Subgroups — #34306718

Order 20224.

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×#19098686	C₂	1	2	yes	maximal
2	C₄×#14579183	C₂	1	1	yes	maximal, characteristic
3	#23771965	C₂	1	2	yes	maximal, complemented
4	#23764153	C₂	1	2	yes	maximal, complemented
5	#23763678	C₂	1	4	yes	maximal, complemented
6	#23763572	C₂	1	1	yes	maximal, characteristic, complemented
7	#23763421	C₂	1	2	yes	maximal, complemented
8	C₇₉×#1770	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#14579183	C₂²	1	1	yes	characteristic
10	C₂×#14579167	C₂²	1	4	yes	—
11	C₄×#11929624	C₂²	1	2	yes	—
12	#19098686	—	2	8	no	—
13	C₄×Dic₃₁₆	C₄	1	1	yes	characteristic, complemented
14	C₄×Dic₃₁₆	C₄	1	1	yes	characteristic, complemented
15	C₄×#11929613	C₄	1	2	yes	complemented
16	C₄×#11929613	C₄	1	2	yes	complemented
17	C₄×D₆₃₂	C₄	1	1	yes	characteristic, complemented
18	C₄×D₆₃₂	C₄	1	1	yes	characteristic, complemented
19	C₂×#14579097	C₂²	1	2	yes	—
20	C₂×#14579097	C₂²	1	2	yes	—
21	#19098601	C₂²	1	1	yes	characteristic
22	#19098589	C₂²	1	4	yes	—
23	#19098588	—	2	4	no	—
24	#19098587	C₂²	1	2	yes	—
25	#19098585	—	2	2	no	—
26	C₄⋊C₈×D₇₉	—	2	2	no	—
27	C₂×#14579089	C₂²	1	4	yes	—
28	#19098560	C₂²	1	2	yes	—
29	#19098323	C₂²	1	4	yes	—
30	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
31	C₂×#97×C₇₉	C₂²	1	2	yes	—
32	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
33	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
34	#336×C₇₉	C₂²	1	2	yes	—
35	C₂×#11929624	C₂³	1	2	yes	—
36	#14579183	D₄	1	4	yes	—
37	#14579183	Q₈	1	4	yes	—
38	C₂×Dic₃₁₆	C₂×C₄	1	1	yes	characteristic
39	C₂×#11929613	C₂×C₄	1	2	yes	—
40	C₂×D₆₃₂	C₂×C₄	1	1	yes	characteristic
41	#14579167	—	2	8	no	—
42	#14579167	—	4	4	no	—
43	C₂×#11929608	C₂³	1	4	yes	—
44	C₂×#11929607	—	2	4	no	—
45	C₂×C₈×D₇₉	—	2	4	no	—
46	C₄×Dic₁₅₈	C₂×C₄	1	2	yes	—
47	C₄×Dic₁₅₈	C₂×C₄	1	2	yes	—
48	C₄×D₃₁₆	C₂×C₄	1	2	yes	—
49	C₄×D₃₁₆	C₂×C₄	1	2	yes	—
50	C₄×C₂²⋊D₇₉	—	2	2	no	—
51	C₄×C₂²⋊D₇₉	—	2	2	no	—
52	#14579120	C₂³	1	2	yes	—
53	#14579118	—	2	2	no	—
54	C₄²×D₇₉	—	2	2	no	—
55	#14579097	—	2	4	no	—
56	#14579097	—	4	2	no	—
57	#14579095	C₂×C₄	1	1	yes	characteristic
58	#14579095	C₂×C₄	1	1	yes	characteristic
59	#14579093	C₂×C₄	1	2	yes	—
60	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
61	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
62	Dic₇₉⋊C₈	—	2	4	no	—
63	Dic₇₉⋊C₈	—	2	4	no	—
64	#14579089	—	2	8	no	—
65	#14579086	C₂×C₄	1	2	yes	—
66	#14579086	C₂×C₄	1	2	yes	—
67	#14579083	C₂×C₄	1	2	yes	—
68	#14579083	C₂×C₄	1	2	yes	—
69	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
71	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
73	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
