Subgroups — C₄×#19151950 #36562406

Order 22784.

878 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151950	C₂	1	1	yes	maximal, characteristic
2	C₄×#15668012	C₂	1	1	yes	maximal, characteristic
3	#26021214	C₂	1	1	yes	maximal, characteristic
4	#26021053	C₂	1	1	yes	maximal, characteristic
5	#26020927	C₂	1	4	yes	maximal
6	#26020379	C₂	1	1	yes	maximal, characteristic
7	C₄×#15667935	C₂	1	4	yes	maximal
8	C₄²×#10623494	C₂	1	1	yes	maximal, characteristic
9	C₄×C₄⋊Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic
10	C₂×#15668012	C₂²	1	1	yes	characteristic
11	C₂×C₄×Dic₁₇₈	C₂²	1	2	yes	—
12	#19151950	C₄	1	8	yes	direct product factor
13	C₂×#15667935	C₂²	1	4	yes	—
14	C₂×#15667935	C₂²	1	4	yes	—
15	C₂×C₄×#10623494	C₂²	1	2	yes	—
16	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
17	C₂×C₄×#10623494	C₂²	1	2	yes	—
18	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
19	#19151504	C₂²	1	2	yes	—
20	#19151496	—	2	1	no	—
21	#19151496	—	2	1	no	—
22	#19151468	C₂²	1	1	yes	characteristic
23	C₄×C₄⋊Dic₈₉	—	2	1	no	—
24	C₄×C₄⋊Dic₈₉	—	2	1	no	—
25	#19151360	C₂²	1	4	yes	—
26	#19151360	C₂²	1	4	yes	—
27	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₈₉	—	2	1	no	—
29	#391×C₈₉	—	2	1	no	—
30	#389×C₈₉	—	2	1	no	—
31	#389×C₈₉	C₂²	1	2	yes	—
32	#384×C₈₉	C₂²	1	1	yes	characteristic
33	C₄×C₄⋊C₄×C₈₉	—	2	1	no	—
34	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
35	C₄³×C₈₉	C₂²	1	1	yes	characteristic
36	C₂²×Dic₁₇₈	C₂³	1	2	yes	—
37	C₂²×#10623494	C₂³	1	2	yes	—
38	C₂²×#10623494	C₂³	1	2	yes	—
39	#15668012	—	2	2	no	—
40	#15668012	C₂×C₄	1	4	yes	—
41	C₄×Dic₁₇₈	—	2	8	no	—
42	C₂×C₄⋊Dic₈₉	—	2	1	no	—
43	C₂×C₄⋊Dic₈₉	—	2	1	no	—
44	C₂×C₄⋊Dic₈₉	—	2	1	no	—
45	C₂×C₄⋊Dic₈₉	—	2	1	no	—
46	C₂×C₄⋊Dic₈₉	C₂³	1	2	yes	—
47	C₂×#13083553	—	2	2	no	—
48	C₂×C₄×Dic₈₉	—	2	2	no	—
49	#15667935	—	2	8	no	—
50	#15667935	C₂×C₄	1	16	yes	—
51	C₄×#10623494	—	2	4	no	—
52	C₄×#10623494	—	2	2	no	—
53	C₄×#10623494	—	2	4	no	—
54	C₄×#10623494	C₂×C₄	1	4	yes	—
55	#15667919	—	2	2	no	—
56	#15667919	—	2	2	no	—
57	C₂²×Q₈×C₈₉	—	2	1	no	—
58	C₄⋊Q₈×C₈₉	—	2	2	no	—
59	C₄⋊Q₈×C₈₉	C₂×C₄	1	4	yes	—
60	C₄×Q₈×C₈₉	—	4	4	no	—
61	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
62	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
64	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
65	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
67	C₂×C₄²×C₈₉	—	2	2	no	—
