Subgroups — C₂×#14558131 #18007948

Order 4736.

1144 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14558131	C₂	1	16	yes	maximal, direct product factor
2	C₂×#11924531	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#11924530	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11924526	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11924521	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11924521	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#11924521	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#11924521	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#11924516	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#11924514	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#11924514	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#11924511	C₂	1	1	yes	maximal, characteristic
13	C₂×C₄×D₁₄₈	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#11924498	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄⋊C₄×D₃₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#125×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×Dic₇₄	C₂²	1	1	yes	characteristic
18	C₂²×D₁₄₈	C₂²	1	1	yes	characteristic
19	C₂²×D₁₄₈	C₂²	1	1	yes	characteristic
20	C₂²×D₁₄₈	C₂²	1	1	yes	characteristic
21	C₂²×C₄×D₃₇	C₂²	1	1	yes	characteristic
22	C₂²×C₄×D₃₇	C₂²	1	1	yes	characteristic
23	C₂²×C₄×D₃₇	C₂²	1	1	yes	characteristic
24	C₂²×C₄×D₃₇	C₂²	1	1	yes	characteristic
25	C₂²×C₄×D₃₇	C₂²	1	1	yes	characteristic
26	#11924531	C₂²	1	8	yes	complemented
27	#11924530	C₂²	1	8	yes	complemented
28	#11924526	C₂²	1	8	yes	complemented
29	#11924521	C₂²	1	8	yes	complemented
30	#11924521	C₂²	1	8	yes	complemented
31	#11924521	C₂²	1	8	yes	complemented
32	#11924521	C₂²	1	8	yes	complemented
33	#11924516	C₂²	1	8	yes	complemented
34	#11924514	C₂²	1	8	yes	complemented
35	#11924514	C₂²	1	8	yes	complemented
36	#11924511	C₂²	1	8	yes	—
37	C₄×D₁₄₈	C₂²	1	8	yes	complemented
38	#11924498	C₂²	1	8	yes	complemented
39	C₂×C₄⋊Dic₃₇	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊Dic₃₇	C₂²	1	1	yes	characteristic
41	C₂×#10596936	C₂²	1	1	yes	characteristic
42	C₂×#10596936	C₂²	1	1	yes	characteristic
43	C₂×#10596936	C₂²	1	1	yes	characteristic
44	C₂×#10596936	C₂²	1	1	yes	characteristic
45	C₂×#10596936	C₂²	1	1	yes	characteristic
46	C₂×#10596936	C₂²	1	1	yes	characteristic
47	C₄⋊C₄×D₃₇	C₂²	1	8	yes	complemented
