Subgroups — #34058571

Order 19072.

992 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750354	C₂	1	1	yes	maximal, characteristic, complemented
2	#23750353	C₂	1	2	yes	maximal, complemented
3	#23750350	C₂	1	1	yes	maximal, characteristic, complemented
4	#23750345	C₂	1	1	yes	maximal, characteristic, complemented
5	#23750344	C₂	1	2	yes	maximal, complemented
6	#23750314	C₂	1	2	yes	maximal, complemented
7	#23750311	C₂	1	4	yes	maximal, complemented
8	#23750309	C₂	1	2	yes	maximal, complemented
9	#23750232	C₂	1	4	yes	maximal, complemented
10	#23750195	C₂	1	2	yes	maximal
11	#23750179	C₂	1	1	yes	maximal, characteristic, complemented
12	#23750178	C₂	1	2	yes	maximal, complemented
13	#23750177	C₂	1	2	yes	maximal, complemented
14	C₄⋊Q₈×D₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#23750101	C₂	1	2	yes	maximal, complemented
16	C₄×#14558735	C₂	1	1	yes	maximal, characteristic
17	#556×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#14558735	C₂²	1	1	yes	characteristic
19	C₂×Q₈×D₁₄₉	C₂²	1	2	yes	—
20	#18011911	C₂²	1	1	yes	characteristic
21	#18011911	C₂²	1	2	yes	—
22	#18011910	C₂²	1	2	yes	—
23	#18011910	C₂²	1	2	yes	—
24	#18011910	C₂²	1	1	yes	characteristic
25	#18011909	C₂²	1	2	yes	—
26	#18011909	C₂²	1	1	yes	characteristic
27	#18011909	C₂²	1	2	yes	—
28	#18011904	C₂²	1	4	yes	—
29	#18011904	C₂²	1	4	yes	—
30	#18011904	C₂²	1	4	yes	—
31	#18011903	C₂²	1	4	yes	—
32	#18011902	C₂²	1	2	yes	—
33	#18011902	C₂²	1	2	yes	—
34	#18011902	C₂²	1	4	yes	—
35	#18011901	C₂²	1	4	yes	—
36	#18011901	C₂²	1	2	yes	—
37	#18011901	C₂²	1	4	yes	—
38	#18011901	C₂²	1	4	yes	—
39	#18011898	C₂²	1	2	yes	—
40	#18011893	C₂²	1	4	yes	—
41	#18011893	C₂²	1	4	yes	—
42	#18011891	C₂²	1	1	yes	characteristic
43	#18011890	C₂²	1	2	yes	—
44	#18011889	C₂²	1	2	yes	—
45	#18011888	C₂²	1	4	yes	—
46	#18011888	C₂²	1	4	yes	—
47	#18011888	C₂²	1	4	yes	—
48	#18011887	C₂²	1	1	yes	characteristic
49	Q₈×Dic₁₄₉	C₂²	1	2	yes	—
50	Q₈×Dic₁₄₉	C₂²	1	2	yes	—
51	C₄×Dic₂₉₈	C₂²	1	4	yes	—
52	C₄×Dic₂₉₈	C₂²	1	4	yes	—
53	C₄×Dic₂₉₈	C₂²	1	2	yes	—
54	C₄×Dic₂₉₈	C₂²	1	1	yes	characteristic
55	C₄×Dic₂₉₈	C₂²	1	2	yes	—
56	C₄×Dic₂₉₈	C₂²	1	1	yes	characteristic
57	#18011876	C₂²	1	4	yes	—
58	#18011876	C₂²	1	2	yes	—
59	#18011876	C₂²	1	2	yes	—
60	#18011876	C₂²	1	1	yes	characteristic
61	D₄×Dic₁₄₉	C₂²	1	1	yes	characteristic
62	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	—
63	#18011871	C₂²	1	2	yes	—
64	#18011870	C₂²	1	2	yes	—
65	#18011869	C₂²	1	4	yes	—
66	#18011869	C₂²	1	1	yes	characteristic
67	#18011868	C₂²	1	2	yes	—
68	#18011868	C₂²	1	4	yes	—
69	#18011867	C₂²	1	4	yes	—
70	#18011867	C₂²	1	2	yes	—
71	C₄⋊C₄×D₁₄₉	C₂²	1	2	yes	—
72	C₄⋊C₄×D₁₄₉	C₂²	1	2	yes	—
73	C₂×C₄×Dic₁₄₉	C₂²	1	2	yes	—
74	C₄²×D₁₄₉	C₂²	1	1	yes	characteristic
75	C₄⋊Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
76	#126×C₁₄₉	C₂²	1	4	yes	—
77	#124×C₁₄₉	C₂²	1	2	yes	—
78	C₂²⋊Q₈×C₁₄₉	C₂²	1	2	yes	—
79	C₄×Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