68	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
75	#95×C₈₉	—	2	2	no	—
76	#95×C₈₉	—	2	2	no	—
77	C₂×Dic₁₇₈	—	2	4	no	—
78	C₂×Dic₁₇₈	—	2	4	no	—
79	C₂×Dic₁₇₈	—	2	2	no	—
80	C₂×Dic₁₇₈	C₂²×C₄	1	4	yes	—
81	C₂²×Dic₈₉	—	2	2	no	—
82	C₂²×Dic₈₉	—	2	2	no	—
83	C₂×#10623494	—	2	2	no	—
84	C₂×#10623494	—	2	2	no	—
85	C₂×#10623494	—	2	2	no	—
86	C₂×#10623494	—	2	2	no	—
87	C₂×#10623494	C₂²×C₄	1	4	yes	—
88	C₂×#10623494	#41	1	4	yes	—
89	C₄⋊Dic₈₉	—	2	4	no	—
90	C₄⋊Dic₈₉	—	2	4	no	—
91	C₄⋊Dic₈₉	—	2	4	no	—
92	C₄⋊Dic₈₉	—	4	2	no	—
93	C₄⋊Dic₈₉	—	4	2	no	—
94	#13083553	—	4	4	no	—
95	C₄×Dic₈₉	—	4	4	no	—
96	C₂×Q₈×C₈₉	—	2	4	no	—
97	C₂×Q₈×C₈₉	—	4	2	no	—
98	C₂×Q₈×C₈₉	—	4	2	no	—
99	C₂²×C₄×C₈₉	—	2	2	no	—
100	C₂²×C₄×C₈₉	—	2	2	no	—
101	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
108	C₄⋊C₄×C₈₉	—	2	4	no	—
109	C₄⋊C₄×C₈₉	—	2	2	no	—
110	C₄⋊C₄×C₈₉	—	2	4	no	—
111	C₄⋊C₄×C₈₉	—	4	4	no	—
112	C₄⋊C₄×C₈₉	—	4	2	no	—
113	C₄⋊C₄×C₈₉	—	4	2	no	—
114	C₄⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
115	C₄²×C₈₉	—	2	2	no	—
116	C₄²×C₈₉	—	2	2	no	—
117	C₄²×C₈₉	—	2	2	no	—
118	C₄²×C₈₉	—	4	4	no	—
119	C₄²×C₈₉	SD₁₆	1	4	yes	—
120	C₄²×C₈₉	Q₁₆	1	4	yes	—
121	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
122	C₄²×C₈₉	#41	1	2	yes	—
123	C₄²×C₈₉	#41	1	4	yes	—
124	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
125	Q₈×C₈₉	—	4	8	no	—
126	C₂×C₄×C₈₉	—	2	1	no	—
127	C₂×C₄×C₈₉	—	2	1	no	—
128	C₂×C₄×C₈₉	—	2	1	no	—
129	C₂×C₄×C₈₉	—	2	1	no	—
130	C₂×C₄×C₈₉	—	2	1	no	—
131	C₂×C₄×C₈₉	—	2	1	no	—
132	C₂×C₄×C₈₉	—	2	4	no	—
133	C₂×C₄×C₈₉	—	4	2	no	—
134	C₂×C₄×C₈₉	—	4	2	no	—
135	C₂×C₄×C₈₉	—	4	2	no	—
136	C₂×C₄×C₈₉	—	4	2	no	—
137	C₂×C₄×C₈₉	—	4	2	no	—
138	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
139	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
140	C₂×C₄×C₈₉	#124	1	2	yes	—
141	C₂×C₄×C₈₉	#124	1	2	yes	—
142	C₂×C₄×C₈₉	C₂×SD₁₆	1	2	yes	—
143	C₂×C₄×C₈₉	C₂×SD₁₆	1	2	yes	—
144	C₂×C₄×C₈₉	C₂×SD₁₆	1	2	yes	—
145	C₂×C₄×C₈₉	C₂×Q₁₆	1	2	yes	—
146	C₂×C₄×C₈₉	C₂×Q₁₆	1	2	yes	—
147	C₂×C₄×C₈₉	C₂×Q₁₆	1	2	yes	—
148	C₂×C₄×C₈₉	#135	1	2	yes	—
149	C₂×C₄×C₈₉	#135	1	2	yes	—
150	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
151	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
152	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
153	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
154	C₂×Dic₈₉	—	2	4	no	—
155	C₂×Dic₈₉	—	4	2	no	—
156	C₂×Dic₈₉	—	4	2	no	—
157	C₂×Dic₈₉	—	4	2	no	—
158	C₂×Dic₈₉	—	4	2	no	—
