Subgroups — C₂×#26019598 #36536746

Order 22784.

786 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151970	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151883	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×Q₈×#10623494	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019598	C₂	1	8	yes	maximal, direct product factor
5	C₂×#19151348	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#19151343	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#19151342	C₂	1	1	yes	maximal, characteristic
8	C₂×#460×C₈₉	C₂	1	1	yes	maximal, characteristic
9	C₂²×#13083562	—	2	1	no	—
10	C₂²×#13083562	—	2	1	no	—
11	C₂×#15668012	C₂²	1	1	yes	characteristic
12	#19151970	—	2	2	no	—
13	#19151970	C₂²	1	4	yes	—
14	#19151883	—	2	2	no	—
15	#19151883	C₂²	1	4	yes	complemented
16	Q₈×#10623494	—	2	2	no	—
17	Q₈×#10623494	C₂²	1	4	yes	complemented
18	C₂×#15667943	—	2	1	no	—
19	C₂×C₄⋊#10623494	—	2	1	no	—
20	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
22	C₂×#15667936	—	2	1	no	—
23	C₂×C₄×#10623494	—	2	1	no	—
24	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
25	#19151348	C₂²	1	4	yes	complemented
26	#19151343	C₂²	1	4	yes	complemented
27	#19151342	C₂²	1	4	yes	—
28	C₂²×SD₁₆×C₈₉	—	2	1	no	—
29	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
31	#460×C₈₉	—	2	2	no	—
32	#460×C₈₉	C₂²	1	4	yes	—
33	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
34	C₂×#102×C₈₉	—	2	1	no	—
35	C₂²×Dic₁₇₈	—	2	1	no	—
36	C₂×#13083562	—	2	4	no	—
37	C₂×#13083562	—	2	4	no	—
38	C₂×#13083562	—	4	4	no	—
39	C₂×#13083562	—	4	4	no	—
40	C₂²×#10623494	—	2	1	no	—
41	C₂²×#10623494	—	2	1	no	—
42	C₂²×#10623494	D₄	1	1	yes	characteristic
43	C₂²×#10623494	D₄	1	1	yes	characteristic
44	#15668012	—	2	1	no	—
45	#15668012	—	2	1	no	—
46	#15668012	—	2	1	no	—
47	#15668012	C₂³	1	2	yes	—
48	C₂×C₄⋊Dic₈₉	—	2	1	no	—
49	C₂×C₄⋊Dic₈₉	—	2	1	no	—
50	#15667943	—	2	4	no	—
51	C₄⋊#10623494	—	2	4	no	—
52	C₄⋊#10623494	—	2	1	no	—
53	C₄⋊#10623494	—	2	1	no	—
54	C₄⋊#10623494	C₂³	1	2	yes	—
55	C₄⋊#10623494	C₂³	1	2	yes	—
56	#15667936	—	2	4	no	—
57	C₄×#10623494	—	2	4	no	—
58	C₄×#10623494	D₄	1	2	yes	—
59	C₄×#10623494	C₂³	1	2	yes	—
60	C₂²×Q₈×C₈₉	D₄	1	1	yes	characteristic
61	C₂²×D₄×C₈₉	—	2	1	no	—
62	C₂²×D₄×C₈₉	—	2	1	no	—
63	C₂²×D₄×C₈₉	—	2	1	no	—
64	C₂×SD₁₆×C₈₉	—	2	4	no	—
65	C₂×SD₁₆×C₈₉	—	4	4	no	—
66	C₂²×C₈×C₈₉	—	2	1	no	—
67	#127×C₈₉	—	2	1	no	—
68	#127×C₈₉	—	2	1	no	—
69	#127×C₈₉	—	2	1	no	—
70	#127×C₈₉	C₂³	1	2	yes	—
71	C₄×Q₈×C₈₉	—	2	1	no	—
72	C₄×Q₈×C₈₉	—	2	1	no	—
73	C₄×Q₈×C₈₉	D₄	1	2	yes	—
74	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
75	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
