Subgroups — #34058437

Order 19072.

1022 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750346	C₂	1	2	yes	maximal, complemented
2	#23750333	C₂	1	2	yes	maximal, complemented
3	#23750317	C₂	1	2	yes	maximal, complemented
4	#23750310	C₂	1	4	yes	maximal, complemented
5	#23750309	C₂	1	2	yes	maximal, complemented
6	#23750301	C₂	1	4	yes	maximal, complemented
7	#23750256	C₂	1	1	yes	maximal, characteristic, complemented
8	#23750248	C₂	1	2	yes	maximal, complemented
9	#23750235	C₂	1	2	yes	maximal, complemented
10	#23750199	C₂	1	1	yes	maximal, characteristic, complemented
11	#23750177	C₂	1	2	yes	maximal, complemented
12	#23750161	C₂	1	2	yes	maximal, complemented
13	#23750136	C₂	1	1	yes	maximal, characteristic
14	#23750106	C₂	1	1	yes	maximal, characteristic, complemented
15	#23750103	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#18011870	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₂²⋊Q₈×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#14558736	C₂²	1	1	yes	characteristic
19	#18011910	C₂²	1	2	yes	complemented
20	#18011910	C₂²	1	2	yes	complemented
21	#18011909	C₂²	1	2	yes	complemented
22	#18011906	C₂²	1	4	yes	complemented
23	#18011906	C₂²	1	4	yes	complemented
24	#18011904	C₂²	1	4	yes	—
25	#18011904	C₂²	1	4	yes	—
26	#18011902	C₂²	1	2	yes	complemented
27	#18011902	C₂²	1	4	yes	complemented
28	#18011902	C₂²	1	2	yes	complemented
29	#18011901	C₂²	1	4	yes	complemented
30	#18011901	C₂²	1	4	yes	complemented
31	#18011900	C₂²	1	2	yes	complemented
32	#18011897	C₂²	1	4	yes	—
33	#18011895	C₂²	1	4	yes	—
34	#18011894	C₂²	1	4	yes	—
35	#18011894	C₂²	1	2	yes	—
36	#18011893	C₂²	1	4	yes	—
37	#18011891	C₂²	1	4	yes	complemented
38	#18011890	C₂²	1	1	yes	characteristic
39	#18011890	C₂²	1	1	yes	characteristic
40	#18011890	C₂²	1	4	yes	—
41	#18011888	C₂²	1	4	yes	—
42	#18011887	C₂²	1	2	yes	complemented
43	#18011887	C₂²	1	2	yes	complemented
44	#18011885	C₂²	1	1	yes	characteristic
45	#18011885	C₂²	1	1	yes	characteristic
46	#18011880	C₂²	1	2	yes	—
47	Q₈×Dic₁₄₉	C₂²	1	2	yes	complemented
48	Q₈×Dic₁₄₉	C₂²	1	2	yes	complemented
49	Q₈×Dic₁₄₉	C₂²	1	2	yes	complemented
50	Q₈×Dic₁₄₉	C₂²	1	2	yes	complemented
51	#18011876	C₂²	1	2	yes	complemented
52	#18011876	C₂²	1	4	yes	complemented
53	#18011873	C₂²	1	2	yes	complemented
54	C₄×C₂²⋊D₁₄₉	C₂²	1	4	yes	—
55	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	—
56	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	—
57	#18011871	C₂²	1	4	yes	—
58	#18011870	C₂²	1	1	yes	characteristic
59	#18011870	C₂²	1	2	yes	—
60	#18011870	C₂²	1	1	yes	characteristic
61	#18011870	C₂²	1	4	yes	—
62	#18011870	C₂²	1	1	yes	characteristic
63	#18011870	C₂²	1	2	yes	—
64	#18011870	C₂²	1	1	yes	characteristic
