Subgroups — #34178893

Order 20224.

698 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₄×Dic₇₉	C₂	1	1	yes	maximal, characteristic
2	#23763255	C₂	1	1	yes	maximal, characteristic, complemented
3	#23763145	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄⋊(C₇₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
5	#23761240	C₂	1	1	yes	maximal, characteristic, complemented
6	#23761239	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×D₄⋊C₈×C₇₉	C₂	1	1	yes	maximal, characteristic
8	C₂×D₄×Dic₇₉	C₄	1	2	yes	—
9	C₂²×C₄×Dic₇₉	—	2	1	no	—
10	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×#14579071	—	2	1	no	—
12	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
13	C₄⋊C₄×Dic₇₉	C₄	1	2	yes	—
14	C₄×C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic
15	C₂²⋊C₄×Dic₇₉	—	2	2	no	—
16	C₄×C₂²⋊Dic₇₉	—	2	1	no	—
17	C₄²×Dic₇₉	C₂²	1	1	yes	characteristic
18	#19098317	—	2	1	no	—
19	#19098317	—	2	2	no	—
20	D₄⋊(C₇₉⋊C₈)	C₄	1	4	yes	complemented
21	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
24	D₄⋊C₈×C₇₉	C₄	1	4	yes	complemented
25	C₂³×Dic₇₉	—	2	2	no	—
26	C₂²×C₇₉⋊C₈	—	2	1	no	—
27	C₂²×C₇₉⋊C₈	—	2	1	no	—
28	D₄×Dic₇₉	—	2	4	no	—
29	D₄×Dic₇₉	—	2	4	no	—
30	C₂×C₄⋊Dic₇₉	C₂×C₄	1	2	yes	—
31	C₂×C₂²⋊Dic₇₉	—	2	2	no	—
32	C₂×C₄×Dic₇₉	—	2	1	no	—
33	C₂×C₄×Dic₇₉	—	2	2	no	—
34	C₂×C₄×Dic₇₉	—	4	2	no	—
35	C₂×C₄×Dic₇₉	—	4	2	no	—
36	C₂×C₄×Dic₇₉	C₂×C₄	1	2	yes	—
37	C₂×C₄×Dic₇₉	D₄	1	1	yes	characteristic
38	C₂×C₄×Dic₇₉	D₄	1	2	yes	—
39	C₂×C₄×Dic₇₉	D₄	1	1	yes	characteristic
40	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
41	C₄⋊(C₇₉⋊C₈)	C₂×C₄	1	2	yes	complemented
42	#14579071	—	4	2	no	—
43	C₄×C₇₉⋊C₈	—	2	1	no	—
44	C₄×C₇₉⋊C₈	C₂×C₄	1	2	yes	complemented
45	C₇₉⋊#95	—	2	1	no	—
46	C₇₉⋊#95	—	2	2	no	—
47	C₂²×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₇₉	—	2	1	no	—
49	C₂²×C₈×C₇₉	—	2	1	no	—
50	C₂²×C₈×C₇₉	—	2	1	no	—
51	C₄×D₄×C₇₉	—	2	1	no	—
52	C₄×D₄×C₇₉	—	2	1	no	—
53	C₄×D₄×C₇₉	C₂×C₄	1	2	yes	—
54	C₄×D₄×C₇₉	C₂×C₄	1	2	yes	—
55	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
56	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
57	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
58	C₄⋊C₈×C₇₉	—	2	1	no	—
59	C₄⋊C₈×C₇₉	C₂×C₄	1	2	yes	complemented
60	C₄×C₈×C₇₉	—	2	1	no	—
61	C₄×C₈×C₇₉	C₂×C₄	1	2	yes	complemented
62	C₂²×Dic₇₉	—	2	8	no	—
63	C₂²×Dic₇₉	—	2	2	no	—
64	C₂²×Dic₇₉	—	4	4	no	—
65	C₂²×Dic₇₉	—	4	4	no	—
66	C₂²×Dic₇₉	C₂²⋊C₄	1	2	yes	—
67	C₂²×Dic₇₉	C₂²⋊C₄	1	2	yes	—
68	C₂×C₇₉⋊C₈	—	2	2	no	—
