Subgroups — #36572877

Order 22784.

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×#19151721	C₂	1	2	yes	maximal
2	C₄×#15668034	C₂	1	1	yes	maximal, characteristic
3	#26028817	C₂	1	2	yes	maximal, complemented
4	#26021005	C₂	1	2	yes	maximal, complemented
5	#26020530	C₂	1	4	yes	maximal, complemented
6	#26020424	C₂	1	1	yes	maximal, characteristic, complemented
7	#26020273	C₂	1	2	yes	maximal, complemented
8	C₈₉×#1770	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#15668034	C₂²	1	1	yes	characteristic
10	C₂×#15668018	C₂²	1	4	yes	—
11	C₄×#13083574	C₂²	1	2	yes	—
12	#19151721	—	2	8	no	—
13	C₄×Dic₃₅₆	C₄	1	1	yes	characteristic, complemented
14	C₄×Dic₃₅₆	C₄	1	1	yes	characteristic, complemented
15	C₄×#13083563	C₄	1	2	yes	complemented
16	C₄×#13083563	C₄	1	2	yes	complemented
17	C₄×D₇₁₂	C₄	1	1	yes	characteristic, complemented
18	C₄×D₇₁₂	C₄	1	1	yes	characteristic, complemented
19	C₂×#15667948	C₂²	1	2	yes	—
20	C₂×#15667948	C₂²	1	2	yes	—
21	#19151636	C₂²	1	1	yes	characteristic
22	#19151624	C₂²	1	4	yes	—
23	#19151623	—	2	4	no	—
24	#19151622	C₂²	1	2	yes	—
25	#19151620	—	2	2	no	—
26	C₄⋊C₈×D₈₉	—	2	2	no	—
27	C₂×#15667940	C₂²	1	4	yes	—
28	#19151595	C₂²	1	2	yes	—
29	#19151358	C₂²	1	4	yes	—
30	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×#97×C₈₉	C₂²	1	2	yes	—
32	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
33	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
34	#336×C₈₉	C₂²	1	2	yes	—
35	C₂×#13083574	C₂³	1	2	yes	—
36	#15668034	D₄	1	4	yes	—
37	#15668034	Q₈	1	4	yes	—
38	C₂×Dic₃₅₆	C₂×C₄	1	1	yes	characteristic
39	C₂×#13083563	C₂×C₄	1	2	yes	—
40	C₂×D₇₁₂	C₂×C₄	1	1	yes	characteristic
41	#15668018	—	2	8	no	—
42	#15668018	—	4	4	no	—
43	C₂×#13083558	C₂³	1	4	yes	—
44	C₂×#13083557	—	2	4	no	—
45	C₂×C₈×D₈₉	—	2	4	no	—
46	C₄×Dic₁₇₈	C₂×C₄	1	2	yes	—
47	C₄×Dic₁₇₈	C₂×C₄	1	2	yes	—
48	C₄×D₃₅₆	C₂×C₄	1	2	yes	—
49	C₄×D₃₅₆	C₂×C₄	1	2	yes	—
50	C₄×C₂²⋊D₈₉	—	2	2	no	—
51	C₄×C₂²⋊D₈₉	—	2	2	no	—
52	#15667971	C₂³	1	2	yes	—
53	#15667969	—	2	2	no	—
54	C₄²×D₈₉	—	2	2	no	—
55	#15667948	—	2	4	no	—
56	#15667948	—	4	2	no	—
57	#15667946	C₂×C₄	1	1	yes	characteristic
58	#15667946	C₂×C₄	1	1	yes	characteristic
59	#15667944	C₂×C₄	1	2	yes	—
60	C₄⋊#10623494	—	2	2	no	—
61	C₄⋊#10623494	—	2	2	no	—
62	#15667941	—	2	4	no	—
63	#15667941	—	2	4	no	—
64	#15667940	—	2	8	no	—
65	#15667937	C₂×C₄	1	2	yes	—
66	#15667937	C₂×C₄	1	2	yes	—
67	#15667934	C₂×C₄	1	2	yes	—
68	#15667934	C₂×C₄	1	2	yes	—
69	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
71	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
73	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
74	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
