Subgroups — C₂×#10590918 #11861068

Order 1152.

1061 conjugacy classes of subgroups.

The subgroup lattice has 428 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×#815	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#63570	C₂	1	2	yes	maximal, complemented
6	#10590918	C₂	1	8	yes	maximal, direct product factor
7	C₂×#4894	—	3	1	no	maximal
8	C₂×#4717	—	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×#815	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×#97	—	3	1	no	—
33	C₂×#825	—	3	2	no	—
34	C₂×#819	D₃	1	1	yes	characteristic, complemented
35	C₂×#815	D₃	1	1	yes	characteristic, complemented
36	C₂×#805	—	3	2	no	—
37	#4894	—	3	8	no	—
38	#4717	—	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	2	yes	—
62	C₂×C₃×C₃⋊C₈	D₄	1	2	yes	—
63	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
64	#3712	—	2	8	no	—
65	#3710	—	2	8	no	—
66	C₂×#444	—	9	1	no	Sylow
67	C₂×#235	—	3	2	no	—
68	C₂×#235	—	3	2	no	—
69	C₂×#235	—	6	2	no	—
70	C₂×C₃×M₁₆	—	3	2	no	—
71	C₂²×C₃×C₈	—	2	1	no	—
72	C₂²×C₃×C₈	—	3	1	no	—
73	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
74	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
75	C₂×C₃×C₄²	—	3	1	no	—
76	C₂×C₄×Dic₃	C₂×D₃	1	1	yes	characteristic
77	C₂×#208	C₂×D₃	1	2	yes	—
78	C₂²×C₃⋊C₈	C₂×D₃	1	1	yes	characteristic
79	#907	—	3	8	no	—
80	#907	—	6	4	no	—
81	C₂×Dic₁₂	—	3	1	no	—
82	C₂×Dic₁₂	—	3	1	no	—
83	C₂×Dic₁₂	—	6	1	no	—
84	#904	—	3	4	no	—
85	#904	—	3	4	no	—
86	#904	—	3	4	no	—
87	#904	—	3	4	no	—
88	#904	—	6	4	no	—
89	#904	—	6	4	no	—
90	C₂×D₂₄	—	3	1	no	—
91	C₂×D₂₄	—	3	1	no	—
92	C₂×D₂₄	—	6	1	no	—
93	C₂×#204	—	3	2	no	—
94	C₂×#204	—	3	2	no	—
95	C₂×#204	—	6	2	no	—
96	#901	—	3	8	no	—
97	#901	—	6	4	no	—
98	C₂×ΓL(1,𝔽₂₅)	—	6	2	no	—
99	C₂×ΓL(1,𝔽₂₅)	—	6	2	no	—
100	C₂×D₃×C₈	—	6	2	no	—
101	C₂×D₃×C₈	—	6	2	no	—
102	C₃×#108	—	3	4	no	—
103	C₃×#97	—	3	4	no	—
104	#825	—	3	8	no	—
105	#819	C₂×D₃	1	4	yes	complemented
106	#815	C₂×D₃	1	4	yes	complemented
107	#805	—	3	8	no	—
108	C₂³×C₃²	#41	1	1	yes	characteristic
109	C₂²×C₃⋊D₃	—	2	2	no	—
110	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
113	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
114	C₂×C₃²×C₄	#41	1	1	yes	characteristic
115	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
116	#638	—	2	4	no	—
117	#638	—	2	4	no	—
118	C₂×C₃⋊Dic₃	—	2	2	no	—
119	C₄⋊(C₃⋊D₃)	—	2	2	no	—
120	C₄⋊(C₃⋊D₃)	C₂²×C₄	1	4	yes	—
