Subgroups — #34058532

Order 19072.

1152 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750323	C₂	1	4	yes	maximal, complemented
2	#23750323	C₂	1	2	yes	maximal, complemented
3	#23750317	C₂	1	2	yes	maximal, complemented
4	#23750302	C₂	1	4	yes	maximal, complemented
5	#23750286	C₂	1	2	yes	maximal, complemented
6	#23750266	C₂	1	2	yes	maximal, complemented
7	#23750224	C₂	1	2	yes	maximal, complemented
8	#23750215	C₂	1	2	yes	maximal, complemented
9	#23750187	C₂	1	2	yes	maximal, complemented
10	#23750161	C₂	1	2	yes	maximal, complemented
11	#23750138	C₂	1	2	yes	maximal, complemented
12	C₂×#18011885	C₂	1	1	yes	maximal, characteristic, complemented
13	#23750098	C₂	1	2	yes	maximal, complemented
14	C₂×C₄×C₂²⋊D₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₂²⋊Q₈×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14558737	C₂²	1	2	yes	complemented
17	C₂²×D₅₉₆	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic
19	C₂²×C₂²⋊D₁₄₉	C₂²	1	2	yes	—
20	C₂²×C₄×D₁₄₉	C₂²	1	1	yes	characteristic, complemented
21	#18011906	C₂²	1	4	yes	complemented
22	#18011906	C₂²	1	4	yes	complemented
23	#18011906	C₂²	1	4	yes	complemented
24	#18011902	C₂²	1	2	yes	complemented
25	#18011902	C₂²	1	4	yes	complemented
26	#18011900	C₂²	1	2	yes	complemented
27	#18011900	C₂²	1	4	yes	complemented
28	#18011896	C₂²	1	4	yes	complemented
29	#18011896	C₂²	1	4	yes	complemented
30	#18011896	C₂²	1	4	yes	complemented
31	#18011895	C₂²	1	4	yes	—
32	#18011895	C₂²	1	4	yes	complemented
33	#18011887	C₂²	1	4	yes	complemented
34	#18011887	C₂²	1	2	yes	complemented
35	#18011886	C₂²	1	4	yes	complemented
36	#18011886	C₂²	1	2	yes	complemented
37	#18011885	C₂²	1	2	yes	—
38	#18011885	C₂²	1	2	yes	—
39	#18011885	C₂²	1	4	yes	complemented
40	#18011885	C₂²	1	4	yes	complemented
41	#18011885	C₂²	1	2	yes	complemented
42	#18011885	C₂²	1	2	yes	complemented
43	#18011881	C₂²	1	4	yes	—
44	#18011881	C₂²	1	4	yes	complemented
45	Q₈×Dic₁₄₉	C₂²	1	2	yes	complemented
46	#18011873	C₂²	1	2	yes	complemented
47	#18011873	C₂²	1	4	yes	complemented
48	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	—
49	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	—
50	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	complemented
51	C₄×C₂²⋊D₁₄₉	C₂²	1	4	yes	complemented
52	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	complemented
