Subgroups — C₂×#22559629 #30838113

Order 17152.

758 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×#16863673	C₂	1	1	yes	maximal, characteristic
2	C₂×#16863598	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×D₂₆₈	C₂	1	1	yes	maximal, characteristic
4	#22559629	C₂	1	8	yes	maximal, direct product factor
5	C₂×#16863147	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16863142	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16863142	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#487×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#11761615	—	2	1	no	—
10	C₂²×C₈×D₆₇	—	2	1	no	—
11	C₂×C₄×D₂₆₈	C₂²	1	1	yes	characteristic
12	#16863673	—	2	2	no	—
13	#16863673	C₂²	1	4	yes	—
14	#16863598	—	2	2	no	—
15	#16863598	C₂²	1	4	yes	—
16	C₈×D₂₆₈	—	2	2	no	—
17	C₈×D₂₆₈	C₂²	1	4	yes	—
18	C₂×#14523976	—	2	1	no	—
19	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
22	C₂×#14523967	—	2	1	no	—
23	C₂×#14523963	—	2	1	no	—
24	C₂×(C₂×D₆₇)⋊C₈	—	2	1	no	—
25	#16863147	C₂²	1	4	yes	complemented
26	#16863142	C₂²	1	4	yes	complemented
27	#16863142	C₂²	1	4	yes	complemented
28	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
30	#487×C₆₇	—	2	2	no	—
31	#487×C₆₇	C₂²	1	4	yes	complemented
32	C₂×#103×C₆₇	—	2	1	no	—
33	C₂×#103×C₆₇	—	2	1	no	—
34	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
35	C₂²×D₂₆₈	D₄	1	1	yes	characteristic
36	C₂²×C₄×D₆₇	—	2	1	no	—
37	C₂×#11761615	—	2	4	no	—
38	C₂×#11761615	—	4	4	no	—
39	C₂²×C₆₇⋊C₈	—	2	1	no	—
40	C₂²×C₆₇⋊C₈	—	2	1	no	—
41	C₂²×C₆₇⋊C₈	—	2	1	no	—
42	C₂×C₈×D₆₇	—	2	4	no	—
43	C₂×C₈×D₆₇	—	4	4	no	—
44	C₄×D₂₆₈	—	2	1	no	—
45	C₄×D₂₆₈	—	2	1	no	—
46	C₄×D₂₆₈	D₄	1	2	yes	—
47	C₄×D₂₆₈	C₂³	1	2	yes	—
48	C₂×C₄⋊Dic₆₇	D₄	1	1	yes	characteristic
49	C₂×(C₂×D₆₇)⋊C₄	—	2	1	no	—
50	#14523976	—	2	4	no	—
51	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
52	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
53	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
54	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
55	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
56	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
57	#14523967	—	2	4	no	—
58	#14523963	—	2	4	no	—
59	(C₂×D₆₇)⋊C₈	—	2	4	no	—
60	C₂²×Q₈×C₆₇	—	2	1	no	—
61	C₂²×Q₈×C₆₇	—	2	1	no	—
62	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
63	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
64	C₄⋊Q₈×C₆₇	—	2	1	no	—
65	C₄⋊Q₈×C₆₇	—	2	1	no	—
66	C₄⋊Q₈×C₆₇	—	2	1	no	—
67	C₄⋊Q₈×C₆₇	—	2	1	no	—
68	C₄⋊Q₈×C₆₇	—	2	1	no	—
69	C₄⋊Q₈×C₆₇	—	2	1	no	—
