Subgroups — #30854416

Order 17152.

1014 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863519	C₂	1	1	yes	maximal, characteristic
2	C₂×#16863512	C₂	1	1	yes	maximal, characteristic
3	#22569009	C₂	1	1	yes	maximal, characteristic
4	#22568636	C₂	1	2	yes	maximal, complemented
5	#22560117	C₂	1	1	yes	maximal, characteristic, complemented
6	#22560090	C₂	1	1	yes	maximal, characteristic, complemented
7	#22560050	C₂	1	2	yes	maximal, complemented
8	#22560048	C₂	1	2	yes	maximal, complemented
9	#22560013	C₂	1	2	yes	maximal, complemented
10	#97×Dic₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#1773	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14524065	C₂²	1	1	yes	characteristic
13	C₂×#14524051	C₂²	1	2	yes	—
14	C₂×#14524049	C₂²	1	2	yes	—
15	#16863864	C₂²	1	2	yes	—
16	#16863519	C₄	1	8	yes	complemented
17	#16863512	C₄	1	8	yes	complemented
18	#16863507	C₄	1	2	yes	complemented
19	#16863502	C₄	1	2	yes	complemented
20	#16863495	C₄	1	4	yes	complemented
21	C₂×#14523979	C₂²	1	1	yes	characteristic
22	C₂×#14523971	C₂²	1	2	yes	—
23	C₂×#14523969	C₂²	1	2	yes	—
24	#16863390	C₂²	1	2	yes	—
25	#16863353	—	2	2	no	—
26	#16863352	C₂²	1	2	yes	—
27	#16863350	—	2	2	no	—
28	M₁₆×Dic₆₇	C₂²	1	2	yes	—
29	C₄×#11761611	—	2	2	no	—
30	C₂×#14523954	C₂²	1	1	yes	characteristic
31	C₂×#14523953	C₂²	1	1	yes	characteristic
32	C₂×#14523953	C₂²	1	1	yes	characteristic
33	#97×D₆₇	—	2	2	no	—
34	C₂×C₈×Dic₆₇	C₂²	1	1	yes	characteristic
35	C₂×C₈×Dic₆₇	C₂²	1	1	yes	characteristic
36	C₄²×Dic₆₇	C₂²	1	1	yes	characteristic
37	#16863160	C₂²	1	2	yes	—
38	#16863155	C₂²	1	2	yes	—
39	C₂×#108×C₆₇	C₂²	1	1	yes	characteristic
40	#427×C₆₇	C₂²	1	1	yes	characteristic
41	#405×C₆₇	C₂²	1	2	yes	—
42	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
43	#339×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	C₂×C₄	1	8	yes	complemented
52	#14524049	—	2	4	no	—
53	#14524049	C₂×C₄	1	8	yes	complemented
54	C₂×#11761612	C₂³	1	2	yes	—
55	C₂×#11761611	—	2	2	no	—
56	C₂×#11761611	—	2	2	no	—
57	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
58	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
59	C₂×C₈×D₆₇	—	2	2	no	—
60	C₂×C₈×D₆₇	—	2	2	no	—
61	#14524008	C₂×C₄	1	4	yes	—
62	#14524005	C₂×C₄	1	4	yes	—
63	(C₂²⋊D₆₇)⋊C₄	—	2	4	no	—
64	#14524000	—	2	2	no	—
65	C₂×C₄×Dic₆₇	—	2	2	no	—
66	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
67	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
68	C₄²×D₆₇	—	2	2	no	—
69	#14523979	C₂×C₄	1	4	yes	complemented
70	#14523971	C₂×C₄	1	8	yes	complemented
71	#14523969	C₂×C₄	1	8	yes	complemented
72	#14523966	C₂×C₄	1	4	yes	—
73	#14523963	C₂×C₄	1	4	yes	—
74	#14523954	—	2	2	no	—
75	#14523954	—	2	2	no	—
76	#14523953	—	2	2	no	—