76	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₈₉	—	2	1	no	—
78	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
79	C₄⋊C₈×C₈₉	—	2	1	no	—
80	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
81	#102×C₈₉	—	2	4	no	—
82	C₂×Dic₁₇₈	—	2	2	no	—
83	C₂×Dic₁₇₈	—	4	2	no	—
84	C₂×Dic₁₇₈	—	4	2	no	—
85	C₂×Dic₁₇₈	—	4	1	no	—
86	C₂²×Dic₈₉	—	4	1	no	—
87	#13083562	—	4	8	no	—
88	#13083562	—	4	8	no	—
89	C₂×#10623494	—	2	2	no	—
90	C₂×#10623494	—	2	2	no	—
91	C₂×#10623494	—	2	2	no	—
92	C₂×#10623494	—	4	2	no	—
93	C₂×#10623494	—	4	2	no	—
94	C₂×#10623494	SD₁₆	1	4	yes	complemented
95	C₂×#10623494	C₂×D₄	1	2	yes	—
96	C₂×#10623494	C₂×D₄	1	2	yes	—
97	C₄⋊Dic₈₉	—	2	2	no	—
98	C₄⋊Dic₈₉	—	2	2	no	—
99	C₄⋊Dic₈₉	—	4	1	no	—
100	C₄⋊Dic₈₉	—	4	1	no	—
101	C₂⁴×C₈₉	—	4	1	no	—
102	C₂×Q₈×C₈₉	—	2	1	no	—
103	C₂×Q₈×C₈₉	—	2	2	no	—
104	C₂×Q₈×C₈₉	SD₁₆	1	4	yes	complemented
105	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
106	C₂×D₄×C₈₉	—	2	2	no	—
107	C₂×D₄×C₈₉	—	2	2	no	—
108	C₂×D₄×C₈₉	—	2	2	no	—
109	C₂×D₄×C₈₉	—	4	1	no	—
110	C₂×D₄×C₈₉	—	4	1	no	—
111	C₂×D₄×C₈₉	—	4	1	no	—
112	C₂×D₄×C₈₉	—	4	2	no	—
113	C₂×D₄×C₈₉	—	4	2	no	—
114	C₂×D₄×C₈₉	—	4	2	no	—
115	C₂×D₄×C₈₉	—	4	2	no	—
116	C₂×D₄×C₈₉	—	8	2	no	—
117	C₂²×C₄×C₈₉	—	2	1	no	—
118	C₂²×C₄×C₈₉	—	2	1	no	—
119	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
122	SD₁₆×C₈₉	—	4	8	no	—
123	C₂×C₈×C₈₉	—	2	2	no	—
124	C₂×C₈×C₈₉	—	4	2	no	—
125	C₄⋊C₄×C₈₉	—	2	2	no	—
126	C₄⋊C₄×C₈₉	—	2	1	no	—
127	C₄⋊C₄×C₈₉	—	2	2	no	—
128	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
129	C₄²×C₈₉	—	2	2	no	—
130	C₄²×C₈₉	—	2	2	no	—
131	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₈₉	#41	1	1	yes	characteristic
134	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
135	C₂³×C₈₉	—	4	2	no	—
136	C₂³×C₈₉	—	8	2	no	—
137	C₂³×C₈₉	—	8	2	no	—
138	C₂³×C₈₉	—	8	2	no	—
139	C₂³×C₈₉	#121	1	1	yes	characteristic
140	Q₈×C₈₉	—	2	2	no	—
141	Q₈×C₈₉	—	2	4	no	—
142	Q₈×C₈₉	C₂×SD₁₆	1	4	yes	complemented
143	D₄×C₈₉	—	4	2	no	—
144	D₄×C₈₉	—	4	2	no	—
145	D₄×C₈₉	—	4	2	no	—
146	D₄×C₈₉	—	4	2	no	—
147	D₄×C₈₉	—	8	2	no	—
148	D₄×C₈₉	—	8	2	no	—
149	D₄×C₈₉	—	8	2	no	—
150	D₄×C₈₉	—	8	2	no	—
151	C₂×C₄×C₈₉	—	2	2	no	—
152	C₂×C₄×C₈₉	—	2	4	no	—
153	C₂×C₄×C₈₉	—	2	2	no	—
154	C₂×C₄×C₈₉	—	2	2	no	—
155	C₂×C₄×C₈₉	—	4	2	no	—
156	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
157	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
158	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
159	C₂×C₄×C₈₉	C₂×SD₁₆	1	2	yes	—
160	C₂×C₄×C₈₉	C₂×SD₁₆	1	2	yes	—
161	C₂×C₄×C₈₉	#135	1	2	yes	—
162	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
