Subgroups — C₂×Q₁₆×D₂₉₂ #33961260

Order 18688.

2742 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	C₂²×Q₁₆×D₇₃	C₂	1	2	yes	maximal, complemented
2	C₂×Q₈×D₂₉₂	C₂	1	2	yes	maximal
3	Q₁₆×D₂₉₂	C₂	1	16	yes	maximal, direct product factor
4	C₂×#17988967	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#17988829	C₂	1	2	yes	maximal, complemented
6	C₂×#17988797	C₂	1	2	yes	maximal, complemented
7	C₂×#17988744	C₂	1	4	yes	maximal, complemented
8	C₂×C₈×D₂₉₂	C₂	1	1	yes	maximal, characteristic
9	C₂×C₄×Q₁₆×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×Q₈×D₇₃	C₂²	1	4	yes	—
11	C₂²×Dic₂₉₂	C₂²	1	2	yes	—
12	C₂²×Dic₂₉₂	C₂²	1	2	yes	—
13	C₂²×#11924018	C₂²	1	4	yes	—
14	C₂×Q₁₆×D₇₃	—	2	16	no	—
15	C₂×Q₁₆×D₇₃	C₂²	1	16	yes	complemented
16	C₂²×C₈×D₇₃	C₂²	1	2	yes	—
17	Q₈×D₂₉₂	—	2	8	no	—
18	Q₈×D₂₉₂	C₂²	1	16	yes	—
19	C₂×#14556591	—	2	2	no	—
20	C₂×#14556591	C₂²	1	2	yes	—
21	C₂×#14556571	—	2	4	no	—
22	C₂×#14556571	C₂²	1	4	yes	—
23	C₂×C₄×D₂₉₂	—	2	2	no	—
24	C₂×C₄×D₂₉₂	C₂²	1	1	yes	characteristic
25	#17988967	C₂²	1	8	yes	complemented
26	#17988829	C₂²	1	16	yes	complemented
27	#17988797	C₂²	1	16	yes	complemented
28	#17988744	C₂²	1	32	yes	complemented
29	C₈×D₂₉₂	C₂²	1	8	yes	—
30	C₂×C₄⋊#10596831	C₂²	1	1	yes	characteristic
31	C₂×#14556514	C₂²	1	4	yes	—
32	C₂×#14556503	C₂²	1	2	yes	—
33	C₂²×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic
34	C₂×C₄×Q₈×C₇₃	C₂²	1	2	yes	—
35	C₄×Q₁₆×C₇₃	C₂²	1	8	yes	complemented
36	C₂×#107×C₇₃	C₂²	1	1	yes	characteristic
37	C₂×#103×C₇₃	C₂²	1	2	yes	—
38	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
39	C₂²×Dic₁₄₆	—	2	4	no	—
40	C₂²×Dic₁₄₆	C₂³	1	4	yes	—
41	C₂×Q₈×D₇₃	—	2	8	no	—
42	C₂×Q₈×D₇₃	—	2	16	no	—
43	C₂×Q₈×D₇₃	—	4	8	no	—
44	C₂×Q₈×D₇₃	C₂³	1	16	yes	—
45	C₂²×D₂₉₂	D₄	1	1	yes	characteristic
46	C₂²×C₄×D₇₃	—	2	4	no	—
47	C₂²×C₄×D₇₃	C₂³	1	2	yes	—
48	C₂×Dic₂₉₂	—	2	8	no	—
49	C₂×Dic₂₉₂	—	4	4	no	—
50	C₂×Dic₂₉₂	C₂³	1	8	yes	—
51	C₂×Dic₂₉₂	C₂³	1	8	yes	—
52	C₂×#11924018	—	2	16	no	—
53	C₂×#11924018	C₂³	1	16	yes	—
54	Q₁₆×D₇₃	—	2	64	no	—
55	C₂²×#10596831	C₂³	1	2	yes	—
56	C₂×C₈×D₇₃	—	2	8	no	—
57	C₂×C₈×D₇₃	C₂³	1	8	yes	—
58	#14556591	—	2	16	no	—
59	#14556591	—	2	4	no	—
60	#14556591	C₂³	1	8	yes	—
61	#14556571	—	2	8	no	—
62	#14556571	—	2	32	no	—
63	#14556571	C₂³	1	16	yes	—
64	C₄×D₂₉₂	—	2	16	no	—
