Subgroups — C₄×SD₁₆×#6923 #30614498

Order 15616.

1230 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×SD₁₆×#6923	C₂	1	2	yes	maximal
2	C₄×Q₈×#6923	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₄×#6923	C₂	1	1	yes	maximal, characteristic
4	#106×#6923	C₂	1	2	yes	maximal, complemented
5	C₄×#14519845	C₂	1	1	yes	maximal, characteristic, complemented
6	#103×#6923	C₂	1	2	yes	maximal, complemented
7	C₄×#14519840	C₂	1	1	yes	maximal, characteristic, complemented
8	#102×#6923	C₂	1	2	yes	maximal
9	C₄×#14519839	C₂	1	1	yes	maximal, characteristic
10	C₄×C₈×#6923	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×SD₁₆×D₆₁	C₂	1	1	yes	maximal, characteristic
12	C₂×Q₈×#6923	C₂²	1	2	yes	—
13	C₂×D₄×#6923	C₂²	1	2	yes	—
14	C₂²×C₄×#6923	—	2	1	no	—
15	SD₁₆×#6923	C₄	1	16	yes	direct product factor
16	C₂×#14519845	C₂²	1	2	yes	—
17	C₂×#14519840	C₂²	1	2	yes	—
18	C₂×#14519839	C₂²	1	2	yes	—
19	C₄×D₆₁⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₈×#6923	C₂²	1	2	yes	—
21	C₂×C₈×#6923	C₂²	1	2	yes	—
22	C₄⋊C₄×#6923	—	2	2	no	—
23	C₄⋊C₄×#6923	C₂²	1	2	yes	—
24	C₄⋊C₄×#6923	C₂²	1	2	yes	—
25	C₄×C₄⋊#6923	—	2	1	no	—
26	C₄×C₄⋊#6923	C₂²	1	1	yes	characteristic
27	C₄×C₄⋊#6923	C₂²	1	1	yes	characteristic
28	C₂²⋊C₄×#6923	—	2	2	no	—
29	C₄×C₂²⋊#6923	—	2	1	no	—
30	C₄²×#6923	—	2	1	no	—
31	C₄²×#6923	C₂²	1	1	yes	characteristic
32	#16840636	C₂²	1	2	yes	—
33	#16840635	C₂²	1	2	yes	—
34	#16840635	C₂²	1	2	yes	—
35	C₂×SD₁₆×D₆₁	C₂²	1	1	yes	characteristic
36	C₄×Q₈×D₆₁	C₂²	1	1	yes	characteristic
37	C₄×D₄×D₆₁	C₂²	1	1	yes	characteristic
38	#16839853	C₄	1	1	yes	characteristic, complemented
39	C₄×#11758190	C₄	1	1	yes	characteristic, complemented
40	SD₁₆×Dic₆₁	C₄	1	1	yes	characteristic, complemented
41	C₄×#11758201	C₄	1	1	yes	characteristic, complemented
42	#16839849	C₄	1	1	yes	characteristic, complemented
43	C₄×#11758200	C₄	1	1	yes	characteristic, complemented
44	#16839847	C₄	1	1	yes	characteristic, complemented
45	#106×D₆₁	C₂²	1	1	yes	characteristic
46	#103×D₆₁	C₂²	1	1	yes	characteristic
47	#102×D₆₁	C₂²	1	1	yes	characteristic
48	C₄×C₈×D₆₁	C₂²	1	1	yes	characteristic
49	C₄×SD₁₆×C₆₁	C₄	1	1	yes	characteristic, complemented
50	C₂³×#6923	—	2	2	no	—
51	C₂×D₆₁⋊C₈	C₂³	1	2	yes	—
52	Q₈×#6923	—	2	4	no	—
53	Q₈×#6923	C₂×C₄	1	8	yes	complemented
54	D₄×#6923	—	2	4	no	—
55	D₄×#6923	C₂×C₄	1	8	yes	—
56	C₂×C₄⋊#6923	—	2	2	no	—
57	C₂×C₄⋊#6923	C₂³	1	2	yes	—
58	C₂×C₄⋊#6923	C₂³	1	2	yes	—
59	C₂×C₂²⋊#6923	—	2	2	no	—
60	C₂×C₄×#6923	—	2	2	no	—
61	C₂×C₄×#6923	—	2	2	no	—
62	C₂×C₄×#6923	—	2	2	no	—
63	C₂×C₄×#6923	—	2	1	no	—
64	C₂×C₄×#6923	—	2	1	no	—
65	C₂×C₄×#6923	—	4	4	no	—