121	C₄×C₃⋊D₃	—	2	4	no	—
122	C₄×C₃⋊D₃	—	2	4	no	—
123	#634	—	2	2	no	—
124	#634	C₂²×C₄	1	4	yes	—
125	C₂×C₃×Dic₃	—	2	2	no	—
126	C₂×C₃×Dic₃	—	4	2	no	—
127	C₃²×C₈	C₂²×C₄	1	2	yes	—
128	C₃²×C₈	C₂²×C₄	1	2	yes	—
129	C₃×C₃⋊C₈	—	2	4	no	—
130	C₃×C₃⋊C₈	C₂×D₄	1	4	yes	—
131	C₂×#135	—	9	1	no	—
132	C₂×#131	—	9	2	no	—
133	#444	—	9	8	no	—
134	C₂×#108	—	3	1	no	—
135	C₂×#104	—	9	2	no	—
136	C₂×#97	—	3	1	no	—
137	C₂²×C₃×C₄	—	2	1	no	—
138	C₂²×C₃×C₄	—	6	1	no	—
139	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
140	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
141	C₂×#67	—	6	2	no	—
142	C₂×#67	—	6	2	no	—
143	C₂×#67	—	12	2	no	—
144	C₂²×Dic₃	—	2	1	no	—
145	#235	—	3	4	no	—
146	#235	—	3	4	no	—
147	#235	—	3	4	no	—
148	#235	—	3	4	no	—
149	#235	—	6	4	no	—
150	#235	—	6	4	no	—
151	#235	—	6	2	no	—
152	#235	—	6	2	no	—
153	#235	—	6	2	no	—
154	#235	—	6	2	no	—
155	#235	—	12	2	no	—
156	#235	—	12	2	no	—
157	C₂×D₁₂	—	3	2	no	—
158	C₂×D₁₂	—	3	2	no	—
159	C₂×D₁₂	—	6	2	no	—
160	C₂×C₄×D₃	—	6	2	no	—
161	C₂×C₄×D₃	—	6	2	no	—
162	C₂×C₄×D₃	—	12	2	no	—
163	C₂×Dic₆	—	3	2	no	—
164	C₂×Dic₆	—	3	2	no	—
165	C₂×Dic₆	—	6	2	no	—
166	C₃×M₁₆	—	3	4	no	—
167	C₃×M₁₆	—	6	2	no	—
168	C₂×C₃×C₈	—	2	1	no	—
169	C₂×C₃×C₈	—	2	1	no	—
170	C₂×C₃×C₈	—	2	2	no	—
171	C₂×C₃×C₈	—	2	2	no	—
172	C₂×C₃×C₈	—	3	2	no	—
173	C₂×C₃×C₈	—	3	2	no	—
174	C₂×C₃×C₈	—	3	2	no	—
175	C₂×C₃×C₈	—	6	2	no	—
176	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
177	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
178	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
179	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
180	C₂×C₃×C₈	C₄×D₃	1	2	yes	—
181	C₂×C₃×C₈	C₄×D₃	1	2	yes	—
182	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
183	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
184	C₃×C₄²	—	3	2	no	—
185	C₃×C₄²	—	6	1	no	—
186	C₄×Dic₃	—	2	1	no	—
187	C₄×Dic₃	C₂²×D₃	1	2	yes	—
188	#208	—	2	2	no	—
189	#208	C₂²×D₃	1	4	yes	—
190	C₂×C₃⋊C₈	—	2	2	no	—
191	C₂×C₃⋊C₈	D₁₂	1	2	yes	—
192	C₂×C₃⋊C₈	D₁₂	1	2	yes	—
193	C₂×C₃⋊C₈	C₂²×D₃	1	2	yes	—
194	Dic₁₂	—	3	4	no	—
195	Dic₁₂	—	3	4	no	—
196	Dic₁₂	—	6	4	no	—
197	D₂₄	—	3	4	no	—
198	D₂₄	—	3	4	no	—
199	D₂₄	—	6	4	no	—
200	#204	—	3	8	no	—
201	#204	—	3	8	no	—
202	#204	—	6	8	no	—
203	ΓL(1,𝔽₂₅)	—	6	8	no	—
204	ΓL(1,𝔽₂₅)	—	6	8	no	—
205	D₃×C₈	—	6	8	no	—
206	D₃×C₈	—	6	8	no	—
207	C₂²×C₃²	—	2	2	no	—
208	C₂²×C₃²	C₄×D₄	1	1	yes	characteristic
