Subgroups — C₂×#23777051 #35196436

Order 20224.

11254 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14579209	C₂	1	1	yes	maximal, characteristic, complemented
2	#23777051	C₂	1	32	yes	maximal, direct product factor
3	C₂×Q₈×C₂²⋊D₇₉	C₂	1	8	yes	maximal, complemented
4	C₂×#19099224	C₂	1	8	yes	maximal, complemented
5	C₂×#19099137	C₂	1	6	yes	maximal, complemented
6	C₂×#19099074	C₂	1	6	yes	maximal, complemented
7	C₂×#19099041	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂⁴×Q₈×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#14579209	—	2	16	no	—
10	C₂×#14579209	C₂²	1	16	yes	complemented
11	C₂²×#11929625	C₂²	1	4	yes	complemented
12	C₂²×#11929624	C₂²	1	6	yes	—
13	C₂²×Q₈×D₇₉	C₂²	1	4	yes	complemented
14	Q₈×C₂²⋊D₇₉	C₂²	1	128	yes	complemented
15	#19099224	C₂²	1	128	yes	complemented
16	#19099137	C₂²	1	96	yes	complemented
17	C₂×#14579159	C₂²	1	12	yes	complemented
18	C₂×#14579150	C₂²	1	12	yes	complemented
19	#19099074	C₂²	1	96	yes	complemented
20	C₂×#14579144	C₂²	1	12	yes	—
21	C₂×#14579140	C₂²	1	12	yes	—
22	C₂×#14579137	C₂²	1	24	yes	complemented
23	C₂×#14579135	C₂²	1	12	yes	—
24	C₂×#14579130	C₂²	1	4	yes	—
25	#19099041	C₂²	1	16	yes	complemented
26	C₂×Q₈×Dic₇₉	C₂²	1	8	yes	complemented
27	C₂×C₄×C₂²⋊D₇₉	C₂²	1	24	yes	—
28	C₂×#14579120	C₂²	1	6	yes	—
29	C₂³×Q₈×C₇₉	—	2	16	no	—
30	C₂³×Q₈×C₇₉	C₂²	1	8	yes	—
31	C₂³×Q₈×C₇₉	C₂²	1	3	yes	—
32	C₂³×Q₈×C₇₉	C₂²	1	1	yes	characteristic
33	C₂³×Q₈×C₇₉	C₂²	1	16	yes	complemented
34	C₂⁴×C₄×C₇₉	C₂²	1	3	yes	—
35	#14579209	—	2	128	no	—
36	C₂×#11929625	—	2	32	no	—
37	C₂×#11929625	C₂³	1	32	yes	complemented
38	C₂×#11929624	—	2	48	no	—
39	C₂×#11929624	C₂³	1	48	yes	—
40	C₂²×Dic₁₅₈	C₂³	1	6	yes	—
41	C₂×Q₈×D₇₉	—	2	32	no	—
42	C₂×Q₈×D₇₉	C₂³	1	32	yes	complemented
43	C₂²×D₃₁₆	C₂³	1	6	yes	—
44	C₂²×C₂²⋊D₇₉	C₂³	1	8	yes	—
45	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
46	C₂²×C₄×D₇₉	C₂³	1	12	yes	—
47	#14579159	C₂³	1	96	yes	complemented
48	#14579150	C₂³	1	96	yes	complemented
49	#14579144	C₂³	1	96	yes	—
50	#14579140	C₂³	1	96	yes	—
51	#14579137	C₂³	1	192	yes	complemented