66	C₂×C₄×#6923	D₄	1	1	yes	characteristic
67	C₂×C₄×#6923	D₄	1	2	yes	—
68	C₂×C₄×#6923	D₄	1	1	yes	characteristic
69	C₂×C₄×#6923	C₂³	1	2	yes	—
70	#14519845	C₂×C₄	1	8	yes	complemented
71	#14519840	C₂×C₄	1	8	yes	complemented
72	#14519839	C₂×C₄	1	8	yes	—
73	C₄×#92420	—	2	1	no	—
74	C₄×#92420	—	2	1	no	—
75	C₈×#6923	—	2	4	no	—
76	C₈×#6923	C₂×C₄	1	8	yes	complemented
77	(C₂×#6923)⋊C₄	—	2	2	no	—
78	(C₂×#6923)⋊C₄	—	2	2	no	—
79	(C₂×#6923)⋊C₄	—	2	1	no	—
80	(C₂×#6923)⋊C₄	—	2	1	no	—
81	C₂×Q₈×D₆₁	C₂³	1	1	yes	characteristic
82	C₂×D₄×D₆₁	C₂³	1	1	yes	characteristic
83	C₂²×C₄×D₆₁	—	2	1	no	—
84	C₂×#11758190	C₂×C₄	1	1	yes	characteristic
85	C₂×#11758200	C₂×C₄	1	1	yes	characteristic
86	C₂×#11758201	C₂×C₄	1	1	yes	characteristic
87	SD₁₆×D₆₁	C₂×C₄	1	8	yes	—
88	C₂×C₈×D₆₁	C₂³	1	1	yes	characteristic
89	C₂×C₈×D₆₁	C₂³	1	1	yes	characteristic
90	Q₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic, complemented
91	C₄×Dic₁₂₂	—	2	1	no	—
92	C₄×Dic₁₂₂	C₂×C₄	1	1	yes	characteristic, complemented
93	#14519742	—	2	1	no	—
94	#14519742	C₂×C₄	1	1	yes	characteristic, complemented
95	C₄×D₂₄₄	C₂×C₄	1	1	yes	characteristic
96	D₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
97	#14519739	C₂×C₄	1	1	yes	characteristic
98	C₄×C₂²⋊D₆₁	—	2	1	no	—
99	#14519737	—	2	1	no	—
100	C₄⋊C₄×D₆₁	—	2	1	no	—
101	C₄⋊C₄×D₆₁	C₂³	1	1	yes	characteristic
102	C₄⋊C₄×D₆₁	C₂³	1	1	yes	characteristic
103	C₂²⋊C₄×D₆₁	—	2	1	no	—
104	C₄²×D₆₁	—	2	1	no	—
105	C₄²×D₆₁	C₂³	1	1	yes	characteristic
106	#14519709	C₂×C₄	1	1	yes	characteristic, complemented
107	#14519708	C₂×C₄	1	1	yes	characteristic, complemented
108	#14519708	C₂×C₄	1	1	yes	characteristic, complemented
109	#14519702	C₂×C₄	1	1	yes	characteristic, complemented
110	#14519701	C₂×C₄	1	1	yes	characteristic, complemented
111	#14519700	C₂×C₄	1	1	yes	characteristic, complemented
112	#14519699	C₂×C₄	1	1	yes	characteristic
113	#14519698	C₂×C₄	1	1	yes	characteristic
114	#14519697	C₂×C₄	1	1	yes	characteristic
115	C₄×#92418	C₂×C₄	1	1	yes	characteristic, complemented
116	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic, complemented
117	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic, complemented
118	C₂×SD₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
119	C₄×Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic, complemented
120	C₄×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
121	#106×C₆₁	C₂×C₄	1	1	yes	characteristic, complemented
122	#103×C₆₁	C₂×C₄	1	1	yes	characteristic, complemented
123	#102×C₆₁	C₂×C₄	1	1	yes	characteristic
124	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic, complemented
