Subgroups — C₄×#19099006 #34441602

Order 20224.

674 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19099006	C₂	1	1	yes	maximal, characteristic
2	C₄×#14579183	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×Dic₃₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#23765272	C₂	1	2	yes	maximal, complemented
5	#23765266	C₂	1	2	yes	maximal, complemented
6	C₄×Dic₆₃₂	C₂	1	2	yes	maximal, complemented
7	C₄×#14579106	C₂	1	2	yes	maximal, complemented
8	#23765188	C₂	1	1	yes	maximal, characteristic, complemented
9	#23765121	C₂	1	1	yes	maximal, characteristic, complemented
10	#23765113	C₂	1	1	yes	maximal, characteristic
11	C₄×M₃₂×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14579183	C₂²	1	1	yes	characteristic
13	C₂²×Dic₃₁₆	C₂²	1	1	yes	characteristic
14	C₄×#11929624	—	2	1	no	—
15	C₂×C₄×Dic₁₅₈	—	2	1	no	—
16	#19099006	C₄	1	8	yes	direct product factor
17	C₂×Dic₆₃₂	C₂²	1	2	yes	—
18	C₂×#14579106	C₂²	1	2	yes	—
19	C₄×Dic₃₁₆	—	2	1	no	—
20	C₄×Dic₃₁₆	—	2	1	no	—
21	C₄×Dic₃₁₆	C₂²	1	2	yes	—
22	C₄×Dic₃₁₆	C₂²	1	2	yes	—
23	C₄×Dic₃₁₆	C₂²	1	1	yes	characteristic
24	C₄×Dic₃₁₆	C₂²	1	1	yes	characteristic
25	C₄×#11929613	—	2	1	no	—
26	C₄×#11929613	—	2	1	no	—
27	C₄×D₆₃₂	C₂²	1	1	yes	characteristic
28	C₄×D₆₃₂	C₂²	1	1	yes	characteristic
29	#19098601	C₂²	1	1	yes	characteristic
30	C₂×#14579095	C₂²	1	1	yes	characteristic
31	#19098560	—	2	1	no	—
32	C₂×#14579086	—	2	1	no	—
33	#19098391	C₂²	1	2	yes	—
34	#19098389	C₂²	1	2	yes	—
35	#19098368	C₂²	1	2	yes	—
36	#19098368	C₂²	1	2	yes	—
37	#19098368	C₂²	1	2	yes	—
38	#19098365	C₂²	1	2	yes	—
39	C₂×M₃₂×C₇₉	C₂²	1	1	yes	characteristic
40	C₂×M₃₂×C₇₉	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
42	#346×C₇₉	C₂²	1	2	yes	—
43	C₄×C₁₆×C₇₉	C₂²	1	2	yes	—
44	C₂×#11929624	—	2	1	no	—
45	C₂²×Dic₁₅₈	—	2	1	no	—
46	#14579183	—	2	2	no	—
47	#14579183	C₂×C₄	1	4	yes	—
48	C₂×Dic₃₁₆	—	2	1	no	—
49	C₂×Dic₃₁₆	—	2	2	no	—
50	C₂×Dic₃₁₆	C₂×C₄	1	4	yes	complemented
51	C₂×Dic₃₁₆	C₂³	1	2	yes	—
52	C₂×Dic₃₁₆	C₂³	1	1	yes	characteristic
53	C₂×#11929613	—	2	1	no	—
54	C₂×D₆₃₂	C₂³	1	1	yes	characteristic
55	C₄×Dic₁₅₈	—	2	1	no	—
56	C₄×Dic₁₅₈	—	2	1	no	—
57	C₄×Dic₁₅₈	—	2	2	no	—
58	C₄×Dic₁₅₈	—	2	2	no	—
59	C₄×Dic₁₅₈	—	4	1	no	—
60	C₄×Dic₁₅₈	—	4	1	no	—
61	C₄×D₃₁₆	—	2	1	no	—
62	C₄×D₃₁₆	—	2	1	no	—
63	C₄×C₂²⋊D₇₉	—	4	1	no	—