52	#14579135	C₂³	1	96	yes	—
53	#14579130	C₂³	1	32	yes	—
54	Q₈×Dic₇₉	C₂³	1	64	yes	complemented
55	C₄×C₂²⋊D₇₉	C₂³	1	192	yes	—
56	#14579120	C₂³	1	48	yes	—
57	C₂×C₄⋊Dic₇₉	C₂³	1	12	yes	—
58	C₂×Dic₇₉⋊C₄	C₂³	1	24	yes	—
59	C₂×C₂²⋊Dic₇₉	C₂³	1	4	yes	—
60	C₂×C₂²⋊Dic₇₉	C₂³	1	8	yes	—
61	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	24	yes	—
62	C₂×C₄×Dic₇₉	C₂³	1	12	yes	—
63	C₂⁵×C₇₉	C₂³	1	1	yes	characteristic
64	C₂²×Q₈×C₇₉	—	2	64	no	—
65	C₂²×Q₈×C₇₉	—	2	128	no	—
66	C₂²×Q₈×C₇₉	—	2	24	no	—
67	C₂²×Q₈×C₇₉	D₄	1	16	yes	complemented
68	C₂²×Q₈×C₇₉	C₂³	1	24	yes	—
69	C₂²×Q₈×C₇₉	C₂³	1	64	yes	—
70	C₂²×Q₈×C₇₉	C₂³	1	12	yes	—
71	C₂²×Q₈×C₇₉	C₂³	1	4	yes	—
72	C₂²×Q₈×C₇₉	C₂³	1	8	yes	—
73	C₂³×C₄×C₇₉	—	2	24	no	—
74	C₂³×C₄×C₇₉	C₂³	1	12	yes	—
75	C₂³×C₄×C₇₉	C₂³	1	3	yes	—
76	C₂³×C₄×C₇₉	C₂³	1	24	yes	—
77	C₂³×C₄×C₇₉	C₂³	1	3	yes	—
78	C₂³×D₇₉	C₂⁴	1	4	yes	—
79	#11929625	—	2	128	no	—
80	#11929624	—	2	192	no	—
81	C₂×Dic₁₅₈	—	2	24	no	—
82	C₂×Dic₁₅₈	C₂⁴	1	24	yes	—
83	Q₈×D₇₉	—	2	128	no	—
84	C₂×D₃₁₆	—	2	24	no	—
85	C₂×D₃₁₆	C₂⁴	1	24	yes	—
86	C₂×C₂²⋊D₇₉	—	2	16	no	—
87	C₂×C₂²⋊D₇₉	—	2	32	no	—
88	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
89	C₂×C₂²⋊D₇₉	C₂⁴	1	32	yes	—
90	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
91	C₂²×Dic₇₉	C₂⁴	1	8	yes	—
92	C₂×C₄×D₇₉	—	2	48	no	—
93	C₂×C₄×D₇₉	C₂⁴	1	48	yes	—
94	C₄⋊Dic₇₉	C₂⁴	1	48	yes	—
95	Dic₇₉⋊C₄	C₂⁴	1	96	yes	—
96	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	—
97	C₂²⋊Dic₇₉	C₂⁴	1	32	yes	—
98	(C₂×D₇₉)⋊C₄	C₂⁴	1	96	yes	—
99	C₄×Dic₇₉	C₂⁴	1	48	yes	—
100	C₂⁴×C₇₉	—	2	4	no	—
101	C₂⁴×C₇₉	—	2	8	no	—
102	C₂⁴×C₇₉	C₂⁴	1	4	yes	—
103	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
104	C₂⁴×C₇₉	C₂⁴	1	2	yes	—
105	C₂×Q₈×C₇₉	—	2	256	no	—
106	C₂×Q₈×C₇₉	—	2	48	no	—
107	C₂×Q₈×C₇₉	—	2	96	no	—
108	C₂×Q₈×C₇₉	C₂×D₄	1	32	yes	—
109	C₂×Q₈×C₇₉	C₂×D₄	1	64	yes	complemented
110	C₂×Q₈×C₇₉	C₂⁴	1	48	yes	—
111	C₂×Q₈×C₇₉	C₂⁴	1	16	yes	—
112	C₂²×C₄×C₇₉	—	2	12	no	—
113	C₂²×C₄×C₇₉	—	2	48	no	—
114	C₂²×C₄×C₇₉	—	2	96	no	—
115	C₂²×C₄×C₇₉	C₂×D₄	1	24	yes	—
116	C₂²×C₄×C₇₉	C₂⁴	1	6	yes	—
