Subgroups — C₂×#10590917 #11861020

Order 1152.

1077 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×#64113	C₂	1	1	yes	maximal, characteristic
2	C₂×#63817	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×#819	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₈×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#63570	C₂	1	2	yes	maximal, complemented
6	#10590917	C₂	1	8	yes	maximal, direct product factor
7	C₂×#4895	—	3	1	no	maximal
8	C₂×#4700	—	3	1	no	maximal
9	C₂×#3828	C₂²	1	2	yes	—
10	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
11	C₂×#3746	C₄	1	1	yes	characteristic, complemented
12	#64113	C₄	1	4	yes	complemented
13	#64113	C₂²	1	4	yes	—
14	C₂×#3745	C₄	1	1	yes	characteristic, complemented
15	C₂×#3744	C₄	1	2	yes	complemented
16	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
17	C₂×C₃×#208	C₂²	1	2	yes	—
18	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×#3712	—	2	2	no	—
20	#63817	—	2	4	no	—
21	#63817	C₂²	1	8	yes	complemented
22	C₂×#3710	—	2	2	no	—
23	C₃×#819	C₂²	1	4	yes	complemented
24	C₃×C₈×Dic₃	C₂²	1	4	yes	complemented
25	#63570	C₂²	1	8	yes	complemented
26	C₂×#907	—	3	2	no	—
27	C₂×#904	—	3	1	no	—
28	C₂×#904	—	3	1	no	—
29	C₂×#904	—	6	1	no	—
30	C₂×#901	—	3	2	no	—
31	C₂×C₃×#108	—	3	1	no	—
32	C₂×C₃×C₄×C₈	—	3	1	no	—
33	C₂×#825	—	3	2	no	—
34	C₂×#819	D₃	1	1	yes	characteristic, complemented
35	C₂×C₈×Dic₃	D₃	1	1	yes	characteristic, complemented
36	C₂×#805	—	3	2	no	—
37	#4895	—	3	8	no	—
38	#4700	—	3	8	no	—
39	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
40	C₂×#638	—	2	2	no	—
41	#3828	—	2	2	no	—
42	#3828	—	2	2	no	—
43	#3828	C₂×C₄	1	4	yes	—
44	#3828	C₂³	1	4	yes	—
45	C₂×C₄⋊(C₃⋊D₃)	C₂×C₄	1	2	yes	—
46	C₂×C₄×C₃⋊D₃	—	2	2	no	—
47	C₂×#634	C₂×C₄	1	2	yes	—
48	C₂²×C₃×Dic₃	—	2	1	no	—
49	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
50	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
51	C₂×C₃²×C₈	C₂×C₄	1	2	yes	—
52	C₂×C₃²×C₈	C₂³	1	2	yes	—
53	#3746	C₂×C₄	1	4	yes	complemented
54	#3745	C₂×C₄	1	4	yes	complemented
55	#3744	C₂×C₄	1	8	yes	complemented
56	C₃×C₄×Dic₃	—	2	1	no	—
57	C₃×C₄×Dic₃	C₂³	1	2	yes	—
58	C₃×#208	—	2	2	no	—
59	C₃×#208	C₂³	1	4	yes	—
60	C₂×C₃×C₃⋊C₈	—	2	2	no	—
61	C₂×C₃×C₃⋊C₈	D₄	1	1	yes	characteristic
62	C₂×C₃×C₃⋊C₈	D₄	1	2	yes	—
63	C₂×C₃×C₃⋊C₈	D₄	1	1	yes	characteristic
64	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
