Subgroups — #15846807

Order 3328.

786 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718746	C₂	1	1	yes	maximal, characteristic, complemented
2	#13124316	C₂	1	1	yes	maximal, characteristic
3	#41×#1055	C₂	1	1	yes	maximal, characteristic, complemented
4	#13114186	C₂	1	4	yes	maximal, complemented
5	#13114179	C₂	1	4	yes	maximal, complemented
6	#13113591	C₂	1	1	yes	maximal, characteristic, complemented
7	#13113521	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113505	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3079	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
11	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
12	C₂×#88203	—	2	1	no	—
13	C₂²×#6106	—	2	2	no	—
14	C₂×#88128	C₂²	1	1	yes	characteristic
15	C₁₃×#477	—	2	1	no	—
16	C₁₃×#476	—	2	1	no	—
17	C₁₃×#475	C₂²	1	2	yes	complemented
18	C₁₃×#474	C₂²	1	2	yes	complemented
19	C₁₃×#428	—	2	1	no	—
20	C₁₃×#423	C₂²	1	1	yes	characteristic
21	C₁₃×#417	—	2	1	no	—
22	#11718746	—	2	1	no	—
23	#11718746	—	2	1	no	—
24	#11718746	C₂²	1	4	yes	—
25	#11718688	—	2	1	no	—
26	#11718688	C₂²	1	2	yes	—
27	Q₈×#1055	C₂²	1	2	yes	complemented
28	#11718676	—	2	1	no	—
29	#11718676	C₂²	1	2	yes	—
30	D₄×#1055	—	2	2	no	—
31	D₄×#1055	C₂²	1	2	yes	complemented
32	#11718662	—	2	1	no	—
33	#11718586	—	2	1	no	—
34	#11718586	C₂²	1	1	yes	characteristic
35	#11718585	C₂²	1	1	yes	characteristic
36	C₂×C₄×#1055	—	2	1	no	—
37	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
38	#11718139	C₂²	1	4	yes	complemented
39	#11718077	C₂²	1	4	yes	—
40	#11718072	C₂²	1	4	yes	complemented
41	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
42	C₂²×Q₈×C₁₃	—	2	1	no	—
43	C₂²×D₅₂	—	2	1	no	—
44	C₂²×D₅₂	—	2	1	no	—
45	C₂²×D₅₂	—	2	1	no	—
46	C₂×C₁₃×M₁₆	—	2	1	no	—
47	C₁₃×C₄⋊Q₈	—	2	1	no	—
48	C₁₃×C₄⋊Q₈	—	2	1	no	—
49	C₁₃×C₄⋊Q₈	—	2	1	no	—
50	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
51	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
52	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
53	C₄×D₄×C₁₃	—	2	1	no	—
54	C₄×D₄×C₁₃	—	2	1	no	—
55	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
56	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
57	C₁₃×#117	—	2	1	no	—
58	C₁₃×#117	D₄	1	1	yes	characteristic
59	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
61	C₂×C₄²×C₁₃	—	2	1	no	—
62	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
63	#88203	—	4	4	no	—
64	C₂×#6106	—	2	2	no	—
65	C₂×#6106	—	2	4	no	—
66	C₂×#6106	—	2	4	no	—
67	C₂×#6106	—	4	8	no	—
68	C₂×#6104	—	2	2	no	—
69	C₂×#6099	—	2	1	no	—
70	C₂²×#1055	—	2	2	no	—
71	C₂²×#1055	D₄	1	2	yes	—
72	#88128	—	2	1	no	—
73	#88128	—	2	1	no	—
74	#88128	—	2	1	no	—
75	#88128	C₂³	1	2	yes	—
76	C₁₃×#107	—	2	2	no	—
77	C₁₃×#106	—	2	2	no	—
78	C₁₃×C₄⋊C₈	—	2	1	no	—
79	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
