Subgroups — #27187648

Order 12928.

660 conjugacy classes of subgroups.

The subgroup lattice has 436 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	#20266121	C₂	1	1	yes	maximal, characteristic, complemented
7	#20266119	C₂	1	1	yes	maximal, characteristic, complemented
8	#20266119	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₄⋊#87938	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²⋊C₄×#87938	C₂	1	2	yes	maximal, 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	—	2	4	no	—
15	C₂×C₄⋊#87938	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊#87938	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊#87938	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊#87938	C₂²	1	2	yes	—
19	C₂×C₄⋊#87938	C₂²	1	1	yes	characteristic
20	C₂×C₂²⋊#87938	C₂²	1	2	yes	—
21	C₂×C₂²⋊#87938	C₂²	1	2	yes	—
22	C₂×C₂²⋊#87938	C₂²	1	2	yes	—
23	C₂×C₄×#87938	C₂²	1	2	yes	—
24	C₂×C₄×#87938	C₂²	1	2	yes	—
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	—	4	2	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	2	no	—
54	C₄⋊#87938	—	2	2	no	—
55	C₄⋊#87938	—	2	2	no	—
56	C₄⋊#87938	D₄	1	4	yes	complemented
57	C₂²⋊#87938	—	2	4	no	—
58	C₂²⋊#87938	—	2	4	no	—
59	C₂²⋊#87938	—	4	2	no	—
60	C₄×#87938	—	2	4	no	—
61	C₄×#87938	—	4	2	no	—
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	2	no	—
68	D₄×D₁₀₁	—	2	2	no	—
69	C₂²×Dic₁₀₁	C₂×C₄	1	1	yes	characteristic
70	C₂²×Dic₁₀₁	C₂×C₄	1	1	yes	characteristic, complemented
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	—	2	2	no	—
75	C₂×C₄×D₁₀₁	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄×D₁₀₁	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄×D₁₀₁	C₂×C₄	1	1	yes	characteristic, complemented
78	C₂×C₄×D₁₀₁	C₂×C₄	1	1	yes	characteristic, complemented
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	C₂×C₄×D₁₀₁	C₂³	1	1	yes	characteristic
84	C₄⋊Dic₁₀₁	C₂×C₄	1	1	yes	characteristic, complemented
85	#13108053	C₂×C₄	1	1	yes	characteristic, complemented
86	#13108053	C₂×C₄	1	1	yes	characteristic, complemented
87	C₂²⋊Dic₁₀₁	C₂×C₄	1	1	yes	characteristic
88	C₂²⋊Dic₁₀₁	C₂×C₄	1	1	yes	characteristic, complemented
89	#13108051	C₂×C₄	1	1	yes	characteristic
90	#13108051	C₂×C₄	1	1	yes	characteristic
91	#13108051	C₂×C₄	1	1	yes	characteristic, complemented
92	#13108051	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	C₄×Dic₁₀₁	C₂×C₄	1	1	yes	characteristic, complemented
96	C₂×D₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic, complemented
99	C₄⋊C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic, complemented
