Subgroups — #27187586

Order 12928.

696 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15692334	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×#87938	C₂	1	1	yes	maximal, characteristic, complemented
3	#20266127	C₂	1	2	yes	maximal, complemented
4	#20266126	C₂	1	2	yes	maximal, complemented
5	#20266125	C₂	1	2	yes	maximal
6	#20266124	C₂	1	2	yes	maximal, complemented
7	C₄×C₄⋊#87938	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×C₂²⋊#87938	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₂²⋊#87938	C₂	1	1	yes	maximal, characteristic, complemented
10	#20266113	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×D₄×D₁₀₁	C₂	1	1	yes	maximal, characteristic
12	C₂³×#87938	C₂²	1	2	yes	—
13	#15692334	—	2	4	no	—
14	C₂×C₄⋊#87938	C₂²	1	2	yes	—
15	C₂×C₄⋊#87938	C₂²	1	2	yes	—
16	C₂×C₂²⋊#87938	C₂²	1	2	yes	—
17	C₂×C₂²⋊#87938	C₂²	1	2	yes	—
18	C₂×C₂²⋊#87938	C₂²	1	2	yes	—
19	C₂×C₄×#87938	—	2	4	no	—
20	C₂×C₄×#87938	C₂²	1	1	yes	characteristic
21	C₂×C₄×#87938	C₂²	1	1	yes	characteristic
22	C₂×C₄×#87938	C₂²	1	1	yes	characteristic
23	C₂×C₄×#87938	C₂²	1	2	yes	—
24	C₂×C₄×#87938	C₂²	1	1	yes	characteristic
25	(C₂×#87938)⋊C₄	C₂²	1	2	yes	—
26	(C₂×#87938)⋊C₄	C₂²	1	2	yes	—
27	(C₂×#87938)⋊C₄	C₂²	1	2	yes	—
28	(C₂×#87938)⋊C₄	C₂²	1	2	yes	—
29	(C₂×#87938)⋊C₄	C₂²	1	2	yes	—
30	C₂×D₄×D₁₀₁	C₂²	1	1	yes	characteristic
31	C₂²×C₄×D₁₀₁	C₂²	1	1	yes	characteristic
32	C₂²×C₄×D₁₀₁	C₂²	1	1	yes	characteristic
33	C₄×D₄₀₄	C₄	1	1	yes	characteristic, complemented
34	D₄×Dic₁₀₁	C₄	1	1	yes	characteristic, complemented
35	#15692217	C₄	1	1	yes	characteristic, complemented
36	C₄×C₂²⋊D₁₀₁	C₄	1	1	yes	characteristic, complemented
37	C₄×C₂²⋊D₁₀₁	C₄	1	1	yes	characteristic, complemented
38	#15692215	C₄	1	1	yes	characteristic, complemented
39	#15692215	C₄	1	1	yes	characteristic, complemented
40	C₄⋊C₄×D₁₀₁	C₂²	1	1	yes	characteristic
41	C₂²⋊C₄×D₁₀₁	C₂²	1	1	yes	characteristic
42	C₂²⋊C₄×D₁₀₁	C₂²	1	1	yes	characteristic
43	C₄²×D₁₀₁	C₂²	1	1	yes	characteristic
44	C₄×D₄×C₁₀₁	C₄	1	1	yes	characteristic, complemented
45	C₂²×#87938	—	2	4	no	—
46	C₂²×#87938	—	2	4	no	—
47	C₂²×#87938	—	2	4	no	—
48	C₂²×#87938	C₂³	1	2	yes	—
49	C₂²×#87938	C₂³	1	2	yes	—
50	C₂²×#87938	C₂³	1	2	yes	—
51	C₂²×#87938	C₂³	1	2	yes	—
52	C₄⋊#87938	—	2	4	no	—
53	C₄⋊#87938	—	2	4	no	—
54	C₂²⋊#87938	—	2	4	no	—
55	C₂²⋊#87938	—	2	4	no	—
56	C₂²⋊#87938	—	2	4	no	—
