Subgroups — #18008207

Order 4736.

1242 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14558268	C₂	1	1	yes	maximal, characteristic, complemented
2	#14558244	C₂	1	1	yes	maximal, characteristic, complemented
3	#14558236	C₂	1	2	yes	maximal, complemented
4	#14558231	C₂	1	2	yes	maximal, complemented
5	#14558210	C₂	1	4	yes	maximal, complemented
6	#14558178	C₂	1	2	yes	maximal, complemented
7	#14558174	C₂	1	2	yes	maximal, complemented
8	D₄×D₁₄₈	C₂	1	1	yes	maximal, characteristic, complemented
9	#14558084	C₂	1	1	yes	maximal, characteristic, complemented
10	#14558069	C₂	1	2	yes	maximal, complemented
11	#14558068	C₂	1	2	yes	maximal, complemented
12	#14558046	C₂	1	4	yes	maximal, complemented
13	C₄×#10596966	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#10596964	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#11924498	C₂	1	2	yes	maximal, complemented
16	C₄×D₄×D₃₇	C₂	1	2	yes	maximal, complemented
17	C₃₇×#554	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#10596966	C₂²	1	1	yes	characteristic
19	C₂×#10596966	C₂²	1	2	yes	complemented
20	C₂×#10596964	C₂²	1	1	yes	characteristic
21	C₂²×D₁₄₈	C₂²	1	2	yes	—
22	C₂×D₄×D₃₇	C₂²	1	2	yes	—
23	C₂²×C₄×D₃₇	C₂²	1	4	yes	complemented
24	#11924533	C₂²	1	1	yes	characteristic
25	#11924531	C₂²	1	4	yes	complemented
26	#11924531	C₂²	1	4	yes	complemented
27	#11924527	C₂²	1	2	yes	complemented
28	#11924525	C₂²	1	2	yes	complemented
29	#11924525	C₂²	1	2	yes	complemented
30	#11924524	C₂²	1	2	yes	complemented
31	#11924521	C₂²	1	4	yes	complemented
32	#11924521	C₂²	1	4	yes	complemented
33	#11924521	C₂²	1	4	yes	complemented
34	#11924520	C₂²	1	4	yes	complemented
35	#11924516	C₂²	1	2	yes	complemented
36	#11924512	C₂²	1	4	yes	complemented
37	#11924511	C₂²	1	2	yes	—
38	#11924511	C₂²	1	2	yes	complemented
39	#11924511	C₂²	1	4	yes	complemented
40	#11924511	C₂²	1	2	yes	complemented
41	#11924510	C₂²	1	2	yes	—
42	#11924510	C₂²	1	4	yes	complemented
43	#11924506	C₂²	1	4	yes	—
44	#11924506	C₂²	1	4	yes	complemented
45	Q₈×Dic₃₇	C₂²	1	1	yes	characteristic, complemented