100	C₂²⋊C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
101	C₂²⋊C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic, complemented
102	C₄²×C₁₀₁	C₂×C₄	1	1	yes	characteristic, complemented
103	C₂³×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
104	C₂³×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
105	C₂²×D₁₀₁	—	2	1	no	—
106	C₂²×D₁₀₁	—	2	1	no	—
107	C₂²×D₁₀₁	—	2	1	no	—
108	C₂²×D₁₀₁	—	2	1	no	—
109	C₂²×D₁₀₁	—	2	1	no	—
110	C₂²×D₁₀₁	—	2	1	no	—
111	C₂²×D₁₀₁	—	2	1	no	—
112	C₂²×D₁₀₁	—	2	1	no	—
113	C₂²×D₁₀₁	—	2	1	no	—
114	C₂²×D₁₀₁	—	2	1	no	—
115	C₂²×D₁₀₁	C₂²×C₄	1	1	yes	characteristic
116	C₂²×D₁₀₁	C₂²×C₄	1	1	yes	characteristic
117	C₂²×D₁₀₁	#41	1	2	yes	—
118	C₂²×D₁₀₁	#41	1	2	yes	—
119	C₂²×D₁₀₁	C₂⁴	1	1	yes	characteristic
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	—	2	2	no	—
127	C₂×#87938	—	2	2	no	—
128	C₂×#87938	—	2	2	no	—
129	C₂×#87938	—	2	2	no	—
130	C₂×#87938	—	2	2	no	—
131	C₂×#87938	—	4	8	no	—
132	C₂×#87938	C₂×D₄	1	4	yes	—
133	D₄×C₁₀₁	—	2	2	no	—
134	C₂×C₄×C₁₀₁	—	2	2	no	—
135	C₂×C₄×C₁₀₁	—	2	2	no	—
136	C₂×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
141	C₂²⋊D₁₀₁	—	2	2	no	—
142	C₂²⋊D₁₀₁	—	2	2	no	—
143	C₂×Dic₁₀₁	—	2	2	no	—
144	C₂×Dic₁₀₁	—	2	2	no	—
145	C₂×Dic₁₀₁	C₂²×C₄	1	1	yes	characteristic
146	C₂×Dic₁₀₁	C₂²×C₄	1	1	yes	characteristic
147	C₂×Dic₁₀₁	C₂²×C₄	1	1	yes	characteristic
148	C₂×Dic₁₀₁	C₂²×C₄	1	1	yes	characteristic
149	C₂×Dic₁₀₁	C₂²×C₄	1	1	yes	characteristic
150	D₄₀₄	—	2	2	no	—
151	C₄×D₁₀₁	—	2	1	no	—
152	C₄×D₁₀₁	—	2	1	no	—
153	C₄×D₁₀₁	—	2	1	no	—
154	C₄×D₁₀₁	—	2	1	no	—
155	C₄×D₁₀₁	—	2	1	no	—
156	C₄×D₁₀₁	—	2	1	no	—
157	C₄×D₁₀₁	—	2	1	no	—
158	C₄×D₁₀₁	—	2	1	no	—
159	C₄×D₁₀₁	—	2	2	no	—
160	C₄×D₁₀₁	—	2	2	no	—
161	C₄×D₁₀₁	—	2	2	no	—
162	C₄×D₁₀₁	—	2	2	no	—
163	C₄×D₁₀₁	C₂×D₄	1	2	yes	—
164	C₄×D₁₀₁	#41	1	2	yes	—
165	C₂²×C₁₀₁	—	2	1	no	—
166	C₂²×C₁₀₁	—	2	1	no	—
167	C₂²×C₁₀₁	—	2	1	no	—
168	C₂²×C₁₀₁	—	2	1	no	—
169	C₂²×C₁₀₁	—	2	1	no	—
170	C₂²×C₁₀₁	#117	1	2	yes	complemented
171	C₂²×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
172	C₂×D₁₀₁	—	2	1	no	—
173	C₂×D₁₀₁	—	2	1	no	—
174	C₂×D₁₀₁	—	2	2	no	—
175	C₂×D₁₀₁	—	2	2	no	—
176	C₂×D₁₀₁	—	2	2	no	—
177	C₂×D₁₀₁	—	2	2	no	—
178	C₂×D₁₀₁	—	2	1	no	—
179	C₂×D₁₀₁	—	2	1	no	—
180	C₂×D₁₀₁	—	2	1	no	—
181	C₂×D₁₀₁	—	4	1	no	—
182	C₂×D₁₀₁	—	4	1	no	—
183	C₂×D₁₀₁	—	4	1	no	—
184	C₂×D₁₀₁	—	4	1	no	—
185	C₂×D₁₀₁	#117	1	2	yes	complemented
186	C₂×D₁₀₁	C₂²×D₄	1	1	yes	characteristic
187	C₂×D₁₀₁	C₂×#41	1	1	yes	characteristic
188	C₂×D₁₀₁	C₂×#41	1	1	yes	characteristic
189	C₂×D₁₀₁	C₂×#41	1	1	yes	characteristic
190	C₂×D₁₀₁	H(5,𝔽₂)	1	1	yes	characteristic