117	C₂²×C₄×C₇₉	C₂⁴	1	48	yes	—
118	C₂²×C₄×C₇₉	C₂⁴	1	12	yes	—
119	C₂²×C₄×C₇₉	C₂⁴	1	6	yes	—
120	C₂²×C₄×C₇₉	C₂⁴	1	12	yes	—
121	C₂³×C₇₉	—	2	32	no	—
122	C₂³×C₇₉	—	2	8	no	—
123	C₂³×C₇₉	—	2	4	no	—
124	C₂³×C₇₉	—	2	4	no	—
125	C₂³×C₇₉	—	2	4	no	—
126	C₂³×C₇₉	—	2	16	no	—
127	C₂³×C₇₉	C₂²×D₄	1	4	yes	—
128	C₂³×C₇₉	2₋¹⁺⁴	1	8	yes	complemented
129	C₂³×C₇₉	C₂⁵	1	2	yes	—
130	C₂³×C₇₉	C₂⁵	1	4	yes	—
131	C₂³×C₇₉	C₂⁵	1	1	yes	characteristic
132	C₂²×D₇₉	—	2	8	no	—
133	C₂²×D₇₉	—	2	16	no	—
134	C₂²×D₇₉	C₂⁵	1	8	yes	—
135	Q₈×C₇₉	—	2	96	no	—
136	Q₈×C₇₉	C₂²×D₄	1	64	yes	—
137	C₂×C₄×C₇₉	—	2	24	no	—
138	C₂×C₄×C₇₉	—	2	12	no	—
139	C₂×C₄×C₇₉	—	2	96	no	—
140	C₂×C₄×C₇₉	C₂²×D₄	1	24	yes	—
141	C₂×C₄×C₇₉	C₂²×D₄	1	48	yes	—
142	C₂×C₄×C₇₉	C₂⁵	1	12	yes	—
143	C₂×C₄×C₇₉	C₂⁵	1	12	yes	—
144	C₂²⋊D₇₉	—	2	32	no	—
145	C₂²⋊D₇₉	—	2	64	no	—
146	C₂×Dic₇₉	—	2	8	no	—
147	C₂×Dic₇₉	—	2	16	no	—
148	C₂×Dic₇₉	C₂⁵	1	16	yes	—
149	C₂×Dic₇₉	C₂⁵	1	8	yes	—
150	D₃₁₆	—	2	48	no	—
151	C₄×D₇₉	—	2	96	no	—
152	Dic₁₅₈	—	2	48	no	—
153	C₂²×C₇₉	—	2	32	no	—
154	C₂²×C₇₉	—	2	4	no	—
155	C₂²×C₇₉	—	2	4	no	—
156	C₂²×C₇₉	—	2	4	no	—
157	C₂²×C₇₉	—	2	8	no	—
158	C₂²×C₇₉	—	2	16	no	—
159	C₂²×C₇₉	C₂³×D₄	1	4	yes	—
160	C₂²×C₇₉	C₂³×D₄	1	2	yes	—
161	C₂²×C₇₉	C₂×2₋¹⁺⁴	1	4	yes	—
162	C₂²×C₇₉	C₂×2₋¹⁺⁴	1	8	yes	complemented
163	C₂²×C₇₉	C₂⁶	1	1	yes	characteristic
164	C₂×D₇₉	—	2	8	no	—
165	C₂×D₇₉	—	2	16	no	—
166	C₂×D₇₉	—	4	16	no	—
167	C₄×C₇₉	—	2	12	no	—
168	C₄×C₇₉	C₂³×D₄	1	24	yes	—
169	Dic₇₉	—	2	8	no	—
170	Dic₇₉	—	2	16	no	—
171	C₂×#3486	—	79	1	no	maximal, Sylow
172	C₂×C₇₉	—	2	4	no	—
173	C₂×C₇₉	—	2	8	no	—
174	C₂×C₇₉	#3486	1	4	yes	complemented
175	C₂×C₇₉	C₂⁴×D₄	1	1	yes	characteristic
176	C₂×C₇₉	C₂²×2₋¹⁺⁴	1	2	yes	—
177	D₇₉	—	4	8	no	—
178	C₂²×2₋¹⁺⁴	—	79	1	no	—
179	C₂⁴×Q₈	D₇₉	1	1	yes	characteristic, complemented
180	#3486	—	79	32	no	—
181	C₂×D₄×Q₈	—	79	8	no	—
182	C₂×#548	—	79	8	no	—
183	C₂×#536	—	79	6	no	—
184	C₂×#525	—	79	6	no	—
185	C₂×#519	—	79	1	no	—
186	C₇₉	C₂×#3486	1	1	yes	characteristic, complemented, Sylow
187	C₂×2₋¹⁺⁴	—	79	16	no	—
188	C₂×2₋¹⁺⁴	—	158	16	no	—
189	C₂²×#41	—	79	4	no	—
