Subgroups — C₂×#23762846 #34270663

Order 20224.

754 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19098911	C₂	1	1	yes	maximal, characteristic
2	C₂×#19098763	C₂	1	1	yes	maximal, characteristic
3	C₂×Q₈×C₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#23762846	C₂	1	8	yes	maximal, direct product factor
5	C₂×#19098315	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#19098309	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#19098306	C₂	1	1	yes	maximal, characteristic
8	C₂×#462×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#11929611	—	2	1	no	—
10	C₂×#14579158	C₂²	1	1	yes	characteristic
11	#19098911	—	2	2	no	—
12	#19098911	C₂²	1	4	yes	—
13	#19098763	—	2	2	no	—
14	#19098763	C₂²	1	4	yes	—
15	Q₈×C₇₉⋊C₈	—	2	2	no	—
16	Q₈×C₇₉⋊C₈	C₂²	1	4	yes	complemented
17	C₂×C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
18	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×#14579081	—	2	1	no	—
21	C₂×#14579081	—	2	1	no	—
22	C₂×#14579081	—	2	1	no	—
23	C₂×C₄×C₇₉⋊C₈	—	2	1	no	—
24	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
25	#19098315	C₂²	1	4	yes	complemented
26	#19098309	C₂²	1	4	yes	complemented
27	#19098306	C₂²	1	4	yes	—
28	C₂²×Q₁₆×C₇₉	—	2	1	no	—
29	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
31	#462×C₇₉	—	2	2	no	—
32	#462×C₇₉	C₂²	1	4	yes	complemented
33	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
34	C₂×#103×C₇₉	—	2	1	no	—
35	C₂²×D₃₁₆	—	2	1	no	—
36	C₂²×D₃₁₆	—	2	1	no	—
37	C₂²×D₃₁₆	—	2	1	no	—
38	C₂×#11929611	—	2	4	no	—
39	C₂×#11929611	—	4	4	no	—
40	C₂²×C₇₉⋊C₈	—	2	1	no	—
41	C₂²×C₇₉⋊C₈	—	2	1	no	—
42	C₂²×C₇₉⋊C₈	D₄	1	1	yes	characteristic
43	C₂²×C₇₉⋊C₈	D₄	1	1	yes	characteristic
44	#14579158	—	2	1	no	—
45	#14579158	—	2	1	no	—
46	#14579158	—	2	1	no	—
47	#14579158	C₂³	1	2	yes	—
48	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
49	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
50	C₄⋊(C₇₉⋊C₈)	—	2	4	no	—
51	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
52	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
53	#14579081	—	2	4	no	—
54	#14579081	—	2	4	no	—
55	#14579081	—	2	4	no	—
56	C₄×C₇₉⋊C₈	—	2	4	no	—
57	C₄×C₇₉⋊C₈	D₄	1	2	yes	—
58	C₄×C₇₉⋊C₈	C₂³	1	2	yes	—
59	C₂²×Q₈×C₇₉	—	2	1	no	—
60	C₂²×Q₈×C₇₉	D₄	1	1	yes	characteristic
61	C₂×Q₁₆×C₇₉	—	2	4	no	—
62	C₂×Q₁₆×C₇₉	—	4	4	no	—
63	C₂²×C₈×C₇₉	—	2	1	no	—
64	C₄⋊Q₈×C₇₉	—	2	1	no	—
65	C₄⋊Q₈×C₇₉	—	2	1	no	—
66	C₄⋊Q₈×C₇₉	—	2	1	no	—
67	C₄⋊Q₈×C₇₉	C₂³	1	2	yes	—
68	C₄×Q₈×C₇₉	—	2	1	no	—
69	C₄×Q₈×C₇₉	—	2	1	no	—
70	C₄×Q₈×C₇₉	D₄	1	2	yes	—
