Subgroups — Q₈×#14579120 #34447698

Order 20224.

2434 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23766357	C₂	1	6	yes	maximal, complemented
2	Q₈×C₄⋊Dic₇₉	C₂	1	2	yes	maximal, complemented
3	#23766277	C₂	1	6	yes	maximal
4	Q₈×C₂²⋊Dic₇₉	C₂	1	2	yes	maximal
5	#23765878	C₂	1	6	yes	maximal, complemented
6	#23765807	C₂	1	3	yes	maximal
7	C₄×Q₈×Dic₇₉	C₂	1	2	yes	maximal, complemented
8	C₄×#14579120	C₂	1	3	yes	maximal
9	C₂²×C₄×Q₈×C₇₉	C₂	1	1	yes	maximal, characteristic
10	C₂×Q₈×Dic₇₉	C₂²	1	4	yes	—
11	C₂×#14579120	C₂²	1	3	yes	—
12	C₂×#14579120	C₂²	1	1	yes	characteristic
13	#19098470	C₂²	1	12	yes	—
14	#19098462	C₂²	1	12	yes	—
15	#19098449	C₂²	1	24	yes	—
16	#19098433	C₂²	1	6	yes	—
17	#19098429	C₂²	1	6	yes	—
18	#19098423	C₂²	1	6	yes	—
19	#19098423	C₂²	1	6	yes	—
20	C₄⋊C₄×Dic₇₉	C₂²	1	12	yes	—
21	C₄×C₄⋊Dic₇₉	C₂²	1	6	yes	—
22	C₄×C₄⋊Dic₇₉	C₂²	1	6	yes	—
23	C₄×C₄⋊Dic₇₉	C₂²	1	6	yes	—
24	C₄×C₄⋊Dic₇₉	C₂²	1	6	yes	—
25	C₄×C₂²⋊Dic₇₉	C₂²	1	6	yes	—
26	C₄×C₂²⋊Dic₇₉	C₂²	1	6	yes	—
27	#19098409	C₂²	1	6	yes	—
28	C₄²×Dic₇₉	C₂²	1	6	yes	—
29	C₂³×Q₈×C₇₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₇₉	C₄	1	16	yes	complemented
31	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₇₉	C₂²	1	3	yes	—
33	C₂×C₄×Q₈×C₇₉	C₂²	1	3	yes	—
34	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
35	C₂²×C₄⋊C₄×C₇₉	C₂²	1	3	yes	—
36	C₂²×C₄²×C₇₉	C₂²	1	3	yes	—
37	Q₈×Dic₇₉	—	2	16	no	—
38	#14579120	—	2	12	no	—
39	#14579120	Q₈	1	8	yes	direct product factor
40	C₂×C₄⋊Dic₇₉	C₂³	1	6	yes	—
41	C₂×C₄⋊Dic₇₉	C₂³	1	12	yes	—
42	C₂×C₄⋊Dic₇₉	C₂³	1	12	yes	—
43	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
44	C₂×C₂²⋊Dic₇₉	C₂³	1	6	yes	—
45	C₂×C₂²⋊Dic₇₉	C₂³	1	2	yes	—
46	C₂×C₄×Dic₇₉	C₂³	1	6	yes	—
47	C₂×C₄×Dic₇₉	C₂³	1	12	yes	—
48	C₂×C₄×Dic₇₉	C₂³	1	12	yes	—
49	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
50	C₇₉⋊#95	C₂³	1	12	yes	—
51	C₇₉⋊#95	C₂³	1	12	yes	—
52	C₇₉⋊#95	C₂³	1	12	yes	—
53	C₇₉⋊#95	C₂³	1	12	yes	—
