Subgroups — C₄×#18011889 #34047224

Order 19072.

656 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#18011889	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Dic₂₉₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄²×D₁₄₉	C₂	1	1	yes	maximal, characteristic
4	#23749529	C₂	1	1	yes	maximal, characteristic, complemented
5	#23749520	C₂	1	1	yes	maximal, characteristic, complemented
6	#23749511	C₂	1	1	yes	maximal, characteristic, complemented
7	#23749507	C₂	1	1	yes	maximal, characteristic, complemented
8	#23749499	C₂	1	1	yes	maximal, characteristic
9	#23749496	C₂	1	1	yes	maximal, characteristic
10	#23749484	C₂	1	1	yes	maximal, characteristic
11	C₄×#14558715	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#14558715	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×#14558713	C₂	1	1	yes	maximal, characteristic
14	C₄×#14558713	C₂	1	1	yes	maximal, characteristic
15	C₄×C₄⋊C₄×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×Dic₂₉₈	C₂²	1	1	yes	characteristic
17	C₂²×C₄×D₁₄₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₁₄₉	C₂²	1	1	yes	characteristic
19	C₂²×C₄×D₁₄₉	C₂²	1	1	yes	characteristic
20	#18011889	C₄	1	8	yes	direct product factor
21	C₄×Dic₂₉₈	—	2	4	no	—
22	C₂×C₄⋊Dic₁₄₉	C₂²	1	1	yes	characteristic
23	C₂×#14558715	C₂²	1	1	yes	characteristic
24	C₂×#14558715	C₂²	1	1	yes	characteristic
25	C₂×#14558715	C₂²	1	1	yes	characteristic
26	C₂×#14558715	C₂²	1	1	yes	characteristic
27	C₂×#14558715	C₂²	1	1	yes	characteristic
28	C₂×#14558715	C₂²	1	1	yes	characteristic
29	C₂×#14558713	C₂²	1	1	yes	characteristic
30	C₂×#14558713	C₂²	1	1	yes	characteristic
31	C₂×#14558713	C₂²	1	1	yes	characteristic
32	C₂×#14558713	C₂²	1	1	yes	characteristic
33	C₂×C₄×Dic₁₄₉	C₂²	1	1	yes	characteristic
34	C₂×C₄×Dic₁₄₉	C₂²	1	1	yes	characteristic
35	C₂×C₄×Dic₁₄₉	C₂²	1	1	yes	characteristic
36	C₂×C₄×Dic₁₄₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×Dic₁₄₉	C₂²	1	1	yes	characteristic
38	C₄²×D₁₄₉	—	2	4	no	—
39	#18011818	C₂²	1	1	yes	characteristic
40	#18011818	C₂²	1	1	yes	characteristic
41	#18011818	C₂²	1	1	yes	characteristic
42	#18011818	C₂²	1	1	yes	characteristic
43	#18011818	C₂²	1	1	yes	characteristic
44	#18011818	C₂²	1	1	yes	characteristic
45	#18011818	C₂²	1	1	yes	characteristic
