Subgroups — #26234727

Order 12032.

858 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689246	C₂	1	2	yes	maximal
2	C₄×#13094046	C₂	1	1	yes	maximal, characteristic
3	#20251953	C₂	1	2	yes	maximal, complemented
4	#20244141	C₂	1	2	yes	maximal, complemented
5	#20243666	C₂	1	4	yes	maximal, complemented
6	#20243560	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243409	C₂	1	2	yes	maximal, complemented
8	C₄₇×#1770	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#13094046	C₂²	1	1	yes	characteristic
10	C₂×#13094030	C₂²	1	4	yes	—
11	C₄×#10625350	C₂²	1	2	yes	—
12	#15689246	—	2	8	no	—
13	C₄×Dic₁₈₈	C₄	1	1	yes	characteristic, complemented
14	C₄×Dic₁₈₈	C₄	1	1	yes	characteristic, complemented
15	C₄×#10625325	C₄	1	2	yes	complemented
16	C₄×#10625325	C₄	1	2	yes	complemented
17	C₄×D₃₇₆	C₄	1	1	yes	characteristic, complemented
18	C₄×D₃₇₆	C₄	1	1	yes	characteristic, complemented
19	C₂×#13093960	C₂²	1	2	yes	—
20	C₂×#13093960	C₂²	1	2	yes	—
21	#15689161	C₂²	1	1	yes	characteristic
22	#15689149	C₂²	1	4	yes	—
23	#15689148	—	2	4	no	—
24	#15689147	C₂²	1	2	yes	—
25	#15689145	—	2	2	no	—
26	C₄⋊C₈×D₄₇	—	2	2	no	—
27	C₂×#13093952	C₂²	1	4	yes	—
28	#15689120	C₂²	1	2	yes	—
29	#15688883	C₂²	1	4	yes	—
30	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
31	C₂×#97×C₄₇	C₂²	1	2	yes	—
32	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
33	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
34	C₄₇×#336	C₂²	1	2	yes	—
35	C₂×#10625350	C₂³	1	2	yes	—
36	#13094046	D₄	1	4	yes	—
37	#13094046	Q₈	1	4	yes	—
38	C₂×Dic₁₈₈	C₂×C₄	1	1	yes	characteristic
39	C₂×#10625325	C₂×C₄	1	2	yes	—
40	C₂×D₃₇₆	C₂×C₄	1	1	yes	characteristic
41	#13094030	—	2	8	no	—
42	#13094030	—	4	4	no	—
43	C₂×#10625329	C₂³	1	4	yes	—
44	C₂×#10625324	—	2	4	no	—
45	C₂×C₈×D₄₇	—	2	4	no	—
46	C₄×Dic₉₄	C₂×C₄	1	2	yes	—
47	C₄×Dic₉₄	C₂×C₄	1	2	yes	—
48	C₄×D₁₈₈	C₂×C₄	1	2	yes	—
49	C₄×D₁₈₈	C₂×C₄	1	2	yes	—
50	C₄×C₂²⋊D₄₇	—	2	2	no	—
51	C₄×C₂²⋊D₄₇	—	2	2	no	—
52	#13093983	C₂³	1	2	yes	—
53	#13093981	—	2	2	no	—
54	C₄²×D₄₇	—	2	2	no	—
55	#13093960	—	2	4	no	—
56	#13093960	—	4	2	no	—
57	#13093958	C₂×C₄	1	1	yes	characteristic
58	#13093958	C₂×C₄	1	1	yes	characteristic
59	#13093956	C₂×C₄	1	2	yes	—
60	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
61	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
62	Dic₄₇⋊C₈	—	2	4	no	—
63	Dic₄₇⋊C₈	—	2	4	no	—
64	#13093952	—	2	8	no	—
65	#13093949	C₂×C₄	1	2	yes	—
66	#13093949	C₂×C₄	1	2	yes	—
67	#13093946	C₂×C₄	1	2	yes	—
68	#13093946	C₂×C₄	1	2	yes	—
69	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
71	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
73	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
74	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
75	C₄⋊C₈×C₄₇	D₄	1	2	yes	—
76	C₄⋊C₈×C₄₇	D₄	1	2	yes	—
77	#97×C₄₇	—	2	4	no	—
78	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
79	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
80	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
81	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
82	#95×C₄₇	—	2	1	no	—
83	C₂²×C₄×C₄₇	—	2	2	no	—
84	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
85	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
86	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
87	C₂×C₂²⋊D₄₇	—	2	2	no	—
88	#10625350	—	2	2	no	—
89	#10625350	—	2	2	no	—
90	#10625350	C₂×D₄	1	4	yes	—
91	#10625350	C₂×Q₈	1	4	yes	—
