Subgroups — #30854393

Order 17152.

1006 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863517	C₂	1	1	yes	maximal, characteristic
2	C₂×#16863512	C₂	1	1	yes	maximal, characteristic
3	#22569011	C₂	1	1	yes	maximal, characteristic
4	C₄×#14524051	C₂	1	2	yes	maximal, complemented
5	#22560096	C₂	1	1	yes	maximal, characteristic, complemented
6	#22560091	C₂	1	1	yes	maximal, characteristic, complemented
7	#22560052	C₂	1	2	yes	maximal, complemented
8	#22560045	C₂	1	2	yes	maximal, complemented
9	#22560022	C₂	1	2	yes	maximal, complemented
10	#22559897	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#1778	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14524065	C₂²	1	1	yes	characteristic
13	C₂×#14524051	C₂²	1	2	yes	—
14	C₂×#14524051	C₂²	1	2	yes	—
15	C₄×#11761628	C₂²	1	2	yes	—
16	#16863517	C₄	1	8	yes	complemented
17	#16863512	C₄	1	8	yes	complemented
18	#16863509	C₄	1	2	yes	complemented
19	#16863504	C₄	1	2	yes	complemented
20	#16863498	C₄	1	4	yes	complemented
21	#16863434	C₂²	1	1	yes	characteristic
22	C₂×#14523969	C₂²	1	2	yes	—
23	C₂×#14523969	C₂²	1	2	yes	—
24	#16863393	C₂²	1	2	yes	—
25	#16863354	C₂²	1	2	yes	—
26	#16863354	C₂²	1	2	yes	—
27	#16863353	—	2	2	no	—
28	#16863353	—	2	2	no	—
29	C₄×#11761611	—	2	2	no	—
30	C₂×#14523953	C₂²	1	1	yes	characteristic
31	C₂×#14523953	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₈×Dic₆₇	C₂²	1	1	yes	characteristic
34	C₂×C₈×Dic₆₇	C₂²	1	1	yes	characteristic
35	C₄×C₈×D₆₇	—	2	2	no	—
36	#16863242	C₂²	1	1	yes	characteristic
37	#16863157	C₂²	1	2	yes	—
38	#16863157	C₂²	1	2	yes	—
39	C₂×#108×C₆₇	C₂²	1	1	yes	characteristic
40	C₂×#108×C₆₇	C₂²	1	1	yes	characteristic
41	C₄×M₁₆×C₆₇	C₂²	1	2	yes	—
42	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
43	#341×C₆₇	C₂²	1	2	yes	—
44	C₂×#11761628	C₂³	1	2	yes	—
45	#14524065	C₂×C₄	1	4	yes	—
46	#14524065	C₂×C₄	1	4	yes	—
47	C₂×Dic₂₆₈	C₂×C₄	1	1	yes	characteristic
48	C₂×#11761617	C₂×C₄	1	2	yes	—
49	C₂×D₅₃₆	C₂×C₄	1	1	yes	characteristic
50	#14524051	—	2	4	no	—
51	#14524051	—	2	4	no	—
52	#14524051	C₂×C₄	1	8	yes	complemented
53	#14524051	C₂×C₄	1	8	yes	complemented
54	C₂×#11761611	—	2	2	no	—
55	C₂×#11761611	—	2	2	no	—
56	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
57	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
58	C₂×C₈×D₆₇	—	2	2	no	—
59	C₂×C₈×D₆₇	—	2	2	no	—
60	C₄×Dic₁₃₄	C₂×C₄	1	4	yes	—
61	C₄×D₂₆₈	C₂×C₄	1	4	yes	—
62	C₄×C₂²⋊D₆₇	—	2	4	no	—
63	#14524002	C₂³	1	2	yes	—
64	#14524000	—	2	2	no	—
65	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
66	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
67	C₄²×D₆₇	—	2	2	no	—
68	#14523977	C₂×C₄	1	2	yes	—
69	#14523975	C₂×C₄	1	2	yes	—
70	#14523969	C₂×C₄	1	8	yes	complemented
71	#14523969	C₂×C₄	1	8	yes	complemented
