Subgroups — #34061208

Order 19072.

588 conjugacy classes of subgroups.

The subgroup lattice has 388 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	#23750570	C₂	1	1	yes	maximal, characteristic, complemented
5	#23750568	C₂	1	1	yes	maximal, characteristic, complemented
6	#23750567	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²⋊C₄×#10597010	C₂	1	2	yes	maximal, complemented
8	C₄×C₂²⋊#10597010	C₂	1	1	yes	maximal, characteristic, complemented
9	#23750561	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×C₂²⋊#10597010	C₂²	1	2	yes	—
15	C₂×C₂²⋊#10597010	C₂²	1	2	yes	—
16	C₂×C₂²⋊#10597010	C₂²	1	2	yes	—
17	C₂×C₄×#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	2	yes	—
24	(C₂×#10597010)⋊C₄	C₂²	1	1	yes	characteristic
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	—	2	4	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	C₂²⋊#10597010	—	2	4	no	—
52	C₂²⋊#10597010	—	2	4	no	—
53	C₂²⋊#10597010	—	4	2	no	—
54	C₄×#10597010	—	2	4	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	2	no	—
62	D₄×D₁₄₉	—	2	2	no	—
63	C₂²×Dic₁₄₉	C₂×C₄	1	1	yes	characteristic
64	C₂²×Dic₁₄₉	C₂×C₄	1	1	yes	characteristic, complemented
65	C₂×C₄×D₁₄₉	—	4	2	no	—
66	C₂×C₄×D₁₄₉	—	4	2	no	—
67	C₂×C₄×D₁₄₉	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄×D₁₄₉	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄×D₁₄₉	C₂×C₄	1	1	yes	characteristic, complemented
70	C₂×C₄×D₁₄₉	C₂×C₄	1	1	yes	characteristic, complemented
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	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
76	C₄⋊Dic₁₄₉	C₂×C₄	1	1	yes	characteristic, complemented
77	#14558715	C₂×C₄	1	1	yes	characteristic, complemented
78	#14558715	C₂×C₄	1	1	yes	characteristic, complemented
79	C₂²⋊Dic₁₄₉	C₂×C₄	1	1	yes	characteristic
80	C₂²⋊Dic₁₄₉	C₂×C₄	1	1	yes	characteristic, complemented
81	#14558713	C₂×C₄	1	1	yes	characteristic
82	#14558713	C₂×C₄	1	1	yes	characteristic
83	#14558713	C₂×C₄	1	1	yes	characteristic, complemented
84	#14558713	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	C₄×Dic₁₄₉	C₂×C₄	1	1	yes	characteristic, complemented
88	C₂×D₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic, complemented
91	C₄⋊C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic, complemented
92	C₂²⋊C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
93	C₂²⋊C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic, complemented
94	C₄²×C₁₄₉	C₂×C₄	1	1	yes	characteristic, complemented