74	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
75	C₄⋊C₈×C₇₉	D₄	1	2	yes	—
76	C₄⋊C₈×C₇₉	D₄	1	2	yes	—
77	#97×C₇₉	—	2	4	no	—
78	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
79	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
80	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
81	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
82	#95×C₇₉	—	2	1	no	—
83	#11929624	—	2	2	no	—
84	#11929624	—	2	2	no	—
85	#11929624	C₂×D₄	1	4	yes	—
86	#11929624	C₂×Q₈	1	4	yes	—
87	C₂×Dic₁₅₈	C₂²×C₄	1	2	yes	—
88	C₂×D₃₁₆	C₂²×C₄	1	2	yes	—
89	C₂×C₂²⋊D₇₉	—	2	2	no	—
90	C₂×C₄×D₇₉	—	2	2	no	—
91	C₂×C₄×D₇₉	—	2	2	no	—
92	C₂×C₄×D₇₉	—	2	2	no	—
93	Dic₃₁₆	C₄⋊C₄	1	4	yes	complemented
94	#11929613	C₄⋊C₄	1	8	yes	complemented
95	D₆₃₂	C₄⋊C₄	1	4	yes	complemented
96	#11929608	—	2	4	no	—
97	#11929608	—	2	4	no	—
98	#11929607	—	4	8	no	—
99	C₂×C₇₉⋊C₈	—	2	4	no	—
100	C₈×D₇₉	—	4	8	no	—
101	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
102	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
103	Dic₇₉⋊C₄	—	2	2	no	—
104	Dic₇₉⋊C₄	—	2	2	no	—
105	C₂²⋊Dic₇₉	—	2	2	no	—
106	(C₂×D₇₉)⋊C₄	—	2	2	no	—
107	(C₂×D₇₉)⋊C₄	—	2	2	no	—
108	C₄×Dic₇₉	—	2	2	no	—
109	C₄×Dic₇₉	—	2	2	no	—
110	C₄×Dic₇₉	—	2	2	no	—
111	C₂²×C₄×C₇₉	—	2	2	no	—
112	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
113	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
114	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
115	C₂×C₈×C₇₉	—	2	2	no	—
116	C₂×C₈×C₇₉	—	2	1	no	—
117	C₂×C₈×C₇₉	—	2	2	no	—
118	C₂×C₈×C₇₉	—	2	1	no	—
119	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
124	C₂×C₈×C₇₉	C₂×D₄	1	4	yes	—
125	C₂×C₈×C₇₉	C₂×Q₈	1	2	yes	—
126	C₄⋊C₄×C₇₉	—	4	2	no	—
127	C₄²×C₇₉	—	2	2	no	—
128	C₄²×C₇₉	—	2	2	no	—
129	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
130	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
131	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
133	C₂³×C₇₉	C₂×#41	1	1	yes	characteristic
134	C₂²×D₇₉	—	2	2	no	—
135	C₂×C₄×C₇₉	—	2	2	no	—
136	C₂×C₄×C₇₉	—	4	1	no	—
137	C₂×C₄×C₇₉	—	4	2	no	—
138	C₂×C₄×C₇₉	—	4	2	no	—
139	C₂×C₄×C₇₉	—	4	2	no	—
140	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
141	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
142	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
143	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
144	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
145	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
146	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
147	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
148	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