46	C₄×Dic₇₄	C₂²	1	1	yes	characteristic, complemented
47	#11924501	C₂²	1	1	yes	characteristic, complemented
48	C₄×D₁₄₈	C₂²	1	1	yes	characteristic
49	C₄×D₁₄₈	C₂²	1	2	yes	complemented
50	C₄×D₁₄₈	C₂²	1	2	yes	complemented
51	D₄×Dic₃₇	C₂²	1	1	yes	characteristic
52	#11924498	C₂²	1	2	yes	—
53	#11924498	C₂²	1	1	yes	characteristic
54	#11924498	C₂²	1	4	yes	complemented
55	#11924498	C₂²	1	2	yes	complemented
56	#11924498	C₂²	1	2	yes	complemented
57	#11924498	C₂²	1	4	yes	complemented
58	#11924498	C₂²	1	2	yes	complemented
59	#11924498	C₂²	1	2	yes	complemented
60	C₄×C₂²⋊D₃₇	C₂²	1	4	yes	complemented
61	C₄×C₂²⋊D₃₇	C₂²	1	2	yes	complemented
62	#11924496	C₂²	1	4	yes	complemented
63	#11924496	C₂²	1	2	yes	complemented
64	#11924494	C₂²	1	2	yes	complemented
65	#11924494	C₂²	1	1	yes	characteristic, complemented
66	#11924494	C₂²	1	1	yes	characteristic, complemented
67	#11924494	C₂²	1	4	yes	complemented
68	#11924492	C₂²	1	2	yes	complemented
69	C₄⋊C₄×D₃₇	C₂²	1	2	yes	complemented
70	C₂×#10596938	C₂²	1	4	yes	complemented
71	C₂²⋊C₄×D₃₇	C₂²	1	4	yes	complemented
72	C₂×C₄×Dic₃₇	C₂²	1	2	yes	complemented
73	C₄²×D₃₇	C₂²	1	2	yes	complemented
74	C₄²×D₃₇	C₂²	1	1	yes	characteristic, complemented
75	C₄⋊Q₈×C₃₇	C₂²	1	1	yes	characteristic, complemented
76	#125×C₃₇	C₂²	1	2	yes	complemented
77	C₂²⋊Q₈×C₃₇	C₂²	1	4	yes	complemented
78	C₂²⋊Q₈×C₃₇	C₂²	1	2	yes	complemented
79	C₄×Q₈×C₃₇	C₂²	1	1	yes	characteristic, complemented
80	C₄×D₄×C₃₇	C₂²	1	2	yes	—
81	C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₃₇	C₂²	1	2	yes	complemented
83	C₂³×D₃₇	C₂³	1	4	yes	—
84	C₂×Q₈×C₃₇	C₂³	1	1	yes	characteristic
85	C₂×Q₈×C₃₇	C₂³	1	2	yes	—
86	C₂×D₄×C₃₇	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₃₇	C₂³	1	2	yes	—
88	C₂²×C₄×C₃₇	C₂³	1	4	yes	—
89	C₂×C₂²⋊D₃₇	C₂³	1	4	yes	—
90	C₂×C₂²⋊D₃₇	C₂³	1	2	yes	—
91	C₂²×Dic₃₇	C₂³	1	2	yes	—
92	C₂²×Dic₃₇	C₂³	1	2	yes	—
93	#10596966	—	2	4	no	—
94	#10596966	—	4	4	no	—
95	#10596964	—	2	4	no	—
96	D₄×D₃₇	—	2	8	no	—
97	C₂×D₁₄₈	—	2	8	no	—
98	C₂×D₁₄₈	C₂³	1	4	yes	—
99	C₂×D₁₄₈	C₂³	1	2	yes	—
100	C₂×D₁₄₈	C₂³	1	2	yes	—
101	C₂×D₁₄₈	C₂³	1	2	yes	—
