Subgroups — #31815857

Order 17792.

496 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17984864	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#17984862	C₂	1	1	yes	maximal, characteristic, complemented
3	#22581499	C₂	1	1	yes	maximal, characteristic, complemented
4	#22581421	C₂	1	1	yes	maximal, characteristic, complemented
5	#22581178	C₂	1	1	yes	maximal, characteristic, complemented
6	#22581174	C₂	1	1	yes	maximal, characteristic, complemented
7	#22581171	C₂	1	1	yes	maximal, characteristic, complemented
8	#22581167	C₂	1	1	yes	maximal, characteristic, complemented
9	#22581162	C₂	1	1	yes	maximal, characteristic, complemented
10	#22581157	C₂	1	1	yes	maximal, characteristic, complemented
11	#22581152	C₂	1	1	yes	maximal, characteristic, complemented
12	#22581147	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×Dic₁₃₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
14	#22580947	C₂	1	1	yes	maximal, characteristic, complemented
15	#416×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14555785	C₂²	1	1	yes	characteristic
17	C₂×#14555785	C₂²	1	1	yes	characteristic
18	#17984864	—	2	4	no	—
19	#17984862	—	2	4	no	—
20	C₂×Dic₅₅₆	C₂²	1	1	yes	characteristic
21	C₂×#14555775	C₂²	1	1	yes	characteristic
22	C₂×#14555774	C₂²	1	1	yes	characteristic
23	C₂×#14555774	C₂²	1	1	yes	characteristic
24	C₂×#14555773	C₂²	1	1	yes	characteristic
25	C₂×#14555772	C₂²	1	1	yes	characteristic
26	C₂×D₁₁₁₂	C₂²	1	1	yes	characteristic
27	C₂×#14555770	C₂²	1	1	yes	characteristic
28	C₂²×C₁₃₉⋊C₈	C₂²	1	1	yes	characteristic
29	#17984840	C₂²	1	1	yes	characteristic
30	#17984838	C₂²	1	1	yes	characteristic
31	#17984831	C₂²	1	1	yes	characteristic
32	#17984829	C₂²	1	1	yes	characteristic
33	#17984814	—	2	1	no	—
34	#17984814	—	2	1	no	—
35	#17984807	C₂²	1	1	yes	characteristic
36	#17984807	C₂²	1	1	yes	characteristic
37	#17984804	C₂²	1	1	yes	characteristic
38	#17984804	C₂²	1	1	yes	characteristic
39	C₄×C₂²⋊D₁₃₉	—	2	1	no	—
40	C₄×C₂²⋊D₁₃₉	—	2	1	no	—
41	(C₂²⋊D₁₃₉)⋊C₄	—	2	1	no	—
42	(C₂²⋊D₁₃₉)⋊C₄	—	2	1	no	—
43	#17984799	—	2	1	no	—
44	C₂×C₄×Dic₁₃₉	C₂²	1	1	yes	characteristic
45	C₄²×D₁₃₉	—	2	1	no	—
46	Dic₁₃₉⋊C₈	C₂²	1	1	yes	characteristic