46	#18011818	C₂²	1	1	yes	characteristic
47	C₂×C₄⋊C₄×C₁₄₉	C₂²	1	1	yes	characteristic
48	C₂×C₄⋊C₄×C₁₄₉	C₂²	1	1	yes	characteristic
49	C₂×C₄²×C₁₄₉	C₂²	1	1	yes	characteristic
50	C₂×C₄²×C₁₄₉	C₂²	1	1	yes	characteristic
51	C₂×C₄²×C₁₄₉	C₂²	1	1	yes	characteristic
52	#95×C₁₄₉	C₂²	1	1	yes	characteristic
53	#95×C₁₄₉	C₂²	1	1	yes	characteristic
54	C₂³×D₁₄₉	C₂³	1	1	yes	characteristic
55	C₂×Dic₂₉₈	—	2	2	no	—
56	C₂×Dic₂₉₈	—	2	2	no	—
57	C₂×Dic₂₉₈	C₂×C₄	1	4	yes	complemented
58	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
59	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
60	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
61	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
62	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
63	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
64	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
65	C₂×C₄×D₁₄₉	—	2	2	no	—
66	C₂×C₄×D₁₄₉	—	2	2	no	—
67	C₂×C₄×D₁₄₉	—	2	2	no	—
68	C₂×C₄×D₁₄₉	—	2	2	no	—
69	C₂×C₄×D₁₄₉	—	2	2	no	—
70	C₂×C₄×D₁₄₉	—	2	2	no	—
71	C₂×C₄×D₁₄₉	—	2	2	no	—
72	C₂×C₄×D₁₄₉	C₂×C₄	1	4	yes	—
73	C₂×C₄×D₁₄₉	Q₈	1	4	yes	complemented
74	C₄⋊Dic₁₄₉	—	2	2	no	—
75	#14558715	—	2	2	no	—
76	#14558715	—	2	2	no	—
77	#14558715	—	2	2	no	—
78	#14558715	—	2	2	no	—
79	#14558715	C₂×C₄	1	4	yes	complemented
80	#14558715	C₂×C₄	1	4	yes	complemented
81	#14558713	—	2	2	no	—
82	#14558713	—	2	2	no	—
83	#14558713	C₂×C₄	1	4	yes	—
84	#14558713	C₂×C₄	1	4	yes	—
85	C₄×Dic₁₄₉	—	2	2	no	—
86	C₄×Dic₁₄₉	—	2	2	no	—
87	C₄×Dic₁₄₉	—	2	2	no	—
88	C₄×Dic₁₄₉	—	2	2	no	—
89	C₄×Dic₁₄₉	D₄	1	4	yes	—
90	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
91	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
92	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
93	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
94	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
95	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
96	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
97	C₄⋊C₄×C₁₄₉	—	2	2	no	—
98	C₄⋊C₄×C₁₄₉	C₂×C₄	1	4	yes	complemented
99	C₄²×C₁₄₉	—	2	2	no	—
100	C₄²×C₁₄₉	—	2	2	no	—
101	C₄²×C₁₄₉	—	2	2	no	—
102	C₂²×D₁₄₉	—	2	1	no	—
103	C₂²×D₁₄₉	—	2	1	no	—
104	C₂²×D₁₄₉	—	2	1	no	—
105	C₂²×D₁₄₉	—	2	1	no	—
106	C₂²×D₁₄₉	C₂²×C₄	1	2	yes	—