80	C₄×Q₈×C₁₄₉	C₂²	1	2	yes	—
81	C₄×D₄×C₁₄₉	C₂²	1	1	yes	characteristic
82	#117×C₁₄₉	C₂²	1	2	yes	—
83	#14558735	—	2	4	no	—
84	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
85	C₂×Dic₂₉₈	C₂³	1	2	yes	—
86	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
87	C₂×Dic₂₉₈	C₂³	1	4	yes	—
88	C₂×Dic₂₉₈	C₂³	1	2	yes	—
89	Q₈×D₁₄₉	—	2	8	no	—
90	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
91	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
92	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
93	C₂×C₄×D₁₄₉	C₂³	1	4	yes	—
94	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
95	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
96	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
97	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
98	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
99	C₄⋊Dic₁₄₉	C₂³	1	4	yes	—
100	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
101	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
102	C₄⋊Dic₁₄₉	C₂³	1	4	yes	—
103	C₄⋊Dic₁₄₉	C₂³	1	4	yes	—
104	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
105	#14558715	C₂³	1	4	yes	—
106	#14558715	C₂³	1	2	yes	—
107	#14558715	C₂³	1	2	yes	—
108	#14558715	C₂³	1	4	yes	—
109	#14558715	C₂³	1	4	yes	—
110	#14558715	C₂³	1	4	yes	—
111	#14558715	C₂³	1	2	yes	—
112	#14558715	C₂³	1	2	yes	—
113	#14558715	C₂³	1	4	yes	—
114	#14558715	C₂³	1	4	yes	—
115	#14558715	C₂³	1	2	yes	—
116	#14558715	C₂³	1	2	yes	—
117	#14558715	C₂³	1	2	yes	—
118	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
119	C₂²⋊Dic₁₄₉	C₂³	1	4	yes	—
120	C₂²⋊Dic₁₄₉	C₂³	1	4	yes	—
121	#14558713	C₂³	1	2	yes	—
122	#14558713	C₂³	1	2	yes	—
123	#14558713	C₂³	1	2	yes	—
124	C₄×Dic₁₄₉	C₂³	1	4	yes	—
125	C₄×Dic₁₄₉	C₂³	1	4	yes	—
126	C₄×Dic₁₄₉	C₂³	1	4	yes	—
127	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
128	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
129	C₄×Dic₁₄₉	C₂³	1	2	yes	—
130	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
131	C₄×Dic₁₄₉	C₂³	1	2	yes	—
132	C₄×Dic₁₄₉	C₂³	1	2	yes	—
133	C₄×Dic₁₄₉	C₂³	1	2	yes	—
134	C₂×Q₈×C₁₄₉	C₂³	1	2	yes	—
135	C₂×Q₈×C₁₄₉	C₂³	1	1	yes	characteristic
136	C₂×D₄×C₁₄₉	C₂³	1	1	yes	characteristic
137	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
138	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
139	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
140	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
141	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
142	C₄⋊C₄×C₁₄₉	C₂³	1	4	yes	—
143	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
144	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
145	C₂²⋊C₄×C₁₄₉	C₂³	1	4	yes	—
146	C₂²⋊C₄×C₁₄₉	C₂³	1	4	yes	—
147	C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
148	C₄²×C₁₄₉	C₂³	1	2	yes	—
149	C₄²×C₁₄₉	C₂³	1	4	yes	—
150	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
151	Dic₂₉₈	—	2	4	no	—