65	#18011870	C₂²	1	1	yes	characteristic
66	#18011869	C₂²	1	4	yes	complemented
67	#18011869	C₂²	1	2	yes	complemented
68	#18011867	C₂²	1	4	yes	—
69	C₂×C₄⋊Dic₁₄₉	C₂²	1	1	yes	characteristic
70	C₂×C₄⋊Dic₁₄₉	C₂²	1	1	yes	characteristic
71	C₄⋊C₄×D₁₄₉	C₂²	1	2	yes	complemented
72	C₂×C₂²⋊Dic₁₄₉	C₂²	1	2	yes	—
73	C₂×C₄×Dic₁₄₉	C₂²	1	2	yes	—
74	C₂²×Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
75	C₂³×C₄×C₁₄₉	C₂²	1	1	yes	characteristic
76	C₂²⋊Q₈×C₁₄₉	C₂²	1	2	yes	—
77	C₂²⋊Q₈×C₁₄₉	C₂²	1	2	yes	—
78	C₂²⋊Q₈×C₁₄₉	C₂²	1	2	yes	—
79	C₂²⋊Q₈×C₁₄₉	C₂²	1	2	yes	—
80	C₂×C₄⋊C₄×C₁₄₉	C₂²	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₁₄₉	C₂²	1	2	yes	—
82	C₂×C₂²⋊C₄×C₁₄₉	C₂²	1	2	yes	—
83	#14558736	—	2	4	no	—
84	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
85	C₂×Dic₂₉₈	C₂³	1	4	yes	—
86	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
87	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
88	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
89	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
90	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
91	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
92	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
93	C₂×C₄×D₁₄₉	C₂³	1	4	yes	—
94	C₄⋊Dic₁₄₉	C₂³	1	4	yes	—
95	C₄⋊Dic₁₄₉	C₂³	1	4	yes	—
96	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
97	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
98	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
99	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
100	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
101	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
102	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
103	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
104	C₄⋊Dic₁₄₉	C₂³	1	4	yes	—
105	#14558715	C₂³	1	4	yes	—
106	#14558715	C₂³	1	4	yes	—
107	#14558715	C₂³	1	4	yes	—
108	#14558715	C₂³	1	4	yes	—
109	#14558715	C₂³	1	4	yes	—
110	#14558715	C₂³	1	2	yes	—
111	#14558715	C₂³	1	2	yes	—
112	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
113	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
114	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
115	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
116	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
117	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
118	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
119	#14558713	C₂³	1	2	yes	—
120	#14558713	C₂³	1	4	yes	—
121	#14558713	C₂³	1	2	yes	—
122	#14558713	C₂³	1	4	yes	—
123	#14558713	C₂³	1	4	yes	—
124	C₄×Dic₁₄₉	C₂³	1	4	yes	—
125	C₄×Dic₁₄₉	C₂³	1	4	yes	—
126	C₄×Dic₁₄₉	C₂³	1	2	yes	—
127	C₄×Dic₁₄₉	C₂³	1	4	yes	—