54	C₂²×Q₈×C₇₉	—	2	8	no	—
55	C₂²×Q₈×C₇₉	C₂×C₄	1	8	yes	—
56	C₂²×Q₈×C₇₉	C₂³	1	3	yes	—
57	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₇₉	C₂³	1	3	yes	—
59	C₂³×C₄×C₇₉	C₂³	1	3	yes	—
60	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
61	C₄×Q₈×C₇₉	C₂×C₄	1	24	yes	—
62	C₄×Q₈×C₇₉	C₂×C₄	1	24	yes	—
63	C₄×Q₈×C₇₉	C₂×C₄	1	8	yes	—
64	C₄×Q₈×C₇₉	C₂×C₄	1	8	yes	—
65	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	24	yes	—
66	C₂×C₄⋊C₄×C₇₉	C₂³	1	3	yes	—
67	C₂×C₄⋊C₄×C₇₉	C₂³	1	6	yes	—
68	C₂×C₄⋊C₄×C₇₉	C₂³	1	3	yes	—
69	C₂×C₄²×C₇₉	C₂×C₄	1	24	yes	—
70	C₂×C₄²×C₇₉	C₂³	1	3	yes	—
71	C₂×C₄²×C₇₉	C₂³	1	3	yes	—
72	C₂×C₄²×C₇₉	C₂³	1	3	yes	—
73	C₂×C₄²×C₇₉	C₂³	1	3	yes	—
74	C₂²×Dic₇₉	C₂⁴	1	12	yes	—
75	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
76	C₄⋊Dic₇₉	—	2	12	no	—
77	C₄⋊Dic₇₉	—	2	24	no	—
78	C₄⋊Dic₇₉	—	4	12	no	—
79	C₄⋊Dic₇₉	C₂×Q₈	1	8	yes	complemented
80	C₂²⋊Dic₇₉	—	2	12	no	—
81	C₂²⋊Dic₇₉	C₂×Q₈	1	8	yes	—
82	C₄×Dic₇₉	—	2	12	no	—
83	C₄×Dic₇₉	—	2	24	no	—
84	C₄×Dic₇₉	—	4	12	no	—
85	C₄×Dic₇₉	C₂×Q₈	1	8	yes	complemented
86	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
87	C₂×Q₈×C₇₉	—	2	32	no	—
88	C₂×Q₈×C₇₉	—	2	12	no	—
89	C₂×Q₈×C₇₉	C₂²×C₄	1	12	yes	—
90	C₂×Q₈×C₇₉	C₂²×C₄	1	4	yes	—
91	C₂×Q₈×C₇₉	#41	1	8	yes	—
92	C₂²×C₄×C₇₉	—	2	12	no	—
93	C₂²×C₄×C₇₉	—	4	6	no	—
94	C₂²×C₄×C₇₉	C₂²×C₄	1	12	yes	—
95	C₂²×C₄×C₇₉	C₂²×C₄	1	12	yes	—
96	C₂²×C₄×C₇₉	C₂²×C₄	1	4	yes	—
97	C₂²×C₄×C₇₉	C₂×Q₈	1	4	yes	—
98	C₂²×C₄×C₇₉	#41	1	4	yes	—
99	C₂²×C₄×C₇₉	C₂⁴	1	3	yes	—
100	C₂²×C₄×C₇₉	C₂⁴	1	3	yes	—
101	C₂²×C₄×C₇₉	C₂⁴	1	3	yes	—
102	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
103	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
104	C₂²×C₄×C₇₉	C₂⁴	1	3	yes	—
105	C₄⋊C₄×C₇₉	C₂²×C₄	1	24	yes	—
106	C₄⋊C₄×C₇₉	C₂²×C₄	1	12	yes	—
107	C₄⋊C₄×C₇₉	C₂²×C₄	1	12	yes	—
108	C₄²×C₇₉	C₂²×C₄	1	12	yes	—
109	C₄²×C₇₉	C₂²×C₄	1	12	yes	—
110	C₄²×C₇₉	C₂²×C₄	1	12	yes	—
111	C₄²×C₇₉	C₂²×C₄	1	12	yes	—
112	C₂³×C₇₉	—	2	2	no	—