48	C₂×#10596938	C₂²	1	1	yes	characteristic
49	C₂×#10596938	C₂²	1	1	yes	characteristic
50	C₂×#10596938	C₂²	1	1	yes	characteristic
51	C₂×#10596938	C₂²	1	1	yes	characteristic
52	C₂×#10596938	C₂²	1	1	yes	characteristic
53	C₂×#10596938	C₂²	1	1	yes	characteristic
54	C₂×#10596938	C₂²	1	1	yes	characteristic
55	C₂×#10596938	C₂²	1	1	yes	characteristic
56	C₂×#10596938	C₂²	1	1	yes	characteristic
57	C₂×#10596938	C₂²	1	1	yes	characteristic
58	C₂×C₄×Dic₃₇	C₂²	1	1	yes	characteristic
59	#125×C₃₇	C₂²	1	8	yes	complemented
60	C₂×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
66	C₂×C₄²×C₃₇	C₂²	1	1	yes	characteristic
67	C₂³×D₃₇	C₂³	1	1	yes	characteristic
68	C₂³×D₃₇	C₂³	1	1	yes	characteristic
69	C₂³×D₃₇	C₂³	1	1	yes	characteristic
70	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
71	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
72	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
73	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
74	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
75	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
76	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
77	C₂²×Dic₃₇	C₂³	1	1	yes	characteristic
78	C₂²×Dic₃₇	C₂³	1	1	yes	characteristic
79	C₂²×Dic₃₇	C₂³	1	1	yes	characteristic
80	C₂²×Dic₃₇	C₂³	1	1	yes	characteristic
81	C₂²×Dic₃₇	C₂³	1	1	yes	characteristic
82	C₂×D₁₄₈	—	2	4	no	—
83	C₂×D₁₄₈	—	2	4	no	—
84	C₂×D₁₄₈	—	4	2	no	—
85	C₂×D₁₄₈	C₂³	1	4	yes	—
86	C₂×D₁₄₈	C₂³	1	4	yes	—
87	C₂×D₁₄₈	C₂³	1	4	yes	—
88	C₂×C₄×D₃₇	—	2	4	no	—
89	C₂×C₄×D₃₇	—	4	2	no	—
90	C₂×C₄×D₃₇	—	4	2	no	—
91	C₂×C₄×D₃₇	—	4	2	no	—
92	C₂×C₄×D₃₇	—	4	2	no	—
93	C₂×C₄×D₃₇	C₂³	1	4	yes	—
94	C₂×C₄×D₃₇	C₂³	1	4	yes	—
95	C₂×C₄×D₃₇	C₂³	1	4	yes	—
96	C₂×C₄×D₃₇	C₂³	1	4	yes	—
97	C₂×C₄×D₃₇	C₂³	1	4	yes	—
98	C₂×Dic₇₄	—	4	2	no	—
99	C₂×Dic₇₄	C₂³	1	4	yes	—
100	C₄⋊C₄×C₃₇	C₂³	1	4	yes	—
101	C₄⋊C₄×C₃₇	C₂³	1	4	yes	—
102	C₄⋊C₄×C₃₇	C₂³	1	4	yes	—
103	C₄⋊C₄×C₃₇	C₂³	1	4	yes	—
104	C₄⋊C₄×C₃₇	C₂³	1	4	yes	—
105	C₄⋊C₄×C₃₇	C₂³	1	4	yes	—
106	C₄²×C₃₇	C₂³	1	4	yes	—
107	#10596938	C₂³	1	4	yes	—
108	#10596938	C₂³	1	4	yes	—
109	#10596938	C₂³	1	4	yes	—
110	#10596938	C₂³	1	4	yes	—
111	#10596938	C₂³	1	4	yes	—
112	#10596938	C₂³	1	4	yes	—
113	#10596938	C₂³	1	4	yes	—
114	#10596938	C₂³	1	4	yes	—
115	#10596938	C₂³	1	4	yes	—
116	#10596938	C₂³	1	4	yes	—
117	C₄⋊Dic₃₇	C₂³	1	4	yes	—
118	C₄⋊Dic₃₇	C₂³	1	4	yes	—
