Subgroups — #16836360

Order 3712.

412 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	#14272197	C₂	1	1	yes	maximal, characteristic, complemented
2	#14272196	C₂	1	1	yes	maximal, characteristic, complemented
3	#14272195	C₂	1	1	yes	maximal, characteristic, complemented
4	#14272193	C₂	1	1	yes	maximal, characteristic, complemented
5	#14272193	C₂	1	1	yes	maximal, characteristic, complemented
6	#14272192	C₂	1	1	yes	maximal, characteristic, complemented
7	#14272191	C₂	1	1	yes	maximal, characteristic, complemented
8	#14272190	C₂	1	1	yes	maximal, characteristic, complemented
9	#14272187	C₂	1	1	yes	maximal, characteristic, complemented
10	#14272187	C₂	1	1	yes	maximal, characteristic, complemented
11	#14272137	C₂	1	1	yes	maximal, characteristic, complemented
12	#14272136	C₂	1	1	yes	maximal, characteristic, complemented
13	#14272134	C₂	1	1	yes	maximal, characteristic, complemented
14	D₂₉⋊(C₂²⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
15	#14271671	C₂	1	1	yes	maximal, characteristic
16	C₂×#90807	C₂²	1	1	yes	characteristic
17	C₂²×C₄×D₂₉	C₂²	1	1	yes	characteristic
18	C₂×#90800	C₂²	1	1	yes	characteristic, complemented
19	C₂²×#6599	C₂²	1	1	yes	characteristic, complemented
20	C₂×#90796	C₂²	1	1	yes	characteristic
21	C₂×#90796	C₂²	1	1	yes	characteristic
22	C₂×#90796	C₂²	1	1	yes	characteristic, complemented
23	C₂×D₂₉⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×D₂₉⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×D₂₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
26	C₂₉×#123	C₄	1	1	yes	characteristic
27	#11745299	C₄	1	1	yes	characteristic
28	#11745291	C₄	1	1	yes	characteristic
29	#11745258	C₄	1	1	yes	characteristic
30	#11745258	C₄	1	1	yes	characteristic
31	#11745255	C₂²	1	1	yes	characteristic
32	#11745255	C₂²	1	1	yes	characteristic
33	#11745246	C₄	1	1	yes	characteristic
34	#11745246	C₄	1	1	yes	characteristic
35	#11745244	C₄	1	1	yes	characteristic
36	#11745243	C₂²	1	1	yes	characteristic
37	#11745243	C₂²	1	1	yes	characteristic
38	#11745239	C₂²	1	1	yes	characteristic
39	C₂²⋊#6599	C₂²	1	1	yes	characteristic
40	C₂²⋊#6599	C₂²	1	1	yes	characteristic
41	C₂²⋊#6599	C₂²	1	1	yes	characteristic
42	C₂²⋊#6599	C₂²	1	1	yes	characteristic
43	C₂²⋊#6599	C₂²	1	1	yes	characteristic, complemented
44	C₂²⋊#6599	C₂²	1	1	yes	characteristic, complemented
45	#11745220	C₂²	1	1	yes	characteristic, complemented
46	#11745220	C₂²	1	1	yes	characteristic, complemented
47	#11745219	C₂²	1	1	yes	characteristic
48	#11745219	C₂²	1	1	yes	characteristic
49	#11745219	C₂²	1	1	yes	characteristic
50	#11745219	C₂²	1	1	yes	characteristic
51	#11745219	C₂²	1	1	yes	characteristic, complemented
52	#11745219	C₂²	1	1	yes	characteristic, complemented
