Subgroups — C₂×#26022331 #36708812

Order 22784.

686 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19152038	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151976	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#19151715	C₂	1	1	yes	maximal, characteristic
4	#26022331	C₂	1	8	yes	maximal, direct product factor
5	C₂×#19151418	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#19151415	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#19151414	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#510×C₈₉	C₂	1	1	yes	maximal, characteristic
9	C₂²×Dic₃₅₆	C₂²	1	1	yes	characteristic
10	C₂²×#13083564	—	2	1	no	—
11	C₂×#15668019	—	2	1	no	—
12	C₂×#15668010	—	2	1	no	—
13	#19152038	—	2	2	no	—
14	#19152038	C₂²	1	4	yes	—
15	C₂×#15667958	—	2	1	no	—
16	C₂×#15667956	—	2	1	no	—
17	C₂×#15667952	C₂²	1	1	yes	characteristic
18	#19151976	—	2	2	no	—
19	#19151976	C₂²	1	4	yes	complemented
20	#19151715	—	2	2	no	—
21	#19151715	C₂²	1	4	yes	—
22	C₂×#15667948	C₂²	1	1	yes	characteristic
23	C₂×#15667939	—	2	1	no	—
24	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
25	#19151418	C₂²	1	4	yes	complemented
26	#19151415	C₂²	1	4	yes	complemented
27	#19151414	C₂²	1	4	yes	complemented
28	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
29	C₂²×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
30	#510×C₈₉	—	2	2	no	—
31	#510×C₈₉	C₂²	1	4	yes	—
32	C₂×Q₃₂×C₈₉	—	2	1	no	—
33	C₂×SD₃₂×C₈₉	—	2	1	no	—
34	C₂×M₃₂×C₈₉	C₂²	1	1	yes	characteristic
35	C₂²×Dic₁₇₈	—	2	1	no	—
36	C₂×Dic₃₅₆	—	2	1	no	—
37	C₂×Dic₃₅₆	—	2	1	no	—
38	C₂×Dic₃₅₆	—	2	1	no	—
39	C₂×Dic₃₅₆	—	2	1	no	—
40	C₂×Dic₃₅₆	—	2	1	no	—
41	C₂×Dic₃₅₆	C₂³	1	2	yes	—
42	C₂×#13083564	—	2	4	no	—
43	C₂×#13083564	—	4	1	no	—
44	C₂×#13083564	—	4	1	no	—
45	C₂×#13083564	—	4	2	no	—
46	#15668019	—	2	4	no	—
47	#15668019	—	4	2	no	—
48	C₂×#13083558	—	2	1	no	—
49	C₂×#13083558	—	4	1	no	—
50	C₂²×#10623494	—	4	1	no	—
51	C₂²×#10623494	D₄	1	1	yes	characteristic
52	#15668010	—	2	4	no	—
53	#15668010	—	4	2	no	—
54	C₂×#13083553	—	4	2	no	—
55	C₂×C₄×Dic₈₉	D₄	1	1	yes	characteristic
56	#15667958	—	2	4	no	—
57	#15667956	—	2	4	no	—
58	#15667952	—	2	1	no	—
59	#15667952	C₂³	1	2	yes	—
60	C₂×#13083549	—	2	1	no	—
61	#15667948	—	2	1	no	—
62	#15667948	C₂³	1	2	yes	—
63	#15667939	—	2	4	no	—
64	C₈×Dic₈₉	D₄	1	2	yes	—
65	C₈×Dic₈₉	C₂³	1	2	yes	—
66	C₂×#41×C₈₉	—	2	1	no	—
67	C₂²×Q₈×C₈₉	—	2	1	no	—
68	#135×C₈₉	—	2	1	no	—
69	#135×C₈₉	—	2	1	no	—
70	#135×C₈₉	D₄	1	2	yes	—
71	#135×C₈₉	C₂³	1	2	yes	—
72	C₂×Q₁₆×C₈₉	—	2	1	no	—
73	C₂×Q₁₆×C₈₉	—	2	1	no	—
74	C₂×Q₁₆×C₈₉	—	2	1	no	—
75	C₂×Q₁₆×C₈₉	—	2	1	no	—
76	C₂×Q₁₆×C₈₉	—	2	1	no	—