119	#10596936	C₂³	1	4	yes	—
120	#10596936	C₂³	1	4	yes	—
121	#10596936	C₂³	1	4	yes	—
122	#10596936	C₂³	1	4	yes	—
123	#10596936	C₂³	1	4	yes	—
124	#10596936	C₂³	1	4	yes	—
125	C₄×Dic₃₇	C₂³	1	4	yes	—
126	C₂³×C₃₇	C₂⁴	1	1	yes	characteristic
127	C₂²×D₃₇	—	2	2	no	—
128	C₂²×D₃₇	—	2	2	no	—
129	C₂²×D₃₇	—	2	2	no	—
130	C₂²×D₃₇	—	2	2	no	—
131	C₂²×D₃₇	—	2	2	no	—
132	C₂²×D₃₇	—	2	2	no	—
133	C₂²×D₃₇	—	2	2	no	—
134	C₂²×D₃₇	—	2	2	no	—
135	C₂²×D₃₇	#41	1	4	yes	—
136	C₂²×D₃₇	C₂⁴	1	2	yes	—
137	C₂²×D₃₇	C₂⁴	1	2	yes	—
138	C₂²×D₃₇	C₂⁴	1	2	yes	—
139	C₂×C₄×C₃₇	—	2	2	no	—
140	C₂×C₄×C₃₇	—	2	2	no	—
141	C₂×C₄×C₃₇	—	2	2	no	—
142	C₂×C₄×C₃₇	—	2	2	no	—
143	C₂×C₄×C₃₇	—	2	2	no	—
144	C₂×C₄×C₃₇	—	2	2	no	—
145	C₂×C₄×C₃₇	—	2	2	no	—
146	C₂×C₄×C₃₇	C₂⁴	1	2	yes	—
147	C₂×C₄×C₃₇	C₂⁴	1	2	yes	—
148	C₂×C₄×C₃₇	C₂⁴	1	2	yes	—
149	C₂×C₄×C₃₇	C₂⁴	1	2	yes	—
150	C₂×C₄×C₃₇	C₂⁴	1	2	yes	—
151	C₂×C₄×C₃₇	C₂⁴	1	2	yes	—
152	C₂×C₄×C₃₇	C₂⁴	1	2	yes	—
153	C₂×Dic₃₇	—	2	2	no	—
154	C₂×Dic₃₇	—	2	2	no	—
155	C₂×Dic₃₇	—	2	2	no	—
156	C₂×Dic₃₇	—	2	2	no	—
157	C₂×Dic₃₇	—	2	2	no	—
158	C₂×Dic₃₇	C₂⁴	1	2	yes	—
159	C₂×Dic₃₇	C₂⁴	1	2	yes	—
160	C₂×Dic₃₇	C₂⁴	1	2	yes	—
161	C₂×Dic₃₇	C₂⁴	1	2	yes	—
162	C₂×Dic₃₇	C₂⁴	1	2	yes	—
163	D₁₄₈	—	2	8	no	—
164	D₁₄₈	—	2	8	no	—
165	D₁₄₈	—	4	4	no	—
166	C₄×D₃₇	—	2	8	no	—
167	C₄×D₃₇	—	4	4	no	—
168	C₄×D₃₇	—	4	4	no	—
169	C₄×D₃₇	—	4	4	no	—
170	C₄×D₃₇	—	4	4	no	—
171	Dic₇₄	—	4	4	no	—
172	C₂²×C₃₇	C₂×#41	1	2	yes	—
173	C₂²×C₃₇	H(5,𝔽₂)	1	2	yes	—
174	C₂²×C₃₇	2₋¹⁺⁴	1	2	yes	—
175	C₂²×C₃₇	C₂⁵	1	1	yes	characteristic
176	C₂×D₃₇	—	2	8	no	—
177	C₂×D₃₇	—	2	2	no	—
178	C₂×D₃₇	—	2	2	no	—
179	C₂×D₃₇	—	2	2	no	—
180	C₂×D₃₇	—	2	2	no	—
181	C₂×D₃₇	—	2	2	no	—
182	C₂×D₃₇	—	2	2	no	—
183	C₂×D₃₇	—	2	2	no	—
184	C₂×D₃₇	—	2	2	no	—
185	C₂×D₃₇	—	4	4	no	—
186	C₂×D₃₇	—	4	4	no	—
187	C₂×D₃₇	C₂×#41	1	4	yes	—
188	C₄×C₃₇	—	2	2	no	—
189	C₄×C₃₇	—	2	2	no	—
190	C₄×C₃₇	—	2	2	no	—
191	C₄×C₃₇	—	2	2	no	—
192	C₄×C₃₇	—	2	2	no	—
193	C₄×C₃₇	—	2	2	no	—
194	C₄×C₃₇	—	2	2	no	—
195	Dic₃₇	—	2	2	no	—
196	Dic₃₇	—	2	2	no	—
197	Dic₃₇	—	2	2	no	—
198	Dic₃₇	—	2	2	no	—
199	Dic₃₇	—	2	2	no	—
200	C₂×#539	—	37	1	no	maximal, Sylow
201	C₂×C₃₇	#539	1	4	yes	complemented
202	C₂×C₃₇	C₂²×#41	1	1	yes	characteristic
203	C₂×C₃₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
204	C₂×C₃₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
205	D₃₇	—	2	4	no	—
206	D₃₇	—	4	2	no	—
207	D₃₇	—	4	2	no	—
