—
153	D₄×C₆₇	—	4	2	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	2	no	—
158	C₂×C₄×C₆₇	—	4	2	no	—
159	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
160	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
161	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
162	C₂×C₄×C₆₇	#135	1	2	yes	—
163	C₂×C₄×C₆₇	AGL(1,ℤ/8)	1	2	yes	—
164	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
167	C₂×Dic₆₇	—	4	2	no	—
168	C₂×Dic₆₇	—	8	2	no	—
169	D₂₆₈	—	4	2	no	—
170	D₂₆₈	—	4	2	no	—
171	D₂₆₈	—	4	4	no	—
172	D₂₆₈	—	8	2	no	—
173	D₂₆₈	—	8	2	no	—
174	D₂₆₈	—	8	2	no	—
175	D₂₆₈	—	8	2	no	—
176	Dic₁₃₄	—	8	2	no	—
177	Dic₁₃₄	—	8	2	no	—
178	C₈×C₆₇	—	2	1	no	—
179	C₈×C₆₇	—	2	1	no	—
180	C₈×C₆₇	—	2	1	no	—
181	C₈×C₆₇	—	2	1	no	—
182	C₈×C₆₇	—	4	2	no	—
183	C₆₇⋊C₈	—	4	2	no	—
184	C₆₇⋊C₈	—	4	2	no	—
185	C₂²×C₆₇	—	2	1	no	—
186	C₂²×C₆₇	—	2	1	no	—
187	C₂²×C₆₇	—	4	2	no	—
188	C₂²×C₆₇	—	4	2	no	—
189	C₂²×C₆₇	—	4	2	no	—
190	C₂²×C₆₇	#463	1	2	yes	—
191	C₂²×C₆₇	C₂×#121	1	1	yes	characteristic
192	C₂×D₆₇	—	8	2	no	—
193	C₂×D₆₇	—	8	2	no	—
194	C₂×D₆₇	—	8	2	no	—
195	C₂×D₆₇	—	16	4	no	—
196	C₄×C₆₇	—	2	1	no	—
197	C₄×C₆₇	—	2	1	no	—
198	C₄×C₆₇	—	4	2	no	—
199	C₄×C₆₇	#463	1	2	yes	—
200	C₄×C₆₇	#472	1	2	yes	—
201	C₄×C₆₇	C₂×#135	1	1	yes	characteristic
202	C₄×C₆₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
203	C₄×C₆₇	#577	1	2	yes	—
204	Dic₆₇	—	8	2	no	—
205	#19196	—	67	1	no	maximal, Sylow
206	C₂×C₆₇	—	2	2	no	—
207	C₂×C₆₇	—	8	2	no	—
208	C₂×C₆₇	C₂×#463	1	1	yes	characteristic
209	C₂×C₆₇	#3057	1	1	yes	characteristic
210	C₂×C₆₇	C₂×#472	1	1	yes	characteristic
211	D₆₇	—	16	2	no	—
212	#3227	—	67	1	no	—
213	#3205	—	67	1	no	—
214	C₂×#486	—	67	1	no	—
215	#2931	D₆₇	1	1	yes	characteristic, complemented
216	#1697	—	67	4	no	—
217	#1677	—	67	4	no	—
218	#1564	—	67	1	no	—
219	#1548	—	67	1	no	—
220	#1545	—	67	1	no	—
221	C₆₇	#19196	1	1	yes	characteristic, complemented, Sylow
222	C₂×#131	—	2	1	no	—
223	#532	C₂×D₆₇	1	1	yes	characteristic
224	C₂×C₄⋊Q₈	—	67	1	no	—
225	C₂×#127	—	67	1	no	—
226	#498	—	134	1	no	—
227	#493	—	134	1	no	—
228	#486	—	67	2	no	—
229	#486	—	67	2	no	—
230	#486	—	134	1	no	—
231	#486	—	134	1	no	—
232	#486	—	134	1	no	—
233	#486	—	134	1	no	—
234	#481	—	134	2	no	—
235	#476	—	67	4	no	—
236	#459	—	67	4	no	—
237	#447	—	134	2	no	—
238	#436	—	2	1	no	—
239	#436	C₂×D₆₇	1	2	yes	complemented
240	C₈×D₄	—	2	1	no	—
241	C₈×D₄	C₂×D₆₇	1	2	yes	complemented
242	#431	—	67	1	no	—
243	#431	—	67	1	no	—
244	#423	C₂×D₆₇	1	1	yes	characteristic
245	C₂×#102	—	134	1	no	—
246	C₂×#102	—	134	1	no	—
247	#408	—	2	1	no	—
248	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
249	#335	—	67	2	no	—
250	#334	—	67	2	no	—
251	#333	—	67	4	no	—
252	#331	—	67	4	no	—
253	C₂×#41	—	2	1	no	—
254	C₂²×Q₈	—	134	1	no	—
255	C₂²×D₄	—	134	1	no	—
256	C₂²×D₄	—	134	1	no	—
