Subgroups — C₂×#135×D₈₃ #24922187

Order 10624.

1504 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×D₈₃	C₂	1	2	yes	maximal, complemented
2	C₂×#14581815	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#14581814	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#14581813	C₂	1	2	yes	maximal, complemented
5	C₂×#14581812	C₂	1	2	yes	maximal, complemented
6	C₂×#14581811	C₂	1	1	yes	maximal, characteristic, complemented
7	#135×D₈₃	C₂	1	16	yes	maximal, direct product factor
8	C₂×Q₁₆×D₈₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×SD₁₆×D₈₃	C₂	1	2	yes	maximal, complemented
10	C₂×D₈×D₈₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₈×D₈₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#135×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#13050591	C₂²	1	2	yes	complemented
14	C₂×#13050590	—	2	2	no	—
15	C₂×#13050590	C₂²	1	2	yes	complemented
16	C₂×#13050589	—	2	2	no	—
17	C₂×#13050589	C₂²	1	2	yes	complemented
18	#41×D₈₃	—	2	8	no	—
19	#41×D₈₃	C₂²	1	16	yes	complemented
20	C₂×Q₈×D₈₃	C₂²	1	2	yes	—
21	C₂×D₄×D₈₃	—	2	2	no	—
22	C₂×D₄×D₈₃	C₂²	1	2	yes	—
23	C₂²×C₄×D₈₃	—	2	2	no	—
24	C₂²×C₄×D₈₃	C₂²	1	1	yes	characteristic
25	#14581815	C₂²	1	8	yes	complemented
26	#14581814	C₂²	1	8	yes	complemented
27	#14581813	C₂²	1	16	yes	complemented
28	#14581812	C₂²	1	16	yes	complemented
29	#14581811	C₂²	1	8	yes	complemented
30	C₂×Dic₃₃₂	C₂²	1	1	yes	characteristic, complemented
31	C₂×#13050580	C₂²	1	2	yes	complemented
32	Q₁₆×D₈₃	C₂²	1	8	yes	complemented
33	C₂×#13050579	C₂²	1	2	yes	complemented
34	C₂×#13050578	C₂²	1	2	yes	complemented
35	C₂×#13050577	C₂²	1	2	yes	complemented
36	SD₁₆×D₈₃	C₂²	1	16	yes	complemented
37	C₂×D₆₆₄	C₂²	1	1	yes	characteristic, complemented
38	C₂×#13050575	C₂²	1	2	yes	complemented
39	D₈×D₈₃	C₂²	1	8	yes	complemented
40	C₂²×C₈₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₈×D₈₃	C₂²	1	1	yes	characteristic
42	C₂×C₈×D₈₃	C₂²	1	1	yes	characteristic
43	C₂×C₈×D₈₃	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₈×D₈₃	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₈×D₈₃	C₂²	1	8	yes	complemented
46	C₂×#41×C₈₃	C₂²	1	2	yes	complemented
47	#135×C₈₃	C₂²	1	8	yes	complemented
48	C₂×Q₁₆×C₈₃	C₂²	1	1	yes	characteristic, complemented
49	C₂×SD₁₆×C₈₃	C₂²	1	2	yes	complemented
50	C₂×D₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
51	C₂²×C₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
