Subgroups — C₄×#41×#6923 #30624545

Order 15616.

4086 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×#6923	C₂	1	2	yes	maximal
2	C₄×Q₈×#6923	C₂	1	4	yes	maximal, complemented
3	C₄×D₄×#6923	C₂	1	12	yes	maximal, complemented
4	#117×#6923	C₂	1	6	yes	maximal, complemented
5	C₄×#14519856	C₂	1	3	yes	maximal, complemented
6	C₂×C₄²×#6923	C₂	1	3	yes	maximal, complemented
7	C₄×#41×D₆₁	C₂	1	1	yes	maximal, characteristic
8	#41×#6923	C₄	1	32	yes	direct product factor
9	C₂×Q₈×#6923	C₂²	1	4	yes	—
10	C₂×D₄×#6923	C₂²	1	12	yes	—
11	C₂×#14519856	C₂²	1	6	yes	—
12	C₂²×C₄×#6923	C₂²	1	12	yes	—
13	C₂²×C₄×#6923	C₂²	1	6	yes	—
14	C₄⋊C₄×#6923	C₂²	1	24	yes	—
15	C₄×C₄⋊#6923	C₂²	1	12	yes	—
16	C₂²⋊C₄×#6923	C₂²	1	24	yes	—
17	C₄×C₂²⋊#6923	C₂²	1	12	yes	—
18	#16840698	C₂²	1	6	yes	—
19	C₄²×#6923	C₂²	1	1	yes	characteristic
20	C₄²×#6923	C₂²	1	3	yes	—
21	C₄²×#6923	C₂²	1	6	yes	—
22	C₄²×#6923	C₂²	1	12	yes	—
23	C₂×#41×D₆₁	C₂²	1	1	yes	characteristic
24	#41×Dic₆₁	C₄	1	1	yes	characteristic, complemented
25	C₄×#11758226	C₄	1	2	yes	complemented
26	C₄×#11758222	C₄	1	3	yes	complemented
27	#16840230	C₄	1	3	yes	complemented
28	C₄×#11758224	C₄	1	6	yes	complemented
29	C₄×Q₈×D₆₁	C₂²	1	2	yes	—
30	C₄×D₄×D₆₁	C₂²	1	6	yes	—
31	#117×D₆₁	C₂²	1	3	yes	—
32	C₂×C₄²×D₆₁	C₂²	1	3	yes	—
33	C₄×#41×C₆₁	C₄	1	1	yes	characteristic, complemented
34	C₂³×#6923	C₂³	1	12	yes	—
35	Q₈×#6923	C₂×C₄	1	32	yes	complemented
36	D₄×#6923	C₂×C₄	1	96	yes	complemented
37	#14519856	C₂×C₄	1	48	yes	complemented
38	C₂×C₄⋊#6923	C₂³	1	12	yes	—
39	C₂×C₂²⋊#6923	C₂³	1	12	yes	—
40	C₂×C₄×#6923	—	2	48	no	—
41	C₂×C₄×#6923	C₂×C₄	1	48	yes	complemented
42	C₂×C₄×#6923	C₂³	1	12	yes	—
43	C₂×C₄×#6923	C₂³	1	24	yes	—
44	C₂×C₄×#6923	C₂³	1	2	yes	—
45	C₂×C₄×#6923	C₂³	1	6	yes	—
46	C₂×C₄×#6923	C₂³	1	12	yes	—
47	C₂×C₄×#6923	C₂³	1	4	yes	—
48	(C₂×#6923)⋊C₄	C₂³	1	24	yes	—
49	C₂×#11758226	C₂×C₄	1	1	yes	characteristic
50	C₂×#11758222	C₂×C₄	1	3	yes	—
51	C₂×#11758224	C₂×C₄	1	3	yes	—
52	#41×D₆₁	C₂×C₄	1	16	yes	—
53	C₂×Q₈×D₆₁	C₂³	1	1	yes	characteristic
54	C₂×D₄×D₆₁	C₂³	1	3	yes	—
55	C₂²×C₄×D₆₁	C₂³	1	6	yes	—