69	C₂×C₇₉⋊C₈	—	2	2	no	—
70	C₂×C₇₉⋊C₈	—	4	2	no	—
71	C₂×C₇₉⋊C₈	—	4	1	no	—
72	C₂×C₇₉⋊C₈	—	4	1	no	—
73	C₄⋊Dic₇₉	—	2	2	no	—
74	C₄⋊Dic₇₉	M₁₆	1	4	yes	—
75	C₂²⋊Dic₇₉	—	2	8	no	—
76	C₄×Dic₇₉	—	2	2	no	—
77	C₄×Dic₇₉	—	2	2	no	—
78	C₄×Dic₇₉	—	2	1	no	—
79	C₄×Dic₇₉	—	2	1	no	—
80	C₄×Dic₇₉	—	4	2	no	—
81	C₄×Dic₇₉	—	4	4	no	—
82	C₄×Dic₇₉	—	4	1	no	—
83	C₄×Dic₇₉	—	4	1	no	—
84	C₄×Dic₇₉	D₈	1	2	yes	—
85	C₄×Dic₇₉	SD₁₆	1	2	yes	—
86	C₂⁴×C₇₉	—	2	1	no	—
87	C₂×D₄×C₇₉	—	2	1	no	—
88	C₂×D₄×C₇₉	—	2	2	no	—
89	C₂×D₄×C₇₉	C₄²	1	2	yes	—
90	C₂×D₄×C₇₉	M₁₆	1	4	yes	—
91	C₂²×C₄×C₇₉	—	2	1	no	—
92	C₂²×C₄×C₇₉	—	2	2	no	—
93	C₂²×C₄×C₇₉	—	2	2	no	—
94	C₂²×C₄×C₇₉	—	4	1	no	—
95	C₂²×C₄×C₇₉	—	4	1	no	—
96	C₂²×C₄×C₇₉	—	4	1	no	—
97	C₂²×C₄×C₇₉	—	4	1	no	—
98	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
101	C₂×C₈×C₇₉	—	2	2	no	—
102	C₂×C₈×C₇₉	—	2	2	no	—
103	C₂×C₈×C₇₉	—	4	2	no	—
104	C₂×C₈×C₇₉	—	4	1	no	—
105	C₂×C₈×C₇₉	—	4	1	no	—
106	C₄⋊C₄×C₇₉	—	2	1	no	—
107	C₄⋊C₄×C₇₉	C₄²	1	2	yes	—
108	C₂²⋊C₄×C₇₉	—	2	2	no	—
109	C₂²⋊C₄×C₇₉	—	2	2	no	—
110	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
111	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
112	C₄²×C₇₉	#41	1	1	yes	characteristic
113	C₄²×C₇₉	#41	1	1	yes	characteristic
114	C₂³×C₇₉	—	2	2	no	—
115	C₂³×C₇₉	—	2	4	no	—
116	C₂³×C₇₉	—	4	1	no	—
117	C₂³×C₇₉	—	4	1	no	—
118	C₂³×C₇₉	—	4	2	no	—
119	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
120	D₄×C₇₉	—	2	2	no	—
121	D₄×C₇₉	—	2	4	no	—
122	D₄×C₇₉	#97	1	4	yes	complemented
123	C₂×C₄×C₇₉	—	2	2	no	—
124	C₂×C₄×C₇₉	—	2	2	no	—
125	C₂×C₄×C₇₉	—	4	1	no	—
126	C₂×C₄×C₇₉	—	4	1	no	—
127	C₂×C₄×C₇₉	—	4	2	no	—
128	C₂×C₄×C₇₉	—	4	2	no	—
129	C₂×C₄×C₇₉	—	4	2	no	—
130	C₂×C₄×C₇₉	—	4	2	no	—
131	C₂×C₄×C₇₉	C₂×C₄²	1	1	yes	characteristic
132	C₂×C₄×C₇₉	#117	1	1	yes	characteristic
133	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
134	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
135	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
136	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
137	C₂×C₄×C₇₉	C₂×M₁₆	1	2	yes	—
138	C₂×C₄×C₇₉	C₂×M₁₆	1	2	yes	—
139	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
140	C₂×C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
141	C₂×C₄×C₇₉	#135	1	1	yes	characteristic
142	C₂×C₄×C₇₉	#135	1	1	yes	characteristic
143	C₂×Dic₇₉	—	2	2	no	—
144	C₂×Dic₇₉	—	2	2	no	—
145	C₂×Dic₇₉	—	2	2	no	—
146	C₂×Dic₇₉	—	2	4	no	—
147	C₂×Dic₇₉	—	2	2	no	—
148	C₂×Dic₇₉	—	2	2	no	—
149	C₂×Dic₇₉	—	4	16	no	—
150	C₂×Dic₇₉	—	4	2	no	—
151	C₂×Dic₇₉	—	4	2	no	—