53	#11745218	C₂²	1	1	yes	characteristic, complemented
54	#11745218	C₂²	1	1	yes	characteristic, complemented
55	C₄⋊#6599	C₂²	1	1	yes	characteristic, complemented
56	C₄⋊#6599	C₂²	1	1	yes	characteristic, complemented
57	C₄×#6599	C₂²	1	1	yes	characteristic, complemented
58	C₄×#6599	C₂²	1	1	yes	characteristic, complemented
59	C₂³×D₂₉	C₂×C₄	1	1	yes	characteristic
60	C₂×D₄×C₂₉	C₂×C₄	1	1	yes	characteristic
61	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
62	C₂×C₂²⋊D₂₉	C₂×C₄	1	1	yes	characteristic
63	C₂×C₂²⋊D₂₉	C₂×C₄	1	1	yes	characteristic
64	C₂×C₂²⋊D₂₉	C₂×C₄	1	1	yes	characteristic
65	C₂×C₂²⋊D₂₉	C₂×C₄	1	1	yes	characteristic
66	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
67	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
68	#90807	—	4	1	no	—
69	#90807	—	4	1	no	—
70	C₂×D₁₁₆	C₂×C₄	1	1	yes	characteristic
71	C₂×D₁₁₆	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄×D₂₉	—	4	1	no	—
73	C₂×C₄×D₂₉	—	4	1	no	—
74	C₂×C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
77	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
78	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
79	C₂×Dic₅₈	C₂×C₄	1	1	yes	characteristic
80	#90800	—	4	1	no	—
81	C₂×#6599	—	4	1	no	—
82	C₂×#6599	C₂³	1	1	yes	characteristic
83	C₂×#6599	C₂³	1	1	yes	characteristic
84	C₂×#6599	C₂³	1	1	yes	characteristic
85	C₂×#6599	C₂³	1	1	yes	characteristic
86	C₂×#6599	C₂³	1	1	yes	characteristic
87	C₂×#6599	C₂³	1	1	yes	characteristic
88	C₂×#6599	C₂³	1	1	yes	characteristic
89	C₂×#6599	C₂³	1	1	yes	characteristic
90	#90796	—	4	1	no	—
91	#90796	—	4	1	no	—
92	#90796	—	4	1	no	—
93	D₂₉⋊C₈	—	4	1	no	—
94	D₂₉⋊C₈	—	4	1	no	—
95	D₂₉⋊C₈	—	4	1	no	—
96	C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
97	C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
98	C₂²⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
99	C₂²⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
100	C₂²⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
101	C₂²⋊Dic₂₉	C₂×C₄	1	1	yes	characteristic
102	#90781	C₂×C₄	1	1	yes	characteristic
103	#90781	C₂×C₄	1	1	yes	characteristic
104	#90781	C₂×C₄	1	1	yes	characteristic
105	#90781	C₂×C₄	1	1	yes	characteristic
106	#90781	C₂×C₄	1	1	yes	characteristic
107	#90781	C₂×C₄	1	1	yes	characteristic
108	#90779	C₂×C₄	1	1	yes	characteristic
109	#90779	C₂×C₄	1	1	yes	characteristic
110	#90779	C₂×C₄	1	1	yes	characteristic
111	#90779	C₂×C₄	1	1	yes	characteristic
112	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
113	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
114	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
115	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
116	C₂²×D₂₉	—	2	2	no	—
117	C₂²×D₂₉	—	4	1	no	—
118	C₂²×D₂₉	—	4	1	no	—
119	C₂²×D₂₉	C₂²×C₄	1	1	yes	characteristic
