Subgroups — C₂×#13113932 #15838648

Order 3328.

1030 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718749	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718688	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718688	C₂	1	1	yes	maximal, characteristic
4	#13113932	C₂	1	8	yes	maximal, direct product factor
5	C₂×#11718139	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Q₈⋊#1055	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×Q₈⋊#1055	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#557	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#557	—	2	2	no	—
10	C₁₃×#557	—	2	2	no	—
11	C₁₃×#557	—	2	2	no	—
12	C₁₃×#557	C₂²	1	4	yes	complemented
13	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
14	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#125	—	2	2	no	—
16	C₂×C₁₃×#125	—	2	1	no	—
17	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
18	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
19	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₂²×#6106	—	2	1	no	—
22	C₂²×#6106	—	2	1	no	—
23	C₂×#88128	C₂²	1	1	yes	characteristic
24	#11718749	—	2	2	no	—
25	#11718749	C₂²	1	4	yes	—
26	#11718688	—	2	2	no	—
27	#11718688	—	2	2	no	—
28	#11718688	C₂²	1	4	yes	—
29	#11718688	C₂²	1	4	yes	—
30	C₂×#88049	—	2	2	no	—
31	C₂×#88049	—	2	1	no	—
32	C₂×#88049	—	2	1	no	—
33	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
35	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
36	#11718139	C₂²	1	4	yes	complemented
37	Q₈⋊#1055	C₂²	1	4	yes	complemented
38	Q₈⋊#1055	C₂²	1	4	yes	complemented
39	C₂²×Q₈×C₁₃	—	2	1	no	—
40	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
41	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
42	C₂²×D₅₂	—	2	1	no	—
43	C₂²×D₅₂	—	2	1	no	—
44	C₂²×D₅₂	—	2	1	no	—
45	C₁₃×C₄⋊Q₈	—	2	4	no	—
46	C₁₃×C₄⋊Q₈	—	2	4	no	—
47	C₁₃×C₄⋊Q₈	—	2	1	no	—
48	C₁₃×C₄⋊Q₈	—	2	1	no	—
49	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
50	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
51	C₁₃×#125	—	2	8	no	—
52	C₁₃×#125	—	2	4	no	—
53	C₁₃×#125	—	2	8	no	—
54	C₁₃×#125	—	2	4	no	—
55	C₄×Q₈×C₁₃	—	2	4	no	—
56	C₄×Q₈×C₁₃	—	2	4	no	—
57	C₄×Q₈×C₁₃	—	2	4	no	—
58	C₄×Q₈×C₁₃	—	2	4	no	—
59	C₄×Q₈×C₁₃	—	2	1	no	—
60	C₄×Q₈×C₁₃	—	2	1	no	—
61	C₄×Q₈×C₁₃	—	2	1	no	—
62	C₄×Q₈×C₁₃	—	2	1	no	—
63	C₄×Q₈×C₁₃	D₄	1	2	yes	—
64	C₄×Q₈×C₁₃	D₄	1	2	yes	—
65	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
66	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