163	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
166	C₂×Dic₈₉	—	4	2	no	—
167	C₂×Dic₈₉	—	8	2	no	—
168	Dic₁₇₈	—	4	2	no	—
169	Dic₁₇₈	—	4	2	no	—
170	Dic₁₇₈	—	8	2	no	—
171	C₈×C₈₉	—	4	2	no	—
172	#10623494	—	2	2	no	—
173	#10623494	—	4	2	no	—
174	#10623494	—	4	2	no	—
175	#10623494	C₂×SD₁₆	1	4	yes	complemented
176	C₂²×C₈₉	—	8	2	no	—
177	C₂²×C₈₉	—	8	2	no	—
178	C₂²×C₈₉	—	8	2	no	—
179	C₂²×C₈₉	—	16	4	no	—
180	C₂²×C₈₉	#460	1	2	yes	—
181	C₂²×C₈₉	#465	1	2	yes	—
182	C₂²×C₈₉	#471	1	2	yes	—
183	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
184	C₄×C₈₉	—	2	4	no	—
185	C₄×C₈₉	—	2	1	no	—
186	C₄×C₈₉	—	2	1	no	—
187	C₄×C₈₉	—	4	2	no	—
188	C₄×C₈₉	#460	1	2	yes	—
189	C₄×C₈₉	#465	1	2	yes	—
190	C₄×C₈₉	C₂²×SD₁₆	1	1	yes	characteristic
191	C₄×C₈₉	C₂²×SD₁₆	1	1	yes	characteristic
192	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
193	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
194	Dic₈₉	—	8	2	no	—
195	C₂×#1666	—	89	1	no	maximal, Sylow
196	C₂×C₈₉	—	16	2	no	—
197	C₂×C₈₉	#1666	1	4	yes	complemented
198	C₂×C₈₉	C₂×#460	1	1	yes	characteristic
199	C₂×C₈₉	C₂×#465	1	1	yes	characteristic
200	C₂×C₈₉	C₂×#471	1	1	yes	characteristic
201	C₂×#492	—	89	1	no	—
202	C₂×#475	—	89	1	no	—
203	C₂×#460	D₈₉	1	1	yes	characteristic
204	C₂×C₈×Q₈	—	89	1	no	—
205	#1666	—	89	8	no	—
206	C₂×#334	—	89	1	no	—
207	C₂×#332	—	89	1	no	—
208	C₂×#331	—	89	1	no	—
209	C₈₉	C₂×#1666	1	1	yes	characteristic, complemented, Sylow
210	C₂²×SD₁₆	—	2	1	no	—
211	C₂²×SD₁₆	—	178	1	no	—
212	C₂²×SD₁₆	—	178	1	no	—
213	C₂×C₄⋊Q₈	—	89	1	no	—
214	C₂×#127	C₂×D₈₉	1	1	yes	characteristic
215	C₂×C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic
216	#492	—	89	4	no	—
217	#492	—	178	2	no	—
218	#475	—	89	4	no	—
219	#475	—	178	2	no	—
220	#460	—	2	2	no	—
221	#460	C₂×D₈₉	1	4	yes	—
222	C₈×Q₈	—	89	4	no	—
223	C₈×Q₈	—	178	2	no	—
224	C₂×#106	—	178	1	no	—
225	C₂×C₄⋊C₈	—	89	1	no	—
226	C₂×C₄⋊C₈	—	89	1	no	—
227	C₂×C₄⋊C₈	—	178	1	no	—
228	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
229	C₂×#103	—	178	1	no	—
230	C₂×#102	—	2	1	no	—
231	C₂×C₄×C₈	—	89	1	no	—
232	C₂×C₄×C₈	—	178	1	no	—
233	#334	—	89	4	no	—
234	#332	—	89	4	no	—
235	#331	—	89	4	no	—
236	C₂²×Q₈	—	178	1	no	—
237	C₂²×Q₈	C₂²⋊D₈₉	1	1	yes	characteristic
238	C₂²×D₄	—	2	1	no	—
239	C₂²×D₄	—	2	1	no	—
240	C₂²×D₄	—	2	1	no	—
241	C₂×SD₁₆	—	2	4	no	—
242	C₂×SD₁₆	—	4	4	no	—
243	C₂×SD₁₆	—	356	4	no	—
244	C₂×SD₁₆	—	356	4	no	—
245	C₂×SD₁₆	—	178	4	no	—
246	C₂×SD₁₆	—	178	4	no	—
247	C₂²×C₈	—	2	1	no	—
248	C₂²×C₈	—	89	1	no	—
249	C₂²×C₈	—	89	1	no	—
250	C₂²×C₈	—	178	1	no	—
251	C₂²×C₈	—	178	1	no	—
252	C₄⋊Q₈	—	89	2	no	—
253	C₄⋊Q₈	—	178	1	no	—
