Subgroups — C₂×#22562339 #31010400

Order 17152.

658 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14523988	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16863671	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16863666	C₂	1	1	yes	maximal, characteristic
4	#22562339	C₂	1	8	yes	maximal, direct product factor
5	C₂×#16863226	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16863213	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16863210	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#504×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#14524073	—	2	1	no	—
10	C₂×#14524068	—	2	1	no	—
11	C₂²×Dic₂₆₈	C₂²	1	1	yes	characteristic
12	C₂²×D₅₃₆	C₂²	1	1	yes	characteristic
13	C₂×#14523988	—	2	1	no	—
14	C₂×#14523988	—	2	1	no	—
15	C₂×#14523988	—	2	2	no	—
16	C₂×#14523988	C₂²	1	4	yes	complemented
17	#16863671	—	2	2	no	—
18	#16863671	C₂²	1	4	yes	complemented
19	#16863666	—	2	2	no	—
20	#16863666	C₂²	1	4	yes	—
21	C₂×#14523979	C₂²	1	1	yes	characteristic
22	C₂×#14523979	C₂²	1	1	yes	characteristic
23	C₂×#14523961	—	2	1	no	—
24	C₂×#14523959	—	2	1	no	—
25	#16863226	C₂²	1	4	yes	complemented
26	#16863213	C₂²	1	4	yes	complemented
27	#16863210	C₂²	1	4	yes	complemented
28	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic
29	#504×C₆₇	—	2	2	no	—
30	#504×C₆₇	C₂²	1	4	yes	complemented
31	C₂×M₃₂×C₆₇	—	2	1	no	—
32	C₂×M₃₂×C₆₇	C₂²	1	1	yes	characteristic
33	C₂²×C₁₆×C₆₇	—	2	1	no	—
34	C₂²×C₁₆×C₆₇	C₂²	1	1	yes	characteristic
35	C₂²×Dic₁₃₄	—	2	1	no	—
36	C₂²×D₂₆₈	—	2	1	no	—
37	#14524073	—	2	4	no	—
38	#14524073	—	4	2	no	—
39	#14524068	—	2	4	no	—
40	#14524068	—	4	2	no	—
41	C₂×Dic₂₆₈	—	2	1	no	—
42	C₂×Dic₂₆₈	—	2	1	no	—
43	C₂×Dic₂₆₈	—	2	1	no	—
44	C₂×Dic₂₆₈	—	2	1	no	—
45	C₂×Dic₂₆₈	—	2	1	no	—
46	C₂×Dic₂₆₈	C₂³	1	2	yes	—
47	C₂×#11761618	—	4	1	no	—
48	C₂×#11761616	—	4	1	no	—
49	C₂×#11761615	—	4	1	no	—
50	C₂×D₅₃₆	—	2	1	no	—
51	C₂×D₅₃₆	—	2	1	no	—
52	C₂×D₅₃₆	—	2	1	no	—
53	C₂×D₅₃₆	—	2	1	no	—
54	C₂×D₅₃₆	—	2	1	no	—
55	C₂×D₅₃₆	C₂³	1	2	yes	—
56	C₂×#11761613	—	4	1	no	—
57	C₂×#11761612	—	2	1	no	—
58	C₂×#11761612	—	2	1	no	—
59	#14523988	—	2	4	no	—
60	#14523988	—	2	4	no	—
61	#14523979	—	2	1	no	—
62	#14523979	—	2	1	no	—