257	C₂²×D₄	—	134	1	no	—
258	C₂×D₈	—	134	4	no	—
259	#131	—	4	4	no	—
260	C₂×M₁₆	—	2	1	no	—
261	C₂×M₁₆	—	2	2	no	—
262	C₂²×C₈	—	2	2	no	—
263	C₂²×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
264	C₂²×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
265	C₄⋊Q₈	—	67	2	no	—
266	C₄⋊Q₈	—	134	1	no	—
267	C₄⋊Q₈	—	134	1	no	—
268	C₄⋊Q₈	—	134	1	no	—
269	C₄⋊Q₈	D₂₆₈	1	1	yes	characteristic
270	#127	—	67	2	no	—
271	#127	—	134	1	no	—
272	#127	—	134	1	no	—
273	#127	—	134	1	no	—
274	#127	D₂₆₈	1	1	yes	characteristic
275	#124	—	2	1	no	—
276	#121	—	2	1	no	—
277	#121	D₂₆₈	1	2	yes	—
278	C₄×D₄	—	2	1	no	—
279	C₄×D₄	C₂²×D₆₇	1	2	yes	—
280	C₂×C₄⋊C₄	—	134	1	no	—
281	C₂×C₄⋊C₄	—	134	1	no	—
282	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
283	#106	—	134	4	no	—
284	C₄⋊C₈	—	2	1	no	—
285	C₄⋊C₈	—	67	2	no	—
286	C₄⋊C₈	—	67	2	no	—
287	C₄⋊C₈	C₂²×D₆₇	1	2	yes	—
288	#102	—	134	4	no	—
289	#102	—	134	2	no	—
290	#102	—	134	2	no	—
291	#102	—	134	2	no	—
292	#102	—	134	2	no	—
293	#102	—	134	4	no	—
294	C₂²⋊C₈	—	2	2	no	—
295	C₂²⋊C₈	—	2	2	no	—
296	C₂²⋊C₈	—	134	1	no	—
297	C₂²⋊C₈	—	134	1	no	—
298	C₄×C₈	—	134	1	no	—
299	C₄×C₈	—	134	1	no	—
300	C₄×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
301	C₄×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
302	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
303	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
304	C₂⁴	—	268	1	no	—
305	#41	—	4	2	no	—
306	#41	—	4	2	no	—
307	C₂×Q₈	—	2	1	no	—
308	C₂×Q₈	—	268	1	no	—
309	C₂×Q₈	—	536	2	no	—
310	C₂×Q₈	—	134	2	no	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	—	2	1	no	—
313	C₂×D₄	—	2	1	no	—
314	C₂×D₄	—	268	1	no	—
315	C₂×D₄	—	268	1	no	—
316	C₂×D₄	—	268	1	no	—
317	C₂×D₄	—	268	2	no	—
318	C₂×D₄	—	268	2	no	—
319	C₂×D₄	—	536	2	no	—
320	C₂×D₄	—	536	2	no	—
321	C₂×D₄	—	134	2	no	—
322	C₂×D₄	—	134	2	no	—
323	C₂×D₄	—	134	2	no	—
324	C₂×D₄	C₂×D₂₆₈	1	2	yes	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	268	1	no	—
327	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
328	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
329	C₂²×C₄	#11761628	1	1	yes	characteristic
330	D₈	—	536	4	no	—
331	M₁₆	—	4	4	no	—
332	M₁₆	—	4	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	4	4	no	—
337	C₂×C₈	—	134	2	no	—
338	C₂×C₈	—	134	2	no	—
339	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
340	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
341	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
342	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	268	1	no	—
345	C₄⋊C₄	—	268	1	no	—
346	C₄⋊C₄	—	134	2	no	—
347	C₄⋊C₄	—	134	2	no	—
348	C₄⋊C₄	C₂×D₂₆₈	1	2	yes	—
349	C₂²⋊C₄	—	2	2	no	—
350	C₂²⋊C₄	—	2	2	no	—
351	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
352	C₄²	C₂×D₂₆₈	1	1	yes	characteristic
353	C₄²	#11761628	1	1	yes	characteristic