152	C₂×Dic₇₉	#102	1	4	yes	—
153	C₈×C₇₉	—	4	2	no	—
154	C₈×C₇₉	—	4	2	no	—
155	C₇₉⋊C₈	—	4	2	no	—
156	C₇₉⋊C₈	—	4	2	no	—
157	C₂²×C₇₉	—	2	4	no	—
158	C₂²×C₇₉	—	4	4	no	—
159	C₂²×C₇₉	—	4	4	no	—
160	C₂²×C₇₉	—	4	2	no	—
161	C₂²×C₇₉	—	4	2	no	—
162	C₂²×C₇₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
163	C₂²×C₇₉	#407	1	2	yes	—
164	C₂²×C₇₉	C₂×#102	1	1	yes	characteristic
165	C₂²×C₇₉	#416	1	1	yes	characteristic
166	C₂²×C₇₉	#421	1	2	yes	—
167	C₄×C₇₉	—	2	1	no	—
168	C₄×C₇₉	—	2	1	no	—
169	C₄×C₇₉	—	4	2	no	—
170	C₄×C₇₉	C₂×#97	1	1	yes	characteristic
171	C₄×C₇₉	C₄×M₁₆	1	1	yes	characteristic
172	C₄×C₇₉	#432	1	2	yes	—
173	C₄×C₇₉	C₄×D₈	1	1	yes	characteristic
174	C₄×C₇₉	C₄×D₈	1	1	yes	characteristic
175	C₄×C₇₉	C₄×SD₁₆	1	1	yes	characteristic
176	C₄×C₇₉	C₄×SD₁₆	1	1	yes	characteristic
177	Dic₇₉	—	2	4	no	—
178	Dic₇₉	—	4	4	no	—
179	Dic₇₉	—	4	2	no	—
180	#8174	—	79	1	no	maximal, Sylow
181	C₂×C₇₉	—	4	4	no	—
182	C₂×C₇₉	#1486	1	2	yes	—
183	C₂×C₇₉	#1488	1	2	yes	—
184	C₂×C₇₉	#1749	1	1	yes	characteristic
185	C₂×C₇₉	#1759	1	1	yes	characteristic
186	C₂×C₇₉	C₄×#102	1	1	yes	characteristic
187	C₄²×D₄	—	79	1	no	—
188	#1767	—	79	1	no	—
189	#1744	—	79	1	no	—
190	C₂×D₄⋊C₈	—	79	1	no	—
191	C₂×D₄⋊C₈	D₇₉	1	1	yes	characteristic
192	#1279	—	79	1	no	—
193	#1279	—	79	1	no	—
194	C₇₉	#8174	1	1	yes	characteristic, complemented, Sylow
195	C₂×C₄×D₄	—	79	2	no	—
196	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
197	C₂²×C₄²	—	158	1	no	—
198	C₂×C₄⋊C₈	—	79	1	no	—
199	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
200	C₂×#97	—	158	1	no	—
201	C₂×C₄×C₈	—	79	1	no	—
202	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
203	C₄×C₄⋊C₄	—	79	2	no	—
204	C₄×C₄⋊C₄	—	79	1	no	—
205	C₄×C₂²⋊C₄	—	158	2	no	—
206	C₄×C₂²⋊C₄	—	158	1	no	—
207	C₄³	—	79	1	no	—
208	#336	—	158	2	no	—
209	#336	—	158	1	no	—
210	D₄⋊C₈	—	79	4	no	—
211	D₄⋊C₈	Dic₇₉	1	4	yes	complemented
212	C₂²×D₄	C₄×D₇₉	1	1	yes	characteristic
213	C₂³×C₄	—	2	1	no	—
214	C₂³×C₄	—	158	2	no	—
215	C₂²×C₈	—	2	1	no	—
216	C₂²×C₈	—	2	1	no	—
217	C₂²×C₈	—	158	1	no	—
218	C₂²×C₈	—	158	1	no	—
219	C₄×D₄	—	2	1	no	—
220	C₄×D₄	—	2	1	no	—
221	C₄×D₄	—	158	4	no	—
222	C₄×D₄	—	158	4	no	—
223	C₄×D₄	C₄×D₇₉	1	2	yes	—
224	C₄×D₄	C₂×Dic₇₉	1	2	yes	—
225	C₂×C₄⋊C₄	—	79	2	no	—
226	C₂×C₄⋊C₄	C₄×D₇₉	1	1	yes	characteristic
227	C₂×C₂²⋊C₄	—	2	1	no	—
228	C₂×C₂²⋊C₄	—	158	2	no	—
229	C₂×C₄²	—	316	2	no	—
230	C₂×C₄²	—	316	2	no	—
231	C₂×C₄²	—	79	2	no	—
232	C₂×C₄²	—	79	1	no	—
233	C₂×C₄²	—	79	2	no	—
234	C₂×C₄²	—	79	1	no	—
