Subgroups — C₂×#22559657 #30838129

Order 17152.

726 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863683	C₂	1	1	yes	maximal, characteristic
2	C₂×#16863673	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×D₂₆₈	C₂	1	1	yes	maximal, characteristic
4	#22559657	C₂	1	8	yes	maximal, direct product factor
5	C₂×#16863149	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16863145	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×C₈×D₆₇	—	2	1	no	—
10	C₂×C₄×D₂₆₈	C₂²	1	1	yes	characteristic
11	#16863683	—	2	2	no	—
12	#16863683	C₂²	1	4	yes	—
13	#16863673	—	2	2	no	—
14	#16863673	C₂²	1	4	yes	—
15	C₈×D₂₆₈	—	2	2	no	—
16	C₈×D₂₆₈	C₂²	1	4	yes	—
17	C₂×#14523976	—	2	1	no	—
18	C₂×#14523974	—	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×#14523963	—	2	1	no	—
23	C₂×#14523963	—	2	1	no	—
24	C₂×(C₂×D₆₇)⋊C₈	—	2	1	no	—
25	#16863149	C₂²	1	4	yes	complemented
26	#16863145	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	C₂²×C₆₇⋊C₈	—	2	1	no	—
38	C₂²×C₆₇⋊C₈	—	2	1	no	—
39	C₂²×C₆₇⋊C₈	—	2	1	no	—
40	C₂×C₈×D₆₇	—	2	4	no	—
41	C₂×C₈×D₆₇	—	4	4	no	—
42	C₄×D₂₆₈	—	2	1	no	—
43	C₄×D₂₆₈	—	2	1	no	—
44	C₄×D₂₆₈	D₄	1	2	yes	—
45	C₄×D₂₆₈	C₂³	1	2	yes	—
46	C₂×C₄⋊Dic₆₇	D₄	1	1	yes	characteristic
47	C₂×(C₂×D₆₇)⋊C₄	—	2	1	no	—
48	#14523976	—	2	4	no	—
49	#14523974	—	2	4	no	—
50	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
51	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
52	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
53	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
54	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
55	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
56	#14523963	—	2	4	no	—
57	#14523963	—	2	4	no	—
58	(C₂×D₆₇)⋊C₈	—	2	4	no	—
59	C₂²×Q₈×C₆₇	—	2	1	no	—
60	C₂²×Q₈×C₆₇	—	2	1	no	—
61	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
62	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
63	C₄⋊Q₈×C₆₇	—	2	1	no	—
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	C₂³	1	2	yes	—
70	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
71	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
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×C₄²×C₆₇	C₂³	1	1	yes	characteristic
76	#103×C₆₇	—	2	4	no	—
77	#103×C₆₇	—	2	4	no	—
78	C₄×C₈×C₆₇	D₄	1	2	yes	—
79	C₄×C₈×C₆₇	C₂³	1	2	yes	—
80	C₂³×D₆₇	—	2	1	no	—
