Subgroups — #34061173

Order 19072.

568 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	#23750575	C₂	1	2	yes	maximal, complemented
2	#23750574	C₂	1	2	yes	maximal, complemented
3	#23750573	C₂	1	2	yes	maximal
4	#23750572	C₂	1	2	yes	maximal, complemented
5	#23750570	C₂	1	1	yes	maximal, characteristic, complemented
6	#23750569	C₂	1	1	yes	maximal, characteristic, complemented
7	#23750568	C₂	1	1	yes	maximal, characteristic, complemented
8	#23750567	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₂²⋊#10597010	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×(C₂×#10597010)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×D₄×D₁₄₉	C₂	1	1	yes	maximal, characteristic
12	C₂³×#10597010	C₂²	1	2	yes	—
13	C₂×C₄⋊#10597010	C₂²	1	2	yes	—
14	C₂×C₄⋊#10597010	C₂²	1	2	yes	—
15	C₂×C₂²⋊#10597010	C₂²	1	2	yes	—
16	C₂×C₂²⋊#10597010	C₂²	1	2	yes	—
17	C₂×C₂²⋊#10597010	C₂²	1	2	yes	—
18	C₂×C₄×#10597010	C₂²	1	2	yes	—
19	(C₂×#10597010)⋊C₄	C₂²	1	1	yes	characteristic
20	(C₂×#10597010)⋊C₄	C₂²	1	1	yes	characteristic
21	(C₂×#10597010)⋊C₄	C₂²	1	2	yes	—
22	(C₂×#10597010)⋊C₄	C₂²	1	1	yes	characteristic
23	(C₂×#10597010)⋊C₄	C₂²	1	1	yes	characteristic
24	(C₂×#10597010)⋊C₄	C₂²	1	2	yes	—
25	(C₂×#10597010)⋊C₄	C₂²	1	2	yes	—
26	(C₂×#10597010)⋊C₄	C₂²	1	2	yes	—
27	(C₂×#10597010)⋊C₄	C₂²	1	2	yes	—
28	C₂×D₄×D₁₄₉	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₁₄₉	C₂²	1	1	yes	characteristic
30	C₂²×C₄×D₁₄₉	C₂²	1	1	yes	characteristic
31	C₄×D₅₉₆	C₄	1	1	yes	characteristic, complemented
32	D₄×Dic₁₄₉	C₄	1	1	yes	characteristic, complemented
33	#18011873	C₄	1	1	yes	characteristic, complemented
34	C₄×C₂²⋊D₁₄₉	C₄	1	1	yes	characteristic, complemented
35	C₄×C₂²⋊D₁₄₉	C₄	1	1	yes	characteristic, complemented
36	#18011871	C₄	1	1	yes	characteristic, complemented
37	#18011871	C₄	1	1	yes	characteristic, complemented
38	C₄⋊C₄×D₁₄₉	C₂²	1	1	yes	characteristic
39	C₂²⋊C₄×D₁₄₉	C₂²	1	1	yes	characteristic
40	C₂²⋊C₄×D₁₄₉	C₂²	1	1	yes	characteristic
41	C₄²×D₁₄₉	C₂²	1	1	yes	characteristic
42	C₄×D₄×C₁₄₉	C₄	1	1	yes	characteristic, complemented
43	C₂²×#10597010	—	2	4	no	—
44	C₂²×#10597010	—	4	2	no	—
45	C₂²×#10597010	—	4	2	no	—
46	C₂²×#10597010	C₂³	1	2	yes	—
47	C₂²×#10597010	C₂³	1	2	yes	—
48	C₂²×#10597010	C₂³	1	2	yes	—
49	C₂²×#10597010	C₂³	1	2	yes	—
50	C₄⋊#10597010	—	4	2	no	—