53	C₄×C₂²⋊D₁₄₉	C₂²	1	4	yes	complemented
54	#18011871	C₂²	1	4	yes	complemented
55	#18011871	C₂²	1	4	yes	complemented
56	#18011869	C₂²	1	4	yes	complemented
57	#18011869	C₂²	1	2	yes	complemented
58	#18011867	C₂²	1	4	yes	complemented
59	C₂×C₄⋊Dic₁₄₉	C₂²	1	1	yes	characteristic, complemented
60	C₂×#14558715	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₂²⋊Dic₁₄₉	C₂²	1	1	yes	characteristic
62	C₂×#14558713	C₂²	1	1	yes	characteristic, complemented
63	C₂×#14558713	C₂²	1	2	yes	complemented
64	C₂²⋊C₄×D₁₄₉	C₂²	1	4	yes	complemented
65	C₂×C₄×Dic₁₄₉	C₂²	1	1	yes	characteristic, complemented
66	C₂²×Q₈×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
67	C₂³×C₄×C₁₄₉	C₂²	1	1	yes	characteristic
68	C₂²⋊Q₈×C₁₄₉	C₂²	1	2	yes	complemented
69	C₂²⋊Q₈×C₁₄₉	C₂²	1	2	yes	complemented
70	C₂²⋊Q₈×C₁₄₉	C₂²	1	2	yes	complemented
71	C₂²⋊Q₈×C₁₄₉	C₂²	1	2	yes	complemented
72	C₂×C₄⋊C₄×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
73	C₂×C₄⋊C₄×C₁₄₉	C₂²	1	2	yes	complemented
74	C₂×C₂²⋊C₄×C₁₄₉	C₂²	1	2	yes	—
75	C₂³×D₁₄₉	C₂³	1	1	yes	characteristic
76	C₂³×D₁₄₉	C₂³	1	2	yes	—
77	#14558737	—	4	4	no	—
78	C₂×D₅₉₆	—	4	2	no	—
79	C₂×D₅₉₆	C₂³	1	2	yes	—
80	C₂×D₅₉₆	C₂³	1	2	yes	—
81	C₂×D₅₉₆	C₂³	1	4	yes	—
82	C₂×D₅₉₆	C₂³	1	4	yes	—
83	C₂×C₂²⋊D₁₄₉	—	2	4	no	—
84	C₂×C₂²⋊D₁₄₉	—	2	8	no	—
85	C₂×C₂²⋊D₁₄₉	C₂³	1	4	yes	—
86	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
87	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
88	C₂×C₂²⋊D₁₄₉	C₂³	1	4	yes	—
89	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
90	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
91	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
92	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
93	C₂×C₄×D₁₄₉	—	4	2	no	—
94	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
95	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
96	C₂×C₄×D₁₄₉	C₂³	1	4	yes	—
97	C₂×C₄×D₁₄₉	C₂³	1	4	yes	—
98	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
99	C₄⋊Dic₁₄₉	C₂³	1	4	yes	—
100	C₄⋊Dic₁₄₉	C₂³	1	4	yes	—
101	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
102	#14558715	C₂³	1	2	yes	—
103	#14558715	C₂³	1	4	yes	—
104	#14558715	C₂³	1	2	yes	—
105	#14558715	C₂³	1	4	yes	—
106	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
107	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
108	#14558713	C₂³	1	2	yes	—
109	#14558713	C₂³	1	4	yes	—