191	C₂×D₁₀₁	2₋¹⁺⁴	1	1	yes	characteristic
192	#87938	—	2	4	no	—
193	#87938	—	4	2	no	—
194	#87938	—	4	2	no	—
195	#87938	—	4	2	no	—
196	C₄×C₁₀₁	—	2	1	no	—
197	C₄×C₁₀₁	—	2	1	no	—
198	C₄×C₁₀₁	—	2	1	no	—
199	C₄×C₁₀₁	—	2	1	no	—
200	C₄×C₁₀₁	C₄×D₄	1	2	yes	—
201	Dic₁₀₁	—	2	1	no	—
202	Dic₁₀₁	—	2	1	no	—
203	Dic₁₀₁	—	2	1	no	—
204	Dic₁₀₁	—	2	1	no	—
205	Dic₁₀₁	C₄×D₄	1	2	yes	—
206	C₂×C₁₀₁	—	2	2	no	—
207	C₂×C₁₀₁	—	4	1	no	—
208	C₂×C₁₀₁	C₂×#117	1	1	yes	characteristic
209	C₂×C₁₀₁	C₂×C₄×D₄	1	1	yes	characteristic
210	C₂×C₁₀₁	#520	1	1	yes	characteristic
211	D₁₀₁	—	2	2	no	—
212	D₁₀₁	—	4	1	no	—
213	D₁₀₁	#546	1	1	yes	characteristic
214	D₁₀₁	#548	1	1	yes	characteristic
215	D₁₀₁	#552	1	1	yes	characteristic
216	D₁₀₁	#553	1	1	yes	characteristic
217	#2352	—	101	1	no	maximal, Sylow
218	C₁₀₁	#2352	1	1	yes	characteristic, complemented, Sylow
219	C₂×C₄×D₄	—	101	1	no	—
220	C₂×#117	—	101	1	no	—
221	C₂²×C₄⋊C₄	—	101	1	no	—
222	#388	—	101	2	no	—
223	#387	—	101	2	no	—
224	#386	—	101	2	no	—
225	#382	—	101	1	no	—
226	#380	—	101	1	no	—
227	#380	—	101	1	no	—
228	C₄×C₄⋊C₄	—	101	1	no	—
229	C₄×C₂²⋊C₄	—	101	2	no	—
230	C₂²×D₄	—	101	1	no	—
231	C₂³×C₄	—	101	1	no	—
232	C₂³×C₄	—	101	1	no	—
233	C₂³×C₄	—	101	2	no	—
234	C₄×D₄	—	101	1	no	—
235	C₄×D₄	—	101	1	no	—
236	C₄×D₄	—	101	1	no	—
237	C₄×D₄	—	101	1	no	—
238	C₄×D₄	—	101	1	no	—
239	C₄×D₄	—	101	1	no	—
240	C₄×D₄	—	101	1	no	—
241	C₄×D₄	#87938	1	1	yes	characteristic, complemented
242	#117	—	202	4	no	—
243	C₂×C₄⋊C₄	—	101	1	no	—
244	C₂×C₄⋊C₄	—	101	1	no	—
245	C₂×C₄⋊C₄	—	101	1	no	—
246	C₂×C₄⋊C₄	—	101	2	no	—
247	C₂×C₄⋊C₄	—	101	1	no	—
248	C₂×C₄⋊C₄	—	101	1	no	—
249	C₂×C₄⋊C₄	—	202	4	no	—
250	C₂×C₂²⋊C₄	—	101	1	no	—
251	C₂×C₂²⋊C₄	—	101	1	no	—
252	C₂×C₂²⋊C₄	—	101	2	no	—
253	C₂×C₂²⋊C₄	—	101	2	no	—
254	C₂×C₂²⋊C₄	—	101	2	no	—
255	C₂×C₄²	—	101	1	no	—
256	C₂×C₄²	—	101	2	no	—
257	C₂×C₄²	—	101	2	no	—
258	#95	—	101	2	no	—
259	#95	—	101	2	no	—
260	#95	—	101	2	no	—
261	#95	—	101	2	no	—
262	#95	—	101	2	no	—
263	C₂⁴	—	101	1	no	—
264	C₂⁴	—	101	1	no	—
265	C₂×D₄	—	101	1	no	—
266	C₂×D₄	—	101	1	no	—
267	C₂×D₄	—	101	1	no	—
268	C₂×D₄	—	202	2	no	—
269	C₂×D₄	—	202	2	no	—
270	C₂×D₄	C₂×#87938	1	1	yes	characteristic
271	C₂²×C₄	—	101	1	no	—
272	C₂²×C₄	—	101	2	no	—
273	C₂²×C₄	—	101	1	no	—
274	C₂²×C₄	—	101	1	no	—
275	C₂²×C₄	—	101	1	no	—
276	C₂²×C₄	—	101	1	no	—
277	C₂²×C₄	—	101	1	no	—
278	C₂²×C₄	—	101	1	no	—
279	C₂²×C₄	—	101	1	no	—
280	C₂²×C₄	—	101	1	no	—
281	C₂²×C₄	—	101	1	no	—
282	C₂²×C₄	—	101	1	no	—
283	C₂²×C₄	—	101	2	no	—
284	C₂²×C₄	—	101	2	no	—
285	C₂²×C₄	—	101	2	no	—
286	C₂²×C₄	—	404	2	no	—
