Subgroups — #30847321

Order 17152.

710 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22572434	C₂	1	2	yes	maximal, complemented
2	D₈×D₂₆₈	C₂	1	1	yes	maximal, characteristic
3	#22559816	C₂	1	1	yes	maximal, characteristic, complemented
4	#22559772	C₂	1	2	yes	maximal, complemented
5	#22559571	C₂	1	1	yes	maximal, characteristic, complemented
6	#22559569	C₂	1	1	yes	maximal, characteristic, complemented
7	#22559386	C₂	1	2	yes	maximal, complemented
8	#22559319	C₂	1	2	yes	maximal, complemented
9	#22559094	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×#11761615	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3393	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×D₈×D₆₇	—	2	1	no	—
13	D₄×D₂₆₈	C₂²	1	2	yes	—
14	#16863773	C₂²	1	1	yes	characteristic
15	#16863744	C₂²	1	2	yes	complemented
16	#16863744	C₂²	1	2	yes	complemented
17	#16863720	—	2	2	no	—
18	#16863673	C₂²	1	2	yes	—
19	#16863644	—	2	2	no	—
20	#16863633	—	2	1	no	—
21	#16863596	C₂²	1	2	yes	complemented
22	#16863591	C₂²	1	2	yes	—
23	#16863546	—	2	2	no	—
24	#16863531	—	2	2	no	—
25	C₄×#11761615	C₂²	1	1	yes	characteristic
26	#16863474	C₂²	1	2	yes	complemented
27	C₈×D₂₆₈	C₂²	1	1	yes	characteristic
28	#16863400	—	2	2	no	—
29	#16863149	C₂²	1	1	yes	characteristic, complemented
30	#16863146	C₂²	1	1	yes	characteristic, complemented
31	#16863142	C₂²	1	2	yes	complemented
32	#16863139	C₂²	1	2	yes	complemented
33	Q₈⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
34	D₄⋊(C₆₇⋊C₈)	C₂²	1	2	yes	complemented
35	#16863123	C₂²	1	1	yes	characteristic
36	C₈×C₆₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
37	#556×C₆₇	C₂²	1	2	yes	complemented
38	#495×C₆₇	—	2	1	no	—
39	#494×C₆₇	C₂²	1	1	yes	characteristic, complemented
40	#464×C₆₇	—	2	2	no	—
41	#461×C₆₇	C₂²	1	2	yes	complemented
42	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
43	C₄×Q₁₆×C₆₇	—	2	1	no	—
44	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
45	C₂²×D₂₆₈	—	2	2	no	—
46	C₂×D₄×D₆₇	—	2	2	no	—
47	C₂×#11761615	—	2	2	no	—
48	C₂×#11761615	D₄	1	1	yes	characteristic
49	C₂×D₅₃₆	—	2	1	no	—
50	C₂×D₅₃₆	—	2	1	no	—
51	C₂×#11761613	—	2	2	no	—
52	D₈×D₆₇	—	4	4	no	—
53	C₂×#11761612	—	2	2	no	—
54	C₂×C₈×D₆₇	—	2	1	no	—
55	#14524040	C₂³	1	2	yes	—
56	#14524018	—	2	2	no	—
57	#14524017	—	2	2	no	—
58	#14524013	—	4	2	no	—
59	C₄×D₂₆₈	C₂³	1	1	yes	characteristic
60	#14523976	—	2	2	no	—
61	#14523974	D₄	1	1	yes	characteristic
62	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
63	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
64	#14523967	D₄	1	1	yes	characteristic
65	#14523963	—	2	2	no	—
66	#14523963	—	2	2	no	—
67	#14523963	—	2	2	no	—
68	#14523963	—	2	2	no	—
69	#14523963	—	2	2	no	—
70	#14523963	—	4	2	no	—
