Subgroups — C₄×#11718569 #16016241

Order 3328.

738 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×#11718569	C₂	1	1	yes	maximal, characteristic
2	C₄×#88158	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×D₁₀₄	C₂	1	1	yes	maximal, characteristic, complemented
4	#13116713	C₂	1	2	yes	maximal, complemented
5	#13116702	C₂	1	2	yes	maximal, complemented
6	C₄×#88040	C₂	1	2	yes	maximal, complemented
7	C₄×D₂₀₈	C₂	1	2	yes	maximal, complemented
8	#13116624	C₂	1	1	yes	maximal, characteristic, complemented
9	#13116553	C₂	1	1	yes	maximal, characteristic, complemented
10	#13116549	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₃×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#88158	C₂²	1	1	yes	characteristic
13	C₂²×D₁₀₄	C₂²	1	1	yes	characteristic
14	C₄×#6127	—	2	1	no	—
15	C₂×C₄×D₅₂	—	2	1	no	—
16	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
19	#11718774	—	2	1	no	—
20	C₂×#88061	—	2	1	no	—
21	#11718767	C₂²	1	1	yes	characteristic
22	C₂×#88058	C₂²	1	1	yes	characteristic
23	#11718569	C₄	1	8	yes	direct product factor
24	C₂×#88040	C₂²	1	2	yes	—
25	C₂×D₂₀₈	C₂²	1	2	yes	—
26	C₄×Dic₅₂	C₂²	1	1	yes	characteristic, complemented
27	C₄×Dic₅₂	C₂²	1	1	yes	characteristic, complemented
28	C₄×D₁₀₄	—	2	1	no	—
29	C₄×D₁₀₄	—	2	1	no	—
30	C₄×D₁₀₄	C₂²	1	2	yes	—
31	C₄×D₁₀₄	C₂²	1	2	yes	—
32	C₄×D₁₀₄	C₂²	1	1	yes	characteristic, complemented
33	C₄×D₁₀₄	C₂²	1	1	yes	characteristic, complemented
34	C₄×#6095	—	2	1	no	—
35	C₄×#6095	—	2	1	no	—
36	C₁₃×#346	C₂²	1	2	yes	complemented
37	C₄×C₁₃×C₁₆	C₂²	1	2	yes	complemented
38	#11718101	C₂²	1	2	yes	—
39	#11718101	C₂²	1	2	yes	—
40	#11718101	C₂²	1	2	yes	complemented
41	#11718097	C₂²	1	2	yes	complemented
42	#11718096	C₂²	1	2	yes	complemented
43	#11718095	C₂²	1	2	yes	complemented
44	C₂×#6127	—	2	1	no	—
45	C₂²×D₅₂	—	2	1	no	—
46	C₂²×C₄×D₁₃	—	4	1	no	—
47	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
48	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
49	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
50	C₄×C₂²⋊D₁₃	—	4	1	no	—
51	C₄×C₂²⋊D₁₃	—	4	1	no	—
52	C₂×#6103	—	4	1	no	—
53	#88180	—	2	1	no	—
54	C₂×C₄⋊Dic₁₃	—	2	1	no	—
55	C₂×Dic₅₂	C₂³	1	1	yes	characteristic
56	#88158	—	2	2	no	—
57	#88158	C₂×C₄	1	4	yes	complemented
58	C₂×D₁₀₄	—	2	1	no	—
59	C₂×D₁₀₄	—	2	2	no	—
60	C₂×D₁₀₄	C₂×C₄	1	4	yes	complemented
61	C₂×D₁₀₄	C₂³	1	2	yes	—
62	C₂×D₁₀₄	C₂³	1	1	yes	characteristic
63	C₂×#6095	—	2	1	no	—
64	C₄×D₅₂	—	2	2	no	—