67	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
68	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
69	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
70	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
71	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
72	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
73	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
74	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
75	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
76	C₂×C₄²×C₁₃	—	2	2	no	—
77	C₂×C₄²×C₁₃	—	2	1	no	—
78	C₂×C₄²×C₁₃	—	2	1	no	—
79	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
80	C₂×#6106	—	2	4	no	—
81	C₂×#6106	—	2	4	no	—
82	C₂×#6106	—	4	4	no	—
83	C₂×#6106	—	4	4	no	—
84	C₂²×#1055	—	2	1	no	—
85	C₂²×#1055	—	2	1	no	—
86	C₂²×#1055	—	2	1	no	—
87	#88128	—	2	1	no	—
88	#88128	—	2	1	no	—
89	#88128	—	2	1	no	—
90	#88128	C₂³	1	2	yes	—
91	#88049	—	2	4	no	—
92	#88049	—	2	4	no	—
93	#88049	—	2	8	no	—
94	C₄⋊#1055	—	2	1	no	—
95	C₄⋊#1055	—	2	1	no	—
96	C₄⋊#1055	C₂³	1	2	yes	—
97	C₄⋊#1055	C₂³	1	2	yes	—
98	C₄×#1055	—	2	1	no	—
99	C₄×#1055	C₂³	1	2	yes	—
100	C₂×#1626	—	13	1	no	maximal, Sylow
101	C₂³×D₁₃	—	4	1	no	—
102	C₂×Q₈×C₁₃	—	2	1	no	—
103	C₂×Q₈×C₁₃	—	2	1	no	—
104	C₂×Q₈×C₁₃	—	2	2	no	—
105	C₂×Q₈×C₁₃	—	2	2	no	—
106	C₂×Q₈×C₁₃	—	2	2	no	—
107	C₂×Q₈×C₁₃	—	2	2	no	—
108	C₂×Q₈×C₁₃	—	2	2	no	—
109	C₂×Q₈×C₁₃	—	4	2	no	—
110	C₂×Q₈×C₁₃	—	4	2	no	—
111	C₂×Q₈×C₁₃	SD₁₆	1	4	yes	complemented
112	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
113	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₁₃	—	2	1	no	—
115	C₂²×C₄×C₁₃	—	2	1	no	—
116	C₂²×C₄×C₁₃	—	2	1	no	—
117	C₂²×C₄×C₁₃	—	2	1	no	—
118	C₂²×C₄×C₁₃	—	2	2	no	—
119	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
122	C₂×D₅₂	—	2	2	no	—
123	C₂×D₅₂	—	2	2	no	—
124	C₂×D₅₂	—	2	2	no	—
125	C₂×D₅₂	—	4	4	no	—
126	C₂×D₅₂	—	4	2	no	—
127	C₂×D₅₂	—	4	2	no	—
128	C₂×D₅₂	—	4	2	no	—
129	C₂×D₅₂	—	4	2	no	—
130	C₂×D₅₂	—	4	1	no	—
131	C₂×D₅₂	—	4	1	no	—
132	C₂×D₅₂	—	4	1	no	—
133	C₁₃×C₄⋊C₄	—	2	8	no	—
134	C₁₃×C₄⋊C₄	—	2	8	no	—
135	C₁₃×C₄⋊C₄	—	2	8	no	—
136	C₁₃×C₄⋊C₄	—	2	2	no	—
137	C₁₃×C₄⋊C₄	—	2	2	no	—
138	C₁₃×C₄⋊C₄	—	2	2	no	—
139	C₁₃×C₄⋊C₄	—	2	1	no	—
140	C₁₃×C₄⋊C₄	—	2	1	no	—
141	C₁₃×C₄⋊C₄	—	2	2	no	—
142	C₁₃×C₄⋊C₄	—	2	2	no	—
143	C₁₃×C₄⋊C₄	—	2	2	no	—
144	C₁₃×C₄⋊C₄	—	2	2	no	—
145	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
146	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