80	C₁₃×#103	—	2	2	no	—
81	C₁₃×#102	—	2	2	no	—
82	C₂²⋊#1055	—	2	1	no	—
83	C₂²⋊#1055	—	2	2	no	—
84	#88049	—	2	2	no	—
85	#88049	—	2	2	no	—
86	C₄⋊#1055	—	2	1	no	—
87	C₄⋊#1055	—	2	2	no	—
88	C₄⋊#1055	C₂³	1	2	yes	—
89	C₄⋊#1055	C₂³	1	2	yes	—
90	C₄×#1055	—	2	1	no	—
91	C₄×#1055	—	2	2	no	—
92	C₄×#1055	D₄	1	1	yes	characteristic
93	C₄×#1055	D₄	1	1	yes	characteristic
94	C₄×#1055	C₂³	1	2	yes	—
95	#19266	—	13	1	no	maximal, Sylow
96	C₂³×D₁₃	—	4	1	no	—
97	C₁₃×#41	—	2	2	no	—
98	C₁₃×#41	SD₁₆	1	4	yes	complemented
99	C₂×Q₈×C₁₃	—	2	2	no	—
100	C₂×Q₈×C₁₃	—	4	4	no	—
101	C₂×Q₈×C₁₃	—	4	1	no	—
102	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
103	C₂×D₄×C₁₃	—	2	1	no	—
104	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	—	2	1	no	—
106	C₂²×C₄×C₁₃	—	2	1	no	—
107	C₂²×C₄×C₁₃	—	2	1	no	—
108	C₂²×C₄×C₁₃	—	4	1	no	—
109	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
112	C₂×D₅₂	—	2	2	no	—
113	C₂×D₅₂	—	2	2	no	—
114	C₂×D₅₂	—	2	2	no	—
115	C₂×D₅₂	—	4	4	no	—
116	C₂×D₅₂	—	4	2	no	—
117	C₂×D₅₂	—	4	2	no	—
118	C₂×D₅₂	—	4	1	no	—
119	C₂×D₅₂	—	4	1	no	—
120	C₂×D₅₂	—	4	1	no	—
121	C₂×D₅₂	—	8	2	no	—
122	C₁₃×M₁₆	—	4	2	no	—
123	C₂×C₈×C₁₃	—	2	2	no	—
124	C₁₃×C₄⋊C₄	—	2	1	no	—
125	C₁₃×C₄⋊C₄	—	2	1	no	—
126	C₁₃×C₄⋊C₄	—	2	2	no	—
127	C₁₃×C₄⋊C₄	—	2	2	no	—
128	C₁₃×C₄⋊C₄	—	4	1	no	—
129	C₁₃×C₄⋊C₄	—	4	1	no	—
130	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
131	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
132	C₁₃×C₂²⋊C₄	—	2	1	no	—
133	C₁₃×C₂²⋊C₄	—	2	1	no	—
134	C₁₃×C₂²⋊C₄	—	2	1	no	—
135	C₄²×C₁₃	—	2	1	no	—
136	C₄²×C₁₃	—	2	1	no	—
137	C₄²×C₁₃	—	2	1	no	—
138	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
139	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₁₃	#41	1	1	yes	characteristic
141	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
142	#6106	—	4	8	no	—
143	#6106	—	4	4	no	—
144	#6106	—	4	8	no	—
145	#6104	—	4	4	no	—
146	#6099	—	4	2	no	—
147	C₂×#1055	—	2	4	no	—
148	C₂×#1055	—	2	2	no	—
149	C₂×#1055	—	2	2	no	—
150	C₂×#1055	—	4	4	no	—
151	C₂×#1055	C₂×D₄	1	2	yes	—
152	C₂×#1055	C₂×D₄	1	2	yes	—
153	C₂×#492	—	13	1	no	—
154	#3079	D₁₃	1	1	yes	characteristic, complemented
155	#3038	—	13	1	no	—
156	C₈×#41	—	13	1	no	—
157	#1666	—	13	4	no	—
158	#1665	—	13	4	no	—
159	#1566	—	13	1	no	—
160	#1549	—	13	1	no	—
161	#1545	—	13	1	no	—
162	C₂³×C₁₃	—	2	1	no	—
163	C₂³×C₁₃	#121	1	1	yes	characteristic
164	C₂²×D₁₃	—	4	2	no	—
165	C₂²×D₁₃	—	8	2	no	—
166	C₂²×D₁₃	—	8	2	no	—
167	C₂²×D₁₃	—	8	2	no	—
168	Q₈×C₁₃	—	2	1	no	—
169	Q₈×C₁₃	—	4	4	no	—
170	Q₈×C₁₃	—	8	2	no	—
171	Q₈×C₁₃	C₂×SD₁₆	1	2	yes	complemented
172	D₄×C₁₃	—	2	4	no	—
173	D₄×C₁₃	—	2	1	no	—
174	D₄×C₁₃	C₂×SD₁₆	1	2	yes	complemented
175	C₂×C₄×C₁₃	—	2	1	no	—
176	C₂×C₄×C₁₃	—	2	2	no	—
177	C₂×C₄×C₁₃	—	2	4	no	—
178	C₂×C₄×C₁₃	—	2	2	no	—
179	C₂×C₄×C₁₃	—	2	1	no	—
