Subgroups — #34058306

Order 19072.

1094 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750353	C₂	1	1	yes	maximal, characteristic, complemented
2	#23750348	C₂	1	1	yes	maximal, characteristic, complemented
3	#23750343	C₂	1	2	yes	maximal, complemented
4	#23750315	C₂	1	2	yes	maximal, complemented
5	#23750308	C₂	1	4	yes	maximal, complemented
6	D₄×Dic₂₉₈	C₂	1	1	yes	maximal, characteristic, complemented
7	#23750284	C₂	1	2	yes	maximal, complemented
8	#23750279	C₂	1	1	yes	maximal, characteristic, complemented
9	#23750274	C₂	1	2	yes	maximal, complemented
10	#23750182	C₂	1	1	yes	maximal, characteristic, complemented
11	#23750179	C₂	1	2	yes	maximal, complemented
12	#23750159	C₂	1	2	yes	maximal, complemented
13	#23750155	C₂	1	4	yes	maximal, complemented
14	C₄×#14558736	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#14558735	C₂	1	2	yes	maximal, complemented
16	C₂×C₄×Dic₂₉₈	C₂	1	2	yes	maximal, complemented
17	C₄×#41×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#14558736	C₂²	1	1	yes	characteristic
19	C₂×#14558735	C₂²	1	2	yes	—
20	C₂²×Dic₂₉₈	C₂²	1	2	yes	—
21	#18011911	C₂²	1	1	yes	characteristic
22	#18011911	C₂²	1	1	yes	characteristic
23	#18011910	C₂²	1	2	yes	—
24	#18011909	C₂²	1	2	yes	—
25	#18011906	C₂²	1	4	yes	—
26	#18011905	C₂²	1	4	yes	—
27	#18011904	C₂²	1	4	yes	—
28	#18011903	C₂²	1	2	yes	—
29	#18011903	C₂²	1	2	yes	—
30	#18011901	C₂²	1	4	yes	—
31	#18011901	C₂²	1	4	yes	—
32	#18011899	C₂²	1	2	yes	—
33	#18011897	C₂²	1	4	yes	—
34	#18011895	C₂²	1	4	yes	—
35	#18011894	C₂²	1	4	yes	—
36	#18011892	C₂²	1	4	yes	—
37	#18011891	C₂²	1	2	yes	—
38	#18011890	C₂²	1	2	yes	—
39	#18011890	C₂²	1	2	yes	—
40	#18011890	C₂²	1	2	yes	—
41	#18011889	C₂²	1	4	yes	—
42	#18011888	C₂²	1	4	yes	—
43	#18011887	C₂²	1	2	yes	—
44	#18011885	C₂²	1	2	yes	—
45	#18011883	C₂²	1	4	yes	—
46	C₄×Dic₂₉₈	C₂²	1	4	yes	—
47	C₄×Dic₂₉₈	C₂²	1	2	yes	—
48	C₄×Dic₂₉₈	C₂²	1	2	yes	—
49	C₄×Dic₂₉₈	C₂²	1	2	yes	—
50	C₄×Dic₂₉₈	C₂²	1	1	yes	characteristic
51	C₄×Dic₂₉₈	C₂²	1	4	yes	—
52	C₄×Dic₂₉₈	C₂²	1	2	yes	—
53	C₄×Dic₂₉₈	C₂²	1	1	yes	characteristic
54	#18011876	C₂²	1	2	yes	—
55	C₄×D₅₉₆	C₂²	1	1	yes	characteristic
56	C₄×D₅₉₆	C₂²	1	1	yes	characteristic
57	D₄×Dic₁₄₉	C₂²	1	2	yes	—
58	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	—
59	C₄×C₂²⋊D₁₄₉	C₂²	1	4	yes	—
60	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	—
61	#18011871	C₂²	1	4	yes	—
62	#18011870	C₂²	1	2	yes	—
63	#18011870	C₂²	1	1	yes	characteristic
64	#18011869	C₂²	1	2	yes	—
65	#18011868	C₂²	1	4	yes	—
66	#18011868	C₂²	1	2	yes	—
67	#18011867	C₂²	1	4	yes	—
68	C₂×C₄⋊Dic₁₄₉	C₂²	1	2	yes	—