125	C₂³×D₆₁	—	2	1	no	—
126	C₂²×#6923	—	2	2	no	—
127	C₂²×#6923	—	2	2	no	—
128	C₂²×#6923	—	2	8	no	—
129	C₂²×#6923	—	4	4	no	—
130	C₂²×#6923	—	4	4	no	—
131	C₂²×#6923	C₂×D₄	1	2	yes	—
132	C₂²×#6923	C₂×D₄	1	2	yes	—
133	C₂×Q₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
134	C₂×D₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₆₁	—	2	1	no	—
136	C₂×C₂²⋊D₆₁	—	2	1	no	—
137	C₂²×Dic₆₁	—	2	1	no	—
138	Q₈×D₆₁	—	2	2	no	—
139	Q₈×D₆₁	C₂²×C₄	1	4	yes	—
140	D₄×D₆₁	—	2	2	no	—
141	D₄×D₆₁	C₂²×C₄	1	4	yes	—
142	C₂×D₂₄₄	C₂²×C₄	1	1	yes	characteristic
143	C₂×C₄×D₆₁	—	2	1	no	—
144	C₂×C₄×D₆₁	—	2	1	no	—
145	C₂×C₄×D₆₁	—	2	1	no	—
146	C₂×C₄×D₆₁	—	2	1	no	—
147	C₂×C₄×D₆₁	—	2	1	no	—
148	C₂×C₄×D₆₁	—	4	2	no	—
149	C₂×C₄×D₆₁	—	4	2	no	—
150	C₂×C₄×D₆₁	C₂×D₄	1	1	yes	characteristic
151	C₂×C₄×D₆₁	C₂×D₄	1	1	yes	characteristic
152	C₂×C₄×D₆₁	C₂⁴	1	1	yes	characteristic
153	C₂×Dic₁₂₂	—	2	1	no	—
154	C₂×Dic₁₂₂	C₂²×C₄	1	1	yes	characteristic
155	C₂²⋊#6923	—	2	8	no	—
156	C₂×#92420	—	2	2	no	—
157	C₄⋊#6923	—	2	8	no	—
158	C₄⋊#6923	—	2	2	no	—
159	C₄⋊#6923	—	2	2	no	—
160	C₄⋊#6923	C₂²×C₄	1	4	yes	—
161	C₄⋊#6923	C₂²×C₄	1	4	yes	—
162	C₄×#6923	—	2	8	no	—
163	C₄×#6923	—	2	4	no	—
164	C₄×#6923	—	2	2	no	—
165	C₄×#6923	—	4	4	no	—
166	C₄×#6923	—	4	4	no	—
167	C₄×#6923	—	4	2	no	—
168	C₄×#6923	—	4	2	no	—
169	C₄×#6923	SD₁₆	1	4	yes	direct product factor
170	C₄×#6923	C₂²×C₄	1	4	yes	—
171	C₄×#6923	#41	1	4	yes	—
172	D₆₁⋊C₈	—	2	2	no	—
173	D₆₁⋊C₈	C₂²×C₄	1	4	yes	—
174	SD₁₆×C₆₁	C₄²	1	4	yes	complemented
175	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
176	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
177	C₄⋊C₄×C₆₁	—	2	1	no	—
178	C₄⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
179	C₄⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
180	C₂²⋊C₄×C₆₁	—	2	1	no	—
181	C₄²×C₆₁	—	2	1	no	—
182	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
183	C₂²⋊Dic₆₁	—	2	1	no	—
184	#11758201	C₄²	1	4	yes	complemented
185	#11758200	C₄²	1	4	yes	complemented
186	#11758198	—	2	1	no	—
187	#11758198	—	2	1	no	—
188	C₄⋊Dic₆₁	—	2	1	no	—
189	C₄⋊Dic₆₁	C₂²×C₄	1	1	yes	characteristic
190	C₄⋊Dic₆₁	C₂²×C₄	1	1	yes	characteristic
191	#11758196	—	2	1	no	—
192	#11758196	—	2	1	no	—
193	#11758196	—	2	1	no	—
194	#11758196	—	2	1	no	—
195	C₄×Dic₆₁	—	2	1	no	—
196	C₄×Dic₆₁	—	2	1	no	—
197	C₄×Dic₆₁	—	2	1	no	—
198	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
199	C₄×Dic₆₁	#41	1	1	yes	characteristic
200	C₄×Dic₆₁	#41	1	1	yes	characteristic
201	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
202	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
203	#11758190	C₄²	1	4	yes	complemented
