Subgroups — C₂×#23762874 #34270863

Order 20224.

766 conjugacy classes of subgroups.

The subgroup lattice has 402 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	C₂×#19098763	C₂	1	1	yes	maximal, characteristic
3	C₂×#19098694	C₂	1	1	yes	maximal, characteristic, complemented
4	#23762874	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×#475×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#11929611	—	2	1	no	—
10	C₂²×#11929611	—	2	1	no	—
11	C₂²×#11929611	—	2	1	no	—
12	C₂×#14579158	C₂²	1	1	yes	characteristic
13	#19098937	—	2	2	no	—
14	#19098937	C₂²	1	4	yes	—
15	#19098763	—	2	2	no	—
16	#19098763	C₂²	1	4	yes	—
17	#19098694	—	2	2	no	—
18	#19098694	C₂²	1	4	yes	complemented
19	C₂×C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
20	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
22	C₂×#14579081	—	2	1	no	—
23	C₂×#14579072	—	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	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
30	#475×C₇₉	—	2	2	no	—
31	#475×C₇₉	C₂²	1	4	yes	complemented
32	C₂×#106×C₇₉	—	2	1	no	—
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	—	2	4	no	—
40	C₂×#11929611	—	2	4	no	—
41	C₂×#11929611	—	4	4	no	—
42	C₂×#11929611	—	4	4	no	—
43	C₂×#11929611	—	4	4	no	—
44	C₂²×C₇₉⋊C₈	—	2	1	no	—
45	C₂²×C₇₉⋊C₈	—	2	1	no	—
46	C₂²×C₇₉⋊C₈	D₄	1	1	yes	characteristic
47	C₂²×C₇₉⋊C₈	D₄	1	1	yes	characteristic
48	#14579158	—	2	1	no	—
49	#14579158	—	2	1	no	—
50	#14579158	—	2	1	no	—
51	#14579158	C₂³	1	2	yes	—
52	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
53	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
54	C₄⋊(C₇₉⋊C₈)	—	2	4	no	—
55	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
56	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
57	#14579081	—	2	4	no	—
58	#14579072	—	2	4	no	—
59	C₄×C₇₉⋊C₈	D₄	1	2	yes	—
60	C₄×C₇₉⋊C₈	C₂³	1	2	yes	—
61	C₂²×Q₈×C₇₉	—	2	1	no	—
62	C₂²×Q₈×C₇₉	D₄	1	1	yes	characteristic
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	#106×C₇₉	—	2	4	no	—
79	C₄⋊C₈×C₇₉	—	2	1	no	—
80	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
81	#103×C₇₉	—	2	4	no	—
82	C₂³×D₇₉	—	4	1	no	—
83	C₂×D₃₁₆	—	2	2	no	—
84	C₂×D₃₁₆	—	2	2	no	—
85	C₂×D₃₁₆	—	2	2	no	—
86	C₂×D₃₁₆	—	4	1	no	—
87	C₂×D₃₁₆	—	4	1	no	—
88	C₂×D₃₁₆	—	4	1	no	—
89	C₂×D₃₁₆	—	4	2	no	—
90	C₂×D₃₁₆	—	4	2	no	—
91	C₂×D₃₁₆	—	4	2	no	—
92	C₂×D₃₁₆	—	4	2	no	—
93	C₂×D₃₁₆	—	8	2	no	—
94	#11929611	—	4	8	no	—