69	C₂×#14558715	C₂²	1	4	yes	—
70	C₂×C₄×Dic₁₄₉	C₂²	1	4	yes	—
71	C₄²×D₁₄₉	C₂²	1	2	yes	—
72	C₂×#41×C₁₄₉	C₂²	1	1	yes	characteristic
73	C₄×Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
74	C₄×Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
75	C₄×D₄×C₁₄₉	C₂²	1	2	yes	—
76	C₄×D₄×C₁₄₉	C₂²	1	1	yes	characteristic
77	C₄×D₄×C₁₄₉	C₂²	1	2	yes	—
78	C₄×D₄×C₁₄₉	C₂²	1	1	yes	characteristic
79	#117×C₁₄₉	C₂²	1	2	yes	—
80	#117×C₁₄₉	C₂²	1	1	yes	characteristic
81	C₂×C₄²×C₁₄₉	C₂²	1	2	yes	—
82	C₂×C₄²×C₁₄₉	C₂²	1	1	yes	characteristic
83	#14558736	—	2	4	no	—
84	#14558735	—	2	8	no	—
85	C₂×Dic₂₉₈	—	2	8	no	—
86	C₂×Dic₂₉₈	C₂³	1	2	yes	—
87	C₂×Dic₂₉₈	C₂³	1	4	yes	—
88	C₂×Dic₂₉₈	C₂³	1	2	yes	—
89	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
90	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
91	C₂×C₂²⋊D₁₄₉	C₂³	1	4	yes	—
92	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
93	C₂²×Dic₁₄₉	C₂³	1	4	yes	—
94	C₂²×Dic₁₄₉	C₂³	1	4	yes	—
95	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
96	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
97	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
98	C₄⋊Dic₁₄₉	C₂³	1	4	yes	—
99	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
100	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
101	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
102	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
103	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
104	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
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	4	yes	—
111	#14558715	C₂³	1	2	yes	—
112	#14558715	C₂³	1	4	yes	—
113	#14558715	C₂³	1	2	yes	—
114	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
115	C₂²⋊Dic₁₄₉	C₂³	1	4	yes	—
116	C₂²⋊Dic₁₄₉	C₂³	1	4	yes	—
117	#14558713	C₂³	1	2	yes	—
118	#14558713	C₂³	1	4	yes	—
119	#14558713	C₂³	1	4	yes	—
120	#14558713	C₂³	1	2	yes	—
121	#14558713	C₂³	1	4	yes	—
122	C₄×Dic₁₄₉	C₂³	1	4	yes	—
123	C₄×Dic₁₄₉	C₂³	1	2	yes	—
124	C₄×Dic₁₄₉	C₂³	1	2	yes	—
125	C₄×Dic₁₄₉	C₂³	1	2	yes	—
126	C₄×Dic₁₄₉	C₂³	1	4	yes	—
127	C₄×Dic₁₄₉	C₂³	1	4	yes	—
128	#41×C₁₄₉	—	2	4	no	—
129	C₂×Q₈×C₁₄₉	C₂³	1	1	yes	characteristic
130	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
131	C₂×D₄×C₁₄₉	C₂³	1	1	yes	characteristic
132	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
133	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
134	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
135	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
137	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