110	#14558713	C₂³	1	4	yes	—
111	#14558713	C₂³	1	4	yes	—
112	#14558713	C₂³	1	4	yes	—
113	#14558713	C₂³	1	4	yes	—
114	#14558713	C₂³	1	4	yes	—
115	#14558713	C₂³	1	4	yes	—
116	#14558713	C₂³	1	2	yes	—
117	#14558713	C₂³	1	4	yes	—
118	C₄×Dic₁₄₉	C₂³	1	2	yes	—
119	C₄×Dic₁₄₉	C₂³	1	4	yes	—
120	C₄×Dic₁₄₉	C₂³	1	4	yes	—
121	C₄×Dic₁₄₉	C₂³	1	2	yes	—
122	C₂⁴×C₁₄₉	C₂³	1	1	yes	characteristic
123	C₂×Q₈×C₁₄₉	—	4	2	no	—
124	C₂×Q₈×C₁₄₉	C₂³	1	2	yes	—
125	C₂×Q₈×C₁₄₉	C₂³	1	2	yes	—
126	C₂²×C₄×C₁₄₉	—	4	2	no	—
127	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
131	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
132	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
133	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
134	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
135	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
136	C₄⋊C₄×C₁₄₉	C₂³	1	4	yes	—
137	C₄⋊C₄×C₁₄₉	C₂³	1	4	yes	—
138	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
139	C₂²⋊C₄×C₁₄₉	C₂³	1	4	yes	—
140	C₂²⋊C₄×C₁₄₉	C₂³	1	4	yes	—
141	C₂²×D₁₄₉	—	2	2	no	—
142	C₂²×D₁₄₉	—	2	4	no	—
143	C₂²×D₁₄₉	—	4	1	no	—
144	C₂²×D₁₄₉	—	4	1	no	—
145	C₂²×D₁₄₉	—	4	2	no	—
146	C₂²×D₁₄₉	—	4	2	no	—
147	C₂²×D₁₄₉	C₂⁴	1	2	yes	—
148	C₂²×D₁₄₉	C₂⁴	1	4	yes	—
149	D₅₉₆	—	2	4	no	—
150	D₅₉₆	—	4	2	no	—
151	D₅₉₆	—	4	4	no	—
152	D₅₉₆	—	4	4	no	—
153	C₂²⋊D₁₄₉	—	2	4	no	—
154	C₂²⋊D₁₄₉	—	2	8	no	—
155	C₂²⋊D₁₄₉	—	2	4	no	—
156	C₂²⋊D₁₄₉	—	2	8	no	—
157	C₂×Dic₁₄₉	—	2	4	no	—
158	C₂×Dic₁₄₉	—	2	2	no	—
159	C₂×Dic₁₄₉	—	4	1	no	—
160	C₂×Dic₁₄₉	—	4	1	no	—
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	4	yes	—
165	C₄×D₁₄₉	—	2	4	no	—
166	C₄×D₁₄₉	—	4	2	no	—
167	C₄×D₁₄₉	—	4	4	no	—
168	C₄×D₁₄₉	—	4	4	no	—
169	C₂³×C₁₄₉	—	4	1	no	—
170	C₂³×C₁₄₉	—	4	1	no	—
171	C₂³×C₁₄₉	#41	1	4	yes	complemented
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	—	4	2	no	—
177	C₂×C₄×C₁₄₉	—	2	2	no	—
178	C₂×C₄×C₁₄₉	—	2	2	no	—
179	C₂×C₄×C₁₄₉	—	2	2	no	—
180	C₂×C₄×C₁₄₉	—	4	1	no	—
181	C₂×C₄×C₁₄₉	—	4	1	no	—
182	C₂×C₄×C₁₄₉	—	4	1	no	—
183	C₂×C₄×C₁₄₉	—	4	2	no	—
184	C₂×C₄×C₁₄₉	—	4	2	no	—
185	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
186	C₂×C₄×C₁₄₉	C₂⁴	1	4	yes	—
187	C₂×C₄×C₁₄₉	C₂⁴	1	4	yes	—
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	—	4	4	no	—
198	C₂²×C₁₄₉	C₂×#41	1	2	yes	—
199	C₂²×C₁₄₉	C₂×#41	1	2	yes	—
200	C₂²×C₁₄₉	C₂×#41	1	2	yes	—
201	C₂²×C₁₄₉	C₂⁵	1	1	yes	characteristic
