Subgroups — #31789487

Order 17536.

492 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	C₂×#17984094	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×M₁₆×D₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#22577912	C₂	1	1	yes	maximal, characteristic
4	#22577481	C₂	1	1	yes	maximal, characteristic, complemented
5	#22577480	C₂	1	1	yes	maximal, characteristic, complemented
6	#22577478	C₂	1	1	yes	maximal, characteristic, complemented
7	#22577478	C₂	1	1	yes	maximal, characteristic, complemented
8	#22577476	C₂	1	1	yes	maximal, characteristic, complemented
9	#22577474	C₂	1	1	yes	maximal, characteristic, complemented
10	#22577472	C₂	1	1	yes	maximal, characteristic, complemented
11	#22577428	C₂	1	1	yes	maximal, characteristic, complemented
12	#22577368	C₂	1	1	yes	maximal, characteristic, complemented
13	#22577365	C₂	1	1	yes	maximal, characteristic, complemented
14	#22577360	C₂	1	1	yes	maximal, characteristic, complemented
15	#435×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14555510	C₂²	1	1	yes	characteristic
17	C₂²×C₄×D₁₃₇	C₂²	1	1	yes	characteristic
18	#17984094	—	2	4	no	—
19	C₂×#14555494	C₂²	1	1	yes	characteristic
20	C₂×#14555494	C₂²	1	1	yes	characteristic, complemented
21	C₂×#14555493	C₂²	1	1	yes	characteristic
22	C₂×#14555493	C₂²	1	1	yes	characteristic
23	C₂×#14555493	C₂²	1	1	yes	characteristic
24	C₂×#14555493	C₂²	1	1	yes	characteristic
25	C₂×#14555493	C₂²	1	1	yes	characteristic, complemented
26	M₁₆×D₁₃₇	—	2	4	no	—
27	C₂×C₈×D₁₃₇	C₂²	1	1	yes	characteristic
28	C₂×C₈×D₁₃₇	C₂²	1	1	yes	characteristic
29	C₂×C₈×D₁₃₇	C₂²	1	1	yes	characteristic, complemented
30	#17984073	C₄	1	1	yes	characteristic
31	#17984070	C₄	1	1	yes	characteristic
32	#17984066	C₄	1	1	yes	characteristic
33	#17984065	C₄	1	1	yes	characteristic
34	#17984061	C₄	1	1	yes	characteristic
35	#17984060	C₄	1	1	yes	characteristic
36	#17984058	C₄	1	1	yes	characteristic
37	#17984056	C₄	1	1	yes	characteristic
38	C₄×D₅₄₈	C₂²	1	1	yes	characteristic
39	C₄×C₂²⋊D₁₃₇	C₂²	1	1	yes	characteristic
40	C₄×C₂²⋊D₁₃₇	C₂²	1	1	yes	characteristic
41	#17984045	C₂²	1	1	yes	characteristic
42	C₄⋊#11764040	C₂²	1	1	yes	characteristic, complemented
43	#17984017	C₂²	1	1	yes	characteristic, complemented
44	#17984017	C₂²	1	1	yes	characteristic, complemented
45	C₂²⋊#11764040	C₂²	1	1	yes	characteristic
46	C₂²⋊#11764040	C₂²	1	1	yes	characteristic, complemented
47	#17984000	C₂²	1	1	yes	characteristic
48	#17984000	C₂²	1	1	yes	characteristic
49	#17984000	C₂²	1	1	yes	characteristic, complemented
50	#17984000	C₂²	1	1	yes	characteristic, complemented
51	#17983998	C₂²	1	1	yes	characteristic, complemented
52	C₄×#11764040	C₂²	1	1	yes	characteristic, complemented
53	C₈×Dic₁₃₇	C₂²	1	1	yes	characteristic, complemented