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	C₂×#10597010	#41	1	4	yes	—
108	C₂²×D₁₄₉	—	2	2	no	—
109	C₂²×D₁₄₉	—	2	2	no	—
110	C₂²×D₁₄₉	—	2	1	no	—
111	C₂²×D₁₄₉	—	2	1	no	—
112	C₂²×D₁₄₉	—	2	2	no	—
113	C₂²×D₁₄₉	—	2	2	no	—
114	C₂²×D₁₄₉	C₂²×C₄	1	1	yes	characteristic
115	C₂²×D₁₄₉	C₂²×C₄	1	1	yes	characteristic
116	C₂²×D₁₄₉	#41	1	2	yes	—
117	C₂²×D₁₄₉	#41	1	2	yes	—
118	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
119	D₅₉₆	—	2	2	no	—
120	C₂²⋊D₁₄₉	—	2	2	no	—
121	C₂²⋊D₁₄₉	—	2	2	no	—
122	C₂×Dic₁₄₉	—	4	1	no	—
123	C₂×Dic₁₄₉	—	4	1	no	—
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	C₂×Dic₁₄₉	C₂²×C₄	1	1	yes	characteristic
129	C₄×D₁₄₉	—	2	1	no	—
130	C₄×D₁₄₉	—	2	1	no	—
131	C₄×D₁₄₉	—	2	2	no	—
132	C₄×D₁₄₉	—	2	2	no	—
133	C₄×D₁₄₉	—	2	2	no	—
134	C₄×D₁₄₉	—	2	2	no	—
135	C₄×D₁₄₉	—	4	1	no	—
136	C₄×D₁₄₉	—	4	1	no	—
137	C₄×D₁₄₉	—	4	1	no	—
138	C₄×D₁₄₉	—	4	1	no	—
139	C₂³×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
140	C₂³×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
141	D₄×C₁₄₉	—	2	2	no	—
142	C₂×C₄×C₁₄₉	—	4	1	no	—
143	C₂×C₄×C₁₄₉	—	4	1	no	—
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	C₂×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
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	—	2	1	no	—
154	C₂²×C₁₄₉	#117	1	2	yes	—
155	C₂²×C₁₄₉	C₂³×C₄	1	1	yes	characteristic
156	C₂×D₁₄₉	—	2	1	no	—
157	C₂×D₁₄₉	—	2	1	no	—
158	C₂×D₁₄₉	—	2	4	no	—
159	C₂×D₁₄₉	—	2	4	no	—
160	C₂×D₁₄₉	—	2	1	no	—
161	C₂×D₁₄₉	—	2	1	no	—
162	C₂×D₁₄₉	—	2	1	no	—
163	C₂×D₁₄₉	—	4	2	no	—
164	C₂×D₁₄₉	—	4	2	no	—
165	C₂×D₁₄₉	#117	1	2	yes	—
166	C₂×D₁₄₉	C₂×#41	1	1	yes	characteristic
167	C₂×D₁₄₉	C₂×#41	1	2	yes	—
168	C₂×D₁₄₉	C₂×#41	1	1	yes	characteristic
169	C₂×D₁₄₉	H(5,𝔽₂)	1	2	yes	—
170	#10597010	—	2	4	no	—
171	#10597010	—	4	2	no	—
172	#10597010	—	4	2	no	—
173	#10597010	—	4	2	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	C₄×C₁₄₉	—	2	1	no	—
179	Dic₁₄₉	—	2	1	no	—
180	Dic₁₄₉	—	2	1	no	—
181	Dic₁₄₉	—	2	1	no	—
182	Dic₁₄₉	—	2	1	no	—
183	Dic₁₄₉	—	2	1	no	—
184	C₂×C₁₄₉	—	2	2	no	—
185	C₂×C₁₄₉	—	4	1	no	—
186	C₂×C₁₄₉	C₂×#117	1	1	yes	characteristic
187	C₂×C₁₄₉	C₄×#41	1	1	yes	characteristic
188	C₂×C₁₄₉	#518	1	1	yes	characteristic
189	D₁₄₉	—	2	2	no	—
190	D₁₄₉	—	4	1	no	—
191	D₁₄₉	#551	1	2	yes	—
192	D₁₄₉	#553	1	2	yes	—
193	C₁₄₉	#2353	1	1	yes	characteristic, complemented, Sylow
194	#2353	—	149	1	no	maximal, Sylow
195	C₂×C₄×D₄	—	149	1	no	—
196	#388	—	149	2	no	—
197	#387	—	149	2	no	—
198	#386	—	149	2	no	—
199	#383	—	149	1	no	—
200	#381	—	149	1	no	—
201	#380	—	149	1	no	—
