Subgroups — #30874280

Order 17152.

858 conjugacy classes of subgroups.

The subgroup lattice has 392 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	2	yes	maximal
2	C₄×#14524065	C₂	1	1	yes	maximal, characteristic
3	#22568774	C₂	1	2	yes	maximal, complemented
4	#22560962	C₂	1	2	yes	maximal, complemented
5	#22560487	C₂	1	4	yes	maximal, complemented
6	#22560381	C₂	1	1	yes	maximal, characteristic, complemented
7	#22560230	C₂	1	2	yes	maximal, complemented
8	C₆₇×#1770	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#14524065	C₂²	1	1	yes	characteristic
10	C₂×#14524049	C₂²	1	4	yes	—
11	C₄×#11761628	C₂²	1	2	yes	—
12	#16863519	—	2	8	no	—
13	C₄×Dic₂₆₈	C₄	1	1	yes	characteristic, complemented
14	C₄×Dic₂₆₈	C₄	1	1	yes	characteristic, complemented
15	C₄×#11761617	C₄	1	2	yes	complemented
16	C₄×#11761617	C₄	1	2	yes	complemented
17	C₄×D₅₃₆	C₄	1	1	yes	characteristic, complemented
18	C₄×D₅₃₆	C₄	1	1	yes	characteristic, complemented
19	C₂×#14523979	C₂²	1	2	yes	—
20	C₂×#14523979	C₂²	1	2	yes	—
21	#16863434	C₂²	1	1	yes	characteristic
22	#16863422	C₂²	1	4	yes	—
23	#16863421	—	2	4	no	—
24	#16863420	C₂²	1	2	yes	—
25	#16863418	—	2	2	no	—
26	C₄⋊C₈×D₆₇	—	2	2	no	—
27	C₂×#14523971	C₂²	1	4	yes	—
28	#16863393	C₂²	1	2	yes	—
29	#16863156	C₂²	1	4	yes	—
30	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×#97×C₆₇	C₂²	1	2	yes	—
32	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
33	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
34	#336×C₆₇	C₂²	1	2	yes	—
35	C₂×#11761628	C₂³	1	2	yes	—
36	#14524065	D₄	1	4	yes	—
37	#14524065	Q₈	1	4	yes	—
38	C₂×Dic₂₆₈	C₂×C₄	1	1	yes	characteristic
39	C₂×#11761617	C₂×C₄	1	2	yes	—
40	C₂×D₅₃₆	C₂×C₄	1	1	yes	characteristic
41	#14524049	—	2	8	no	—
42	#14524049	—	4	4	no	—
43	C₂×#11761612	C₂³	1	4	yes	—
44	C₂×#11761611	—	2	4	no	—
45	C₂×C₈×D₆₇	—	2	4	no	—
46	C₄×Dic₁₃₄	C₂×C₄	1	2	yes	—
47	C₄×Dic₁₃₄	C₂×C₄	1	2	yes	—
48	C₄×D₂₆₈	C₂×C₄	1	2	yes	—
49	C₄×D₂₆₈	C₂×C₄	1	2	yes	—
50	C₄×C₂²⋊D₆₇	—	2	2	no	—
51	C₄×C₂²⋊D₆₇	—	2	2	no	—
52	#14524002	C₂³	1	2	yes	—
53	#14524000	—	2	2	no	—
54	C₄²×D₆₇	—	2	2	no	—
55	#14523979	—	2	4	no	—
56	#14523979	—	4	2	no	—
57	#14523977	C₂×C₄	1	1	yes	characteristic
58	#14523977	C₂×C₄	1	1	yes	characteristic
59	#14523975	C₂×C₄	1	2	yes	—
60	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
61	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
62	Dic₆₇⋊C₈	—	2	4	no	—
63	Dic₆₇⋊C₈	—	2	4	no	—
64	#14523971	—	2	8	no	—
65	#14523968	C₂×C₄	1	2	yes	—
66	#14523968	C₂×C₄	1	2	yes	—
67	#14523965	C₂×C₄	1	2	yes	—
68	#14523965	C₂×C₄	1	2	yes	—
69	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
71	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
