Subgroups — #34058900

Order 19072.

1038 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750376	C₂	1	2	yes	maximal, complemented
2	#23750371	C₂	1	2	yes	maximal, complemented
3	#23750329	C₂	1	2	yes	maximal, complemented
4	#23750310	C₂	1	2	yes	maximal, complemented
5	#23750302	C₂	1	2	yes	maximal, complemented
6	#23750301	C₂	1	2	yes	maximal, complemented
7	#23750276	C₂	1	2	yes	maximal, complemented
8	#23750265	C₂	1	2	yes	maximal, complemented
9	#23750254	C₂	1	1	yes	maximal, characteristic, complemented
10	#23750250	C₂	1	1	yes	maximal, characteristic, complemented
11	#23750245	C₂	1	2	yes	maximal, complemented
12	#23750224	C₂	1	1	yes	maximal, characteristic, complemented
13	#23750222	C₂	1	2	yes	maximal, complemented
14	#23750221	C₂	1	2	yes	maximal, complemented
15	#23750215	C₂	1	1	yes	maximal, characteristic, complemented
16	#23750199	C₂	1	2	yes	maximal, complemented
17	#23750136	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#18011894	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₂²⋊Q₈×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#14558736	C₂²	1	2	yes	—
21	C₂×#14558736	C₂²	1	1	yes	characteristic, complemented
22	C₂²×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic
23	#18011910	C₂²	1	2	yes	complemented
24	#18011909	C₂²	1	2	yes	complemented
25	#18011909	C₂²	1	2	yes	complemented
26	#18011906	C₂²	1	2	yes	complemented
27	#18011906	C₂²	1	2	yes	complemented
28	#18011906	C₂²	1	2	yes	complemented
29	#18011906	C₂²	1	2	yes	complemented
30	#18011904	C₂²	1	2	yes	complemented
31	#18011904	C₂²	1	2	yes	complemented
32	#18011902	C₂²	1	2	yes	complemented
33	#18011901	C₂²	1	2	yes	complemented
34	#18011901	C₂²	1	2	yes	complemented
35	#18011901	C₂²	1	2	yes	complemented
36	#18011901	C₂²	1	2	yes	complemented
37	#18011900	C₂²	1	2	yes	complemented
38	#18011900	C₂²	1	2	yes	complemented
39	#18011897	C₂²	1	2	yes	—
40	#18011897	C₂²	1	2	yes	complemented
41	#18011896	C₂²	1	2	yes	complemented
42	#18011896	C₂²	1	2	yes	complemented
43	#18011896	C₂²	1	2	yes	complemented
44	#18011896	C₂²	1	2	yes	complemented
45	#18011895	C₂²	1	2	yes	—
46	#18011894	C₂²	1	2	yes	—
47	#18011894	C₂²	1	2	yes	—
48	#18011894	C₂²	1	2	yes	—
49	#18011894	C₂²	1	2	yes	—
50	#18011894	C₂²	1	2	yes	—
51	#18011894	C₂²	1	2	yes	complemented
52	#18011894	C₂²	1	2	yes	complemented
53	#18011893	C₂²	1	2	yes	—
54	#18011893	C₂²	1	2	yes	complemented
55	#18011891	C₂²	1	2	yes	complemented
56	#18011890	C₂²	1	1	yes	characteristic
57	#18011890	C₂²	1	2	yes	complemented
58	#18011890	C₂²	1	1	yes	characteristic, complemented
59	#18011889	C₂²	1	2	yes	complemented
60	#18011889	C₂²	1	2	yes	complemented
61	#18011889	C₂²	1	2	yes	complemented
62	#18011889	C₂²	1	2	yes	complemented
63	#18011888	C₂²	1	2	yes	—
64	#18011888	C₂²	1	2	yes	—
65	#18011887	C₂²	1	2	yes	complemented
