Subgroups — C₂×#23777055 #35196513

Order 20224.

11510 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#11929625	C₂	1	1	yes	maximal, characteristic, complemented
2	#23777055	C₂	1	32	yes	maximal, direct product factor
3	C₂×#19099232	C₂	1	8	yes	maximal, complemented
4	C₂×#19099224	C₂	1	8	yes	maximal, complemented
5	C₂×#19099127	C₂	1	6	yes	maximal, complemented
6	C₂×#19099070	C₂	1	6	yes	maximal, complemented
7	C₂×#19099041	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×2₋¹⁺⁴×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#11929625	—	2	16	no	—
10	C₂²×#11929625	C₂²	1	8	yes	—
11	C₂²×#11929625	C₂²	1	16	yes	complemented
12	C₂³×D₃₁₆	C₂²	1	3	yes	—
13	C₂³×C₄×D₇₉	C₂²	1	3	yes	—
14	#19099232	C₂²	1	128	yes	complemented
15	#19099224	C₂²	1	128	yes	complemented
16	#19099127	C₂²	1	96	yes	complemented
17	C₂×#14579157	C₂²	1	12	yes	complemented
18	C₂×#14579150	C₂²	1	12	yes	complemented
19	#19099070	C₂²	1	96	yes	complemented
20	C₂×#14579142	C₂²	1	4	yes	—
21	C₂×#14579137	C₂²	1	12	yes	complemented
22	C₂×#14579135	C₂²	1	24	yes	complemented
23	C₂×#14579132	C₂²	1	12	yes	complemented
24	C₂×#14579129	C₂²	1	12	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	complemented
28	C₂×#14579120	C₂²	1	6	yes	—
29	C₂×2₋¹⁺⁴×C₇₉	—	2	16	no	—
30	C₂×2₋¹⁺⁴×C₇₉	C₂²	1	16	yes	complemented
31	C₂²×#41×C₇₉	C₂²	1	6	yes	—
32	C₂²×#41×C₇₉	C₂²	1	4	yes	complemented
33	C₂³×Q₈×C₇₉	C₂²	1	1	yes	characteristic
34	C₂³×Q₈×C₇₉	C₂²	1	4	yes	complemented
35	C₂⁴×D₇₉	C₂³	1	3	yes	—
36	C₂×#11929625	—	2	64	no	—
37	C₂×#11929625	—	2	128	no	—
38	C₂×#11929625	C₂³	1	64	yes	—
39	C₂²×D₃₁₆	—	2	24	no	—
40	C₂²×D₃₁₆	C₂³	1	12	yes	—
41	C₂²×D₃₁₆	C₂³	1	24	yes	—
42	C₂²×C₂²⋊D₇₉	C₂³	1	24	yes	—
43	C₂³×Dic₇₉	C₂³	1	1	yes	characteristic
44	C₂²×C₄×D₇₉	—	2	24	no	—
45	C₂²×C₄×D₇₉	C₂³	1	12	yes	—
46	C₂²×C₄×D₇₉	C₂³	1	24	yes	—
47	#14579157	C₂³	1	96	yes	complemented
48	#14579150	C₂³	1	96	yes	complemented
49	#14579142	C₂³	1	32	yes	—
50	#14579137	C₂³	1	96	yes	complemented
51	#14579135	C₂³	1	192	yes	complemented
52	#14579132	C₂³	1	96	yes	complemented
