Subgroups — #31010224

Order 17152.

696 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	#22573343	C₂	1	2	yes	maximal, complemented
2	#22570637	C₂	1	1	yes	maximal, characteristic, complemented
3	#22562290	C₂	1	2	yes	maximal, complemented
4	#22562285	C₂	1	2	yes	maximal, complemented
5	#22562278	C₂	1	4	yes	maximal, complemented
6	C₂×#16863217	C₂	1	1	yes	maximal, characteristic, complemented
7	#22561956	C₂	1	2	yes	maximal, complemented
8	C₂×#443×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#14524065	—	2	1	no	—
10	C₂×#14524065	C₂²	1	2	yes	—
11	#16863946	—	2	1	no	—
12	#16863837	—	2	2	no	—
13	#16863836	C₂²	1	4	yes	—
14	#16863832	—	2	2	no	—
15	#16863831	C₂²	1	4	yes	—
16	#16863826	—	2	4	no	—
17	C₂×#14523983	C₂²	1	2	yes	—
18	#16863780	—	2	1	no	—
19	#16863780	C₂²	1	2	yes	complemented
20	#16863776	C₂²	1	1	yes	characteristic, complemented
21	#16863773	C₂²	1	1	yes	characteristic, complemented
22	#16863769	—	2	1	no	—
23	#16863217	C₂²	1	2	yes	complemented
24	#16863217	C₂²	1	2	yes	complemented
25	#16863211	C₂²	1	4	yes	complemented
26	#16863208	C₂²	1	4	yes	complemented
27	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×#131×C₆₇	—	2	1	no	—
29	#443×C₆₇	—	2	1	no	—
30	#443×C₆₇	—	2	1	no	—
31	#443×C₆₇	C₂²	1	2	yes	—
32	#443×C₆₇	C₂²	1	2	yes	—
33	C₂×#108×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×#104×C₆₇	—	2	1	no	—
35	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×#11761628	—	2	2	no	—
37	#14524065	—	2	2	no	—
38	#14524065	—	2	2	no	—
39	#14524065	—	2	2	no	—
40	#14524065	—	2	2	no	—
41	#14524065	—	4	1	no	—
42	#14524065	—	4	1	no	—
43	#14524065	—	4	1	no	—
44	#14524065	—	4	1	no	—
45	C₂×Dic₂₆₈	—	2	1	no	—
46	C₂×Dic₂₆₈	C₂³	1	2	yes	—
47	C₂×#11761617	—	2	2	no	—
48	C₂×#11761617	—	2	2	no	—
49	C₂×D₅₃₆	—	2	1	no	—
50	C₂×D₅₃₆	C₂³	1	2	yes	—
51	#14524043	—	2	1	no	—
52	#14524040	—	2	1	no	—
53	#14524031	—	2	2	no	—
54	#14524017	—	4	2	no	—
55	C₄×D₂₆₈	—	4	2	no	—
56	#14523989	—	2	4	no	—
57	#14523987	—	2	4	no	—
58	#14523986	—	2	4	no	—
59	#14523984	—	2	4	no	—
60	#14523983	—	2	2	no	—
61	#14523983	C₂³	1	4	yes	—
62	C₂×C₆₇⋊C₁₆	—	2	2	no	—
63	C₂×#41×C₆₇	—	2	1	no	—
64	#135×C₆₇	—	2	1	no	—
65	#135×C₆₇	—	2	1	no	—
66	#135×C₆₇	D₄	1	2	yes	complemented
67	#135×C₆₇	C₂³	1	2	yes	—
68	C₂×Q₁₆×C₆₇	D₄	1	1	yes	characteristic, complemented
69	C₂×SD₁₆×C₆₇	—	2	1	no	—
70	C₂×D₈×C₆₇	D₄	1	1	yes	characteristic, complemented
71	#131×C₆₇	—	2	2	no	—
72	#131×C₆₇	—	2	2	no	—
73	#131×C₆₇	—	4	1	no	—
74	#131×C₆₇	—	4	1	no	—
75	C₂×M₁₆×C₆₇	—	2	1	no	—
76	C₂×M₁₆×C₆₇	—	4	1	no	—
77	C₂²×C₈×C₆₇	—	4	1	no	—
78	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
79	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
81	#108×C₆₇	—	2	1	no	—
82	#108×C₆₇	C₂³	1	2	yes	—
83	#104×C₆₇	—	2	2	no	—
84	#104×C₆₇	—	2	2	no	—
85	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
