Subgroups — C₂×#22559708 #30838352

Order 17152.

726 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863794	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16863686	C₂	1	1	yes	maximal, characteristic
3	C₂×#16863601	C₂	1	1	yes	maximal, characteristic
4	#22559708	C₂	1	8	yes	maximal, direct product factor
5	C₂×#16863149	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16863144	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16863141	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#436×C₆₇	C₂	1	1	yes	maximal, characteristic
9	C₂²×#11761616	—	2	1	no	—
10	C₂×#14524043	C₂²	1	1	yes	characteristic
11	C₂×#14524043	C₂²	1	1	yes	characteristic
12	#16863794	—	2	2	no	—
13	#16863794	C₂²	1	4	yes	complemented
14	#16863686	—	2	2	no	—
15	#16863686	C₂²	1	4	yes	—
16	#16863601	—	2	2	no	—
17	#16863601	C₂²	1	4	yes	—
18	C₂×#14523975	—	2	1	no	—
19	C₂×#14523975	—	2	1	no	—
20	C₂×#14523974	—	2	1	no	—
21	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
23	C₂×#14523966	—	2	1	no	—
24	C₂×#14523964	—	2	1	no	—
25	#16863149	C₂²	1	4	yes	complemented
26	#16863144	C₂²	1	4	yes	complemented
27	#16863141	C₂²	1	4	yes	complemented
28	C₂²×M₁₆×C₆₇	—	2	1	no	—
29	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
30	#436×C₆₇	—	2	2	no	—
31	#436×C₆₇	C₂²	1	4	yes	—
32	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊C₈×C₆₇	—	2	1	no	—
34	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
35	C₂²×Dic₁₃₄	—	2	1	no	—
36	C₂²×Dic₁₃₄	—	2	1	no	—
37	C₂×#11761616	—	2	4	no	—
38	C₂×#11761616	—	4	4	no	—
39	C₂²×C₆₇⋊C₈	—	2	1	no	—
40	C₂²×C₆₇⋊C₈	—	2	1	no	—
41	#14524043	—	2	1	no	—
42	#14524043	—	2	1	no	—
43	#14524043	—	2	1	no	—
44	#14524043	—	2	1	no	—
45	#14524043	—	2	1	no	—
46	#14524043	—	2	1	no	—
47	#14524043	C₂³	1	2	yes	—
48	#14524043	C₂³	1	2	yes	—
49	C₂×C₄⋊Dic₆₇	—	2	1	no	—
50	C₂×C₄⋊Dic₆₇	—	2	1	no	—
51	C₂×C₄⋊Dic₆₇	—	2	1	no	—
52	C₂×C₄⋊Dic₆₇	—	2	1	no	—
53	#14523975	—	2	4	no	—
54	#14523975	—	2	4	no	—
55	#14523974	—	2	4	no	—
56	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
57	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
58	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
59	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
60	#14523966	—	2	4	no	—
61	#14523964	—	2	4	no	—
62	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
63	C₂³×C₄×C₆₇	—	2	1	no	—
64	C₂×M₁₆×C₆₇	—	2	4	no	—
65	C₂×M₁₆×C₆₇	—	4	4	no	—
66	C₂²×C₈×C₆₇	—	2	1	no	—
67	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
68	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