152	Dic₂₉₈	—	2	2	no	—
153	Dic₂₉₈	—	2	2	no	—
154	Dic₂₉₈	—	2	8	no	—
155	Dic₂₉₈	—	2	4	no	—
156	C₂²⋊D₁₄₉	—	2	4	no	—
157	C₂×Dic₁₄₉	—	2	4	no	—
158	C₂×Dic₁₄₉	—	2	4	no	—
159	C₂×Dic₁₄₉	C₂⁴	1	4	yes	—
160	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
161	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
162	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
163	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
164	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
165	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
166	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
167	C₄×D₁₄₉	—	2	8	no	—
168	C₄×D₁₄₉	—	2	2	no	—
169	C₄×D₁₄₉	—	2	2	no	—
170	C₄×D₁₄₉	#41	1	4	yes	—
171	C₂³×C₁₄₉	C₂⁴	1	2	yes	—
172	Q₈×C₁₄₉	—	2	4	no	—
173	Q₈×C₁₄₉	—	2	2	no	—
174	D₄×C₁₄₉	—	2	2	no	—
175	C₂×C₄×C₁₄₉	—	2	4	no	—
176	C₂×C₄×C₁₄₉	C₂⁴	1	4	yes	—
177	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
178	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
179	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
180	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
181	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
182	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
183	C₂²×C₁₄₉	—	2	2	no	—
184	C₂²×C₁₄₉	—	2	2	no	—
185	C₂²×C₁₄₉	—	2	2	no	—
186	C₂²×C₁₄₉	C₂⁵	1	1	yes	characteristic
187	C₂×D₁₄₉	—	2	1	no	—
188	C₂×D₁₄₉	—	2	1	no	—
189	C₂×D₁₄₉	C₂×#41	1	2	yes	—
190	C₄×C₁₄₉	—	2	4	no	—
191	C₄×C₁₄₉	—	2	2	no	—
192	C₄×C₁₄₉	—	2	2	no	—
193	C₄×C₁₄₉	—	2	1	no	—
194	C₄×C₁₄₉	—	2	2	no	—
195	C₄×C₁₄₉	C₂×#41	1	2	yes	—
196	C₄×C₁₄₉	2₋¹⁺⁴	1	2	yes	—
197	Dic₁₄₉	—	2	4	no	—
198	Dic₁₄₉	—	2	2	no	—
199	Dic₁₄₉	—	2	1	no	—
200	Dic₁₄₉	—	2	2	no	—
201	Dic₁₄₉	—	2	2	no	—
202	Dic₁₄₉	—	2	2	no	—
203	Dic₁₄₉	C₂×#41	1	2	yes	—
204	Dic₁₄₉	2₋¹⁺⁴	1	2	yes	—
205	C₂×C₁₄₉	—	4	2	no	—
206	C₂×C₁₄₉	C₂²×#41	1	1	yes	characteristic
207	C₂×C₁₄₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
208	C₂×C₁₄₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
209	D₁₄₉	—	2	2	no	—
210	C₁₄₉	#3509	1	1	yes	characteristic, complemented, Sylow
211	#3509	—	149	1	no	maximal, Sylow
212	#557	—	149	1	no	—
213	#557	—	149	2	no	—
214	#557	—	149	1	no	—
215	#556	—	149	2	no	—
216	#556	—	149	1	no	—
217	#556	D₁₄₉	1	1	yes	characteristic, complemented
218	#552	—	149	4	no	—
219	#552	—	149	2	no	—
220	#552	—	149	2	no	—
221	#541	—	149	4	no	—
222	#536	—	149	2	no	—
223	#533	—	149	2	no	—
224	#533	—	149	1	no	—
225	#533	—	149	2	no	—
226	C₂×C₄⋊Q₈	—	149	1	no	—
227	#519	—	149	2	no	—
228	C₄×#41	—	149	1	no	—
229	C₂×#41	—	149	1	no	—
230	C₂²×Q₈	—	149	2	no	—
231	C₄⋊Q₈	—	149	2	no	—
232	C₄⋊Q₈	—	149	1	no	—
233	C₄⋊Q₈	—	149	2	no	—
234	C₄⋊Q₈	—	149	2	no	—
235	C₄⋊Q₈	—	149	2	no	—
236	C₄⋊Q₈	—	149	1	no	—
237	C₄⋊Q₈	—	149	1	no	—
238	C₄⋊Q₈	—	149	2	no	—
239	C₄⋊Q₈	C₂×D₁₄₉	1	1	yes	characteristic
240	#126	—	149	4	no	—
241	#126	—	149	4	no	—
242	#126	—	149	4	no	—
243	#126	C₂×D₁₄₉	1	4	yes	—
244	#125	—	149	2	no	—
245	#125	—	149	4	no	—