53	#14579129	C₂³	1	96	yes	—
54	Q₈×Dic₇₉	C₂³	1	64	yes	complemented
55	C₄×C₂²⋊D₇₉	C₂³	1	192	yes	complemented
56	#14579120	C₂³	1	48	yes	—
57	C₂×C₄⋊Dic₇₉	C₂³	1	12	yes	—
58	C₂×Dic₇₉⋊C₄	C₂³	1	8	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	2₋¹⁺⁴×C₇₉	—	2	128	no	—
64	C₂×#41×C₇₉	—	2	32	no	—
65	C₂×#41×C₇₉	—	2	48	no	—
66	C₂×#41×C₇₉	C₂³	1	48	yes	—
67	C₂×#41×C₇₉	C₂³	1	32	yes	complemented
68	C₂²×Q₈×C₇₉	—	2	32	no	—
69	C₂²×Q₈×C₇₉	D₄	1	16	yes	complemented
70	C₂²×Q₈×C₇₉	C₂³	1	6	yes	—
71	C₂²×Q₈×C₇₉	C₂³	1	4	yes	—
72	C₂²×Q₈×C₇₉	C₂³	1	8	yes	—
73	C₂²×Q₈×C₇₉	C₂³	1	32	yes	complemented
74	C₂²×D₄×C₇₉	C₂³	1	4	yes	—
75	C₂²×D₄×C₇₉	C₂³	1	6	yes	—
76	C₂³×C₄×C₇₉	C₂³	1	12	yes	—
77	C₂³×C₄×C₇₉	C₂³	1	3	yes	—
78	C₂³×D₇₉	—	2	12	no	—
79	C₂³×D₇₉	—	4	12	no	—
80	C₂³×D₇₉	C₂⁴	1	6	yes	—
81	C₂³×D₇₉	C₂⁴	1	12	yes	—
82	#11929625	—	2	256	no	—
83	C₂×D₃₁₆	—	2	48	no	—
84	C₂×D₃₁₆	—	2	96	no	—
85	C₂×D₃₁₆	C₂⁴	1	48	yes	—
86	C₂×C₂²⋊D₇₉	—	4	48	no	—
87	C₂×C₂²⋊D₇₉	C₂⁴	1	96	yes	—
88	C₂²×Dic₇₉	—	2	4	no	—
89	C₂²×Dic₇₉	C₂⁴	1	8	yes	—
90	C₂²×Dic₇₉	C₂⁴	1	2	yes	—
91	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
92	C₂×C₄×D₇₉	—	2	48	no	—
93	C₂×C₄×D₇₉	—	2	96	no	—
94	C₂×C₄×D₇₉	C₂⁴	1	48	yes	—
95	C₄⋊Dic₇₉	C₂⁴	1	48	yes	—
96	Dic₇₉⋊C₄	C₂⁴	1	32	yes	—
97	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	—
98	C₂²⋊Dic₇₉	C₂⁴	1	32	yes	—
99	(C₂×D₇₉)⋊C₄	C₂⁴	1	96	yes	—
100	C₄×Dic₇₉	C₂⁴	1	48	yes	—
101	C₂⁴×C₇₉	C₂⁴	1	4	yes	—
102	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
103	#41×C₇₉	—	2	128	no	—
104	#41×C₇₉	—	2	192	no	—
105	C₂×Q₈×C₇₉	—	2	128	no	—
106	C₂×Q₈×C₇₉	—	2	24	no	—
107	C₂×Q₈×C₇₉	C₂×D₄	1	32	yes	—
108	C₂×Q₈×C₇₉	C₂×D₄	1	64	yes	complemented
109	C₂×Q₈×C₇₉	C₂⁴	1	24	yes	—
110	C₂×Q₈×C₇₉	C₂⁴	1	16	yes	—
111	C₂×D₄×C₇₉	—	2	16	no	—
112	C₂×D₄×C₇₉	—	2	24	no	—
113	C₂×D₄×C₇₉	C₂⁴	1	16	yes	—
114	C₂×D₄×C₇₉	C₂⁴	1	24	yes	—
115	C₂²×C₄×C₇₉	—	2	48	no	—
116	C₂²×C₄×C₇₉	C₂×D₄	1	24	yes	—
117	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
118	C₂²×C₄×C₇₉	C₂⁴	1	48	yes	—
119	C₂²×C₄×C₇₉	C₂⁴	1	6	yes	—
120	C₂²×C₄×C₇₉	C₂⁴	1	12	yes	—
