Subgroups — #31789814

Order 17536.

456 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₄×D₁₃₇	C₂	1	1	yes	maximal, characteristic
2	#22577477	C₂	1	1	yes	maximal, characteristic, complemented
3	#22577476	C₂	1	1	yes	maximal, characteristic, complemented
4	#22577475	C₂	1	1	yes	maximal, characteristic, complemented
5	#22577474	C₂	1	1	yes	maximal, characteristic, complemented
6	#22577473	C₂	1	1	yes	maximal, characteristic, complemented
7	#22577472	C₂	1	1	yes	maximal, characteristic, complemented
8	#22577471	C₂	1	1	yes	maximal, characteristic, complemented
9	#22577459	C₂	1	1	yes	maximal, characteristic, complemented
10	#22577458	C₂	1	1	yes	maximal, characteristic, complemented
11	#22577366	C₂	1	1	yes	maximal, characteristic, complemented
12	#22577365	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#17984000	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²⋊C₈×D₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
15	#435×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×D₄×D₁₃₇	C₄	1	1	yes	characteristic
17	C₂²×C₄×D₁₃₇	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₁₃₇	C₂²	1	1	yes	characteristic
19	C₂×#14555494	C₂²	1	1	yes	characteristic, complemented
20	C₂×#14555493	C₂²	1	1	yes	characteristic, complemented
21	C₂×#14555493	C₂²	1	1	yes	characteristic, complemented
22	C₂²×#11764040	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₈×D₁₃₇	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₈×D₁₃₇	C₂²	1	1	yes	characteristic, complemented
25	C₄×D₅₄₈	C₂²	1	1	yes	characteristic
26	D₄×Dic₁₃₇	C₄	1	1	yes	characteristic
27	#17984050	C₄	1	1	yes	characteristic
28	C₄×C₂²⋊D₁₃₇	C₂²	1	1	yes	characteristic
29	C₄×C₂²⋊D₁₃₇	C₂²	1	1	yes	characteristic
30	#17984048	C₄	1	1	yes	characteristic
31	#17984048	C₄	1	1	yes	characteristic
32	C₄⋊C₄×D₁₃₇	C₄	1	1	yes	characteristic
33	C₂²⋊C₄×D₁₃₇	C₄	1	1	yes	characteristic
34	C₂²⋊C₄×D₁₃₇	C₄	1	1	yes	characteristic
35	C₄²×D₁₃₇	C₂²	1	1	yes	characteristic
36	C₄⋊#11764040	C₂²	1	1	yes	characteristic, complemented
37	#17984017	C₂²	1	1	yes	characteristic, complemented
38	#17984017	C₂²	1	1	yes	characteristic, complemented
39	C₂²⋊#11764040	C₂²	1	1	yes	characteristic, complemented
40	C₂²⋊#11764040	C₂²	1	1	yes	characteristic, complemented
41	#17984000	C₂²	1	1	yes	characteristic
42	#17984000	C₂²	1	1	yes	characteristic
43	#17984000	C₂²	1	1	yes	characteristic
44	#17984000	C₂²	1	1	yes	characteristic
45	#17984000	C₂²	1	1	yes	characteristic, complemented
46	#17984000	C₂²	1	1	yes	characteristic, complemented
47	#17984000	C₂²	1	1	yes	characteristic, complemented