102	C₂×D₁₄₈	C₂³	1	2	yes	—
103	C₂×D₁₄₈	C₂³	1	4	yes	—
104	C₂×D₁₄₈	C₂³	1	1	yes	characteristic
105	C₂×C₄×D₃₇	—	4	8	no	—
106	C₂×C₄×D₃₇	C₂³	1	2	yes	—
107	C₂×C₄×D₃₇	C₂³	1	2	yes	—
108	C₂×C₄×D₃₇	C₂³	1	1	yes	characteristic
109	C₂×C₄×D₃₇	C₂³	1	1	yes	characteristic
110	C₂×C₄×D₃₇	C₂³	1	1	yes	characteristic
111	C₂×C₄×D₃₇	C₂³	1	2	yes	—
112	C₂×C₄×D₃₇	C₂³	1	4	yes	—
113	C₂×C₄×D₃₇	C₂³	1	4	yes	—
114	C₂×C₄×D₃₇	C₂³	1	4	yes	—
115	C₂×Dic₇₄	C₂³	1	1	yes	characteristic
116	C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
117	C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
118	C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
119	C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
120	C₄⋊C₄×C₃₇	C₂³	1	4	yes	—
121	C₄⋊C₄×C₃₇	C₂³	1	2	yes	—
122	C₄⋊C₄×C₃₇	C₂³	1	4	yes	—
123	C₂²⋊C₄×C₃₇	C₂³	1	4	yes	—
124	C₂²⋊C₄×C₃₇	C₂³	1	2	yes	—
125	C₄²×C₃₇	C₂³	1	1	yes	characteristic
126	C₄²×C₃₇	C₂³	1	2	yes	—
127	C₂²⋊Dic₃₇	C₂³	1	2	yes	—
128	#10596938	C₂³	1	4	yes	—
129	#10596938	C₂³	1	4	yes	—
130	#10596938	C₂³	1	2	yes	—
131	#10596938	C₂³	1	4	yes	—
132	#10596938	C₂³	1	4	yes	—
133	#10596938	C₂³	1	4	yes	—
134	#10596938	C₂³	1	2	yes	—
135	#10596938	C₂³	1	2	yes	—
136	#10596938	C₂³	1	2	yes	—
137	#10596938	C₂³	1	4	yes	—
138	#10596938	C₂³	1	4	yes	—
139	C₄⋊Dic₃₇	C₂³	1	1	yes	characteristic
140	C₄⋊Dic₃₇	C₂³	1	1	yes	characteristic
141	C₄⋊Dic₃₇	C₂³	1	2	yes	—
142	C₄⋊Dic₃₇	C₂³	1	4	yes	—
143	#10596936	C₂³	1	4	yes	—
144	#10596936	C₂³	1	2	yes	—
145	#10596936	C₂³	1	2	yes	—
146	C₄×Dic₃₇	C₂³	1	1	yes	characteristic
147	C₄×Dic₃₇	C₂³	1	1	yes	characteristic
148	C₄×Dic₃₇	C₂³	1	1	yes	characteristic
149	C₄×Dic₃₇	C₂³	1	2	yes	—
150	C₄×Dic₃₇	C₂³	1	2	yes	—
151	C₄×Dic₃₇	C₂³	1	2	yes	—
152	C₄×Dic₃₇	C₂³	1	2	yes	—
153	C₄×Dic₃₇	C₂³	1	2	yes	—
154	C₂³×C₃₇	C₂⁴	1	2	yes	—
155	C₂²×D₃₇	—	2	8	no	—
156	C₂²×D₃₇	—	2	8	no	—
157	C₂²×D₃₇	—	4	4	no	—
158	C₂²×D₃₇	C₂⁴	1	4	yes	—
159	C₂²×D₃₇	C₂⁴	1	1	yes	characteristic
160	C₂²×D₃₇	C₂⁴	1	2	yes	—
161	Q₈×C₃₇	—	2	2	no	—
162	Q₈×C₃₇	—	4	2	no	—
163	D₄×C₃₇	#41	1	4	yes	complemented
164	C₂×C₄×C₃₇	—	2	4	no	—
165	C₂×C₄×C₃₇	—	4	4	no	—
166	C₂×C₄×C₃₇	C₂⁴	1	2	yes	—