128	C₄×Dic₁₄₉	C₂³	1	2	yes	—
129	C₄×Dic₁₄₉	C₂³	1	2	yes	—
130	C₄×Dic₁₄₉	C₂³	1	2	yes	—
131	C₄×Dic₁₄₉	C₂³	1	2	yes	—
132	C₂⁴×C₁₄₉	C₂³	1	1	yes	characteristic
133	C₂×Q₈×C₁₄₉	—	2	4	no	—
134	C₂×Q₈×C₁₄₉	C₂³	1	2	yes	—
135	C₂×Q₈×C₁₄₉	C₂³	1	2	yes	—
136	C₂²×C₄×C₁₄₉	—	2	4	no	—
137	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
138	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
139	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
140	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
141	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
142	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
143	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
144	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
145	C₄⋊C₄×C₁₄₉	C₂³	1	4	yes	—
146	C₄⋊C₄×C₁₄₉	C₂³	1	4	yes	—
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	4	yes	—
151	C₂²×D₁₄₉	C₂⁴	1	2	yes	—
152	Dic₂₉₈	—	2	2	no	—
153	Dic₂₉₈	—	4	4	no	—
154	D₅₉₆	—	2	2	no	—
155	C₂²⋊D₁₄₉	—	2	4	no	—
156	C₂²⋊D₁₄₉	—	2	4	no	—
157	C₂²⋊D₁₄₉	—	4	2	no	—
158	C₂×Dic₁₄₉	—	2	4	no	—
159	C₂×Dic₁₄₉	—	4	2	no	—
160	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
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	2	yes	—
166	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
167	C₄×D₁₄₉	—	2	4	no	—
168	C₄×D₁₄₉	—	4	4	no	—
169	C₂³×C₁₄₉	—	2	2	no	—
170	C₂³×C₁₄₉	—	2	2	no	—
171	C₂³×C₁₄₉	—	4	1	no	—
172	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
173	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
174	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
175	Q₈×C₁₄₉	—	2	4	no	—
176	Q₈×C₁₄₉	—	2	4	no	—
177	C₂×C₄×C₁₄₉	—	2	2	no	—
178	C₂×C₄×C₁₄₉	—	2	4	no	—
179	C₂×C₄×C₁₄₉	—	2	2	no	—
180	C₂×C₄×C₁₄₉	—	2	2	no	—
181	C₂×C₄×C₁₄₉	—	2	2	no	—
182	C₂×C₄×C₁₄₉	—	2	2	no	—
183	C₂×C₄×C₁₄₉	—	4	2	no	—
184	C₂×C₄×C₁₄₉	#41	1	4	yes	—
185	C₂×C₄×C₁₄₉	C₂⁴	1	4	yes	—
186	C₂×C₄×C₁₄₉	C₂⁴	1	4	yes	—
187	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
188	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
189	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
190	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
191	C₂²×C₁₄₉	—	2	1	no	—
192	C₂²×C₁₄₉	—	2	1	no	—
193	C₂²×C₁₄₉	—	2	1	no	—
194	C₂²×C₁₄₉	—	2	1	no	—
195	C₂²×C₁₄₉	—	2	1	no	—
196	C₂²×C₁₄₉	—	2	1	no	—
197	C₂²×C₁₄₉	—	2	1	no	—
198	C₂²×C₁₄₉	—	4	4	no	—
199	C₂²×C₁₄₉	C₂×#41	1	2	yes	—
200	C₂²×C₁₄₉	2₋¹⁺⁴	1	2	yes	—
201	C₂²×C₁₄₉	C₂⁵	1	1	yes	characteristic
202	C₂×D₁₄₉	—	2	2	no	—
203	C₂×D₁₄₉	—	2	2	no	—
204	C₂×D₁₄₉	—	2	2	no	—
205	C₄×C₁₄₉	—	2	1	no	—
206	C₄×C₁₄₉	—	2	1	no	—
207	C₄×C₁₄₉	—	2	4	no	—
208	C₄×C₁₄₉	—	2	4	no	—
209	C₄×C₁₄₉	C₂×#41	1	2	yes	—
210	C₄×C₁₄₉	C₂×#41	1	2	yes	—
211	Dic₁₄₉	—	2	2	no	—
212	Dic₁₄₉	—	2	2	no	—