65	C₄×D₅₂	—	2	2	no	—
66	C₄×D₅₂	—	2	1	no	—
67	C₄×D₅₂	—	2	1	no	—
68	C₄×D₅₂	—	4	1	no	—
69	C₄×D₅₂	—	4	1	no	—
70	#88126	—	4	1	no	—
71	C₄²×D₁₃	—	4	1	no	—
72	C₄×Dic₂₆	—	2	1	no	—
73	C₄×Dic₂₆	—	2	1	no	—
74	C₁₃×M₃₂	—	2	2	no	—
75	C₁₃×M₃₂	C₂×C₄	1	4	yes	complemented
76	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
77	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
78	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
79	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
80	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
81	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
82	#88061	—	2	2	no	—
83	#88061	—	2	2	no	—
84	#88061	—	2	1	no	—
85	#88061	—	2	1	no	—
86	#88058	—	2	1	no	—
87	#88058	C₂³	1	2	yes	—
88	#88058	C₂³	1	1	yes	characteristic
89	#88058	C₂³	1	1	yes	characteristic
90	#88057	—	2	1	no	—
91	#88056	—	2	1	no	—
92	#88056	—	2	1	no	—
93	#88040	C₂×C₄	1	8	yes	complemented
94	D₂₀₈	C₂×C₄	1	8	yes	complemented
95	C₄×#509	—	13	1	no	maximal, Sylow
96	C₂³×D₁₃	—	4	1	no	—
97	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
100	C₂×C₂²⋊D₁₃	—	4	1	no	—
101	C₂²×Dic₁₃	—	4	1	no	—
102	#6127	—	2	4	no	—
103	#6127	—	4	2	no	—
104	C₂×D₅₂	—	2	4	no	—
105	C₂×D₅₂	—	2	1	no	—
106	C₂×D₅₂	—	2	2	no	—
107	C₂×D₅₂	—	4	1	no	—
108	C₂×D₅₂	—	4	2	no	—
109	C₂×C₄×D₁₃	—	4	1	no	—
110	C₂×C₄×D₁₃	—	4	1	no	—
111	C₂×C₄×D₁₃	—	4	1	no	—
112	C₂×C₄×D₁₃	—	4	2	no	—
113	C₂×C₄×D₁₃	—	4	2	no	—
114	C₂×C₄×D₁₃	—	8	4	no	—
115	C₂×Dic₂₆	—	2	1	no	—
116	C₂×C₈×C₁₃	—	2	2	no	—
117	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
118	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₁₃	#41	1	2	yes	—
122	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
123	C₄²×C₁₃	D₈	1	1	yes	characteristic
124	C₄²×C₁₃	D₈	1	1	yes	characteristic
125	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
127	C₂²⋊Dic₁₃	—	4	1	no	—
128	#6103	—	4	1	no	—
129	#6103	—	4	1	no	—
130	#6103	—	4	2	no	—
131	#6103	—	4	2	no	—
132	C₄⋊Dic₁₃	—	2	1	no	—
133	C₄⋊Dic₁₃	—	2	1	no	—
134	C₄⋊Dic₁₃	—	2	2	no	—
135	C₄⋊Dic₁₃	—	4	1	no	—
136	#6101	—	4	1	no	—
137	#6101	—	4	1	no	—
138	C₄×Dic₁₃	—	4	1	no	—
139	C₄×Dic₁₃	—	4	1	no	—
140	C₄×Dic₁₃	—	4	1	no	—
141	Dic₅₂	—	2	1	no	—
142	Dic₅₂	C₂²×C₄	1	2	yes	complemented
143	D₁₀₄	—	2	4	no	—
144	D₁₀₄	—	2	2	no	—
145	D₁₀₄	—	2	1	no	—
146	D₁₀₄	C₂²×C₄	1	4	yes	—
147	D₁₀₄	C₂²×C₄	1	2	yes	complemented
148	#6095	—	2	4	no	—
149	C₁₃×C₁₆	—	2	2	no	—
150	C₁₃×C₁₆	C₂²×C₄	1	4	yes	complemented