56	C₂²×C₄×D₆₁	C₂³	1	3	yes	—
57	Q₈×Dic₆₁	C₂×C₄	1	2	yes	complemented
58	C₄×Dic₁₂₂	C₂×C₄	1	6	yes	complemented
59	#14519742	C₂×C₄	1	6	yes	complemented
60	C₄×D₂₄₄	C₂×C₄	1	6	yes	complemented
61	D₄×Dic₆₁	C₂×C₄	1	6	yes	complemented
62	#14519739	C₂×C₄	1	6	yes	complemented
63	C₄×C₂²⋊D₆₁	C₂×C₄	1	12	yes	complemented
64	#14519737	C₂×C₄	1	12	yes	complemented
65	#14519736	C₂×C₄	1	3	yes	complemented
66	#14519735	C₂×C₄	1	6	yes	complemented
67	#14519734	C₂×C₄	1	6	yes	complemented
68	#14519733	C₂×C₄	1	6	yes	complemented
69	C₄⋊C₄×D₆₁	C₂³	1	6	yes	—
70	C₂²⋊C₄×D₆₁	C₂³	1	6	yes	—
71	C₂×C₄×Dic₆₁	C₂×C₄	1	6	yes	complemented
72	C₂×C₄×Dic₆₁	C₂×C₄	1	3	yes	complemented
73	C₄²×D₆₁	C₂×C₄	1	6	yes	complemented
74	C₄²×D₆₁	C₂×C₄	1	3	yes	complemented
75	C₄²×D₆₁	C₂×C₄	1	3	yes	complemented
76	C₄²×D₆₁	C₂³	1	1	yes	characteristic
77	C₄²×D₆₁	C₂³	1	3	yes	—
78	C₄²×D₆₁	C₂³	1	6	yes	—
79	C₂×#41×C₆₁	C₂×C₄	1	1	yes	characteristic
80	C₄×Q₈×C₆₁	C₂×C₄	1	2	yes	complemented
81	C₄×D₄×C₆₁	C₂×C₄	1	6	yes	complemented
82	#117×C₆₁	C₂×C₄	1	3	yes	complemented
83	C₂×C₄²×C₆₁	C₂×C₄	1	3	yes	complemented
84	C₂³×D₆₁	C₂⁴	1	3	yes	—
85	C₂²×#6923	—	2	48	no	—
86	C₂²×#6923	C₂²×C₄	1	48	yes	—
87	C₂²×#6923	C₂⁴	1	12	yes	—
88	C₂²×#6923	C₂⁴	1	4	yes	—
89	#41×C₆₁	C₄²	1	8	yes	complemented
90	C₂×Q₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
91	C₂×D₄×C₆₁	C₂²×C₄	1	3	yes	—
92	C₂²×C₄×C₆₁	C₂²×C₄	1	6	yes	—
93	C₂²×C₄×C₆₁	C₂²×C₄	1	3	yes	—
94	C₂×C₂²⋊D₆₁	C₂²×C₄	1	6	yes	—
95	C₂²×Dic₆₁	C₂²×C₄	1	6	yes	—
96	C₂²×Dic₆₁	C₂²×C₄	1	3	yes	—
97	#11758226	C₄²	1	8	yes	complemented
98	Q₈×D₆₁	C₂²×C₄	1	8	yes	—
99	#11758224	C₄²	1	24	yes	complemented
100	D₄×D₆₁	C₂²×C₄	1	24	yes	—
101	#11758222	C₄²	1	24	yes	complemented
102	C₂×D₂₄₄	C₂²×C₄	1	3	yes	—
103	C₂×C₄×D₆₁	—	2	24	no	—
104	C₂×C₄×D₆₁	C₂²×C₄	1	6	yes	—
105	C₂×C₄×D₆₁	C₂²×C₄	1	6	yes	—
106	C₂×C₄×D₆₁	C₂²×C₄	1	3	yes	—
107	C₂×C₄×D₆₁	C₂²×C₄	1	3	yes	—
108	C₂×C₄×D₆₁	C₂²×C₄	1	24	yes	—
109	C₂×C₄×D₆₁	C₂⁴	1	6	yes	—
110	C₂×C₄×D₆₁	C₂⁴	1	1	yes	characteristic
111	C₂×C₄×D₆₁	C₂⁴	1	3	yes	—
112	C₂×C₄×D₆₁	C₂⁴	1	2	yes	—
113	C₂×Dic₁₂₂	C₂²×C₄	1	3	yes	—
114	C₂²⋊#6923	C₂²×C₄	1	48	yes	—