81	C₂×D₂₆₈	—	2	1	no	—
82	C₂×D₂₆₈	—	2	2	no	—
83	C₂×D₂₆₈	Q₁₆	1	4	yes	—
84	C₂×D₂₆₈	C₂×D₄	1	2	yes	—
85	C₂²×Dic₆₇	—	2	1	no	—
86	C₂×C₄×D₆₇	—	2	2	no	—
87	C₂×C₄×D₆₇	—	2	2	no	—
88	C₂×C₄×D₆₇	—	4	2	no	—
89	C₂×C₄×D₆₇	—	4	2	no	—
90	C₂×C₆₇⋊C₈	—	2	2	no	—
91	C₂×C₆₇⋊C₈	—	2	2	no	—
92	C₂×C₆₇⋊C₈	—	2	2	no	—
93	C₂×C₆₇⋊C₈	—	4	2	no	—
94	C₂×C₆₇⋊C₈	—	4	2	no	—
95	C₂×C₆₇⋊C₈	—	4	2	no	—
96	C₈×D₆₇	—	4	8	no	—
97	C₄⋊Dic₆₇	—	2	1	no	—
98	C₄⋊Dic₆₇	C₂×D₄	1	2	yes	—
99	(C₂×D₆₇)⋊C₄	—	2	2	no	—
100	(C₂×D₆₇)⋊C₄	—	2	2	no	—
101	C₂×Q₈×C₆₇	—	2	2	no	—
102	C₂×Q₈×C₆₇	—	2	2	no	—
103	C₂×Q₈×C₆₇	—	4	1	no	—
104	C₂×Q₈×C₆₇	—	4	1	no	—
105	C₂×Q₈×C₆₇	—	4	2	no	—
106	C₂×Q₈×C₆₇	—	4	2	no	—
107	C₂×Q₈×C₆₇	—	8	2	no	—
108	C₂²×C₄×C₆₇	—	4	1	no	—
109	C₂²×C₄×C₆₇	—	4	1	no	—
110	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
113	C₂×C₈×C₆₇	—	2	2	no	—
114	C₂×C₈×C₆₇	—	2	2	no	—
115	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
116	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
117	C₄⋊C₄×C₆₇	—	2	2	no	—
118	C₄⋊C₄×C₆₇	—	2	2	no	—
119	C₄⋊C₄×C₆₇	—	2	2	no	—
120	C₄⋊C₄×C₆₇	—	2	2	no	—
121	C₄⋊C₄×C₆₇	—	4	1	no	—
122	C₄⋊C₄×C₆₇	—	4	1	no	—
123	C₄⋊C₄×C₆₇	—	4	1	no	—
124	C₄⋊C₄×C₆₇	—	4	1	no	—
125	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₆₇	#41	1	1	yes	characteristic
128	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
129	C₂³×C₆₇	#121	1	1	yes	characteristic
130	C₂²×D₆₇	—	2	2	no	—
131	C₂²×D₆₇	—	2	4	no	—
132	C₂²×D₆₇	—	4	2	no	—
133	C₂²×D₆₇	—	4	2	no	—
134	Q₈×C₆₇	—	4	2	no	—
135	Q₈×C₆₇	—	4	2	no	—
136	Q₈×C₆₇	—	8	2	no	—
137	Q₈×C₆₇	—	8	2	no	—
138	Q₈×C₆₇	—	8	2	no	—
139	C₂×C₄×C₆₇	—	2	2	no	—
140	C₂×C₄×C₆₇	—	4	2	no	—
141	C₂×C₄×C₆₇	—	4	2	no	—
142	C₂×C₄×C₆₇	—	8	2	no	—
143	C₂×C₄×C₆₇	—	8	2	no	—
144	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
145	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
146	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
147	C₂×C₄×C₆₇	C₂×Q₁₆	1	2	yes	—
148	C₂×C₄×C₆₇	#135	1	2	yes	—
149	C₂×C₄×C₆₇	#135	1	2	yes	—
150	C₂×C₄×C₆₇	AGL(1,ℤ/8)	1	2	yes	—
151	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
152	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
153	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
154	C₂×Dic₆₇	—	2	2	no	—
155	C₂×Dic₆₇	—	4	2	no	—
156	D₂₆₈	—	2	2	no	—
157	D₂₆₈	—	2	4	no	—
158	D₂₆₈	C₂×Q₁₆	1	4	yes	—
159	C₄×D₆₇	—	4	2	no	—