138	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
139	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
140	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
141	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
142	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
143	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
144	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
145	C₄²×C₁₄₉	C₂³	1	2	yes	—
146	C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
147	C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
148	C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
149	C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
150	C₄²×C₁₄₉	C₂³	1	2	yes	—
151	C₄²×C₁₄₉	C₂³	1	2	yes	—
152	C₂²×D₁₄₉	C₂⁴	1	2	yes	—
153	Dic₂₉₈	—	2	4	no	—
154	Dic₂₉₈	—	2	4	no	—
155	Dic₂₉₈	—	2	8	no	—
156	Dic₂₉₈	#41	1	4	yes	complemented
157	D₅₉₆	—	2	2	no	—
158	C₂²⋊D₁₄₉	—	2	8	no	—
159	C₂²⋊D₁₄₉	—	2	4	no	—
160	C₂×Dic₁₄₉	—	2	8	no	—
161	C₂×Dic₁₄₉	—	2	8	no	—
162	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
163	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
164	C₂×Dic₁₄₉	C₂⁴	1	4	yes	—
165	C₂×Dic₁₄₉	C₂⁴	1	4	yes	—
166	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
167	C₄×D₁₄₉	—	2	4	no	—
168	C₄×D₁₄₉	—	2	4	no	—
169	C₄×D₁₄₉	—	2	4	no	—
170	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
171	C₂³×C₁₄₉	C₂⁴	1	2	yes	—
172	Q₈×C₁₄₉	—	2	2	no	—
173	D₄×C₁₄₉	—	2	4	no	—
174	D₄×C₁₄₉	#41	1	4	yes	complemented
175	C₂×C₄×C₁₄₉	—	2	4	no	—
176	C₂×C₄×C₁₄₉	—	2	4	no	—
177	C₂×C₄×C₁₄₉	—	2	2	no	—
178	C₂×C₄×C₁₄₉	—	2	2	no	—
179	C₂×C₄×C₁₄₉	—	2	4	no	—
180	C₂×C₄×C₁₄₉	—	2	2	no	—
181	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
182	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
183	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
184	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
185	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
186	C₂×C₄×C₁₄₉	C₂⁴	1	2	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	C₂²×C₁₄₉	—	2	2	no	—
191	C₂²×C₁₄₉	—	2	2	no	—
192	C₂²×C₁₄₉	—	2	1	no	—
193	C₂²×C₁₄₉	—	2	1	no	—
194	C₂²×C₁₄₉	—	2	1	no	—
195	C₂²×C₁₄₉	C₂×#41	1	4	yes	—
196	C₂²×C₁₄₉	C₂⁵	1	1	yes	characteristic
197	C₂×D₁₄₉	—	2	2	no	—
198	C₂×D₁₄₉	—	2	2	no	—
199	C₂×D₁₄₉	—	2	2	no	—
200	C₄×C₁₄₉	—	2	1	no	—
201	C₄×C₁₄₉	—	2	2	no	—
202	C₄×C₁₄₉	—	2	1	no	—
203	C₄×C₁₄₉	—	2	2	no	—
204	C₄×C₁₄₉	—	2	2	no	—
205	C₄×C₁₄₉	—	2	1	no	—
206	C₄×C₁₄₉	C₂×#41	1	2	yes	—
207	C₄×C₁₄₉	C₂×#41	1	2	yes	—
208	C₄×C₁₄₉	2₋¹⁺⁴	1	2	yes	—
209	Dic₁₄₉	—	2	2	no	—
210	Dic₁₄₉	—	2	4	no	—
211	Dic₁₄₉	—	2	4	no	—
212	Dic₁₄₉	—	2	2	no	—
213	Dic₁₄₉	C₂×#41	1	4	yes	—
