Subgroups — C₂×#22562283 #31010209

Order 17152.

790 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863831	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16863771	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16863513	C₂	1	1	yes	maximal, characteristic, complemented
4	#22562283	C₂	1	8	yes	maximal, direct product factor
5	C₂×#16863216	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16863210	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16863209	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#509×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×D₅₃₆	C₂²	1	1	yes	characteristic
10	C₂²×#11761613	—	2	1	no	—
11	C₂×#14524050	—	2	1	no	—
12	C₂×#14524039	—	2	1	no	—
13	#16863831	—	2	2	no	—
14	#16863831	C₂²	1	4	yes	complemented
15	C₂×#14523986	—	2	1	no	—
16	C₂×#14523984	—	2	1	no	—
17	C₂×#14523983	C₂²	1	1	yes	characteristic
18	#16863771	—	2	2	no	—
19	#16863771	C₂²	1	4	yes	complemented
20	#16863513	—	2	2	no	—
21	#16863513	C₂²	1	4	yes	complemented
22	C₂×#14523979	C₂²	1	1	yes	characteristic
23	C₂×#14523970	—	2	1	no	—
24	C₂×C₈×Dic₆₇	C₂²	1	1	yes	characteristic
25	#16863216	C₂²	1	4	yes	complemented
26	#16863210	C₂²	1	4	yes	complemented
27	#16863209	C₂²	1	4	yes	complemented
28	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
29	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic
30	#509×C₆₇	—	2	2	no	—
31	#509×C₆₇	C₂²	1	4	yes	complemented
32	C₂×SD₃₂×C₆₇	—	2	1	no	—
33	C₂×D₁₆×C₆₇	—	2	1	no	—
34	C₂×M₃₂×C₆₇	C₂²	1	1	yes	characteristic
35	C₂²×D₂₆₈	—	2	1	no	—
36	C₂²×C₂²⋊D₆₇	—	4	2	no	—
37	C₂×D₅₃₆	—	2	1	no	—
38	C₂×D₅₃₆	—	2	1	no	—
39	C₂×D₅₃₆	—	2	1	no	—
40	C₂×D₅₃₆	—	2	1	no	—
41	C₂×D₅₃₆	—	2	1	no	—
42	C₂×D₅₃₆	C₂³	1	2	yes	—
43	C₂×#11761613	—	2	4	no	—
44	C₂×#11761613	—	4	1	no	—
45	C₂×#11761613	—	4	1	no	—
46	C₂×#11761613	—	4	2	no	—
47	#14524050	—	2	4	no	—
48	#14524050	—	4	2	no	—
49	C₂×#11761612	—	2	1	no	—
50	C₂×#11761612	—	4	1	no	—
51	C₂²×C₆₇⋊C₈	—	4	1	no	—
52	C₂²×C₆₇⋊C₈	D₄	1	1	yes	characteristic
53	#14524039	—	2	4	no	—
54	#14524039	—	4	2	no	—
55	C₂×C₄×Dic₆₇	D₄	1	1	yes	characteristic
56	#14523986	—	2	4	no	—
57	#14523984	—	2	4	no	—
58	#14523983	—	2	1	no	—
59	#14523983	C₂³	1	2	yes	—
60	C₂×C₆₇⋊C₁₆	—	2	1	no	—
61	#14523979	—	2	1	no	—
62	#14523979	C₂³	1	2	yes	—
63	#14523970	—	2	4	no	—
64	C₈×Dic₆₇	D₄	1	2	yes	—
65	C₈×Dic₆₇	C₂³	1	2	yes	—