51	C₄⋊#10597010	—	4	2	no	—
52	C₂²⋊#10597010	—	2	4	no	—
53	C₂²⋊#10597010	—	4	2	no	—
54	C₂²⋊#10597010	—	4	2	no	—
55	C₄×#10597010	—	4	2	no	—
56	C₂³×D₁₄₉	C₂³	1	1	yes	characteristic
57	C₂³×D₁₄₉	C₂³	1	1	yes	characteristic
58	C₂×D₅₉₆	C₂×C₄	1	1	yes	characteristic
59	C₂×C₂²⋊D₁₄₉	C₂×C₄	1	1	yes	characteristic
60	C₂×C₂²⋊D₁₄₉	C₂×C₄	1	1	yes	characteristic
61	D₄×D₁₄₉	—	2	4	no	—
62	C₂²×Dic₁₄₉	C₂×C₄	1	1	yes	characteristic
63	C₂²×Dic₁₄₉	C₂×C₄	1	1	yes	characteristic, complemented
64	C₂×C₄×D₁₄₉	—	4	2	no	—
65	C₂×C₄×D₁₄₉	—	4	2	no	—
66	C₂×C₄×D₁₄₉	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄×D₁₄₉	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄×D₁₄₉	C₂×C₄	1	1	yes	characteristic, complemented
69	C₂×C₄×D₁₄₉	C₂×C₄	1	1	yes	characteristic, complemented
70	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
71	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
72	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
73	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
74	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
75	C₄⋊Dic₁₄₉	C₂×C₄	1	1	yes	characteristic, complemented
76	#14558715	C₂×C₄	1	1	yes	characteristic, complemented
77	#14558715	C₂×C₄	1	1	yes	characteristic, complemented
78	C₂²⋊Dic₁₄₉	C₂×C₄	1	1	yes	characteristic
79	C₂²⋊Dic₁₄₉	C₂×C₄	1	1	yes	characteristic, complemented
80	#14558713	C₂×C₄	1	1	yes	characteristic
81	#14558713	C₂×C₄	1	1	yes	characteristic
82	#14558713	C₂×C₄	1	1	yes	characteristic, complemented
83	#14558713	C₂×C₄	1	1	yes	characteristic, complemented
84	C₄×Dic₁₄₉	C₂×C₄	1	1	yes	characteristic, complemented
85	C₄×Dic₁₄₉	C₂×C₄	1	1	yes	characteristic, complemented
86	C₄×Dic₁₄₉	C₂×C₄	1	1	yes	characteristic, complemented
87	C₂×D₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic, complemented
90	C₄⋊C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic, complemented
91	C₂²⋊C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
92	C₂²⋊C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic, complemented
93	C₄²×C₁₄₉	C₂×C₄	1	1	yes	characteristic, complemented
94	C₂×#10597010	—	2	2	no	—
95	C₂×#10597010	—	2	2	no	—
96	C₂×#10597010	—	2	2	no	—
97	C₂×#10597010	—	2	2	no	—
98	C₂×#10597010	—	2	2	no	—
99	C₂×#10597010	—	2	2	no	—
100	C₂×#10597010	—	2	2	no	—
101	C₂×#10597010	—	2	2	no	—
102	C₂×#10597010	—	2	2	no	—