64	C₄×C₂²⋊D₇₉	—	4	1	no	—
65	#14579120	—	2	1	no	—
66	#14579118	—	4	1	no	—
67	C₂×C₄⋊Dic₇₉	—	2	1	no	—
68	C₂×Dic₇₉⋊C₄	—	4	1	no	—
69	C₂×C₄×Dic₇₉	—	4	1	no	—
70	C₄²×D₇₉	—	4	1	no	—
71	Dic₆₃₂	C₂×C₄	1	8	yes	complemented
72	#14579106	C₂×C₄	1	8	yes	complemented
73	#14579095	—	2	1	no	—
74	#14579095	C₂³	1	1	yes	characteristic
75	#14579095	C₂³	1	1	yes	characteristic
76	#14579095	C₂³	1	2	yes	—
77	#14579093	—	2	1	no	—
78	#14579086	—	2	1	no	—
79	#14579086	—	2	1	no	—
80	#14579086	—	2	2	no	—
81	#14579086	—	2	2	no	—
82	#14579083	—	2	1	no	—
83	#14579083	—	2	1	no	—
84	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
85	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
87	M₃₂×C₇₉	—	2	2	no	—
88	M₃₂×C₇₉	C₂×C₄	1	4	yes	complemented
89	C₂×C₁₆×C₇₉	C₂³	1	2	yes	—
90	C₂×C₁₆×C₇₉	C₂³	1	2	yes	—
91	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
92	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
93	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
95	#11929624	—	2	4	no	—
96	#11929624	—	4	2	no	—
97	C₂×Dic₁₅₈	—	2	4	no	—
98	C₂×Dic₁₅₈	—	2	2	no	—
99	C₂×Dic₁₅₈	—	2	1	no	—
100	C₂×Dic₁₅₈	—	4	1	no	—
101	C₂×Dic₁₅₈	—	4	2	no	—
102	C₂×D₃₁₆	—	2	1	no	—
103	C₂×C₂²⋊D₇₉	—	4	1	no	—
104	C₂²×Dic₇₉	—	4	1	no	—
105	C₂²×Dic₇₉	—	4	1	no	—
106	C₂×C₄×D₇₉	—	4	1	no	—
107	C₂×C₄×D₇₉	—	4	1	no	—
108	C₂×C₄×D₇₉	—	4	1	no	—
109	Dic₃₁₆	—	2	4	no	—
110	Dic₃₁₆	—	2	2	no	—
111	Dic₃₁₆	—	2	1	no	—
112	Dic₃₁₆	C₂²×C₄	1	4	yes	—
113	Dic₃₁₆	C₂²×C₄	1	2	yes	—
114	#11929613	—	2	4	no	—
115	D₆₃₂	—	2	1	no	—
116	D₆₃₂	C₂²×C₄	1	2	yes	—
117	C₄⋊Dic₇₉	—	2	1	no	—
118	C₄⋊Dic₇₉	—	2	1	no	—
119	C₄⋊Dic₇₉	—	2	2	no	—
120	C₄⋊Dic₇₉	—	4	1	no	—
121	Dic₇₉⋊C₄	—	4	2	no	—
122	Dic₇₉⋊C₄	—	4	2	no	—
123	Dic₇₉⋊C₄	—	4	1	no	—
124	Dic₇₉⋊C₄	—	4	1	no	—
125	C₂²⋊Dic₇₉	—	4	1	no	—
126	(C₂×D₇₉)⋊C₄	—	4	1	no	—
127	(C₂×D₇₉)⋊C₄	—	4	1	no	—
128	C₄×Dic₇₉	—	4	1	no	—
129	C₄×Dic₇₉	—	4	1	no	—
130	C₄×Dic₇₉	—	4	1	no	—
131	C₄×Dic₇₉	—	4	2	no	—
132	C₄×Dic₇₉	—	4	2	no	—
133	C₂²×C₄×C₇₉	D₈	1	1	yes	characteristic
134	C₂²×C₄×C₇₉	D₈	1	1	yes	characteristic
135	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
136	C₂×C₈×C₇₉	—	2	2	no	—
137	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
138	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
139	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