66	C₂×#41×C₆₇	—	2	1	no	—
67	C₂²×D₄×C₆₇	—	2	1	no	—
68	#135×C₆₇	—	2	1	no	—
69	#135×C₆₇	—	2	1	no	—
70	#135×C₆₇	D₄	1	2	yes	complemented
71	#135×C₆₇	C₂³	1	2	yes	—
72	C₂×Q₁₆×C₆₇	D₄	1	1	yes	characteristic, complemented
73	C₂×SD₁₆×C₆₇	—	2	1	no	—
74	C₂×D₈×C₆₇	—	2	1	no	—
75	C₂×D₈×C₆₇	—	2	1	no	—
76	C₂×D₈×C₆₇	—	2	1	no	—
77	C₂×D₈×C₆₇	—	2	1	no	—
78	C₂×D₈×C₆₇	—	2	1	no	—
79	C₂×D₈×C₆₇	D₄	1	1	yes	characteristic, complemented
80	C₂×D₈×C₆₇	C₂³	1	2	yes	—
81	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
82	SD₃₂×C₆₇	—	2	4	no	—
83	D₁₆×C₆₇	—	2	4	no	—
84	M₃₂×C₆₇	—	2	1	no	—
85	M₃₂×C₆₇	C₂³	1	2	yes	—
86	C₂×C₁₆×C₆₇	—	2	1	no	—
87	C₂³×D₆₇	—	4	1	no	—
88	C₂×D₂₆₈	—	2	2	no	—
89	C₂×D₂₆₈	—	4	1	no	—
90	C₂×D₂₆₈	—	4	1	no	—
91	C₂×D₂₆₈	—	4	1	no	—
92	C₂×D₂₆₈	—	4	1	no	—
93	C₂×D₂₆₈	—	4	1	no	—
94	C₂×C₂²⋊D₆₇	—	4	8	no	—
95	C₂×C₂²⋊D₆₇	—	8	8	no	—
96	C₂²×Dic₆₇	—	2	1	no	—
97	D₅₃₆	—	2	2	no	—
98	D₅₃₆	—	2	2	no	—
99	D₅₃₆	—	4	1	no	—
100	D₅₃₆	—	4	1	no	—
101	#11761613	—	4	4	no	—
102	#11761613	—	4	4	no	—
103	#11761612	—	2	2	no	—
104	#11761612	—	4	1	no	—
105	#11761612	—	4	4	no	—
106	C₂×C₆₇⋊C₈	—	4	1	no	—
107	C₂×C₆₇⋊C₈	—	4	4	no	—
108	C₂×C₆₇⋊C₈	D₈	1	1	yes	characteristic
109	C₂×C₆₇⋊C₈	D₈	1	1	yes	characteristic
110	C₂×C₆₇⋊C₈	D₈	1	2	yes	—
111	C₂×C₆₇⋊C₈	C₂×D₄	1	2	yes	—
112	C₄×Dic₆₇	—	2	1	no	—
113	C₄×Dic₆₇	C₂×D₄	1	2	yes	—
114	C₆₇⋊C₁₆	—	2	2	no	—
115	C₂⁴×C₆₇	—	4	1	no	—
116	#41×C₆₇	—	2	2	no	—
117	#41×C₆₇	—	2	2	no	—
118	#41×C₆₇	—	4	1	no	—
119	#41×C₆₇	—	4	1	no	—
120	C₂×Q₈×C₆₇	—	2	1	no	—
121	C₂×D₄×C₆₇	—	2	1	no	—
122	C₂×D₄×C₆₇	—	2	2	no	—
123	C₂×D₄×C₆₇	—	4	1	no	—
124	C₂×D₄×C₆₇	—	4	1	no	—
125	C₂×D₄×C₆₇	—	4	1	no	—
126	C₂×D₄×C₆₇	—	4	1	no	—
127	C₂×D₄×C₆₇	—	4	1	no	—
128	C₂×D₄×C₆₇	—	4	1	no	—
129	C₂²×C₄×C₆₇	—	4	1	no	—
130	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
131	Q₁₆×C₆₇	—	2	1	no	—
132	Q₁₆×C₆₇	C₂×D₄	1	2	yes	complemented
133	SD₁₆×C₆₇	—	2	2	no	—
134	SD₁₆×C₆₇	—	2	2	no	—
135	D₈×C₆₇	—	2	1	no	—
136	D₈×C₆₇	—	2	2	no	—
137	D₈×C₆₇	—	2	2	no	—
138	D₈×C₆₇	—	4	1	no	—
139	D₈×C₆₇	—	4	1	no	—
140	D₈×C₆₇	C₂×D₄	1	2	yes	complemented
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	#41	1	1	yes	characteristic
145	C₂×C₈×C₆₇	#41	1	1	yes	characteristic
146	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
147	C₁₆×C₆₇	—	2	2	no	—
148	C₂³×C₆₇	—	4	1	no	—
149	C₂³×C₆₇	—	4	2	no	—
150	C₂³×C₆₇	—	8	4	no	—
151	C₂³×C₆₇	—	8	1	no	—