115	C₄⋊#6923	C₂²×C₄	1	48	yes	—
116	C₄×#6923	—	2	48	no	—
117	C₄×#6923	—	2	24	no	—
118	C₄×#6923	C₂²×C₄	1	8	yes	—
119	C₄×#6923	C₂²×C₄	1	24	yes	—
120	C₄×#6923	C₂²×C₄	1	48	yes	—
121	C₄×#6923	#41	1	16	yes	direct product factor
122	C₄⋊C₄×C₆₁	C₂²×C₄	1	6	yes	—
123	C₂²⋊C₄×C₆₁	C₂²×C₄	1	6	yes	—
124	C₄²×C₆₁	C₂²×C₄	1	3	yes	—
125	C₄²×C₆₁	C₂²×C₄	1	6	yes	—
126	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
127	C₂²⋊Dic₆₁	C₂²×C₄	1	6	yes	—
128	#11758198	C₂²×C₄	1	12	yes	—
129	C₄⋊Dic₆₁	C₂²×C₄	1	6	yes	—
130	#11758196	C₂²×C₄	1	12	yes	—
131	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
132	C₄×Dic₆₁	C₂²×C₄	1	2	yes	—
133	C₄×Dic₆₁	C₂²×C₄	1	6	yes	—
134	C₄×Dic₆₁	C₂²×C₄	1	3	yes	—
135	C₄×Dic₆₁	C₂²×C₄	1	6	yes	—
136	C₄×Dic₆₁	C₂²×C₄	1	6	yes	—
137	C₄×Dic₆₁	C₂²×C₄	1	6	yes	—
138	C₂³×C₆₁	C₂³×C₄	1	3	yes	—
139	C₂²×D₆₁	—	2	12	no	—
140	C₂²×D₆₁	C₂³×C₄	1	12	yes	—
141	C₂²×D₆₁	C₂³×C₄	1	3	yes	—
142	C₂²×D₆₁	C₂⁵	1	1	yes	characteristic
143	C₂×#6923	—	2	24	no	—
144	C₂×#6923	—	2	96	no	—
145	C₂×#6923	C₂³×C₄	1	24	yes	—
146	C₂×#6923	C₂³×C₄	1	8	yes	—
147	C₂×#6923	C₂×#41	1	16	yes	—
148	Q₈×C₆₁	C₂×C₄²	1	4	yes	complemented
149	D₄×C₆₁	C₂×C₄²	1	12	yes	complemented
150	C₂×C₄×C₆₁	—	2	12	no	—
151	C₂×C₄×C₆₁	C₂×C₄²	1	12	yes	complemented
152	C₂×C₄×C₆₁	C₂³×C₄	1	6	yes	—
153	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
154	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
155	C₂×C₄×C₆₁	C₂³×C₄	1	3	yes	—
156	C₂²⋊D₆₁	C₂×C₄²	1	24	yes	complemented
157	C₂×Dic₆₁	—	2	12	no	—
158	C₂×Dic₆₁	C₂×C₄²	1	12	yes	complemented
159	C₂×Dic₆₁	C₂³×C₄	1	6	yes	—
160	C₂×Dic₆₁	C₂³×C₄	1	2	yes	—
161	C₂×Dic₆₁	C₂³×C₄	1	1	yes	characteristic
162	C₂×Dic₆₁	C₂³×C₄	1	3	yes	—
163	D₂₄₄	C₂×C₄²	1	12	yes	complemented
164	C₄×D₆₁	—	2	12	no	—
165	C₄×D₆₁	—	2	12	no	—
166	C₄×D₆₁	—	2	12	no	—
167	C₄×D₆₁	C₂×C₄²	1	12	yes	complemented
168	C₄×D₆₁	C₂×C₄²	1	12	yes	complemented
169	C₄×D₆₁	C₂³×C₄	1	4	yes	—
170	C₄×D₆₁	C₂³×C₄	1	12	yes	—
171	C₄×D₆₁	C₂×#41	1	8	yes	—
172	Dic₁₂₂	C₂×C₄²	1	12	yes	complemented
173	C₄²×#41	—	61	1	no	maximal, Sylow
174	C₂²×C₆₁	—	2	6	no	—
175	C₂²×C₆₁	C₂²×C₄²	1	6	yes	—