71	#14523963	D₄	1	1	yes	characteristic
72	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
73	(C₂×D₆₇)⋊C₈	—	2	1	no	—
74	C₄×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
75	C₄×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
76	C₂×Q₁₆×C₆₇	—	2	1	no	—
77	C₂×Q₁₆×C₆₇	—	2	1	no	—
78	C₂×SD₁₆×C₆₇	—	2	2	no	—
79	C₂×D₈×C₆₇	D₄	1	1	yes	characteristic
80	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
81	#126×C₆₇	—	4	2	no	—
82	#124×C₆₇	—	2	2	no	—
83	C₂²⋊Q₈×C₆₇	—	2	2	no	—
84	C₄×Q₈×C₆₇	—	2	2	no	—
85	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
86	C₄×D₄×C₆₇	C₂³	1	2	yes	—
87	#117×C₆₇	—	2	2	no	—
88	#107×C₆₇	D₄	1	1	yes	characteristic
89	C₄⋊C₈×C₆₇	—	2	1	no	—
90	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
91	#103×C₆₇	—	2	2	no	—
92	#102×C₆₇	D₄	1	2	yes	—
93	C₄×C₈×C₆₇	—	2	1	no	—
94	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
95	C₂³×D₆₇	—	4	2	no	—
96	C₂×D₂₆₈	—	2	2	no	—
97	C₂×D₂₆₈	—	2	2	no	—
98	C₂×D₂₆₈	—	2	2	no	—
99	C₂×D₂₆₈	—	4	4	no	—
100	C₂×D₂₆₈	—	4	2	no	—
101	C₂×D₂₆₈	—	8	2	no	—
102	C₂×D₂₆₈	C₂×D₄	1	1	yes	characteristic
103	C₂×C₂²⋊D₆₇	—	4	2	no	—
104	D₄×D₆₇	—	4	4	no	—
105	D₄×D₆₇	—	8	2	no	—
106	C₂×C₄×D₆₇	—	2	1	no	—
107	#11761615	—	2	2	no	—
108	#11761615	—	8	2	no	—
109	D₅₃₆	—	4	2	no	—
110	D₅₃₆	—	8	1	no	—
111	#11761613	—	4	4	no	—
112	#11761612	—	8	2	no	—
113	C₂×C₆₇⋊C₈	—	2	1	no	—
114	C₂×C₆₇⋊C₈	—	2	2	no	—
115	C₂×C₆₇⋊C₈	—	2	1	no	—
116	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
117	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
118	C₈×D₆₇	—	4	2	no	—
119	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
120	(C₂×D₆₇)⋊C₄	—	2	1	no	—
121	(C₂×D₆₇)⋊C₄	—	4	2	no	—
122	C₂×Q₈×C₆₇	—	2	2	no	—
123	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
124	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₆₇	—	2	2	no	—
126	Q₁₆×C₆₇	—	4	2	no	—
127	Q₁₆×C₆₇	—	8	1	no	—
128	SD₁₆×C₆₇	—	8	2	no	—
129	D₈×C₆₇	—	2	2	no	—
130	C₂×C₈×C₆₇	—	2	1	no	—
131	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
133	C₄⋊C₄×C₆₇	—	2	1	no	—
134	C₄⋊C₄×C₆₇	—	2	2	no	—
135	C₄⋊C₄×C₆₇	—	2	2	no	—
136	C₄⋊C₄×C₆₇	—	4	2	no	—
137	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
138	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
139	C₂²⋊C₄×C₆₇	—	2	2	no	—
140	C₂²⋊C₄×C₆₇	—	4	2	no	—
141	C₂²⋊C₄×C₆₇	—	4	2	no	—
142	C₄²×C₆₇	—	2	1	no	—
143	C₄²×C₆₇	—	4	2	no	—
144	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
145	C₂³×C₆₇	—	2	2	no	—
146	C₂²×D₆₇	—	2	1	no	—
147	C₂²×D₆₇	—	4	2	no	—
148	C₂²×D₆₇	—	8	4	no	—
149	C₂²×D₆₇	—	8	4	no	—
150	C₂²×D₆₇	—	16	2	no	—
151	Q₈×C₆₇	—	2	1	no	—
152	Q₈×C₆₇	—	2	1	no	—
153	Q₈×C₆₇	—	4	2	no	—
154	Q₈×C₆₇	—	4	2	no	—
155	D₄×C₆₇	—	2	2	no	—
156	D₄×C₆₇	—	2	2	no	—
157	C₂×C₄×C₆₇	—	2	1	no	—