71	C₄×Q₈×C₇₉	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
73	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
74	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
75	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₇₉	—	2	1	no	—
77	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
78	C₄⋊C₈×C₇₉	—	2	1	no	—
79	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
80	#103×C₇₉	—	2	4	no	—
81	C₂³×D₇₉	—	4	1	no	—
82	C₂×D₃₁₆	—	2	2	no	—
83	C₂×D₃₁₆	—	2	2	no	—
84	C₂×D₃₁₆	—	2	2	no	—
85	C₂×D₃₁₆	—	4	1	no	—
86	C₂×D₃₁₆	—	4	1	no	—
87	C₂×D₃₁₆	—	4	1	no	—
88	C₂×D₃₁₆	—	4	2	no	—
89	C₂×D₃₁₆	—	4	2	no	—
90	C₂×D₃₁₆	—	4	2	no	—
91	C₂×D₃₁₆	—	4	2	no	—
92	C₂×D₃₁₆	—	8	2	no	—
93	#11929611	—	4	8	no	—
94	C₂×C₇₉⋊C₈	—	2	2	no	—
95	C₂×C₇₉⋊C₈	—	2	2	no	—
96	C₂×C₇₉⋊C₈	—	2	2	no	—
97	C₂×C₇₉⋊C₈	—	2	2	no	—
98	C₂×C₇₉⋊C₈	—	4	2	no	—
99	C₂×C₇₉⋊C₈	—	4	2	no	—
100	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
101	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
102	C₂×Q₈×C₇₉	—	2	1	no	—
103	C₂×Q₈×C₇₉	—	2	2	no	—
104	C₂×Q₈×C₇₉	—	2	2	no	—
105	C₂×Q₈×C₇₉	—	4	1	no	—
106	C₂×Q₈×C₇₉	—	4	2	no	—
107	C₂×Q₈×C₇₉	—	4	2	no	—
108	C₂×Q₈×C₇₉	D₈	1	4	yes	—
109	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₇₉	—	2	1	no	—
111	C₂²×C₄×C₇₉	—	2	1	no	—
112	C₂²×C₄×C₇₉	—	4	1	no	—
113	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
116	Q₁₆×C₇₉	—	4	8	no	—
117	C₂×C₈×C₇₉	—	2	2	no	—
118	C₂×C₈×C₇₉	—	4	2	no	—
119	C₄⋊C₄×C₇₉	—	2	2	no	—
120	C₄⋊C₄×C₇₉	—	2	1	no	—
121	C₄⋊C₄×C₇₉	—	2	2	no	—
122	C₄⋊C₄×C₇₉	—	2	2	no	—
123	C₄⋊C₄×C₇₉	—	2	2	no	—
124	C₄⋊C₄×C₇₉	—	4	1	no	—
125	C₄⋊C₄×C₇₉	—	4	1	no	—
126	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
127	C₄²×C₇₉	—	2	2	no	—
128	C₄²×C₇₉	—	2	2	no	—
129	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₇₉	#41	1	1	yes	characteristic
132	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
133	C₂³×C₇₉	#121	1	1	yes	characteristic
134	C₂²×D₇₉	—	4	2	no	—
135	C₂²×D₇₉	—	8	2	no	—
136	C₂²×D₇₉	—	8	2	no	—
137	C₂²×D₇₉	—	8	2	no	—
138	Q₈×C₇₉	—	2	2	no	—
139	Q₈×C₇₉	—	2	4	no	—
140	Q₈×C₇₉	—	4	2	no	—
141	Q₈×C₇₉	—	4	2	no	—
142	Q₈×C₇₉	—	8	2	no	—
143	Q₈×C₇₉	C₂×D₈	1	4	yes	—
144	C₂×C₄×C₇₉	—	2	2	no	—
145	C₂×C₄×C₇₉	—	2	4	no	—
146	C₂×C₄×C₇₉	—	2	2	no	—
147	C₂×C₄×C₇₉	—	2	2	no	—
148	C₂×C₄×C₇₉	—	4	2	no	—
149	C₂×C₄×C₇₉	—	4	2	no	—
150	C₂×C₄×C₇₉	—	8	2	no	—
151	C₂×C₄×C₇₉	#121	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	C₂×D₈	1	2	yes	—
155	C₂×C₄×C₇₉	#135	1	2	yes	—
156	C₂×C₄×C₇₉	#135	1	2	yes	—
157	C₂×C₄×C₇₉	#137	1	2	yes	—