66	#18011887	C₂²	1	2	yes	complemented
67	#18011887	C₂²	1	2	yes	complemented
68	#18011887	C₂²	1	2	yes	complemented
69	#18011886	C₂²	1	2	yes	complemented
70	#18011885	C₂²	1	1	yes	characteristic
71	#18011885	C₂²	1	2	yes	—
72	#18011885	C₂²	1	1	yes	characteristic, complemented
73	#18011884	C₂²	1	2	yes	—
74	#18011884	C₂²	1	2	yes	—
75	#18011881	C₂²	1	2	yes	—
76	#18011880	C₂²	1	2	yes	—
77	#18011876	C₂²	1	2	yes	complemented
78	#18011873	C₂²	1	2	yes	complemented
79	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	—
80	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	—
81	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	complemented
82	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	complemented
83	#18011871	C₂²	1	2	yes	—
84	#18011871	C₂²	1	2	yes	—
85	#18011870	C₂²	1	2	yes	complemented
86	#18011870	C₂²	1	1	yes	characteristic, complemented
87	#18011869	C₂²	1	2	yes	complemented
88	#18011867	C₂²	1	2	yes	—
89	C₂×#14558715	C₂²	1	1	yes	characteristic
90	C₂×#14558715	C₂²	1	1	yes	characteristic
91	C₄⋊C₄×D₁₄₉	C₂²	1	2	yes	complemented
92	C₂×C₂²⋊Dic₁₄₉	C₂²	1	1	yes	characteristic
93	C₂×#14558713	C₂²	1	1	yes	characteristic
94	C₂×#14558713	C₂²	1	1	yes	characteristic
95	C₂²⋊C₄×D₁₄₉	C₂²	1	2	yes	—
96	C₂²×Q₈×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
97	C₂³×C₄×C₁₄₉	C₂²	1	1	yes	characteristic
98	C₂²⋊Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
99	C₂²⋊Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
100	C₂²⋊Q₈×C₁₄₉	C₂²	1	2	yes	—
101	C₂²⋊Q₈×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
102	C₂²⋊Q₈×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
103	C₂²⋊Q₈×C₁₄₉	C₂²	1	2	yes	complemented
104	C₂×C₄⋊C₄×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
105	C₂×C₄⋊C₄×C₁₄₉	C₂²	1	2	yes	complemented
106	C₂×C₂²⋊C₄×C₁₄₉	C₂²	1	2	yes	—
107	C₂³×D₁₄₉	C₂³	1	1	yes	characteristic
108	#14558736	—	4	4	no	—
109	#14558736	—	4	2	no	—
110	C₂×Dic₂₉₈	C₂³	1	2	yes	—
111	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
112	C₂×Dic₂₉₈	C₂³	1	2	yes	—
113	C₂×D₅₉₆	C₂³	1	2	yes	—
114	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
115	C₂×D₅₉₆	C₂³	1	2	yes	—
116	C₂×C₂²⋊D₁₄₉	—	4	2	no	—
117	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
118	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
119	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
120	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
121	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
122	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
123	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
124	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
125	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
126	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
127	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