121	C₂³×C₇₉	—	2	4	no	—
122	C₂³×C₇₉	—	2	8	no	—
123	C₂³×C₇₉	—	2	16	no	—
124	C₂³×C₇₉	C₂²×D₄	1	4	yes	—
125	C₂³×C₇₉	C₂⁵	1	8	yes	—
126	C₂³×C₇₉	C₂⁵	1	2	yes	—
127	C₂³×C₇₉	C₂⁵	1	1	yes	characteristic
128	C₂²×D₇₉	—	2	24	no	—
129	C₂²×D₇₉	—	2	12	no	—
130	C₂²×D₇₉	—	2	24	no	—
131	C₂²×D₇₉	—	4	24	no	—
132	C₂²×D₇₉	—	4	48	no	—
133	C₂²×D₇₉	C₂⁵	1	12	yes	—
134	Q₈×C₇₉	—	2	48	no	—
135	Q₈×C₇₉	C₂²×D₄	1	64	yes	—
136	D₄×C₇₉	—	2	32	no	—
137	D₄×C₇₉	—	2	48	no	—
138	C₂×C₄×C₇₉	—	2	8	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	8	yes	—
143	C₂×C₄×C₇₉	C₂⁵	1	12	yes	—
144	C₂²⋊D₇₉	—	4	96	no	—
145	C₂×Dic₇₉	—	2	8	no	—
146	C₂×Dic₇₉	—	2	4	no	—
147	C₂×Dic₇₉	—	2	16	no	—
148	C₂×Dic₇₉	C₂⁵	1	16	yes	—
149	C₂×Dic₇₉	C₂⁵	1	4	yes	—
150	D₃₁₆	—	2	96	no	—
151	C₄×D₇₉	—	2	96	no	—
152	C₂²×C₇₉	—	2	4	no	—
153	C₂²×C₇₉	—	2	8	no	—
154	C₂²×C₇₉	—	2	8	no	—
155	C₂²×C₇₉	—	2	16	no	—
156	C₂²×C₇₉	—	4	16	no	—
157	C₂²×C₇₉	C₂³×D₄	1	4	yes	—
158	C₂²×C₇₉	C₂³×D₄	1	2	yes	—
159	C₂²×C₇₉	#585	1	4	yes	—
160	C₂²×C₇₉	C₂⁶	1	1	yes	characteristic
161	C₂×D₇₉	—	2	12	no	—
162	C₂×D₇₉	—	2	24	no	—
163	C₂×D₇₉	—	4	48	no	—
164	C₂×D₇₉	—	4	24	no	—
165	C₄×C₇₉	—	2	8	no	—
166	C₄×C₇₉	C₂³×D₄	1	24	yes	—
167	Dic₇₉	—	2	4	no	—
168	Dic₇₉	—	2	16	no	—
169	C₂×#3487	—	79	1	no	maximal, Sylow
170	C₂×C₇₉	—	2	4	no	—
171	C₂×C₇₉	—	4	8	no	—
172	C₂×C₇₉	#3487	1	4	yes	complemented
173	C₂×C₇₉	C₂⁴×D₄	1	1	yes	characteristic
174	C₂×C₇₉	C₂×#585	1	2	yes	—
175	D₇₉	—	4	12	no	—
176	C₂²×2₋¹⁺⁴	D₇₉	1	1	yes	characteristic, complemented
177	C₂³×#41	—	79	1	no	—
178	#3487	—	79	32	no	—
179	C₂×#550	—	79	8	no	—
180	C₂×#548	—	79	8	no	—
181	C₂×#535	—	79	6	no	—
182	C₂×#525	—	79	6	no	—
183	C₂×#519	—	79	1	no	—
184	C₇₉	C₂×#3487	1	1	yes	characteristic, complemented, Sylow
185	C₂×2₋¹⁺⁴	—	2	16	no	—
186	C₂×2₋¹⁺⁴	C₂×D₇₉	1	16	yes	complemented
187	C₂²×#41	—	79	8	no	—
188	C₂²×#41	—	79	16	no	—
189	C₂²×#41	—	158	16	no	—
190	C₂²×#41	C₂×D₇₉	1	6	yes	—
191	C₂²×#41	C₂×D₇₉	1	4	yes	complemented
192	C₂³×Q₈	C₂×D₇₉	1	1	yes	characteristic
193	C₂³×Q₈	C₂×D₇₉	1	4	yes	complemented
194	C₂³×D₄	—	79	3	no	—
