Subgroups — #29698480

Order 15616.

870 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16839879	C₂	1	2	yes	maximal
2	#21454387	C₂	1	2	yes	maximal, complemented
3	#21446568	C₂	1	2	yes	maximal, complemented
4	#21446096	C₂	1	4	yes	maximal, complemented
5	#21445991	C₂	1	1	yes	maximal, characteristic, complemented
6	#21445839	C₂	1	2	yes	maximal, complemented
7	C₈×C₄⋊Dic₆₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×#135×C₆₁	C₂	1	1	yes	maximal, characteristic
9	C₂×#14519784	C₂²	1	4	yes	—
10	#16839879	—	2	8	no	—
11	C₂×#14519713	C₂²	1	2	yes	—
12	C₂×#14519713	C₂²	1	2	yes	—
13	#16839789	—	2	4	no	—
14	#16839789	C₂²	1	4	yes	—
15	#16839786	—	2	2	no	—
16	#16839786	C₂²	1	2	yes	—
17	C₂×C₄⋊#92418	—	2	2	no	—
18	C₂×C₄⋊#92418	C₂²	1	1	yes	characteristic
19	C₂×#14519704	C₂²	1	4	yes	—
20	C₂×C₈×Dic₆₁	C₂²	1	2	yes	—
21	C₄×C₄⋊Dic₆₁	C₂²	1	1	yes	characteristic
22	#16839521	C₂²	1	4	yes	—
23	#16839516	C₂²	1	2	yes	—
24	C₂×#135×C₆₁	C₂²	1	1	yes	characteristic
25	C₄×#41×C₆₁	C₂²	1	2	yes	—
26	C₄×Q₁₆×C₆₁	C₄	1	1	yes	characteristic, complemented
27	C₄×Q₁₆×C₆₁	C₄	1	1	yes	characteristic, complemented
28	C₄×SD₁₆×C₆₁	C₄	1	2	yes	complemented
29	C₄×SD₁₆×C₆₁	C₄	1	2	yes	complemented
30	C₄×D₈×C₆₁	C₄	1	1	yes	characteristic, complemented
31	C₄×D₈×C₆₁	C₄	1	1	yes	characteristic, complemented
32	C₆₁×#427	C₂²	1	1	yes	characteristic
33	C₆₁×#416	C₂²	1	2	yes	—
34	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
35	#14519784	—	2	8	no	—
36	#14519784	—	4	4	no	—
37	C₂×#11758194	—	2	4	no	—
38	C₂×#11758194	C₂³	1	4	yes	—
39	C₂²×#92418	—	2	4	no	—
40	C₂²×#92418	C₂³	1	2	yes	—
41	C₂×C₄⋊Dic₆₁	—	2	1	no	—
42	C₂×C₄×Dic₆₁	C₂³	1	2	yes	—
43	#14519713	—	2	4	no	—
44	#14519713	—	4	2	no	—
45	C₄⋊#92418	—	2	2	no	—
46	C₄⋊#92418	—	2	2	no	—
47	C₄⋊#92418	—	2	4	no	—
48	C₄⋊#92418	—	2	4	no	—
49	C₄⋊#92418	D₄	1	1	yes	characteristic
50	C₄⋊#92418	D₄	1	1	yes	characteristic
51	C₄⋊#92418	D₄	1	2	yes	—
52	#14519704	—	2	8	no	—
53	C₈×Dic₆₁	—	2	4	no	—
54	#14519684	—	2	1	no	—
55	C₂×#41×C₆₁	C₂³	1	2	yes	—
56	#135×C₆₁	D₄	1	4	yes	—
57	#135×C₆₁	Q₈	1	4	yes	—
58	C₂×Q₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
59	C₂×SD₁₆×C₆₁	C₂×C₄	1	2	yes	—
60	C₂×D₈×C₆₁	C₂×C₄	1	1	yes	characteristic
61	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
63	C₄×Q₈×C₆₁	C₂×C₄	1	2	yes	—
