Subgroups — #107×D₃₁₆ #34306388

Order 20224.

1126 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₃₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×#107×D₇₉	C₂	1	2	yes	maximal, complemented
3	C₄⋊C₄×D₃₁₆	C₂	1	2	yes	maximal
4	#23764158	C₂	1	2	yes	maximal, complemented
5	#23763589	C₂	1	4	yes	maximal, complemented
6	#23763560	C₂	1	1	yes	maximal, characteristic, complemented
7	#23763426	C₂	1	2	yes	maximal, complemented
8	C₄×#107×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₈×D₇₉	C₂²	1	2	yes	—
10	C₂×C₄×D₃₁₆	—	2	2	no	—
11	C₂×C₄×D₃₁₆	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊C₄×D₇₉	C₂²	1	4	yes	—
13	C₈×D₃₁₆	C₄	1	8	yes	complemented
14	C₂×#14579095	C₂²	1	2	yes	—
15	C₂×#14579095	C₂²	1	2	yes	—
16	C₂×#14579094	C₂²	1	4	yes	—
17	#107×D₇₉	—	2	8	no	—
18	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×(C₂×D₇₉)⋊C₈	C₂²	1	2	yes	—
20	#19098461	—	2	2	no	—
21	#19098437	—	2	4	no	—
22	#19098433	C₂²	1	2	yes	—
23	#19098420	C₂²	1	4	yes	—
24	#19098325	C₂²	1	4	yes	—
25	C₂×#107×C₇₉	C₂²	1	1	yes	characteristic
26	C₂×#107×C₇₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
28	C₄×C₄⋊C₄×C₇₉	C₂²	1	2	yes	—
29	#340×C₇₉	C₂²	1	2	yes	—
30	C₂²×D₃₁₆	D₄	1	1	yes	characteristic
31	C₂²×C₄×D₇₉	—	2	4	no	—
32	C₂²×C₄×D₇₉	C₂³	1	2	yes	—
33	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
34	C₂×C₈×D₇₉	—	2	4	no	—
35	C₂×C₈×D₇₉	—	2	4	no	—
36	C₂×C₈×D₇₉	C₂×C₄	1	8	yes	complemented
37	C₄×D₃₁₆	—	4	8	no	—
38	C₄×D₃₁₆	C₂×C₄	1	4	yes	—
39	C₄×D₃₁₆	Q₈	1	4	yes	—
40	C₂×C₄⋊Dic₇₉	—	2	2	no	—
41	C₂×C₄⋊Dic₇₉	—	2	2	no	—
42	C₂×C₄⋊Dic₇₉	D₄	1	1	yes	characteristic
43	C₂×C₄⋊Dic₇₉	C₂³	1	4	yes	—
44	C₂×Dic₇₉⋊C₄	—	2	4	no	—
45	C₄⋊C₄×D₇₉	—	2	8	no	—
46	C₄⋊C₄×D₇₉	—	4	4	no	—
47	C₂×(C₂×D₇₉)⋊C₄	—	2	4	no	—
48	C₂×(C₂×D₇₉)⋊C₄	D₄	1	2	yes	—
49	#14579095	—	2	4	no	—
50	#14579095	—	4	2	no	—
51	#14579094	—	2	8	no	—
52	C₄⋊(C₇₉⋊C₈)	C₂×C₄	1	4	yes	complemented
53	(C₂×D₇₉)⋊C₈	C₂×C₄	1	8	yes	complemented
54	C₇₉⋊#95	—	2	4	no	—
55	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
57	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
58	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
59	C₂×C₄²×C₇₉	—	2	2	no	—
60	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
61	#107×C₇₉	—	2	2	no	—
62	#107×C₇₉	D₄	1	4	yes	complemented
63	C₄×C₈×C₇₉	C₂×C₄	1	4	yes	complemented
64	#95×C₇₉	—	2	2	no	—
65	C₂³×D₇₉	C₂×D₄	1	2	yes	—
66	C₂×D₃₁₆	C₄⋊C₄	1	4	yes	—
67	C₂×D₃₁₆	D₈	1	4	yes	—
68	C₂×D₃₁₆	Q₁₆	1	4	yes	—
69	C₂²×Dic₇₉	—	2	4	no	—
70	C₂²×Dic₇₉	C₂×D₄	1	2	yes	—
71	C₂×C₄×D₇₉	—	2	2	no	—
72	C₂×C₄×D₇₉	—	2	2	no	—
73	C₂×C₄×D₇₉	—	2	2	no	—