190	C₂²×#41	—	79	6	no	—
191	C₂³×Q₈	—	2	16	no	—
192	C₂³×Q₈	—	79	4	no	—
193	C₂³×Q₈	C₂×D₇₉	1	3	yes	—
194	C₂³×Q₈	C₂×D₇₉	1	8	yes	—
195	C₂³×Q₈	C₂×D₇₉	1	1	yes	characteristic
196	C₂³×Q₈	C₂×D₇₉	1	16	yes	complemented
197	C₂⁴×C₄	C₂×D₇₉	1	3	yes	—
198	D₄×Q₈	—	79	128	no	—
199	#548	—	79	128	no	—
200	#536	—	79	96	no	—
201	C₂×C₄⋊Q₈	—	79	12	no	—
202	C₂×#124	—	79	12	no	—
203	#525	—	79	96	no	—
204	C₂×#123	—	79	12	no	—
205	C₂×C₂²⋊Q₈	—	79	24	no	—
206	C₂×C₂²⋊Q₈	—	79	12	no	—
207	C₂×#121	—	79	12	no	—
208	C₂×#120	—	79	4	no	—
209	#519	—	79	16	no	—
210	C₂×C₄×Q₈	—	79	8	no	—
211	C₂×C₄×D₄	—	79	24	no	—
212	C₂×#117	—	79	6	no	—
213	C₂⁵	C₂²×D₇₉	1	1	yes	characteristic
214	2₋¹⁺⁴	—	158	128	no	—
215	C₂×#41	—	79	32	no	—
216	C₂×#41	—	79	48	no	—
217	C₂×#41	—	158	32	no	—
218	C₂×#41	—	158	48	no	—
219	C₂²×Q₈	—	2	64	no	—
220	C₂²×Q₈	—	2	128	no	—
221	C₂²×Q₈	—	2	24	no	—
222	C₂²×Q₈	—	79	32	no	—
223	C₂²×Q₈	—	79	6	no	—
224	C₂²×Q₈	—	158	32	no	—
225	C₂²×Q₈	C₂²⋊D₇₉	1	16	yes	complemented
226	C₂²×Q₈	C₂²×D₇₉	1	12	yes	—
227	C₂²×Q₈	C₂²×D₇₉	1	24	yes	—
228	C₂²×Q₈	C₂²×D₇₉	1	64	yes	—
229	C₂²×Q₈	C₂²×D₇₉	1	4	yes	—
230	C₂²×Q₈	C₂²×D₇₉	1	8	yes	—
231	C₂²×D₄	—	79	8	no	—
232	C₂²×D₄	—	79	4	no	—
233	C₂²×D₄	—	79	6	no	—
234	C₂³×C₄	—	2	24	no	—
235	C₂³×C₄	—	79	12	no	—
236	C₂³×C₄	C₂²×D₇₉	1	12	yes	—
237	C₂³×C₄	C₂²×D₇₉	1	3	yes	—
238	C₂³×C₄	C₂²×D₇₉	1	24	yes	—
239	C₂³×C₄	C₂²×D₇₉	1	3	yes	—
240	C₄⋊Q₈	—	79	96	no	—
241	#124	—	79	96	no	—
242	#123	—	79	96	no	—
243	C₂²⋊Q₈	—	79	192	no	—
244	C₂²⋊Q₈	—	79	96	no	—
245	#121	—	79	96	no	—
246	#120	—	79	32	no	—
247	C₄×Q₈	—	79	64	no	—
248	C₄×D₄	—	79	192	no	—
249	#117	—	79	48	no	—
250	C₂×C₄⋊C₄	—	79	12	no	—
251	C₂×C₄⋊C₄	—	79	24	no	—
252	C₂×C₂²⋊C₄	—	79	4	no	—
253	C₂×C₂²⋊C₄	—	79	8	no	—
254	C₂×C₂²⋊C₄	—	79	24	no	—
255	C₂×C₄²	—	79	12	no	—
256	C₂⁴	—	2	8	no	—
257	C₂⁴	—	2	4	no	—
258	C₂⁴	—	79	4	no	—
259	C₂⁴	C₂³×D₇₉	1	4	yes	—
260	C₂⁴	C₂³×D₇₉	1	2	yes	—
261	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
262	#41	—	158	128	no	—
263	#41	—	158	192	no	—
264	C₂×Q₈	—	2	256	no	—
265	C₂×Q₈	—	2	48	no	—
266	C₂×Q₈	—	2	96	no	—