113	C₂³×C₇₉	—	2	2	no	—
114	C₂³×C₇₉	C₂³×C₄	1	2	yes	—
115	C₂³×C₇₉	C₂²×Q₈	1	2	yes	—
116	C₂³×C₇₉	C₂×#41	1	2	yes	—
117	C₂³×C₇₉	C₂⁵	1	1	yes	characteristic
118	Q₈×C₇₉	—	2	24	no	—
119	Q₈×C₇₉	#117	1	16	yes	complemented
120	C₂×C₄×C₇₉	—	2	6	no	—
121	C₂×C₄×C₇₉	—	2	6	no	—
122	C₂×C₄×C₇₉	—	2	6	no	—
123	C₂×C₄×C₇₉	—	2	24	no	—
124	C₂×C₄×C₇₉	—	4	12	no	—
125	C₂×C₄×C₇₉	C₄×Q₈	1	16	yes	complemented
126	C₂×C₄×C₇₉	C₂³×C₄	1	6	yes	—
127	C₂×C₄×C₇₉	C₂³×C₄	1	6	yes	—
128	C₂×C₄×C₇₉	C₂³×C₄	1	6	yes	—
129	C₂×C₄×C₇₉	C₂³×C₄	1	6	yes	—
130	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
131	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
132	C₂×C₄×C₇₉	C₂²×Q₈	1	2	yes	—
133	C₂×C₄×C₇₉	C₂²×Q₈	1	2	yes	—
134	C₂×C₄×C₇₉	C₂×#41	1	12	yes	—
135	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
136	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
137	C₂×Dic₇₉	—	2	4	no	—
138	C₂×Dic₇₉	—	2	4	no	—
139	C₂×Dic₇₉	—	2	12	no	—
140	C₂×Dic₇₉	—	2	12	no	—
141	C₂×Dic₇₉	—	2	12	no	—
142	C₂×Dic₇₉	C₂²×Q₈	1	8	yes	—
143	C₂²×C₇₉	—	2	2	no	—
144	C₂²×C₇₉	—	2	2	no	—
145	C₂²×C₇₉	—	2	4	no	—
146	C₂²×C₇₉	—	2	4	no	—
147	C₂²×C₇₉	C₂×C₄×Q₈	1	4	yes	—
148	C₂²×C₇₉	C₂⁴×C₄	1	1	yes	characteristic
149	C₂²×C₇₉	C₂³×Q₈	1	1	yes	characteristic
150	C₂²×C₇₉	C₂²×#41	1	2	yes	—
151	C₂²×C₇₉	C₂²×#41	1	1	yes	characteristic
152	C₂²×C₇₉	#585	1	2	yes	—
153	C₄×C₇₉	—	2	6	no	—
154	C₄×C₇₉	—	2	6	no	—
155	C₄×C₇₉	—	2	6	no	—
156	C₄×C₇₉	C₂×#117	1	12	yes	—
157	C₄×C₇₉	C₂×C₄×Q₈	1	4	yes	—
158	C₄×C₇₉	C₂×C₄×Q₈	1	4	yes	—
159	Dic₇₉	—	2	8	no	—
160	Dic₇₉	—	4	12	no	—
161	Q₈×#117	—	79	1	no	maximal, Sylow
162	C₂×C₇₉	—	2	4	no	—
163	C₂×C₇₉	C₂²×#117	1	1	yes	characteristic
164	C₂×C₇₉	C₂²×C₄×Q₈	1	1	yes	characteristic
165	C₂×C₇₉	#3428	1	1	yes	characteristic
166	C₂×C₇₉	Q₈×#41	1	2	yes	—
167	C₂×C₇₉	#3480	1	2	yes	—
168	C₂²×C₄×Q₈	D₇₉	1	1	yes	characteristic
169	#2355	—	79	6	no	—
170	Q₈×C₄⋊C₄	—	79	2	no	—
171	#2345	—	79	6	no	—
172	Q₈×C₂²⋊C₄	—	79	2	no	—
173	#2295	—	79	6	no	—
174	#2285	—	79	3	no	—