103	C₂×#10597010	—	2	2	no	—
104	C₂×#10597010	—	2	2	no	—
105	C₂×#10597010	—	2	2	no	—
106	C₂×#10597010	—	4	8	no	—
107	C₂²×D₁₄₉	—	2	2	no	—
108	C₂²×D₁₄₉	—	2	1	no	—
109	C₂²×D₁₄₉	—	2	1	no	—
110	C₂²×D₁₄₉	—	2	2	no	—
111	C₂²×D₁₄₉	—	2	2	no	—
112	C₂²×D₁₄₉	—	2	1	no	—
113	C₂²×D₁₄₉	—	2	1	no	—
114	C₂²×D₁₄₉	C₂²×C₄	1	1	yes	characteristic
115	C₂²×D₁₄₉	C₂²×C₄	1	1	yes	characteristic
116	C₂²×D₁₄₉	#41	1	4	yes	—
117	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
118	D₅₉₆	—	2	2	no	—
119	C₂²⋊D₁₄₉	—	2	2	no	—
120	C₂²⋊D₁₄₉	—	2	2	no	—
121	C₂×Dic₁₄₉	—	4	1	no	—
122	C₂×Dic₁₄₉	—	4	1	no	—
123	C₂×Dic₁₄₉	C₂²×C₄	1	1	yes	characteristic
124	C₂×Dic₁₄₉	C₂²×C₄	1	1	yes	characteristic
125	C₂×Dic₁₄₉	C₂²×C₄	1	1	yes	characteristic
126	C₂×Dic₁₄₉	C₂²×C₄	1	1	yes	characteristic
127	C₂×Dic₁₄₉	C₂²×C₄	1	1	yes	characteristic
128	C₄×D₁₄₉	—	2	2	no	—
129	C₄×D₁₄₉	—	2	2	no	—
130	C₄×D₁₄₉	—	2	2	no	—
131	C₄×D₁₄₉	—	2	2	no	—
132	C₄×D₁₄₉	—	2	1	no	—
133	C₄×D₁₄₉	—	2	1	no	—
134	C₄×D₁₄₉	—	4	1	no	—
135	C₄×D₁₄₉	—	4	1	no	—
136	C₄×D₁₄₉	—	4	1	no	—
137	C₄×D₁₄₉	—	4	1	no	—
138	C₂³×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
139	C₂³×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
140	D₄×C₁₄₉	—	2	2	no	—
141	C₂×C₄×C₁₄₉	—	4	1	no	—
142	C₂×C₄×C₁₄₉	—	4	1	no	—
143	C₂×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
144	C₂×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₁₄₉	—	2	1	no	—
149	C₂²×C₁₄₉	—	2	1	no	—
150	C₂²×C₁₄₉	—	2	1	no	—
151	C₂²×C₁₄₉	—	2	1	no	—
152	C₂²×C₁₄₉	—	2	1	no	—
153	C₂²×C₁₄₉	#117	1	2	yes	—
154	C₂²×C₁₄₉	C₂³×C₄	1	1	yes	characteristic
155	C₂×D₁₄₉	—	2	1	no	—
156	C₂×D₁₄₉	—	2	1	no	—
157	C₂×D₁₄₉	—	2	4	no	—
158	C₂×D₁₄₉	—	2	4	no	—
159	C₂×D₁₄₉	—	2	1	no	—
160	C₂×D₁₄₉	—	2	1	no	—
161	C₂×D₁₄₉	—	2	1	no	—
162	C₂×D₁₄₉	—	4	2	no	—
163	C₂×D₁₄₉	—	4	2	no	—
164	C₂×D₁₄₉	#117	1	2	yes	—
165	C₂×D₁₄₉	C₂×#41	1	2	yes	—
166	C₂×D₁₄₉	H(5,𝔽₂)	1	1	yes	characteristic
167	C₂×D₁₄₉	H(5,𝔽₂)	1	2	yes	—
168	C₂×D₁₄₉	2₋¹⁺⁴	1	1	yes	characteristic
169	#10597010	—	4	2	no	—
170	#10597010	—	4	2	no	—
171	#10597010	—	4	2	no	—
172	#10597010	—	4	2	no	—
173	C₄×C₁₄₉	—	2	1	no	—
174	C₄×C₁₄₉	—	2	1	no	—
175	C₄×C₁₄₉	—	2	1	no	—
176	C₄×C₁₄₉	—	2	1	no	—
177	C₄×C₁₄₉	—	2	1	no	—
178	Dic₁₄₉	—	2	1	no	—
179	Dic₁₄₉	—	2	1	no	—
180	Dic₁₄₉	—	2	1	no	—
181	Dic₁₄₉	—	2	1	no	—
182	Dic₁₄₉	—	2	1	no	—
183	C₂×C₁₄₉	—	2	2	no	—
