Subgroups — #34058302

Order 19072.

1242 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750360	C₂	1	1	yes	maximal, characteristic, complemented
2	#23750336	C₂	1	1	yes	maximal, characteristic, complemented
3	#23750328	C₂	1	2	yes	maximal, complemented
4	#23750323	C₂	1	2	yes	maximal, complemented
5	#23750302	C₂	1	4	yes	maximal, complemented
6	#23750270	C₂	1	2	yes	maximal, complemented
7	#23750266	C₂	1	2	yes	maximal, complemented
8	D₄×D₅₉₆	C₂	1	1	yes	maximal, characteristic, complemented
9	#23750176	C₂	1	1	yes	maximal, characteristic, complemented
10	#23750161	C₂	1	2	yes	maximal, complemented
11	#23750160	C₂	1	2	yes	maximal, complemented
12	#23750138	C₂	1	4	yes	maximal, complemented
13	C₄×#14558737	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#14558735	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#18011873	C₂	1	2	yes	maximal, complemented
16	C₄×D₄×D₁₄₉	C₂	1	2	yes	maximal, complemented
17	#554×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#14558737	C₂²	1	1	yes	characteristic
19	C₂×#14558737	C₂²	1	2	yes	complemented
20	C₂×#14558735	C₂²	1	1	yes	characteristic
21	C₂²×D₅₉₆	C₂²	1	2	yes	—
22	C₂×D₄×D₁₄₉	C₂²	1	2	yes	—
23	C₂²×C₄×D₁₄₉	C₂²	1	4	yes	complemented
24	#18011908	C₂²	1	1	yes	characteristic
25	#18011906	C₂²	1	4	yes	complemented
26	#18011906	C₂²	1	4	yes	complemented
27	#18011902	C₂²	1	2	yes	complemented
28	#18011900	C₂²	1	2	yes	complemented
29	#18011900	C₂²	1	2	yes	complemented
30	#18011899	C₂²	1	2	yes	complemented
31	#18011896	C₂²	1	4	yes	complemented
32	#18011896	C₂²	1	4	yes	complemented
33	#18011896	C₂²	1	4	yes	complemented
34	#18011895	C₂²	1	4	yes	complemented
35	#18011891	C₂²	1	2	yes	complemented
36	#18011887	C₂²	1	4	yes	complemented
37	#18011886	C₂²	1	2	yes	—
38	#18011886	C₂²	1	2	yes	complemented
39	#18011886	C₂²	1	2	yes	complemented
40	#18011886	C₂²	1	4	yes	complemented
41	#18011885	C₂²	1	2	yes	—
42	#18011885	C₂²	1	4	yes	complemented
43	#18011881	C₂²	1	4	yes	—
44	#18011881	C₂²	1	4	yes	complemented
45	Q₈×Dic₁₄₉	C₂²	1	1	yes	characteristic, complemented
46	C₄×Dic₂₉₈	C₂²	1	1	yes	characteristic, complemented
47	#18011876	C₂²	1	1	yes	characteristic, complemented
48	C₄×D₅₉₆	C₂²	1	1	yes	characteristic
49	C₄×D₅₉₆	C₂²	1	2	yes	complemented
50	C₄×D₅₉₆	C₂²	1	2	yes	complemented
51	D₄×Dic₁₄₉	C₂²	1	1	yes	characteristic
52	#18011873	C₂²	1	2	yes	—
53	#18011873	C₂²	1	1	yes	characteristic
54	#18011873	C₂²	1	2	yes	complemented
55	#18011873	C₂²	1	4	yes	complemented
56	#18011873	C₂²	1	2	yes	complemented
57	#18011873	C₂²	1	4	yes	complemented