176	C₂²×C₆₁	C₂⁴×C₄	1	1	yes	characteristic
177	C₂×D₆₁	—	2	6	no	—
178	C₂×D₆₁	—	2	24	no	—
179	C₂×D₆₁	C₂²×C₄²	1	6	yes	—
180	C₂×D₆₁	C₂⁴×C₄	1	2	yes	—
181	C₂×D₆₁	C₂²×#41	1	4	yes	—
182	#6923	—	2	24	no	—
183	#6923	C₄×#41	1	16	yes	direct product factor
184	C₄×C₆₁	—	2	6	no	—
185	C₄×C₆₁	C₂²×C₄²	1	6	yes	—
186	C₄×C₆₁	C₂²×C₄²	1	2	yes	—
187	C₄×C₆₁	C₄×#41	1	4	yes	complemented
188	Dic₆₁	—	2	6	no	—
189	Dic₆₁	C₂²×C₄²	1	6	yes	—
190	Dic₆₁	C₂²×C₄²	1	2	yes	—
191	Dic₆₁	C₄×#41	1	4	yes	complemented
192	C₂×C₄×#41	—	61	2	no	—
193	C₂×C₄×#41	—	61	1	no	—
194	C₄²×Q₈	—	61	4	no	—
195	C₄²×D₄	—	61	12	no	—
196	C₄×#117	—	61	3	no	—
197	C₄×#117	—	61	6	no	—
198	C₂×C₄³	—	61	3	no	—
199	C₂×C₆₁	—	2	6	no	—
200	C₂×C₆₁	C₂³×C₄²	1	1	yes	characteristic
201	C₂×C₆₁	C₂×C₄×#41	1	2	yes	—
202	D₆₁	—	2	6	no	—
203	D₆₁	C₂×C₄×#41	1	4	yes	—
204	C₂²×#41	—	61	1	no	—
205	C₄×#41	—	61	32	no	—
206	C₄×#41	—	61	1	no	—
207	C₄×#41	—	61	2	no	—
208	C₄×#41	—	61	6	no	—
209	C₄×#41	—	61	3	no	—
210	C₄×#41	—	61	3	no	—
211	C₄×#41	#6923	1	1	yes	characteristic, direct product factor
212	C₂×C₄×Q₈	—	61	4	no	—
213	C₂×C₄×Q₈	—	61	2	no	—
214	C₂×C₄×D₄	—	61	12	no	—
215	C₂×C₄×D₄	—	61	6	no	—
216	C₂×#117	—	61	6	no	—
217	C₂×#117	—	61	3	no	—
218	C₂²×C₄²	—	61	6	no	—
219	C₂²×C₄²	—	61	3	no	—
220	C₂²×C₄²	—	61	12	no	—
221	C₄×C₄⋊C₄	—	61	12	no	—
222	C₄×C₄⋊C₄	—	61	24	no	—
223	C₄×C₂²⋊C₄	—	61	12	no	—
224	C₄×C₂²⋊C₄	—	61	24	no	—
225	#376	—	61	6	no	—
226	C₄³	—	61	1	no	—
227	C₄³	—	61	3	no	—
228	C₄³	—	61	6	no	—
229	C₄³	—	61	12	no	—
230	C₆₁	C₄²×#41	1	1	yes	characteristic, complemented, Sylow
231	C₂×#41	—	61	16	no	—
232	C₂×#41	—	61	1	no	—
233	C₂×#41	—	61	3	no	—
234	C₂×#41	—	61	3	no	—
235	C₂×#41	C₂×#6923	1	1	yes	characteristic
236	C₂²×Q₈	—	61	1	no	—
237	C₂²×D₄	—	61	3	no	—
238	C₂³×C₄	—	61	3	no	—
239	C₂³×C₄	—	61	12	no	—
240	C₂³×C₄	—	61	6	no	—
241	C₄×Q₈	—	61	32	no	—
242	C₄×Q₈	—	61	2	no	—
243	C₄×Q₈	—	61	6	no	—
244	C₄×Q₈	—	61	6	no	—
245	C₄×Q₈	C₂×#6923	1	2	yes	complemented
246	C₄×D₄	—	61	96	no	—
247	C₄×D₄	—	61	6	no	—
248	C₄×D₄	—	61	12	no	—
249	C₄×D₄	—	61	6	no	—
250	C₄×D₄	—	61	12	no	—
251	C₄×D₄	—	61	6	no	—
