Subgroups — #30854417

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×#16863514	C₂	1	1	yes	maximal, characteristic
3	#22569011	C₂	1	1	yes	maximal, characteristic
4	#22568634	C₂	1	2	yes	maximal, complemented
5	#22560115	C₂	1	1	yes	maximal, characteristic, complemented
6	#22560093	C₂	1	1	yes	maximal, characteristic, complemented
7	#22560088	C₂	1	1	yes	maximal, characteristic, complemented
8	#22560053	C₂	1	2	yes	maximal, complemented
9	#22560046	C₂	1	2	yes	maximal, complemented
10	C₄×#14523971	C₂	1	2	yes	maximal, complemented
11	C₄×#97×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14524065	C₂²	1	1	yes	characteristic
13	C₂×#14524049	C₂²	1	2	yes	—
14	C₂×#14524049	C₂²	1	2	yes	—
15	C₄×#11761628	C₂²	1	2	yes	—
16	#16863519	C₄	1	8	yes	complemented
17	#16863514	C₄	1	8	yes	complemented
18	#16863509	C₄	1	2	yes	complemented
19	#16863504	C₄	1	2	yes	complemented
20	#16863498	C₄	1	4	yes	complemented
21	C₂×#14523979	C₂²	1	1	yes	characteristic
22	C₂×#14523979	C₂²	1	1	yes	characteristic
23	#16863434	C₂²	1	1	yes	characteristic
24	C₂×#14523971	C₂²	1	2	yes	—
25	C₂×#14523971	C₂²	1	2	yes	—
26	#16863393	C₂²	1	2	yes	—
27	#16863353	—	2	2	no	—
28	#16863353	—	2	2	no	—
29	#16863351	C₂²	1	2	yes	—
30	#16863351	C₂²	1	2	yes	—
31	C₄×#11761612	C₂²	1	2	yes	—
32	#16863348	—	2	2	no	—
33	#97×D₆₇	—	2	2	no	—
34	#16863161	C₂²	1	2	yes	—
35	#16863156	C₂²	1	2	yes	—
36	#16863156	C₂²	1	2	yes	—
37	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
40	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
43	C₄³×C₆₇	C₂²	1	1	yes	characteristic
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	#14524049	—	2	4	no	—
51	#14524049	—	2	4	no	—
52	#14524049	C₂×C₄	1	8	yes	complemented
53	#14524049	C₂×C₄	1	8	yes	complemented
54	C₂×#11761612	C₂³	1	2	yes	—
55	C₂×#11761612	C₂³	1	2	yes	—
56	C₂×#11761611	—	2	2	no	—
57	C₂×#11761611	—	2	2	no	—
58	C₂×C₈×D₆₇	—	2	2	no	—
59	C₂×C₈×D₆₇	—	2	2	no	—
60	C₄×Dic₁₃₄	C₂×C₄	1	4	yes	—
61	C₄×D₂₆₈	C₂×C₄	1	4	yes	—
62	C₄×C₂²⋊D₆₇	—	2	4	no	—
63	#14524002	C₂³	1	2	yes	—
64	#14524000	—	2	2	no	—
65	C₄²×D₆₇	—	2	2	no	—
66	#14523979	C₂×C₄	1	4	yes	complemented
67	#14523979	C₂×C₄	1	4	yes	complemented
68	#14523977	C₂×C₄	1	2	yes	—
69	#14523975	C₂×C₄	1	2	yes	—
70	#14523971	C₂×C₄	1	8	yes	complemented
71	#14523971	C₂×C₄	1	8	yes	complemented
72	#14523968	C₂×C₄	1	4	yes	—
73	#14523965	C₂×C₄	1	4	yes	—
74	#14523954	—	2	2	no	—
75	#14523953	—	2	2	no	—
76	#14523953	—	2	2	no	—
77	C₄×C₆₇⋊C₈	—	2	2	no	—
78	C₈×Dic₆₇	—	2	2	no	—
79	C₈×Dic₆₇	—	2	2	no	—
80	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₆₇	—	2	2	no	—
85	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
88	#97×C₆₇	—	2	2	no	—
89	#97×C₆₇	C₂×C₄	1	2	yes	—
90	#97×C₆₇	C₂×C₄	1	2	yes	—
91	#97×C₆₇	C₂×C₄	1	4	yes	complemented
92	#97×C₆₇	D₄	1	2	yes	—
93	#97×C₆₇	D₄	1	2	yes	—
94	C₄×C₈×C₆₇	—	2	2	no	—
95	C₄×C₈×C₆₇	C₂×C₄	1	4	yes	complemented