140	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
141	C₂×C₈×C₇₉	#41	1	2	yes	—
142	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
143	C₄²×C₇₉	D₈	1	1	yes	characteristic
144	C₄²×C₇₉	D₈	1	1	yes	characteristic
145	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
146	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
147	C₁₆×C₇₉	—	2	2	no	—
148	C₁₆×C₇₉	C₂²×C₄	1	4	yes	—
149	C₂³×C₇₉	C₂×D₈	1	1	yes	characteristic
150	C₂²×D₇₉	—	4	1	no	—
151	C₂×C₄×C₇₉	—	2	2	no	—
152	C₂×C₄×C₇₉	—	4	1	no	—
153	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
154	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
155	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
156	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
157	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
158	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
159	C₂×C₄×C₇₉	#135	1	2	yes	—
160	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
161	C₂²⋊D₇₉	—	4	4	no	—
162	C₂×Dic₇₉	—	4	1	no	—
163	C₂×Dic₇₉	—	4	2	no	—
164	C₂×Dic₇₉	—	4	4	no	—
165	C₂×Dic₇₉	—	4	1	no	—
166	C₂×Dic₇₉	—	4	1	no	—
167	C₂×Dic₇₉	—	4	2	no	—
168	C₂×Dic₇₉	—	8	2	no	—
169	D₃₁₆	—	2	2	no	—
170	D₃₁₆	—	4	1	no	—
171	C₄×D₇₉	—	4	4	no	—
172	C₄×D₇₉	—	8	2	no	—
173	C₄×D₇₉	—	8	2	no	—
174	Dic₁₅₈	—	2	2	no	—
175	Dic₁₅₈	—	2	4	no	—
176	Dic₁₅₈	—	4	2	no	—
177	Dic₁₅₈	—	4	1	no	—
178	Dic₁₅₈	—	4	4	no	—
179	C₈×C₇₉	—	2	1	no	—
180	C₈×C₇₉	—	2	1	no	—
181	C₈×C₇₉	C₄×D₄	1	2	yes	—
182	C₈×C₇₉	C₂³×C₄	1	1	yes	characteristic
183	C₈×C₇₉	C₂×#41	1	1	yes	characteristic
184	C₂²×C₇₉	—	2	1	no	—
185	C₂²×C₇₉	—	2	1	no	—
186	C₂²×C₇₉	C₄×D₈	1	2	yes	—
187	C₂²×C₇₉	C₂²×D₈	1	1	yes	characteristic
188	C₂×D₇₉	—	4	2	no	—
189	C₂×D₇₉	—	8	1	no	—
190	C₂×D₇₉	—	8	1	no	—
191	C₄×C₇₉	—	2	1	no	—
192	C₄×C₇₉	—	2	1	no	—
193	C₄×C₇₉	—	2	1	no	—
194	C₄×C₇₉	C₄×D₈	1	2	yes	—
195	C₄×C₇₉	#510	1	2	yes	complemented
196	C₄×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
197	C₄×C₇₉	C₂×#135	1	1	yes	characteristic
198	Dic₇₉	—	4	2	no	—
199	Dic₇₉	—	4	4	no	—
200	Dic₇₉	—	8	1	no	—
201	Dic₇₉	—	8	1	no	—
202	Dic₇₉	—	8	2	no	—
203	C₄×#510	—	79	1	no	maximal, Sylow
204	C₂×C₇₉	—	2	2	no	—
205	C₂×C₇₉	C₂×C₄×D₈	1	1	yes	characteristic
206	C₂×C₇₉	C₂×#510	1	1	yes	characteristic
207	C₂×C₇₉	#3414	1	1	yes	characteristic
208	D₇₉	—	8	2	no	—
209	C₂×#510	—	79	1	no	—
210	C₄×#135	—	79	1	no	—