69	C₄×D₄×C₆₇	—	2	1	no	—
70	C₄×D₄×C₆₇	—	2	1	no	—
71	C₄×D₄×C₆₇	D₄	1	2	yes	—
72	C₄×D₄×C₆₇	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
74	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
75	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
76	C₄⋊C₈×C₆₇	—	2	1	no	—
77	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
78	C₂²⋊C₈×C₆₇	—	2	4	no	—
79	C₄×C₈×C₆₇	D₄	1	2	yes	—
80	C₄×C₈×C₆₇	C₂³	1	2	yes	—
81	C₂×Dic₁₃₄	—	2	2	no	—
82	C₂×Dic₁₃₄	—	2	2	no	—
83	C₂×Dic₁₃₄	—	4	2	no	—
84	C₂×Dic₁₃₄	—	4	2	no	—
85	C₂×Dic₁₃₄	—	4	1	no	—
86	C₂×Dic₁₃₄	—	4	1	no	—
87	C₂×Dic₁₃₄	—	8	2	no	—
88	C₂²×Dic₆₇	—	4	1	no	—
89	C₂²×Dic₆₇	—	4	1	no	—
90	#11761616	—	4	8	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	C₄⋊Dic₆₇	—	2	2	no	—
96	C₄⋊Dic₆₇	—	2	2	no	—
97	C₄⋊Dic₆₇	—	2	2	no	—
98	C₄⋊Dic₆₇	—	2	2	no	—
99	C₄⋊Dic₆₇	—	4	1	no	—
100	C₄⋊Dic₆₇	—	4	1	no	—
101	C₄⋊Dic₆₇	—	4	1	no	—
102	C₄⋊Dic₆₇	—	4	1	no	—
103	C₂⁴×C₆₇	—	2	1	no	—
104	C₂×D₄×C₆₇	—	2	1	no	—
105	C₂×D₄×C₆₇	—	2	2	no	—
106	C₂×D₄×C₆₇	—	2	2	no	—
107	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₆₇	—	2	1	no	—
109	C₂²×C₄×C₆₇	—	2	2	no	—
110	C₂²×C₄×C₆₇	—	2	2	no	—
111	C₂²×C₄×C₆₇	—	4	2	no	—
112	C₂²×C₄×C₆₇	—	4	2	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	M₁₆×C₆₇	—	4	8	no	—
117	C₂×C₈×C₆₇	—	2	2	no	—
118	C₂×C₈×C₆₇	—	2	2	no	—
119	C₂×C₈×C₆₇	—	4	2	no	—
120	C₂×C₈×C₆₇	SD₁₆	1	4	yes	complemented
121	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
122	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
123	C₄⋊C₄×C₆₇	—	2	1	no	—
124	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
125	C₂²⋊C₄×C₆₇	—	2	2	no	—
126	C₂²⋊C₄×C₆₇	—	2	2	no	—
127	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₆₇	#41	1	1	yes	characteristic
130	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
131	C₂³×C₆₇	—	2	2	no	—
132	C₂³×C₆₇	—	4	2	no	—
133	C₂³×C₆₇	—	4	2	no	—
134	C₂³×C₆₇	—	4	2	no	—
135	C₂³×C₆₇	#121	1	1	yes	characteristic
136	D₄×C₆₇	—	2	2	no	—
137	D₄×C₆₇	—	2	2	no	—
138	D₄×C₆₇	—	4	2	no	—
139	C₂×C₄×C₆₇	—	2	2	no	—
140	C₂×C₄×C₆₇	—	2	2	no	—
141	C₂×C₄×C₆₇	—	4	2	no	—
142	C₂×C₄×C₆₇	—	4	2	no	—
143	C₂×C₄×C₆₇	—	4	2	no	—
144	C₂×C₄×C₆₇	—	4	4	no	—
145	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
146	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
147	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
148	C₂×C₄×C₆₇	C₂×SD₁₆	1	2	yes	—
149	C₂×C₄×C₆₇	AGL(1,ℤ/8)	1	2	yes	—
150	C₂×C₄×C₆₇	#137	1	2	yes	—
151	C₂×C₄×C₆₇	#137	1	2	yes	—
152	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
153	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