77	#14523953	C₂×C₄	1	2	yes	—
78	#14523953	C₂×C₄	1	2	yes	—
79	#14523953	D₄	1	2	yes	—
80	#14523953	D₄	1	2	yes	—
81	C₄×C₆₇⋊C₈	—	2	2	no	—
82	C₈×Dic₆₇	—	2	2	no	—
83	C₈×Dic₆₇	—	2	2	no	—
84	C₈×Dic₆₇	C₂×C₄	1	4	yes	complemented
85	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
86	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
88	#117×C₆₇	C₂³	1	2	yes	—
89	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
90	#108×C₆₇	C₂×C₄	1	4	yes	complemented
91	#107×C₆₇	C₂×C₄	1	2	yes	—
92	#106×C₆₇	C₂×C₄	1	2	yes	—
93	#97×C₆₇	—	2	2	no	—
94	#97×C₆₇	C₂×C₄	1	4	yes	complemented
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	#41	1	2	yes	—
105	C₂×C₄×D₆₇	—	2	2	no	—
106	C₂×C₄×D₆₇	—	2	4	no	—
107	Dic₂₆₈	C₄²	1	4	yes	complemented
108	#11761617	C₄²	1	8	yes	complemented
109	D₅₃₆	C₄²	1	4	yes	complemented
110	#11761612	—	2	2	no	—
111	#11761612	C₂²×C₄	1	4	yes	—
112	#11761611	—	2	8	no	—
113	#11761611	—	2	8	no	—
114	C₂×C₆₇⋊C₈	—	2	2	no	—
115	C₂×C₆₇⋊C₈	—	2	1	no	—
116	C₂×C₆₇⋊C₈	—	2	1	no	—
117	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
118	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
119	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
120	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
121	C₂×C₆₇⋊C₈	#41	1	2	yes	—
122	C₈×D₆₇	—	2	8	no	—
123	C₈×D₆₇	—	2	8	no	—
124	Dic₆₇⋊C₄	—	2	4	no	—
125	(C₂×D₆₇)⋊C₄	—	2	4	no	—
126	C₄×Dic₆₇	—	2	1	no	—
127	C₄×Dic₆₇	—	2	4	no	—
128	C₄×Dic₆₇	—	4	4	no	—
129	C₄×Dic₆₇	C₂²×C₄	1	2	yes	—
130	C₄×Dic₆₇	C₂²×C₄	1	2	yes	—
131	C₄×Dic₆₇	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₆₇	—	2	1	no	—
133	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
134	M₁₆×C₆₇	—	2	2	no	—
135	M₁₆×C₆₇	C₂²×C₄	1	4	yes	—
136	C₂×C₈×C₆₇	—	2	2	no	—
137	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
140	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
141	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
142	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
143	C₂×C₈×C₆₇	#41	1	2	yes	—
144	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
145	C₂²⋊C₄×C₆₇	—	2	2	no	—
146	C₄²×C₆₇	—	2	2	no	—
147	C₄²×C₆₇	—	2	1	no	—
148	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
149	C₂³×C₆₇	C₂×#41	1	1	yes	characteristic
150	C₂²×D₆₇	—	2	2	no	—
151	C₂×C₄×C₆₇	—	2	4	no	—
152	C₂×C₄×C₆₇	—	2	2	no	—
153	C₂×C₄×C₆₇	—	4	2	no	—
154	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
155	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
156	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
157	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
159	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
160	C₂²⋊D₆₇	—	2	4	no	—
161	C₂²⋊D₆₇	—	2	4	no	—
162	C₂×Dic₆₇	—	2	4	no	—