235	C₂×C₄²	—	158	2	no	—
236	C₂×C₄²	—	158	1	no	—
237	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
238	C₄⋊C₈	—	2	1	no	—
239	C₄⋊C₈	—	79	2	no	—
240	C₄⋊C₈	—	158	1	no	—
241	C₄⋊C₈	C₂×Dic₇₉	1	2	yes	complemented
242	#97	—	316	2	no	—
243	C₄×C₈	—	2	1	no	—
244	C₄×C₈	—	79	2	no	—
245	C₄×C₈	—	158	1	no	—
246	C₄×C₈	C₂×Dic₇₉	1	2	yes	complemented
247	#95	—	158	2	no	—
248	#95	—	158	1	no	—
249	C₂⁴	—	2	1	no	—
250	C₂×D₄	—	2	1	no	—
251	C₂×D₄	—	2	2	no	—
252	C₂×D₄	C₄×Dic₇₉	1	2	yes	—
253	C₂×D₄	#11929607	1	4	yes	—
254	C₂²×C₄	—	2	1	no	—
255	C₂²×C₄	—	2	2	no	—
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	4	1	no	—
258	C₂²×C₄	—	4	1	no	—
259	C₂²×C₄	—	4	1	no	—
260	C₂²×C₄	—	4	1	no	—
261	C₂²×C₄	—	316	4	no	—
262	C₂²×C₄	—	316	4	no	—
263	C₂²×C₄	—	79	2	no	—
264	C₂²×C₄	—	79	2	no	—
265	C₂²×C₄	—	158	8	no	—
266	C₂²×C₄	—	158	2	no	—
267	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
268	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
269	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
270	C₂×C₈	—	2	2	no	—
271	C₂×C₈	—	2	2	no	—
272	C₂×C₈	—	4	2	no	—
273	C₂×C₈	—	4	1	no	—
274	C₂×C₈	—	4	1	no	—
275	C₂×C₈	—	316	2	no	—
276	C₂×C₈	—	316	1	no	—
277	C₂×C₈	—	316	1	no	—
278	C₂×C₈	—	158	2	no	—
279	C₂×C₈	—	158	2	no	—
280	C₄⋊C₄	—	2	1	no	—
281	C₄⋊C₄	—	79	4	no	—
282	C₄⋊C₄	—	158	2	no	—
283	C₄⋊C₄	C₄×Dic₇₉	1	2	yes	—
284	C₂²⋊C₄	—	2	2	no	—
285	C₂²⋊C₄	—	2	2	no	—
286	C₂²⋊C₄	—	158	8	no	—
287	C₄²	—	316	2	no	—
288	C₄²	—	316	4	no	—
289	C₄²	—	316	1	no	—
290	C₄²	—	316	1	no	—
291	C₄²	—	79	2	no	—
292	C₄²	—	79	2	no	—
293	C₄²	—	158	2	no	—
294	C₄²	—	158	2	no	—
295	C₄²	—	158	1	no	—
296	C₄²	—	158	1	no	—
297	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
298	C₄²	C₂²×Dic₇₉	1	1	yes	characteristic
299	C₄²	#11929623	1	1	yes	characteristic
300	C₄²	#11929623	1	1	yes	characteristic
301	C₂³	—	2	2	no	—
302	C₂³	—	2	4	no	—
303	C₂³	—	4	1	no	—
304	C₂³	—	4	1	no	—
305	C₂³	—	4	2	no	—
306	C₂³	C₂²⋊C₄×D₇₉	1	1	yes	characteristic
307	D₄	—	2	2	no	—
308	D₄	—	2	4	no	—
309	D₄	#14579071	1	4	yes	complemented
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	4	1	no	—
313	C₂×C₄	—	4	1	no	—
314	C₂×C₄	—	4	2	no	—
315	C₂×C₄	—	4	2	no	—
316	C₂×C₄	—	4	2	no	—
317	C₂×C₄	—	4	2	no	—
318	C₂×C₄	—	316	2	no	—
319	C₂×C₄	—	316	2	no	—
320	C₂×C₄	—	316	16	no	—
321	C₂×C₄	—	79	4	no	—
322	C₂×C₄	—	158	2	no	—
323	C₂×C₄	—	158	4	no	—
324	C₂×C₄	—	158	2	no	—
325	C₂×C₄	—	158	2	no	—
326	C₂×C₄	—	158	2	no	—
327	C₂×C₄	—	158	2	no	—
328	C₂×C₄	C₂×C₄×Dic₇₉	1	1	yes	characteristic