95	#11929611	—	4	8	no	—
96	#11929611	—	4	8	no	—
97	C₂×C₇₉⋊C₈	—	2	2	no	—
98	C₂×C₇₉⋊C₈	—	2	2	no	—
99	C₂×C₇₉⋊C₈	—	2	2	no	—
100	C₂×C₇₉⋊C₈	—	4	2	no	—
101	C₂×C₇₉⋊C₈	—	4	2	no	—
102	C₂×C₇₉⋊C₈	SD₁₆	1	4	yes	complemented
103	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
104	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
105	C₂×Q₈×C₇₉	—	2	1	no	—
106	C₂×Q₈×C₇₉	—	2	2	no	—
107	C₂×Q₈×C₇₉	—	2	2	no	—
108	C₂×Q₈×C₇₉	—	2	2	no	—
109	C₂×Q₈×C₇₉	—	4	1	no	—
110	C₂×Q₈×C₇₉	—	4	2	no	—
111	C₂×Q₈×C₇₉	—	4	2	no	—
112	C₂×Q₈×C₇₉	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₇₉	—	2	1	no	—
114	C₂²×C₄×C₇₉	—	2	1	no	—
115	C₂²×C₄×C₇₉	—	4	1	no	—
116	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
119	C₂×C₈×C₇₉	—	2	2	no	—
120	C₂×C₈×C₇₉	—	4	2	no	—
121	C₄⋊C₄×C₇₉	—	2	2	no	—
122	C₄⋊C₄×C₇₉	—	2	1	no	—
123	C₄⋊C₄×C₇₉	—	2	2	no	—
124	C₄⋊C₄×C₇₉	—	2	2	no	—
125	C₄⋊C₄×C₇₉	—	2	2	no	—
126	C₄⋊C₄×C₇₉	—	4	1	no	—
127	C₄⋊C₄×C₇₉	—	4	1	no	—
128	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
129	C₄²×C₇₉	—	2	2	no	—
130	C₄²×C₇₉	—	2	2	no	—
131	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₇₉	#41	1	1	yes	characteristic
134	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
135	C₂³×C₇₉	#121	1	1	yes	characteristic
136	C₂²×D₇₉	—	4	2	no	—
137	C₂²×D₇₉	—	8	2	no	—
138	C₂²×D₇₉	—	8	2	no	—
139	C₂²×D₇₉	—	8	2	no	—
140	Q₈×C₇₉	—	2	2	no	—
141	Q₈×C₇₉	—	2	2	no	—
142	Q₈×C₇₉	—	4	2	no	—
143	Q₈×C₇₉	—	4	2	no	—
144	Q₈×C₇₉	—	4	2	no	—
145	Q₈×C₇₉	—	8	2	no	—
146	C₂×C₄×C₇₉	—	2	2	no	—
147	C₂×C₄×C₇₉	—	2	2	no	—
148	C₂×C₄×C₇₉	—	2	2	no	—
149	C₂×C₄×C₇₉	—	4	2	no	—
150	C₂×C₄×C₇₉	—	4	2	no	—
151	C₂×C₄×C₇₉	—	4	2	no	—
152	C₂×C₄×C₇₉	—	8	2	no	—
153	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
154	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
155	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
156	C₂×C₄×C₇₉	C₂×SD₁₆	1	2	yes	—
157	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
158	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
159	C₂×C₄×C₇₉	#137	1	2	yes	—
160	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
163	D₃₁₆	—	4	2	no	—
164	D₃₁₆	—	4	2	no	—
165	D₃₁₆	—	4	2	no	—
166	D₃₁₆	—	4	2	no	—
167	D₃₁₆	—	8	2	no	—
168	D₃₁₆	—	8	2	no	—
169	D₃₁₆	—	8	2	no	—
170	D₃₁₆	—	8	2	no	—
171	C₈×C₇₉	—	4	2	no	—
172	C₇₉⋊C₈	—	2	2	no	—
173	C₇₉⋊C₈	—	4	2	no	—
174	C₇₉⋊C₈	—	4	2	no	—
175	C₇₉⋊C₈	C₂×SD₁₆	1	4	yes	complemented
176	C₂²×C₇₉	#460	1	2	yes	—
177	C₂²×C₇₉	#468	1	2	yes	—
