Subgroups — #30875536

Order 17152.

710 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22568875	C₂	1	2	yes	maximal, complemented
2	#22561103	C₂	1	2	yes	maximal
3	#22560859	C₂	1	4	yes	maximal, complemented
4	#22560381	C₂	1	1	yes	maximal, characteristic, complemented
5	#22560229	C₂	1	2	yes	maximal, complemented
6	#22560095	C₂	1	2	yes	maximal, complemented
7	#22560076	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×#135×C₆₇	C₂	1	1	yes	maximal, characteristic
9	#16863457	—	2	4	no	—
10	#16863453	—	2	2	no	—
11	#16863449	—	2	2	no	—
12	C₂×#14523979	C₂²	1	2	yes	—
13	C₂×#14523979	C₂²	1	2	yes	—
14	#16863420	C₂²	1	2	yes	—
15	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×#14523970	C₂²	1	4	yes	—
17	#16863363	C₂²	1	4	yes	—
18	#16863352	C₂²	1	4	yes	—
19	C₂×#14523953	C₂²	1	2	yes	—
20	C₄×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic
21	#16863155	C₂²	1	4	yes	—
22	#16863150	C₂²	1	2	yes	—
23	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
24	C₄×#41×C₆₇	C₂²	1	2	yes	—
25	C₄×Q₁₆×C₆₇	C₄	1	1	yes	characteristic, complemented
26	C₄×Q₁₆×C₆₇	C₄	1	1	yes	characteristic, complemented
27	C₄×SD₁₆×C₆₇	C₄	1	2	yes	complemented
28	C₄×SD₁₆×C₆₇	C₄	1	2	yes	complemented
29	C₄×D₈×C₆₇	C₄	1	1	yes	characteristic, complemented
30	C₄×D₈×C₆₇	C₄	1	1	yes	characteristic, complemented
31	#427×C₆₇	C₂²	1	1	yes	characteristic
32	#416×C₆₇	C₂²	1	2	yes	—
33	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×#11761612	C₂³	1	4	yes	—
35	C₂²×C₆₇⋊C₈	C₂³	1	2	yes	—
36	C₂×C₄⋊Dic₆₇	—	2	1	no	—
37	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
38	#14523979	—	2	4	no	—
39	#14523979	—	4	2	no	—
40	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
41	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
42	C₄⋊(C₆₇⋊C₈)	D₄	1	2	yes	—
43	C₄⋊(C₆₇⋊C₈)	D₄	1	2	yes	—
44	#14523970	—	4	4	no	—
45	C₂²⋊(C₆₇⋊C₈)	—	2	4	no	—
46	C₂²⋊(C₆₇⋊C₈)	—	2	4	no	—
47	#14523954	—	2	4	no	—
48	#14523953	—	2	4	no	—
49	C₄×C₆₇⋊C₈	—	2	4	no	—
50	C₆₇⋊#95	—	2	1	no	—
51	C₂×#41×C₆₇	C₂³	1	2	yes	—
52	#135×C₆₇	—	2	2	no	—
53	#135×C₆₇	—	2	2	no	—
54	C₂×Q₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic
55	C₂×SD₁₆×C₆₇	C₂×C₄	1	2	yes	—
56	C₂×D₈×C₆₇	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
59	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
60	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
61	C₄×D₄×C₆₇	—	2	2	no	—
62	C₄×D₄×C₆₇	—	2	2	no	—
63	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
64	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
65	#117×C₆₇	—	2	2	no	—
66	#117×C₆₇	C₂³	1	2	yes	—
67	C₂×C₄²×C₆₇	—	2	2	no	—
68	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
69	#107×C₆₇	C₂×C₄	1	1	yes	characteristic