47	Dic₁₃₉⋊C₈	C₂²	1	1	yes	characteristic
48	Dic₁₃₉⋊C₈	C₂²	1	1	yes	characteristic
49	Dic₁₃₉⋊C₈	C₂²	1	1	yes	characteristic
50	#17984765	C₂²	1	1	yes	characteristic
51	#17984765	C₂²	1	1	yes	characteristic
52	#17984762	C₂²	1	1	yes	characteristic
53	#17984762	C₂²	1	1	yes	characteristic
54	C₂×#41×C₁₃₉	C₂²	1	1	yes	characteristic
55	C₂²×C₈×C₁₃₉	C₂²	1	1	yes	characteristic
56	#117×C₁₃₉	C₂²	1	1	yes	characteristic
57	#103×C₁₃₉	C₂²	1	1	yes	characteristic
58	#103×C₁₃₉	C₂²	1	1	yes	characteristic
59	#102×C₁₃₉	C₂²	1	1	yes	characteristic
60	#102×C₁₃₉	C₂²	1	1	yes	characteristic
61	#14555785	—	2	2	no	—
62	#14555785	—	2	2	no	—
63	#14555785	—	2	2	no	—
64	#14555785	D₄	1	4	yes	complemented
65	C₂×Dic₂₇₈	C₂³	1	1	yes	characteristic
66	C₂×Dic₂₇₈	C₂³	1	1	yes	characteristic
67	C₂×D₅₅₆	C₂³	1	1	yes	characteristic
68	C₂×D₅₅₆	C₂³	1	1	yes	characteristic
69	C₂×C₂²⋊D₁₃₉	—	2	1	no	—
70	C₂×C₂²⋊D₁₃₉	—	2	1	no	—
71	C₂×C₂²⋊D₁₃₉	—	2	1	no	—
72	C₂×C₂²⋊D₁₃₉	—	2	1	no	—
73	C₂²×Dic₁₃₉	D₄	1	1	yes	characteristic
74	C₂²×Dic₁₃₉	D₄	1	1	yes	characteristic
75	C₂×C₄×D₁₃₉	—	2	1	no	—
76	C₂×C₄×D₁₃₉	—	2	1	no	—
77	C₂×C₄×D₁₃₉	—	2	1	no	—
78	C₂×C₄×D₁₃₉	—	2	1	no	—
79	Dic₅₅₆	—	2	2	no	—
80	#14555775	—	2	2	no	—
81	#14555774	—	2	2	no	—
82	#14555774	—	2	2	no	—
83	#14555773	—	2	2	no	—
84	#14555772	—	2	2	no	—
85	D₁₁₁₂	—	2	2	no	—
86	#14555770	—	2	2	no	—
87	C₂×C₁₃₉⋊C₈	—	2	2	no	—
88	C₂×C₁₃₉⋊C₈	C₂³	1	1	yes	characteristic
89	C₂×C₁₃₉⋊C₈	C₂³	1	1	yes	characteristic
90	Dic₁₃₉⋊C₄	—	2	1	no	—
91	Dic₁₃₉⋊C₄	—	2	1	no	—
92	Dic₁₃₉⋊C₄	—	2	1	no	—
93	Dic₁₃₉⋊C₄	—	2	1	no	—
94	C₂²⋊Dic₁₃₉	—	2	1	no	—
95	C₂²⋊Dic₁₃₉	—	2	1	no	—
96	(C₂×D₁₃₉)⋊C₄	—	2	1	no	—
97	(C₂×D₁₃₉)⋊C₄	—	2	1	no	—
98	(C₂×D₁₃₉)⋊C₄	—	2	1	no	—
99	(C₂×D₁₃₉)⋊C₄	—	2	1	no	—
100	C₄×Dic₁₃₉	—	2	1	no	—
101	C₄×Dic₁₃₉	—	2	1	no	—
102	C₄×Dic₁₃₉	D₄	1	1	yes	characteristic
103	C₄×Dic₁₃₉	D₄	1	1	yes	characteristic
104	C₄×Dic₁₃₉	C₂³	1	1	yes	characteristic
105	C₄×Dic₁₃₉	C₂³	1	1	yes	characteristic
106	#41×C₁₃₉	—	2	2	no	—
107	#41×C₁₃₉	—	2	2	no	—
108	C₂×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
109	C₂×D₄×C₁₃₉	—	2	1	no	—
110	C₂×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
111	C₂²×C₄×C₁₃₉	—	2	1	no	—
112	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