202	C₂×D₁₄₉	—	2	2	no	—
203	C₂×D₁₄₉	—	2	4	no	—
204	C₂×D₁₄₉	—	2	2	no	—
205	C₂×D₁₄₉	—	2	4	no	—
206	C₂×D₁₄₉	—	2	4	no	—
207	C₂×D₁₄₉	—	2	2	no	—
208	C₂×D₁₄₉	—	4	4	no	—
209	C₂×D₁₄₉	—	8	4	no	—
210	C₄×C₁₄₉	—	2	1	no	—
211	C₄×C₁₄₉	—	2	1	no	—
212	C₄×C₁₄₉	—	2	1	no	—
213	C₄×C₁₄₉	—	2	4	no	—
214	C₄×C₁₄₉	—	2	4	no	—
215	C₄×C₁₄₉	H(5,𝔽₂)	1	2	yes	—
216	Dic₁₄₉	—	2	4	no	—
217	Dic₁₄₉	—	2	2	no	—
218	Dic₁₄₉	—	2	2	no	—
219	Dic₁₄₉	—	2	2	no	—
220	C₂×C₁₄₉	—	2	2	no	—
221	C₂×C₁₄₉	—	2	2	no	—
222	C₂×C₁₄₉	—	2	2	no	—
223	C₂×C₁₄₉	C₂²×#41	1	1	yes	characteristic
224	C₂×C₁₄₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
225	C₂×C₁₄₉	#585	1	1	yes	characteristic
226	D₁₄₉	—	4	2	no	—
227	D₁₄₉	—	4	4	no	—
228	C₁₄₉	#3505	1	1	yes	characteristic, complemented, Sylow
229	#3505	—	149	1	no	maximal, Sylow
230	#553	—	149	2	no	—
231	#553	—	149	4	no	—
232	#552	—	149	2	no	—
233	#551	—	149	4	no	—
234	#548	—	149	2	no	—
235	#546	—	149	2	no	—
236	#539	—	149	2	no	—
237	#538	—	149	2	no	—
238	#534	—	149	2	no	—
239	#529	—	149	2	no	—
240	#525	—	149	2	no	—
241	C₂×C₂²⋊Q₈	D₁₄₉	1	1	yes	characteristic, complemented
242	C₂×#121	—	149	1	no	—
243	#518	—	149	2	no	—
244	C₂×C₄×D₄	—	149	1	no	—
245	C₂×#41	—	149	2	no	—
246	C₂²×Q₈	C₂×D₁₄₉	1	1	yes	characteristic, complemented
247	C₂²×D₄	—	149	1	no	—
248	C₂²×D₄	—	149	2	no	—
249	C₂²×D₄	—	149	1	no	—
250	C₂³×C₄	—	149	1	no	—
251	C₂³×C₄	C₂×D₁₄₉	1	1	yes	characteristic
252	#126	—	149	4	no	—
253	#126	—	149	4	no	—
254	#126	—	149	4	no	—
255	#125	—	149	2	no	—
256	#125	—	149	4	no	—
257	#124	—	149	2	no	—
258	#124	—	149	4	no	—
259	#123	—	149	4	no	—
260	#123	—	149	4	no	—
261	#123	—	149	4	no	—
262	#123	—	149	4	no	—
263	#123	—	149	4	no	—
264	C₂²⋊Q₈	—	149	2	no	—
265	C₂²⋊Q₈	—	149	4	no	—
266	C₂²⋊Q₈	C₂×D₁₄₉	1	2	yes	complemented
267	C₂²⋊Q₈	C₂×D₁₄₉	1	2	yes	complemented
268	C₂²⋊Q₈	C₂×D₁₄₉	1	2	yes	complemented
269	C₂²⋊Q₈	C₂×D₁₄₉	1	2	yes	complemented
270	#121	—	149	2	no	—
271	#121	—	149	2	no	—
272	#121	—	149	2	no	—
273	#121	—	149	2	no	—
274	#121	—	149	4	no	—
275	#121	—	149	4	no	—
276	#121	—	149	2	no	—
277	#121	—	149	4	no	—
278	#120	—	149	4	no	—
279	#120	—	149	4	no	—
280	C₄×Q₈	—	149	2	no	—
281	C₄×D₄	—	149	2	no	—
282	C₄×D₄	—	149	2	no	—
283	C₄×D₄	—	149	2	no	—
284	C₄×D₄	—	149	2	no	—
285	C₄×D₄	—	149	4	no	—
286	C₄×D₄	—	149	4	no	—
287	C₄×D₄	—	149	4	no	—
288	C₄×D₄	—	149	2	no	—
289	C₄×D₄	—	149	4	no	—
290	C₄×D₄	—	149	4	no	—