195	C₂⁴×C₄	—	79	3	no	—
196	#550	—	79	128	no	—
197	#548	—	79	128	no	—
198	#535	—	79	96	no	—
199	C₂×#127	—	79	12	no	—
200	C₂×#124	—	79	12	no	—
201	#525	—	79	96	no	—
202	C₂×#123	—	79	4	no	—
203	C₂×C₂²⋊Q₈	—	79	12	no	—
204	C₂×#121	—	79	12	no	—
205	C₂×#121	—	79	24	no	—
206	C₂×#120	—	79	12	no	—
207	#519	—	79	16	no	—
208	C₂×C₄×Q₈	—	79	8	no	—
209	C₂×C₄×D₄	—	79	24	no	—
210	C₂×#117	—	79	6	no	—
211	C₂⁵	—	79	3	no	—
212	2₋¹⁺⁴	—	2	128	no	—
213	C₂×#41	—	2	32	no	—
214	C₂×#41	—	2	48	no	—
215	C₂×#41	—	79	64	no	—
216	C₂×#41	—	158	64	no	—
217	C₂×#41	—	158	128	no	—
218	C₂×#41	C₂²×D₇₉	1	48	yes	—
219	C₂×#41	C₂²×D₇₉	1	32	yes	complemented
220	C₂²×Q₈	—	2	32	no	—
221	C₂²×Q₈	C₂²⋊D₇₉	1	16	yes	complemented
222	C₂²×Q₈	C₂²×D₇₉	1	6	yes	—
223	C₂²×Q₈	C₂²×D₇₉	1	4	yes	—
224	C₂²×Q₈	C₂²×D₇₉	1	8	yes	—
225	C₂²×Q₈	C₂²×D₇₉	1	32	yes	complemented
226	C₂²×D₄	—	79	24	no	—
227	C₂²×D₄	—	79	12	no	—
228	C₂²×D₄	—	79	24	no	—
229	C₂²×D₄	—	158	24	no	—
230	C₂²×D₄	C₂²×D₇₉	1	4	yes	—
231	C₂²×D₄	C₂²×D₇₉	1	6	yes	—
232	C₂³×C₄	—	79	1	no	—
233	C₂³×C₄	—	79	12	no	—
234	C₂³×C₄	—	79	24	no	—
235	C₂³×C₄	—	158	24	no	—
236	C₂³×C₄	C₂²×D₇₉	1	12	yes	—
237	C₂³×C₄	C₂²×D₇₉	1	3	yes	—
238	#127	—	79	96	no	—
239	#124	—	79	96	no	—
240	#123	—	79	32	no	—
241	C₂²⋊Q₈	—	79	96	no	—
242	#121	—	79	96	no	—
243	#121	—	79	192	no	—
244	#120	—	79	96	no	—
245	C₄×Q₈	—	79	64	no	—
246	C₄×D₄	—	79	192	no	—
247	#117	—	79	48	no	—
248	C₂×C₄⋊C₄	—	79	12	no	—
249	C₂×C₄⋊C₄	—	79	8	no	—
250	C₂×C₂²⋊C₄	—	79	4	no	—
251	C₂×C₂²⋊C₄	—	79	8	no	—
252	C₂×C₂²⋊C₄	—	79	24	no	—
253	C₂×C₄²	—	79	12	no	—
254	C₂⁴	—	316	12	no	—
255	C₂⁴	—	79	12	no	—
256	C₂⁴	—	79	6	no	—
257	C₂⁴	—	158	12	no	—
258	C₂⁴	C₂³×D₇₉	1	4	yes	—
259	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
260	#41	—	2	128	no	—
261	#41	—	2	192	no	—
262	#41	—	158	256	no	—
263	C₂×Q₈	—	2	128	no	—
264	C₂×Q₈	—	2	24	no	—
265	C₂×Q₈	C₂×C₂²⋊D₇₉	1	32	yes	—
266	C₂×Q₈	C₂×C₂²⋊D₇₉	1	64	yes	complemented
267	C₂×Q₈	C₂³×D₇₉	1	24	yes	—
268	C₂×Q₈	C₂³×D₇₉	1	16	yes	—
269	C₂×D₄	—	2	16	no	—
270	C₂×D₄	—	2	24	no	—
271	C₂×D₄	—	316	48	no	—
272	C₂×D₄	—	79	96	no	—
