Subgroups — C₂²×Q₈×C₂²⋊D₇₉ #35195183

Order 20224.

11798 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×Q₈×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×Q₈×C₂²⋊D₇₉	C₂	1	48	yes	maximal, direct product factor
3	C₂²×#14579159	C₂	1	3	yes	maximal, complemented
4	C₂²×#14579140	C₂	1	3	yes	maximal, complemented
5	C₂²×#14579137	C₂	1	3	yes	maximal, complemented
6	C₂²×Q₈×Dic₇₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₄×C₂²⋊D₇₉	C₂	1	3	yes	maximal
8	C₂⁴×Q₈×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×Dic₁₅₈	C₂²	1	3	yes	—
10	C₂²×Q₈×D₇₉	—	2	16	no	—
11	C₂²×Q₈×D₇₉	C₂²	1	24	yes	complemented
12	C₂³×C₂²⋊D₇₉	C₂²	1	1	yes	characteristic
13	C₂³×C₄×D₇₉	C₂²	1	3	yes	—
14	Q₈×C₂²⋊D₇₉	C₂²	1	256	yes	direct product factor
15	C₂×#14579159	C₂²	1	72	yes	complemented
16	C₂×#14579140	C₂²	1	72	yes	complemented
17	C₂×#14579137	C₂²	1	72	yes	complemented
18	C₂×Q₈×Dic₇₉	C₂²	1	24	yes	complemented
19	C₂×C₄×C₂²⋊D₇₉	C₂²	1	72	yes	—
20	C₂²×C₄⋊Dic₇₉	C₂²	1	3	yes	—
21	C₂²×Dic₇₉⋊C₄	C₂²	1	3	yes	—
22	C₂²×Dic₇₉⋊C₄	C₂²	1	6	yes	—
23	C₂²×C₂²⋊Dic₇₉	C₂²	1	3	yes	—
24	C₂²×(C₂×D₇₉)⋊C₄	C₂²	1	3	yes	—
25	C₂²×C₄×Dic₇₉	C₂²	1	3	yes	—
26	C₂³×Q₈×C₇₉	—	2	16	no	—
27	C₂³×Q₈×C₇₉	C₂²	1	3	yes	—
28	C₂³×Q₈×C₇₉	C₂²	1	1	yes	characteristic
29	C₂³×Q₈×C₇₉	C₂²	1	24	yes	complemented
30	C₂⁴×C₄×C₇₉	C₂²	1	3	yes	—
31	C₂⁴×D₇₉	C₂³	1	1	yes	characteristic
32	C₂²×Dic₁₅₈	—	2	24	no	—
33	C₂²×Dic₁₅₈	C₂³	1	36	yes	—
34	C₂×Q₈×D₇₉	—	2	192	no	—
35	C₂×Q₈×D₇₉	C₂³	1	64	yes	complemented
36	C₂²×C₂²⋊D₇₉	Q₈	1	16	yes	direct product factor
37	C₂²×C₂²⋊D₇₉	C₂³	1	12	yes	—
38	C₂³×Dic₇₉	C₂³	1	3	yes	—
39	C₂³×Dic₇₉	C₂³	1	3	yes	—
40	C₂³×Dic₇₉	C₂³	1	1	yes	characteristic
41	C₂²×C₄×D₇₉	—	2	24	no	—
42	C₂²×C₄×D₇₉	C₂³	1	36	yes	—
43	#14579159	C₂³	1	192	yes	complemented
44	#14579140	C₂³	1	192	yes	complemented
45	#14579137	C₂³	1	192	yes	complemented
46	Q₈×Dic₇₉	C₂³	1	64	yes	complemented
47	C₄×C₂²⋊D₇₉	C₂³	1	192	yes	—
48	C₂×C₄⋊Dic₇₉	C₂³	1	36	yes	—
49	C₂×Dic₇₉⋊C₄	C₂³	1	36	yes	—
50	C₂×Dic₇₉⋊C₄	C₂³	1	72	yes	—