77	C₂×Q₁₆×C₈₉	D₄	1	1	yes	characteristic
78	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
79	C₂×SD₁₆×C₈₉	—	2	1	no	—
80	C₂×D₈×C₈₉	D₄	1	1	yes	characteristic
81	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
82	Q₃₂×C₈₉	—	2	4	no	—
83	SD₃₂×C₈₉	—	2	4	no	—
84	M₃₂×C₈₉	—	2	1	no	—
85	M₃₂×C₈₉	C₂³	1	2	yes	—
86	C₂×C₁₆×C₈₉	—	2	1	no	—
87	C₂×Dic₁₇₈	—	2	2	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×Dic₁₇₈	—	4	1	no	—
93	C₂²×Dic₈₉	—	2	1	no	—
94	C₂²×Dic₈₉	—	4	1	no	—
95	Dic₃₅₆	—	2	2	no	—
96	Dic₃₅₆	—	2	2	no	—
97	Dic₃₅₆	—	4	1	no	—
98	Dic₃₅₆	—	4	1	no	—
99	#13083564	—	4	4	no	—
100	#13083564	—	4	4	no	—
101	#13083558	—	2	2	no	—
102	#13083558	—	4	1	no	—
103	#13083558	—	4	4	no	—
104	C₂×#10623494	—	4	1	no	—
105	C₂×#10623494	—	4	4	no	—
106	C₂×#10623494	D₈	1	1	yes	characteristic
107	C₂×#10623494	D₈	1	1	yes	characteristic
108	C₂×#10623494	D₈	1	2	yes	—
109	C₂×#10623494	C₂×D₄	1	2	yes	—
110	#13083553	—	4	8	no	—
111	C₄×Dic₈₉	—	2	1	no	—
112	C₄×Dic₈₉	C₂×D₄	1	2	yes	—
113	#13083549	—	2	2	no	—
114	#41×C₈₉	—	2	2	no	—
115	#41×C₈₉	—	2	2	no	—
116	#41×C₈₉	—	4	1	no	—
117	#41×C₈₉	—	4	1	no	—
118	C₂×Q₈×C₈₉	—	2	1	no	—
119	C₂×Q₈×C₈₉	—	2	2	no	—
120	C₂×Q₈×C₈₉	—	4	1	no	—
121	C₂×Q₈×C₈₉	—	4	1	no	—
122	C₂×Q₈×C₈₉	—	4	1	no	—
123	C₂×Q₈×C₈₉	—	4	1	no	—
124	C₂×Q₈×C₈₉	—	4	1	no	—
125	C₂×D₄×C₈₉	—	2	1	no	—
126	C₂×D₄×C₈₉	—	4	1	no	—
127	C₂²×C₄×C₈₉	—	4	1	no	—
128	C₂²×C₄×C₈₉	—	4	1	no	—
129	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
130	Q₁₆×C₈₉	—	2	1	no	—
131	Q₁₆×C₈₉	—	2	2	no	—
132	Q₁₆×C₈₉	—	2	2	no	—
133	Q₁₆×C₈₉	—	4	1	no	—
134	Q₁₆×C₈₉	—	4	1	no	—
135	Q₁₆×C₈₉	C₂×D₄	1	2	yes	—
136	SD₁₆×C₈₉	—	2	2	no	—
137	SD₁₆×C₈₉	—	2	2	no	—
138	D₈×C₈₉	—	2	1	no	—
139	D₈×C₈₉	C₂×D₄	1	2	yes	—
140	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
141	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
142	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
144	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
145	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
146	C₁₆×C₈₉	—	2	2	no	—
147	C₂³×C₈₉	—	4	1	no	—
148	C₂³×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
149	Q₈×C₈₉	—	2	2	no	—
150	Q₈×C₈₉	—	4	1	no	—
151	Q₈×C₈₉	—	4	2	no	—
152	Q₈×C₈₉	—	4	2	no	—
153	Q₈×C₈₉	—	8	1	no	—
154	Q₈×C₈₉	—	8	1	no	—
155	D₄×C₈₉	—	2	2	no	—
156	D₄×C₈₉	—	4	2	no	—
157	D₄×C₈₉	—	4	2	no	—
158	D₄×C₈₉	—	4	1	no	—
159	C₂×C₄×C₈₉	—	4	1	no	—
160	C₂×C₄×C₈₉	—	4	2	no	—
161	C₂×C₄×C₈₉	—	4	2	no	—
162	C₂×C₄×C₈₉	—	4	2	no	—
163	C₂×C₄×C₈₉	—	8	1	no	—
164	C₂×C₄×C₈₉	—	8	1	no	—
165	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
166	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