252	C₄×D₄	C₂×#6923	1	6	yes	complemented
253	#117	—	61	48	no	—
254	#117	—	61	3	no	—
255	#117	—	61	6	no	—
256	#117	—	61	6	no	—
257	#117	—	61	6	no	—
258	#117	C₂×#6923	1	3	yes	complemented
259	C₂×C₄⋊C₄	—	61	12	no	—
260	C₂×C₄⋊C₄	—	61	6	no	—
261	C₂×C₂²⋊C₄	—	61	12	no	—
262	C₂×C₂²⋊C₄	—	61	6	no	—
263	C₂×C₄²	—	61	6	no	—
264	C₂×C₄²	—	61	12	no	—
265	C₂×C₄²	—	61	48	no	—
266	C₂×C₄²	—	61	2	no	—
267	C₂×C₄²	—	61	4	no	—
268	C₂×C₄²	—	61	6	no	—
269	C₂×C₄²	—	61	3	no	—
270	C₂×C₄²	—	61	3	no	—
271	C₂×C₄²	—	61	6	no	—
272	C₂×C₄²	—	61	6	no	—
273	C₂×C₄²	—	61	3	no	—
274	C₂×C₄²	—	61	3	no	—
275	C₂×C₄²	—	61	1	no	—
276	C₂×C₄²	—	61	24	no	—
277	C₂×C₄²	—	61	12	no	—
278	C₂×C₄²	—	122	48	no	—
279	C₂×C₄²	C₂×#6923	1	3	yes	complemented
280	#95	—	61	24	no	—
281	C₂⁴	—	61	3	no	—
282	#41	—	61	8	no	—
283	#41	—	61	24	no	—
284	#41	—	61	24	no	—
285	#41	C₄×#6923	1	8	yes	direct product factor
286	C₂×Q₈	—	61	8	no	—
287	C₂×Q₈	—	61	3	no	—
288	C₂×Q₈	C₂²×#6923	1	1	yes	characteristic
289	C₂×D₄	—	61	6	no	—
290	C₂×D₄	—	61	24	no	—
291	C₂×D₄	—	61	3	no	—
292	C₂×D₄	C₂²×#6923	1	3	yes	—
293	C₂²×C₄	—	61	4	no	—
294	C₂²×C₄	—	61	3	no	—
295	C₂²×C₄	—	61	24	no	—
296	C₂²×C₄	—	61	1	no	—
297	C₂²×C₄	—	61	2	no	—
298	C₂²×C₄	—	61	3	no	—
299	C₂²×C₄	—	61	3	no	—
300	C₂²×C₄	—	61	3	no	—
301	C₂²×C₄	—	61	12	no	—
302	C₂²×C₄	—	61	48	no	—
303	C₂²×C₄	—	61	6	no	—
304	C₂²×C₄	—	61	6	no	—
305	C₂²×C₄	—	61	6	no	—
306	C₂²×C₄	—	61	6	no	—
307	C₂²×C₄	—	122	24	no	—
308	C₂²×C₄	—	122	48	no	—
309	C₂²×C₄	C₂²×#6923	1	6	yes	—
310	C₂²×C₄	C₂²×#6923	1	3	yes	—
311	C₄⋊C₄	—	61	48	no	—
312	C₄⋊C₄	—	61	12	no	—
313	C₄⋊C₄	—	61	6	no	—
314	C₄⋊C₄	C₂²×#6923	1	6	yes	—
315	C₂²⋊C₄	—	61	48	no	—
316	C₂²⋊C₄	—	61	6	no	—
317	C₂²⋊C₄	—	61	12	no	—
318	C₂²⋊C₄	C₂²×#6923	1	6	yes	—
319	C₄²	—	61	8	no	—
320	C₄²	—	61	24	no	—
321	C₄²	—	61	48	no	—
322	C₄²	—	61	16	no	—
323	C₄²	—	61	1	no	—
324	C₄²	—	61	2	no	—
325	C₄²	—	61	6	no	—
326	C₄²	—	61	3	no	—
327	C₄²	—	61	6	no	—
328	C₄²	—	61	6	no	—
329	C₄²	—	61	6	no	—
330	C₄²	—	122	48	no	—
331	C₄²	—	122	24	no	—
332	C₄²	C₂²×#6923	1	3	yes	—
333	C₄²	C₂²×#6923	1	6	yes	—
334	C₄²	C₂²×#6923	1	1	yes	characteristic