211	C₂×C₄×Q₁₆	—	79	1	no	—
212	#2176	—	79	2	no	—
213	#2175	—	79	2	no	—
214	C₄×Q₃₂	—	79	2	no	—
215	C₄×SD₃₂	—	79	2	no	—
216	#2159	—	79	1	no	—
217	#2141	—	79	1	no	—
218	#2139	—	79	1	no	—
219	C₄×M₃₂	D₇₉	1	1	yes	characteristic, complemented
220	C₇₉	C₄×#510	1	1	yes	characteristic, complemented, Sylow
221	C₂×#135	—	79	1	no	—
222	C₂²×Q₁₆	—	79	1	no	—
223	C₄×#41	—	158	1	no	—
224	C₂×C₄×Q₈	—	158	1	no	—
225	#510	—	79	8	no	—
226	C₂×Q₃₂	—	79	2	no	—
227	C₂×SD₃₂	—	79	2	no	—
228	C₂×M₃₂	C₂×D₇₉	1	1	yes	characteristic
229	C₂×M₃₂	C₂×D₇₉	1	1	yes	characteristic
230	C₄×Q₁₆	—	79	2	no	—
231	C₄×Q₁₆	—	79	2	no	—
232	C₄×Q₁₆	—	79	1	no	—
233	C₄×Q₁₆	—	79	1	no	—
234	C₄×Q₁₆	—	158	1	no	—
235	C₄×Q₁₆	—	158	1	no	—
236	C₄×SD₁₆	—	158	1	no	—
237	C₄×SD₁₆	—	158	1	no	—
238	C₄×D₈	—	79	1	no	—
239	C₄×D₈	—	79	1	no	—
240	#427	—	79	1	no	—
241	C₂×#107	—	79	1	no	—
242	#416	—	158	1	no	—
243	C₂×#103	—	158	1	no	—
244	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
245	#367	—	79	2	no	—
246	#366	—	79	2	no	—
247	#358	—	79	2	no	—
248	#358	—	79	2	no	—
249	#358	—	79	2	no	—
250	#357	—	79	2	no	—
251	#346	C₂×D₇₉	1	2	yes	—
252	C₄×C₁₆	C₂×D₇₉	1	2	yes	—
253	C₂×#41	—	158	1	no	—
254	C₂²×Q₈	—	158	1	no	—
255	#135	—	79	4	no	—
256	#135	—	158	2	no	—
257	C₂×Q₁₆	—	79	4	no	—
258	C₂×Q₁₆	—	79	2	no	—
259	C₂×Q₁₆	—	79	1	no	—
260	C₂×Q₁₆	—	158	1	no	—
261	C₂×Q₁₆	—	158	2	no	—
262	C₂×SD₁₆	—	158	1	no	—
263	C₂×D₈	—	79	1	no	—
264	C₂²×C₈	D₃₁₆	1	1	yes	characteristic
265	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
266	C₄×Q₈	—	316	1	no	—
267	C₄×Q₈	—	316	1	no	—
268	C₄×Q₈	—	158	2	no	—
269	C₄×Q₈	—	158	2	no	—
270	C₄×Q₈	—	158	1	no	—
271	C₄×Q₈	—	158	1	no	—
272	C₄×D₄	—	316	1	no	—
273	C₄×D₄	—	316	1	no	—
274	C₄×D₄	—	158	1	no	—
275	C₄×D₄	—	158	1	no	—
276	#117	—	316	1	no	—
277	#117	—	158	1	no	—
278	C₂×C₄⋊C₄	—	316	1	no	—
279	C₂×C₄⋊C₄	—	158	1	no	—
280	C₂×C₄²	—	316	1	no	—
281	C₂×C₄²	—	316	1	no	—
282	C₂×C₄²	D₃₁₆	1	1	yes	characteristic
283	Q₃₂	—	79	8	no	—
284	SD₃₂	—	79	8	no	—
285	M₃₂	—	2	2	no	—
286	M₃₂	C₄×D₇₉	1	4	yes	complemented
287	C₂×C₁₆	C₂²×D₇₉	1	2	yes	—
288	C₂×C₁₆	C₂²×D₇₉	1	2	yes	—
289	#107	—	79	2	no	—
290	#107	—	79	1	no	—
291	#107	—	79	1	no	—
292	#107	—	158	1	no	—
293	#106	—	158	1	no	—
294	#103	—	158	2	no	—
295	#103	—	158	2	no	—
296	#103	—	158	1	no	—
297	#103	—	158	1	no	—
298	#102	—	158	1	no	—
