Subgroups — #34189386

Order 20224.

702 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19098937	C₂	1	1	yes	maximal, characteristic
2	#23768399	C₂	1	1	yes	maximal, characteristic
3	#23764349	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#19098306	C₂	1	1	yes	maximal, characteristic
5	C₂×Q₈⋊(C₇₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
6	#23761239	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#477×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#11929611	—	2	2	no	—
9	C₂×#14579158	C₂²	1	1	yes	characteristic
10	C₂×#14579150	—	2	1	no	—
11	#19098937	—	2	2	no	—
12	#19098937	—	2	2	no	—
13	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
15	#19098480	—	2	2	no	—
16	#19098465	—	2	2	no	—
17	#19098464	—	2	1	no	—
18	C₄×C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic
19	#19098325	—	2	2	no	—
20	#19098306	—	2	2	no	—
21	Q₈⋊(C₇₉⋊C₈)	—	2	2	no	—
22	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
24	#477×C₇₉	—	2	2	no	—
25	#477×C₇₉	—	2	2	no	—
26	C₂×#107×C₇₉	—	2	1	no	—
27	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
28	C₂×#103×C₇₉	—	2	1	no	—
29	C₂²×D₃₁₆	—	2	1	no	—
30	C₂²×D₃₁₆	—	2	1	no	—
31	C₂²×D₃₁₆	D₄	1	2	yes	—
32	C₂×#11929611	—	2	8	no	—
33	C₂×#11929611	—	4	8	no	—
34	C₂²×C₇₉⋊C₈	—	2	1	no	—
35	C₂²×C₇₉⋊C₈	—	2	1	no	—
36	#14579158	—	2	1	no	—
37	#14579158	—	2	1	no	—
38	#14579158	—	2	1	no	—
39	#14579158	—	2	1	no	—
40	#14579150	—	4	2	no	—
41	#14579150	—	4	2	no	—
42	C₂×C₄⋊Dic₇₉	D₄	1	2	yes	—
43	C₂×(C₂×D₇₉)⋊C₄	—	2	4	no	—
44	C₂×(C₂×D₇₉)⋊C₄	—	2	4	no	—
45	C₂×C₄×Dic₇₉	—	2	1	no	—
46	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
47	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
48	C₄×C₇₉⋊C₈	—	2	1	no	—
49	C₄×C₇₉⋊C₈	D₄	1	2	yes	—
50	C₇₉⋊#95	—	2	1	no	—
51	C₂²×Q₈×C₇₉	—	2	1	no	—
52	C₂²×Q₈×C₇₉	D₄	1	1	yes	characteristic
53	C₂²×C₈×C₇₉	—	2	1	no	—
54	C₄⋊Q₈×C₇₉	—	2	1	no	—
55	C₄⋊Q₈×C₇₉	—	2	1	no	—
56	C₄⋊Q₈×C₇₉	—	2	1	no	—
57	C₄⋊Q₈×C₇₉	D₄	1	2	yes	—
58	C₄×Q₈×C₇₉	—	2	1	no	—
59	C₄×Q₈×C₇₉	—	2	1	no	—
60	C₄×Q₈×C₇₉	—	2	1	no	—
61	C₄×Q₈×C₇₉	—	2	1	no	—
62	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
64	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
65	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₇₉	—	2	1	no	—
67	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
68	#107×C₇₉	—	2	4	no	—
69	C₄⋊C₈×C₇₉	—	2	1	no	—
70	C₄⋊C₈×C₇₉	D₄	1	2	yes	—
71	#103×C₇₉	—	2	4	no	—
72	C₂³×D₇₉	—	2	2	no	—
73	C₂×D₃₁₆	—	2	2	no	—
74	C₂×D₃₁₆	—	2	2	no	—
75	C₂×D₃₁₆	—	4	4	no	—