58	#18011873	C₂²	1	2	yes	complemented
59	#18011873	C₂²	1	2	yes	complemented
60	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	complemented
61	C₄×C₂²⋊D₁₄₉	C₂²	1	4	yes	complemented
62	#18011871	C₂²	1	4	yes	complemented
63	#18011871	C₂²	1	2	yes	complemented
64	#18011869	C₂²	1	4	yes	complemented
65	#18011869	C₂²	1	2	yes	complemented
66	#18011869	C₂²	1	1	yes	characteristic, complemented
67	#18011869	C₂²	1	1	yes	characteristic, complemented
68	#18011867	C₂²	1	2	yes	complemented
69	C₄⋊C₄×D₁₄₉	C₂²	1	2	yes	complemented
70	C₂×#14558713	C₂²	1	4	yes	complemented
71	C₂²⋊C₄×D₁₄₉	C₂²	1	4	yes	complemented
72	C₂×C₄×Dic₁₄₉	C₂²	1	2	yes	complemented
73	C₄²×D₁₄₉	C₂²	1	2	yes	complemented
74	C₄²×D₁₄₉	C₂²	1	1	yes	characteristic, complemented
75	C₄⋊Q₈×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
76	#125×C₁₄₉	C₂²	1	2	yes	complemented
77	C₂²⋊Q₈×C₁₄₉	C₂²	1	2	yes	complemented
78	C₂²⋊Q₈×C₁₄₉	C₂²	1	4	yes	complemented
79	C₄×Q₈×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
80	C₄×D₄×C₁₄₉	C₂²	1	1	yes	characteristic
81	C₄×D₄×C₁₄₉	C₂²	1	2	yes	—
82	C₂×C₄⋊C₄×C₁₄₉	C₂²	1	2	yes	complemented
83	C₂³×D₁₄₉	C₂³	1	4	yes	—
84	#14558737	—	2	4	no	—
85	#14558737	—	4	4	no	—
86	#14558735	—	2	4	no	—
87	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
88	C₂×D₅₉₆	—	2	8	no	—
89	C₂×D₅₉₆	C₂³	1	2	yes	—
90	C₂×D₅₉₆	C₂³	1	2	yes	—
91	C₂×D₅₉₆	C₂³	1	4	yes	—
92	C₂×D₅₉₆	C₂³	1	2	yes	—
93	C₂×D₅₉₆	C₂³	1	2	yes	—
94	C₂×D₅₉₆	C₂³	1	4	yes	—
95	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
96	C₂×C₂²⋊D₁₄₉	C₂³	1	4	yes	—
97	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
98	D₄×D₁₄₉	—	2	8	no	—
99	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
100	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
101	C₂×C₄×D₁₄₉	—	4	8	no	—
102	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
103	C₂×C₄×D₁₄₉	C₂³	1	4	yes	—
104	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
105	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
106	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
107	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
108	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
109	C₂×C₄×D₁₄₉	C₂³	1	4	yes	—
110	C₂×C₄×D₁₄₉	C₂³	1	4	yes	—
111	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
112	C₄⋊Dic₁₄₉	C₂³	1	4	yes	—
113	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
114	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
115	#14558715	C₂³	1	2	yes	—
116	#14558715	C₂³	1	4	yes	—
117	#14558715	C₂³	1	2	yes	—
118	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
