Subgroups — #18008641

Order 4736.

1124 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14558255	C₂	1	1	yes	maximal, characteristic, complemented
2	#14558238	C₂	1	1	yes	maximal, characteristic, complemented
3	#14558215	C₂	1	2	yes	maximal, complemented
4	#14558212	C₂	1	2	yes	maximal, complemented
5	#14558210	C₂	1	2	yes	maximal, complemented
6	#14558198	C₂	1	1	yes	maximal, characteristic, complemented
7	#14558193	C₂	1	2	yes	maximal, complemented
8	#14558185	C₂	1	1	yes	maximal, characteristic, complemented
9	#14558184	C₂	1	1	yes	maximal, characteristic, complemented
10	#14558179	C₂	1	1	yes	maximal, characteristic, complemented
11	#14558174	C₂	1	1	yes	maximal, characteristic, complemented
12	#14558157	C₂	1	1	yes	maximal, characteristic, complemented
13	#14558156	C₂	1	1	yes	maximal, characteristic, complemented
14	#14558131	C₂	1	2	yes	maximal, complemented
15	#14558129	C₂	1	2	yes	maximal, complemented
16	#14558085	C₂	1	1	yes	maximal, characteristic, complemented
17	#14558063	C₂	1	1	yes	maximal, characteristic, complemented
18	#14558042	C₂	1	2	yes	maximal, complemented
19	C₂²⋊Q₈×D₃₇	C₂	1	2	yes	maximal, complemented
20	#14558015	C₂	1	1	yes	maximal, characteristic, complemented
21	#14558014	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#11924498	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₇×#554	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#10596966	C₂²	1	1	yes	characteristic
25	C₂×#10596962	C₂²	1	1	yes	characteristic
26	C₂×#10596962	C₂²	1	2	yes	complemented
27	C₂×Q₈×D₃₇	C₂²	1	2	yes	complemented
28	C₂²×D₁₄₈	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₃₇	C₂²	1	2	yes	—
30	#11924535	C₂²	1	1	yes	characteristic, complemented
31	#11924535	C₂²	1	1	yes	characteristic, complemented
32	#11924534	C₂²	1	1	yes	characteristic, complemented
33	#11924531	C₂²	1	2	yes	complemented
34	#11924531	C₂²	1	2	yes	complemented
35	#11924531	C₂²	1	2	yes	complemented
36	#11924531	C₂²	1	1	yes	characteristic, complemented
37	#11924530	C₂²	1	2	yes	complemented
38	#11924529	C₂²	1	1	yes	characteristic, complemented
39	#11924526	C₂²	1	1	yes	characteristic, complemented
40	#11924526	C₂²	1	2	yes	complemented
41	#11924526	C₂²	1	2	yes	complemented
42	#11924525	C₂²	1	1	yes	characteristic
43	#11924525	C₂²	1	2	yes	complemented
44	#11924524	C₂²	1	1	yes	characteristic
45	#11924522	C₂²	1	2	yes	complemented
46	#11924522	C₂²	1	1	yes	characteristic, complemented
47	#11924521	C₂²	1	2	yes	—
48	#11924521	C₂²	1	2	yes	—
49	#11924521	C₂²	1	2	yes	complemented
50	#11924521	C₂²	1	2	yes	complemented
51	#11924521	C₂²	1	2	yes	complemented
52	#11924520	C₂²	1	1	yes	characteristic
53	#11924519	C₂²	1	2	yes	complemented
54	#11924518	C₂²	1	2	yes	complemented
55	#11924518	C₂²	1	2	yes	complemented
56	#11924517	C₂²	1	1	yes	characteristic
57	#11924516	C₂²	1	1	yes	characteristic, complemented
58	#11924516	C₂²	1	2	yes	complemented
59	#11924515	C₂²	1	2	yes	—