159	C₂×Dic₈₉	—	4	2	no	—
160	Dic₁₇₈	—	2	8	no	—
161	Dic₁₇₈	—	4	4	no	—
162	#10623494	—	2	4	no	—
163	#10623494	—	2	4	no	—
164	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
165	C₂²×C₈₉	C₂×#124	1	1	yes	characteristic
166	C₂²×C₈₉	#532	1	1	yes	characteristic
167	C₂²×C₈₉	C₂²×SD₁₆	1	1	yes	characteristic
168	C₂²×C₈₉	C₂²×Q₁₆	1	1	yes	characteristic
169	C₂²×C₈₉	C₂×#135	1	1	yes	characteristic
170	C₂²×C₈₉	C₂×#135	1	1	yes	characteristic
171	C₄×C₈₉	—	2	2	no	—
172	C₄×C₈₉	—	2	2	no	—
173	C₄×C₈₉	—	2	2	no	—
174	C₄×C₈₉	—	4	4	no	—
175	C₄×C₈₉	—	8	2	no	—
176	C₄×C₈₉	C₄×SD₁₆	1	4	yes	—
177	C₄×C₈₉	C₄×Q₁₆	1	4	yes	—
178	C₄×C₈₉	#487	1	4	yes	complemented
179	C₄×C₈₉	C₄×#41	1	2	yes	—
180	C₄×C₈₉	#529	1	2	yes	—
181	Dic₈₉	—	4	4	no	—
182	Dic₈₉	—	8	2	no	—
183	C₄×#487	—	89	1	no	maximal, Sylow
184	C₂×C₈₉	C₄×#124	1	1	yes	characteristic
185	C₂×C₈₉	C₂×C₄×SD₁₆	1	1	yes	characteristic
186	C₂×C₈₉	C₂×C₄×Q₁₆	1	1	yes	characteristic
187	C₂×C₈₉	C₂×#487	1	1	yes	characteristic
188	C₂×C₈₉	#3131	1	1	yes	characteristic
189	C₂×C₈₉	#3167	1	1	yes	characteristic
190	C₂×C₈₉	#3170	1	1	yes	characteristic
191	C₂×#487	—	89	1	no	—
192	C₄×C₄⋊Q₈	—	89	1	no	—
193	C₄×C₄⋊Q₈	D₈₉	1	1	yes	characteristic
194	#1990	—	89	1	no	—
195	#1956	—	89	1	no	—
196	#1933	—	89	4	no	—
197	#1834	—	89	1	no	—
198	C₄×#103	—	89	4	no	—
199	C₄²×C₈	—	89	1	no	—
200	C₈₉	C₄×#487	1	1	yes	characteristic, complemented, Sylow
201	C₂×C₄⋊Q₈	—	89	1	no	—
202	C₂×C₄⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
203	C₂×C₄×Q₈	—	2	1	no	—
204	C₂×C₄×Q₈	—	89	2	no	—
205	#487	—	89	8	no	—
206	C₂×#103	—	89	4	no	—
207	C₂×#103	—	89	4	no	—
208	C₂×C₄×C₈	—	89	1	no	—
209	C₂×C₄×C₈	—	89	2	no	—
210	C₂×C₄×C₈	—	89	1	no	—
211	C₂×C₄×C₈	—	89	2	no	—
212	#391	—	2	1	no	—
213	#391	—	89	2	no	—
214	#389	—	2	1	no	—
215	#389	—	178	1	no	—
216	#389	—	178	1	no	—
217	#389	C₂×D₈₉	1	2	yes	—
218	#384	—	89	1	no	—
219	#384	C₂×D₈₉	1	1	yes	characteristic
220	C₄×C₄⋊C₄	—	2	1	no	—
221	C₄×C₄⋊C₄	—	178	1	no	—
222	C₄×C₄⋊C₄	—	178	1	no	—
223	C₄×C₄⋊C₄	C₂×D₈₉	1	2	yes	—
224	C₄³	C₂×D₈₉	1	1	yes	characteristic
225	#340	—	89	4	no	—
226	#340	—	89	4	no	—
227	C₂²×Q₈	—	2	1	no	—
228	C₂²×Q₈	—	89	2	no	—
229	C₂²×C₈	—	89	2	no	—
230	C₂²×C₈	—	89	2	no	—
231	C₄⋊Q₈	—	2	2	no	—
232	C₄⋊Q₈	—	89	4	no	—
233	C₄⋊Q₈	—	178	2	no	—
234	C₄⋊Q₈	C₄×D₈₉	1	4	yes	—
235	C₄×Q₈	—	4	4	no	—
236	C₄×Q₈	—	178	8	no	—
237	C₂×C₄⋊C₄	—	2	1	no	—
238	C₂×C₄⋊C₄	—	2	1	no	—
239	C₂×C₄⋊C₄	—	2	2	no	—
240	C₂×C₄⋊C₄	—	2	1	no	—