70	#107×C₆₇	C₂×C₄	1	1	yes	characteristic
71	#106×C₆₇	C₂×C₄	1	2	yes	—
72	#103×C₆₇	C₂×C₄	1	2	yes	—
73	#103×C₆₇	C₂×C₄	1	2	yes	—
74	#102×C₆₇	C₂×C₄	1	2	yes	—
75	#102×C₆₇	C₂×C₄	1	2	yes	—
76	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
77	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
78	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
79	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
80	C₂²×Dic₆₇	—	2	2	no	—
81	#11761612	—	2	4	no	—
82	#11761612	—	2	4	no	—
83	C₂×C₆₇⋊C₈	—	2	2	no	—
84	C₂×C₆₇⋊C₈	—	2	2	no	—
85	C₂×C₆₇⋊C₈	—	2	4	no	—
86	C₂×C₆₇⋊C₈	C₂×D₄	1	4	yes	—
87	C₄⋊Dic₆₇	—	4	2	no	—
88	C₄×Dic₆₇	—	2	2	no	—
89	C₄×Dic₆₇	—	2	2	no	—
90	#41×C₆₇	—	2	2	no	—
91	#41×C₆₇	—	2	2	no	—
92	#41×C₆₇	—	2	2	no	—
93	#41×C₆₇	—	2	2	no	—
94	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
95	C₂×D₄×C₆₇	—	2	2	no	—
96	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₆₇	—	2	2	no	—
98	C₂²×C₄×C₆₇	—	2	2	no	—
99	C₂²×C₄×C₆₇	—	2	2	no	—
100	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
101	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
102	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
103	Q₁₆×C₆₇	—	2	2	no	—
104	SD₁₆×C₆₇	—	2	4	no	—
105	D₈×C₆₇	—	2	2	no	—
106	C₂×C₈×C₆₇	—	2	1	no	—
107	C₂×C₈×C₆₇	—	2	1	no	—
108	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₈×C₆₇	#41	1	2	yes	—
113	C₂×C₈×C₆₇	#41	1	2	yes	—
114	C₄⋊C₄×C₆₇	—	2	2	no	—
115	C₄⋊C₄×C₆₇	—	2	2	no	—
116	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
117	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
118	C₂²⋊C₄×C₆₇	—	2	2	no	—
119	C₂²⋊C₄×C₆₇	—	2	2	no	—
120	C₂²⋊C₄×C₆₇	—	2	2	no	—
121	C₄²×C₆₇	—	2	2	no	—
122	C₄²×C₆₇	—	2	2	no	—
123	C₄²×C₆₇	—	2	2	no	—
124	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
125	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
126	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
128	C₂³×C₆₇	—	2	2	no	—
129	C₂³×C₆₇	C₂×#41	1	1	yes	characteristic
130	Q₈×C₆₇	—	2	2	no	—
131	Q₈×C₆₇	—	2	2	no	—
132	D₄×C₆₇	—	2	2	no	—
133	D₄×C₆₇	—	2	2	no	—
134	D₄×C₆₇	—	4	2	no	—
135	D₄×C₆₇	—	4	2	no	—
136	C₂×C₄×C₆₇	—	2	2	no	—
137	C₂×C₄×C₆₇	—	2	2	no	—
138	C₂×C₄×C₆₇	—	2	2	no	—
139	C₂×C₄×C₆₇	—	2	2	no	—
140	C₂×C₄×C₆₇	—	4	1	no	—
141	C₂×C₄×C₆₇	—	4	2	no	—
142	C₂×C₄×C₆₇	—	4	2	no	—
143	C₂×C₄×C₆₇	—	4	4	no	—
144	C₂×C₄×C₆₇	—	8	2	no	—
145	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
146	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
147	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
148	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
149	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
150	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