180	C₂×C₄×C₁₃	—	2	1	no	—
181	C₂×C₄×C₁₃	—	4	2	no	—
182	C₂×C₄×C₁₃	—	4	2	no	—
183	C₂×C₄×C₁₃	—	4	2	no	—
184	C₂×C₄×C₁₃	—	8	2	no	—
185	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
186	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
187	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
188	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
189	C₂×C₄×C₁₃	#135	1	2	yes	—
190	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
193	D₅₂	—	4	2	no	—
194	D₅₂	—	4	2	no	—
195	D₅₂	—	4	4	no	—
196	D₅₂	—	8	2	no	—
197	D₅₂	—	8	2	no	—
198	D₅₂	—	8	2	no	—
199	D₅₂	—	8	2	no	—
200	C₈×C₁₃	—	4	2	no	—
201	#1055	—	2	2	no	—
202	#1055	—	4	2	no	—
203	#1055	—	4	2	no	—
204	#1055	AGL(1,ℤ/8)	1	4	yes	complemented
205	C₂×AGL(1,ℤ/8)	—	26	1	no	—
206	C₂²×SD₁₆	—	26	2	no	—
207	C₂×C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
208	C₂×#127	—	13	1	no	—
209	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
210	#492	—	13	4	no	—
211	#492	—	26	1	no	—
212	#492	—	26	1	no	—
213	#477	—	2	1	no	—
214	#476	—	2	1	no	—
215	#475	C₂×D₁₃	1	2	yes	complemented
216	#474	C₂×D₁₃	1	2	yes	complemented
217	#460	—	13	2	no	—
218	#460	—	26	1	no	—
219	#459	—	13	2	no	—
220	#459	—	26	1	no	—
221	C₈×Q₈	—	13	2	no	—
222	C₈×D₄	—	13	2	no	—
223	C₈×D₄	—	26	2	no	—
224	#431	—	13	1	no	—
225	#431	—	26	1	no	—
226	#428	—	2	1	no	—
227	#423	—	13	1	no	—
228	#423	C₂×D₁₃	1	1	yes	characteristic
229	#418	—	26	1	no	—
230	#417	—	2	1	no	—
231	C₂×C₄×C₈	—	13	1	no	—
232	C₂×C₄×C₈	—	26	1	no	—
233	#334	—	13	4	no	—
234	#332	—	13	4	no	—
235	#331	—	13	4	no	—
236	C₂²×C₁₃	—	2	1	no	—
237	C₂²×C₁₃	—	2	1	no	—
238	C₂²×C₁₃	—	2	2	no	—
239	C₂²×C₁₃	—	4	1	no	—
240	C₂²×C₁₃	—	4	1	no	—
241	C₂²×C₁₃	#465	1	2	yes	—
242	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
243	C₂×D₁₃	—	8	2	no	—
244	C₂×D₁₃	—	8	2	no	—
245	C₂×D₁₃	—	8	2	no	—
246	C₂×D₁₃	—	16	4	no	—
247	C₄×C₁₃	—	2	1	no	—
248	C₄×C₁₃	—	2	2	no	—
249	C₄×C₁₃	—	2	1	no	—
250	C₄×C₁₃	—	4	1	no	—
251	C₄×C₁₃	—	4	1	no	—
252	C₄×C₁₃	—	8	2	no	—
253	C₄×C₁₃	#465	1	2	yes	—
254	C₄×C₁₃	#471	1	2	yes	—
255	C₄×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
256	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
257	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
258	C₂×#41	C₂²⋊D₁₃	1	1	yes	characteristic
259	C₂²×Q₈	—	2	1	no	—
260	C₂²×D₄	—	26	1	no	—
261	C₂²×D₄	—	26	1	no	—
262	C₂²×D₄	—	26	1	no	—
263	AGL(1,ℤ/8)	—	52	4	no	—
264	C₂×SD₁₆	—	26	4	no	—
265	C₂×SD₁₆	—	26	4	no	—
266	C₂×SD₁₆	—	26	2	no	—
267	C₂×SD₁₆	—	52	8	no	—
268	C₂×D₈	—	26	2	no	—
269	C₂×M₁₆	—	2	1	no	—
270	C₂×M₁₆	—	26	1	no	—
271	C₂²×C₈	—	13	2	no	—
272	C₂²×C₈	—	26	2	no	—
273	C₄⋊Q₈	—	2	1	no	—
274	C₄⋊Q₈	—	2	1	no	—
275	C₄⋊Q₈	—	2	1	no	—
276	C₄⋊Q₈	C₂²×D₁₃	1	2	yes	—
277	#127	—	13	2	no	—
278	#127	—	26	1	no	—
279	#127	—	26	1	no	—
280	#127	—	26	1	no	—