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	C₂×C₄×D₆₇	—	2	2	no	—
104	C₂×C₄×D₆₇	—	2	4	no	—
105	Dic₂₆₈	C₄²	1	4	yes	complemented
106	#11761617	C₄²	1	8	yes	complemented
107	D₅₃₆	C₄²	1	4	yes	complemented
108	#11761612	—	2	2	no	—
109	#11761612	—	2	2	no	—
110	#11761612	C₂²×C₄	1	4	yes	—
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	2	no	—
116	C₈×D₆₇	—	2	8	no	—
117	C₈×D₆₇	—	2	8	no	—
118	C₄⋊Dic₆₇	C₂²×C₄	1	4	yes	—
119	Dic₆₇⋊C₄	—	2	4	no	—
120	C₂²⋊Dic₆₇	—	2	2	no	—
121	(C₂×D₆₇)⋊C₄	—	2	4	no	—
122	C₄×Dic₆₇	—	2	4	no	—
123	C₄×Dic₆₇	—	2	2	no	—
124	C₂²×C₄×C₆₇	—	2	1	no	—
125	C₂²×C₄×C₆₇	—	2	1	no	—
126	C₂²×C₄×C₆₇	#41	1	2	yes	—
127	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
128	C₂×C₈×C₆₇	—	2	1	no	—
129	C₂×C₈×C₆₇	—	2	1	no	—
130	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
131	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
134	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
135	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
136	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
137	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
138	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
139	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
140	C₂×C₈×C₆₇	#41	1	2	yes	—
141	C₂×C₈×C₆₇	#41	1	2	yes	—
142	C₄²×C₆₇	—	2	1	no	—
143	C₄²×C₆₇	—	2	1	no	—
144	C₄²×C₆₇	—	4	4	no	—
145	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
146	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
147	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
148	C₄²×C₆₇	C₂×D₄	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	—	2	2	no	—
154	C₂×C₄×C₆₇	—	4	2	no	—
155	C₂×C₄×C₆₇	—	4	2	no	—
156	C₂×C₄×C₆₇	C₄×D₄	1	4	yes	—
157	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
158	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
159	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
160	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
162	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
163	C₂²⋊D₆₇	—	2	4	no	—
164	C₂²⋊D₆₇	—	2	4	no	—
165	C₂×Dic₆₇	—	2	2	no	—
166	C₂×Dic₆₇	—	2	4	no	—
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	2	no	—
175	C₈×C₆₇	C₂×C₄²	1	2	yes	—
176	C₈×C₆₇	C₂×C₄²	1	2	yes	—
177	C₈×C₆₇	C₄×D₄	1	2	yes	—
178	C₈×C₆₇	C₄×D₄	1	4	yes	—
179	C₈×C₆₇	C₄×D₄	1	2	yes	—
180	C₆₇⋊C₈	—	2	4	no	—
181	C₆₇⋊C₈	—	2	4	no	—
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	—	2	4	no	—
189	C₄×C₆₇	—	2	4	no	—
190	C₄×C₆₇	—	4	2	no	—
191	C₄×C₆₇	C₂²×C₄²	1	1	yes	characteristic
192	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
193	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
194	C₄×C₆₇	C₄×#41	1	1	yes	characteristic
195	Dic₆₇	—	2	4	no	—
196	Dic₆₇	—	4	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	—	67	1	no	—
209	#1772	—	67	1	no	—
210	#1765	—	67	2	no	—
211	#1764	—	67	2	no	—
212	C₄×#104	—	67	2	no	—
213	C₄×#97	D₆₇	1	1	yes	characteristic, complemented