48	#17984000	C₂²	1	1	yes	characteristic, complemented
49	#17983999	C₂²	1	1	yes	characteristic, complemented
50	#17983998	C₂²	1	1	yes	characteristic, complemented
51	#17983998	C₂²	1	1	yes	characteristic, complemented
52	C₂×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
53	C₂²×C₈×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
54	C₄×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
55	C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
56	C₂²⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
57	C₂²⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
58	#97×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
59	C₂³×D₁₃₇	C₂×C₄	1	1	yes	characteristic
60	C₂³×D₁₃₇	C₂×C₄	1	1	yes	characteristic
61	C₂×D₅₄₈	C₂×C₄	1	1	yes	characteristic
62	C₂×C₂²⋊D₁₃₇	C₂×C₄	1	1	yes	characteristic
63	C₂×C₂²⋊D₁₃₇	C₂×C₄	1	1	yes	characteristic
64	D₄×D₁₃₇	—	2	4	no	—
65	C₂²×Dic₁₃₇	C₂×C₄	1	1	yes	characteristic
66	C₂²×Dic₁₃₇	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄×D₁₃₇	—	4	1	no	—
68	C₂×C₄×D₁₃₇	—	4	1	no	—
69	C₂×C₄×D₁₃₇	—	4	1	no	—
70	C₂×C₄×D₁₃₇	—	4	1	no	—
71	C₂×C₄×D₁₃₇	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄×D₁₃₇	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄×D₁₃₇	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄×D₁₃₇	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄×D₁₃₇	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄×D₁₃₇	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄×D₁₃₇	C₂³	1	1	yes	characteristic
78	C₂×C₄×D₁₃₇	C₂³	1	1	yes	characteristic
79	C₂×C₄×D₁₃₇	C₂³	1	1	yes	characteristic
80	#14555494	—	4	1	no	—
81	#14555493	—	4	1	no	—
82	#14555493	—	4	1	no	—
83	C₂×#11764040	—	4	1	no	—
84	C₂×#11764040	C₂³	1	1	yes	characteristic
85	C₂×#11764040	C₂³	1	1	yes	characteristic
86	C₂×#11764040	C₂³	1	1	yes	characteristic
87	C₂×#11764040	C₂³	1	1	yes	characteristic
88	C₈×D₁₃₇	—	4	1	no	—
89	C₈×D₁₃₇	—	4	1	no	—
90	C₄⋊Dic₁₃₇	C₂×C₄	1	1	yes	characteristic
91	#14555489	C₂×C₄	1	1	yes	characteristic
92	#14555489	C₂×C₄	1	1	yes	characteristic
93	C₂²⋊Dic₁₃₇	C₂×C₄	1	1	yes	characteristic
94	C₂²⋊Dic₁₃₇	C₂×C₄	1	1	yes	characteristic
95	#14555487	C₂×C₄	1	1	yes	characteristic
96	#14555487	C₂×C₄	1	1	yes	characteristic
97	#14555487	C₂×C₄	1	1	yes	characteristic
98	#14555487	C₂×C₄	1	1	yes	characteristic
99	C₄×Dic₁₃₇	C₂×C₄	1	1	yes	characteristic
100	C₄×Dic₁₃₇	C₂×C₄	1	1	yes	characteristic
101	C₄×Dic₁₃₇	C₂³	1	1	yes	characteristic
102	C₂×D₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
104	C₂²×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