119	#14558713	C₂³	1	4	yes	—
120	#14558713	C₂³	1	4	yes	—
121	#14558713	C₂³	1	4	yes	—
122	#14558713	C₂³	1	4	yes	—
123	#14558713	C₂³	1	4	yes	—
124	#14558713	C₂³	1	2	yes	—
125	#14558713	C₂³	1	4	yes	—
126	#14558713	C₂³	1	2	yes	—
127	#14558713	C₂³	1	2	yes	—
128	#14558713	C₂³	1	2	yes	—
129	#14558713	C₂³	1	4	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	1	yes	characteristic
134	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
135	C₄×Dic₁₄₉	C₂³	1	2	yes	—
136	C₄×Dic₁₄₉	C₂³	1	2	yes	—
137	C₄×Dic₁₄₉	C₂³	1	2	yes	—
138	C₂×Q₈×C₁₄₉	C₂³	1	1	yes	characteristic
139	C₂×Q₈×C₁₄₉	C₂³	1	2	yes	—
140	C₂×D₄×C₁₄₉	C₂³	1	1	yes	characteristic
141	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
142	C₂²×C₄×C₁₄₉	C₂³	1	4	yes	—
143	C₄⋊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	2	yes	—
147	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
148	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
149	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
150	C₂²⋊C₄×C₁₄₉	C₂³	1	4	yes	—
151	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
152	C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
153	C₄²×C₁₄₉	C₂³	1	2	yes	—
154	C₂²×D₁₄₉	—	2	8	no	—
155	C₂²×D₁₄₉	—	2	8	no	—
156	C₂²×D₁₄₉	—	4	4	no	—
157	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
158	C₂²×D₁₄₉	C₂⁴	1	4	yes	—
159	C₂²×D₁₄₉	C₂⁴	1	2	yes	—
160	Dic₂₉₈	—	2	2	no	—
161	D₅₉₆	—	2	8	no	—
162	D₅₉₆	—	2	4	no	—
163	D₅₉₆	—	2	4	no	—
164	D₅₉₆	—	2	4	no	—
165	D₅₉₆	—	4	4	no	—
166	D₅₉₆	—	4	2	no	—
167	D₅₉₆	#41	1	4	yes	complemented
168	C₂²⋊D₁₄₉	—	2	8	no	—
169	C₂²⋊D₁₄₉	—	2	4	no	—
170	C₂×Dic₁₄₉	—	2	4	no	—
171	C₂×Dic₁₄₉	—	2	4	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	2	yes	—
177	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
178	C₄×D₁₄₉	—	2	4	no	—
179	C₄×D₁₄₉	—	2	4	no	—
180	C₄×D₁₄₉	—	2	2	no	—
181	C₄×D₁₄₉	—	2	2	no	—
182	C₄×D₁₄₉	—	2	4	no	—
183	C₄×D₁₄₉	—	2	8	no	—
184	C₄×D₁₄₉	—	2	2	no	—
185	C₄×D₁₄₉	—	4	4	no	—
186	C₄×D₁₄₉	—	4	4	no	—
187	C₂³×C₁₄₉	C₂⁴	1	2	yes	—
188	Q₈×C₁₄₉	—	2	2	no	—
189	Q₈×C₁₄₉	—	4	2	no	—
190	D₄×C₁₄₉	#41	1	4	yes	complemented
191	C₂×C₄×C₁₄₉	—	2	4	no	—
192	C₂×C₄×C₁₄₉	—	4	4	no	—
193	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
194	C₂×C₄×C₁₄₉	C₂⁴	1	4	yes	—
195	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
196	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
197	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
198	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
199	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
200	C₂²×C₁₄₉	—	2	2	no	—
201	C₂²×C₁₄₉	—	2	2	no	—