151	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
152	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
153	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
154	C₂×C₄×C₆₇	2₋¹⁺⁴	1	1	yes	characteristic
155	C₂×Dic₆₇	—	4	2	no	—
156	C₂×Dic₆₇	—	4	2	no	—
157	C₂×Dic₆₇	—	4	2	no	—
158	C₈×C₆₇	—	2	1	no	—
159	C₈×C₆₇	—	2	1	no	—
160	C₈×C₆₇	#117	1	2	yes	—
161	C₈×C₆₇	#117	1	2	yes	—
162	C₆₇⋊C₈	—	2	4	no	—
163	C₆₇⋊C₈	—	4	4	no	—
164	C₂²×C₆₇	—	2	1	no	—
165	C₂²×C₆₇	—	2	1	no	—
166	C₂²×C₆₇	—	4	2	no	—
167	C₂²×C₆₇	—	4	2	no	—
168	C₂²×C₆₇	—	4	2	no	—
169	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
170	C₂²×C₆₇	#555	1	1	yes	characteristic
171	C₂²×C₆₇	#556	1	1	yes	characteristic
172	C₄×C₆₇	—	2	1	no	—
173	C₄×C₆₇	—	2	1	no	—
174	C₄×C₆₇	—	2	1	no	—
175	C₄×C₆₇	—	4	2	no	—
176	C₄×C₆₇	—	4	2	no	—
177	C₄×C₆₇	—	4	2	no	—
178	C₄×C₆₇	#444	1	2	yes	—
179	C₄×C₆₇	C₂×#117	1	1	yes	characteristic
180	C₄×C₆₇	#520	1	1	yes	characteristic
181	C₄×C₆₇	#547	1	1	yes	characteristic
182	C₄×C₆₇	#550	1	1	yes	characteristic
183	Dic₆₇	—	8	2	no	—
184	#22803	—	67	1	no	maximal, Sylow
185	C₂×C₆₇	—	2	1	no	—
186	C₂×C₆₇	—	2	1	no	—
187	C₂×C₆₇	—	8	2	no	—
188	C₂×C₆₇	#2354	1	1	yes	characteristic
189	C₂×C₆₇	C₂×#444	1	1	yes	characteristic
190	C₂×C₆₇	#2957	1	1	yes	characteristic
191	C₄×#135	D₆₇	1	1	yes	characteristic
192	#2925	—	67	2	no	—
193	#1975	—	67	2	no	—
194	#1929	—	67	4	no	—
195	#1848	—	67	1	no	—
196	#1806	—	67	2	no	—
197	#1773	—	67	2	no	—
198	#1770	—	67	1	no	—
199	C₆₇	#22803	1	1	yes	characteristic, complemented, Sylow
200	C₂×#135	C₂×D₆₇	1	1	yes	characteristic
201	C₄×#41	C₂×D₆₇	1	2	yes	—
202	C₄×Q₁₆	Dic₆₇	1	1	yes	characteristic, complemented
203	C₄×Q₁₆	Dic₆₇	1	1	yes	characteristic, complemented
204	C₄×SD₁₆	Dic₆₇	1	2	yes	complemented
205	C₄×SD₁₆	Dic₆₇	1	2	yes	complemented
206	C₄×D₈	Dic₆₇	1	1	yes	characteristic, complemented
207	C₄×D₈	Dic₆₇	1	1	yes	characteristic, complemented
208	#433	—	134	4	no	—
209	#432	—	134	2	no	—
210	#431	—	134	2	no	—
211	C₂×#108	—	67	2	no	—
212	C₂×#108	—	67	2	no	—
213	#427	C₂×D₆₇	1	1	yes	characteristic
214	#423	—	67	2	no	—
215	C₂×C₄⋊C₈	—	67	1	no	—
216	C₂×#104	—	67	4	no	—
217	#416	C₂×D₆₇	1	2	yes	—
218	#408	—	67	4	no	—
219	#405	—	67	4	no	—
220	C₂×#97	—	67	2	no	—
221	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
222	C₄×C₄⋊C₄	—	67	1	no	—
223	#339	—	67	4	no	—
224	#336	—	67	2	no	—
225	C₂×#41	C₂²×D₆₇	1	2	yes	—
226	#135	—	2	2	no	—
227	#135	—	2	2	no	—
228	C₂×Q₁₆	C₂×Dic₆₇	1	1	yes	characteristic
229	C₂×SD₁₆	C₂×Dic₆₇	1	2	yes	—
230	C₂×D₈	C₂×Dic₆₇	1	1	yes	characteristic
231	C₂×M₁₆	—	67	4	no	—
232	C₂²×C₈	—	67	2	no	—
233	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
234	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