54	C₂×M₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
55	C₂²×C₈×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
56	C₄×D₄×C₁₃₇	C₂²	1	1	yes	characteristic
57	C₄⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
58	C₂²⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic
59	C₂²⋊C₈×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
60	#97×C₁₃₇	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₁₃₇	C₂×C₄	1	1	yes	characteristic
62	#14555510	—	2	2	no	—
63	#14555510	—	2	2	no	—
64	C₂×Dic₂₇₄	C₂×C₄	1	1	yes	characteristic
65	C₂×D₅₄₈	C₂×C₄	1	1	yes	characteristic
66	C₂×D₅₄₈	C₂×C₄	1	1	yes	characteristic
67	C₂×C₂²⋊D₁₃₇	C₂×C₄	1	1	yes	characteristic
68	C₂×C₂²⋊D₁₃₇	C₂×C₄	1	1	yes	characteristic
69	C₂×C₂²⋊D₁₃₇	C₂×C₄	1	1	yes	characteristic
70	C₂×C₂²⋊D₁₃₇	C₂×C₄	1	1	yes	characteristic
71	C₂²×Dic₁₃₇	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄×D₁₃₇	—	2	2	no	—
73	C₂×C₄×D₁₃₇	—	2	2	no	—
74	C₂×C₄×D₁₃₇	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄×D₁₃₇	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄×D₁₃₇	C₂³	1	1	yes	characteristic
77	C₂×C₄×D₁₃₇	C₂³	1	1	yes	characteristic
78	C₂×C₄×D₁₃₇	C₂³	1	1	yes	characteristic
79	#14555494	—	2	2	no	—
80	#14555494	—	2	2	no	—
81	#14555493	—	2	2	no	—
82	#14555493	—	2	2	no	—
83	#14555493	—	2	2	no	—
84	#14555493	—	2	2	no	—
85	#14555493	—	2	2	no	—
86	C₂×#11764040	C₂³	1	1	yes	characteristic
87	C₂×#11764040	C₂³	1	1	yes	characteristic
88	C₂×#11764040	C₂³	1	1	yes	characteristic
89	C₂×#11764040	C₂³	1	1	yes	characteristic
90	C₈×D₁₃₇	—	2	2	no	—
91	C₈×D₁₃₇	—	2	2	no	—
92	C₈×D₁₃₇	D₄	1	4	yes	complemented
93	C₄⋊Dic₁₃₇	C₂×C₄	1	1	yes	characteristic
94	#14555489	C₂×C₄	1	1	yes	characteristic
95	#14555489	C₂×C₄	1	1	yes	characteristic
96	#14555489	C₂×C₄	1	1	yes	characteristic
97	#14555489	C₂×C₄	1	1	yes	characteristic
98	C₂²⋊Dic₁₃₇	C₂×C₄	1	1	yes	characteristic
99	C₂²⋊Dic₁₃₇	C₂×C₄	1	1	yes	characteristic
100	#14555487	C₂×C₄	1	1	yes	characteristic
101	#14555487	C₂×C₄	1	1	yes	characteristic
102	#14555487	C₂×C₄	1	1	yes	characteristic
103	#14555487	C₂×C₄	1	1	yes	characteristic
104	#14555487	C₂×C₄	1	1	yes	characteristic
105	#14555487	C₂×C₄	1	1	yes	characteristic
106	C₄×Dic₁₃₇	C₂³	1	1	yes	characteristic
107	C₂×D₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
109	C₂²×C₄×C₁₃₇	C₂³	1	1	yes	characteristic
110	M₁₆×C₁₃₇	—	2	2	no	—
111	C₂×C₈×C₁₃₇	—	2	2	no	—
112	C₂×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
113	C₂×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
114	C₂×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
115	C₂×C₈×C₁₃₇	C₂³	1	1	yes	characteristic
116	C₄⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
117	C₂²⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