175	C₄²×Q₈	—	79	2	no	—
176	C₄×#117	—	79	3	no	—
177	C₇₉	Q₈×#117	1	1	yes	characteristic, complemented, Sylow
178	C₂³×Q₈	C₂×D₇₉	1	1	yes	characteristic
179	C₂×C₄×Q₈	—	79	4	no	—
180	C₂×C₄×Q₈	Dic₇₉	1	16	yes	complemented
181	C₂×C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic
182	C₂×C₄×Q₈	C₂×D₇₉	1	3	yes	—
183	C₂×C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic
184	C₂×C₄×Q₈	C₂×D₇₉	1	3	yes	—
185	C₂×#117	—	79	1	no	—
186	C₂×#117	—	79	3	no	—
187	C₂²×C₄⋊C₄	C₂×D₇₉	1	3	yes	—
188	C₂²×C₄²	C₂×D₇₉	1	3	yes	—
189	#391	—	79	12	no	—
190	#389	—	79	12	no	—
191	#387	—	79	24	no	—
192	#384	—	79	6	no	—
193	#382	—	79	6	no	—
194	#380	—	79	6	no	—
195	#380	—	79	6	no	—
196	C₄×C₄⋊C₄	—	79	12	no	—
197	C₄×C₄⋊C₄	—	79	6	no	—
198	C₄×C₄⋊C₄	—	79	6	no	—
199	C₄×C₄⋊C₄	—	79	6	no	—
200	C₄×C₄⋊C₄	—	79	6	no	—
201	C₄×C₂²⋊C₄	—	79	6	no	—
202	C₄×C₂²⋊C₄	—	79	6	no	—
203	#376	—	79	6	no	—
204	C₄³	—	79	6	no	—
205	C₂²×Q₈	—	2	8	no	—
206	C₂²×Q₈	C₂×Dic₇₉	1	8	yes	—
207	C₂²×Q₈	C₂²×D₇₉	1	3	yes	—
208	C₂²×Q₈	C₂²×D₇₉	1	1	yes	characteristic
209	C₂³×C₄	C₂²×D₇₉	1	3	yes	—
210	C₂³×C₄	C₂²×D₇₉	1	3	yes	—
211	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
212	C₄×Q₈	—	158	16	no	—
213	C₄×Q₈	C₂×Dic₇₉	1	24	yes	—
214	C₄×Q₈	C₂×Dic₇₉	1	24	yes	—
215	C₄×Q₈	C₂×Dic₇₉	1	8	yes	—
216	C₄×Q₈	C₂×Dic₇₉	1	8	yes	—
217	#117	—	79	8	no	—
218	#117	—	158	12	no	—
219	C₂×C₄⋊C₄	—	79	12	no	—
220	C₂×C₄⋊C₄	—	79	2	no	—
221	C₂×C₄⋊C₄	—	79	6	no	—
222	C₂×C₄⋊C₄	—	79	12	no	—
223	C₂×C₄⋊C₄	C₂×Dic₇₉	1	24	yes	—
224	C₂×C₄⋊C₄	C₂²×D₇₉	1	3	yes	—
225	C₂×C₄⋊C₄	C₂²×D₇₉	1	6	yes	—
226	C₂×C₄⋊C₄	C₂²×D₇₉	1	3	yes	—
227	C₂×C₂²⋊C₄	—	79	2	no	—
228	C₂×C₂²⋊C₄	—	79	6	no	—
229	C₂×C₄²	—	79	12	no	—
230	C₂×C₄²	—	79	2	no	—
231	C₂×C₄²	—	79	12	no	—
232	C₂×C₄²	—	79	6	no	—
233	C₂×C₄²	C₂×Dic₇₉	1	24	yes	—
234	C₂×C₄²	C₂²×D₇₉	1	3	yes	—
235	C₂×C₄²	C₂²×D₇₉	1	3	yes	—
236	C₂×C₄²	C₂²×D₇₉	1	3	yes	—
237	C₂×C₄²	C₂²×D₇₉	1	3	yes	—
238	#95	—	79	12	no	—
239	#95	—	79	12	no	—
240	#95	—	79	12	no	—