167	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
168	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
169	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
170	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
171	C₂×Dic₈₉	—	2	4	no	—
172	C₂×Dic₈₉	—	2	2	no	—
173	C₂×Dic₈₉	—	4	2	no	—
174	C₂×Dic₈₉	—	8	1	no	—
175	C₂×Dic₈₉	—	8	1	no	—
176	Dic₁₇₈	—	4	2	no	—
177	Dic₁₇₈	—	4	2	no	—
178	Dic₁₇₈	—	8	1	no	—
179	Dic₁₇₈	—	8	1	no	—
180	C₈×C₈₉	#121	1	1	yes	characteristic
181	C₈×C₈₉	#121	1	1	yes	characteristic
182	C₈×C₈₉	C₂²×D₄	1	1	yes	characteristic
183	C₈×C₈₉	C₂×#41	1	1	yes	characteristic
184	#10623494	—	4	2	no	—
185	#10623494	C₂×D₈	1	2	yes	—
186	#10623494	C₂×D₈	1	2	yes	—
187	C₂²×C₈₉	—	2	2	no	—
188	C₂²×C₈₉	—	4	2	no	—
189	C₂²×C₈₉	—	8	2	no	—
190	C₂²×C₈₉	#459	1	1	yes	characteristic
191	C₂²×C₈₉	#459	1	1	yes	characteristic
192	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
193	C₄×C₈₉	—	4	2	no	—
194	C₄×C₈₉	—	8	2	no	—
195	C₄×C₈₉	#459	1	1	yes	characteristic
196	C₄×C₈₉	#459	1	1	yes	characteristic
197	C₄×C₈₉	C₂×#121	1	1	yes	characteristic
198	C₄×C₈₉	C₂²×D₈	1	1	yes	characteristic
199	Dic₈₉	—	2	4	no	—
200	Dic₈₉	—	8	2	no	—
201	C₂×#2214	—	89	1	no	maximal, Sylow
202	C₂×C₈₉	—	2	1	no	—
203	C₂×C₈₉	—	2	1	no	—
204	C₂×C₈₉	—	8	2	no	—
205	C₂×C₈₉	#2214	1	2	yes	complemented
206	C₂×C₈₉	C₂×#459	1	1	yes	characteristic
207	C₂×#510	—	89	1	no	—
208	C₂×#510	D₈₉	1	1	yes	characteristic
209	C₂×#494	—	89	1	no	—
210	C₂×#443	—	89	1	no	—
211	#2214	—	89	8	no	—
212	C₂×#364	—	89	1	no	—
213	C₂×#362	—	89	1	no	—
214	C₂×#362	—	89	1	no	—
215	C₈₉	C₂×#2214	1	1	yes	characteristic, complemented, Sylow
216	C₂×#135	C₂×D₈₉	1	1	yes	characteristic
217	C₂²×Q₁₆	—	89	1	no	—
218	C₂²×Q₁₆	—	178	1	no	—
219	C₂²×Q₁₆	C₂×D₈₉	1	1	yes	characteristic
220	C₂×#131	—	178	1	no	—
221	C₂×C₄⋊Q₈	—	178	1	no	—
222	#510	—	2	2	no	—
223	#510	—	89	4	no	—
224	#510	—	178	2	no	—
225	#510	C₂×D₈₉	1	4	yes	—
226	C₂×Q₃₂	—	2	1	no	—
227	C₂×Q₃₂	—	178	1	no	—
228	C₂×SD₃₂	—	2	1	no	—
229	C₂×SD₃₂	—	178	1	no	—
230	C₂×M₃₂	—	89	1	no	—
231	C₂×M₃₂	C₂×D₈₉	1	1	yes	characteristic
232	#494	—	89	4	no	—
233	#494	—	178	2	no	—
234	#443	—	89	4	no	—
235	#443	—	178	2	no	—
236	C₂×#108	—	89	1	no	—
237	C₂×#104	—	178	1	no	—
238	C₂×C₄×C₈	—	89	1	no	—
239	#364	—	89	4	no	—
240	#362	—	89	4	no	—
241	#362	—	89	4	no	—
242	C₂×#41	—	2	1	no	—
243	C₂²×Q₈	—	2	1	no	—
244	C₂²×Q₈	—	178	1	no	—
245	#135	—	2	1	no	—
246	#135	—	2	1	no	—
247	#135	C₂²⋊D₈₉	1	2	yes	—
248	#135	C₂²×D₈₉	1	2	yes	—
249	C₂×Q₁₆	—	2	1	no	—
250	C₂×Q₁₆	—	2	1	no	—
251	C₂×Q₁₆	—	2	1	no	—
252	C₂×Q₁₆	—	2	1	no	—
253	C₂×Q₁₆	—	2	1	no	—
254	C₂×Q₁₆	—	89	2	no	—