152	C₂³×C₆₇	—	8	1	no	—
153	C₂³×C₆₇	AGL(1,ℤ/8)	1	1	yes	characteristic
154	C₂²×D₆₇	—	4	2	no	—
155	C₂²×D₆₇	—	8	4	no	—
156	C₂²×D₆₇	—	8	1	no	—
157	C₂²×D₆₇	—	8	1	no	—
158	Q₈×C₆₇	—	2	2	no	—
159	Q₈×C₆₇	—	4	1	no	—
160	D₄×C₆₇	—	2	2	no	—
161	D₄×C₆₇	—	4	2	no	—
162	D₄×C₆₇	—	4	2	no	—
163	D₄×C₆₇	—	4	2	no	—
164	D₄×C₆₇	—	4	2	no	—
165	D₄×C₆₇	—	4	1	no	—
166	D₄×C₆₇	—	8	1	no	—
167	D₄×C₆₇	—	8	1	no	—
168	C₂×C₄×C₆₇	—	4	1	no	—
169	C₂×C₄×C₆₇	—	4	2	no	—
170	C₂×C₄×C₆₇	—	4	2	no	—
171	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
172	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
173	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
174	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
175	C₂×C₄×C₆₇	AGL(1,ℤ/8)	1	1	yes	characteristic
176	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
177	C₂²⋊D₆₇	—	8	16	no	—
178	C₂×Dic₆₇	—	2	4	no	—
179	C₂×Dic₆₇	—	2	2	no	—
180	D₂₆₈	—	4	2	no	—
181	D₂₆₈	—	4	2	no	—
182	D₂₆₈	—	8	1	no	—
183	D₂₆₈	—	8	1	no	—
184	C₈×C₆₇	#121	1	1	yes	characteristic
185	C₈×C₆₇	#121	1	1	yes	characteristic
186	C₈×C₆₇	C₂²×D₄	1	1	yes	characteristic
187	C₈×C₆₇	C₂×#41	1	1	yes	characteristic
188	C₆₇⋊C₈	—	4	2	no	—
189	C₆₇⋊C₈	C₂×D₈	1	2	yes	—
190	C₆₇⋊C₈	C₂×D₈	1	2	yes	—
191	C₂²×C₆₇	—	2	2	no	—
192	C₂²×C₆₇	—	4	2	no	—
193	C₂²×C₆₇	—	8	4	no	—
194	C₂²×C₆₇	—	8	2	no	—
195	C₂²×C₆₇	—	8	2	no	—
196	C₂²×C₆₇	—	16	2	no	—
197	C₂²×C₆₇	—	16	2	no	—
198	C₂²×C₆₇	#459	1	1	yes	characteristic
199	C₂²×C₆₇	#459	1	1	yes	characteristic
200	C₂²×C₆₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
201	C₂×D₆₇	—	8	4	no	—
202	C₂×D₆₇	—	8	2	no	—
203	C₂×D₆₇	—	16	2	no	—
204	C₂×D₆₇	—	16	2	no	—
205	C₄×C₆₇	—	4	2	no	—
206	C₄×C₆₇	#459	1	1	yes	characteristic
207	C₄×C₆₇	#459	1	1	yes	characteristic
208	C₄×C₆₇	C₂×#121	1	1	yes	characteristic
209	C₄×C₆₇	C₂²×D₈	1	1	yes	characteristic
210	Dic₆₇	—	2	4	no	—
211	C₂×#2213	—	67	1	no	maximal, Sylow
212	C₂×C₆₇	—	2	1	no	—
213	C₂×C₆₇	—	2	1	no	—
214	C₂×C₆₇	—	8	2	no	—
215	C₂×C₆₇	—	16	2	no	—
216	C₂×C₆₇	#2213	1	2	yes	complemented
217	C₂×C₆₇	C₂×#459	1	1	yes	characteristic
218	D₆₇	—	16	2	no	—
219	C₂×#509	—	67	1	no	—
220	C₂×#509	D₆₇	1	1	yes	characteristic, complemented
221	C₂×#493	—	67	1	no	—
222	C₂×#443	—	67	1	no	—
223	#2213	—	67	8	no	—
224	C₂×#364	—	67	1	no	—
225	C₂×#361	—	67	1	no	—
226	C₂×#361	—	67	1	no	—
227	C₆₇	C₂×#2213	1	1	yes	characteristic, complemented, Sylow