128	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
129	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
130	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
131	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
132	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
133	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
134	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
135	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
136	#14558715	C₂³	1	2	yes	—
137	#14558715	C₂³	1	2	yes	—
138	#14558715	C₂³	1	2	yes	—
139	#14558715	C₂³	1	2	yes	—
140	#14558715	C₂³	1	2	yes	—
141	#14558715	C₂³	1	2	yes	—
142	#14558715	C₂³	1	2	yes	—
143	#14558715	C₂³	1	2	yes	—
144	#14558715	C₂³	1	2	yes	—
145	#14558715	C₂³	1	2	yes	—
146	#14558715	C₂³	1	2	yes	—
147	#14558715	C₂³	1	2	yes	—
148	#14558715	C₂³	1	2	yes	—
149	#14558715	C₂³	1	2	yes	—
150	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
151	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
152	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
153	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
154	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
155	#14558713	C₂³	1	2	yes	—
156	#14558713	C₂³	1	2	yes	—
157	#14558713	C₂³	1	2	yes	—
158	#14558713	C₂³	1	2	yes	—
159	#14558713	C₂³	1	2	yes	—
160	#14558713	C₂³	1	2	yes	—
161	#14558713	C₂³	1	2	yes	—
162	#14558713	C₂³	1	2	yes	—
163	#14558713	C₂³	1	2	yes	—
164	#14558713	C₂³	1	2	yes	—
165	#14558713	C₂³	1	2	yes	—
166	#14558713	C₂³	1	2	yes	—
167	#14558713	C₂³	1	2	yes	—
168	#14558713	C₂³	1	2	yes	—
169	C₄×Dic₁₄₉	C₂³	1	2	yes	—
170	C₄×Dic₁₄₉	C₂³	1	2	yes	—
171	C₄×Dic₁₄₉	C₂³	1	2	yes	—
172	C₄×Dic₁₄₉	C₂³	1	2	yes	—
173	C₄×Dic₁₄₉	C₂³	1	2	yes	—
174	C₂⁴×C₁₄₉	C₂³	1	1	yes	characteristic
175	C₂×Q₈×C₁₄₉	—	4	2	no	—
176	C₂×Q₈×C₁₄₉	C₂³	1	1	yes	characteristic
177	C₂×Q₈×C₁₄₉	C₂³	1	2	yes	—
178	C₂×Q₈×C₁₄₉	C₂³	1	1	yes	characteristic
179	C₂²×C₄×C₁₄₉	—	4	2	no	—
180	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
181	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
182	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
183	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
184	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
185	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
186	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
187	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
188	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
189	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
190	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
191	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
192	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
193	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
194	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