60	#11924515	C₂²	1	1	yes	characteristic
61	#11924514	C₂²	1	2	yes	complemented
62	#11924514	C₂²	1	2	yes	complemented
63	#11924514	C₂²	1	2	yes	complemented
64	#11924514	C₂²	1	2	yes	complemented
65	#11924514	C₂²	1	2	yes	complemented
66	#11924513	C₂²	1	1	yes	characteristic
67	#11924513	C₂²	1	2	yes	—
68	#11924512	C₂²	1	2	yes	complemented
69	#11924512	C₂²	1	2	yes	complemented
70	#11924511	C₂²	1	2	yes	—
71	#11924511	C₂²	1	1	yes	characteristic
72	#11924510	C₂²	1	1	yes	characteristic
73	#11924509	C₂²	1	2	yes	—
74	#11924509	C₂²	1	2	yes	complemented
75	#11924508	C₂²	1	1	yes	characteristic
76	#11924506	C₂²	1	2	yes	—
77	#11924504	C₂²	1	2	yes	—
78	Q₈×Dic₃₇	C₂²	1	1	yes	characteristic, complemented
79	C₄×Dic₇₄	C₂²	1	1	yes	characteristic, complemented
80	#11924501	C₂²	1	2	yes	complemented
81	#11924501	C₂²	1	1	yes	characteristic, complemented
82	#11924501	C₂²	1	1	yes	characteristic, complemented
83	C₄×D₁₄₈	C₂²	1	1	yes	characteristic
84	C₄×D₁₄₈	C₂²	1	2	yes	complemented
85	#11924498	C₂²	1	2	yes	—
86	#11924498	C₂²	1	1	yes	characteristic
87	#11924498	C₂²	1	1	yes	characteristic
88	#11924498	C₂²	1	2	yes	—
89	#11924498	C₂²	1	1	yes	characteristic
90	#11924498	C₂²	1	1	yes	characteristic
91	#11924498	C₂²	1	1	yes	characteristic
92	#11924498	C₂²	1	2	yes	complemented
93	C₄×C₂²⋊D₃₇	C₂²	1	2	yes	—
94	C₄×C₂²⋊D₃₇	C₂²	1	1	yes	characteristic
95	C₄×C₂²⋊D₃₇	C₂²	1	2	yes	complemented
96	C₄×C₂²⋊D₃₇	C₂²	1	2	yes	complemented
97	C₄×C₂²⋊D₃₇	C₂²	1	1	yes	characteristic, complemented
98	#11924495	C₂²	1	1	yes	characteristic, complemented
99	#11924494	C₂²	1	2	yes	complemented
100	#11924493	C₂²	1	2	yes	complemented
101	#11924493	C₂²	1	2	yes	complemented
102	#11924493	C₂²	1	1	yes	characteristic, complemented
103	#11924492	C₂²	1	2	yes	—
104	C₄⋊C₄×D₃₇	C₂²	1	2	yes	complemented
105	C₄⋊C₄×D₃₇	C₂²	1	1	yes	characteristic, complemented
106	C₄⋊C₄×D₃₇	C₂²	1	2	yes	complemented
107	C₄⋊C₄×D₃₇	C₂²	1	2	yes	complemented
108	C₂×#10596938	C₂²	1	2	yes	—
109	C₂²⋊C₄×D₃₇	C₂²	1	2	yes	—
110	C₂²⋊C₄×D₃₇	C₂²	1	2	yes	—
111	C₂×C₄×Dic₃₇	C₂²	1	1	yes	characteristic
112	C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic, complemented
113	#125×C₃₇	C₂²	1	2	yes	complemented
114	C₂²⋊Q₈×C₃₇	C₂²	1	2	yes	—
115	C₂²⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic
116	C₂²⋊Q₈×C₃₇	C₂²	1	2	yes	complemented
117	C₂²⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic, complemented
118	C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₄×C₃₇	C₂²	1	2	yes	—
120	C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₃₇	C₂³	1	2	yes	—
124	C₂×Q₈×C₃₇	C₂³	1	1	yes	characteristic
125	C₂×Q₈×C₃₇	C₂³	1	2	yes	—
126	C₂×D₄×C₃₇	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₃₇	C₂³	1	2	yes	—
130	C₂²×C₄×C₃₇	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₃₇	C₂³	1	1	yes	characteristic
132	C₂×C₂²⋊D₃₇	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₃₇	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊D₃₇	C₂³	1	2	yes	—
