Subgroups — #26034049

Order 11392.

1100 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152309	C₂	1	1	yes	maximal, characteristic, complemented
2	#19152306	C₂	1	4	yes	maximal, complemented
3	#19152305	C₂	1	2	yes	maximal, complemented
4	#19152304	C₂	1	2	yes	maximal, complemented
5	#19152303	C₂	1	2	yes	maximal, complemented
6	Q₈×D₃₅₆	C₂	1	1	yes	maximal, characteristic, complemented
7	D₄×Dic₁₇₈	C₂	1	1	yes	maximal, characteristic, complemented
8	#19152261	C₂	1	2	yes	maximal, complemented
9	#19152228	C₂	1	2	yes	maximal, complemented
10	#19152223	C₂	1	4	yes	maximal, complemented
11	#19152153	C₂	1	1	yes	maximal, characteristic, complemented
12	#19152152	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#15667992	C₂	1	2	yes	maximal, complemented
14	C₂²⋊Q₈×D₈₉	C₂	1	2	yes	maximal, complemented
15	#19152070	C₂	1	2	yes	maximal
16	C₄×D₄×D₈₉	C₂	1	1	yes	maximal, characteristic
17	#554×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×Dic₁₇₈	C₂²	1	2	yes	complemented
19	C₂×Q₈×D₈₉	C₂²	1	2	yes	complemented
20	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic
21	C₂²×C₄×D₈₉	C₂²	1	2	yes	—
22	#15668012	C₂²	1	1	yes	characteristic, complemented
23	#15668012	C₂²	1	2	yes	complemented
24	#15668011	C₂²	1	1	yes	characteristic, complemented
25	#15668011	C₂²	1	4	yes	complemented
26	#15668011	C₂²	1	2	yes	complemented
27	#15668010	C₂²	1	1	yes	characteristic, complemented
28	#15668003	C₂²	1	2	yes	complemented
29	#15668003	C₂²	1	2	yes	complemented
30	#15668002	C₂²	1	2	yes	complemented
31	#15668002	C₂²	1	4	yes	complemented
32	#15667992	C₂²	1	1	yes	characteristic
33	#15667992	C₂²	1	2	yes	—
34	#15667992	C₂²	1	4	yes	—
35	#15667992	C₂²	1	4	yes	complemented
36	#15667992	C₂²	1	2	yes	complemented
37	#15667992	C₂²	1	2	yes	complemented
38	#15667992	C₂²	1	4	yes	complemented
39	#15667991	C₂²	1	4	yes	complemented
40	#15667991	C₂²	1	2	yes	complemented
41	#15667990	C₂²	1	2	yes	—
42	#15667990	C₂²	1	4	yes	—
43	#15667990	C₂²	1	4	yes	complemented
44	#15667990	C₂²	1	4	yes	complemented
45	#15667989	C₂²	1	4	yes	complemented
46	#15667989	C₂²	1	4	yes	complemented
47	#15667989	C₂²	1	4	yes	complemented
48	#15667988	C₂²	1	1	yes	characteristic
49	#15667988	C₂²	1	2	yes	—
50	#15667988	C₂²	1	4	yes	complemented
51	Q₈×Dic₈₉	C₂²	1	2	yes	complemented
52	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
53	C₄×Dic₁₇₈	C₂²	1	2	yes	complemented
54	#15667977	C₂²	1	2	yes	complemented
