Subgroups — C₄×#15668039 #26029061

Order 11392.

548 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15668039	C₂	1	1	yes	maximal, characteristic
2	C₄×#13083575	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₄×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#19151709	C₂	1	1	yes	maximal, characteristic, complemented
5	#19151707	C₂	1	1	yes	maximal, characteristic, complemented
6	#19151701	C₂	1	1	yes	maximal, characteristic, complemented
7	#19151699	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×#13083561	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×D₇₁₂	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#13083559	C₂	1	1	yes	maximal, characteristic, complemented
11	#19151637	C₂	1	1	yes	maximal, characteristic, complemented
12	#19151601	C₂	1	1	yes	maximal, characteristic, complemented
13	#19151598	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#13083557	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×SD₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13083575	C₂²	1	1	yes	characteristic
17	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₈₉	—	2	1	no	—
19	#15668039	C₄	1	8	yes	direct product factor
20	C₂×#13083561	C₂²	1	1	yes	characteristic
21	C₂×D₇₁₂	C₂²	1	1	yes	characteristic
22	C₂×#13083559	C₂²	1	1	yes	characteristic
23	C₂×#13083557	C₂²	1	1	yes	characteristic
24	C₂×#13083557	C₂²	1	1	yes	characteristic
25	Q₈×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
26	C₄×D₃₅₆	—	2	1	no	—
27	C₄×D₃₅₆	C₂²	1	1	yes	characteristic
28	C₄×D₃₅₆	C₂²	1	1	yes	characteristic, complemented
29	D₄×Dic₈₉	C₂²	1	1	yes	characteristic
30	#15667974	—	2	1	no	—
31	#15667974	C₂²	1	1	yes	characteristic
32	#15667974	C₂²	1	1	yes	characteristic, complemented
33	C₄×C₂²⋊D₈₉	—	2	1	no	—
34	#15667972	—	2	1	no	—
35	#15667970	—	2	1	no	—
36	#15667970	C₂²	1	1	yes	characteristic
37	C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
38	C₂²⋊C₄×D₈₉	—	2	1	no	—
39	C₄²×D₈₉	—	2	1	no	—
40	C₄²×D₈₉	C₂²	1	1	yes	characteristic
41	#15667946	C₂²	1	1	yes	characteristic, complemented
42	#15667945	C₂²	1	1	yes	characteristic, complemented
43	#15667943	C₂²	1	1	yes	characteristic, complemented
44	#15667936	C₂²	1	1	yes	characteristic, complemented
45	#15667934	C₂²	1	1	yes	characteristic
46	#15667934	C₂²	1	1	yes	characteristic, complemented
47	#15667933	C₂²	1	1	yes	characteristic
48	#15667932	C₂²	1	1	yes	characteristic
49	#15667932	C₂²	1	1	yes	characteristic, complemented
50	#15667922	C₂²	1	1	yes	characteristic, complemented
51	#15667922	C₂²	1	1	yes	characteristic, complemented
52	C₄×#10623494	C₂²	1	1	yes	characteristic, complemented
53	C₂×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
54	C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
55	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
56	#106×C₈₉	C₂²	1	1	yes	characteristic, complemented
57	#103×C₈₉	C₂²	1	1	yes	characteristic, complemented
58	#102×C₈₉	C₂²	1	1	yes	characteristic