213	Dic₁₄₉	—	2	2	no	—
214	Dic₁₄₉	—	2	2	no	—
215	Dic₁₄₉	—	2	2	no	—
216	Dic₁₄₉	—	2	2	no	—
217	Dic₁₄₉	—	2	2	no	—
218	C₂×C₁₄₉	—	2	2	no	—
219	C₂×C₁₄₉	—	2	2	no	—
220	C₂×C₁₄₉	—	4	1	no	—
221	C₂×C₁₄₉	C₂²×#41	1	1	yes	characteristic
222	C₂×C₁₄₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
223	C₂×C₁₄₉	#585	1	1	yes	characteristic
224	D₁₄₉	—	4	2	no	—
225	C₁₄₉	#3495	1	1	yes	characteristic, complemented, Sylow
226	#3495	—	149	1	no	maximal, Sylow
227	#556	—	149	2	no	—
228	#554	—	149	2	no	—
229	#552	—	149	2	no	—
230	#552	—	149	2	no	—
231	#552	—	149	4	no	—
232	#551	—	149	4	no	—
233	#544	—	149	1	no	—
234	#542	—	149	2	no	—
235	#541	—	149	2	no	—
236	#536	—	149	1	no	—
237	#533	—	149	2	no	—
238	#529	—	149	2	no	—
239	#525	—	149	1	no	—
240	C₂×C₂²⋊Q₈	D₁₄₉	1	1	yes	characteristic, complemented
241	#520	—	149	1	no	—
242	#519	—	149	1	no	—
243	C₂×#117	—	149	1	no	—
244	C₂×#41	—	149	1	no	—
245	C₂²×Q₈	C₂×D₁₄₉	1	1	yes	characteristic
246	C₂³×C₄	C₂×D₁₄₉	1	1	yes	characteristic
247	C₄⋊Q₈	—	149	2	no	—
248	C₄⋊Q₈	—	149	2	no	—
249	C₄⋊Q₈	—	149	2	no	—
250	#126	—	149	4	no	—
251	#126	—	149	4	no	—
252	#126	—	149	4	no	—
253	#126	—	149	4	no	—
254	#125	—	149	2	no	—
255	#125	—	149	4	no	—
256	#125	—	149	4	no	—
257	#125	—	149	4	no	—
258	#125	—	149	2	no	—
259	#124	—	149	2	no	—
260	#124	—	149	4	no	—
261	#123	—	149	2	no	—
262	#123	—	149	4	no	—
263	#123	—	149	4	no	—
264	#123	—	149	4	no	—
265	C₂²⋊Q₈	—	149	2	no	—
266	C₂²⋊Q₈	—	149	2	no	—
267	C₂²⋊Q₈	—	149	1	no	—
268	C₂²⋊Q₈	—	149	1	no	—
269	C₂²⋊Q₈	—	149	4	no	—
270	C₂²⋊Q₈	—	149	4	no	—
271	C₂²⋊Q₈	—	149	4	no	—
272	C₂²⋊Q₈	C₂×D₁₄₉	1	2	yes	—
273	C₂²⋊Q₈	C₂×D₁₄₉	1	2	yes	—
274	C₂²⋊Q₈	C₂×D₁₄₉	1	2	yes	—
275	C₂²⋊Q₈	C₂×D₁₄₉	1	2	yes	—
276	#121	—	149	1	no	—
277	#121	—	149	1	no	—
278	#120	—	149	2	no	—
279	C₄×Q₈	—	149	2	no	—
280	C₄×Q₈	—	149	2	no	—
281	C₄×Q₈	—	149	2	no	—
282	C₄×Q₈	—	149	2	no	—
283	C₄×Q₈	—	149	2	no	—
284	C₄×Q₈	—	149	4	no	—
285	C₄×D₄	—	149	4	no	—
286	C₄×D₄	—	149	2	no	—
287	C₄×D₄	—	149	2	no	—
288	C₄×D₄	—	149	2	no	—
289	C₄×D₄	—	149	4	no	—
290	#117	—	149	1	no	—
291	#117	—	149	1	no	—
292	#117	—	149	2	no	—
293	#117	—	149	1	no	—
294	#117	—	149	2	no	—
295	#117	—	149	1	no	—
296	#117	—	149	1	no	—
297	#117	—	149	4	no	—
298	#117	—	149	2	no	—
299	#117	—	149	4	no	—
300	#117	—	149	4	no	—
301	C₂×C₄⋊C₄	—	149	1	no	—
302	C₂×C₄⋊C₄	—	149	1	no	—
303	C₂×C₄⋊C₄	—	149	2	no	—
304	C₂×C₄⋊C₄	C₂×D₁₄₉	1	1	yes	characteristic
305	C₂×C₄⋊C₄	C₂×D₁₄₉	1	2	yes	—
306	C₂×C₂²⋊C₄	—	149	2	no	—
307	C₂×C₂²⋊C₄	C₂×D₁₄₉	1	2	yes	—
308	C₂×C₄²	—	149	2	no	—
309	C₂⁴	C₂²×D₁₄₉	1	1	yes	characteristic
310	#41	—	298	4	no	—
311	C₂×Q₈	—	2	4	no	—
312	C₂×Q₈	—	149	1	no	—
313	C₂×Q₈	—	149	4	no	—
314	C₂×Q₈	C₂²×D₁₄₉	1	2	yes	—
315	C₂×Q₈	C₂²×D₁₄₉	1	2	yes	—