208	#539	—	37	16	no	—
209	C₂×#126	—	37	1	no	—
210	C₂×#126	—	37	1	no	—
211	C₂×#125	—	37	1	no	—
212	C₂×#125	D₃₇	1	1	yes	characteristic, complemented
213	C₂×#123	—	37	1	no	—
214	C₂×#123	—	37	1	no	—
215	C₂×#123	—	37	1	no	—
216	C₂×#123	—	37	1	no	—
217	C₂×C₂²⋊Q₈	—	37	1	no	—
218	C₂×C₂²⋊Q₈	—	37	1	no	—
219	C₂×C₂²⋊Q₈	—	37	1	no	—
220	C₂×#121	—	37	1	no	—
221	C₂×C₄×D₄	—	37	1	no	—
222	C₂×C₄×D₄	—	37	1	no	—
223	C₂²×C₄⋊C₄	—	37	1	no	—
224	C₃₇	C₂×#539	1	1	yes	characteristic, complemented, Sylow
225	C₂²×Q₈	—	37	1	no	—
226	C₂²×D₄	—	37	1	no	—
227	C₂²×D₄	—	37	1	no	—
228	C₂²×D₄	—	37	1	no	—
229	C₂³×C₄	—	37	1	no	—
230	C₂³×C₄	—	37	1	no	—
231	C₂³×C₄	—	37	1	no	—
232	C₂³×C₄	—	37	1	no	—
233	C₂³×C₄	—	37	1	no	—
234	#126	—	37	8	no	—
235	#126	—	37	8	no	—
236	#125	—	37	8	no	—
237	#125	C₂×D₃₇	1	8	yes	complemented
238	#123	—	37	8	no	—
239	#123	—	37	8	no	—
240	#123	—	37	8	no	—
241	#123	—	37	8	no	—
242	C₂²⋊Q₈	—	37	8	no	—
243	C₂²⋊Q₈	—	37	8	no	—
244	C₂²⋊Q₈	—	37	8	no	—
245	#121	—	37	8	no	—
246	C₄×D₄	—	37	8	no	—
247	C₄×D₄	—	37	8	no	—
248	C₂×C₄⋊C₄	—	37	1	no	—
249	C₂×C₄⋊C₄	—	37	1	no	—
250	C₂×C₄⋊C₄	—	37	1	no	—
251	C₂×C₄⋊C₄	—	37	1	no	—
252	C₂×C₄⋊C₄	—	37	1	no	—
253	C₂×C₄⋊C₄	—	37	1	no	—
254	C₂×C₄⋊C₄	—	37	1	no	—
255	C₂×C₄⋊C₄	—	37	1	no	—
256	C₂×C₄⋊C₄	—	37	8	no	—
257	C₂×C₄⋊C₄	C₂×D₃₇	1	1	yes	characteristic
258	C₂×C₄⋊C₄	C₂×D₃₇	1	1	yes	characteristic
259	C₂×C₄⋊C₄	C₂×D₃₇	1	1	yes	characteristic
260	C₂×C₄⋊C₄	C₂×D₃₇	1	1	yes	characteristic
261	C₂×C₄⋊C₄	C₂×D₃₇	1	1	yes	characteristic
262	C₂×C₄⋊C₄	C₂×D₃₇	1	1	yes	characteristic
263	C₂×C₂²⋊C₄	—	37	1	no	—
264	C₂×C₂²⋊C₄	—	37	1	no	—
265	C₂×C₂²⋊C₄	—	37	1	no	—
266	C₂×C₂²⋊C₄	—	37	1	no	—
267	C₂×C₂²⋊C₄	—	37	1	no	—
268	C₂×C₂²⋊C₄	—	37	1	no	—
269	C₂×C₂²⋊C₄	—	37	1	no	—
270	C₂×C₂²⋊C₄	—	37	1	no	—
271	C₂×C₂²⋊C₄	—	37	1	no	—
272	C₂×C₂²⋊C₄	—	37	1	no	—
273	C₂×C₄²	—	37	1	no	—
274	C₂×C₄²	C₂×D₃₇	1	1	yes	characteristic
275	C₂⁴	—	37	1	no	—
276	C₂⁴	—	37	1	no	—
277	C₂⁴	—	37	1	no	—
278	C₂×Q₈	—	37	4	no	—
279	C₂×Q₈	—	148	2	no	—
280	C₂×D₄	—	37	4	no	—
281	C₂×D₄	—	37	4	no	—
282	C₂×D₄	—	37	4	no	—
283	C₂×D₄	—	74	4	no	—
284	C₂×D₄	—	74	4	no	—
285	C₂×D₄	—	148	2	no	—
286	C₂²×C₄	—	37	1	no	—
287	C₂²×C₄	—	37	1	no	—
288	C₂²×C₄	—	37	1	no	—
289	C₂²×C₄	—	37	1	no	—
290	C₂²×C₄	—	37	1	no	—
291	C₂²×C₄	—	37	4	no	—
292	C₂²×C₄	—	37	4	no	—
293	C₂²×C₄	—	37	4	no	—
294	C₂²×C₄	—	37	4	no	—
295	C₂²×C₄	—	37	4	no	—
296	C₂²×C₄	—	74	4	no	—