235	C₄×Q₈	C₂×Dic₆₇	1	2	yes	—
236	C₄×Q₈	C₂×Dic₆₇	1	2	yes	—
237	C₄×D₄	—	2	2	no	—
238	C₄×D₄	—	2	2	no	—
239	C₄×D₄	C₂×Dic₆₇	1	2	yes	—
240	C₄×D₄	C₂×Dic₆₇	1	2	yes	—
241	#117	—	2	2	no	—
242	#117	C₂²×D₆₇	1	2	yes	—
243	C₂×C₄⋊C₄	—	134	1	no	—
244	C₂×C₄²	—	2	2	no	—
245	C₂×C₄²	—	67	2	no	—
246	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
247	#108	—	268	2	no	—
248	#108	—	134	4	no	—
249	#107	C₂×Dic₆₇	1	1	yes	characteristic
250	#107	C₂×Dic₆₇	1	1	yes	characteristic
251	#106	C₂×Dic₆₇	1	2	yes	—
252	C₄⋊C₈	—	67	2	no	—
253	C₄⋊C₈	—	67	2	no	—
254	C₄⋊C₈	—	134	2	no	—
255	C₄⋊C₈	—	134	2	no	—
256	#104	—	268	4	no	—
257	#103	C₂×Dic₆₇	1	2	yes	—
258	#103	C₂×Dic₆₇	1	2	yes	—
259	#102	C₂×Dic₆₇	1	2	yes	—
260	#102	C₂×Dic₆₇	1	2	yes	—
261	C₂²⋊C₈	—	134	4	no	—
262	C₂²⋊C₈	—	134	4	no	—
263	#97	—	134	4	no	—
264	#97	—	134	4	no	—
265	C₄×C₈	—	134	4	no	—
266	C₄×C₈	C₂×Dic₆₇	1	1	yes	characteristic
267	C₄×C₈	C₂×Dic₆₇	1	1	yes	characteristic
268	C₄×C₈	C₂×Dic₆₇	1	1	yes	characteristic
269	C₄×C₈	C₂×Dic₆₇	1	1	yes	characteristic
270	#95	—	134	1	no	—
271	#41	—	2	2	no	—
272	#41	—	2	2	no	—
273	#41	—	2	2	no	—
274	#41	—	2	2	no	—
275	C₂×Q₈	C₂²×Dic₆₇	1	2	yes	—
276	C₂×D₄	—	2	2	no	—
277	C₂×D₄	C₂²×Dic₆₇	1	2	yes	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	134	2	no	—
282	C₂²×C₄	#11761627	1	1	yes	characteristic
283	C₂²×C₄	#11761627	1	1	yes	characteristic
284	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
285	Q₁₆	—	2	2	no	—
286	SD₁₆	—	2	4	no	—
287	D₈	—	2	2	no	—
288	M₁₆	—	134	4	no	—
289	M₁₆	—	134	4	no	—
290	C₂×C₈	—	2	1	no	—
291	C₂×C₈	—	2	1	no	—
292	C₂×C₈	—	67	4	no	—
293	C₂×C₈	—	134	4	no	—
294	C₂×C₈	—	134	2	no	—
295	C₂×C₈	—	134	2	no	—
296	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
297	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
298	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
299	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
300	C₂×C₈	#11761628	1	2	yes	—
301	C₂×C₈	#11761628	1	2	yes	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	—	268	2	no	—
305	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
306	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
307	C₂²⋊C₄	—	2	2	no	—
308	C₂²⋊C₄	—	2	2	no	—
309	C₂²⋊C₄	—	2	2	no	—
310	C₄²	—	2	2	no	—
311	C₄²	—	2	2	no	—
312	C₄²	—	2	2	no	—
313	C₄²	—	134	2	no	—
314	C₄²	—	134	2	no	—
315	C₄²	C₂²×Dic₆₇	1	1	yes	characteristic
316	C₄²	C₂²×Dic₆₇	1	1	yes	characteristic
317	C₄²	D₄×D₆₇	1	1	yes	characteristic
318	C₄²	D₄×D₆₇	1	1	yes	characteristic
319	C₂³	—	2	2	no	—
320	C₂³	C₂×#11761627	1	1	yes	characteristic
321	Q₈	—	2	2	no	—
322	Q₈	—	2	2	no	—
323	D₄	—	2	2	no	—
324	D₄	—	2	2	no	—
325	D₄	—	4	2	no	—