316	C₂×D₄	—	149	2	no	—
317	C₂×D₄	—	149	2	no	—
318	C₂×D₄	—	149	2	no	—
319	C₂×D₄	—	149	1	no	—
320	C₂²×C₄	—	2	4	no	—
321	C₂²×C₄	—	149	2	no	—
322	C₂²×C₄	—	149	2	no	—
323	C₂²×C₄	—	149	2	no	—
324	C₂²×C₄	—	149	4	no	—
325	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
326	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
327	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
328	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
329	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
330	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
331	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
332	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
333	C₄⋊C₄	—	149	1	no	—
334	C₄⋊C₄	—	149	1	no	—
335	C₄⋊C₄	—	149	2	no	—
336	C₄⋊C₄	—	149	1	no	—
337	C₄⋊C₄	—	149	1	no	—
338	C₄⋊C₄	—	149	2	no	—
339	C₄⋊C₄	—	149	4	no	—
340	C₄⋊C₄	—	149	1	no	—
341	C₄⋊C₄	—	149	1	no	—
342	C₄⋊C₄	—	149	4	no	—
343	C₄⋊C₄	—	149	4	no	—
344	C₄⋊C₄	—	149	4	no	—
345	C₄⋊C₄	—	149	4	no	—
346	C₄⋊C₄	—	149	4	no	—
347	C₄⋊C₄	—	149	2	no	—
348	C₄⋊C₄	—	149	2	no	—
349	C₄⋊C₄	—	149	4	no	—
350	C₄⋊C₄	—	149	4	no	—
351	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
352	C₄⋊C₄	C₂²×D₁₄₉	1	4	yes	—
353	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
354	C₄⋊C₄	C₂²×D₁₄₉	1	4	yes	—
355	C₂²⋊C₄	—	149	2	no	—
356	C₂²⋊C₄	—	149	2	no	—
357	C₂²⋊C₄	—	149	2	no	—
358	C₂²⋊C₄	—	149	2	no	—
359	C₂²⋊C₄	—	149	2	no	—
360	C₂²⋊C₄	—	149	2	no	—
361	C₂²⋊C₄	—	149	2	no	—
362	C₂²⋊C₄	—	149	2	no	—
363	C₂²⋊C₄	—	149	4	no	—
364	C₂²⋊C₄	—	149	4	no	—
365	C₂²⋊C₄	—	149	2	no	—
366	C₂²⋊C₄	—	149	4	no	—
367	C₂²⋊C₄	C₂²×D₁₄₉	1	4	yes	—
368	C₂²⋊C₄	C₂²×D₁₄₉	1	4	yes	—
369	C₄²	—	149	2	no	—
370	C₄²	—	149	2	no	—
371	C₄²	—	149	2	no	—
372	C₄²	—	149	2	no	—
373	C₄²	—	149	4	no	—
374	C₄²	—	149	4	no	—
375	C₄²	—	149	4	no	—
376	C₄²	—	149	2	no	—
377	C₂³	—	2	2	no	—
378	C₂³	—	2	2	no	—
379	C₂³	—	4	1	no	—
380	C₂³	—	149	2	no	—
381	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
382	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
383	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
384	Q₈	—	2	4	no	—
385	Q₈	—	2	4	no	—
386	Q₈	—	298	2	no	—
387	Q₈	—	596	4	no	—
388	D₄	—	298	4	no	—
389	D₄	—	298	4	no	—
390	D₄	—	298	2	no	—
391	D₄	—	596	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	298	4	no	—
400	C₂×C₄	—	298	4	no	—
401	C₂×C₄	—	596	4	no	—
402	C₂×C₄	—	596	2	no	—
403	C₂×C₄	—	149	2	no	—
404	C₂×C₄	—	149	2	no	—
405	C₂×C₄	—	149	2	no	—
406	C₂×C₄	—	149	2	no	—
407	C₂×C₄	—	149	2	no	—
408	C₂×C₄	—	149	2	no	—
409	C₂×C₄	—	149	2	no	—
410	C₂×C₄	#14558735	1	4	yes	—
411	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
412	C₂×C₄	C₂³×D₁₄₉	1	4	yes	—
413	C₂×C₄	C₂³×D₁₄₉	1	4	yes	—