135	C₂²×Dic₃₇	C₂³	1	1	yes	characteristic
136	C₂²×Dic₃₇	C₂³	1	1	yes	characteristic
137	#10596966	—	2	4	no	—
138	Q₈×D₃₇	—	4	4	no	—
139	#10596962	—	2	4	no	—
140	#10596962	—	4	4	no	—
141	C₂×D₁₄₈	—	2	4	no	—
142	C₂×D₁₄₈	C₂³	1	2	yes	—
143	C₂×D₁₄₈	C₂³	1	1	yes	characteristic
144	C₂×D₁₄₈	C₂³	1	2	yes	—
145	C₂×D₁₄₈	C₂³	1	2	yes	—
146	C₂×D₁₄₈	C₂³	1	1	yes	characteristic
147	C₂×C₄×D₃₇	—	4	4	no	—
148	C₂×C₄×D₃₇	C₂³	1	2	yes	—
149	C₂×C₄×D₃₇	C₂³	1	2	yes	—
150	C₂×C₄×D₃₇	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₃₇	C₂³	1	2	yes	—
152	C₂×C₄×D₃₇	C₂³	1	2	yes	—
153	C₂×C₄×D₃₇	C₂³	1	2	yes	—
154	C₂×C₄×D₃₇	C₂³	1	2	yes	—
155	C₂×C₄×D₃₇	C₂³	1	2	yes	—
156	C₂×C₄×D₃₇	C₂³	1	2	yes	—
157	C₂×C₄×D₃₇	C₂³	1	2	yes	—
158	C₂×Dic₇₄	C₂³	1	1	yes	characteristic
159	C₂×Dic₇₄	C₂³	1	2	yes	—
160	C₂×Dic₇₄	C₂³	1	1	yes	characteristic
161	C₂×Dic₇₄	C₂³	1	2	yes	—
162	C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
163	C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
164	C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
165	C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
166	C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
167	C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
168	C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
169	C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
170	C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
171	C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
172	C₂²⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
173	C₂²⋊C₄×C₃₇	C₂³	1	2	yes	—
174	C₂²⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
175	C₂²⋊C₄×C₃₇	C₂³	1	2	yes	—
176	C₄²×C₃₇	C₂³	1	2	yes	—
177	C₄²×C₃₇	C₂³	1	1	yes	characteristic
178	C₂²⋊Dic₃₇	C₂³	1	1	yes	characteristic
179	C₂²⋊Dic₃₇	C₂³	1	2	yes	—
180	C₂²⋊Dic₃₇	C₂³	1	1	yes	characteristic
181	C₂²⋊Dic₃₇	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₃₇	C₂³	1	1	yes	characteristic
183	#10596938	C₂³	1	2	yes	—
184	#10596938	C₂³	1	2	yes	—
185	#10596938	C₂³	1	2	yes	—
186	#10596938	C₂³	1	2	yes	—
187	#10596938	C₂³	1	2	yes	—
188	#10596938	C₂³	1	2	yes	—
189	#10596938	C₂³	1	2	yes	—
190	#10596938	C₂³	1	2	yes	—
191	#10596938	C₂³	1	1	yes	characteristic
192	#10596938	C₂³	1	2	yes	—
193	#10596938	C₂³	1	1	yes	characteristic
194	#10596938	C₂³	1	2	yes	—
195	#10596938	C₂³	1	2	yes	—
196	#10596938	C₂³	1	2	yes	—
197	#10596938	C₂³	1	2	yes	—
198	#10596938	C₂³	1	1	yes	characteristic
199	#10596938	C₂³	1	1	yes	characteristic
200	C₄⋊Dic₃₇	C₂³	1	1	yes	characteristic
201	C₄⋊Dic₃₇	C₂³	1	1	yes	characteristic
202	C₄⋊Dic₃₇	C₂³	1	2	yes	—
203	C₄⋊Dic₃₇	C₂³	1	2	yes	—
204	C₄⋊Dic₃₇	C₂³	1	1	yes	characteristic
205	C₄⋊Dic₃₇	C₂³	1	1	yes	characteristic
206	#10596936	C₂³	1	1	yes	characteristic
207	#10596936	C₂³	1	2	yes	—
208	#10596936	C₂³	1	1	yes	characteristic
209	#10596936	C₂³	1	2	yes	—
210	#10596936	C₂³	1	2	yes	—
211	#10596936	C₂³	1	2	yes	—
212	#10596936	C₂³	1	2	yes	—
213	#10596936	C₂³	1	2	yes	—