335	C₂³	—	61	1	no	—
336	C₂³	—	61	12	no	—
337	C₂³	—	61	3	no	—
338	C₂³	—	122	12	no	—
339	C₂³	C₂³×#6923	1	3	yes	—
340	Q₈	—	61	12	no	—
341	Q₈	C₂×C₄×#6923	1	4	yes	complemented
342	D₄	—	61	24	no	—
343	D₄	—	61	12	no	—
344	D₄	C₂×C₄×#6923	1	12	yes	complemented
345	C₂×C₄	—	2	12	no	—
346	C₂×C₄	—	61	8	no	—
347	C₂×C₄	—	61	16	no	—
348	C₂×C₄	—	61	12	no	—
349	C₂×C₄	—	61	1	no	—
350	C₂×C₄	—	61	2	no	—
351	C₂×C₄	—	61	3	no	—
352	C₂×C₄	—	61	12	no	—
353	C₂×C₄	—	61	12	no	—
354	C₂×C₄	—	61	4	no	—
355	C₂×C₄	—	61	12	no	—
356	C₂×C₄	—	61	8	no	—
357	C₂×C₄	—	61	24	no	—
358	C₂×C₄	—	61	6	no	—
359	C₂×C₄	—	122	12	no	—
360	C₂×C₄	—	122	12	no	—
361	C₂×C₄	—	122	12	no	—
362	C₂×C₄	—	122	96	no	—
363	C₂×C₄	—	122	24	no	—
364	C₂×C₄	—	122	12	no	—
365	C₂×C₄	C₂×C₄×#6923	1	12	yes	complemented
366	C₂×C₄	C₂³×#6923	1	6	yes	—
367	C₂×C₄	C₂³×#6923	1	1	yes	characteristic
368	C₂×C₄	C₂³×#6923	1	3	yes	—
369	C₂×C₄	C₂³×#6923	1	2	yes	—
370	C₂²	—	2	6	no	—
371	C₂²	—	61	2	no	—
372	C₂²	—	61	4	no	—
373	C₂²	—	61	6	no	—
374	C₂²	—	122	24	no	—
375	C₂²	—	122	6	no	—
376	C₂²	C₂²×C₄×#6923	1	6	yes	—
377	C₂²	C₂⁴×#6923	1	1	yes	characteristic
378	C₄	—	2	6	no	—
379	C₄	—	61	16	no	—
380	C₄	—	61	2	no	—
381	C₄	—	61	6	no	—
382	C₄	—	61	4	no	—
383	C₄	—	122	24	no	—
384	C₄	—	122	6	no	—
385	C₄	C₂²×C₄×#6923	1	2	yes	—
386	C₄	C₂²×C₄×#6923	1	6	yes	—
387	C₄	#41×#6923	1	4	yes	direct product factor
388	C₂	—	2	6	no	—
389	C₂	—	61	4	no	—
390	C₂	—	122	6	no	—
391	C₂	C₂³×C₄×#6923	1	1	yes	characteristic
392	C₂	C₂×#41×#6923	1	2	yes	—

	subgroup	G/H
center	C₄²	C₂²×#6923
commutator	C₂×C₆₁	C₂³×C₄²
Frattini	C₂²	C₂⁴×#6923
Fitting	C₄×#41×C₆₁	C₄
socle	C₂²×C₆₁	C₂⁴×C₄
prime radical	C₂×#41×D₆₁	C₂²
cosocle	C₂²×D₆₁	C₂⁵
hypercenter	C₄×#41	#6923
hypocenter	C₆₁	C₄²×#41
LCS	G ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄² ◁ C₄×#41

Complements

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

N	H ≅ G/N	type
2. C₄×Q₈×#6923	C₂	semidirect
3. C₄×D₄×#6923	C₂	semidirect
4. #117×#6923	C₂	semidirect
5. C₄×#14519856	C₂	semidirect
6. C₂×C₄²×#6923	C₂	semidirect
8. #41×#6923	C₄	direct (N × H)
24. #41×Dic₆₁	C₄	semidirect