76	C₂×D₃₁₆	—	4	1	no	—
77	C₂×D₃₁₆	—	4	1	no	—
78	C₂×D₃₁₆	—	4	1	no	—
79	C₂×D₃₁₆	—	4	1	no	—
80	C₂×D₃₁₆	—	4	1	no	—
81	C₂×D₃₁₆	—	4	1	no	—
82	C₂×D₃₁₆	—	4	2	no	—
83	C₂×D₃₁₆	—	4	1	no	—
84	C₂×D₃₁₆	—	4	1	no	—
85	C₂×D₃₁₆	—	4	2	no	—
86	C₂²×Dic₇₉	—	2	2	no	—
87	#11929611	—	4	16	no	—
88	C₂×C₇₉⋊C₈	—	2	4	no	—
89	C₂×C₇₉⋊C₈	—	2	2	no	—
90	C₂×C₇₉⋊C₈	—	4	1	no	—
91	C₂×C₇₉⋊C₈	—	4	2	no	—
92	C₄⋊Dic₇₉	—	2	2	no	—
93	C₄⋊Dic₇₉	—	2	2	no	—
94	(C₂×D₇₉)⋊C₄	—	4	8	no	—
95	(C₂×D₇₉)⋊C₄	—	8	4	no	—
96	C₄×Dic₇₉	—	4	1	no	—
97	C₄×Dic₇₉	—	4	1	no	—
98	C₂×Q₈×C₇₉	—	2	1	no	—
99	C₂×Q₈×C₇₉	—	2	1	no	—
100	C₂×Q₈×C₇₉	—	2	2	no	—
101	C₂×Q₈×C₇₉	—	2	1	no	—
102	C₂×Q₈×C₇₉	—	2	1	no	—
103	C₂×Q₈×C₇₉	—	2	1	no	—
104	C₂×Q₈×C₇₉	—	4	4	no	—
105	C₂×Q₈×C₇₉	—	4	1	no	—
106	C₂×Q₈×C₇₉	SD₁₆	1	2	yes	complemented
107	C₂²×C₄×C₇₉	—	2	1	no	—
108	C₂²×C₄×C₇₉	—	2	1	no	—
109	C₂²×C₄×C₇₉	—	4	1	no	—
110	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
113	C₂×C₈×C₇₉	—	2	2	no	—
114	C₂×C₈×C₇₉	—	4	1	no	—
115	C₂×C₈×C₇₉	—	4	1	no	—
116	C₄⋊C₄×C₇₉	—	2	2	no	—
117	C₄⋊C₄×C₇₉	—	2	1	no	—
118	C₄⋊C₄×C₇₉	—	2	2	no	—
119	C₄⋊C₄×C₇₉	—	2	1	no	—
120	C₄⋊C₄×C₇₉	—	4	1	no	—
121	C₄⋊C₄×C₇₉	—	4	1	no	—
122	C₄⋊C₄×C₇₉	—	4	1	no	—
123	C₄⋊C₄×C₇₉	—	4	1	no	—
124	C₄²×C₇₉	—	4	1	no	—
125	C₄²×C₇₉	—	4	1	no	—
126	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₇₉	#41	1	1	yes	characteristic
130	C₂³×C₇₉	#120	1	1	yes	characteristic
131	C₂²×D₇₉	—	4	2	no	—
132	C₂²×D₇₉	—	4	2	no	—
133	C₂²×D₇₉	—	4	2	no	—
134	C₂²×D₇₉	—	4	4	no	—
135	C₂²×D₇₉	—	4	4	no	—
136	Q₈×C₇₉	—	2	2	no	—
137	Q₈×C₇₉	—	2	2	no	—
138	Q₈×C₇₉	—	4	4	no	—
139	Q₈×C₇₉	—	4	1	no	—
140	Q₈×C₇₉	—	4	1	no	—
141	Q₈×C₇₉	—	8	2	no	—
142	C₂×C₄×C₇₉	—	2	2	no	—
143	C₂×C₄×C₇₉	—	2	2	no	—
144	C₂×C₄×C₇₉	—	4	1	no	—
145	C₂×C₄×C₇₉	—	4	1	no	—
146	C₂×C₄×C₇₉	—	4	1	no	—
147	C₂×C₄×C₇₉	—	4	2	no	—
148	C₂×C₄×C₇₉	—	4	2	no	—
149	C₂×C₄×C₇₉	—	8	2	no	—
150	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
151	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
152	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
153	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
154	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
155	C₂×C₄×C₇₉	#127	1	1	yes	characteristic
156	C₂×C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
157	C₂×C₄×C₇₉	#135	1	1	yes	characteristic
158	C₂×C₄×C₇₉	#135	1	2	yes	—
159	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
160	C₂×C₄×C₇₉	#137	1	1	yes	characteristic
161	C₂×C₄×C₇₉	#137	1	2	yes	—
162	C₂×Dic₇₉	—	4	2	no	—
163	C₂×Dic₇₉	—	4	2	no	—
164	C₂×Dic₇₉	—	4	2	no	—