64	C₄×Q₈×C₆₁	C₂×C₄	1	2	yes	—
65	C₄×D₄×C₆₁	—	2	2	no	—
66	C₄×D₄×C₆₁	—	2	2	no	—
67	C₄×D₄×C₆₁	C₂×C₄	1	2	yes	—
68	C₄×D₄×C₆₁	C₂×C₄	1	2	yes	—
69	#117×C₆₁	—	2	2	no	—
70	#117×C₆₁	C₂³	1	2	yes	—
71	C₂×C₄²×C₆₁	—	2	2	no	—
72	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
73	#107×C₆₁	C₂×C₄	1	1	yes	characteristic
74	#107×C₆₁	C₂×C₄	1	1	yes	characteristic
75	#106×C₆₁	C₂×C₄	1	2	yes	—
76	#103×C₆₁	C₂×C₄	1	2	yes	—
77	#103×C₆₁	C₂×C₄	1	2	yes	—
78	#102×C₆₁	C₂×C₄	1	2	yes	—
79	#102×C₆₁	C₂×C₄	1	2	yes	—
80	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
81	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
82	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
83	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
84	#41×C₆₁	—	2	2	no	—
85	#41×C₆₁	—	2	2	no	—
86	#41×C₆₁	C₂×D₄	1	4	yes	—
87	#41×C₆₁	C₂×Q₈	1	4	yes	—
88	C₂×Q₈×C₆₁	C₂²×C₄	1	2	yes	—
89	C₂×D₄×C₆₁	—	2	2	no	—
90	C₂×D₄×C₆₁	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₆₁	—	2	2	no	—
92	C₂²×C₄×C₆₁	—	2	2	no	—
93	C₂²×C₄×C₆₁	—	2	2	no	—
94	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
95	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
96	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
97	C₂²×Dic₆₁	—	2	2	no	—
98	Q₁₆×C₆₁	C₄⋊C₄	1	4	yes	complemented
99	SD₁₆×C₆₁	C₄⋊C₄	1	8	yes	complemented
100	D₈×C₆₁	C₄⋊C₄	1	4	yes	complemented
101	C₂×C₈×C₆₁	—	2	1	no	—
102	C₂×C₈×C₆₁	—	2	1	no	—
103	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
108	C₂×C₈×C₆₁	C₂×Q₈	1	2	yes	—
109	C₄⋊C₄×C₆₁	—	2	2	no	—
110	C₄⋊C₄×C₆₁	—	2	2	no	—
111	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
112	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
113	C₂²⋊C₄×C₆₁	—	2	2	no	—
114	C₂²⋊C₄×C₆₁	—	2	2	no	—
115	C₂²⋊C₄×C₆₁	—	2	2	no	—
116	C₄²×C₆₁	—	2	2	no	—
117	C₄²×C₆₁	—	2	2	no	—
118	C₄²×C₆₁	—	2	2	no	—
119	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
120	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
121	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
123	C₄⋊Dic₆₁	—	2	4	no	—
124	C₄×Dic₆₁	—	2	2	no	—
125	C₄×Dic₆₁	—	2	2	no	—
126	#11758194	—	2	4	no	—
127	#11758194	—	2	4	no	—
128	#11758194	—	4	8	no	—
129	C₂×#92418	—	2	2	no	—
130	C₂×#92418	—	2	2	no	—
131	C₂×#92418	—	2	4	no	—
132	C₂×#92418	—	4	8	no	—
133	C₂×#92418	C₂×D₄	1	2	yes	—
134	C₂×#92418	C₂×D₄	1	2	yes	—