92	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
93	C₂×C₄×D₄₇	—	2	2	no	—
94	C₂×C₄×D₄₇	—	2	2	no	—
95	C₂×C₄×D₄₇	—	2	2	no	—
96	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
97	C₂×C₈×C₄₇	—	2	2	no	—
98	C₂×C₈×C₄₇	—	2	1	no	—
99	C₂×C₈×C₄₇	—	2	2	no	—
100	C₂×C₈×C₄₇	—	2	1	no	—
101	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
106	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
107	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	—
108	C₄⋊C₄×C₄₇	—	4	2	no	—
109	C₄²×C₄₇	—	2	2	no	—
110	C₄²×C₄₇	—	2	2	no	—
111	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
112	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
113	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
114	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
115	C₂²⋊Dic₄₇	—	2	2	no	—
116	(C₂×D₄₇)⋊C₄	—	2	2	no	—
117	(C₂×D₄₇)⋊C₄	—	2	2	no	—
118	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
119	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
120	Dic₄₇⋊C₄	—	2	2	no	—
121	Dic₄₇⋊C₄	—	2	2	no	—
122	C₄×Dic₄₇	—	2	2	no	—
123	C₄×Dic₄₇	—	2	2	no	—
124	C₄×Dic₄₇	—	2	2	no	—
125	#10625329	—	2	4	no	—
126	#10625329	—	2	4	no	—
127	C₂×C₄₇⋊C₈	—	2	4	no	—
128	Dic₁₈₈	C₄⋊C₄	1	4	yes	complemented
129	D₃₇₆	C₄⋊C₄	1	4	yes	complemented
130	#10625325	C₄⋊C₄	1	8	yes	complemented
131	#10625324	—	4	8	no	—
132	C₈×D₄₇	—	4	8	no	—
133	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
134	C₂²×D₄₇	—	2	2	no	—
135	C₂×C₄×C₄₇	—	2	2	no	—
136	C₂×C₄×C₄₇	—	4	1	no	—
137	C₂×C₄×C₄₇	—	4	2	no	—
138	C₂×C₄×C₄₇	—	4	2	no	—
139	C₂×C₄×C₄₇	—	4	2	no	—
140	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
141	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
142	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
143	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
144	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
145	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
146	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
147	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
148	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
149	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
150	C₂²⋊D₄₇	—	2	4	no	—
151	C₂²⋊D₄₇	—	2	4	no	—
152	C₂×Dic₄₇	—	2	2	no	—
153	C₂×Dic₄₇	—	2	2	no	—
154	C₂×Dic₄₇	—	2	2	no	—
155	D₁₈₈	—	2	2	no	—
156	D₁₈₈	C₂×C₄⋊C₄	1	4	yes	—
157	C₄×D₄₇	—	2	4	no	—
158	C₄×D₄₇	—	2	4	no	—
159	C₄×D₄₇	—	4	4	no	—
160	C₄×D₄₇	—	8	2	no	—
161	Dic₉₄	—	2	2	no	—
162	Dic₉₄	C₂×C₄⋊C₄	1	4	yes	—
163	C₈×C₄₇	—	2	1	no	—
164	C₈×C₄₇	—	2	1	no	—
165	C₈×C₄₇	—	2	4	no	—
166	C₈×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
167	C₈×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
168	C₄₇⋊C₈	—	4	4	no	—
169	#22686	—	47	1	no	maximal, Sylow
170	C₂²×C₄₇	—	2	1	no	—
171	C₂²×C₄₇	—	2	1	no	—
172	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
173	C₂²×C₄₇	#547	1	1	yes	characteristic
174	C₂²×C₄₇	#554	1	1	yes	characteristic
175	C₂×D₄₇	—	2	4	no	—
176	C₂×D₄₇	—	4	2	no	—
177	C₂×D₄₇	—	4	2	no	—
178	C₄×C₄₇	—	2	1	no	—
179	C₄×C₄₇	—	2	1	no	—
180	C₄×C₄₇	—	2	1	no	—
181	C₄×C₄₇	—	8	2	no	—
182	C₄×C₄₇	#444	1	2	yes	complemented
183	C₄×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
184	C₄×C₄₇	#520	1	1	yes	characteristic
185	C₄×C₄₇	D₄²	1	1	yes	characteristic
186	C₄×C₄₇	D₄×Q₈	1	1	yes	characteristic
187	Dic₄₇	—	2	4	no	—
188	Dic₄₇	—	4	2	no	—
189	Dic₄₇	—	4	2	no	—
190	C₂×#444	—	47	2	no	—
191	C₄×#135	—	47	1	no	—