147	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
148	C₄²×C₁₃	—	2	8	no	—
149	C₄²×C₁₃	—	2	2	no	—
150	C₄²×C₁₃	—	2	2	no	—
151	C₄²×C₁₃	—	2	2	no	—
152	C₄²×C₁₃	—	2	2	no	—
153	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
154	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
156	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
157	#6106	—	4	8	no	—
158	#6106	—	4	8	no	—
159	C₂×#1055	—	2	2	no	—
160	C₂×#1055	—	2	2	no	—
161	C₂×#1055	—	2	2	no	—
162	C₂×#1055	—	4	2	no	—
163	C₂×#1055	—	4	2	no	—
164	C₂×#1055	—	4	2	no	—
165	C₂×#557	D₁₃	1	1	yes	characteristic, complemented
166	C₂×#486	—	13	1	no	—
167	C₂×#460	—	13	1	no	—
168	C₂×#460	—	13	1	no	—
169	#1626	—	13	8	no	—
170	C₂×#332	—	13	1	no	—
171	C₂×Q₈⋊C₈	—	13	1	no	—
172	C₂×Q₈⋊C₈	—	13	1	no	—
173	C₂³×C₁₃	#120	1	1	yes	characteristic
174	C₂²×D₁₃	—	4	2	no	—
175	C₂²×D₁₃	—	8	2	no	—
176	C₂²×D₁₃	—	8	2	no	—
177	C₂²×D₁₃	—	8	2	no	—
178	Q₈×C₁₃	—	2	2	no	—
179	Q₈×C₁₃	—	2	4	no	—
180	Q₈×C₁₃	—	2	2	no	—
181	Q₈×C₁₃	—	2	2	no	—
182	Q₈×C₁₃	—	4	2	no	—
183	Q₈×C₁₃	—	4	2	no	—
184	Q₈×C₁₃	—	4	2	no	—
185	Q₈×C₁₃	—	4	4	no	—
186	Q₈×C₁₃	C₂×SD₁₆	1	4	yes	complemented
187	C₂×C₄×C₁₃	—	2	2	no	—
188	C₂×C₄×C₁₃	—	2	4	no	—
189	C₂×C₄×C₁₃	—	2	2	no	—
190	C₂×C₄×C₁₃	—	2	2	no	—
191	C₂×C₄×C₁₃	—	2	2	no	—
192	C₂×C₄×C₁₃	—	2	2	no	—
193	C₂×C₄×C₁₃	—	2	4	no	—
194	C₂×C₄×C₁₃	—	4	2	no	—
195	C₂×C₄×C₁₃	—	4	4	no	—
196	C₂×C₄×C₁₃	—	4	2	no	—
197	C₂×C₄×C₁₃	—	4	2	no	—
198	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
199	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
200	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
201	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
202	C₂×C₄×C₁₃	#135	1	2	yes	—
203	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
204	C₂×C₄×C₁₃	#137	1	2	yes	—
205	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
208	D₅₂	—	4	4	no	—
209	D₅₂	—	4	2	no	—
210	D₅₂	—	4	2	no	—
211	D₅₂	—	4	2	no	—
212	D₅₂	—	4	2	no	—
213	D₅₂	—	8	2	no	—
214	D₅₂	—	8	2	no	—
215	D₅₂	—	8	2	no	—
216	#1055	—	4	2	no	—
217	#1055	—	4	2	no	—
218	#1055	—	4	2	no	—
219	C₂²×SD₁₆	—	26	1	no	—
220	C₂²×SD₁₆	—	26	1	no	—
221	#557	—	2	2	no	—
222	#557	—	2	2	no	—
223	#557	—	2	2	no	—
224	#557	C₂×D₁₃	1	4	yes	complemented
225	C₂×C₄⋊Q₈	—	2	1	no	—
226	C₂×C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
227	C₂×#127	—	13	1	no	—
228	C₂×#125	—	2	2	no	—
229	C₂×#125	—	2	1	no	—
230	C₂×C₄×Q₈	—	2	1	no	—
231	C₂×C₄×Q₈	—	2	1	no	—