105	M₁₆×C₁₃₇	—	4	1	no	—
106	C₂×C₈×C₁₃₇	—	4	1	no	—
107	C₂×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
108	C₂×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
109	C₂×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
110	C₂×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
111	C₄⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
112	C₂²⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
113	C₂²⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
114	C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
115	C₂²×D₁₃₇	—	2	2	no	—
116	C₂²×D₁₃₇	—	4	1	no	—
117	C₂²×D₁₃₇	—	4	1	no	—
118	C₂²×D₁₃₇	—	4	1	no	—
119	C₂²×D₁₃₇	—	4	1	no	—
120	C₂²×D₁₃₇	M₁₆	1	4	yes	complemented
121	C₂²×D₁₃₇	C₂²×C₄	1	1	yes	characteristic
122	C₂²×D₁₃₇	C₂²×C₄	1	1	yes	characteristic
123	C₂²×D₁₃₇	C₂²×C₄	1	1	yes	characteristic
124	D₅₄₈	—	2	2	no	—
125	C₂²⋊D₁₃₇	—	2	2	no	—
126	C₂²⋊D₁₃₇	—	2	2	no	—
127	C₂×Dic₁₃₇	—	4	1	no	—
128	C₂×Dic₁₃₇	—	4	1	no	—
129	C₂×Dic₁₃₇	C₂²×C₄	1	1	yes	characteristic
130	C₂×Dic₁₃₇	C₂²×C₄	1	1	yes	characteristic
131	C₂×Dic₁₃₇	C₂²×C₄	1	1	yes	characteristic
132	C₂×Dic₁₃₇	C₂²×C₄	1	1	yes	characteristic
133	C₂×Dic₁₃₇	C₂²×C₄	1	1	yes	characteristic
134	C₄×D₁₃₇	—	2	2	no	—
135	C₄×D₁₃₇	—	2	1	no	—
136	C₄×D₁₃₇	—	2	1	no	—
137	C₄×D₁₃₇	—	2	1	no	—
138	C₄×D₁₃₇	—	2	1	no	—
139	C₄×D₁₃₇	—	2	1	no	—
140	C₄×D₁₃₇	—	2	1	no	—
141	C₄×D₁₃₇	—	4	1	no	—
142	C₄×D₁₃₇	—	4	1	no	—
143	C₄×D₁₃₇	—	4	1	no	—
144	C₄×D₁₃₇	—	4	1	no	—
145	C₄×D₁₃₇	—	4	1	no	—
146	#11764040	—	2	1	no	—
147	#11764040	—	2	1	no	—
148	#11764040	—	2	1	no	—
149	#11764040	—	2	1	no	—
150	C₂³×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
151	C₂³×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
152	D₄×C₁₃₇	—	2	2	no	—
153	C₂×C₄×C₁₃₇	—	2	1	no	—
154	C₂×C₄×C₁₃₇	—	2	1	no	—
155	C₂×C₄×C₁₃₇	—	2	1	no	—
156	C₂×C₄×C₁₃₇	—	2	1	no	—
157	C₂×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
162	C₈×C₁₃₇	—	2	1	no	—
163	C₈×C₁₃₇	—	2	1	no	—
164	C₈×C₁₃₇	—	2	1	no	—
165	C₈×C₁₃₇	—	2	1	no	—
166	C₂²×C₁₃₇	—	2	1	no	—
167	C₂²×C₁₃₇	—	2	1	no	—
168	C₂²×C₁₃₇	—	2	1	no	—
169	C₂²×C₁₃₇	—	2	1	no	—
170	C₂²×C₁₃₇	—	2	1	no	—
171	C₂²×C₁₃₇	C₂×M₁₆	1	2	yes	—
172	C₂²×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
173	C₂×D₁₃₇	—	2	1	no	—
174	C₂×D₁₃₇	—	2	1	no	—
175	C₂×D₁₃₇	—	2	1	no	—
176	C₂×D₁₃₇	—	2	1	no	—
177	C₂×D₁₃₇	—	2	1	no	—
178	C₂×D₁₃₇	—	2	1	no	—
179	C₂×D₁₃₇	—	2	1	no	—
180	C₂×D₁₃₇	—	4	4	no	—
181	C₂×D₁₃₇	—	4	4	no	—
182	C₂×D₁₃₇	C₂×M₁₆	1	2	yes	—
183	C₂×D₁₃₇	C₂×M₁₆	1	2	yes	—
184	C₄×C₁₃₇	—	2	1	no	—
185	C₄×C₁₃₇	—	2	1	no	—
186	C₄×C₁₃₇	—	2	1	no	—
187	C₄×C₁₃₇	—	2	1	no	—