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	—	67	1	no	—
226	#427	—	67	1	no	—
227	C₂×#104	—	67	2	no	—
228	C₂×#104	—	67	2	no	—
229	#416	—	67	2	no	—
230	#405	—	67	2	no	—
231	#405	—	67	2	no	—
232	#405	—	134	2	no	—
233	#405	—	134	2	no	—
234	C₄×M₁₆	—	67	2	no	—
235	C₄×M₁₆	—	134	2	no	—
236	C₂×#97	—	134	2	no	—
237	C₂×#97	C₂×D₆₇	1	1	yes	characteristic
238	C₂×#97	C₂×D₆₇	1	1	yes	characteristic
239	C₂×#97	C₂×D₆₇	1	1	yes	characteristic
240	C₂×#97	C₂×D₆₇	1	1	yes	characteristic
241	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
242	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
243	C₄³	C₂×D₆₇	1	1	yes	characteristic
244	#341	—	67	2	no	—
245	#339	—	67	2	no	—
246	#339	—	67	2	no	—
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	—	67	2	no	—
259	C₂×M₁₆	—	134	2	no	—
260	C₂×M₁₆	—	134	2	no	—
261	C₂²×C₈	—	134	2	no	—
262	C₂²×C₈	—	134	2	no	—
263	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
264	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
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	—	67	2	no	—
271	#117	—	134	2	no	—
272	C₂×C₄²	—	2	2	no	—
273	C₂×C₄²	—	134	2	no	—
274	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
275	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
276	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
277	#108	—	67	4	no	—
278	#108	—	67	4	no	—
279	#107	—	67	2	no	—
280	#106	—	67	2	no	—
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	—	134	2	no	—
287	#97	—	134	2	no	—
288	#97	—	134	2	no	—
289	#97	C₄×D₆₇	1	2	yes	—
290	#97	C₄×D₆₇	1	2	yes	—
291	#97	C₄×D₆₇	1	4	yes	complemented
292	#97	D₂₆₈	1	2	yes	—
293	#97	D₂₆₈	1	2	yes	—
294	C₄×C₈	—	2	2	no	—
295	C₄×C₈	—	134	2	no	—
296	C₄×C₈	—	134	2	no	—
297	C₄×C₈	—	134	2	no	—
298	C₄×C₈	C₄×D₆₇	1	4	yes	complemented
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	—	2	1	no	—
308	C₂²×C₄	—	134	4	no	—
309	C₂²×C₄	—	134	2	no	—
310	C₂²×C₄	#11761628	1	2	yes	—
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	—	67	4	no	—
316	M₁₆	—	67	4	no	—
317	M₁₆	—	134	2	no	—
318	M₁₆	—	134	2	no	—
319	M₁₆	—	134	8	no	—
320	M₁₆	—	134	8	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	134	2	no	—
324	C₂×C₈	—	134	2	no	—
325	C₂×C₈	—	134	8	no	—
326	C₂×C₈	—	134	8	no	—
327	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
328	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
329	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
330	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
331	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
332	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
333	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
334	C₂×C₈	C₂×D₂₆₈	1	1	yes	characteristic
335	C₂×C₈	C₂×D₂₆₈	1	2	yes	—
336	C₂×C₈	C₂×D₂₆₈	1	1	yes	characteristic
337	C₂×C₈	#11761628	1	2	yes	—
338	C₂×C₈	#11761628	1	2	yes	—
339	C₄⋊C₄	—	67	4	no	—
340	C₄⋊C₄	—	134	4	no	—
341	C₂²⋊C₄	—	134	2	no	—
342	C₂²⋊C₄	—	134	4	no	—
343	C₄²	—	2	1	no	—