59	C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
60	C₂³×D₈₉	—	2	1	no	—
61	#13083575	—	2	2	no	—
62	#13083575	C₂×C₄	1	4	yes	complemented
63	C₂×D₃₅₆	—	2	1	no	—
64	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
65	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
66	C₂×C₂²⋊D₈₉	—	2	1	no	—
67	D₄×D₈₉	—	2	2	no	—
68	D₄×D₈₉	C₂×C₄	1	4	yes	complemented
69	C₂²×Dic₈₉	—	2	1	no	—
70	C₂×C₄×D₈₉	—	2	1	no	—
71	C₂×C₄×D₈₉	—	2	1	no	—
72	C₂×C₄×D₈₉	—	2	1	no	—
73	C₂×C₄×D₈₉	—	2	1	no	—
74	C₂×C₄×D₈₉	—	2	1	no	—
75	C₂×C₄×D₈₉	—	2	1	no	—
76	C₂×C₄×D₈₉	—	4	4	no	—
77	C₂×C₄×D₈₉	D₄	1	1	yes	characteristic
78	C₂×C₄×D₈₉	D₄	1	1	yes	characteristic
79	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
80	#13083561	C₂×C₄	1	4	yes	complemented
81	D₇₁₂	C₂×C₄	1	4	yes	complemented
82	#13083559	C₂×C₄	1	4	yes	complemented
83	#13083557	—	2	2	no	—
84	#13083557	C₂×C₄	1	4	yes	complemented
85	C₂×#10623494	C₂³	1	1	yes	characteristic
86	C₂×#10623494	C₂³	1	1	yes	characteristic
87	C₄⋊Dic₈₉	—	2	1	no	—
88	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
89	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
90	#13083553	—	2	1	no	—
91	C₂²⋊Dic₈₉	—	2	1	no	—
92	#13083551	—	2	1	no	—
93	#13083551	—	2	1	no	—
94	#13083551	—	2	1	no	—
95	#13083551	—	2	1	no	—
96	#13083551	—	2	1	no	—
97	C₄×Dic₈₉	—	2	1	no	—
98	C₄×Dic₈₉	—	2	1	no	—
99	C₄×Dic₈₉	D₄	1	1	yes	characteristic
100	C₄×Dic₈₉	D₄	1	1	yes	characteristic
101	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
102	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
103	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
104	C₂²×C₄×C₈₉	—	2	1	no	—
105	SD₁₆×C₈₉	C₂×C₄	1	4	yes	complemented
106	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
107	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
108	C₄⋊C₄×C₈₉	—	2	1	no	—
109	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
110	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
111	C₂²⋊C₄×C₈₉	—	2	1	no	—
112	C₄²×C₈₉	—	2	1	no	—
113	C₄²×C₈₉	C₂³	1	1	yes	characteristic
114	C₂³×C₈₉	—	2	1	no	—
115	C₂²×D₈₉	—	2	1	no	—
116	C₂²×D₈₉	—	2	1	no	—
117	C₂²×D₈₉	—	2	4	no	—
118	C₂²×D₈₉	—	4	2	no	—
119	C₂²×D₈₉	—	4	2	no	—
120	C₂²×D₈₉	C₂×D₄	1	1	yes	characteristic
121	Q₈×C₈₉	—	2	1	no	—
122	Q₈×C₈₉	C₂²×C₄	1	2	yes	complemented
123	D₄×C₈₉	—	2	1	no	—
124	D₄×C₈₉	C₂²×C₄	1	2	yes	—
125	C₂×C₄×C₈₉	—	2	1	no	—
126	C₂×C₄×C₈₉	—	2	1	no	—
127	C₂×C₄×C₈₉	—	2	1	no	—
128	C₂×C₄×C₈₉	—	4	2	no	—
129	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
130	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
131	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
132	C₂²⋊D₈₉	—	2	4	no	—
133	C₂×Dic₈₉	—	2	1	no	—
134	C₂×Dic₈₉	—	2	1	no	—
135	C₂×Dic₈₉	—	4	2	no	—
136	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
137	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
138	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
139	D₃₅₆	—	2	4	no	—
140	D₃₅₆	—	2	1	no	—
141	D₃₅₆	—	2	1	no	—