151	C₂×#509	—	13	1	no	—
152	C₄×#135	—	13	1	no	—
153	C₂×C₄×D₈	—	13	1	no	—
154	#2177	—	13	2	no	—
155	#2175	—	13	2	no	—
156	C₄×SD₃₂	—	13	2	no	—
157	C₄×D₁₆	—	13	2	no	—
158	#2159	—	13	1	no	—
159	#2140	—	13	1	no	—
160	#2139	—	13	1	no	—
161	C₄×M₃₂	D₁₃	1	1	yes	characteristic, complemented
162	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
163	C₂²×D₁₃	—	4	1	no	—
164	C₂²×D₁₃	—	4	2	no	—
165	C₂²×D₁₃	—	4	4	no	—
166	C₂²×D₁₃	—	8	2	no	—
167	C₂²×D₁₃	—	8	2	no	—
168	C₂×C₄×C₁₃	—	2	2	no	—
169	C₂×C₄×C₁₃	—	4	1	no	—
170	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
171	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
172	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
173	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
174	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
175	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
176	C₂×C₄×C₁₃	#135	1	2	yes	—
177	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
178	C₂²⋊D₁₃	—	4	4	no	—
179	C₂×Dic₁₃	—	4	1	no	—
180	C₂×Dic₁₃	—	4	1	no	—
181	C₂×Dic₁₃	—	4	1	no	—
182	C₂×Dic₁₃	—	4	2	no	—
183	C₂×Dic₁₃	—	8	2	no	—
184	D₅₂	—	2	2	no	—
185	D₅₂	—	2	4	no	—
186	D₅₂	—	4	2	no	—
187	D₅₂	—	4	1	no	—
188	D₅₂	—	4	4	no	—
189	C₄×D₁₃	—	4	4	no	—
190	C₄×D₁₃	—	8	2	no	—
191	C₄×D₁₃	—	8	4	no	—
192	C₄×D₁₃	—	8	2	no	—
193	C₄×D₁₃	—	8	4	no	—
194	Dic₂₆	—	2	2	no	—
195	Dic₂₆	—	4	1	no	—
196	C₈×C₁₃	—	2	1	no	—
197	C₈×C₁₃	—	2	1	no	—
198	C₈×C₁₃	C₄×D₄	1	2	yes	—
199	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
200	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
201	C₂×#135	—	13	1	no	—
202	C₂²×D₈	—	13	1	no	—
203	C₄×#41	—	26	1	no	—
204	C₂×C₄×D₄	—	26	1	no	—
205	#509	—	13	8	no	—
206	C₂×SD₃₂	—	13	2	no	—
207	C₂×D₁₆	—	13	2	no	—
208	C₂×M₃₂	C₂×D₁₃	1	1	yes	characteristic
209	C₂×M₃₂	C₂×D₁₃	1	1	yes	characteristic
210	C₄×Q₁₆	—	13	1	no	—
211	C₄×Q₁₆	—	13	1	no	—
212	C₄×SD₁₆	—	26	1	no	—
213	C₄×SD₁₆	—	26	1	no	—
214	C₄×D₈	—	13	2	no	—
215	C₄×D₈	—	13	2	no	—
216	C₄×D₈	—	13	1	no	—
217	C₄×D₈	—	13	1	no	—
218	C₄×D₈	—	26	1	no	—
219	C₄×D₈	—	26	1	no	—
220	#427	—	13	1	no	—
221	C₂×#107	—	13	1	no	—
222	#416	—	26	1	no	—
223	C₂×#102	—	26	1	no	—
224	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
225	#367	—	13	2	no	—
226	#366	—	13	2	no	—
227	#358	—	13	2	no	—
228	#357	—	13	2	no	—
229	#357	—	13	2	no	—
230	#357	—	13	2	no	—
231	#346	C₂×D₁₃	1	2	yes	complemented
232	C₄×C₁₆	C₂×D₁₃	1	2	yes	complemented
233	C₂²×C₁₃	—	2	1	no	—
234	C₂²×C₁₃	—	2	1	no	—