246	#125	—	149	2	no	—
247	#125	—	149	2	no	—
248	#125	—	149	4	no	—
249	#125	—	149	4	no	—
250	#125	—	149	4	no	—
251	#125	—	149	4	no	—
252	#124	—	149	2	no	—
253	#124	C₂×D₁₄₉	1	2	yes	—
254	#123	—	149	4	no	—
255	#123	—	149	4	no	—
256	C₂²⋊Q₈	—	149	1	no	—
257	C₂²⋊Q₈	—	149	2	no	—
258	C₂²⋊Q₈	—	149	2	no	—
259	C₂²⋊Q₈	—	149	1	no	—
260	C₂²⋊Q₈	—	149	4	no	—
261	C₂²⋊Q₈	—	149	4	no	—
262	C₂²⋊Q₈	—	149	4	no	—
263	C₂²⋊Q₈	C₂×D₁₄₉	1	2	yes	—
264	C₄×Q₈	—	149	2	no	—
265	C₄×Q₈	—	149	2	no	—
266	C₄×Q₈	—	149	1	no	—
267	C₄×Q₈	—	149	4	no	—
268	C₄×Q₈	—	149	2	no	—
269	C₄×Q₈	—	149	2	no	—
270	C₄×Q₈	—	149	1	no	—
271	C₄×Q₈	—	149	4	no	—
272	C₄×Q₈	—	149	2	no	—
273	C₄×Q₈	—	149	4	no	—
274	C₄×Q₈	—	149	2	no	—
275	C₄×Q₈	—	149	1	no	—
276	C₄×Q₈	C₂×D₁₄₉	1	2	yes	—
277	C₄×Q₈	C₂×D₁₄₉	1	1	yes	characteristic
278	C₄×D₄	—	149	1	no	—
279	C₄×D₄	—	149	2	no	—
280	C₄×D₄	—	149	2	no	—
281	C₄×D₄	C₂×D₁₄₉	1	1	yes	characteristic
282	#117	—	149	2	no	—
283	#117	—	149	1	no	—
284	#117	—	149	4	no	—
285	#117	—	149	2	no	—
286	#117	—	149	4	no	—
287	#117	—	149	2	no	—
288	#117	—	149	4	no	—
289	#117	C₂×D₁₄₉	1	2	yes	—
290	C₂×C₄⋊C₄	—	149	2	no	—
291	C₂×C₄⋊C₄	—	149	2	no	—
292	C₂×C₄²	—	149	2	no	—
293	C₂×C₄²	—	149	1	no	—
294	#41	—	298	4	no	—
295	C₂×Q₈	—	298	8	no	—
296	C₂×Q₈	—	149	1	no	—
297	C₂×Q₈	—	149	2	no	—
298	C₂×Q₈	—	149	4	no	—
299	C₂×Q₈	—	149	2	no	—
300	C₂×Q₈	—	149	1	no	—
301	C₂×Q₈	C₂²×D₁₄₉	1	1	yes	characteristic
302	C₂×Q₈	C₂²×D₁₄₉	1	2	yes	—
303	C₂×D₄	—	149	2	no	—
304	C₂×D₄	C₂²×D₁₄₉	1	1	yes	characteristic
305	C₂²×C₄	—	149	2	no	—
306	C₂²×C₄	—	149	2	no	—
307	C₂²×C₄	—	149	1	no	—
308	C₂²×C₄	—	149	1	no	—
309	C₂²×C₄	—	149	4	no	—
310	C₂²×C₄	—	149	1	no	—
311	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
312	C₄⋊C₄	—	149	4	no	—
313	C₄⋊C₄	—	149	2	no	—
314	C₄⋊C₄	—	149	4	no	—
315	C₄⋊C₄	—	149	2	no	—
316	C₄⋊C₄	—	149	2	no	—
317	C₄⋊C₄	—	149	1	no	—
318	C₄⋊C₄	—	149	1	no	—
319	C₄⋊C₄	—	149	2	no	—
320	C₄⋊C₄	—	149	2	no	—
321	C₄⋊C₄	—	149	2	no	—
322	C₄⋊C₄	—	149	2	no	—
323	C₄⋊C₄	—	149	4	no	—
324	C₄⋊C₄	—	149	4	no	—
325	C₄⋊C₄	—	149	4	no	—
326	C₄⋊C₄	—	149	4	no	—
327	C₄⋊C₄	—	149	4	no	—
328	C₄⋊C₄	—	149	4	no	—
329	C₄⋊C₄	—	149	4	no	—
330	C₄⋊C₄	—	149	2	no	—
331	C₄⋊C₄	—	149	2	no	—
332	C₄⋊C₄	—	149	2	no	—
333	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
334	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
335	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
336	C₄⋊C₄	C₂²×D₁₄₉	1	4	yes	—
337	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
338	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
339	C₂²⋊C₄	—	149	2	no	—
340	C₂²⋊C₄	—	149	4	no	—
341	C₂²⋊C₄	—	149	4	no	—
342	C₂²⋊C₄	—	149	2	no	—
343	C₂²⋊C₄	—	149	2	no	—
344	C₂²⋊C₄	—	149	2	no	—
345	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
346	C₂²⋊C₄	C₂²×D₁₄₉	1	4	yes	—
347	C₂²⋊C₄	C₂²×D₁₄₉	1	4	yes	—
348	C₄²	—	149	1	no	—
349	C₄²	—	149	2	no	—
350	C₄²	—	149	1	no	—
351	C₄²	—	149	2	no	—
352	C₄²	—	149	2	no	—
353	C₄²	—	149	1	no	—