57	C₄×#87938	—	2	4	no	—
58	C₄×#87938	—	2	2	no	—
59	C₄×#87938	—	2	2	no	—
60	C₄×#87938	—	2	2	no	—
61	C₄×#87938	D₄	1	4	yes	complemented
62	C₂³×D₁₀₁	C₂³	1	1	yes	characteristic
63	C₂³×D₁₀₁	C₂³	1	1	yes	characteristic
64	C₂×D₄₀₄	C₂×C₄	1	1	yes	characteristic
65	C₂×C₂²⋊D₁₀₁	C₂×C₄	1	1	yes	characteristic
66	C₂×C₂²⋊D₁₀₁	C₂×C₄	1	1	yes	characteristic
67	D₄×D₁₀₁	—	2	4	no	—
68	C₂²×Dic₁₀₁	C₂×C₄	1	1	yes	characteristic
69	C₂²×Dic₁₀₁	C₂×C₄	1	1	yes	characteristic, complemented
70	C₂×C₄×D₁₀₁	—	2	2	no	—
71	C₂×C₄×D₁₀₁	—	2	2	no	—
72	C₂×C₄×D₁₀₁	—	2	2	no	—
73	C₂×C₄×D₁₀₁	—	2	2	no	—
74	C₂×C₄×D₁₀₁	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄×D₁₀₁	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄×D₁₀₁	C₂×C₄	1	1	yes	characteristic, complemented
77	C₂×C₄×D₁₀₁	C₂×C₄	1	1	yes	characteristic, complemented
78	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
79	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
80	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
81	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
82	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
83	C₄⋊Dic₁₀₁	C₂×C₄	1	1	yes	characteristic, complemented
84	#13108053	C₂×C₄	1	1	yes	characteristic, complemented
85	#13108053	C₂×C₄	1	1	yes	characteristic, complemented
86	C₂²⋊Dic₁₀₁	C₂×C₄	1	1	yes	characteristic
87	C₂²⋊Dic₁₀₁	C₂×C₄	1	1	yes	characteristic, complemented
88	#13108051	C₂×C₄	1	1	yes	characteristic
89	#13108051	C₂×C₄	1	1	yes	characteristic
90	#13108051	C₂×C₄	1	1	yes	characteristic, complemented
91	#13108051	C₂×C₄	1	1	yes	characteristic, complemented
92	C₄×Dic₁₀₁	C₂×C₄	1	1	yes	characteristic, complemented
93	C₄×Dic₁₀₁	C₂×C₄	1	1	yes	characteristic, complemented
94	C₄×Dic₁₀₁	C₂×C₄	1	1	yes	characteristic, complemented
95	C₂×D₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic, complemented
98	C₄⋊C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic, complemented
99	C₂²⋊C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
100	C₂²⋊C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic, complemented
101	C₄²×C₁₀₁	C₂×C₄	1	1	yes	characteristic, complemented
102	C₂³×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
103	C₂³×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
104	C₂²×D₁₀₁	—	2	1	no	—
105	C₂²×D₁₀₁	—	2	1	no	—
106	C₂²×D₁₀₁	—	2	2	no	—
107	C₂²×D₁₀₁	—	2	1	no	—
108	C₂²×D₁₀₁	—	2	1	no	—
109	C₂²×D₁₀₁	—	2	2	no	—