73	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
74	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
75	C₄⋊C₈×C₆₇	D₄	1	2	yes	—
76	C₄⋊C₈×C₆₇	D₄	1	2	yes	—
77	#97×C₆₇	—	2	4	no	—
78	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
79	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
80	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
81	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
82	#95×C₆₇	—	2	1	no	—
83	#11761628	—	2	2	no	—
84	#11761628	—	2	2	no	—
85	#11761628	C₂×D₄	1	4	yes	—
86	#11761628	C₂×Q₈	1	4	yes	—
87	C₂×Dic₁₃₄	C₂²×C₄	1	2	yes	—
88	C₂×D₂₆₈	C₂²×C₄	1	2	yes	—
89	C₂×C₂²⋊D₆₇	—	2	2	no	—
90	C₂×C₄×D₆₇	—	2	2	no	—
91	C₂×C₄×D₆₇	—	2	2	no	—
92	C₂×C₄×D₆₇	—	2	2	no	—
93	Dic₂₆₈	C₄⋊C₄	1	4	yes	complemented
94	#11761617	C₄⋊C₄	1	8	yes	complemented
95	D₅₃₆	C₄⋊C₄	1	4	yes	complemented
96	#11761612	—	2	4	no	—
97	#11761612	—	2	4	no	—
98	#11761611	—	4	8	no	—
99	C₂×C₆₇⋊C₈	—	2	4	no	—
100	C₈×D₆₇	—	4	8	no	—
101	C₄⋊Dic₆₇	C₂²×C₄	1	2	yes	—
102	C₄⋊Dic₆₇	C₂²×C₄	1	2	yes	—
103	Dic₆₇⋊C₄	—	2	2	no	—
104	Dic₆₇⋊C₄	—	2	2	no	—
105	C₂²⋊Dic₆₇	—	2	2	no	—
106	(C₂×D₆₇)⋊C₄	—	2	2	no	—
107	(C₂×D₆₇)⋊C₄	—	2	2	no	—
108	C₄×Dic₆₇	—	2	2	no	—
109	C₄×Dic₆₇	—	2	2	no	—
110	C₄×Dic₆₇	—	2	2	no	—
111	C₂²×C₄×C₆₇	—	2	2	no	—
112	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
113	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
114	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
115	C₂×C₈×C₆₇	—	2	2	no	—
116	C₂×C₈×C₆₇	—	2	1	no	—
117	C₂×C₈×C₆₇	—	2	2	no	—
118	C₂×C₈×C₆₇	—	2	1	no	—
119	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
124	C₂×C₈×C₆₇	C₂×D₄	1	4	yes	—
125	C₂×C₈×C₆₇	C₂×Q₈	1	2	yes	—
126	C₄⋊C₄×C₆₇	—	4	2	no	—
127	C₄²×C₆₇	—	2	2	no	—
128	C₄²×C₆₇	—	2	2	no	—
129	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
130	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
131	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
133	C₂³×C₆₇	C₂×#41	1	1	yes	characteristic
134	C₂²×D₆₇	—	2	2	no	—
135	C₂×C₄×C₆₇	—	2	2	no	—
136	C₂×C₄×C₆₇	—	4	1	no	—
137	C₂×C₄×C₆₇	—	4	2	no	—
138	C₂×C₄×C₆₇	—	4	2	no	—
139	C₂×C₄×C₆₇	—	4	2	no	—
140	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
141	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
142	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
143	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
144	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
145	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
146	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
147	C₂×C₄×C₆₇	C₂²×Q₈	1	1	yes	characteristic
148	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