267	C₂×Q₈	—	79	24	no	—
268	C₂×Q₈	—	158	128	no	—
269	C₂×Q₈	—	158	24	no	—
270	C₂×Q₈	C₂×C₂²⋊D₇₉	1	32	yes	—
271	C₂×Q₈	C₂×C₂²⋊D₇₉	1	64	yes	complemented
272	C₂×Q₈	C₂³×D₇₉	1	48	yes	—
273	C₂×Q₈	C₂³×D₇₉	1	16	yes	—
274	C₂×D₄	—	79	32	no	—
275	C₂×D₄	—	79	16	no	—
276	C₂×D₄	—	79	24	no	—
277	C₂×D₄	—	158	32	no	—
278	C₂×D₄	—	158	16	no	—
279	C₂×D₄	—	158	24	no	—
280	C₂²×C₄	—	2	12	no	—
281	C₂²×C₄	—	2	48	no	—
282	C₂²×C₄	—	2	96	no	—
283	C₂²×C₄	—	79	8	no	—
284	C₂²×C₄	—	79	4	no	—
285	C₂²×C₄	—	79	48	no	—
286	C₂²×C₄	—	158	48	no	—
287	C₂²×C₄	C₂×C₂²⋊D₇₉	1	24	yes	—
288	C₂²×C₄	C₂³×D₇₉	1	48	yes	—
289	C₂²×C₄	C₂³×D₇₉	1	12	yes	—
290	C₂²×C₄	C₂³×D₇₉	1	6	yes	—
291	C₂²×C₄	C₂³×D₇₉	1	12	yes	—
292	C₂²×C₄	C₂³×D₇₉	1	6	yes	—
293	C₄⋊C₄	—	79	96	no	—
294	C₄⋊C₄	—	79	48	no	—
295	C₂²⋊C₄	—	79	16	no	—
296	C₂²⋊C₄	—	79	32	no	—
297	C₂²⋊C₄	—	79	96	no	—
298	C₄²	—	79	48	no	—
299	C₂³	—	2	32	no	—
300	C₂³	—	2	4	no	—
301	C₂³	—	2	4	no	—
302	C₂³	—	2	16	no	—
303	C₂³	—	2	8	no	—
304	C₂³	—	2	4	no	—
305	C₂³	—	79	8	no	—
306	C₂³	—	158	16	no	—
307	C₂³	—	158	8	no	—
308	C₂³	C₂²×C₂²⋊D₇₉	1	4	yes	—
309	C₂³	#14579209	1	8	yes	complemented
310	C₂³	C₂⁴×D₇₉	1	4	yes	—
311	C₂³	C₂⁴×D₇₉	1	2	yes	—
312	C₂³	C₂⁴×D₇₉	1	1	yes	characteristic
313	Q₈	—	2	96	no	—
314	Q₈	—	158	48	no	—
315	Q₈	C₂²×C₂²⋊D₇₉	1	64	yes	—
316	D₄	—	158	64	no	—
317	D₄	—	158	32	no	—
318	D₄	—	158	48	no	—
319	C₂×C₄	—	2	24	no	—
320	C₂×C₄	—	2	12	no	—
321	C₂×C₄	—	2	96	no	—
322	C₂×C₄	—	79	16	no	—
323	C₂×C₄	—	79	8	no	—
324	C₂×C₄	—	158	16	no	—
325	C₂×C₄	—	158	8	no	—
326	C₂×C₄	—	158	96	no	—
327	C₂×C₄	C₂²×C₂²⋊D₇₉	1	24	yes	—
328	C₂×C₄	C₂²×C₂²⋊D₇₉	1	48	yes	—
329	C₂×C₄	C₂⁴×D₇₉	1	12	yes	—
330	C₂×C₄	C₂⁴×D₇₉	1	12	yes	—
331	C₂²	—	2	32	no	—
332	C₂²	—	2	16	no	—
333	C₂²	—	2	8	no	—
334	C₂²	—	2	4	no	—
335	C₂²	—	2	4	no	—
336	C₂²	—	2	4	no	—
337	C₂²	—	316	16	no	—
338	C₂²	—	158	8	no	—
339	C₂²	—	158	16	no	—
340	C₂²	C₂³×C₂²⋊D₇₉	1	4	yes	—
341	C₂²	C₂³×C₂²⋊D₇₉	1	2	yes	—
342	C₂²	C₂×#14579209	1	4	yes	—
343	C₂²	C₂×#14579209	1	8	yes	complemented
344	C₂²	C₂⁵×D₇₉	1	1	yes	characteristic
345	C₄	—	2	12	no	—
346	C₄	—	158	8	no	—