281	C₄×Q₈	C₂²⋊D₁₃	1	1	yes	characteristic
282	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
283	C₄×D₄	—	2	1	no	—
284	C₄×D₄	—	2	1	no	—
285	C₄×D₄	C₂²⋊D₁₃	1	1	yes	characteristic
286	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
287	#117	—	2	1	no	—
288	#117	C₂²⋊D₁₃	1	1	yes	characteristic
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₄⋊C₄	—	2	1	no	—
291	C₂×C₄²	—	2	1	no	—
292	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
293	#107	—	2	2	no	—
294	#106	—	2	2	no	—
295	C₄⋊C₈	—	2	1	no	—
296	C₄⋊C₈	—	13	2	no	—
297	C₄⋊C₈	—	13	2	no	—
298	C₄⋊C₈	—	26	2	no	—
299	C₄⋊C₈	—	26	1	no	—
300	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
301	#103	—	2	2	no	—
302	#102	—	2	2	no	—
303	#102	—	26	2	no	—
304	#102	—	26	2	no	—
305	C₂²⋊C₈	—	26	2	no	—
306	C₂²⋊C₈	—	26	1	no	—
307	C₄×C₈	—	13	1	no	—
308	C₄×C₈	—	13	1	no	—
309	C₄×C₈	—	13	2	no	—
310	C₄×C₈	—	26	2	no	—
311	C₄×C₈	—	26	1	no	—
312	C₂×C₁₃	—	2	2	no	—
313	C₂×C₁₃	—	4	2	no	—
314	C₂×C₁₃	#3038	1	1	yes	characteristic
315	C₂×C₁₃	C₂×#465	1	1	yes	characteristic
316	C₂×C₁₃	C₂×#471	1	1	yes	characteristic
317	D₁₃	—	16	2	no	—
318	C₂⁴	—	52	1	no	—
319	#41	—	2	2	no	—
320	#41	#6106	1	4	yes	complemented
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	4	4	no	—
323	C₂×Q₈	—	4	1	no	—
324	C₂×Q₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	—	26	2	no	—
327	C₂×D₄	—	26	2	no	—
328	C₂×D₄	—	26	2	no	—
329	C₂×D₄	—	52	4	no	—
330	C₂×D₄	—	52	1	no	—
331	C₂×D₄	—	52	1	no	—
332	C₂×D₄	—	52	1	no	—
333	C₂×D₄	—	52	2	no	—
334	C₂×D₄	—	52	2	no	—
335	C₂×D₄	—	104	2	no	—
336	C₂×D₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	4	1	no	—
341	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
342	C₂²×C₄	#6129	1	1	yes	characteristic
343	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
344	SD₁₆	—	52	8	no	—
345	SD₁₆	—	52	8	no	—
346	SD₁₆	—	52	4	no	—
347	D₈	—	52	4	no	—
348	M₁₆	—	4	2	no	—
349	M₁₆	—	52	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	13	2	no	—
352	C₂×C₈	—	13	2	no	—
353	C₂×C₈	—	26	4	no	—
354	C₂×C₈	—	26	2	no	—
355	C₂×C₈	—	26	2	no	—
356	C₂×C₈	—	52	4	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	4	1	no	—
362	C₄⋊C₄	—	4	1	no	—
363	C₄⋊C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
364	C₄⋊C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
365	C₂²⋊C₄	—	2	1	no	—
366	C₂²⋊C₄	—	2	1	no	—
367	C₂²⋊C₄	—	2	1	no	—
368	C₄²	—	2	1	no	—
369	C₄²	—	2	1	no	—
370	C₄²	—	2	1	no	—
371	C₄²	D₄×D₁₃	1	1	yes	characteristic
372	C₄²	#6129	1	1	yes	characteristic
373	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
374	C₄²	C₂³×D₁₃	1	1	yes	characteristic
375	C₁₃	#19266	1	1	yes	characteristic, complemented, Sylow
376	C₂³	—	2	1	no	—
377	C₂³	—	52	2	no	—
378	C₂³	—	104	2	no	—
379	C₂³	—	104	2	no	—
380	C₂³	—	104	2	no	—
381	C₂³	#88193	1	1	yes	characteristic