160	C₄×D₆₇	—	4	2	no	—
161	C₄×D₆₇	—	4	4	no	—
162	C₈×C₆₇	—	2	2	no	—
163	C₈×C₆₇	—	2	2	no	—
164	C₆₇⋊C₈	—	4	2	no	—
165	C₆₇⋊C₈	—	4	2	no	—
166	C₆₇⋊C₈	—	4	2	no	—
167	C₂²×C₆₇	#463	1	2	yes	—
168	C₂²×C₆₇	#467	1	2	yes	—
169	C₂²×C₆₇	#471	1	2	yes	—
170	C₂²×C₆₇	C₂×#121	1	1	yes	characteristic
171	C₂×D₆₇	—	2	4	no	—
172	C₂×D₆₇	—	4	8	no	—
173	C₂×D₆₇	—	4	2	no	—
174	C₂×D₆₇	—	4	2	no	—
175	C₄×C₆₇	—	2	1	no	—
176	C₄×C₆₇	—	2	1	no	—
177	C₄×C₆₇	—	8	2	no	—
178	C₄×C₆₇	—	8	2	no	—
179	C₄×C₆₇	#463	1	2	yes	—
180	C₄×C₆₇	#467	1	2	yes	—
181	C₄×C₆₇	C₂²×Q₁₆	1	1	yes	characteristic
182	C₄×C₆₇	C₂×#135	1	1	yes	characteristic
183	C₄×C₆₇	C₂×#135	1	1	yes	characteristic
184	C₄×C₆₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
185	Dic₆₇	—	4	2	no	—
186	C₂×#1683	—	67	1	no	maximal, Sylow
187	C₂×C₆₇	#1683	1	4	yes	complemented
188	C₂×C₆₇	C₂×#463	1	1	yes	characteristic
189	C₂×C₆₇	C₂×#467	1	1	yes	characteristic
190	C₂×C₆₇	C₂×#471	1	1	yes	characteristic
191	D₆₇	—	4	4	no	—
192	C₂×#487	D₆₇	1	1	yes	characteristic, complemented
193	C₂×#476	—	67	1	no	—
194	C₂×#474	—	67	1	no	—
195	C₂×C₈×D₄	—	67	1	no	—
196	#1683	—	67	8	no	—
197	C₂×#335	—	67	1	no	—
198	C₂×#333	—	67	1	no	—
199	C₂×#332	—	67	1	no	—
200	C₆₇	C₂×#1683	1	1	yes	characteristic, complemented, Sylow
201	C₂³×C₈	—	134	1	no	—
202	C₂×C₄⋊Q₈	C₂×D₆₇	1	1	yes	characteristic
203	C₂×C₄⋊Q₈	C₂×D₆₇	1	1	yes	characteristic
204	C₂×C₄×D₄	—	67	1	no	—
205	#487	—	2	2	no	—
206	#487	C₂×D₆₇	1	4	yes	complemented
207	#476	—	67	4	no	—
208	#476	—	134	2	no	—
209	#474	—	67	4	no	—
210	#474	—	134	2	no	—
211	C₈×D₄	—	67	4	no	—
212	C₈×D₄	—	134	2	no	—
213	C₂×#107	—	134	1	no	—
214	C₂×#106	—	134	1	no	—
215	C₂×C₄⋊C₈	—	67	1	no	—
216	C₂×C₄⋊C₈	—	67	1	no	—
217	C₂×C₄⋊C₈	—	67	1	no	—
218	C₂×#103	—	2	1	no	—
219	C₂×#103	—	2	1	no	—
220	C₂×#102	—	134	1	no	—
221	C₂×#102	—	134	1	no	—
222	C₂×C₂²⋊C₈	—	134	1	no	—
223	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
224	#335	—	67	4	no	—
225	#333	—	67	4	no	—
226	#332	—	67	4	no	—
227	C₂²×Q₈	—	2	1	no	—
228	C₂²×Q₈	—	2	1	no	—
229	C₂²×D₄	—	67	1	no	—
230	C₂³×C₄	—	134	1	no	—
231	C₂²×C₈	—	268	4	no	—
232	C₂²×C₈	—	134	1	no	—
233	C₂²×C₈	—	134	1	no	—
234	C₂²×C₈	—	134	1	no	—
235	C₂²×C₈	—	134	4	no	—
236	C₂²×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
237	C₂²×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