55	C₄×D₃₅₆	C₂²	1	2	yes	—
56	C₄×D₃₅₆	C₂²	1	1	yes	characteristic
57	D₄×Dic₈₉	C₂²	1	2	yes	—
58	D₄×Dic₈₉	C₂²	1	1	yes	characteristic
59	#15667974	C₂²	1	1	yes	characteristic
60	#15667974	C₂²	1	2	yes	—
61	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	—
62	C₄×C₂²⋊D₈₉	C₂²	1	4	yes	—
63	#15667972	C₂²	1	4	yes	—
64	#15667972	C₂²	1	2	yes	—
65	#15667970	C₂²	1	2	yes	—
66	#15667969	C₂²	1	2	yes	—
67	C₂×C₄⋊Dic₈₉	C₂²	1	4	yes	complemented
68	C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
69	C₄⋊C₄×D₈₉	C₂²	1	2	yes	complemented
70	C₄⋊C₄×D₈₉	C₂²	1	4	yes	complemented
71	C₂×#13083551	C₂²	1	4	yes	—
72	C₂²⋊C₄×D₈₉	C₂²	1	2	yes	—
73	C₂²⋊C₄×D₈₉	C₂²	1	4	yes	—
74	C₄²×D₈₉	C₂²	1	1	yes	characteristic
75	C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
76	#125×C₈₉	C₂²	1	2	yes	complemented
77	C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	complemented
78	C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	complemented
79	C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
80	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
81	C₄×D₄×C₈₉	C₂²	1	2	yes	—
82	C₂×C₄⋊C₄×C₈₉	C₂²	1	2	yes	complemented
83	C₂³×D₈₉	C₂³	1	2	yes	—
84	C₂×Dic₁₇₈	—	4	4	no	—
85	C₂×Dic₁₇₈	C₂³	1	2	yes	—
86	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
87	C₂×Dic₁₇₈	C₂³	1	2	yes	—
88	C₂×Dic₁₇₈	C₂³	1	4	yes	—
89	C₂×Dic₁₇₈	C₂³	1	4	yes	—
90	Q₈×D₈₉	—	4	4	no	—
91	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
92	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
93	D₄×D₈₉	Q₈	1	8	yes	complemented
94	C₂²×Dic₈₉	C₂³	1	2	yes	—
95	C₂²×Dic₈₉	C₂³	1	4	yes	—
96	C₂×C₄×D₈₉	—	4	4	no	—
97	C₂×C₄×D₈₉	C₂³	1	2	yes	—
98	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
99	C₂×C₄×D₈₉	C₂³	1	2	yes	—
100	C₂×C₄×D₈₉	C₂³	1	4	yes	—
101	C₂×C₄×D₈₉	C₂³	1	4	yes	—
102	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
103	C₂×C₄×D₈₉	C₂³	1	2	yes	—
104	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
105	C₄⋊Dic₈₉	C₂³	1	2	yes	—
106	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
107	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
108	C₄⋊Dic₈₉	C₂³	1	2	yes	—
109	C₄⋊Dic₈₉	C₂³	1	2	yes	—
110	C₄⋊Dic₈₉	C₂³	1	4	yes	—
111	C₄⋊Dic₈₉	C₂³	1	4	yes	—
112	C₄⋊Dic₈₉	C₂³	1	4	yes	—
113	#13083553	C₂³	1	2	yes	—
114	#13083553	C₂³	1	2	yes	—
115	#13083553	C₂³	1	2	yes	—
116	#13083553	C₂³	1	4	yes	—
117	#13083553	C₂³	1	2	yes	—
118	#13083553	C₂³	1	2	yes	—
119	#13083553	C₂³	1	2	yes	—
120	#13083553	C₂³	1	4	yes	—