63	#14523979	C₂³	1	2	yes	—
64	#14523979	C₂³	1	2	yes	—
65	#14523961	—	2	4	no	—
66	#14523959	—	2	4	no	—
67	C₂×#41×C₆₇	D₄	1	1	yes	characteristic
68	#131×C₆₇	—	2	1	no	—
69	#131×C₆₇	—	2	1	no	—
70	#131×C₆₇	D₄	1	2	yes	—
71	#131×C₆₇	C₂³	1	2	yes	—
72	C₂×M₁₆×C₆₇	—	2	1	no	—
73	C₂×M₁₆×C₆₇	D₄	1	1	yes	characteristic
74	C₂²×C₈×C₆₇	—	2	1	no	—
75	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
76	M₃₂×C₆₇	—	2	1	no	—
77	M₃₂×C₆₇	—	2	4	no	—
78	M₃₂×C₆₇	C₂³	1	2	yes	—
79	C₂×C₁₆×C₆₇	—	2	1	no	—
80	C₂×C₁₆×C₆₇	—	2	4	no	—
81	C₂×C₁₆×C₆₇	D₄	1	1	yes	characteristic
82	C₂×C₁₆×C₆₇	D₄	1	1	yes	characteristic
83	C₂×C₁₆×C₆₇	D₄	1	2	yes	—
84	C₂×C₁₆×C₆₇	C₂³	1	2	yes	—
85	C₂³×D₆₇	—	4	1	no	—
86	C₂×Dic₁₃₄	—	2	2	no	—
87	C₂×Dic₁₃₄	—	4	1	no	—
88	C₂×Dic₁₃₄	—	4	1	no	—
89	C₂×Dic₁₃₄	—	4	1	no	—
90	C₂×Dic₁₃₄	—	4	1	no	—
91	C₂×Dic₁₃₄	—	4	1	no	—
92	C₂×D₂₆₈	—	2	2	no	—
93	C₂×D₂₆₈	—	4	1	no	—
94	C₂×D₂₆₈	—	4	1	no	—
95	C₂×D₂₆₈	—	4	1	no	—
96	C₂×D₂₆₈	—	4	1	no	—
97	C₂×D₂₆₈	—	4	1	no	—
98	C₂²×Dic₆₇	—	4	1	no	—
99	Dic₂₆₈	—	2	2	no	—
100	Dic₂₆₈	—	2	2	no	—
101	Dic₂₆₈	—	4	1	no	—
102	Dic₂₆₈	—	4	1	no	—
103	#11761618	—	4	4	no	—
104	#11761616	—	4	4	no	—
105	#11761615	—	4	4	no	—
106	D₅₃₆	—	2	2	no	—
107	D₅₃₆	—	2	2	no	—
108	D₅₃₆	—	4	1	no	—
109	D₅₃₆	—	4	1	no	—
110	#11761613	—	4	4	no	—
111	#11761612	—	2	2	no	—
112	#11761612	—	2	2	no	—
113	#11761612	—	4	1	no	—
114	#11761612	—	4	1	no	—
115	C₂×C₆₇⋊C₈	—	4	1	no	—
116	C₂×C₆₇⋊C₈	—	4	1	no	—
117	#41×C₆₇	—	2	1	no	—
118	#41×C₆₇	—	2	1	no	—
119	#41×C₆₇	D₈	1	2	yes	—
120	#41×C₆₇	C₂×D₄	1	2	yes	—
121	C₂×Q₈×C₆₇	D₈	1	1	yes	characteristic
122	C₂×D₄×C₆₇	—	2	1	no	—
123	C₂×D₄×C₆₇	D₈	1	1	yes	characteristic
124	C₂²×C₄×C₆₇	—	2	1	no	—
125	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
126	M₁₆×C₆₇	—	2	1	no	—
127	M₁₆×C₆₇	—	2	2	no	—
128	M₁₆×C₆₇	—	2	2	no	—
129	M₁₆×C₆₇	C₂×D₄	1	2	yes	—
130	C₂×C₈×C₆₇	—	2	1	no	—
131	C₂×C₈×C₆₇	—	2	2	no	—
132	C₂×C₈×C₆₇	—	2	2	no	—
133	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
134	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
135	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
136	C₂×C₈×C₆₇	#41	1	1	yes	characteristic
137	C₂×C₈×C₆₇	#41	1	1	yes	characteristic
138	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