238	C₄⋊Q₈	—	2	1	no	—
239	C₄⋊Q₈	—	2	1	no	—
240	C₄⋊Q₈	—	2	1	no	—
241	C₄⋊Q₈	—	2	1	no	—
242	C₄⋊Q₈	—	2	1	no	—
243	C₄⋊Q₈	—	2	1	no	—
244	C₄⋊Q₈	C₂²×D₆₇	1	2	yes	—
245	C₄⋊Q₈	C₂²×D₆₇	1	2	yes	—
246	C₄×D₄	—	67	2	no	—
247	C₄×D₄	—	67	2	no	—
248	C₄×D₄	—	134	1	no	—
249	C₄×D₄	—	134	1	no	—
250	C₂×C₄⋊C₄	—	2	1	no	—
251	C₂×C₄⋊C₄	—	2	1	no	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	—	67	1	no	—
255	C₂×C₂²⋊C₄	—	134	1	no	—
256	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
257	#107	—	134	4	no	—
258	#106	—	134	4	no	—
259	C₄⋊C₈	—	67	2	no	—
260	C₄⋊C₈	—	67	2	no	—
261	C₄⋊C₈	—	67	2	no	—
262	C₄⋊C₈	—	134	1	no	—
263	C₄⋊C₈	—	134	1	no	—
264	C₄⋊C₈	—	134	1	no	—
265	#103	—	2	4	no	—
266	#103	—	2	4	no	—
267	#102	—	134	4	no	—
268	#102	—	134	4	no	—
269	C₂²⋊C₈	—	134	4	no	—
270	C₄×C₈	C₂²⋊D₆₇	1	2	yes	—
271	C₄×C₈	C₂²×D₆₇	1	2	yes	—
272	C₂⁴	—	134	1	no	—
273	C₂×Q₈	—	2	2	no	—
274	C₂×Q₈	—	2	2	no	—
275	C₂×Q₈	—	4	1	no	—
276	C₂×Q₈	—	4	1	no	—
277	C₂×Q₈	—	4	2	no	—
278	C₂×Q₈	—	4	2	no	—
279	C₂×Q₈	—	8	2	no	—
280	C₂×D₄	—	67	4	no	—
281	C₂×D₄	—	67	2	no	—
282	C₂×D₄	—	134	1	no	—
283	C₂×D₄	—	134	2	no	—
284	C₂²×C₄	—	4	1	no	—
285	C₂²×C₄	—	4	1	no	—
286	C₂²×C₄	—	268	2	no	—
287	C₂²×C₄	—	268	2	no	—
288	C₂²×C₄	—	134	1	no	—
289	C₂²×C₄	—	134	2	no	—
290	C₂²×C₄	—	134	2	no	—
291	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
292	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
293	C₂²×C₄	#11761627	1	1	yes	characteristic
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	268	8	no	—
297	C₂×C₈	—	268	2	no	—
298	C₂×C₈	—	268	2	no	—
299	C₂×C₈	—	268	2	no	—
300	C₂×C₈	—	134	2	no	—
301	C₂×C₈	—	134	2	no	—
302	C₂×C₈	—	134	2	no	—
303	C₂×C₈	C₂×C₂²⋊D₆₇	1	2	yes	—
304	C₂×C₈	C₂×C₂²⋊D₆₇	1	2	yes	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	4	1	no	—
310	C₄⋊C₄	—	4	1	no	—
311	C₄⋊C₄	—	4	1	no	—
312	C₄⋊C₄	—	4	1	no	—
313	C₄⋊C₄	—	67	2	no	—
314	C₄⋊C₄	—	134	1	no	—
315	C₂²⋊C₄	—	134	2	no	—
316	C₂²⋊C₄	—	134	2	no	—
317	C₄²	D₄×D₆₇	1	1	yes	characteristic
318	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
319	C₄²	#11761627	1	1	yes	characteristic
320	C₄²	C₂³×D₆₇	1	1	yes	characteristic
321	C₂³	—	268	2	no	—
322	C₂³	—	268	2	no	—
323	C₂³	—	134	2	no	—
324	C₂³	—	134	4	no	—
325	C₂³	#14524014	1	1	yes	characteristic
326	Q₈	—	4	2	no	—
327	Q₈	—	4	2	no	—
328	Q₈	—	8	2	no	—
329	Q₈	—	8	2	no	—
330	Q₈	—	8	2	no	—