241	C₂×C₄⋊C₄	—	89	2	no	—
242	C₂×C₄⋊C₄	—	178	2	no	—
243	C₂×C₄⋊C₄	—	178	1	no	—
244	C₂×C₄⋊C₄	—	178	1	no	—
245	C₂×C₄⋊C₄	—	178	1	no	—
246	C₂×C₄⋊C₄	—	178	1	no	—
247	C₂×C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
248	C₂×C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
249	C₂×C₄²	—	2	2	no	—
250	C₂×C₄²	—	178	2	no	—
251	C₂×C₄²	C₂²⋊D₈₉	1	1	yes	characteristic
252	C₂×C₄²	C₂²⋊D₈₉	1	1	yes	characteristic
253	C₂×C₄²	C₂²⋊D₈₉	1	1	yes	characteristic
254	C₂×C₄²	C₂²⋊D₈₉	1	1	yes	characteristic
255	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
256	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
257	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
258	#103	—	89	16	no	—
259	#103	—	178	8	no	—
260	C₄×C₈	—	89	4	no	—
261	C₄×C₈	—	178	4	no	—
262	C₄×C₈	—	178	2	no	—
263	C₄×C₈	—	178	4	no	—
264	#95	—	2	2	no	—
265	#95	—	2	2	no	—
266	#95	—	178	2	no	—
267	#95	—	178	2	no	—
268	C₂×Q₈	—	2	4	no	—
269	C₂×Q₈	—	4	2	no	—
270	C₂×Q₈	—	4	2	no	—
271	C₂×Q₈	—	89	4	no	—
272	C₂×Q₈	—	178	4	no	—
273	C₂×Q₈	—	178	4	no	—
274	C₂×Q₈	—	178	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	178	2	no	—
278	C₂²×C₄	—	178	2	no	—
279	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
280	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
281	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
282	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
283	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
284	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
285	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
286	C₂×C₈	—	89	4	no	—
287	C₂×C₈	—	89	4	no	—
288	C₂×C₈	—	178	2	no	—
289	C₂×C₈	—	178	2	no	—
290	C₂×C₈	—	178	2	no	—
291	C₂×C₈	—	178	2	no	—
292	C₄⋊C₄	—	2	4	no	—
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	—	2	4	no	—
295	C₄⋊C₄	—	4	4	no	—
296	C₄⋊C₄	—	4	2	no	—
297	C₄⋊C₄	—	4	2	no	—
298	C₄⋊C₄	—	356	4	no	—
299	C₄⋊C₄	—	356	2	no	—
300	C₄⋊C₄	—	356	2	no	—
301	C₄⋊C₄	—	178	4	no	—
302	C₄⋊C₄	—	178	4	no	—
303	C₄⋊C₄	—	178	4	no	—
304	C₄⋊C₄	C₂×C₄×D₈₉	1	4	yes	—
305	C₄²	—	2	2	no	—
306	C₄²	—	2	2	no	—
307	C₄²	—	2	2	no	—
308	C₄²	—	4	4	no	—
309	C₄²	—	356	4	no	—
310	C₄²	#13083562	1	4	yes	—
311	C₄²	#13083564	1	4	yes	—
312	C₄²	C₂×C₄×D₈₉	1	2	yes	—
313	C₄²	#13083574	1	2	yes	—
314	C₄²	#13083575	1	4	yes	—
315	C₂³	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
316	Q₈	—	4	8	no	—
317	Q₈	—	356	4	no	—