135	C₂³×C₆₁	—	2	2	no	—
136	C₂³×C₆₁	C₂×#41	1	1	yes	characteristic
137	Q₈×C₆₁	—	2	2	no	—
138	Q₈×C₆₁	C₂×C₄⋊C₄	1	4	yes	—
139	D₄×C₆₁	—	2	4	no	—
140	D₄×C₆₁	—	2	4	no	—
141	D₄×C₆₁	—	2	2	no	—
142	D₄×C₆₁	C₂×C₄⋊C₄	1	4	yes	—
143	C₂×C₄×C₆₁	—	2	2	no	—
144	C₂×C₄×C₆₁	—	2	4	no	—
145	C₂×C₄×C₆₁	—	2	4	no	—
146	C₂×C₄×C₆₁	—	2	2	no	—
147	C₂×C₄×C₆₁	—	2	2	no	—
148	C₂×C₄×C₆₁	—	2	2	no	—
149	C₂×C₄×C₆₁	—	4	1	no	—
150	C₂×C₄×C₆₁	—	4	4	no	—
151	C₂×C₄×C₆₁	—	8	2	no	—
152	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
153	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
154	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
155	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
156	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
157	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
159	C₂×C₄×C₆₁	C₂²×Q₈	1	1	yes	characteristic
160	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
161	C₂×C₄×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
162	C₂×Dic₆₁	—	2	4	no	—
163	C₂×Dic₆₁	—	4	2	no	—
164	C₂×Dic₆₁	—	4	2	no	—
165	C₈×C₆₁	—	2	1	no	—
166	C₈×C₆₁	—	2	1	no	—
167	C₈×C₆₁	C₂×C₄⋊C₄	1	2	yes	—
168	C₈×C₆₁	C₂×C₄⋊C₄	1	2	yes	—
169	#92418	—	2	2	no	—
170	#92418	—	2	2	no	—
171	#92418	—	4	4	no	—
172	#22688	—	61	1	no	maximal, Sylow
173	C₂²×C₆₁	—	2	1	no	—
174	C₂²×C₆₁	—	2	1	no	—
175	C₂²×C₆₁	—	2	4	no	—
176	C₂²×C₆₁	—	4	2	no	—
177	C₂²×C₆₁	—	4	2	no	—
178	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
179	C₂²×C₆₁	#547	1	1	yes	characteristic
180	C₂²×C₆₁	#554	1	1	yes	characteristic
181	C₄×C₆₁	—	2	4	no	—
182	C₄×C₆₁	—	2	1	no	—
183	C₄×C₆₁	—	2	1	no	—
184	C₄×C₆₁	—	2	1	no	—
185	C₄×C₆₁	—	4	2	no	—
186	C₄×C₆₁	—	4	2	no	—
187	C₄×C₆₁	#443	1	2	yes	complemented
188	C₄×C₆₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
189	C₄×C₆₁	#520	1	1	yes	characteristic
190	C₄×C₆₁	D₄²	1	1	yes	characteristic
191	C₄×C₆₁	D₄×Q₈	1	1	yes	characteristic
192	Dic₆₁	—	4	4	no	—
193	C₂×#443	—	61	2	no	—
194	C₄×#135	D₆₁	1	1	yes	characteristic
195	#2906	—	61	2	no	—
196	#1945	—	61	2	no	—
197	#1866	—	61	4	no	—
198	#1848	—	61	1	no	—
199	#1806	—	61	2	no	—
200	C₈×C₄⋊C₄	—	61	1	no	—
201	C₂×C₆₁	—	2	1	no	—
202	C₂×C₆₁	—	2	1	no	—
203	C₂×C₆₁	—	4	4	no	—
204	C₂×C₆₁	D₄×C₄⋊C₄	1	1	yes	characteristic
205	C₂×C₆₁	C₂×#443	1	1	yes	characteristic
206	C₂×C₆₁	#2957	1	1	yes	characteristic