120	C₂²×D₂₉	C₂²×C₄	1	1	yes	characteristic
121	C₂²×D₂₉	C₂²×C₄	1	1	yes	characteristic
122	D₄×C₂₉	—	4	1	no	—
123	C₂×C₄×C₂₉	—	4	1	no	—
124	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
129	C₂²⋊D₂₉	—	2	2	no	—
130	C₂²⋊D₂₉	—	4	1	no	—
131	C₂²⋊D₂₉	—	4	1	no	—
132	C₂²⋊D₂₉	—	4	1	no	—
133	C₂×Dic₂₉	—	2	1	no	—
134	C₂×Dic₂₉	—	2	1	no	—
135	C₂×Dic₂₉	—	2	1	no	—
136	C₂×Dic₂₉	—	2	1	no	—
137	C₂×Dic₂₉	C₂²×C₄	1	1	yes	characteristic
138	C₂×Dic₂₉	C₂²×C₄	1	1	yes	characteristic
139	C₂×Dic₂₉	C₂²×C₄	1	1	yes	characteristic
140	C₂×Dic₂₉	C₂²×C₄	1	1	yes	characteristic
141	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
142	D₁₁₆	—	2	2	no	—
143	D₁₁₆	—	4	1	no	—
144	C₄×D₂₉	—	2	1	no	—
145	C₄×D₂₉	—	2	1	no	—
146	C₄×D₂₉	—	2	1	no	—
147	C₄×D₂₉	—	2	1	no	—
148	C₄×D₂₉	—	2	1	no	—
149	C₄×D₂₉	—	2	1	no	—
150	C₄×D₂₉	—	4	1	no	—
151	C₄×D₂₉	—	4	1	no	—
152	Dic₅₈	—	4	1	no	—
153	#6599	—	2	1	no	—
154	#6599	—	2	1	no	—
155	#6599	—	2	1	no	—
156	#6599	—	2	1	no	—
157	#6599	—	2	1	no	—
158	#6599	—	2	1	no	—
159	#6599	—	2	1	no	—
160	#6599	—	2	1	no	—
161	#2976	—	29	1	no	maximal, Sylow
162	C₂²×C₂₉	—	2	1	no	—
163	C₂²×C₂₉	—	2	1	no	—
164	C₂²×C₂₉	—	2	1	no	—
165	C₂²×C₂₉	—	2	1	no	—
166	C₂²×C₂₉	—	2	1	no	—
167	C₂²×C₂₉	—	2	1	no	—
168	C₂²×C₂₉	C₂³×C₄	1	1	yes	characteristic
169	C₂×D₂₉	—	2	1	no	—
170	C₂×D₂₉	—	2	1	no	—
171	C₂×D₂₉	—	2	1	no	—
172	C₂×D₂₉	—	2	1	no	—
173	C₂×D₂₉	—	2	1	no	—
174	C₂×D₂₉	—	2	1	no	—
175	C₂×D₂₉	—	2	1	no	—
176	C₂×D₂₉	—	2	1	no	—
177	C₂×D₂₉	—	4	4	no	—
178	C₂×D₂₉	#131	1	2	yes	—
179	C₄×C₂₉	—	2	1	no	—
180	C₄×C₂₉	—	2	1	no	—
181	C₄×C₂₉	—	2	1	no	—
182	C₄×C₂₉	—	2	1	no	—
183	C₄×C₂₉	—	2	1	no	—
184	Dic₂₉	—	2	1	no	—
185	Dic₂₉	—	2	1	no	—
186	Dic₂₉	—	2	1	no	—
187	Dic₂₉	—	2	1	no	—
188	Dic₂₉	H(5,𝔽₂)	1	1	yes	characteristic
189	Dic₂₉	H(5,𝔽₂)	1	1	yes	characteristic
190	#525	—	29	1	no	—
191	#436	—	29	1	no	—
192	#436	—	29	1	no	—
193	#435	—	29	1	no	—
194	#435	—	29	1	no	—
195	#435	—	29	1	no	—
196	#435	—	29	1	no	—
197	C₈×D₄	—	29	1	no	—
198	C₈×D₄	—	29	1	no	—
199	#433	—	29	1	no	—
200	#433	—	29	1	no	—
201	#408	—	29	1	no	—
202	#408	—	29	1	no	—
203	#407	—	29	1	no	—
204	C₂×C₂²⋊C₈	—	29	1	no	—
205	C₂×C₂₉	—	4	1	no	—
206	C₂×C₂₉	—	4	1	no	—
207	C₂×C₂₉	#518	1	1	yes	characteristic
208	C₂×C₂₉	C₂×#131	1	1	yes	characteristic
209	C₂×C₂₉	#568	1	1	yes	characteristic
210	D₂₉	—	2	2	no	—
211	D₂₉	—	4	1	no	—
212	D₂₉	—	4	1	no	—
213	C₂×#41	—	29	1	no	—
214	C₂³×C₄	—	29	1	no	—
215	C₂×M₁₆	—	29	1	no	—
216	C₂×M₁₆	—	29	1	no	—
217	C₂×M₁₆	—	29	1	no	—
218	C₂×M₁₆	—	29	1	no	—
219	C₂²×C₈	—	29	1	no	—
220	C₂²×C₈	—	29	1	no	—
221	C₂²×C₈	—	29	1	no	—
222	C₂²×C₈	—	29	1	no	—
223	#123	—	29	1	no	—
224	#123	#1181	1	1	yes	characteristic
225	C₂²⋊Q₈	—	29	1	no	—
226	C₂²⋊Q₈	—	29	1	no	—
227	#121	—	29	1	no	—
228	#121	—	29	1	no	—
229	#120	—	29	1	no	—
230	#120	—	29	1	no	—
