Subgroups — #26032274

Order 11392.

450 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152287	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×C₂²⋊D₈₉	C₂	1	1	yes	maximal, characteristic
3	#19151961	C₂	1	1	yes	maximal, characteristic, complemented
4	#19151922	C₂	1	1	yes	maximal, characteristic, complemented
5	#19151910	C₂	1	1	yes	maximal, characteristic, complemented
6	#19151896	C₂	1	1	yes	maximal, characteristic, complemented
7	#19151844	C₂	1	1	yes	maximal, characteristic, complemented
8	#19151826	C₂	1	1	yes	maximal, characteristic, complemented
9	#19151797	C₂	1	1	yes	maximal, characteristic, complemented
10	#19151750	C₂	1	1	yes	maximal, characteristic, complemented
11	#19151749	C₂	1	1	yes	maximal, characteristic, complemented
12	#19151695	C₂	1	1	yes	maximal, characteristic, complemented
13	#19151667	C₂	1	1	yes	maximal, characteristic, complemented
14	#102×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#418×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₂²⋊D₈₉	—	2	1	no	—
17	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic
18	C₂×#13083563	C₂²	1	1	yes	characteristic, complemented
19	C₂×#13083562	C₂²	1	1	yes	characteristic
20	C₂×#13083562	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₈×D₈₉	C₂²	1	1	yes	characteristic, complemented
22	#15668008	C₂²	1	1	yes	characteristic
23	#15668005	—	2	1	no	—
24	#15668004	—	2	1	no	—
25	#15668003	C₂²	1	1	yes	characteristic, complemented
26	#15667994	—	2	1	no	—
27	#15667992	C₂²	1	1	yes	characteristic, complemented
28	#15667991	C₂²	1	1	yes	characteristic, complemented
29	#15667986	C₂²	1	1	yes	characteristic
30	#15667984	—	2	1	no	—
31	#15667983	C₂²	1	1	yes	characteristic
32	#15667981	—	2	1	no	—
33	#15667980	—	2	1	no	—
34	#15667977	C₂²	1	1	yes	characteristic, complemented
35	D₄×Dic₈₉	C₂²	1	1	yes	characteristic
36	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
37	#15667969	—	2	1	no	—
38	C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic, complemented
39	#15667946	C₂²	1	1	yes	characteristic, complemented
40	#15667945	C₂²	1	1	yes	characteristic, complemented
41	#15667943	C₂²	1	1	yes	characteristic, complemented
42	#15667941	C₂²	1	1	yes	characteristic, complemented
43	#15667937	C₂²	1	1	yes	characteristic, complemented
44	#15667934	C₂²	1	1	yes	characteristic, complemented
45	#15667933	C₂²	1	1	yes	characteristic
46	#15667933	C₂²	1	1	yes	characteristic, complemented
47	#15667932	C₂²	1	1	yes	characteristic, complemented
48	#15667932	C₂²	1	1	yes	characteristic, complemented
49	C₂²⋊#10623494	C₂²	1	1	yes	characteristic, complemented
50	#15667924	C₂²	1	1	yes	characteristic, complemented
51	#15667922	C₂²	1	1	yes	characteristic, complemented
52	C₂²×D₄×C₈₉	C₂²	1	1	yes	characteristic