52	C₂³×D₈₃	—	2	2	no	—
53	C₂³×D₈₃	D₄	1	1	yes	characteristic
54	#13050591	—	2	4	no	—
55	#13050591	C₂³	1	8	yes	complemented
56	#13050590	—	2	4	no	—
57	#13050590	—	2	16	no	—
58	#13050590	C₂³	1	8	yes	complemented
59	#13050589	—	2	16	no	—
60	#13050589	—	2	4	no	—
61	#13050589	C₂³	1	8	yes	complemented
62	C₂×Dic₁₆₆	—	2	2	no	—
63	C₂×Dic₁₆₆	C₂³	1	2	yes	—
64	Q₈×D₈₃	—	2	4	no	—
65	Q₈×D₈₃	C₂³	1	8	yes	—
66	C₂×D₃₃₂	—	2	2	no	—
67	C₂×D₃₃₂	C₂³	1	2	yes	—
68	C₂×C₂²⋊D₈₃	—	2	2	no	—
69	C₂×C₂²⋊D₈₃	—	2	2	no	—
70	C₂×C₂²⋊D₈₃	—	2	2	no	—
71	D₄×D₈₃	—	2	16	no	—
72	D₄×D₈₃	—	2	4	no	—
73	D₄×D₈₃	C₂³	1	8	yes	—
74	C₂²×Dic₈₃	—	2	2	no	—
75	C₂²×Dic₈₃	D₄	1	1	yes	characteristic
76	C₂×C₄×D₈₃	—	2	2	no	—
77	C₂×C₄×D₈₃	—	2	2	no	—
78	C₂×C₄×D₈₃	—	2	2	no	—
79	C₂×C₄×D₈₃	—	2	16	no	—
80	C₂×C₄×D₈₃	D₄	1	1	yes	characteristic
81	C₂×C₄×D₈₃	D₄	1	4	yes	—
82	C₂×C₄×D₈₃	D₄	1	1	yes	characteristic
83	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
84	C₂×C₄×D₈₃	C₂³	1	4	yes	—
85	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
86	Dic₃₃₂	C₂³	1	4	yes	complemented
87	#13050580	C₂³	1	8	yes	complemented
88	#13050579	C₂³	1	8	yes	complemented
89	#13050578	C₂³	1	8	yes	complemented
90	#13050577	C₂³	1	8	yes	complemented
91	D₆₆₄	C₂³	1	4	yes	complemented
92	#13050575	C₂³	1	8	yes	complemented
93	C₂×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
94	C₂×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
95	C₂×C₈₃⋊C₈	C₂³	1	4	yes	complemented
96	C₈×D₈₃	C₂³	1	4	yes	—
97	C₈×D₈₃	C₂³	1	4	yes	—
98	C₈×D₈₃	C₂³	1	4	yes	complemented
99	C₈×D₈₃	C₂³	1	4	yes	complemented
100	#41×C₈₃	—	2	4	no	—
101	#41×C₈₃	C₂³	1	8	yes	complemented
102	C₂×Q₈×C₈₃	C₂³	1	2	yes	—
103	C₂×D₄×C₈₃	—	2	2	no	—
104	C₂×D₄×C₈₃	C₂³	1	2	yes	—
105	C₂²×C₄×C₈₃	—	2	2	no	—
106	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
107	Q₁₆×C₈₃	C₂³	1	4	yes	complemented
108	SD₁₆×C₈₃	C₂³	1	8	yes	complemented
109	D₈×C₈₃	C₂³	1	4	yes	complemented
110	C₂×C₈×C₈₃	C₂³	1	1	yes	characteristic
111	C₂×C₈×C₈₃	C₂³	1	1	yes	characteristic
112	C₂×C₈×C₈₃	C₂³	1	4	yes	complemented
113	C₂³×C₈₃	—	2	2	no	—
114	C₂³×C₈₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×D₈₃	—	2	4	no	—
116	C₂²×D₈₃	—	2	2	no	—
117	C₂²×D₈₃	—	2	8	no	—
118	C₂²×D₈₃	—	4	8	no	—
119	C₂²×D₈₃	C₂×D₄	1	4	yes	—
120	C₂²×D₈₃	C₂×D₄	1	1	yes	characteristic
121	C₂²×D₈₃	C₂×D₄	1	1	yes	characteristic
122	Q₈×C₈₃	—	2	2	no	—
123	Q₈×C₈₃	C₂⁴	1	4	yes	—
124	D₄×C₈₃	—	2	8	no	—