178	C₂²×C₇₉	#471	1	2	yes	—
179	C₂²×C₇₉	C₂×#121	1	1	yes	characteristic
180	C₂×D₇₉	—	8	2	no	—
181	C₂×D₇₉	—	8	2	no	—
182	C₂×D₇₉	—	8	2	no	—
183	C₂×D₇₉	—	16	4	no	—
184	C₄×C₇₉	—	2	1	no	—
185	C₄×C₇₉	—	2	1	no	—
186	C₄×C₇₉	—	4	2	no	—
187	C₄×C₇₉	—	4	2	no	—
188	C₄×C₇₉	—	8	2	no	—
189	C₄×C₇₉	#460	1	2	yes	—
190	C₄×C₇₉	#468	1	2	yes	—
191	C₄×C₇₉	C₂²×SD₁₆	1	1	yes	characteristic
192	C₄×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
193	C₄×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
194	C₄×C₇₉	C₂×#137	1	1	yes	characteristic
195	C₂×#1686	—	79	1	no	maximal, Sylow
196	C₂×C₇₉	#1686	1	4	yes	complemented
197	C₂×C₇₉	C₂×#460	1	1	yes	characteristic
198	C₂×C₇₉	C₂×#468	1	1	yes	characteristic
199	C₂×C₇₉	C₂×#471	1	1	yes	characteristic
200	D₇₉	—	16	2	no	—
201	C₂×#492	—	79	1	no	—
202	C₂×#475	D₇₉	1	1	yes	characteristic, complemented
203	C₂×#460	—	79	1	no	—
204	C₂×#446	—	79	1	no	—
205	#1686	—	79	8	no	—
206	C₂×#335	—	79	1	no	—
207	C₂×#332	—	79	1	no	—
208	C₂×#331	—	79	1	no	—
209	C₇₉	C₂×#1686	1	1	yes	characteristic, complemented, Sylow
210	C₂²×SD₁₆	—	158	1	no	—
211	C₂²×SD₁₆	—	158	1	no	—
212	C₂²×SD₁₆	—	158	1	no	—
213	C₂×C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
214	C₂×#127	—	79	1	no	—
215	C₂×C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic
216	#492	—	79	4	no	—
217	#492	—	158	2	no	—
218	#475	—	2	2	no	—
219	#475	C₂×D₇₉	1	4	yes	complemented
220	#460	—	79	4	no	—
221	#460	—	158	2	no	—
222	#446	—	79	4	no	—
223	#446	—	158	2	no	—
224	C₂×#106	—	2	1	no	—
225	C₂×C₄⋊C₈	—	79	1	no	—
226	C₂×C₄⋊C₈	—	79	1	no	—
227	C₂×C₄⋊C₈	—	158	1	no	—
228	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
229	C₂×#103	—	2	1	no	—
230	C₂×#102	—	158	1	no	—
231	C₂×#97	—	158	1	no	—
232	C₂×C₄×C₈	—	79	1	no	—
233	#335	—	79	4	no	—
234	#332	—	79	4	no	—
235	#331	—	79	4	no	—
236	C₂²×Q₈	—	2	1	no	—
237	C₂²×Q₈	C₂²⋊D₇₉	1	1	yes	characteristic
238	C₂²×D₄	—	158	1	no	—
239	C₂²×D₄	—	158	1	no	—
240	C₂²×D₄	—	158	1	no	—
241	C₂×SD₁₆	—	316	4	no	—
242	C₂×SD₁₆	—	316	4	no	—
243	C₂×SD₁₆	—	316	4	no	—
244	C₂×SD₁₆	—	158	4	no	—
245	C₂×SD₁₆	—	158	4	no	—
246	C₂×SD₁₆	—	158	4	no	—
247	C₂²×C₈	—	2	1	no	—
248	C₂²×C₈	—	79	1	no	—
249	C₂²×C₈	—	79	1	no	—
250	C₂²×C₈	—	158	1	no	—
251	C₂²×C₈	—	158	1	no	—
252	C₄⋊Q₈	—	2	1	no	—
253	C₄⋊Q₈	—	2	1	no	—
254	C₄⋊Q₈	—	2	1	no	—
255	C₄⋊Q₈	C₂²×D₇₉	1	2	yes	—
256	#127	—	79	2	no	—
257	#127	—	158	1	no	—
258	#127	—	158	1	no	—
259	#127	—	158	1	no	—