53	C₂×M₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
54	#117×C₈₉	C₂²	1	1	yes	characteristic, complemented
55	#102×C₈₉	C₂²	1	1	yes	characteristic
56	#102×C₈₉	C₂²	1	1	yes	characteristic
57	#102×C₈₉	C₂²	1	1	yes	characteristic, complemented
58	#102×C₈₉	C₂²	1	1	yes	characteristic, complemented
59	C₂³×D₈₉	—	2	1	no	—
60	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
61	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
62	C₂×C₂²⋊D₈₉	—	2	1	no	—
63	C₂×C₂²⋊D₈₉	—	2	1	no	—
64	C₂×C₂²⋊D₈₉	—	2	1	no	—
65	C₂×C₂²⋊D₈₉	—	2	1	no	—
66	C₂×C₂²⋊D₈₉	—	2	1	no	—
67	C₂×C₂²⋊D₈₉	—	4	4	no	—
68	C₂×C₂²⋊D₈₉	D₄	1	1	yes	characteristic
69	D₄×D₈₉	—	2	2	no	—
70	D₄×D₈₉	—	4	1	no	—
71	C₂²×Dic₈₉	—	2	1	no	—
72	C₂×C₄×D₈₉	—	2	1	no	—
73	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
74	#13083563	—	4	1	no	—
75	#13083562	—	2	2	no	—
76	#13083562	—	4	1	no	—
77	C₂×#10623494	C₂³	1	1	yes	characteristic
78	C₂×#10623494	C₂³	1	1	yes	characteristic
79	C₈×D₈₉	—	4	1	no	—
80	C₄⋊Dic₈₉	—	2	1	no	—
81	C₄⋊Dic₈₉	—	2	1	no	—
82	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
83	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
84	#13083553	—	2	1	no	—
85	#13083553	—	2	1	no	—
86	#13083553	—	2	1	no	—
87	#13083553	—	2	1	no	—
88	#13083553	D₄	1	1	yes	characteristic
89	C₂²⋊Dic₈₉	—	2	1	no	—
90	C₂²⋊Dic₈₉	—	2	1	no	—
91	C₂²⋊Dic₈₉	—	2	1	no	—
92	C₂²⋊Dic₈₉	D₄	1	1	yes	characteristic
93	#13083551	—	2	1	no	—
94	#13083551	—	2	1	no	—
95	#13083551	D₄	1	1	yes	characteristic
96	C₄×Dic₈₉	—	2	1	no	—
97	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
98	C₂⁴×C₈₉	—	2	1	no	—
99	C₂×D₄×C₈₉	—	2	2	no	—
100	C₂×D₄×C₈₉	—	2	1	no	—
101	C₂×D₄×C₈₉	—	4	1	no	—
102	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
103	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
104	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
105	M₁₆×C₈₉	—	4	1	no	—
106	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
107	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
108	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
109	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
110	C₂²⋊C₄×C₈₉	—	2	1	no	—
111	C₄²×C₈₉	—	2	1	no	—
112	C₂³×C₈₉	—	2	1	no	—
113	C₂³×C₈₉	—	2	1	no	—
114	C₂³×C₈₉	—	4	2	no	—
115	C₂³×C₈₉	—	4	2	no	—
116	C₂³×C₈₉	—	8	1	no	—
117	C₂³×C₈₉	C₂×D₄	1	1	yes	characteristic
118	C₂²×D₈₉	—	2	1	no	—
119	C₂²×D₈₉	—	4	2	no	—
120	C₂²×D₈₉	—	4	2	no	—
121	C₂²×D₈₉	—	8	1	no	—
122	C₂²×D₈₉	C₂×D₄	1	1	yes	characteristic
123	D₄×C₈₉	—	2	1	no	—
124	D₄×C₈₉	—	2	1	no	—
125	D₄×C₈₉	—	2	1	no	—
126	D₄×C₈₉	—	4	2	no	—
127	D₄×C₈₉	#41	1	2	yes	—
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	C₂×D₄	1	1	yes	characteristic
133	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
134	C₂²⋊D₈₉	—	2	2	no	—
135	C₂²⋊D₈₉	—	4	2	no	—
136	C₂²⋊D₈₉	—	4	2	no	—
137	C₂²⋊D₈₉	—	4	2	no	—