113	C₂×C₈×C₁₃₉	—	2	2	no	—
114	C₂×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
115	C₂×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
116	C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
117	C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
118	C₂²⋊C₄×C₁₃₉	—	2	1	no	—
119	C₄²×C₁₃₉	—	2	1	no	—
120	C₂²×D₁₃₉	—	2	1	no	—
121	C₂²×D₁₃₉	—	2	1	no	—
122	Dic₂₇₈	—	2	1	no	—
123	Dic₂₇₈	—	2	1	no	—
124	Dic₂₇₈	—	2	1	no	—
125	Dic₂₇₈	C₂×D₄	1	2	yes	—
126	D₅₅₆	—	2	1	no	—
127	D₅₅₆	—	2	1	no	—
128	D₅₅₆	—	2	1	no	—
129	D₅₅₆	C₂×D₄	1	2	yes	—
130	C₂²⋊D₁₃₉	—	2	4	no	—
131	C₂²⋊D₁₃₉	—	4	2	no	—
132	C₂²⋊D₁₃₉	—	4	2	no	—
133	C₂²⋊D₁₃₉	—	4	2	no	—
134	C₂×Dic₁₃₉	—	2	1	no	—
135	C₂×Dic₁₃₉	—	2	2	no	—
136	C₂×Dic₁₃₉	—	2	1	no	—
137	C₂×Dic₁₃₉	—	4	1	no	—
138	C₂×Dic₁₃₉	C₂×D₄	1	1	yes	characteristic
139	C₂×Dic₁₃₉	C₂×D₄	1	1	yes	characteristic
140	C₂×Dic₁₃₉	C₂×D₄	1	1	yes	characteristic
141	C₂×Dic₁₃₉	C₂×D₄	1	1	yes	characteristic
142	C₄×D₁₃₉	—	2	4	no	—
143	C₄×D₁₃₉	—	4	2	no	—
144	C₄×D₁₃₉	—	4	2	no	—
145	C₄×D₁₃₉	—	4	2	no	—
146	C₁₃₉⋊C₈	—	2	1	no	—
147	C₁₃₉⋊C₈	—	2	1	no	—
148	C₂³×C₁₃₉	—	2	1	no	—
149	C₂³×C₁₃₉	C₂×D₄	1	1	yes	characteristic
150	Q₈×C₁₃₉	—	2	1	no	—
151	Q₈×C₁₃₉	—	2	1	no	—
152	D₄×C₁₃₉	—	2	1	no	—
153	D₄×C₁₃₉	—	2	1	no	—
154	D₄×C₁₃₉	—	4	2	no	—
155	C₂×C₄×C₁₃₉	—	2	1	no	—
156	C₂×C₄×C₁₃₉	—	2	1	no	—
157	C₂×C₄×C₁₃₉	—	2	1	no	—
158	C₂×C₄×C₁₃₉	—	4	2	no	—
159	C₂×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
160	C₂×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
161	C₂×C₄×C₁₃₉	#41	1	2	yes	—
162	C₂×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
163	C₈×C₁₃₉	—	2	1	no	—
164	C₈×C₁₃₉	—	2	1	no	—
165	C₂²×C₁₃₉	—	2	1	no	—
166	C₂²×C₁₃₉	—	2	1	no	—
167	C₂²×C₁₃₉	—	4	1	no	—
168	C₂²×C₁₃₉	—	4	1	no	—
169	C₂²×C₁₃₉	—	4	1	no	—
170	C₂²×C₁₃₉	#121	1	2	yes	—
171	C₂²×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
172	C₂×D₁₃₉	—	2	2	no	—
173	C₂×D₁₃₉	—	4	1	no	—
174	C₂×D₁₃₉	—	4	1	no	—
175	C₂×D₁₃₉	—	4	1	no	—
176	C₂×D₁₃₉	—	4	1	no	—
177	C₂×D₁₃₉	—	4	1	no	—
178	C₄×C₁₃₉	—	4	1	no	—
179	C₄×C₁₃₉	—	4	1	no	—
180	C₄×C₁₃₉	—	4	1	no	—
181	C₄×C₁₃₉	#121	1	2	yes	—
182	C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