235	C₂²×C₁₃	C₄×D₈	1	2	yes	—
236	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
237	C₂×D₁₃	—	4	2	no	—
238	C₂×D₁₃	—	4	4	no	—
239	C₂×D₁₃	—	8	8	no	—
240	C₂×D₁₃	—	8	2	no	—
241	C₂×D₁₃	—	8	1	no	—
242	C₂×D₁₃	—	8	1	no	—
243	C₂×D₁₃	—	8	2	no	—
244	C₄×C₁₃	—	2	1	no	—
245	C₄×C₁₃	—	2	1	no	—
246	C₄×C₁₃	—	2	1	no	—
247	C₄×C₁₃	C₄×D₈	1	2	yes	—
248	C₄×C₁₃	#509	1	2	yes	complemented
249	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
250	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
251	Dic₁₃	—	4	2	no	—
252	Dic₁₃	—	8	2	no	—
253	Dic₁₃	—	8	1	no	—
254	Dic₁₃	—	8	1	no	—
255	C₂×#41	—	26	1	no	—
256	C₂²×D₄	—	26	1	no	—
257	C₂³×C₄	—	52	1	no	—
258	#135	—	13	4	no	—
259	#135	—	26	2	no	—
260	C₂×Q₁₆	—	13	1	no	—
261	C₂×SD₁₆	—	26	1	no	—
262	C₂×D₈	—	13	4	no	—
263	C₂×D₈	—	13	2	no	—
264	C₂×D₈	—	13	1	no	—
265	C₂×D₈	—	26	1	no	—
266	C₂×D₈	—	26	2	no	—
267	C₂²×C₈	D₅₂	1	1	yes	characteristic
268	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
269	C₄×Q₈	—	26	1	no	—
270	C₄×Q₈	—	26	1	no	—
271	C₄×D₄	—	26	2	no	—
272	C₄×D₄	—	26	2	no	—
273	C₄×D₄	—	26	1	no	—
274	C₄×D₄	—	26	1	no	—
275	C₄×D₄	—	52	1	no	—
276	C₄×D₄	—	52	1	no	—
277	C₄×D₄	—	52	1	no	—
278	C₄×D₄	—	52	1	no	—
279	#117	—	26	1	no	—
280	#117	—	52	1	no	—
281	C₂×C₄⋊C₄	—	26	1	no	—
282	C₂×C₂²⋊C₄	—	52	1	no	—
283	C₂×C₄²	—	52	1	no	—
284	C₂×C₄²	D₅₂	1	1	yes	characteristic
285	SD₃₂	—	13	8	no	—
286	D₁₆	—	13	8	no	—
287	M₃₂	—	2	2	no	—
288	M₃₂	C₄×D₁₃	1	4	yes	complemented
289	C₂×C₁₆	C₂²×D₁₃	1	2	yes	—
290	C₂×C₁₆	C₂²×D₁₃	1	2	yes	—
291	#107	—	13	1	no	—
292	#107	—	13	1	no	—
293	#107	—	13	2	no	—
294	#107	—	26	1	no	—
295	#106	—	26	1	no	—
296	#103	—	26	1	no	—
297	#103	—	26	1	no	—
298	#102	—	26	2	no	—
299	#102	—	26	2	no	—
300	#102	—	26	1	no	—
301	#102	—	26	1	no	—
302	C₄×C₈	D₅₂	1	1	yes	characteristic
303	C₄×C₈	D₅₂	1	1	yes	characteristic
304	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
305	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
306	C₂×C₁₃	—	2	2	no	—
307	C₂×C₁₃	C₂×C₄×D₈	1	1	yes	characteristic
308	C₂×C₁₃	C₂×#509	1	1	yes	characteristic
309	C₂×C₁₃	#3414	1	1	yes	characteristic
310	D₁₃	—	8	2	no	—
311	D₁₃	—	8	4	no	—
312	C₂⁴	—	52	1	no	—
313	#41	—	26	4	no	—
314	#41	—	52	2	no	—
315	C₂×Q₈	—	26	1	no	—
316	C₂×D₄	—	26	4	no	—
317	C₂×D₄	—	26	2	no	—
318	C₂×D₄	—	26	1	no	—
319	C₂×D₄	—	52	1	no	—
320	C₂×D₄	—	52	1	no	—
321	C₂×D₄	—	52	2	no	—
322	C₂²×C₄	—	52	1	no	—
323	C₂²×C₄	—	52	1	no	—
324	C₂²×C₄	—	52	1	no	—