202	C₂²×C₁₄₉	C₂×#41	1	4	yes	—
203	C₂²×C₁₄₉	C₂⁵	1	1	yes	characteristic
204	C₂×D₁₄₉	—	2	2	no	—
205	C₂×D₁₄₉	—	2	2	no	—
206	C₂×D₁₄₉	—	2	1	no	—
207	C₂×D₁₄₉	—	2	1	no	—
208	C₂×D₁₄₉	—	2	4	no	—
209	C₂×D₁₄₉	—	2	4	no	—
210	C₂×D₁₄₉	—	2	4	no	—
211	C₂×D₁₄₉	—	2	1	no	—
212	C₂×D₁₄₉	—	4	16	no	—
213	C₂×D₁₄₉	C₂×#41	1	4	yes	—
214	C₄×C₁₄₉	—	2	2	no	—
215	C₄×C₁₄₉	—	2	2	no	—
216	C₄×C₁₄₉	—	2	2	no	—
217	C₄×C₁₄₉	—	2	4	no	—
218	C₄×C₁₄₉	—	2	1	no	—
219	C₄×C₁₄₉	C₂×#41	1	2	yes	—
220	C₄×C₁₄₉	C₂×#41	1	2	yes	—
221	Dic₁₄₉	—	2	1	no	—
222	Dic₁₄₉	—	2	1	no	—
223	Dic₁₄₉	—	2	2	no	—
224	Dic₁₄₉	—	2	2	no	—
225	Dic₁₄₉	—	2	2	no	—
226	Dic₁₄₉	H(5,𝔽₂)	1	2	yes	—
227	C₂×C₁₄₉	—	2	4	no	—
228	C₂×C₁₄₉	C₂²×#41	1	1	yes	characteristic
229	C₂×C₁₄₉	C₂²×#41	1	1	yes	characteristic
230	C₂×C₁₄₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
231	D₁₄₉	—	2	4	no	—
232	D₁₄₉	—	4	1	no	—
233	D₁₄₉	—	4	4	no	—
234	C₁₄₉	#3481	1	1	yes	characteristic, complemented, Sylow
235	#3481	—	149	1	no	maximal, Sylow
236	#559	—	149	1	no	—
237	#554	—	149	1	no	—
238	#554	D₁₄₉	1	1	yes	characteristic, complemented
239	#553	—	149	2	no	—
240	#553	—	149	2	no	—
241	#551	—	149	4	no	—
242	#546	—	149	2	no	—
243	#546	—	149	2	no	—
244	D₄²	—	149	1	no	—
245	#532	—	149	1	no	—
246	#529	—	149	2	no	—
247	#529	—	149	2	no	—
248	#525	—	149	4	no	—
249	C₄×#41	—	149	1	no	—
250	C₄×#41	—	149	1	no	—
251	C₂×C₄×D₄	—	149	2	no	—
252	C₂×C₄×D₄	—	149	2	no	—
253	C₂×#41	—	149	1	no	—
254	C₂×#41	—	149	2	no	—
255	C₂×#41	—	149	1	no	—
256	C₂²×D₄	—	149	2	no	—
257	C₂²×D₄	—	149	2	no	—
258	C₂³×C₄	—	149	4	no	—
259	C₄⋊Q₈	C₂×D₁₄₉	1	1	yes	characteristic, complemented
260	#127	—	149	1	no	—
261	#126	—	149	4	no	—
262	#126	—	149	4	no	—
263	#125	—	149	2	no	—
264	#125	C₂×D₁₄₉	1	2	yes	complemented
265	#124	—	149	2	no	—
266	#124	—	149	2	no	—
267	#124	—	149	2	no	—
268	#123	—	149	4	no	—
269	#123	—	149	4	no	—
270	#123	—	149	4	no	—
271	#123	—	149	4	no	—
272	C₂²⋊Q₈	—	149	4	no	—
273	C₂²⋊Q₈	—	149	2	no	—
274	C₂²⋊Q₈	C₂×D₁₄₉	1	4	yes	complemented
275	C₂²⋊Q₈	C₂×D₁₄₉	1	2	yes	complemented
276	#121	—	149	4	no	—
277	#121	—	149	2	no	—
278	#121	—	149	4	no	—
279	#121	—	149	2	no	—
280	#121	—	149	2	no	—
281	#121	—	149	2	no	—
282	#120	—	149	4	no	—
283	#120	—	149	4	no	—
284	C₄×Q₈	—	149	1	no	—
285	C₄×Q₈	—	149	1	no	—
286	C₄×Q₈	—	149	1	no	—
287	C₄×Q₈	C₂×D₁₄₉	1	1	yes	characteristic, complemented
288	C₄×D₄	—	149	1	no	—
289	C₄×D₄	—	149	4	no	—
290	C₄×D₄	—	149	2	no	—
291	C₄×D₄	—	149	1	no	—
292	C₄×D₄	—	149	4	no	—
293	C₄×D₄	—	149	2	no	—
294	C₄×D₄	—	149	2	no	—
295	C₄×D₄	—	149	2	no	—
296	C₄×D₄	—	149	4	no	—
297	C₄×D₄	—	149	2	no	—