184	C₂×C₁₄₉	—	4	1	no	—
185	C₂×C₁₄₉	C₂×#117	1	1	yes	characteristic
186	C₂×C₁₄₉	#518	1	1	yes	characteristic
187	C₂×C₁₄₉	#520	1	1	yes	characteristic
188	D₁₄₉	—	2	2	no	—
189	D₁₄₉	—	4	1	no	—
190	D₁₄₉	#538	1	2	yes	—
191	D₁₄₉	#539	1	2	yes	—
192	C₁₄₉	#2318	1	1	yes	characteristic, complemented, Sylow
193	#2318	—	149	1	no	maximal, Sylow
194	C₂×C₄×D₄	—	149	1	no	—
195	#388	—	149	2	no	—
196	#387	—	149	2	no	—
197	#386	—	149	2	no	—
198	#385	—	149	2	no	—
199	#383	—	149	1	no	—
200	#382	—	149	1	no	—
201	#381	—	149	1	no	—
202	#380	—	149	1	no	—
203	C₄×C₂²⋊C₄	—	149	1	no	—
204	C₂×#95	—	149	1	no	—
205	C₂²×D₄	—	149	1	no	—
206	C₂³×C₄	—	149	2	no	—
207	C₂³×C₄	—	149	1	no	—
208	C₂³×C₄	—	149	1	no	—
209	C₄×D₄	—	149	1	no	—
210	C₄×D₄	—	149	1	no	—
211	C₄×D₄	—	149	1	no	—
212	C₄×D₄	—	149	1	no	—
213	C₄×D₄	—	149	1	no	—
214	C₄×D₄	—	149	1	no	—
215	C₄×D₄	—	149	1	no	—
216	C₄×D₄	#10597010	1	1	yes	characteristic, complemented
217	C₂×C₄⋊C₄	—	149	2	no	—
218	C₂×C₄⋊C₄	—	149	2	no	—
219	C₂×C₄⋊C₄	—	149	1	no	—
220	C₂×C₂²⋊C₄	—	149	2	no	—
221	C₂×C₂²⋊C₄	—	149	2	no	—
222	C₂×C₂²⋊C₄	—	149	2	no	—
223	C₂×C₂²⋊C₄	—	149	1	no	—
224	C₂×C₂²⋊C₄	—	149	1	no	—
225	C₂×C₄²	—	149	2	no	—
226	C₂×C₄²	—	149	1	no	—
227	#95	—	149	1	no	—
228	#95	—	149	1	no	—
229	#95	—	149	2	no	—
230	#95	—	149	1	no	—
231	#95	—	149	1	no	—
232	#95	—	149	2	no	—
233	#95	—	149	2	no	—
234	#95	—	149	2	no	—
235	#95	—	149	2	no	—
236	C₂⁴	—	149	1	no	—
237	C₂⁴	—	149	1	no	—
238	C₂×D₄	—	298	4	no	—
239	C₂×D₄	—	149	1	no	—
240	C₂×D₄	—	149	1	no	—
241	C₂×D₄	—	149	1	no	—
242	C₂×D₄	C₂×#10597010	1	1	yes	characteristic
243	C₂²×C₄	—	298	4	no	—
244	C₂²×C₄	—	596	2	no	—
245	C₂²×C₄	—	596	2	no	—
246	C₂²×C₄	—	596	2	no	—
247	C₂²×C₄	—	596	2	no	—
248	C₂²×C₄	—	149	2	no	—
249	C₂²×C₄	—	149	2	no	—
250	C₂²×C₄	—	149	2	no	—
251	C₂²×C₄	—	149	2	no	—
252	C₂²×C₄	—	149	1	no	—
253	C₂²×C₄	—	149	1	no	—
254	C₂²×C₄	—	149	1	no	—
255	C₂²×C₄	—	149	1	no	—
256	C₂²×C₄	—	149	1	no	—
257	C₂²×C₄	—	149	1	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	C₂×#10597010	1	1	yes	characteristic
264	C₂²×C₄	C₂×#10597010	1	1	yes	characteristic, complemented
265	C₄⋊C₄	—	596	2	no	—
266	C₄⋊C₄	—	596	2	no	—
267	C₄⋊C₄	—	149	1	no	—
268	C₄⋊C₄	—	149	1	no	—
269	C₄⋊C₄	—	149	1	no	—
270	C₄⋊C₄	C₂×#10597010	1	1	yes	characteristic, complemented
271	C₂²⋊C₄	—	298	4	no	—
272	C₂²⋊C₄	—	596	2	no	—