125	D₄×C₈₃	—	2	2	no	—
126	D₄×C₈₃	C₂⁴	1	4	yes	—
127	C₂×C₄×C₈₃	—	2	2	no	—
128	C₂×C₄×C₈₃	—	2	8	no	—
129	C₂×C₄×C₈₃	C₂×D₄	1	2	yes	—
130	C₂×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
131	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
132	C₂×C₄×C₈₃	C₂⁴	1	2	yes	—
133	C₂²⋊D₈₃	—	2	8	no	—
134	C₂²⋊D₈₃	—	2	8	no	—
135	C₂²⋊D₈₃	—	2	8	no	—
136	C₂×Dic₈₃	—	2	2	no	—
137	C₂×Dic₈₃	—	2	8	no	—
138	C₂×Dic₈₃	C₂×D₄	1	1	yes	characteristic
139	C₂×Dic₈₃	C₂×D₄	1	1	yes	characteristic
140	C₂×Dic₈₃	C₂×D₄	1	4	yes	—
141	D₃₃₂	—	2	8	no	—
142	D₃₃₂	—	2	2	no	—
143	D₃₃₂	C₂⁴	1	4	yes	—
144	C₄×D₈₃	—	2	8	no	—
145	C₄×D₈₃	—	2	8	no	—
146	C₄×D₈₃	—	2	8	no	—
147	C₄×D₈₃	C₂×D₄	1	4	yes	—
148	C₄×D₈₃	C₂×D₄	1	2	yes	—
149	C₄×D₈₃	C₂×D₄	1	2	yes	—
150	C₄×D₈₃	C₂×D₄	1	4	yes	—
151	C₄×D₈₃	C₂⁴	1	2	yes	—
152	C₄×D₈₃	C₂⁴	1	2	yes	—
153	Dic₁₆₆	—	2	2	no	—
154	Dic₁₆₆	—	2	8	no	—
155	Dic₁₆₆	C₂⁴	1	4	yes	—
156	C₈×C₈₃	C₂⁴	1	2	yes	—
157	C₈×C₈₃	C₂⁴	1	2	yes	—
158	C₈₃⋊C₈	C₂⁴	1	2	yes	—
159	C₈₃⋊C₈	C₂⁴	1	2	yes	—
160	C₂²×C₈₃	—	2	2	no	—
161	C₂²×C₈₃	—	2	4	no	—
162	C₂²×C₈₃	—	4	4	no	—
163	C₂²×C₈₃	C₂²×D₄	1	2	yes	—
164	C₂²×C₈₃	C₂²×D₄	1	1	yes	characteristic
165	C₂×D₈₃	—	2	2	no	—
166	C₂×D₈₃	—	2	8	no	—
167	C₂×D₈₃	—	2	4	no	—
168	C₂×D₈₃	—	4	4	no	—
169	C₂×D₈₃	—	4	16	no	—
170	C₂×D₈₃	#135	1	4	yes	direct product factor
171	C₂×D₈₃	C₂²×D₄	1	2	yes	—
172	C₂×D₈₃	C₂²×D₄	1	2	yes	—
173	C₄×C₈₃	—	2	4	no	—
174	C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
175	C₄×C₈₃	C₂²×D₄	1	2	yes	—
176	C₄×C₈₃	C₂⁵	1	1	yes	characteristic
177	Dic₈₃	—	2	4	no	—
178	Dic₈₃	C₂²×D₄	1	2	yes	—
179	Dic₈₃	C₂²×D₄	1	2	yes	—
180	C₂×C₈₃	—	2	2	no	—
181	C₂×C₈₃	—	4	4	no	—
182	C₂×C₈₃	C₂×#135	1	2	yes	complemented
183	C₂×C₈₃	C₂³×D₄	1	1	yes	characteristic
184	D₈₃	—	2	2	no	—
185	D₈₃	—	4	4	no	—
186	D₈₃	C₂×#135	1	4	yes	direct product factor
187	C₂²×#135	—	83	1	no	maximal, Sylow
188	C₈₃	C₂²×#135	1	1	yes	characteristic, complemented, Sylow
189	C₂²×#41	—	83	2	no	—
190	C₂×#135	—	83	2	no	—
191	C₂×#135	—	83	16	no	—
192	C₂×#135	—	83	1	no	—
193	C₂×#135	—	83	2	no	—
194	C₂×#135	—	83	1	no	—
195	C₂×#135	—	83	1	no	—
196	C₂×#135	D₈₃	1	1	yes	characteristic, direct product factor
197	C₂²×Q₁₆	—	83	1	no	—
198	C₂²×SD₁₆	—	83	2	no	—
199	C₂²×D₈	—	83	1	no	—
200	C₂³×C₈	—	83	1	no	—
201	C₂×#41	—	83	16	no	—
202	C₂×#41	—	83	2	no	—
203	C₂×#41	—	83	2	no	—
204	C₂×#41	—	83	2	no	—
205	C₂×#41	—	166	2	no	—
206	C₂×#41	—	166	2	no	—
207	C₂×#41	—	166	8	no	—