287	C₂²×C₄	—	202	2	no	—
288	C₂²×C₄	—	202	2	no	—
289	C₂²×C₄	—	202	2	no	—
290	C₂²×C₄	—	202	2	no	—
291	C₂²×C₄	—	202	4	no	—
292	C₂²×C₄	—	202	4	no	—
293	C₂²×C₄	C₂×#87938	1	1	yes	characteristic
294	C₂²×C₄	C₂×#87938	1	1	yes	characteristic, complemented
295	C₄⋊C₄	—	101	4	no	—
296	C₄⋊C₄	—	101	1	no	—
297	C₄⋊C₄	—	101	1	no	—
298	C₄⋊C₄	—	101	1	no	—
299	C₄⋊C₄	—	202	2	no	—
300	C₄⋊C₄	—	202	2	no	—
301	C₄⋊C₄	—	202	4	no	—
302	C₄⋊C₄	—	202	2	no	—
303	C₄⋊C₄	C₂×#87938	1	1	yes	characteristic, complemented
304	C₂²⋊C₄	—	101	1	no	—
305	C₂²⋊C₄	—	101	1	no	—
306	C₂²⋊C₄	—	101	1	no	—
307	C₂²⋊C₄	—	101	1	no	—
308	C₂²⋊C₄	—	101	1	no	—
309	C₂²⋊C₄	—	101	1	no	—
310	C₂²⋊C₄	—	404	2	no	—
311	C₂²⋊C₄	—	202	4	no	—
312	C₂²⋊C₄	—	202	4	no	—
313	C₂²⋊C₄	C₂×#87938	1	1	yes	characteristic
314	C₂²⋊C₄	C₂×#87938	1	1	yes	characteristic, complemented
315	C₄²	—	101	1	no	—
316	C₄²	—	101	1	no	—
317	C₄²	—	101	1	no	—
318	C₄²	—	404	2	no	—
319	C₄²	—	202	4	no	—
320	C₄²	C₂×#87938	1	1	yes	characteristic, complemented
321	C₂³	—	101	1	no	—
322	C₂³	—	101	2	no	—
323	C₂³	—	101	2	no	—
324	C₂³	—	101	1	no	—
325	C₂³	—	101	1	no	—
326	C₂³	—	202	1	no	—
327	C₂³	—	202	1	no	—
328	C₂³	—	202	1	no	—
329	C₂³	—	202	1	no	—
330	C₂³	—	202	1	no	—
331	C₂³	—	202	1	no	—
332	C₂³	—	202	1	no	—
333	C₂³	—	202	1	no	—
334	C₂³	—	202	1	no	—
335	C₂³	—	202	1	no	—
336	C₂³	C₂²×#87938	1	1	yes	characteristic
337	C₂³	C₂²×#87938	1	1	yes	characteristic
338	D₄	—	2	2	no	—
339	D₄	—	202	2	no	—
340	D₄	—	202	2	no	—
341	D₄	—	202	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	101	1	no	—
345	C₂×C₄	—	101	2	no	—
346	C₂×C₄	—	101	2	no	—
347	C₂×C₄	—	101	4	no	—
348	C₂×C₄	—	101	1	no	—
349	C₂×C₄	—	101	1	no	—
350	C₂×C₄	—	101	1	no	—
351	C₂×C₄	—	101	1	no	—
352	C₂×C₄	—	404	8	no	—
353	C₂×C₄	—	202	2	no	—
354	C₂×C₄	—	202	2	no	—
355	C₂×C₄	—	202	1	no	—
356	C₂×C₄	—	202	1	no	—
357	C₂×C₄	—	202	1	no	—
358	C₂×C₄	—	202	1	no	—
359	C₂×C₄	—	202	1	no	—
360	C₂×C₄	—	202	1	no	—
361	C₂×C₄	—	202	1	no	—
362	C₂×C₄	—	202	1	no	—
363	C₂×C₄	—	202	2	no	—
364	C₂×C₄	—	202	2	no	—
365	C₂×C₄	—	202	2	no	—
366	C₂×C₄	—	202	2	no	—
367	C₂×C₄	—	202	2	no	—
368	C₂×C₄	—	202	2	no	—
369	C₂×C₄	—	202	2	no	—
370	C₂×C₄	—	202	2	no	—
371	C₂×C₄	—	202	2	no	—
372	C₂×C₄	—	202	2	no	—
373	C₂×C₄	—	202	2	no	—
374	C₂×C₄	—	202	2	no	—
375	C₂×C₄	—	202	2	no	—
376	C₂×C₄	—	202	2	no	—
377	C₂×C₄	—	202	2	no	—
378	C₂×C₄	C₂²×#87938	1	1	yes	characteristic
379	C₂×C₄	C₂²×#87938	1	1	yes	characteristic
380	C₂×C₄	C₂²×#87938	1	1	yes	characteristic
381	C₂×C₄	C₂²×#87938	1	1	yes	characteristic
382	C₂×C₄	C₂²×#87938	1	1	yes	characteristic