110	C₂²×D₁₀₁	—	2	2	no	—
111	C₂²×D₁₀₁	C₂²×C₄	1	1	yes	characteristic
112	C₂²×D₁₀₁	C₂²×C₄	1	1	yes	characteristic
113	C₂²×D₁₀₁	#41	1	4	yes	—
114	C₂²×D₁₀₁	C₂⁴	1	1	yes	characteristic
115	C₂×#87938	—	2	16	no	—
116	C₂×#87938	—	2	2	no	—
117	C₂×#87938	—	2	2	no	—
118	C₂×#87938	—	2	2	no	—
119	C₂×#87938	—	2	2	no	—
120	C₂×#87938	—	2	2	no	—
121	C₂×#87938	—	2	2	no	—
122	C₂×#87938	—	2	2	no	—
123	C₂×#87938	—	2	2	no	—
124	C₂×#87938	—	2	2	no	—
125	C₂×#87938	—	2	2	no	—
126	C₂×#87938	C₂×D₄	1	4	yes	—
127	C₂×#87938	#41	1	4	yes	—
128	D₄×C₁₀₁	—	2	2	no	—
129	C₂×C₄×C₁₀₁	—	2	2	no	—
130	C₂×C₄×C₁₀₁	—	2	2	no	—
131	C₂×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
136	C₂²⋊D₁₀₁	—	2	2	no	—
137	C₂²⋊D₁₀₁	—	2	2	no	—
138	C₂×Dic₁₀₁	—	2	2	no	—
139	C₂×Dic₁₀₁	—	2	2	no	—
140	C₂×Dic₁₀₁	C₂²×C₄	1	1	yes	characteristic
141	C₂×Dic₁₀₁	C₂²×C₄	1	1	yes	characteristic
142	C₂×Dic₁₀₁	C₂²×C₄	1	1	yes	characteristic
143	C₂×Dic₁₀₁	C₂²×C₄	1	1	yes	characteristic
144	C₂×Dic₁₀₁	C₂²×C₄	1	1	yes	characteristic
145	D₄₀₄	—	2	2	no	—
146	C₄×D₁₀₁	—	2	1	no	—
147	C₄×D₁₀₁	—	2	1	no	—
148	C₄×D₁₀₁	—	2	1	no	—
149	C₄×D₁₀₁	—	2	1	no	—
150	C₄×D₁₀₁	—	2	2	no	—
151	C₄×D₁₀₁	—	2	2	no	—
152	C₄×D₁₀₁	—	2	2	no	—
153	C₄×D₁₀₁	—	2	2	no	—
154	C₄×D₁₀₁	—	2	2	no	—
155	C₄×D₁₀₁	—	2	2	no	—
156	C₄×D₁₀₁	C₂×D₄	1	2	yes	—
157	C₄×D₁₀₁	#41	1	2	yes	—
158	C₂²×C₁₀₁	—	2	1	no	—
159	C₂²×C₁₀₁	—	2	1	no	—
160	C₂²×C₁₀₁	—	2	1	no	—
161	C₂²×C₁₀₁	—	2	1	no	—
162	C₂²×C₁₀₁	—	2	1	no	—
163	C₂²×C₁₀₁	#117	1	2	yes	complemented
164	C₂²×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
165	C₂×D₁₀₁	—	2	1	no	—
166	C₂×D₁₀₁	—	2	1	no	—
167	C₂×D₁₀₁	—	2	4	no	—
168	C₂×D₁₀₁	—	2	4	no	—
169	C₂×D₁₀₁	—	2	1	no	—
170	C₂×D₁₀₁	—	2	1	no	—
171	C₂×D₁₀₁	—	2	1	no	—
172	C₂×D₁₀₁	—	4	2	no	—
173	C₂×D₁₀₁	—	4	2	no	—
174	C₂×D₁₀₁	#117	1	2	yes	complemented
175	C₂×D₁₀₁	C₂²×D₄	1	1	yes	characteristic
176	C₂×D₁₀₁	C₂×#41	1	2	yes	—
177	C₂×D₁₀₁	C₂×#41	1	2	yes	—
178	C₂×D₁₀₁	C₂×#41	1	1	yes	characteristic
179	#87938	—	2	4	no	—
180	#87938	—	2	4	no	—
181	#87938	—	4	2	no	—
182	#87938	—	4	2	no	—
183	C₄×C₁₀₁	—	2	1	no	—
184	C₄×C₁₀₁	—	2	1	no	—
185	C₄×C₁₀₁	—	2	1	no	—
186	C₄×C₁₀₁	—	2	1	no	—
187	C₄×C₁₀₁	C₄×D₄	1	2	yes	—
188	Dic₁₀₁	—	2	1	no	—
189	Dic₁₀₁	—	2	1	no	—
190	Dic₁₀₁	—	2	1	no	—
191	Dic₁₀₁	—	2	1	no	—
192	Dic₁₀₁	C₄×D₄	1	2	yes	—
193	C₂×C₁₀₁	—	2	2	no	—
194	C₂×C₁₀₁	—	4	1	no	—
195	C₂×C₁₀₁	C₂×#117	1	1	yes	characteristic