354	C₄²	—	149	4	no	—
355	C₄²	—	149	4	no	—
356	C₄²	—	149	4	no	—
357	C₄²	—	149	2	no	—
358	C₄²	C₂²×D₁₄₉	1	1	yes	characteristic
359	C₄²	C₂²×D₁₄₉	1	4	yes	—
360	C₄²	C₂²×D₁₄₉	1	2	yes	—
361	C₂³	—	149	1	no	—
362	C₂³	C₂³×D₁₄₉	1	2	yes	—
363	Q₈	—	2	4	no	—
364	Q₈	—	2	2	no	—
365	Q₈	—	298	8	no	—
366	Q₈	—	298	4	no	—
367	Q₈	—	298	4	no	—
368	Q₈	—	298	2	no	—
369	Q₈	—	298	2	no	—
370	D₄	—	2	2	no	—
371	D₄	—	298	4	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	298	8	no	—
374	C₂×C₄	—	298	2	no	—
375	C₂×C₄	—	298	4	no	—
376	C₂×C₄	—	298	4	no	—
377	C₂×C₄	—	298	2	no	—
378	C₂×C₄	—	149	2	no	—
379	C₂×C₄	—	149	2	no	—
380	C₂×C₄	—	149	2	no	—
381	C₂×C₄	—	149	1	no	—
382	C₂×C₄	—	149	4	no	—
383	C₂×C₄	—	149	2	no	—
384	C₂×C₄	—	149	1	no	—
385	C₂×C₄	—	149	1	no	—
386	C₂×C₄	—	149	4	no	—
387	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
388	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
389	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
390	C₂×C₄	C₂³×D₁₄₉	1	4	yes	—
391	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
392	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
393	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
394	C₂²	—	2	2	no	—
395	C₂²	—	2	2	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	298	1	no	—
398	C₂²	—	298	1	no	—
399	C₂²	—	149	2	no	—
400	C₂²	C₂⁴×D₁₄₉	1	1	yes	characteristic
401	C₄	—	2	4	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	2	no	—
404	C₄	—	2	2	no	—
405	C₄	—	2	2	no	—
406	C₄	—	298	2	no	—
407	C₄	—	298	4	no	—
408	C₄	—	298	2	no	—
409	C₄	—	298	2	no	—
410	C₄	—	298	1	no	—
411	C₄	—	298	2	no	—
412	C₄	—	149	2	no	—
413	C₄	—	149	2	no	—
414	C₄	#41×D₁₄₉	1	2	yes	—
415	C₄	#18011958	1	2	yes	—
416	C₂	—	4	2	no	—
417	C₂	—	298	2	no	—
418	C₂	C₂×#41×D₁₄₉	1	1	yes	characteristic
419	C₂	2₋¹⁺⁴×D₁₄₉	1	1	yes	characteristic
420	C₂	C₂×#18011958	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₄₉
commutator, socle, cosocle	C₂²×C₁₄₉	C₂⁵
Fitting	#556×C₁₄₉	C₂
prime radical	C₂×#14558735	C₂²
hypercenter	#556	D₁₄₉
hypocenter	C₁₄₉	#3509
LCS	G ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ #556

Complements

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

N	H ≅ G/N	type
1. #23750354	C₂	semidirect
2. #23750353	C₂	semidirect
3. #23750350	C₂	semidirect
4. #23750345	C₂	semidirect
5. #23750344	C₂	semidirect
6. #23750314	C₂	semidirect
7. #23750311	C₂	semidirect
8. #23750309	C₂	semidirect
9. #23750232	C₂	semidirect
11. #23750179	C₂	semidirect
12. #23750178	C₂	semidirect
13. #23750177	C₂	semidirect
14. C₄⋊Q₈×D₁₄₉	C₂	semidirect
15. #23750101	C₂	semidirect
17. #556×C₁₄₉	C₂	semidirect
210. C₁₄₉	#3509	semidirect
217. #556	D₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
#23750354	2
#23750353	2
#23750350	2
#23750345	2
#23750344	2
#23750314	2
#23750311	2
#23750309	2
#23750232	2
#23750195	2
#23750179	2
#23750178	2
#23750177	2
C₄⋊Q₈×D₁₄₉	2
#23750101	2
C₄×#14558735	2
#556×C₁₄₉	2
#3509	149