65	C₄×D₂₉₂	D₄	1	4	yes	—
66	C₄×D₂₉₂	C₂³	1	4	yes	—
67	C₂×C₄⋊Dic₇₃	—	2	4	no	—
68	C₂×C₄⋊Dic₇₃	—	2	2	no	—
69	C₂×C₄⋊Dic₇₃	—	2	2	no	—
70	C₂×C₄⋊Dic₇₃	D₄	1	1	yes	characteristic
71	C₂×#11924005	—	2	4	no	—
72	C₂×#11924005	D₄	1	2	yes	—
73	C₄⋊#10596831	C₂³	1	4	yes	—
74	#14556514	C₂³	1	16	yes	—
75	#14556503	C₂³	1	8	yes	—
76	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
77	C₂×Q₁₆×C₇₃	D₄	1	8	yes	complemented
78	C₂×Q₁₆×C₇₃	C₂³	1	4	yes	—
79	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
81	C₄×Q₈×C₇₃	—	2	4	no	—
82	C₄×Q₈×C₇₃	C₂³	1	8	yes	—
83	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
84	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
85	C₂×C₄²×C₇₃	—	2	2	no	—
86	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
87	#107×C₇₃	C₂³	1	4	yes	—
88	#103×C₇₃	C₂³	1	8	yes	—
89	C₄×C₈×C₇₃	C₂³	1	4	yes	—
90	C₂³×D₇₃	C₂×D₄	1	2	yes	—
91	C₂×Dic₁₄₆	—	2	8	no	—
92	C₂×Dic₁₄₆	—	2	8	no	—
93	C₂×Dic₁₄₆	—	2	4	no	—
94	C₂×Dic₁₄₆	—	2	16	no	—
95	C₂×Dic₁₄₆	—	4	16	no	—
96	C₂×Dic₁₄₆	C₂⁴	1	8	yes	—
97	Q₈×D₇₃	—	2	32	no	—
98	Q₈×D₇₃	—	4	16	no	—
99	Q₈×D₇₃	—	4	32	no	—
100	C₂×D₂₉₂	Q₁₆	1	8	yes	direct product factor
101	C₂×D₂₉₂	C₂×D₄	1	4	yes	—
102	C₂²×Dic₇₃	—	2	4	no	—
103	C₂²×Dic₇₃	C₂×D₄	1	2	yes	—
104	C₂×C₄×D₇₃	—	2	4	no	—
105	C₂×C₄×D₇₃	—	2	4	no	—
106	C₂×C₄×D₇₃	—	2	16	no	—
107	C₂×C₄×D₇₃	—	4	16	no	—
108	C₂×C₄×D₇₃	C₂×D₄	1	4	yes	—
109	C₂×C₄×D₇₃	C₂⁴	1	4	yes	—
110	Dic₂₉₂	—	2	16	no	—
111	Dic₂₉₂	—	4	8	no	—
112	#11924018	—	2	32	no	—
113	C₂×#10596831	—	2	4	no	—
114	C₂×#10596831	C₂⁴	1	4	yes	—
115	C₈×D₇₃	—	2	16	no	—
116	C₄⋊Dic₇₃	—	2	8	no	—
117	C₄⋊Dic₇₃	—	2	8	no	—
118	C₄⋊Dic₇₃	—	2	16	no	—
119	C₄⋊Dic₇₃	C₂×D₄	1	4	yes	—
120	#11924005	—	2	16	no	—
121	#11924005	C₂×D₄	1	8	yes	—
122	C₂×Q₈×C₇₃	—	2	2	no	—
123	C₂×Q₈×C₇₃	—	2	4	no	—
124	C₂×Q₈×C₇₃	C₂×D₄	1	8	yes	—
125	C₂×Q₈×C₇₃	C₂⁴	1	4	yes	—
126	C₂²×C₄×C₇₃	—	2	2	no	—
127	C₂²×C₄×C₇₃	—	2	2	no	—
128	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
131	Q₁₆×C₇₃	C₂×D₄	1	16	yes	complemented
132	C₂×C₈×C₇₃	—	2	2	no	—
133	C₂×C₈×C₇₃	C₂×D₄	1	4	yes	—
134	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
135	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
136	C₄⋊C₄×C₇₃	—	2	8	no	—
137	C₄⋊C₄×C₇₃	—	2	2	no	—
138	C₄⋊C₄×C₇₃	C₂⁴	1	4	yes	—
139	C₄²×C₇₃	—	2	8	no	—
140	C₄²×C₇₃	C₂×D₄	1	2	yes	—