149	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
150	C₂²⋊D₇₉	—	2	4	no	—
151	C₂²⋊D₇₉	—	2	4	no	—
152	C₂×Dic₇₉	—	2	2	no	—
153	C₂×Dic₇₉	—	2	2	no	—
154	C₂×Dic₇₉	—	2	2	no	—
155	D₃₁₆	—	2	2	no	—
156	D₃₁₆	C₂×C₄⋊C₄	1	4	yes	—
157	C₄×D₇₉	—	2	4	no	—
158	C₄×D₇₉	—	2	4	no	—
159	C₄×D₇₉	—	4	4	no	—
160	C₄×D₇₉	—	8	2	no	—
161	Dic₁₅₈	—	2	2	no	—
162	Dic₁₅₈	C₂×C₄⋊C₄	1	4	yes	—
163	C₈×C₇₉	—	2	1	no	—
164	C₈×C₇₉	—	2	1	no	—
165	C₈×C₇₉	—	2	4	no	—
166	C₈×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
167	C₈×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
168	C₇₉⋊C₈	—	4	4	no	—
169	C₂²×C₇₉	—	2	1	no	—
170	C₂²×C₇₉	—	2	1	no	—
171	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
172	C₂²×C₇₉	#547	1	1	yes	characteristic
173	C₂²×C₇₉	#554	1	1	yes	characteristic
174	C₂×D₇₉	—	2	4	no	—
175	C₂×D₇₉	—	4	2	no	—
176	C₂×D₇₉	—	4	2	no	—
177	C₄×C₇₉	—	2	1	no	—
178	C₄×C₇₉	—	2	1	no	—
179	C₄×C₇₉	—	2	1	no	—
180	C₄×C₇₉	—	8	2	no	—
181	C₄×C₇₉	#444	1	2	yes	complemented
182	C₄×C₇₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
183	C₄×C₇₉	#520	1	1	yes	characteristic
184	C₄×C₇₉	D₄²	1	1	yes	characteristic
185	C₄×C₇₉	D₄×Q₈	1	1	yes	characteristic
186	Dic₇₉	—	2	4	no	—
187	Dic₇₉	—	4	2	no	—
188	Dic₇₉	—	4	2	no	—
189	#22686	—	79	1	no	maximal, Sylow
190	C₂×C₇₉	—	2	1	no	—
191	C₂×C₇₉	—	2	1	no	—
192	C₂×C₇₉	D₄×C₄⋊C₄	1	1	yes	characteristic
193	C₂×C₇₉	C₂×#444	1	1	yes	characteristic
194	C₂×C₇₉	#2957	1	1	yes	characteristic
195	D₇₉	—	4	4	no	—
196	C₂×#444	—	79	2	no	—
197	C₄×#135	—	79	1	no	—
198	#2906	—	79	2	no	—
199	#1946	—	79	2	no	—
200	#1866	—	79	4	no	—
201	#1848	—	79	1	no	—
202	#1806	—	79	2	no	—
203	#1770	D₇₉	1	1	yes	characteristic, complemented
204	C₇₉	#22686	1	1	yes	characteristic, complemented, Sylow
205	C₂×#135	—	79	1	no	—
206	C₂×#131	—	79	4	no	—
207	C₄×#41	—	79	2	no	—
208	#444	—	158	8	no	—
209	C₄×Q₁₆	—	79	1	no	—
210	C₄×Q₁₆	—	79	1	no	—
211	C₄×SD₁₆	—	79	2	no	—
212	C₄×SD₁₆	—	79	2	no	—
213	C₄×D₈	—	79	1	no	—
214	C₄×D₈	—	79	1	no	—
215	C₂×#108	—	79	2	no	—
216	C₂×#108	—	79	2	no	—
217	#427	—	79	1	no	—
218	#424	—	79	4	no	—
219	#424	—	158	4	no	—
220	#423	—	79	2	no	—
221	#423	—	158	2	no	—
222	C₂×C₄⋊C₈	—	158	2	no	—
223	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
224	C₂×#104	—	79	4	no	—
225	#416	—	79	2	no	—
226	C₂×#97	C₂×D₇₉	1	2	yes	—
227	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
228	C₄×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
229	#339	—	79	4	no	—
230	#336	C₂×D₇₉	1	2	yes	—
231	C₂×#41	—	79	2	no	—
232	#135	—	79	4	no	—
233	#135	—	79	4	no	—
234	C₂×Q₁₆	—	79	1	no	—
235	C₂×SD₁₆	—	79	2	no	—
236	C₂×D₈	—	79	1	no	—
237	#131	—	316	4	no	—
238	#131	—	158	8	no	—
239	C₂×M₁₆	—	79	4	no	—