51	C₂×C₂²⋊Dic₇₉	C₂³	1	36	yes	—
52	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	36	yes	—
53	C₂×C₄×Dic₇₉	C₂³	1	36	yes	—
54	C₂⁵×C₇₉	C₂³	1	1	yes	characteristic
55	C₂²×Q₈×C₇₉	—	2	192	no	—
56	C₂²×Q₈×C₇₉	—	2	24	no	—
57	C₂²×Q₈×C₇₉	D₄	1	16	yes	complemented
58	C₂²×Q₈×C₇₉	C₂³	1	36	yes	—
59	C₂²×Q₈×C₇₉	C₂³	1	12	yes	—
60	C₂²×Q₈×C₇₉	C₂³	1	64	yes	complemented
61	C₂³×C₄×C₇₉	—	2	24	no	—
62	C₂³×C₄×C₇₉	C₂³	1	3	yes	—
63	C₂³×C₄×C₇₉	C₂³	1	36	yes	—
64	C₂³×C₄×C₇₉	C₂³	1	3	yes	—
65	C₂³×D₇₉	—	2	4	no	—
66	C₂³×D₇₉	—	2	4	no	—
67	C₂³×D₇₉	C₂×Q₈	1	8	yes	complemented
68	C₂³×D₇₉	C₂⁴	1	6	yes	—
69	C₂×Dic₁₅₈	—	2	144	no	—
70	C₂×Dic₁₅₈	C₂⁴	1	48	yes	—
71	Q₈×D₇₉	—	2	256	no	—
72	C₂×C₂²⋊D₇₉	C₂×Q₈	1	96	yes	direct product factor
73	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
74	C₂²×Dic₇₉	—	2	12	no	—
75	C₂²×Dic₇₉	—	2	12	no	—
76	C₂²×Dic₇₉	C₂×Q₈	1	8	yes	complemented
77	C₂²×Dic₇₉	C₂⁴	1	18	yes	—
78	C₂²×Dic₇₉	C₂⁴	1	18	yes	—
79	C₂²×Dic₇₉	C₂⁴	1	6	yes	—
80	C₂×C₄×D₇₉	—	2	144	no	—
81	C₂×C₄×D₇₉	C₂⁴	1	48	yes	—
82	C₄⋊Dic₇₉	C₂⁴	1	48	yes	—
83	Dic₇₉⋊C₄	C₂⁴	1	48	yes	—
84	Dic₇₉⋊C₄	C₂⁴	1	96	yes	—
85	C₂²⋊Dic₇₉	C₂⁴	1	48	yes	—
86	(C₂×D₇₉)⋊C₄	C₂⁴	1	48	yes	—
87	C₄×Dic₇₉	C₂⁴	1	48	yes	—
88	C₂⁴×C₇₉	—	2	4	no	—
89	C₂⁴×C₇₉	—	2	4	no	—
90	C₂⁴×C₇₉	C₂×Q₈	1	8	yes	complemented
91	C₂⁴×C₇₉	C₂⁴	1	6	yes	—
92	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
93	C₂×Q₈×C₇₉	—	2	256	no	—
94	C₂×Q₈×C₇₉	—	2	144	no	—
95	C₂×Q₈×C₇₉	C₂×D₄	1	96	yes	complemented
96	C₂×Q₈×C₇₉	C₂⁴	1	48	yes	—
97	C₂×Q₈×C₇₉	C₂⁴	1	16	yes	—
98	C₂²×C₄×C₇₉	—	2	12	no	—
99	C₂²×C₄×C₇₉	—	2	144	no	—
100	C₂²×C₄×C₇₉	C₂×D₄	1	24	yes	—
101	C₂²×C₄×C₇₉	C₂⁴	1	18	yes	—
102	C₂²×C₄×C₇₉	C₂⁴	1	48	yes	—
103	C₂²×C₄×C₇₉	C₂⁴	1	18	yes	—
104	C₂³×C₇₉	—	2	32	no	—
105	C₂³×C₇₉	—	2	12	no	—
106	C₂³×C₇₉	—	2	12	no	—
107	C₂³×C₇₉	C₂²×D₄	1	4	yes	—
108	C₂³×C₇₉	C₂²×Q₈	1	4	yes	—
109	C₂³×C₇₉	C₂²×Q₈	1	24	yes	complemented
110	C₂³×C₇₉	2₋¹⁺⁴	1	4	yes	—
111	C₂³×C₇₉	C₂⁵	1	4	yes	—
112	C₂³×C₇₉	C₂⁵	1	3	yes	—
113	C₂²×D₇₉	—	2	32	no	—
