Subgroups — #34058541

Order 19072.

1140 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750359	C₂	1	4	yes	maximal, complemented
2	#23750346	C₂	1	2	yes	maximal, complemented
3	#23750340	C₂	1	1	yes	maximal, characteristic, complemented
4	#23750340	C₂	1	1	yes	maximal, characteristic, complemented
5	#23750323	C₂	1	2	yes	maximal, complemented
6	#23750322	C₂	1	2	yes	maximal, complemented
7	#23750294	C₂	1	2	yes	maximal, complemented
8	#23750278	C₂	1	1	yes	maximal, characteristic, complemented
9	#23750211	C₂	1	4	yes	maximal, complemented
10	#23750191	C₂	1	2	yes	maximal, complemented
11	#23750180	C₂	1	1	yes	maximal, characteristic, complemented
12	#23750172	C₂	1	1	yes	maximal, characteristic, complemented
13	#23750138	C₂	1	2	yes	maximal, complemented
14	#23750132	C₂	1	2	yes	maximal, complemented
15	#23750106	C₂	1	2	yes	maximal, complemented
16	C₄×D₄×D₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
17	#547×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#14558737	C₂²	1	2	yes	complemented
19	C₂×#14558736	C₂²	1	2	yes	—
20	C₂×D₄×D₁₄₉	C₂²	1	1	yes	characteristic
21	C₂²×C₄×D₁₄₉	C₂²	1	2	yes	—
22	#18011911	C₂²	1	1	yes	characteristic, complemented
23	#18011910	C₂²	1	1	yes	characteristic, complemented
24	#18011907	C₂²	1	4	yes	—
25	#18011907	C₂²	1	1	yes	characteristic, complemented
26	#18011906	C₂²	1	4	yes	complemented
27	#18011904	C₂²	1	4	yes	complemented
28	#18011902	C₂²	1	2	yes	complemented
29	#18011897	C₂²	1	4	yes	—
30	#18011897	C₂²	1	2	yes	complemented
31	#18011897	C₂²	1	4	yes	complemented
32	#18011897	C₂²	1	4	yes	complemented
33	#18011896	C₂²	1	4	yes	complemented
34	#18011896	C₂²	1	4	yes	complemented
35	#18011892	C₂²	1	4	yes	complemented
36	#18011891	C₂²	1	2	yes	—
37	#18011887	C₂²	1	2	yes	—
38	#18011887	C₂²	1	2	yes	complemented
39	#18011886	C₂²	1	1	yes	characteristic
40	#18011886	C₂²	1	2	yes	—
41	#18011885	C₂²	1	2	yes	—
42	#18011885	C₂²	1	4	yes	complemented
43	#18011885	C₂²	1	2	yes	complemented
44	#18011884	C₂²	1	2	yes	—
45	#18011882	C₂²	1	1	yes	characteristic
46	#18011882	C₂²	1	2	yes	—
47	#18011882	C₂²	1	4	yes	complemented
48	#18011882	C₂²	1	2	yes	complemented
49	#18011881	C₂²	1	4	yes	—
50	#18011879	C₂²	1	4	yes	—
51	Q₈×Dic₁₄₉	C₂²	1	2	yes	complemented
52	#18011876	C₂²	1	2	yes	complemented
53	#18011876	C₂²	1	4	yes	complemented
54	C₄×D₅₉₆	C₂²	1	1	yes	characteristic
55	C₄×D₅₉₆	C₂²	1	1	yes	characteristic, complemented
56	D₄×Dic₁₄₉	C₂²	1	1	yes	characteristic
57	#18011873	C₂²	1	4	yes	—
58	#18011873	C₂²	1	1	yes	characteristic
59	C₄×C₂²⋊D₁₄₉	C₂²	1	4	yes	—
