Subgroups — C₂×#26022131 #36707826

Order 22784.

662 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19152028	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151716	C₂	1	1	yes	maximal, characteristic, complemented
3	#26022131	C₂	1	8	yes	maximal, direct product factor
4	C₂×#19151427	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#19151405	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#19151404	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄×#13083549	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#443×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#15668034	C₂²	1	1	yes	characteristic
10	C₂×#15668018	—	2	1	no	—
11	#19152028	C₄	1	4	yes	complemented
12	#19152028	C₂²	1	4	yes	—
13	C₂×#15667958	C₄	1	1	yes	characteristic, complemented
14	C₂×#15667956	C₄	1	1	yes	characteristic, complemented
15	C₂×#15667955	C₄	1	1	yes	characteristic, complemented
16	C₂×#15667953	C₄	1	1	yes	characteristic, complemented
17	C₂²×#13083549	C₂²	1	1	yes	characteristic
18	C₂²×#13083549	C₂²	1	1	yes	characteristic
19	#19151716	—	2	2	no	—
20	#19151716	C₂²	1	4	yes	complemented
21	C₂×#15667948	C₂²	1	1	yes	characteristic
22	C₂×#15667940	—	2	1	no	—
23	#19151427	C₂²	1	4	yes	complemented
24	#19151405	C₂²	1	4	yes	complemented
25	#19151404	C₂²	1	4	yes	complemented
26	C₄×#13083549	C₂²	1	4	yes	complemented
27	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×#131×C₈₉	—	2	1	no	—
29	#443×C₈₉	—	2	2	no	—
30	#443×C₈₉	C₂²	1	4	yes	complemented
31	C₂×#108×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×#104×C₈₉	—	2	1	no	—
33	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
34	C₂×#13083574	—	2	1	no	—
35	#15668034	—	2	1	no	—
36	#15668034	—	2	1	no	—
37	#15668034	C₂×C₄	1	2	yes	—
38	#15668034	C₂³	1	2	yes	—
39	C₂×Dic₃₅₆	C₂×C₄	1	1	yes	characteristic
40	C₂×#13083563	—	2	1	no	—
41	C₂×D₇₁₂	C₂×C₄	1	1	yes	characteristic
42	#15668018	—	2	4	no	—
43	#15668018	—	4	2	no	—
44	C₂×#13083558	—	2	1	no	—
45	C₂×#13083557	—	4	1	no	—
46	C₂×C₈×D₈₉	—	4	1	no	—
47	#15667958	C₂×C₄	1	4	yes	complemented
48	#15667956	C₂×C₄	1	4	yes	complemented
49	#15667955	C₂×C₄	1	4	yes	complemented
50	#15667953	C₂×C₄	1	4	yes	complemented
51	C₂×#13083549	—	2	1	no	—
52	C₂×#13083549	—	2	1	no	—
53	C₂×#13083549	C₂×C₄	1	1	yes	characteristic
54	C₂×#13083549	C₂×C₄	1	1	yes	characteristic
55	C₂×#13083549	C₂×C₄	1	2	yes	—
56	C₂×#13083549	C₂³	1	2	yes	—
57	C₂×#13083549	C₂³	1	2	yes	—
58	#15667948	—	2	1	no	—
59	#15667948	C₂³	1	2	yes	—
60	#15667940	—	2	4	no	—
61	C₂×#41×C₈₉	—	2	1	no	—
62	#135×C₈₉	—	2	1	no	—
63	#135×C₈₉	—	2	1	no	—
64	#135×C₈₉	C₂×C₄	1	2	yes	—
65	#135×C₈₉	C₂³	1	2	yes	—
66	C₂×Q₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
67	C₂×SD₁₆×C₈₉	—	2	1	no	—