86	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
87	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
88	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
89	#11761628	—	4	2	no	—
90	#11761628	—	4	2	no	—
91	#11761628	—	4	2	no	—
92	#11761628	—	4	2	no	—
93	C₂×Dic₁₃₄	—	2	2	no	—
94	C₂×D₂₆₈	—	2	2	no	—
95	C₂×D₂₆₈	—	4	2	no	—
96	C₂×C₂²⋊D₆₇	—	4	2	no	—
97	C₂×C₄×D₆₇	—	4	2	no	—
98	Dic₂₆₈	—	2	2	no	—
99	Dic₂₆₈	—	2	2	no	—
100	Dic₂₆₈	—	4	1	no	—
101	Dic₂₆₈	—	4	1	no	—
102	#11761617	—	4	2	no	—
103	#11761617	—	4	2	no	—
104	#11761617	—	4	2	no	—
105	#11761617	—	4	2	no	—
106	D₅₃₆	—	2	2	no	—
107	D₅₃₆	—	2	2	no	—
108	D₅₃₆	—	4	1	no	—
109	D₅₃₆	—	4	1	no	—
110	C₄⋊Dic₆₇	—	4	2	no	—
111	(C₂×D₆₇)⋊C₄	—	4	4	no	—
112	C₆₇⋊C₁₆	—	2	4	no	—
113	#41×C₆₇	—	2	2	no	—
114	#41×C₆₇	—	2	2	no	—
115	#41×C₆₇	—	4	1	no	—
116	#41×C₆₇	—	4	1	no	—
117	C₂×Q₈×C₆₇	—	2	1	no	—
118	C₂×D₄×C₆₇	—	2	1	no	—
119	C₂×D₄×C₆₇	—	4	1	no	—
120	C₂²×C₄×C₆₇	—	2	1	no	—
121	C₂²×C₄×C₆₇	—	4	1	no	—
122	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
123	Q₁₆×C₆₇	—	2	1	no	—
124	Q₁₆×C₆₇	C₂×D₄	1	2	yes	—
125	SD₁₆×C₆₇	—	2	2	no	—
126	SD₁₆×C₆₇	—	2	2	no	—
127	D₈×C₆₇	—	2	1	no	—
128	D₈×C₆₇	C₂×D₄	1	2	yes	—
129	M₁₆×C₆₇	—	2	2	no	—
130	M₁₆×C₆₇	—	4	1	no	—
131	M₁₆×C₆₇	—	4	2	no	—
132	M₁₆×C₆₇	—	4	2	no	—
133	C₂×C₈×C₆₇	—	4	1	no	—
134	C₂×C₈×C₆₇	—	4	2	no	—
135	C₂×C₈×C₆₇	—	4	2	no	—
136	C₂×C₈×C₆₇	D₈	1	1	yes	characteristic
137	C₂×C₈×C₆₇	D₈	1	1	yes	characteristic
138	C₂×C₈×C₆₇	D₈	1	1	yes	characteristic
139	C₂×C₈×C₆₇	D₈	1	1	yes	characteristic
140	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
141	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
142	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
145	C₂×C₈×C₆₇	#41	1	1	yes	characteristic
146	C₂×C₈×C₆₇	#41	1	1	yes	characteristic
147	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
148	C₄²×C₆₇	—	2	1	no	—
149	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
151	C₂³×C₆₇	—	4	1	no	—
152	C₂³×C₆₇	AGL(1,ℤ/8)	1	1	yes	characteristic
153	C₂²×D₆₇	—	4	2	no	—
154	Q₈×C₆₇	—	2	2	no	—
155	Q₈×C₆₇	—	4	1	no	—
156	D₄×C₆₇	—	2	2	no	—
157	D₄×C₆₇	—	4	2	no	—
158	D₄×C₆₇	—	4	2	no	—
159	D₄×C₆₇	—	4	1	no	—
160	C₂×C₄×C₆₇	—	2	1	no	—
161	C₂×C₄×C₆₇	—	2	1	no	—
162	C₂×C₄×C₆₇	—	4	2	no	—
163	C₂×C₄×C₆₇	—	4	1	no	—
164	C₂×C₄×C₆₇	—	4	2	no	—
165	C₂×C₄×C₆₇	—	4	2	no	—
166	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
167	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
168	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
169	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
170	C₂×C₄×C₆₇	AGL(1,ℤ/8)	1	1	yes	characteristic
171	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
172	C₂²⋊D₆₇	—	8	2	no	—
173	C₂²⋊D₆₇	—	8	2	no	—
174	C₂×Dic₆₇	—	4	2	no	—
175	D₂₆₈	—	4	2	no	—
176	D₂₆₈	—	4	2	no	—
177	D₂₆₈	—	8	4	no	—