207	C₂×#135	C₂×D₆₁	1	1	yes	characteristic
208	C₂×#131	—	61	4	no	—
209	C₄×#41	C₂×D₆₁	1	2	yes	—
210	#443	—	122	8	no	—
211	C₄×Q₁₆	Dic₆₁	1	1	yes	characteristic, complemented
212	C₄×Q₁₆	Dic₆₁	1	1	yes	characteristic, complemented
213	C₄×SD₁₆	Dic₆₁	1	2	yes	complemented
214	C₄×SD₁₆	Dic₆₁	1	2	yes	complemented
215	C₄×D₈	Dic₆₁	1	1	yes	characteristic, complemented
216	C₄×D₈	Dic₆₁	1	1	yes	characteristic, complemented
217	C₂×#108	—	61	2	no	—
218	C₂×#108	—	61	2	no	—
219	#427	C₂×D₆₁	1	1	yes	characteristic
220	#424	—	61	4	no	—
221	#424	—	122	4	no	—
222	#423	—	61	2	no	—
223	#423	—	122	2	no	—
224	C₂×C₄⋊C₈	—	61	1	no	—
225	C₂×C₄⋊C₈	—	122	2	no	—
226	C₂×#104	—	61	4	no	—
227	#416	C₂×D₆₁	1	2	yes	—
228	C₂×C₄×C₈	—	61	2	no	—
229	C₂×C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
230	C₄×C₄⋊C₄	—	61	1	no	—
231	#339	—	61	4	no	—
232	#336	—	61	2	no	—
233	C₆₁	#22688	1	1	yes	characteristic, complemented, Sylow
234	C₂×#41	C₂²×D₆₁	1	2	yes	—
235	#135	Dic₁₂₂	1	4	yes	—
236	#135	D₂₄₄	1	4	yes	—
237	C₂×Q₁₆	C₂×Dic₆₁	1	1	yes	characteristic
238	C₂×SD₁₆	C₂×Dic₆₁	1	2	yes	—
239	C₂×D₈	C₂×Dic₆₁	1	1	yes	characteristic
240	#131	—	122	8	no	—
241	#131	—	244	4	no	—
242	C₂×M₁₆	—	61	4	no	—
243	C₂×M₁₆	—	122	4	no	—
244	C₂²×C₈	—	61	2	no	—
245	C₂²×C₈	—	122	4	no	—
246	C₂²×C₈	C₂²×D₆₁	1	1	yes	characteristic
247	C₂²×C₈	C₂²×D₆₁	1	1	yes	characteristic
248	C₄×Q₈	C₂×Dic₆₁	1	2	yes	—
249	C₄×Q₈	C₂×Dic₆₁	1	2	yes	—
250	C₄×D₄	—	2	2	no	—
251	C₄×D₄	—	2	2	no	—
252	C₄×D₄	C₂×Dic₆₁	1	2	yes	—
253	C₄×D₄	C₂×Dic₆₁	1	2	yes	—
254	#117	—	2	2	no	—
255	#117	C₂²×D₆₁	1	2	yes	—
256	C₂×C₄⋊C₄	—	122	1	no	—
257	C₂×C₄²	—	2	2	no	—
258	C₂×C₄²	—	61	2	no	—
259	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
260	#108	—	122	4	no	—
261	#108	—	244	2	no	—
262	#107	C₂×Dic₆₁	1	1	yes	characteristic
263	#107	C₂×Dic₆₁	1	1	yes	characteristic
264	#106	C₂×Dic₆₁	1	2	yes	—
265	C₄⋊C₈	—	61	1	no	—
266	C₄⋊C₈	—	61	1	no	—
267	C₄⋊C₈	—	61	2	no	—
268	C₄⋊C₈	—	122	4	no	—
269	C₄⋊C₈	—	122	4	no	—
270	C₄⋊C₈	—	122	2	no	—
271	C₄⋊C₈	—	122	2	no	—
272	#104	—	122	8	no	—
273	#103	C₂×Dic₆₁	1	2	yes	—
274	#103	C₂×Dic₆₁	1	2	yes	—
275	#102	C₂×Dic₆₁	1	2	yes	—
276	#102	C₂×Dic₆₁	1	2	yes	—
277	C₄×C₈	—	122	4	no	—
278	C₄×C₈	C₂×Dic₆₁	1	1	yes	characteristic
279	C₄×C₈	C₂×Dic₆₁	1	1	yes	characteristic
280	C₄×C₈	C₂×Dic₆₁	1	1	yes	characteristic