204	C₈×D₆₁	—	2	2	no	—
205	C₈×D₆₁	C₂²×C₄	1	4	yes	—
206	C₂³×C₆₁	—	2	1	no	—
207	C₂²×D₆₁	—	2	1	no	—
208	C₂²×D₆₁	—	2	4	no	—
209	C₂²×D₆₁	—	4	1	no	—
210	C₂²×D₆₁	—	4	1	no	—
211	C₂²×D₆₁	—	4	2	no	—
212	C₂²×D₆₁	C₂²×D₄	1	1	yes	characteristic
213	C₂×#6923	—	2	2	no	—
214	C₂×#6923	—	2	2	no	—
215	C₂×#6923	—	2	4	no	—
216	C₂×#6923	—	2	4	no	—
217	C₂×#6923	—	4	2	no	—
218	C₂×#6923	—	4	2	no	—
219	C₂×#6923	—	4	2	no	—
220	C₂×#6923	—	4	2	no	—
221	C₂×#6923	—	4	16	no	—
222	C₂×#6923	C₄×D₄	1	4	yes	—
223	C₂×#6923	C₄×D₄	1	4	yes	—
224	C₂×#6923	C₂×SD₁₆	1	4	yes	—
225	C₂×#6923	#135	1	4	yes	—
226	Q₈×C₆₁	—	2	1	no	—
227	Q₈×C₆₁	C₂×C₄²	1	2	yes	complemented
228	D₄×C₆₁	—	2	1	no	—
229	D₄×C₆₁	C₂×C₄²	1	2	yes	—
230	C₂×C₄×C₆₁	—	2	1	no	—
231	C₂×C₄×C₆₁	—	2	1	no	—
232	C₂×C₄×C₆₁	—	2	1	no	—
233	C₂×C₄×C₆₁	—	4	2	no	—
234	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
235	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
236	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
237	C₂²⋊D₆₁	—	2	4	no	—
238	C₂×Dic₆₁	—	2	1	no	—
239	C₂×Dic₆₁	—	2	1	no	—
240	C₂×Dic₆₁	—	2	1	no	—
241	C₂×Dic₆₁	—	4	2	no	—
242	C₂×Dic₆₁	C₄×D₄	1	1	yes	characteristic
243	C₂×Dic₆₁	C₄×D₄	1	1	yes	characteristic
244	C₂×Dic₆₁	C₂×#41	1	1	yes	characteristic
245	D₂₄₄	—	2	1	no	—
246	D₂₄₄	C₂×C₄²	1	2	yes	—
247	C₄×D₆₁	—	2	4	no	—
248	C₄×D₆₁	—	2	2	no	—
249	C₄×D₆₁	—	4	1	no	—
250	C₄×D₆₁	—	4	2	no	—
251	C₄×D₆₁	—	4	1	no	—
252	C₄×D₆₁	—	4	2	no	—
253	C₄×D₆₁	—	4	2	no	—
254	C₄×D₆₁	C₂×SD₁₆	1	2	yes	—
255	C₄×D₆₁	#135	1	2	yes	—
256	C₄×D₆₁	C₂³×C₄	1	2	yes	—
257	C₄×D₆₁	C₂×#41	1	2	yes	—
258	Dic₁₂₂	—	2	1	no	—
259	Dic₁₂₂	—	2	4	no	—
260	Dic₁₂₂	C₂×C₄²	1	2	yes	complemented
261	#92420	—	2	4	no	—
262	C₈×C₆₁	—	2	1	no	—
263	C₈×C₆₁	C₂×C₄²	1	2	yes	complemented
264	#92418	—	2	1	no	—
265	#92418	C₂×C₄²	1	2	yes	complemented
266	C₄²×SD₁₆	—	61	1	no	maximal, Sylow
267	C₂²×C₆₁	—	2	2	no	—
268	C₂²×C₆₁	—	4	1	no	—
269	C₂²×C₆₁	—	4	1	no	—
270	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
271	C₂×D₆₁	—	2	2	no	—
272	C₂×D₆₁	—	4	1	no	—
273	C₂×D₆₁	—	4	1	no	—
274	C₂×D₆₁	—	4	4	no	—
275	C₂×D₆₁	—	4	4	no	—
276	C₂×D₆₁	C₂×C₄×D₄	1	2	yes	—
277	C₂×D₆₁	C₂²×SD₁₆	1	1	yes	characteristic
278	C₂×D₆₁	C₂×#135	1	2	yes	—
279	C₂×D₆₁	C₂×#135	1	1	yes	characteristic
280	#6923	—	2	4	no	—
281	#6923	—	4	4	no	—
282	#6923	—	4	4	no	—
283	#6923	C₄×SD₁₆	1	8	yes	direct product factor
284	C₄×C₆₁	—	2	1	no	—
285	C₄×C₆₁	—	2	2	no	—
286	C₄×C₆₁	—	4	1	no	—
287	C₄×C₆₁	—	4	1	no	—
288	C₄×C₆₁	C₄×SD₁₆	1	2	yes	complemented
289	C₄×C₆₁	C₂²×C₄²	1	1	yes	characteristic
290	C₄×C₆₁	C₄×#41	1	1	yes	characteristic
291	Dic₆₁	—	2	1	no	—
292	Dic₆₁	—	2	2	no	—
293	Dic₆₁	—	4	1	no	—
294	Dic₆₁	—	4	1	no	—