195	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
196	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
197	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
198	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
199	C₂²×D₁₄₉	—	2	2	no	—
200	C₂²×D₁₄₉	—	4	1	no	—
201	C₂²×D₁₄₉	—	4	1	no	—
202	C₂²×D₁₄₉	C₂⁴	1	2	yes	—
203	C₂²×D₁₄₉	C₂⁴	1	2	yes	—
204	Dic₂₉₈	—	4	2	no	—
205	Dic₂₉₈	—	4	1	no	—
206	Dic₂₉₈	—	4	2	no	—
207	D₅₉₆	—	4	2	no	—
208	D₅₉₆	—	4	1	no	—
209	D₅₉₆	—	4	2	no	—
210	C₂²⋊D₁₄₉	—	2	4	no	—
211	C₂²⋊D₁₄₉	—	2	4	no	—
212	C₂²⋊D₁₄₉	—	2	4	no	—
213	C₂²⋊D₁₄₉	—	4	2	no	—
214	C₂²⋊D₁₄₉	—	4	2	no	—
215	C₂×Dic₁₄₉	—	2	2	no	—
216	C₂×Dic₁₄₉	—	4	1	no	—
217	C₂×Dic₁₄₉	—	4	1	no	—
218	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
219	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
220	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
221	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
222	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
223	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
224	C₄×D₁₄₉	—	4	2	no	—
225	C₄×D₁₄₉	—	4	2	no	—
226	C₄×D₁₄₉	—	4	2	no	—
227	C₄×D₁₄₉	—	4	2	no	—
228	C₄×D₁₄₉	—	4	2	no	—
229	C₂³×C₁₄₉	—	2	2	no	—
230	C₂³×C₁₄₉	—	2	2	no	—
231	C₂³×C₁₄₉	—	4	1	no	—
232	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
233	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
234	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
235	Q₈×C₁₄₉	—	4	1	no	—
236	Q₈×C₁₄₉	—	4	2	no	—
237	Q₈×C₁₄₉	—	4	1	no	—
238	C₂×C₄×C₁₄₉	—	2	2	no	—
239	C₂×C₄×C₁₄₉	—	2	4	no	—
240	C₂×C₄×C₁₄₉	—	2	2	no	—
241	C₂×C₄×C₁₄₉	—	4	1	no	—
242	C₂×C₄×C₁₄₉	—	4	1	no	—
243	C₂×C₄×C₁₄₉	—	4	1	no	—
244	C₂×C₄×C₁₄₉	—	4	1	no	—
245	C₂×C₄×C₁₄₉	—	4	2	no	—
246	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
247	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
249	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
250	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
251	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
252	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
253	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
254	C₂²×C₁₄₉	—	2	1	no	—
255	C₂²×C₁₄₉	—	2	1	no	—
256	C₂²×C₁₄₉	—	2	1	no	—
257	C₂²×C₁₄₉	—	2	1	no	—
258	C₂²×C₁₄₉	—	2	1	no	—
259	C₂²×C₁₄₉	—	2	1	no	—
260	C₂²×C₁₄₉	—	2	1	no	—
261	C₂²×C₁₄₉	—	4	4	no	—
262	C₂²×C₁₄₉	H(5,𝔽₂)	1	2	yes	—
263	C₂²×C₁₄₉	2₋¹⁺⁴	1	2	yes	—
264	C₂²×C₁₄₉	C₂⁵	1	1	yes	characteristic
265	C₂×D₁₄₉	—	2	2	no	—
266	C₂×D₁₄₉	—	2	2	no	—
267	C₂×D₁₄₉	—	2	2	no	—
268	C₂×D₁₄₉	—	2	2	no	—
269	C₂×D₁₄₉	—	2	2	no	—
270	C₂×D₁₄₉	—	2	2	no	—
271	C₂×D₁₄₉	—	8	2	no	—
272	C₄×C₁₄₉	—	2	1	no	—
273	C₄×C₁₄₉	—	2	1	no	—
274	C₄×C₁₄₉	—	2	1	no	—
275	C₄×C₁₄₉	—	2	1	no	—
276	C₄×C₁₄₉	—	2	2	no	—
277	C₄×C₁₄₉	—	2	2	no	—
278	C₄×C₁₄₉	—	2	2	no	—
279	C₄×C₁₄₉	—	2	2	no	—
280	Dic₁₄₉	—	2	2	no	—
281	Dic₁₄₉	—	2	2	no	—
282	Dic₁₄₉	—	2	2	no	—
283	Dic₁₄₉	—	2	2	no	—