154	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
155	C₂×Dic₆₇	—	4	2	no	—
156	C₂×Dic₆₇	—	4	2	no	—
157	C₂×Dic₆₇	—	8	2	no	—
158	C₂×Dic₆₇	—	8	2	no	—
159	Dic₁₃₄	—	4	2	no	—
160	Dic₁₃₄	—	4	2	no	—
161	Dic₁₃₄	—	8	2	no	—
162	Dic₁₃₄	—	8	2	no	—
163	Dic₁₃₄	—	8	2	no	—
164	C₈×C₆₇	—	2	2	no	—
165	C₈×C₆₇	—	4	2	no	—
166	C₈×C₆₇	C₂×SD₁₆	1	4	yes	complemented
167	C₆₇⋊C₈	—	4	2	no	—
168	C₆₇⋊C₈	—	4	2	no	—
169	C₂²×C₆₇	—	4	2	no	—
170	C₂²×C₆₇	—	4	2	no	—
171	C₂²×C₆₇	—	4	2	no	—
172	C₂²×C₆₇	—	8	4	no	—
173	C₂²×C₆₇	#461	1	2	yes	—
174	C₂²×C₆₇	#468	1	2	yes	—
175	C₂²×C₆₇	#471	1	2	yes	—
176	C₂²×C₆₇	C₂×#121	1	1	yes	characteristic
177	C₄×C₆₇	—	2	1	no	—
178	C₄×C₆₇	—	2	1	no	—
179	C₄×C₆₇	—	4	2	no	—
180	C₄×C₆₇	#461	1	2	yes	—
181	C₄×C₆₇	#468	1	2	yes	—
182	C₄×C₆₇	C₂²×SD₁₆	1	1	yes	characteristic
183	C₄×C₆₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
184	C₄×C₆₇	C₂×#137	1	1	yes	characteristic
185	C₄×C₆₇	C₂×#137	1	1	yes	characteristic
186	Dic₆₇	—	8	2	no	—
187	Dic₆₇	—	8	2	no	—
188	C₂×#1691	—	67	1	no	maximal, Sylow
189	C₂×C₆₇	—	8	2	no	—
190	C₂×C₆₇	#1691	1	4	yes	complemented
191	C₂×C₆₇	C₂×#461	1	1	yes	characteristic
192	C₂×C₆₇	C₂×#468	1	1	yes	characteristic
193	C₂×C₆₇	C₂×#471	1	1	yes	characteristic
194	C₂×#498	—	67	1	no	—
195	C₂×#476	—	67	1	no	—
196	C₂×#461	—	67	1	no	—
197	C₂×#436	D₆₇	1	1	yes	characteristic
198	#1691	—	67	8	no	—
199	C₂×#335	—	67	1	no	—
200	C₂×#333	—	67	1	no	—
201	C₂×#332	—	67	1	no	—
202	C₆₇	C₂×#1691	1	1	yes	characteristic, complemented, Sylow
203	C₂²×SD₁₆	—	134	1	no	—
204	C₂²×M₁₆	—	2	1	no	—
205	C₂×C₄⋊Q₈	—	67	1	no	—
206	C₂×C₄⋊Q₈	—	67	1	no	—
207	C₂×C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
208	#498	—	67	4	no	—
209	#498	—	134	2	no	—
210	#476	—	67	4	no	—
211	#476	—	134	2	no	—
212	#461	—	67	4	no	—
213	#461	—	134	2	no	—
214	#436	—	2	2	no	—
215	#436	C₂×D₆₇	1	4	yes	—
216	C₂×#106	—	134	1	no	—
217	C₂×#106	—	134	1	no	—
218	C₂×#106	—	134	1	no	—
219	C₂×C₄⋊C₈	—	67	1	no	—
220	C₂×C₄⋊C₈	—	67	1	no	—
221	C₂×C₄⋊C₈	C₂×D₆₇	1	1	yes	characteristic
222	C₂×#103	—	134	1	no	—
223	C₂×#102	—	134	1	no	—
224	C₂×C₂²⋊C₈	—	2	1	no	—
225	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
226	#335	—	67	4	no	—
227	#333	—	67	4	no	—
228	#332	—	67	4	no	—
229	C₂²×Q₈	—	134	1	no	—
230	C₂²×Q₈	—	134	1	no	—
231	C₂²×D₄	D₂₆₈	1	1	yes	characteristic
232	C₂³×C₄	—	2	1	no	—
233	C₂×SD₁₆	—	268	4	no	—
234	C₂×SD₁₆	—	134	4	no	—
235	C₂×M₁₆	—	2	4	no	—
236	C₂×M₁₆	—	4	4	no	—
237	C₂²×C₈	—	2	1	no	—
238	C₂²×C₈	—	134	1	no	—
239	C₂²×C₈	—	134	1	no	—
240	C₂²×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