139	C₁₆×C₆₇	—	2	2	no	—
140	C₁₆×C₆₇	C₂×D₄	1	2	yes	—
141	C₁₆×C₆₇	C₂×D₄	1	2	yes	—
142	C₂³×C₆₇	—	2	1	no	—
143	C₂³×C₆₇	#135	1	1	yes	characteristic
144	C₂²×D₆₇	—	4	2	no	—
145	C₂²×D₆₇	—	8	1	no	—
146	C₂²×D₆₇	—	8	1	no	—
147	C₂²×D₆₇	—	16	2	no	—
148	Q₈×C₆₇	—	2	1	no	—
149	Q₈×C₆₇	C₂×D₈	1	2	yes	—
150	D₄×C₆₇	—	2	2	no	—
151	D₄×C₆₇	—	2	2	no	—
152	D₄×C₆₇	—	2	1	no	—
153	D₄×C₆₇	C₂×D₈	1	2	yes	—
154	C₂×C₄×C₆₇	—	2	1	no	—
155	C₂×C₄×C₆₇	—	2	2	no	—
156	C₂×C₄×C₆₇	—	2	2	no	—
157	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
158	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
159	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
160	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
161	C₂×C₄×C₆₇	#135	1	1	yes	characteristic
162	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
163	C₂×Dic₆₇	—	4	2	no	—
164	C₂×Dic₆₇	—	8	1	no	—
165	C₂×Dic₆₇	—	8	1	no	—
166	D₂₆₈	—	4	2	no	—
167	D₂₆₈	—	4	2	no	—
168	D₂₆₈	—	8	1	no	—
169	D₂₆₈	—	8	1	no	—
170	Dic₁₃₄	—	4	2	no	—
171	Dic₁₃₄	—	4	2	no	—
172	Dic₁₃₄	—	8	1	no	—
173	Dic₁₃₄	—	8	1	no	—
174	C₈×C₆₇	—	2	2	no	—
175	C₈×C₆₇	#121	1	1	yes	characteristic
176	C₈×C₆₇	#121	1	1	yes	characteristic
177	C₈×C₆₇	C₂²×D₄	1	1	yes	characteristic
178	C₈×C₆₇	C₂×#41	1	1	yes	characteristic
179	C₆₇⋊C₈	—	4	2	no	—
180	C₆₇⋊C₈	—	4	2	no	—
181	C₂²×C₆₇	—	2	2	no	—
182	C₂²×C₆₇	—	2	2	no	—
183	C₂²×C₆₇	—	4	2	no	—
184	C₂²×C₆₇	#466	1	1	yes	characteristic
185	C₂²×C₆₇	#466	1	1	yes	characteristic
186	C₂²×C₆₇	C₂×#135	1	1	yes	characteristic
187	C₂×D₆₇	—	8	2	no	—
188	C₂×D₆₇	—	16	2	no	—
189	C₂×D₆₇	—	16	2	no	—
190	C₂×D₆₇	—	16	2	no	—
191	C₄×C₆₇	—	2	2	no	—
192	C₄×C₆₇	#466	1	1	yes	characteristic
193	C₄×C₆₇	#466	1	1	yes	characteristic
194	C₄×C₆₇	C₂×#121	1	1	yes	characteristic
195	C₄×C₆₇	C₂²×D₈	1	1	yes	characteristic
196	Dic₆₇	—	8	2	no	—
197	C₂×#2223	—	67	1	no	maximal, Sylow
198	C₂×C₆₇	—	2	1	no	—
199	C₂×C₆₇	—	2	1	no	—
200	C₂×C₆₇	—	4	2	no	—
201	C₂×C₆₇	#2223	1	2	yes	complemented
202	C₂×C₆₇	C₂×#466	1	1	yes	characteristic
203	D₆₇	—	16	2	no	—
204	C₂²×SD₃₂	—	67	1	no	—
205	C₂×#504	D₆₇	1	1	yes	characteristic, complemented
206	C₂×#473	—	67	1	no	—
207	C₂×#472	—	67	1	no	—
208	#2223	—	67	8	no	—
209	C₂×#368	—	67	1	no	—