60	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	—
61	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	complemented
62	C₄×C₂²⋊D₁₄₉	C₂²	1	4	yes	complemented
63	C₄×C₂²⋊D₁₄₉	C₂²	1	4	yes	complemented
64	#18011871	C₂²	1	2	yes	—
65	#18011871	C₂²	1	4	yes	complemented
66	#18011870	C₂²	1	2	yes	complemented
67	#18011870	C₂²	1	2	yes	complemented
68	#18011869	C₂²	1	2	yes	—
69	#18011869	C₂²	1	2	yes	complemented
70	#18011869	C₂²	1	2	yes	complemented
71	C₄⋊C₄×D₁₄₉	C₂²	1	1	yes	characteristic
72	C₄⋊C₄×D₁₄₉	C₂²	1	2	yes	complemented
73	C₂²⋊C₄×D₁₄₉	C₂²	1	2	yes	—
74	C₄²×D₁₄₉	C₂²	1	1	yes	characteristic
75	C₂×#41×C₁₄₉	C₂²	1	2	yes	complemented
76	C₄⋊Q₈×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
77	#123×C₁₄₉	C₂²	1	4	yes	complemented
78	C₂²⋊Q₈×C₁₄₉	C₂²	1	2	yes	complemented
79	#121×C₁₄₉	C₂²	1	2	yes	—
80	C₄×D₄×C₁₄₉	C₂²	1	1	yes	characteristic
81	C₄×D₄×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
82	C₂×C₄⋊C₄×C₁₄₉	C₂²	1	2	yes	complemented
83	C₂³×D₁₄₉	C₂³	1	2	yes	—
84	#14558737	—	4	4	no	—
85	#14558736	—	2	8	no	—
86	C₂×Dic₂₉₈	C₂³	1	2	yes	—
87	C₂×Dic₂₉₈	C₂³	1	2	yes	—
88	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
89	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
90	C₂×D₅₉₆	C₂³	1	2	yes	—
91	C₂×D₅₉₆	C₂³	1	4	yes	—
92	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
93	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
94	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
95	C₂×C₂²⋊D₁₄₉	C₂³	1	4	yes	—
96	C₂×C₂²⋊D₁₄₉	C₂³	1	4	yes	—
97	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
98	D₄×D₁₄₉	—	2	4	no	—
99	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
100	C₂×C₄×D₁₄₉	—	4	4	no	—
101	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
102	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
103	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
104	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
105	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
106	C₂×C₄×D₁₄₉	C₂³	1	4	yes	—
107	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
108	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
109	C₄⋊Dic₁₄₉	C₂³	1	4	yes	—
110	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
111	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
112	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
113	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
114	#14558715	C₂³	1	2	yes	—
115	#14558715	C₂³	1	4	yes	—
116	#14558715	C₂³	1	2	yes	—
117	#14558715	C₂³	1	4	yes	—
118	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