192	#2906	—	47	2	no	—
193	#1946	—	47	2	no	—
194	#1866	—	47	4	no	—
195	#1848	—	47	1	no	—
196	#1806	—	47	2	no	—
197	#1770	D₄₇	1	1	yes	characteristic, complemented
198	C₂×C₄₇	—	2	1	no	—
199	C₂×C₄₇	—	2	1	no	—
200	C₂×C₄₇	D₄×C₄⋊C₄	1	1	yes	characteristic
201	C₂×C₄₇	C₂×#444	1	1	yes	characteristic
202	C₂×C₄₇	#2957	1	1	yes	characteristic
203	D₄₇	—	4	4	no	—
204	C₂×#135	—	47	1	no	—
205	C₂×#131	—	47	4	no	—
206	C₄×#41	—	47	2	no	—
207	#444	—	94	8	no	—
208	C₄×Q₁₆	—	47	1	no	—
209	C₄×Q₁₆	—	47	1	no	—
210	C₄×SD₁₆	—	47	2	no	—
211	C₄×SD₁₆	—	47	2	no	—
212	C₄×D₈	—	47	1	no	—
213	C₄×D₈	—	47	1	no	—
214	C₂×#108	—	47	2	no	—
215	C₂×#108	—	47	2	no	—
216	#427	—	47	1	no	—
217	#424	—	47	4	no	—
218	#424	—	94	4	no	—
219	#423	—	47	2	no	—
220	#423	—	94	2	no	—
221	C₂×C₄⋊C₈	—	94	2	no	—
222	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
223	C₂×#104	—	47	4	no	—
224	#416	—	47	2	no	—
225	C₂×#97	C₂×D₄₇	1	2	yes	—
226	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
227	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
228	#339	—	47	4	no	—
229	#336	C₂×D₄₇	1	2	yes	—
230	C₄₇	#22686	1	1	yes	characteristic, complemented, Sylow
231	C₂×#41	—	47	2	no	—
232	#135	—	47	4	no	—
233	#135	—	47	4	no	—
234	C₂×Q₁₆	—	47	1	no	—
235	C₂×SD₁₆	—	47	2	no	—
236	C₂×D₈	—	47	1	no	—
237	#131	—	94	8	no	—
238	#131	—	188	4	no	—
239	C₂×M₁₆	—	47	4	no	—
240	C₂×M₁₆	—	94	4	no	—
241	C₂²×C₈	—	94	4	no	—
242	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
243	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
244	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
245	C₄×Q₈	—	47	2	no	—
246	C₄×Q₈	—	47	2	no	—
247	C₄×D₄	—	47	2	no	—
248	C₄×D₄	—	47	2	no	—
249	C₄×D₄	—	94	2	no	—
250	C₄×D₄	—	94	2	no	—
251	#117	—	47	2	no	—
252	#117	—	94	2	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄²	—	94	2	no	—
255	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
256	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
257	#108	—	94	4	no	—
258	#108	—	188	2	no	—
259	#107	—	47	1	no	—
260	#107	—	47	1	no	—
261	#106	—	47	2	no	—
262	C₄⋊C₈	—	94	4	no	—
263	C₄⋊C₈	—	94	4	no	—
264	C₄⋊C₈	—	94	2	no	—
265	C₄⋊C₈	—	94	2	no	—
266	C₄⋊C₈	D₁₈₈	1	2	yes	—
267	C₄⋊C₈	D₁₈₈	1	2	yes	—
268	#104	—	94	8	no	—
269	#103	—	47	2	no	—
270	#103	—	47	2	no	—
271	#102	—	47	2	no	—
272	#102	—	47	2	no	—
273	#97	—	2	4	no	—
274	C₄×C₈	C₄×D₄₇	1	1	yes	characteristic
275	C₄×C₈	C₄×D₄₇	1	1	yes	characteristic
276	C₄×C₈	C₄×D₄₇	1	1	yes	characteristic
277	C₄×C₈	C₄×D₄₇	1	1	yes	characteristic
278	#95	—	2	1	no	—
279	#41	—	47	4	no	—
280	#41	—	47	4	no	—
281	#41	—	94	2	no	—
282	#41	—	94	2	no	—
283	C₂×Q₈	—	47	2	no	—
284	C₂×D₄	—	47	2	no	—
285	C₂×D₄	—	94	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	94	2	no	—
288	C₂²×C₄	—	94	2	no	—
289	C₂²×C₄	—	94	2	no	—
290	C₂²×C₄	#10625350	1	1	yes	characteristic
291	C₂²×C₄	#10625350	1	1	yes	characteristic
292	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
293	Q₁₆	—	47	4	no	—
294	SD₁₆	—	47	8	no	—
295	D₈	—	47	4	no	—
296	M₁₆	—	94	4	no	—
297	M₁₆	—	94	4	no	—
298	M₁₆	—	188	8	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	94	4	no	—
304	C₂×C₈	—	188	8	no	—
305	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
306	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
307	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
308	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
309	C₂×C₈	C₂×D₁₈₈	1	4	yes	—
310	C₂×C₈	D₄×D₄₇	1	2	yes	—
311	C₂×C₈	Q₈×D₄₇	1	2	yes	—