72	#14523968	C₂×C₄	1	4	yes	—
73	#14523965	C₂×C₄	1	4	yes	—
74	#14523953	—	2	2	no	—
75	#14523953	—	2	2	no	—
76	#14523953	—	2	2	no	—
77	#14523953	C₂×C₄	1	4	yes	complemented
78	C₄×C₆₇⋊C₈	D₄	1	2	yes	—
79	C₄×C₆₇⋊C₈	D₄	1	2	yes	—
80	C₈×Dic₆₇	—	2	2	no	—
81	C₈×Dic₆₇	—	2	2	no	—
82	C₈×Dic₆₇	—	2	2	no	—
83	C₈×Dic₆₇	C₂×C₄	1	4	yes	complemented
84	C₆₇⋊#95	—	2	2	no	—
85	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
86	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
87	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
90	#108×C₆₇	C₂×C₄	1	4	yes	complemented
91	#108×C₆₇	C₂×C₄	1	4	yes	complemented
92	#97×C₆₇	—	2	2	no	—
93	#97×C₆₇	C₂×C₄	1	2	yes	—
94	#97×C₆₇	C₂×C₄	1	2	yes	—
95	C₄×C₈×C₆₇	—	2	2	no	—
96	#11761628	—	2	2	no	—
97	#11761628	—	2	2	no	—
98	#11761628	C₂²×C₄	1	4	yes	—
99	#11761628	C₂²×C₄	1	4	yes	—
100	C₂×Dic₁₃₄	C₂²×C₄	1	2	yes	—
101	C₂×D₂₆₈	C₂²×C₄	1	2	yes	—
102	C₂×C₂²⋊D₆₇	—	2	2	no	—
103	C₂²×Dic₆₇	—	2	1	no	—
104	C₂²×Dic₆₇	—	2	1	no	—
105	C₂×C₄×D₆₇	—	2	2	no	—
106	C₂×C₄×D₆₇	—	2	4	no	—
107	Dic₂₆₈	C₄²	1	4	yes	—
108	#11761617	C₄²	1	8	yes	—
109	D₅₃₆	C₄²	1	4	yes	—
110	#11761611	—	2	8	no	—
111	#11761611	—	2	8	no	—
112	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
113	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
114	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
115	C₂×C₆₇⋊C₈	C₂×D₄	1	2	yes	—
116	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
117	C₂×C₆₇⋊C₈	#41	1	2	yes	—
118	C₂×C₆₇⋊C₈	#41	1	2	yes	—
119	C₈×D₆₇	—	2	8	no	—
120	C₈×D₆₇	—	2	8	no	—
121	C₄⋊Dic₆₇	C₂²×C₄	1	4	yes	—
122	Dic₆₇⋊C₄	—	2	4	no	—
123	C₂²⋊Dic₆₇	—	2	2	no	—
124	(C₂×D₆₇)⋊C₄	—	2	4	no	—
125	C₄×Dic₆₇	—	2	4	no	—
126	C₄×Dic₆₇	—	2	2	no	—
127	C₄×Dic₆₇	—	2	1	no	—
128	C₄×Dic₆₇	—	2	1	no	—
129	C₄×Dic₆₇	C₂²×C₄	1	2	yes	—
130	C₄×Dic₆₇	C₂²×C₄	1	2	yes	—
131	C₂²×C₄×C₆₇	#41	1	2	yes	—
132	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
133	M₁₆×C₆₇	—	2	2	no	—
134	M₁₆×C₆₇	—	2	2	no	—
135	M₁₆×C₆₇	C₂²×C₄	1	4	yes	—
136	M₁₆×C₆₇	C₂²×C₄	1	4	yes	—
137	C₂×C₈×C₆₇	—	2	2	no	—
138	C₂×C₈×C₆₇	—	2	2	no	—
139	C₂×C₈×C₆₇	—	2	1	no	—
140	C₂×C₈×C₆₇	—	2	1	no	—
141	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
142	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
143	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
144	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
146	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
147	C₄²×C₆₇	C₂×D₄	1	2	yes	—
148	C₂³×C₆₇	C₂×#41	1	1	yes	characteristic
149	C₂²×D₆₇	—	2	2	no	—
150	C₂×C₄×C₆₇	—	4	2	no	—
151	C₂×C₄×C₆₇	C₄×D₄	1	4	yes	—
152	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
153	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
154	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