119	C₂²⋊Dic₁₄₉	C₂³	1	4	yes	—
120	C₂²⋊Dic₁₄₉	C₂³	1	4	yes	—
121	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
122	#14558713	C₂³	1	2	yes	—
123	#14558713	C₂³	1	4	yes	—
124	#14558713	C₂³	1	4	yes	—
125	#14558713	C₂³	1	2	yes	—
126	#14558713	C₂³	1	4	yes	—
127	#14558713	C₂³	1	4	yes	—
128	#14558713	C₂³	1	2	yes	—
129	#14558713	C₂³	1	2	yes	—
130	C₄×Dic₁₄₉	C₂³	1	4	yes	—
131	C₄×Dic₁₄₉	C₂³	1	4	yes	—
132	C₄×Dic₁₄₉	C₂³	1	4	yes	—
133	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
134	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
135	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
136	#41×C₁₄₉	—	4	4	no	—
137	C₂×Q₈×C₁₄₉	C₂³	1	2	yes	—
138	C₂×D₄×C₁₄₉	C₂³	1	1	yes	characteristic
139	C₂×D₄×C₁₄₉	C₂³	1	1	yes	characteristic
140	C₂×D₄×C₁₄₉	C₂³	1	4	yes	—
141	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
142	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
143	C₂²×C₄×C₁₄₉	C₂³	1	4	yes	—
144	C₄⋊C₄×C₁₄₉	C₂³	1	4	yes	—
145	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
146	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
147	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
148	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
149	C₂²⋊C₄×C₁₄₉	C₂³	1	4	yes	—
150	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
151	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
152	C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
153	C₂²×D₁₄₉	—	2	4	no	—
154	C₂²×D₁₄₉	—	4	2	no	—
155	C₂²×D₁₄₉	—	4	2	no	—
156	C₂²×D₁₄₉	C₂⁴	1	2	yes	—
157	C₂²×D₁₄₉	C₂⁴	1	2	yes	—
158	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
159	Dic₂₉₈	—	2	4	no	—
160	Dic₂₉₈	—	4	2	no	—
161	D₅₉₆	—	2	4	no	—
162	D₅₉₆	—	2	2	no	—
163	D₅₉₆	—	2	2	no	—
164	D₅₉₆	—	4	4	no	—
165	C₂²⋊D₁₄₉	—	2	4	no	—
166	C₂²⋊D₁₄₉	—	2	4	no	—
167	C₂²⋊D₁₄₉	—	2	4	no	—
168	C₂²⋊D₁₄₉	—	4	2	no	—
169	C₂²⋊D₁₄₉	—	4	4	no	—
170	C₂²⋊D₁₄₉	—	4	4	no	—
171	C₂×Dic₁₄₉	—	4	2	no	—
172	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
173	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
174	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
175	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
176	C₂×Dic₁₄₉	C₂⁴	1	4	yes	—
177	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
178	C₄×D₁₄₉	—	2	4	no	—
179	C₄×D₁₄₉	—	2	2	no	—
180	C₄×D₁₄₉	—	2	4	no	—
181	C₄×D₁₄₉	—	4	2	no	—
182	C₄×D₁₄₉	—	4	2	no	—
183	C₄×D₁₄₉	—	4	1	no	—
184	C₄×D₁₄₉	—	4	4	no	—
185	C₄×D₁₄₉	#41	1	4	yes	complemented
186	C₂³×C₁₄₉	C₂⁴	1	2	yes	—
187	C₂³×C₁₄₉	C₂⁴	1	2	yes	—
188	Q₈×C₁₄₉	—	2	4	no	—
189	D₄×C₁₄₉	—	2	2	no	—
190	D₄×C₁₄₉	—	2	2	no	—