273	C₂²⋊C₄	—	596	2	no	—
274	C₂²⋊C₄	—	149	1	no	—
275	C₂²⋊C₄	—	149	1	no	—
276	C₂²⋊C₄	—	149	1	no	—
277	C₂²⋊C₄	—	149	1	no	—
278	C₂²⋊C₄	—	149	1	no	—
279	C₂²⋊C₄	—	149	1	no	—
280	C₂²⋊C₄	C₂×#10597010	1	1	yes	characteristic
281	C₂²⋊C₄	C₂×#10597010	1	1	yes	characteristic, complemented
282	C₄²	—	596	2	no	—
283	C₄²	—	149	1	no	—
284	C₄²	—	149	1	no	—
285	C₄²	—	149	1	no	—
286	C₄²	C₂×#10597010	1	1	yes	characteristic, complemented
287	C₂³	—	298	2	no	—
288	C₂³	—	298	1	no	—
289	C₂³	—	298	1	no	—
290	C₂³	—	298	1	no	—
291	C₂³	—	298	2	no	—
292	C₂³	—	298	2	no	—
293	C₂³	—	298	1	no	—
294	C₂³	—	149	1	no	—
295	C₂³	—	149	4	no	—
296	C₂³	—	149	1	no	—
297	C₂³	—	149	1	no	—
298	C₂³	C₂²×#10597010	1	1	yes	characteristic
299	C₂³	C₂²×#10597010	1	1	yes	characteristic
300	D₄	—	2	2	no	—
301	D₄	—	298	2	no	—
302	D₄	—	298	2	no	—
303	D₄	—	298	2	no	—
304	C₂×C₄	—	4	1	no	—
305	C₂×C₄	—	4	1	no	—
306	C₂×C₄	—	298	2	no	—
307	C₂×C₄	—	298	1	no	—
308	C₂×C₄	—	298	2	no	—
309	C₂×C₄	—	298	2	no	—
310	C₂×C₄	—	298	1	no	—
311	C₂×C₄	—	298	2	no	—
312	C₂×C₄	—	298	2	no	—
313	C₂×C₄	—	298	2	no	—
314	C₂×C₄	—	298	2	no	—
315	C₂×C₄	—	298	2	no	—
316	C₂×C₄	—	298	2	no	—
317	C₂×C₄	—	298	2	no	—
318	C₂×C₄	—	298	2	no	—
319	C₂×C₄	—	298	2	no	—
320	C₂×C₄	—	298	2	no	—
321	C₂×C₄	—	298	2	no	—
322	C₂×C₄	—	298	2	no	—
323	C₂×C₄	—	298	2	no	—
324	C₂×C₄	—	596	1	no	—
325	C₂×C₄	—	596	1	no	—
326	C₂×C₄	—	596	1	no	—
327	C₂×C₄	—	596	1	no	—
328	C₂×C₄	—	596	1	no	—
329	C₂×C₄	—	596	1	no	—
330	C₂×C₄	—	596	8	no	—
331	C₂×C₄	—	149	1	no	—
332	C₂×C₄	—	149	1	no	—
333	C₂×C₄	—	149	1	no	—
334	C₂×C₄	—	149	1	no	—
335	C₂×C₄	—	149	1	no	—
336	C₂×C₄	C₂²×#10597010	1	1	yes	characteristic
337	C₂×C₄	C₂²×#10597010	1	1	yes	characteristic
338	C₂×C₄	C₂²×#10597010	1	1	yes	characteristic
339	C₂×C₄	C₂²×#10597010	1	1	yes	characteristic
340	C₂×C₄	C₂²×#10597010	1	1	yes	characteristic
341	C₂²	—	2	1	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	2	1	no	—
345	C₂²	—	2	1	no	—
346	C₂²	—	298	4	no	—
347	C₂²	—	298	4	no	—
348	C₂²	—	298	1	no	—
349	C₂²	—	298	1	no	—
350	C₂²	—	298	1	no	—
351	C₂²	—	298	1	no	—
352	C₂²	—	298	1	no	—
353	C₂²	—	596	2	no	—
354	C₂²	—	596	2	no	—
355	C₂²	—	149	2	no	—
356	C₂²	—	149	2	no	—
357	C₂²	—	149	2	no	—
358	C₂²	—	149	1	no	—
359	C₂²	—	149	1	no	—
360	C₂²	#18011990	1	2	yes	—
361	C₂²	C₂³×#10597010	1	1	yes	characteristic
362	C₄	—	2	1	no	—