158	C₂×C₄×C₆₇	—	2	1	no	—
159	C₂×C₄×C₆₇	—	2	2	no	—
160	C₂×C₄×C₆₇	—	4	2	no	—
161	C₂×C₄×C₆₇	—	4	2	no	—
162	C₂×C₄×C₆₇	—	4	2	no	—
163	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
166	C₂²⋊D₆₇	—	8	4	no	—
167	C₂×Dic₆₇	—	2	1	no	—
168	D₂₆₈	—	2	1	no	—
169	D₂₆₈	—	4	2	no	—
170	D₂₆₈	—	4	2	no	—
171	D₂₆₈	—	4	2	no	—
172	D₂₆₈	—	4	2	no	—
173	D₂₆₈	—	8	2	no	—
174	D₂₆₈	—	8	4	no	—
175	D₂₆₈	#135	1	2	yes	—
176	C₄×D₆₇	—	4	1	no	—
177	C₄×D₆₇	—	4	1	no	—
178	C₈×C₆₇	—	2	1	no	—
179	C₈×C₆₇	—	4	1	no	—
180	C₈×C₆₇	AGL(1,ℤ/8)	1	2	yes	—
181	C₆₇⋊C₈	—	2	1	no	—
182	C₆₇⋊C₈	—	2	1	no	—
183	C₆₇⋊C₈	—	4	1	no	—
184	C₆₇⋊C₈	—	4	1	no	—
185	C₆₇⋊C₈	—	4	2	no	—
186	C₂²×C₆₇	—	4	2	no	—
187	C₂²×C₆₇	—	4	2	no	—
188	C₂²×C₆₇	—	4	2	no	—
189	C₂²×C₆₇	D₄²	1	1	yes	characteristic
190	C₂×D₆₇	—	2	2	no	—
191	C₂×D₆₇	—	4	1	no	—
192	C₂×D₆₇	—	4	1	no	—
193	C₂×D₆₇	—	8	2	no	—
194	C₂×D₆₇	—	8	2	no	—
195	C₂×D₆₇	—	8	2	no	—
196	C₂×D₆₇	—	16	8	no	—
197	C₄×C₆₇	—	2	1	no	—
198	C₄×C₆₇	—	4	2	no	—
199	C₄×C₆₇	—	4	1	no	—
200	C₄×C₆₇	—	4	1	no	—
201	C₄×C₆₇	—	8	2	no	—
202	C₄×C₆₇	C₂×#135	1	1	yes	characteristic
203	C₄×C₆₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
204	C₄×C₆₇	#576	1	1	yes	characteristic
205	C₄×C₆₇	#576	1	1	yes	characteristic
206	Dic₆₇	—	4	1	no	—
207	#19900	—	67	1	no	maximal, Sylow
208	C₂×C₆₇	—	8	2	no	—
209	C₂×C₆₇	#3274	1	1	yes	characteristic
210	C₂×C₆₇	#3280	1	1	yes	characteristic
211	C₂×C₆₇	#3290	1	1	yes	characteristic
212	D₆₇	—	4	2	no	—
213	D₆₇	—	16	2	no	—
214	#3393	D₆₇	1	1	yes	characteristic, complemented
215	#3324	—	67	2	no	—
216	D₄×D₈	—	67	1	no	—
217	#1709	—	67	1	no	—
218	#1701	—	67	2	no	—
219	#1669	—	67	1	no	—
220	#1668	—	67	1	no	—
221	#1639	—	67	2	no	—
222	#1628	—	67	2	no	—
223	#1589	—	67	1	no	—
224	C₈×SD₁₆	—	67	1	no	—
225	C₆₇	#19900	1	1	yes	characteristic, complemented, Sylow
226	C₂²×D₈	—	134	1	no	—
227	#556	C₂×D₆₇	1	2	yes	complemented
228	D₄²	—	67	2	no	—
229	#495	—	2	1	no	—
230	#494	C₂×D₆₇	1	1	yes	characteristic, complemented
231	#493	—	67	1	no	—
232	#486	—	67	2	no	—
233	#486	—	67	2	no	—
234	#482	—	134	2	no	—
235	#474	—	67	2	no	—
236	#468	—	134	2	no	—
237	#466	—	134	1	no	—
238	#464	—	2	2	no	—
239	#461	C₂×D₆₇	1	2	yes	complemented
240	#460	—	67	2	no	—
241	#459	—	67	2	no	—
242	#450	—	134	2	no	—
243	#447	—	134	2	no	—
244	C₈×Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
245	C₄×Q₁₆	—	2	1	no	—
246	C₄×SD₁₆	—	67	1	no	—
247	C₄×D₈	C₂×D₆₇	1	1	yes	characteristic
248	#436	—	67	2	no	—
249	C₈×D₄	—	67	1	no	—
250	#418	—	134	2	no	—
251	#335	—	67	1	no	—
252	#334	—	67	1	no	—
253	#332	—	67	2	no	—
254	#331	—	67	2	no	—
255	Q₈⋊C₈	—	67	1	no	—
256	D₄⋊C₈	—	67	2	no	—
257	D₄⋊C₈	—	67	1	no	—
258	C₈²	—	67	1	no	—
259	C₂²×D₄	—	134	2	no	—
260	C₂²×D₄	—	134	2	no	—
261	C₂×Q₁₆	—	2	1	no	—
262	C₂×Q₁₆	—	2	1	no	—
