Subgroups — #26034204

Order 11392.

1142 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152334	C₂	1	1	yes	maximal, characteristic, complemented
2	#19152318	C₂	1	1	yes	maximal, characteristic, complemented
3	#19152312	C₂	1	2	yes	maximal, complemented
4	#19152279	C₂	1	4	yes	maximal, complemented
5	D₄×Dic₁₇₈	C₂	1	1	yes	maximal, characteristic, complemented
6	#19152254	C₂	1	2	yes	maximal, complemented
7	#19152242	C₂	1	2	yes	maximal, complemented
8	#19152242	C₂	1	2	yes	maximal, complemented
9	#19152215	C₂	1	2	yes	maximal, complemented
10	#19152183	C₂	1	4	yes	maximal, complemented
11	#19152146	C₂	1	1	yes	maximal, characteristic, complemented
12	#19152130	C₂	1	1	yes	maximal, characteristic, complemented
13	#19152129	C₂	1	2	yes	maximal, complemented
14	C₂×#15667999	C₂	1	2	yes	maximal, complemented
15	#19152073	C₂	1	2	yes	maximal, complemented
16	C₄×#13083573	C₂	1	1	yes	maximal, characteristic, complemented
17	D₄²×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#13083573	C₂²	1	1	yes	characteristic
19	C₂×#13083573	C₂²	1	2	yes	complemented
20	C₂²×Dic₁₇₈	C₂²	1	2	yes	complemented
21	#15668012	C₂²	1	1	yes	characteristic, complemented
22	#15668011	C₂²	1	2	yes	complemented
23	#15668005	C₂²	1	4	yes	complemented
24	#15668005	C₂²	1	2	yes	complemented
25	#15668005	C₂²	1	4	yes	complemented
26	#15668003	C₂²	1	1	yes	characteristic, complemented
27	#15667999	C₂²	1	1	yes	characteristic
28	#15667999	C₂²	1	2	yes	—
29	#15667999	C₂²	1	2	yes	complemented
30	#15667999	C₂²	1	4	yes	complemented
31	#15667999	C₂²	1	2	yes	complemented
32	#15667999	C₂²	1	2	yes	complemented
33	#15667999	C₂²	1	4	yes	complemented
34	#15667998	C₂²	1	4	yes	complemented
35	#15667994	C₂²	1	2	yes	complemented
36	#15667993	C₂²	1	4	yes	complemented
37	#15667993	C₂²	1	4	yes	complemented
38	#15667993	C₂²	1	4	yes	complemented
39	#15667992	C₂²	1	1	yes	characteristic, complemented
40	#15667991	C₂²	1	2	yes	complemented
41	#15667991	C₂²	1	2	yes	complemented
42	#15667989	C₂²	1	4	yes	complemented
43	#15667989	C₂²	1	4	yes	complemented
44	#15667984	C₂²	1	4	yes	complemented
45	#15667984	C₂²	1	4	yes	complemented
46	#15667983	C₂²	1	1	yes	characteristic
47	#15667983	C₂²	1	2	yes	complemented
48	#15667983	C₂²	1	2	yes	complemented
49	#15667981	C₂²	1	4	yes	complemented
50	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
51	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
52	#15667977	C₂²	1	2	yes	complemented