241	#95	—	79	12	no	—
242	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
243	C₂×Q₈	—	2	32	no	—
244	C₂×Q₈	—	2	12	no	—
245	C₂×Q₈	C₂²×Dic₇₉	1	12	yes	—
246	C₂×Q₈	C₂²×Dic₇₉	1	4	yes	—
247	C₂×Q₈	#11929624	1	8	yes	—
248	C₂²×C₄	—	2	12	no	—
249	C₂²×C₄	—	4	6	no	—
250	C₂²×C₄	—	79	4	no	—
251	C₂²×C₄	—	79	12	no	—
252	C₂²×C₄	C₂²×Dic₇₉	1	12	yes	—
253	C₂²×C₄	C₂²×Dic₇₉	1	12	yes	—
254	C₂²×C₄	C₂²×Dic₇₉	1	4	yes	—
255	C₂²×C₄	Q₈×D₇₉	1	4	yes	—
256	C₂²×C₄	#11929625	1	4	yes	—
257	C₂²×C₄	C₂³×D₇₉	1	3	yes	—
258	C₂²×C₄	C₂³×D₇₉	1	3	yes	—
259	C₂²×C₄	C₂³×D₇₉	1	3	yes	—
260	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
261	C₂²×C₄	C₂³×D₇₉	1	3	yes	—
262	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
263	C₄⋊C₄	—	316	12	no	—
264	C₄⋊C₄	—	79	8	no	—
265	C₄⋊C₄	—	158	24	no	—
266	C₄⋊C₄	—	158	12	no	—
267	C₄⋊C₄	C₂²×Dic₇₉	1	24	yes	—
268	C₄⋊C₄	C₂²×Dic₇₉	1	12	yes	—
269	C₄⋊C₄	C₂²×Dic₇₉	1	12	yes	—
270	C₂²⋊C₄	—	79	8	no	—
271	C₂²⋊C₄	—	158	12	no	—
272	C₄²	—	316	12	no	—
273	C₄²	—	79	8	no	—
274	C₄²	—	158	24	no	—
275	C₄²	—	158	12	no	—
276	C₄²	C₂²×Dic₇₉	1	12	yes	—
277	C₄²	C₂²×Dic₇₉	1	12	yes	—
278	C₄²	C₂²×Dic₇₉	1	12	yes	—
279	C₄²	C₂²×Dic₇₉	1	12	yes	—
280	C₂³	—	2	2	no	—
281	C₂³	—	2	2	no	—
282	C₂³	C₂³×Dic₇₉	1	2	yes	—
283	C₂³	C₂×Q₈×D₇₉	1	2	yes	—
284	C₂³	C₂×#11929625	1	2	yes	—
285	C₂³	C₂⁴×D₇₉	1	1	yes	characteristic
286	Q₈	—	2	24	no	—
287	Q₈	#14579120	1	16	yes	direct product factor
288	C₂×C₄	—	2	6	no	—
289	C₂×C₄	—	2	6	no	—
290	C₂×C₄	—	2	6	no	—
291	C₂×C₄	—	2	24	no	—
292	C₂×C₄	—	4	12	no	—
293	C₂×C₄	—	79	8	no	—
294	C₂×C₄	—	158	12	no	—
295	C₂×C₄	—	158	12	no	—
296	C₂×C₄	—	158	12	no	—
297	C₂×C₄	—	158	4	no	—
298	C₂×C₄	—	158	4	no	—
299	C₂×C₄	Q₈×Dic₇₉	1	16	yes	complemented
300	C₂×C₄	C₂³×Dic₇₉	1	6	yes	—
301	C₂×C₄	C₂³×Dic₇₉	1	6	yes	—
302	C₂×C₄	C₂³×Dic₇₉	1	6	yes	—
303	C₂×C₄	C₂³×Dic₇₉	1	6	yes	—
304	C₂×C₄	C₂³×Dic₇₉	1	2	yes	—
305	C₂×C₄	C₂³×Dic₇₉	1	2	yes	—
306	C₂×C₄	C₂×Q₈×D₇₉	1	2	yes	—
307	C₂×C₄	C₂×Q₈×D₇₉	1	2	yes	—