121	#13083553	C₂³	1	4	yes	—
122	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
123	C₂²⋊Dic₈₉	C₂³	1	4	yes	—
124	#13083551	C₂³	1	2	yes	—
125	#13083551	C₂³	1	2	yes	—
126	#13083551	C₂³	1	4	yes	—
127	#13083551	C₂³	1	4	yes	—
128	#13083551	C₂³	1	2	yes	—
129	#13083551	C₂³	1	2	yes	—
130	#13083551	C₂³	1	4	yes	—
131	C₄×Dic₈₉	C₂³	1	2	yes	—
132	C₄×Dic₈₉	C₂³	1	4	yes	—
133	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
134	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
135	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
136	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
137	C₂×Q₈×C₈₉	C₂³	1	2	yes	—
138	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
139	C₂²×C₄×C₈₉	C₂³	1	2	yes	—
140	C₂²×C₄×C₈₉	C₂³	1	4	yes	—
141	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
142	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
143	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
144	C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
145	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
146	C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
147	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
148	C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
149	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
150	C₄²×C₈₉	C₂³	1	2	yes	—
151	C₄²×C₈₉	C₂³	1	1	yes	characteristic
152	C₂³×C₈₉	C₂⁴	1	2	yes	—
153	C₂²×D₈₉	—	4	2	no	—
154	C₂²×D₈₉	—	4	2	no	—
155	C₂²×D₈₉	C₂×Q₈	1	8	yes	complemented
156	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
157	C₂²×D₈₉	C₂⁴	1	2	yes	—
158	Q₈×C₈₉	—	2	2	no	—
159	Q₈×C₈₉	—	4	2	no	—
160	D₄×C₈₉	C₂×Q₈	1	4	yes	complemented
161	C₂×C₄×C₈₉	—	2	4	no	—
162	C₂×C₄×C₈₉	—	4	4	no	—
163	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
164	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
165	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
166	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
167	C₂×C₄×C₈₉	C₂⁴	1	4	yes	—
168	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
169	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
170	C₂²⋊D₈₉	C₂×Q₈	1	8	yes	complemented
171	C₂×Dic₈₉	—	4	2	no	—
172	C₂×Dic₈₉	—	4	4	no	—
173	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
174	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
175	C₂×Dic₈₉	C₂⁴	1	2	yes	—
176	C₂×Dic₈₉	C₂⁴	1	4	yes	—
177	C₂×Dic₈₉	C₂⁴	1	2	yes	—
178	C₂×Dic₈₉	C₂⁴	1	2	yes	—
179	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