158	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
159	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
161	D₃₁₆	—	4	2	no	—
162	D₃₁₆	—	4	2	no	—
163	D₃₁₆	—	4	2	no	—
164	D₃₁₆	—	4	2	no	—
165	D₃₁₆	—	8	2	no	—
166	D₃₁₆	—	8	2	no	—
167	D₃₁₆	—	8	2	no	—
168	D₃₁₆	—	8	2	no	—
169	C₈×C₇₉	—	4	2	no	—
170	C₇₉⋊C₈	—	2	2	no	—
171	C₇₉⋊C₈	—	2	2	no	—
172	C₇₉⋊C₈	—	4	2	no	—
173	C₇₉⋊C₈	—	4	2	no	—
174	C₂²×C₇₉	#464	1	2	yes	—
175	C₂²×C₇₉	#466	1	2	yes	—
176	C₂²×C₇₉	#471	1	2	yes	—
177	C₂²×C₇₉	C₂×#121	1	1	yes	characteristic
178	C₂×D₇₉	—	8	2	no	—
179	C₂×D₇₉	—	8	2	no	—
180	C₂×D₇₉	—	8	2	no	—
181	C₂×D₇₉	—	16	4	no	—
182	C₄×C₇₉	—	2	4	no	—
183	C₄×C₇₉	—	2	1	no	—
184	C₄×C₇₉	—	2	1	no	—
185	C₄×C₇₉	—	4	2	no	—
186	C₄×C₇₉	—	8	2	no	—
187	C₄×C₇₉	#464	1	2	yes	—
188	C₄×C₇₉	#466	1	2	yes	—
189	C₄×C₇₉	C₂²×D₈	1	1	yes	characteristic
190	C₄×C₇₉	C₂×#135	1	1	yes	characteristic
191	C₄×C₇₉	C₂×#135	1	1	yes	characteristic
192	C₄×C₇₉	C₂×#137	1	1	yes	characteristic
193	C₂×#1682	—	79	1	no	maximal, Sylow
194	C₂×C₇₉	#1682	1	4	yes	complemented
195	C₂×C₇₉	C₂×#464	1	1	yes	characteristic
196	C₂×C₇₉	C₂×#466	1	1	yes	characteristic
197	C₂×C₇₉	C₂×#471	1	1	yes	characteristic
198	D₇₉	—	16	2	no	—
199	C₂×#486	—	79	1	no	—
200	C₂×#462	D₇₉	1	1	yes	characteristic, complemented
201	C₂×#460	—	79	1	no	—
202	C₂×C₈×Q₈	—	79	1	no	—
203	#1682	—	79	8	no	—
204	C₂×#335	—	79	1	no	—
205	C₂×#332	—	79	1	no	—
206	C₂×#331	—	79	1	no	—
207	C₇₉	C₂×#1682	1	1	yes	characteristic, complemented, Sylow
208	C₂²×Q₁₆	—	2	1	no	—
209	C₂²×SD₁₆	—	158	1	no	—
210	C₂×C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
211	C₂×#127	—	79	1	no	—
212	C₂×C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic
213	#486	—	79	4	no	—
214	#486	—	158	2	no	—
215	#462	—	2	2	no	—
216	#462	C₂×D₇₉	1	4	yes	complemented
217	#460	—	79	4	no	—
218	#460	—	158	2	no	—
219	C₈×Q₈	—	79	4	no	—
220	C₈×Q₈	—	158	2	no	—
221	C₂×C₄⋊C₈	—	79	1	no	—
222	C₂×C₄⋊C₈	—	79	1	no	—
223	C₂×C₄⋊C₈	—	158	1	no	—
224	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
225	C₂×#103	—	2	1	no	—
226	C₂×#102	—	158	1	no	—
227	C₂×#102	—	158	1	no	—
228	C₂×#102	—	158	1	no	—
229	C₂×C₄×C₈	—	79	1	no	—
230	C₂×C₄×C₈	—	158	1	no	—
231	#335	—	79	4	no	—
232	#332	—	79	4	no	—
233	#331	—	79	4	no	—
234	C₂²×Q₈	—	2	1	no	—
235	C₂²×Q₈	C₂²⋊D₇₉	1	1	yes	characteristic
236	C₂²×D₄	—	158	1	no	—
237	C₂²×D₄	—	158	1	no	—
238	C₂²×D₄	—	158	1	no	—
239	C₂×Q₁₆	—	2	4	no	—
240	C₂×Q₁₆	—	4	4	no	—
241	C₂×SD₁₆	—	316	4	no	—
242	C₂×SD₁₆	—	158	4	no	—
243	C₂²×C₈	—	2	1	no	—
244	C₂²×C₈	—	79	1	no	—
245	C₂²×C₈	—	79	1	no	—