325	C₂²×C₄	—	52	2	no	—
326	C₂²×C₄	—	52	1	no	—
327	C₂²×C₄	—	52	2	no	—
328	C₂²×C₄	—	104	4	no	—
329	C₂²×C₄	D₁₀₄	1	1	yes	characteristic
330	C₂²×C₄	D₁₀₄	1	1	yes	characteristic
331	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
332	Q₁₆	—	13	2	no	—
333	Q₁₆	—	26	1	no	—
334	SD₁₆	—	26	4	no	—
335	D₈	—	13	2	no	—
336	D₈	—	13	4	no	—
337	D₈	—	26	4	no	—
338	D₈	—	26	2	no	—
339	D₈	—	26	1	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
342	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
343	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
344	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
345	C₂×C₈	#6127	1	2	yes	—
346	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
347	C₄⋊C₄	—	26	2	no	—
348	C₄⋊C₄	—	26	1	no	—
349	C₄⋊C₄	—	26	1	no	—
350	C₄⋊C₄	—	52	1	no	—
351	C₄⋊C₄	—	52	1	no	—
352	C₄⋊C₄	—	52	1	no	—
353	C₂²⋊C₄	—	52	1	no	—
354	C₂²⋊C₄	—	52	2	no	—
355	C₂²⋊C₄	—	52	2	no	—
356	C₂²⋊C₄	—	52	1	no	—
357	C₂²⋊C₄	—	52	1	no	—
358	C₄²	—	52	1	no	—
359	C₄²	—	52	1	no	—
360	C₄²	—	52	1	no	—
361	C₄²	D₁₀₄	1	1	yes	characteristic
362	C₄²	D₁₀₄	1	1	yes	characteristic
363	C₄²	C₂×D₅₂	1	1	yes	characteristic
364	C₄²	C₂×D₅₂	1	1	yes	characteristic
365	C₁₆	—	2	2	no	—
366	C₁₆	C₂×C₄×D₁₃	1	4	yes	complemented
367	C₁₃	C₄×#509	1	1	yes	characteristic, complemented, Sylow
368	C₂³	—	52	1	no	—
369	C₂³	—	52	2	no	—
370	C₂³	—	52	4	no	—
371	C₂³	—	104	2	no	—
372	C₂³	—	104	2	no	—
373	C₂³	C₂×D₁₀₄	1	1	yes	characteristic
374	Q₈	—	26	2	no	—
375	Q₈	—	52	1	no	—
376	D₄	—	26	4	no	—
377	D₄	—	26	2	no	—
378	D₄	—	52	4	no	—
379	D₄	—	52	2	no	—
380	D₄	—	52	1	no	—
381	D₄	—	52	4	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	52	1	no	—
385	C₂×C₄	—	52	4	no	—
386	C₂×C₄	—	52	1	no	—
387	C₂×C₄	—	52	1	no	—
388	C₂×C₄	—	52	2	no	—
389	C₂×C₄	—	104	2	no	—
390	C₂×C₄	—	104	4	no	—
391	C₂×C₄	—	104	2	no	—
392	C₂×C₄	—	104	2	no	—
393	C₂×C₄	—	104	4	no	—
394	C₂×C₄	C₄×D₅₂	1	2	yes	—
395	C₂×C₄	C₂×D₁₀₄	1	1	yes	characteristic
396	C₂×C₄	C₂×D₁₀₄	1	1	yes	characteristic
397	C₂×C₄	C₂×D₁₀₄	1	1	yes	characteristic
398	C₂×C₄	C₂×D₁₀₄	1	1	yes	characteristic
399	C₂×C₄	C₂×D₁₀₄	1	1	yes	characteristic
400	C₂×C₄	#88158	1	2	yes	—
401	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
402	C₈	—	2	1	no	—
403	C₈	—	2	1	no	—
404	C₈	C₄×D₅₂	1	2	yes	—
405	C₈	C₂²×C₄×D₁₃	1	1	yes	characteristic
406	C₈	C₂×#6127	1	1	yes	characteristic
407	C₂²	—	2	1	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	52	2	no	—
410	C₂²	—	52	4	no	—