149	C₂×C₄×C₆₇	2₋¹⁺⁴	1	1	yes	characteristic
150	C₂²⋊D₆₇	—	2	4	no	—
151	C₂²⋊D₆₇	—	2	4	no	—
152	C₂×Dic₆₇	—	2	2	no	—
153	C₂×Dic₆₇	—	2	2	no	—
154	C₂×Dic₆₇	—	2	2	no	—
155	D₂₆₈	—	2	2	no	—
156	D₂₆₈	C₂×C₄⋊C₄	1	4	yes	—
157	C₄×D₆₇	—	2	4	no	—
158	C₄×D₆₇	—	2	4	no	—
159	C₄×D₆₇	—	4	4	no	—
160	C₄×D₆₇	—	8	2	no	—
161	Dic₁₃₄	—	2	2	no	—
162	Dic₁₃₄	C₂×C₄⋊C₄	1	4	yes	—
163	C₈×C₆₇	—	2	1	no	—
164	C₈×C₆₇	—	2	1	no	—
165	C₈×C₆₇	—	2	4	no	—
166	C₈×C₆₇	C₂×C₄⋊C₄	1	2	yes	—
167	C₈×C₆₇	C₂×C₄⋊C₄	1	2	yes	—
168	C₆₇⋊C₈	—	4	4	no	—
169	C₂²×C₆₇	—	2	1	no	—
170	C₂²×C₆₇	—	2	1	no	—
171	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
172	C₂²×C₆₇	#547	1	1	yes	characteristic
173	C₂²×C₆₇	#554	1	1	yes	characteristic
174	C₂×D₆₇	—	2	4	no	—
175	C₂×D₆₇	—	4	2	no	—
176	C₂×D₆₇	—	4	2	no	—
177	C₄×C₆₇	—	2	1	no	—
178	C₄×C₆₇	—	2	1	no	—
179	C₄×C₆₇	—	2	1	no	—
180	C₄×C₆₇	—	8	2	no	—
181	C₄×C₆₇	#444	1	2	yes	complemented
182	C₄×C₆₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
183	C₄×C₆₇	#520	1	1	yes	characteristic
184	C₄×C₆₇	D₄²	1	1	yes	characteristic
185	C₄×C₆₇	D₄×Q₈	1	1	yes	characteristic
186	Dic₆₇	—	2	4	no	—
187	Dic₆₇	—	4	2	no	—
188	Dic₆₇	—	4	2	no	—
189	#22686	—	67	1	no	maximal, Sylow
190	C₂×C₆₇	—	2	1	no	—
191	C₂×C₆₇	—	2	1	no	—
192	C₂×C₆₇	D₄×C₄⋊C₄	1	1	yes	characteristic
193	C₂×C₆₇	C₂×#444	1	1	yes	characteristic
194	C₂×C₆₇	#2957	1	1	yes	characteristic
195	D₆₇	—	4	4	no	—
196	C₂×#444	—	67	2	no	—
197	C₄×#135	—	67	1	no	—
198	#2906	—	67	2	no	—
199	#1946	—	67	2	no	—
200	#1866	—	67	4	no	—
201	#1848	—	67	1	no	—
202	#1806	—	67	2	no	—
203	#1770	D₆₇	1	1	yes	characteristic, complemented
204	C₆₇	#22686	1	1	yes	characteristic, complemented, Sylow
205	C₂×#135	—	67	1	no	—
206	C₂×#131	—	67	4	no	—
207	C₄×#41	—	67	2	no	—
208	#444	—	134	8	no	—
209	C₄×Q₁₆	—	67	1	no	—
210	C₄×Q₁₆	—	67	1	no	—
211	C₄×SD₁₆	—	67	2	no	—
212	C₄×SD₁₆	—	67	2	no	—
213	C₄×D₈	—	67	1	no	—
214	C₄×D₈	—	67	1	no	—
215	C₂×#108	—	67	2	no	—
216	C₂×#108	—	67	2	no	—
217	#427	—	67	1	no	—
218	#424	—	67	4	no	—
219	#424	—	134	4	no	—
220	#423	—	67	2	no	—
221	#423	—	134	2	no	—
222	C₂×C₄⋊C₈	—	134	2	no	—
223	C₂×C₄⋊C₈	C₂×D₆₇	1	1	yes	characteristic
224	C₂×#104	—	67	4	no	—
225	#416	—	67	2	no	—
226	C₂×#97	C₂×D₆₇	1	2	yes	—
227	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
228	C₄×C₄⋊C₄	C₂×D₆₇	1	1	yes	characteristic
229	#339	—	67	4	no	—
230	#336	C₂×D₆₇	1	2	yes	—
231	C₂×#41	—	67	2	no	—
232	#135	—	67	4	no	—
233	#135	—	67	4	no	—
234	C₂×Q₁₆	—	67	1	no	—
235	C₂×SD₁₆	—	67	2	no	—
236	C₂×D₈	—	67	1	no	—
237	#131	—	268	4	no	—
238	#131	—	134	8	no	—
239	C₂×M₁₆	—	67	4	no	—
240	C₂×M₁₆	—	134	4	no	—
241	C₂²×C₈	—	134	4	no	—
242	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