53	#15667977	C₂²	1	1	yes	characteristic, complemented
54	D₄×Dic₈₉	C₂²	1	2	yes	—
55	D₄×Dic₈₉	C₂²	1	1	yes	characteristic
56	D₄×Dic₈₉	C₂²	1	4	yes	complemented
57	D₄×Dic₈₉	C₂²	1	2	yes	complemented
58	D₄×Dic₈₉	C₂²	1	2	yes	complemented
59	D₄×Dic₈₉	C₂²	1	2	yes	complemented
60	D₄×Dic₈₉	C₂²	1	4	yes	complemented
61	D₄×Dic₈₉	C₂²	1	2	yes	complemented
62	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	complemented
63	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	complemented
64	#15667972	C₂²	1	2	yes	complemented
65	#15667971	C₂²	1	2	yes	complemented
66	#15667971	C₂²	1	2	yes	complemented
67	#15667970	C₂²	1	1	yes	characteristic, complemented
68	#15667968	C₂²	1	4	yes	complemented
69	#15667968	C₂²	1	2	yes	complemented
70	C₂×C₂²⋊Dic₈₉	C₂²	1	4	yes	complemented
71	C₂×C₂²⋊Dic₈₉	C₂²	1	4	yes	complemented
72	C₂×C₂²⋊Dic₈₉	C₂²	1	4	yes	complemented
73	C₂×C₄×Dic₈₉	C₂²	1	2	yes	complemented
74	C₄²×D₈₉	C₂²	1	1	yes	characteristic, complemented
75	C₂²×D₄×C₈₉	C₂²	1	2	yes	—
76	C₂²×D₄×C₈₉	C₂²	1	2	yes	—
77	#127×C₈₉	C₂²	1	1	yes	characteristic
78	#121×C₈₉	C₂²	1	2	yes	—
79	#121×C₈₉	C₂²	1	2	yes	—
80	#120×C₈₉	C₂²	1	4	yes	—
81	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
82	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
83	#13083573	—	2	4	no	—
84	#13083573	—	4	4	no	—
85	C₂×Dic₁₇₈	—	4	4	no	—
86	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
87	C₂×Dic₁₇₈	C₂³	1	2	yes	—
88	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
89	C₂×Dic₁₇₈	C₂³	1	4	yes	—
90	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
91	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
92	C₂×C₂²⋊D₈₉	C₂³	1	4	yes	—
93	C₂²×Dic₈₉	C₂³	1	2	yes	—
94	C₂²×Dic₈₉	C₂³	1	4	yes	—
95	C₂²×Dic₈₉	C₂³	1	2	yes	—
96	C₂²×Dic₈₉	C₂³	1	4	yes	—
97	C₂²×Dic₈₉	C₂³	1	4	yes	—
98	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
99	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
100	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
101	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
102	C₄⋊Dic₈₉	C₂³	1	2	yes	—
103	C₄⋊Dic₈₉	C₂³	1	2	yes	—
104	C₄⋊Dic₈₉	C₂³	1	2	yes	—
105	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
106	C₄⋊Dic₈₉	C₂³	1	2	yes	—
107	#13083553	C₂³	1	2	yes	—
108	#13083553	C₂³	1	2	yes	—
109	#13083553	C₂³	1	2	yes	—
110	#13083553	C₂³	1	4	yes	—
111	#13083553	C₂³	1	4	yes	—
112	#13083553	C₂³	1	2	yes	—
113	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
114	C₂²⋊Dic₈₉	C₂³	1	4	yes	—
115	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