70	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
71	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
73	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
74	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
75	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
76	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
77	#103×C₆₇	—	2	4	no	—
78	#103×C₆₇	—	2	4	no	—
79	C₄×C₈×C₆₇	D₄	1	2	yes	—
80	C₄×C₈×C₆₇	C₂³	1	2	yes	—
81	C₂³×D₆₇	—	2	1	no	—
82	C₂×D₂₆₈	—	2	1	no	—
83	C₂×D₂₆₈	—	2	2	no	—
84	C₂×D₂₆₈	SD₁₆	1	4	yes	—
85	C₂×D₂₆₈	C₂×D₄	1	2	yes	—
86	C₂²×Dic₆₇	—	2	1	no	—
87	C₂×C₄×D₆₇	—	2	2	no	—
88	C₂×C₄×D₆₇	—	2	2	no	—
89	C₂×C₄×D₆₇	—	4	2	no	—
90	C₂×C₄×D₆₇	—	4	2	no	—
91	#11761615	—	4	8	no	—
92	C₂×C₆₇⋊C₈	—	2	2	no	—
93	C₂×C₆₇⋊C₈	—	2	2	no	—
94	C₂×C₆₇⋊C₈	—	2	2	no	—
95	C₂×C₆₇⋊C₈	—	4	2	no	—
96	C₂×C₆₇⋊C₈	—	4	2	no	—
97	C₂×C₆₇⋊C₈	—	4	2	no	—
98	C₈×D₆₇	—	4	8	no	—
99	C₄⋊Dic₆₇	—	2	1	no	—
100	C₄⋊Dic₆₇	C₂×D₄	1	2	yes	—
101	(C₂×D₆₇)⋊C₄	—	2	2	no	—
102	(C₂×D₆₇)⋊C₄	—	2	2	no	—
103	C₂×Q₈×C₆₇	—	2	2	no	—
104	C₂×Q₈×C₆₇	—	2	2	no	—
105	C₂×Q₈×C₆₇	—	4	1	no	—
106	C₂×Q₈×C₆₇	—	4	1	no	—
107	C₂×Q₈×C₆₇	—	4	2	no	—
108	C₂×Q₈×C₆₇	—	4	2	no	—
109	C₂×Q₈×C₆₇	—	4	2	no	—
110	C₂×Q₈×C₆₇	—	4	2	no	—
111	C₂²×C₄×C₆₇	—	4	1	no	—
112	C₂²×C₄×C₆₇	—	4	1	no	—
113	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
116	C₂×C₈×C₆₇	—	2	2	no	—
117	C₂×C₈×C₆₇	—	2	2	no	—
118	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
119	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
120	C₄⋊C₄×C₆₇	—	2	2	no	—
121	C₄⋊C₄×C₆₇	—	2	2	no	—
122	C₄⋊C₄×C₆₇	—	2	2	no	—
123	C₄⋊C₄×C₆₇	—	2	2	no	—
124	C₄⋊C₄×C₆₇	—	4	1	no	—
125	C₄⋊C₄×C₆₇	—	4	1	no	—
126	C₄⋊C₄×C₆₇	—	4	1	no	—
127	C₄⋊C₄×C₆₇	—	4	1	no	—
128	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₆₇	#41	1	1	yes	characteristic
131	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
132	C₂³×C₆₇	#121	1	1	yes	characteristic
133	C₂²×D₆₇	—	2	2	no	—
134	C₂²×D₆₇	—	2	4	no	—
135	C₂²×D₆₇	—	4	2	no	—
136	C₂²×D₆₇	—	4	2	no	—
137	Q₈×C₆₇	—	4	2	no	—
138	Q₈×C₆₇	—	4	2	no	—
139	Q₈×C₆₇	—	4	2	no	—
140	Q₈×C₆₇	—	4	2	no	—
141	Q₈×C₆₇	—	8	2	no	—
142	Q₈×C₆₇	—	8	2	no	—
143	C₂×C₄×C₆₇	—	2	2	no	—
144	C₂×C₄×C₆₇	—	4	2	no	—
145	C₂×C₄×C₆₇	—	4	2	no	—
146	C₂×C₄×C₆₇	—	8	2	no	—
147	C₂×C₄×C₆₇	—	8	2	no	—
148	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
149	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
150	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
151	C₂×C₄×C₆₇	C₂×SD₁₆	1	2	yes	—
152	C₂×C₄×C₆₇	#135	1	2	yes	—
153	C₂×C₄×C₆₇	#135	1	2	yes	—
154	C₂×C₄×C₆₇	AGL(1,ℤ/8)	1	2	yes	—