214	C₂×C₁₄₉	—	2	4	no	—
215	C₂×C₁₄₉	—	4	1	no	—
216	C₂×C₁₄₉	C₂²×#41	1	1	yes	characteristic
217	C₂×C₁₄₉	C₂²×#41	1	1	yes	characteristic
218	C₂×C₁₄₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
219	D₁₄₉	—	4	2	no	—
220	C₁₄₉	#3482	1	1	yes	characteristic, complemented, Sylow
221	#3482	—	149	1	no	maximal, Sylow
222	#557	—	149	1	no	—
223	#556	—	149	1	no	—
224	#556	—	149	2	no	—
225	#552	—	149	2	no	—
226	#552	—	149	4	no	—
227	D₄×Q₈	—	149	1	no	—
228	#548	—	149	2	no	—
229	#547	—	149	2	no	—
230	#547	—	149	1	no	—
231	#533	—	149	2	no	—
232	#533	—	149	1	no	—
233	#529	—	149	4	no	—
234	#529	—	149	2	no	—
235	C₄×#41	—	149	2	no	—
236	C₄×#41	—	149	1	no	—
237	C₄×#41	D₁₄₉	1	1	yes	characteristic, complemented
238	C₂×C₄×Q₈	—	149	2	no	—
239	C₂×#41	—	149	2	no	—
240	C₂×#41	—	149	1	no	—
241	C₂×#41	C₂×D₁₄₉	1	1	yes	characteristic
242	C₂²×Q₈	—	149	2	no	—
243	C₄⋊Q₈	—	149	2	no	—
244	C₄⋊Q₈	—	149	2	no	—
245	C₄⋊Q₈	—	149	1	no	—
246	C₄⋊Q₈	—	149	1	no	—
247	#126	—	149	4	no	—
248	#126	—	149	4	no	—
249	#126	—	149	4	no	—
250	#125	—	149	4	no	—
251	#125	—	149	4	no	—
252	#125	—	149	2	no	—
253	#125	—	149	2	no	—
254	#124	—	149	4	no	—
255	#124	—	149	2	no	—
256	#123	—	149	4	no	—
257	#123	—	149	4	no	—
258	#123	—	149	4	no	—
259	C₂²⋊Q₈	—	149	2	no	—
260	C₂²⋊Q₈	—	149	2	no	—
261	C₂²⋊Q₈	—	149	2	no	—
262	C₂²⋊Q₈	—	149	2	no	—
263	C₂²⋊Q₈	—	149	2	no	—
264	C₂²⋊Q₈	—	149	4	no	—
265	C₂²⋊Q₈	—	149	4	no	—
266	#121	—	149	4	no	—
267	#121	—	149	2	no	—
268	C₄×Q₈	—	149	2	no	—
269	C₄×Q₈	—	149	1	no	—
270	C₄×Q₈	—	149	4	no	—
271	C₄×Q₈	—	149	2	no	—
272	C₄×Q₈	—	149	2	no	—
273	C₄×Q₈	—	149	2	no	—
274	C₄×Q₈	—	149	4	no	—
275	C₄×Q₈	—	149	2	no	—
276	C₄×Q₈	—	149	1	no	—
277	C₄×Q₈	C₂×D₁₄₉	1	1	yes	characteristic
278	C₄×Q₈	C₂×D₁₄₉	1	1	yes	characteristic
279	C₄×D₄	—	149	2	no	—
280	C₄×D₄	—	149	2	no	—
281	C₄×D₄	—	149	4	no	—
282	C₄×D₄	—	149	2	no	—
283	C₄×D₄	—	149	4	no	—
284	C₄×D₄	—	149	1	no	—
285	C₄×D₄	—	149	1	no	—
286	C₄×D₄	C₂×D₁₄₉	1	1	yes	characteristic
287	C₄×D₄	C₂×D₁₄₉	1	2	yes	—
288	C₄×D₄	C₂×D₁₄₉	1	1	yes	characteristic
289	C₄×D₄	C₂×D₁₄₉	1	2	yes	—
290	#117	—	149	1	no	—
291	#117	—	149	2	no	—
292	#117	—	149	2	no	—
293	#117	—	149	4	no	—
294	#117	—	149	2	no	—
295	#117	—	149	4	no	—
296	#117	C₂×D₁₄₉	1	2	yes	—
297	#117	C₂×D₁₄₉	1	1	yes	characteristic
298	C₂×C₄⋊C₄	—	149	4	no	—
299	C₂×C₄⋊C₄	—	149	2	no	—
300	C₂×C₄²	—	149	4	no	—
301	C₂×C₄²	—	149	2	no	—
302	C₂×C₄²	C₂×D₁₄₉	1	2	yes	—
303	C₂×C₄²	C₂×D₁₄₉	1	1	yes	characteristic
304	#41	—	2	4	no	—
305	#41	—	298	4	no	—
306	#41	—	298	8	no	—
307	C₂×Q₈	—	298	8	no	—
308	C₂×Q₈	—	149	2	no	—
309	C₂×Q₈	—	149	4	no	—
310	C₂×Q₈	—	149	2	no	—
311	C₂×Q₈	—	149	1	no	—