141	C₄²×C₇₃	C₂⁴	1	2	yes	—
142	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
143	C₂²×D₇₃	—	2	4	no	—
144	C₂²×D₇₃	—	2	4	no	—
145	C₂²×D₇₃	C₂×Q₁₆	1	8	yes	complemented
146	C₂²×D₇₃	C₂²×D₄	1	4	yes	—
147	Q₈×C₇₃	—	2	8	no	—
148	Q₈×C₇₃	—	2	4	no	—
149	Q₈×C₇₃	C₂²×D₄	1	8	yes	—
150	C₂×C₄×C₇₃	—	2	8	no	—
151	C₂×C₄×C₇₃	—	2	2	no	—
152	C₂×C₄×C₇₃	—	2	4	no	—
153	C₂×C₄×C₇₃	—	2	4	no	—
154	C₂×C₄×C₇₃	—	4	4	no	—
155	C₂×C₄×C₇₃	C₂×Q₁₆	1	4	yes	complemented
156	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
157	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
159	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
160	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
161	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
162	C₂×Dic₇₃	—	2	4	no	—
163	C₂×Dic₇₃	—	2	8	no	—
164	C₂×Dic₇₃	—	4	8	no	—
165	C₂×Dic₇₃	C₂²×D₄	1	4	yes	—
166	D₂₉₂	C₂×Q₁₆	1	16	yes	direct product factor
167	C₄×D₇₃	—	2	8	no	—
168	C₄×D₇₃	—	2	4	no	—
169	C₄×D₇₃	—	2	4	no	—
170	C₄×D₇₃	—	4	32	no	—
171	Dic₁₄₆	—	2	8	no	—
172	Dic₁₄₆	—	2	8	no	—
173	Dic₁₄₆	—	4	32	no	—
174	Dic₁₄₆	—	4	8	no	—
175	C₈×C₇₃	—	2	2	no	—
176	C₈×C₇₃	C₂²×D₄	1	4	yes	—
177	#10596831	—	2	4	no	—
178	C₂²×C₇₃	D₄²	1	2	yes	—
179	C₂²×C₇₃	C₂²×Q₁₆	1	2	yes	—
180	C₂²×C₇₃	#578	1	2	yes	—
181	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
182	C₂×D₇₃	—	2	4	no	—
183	C₂×D₇₃	—	2	16	no	—
184	C₂×D₇₃	—	2	4	no	—
185	C₂×D₇₃	C₂²×Q₁₆	1	8	yes	complemented
186	C₄×C₇₃	—	2	8	no	—
187	C₄×C₇₃	—	2	2	no	—
188	C₄×C₇₃	—	4	4	no	—
189	C₄×C₇₃	D₄²	1	2	yes	—
190	C₄×C₇₃	C₂²×Q₁₆	1	4	yes	complemented
191	C₄×C₇₃	C₂³×D₄	1	1	yes	characteristic
192	C₄×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
193	Dic₇₃	—	2	4	no	—
194	Dic₇₃	—	4	8	no	—
195	C₂×D₄×Q₁₆	—	73	1	no	maximal, Sylow
196	C₂×C₇₃	D₄×Q₁₆	1	4	yes	complemented
197	C₂×C₇₃	C₂×D₄²	1	1	yes	characteristic
198	C₂×C₇₃	C₂³×Q₁₆	1	1	yes	characteristic
199	C₂×C₇₃	C₂×#578	1	1	yes	characteristic
200	D₇₃	—	2	8	no	—
201	C₂³×Q₁₆	—	73	2	no	—
202	C₂×D₄×Q₈	—	73	2	no	—
203	D₄×Q₁₆	—	73	16	no	—
204	C₂×#494	—	73	1	no	—
205	C₂×#467	—	73	2	no	—
206	C₂×#462	—	73	2	no	—
207	C₂×#451	—	73	4	no	—
208	C₂×C₄×Q₁₆	D₇₃	1	1	yes	characteristic, complemented
209	C₂×C₈×D₄	—	73	1	no	—
210	C₇₃	C₂×D₄×Q₁₆	1	1	yes	characteristic, complemented, Sylow
211	C₂³×Q₈	—	73	4	no	—
212	C₂²×Q₁₆	—	73	4	no	—
