Subgroups — C₂×#26022382 #36708997

Order 22784.

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×#15667957	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#19151873	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#19151868	C₂	1	1	yes	maximal, characteristic
4	#26022382	C₂	1	8	yes	maximal, direct product factor
5	C₂×#19151428	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#19151415	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#19151412	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#504×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#15668042	—	2	1	no	—
10	C₂×#15668037	—	2	1	no	—
11	C₂²×Dic₃₅₆	C₂²	1	1	yes	characteristic
12	C₂²×D₇₁₂	C₂²	1	1	yes	characteristic
13	C₂×#15667957	—	2	1	no	—
14	C₂×#15667957	—	2	1	no	—
15	C₂×#15667957	—	2	2	no	—
16	C₂×#15667957	C₂²	1	4	yes	complemented
17	#19151873	—	2	2	no	—
18	#19151873	C₂²	1	4	yes	complemented
19	#19151868	—	2	2	no	—
20	#19151868	C₂²	1	4	yes	—
21	C₂×#15667948	C₂²	1	1	yes	characteristic
22	C₂×#15667948	C₂²	1	1	yes	characteristic
23	C₂×#15667930	—	2	1	no	—
24	C₂×#15667928	—	2	1	no	—
25	#19151428	C₂²	1	4	yes	complemented
26	#19151415	C₂²	1	4	yes	complemented
27	#19151412	C₂²	1	4	yes	complemented
28	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic
29	#504×C₈₉	—	2	2	no	—
30	#504×C₈₉	C₂²	1	4	yes	complemented
31	C₂×M₃₂×C₈₉	—	2	1	no	—
32	C₂×M₃₂×C₈₉	C₂²	1	1	yes	characteristic
33	C₂²×C₁₆×C₈₉	—	2	1	no	—
34	C₂²×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
35	C₂²×Dic₁₇₈	—	2	1	no	—
36	C₂²×D₃₅₆	—	2	1	no	—
37	#15668042	—	2	4	no	—
38	#15668042	—	4	2	no	—
39	#15668037	—	2	4	no	—
40	#15668037	—	4	2	no	—
41	C₂×Dic₃₅₆	—	2	1	no	—
42	C₂×Dic₃₅₆	—	2	1	no	—
43	C₂×Dic₃₅₆	—	2	1	no	—
44	C₂×Dic₃₅₆	—	2	1	no	—
45	C₂×Dic₃₅₆	—	2	1	no	—
46	C₂×Dic₃₅₆	C₂³	1	2	yes	—
47	C₂×#13083564	—	4	1	no	—
48	C₂×#13083562	—	4	1	no	—
49	C₂×#13083561	—	4	1	no	—
50	C₂×D₇₁₂	—	2	1	no	—
51	C₂×D₇₁₂	—	2	1	no	—
52	C₂×D₇₁₂	—	2	1	no	—
53	C₂×D₇₁₂	—	2	1	no	—
54	C₂×D₇₁₂	—	2	1	no	—
55	C₂×D₇₁₂	C₂³	1	2	yes	—
56	C₂×#13083559	—	4	1	no	—
57	C₂×#13083558	—	2	1	no	—
58	C₂×#13083558	—	2	1	no	—
59	#15667957	—	2	4	no	—
60	#15667957	—	2	4	no	—
61	#15667948	—	2	1	no	—
62	#15667948	—	2	1	no	—
63	#15667948	C₂³	1	2	yes	—
64	#15667948	C₂³	1	2	yes	—
65	#15667930	—	2	4	no	—
66	#15667928	—	2	4	no	—
67	C₂×#41×C₈₉	D₄	1	1	yes	characteristic
68	#131×C₈₉	—	2	1	no	—
69	#131×C₈₉	—	2	1	no	—
70	#131×C₈₉	D₄	1	2	yes	—
71	#131×C₈₉	C₂³	1	2	yes	—
72	C₂×M₁₆×C₈₉	—	2	1	no	—
73	C₂×M₁₆×C₈₉	D₄	1	1	yes	characteristic
74	C₂²×C₈×C₈₉	—	2	1	no	—
75	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
76	M₃₂×C₈₉	—	2	1	no	—