202	C₄×C₂²⋊C₄	—	149	1	no	—
203	C₄×C₂²⋊C₄	—	149	2	no	—
204	#376	—	149	1	no	—
205	C₂×#95	—	149	1	no	—
206	C₂²×D₄	—	149	1	no	—
207	C₂³×C₄	—	149	2	no	—
208	C₂³×C₄	—	149	1	no	—
209	C₂³×C₄	—	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	—	149	1	no	—
217	C₄×D₄	#10597010	1	1	yes	characteristic, complemented
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	2	no	—
227	C₂×C₄²	—	149	1	no	—
228	#95	—	149	1	no	—
229	#95	—	149	1	no	—
230	#95	—	149	2	no	—
231	#95	—	149	1	no	—
232	#95	—	149	2	no	—
233	#95	—	149	1	no	—
234	#95	—	149	2	no	—
235	#95	—	149	2	no	—
236	#95	—	149	2	no	—
237	C₂⁴	—	149	1	no	—
238	C₂⁴	—	149	1	no	—
239	C₂×D₄	—	298	2	no	—
240	C₂×D₄	—	298	2	no	—
241	C₂×D₄	—	149	1	no	—
242	C₂×D₄	—	149	1	no	—
243	C₂×D₄	—	149	1	no	—
244	C₂×D₄	C₂×#10597010	1	1	yes	characteristic
245	C₂²×C₄	—	298	4	no	—
246	C₂²×C₄	—	298	4	no	—
247	C₂²×C₄	—	596	2	no	—
248	C₂²×C₄	—	596	2	no	—
249	C₂²×C₄	—	596	2	no	—
250	C₂²×C₄	—	149	2	no	—
251	C₂²×C₄	—	149	2	no	—
252	C₂²×C₄	—	149	2	no	—
253	C₂²×C₄	—	149	2	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	—	149	1	no	—
264	C₂²×C₄	—	149	1	no	—
265	C₂²×C₄	C₂×#10597010	1	1	yes	characteristic
266	C₂²×C₄	C₂×#10597010	1	1	yes	characteristic, complemented
267	C₄⋊C₄	—	596	2	no	—
268	C₄⋊C₄	—	149	1	no	—
269	C₄⋊C₄	—	149	1	no	—
270	C₄⋊C₄	—	149	1	no	—
271	C₄⋊C₄	C₂×#10597010	1	1	yes	characteristic, complemented
272	C₂²⋊C₄	—	298	4	no	—
273	C₂²⋊C₄	—	298	4	no	—
274	C₂²⋊C₄	—	596	2	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	—	149	1	no	—
281	C₂²⋊C₄	C₂×#10597010	1	1	yes	characteristic
282	C₂²⋊C₄	C₂×#10597010	1	1	yes	characteristic, complemented
283	C₄²	—	298	4	no	—
284	C₄²	—	596	2	no	—
285	C₄²	—	149	1	no	—
286	C₄²	—	149	1	no	—
287	C₄²	—	149	1	no	—
288	C₄²	C₂×#10597010	1	1	yes	characteristic, complemented
289	C₂³	—	298	2	no	—
290	C₂³	—	298	2	no	—
291	C₂³	—	298	2	no	—
292	C₂³	—	298	2	no	—
293	C₂³	—	298	1	no	—
294	C₂³	—	298	1	no	—
295	C₂³	—	149	1	no	—
296	C₂³	—	149	2	no	—
297	C₂³	—	149	2	no	—
298	C₂³	—	149	1	no	—
299	C₂³	—	149	1	no	—
300	C₂³	C₂²×#10597010	1	1	yes	characteristic
301	C₂³	C₂²×#10597010	1	1	yes	characteristic
302	D₄	—	2	2	no	—
303	D₄	—	298	2	no	—
304	D₄	—	298	2	no	—
305	D₄	—	298	2	no	—
306	C₂×C₄	—	4	1	no	—
307	C₂×C₄	—	4	1	no	—
308	C₂×C₄	—	298	2	no	—
309	C₂×C₄	—	298	2	no	—
310	C₂×C₄	—	298	2	no	—
311	C₂×C₄	—	298	2	no	—
312	C₂×C₄	—	298	1	no	—
313	C₂×C₄	—	298	1	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	—	298	2	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	1	no	—