298	C₄×D₄	—	149	2	no	—
299	C₄×D₄	—	149	4	no	—
300	C₄×D₄	—	149	2	no	—
301	C₄×D₄	—	149	2	no	—
302	C₄×D₄	—	149	1	no	—
303	C₄×D₄	—	149	2	no	—
304	C₄×D₄	C₂×D₁₄₉	1	2	yes	—
305	C₄×D₄	C₂×D₁₄₉	1	1	yes	characteristic
306	#117	—	149	2	no	—
307	#117	—	149	1	no	—
308	#117	—	149	1	no	—
309	#117	—	149	4	no	—
310	#117	—	149	2	no	—
311	C₂×C₄⋊C₄	—	149	2	no	—
312	C₂×C₄⋊C₄	C₂×D₁₄₉	1	2	yes	complemented
313	C₂×C₂²⋊C₄	—	149	4	no	—
314	C₂×C₂²⋊C₄	—	149	4	no	—
315	C₂×C₄²	—	149	2	no	—
316	C₂×C₄²	—	149	2	no	—
317	C₂×C₄²	—	149	1	no	—
318	C₂⁴	—	149	4	no	—
319	#41	—	298	4	no	—
320	#41	—	298	4	no	—
321	#41	—	596	4	no	—
322	C₂×Q₈	—	149	1	no	—
323	C₂×Q₈	C₂²×D₁₄₉	1	1	yes	characteristic
324	C₂×Q₈	C₂²×D₁₄₉	1	2	yes	—
325	C₂×D₄	—	298	8	no	—
326	C₂×D₄	—	298	8	no	—
327	C₂×D₄	—	149	2	no	—
328	C₂×D₄	—	149	4	no	—
329	C₂×D₄	—	149	2	no	—
330	C₂×D₄	—	149	4	no	—
331	C₂×D₄	—	149	2	no	—
332	C₂×D₄	—	149	2	no	—
333	C₂×D₄	—	149	2	no	—
334	C₂×D₄	—	149	4	no	—
335	C₂×D₄	—	149	1	no	—
336	C₂×D₄	C₂²×D₁₄₉	1	1	yes	characteristic
337	C₂²×C₄	—	596	8	no	—
338	C₂²×C₄	—	149	2	no	—
339	C₂²×C₄	—	149	2	no	—
340	C₂²×C₄	—	149	2	no	—
341	C₂²×C₄	—	149	2	no	—
342	C₂²×C₄	—	149	1	no	—
343	C₂²×C₄	—	149	1	no	—
344	C₂²×C₄	—	149	2	no	—
345	C₂²×C₄	—	149	1	no	—
346	C₂²×C₄	—	149	4	no	—
347	C₂²×C₄	—	149	4	no	—
348	C₂²×C₄	—	149	4	no	—
349	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
350	C₂²×C₄	C₂²×D₁₄₉	1	4	yes	—
351	C₄⋊C₄	—	149	1	no	—
352	C₄⋊C₄	—	149	4	no	—
353	C₄⋊C₄	—	149	1	no	—
354	C₄⋊C₄	—	149	2	no	—
355	C₄⋊C₄	—	149	2	no	—
356	C₄⋊C₄	—	149	2	no	—
357	C₄⋊C₄	—	149	4	no	—
358	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
359	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
360	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
361	C₄⋊C₄	C₂²×D₁₄₉	1	4	yes	—
362	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
363	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
364	C₄⋊C₄	C₂²×D₁₄₉	1	4	yes	—
365	C₂²⋊C₄	—	149	2	no	—
366	C₂²⋊C₄	—	149	2	no	—
367	C₂²⋊C₄	—	149	4	no	—
368	C₂²⋊C₄	—	149	4	no	—
369	C₂²⋊C₄	—	149	4	no	—
370	C₂²⋊C₄	—	149	4	no	—
371	C₂²⋊C₄	—	149	4	no	—
372	C₂²⋊C₄	—	149	2	no	—
373	C₂²⋊C₄	—	149	2	no	—
374	C₂²⋊C₄	—	149	2	no	—
375	C₂²⋊C₄	—	149	4	no	—
376	C₂²⋊C₄	—	149	4	no	—
377	C₂²⋊C₄	C₂²×D₁₄₉	1	4	yes	—
378	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
379	C₄²	—	149	1	no	—
380	C₄²	—	149	1	no	—
381	C₄²	—	149	1	no	—
382	C₄²	—	149	2	no	—
383	C₄²	—	149	2	no	—
384	C₄²	—	149	2	no	—
385	C₄²	—	149	2	no	—
386	C₄²	—	149	2	no	—
387	C₄²	C₂²×D₁₄₉	1	2	yes	—
388	C₄²	C₂²×D₁₄₉	1	1	yes	characteristic
389	C₂³	—	298	8	no	—