297	C₂²×C₄	—	148	2	no	—
298	C₂²×C₄	—	148	2	no	—
299	C₂²×C₄	—	148	2	no	—
300	C₂²×C₄	—	148	2	no	—
301	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
302	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
303	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
304	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
305	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
306	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
307	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
308	C₄⋊C₄	—	37	4	no	—
309	C₄⋊C₄	—	37	4	no	—
310	C₄⋊C₄	—	37	4	no	—
311	C₄⋊C₄	—	37	4	no	—
312	C₄⋊C₄	—	37	4	no	—
313	C₄⋊C₄	—	37	4	no	—
314	C₄⋊C₄	—	37	4	no	—
315	C₄⋊C₄	—	37	4	no	—
316	C₄⋊C₄	C₂²×D₃₇	1	4	yes	—
317	C₄⋊C₄	C₂²×D₃₇	1	4	yes	—
318	C₄⋊C₄	C₂²×D₃₇	1	4	yes	—
319	C₄⋊C₄	C₂²×D₃₇	1	4	yes	—
320	C₄⋊C₄	C₂²×D₃₇	1	4	yes	—
321	C₄⋊C₄	C₂²×D₃₇	1	4	yes	—
322	C₂²⋊C₄	—	37	4	no	—
323	C₂²⋊C₄	—	37	4	no	—
324	C₂²⋊C₄	—	37	4	no	—
325	C₂²⋊C₄	—	37	4	no	—
326	C₂²⋊C₄	—	37	4	no	—
327	C₂²⋊C₄	—	37	4	no	—
328	C₂²⋊C₄	—	37	4	no	—
329	C₂²⋊C₄	—	37	4	no	—
330	C₂²⋊C₄	—	37	4	no	—
331	C₂²⋊C₄	—	37	4	no	—
332	C₄²	—	37	4	no	—
333	C₄²	C₂²×D₃₇	1	4	yes	—
334	C₂³	—	37	4	no	—
335	C₂³	—	37	2	no	—
336	C₂³	—	37	2	no	—
337	C₂³	—	37	2	no	—
338	C₂³	—	74	2	no	—
339	C₂³	—	74	2	no	—
340	C₂³	—	74	2	no	—
341	C₂³	—	74	2	no	—
342	C₂³	—	74	2	no	—
343	C₂³	—	74	2	no	—
344	C₂³	—	74	2	no	—
345	C₂³	—	74	2	no	—
346	C₂³	C₂³×D₃₇	1	1	yes	characteristic
347	Q₈	—	148	4	no	—
348	D₄	—	74	8	no	—
349	D₄	—	74	8	no	—
350	D₄	—	148	4	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	37	2	no	—
359	C₂×C₄	—	37	2	no	—
360	C₂×C₄	—	37	2	no	—
361	C₂×C₄	—	37	2	no	—
362	C₂×C₄	—	37	2	no	—
363	C₂×C₄	—	74	8	no	—
364	C₂×C₄	—	74	2	no	—
365	C₂×C₄	—	74	2	no	—
366	C₂×C₄	—	74	2	no	—
367	C₂×C₄	—	74	2	no	—
368	C₂×C₄	—	74	2	no	—
369	C₂×C₄	—	148	4	no	—
370	C₂×C₄	—	148	4	no	—
371	C₂×C₄	—	148	4	no	—
372	C₂×C₄	—	148	4	no	—
373	C₂×C₄	C₂³×D₃₇	1	2	yes	—
374	C₂×C₄	C₂³×D₃₇	1	2	yes	—
375	C₂×C₄	C₂³×D₃₇	1	2	yes	—
376	C₂×C₄	C₂³×D₃₇	1	2	yes	—
377	C₂×C₄	C₂³×D₃₇	1	2	yes	—
378	C₂×C₄	C₂³×D₃₇	1	2	yes	—
379	C₂×C₄	C₂³×D₃₇	1	2	yes	—
380	C₂²	—	37	4	no	—
381	C₂²	—	74	2	no	—
382	C₂²	—	74	2	no	—
383	C₂²	—	74	8	no	—
384	C₂²	—	74	2	no	—
385	C₂²	—	74	2	no	—
386	C₂²	—	74	2	no	—
387	C₂²	—	74	2	no	—
388	C₂²	—	74	2	no	—
389	C₂²	—	74	2	no	—
390	C₂²	—	148	4	no	—
391	C₂²	—	148	4	no	—
392	C₂²	#41×D₃₇	1	2	yes	—