295	Dic₆₁	C₄×SD₁₆	1	2	yes	complemented
296	Dic₆₁	C₄×#41	1	2	yes	—
297	C₂×C₄×SD₁₆	—	61	2	no	—
298	C₂×C₄×SD₁₆	—	61	1	no	—
299	C₄²×Q₈	—	61	1	no	—
300	C₄²×D₄	—	61	1	no	—
301	C₄×#106	—	61	1	no	—
302	C₄×#106	—	61	2	no	—
303	C₄×#103	—	61	1	no	—
304	C₄×#103	—	61	2	no	—
305	C₄×#102	—	61	1	no	—
306	C₄×#102	—	61	2	no	—
307	C₄²×C₈	—	61	1	no	—
308	C₂×C₆₁	—	4	2	no	—
309	C₂×C₆₁	C₄²×D₄	1	1	yes	characteristic
310	C₂×C₆₁	C₂×C₄×SD₁₆	1	1	yes	characteristic
311	C₂×C₆₁	C₄×#135	1	1	yes	characteristic
312	D₆₁	—	4	2	no	—
313	D₆₁	C₂×C₄×SD₁₆	1	2	yes	—
314	D₆₁	C₄×#135	1	2	yes	—
315	C₂²×SD₁₆	—	61	1	no	—
316	C₂×C₄×Q₈	—	61	2	no	—
317	C₂×C₄×Q₈	—	61	1	no	—
318	C₂×C₄×D₄	—	61	2	no	—
319	C₂×C₄×D₄	—	61	1	no	—
320	C₂²×C₄²	—	122	1	no	—
321	C₄×SD₁₆	—	61	16	no	—
322	C₄×SD₁₆	—	61	1	no	—
323	C₄×SD₁₆	—	61	1	no	—
324	C₄×SD₁₆	—	61	1	no	—
325	C₄×SD₁₆	—	61	1	no	—
326	C₄×SD₁₆	—	61	1	no	—
327	C₄×SD₁₆	—	61	1	no	—
328	C₄×SD₁₆	—	61	1	no	—
329	C₄×SD₁₆	#6923	1	1	yes	characteristic, direct product factor
330	C₂×#106	—	61	2	no	—
331	C₂×#106	—	61	1	no	—
332	C₂×#103	—	61	2	no	—
333	C₂×#103	—	61	1	no	—
334	C₂×#102	—	61	2	no	—
335	C₂×#102	—	61	1	no	—
336	C₂×C₄×C₈	—	61	2	no	—
337	C₂×C₄×C₈	—	61	1	no	—
338	C₂×C₄×C₈	—	61	2	no	—
339	C₂×C₄×C₈	—	61	1	no	—
340	C₄×C₄⋊C₄	—	61	1	no	—
341	C₄×C₄⋊C₄	—	61	2	no	—
342	C₄×C₄⋊C₄	—	61	1	no	—
343	C₄×C₄⋊C₄	—	61	2	no	—
344	C₄×C₄⋊C₄	—	122	1	no	—
345	C₄×C₄⋊C₄	—	122	2	no	—
346	C₄×C₂²⋊C₄	—	122	1	no	—
347	C₄×C₂²⋊C₄	—	122	2	no	—
348	C₄³	—	61	1	no	—
349	C₄³	—	122	1	no	—
350	#340	—	61	2	no	—
351	#340	—	61	2	no	—
352	#340	—	61	2	no	—
353	C₆₁	C₄²×SD₁₆	1	1	yes	characteristic, complemented, Sylow
354	C₂²×Q₈	—	61	1	no	—
355	C₂²×D₄	—	61	1	no	—
356	C₂³×C₄	—	122	1	no	—
357	C₂³×C₄	—	122	2	no	—
358	C₂×SD₁₆	—	61	1	no	—
359	C₂×SD₁₆	—	61	1	no	—
360	C₂×SD₁₆	—	61	8	no	—
361	C₂×SD₁₆	—	61	1	no	—
362	C₂×SD₁₆	C₂×#6923	1	1	yes	characteristic
363	C₂²×C₈	—	61	1	no	—
364	C₂²×C₈	—	61	2	no	—
365	C₂²×C₈	—	61	1	no	—
366	C₄×Q₈	—	61	8	no	—
367	C₄×Q₈	—	61	1	no	—
368	C₄×Q₈	—	61	1	no	—
369	C₄×Q₈	—	61	1	no	—
370	C₄×Q₈	—	122	1	no	—
371	C₄×Q₈	—	122	1	no	—
372	C₄×Q₈	—	122	4	no	—
373	C₄×Q₈	C₂×#6923	1	1	yes	characteristic, complemented
374	C₄×D₄	—	61	8	no	—
375	C₄×D₄	—	61	1	no	—
376	C₄×D₄	—	61	1	no	—
377	C₄×D₄	—	61	1	no	—
378	C₄×D₄	—	122	1	no	—
379	C₄×D₄	—	122	1	no	—
380	C₄×D₄	—	122	4	no	—
381	C₄×D₄	C₂×#6923	1	1	yes	characteristic
382	C₂×C₄⋊C₄	—	61	2	no	—
383	C₂×C₄⋊C₄	—	61	2	no	—
384	C₂×C₄⋊C₄	—	61	1	no	—
385	C₂×C₄⋊C₄	—	61	1	no	—
386	C₂×C₄⋊C₄	—	122	1	no	—
387	C₂×C₄⋊C₄	—	122	2	no	—
388	C₂×C₂²⋊C₄	—	122	1	no	—
389	C₂×C₂²⋊C₄	—	122	2	no	—
390	C₂×C₄²	—	61	2	no	—
391	C₂×C₄²	—	61	1	no	—