180	D₃₅₆	C₂×Q₈	1	4	yes	complemented
181	C₄×D₈₉	—	2	2	no	—
182	C₄×D₈₉	—	2	4	no	—
183	C₄×D₈₉	—	4	2	no	—
184	C₄×D₈₉	—	4	2	no	—
185	C₄×D₈₉	—	4	1	no	—
186	C₄×D₈₉	—	4	4	no	—
187	C₄×D₈₉	—	4	4	no	—
188	C₄×D₈₉	C₂×Q₈	1	4	yes	complemented
189	Dic₁₇₈	—	2	4	no	—
190	Dic₁₇₈	—	2	2	no	—
191	Dic₁₇₈	—	4	4	no	—
192	Dic₁₇₈	—	4	4	no	—
193	Dic₁₇₈	—	4	2	no	—
194	C₂²×C₈₉	—	2	2	no	—
195	C₂²×C₈₉	—	2	2	no	—
196	C₂²×C₈₉	C₂²×Q₈	1	4	yes	—
197	C₂²×C₈₉	C₂⁵	1	1	yes	characteristic
198	C₂×D₈₉	—	2	2	no	—
199	C₂×D₈₉	—	2	1	no	—
200	C₂×D₈₉	—	2	2	no	—
201	C₂×D₈₉	—	2	1	no	—
202	C₂×D₈₉	—	4	8	no	—
203	C₂×D₈₉	C₂²×Q₈	1	2	yes	—
204	C₂×D₈₉	C₂²×Q₈	1	4	yes	—
205	C₄×C₈₉	—	2	2	no	—
206	C₄×C₈₉	—	2	2	no	—
207	C₄×C₈₉	—	2	2	no	—
208	C₄×C₈₉	—	2	4	no	—
209	C₄×C₈₉	—	2	1	no	—
210	C₄×C₈₉	C₂²×Q₈	1	2	yes	—
211	C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
212	Dic₈₉	—	2	4	no	—
213	Dic₈₉	—	2	2	no	—
214	Dic₈₉	—	2	2	no	—
215	Dic₈₉	—	2	1	no	—
216	Dic₈₉	—	2	1	no	—
217	Dic₈₉	—	2	2	no	—
218	Dic₈₉	C₂²×Q₈	1	2	yes	—
219	C₂×C₈₉	—	2	4	no	—
220	C₂×C₈₉	C₂³×Q₈	1	1	yes	characteristic
221	C₂×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
222	C₂×C₈₉	#585	1	1	yes	characteristic
223	D₈₉	—	2	2	no	—
224	D₈₉	—	2	4	no	—
225	#3501	—	89	1	no	maximal, Sylow
226	C₈₉	#3501	1	1	yes	characteristic, complemented, Sylow
227	#554	—	89	1	no	—
228	#554	—	89	2	no	—
229	#554	—	89	4	no	—
230	#554	—	89	2	no	—
231	#554	—	89	2	no	—
232	#554	D₈₉	1	1	yes	characteristic, complemented
233	D₄×Q₈	—	89	2	no	—
234	D₄×Q₈	—	89	1	no	—
235	D₄×Q₈	—	89	1	no	—
236	#544	—	89	2	no	—
237	#543	—	89	4	no	—
238	#533	—	89	1	no	—
239	#533	—	89	1	no	—
240	C₂×C₂²⋊Q₈	—	89	2	no	—
241	C₂×C₂²⋊Q₈	—	89	2	no	—
242	#518	—	89	2	no	—
243	C₂×C₄×D₄	—	89	1	no	—
244	C₂²×Q₈	—	89	2	no	—
245	C₂²×Q₈	—	89	2	no	—
246	C₂²×D₄	—	89	1	no	—
247	C₂³×C₄	—	89	2	no	—
248	C₄⋊Q₈	—	89	1	no	—
249	C₄⋊Q₈	—	89	1	no	—
250	C₄⋊Q₈	—	89	4	no	—
251	C₄⋊Q₈	—	89	2	no	—
252	C₄⋊Q₈	—	89	1	no	—
253	C₄⋊Q₈	—	89	2	no	—
254	C₄⋊Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
255	#125	—	89	2	no	—
256	#125	—	89	2	no	—
257	#125	—	89	4	no	—
258	#125	—	89	2	no	—
259	#125	C₂×D₈₉	1	2	yes	complemented
260	C₂²⋊Q₈	—	89	1	no	—
261	C₂²⋊Q₈	—	89	2	no	—
262	C₂²⋊Q₈	—	89	4	no	—
263	C₂²⋊Q₈	—	89	2	no	—
264	C₂²⋊Q₈	—	89	4	no	—
265	C₂²⋊Q₈	—	89	2	no	—
266	C₂²⋊Q₈	—	89	1	no	—
267	C₂²⋊Q₈	—	89	4	no	—
268	C₂²⋊Q₈	—	89	4	no	—
269	C₂²⋊Q₈	—	89	2	no	—
270	C₂²⋊Q₈	—	89	2	no	—
271	C₂²⋊Q₈	—	89	4	no	—