155	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
156	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
157	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
158	C₂²⋊D₆₇	—	2	4	no	—
159	C₂²⋊D₆₇	—	2	4	no	—
160	C₂×Dic₆₇	—	2	2	no	—
161	C₂×Dic₆₇	—	2	4	no	—
162	C₂×Dic₆₇	—	2	2	no	—
163	C₂×Dic₆₇	—	2	2	no	—
164	C₂×Dic₆₇	—	4	2	no	—
165	C₂×Dic₆₇	—	4	2	no	—
166	D₂₆₈	—	2	2	no	—
167	D₂₆₈	C₂×C₄²	1	4	yes	—
168	C₄×D₆₇	—	2	4	no	—
169	C₄×D₆₇	—	2	4	no	—
170	C₄×D₆₇	—	4	8	no	—
171	Dic₁₃₄	—	2	2	no	—
172	Dic₁₃₄	C₂×C₄²	1	4	yes	—
173	C₈×C₆₇	—	2	4	no	—
174	C₈×C₆₇	—	2	4	no	—
175	C₈×C₆₇	—	2	2	no	—
176	C₈×C₆₇	C₂×C₄²	1	2	yes	—
177	C₈×C₆₇	C₂×C₄²	1	2	yes	—
178	C₆₇⋊C₈	C₄×D₄	1	2	yes	—
179	C₆₇⋊C₈	C₄×D₄	1	4	yes	—
180	C₆₇⋊C₈	C₄×D₄	1	2	yes	—
181	C₂²×C₆₇	—	2	2	no	—
182	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
183	C₂²×C₆₇	C₄×#41	1	1	yes	characteristic
184	C₂²×C₆₇	C₄×#41	1	1	yes	characteristic
185	C₂×D₆₇	—	2	4	no	—
186	C₂×D₆₇	—	4	4	no	—
187	C₄×C₆₇	—	2	4	no	—
188	C₄×C₆₇	C₂²×C₄²	1	1	yes	characteristic
189	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
190	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
191	C₄×C₆₇	C₄×#41	1	1	yes	characteristic
192	Dic₆₇	—	2	4	no	—
193	Dic₆₇	—	4	2	no	—
194	Dic₆₇	—	4	2	no	—
195	Dic₆₇	—	4	4	no	—
196	#20510	—	67	1	no	maximal, Sylow
197	C₂×C₆₇	—	2	1	no	—
198	C₂×C₆₇	—	2	1	no	—
199	C₂×C₆₇	C₄²×D₄	1	1	yes	characteristic
200	C₂×C₆₇	#2955	1	2	yes	—
201	D₆₇	—	4	4	no	—
202	C₂×#444	—	67	1	no	—
203	C₂×#443	—	67	1	no	—
204	#2943	—	67	1	no	—
205	C₄×#131	—	67	2	no	—
206	#1778	D₆₇	1	1	yes	characteristic, complemented
207	#1773	—	67	1	no	—
208	#1772	—	67	1	no	—
209	#1765	—	67	2	no	—
210	#1764	—	67	2	no	—
211	#1759	—	67	2	no	—
212	#1726	—	67	1	no	—
213	C₆₇	#20510	1	1	yes	characteristic, complemented, Sylow
214	C₂×#135	—	67	1	no	—
215	C₂×#131	—	67	2	no	—
216	C₂×#131	—	67	2	no	—
217	C₄×#41	—	67	2	no	—
218	#444	—	67	8	no	—
219	#443	—	67	8	no	—
220	#442	—	67	2	no	—
221	#441	—	67	2	no	—
222	#440	—	67	4	no	—
223	C₂×#108	C₂×D₆₇	1	1	yes	characteristic
224	C₂×#108	C₂×D₆₇	1	1	yes	characteristic
225	#427	—	67	1	no	—
226	C₂×#104	—	67	2	no	—
227	C₂×#104	—	67	2	no	—
228	#416	—	67	2	no	—
229	#405	—	67	2	no	—
230	#405	—	67	2	no	—
231	#405	—	134	2	no	—
232	#405	—	134	2	no	—
233	C₄×M₁₆	—	134	2	no	—
234	C₄×M₁₆	C₂×D₆₇	1	2	yes	—
235	C₂×#97	—	67	1	no	—
236	C₂×#97	—	67	1	no	—
237	C₂×#97	C₂×D₆₇	1	1	yes	characteristic
238	C₂×C₄×C₈	—	67	1	no	—
239	C₂×C₄×C₈	—	67	1	no	—
240	C₂×C₄×C₈	—	67	1	no	—
241	C₂×C₄×C₈	—	134	2	no	—
242	#376	—	67	1	no	—
243	#341	C₂×D₆₇	1	2	yes	—
244	#339	—	67	2	no	—
245	#339	—	67	2	no	—
246	C₂×#41	—	67	2	no	—
247	#135	—	67	4	no	—
248	#135	—	67	4	no	—
249	C₂×Q₁₆	—	67	1	no	—
250	C₂×SD₁₆	—	67	2	no	—
251	C₂×D₈	—	67	1	no	—
252	#131	—	67	8	no	—