392	C₂×C₄²	—	61	1	no	—
393	C₂×C₄²	—	61	2	no	—
394	C₂×C₄²	—	61	1	no	—
395	C₂×C₄²	—	122	1	no	—
396	C₂×C₄²	—	122	2	no	—
397	C₂×C₄²	—	122	2	no	—
398	C₂×C₄²	—	122	1	no	—
399	C₂×C₄²	—	122	2	no	—
400	C₂×C₄²	—	122	1	no	—
401	C₂×C₄²	—	244	4	no	—
402	#106	—	61	8	no	—
403	#106	—	61	1	no	—
404	#106	—	61	1	no	—
405	#106	—	61	1	no	—
406	#106	C₂×#6923	1	1	yes	characteristic, complemented
407	#103	—	61	8	no	—
408	#103	—	61	1	no	—
409	#103	—	61	1	no	—
410	#103	—	61	1	no	—
411	#103	C₂×#6923	1	1	yes	characteristic, complemented
412	#102	—	61	8	no	—
413	#102	—	61	1	no	—
414	#102	—	61	1	no	—
415	#102	—	61	1	no	—
416	#102	C₂×#6923	1	1	yes	characteristic
417	C₄×C₈	—	61	8	no	—
418	C₄×C₈	—	61	1	no	—
419	C₄×C₈	—	61	1	no	—
420	C₄×C₈	—	61	1	no	—
421	C₄×C₈	—	122	4	no	—
422	C₄×C₈	—	122	1	no	—
423	C₄×C₈	—	122	1	no	—
424	C₄×C₈	C₂×#6923	1	1	yes	characteristic, complemented
425	#95	—	122	2	no	—
426	#95	—	122	1	no	—
427	#95	—	122	2	no	—
428	#95	—	122	1	no	—
429	C₂⁴	—	122	1	no	—
430	C₂×Q₈	—	61	4	no	—
431	C₂×Q₈	—	61	1	no	—
432	C₂×Q₈	—	122	1	no	—
433	C₂×Q₈	—	122	2	no	—
434	C₂×Q₈	C₂²×#6923	1	1	yes	characteristic
435	C₂×D₄	—	61	4	no	—
436	C₂×D₄	—	61	1	no	—
437	C₂×D₄	—	122	2	no	—
438	C₂×D₄	—	122	1	no	—
439	C₂×D₄	C₂²×#6923	1	1	yes	characteristic
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	61	2	no	—
442	C₂²×C₄	—	61	1	no	—
443	C₂²×C₄	—	61	1	no	—
444	C₂²×C₄	—	61	2	no	—
445	C₂²×C₄	—	61	1	no	—
446	C₂²×C₄	—	122	1	no	—
447	C₂²×C₄	—	122	1	no	—
448	C₂²×C₄	—	122	1	no	—
449	C₂²×C₄	—	122	1	no	—
450	C₂²×C₄	—	122	1	no	—
451	C₂²×C₄	—	122	8	no	—
452	C₂²×C₄	—	122	2	no	—
453	C₂²×C₄	—	122	2	no	—
454	C₂²×C₄	—	122	1	no	—
455	C₂²×C₄	—	244	2	no	—
456	C₂²×C₄	—	244	2	no	—
457	C₂²×C₄	—	244	4	no	—
458	C₂²×C₄	—	244	4	no	—
459	SD₁₆	—	61	4	no	—
460	SD₁₆	—	61	4	no	—
461	SD₁₆	—	61	4	no	—
462	SD₁₆	C₄×#6923	1	4	yes	direct product factor
463	C₂×C₈	—	61	1	no	—
464	C₂×C₈	—	61	4	no	—
465	C₂×C₈	—	61	4	no	—
466	C₂×C₈	—	61	1	no	—
467	C₂×C₈	—	122	2	no	—
468	C₂×C₈	—	122	2	no	—
469	C₂×C₈	—	122	2	no	—
470	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
471	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	61	4	no	—
474	C₄⋊C₄	—	61	4	no	—
475	C₄⋊C₄	—	61	1	no	—
476	C₄⋊C₄	—	61	1	no	—
477	C₄⋊C₄	—	122	1	no	—
478	C₄⋊C₄	—	122	1	no	—
479	C₄⋊C₄	—	122	1	no	—
480	C₄⋊C₄	—	122	1	no	—
481	C₄⋊C₄	—	122	2	no	—
482	C₄⋊C₄	—	122	2	no	—
483	C₄⋊C₄	—	122	8	no	—
484	C₄⋊C₄	—	122	1	no	—
485	C₄⋊C₄	C₂²×#6923	1	1	yes	characteristic
486	C₄⋊C₄	C₂²×#6923	1	1	yes	characteristic
487	C₂²⋊C₄	—	2	1	no	—
488	C₂²⋊C₄	—	122	1	no	—
489	C₂²⋊C₄	—	122	1	no	—
490	C₂²⋊C₄	—	122	8	no	—
491	C₂²⋊C₄	—	122	1	no	—