167	C₂×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
168	C₂×C₄×C₃₇	C₂⁴	1	2	yes	—
169	C₂×C₄×C₃₇	C₂⁴	1	2	yes	—
170	C₂×C₄×C₃₇	C₂⁴	1	4	yes	—
171	C₂×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
172	C₂×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
173	C₂²⋊D₃₇	—	2	8	no	—
174	C₂²⋊D₃₇	—	2	4	no	—
175	C₂×Dic₃₇	—	2	4	no	—
176	C₂×Dic₃₇	—	2	4	no	—
177	C₂×Dic₃₇	C₂⁴	1	1	yes	characteristic
178	C₂×Dic₃₇	C₂⁴	1	1	yes	characteristic
179	C₂×Dic₃₇	C₂⁴	1	2	yes	—
180	C₂×Dic₃₇	C₂⁴	1	2	yes	—
181	C₂×Dic₃₇	C₂⁴	1	2	yes	—
182	C₂×Dic₃₇	C₂⁴	1	1	yes	characteristic
183	D₁₄₈	—	2	8	no	—
184	D₁₄₈	—	2	4	no	—
185	D₁₄₈	—	2	4	no	—
186	D₁₄₈	—	2	4	no	—
187	D₁₄₈	—	4	4	no	—
188	D₁₄₈	—	4	2	no	—
189	D₁₄₈	#41	1	4	yes	complemented
190	C₄×D₃₇	—	2	4	no	—
191	C₄×D₃₇	—	2	4	no	—
192	C₄×D₃₇	—	2	2	no	—
193	C₄×D₃₇	—	2	2	no	—
194	C₄×D₃₇	—	2	4	no	—
195	C₄×D₃₇	—	2	8	no	—
196	C₄×D₃₇	—	2	2	no	—
197	C₄×D₃₇	—	4	4	no	—
198	C₄×D₃₇	—	4	4	no	—
199	Dic₇₄	—	2	2	no	—
200	C₂²×C₃₇	—	2	2	no	—
201	C₂²×C₃₇	—	2	2	no	—
202	C₂²×C₃₇	C₂×#41	1	4	yes	—
203	C₂²×C₃₇	C₂⁵	1	1	yes	characteristic
204	C₂×D₃₇	—	2	2	no	—
205	C₂×D₃₇	—	2	2	no	—
206	C₂×D₃₇	—	2	1	no	—
207	C₂×D₃₇	—	2	1	no	—
208	C₂×D₃₇	—	2	4	no	—
209	C₂×D₃₇	—	2	4	no	—
210	C₂×D₃₇	—	2	4	no	—
211	C₂×D₃₇	—	2	1	no	—
212	C₂×D₃₇	—	4	16	no	—
213	C₂×D₃₇	C₂×#41	1	4	yes	—
214	C₄×C₃₇	—	2	2	no	—
215	C₄×C₃₇	—	2	2	no	—
216	C₄×C₃₇	—	2	2	no	—
217	C₄×C₃₇	—	2	4	no	—
218	C₄×C₃₇	—	2	1	no	—
219	C₄×C₃₇	C₂×#41	1	2	yes	—
220	C₄×C₃₇	C₂×#41	1	2	yes	—
221	Dic₃₇	—	2	2	no	—
222	Dic₃₇	—	2	1	no	—
223	Dic₃₇	—	2	1	no	—
224	Dic₃₇	—	2	2	no	—
225	Dic₃₇	—	2	2	no	—
226	Dic₃₇	H(5,𝔽₂)	1	2	yes	—
227	#3481	—	37	1	no	maximal, Sylow
228	C₂×C₃₇	—	2	4	no	—
229	C₂×C₃₇	C₂²×#41	1	1	yes	characteristic
230	C₂×C₃₇	C₂²×#41	1	1	yes	characteristic
231	C₂×C₃₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
232	D₃₇	—	2	4	no	—
233	D₃₇	—	4	1	no	—
234	D₃₇	—	4	4	no	—
235	#559	—	37	1	no	—
236	#554	—	37	1	no	—
237	#554	D₃₇	1	1	yes	characteristic, complemented
238	#553	—	37	2	no	—
239	#553	—	37	2	no	—
240	#551	—	37	4	no	—
241	#546	—	37	2	no	—
242	#546	—	37	2	no	—