178	C₄×D₆₇	—	8	2	no	—
179	C₄×D₆₇	—	8	2	no	—
180	Dic₁₃₄	—	4	2	no	—
181	Dic₁₃₄	—	4	2	no	—
182	C₈×C₆₇	—	4	2	no	—
183	C₈×C₆₇	#121	1	1	yes	characteristic
184	C₈×C₆₇	#121	1	1	yes	characteristic
185	C₈×C₆₇	C₂×D₈	1	1	yes	characteristic
186	C₈×C₆₇	C₂×D₈	1	1	yes	characteristic
187	C₈×C₆₇	C₂×D₈	1	1	yes	characteristic
188	C₈×C₆₇	C₂×D₈	1	1	yes	characteristic
189	C₈×C₆₇	C₂²×D₄	1	1	yes	characteristic
190	C₈×C₆₇	C₂×#41	1	1	yes	characteristic
191	C₂²×C₆₇	—	4	1	no	—
192	C₂²×C₆₇	—	4	2	no	—
193	C₂²×C₆₇	—	8	2	no	—
194	C₂²×C₆₇	#459	1	1	yes	characteristic
195	C₂²×C₆₇	#459	1	1	yes	characteristic
196	C₂²×C₆₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
197	C₂×D₆₇	—	8	4	no	—
198	C₂×D₆₇	—	8	2	no	—
199	C₄×C₆₇	—	2	2	no	—
200	C₄×C₆₇	—	4	1	no	—
201	C₄×C₆₇	—	4	2	no	—
202	C₄×C₆₇	#459	1	1	yes	characteristic
203	C₄×C₆₇	#459	1	1	yes	characteristic
204	C₄×C₆₇	C₂×#121	1	1	yes	characteristic
205	C₄×C₆₇	C₂²×D₈	1	1	yes	characteristic
206	Dic₆₇	—	8	2	no	—
207	#33594	—	67	1	no	maximal, Sylow
208	C₂×C₆₇	—	2	1	no	—
209	C₂×C₆₇	—	2	1	no	—
210	C₂×C₆₇	—	2	1	no	—
211	C₂×C₆₇	—	8	2	no	—
212	C₂×C₆₇	C₂×#459	1	1	yes	characteristic
213	D₆₇	—	16	2	no	—
214	#3414	—	67	2	no	—
215	#3147	—	67	1	no	—
216	C₂×#443	D₆₇	1	1	yes	characteristic, complemented
217	#2214	—	67	2	no	—
218	#2213	—	67	2	no	—
219	#2212	—	67	4	no	—
220	C₂×#364	—	67	1	no	—
221	#2148	—	67	2	no	—
222	C₆₇	#33594	1	1	yes	characteristic, complemented, Sylow
223	C₂×#135	—	67	2	no	—
224	C₂×#135	—	134	1	no	—
225	C₂×#135	C₂×D₆₇	1	1	yes	characteristic
226	C₂×#131	—	2	1	no	—
227	#532	—	134	1	no	—
228	#510	—	67	4	no	—
229	#510	—	134	2	no	—
230	#509	—	67	4	no	—
231	#509	—	134	2	no	—
232	#508	—	134	4	no	—
233	C₂×M₃₂	—	67	2	no	—
234	#495	—	67	2	no	—
235	#495	—	134	1	no	—
236	#494	—	67	1	no	—
237	#493	—	67	1	no	—
238	#492	—	134	1	no	—
239	#443	—	2	1	no	—
240	#443	—	2	1	no	—
241	#443	C₂×D₆₇	1	2	yes	—
242	#443	C₂×D₆₇	1	2	yes	—
243	C₂×#108	C₂×D₆₇	1	1	yes	characteristic
244	C₂×#104	—	2	1	no	—
245	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
246	#364	—	67	2	no	—
247	#364	—	67	2	no	—
248	#362	—	67	4	no	—
249	#361	—	67	4	no	—
250	C₂×#41	—	2	1	no	—
251	C₂×#41	—	134	2	no	—
252	#135	—	2	1	no	—
253	#135	—	2	1	no	—
254	#135	—	268	1	no	—
255	#135	—	268	1	no	—
256	#135	—	268	1	no	—
257	#135	—	268	1	no	—
258	#135	—	134	2	no	—
259	#135	—	134	2	no	—
260	#135	—	134	2	no	—
261	#135	—	134	2	no	—
262	#135	D₂₆₈	1	2	yes	complemented
263	#135	C₂²×D₆₇	1	2	yes	—
264	C₂×Q₁₆	—	67	2	no	—
265	C₂×Q₁₆	—	134	1	no	—
266	C₂×Q₁₆	D₂₆₈	1	1	yes	characteristic, complemented
267	C₂×SD₁₆	—	2	1	no	—
268	C₂×SD₁₆	—	134	2	no	—
269	C₂×SD₁₆	—	134	2	no	—
270	C₂×D₈	—	67	2	no	—
271	C₂×D₈	—	134	1	no	—
272	C₂×D₈	D₂₆₈	1	1	yes	characteristic, complemented
273	#131	—	2	2	no	—
274	#131	—	2	2	no	—
275	#131	—	4	1	no	—