272	C₂²⋊Q₈	—	89	2	no	—
273	C₂²⋊Q₈	—	89	4	no	—
274	C₂²⋊Q₈	—	89	4	no	—
275	C₂²⋊Q₈	—	89	4	no	—
276	C₂²⋊Q₈	—	89	4	no	—
277	C₂²⋊Q₈	—	89	4	no	—
278	C₂²⋊Q₈	—	89	4	no	—
279	C₂²⋊Q₈	C₂×D₈₉	1	2	yes	complemented
280	C₂²⋊Q₈	C₂×D₈₉	1	4	yes	complemented
281	C₄×Q₈	—	89	2	no	—
282	C₄×Q₈	—	89	2	no	—
283	C₄×Q₈	—	89	1	no	—
284	C₄×Q₈	—	89	2	no	—
285	C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
286	C₄×D₄	—	89	1	no	—
287	C₄×D₄	—	89	2	no	—
288	C₄×D₄	—	89	2	no	—
289	C₄×D₄	—	89	4	no	—
290	C₄×D₄	—	89	1	no	—
291	C₄×D₄	—	89	2	no	—
292	C₄×D₄	—	89	2	no	—
293	C₄×D₄	—	89	4	no	—
294	C₄×D₄	—	89	1	no	—
295	C₄×D₄	—	89	2	no	—
296	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
297	C₄×D₄	C₂×D₈₉	1	2	yes	—
298	#117	—	89	2	no	—
299	#117	—	89	2	no	—
300	C₂×C₄⋊C₄	—	89	4	no	—
301	C₂×C₄⋊C₄	—	89	1	no	—
302	C₂×C₄⋊C₄	—	89	4	no	—
303	C₂×C₄⋊C₄	—	89	2	no	—
304	C₂×C₄⋊C₄	C₂×D₈₉	1	2	yes	complemented
305	C₂×C₂²⋊C₄	—	89	4	no	—
306	C₂×C₂²⋊C₄	—	89	2	no	—
307	C₂×C₂²⋊C₄	—	89	4	no	—
308	C₂×C₄²	—	89	1	no	—
309	C₂⁴	—	89	2	no	—
310	C₂×Q₈	—	89	2	no	—
311	C₂×Q₈	—	89	4	no	—
312	C₂×Q₈	—	89	4	no	—
313	C₂×Q₈	—	89	2	no	—
314	C₂×Q₈	—	89	1	no	—
315	C₂×Q₈	—	356	4	no	—
316	C₂×Q₈	—	356	4	no	—
317	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
318	C₂×Q₈	C₂²×D₈₉	1	2	yes	—
319	C₂×D₄	—	89	2	no	—
320	C₂×D₄	—	89	8	no	—
321	C₂×D₄	—	89	1	no	—
322	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
323	C₂²×C₄	—	89	1	no	—
324	C₂²×C₄	—	89	4	no	—
325	C₂²×C₄	—	89	2	no	—
326	C₂²×C₄	—	89	1	no	—
327	C₂²×C₄	—	89	4	no	—
328	C₂²×C₄	—	89	4	no	—
329	C₂²×C₄	—	89	2	no	—
330	C₂²×C₄	—	89	2	no	—
331	C₂²×C₄	—	89	1	no	—
332	C₂²×C₄	—	89	2	no	—
333	C₂²×C₄	—	356	4	no	—
334	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
335	C₂²×C₄	C₂²×D₈₉	1	4	yes	—
336	C₄⋊C₄	—	89	2	no	—
337	C₄⋊C₄	—	89	4	no	—
338	C₄⋊C₄	—	89	2	no	—
339	C₄⋊C₄	—	89	1	no	—
340	C₄⋊C₄	—	89	2	no	—
341	C₄⋊C₄	—	89	1	no	—
342	C₄⋊C₄	—	89	4	no	—
343	C₄⋊C₄	—	89	4	no	—
344	C₄⋊C₄	—	89	4	no	—
345	C₄⋊C₄	—	89	4	no	—
346	C₄⋊C₄	—	89	2	no	—
347	C₄⋊C₄	—	89	2	no	—
348	C₄⋊C₄	—	89	2	no	—
349	C₄⋊C₄	—	89	4	no	—
350	C₄⋊C₄	—	89	2	no	—
351	C₄⋊C₄	—	89	2	no	—
352	C₄⋊C₄	—	89	2	no	—
353	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
354	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
355	C₄⋊C₄	C₂²×D₈₉	1	4	yes	—
356	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
357	C₄⋊C₄	C₂²×D₈₉	1	4	yes	—
358	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