284	Dic₁₄₉	—	2	2	no	—
285	Dic₁₄₉	—	2	2	no	—
286	C₂×C₁₄₉	—	2	2	no	—
287	C₂×C₁₄₉	—	2	2	no	—
288	C₂×C₁₄₉	—	4	1	no	—
289	C₂×C₁₄₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
290	C₂×C₁₄₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
291	C₂×C₁₄₉	#585	1	1	yes	characteristic
292	D₁₄₉	—	4	2	no	—
293	D₁₄₉	—	4	2	no	—
294	C₁₄₉	#3535	1	1	yes	characteristic, complemented, Sylow
295	#3535	—	149	1	no	maximal, Sylow
296	#563	—	149	2	no	—
297	#562	—	149	2	no	—
298	#554	—	149	2	no	—
299	#552	—	149	2	no	—
300	#551	—	149	2	no	—
301	#551	—	149	2	no	—
302	#547	—	149	2	no	—
303	#546	—	149	2	no	—
304	#544	—	149	1	no	—
305	#543	—	149	1	no	—
306	#542	—	149	2	no	—
307	#539	—	149	1	no	—
308	#539	—	149	2	no	—
309	#539	—	149	2	no	—
310	#538	—	149	1	no	—
311	#536	—	149	2	no	—
312	#525	—	149	1	no	—
313	C₂×#123	—	149	1	no	—
314	C₂×C₂²⋊Q₈	D₁₄₉	1	1	yes	characteristic, complemented
315	C₂×#41	—	149	1	no	—
316	C₂×#41	—	149	2	no	—
317	C₂²×Q₈	C₂×D₁₄₉	1	1	yes	characteristic, complemented
318	C₂²×D₄	—	149	1	no	—
319	C₂³×C₄	C₂×D₁₄₉	1	1	yes	characteristic
320	C₄⋊Q₈	—	149	2	no	—
321	C₄⋊Q₈	—	149	2	no	—
322	C₄⋊Q₈	—	149	2	no	—
323	#126	—	149	2	no	—
324	#126	—	149	2	no	—
325	#126	—	149	2	no	—
326	#126	—	149	2	no	—
327	#126	—	149	2	no	—
328	#126	—	149	2	no	—
329	#125	—	149	2	no	—
330	#125	—	149	2	no	—
331	#125	—	149	2	no	—
332	#125	—	149	2	no	—
333	#125	—	149	2	no	—
334	#124	—	149	2	no	—
335	#124	—	149	2	no	—
336	#124	—	149	2	no	—
337	#124	—	149	2	no	—
338	#123	—	149	2	no	—
339	#123	—	149	2	no	—
340	#123	—	149	2	no	—
341	#123	—	149	2	no	—
342	#123	—	149	2	no	—
343	#123	—	149	2	no	—
344	#123	—	149	2	no	—
345	#123	—	149	2	no	—
346	#123	—	149	2	no	—
347	#123	—	149	2	no	—
348	#123	—	149	2	no	—
349	#123	—	149	2	no	—
350	#123	—	149	2	no	—
351	#123	—	149	2	no	—
352	C₂²⋊Q₈	—	149	2	no	—
353	C₂²⋊Q₈	—	149	2	no	—
354	C₂²⋊Q₈	—	149	2	no	—
355	C₂²⋊Q₈	—	149	2	no	—
356	C₂²⋊Q₈	—	149	1	no	—
357	C₂²⋊Q₈	—	149	1	no	—
358	C₂²⋊Q₈	—	149	2	no	—
359	C₂²⋊Q₈	—	149	2	no	—
360	C₂²⋊Q₈	—	149	2	no	—
361	C₂²⋊Q₈	—	149	2	no	—
362	C₂²⋊Q₈	—	149	2	no	—
363	C₂²⋊Q₈	—	149	2	no	—
364	C₂²⋊Q₈	—	149	2	no	—
365	C₂²⋊Q₈	—	149	2	no	—
366	C₂²⋊Q₈	C₂×D₁₄₉	1	1	yes	characteristic
367	C₂²⋊Q₈	C₂×D₁₄₉	1	1	yes	characteristic
368	C₂²⋊Q₈	C₂×D₁₄₉	1	2	yes	—
369	C₂²⋊Q₈	C₂×D₁₄₉	1	1	yes	characteristic, complemented
370	C₂²⋊Q₈	C₂×D₁₄₉	1	1	yes	characteristic, complemented
371	C₂²⋊Q₈	C₂×D₁₄₉	1	2	yes	complemented
372	#121	—	149	1	no	—
373	#121	—	149	1	no	—
374	#121	—	149	2	no	—
375	#121	—	149	2	no	—
376	#121	—	149	2	no	—
377	#121	—	149	2	no	—
378	#120	—	149	2	no	—
379	#120	—	149	2	no	—
380	C₄×Q₈	—	149	2	no	—
381	C₄×D₄	—	149	2	no	—
382	C₄×D₄	—	149	2	no	—
383	C₄×D₄	—	149	2	no	—
384	C₄×D₄	—	149	2	no	—
385	C₄×D₄	—	149	2	no	—
386	C₄×D₄	—	149	2	no	—
387	C₄×D₄	—	149	2	no	—
388	#117	—	149	1	no	—
389	#117	—	149	2	no	—