142	D₃₅₆	C₂²×C₄	1	2	yes	—
143	D₃₅₆	C₂²×C₄	1	2	yes	complemented
144	C₄×D₈₉	—	2	2	no	—
145	C₄×D₈₉	—	2	4	no	—
146	C₄×D₈₉	—	4	1	no	—
147	C₄×D₈₉	—	4	2	no	—
148	C₄×D₈₉	—	4	2	no	—
149	C₄×D₈₉	—	4	2	no	—
150	C₄×D₈₉	—	4	2	no	—
151	C₄×D₈₉	—	4	2	no	—
152	C₄×D₈₉	C₂²×C₄	1	2	yes	—
153	C₄×D₈₉	#41	1	2	yes	—
154	C₈×C₈₉	—	2	1	no	—
155	C₈×C₈₉	C₂²×C₄	1	2	yes	complemented
156	#10623494	—	2	1	no	—
157	#10623494	C₂²×C₄	1	2	yes	complemented
158	C₂²×C₈₉	—	2	2	no	—
159	C₂²×C₈₉	—	4	1	no	—
160	C₂²×C₈₉	—	4	1	no	—
161	C₂²×C₈₉	C₂²×D₄	1	1	yes	characteristic
162	C₂×D₈₉	—	2	1	no	—
163	C₂×D₈₉	—	2	1	no	—
164	C₂×D₈₉	—	2	2	no	—
165	C₂×D₈₉	—	2	2	no	—
166	C₂×D₈₉	—	4	8	no	—
167	C₂×D₈₉	—	4	1	no	—
168	C₂×D₈₉	—	4	1	no	—
169	C₂×D₈₉	—	4	1	no	—
170	C₂×D₈₉	—	4	1	no	—
171	C₂×D₈₉	C₄×D₄	1	2	yes	—
172	C₄×C₈₉	—	2	2	no	—
173	C₄×C₈₉	—	2	1	no	—
174	C₄×C₈₉	—	4	1	no	—
175	C₄×C₈₉	—	4	1	no	—
176	C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	complemented
177	C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
178	C₄×C₈₉	C₂×#41	1	1	yes	characteristic
179	Dic₈₉	—	2	1	no	—
180	Dic₈₉	—	2	1	no	—
181	Dic₈₉	—	4	1	no	—
182	Dic₈₉	—	4	1	no	—
183	Dic₈₉	C₄×D₄	1	2	yes	—
184	C₂×C₈₉	—	4	2	no	—
185	C₂×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
186	C₂×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
187	C₂×C₈₉	#575	1	1	yes	characteristic
188	D₈₉	—	2	2	no	—
189	D₈₉	—	4	2	no	—
190	D₈₉	—	4	2	no	—
191	C₄×AGL(1,ℤ/8)	—	89	1	no	maximal, Sylow
192	C₈₉	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
193	C₂×AGL(1,ℤ/8)	—	89	1	no	—
194	C₄×#41	—	89	1	no	—
195	C₂×C₄×D₄	—	89	1	no	—
196	#442	—	89	1	no	—
197	#442	—	89	1	no	—
198	#440	—	89	1	no	—
199	#440	—	89	1	no	—
200	C₄×SD₁₆	—	89	1	no	—
201	C₄×SD₁₆	D₈₉	1	1	yes	characteristic, complemented
202	C₄×D₈	—	89	1	no	—
203	C₄×D₈	—	89	1	no	—
204	#428	—	89	1	no	—
205	#418	—	89	1	no	—
206	#417	—	89	1	no	—
207	C₄×M₁₆	—	89	1	no	—
208	C₂×#41	—	89	1	no	—
209	C₂²×D₄	—	89	1	no	—
210	C₂³×C₄	—	178	1	no	—
211	AGL(1,ℤ/8)	—	89	8	no	—
212	C₂×SD₁₆	—	89	1	no	—
213	C₂×SD₁₆	C₂×D₈₉	1	1	yes	characteristic
214	C₂×D₈	—	89	1	no	—
215	C₂×D₈	—	89	1	no	—
216	C₂×M₁₆	—	89	1	no	—
217	C₂×M₁₆	—	89	1	no	—
218	C₄×Q₈	—	89	1	no	—
219	C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
220	C₄×D₄	—	89	1	no	—
221	C₄×D₄	—	89	1	no	—
222	C₄×D₄	—	89	1	no	—
223	C₄×D₄	—	89	1	no	—
224	C₄×D₄	—	89	1	no	—
225	C₄×D₄	—	178	1	no	—
226	C₄×D₄	—	178	1	no	—
227	C₄×D₄	—	178	1	no	—
228	C₄×D₄	—	178	1	no	—
229	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
230	#117	—	89	1	no	—
231	#117	—	178	1	no	—
232	C₂×C₄⋊C₄	—	89	1	no	—
233	C₂×C₂²⋊C₄	—	178	1	no	—
234	C₂×C₄²	—	89	1	no	—
235	C₂×C₄²	—	178	1	no	—
236	#107	—	89	1	no	—
237	#107	—	89	1	no	—
238	#106	—	89	1	no	—
239	#106	C₂×D₈₉	1	1	yes	characteristic, complemented
240	#103	—	89	1	no	—
241	#103	C₂×D₈₉	1	1	yes	characteristic, complemented
242	#102	—	89	1	no	—
243	#102	—	89	1	no	—
244	#102	—	89	1	no	—
245	#102	—	89	1	no	—
246	#102	—	89	1	no	—