411	C₂²	—	104	8	no	—
412	C₂²	—	104	2	no	—
413	C₂²	—	104	1	no	—
414	C₂²	—	104	1	no	—
415	C₂²	—	104	2	no	—
416	C₂²	C₄×D₁₀₄	1	2	yes	—
417	C₂²	C₂²×D₁₀₄	1	1	yes	characteristic
418	C₄	—	2	1	no	—
419	C₄	—	2	1	no	—
420	C₄	—	2	1	no	—
421	C₄	—	52	2	no	—
422	C₄	—	104	1	no	—
423	C₄	—	104	2	no	—
424	C₄	—	104	1	no	—
425	C₄	C₄×D₁₀₄	1	2	yes	—
426	C₄	#11718569	1	2	yes	direct product factor
427	C₄	C₂×C₄×D₅₂	1	1	yes	characteristic
428	C₄	C₂×#88158	1	1	yes	characteristic
429	C₂	—	2	2	no	—
430	C₂	—	104	4	no	—
431	C₂	—	104	2	no	—
432	C₂	C₂×C₄×D₁₀₄	1	1	yes	characteristic
433	C₂	C₂×#11718569	1	1	yes	characteristic
434	C₂	#13127972	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₁₀₄
commutator	C₈×C₁₃	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₄×C₁₃×M₃₂	C₂
socle	C₂²×C₁₃	C₂²×D₈
prime radical	C₂×#11718569	C₂
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	C₄×M₃₂	D₁₃
hypocenter	C₁₃	C₄×#509
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₄×M₃₂

Complements

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

N	H ≅ G/N	type
2. C₄×#88158	C₂	semidirect
3. C₂×C₄×D₁₀₄	C₂	semidirect
4. #13116713	C₂	semidirect
5. #13116702	C₂	semidirect
6. C₄×#88040	C₂	semidirect
7. C₄×D₂₀₈	C₂	semidirect
8. #13116624	C₂	semidirect
9. #13116553	C₂	semidirect
10. #13116549	C₂	semidirect
11. C₄×C₁₃×M₃₂	C₂	semidirect
23. #11718569	C₄	direct (N × H)
26. C₄×Dic₅₂	C₂²	semidirect
27. C₄×Dic₅₂	C₂²	semidirect
32. C₄×D₁₀₄	C₂²	semidirect
33. C₄×D₁₀₄	C₂²	semidirect
36. C₁₃×#346	C₂²	semidirect
37. C₄×C₁₃×C₁₆	C₂²	semidirect
40. #11718101	C₂²	semidirect
41. #11718097	C₂²	semidirect
42. #11718096	C₂²	semidirect
43. #11718095	C₂²	semidirect
57. #88158	C₂×C₄	semidirect
60. C₂×D₁₀₄	C₂×C₄	semidirect
75. C₁₃×M₃₂	C₂×C₄	semidirect
93. #88040	C₂×C₄	semidirect
94. D₂₀₈	C₂×C₄	semidirect
142. Dic₅₂	C₂²×C₄	semidirect
147. D₁₀₄	C₂²×C₄	semidirect
150. C₁₃×C₁₆	C₂²×C₄	semidirect
161. C₄×M₃₂	D₁₃	semidirect
231. #346	C₂×D₁₃	semidirect
232. C₄×C₁₆	C₂×D₁₃	semidirect
248. C₄×C₁₃	#509	semidirect
288. M₃₂	C₄×D₁₃	semidirect
366. C₁₆	C₂×C₄×D₁₃	semidirect
367. C₁₃	C₄×#509	semidirect
426. C₄	#11718569	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×#11718569	2
C₄×#88158	2
C₂×C₄×D₁₀₄	2
#13116713	2
#13116702	2
C₄×#88040	2
C₄×D₂₀₈	2
#13116624	2
#13116553	2
#13116549	2
C₄×C₁₃×M₃₂	2
C₄×#509	13

Subgroups — C4×#11718569 #16016241

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11718569 #16016241