312	C₄⋊C₄	—	4	2	no	—
313	C₄⋊C₄	—	47	2	no	—
314	C₄⋊C₄	—	47	2	no	—
315	C₄⋊C₄	—	94	2	no	—
316	C₄⋊C₄	—	94	2	no	—
317	C₂²⋊C₄	—	94	2	no	—
318	C₂²⋊C₄	—	94	2	no	—
319	C₂²⋊C₄	—	94	2	no	—
320	C₄²	—	2	2	no	—
321	C₄²	—	2	2	no	—
322	C₄²	—	94	2	no	—
323	C₄²	—	94	2	no	—
324	C₄²	—	94	2	no	—
325	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
326	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
327	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
328	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
329	C₂³	—	94	2	no	—
330	C₂³	C₂×#10625350	1	1	yes	characteristic
331	Q₈	—	47	4	no	—
332	Q₈	—	94	2	no	—
333	D₄	—	47	4	no	—
334	D₄	—	94	4	no	—
335	D₄	—	94	4	no	—
336	D₄	—	94	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	94	2	no	—
343	C₂×C₄	—	94	4	no	—
344	C₂×C₄	—	94	4	no	—
345	C₂×C₄	—	94	2	no	—
346	C₂×C₄	—	94	2	no	—
347	C₂×C₄	—	376	2	no	—
348	C₂×C₄	—	188	4	no	—
349	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
350	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
351	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
352	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
353	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
354	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
355	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
356	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
357	C₂×C₄	#13094070	1	1	yes	characteristic
358	C₂×C₄	#13094071	1	1	yes	characteristic
359	C₈	—	2	4	no	—
360	C₈	—	2	1	no	—
361	C₈	—	2	1	no	—
362	C₈	—	188	4	no	—
363	C₈	C₄⋊C₄×D₄₇	1	2	yes	—
364	C₈	C₄⋊C₄×D₄₇	1	2	yes	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	94	4	no	—
368	C₂²	—	188	2	no	—
369	C₂²	—	188	2	no	—
370	C₂²	C₂×C₄×D₁₈₈	1	1	yes	characteristic
371	C₂²	#15689778	1	1	yes	characteristic
372	C₂²	#15689833	1	1	yes	characteristic
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	8	2	no	—
377	C₄	—	94	4	no	—
378	C₄	—	188	2	no	—
379	C₄	—	188	2	no	—
380	C₄	#15689246	1	2	yes	complemented
381	C₄	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
382	C₄	#15689603	1	1	yes	characteristic
383	C₄	D₄×D₁₈₈	1	1	yes	characteristic
384	C₄	Q₈×D₁₈₈	1	1	yes	characteristic
385	C₂	—	2	1	no	—
386	C₂	—	2	1	no	—
387	C₂	—	188	4	no	—
388	C₂	C₄⋊C₄×D₁₈₈	1	1	yes	characteristic
389	C₂	C₂×#15689246	1	1	yes	characteristic
390	C₂	#20252306	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1770	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂×#13094046	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1770	D₄₇
hypocenter	C₄₇	#22686
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄⋊C₈ ◁ #1770

Complements

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

N	H ≅ G/N	type
3. #20251953	C₂	semidirect
4. #20244141	C₂	semidirect
5. #20243666	C₂	semidirect
6. #20243560	C₂	semidirect
7. #20243409	C₂	semidirect
8. C₄₇×#1770	C₂	semidirect
13. C₄×Dic₁₈₈	C₄	semidirect
14. C₄×Dic₁₈₈	C₄	semidirect
15. C₄×#10625325	C₄	semidirect
16. C₄×#10625325	C₄	semidirect
17. C₄×D₃₇₆	C₄	semidirect
18. C₄×D₃₇₆	C₄	semidirect
128. Dic₁₈₈	C₄⋊C₄	semidirect
129. D₃₇₆	C₄⋊C₄	semidirect
130. #10625325	C₄⋊C₄	semidirect
182. C₄×C₄₇	#444	semidirect
197. #1770	D₄₇	semidirect
230. C₄₇	#22686	semidirect
380. C₄	#15689246	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689246	2
C₄×#13094046	2
#20251953	2
#20244141	2
#20243666	2
#20243560	2
#20243409	2
C₄₇×#1770	2
#22686	47