209	C₂²×C₃²	C₄×D₄	1	1	yes	characteristic
210	C₂²×C₃²	C₂×#41	1	1	yes	characteristic
211	C₂×C₃⋊D₃	—	2	4	no	—
212	C₂×C₃⋊D₃	—	4	4	no	—
213	C₃²×C₄	C₄×D₄	1	1	yes	characteristic
214	C₃²×C₄	C₄×D₄	1	1	yes	characteristic
215	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
216	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
217	C₃⋊Dic₃	—	2	4	no	—
218	C₃×Dic₃	—	4	2	no	—
219	C₂×#41	—	9	2	no	—
220	#135	—	9	4	no	—
221	#135	—	9	4	no	—
222	C₂×Q₁₆	—	9	1	no	—
223	C₂×SD₁₆	—	9	2	no	—
224	C₂×D₈	—	9	1	no	—
225	#131	—	9	8	no	—
226	#131	—	18	4	no	—
227	C₂×M₁₆	—	3	2	no	—
228	C₂×M₁₆	—	18	2	no	—
229	C₂²×C₈	—	3	1	no	—
230	C₂²×C₈	—	18	2	no	—
231	C₂²×C₈	D₃²	1	1	yes	characteristic
232	C₂×C₄²	—	3	1	no	—
233	#108	—	3	4	no	—
234	#104	—	9	8	no	—
235	#97	—	3	4	no	—
236	C₂³×C₃	—	2	1	no	—
237	C₂³×C₃	#235	1	1	yes	characteristic
238	C₂³×C₃	#239	1	1	yes	characteristic
239	C₂²×D₃	—	6	2	no	—
240	C₂²×D₃	—	6	2	no	—
241	C₂²×D₃	—	12	2	no	—
242	C₂×C₃×C₄	—	2	1	no	—
243	C₂×C₃×C₄	—	2	1	no	—
244	C₂×C₃×C₄	—	2	1	no	—
245	C₂×C₃×C₄	—	2	1	no	—
246	C₂×C₃×C₄	—	2	1	no	—
247	C₂×C₃×C₄	—	2	1	no	—
248	C₂×C₃×C₄	—	6	2	no	—
249	C₂×C₃×C₄	—	12	2	no	—
250	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
251	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
252	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
253	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
254	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
255	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
256	C₂×C₃×C₄	#235	1	1	yes	characteristic
257	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
258	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
259	C₂×C₃×C₄	#239	1	1	yes	characteristic
260	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
261	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
262	#67	—	6	4	no	—
263	#67	—	6	4	no	—
264	#67	—	6	4	no	—
265	#67	—	6	4	no	—
266	#67	—	12	4	no	—
267	#67	—	12	4	no	—
268	C₂×Dic₃	—	2	2	no	—
269	C₂×Dic₃	—	4	2	no	—
270	C₂×Dic₃	—	6	2	no	—
271	C₂×Dic₃	—	6	2	no	—
272	C₂×Dic₃	—	12	2	no	—
273	D₁₂	—	3	4	no	—
274	D₁₂	—	3	4	no	—
275	D₁₂	—	6	4	no	—
276	D₁₂	—	6	2	no	—
277	D₁₂	—	6	2	no	—
278	D₁₂	—	12	2	no	—
279	C₄×D₃	—	6	4	no	—
280	C₄×D₃	—	6	4	no	—
281	C₄×D₃	—	6	4	no	—
282	C₄×D₃	—	6	4	no	—
283	C₄×D₃	—	12	4	no	—
284	C₄×D₃	—	12	4	no	—
285	Dic₆	—	3	4	no	—
286	Dic₆	—	3	4	no	—
287	Dic₆	—	6	4	no	—
288	Dic₆	—	6	2	no	—