188	C₄×C₁₃₇	H(5,𝔽₂)	1	1	yes	characteristic
189	C₄×C₁₃₇	H(5,𝔽₂)	1	1	yes	characteristic
190	Dic₁₃₇	—	2	1	no	—
191	Dic₁₃₇	—	2	1	no	—
192	Dic₁₃₇	—	2	1	no	—
193	Dic₁₃₇	—	2	1	no	—
194	Dic₁₃₇	—	2	1	no	—
195	C₂×C₁₃₇	—	2	2	no	—
196	C₂×C₁₃₇	—	4	1	no	—
197	C₂×C₁₃₇	#518	1	1	yes	characteristic
198	C₂×C₁₃₇	C₂²×M₁₆	1	1	yes	characteristic
199	C₂×C₁₃₇	#568	1	1	yes	characteristic
200	D₁₃₇	—	2	2	no	—
201	D₁₃₇	—	2	2	no	—
202	D₁₃₇	—	4	1	no	—
203	C₁₃₇	#2973	1	1	yes	characteristic, complemented, Sylow
204	#2973	—	137	1	no	maximal, Sylow
205	C₂×C₄×D₄	—	137	1	no	—
206	#435	—	137	1	no	—
207	#435	—	137	1	no	—
208	#435	—	137	1	no	—
209	#435	—	137	1	no	—
210	#435	—	137	1	no	—
211	#435	—	137	1	no	—
212	#435	—	137	1	no	—
213	#435	D₁₃₇	1	1	yes	characteristic, complemented
214	#432	—	137	1	no	—
215	#432	—	137	1	no	—
216	#407	—	137	1	no	—
217	#407	—	137	1	no	—
218	C₂×C₂²⋊C₈	—	137	1	no	—
219	C₂×C₂²⋊C₈	—	137	1	no	—
220	C₂²×D₄	—	137	1	no	—
221	C₂³×C₄	—	137	1	no	—
222	C₂³×C₄	—	137	1	no	—
223	C₂×M₁₆	—	137	1	no	—
224	C₂×M₁₆	—	137	1	no	—
225	C₂×M₁₆	—	137	1	no	—
226	C₂×M₁₆	C₂×D₁₃₇	1	1	yes	characteristic, complemented
227	C₂²×C₈	—	137	1	no	—
228	C₂²×C₈	—	137	1	no	—
229	C₂²×C₈	—	137	1	no	—
230	C₂²×C₈	C₂×D₁₃₇	1	1	yes	characteristic, complemented
231	C₄×D₄	—	137	1	no	—
232	C₄×D₄	—	137	1	no	—
233	C₄×D₄	—	137	1	no	—
234	C₄×D₄	—	137	1	no	—
235	C₄×D₄	—	137	1	no	—
236	C₄×D₄	—	137	1	no	—
237	C₄×D₄	—	137	1	no	—
238	C₄×D₄	C₂×D₁₃₇	1	1	yes	characteristic
239	C₂×C₄⋊C₄	—	137	1	no	—
240	C₂×C₂²⋊C₄	—	137	1	no	—
241	C₂×C₂²⋊C₄	—	137	1	no	—
242	C₂×C₄²	—	137	1	no	—
243	C₄⋊C₈	—	137	1	no	—
244	C₄⋊C₈	—	137	1	no	—
245	C₄⋊C₈	—	137	1	no	—
246	C₄⋊C₈	C₂×D₁₃₇	1	1	yes	characteristic, complemented
247	C₂²⋊C₈	—	137	1	no	—
248	C₂²⋊C₈	—	137	1	no	—
249	C₂²⋊C₈	—	137	1	no	—
250	C₂²⋊C₈	—	137	1	no	—
251	C₂²⋊C₈	—	137	1	no	—
252	C₂²⋊C₈	—	137	1	no	—
253	C₂²⋊C₈	—	137	1	no	—
254	C₂²⋊C₈	—	137	1	no	—
255	C₂²⋊C₈	—	137	1	no	—
256	C₂²⋊C₈	—	137	1	no	—
257	C₂²⋊C₈	C₂×D₁₃₇	1	1	yes	characteristic, complemented
258	C₂²⋊C₈	C₂×D₁₃₇	1	1	yes	characteristic, complemented
259	#97	—	137	1	no	—
260	#97	—	137	1	no	—
261	#97	—	137	1	no	—
262	#97	C₂×D₁₃₇	1	1	yes	characteristic, complemented
263	C₂⁴	—	137	1	no	—
264	C₂⁴	—	137	1	no	—
265	C₂×D₄	—	274	4	no	—
266	C₂×D₄	—	137	1	no	—
267	C₂×D₄	—	137	1	no	—
268	C₂×D₄	—	137	1	no	—
269	C₂×D₄	C₄×D₁₃₇	1	1	yes	characteristic
270	C₂²×C₄	—	548	1	no	—
271	C₂²×C₄	—	548	1	no	—
272	C₂²×C₄	—	548	1	no	—
273	C₂²×C₄	—	548	1	no	—
274	C₂²×C₄	—	137	1	no	—
275	C₂²×C₄	—	137	1	no	—
276	C₂²×C₄	—	137	1	no	—
277	C₂²×C₄	—	137	1	no	—
278	C₂²×C₄	—	137	1	no	—