260	C₄×Q₈	—	2	1	no	—
261	C₄×Q₈	—	2	1	no	—
262	C₄×Q₈	C₂²⋊D₇₉	1	2	yes	—
263	C₄×Q₈	C₂²×D₇₉	1	2	yes	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	C₂²⋊D₇₉	1	1	yes	characteristic
268	C₂×C₄²	—	2	1	no	—
269	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
270	#106	—	2	4	no	—
271	C₄⋊C₈	—	2	1	no	—
272	C₄⋊C₈	—	79	2	no	—
273	C₄⋊C₈	—	79	2	no	—
274	C₄⋊C₈	—	158	4	no	—
275	C₄⋊C₈	—	158	1	no	—
276	C₄⋊C₈	—	158	1	no	—
277	C₄⋊C₈	C₂²×D₇₉	1	2	yes	—
278	#103	—	2	4	no	—
279	#102	—	158	4	no	—
280	#97	—	158	4	no	—
281	C₄×C₈	—	79	2	no	—
282	C₄×C₈	—	79	2	no	—
283	C₂⁴	—	316	1	no	—
284	C₂×Q₈	—	2	1	no	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	4	1	no	—
289	C₂×Q₈	—	4	2	no	—
290	C₂×Q₈	—	4	2	no	—
291	C₂×Q₈	C₂×C₂²⋊D₇₉	1	2	yes	—
292	C₂×D₄	—	316	1	no	—
293	C₂×D₄	—	316	1	no	—
294	C₂×D₄	—	316	1	no	—
295	C₂×D₄	—	316	2	no	—
296	C₂×D₄	—	316	2	no	—
297	C₂×D₄	—	316	2	no	—
298	C₂×D₄	—	316	2	no	—
299	C₂×D₄	—	632	2	no	—
300	C₂×D₄	—	158	2	no	—
301	C₂×D₄	—	158	2	no	—
302	C₂×D₄	—	158	2	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	4	1	no	—
306	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
307	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
308	C₂²×C₄	#11929623	1	1	yes	characteristic
309	SD₁₆	—	316	8	no	—
310	SD₁₆	—	316	8	no	—
311	SD₁₆	—	316	8	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	4	2	no	—
314	C₂×C₈	—	316	2	no	—
315	C₂×C₈	—	316	2	no	—
316	C₂×C₈	—	79	4	no	—
317	C₂×C₈	—	79	2	no	—
318	C₂×C₈	—	79	2	no	—
319	C₂×C₈	—	158	2	no	—
320	C₂×C₈	—	158	2	no	—
321	C₂×C₈	—	158	2	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	1	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	4	1	no	—
328	C₄⋊C₄	—	4	1	no	—
329	C₄⋊C₄	C₂×C₂²⋊D₇₉	1	2	yes	—
330	C₄²	—	2	2	no	—
331	C₄²	—	2	2	no	—
332	C₄²	D₄×D₇₉	1	1	yes	characteristic
333	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
334	C₄²	#11929623	1	1	yes	characteristic
335	C₄²	C₂³×D₇₉	1	1	yes	characteristic
336	C₂³	—	316	2	no	—
337	C₂³	—	632	2	no	—
338	C₂³	—	632	2	no	—
339	C₂³	—	632	2	no	—
340	C₂³	#14579133	1	1	yes	characteristic
341	Q₈	—	2	2	no	—
342	Q₈	—	2	2	no	—
343	Q₈	—	4	2	no	—
344	Q₈	—	4	2	no	—
345	Q₈	—	4	2	no	—
346	Q₈	—	8	2	no	—
347	D₄	—	316	2	no	—
348	D₄	—	316	2	no	—
349	D₄	—	316	2	no	—
350	D₄	—	316	2	no	—
351	D₄	—	632	2	no	—
352	D₄	—	632	2	no	—
353	D₄	—	632	2	no	—
354	D₄	—	632	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	8	2	no	—