308	C₂×C₄	C₂×#11929624	1	12	yes	—
309	C₂×C₄	C₂×#11929625	1	2	yes	—
310	C₂×C₄	C₂×#11929625	1	2	yes	—
311	C₂²	—	2	2	no	—
312	C₂²	—	2	2	no	—
313	C₂²	—	2	4	no	—
314	C₂²	—	2	4	no	—
315	C₂²	C₂×Q₈×Dic₇₉	1	4	yes	—
316	C₂²	C₂⁴×Dic₇₉	1	1	yes	characteristic
317	C₂²	C₂²×Q₈×D₇₉	1	1	yes	characteristic
318	C₂²	C₂²×#11929624	1	2	yes	—
319	C₂²	C₂²×#11929625	1	1	yes	characteristic
320	C₂²	#19099399	1	2	yes	—
321	C₄	—	2	6	no	—
322	C₄	—	2	6	no	—
323	C₄	—	2	6	no	—
324	C₄	—	316	12	no	—
325	C₄	—	158	8	no	—
326	C₄	C₂×#14579120	1	12	yes	—
327	C₄	C₂×Q₈×Dic₇₉	1	4	yes	—
328	C₄	C₂×Q₈×Dic₇₉	1	4	yes	—
329	C₂	—	2	4	no	—
330	C₂	C₂²×#14579120	1	1	yes	characteristic
331	C₂	C₂²×Q₈×Dic₇₉	1	1	yes	characteristic
332	C₂	#23776603	1	1	yes	characteristic
333	C₂	Q₈×#11929624	1	2	yes	—
334	C₂	#23776995	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂³×D₇₉
commutator	C₂²×C₇₉	C₂⁴×C₄
Frattini	C₂³	C₂⁴×D₇₉
Fitting	C₂²×C₄×Q₈×C₇₉	C₂
socle, cosocle	C₂³×C₇₉	C₂⁵
prime radical	C₂⁴×C₇₉	C₂⁴
hypercenter	C₂²×C₄×Q₈	D₇₉
hypocenter	C₇₉	Q₈×#117
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄×Q₈

Complements

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

N	H ≅ G/N	type
1. #23766357	C₂	semidirect
2. Q₈×C₄⋊Dic₇₉	C₂	semidirect
5. #23765878	C₂	semidirect
7. C₄×Q₈×Dic₇₉	C₂	semidirect
30. C₂×C₄×Q₈×C₇₉	C₄	semidirect
39. #14579120	Q₈	direct (N × H)
79. C₄⋊Dic₇₉	C₂×Q₈	semidirect
85. C₄×Dic₇₉	C₂×Q₈	semidirect
119. Q₈×C₇₉	#117	semidirect
125. C₂×C₄×C₇₉	C₄×Q₈	semidirect
177. C₇₉	Q₈×#117	semidirect
180. C₂×C₄×Q₈	Dic₇₉	semidirect
287. Q₈	#14579120	direct (N × H)
299. C₂×C₄	Q₈×Dic₇₉	semidirect

Maximal subgroups

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

subgroup	index
#23766357	2
Q₈×C₄⋊Dic₇₉	2
#23766277	2
Q₈×C₂²⋊Dic₇₉	2
#23765878	2
#23765807	2
C₄×Q₈×Dic₇₉	2
C₄×#14579120	2
C₂²×C₄×Q₈×C₇₉	2
Q₈×#117	79

Subgroups — Q8×#14579120 #34447698

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×#14579120 #34447698