247	#102	C₂×D₈₉	1	1	yes	characteristic
248	#97	—	89	1	no	—
249	#97	—	89	1	no	—
250	C₄×C₈	—	89	1	no	—
251	C₄×C₈	C₂×D₈₉	1	1	yes	characteristic, complemented
252	C₂⁴	—	178	1	no	—
253	#41	—	89	4	no	—
254	#41	—	178	2	no	—
255	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
256	C₂×D₄	—	89	4	no	—
257	C₂×D₄	—	89	1	no	—
258	C₂×D₄	—	89	1	no	—
259	C₂×D₄	—	178	1	no	—
260	C₂×D₄	—	178	2	no	—
261	C₂×D₄	—	178	1	no	—
262	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
263	C₂²×C₄	—	2	1	no	—
264	C₂²×C₄	—	89	1	no	—
265	C₂²×C₄	—	89	1	no	—
266	C₂²×C₄	—	89	1	no	—
267	C₂²×C₄	—	356	4	no	—
268	C₂²×C₄	—	178	1	no	—
269	C₂²×C₄	—	178	1	no	—
270	C₂²×C₄	—	178	1	no	—
271	C₂²×C₄	—	178	1	no	—
272	C₂²×C₄	—	178	1	no	—
273	C₂²×C₄	—	178	1	no	—
274	C₂²×C₄	—	178	1	no	—
275	SD₁₆	—	89	4	no	—
276	SD₁₆	C₄×D₈₉	1	4	yes	complemented
277	D₈	—	89	4	no	—
278	D₈	—	89	4	no	—
279	M₁₆	—	89	4	no	—
280	M₁₆	—	178	2	no	—
281	C₂×C₈	—	89	1	no	—
282	C₂×C₈	—	89	1	no	—
283	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
284	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
285	C₄⋊C₄	—	2	1	no	—
286	C₄⋊C₄	—	89	1	no	—
287	C₄⋊C₄	—	89	1	no	—
288	C₄⋊C₄	—	178	1	no	—
289	C₄⋊C₄	—	178	1	no	—
290	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
291	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
292	C₂²⋊C₄	—	2	1	no	—
293	C₂²⋊C₄	—	178	1	no	—
294	C₂²⋊C₄	—	178	1	no	—
295	C₂²⋊C₄	—	178	1	no	—
296	C₂²⋊C₄	—	178	1	no	—
297	C₂²⋊C₄	—	178	1	no	—
298	C₂²⋊C₄	—	178	1	no	—
299	C₄²	—	2	1	no	—
300	C₄²	—	89	1	no	—
301	C₄²	—	89	1	no	—
302	C₄²	—	89	1	no	—
303	C₄²	—	178	1	no	—
304	C₄²	—	178	1	no	—
305	C₄²	C₂²×D₈₉	1	1	yes	characteristic
306	C₂³	—	2	1	no	—
307	C₂³	—	89	1	no	—
308	C₂³	—	356	2	no	—
309	C₂³	—	356	2	no	—
310	C₂³	—	178	4	no	—
311	C₂³	—	178	1	no	—
312	C₂³	—	178	1	no	—
313	Q₈	—	2	1	no	—
314	Q₈	C₂×C₄×D₈₉	1	2	yes	complemented
315	D₄	—	2	1	no	—
316	D₄	—	89	2	no	—
317	D₄	—	89	2	no	—
318	D₄	—	178	4	no	—
319	D₄	—	178	4	no	—
320	D₄	—	178	1	no	—
321	D₄	—	178	1	no	—
322	D₄	C₂×C₄×D₈₉	1	2	yes	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	89	1	no	—
328	C₂×C₄	—	89	2	no	—
329	C₂×C₄	—	89	2	no	—
330	C₂×C₄	—	89	1	no	—
331	C₂×C₄	—	89	1	no	—
332	C₂×C₄	—	356	1	no	—
333	C₂×C₄	—	356	2	no	—
334	C₂×C₄	—	356	2	no	—
335	C₂×C₄	—	356	2	no	—
336	C₂×C₄	—	356	2	no	—
337	C₂×C₄	—	356	2	no	—
338	C₂×C₄	—	356	2	no	—
339	C₂×C₄	—	178	4	no	—
340	C₂×C₄	—	178	1	no	—
341	C₂×C₄	—	178	1	no	—
342	C₂×C₄	—	178	2	no	—
343	C₂×C₄	D₄×D₈₉	1	1	yes	characteristic
344	C₂×C₄	D₄×D₈₉	1	1	yes	characteristic
345	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
346	C₈	—	2	1	no	—
347	C₈	—	89	2	no	—
348	C₈	—	178	1	no	—
349	C₈	C₂×C₄×D₈₉	1	2	yes	complemented
350	C₂²	—	2	2	no	—
351	C₂²	—	4	1	no	—
352	C₂²	—	4	1	no	—
353	C₂²	—	89	2	no	—
354	C₂²	—	356	8	no	—
355	C₂²	—	356	1	no	—
356	C₂²	—	356	1	no	—
357	C₂²	—	356	1	no	—
358	C₂²	—	356	1	no	—
359	C₂²	—	178	2	no	—
360	C₂²	—	178	2	no	—
361	C₂²	—	178	1	no	—
362	C₂²	—	178	1	no	—