77	M₃₂×C₈₉	—	2	4	no	—
78	M₃₂×C₈₉	C₂³	1	2	yes	—
79	C₂×C₁₆×C₈₉	—	2	1	no	—
80	C₂×C₁₆×C₈₉	—	2	4	no	—
81	C₂×C₁₆×C₈₉	D₄	1	1	yes	characteristic
82	C₂×C₁₆×C₈₉	D₄	1	1	yes	characteristic
83	C₂×C₁₆×C₈₉	D₄	1	2	yes	—
84	C₂×C₁₆×C₈₉	C₂³	1	2	yes	—
85	C₂³×D₈₉	—	4	1	no	—
86	C₂×Dic₁₇₈	—	2	2	no	—
87	C₂×Dic₁₇₈	—	4	1	no	—
88	C₂×Dic₁₇₈	—	4	1	no	—
89	C₂×Dic₁₇₈	—	4	1	no	—
90	C₂×Dic₁₇₈	—	4	1	no	—
91	C₂×Dic₁₇₈	—	4	1	no	—
92	C₂×D₃₅₆	—	2	2	no	—
93	C₂×D₃₅₆	—	4	1	no	—
94	C₂×D₃₅₆	—	4	1	no	—
95	C₂×D₃₅₆	—	4	1	no	—
96	C₂×D₃₅₆	—	4	1	no	—
97	C₂×D₃₅₆	—	4	1	no	—
98	C₂²×Dic₈₉	—	4	1	no	—
99	Dic₃₅₆	—	2	2	no	—
100	Dic₃₅₆	—	2	2	no	—
101	Dic₃₅₆	—	4	1	no	—
102	Dic₃₅₆	—	4	1	no	—
103	#13083564	—	4	4	no	—
104	#13083562	—	4	4	no	—
105	#13083561	—	4	4	no	—
106	D₇₁₂	—	2	2	no	—
107	D₇₁₂	—	2	2	no	—
108	D₇₁₂	—	4	1	no	—
109	D₇₁₂	—	4	1	no	—
110	#13083559	—	4	4	no	—
111	#13083558	—	2	2	no	—
112	#13083558	—	2	2	no	—
113	#13083558	—	4	1	no	—
114	#13083558	—	4	1	no	—
115	C₂×#10623494	—	4	1	no	—
116	C₂×#10623494	—	4	1	no	—
117	#41×C₈₉	—	2	1	no	—
118	#41×C₈₉	—	2	1	no	—
119	#41×C₈₉	D₈	1	2	yes	—
120	#41×C₈₉	C₂×D₄	1	2	yes	—
121	C₂×Q₈×C₈₉	D₈	1	1	yes	characteristic
122	C₂×D₄×C₈₉	—	2	1	no	—
123	C₂×D₄×C₈₉	D₈	1	1	yes	characteristic
124	C₂²×C₄×C₈₉	—	2	1	no	—
125	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
126	M₁₆×C₈₉	—	2	1	no	—
127	M₁₆×C₈₉	—	2	2	no	—
128	M₁₆×C₈₉	—	2	2	no	—
129	M₁₆×C₈₉	C₂×D₄	1	2	yes	—
130	C₂×C₈×C₈₉	—	2	1	no	—
131	C₂×C₈×C₈₉	—	2	2	no	—
132	C₂×C₈×C₈₉	—	2	2	no	—
133	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
134	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
135	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
136	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
137	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
138	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
139	C₁₆×C₈₉	—	2	2	no	—
140	C₁₆×C₈₉	C₂×D₄	1	2	yes	—
141	C₁₆×C₈₉	C₂×D₄	1	2	yes	—
142	C₂³×C₈₉	—	2	1	no	—
143	C₂³×C₈₉	#135	1	1	yes	characteristic
144	C₂²×D₈₉	—	4	2	no	—
145	C₂²×D₈₉	—	8	1	no	—
146	C₂²×D₈₉	—	8	1	no	—
147	C₂²×D₈₉	—	16	2	no	—
148	Q₈×C₈₉	—	2	1	no	—
149	Q₈×C₈₉	C₂×D₈	1	2	yes	—
150	D₄×C₈₉	—	2	2	no	—
151	D₄×C₈₉	—	2	2	no	—
152	D₄×C₈₉	—	2	1	no	—
153	D₄×C₈₉	C₂×D₈	1	2	yes	—
154	C₂×C₄×C₈₉	—	2	1	no	—
155	C₂×C₄×C₈₉	—	2	2	no	—
156	C₂×C₄×C₈₉	—	2	2	no	—
157	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
158	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
159	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
160	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
161	C₂×C₄×C₈₉	#135	1	1	yes	characteristic
162	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
163	C₂×Dic₈₉	—	4	2	no	—