116	C₂²⋊Dic₈₉	C₂³	1	4	yes	—
117	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
118	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
119	C₂²⋊Dic₈₉	C₂³	1	4	yes	—
120	C₂²⋊Dic₈₉	C₂³	1	4	yes	—
121	C₂²⋊Dic₈₉	C₂³	1	4	yes	—
122	C₂²⋊Dic₈₉	C₂³	1	4	yes	—
123	C₂²⋊Dic₈₉	C₂³	1	4	yes	—
124	C₂²⋊Dic₈₉	C₂³	1	4	yes	—
125	#13083551	C₂³	1	2	yes	—
126	#13083551	C₂³	1	2	yes	—
127	C₄×Dic₈₉	C₂³	1	2	yes	—
128	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
129	C₄×Dic₈₉	C₂³	1	4	yes	—
130	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
131	C₄×Dic₈₉	C₂³	1	2	yes	—
132	C₄×Dic₈₉	C₂³	1	2	yes	—
133	C₄×Dic₈₉	C₂³	1	2	yes	—
134	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
135	C₂⁴×C₈₉	C₂³	1	4	yes	—
136	C₂×D₄×C₈₉	—	2	8	no	—
137	C₂×D₄×C₈₉	—	4	4	no	—
138	C₂×D₄×C₈₉	C₂³	1	2	yes	—
139	C₂×D₄×C₈₉	C₂³	1	4	yes	—
140	C₂×D₄×C₈₉	C₂³	1	2	yes	—
141	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
142	C₂×D₄×C₈₉	C₂³	1	2	yes	—
143	C₂×D₄×C₈₉	C₂³	1	4	yes	—
144	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
145	C₂²×C₄×C₈₉	C₂³	1	2	yes	—
146	C₂²×C₄×C₈₉	C₂³	1	2	yes	—
147	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
148	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
149	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
150	C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
151	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
152	C₄²×C₈₉	C₂³	1	1	yes	characteristic
153	C₂³×C₈₉	—	2	8	no	—
154	C₂³×C₈₉	—	4	4	no	—
155	C₂³×C₈₉	—	4	4	no	—
156	C₂³×C₈₉	C₂⁴	1	2	yes	—
157	C₂³×C₈₉	C₂⁴	1	4	yes	—
158	C₂³×C₈₉	C₂⁴	1	2	yes	—
159	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
160	D₄×C₈₉	—	2	8	no	—
161	D₄×C₈₉	—	2	4	no	—
162	D₄×C₈₉	—	2	2	no	—
163	D₄×C₈₉	—	2	4	no	—
164	D₄×C₈₉	—	4	4	no	—
165	D₄×C₈₉	—	4	2	no	—
166	D₄×C₈₉	#41	1	4	yes	complemented
167	C₂×C₄×C₈₉	—	2	4	no	—
168	C₂×C₄×C₈₉	—	2	4	no	—
169	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
170	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
171	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
172	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
173	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
174	C₂²⋊D₈₉	—	2	4	no	—
175	C₂²⋊D₈₉	—	4	2	no	—
176	C₂²⋊D₈₉	—	4	4	no	—
177	C₂×Dic₈₉	—	2	4	no	—
178	C₂×Dic₈₉	—	4	2	no	—
179	C₂×Dic₈₉	—	4	4	no	—
180	C₂×Dic₈₉	—	4	4	no	—
181	C₂×Dic₈₉	—	4	4	no	—
182	C₂×Dic₈₉	C₂⁴	1	2	yes	—
183	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