255	C₂×Q₁₆	—	356	1	no	—
256	C₂×Q₁₆	—	356	1	no	—
257	C₂×Q₁₆	—	356	2	no	—
258	C₂×Q₁₆	—	178	4	no	—
259	C₂×Q₁₆	—	178	1	no	—
260	C₂×Q₁₆	—	178	1	no	—
261	C₂×Q₁₆	—	178	1	no	—
262	C₂×Q₁₆	—	178	1	no	—
263	C₂×Q₁₆	—	178	1	no	—
264	C₂×Q₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
265	C₂×Q₁₆	C₂²×D₈₉	1	2	yes	—
266	C₂×SD₁₆	—	2	1	no	—
267	C₂×D₈	C₂²⋊D₈₉	1	1	yes	characteristic
268	#131	—	356	2	no	—
269	#131	—	178	4	no	—
270	C₂×M₁₆	—	356	1	no	—
271	C₂×M₁₆	—	178	1	no	—
272	C₂²×C₈	—	89	1	no	—
273	C₂²×C₈	—	356	1	no	—
274	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
275	C₄⋊Q₈	—	356	2	no	—
276	C₄⋊Q₈	—	178	4	no	—
277	C₂×C₄⋊C₄	—	356	2	no	—
278	C₂×C₄²	—	89	1	no	—
279	Q₃₂	—	2	4	no	—
280	Q₃₂	—	178	4	no	—
281	SD₃₂	—	2	4	no	—
282	SD₃₂	—	178	4	no	—
283	M₃₂	—	2	1	no	—
284	M₃₂	—	89	2	no	—
285	M₃₂	—	178	1	no	—
286	M₃₂	C₂²×D₈₉	1	2	yes	—
287	C₂×C₁₆	—	2	1	no	—
288	C₂×C₁₆	—	178	1	no	—
289	#108	—	89	2	no	—
290	#108	—	178	1	no	—
291	#104	—	178	4	no	—
292	C₄×C₈	—	89	2	no	—
293	C₄×C₈	—	89	2	no	—
294	#41	—	2	2	no	—
295	#41	—	2	2	no	—
296	#41	—	4	1	no	—
297	#41	—	4	1	no	—
298	C₂×Q₈	—	2	1	no	—
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	—	4	1	no	—
301	C₂×Q₈	—	4	1	no	—
302	C₂×Q₈	—	4	1	no	—
303	C₂×Q₈	—	4	1	no	—
304	C₂×Q₈	—	4	1	no	—
305	C₂×Q₈	—	356	1	no	—
306	C₂×Q₈	—	356	1	no	—
307	C₂×Q₈	—	356	1	no	—
308	C₂×Q₈	—	356	1	no	—
309	C₂×Q₈	—	356	1	no	—
310	C₂×Q₈	—	178	2	no	—
311	C₂×D₄	—	2	1	no	—
312	C₂×D₄	—	4	1	no	—
313	C₂²×C₄	—	4	1	no	—
314	C₂²×C₄	—	4	1	no	—
315	C₂²×C₄	—	356	1	no	—
316	C₂²×C₄	—	178	1	no	—
317	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
318	Q₁₆	—	2	1	no	—
319	Q₁₆	—	2	2	no	—
320	Q₁₆	—	2	2	no	—
321	Q₁₆	—	4	1	no	—
322	Q₁₆	—	4	1	no	—
323	Q₁₆	—	356	4	no	—
324	Q₁₆	—	356	4	no	—
325	Q₁₆	—	356	1	no	—
326	Q₁₆	—	356	1	no	—
327	Q₁₆	—	178	2	no	—
328	Q₁₆	—	178	2	no	—
329	Q₁₆	C₂×C₂²⋊D₈₉	1	2	yes	—
330	SD₁₆	—	2	2	no	—
331	SD₁₆	—	2	2	no	—
332	D₈	—	2	1	no	—
333	D₈	C₂×C₂²⋊D₈₉	1	2	yes	—
334	M₁₆	—	356	4	no	—
335	M₁₆	—	356	1	no	—
336	M₁₆	—	178	2	no	—
337	C₂×C₈	—	89	1	no	—
338	C₂×C₈	—	89	1	no	—
339	C₂×C₈	—	89	2	no	—
340	C₂×C₈	—	89	2	no	—
341	C₂×C₈	—	356	4	no	—
342	C₂×C₈	—	356	1	no	—
343	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
344	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
345	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
346	C₂×C₈	#13083573	1	1	yes	characteristic
347	C₂×C₈	#13083573	1	1	yes	characteristic
348	C₂×C₈	C₂³×D₈₉	1	1	yes	characteristic
349	C₄⋊C₄	—	356	8	no	—
350	C₄²	—	89	2	no	—
351	C₄²	—	178	1	no	—
352	C₁₆	—	2	2	no	—
353	C₁₆	—	178	2	no	—
354	C₂³	—	4	1	no	—
355	C₂³	#15668036	1	1	yes	characteristic