68	C₂×D₈×C₈₉	C₂×C₄	1	1	yes	characteristic
69	#131×C₈₉	—	2	4	no	—
70	#131×C₈₉	—	4	2	no	—
71	C₂×M₁₆×C₈₉	—	2	1	no	—
72	C₂×M₁₆×C₈₉	—	4	1	no	—
73	C₂²×C₈×C₈₉	—	4	1	no	—
74	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
75	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
77	#108×C₈₉	—	2	1	no	—
78	#108×C₈₉	C₂³	1	2	yes	—
79	#104×C₈₉	—	2	4	no	—
80	C₄×C₈×C₈₉	D₄	1	2	yes	—
81	C₄×C₈×C₈₉	C₂³	1	2	yes	—
82	#13083574	—	2	2	no	—
83	#13083574	—	2	2	no	—
84	#13083574	—	4	1	no	—
85	#13083574	—	4	1	no	—
86	C₂×Dic₁₇₈	—	2	1	no	—
87	C₂×D₃₅₆	—	2	1	no	—
88	C₂×C₂²⋊D₈₉	—	4	1	no	—
89	C₂×C₄×D₈₉	—	4	1	no	—
90	Dic₃₅₆	—	2	1	no	—
91	Dic₃₅₆	C₂²×C₄	1	2	yes	—
92	#13083563	—	2	2	no	—
93	#13083563	—	2	2	no	—
94	D₇₁₂	—	2	1	no	—
95	D₇₁₂	C₂²×C₄	1	2	yes	—
96	#13083558	—	2	2	no	—
97	#13083558	—	4	1	no	—
98	#13083557	—	4	4	no	—
99	C₂×#10623494	—	4	1	no	—
100	C₈×D₈₉	—	4	4	no	—
101	#13083549	—	2	2	no	—
102	#13083549	C₂²×C₄	1	2	yes	—
103	#13083549	C₂²×C₄	1	2	yes	—
104	#41×C₈₉	—	2	2	no	—
105	#41×C₈₉	—	2	2	no	—
106	#41×C₈₉	—	4	1	no	—
107	#41×C₈₉	—	4	1	no	—
108	C₂×Q₈×C₈₉	—	2	1	no	—
109	C₂×D₄×C₈₉	—	2	1	no	—
110	C₂×D₄×C₈₉	—	4	1	no	—
111	C₂²×C₄×C₈₉	—	2	1	no	—
112	C₂²×C₄×C₈₉	—	4	1	no	—
113	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
114	Q₁₆×C₈₉	—	2	1	no	—
115	Q₁₆×C₈₉	C₂²×C₄	1	2	yes	—
116	SD₁₆×C₈₉	—	2	2	no	—
117	SD₁₆×C₈₉	—	2	2	no	—
118	D₈×C₈₉	—	2	1	no	—
119	D₈×C₈₉	C₂²×C₄	1	2	yes	—
120	M₁₆×C₈₉	—	2	2	no	—
121	M₁₆×C₈₉	—	4	1	no	—
122	M₁₆×C₈₉	—	4	4	no	—
123	C₂×C₈×C₈₉	—	4	1	no	—
124	C₂×C₈×C₈₉	—	4	4	no	—
125	C₂×C₈×C₈₉	D₈	1	1	yes	characteristic
126	C₂×C₈×C₈₉	D₈	1	2	yes	—
127	C₂×C₈×C₈₉	D₈	1	1	yes	characteristic
128	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
131	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
132	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
133	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
134	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
135	C₄²×C₈₉	—	2	1	no	—
136	C₄²×C₈₉	C₂×D₄	1	2	yes	—
137	C₂³×C₈₉	—	4	1	no	—
138	C₂³×C₈₉	#135	1	1	yes	characteristic
139	C₂²×D₈₉	—	4	1	no	—
140	Q₈×C₈₉	—	2	2	no	—
141	Q₈×C₈₉	—	4	1	no	—
142	D₄×C₈₉	—	2	2	no	—
143	D₄×C₈₉	—	4	2	no	—
144	D₄×C₈₉	—	4	2	no	—
145	D₄×C₈₉	—	4	1	no	—
146	C₂×C₄×C₈₉	—	2	4	no	—
147	C₂×C₄×C₈₉	—	2	2	no	—
148	C₂×C₄×C₈₉	—	4	1	no	—
149	C₂×C₄×C₈₉	—	4	2	no	—
150	C₂×C₄×C₈₉	—	4	2	no	—
151	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
152	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
153	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
154	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
155	C₂×C₄×C₈₉	#135	1	1	yes	characteristic
156	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
157	C₂²⋊D₈₉	—	4	2	no	—
158	C₂²⋊D₈₉	—	4	2	no	—