228	C₂×#135	C₂×D₆₇	1	1	yes	characteristic
229	C₂²×D₈	—	67	1	no	—
230	C₂²×D₈	—	134	1	no	—
231	C₂²×D₈	C₂×D₆₇	1	1	yes	characteristic
232	C₂×#131	—	134	1	no	—
233	C₂×#127	—	134	1	no	—
234	#509	—	2	2	no	—
235	#509	—	67	4	no	—
236	#509	—	134	2	no	—
237	#509	C₂×D₆₇	1	4	yes	complemented
238	C₂×SD₃₂	—	2	1	no	—
239	C₂×SD₃₂	—	134	1	no	—
240	C₂×D₁₆	—	2	1	no	—
241	C₂×D₁₆	—	134	1	no	—
242	C₂×M₃₂	—	67	1	no	—
243	C₂×M₃₂	C₂×D₆₇	1	1	yes	characteristic
244	#493	—	67	4	no	—
245	#493	—	134	2	no	—
246	#443	—	67	4	no	—
247	#443	—	134	2	no	—
248	C₂×#108	—	67	1	no	—
249	C₂×#104	—	134	1	no	—
250	C₂×C₄×C₈	—	67	1	no	—
251	#364	—	67	4	no	—
252	#361	—	67	4	no	—
253	#361	—	67	4	no	—
254	C₂×#41	—	2	1	no	—
255	C₂²×D₄	—	2	1	no	—
256	C₂²×D₄	—	268	2	no	—
257	C₂²×D₄	—	134	1	no	—
258	#135	—	2	1	no	—
259	#135	—	2	1	no	—
260	#135	C₂²⋊D₆₇	1	2	yes	complemented
261	#135	C₂²×D₆₇	1	2	yes	—
262	C₂×Q₁₆	C₂²⋊D₆₇	1	1	yes	characteristic, complemented
263	C₂×SD₁₆	—	2	1	no	—
264	C₂×D₈	—	2	1	no	—
265	C₂×D₈	—	2	1	no	—
266	C₂×D₈	—	2	1	no	—
267	C₂×D₈	—	2	1	no	—
268	C₂×D₈	—	2	1	no	—
269	C₂×D₈	—	268	1	no	—
270	C₂×D₈	—	268	1	no	—
271	C₂×D₈	—	268	2	no	—
272	C₂×D₈	—	67	2	no	—
273	C₂×D₈	—	134	4	no	—
274	C₂×D₈	—	134	1	no	—
275	C₂×D₈	—	134	1	no	—
276	C₂×D₈	—	134	1	no	—
277	C₂×D₈	—	134	1	no	—
278	C₂×D₈	—	134	1	no	—
279	C₂×D₈	C₂²⋊D₆₇	1	1	yes	characteristic, complemented
280	C₂×D₈	C₂²×D₆₇	1	2	yes	—
281	#131	—	268	2	no	—
282	#131	—	134	4	no	—
283	C₂×M₁₆	—	268	1	no	—
284	C₂×M₁₆	—	134	1	no	—
285	C₂²×C₈	—	268	1	no	—
286	C₂²×C₈	—	67	1	no	—
287	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
288	#127	—	268	2	no	—
289	#127	—	134	4	no	—
290	C₂×C₄²	—	67	1	no	—
291	SD₃₂	—	2	4	no	—
292	SD₃₂	—	134	4	no	—
293	D₁₆	—	2	4	no	—
294	D₁₆	—	134	4	no	—
295	M₃₂	—	2	1	no	—
296	M₃₂	—	67	2	no	—
297	M₃₂	—	134	1	no	—
298	M₃₂	C₂²×D₆₇	1	2	yes	—
299	C₂×C₁₆	—	2	1	no	—
300	C₂×C₁₆	—	134	1	no	—
301	#108	—	67	2	no	—
302	#108	—	134	1	no	—
303	#104	—	134	4	no	—
304	C₄×C₈	—	67	2	no	—
305	C₄×C₈	—	67	2	no	—
306	C₂⁴	—	4	1	no	—
307	C₂⁴	—	268	1	no	—
308	#41	—	2	2	no	—
309	#41	—	2	2	no	—
310	#41	—	4	1	no	—
311	#41	—	4	1	no	—
312	C₂×Q₈	—	2	1	no	—
313	C₂×D₄	—	2	1	no	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	—	4	1	no	—
316	C₂×D₄	—	4	1	no	—
317	C₂×D₄	—	4	1	no	—
318	C₂×D₄	—	4	1	no	—
319	C₂×D₄	—	4	1	no	—
320	C₂×D₄	—	4	1	no	—