210	C₂×#362	—	67	1	no	—
211	C₂×#361	—	67	1	no	—
212	C₆₇	C₂×#2223	1	1	yes	characteristic, complemented, Sylow
213	C₂×#137	—	134	1	no	—
214	C₂×AGL(1,ℤ/8)	—	134	1	no	—
215	C₂²×Q₁₆	—	67	1	no	—
216	C₂²×D₈	—	67	1	no	—
217	C₂×#131	C₂×D₆₇	1	1	yes	characteristic
218	C₂×SD₃₂	—	67	4	no	—
219	C₂×SD₃₂	—	134	1	no	—
220	C₂×SD₃₂	—	134	1	no	—
221	C₂×SD₃₂	—	134	2	no	—
222	#504	—	2	2	no	—
223	#504	C₂×D₆₇	1	4	yes	complemented
224	C₂×M₃₂	—	2	1	no	—
225	C₂×M₃₂	C₂×D₆₇	1	1	yes	characteristic
226	C₂²×C₁₆	—	2	1	no	—
227	C₂²×C₁₆	C₂×D₆₇	1	1	yes	characteristic
228	#473	—	67	4	no	—
229	#473	—	134	2	no	—
230	#472	—	67	4	no	—
231	#472	—	134	2	no	—
232	C₂×#108	—	67	1	no	—
233	C₂×#108	—	67	1	no	—
234	C₂×#101	—	134	1	no	—
235	C₂×#100	—	134	1	no	—
236	#368	—	67	4	no	—
237	#362	—	67	4	no	—
238	#361	—	67	4	no	—
239	C₂×#41	D₂₆₈	1	1	yes	characteristic
240	C₂²×Q₈	—	134	1	no	—
241	C₂²×D₄	—	134	1	no	—
242	#137	—	268	2	no	—
243	#137	—	134	4	no	—
244	AGL(1,ℤ/8)	—	268	2	no	—
245	AGL(1,ℤ/8)	—	134	4	no	—
246	C₂×Q₁₆	—	268	1	no	—
247	C₂×Q₁₆	—	67	2	no	—
248	C₂×Q₁₆	—	134	1	no	—
249	C₂×Q₁₆	—	134	1	no	—
250	C₂×Q₁₆	—	134	1	no	—
251	C₂×Q₁₆	—	134	1	no	—
252	C₂×Q₁₆	—	134	1	no	—
253	C₂×SD₁₆	—	268	1	no	—
254	C₂×SD₁₆	—	268	1	no	—
255	C₂×D₈	—	268	1	no	—
256	C₂×D₈	—	67	2	no	—
257	C₂×D₈	—	134	1	no	—
258	C₂×D₈	—	134	1	no	—
259	C₂×D₈	—	134	1	no	—
260	C₂×D₈	—	134	1	no	—
261	C₂×D₈	—	134	1	no	—
262	#131	—	2	1	no	—
263	#131	—	2	1	no	—
264	#131	D₂₆₈	1	2	yes	—
265	#131	C₂²×D₆₇	1	2	yes	—
266	C₂×M₁₆	—	2	1	no	—
267	C₂×M₁₆	—	134	1	no	—
268	C₂×M₁₆	—	134	1	no	—
269	C₂×M₁₆	D₂₆₈	1	1	yes	characteristic
270	C₂²×C₈	—	2	1	no	—
271	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
272	SD₃₂	—	134	4	no	—
273	SD₃₂	—	134	4	no	—
274	M₃₂	—	2	1	no	—
275	M₃₂	—	2	4	no	—
276	M₃₂	C₂²×D₆₇	1	2	yes	—
277	C₂×C₁₆	—	2	1	no	—
278	C₂×C₁₆	—	2	4	no	—
279	C₂×C₁₆	C₂²⋊D₆₇	1	1	yes	characteristic
280	C₂×C₁₆	C₂²⋊D₆₇	1	1	yes	characteristic
281	C₂×C₁₆	C₂²⋊D₆₇	1	2	yes	—
282	C₂×C₁₆	C₂²×D₆₇	1	2	yes	—
283	#108	—	67	2	no	—
284	#108	—	67	2	no	—
285	#108	—	134	1	no	—
286	#108	—	134	1	no	—
287	#101	—	134	4	no	—
288	#100	—	134	4	no	—
289	C₂⁴	—	268	1	no	—
290	#41	—	2	1	no	—
291	#41	—	2	1	no	—
292	#41	D₅₃₆	1	2	yes	—
