Subgroups — C₂×#22562336 #31010397

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	C₂×#16863812	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16863668	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16863663	C₂	1	1	yes	maximal, characteristic
4	#22562336	C₂	1	8	yes	maximal, direct product factor
5	C₂×#16863226	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16863212	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16863209	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×SD₃₂×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#14524074	—	2	1	no	—
10	C₂×#14524069	—	2	1	no	—
11	C₂×#14524049	C₂²	1	1	yes	characteristic
12	#16863812	—	2	2	no	—
13	#16863812	C₂²	1	4	yes	complemented
14	C₂×#14523983	C₂²	1	1	yes	characteristic
15	C₂×#14523982	—	2	1	no	—
16	C₂×C₁₆×D₆₇	—	2	1	no	—
17	#16863668	—	2	2	no	—
18	#16863668	C₂²	1	4	yes	complemented
19	#16863663	—	2	2	no	—
20	#16863663	C₂²	1	4	yes	—
21	C₂×#14523979	C₂²	1	1	yes	characteristic
22	C₂×#14523979	C₂²	1	1	yes	characteristic
23	C₂×#14523962	—	2	1	no	—
24	C₂×#14523960	—	2	1	no	—
25	#16863226	C₂²	1	4	yes	complemented
26	#16863212	C₂²	1	4	yes	complemented
27	#16863209	C₂²	1	4	yes	complemented
28	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
29	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×SD₃₂×C₆₇	—	2	1	no	—
31	C₂×SD₃₂×C₆₇	—	2	1	no	—
32	C₂×SD₃₂×C₆₇	—	2	2	no	—
33	C₂×SD₃₂×C₆₇	C₂²	1	4	yes	complemented
34	C₂²×C₁₆×C₆₇	C₂²	1	1	yes	characteristic
35	C₂×#11761628	D₄	1	1	yes	characteristic
36	#14524074	—	2	4	no	—
37	#14524074	—	4	2	no	—
38	#14524069	—	2	4	no	—
39	#14524069	—	4	2	no	—
40	C₂×#11761618	—	4	1	no	—
41	C₂×#11761616	—	4	1	no	—
42	C₂×#11761615	—	4	1	no	—
43	C₂×#11761613	—	4	1	no	—
44	#14524049	—	2	1	no	—
45	#14524049	—	2	1	no	—
46	#14524049	D₄	1	2	yes	—
47	#14524049	C₂³	1	2	yes	—
48	C₂×#11761612	—	2	1	no	—
49	C₂×#11761612	—	2	1	no	—
50	C₂×#11761612	D₄	1	1	yes	characteristic
51	C₂×#11761611	—	2	1	no	—
52	C₂×C₈×D₆₇	—	2	1	no	—
53	#14523983	—	2	1	no	—
54	#14523983	C₂³	1	2	yes	—
55	#14523982	—	2	4	no	—
56	C₂×C₆₇⋊C₁₆	—	2	1	no	—
57	C₁₆×D₆₇	—	2	4	no	—
58	#14523979	—	2	1	no	—
59	#14523979	—	2	1	no	—
60	#14523979	C₂³	1	2	yes	—
61	#14523979	C₂³	1	2	yes	—
62	#14523962	—	2	4	no	—
63	#14523960	—	2	4	no	—
64	C₂²×Q₈×C₆₇	—	2	1	no	—
65	C₂²×D₄×C₆₇	—	2	1	no	—
66	C₂×Q₁₆×C₆₇	—	2	1	no	—
67	C₂×Q₁₆×C₆₇	—	2	1	no	—
68	C₂×Q₁₆×C₆₇	—	2	1	no	—
69	C₂×Q₁₆×C₆₇	—	2	1	no	—