243	C₂²×C₈	C₂²×D₆₇	1	2	yes	—
244	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
245	C₄×Q₈	—	67	2	no	—
246	C₄×Q₈	—	67	2	no	—
247	C₄×D₄	—	67	2	no	—
248	C₄×D₄	—	67	2	no	—
249	C₄×D₄	—	134	2	no	—
250	C₄×D₄	—	134	2	no	—
251	#117	—	67	2	no	—
252	#117	—	134	2	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄²	—	134	2	no	—
255	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
256	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
257	#108	—	268	2	no	—
258	#108	—	134	4	no	—
259	#107	—	67	1	no	—
260	#107	—	67	1	no	—
261	#106	—	67	2	no	—
262	C₄⋊C₈	—	134	4	no	—
263	C₄⋊C₈	—	134	4	no	—
264	C₄⋊C₈	—	134	2	no	—
265	C₄⋊C₈	—	134	2	no	—
266	C₄⋊C₈	D₂₆₈	1	2	yes	—
267	C₄⋊C₈	D₂₆₈	1	2	yes	—
268	#104	—	134	8	no	—
269	#103	—	67	2	no	—
270	#103	—	67	2	no	—
271	#102	—	67	2	no	—
272	#102	—	67	2	no	—
273	#97	—	2	4	no	—
274	C₄×C₈	C₄×D₆₇	1	1	yes	characteristic
275	C₄×C₈	C₄×D₆₇	1	1	yes	characteristic
276	C₄×C₈	C₄×D₆₇	1	1	yes	characteristic
277	C₄×C₈	C₄×D₆₇	1	1	yes	characteristic
278	#95	—	2	1	no	—
279	#41	—	67	4	no	—
280	#41	—	67	4	no	—
281	#41	—	134	2	no	—
282	#41	—	134	2	no	—
283	C₂×Q₈	—	67	2	no	—
284	C₂×D₄	—	67	2	no	—
285	C₂×D₄	—	134	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	134	2	no	—
288	C₂²×C₄	—	134	2	no	—
289	C₂²×C₄	—	134	2	no	—
290	C₂²×C₄	#11761628	1	1	yes	characteristic
291	C₂²×C₄	#11761628	1	1	yes	characteristic
292	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
293	Q₁₆	—	67	4	no	—
294	SD₁₆	—	67	8	no	—
295	D₈	—	67	4	no	—
296	M₁₆	—	268	8	no	—
297	M₁₆	—	134	4	no	—
298	M₁₆	—	134	4	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	268	8	no	—
304	C₂×C₈	—	134	4	no	—
305	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
306	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
307	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
308	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
309	C₂×C₈	D₄×D₆₇	1	2	yes	—
310	C₂×C₈	C₂×D₂₆₈	1	4	yes	—
311	C₂×C₈	Q₈×D₆₇	1	2	yes	—
312	C₄⋊C₄	—	4	2	no	—
313	C₄⋊C₄	—	67	2	no	—
314	C₄⋊C₄	—	67	2	no	—
315	C₄⋊C₄	—	134	2	no	—
316	C₄⋊C₄	—	134	2	no	—
317	C₂²⋊C₄	—	134	2	no	—
318	C₂²⋊C₄	—	134	2	no	—
319	C₂²⋊C₄	—	134	2	no	—
320	C₄²	—	2	2	no	—
321	C₄²	—	2	2	no	—
322	C₄²	—	134	2	no	—
323	C₄²	—	134	2	no	—
324	C₄²	—	134	2	no	—
325	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
326	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
327	C₄²	C₂×D₂₆₈	1	1	yes	characteristic
328	C₄²	C₂×D₂₆₈	1	1	yes	characteristic
329	C₂³	—	134	2	no	—
330	C₂³	C₂×#11761628	1	1	yes	characteristic
331	Q₈	—	67	4	no	—
332	Q₈	—	134	2	no	—
333	D₄	—	67	4	no	—
334	D₄	—	134	4	no	—
335	D₄	—	134	4	no	—