184	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
185	C₂×Dic₈₉	C₂⁴	1	2	yes	—
186	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
187	C₂×Dic₈₉	C₂⁴	1	2	yes	—
188	C₂×Dic₈₉	C₂⁴	1	2	yes	—
189	C₂×Dic₈₉	C₂⁴	1	4	yes	—
190	C₄×D₈₉	—	2	2	no	—
191	C₄×D₈₉	—	2	2	no	—
192	C₄×D₈₉	—	4	1	no	—
193	Dic₁₇₈	—	2	2	no	—
194	Dic₁₇₈	—	2	2	no	—
195	Dic₁₇₈	—	2	4	no	—
196	Dic₁₇₈	—	4	4	no	—
197	C₂²×C₈₉	—	2	2	no	—
198	C₂²×C₈₉	—	2	2	no	—
199	C₂²×C₈₉	—	2	2	no	—
200	C₂²×C₈₉	—	2	4	no	—
201	C₂²×C₈₉	—	2	4	no	—
202	C₂²×C₈₉	—	2	2	no	—
203	C₂²×C₈₉	—	2	4	no	—
204	C₂²×C₈₉	—	2	2	no	—
205	C₂²×C₈₉	—	8	8	no	—
206	C₂²×C₈₉	C₂×#41	1	4	yes	—
207	C₂²×C₈₉	C₂⁵	1	1	yes	characteristic
208	C₂×D₈₉	—	2	1	no	—
209	C₂×D₈₉	—	2	1	no	—
210	C₂×D₈₉	—	2	1	no	—
211	C₄×C₈₉	—	2	2	no	—
212	C₄×C₈₉	—	2	2	no	—
213	C₄×C₈₉	—	2	1	no	—
214	C₄×C₈₉	C₂×#41	1	2	yes	—
215	C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
216	Dic₈₉	—	2	2	no	—
217	Dic₈₉	—	2	1	no	—
218	Dic₈₉	—	2	2	no	—
219	Dic₈₉	—	2	4	no	—
220	Dic₈₉	—	2	1	no	—
221	Dic₈₉	—	2	1	no	—
222	Dic₈₉	—	2	2	no	—
223	Dic₈₉	—	2	2	no	—
224	C₂×C₈₉	—	2	4	no	—
225	C₂×C₈₉	—	4	4	no	—
226	C₂×C₈₉	—	4	2	no	—
227	C₂×C₈₉	C₂²×#41	1	1	yes	characteristic
228	C₂×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
229	C₂×C₈₉	#585	1	1	yes	characteristic
230	D₈₉	—	4	1	no	—
231	#3514	—	89	1	no	maximal, Sylow
232	C₈₉	#3514	1	1	yes	characteristic, complemented, Sylow
233	#559	—	89	1	no	—
234	#556	—	89	1	no	—
235	#555	—	89	2	no	—
236	#551	—	89	4	no	—
237	D₄×Q₈	—	89	1	no	—
238	#548	—	89	2	no	—
239	#546	—	89	2	no	—
240	#546	—	89	2	no	—
241	D₄²	D₈₉	1	1	yes	characteristic, complemented
242	#542	—	89	2	no	—
243	#538	—	89	4	no	—
244	#532	—	89	1	no	—
245	#529	—	89	2	no	—
246	#529	—	89	1	no	—
247	C₂×#124	—	89	2	no	—
248	#518	—	89	2	no	—
249	C₄×#41	—	89	1	no	—
250	C₂×#41	—	89	2	no	—
251	C₂×#41	—	89	1	no	—
252	C₂²×Q₈	—	89	2	no	—
253	C₂²×D₄	C₂×D₈₉	1	2	yes	—
254	C₂²×D₄	C₂×D₈₉	1	2	yes	—
255	C₄⋊Q₈	—	89	2	no	—
256	C₄⋊Q₈	—	89	1	no	—
257	#127	C₂×D₈₉	1	1	yes	characteristic
258	#126	—	89	4	no	—
259	#126	—	89	2	no	—
260	#126	—	89	4	no	—
261	#125	—	89	1	no	—
262	#124	—	89	1	no	—
263	#124	—	89	2	no	—
264	#124	—	89	4	no	—
265	#124	—	89	2	no	—
266	#124	—	89	2	no	—
267	#124	—	89	4	no	—
268	#124	—	89	2	no	—
269	#124	—	89	4	no	—
270	#123	—	89	4	no	—
271	#123	—	89	4	no	—
272	#123	—	89	4	no	—
273	#123	—	89	2	no	—
274	C₂²⋊Q₈	—	89	2	no	—
275	C₂²⋊Q₈	—	89	2	no	—
276	C₂²⋊Q₈	—	89	1	no	—
277	C₂²⋊Q₈	—	89	4	no	—
278	C₂²⋊Q₈	—	89	4	no	—