362	C₂×C₄	#14579133	1	1	yes	characteristic
363	C₂×C₄	#14579133	1	1	yes	characteristic
364	C₂×C₄	#14579133	1	1	yes	characteristic
365	C₂×C₄	SD₁₆×D₇₉	1	2	yes	—
366	C₂×C₄	#14579186	1	2	yes	—
367	C₂×C₄	#14579188	1	2	yes	—
368	C₂×C₄	#14579192	1	2	yes	—
369	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
370	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
371	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
372	C₈	—	4	2	no	—
373	C₈	—	316	2	no	—
374	C₈	—	316	2	no	—
375	C₈	—	79	4	no	—
376	C₈	—	158	2	no	—
377	C₂²	—	632	2	no	—
378	C₂²	—	632	2	no	—
379	C₂²	—	632	2	no	—
380	C₂²	—	1264	4	no	—
381	C₂²	#19098761	1	2	yes	—
382	C₂²	#19098811	1	2	yes	—
383	C₂²	#19098828	1	2	yes	—
384	C₂²	C₂×#14579133	1	1	yes	characteristic
385	C₄	—	2	1	no	—
386	C₄	—	2	1	no	—
387	C₄	—	4	2	no	—
388	C₄	—	4	2	no	—
389	C₄	—	8	2	no	—
390	C₄	#19098761	1	2	yes	—
391	C₄	#19098811	1	2	yes	—
392	C₄	C₂×SD₁₆×D₇₉	1	1	yes	characteristic
393	C₄	C₂×#14579186	1	1	yes	characteristic
394	C₄	C₂×#14579188	1	1	yes	characteristic
395	C₄	C₂×#14579192	1	1	yes	characteristic
396	C₂	—	1264	2	no	—
397	C₂	#23762874	1	4	yes	direct product factor
398	C₂	C₂×#19098761	1	1	yes	characteristic
399	C₂	C₂×#19098811	1	1	yes	characteristic
400	C₂	C₂×#19098828	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#14579133
commutator, cosocle	C₄²×C₇₉	C₂⁴
Frattini	C₄²	C₂³×D₇₉
Fitting	C₂×#475×C₇₉	C₂
socle	C₂³×C₇₉	#121
prime radical	C₂×#14579158	C₂²
hypercenter	C₂×#475	D₇₉
hypocenter	C₇₉	C₂×#1686
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#475

Complements

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

N	H ≅ G/N	type
3. C₂×#19098694	C₂	semidirect
4. #23762874	C₂	direct (N × H)
5. C₂×#19098315	C₂	semidirect
6. C₂×#19098309	C₂	semidirect
8. C₂×#475×C₇₉	C₂	semidirect
18. #19098694	C₂²	semidirect
25. #19098315	C₂²	semidirect
26. #19098309	C₂²	semidirect
31. #475×C₇₉	C₂²	semidirect
102. C₂×C₇₉⋊C₈	SD₁₆	semidirect
175. C₇₉⋊C₈	C₂×SD₁₆	semidirect
196. C₂×C₇₉	#1686	semidirect
202. C₂×#475	D₇₉	semidirect
209. C₇₉	C₂×#1686	semidirect
219. #475	C₂×D₇₉	semidirect
397. C₂	#23762874	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×#19098937	2
C₂×#19098763	2
C₂×#19098694	2
#23762874	2
C₂×#19098315	2
C₂×#19098309	2
C₂×#19098306	2
C₂×#475×C₇₉	2
C₂×#1686	79

Subgroups — C2×#23762874 #34270863

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#23762874 #34270863