65	#3712	—	2	8	no	—
66	#3710	—	2	8	no	—
67	C₂×#443	—	9	1	no	Sylow
68	C₂×#235	—	3	2	no	—
69	C₂×#235	—	3	2	no	—
70	C₂×#235	—	6	2	no	—
71	C₂×C₃×M₁₆	—	3	2	no	—
72	C₂²×C₃×C₈	—	2	1	no	—
73	C₂²×C₃×C₈	—	3	1	no	—
74	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
75	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
76	C₂×C₃×C₄²	—	3	1	no	—
77	C₂×C₄×Dic₃	C₂×D₃	1	1	yes	characteristic
78	C₂×#208	C₂×D₃	1	2	yes	—
79	C₂²×C₃⋊C₈	C₂×D₃	1	1	yes	characteristic
80	#907	—	3	8	no	—
81	#907	—	6	4	no	—
82	C₂×Dic₁₂	—	3	1	no	—
83	C₂×Dic₁₂	—	3	1	no	—
84	C₂×Dic₁₂	—	6	1	no	—
85	#904	—	3	4	no	—
86	#904	—	3	4	no	—
87	#904	—	3	4	no	—
88	#904	—	3	4	no	—
89	#904	—	6	4	no	—
90	#904	—	6	4	no	—
91	C₂×D₂₄	—	3	1	no	—
92	C₂×D₂₄	—	3	1	no	—
93	C₂×D₂₄	—	6	1	no	—
94	C₂×#204	—	3	2	no	—
95	C₂×#204	—	3	2	no	—
96	C₂×#204	—	6	2	no	—
97	#901	—	3	8	no	—
98	#901	—	6	4	no	—
99	C₂×ΓL(1,𝔽₂₅)	—	6	2	no	—
100	C₂×ΓL(1,𝔽₂₅)	—	6	2	no	—
101	C₂×D₃×C₈	—	6	2	no	—
102	C₂×D₃×C₈	—	6	2	no	—
103	C₃×#108	—	3	4	no	—
104	C₃×C₄×C₈	—	3	4	no	—
105	#825	—	3	8	no	—
106	#819	C₂×D₃	1	4	yes	complemented
107	C₈×Dic₃	C₂×D₃	1	4	yes	complemented
108	#805	—	3	8	no	—
109	C₂³×C₃²	#41	1	1	yes	characteristic
110	C₂²×C₃⋊D₃	—	2	2	no	—
111	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
114	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
115	C₂×C₃²×C₄	#41	1	1	yes	characteristic
116	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
117	#638	—	2	4	no	—
118	#638	—	2	4	no	—
119	C₂×C₃⋊Dic₃	—	2	2	no	—
120	C₄⋊(C₃⋊D₃)	—	2	2	no	—
121	C₄⋊(C₃⋊D₃)	C₂²×C₄	1	4	yes	—
122	C₄×C₃⋊D₃	—	2	4	no	—
123	C₄×C₃⋊D₃	—	2	4	no	—
124	#634	—	2	2	no	—
125	#634	C₂²×C₄	1	4	yes	—
126	C₂×C₃×Dic₃	—	2	4	no	—
127	C₂×C₃×Dic₃	—	2	2	no	—
128	C₃²×C₈	C₂²×C₄	1	2	yes	—
129	C₃²×C₈	C₂²×C₄	1	2	yes	—
130	C₃×C₃⋊C₈	—	2	4	no	—
131	C₃×C₃⋊C₈	C₂×D₄	1	2	yes	—
132	C₃×C₃⋊C₈	C₂×D₄	1	2	yes	—
133	C₂×#135	—	9	1	no	—
134	C₂×#131	—	9	2	no	—
135	#443	—	9	8	no	—
136	C₂×#108	—	3	1	no	—
137	C₂×#104	—	9	2	no	—
138	C₂×C₄×C₈	—	3	1	no	—
139	C₂²×C₃×C₄	—	2	1	no	—
140	C₂²×C₃×C₄	—	6	1	no	—
141	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
142	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
143	C₂×#67	—	6	2	no	—
144	C₂×#67	—	6	2	no	—
145	C₂×#67	—	12	2	no	—
146	C₂²×Dic₃	—	2	1	no	—
147	#235	—	3	4	no	—
148	#235	—	3	4	no	—
149	#235	—	3	4	no	—
150	#235	—	3	4	no	—