382	Q₈	—	2	1	no	—
383	Q₈	—	4	4	no	—
384	Q₈	—	8	2	no	—
385	Q₈	C₂×#6106	1	2	yes	complemented
386	D₄	—	2	4	no	—
387	D₄	—	2	1	no	—
388	D₄	—	52	4	no	—
389	D₄	—	52	2	no	—
390	D₄	—	52	2	no	—
391	D₄	—	104	2	no	—
392	D₄	—	104	2	no	—
393	D₄	—	104	2	no	—
394	D₄	—	104	2	no	—
395	D₄	C₂×#6106	1	2	yes	complemented
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	8	2	no	—
406	C₂×C₄	#88193	1	1	yes	characteristic
407	C₂×C₄	#88193	1	1	yes	characteristic
408	C₂×C₄	#88193	1	1	yes	characteristic
409	C₂×C₄	C₂×#6106	1	2	yes	—
410	C₂×C₄	#88204	1	2	yes	—
411	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
412	C₂×C₄	C₂×#6129	1	1	yes	characteristic
413	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
414	C₈	—	4	2	no	—
415	C₈	—	13	4	no	—
416	C₈	—	26	2	no	—
417	C₈	—	52	2	no	—
418	C₈	—	52	2	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	2	2	no	—
422	C₂²	—	4	1	no	—
423	C₂²	—	4	1	no	—
424	C₂²	—	104	2	no	—
425	C₂²	—	104	2	no	—
426	C₂²	—	104	2	no	—
427	C₂²	—	208	4	no	—
428	C₂²	#11718709	1	2	yes	—
429	C₂²	C₂×#88193	1	1	yes	characteristic
430	C₄	—	2	2	no	—
431	C₄	—	2	1	no	—
432	C₄	—	2	1	no	—
433	C₄	—	4	1	no	—
434	C₄	—	4	1	no	—
435	C₄	—	8	2	no	—
436	C₄	#11718709	1	2	yes	—
437	C₄	#11718864	1	2	yes	—
438	C₄	D₁₃×AGL(1,ℤ/8)	1	2	yes	—
439	C₄	C₂²×#6106	1	1	yes	characteristic
440	C₄	C₂×#88204	1	1	yes	characteristic
441	C₂	—	2	2	no	—
442	C₂	—	4	2	no	—
443	C₂	—	208	2	no	—
444	C₂	#13124314	1	1	yes	characteristic
445	C₂	C₂×#11718709	1	1	yes	characteristic
446	C₂	C₂×#11718864	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#88193
commutator, cosocle	C₄²×C₁₃	C₂⁴
Frattini	C₄²	C₂³×D₁₃
Fitting	C₁₃×#3079	C₂
socle	C₂²×C₁₃	C₂×#121
prime radical	#13124316	C₂
hypercenter	#3079	D₁₃
hypocenter	C₁₃	#19266
LCS	G ▷ C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3079

Complements

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

N	H ≅ G/N	type
1. C₂×#11718746	C₂	semidirect
3. #41×#1055	C₂	semidirect
4. #13114186	C₂	semidirect
5. #13114179	C₂	semidirect
6. #13113591	C₂	semidirect
7. #13113521	C₂	semidirect
8. #13113505	C₂	semidirect
9. C₁₃×#3079	C₂	semidirect
17. C₁₃×#475	C₂²	semidirect
18. C₁₃×#474	C₂²	semidirect
27. Q₈×#1055	C₂²	semidirect
31. D₄×#1055	C₂²	semidirect
38. #11718139	C₂²	semidirect
40. #11718072	C₂²	semidirect
98. C₁₃×#41	SD₁₆	semidirect
154. #3079	D₁₃	semidirect
171. Q₈×C₁₃	C₂×SD₁₆	semidirect
174. D₄×C₁₃	C₂×SD₁₆	semidirect
204. #1055	AGL(1,ℤ/8)	semidirect
215. #475	C₂×D₁₃	semidirect
216. #474	C₂×D₁₃	semidirect
320. #41	#6106	semidirect
375. C₁₃	#19266	semidirect
385. Q₈	C₂×#6106	semidirect
395. D₄	C₂×#6106	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#11718746	2
#13124316	2
#41×#1055	2
#13114186	2
#13114179	2
#13113591	2
#13113521	2
#13113505	2
C₁₃×#3079	2
#19266	13