208	C₂×#41	C₂×D₈₃	1	2	yes	complemented
209	C₂²×Q₈	—	83	2	no	—
210	C₂²×D₄	—	83	2	no	—
211	C₂²×D₄	—	166	2	no	—
212	C₂³×C₄	—	83	1	no	—
213	C₂³×C₄	—	166	2	no	—
214	#135	—	83	16	no	—
215	#135	—	83	8	no	—
216	#135	—	83	16	no	—
217	#135	—	83	8	no	—
218	#135	—	83	8	no	—
219	#135	C₂×D₈₃	1	8	yes	direct product factor
220	C₂×Q₁₆	—	83	2	no	—
221	C₂×Q₁₆	—	83	8	no	—
222	C₂×Q₁₆	—	83	1	no	—
223	C₂×Q₁₆	C₂×D₈₃	1	1	yes	characteristic, complemented
224	C₂×SD₁₆	—	83	2	no	—
225	C₂×SD₁₆	—	83	2	no	—
226	C₂×SD₁₆	—	83	16	no	—
227	C₂×SD₁₆	—	83	2	no	—
228	C₂×SD₁₆	C₂×D₈₃	1	2	yes	complemented
229	C₂×D₈	—	83	2	no	—
230	C₂×D₈	—	83	8	no	—
231	C₂×D₈	—	83	1	no	—
232	C₂×D₈	C₂×D₈₃	1	1	yes	characteristic, complemented
233	C₂²×C₈	—	83	1	no	—
234	C₂²×C₈	—	83	1	no	—
235	C₂²×C₈	—	83	1	no	—
236	C₂²×C₈	—	83	1	no	—
237	C₂²×C₈	—	83	1	no	—
238	C₂²×C₈	—	83	8	no	—
239	C₂²×C₈	C₂×D₈₃	1	1	yes	characteristic, complemented
240	C₂⁴	—	83	1	no	—
241	C₂⁴	—	166	2	no	—
242	#41	—	2	4	no	—
243	#41	—	83	8	no	—
244	#41	—	83	8	no	—
245	#41	—	83	8	no	—
246	#41	—	166	16	no	—
247	#41	—	166	16	no	—
248	#41	—	166	4	no	—
249	#41	—	166	4	no	—
250	#41	—	166	4	no	—
251	#41	C₂²×D₈₃	1	8	yes	complemented
252	C₂×Q₈	—	83	8	no	—
253	C₂×Q₈	—	83	2	no	—
254	C₂×Q₈	—	166	2	no	—
255	C₂×Q₈	—	166	4	no	—
256	C₂×Q₈	C₂²×D₈₃	1	2	yes	—
257	C₂×D₄	—	2	2	no	—
258	C₂×D₄	—	83	8	no	—
259	C₂×D₄	—	83	2	no	—
260	C₂×D₄	—	166	2	no	—
261	C₂×D₄	—	166	4	no	—
262	C₂×D₄	—	166	2	no	—
263	C₂×D₄	—	166	16	no	—
264	C₂×D₄	—	166	2	no	—
265	C₂×D₄	—	166	2	no	—
266	C₂×D₄	C₂²×D₈₃	1	2	yes	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	83	1	no	—
269	C₂²×C₄	—	83	4	no	—
270	C₂²×C₄	—	83	1	no	—
271	C₂²×C₄	—	83	1	no	—
272	C₂²×C₄	—	83	1	no	—
273	C₂²×C₄	—	83	1	no	—
274	C₂²×C₄	—	83	4	no	—
275	C₂²×C₄	—	166	2	no	—
276	C₂²×C₄	—	166	16	no	—
277	C₂²×C₄	—	166	2	no	—
278	C₂²×C₄	—	166	2	no	—
279	C₂²×C₄	—	166	2	no	—
280	C₂²×C₄	C₂²×D₈₃	1	1	yes	characteristic
281	Q₁₆	—	83	8	no	—
282	Q₁₆	—	83	4	no	—
283	Q₁₆	C₂²×D₈₃	1	4	yes	complemented
284	SD₁₆	—	83	8	no	—
285	SD₁₆	—	83	8	no	—
286	SD₁₆	—	83	8	no	—
287	SD₁₆	C₂²×D₈₃	1	8	yes	complemented
288	D₈	—	83	8	no	—
289	D₈	—	83	4	no	—
290	D₈	C₂²×D₈₃	1	4	yes	complemented
291	C₂×C₈	—	83	1	no	—
292	C₂×C₈	—	83	1	no	—
293	C₂×C₈	—	83	4	no	—
294	C₂×C₈	—	83	4	no	—
295	C₂×C₈	—	83	4	no	—
296	C₂×C₈	—	83	4	no	—
297	C₂×C₈	—	83	4	no	—
298	C₂×C₈	C₂²×D₈₃	1	1	yes	characteristic
299	C₂×C₈	C₂²×D₈₃	1	1	yes	characteristic