243	D₄²	—	37	1	no	—
244	#532	—	37	1	no	—
245	#529	—	37	2	no	—
246	#529	—	37	2	no	—
247	#525	—	37	4	no	—
248	C₄×#41	—	37	1	no	—
249	C₄×#41	—	37	1	no	—
250	C₂×C₄×D₄	—	37	2	no	—
251	C₂×C₄×D₄	—	37	2	no	—
252	C₃₇	#3481	1	1	yes	characteristic, complemented, Sylow
253	C₂×#41	—	37	1	no	—
254	C₂×#41	—	37	2	no	—
255	C₂×#41	—	37	1	no	—
256	C₂²×D₄	—	37	2	no	—
257	C₂²×D₄	—	37	2	no	—
258	C₂³×C₄	—	37	4	no	—
259	C₄⋊Q₈	C₂×D₃₇	1	1	yes	characteristic, complemented
260	#127	—	37	1	no	—
261	#126	—	37	4	no	—
262	#126	—	37	4	no	—
263	#125	—	37	2	no	—
264	#125	C₂×D₃₇	1	2	yes	complemented
265	#124	—	37	2	no	—
266	#124	—	37	2	no	—
267	#124	—	37	2	no	—
268	#123	—	37	4	no	—
269	#123	—	37	4	no	—
270	#123	—	37	4	no	—
271	#123	—	37	4	no	—
272	C₂²⋊Q₈	—	37	4	no	—
273	C₂²⋊Q₈	—	37	2	no	—
274	C₂²⋊Q₈	C₂×D₃₇	1	4	yes	complemented
275	C₂²⋊Q₈	C₂×D₃₇	1	2	yes	complemented
276	#121	—	37	4	no	—
277	#121	—	37	2	no	—
278	#121	—	37	4	no	—
279	#121	—	37	2	no	—
280	#121	—	37	2	no	—
281	#121	—	37	2	no	—
282	#120	—	37	4	no	—
283	#120	—	37	4	no	—
284	C₄×Q₈	—	37	1	no	—
285	C₄×Q₈	—	37	1	no	—
286	C₄×Q₈	—	37	1	no	—
287	C₄×Q₈	C₂×D₃₇	1	1	yes	characteristic, complemented
288	C₄×D₄	—	37	1	no	—
289	C₄×D₄	—	37	4	no	—
290	C₄×D₄	—	37	2	no	—
291	C₄×D₄	—	37	1	no	—
292	C₄×D₄	—	37	4	no	—
293	C₄×D₄	—	37	2	no	—
294	C₄×D₄	—	37	2	no	—
295	C₄×D₄	—	37	2	no	—
296	C₄×D₄	—	37	4	no	—
297	C₄×D₄	—	37	2	no	—
298	C₄×D₄	—	37	2	no	—
299	C₄×D₄	—	37	4	no	—
300	C₄×D₄	—	37	2	no	—
301	C₄×D₄	—	37	2	no	—
302	C₄×D₄	—	37	1	no	—
303	C₄×D₄	—	37	2	no	—
304	C₄×D₄	C₂×D₃₇	1	2	yes	—
305	C₄×D₄	C₂×D₃₇	1	1	yes	characteristic
306	#117	—	37	2	no	—
307	#117	—	37	1	no	—
308	#117	—	37	1	no	—
309	#117	—	37	4	no	—
310	#117	—	37	2	no	—
311	C₂×C₄⋊C₄	—	37	2	no	—
312	C₂×C₄⋊C₄	C₂×D₃₇	1	2	yes	complemented
313	C₂×C₂²⋊C₄	—	37	4	no	—
314	C₂×C₂²⋊C₄	—	37	4	no	—
315	C₂×C₄²	—	37	2	no	—
316	C₂×C₄²	—	37	2	no	—
317	C₂×C₄²	—	37	1	no	—
318	C₂⁴	—	37	4	no	—
319	#41	—	74	4	no	—
320	#41	—	74	4	no	—
321	#41	—	148	4	no	—
322	C₂×Q₈	—	37	1	no	—
323	C₂×Q₈	C₂²×D₃₇	1	1	yes	characteristic
324	C₂×Q₈	C₂²×D₃₇	1	2	yes	—