196	C₂×C₁₀₁	C₂×C₄×D₄	1	1	yes	characteristic
197	C₂×C₁₀₁	C₄×#41	1	1	yes	characteristic
198	D₁₀₁	—	2	2	no	—
199	D₁₀₁	—	4	1	no	—
200	D₁₀₁	#525	1	2	yes	—
201	D₁₀₁	#529	1	2	yes	—
202	#2290	—	101	1	no	maximal, Sylow
203	C₁₀₁	#2290	1	1	yes	characteristic, complemented, Sylow
204	C₂×C₄×D₄	—	101	1	no	—
205	C₂×#117	—	101	1	no	—
206	C₂²×C₄²	—	101	1	no	—
207	#388	—	101	2	no	—
208	#387	—	101	2	no	—
209	#386	—	101	2	no	—
210	#385	—	101	2	no	—
211	C₄×C₄⋊C₄	—	101	1	no	—
212	C₄×C₂²⋊C₄	—	101	1	no	—
213	C₄×C₂²⋊C₄	—	101	1	no	—
214	#376	—	101	1	no	—
215	C₂²×D₄	—	101	1	no	—
216	C₂³×C₄	—	101	1	no	—
217	C₂³×C₄	—	101	1	no	—
218	C₂³×C₄	—	101	2	no	—
219	C₄×D₄	—	101	1	no	—
220	C₄×D₄	—	101	1	no	—
221	C₄×D₄	—	101	1	no	—
222	C₄×D₄	—	101	1	no	—
223	C₄×D₄	—	101	1	no	—
224	C₄×D₄	—	101	1	no	—
225	C₄×D₄	—	101	1	no	—
226	C₄×D₄	#87938	1	1	yes	characteristic, complemented
227	#117	—	202	4	no	—
228	C₂×C₄⋊C₄	—	101	1	no	—
229	C₂×C₄⋊C₄	—	101	2	no	—
230	C₂×C₄⋊C₄	—	101	2	no	—
231	C₂×C₂²⋊C₄	—	101	1	no	—
232	C₂×C₂²⋊C₄	—	101	1	no	—
233	C₂×C₂²⋊C₄	—	101	2	no	—
234	C₂×C₂²⋊C₄	—	101	2	no	—
235	C₂×C₂²⋊C₄	—	101	2	no	—
236	C₂×C₄²	—	101	1	no	—
237	C₂×C₄²	—	101	1	no	—
238	C₂×C₄²	—	101	1	no	—
239	C₂×C₄²	—	101	1	no	—
240	C₂×C₄²	—	101	1	no	—
241	C₂×C₄²	—	101	2	no	—
242	C₂×C₄²	—	202	4	no	—
243	#95	—	101	2	no	—
244	#95	—	101	2	no	—
245	#95	—	101	2	no	—
246	#95	—	101	2	no	—
247	#95	—	101	2	no	—
248	C₂⁴	—	101	1	no	—
249	C₂⁴	—	101	1	no	—
250	C₂×D₄	—	101	1	no	—
251	C₂×D₄	—	101	1	no	—
252	C₂×D₄	—	101	1	no	—
253	C₂×D₄	—	202	4	no	—
254	C₂×D₄	C₂×#87938	1	1	yes	characteristic
255	C₂²×C₄	—	101	1	no	—
256	C₂²×C₄	—	101	2	no	—
257	C₂²×C₄	—	101	2	no	—
258	C₂²×C₄	—	101	1	no	—
259	C₂²×C₄	—	101	1	no	—
260	C₂²×C₄	—	101	1	no	—
261	C₂²×C₄	—	101	1	no	—
262	C₂²×C₄	—	101	1	no	—
263	C₂²×C₄	—	101	1	no	—
264	C₂²×C₄	—	101	1	no	—
265	C₂²×C₄	—	101	1	no	—
266	C₂²×C₄	—	101	1	no	—
267	C₂²×C₄	—	101	1	no	—
268	C₂²×C₄	—	101	2	no	—
269	C₂²×C₄	—	101	2	no	—
270	C₂²×C₄	—	202	2	no	—
271	C₂²×C₄	—	202	2	no	—
272	C₂²×C₄	—	202	2	no	—
273	C₂²×C₄	—	202	2	no	—
274	C₂²×C₄	—	202	4	no	—
275	C₂²×C₄	—	202	4	no	—
276	C₂²×C₄	—	202	4	no	—
277	C₂²×C₄	C₂×#87938	1	1	yes	characteristic
278	C₂²×C₄	C₂×#87938	1	1	yes	characteristic, complemented
279	C₄⋊C₄	—	101	1	no	—
280	C₄⋊C₄	—	101	1	no	—
281	C₄⋊C₄	—	101	1	no	—
282	C₄⋊C₄	—	202	4	no	—
283	C₄⋊C₄	—	202	4	no	—
284	C₄⋊C₄	C₂×#87938	1	1	yes	characteristic, complemented