191	D₄×C₁₄₉	—	4	4	no	—
192	C₂×C₄×C₁₄₉	—	2	4	no	—
193	C₂×C₄×C₁₄₉	—	2	4	no	—
194	C₂×C₄×C₁₄₉	—	4	4	no	—
195	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
196	C₂×C₄×C₁₄₉	C₂⁴	1	4	yes	—
197	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
198	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
199	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
200	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
201	C₂²×C₁₄₉	—	2	2	no	—
202	C₂²×C₁₄₉	—	2	2	no	—
203	C₂²×C₁₄₉	—	2	2	no	—
204	C₂²×C₁₄₉	—	2	2	no	—
205	C₂²×C₁₄₉	—	2	2	no	—
206	C₂²×C₁₄₉	—	2	2	no	—
207	C₂²×C₁₄₉	C₂⁵	1	1	yes	characteristic
208	C₂×D₁₄₉	—	2	1	no	—
209	C₂×D₁₄₉	—	2	1	no	—
210	C₂×D₁₄₉	—	2	2	no	—
211	C₂×D₁₄₉	—	2	2	no	—
212	C₂×D₁₄₉	—	2	2	no	—
213	C₂×D₁₄₉	—	2	2	no	—
214	C₂×D₁₄₉	—	2	2	no	—
215	C₂×D₁₄₉	—	2	2	no	—
216	C₂×D₁₄₉	—	4	8	no	—
217	C₂×D₁₄₉	C₂×#41	1	2	yes	—
218	C₄×C₁₄₉	—	2	2	no	—
219	C₄×C₁₄₉	—	2	2	no	—
220	C₄×C₁₄₉	—	2	4	no	—
221	C₄×C₁₄₉	—	2	1	no	—
222	C₄×C₁₄₉	C₂×#41	1	2	yes	—
223	C₄×C₁₄₉	H(5,𝔽₂)	1	2	yes	—
224	Dic₁₄₉	—	2	2	no	—
225	Dic₁₄₉	—	2	2	no	—
226	Dic₁₄₉	—	2	1	no	—
227	Dic₁₄₉	—	2	1	no	—
228	Dic₁₄₉	—	2	4	no	—
229	Dic₁₄₉	C₂×#41	1	2	yes	—
230	C₂×C₁₄₉	—	4	2	no	—
231	C₂×C₁₄₉	—	4	2	no	—
232	C₂×C₁₄₉	C₂²×#41	1	1	yes	characteristic
233	C₂×C₁₄₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
234	C₂×C₁₄₉	#585	1	1	yes	characteristic
235	D₁₄₉	—	2	2	no	—
236	D₁₄₉	—	4	2	no	—
237	D₁₄₉	—	4	2	no	—
238	C₁₄₉	#3506	1	1	yes	characteristic, complemented, Sylow
239	#3506	—	149	1	no	maximal, Sylow
240	#559	—	149	4	no	—
241	#556	—	149	2	no	—
242	#555	—	149	1	no	—
243	#555	—	149	1	no	—
244	#553	—	149	2	no	—
245	#553	—	149	2	no	—
246	#550	—	149	2	no	—
247	#547	—	149	1	no	—
248	#547	D₁₄₉	1	1	yes	characteristic, complemented
249	#538	—	149	4	no	—
250	#535	—	149	2	no	—
251	#533	—	149	1	no	—
252	#532	—	149	1	no	—
253	#525	—	149	2	no	—
254	#525	—	149	2	no	—
255	#520	—	149	2	no	—
256	C₂×C₄×D₄	—	149	1	no	—
257	C₂×#41	—	149	2	no	—
258	C₂×#41	—	149	2	no	—
259	C₂×#41	C₂×D₁₄₉	1	2	yes	complemented
260	C₂²×D₄	—	149	1	no	—
261	C₂³×C₄	—	149	2	no	—
262	C₄⋊Q₈	—	149	1	no	—
263	C₄⋊Q₈	—	149	1	no	—
264	C₄⋊Q₈	C₂×D₁₄₉	1	1	yes	characteristic, complemented
265	#127	—	149	4	no	—
266	#127	—	149	1	no	—
267	#126	—	149	4	no	—
268	#126	—	149	4	no	—
269	#125	—	149	2	no	—
270	#124	—	149	2	no	—
271	#124	—	149	4	no	—
272	#124	—	149	4	no	—
273	#124	—	149	4	no	—
274	#123	—	149	4	no	—
275	#123	—	149	4	no	—
276	#123	—	149	4	no	—
277	#123	C₂×D₁₄₉	1	4	yes	complemented
278	C₂²⋊Q₈	—	149	2	no	—
279	C₂²⋊Q₈	—	149	2	no	—
280	C₂²⋊Q₈	—	149	2	no	—