359	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
360	C₂²⋊C₄	—	89	2	no	—
361	C₂²⋊C₄	—	89	4	no	—
362	C₂²⋊C₄	—	89	2	no	—
363	C₂²⋊C₄	—	89	4	no	—
364	C₂²⋊C₄	—	89	2	no	—
365	C₂²⋊C₄	—	89	2	no	—
366	C₂²⋊C₄	—	89	4	no	—
367	C₂²⋊C₄	—	89	4	no	—
368	C₂²⋊C₄	—	89	2	no	—
369	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
370	C₂²⋊C₄	C₂²×D₈₉	1	4	yes	—
371	C₄²	—	89	1	no	—
372	C₄²	—	89	1	no	—
373	C₄²	—	89	1	no	—
374	C₄²	—	89	4	no	—
375	C₄²	—	89	2	no	—
376	C₄²	C₂²×D₈₉	1	1	yes	characteristic
377	C₄²	C₂²×D₈₉	1	2	yes	—
378	C₂³	—	89	8	no	—
379	C₂³	—	89	1	no	—
380	C₂³	—	89	2	no	—
381	C₂³	—	356	2	no	—
382	C₂³	—	356	2	no	—
383	C₂³	C₂³×D₈₉	1	2	yes	—
384	Q₈	—	2	2	no	—
385	Q₈	—	4	2	no	—
386	Q₈	—	356	2	no	—
387	Q₈	—	356	4	no	—
388	Q₈	—	356	4	no	—
389	Q₈	—	178	4	no	—
390	Q₈	—	178	2	no	—
391	D₄	—	89	8	no	—
392	D₄	—	89	4	no	—
393	D₄	Q₈×D₈₉	1	4	yes	complemented
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	4	4	no	—
396	C₂×C₄	—	89	1	no	—
397	C₂×C₄	—	89	4	no	—
398	C₂×C₄	—	89	1	no	—
399	C₂×C₄	—	89	1	no	—
400	C₂×C₄	—	89	2	no	—
401	C₂×C₄	—	89	2	no	—
402	C₂×C₄	—	89	4	no	—
403	C₂×C₄	—	89	2	no	—
404	C₂×C₄	—	356	4	no	—
405	C₂×C₄	—	356	1	no	—
406	C₂×C₄	—	356	2	no	—
407	C₂×C₄	—	356	2	no	—
408	C₂×C₄	—	356	4	no	—
409	C₂×C₄	—	356	2	no	—
410	C₂×C₄	—	356	4	no	—
411	C₂×C₄	—	178	2	no	—
412	C₂×C₄	—	178	4	no	—
413	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
414	C₂×C₄	C₂³×D₈₉	1	4	yes	—
415	C₂×C₄	C₂³×D₈₉	1	2	yes	—
416	C₂×C₄	C₂³×D₈₉	1	2	yes	—
417	C₂×C₄	C₂³×D₈₉	1	2	yes	—
418	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
419	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
420	C₂²	—	2	2	no	—
421	C₂²	—	2	2	no	—
422	C₂²	—	89	2	no	—
423	C₂²	—	89	4	no	—
424	C₂²	—	356	8	no	—
425	C₂²	—	178	2	no	—
426	C₂²	—	178	1	no	—
427	C₂²	—	178	2	no	—
428	C₂²	—	178	1	no	—
429	C₂²	C₂×Q₈×D₈₉	1	4	yes	—
430	C₂²	C₂⁴×D₈₉	1	1	yes	characteristic
431	C₄	—	2	2	no	—
432	C₄	—	2	2	no	—
433	C₄	—	2	2	no	—
434	C₄	—	2	4	no	—
435	C₄	—	2	1	no	—
436	C₄	—	89	2	no	—
437	C₄	—	178	1	no	—
438	C₄	—	178	2	no	—
439	C₄	—	178	4	no	—
440	C₄	—	178	2	no	—
441	C₄	—	178	2	no	—
442	C₄	—	178	1	no	—
443	C₄	C₂×Q₈×D₈₉	1	2	yes	—
444	C₄	#15668058	1	2	yes	—
445	C₂	—	2	4	no	—
446	C₂	—	178	2	no	—
447	C₂	—	178	4	no	—
448	C₂	C₂²×Q₈×D₈₉	1	1	yes	characteristic
449	C₂	C₂×#15668058	1	1	yes	characteristic
450	C₂	#19152433	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₉
commutator, socle, cosocle	C₂²×C₈₉	C₂⁵
Fitting	#554×C₈₉	C₂