293	#41	C₂×D₂₆₈	1	2	yes	—
294	C₂×Q₈	—	268	1	no	—
295	C₂×Q₈	—	268	1	no	—
296	C₂×Q₈	—	268	1	no	—
297	C₂×Q₈	—	268	1	no	—
298	C₂×Q₈	—	268	1	no	—
299	C₂×Q₈	—	134	2	no	—
300	C₂×Q₈	D₅₃₆	1	1	yes	characteristic
301	C₂×D₄	—	2	1	no	—
302	C₂×D₄	—	268	1	no	—
303	C₂×D₄	—	268	1	no	—
304	C₂×D₄	—	268	1	no	—
305	C₂×D₄	—	268	1	no	—
306	C₂×D₄	—	268	1	no	—
307	C₂×D₄	—	134	2	no	—
308	C₂×D₄	D₅₃₆	1	1	yes	characteristic
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	268	1	no	—
311	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
312	Q₁₆	—	268	4	no	—
313	Q₁₆	—	268	1	no	—
314	Q₁₆	—	268	1	no	—
315	Q₁₆	—	134	2	no	—
316	Q₁₆	—	134	2	no	—
317	SD₁₆	—	268	4	no	—
318	SD₁₆	—	268	4	no	—
319	D₈	—	268	4	no	—
320	D₈	—	268	1	no	—
321	D₈	—	268	1	no	—
322	D₈	—	134	2	no	—
323	D₈	—	134	2	no	—
324	M₁₆	—	2	1	no	—
325	M₁₆	—	2	2	no	—
326	M₁₆	—	2	2	no	—
327	M₁₆	—	268	1	no	—
328	M₁₆	—	268	1	no	—
329	M₁₆	—	134	2	no	—
330	M₁₆	—	134	2	no	—
331	M₁₆	C₂×D₂₆₈	1	2	yes	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	268	1	no	—
336	C₂×C₈	—	268	1	no	—
337	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
338	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
339	C₂×C₈	C₂×D₂₆₈	1	1	yes	characteristic
340	C₂×C₈	#11761628	1	1	yes	characteristic
341	C₂×C₈	#11761628	1	1	yes	characteristic
342	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
343	C₁₆	—	2	2	no	—
344	C₁₆	C₂×C₂²⋊D₆₇	1	2	yes	—
345	C₁₆	C₂×C₂²⋊D₆₇	1	2	yes	—
346	C₂³	—	2	1	no	—
347	C₂³	—	268	2	no	—
348	C₂³	—	536	1	no	—
349	C₂³	—	536	1	no	—
350	C₂³	—	1072	2	no	—
351	C₂³	#14524065	1	1	yes	characteristic
352	Q₈	—	2	1	no	—
353	Q₈	—	268	2	no	—
354	Q₈	—	268	2	no	—
355	Q₈	—	536	1	no	—
356	Q₈	—	536	1	no	—
357	Q₈	C₂×D₅₃₆	1	2	yes	—
358	D₄	—	2	2	no	—
359	D₄	—	2	2	no	—
360	D₄	—	2	1	no	—
361	D₄	—	268	2	no	—
362	D₄	—	268	2	no	—
363	D₄	—	536	1	no	—
364	D₄	—	536	1	no	—
365	D₄	C₂×D₅₃₆	1	2	yes	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	268	2	no	—
370	C₂×C₄	—	536	1	no	—
371	C₂×C₄	—	536	1	no	—
372	C₂×C₄	#14524017	1	1	yes	characteristic
373	C₂×C₄	#14524017	1	1	yes	characteristic
374	C₂×C₄	C₂×D₅₃₆	1	1	yes	characteristic
375	C₂×C₄	C₂×D₅₃₆	1	1	yes	characteristic
376	C₂×C₄	#14524065	1	1	yes	characteristic