164	C₂×Dic₈₉	—	8	1	no	—
165	C₂×Dic₈₉	—	8	1	no	—
166	D₃₅₆	—	4	2	no	—
167	D₃₅₆	—	4	2	no	—
168	D₃₅₆	—	8	1	no	—
169	D₃₅₆	—	8	1	no	—
170	Dic₁₇₈	—	4	2	no	—
171	Dic₁₇₈	—	4	2	no	—
172	Dic₁₇₈	—	8	1	no	—
173	Dic₁₇₈	—	8	1	no	—
174	C₈×C₈₉	—	2	2	no	—
175	C₈×C₈₉	#121	1	1	yes	characteristic
176	C₈×C₈₉	#121	1	1	yes	characteristic
177	C₈×C₈₉	C₂²×D₄	1	1	yes	characteristic
178	C₈×C₈₉	C₂×#41	1	1	yes	characteristic
179	#10623494	—	4	2	no	—
180	#10623494	—	4	2	no	—
181	C₂²×C₈₉	—	2	2	no	—
182	C₂²×C₈₉	—	2	2	no	—
183	C₂²×C₈₉	—	4	2	no	—
184	C₂²×C₈₉	#466	1	1	yes	characteristic
185	C₂²×C₈₉	#466	1	1	yes	characteristic
186	C₂²×C₈₉	C₂×#135	1	1	yes	characteristic
187	C₂×D₈₉	—	8	2	no	—
188	C₂×D₈₉	—	16	2	no	—
189	C₂×D₈₉	—	16	2	no	—
190	C₂×D₈₉	—	16	2	no	—
191	C₄×C₈₉	—	2	2	no	—
192	C₄×C₈₉	#466	1	1	yes	characteristic
193	C₄×C₈₉	#466	1	1	yes	characteristic
194	C₄×C₈₉	C₂×#121	1	1	yes	characteristic
195	C₄×C₈₉	C₂²×D₈	1	1	yes	characteristic
196	Dic₈₉	—	8	2	no	—
197	C₂×#2223	—	89	1	no	maximal, Sylow
198	C₂×C₈₉	—	2	1	no	—
199	C₂×C₈₉	—	2	1	no	—
200	C₂×C₈₉	—	4	2	no	—
201	C₂×C₈₉	#2223	1	2	yes	complemented
202	C₂×C₈₉	C₂×#466	1	1	yes	characteristic
203	D₈₉	—	16	2	no	—
204	C₂²×SD₃₂	—	89	1	no	—
205	C₂×#504	D₈₉	1	1	yes	characteristic, complemented
206	C₂×#473	—	89	1	no	—
207	C₂×#472	—	89	1	no	—
208	#2223	—	89	8	no	—
209	C₂×#368	—	89	1	no	—
210	C₂×#362	—	89	1	no	—
211	C₂×#361	—	89	1	no	—
212	C₈₉	C₂×#2223	1	1	yes	characteristic, complemented, Sylow
213	C₂×#137	—	178	1	no	—
214	C₂×AGL(1,ℤ/8)	—	178	1	no	—
215	C₂²×Q₁₆	—	89	1	no	—
216	C₂²×D₈	—	89	1	no	—
217	C₂×#131	C₂×D₈₉	1	1	yes	characteristic
218	C₂×SD₃₂	—	89	4	no	—
219	C₂×SD₃₂	—	178	1	no	—
220	C₂×SD₃₂	—	178	1	no	—
221	C₂×SD₃₂	—	178	2	no	—
222	#504	—	2	2	no	—
223	#504	C₂×D₈₉	1	4	yes	complemented
224	C₂×M₃₂	—	2	1	no	—
225	C₂×M₃₂	C₂×D₈₉	1	1	yes	characteristic
226	C₂²×C₁₆	—	2	1	no	—
227	C₂²×C₁₆	C₂×D₈₉	1	1	yes	characteristic
228	#473	—	89	4	no	—
229	#473	—	178	2	no	—
230	#472	—	89	4	no	—
231	#472	—	178	2	no	—
232	C₂×#108	—	89	1	no	—
233	C₂×#108	—	89	1	no	—
234	C₂×#101	—	178	1	no	—
235	C₂×#100	—	178	1	no	—
236	#368	—	89	4	no	—
237	#362	—	89	4	no	—
238	#361	—	89	4	no	—
239	C₂×#41	D₃₅₆	1	1	yes	characteristic
240	C₂²×Q₈	—	178	1	no	—
241	C₂²×D₄	—	178	1	no	—
242	#137	—	356	2	no	—
243	#137	—	178	4	no	—
244	AGL(1,ℤ/8)	—	356	2	no	—
245	AGL(1,ℤ/8)	—	178	4	no	—
246	C₂×Q₁₆	—	89	2	no	—
247	C₂×Q₁₆	—	356	1	no	—
248	C₂×Q₁₆	—	178	1	no	—
249	C₂×Q₁₆	—	178	1	no	—
250	C₂×Q₁₆	—	178	1	no	—
251	C₂×Q₁₆	—	178	1	no	—
252	C₂×Q₁₆	—	178	1	no	—
253	C₂×SD₁₆	—	356	1	no	—
254	C₂×SD₁₆	—	356	1	no	—
255	C₂×D₈	—	89	2	no	—
256	C₂×D₈	—	356	1	no	—
257	C₂×D₈	—	178	1	no	—