183	C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
184	Dic₁₃₉	—	2	2	no	—
185	Dic₁₃₉	—	2	1	no	—
186	Dic₁₃₉	—	2	1	no	—
187	Dic₁₃₉	—	2	1	no	—
188	Dic₁₃₉	—	4	1	no	—
189	Dic₁₃₉	#135	1	2	yes	complemented
190	C₂×C₁₃₉	—	2	2	no	—
191	C₂×C₁₃₉	—	8	1	no	—
192	C₂×C₁₃₉	C₂×#121	1	1	yes	characteristic
193	C₂×C₁₃₉	C₂×#135	1	1	yes	characteristic
194	C₂×C₁₃₉	#575	1	1	yes	characteristic
195	D₁₃₉	—	4	2	no	—
196	D₁₃₉	—	8	1	no	—
197	C₁₃₉	#3035	1	1	yes	characteristic, complemented, Sylow
198	#3035	—	139	1	no	maximal, Sylow
199	C₂×#135	—	139	1	no	—
200	C₂×#135	—	139	1	no	—
201	#532	—	139	1	no	—
202	C₄×#41	—	139	1	no	—
203	#464	—	139	1	no	—
204	#464	—	139	1	no	—
205	#463	—	139	1	no	—
206	#463	—	139	1	no	—
207	#462	—	139	1	no	—
208	#461	—	139	1	no	—
209	#460	—	139	1	no	—
210	#459	—	139	1	no	—
211	C₂×C₄⋊C₈	—	139	1	no	—
212	#416	—	139	1	no	—
213	#416	D₁₃₉	1	1	yes	characteristic, complemented
214	C₂×#41	—	139	1	no	—
215	C₂×#41	—	139	1	no	—
216	C₂×#41	C₂×D₁₃₉	1	1	yes	characteristic
217	#135	—	278	4	no	—
218	#135	—	278	4	no	—
219	C₂×Q₁₆	—	139	1	no	—
220	C₂×Q₁₆	—	139	1	no	—
221	C₂×SD₁₆	—	139	1	no	—
222	C₂×SD₁₆	—	139	1	no	—
223	C₂×SD₁₆	—	139	1	no	—
224	C₂×SD₁₆	—	139	1	no	—
225	C₂×D₈	—	139	1	no	—
226	C₂×D₈	—	139	1	no	—
227	C₂²×C₈	—	139	1	no	—
228	C₂²×C₈	C₂×D₁₃₉	1	1	yes	characteristic
229	C₄⋊Q₈	—	139	1	no	—
230	#127	—	139	1	no	—
231	#124	—	139	1	no	—
232	#124	—	139	1	no	—
233	#121	—	278	1	no	—
234	#121	—	278	1	no	—
235	C₄×Q₈	—	139	1	no	—
236	C₄×Q₈	—	139	1	no	—
237	C₄×D₄	—	278	1	no	—
238	C₄×D₄	—	278	1	no	—
239	C₄×D₄	—	278	1	no	—
240	C₄×D₄	—	278	1	no	—
241	C₄×D₄	—	139	1	no	—
242	C₄×D₄	—	139	1	no	—
243	#117	—	278	1	no	—
244	#117	C₂×D₁₃₉	1	1	yes	characteristic
245	C₂×C₄²	—	278	1	no	—
246	C₂×C₄²	—	139	1	no	—
247	C₄⋊C₈	—	139	1	no	—
248	C₄⋊C₈	—	139	1	no	—
249	C₄⋊C₈	—	139	1	no	—
250	C₄⋊C₈	—	139	1	no	—
251	#103	—	139	1	no	—
252	#103	—	139	1	no	—
253	#103	C₂×D₁₃₉	1	1	yes	characteristic
254	#103	C₂×D₁₃₉	1	1	yes	characteristic
255	#102	—	139	1	no	—
256	#102	—	139	1	no	—
257	#102	C₂×D₁₃₉	1	1	yes	characteristic
258	#102	C₂×D₁₃₉	1	1	yes	characteristic
259	#41	—	2	2	no	—
260	#41	—	2	2	no	—
261	#41	—	278	2	no	—
262	#41	—	278	2	no	—