279	#121	—	89	1	no	—
280	#121	—	89	2	no	—
281	#121	—	89	2	no	—
282	#121	—	89	4	no	—
283	#121	—	89	4	no	—
284	#121	C₂×D₈₉	1	2	yes	—
285	#121	C₂×D₈₉	1	2	yes	—
286	#120	—	89	4	no	—
287	#120	C₂×D₈₉	1	4	yes	—
288	C₄×Q₈	—	89	1	no	—
289	C₄×Q₈	—	89	2	no	—
290	C₄×Q₈	—	89	1	no	—
291	C₄×Q₈	—	89	1	no	—
292	C₄×D₄	—	89	1	no	—
293	C₄×D₄	—	89	2	no	—
294	C₄×D₄	—	89	4	no	—
295	C₄×D₄	—	89	2	no	—
296	C₄×D₄	—	89	4	no	—
297	C₄×D₄	—	89	2	no	—
298	C₄×D₄	—	89	2	no	—
299	C₄×D₄	—	89	2	no	—
300	C₄×D₄	—	89	2	no	—
301	C₄×D₄	—	89	2	no	—
302	C₄×D₄	—	89	2	no	—
303	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
304	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
305	#117	—	89	2	no	—
306	#117	—	89	2	no	—
307	#117	—	89	1	no	—
308	#117	—	89	2	no	—
309	#117	—	89	4	no	—
310	C₂×C₂²⋊C₄	—	89	4	no	—
311	C₂×C₂²⋊C₄	—	89	4	no	—
312	C₂×C₂²⋊C₄	—	89	4	no	—
313	C₂×C₄²	—	89	2	no	—
314	C₂×C₄²	—	89	1	no	—
315	C₂⁴	C₂²×D₈₉	1	4	yes	—
316	#41	—	356	4	no	—
317	#41	—	178	4	no	—
318	C₂×Q₈	—	89	4	no	—
319	C₂×Q₈	—	89	1	no	—
320	C₂×Q₈	—	89	1	no	—
321	C₂×Q₈	—	89	2	no	—
322	C₂×Q₈	—	356	4	no	—
323	C₂×D₄	—	2	8	no	—
324	C₂×D₄	—	4	4	no	—
325	C₂×D₄	—	89	2	no	—
326	C₂×D₄	—	89	4	no	—
327	C₂×D₄	—	89	2	no	—
328	C₂×D₄	C₂²×D₈₉	1	4	yes	—
329	C₂×D₄	C₂²×D₈₉	1	2	yes	—
330	C₂×D₄	C₂²×D₈₉	1	2	yes	—
331	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
332	C₂×D₄	C₂²×D₈₉	1	2	yes	—
333	C₂×D₄	C₂²×D₈₉	1	4	yes	—
334	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
335	C₂²×C₄	—	89	2	no	—
336	C₂²×C₄	—	89	4	no	—
337	C₂²×C₄	—	89	4	no	—
338	C₂²×C₄	—	89	4	no	—
339	C₂²×C₄	—	89	2	no	—
340	C₂²×C₄	—	89	1	no	—
341	C₂²×C₄	—	89	1	no	—
342	C₂²×C₄	—	89	1	no	—
343	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
344	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
345	C₄⋊C₄	—	89	1	no	—
346	C₄⋊C₄	—	89	2	no	—
347	C₄⋊C₄	—	89	2	no	—
348	C₄⋊C₄	—	89	2	no	—
349	C₄⋊C₄	—	89	2	no	—
350	C₄⋊C₄	—	89	2	no	—
351	C₄⋊C₄	—	89	2	no	—
352	C₄⋊C₄	—	89	4	no	—
353	C₄⋊C₄	—	89	1	no	—
354	C₄⋊C₄	—	89	2	no	—
355	C₄⋊C₄	—	89	4	no	—
356	C₄⋊C₄	—	89	2	no	—
357	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
358	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
359	C₂²⋊C₄	—	89	2	no	—
360	C₂²⋊C₄	—	89	2	no	—
361	C₂²⋊C₄	—	89	4	no	—
362	C₂²⋊C₄	—	89	2	no	—
363	C₂²⋊C₄	—	89	2	no	—
364	C₂²⋊C₄	—	89	4	no	—
365	C₂²⋊C₄	—	89	4	no	—
366	C₂²⋊C₄	—	89	4	no	—
367	C₂²⋊C₄	—	89	4	no	—
368	C₂²⋊C₄	—	89	4	no	—
369	C₂²⋊C₄	—	89	4	no	—
370	C₂²⋊C₄	—	89	4	no	—
371	C₂²⋊C₄	—	89	2	no	—
372	C₂²⋊C₄	—	89	2	no	—