213	C₂²×Q₁₆	—	73	16	no	—
214	C₂²×Q₁₆	—	73	2	no	—
215	C₂²×Q₁₆	—	73	2	no	—
216	C₂²×Q₁₆	—	146	16	no	—
217	C₂²×Q₁₆	C₂×D₇₃	1	1	yes	characteristic
218	C₂³×C₈	—	73	2	no	—
219	D₄×Q₈	—	73	16	no	—
220	D₄×Q₈	—	146	8	no	—
221	C₂×C₄⋊Q₈	—	73	2	no	—
222	C₂×C₄⋊Q₈	—	146	2	no	—
223	C₂×C₂²⋊Q₈	—	73	4	no	—
224	C₂×C₂²⋊Q₈	—	146	4	no	—
225	C₂×C₄×Q₈	C₂×D₇₃	1	2	yes	—
226	C₂×C₄×D₄	—	73	1	no	—
227	C₂×C₄×D₄	—	146	2	no	—
228	#494	—	73	8	no	—
229	#467	—	73	16	no	—
230	#462	—	73	16	no	—
231	#451	—	73	32	no	—
232	C₄×Q₁₆	C₂×D₇₃	1	8	yes	complemented
233	C₈×D₄	—	73	8	no	—
234	C₂×#107	C₂×D₇₃	1	1	yes	characteristic
235	C₂×C₄⋊C₈	—	73	1	no	—
236	C₂×#103	—	73	4	no	—
237	C₂×#103	C₂×D₇₃	1	2	yes	—
238	C₂×C₂²⋊C₈	—	73	2	no	—
239	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
240	C₂²×Q₈	—	292	8	no	—
241	C₂²×Q₈	—	73	16	no	—
242	C₂²×Q₈	—	73	4	no	—
243	C₂²×Q₈	—	146	4	no	—
244	C₂²×Q₈	—	146	16	no	—
245	C₂²×Q₈	—	146	8	no	—
246	C₂²×Q₈	C₂²×D₇₃	1	2	yes	—
247	C₂²×D₄	—	73	1	no	—
248	C₂³×C₄	—	73	2	no	—
249	C₂³×C₄	—	146	4	no	—
250	C₂×Q₁₆	—	292	4	no	—
251	C₂×Q₁₆	—	73	16	no	—
252	C₂×Q₁₆	—	73	8	no	—
253	C₂×Q₁₆	—	73	8	no	—
254	C₂×Q₁₆	—	146	16	no	—
255	C₂×Q₁₆	—	146	64	no	—
256	C₂×Q₁₆	—	146	8	no	—
257	C₂×Q₁₆	D₂₉₂	1	8	yes	direct product factor
258	C₂×Q₁₆	C₂²×D₇₃	1	4	yes	—
259	C₂²×C₈	—	73	2	no	—
260	C₂²×C₈	—	73	8	no	—
261	C₂²×C₈	—	146	8	no	—
262	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
263	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
264	C₄⋊Q₈	—	73	8	no	—
265	C₄⋊Q₈	—	146	16	no	—
266	C₄⋊Q₈	—	146	4	no	—
267	C₂²⋊Q₈	—	73	16	no	—
268	C₂²⋊Q₈	—	146	32	no	—
269	C₂²⋊Q₈	—	146	8	no	—
270	C₄×Q₈	—	2	4	no	—
271	C₄×Q₈	C₂²×D₇₃	1	8	yes	—
272	C₄×D₄	—	73	4	no	—
273	C₄×D₄	—	73	4	no	—
274	C₄×D₄	—	146	16	no	—
275	C₂×C₄⋊C₄	—	2	2	no	—
276	C₂×C₄⋊C₄	—	73	1	no	—
277	C₂×C₄⋊C₄	—	146	4	no	—
278	C₂×C₄⋊C₄	—	146	2	no	—
279	C₂×C₄⋊C₄	—	146	2	no	—
280	C₂×C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
281	C₂×C₂²⋊C₄	—	73	2	no	—
282	C₂×C₂²⋊C₄	—	146	4	no	—
283	C₂×C₄²	—	2	2	no	—
284	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
285	#107	C₂²×D₇₃	1	4	yes	—
286	C₄⋊C₈	—	73	4	no	—
287	#103	—	73	16	no	—
288	#103	C₂²×D₇₃	1	8	yes	—
289	C₂²⋊C₈	—	73	8	no	—
290	C₄×C₈	C₂²×D₇₃	1	4	yes	—
291	C₂⁴	—	73	2	no	—
292	C₂×Q₈	—	2	2	no	—
293	C₂×Q₈	—	2	4	no	—