232	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic
233	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic
234	#486	—	13	4	no	—
235	#486	—	26	2	no	—
236	#460	—	13	4	no	—
237	#460	—	13	4	no	—
238	#460	—	26	2	no	—
239	#460	—	26	2	no	—
240	C₂×C₄⋊C₈	—	13	1	no	—
241	C₂×C₄⋊C₈	—	13	1	no	—
242	C₂×#102	—	26	2	no	—
243	C₂×#102	—	26	1	no	—
244	C₂×#102	—	26	1	no	—
245	C₂×C₄×C₈	—	13	1	no	—
246	#332	—	13	4	no	—
247	Q₈⋊C₈	—	13	4	no	—
248	Q₈⋊C₈	—	13	4	no	—
249	C₂²×C₁₃	#448	1	2	yes	—
250	C₂²×C₁₃	#449	1	2	yes	—
251	C₂²×C₁₃	#454	1	2	yes	—
252	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
253	C₂×D₁₃	—	8	2	no	—
254	C₂×D₁₃	—	8	2	no	—
255	C₂×D₁₃	—	8	2	no	—
256	C₂×D₁₃	—	16	4	no	—
257	C₄×C₁₃	—	2	4	no	—
258	C₄×C₁₃	—	2	1	no	—
259	C₄×C₁₃	—	2	1	no	—
260	C₄×C₁₃	—	4	2	no	—
261	C₄×C₁₃	—	4	4	no	—
262	C₄×C₁₃	—	4	2	no	—
263	C₄×C₁₃	—	4	2	no	—
264	C₄×C₁₃	#448	1	2	yes	—
265	C₄×C₁₃	#449	1	2	yes	—
266	C₄×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
267	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
268	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
269	C₄×C₁₃	C₂×#137	1	1	yes	characteristic
270	C₂²×Q₈	—	2	1	no	—
271	C₂²×Q₈	C₂²⋊D₁₃	1	1	yes	characteristic
272	C₂²×Q₈	C₂²⋊D₁₃	1	1	yes	characteristic
273	C₂²×D₄	—	26	1	no	—
274	C₂²×D₄	—	26	1	no	—
275	C₂²×D₄	—	26	1	no	—
276	C₂×SD₁₆	—	26	4	no	—
277	C₂×SD₁₆	—	26	4	no	—
278	C₂×SD₁₆	—	52	4	no	—
279	C₂×SD₁₆	—	52	4	no	—
280	C₂²×C₈	—	26	1	no	—
281	C₂²×C₈	—	26	1	no	—
282	C₂²×C₈	—	26	1	no	—
283	C₄⋊Q₈	—	2	4	no	—
284	C₄⋊Q₈	—	2	4	no	—
285	C₄⋊Q₈	—	2	1	no	—
286	C₄⋊Q₈	—	2	1	no	—
287	C₄⋊Q₈	C₂²⋊D₁₃	1	2	yes	—
288	C₄⋊Q₈	C₂²×D₁₃	1	2	yes	—
289	#127	—	13	2	no	—
290	#127	—	26	1	no	—
291	#127	—	26	1	no	—
292	#127	—	26	1	no	—
293	#125	—	2	8	no	—
294	#125	—	2	4	no	—
295	#125	—	2	8	no	—
296	#125	—	2	4	no	—
297	C₄×Q₈	—	2	4	no	—
298	C₄×Q₈	—	2	4	no	—
299	C₄×Q₈	—	2	4	no	—
300	C₄×Q₈	—	2	4	no	—
301	C₄×Q₈	—	2	1	no	—
302	C₄×Q₈	—	2	1	no	—
303	C₄×Q₈	—	2	1	no	—
304	C₄×Q₈	—	2	1	no	—
305	C₄×Q₈	C₂²⋊D₁₃	1	2	yes	—
306	C₄×Q₈	C₂²⋊D₁₃	1	2	yes	—
307	C₄×Q₈	C₂²×D₁₃	1	2	yes	—
308	C₄×Q₈	C₂²×D₁₃	1	2	yes	—
309	C₂×C₄⋊C₄	—	2	2	no	—
310	C₂×C₄⋊C₄	—	2	2	no	—
311	C₂×C₄⋊C₄	—	2	2	no	—
312	C₂×C₄⋊C₄	—	2	1	no	—
313	C₂×C₄⋊C₄	—	2	1	no	—
314	C₂×C₄⋊C₄	—	2	1	no	—
315	C₂×C₄⋊C₄	C₂²⋊D₁₃	1	1	yes	characteristic
316	C₂×C₄⋊C₄	C₂²⋊D₁₃	1	1	yes	characteristic
317	C₂×C₄⋊C₄	C₂²⋊D₁₃	1	2	yes	—
318	C₂×C₄²	—	2	2	no	—
319	C₂×C₄²	—	2	1	no	—
320	C₂×C₄²	—	2	1	no	—