300	C₂×C₈	C₂²×D₈₃	1	4	yes	complemented
301	C₂³	—	2	2	no	—
302	C₂³	—	332	8	no	—
303	C₂³	—	83	1	no	—
304	C₂³	—	83	4	no	—
305	C₂³	—	83	1	no	—
306	C₂³	—	166	8	no	—
307	C₂³	—	166	4	no	—
308	C₂³	—	166	2	no	—
309	C₂³	D₄×D₈₃	1	1	yes	characteristic
310	Q₈	—	2	2	no	—
311	Q₈	—	83	4	no	—
312	Q₈	—	166	8	no	—
313	Q₈	—	166	2	no	—
314	Q₈	C₂³×D₈₃	1	4	yes	—
315	D₄	—	2	8	no	—
316	D₄	—	2	2	no	—
317	D₄	—	83	4	no	—
318	D₄	—	166	8	no	—
319	D₄	—	166	8	no	—
320	D₄	—	166	8	no	—
321	D₄	—	166	8	no	—
322	D₄	—	166	2	no	—
323	D₄	C₂³×D₈₃	1	4	yes	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	8	no	—
326	C₂×C₄	—	83	1	no	—
327	C₂×C₄	—	83	1	no	—
328	C₂×C₄	—	83	4	no	—
329	C₂×C₄	—	83	4	no	—
330	C₂×C₄	—	83	2	no	—
331	C₂×C₄	—	83	2	no	—
332	C₂×C₄	—	83	4	no	—
333	C₂×C₄	—	83	2	no	—
334	C₂×C₄	—	83	2	no	—
335	C₂×C₄	—	166	8	no	—
336	C₂×C₄	—	166	8	no	—
337	C₂×C₄	—	166	8	no	—
338	C₂×C₄	—	166	2	no	—
339	C₂×C₄	—	166	8	no	—
340	C₂×C₄	D₄×D₈₃	1	2	yes	—
341	C₂×C₄	D₄×D₈₃	1	1	yes	characteristic
342	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
343	C₂×C₄	C₂³×D₈₃	1	2	yes	—
344	C₈	—	83	2	no	—
345	C₈	—	83	2	no	—
346	C₈	C₂³×D₈₃	1	2	yes	—
347	C₈	C₂³×D₈₃	1	2	yes	—
348	C₂²	—	2	2	no	—
349	C₂²	—	2	4	no	—
350	C₂²	—	4	4	no	—
351	C₂²	—	332	16	no	—
352	C₂²	—	332	4	no	—
353	C₂²	—	83	4	no	—
354	C₂²	—	83	2	no	—
355	C₂²	—	83	2	no	—
356	C₂²	—	166	8	no	—
357	C₂²	—	166	4	no	—
358	C₂²	—	166	2	no	—
359	C₂²	C₂×D₄×D₈₃	1	2	yes	—
360	C₂²	C₂×D₄×D₈₃	1	1	yes	characteristic
361	C₄	—	2	4	no	—
362	C₄	—	83	2	no	—
363	C₄	—	83	2	no	—
364	C₄	—	166	4	no	—
365	C₄	C₂×D₄×D₈₃	1	2	yes	—
366	C₄	C₂×D₄×D₈₃	1	1	yes	characteristic
367	C₄	C₂⁴×D₈₃	1	1	yes	characteristic
368	C₂	—	2	2	no	—
369	C₂	—	4	4	no	—
370	C₂	—	332	4	no	—
371	C₂	—	83	4	no	—
372	C₂	—	166	2	no	—
373	C₂	#135×D₈₃	1	2	yes	direct product factor
374	C₂	C₂²×D₄×D₈₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₄×D₈₃
commutator, cosocle	C₄×C₈₃	C₂⁵
Frattini	C₄	C₂⁴×D₈₃
Fitting	C₂×#135×C₈₃	C₂
socle	C₂²×C₈₃	C₂²×D₄
hypercenter	C₂×#135	D₈₃
hypocenter	C₈₃	C₂²×#135
LCS	G ▷ C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#135

Complements

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

N	H ≅ G/N	type
1. C₂×#41×D₈₃	C₂	semidirect
2. C₂×#14581815	C₂	semidirect
3. C₂×#14581814	C₂	semidirect
4. C₂×#14581813	C₂	semidirect
5. C₂×#14581812	C₂	semidirect
6. C₂×#14581811	C₂	semidirect
7. #135×D₈₃	C₂	direct (N × H)