312	C₂×Q₈	C₂²×D₁₄₉	1	1	yes	characteristic
313	C₂×D₄	—	149	4	no	—
314	C₂×D₄	—	149	2	no	—
315	C₂×D₄	—	149	1	no	—
316	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
317	C₂×D₄	C₂²×D₁₄₉	1	1	yes	characteristic
318	C₂²×C₄	—	149	4	no	—
319	C₂²×C₄	—	149	4	no	—
320	C₂²×C₄	—	149	2	no	—
321	C₂²×C₄	—	149	2	no	—
322	C₂²×C₄	—	149	2	no	—
323	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
324	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
325	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
326	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
327	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
328	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
329	C₄⋊C₄	—	149	2	no	—
330	C₄⋊C₄	—	149	1	no	—
331	C₄⋊C₄	—	149	4	no	—
332	C₄⋊C₄	—	149	2	no	—
333	C₄⋊C₄	—	149	4	no	—
334	C₄⋊C₄	—	149	4	no	—
335	C₄⋊C₄	—	149	4	no	—
336	C₄⋊C₄	—	149	2	no	—
337	C₄⋊C₄	—	149	4	no	—
338	C₄⋊C₄	—	149	1	no	—
339	C₄⋊C₄	—	149	2	no	—
340	C₄⋊C₄	—	149	4	no	—
341	C₄⋊C₄	—	149	4	no	—
342	C₄⋊C₄	—	149	2	no	—
343	C₄⋊C₄	—	149	4	no	—
344	C₄⋊C₄	—	149	2	no	—
345	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
346	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
347	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
348	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
349	C₂²⋊C₄	—	149	4	no	—
350	C₂²⋊C₄	—	149	2	no	—
351	C₂²⋊C₄	—	149	4	no	—
352	C₂²⋊C₄	—	149	2	no	—
353	C₂²⋊C₄	—	149	2	no	—
354	C₂²⋊C₄	—	149	4	no	—
355	C₂²⋊C₄	—	149	4	no	—
356	C₂²⋊C₄	—	149	4	no	—
357	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
358	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
359	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
360	C₄²	—	149	2	no	—
361	C₄²	—	149	4	no	—
362	C₄²	—	149	2	no	—
363	C₄²	—	149	4	no	—
364	C₄²	—	149	2	no	—
365	C₄²	—	149	4	no	—
366	C₄²	C₂²×D₁₄₉	1	1	yes	characteristic
367	C₄²	C₂²×D₁₄₉	1	2	yes	—
368	C₄²	C₂²×D₁₄₉	1	1	yes	characteristic
369	C₄²	C₂²×D₁₄₉	1	2	yes	—
370	C₄²	C₂²×D₁₄₉	1	1	yes	characteristic
371	C₄²	C₂²×D₁₄₉	1	1	yes	characteristic
372	C₄²	C₂²×D₁₄₉	1	2	yes	—
373	C₂³	—	149	2	no	—
374	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
375	C₂³	C₂³×D₁₄₉	1	2	yes	—
376	Q₈	—	2	2	no	—
377	Q₈	—	298	8	no	—
378	Q₈	—	298	4	no	—
379	Q₈	—	298	4	no	—
380	Q₈	—	149	4	no	—
381	D₄	—	2	4	no	—
382	D₄	—	298	8	no	—
383	D₄	—	298	4	no	—
384	D₄	—	298	2	no	—
385	D₄	#14558736	1	4	yes	complemented
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	298	4	no	—
393	C₂×C₄	—	298	8	no	—
394	C₂×C₄	—	298	8	no	—
395	C₂×C₄	—	298	4	no	—
396	C₂×C₄	—	298	4	no	—
397	C₂×C₄	—	149	2	no	—
398	C₂×C₄	—	149	2	no	—