70	C₂×Q₁₆×C₆₇	—	2	1	no	—
71	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
72	C₂×D₈×C₆₇	—	2	1	no	—
73	C₂×D₈×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	C₂³	1	2	yes	—
78	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
79	SD₃₂×C₆₇	—	2	4	no	—
80	SD₃₂×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	#11761628	—	2	1	no	—
86	#11761628	—	2	1	no	—
87	#11761628	D₈	1	2	yes	—
88	#11761628	C₂×D₄	1	2	yes	—
89	C₂×Dic₁₃₄	D₈	1	1	yes	characteristic
90	C₂×D₂₆₈	D₈	1	1	yes	characteristic
91	C₂×C₂²⋊D₆₇	—	2	1	no	—
92	C₂×C₄×D₆₇	—	2	1	no	—
93	#11761618	—	4	4	no	—
94	#11761616	—	4	4	no	—
95	#11761615	—	4	4	no	—
96	#11761613	—	4	4	no	—
97	#11761612	—	2	1	no	—
98	#11761612	—	2	2	no	—
99	#11761612	—	2	2	no	—
100	#11761612	—	4	1	no	—
101	#11761612	—	4	1	no	—
102	#11761612	C₂×D₄	1	2	yes	—
103	#11761611	—	2	2	no	—
104	#11761611	—	2	2	no	—
105	C₂×C₆₇⋊C₈	—	2	1	no	—
106	C₂×C₆₇⋊C₈	—	4	1	no	—
107	C₂×C₆₇⋊C₈	—	4	1	no	—
108	C₈×D₆₇	—	2	2	no	—
109	C₈×D₆₇	—	2	2	no	—
110	C₆₇⋊C₁₆	—	2	2	no	—
111	C₂⁴×C₆₇	—	4	1	no	—
112	C₂×Q₈×C₆₇	—	2	2	no	—
113	C₂×Q₈×C₆₇	—	4	1	no	—
114	C₂×Q₈×C₆₇	—	4	1	no	—
115	C₂×Q₈×C₆₇	—	4	1	no	—
116	C₂×Q₈×C₆₇	—	4	1	no	—
117	C₂×Q₈×C₆₇	—	4	1	no	—
118	C₂×D₄×C₆₇	—	2	2	no	—
119	C₂×D₄×C₆₇	—	4	1	no	—
120	C₂×D₄×C₆₇	—	4	1	no	—
121	C₂×D₄×C₆₇	—	4	1	no	—
122	C₂×D₄×C₆₇	—	4	1	no	—
123	C₂×D₄×C₆₇	—	4	1	no	—
124	C₂²×C₄×C₆₇	—	4	1	no	—
125	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
126	Q₁₆×C₆₇	—	2	2	no	—
127	Q₁₆×C₆₇	—	2	2	no	—
128	Q₁₆×C₆₇	—	4	1	no	—
129	Q₁₆×C₆₇	—	4	1	no	—
130	D₈×C₆₇	—	2	2	no	—
131	D₈×C₆₇	—	2	2	no	—
132	D₈×C₆₇	—	4	1	no	—
133	D₈×C₆₇	—	4	1	no	—
134	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
135	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
136	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
137	C₂×C₈×C₆₇	#41	1	1	yes	characteristic
138	C₂×C₈×C₆₇	#41	1	1	yes	characteristic
139	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
140	C₁₆×C₆₇	C₂×D₄	1	2	yes	—
141	C₁₆×C₆₇	C₂×D₄	1	2	yes	—
142	C₂³×C₆₇	—	4	2	no	—
143	C₂³×C₆₇	—	8	1	no	—
144	C₂³×C₆₇	—	8	1	no	—
145	C₂³×C₆₇	—	16	2	no	—
146	C₂³×C₆₇	#135	1	1	yes	characteristic
147	C₂²×D₆₇	—	2	1	no	—
148	Q₈×C₆₇	—	4	2	no	—
149	Q₈×C₆₇	—	4	2	no	—
150	Q₈×C₆₇	—	8	1	no	—
151	Q₈×C₆₇	—	8	1	no	—
152	D₄×C₆₇	—	4	2	no	—
153	D₄×C₆₇	—	4	2	no	—
154	D₄×C₆₇	—	8	1	no	—
155	D₄×C₆₇	—	8	1	no	—
156	C₂×C₄×C₆₇	—	4	2	no	—
157	C₂×C₄×C₆₇	—	8	1	no	—
158	C₂×C₄×C₆₇	—	8	1	no	—