354	C₄²	C₂³×D₆₇	1	1	yes	characteristic
355	C₂³	—	2	2	no	—
356	C₂³	—	268	2	no	—
357	C₂³	—	536	2	no	—
358	C₂³	—	536	2	no	—
359	C₂³	—	536	2	no	—
360	C₂³	#14524017	1	1	yes	characteristic
361	Q₈	—	4	2	no	—
362	Q₈	—	536	2	no	—
363	Q₈	—	536	2	no	—
364	D₄	—	2	4	no	—
365	D₄	—	4	4	no	—
366	D₄	—	4	2	no	—
367	D₄	—	4	2	no	—
368	D₄	—	268	2	no	—
369	D₄	—	268	2	no	—
370	D₄	—	268	4	no	—
371	D₄	—	536	2	no	—
372	D₄	—	536	2	no	—
373	D₄	—	536	2	no	—
374	D₄	—	536	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	268	2	no	—
381	C₂×C₄	—	536	2	no	—
382	C₂×C₄	#14524017	1	1	yes	characteristic
383	C₂×C₄	#14524017	1	1	yes	characteristic
384	C₂×C₄	#14524017	1	1	yes	characteristic
385	C₂×C₄	#14524063	1	2	yes	—
386	C₂×C₄	#14524069	1	2	yes	—
387	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
388	C₂×C₄	C₂²×D₂₆₈	1	1	yes	characteristic
389	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
390	C₈	—	2	1	no	—
391	C₈	—	2	1	no	—
392	C₈	—	2	1	no	—
393	C₈	—	2	1	no	—
394	C₈	—	4	2	no	—
395	C₈	—	268	2	no	—
396	C₈	—	268	2	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	4	2	no	—
400	C₂²	—	4	2	no	—
401	C₂²	—	4	2	no	—
402	C₂²	—	536	2	no	—
403	C₂²	—	536	2	no	—
404	C₂²	—	536	2	no	—
405	C₂²	—	1072	4	no	—
406	C₂²	#16863611	1	2	yes	—
407	C₂²	C₂×#14524017	1	1	yes	characteristic
408	C₄	—	2	1	no	—
409	C₄	—	2	1	no	—
410	C₄	—	4	2	no	—
411	C₄	—	536	2	no	—
412	C₄	#16863611	1	2	yes	—
413	C₄	#16863666	1	2	yes	—
414	C₄	C₂×#14524063	1	1	yes	characteristic
415	C₄	C₂×#14524069	1	1	yes	characteristic
416	C₄	#16864208	1	2	yes	—
417	C₂	—	2	2	no	—
418	C₂	—	8	2	no	—
419	C₂	—	1072	2	no	—
420	C₂	C₂×#16863611	1	1	yes	characteristic
421	C₂	#22569848	1	1	yes	characteristic
422	C₂	C₂×#16863666	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#14524017
commutator, cosocle	C₄²×C₆₇	C₂⁴
Frattini	C₄²	C₂³×D₆₇
Fitting	C₆₇×#2931	C₂
socle	C₂²×C₆₇	C₂×#121
prime radical	#22571124	C₂
hypercenter	#2931	D₆₇
hypocenter	C₆₇	#19196
LCS	G ▷ C₄²×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2931

Complements

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

N	H ≅ G/N	type
1. #22571334	C₂	semidirect
3. C₂×#16863743	C₂	semidirect
4. #22559742	C₂	semidirect
5. #22559618	C₂	semidirect
6. #22558957	C₂	semidirect
7. #22558891	C₂	semidirect
8. #22558878	C₂	semidirect
9. C₆₇×#2931	C₂	semidirect
21. #16863686	C₂²	semidirect
28. #16863149	C₂²	semidirect
29. #16863147	C₂²	semidirect
30. #16863144	C₂²	semidirect
35. #436×C₆₇	C₂²	semidirect
37. C₈×D₄×C₆₇	C₂²	semidirect
215. #2931	D₆₇	semidirect
221. C₆₇	#19196	semidirect
239. #436	C₂×D₆₇	semidirect
241. C₈×D₄	C₂×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
#22571334	2
#22571124	2
C₂×#16863743	2
#22559742	2
#22559618	2
#22558957	2
#22558891	2
#22558878	2
C₆₇×#2931	2
#19196	67