74	C₂×C₄×D₇₉	—	2	2	no	—
75	C₂×C₄×D₇₉	—	4	8	no	—
76	C₂×C₄×D₇₉	—	4	8	no	—
77	C₂×C₄×D₇₉	—	8	4	no	—
78	C₂×C₄×D₇₉	C₂²×C₄	1	4	yes	—
79	C₂×C₄×D₇₉	C₂×Q₈	1	4	yes	—
80	C₂×C₇₉⋊C₈	—	2	2	no	—
81	C₂×C₇₉⋊C₈	—	2	2	no	—
82	C₂×C₇₉⋊C₈	C₂²×C₄	1	4	yes	—
83	C₈×D₇₉	—	2	16	no	—
84	C₄⋊Dic₇₉	—	2	4	no	—
85	C₄⋊Dic₇₉	—	2	4	no	—
86	C₄⋊Dic₇₉	—	4	4	no	—
87	C₄⋊Dic₇₉	—	8	2	no	—
88	C₄⋊Dic₇₉	C₄⋊C₄	1	4	yes	—
89	Dic₇₉⋊C₄	—	4	8	no	—
90	(C₂×D₇₉)⋊C₄	—	4	8	no	—
91	(C₂×D₇₉)⋊C₄	C₄⋊C₄	1	8	yes	—
92	C₂²×C₄×C₇₉	—	2	2	no	—
93	C₂²×C₄×C₇₉	—	2	2	no	—
94	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
97	C₂×C₈×C₇₉	—	2	1	no	—
98	C₂×C₈×C₇₉	—	2	1	no	—
99	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
100	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
101	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
102	C₂×C₈×C₇₉	#41	1	2	yes	—
103	C₄⋊C₄×C₇₉	—	2	2	no	—
104	C₄⋊C₄×C₇₉	—	2	2	no	—
105	C₄⋊C₄×C₇₉	—	2	2	no	—
106	C₄⋊C₄×C₇₉	C₂×D₄	1	4	yes	—
107	C₄²×C₇₉	—	4	4	no	—
108	C₄²×C₇₉	C₂²×C₄	1	2	yes	—
109	C₄²×C₇₉	C₂×Q₈	1	2	yes	—
110	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
111	C₂²×D₇₉	—	2	2	no	—
112	C₂²×D₇₉	—	2	2	no	—
113	C₂²×D₇₉	—	2	2	no	—
114	C₂²×D₇₉	—	2	2	no	—
115	C₂²×D₇₉	C₂×C₄⋊C₄	1	4	yes	—
116	C₂²×D₇₉	C₂×D₈	1	4	yes	—
117	C₂²×D₇₉	C₂×Q₁₆	1	4	yes	—
118	C₂×C₄×C₇₉	—	2	1	no	—
119	C₂×C₄×C₇₉	—	2	1	no	—
120	C₂×C₄×C₇₉	—	2	4	no	—
121	C₂×C₄×C₇₉	—	4	2	no	—
122	C₂×C₄×C₇₉	—	4	2	no	—
123	C₂×C₄×C₇₉	—	4	2	no	—
124	C₂×C₄×C₇₉	—	4	2	no	—
125	C₂×C₄×C₇₉	—	4	2	no	—
126	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
127	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
128	C₂×C₄×C₇₉	C₂×D₈	1	2	yes	—
129	C₂×C₄×C₇₉	C₂×Q₁₆	1	2	yes	—
130	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
131	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
132	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
133	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
134	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
135	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
136	C₂×Dic₇₉	—	2	2	no	—
137	C₂×Dic₇₉	—	2	2	no	—
138	C₂×Dic₇₉	—	4	4	no	—
139	C₂×Dic₇₉	—	4	4	no	—
140	C₂×Dic₇₉	—	4	4	no	—
141	C₂×Dic₇₉	C₂×C₄⋊C₄	1	4	yes	—
142	D₃₁₆	#107	1	16	yes	direct product factor
143	C₄×D₇₉	—	2	4	no	—
144	C₄×D₇₉	—	2	4	no	—
145	C₄×D₇₉	—	2	4	no	—
146	C₄×D₇₉	—	2	4	no	—
147	C₄×D₇₉	—	8	16	no	—
148	C₈×C₇₉	—	2	2	no	—
149	C₈×C₇₉	C₄×D₄	1	4	yes	complemented
150	C₇₉⋊C₈	—	2	4	no	—
151	C₂²×C₇₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
152	C₂²×C₇₉	D₄²	1	1	yes	characteristic
153	C₂²×C₇₉	#547	1	1	yes	characteristic