159	C₂×Dic₈₉	—	4	1	no	—
160	D₃₅₆	—	2	2	no	—
161	D₃₅₆	—	4	1	no	—
162	C₄×D₈₉	—	4	2	no	—
163	C₄×D₈₉	—	4	2	no	—
164	Dic₁₇₈	—	2	2	no	—
165	Dic₁₇₈	—	4	1	no	—
166	C₈×C₈₉	—	4	2	no	—
167	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
168	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
169	C₈×C₈₉	C₂×D₈	1	2	yes	—
170	C₈×C₈₉	C₂×D₈	1	2	yes	—
171	C₈×C₈₉	C₂³×C₄	1	1	yes	characteristic
172	C₈×C₈₉	C₂×#41	1	1	yes	characteristic
173	#10623494	—	4	2	no	—
174	C₂²×C₈₉	—	2	2	no	—
175	C₂²×C₈₉	—	4	2	no	—
176	C₂²×C₈₉	—	8	2	no	—
177	C₂²×C₈₉	C₄×D₈	1	1	yes	characteristic
178	C₂²×C₈₉	C₄×D₈	1	1	yes	characteristic
179	C₂²×C₈₉	C₂×#135	1	1	yes	characteristic
180	C₂×D₈₉	—	4	2	no	—
181	C₂×D₈₉	—	8	2	no	—
182	C₄×C₈₉	—	2	4	no	—
183	C₄×C₈₉	—	4	2	no	—
184	C₄×C₈₉	C₄×D₈	1	1	yes	characteristic
185	C₄×C₈₉	C₄×D₈	1	1	yes	characteristic
186	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
187	C₄×C₈₉	C₂²×D₈	1	1	yes	characteristic
188	Dic₈₉	—	4	2	no	—
189	C₂×#2178	—	89	1	no	maximal, Sylow
190	C₂×C₈₉	—	2	1	no	—
191	C₂×C₈₉	—	2	1	no	—
192	C₂×C₈₉	—	8	2	no	—
193	C₂×C₈₉	#2178	1	2	yes	complemented
194	C₂×C₈₉	C₂×C₄×D₈	1	1	yes	characteristic
195	D₈₉	—	8	2	no	—
196	C₂×#508	—	89	1	no	—
197	C₂×#443	—	89	1	no	—
198	C₂×#443	D₈₉	1	1	yes	characteristic, complemented
199	#2178	—	89	8	no	—
200	C₂×#368	—	89	1	no	—
201	C₂×#359	—	89	1	no	—
202	C₂×#359	—	89	1	no	—
203	C₂×C₄×C₁₆	—	89	1	no	—
204	C₈₉	C₂×#2178	1	1	yes	characteristic, complemented, Sylow
205	C₂×#135	—	89	1	no	—
206	C₂×#135	C₂×D₈₉	1	1	yes	characteristic
207	C₂×#131	—	2	1	no	—
208	C₂×#131	—	178	1	no	—
209	#508	—	89	4	no	—
210	#508	—	89	4	no	—
211	C₂×Q₃₂	—	89	1	no	—
212	C₂×SD₃₂	—	89	1	no	—
213	C₂×SD₃₂	—	89	1	no	—
214	C₂×D₁₆	—	89	1	no	—
215	C₂²×C₁₆	—	89	1	no	—
216	C₂²×C₁₆	—	89	1	no	—
217	#443	—	2	2	no	—
218	#443	—	89	4	no	—
219	#443	—	178	2	no	—
220	#443	C₂×D₈₉	1	4	yes	complemented
221	C₂×#108	—	89	1	no	—
222	C₂×#108	C₂×D₈₉	1	1	yes	characteristic
223	C₂×#104	—	2	1	no	—
224	C₂×#104	—	178	1	no	—
225	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
226	#368	—	89	4	no	—
227	#359	—	89	4	no	—
228	#359	—	89	4	no	—
229	C₄×C₁₆	—	89	4	no	—
230	C₂×#41	—	2	1	no	—
231	C₂×#41	—	178	1	no	—
232	#135	—	2	1	no	—
233	#135	—	2	1	no	—
234	#135	—	89	2	no	—
235	#135	—	89	2	no	—
236	#135	—	178	1	no	—
237	#135	—	178	1	no	—
238	#135	C₄×D₈₉	1	2	yes	—
239	#135	C₂²×D₈₉	1	2	yes	—
240	C₂×Q₁₆	—	89	1	no	—
241	C₂×Q₁₆	C₄×D₈₉	1	1	yes	characteristic
242	C₂×SD₁₆	—	2	1	no	—
243	C₂×SD₁₆	—	178	1	no	—
244	C₂×D₈	—	89	1	no	—
245	C₂×D₈	C₄×D₈₉	1	1	yes	characteristic
246	#131	—	2	4	no	—
247	#131	—	4	2	no	—
248	#131	—	356	2	no	—
249	#131	—	178	4	no	—
250	C₂×M₁₆	—	2	1	no	—
251	C₂×M₁₆	—	4	1	no	—
252	C₂×M₁₆	—	356	1	no	—
253	C₂×M₁₆	—	178	1	no	—