138	C₂²⋊D₈₉	—	4	2	no	—
139	C₂²⋊D₈₉	—	8	1	no	—
140	C₂×Dic₈₉	—	2	1	no	—
141	C₂×Dic₈₉	—	2	1	no	—
142	C₂×Dic₈₉	—	2	1	no	—
143	C₂×Dic₈₉	—	4	2	no	—
144	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
145	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
146	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
147	D₃₅₆	—	2	1	no	—
148	D₃₅₆	—	2	1	no	—
149	C₄×D₈₉	—	2	1	no	—
150	C₄×D₈₉	—	2	1	no	—
151	C₄×D₈₉	—	4	2	no	—
152	Dic₁₇₈	—	2	1	no	—
153	Dic₁₇₈	—	2	1	no	—
154	C₈×C₈₉	—	2	1	no	—
155	C₈×C₈₉	—	2	1	no	—
156	#10623494	—	2	1	no	—
157	#10623494	—	2	1	no	—
158	C₂²×C₈₉	—	2	2	no	—
159	C₂²×C₈₉	—	2	1	no	—
160	C₂²×C₈₉	—	2	1	no	—
161	C₂²×C₈₉	—	2	1	no	—
162	C₂²×C₈₉	—	4	1	no	—
163	C₂²×C₈₉	—	4	1	no	—
164	C₂²×C₈₉	—	4	1	no	—
165	C₂²×C₈₉	—	4	1	no	—
166	C₂²×C₈₉	—	4	1	no	—
167	C₂²×C₈₉	—	8	4	no	—
168	C₂²×C₈₉	C₂²×D₄	1	1	yes	characteristic
169	C₂×D₈₉	—	2	1	no	—
170	C₂×D₈₉	—	2	1	no	—
171	C₂×D₈₉	—	4	1	no	—
172	C₂×D₈₉	—	4	1	no	—
173	C₂×D₈₉	—	4	1	no	—
174	C₂×D₈₉	—	8	4	no	—
175	C₂×D₈₉	AGL(1,ℤ/8)	1	2	yes	—
176	C₄×C₈₉	—	2	1	no	—
177	C₄×C₈₉	—	4	1	no	—
178	C₄×C₈₉	—	4	1	no	—
179	C₄×C₈₉	C₂×#41	1	1	yes	characteristic
180	C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
181	Dic₈₉	—	2	1	no	—
182	Dic₈₉	—	2	1	no	—
183	Dic₈₉	—	2	1	no	—
184	Dic₈₉	—	4	1	no	—
185	Dic₈₉	—	4	1	no	—
186	Dic₈₉	—	4	1	no	—
187	C₂×C₈₉	—	4	2	no	—
188	C₂×C₈₉	—	4	1	no	—
189	C₂×C₈₉	—	8	1	no	—
190	C₂×C₈₉	#546	1	1	yes	characteristic
191	C₂×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
192	C₂×C₈₉	#577	1	1	yes	characteristic
193	D₈₉	—	2	2	no	—
194	D₈₉	—	8	1	no	—
195	#3310	—	89	1	no	maximal, Sylow
196	C₈₉	#3310	1	1	yes	characteristic, complemented, Sylow
197	#552	—	89	1	no	—
198	D₄²	—	89	1	no	—
199	#490	—	89	1	no	—
200	#482	—	89	1	no	—
201	#480	—	89	1	no	—
202	#478	—	89	1	no	—
203	#468	—	89	1	no	—
204	#465	—	89	1	no	—
205	#460	—	89	1	no	—
206	#450	—	89	1	no	—
207	#450	—	89	1	no	—
208	#440	—	89	1	no	—
209	#435	—	89	1	no	—
210	#418	D₈₉	1	1	yes	characteristic, complemented
211	C₂×#102	—	89	1	no	—
212	C₂²×D₄	—	89	1	no	—
213	C₂²×D₄	—	178	1	no	—
214	C₂²×D₄	C₂×D₈₉	1	1	yes	characteristic
215	C₂×SD₁₆	—	89	1	no	—
216	C₂×SD₁₆	—	89	1	no	—
217	C₂×SD₁₆	—	89	1	no	—
218	C₂×M₁₆	C₂×D₈₉	1	1	yes	characteristic, complemented
219	C₂²×C₈	—	89	1	no	—
220	#127	—	89	1	no	—
221	#126	—	178	1	no	—
222	#125	—	89	1	no	—
223	#125	—	178	1	no	—
224	#123	—	178	1	no	—
225	C₂²⋊Q₈	—	89	1	no	—
226	C₂²⋊Q₈	—	89	1	no	—
227	#121	—	89	1	no	—
228	#121	—	89	1	no	—
229	#121	—	178	1	no	—
230	#120	—	178	1	no	—
231	#120	—	178	1	no	—
232	C₄×Q₈	—	89	1	no	—
233	C₄×D₄	—	89	1	no	—
234	C₄×D₄	—	89	1	no	—
235	#117	—	178	1	no	—
236	#117	C₂×D₈₉	1	1	yes	characteristic, complemented
237	C₂×C₄⋊C₄	—	89	1	no	—
238	#107	—	89	1	no	—
239	#107	—	89	1	no	—
240	#106	—	89	1	no	—
241	C₄⋊C₈	—	89	1	no	—