390	C₂³	—	298	8	no	—
391	C₂³	—	596	4	no	—
392	C₂³	—	149	4	no	—
393	C₂³	—	149	1	no	—
394	C₂³	—	149	2	no	—
395	C₂³	C₂³×D₁₄₉	1	2	yes	—
396	Q₈	—	2	2	no	—
397	Q₈	—	4	2	no	—
398	Q₈	—	298	2	no	—
399	D₄	—	298	8	no	—
400	D₄	—	298	4	no	—
401	D₄	—	298	8	no	—
402	D₄	—	298	4	no	—
403	D₄	—	298	4	no	—
404	D₄	—	298	4	no	—
405	D₄	—	596	4	no	—
406	D₄	—	596	2	no	—
407	D₄	—	149	4	no	—
408	D₄	#14558737	1	4	yes	complemented
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	4	4	no	—
411	C₂×C₄	—	298	4	no	—
412	C₂×C₄	—	298	4	no	—
413	C₂×C₄	—	298	8	no	—
414	C₂×C₄	—	298	2	no	—
415	C₂×C₄	—	298	4	no	—
416	C₂×C₄	—	298	4	no	—
417	C₂×C₄	—	298	2	no	—
418	C₂×C₄	—	298	4	no	—
419	C₂×C₄	—	298	2	no	—
420	C₂×C₄	—	596	4	no	—
421	C₂×C₄	—	596	4	no	—
422	C₂×C₄	—	149	1	no	—
423	C₂×C₄	—	149	1	no	—
424	C₂×C₄	—	149	2	no	—
425	C₂×C₄	—	149	2	no	—
426	C₂×C₄	—	149	2	no	—
427	C₂×C₄	—	149	1	no	—
428	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
429	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
430	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
431	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
432	C₂×C₄	C₂³×D₁₄₉	1	4	yes	—
433	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
434	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
435	C₂²	—	2	2	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	298	2	no	—
438	C₂²	—	298	2	no	—
439	C₂²	—	298	1	no	—
440	C₂²	—	298	4	no	—
441	C₂²	—	298	1	no	—
442	C₂²	—	298	4	no	—
443	C₂²	—	298	4	no	—
444	C₂²	—	298	1	no	—
445	C₂²	—	596	16	no	—
446	C₂²	—	149	4	no	—
447	C₂²	C₂×#14558737	1	4	yes	—
448	C₂²	C₂⁴×D₁₄₉	1	1	yes	characteristic
449	C₄	—	2	2	no	—
450	C₄	—	2	2	no	—
451	C₄	—	2	2	no	—
452	C₄	—	2	4	no	—
453	C₄	—	2	1	no	—
454	C₄	—	298	1	no	—
455	C₄	—	298	1	no	—
456	C₄	—	298	2	no	—
457	C₄	—	298	2	no	—
458	C₄	—	298	2	no	—
459	C₄	—	149	2	no	—
460	C₄	#41×D₁₄₉	1	2	yes	—
461	C₄	C₂×#14558737	1	2	yes	—
462	C₂	—	2	4	no	—
463	C₂	—	298	4	no	—
464	C₂	—	596	4	no	—
465	C₂	—	596	1	no	—
466	C₂	C₂×#41×D₁₄₉	1	1	yes	characteristic
467	C₂	C₂²×#14558737	1	1	yes	characteristic
468	C₂	H(5,𝔽₂)×D₁₄₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₄₉
commutator, socle, cosocle	C₂²×C₁₄₉	C₂⁵
Fitting	#554×C₁₄₉	C₂
hypercenter	#554	D₁₄₉
hypocenter	C₁₄₉	#3481
LCS	G ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ #554

Complements

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

N	H ≅ G/N	type
1. #23750360	C₂	semidirect
2. #23750336	C₂	semidirect
3. #23750328	C₂	semidirect
4. #23750323	C₂	semidirect
5. #23750302	C₂	semidirect
6. #23750270	C₂	semidirect