291	#117	—	149	2	no	—
292	#117	—	149	4	no	—
293	#117	—	149	4	no	—
294	C₂×C₄⋊C₄	—	149	1	no	—
295	C₂×C₄⋊C₄	—	149	1	no	—
296	C₂×C₄⋊C₄	C₂×D₁₄₉	1	1	yes	characteristic, complemented
297	C₂×C₄⋊C₄	C₂×D₁₄₉	1	2	yes	complemented
298	C₂×C₂²⋊C₄	—	149	1	no	—
299	C₂×C₂²⋊C₄	—	149	1	no	—
300	C₂×C₂²⋊C₄	—	149	2	no	—
301	C₂×C₂²⋊C₄	—	149	4	no	—
302	C₂×C₂²⋊C₄	C₂×D₁₄₉	1	2	yes	—
303	C₂×C₄²	—	149	1	no	—
304	C₂⁴	—	149	2	no	—
305	C₂⁴	—	149	1	no	—
306	C₂⁴	C₂²×D₁₄₉	1	1	yes	characteristic
307	#41	—	596	4	no	—
308	C₂×Q₈	—	4	2	no	—
309	C₂×Q₈	C₂²×D₁₄₉	1	2	yes	—
310	C₂×Q₈	C₂²×D₁₄₉	1	2	yes	—
311	C₂×D₄	—	298	4	no	—
312	C₂×D₄	—	298	8	no	—
313	C₂×D₄	—	596	2	no	—
314	C₂×D₄	—	149	2	no	—
315	C₂×D₄	—	149	4	no	—
316	C₂×D₄	—	149	2	no	—
317	C₂×D₄	—	149	4	no	—
318	C₂×D₄	—	149	2	no	—
319	C₂×D₄	—	149	4	no	—
320	C₂×D₄	—	149	4	no	—
321	C₂×D₄	—	149	2	no	—
322	C₂²×C₄	—	4	2	no	—
323	C₂²×C₄	—	596	2	no	—
324	C₂²×C₄	—	149	1	no	—
325	C₂²×C₄	—	149	2	no	—
326	C₂²×C₄	—	149	2	no	—
327	C₂²×C₄	—	149	1	no	—
328	C₂²×C₄	—	149	1	no	—
329	C₂²×C₄	—	149	4	no	—
330	C₂²×C₄	—	149	4	no	—
331	C₂²×C₄	—	149	2	no	—
332	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
333	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
334	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
335	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
336	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
337	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
338	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
339	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
340	C₄⋊C₄	—	149	2	no	—
341	C₄⋊C₄	—	149	2	no	—
342	C₄⋊C₄	—	149	2	no	—
343	C₄⋊C₄	—	149	2	no	—
344	C₄⋊C₄	—	149	4	no	—
345	C₄⋊C₄	—	149	4	no	—
346	C₄⋊C₄	—	149	4	no	—
347	C₄⋊C₄	—	149	4	no	—
348	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
349	C₄⋊C₄	C₂²×D₁₄₉	1	4	yes	—
350	C₄⋊C₄	C₂²×D₁₄₉	1	4	yes	—
351	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
352	C₂²⋊C₄	—	149	2	no	—
353	C₂²⋊C₄	—	149	2	no	—
354	C₂²⋊C₄	—	149	4	no	—
355	C₂²⋊C₄	—	149	2	no	—
356	C₂²⋊C₄	—	149	4	no	—
357	C₂²⋊C₄	—	149	4	no	—
358	C₂²⋊C₄	—	149	2	no	—
359	C₂²⋊C₄	—	149	4	no	—
360	C₂²⋊C₄	—	149	4	no	—
361	C₂²⋊C₄	—	149	4	no	—
362	C₂²⋊C₄	—	149	4	no	—
363	C₂²⋊C₄	—	149	4	no	—
364	C₂²⋊C₄	C₂²×D₁₄₉	1	4	yes	—
365	C₂²⋊C₄	C₂²×D₁₄₉	1	4	yes	—
366	C₄²	—	149	2	no	—
367	C₄²	—	149	2	no	—
368	C₄²	—	149	4	no	—
369	C₄²	—	149	4	no	—