151	#235	—	6	4	no	—
152	#235	—	6	4	no	—
153	#235	—	6	2	no	—
154	#235	—	6	2	no	—
155	#235	—	6	2	no	—
156	#235	—	6	2	no	—
157	#235	—	12	2	no	—
158	#235	—	12	2	no	—
159	C₂×D₁₂	—	3	2	no	—
160	C₂×D₁₂	—	3	2	no	—
161	C₂×D₁₂	—	6	2	no	—
162	C₂×C₄×D₃	—	6	2	no	—
163	C₂×C₄×D₃	—	6	2	no	—
164	C₂×C₄×D₃	—	12	2	no	—
165	C₂×Dic₆	—	3	2	no	—
166	C₂×Dic₆	—	3	2	no	—
167	C₂×Dic₆	—	6	2	no	—
168	C₃×M₁₆	—	3	4	no	—
169	C₃×M₁₆	—	6	2	no	—
170	C₂×C₃×C₈	—	2	1	no	—
171	C₂×C₃×C₈	—	2	1	no	—
172	C₂×C₃×C₈	—	2	2	no	—
173	C₂×C₃×C₈	—	2	2	no	—
174	C₂×C₃×C₈	—	3	1	no	—
175	C₂×C₃×C₈	—	3	1	no	—
176	C₂×C₃×C₈	—	3	2	no	—
177	C₂×C₃×C₈	—	3	2	no	—
178	C₂×C₃×C₈	—	6	2	no	—
179	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
180	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
181	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
182	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
183	C₂×C₃×C₈	C₄×D₃	1	2	yes	—
184	C₂×C₃×C₈	C₄×D₃	1	2	yes	—
185	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
186	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
187	C₃×C₄²	—	3	2	no	—
188	C₃×C₄²	—	6	1	no	—
189	C₄×Dic₃	—	2	1	no	—
190	C₄×Dic₃	C₂²×D₃	1	2	yes	—
191	#208	—	2	2	no	—
192	#208	C₂²×D₃	1	4	yes	—
193	C₂×C₃⋊C₈	—	2	2	no	—
194	C₂×C₃⋊C₈	D₁₂	1	1	yes	characteristic
195	C₂×C₃⋊C₈	D₁₂	1	1	yes	characteristic
196	C₂×C₃⋊C₈	D₁₂	1	2	yes	—
197	C₂×C₃⋊C₈	C₂²×D₃	1	2	yes	—
198	Dic₁₂	—	3	4	no	—
199	Dic₁₂	—	3	4	no	—
200	Dic₁₂	—	6	4	no	—
201	D₂₄	—	3	4	no	—
202	D₂₄	—	3	4	no	—
203	D₂₄	—	6	4	no	—
204	#204	—	3	8	no	—
205	#204	—	3	8	no	—
206	#204	—	6	8	no	—
207	ΓL(1,𝔽₂₅)	—	6	8	no	—
208	ΓL(1,𝔽₂₅)	—	6	8	no	—
209	D₃×C₈	—	6	8	no	—
210	D₃×C₈	—	6	8	no	—
211	C₂²×C₃²	—	2	2	no	—
212	C₂²×C₃²	C₄×D₄	1	1	yes	characteristic
213	C₂²×C₃²	C₄×D₄	1	1	yes	characteristic
214	C₂²×C₃²	C₂×#41	1	1	yes	characteristic
215	C₂×C₃⋊D₃	—	2	4	no	—
216	C₂×C₃⋊D₃	—	4	4	no	—
217	C₃²×C₄	C₄×D₄	1	1	yes	characteristic
218	C₃²×C₄	C₄×D₄	1	1	yes	characteristic
219	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
220	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
221	C₃⋊Dic₃	—	2	4	no	—
222	C₃×Dic₃	—	2	4	no	—
223	C₂×#41	—	9	2	no	—
224	#135	—	9	4	no	—
225	#135	—	9	4	no	—
226	C₂×Q₁₆	—	9	1	no	—
227	C₂×SD₁₆	—	9	2	no	—
228	C₂×D₈	—	9	1	no	—
229	#131	—	9	8	no	—
230	#131	—	18	4	no	—
231	C₂×M₁₆	—	3	2	no	—
232	C₂×M₁₆	—	18	2	no	—
233	C₂²×C₈	—	3	1	no	—