414	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
415	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
416	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	2	1	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	2	1	no	—
424	C₂²	—	4	4	no	—
425	C₂²	—	298	2	no	—
426	C₂²	—	298	2	no	—
427	C₂²	—	298	2	no	—
428	C₂²	C₂×#14558735	1	2	yes	—
429	C₂²	#18011959	1	2	yes	—
430	C₂²	C₂⁴×D₁₄₉	1	1	yes	characteristic
431	C₄	—	2	1	no	—
432	C₄	—	2	1	no	—
433	C₄	—	2	4	no	—
434	C₄	—	2	4	no	—
435	C₄	—	298	2	no	—
436	C₄	—	298	2	no	—
437	C₄	—	298	2	no	—
438	C₄	—	298	2	no	—
439	C₄	—	298	2	no	—
440	C₄	—	298	2	no	—
441	C₄	—	298	2	no	—
442	C₄	C₂×#14558735	1	2	yes	—
443	C₄	C₂×#14558735	1	2	yes	—
444	C₂	—	2	2	no	—
445	C₂	—	2	2	no	—
446	C₂	—	4	1	no	—
447	C₂	—	596	2	no	—
448	C₂	C₂²×#14558735	1	1	yes	characteristic
449	C₂	C₂×#18011959	1	1	yes	characteristic
450	C₂	#23750461	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₄₉
commutator, socle, cosocle	C₂²×C₁₄₉	C₂⁵
Fitting	C₂×C₂²⋊Q₈×C₁₄₉	C₂
prime radical	#23750136	C₂
hypercenter	C₂×C₂²⋊Q₈	D₁₄₉
hypocenter	C₁₄₉	#3495
LCS	G ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ C₂×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. #23750346	C₂	semidirect
2. #23750333	C₂	semidirect
3. #23750317	C₂	semidirect
4. #23750310	C₂	semidirect
5. #23750309	C₂	semidirect
6. #23750301	C₂	semidirect
7. #23750256	C₂	semidirect
8. #23750248	C₂	semidirect
9. #23750235	C₂	semidirect
10. #23750199	C₂	semidirect
11. #23750177	C₂	semidirect
12. #23750161	C₂	semidirect
14. #23750106	C₂	semidirect
15. #23750103	C₂	semidirect
16. C₂×#18011870	C₂	semidirect
17. C₂×C₂²⋊Q₈×C₁₄₉	C₂	semidirect
19. #18011910	C₂²	semidirect
20. #18011910	C₂²	semidirect
21. #18011909	C₂²	semidirect
22. #18011906	C₂²	semidirect
23. #18011906	C₂²	semidirect
26. #18011902	C₂²	semidirect
27. #18011902	C₂²	semidirect
28. #18011902	C₂²	semidirect
29. #18011901	C₂²	semidirect
30. #18011901	C₂²	semidirect
31. #18011900	C₂²	semidirect
37. #18011891	C₂²	semidirect
42. #18011887	C₂²	semidirect
43. #18011887	C₂²	semidirect
47. Q₈×Dic₁₄₉	C₂²	semidirect
48. Q₈×Dic₁₄₉	C₂²	semidirect
49. Q₈×Dic₁₄₉	C₂²	semidirect
50. Q₈×Dic₁₄₉	C₂²	semidirect
51. #18011876	C₂²	semidirect
52. #18011876	C₂²	semidirect
53. #18011873	C₂²	semidirect
66. #18011869	C₂²	semidirect
67. #18011869	C₂²	semidirect
71. C₄⋊C₄×D₁₄₉	C₂²	semidirect
225. C₁₄₉	#3495	semidirect
240. C₂×C₂²⋊Q₈	D₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
#23750346	2
#23750333	2
#23750317	2
#23750310	2
#23750309	2
#23750301	2
#23750256	2
#23750248	2
#23750235	2
#23750199	2
#23750177	2
#23750161	2
#23750136	2
#23750106	2
#23750103	2
C₂×#18011870	2
C₂×C₂²⋊Q₈×C₁₄₉	2
#3495	149