393	C₂²	#11924582	1	2	yes	—
394	C₂²	#11924584	1	2	yes	—
395	C₂²	C₂⁴×D₃₇	1	1	yes	characteristic
396	C₄	—	2	2	no	—
397	C₄	—	2	2	no	—
398	C₄	—	2	2	no	—
399	C₄	—	2	2	no	—
400	C₄	—	2	2	no	—
401	C₄	—	2	2	no	—
402	C₄	—	2	2	no	—
403	C₄	—	74	2	no	—
404	C₄	—	74	2	no	—
405	C₄	—	74	2	no	—
406	C₄	—	74	2	no	—
407	C₄	—	74	2	no	—
408	C₂	—	74	4	no	—
409	C₂	—	148	2	no	—
410	C₂	—	148	2	no	—
411	C₂	#14558131	1	4	yes	direct product factor
412	C₂	C₂×#41×D₃₇	1	1	yes	characteristic
413	C₂	C₂×#11924582	1	1	yes	characteristic
414	C₂	C₂×#11924584	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₃₇
commutator, cosocle	C₂²×C₃₇	C₂⁵
Frattini	C₂²	C₂⁴×D₃₇
Fitting	C₂×#125×C₃₇	C₂
socle	C₂³×C₃₇	C₂⁴
prime radical	C₂×#11924511	C₂
hypercenter	C₂×#125	D₃₇
hypocenter	C₃₇	C₂×#539
LCS	G ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂³ ◁ C₂×#125

Complements

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

N	H ≅ G/N	type
1. #14558131	C₂	direct (N × H)
2. C₂×#11924531	C₂	semidirect
3. C₂×#11924530	C₂	semidirect
4. C₂×#11924526	C₂	semidirect
5. C₂×#11924521	C₂	semidirect
6. C₂×#11924521	C₂	semidirect
7. C₂×#11924521	C₂	semidirect
8. C₂×#11924521	C₂	semidirect
9. C₂×#11924516	C₂	semidirect
10. C₂×#11924514	C₂	semidirect
11. C₂×#11924514	C₂	semidirect
13. C₂×C₄×D₁₄₈	C₂	semidirect
14. C₂×#11924498	C₂	semidirect
15. C₂×C₄⋊C₄×D₃₇	C₂	semidirect
16. C₂×#125×C₃₇	C₂	semidirect
26. #11924531	C₂²	semidirect
27. #11924530	C₂²	semidirect
28. #11924526	C₂²	semidirect
29. #11924521	C₂²	semidirect
30. #11924521	C₂²	semidirect
31. #11924521	C₂²	semidirect
32. #11924521	C₂²	semidirect
33. #11924516	C₂²	semidirect
34. #11924514	C₂²	semidirect
35. #11924514	C₂²	semidirect
37. C₄×D₁₄₈	C₂²	semidirect
38. #11924498	C₂²	semidirect
47. C₄⋊C₄×D₃₇	C₂²	semidirect
59. #125×C₃₇	C₂²	semidirect
201. C₂×C₃₇	#539	semidirect
212. C₂×#125	D₃₇	semidirect
224. C₃₇	C₂×#539	semidirect
237. #125	C₂×D₃₇	semidirect
411. C₂	#14558131	direct (N × H)

Maximal subgroups

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

subgroup	index
#14558131	2
C₂×#11924531	2
C₂×#11924530	2
C₂×#11924526	2
C₂×#11924521	2
C₂×#11924516	2
C₂×#11924514	2
C₂×#11924511	2
C₂×C₄×D₁₄₈	2
C₂×#11924498	2
C₂×C₄⋊C₄×D₃₇	2
C₂×#125×C₃₇	2
C₂×#539	37

Subgroups — C2×#14558131 #18007948

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14558131 #18007948