165	D₃₁₆	—	4	4	no	—
166	D₃₁₆	—	8	2	no	—
167	D₃₁₆	—	8	1	no	—
168	D₃₁₆	—	8	1	no	—
169	D₃₁₆	—	8	2	no	—
170	D₃₁₆	—	8	1	no	—
171	D₃₁₆	—	8	1	no	—
172	D₃₁₆	—	8	1	no	—
173	D₃₁₆	—	8	1	no	—
174	C₈×C₇₉	—	4	2	no	—
175	C₇₉⋊C₈	—	2	4	no	—
176	C₇₉⋊C₈	—	8	1	no	—
177	C₂²×C₇₉	#392	1	1	yes	characteristic
178	C₂²×C₇₉	#450	1	1	yes	characteristic
179	C₂²×C₇₉	#452	1	1	yes	characteristic
180	C₂²×C₇₉	#452	1	2	yes	—
181	C₂²×C₇₉	#453	1	2	yes	—
182	C₂×D₇₉	—	8	4	no	—
183	C₂×D₇₉	—	8	4	no	—
184	C₂×D₇₉	—	8	2	no	—
185	C₂×D₇₉	—	8	2	no	—
186	C₂×D₇₉	—	8	2	no	—
187	C₄×C₇₉	—	2	1	no	—
188	C₄×C₇₉	—	2	1	no	—
189	C₄×C₇₉	—	4	2	no	—
190	C₄×C₇₉	—	8	1	no	—
191	C₄×C₇₉	—	8	2	no	—
192	C₄×C₇₉	#448	1	1	yes	characteristic
193	C₄×C₇₉	#449	1	1	yes	characteristic
194	C₄×C₇₉	#464	1	2	yes	—
195	C₄×C₇₉	#465	1	1	yes	characteristic
196	C₄×C₇₉	#468	1	1	yes	characteristic
197	C₄×C₇₉	#495	1	1	yes	characteristic
198	C₄×C₇₉	#497	1	1	yes	characteristic
199	Dic₇₉	—	8	2	no	—
200	#10055	—	79	1	no	maximal, Sylow
201	C₂×C₇₉	#1630	1	2	yes	—
202	C₂×C₇₉	#1631	1	2	yes	—
203	C₂×C₇₉	#2000	1	1	yes	characteristic
204	C₂×C₇₉	#2002	1	1	yes	characteristic
205	C₂×C₇₉	#2015	1	1	yes	characteristic
206	D₇₉	—	16	2	no	—
207	C₂×#492	—	79	1	no	—
208	C₂×#477	D₇₉	1	1	yes	characteristic, complemented
209	#2548	—	79	1	no	—
210	#1987	—	79	1	no	—
211	C₂×#331	—	79	1	no	—
212	C₂×Q₈⋊C₈	—	79	1	no	—
213	#1279	—	79	1	no	—
214	C₇₉	#10055	1	1	yes	characteristic, complemented, Sylow
215	C₂²×SD₁₆	—	158	2	no	—
216	C₂×C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
217	C₂×#127	—	79	1	no	—
218	C₂×#124	—	158	1	no	—
219	C₂×C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic
220	#492	—	158	2	no	—
221	#492	—	158	2	no	—
222	#477	—	2	2	no	—
223	#477	—	2	2	no	—
224	C₂×#107	—	2	1	no	—
225	C₂×C₄⋊C₈	—	79	1	no	—
226	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
227	C₂×#103	—	2	1	no	—
228	C₂×C₄×C₈	—	79	1	no	—
229	#394	—	158	2	no	—
230	#390	—	158	2	no	—
231	#390	—	158	1	no	—
232	C₄×C₄⋊C₄	—	79	1	no	—
233	#340	—	158	2	no	—
234	#331	—	158	2	no	—
235	Q₈⋊C₈	—	158	2	no	—
236	C₂²×Q₈	—	2	1	no	—
237	C₂²×Q₈	C₂²⋊D₇₉	1	1	yes	characteristic
238	C₂²×D₄	—	79	2	no	—
239	C₂²×D₄	—	158	1	no	—
240	C₂²×D₄	—	158	1	no	—
241	C₂×SD₁₆	—	316	8	no	—
242	C₂×SD₁₆	—	158	8	no	—
243	C₂²×C₈	—	2	1	no	—
244	C₂²×C₈	—	158	1	no	—
245	C₂²×C₈	—	158	1	no	—
246	C₄⋊Q₈	—	2	1	no	—
247	C₄⋊Q₈	—	2	1	no	—
248	C₄⋊Q₈	—	2	1	no	—
249	C₄⋊Q₈	C₂²⋊D₇₉	1	2	yes	—
250	#127	—	158	1	no	—
251	#127	—	158	1	no	—
252	#127	—	158	1	no	—
253	#127	—	158	1	no	—