234	C₂²×C₈	—	18	2	no	—
235	C₂²×C₈	D₃²	1	1	yes	characteristic
236	C₂×C₄²	—	3	1	no	—
237	#108	—	3	4	no	—
238	#104	—	9	8	no	—
239	C₄×C₈	—	3	4	no	—
240	C₂³×C₃	—	2	1	no	—
241	C₂³×C₃	#235	1	1	yes	characteristic
242	C₂³×C₃	#239	1	1	yes	characteristic
243	C₂²×D₃	—	6	2	no	—
244	C₂²×D₃	—	6	2	no	—
245	C₂²×D₃	—	12	2	no	—
246	C₂×C₃×C₄	—	2	1	no	—
247	C₂×C₃×C₄	—	2	1	no	—
248	C₂×C₃×C₄	—	2	1	no	—
249	C₂×C₃×C₄	—	2	1	no	—
250	C₂×C₃×C₄	—	2	1	no	—
251	C₂×C₃×C₄	—	2	1	no	—
252	C₂×C₃×C₄	—	6	4	no	—
253	C₂×C₃×C₄	—	6	2	no	—
254	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
255	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
256	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
257	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
258	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
259	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
260	C₂×C₃×C₄	#235	1	1	yes	characteristic
261	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
262	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
263	C₂×C₃×C₄	#239	1	1	yes	characteristic
264	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
265	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
266	#67	—	6	4	no	—
267	#67	—	6	4	no	—
268	#67	—	6	4	no	—
269	#67	—	6	4	no	—
270	#67	—	12	4	no	—
271	#67	—	12	4	no	—
272	C₂×Dic₃	—	2	4	no	—
273	C₂×Dic₃	—	2	2	no	—
274	C₂×Dic₃	—	6	2	no	—
275	C₂×Dic₃	—	6	2	no	—
276	C₂×Dic₃	—	12	2	no	—
277	D₁₂	—	3	4	no	—
278	D₁₂	—	3	4	no	—
279	D₁₂	—	6	4	no	—
280	D₁₂	—	6	2	no	—
281	D₁₂	—	6	2	no	—
282	D₁₂	—	12	2	no	—
283	C₄×D₃	—	6	4	no	—
284	C₄×D₃	—	6	4	no	—
285	C₄×D₃	—	6	4	no	—
286	C₄×D₃	—	6	4	no	—
287	C₄×D₃	—	12	4	no	—
288	C₄×D₃	—	12	4	no	—
289	Dic₆	—	3	4	no	—
290	Dic₆	—	3	4	no	—
291	Dic₆	—	6	4	no	—
292	Dic₆	—	6	2	no	—
293	Dic₆	—	6	2	no	—
294	Dic₆	—	12	2	no	—
295	C₃×C₈	—	2	2	no	—
296	C₃×C₈	—	2	2	no	—
297	C₃×C₈	—	3	2	no	—
298	C₃×C₈	—	3	2	no	—
299	C₃×C₈	—	6	4	no	—
300	C₃×C₈	C₂×C₄×D₃	1	2	yes	—
301	C₃×C₈	C₂×C₄×D₃	1	2	yes	—
302	C₃×C₈	C₂×C₄×D₃	1	2	yes	—
303	C₃×C₈	C₂×C₄×D₃	1	2	yes	—
304	C₃⋊C₈	—	2	4	no	—
305	C₃⋊C₈	C₂×D₁₂	1	2	yes	—
306	C₃⋊C₈	C₂×D₁₂	1	2	yes	—
307	C₂×C₃²	—	2	1	no	—
308	C₂×C₃²	—	2	1	no	—
309	C₂×C₃²	#443	1	2	yes	complemented
310	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
311	C₃⋊D₃	—	4	4	no	—
312	#41	—	9	4	no	—
313	#41	—	9	4	no	—
314	#41	—	18	2	no	—
315	#41	—	18	2	no	—