289	Dic₆	—	6	2	no	—
290	Dic₆	—	12	2	no	—
291	C₃×C₈	—	2	2	no	—
292	C₃×C₈	—	2	2	no	—
293	C₃×C₈	—	3	4	no	—
294	C₃×C₈	—	6	4	no	—
295	C₃×C₈	C₂×C₄×D₃	1	2	yes	—
296	C₃×C₈	C₂×C₄×D₃	1	2	yes	—
297	C₃×C₈	C₂×C₄×D₃	1	2	yes	—
298	C₃×C₈	C₂×C₄×D₃	1	2	yes	—
299	C₃⋊C₈	—	2	4	no	—
300	C₃⋊C₈	C₂×D₁₂	1	4	yes	—
301	C₂×C₃²	—	2	1	no	—
302	C₂×C₃²	—	2	1	no	—
303	C₂×C₃²	#444	1	2	yes	complemented
304	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
305	C₃⋊D₃	—	4	4	no	—
306	#41	—	9	4	no	—
307	#41	—	9	4	no	—
308	#41	—	18	2	no	—
309	#41	—	18	2	no	—
310	C₂×Q₈	—	9	2	no	—
311	C₂×D₄	—	9	2	no	—
312	C₂×D₄	—	18	2	no	—
313	C₂²×C₄	—	6	1	no	—
314	C₂²×C₄	—	18	2	no	—
315	C₂²×C₄	C₂×D₃²	1	1	yes	characteristic
316	Q₁₆	—	9	4	no	—
317	SD₁₆	—	9	8	no	—
318	D₈	—	9	4	no	—
319	M₁₆	—	3	4	no	—
320	M₁₆	—	6	2	no	—
321	M₁₆	—	18	8	no	—
322	C₂×C₈	—	3	2	no	—
323	C₂×C₈	—	3	2	no	—
324	C₂×C₈	—	3	2	no	—
325	C₂×C₈	—	6	2	no	—
326	C₂×C₈	—	18	8	no	—
327	C₂×C₈	#624	1	1	yes	characteristic
328	C₂×C₈	#624	1	1	yes	characteristic
329	C₂×C₈	#624	1	2	yes	—
330	C₂×C₈	C₂×D₃²	1	2	yes	—
331	C₄²	—	3	2	no	—
332	C₄²	—	6	1	no	—
333	C₂²×C₃	—	2	2	no	—
334	C₂²×C₃	—	2	2	no	—
335	C₂²×C₃	—	2	1	no	—
336	C₂²×C₃	—	2	1	no	—
337	C₂²×C₃	—	2	1	no	—
338	C₂²×C₃	—	4	2	no	—
339	C₂²×C₃	C₄×D₁₂	1	1	yes	characteristic
340	C₂²×C₃	C₄×D₁₂	1	1	yes	characteristic
341	C₂²×C₃	#893	1	1	yes	characteristic
342	C₂²×C₃	#893	1	1	yes	characteristic
343	C₂²×C₃	C₂×#235	1	1	yes	characteristic
344	C₂²×C₃	C₂×#239	1	1	yes	characteristic
345	C₂×D₃	—	6	4	no	—
346	C₂×D₃	—	6	4	no	—
347	C₂×D₃	—	12	4	no	—
348	C₂×D₃	—	12	4	no	—
349	C₂×D₃	—	12	4	no	—
350	C₂×D₃	—	24	4	no	—
351	C₃×C₄	—	2	1	no	—
352	C₃×C₄	—	2	1	no	—
353	C₃×C₄	—	2	1	no	—
354	C₃×C₄	—	2	1	no	—
355	C₃×C₄	—	12	2	no	—
356	C₃×C₄	C₄×D₁₂	1	1	yes	characteristic
357	C₃×C₄	C₄×D₁₂	1	1	yes	characteristic
358	C₃×C₄	#893	1	1	yes	characteristic
359	C₃×C₄	#893	1	1	yes	characteristic
360	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
361	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
362	C₃×C₄	C₂²×D₁₂	1	1	yes	characteristic
363	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
364	Dic₃	—	4	2	no	—
365	Dic₃	—	6	4	no	—
366	Dic₃	—	6	4	no	—
367	Dic₃	—	12	4	no	—
368	C₃²	C₂×#444	1	1	yes	characteristic, complemented, Sylow
369	C₂³	—	18	2	no	—
370	C₂³	#3799	1	1	yes	characteristic
371	Q₈	—	9	4	no	—
372	Q₈	—	18	2	no	—
373	D₄	—	9	4	no	—
374	D₄	—	18	4	no	—