331	D₄	—	67	4	no	—
332	D₄	—	134	4	no	—
333	D₄	—	134	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	8	2	no	—
338	C₂×C₄	—	8	2	no	—
339	C₂×C₄	—	268	2	no	—
340	C₂×C₄	—	268	4	no	—
341	C₂×C₄	—	268	2	no	—
342	C₂×C₄	—	268	2	no	—
343	C₂×C₄	—	134	2	no	—
344	C₂×C₄	#14524014	1	1	yes	characteristic
345	C₂×C₄	#14524014	1	1	yes	characteristic
346	C₂×C₄	#14524014	1	1	yes	characteristic
347	C₂×C₄	Q₁₆×D₆₇	1	2	yes	—
348	C₂×C₄	#14524063	1	2	yes	—
349	C₂×C₄	#14524066	1	2	yes	—
350	C₂×C₄	#14524068	1	2	yes	—
351	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
352	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
353	C₂×C₄	C₂×#11761627	1	1	yes	characteristic
354	C₈	—	2	2	no	—
355	C₈	—	2	2	no	—
356	C₈	—	268	2	no	—
357	C₈	—	268	2	no	—
358	C₈	—	268	2	no	—
359	C₂²	—	268	2	no	—
360	C₂²	—	268	8	no	—
361	C₂²	—	268	2	no	—
362	C₂²	—	134	4	no	—
363	C₂²	#16863608	1	2	yes	—
364	C₂²	#16863634	1	2	yes	—
365	C₂²	#16863656	1	2	yes	—
366	C₂²	C₂×#14524014	1	1	yes	characteristic
367	C₄	—	2	1	no	—
368	C₄	—	2	1	no	—
369	C₄	—	8	2	no	—
370	C₄	—	8	2	no	—
371	C₄	—	268	2	no	—
372	C₄	#16863608	1	2	yes	—
373	C₄	#16863634	1	2	yes	—
374	C₄	C₂×Q₁₆×D₆₇	1	1	yes	characteristic
375	C₄	C₂×#14524063	1	1	yes	characteristic
376	C₄	C₂×#14524066	1	1	yes	characteristic
377	C₄	C₂×#14524068	1	1	yes	characteristic
378	C₂	—	268	4	no	—
379	C₂	#22559657	1	4	yes	direct product factor
380	C₂	C₂×#16863608	1	1	yes	characteristic
381	C₂	C₂×#16863634	1	1	yes	characteristic
382	C₂	C₂×#16863656	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×#1683
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. #22559657	C₂	direct (N × H)
5. C₂×#16863149	C₂	semidirect
6. C₂×#16863145	C₂	semidirect
7. C₂×#16863142	C₂	semidirect
8. C₂×#487×C₆₇	C₂	semidirect
25. #16863149	C₂²	semidirect
26. #16863145	C₂²	semidirect
27. #16863142	C₂²	semidirect
31. #487×C₆₇	C₂²	semidirect
187. C₂×C₆₇	#1683	semidirect
192. C₂×#487	D₆₇	semidirect
200. C₆₇	C₂×#1683	semidirect
206. #487	C₂×D₆₇	semidirect
379. C₂	#22559657	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×#16863683	2
C₂×#16863673	2
C₂×C₈×D₂₆₈	2
#22559657	2
C₂×#16863149	2
C₂×#16863145	2
C₂×#16863142	2
C₂×#487×C₆₇	2
C₂×#1683	67

Subgroups — C2×#22559657 #30838129

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22559657 #30838129