241	C₂²×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
242	C₄⋊Q₈	—	67	2	no	—
243	C₄⋊Q₈	—	67	2	no	—
244	C₄⋊Q₈	—	134	1	no	—
245	C₄⋊Q₈	—	134	1	no	—
246	C₄⋊Q₈	—	134	1	no	—
247	C₄⋊Q₈	—	134	1	no	—
248	C₄⋊Q₈	—	134	1	no	—
249	C₄⋊Q₈	—	134	1	no	—
250	C₄×D₄	—	2	1	no	—
251	C₄×D₄	—	2	1	no	—
252	C₄×D₄	D₂₆₈	1	2	yes	—
253	C₄×D₄	C₂²×D₆₇	1	2	yes	—
254	C₂×C₄⋊C₄	—	134	1	no	—
255	C₂×C₄⋊C₄	—	134	1	no	—
256	C₂×C₄⋊C₄	—	134	1	no	—
257	C₂×C₄⋊C₄	—	134	1	no	—
258	C₂×C₄⋊C₄	D₂₆₈	1	1	yes	characteristic
259	C₂×C₂²⋊C₄	—	2	1	no	—
260	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
261	#106	—	134	4	no	—
262	#106	—	134	4	no	—
263	#106	—	134	4	no	—
264	C₄⋊C₈	—	2	1	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	C₂²×D₆₇	1	2	yes	—
270	#103	—	134	4	no	—
271	#102	—	134	4	no	—
272	C₂²⋊C₈	—	2	4	no	—
273	C₄×C₈	C₂²⋊D₆₇	1	2	yes	—
274	C₄×C₈	C₂²×D₆₇	1	2	yes	—
275	C₂⁴	—	2	1	no	—
276	C₂×Q₈	—	268	1	no	—
277	C₂×Q₈	—	268	1	no	—
278	C₂×Q₈	—	268	2	no	—
279	C₂×Q₈	—	268	2	no	—
280	C₂×Q₈	—	536	2	no	—
281	C₂×Q₈	—	134	2	no	—
282	C₂×Q₈	—	134	2	no	—
283	C₂×D₄	—	2	1	no	—
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	C₂×D₂₆₈	1	2	yes	—
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	4	2	no	—
291	C₂²×C₄	—	4	2	no	—
292	C₂²×C₄	—	268	1	no	—
293	C₂²×C₄	—	268	1	no	—
294	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
295	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
296	C₂²×C₄	#11761628	1	1	yes	characteristic
297	SD₁₆	—	268	8	no	—
298	M₁₆	—	4	8	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	4	2	no	—
302	C₂×C₈	—	268	2	no	—
303	C₂×C₈	—	268	2	no	—
304	C₂×C₈	—	134	2	no	—
305	C₂×C₈	—	134	2	no	—
306	C₂×C₈	#11761616	1	4	yes	complemented
307	C₂×C₈	C₂×C₂²⋊D₆₇	1	2	yes	—
308	C₂×C₈	C₂×C₂²⋊D₆₇	1	2	yes	—
309	C₄⋊C₄	—	2	1	no	—
310	C₄⋊C₄	—	268	1	no	—
311	C₄⋊C₄	—	268	1	no	—
312	C₄⋊C₄	—	268	1	no	—
313	C₄⋊C₄	—	268	1	no	—
314	C₄⋊C₄	—	134	2	no	—
315	C₄⋊C₄	—	134	2	no	—
316	C₄⋊C₄	—	134	2	no	—
317	C₄⋊C₄	—	134	2	no	—
318	C₄⋊C₄	C₂×D₂₆₈	1	2	yes	—
319	C₂²⋊C₄	—	2	2	no	—
320	C₂²⋊C₄	—	2	2	no	—
321	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
322	C₄²	C₂×D₂₆₈	1	1	yes	characteristic
323	C₄²	#11761628	1	1	yes	characteristic
324	C₄²	C₂³×D₆₇	1	1	yes	characteristic
325	C₂³	—	2	2	no	—
326	C₂³	—	4	2	no	—
327	C₂³	—	4	2	no	—
328	C₂³	—	4	2	no	—
329	C₂³	#14524017	1	1	yes	characteristic
330	Q₈	—	268	2	no	—
331	Q₈	—	268	2	no	—
332	Q₈	—	536	2	no	—
333	Q₈	—	536	2	no	—
334	Q₈	—	536	2	no	—
335	D₄	—	2	2	no	—
336	D₄	—	2	2	no	—