8. C₂×Q₁₆×D₈₃	C₂	semidirect
9. C₂×SD₁₆×D₈₃	C₂	semidirect
10. C₂×D₈×D₈₃	C₂	semidirect
11. C₂²×C₈×D₈₃	C₂	semidirect
12. C₂×#135×C₈₃	C₂	semidirect
13. C₂×#13050591	C₂²	semidirect
15. C₂×#13050590	C₂²	semidirect
17. C₂×#13050589	C₂²	semidirect
19. #41×D₈₃	C₂²	semidirect
25. #14581815	C₂²	semidirect
26. #14581814	C₂²	semidirect
27. #14581813	C₂²	semidirect
28. #14581812	C₂²	semidirect
29. #14581811	C₂²	semidirect
30. C₂×Dic₃₃₂	C₂²	semidirect
31. C₂×#13050580	C₂²	semidirect
32. Q₁₆×D₈₃	C₂²	semidirect
33. C₂×#13050579	C₂²	semidirect
34. C₂×#13050578	C₂²	semidirect
35. C₂×#13050577	C₂²	semidirect
36. SD₁₆×D₈₃	C₂²	semidirect
37. C₂×D₆₆₄	C₂²	semidirect
38. C₂×#13050575	C₂²	semidirect
39. D₈×D₈₃	C₂²	semidirect
40. C₂²×C₈₃⋊C₈	C₂²	semidirect
43. C₂×C₈×D₈₃	C₂²	semidirect
44. C₂×C₈×D₈₃	C₂²	semidirect
45. C₂×C₈×D₈₃	C₂²	semidirect
46. C₂×#41×C₈₃	C₂²	semidirect
47. #135×C₈₃	C₂²	semidirect
48. C₂×Q₁₆×C₈₃	C₂²	semidirect
49. C₂×SD₁₆×C₈₃	C₂²	semidirect
50. C₂×D₈×C₈₃	C₂²	semidirect
51. C₂²×C₈×C₈₃	C₂²	semidirect
55. #13050591	C₂³	semidirect
58. #13050590	C₂³	semidirect
61. #13050589	C₂³	semidirect
86. Dic₃₃₂	C₂³	semidirect
87. #13050580	C₂³	semidirect
88. #13050579	C₂³	semidirect
89. #13050578	C₂³	semidirect
90. #13050577	C₂³	semidirect
91. D₆₆₄	C₂³	semidirect
92. #13050575	C₂³	semidirect
95. C₂×C₈₃⋊C₈	C₂³	semidirect
98. C₈×D₈₃	C₂³	semidirect
99. C₈×D₈₃	C₂³	semidirect
101. #41×C₈₃	C₂³	semidirect
107. Q₁₆×C₈₃	C₂³	semidirect
108. SD₁₆×C₈₃	C₂³	semidirect
109. D₈×C₈₃	C₂³	semidirect
112. C₂×C₈×C₈₃	C₂³	semidirect
170. C₂×D₈₃	#135	direct (N × H)
182. C₂×C₈₃	C₂×#135	semidirect
186. D₈₃	C₂×#135	direct (N × H)
188. C₈₃	C₂²×#135	semidirect
196. C₂×#135	D₈₃	direct (N × H)
208. C₂×#41	C₂×D₈₃	semidirect
219. #135	C₂×D₈₃	direct (N × H)
223. C₂×Q₁₆	C₂×D₈₃	semidirect
228. C₂×SD₁₆	C₂×D₈₃	semidirect
232. C₂×D₈	C₂×D₈₃	semidirect
239. C₂²×C₈	C₂×D₈₃	semidirect
251. #41	C₂²×D₈₃	semidirect
283. Q₁₆	C₂²×D₈₃	semidirect
287. SD₁₆	C₂²×D₈₃	semidirect
290. D₈	C₂²×D₈₃	semidirect
300. C₂×C₈	C₂²×D₈₃	semidirect
373. C₂	#135×D₈₃	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×#41×D₈₃	2
C₂×#14581815	2
C₂×#14581814	2
C₂×#14581813	2
C₂×#14581812	2
C₂×#14581811	2
#135×D₈₃	2
C₂×Q₁₆×D₈₃	2
C₂×SD₁₆×D₈₃	2
C₂×D₈×D₈₃	2
C₂²×C₈×D₈₃	2
C₂×#135×C₈₃	2
C₂²×#135	83

Subgroups — C2×#135×D83 #24922187

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#135×D₈₃ #24922187