321	C₂×D₄	—	268	8	no	—
322	C₂×D₄	—	268	1	no	—
323	C₂×D₄	—	268	1	no	—
324	C₂×D₄	—	268	1	no	—
325	C₂×D₄	—	268	1	no	—
326	C₂×D₄	—	268	1	no	—
327	C₂×D₄	—	536	8	no	—
328	C₂×D₄	—	134	2	no	—
329	C₂²×C₄	—	4	1	no	—
330	C₂²×C₄	—	134	1	no	—
331	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
332	Q₁₆	—	2	1	no	—
333	Q₁₆	C₂×C₂²⋊D₆₇	1	2	yes	complemented
334	SD₁₆	—	2	2	no	—
335	SD₁₆	—	2	2	no	—
336	D₈	—	2	1	no	—
337	D₈	—	2	2	no	—
338	D₈	—	2	2	no	—
339	D₈	—	4	1	no	—
340	D₈	—	4	1	no	—
341	D₈	—	268	4	no	—
342	D₈	—	268	4	no	—
343	D₈	—	268	1	no	—
344	D₈	—	268	1	no	—
345	D₈	—	134	2	no	—
346	D₈	—	134	2	no	—
347	D₈	C₂×C₂²⋊D₆₇	1	2	yes	complemented
348	M₁₆	—	268	1	no	—
349	M₁₆	—	268	4	no	—
350	M₁₆	—	134	2	no	—
351	C₂×C₈	—	268	1	no	—
352	C₂×C₈	—	268	4	no	—
353	C₂×C₈	—	67	1	no	—
354	C₂×C₈	—	67	1	no	—
355	C₂×C₈	—	67	2	no	—
356	C₂×C₈	—	67	2	no	—
357	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
358	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
359	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
360	C₂×C₈	#11761627	1	1	yes	characteristic
361	C₂×C₈	#11761627	1	1	yes	characteristic
362	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
363	C₄²	—	67	2	no	—
364	C₄²	—	134	1	no	—
365	C₁₆	—	2	2	no	—
366	C₁₆	—	134	2	no	—
367	C₂³	—	4	1	no	—
368	C₂³	—	4	2	no	—
369	C₂³	—	8	4	no	—
370	C₂³	—	8	1	no	—
371	C₂³	—	8	1	no	—
372	C₂³	—	268	2	no	—
373	C₂³	—	536	4	no	—
374	C₂³	—	536	1	no	—
375	C₂³	—	536	1	no	—
376	C₂³	#14524067	1	1	yes	characteristic
377	Q₈	—	2	2	no	—
378	Q₈	—	4	1	no	—
379	D₄	—	2	2	no	—
380	D₄	—	4	2	no	—
381	D₄	—	4	2	no	—
382	D₄	—	4	1	no	—
383	D₄	—	4	2	no	—
384	D₄	—	4	2	no	—
385	D₄	—	8	1	no	—
386	D₄	—	8	1	no	—
387	D₄	—	268	2	no	—
388	D₄	—	268	2	no	—
389	D₄	—	536	16	no	—
390	D₄	—	536	1	no	—
391	D₄	—	536	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	134	4	no	—
396	C₂×C₄	—	134	2	no	—
397	C₂×C₄	#14524015	1	1	yes	characteristic
398	C₂×C₄	#14524015	1	1	yes	characteristic
399	C₂×C₄	D₈×D₆₇	1	1	yes	characteristic
400	C₂×C₄	D₈×D₆₇	1	1	yes	characteristic
401	C₂×C₄	#14524067	1	1	yes	characteristic
402	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
403	C₈	—	268	2	no	—
404	C₈	—	67	2	no	—
405	C₈	—	67	2	no	—
406	C₈	#14524015	1	1	yes	characteristic
407	C₈	#14524015	1	1	yes	characteristic
408	C₈	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