7. #23750266	C₂	semidirect
8. D₄×D₅₉₆	C₂	semidirect
9. #23750176	C₂	semidirect
10. #23750161	C₂	semidirect
11. #23750160	C₂	semidirect
12. #23750138	C₂	semidirect
13. C₄×#14558737	C₂	semidirect
14. C₄×#14558735	C₂	semidirect
15. C₂×#18011873	C₂	semidirect
16. C₄×D₄×D₁₄₉	C₂	semidirect
17. #554×C₁₄₉	C₂	semidirect
19. C₂×#14558737	C₂²	semidirect
23. C₂²×C₄×D₁₄₉	C₂²	semidirect
25. #18011906	C₂²	semidirect
26. #18011906	C₂²	semidirect
27. #18011902	C₂²	semidirect
28. #18011900	C₂²	semidirect
29. #18011900	C₂²	semidirect
30. #18011899	C₂²	semidirect
31. #18011896	C₂²	semidirect
32. #18011896	C₂²	semidirect
33. #18011896	C₂²	semidirect
34. #18011895	C₂²	semidirect
35. #18011891	C₂²	semidirect
36. #18011887	C₂²	semidirect
38. #18011886	C₂²	semidirect
39. #18011886	C₂²	semidirect
40. #18011886	C₂²	semidirect
42. #18011885	C₂²	semidirect
44. #18011881	C₂²	semidirect
45. Q₈×Dic₁₄₉	C₂²	semidirect
46. C₄×Dic₂₉₈	C₂²	semidirect
47. #18011876	C₂²	semidirect
49. C₄×D₅₉₆	C₂²	semidirect
50. C₄×D₅₉₆	C₂²	semidirect
54. #18011873	C₂²	semidirect
55. #18011873	C₂²	semidirect
56. #18011873	C₂²	semidirect
57. #18011873	C₂²	semidirect
58. #18011873	C₂²	semidirect
59. #18011873	C₂²	semidirect
60. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
61. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
62. #18011871	C₂²	semidirect
63. #18011871	C₂²	semidirect
64. #18011869	C₂²	semidirect
65. #18011869	C₂²	semidirect
66. #18011869	C₂²	semidirect
67. #18011869	C₂²	semidirect
68. #18011867	C₂²	semidirect
69. C₄⋊C₄×D₁₄₉	C₂²	semidirect
70. C₂×#14558713	C₂²	semidirect
71. C₂²⋊C₄×D₁₄₉	C₂²	semidirect
72. C₂×C₄×Dic₁₄₉	C₂²	semidirect
73. C₄²×D₁₄₉	C₂²	semidirect
74. C₄²×D₁₄₉	C₂²	semidirect
75. C₄⋊Q₈×C₁₄₉	C₂²	semidirect
76. #125×C₁₄₉	C₂²	semidirect
77. C₂²⋊Q₈×C₁₄₉	C₂²	semidirect
78. C₂²⋊Q₈×C₁₄₉	C₂²	semidirect
79. C₄×Q₈×C₁₄₉	C₂²	semidirect
82. C₂×C₄⋊C₄×C₁₄₉	C₂²	semidirect
167. D₅₉₆	#41	semidirect
190. D₄×C₁₄₉	#41	semidirect
234. C₁₄₉	#3481	semidirect
238. #554	D₁₄₉	semidirect
259. C₄⋊Q₈	C₂×D₁₄₉	semidirect
264. #125	C₂×D₁₄₉	semidirect
274. C₂²⋊Q₈	C₂×D₁₄₉	semidirect
275. C₂²⋊Q₈	C₂×D₁₄₉	semidirect
287. C₄×Q₈	C₂×D₁₄₉	semidirect
312. C₂×C₄⋊C₄	C₂×D₁₄₉	semidirect
408. D₄	#14558737	semidirect

Maximal subgroups

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

subgroup	index
#23750360	2
#23750336	2
#23750328	2
#23750323	2
#23750302	2
#23750270	2
#23750266	2
D₄×D₅₉₆	2
#23750176	2
#23750161	2
#23750160	2
#23750138	2
C₄×#14558737	2
C₄×#14558735	2
C₂×#18011873	2
C₄×D₄×D₁₄₉	2
#554×C₁₄₉	2
#3481	149