390	#117	—	149	2	no	—
391	#117	—	149	2	no	—
392	C₂×C₄⋊C₄	—	149	1	no	—
393	C₂×C₄⋊C₄	—	149	1	no	—
394	C₂×C₄⋊C₄	—	149	2	no	—
395	C₂×C₄⋊C₄	C₂×D₁₄₉	1	1	yes	characteristic, complemented
396	C₂×C₄⋊C₄	C₂×D₁₄₉	1	2	yes	complemented
397	C₂×C₂²⋊C₄	—	149	1	no	—
398	C₂×C₂²⋊C₄	—	149	1	no	—
399	C₂×C₂²⋊C₄	—	149	1	no	—
400	C₂×C₂²⋊C₄	—	149	2	no	—
401	C₂×C₂²⋊C₄	C₂×D₁₄₉	1	2	yes	—
402	C₂⁴	—	149	1	no	—
403	C₂⁴	C₂²×D₁₄₉	1	1	yes	characteristic
404	#41	—	596	2	no	—
405	#41	—	596	4	no	—
406	C₂×Q₈	—	4	2	no	—
407	C₂×Q₈	—	149	2	no	—
408	C₂×Q₈	—	149	1	no	—
409	C₂×Q₈	—	149	2	no	—
410	C₂×Q₈	C₂²×D₁₄₉	1	1	yes	characteristic
411	C₂×Q₈	C₂²×D₁₄₉	1	2	yes	—
412	C₂×Q₈	C₂²×D₁₄₉	1	1	yes	characteristic
413	C₂×D₄	—	596	2	no	—
414	C₂×D₄	—	149	2	no	—
415	C₂×D₄	—	149	2	no	—
416	C₂×D₄	—	149	2	no	—
417	C₂×D₄	—	149	2	no	—
418	C₂×D₄	—	149	2	no	—
419	C₂×D₄	—	149	2	no	—
420	C₂×D₄	—	149	2	no	—
421	C₂×D₄	—	149	1	no	—
422	C₂²×C₄	—	4	2	no	—
423	C₂²×C₄	—	149	1	no	—
424	C₂²×C₄	—	149	1	no	—
425	C₂²×C₄	—	149	1	no	—
426	C₂²×C₄	—	149	2	no	—
427	C₂²×C₄	—	149	2	no	—
428	C₂²×C₄	—	149	2	no	—
429	C₂²×C₄	—	149	2	no	—
430	C₂²×C₄	—	149	2	no	—
431	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
432	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
433	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
434	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
435	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
436	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
437	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
438	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
439	C₄⋊C₄	—	149	2	no	—
440	C₄⋊C₄	—	149	2	no	—
441	C₄⋊C₄	—	149	2	no	—
442	C₄⋊C₄	—	149	2	no	—
443	C₄⋊C₄	—	149	2	no	—
444	C₄⋊C₄	—	149	2	no	—
445	C₄⋊C₄	—	149	1	no	—
446	C₄⋊C₄	—	149	1	no	—
447	C₄⋊C₄	—	149	2	no	—
448	C₄⋊C₄	—	149	2	no	—
449	C₄⋊C₄	—	149	2	no	—
450	C₄⋊C₄	—	149	2	no	—
451	C₄⋊C₄	—	149	2	no	—
452	C₄⋊C₄	—	149	2	no	—
453	C₄⋊C₄	—	149	2	no	—
454	C₄⋊C₄	—	149	2	no	—
455	C₄⋊C₄	—	149	2	no	—
456	C₄⋊C₄	—	149	2	no	—
457	C₄⋊C₄	—	149	2	no	—
458	C₄⋊C₄	—	149	2	no	—
459	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
460	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
461	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
462	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
463	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
464	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
465	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
466	C₂²⋊C₄	—	149	2	no	—
467	C₂²⋊C₄	—	149	2	no	—
468	C₂²⋊C₄	—	149	2	no	—
469	C₂²⋊C₄	—	149	2	no	—
470	C₂²⋊C₄	—	149	2	no	—
471	C₂²⋊C₄	—	149	2	no	—
472	C₂²⋊C₄	—	149	2	no	—
473	C₂²⋊C₄	—	149	2	no	—
474	C₂²⋊C₄	—	149	2	no	—
475	C₂²⋊C₄	—	149	2	no	—
476	C₂²⋊C₄	—	149	2	no	—
477	C₂²⋊C₄	—	149	2	no	—
478	C₂²⋊C₄	—	149	2	no	—
479	C₂²⋊C₄	—	149	2	no	—
480	C₂²⋊C₄	—	149	2	no	—