242	#103	—	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	—	89	1	no	—
248	#102	C₂×D₈₉	1	1	yes	characteristic
249	#102	C₂×D₈₉	1	1	yes	characteristic
250	#102	C₂×D₈₉	1	1	yes	characteristic, complemented
251	#102	C₂×D₈₉	1	1	yes	characteristic, complemented
252	C₂²⋊C₈	—	89	1	no	—
253	C₂²⋊C₈	—	89	1	no	—
254	#97	—	89	1	no	—
255	C₂⁴	—	2	1	no	—
256	C₂⁴	—	178	1	no	—
257	C₂×Q₈	—	89	1	no	—
258	C₂×D₄	—	2	2	no	—
259	C₂×D₄	—	2	1	no	—
260	C₂×D₄	—	4	1	no	—
261	C₂×D₄	—	89	1	no	—
262	C₂×D₄	—	89	1	no	—
263	C₂×D₄	—	356	4	no	—
264	C₂×D₄	—	356	1	no	—
265	C₂×D₄	—	178	1	no	—
266	C₂×D₄	—	178	1	no	—
267	C₂×D₄	—	178	1	no	—
268	C₂×D₄	—	178	1	no	—
269	C₂×D₄	—	178	1	no	—
270	C₂×D₄	—	178	2	no	—
271	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
272	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
273	C₂²×C₄	—	89	1	no	—
274	C₂²×C₄	—	178	1	no	—
275	C₂²×C₄	—	178	1	no	—
276	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
277	SD₁₆	—	356	1	no	—
278	SD₁₆	—	356	1	no	—
279	SD₁₆	—	178	2	no	—
280	M₁₆	—	4	1	no	—
281	C₂×C₈	—	89	1	no	—
282	C₂×C₈	—	89	1	no	—
283	C₂×C₈	—	356	1	no	—
284	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
285	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
286	C₄⋊C₄	—	89	1	no	—
287	C₄⋊C₄	—	89	1	no	—
288	C₄⋊C₄	—	89	1	no	—
289	C₄⋊C₄	—	178	1	no	—
290	C₄⋊C₄	—	178	1	no	—
291	C₄⋊C₄	—	178	1	no	—
292	C₄⋊C₄	—	178	1	no	—
293	C₄⋊C₄	—	178	1	no	—
294	C₄⋊C₄	—	178	1	no	—
295	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
296	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
297	C₂²⋊C₄	—	2	1	no	—
298	C₂²⋊C₄	—	89	1	no	—
299	C₂²⋊C₄	—	89	1	no	—
300	C₂²⋊C₄	—	178	1	no	—
301	C₂²⋊C₄	—	178	1	no	—
302	C₂²⋊C₄	—	178	1	no	—
303	C₂²⋊C₄	—	178	1	no	—
304	C₂²⋊C₄	—	178	1	no	—
305	C₄²	—	2	1	no	—
306	C₄²	—	89	1	no	—
307	C₄²	—	178	1	no	—
308	C₂³	—	2	1	no	—
309	C₂³	—	2	1	no	—
310	C₂³	—	4	2	no	—
311	C₂³	—	4	2	no	—
312	C₂³	—	8	1	no	—
313	C₂³	—	89	1	no	—
314	C₂³	—	356	2	no	—
315	C₂³	—	356	2	no	—
316	C₂³	—	178	1	no	—
317	C₂³	—	712	1	no	—
318	C₂³	D₄×D₈₉	1	1	yes	characteristic
319	Q₈	—	178	1	no	—
320	Q₈	—	178	1	no	—
321	D₄	—	2	1	no	—
322	D₄	—	2	1	no	—
323	D₄	—	2	1	no	—
324	D₄	—	4	2	no	—
325	D₄	—	356	2	no	—
326	D₄	—	356	2	no	—
327	D₄	—	356	2	no	—
328	D₄	—	356	2	no	—
329	D₄	—	178	2	no	—
330	D₄	—	178	1	no	—
331	D₄	—	178	1	no	—
332	D₄	—	712	1	no	—
333	D₄	#13083574	1	2	yes	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	89	1	no	—
339	C₂×C₄	—	89	1	no	—
340	C₂×C₄	—	89	1	no	—
341	C₂×C₄	—	356	2	no	—
342	C₂×C₄	—	356	2	no	—
343	C₂×C₄	—	178	1	no	—
344	C₂×C₄	—	178	1	no	—
345	C₂×C₄	—	178	1	no	—
346	C₂×C₄	—	178	1	no	—
347	C₂×C₄	—	178	1	no	—
348	C₂×C₄	D₄×D₈₉	1	1	yes	characteristic
349	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
350	C₈	—	2	1	no	—
351	C₈	—	2	1	no	—
352	C₈	—	178	1	no	—