254	C₄⋊Q₈	—	178	1	no	—
255	C₄⋊Q₈	—	178	1	no	—
256	#127	—	2	1	no	—
257	#127	—	2	1	no	—
258	#127	—	2	1	no	—
259	#127	C₂²×D₈₉	1	2	yes	—
260	C₄×Q₈	—	2	1	no	—
261	C₄×Q₈	—	2	1	no	—
262	C₄×Q₈	C₂²⋊D₈₉	1	2	yes	—
263	C₄×Q₈	C₂²×D₈₉	1	2	yes	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	—	178	1	no	—
266	C₂×C₄⋊C₄	—	178	1	no	—
267	C₂×C₄⋊C₄	C₂²⋊D₈₉	1	1	yes	characteristic
268	C₂×C₄²	—	2	1	no	—
269	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
270	#106	—	178	4	no	—
271	C₄⋊C₈	—	2	1	no	—
272	C₄⋊C₈	—	89	2	no	—
273	C₄⋊C₈	—	89	2	no	—
274	C₄⋊C₈	—	178	4	no	—
275	C₄⋊C₈	—	178	1	no	—
276	C₄⋊C₈	—	178	1	no	—
277	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
278	#103	—	178	4	no	—
279	#102	—	2	4	no	—
280	C₄×C₈	—	89	2	no	—
281	C₄×C₈	—	89	2	no	—
282	C₄×C₈	—	178	4	no	—
283	C₂⁴	—	4	1	no	—
284	C₂×Q₈	—	2	1	no	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	356	1	no	—
287	C₂×Q₈	—	356	2	no	—
288	C₂×Q₈	—	356	2	no	—
289	C₂×Q₈	—	178	2	no	—
290	C₂×Q₈	#13083562	1	4	yes	complemented
291	C₂×Q₈	C₂×C₂²⋊D₈₉	1	2	yes	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	4	1	no	—
296	C₂×D₄	—	4	1	no	—
297	C₂×D₄	—	4	1	no	—
298	C₂×D₄	—	4	2	no	—
299	C₂×D₄	—	4	2	no	—
300	C₂×D₄	—	4	2	no	—
301	C₂×D₄	—	4	2	no	—
302	C₂×D₄	—	8	2	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	356	1	no	—
306	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
307	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
308	C₂²×C₄	#13083573	1	1	yes	characteristic
309	SD₁₆	—	4	8	no	—
310	SD₁₆	—	356	8	no	—
311	SD₁₆	—	356	8	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	4	2	no	—
314	C₂×C₈	—	89	4	no	—
315	C₂×C₈	—	89	2	no	—
316	C₂×C₈	—	89	2	no	—
317	C₂×C₈	—	356	2	no	—
318	C₂×C₈	—	356	2	no	—
319	C₂×C₈	—	178	2	no	—
320	C₂×C₈	—	178	2	no	—
321	C₂×C₈	—	178	2	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	1	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	356	1	no	—
326	C₄⋊C₄	—	356	1	no	—
327	C₄⋊C₄	—	178	2	no	—
328	C₄⋊C₄	—	178	2	no	—
329	C₄⋊C₄	C₂×C₂²⋊D₈₉	1	2	yes	—
330	C₄²	—	2	2	no	—
331	C₄²	—	2	2	no	—
332	C₄²	D₄×D₈₉	1	1	yes	characteristic
333	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
334	C₄²	#13083573	1	1	yes	characteristic
335	C₄²	C₂³×D₈₉	1	1	yes	characteristic
336	C₂³	—	4	2	no	—
337	C₂³	—	8	2	no	—
338	C₂³	—	8	2	no	—
339	C₂³	—	8	2	no	—
340	C₂³	#15667984	1	1	yes	characteristic
341	Q₈	—	2	4	no	—
342	Q₈	—	2	2	no	—
343	Q₈	—	356	2	no	—
344	Q₈	—	356	2	no	—
345	Q₈	—	712	2	no	—
346	Q₈	C₂×#13083562	1	4	yes	complemented
347	D₄	—	4	2	no	—
348	D₄	—	4	2	no	—
349	D₄	—	4	2	no	—
350	D₄	—	4	2	no	—
351	D₄	—	8	2	no	—
352	D₄	—	8	2	no	—