75	C₄⋊C₈×C₈₉	D₄	1	2	yes	—
76	C₄⋊C₈×C₈₉	D₄	1	2	yes	—
77	#97×C₈₉	—	2	4	no	—
78	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
79	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
80	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
81	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
82	#95×C₈₉	—	2	1	no	—
83	#13083574	—	2	2	no	—
84	#13083574	—	2	2	no	—
85	#13083574	C₂×D₄	1	4	yes	—
86	#13083574	C₂×Q₈	1	4	yes	—
87	C₂×Dic₁₇₈	C₂²×C₄	1	2	yes	—
88	C₂×D₃₅₆	C₂²×C₄	1	2	yes	—
89	C₂×C₂²⋊D₈₉	—	2	2	no	—
90	C₂×C₄×D₈₉	—	2	2	no	—
91	C₂×C₄×D₈₉	—	2	2	no	—
92	C₂×C₄×D₈₉	—	2	2	no	—
93	Dic₃₅₆	C₄⋊C₄	1	4	yes	complemented
94	#13083563	C₄⋊C₄	1	8	yes	complemented
95	D₇₁₂	C₄⋊C₄	1	4	yes	complemented
96	#13083558	—	2	4	no	—
97	#13083558	—	2	4	no	—
98	#13083557	—	4	8	no	—
99	C₂×#10623494	—	2	4	no	—
100	C₈×D₈₉	—	4	8	no	—
101	C₄⋊Dic₈₉	C₂²×C₄	1	2	yes	—
102	C₄⋊Dic₈₉	C₂²×C₄	1	2	yes	—
103	#13083553	—	2	2	no	—
104	#13083553	—	2	2	no	—
105	C₂²⋊Dic₈₉	—	2	2	no	—
106	#13083551	—	2	2	no	—
107	#13083551	—	2	2	no	—
108	C₄×Dic₈₉	—	2	2	no	—
109	C₄×Dic₈₉	—	2	2	no	—
110	C₄×Dic₈₉	—	2	2	no	—
111	C₂²×C₄×C₈₉	—	2	2	no	—
112	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
113	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
114	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
115	C₂×C₈×C₈₉	—	2	2	no	—
116	C₂×C₈×C₈₉	—	2	2	no	—
117	C₂×C₈×C₈₉	—	2	1	no	—
118	C₂×C₈×C₈₉	—	2	1	no	—
119	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₈×C₈₉	C₂×D₄	1	4	yes	—
124	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
125	C₂×C₈×C₈₉	C₂×Q₈	1	2	yes	—
126	C₄⋊C₄×C₈₉	—	4	2	no	—
127	C₄²×C₈₉	—	2	2	no	—
128	C₄²×C₈₉	—	2	2	no	—
129	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
130	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
131	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
133	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
134	C₂²×D₈₉	—	2	2	no	—
135	C₂×C₄×C₈₉	—	2	2	no	—
136	C₂×C₄×C₈₉	—	4	1	no	—
137	C₂×C₄×C₈₉	—	4	2	no	—
138	C₂×C₄×C₈₉	—	4	2	no	—
139	C₂×C₄×C₈₉	—	4	2	no	—
140	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
141	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
142	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
143	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
144	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
145	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
146	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
147	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
148	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
149	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