326	D₄	—	4	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	4	4	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	8	2	no	—
336	C₂×C₄	—	268	2	no	—
337	C₂×C₄	—	268	2	no	—
338	C₂×C₄	—	268	2	no	—
339	C₂×C₄	D₄×Dic₆₇	1	1	yes	characteristic
340	C₂×C₄	D₄×Dic₆₇	1	1	yes	characteristic
341	C₂×C₄	D₄×Dic₆₇	1	1	yes	characteristic
342	C₂×C₄	D₄×Dic₆₇	1	1	yes	characteristic
343	C₂×C₄	C₂³×Dic₆₇	1	1	yes	characteristic
344	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
345	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
346	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
347	C₂×C₄	#14524089	1	1	yes	characteristic
348	C₂×C₄	#14524090	1	1	yes	characteristic
349	C₈	—	2	1	no	—
350	C₈	—	2	1	no	—
351	C₈	—	268	4	no	—
352	C₈	—	134	4	no	—
353	C₈	#14524002	1	2	yes	—
354	C₈	#14524002	1	2	yes	—
355	C₂²	—	2	1	no	—
356	C₂²	—	2	1	no	—
357	C₂²	—	4	2	no	—
358	C₂²	—	4	2	no	—
359	C₂²	—	4	2	no	—
360	C₂²	C₂×D₄×Dic₆₇	1	1	yes	characteristic
361	C₂²	#16864111	1	1	yes	characteristic
362	C₂²	#16864116	1	1	yes	characteristic
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	4	2	no	—
367	C₄	—	4	2	no	—
368	C₄	—	4	2	no	—
369	C₄	—	536	2	no	—
370	C₄	#16863518	1	2	yes	—
371	C₄	C₂×#14524002	1	1	yes	characteristic
372	C₄	#16863879	1	1	yes	characteristic
373	C₄	#16864051	1	1	yes	characteristic
374	C₄	#16864067	1	1	yes	characteristic
375	C₂	—	2	1	no	—
376	C₂	—	2	1	no	—
377	C₂	—	8	2	no	—
378	C₂	#22563158	1	1	yes	characteristic
379	C₂	C₂×#16863518	1	1	yes	characteristic
380	C₂	#22569126	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₆₇
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting	C₄×#135×C₆₇	C₂
socle	C₂²×C₆₇	C₂×C₄×D₄
prime radical	C₂×#135×C₆₇	C₂²
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	C₄×#135	D₆₇
hypocenter	C₆₇	#22803
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#135

Complements

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

N	H ≅ G/N	type
1. #22568875	C₂	semidirect
3. #22560859	C₂	semidirect
4. #22560381	C₂	semidirect
5. #22560229	C₂	semidirect
6. #22560095	C₂	semidirect
7. #22560076	C₂	semidirect
25. C₄×Q₁₆×C₆₇	C₄	semidirect
26. C₄×Q₁₆×C₆₇	C₄	semidirect
27. C₄×SD₁₆×C₆₇	C₄	semidirect
28. C₄×SD₁₆×C₆₇	C₄	semidirect
29. C₄×D₈×C₆₇	C₄	semidirect
30. C₄×D₈×C₆₇	C₄	semidirect
199. C₆₇	#22803	semidirect
202. C₄×Q₁₆	Dic₆₇	semidirect
203. C₄×Q₁₆	Dic₆₇	semidirect
204. C₄×SD₁₆	Dic₆₇	semidirect
205. C₄×SD₁₆	Dic₆₇	semidirect
206. C₄×D₈	Dic₆₇	semidirect
207. C₄×D₈	Dic₆₇	semidirect

Maximal subgroups

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

subgroup	index
#22568875	2
#22561103	2
#22560859	2
#22560381	2
#22560229	2
#22560095	2
#22560076	2
C₄×#135×C₆₇	2
#22803	67