253	#131	—	67	8	no	—
254	#131	—	134	4	no	—
255	#131	—	134	4	no	—
256	C₂×M₁₆	—	134	2	no	—
257	C₂×M₁₆	—	134	2	no	—
258	C₂×M₁₆	C₂²×D₆₇	1	2	yes	—
259	C₂×M₁₆	C₂²×D₆₇	1	2	yes	—
260	C₂²×C₈	—	67	1	no	—
261	C₂²×C₈	—	67	1	no	—
262	C₂²×C₈	—	134	2	no	—
263	C₂²×C₈	—	134	2	no	—
264	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
265	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
266	C₄×Q₈	—	67	4	no	—
267	C₄×D₄	—	67	4	no	—
268	C₄×D₄	—	134	4	no	—
269	#117	—	67	2	no	—
270	#117	—	134	2	no	—
271	C₂×C₄²	—	67	1	no	—
272	C₂×C₄²	—	67	1	no	—
273	C₂×C₄²	—	134	2	no	—
274	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
275	#108	C₄×D₆₇	1	4	yes	complemented
276	#108	C₄×D₆₇	1	4	yes	complemented
277	#107	—	67	2	no	—
278	#106	—	67	2	no	—
279	#104	—	67	8	no	—
280	#104	—	67	8	no	—
281	#103	—	67	4	no	—
282	#102	—	67	4	no	—
283	#97	—	2	2	no	—
284	#97	—	67	4	no	—
285	#97	—	134	2	no	—
286	#97	—	134	2	no	—
287	#97	—	134	2	no	—
288	#97	C₄×D₆₇	1	2	yes	—
289	#97	C₄×D₆₇	1	2	yes	—
290	C₄×C₈	—	2	2	no	—
291	C₄×C₈	—	67	4	no	—
292	C₄×C₈	—	67	2	no	—
293	C₄×C₈	—	67	2	no	—
294	C₄×C₈	—	134	2	no	—
295	C₄×C₈	—	134	2	no	—
296	C₄×C₈	—	134	2	no	—
297	#95	—	134	2	no	—
298	#41	—	67	4	no	—
299	#41	—	67	4	no	—
300	#41	—	134	2	no	—
301	#41	—	134	2	no	—
302	C₂×Q₈	—	67	2	no	—
303	C₂×D₄	—	67	2	no	—
304	C₂×D₄	—	134	2	no	—
305	C₂²×C₄	—	134	1	no	—
306	C₂²×C₄	—	134	1	no	—
307	C₂²×C₄	—	134	4	no	—
308	C₂²×C₄	—	134	2	no	—
309	C₂²×C₄	#11761629	1	2	yes	—
310	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
311	Q₁₆	—	67	4	no	—
312	SD₁₆	—	67	8	no	—
313	D₈	—	67	4	no	—
314	M₁₆	—	2	2	no	—
315	M₁₆	—	2	2	no	—
316	M₁₆	—	134	8	no	—
317	M₁₆	—	134	8	no	—
318	M₁₆	C₂×C₄×D₆₇	1	4	yes	—
319	M₁₆	C₂×C₄×D₆₇	1	4	yes	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	67	2	no	—
325	C₂×C₈	—	67	2	no	—
326	C₂×C₈	—	67	1	no	—
327	C₂×C₈	—	67	2	no	—
328	C₂×C₈	—	67	1	no	—
329	C₂×C₈	—	67	2	no	—
330	C₂×C₈	—	67	2	no	—
331	C₂×C₈	—	134	8	no	—
332	C₂×C₈	—	134	8	no	—
333	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
334	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
335	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
336	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
337	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
338	C₄⋊C₄	—	67	4	no	—
339	C₄⋊C₄	—	134	4	no	—
340	C₂²⋊C₄	—	134	2	no	—
341	C₂²⋊C₄	—	134	4	no	—
342	C₄²	—	67	2	no	—
343	C₄²	—	67	2	no	—
344	C₄²	—	134	4	no	—
345	C₄²	—	134	2	no	—
346	C₄²	—	134	1	no	—
347	C₄²	—	134	1	no	—
348	C₄²	C₂×C₄×D₆₇	1	2	yes	—
349	C₄²	D₄×D₆₇	1	2	yes	—
350	C₂³	—	134	2	no	—
351	C₂³	C₂×#11761629	1	1	yes	characteristic
352	Q₈	—	67	4	no	—
353	Q₈	—	134	2	no	—
354	D₄	—	67	4	no	—
355	D₄	—	134	4	no	—
356	D₄	—	134	4	no	—