294	C₂×Q₈	—	292	16	no	—
295	C₂×Q₈	—	292	32	no	—
296	C₂×Q₈	—	292	16	no	—
297	C₂×Q₈	—	73	8	no	—
298	C₂×Q₈	—	146	16	no	—
299	C₂×Q₈	—	146	32	no	—
300	C₂×Q₈	—	146	8	no	—
301	C₂×Q₈	—	146	8	no	—
302	C₂×Q₈	—	146	4	no	—
303	C₂×Q₈	C₂×D₂₉₂	1	8	yes	—
304	C₂×Q₈	C₂³×D₇₃	1	4	yes	—
305	C₂×D₄	—	73	8	no	—
306	C₂×D₄	—	73	4	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	292	16	no	—
310	C₂²×C₄	—	73	2	no	—
311	C₂²×C₄	—	73	4	no	—
312	C₂²×C₄	—	73	4	no	—
313	C₂²×C₄	—	146	16	no	—
314	C₂²×C₄	—	146	4	no	—
315	C₂²×C₄	—	146	4	no	—
316	C₂²×C₄	—	146	4	no	—
317	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
318	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
319	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
320	Q₁₆	—	292	8	no	—
321	Q₁₆	—	146	32	no	—
322	Q₁₆	—	146	16	no	—
323	Q₁₆	C₂×D₂₉₂	1	16	yes	direct product factor
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	73	4	no	—
326	C₂×C₈	—	146	4	no	—
327	C₂×C₈	—	146	16	no	—
328	C₂×C₈	C₂×D₂₉₂	1	4	yes	—
329	C₂×C₈	C₂³×D₇₃	1	2	yes	—
330	C₂×C₈	C₂³×D₇₃	1	2	yes	—
331	C₄⋊C₄	—	2	8	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	73	4	no	—
334	C₄⋊C₄	—	146	16	no	—
335	C₄⋊C₄	—	146	8	no	—
336	C₄⋊C₄	—	146	8	no	—
337	C₄⋊C₄	C₂³×D₇₃	1	4	yes	—
338	C₂²⋊C₄	—	73	8	no	—
339	C₂²⋊C₄	—	146	16	no	—
340	C₄²	—	2	8	no	—
341	C₄²	D₄×D₇₃	1	2	yes	—
342	C₄²	C₂³×D₇₃	1	2	yes	—
343	C₂³	—	73	4	no	—
344	C₂³	—	73	8	no	—
345	C₂³	—	146	4	no	—
346	C₂³	—	146	4	no	—
347	C₂³	C₂×D₄×D₇₃	1	1	yes	characteristic
348	Q₈	—	2	4	no	—
349	Q₈	—	2	8	no	—
350	Q₈	—	292	32	no	—
351	Q₈	—	292	8	no	—
352	Q₈	—	146	8	no	—
353	Q₈	—	146	8	no	—
354	Q₈	C₂²×D₂₉₂	1	8	yes	—
355	D₄	—	73	16	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	8	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	4	4	no	—
361	C₂×C₄	—	292	32	no	—
362	C₂×C₄	—	292	8	no	—
363	C₂×C₄	—	73	4	no	—
364	C₂×C₄	—	146	8	no	—
365	C₂×C₄	—	146	4	no	—
366	C₂×C₄	—	146	4	no	—
367	C₂×C₄	—	146	4	no	—
368	C₂×C₄	—	146	8	no	—
369	C₂×C₄	Q₁₆×D₇₃	1	4	yes	complemented
370	C₂×C₄	C₂×D₄×D₇₃	1	2	yes	—
371	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
372	C₂×C₄	C₂×D₄×D₇₃	1	2	yes	—
373	C₂×C₄	C₂²×D₂₉₂	1	2	yes	—
374	C₂×C₄	#14556637	1	2	yes	—
375	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
376	C₈	—	2	2	no	—
377	C₈	—	146	4	no	—
378	C₈	C₂²×D₂₉₂	1	4	yes	—