159	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
160	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
161	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
162	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
163	C₂×C₄×C₆₇	#135	1	1	yes	characteristic
164	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
165	C₂²⋊D₆₇	—	2	2	no	—
166	C₂²⋊D₆₇	—	2	2	no	—
167	C₂×Dic₆₇	—	2	1	no	—
168	D₂₆₈	—	2	1	no	—
169	D₂₆₈	C₂×D₈	1	2	yes	—
170	C₄×D₆₇	—	2	2	no	—
171	C₄×D₆₇	—	2	2	no	—
172	Dic₁₃₄	—	2	1	no	—
173	Dic₁₃₄	C₂×D₈	1	2	yes	—
174	C₈×C₆₇	#121	1	1	yes	characteristic
175	C₈×C₆₇	#121	1	1	yes	characteristic
176	C₈×C₆₇	C₂²×D₄	1	1	yes	characteristic
177	C₈×C₆₇	C₂×#41	1	1	yes	characteristic
178	C₆₇⋊C₈	—	2	2	no	—
179	C₆₇⋊C₈	—	4	2	no	—
180	C₆₇⋊C₈	—	4	2	no	—
181	C₂²×C₆₇	—	2	2	no	—
182	C₂²×C₆₇	—	8	2	no	—
183	C₂²×C₆₇	—	16	2	no	—
184	C₂²×C₆₇	—	16	2	no	—
185	C₂²×C₆₇	—	16	2	no	—
186	C₂²×C₆₇	#466	1	1	yes	characteristic
187	C₂²×C₆₇	#466	1	1	yes	characteristic
188	C₂²×C₆₇	C₂×#135	1	1	yes	characteristic
189	C₂×D₆₇	—	2	2	no	—
190	C₂×D₆₇	—	4	2	no	—
191	C₄×C₆₇	—	8	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	—	2	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	—	16	2	no	—
201	C₂×C₆₇	#2223	1	2	yes	complemented
202	C₂×C₆₇	C₂×#466	1	1	yes	characteristic
203	D₆₇	—	4	2	no	—
204	C₂²×SD₃₂	D₆₇	1	1	yes	characteristic, complemented
205	C₂×#504	—	67	1	no	—
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	C₂×D₆₇	1	1	yes	characteristic
216	C₂²×D₈	C₂×D₆₇	1	1	yes	characteristic
217	C₂×#131	—	67	1	no	—
218	C₂×SD₃₂	—	2	1	no	—
219	C₂×SD₃₂	—	2	1	no	—
220	C₂×SD₃₂	—	2	2	no	—
221	C₂×SD₃₂	C₂×D₆₇	1	4	yes	complemented
222	#504	—	67	4	no	—
223	#504	—	134	2	no	—
224	C₂×M₃₂	—	67	1	no	—
225	C₂×M₃₂	—	134	1	no	—
226	C₂²×C₁₆	—	134	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	—	67	1	no	—
240	C₂²×Q₈	—	2	1	no	—
241	C₂²×D₄	—	2	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	—	2	1	no	—
247	C₂×Q₁₆	—	2	1	no	—
248	C₂×Q₁₆	—	2	1	no	—
249	C₂×Q₁₆	—	2	1	no	—
250	C₂×Q₁₆	—	2	1	no	—
251	C₂×Q₁₆	—	268	1	no	—
252	C₂×Q₁₆	C₂²×D₆₇	1	2	yes	—
253	C₂×SD₁₆	—	268	1	no	—
254	C₂×SD₁₆	—	268	1	no	—
255	C₂×D₈	—	2	1	no	—
256	C₂×D₈	—	2	1	no	—
257	C₂×D₈	—	2	1	no	—
258	C₂×D₈	—	2	1	no	—
259	C₂×D₈	—	2	1	no	—
260	C₂×D₈	—	268	1	no	—
261	C₂×D₈	C₂²×D₆₇	1	2	yes	—
262	#131	—	67	2	no	—
263	#131	—	67	2	no	—
264	#131	—	134	1	no	—
265	#131	—	134	1	no	—
266	C₂×M₁₆	—	67	1	no	—