318	Q₈	—	178	8	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	356	2	no	—
332	C₂×C₄	—	356	2	no	—
333	C₂×C₄	—	356	2	no	—
334	C₂×C₄	—	356	2	no	—
335	C₂×C₄	—	356	2	no	—
336	C₂×C₄	—	178	4	no	—
337	C₂×C₄	C₄×C₂²⋊D₈₉	1	2	yes	—
338	C₂×C₄	C₄×C₂²⋊D₈₉	1	2	yes	—
339	C₂×C₄	#15668001	1	2	yes	—
340	C₂×C₄	#15668001	1	2	yes	—
341	C₂×C₄	C₂×#13083562	1	2	yes	—
342	C₂×C₄	C₂×#13083562	1	2	yes	—
343	C₂×C₄	C₂×#13083562	1	2	yes	—
344	C₂×C₄	C₂×#13083564	1	2	yes	—
345	C₂×C₄	C₂×#13083564	1	2	yes	—
346	C₂×C₄	C₂×#13083564	1	2	yes	—
347	C₂×C₄	#15668032	1	2	yes	—
348	C₂×C₄	#15668032	1	2	yes	—
349	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
350	C₂×C₄	#41×D₈₉	1	2	yes	—
351	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
352	C₂×C₄	C₂×#13083575	1	2	yes	—
353	C₈	—	178	4	no	—
354	C₈	—	178	4	no	—
355	C₂²	C₂×C₄×C₂²⋊D₈₉	1	1	yes	characteristic
356	C₂²	C₂×#15668001	1	1	yes	characteristic
357	C₂²	#19152144	1	1	yes	characteristic
358	C₂²	C₂²×#13083562	1	1	yes	characteristic
359	C₂²	C₂²×#13083564	1	1	yes	characteristic
360	C₂²	C₂×#15668032	1	1	yes	characteristic
361	C₂²	C₂×#15668032	1	1	yes	characteristic
362	C₄	—	2	2	no	—
363	C₄	—	2	2	no	—
364	C₄	—	2	2	no	—
365	C₄	—	4	4	no	—
366	C₄	—	8	2	no	—
367	C₄	—	356	4	no	—
368	C₄	—	712	2	no	—
369	C₄	C₄×#13083562	1	4	yes	—
370	C₄	C₄×#13083564	1	4	yes	—
371	C₄	#19151950	1	4	yes	direct product factor
372	C₄	C₄×#13083575	1	2	yes	—
373	C₄	#19152135	1	2	yes	—
374	C₂	C₄×#15668001	1	1	yes	characteristic
375	C₂	C₂×C₄×#13083562	1	1	yes	characteristic
376	C₂	C₂×C₄×#13083564	1	1	yes	characteristic
377	C₂	C₂×#19151950	1	1	yes	characteristic
378	C₂	#26030577	1	1	yes	characteristic
379	C₂	#26030807	1	1	yes	characteristic
380	C₂	#26030834	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₄×C₄⋊Q₈×C₈₉	C₂
socle, prime radical	C₂³×C₈₉	C₂²×D₄
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	C₄×C₄⋊Q₈	D₈₉
hypocenter	C₈₉	C₄×#487
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ C₄×C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
12. #19151950	C₄	direct (N × H)
178. C₄×C₈₉	#487	semidirect
200. C₈₉	C₄×#487	semidirect
371. C₄	#19151950	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×#19151950	2
C₄×#15668012	2
#26021214	2
#26021053	2
#26020927	2
#26020379	2
C₄×#15667935	2
C₄²×#10623494	2
C₄×C₄⋊Q₈×C₈₉	2
C₄×#487	89

Subgroups — C4×#19151950 #36562406

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#19151950 #36562406