353	D₄	—	8	2	no	—
354	D₄	—	8	2	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	356	2	no	—
361	C₂×C₄	—	712	2	no	—
362	C₂×C₄	#15667984	1	1	yes	characteristic
363	C₂×C₄	#15667984	1	1	yes	characteristic
364	C₂×C₄	#15667984	1	1	yes	characteristic
365	C₂×C₄	SD₁₆×D₈₉	1	2	yes	—
366	C₂×C₄	C₂×#13083562	1	2	yes	—
367	C₂×C₄	#15668032	1	2	yes	—
368	C₂×C₄	#15668039	1	2	yes	—
369	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
370	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
371	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
372	C₈	—	4	2	no	—
373	C₈	—	89	4	no	—
374	C₈	—	356	2	no	—
375	C₈	—	356	2	no	—
376	C₈	—	178	2	no	—
377	C₂²	—	8	2	no	—
378	C₂²	—	8	2	no	—
379	C₂²	—	8	2	no	—
380	C₂²	—	16	4	no	—
381	C₂²	#19151796	1	2	yes	—
382	C₂²	#19151825	1	2	yes	—
383	C₂²	#19151859	1	2	yes	—
384	C₂²	C₂×#15667984	1	1	yes	characteristic
385	C₄	—	2	1	no	—
386	C₄	—	2	1	no	—
387	C₄	—	2	4	no	—
388	C₄	—	4	2	no	—
389	C₄	—	712	2	no	—
390	C₄	#19151796	1	2	yes	—
391	C₄	#19151825	1	2	yes	—
392	C₄	C₂×SD₁₆×D₈₉	1	1	yes	characteristic
393	C₄	C₂²×#13083562	1	1	yes	characteristic
394	C₄	C₂×#15668032	1	1	yes	characteristic
395	C₄	C₂×#15668039	1	1	yes	characteristic
396	C₂	—	16	2	no	—
397	C₂	#26019598	1	4	yes	direct product factor
398	C₂	C₂×#19151796	1	1	yes	characteristic
399	C₂	C₂×#19151825	1	1	yes	characteristic
400	C₂	C₂×#19151859	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#15667984
commutator, cosocle	C₄²×C₈₉	C₂⁴
Frattini	C₄²	C₂³×D₈₉
Fitting	C₂×#460×C₈₉	C₂
socle	C₂³×C₈₉	#121
prime radical	C₂×#127×C₈₉	C₂²
hypercenter	C₂×#460	D₈₉
hypocenter	C₈₉	C₂×#1666
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#460

Complements

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

N	H ≅ G/N	type
2. C₂×#19151883	C₂	semidirect
3. C₂×Q₈×#10623494	C₂	semidirect
4. #26019598	C₂	direct (N × H)
5. C₂×#19151348	C₂	semidirect
6. C₂×#19151343	C₂	semidirect
15. #19151883	C₂²	semidirect
17. Q₈×#10623494	C₂²	semidirect
25. #19151348	C₂²	semidirect
26. #19151343	C₂²	semidirect
94. C₂×#10623494	SD₁₆	semidirect
104. C₂×Q₈×C₈₉	SD₁₆	semidirect
142. Q₈×C₈₉	C₂×SD₁₆	semidirect
175. #10623494	C₂×SD₁₆	semidirect
197. C₂×C₈₉	#1666	semidirect
209. C₈₉	C₂×#1666	semidirect
290. C₂×Q₈	#13083562	semidirect
346. Q₈	C₂×#13083562	semidirect
397. C₂	#26019598	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×#19151970	2
C₂×#19151883	2
C₂×Q₈×#10623494	2
#26019598	2
C₂×#19151348	2
C₂×#19151343	2
C₂×#19151342	2
C₂×#460×C₈₉	2
C₂×#1666	89

Subgroups — C2×#26019598 #36536746

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#26019598 #36536746