409	C₈	C₂×#11761627	1	1	yes	characteristic
410	C₂²	—	2	2	no	—
411	C₂²	—	4	2	no	—
412	C₂²	—	8	4	no	—
413	C₂²	—	8	2	no	—
414	C₂²	—	8	2	no	—
415	C₂²	—	16	2	no	—
416	C₂²	—	16	2	no	—
417	C₂²	—	536	4	no	—
418	C₂²	—	536	2	no	—
419	C₂²	—	1072	2	no	—
420	C₂²	—	1072	2	no	—
421	C₂²	#16863589	1	1	yes	characteristic
422	C₂²	#16863589	1	1	yes	characteristic
423	C₂²	C₂×#14524067	1	1	yes	characteristic
424	C₄	—	4	2	no	—
425	C₄	—	134	4	no	—
426	C₄	#16863589	1	1	yes	characteristic
427	C₄	#16863589	1	1	yes	characteristic
428	C₄	C₂×#14524015	1	1	yes	characteristic
429	C₄	C₂×D₈×D₆₇	1	1	yes	characteristic
430	C₂	—	2	1	no	—
431	C₂	—	2	1	no	—
432	C₂	—	8	2	no	—
433	C₂	—	16	2	no	—
434	C₂	—	1072	2	no	—
435	C₂	#22562283	1	2	yes	direct product factor
436	C₂	C₂×#16863589	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#16863589
commutator, cosocle	C₂×C₈×C₆₇	C₂⁴
Frattini	C₂×C₈	C₂³×D₆₇
Fitting	C₂×#509×C₆₇	C₂
socle	C₂²×C₆₇	#459
hypercenter	C₂×#509	D₆₇
hypocenter	C₆₇	C₂×#2213
LCS	G ▷ C₂×C₈×C₆₇ ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#509

Complements

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

N	H ≅ G/N	type
1. C₂×#16863831	C₂	semidirect
2. C₂×#16863771	C₂	semidirect
3. C₂×#16863513	C₂	semidirect
4. #22562283	C₂	direct (N × H)
5. C₂×#16863216	C₂	semidirect
6. C₂×#16863210	C₂	semidirect
7. C₂×#16863209	C₂	semidirect
8. C₂×#509×C₆₇	C₂	semidirect
14. #16863831	C₂²	semidirect
19. #16863771	C₂²	semidirect
21. #16863513	C₂²	semidirect
25. #16863216	C₂²	semidirect
26. #16863210	C₂²	semidirect
27. #16863209	C₂²	semidirect
31. #509×C₆₇	C₂²	semidirect
70. #135×C₆₇	D₄	semidirect
72. C₂×Q₁₆×C₆₇	D₄	semidirect
79. C₂×D₈×C₆₇	D₄	semidirect
132. Q₁₆×C₆₇	C₂×D₄	semidirect
140. D₈×C₆₇	C₂×D₄	semidirect
216. C₂×C₆₇	#2213	semidirect
220. C₂×#509	D₆₇	semidirect
227. C₆₇	C₂×#2213	semidirect
237. #509	C₂×D₆₇	semidirect
260. #135	C₂²⋊D₆₇	semidirect
262. C₂×Q₁₆	C₂²⋊D₆₇	semidirect
279. C₂×D₈	C₂²⋊D₆₇	semidirect
333. Q₁₆	C₂×C₂²⋊D₆₇	semidirect
347. D₈	C₂×C₂²⋊D₆₇	semidirect
435. C₂	#22562283	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×#16863831	2
C₂×#16863771	2
C₂×#16863513	2
#22562283	2
C₂×#16863216	2
C₂×#16863210	2
C₂×#16863209	2
C₂×#509×C₆₇	2
C₂×#2213	67

Subgroups — C2×#22562283 #31010209

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22562283 #31010209