214	#10596936	C₂³	1	1	yes	characteristic
215	#10596936	C₂³	1	1	yes	characteristic
216	#10596936	C₂³	1	2	yes	—
217	#10596936	C₂³	1	1	yes	characteristic
218	#10596936	C₂³	1	2	yes	—
219	#10596936	C₂³	1	1	yes	characteristic
220	C₄×Dic₃₇	C₂³	1	1	yes	characteristic
221	C₄×Dic₃₇	C₂³	1	1	yes	characteristic
222	C₄×Dic₃₇	C₂³	1	1	yes	characteristic
223	C₄×Dic₃₇	C₂³	1	1	yes	characteristic
224	C₄×Dic₃₇	C₂³	1	2	yes	—
225	C₄×Dic₃₇	C₂³	1	2	yes	—
226	C₄×Dic₃₇	C₂³	1	2	yes	—
227	C₄×Dic₃₇	C₂³	1	1	yes	characteristic
228	C₂³×C₃₇	C₂⁴	1	1	yes	characteristic
229	C₂³×C₃₇	C₂⁴	1	1	yes	characteristic
230	C₂²×D₃₇	—	2	4	no	—
231	C₂²×D₃₇	—	2	4	no	—
232	C₂²×D₃₇	—	4	2	no	—
233	C₂²×D₃₇	C₂⁴	1	2	yes	—
234	C₂²×D₃₇	C₂⁴	1	1	yes	characteristic
235	C₂²×D₃₇	C₂⁴	1	2	yes	—
236	Q₈×C₃₇	—	2	2	no	—
237	Q₈×C₃₇	—	4	2	no	—
238	D₄×C₃₇	—	2	2	no	—
239	C₂×C₄×C₃₇	—	2	2	no	—
240	C₂×C₄×C₃₇	—	2	2	no	—
241	C₂×C₄×C₃₇	—	4	2	no	—
242	C₂×C₄×C₃₇	—	4	2	no	—
243	C₂×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₃₇	C₂⁴	1	2	yes	—
245	C₂×C₄×C₃₇	C₂⁴	1	2	yes	—
246	C₂×C₄×C₃₇	C₂⁴	1	2	yes	—
247	C₂×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₃₇	C₂⁴	1	2	yes	—
251	C₂×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
252	C₂²⋊D₃₇	—	2	2	no	—
253	C₂²⋊D₃₇	—	2	4	no	—
254	C₂²⋊D₃₇	—	2	2	no	—
255	C₂²⋊D₃₇	—	4	2	no	—
256	C₂×Dic₃₇	—	2	2	no	—
257	C₂×Dic₃₇	—	2	2	no	—
258	C₂×Dic₃₇	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₃₇	C₂⁴	1	1	yes	characteristic
260	C₂×Dic₃₇	C₂⁴	1	1	yes	characteristic
261	C₂×Dic₃₇	C₂⁴	1	2	yes	—
262	C₂×Dic₃₇	C₂⁴	1	1	yes	characteristic
263	C₂×Dic₃₇	C₂⁴	1	2	yes	—
264	C₂×Dic₃₇	C₂⁴	1	1	yes	characteristic
265	C₂×Dic₃₇	C₂⁴	1	1	yes	characteristic
266	C₂×Dic₃₇	C₂⁴	1	1	yes	characteristic
267	D₁₄₈	—	2	4	no	—
268	D₁₄₈	—	2	4	no	—
269	D₁₄₈	—	2	2	no	—
270	D₁₄₈	—	4	2	no	—
271	D₁₄₈	#41	1	4	yes	complemented
272	C₄×D₃₇	—	2	4	no	—
273	C₄×D₃₇	—	2	4	no	—
274	C₄×D₃₇	—	2	2	no	—
275	C₄×D₃₇	—	2	4	no	—
276	C₄×D₃₇	—	2	4	no	—
277	C₄×D₃₇	—	4	2	no	—
278	C₄×D₃₇	—	4	2	no	—
279	C₄×D₃₇	—	4	2	no	—
280	C₄×D₃₇	—	4	2	no	—
281	C₄×D₃₇	—	4	2	no	—
282	Dic₇₄	—	2	2	no	—
283	Dic₇₄	—	2	4	no	—
284	Dic₇₄	—	2	2	no	—
285	Dic₇₄	—	4	2	no	—
286	C₂²×C₃₇	—	2	1	no	—
287	C₂²×C₃₇	—	2	1	no	—
288	C₂²×C₃₇	—	2	1	no	—
289	C₂²×C₃₇	—	2	1	no	—
290	C₂²×C₃₇	—	2	1	no	—
291	C₂²×C₃₇	2₋¹⁺⁴	1	2	yes	—
292	C₂²×C₃₇	C₂⁵	1	1	yes	characteristic
293	C₂×D₃₇	—	2	2	no	—
294	C₂×D₃₇	—	2	2	no	—
295	C₂×D₃₇	—	2	1	no	—
296	C₂×D₃₇	—	2	2	no	—
297	C₂×D₃₇	—	2	2	no	—
298	C₂×D₃₇	—	2	1	no	—
299	C₂×D₃₇	—	2	1	no	—
300	C₂×D₃₇	—	2	2	no	—
301	C₂×D₃₇	—	4	8	no	—
302	C₂×D₃₇	C₂×#41	1	4	yes	—
303	C₄×C₃₇	—	2	1	no	—
304	C₄×C₃₇	—	2	2	no	—
305	C₄×C₃₇	—	2	1	no	—
306	C₄×C₃₇	—	2	1	no	—
307	C₄×C₃₇	—	2	2	no	—
308	C₄×C₃₇	—	2	2	no	—
309	C₄×C₃₇	—	2	2	no	—
310	C₄×C₃₇	—	2	1	no	—
311	C₄×C₃₇	C₂×#41	1	2	yes	—
312	Dic₃₇	—	2	2	no	—
313	Dic₃₇	—	2	1	no	—
314	Dic₃₇	—	2	1	no	—
315	Dic₃₇	—	2	2	no	—
316	Dic₃₇	—	2	1	no	—
317	Dic₃₇	—	2	1	no	—
318	Dic₃₇	—	2	1	no	—
319	Dic₃₇	—	2	1	no	—
320	Dic₃₇	H(5,𝔽₂)	1	2	yes	—