276	#131	—	4	1	no	—
277	C₂×M₁₆	—	2	1	no	—
278	C₂×M₁₆	—	4	1	no	—
279	C₂²×C₈	—	4	1	no	—
280	C₂²×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
281	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
282	C₄⋊Q₈	—	134	1	no	—
283	#127	—	134	1	no	—
284	#124	—	134	2	no	—
285	#121	—	268	2	no	—
286	C₄×D₄	—	268	2	no	—
287	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
288	Q₃₂	—	134	4	no	—
289	SD₃₂	—	134	4	no	—
290	SD₃₂	—	134	4	no	—
291	D₁₆	—	134	4	no	—
292	M₃₂	—	67	4	no	—
293	M₃₂	—	134	2	no	—
294	C₂×C₁₆	—	134	2	no	—
295	#108	—	2	1	no	—
296	#108	C₂²×D₆₇	1	2	yes	—
297	#104	—	2	2	no	—
298	#104	—	2	2	no	—
299	C₄×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
300	C₄×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
301	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
302	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
303	#41	—	2	2	no	—
304	#41	—	2	2	no	—
305	#41	—	4	1	no	—
306	#41	—	4	1	no	—
307	#41	—	268	2	no	—
308	#41	—	268	2	no	—
309	#41	—	268	2	no	—
310	#41	—	268	2	no	—
311	C₂×Q₈	—	2	1	no	—
312	C₂×Q₈	—	134	2	no	—
313	C₂×D₄	—	2	1	no	—
314	C₂×D₄	—	4	1	no	—
315	C₂×D₄	—	268	2	no	—
316	C₂×D₄	—	268	2	no	—
317	C₂×D₄	—	134	2	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	4	1	no	—
320	C₂²×C₄	—	268	2	no	—
321	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
322	Q₁₆	—	2	1	no	—
323	Q₁₆	—	268	1	no	—
324	Q₁₆	—	268	1	no	—
325	Q₁₆	—	134	2	no	—
326	Q₁₆	—	134	2	no	—
327	Q₁₆	C₂×D₂₆₈	1	2	yes	—
328	SD₁₆	—	2	2	no	—
329	SD₁₆	—	2	2	no	—
330	SD₁₆	—	268	2	no	—
331	SD₁₆	—	268	2	no	—
332	SD₁₆	—	268	2	no	—
333	SD₁₆	—	268	2	no	—
334	D₈	—	2	1	no	—
335	D₈	—	268	1	no	—
336	D₈	—	268	1	no	—
337	D₈	—	134	2	no	—
338	D₈	—	134	2	no	—
339	D₈	C₂×D₂₆₈	1	2	yes	—
340	M₁₆	—	2	2	no	—
341	M₁₆	—	4	1	no	—
342	M₁₆	—	4	2	no	—
343	M₁₆	—	4	2	no	—
344	C₂×C₈	—	4	1	no	—
345	C₂×C₈	—	4	2	no	—
346	C₂×C₈	—	4	2	no	—
347	C₂×C₈	#11761613	1	1	yes	characteristic
348	C₂×C₈	#11761613	1	1	yes	characteristic
349	C₂×C₈	#11761613	1	1	yes	characteristic
350	C₂×C₈	#11761613	1	1	yes	characteristic
351	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
352	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
353	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
354	C₂×C₈	C₂×D₂₆₈	1	1	yes	characteristic
355	C₂×C₈	C₂×D₂₆₈	1	1	yes	characteristic
356	C₂×C₈	#11761628	1	1	yes	characteristic
357	C₂×C₈	#11761628	1	1	yes	characteristic
358	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
359	C₄⋊C₄	—	268	2	no	—
360	C₂²⋊C₄	—	268	4	no	—
361	C₄²	—	2	1	no	—
362	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
363	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
364	C₁₆	—	134	4	no	—
365	C₂³	—	4	1	no	—
366	C₂³	—	268	2	no	—
367	C₂³	#14524068	1	1	yes	characteristic
368	Q₈	—	2	2	no	—
369	Q₈	—	4	1	no	—
370	Q₈	—	268	2	no	—