347	C₄	—	158	16	no	—
348	C₄	C₂³×C₂²⋊D₇₉	1	24	yes	—
349	C₂	—	2	8	no	—
350	C₂	—	2	4	no	—
351	C₂	—	316	8	no	—
352	C₂	#23777051	1	4	yes	direct product factor
353	C₂	C₂⁴×C₂²⋊D₇₉	1	1	yes	characteristic
354	C₂	C₂²×#14579209	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₇₉
commutator, cosocle	C₂²×C₇₉	C₂⁶
Frattini	C₂²	C₂⁵×D₇₉
Fitting	C₂⁴×Q₈×C₇₉	C₂
socle	C₂³×C₇₉	C₂⁵
hypercenter	C₂⁴×Q₈	D₇₉
hypocenter	C₇₉	C₂×#3486
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂⁴×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂²×#14579209	C₂	semidirect
2. #23777051	C₂	direct (N × H)
3. C₂×Q₈×C₂²⋊D₇₉	C₂	semidirect
4. C₂×#19099224	C₂	semidirect
5. C₂×#19099137	C₂	semidirect
6. C₂×#19099074	C₂	semidirect
7. C₂×#19099041	C₂	semidirect
8. C₂⁴×Q₈×C₇₉	C₂	semidirect
10. C₂×#14579209	C₂²	semidirect
11. C₂²×#11929625	C₂²	semidirect
13. C₂²×Q₈×D₇₉	C₂²	semidirect
14. Q₈×C₂²⋊D₇₉	C₂²	semidirect
15. #19099224	C₂²	semidirect
16. #19099137	C₂²	semidirect
17. C₂×#14579159	C₂²	semidirect
18. C₂×#14579150	C₂²	semidirect
19. #19099074	C₂²	semidirect
22. C₂×#14579137	C₂²	semidirect
25. #19099041	C₂²	semidirect
26. C₂×Q₈×Dic₇₉	C₂²	semidirect
33. C₂³×Q₈×C₇₉	C₂²	semidirect
37. C₂×#11929625	C₂³	semidirect
42. C₂×Q₈×D₇₉	C₂³	semidirect
47. #14579159	C₂³	semidirect
48. #14579150	C₂³	semidirect
51. #14579137	C₂³	semidirect
54. Q₈×Dic₇₉	C₂³	semidirect
67. C₂²×Q₈×C₇₉	D₄	semidirect
109. C₂×Q₈×C₇₉	C₂×D₄	semidirect
128. C₂³×C₇₉	2₋¹⁺⁴	semidirect
162. C₂²×C₇₉	C₂×2₋¹⁺⁴	semidirect
174. C₂×C₇₉	#3486	semidirect
179. C₂⁴×Q₈	D₇₉	semidirect
186. C₇₉	C₂×#3486	semidirect
196. C₂³×Q₈	C₂×D₇₉	semidirect
225. C₂²×Q₈	C₂²⋊D₇₉	semidirect
271. C₂×Q₈	C₂×C₂²⋊D₇₉	semidirect
309. C₂³	#14579209	semidirect
343. C₂²	C₂×#14579209	semidirect
352. C₂	#23777051	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#14579209	2
#23777051	2
C₂×Q₈×C₂²⋊D₇₉	2
C₂×#19099224	2
C₂×#19099137	2
C₂×#19099074	2
C₂×#19099041	2
C₂⁴×Q₈×C₇₉	2
C₂×#3486	79

Subgroups — C2×#23777051 #35196436

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#23777051 #35196436