118	C₂²⋊C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
119	C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
120	C₂²×D₁₃₇	—	2	2	no	—
121	C₂²×D₁₃₇	—	4	1	no	—
122	C₂²×D₁₃₇	—	4	1	no	—
123	C₂²×D₁₃₇	C₂²×C₄	1	1	yes	characteristic
124	C₂²×D₁₃₇	C₂²×C₄	1	1	yes	characteristic
125	C₂²×D₁₃₇	C₂²×C₄	1	1	yes	characteristic
126	Dic₂₇₄	—	2	2	no	—
127	D₅₄₈	—	2	2	no	—
128	D₅₄₈	—	4	1	no	—
129	C₂²⋊D₁₃₇	—	2	2	no	—
130	C₂²⋊D₁₃₇	—	2	2	no	—
131	C₂²⋊D₁₃₇	—	4	1	no	—
132	C₂²⋊D₁₃₇	—	4	1	no	—
133	C₂×Dic₁₃₇	—	2	2	no	—
134	C₂×Dic₁₃₇	C₂²×C₄	1	1	yes	characteristic
135	C₂×Dic₁₃₇	C₂²×C₄	1	1	yes	characteristic
136	C₂×Dic₁₃₇	C₂²×C₄	1	1	yes	characteristic
137	C₂×Dic₁₃₇	C₂²×C₄	1	1	yes	characteristic
138	C₂×Dic₁₃₇	C₂²×C₄	1	1	yes	characteristic
139	C₄×D₁₃₇	—	2	2	no	—
140	C₄×D₁₃₇	—	2	1	no	—
141	C₄×D₁₃₇	—	2	1	no	—
142	C₄×D₁₃₇	—	2	1	no	—
143	C₄×D₁₃₇	—	2	1	no	—
144	C₄×D₁₃₇	—	2	2	no	—
145	C₄×D₁₃₇	C₂×D₄	1	2	yes	—
146	C₄×D₁₃₇	#41	1	2	yes	—
147	#11764040	—	2	1	no	—
148	#11764040	—	2	1	no	—
149	#11764040	—	2	1	no	—
150	#11764040	C₂×D₄	1	2	yes	—
151	C₂³×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
152	C₂³×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
153	D₄×C₁₃₇	—	4	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	—	2	1	no	—
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	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₄×C₁₃₇	C₂⁴	1	1	yes	characteristic
163	C₈×C₁₃₇	—	2	1	no	—
164	C₈×C₁₃₇	—	2	1	no	—
165	C₈×C₁₃₇	—	2	1	no	—
166	C₈×C₁₃₇	C₂×D₄	1	2	yes	—
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	—	2	1	no	—
172	C₂²×C₁₃₇	—	2	1	no	—
173	C₂²×C₁₃₇	C₂³×C₄	1	1	yes	characteristic
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	—	2	1	no	—
181	C₂×D₁₃₇	—	2	1	no	—
182	C₂×D₁₃₇	—	4	4	no	—
183	C₂×D₁₃₇	C₄×D₄	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	C₂²×D₄	1	1	yes	characteristic
189	C₄×C₁₃₇	C₂×#41	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	C₄×D₄	1	2	yes	—
195	C₂×C₁₃₇	—	4	1	no	—
196	C₂×C₁₃₇	—	4	1	no	—
197	C₂×C₁₃₇	C₂×C₄×D₄	1	1	yes	characteristic
198	C₂×C₁₃₇	#568	1	1	yes	characteristic
199	C₂×C₁₃₇	#568	1	1	yes	characteristic
200	D₁₃₇	—	2	2	no	—
201	D₁₃₇	—	4	1	no	—
202	D₁₃₇	—	4	1	no	—
203	C₁₃₇	#2930	1	1	yes	characteristic, complemented, Sylow
204	#2930	—	137	1	no	maximal, Sylow
205	C₂×#131	—	137	1	no	—
206	C₂²×M₁₆	—	137	1	no	—
207	#525	—	137	1	no	—
208	#436	—	137	1	no	—
209	#436	—	137	1	no	—
210	#436	—	137	1	no	—
211	#436	—	137	1	no	—
212	#435	—	137	1	no	—
213	#435	—	137	1	no	—
214	#435	—	137	1	no	—
215	#435	D₁₃₇	1	1	yes	characteristic, complemented
216	#424	—	137	1	no	—
217	#408	—	137	1	no	—
218	#407	—	137	1	no	—
219	#405	—	137	1	no	—
220	C₂×#41	—	137	1	no	—
221	C₂³×C₄	—	137	1	no	—
222	#131	—	274	4	no	—
223	C₂×M₁₆	—	274	4	no	—
224	C₂×M₁₆	—	137	1	no	—