107	C₂²×D₁₄₉	C₂×Q₈	1	2	yes	—
108	C₂²×D₁₄₉	#41	1	2	yes	—
109	Dic₂₉₈	—	2	8	no	—
110	C₂×Dic₁₄₉	—	2	1	no	—
111	C₂×Dic₁₄₉	—	2	1	no	—
112	C₂×Dic₁₄₉	—	2	1	no	—
113	C₂×Dic₁₄₉	—	2	1	no	—
114	C₂×Dic₁₄₉	—	2	1	no	—
115	C₂×Dic₁₄₉	—	2	1	no	—
116	C₂×Dic₁₄₉	—	2	1	no	—
117	C₂×Dic₁₄₉	—	2	1	no	—
118	C₂×Dic₁₄₉	—	2	1	no	—
119	C₂×Dic₁₄₉	—	2	1	no	—
120	C₂×Dic₁₄₉	—	2	1	no	—
121	C₂×Dic₁₄₉	—	2	1	no	—
122	C₂×Dic₁₄₉	—	2	1	no	—
123	C₂×Dic₁₄₉	—	2	1	no	—
124	C₂×Dic₁₄₉	C₂²×C₄	1	2	yes	—
125	C₂×Dic₁₄₉	C₂²×C₄	1	2	yes	—
126	C₂×Dic₁₄₉	C₂²×C₄	1	2	yes	—
127	C₂×Dic₁₄₉	C₂×D₄	1	2	yes	—
128	C₂×Dic₁₄₉	C₂×D₄	1	2	yes	—
129	C₂×Dic₁₄₉	C₂×Q₈	1	2	yes	—
130	C₂×Dic₁₄₉	#41	1	2	yes	—
131	C₄×D₁₄₉	—	2	8	no	—
132	C₄×D₁₄₉	—	2	8	no	—
133	C₄×D₁₄₉	—	2	8	no	—
134	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
135	C₂×C₄×C₁₄₉	—	2	1	no	—
136	C₂×C₄×C₁₄₉	—	2	1	no	—
137	C₂×C₄×C₁₄₉	—	2	1	no	—
138	C₂×C₄×C₁₄₉	—	2	1	no	—
139	C₂×C₄×C₁₄₉	—	2	1	no	—
140	C₂×C₄×C₁₄₉	—	2	1	no	—
141	C₂×C₄×C₁₄₉	—	2	1	no	—
142	C₂×C₄×C₁₄₉	—	2	1	no	—
143	C₂×C₄×C₁₄₉	—	2	1	no	—
144	C₂×C₄×C₁₄₉	—	2	1	no	—
145	C₂×C₄×C₁₄₉	—	2	1	no	—
146	C₂×C₄×C₁₄₉	—	2	1	no	—
147	C₂×C₄×C₁₄₉	—	2	1	no	—
148	C₂×C₄×C₁₄₉	—	2	1	no	—
149	C₂×C₄×C₁₄₉	C₂²×C₄	1	2	yes	—
150	C₂×C₄×C₁₄₉	C₂²×C₄	1	2	yes	—
151	C₂×C₄×C₁₄₉	C₂²×C₄	1	2	yes	—
152	C₂×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
153	C₂×C₄×C₁₄₉	C₂×Q₈	1	2	yes	—
154	C₂×C₄×C₁₄₉	#41	1	2	yes	—
155	C₂×C₄×C₁₄₉	#41	1	2	yes	—
156	C₂²×C₁₄₉	C₂³×C₄	1	1	yes	characteristic
157	C₂²×C₁₄₉	C₂²×D₄	1	1	yes	characteristic
158	C₂²×C₁₄₉	C₂²×Q₈	1	1	yes	characteristic
159	C₂²×C₁₄₉	C₂×#41	1	1	yes	characteristic
160	C₂²×C₁₄₉	C₂×#41	1	1	yes	characteristic
161	C₂²×C₁₄₉	C₂×#41	1	1	yes	characteristic
162	C₂²×C₁₄₉	C₂×#41	1	1	yes	characteristic
163	C₂×D₁₄₉	—	2	2	no	—
164	C₂×D₁₄₉	—	2	2	no	—
165	C₂×D₁₄₉	—	2	2	no	—
166	C₂×D₁₄₉	—	2	2	no	—
167	C₂×D₁₄₉	—	2	2	no	—
168	C₂×D₁₄₉	—	2	2	no	—
169	C₂×D₁₄₉	C₄×Q₈	1	4	yes	complemented
170	C₄×C₁₄₉	—	2	2	no	—
171	C₄×C₁₄₉	—	2	2	no	—
172	C₄×C₁₄₉	—	2	2	no	—
173	C₄×C₁₄₉	—	2	2	no	—
174	C₄×C₁₄₉	—	4	1	no	—
175	C₄×C₁₄₉	—	4	1	no	—
176	C₄×C₁₄₉	C₂²⋊Q₈	1	4	yes	complemented
177	Dic₁₄₉	—	2	2	no	—
178	Dic₁₄₉	—	2	2	no	—
179	Dic₁₄₉	—	2	2	no	—
180	Dic₁₄₉	—	2	2	no	—
181	Dic₁₄₉	—	4	1	no	—
182	Dic₁₄₉	—	4	1	no	—
183	Dic₁₄₉	C₄×D₄	1	4	yes	—
184	C₂×C₁₄₉	C₂×C₄×D₄	1	1	yes	characteristic