325	C₂×D₄	—	37	2	no	—
326	C₂×D₄	—	37	4	no	—
327	C₂×D₄	—	37	1	no	—
328	C₂×D₄	—	37	2	no	—
329	C₂×D₄	—	37	4	no	—
330	C₂×D₄	—	37	2	no	—
331	C₂×D₄	—	37	2	no	—
332	C₂×D₄	—	37	2	no	—
333	C₂×D₄	—	37	4	no	—
334	C₂×D₄	—	74	8	no	—
335	C₂×D₄	—	74	8	no	—
336	C₂×D₄	C₂²×D₃₇	1	1	yes	characteristic
337	C₂²×C₄	—	37	2	no	—
338	C₂²×C₄	—	37	2	no	—
339	C₂²×C₄	—	37	2	no	—
340	C₂²×C₄	—	37	2	no	—
341	C₂²×C₄	—	37	1	no	—
342	C₂²×C₄	—	37	1	no	—
343	C₂²×C₄	—	37	2	no	—
344	C₂²×C₄	—	37	1	no	—
345	C₂²×C₄	—	37	4	no	—
346	C₂²×C₄	—	37	4	no	—
347	C₂²×C₄	—	37	4	no	—
348	C₂²×C₄	—	148	8	no	—
349	C₂²×C₄	C₂²×D₃₇	1	2	yes	—
350	C₂²×C₄	C₂²×D₃₇	1	4	yes	—
351	C₄⋊C₄	—	37	4	no	—
352	C₄⋊C₄	—	37	2	no	—
353	C₄⋊C₄	—	37	2	no	—
354	C₄⋊C₄	—	37	1	no	—
355	C₄⋊C₄	—	37	1	no	—
356	C₄⋊C₄	—	37	2	no	—
357	C₄⋊C₄	—	37	4	no	—
358	C₄⋊C₄	C₂²×D₃₇	1	2	yes	—
359	C₄⋊C₄	C₂²×D₃₇	1	1	yes	characteristic
360	C₄⋊C₄	C₂²×D₃₇	1	2	yes	—
361	C₄⋊C₄	C₂²×D₃₇	1	4	yes	—
362	C₄⋊C₄	C₂²×D₃₇	1	2	yes	—
363	C₄⋊C₄	C₂²×D₃₇	1	1	yes	characteristic
364	C₄⋊C₄	C₂²×D₃₇	1	4	yes	—
365	C₂²⋊C₄	—	37	2	no	—
366	C₂²⋊C₄	—	37	2	no	—
367	C₂²⋊C₄	—	37	4	no	—
368	C₂²⋊C₄	—	37	4	no	—
369	C₂²⋊C₄	—	37	4	no	—
370	C₂²⋊C₄	—	37	4	no	—
371	C₂²⋊C₄	—	37	4	no	—
372	C₂²⋊C₄	—	37	2	no	—
373	C₂²⋊C₄	—	37	2	no	—
374	C₂²⋊C₄	—	37	2	no	—
375	C₂²⋊C₄	—	37	4	no	—
376	C₂²⋊C₄	—	37	4	no	—
377	C₂²⋊C₄	C₂²×D₃₇	1	4	yes	—
378	C₂²⋊C₄	C₂²×D₃₇	1	2	yes	—
379	C₄²	—	37	1	no	—
380	C₄²	—	37	1	no	—
381	C₄²	—	37	1	no	—
382	C₄²	—	37	2	no	—
383	C₄²	—	37	2	no	—
384	C₄²	—	37	2	no	—
385	C₄²	—	37	2	no	—
386	C₄²	—	37	2	no	—
387	C₄²	C₂²×D₃₇	1	2	yes	—
388	C₄²	C₂²×D₃₇	1	1	yes	characteristic
389	C₂³	—	37	2	no	—
390	C₂³	—	37	4	no	—
391	C₂³	—	37	1	no	—
392	C₂³	—	74	8	no	—
393	C₂³	—	74	8	no	—
394	C₂³	—	148	4	no	—
395	C₂³	C₂³×D₃₇	1	2	yes	—
396	Q₈	—	2	2	no	—
397	Q₈	—	4	2	no	—
398	Q₈	—	74	2	no	—
399	D₄	—	37	4	no	—
400	D₄	—	74	8	no	—
401	D₄	—	74	4	no	—
402	D₄	—	74	8	no	—
403	D₄	—	74	4	no	—
404	D₄	—	74	4	no	—
405	D₄	—	74	4	no	—
406	D₄	—	148	4	no	—
407	D₄	—	148	2	no	—
408	D₄	#10596966	1	4	yes	complemented
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	4	4	no	—