254	C₂²×C₈	—	4	1	no	—
255	C₂²×C₈	—	356	1	no	—
256	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
257	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
258	C₂×C₄²	C₂²⋊D₈₉	1	1	yes	characteristic
259	Q₃₂	—	89	4	no	—
260	SD₃₂	—	89	4	no	—
261	SD₃₂	—	89	4	no	—
262	D₁₆	—	89	4	no	—
263	C₂×C₁₆	—	89	1	no	—
264	C₂×C₁₆	—	89	1	no	—
265	C₂×C₁₆	—	89	2	no	—
266	C₂×C₁₆	—	89	2	no	—
267	C₂×C₁₆	—	89	2	no	—
268	C₂×C₁₆	—	178	1	no	—
269	C₂×C₁₆	—	178	1	no	—
270	#108	—	2	1	no	—
271	#108	—	89	2	no	—
272	#108	—	178	1	no	—
273	#108	C₂²×D₈₉	1	2	yes	—
274	#104	—	2	4	no	—
275	#104	—	178	4	no	—
276	C₄×C₈	C₂²⋊D₈₉	1	2	yes	—
277	C₄×C₈	C₂²×D₈₉	1	2	yes	—
278	#41	—	2	2	no	—
279	#41	—	2	2	no	—
280	#41	—	4	1	no	—
281	#41	—	4	1	no	—
282	#41	—	356	1	no	—
283	#41	—	356	1	no	—
284	#41	—	178	2	no	—
285	#41	—	178	2	no	—
286	C₂×Q₈	—	2	1	no	—
287	C₂×Q₈	—	178	1	no	—
288	C₂×D₄	—	2	1	no	—
289	C₂×D₄	—	4	1	no	—
290	C₂×D₄	—	356	1	no	—
291	C₂×D₄	—	178	1	no	—
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	—	4	1	no	—
294	C₂²×C₄	—	356	1	no	—
295	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
296	Q₁₆	—	2	1	no	—
297	Q₁₆	—	89	2	no	—
298	Q₁₆	—	178	1	no	—
299	Q₁₆	C₂×C₄×D₈₉	1	2	yes	—
300	SD₁₆	—	2	2	no	—
301	SD₁₆	—	2	2	no	—
302	SD₁₆	—	178	2	no	—
303	SD₁₆	—	178	2	no	—
304	D₈	—	2	1	no	—
305	D₈	—	89	2	no	—
306	D₈	—	178	1	no	—
307	D₈	C₂×C₄×D₈₉	1	2	yes	—
308	M₁₆	—	2	2	no	—
309	M₁₆	—	4	1	no	—
310	M₁₆	—	4	4	no	—
311	M₁₆	—	356	1	no	—
312	M₁₆	—	356	4	no	—
313	M₁₆	—	178	2	no	—
314	C₂×C₈	—	4	1	no	—
315	C₂×C₈	—	4	4	no	—
316	C₂×C₈	—	356	1	no	—
317	C₂×C₈	—	356	4	no	—
318	C₂×C₈	#13083559	1	1	yes	characteristic
319	C₂×C₈	#13083559	1	2	yes	—
320	C₂×C₈	#13083559	1	1	yes	characteristic
321	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
322	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
323	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
324	C₂×C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
325	C₂×C₈	#13083574	1	1	yes	characteristic
326	C₂×C₈	#13083574	1	1	yes	characteristic
327	C₂×C₈	C₂³×D₈₉	1	1	yes	characteristic
328	C₄²	—	2	1	no	—
329	C₄²	C₂×C₂²⋊D₈₉	1	2	yes	—
330	C₁₆	—	89	2	no	—
331	C₁₆	—	89	2	no	—
332	C₁₆	—	178	2	no	—
333	C₂³	—	4	1	no	—
334	C₂³	—	356	1	no	—
335	C₂³	#15668032	1	1	yes	characteristic
336	Q₈	—	2	2	no	—
337	Q₈	—	4	1	no	—
338	Q₈	—	356	1	no	—
339	Q₈	—	178	2	no	—
340	D₄	—	2	2	no	—
341	D₄	—	4	2	no	—
342	D₄	—	4	2	no	—
343	D₄	—	4	1	no	—
344	D₄	—	356	2	no	—
345	D₄	—	356	2	no	—
346	D₄	—	356	1	no	—
347	D₄	—	178	2	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	356	1	no	—
354	C₂×C₄	—	356	2	no	—
355	C₂×C₄	—	356	2	no	—
356	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
357	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