321	#3520	—	37	1	no	maximal, Sylow
322	C₂×C₃₇	—	2	2	no	—
323	C₂×C₃₇	—	4	1	no	—
324	C₂×C₃₇	C₂²×#41	1	1	yes	characteristic
325	C₂×C₃₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
326	C₂×C₃₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
327	D₃₇	—	2	4	no	—
328	D₃₇	—	4	1	no	—
329	D₃₇	—	4	2	no	—
330	#556	—	37	1	no	—
331	#554	—	37	1	no	—
332	#554	D₃₇	1	1	yes	characteristic, complemented
333	#552	—	37	2	no	—
334	#551	—	37	2	no	—
335	#551	—	37	2	no	—
336	D₄×Q₈	—	37	1	no	—
337	#548	—	37	2	no	—
338	#547	—	37	1	no	—
339	#547	—	37	1	no	—
340	#546	—	37	1	no	—
341	#546	—	37	1	no	—
342	#542	—	37	1	no	—
343	#542	—	37	1	no	—
344	#539	—	37	2	no	—
345	#539	—	37	2	no	—
346	#533	—	37	1	no	—
347	#529	—	37	1	no	—
348	#525	—	37	2	no	—
349	C₂×C₂²⋊Q₈	—	37	2	no	—
350	#520	—	37	1	no	—
351	#520	—	37	1	no	—
352	C₂×C₄×D₄	—	37	1	no	—
353	C₃₇	#3520	1	1	yes	characteristic, complemented, Sylow
354	C₂×#41	—	37	1	no	—
355	C₂×#41	—	37	1	no	—
356	C₂×#41	—	37	2	no	—
357	C₂²×Q₈	—	37	2	no	—
358	C₂²×D₄	—	37	1	no	—
359	C₂³×C₄	—	37	2	no	—
360	C₄⋊Q₈	—	37	1	no	—
361	C₄⋊Q₈	—	37	1	no	—
362	C₄⋊Q₈	—	37	1	no	—
363	C₄⋊Q₈	C₂×D₃₇	1	1	yes	characteristic, complemented
364	#126	—	37	1	no	—
365	#126	—	37	2	no	—
366	#126	—	37	2	no	—
367	#126	—	37	2	no	—
368	#126	—	37	1	no	—
369	#126	—	37	2	no	—
370	#125	—	37	1	no	—
371	#125	—	37	2	no	—
372	#125	—	37	2	no	—
373	#125	C₂×D₃₇	1	2	yes	complemented
374	#124	—	37	1	no	—
375	#124	—	37	2	no	—
376	#124	—	37	1	no	—
377	#124	—	37	2	no	—
378	#124	—	37	1	no	—
379	#123	—	37	1	no	—
380	#123	—	37	2	no	—
381	#123	—	37	2	no	—
382	#123	—	37	2	no	—
383	#123	—	37	2	no	—
384	#123	—	37	2	no	—
385	#123	—	37	2	no	—
386	#123	—	37	2	no	—
387	#123	—	37	1	no	—
388	#123	—	37	2	no	—
389	C₂²⋊Q₈	—	37	2	no	—
390	C₂²⋊Q₈	—	37	2	no	—
391	C₂²⋊Q₈	—	37	2	no	—
392	C₂²⋊Q₈	—	37	1	no	—
393	C₂²⋊Q₈	—	37	2	no	—
394	C₂²⋊Q₈	—	37	2	no	—
395	C₂²⋊Q₈	—	37	2	no	—
396	C₂²⋊Q₈	—	37	2	no	—
397	C₂²⋊Q₈	—	37	2	no	—
398	C₂²⋊Q₈	—	37	2	no	—
399	C₂²⋊Q₈	—	37	1	no	—
400	C₂²⋊Q₈	—	37	1	no	—
401	C₂²⋊Q₈	—	37	2	no	—
402	C₂²⋊Q₈	C₂×D₃₇	1	2	yes	—
403	C₂²⋊Q₈	C₂×D₃₇	1	1	yes	characteristic
404	C₂²⋊Q₈	C₂×D₃₇	1	2	yes	complemented
405	C₂²⋊Q₈	C₂×D₃₇	1	1	yes	characteristic, complemented
406	#121	—	37	1	no	—
407	#121	—	37	1	no	—
408	#121	—	37	2	no	—
409	#121	—	37	1	no	—
410	#121	—	37	2	no	—
411	#121	—	37	2	no	—
412	#120	—	37	2	no	—
413	#120	—	37	2	no	—
414	C₄×Q₈	—	37	1	no	—
415	C₄×Q₈	—	37	1	no	—
416	C₄×Q₈	—	37	1	no	—
417	C₄×Q₈	—	37	2	no	—
418	C₄×Q₈	—	37	1	no	—
419	C₄×Q₈	C₂×D₃₇	1	1	yes	characteristic, complemented
420	C₄×D₄	—	37	2	no	—
421	C₄×D₄	—	37	2	no	—
422	C₄×D₄	—	37	2	no	—
423	C₄×D₄	—	37	1	no	—
424	C₄×D₄	—	37	1	no	—
425	C₄×D₄	—	37	1	no	—
426	C₄×D₄	—	37	2	no	—
427	C₄×D₄	—	37	1	no	—
428	C₄×D₄	—	37	1	no	—
429	C₄×D₄	—	37	1	no	—
430	C₄×D₄	—	37	2	no	—
431	C₄×D₄	—	37	1	no	—
432	C₄×D₄	—	37	2	no	—
433	C₄×D₄	—	37	2	no	—
434	C₄×D₄	—	37	1	no	—
435	C₄×D₄	C₂×D₃₇	1	2	yes	—
436	C₄×D₄	C₂×D₃₇	1	1	yes	characteristic