399	C₂×C₄	—	149	4	no	—
400	C₂×C₄	—	149	4	no	—
401	C₂×C₄	—	149	2	no	—
402	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
403	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
404	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
405	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
406	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
407	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
408	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
409	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
410	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
411	C₂²	—	2	2	no	—
412	C₂²	—	2	2	no	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	298	2	no	—
417	C₂²	—	298	2	no	—
418	C₂²	—	298	2	no	—
419	C₂²	C₂×#14558736	1	4	yes	—
420	C₂²	C₂⁴×D₁₄₉	1	1	yes	characteristic
421	C₄	—	2	1	no	—
422	C₄	—	2	2	no	—
423	C₄	—	2	1	no	—
424	C₄	—	2	2	no	—
425	C₄	—	2	2	no	—
426	C₄	—	2	1	no	—
427	C₄	—	298	4	no	—
428	C₄	—	298	2	no	—
429	C₄	—	298	4	no	—
430	C₄	—	298	2	no	—
431	C₄	—	149	4	no	—
432	C₄	#41×D₁₄₉	1	2	yes	—
433	C₄	C₂×#14558736	1	2	yes	—
434	C₄	#18011958	1	2	yes	—
435	C₂	—	2	4	no	—
436	C₂	—	4	1	no	—
437	C₂	—	596	2	no	—
438	C₂	C₂×#41×D₁₄₉	1	1	yes	characteristic
439	C₂	C₂²×#14558736	1	1	yes	characteristic
440	C₂	C₂×#18011958	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₁₄₉
commutator, socle, cosocle	C₂²×C₁₄₉	C₂⁵
Frattini	C₂²	C₂⁴×D₁₄₉
Fitting	C₄×#41×C₁₄₉	C₂
hypercenter	C₄×#41	D₁₄₉
hypocenter	C₁₄₉	#3482
LCS	G ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41

Complements

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

N	H ≅ G/N	type
1. #23750353	C₂	semidirect
2. #23750348	C₂	semidirect
3. #23750343	C₂	semidirect
4. #23750315	C₂	semidirect
5. #23750308	C₂	semidirect
6. D₄×Dic₂₉₈	C₂	semidirect
7. #23750284	C₂	semidirect
8. #23750279	C₂	semidirect
9. #23750274	C₂	semidirect
10. #23750182	C₂	semidirect
11. #23750179	C₂	semidirect
12. #23750159	C₂	semidirect
13. #23750155	C₂	semidirect
14. C₄×#14558736	C₂	semidirect
15. C₄×#14558735	C₂	semidirect
16. C₂×C₄×Dic₂₉₈	C₂	semidirect
17. C₄×#41×C₁₄₉	C₂	semidirect
156. Dic₂₉₈	#41	semidirect
174. D₄×C₁₄₉	#41	semidirect
220. C₁₄₉	#3482	semidirect
237. C₄×#41	D₁₄₉	semidirect
385. D₄	#14558736	semidirect

Maximal subgroups

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

subgroup	index
#23750353	2
#23750348	2
#23750343	2
#23750315	2
#23750308	2
D₄×Dic₂₉₈	2
#23750284	2
#23750279	2
#23750274	2
#23750182	2
#23750179	2
#23750159	2
#23750155	2
C₄×#14558736	2
C₄×#14558735	2
C₂×C₄×Dic₂₉₈	2
C₄×#41×C₁₄₉	2
#3482	149