267	C₂×M₁₆	—	134	1	no	—
268	C₂×M₁₆	—	134	1	no	—
269	C₂×M₁₆	—	134	1	no	—
270	C₂²×C₈	—	134	1	no	—
271	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
272	SD₃₂	—	2	4	no	—
273	SD₃₂	—	2	4	no	—
274	M₃₂	—	67	2	no	—
275	M₃₂	—	134	1	no	—
276	M₃₂	—	134	4	no	—
277	C₂×C₁₆	—	134	1	no	—
278	C₂×C₁₆	—	134	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	—	4	1	no	—
290	#41	—	67	2	no	—
291	#41	—	67	2	no	—
292	#41	—	134	1	no	—
293	#41	—	134	1	no	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	—	4	1	no	—
296	C₂×Q₈	—	4	1	no	—
297	C₂×Q₈	—	4	1	no	—
298	C₂×Q₈	—	4	1	no	—
299	C₂×Q₈	—	4	1	no	—
300	C₂×Q₈	—	67	1	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	4	1	no	—
303	C₂×D₄	—	4	1	no	—
304	C₂×D₄	—	4	1	no	—
305	C₂×D₄	—	4	1	no	—
306	C₂×D₄	—	4	1	no	—
307	C₂×D₄	—	67	1	no	—
308	C₂×D₄	—	134	1	no	—
309	C₂²×C₄	—	4	1	no	—
310	C₂²×C₄	—	134	1	no	—
311	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
312	Q₁₆	—	2	2	no	—
313	Q₁₆	—	2	2	no	—
314	Q₁₆	—	4	1	no	—
315	Q₁₆	—	4	1	no	—
316	Q₁₆	—	268	4	no	—
317	SD₁₆	—	268	4	no	—
318	SD₁₆	—	268	4	no	—
319	D₈	—	2	2	no	—
320	D₈	—	2	2	no	—
321	D₈	—	4	1	no	—
322	D₈	—	4	1	no	—
323	D₈	—	268	4	no	—
324	M₁₆	—	268	1	no	—
325	M₁₆	—	268	1	no	—
326	M₁₆	—	67	2	no	—
327	M₁₆	—	134	2	no	—
328	M₁₆	—	134	2	no	—
329	M₁₆	—	134	1	no	—
330	M₁₆	—	134	2	no	—
331	M₁₆	—	134	2	no	—
332	C₂×C₈	—	268	1	no	—
333	C₂×C₈	—	268	1	no	—
334	C₂×C₈	—	134	1	no	—
335	C₂×C₈	—	134	2	no	—
336	C₂×C₈	—	134	2	no	—
337	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
338	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
339	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
340	C₂×C₈	#11761627	1	1	yes	characteristic
341	C₂×C₈	#11761627	1	1	yes	characteristic
342	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
343	C₁₆	—	134	2	no	—
344	C₁₆	C₂×C₂²⋊D₆₇	1	2	yes	—
345	C₁₆	C₂×C₂²⋊D₆₇	1	2	yes	—
346	C₂³	—	4	2	no	—
347	C₂³	—	8	1	no	—
348	C₂³	—	8	1	no	—
349	C₂³	—	16	2	no	—
350	C₂³	—	134	1	no	—
351	C₂³	#14524062	1	1	yes	characteristic
352	Q₈	—	4	2	no	—
353	Q₈	—	4	2	no	—
354	Q₈	—	8	1	no	—
355	Q₈	—	8	1	no	—
356	Q₈	—	67	2	no	—
357	Q₈	—	134	1	no	—
358	D₄	—	4	2	no	—
359	D₄	—	4	2	no	—
360	D₄	—	8	1	no	—
361	D₄	—	8	1	no	—
362	D₄	—	67	2	no	—
363	D₄	—	134	2	no	—
364	D₄	—	134	2	no	—
365	D₄	—	134	1	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	8	1	no	—
368	C₂×C₄	—	8	1	no	—
369	C₂×C₄	—	134	1	no	—
370	C₂×C₄	—	134	2	no	—
371	C₂×C₄	—	134	2	no	—