370	C₂³	—	4	1	no	—
371	C₂³	—	4	1	no	—
372	C₂³	—	298	2	no	—
373	C₂³	—	298	4	no	—
374	C₂³	—	596	1	no	—
375	C₂³	—	596	1	no	—
376	C₂³	—	596	2	no	—
377	C₂³	—	596	2	no	—
378	C₂³	—	149	2	no	—
379	C₂³	—	149	4	no	—
380	C₂³	#14558737	1	4	yes	complemented
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	—	4	2	no	—
386	D₄	—	298	4	no	—
387	D₄	—	298	8	no	—
388	D₄	—	298	4	no	—
389	D₄	—	298	8	no	—
390	D₄	—	298	4	no	—
391	D₄	—	596	2	no	—
392	D₄	—	596	4	no	—
393	D₄	—	596	4	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	298	4	no	—
403	C₂×C₄	—	298	2	no	—
404	C₂×C₄	—	298	4	no	—
405	C₂×C₄	—	596	2	no	—
406	C₂×C₄	—	596	4	no	—
407	C₂×C₄	—	596	4	no	—
408	C₂×C₄	—	596	1	no	—
409	C₂×C₄	—	596	1	no	—
410	C₂×C₄	—	149	2	no	—
411	C₂×C₄	—	149	2	no	—
412	C₂×C₄	—	149	4	no	—
413	C₂×C₄	—	149	2	no	—
414	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
415	C₂×C₄	C₂³×D₁₄₉	1	4	yes	—
416	C₂×C₄	C₂³×D₁₄₉	1	4	yes	—
417	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
418	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
419	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
420	C₂²	—	2	1	no	—
421	C₂²	—	2	1	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	2	1	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	4	4	no	—
427	C₂²	—	298	2	no	—
428	C₂²	—	298	4	no	—
429	C₂²	—	298	2	no	—
430	C₂²	—	298	4	no	—
431	C₂²	—	298	4	no	—
432	C₂²	—	298	2	no	—
433	C₂²	—	596	4	no	—
434	C₂²	—	1192	4	no	—
435	C₂²	C₂×#14558737	1	2	yes	—
436	C₂²	C₂×#14558737	1	2	yes	—
437	C₂²	C₂×#14558737	1	2	yes	—
438	C₂²	C₂⁴×D₁₄₉	1	1	yes	characteristic
439	C₄	—	2	1	no	—
440	C₄	—	2	1	no	—
441	C₄	—	2	1	no	—
442	C₄	—	2	4	no	—
443	C₄	—	2	4	no	—
444	C₄	—	298	4	no	—
445	C₄	—	298	2	no	—
446	C₄	—	298	2	no	—
447	C₄	—	298	2	no	—
448	C₄	#18011956	1	2	yes	—
449	C₂	—	2	2	no	—
450	C₂	—	2	2	no	—
451	C₂	—	2	2	no	—
452	C₂	—	596	2	no	—
453	C₂	—	596	4	no	—
454	C₂	C₂²×#14558737	1	1	yes	characteristic
455	C₂	C₂×#18011956	1	1	yes	characteristic
456	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	#3505
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. #23750323	C₂	semidirect
2. #23750323	C₂	semidirect
3. #23750317	C₂	semidirect
4. #23750302	C₂	semidirect
5. #23750286	C₂	semidirect
6. #23750266	C₂	semidirect
7. #23750224	C₂	semidirect
8. #23750215	C₂	semidirect
9. #23750187	C₂	semidirect
10. #23750161	C₂	semidirect