150	C₂²⋊D₈₉	—	2	4	no	—
151	C₂²⋊D₈₉	—	2	4	no	—
152	C₂×Dic₈₉	—	2	2	no	—
153	C₂×Dic₈₉	—	2	2	no	—
154	C₂×Dic₈₉	—	2	2	no	—
155	D₃₅₆	—	2	2	no	—
156	D₃₅₆	C₂×C₄⋊C₄	1	4	yes	—
157	C₄×D₈₉	—	2	4	no	—
158	C₄×D₈₉	—	2	4	no	—
159	C₄×D₈₉	—	4	4	no	—
160	C₄×D₈₉	—	8	2	no	—
161	Dic₁₇₈	—	2	2	no	—
162	Dic₁₇₈	C₂×C₄⋊C₄	1	4	yes	—
163	C₈×C₈₉	—	2	1	no	—
164	C₈×C₈₉	—	2	1	no	—
165	C₈×C₈₉	—	2	4	no	—
166	C₈×C₈₉	C₂×C₄⋊C₄	1	2	yes	—
167	C₈×C₈₉	C₂×C₄⋊C₄	1	2	yes	—
168	#10623494	—	4	4	no	—
169	C₂²×C₈₉	—	2	1	no	—
170	C₂²×C₈₉	—	2	1	no	—
171	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
172	C₂²×C₈₉	#547	1	1	yes	characteristic
173	C₂²×C₈₉	#554	1	1	yes	characteristic
174	C₂×D₈₉	—	2	4	no	—
175	C₂×D₈₉	—	4	2	no	—
176	C₂×D₈₉	—	4	2	no	—
177	C₄×C₈₉	—	2	1	no	—
178	C₄×C₈₉	—	2	1	no	—
179	C₄×C₈₉	—	2	1	no	—
180	C₄×C₈₉	—	8	2	no	—
181	C₄×C₈₉	#444	1	2	yes	complemented
182	C₄×C₈₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
183	C₄×C₈₉	#520	1	1	yes	characteristic
184	C₄×C₈₉	D₄²	1	1	yes	characteristic
185	C₄×C₈₉	D₄×Q₈	1	1	yes	characteristic
186	Dic₈₉	—	2	4	no	—
187	Dic₈₉	—	4	2	no	—
188	Dic₈₉	—	4	2	no	—
189	#22686	—	89	1	no	maximal, Sylow
190	C₂×C₈₉	—	2	1	no	—
191	C₂×C₈₉	—	2	1	no	—
192	C₂×C₈₉	D₄×C₄⋊C₄	1	1	yes	characteristic
193	C₂×C₈₉	C₂×#444	1	1	yes	characteristic
194	C₂×C₈₉	#2957	1	1	yes	characteristic
195	D₈₉	—	4	4	no	—
196	C₂×#444	—	89	2	no	—
197	C₄×#135	—	89	1	no	—
198	#2906	—	89	2	no	—
199	#1946	—	89	2	no	—
200	#1866	—	89	4	no	—
201	#1848	—	89	1	no	—
202	#1806	—	89	2	no	—
203	#1770	D₈₉	1	1	yes	characteristic, complemented
204	C₈₉	#22686	1	1	yes	characteristic, complemented, Sylow
205	C₂×#135	—	89	1	no	—
206	C₂×#131	—	89	4	no	—
207	C₄×#41	—	89	2	no	—
208	#444	—	178	8	no	—
209	C₄×Q₁₆	—	89	1	no	—
210	C₄×Q₁₆	—	89	1	no	—
211	C₄×SD₁₆	—	89	2	no	—
212	C₄×SD₁₆	—	89	2	no	—
213	C₄×D₈	—	89	1	no	—
214	C₄×D₈	—	89	1	no	—
215	C₂×#108	—	89	2	no	—
216	C₂×#108	—	89	2	no	—
217	#427	—	89	1	no	—
218	#424	—	89	4	no	—
219	#424	—	178	4	no	—
220	#423	—	89	2	no	—
221	#423	—	178	2	no	—
222	C₂×C₄⋊C₈	—	178	2	no	—
223	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
224	C₂×#104	—	89	4	no	—
225	#416	—	89	2	no	—
226	C₂×#97	C₂×D₈₉	1	2	yes	—
227	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
228	C₄×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
229	#339	—	89	4	no	—
230	#336	C₂×D₈₉	1	2	yes	—
231	C₂×#41	—	89	2	no	—
232	#135	—	89	4	no	—
233	#135	—	89	4	no	—
234	C₂×Q₁₆	—	89	1	no	—
235	C₂×SD₁₆	—	89	2	no	—
236	C₂×D₈	—	89	1	no	—
237	#131	—	356	4	no	—
238	#131	—	178	8	no	—
239	C₂×M₁₆	—	89	4	no	—
240	C₂×M₁₆	—	178	4	no	—
241	C₂²×C₈	—	178	4	no	—
242	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