437	#117	—	37	1	no	—
438	#117	—	37	2	no	—
439	#117	—	37	2	no	—
440	#117	—	37	1	no	—
441	#117	—	37	2	no	—
442	#117	—	37	2	no	—
443	C₂×C₄⋊C₄	—	37	2	no	—
444	C₂×C₄⋊C₄	—	37	2	no	—
445	C₂×C₄⋊C₄	—	37	1	no	—
446	C₂×C₄⋊C₄	—	37	2	no	—
447	C₂×C₄⋊C₄	C₂×D₃₇	1	1	yes	characteristic
448	C₂×C₄⋊C₄	C₂×D₃₇	1	1	yes	characteristic, complemented
449	C₂×C₂²⋊C₄	—	37	2	no	—
450	C₂×C₂²⋊C₄	—	37	2	no	—
451	C₂×C₂²⋊C₄	—	37	2	no	—
452	C₂×C₄²	—	37	1	no	—
453	C₂⁴	—	37	2	no	—
454	#41	—	74	4	no	—
455	#41	—	74	4	no	—
456	#41	—	148	4	no	—
457	C₂×Q₈	—	37	1	no	—
458	C₂×Q₈	—	37	1	no	—
459	C₂×Q₈	—	37	2	no	—
460	C₂×Q₈	—	37	2	no	—
461	C₂×Q₈	—	148	4	no	—
462	C₂×Q₈	C₂²×D₃₇	1	1	yes	characteristic
463	C₂×Q₈	C₂²×D₃₇	1	2	yes	—
464	C₂×D₄	—	37	1	no	—
465	C₂×D₄	—	37	2	no	—
466	C₂×D₄	—	37	1	no	—
467	C₂×D₄	—	37	2	no	—
468	C₂×D₄	—	37	1	no	—
469	C₂×D₄	—	37	2	no	—
470	C₂×D₄	—	37	2	no	—
471	C₂×D₄	—	37	1	no	—
472	C₂×D₄	—	37	2	no	—
473	C₂×D₄	—	74	4	no	—
474	C₂×D₄	C₂²×D₃₇	1	1	yes	characteristic
475	C₂²×C₄	—	37	1	no	—
476	C₂²×C₄	—	37	1	no	—
477	C₂²×C₄	—	37	2	no	—
478	C₂²×C₄	—	37	2	no	—
479	C₂²×C₄	—	37	1	no	—
480	C₂²×C₄	—	37	2	no	—
481	C₂²×C₄	—	37	2	no	—
482	C₂²×C₄	—	37	2	no	—
483	C₂²×C₄	—	37	2	no	—
484	C₂²×C₄	—	37	2	no	—
485	C₂²×C₄	—	37	2	no	—
486	C₂²×C₄	—	37	2	no	—
487	C₂²×C₄	—	148	4	no	—
488	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
489	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
490	C₂²×C₄	C₂²×D₃₇	1	2	yes	—
491	C₂²×C₄	C₂²×D₃₇	1	2	yes	—
492	C₄⋊C₄	—	37	1	no	—
493	C₄⋊C₄	—	37	2	no	—
494	C₄⋊C₄	—	37	1	no	—
495	C₄⋊C₄	—	37	2	no	—
496	C₄⋊C₄	—	37	2	no	—
497	C₄⋊C₄	—	37	2	no	—
498	C₄⋊C₄	—	37	1	no	—
499	C₄⋊C₄	—	37	1	no	—
500	C₄⋊C₄	—	37	2	no	—
501	C₄⋊C₄	—	37	2	no	—
502	C₄⋊C₄	—	37	2	no	—
503	C₄⋊C₄	—	37	1	no	—
504	C₄⋊C₄	—	37	2	no	—
505	C₄⋊C₄	—	37	1	no	—
506	C₄⋊C₄	—	37	1	no	—
507	C₄⋊C₄	—	37	1	no	—
508	C₄⋊C₄	—	37	2	no	—
509	C₄⋊C₄	—	37	2	no	—
510	C₄⋊C₄	—	37	1	no	—
511	C₄⋊C₄	—	37	1	no	—
512	C₄⋊C₄	C₂²×D₃₇	1	1	yes	characteristic
513	C₄⋊C₄	C₂²×D₃₇	1	2	yes	—
514	C₄⋊C₄	C₂²×D₃₇	1	2	yes	—
515	C₄⋊C₄	C₂²×D₃₇	1	2	yes	—
516	C₄⋊C₄	C₂²×D₃₇	1	2	yes	—
517	C₄⋊C₄	C₂²×D₃₇	1	1	yes	characteristic
518	C₄⋊C₄	C₂²×D₃₇	1	1	yes	characteristic
519	C₄⋊C₄	C₂²×D₃₇	1	2	yes	—
520	C₄⋊C₄	C₂²×D₃₇	1	1	yes	characteristic
521	C₄⋊C₄	C₂²×D₃₇	1	2	yes	—
522	C₂²⋊C₄	—	37	1	no	—
523	C₂²⋊C₄	—	37	2	no	—
524	C₂²⋊C₄	—	37	1	no	—
525	C₂²⋊C₄	—	37	1	no	—
526	C₂²⋊C₄	—	37	1	no	—
527	C₂²⋊C₄	—	37	2	no	—
528	C₂²⋊C₄	—	37	2	no	—
529	C₂²⋊C₄	—	37	2	no	—
530	C₂²⋊C₄	—	37	2	no	—
531	C₂²⋊C₄	—	37	2	no	—
532	C₂²⋊C₄	—	37	2	no	—
533	C₂²⋊C₄	—	37	2	no	—
534	C₂²⋊C₄	—	37	2	no	—
535	C₂²⋊C₄	—	37	2	no	—
536	C₂²⋊C₄	—	37	2	no	—
537	C₂²⋊C₄	—	37	1	no	—
538	C₂²⋊C₄	—	37	1	no	—
539	C₂²⋊C₄	—	37	2	no	—
540	C₂²⋊C₄	—	37	2	no	—
541	C₂²⋊C₄	—	37	1	no	—
542	C₂²⋊C₄	—	37	2	no	—
543	C₂²⋊C₄	—	37	1	no	—
544	C₂²⋊C₄	C₂²×D₃₇	1	1	yes	characteristic
545	C₂²⋊C₄	C₂²×D₃₇	1	2	yes	—
546	C₂²⋊C₄	C₂²×D₃₇	1	1	yes	characteristic
547	C₂²⋊C₄	C₂²×D₃₇	1	2	yes	—
548	C₄²	—	37	1	no	—
549	C₄²	—	37	1	no	—