263	#41	—	278	2	no	—
264	#41	—	139	4	no	—
265	C₂×Q₈	—	139	1	no	—
266	C₂×Q₈	—	139	1	no	—
267	C₂×Q₈	C₂²×D₁₃₉	1	1	yes	characteristic
268	C₂×D₄	—	2	1	no	—
269	C₂×D₄	—	278	1	no	—
270	C₂×D₄	—	278	1	no	—
271	C₂×D₄	—	278	1	no	—
272	C₂×D₄	—	278	1	no	—
273	C₂×D₄	—	139	1	no	—
274	C₂×D₄	—	139	1	no	—
275	C₂×D₄	C₂²×D₁₃₉	1	1	yes	characteristic
276	C₂²×C₄	—	2	1	no	—
277	C₂²×C₄	—	278	1	no	—
278	C₂²×C₄	—	278	1	no	—
279	C₂²×C₄	—	278	1	no	—
280	C₂²×C₄	—	278	1	no	—
281	C₂²×C₄	—	139	1	no	—
282	C₂²×C₄	—	139	1	no	—
283	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
284	Q₁₆	—	278	2	no	—
285	Q₁₆	—	278	2	no	—
286	SD₁₆	—	278	2	no	—
287	SD₁₆	—	278	2	no	—
288	SD₁₆	—	278	2	no	—
289	SD₁₆	—	278	2	no	—
290	D₈	—	278	2	no	—
291	D₈	—	278	2	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	278	2	no	—
294	C₂×C₈	—	139	1	no	—
295	C₂×C₈	—	139	1	no	—
296	C₂×C₈	C₂²×D₁₃₉	1	1	yes	characteristic
297	C₂×C₈	C₂²×D₁₃₉	1	1	yes	characteristic
298	C₄⋊C₄	—	278	1	no	—
299	C₄⋊C₄	—	278	1	no	—
300	C₄⋊C₄	—	278	1	no	—
301	C₄⋊C₄	—	278	1	no	—
302	C₄⋊C₄	C₂²×D₁₃₉	1	1	yes	characteristic
303	C₄⋊C₄	C₂²×D₁₃₉	1	1	yes	characteristic
304	C₂²⋊C₄	—	2	1	no	—
305	C₂²⋊C₄	—	278	1	no	—
306	C₂²⋊C₄	—	278	1	no	—
307	C₂²⋊C₄	—	278	1	no	—
308	C₂²⋊C₄	—	278	1	no	—
309	C₂²⋊C₄	—	278	1	no	—
310	C₂²⋊C₄	—	278	1	no	—
311	C₄²	—	2	1	no	—
312	C₄²	—	278	1	no	—
313	C₄²	—	278	1	no	—
314	C₄²	—	139	1	no	—
315	C₄²	—	139	1	no	—
316	C₄²	—	139	1	no	—
317	C₄²	—	139	1	no	—
318	C₂³	—	2	1	no	—
319	C₂³	—	278	1	no	—
320	C₂³	—	278	1	no	—
321	C₂³	D₄×D₁₃₉	1	1	yes	characteristic
322	Q₈	—	2	1	no	—
323	Q₈	—	2	1	no	—
324	Q₈	—	278	1	no	—
325	Q₈	—	278	1	no	—
326	Q₈	—	278	1	no	—
327	Q₈	—	139	2	no	—
328	D₄	—	2	1	no	—
329	D₄	—	2	1	no	—
330	D₄	—	4	2	no	—
331	D₄	—	278	4	no	—
332	D₄	—	278	1	no	—
333	D₄	—	278	1	no	—
334	D₄	—	278	1	no	—
335	D₄	—	556	2	no	—
336	D₄	—	556	2	no	—
337	D₄	—	556	2	no	—
338	D₄	—	139	2	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	278	1	no	—
344	C₂×C₄	—	278	2	no	—
345	C₂×C₄	—	278	4	no	—
346	C₂×C₄	—	278	1	no	—
347	C₂×C₄	—	556	2	no	—
348	C₂×C₄	—	556	2	no	—
349	C₂×C₄	—	556	1	no	—
350	C₂×C₄	—	556	2	no	—
351	C₂×C₄	—	139	1	no	—
352	C₂×C₄	—	139	1	no	—
353	C₂×C₄	—	139	1	no	—
354	C₂×C₄	—	139	1	no	—