329	C₂×C₄	#14579117	1	1	yes	characteristic
330	C₂×C₄	(C₂²⋊D₇₉)⋊C₄	1	1	yes	characteristic
331	C₂×C₄	(C₂²⋊D₇₉)⋊C₄	1	1	yes	characteristic
332	C₂×C₄	D₄×Dic₇₉	1	1	yes	characteristic
333	C₂×C₄	D₄×Dic₇₉	1	1	yes	characteristic
334	C₂×C₄	M₁₆×D₇₉	1	2	yes	—
335	C₂×C₄	C₂×#11929607	1	2	yes	—
336	C₂×C₄	D₈×D₇₉	1	1	yes	characteristic
337	C₂×C₄	SD₁₆×D₇₉	1	1	yes	characteristic
338	C₂×C₄	#14579180	1	1	yes	characteristic
339	C₂×C₄	#14579182	1	1	yes	characteristic
340	C₈	—	4	2	no	—
341	C₈	—	4	2	no	—
342	C₈	—	316	2	no	—
343	C₈	—	316	2	no	—
344	C₂²	—	2	4	no	—
345	C₂²	—	4	2	no	—
346	C₂²	—	4	2	no	—
347	C₂²	—	4	4	no	—
348	C₂²	—	4	4	no	—
349	C₂²	C₂²⋊C₄×Dic₇₉	1	1	yes	characteristic
350	C₂²	#19098525	1	2	yes	—
351	C₂²	#102×D₇₉	1	1	yes	characteristic
352	C₂²	#19098556	1	1	yes	characteristic
353	C₂²	#19098578	1	2	yes	—
354	C₄	—	2	1	no	—
355	C₄	—	2	1	no	—
356	C₄	—	4	2	no	—
357	C₄	—	316	4	no	—
358	C₄	—	316	2	no	—
359	C₄	—	158	4	no	—
360	C₄	C₂×#14579071	1	1	yes	characteristic
361	C₄	M₁₆×Dic₇₉	1	1	yes	characteristic
362	C₄	#19098617	1	2	yes	—
363	C₄	#19098643	1	1	yes	characteristic
364	C₄	D₈×Dic₇₉	1	1	yes	characteristic
365	C₄	SD₁₆×Dic₇₉	1	1	yes	characteristic
366	C₄	#19098654	1	1	yes	characteristic
367	C₂	—	4	4	no	—
368	C₂	#23761823	1	2	yes	—
369	C₂	#23761831	1	2	yes	—
370	C₂	#23763164	1	1	yes	characteristic
371	C₂	#23763212	1	1	yes	characteristic
372	C₂	#102×Dic₇₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₇₉
commutator	C₂×C₄×C₇₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₂×D₄⋊C₈×C₇₉	C₂
socle	C₂³×C₇₉	C₂×C₂²⋊C₄
prime radical	C₂²×D₄×C₇₉	C₂×C₄
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	C₂×D₄⋊C₈	D₇₉
hypocenter	C₇₉	#8174
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×D₄⋊C₈

Complements

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

N	H ≅ G/N	type
2. #23763255	C₂	semidirect
3. #23763145	C₂	semidirect
5. #23761240	C₂	semidirect
6. #23761239	C₂	semidirect
20. D₄⋊(C₇₉⋊C₈)	C₄	semidirect
24. D₄⋊C₈×C₇₉	C₄	semidirect
41. C₄⋊(C₇₉⋊C₈)	C₂×C₄	semidirect
44. C₄×C₇₉⋊C₈	C₂×C₄	semidirect
59. C₄⋊C₈×C₇₉	C₂×C₄	semidirect
61. C₄×C₈×C₇₉	C₂×C₄	semidirect
122. D₄×C₇₉	#97	semidirect
194. C₇₉	#8174	semidirect
211. D₄⋊C₈	Dic₇₉	semidirect
241. C₄⋊C₈	C₂×Dic₇₉	semidirect
246. C₄×C₈	C₂×Dic₇₉	semidirect
309. D₄	#14579071	semidirect

Maximal subgroups

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

subgroup	index
C₄×D₄×Dic₇₉	2
#23763255	2
#23763145	2
C₂×D₄⋊(C₇₉⋊C₈)	2
#23761240	2
#23761239	2
C₂×D₄⋊C₈×C₇₉	2
#8174	79