prime radical	C₂×D₄×D₈₉	C₂²
hypercenter	#554	D₈₉
hypocenter	C₈₉	#3501
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ #554

Complements

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

N	H ≅ G/N	type
1. #19152309	C₂	semidirect
2. #19152306	C₂	semidirect
3. #19152305	C₂	semidirect
4. #19152304	C₂	semidirect
5. #19152303	C₂	semidirect
6. Q₈×D₃₅₆	C₂	semidirect
7. D₄×Dic₁₇₈	C₂	semidirect
8. #19152261	C₂	semidirect
9. #19152228	C₂	semidirect
10. #19152223	C₂	semidirect
11. #19152153	C₂	semidirect
12. #19152152	C₂	semidirect
13. C₂×#15667992	C₂	semidirect
14. C₂²⋊Q₈×D₈₉	C₂	semidirect
17. #554×C₈₉	C₂	semidirect
18. C₂²×Dic₁₇₈	C₂²	semidirect
19. C₂×Q₈×D₈₉	C₂²	semidirect
22. #15668012	C₂²	semidirect
23. #15668012	C₂²	semidirect
24. #15668011	C₂²	semidirect
25. #15668011	C₂²	semidirect
26. #15668011	C₂²	semidirect
27. #15668010	C₂²	semidirect
28. #15668003	C₂²	semidirect
29. #15668003	C₂²	semidirect
30. #15668002	C₂²	semidirect
31. #15668002	C₂²	semidirect
35. #15667992	C₂²	semidirect
36. #15667992	C₂²	semidirect
37. #15667992	C₂²	semidirect
38. #15667992	C₂²	semidirect
39. #15667991	C₂²	semidirect
40. #15667991	C₂²	semidirect
43. #15667990	C₂²	semidirect
44. #15667990	C₂²	semidirect
45. #15667989	C₂²	semidirect
46. #15667989	C₂²	semidirect
47. #15667989	C₂²	semidirect
50. #15667988	C₂²	semidirect
51. Q₈×Dic₈₉	C₂²	semidirect
52. C₄×Dic₁₇₈	C₂²	semidirect
53. C₄×Dic₁₇₈	C₂²	semidirect
54. #15667977	C₂²	semidirect
67. C₂×C₄⋊Dic₈₉	C₂²	semidirect
69. C₄⋊C₄×D₈₉	C₂²	semidirect
70. C₄⋊C₄×D₈₉	C₂²	semidirect
75. C₄⋊Q₈×C₈₉	C₂²	semidirect
76. #125×C₈₉	C₂²	semidirect
77. C₂²⋊Q₈×C₈₉	C₂²	semidirect
78. C₂²⋊Q₈×C₈₉	C₂²	semidirect
79. C₄×Q₈×C₈₉	C₂²	semidirect
82. C₂×C₄⋊C₄×C₈₉	C₂²	semidirect
93. D₄×D₈₉	Q₈	semidirect
155. C₂²×D₈₉	C₂×Q₈	semidirect
160. D₄×C₈₉	C₂×Q₈	semidirect
170. C₂²⋊D₈₉	C₂×Q₈	semidirect
180. D₃₅₆	C₂×Q₈	semidirect
188. C₄×D₈₉	C₂×Q₈	semidirect
226. C₈₉	#3501	semidirect
232. #554	D₈₉	semidirect
254. C₄⋊Q₈	C₂×D₈₉	semidirect
259. #125	C₂×D₈₉	semidirect
279. C₂²⋊Q₈	C₂×D₈₉	semidirect
280. C₂²⋊Q₈	C₂×D₈₉	semidirect
285. C₄×Q₈	C₂×D₈₉	semidirect
304. C₂×C₄⋊C₄	C₂×D₈₉	semidirect
393. D₄	Q₈×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#19152309	2
#19152306	2
#19152305	2
#19152304	2
#19152303	2
Q₈×D₃₅₆	2
D₄×Dic₁₇₈	2
#19152261	2
#19152228	2
#19152223	2
#19152153	2
#19152152	2
C₂×#15667992	2
C₂²⋊Q₈×D₈₉	2
#19152070	2
C₄×D₄×D₈₉	2
#554×C₈₉	2
#3501	89