281	C₂²⋊Q₈	C₂×D₁₄₉	1	2	yes	complemented
282	#121	—	149	1	no	—
283	#121	—	149	2	no	—
284	#121	—	149	2	no	—
285	#121	—	149	4	no	—
286	#121	—	149	2	no	—
287	#121	—	149	2	no	—
288	#121	—	149	4	no	—
289	#121	—	149	1	no	—
290	#121	—	149	2	no	—
291	#121	—	149	2	no	—
292	#121	C₂×D₁₄₉	1	2	yes	—
293	#120	—	149	4	no	—
294	#120	—	149	4	no	—
295	C₄×Q₈	—	149	2	no	—
296	C₄×Q₈	—	149	4	no	—
297	C₄×Q₈	—	149	2	no	—
298	C₄×D₄	—	149	1	no	—
299	C₄×D₄	—	149	2	no	—
300	C₄×D₄	—	149	4	no	—
301	C₄×D₄	—	149	4	no	—
302	C₄×D₄	—	149	4	no	—
303	C₄×D₄	—	149	2	no	—
304	C₄×D₄	—	149	1	no	—
305	C₄×D₄	—	149	4	no	—
306	C₄×D₄	—	149	2	no	—
307	C₄×D₄	—	149	4	no	—
308	C₄×D₄	—	149	1	no	—
309	C₄×D₄	—	149	1	no	—
310	C₄×D₄	C₂×D₁₄₉	1	1	yes	characteristic
311	C₄×D₄	C₂×D₁₄₉	1	1	yes	characteristic, complemented
312	#117	—	149	2	no	—
313	#117	—	149	2	no	—
314	#117	—	149	2	no	—
315	#117	—	149	2	no	—
316	#117	—	149	2	no	—
317	C₂×C₄⋊C₄	—	149	1	no	—
318	C₂×C₄⋊C₄	—	149	2	no	—
319	C₂×C₄⋊C₄	C₂×D₁₄₉	1	2	yes	complemented
320	C₂×C₂²⋊C₄	—	149	2	no	—
321	C₂×C₄²	—	149	1	no	—
322	C₂⁴	—	149	2	no	—
323	#41	—	4	4	no	—
324	#41	—	298	8	no	—
325	#41	—	596	4	no	—
326	C₂×Q₈	—	149	2	no	—
327	C₂×Q₈	—	149	2	no	—
328	C₂×Q₈	C₂²×D₁₄₉	1	2	yes	—
329	C₂×D₄	—	298	4	no	—
330	C₂×D₄	—	149	2	no	—
331	C₂×D₄	—	149	2	no	—
332	C₂×D₄	—	149	2	no	—
333	C₂×D₄	—	149	4	no	—
334	C₂×D₄	—	149	4	no	—
335	C₂×D₄	—	149	2	no	—
336	C₂×D₄	—	149	2	no	—
337	C₂×D₄	—	149	1	no	—
338	C₂×D₄	—	149	1	no	—
339	C₂×D₄	—	149	4	no	—
340	C₂×D₄	C₂²×D₁₄₉	1	1	yes	characteristic
341	C₂×D₄	C₂²×D₁₄₉	1	1	yes	characteristic
342	C₂×D₄	C₂²×D₁₄₉	1	4	yes	—
343	C₂²×C₄	—	596	4	no	—
344	C₂²×C₄	—	149	1	no	—
345	C₂²×C₄	—	149	2	no	—
346	C₂²×C₄	—	149	2	no	—
347	C₂²×C₄	—	149	2	no	—
348	C₂²×C₄	—	149	1	no	—
349	C₂²×C₄	—	149	2	no	—
350	C₂²×C₄	—	149	4	no	—
351	C₂²×C₄	—	149	2	no	—
352	C₂²×C₄	—	149	1	no	—
353	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
354	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
355	C₂²×C₄	C₂²×D₁₄₉	1	4	yes	—
356	C₄⋊C₄	—	149	1	no	—
357	C₄⋊C₄	—	149	2	no	—
358	C₄⋊C₄	—	149	4	no	—
359	C₄⋊C₄	—	149	2	no	—
360	C₄⋊C₄	—	149	1	no	—
361	C₄⋊C₄	—	149	2	no	—
362	C₄⋊C₄	—	149	4	no	—
363	C₄⋊C₄	—	149	2	no	—
364	C₄⋊C₄	—	149	4	no	—
365	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
366	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
367	C₄⋊C₄	C₂²×D₁₄₉	1	4	yes	—
368	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
369	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
370	C₂²⋊C₄	—	149	2	no	—
371	C₂²⋊C₄	—	149	4	no	—
372	C₂²⋊C₄	—	149	4	no	—
373	C₂²⋊C₄	—	149	2	no	—
