Finite Group Databasebeta

← #15872453

Subgroups — #15872453

Order 3328.

1238 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D13×C4⋊Q8C211yesmaximal, characteristic
2C2×#11718496C211yesmaximal, characteristic
3#13117232C211yesmaximal, characteristic
4#13115807C214yesmaximal, complemented
5#13115789C211yesmaximal, characteristic, complemented
6#13115788C211yesmaximal, characteristic, complemented
7#13115787C211yesmaximal, characteristic, complemented
8#13114925C214yesmaximal
9C13×#1988C211yesmaximal, characteristic, complemented
10C22×Q8×D13—21no—
11C2×C13×C4⋊Q8C2211yescharacteristic
12C2×#88198—21no—
13D13×C4⋊Q8—24no—
14D13×C4⋊Q8C418yescomplemented
15C2×C4⋊C4×D13—21no—
16C2×C4⋊C4×D13C2212yes—
17C2×#88142—21no—
18C2×#88142C2212yes—
19C2×C42×D13C2211yescharacteristic
20C2×#88123C2211yescharacteristic
21C2×C13×C4⋊C8C2211yescharacteristic
22C4×C13×C4⋊C4C2211yescharacteristic
23C2×#88060C2212yes—
24C2×#88055C2212yes—
25#11718648C2212yes—
26#11718638C2212yes—
27C4×#6103—21no—
28C4×C4⋊Dic13C2211yescharacteristic
29#11718593—21no—
30C2×C4⋊#1055C2211yescharacteristic
31#11718496—24no—
32#11718325—21no—
33#11718312—21no—
34C13×#340C2214yes—
35#11718143C2214yes—
36#11718121C2214yes—
37#11718121C2214yes—
38C22×Q8×C13—21no—
39C2×Q8×D13—28no—
40C2×Q8×D13—44no—
41C2×Q8×D13—44no—
42C22×C4×D13—22no—
43C22×C4×D13D411yescharacteristic
44C22×C4×D13D411yescharacteristic
45C22×C4×D13C2311yescharacteristic
46C22×Dic26—21no—
47C22×Dic26—22no—
48C22×C8×C13C2312yes—
49C13×C4⋊Q8—22no—
50C13×C4⋊Q8C2×C414yes—
51C2×C13×C4⋊C4—21no—
52C2×C13×C4⋊C4C2312yes—
53C2×C13×C4⋊C4C2312yes—
54C2×C42×C13—21no—
55C2×C42×C13C2311yescharacteristic
56#88198—28no—
57C2×#6103—22no—
58C2×C4⋊Dic13—21no—
59C2×C4⋊Dic13C2312yes—
60C2×C4⋊Dic13C2312yes—
61C2×#6101—22no—
62C2×#6101—22no—
63C2×C4×Dic13—21no—
64C2×C4×Dic13D411yescharacteristic
65C2×C4×Dic13D411yescharacteristic
66C2×C4×Dic13C2311yescharacteristic
67C22×#1055C2312yes—
68C4⋊C4×D13—28no—
69C4⋊C4×D13—24no—
70C4⋊C4×D13C2×C418yes—
71#88142—28no—
72#88142—24no—
73#88142C2×C418yes—
74C42×D13C2×C414yes—
75C42×D13D414yes—
76#88123—22no—
77#88123C2×C414yes—
78C13×C4⋊C8—22no—
79C13×#95—21no—
80#88071—21no—
81#88071—22no—
82#88071—22no—
83#88071—22no—
84#88060—24no—
85#88055—24no—
86C4⋊#1055—22no—
87#21841—131nomaximal, Sylow
88C23×D13C2×D411yescharacteristic
89C2×Q8×C13—24no—
90C2×Q8×C13—42no—
91C2×Q8×C13—42no—
92C22×C4×C13—22no—
93C22×C4×C13—22no—
94C22×C4×C13C2×D411yescharacteristic
95C22×C4×C13C2×D411yescharacteristic