114	C₂²×D₇₉	—	2	12	no	—
115	C₂²×D₇₉	—	2	12	no	—
116	C₂²×D₇₉	C₂²×Q₈	1	24	yes	complemented
117	C₂²×D₇₉	C₂⁵	1	4	yes	—
118	Q₈×C₇₉	—	2	96	no	—
119	Q₈×C₇₉	C₂²×D₄	1	64	yes	complemented
120	C₂×C₄×C₇₉	—	2	36	no	—
121	C₂×C₄×C₇₉	—	2	96	no	—
122	C₂×C₄×C₇₉	C₂²×D₄	1	72	yes	—
123	C₂×C₄×C₇₉	C₂⁵	1	12	yes	—
124	C₂×C₄×C₇₉	C₂⁵	1	12	yes	—
125	C₂²⋊D₇₉	C₂²×Q₈	1	64	yes	direct product factor
126	C₂×Dic₇₉	—	2	36	no	—
127	C₂×Dic₇₉	—	2	36	no	—
128	C₂×Dic₇₉	C₂²×Q₈	1	24	yes	complemented
129	C₂×Dic₇₉	C₂⁵	1	12	yes	—
130	C₂×Dic₇₉	C₂⁵	1	12	yes	—
131	C₂×Dic₇₉	C₂⁵	1	4	yes	—
132	C₄×D₇₉	—	2	96	no	—
133	Dic₁₅₈	—	2	96	no	—
134	C₂²×C₇₉	—	2	4	no	—
135	C₂²×C₇₉	—	2	4	no	—
136	C₂²×C₇₉	—	2	48	no	—
137	C₂²×C₇₉	D₄×Q₈	1	16	yes	complemented
138	C₂²×C₇₉	C₂³×D₄	1	6	yes	—
139	C₂²×C₇₉	C₂³×Q₈	1	6	yes	—
140	C₂²×C₇₉	C₂³×Q₈	1	8	yes	complemented
141	C₂²×C₇₉	C₂×2₋¹⁺⁴	1	6	yes	—
142	C₂²×C₇₉	C₂⁶	1	1	yes	characteristic
143	C₂×D₇₉	—	2	4	no	—
144	C₂×D₇₉	—	2	4	no	—
145	C₂×D₇₉	—	2	48	no	—
146	C₂×D₇₉	C₂³×Q₈	1	8	yes	complemented
147	C₄×C₇₉	—	2	12	no	—
148	C₄×C₇₉	C₂³×D₄	1	24	yes	—
149	Dic₇₉	—	2	12	no	—
150	Dic₇₉	—	2	12	no	—
151	Dic₇₉	C₂³×Q₈	1	8	yes	complemented
152	C₂²×D₄×Q₈	—	79	1	no	maximal, Sylow
153	C₂×C₇₉	—	2	8	no	—
154	C₂×C₇₉	C₂×D₄×Q₈	1	12	yes	complemented
155	C₂×C₇₉	C₂⁴×D₄	1	1	yes	characteristic
156	C₂×C₇₉	C₂⁴×Q₈	1	1	yes	characteristic
157	C₂×C₇₉	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
158	D₇₉	—	2	8	no	—
159	C₂⁴×Q₈	—	79	1	no	—
160	C₂⁴×Q₈	D₇₉	1	1	yes	characteristic, complemented
161	C₂×D₄×Q₈	—	79	48	no	—
162	C₂²×C₄⋊Q₈	—	79	3	no	—
163	C₂²×C₂²⋊Q₈	—	79	3	no	—
164	C₂²×C₂²⋊Q₈	—	79	3	no	—
165	C₂²×C₄×Q₈	—	79	1	no	—
166	C₂²×C₄×D₄	—	79	3	no	—
167	C₇₉	C₂²×D₄×Q₈	1	1	yes	characteristic, complemented, Sylow
168	C₂³×Q₈	—	2	16	no	—
169	C₂³×Q₈	—	79	24	no	—
170	C₂³×Q₈	—	79	3	no	—
171	C₂³×Q₈	—	158	16	no	—
172	C₂³×Q₈	C₂×D₇₉	1	3	yes	—
173	C₂³×Q₈	C₂×D₇₉	1	1	yes	characteristic
174	C₂³×Q₈	C₂×D₇₉	1	24	yes	complemented
175	C₂³×D₄	—	79	1	no	—
176	C₂⁴×C₄	—	79	3	no	—
177	C₂⁴×C₄	C₂×D₇₉	1	3	yes	—