154	C₂²×C₇₉	C₂²×D₈	1	1	yes	characteristic
155	C₂²×C₇₉	C₂²×Q₁₆	1	1	yes	characteristic
156	C₂²×C₇₉	#576	1	1	yes	characteristic
157	C₂²×C₇₉	#578	1	1	yes	characteristic
158	C₂×D₇₉	—	2	4	no	—
159	C₂×D₇₉	—	2	4	no	—
160	C₂×D₇₉	—	2	4	no	—
161	C₂×D₇₉	—	2	4	no	—
162	C₂×D₇₉	—	2	4	no	—
163	C₂×D₇₉	—	2	4	no	—
164	C₂×D₇₉	C₂×#107	1	8	yes	complemented
165	C₄×C₇₉	—	2	2	no	—
166	C₄×C₇₉	—	4	4	no	—
167	C₄×C₇₉	—	8	2	no	—
168	C₄×C₇₉	C₂×#107	1	4	yes	complemented
169	C₄×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
170	C₄×C₇₉	#520	1	1	yes	characteristic
171	C₄×C₇₉	D₄×Q₈	1	1	yes	characteristic
172	C₄×C₇₉	#554	1	1	yes	characteristic
173	Dic₇₉	—	2	4	no	—
174	Dic₇₉	—	8	4	no	—
175	D₄×#107	—	79	1	no	maximal, Sylow
176	C₂×C₇₉	D₄×C₄⋊C₄	1	1	yes	characteristic
177	C₂×C₇₉	C₂²×#107	1	1	yes	characteristic
178	C₂×C₇₉	#2913	1	1	yes	characteristic
179	C₂×C₇₉	D₄×D₈	1	1	yes	characteristic
180	C₂×C₇₉	D₄×Q₁₆	1	1	yes	characteristic
181	C₂×C₇₉	#3334	1	1	yes	characteristic
182	C₂×C₇₉	#3338	1	1	yes	characteristic
183	D₇₉	—	2	8	no	—
184	C₂×C₈×D₄	—	79	1	no	—
185	C₂²×#107	—	79	2	no	—
186	D₄×C₄⋊C₄	—	79	2	no	—
187	#1947	—	79	2	no	—
188	#1852	—	79	4	no	—
189	#1845	—	79	1	no	—
190	#1808	—	79	2	no	—
191	C₄×#107	D₇₉	1	1	yes	characteristic, complemented
192	C₇₉	D₄×#107	1	1	yes	characteristic, complemented, Sylow
193	C₂³×C₈	—	79	2	no	—
194	C₂×C₄×D₄	—	79	1	no	—
195	C₂×C₄×D₄	—	158	2	no	—
196	C₂²×C₄⋊C₄	—	79	4	no	—
197	C₈×D₄	—	79	8	no	—
198	C₂×#107	—	79	2	no	—
199	C₂×#107	—	79	2	no	—
200	C₂×#107	—	79	4	no	—
201	C₂×#107	—	158	8	no	—
202	C₂×#107	C₂×D₇₉	1	1	yes	characteristic
203	C₂×#107	C₂×D₇₉	1	1	yes	characteristic
204	C₂×C₄⋊C₈	—	79	1	no	—
205	C₂×C₂²⋊C₈	—	79	2	no	—
206	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
207	#389	—	158	2	no	—
208	#385	—	158	4	no	—
209	#384	—	79	2	no	—
210	#380	—	79	4	no	—
211	C₄×C₄⋊C₄	C₂×D₇₉	1	2	yes	—
212	#340	—	79	4	no	—
213	#340	C₂×D₇₉	1	2	yes	—
214	C₂²×D₄	—	79	1	no	—
215	C₂³×C₄	—	79	2	no	—
216	C₂³×C₄	—	158	4	no	—
217	C₂²×C₈	—	79	2	no	—
218	C₂²×C₈	—	79	8	no	—
219	C₂²×C₈	—	158	4	no	—
220	C₂²×C₈	—	158	4	no	—
221	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
222	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
223	C₄×D₄	—	316	8	no	—
224	C₄×D₄	—	79	4	no	—
225	C₄×D₄	—	79	4	no	—
226	C₂×C₄⋊C₄	—	316	4	no	—
227	C₂×C₄⋊C₄	—	79	1	no	—
228	C₂×C₄⋊C₄	—	79	4	no	—
229	C₂×C₄⋊C₄	—	158	4	no	—
230	C₂×C₄⋊C₄	—	158	2	no	—
231	C₂×C₄⋊C₄	—	158	8	no	—
232	C₂×C₄⋊C₄	—	158	2	no	—
233	C₂×C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
234	C₂×C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