353	C₈	—	178	1	no	—
354	C₂²	—	2	1	no	—
355	C₂²	—	2	1	no	—
356	C₂²	—	2	2	no	—
357	C₂²	—	2	1	no	—
358	C₂²	—	4	1	no	—
359	C₂²	—	4	1	no	—
360	C₂²	—	4	1	no	—
361	C₂²	—	4	1	no	—
362	C₂²	—	4	1	no	—
363	C₂²	—	8	4	no	—
364	C₂²	—	89	2	no	—
365	C₂²	—	356	1	no	—
366	C₂²	—	356	1	no	—
367	C₂²	—	356	1	no	—
368	C₂²	—	178	1	no	—
369	C₂²	—	178	1	no	—
370	C₂²	—	712	4	no	—
371	C₂²	C₂×D₄×D₈₉	1	1	yes	characteristic
372	C₄	—	2	1	no	—
373	C₄	—	4	1	no	—
374	C₄	—	4	1	no	—
375	C₄	—	356	1	no	—
376	C₄	—	356	1	no	—
377	C₄	—	356	1	no	—
378	C₄	—	178	1	no	—
379	C₄	—	178	1	no	—
380	C₄	—	178	1	no	—
381	C₄	C₂×#13083574	1	1	yes	characteristic
382	C₄	#15668057	1	1	yes	characteristic
383	C₂	—	4	1	no	—
384	C₂	—	4	2	no	—
385	C₂	—	8	1	no	—
386	C₂	—	178	2	no	—
387	C₂	—	712	1	no	—
388	C₂	#19152238	1	1	yes	characteristic
389	C₂	AGL(1,ℤ/8)×D₈₉	1	1	yes	characteristic
390	C₂	#19152408	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₈₉
commutator, cosocle	C₂×C₄×C₈₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₈₉
Fitting	#418×C₈₉	C₂
socle	C₂²×C₈₉	C₂²×D₄
prime radical	D₄×C₂²⋊D₈₉	C₂
hypercenter	#418	D₈₉
hypocenter	C₈₉	#3310
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #418

Complements

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

N	H ≅ G/N	type
1. #19152287	C₂	semidirect
3. #19151961	C₂	semidirect
4. #19151922	C₂	semidirect
5. #19151910	C₂	semidirect
6. #19151896	C₂	semidirect
7. #19151844	C₂	semidirect
8. #19151826	C₂	semidirect
9. #19151797	C₂	semidirect
10. #19151750	C₂	semidirect
11. #19151749	C₂	semidirect
12. #19151695	C₂	semidirect
13. #19151667	C₂	semidirect
14. #102×D₈₉	C₂	semidirect
15. #418×C₈₉	C₂	semidirect
18. C₂×#13083563	C₂²	semidirect
20. C₂×#13083562	C₂²	semidirect
21. C₂×C₈×D₈₉	C₂²	semidirect
25. #15668003	C₂²	semidirect
27. #15667992	C₂²	semidirect
28. #15667991	C₂²	semidirect
34. #15667977	C₂²	semidirect
38. C₄⋊C₄×D₈₉	C₂²	semidirect
39. #15667946	C₂²	semidirect
40. #15667945	C₂²	semidirect
41. #15667943	C₂²	semidirect
42. #15667941	C₂²	semidirect
43. #15667937	C₂²	semidirect
44. #15667934	C₂²	semidirect
46. #15667933	C₂²	semidirect
47. #15667932	C₂²	semidirect
48. #15667932	C₂²	semidirect
49. C₂²⋊#10623494	C₂²	semidirect
50. #15667924	C₂²	semidirect
51. #15667922	C₂²	semidirect
53. C₂×M₁₆×C₈₉	C₂²	semidirect
54. #117×C₈₉	C₂²	semidirect
57. #102×C₈₉	C₂²	semidirect
58. #102×C₈₉	C₂²	semidirect
196. C₈₉	#3310	semidirect
210. #418	D₈₉	semidirect
218. C₂×M₁₆	C₂×D₈₉	semidirect
236. #117	C₂×D₈₉	semidirect
250. #102	C₂×D₈₉	semidirect
251. #102	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#19152287	2
D₄×C₂²⋊D₈₉	2
#19151961	2
#19151922	2
#19151910	2
#19151896	2
#19151844	2
#19151826	2
#19151797	2
#19151750	2
#19151749	2
#19151695	2
#19151667	2
#102×D₈₉	2
#418×C₈₉	2
#3310	89