25. C₄×#11758226	C₄	semidirect
26. C₄×#11758222	C₄	semidirect
27. #16840230	C₄	semidirect
28. C₄×#11758224	C₄	semidirect
33. C₄×#41×C₆₁	C₄	semidirect
35. Q₈×#6923	C₂×C₄	semidirect
36. D₄×#6923	C₂×C₄	semidirect
37. #14519856	C₂×C₄	semidirect
41. C₂×C₄×#6923	C₂×C₄	semidirect
57. Q₈×Dic₆₁	C₂×C₄	semidirect
58. C₄×Dic₁₂₂	C₂×C₄	semidirect
59. #14519742	C₂×C₄	semidirect
60. C₄×D₂₄₄	C₂×C₄	semidirect
61. D₄×Dic₆₁	C₂×C₄	semidirect
62. #14519739	C₂×C₄	semidirect
63. C₄×C₂²⋊D₆₁	C₂×C₄	semidirect
64. #14519737	C₂×C₄	semidirect
65. #14519736	C₂×C₄	semidirect
66. #14519735	C₂×C₄	semidirect
67. #14519734	C₂×C₄	semidirect
68. #14519733	C₂×C₄	semidirect
71. C₂×C₄×Dic₆₁	C₂×C₄	semidirect
72. C₂×C₄×Dic₆₁	C₂×C₄	semidirect
73. C₄²×D₆₁	C₂×C₄	semidirect
74. C₄²×D₆₁	C₂×C₄	semidirect
75. C₄²×D₆₁	C₂×C₄	semidirect
80. C₄×Q₈×C₆₁	C₂×C₄	semidirect
81. C₄×D₄×C₆₁	C₂×C₄	semidirect
82. #117×C₆₁	C₂×C₄	semidirect
83. C₂×C₄²×C₆₁	C₂×C₄	semidirect
89. #41×C₆₁	C₄²	semidirect
97. #11758226	C₄²	semidirect
99. #11758224	C₄²	semidirect
101. #11758222	C₄²	semidirect
121. C₄×#6923	#41	direct (N × H)
148. Q₈×C₆₁	C₂×C₄²	semidirect
149. D₄×C₆₁	C₂×C₄²	semidirect
151. C₂×C₄×C₆₁	C₂×C₄²	semidirect
156. C₂²⋊D₆₁	C₂×C₄²	semidirect
158. C₂×Dic₆₁	C₂×C₄²	semidirect
163. D₂₄₄	C₂×C₄²	semidirect
167. C₄×D₆₁	C₂×C₄²	semidirect
168. C₄×D₆₁	C₂×C₄²	semidirect
172. Dic₁₂₂	C₂×C₄²	semidirect
183. #6923	C₄×#41	direct (N × H)
187. C₄×C₆₁	C₄×#41	semidirect
191. Dic₆₁	C₄×#41	semidirect
211. C₄×#41	#6923	direct (N × H)
230. C₆₁	C₄²×#41	semidirect
245. C₄×Q₈	C₂×#6923	semidirect
252. C₄×D₄	C₂×#6923	semidirect
258. #117	C₂×#6923	semidirect
279. C₂×C₄²	C₂×#6923	semidirect
285. #41	C₄×#6923	direct (N × H)
341. Q₈	C₂×C₄×#6923	semidirect
344. D₄	C₂×C₄×#6923	semidirect
365. C₂×C₄	C₂×C₄×#6923	semidirect
387. C₄	#41×#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×#41×#6923	2
C₄×Q₈×#6923	2
C₄×D₄×#6923	2
#117×#6923	2
C₄×#14519856	2
C₂×C₄²×#6923	2
C₄×#41×D₆₁	2
C₄²×#41	61

Subgroups — C4×#41×#6923 #30624545

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#41×#6923 #30624545