254	#124	—	316	2	no	—
255	#124	—	316	2	no	—
256	C₄×Q₈	—	2	1	no	—
257	C₄×Q₈	—	2	1	no	—
258	C₄×Q₈	—	2	1	no	—
259	C₄×Q₈	—	2	1	no	—
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	—	79	2	no	—
264	C₂×C₄⋊C₄	C₂²⋊D₇₉	1	1	yes	characteristic
265	C₂×C₂²⋊C₄	—	158	4	no	—
266	C₂×C₂²⋊C₄	—	158	4	no	—
267	C₂×C₄²	—	2	1	no	—
268	C₂×C₄²	—	158	1	no	—
269	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
270	#107	—	2	4	no	—
271	C₄⋊C₈	—	2	1	no	—
272	C₄⋊C₈	—	158	1	no	—
273	C₄⋊C₈	—	158	1	no	—
274	C₄⋊C₈	C₂²⋊D₇₉	1	2	yes	—
275	#103	—	2	4	no	—
276	C₄×C₈	—	79	2	no	—
277	C₄×C₈	—	158	1	no	—
278	#95	—	158	1	no	—
279	C₂⁴	—	158	2	no	—
280	C₂×Q₈	—	2	1	no	—
281	C₂×Q₈	—	2	2	no	—
282	C₂×Q₈	—	2	1	no	—
283	C₂×Q₈	—	2	1	no	—
284	C₂×Q₈	—	2	1	no	—
285	C₂×Q₈	—	2	1	no	—
286	C₂×Q₈	—	4	4	no	—
287	C₂×Q₈	—	4	1	no	—
288	C₂×Q₈	#11929611	1	2	yes	complemented
289	C₂×D₄	—	316	4	no	—
290	C₂×D₄	—	316	1	no	—
291	C₂×D₄	—	316	1	no	—
292	C₂×D₄	—	316	1	no	—
293	C₂×D₄	—	316	1	no	—
294	C₂×D₄	—	316	1	no	—
295	C₂×D₄	—	316	1	no	—
296	C₂×D₄	—	316	2	no	—
297	C₂×D₄	—	316	1	no	—
298	C₂×D₄	—	316	1	no	—
299	C₂×D₄	—	316	2	no	—
300	C₂×D₄	—	158	2	no	—
301	C₂×D₄	—	158	2	no	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	4	1	no	—
305	C₂²×C₄	—	158	2	no	—
306	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
307	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
308	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
309	SD₁₆	—	316	16	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	4	1	no	—
312	C₂×C₈	—	4	1	no	—
313	C₂×C₈	—	316	1	no	—
314	C₂×C₈	—	316	2	no	—
315	C₂×C₈	—	158	4	no	—
316	C₂×C₈	—	158	2	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	1	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	1	no	—
321	C₄⋊C₄	—	4	1	no	—
322	C₄⋊C₄	—	4	1	no	—
323	C₄⋊C₄	—	4	1	no	—
324	C₄⋊C₄	—	4	1	no	—
325	C₄⋊C₄	—	158	2	no	—
326	C₄⋊C₄	—	158	2	no	—
327	C₂²⋊C₄	—	316	8	no	—
328	C₂²⋊C₄	—	632	4	no	—
329	C₄²	—	4	1	no	—
330	C₄²	—	4	1	no	—
331	C₄²	—	316	1	no	—
332	C₄²	—	316	1	no	—
333	C₄²	D₄×D₇₉	1	1	yes	characteristic
334	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
335	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
336	C₄²	#11929623	1	1	yes	characteristic
337	C₂³	—	316	2	no	—
338	C₂³	—	316	2	no	—
339	C₂³	—	316	4	no	—
340	C₂³	—	316	2	no	—
341	C₂³	—	316	4	no	—
342	C₂³	#14579129	1	1	yes	characteristic
343	Q₈	—	2	2	no	—
344	Q₈	—	2	2	no	—
345	Q₈	—	4	4	no	—
346	Q₈	—	4	1	no	—
347	Q₈	—	4	1	no	—
348	Q₈	—	8	2	no	—
349	D₄	—	316	4	no	—
350	D₄	—	632	2	no	—