225	C₂×M₁₆	—	137	1	no	—
226	C₂×M₁₆	—	137	1	no	—
227	C₂×M₁₆	—	137	1	no	—
228	C₂×M₁₆	—	137	1	no	—
229	C₂×M₁₆	—	137	1	no	—
230	C₂×M₁₆	—	137	1	no	—
231	C₂×M₁₆	C₂×D₁₃₇	1	1	yes	characteristic
232	C₂²×C₈	—	137	1	no	—
233	C₂²×C₈	—	137	1	no	—
234	C₂²×C₈	—	137	1	no	—
235	C₂²×C₈	C₂×D₁₃₇	1	1	yes	characteristic, complemented
236	#123	—	137	1	no	—
237	#123	—	137	1	no	—
238	C₂²⋊Q₈	—	137	1	no	—
239	C₂²⋊Q₈	—	137	1	no	—
240	#121	—	137	1	no	—
241	#121	—	137	1	no	—
242	#120	—	137	1	no	—
243	#120	—	137	1	no	—
244	C₄×D₄	—	137	1	no	—
245	C₄×D₄	—	137	1	no	—
246	C₄×D₄	—	137	1	no	—
247	C₄×D₄	C₂×D₁₃₇	1	1	yes	characteristic
248	#117	—	137	1	no	—
249	C₄⋊C₈	—	137	1	no	—
250	C₄⋊C₈	—	137	1	no	—
251	C₄⋊C₈	—	137	1	no	—
252	C₄⋊C₈	C₂×D₁₃₇	1	1	yes	characteristic, complemented
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	—	137	1	no	—
258	C₂²⋊C₈	—	137	1	no	—
259	C₂²⋊C₈	C₂×D₁₃₇	1	1	yes	characteristic
260	C₂²⋊C₈	C₂×D₁₃₇	1	1	yes	characteristic, complemented
261	#97	—	137	1	no	—
262	#97	C₂×D₁₃₇	1	1	yes	characteristic, complemented
263	C₄×C₈	—	137	1	no	—
264	C₄×C₈	—	137	1	no	—
265	C₂⁴	—	137	1	no	—
266	#41	—	274	2	no	—
267	#41	—	274	2	no	—
268	C₂×Q₈	—	137	1	no	—
269	C₂×D₄	—	137	1	no	—
270	C₂×D₄	—	137	1	no	—
271	C₂×D₄	—	137	1	no	—
272	C₂×D₄	—	137	1	no	—
273	C₂×D₄	—	137	1	no	—
274	C₂×D₄	—	137	1	no	—
275	C₂×D₄	C₄×D₁₃₇	1	1	yes	characteristic
276	C₂²×C₄	—	274	2	no	—
277	C₂²×C₄	—	274	2	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	C₂²×D₁₃₇	1	1	yes	characteristic
285	C₂²×C₄	C₂²×D₁₃₇	1	1	yes	characteristic
286	M₁₆	—	2	2	no	—
287	M₁₆	—	274	2	no	—
288	M₁₆	—	274	2	no	—
289	M₁₆	—	274	2	no	—
290	M₁₆	—	274	2	no	—
291	M₁₆	—	274	2	no	—
292	M₁₆	—	274	2	no	—
293	M₁₆	—	274	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	274	2	no	—
296	C₂×C₈	—	274	2	no	—
297	C₂×C₈	—	137	1	no	—
298	C₂×C₈	—	137	1	no	—
299	C₂×C₈	—	137	1	no	—
300	C₂×C₈	—	137	1	no	—
301	C₂×C₈	—	137	4	no	—
302	C₂×C₈	C₂²×D₁₃₇	1	1	yes	characteristic
303	C₂×C₈	C₂²×D₁₃₇	1	1	yes	characteristic
304	C₂×C₈	C₂²×D₁₃₇	1	1	yes	characteristic
305	C₂×C₈	C₂²×D₁₃₇	1	1	yes	characteristic
306	C₄⋊C₄	—	137	1	no	—
307	C₄⋊C₄	—	137	1	no	—
308	C₄⋊C₄	—	137	1	no	—
309	C₄⋊C₄	—	137	1	no	—
310	C₄⋊C₄	—	137	1	no	—
311	C₄⋊C₄	C₄×D₁₃₇	1	1	yes	characteristic
312	C₂²⋊C₄	—	137	1	no	—
313	C₂²⋊C₄	—	137	1	no	—
314	C₂²⋊C₄	—	137	1	no	—
315	C₂²⋊C₄	—	137	1	no	—
316	C₂²⋊C₄	—	137	1	no	—
317	C₂²⋊C₄	—	137	1	no	—
318	C₂²⋊C₄	—	137	1	no	—
319	C₂²⋊C₄	—	137	1	no	—
320	C₂²⋊C₄	C₄×D₁₃₇	1	1	yes	characteristic
321	C₂²⋊C₄	C₄×D₁₃₇	1	1	yes	characteristic
322	C₄²	—	137	1	no	—
323	C₄²	C₂²×D₁₃₇	1	1	yes	characteristic
324	C₂³	—	274	2	no	—
325	C₂³	—	548	1	no	—
326	C₂³	—	548	1	no	—
327	C₂³	—	137	1	no	—
328	C₂³	—	137	1	no	—
329	C₂³	—	137	1	no	—
330	C₂³	C₂×C₄×D₁₃₇	1	1	yes	characteristic