285	C₂²⋊C₄	—	101	1	no	—
286	C₂²⋊C₄	—	101	1	no	—
287	C₂²⋊C₄	—	101	1	no	—
288	C₂²⋊C₄	—	101	1	no	—
289	C₂²⋊C₄	—	101	1	no	—
290	C₂²⋊C₄	—	101	1	no	—
291	C₂²⋊C₄	—	202	4	no	—
292	C₂²⋊C₄	—	202	4	no	—
293	C₂²⋊C₄	—	202	4	no	—
294	C₂²⋊C₄	C₂×#87938	1	1	yes	characteristic
295	C₂²⋊C₄	C₂×#87938	1	1	yes	characteristic, complemented
296	C₄²	—	101	4	no	—
297	C₄²	—	101	1	no	—
298	C₄²	—	101	1	no	—
299	C₄²	—	101	1	no	—
300	C₄²	—	202	2	no	—
301	C₄²	—	202	2	no	—
302	C₄²	—	202	4	no	—
303	C₄²	—	202	2	no	—
304	C₄²	C₂×#87938	1	1	yes	characteristic, complemented
305	C₂³	—	101	1	no	—
306	C₂³	—	101	4	no	—
307	C₂³	—	101	1	no	—
308	C₂³	—	101	1	no	—
309	C₂³	—	202	1	no	—
310	C₂³	—	202	2	no	—
311	C₂³	—	202	1	no	—
312	C₂³	—	202	2	no	—
313	C₂³	—	202	1	no	—
314	C₂³	—	202	1	no	—
315	C₂³	—	202	2	no	—
316	C₂³	C₂²×#87938	1	1	yes	characteristic
317	C₂³	C₂²×#87938	1	1	yes	characteristic
318	D₄	—	2	2	no	—
319	D₄	—	202	2	no	—
320	D₄	—	202	2	no	—
321	D₄	—	202	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	101	1	no	—
325	C₂×C₄	—	101	2	no	—
326	C₂×C₄	—	101	2	no	—
327	C₂×C₄	—	101	4	no	—
328	C₂×C₄	—	101	4	no	—
329	C₂×C₄	—	101	1	no	—
330	C₂×C₄	—	101	1	no	—
331	C₂×C₄	—	101	1	no	—
332	C₂×C₄	—	101	1	no	—
333	C₂×C₄	—	202	2	no	—
334	C₂×C₄	—	202	2	no	—
335	C₂×C₄	—	202	1	no	—
336	C₂×C₄	—	202	1	no	—
337	C₂×C₄	—	202	2	no	—
338	C₂×C₄	—	202	1	no	—
339	C₂×C₄	—	202	1	no	—
340	C₂×C₄	—	202	2	no	—
341	C₂×C₄	—	202	2	no	—
342	C₂×C₄	—	202	2	no	—
343	C₂×C₄	—	202	2	no	—
344	C₂×C₄	—	202	2	no	—
345	C₂×C₄	—	202	2	no	—
346	C₂×C₄	—	202	2	no	—
347	C₂×C₄	—	202	2	no	—
348	C₂×C₄	—	202	2	no	—
349	C₂×C₄	—	202	2	no	—
350	C₂×C₄	—	202	2	no	—
351	C₂×C₄	—	202	2	no	—
352	C₂×C₄	—	202	2	no	—
353	C₂×C₄	—	202	16	no	—
354	C₂×C₄	—	202	2	no	—
355	C₂×C₄	—	202	2	no	—
356	C₂×C₄	C₂²×#87938	1	1	yes	characteristic
357	C₂×C₄	C₂²×#87938	1	1	yes	characteristic
358	C₂×C₄	C₂²×#87938	1	1	yes	characteristic
359	C₂×C₄	C₂²×#87938	1	1	yes	characteristic
360	C₂×C₄	C₂²×#87938	1	1	yes	characteristic
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	101	2	no	—
367	C₂²	—	101	1	no	—
368	C₂²	—	101	1	no	—
369	C₂²	—	101	2	no	—
370	C₂²	—	101	2	no	—
371	C₂²	—	404	2	no	—
372	C₂²	—	404	2	no	—
373	C₂²	—	202	4	no	—
374	C₂²	—	202	4	no	—
375	C₂²	—	202	1	no	—
376	C₂²	—	202	1	no	—
377	C₂²	—	202	1	no	—
378	C₂²	—	202	1	no	—
379	C₂²	—	202	1	no	—
380	C₂²	#15692334	1	2	yes	complemented