263	C₂×SD₁₆	—	2	2	no	—
264	C₂×SD₁₆	—	67	1	no	—
265	C₂×SD₁₆	—	134	2	no	—
266	C₂×D₈	—	268	4	no	—
267	C₂×D₈	—	134	2	no	—
268	C₂×D₈	—	134	1	no	—
269	C₂×D₈	—	134	1	no	—
270	C₂×D₈	C₂²⋊D₆₇	1	1	yes	characteristic
271	C₂×M₁₆	—	134	2	no	—
272	C₂²×C₈	—	134	1	no	—
273	C₄⋊Q₈	C₂²×D₆₇	1	2	yes	—
274	#127	—	67	2	no	—
275	#126	—	4	2	no	—
276	#124	—	2	2	no	—
277	C₂²⋊Q₈	—	2	2	no	—
278	#121	—	134	2	no	—
279	#121	—	134	2	no	—
280	#120	—	268	2	no	—
281	C₄×Q₈	—	2	2	no	—
282	C₄×Q₈	C₂²×D₆₇	1	1	yes	characteristic
283	C₄×D₄	—	67	1	no	—
284	C₄×D₄	C₂²×D₆₇	1	2	yes	—
285	#117	—	2	2	no	—
286	#107	—	134	2	no	—
287	#107	C₂²⋊D₆₇	1	1	yes	characteristic
288	#106	—	67	1	no	—
289	C₄⋊C₈	—	2	1	no	—
290	C₄⋊C₈	—	67	2	no	—
291	C₄⋊C₈	—	67	1	no	—
292	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
293	#103	—	2	2	no	—
294	#103	—	67	1	no	—
295	#102	—	268	2	no	—
296	#102	—	67	1	no	—
297	#102	—	134	2	no	—
298	#102	—	134	2	no	—
299	#102	—	134	2	no	—
300	#102	—	134	2	no	—
301	#102	—	134	2	no	—
302	#102	C₂²⋊D₆₇	1	2	yes	—
303	C₂²⋊C₈	—	134	2	no	—
304	C₂²⋊C₈	—	134	1	no	—
305	C₄×C₈	—	2	1	no	—
306	C₄×C₈	—	67	1	no	—
307	C₄×C₈	—	67	1	no	—
308	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
309	C₂⁴	—	268	2	no	—
310	C₂×Q₈	—	2	2	no	—
311	C₂×Q₈	D₄×D₆₇	1	1	yes	characteristic
312	C₂×D₄	—	268	2	no	—
313	C₂×D₄	—	268	4	no	—
314	C₂×D₄	—	268	4	no	—
315	C₂×D₄	—	268	2	no	—
316	C₂×D₄	—	536	2	no	—
317	C₂×D₄	—	536	2	no	—
318	C₂×D₄	—	67	1	no	—
319	C₂×D₄	—	134	2	no	—
320	C₂×D₄	—	134	2	no	—
321	C₂×D₄	—	134	2	no	—
322	C₂×D₄	C₂×C₂²⋊D₆₇	1	2	yes	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	134	1	no	—
325	Q₁₆	—	4	2	no	—
326	Q₁₆	—	8	1	no	—
327	SD₁₆	—	8	2	no	—
328	SD₁₆	—	536	2	no	—
329	SD₁₆	—	134	2	no	—
330	D₈	—	2	2	no	—
331	D₈	—	268	4	no	—
332	D₈	—	268	2	no	—
333	D₈	—	536	1	no	—
334	M₁₆	—	536	2	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	268	2	no	—
337	C₂×C₈	—	67	1	no	—
338	C₂×C₈	—	67	1	no	—
339	C₂×C₈	—	134	2	no	—
340	C₂×C₈	—	134	1	no	—
341	C₂×C₈	—	134	1	no	—
342	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
343	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	4	2	no	—
348	C₄⋊C₄	—	67	1	no	—
349	C₄⋊C₄	D₄×D₆₇	1	1	yes	characteristic
350	C₄⋊C₄	C₂×C₂²⋊D₆₇	1	2	yes	—
351	C₂²⋊C₄	—	2	2	no	—
352	C₂²⋊C₄	—	4	2	no	—
353	C₂²⋊C₄	—	4	2	no	—
354	C₂²⋊C₄	—	268	2	no	—
355	C₂²⋊C₄	—	134	1	no	—
356	C₄²	—	2	1	no	—
357	C₄²	—	4	2	no	—
358	C₄²	C₂³×D₆₇	1	1	yes	characteristic
359	C₂³	—	2	2	no	—
360	C₂³	—	268	2	no	—
361	C₂³	—	536	4	no	—
362	C₂³	—	536	4	no	—
363	C₂³	—	1072	2	no	—
364	C₂³	—	134	1	no	—
365	Q₈	—	2	1	no	—
366	Q₈	—	2	1	no	—
367	Q₈	—	4	2	no	—
368	Q₈	—	4	2	no	—
369	D₄	—	2	2	no	—
370	D₄	—	2	2	no	—
371	D₄	—	268	2	no	—
372	D₄	—	268	2	no	—
373	D₄	—	268	2	no	—