246	C₂²×C₈	—	158	1	no	—
247	C₂²×C₈	—	158	1	no	—
248	C₄⋊Q₈	—	2	1	no	—
249	C₄⋊Q₈	—	2	1	no	—
250	C₄⋊Q₈	—	2	1	no	—
251	C₄⋊Q₈	C₂²×D₇₉	1	2	yes	—
252	#127	—	79	2	no	—
253	#127	—	158	1	no	—
254	#127	—	158	1	no	—
255	#127	—	158	1	no	—
256	C₄×Q₈	—	2	1	no	—
257	C₄×Q₈	—	2	1	no	—
258	C₄×Q₈	C₂²⋊D₇₉	1	2	yes	—
259	C₄×Q₈	C₂²×D₇₉	1	2	yes	—
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	C₂²⋊D₇₉	1	1	yes	characteristic
264	C₂×C₄²	—	2	1	no	—
265	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
266	C₄⋊C₈	—	2	1	no	—
267	C₄⋊C₈	—	79	2	no	—
268	C₄⋊C₈	—	79	2	no	—
269	C₄⋊C₈	—	158	4	no	—
270	C₄⋊C₈	—	158	1	no	—
271	C₄⋊C₈	—	158	1	no	—
272	C₄⋊C₈	C₂²×D₇₉	1	2	yes	—
273	#103	—	2	4	no	—
274	#102	—	158	4	no	—
275	#102	—	158	4	no	—
276	#102	—	158	4	no	—
277	C₄×C₈	—	79	2	no	—
278	C₄×C₈	—	79	2	no	—
279	C₄×C₈	—	158	4	no	—
280	C₂⁴	—	316	1	no	—
281	C₂×Q₈	—	2	1	no	—
282	C₂×Q₈	—	2	2	no	—
283	C₂×Q₈	—	2	2	no	—
284	C₂×Q₈	—	4	1	no	—
285	C₂×Q₈	—	4	2	no	—
286	C₂×Q₈	—	4	2	no	—
287	C₂×Q₈	#11929609	1	4	yes	—
288	C₂×Q₈	C₂×C₂²⋊D₇₉	1	2	yes	—
289	C₂×D₄	—	316	1	no	—
290	C₂×D₄	—	316	1	no	—
291	C₂×D₄	—	316	1	no	—
292	C₂×D₄	—	316	2	no	—
293	C₂×D₄	—	316	2	no	—
294	C₂×D₄	—	316	2	no	—
295	C₂×D₄	—	316	2	no	—
296	C₂×D₄	—	632	2	no	—
297	C₂×D₄	—	158	2	no	—
298	C₂×D₄	—	158	2	no	—
299	C₂×D₄	—	158	2	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	4	1	no	—
303	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
304	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
305	C₂²×C₄	#11929623	1	1	yes	characteristic
306	Q₁₆	—	4	8	no	—
307	SD₁₆	—	316	8	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	4	2	no	—
310	C₂×C₈	—	316	2	no	—
311	C₂×C₈	—	316	2	no	—
312	C₂×C₈	—	79	2	no	—
313	C₂×C₈	—	79	2	no	—
314	C₂×C₈	—	158	2	no	—
315	C₂×C₈	—	158	2	no	—
316	C₂×C₈	—	158	2	no	—
317	C₂×C₈	—	158	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	1	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	4	1	no	—
324	C₄⋊C₄	—	4	1	no	—
325	C₄⋊C₄	C₂×C₂²⋊D₇₉	1	2	yes	—
326	C₄²	—	2	2	no	—
327	C₄²	—	2	2	no	—
328	C₄²	D₄×D₇₉	1	1	yes	characteristic
329	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
330	C₄²	#11929623	1	1	yes	characteristic
331	C₄²	C₂³×D₇₉	1	1	yes	characteristic
332	C₂³	—	316	2	no	—
333	C₂³	—	632	2	no	—
334	C₂³	—	632	2	no	—
335	C₂³	—	632	2	no	—
336	C₂³	#14579133	1	1	yes	characteristic
337	Q₈	—	2	4	no	—
338	Q₈	—	2	2	no	—
339	Q₈	—	4	2	no	—
340	Q₈	—	4	2	no	—
341	Q₈	—	8	2	no	—
342	Q₈	C₂×#11929609	1	4	yes	—
343	D₄	—	316	2	no	—
344	D₄	—	316	2	no	—
345	D₄	—	316	2	no	—