331	C₂³	C₂×C₄×D₁₃₇	1	1	yes	characteristic
332	Q₈	—	274	2	no	—
333	D₄	—	4	1	no	—
334	D₄	—	274	2	no	—
335	D₄	—	274	2	no	—
336	D₄	—	274	2	no	—
337	D₄	—	548	1	no	—
338	D₄	—	548	1	no	—
339	D₄	—	548	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	274	2	no	—
345	C₂×C₄	—	274	2	no	—
346	C₂×C₄	—	274	2	no	—
347	C₂×C₄	—	274	1	no	—
348	C₂×C₄	—	274	1	no	—
349	C₂×C₄	—	274	1	no	—
350	C₂×C₄	—	274	1	no	—
351	C₂×C₄	—	137	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	2	no	—
357	C₂×C₄	—	137	2	no	—
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	C₂×C₄×D₁₃₇	1	1	yes	characteristic
362	C₂×C₄	C₂³×D₁₃₇	1	1	yes	characteristic
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	—	137	2	no	—
370	C₈	D₄×D₁₃₇	1	2	yes	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	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	—	274	1	no	—
383	C₂²	—	274	1	no	—
384	C₂²	—	274	1	no	—
385	C₂²	—	548	4	no	—
386	C₂²	—	137	2	no	—
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	—	137	2	no	—
397	C₄	C₂×D₄×D₁₃₇	1	1	yes	characteristic
398	C₄	#41×D₁₃₇	1	1	yes	characteristic
399	C₂	—	4	1	no	—
400	C₂	—	4	1	no	—
401	C₂	—	274	2	no	—
402	C₂	—	548	1	no	—
403	C₂	—	548	1	no	—
404	C₂	C₄×D₄×D₁₃₇	1	1	yes	characteristic
405	C₂	#22578168	1	1	yes	characteristic
406	C₂	#22578169	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	#22577912	C₂
cosocle	C₂×C₄×C₁₃₇	C₂⁴
hypercenter	#435	D₁₃₇
hypocenter	C₁₃₇	#2930
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
1. C₂×#17984094	C₂	semidirect
2. C₂×M₁₆×D₁₃₇	C₂	semidirect
4. #22577481	C₂	semidirect
5. #22577480	C₂	semidirect
6. #22577478	C₂	semidirect
7. #22577478	C₂	semidirect
8. #22577476	C₂	semidirect
9. #22577474	C₂	semidirect
10. #22577472	C₂	semidirect
11. #22577428	C₂	semidirect
12. #22577368	C₂	semidirect
13. #22577365	C₂	semidirect
14. #22577360	C₂	semidirect
15. #435×C₁₃₇	C₂	semidirect
20. C₂×#14555494	C₂²	semidirect
25. C₂×#14555493	C₂²	semidirect
29. C₂×C₈×D₁₃₇	C₂²	semidirect
42. C₄⋊#11764040	C₂²	semidirect
43. #17984017	C₂²	semidirect
44. #17984017	C₂²	semidirect
46. C₂²⋊#11764040	C₂²	semidirect
49. #17984000	C₂²	semidirect
50. #17984000	C₂²	semidirect
51. #17983998	C₂²	semidirect
52. C₄×#11764040	C₂²	semidirect
53. C₈×Dic₁₃₇	C₂²	semidirect
55. C₂²×C₈×C₁₃₇	C₂²	semidirect
57. C₄⋊C₈×C₁₃₇	C₂²	semidirect
59. C₂²⋊C₈×C₁₃₇	C₂²	semidirect
60. #97×C₁₃₇	C₂²	semidirect
92. C₈×D₁₃₇	D₄	semidirect
203. C₁₃₇	#2930	semidirect
215. #435	D₁₃₇	semidirect
235. C₂²×C₈	C₂×D₁₃₇	semidirect
252. C₄⋊C₈	C₂×D₁₃₇	semidirect
260. 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
C₂×#17984094	2
C₂×M₁₆×D₁₃₇	2
#22577912	2
#22577481	2
#22577480	2
#22577478	2
#22577476	2
#22577474	2
#22577472	2
#22577428	2
#22577368	2
#22577365	2
#22577360	2
#435×C₁₃₇	2
#2930	137