235	C₂×C₂²⋊C₄	—	79	2	no	—
236	C₂×C₂²⋊C₄	—	158	4	no	—
237	C₂×C₄²	—	2	2	no	—
238	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
239	#107	—	2	2	no	—
240	#107	—	316	2	no	—
241	#107	—	158	4	no	—
242	#107	—	158	8	no	—
243	#107	D₃₁₆	1	4	yes	direct product factor
244	C₄⋊C₈	—	79	4	no	—
245	C₂²⋊C₈	—	79	8	no	—
246	C₄×C₈	C₄×D₇₉	1	4	yes	complemented
247	#95	—	2	2	no	—
248	#95	—	158	4	no	—
249	C₂⁴	—	79	2	no	—
250	C₂×D₄	—	79	4	no	—
251	C₂×D₄	—	79	4	no	—
252	C₂×D₄	—	79	4	no	—
253	C₂²×C₄	—	2	2	no	—
254	C₂²×C₄	—	2	2	no	—
255	C₂²×C₄	—	316	8	no	—
256	C₂²×C₄	—	316	8	no	—
257	C₂²×C₄	—	79	2	no	—
258	C₂²×C₄	—	79	4	no	—
259	C₂²×C₄	—	79	4	no	—
260	C₂²×C₄	—	632	4	no	—
261	C₂²×C₄	—	158	4	no	—
262	C₂²×C₄	—	158	2	no	—
263	C₂²×C₄	—	158	2	no	—
264	C₂²×C₄	—	158	2	no	—
265	C₂²×C₄	—	158	2	no	—
266	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
267	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
268	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
269	C₂×C₈	—	2	1	no	—
270	C₂×C₈	—	2	1	no	—
271	C₂×C₈	—	79	4	no	—
272	C₂×C₈	—	158	2	no	—
273	C₂×C₈	—	158	2	no	—
274	C₂×C₈	—	158	16	no	—
275	C₂×C₈	C₂×C₄×D₇₉	1	2	yes	—
276	C₂×C₈	C₂×C₄×D₇₉	1	2	yes	—
277	C₂×C₈	C₂×D₃₁₆	1	2	yes	—
278	C₂×C₈	#11929624	1	2	yes	—
279	C₄⋊C₄	—	2	2	no	—
280	C₄⋊C₄	—	2	2	no	—
281	C₄⋊C₄	—	2	2	no	—
282	C₄⋊C₄	—	316	8	no	—
283	C₄⋊C₄	—	316	4	no	—
284	C₄⋊C₄	—	79	4	no	—
285	C₄⋊C₄	—	632	2	no	—
286	C₄⋊C₄	—	158	4	no	—
287	C₄⋊C₄	—	158	4	no	—
288	C₄⋊C₄	C₂×D₃₁₆	1	4	yes	—
289	C₂²⋊C₄	—	316	8	no	—
290	C₂²⋊C₄	—	79	8	no	—
291	C₄²	—	4	4	no	—
292	C₄²	C₂×C₄×D₇₉	1	2	yes	—
293	C₄²	Q₈×D₇₉	1	2	yes	—
294	C₂³	—	79	4	no	—
295	C₂³	—	79	4	no	—
296	C₂³	—	79	4	no	—
297	C₂³	—	158	2	no	—
298	C₂³	—	158	2	no	—
299	C₂³	—	158	2	no	—
300	C₂³	—	158	2	no	—
301	C₂³	C₂×D₄×D₇₉	1	1	yes	characteristic
302	D₄	—	79	16	no	—
303	C₂×C₄	—	2	1	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	4	no	—
306	C₂×C₄	—	4	2	no	—
307	C₂×C₄	—	4	2	no	—
308	C₂×C₄	—	4	2	no	—
309	C₂×C₄	—	4	2	no	—
310	C₂×C₄	—	4	2	no	—
311	C₂×C₄	—	316	4	no	—
312	C₂×C₄	—	316	4	no	—
313	C₂×C₄	—	316	4	no	—
314	C₂×C₄	—	79	4	no	—
315	C₂×C₄	—	632	16	no	—
316	C₂×C₄	—	158	2	no	—
317	C₂×C₄	—	158	2	no	—
318	C₂×C₄	—	158	4	no	—
319	C₂×C₄	—	158	4	no	—
320	C₂×C₄	—	158	4	no	—
321	C₂×C₄	—	158	4	no	—
322	C₂×C₄	C₄⋊C₄×D₇₉	1	2	yes	—
323	C₂×C₄	C₄⋊C₄×D₇₉	1	2	yes	—
324	C₂×C₄	D₈×D₇₉	1	2	yes	—
325	C₂×C₄	Q₁₆×D₇₉	1	2	yes	—
326	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
327	C₂×C₄	C₂²×D₃₁₆	1	1	yes	characteristic
328	C₂×C₄	C₂×Q₈×D₇₉	1	1	yes	characteristic