273	C₂×D₄	—	79	48	no	—
274	C₂×D₄	—	158	48	no	—
275	C₂×D₄	—	158	96	no	—
276	C₂×D₄	C₂³×D₇₉	1	16	yes	—
277	C₂×D₄	C₂³×D₇₉	1	24	yes	—
278	C₂²×C₄	—	2	48	no	—
279	C₂²×C₄	—	79	4	no	—
280	C₂²×C₄	—	79	8	no	—
281	C₂²×C₄	—	79	2	no	—
282	C₂²×C₄	—	79	48	no	—
283	C₂²×C₄	—	158	4	no	—
284	C₂²×C₄	—	158	48	no	—
285	C₂²×C₄	—	158	96	no	—
286	C₂²×C₄	C₂×C₂²⋊D₇₉	1	24	yes	—
287	C₂²×C₄	C₂³×D₇₉	1	48	yes	—
288	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
289	C₂²×C₄	C₂³×D₇₉	1	12	yes	—
290	C₂²×C₄	C₂³×D₇₉	1	6	yes	—
291	C₄⋊C₄	—	79	32	no	—
292	C₄⋊C₄	—	79	48	no	—
293	C₂²⋊C₄	—	79	16	no	—
294	C₂²⋊C₄	—	79	32	no	—
295	C₂²⋊C₄	—	79	96	no	—
296	C₄²	—	79	48	no	—
297	C₂³	—	2	4	no	—
298	C₂³	—	2	16	no	—
299	C₂³	—	2	8	no	—
300	C₂³	—	316	48	no	—
301	C₂³	—	316	24	no	—
302	C₂³	—	79	12	no	—
303	C₂³	—	158	24	no	—
304	C₂³	—	158	24	no	—
305	C₂³	—	158	12	no	—
306	C₂³	C₂²×C₂²⋊D₇₉	1	4	yes	—
307	C₂³	C₂⁴×D₇₉	1	8	yes	—
308	C₂³	C₂⁴×D₇₉	1	2	yes	—
309	C₂³	C₂⁴×D₇₉	1	1	yes	characteristic
310	Q₈	—	2	48	no	—
311	Q₈	C₂²×C₂²⋊D₇₉	1	64	yes	—
312	D₄	—	2	32	no	—
313	D₄	—	2	48	no	—
314	D₄	—	316	96	no	—
315	D₄	—	158	96	no	—
316	C₂×C₄	—	2	8	no	—
317	C₂×C₄	—	2	96	no	—
318	C₂×C₄	—	79	16	no	—
319	C₂×C₄	—	79	4	no	—
320	C₂×C₄	—	158	16	no	—
321	C₂×C₄	—	158	8	no	—
322	C₂×C₄	—	158	4	no	—
323	C₂×C₄	—	158	96	no	—
324	C₂×C₄	C₂²×C₂²⋊D₇₉	1	24	yes	—
325	C₂×C₄	C₂²×C₂²⋊D₇₉	1	48	yes	—
326	C₂×C₄	C₂⁴×D₇₉	1	8	yes	—
327	C₂×C₄	C₂⁴×D₇₉	1	12	yes	—
328	C₂²	—	2	8	no	—
329	C₂²	—	2	4	no	—
330	C₂²	—	2	8	no	—
331	C₂²	—	2	16	no	—
332	C₂²	—	4	16	no	—
333	C₂²	—	316	48	no	—
334	C₂²	—	316	24	no	—
335	C₂²	—	158	12	no	—
336	C₂²	—	158	24	no	—
337	C₂²	C₂³×C₂²⋊D₇₉	1	4	yes	—
338	C₂²	C₂³×C₂²⋊D₇₉	1	2	yes	—
339	C₂²	#19099400	1	4	yes	—
340	C₂²	C₂⁵×D₇₉	1	1	yes	characteristic
341	C₄	—	2	8	no	—
342	C₄	—	158	4	no	—
343	C₄	—	158	16	no	—
344	C₄	C₂³×C₂²⋊D₇₉	1	24	yes	—
345	C₂	—	2	4	no	—
346	C₂	—	4	8	no	—
347	C₂	—	316	12	no	—
348	C₂	#23777055	1	4	yes	direct product factor
349	C₂	C₂⁴×C₂²⋊D₇₉	1	1	yes	characteristic
350	C₂	C₂×#19099400	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₇₉