11. #23750138	C₂	semidirect
12. C₂×#18011885	C₂	semidirect
13. #23750098	C₂	semidirect
14. C₂×C₄×C₂²⋊D₁₄₉	C₂	semidirect
15. C₂×C₂²⋊Q₈×C₁₄₉	C₂	semidirect
16. C₂×#14558737	C₂²	semidirect
17. C₂²×D₅₉₆	C₂²	semidirect
20. C₂²×C₄×D₁₄₉	C₂²	semidirect
21. #18011906	C₂²	semidirect
22. #18011906	C₂²	semidirect
23. #18011906	C₂²	semidirect
24. #18011902	C₂²	semidirect
25. #18011902	C₂²	semidirect
26. #18011900	C₂²	semidirect
27. #18011900	C₂²	semidirect
28. #18011896	C₂²	semidirect
29. #18011896	C₂²	semidirect
30. #18011896	C₂²	semidirect
32. #18011895	C₂²	semidirect
33. #18011887	C₂²	semidirect
34. #18011887	C₂²	semidirect
35. #18011886	C₂²	semidirect
36. #18011886	C₂²	semidirect
39. #18011885	C₂²	semidirect
40. #18011885	C₂²	semidirect
41. #18011885	C₂²	semidirect
42. #18011885	C₂²	semidirect
44. #18011881	C₂²	semidirect
45. Q₈×Dic₁₄₉	C₂²	semidirect
46. #18011873	C₂²	semidirect
47. #18011873	C₂²	semidirect
50. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
51. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
52. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
53. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
54. #18011871	C₂²	semidirect
55. #18011871	C₂²	semidirect
56. #18011869	C₂²	semidirect
57. #18011869	C₂²	semidirect
58. #18011867	C₂²	semidirect
59. C₂×C₄⋊Dic₁₄₉	C₂²	semidirect
60. C₂×#14558715	C₂²	semidirect
62. C₂×#14558713	C₂²	semidirect
63. C₂×#14558713	C₂²	semidirect
64. C₂²⋊C₄×D₁₄₉	C₂²	semidirect
65. C₂×C₄×Dic₁₄₉	C₂²	semidirect
66. C₂²×Q₈×C₁₄₉	C₂²	semidirect
68. C₂²⋊Q₈×C₁₄₉	C₂²	semidirect
69. C₂²⋊Q₈×C₁₄₉	C₂²	semidirect
70. C₂²⋊Q₈×C₁₄₉	C₂²	semidirect
71. C₂²⋊Q₈×C₁₄₉	C₂²	semidirect
72. C₂×C₄⋊C₄×C₁₄₉	C₂²	semidirect
73. C₂×C₄⋊C₄×C₁₄₉	C₂²	semidirect
171. C₂³×C₁₄₉	#41	semidirect
228. C₁₄₉	#3505	semidirect
241. C₂×C₂²⋊Q₈	D₁₄₉	semidirect
246. C₂²×Q₈	C₂×D₁₄₉	semidirect
266. C₂²⋊Q₈	C₂×D₁₄₉	semidirect
267. C₂²⋊Q₈	C₂×D₁₄₉	semidirect
268. C₂²⋊Q₈	C₂×D₁₄₉	semidirect
269. C₂²⋊Q₈	C₂×D₁₄₉	semidirect
296. C₂×C₄⋊C₄	C₂×D₁₄₉	semidirect
297. C₂×C₄⋊C₄	C₂×D₁₄₉	semidirect
380. C₂³	#14558737	semidirect

Maximal subgroups

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

subgroup	index
#23750323	2
#23750317	2
#23750302	2
#23750286	2
#23750266	2
#23750224	2
#23750215	2
#23750187	2
#23750161	2
#23750138	2
C₂×#18011885	2
#23750098	2
C₂×C₄×C₂²⋊D₁₄₉	2
C₂×C₂²⋊Q₈×C₁₄₉	2
#3505	149