358	C₂×C₄	C₂×#13083559	1	1	yes	characteristic
359	C₂×C₄	C₂×#13083559	1	1	yes	characteristic
360	C₂×C₄	#15668032	1	1	yes	characteristic
361	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
362	C₈	—	4	2	no	—
363	C₈	—	356	2	no	—
364	C₈	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
365	C₈	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
366	C₈	C₂×#13083559	1	2	yes	—
367	C₈	C₂×#13083559	1	2	yes	—
368	C₈	C₂²×C₄×D₈₉	1	1	yes	characteristic
369	C₈	C₂×#13083574	1	1	yes	characteristic
370	C₂²	—	2	2	no	—
371	C₂²	—	4	2	no	—
372	C₂²	—	8	2	no	—
373	C₂²	—	356	2	no	—
374	C₂²	—	712	2	no	—
375	C₂²	C₄×#13083559	1	1	yes	characteristic
376	C₂²	C₄×#13083559	1	1	yes	characteristic
377	C₂²	C₂×#15668032	1	1	yes	characteristic
378	C₄	—	2	4	no	—
379	C₄	—	4	2	no	—
380	C₄	—	356	2	no	—
381	C₄	C₄×#13083559	1	1	yes	characteristic
382	C₄	C₄×#13083559	1	1	yes	characteristic
383	C₄	C₂×C₄×C₂²⋊D₈₉	1	1	yes	characteristic
384	C₄	C₂²×#13083559	1	1	yes	characteristic
385	C₂	—	2	1	no	—
386	C₂	—	2	1	no	—
387	C₂	—	8	2	no	—
388	C₂	—	712	2	no	—
389	C₂	#26022131	1	2	yes	direct product factor
390	C₂	C₂×C₄×#13083559	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	#13083559
commutator	C₈×C₈₉	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₈₉
Fitting	C₂×#443×C₈₉	C₂
socle	C₂²×C₈₉	C₄×D₈
prime radical	C₂×#19152028	C₂
cosocle	C₂×C₈×C₈₉	C₂⁴
hypercenter	C₂×#443	D₈₉
hypocenter	C₈₉	C₂×#2178
LCS	G ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ C₂×C₄×C₈ ◁ C₂×#443

Complements

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

N	H ≅ G/N	type
2. C₂×#19151716	C₂	semidirect
3. #26022131	C₂	direct (N × H)
4. C₂×#19151427	C₂	semidirect
5. C₂×#19151405	C₂	semidirect
6. C₂×#19151404	C₂	semidirect
7. C₂×C₄×#13083549	C₂	semidirect
8. C₂×#443×C₈₉	C₂	semidirect
11. #19152028	C₄	semidirect
13. C₂×#15667958	C₄	semidirect
14. C₂×#15667956	C₄	semidirect
15. C₂×#15667955	C₄	semidirect
16. C₂×#15667953	C₄	semidirect
20. #19151716	C₂²	semidirect
23. #19151427	C₂²	semidirect
24. #19151405	C₂²	semidirect
25. #19151404	C₂²	semidirect
26. C₄×#13083549	C₂²	semidirect
30. #443×C₈₉	C₂²	semidirect
47. #15667958	C₂×C₄	semidirect
48. #15667956	C₂×C₄	semidirect
49. #15667955	C₂×C₄	semidirect
50. #15667953	C₂×C₄	semidirect
193. C₂×C₈₉	#2178	semidirect
198. C₂×#443	D₈₉	semidirect
204. C₈₉	C₂×#2178	semidirect
220. #443	C₂×D₈₉	semidirect
389. C₂	#26022131	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×#19152028	2
C₂×#19151716	2
#26022131	2
C₂×#19151427	2
C₂×#19151405	2
C₂×#19151404	2
C₂×C₄×#13083549	2
C₂×#443×C₈₉	2
C₂×#2178	89

Subgroups — C2×#26022131 #36707826

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#26022131 #36707826