commutator, cosocle	C₂²×C₇₉	C₂⁶
Frattini	C₂²	C₂⁵×D₇₉
Fitting	C₂²×2₋¹⁺⁴×C₇₉	C₂
socle	C₂³×C₇₉	C₂⁵
hypercenter	C₂²×2₋¹⁺⁴	D₇₉
hypocenter	C₇₉	C₂×#3487
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂²×2₋¹⁺⁴

Complements

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

N	H ≅ G/N	type
1. C₂³×#11929625	C₂	semidirect
2. #23777055	C₂	direct (N × H)
3. C₂×#19099232	C₂	semidirect
4. C₂×#19099224	C₂	semidirect
5. C₂×#19099127	C₂	semidirect
6. C₂×#19099070	C₂	semidirect
7. C₂×#19099041	C₂	semidirect
8. C₂²×2₋¹⁺⁴×C₇₉	C₂	semidirect
11. C₂²×#11929625	C₂²	semidirect
14. #19099232	C₂²	semidirect
15. #19099224	C₂²	semidirect
16. #19099127	C₂²	semidirect
17. C₂×#14579157	C₂²	semidirect
18. C₂×#14579150	C₂²	semidirect
19. #19099070	C₂²	semidirect
21. C₂×#14579137	C₂²	semidirect
22. C₂×#14579135	C₂²	semidirect
23. C₂×#14579132	C₂²	semidirect
25. #19099041	C₂²	semidirect
26. C₂×Q₈×Dic₇₉	C₂²	semidirect
27. C₂×C₄×C₂²⋊D₇₉	C₂²	semidirect
30. C₂×2₋¹⁺⁴×C₇₉	C₂²	semidirect
32. C₂²×#41×C₇₉	C₂²	semidirect
34. C₂³×Q₈×C₇₉	C₂²	semidirect
47. #14579157	C₂³	semidirect
48. #14579150	C₂³	semidirect
50. #14579137	C₂³	semidirect
51. #14579135	C₂³	semidirect
52. #14579132	C₂³	semidirect
54. Q₈×Dic₇₉	C₂³	semidirect
55. C₄×C₂²⋊D₇₉	C₂³	semidirect
67. C₂×#41×C₇₉	C₂³	semidirect
69. C₂²×Q₈×C₇₉	D₄	semidirect
73. C₂²×Q₈×C₇₉	C₂³	semidirect
108. C₂×Q₈×C₇₉	C₂×D₄	semidirect
172. C₂×C₇₉	#3487	semidirect
176. C₂²×2₋¹⁺⁴	D₇₉	semidirect
184. C₇₉	C₂×#3487	semidirect
186. C₂×2₋¹⁺⁴	C₂×D₇₉	semidirect
191. C₂²×#41	C₂×D₇₉	semidirect
193. C₂³×Q₈	C₂×D₇₉	semidirect
219. C₂×#41	C₂²×D₇₉	semidirect
221. C₂²×Q₈	C₂²⋊D₇₉	semidirect
225. C₂²×Q₈	C₂²×D₇₉	semidirect
266. C₂×Q₈	C₂×C₂²⋊D₇₉	semidirect
348. C₂	#23777055	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×#11929625	2
#23777055	2
C₂×#19099232	2
C₂×#19099224	2
C₂×#19099127	2
C₂×#19099070	2
C₂×#19099041	2
C₂²×2₋¹⁺⁴×C₇₉	2
C₂×#3487	79

Subgroups — C2×#23777055 #35196513

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#23777055 #35196513