374	C₂²⋊C₄	—	149	2	no	—
375	C₂²⋊C₄	—	149	2	no	—
376	C₂²⋊C₄	—	149	4	no	—
377	C₂²⋊C₄	—	149	4	no	—
378	C₂²⋊C₄	—	149	4	no	—
379	C₂²⋊C₄	—	149	2	no	—
380	C₂²⋊C₄	—	149	4	no	—
381	C₂²⋊C₄	—	149	2	no	—
382	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
383	C₂²⋊C₄	C₂²×D₁₄₉	1	4	yes	—
384	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
385	C₄²	—	149	1	no	—
386	C₄²	—	149	1	no	—
387	C₄²	—	149	1	no	—
388	C₄²	—	149	4	no	—
389	C₄²	—	149	4	no	—
390	C₄²	—	149	4	no	—
391	C₄²	C₂²×D₁₄₉	1	1	yes	characteristic
392	C₂³	—	298	4	no	—
393	C₂³	—	596	2	no	—
394	C₂³	—	596	2	no	—
395	C₂³	—	149	2	no	—
396	C₂³	—	149	2	no	—
397	C₂³	—	149	1	no	—
398	C₂³	C₂³×D₁₄₉	1	2	yes	—
399	C₂³	C₂³×D₁₄₉	1	2	yes	—
400	Q₈	—	2	4	no	—
401	Q₈	—	298	4	no	—
402	Q₈	—	596	2	no	—
403	D₄	—	2	2	no	—
404	D₄	—	2	2	no	—
405	D₄	—	4	4	no	—
406	D₄	—	298	4	no	—
407	D₄	—	298	4	no	—
408	D₄	—	298	4	no	—
409	D₄	—	298	4	no	—
410	D₄	—	298	2	no	—
411	D₄	—	298	2	no	—
412	D₄	—	596	4	no	—
413	D₄	—	596	2	no	—
414	D₄	—	596	4	no	—
415	D₄	—	596	4	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	4	4	no	—
419	C₂×C₄	—	298	4	no	—
420	C₂×C₄	—	298	2	no	—
421	C₂×C₄	—	298	4	no	—
422	C₂×C₄	—	596	2	no	—
423	C₂×C₄	—	596	2	no	—
424	C₂×C₄	—	596	1	no	—
425	C₂×C₄	—	596	4	no	—
426	C₂×C₄	—	596	2	no	—
427	C₂×C₄	—	149	4	no	—
428	C₂×C₄	—	149	2	no	—
429	C₂×C₄	—	149	1	no	—
430	C₂×C₄	—	149	2	no	—
431	C₂×C₄	—	149	1	no	—
432	C₂×C₄	—	149	1	no	—
433	C₂×C₄	—	149	4	no	—
434	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
435	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
436	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
437	C₂×C₄	C₂³×D₁₄₉	1	4	yes	—
438	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
439	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
440	C₂²	—	2	2	no	—
441	C₂²	—	2	2	no	—
442	C₂²	—	2	2	no	—
443	C₂²	—	2	2	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	298	1	no	—
447	C₂²	—	298	1	no	—
448	C₂²	—	298	2	no	—
449	C₂²	—	298	2	no	—
450	C₂²	—	298	2	no	—
451	C₂²	—	298	2	no	—
452	C₂²	—	298	2	no	—
453	C₂²	—	298	2	no	—
454	C₂²	—	596	8	no	—
455	C₂²	—	149	2	no	—
456	C₂²	C₂⁴×D₁₄₉	1	1	yes	characteristic
457	C₄	—	2	2	no	—
458	C₄	—	2	2	no	—
459	C₄	—	2	4	no	—
460	C₄	—	2	1	no	—
461	C₄	—	298	2	no	—
462	C₄	—	298	1	no	—
463	C₄	—	298	2	no	—
464	C₄	—	298	1	no	—
465	C₄	—	298	4	no	—
466	C₄	—	149	2	no	—
467	C₄	#41×D₁₄₉	1	2	yes	—
468	C₄	#18011956	1	2	yes	—
469	C₂	—	4	2	no	—
470	C₂	—	4	2	no	—
471	C₂	—	298	2	no	—
472	C₂	—	596	2	no	—
473	C₂	—	596	2	no	—
474	C₂	C₂×#41×D₁₄₉	1	1	yes	characteristic