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	298	1	no	—
368	C₄	—	298	1	no	—
369	C₄	—	298	1	no	—
370	C₄	—	298	1	no	—
371	C₄	—	298	1	no	—
372	C₄	—	596	2	no	—
373	C₄	—	596	2	no	—
374	C₄	—	596	2	no	—
375	C₄	—	596	2	no	—
376	C₂	—	2	2	no	—
377	C₂	—	4	1	no	—
378	C₂	—	298	2	no	—
379	C₂	—	596	1	no	—
380	C₂	—	149	2	no	—
381	C₂	—	149	2	no	—
382	C₂	C₂×#18011990	1	1	yes	characteristic
383	C₂	#23750692	1	1	yes	characteristic
384	C₂	#23750694	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×#10597010
commutator, socle	C₂²×C₁₄₉	C₂³×C₄
Fitting	C₄×D₄×C₁₄₉	C₄
prime radical	C₂×D₄×D₁₄₉	C₂²
cosocle	C₂²×D₁₄₉	C₂⁴
hypercenter	C₄×D₄	#10597010
hypocenter	C₁₄₉	#2318
LCS	G ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ C₄×D₄

Complements

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

N	H ≅ G/N	type
1. #23750575	C₂	semidirect
2. #23750574	C₂	semidirect
4. #23750572	C₂	semidirect
5. #23750570	C₂	semidirect
6. #23750569	C₂	semidirect
7. #23750568	C₂	semidirect
8. #23750567	C₂	semidirect
9. C₄×C₂²⋊#10597010	C₂	semidirect
10. C₂×(C₂×#10597010)⋊C₄	C₂	semidirect
31. C₄×D₅₉₆	C₄	semidirect
32. D₄×Dic₁₄₉	C₄	semidirect
33. #18011873	C₄	semidirect
34. C₄×C₂²⋊D₁₄₉	C₄	semidirect
35. C₄×C₂²⋊D₁₄₉	C₄	semidirect
36. #18011871	C₄	semidirect
37. #18011871	C₄	semidirect
42. C₄×D₄×C₁₄₉	C₄	semidirect
63. C₂²×Dic₁₄₉	C₂×C₄	semidirect
68. C₂×C₄×D₁₄₉	C₂×C₄	semidirect
69. C₂×C₄×D₁₄₉	C₂×C₄	semidirect
75. C₄⋊Dic₁₄₉	C₂×C₄	semidirect
76. #14558715	C₂×C₄	semidirect
77. #14558715	C₂×C₄	semidirect
79. C₂²⋊Dic₁₄₉	C₂×C₄	semidirect
82. #14558713	C₂×C₄	semidirect
83. #14558713	C₂×C₄	semidirect
84. C₄×Dic₁₄₉	C₂×C₄	semidirect
85. C₄×Dic₁₄₉	C₂×C₄	semidirect
86. C₄×Dic₁₄₉	C₂×C₄	semidirect
89. C₂²×C₄×C₁₄₉	C₂×C₄	semidirect
90. C₄⋊C₄×C₁₄₉	C₂×C₄	semidirect
92. C₂²⋊C₄×C₁₄₉	C₂×C₄	semidirect
93. C₄²×C₁₄₉	C₂×C₄	semidirect
192. C₁₄₉	#2318	semidirect
216. C₄×D₄	#10597010	semidirect
264. C₂²×C₄	C₂×#10597010	semidirect
270. C₄⋊C₄	C₂×#10597010	semidirect
281. C₂²⋊C₄	C₂×#10597010	semidirect
286. C₄²	C₂×#10597010	semidirect

Maximal subgroups

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

subgroup	index
#23750575	2
#23750574	2
#23750573	2
#23750572	2
#23750570	2
#23750569	2
#23750568	2
#23750567	2
C₄×C₂²⋊#10597010	2
C₂×(C₂×#10597010)⋊C₄	2
C₄×D₄×D₁₄₉	2
#2318	149