331	C₂×C₄	—	596	8	no	—
332	C₂×C₄	—	149	4	no	—
333	C₂×C₄	—	149	1	no	—
334	C₂×C₄	—	149	1	no	—
335	C₂×C₄	—	149	1	no	—
336	C₂×C₄	—	149	1	no	—
337	C₂×C₄	—	149	1	no	—
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	C₂×C₄	C₂²×#10597010	1	1	yes	characteristic
342	C₂×C₄	C₂²×#10597010	1	1	yes	characteristic
343	C₂²	—	2	1	no	—
344	C₂²	—	2	1	no	—
345	C₂²	—	2	1	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	2	1	no	—
348	C₂²	—	298	4	no	—
349	C₂²	—	298	4	no	—
350	C₂²	—	298	1	no	—
351	C₂²	—	298	1	no	—
352	C₂²	—	298	1	no	—
353	C₂²	—	298	1	no	—
354	C₂²	—	298	1	no	—
355	C₂²	—	596	2	no	—
356	C₂²	—	596	2	no	—
357	C₂²	—	149	2	no	—
358	C₂²	—	149	1	no	—
359	C₂²	—	149	1	no	—
360	C₂²	—	149	2	no	—
361	C₂²	—	149	2	no	—
362	C₂²	#18011990	1	2	yes	—
363	C₂²	C₂³×#10597010	1	1	yes	characteristic
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	2	1	no	—
368	C₄	—	2	1	no	—
369	C₄	—	298	4	no	—
370	C₄	—	298	1	no	—
371	C₄	—	298	1	no	—
372	C₄	—	298	1	no	—
373	C₄	—	298	1	no	—
374	C₄	—	298	1	no	—
375	C₄	—	596	2	no	—
376	C₄	—	596	2	no	—
377	C₄	—	596	2	no	—
378	C₂	—	2	2	no	—
379	C₂	—	4	1	no	—
380	C₂	—	298	2	no	—
381	C₂	—	596	1	no	—
382	C₂	—	149	2	no	—
383	C₂	—	149	2	no	—
384	C₂	C₂×#18011990	1	1	yes	characteristic
385	C₂	#41×#10597010	1	1	yes	characteristic
386	C₂	#23750692	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	#2353
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. #23750570	C₂	semidirect
5. #23750568	C₂	semidirect
6. #23750567	C₂	semidirect
7. C₂²⋊C₄×#10597010	C₂	semidirect
8. C₄×C₂²⋊#10597010	C₂	semidirect
9. #23750561	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
64. C₂²×Dic₁₄₉	C₂×C₄	semidirect
69. C₂×C₄×D₁₄₉	C₂×C₄	semidirect
70. C₂×C₄×D₁₄₉	C₂×C₄	semidirect
76. C₄⋊Dic₁₄₉	C₂×C₄	semidirect
77. #14558715	C₂×C₄	semidirect
78. #14558715	C₂×C₄	semidirect
80. C₂²⋊Dic₁₄₉	C₂×C₄	semidirect
83. #14558713	C₂×C₄	semidirect
84. #14558713	C₂×C₄	semidirect
85. C₄×Dic₁₄₉	C₂×C₄	semidirect
86. C₄×Dic₁₄₉	C₂×C₄	semidirect
87. C₄×Dic₁₄₉	C₂×C₄	semidirect
90. C₂²×C₄×C₁₄₉	C₂×C₄	semidirect
91. C₄⋊C₄×C₁₄₉	C₂×C₄	semidirect
93. C₂²⋊C₄×C₁₄₉	C₂×C₄	semidirect
94. C₄²×C₁₄₉	C₂×C₄	semidirect
193. C₁₄₉	#2353	semidirect
217. C₄×D₄	#10597010	semidirect
266. C₂²×C₄	C₂×#10597010	semidirect
271. C₄⋊C₄	C₂×#10597010	semidirect
282. C₂²⋊C₄	C₂×#10597010	semidirect
288. 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
#23750570	2
#23750568	2
#23750567	2
C₂²⋊C₄×#10597010	2
C₄×C₂²⋊#10597010	2
#23750561	2
C₂×(C₂×#10597010)⋊C₄	2
C₄×D₄×D₁₄₉	2
#2353	149