279	C₂²×C₄	—	137	1	no	—
280	C₂²×C₄	—	137	1	no	—
281	C₂²×C₄	—	137	1	no	—
282	C₂²×C₄	—	137	1	no	—
283	C₂²×C₄	—	137	1	no	—
284	C₂²×C₄	—	137	1	no	—
285	C₂²×C₄	C₂²×D₁₃₇	1	1	yes	characteristic
286	C₂²×C₄	C₂²×D₁₃₇	1	1	yes	characteristic
287	M₁₆	—	4	1	no	—
288	M₁₆	—	548	1	no	—
289	M₁₆	—	548	1	no	—
290	M₁₆	—	548	1	no	—
291	C₂×C₈	—	4	1	no	—
292	C₂×C₈	—	548	1	no	—
293	C₂×C₈	—	548	1	no	—
294	C₂×C₈	—	548	1	no	—
295	C₂×C₈	—	137	1	no	—
296	C₂×C₈	—	137	1	no	—
297	C₂×C₈	—	137	1	no	—
298	C₂×C₈	—	137	1	no	—
299	C₂×C₈	C₂²×D₁₃₇	1	1	yes	characteristic
300	C₂×C₈	C₂²×D₁₃₇	1	1	yes	characteristic
301	C₂×C₈	C₂²×D₁₃₇	1	1	yes	characteristic
302	C₂×C₈	C₂²×D₁₃₇	1	1	yes	characteristic
303	C₄⋊C₄	—	137	1	no	—
304	C₄⋊C₄	—	137	1	no	—
305	C₄⋊C₄	—	137	1	no	—
306	C₄⋊C₄	C₄×D₁₃₇	1	1	yes	characteristic
307	C₂²⋊C₄	—	137	1	no	—
308	C₂²⋊C₄	—	137	1	no	—
309	C₂²⋊C₄	—	137	1	no	—
310	C₂²⋊C₄	—	137	1	no	—
311	C₂²⋊C₄	—	137	1	no	—
312	C₂²⋊C₄	—	137	1	no	—
313	C₂²⋊C₄	C₄×D₁₃₇	1	1	yes	characteristic
314	C₂²⋊C₄	C₄×D₁₃₇	1	1	yes	characteristic
315	C₄²	—	137	1	no	—
316	C₄²	—	137	1	no	—
317	C₄²	—	137	1	no	—
318	C₄²	C₂²×D₁₃₇	1	1	yes	characteristic
319	C₂³	—	274	2	no	—
320	C₂³	—	548	1	no	—
321	C₂³	—	548	1	no	—
322	C₂³	—	548	1	no	—
323	C₂³	—	548	1	no	—
324	C₂³	—	137	1	no	—
325	C₂³	—	137	1	no	—
326	C₂³	—	137	1	no	—
327	C₂³	—	137	4	no	—
328	C₂³	C₂×C₄×D₁₃₇	1	1	yes	characteristic
329	C₂³	C₂×C₄×D₁₃₇	1	1	yes	characteristic
330	D₄	—	2	2	no	—
331	D₄	—	274	2	no	—
332	D₄	—	274	2	no	—
333	D₄	—	274	2	no	—
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	—	274	2	no	—
339	C₂×C₄	—	274	1	no	—
340	C₂×C₄	—	274	1	no	—
341	C₂×C₄	—	274	1	no	—
342	C₂×C₄	—	274	1	no	—
343	C₂×C₄	—	274	1	no	—
344	C₂×C₄	—	274	1	no	—
345	C₂×C₄	—	548	1	no	—
346	C₂×C₄	—	548	1	no	—
347	C₂×C₄	—	548	1	no	—
348	C₂×C₄	—	548	1	no	—
349	C₂×C₄	—	548	1	no	—
350	C₂×C₄	—	548	1	no	—
351	C₂×C₄	—	548	1	no	—
352	C₂×C₄	—	137	1	no	—
353	C₂×C₄	—	137	1	no	—
354	C₂×C₄	—	137	1	no	—
355	C₂×C₄	—	137	1	no	—
356	C₂×C₄	—	137	1	no	—
357	C₂×C₄	C₂×C₄×D₁₃₇	1	1	yes	characteristic
358	C₂×C₄	C₂×C₄×D₁₃₇	1	1	yes	characteristic
359	C₂×C₄	C₂×C₄×D₁₃₇	1	1	yes	characteristic
360	C₂×C₄	C₂×C₄×D₁₃₇	1	1	yes	characteristic
361	C₂×C₄	C₂³×D₁₃₇	1	1	yes	characteristic
362	C₈	—	2	1	no	—
363	C₈	—	2	1	no	—
364	C₈	—	2	1	no	—
365	C₈	—	2	1	no	—
366	C₈	—	274	1	no	—
367	C₈	—	274	1	no	—
368	C₈	—	274	1	no	—
369	C₈	—	274	1	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	274	1	no	—
376	C₂²	—	274	1	no	—
377	C₂²	—	274	1	no	—
378	C₂²	—	274	1	no	—
379	C₂²	—	274	1	no	—
380	C₂²	—	274	1	no	—
381	C₂²	—	274	1	no	—
382	C₂²	—	548	4	no	—