411	C₂×C₄	—	37	1	no	—
412	C₂×C₄	—	37	1	no	—
413	C₂×C₄	—	37	1	no	—
414	C₂×C₄	—	37	2	no	—
415	C₂×C₄	—	37	2	no	—
416	C₂×C₄	—	37	2	no	—
417	C₂×C₄	—	74	4	no	—
418	C₂×C₄	—	74	8	no	—
419	C₂×C₄	—	74	2	no	—
420	C₂×C₄	—	74	4	no	—
421	C₂×C₄	—	74	4	no	—
422	C₂×C₄	—	74	4	no	—
423	C₂×C₄	—	74	2	no	—
424	C₂×C₄	—	74	4	no	—
425	C₂×C₄	—	74	2	no	—
426	C₂×C₄	—	148	4	no	—
427	C₂×C₄	—	148	4	no	—
428	C₂×C₄	C₂³×D₃₇	1	2	yes	—
429	C₂×C₄	C₂³×D₃₇	1	2	yes	—
430	C₂×C₄	C₂³×D₃₇	1	2	yes	—
431	C₂×C₄	C₂³×D₃₇	1	1	yes	characteristic
432	C₂×C₄	C₂³×D₃₇	1	4	yes	—
433	C₂×C₄	C₂³×D₃₇	1	1	yes	characteristic
434	C₂×C₄	C₂³×D₃₇	1	1	yes	characteristic
435	C₂²	—	2	2	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	37	4	no	—
438	C₂²	—	74	2	no	—
439	C₂²	—	74	2	no	—
440	C₂²	—	74	1	no	—
441	C₂²	—	74	4	no	—
442	C₂²	—	74	1	no	—
443	C₂²	—	74	4	no	—
444	C₂²	—	74	4	no	—
445	C₂²	—	74	1	no	—
446	C₂²	—	148	16	no	—
447	C₂²	C₂×#10596966	1	4	yes	—
448	C₂²	C₂⁴×D₃₇	1	1	yes	characteristic
449	C₄	—	2	2	no	—
450	C₄	—	2	2	no	—
451	C₄	—	2	2	no	—
452	C₄	—	2	4	no	—
453	C₄	—	2	1	no	—
454	C₄	—	37	2	no	—
455	C₄	—	74	1	no	—
456	C₄	—	74	1	no	—
457	C₄	—	74	2	no	—
458	C₄	—	74	2	no	—
459	C₄	—	74	2	no	—
460	C₄	#41×D₃₇	1	2	yes	—
461	C₄	C₂×#10596966	1	2	yes	—
462	C₂	—	2	4	no	—
463	C₂	—	74	4	no	—
464	C₂	—	148	4	no	—
465	C₂	—	148	1	no	—
466	C₂	C₂×#41×D₃₇	1	1	yes	characteristic
467	C₂	C₂²×#10596966	1	1	yes	characteristic
468	C₂	H(5,𝔽₂)×D₃₇	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	#3481
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. #14558268	C₂	semidirect
2. #14558244	C₂	semidirect
3. #14558236	C₂	semidirect
4. #14558231	C₂	semidirect
5. #14558210	C₂	semidirect
6. #14558178	C₂	semidirect
7. #14558174	C₂	semidirect
8. D₄×D₁₄₈	C₂	semidirect
9. #14558084	C₂	semidirect
10. #14558069	C₂	semidirect
11. #14558068	C₂	semidirect
12. #14558046	C₂	semidirect
13. C₄×#10596966	C₂	semidirect
14. C₄×#10596964	C₂	semidirect
15. C₂×#11924498	C₂	semidirect
16. C₄×D₄×D₃₇	C₂	semidirect
17. C₃₇×#554	C₂	semidirect
19. C₂×#10596966	C₂²	semidirect
23. C₂²×C₄×D₃₇	C₂²	semidirect