163	C₂×Dic₆₇	—	2	2	no	—
164	C₂×Dic₆₇	—	2	2	no	—
165	C₂×Dic₆₇	—	4	2	no	—
166	C₂×Dic₆₇	C₄×D₄	1	4	yes	—
167	D₂₆₈	—	2	2	no	—
168	D₂₆₈	C₂×C₄²	1	4	yes	—
169	C₄×D₆₇	—	2	4	no	—
170	C₄×D₆₇	—	2	4	no	—
171	C₄×D₆₇	—	8	4	no	—
172	Dic₁₃₄	—	2	2	no	—
173	Dic₁₃₄	C₂×C₄²	1	4	yes	—
174	C₈×C₆₇	—	2	4	no	—
175	C₈×C₆₇	C₂×C₄²	1	2	yes	—
176	C₈×C₆₇	C₂×C₄²	1	2	yes	—
177	C₈×C₆₇	C₄×D₄	1	4	yes	—
178	C₆₇⋊C₈	—	2	4	no	—
179	C₆₇⋊C₈	—	2	2	no	—
180	C₆₇⋊C₈	C₄×D₄	1	2	yes	—
181	C₆₇⋊C₈	C₄×D₄	1	2	yes	—
182	C₂²×C₆₇	—	2	2	no	—
183	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
184	C₂²×C₆₇	C₄×#41	1	1	yes	characteristic
185	C₂²×C₆₇	C₄×#41	1	1	yes	characteristic
186	C₂×D₆₇	—	2	4	no	—
187	C₂×D₆₇	—	4	4	no	—
188	C₄×C₆₇	—	4	2	no	—
189	C₄×C₆₇	—	4	4	no	—
190	C₄×C₆₇	C₂²×C₄²	1	1	yes	characteristic
191	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
192	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
193	C₄×C₆₇	C₄×#41	1	1	yes	characteristic
194	Dic₆₇	—	2	4	no	—
195	Dic₆₇	—	2	4	no	—
196	Dic₆₇	—	2	4	no	—
197	#20512	—	67	1	no	maximal, Sylow
198	C₂×C₆₇	—	2	1	no	—
199	C₂×C₆₇	—	2	1	no	—
200	C₂×C₆₇	C₄²×D₄	1	1	yes	characteristic
201	C₂×C₆₇	#2956	1	2	yes	—
202	D₆₇	—	4	4	no	—
203	C₂×#444	—	67	1	no	—
204	C₂×#443	—	67	1	no	—
205	#2943	—	67	1	no	—
206	#2875	—	67	2	no	—
207	#1778	—	67	1	no	—
208	#1773	D₆₇	1	1	yes	characteristic, complemented
209	#1772	—	67	1	no	—
210	#1765	—	67	2	no	—
211	#1764	—	67	2	no	—
212	C₄×#104	—	67	2	no	—
213	C₄×#97	—	67	1	no	—
214	C₆₇	#20512	1	1	yes	characteristic, complemented, Sylow
215	C₂×#135	—	67	1	no	—
216	C₂×#131	—	67	2	no	—
217	C₂×#131	—	67	2	no	—
218	C₄×#41	—	67	2	no	—
219	#444	—	67	8	no	—
220	#443	—	67	8	no	—
221	#442	—	67	2	no	—
222	#441	—	67	2	no	—
223	#440	—	67	4	no	—
224	C₂×#108	—	67	1	no	—
225	C₂×#108	C₂×D₆₇	1	1	yes	characteristic
226	#427	C₂×D₆₇	1	1	yes	characteristic
227	C₂×#104	—	67	2	no	—
228	C₂×#104	—	67	2	no	—
229	#416	—	67	2	no	—
230	#405	—	67	2	no	—
231	#405	—	134	2	no	—
232	#405	—	134	2	no	—
233	#405	C₂×D₆₇	1	2	yes	—
234	C₄×M₁₆	—	67	2	no	—
235	C₄×M₁₆	—	134	2	no	—
236	C₂×#97	—	67	1	no	—
237	C₂×#97	—	67	1	no	—
238	C₂×#97	—	67	1	no	—
239	C₂×#97	—	134	2	no	—
240	C₂×#97	C₂×D₆₇	1	1	yes	characteristic
241	C₂×C₄×C₈	—	67	1	no	—
242	C₂×C₄×C₈	—	67	1	no	—
243	C₄³	—	67	1	no	—
244	#341	—	67	2	no	—
245	#339	—	67	2	no	—
246	#339	C₂×D₆₇	1	2	yes	—
247	C₂×#41	—	67	2	no	—
248	#135	—	67	4	no	—
249	#135	—	67	4	no	—
250	C₂×Q₁₆	—	67	1	no	—
251	C₂×SD₁₆	—	67	2	no	—
252	C₂×D₈	—	67	1	no	—
253	#131	—	67	8	no	—
254	#131	—	67	8	no	—
255	#131	—	134	4	no	—
256	#131	—	134	4	no	—
257	C₂×M₁₆	—	67	2	no	—
258	C₂×M₁₆	—	134	2	no	—
259	C₂×M₁₆	—	134	2	no	—
260	C₂×M₁₆	C₂²×D₆₇	1	2	yes	—
261	C₂²×C₈	—	67	1	no	—