240	C₂×M₁₆	—	158	4	no	—
241	C₂²×C₈	—	158	4	no	—
242	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
243	C₂²×C₈	C₂²×D₇₉	1	2	yes	—
244	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
245	C₄×Q₈	—	79	2	no	—
246	C₄×Q₈	—	79	2	no	—
247	C₄×D₄	—	79	2	no	—
248	C₄×D₄	—	79	2	no	—
249	C₄×D₄	—	158	2	no	—
250	C₄×D₄	—	158	2	no	—
251	#117	—	79	2	no	—
252	#117	—	158	2	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄²	—	158	2	no	—
255	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
256	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
257	#108	—	316	2	no	—
258	#108	—	158	4	no	—
259	#107	—	79	1	no	—
260	#107	—	79	1	no	—
261	#106	—	79	2	no	—
262	C₄⋊C₈	—	158	4	no	—
263	C₄⋊C₈	—	158	4	no	—
264	C₄⋊C₈	—	158	2	no	—
265	C₄⋊C₈	—	158	2	no	—
266	C₄⋊C₈	D₃₁₆	1	2	yes	—
267	C₄⋊C₈	D₃₁₆	1	2	yes	—
268	#104	—	158	8	no	—
269	#103	—	79	2	no	—
270	#103	—	79	2	no	—
271	#102	—	79	2	no	—
272	#102	—	79	2	no	—
273	#97	—	2	4	no	—
274	C₄×C₈	C₄×D₇₉	1	1	yes	characteristic
275	C₄×C₈	C₄×D₇₉	1	1	yes	characteristic
276	C₄×C₈	C₄×D₇₉	1	1	yes	characteristic
277	C₄×C₈	C₄×D₇₉	1	1	yes	characteristic
278	#95	—	2	1	no	—
279	#41	—	79	4	no	—
280	#41	—	79	4	no	—
281	#41	—	158	2	no	—
282	#41	—	158	2	no	—
283	C₂×Q₈	—	79	2	no	—
284	C₂×D₄	—	79	2	no	—
285	C₂×D₄	—	158	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	158	2	no	—
288	C₂²×C₄	—	158	2	no	—
289	C₂²×C₄	—	158	2	no	—
290	C₂²×C₄	#11929624	1	1	yes	characteristic
291	C₂²×C₄	#11929624	1	1	yes	characteristic
292	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
293	Q₁₆	—	79	4	no	—
294	SD₁₆	—	79	8	no	—
295	D₈	—	79	4	no	—
296	M₁₆	—	316	8	no	—
297	M₁₆	—	158	4	no	—
298	M₁₆	—	158	4	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	316	8	no	—
304	C₂×C₈	—	158	4	no	—
305	C₂×C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
306	C₂×C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
307	C₂×C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
308	C₂×C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
309	C₂×C₈	D₄×D₇₉	1	2	yes	—
310	C₂×C₈	C₂×D₃₁₆	1	4	yes	—
311	C₂×C₈	Q₈×D₇₉	1	2	yes	—
312	C₄⋊C₄	—	4	2	no	—
313	C₄⋊C₄	—	79	2	no	—
314	C₄⋊C₄	—	79	2	no	—
315	C₄⋊C₄	—	158	2	no	—
316	C₄⋊C₄	—	158	2	no	—
317	C₂²⋊C₄	—	158	2	no	—
318	C₂²⋊C₄	—	158	2	no	—
319	C₂²⋊C₄	—	158	2	no	—
320	C₄²	—	2	2	no	—
321	C₄²	—	2	2	no	—
322	C₄²	—	158	2	no	—
323	C₄²	—	158	2	no	—
324	C₄²	—	158	2	no	—
325	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
326	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
327	C₄²	C₂×D₃₁₆	1	1	yes	characteristic
328	C₄²	C₂×D₃₁₆	1	1	yes	characteristic
329	C₂³	—	158	2	no	—
330	C₂³	C₂×#11929624	1	1	yes	characteristic
331	Q₈	—	79	4	no	—