351	D₄	—	632	1	no	—
352	D₄	—	632	1	no	—
353	D₄	—	632	1	no	—
354	D₄	—	632	1	no	—
355	D₄	—	632	2	no	—
356	D₄	—	632	1	no	—
357	D₄	—	632	1	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	8	2	no	—
366	C₂×C₄	—	316	2	no	—
367	C₂×C₄	—	316	2	no	—
368	C₂×C₄	—	316	2	no	—
369	C₂×C₄	#14579129	1	1	yes	characteristic
370	C₂×C₄	#14579130	1	1	yes	characteristic
371	C₂×C₄	#14579132	1	1	yes	characteristic
372	C₂×C₄	#14579133	1	1	yes	characteristic
373	C₂×C₄	#14579133	1	1	yes	characteristic
374	C₂×C₄	#14579157	1	1	yes	characteristic
375	C₂×C₄	C₂×#11929611	1	1	yes	characteristic
376	C₂×C₄	#14579181	1	1	yes	characteristic
377	C₂×C₄	#14579184	1	2	yes	—
378	C₂×C₄	#14579186	1	1	yes	characteristic
379	C₂×C₄	#14579192	1	1	yes	characteristic
380	C₂×C₄	#14579193	1	2	yes	—
381	C₈	—	4	2	no	—
382	C₈	—	632	1	no	—
383	C₈	—	158	4	no	—
384	C₂²	—	632	2	no	—
385	C₂²	—	632	4	no	—
386	C₂²	—	632	4	no	—
387	C₂²	—	632	2	no	—
388	C₂²	—	632	2	no	—
389	C₂²	#19098471	1	1	yes	characteristic
390	C₂²	#19098713	1	1	yes	characteristic
391	C₂²	#19098723	1	1	yes	characteristic
392	C₂²	#19098724	1	2	yes	—
393	C₂²	#19098729	1	2	yes	—
394	C₄	—	2	1	no	—
395	C₄	—	2	1	no	—
396	C₄	—	4	2	no	—
397	C₄	—	8	1	no	—
398	C₄	—	8	2	no	—
399	C₄	—	632	2	no	—
400	C₄	#19098702	1	1	yes	characteristic
401	C₄	#19098708	1	1	yes	characteristic
402	C₄	#19098787	1	2	yes	—
403	C₄	#19098794	1	1	yes	characteristic
404	C₄	#19098811	1	1	yes	characteristic
405	C₄	#19098948	1	1	yes	characteristic
406	C₄	#19098956	1	1	yes	characteristic
407	C₂	—	1264	2	no	—
408	C₂	#23762520	1	2	yes	—
409	C₂	#23762525	1	2	yes	—
410	C₂	#23764401	1	1	yes	characteristic
411	C₂	#23764412	1	1	yes	characteristic
412	C₂	#23764491	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#14579129
commutator, cosocle	C₂×C₄²×C₇₉	C₂³
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₂×#477×C₇₉	C₂
socle	C₂³×C₇₉	#120
prime radical	C₂×#14579158	C₂²
hypercenter	C₂×#477	D₇₉
hypocenter	C₇₉	#10055
LCS	G ▷ C₂×C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#477

Complements

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

N	H ≅ G/N	type
3. #23764349	C₂	semidirect
5. C₂×Q₈⋊(C₇₉⋊C₈)	C₂	semidirect
6. #23761239	C₂	semidirect
7. C₂×#477×C₇₉	C₂	semidirect
106. C₂×Q₈×C₇₉	SD₁₆	semidirect
208. C₂×#477	D₇₉	semidirect
214. C₇₉	#10055	semidirect
288. C₂×Q₈	#11929611	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19098937	2
#23768399	2
#23764349	2
C₂×#19098306	2
C₂×Q₈⋊(C₇₉⋊C₈)	2
#23761239	2
C₂×#477×C₇₉	2
#10055	79