344	C₄²	—	2	1	no	—
345	C₄²	—	4	4	no	—
346	C₄²	—	134	4	no	—
347	C₄²	—	134	2	no	—
348	C₄²	C₂×C₄×D₆₇	1	2	yes	—
349	C₄²	C₂×C₄×D₆₇	1	2	yes	—
350	C₄²	C₂×C₄×D₆₇	1	2	yes	—
351	C₄²	C₂×D₂₆₈	1	2	yes	—
352	C₂³	—	134	2	no	—
353	C₂³	C₂×#11761628	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	—	2	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	536	4	no	—
366	C₂×C₄	—	134	4	no	—
367	C₂×C₄	—	134	2	no	—
368	C₂×C₄	—	134	4	no	—
369	C₂×C₄	—	134	4	no	—
370	C₂×C₄	C₄×D₂₆₈	1	4	yes	—
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	C₂²×D₂₆₈	1	1	yes	characteristic
375	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
376	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
377	C₈	—	2	2	no	—
378	C₈	—	134	4	no	—
379	C₈	—	134	4	no	—
380	C₈	C₄²×D₆₇	1	2	yes	—
381	C₈	C₄²×D₆₇	1	2	yes	—
382	C₈	C₄×D₂₆₈	1	2	yes	—
383	C₈	C₄×D₂₆₈	1	4	yes	—
384	C₈	C₄×D₂₆₈	1	2	yes	—
385	C₂²	—	2	2	no	—
386	C₂²	—	268	4	no	—
387	C₂²	—	134	4	no	—
388	C₂²	C₂×C₄×D₂₆₈	1	1	yes	characteristic
389	C₂²	C₄×#11761628	1	1	yes	characteristic
390	C₂²	C₄×#11761628	1	1	yes	characteristic
391	C₄	—	2	4	no	—
392	C₄	—	2	4	no	—
393	C₄	—	4	2	no	—
394	C₄	—	268	4	no	—
395	C₄	—	134	4	no	—
396	C₄	C₂×C₄²×D₆₇	1	1	yes	characteristic
397	C₄	C₂×C₄×D₂₆₈	1	1	yes	characteristic
398	C₄	C₂×C₄×D₂₆₈	1	1	yes	characteristic
399	C₄	C₄×#11761628	1	1	yes	characteristic
400	C₂	—	2	1	no	—
401	C₂	—	2	1	no	—
402	C₂	—	268	4	no	—
403	C₂	C₄²×D₂₆₈	1	1	yes	characteristic
404	C₂	#22569120	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²×D₂₆₈
commutator	C₄×C₆₇	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting	C₄×#97×C₆₇	C₂
socle	C₂²×C₆₇	C₂×C₄×D₄
prime radical	C₂×#14524065	C₂²
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	C₄×#97	D₆₇
hypocenter	C₆₇	#20512
LCS	G ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#97 ◁ C₄×#97

Complements

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

N	H ≅ G/N	type
4. #22568634	C₂	semidirect
5. #22560115	C₂	semidirect
6. #22560093	C₂	semidirect
7. #22560088	C₂	semidirect
8. #22560053	C₂	semidirect
9. #22560046	C₂	semidirect
10. C₄×#14523971	C₂	semidirect
11. C₄×#97×C₆₇	C₂	semidirect
16. #16863519	C₄	semidirect
17. #16863514	C₄	semidirect
18. #16863509	C₄	semidirect
19. #16863504	C₄	semidirect
20. #16863498	C₄	semidirect
52. #14524049	C₂×C₄	semidirect
53. #14524049	C₂×C₄	semidirect
66. #14523979	C₂×C₄	semidirect
67. #14523979	C₂×C₄	semidirect
70. #14523971	C₂×C₄	semidirect
71. #14523971	C₂×C₄	semidirect
91. #97×C₆₇	C₂×C₄	semidirect
95. C₄×C₈×C₆₇	C₂×C₄	semidirect
105. Dic₂₆₈	C₄²	semidirect
106. #11761617	C₄²	semidirect
107. D₅₃₆	C₄²	semidirect
213. C₄×#97	D₆₇	semidirect
214. C₆₇	#20512	semidirect
291. #97	C₄×D₆₇	semidirect
298. C₄×C₈	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×#16863514	2
#22569011	2
#22568634	2
#22560115	2
#22560093	2
#22560088	2
#22560053	2
#22560046	2
C₄×#14523971	2
C₄×#97×C₆₇	2
#20512	67