356	Q₈	—	2	2	no	—
357	Q₈	—	4	1	no	—
358	Q₈	—	4	2	no	—
359	Q₈	—	4	2	no	—
360	Q₈	—	8	1	no	—
361	Q₈	—	8	1	no	—
362	Q₈	—	356	2	no	—
363	Q₈	—	356	2	no	—
364	Q₈	—	712	1	no	—
365	Q₈	—	712	1	no	—
366	D₄	—	2	2	no	—
367	D₄	—	4	2	no	—
368	D₄	—	4	2	no	—
369	D₄	—	4	1	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	8	1	no	—
375	C₂×C₄	—	8	1	no	—
376	C₂×C₄	—	356	2	no	—
377	C₂×C₄	—	178	4	no	—
378	C₂×C₄	—	178	2	no	—
379	C₂×C₄	—	712	1	no	—
380	C₂×C₄	—	712	1	no	—
381	C₂×C₄	#15667984	1	1	yes	characteristic
382	C₂×C₄	#15667984	1	1	yes	characteristic
383	C₂×C₄	D₈×D₈₉	1	1	yes	characteristic
384	C₂×C₄	D₈×D₈₉	1	1	yes	characteristic
385	C₂×C₄	#15668036	1	1	yes	characteristic
386	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
387	C₈	—	89	2	no	—
388	C₈	—	89	2	no	—
389	C₈	—	356	2	no	—
390	C₈	#15667984	1	1	yes	characteristic
391	C₈	#15667984	1	1	yes	characteristic
392	C₈	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
393	C₈	C₂×#13083573	1	1	yes	characteristic
394	C₂²	—	2	2	no	—
395	C₂²	—	4	2	no	—
396	C₂²	—	8	2	no	—
397	C₂²	#19151791	1	1	yes	characteristic
398	C₂²	#19151791	1	1	yes	characteristic
399	C₂²	C₂×#15668036	1	1	yes	characteristic
400	C₄	—	4	2	no	—
401	C₄	—	8	2	no	—
402	C₄	—	178	4	no	—
403	C₄	—	712	2	no	—
404	C₄	#19151791	1	1	yes	characteristic
405	C₄	#19151791	1	1	yes	characteristic
406	C₄	C₂×#15667984	1	1	yes	characteristic
407	C₄	C₂×D₈×D₈₉	1	1	yes	characteristic
408	C₂	—	2	1	no	—
409	C₂	—	2	1	no	—
410	C₂	—	8	2	no	—
411	C₂	#26022331	1	2	yes	direct product factor
412	C₂	C₂×#19151791	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#19151791
commutator, cosocle	C₂×C₈×C₈₉	C₂⁴
Frattini	C₂×C₈	C₂³×D₈₉
Fitting	C₂×#510×C₈₉	C₂
socle	C₂²×C₈₉	#459
prime radical	C₂×#135×C₈₉	C₂²
hypercenter	C₂×#510	D₈₉
hypocenter	C₈₉	C₂×#2214
LCS	G ▷ C₂×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#510

Complements

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

N	H ≅ G/N	type
2. C₂×#19151976	C₂	semidirect
4. #26022331	C₂	direct (N × H)
5. C₂×#19151418	C₂	semidirect
6. C₂×#19151415	C₂	semidirect
7. C₂×#19151414	C₂	semidirect
19. #19151976	C₂²	semidirect
25. #19151418	C₂²	semidirect
26. #19151415	C₂²	semidirect
27. #19151414	C₂²	semidirect
205. C₂×C₈₉	#2214	semidirect
215. C₈₉	C₂×#2214	semidirect
411. C₂	#26022331	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×#19152038	2
C₂×#19151976	2
C₂×#19151715	2
#26022331	2
C₂×#19151418	2
C₂×#19151415	2
C₂×#19151414	2
C₂×#510×C₈₉	2
C₂×#2214	89

Subgroups — C2×#26022331 #36708812

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#26022331 #36708812