262	C₂²×C₈	—	67	1	no	—
263	C₂²×C₈	—	134	2	no	—
264	C₂²×C₈	—	134	2	no	—
265	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
266	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
267	C₄×Q₈	—	67	4	no	—
268	C₄×D₄	—	67	4	no	—
269	C₄×D₄	—	134	4	no	—
270	#117	—	134	2	no	—
271	#117	C₂²×D₆₇	1	2	yes	—
272	C₂×C₄²	—	67	1	no	—
273	C₂×C₄²	—	67	1	no	—
274	C₂×C₄²	—	134	2	no	—
275	C₂×C₄²	—	134	2	no	—
276	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
277	#108	—	67	4	no	—
278	#108	C₄×D₆₇	1	4	yes	complemented
279	#107	C₄×D₆₇	1	2	yes	—
280	#106	C₄×D₆₇	1	2	yes	—
281	#104	—	67	8	no	—
282	#104	—	67	8	no	—
283	#103	—	67	4	no	—
284	#102	—	67	4	no	—
285	#97	—	2	2	no	—
286	#97	—	67	2	no	—
287	#97	—	67	2	no	—
288	#97	—	67	2	no	—
289	#97	—	67	2	no	—
290	#97	—	134	2	no	—
291	#97	—	134	2	no	—
292	#97	—	134	2	no	—
293	#97	C₄×D₆₇	1	4	yes	complemented
294	C₄×C₈	—	2	2	no	—
295	C₄×C₈	—	67	4	no	—
296	C₄×C₈	—	134	2	no	—
297	C₄×C₈	—	134	2	no	—
298	C₄×C₈	—	134	2	no	—
299	#41	—	67	4	no	—
300	#41	—	67	4	no	—
301	#41	—	134	2	no	—
302	#41	—	134	2	no	—
303	C₂×Q₈	—	67	2	no	—
304	C₂×D₄	—	67	2	no	—
305	C₂×D₄	—	134	2	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	67	2	no	—
308	C₂²×C₄	—	134	4	no	—
309	C₂²×C₄	—	134	1	no	—
310	C₂²×C₄	—	134	2	no	—
311	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
312	Q₁₆	—	67	4	no	—
313	SD₁₆	—	67	8	no	—
314	D₈	—	67	4	no	—
315	M₁₆	—	2	2	no	—
316	M₁₆	—	67	4	no	—
317	M₁₆	—	134	8	no	—
318	M₁₆	—	134	2	no	—
319	M₁₆	—	134	8	no	—
320	M₁₆	C₂×C₄×D₆₇	1	4	yes	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	67	2	no	—
323	C₂×C₈	—	67	1	no	—
324	C₂×C₈	—	67	1	no	—
325	C₂×C₈	—	67	2	no	—
326	C₂×C₈	—	67	2	no	—
327	C₂×C₈	—	134	8	no	—
328	C₂×C₈	—	134	2	no	—
329	C₂×C₈	—	134	1	no	—
330	C₂×C₈	—	134	1	no	—
331	C₂×C₈	—	134	8	no	—
332	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
333	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
334	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
335	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
336	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
337	C₂×C₈	D₄×D₆₇	1	2	yes	—
338	C₂×C₈	#11761629	1	2	yes	—
339	C₄⋊C₄	—	134	4	no	—
340	C₄⋊C₄	C₂×C₄×D₆₇	1	4	yes	—
341	C₂²⋊C₄	—	2	2	no	—
342	C₂²⋊C₄	—	134	4	no	—
343	C₄²	—	2	2	no	—
344	C₄²	—	2	1	no	—
345	C₄²	—	268	4	no	—
346	C₄²	—	67	2	no	—
347	C₄²	—	67	2	no	—
348	C₄²	—	67	2	no	—
349	C₄²	—	134	4	no	—
350	C₄²	—	134	1	no	—
351	C₄²	C₂×C₄×D₆₇	1	2	yes	—
352	C₂³	—	134	2	no	—
353	C₂³	#41×D₆₇	1	1	yes	characteristic
354	Q₈	—	67	4	no	—
355	Q₈	—	134	2	no	—
356	D₄	—	67	4	no	—
357	D₄	—	134	4	no	—
358	D₄	—	134	4	no	—
359	D₄	—	134	2	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	268	2	no	—