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	2	1	no	—
387	C₂²	—	2	1	no	—
388	C₂²	—	101	1	no	—
389	C₂²	—	101	1	no	—
390	C₂²	—	101	1	no	—
391	C₂²	—	101	1	no	—
392	C₂²	—	101	1	no	—
393	C₂²	—	101	1	no	—
394	C₂²	—	101	2	no	—
395	C₂²	—	404	1	no	—
396	C₂²	—	404	1	no	—
397	C₂²	—	404	1	no	—
398	C₂²	—	404	1	no	—
399	C₂²	—	202	2	no	—
400	C₂²	—	202	2	no	—
401	C₂²	—	202	2	no	—
402	C₂²	—	202	2	no	—
403	C₂²	—	202	1	no	—
404	C₂²	—	202	1	no	—
405	C₂²	—	202	1	no	—
406	C₂²	—	202	1	no	—
407	C₂²	—	202	1	no	—
408	C₂²	#15692334	1	2	yes	complemented
409	C₂²	C₂³×#87938	1	1	yes	characteristic
410	C₄	—	2	1	no	—
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	101	2	no	—
415	C₄	—	404	2	no	—
416	C₄	—	404	2	no	—
417	C₄	—	404	2	no	—
418	C₄	—	202	4	no	—
419	C₄	—	202	1	no	—
420	C₄	—	202	1	no	—
421	C₄	—	202	1	no	—
422	C₄	—	202	1	no	—
423	C₄	D₄×#87938	1	2	yes	—
424	C₂	—	2	2	no	—
425	C₂	—	4	1	no	—
426	C₂	—	101	1	no	—
427	C₂	—	101	1	no	—
428	C₂	—	101	1	no	—
429	C₂	—	101	1	no	—
430	C₂	—	404	1	no	—
431	C₂	—	202	2	no	—
432	C₂	C₂×#15692334	1	1	yes	characteristic
433	C₂	C₂×D₄×#87938	1	1	yes	characteristic
434	C₂	#20266246	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×#87938
commutator, socle	C₂²×C₁₀₁	C₂³×C₄
Fitting	C₄×D₄×C₁₀₁	C₄
prime radical	C₂×D₄×D₁₀₁	C₂²
cosocle	C₂²×D₁₀₁	C₂⁴
hypercenter	C₄×D₄	#87938
hypocenter	C₁₀₁	#2352
LCS	G ▷ C₂²×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ 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. #20266121	C₂	semidirect
7. #20266119	C₂	semidirect
8. #20266119	C₂	semidirect
9. C₄×C₄⋊#87938	C₂	semidirect
10. C₂²⋊C₄×#87938	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
56. C₄⋊#87938	D₄	semidirect
70. C₂²×Dic₁₀₁	C₂×C₄	semidirect
77. C₂×C₄×D₁₀₁	C₂×C₄	semidirect
78. C₂×C₄×D₁₀₁	C₂×C₄	semidirect
84. C₄⋊Dic₁₀₁	C₂×C₄	semidirect
85. #13108053	C₂×C₄	semidirect
86. #13108053	C₂×C₄	semidirect
88. C₂²⋊Dic₁₀₁	C₂×C₄	semidirect
91. #13108051	C₂×C₄	semidirect
92. #13108051	C₂×C₄	semidirect
93. C₄×Dic₁₀₁	C₂×C₄	semidirect
94. C₄×Dic₁₀₁	C₂×C₄	semidirect
95. C₄×Dic₁₀₁	C₂×C₄	semidirect
98. C₂²×C₄×C₁₀₁	C₂×C₄	semidirect
99. C₄⋊C₄×C₁₀₁	C₂×C₄	semidirect
101. C₂²⋊C₄×C₁₀₁	C₂×C₄	semidirect
102. C₄²×C₁₀₁	C₂×C₄	semidirect
170. C₂²×C₁₀₁	#117	semidirect
185. C₂×D₁₀₁	#117	semidirect
218. C₁₀₁	#2352	semidirect
241. C₄×D₄	#87938	semidirect
294. C₂²×C₄	C₂×#87938	semidirect
303. C₄⋊C₄	C₂×#87938	semidirect
314. C₂²⋊C₄	C₂×#87938	semidirect
320. C₄²	C₂×#87938	semidirect
408. 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
#20266121	2
#20266119	2
C₄×C₄⋊#87938	2
C₂²⋊C₄×#87938	2
C₄×D₄×D₁₀₁	2
#2352	101