381	C₂²	C₂³×#87938	1	1	yes	characteristic
382	C₄	—	2	1	no	—
383	C₄	—	2	1	no	—
384	C₄	—	2	1	no	—
385	C₄	—	2	1	no	—
386	C₄	—	101	2	no	—
387	C₄	—	404	2	no	—
388	C₄	—	404	2	no	—
389	C₄	—	202	4	no	—
390	C₄	—	202	4	no	—
391	C₄	—	202	1	no	—
392	C₄	—	202	1	no	—
393	C₄	—	202	1	no	—
394	C₄	—	202	1	no	—
395	C₄	D₄×#87938	1	2	yes	—
396	C₂	—	2	2	no	—
397	C₂	—	4	1	no	—
398	C₂	—	101	2	no	—
399	C₂	—	101	2	no	—
400	C₂	—	404	1	no	—
401	C₂	—	202	2	no	—
402	C₂	C₂×#15692334	1	1	yes	characteristic
403	C₂	C₂×D₄×#87938	1	1	yes	characteristic
404	C₂	#41×#87938	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×#87938
commutator, socle	C₂²×C₁₀₁	C₂³×C₄
Frattini	C₂²	C₂³×#87938
Fitting	C₄×D₄×C₁₀₁	C₄
prime radical	C₂×D₄×D₁₀₁	C₂²
cosocle	C₂²×D₁₀₁	C₂⁴
hypercenter	C₄×D₄	#87938
hypocenter	C₁₀₁	#2290
LCS	G ▷ C₂²×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×#15692334	C₂	semidirect
2. C₂²×C₄×#87938	C₂	semidirect
3. #20266127	C₂	semidirect
4. #20266126	C₂	semidirect
6. #20266124	C₂	semidirect
7. C₄×C₄⋊#87938	C₂	semidirect
8. C₄×C₂²⋊#87938	C₂	semidirect
9. C₄×C₂²⋊#87938	C₂	semidirect
10. #20266113	C₂	semidirect
33. C₄×D₄₀₄	C₄	semidirect
34. D₄×Dic₁₀₁	C₄	semidirect
35. #15692217	C₄	semidirect
36. C₄×C₂²⋊D₁₀₁	C₄	semidirect
37. C₄×C₂²⋊D₁₀₁	C₄	semidirect
38. #15692215	C₄	semidirect
39. #15692215	C₄	semidirect
44. C₄×D₄×C₁₀₁	C₄	semidirect
61. C₄×#87938	D₄	semidirect
69. C₂²×Dic₁₀₁	C₂×C₄	semidirect
76. C₂×C₄×D₁₀₁	C₂×C₄	semidirect
77. C₂×C₄×D₁₀₁	C₂×C₄	semidirect
83. C₄⋊Dic₁₀₁	C₂×C₄	semidirect
84. #13108053	C₂×C₄	semidirect
85. #13108053	C₂×C₄	semidirect
87. C₂²⋊Dic₁₀₁	C₂×C₄	semidirect
90. #13108051	C₂×C₄	semidirect
91. #13108051	C₂×C₄	semidirect
92. C₄×Dic₁₀₁	C₂×C₄	semidirect
93. C₄×Dic₁₀₁	C₂×C₄	semidirect
94. C₄×Dic₁₀₁	C₂×C₄	semidirect
97. C₂²×C₄×C₁₀₁	C₂×C₄	semidirect
98. C₄⋊C₄×C₁₀₁	C₂×C₄	semidirect
100. C₂²⋊C₄×C₁₀₁	C₂×C₄	semidirect
101. C₄²×C₁₀₁	C₂×C₄	semidirect
163. C₂²×C₁₀₁	#117	semidirect
174. C₂×D₁₀₁	#117	semidirect
203. C₁₀₁	#2290	semidirect
226. C₄×D₄	#87938	semidirect
278. C₂²×C₄	C₂×#87938	semidirect
284. C₄⋊C₄	C₂×#87938	semidirect
295. C₂²⋊C₄	C₂×#87938	semidirect
304. C₄²	C₂×#87938	semidirect
380. C₂²	#15692334	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15692334	2
C₂²×C₄×#87938	2
#20266127	2
#20266126	2
#20266125	2
#20266124	2
C₄×C₄⋊#87938	2
C₄×C₂²⋊#87938	2
#20266113	2
C₄×D₄×D₁₀₁	2
#2290	101