371	Q₈	—	268	2	no	—
372	D₄	—	2	2	no	—
373	D₄	—	4	2	no	—
374	D₄	—	4	2	no	—
375	D₄	—	4	1	no	—
376	D₄	—	268	2	no	—
377	D₄	—	268	2	no	—
378	D₄	—	536	4	no	—
379	D₄	—	536	2	no	—
380	D₄	—	536	2	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	268	2	no	—
388	C₂×C₄	—	536	2	no	—
389	C₂×C₄	—	536	2	no	—
390	C₂×C₄	#14524017	1	1	yes	characteristic
391	C₂×C₄	#14524017	1	1	yes	characteristic
392	C₂×C₄	C₂×#11761613	1	1	yes	characteristic
393	C₂×C₄	C₂×#11761613	1	1	yes	characteristic
394	C₂×C₄	#14524068	1	1	yes	characteristic
395	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
396	C₈	—	4	2	no	—
397	C₈	#14524017	1	1	yes	characteristic
398	C₈	#14524017	1	1	yes	characteristic
399	C₈	C₂×#11761613	1	1	yes	characteristic
400	C₈	C₂×#11761613	1	1	yes	characteristic
401	C₈	C₂×#11761613	1	1	yes	characteristic
402	C₈	C₂×#11761613	1	1	yes	characteristic
403	C₈	C₂²×D₂₆₈	1	1	yes	characteristic
404	C₈	C₂×#11761628	1	1	yes	characteristic
405	C₂²	—	4	1	no	—
406	C₂²	—	4	2	no	—
407	C₂²	—	8	2	no	—
408	C₂²	—	536	4	no	—
409	C₂²	—	536	2	no	—
410	C₂²	#16863591	1	1	yes	characteristic
411	C₂²	#16863591	1	1	yes	characteristic
412	C₂²	C₂×#14524068	1	1	yes	characteristic
413	C₄	—	2	2	no	—
414	C₄	—	4	1	no	—
415	C₄	—	4	2	no	—
416	C₄	—	536	2	no	—
417	C₄	#16863591	1	1	yes	characteristic
418	C₄	#16863591	1	1	yes	characteristic
419	C₄	C₂×#14524017	1	1	yes	characteristic
420	C₄	C₂²×#11761613	1	1	yes	characteristic
421	C₂	—	2	1	no	—
422	C₂	—	2	1	no	—
423	C₂	—	2	1	no	—
424	C₂	—	8	2	no	—
425	C₂	—	1072	2	no	—
426	C₂	C₂×#16863591	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#16863591
commutator, cosocle	C₂×C₈×C₆₇	C₂⁴
Frattini	C₂×C₈	C₂³×D₆₇
Fitting	C₂×#443×C₆₇	C₂
socle	C₂×C₆₇	C₂×#459
hypercenter	C₂×#443	D₆₇
hypocenter	C₆₇	#33594
LCS	G ▷ C₂×C₈×C₆₇ ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ C₂×#443

Complements

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

N	H ≅ G/N	type
1. #22573343	C₂	semidirect
2. #22570637	C₂	semidirect
3. #22562290	C₂	semidirect
4. #22562285	C₂	semidirect
5. #22562278	C₂	semidirect
6. C₂×#16863217	C₂	semidirect
7. #22561956	C₂	semidirect
8. C₂×#443×C₆₇	C₂	semidirect
19. #16863780	C₂²	semidirect
20. #16863776	C₂²	semidirect
21. #16863773	C₂²	semidirect
23. #16863217	C₂²	semidirect
24. #16863217	C₂²	semidirect
25. #16863211	C₂²	semidirect
26. #16863208	C₂²	semidirect
66. #135×C₆₇	D₄	semidirect
68. C₂×Q₁₆×C₆₇	D₄	semidirect
70. C₂×D₈×C₆₇	D₄	semidirect
216. C₂×#443	D₆₇	semidirect
222. C₆₇	#33594	semidirect
262. #135	D₂₆₈	semidirect
266. C₂×Q₁₆	D₂₆₈	semidirect
272. C₂×D₈	D₂₆₈	semidirect

Maximal subgroups

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

subgroup	index
#22573343	2
#22570637	2
#22562290	2
#22562285	2
#22562278	2
C₂×#16863217	2
#22561956	2
C₂×#443×C₆₇	2
#33594	67