375	D₄	—	18	4	no	—
376	D₄	—	18	2	no	—
377	C₂×C₄	—	6	2	no	—
378	C₂×C₄	—	12	2	no	—
379	C₂×C₄	—	18	2	no	—
380	C₂×C₄	—	18	4	no	—
381	C₂×C₄	—	18	4	no	—
382	C₂×C₄	#3799	1	1	yes	characteristic
383	C₂×C₄	D₃×D₁₂	1	1	yes	characteristic
384	C₂×C₄	D₃×D₁₂	1	1	yes	characteristic
385	C₂×C₄	C₂×#624	1	1	yes	characteristic
386	C₂×C₄	C₂×#624	1	1	yes	characteristic
387	C₂×C₄	C₂²×D₃²	1	1	yes	characteristic
388	C₈	—	3	4	no	—
389	C₈	—	6	4	no	—
390	C₈	C₂×#624	1	2	yes	—
391	C₈	C₂×#624	1	2	yes	—
392	C₂×C₃	—	2	1	no	—
393	C₂×C₃	—	2	1	no	—
394	C₂×C₃	—	2	1	no	—
395	C₂×C₃	—	2	1	no	—
396	C₂×C₃	—	2	1	no	—
397	C₂×C₃	—	2	2	no	—
398	C₂×C₃	—	4	1	no	—
399	C₂×C₃	—	4	1	no	—
400	C₂×C₃	#4717	1	2	yes	complemented
401	C₂×C₃	#4894	1	2	yes	complemented
402	C₂×C₃	C₂×C₄×D₁₂	1	1	yes	characteristic
403	C₂×C₃	C₂×#893	1	1	yes	characteristic
404	D₃	—	12	4	no	—
405	D₃	—	12	4	no	—
406	D₃	—	24	4	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	18	4	no	—
409	C₂²	—	36	4	no	—
410	C₂²	#63894	1	1	yes	characteristic
411	C₂²	#63894	1	1	yes	characteristic
412	C₂²	C₂×#3799	1	1	yes	characteristic
413	C₄	—	12	2	no	—
414	C₄	—	18	4	no	—
415	C₄	#63894	1	1	yes	characteristic
416	C₄	#63894	1	1	yes	characteristic
417	C₄	C₂×D₃×D₁₂	1	1	yes	characteristic
418	C₄	C₂²×#624	1	1	yes	characteristic
419	C₃	—	2	1	no	—
420	C₃	C₂×#4717	1	1	yes	characteristic, complemented
421	C₃	C₂×#4894	1	1	yes	characteristic, complemented
422	C₂	—	2	1	no	—
423	C₂	—	2	1	no	—
424	C₂	—	36	4	no	—
425	C₂	#10590918	1	2	yes	direct product factor
426	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×#444
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×#815	C₂	semidirect
5. C₂×#63570	C₂	semidirect
6. #10590918	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×#815	C₂²	semidirect
25. #63570	C₂²	semidirect
34. C₂×#819	D₃	semidirect
35. C₂×#815	D₃	semidirect
53. #3746	C₂×C₄	semidirect
54. #3745	C₂×C₄	semidirect
55. #3744	C₂×C₄	semidirect
105. #819	C₂×D₃	semidirect
106. #815	C₂×D₃	semidirect
303. C₂×C₃²	#444	semidirect
368. C₃²	C₂×#444	semidirect
400. C₂×C₃	#4717	semidirect
401. C₂×C₃	#4894	semidirect
420. C₃	C₂×#4717	semidirect
421. C₃	C₂×#4894	semidirect
425. C₂	#10590918	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×#815	2
C₂×#63570	2
#10590918	2
C₂×#4894	3
C₂×#4717	3

Subgroups — C2×#10590918 #11861068

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10590918 #11861068