379	C₂²	—	73	8	no	—
380	C₂²	—	146	4	no	—
381	C₂²	—	146	4	no	—
382	C₂²	—	146	16	no	—
383	C₂²	D₄×D₂₉₂	1	2	yes	—
384	C₂²	C₂×Q₁₆×D₇₃	1	2	yes	—
385	C₂²	#17989401	1	2	yes	—
386	C₂²	C₂²×D₄×D₇₃	1	1	yes	characteristic
387	C₄	—	2	8	no	—
388	C₄	—	2	2	no	—
389	C₄	—	4	4	no	—
390	C₄	—	292	8	no	—
391	C₄	—	146	4	no	—
392	C₄	D₄×D₂₉₂	1	2	yes	—
393	C₄	C₂×Q₁₆×D₇₃	1	4	yes	complemented
394	C₄	C₂³×D₂₉₂	1	1	yes	characteristic
395	C₄	C₂×#14556637	1	1	yes	characteristic
396	C₂	—	146	8	no	—
397	C₂	Q₁₆×D₂₉₂	1	4	yes	direct product factor
398	C₂	C₂×D₄×D₂₉₂	1	1	yes	characteristic
399	C₂	C₂²×Q₁₆×D₇₃	1	1	yes	characteristic
400	C₂	C₂×#17989401	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₇₃
commutator, cosocle	C₂×C₄×C₇₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₇₃
Fitting	C₂×C₄×Q₁₆×C₇₃	C₂
socle	C₂³×C₇₃	C₂²×D₄
prime radical	C₂²×D₂₉₂	D₄
hypercenter	C₂×C₄×Q₁₆	D₇₃
hypocenter	C₇₃	C₂×D₄×Q₁₆
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×Q₁₆

Complements

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

N	H ≅ G/N	type
1. C₂²×Q₁₆×D₇₃	C₂	semidirect
3. Q₁₆×D₂₉₂	C₂	direct (N × H)
4. C₂×#17988967	C₂	semidirect
5. C₂×#17988829	C₂	semidirect
6. C₂×#17988797	C₂	semidirect
7. C₂×#17988744	C₂	semidirect
9. C₂×C₄×Q₁₆×C₇₃	C₂	semidirect
15. C₂×Q₁₆×D₇₃	C₂²	semidirect
25. #17988967	C₂²	semidirect
26. #17988829	C₂²	semidirect
27. #17988797	C₂²	semidirect
28. #17988744	C₂²	semidirect
35. C₄×Q₁₆×C₇₃	C₂²	semidirect
77. C₂×Q₁₆×C₇₃	D₄	semidirect
100. C₂×D₂₉₂	Q₁₆	direct (N × H)
131. Q₁₆×C₇₃	C₂×D₄	semidirect
145. C₂²×D₇₃	C₂×Q₁₆	semidirect
155. C₂×C₄×C₇₃	C₂×Q₁₆	semidirect
166. D₂₉₂	C₂×Q₁₆	direct (N × H)
185. C₂×D₇₃	C₂²×Q₁₆	semidirect
190. C₄×C₇₃	C₂²×Q₁₆	semidirect
196. C₂×C₇₃	D₄×Q₁₆	semidirect
208. C₂×C₄×Q₁₆	D₇₃	semidirect
210. C₇₃	C₂×D₄×Q₁₆	semidirect
232. C₄×Q₁₆	C₂×D₇₃	semidirect
257. C₂×Q₁₆	D₂₉₂	direct (N × H)
323. Q₁₆	C₂×D₂₉₂	direct (N × H)
369. C₂×C₄	Q₁₆×D₇₃	semidirect
393. C₄	C₂×Q₁₆×D₇₃	semidirect
397. C₂	Q₁₆×D₂₉₂	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×Q₁₆×D₇₃	2
C₂×Q₈×D₂₉₂	2
Q₁₆×D₂₉₂	2
C₂×#17988967	2
C₂×#17988829	2
C₂×#17988797	2
C₂×#17988744	2
C₂×C₈×D₂₉₂	2
C₂×C₄×Q₁₆×C₇₃	2
C₂×D₄×Q₁₆	73

Subgroups — C2×Q16×D292 #33961260

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Q₁₆×D₂₉₂ #33961260