321	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
322	C₄⋊C₈	—	13	2	no	—
323	C₄⋊C₈	—	13	2	no	—
324	C₄⋊C₈	—	26	1	no	—
325	C₄⋊C₈	—	26	1	no	—
326	#102	—	26	4	no	—
327	#102	—	26	4	no	—
328	#102	—	26	8	no	—
329	C₄×C₈	—	13	2	no	—
330	C₄×C₈	—	26	1	no	—
331	C₂×C₁₃	#1626	1	4	yes	complemented
332	C₂×C₁₃	C₂×#448	1	1	yes	characteristic
333	C₂×C₁₃	C₂×#449	1	1	yes	characteristic
334	C₂×C₁₃	C₂×#454	1	1	yes	characteristic
335	D₁₃	—	16	2	no	—
336	C₂⁴	—	52	1	no	—
337	C₂×Q₈	—	2	2	no	—
338	C₂×Q₈	—	2	1	no	—
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	4	2	no	—
345	C₂×Q₈	—	4	2	no	—
346	C₂×Q₈	#6106	1	4	yes	complemented
347	C₂×Q₈	C₂×C₂²⋊D₁₃	1	2	yes	—
348	C₂×Q₈	C₂×C₂²⋊D₁₃	1	2	yes	—
349	C₂×D₄	—	26	2	no	—
350	C₂×D₄	—	26	2	no	—
351	C₂×D₄	—	26	2	no	—
352	C₂×D₄	—	52	4	no	—
353	C₂×D₄	—	52	2	no	—
354	C₂×D₄	—	52	2	no	—
355	C₂×D₄	—	52	2	no	—
356	C₂×D₄	—	52	2	no	—
357	C₂×D₄	—	52	1	no	—
358	C₂×D₄	—	52	1	no	—
359	C₂×D₄	—	52	1	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
366	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
367	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
368	SD₁₆	—	52	8	no	—
369	SD₁₆	—	52	8	no	—
370	C₂×C₈	—	26	2	no	—
371	C₂×C₈	—	26	2	no	—
372	C₂×C₈	—	26	2	no	—
373	C₂×C₈	—	52	2	no	—
374	C₂×C₈	—	52	2	no	—
375	C₂×C₈	—	52	2	no	—
376	C₄⋊C₄	—	2	8	no	—
377	C₄⋊C₄	—	2	8	no	—
378	C₄⋊C₄	—	2	8	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	C₂×C₂²⋊D₁₃	1	2	yes	—
389	C₄⋊C₄	C₂×C₂²⋊D₁₃	1	2	yes	—
390	C₄⋊C₄	C₂×C₂²⋊D₁₃	1	4	yes	—
391	C₄²	—	2	8	no	—
392	C₄²	—	2	2	no	—
393	C₄²	—	2	2	no	—
394	C₄²	—	2	2	no	—
395	C₄²	—	2	2	no	—
396	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
397	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
398	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
399	C₄²	C₂³×D₁₃	1	1	yes	characteristic
400	C₁₃	C₂×#1626	1	1	yes	characteristic, complemented, Sylow
401	C₂³	—	52	2	no	—
402	C₂³	—	104	2	no	—
403	C₂³	—	104	2	no	—
404	C₂³	—	104	2	no	—
405	C₂³	#88207	1	1	yes	characteristic
406	Q₈	—	2	2	no	—
407	Q₈	—	2	4	no	—
408	Q₈	—	2	2	no	—
409	Q₈	—	2	2	no	—
410	Q₈	—	4	2	no	—
411	Q₈	—	4	2	no	—
412	Q₈	—	4	2	no	—
413	Q₈	—	4	4	no	—
414	Q₈	C₂×#6106	1	4	yes	complemented
415	D₄	—	52	4	no	—
416	D₄	—	52	2	no	—
417	D₄	—	52	2	no	—
418	D₄	—	52	2	no	—
419	D₄	—	52	2	no	—
420	D₄	—	104	2	no	—
421	D₄	—	104	2	no	—
422	D₄	—	104	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	4	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	4	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	C₂×#6106	1	2	yes	—