178	D₄×Q₈	—	79	256	no	—
179	C₂×C₄⋊Q₈	—	79	72	no	—
180	C₂×C₂²⋊Q₈	—	79	72	no	—
181	C₂×C₂²⋊Q₈	—	79	72	no	—
182	C₂×C₄×Q₈	—	79	24	no	—
183	C₂×C₄×D₄	—	79	72	no	—
184	C₂²×C₄⋊C₄	—	79	3	no	—
185	C₂²×C₄⋊C₄	—	79	3	no	—
186	C₂²×C₄⋊C₄	—	79	6	no	—
187	C₂²×C₂²⋊C₄	—	79	3	no	—
188	C₂²×C₂²⋊C₄	—	79	3	no	—
189	C₂²×C₄²	—	79	3	no	—
190	C₂⁵	—	79	1	no	—
191	C₂⁵	C₂²×D₇₉	1	1	yes	characteristic
192	C₂²×Q₈	—	2	192	no	—
193	C₂²×Q₈	—	2	24	no	—
194	C₂²×Q₈	—	79	64	no	—
195	C₂²×Q₈	—	79	36	no	—
196	C₂²×Q₈	—	158	192	no	—
197	C₂²×Q₈	—	158	24	no	—
198	C₂²×Q₈	C₂²⋊D₇₉	1	16	yes	direct product factor
199	C₂²×Q₈	C₂²×D₇₉	1	36	yes	—
200	C₂²×Q₈	C₂²×D₇₉	1	12	yes	—
201	C₂²×Q₈	C₂²×D₇₉	1	64	yes	complemented
202	C₂²×D₄	—	79	16	no	—
203	C₂²×D₄	—	79	12	no	—
204	C₂³×C₄	—	2	24	no	—
205	C₂³×C₄	—	79	1	no	—
206	C₂³×C₄	—	79	3	no	—
207	C₂³×C₄	—	79	3	no	—
208	C₂³×C₄	—	79	36	no	—
209	C₂³×C₄	—	158	24	no	—
210	C₂³×C₄	C₂²×D₇₉	1	36	yes	—
211	C₂³×C₄	C₂²×D₇₉	1	3	yes	—
212	C₂³×C₄	C₂²×D₇₉	1	3	yes	—
213	C₄⋊Q₈	—	79	192	no	—
214	C₂²⋊Q₈	—	79	192	no	—
215	C₂²⋊Q₈	—	79	192	no	—
216	C₄×Q₈	—	79	64	no	—
217	C₄×D₄	—	79	192	no	—
218	C₂×C₄⋊C₄	—	79	36	no	—
219	C₂×C₄⋊C₄	—	79	36	no	—
220	C₂×C₄⋊C₄	—	79	72	no	—
221	C₂×C₂²⋊C₄	—	79	36	no	—
222	C₂×C₂²⋊C₄	—	79	36	no	—
223	C₂×C₄²	—	79	36	no	—
224	C₂⁴	—	2	4	no	—
225	C₂⁴	—	2	4	no	—
226	C₂⁴	—	79	8	no	—
227	C₂⁴	—	79	6	no	—
228	C₂⁴	—	158	4	no	—
229	C₂⁴	—	158	4	no	—
230	C₂⁴	Q₈×D₇₉	1	8	yes	complemented
231	C₂⁴	C₂³×D₇₉	1	6	yes	—
232	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
233	C₂×Q₈	—	2	256	no	—
234	C₂×Q₈	—	2	144	no	—
235	C₂×Q₈	—	79	48	no	—
236	C₂×Q₈	—	158	256	no	—
237	C₂×Q₈	—	158	144	no	—
238	C₂×Q₈	C₂×C₂²⋊D₇₉	1	96	yes	direct product factor
239	C₂×Q₈	C₂³×D₇₉	1	48	yes	—
240	C₂×Q₈	C₂³×D₇₉	1	16	yes	—
241	C₂×D₄	—	79	96	no	—
242	C₂×D₄	—	79	16	no	—
243	C₂²×C₄	—	2	12	no	—
244	C₂²×C₄	—	2	144	no	—
245	C₂²×C₄	—	79	8	no	—
246	C₂²×C₄	—	79	6	no	—
247	C₂²×C₄	—	79	18	no	—
248	C₂²×C₄	—	79	18	no	—
249	C₂²×C₄	—	79	48	no	—
250	C₂²×C₄	—	158	12	no	—