364	C₂×C₄	—	536	4	no	—
365	C₂×C₄	—	67	4	no	—
366	C₂×C₄	—	134	4	no	—
367	C₂×C₄	—	134	2	no	—
368	C₂×C₄	—	134	2	no	—
369	C₂×C₄	—	134	4	no	—
370	C₂×C₄	—	134	4	no	—
371	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
372	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
373	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
374	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
375	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
376	C₂×C₄	C₂×#11761629	1	1	yes	characteristic
377	C₈	—	2	4	no	—
378	C₈	—	67	2	no	—
379	C₈	—	67	2	no	—
380	C₈	—	134	4	no	—
381	C₈	—	134	2	no	—
382	C₈	C₄²×D₆₇	1	2	yes	—
383	C₈	C₄²×D₆₇	1	2	yes	—
384	C₈	#14524005	1	4	yes	—
385	C₂²	—	2	2	no	—
386	C₂²	—	268	4	no	—
387	C₂²	—	134	4	no	—
388	C₂²	C₄×D₄×D₆₇	1	1	yes	characteristic
389	C₂²	#16863864	1	1	yes	characteristic
390	C₂²	C₄×#11761629	1	1	yes	characteristic
391	C₄	—	4	2	no	—
392	C₄	—	4	4	no	—
393	C₄	—	134	4	no	—
394	C₄	—	134	4	no	—
395	C₄	—	134	4	no	—
396	C₄	C₂×C₄²×D₆₇	1	1	yes	characteristic
397	C₄	C₄×D₄×D₆₇	1	1	yes	characteristic
398	C₄	C₂×#14524005	1	1	yes	characteristic
399	C₄	C₄×#11761629	1	1	yes	characteristic
400	C₂	—	2	1	no	—
401	C₂	—	2	1	no	—
402	C₂	—	268	4	no	—
403	C₂	C₄×#14524005	1	1	yes	characteristic
404	C₂	#22569117	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₆₇
commutator	C₄×C₆₇	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting	C₆₇×#1773	C₂
socle	C₂²×C₆₇	C₂×C₄×D₄
prime radical	C₂×#14524065	C₂²
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	#1773	D₆₇
hypocenter	C₆₇	#20512
LCS	G ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1773

Complements

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

N	H ≅ G/N	type
4. #22568636	C₂	semidirect
5. #22560117	C₂	semidirect
6. #22560090	C₂	semidirect
7. #22560050	C₂	semidirect
8. #22560048	C₂	semidirect
9. #22560013	C₂	semidirect
10. #97×Dic₆₇	C₂	semidirect
11. C₆₇×#1773	C₂	semidirect
16. #16863519	C₄	semidirect
17. #16863512	C₄	semidirect
18. #16863507	C₄	semidirect
19. #16863502	C₄	semidirect
20. #16863495	C₄	semidirect
51. #14524051	C₂×C₄	semidirect
53. #14524049	C₂×C₄	semidirect
69. #14523979	C₂×C₄	semidirect
70. #14523971	C₂×C₄	semidirect
71. #14523969	C₂×C₄	semidirect
84. C₈×Dic₆₇	C₂×C₄	semidirect
90. #108×C₆₇	C₂×C₄	semidirect
94. #97×C₆₇	C₂×C₄	semidirect
107. Dic₂₆₈	C₄²	semidirect
108. #11761617	C₄²	semidirect
109. D₅₃₆	C₄²	semidirect
208. #1773	D₆₇	semidirect
214. C₆₇	#20512	semidirect
278. #108	C₄×D₆₇	semidirect
293. #97	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×#16863519	2
C₂×#16863512	2
#22569009	2
#22568636	2
#22560117	2
#22560090	2
#22560050	2
#22560048	2
#22560013	2
#97×Dic₆₇	2
C₆₇×#1773	2
#20512	67