475	C₂	C₂×#18011956	1	1	yes	characteristic
476	C₂	#23750462	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₄₉
commutator, socle, cosocle	C₂²×C₁₄₉	C₂⁵
Fitting	#547×C₁₄₉	C₂
hypercenter	#547	D₁₄₉
hypocenter	C₁₄₉	#3506
LCS	G ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ #547

Complements

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

N	H ≅ G/N	type
1. #23750359	C₂	semidirect
2. #23750346	C₂	semidirect
3. #23750340	C₂	semidirect
4. #23750340	C₂	semidirect
5. #23750323	C₂	semidirect
6. #23750322	C₂	semidirect
7. #23750294	C₂	semidirect
8. #23750278	C₂	semidirect
9. #23750211	C₂	semidirect
10. #23750191	C₂	semidirect
11. #23750180	C₂	semidirect
12. #23750172	C₂	semidirect
13. #23750138	C₂	semidirect
14. #23750132	C₂	semidirect
15. #23750106	C₂	semidirect
16. C₄×D₄×D₁₄₉	C₂	semidirect
17. #547×C₁₄₉	C₂	semidirect
18. C₂×#14558737	C₂²	semidirect
22. #18011911	C₂²	semidirect
23. #18011910	C₂²	semidirect
25. #18011907	C₂²	semidirect
26. #18011906	C₂²	semidirect
27. #18011904	C₂²	semidirect
28. #18011902	C₂²	semidirect
30. #18011897	C₂²	semidirect
31. #18011897	C₂²	semidirect
32. #18011897	C₂²	semidirect
33. #18011896	C₂²	semidirect
34. #18011896	C₂²	semidirect
35. #18011892	C₂²	semidirect
38. #18011887	C₂²	semidirect
42. #18011885	C₂²	semidirect
43. #18011885	C₂²	semidirect
47. #18011882	C₂²	semidirect
48. #18011882	C₂²	semidirect
51. Q₈×Dic₁₄₉	C₂²	semidirect
52. #18011876	C₂²	semidirect
53. #18011876	C₂²	semidirect
55. C₄×D₅₉₆	C₂²	semidirect
61. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
62. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
63. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
65. #18011871	C₂²	semidirect
66. #18011870	C₂²	semidirect
67. #18011870	C₂²	semidirect
69. #18011869	C₂²	semidirect
70. #18011869	C₂²	semidirect
72. C₄⋊C₄×D₁₄₉	C₂²	semidirect
75. C₂×#41×C₁₄₉	C₂²	semidirect
76. C₄⋊Q₈×C₁₄₉	C₂²	semidirect
77. #123×C₁₄₉	C₂²	semidirect
78. C₂²⋊Q₈×C₁₄₉	C₂²	semidirect
81. C₄×D₄×C₁₄₉	C₂²	semidirect
82. C₂×C₄⋊C₄×C₁₄₉	C₂²	semidirect
185. C₄×D₁₄₉	#41	semidirect
238. C₁₄₉	#3506	semidirect
248. #547	D₁₄₉	semidirect
259. C₂×#41	C₂×D₁₄₉	semidirect
264. C₄⋊Q₈	C₂×D₁₄₉	semidirect
277. #123	C₂×D₁₄₉	semidirect
281. C₂²⋊Q₈	C₂×D₁₄₉	semidirect
311. C₄×D₄	C₂×D₁₄₉	semidirect
319. C₂×C₄⋊C₄	C₂×D₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
#23750359	2
#23750346	2
#23750340	2
#23750323	2
#23750322	2
#23750294	2
#23750278	2
#23750211	2
#23750191	2
#23750180	2
#23750172	2
#23750138	2
#23750132	2
#23750106	2
C₄×D₄×D₁₄₉	2
#547×C₁₄₉	2
#3506	149