481	C₂²⋊C₄	—	149	2	no	—
482	C₂²⋊C₄	—	149	2	no	—
483	C₂²⋊C₄	—	149	2	no	—
484	C₂²⋊C₄	—	149	2	no	—
485	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
486	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
487	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
488	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
489	C₄²	—	149	2	no	—
490	C₄²	—	149	2	no	—
491	C₄²	—	149	2	no	—
492	C₄²	—	149	2	no	—
493	C₄²	—	149	2	no	—
494	C₂³	—	2	2	no	—
495	C₂³	—	2	2	no	—
496	C₂³	—	4	1	no	—
497	C₂³	—	298	2	no	—
498	C₂³	—	596	1	no	—
499	C₂³	—	596	1	no	—
500	C₂³	—	149	2	no	—
501	C₂³	—	149	2	no	—
502	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
503	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
504	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
505	Q₈	—	4	1	no	—
506	Q₈	—	4	2	no	—
507	Q₈	—	4	1	no	—
508	Q₈	—	596	2	no	—
509	Q₈	—	596	1	no	—
510	Q₈	—	596	2	no	—
511	D₄	—	298	4	no	—
512	D₄	—	298	4	no	—
513	D₄	—	298	4	no	—
514	D₄	—	596	2	no	—
515	D₄	—	596	1	no	—
516	D₄	—	596	2	no	—
517	D₄	—	596	2	no	—
518	D₄	—	596	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	298	2	no	—
528	C₂×C₄	—	596	2	no	—
529	C₂×C₄	—	596	2	no	—
530	C₂×C₄	—	596	2	no	—
531	C₂×C₄	—	596	2	no	—
532	C₂×C₄	—	596	2	no	—
533	C₂×C₄	—	596	1	no	—
534	C₂×C₄	—	596	1	no	—
535	C₂×C₄	—	149	2	no	—
536	C₂×C₄	—	149	2	no	—
537	C₂×C₄	—	149	2	no	—
538	C₂×C₄	—	149	2	no	—
539	C₂×C₄	—	149	2	no	—
540	C₂×C₄	—	149	2	no	—
541	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
542	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
543	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
544	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
545	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
546	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
547	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
548	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
549	C₂²	—	2	1	no	—
550	C₂²	—	2	1	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	2	1	no	—
553	C₂²	—	2	1	no	—
554	C₂²	—	2	1	no	—
555	C₂²	—	2	1	no	—
556	C₂²	—	4	4	no	—
557	C₂²	—	298	2	no	—
558	C₂²	—	298	2	no	—
559	C₂²	—	298	2	no	—
560	C₂²	—	298	2	no	—
561	C₂²	—	298	2	no	—
562	C₂²	—	298	2	no	—
563	C₂²	—	1192	2	no	—
564	C₂²	#18011956	1	2	yes	—
565	C₂²	#18011959	1	2	yes	—
566	C₂²	C₂⁴×D₁₄₉	1	1	yes	characteristic
567	C₄	—	2	1	no	—
568	C₄	—	2	1	no	—
569	C₄	—	2	1	no	—
570	C₄	—	2	1	no	—
571	C₄	—	2	2	no	—
572	C₄	—	2	2	no	—
573	C₄	—	2	2	no	—
574	C₄	—	2	2	no	—
575	C₄	—	298	2	no	—
576	C₄	—	298	2	no	—
577	C₄	—	298	2	no	—
578	C₄	—	298	2	no	—
579	C₄	—	298	2	no	—
580	C₄	—	298	2	no	—
581	C₂	—	2	2	no	—
582	C₂	—	2	2	no	—
583	C₂	—	4	1	no	—
584	C₂	—	596	2	no	—
585	C₂	—	596	2	no	—
586	C₂	C₂×#18011956	1	1	yes	characteristic
587	C₂	C₂×#18011959	1	1	yes	characteristic
588	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