243	C₂²×C₈	C₂²×D₈₉	1	2	yes	—
244	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
245	C₄×Q₈	—	89	2	no	—
246	C₄×Q₈	—	89	2	no	—
247	C₄×D₄	—	89	2	no	—
248	C₄×D₄	—	89	2	no	—
249	C₄×D₄	—	178	2	no	—
250	C₄×D₄	—	178	2	no	—
251	#117	—	89	2	no	—
252	#117	—	178	2	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄²	—	178	2	no	—
255	C₂×C₄²	C₂²×D₈₉	1	2	yes	—
256	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
257	#108	—	356	2	no	—
258	#108	—	178	4	no	—
259	#107	—	89	1	no	—
260	#107	—	89	1	no	—
261	#106	—	89	2	no	—
262	C₄⋊C₈	—	178	4	no	—
263	C₄⋊C₈	—	178	4	no	—
264	C₄⋊C₈	—	178	2	no	—
265	C₄⋊C₈	—	178	2	no	—
266	C₄⋊C₈	D₃₅₆	1	2	yes	—
267	C₄⋊C₈	D₃₅₆	1	2	yes	—
268	#104	—	178	8	no	—
269	#103	—	89	2	no	—
270	#103	—	89	2	no	—
271	#102	—	89	2	no	—
272	#102	—	89	2	no	—
273	#97	—	2	4	no	—
274	C₄×C₈	C₄×D₈₉	1	1	yes	characteristic
275	C₄×C₈	C₄×D₈₉	1	1	yes	characteristic
276	C₄×C₈	C₄×D₈₉	1	1	yes	characteristic
277	C₄×C₈	C₄×D₈₉	1	1	yes	characteristic
278	#95	—	2	1	no	—
279	#41	—	89	4	no	—
280	#41	—	89	4	no	—
281	#41	—	178	2	no	—
282	#41	—	178	2	no	—
283	C₂×Q₈	—	89	2	no	—
284	C₂×D₄	—	89	2	no	—
285	C₂×D₄	—	178	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	178	2	no	—
288	C₂²×C₄	—	178	2	no	—
289	C₂²×C₄	—	178	2	no	—
290	C₂²×C₄	#13083574	1	1	yes	characteristic
291	C₂²×C₄	#13083574	1	1	yes	characteristic
292	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
293	Q₁₆	—	89	4	no	—
294	SD₁₆	—	89	8	no	—
295	D₈	—	89	4	no	—
296	M₁₆	—	356	8	no	—
297	M₁₆	—	178	4	no	—
298	M₁₆	—	178	4	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	—	356	8	no	—
304	C₂×C₈	—	178	4	no	—
305	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
306	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
307	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
308	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
309	C₂×C₈	D₄×D₈₉	1	2	yes	—
310	C₂×C₈	C₂×D₃₅₆	1	4	yes	—
311	C₂×C₈	Q₈×D₈₉	1	2	yes	—
312	C₄⋊C₄	—	4	2	no	—
313	C₄⋊C₄	—	89	2	no	—
314	C₄⋊C₄	—	89	2	no	—
315	C₄⋊C₄	—	178	2	no	—
316	C₄⋊C₄	—	178	2	no	—
317	C₂²⋊C₄	—	178	2	no	—
318	C₂²⋊C₄	—	178	2	no	—
319	C₂²⋊C₄	—	178	2	no	—
320	C₄²	—	2	2	no	—
321	C₄²	—	2	2	no	—
322	C₄²	—	178	2	no	—
323	C₄²	—	178	2	no	—
324	C₄²	—	178	2	no	—
325	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
326	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
327	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
328	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
329	C₂³	—	178	2	no	—
330	C₂³	C₂×#13083574	1	1	yes	characteristic
331	Q₈	—	89	4	no	—
332	Q₈	—	178	2	no	—
333	D₄	—	89	4	no	—
334	D₄	—	178	4	no	—
335	D₄	—	178	4	no	—