337	D₄	—	4	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	268	2	no	—
345	C₂×C₄	—	268	2	no	—
346	C₂×C₄	—	536	2	no	—
347	C₂×C₄	—	536	2	no	—
348	C₂×C₄	#14524017	1	1	yes	characteristic
349	C₂×C₄	#14524017	1	1	yes	characteristic
350	C₂×C₄	#14524017	1	1	yes	characteristic
351	C₂×C₄	C₂×#11761616	1	2	yes	—
352	C₂×C₄	#14524071	1	2	yes	—
353	C₂×C₄	#14524073	1	2	yes	—
354	C₂×C₄	#14524076	1	2	yes	—
355	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
356	C₂×C₄	C₂²×D₂₆₈	1	1	yes	characteristic
357	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
358	C₈	—	2	2	no	—
359	C₈	—	4	2	no	—
360	C₈	—	268	2	no	—
361	C₈	—	268	2	no	—
362	C₈	C₂×#11761616	1	4	yes	complemented
363	C₂²	—	4	2	no	—
364	C₂²	—	4	2	no	—
365	C₂²	—	4	2	no	—
366	C₂²	—	8	4	no	—
367	C₂²	#16863601	1	2	yes	—
368	C₂²	#16863642	1	2	yes	—
369	C₂²	#16863659	1	2	yes	—
370	C₂²	C₂×#14524017	1	1	yes	characteristic
371	C₄	—	2	1	no	—
372	C₄	—	2	1	no	—
373	C₄	—	4	2	no	—
374	C₄	—	536	2	no	—
375	C₄	—	536	2	no	—
376	C₄	#16863601	1	2	yes	—
377	C₄	#16863642	1	2	yes	—
378	C₄	C₂²×#11761616	1	1	yes	characteristic
379	C₄	C₂×#14524071	1	1	yes	characteristic
380	C₄	C₂×#14524073	1	1	yes	characteristic
381	C₄	C₂×#14524076	1	1	yes	characteristic
382	C₂	—	8	2	no	—
383	C₂	#22559708	1	4	yes	direct product factor
384	C₂	C₂×#16863601	1	1	yes	characteristic
385	C₂	C₂×#16863642	1	1	yes	characteristic
386	C₂	C₂×#16863659	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#14524017
commutator, cosocle	C₄²×C₆₇	C₂⁴
Frattini	C₄²	C₂³×D₆₇
Fitting	C₂×#436×C₆₇	C₂
socle	C₂³×C₆₇	#121
prime radical	C₂²×D₄×C₆₇	D₄
hypercenter	C₂×#436	D₆₇
hypocenter	C₆₇	C₂×#1691
LCS	G ▷ C₄²×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#436

Complements

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

N	H ≅ G/N	type
1. C₂×#16863794	C₂	semidirect
4. #22559708	C₂	direct (N × H)
5. C₂×#16863149	C₂	semidirect
6. C₂×#16863144	C₂	semidirect
7. C₂×#16863141	C₂	semidirect
13. #16863794	C₂²	semidirect
25. #16863149	C₂²	semidirect
26. #16863144	C₂²	semidirect
27. #16863141	C₂²	semidirect
120. C₂×C₈×C₆₇	SD₁₆	semidirect
166. C₈×C₆₇	C₂×SD₁₆	semidirect
190. C₂×C₆₇	#1691	semidirect
202. C₆₇	C₂×#1691	semidirect
306. C₂×C₈	#11761616	semidirect
362. C₈	C₂×#11761616	semidirect
383. C₂	#22559708	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×#16863794	2
C₂×#16863686	2
C₂×#16863601	2
#22559708	2
C₂×#16863149	2
C₂×#16863144	2
C₂×#16863141	2
C₂×#436×C₆₇	2
C₂×#1691	67

Subgroups — C2×#22559708 #30838352

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22559708 #30838352