299	#102	—	158	1	no	—
300	C₄×C₈	D₃₁₆	1	1	yes	characteristic
301	C₄×C₈	D₃₁₆	1	1	yes	characteristic
302	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
303	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
304	#41	—	316	2	no	—
305	#41	—	158	4	no	—
306	C₂×Q₈	—	316	1	no	—
307	C₂×Q₈	—	316	2	no	—
308	C₂×Q₈	—	158	4	no	—
309	C₂×Q₈	—	158	1	no	—
310	C₂×Q₈	—	158	2	no	—
311	C₂×D₄	—	316	1	no	—
312	C₂×D₄	—	158	1	no	—
313	C₂²×C₄	—	316	1	no	—
314	C₂²×C₄	—	316	1	no	—
315	C₂²×C₄	—	316	1	no	—
316	C₂²×C₄	—	316	1	no	—
317	C₂²×C₄	—	316	1	no	—
318	C₂²×C₄	D₆₃₂	1	1	yes	characteristic
319	C₂²×C₄	D₆₃₂	1	1	yes	characteristic
320	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
321	Q₁₆	—	79	4	no	—
322	Q₁₆	—	79	2	no	—
323	Q₁₆	—	158	2	no	—
324	Q₁₆	—	158	1	no	—
325	Q₁₆	—	158	4	no	—
326	SD₁₆	—	158	4	no	—
327	D₈	—	79	2	no	—
328	D₈	—	158	1	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	C₂×C₄×D₇₉	1	2	yes	—
331	C₂×C₈	C₂×D₃₁₆	1	1	yes	characteristic
332	C₂×C₈	C₂×D₃₁₆	1	1	yes	characteristic
333	C₂×C₈	C₂×D₃₁₆	1	1	yes	characteristic
334	C₂×C₈	#11929624	1	2	yes	—
335	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
336	C₄⋊C₄	—	316	2	no	—
337	C₄⋊C₄	—	316	2	no	—
338	C₄⋊C₄	—	316	1	no	—
339	C₄⋊C₄	—	316	1	no	—
340	C₄⋊C₄	—	316	1	no	—
341	C₄⋊C₄	—	158	1	no	—
342	C₄⋊C₄	—	158	1	no	—
343	C₄⋊C₄	—	158	2	no	—
344	C₂²⋊C₄	—	316	1	no	—
345	C₂²⋊C₄	—	316	1	no	—
346	C₂²⋊C₄	—	316	1	no	—
347	C₄²	—	316	1	no	—
348	C₄²	—	316	1	no	—
349	C₄²	—	316	2	no	—
350	C₄²	—	316	1	no	—
351	C₄²	—	316	2	no	—
352	C₄²	D₆₃₂	1	1	yes	characteristic
353	C₄²	D₆₃₂	1	1	yes	characteristic
354	C₄²	C₂×D₃₁₆	1	1	yes	characteristic
355	C₄²	C₂×D₃₁₆	1	1	yes	characteristic
356	C₁₆	—	2	2	no	—
357	C₁₆	C₂×C₄×D₇₉	1	4	yes	—
358	C₂³	—	316	1	no	—
359	C₂³	C₂×D₆₃₂	1	1	yes	characteristic
360	Q₈	—	316	4	no	—
361	Q₈	—	316	2	no	—
362	Q₈	—	316	1	no	—
363	Q₈	—	158	2	no	—
364	Q₈	—	158	4	no	—
365	D₄	—	316	4	no	—
366	D₄	—	316	1	no	—
367	D₄	—	158	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	316	4	no	—
371	C₂×C₄	—	316	1	no	—
372	C₂×C₄	—	316	2	no	—
373	C₂×C₄	—	316	4	no	—
374	C₂×C₄	—	316	1	no	—
375	C₂×C₄	—	316	1	no	—
376	C₂×C₄	—	316	2	no	—
377	C₂×C₄	—	632	2	no	—
378	C₂×C₄	—	632	2	no	—
379	C₂×C₄	—	632	2	no	—
380	C₂×C₄	C₄×D₃₁₆	1	2	yes	—
381	C₂×C₄	C₂×D₆₃₂	1	1	yes	characteristic