258	C₂×D₈	—	178	1	no	—
259	C₂×D₈	—	178	1	no	—
260	C₂×D₈	—	178	1	no	—
261	C₂×D₈	—	178	1	no	—
262	#131	—	2	1	no	—
263	#131	—	2	1	no	—
264	#131	D₃₅₆	1	2	yes	—
265	#131	C₂²×D₈₉	1	2	yes	—
266	C₂×M₁₆	—	2	1	no	—
267	C₂×M₁₆	—	178	1	no	—
268	C₂×M₁₆	—	178	1	no	—
269	C₂×M₁₆	D₃₅₆	1	1	yes	characteristic
270	C₂²×C₈	—	2	1	no	—
271	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
272	SD₃₂	—	178	4	no	—
273	SD₃₂	—	178	4	no	—
274	M₃₂	—	2	1	no	—
275	M₃₂	—	2	4	no	—
276	M₃₂	C₂²×D₈₉	1	2	yes	—
277	C₂×C₁₆	—	2	1	no	—
278	C₂×C₁₆	—	2	4	no	—
279	C₂×C₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
280	C₂×C₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
281	C₂×C₁₆	C₂²⋊D₈₉	1	2	yes	—
282	C₂×C₁₆	C₂²×D₈₉	1	2	yes	—
283	#108	—	89	2	no	—
284	#108	—	89	2	no	—
285	#108	—	178	1	no	—
286	#108	—	178	1	no	—
287	#101	—	178	4	no	—
288	#100	—	178	4	no	—
289	C₂⁴	—	356	1	no	—
290	#41	—	2	1	no	—
291	#41	—	2	1	no	—
292	#41	D₇₁₂	1	2	yes	—
293	#41	C₂×D₃₅₆	1	2	yes	—
294	C₂×Q₈	—	356	1	no	—
295	C₂×Q₈	—	356	1	no	—
296	C₂×Q₈	—	356	1	no	—
297	C₂×Q₈	—	356	1	no	—
298	C₂×Q₈	—	356	1	no	—
299	C₂×Q₈	—	178	2	no	—
300	C₂×Q₈	D₇₁₂	1	1	yes	characteristic
301	C₂×D₄	—	2	1	no	—
302	C₂×D₄	—	356	1	no	—
303	C₂×D₄	—	356	1	no	—
304	C₂×D₄	—	356	1	no	—
305	C₂×D₄	—	356	1	no	—
306	C₂×D₄	—	356	1	no	—
307	C₂×D₄	—	178	2	no	—
308	C₂×D₄	D₇₁₂	1	1	yes	characteristic
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	356	1	no	—
311	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
312	Q₁₆	—	356	4	no	—
313	Q₁₆	—	356	1	no	—
314	Q₁₆	—	356	1	no	—
315	Q₁₆	—	178	2	no	—
316	Q₁₆	—	178	2	no	—
317	SD₁₆	—	356	4	no	—
318	SD₁₆	—	356	4	no	—
319	D₈	—	356	4	no	—
320	D₈	—	356	1	no	—
321	D₈	—	356	1	no	—
322	D₈	—	178	2	no	—
323	D₈	—	178	2	no	—
324	M₁₆	—	2	1	no	—
325	M₁₆	—	2	2	no	—
326	M₁₆	—	2	2	no	—
327	M₁₆	—	356	1	no	—
328	M₁₆	—	356	1	no	—
329	M₁₆	—	178	2	no	—
330	M₁₆	—	178	2	no	—
331	M₁₆	C₂×D₃₅₆	1	2	yes	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	356	1	no	—
336	C₂×C₈	—	356	1	no	—
337	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
338	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
339	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
340	C₂×C₈	#13083574	1	1	yes	characteristic
341	C₂×C₈	#13083574	1	1	yes	characteristic
342	C₂×C₈	C₂³×D₈₉	1	1	yes	characteristic
343	C₁₆	—	2	2	no	—
344	C₁₆	C₂×C₂²⋊D₈₉	1	2	yes	—
345	C₁₆	C₂×C₂²⋊D₈₉	1	2	yes	—
346	C₂³	—	2	1	no	—
347	C₂³	—	356	2	no	—
348	C₂³	—	1424	2	no	—
349	C₂³	—	712	1	no	—
350	C₂³	—	712	1	no	—
351	C₂³	#15668034	1	1	yes	characteristic
352	Q₈	—	2	1	no	—
353	Q₈	—	356	2	no	—
354	Q₈	—	356	2	no	—
355	Q₈	—	712	1	no	—
356	Q₈	—	712	1	no	—