155	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
156	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
157	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
158	C₂×Dic₆₇	—	2	2	no	—
159	C₂×Dic₆₇	—	4	2	no	—
160	D₂₆₈	—	2	2	no	—
161	D₂₆₈	—	2	4	no	—
162	D₂₆₈	C₂×SD₁₆	1	4	yes	—
163	C₄×D₆₇	—	4	2	no	—
164	C₄×D₆₇	—	4	2	no	—
165	C₄×D₆₇	—	4	4	no	—
166	C₈×C₆₇	—	2	2	no	—
167	C₈×C₆₇	—	2	2	no	—
168	C₆₇⋊C₈	—	4	2	no	—
169	C₆₇⋊C₈	—	4	2	no	—
170	C₆₇⋊C₈	—	4	2	no	—
171	C₂²×C₆₇	#463	1	2	yes	—
172	C₂²×C₆₇	#465	1	2	yes	—
173	C₂²×C₆₇	#473	1	2	yes	—
174	C₂²×C₆₇	C₂×#121	1	1	yes	characteristic
175	C₂×D₆₇	—	2	4	no	—
176	C₂×D₆₇	—	4	8	no	—
177	C₂×D₆₇	—	4	2	no	—
178	C₂×D₆₇	—	4	2	no	—
179	C₄×C₆₇	—	2	1	no	—
180	C₄×C₆₇	—	2	1	no	—
181	C₄×C₆₇	—	8	2	no	—
182	C₄×C₆₇	—	8	2	no	—
183	C₄×C₆₇	#463	1	2	yes	—
184	C₄×C₆₇	#465	1	2	yes	—
185	C₄×C₆₇	C₂²×SD₁₆	1	1	yes	characteristic
186	C₄×C₆₇	C₂×#135	1	1	yes	characteristic
187	C₄×C₆₇	C₂×#135	1	1	yes	characteristic
188	C₄×C₆₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
189	Dic₆₇	—	4	2	no	—
190	C₂×#1679	—	67	1	no	maximal, Sylow
191	C₂×C₆₇	#1679	1	4	yes	complemented
192	C₂×C₆₇	C₂×#463	1	1	yes	characteristic
193	C₂×C₆₇	C₂×#465	1	1	yes	characteristic
194	C₂×C₆₇	C₂×#473	1	1	yes	characteristic
195	D₆₇	—	4	4	no	—
196	C₂×#487	D₆₇	1	1	yes	characteristic, complemented
197	C₂×#474	—	67	1	no	—
198	C₂×#461	—	67	1	no	—
199	C₂×C₈×D₄	—	67	1	no	—
200	#1679	—	67	8	no	—
201	C₂×#334	—	67	1	no	—
202	C₂×#332	—	67	1	no	—
203	C₂×#332	—	67	1	no	—
204	C₆₇	C₂×#1679	1	1	yes	characteristic, complemented, Sylow
205	C₂²×SD₁₆	—	134	1	no	—
206	C₂³×C₈	—	134	1	no	—
207	C₂×C₄⋊Q₈	C₂×D₆₇	1	1	yes	characteristic
208	C₂×C₄⋊Q₈	C₂×D₆₇	1	1	yes	characteristic
209	C₂×C₄×D₄	—	67	1	no	—
210	#487	—	2	2	no	—
211	#487	C₂×D₆₇	1	4	yes	complemented
212	#474	—	67	4	no	—
213	#474	—	134	2	no	—
214	#461	—	67	4	no	—
215	#461	—	134	2	no	—
216	C₈×D₄	—	67	4	no	—
217	C₈×D₄	—	134	2	no	—
218	C₂×#107	—	134	1	no	—
219	C₂×C₄⋊C₈	—	67	1	no	—
220	C₂×C₄⋊C₈	—	67	1	no	—
221	C₂×C₄⋊C₈	—	67	1	no	—
222	C₂×#103	—	2	1	no	—
223	C₂×#103	—	2	1	no	—
224	C₂×#103	—	134	1	no	—
225	C₂×#102	—	134	1	no	—
226	C₂×C₂²⋊C₈	—	134	1	no	—
227	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
228	#334	—	67	4	no	—
229	#332	—	67	4	no	—
230	#332	—	67	4	no	—
231	C₂²×Q₈	—	2	1	no	—
232	C₂²×Q₈	—	2	1	no	—
233	C₂²×D₄	—	67	1	no	—
234	C₂³×C₄	—	134	1	no	—
235	C₂×SD₁₆	—	268	4	no	—
236	C₂×SD₁₆	—	134	4	no	—
237	C₂²×C₈	—	268	4	no	—
238	C₂²×C₈	—	134	1	no	—
239	C₂²×C₈	—	134	1	no	—