hypercenter	C₂×C₂²⋊Q₈	D₁₄₉
hypocenter	C₁₄₉	#3535
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. #23750376	C₂	semidirect
2. #23750371	C₂	semidirect
3. #23750329	C₂	semidirect
4. #23750310	C₂	semidirect
5. #23750302	C₂	semidirect
6. #23750301	C₂	semidirect
7. #23750276	C₂	semidirect
8. #23750265	C₂	semidirect
9. #23750254	C₂	semidirect
10. #23750250	C₂	semidirect
11. #23750245	C₂	semidirect
12. #23750224	C₂	semidirect
13. #23750222	C₂	semidirect
14. #23750221	C₂	semidirect
15. #23750215	C₂	semidirect
16. #23750199	C₂	semidirect
17. #23750136	C₂	semidirect
18. C₂×#18011894	C₂	semidirect
19. C₂×C₂²⋊Q₈×C₁₄₉	C₂	semidirect
21. C₂×#14558736	C₂²	semidirect
23. #18011910	C₂²	semidirect
24. #18011909	C₂²	semidirect
25. #18011909	C₂²	semidirect
26. #18011906	C₂²	semidirect
27. #18011906	C₂²	semidirect
28. #18011906	C₂²	semidirect
29. #18011906	C₂²	semidirect
30. #18011904	C₂²	semidirect
31. #18011904	C₂²	semidirect
32. #18011902	C₂²	semidirect
33. #18011901	C₂²	semidirect
34. #18011901	C₂²	semidirect
35. #18011901	C₂²	semidirect
36. #18011901	C₂²	semidirect
37. #18011900	C₂²	semidirect
38. #18011900	C₂²	semidirect
40. #18011897	C₂²	semidirect
41. #18011896	C₂²	semidirect
42. #18011896	C₂²	semidirect
43. #18011896	C₂²	semidirect
44. #18011896	C₂²	semidirect
51. #18011894	C₂²	semidirect
52. #18011894	C₂²	semidirect
54. #18011893	C₂²	semidirect
55. #18011891	C₂²	semidirect
57. #18011890	C₂²	semidirect
58. #18011890	C₂²	semidirect
59. #18011889	C₂²	semidirect
60. #18011889	C₂²	semidirect
61. #18011889	C₂²	semidirect
62. #18011889	C₂²	semidirect
65. #18011887	C₂²	semidirect
66. #18011887	C₂²	semidirect
67. #18011887	C₂²	semidirect
68. #18011887	C₂²	semidirect
69. #18011886	C₂²	semidirect
72. #18011885	C₂²	semidirect
77. #18011876	C₂²	semidirect
78. #18011873	C₂²	semidirect
81. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
82. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
85. #18011870	C₂²	semidirect
86. #18011870	C₂²	semidirect
87. #18011869	C₂²	semidirect
91. C₄⋊C₄×D₁₄₉	C₂²	semidirect
96. C₂²×Q₈×C₁₄₉	C₂²	semidirect
101. C₂²⋊Q₈×C₁₄₉	C₂²	semidirect
102. C₂²⋊Q₈×C₁₄₉	C₂²	semidirect
103. C₂²⋊Q₈×C₁₄₉	C₂²	semidirect
104. C₂×C₄⋊C₄×C₁₄₉	C₂²	semidirect
105. C₂×C₄⋊C₄×C₁₄₉	C₂²	semidirect
294. C₁₄₉	#3535	semidirect
314. C₂×C₂²⋊Q₈	D₁₄₉	semidirect
317. C₂²×Q₈	C₂×D₁₄₉	semidirect
369. C₂²⋊Q₈	C₂×D₁₄₉	semidirect
370. C₂²⋊Q₈	C₂×D₁₄₉	semidirect
371. C₂²⋊Q₈	C₂×D₁₄₉	semidirect
395. C₂×C₄⋊C₄	C₂×D₁₄₉	semidirect
396. 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
#23750376	2
#23750371	2
#23750329	2
#23750310	2
#23750302	2
#23750301	2
#23750276	2
#23750265	2
#23750254	2
#23750250	2
#23750245	2
#23750224	2
#23750222	2
#23750221	2
#23750215	2
#23750199	2
#23750136	2
C₂×#18011894	2
C₂×C₂²⋊Q₈×C₁₄₉	2
#3535	149