550	C₄²	—	37	1	no	—
551	C₄²	—	37	1	no	—
552	C₄²	—	37	2	no	—
553	C₄²	—	37	2	no	—
554	C₄²	—	37	2	no	—
555	C₄²	—	37	1	no	—
556	C₄²	C₂²×D₃₇	1	2	yes	—
557	C₄²	C₂²×D₃₇	1	1	yes	characteristic
558	C₂³	—	37	2	no	—
559	C₂³	—	37	2	no	—
560	C₂³	—	37	1	no	—
561	C₂³	—	74	4	no	—
562	C₂³	—	74	4	no	—
563	C₂³	—	148	2	no	—
564	C₂³	C₂³×D₃₇	1	1	yes	characteristic
565	C₂³	C₂³×D₃₇	1	1	yes	characteristic
566	Q₈	—	2	2	no	—
567	Q₈	—	4	2	no	—
568	Q₈	—	74	2	no	—
569	Q₈	—	74	4	no	—
570	Q₈	—	74	2	no	—
571	Q₈	—	148	2	no	—
572	D₄	—	2	2	no	—
573	D₄	—	37	4	no	—
574	D₄	—	74	4	no	—
575	D₄	—	74	4	no	—
576	D₄	—	74	2	no	—
577	D₄	—	74	4	no	—
578	D₄	—	74	2	no	—
579	D₄	—	74	2	no	—
580	D₄	—	148	2	no	—
581	D₄	—	148	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	4	2	no	—
585	C₂×C₄	—	4	2	no	—
586	C₂×C₄	—	37	1	no	—
587	C₂×C₄	—	37	1	no	—
588	C₂×C₄	—	37	1	no	—
589	C₂×C₄	—	37	1	no	—
590	C₂×C₄	—	37	2	no	—
591	C₂×C₄	—	37	1	no	—
592	C₂×C₄	—	37	1	no	—
593	C₂×C₄	—	37	2	no	—
594	C₂×C₄	—	37	1	no	—
595	C₂×C₄	—	74	4	no	—
596	C₂×C₄	—	74	4	no	—
597	C₂×C₄	—	74	4	no	—
598	C₂×C₄	—	74	4	no	—
599	C₂×C₄	—	74	2	no	—
600	C₂×C₄	—	74	2	no	—
601	C₂×C₄	—	74	2	no	—
602	C₂×C₄	—	148	2	no	—
603	C₂×C₄	—	148	2	no	—
604	C₂×C₄	—	148	2	no	—
605	C₂×C₄	—	148	2	no	—
606	C₂×C₄	—	148	2	no	—
607	C₂×C₄	C₂³×D₃₇	1	1	yes	characteristic
608	C₂×C₄	C₂³×D₃₇	1	2	yes	—
609	C₂×C₄	C₂³×D₃₇	1	2	yes	—
610	C₂×C₄	C₂³×D₃₇	1	2	yes	—
611	C₂×C₄	C₂³×D₃₇	1	1	yes	characteristic
612	C₂×C₄	C₂³×D₃₇	1	1	yes	characteristic
613	C₂×C₄	C₂³×D₃₇	1	1	yes	characteristic
614	C₂×C₄	C₂³×D₃₇	1	2	yes	—
615	C₂×C₄	C₂³×D₃₇	1	1	yes	characteristic
616	C₂²	—	2	1	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	2	1	no	—
619	C₂²	—	2	1	no	—
620	C₂²	—	2	1	no	—
621	C₂²	—	37	4	no	—
622	C₂²	—	74	2	no	—
623	C₂²	—	74	2	no	—
624	C₂²	—	74	1	no	—
625	C₂²	—	74	2	no	—
626	C₂²	—	74	2	no	—
627	C₂²	—	74	1	no	—
628	C₂²	—	74	1	no	—
629	C₂²	—	74	2	no	—
630	C₂²	—	148	8	no	—
631	C₂²	#11924584	1	2	yes	—
632	C₂²	C₂⁴×D₃₇	1	1	yes	characteristic
633	C₄	—	2	1	no	—
634	C₄	—	2	1	no	—
635	C₄	—	2	2	no	—
636	C₄	—	2	2	no	—
637	C₄	—	2	2	no	—
638	C₄	—	2	2	no	—
639	C₄	—	2	1	no	—
640	C₄	—	2	1	no	—
641	C₄	—	37	2	no	—
642	C₄	—	74	1	no	—
643	C₄	—	74	2	no	—
644	C₄	—	74	1	no	—
645	C₄	—	74	2	no	—
646	C₄	—	74	1	no	—
647	C₄	—	74	1	no	—
648	C₄	—	74	1	no	—
649	C₄	—	74	1	no	—
650	C₄	#41×D₃₇	1	2	yes	—
651	C₂	—	2	2	no	—
652	C₂	—	4	1	no	—
653	C₂	—	74	4	no	—
654	C₂	—	148	2	no	—
655	C₂	—	148	1	no	—
656	C₂	C₂×#41×D₃₇	1	1	yes	characteristic
657	C₂	H(5,𝔽₂)×D₃₇	1	1	yes	characteristic
658	C₂	C₂×#11924584	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₃₇
commutator, socle, cosocle	C₂²×C₃₇	C₂⁵
Fitting	C₃₇×#554	C₂
hypercenter	#554	D₃₇
hypocenter	C₃₇	#3520
LCS	G ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ #554

Complements

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

N	H ≅ G/N	type
1. #14558255	C₂	semidirect
2. #14558238	C₂	semidirect
3. #14558215	C₂	semidirect