372	C₂×C₄	#14524014	1	1	yes	characteristic
373	C₂×C₄	#14524014	1	1	yes	characteristic
374	C₂×C₄	D₈×D₆₇	1	1	yes	characteristic
375	C₂×C₄	D₈×D₆₇	1	1	yes	characteristic
376	C₂×C₄	#14524062	1	1	yes	characteristic
377	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
378	C₈	—	268	2	no	—
379	C₈	—	268	2	no	—
380	C₈	—	134	2	no	—
381	C₈	#14524014	1	1	yes	characteristic
382	C₈	#14524014	1	1	yes	characteristic
383	C₈	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
384	C₈	C₂×#11761627	1	1	yes	characteristic
385	C₂²	—	2	2	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	268	2	no	—
388	C₂²	—	16	2	no	—
389	C₂²	—	16	2	no	—
390	C₂²	—	16	2	no	—
391	C₂²	—	134	2	no	—
392	C₂²	#16863629	1	1	yes	characteristic
393	C₂²	#16863629	1	1	yes	characteristic
394	C₂²	C₂×#14524062	1	1	yes	characteristic
395	C₄	—	8	2	no	—
396	C₄	—	134	2	no	—
397	C₄	#16863629	1	1	yes	characteristic
398	C₄	#16863629	1	1	yes	characteristic
399	C₄	C₂×#14524014	1	1	yes	characteristic
400	C₄	C₂×D₈×D₆₇	1	1	yes	characteristic
401	C₂	—	2	1	no	—
402	C₂	—	2	1	no	—
403	C₂	—	268	2	no	—
404	C₂	—	16	2	no	—
405	C₂	#22562336	1	2	yes	direct product factor
406	C₂	C₂×#16863629	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#16863629
commutator, cosocle	C₂×C₈×C₆₇	C₂⁴
Frattini	C₂×C₈	C₂³×D₆₇
Fitting	C₂²×SD₃₂×C₆₇	C₂
socle	C₂²×C₆₇	#466
prime radical	C₂×#16863663	C₂
hypercenter	C₂²×SD₃₂	D₆₇
hypocenter	C₆₇	C₂×#2223
LCS	G ▷ C₂×C₈×C₆₇ ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×SD₃₂

Complements

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

N	H ≅ G/N	type
1. C₂×#16863812	C₂	semidirect
2. C₂×#16863668	C₂	semidirect
4. #22562336	C₂	direct (N × H)
5. C₂×#16863226	C₂	semidirect
6. C₂×#16863212	C₂	semidirect
7. C₂×#16863209	C₂	semidirect
8. C₂²×SD₃₂×C₆₇	C₂	semidirect
13. #16863812	C₂²	semidirect
18. #16863668	C₂²	semidirect
25. #16863226	C₂²	semidirect
26. #16863212	C₂²	semidirect
27. #16863209	C₂²	semidirect
33. C₂×SD₃₂×C₆₇	C₂²	semidirect
201. C₂×C₆₇	#2223	semidirect
204. C₂²×SD₃₂	D₆₇	semidirect
212. C₆₇	C₂×#2223	semidirect
221. C₂×SD₃₂	C₂×D₆₇	semidirect
405. C₂	#22562336	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×#16863812	2
C₂×#16863668	2
C₂×#16863663	2
#22562336	2
C₂×#16863226	2
C₂×#16863212	2
C₂×#16863209	2
C₂²×SD₃₂×C₆₇	2
C₂×#2223	67

Subgroups — C2×#22562336 #31010397

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22562336 #31010397