251	C₂²×C₄	—	158	12	no	—
252	C₂²×C₄	—	158	144	no	—
253	C₂²×C₄	C₂×C₂²⋊D₇₉	1	24	yes	—
254	C₂²×C₄	C₂³×D₇₉	1	18	yes	—
255	C₂²×C₄	C₂³×D₇₉	1	48	yes	—
256	C₂²×C₄	C₂³×D₇₉	1	18	yes	—
257	C₄⋊C₄	—	79	48	no	—
258	C₄⋊C₄	—	79	96	no	—
259	C₄⋊C₄	—	79	48	no	—
260	C₂²⋊C₄	—	79	48	no	—
261	C₂²⋊C₄	—	79	48	no	—
262	C₄²	—	79	48	no	—
263	C₂³	—	2	12	no	—
264	C₂³	—	2	32	no	—
265	C₂³	—	2	12	no	—
266	C₂³	—	79	4	no	—
267	C₂³	—	79	24	no	—
268	C₂³	—	158	12	no	—
269	C₂³	—	158	32	no	—
270	C₂³	—	158	12	no	—
271	C₂³	C₂²×C₂²⋊D₇₉	1	4	yes	—
272	C₂³	C₂×Q₈×D₇₉	1	4	yes	—
273	C₂³	C₂×Q₈×D₇₉	1	24	yes	complemented
274	C₂³	#14579209	1	4	yes	—
275	C₂³	C₂⁴×D₇₉	1	4	yes	—
276	C₂³	C₂⁴×D₇₉	1	3	yes	—
277	Q₈	—	2	96	no	—
278	Q₈	—	158	96	no	—
279	Q₈	C₂²×C₂²⋊D₇₉	1	64	yes	direct product factor
280	D₄	—	79	64	no	—
281	C₂×C₄	—	2	36	no	—
282	C₂×C₄	—	2	96	no	—
283	C₂×C₄	—	79	4	no	—
284	C₂×C₄	—	79	24	no	—
285	C₂×C₄	—	79	12	no	—
286	C₂×C₄	—	79	12	no	—
287	C₂×C₄	—	158	36	no	—
288	C₂×C₄	—	158	36	no	—
289	C₂×C₄	—	158	96	no	—
290	C₂×C₄	C₂²×C₂²⋊D₇₉	1	72	yes	—
291	C₂×C₄	C₂⁴×D₇₉	1	12	yes	—
292	C₂×C₄	C₂⁴×D₇₉	1	12	yes	—
293	C₂²	—	2	48	no	—
294	C₂²	—	2	4	no	—
295	C₂²	—	2	4	no	—
296	C₂²	—	79	8	no	—
297	C₂²	—	158	48	no	—
298	C₂²	—	158	4	no	—
299	C₂²	—	158	4	no	—
300	C₂²	Q₈×C₂²⋊D₇₉	1	16	yes	direct product factor
301	C₂²	C₂³×C₂²⋊D₇₉	1	6	yes	—
302	C₂²	C₂²×Q₈×D₇₉	1	6	yes	—
303	C₂²	C₂²×Q₈×D₇₉	1	8	yes	complemented
304	C₂²	C₂×#14579209	1	6	yes	—
305	C₂²	C₂⁵×D₇₉	1	1	yes	characteristic
306	C₄	—	2	12	no	—
307	C₄	—	79	8	no	—
308	C₄	—	158	12	no	—
309	C₄	—	158	12	no	—
310	C₄	C₂³×C₂²⋊D₇₉	1	24	yes	—
311	C₂	—	2	8	no	—
312	C₂	—	158	8	no	—
313	C₂	C₂×Q₈×C₂²⋊D₇₉	1	12	yes	direct product factor
314	C₂	C₂⁴×C₂²⋊D₇₉	1	1	yes	characteristic
315	C₂	C₂³×Q₈×D₇₉	1	1	yes	characteristic
316	C₂	C₂²×#14579209	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂³×D₇₉
commutator, cosocle	C₂²×C₇₉	C₂⁶
Frattini	C₂²	C₂⁵×D₇₉
Fitting	C₂⁴×Q₈×C₇₉	C₂
socle	C₂⁴×C₇₉	C₂⁴
prime radical	C₂³×C₂²⋊D₇₉	C₂²
hypercenter	C₂⁴×Q₈	D₇₉