336	D₄	—	178	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	—	356	4	no	—
343	C₂×C₄	—	178	2	no	—
344	C₂×C₄	—	178	2	no	—
345	C₂×C₄	—	178	2	no	—
346	C₂×C₄	—	178	4	no	—
347	C₂×C₄	—	178	4	no	—
348	C₂×C₄	—	712	2	no	—
349	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
350	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
351	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
352	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
353	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
354	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
355	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
356	C₂×C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
357	C₂×C₄	#15668058	1	1	yes	characteristic
358	C₂×C₄	#15668059	1	1	yes	characteristic
359	C₈	—	2	4	no	—
360	C₈	—	2	1	no	—
361	C₈	—	2	1	no	—
362	C₈	—	356	4	no	—
363	C₈	C₄⋊C₄×D₈₉	1	2	yes	—
364	C₈	C₄⋊C₄×D₈₉	1	2	yes	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	356	2	no	—
368	C₂²	—	356	2	no	—
369	C₂²	—	178	4	no	—
370	C₂²	C₂×C₄×D₃₅₆	1	1	yes	characteristic
371	C₂²	#19152253	1	1	yes	characteristic
372	C₂²	#19152308	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	—	356	2	no	—
378	C₄	—	356	2	no	—
379	C₄	—	178	4	no	—
380	C₄	#19151721	1	2	yes	complemented
381	C₄	C₂×C₄⋊C₄×D₈₉	1	1	yes	characteristic
382	C₄	#19152078	1	1	yes	characteristic
383	C₄	D₄×D₃₅₆	1	1	yes	characteristic
384	C₄	Q₈×D₃₅₆	1	1	yes	characteristic
385	C₂	—	2	1	no	—
386	C₂	—	2	1	no	—
387	C₂	—	356	4	no	—
388	C₂	C₄⋊C₄×D₃₅₆	1	1	yes	characteristic
389	C₂	C₂×#19151721	1	1	yes	characteristic
390	C₂	#26029170	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₃₅₆
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₈₉×#1770	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×#15668034	C₂²
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#1770	D₈₉
hypocenter	C₈₉	#22686
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
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. #26028817	C₂	semidirect
4. #26021005	C₂	semidirect
5. #26020530	C₂	semidirect
6. #26020424	C₂	semidirect
7. #26020273	C₂	semidirect
8. C₈₉×#1770	C₂	semidirect
13. C₄×Dic₃₅₆	C₄	semidirect
14. C₄×Dic₃₅₆	C₄	semidirect
15. C₄×#13083563	C₄	semidirect
16. C₄×#13083563	C₄	semidirect
17. C₄×D₇₁₂	C₄	semidirect
18. C₄×D₇₁₂	C₄	semidirect
93. Dic₃₅₆	C₄⋊C₄	semidirect
94. #13083563	C₄⋊C₄	semidirect
95. D₇₁₂	C₄⋊C₄	semidirect
181. C₄×C₈₉	#444	semidirect
203. #1770	D₈₉	semidirect
204. C₈₉	#22686	semidirect
380. C₄	#19151721	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19151721	2
C₄×#15668034	2
#26028817	2
#26021005	2
#26020530	2
#26020424	2
#26020273	2
C₈₉×#1770	2
#22686	89