185	C₂×C₁₄₉	C₂×C₄×Q₈	1	1	yes	characteristic
186	C₂×C₁₄₉	C₄×#41	1	1	yes	characteristic
187	C₂×C₁₄₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
188	C₂×C₁₄₉	#525	1	1	yes	characteristic
189	C₂×C₁₄₉	#529	1	1	yes	characteristic
190	C₂×C₁₄₉	#533	1	1	yes	characteristic
191	D₁₄₉	—	2	4	no	—
192	C₁₄₉	C₄×C₂²⋊Q₈	1	1	yes	characteristic, complemented, Sylow
193	C₄×C₂²⋊Q₈	—	149	1	no	maximal, Sylow
194	C₂×C₂²⋊Q₈	—	149	1	no	—
195	C₂×C₄×Q₈	—	149	1	no	—
196	C₂²×C₄²	—	149	1	no	—
197	#391	—	149	1	no	—
198	#389	—	149	1	no	—
199	#387	—	149	1	no	—
200	#387	—	149	1	no	—
201	#385	—	149	1	no	—
202	#385	—	149	1	no	—
203	#380	—	149	1	no	—
204	C₄×C₄⋊C₄	—	149	1	no	—
205	C₄×C₄⋊C₄	—	149	1	no	—
206	C₄×C₄⋊C₄	D₁₄₉	1	1	yes	characteristic, complemented
207	C₄×C₂²⋊C₄	—	149	1	no	—
208	C₄×C₂²⋊C₄	—	149	1	no	—
209	C₂²×Q₈	—	149	1	no	—
210	C₂³×C₄	—	149	1	no	—
211	C₂³×C₄	—	149	1	no	—
212	C₂³×C₄	—	149	1	no	—
213	C₂²⋊Q₈	—	149	8	no	—
214	C₄×Q₈	—	298	4	no	—
215	C₂×C₄⋊C₄	—	149	1	no	—
216	C₂×C₄⋊C₄	—	149	1	no	—
217	C₂×C₄⋊C₄	—	149	1	no	—
218	C₂×C₄⋊C₄	—	149	1	no	—
219	C₂×C₄⋊C₄	—	149	1	no	—
220	C₂×C₄⋊C₄	—	149	1	no	—
221	C₂×C₄⋊C₄	—	149	1	no	—
222	C₂×C₄⋊C₄	C₂×D₁₄₉	1	1	yes	characteristic
223	C₂×C₄⋊C₄	C₂×D₁₄₉	1	1	yes	characteristic
224	C₂×C₂²⋊C₄	—	149	1	no	—
225	C₂×C₂²⋊C₄	—	149	1	no	—
226	C₂×C₂²⋊C₄	—	149	1	no	—
227	C₂×C₂²⋊C₄	—	149	1	no	—
228	C₂×C₄²	—	298	4	no	—
229	C₂×C₄²	—	149	1	no	—
230	C₂×C₄²	—	149	1	no	—
231	C₂×C₄²	—	149	1	no	—
232	C₂×C₄²	—	149	1	no	—
233	C₂×C₄²	—	149	1	no	—
234	C₂×C₄²	C₂×D₁₄₉	1	1	yes	characteristic
235	C₂×C₄²	C₂×D₁₄₉	1	1	yes	characteristic
236	C₂×C₄²	C₂×D₁₄₉	1	1	yes	characteristic
237	#95	—	149	1	no	—
238	#95	—	149	1	no	—
239	#95	—	149	1	no	—
240	#95	—	149	1	no	—
241	#95	—	149	1	no	—
242	#95	—	149	1	no	—
243	#95	—	149	1	no	—
244	#95	—	149	1	no	—
245	#95	C₂×D₁₄₉	1	1	yes	characteristic
246	#95	C₂×D₁₄₉	1	1	yes	characteristic
247	C₂⁴	—	149	1	no	—
248	C₂×Q₈	—	298	2	no	—
249	C₂×Q₈	—	298	2	no	—
250	C₂×Q₈	—	149	4	no	—
251	C₂²×C₄	—	298	2	no	—
252	C₂²×C₄	—	298	2	no	—
253	C₂²×C₄	—	298	2	no	—
254	C₂²×C₄	—	298	2	no	—
255	C₂²×C₄	—	298	2	no	—
256	C₂²×C₄	—	298	2	no	—
257	C₂²×C₄	—	298	2	no	—
258	C₂²×C₄	—	149	1	no	—
259	C₂²×C₄	—	149	1	no	—
260	C₂²×C₄	—	149	1	no	—
261	C₂²×C₄	—	149	1	no	—