492	C₄²	—	2	1	no	—
493	C₄²	—	61	4	no	—
494	C₄²	—	61	4	no	—
495	C₄²	—	61	4	no	—
496	C₄²	—	61	1	no	—
497	C₄²	—	61	1	no	—
498	C₄²	—	61	1	no	—
499	C₄²	—	122	1	no	—
500	C₄²	—	122	1	no	—
501	C₄²	—	122	4	no	—
502	C₄²	—	122	2	no	—
503	C₄²	—	122	8	no	—
504	C₄²	—	122	1	no	—
505	C₄²	—	244	4	no	—
506	C₄²	—	244	2	no	—
507	C₄²	—	244	4	no	—
508	C₄²	—	244	2	no	—
509	C₄²	C₂²×#6923	1	1	yes	characteristic
510	C₂³	—	2	1	no	—
511	C₂³	—	61	1	no	—
512	C₂³	—	122	4	no	—
513	C₂³	—	122	1	no	—
514	C₂³	—	244	1	no	—
515	C₂³	—	244	1	no	—
516	C₂³	—	244	2	no	—
517	Q₈	—	2	1	no	—
518	Q₈	—	61	2	no	—
519	Q₈	—	122	4	no	—
520	Q₈	—	122	1	no	—
521	Q₈	C₂×C₄×#6923	1	2	yes	complemented
522	D₄	—	2	1	no	—
523	D₄	—	61	2	no	—
524	D₄	—	122	4	no	—
525	D₄	—	122	1	no	—
526	D₄	C₂×C₄×#6923	1	2	yes	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	61	4	no	—
532	C₂×C₄	—	61	4	no	—
533	C₂×C₄	—	61	4	no	—
534	C₂×C₄	—	61	1	no	—
535	C₂×C₄	—	61	1	no	—
536	C₂×C₄	—	61	2	no	—
537	C₂×C₄	—	61	2	no	—
538	C₂×C₄	—	61	2	no	—
539	C₂×C₄	—	61	2	no	—
540	C₂×C₄	—	61	4	no	—
541	C₂×C₄	—	61	1	no	—
542	C₂×C₄	—	122	4	no	—
543	C₂×C₄	—	122	2	no	—
544	C₂×C₄	—	122	2	no	—
545	C₂×C₄	—	122	2	no	—
546	C₂×C₄	—	122	1	no	—
547	C₂×C₄	—	122	4	no	—
548	C₂×C₄	—	122	4	no	—
549	C₂×C₄	—	122	1	no	—
550	C₂×C₄	—	122	1	no	—
551	C₂×C₄	—	244	2	no	—
552	C₂×C₄	—	244	1	no	—
553	C₂×C₄	—	244	2	no	—
554	C₂×C₄	—	244	1	no	—
555	C₂×C₄	—	244	2	no	—
556	C₂×C₄	—	244	16	no	—
557	C₂×C₄	—	244	2	no	—
558	C₂×C₄	—	244	2	no	—
559	C₂×C₄	—	244	2	no	—
560	C₂×C₄	—	244	2	no	—
561	C₂×C₄	—	244	2	no	—
562	C₂×C₄	D₄×#6923	1	1	yes	characteristic
563	C₂×C₄	D₄×#6923	1	1	yes	characteristic
564	C₂×C₄	C₂³×#6923	1	1	yes	characteristic
565	C₈	—	2	1	no	—
566	C₈	—	61	2	no	—
567	C₈	—	122	4	no	—
568	C₈	—	122	1	no	—
569	C₈	C₂×C₄×#6923	1	2	yes	complemented
570	C₂²	—	2	2	no	—
571	C₂²	—	4	1	no	—
572	C₂²	—	4	1	no	—
573	C₂²	—	61	1	no	—
574	C₂²	—	61	1	no	—
575	C₂²	—	61	2	no	—
576	C₂²	—	61	2	no	—
577	C₂²	—	122	2	no	—
578	C₂²	—	244	4	no	—
579	C₂²	—	244	4	no	—
580	C₂²	—	244	1	no	—
581	C₂²	—	244	1	no	—
582	C₂²	C₂×D₄×#6923	1	1	yes	characteristic
583	C₄	—	2	1	no	—
584	C₄	—	2	2	no	—
585	C₄	—	4	1	no	—
586	C₄	—	4	1	no	—
587	C₄	—	61	8	no	—
588	C₄	—	61	2	no	—
589	C₄	—	61	2	no	—
590	C₄	—	122	4	no	—
591	C₄	—	122	1	no	—
592	C₄	—	122	2	no	—
593	C₄	—	244	4	no	—
594	C₄	—	244	4	no	—
595	C₄	—	244	1	no	—
596	C₄	—	244	1	no	—
597	C₄	SD₁₆×#6923	1	2	yes	direct product factor
598	C₄	C₂²×C₄×#6923	1	1	yes	characteristic
599	C₄	#41×#6923	1	1	yes	characteristic
600	C₂	—	4	2	no	—
601	C₂	—	61	2	no	—
602	C₂	—	61	2	no	—
603	C₂	—	244	2	no	—
604	C₂	C₄×D₄×#6923	1	1	yes	characteristic