329	C₂×C₄	C₂×#11929624	1	1	yes	characteristic
330	C₂×C₄	#14579207	1	1	yes	characteristic
331	C₂×C₄	#14579208	1	1	yes	characteristic
332	C₈	—	2	2	no	—
333	C₈	—	158	4	no	—
334	C₈	C₄×D₃₁₆	1	4	yes	complemented
335	C₂²	—	79	8	no	—
336	C₂²	—	158	4	no	—
337	C₂²	—	158	4	no	—
338	C₂²	—	158	4	no	—
339	C₂²	—	158	4	no	—
340	C₂²	—	158	4	no	—
341	C₂²	—	158	4	no	—
342	C₂²	C₂×C₄⋊C₄×D₇₉	1	1	yes	characteristic
343	C₂²	D₄×D₃₁₆	1	1	yes	characteristic
344	C₂²	#19099218	1	1	yes	characteristic
345	C₂²	C₂×D₈×D₇₉	1	1	yes	characteristic
346	C₂²	C₂×Q₁₆×D₇₉	1	1	yes	characteristic
347	C₂²	#19099365	1	1	yes	characteristic
348	C₂²	#19099377	1	1	yes	characteristic
349	C₄	—	2	2	no	—
350	C₄	—	4	4	no	—
351	C₄	—	8	2	no	—
352	C₄	—	632	4	no	—
353	C₄	—	158	4	no	—
354	C₄	#107×D₇₉	1	4	yes	complemented
355	C₄	C₂×C₄×D₃₁₆	1	1	yes	characteristic
356	C₄	#19099043	1	1	yes	characteristic
357	C₄	Q₈×D₃₁₆	1	1	yes	characteristic
358	C₄	#19099273	1	1	yes	characteristic
359	C₂	—	158	8	no	—
360	C₂	C₄⋊C₄×D₃₁₆	1	1	yes	characteristic
361	C₂	C₂×#107×D₇₉	1	1	yes	characteristic
362	C₂	#23771997	1	1	yes	characteristic
363	C₂	D₈×D₃₁₆	1	1	yes	characteristic
364	C₂	Q₁₆×D₃₁₆	1	1	yes	characteristic
365	C₂	#23775749	1	1	yes	characteristic
366	C₂	#23775794	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₇₉
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting	C₄×#107×C₇₉	C₂
socle	C₂³×C₇₉	C₂²×D₄
prime radical	C₂²×D₃₁₆	D₄
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	C₄×#107	D₇₉
hypocenter	C₇₉	D₄×#107
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₄×#107

Complements

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

N	H ≅ G/N	type
2. C₂×#107×D₇₉	C₂	semidirect
4. #23764158	C₂	semidirect
5. #23763589	C₂	semidirect
6. #23763560	C₂	semidirect
7. #23763426	C₂	semidirect
8. C₄×#107×C₇₉	C₂	semidirect
13. C₈×D₃₁₆	C₄	semidirect
36. C₂×C₈×D₇₉	C₂×C₄	semidirect
52. C₄⋊(C₇₉⋊C₈)	C₂×C₄	semidirect
53. (C₂×D₇₉)⋊C₈	C₂×C₄	semidirect
62. #107×C₇₉	D₄	semidirect
63. C₄×C₈×C₇₉	C₂×C₄	semidirect
142. D₃₁₆	#107	direct (N × H)
149. C₈×C₇₉	C₄×D₄	semidirect
164. C₂×D₇₉	C₂×#107	semidirect
168. C₄×C₇₉	C₂×#107	semidirect
191. C₄×#107	D₇₉	semidirect
192. C₇₉	D₄×#107	semidirect
243. #107	D₃₁₆	direct (N × H)
246. C₄×C₈	C₄×D₇₉	semidirect
334. C₈	C₄×D₃₁₆	semidirect
354. C₄	#107×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×D₃₁₆	2
C₂×#107×D₇₉	2
C₄⋊C₄×D₃₁₆	2
#23764158	2
#23763589	2
#23763560	2
#23763426	2
C₄×#107×C₇₉	2
D₄×#107	79

Subgroups — #107×D316 #34306388

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #107×D₃₁₆ #34306388