262	C₂²×C₄	—	149	1	no	—
263	C₂²×C₄	—	149	1	no	—
264	C₂²×C₄	—	149	4	no	—
265	C₂²×C₄	—	149	4	no	—
266	C₂²×C₄	—	149	1	no	—
267	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
268	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
269	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
270	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
271	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
272	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
273	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
274	C₄⋊C₄	—	2	2	no	—
275	C₄⋊C₄	—	298	2	no	—
276	C₄⋊C₄	—	298	2	no	—
277	C₄⋊C₄	—	298	2	no	—
278	C₄⋊C₄	—	298	2	no	—
279	C₄⋊C₄	—	298	2	no	—
280	C₄⋊C₄	—	149	4	no	—
281	C₄⋊C₄	—	149	4	no	—
282	C₄⋊C₄	C₄×D₁₄₉	1	4	yes	complemented
283	C₂²⋊C₄	—	298	2	no	—
284	C₂²⋊C₄	—	298	2	no	—
285	C₂²⋊C₄	—	149	4	no	—
286	C₂²⋊C₄	—	149	4	no	—
287	C₄²	—	2	2	no	—
288	C₄²	—	2	2	no	—
289	C₄²	—	2	2	no	—
290	C₄²	—	298	2	no	—
291	C₄²	—	298	2	no	—
292	C₄²	—	298	2	no	—
293	C₄²	—	298	2	no	—
294	C₄²	—	149	4	no	—
295	C₂³	—	298	1	no	—
296	C₂³	—	298	1	no	—
297	C₂³	—	298	1	no	—
298	C₂³	—	298	1	no	—
299	C₂³	—	149	2	no	—
300	C₂³	—	149	2	no	—
301	C₂³	—	149	2	no	—
302	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
303	Q₈	—	298	8	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	1	no	—
306	C₂×C₄	—	2	1	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	1	no	—
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	298	8	no	—
319	C₂×C₄	—	298	8	no	—
320	C₂×C₄	—	298	1	no	—
321	C₂×C₄	—	298	1	no	—
322	C₂×C₄	—	298	1	no	—
323	C₂×C₄	—	298	1	no	—
324	C₂×C₄	—	298	1	no	—
325	C₂×C₄	—	298	1	no	—
326	C₂×C₄	—	298	1	no	—
327	C₂×C₄	—	298	1	no	—
328	C₂×C₄	—	298	8	no	—
329	C₂×C₄	—	298	1	no	—
330	C₂×C₄	—	298	1	no	—
331	C₂×C₄	—	298	1	no	—
332	C₂×C₄	—	298	1	no	—
333	C₂×C₄	—	298	1	no	—
334	C₂×C₄	—	298	1	no	—
335	C₂×C₄	—	149	2	no	—
336	C₂×C₄	—	149	2	no	—
337	C₂×C₄	—	149	2	no	—
338	C₂×C₄	—	149	2	no	—
339	C₂×C₄	—	149	2	no	—
340	C₂×C₄	—	149	2	no	—
341	C₂×C₄	—	149	2	no	—
342	C₂×C₄	C₂×C₄×D₁₄₉	1	2	yes	—
343	C₂×C₄	C₂×C₄×D₁₄₉	1	2	yes	—
344	C₂×C₄	C₂×C₄×D₁₄₉	1	2	yes	—
345	C₂×C₄	D₄×D₁₄₉	1	2	yes	—
346	C₂×C₄	Q₈×D₁₄₉	1	2	yes	—
347	C₂×C₄	#14558736	1	2	yes	—
348	C₂×C₄	#14558736	1	2	yes	—
349	C₂²	—	298	2	no	—
350	C₂²	—	298	2	no	—