357	Q₈	C₂×D₇₁₂	1	2	yes	—
358	D₄	—	2	2	no	—
359	D₄	—	2	2	no	—
360	D₄	—	2	1	no	—
361	D₄	—	356	2	no	—
362	D₄	—	356	2	no	—
363	D₄	—	712	1	no	—
364	D₄	—	712	1	no	—
365	D₄	C₂×D₇₁₂	1	2	yes	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	356	2	no	—
370	C₂×C₄	—	712	1	no	—
371	C₂×C₄	—	712	1	no	—
372	C₂×C₄	#15667986	1	1	yes	characteristic
373	C₂×C₄	#15667986	1	1	yes	characteristic
374	C₂×C₄	C₂×D₇₁₂	1	1	yes	characteristic
375	C₂×C₄	C₂×D₇₁₂	1	1	yes	characteristic
376	C₂×C₄	#15668034	1	1	yes	characteristic
377	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
378	C₈	—	2	2	no	—
379	C₈	—	356	2	no	—
380	C₈	—	356	2	no	—
381	C₈	#15667986	1	1	yes	characteristic
382	C₈	#15667986	1	1	yes	characteristic
383	C₈	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
384	C₈	C₂×#13083574	1	1	yes	characteristic
385	C₂²	—	2	2	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	1424	2	no	—
389	C₂²	—	1424	2	no	—
390	C₂²	—	1424	2	no	—
391	C₂²	—	712	2	no	—
392	C₂²	#19151834	1	1	yes	characteristic
393	C₂²	#19151834	1	1	yes	characteristic
394	C₂²	C₂×#15668034	1	1	yes	characteristic
395	C₄	—	2	2	no	—
396	C₄	—	712	2	no	—
397	C₄	#19151834	1	1	yes	characteristic
398	C₄	#19151834	1	1	yes	characteristic
399	C₄	C₂×#15667986	1	1	yes	characteristic
400	C₄	C₂²×D₇₁₂	1	1	yes	characteristic
401	C₂	—	2	1	no	—
402	C₂	—	2	1	no	—
403	C₂	—	4	2	no	—
404	C₂	—	1424	2	no	—
405	C₂	#26022382	1	2	yes	direct product factor
406	C₂	C₂×#19151834	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#19151834
commutator, cosocle	C₂×C₈×C₈₉	C₂⁴
Frattini	C₂×C₈	C₂³×D₈₉
Fitting	C₂×#504×C₈₉	C₂
socle	C₂²×C₈₉	#466
prime radical	C₂×#19151868	C₂
hypercenter	C₂×#504	D₈₉
hypocenter	C₈₉	C₂×#2223
LCS	G ▷ C₂×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
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×#15667957	C₂	semidirect
2. C₂×#19151873	C₂	semidirect
4. #26022382	C₂	direct (N × H)
5. C₂×#19151428	C₂	semidirect
6. C₂×#19151415	C₂	semidirect
7. C₂×#19151412	C₂	semidirect
8. C₂×#504×C₈₉	C₂	semidirect
16. C₂×#15667957	C₂²	semidirect
18. #19151873	C₂²	semidirect
25. #19151428	C₂²	semidirect
26. #19151415	C₂²	semidirect
27. #19151412	C₂²	semidirect
30. #504×C₈₉	C₂²	semidirect
201. C₂×C₈₉	#2223	semidirect
205. C₂×#504	D₈₉	semidirect
212. C₈₉	C₂×#2223	semidirect
223. #504	C₂×D₈₉	semidirect
405. C₂	#26022382	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×#15667957	2
C₂×#19151873	2
C₂×#19151868	2
#26022382	2
C₂×#19151428	2
C₂×#19151415	2
C₂×#19151412	2
C₂×#504×C₈₉	2
C₂×#2223	89

Subgroups — C2×#26022382 #36708997

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#26022382 #36708997