316	C₂×Q₈	—	9	2	no	—
317	C₂×D₄	—	9	2	no	—
318	C₂×D₄	—	18	2	no	—
319	C₂²×C₄	—	6	1	no	—
320	C₂²×C₄	—	18	2	no	—
321	C₂²×C₄	C₂×D₃²	1	1	yes	characteristic
322	Q₁₆	—	9	4	no	—
323	SD₁₆	—	9	8	no	—
324	D₈	—	9	4	no	—
325	M₁₆	—	3	4	no	—
326	M₁₆	—	6	2	no	—
327	M₁₆	—	18	8	no	—
328	C₂×C₈	—	3	2	no	—
329	C₂×C₈	—	3	2	no	—
330	C₂×C₈	—	3	1	no	—
331	C₂×C₈	—	3	1	no	—
332	C₂×C₈	—	6	2	no	—
333	C₂×C₈	—	18	8	no	—
334	C₂×C₈	#624	1	1	yes	characteristic
335	C₂×C₈	#624	1	1	yes	characteristic
336	C₂×C₈	#624	1	2	yes	—
337	C₂×C₈	C₂×D₃²	1	2	yes	—
338	C₄²	—	3	2	no	—
339	C₄²	—	6	1	no	—
340	C₂²×C₃	—	2	2	no	—
341	C₂²×C₃	—	2	2	no	—
342	C₂²×C₃	—	2	1	no	—
343	C₂²×C₃	—	2	1	no	—
344	C₂²×C₃	—	2	1	no	—
345	C₂²×C₃	—	4	2	no	—
346	C₂²×C₃	C₄×D₁₂	1	1	yes	characteristic
347	C₂²×C₃	C₄×D₁₂	1	1	yes	characteristic
348	C₂²×C₃	#893	1	1	yes	characteristic
349	C₂²×C₃	#893	1	1	yes	characteristic
350	C₂²×C₃	C₂×#235	1	1	yes	characteristic
351	C₂²×C₃	C₂×#239	1	1	yes	characteristic
352	C₂×D₃	—	6	4	no	—
353	C₂×D₃	—	6	4	no	—
354	C₂×D₃	—	12	4	no	—
355	C₂×D₃	—	12	4	no	—
356	C₂×D₃	—	12	4	no	—
357	C₂×D₃	—	24	4	no	—
358	C₃×C₄	—	2	1	no	—
359	C₃×C₄	—	2	1	no	—
360	C₃×C₄	—	2	1	no	—
361	C₃×C₄	—	2	1	no	—
362	C₃×C₄	—	6	4	no	—
363	C₃×C₄	C₄×D₁₂	1	1	yes	characteristic
364	C₃×C₄	C₄×D₁₂	1	1	yes	characteristic
365	C₃×C₄	#893	1	1	yes	characteristic
366	C₃×C₄	#893	1	1	yes	characteristic
367	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
368	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
369	C₃×C₄	C₂²×D₁₂	1	1	yes	characteristic
370	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
371	Dic₃	—	2	4	no	—
372	Dic₃	—	6	4	no	—
373	Dic₃	—	6	4	no	—
374	Dic₃	—	12	4	no	—
375	C₃²	C₂×#443	1	1	yes	characteristic, complemented, Sylow
376	C₂³	—	18	2	no	—
377	C₂³	#3799	1	1	yes	characteristic
378	Q₈	—	9	4	no	—
379	Q₈	—	18	2	no	—
380	D₄	—	9	4	no	—
381	D₄	—	18	4	no	—
382	D₄	—	18	4	no	—
383	D₄	—	18	2	no	—
384	C₂×C₄	—	6	4	no	—
385	C₂×C₄	—	6	2	no	—
386	C₂×C₄	—	18	2	no	—
387	C₂×C₄	—	18	4	no	—
388	C₂×C₄	—	18	4	no	—
389	C₂×C₄	#3799	1	1	yes	characteristic
390	C₂×C₄	D₃×D₁₂	1	1	yes	characteristic
391	C₂×C₄	D₃×D₁₂	1	1	yes	characteristic
392	C₂×C₄	C₂×#624	1	1	yes	characteristic
393	C₂×C₄	C₂×#624	1	1	yes	characteristic
394	C₂×C₄	C₂²×D₃²	1	1	yes	characteristic
395	C₈	—	3	2	no	—
396	C₈	—	3	2	no	—
397	C₈	—	6	4	no	—
398	C₈	C₂×#624	1	2	yes	—
399	C₈	C₂×#624	1	2	yes	—