363	C₂²	C₂×D₄×D₈₉	1	1	yes	characteristic
364	C₄	—	2	1	no	—
365	C₄	—	2	2	no	—
366	C₄	—	4	1	no	—
367	C₄	—	4	1	no	—
368	C₄	—	89	2	no	—
369	C₄	—	356	1	no	—
370	C₄	—	356	1	no	—
371	C₄	—	178	1	no	—
372	C₄	—	178	1	no	—
373	C₄	#15668039	1	2	yes	direct product factor
374	C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
375	C₄	#41×D₈₉	1	1	yes	characteristic
376	C₂	—	4	2	no	—
377	C₂	—	356	2	no	—
378	C₂	—	356	2	no	—
379	C₂	—	178	2	no	—
380	C₂	C₄×D₄×D₈₉	1	1	yes	characteristic
381	C₂	C₂×#15668039	1	1	yes	characteristic
382	C₂	#19152395	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₄×D₈₉
commutator	C₄×C₈₉	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₈₉
Fitting	C₄×SD₁₆×C₈₉	C₂
socle	C₂²×C₈₉	C₂²×D₄
prime radical	C₂×#15668039	C₂
cosocle	C₂×C₄×C₈₉	C₂⁴
hypercenter	C₄×SD₁₆	D₈₉
hypocenter	C₈₉	C₄×AGL(1,ℤ/8)
LCS	G ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×SD₁₆

Complements

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

N	H ≅ G/N	type
2. C₄×#13083575	C₂	semidirect
3. C₄×D₄×D₈₉	C₂	semidirect
4. #19151709	C₂	semidirect
5. #19151707	C₂	semidirect
6. #19151701	C₂	semidirect
7. #19151699	C₂	semidirect
8. C₄×#13083561	C₂	semidirect
9. C₄×D₇₁₂	C₂	semidirect
10. C₄×#13083559	C₂	semidirect
11. #19151637	C₂	semidirect
12. #19151601	C₂	semidirect
13. #19151598	C₂	semidirect
14. C₄×#13083557	C₂	semidirect
15. C₄×SD₁₆×C₈₉	C₂	semidirect
19. #15668039	C₄	direct (N × H)
25. Q₈×Dic₈₉	C₂²	semidirect
28. C₄×D₃₅₆	C₂²	semidirect
32. #15667974	C₂²	semidirect
41. #15667946	C₂²	semidirect
42. #15667945	C₂²	semidirect
43. #15667943	C₂²	semidirect
44. #15667936	C₂²	semidirect
46. #15667934	C₂²	semidirect
49. #15667932	C₂²	semidirect
50. #15667922	C₂²	semidirect
51. #15667922	C₂²	semidirect
52. C₄×#10623494	C₂²	semidirect
54. C₄×Q₈×C₈₉	C₂²	semidirect
56. #106×C₈₉	C₂²	semidirect
57. #103×C₈₉	C₂²	semidirect
59. C₄×C₈×C₈₉	C₂²	semidirect
62. #13083575	C₂×C₄	semidirect
68. D₄×D₈₉	C₂×C₄	semidirect
80. #13083561	C₂×C₄	semidirect
81. D₇₁₂	C₂×C₄	semidirect
82. #13083559	C₂×C₄	semidirect
84. #13083557	C₂×C₄	semidirect
105. SD₁₆×C₈₉	C₂×C₄	semidirect
122. Q₈×C₈₉	C₂²×C₄	semidirect
143. D₃₅₆	C₂²×C₄	semidirect
155. C₈×C₈₉	C₂²×C₄	semidirect
157. #10623494	C₂²×C₄	semidirect
176. C₄×C₈₉	AGL(1,ℤ/8)	semidirect
192. C₈₉	C₄×AGL(1,ℤ/8)	semidirect
201. C₄×SD₁₆	D₈₉	semidirect
219. C₄×Q₈	C₂×D₈₉	semidirect
239. #106	C₂×D₈₉	semidirect
241. #103	C₂×D₈₉	semidirect
251. C₄×C₈	C₂×D₈₉	semidirect
276. SD₁₆	C₄×D₈₉	semidirect
314. Q₈	C₂×C₄×D₈₉	semidirect
349. C₈	C₂×C₄×D₈₉	semidirect
373. C₄	#15668039	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×#15668039	2
C₄×#13083575	2
C₄×D₄×D₈₉	2
#19151709	2
#19151707	2
#19151701	2
#19151699	2
C₄×#13083561	2
C₄×D₇₁₂	2
C₄×#13083559	2
#19151637	2
#19151601	2
#19151598	2
C₄×#13083557	2
C₄×SD₁₆×C₈₉	2
C₄×AGL(1,ℤ/8)	89

Subgroups — C4×#15668039 #26029061

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#15668039 #26029061