hypocenter	C₇₉	C₂²×D₄×Q₈
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂⁴ ◁ C₂⁴×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂³×Q₈×D₇₉	C₂	semidirect
2. C₂×Q₈×C₂²⋊D₇₉	C₂	direct (N × H)
3. C₂²×#14579159	C₂	semidirect
4. C₂²×#14579140	C₂	semidirect
5. C₂²×#14579137	C₂	semidirect
6. C₂²×Q₈×Dic₇₉	C₂	semidirect
8. C₂⁴×Q₈×C₇₉	C₂	semidirect
11. C₂²×Q₈×D₇₉	C₂²	semidirect
14. Q₈×C₂²⋊D₇₉	C₂²	direct (N × H)
15. C₂×#14579159	C₂²	semidirect
16. C₂×#14579140	C₂²	semidirect
17. C₂×#14579137	C₂²	semidirect
18. C₂×Q₈×Dic₇₉	C₂²	semidirect
29. C₂³×Q₈×C₇₉	C₂²	semidirect
35. C₂×Q₈×D₇₉	C₂³	semidirect
36. C₂²×C₂²⋊D₇₉	Q₈	direct (N × H)
43. #14579159	C₂³	semidirect
44. #14579140	C₂³	semidirect
45. #14579137	C₂³	semidirect
46. Q₈×Dic₇₉	C₂³	semidirect
57. C₂²×Q₈×C₇₉	D₄	semidirect
60. C₂²×Q₈×C₇₉	C₂³	semidirect
67. C₂³×D₇₉	C₂×Q₈	semidirect
72. C₂×C₂²⋊D₇₉	C₂×Q₈	direct (N × H)
76. C₂²×Dic₇₉	C₂×Q₈	semidirect
90. C₂⁴×C₇₉	C₂×Q₈	semidirect
95. C₂×Q₈×C₇₉	C₂×D₄	semidirect
109. C₂³×C₇₉	C₂²×Q₈	semidirect
116. C₂²×D₇₉	C₂²×Q₈	semidirect
119. Q₈×C₇₉	C₂²×D₄	semidirect
125. C₂²⋊D₇₉	C₂²×Q₈	direct (N × H)
128. C₂×Dic₇₉	C₂²×Q₈	semidirect
137. C₂²×C₇₉	D₄×Q₈	semidirect
140. C₂²×C₇₉	C₂³×Q₈	semidirect
146. C₂×D₇₉	C₂³×Q₈	semidirect
151. Dic₇₉	C₂³×Q₈	semidirect
154. C₂×C₇₉	C₂×D₄×Q₈	semidirect
160. C₂⁴×Q₈	D₇₉	semidirect
167. C₇₉	C₂²×D₄×Q₈	semidirect
174. C₂³×Q₈	C₂×D₇₉	semidirect
198. C₂²×Q₈	C₂²⋊D₇₉	direct (N × H)
201. C₂²×Q₈	C₂²×D₇₉	semidirect
230. C₂⁴	Q₈×D₇₉	semidirect
238. C₂×Q₈	C₂×C₂²⋊D₇₉	direct (N × H)
273. C₂³	C₂×Q₈×D₇₉	semidirect
279. Q₈	C₂²×C₂²⋊D₇₉	direct (N × H)
300. C₂²	Q₈×C₂²⋊D₇₉	direct (N × H)
303. C₂²	C₂²×Q₈×D₇₉	semidirect
313. C₂	C₂×Q₈×C₂²⋊D₇₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×Q₈×D₇₉	2
C₂×Q₈×C₂²⋊D₇₉	2
C₂²×#14579159	2
C₂²×#14579140	2
C₂²×#14579137	2
C₂²×Q₈×Dic₇₉	2
C₂²×C₄×C₂²⋊D₇₉	2
C₂⁴×Q₈×C₇₉	2
C₂²×D₄×Q₈	79

Subgroups — C22×Q8×C22⋊D79 #35195183

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×Q₈×C₂²⋊D₇₉ #35195183