383	C₂²	—	548	4	no	—
384	C₂²	—	137	2	no	—
385	C₂²	—	137	2	no	—
386	C₂²	M₁₆×D₁₃₇	1	2	yes	—
387	C₂²	C₂²×C₄×D₁₃₇	1	1	yes	characteristic
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	274	1	no	—
393	C₄	—	274	1	no	—
394	C₄	—	274	1	no	—
395	C₄	—	274	1	no	—
396	C₄	—	274	1	no	—
397	C₄	#17984133	1	1	yes	characteristic
398	C₄	#17984134	1	1	yes	characteristic
399	C₂	—	2	2	no	—
400	C₂	—	4	1	no	—
401	C₂	—	274	2	no	—
402	C₂	—	274	2	no	—
403	C₂	—	548	1	no	—
404	C₂	#22577875	1	1	yes	characteristic
405	C₂	C₂×M₁₆×D₁₃₇	1	1	yes	characteristic
406	C₂	#22578168	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₁₃₇
commutator, socle	C₂²×C₁₃₇	C₂³×C₄
Fitting	#435×C₁₃₇	C₂
prime radical	C₂×D₄×D₁₃₇	C₄
cosocle	C₂×C₄×C₁₃₇	C₂⁴
hypercenter	#435	D₁₃₇
hypocenter	C₁₃₇	#2973
LCS	G ▷ C₂²×C₁₃₇ ▷ C₁₃₇
UCS	C₁ ◁ C₂×C₄ ◁ #435

Complements

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

N	H ≅ G/N	type
2. #22577477	C₂	semidirect
3. #22577476	C₂	semidirect
4. #22577475	C₂	semidirect
5. #22577474	C₂	semidirect
6. #22577473	C₂	semidirect
7. #22577472	C₂	semidirect
8. #22577471	C₂	semidirect
9. #22577459	C₂	semidirect
10. #22577458	C₂	semidirect
11. #22577366	C₂	semidirect
12. #22577365	C₂	semidirect
13. C₂×#17984000	C₂	semidirect
14. C₂²⋊C₈×D₁₃₇	C₂	semidirect
15. #435×C₁₃₇	C₂	semidirect
19. C₂×#14555494	C₂²	semidirect
20. C₂×#14555493	C₂²	semidirect
21. C₂×#14555493	C₂²	semidirect
22. C₂²×#11764040	C₂²	semidirect
23. C₂×C₈×D₁₃₇	C₂²	semidirect
24. C₂×C₈×D₁₃₇	C₂²	semidirect
36. C₄⋊#11764040	C₂²	semidirect
37. #17984017	C₂²	semidirect
38. #17984017	C₂²	semidirect
39. C₂²⋊#11764040	C₂²	semidirect
40. C₂²⋊#11764040	C₂²	semidirect
45. #17984000	C₂²	semidirect
46. #17984000	C₂²	semidirect
47. #17984000	C₂²	semidirect
48. #17984000	C₂²	semidirect
49. #17983999	C₂²	semidirect
50. #17983998	C₂²	semidirect
51. #17983998	C₂²	semidirect
52. C₂×M₁₆×C₁₃₇	C₂²	semidirect
53. C₂²×C₈×C₁₃₇	C₂²	semidirect
55. C₄⋊C₈×C₁₃₇	C₂²	semidirect
56. C₂²⋊C₈×C₁₃₇	C₂²	semidirect
57. C₂²⋊C₈×C₁₃₇	C₂²	semidirect
58. #97×C₁₃₇	C₂²	semidirect
120. C₂²×D₁₃₇	M₁₆	semidirect
203. C₁₃₇	#2973	semidirect
213. #435	D₁₃₇	semidirect
226. C₂×M₁₆	C₂×D₁₃₇	semidirect
230. C₂²×C₈	C₂×D₁₃₇	semidirect
246. C₄⋊C₈	C₂×D₁₃₇	semidirect
257. C₂²⋊C₈	C₂×D₁₃₇	semidirect
258. C₂²⋊C₈	C₂×D₁₃₇	semidirect
262. #97	C₂×D₁₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₄×D₄×D₁₃₇	2
#22577477	2
#22577476	2
#22577475	2
#22577474	2
#22577473	2
#22577472	2
#22577471	2
#22577459	2
#22577458	2
#22577366	2
#22577365	2
C₂×#17984000	2
C₂²⋊C₈×D₁₃₇	2
#435×C₁₃₇	2
#2973	137