357	D₄	—	134	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	268	8	no	—
360	C₂×C₄	—	268	2	no	—
361	C₂×C₄	—	268	2	no	—
362	C₂×C₄	—	134	4	no	—
363	C₂×C₄	—	134	2	no	—
364	C₂×C₄	—	134	2	no	—
365	C₂×C₄	—	134	2	no	—
366	C₂×C₄	—	134	4	no	—
367	C₂×C₄	—	134	4	no	—
368	C₂×C₄	#14524005	1	4	yes	—
369	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
370	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
371	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
372	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
373	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
374	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
375	C₈	—	2	4	no	—
376	C₈	—	2	4	no	—
377	C₈	—	2	2	no	—
378	C₈	—	67	2	no	—
379	C₈	—	67	4	no	—
380	C₈	—	67	2	no	—
381	C₈	C₄²×D₆₇	1	2	yes	—
382	C₈	C₄²×D₆₇	1	2	yes	—
383	C₂²	—	2	2	no	—
384	C₂²	—	268	4	no	—
385	C₂²	—	134	4	no	—
386	C₂²	C₂×#14524005	1	1	yes	characteristic
387	C₂²	C₄×#11761629	1	1	yes	characteristic
388	C₂²	C₄×#11761629	1	1	yes	characteristic
389	C₄	—	2	4	no	—
390	C₄	—	268	2	no	—
391	C₄	—	268	2	no	—
392	C₄	—	268	4	no	—
393	C₄	—	134	4	no	—
394	C₄	C₂×C₄²×D₆₇	1	1	yes	characteristic
395	C₄	C₄×D₄×D₆₇	1	1	yes	characteristic
396	C₄	C₄×D₄×D₆₇	1	1	yes	characteristic
397	C₄	#16863864	1	1	yes	characteristic
398	C₂	—	2	1	no	—
399	C₂	—	2	1	no	—
400	C₂	—	268	4	no	—
401	C₂	C₄×#14524005	1	1	yes	characteristic
402	C₂	#22569111	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₆₇
commutator	C₄×C₆₇	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting	C₆₇×#1778	C₂
socle	C₂²×C₆₇	C₂×C₄×D₄
prime radical	C₂×#14524065	C₂²
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	#1778	D₆₇
hypocenter	C₆₇	#20510
LCS	G ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1778

Complements

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

N	H ≅ G/N	type
4. C₄×#14524051	C₂	semidirect
5. #22560096	C₂	semidirect
6. #22560091	C₂	semidirect
7. #22560052	C₂	semidirect
8. #22560045	C₂	semidirect
9. #22560022	C₂	semidirect
10. #22559897	C₂	semidirect
11. C₆₇×#1778	C₂	semidirect
16. #16863517	C₄	semidirect
17. #16863512	C₄	semidirect
18. #16863509	C₄	semidirect
19. #16863504	C₄	semidirect
20. #16863498	C₄	semidirect
52. #14524051	C₂×C₄	semidirect
53. #14524051	C₂×C₄	semidirect
70. #14523969	C₂×C₄	semidirect
71. #14523969	C₂×C₄	semidirect
77. #14523953	C₂×C₄	semidirect
83. C₈×Dic₆₇	C₂×C₄	semidirect
90. #108×C₆₇	C₂×C₄	semidirect
91. #108×C₆₇	C₂×C₄	semidirect
206. #1778	D₆₇	semidirect
213. C₆₇	#20510	semidirect
275. #108	C₄×D₆₇	semidirect
276. #108	C₄×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16863517	2
C₂×#16863512	2
#22569011	2
C₄×#14524051	2
#22560096	2
#22560091	2
#22560052	2
#22560045	2
#22560022	2
#22559897	2
C₆₇×#1778	2
#20510	67