373	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
374	C₂²⋊C₄	C₂²×D₈₉	1	4	yes	—
375	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
376	C₄²	—	89	1	no	—
377	C₄²	—	89	2	no	—
378	C₄²	—	89	1	no	—
379	C₄²	—	89	1	no	—
380	C₄²	—	89	2	no	—
381	C₄²	—	89	2	no	—
382	C₄²	—	89	4	no	—
383	C₄²	—	89	2	no	—
384	C₄²	C₂²×D₈₉	1	1	yes	characteristic
385	C₂³	—	2	8	no	—
386	C₂³	—	4	4	no	—
387	C₂³	—	4	4	no	—
388	C₂³	—	89	1	no	—
389	C₂³	C₂³×D₈₉	1	2	yes	—
390	C₂³	C₂³×D₈₉	1	4	yes	—
391	C₂³	C₂³×D₈₉	1	2	yes	—
392	Q₈	—	356	4	no	—
393	Q₈	—	178	2	no	—
394	Q₈	—	178	2	no	—
395	Q₈	—	178	4	no	—
396	D₄	—	2	8	no	—
397	D₄	—	2	4	no	—
398	D₄	—	2	2	no	—
399	D₄	—	2	4	no	—
400	D₄	—	4	4	no	—
401	D₄	—	4	2	no	—
402	D₄	—	356	2	no	—
403	D₄	—	356	4	no	—
404	D₄	—	178	4	no	—
405	D₄	#13083573	1	4	yes	complemented
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	89	1	no	—
409	C₂×C₄	—	89	2	no	—
410	C₂×C₄	—	89	1	no	—
411	C₂×C₄	—	89	2	no	—
412	C₂×C₄	—	89	1	no	—
413	C₂×C₄	—	89	2	no	—
414	C₂×C₄	—	89	2	no	—
415	C₂×C₄	—	89	4	no	—
416	C₂×C₄	—	356	1	no	—
417	C₂×C₄	—	356	2	no	—
418	C₂×C₄	—	356	4	no	—
419	C₂×C₄	—	356	4	no	—
420	C₂×C₄	—	356	4	no	—
421	C₂×C₄	—	178	4	no	—
422	C₂×C₄	—	178	2	no	—
423	C₂×C₄	—	178	2	no	—
424	C₂×C₄	C₂³×D₈₉	1	2	yes	—
425	C₂×C₄	C₂³×D₈₉	1	2	yes	—
426	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
427	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
428	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
429	C₂²	—	2	2	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	4	no	—
433	C₂²	—	2	4	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	2	4	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	8	8	no	—
438	C₂²	—	178	1	no	—
439	C₂²	—	178	1	no	—
440	C₂²	—	178	1	no	—
441	C₂²	C₂×#13083573	1	4	yes	—
442	C₂²	C₂⁴×D₈₉	1	1	yes	characteristic
443	C₄	—	2	2	no	—
444	C₄	—	2	2	no	—
445	C₄	—	2	1	no	—
446	C₄	—	178	1	no	—
447	C₄	—	178	2	no	—
448	C₄	—	178	1	no	—
449	C₄	—	178	4	no	—
450	C₄	—	178	2	no	—
451	C₄	—	178	1	no	—
452	C₄	—	178	2	no	—
453	C₄	—	178	2	no	—
454	C₄	C₂×#13083573	1	2	yes	—
455	C₄	#15668057	1	2	yes	—
456	C₂	—	2	4	no	—
457	C₂	—	4	4	no	—
458	C₂	—	4	2	no	—
459	C₂	—	356	1	no	—
460	C₂	C₂²×#13083573	1	1	yes	characteristic
461	C₂	C₂×#15668057	1	1	yes	characteristic
462	C₂	#19152433	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₉
commutator, socle, cosocle	C₂²×C₈₉	C₂⁵
Fitting	D₄²×C₈₉	C₂
hypercenter	D₄²	D₈₉
hypocenter	C₈₉	#3514
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ D₄²