25. #11924531	C₂²	semidirect
26. #11924531	C₂²	semidirect
27. #11924527	C₂²	semidirect
28. #11924525	C₂²	semidirect
29. #11924525	C₂²	semidirect
30. #11924524	C₂²	semidirect
31. #11924521	C₂²	semidirect
32. #11924521	C₂²	semidirect
33. #11924521	C₂²	semidirect
34. #11924520	C₂²	semidirect
35. #11924516	C₂²	semidirect
36. #11924512	C₂²	semidirect
38. #11924511	C₂²	semidirect
39. #11924511	C₂²	semidirect
40. #11924511	C₂²	semidirect
42. #11924510	C₂²	semidirect
44. #11924506	C₂²	semidirect
45. Q₈×Dic₃₇	C₂²	semidirect
46. C₄×Dic₇₄	C₂²	semidirect
47. #11924501	C₂²	semidirect
49. C₄×D₁₄₈	C₂²	semidirect
50. C₄×D₁₄₈	C₂²	semidirect
54. #11924498	C₂²	semidirect
55. #11924498	C₂²	semidirect
56. #11924498	C₂²	semidirect
57. #11924498	C₂²	semidirect
58. #11924498	C₂²	semidirect
59. #11924498	C₂²	semidirect
60. C₄×C₂²⋊D₃₇	C₂²	semidirect
61. C₄×C₂²⋊D₃₇	C₂²	semidirect
62. #11924496	C₂²	semidirect
63. #11924496	C₂²	semidirect
64. #11924494	C₂²	semidirect
65. #11924494	C₂²	semidirect
66. #11924494	C₂²	semidirect
67. #11924494	C₂²	semidirect
68. #11924492	C₂²	semidirect
69. C₄⋊C₄×D₃₇	C₂²	semidirect
70. C₂×#10596938	C₂²	semidirect
71. C₂²⋊C₄×D₃₇	C₂²	semidirect
72. C₂×C₄×Dic₃₇	C₂²	semidirect
73. C₄²×D₃₇	C₂²	semidirect
74. C₄²×D₃₇	C₂²	semidirect
75. C₄⋊Q₈×C₃₇	C₂²	semidirect
76. #125×C₃₇	C₂²	semidirect
77. C₂²⋊Q₈×C₃₇	C₂²	semidirect
78. C₂²⋊Q₈×C₃₇	C₂²	semidirect
79. C₄×Q₈×C₃₇	C₂²	semidirect
82. C₂×C₄⋊C₄×C₃₇	C₂²	semidirect
163. D₄×C₃₇	#41	semidirect
189. D₁₄₈	#41	semidirect
237. #554	D₃₇	semidirect
252. C₃₇	#3481	semidirect
259. C₄⋊Q₈	C₂×D₃₇	semidirect
264. #125	C₂×D₃₇	semidirect
274. C₂²⋊Q₈	C₂×D₃₇	semidirect
275. C₂²⋊Q₈	C₂×D₃₇	semidirect
287. C₄×Q₈	C₂×D₃₇	semidirect
312. C₂×C₄⋊C₄	C₂×D₃₇	semidirect
408. D₄	#10596966	semidirect

Maximal subgroups

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

subgroup	index
#14558268	2
#14558244	2
#14558236	2
#14558231	2
#14558210	2
#14558178	2
#14558174	2
D₄×D₁₄₈	2
#14558084	2
#14558069	2
#14558068	2
#14558046	2
C₄×#10596966	2
C₄×#10596964	2
C₂×#11924498	2
C₄×D₄×D₃₇	2
C₃₇×#554	2
#3481	37