382	C₂×C₄	C₂×D₆₃₂	1	1	yes	characteristic
383	C₂×C₄	C₂×D₆₃₂	1	1	yes	characteristic
384	C₂×C₄	C₂×D₆₃₂	1	1	yes	characteristic
385	C₂×C₄	C₂×D₆₃₂	1	1	yes	characteristic
386	C₂×C₄	#14579183	1	2	yes	—
387	C₂×C₄	C₂²×D₃₁₆	1	1	yes	characteristic
388	C₈	—	2	1	no	—
389	C₈	—	2	1	no	—
390	C₈	C₄×D₃₁₆	1	2	yes	—
391	C₈	C₂²×C₄×D₇₉	1	1	yes	characteristic
392	C₈	C₂×#11929624	1	1	yes	characteristic
393	C₂²	—	2	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	316	2	no	—
396	C₂²	—	632	1	no	—
397	C₂²	—	632	1	no	—
398	C₂²	C₄×D₆₃₂	1	2	yes	—
399	C₂²	C₂²×D₆₃₂	1	1	yes	characteristic
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	316	2	no	—
404	C₄	—	316	4	no	—
405	C₄	—	632	1	no	—
406	C₄	—	632	1	no	—
407	C₄	—	632	2	no	—
408	C₄	C₄×D₆₃₂	1	2	yes	—
409	C₄	#19099006	1	2	yes	direct product factor
410	C₄	C₂×C₄×D₃₁₆	1	1	yes	characteristic
411	C₄	C₂×#14579183	1	1	yes	characteristic
412	C₂	—	2	2	no	—
413	C₂	—	632	2	no	—
414	C₂	C₂×C₄×D₆₃₂	1	1	yes	characteristic
415	C₂	C₂×#19099006	1	1	yes	characteristic
416	C₂	#23776536	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₆₃₂
commutator	C₈×C₇₉	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₇₉
Fitting	C₄×M₃₂×C₇₉	C₂
socle	C₂²×C₇₉	C₂²×D₈
prime radical	C₂×#14579183	C₂²
cosocle	C₂×C₈×C₇₉	C₂⁴
hypercenter	C₄×M₃₂	D₇₉
hypocenter	C₇₉	C₄×#510
LCS	G ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₄×M₃₂

Complements

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

N	H ≅ G/N	type
3. C₂×C₄×Dic₃₁₆	C₂	semidirect
4. #23765272	C₂	semidirect
5. #23765266	C₂	semidirect
6. C₄×Dic₆₃₂	C₂	semidirect
7. C₄×#14579106	C₂	semidirect
8. #23765188	C₂	semidirect
9. #23765121	C₂	semidirect
11. C₄×M₃₂×C₇₉	C₂	semidirect
16. #19099006	C₄	direct (N × H)
50. C₂×Dic₃₁₆	C₂×C₄	semidirect
71. Dic₆₃₂	C₂×C₄	semidirect
72. #14579106	C₂×C₄	semidirect
88. M₃₂×C₇₉	C₂×C₄	semidirect
195. C₄×C₇₉	#510	semidirect
219. C₄×M₃₂	D₇₉	semidirect
220. C₇₉	C₄×#510	semidirect
286. M₃₂	C₄×D₇₉	semidirect
409. C₄	#19099006	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×#19099006	2
C₄×#14579183	2
C₂×C₄×Dic₃₁₆	2
#23765272	2
#23765266	2
C₄×Dic₆₃₂	2
C₄×#14579106	2
#23765188	2
#23765121	2
#23765113	2
C₄×M₃₂×C₇₉	2
C₄×#510	79

Subgroups — C4×#19099006 #34441602

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#19099006 #34441602