281	C₄×C₈	C₂×Dic₆₁	1	1	yes	characteristic
282	#95	—	122	1	no	—
283	#41	—	2	2	no	—
284	#41	—	2	2	no	—
285	#41	C₂×Dic₁₂₂	1	4	yes	—
286	#41	C₂×D₂₄₄	1	4	yes	—
287	C₂×Q₈	C₂²×Dic₆₁	1	2	yes	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	C₂²×Dic₆₁	1	2	yes	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	122	2	no	—
294	C₂²×C₄	#11758224	1	1	yes	characteristic
295	C₂²×C₄	#11758224	1	1	yes	characteristic
296	C₂²×C₄	C₂³×D₆₁	1	1	yes	characteristic
297	Q₁₆	C₄⋊Dic₆₁	1	4	yes	complemented
298	SD₁₆	C₄⋊Dic₆₁	1	8	yes	complemented
299	D₈	C₄⋊Dic₆₁	1	4	yes	complemented
300	M₁₆	—	122	4	no	—
301	M₁₆	—	122	4	no	—
302	M₁₆	—	244	8	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	2	1	no	—
305	C₂×C₈	—	61	2	no	—
306	C₂×C₈	—	61	2	no	—
307	C₂×C₈	—	122	2	no	—
308	C₂×C₈	—	122	2	no	—
309	C₂×C₈	—	122	4	no	—
310	C₂×C₈	—	244	8	no	—
311	C₂×C₈	C₂×Dic₁₂₂	1	2	yes	—
312	C₂×C₈	C₂×D₂₄₄	1	2	yes	—
313	C₂×C₈	C₂²×Dic₆₁	1	1	yes	characteristic
314	C₂×C₈	C₂²×Dic₆₁	1	1	yes	characteristic
315	C₂×C₈	C₂²×Dic₆₁	1	1	yes	characteristic
316	C₂×C₈	C₂²×Dic₆₁	1	1	yes	characteristic
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	122	4	no	—
320	C₄⋊C₄	C₂²×Dic₆₁	1	2	yes	—
321	C₄⋊C₄	C₂²×Dic₆₁	1	2	yes	—
322	C₂²⋊C₄	—	2	2	no	—
323	C₂²⋊C₄	—	2	2	no	—
324	C₂²⋊C₄	—	2	2	no	—
325	C₄²	—	2	2	no	—
326	C₄²	—	2	2	no	—
327	C₄²	—	2	2	no	—
328	C₄²	—	122	2	no	—
329	C₄²	—	122	2	no	—
330	C₄²	D₄×D₆₁	1	1	yes	characteristic
331	C₄²	D₄×D₆₁	1	1	yes	characteristic
332	C₄²	C₂²×Dic₆₁	1	1	yes	characteristic
333	C₄²	C₂²×Dic₆₁	1	1	yes	characteristic
334	C₂³	—	2	2	no	—
335	C₂³	C₂×#11758224	1	1	yes	characteristic
336	Q₈	—	2	2	no	—
337	Q₈	C₂×C₄⋊Dic₆₁	1	4	yes	—
338	D₄	—	2	4	no	—
339	D₄	—	2	4	no	—
340	D₄	—	2	2	no	—
341	D₄	C₂×C₄⋊Dic₆₁	1	4	yes	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	4	no	—
350	C₂×C₄	—	8	2	no	—
351	C₂×C₄	—	122	4	no	—
352	C₂×C₄	—	244	2	no	—
353	C₂×C₄	—	244	2	no	—
354	C₂×C₄	D₄×Dic₆₁	1	1	yes	characteristic
355	C₂×C₄	D₄×Dic₆₁	1	1	yes	characteristic
356	C₂×C₄	D₄×Dic₆₁	1	1	yes	characteristic
357	C₂×C₄	D₄×Dic₆₁	1	1	yes	characteristic
358	C₂×C₄	C₂³×Dic₆₁	1	1	yes	characteristic
359	C₂×C₄	C₂×D₄×D₆₁	1	1	yes	characteristic
360	C₂×C₄	C₂²×D₂₄₄	1	1	yes	characteristic
361	C₂×C₄	C₂²×Dic₁₂₂	1	1	yes	characteristic
362	C₂×C₄	#14519823	1	1	yes	characteristic