240	C₂²×C₈	—	134	1	no	—
241	C₂²×C₈	—	134	4	no	—
242	C₂²×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
243	C₂²×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
244	C₄⋊Q₈	—	2	1	no	—
245	C₄⋊Q₈	—	2	1	no	—
246	C₄⋊Q₈	—	2	1	no	—
247	C₄⋊Q₈	—	2	1	no	—
248	C₄⋊Q₈	—	2	1	no	—
249	C₄⋊Q₈	—	2	1	no	—
250	C₄⋊Q₈	C₂²×D₆₇	1	2	yes	—
251	C₄⋊Q₈	C₂²×D₆₇	1	2	yes	—
252	C₄×D₄	—	67	2	no	—
253	C₄×D₄	—	67	2	no	—
254	C₄×D₄	—	134	1	no	—
255	C₄×D₄	—	134	1	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	—	67	1	no	—
261	C₂×C₂²⋊C₄	—	134	1	no	—
262	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
263	#107	—	134	4	no	—
264	C₄⋊C₈	—	67	2	no	—
265	C₄⋊C₈	—	67	2	no	—
266	C₄⋊C₈	—	67	2	no	—
267	C₄⋊C₈	—	134	1	no	—
268	C₄⋊C₈	—	134	1	no	—
269	C₄⋊C₈	—	134	1	no	—
270	#103	—	2	4	no	—
271	#103	—	2	4	no	—
272	#103	—	134	4	no	—
273	#102	—	134	4	no	—
274	C₂²⋊C₈	—	134	4	no	—
275	C₄×C₈	C₂²⋊D₆₇	1	2	yes	—
276	C₄×C₈	C₂²×D₆₇	1	2	yes	—
277	C₂⁴	—	134	1	no	—
278	C₂×Q₈	—	2	2	no	—
279	C₂×Q₈	—	2	2	no	—
280	C₂×Q₈	—	4	1	no	—
281	C₂×Q₈	—	4	1	no	—
282	C₂×Q₈	—	4	2	no	—
283	C₂×Q₈	—	4	2	no	—
284	C₂×Q₈	—	4	2	no	—
285	C₂×Q₈	—	4	2	no	—
286	C₂×D₄	—	67	4	no	—
287	C₂×D₄	—	67	2	no	—
288	C₂×D₄	—	134	1	no	—
289	C₂×D₄	—	134	2	no	—
290	C₂²×C₄	—	4	1	no	—
291	C₂²×C₄	—	4	1	no	—
292	C₂²×C₄	—	268	2	no	—
293	C₂²×C₄	—	268	2	no	—
294	C₂²×C₄	—	134	1	no	—
295	C₂²×C₄	—	134	2	no	—
296	C₂²×C₄	—	134	2	no	—
297	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
298	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
299	C₂²×C₄	#11761627	1	1	yes	characteristic
300	SD₁₆	—	268	8	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	268	8	no	—
304	C₂×C₈	—	268	2	no	—
305	C₂×C₈	—	268	2	no	—
306	C₂×C₈	—	268	2	no	—
307	C₂×C₈	—	134	2	no	—
308	C₂×C₈	—	134	2	no	—
309	C₂×C₈	—	134	2	no	—
310	C₂×C₈	C₂×C₂²⋊D₆₇	1	2	yes	—
311	C₂×C₈	C₂×C₂²⋊D₆₇	1	2	yes	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	4	1	no	—
317	C₄⋊C₄	—	4	1	no	—
318	C₄⋊C₄	—	4	1	no	—
319	C₄⋊C₄	—	4	1	no	—
320	C₄⋊C₄	—	67	2	no	—
321	C₄⋊C₄	—	134	1	no	—
322	C₂²⋊C₄	—	134	2	no	—
323	C₂²⋊C₄	—	134	2	no	—
324	C₄²	D₄×D₆₇	1	1	yes	characteristic
325	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
326	C₄²	#11761627	1	1	yes	characteristic
327	C₄²	C₂³×D₆₇	1	1	yes	characteristic
328	C₂³	—	268	2	no	—
329	C₂³	—	268	2	no	—
330	C₂³	—	134	4	no	—
331	C₂³	—	134	2	no	—
332	C₂³	#14524014	1	1	yes	characteristic
333	Q₈	—	4	2	no	—
334	Q₈	—	4	2	no	—
335	Q₈	—	4	2	no	—
336	Q₈	—	4	2	no	—
337	Q₈	—	8	2	no	—
338	Q₈	—	8	2	no	—
339	D₄	—	67	4	no	—
340	D₄	—	134	4	no	—