605	C₂	C₂×SD₁₆×#6923	1	1	yes	characteristic
606	C₂	#135×#6923	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₄×#6923
commutator	C₄×C₆₁	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#6923
Fitting	C₄×SD₁₆×C₆₁	C₄
socle	C₂²×C₆₁	C₂×C₄×D₄
prime radical	C₂×D₄×D₆₁	C₂³
cosocle	C₂×C₄×D₆₁	C₂⁴
hypercenter	C₄×SD₁₆	#6923
hypocenter	C₆₁	C₄²×SD₁₆
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×SD₁₆

Complements

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

N	H ≅ G/N	type
2. C₄×Q₈×#6923	C₂	semidirect
4. #106×#6923	C₂	semidirect
5. C₄×#14519845	C₂	semidirect
6. #103×#6923	C₂	semidirect
7. C₄×#14519840	C₂	semidirect
10. C₄×C₈×#6923	C₂	semidirect
15. SD₁₆×#6923	C₄	direct (N × H)
38. #16839853	C₄	semidirect
39. C₄×#11758190	C₄	semidirect
40. SD₁₆×Dic₆₁	C₄	semidirect
41. C₄×#11758201	C₄	semidirect
42. #16839849	C₄	semidirect
43. C₄×#11758200	C₄	semidirect
44. #16839847	C₄	semidirect
49. C₄×SD₁₆×C₆₁	C₄	semidirect
53. Q₈×#6923	C₂×C₄	semidirect
70. #14519845	C₂×C₄	semidirect
71. #14519840	C₂×C₄	semidirect
76. C₈×#6923	C₂×C₄	semidirect
90. Q₈×Dic₆₁	C₂×C₄	semidirect
92. C₄×Dic₁₂₂	C₂×C₄	semidirect
94. #14519742	C₂×C₄	semidirect
106. #14519709	C₂×C₄	semidirect
107. #14519708	C₂×C₄	semidirect
108. #14519708	C₂×C₄	semidirect
109. #14519702	C₂×C₄	semidirect
110. #14519701	C₂×C₄	semidirect
111. #14519700	C₂×C₄	semidirect
115. C₄×#92418	C₂×C₄	semidirect
116. C₈×Dic₆₁	C₂×C₄	semidirect
117. C₈×Dic₆₁	C₂×C₄	semidirect
119. C₄×Q₈×C₆₁	C₂×C₄	semidirect
121. #106×C₆₁	C₂×C₄	semidirect
122. #103×C₆₁	C₂×C₄	semidirect
124. C₄×C₈×C₆₁	C₂×C₄	semidirect
169. C₄×#6923	SD₁₆	direct (N × H)
174. SD₁₆×C₆₁	C₄²	semidirect
184. #11758201	C₄²	semidirect
185. #11758200	C₄²	semidirect
203. #11758190	C₄²	semidirect
227. Q₈×C₆₁	C₂×C₄²	semidirect
260. Dic₁₂₂	C₂×C₄²	semidirect
263. C₈×C₆₁	C₂×C₄²	semidirect
265. #92418	C₂×C₄²	semidirect
283. #6923	C₄×SD₁₆	direct (N × H)
288. C₄×C₆₁	C₄×SD₁₆	semidirect
295. Dic₆₁	C₄×SD₁₆	semidirect
329. C₄×SD₁₆	#6923	direct (N × H)
353. C₆₁	C₄²×SD₁₆	semidirect
373. C₄×Q₈	C₂×#6923	semidirect
406. #106	C₂×#6923	semidirect
411. #103	C₂×#6923	semidirect
424. C₄×C₈	C₂×#6923	semidirect
462. SD₁₆	C₄×#6923	direct (N × H)
521. Q₈	C₂×C₄×#6923	semidirect
569. C₈	C₂×C₄×#6923	semidirect
597. C₄	SD₁₆×#6923	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×SD₁₆×#6923	2
C₄×Q₈×#6923	2
C₄×D₄×#6923	2
#106×#6923	2
C₄×#14519845	2
#103×#6923	2
C₄×#14519840	2
#102×#6923	2
C₄×#14519839	2
C₄×C₈×#6923	2
C₄×SD₁₆×D₆₁	2
C₄²×SD₁₆	61

Subgroups — C4×SD16×#6923 #30614498

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×SD₁₆×#6923 #30614498