332	Q₈	—	158	2	no	—
333	D₄	—	79	4	no	—
334	D₄	—	158	4	no	—
335	D₄	—	158	4	no	—
336	D₄	—	158	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	—	316	4	no	—
343	C₂×C₄	—	632	2	no	—
344	C₂×C₄	—	158	2	no	—
345	C₂×C₄	—	158	2	no	—
346	C₂×C₄	—	158	2	no	—
347	C₂×C₄	—	158	4	no	—
348	C₂×C₄	—	158	4	no	—
349	C₂×C₄	C₄×D₃₁₆	1	1	yes	characteristic
350	C₂×C₄	C₄×D₃₁₆	1	1	yes	characteristic
351	C₂×C₄	C₄×D₃₁₆	1	1	yes	characteristic
352	C₂×C₄	C₄×D₃₁₆	1	1	yes	characteristic
353	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
354	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
355	C₂×C₄	C₂²×D₃₁₆	1	1	yes	characteristic
356	C₂×C₄	C₂×Q₈×D₇₉	1	1	yes	characteristic
357	C₂×C₄	#14579207	1	1	yes	characteristic
358	C₂×C₄	#14579208	1	1	yes	characteristic
359	C₈	—	2	4	no	—
360	C₈	—	2	1	no	—
361	C₈	—	2	1	no	—
362	C₈	—	316	4	no	—
363	C₈	C₄⋊C₄×D₇₉	1	2	yes	—
364	C₈	C₄⋊C₄×D₇₉	1	2	yes	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	316	2	no	—
368	C₂²	—	316	2	no	—
369	C₂²	—	158	4	no	—
370	C₂²	C₂×C₄×D₃₁₆	1	1	yes	characteristic
371	C₂²	#19099218	1	1	yes	characteristic
372	C₂²	#19099273	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	—	316	2	no	—
378	C₄	—	316	2	no	—
379	C₄	—	158	4	no	—
380	C₄	#19098686	1	2	yes	complemented
381	C₄	C₂×C₄⋊C₄×D₇₉	1	1	yes	characteristic
382	C₄	#19099043	1	1	yes	characteristic
383	C₄	D₄×D₃₁₆	1	1	yes	characteristic
384	C₄	Q₈×D₃₁₆	1	1	yes	characteristic
385	C₂	—	2	1	no	—
386	C₂	—	2	1	no	—
387	C₂	—	316	4	no	—
388	C₂	C₄⋊C₄×D₃₁₆	1	1	yes	characteristic
389	C₂	C₂×#19098686	1	1	yes	characteristic
390	C₂	#23772318	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₃₁₆
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting	C₇₉×#1770	C₂
socle	C₂²×C₇₉	C₂×C₄×D₄
prime radical	C₂×#14579183	C₂²
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	#1770	D₇₉
hypocenter	C₇₉	#22686
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
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. #23771965	C₂	semidirect
4. #23764153	C₂	semidirect
5. #23763678	C₂	semidirect
6. #23763572	C₂	semidirect
7. #23763421	C₂	semidirect
8. C₇₉×#1770	C₂	semidirect
13. C₄×Dic₃₁₆	C₄	semidirect
14. C₄×Dic₃₁₆	C₄	semidirect
15. C₄×#11929613	C₄	semidirect
16. C₄×#11929613	C₄	semidirect
17. C₄×D₆₃₂	C₄	semidirect
18. C₄×D₆₃₂	C₄	semidirect
93. Dic₃₁₆	C₄⋊C₄	semidirect
94. #11929613	C₄⋊C₄	semidirect
95. D₆₃₂	C₄⋊C₄	semidirect
181. C₄×C₇₉	#444	semidirect
203. #1770	D₇₉	semidirect
204. C₇₉	#22686	semidirect
380. C₄	#19098686	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19098686	2
C₄×#14579183	2
#23771965	2
#23764153	2
#23763678	2
#23763572	2
#23763421	2
C₇₉×#1770	2
#22686	79