355	C₂×C₄	D₄×D₁₃₉	1	2	yes	—
356	C₂×C₄	D₄×D₁₃₉	1	1	yes	characteristic
357	C₂×C₄	#14555785	1	2	yes	—
358	C₂×C₄	C₂³×D₁₃₉	1	1	yes	characteristic
359	C₈	—	2	1	no	—
360	C₈	—	2	1	no	—
361	C₈	—	278	1	no	—
362	C₈	—	278	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	4	1	no	—
366	C₂²	—	4	1	no	—
367	C₂²	—	4	1	no	—
368	C₂²	—	278	2	no	—
369	C₂²	—	556	1	no	—
370	C₂²	—	556	1	no	—
371	C₂²	—	556	1	no	—
372	C₂²	—	556	1	no	—
373	C₂²	—	556	1	no	—
374	C₂²	#17984815	1	2	yes	—
375	C₂²	C₂×D₄×D₁₃₉	1	1	yes	characteristic
376	C₄	—	4	1	no	—
377	C₄	—	4	1	no	—
378	C₄	—	4	1	no	—
379	C₄	—	278	2	no	—
380	C₄	—	278	1	no	—
381	C₄	—	278	1	no	—
382	C₄	—	278	1	no	—
383	C₄	—	556	1	no	—
384	C₄	—	139	2	no	—
385	C₄	#17984815	1	2	yes	—
386	C₄	C₂×D₄×D₁₃₉	1	1	yes	characteristic
387	C₄	C₂×#14555785	1	1	yes	characteristic
388	C₂	—	2	2	no	—
389	C₂	—	8	1	no	—
390	C₂	—	556	2	no	—
391	C₂	—	1112	1	no	—
392	C₂	C₂×#17984815	1	1	yes	characteristic
393	C₂	#135×D₁₃₉	1	1	yes	characteristic
394	C₂	#22581750	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₄×D₁₃₉
commutator, cosocle	C₂×C₄×C₁₃₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₃₉
Fitting	#416×C₁₃₉	C₂
socle	C₂²×C₁₃₉	C₂²×D₄
hypercenter	#416	D₁₃₉
hypocenter	C₁₃₉	#3035
LCS	G ▷ C₂×C₄×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #416

Complements

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

N	H ≅ G/N	type
1. C₂×#17984864	C₂	semidirect
2. C₂×#17984862	C₂	semidirect
3. #22581499	C₂	semidirect
4. #22581421	C₂	semidirect
5. #22581178	C₂	semidirect
6. #22581174	C₂	semidirect
7. #22581171	C₂	semidirect
8. #22581167	C₂	semidirect
9. #22581162	C₂	semidirect
10. #22581157	C₂	semidirect
11. #22581152	C₂	semidirect
12. #22581147	C₂	semidirect
13. C₂×Dic₁₃₉⋊C₈	C₂	semidirect
14. #22580947	C₂	semidirect
15. #416×C₁₃₉	C₂	semidirect
64. #14555785	D₄	semidirect
189. Dic₁₃₉	#135	semidirect
197. C₁₃₉	#3035	semidirect
213. #416	D₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17984864	2
C₂×#17984862	2
#22581499	2
#22581421	2
#22581178	2
#22581174	2
#22581171	2
#22581167	2
#22581162	2
#22581157	2
#22581152	2
#22581147	2
C₂×Dic₁₃₉⋊C₈	2
#22580947	2
#416×C₁₃₉	2
#3035	139