351	C₂²	—	298	2	no	—
352	C₂²	—	298	2	no	—
353	C₂²	—	298	2	no	—
354	C₂²	—	298	2	no	—
355	C₂²	—	149	4	no	—
356	C₂²	C₂²×C₄×D₁₄₉	1	1	yes	characteristic
357	C₂²	C₂×D₄×D₁₄₉	1	1	yes	characteristic
358	C₂²	C₂×Q₈×D₁₄₉	1	1	yes	characteristic
359	C₂²	#41×D₁₄₉	1	1	yes	characteristic
360	C₂²	#41×D₁₄₉	1	1	yes	characteristic
361	C₂²	C₂×#14558736	1	1	yes	characteristic
362	C₂²	C₂×#14558736	1	1	yes	characteristic
363	C₄	—	2	2	no	—
364	C₄	—	2	2	no	—
365	C₄	—	2	2	no	—
366	C₄	—	2	2	no	—
367	C₄	—	4	1	no	—
368	C₄	—	4	1	no	—
369	C₄	—	298	2	no	—
370	C₄	—	298	2	no	—
371	C₄	—	298	2	no	—
372	C₄	—	298	2	no	—
373	C₄	—	596	1	no	—
374	C₄	—	596	1	no	—
375	C₄	—	149	4	no	—
376	C₄	#18011889	1	4	yes	direct product factor
377	C₂	—	298	4	no	—
378	C₂	C₄×D₄×D₁₄₉	1	1	yes	characteristic
379	C₂	C₄×Q₈×D₁₄₉	1	1	yes	characteristic
380	C₂	C₄×#14558736	1	1	yes	characteristic
381	C₂	C₂×#18011889	1	1	yes	characteristic
382	C₂	#23750134	1	1	yes	characteristic
383	C₂	#23750153	1	1	yes	characteristic
384	C₂	#23750179	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²×D₁₄₉
commutator	C₂²×C₁₄₉	C₂³×C₄
Frattini	C₂³	C₂³×D₁₄₉
Fitting	C₄×C₄⋊C₄×C₁₄₉	C₂
socle, cosocle	C₂³×C₁₄₉	C₂⁴
prime radical	C₂³×D₁₄₉	C₂³
hypercenter	C₄×C₄⋊C₄	D₁₄₉
hypocenter	C₁₄₉	C₄×C₂²⋊Q₈
LCS	G ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×Dic₂₉₈	C₂	semidirect
4. #23749529	C₂	semidirect
5. #23749520	C₂	semidirect
6. #23749511	C₂	semidirect
7. #23749507	C₂	semidirect
11. C₄×#14558715	C₂	semidirect
12. C₄×#14558715	C₂	semidirect
15. C₄×C₄⋊C₄×C₁₄₉	C₂	semidirect
20. #18011889	C₄	direct (N × H)
57. C₂×Dic₂₉₈	C₂×C₄	semidirect
73. C₂×C₄×D₁₄₉	Q₈	semidirect
79. #14558715	C₂×C₄	semidirect
80. #14558715	C₂×C₄	semidirect
98. C₄⋊C₄×C₁₄₉	C₂×C₄	semidirect
169. C₂×D₁₄₉	C₄×Q₈	semidirect
176. C₄×C₁₄₉	C₂²⋊Q₈	semidirect
192. C₁₄₉	C₄×C₂²⋊Q₈	semidirect
206. C₄×C₄⋊C₄	D₁₄₉	semidirect
282. C₄⋊C₄	C₄×D₁₄₉	semidirect
376. C₄	#18011889	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#18011889	2
C₂×C₄×Dic₂₉₈	2
C₂×C₄²×D₁₄₉	2
#23749529	2
#23749520	2
#23749511	2
#23749507	2
#23749499	2
#23749496	2
#23749484	2
C₄×#14558715	2
C₄×#14558713	2
C₄×C₄⋊C₄×C₁₄₉	2
C₄×C₂²⋊Q₈	149

Subgroups — C4×#18011889 #34047224

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#18011889 #34047224