346	D₄	—	316	2	no	—
347	D₄	—	632	2	no	—
348	D₄	—	632	2	no	—
349	D₄	—	632	2	no	—
350	D₄	—	632	2	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	8	2	no	—
358	C₂×C₄	#14579133	1	1	yes	characteristic
359	C₂×C₄	#14579133	1	1	yes	characteristic
360	C₂×C₄	#14579133	1	1	yes	characteristic
361	C₂×C₄	C₂×#11929609	1	2	yes	—
362	C₂×C₄	#14579181	1	2	yes	—
363	C₂×C₄	#14579184	1	2	yes	—
364	C₂×C₄	#14579193	1	2	yes	—
365	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
366	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
367	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
368	C₈	—	4	2	no	—
369	C₈	—	316	2	no	—
370	C₈	—	316	2	no	—
371	C₈	—	158	2	no	—
372	C₈	—	158	2	no	—
373	C₂²	—	632	2	no	—
374	C₂²	—	632	2	no	—
375	C₂²	—	632	2	no	—
376	C₂²	—	1264	4	no	—
377	C₂²	#19098787	1	2	yes	—
378	C₂²	#19098797	1	2	yes	—
379	C₂²	#19098828	1	2	yes	—
380	C₂²	C₂×#14579133	1	1	yes	characteristic
381	C₄	—	2	4	no	—
382	C₄	—	2	1	no	—
383	C₄	—	2	1	no	—
384	C₄	—	4	2	no	—
385	C₄	—	8	2	no	—
386	C₄	#19098787	1	2	yes	—
387	C₄	#19098797	1	2	yes	—
388	C₄	C₂²×#11929609	1	1	yes	characteristic
389	C₄	C₂×#14579181	1	1	yes	characteristic
390	C₄	C₂×#14579184	1	1	yes	characteristic
391	C₄	C₂×#14579193	1	1	yes	characteristic
392	C₂	—	1264	2	no	—
393	C₂	#23762846	1	4	yes	direct product factor
394	C₂	C₂×#19098787	1	1	yes	characteristic
395	C₂	C₂×#19098797	1	1	yes	characteristic
396	C₂	C₂×#19098828	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#14579133
commutator, cosocle	C₄²×C₇₉	C₂⁴
Frattini	C₄²	C₂³×D₇₉
Fitting	C₂×#462×C₇₉	C₂
socle	C₂³×C₇₉	#121
prime radical	C₂×#14579158	C₂²
hypercenter	C₂×#462	D₇₉
hypocenter	C₇₉	C₂×#1682
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#462

Complements

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

N	H ≅ G/N	type
3. C₂×Q₈×C₇₉⋊C₈	C₂	semidirect
4. #23762846	C₂	direct (N × H)
5. C₂×#19098315	C₂	semidirect
6. C₂×#19098309	C₂	semidirect
8. C₂×#462×C₇₉	C₂	semidirect
16. Q₈×C₇₉⋊C₈	C₂²	semidirect
25. #19098315	C₂²	semidirect
26. #19098309	C₂²	semidirect
32. #462×C₇₉	C₂²	semidirect
194. C₂×C₇₉	#1682	semidirect
200. C₂×#462	D₇₉	semidirect
207. C₇₉	C₂×#1682	semidirect
216. #462	C₂×D₇₉	semidirect
393. C₂	#23762846	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#19098911	2
C₂×#19098763	2
C₂×Q₈×C₇₉⋊C₈	2
#23762846	2
C₂×#19098315	2
C₂×#19098309	2
C₂×#19098306	2
C₂×#462×C₇₉	2
C₂×#1682	79

Subgroups — C2×#23762846 #34270663

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#23762846 #34270663