Complements

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

N	H ≅ G/N	type
1. #19152334	C₂	semidirect
2. #19152318	C₂	semidirect
3. #19152312	C₂	semidirect
4. #19152279	C₂	semidirect
5. D₄×Dic₁₇₈	C₂	semidirect
6. #19152254	C₂	semidirect
7. #19152242	C₂	semidirect
8. #19152242	C₂	semidirect
9. #19152215	C₂	semidirect
10. #19152183	C₂	semidirect
11. #19152146	C₂	semidirect
12. #19152130	C₂	semidirect
13. #19152129	C₂	semidirect
14. C₂×#15667999	C₂	semidirect
15. #19152073	C₂	semidirect
16. C₄×#13083573	C₂	semidirect
17. D₄²×C₈₉	C₂	semidirect
19. C₂×#13083573	C₂²	semidirect
20. C₂²×Dic₁₇₈	C₂²	semidirect
21. #15668012	C₂²	semidirect
22. #15668011	C₂²	semidirect
23. #15668005	C₂²	semidirect
24. #15668005	C₂²	semidirect
25. #15668005	C₂²	semidirect
26. #15668003	C₂²	semidirect
29. #15667999	C₂²	semidirect
30. #15667999	C₂²	semidirect
31. #15667999	C₂²	semidirect
32. #15667999	C₂²	semidirect
33. #15667999	C₂²	semidirect
34. #15667998	C₂²	semidirect
35. #15667994	C₂²	semidirect
36. #15667993	C₂²	semidirect
37. #15667993	C₂²	semidirect
38. #15667993	C₂²	semidirect
39. #15667992	C₂²	semidirect
40. #15667991	C₂²	semidirect
41. #15667991	C₂²	semidirect
42. #15667989	C₂²	semidirect
43. #15667989	C₂²	semidirect
44. #15667984	C₂²	semidirect
45. #15667984	C₂²	semidirect
47. #15667983	C₂²	semidirect
48. #15667983	C₂²	semidirect
49. #15667981	C₂²	semidirect
50. C₄×Dic₁₇₈	C₂²	semidirect
51. C₄×Dic₁₇₈	C₂²	semidirect
52. #15667977	C₂²	semidirect
53. #15667977	C₂²	semidirect
56. D₄×Dic₈₉	C₂²	semidirect
57. D₄×Dic₈₉	C₂²	semidirect
58. D₄×Dic₈₉	C₂²	semidirect
59. D₄×Dic₈₉	C₂²	semidirect
60. D₄×Dic₈₉	C₂²	semidirect
61. D₄×Dic₈₉	C₂²	semidirect
62. C₄×C₂²⋊D₈₉	C₂²	semidirect
63. C₄×C₂²⋊D₈₉	C₂²	semidirect
64. #15667972	C₂²	semidirect
65. #15667971	C₂²	semidirect
66. #15667971	C₂²	semidirect
67. #15667970	C₂²	semidirect
68. #15667968	C₂²	semidirect
69. #15667968	C₂²	semidirect
70. C₂×C₂²⋊Dic₈₉	C₂²	semidirect
71. C₂×C₂²⋊Dic₈₉	C₂²	semidirect
72. C₂×C₂²⋊Dic₈₉	C₂²	semidirect
73. C₂×C₄×Dic₈₉	C₂²	semidirect
74. C₄²×D₈₉	C₂²	semidirect
166. D₄×C₈₉	#41	semidirect
232. C₈₉	#3514	semidirect
241. D₄²	D₈₉	semidirect
405. D₄	#13083573	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#19152334	2
#19152318	2
#19152312	2
#19152279	2
D₄×Dic₁₇₈	2
#19152254	2
#19152242	2
#19152215	2
#19152183	2
#19152146	2
#19152130	2
#19152129	2
C₂×#15667999	2
#19152073	2
C₄×#13083573	2
D₄²×C₈₉	2
#3514	89