363	C₂×C₄	#14519824	1	1	yes	characteristic
364	C₈	—	2	1	no	—
365	C₈	—	2	1	no	—
366	C₈	—	122	2	no	—
367	C₈	—	122	2	no	—
368	C₈	—	244	4	no	—
369	C₈	C₂×C₄⋊Dic₆₁	1	2	yes	—
370	C₈	C₂×C₄⋊Dic₆₁	1	2	yes	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	4	no	—
374	C₂²	—	4	2	no	—
375	C₂²	—	4	2	no	—
376	C₂²	C₂×D₄×Dic₆₁	1	1	yes	characteristic
377	C₂²	#16840416	1	1	yes	characteristic
378	C₂²	#16840469	1	1	yes	characteristic
379	C₄	—	2	4	no	—
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	2	1	no	—
383	C₄	—	4	2	no	—
384	C₄	—	4	2	no	—
385	C₄	—	244	4	no	—
386	C₄	#16839879	1	2	yes	complemented
387	C₄	C₂²×C₄⋊Dic₆₁	1	1	yes	characteristic
388	C₄	#16840245	1	1	yes	characteristic
389	C₄	D₄×D₂₄₄	1	1	yes	characteristic
390	C₄	D₄×Dic₁₂₂	1	1	yes	characteristic
391	C₂	—	2	1	no	—
392	C₂	—	2	1	no	—
393	C₂	—	4	4	no	—
394	C₂	D₄×C₄⋊Dic₆₁	1	1	yes	characteristic
395	C₂	C₂×#16839879	1	1	yes	characteristic
396	C₂	#21454736	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₆₁
commutator	C₂×C₄×C₆₁	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₆₁
Fitting	C₄×#135×C₆₁	C₂
socle	C₂²×C₆₁	C₂×C₄×D₄
prime radical	C₂×#135×C₆₁	C₂²
cosocle	C₂²×C₄×C₆₁	C₂⁴
hypercenter	C₄×#135	D₆₁
hypocenter	C₆₁	#22688
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#135

Complements

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

N	H ≅ G/N	type
2. #21454387	C₂	semidirect
3. #21446568	C₂	semidirect
4. #21446096	C₂	semidirect
5. #21445991	C₂	semidirect
6. #21445839	C₂	semidirect
7. C₈×C₄⋊Dic₆₁	C₂	semidirect
26. C₄×Q₁₆×C₆₁	C₄	semidirect
27. C₄×Q₁₆×C₆₁	C₄	semidirect
28. C₄×SD₁₆×C₆₁	C₄	semidirect
29. C₄×SD₁₆×C₆₁	C₄	semidirect
30. C₄×D₈×C₆₁	C₄	semidirect
31. C₄×D₈×C₆₁	C₄	semidirect
98. Q₁₆×C₆₁	C₄⋊C₄	semidirect
99. SD₁₆×C₆₁	C₄⋊C₄	semidirect
100. D₈×C₆₁	C₄⋊C₄	semidirect
187. C₄×C₆₁	#443	semidirect
211. C₄×Q₁₆	Dic₆₁	semidirect
212. C₄×Q₁₆	Dic₆₁	semidirect
213. C₄×SD₁₆	Dic₆₁	semidirect
214. C₄×SD₁₆	Dic₆₁	semidirect
215. C₄×D₈	Dic₆₁	semidirect
216. C₄×D₈	Dic₆₁	semidirect
233. C₆₁	#22688	semidirect
297. Q₁₆	C₄⋊Dic₆₁	semidirect
298. SD₁₆	C₄⋊Dic₆₁	semidirect
299. D₈	C₄⋊Dic₆₁	semidirect
386. C₄	#16839879	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16839879	2
#21454387	2
#21446568	2
#21446096	2
#21445991	2
#21445839	2
C₈×C₄⋊Dic₆₁	2
C₄×#135×C₆₁	2
#22688	61