435	C₂×C₄	#88196	1	2	yes	—
436	C₂×C₄	#88203	1	2	yes	—
437	C₂×C₄	#88204	1	2	yes	—
438	C₂×C₄	#88207	1	1	yes	characteristic
439	C₂×C₄	#88207	1	1	yes	characteristic
440	C₂×C₄	#88207	1	1	yes	characteristic
441	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
442	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
443	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
444	C₈	—	52	2	no	—
445	C₈	—	52	2	no	—
446	C₈	—	52	2	no	—
447	C₂²	—	104	2	no	—
448	C₂²	—	104	2	no	—
449	C₂²	—	104	2	no	—
450	C₂²	—	208	4	no	—
451	C₂²	#11718888	1	2	yes	—
452	C₂²	#11718899	1	2	yes	—
453	C₂²	#11718906	1	2	yes	—
454	C₂²	C₂×#88207	1	1	yes	characteristic
455	C₄	—	2	1	no	—
456	C₄	—	2	1	no	—
457	C₄	—	2	4	no	—
458	C₄	—	4	2	no	—
459	C₄	—	4	2	no	—
460	C₄	—	4	2	no	—
461	C₄	—	4	4	no	—
462	C₄	#11718888	1	2	yes	—
463	C₄	#11718899	1	2	yes	—
464	C₄	C₂²×#6106	1	1	yes	characteristic
465	C₄	C₂×#88196	1	1	yes	characteristic
466	C₄	C₂×#88203	1	1	yes	characteristic
467	C₄	C₂×#88204	1	1	yes	characteristic
468	C₂	—	208	2	no	—
469	C₂	#13113932	1	4	yes	direct product factor
470	C₂	C₂×#11718888	1	1	yes	characteristic
471	C₂	C₂×#11718899	1	1	yes	characteristic
472	C₂	C₂×#11718906	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#88207
commutator, cosocle	C₄²×C₁₃	C₂⁴
Frattini	C₄²	C₂³×D₁₃
Fitting	C₂×C₁₃×#557	C₂
socle	C₂³×C₁₃	#120
prime radical	C₂×#88128	C₂²
hypercenter	C₂×#557	D₁₃
hypocenter	C₁₃	C₂×#1626
LCS	G ▷ C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#557

Complements

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

N	H ≅ G/N	type
4. #13113932	C₂	direct (N × H)
5. C₂×#11718139	C₂	semidirect
6. C₂×Q₈⋊#1055	C₂	semidirect
7. C₂×Q₈⋊#1055	C₂	semidirect
8. C₂×C₁₃×#557	C₂	semidirect
12. C₁₃×#557	C₂²	semidirect
36. #11718139	C₂²	semidirect
37. Q₈⋊#1055	C₂²	semidirect
38. Q₈⋊#1055	C₂²	semidirect
111. C₂×Q₈×C₁₃	SD₁₆	semidirect
165. C₂×#557	D₁₃	semidirect
186. Q₈×C₁₃	C₂×SD₁₆	semidirect
224. #557	C₂×D₁₃	semidirect
331. C₂×C₁₃	#1626	semidirect
346. C₂×Q₈	#6106	semidirect
400. C₁₃	C₂×#1626	semidirect
414. Q₈	C₂×#6106	semidirect
469. C₂	#13113932	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×#11718749	2
C₂×#11718688	2
#13113932	2
C₂×#11718139	2
C₂×Q₈⋊#1055	2
C₂×C₁₃×#557	2
C₂×#1626	13

Subgroups — C2×#13113932 #15838648

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13113932 #15838648