336	D₄	—	134	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	268	4	no	—
343	C₂×C₄	—	536	2	no	—
344	C₂×C₄	—	134	2	no	—
345	C₂×C₄	—	134	2	no	—
346	C₂×C₄	—	134	2	no	—
347	C₂×C₄	—	134	4	no	—
348	C₂×C₄	—	134	4	no	—
349	C₂×C₄	C₄×D₂₆₈	1	1	yes	characteristic
350	C₂×C₄	C₄×D₂₆₈	1	1	yes	characteristic
351	C₂×C₄	C₄×D₂₆₈	1	1	yes	characteristic
352	C₂×C₄	C₄×D₂₆₈	1	1	yes	characteristic
353	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
354	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
355	C₂×C₄	C₂²×D₂₆₈	1	1	yes	characteristic
356	C₂×C₄	C₂×Q₈×D₆₇	1	1	yes	characteristic
357	C₂×C₄	#14524089	1	1	yes	characteristic
358	C₂×C₄	#14524090	1	1	yes	characteristic
359	C₈	—	2	4	no	—
360	C₈	—	2	1	no	—
361	C₈	—	2	1	no	—
362	C₈	—	268	4	no	—
363	C₈	C₄⋊C₄×D₆₇	1	2	yes	—
364	C₈	C₄⋊C₄×D₆₇	1	2	yes	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	268	2	no	—
368	C₂²	—	268	2	no	—
369	C₂²	—	134	4	no	—
370	C₂²	C₂×C₄×D₂₆₈	1	1	yes	characteristic
371	C₂²	#16864051	1	1	yes	characteristic
372	C₂²	#16864106	1	1	yes	characteristic
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	8	2	no	—
377	C₄	—	268	2	no	—
378	C₄	—	268	2	no	—
379	C₄	—	134	4	no	—
380	C₄	#16863519	1	2	yes	complemented
381	C₄	C₂×C₄⋊C₄×D₆₇	1	1	yes	characteristic
382	C₄	#16863876	1	1	yes	characteristic
383	C₄	D₄×D₂₆₈	1	1	yes	characteristic
384	C₄	Q₈×D₂₆₈	1	1	yes	characteristic
385	C₂	—	2	1	no	—
386	C₂	—	2	1	no	—
387	C₂	—	268	4	no	—
388	C₂	C₄⋊C₄×D₂₆₈	1	1	yes	characteristic
389	C₂	C₂×#16863519	1	1	yes	characteristic
390	C₂	#22569127	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₂₆₈
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting	C₆₇×#1770	C₂
socle	C₂²×C₆₇	C₂×C₄×D₄
prime radical	C₂×#14524065	C₂²
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	#1770	D₆₇
hypocenter	C₆₇	#22686
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄⋊C₈ ◁ #1770

Complements

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

N	H ≅ G/N	type
3. #22568774	C₂	semidirect
4. #22560962	C₂	semidirect
5. #22560487	C₂	semidirect
6. #22560381	C₂	semidirect
7. #22560230	C₂	semidirect
8. C₆₇×#1770	C₂	semidirect
13. C₄×Dic₂₆₈	C₄	semidirect
14. C₄×Dic₂₆₈	C₄	semidirect
15. C₄×#11761617	C₄	semidirect
16. C₄×#11761617	C₄	semidirect
17. C₄×D₅₃₆	C₄	semidirect
18. C₄×D₅₃₆	C₄	semidirect
93. Dic₂₆₈	C₄⋊C₄	semidirect
94. #11761617	C₄⋊C₄	semidirect
95. D₅₃₆	C₄⋊C₄	semidirect
181. C₄×C₆₇	#444	semidirect
203. #1770	D₆₇	semidirect
204. C₆₇	#22686	semidirect
380. C₄	#16863519	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
C₄×#14524065	2
#22568774	2
#22560962	2
#22560487	2
#22560381	2
#22560230	2
C₆₇×#1770	2
#22686	67