231	C₄×D₄	—	29	1	no	—
232	C₄×D₄	—	29	1	no	—
233	C₄×D₄	—	29	1	no	—
234	C₄×D₄	—	29	1	no	—
235	#117	—	29	1	no	—
236	C₄⋊C₈	—	29	1	no	—
237	C₄⋊C₈	—	29	1	no	—
238	C₄⋊C₈	—	29	1	no	—
239	C₄⋊C₈	—	29	1	no	—
240	C₂²⋊C₈	—	29	1	no	—
241	C₂²⋊C₈	—	29	1	no	—
242	C₂²⋊C₈	—	29	1	no	—
243	C₂²⋊C₈	—	29	1	no	—
244	C₂²⋊C₈	—	29	1	no	—
245	C₂²⋊C₈	—	29	1	no	—
246	C₂²⋊C₈	—	29	1	no	—
247	C₂²⋊C₈	—	29	1	no	—
248	C₂²⋊C₈	—	29	1	no	—
249	C₂²⋊C₈	—	29	1	no	—
250	C₂²⋊C₈	—	29	1	no	—
251	C₂²⋊C₈	—	29	1	no	—
252	#97	—	29	1	no	—
253	#97	—	29	1	no	—
254	C₄×C₈	—	29	1	no	—
255	C₄×C₈	—	29	1	no	—
256	C₂₉	#2976	1	1	yes	characteristic, complemented, Sylow
257	C₂⁴	—	29	1	no	—
258	#41	—	116	1	no	—
259	#41	—	116	1	no	—
260	C₂×Q₈	—	29	1	no	—
261	C₂×D₄	—	29	1	no	—
262	C₂×D₄	—	29	1	no	—
263	C₂×D₄	—	29	1	no	—
264	C₂×D₄	—	29	1	no	—
265	C₂×D₄	—	29	1	no	—
266	C₂×D₄	—	29	1	no	—
267	C₂×D₄	C₂×#1181	1	1	yes	characteristic
268	C₂²×C₄	—	29	1	no	—
269	C₂²×C₄	—	29	1	no	—
270	C₂²×C₄	—	29	1	no	—
271	C₂²×C₄	—	29	1	no	—
272	C₂²×C₄	—	29	1	no	—
273	C₂²×C₄	—	29	1	no	—
274	C₂²×C₄	—	29	1	no	—
275	C₂²×C₄	—	116	1	no	—
276	C₂²×C₄	—	116	1	no	—
277	C₂²×C₄	C₂×#1181	1	1	yes	characteristic
278	M₁₆	—	116	1	no	—
279	M₁₆	—	116	1	no	—
280	M₁₆	—	116	1	no	—
281	M₁₆	—	116	1	no	—
282	C₂×C₈	—	29	1	no	—
283	C₂×C₈	—	29	1	no	—
284	C₂×C₈	—	29	1	no	—
285	C₂×C₈	—	29	1	no	—
286	C₂×C₈	—	29	1	no	—
287	C₂×C₈	—	29	1	no	—
288	C₂×C₈	—	29	1	no	—
289	C₂×C₈	—	29	1	no	—
290	C₂×C₈	—	116	1	no	—
291	C₂×C₈	—	116	1	no	—
292	C₂×C₈	—	116	1	no	—
293	C₂×C₈	—	116	1	no	—
294	C₄⋊C₄	—	29	1	no	—
295	C₄⋊C₄	—	29	1	no	—
296	C₄⋊C₄	—	29	1	no	—
297	C₄⋊C₄	—	29	1	no	—
298	C₄⋊C₄	C₂×#1181	1	1	yes	characteristic
299	C₄⋊C₄	C₂×#1181	1	1	yes	characteristic
300	C₂²⋊C₄	—	29	1	no	—
301	C₂²⋊C₄	—	29	1	no	—
302	C₂²⋊C₄	—	29	1	no	—
303	C₂²⋊C₄	—	29	1	no	—
304	C₂²⋊C₄	—	29	1	no	—
305	C₂²⋊C₄	—	29	1	no	—
306	C₂²⋊C₄	—	29	1	no	—
307	C₂²⋊C₄	C₂×#1181	1	1	yes	characteristic
308	C₂²⋊C₄	C₂×#1181	1	1	yes	characteristic
309	C₂²⋊C₄	C₂×#1181	1	1	yes	characteristic
310	C₄²	—	29	1	no	—
311	C₄²	—	29	1	no	—
312	C₂³	—	29	1	no	—
313	C₂³	—	29	1	no	—
314	C₂³	—	29	1	no	—
315	C₂³	—	58	2	no	—
316	C₂³	—	116	1	no	—
317	C₂³	—	116	1	no	—
318	C₂³	C₂²×#1181	1	1	yes	characteristic
319	C₂³	C₂²×#1181	1	1	yes	characteristic
320	Q₈	—	116	1	no	—
321	D₄	—	4	1	no	—
322	D₄	—	58	2	no	—
323	D₄	—	58	2	no	—
324	D₄	—	116	1	no	—
325	D₄	—	116	1	no	—
326	D₄	—	116	1	no	—
327	D₄	—	116	1	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	29	1	no	—
330	C₂×C₄	—	29	1	no	—
331	C₂×C₄	—	29	1	no	—
332	C₂×C₄	—	29	1	no	—
333	C₂×C₄	—	29	1	no	—
334	C₂×C₄	—	58	1	no	—
335	C₂×C₄	—	58	1	no	—
336	C₂×C₄	—	58	1	no	—
337	C₂×C₄	—	58	1	no	—
338	C₂×C₄	—	58	1	no	—
339	C₂×C₄	—	58	1	no	—
340	C₂×C₄	—	58	1	no	—
341	C₂×C₄	—	58	1	no	—
342	C₂×C₄	—	58	1	no	—