374	D₄	—	268	2	no	—
375	D₄	—	536	2	no	—
376	D₄	—	536	4	no	—
377	D₄	—	536	4	no	—
378	D₄	—	67	2	no	—
379	D₄	—	134	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	268	1	no	—
387	C₂×C₄	—	268	1	no	—
388	C₂×C₄	—	134	1	no	—
389	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
390	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
391	C₂×C₄	#14524088	1	1	yes	characteristic
392	C₈	—	2	1	no	—
393	C₈	—	4	1	no	—
394	C₈	—	268	1	no	—
395	C₈	—	268	1	no	—
396	C₈	—	268	2	no	—
397	C₈	—	134	1	no	—
398	C₈	—	134	1	no	—
399	C₈	#14524068	1	2	yes	—
400	C₂²	—	4	2	no	—
401	C₂²	—	4	2	no	—
402	C₂²	—	4	2	no	—
403	C₂²	—	268	1	no	—
404	C₂²	—	268	1	no	—
405	C₂²	—	536	2	no	—
406	C₂²	—	536	2	no	—
407	C₂²	—	536	2	no	—
408	C₂²	—	1072	8	no	—
409	C₂²	—	134	2	no	—
410	C₂²	D₄×C₂²⋊D₆₇	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	4	2	no	—
413	C₄	—	4	1	no	—
414	C₄	—	4	1	no	—
415	C₄	—	8	2	no	—
416	C₄	—	268	1	no	—
417	C₄	#135×D₆₇	1	1	yes	characteristic
418	C₄	C₂×#14524068	1	1	yes	characteristic
419	C₄	#16864198	1	1	yes	characteristic
420	C₄	#16864199	1	1	yes	characteristic
421	C₂	—	8	2	no	—
422	C₂	—	268	2	no	—
423	C₂	—	1072	2	no	—
424	C₂	#22571829	1	1	yes	characteristic
425	C₂	#22571888	1	1	yes	characteristic
426	C₂	#22571995	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×C₂²⋊D₆₇
commutator, cosocle	C₄²×C₆₇	C₂⁴
Frattini	C₄²	C₂³×D₆₇
Fitting	C₆₇×#3393	C₂
socle	C₂²×C₆₇	D₄²
prime radical	D₈×D₂₆₈	C₂
hypercenter	#3393	D₆₇
hypocenter	C₆₇	#19900
LCS	G ▷ C₄²×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #3393

Complements

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

N	H ≅ G/N	type
1. #22572434	C₂	semidirect
3. #22559816	C₂	semidirect
4. #22559772	C₂	semidirect
5. #22559571	C₂	semidirect
6. #22559569	C₂	semidirect
7. #22559386	C₂	semidirect
8. #22559319	C₂	semidirect
9. #22559094	C₂	semidirect
10. C₈×#11761615	C₂	semidirect
11. C₆₇×#3393	C₂	semidirect
15. #16863744	C₂²	semidirect
16. #16863744	C₂²	semidirect
21. #16863596	C₂²	semidirect
26. #16863474	C₂²	semidirect
29. #16863149	C₂²	semidirect
30. #16863146	C₂²	semidirect
31. #16863142	C₂²	semidirect
32. #16863139	C₂²	semidirect
33. Q₈⋊(C₆₇⋊C₈)	C₂²	semidirect
34. D₄⋊(C₆₇⋊C₈)	C₂²	semidirect
36. C₈×C₆₇⋊C₈	C₂²	semidirect
37. #556×C₆₇	C₂²	semidirect
39. #494×C₆₇	C₂²	semidirect
41. #461×C₆₇	C₂²	semidirect
42. C₈×Q₈×C₆₇	C₂²	semidirect
214. #3393	D₆₇	semidirect
225. C₆₇	#19900	semidirect
227. #556	C₂×D₆₇	semidirect
230. #494	C₂×D₆₇	semidirect
239. #461	C₂×D₆₇	semidirect
244. C₈×Q₈	C₂×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
#22572434	2
D₈×D₂₆₈	2
#22559816	2
#22559772	2
#22559571	2
#22559569	2
#22559386	2
#22559319	2
#22559094	2
C₈×#11761615	2
C₆₇×#3393	2
#19900	67