341	D₄	—	134	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	8	2	no	—
346	C₂×C₄	—	8	2	no	—
347	C₂×C₄	—	268	2	no	—
348	C₂×C₄	—	268	4	no	—
349	C₂×C₄	—	268	2	no	—
350	C₂×C₄	—	268	2	no	—
351	C₂×C₄	—	134	2	no	—
352	C₂×C₄	#14524014	1	1	yes	characteristic
353	C₂×C₄	#14524014	1	1	yes	characteristic
354	C₂×C₄	#14524014	1	1	yes	characteristic
355	C₂×C₄	SD₁₆×D₆₇	1	2	yes	—
356	C₂×C₄	#14524063	1	2	yes	—
357	C₂×C₄	#14524064	1	2	yes	—
358	C₂×C₄	#14524068	1	2	yes	—
359	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
360	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
361	C₂×C₄	C₂×#11761627	1	1	yes	characteristic
362	C₈	—	2	2	no	—
363	C₈	—	2	2	no	—
364	C₈	—	268	2	no	—
365	C₈	—	268	2	no	—
366	C₈	—	268	2	no	—
367	C₂²	—	268	8	no	—
368	C₂²	—	268	2	no	—
369	C₂²	—	268	2	no	—
370	C₂²	—	134	4	no	—
371	C₂²	#16863608	1	2	yes	—
372	C₂²	#16863622	1	2	yes	—
373	C₂²	#16863668	1	2	yes	—
374	C₂²	C₂×#14524014	1	1	yes	characteristic
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	8	2	no	—
378	C₄	—	8	2	no	—
379	C₄	—	268	2	no	—
380	C₄	#16863608	1	2	yes	—
381	C₄	#16863622	1	2	yes	—
382	C₄	C₂×SD₁₆×D₆₇	1	1	yes	characteristic
383	C₄	C₂×#14524063	1	1	yes	characteristic
384	C₄	C₂×#14524064	1	1	yes	characteristic
385	C₄	C₂×#14524068	1	1	yes	characteristic
386	C₂	—	268	4	no	—
387	C₂	#22559629	1	4	yes	direct product factor
388	C₂	C₂×#16863608	1	1	yes	characteristic
389	C₂	C₂×#16863622	1	1	yes	characteristic
390	C₂	C₂×#16863668	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#14524014
commutator, cosocle	C₄²×C₆₇	C₂⁴
Frattini	C₄²	C₂³×D₆₇
Fitting	C₂×#487×C₆₇	C₂
socle	C₂³×C₆₇	#121
prime radical	C₂²×D₂₆₈	D₄
hypercenter	C₂×#487	D₆₇
hypocenter	C₆₇	C₂×#1679
LCS	G ▷ C₄²×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#487

Complements

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

N	H ≅ G/N	type
4. #22559629	C₂	direct (N × H)
5. C₂×#16863147	C₂	semidirect
6. C₂×#16863142	C₂	semidirect
7. C₂×#16863142	C₂	semidirect
8. C₂×#487×C₆₇	C₂	semidirect
25. #16863147	C₂²	semidirect
26. #16863142	C₂²	semidirect
27. #16863142	C₂²	semidirect
31. #487×C₆₇	C₂²	semidirect
191. C₂×C₆₇	#1679	semidirect
196. C₂×#487	D₆₇	semidirect
204. C₆₇	C₂×#1679	semidirect
211. #487	C₂×D₆₇	semidirect
387. C₂	#22559629	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#16863673	2
C₂×#16863598	2
C₂×C₈×D₂₆₈	2
#22559629	2
C₂×#16863147	2
C₂×#16863142	2
C₂×#487×C₆₇	2
C₂×#1679	67

Subgroups — C2×#22559629 #30838113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22559629 #30838113