343	C₂×C₄	—	58	1	no	—
344	C₂×C₄	—	116	1	no	—
345	C₂×C₄	—	116	1	no	—
346	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
347	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
348	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
349	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
350	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
351	C₈	—	58	1	no	—
352	C₈	—	58	1	no	—
353	C₈	—	58	1	no	—
354	C₈	—	58	1	no	—
355	C₈	—	58	1	no	—
356	C₈	—	58	1	no	—
357	C₈	—	58	1	no	—
358	C₈	—	58	1	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	29	2	no	—
366	C₂²	—	58	1	no	—
367	C₂²	—	58	1	no	—
368	C₂²	—	58	1	no	—
369	C₂²	—	58	1	no	—
370	C₂²	—	58	1	no	—
371	C₂²	—	58	1	no	—
372	C₂²	—	58	1	no	—
373	C₂²	—	58	1	no	—
374	C₂²	—	116	4	no	—
375	C₂²	C₂³×#1181	1	1	yes	characteristic
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	2	1	no	—
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	29	1	no	—
382	C₄	—	29	1	no	—
383	C₄	—	58	1	no	—
384	C₄	—	58	1	no	—
385	C₄	—	58	1	no	—
386	C₄	—	58	1	no	—
387	C₂	—	4	1	no	—
388	C₂	—	4	1	no	—
389	C₂	—	58	2	no	—
390	C₂	—	116	1	no	—
391	C₂	—	116	1	no	—
392	C₂	#14272230	1	1	yes	characteristic
393	C₂	D₂₉⋊#131	1	1	yes	characteristic
394	C₂	#14272242	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×#1181
commutator, socle	C₂²×C₂₉	C₂³×C₄
Fitting	C₂₉×#123	C₄
prime radical	#14271671	C₂
cosocle	C₂×Dic₂₉	C₂⁴
hypercenter	#123	#1181
hypocenter	C₂₉	#2976
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ #123

Complements

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

N	H ≅ G/N	type
1. #14272197	C₂	semidirect
2. #14272196	C₂	semidirect
3. #14272195	C₂	semidirect
4. #14272193	C₂	semidirect
5. #14272193	C₂	semidirect
6. #14272192	C₂	semidirect
7. #14272191	C₂	semidirect
8. #14272190	C₂	semidirect
9. #14272187	C₂	semidirect
10. #14272187	C₂	semidirect
11. #14272137	C₂	semidirect
12. #14272136	C₂	semidirect
13. #14272134	C₂	semidirect
14. D₂₉⋊(C₂²⋊C₈)	C₂	semidirect
18. C₂×#90800	C₂²	semidirect
19. C₂²×#6599	C₂²	semidirect
22. C₂×#90796	C₂²	semidirect
25. C₂×D₂₉⋊C₈	C₂²	semidirect
43. C₂²⋊#6599	C₂²	semidirect
44. C₂²⋊#6599	C₂²	semidirect
45. #11745220	C₂²	semidirect
46. #11745220	C₂²	semidirect
51. #11745219	C₂²	semidirect
52. #11745219	C₂²	semidirect
53. #11745218	C₂²	semidirect
54. #11745218	C₂²	semidirect
55. C₄⋊#6599	C₂²	semidirect
56. C₄⋊#6599	C₂²	semidirect
57. C₄×#6599	C₂²	semidirect
58. C₄×#6599	C₂²	semidirect
256. C₂₉	#2976	semidirect

Maximal subgroups

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

subgroup	index
#14272197	2
#14272196	2
#14272195	2
#14272193	2
#14272192	2
#14272191	2
#14272190	2
#14272187	2
#14272137	2
#14272136	2
#14272134	2
D₂₉⋊(C₂²⋊C₈)	2
#14271671	2
#2976	29