4. #14558212	C₂	semidirect
5. #14558210	C₂	semidirect
6. #14558198	C₂	semidirect
7. #14558193	C₂	semidirect
8. #14558185	C₂	semidirect
9. #14558184	C₂	semidirect
10. #14558179	C₂	semidirect
11. #14558174	C₂	semidirect
12. #14558157	C₂	semidirect
13. #14558156	C₂	semidirect
14. #14558131	C₂	semidirect
15. #14558129	C₂	semidirect
16. #14558085	C₂	semidirect
17. #14558063	C₂	semidirect
18. #14558042	C₂	semidirect
19. C₂²⋊Q₈×D₃₇	C₂	semidirect
20. #14558015	C₂	semidirect
21. #14558014	C₂	semidirect
22. C₂×#11924498	C₂	semidirect
23. C₃₇×#554	C₂	semidirect
26. C₂×#10596962	C₂²	semidirect
27. C₂×Q₈×D₃₇	C₂²	semidirect
30. #11924535	C₂²	semidirect
31. #11924535	C₂²	semidirect
32. #11924534	C₂²	semidirect
33. #11924531	C₂²	semidirect
34. #11924531	C₂²	semidirect
35. #11924531	C₂²	semidirect
36. #11924531	C₂²	semidirect
37. #11924530	C₂²	semidirect
38. #11924529	C₂²	semidirect
39. #11924526	C₂²	semidirect
40. #11924526	C₂²	semidirect
41. #11924526	C₂²	semidirect
43. #11924525	C₂²	semidirect
45. #11924522	C₂²	semidirect
46. #11924522	C₂²	semidirect
49. #11924521	C₂²	semidirect
50. #11924521	C₂²	semidirect
51. #11924521	C₂²	semidirect
53. #11924519	C₂²	semidirect
54. #11924518	C₂²	semidirect
55. #11924518	C₂²	semidirect
57. #11924516	C₂²	semidirect
58. #11924516	C₂²	semidirect
61. #11924514	C₂²	semidirect
62. #11924514	C₂²	semidirect
63. #11924514	C₂²	semidirect
64. #11924514	C₂²	semidirect
65. #11924514	C₂²	semidirect
68. #11924512	C₂²	semidirect
69. #11924512	C₂²	semidirect
74. #11924509	C₂²	semidirect
78. Q₈×Dic₃₇	C₂²	semidirect
79. C₄×Dic₇₄	C₂²	semidirect
80. #11924501	C₂²	semidirect
81. #11924501	C₂²	semidirect
82. #11924501	C₂²	semidirect
84. C₄×D₁₄₈	C₂²	semidirect
92. #11924498	C₂²	semidirect
95. C₄×C₂²⋊D₃₇	C₂²	semidirect
96. C₄×C₂²⋊D₃₇	C₂²	semidirect
97. C₄×C₂²⋊D₃₇	C₂²	semidirect
98. #11924495	C₂²	semidirect
99. #11924494	C₂²	semidirect
100. #11924493	C₂²	semidirect
101. #11924493	C₂²	semidirect
102. #11924493	C₂²	semidirect
104. C₄⋊C₄×D₃₇	C₂²	semidirect
105. C₄⋊C₄×D₃₇	C₂²	semidirect
106. C₄⋊C₄×D₃₇	C₂²	semidirect
107. C₄⋊C₄×D₃₇	C₂²	semidirect
112. C₄⋊Q₈×C₃₇	C₂²	semidirect
113. #125×C₃₇	C₂²	semidirect
116. C₂²⋊Q₈×C₃₇	C₂²	semidirect
117. C₂²⋊Q₈×C₃₇	C₂²	semidirect
118. C₄×Q₈×C₃₇	C₂²	semidirect
122. C₂×C₄⋊C₄×C₃₇	C₂²	semidirect
271. D₁₄₈	#41	semidirect
332. #554	D₃₇	semidirect
353. C₃₇	#3520	semidirect
363. C₄⋊Q₈	C₂×D₃₇	semidirect
373. #125	C₂×D₃₇	semidirect
404. C₂²⋊Q₈	C₂×D₃₇	semidirect
405. C₂²⋊Q₈	C₂×D₃₇	semidirect
419. C₄×Q₈	C₂×D₃₇	semidirect
448. C₂×C₄⋊C₄	C₂×D₃₇	semidirect

Maximal subgroups

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

subgroup	index
#14558255	2
#14558238	2
#14558215	2
#14558212	2
#14558210	2
#14558198	2
#14558193	2
#14558185	2
#14558184	2
#14558179	2
#14558174	2
#14558157	2
#14558156	2
#14558131	2
#14558129	2
#14558085	2
#14558063	2
#14558042	2
C₂²⋊Q₈×D₃₇	2
#14558015	2
#14558014	2
C₂×#11924498	2
C₃₇×#554	2
#3520	37