400	C₂×C₃	—	2	1	no	—
401	C₂×C₃	—	2	1	no	—
402	C₂×C₃	—	2	1	no	—
403	C₂×C₃	—	2	1	no	—
404	C₂×C₃	—	2	1	no	—
405	C₂×C₃	—	2	2	no	—
406	C₂×C₃	—	4	1	no	—
407	C₂×C₃	—	4	1	no	—
408	C₂×C₃	#4700	1	2	yes	complemented
409	C₂×C₃	#4895	1	2	yes	complemented
410	C₂×C₃	C₂×C₄×D₁₂	1	1	yes	characteristic
411	C₂×C₃	C₂×#893	1	1	yes	characteristic
412	D₃	—	12	4	no	—
413	D₃	—	12	4	no	—
414	D₃	—	24	4	no	—
415	C₂²	—	2	2	no	—
416	C₂²	—	18	4	no	—
417	C₂²	—	36	4	no	—
418	C₂²	#63894	1	1	yes	characteristic
419	C₂²	#63894	1	1	yes	characteristic
420	C₂²	C₂×#3799	1	1	yes	characteristic
421	C₄	—	6	4	no	—
422	C₄	—	18	4	no	—
423	C₄	#63894	1	1	yes	characteristic
424	C₄	#63894	1	1	yes	characteristic
425	C₄	C₂×D₃×D₁₂	1	1	yes	characteristic
426	C₄	C₂²×#624	1	1	yes	characteristic
427	C₃	—	2	1	no	—
428	C₃	C₂×#4700	1	1	yes	characteristic, complemented
429	C₃	C₂×#4895	1	1	yes	characteristic, complemented
430	C₂	—	2	1	no	—
431	C₂	—	2	1	no	—
432	C₂	—	36	4	no	—
433	C₂	#10590917	1	2	yes	direct product factor
434	C₂	C₂×#63894	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₃×D₁₂
commutator	C₃²×C₄	C₂³×C₄
Frattini	C₂×C₄	C₂²×D₃²
Fitting	C₂²×C₃²×C₈	C₂²
socle	C₂²×C₃²	C₄×D₄
prime radical	C₂×#64113	C₂
cosocle	C₂×C₃²×C₄	C₂⁴
hypercenter	C₂²×C₈	D₃²
hypocenter	C₃²	C₂×#443
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×#63817	C₂	semidirect
3. C₂×C₃×#819	C₂	semidirect
4. C₂×C₃×C₈×Dic₃	C₂	semidirect
5. C₂×#63570	C₂	semidirect
6. #10590917	C₂	direct (N × H)
11. C₂×#3746	C₄	semidirect
12. #64113	C₄	semidirect
14. C₂×#3745	C₄	semidirect
15. C₂×#3744	C₄	semidirect
21. #63817	C₂²	semidirect
23. C₃×#819	C₂²	semidirect
24. C₃×C₈×Dic₃	C₂²	semidirect
25. #63570	C₂²	semidirect
34. C₂×#819	D₃	semidirect
35. C₂×C₈×Dic₃	D₃	semidirect
53. #3746	C₂×C₄	semidirect
54. #3745	C₂×C₄	semidirect
55. #3744	C₂×C₄	semidirect
106. #819	C₂×D₃	semidirect
107. C₈×Dic₃	C₂×D₃	semidirect
309. C₂×C₃²	#443	semidirect
375. C₃²	C₂×#443	semidirect
408. C₂×C₃	#4700	semidirect
409. C₂×C₃	#4895	semidirect
428. C₃	C₂×#4700	semidirect
429. C₃	C₂×#4895	semidirect
433. C₂	#10590917	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×#64113	2
C₂×#63817	2
C₂×C₃×#819	2
C₂×C₃×C₈×Dic₃	2
C₂×#63570	2
#10590917	2
C₂×#4895	3
C₂×#4700	3

Subgroups — C2×#10590917 #11861020

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10590917 #11861020