377	C₂×C₄	C₂²×D₂₆₈	1	1	yes	characteristic
378	C₈	—	2	2	no	—
379	C₈	—	268	2	no	—
380	C₈	—	268	2	no	—
381	C₈	#14524017	1	1	yes	characteristic
382	C₈	#14524017	1	1	yes	characteristic
383	C₈	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
384	C₈	C₂×#11761628	1	1	yes	characteristic
385	C₂²	—	2	2	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	536	2	no	—
389	C₂²	—	1072	2	no	—
390	C₂²	—	1072	2	no	—
391	C₂²	—	1072	2	no	—
392	C₂²	#16863632	1	1	yes	characteristic
393	C₂²	#16863632	1	1	yes	characteristic
394	C₂²	C₂×#14524065	1	1	yes	characteristic
395	C₄	—	2	2	no	—
396	C₄	—	536	2	no	—
397	C₄	#16863632	1	1	yes	characteristic
398	C₄	#16863632	1	1	yes	characteristic
399	C₄	C₂×#14524017	1	1	yes	characteristic
400	C₄	C₂²×D₅₃₆	1	1	yes	characteristic
401	C₂	—	2	1	no	—
402	C₂	—	2	1	no	—
403	C₂	—	4	2	no	—
404	C₂	—	1072	2	no	—
405	C₂	#22562339	1	2	yes	direct product factor
406	C₂	C₂×#16863632	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#16863632
commutator, cosocle	C₂×C₈×C₆₇	C₂⁴
Frattini	C₂×C₈	C₂³×D₆₇
Fitting	C₂×#504×C₆₇	C₂
socle	C₂²×C₆₇	#466
prime radical	C₂×#16863666	C₂
hypercenter	C₂×#504	D₆₇
hypocenter	C₆₇	C₂×#2223
LCS	G ▷ C₂×C₈×C₆₇ ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#131 ◁ C₂×#504

Complements

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

N	H ≅ G/N	type
1. C₂²×#14523988	C₂	semidirect
2. C₂×#16863671	C₂	semidirect
4. #22562339	C₂	direct (N × H)
5. C₂×#16863226	C₂	semidirect
6. C₂×#16863213	C₂	semidirect
7. C₂×#16863210	C₂	semidirect
8. C₂×#504×C₆₇	C₂	semidirect
16. C₂×#14523988	C₂²	semidirect
18. #16863671	C₂²	semidirect
25. #16863226	C₂²	semidirect
26. #16863213	C₂²	semidirect
27. #16863210	C₂²	semidirect
30. #504×C₆₇	C₂²	semidirect
201. C₂×C₆₇	#2223	semidirect
205. C₂×#504	D₆₇	semidirect
212. C₆₇	C₂×#2223	semidirect
223. #504	C₂×D₆₇	semidirect
405. C₂	#22562339	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#14523988	2
C₂×#16863671	2
C₂×#16863666	2
#22562339	2
C₂×#16863226	2
C₂×#16863213	2
C₂×#16863210	2
C₂×#504×C₆₇	2
C₂×#2223	67

Subgroups — C2×#22562339 #31010400

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22562339 #31010400