96C22×C4×C13C2411yescharacteristic
97C22×Dic13—22no—
98C22×Dic13—22no—
99C22×Dic13C2×D411yescharacteristic
100C22×Dic13C2×D411yescharacteristic
101C22×Dic13C2×D411yescharacteristic
102Q8×D13—432no—
103C2×C4×D13—24no—
104C2×C4×D13—22no—
105C2×C4×D13—22no—
106C2×C4×D13—22no—
107C2×C4×D13—22no—
108C2×C4×D13—28no—
109C2×C4×D13—44no—
110C2×C4×D13—44no—
111C2×C4×D13C22⋊C414yes—
112C2×C4×D13C22⋊C414yes—
113C2×C4×D13C22×C412yes—
114C2×C4×D13C2×D412yes—
115C2×Dic26—24no—
116C2×Dic26—28no—
117C2×Dic26—44no—
118C2×Dic26—44no—
119C2×Dic26—42no—
120C2×Dic26—42no—
121C2×C8×C13—22no—
122C2×C8×C13—24no—
123C13×C4⋊C4—24no—
124C13×C4⋊C4—22no—
125C13×C4⋊C4—22no—
126C13×C4⋊C4—22no—
127C13×C4⋊C4C22×C414yes—
128C42×C13—42no—
129C42×C13C22×C412yes—
130C42×C13C2×D412yes—
131#6103—44no—
132C4⋊Dic13—24no—
133C4⋊Dic13—22no—
134C4⋊Dic13—22no—
135C4⋊Dic13—22no—
136C4⋊Dic13C22×C414yes—
137#6101—28no—
138#6101—28no—
139C4×Dic13—42no—
140C4×Dic13C22⋊C414yes—
141C4×Dic13C22⋊C414yes—
142C4×Dic13C22×C412yes—
143C4×Dic13C2×D412yes—
144C2×#1055—22no—
145C2×#1055—24no—
146C22×C4⋊Q8—131no—
147C2×#432—131no—
148#2283—131no—
149#1993—134no—
150#1988—131no—
151#1988—131no—
152#1988—131no—
153#1988D1311yescharacteristic, complemented
154#1824—134no—
155C23×C13C22×D411yescharacteristic
156C22×D13—22no—
157C22×D13—21no—
158C22×D13—21no—
159C22×D13C2×C22⋊C412yes—
160C22×D13#13714yes—
161Q8×C13—48no—
162C2×C4×C13—22no—
163C2×C4×C13—24no—
164C2×C4×C13—42no—
165C2×C4×C13—42no—
166C2×C4×C13—42no—
167C2×C4×C13—42no—
168C2×C4×C13—42no—
169C2×C4×C13C2×C22⋊C412yes—
170C2×C4×C13C2×C22⋊C412yes—
171C2×C4×C13AGL(1,ℤ/8)12yes—
172C2×C4×C13AGL(1,ℤ/8)12yes—
173C2×C4×C13C23×C411yescharacteristic
174C2×C4×C13C22×D411yescharacteristic
175C2×C4×C132−1+412yes—
176C2×C4×C132−1+412yes—
177C2×Dic13—22no—
178C2×Dic13—21no—
179C2×Dic13—21no—
180C2×Dic13—22no—
181C2×Dic13—24no—
182C2×Dic13—42no—
183C2×Dic13—42no—
184C2×Dic13—42no—
185C2×Dic13—42no—
186C2×Dic13—42no—
187C2×Dic13C2×C22⋊C412yes—
188C2×Dic13C2×C22⋊C412yes—
189C2×Dic13C2×C22⋊C412yes—
190C4×D13—28no—
191C4×D13—24no—
192C4×D13—22no—
193C4×D13—22no—
194C4×D13—28no—
195C4×D13—416no—
196Dic26—416no—
197Dic26—48no—
198C8×C13—42no—
199#1055—42no—
200C23×Q8—261no—
201C2×C4⋊Q8—138no—
202C2×C4⋊Q8—132no—
203C2×C4⋊Q8—131no—
204C2×C4⋊Q8—261no—
205C2×C4⋊Q8—264no—
206C2×C4⋊Q8—261no—
207C2×C4⋊Q8C2×D1311yescharacteristic
208C22×C4⋊C4—132no—
209C22×C4⋊C4—261no—
210C22×C42—131no—
211#432—264no—
212C2×C4⋊C8—131no—
213C2×C4⋊C8C2×D1311yescharacteristic
214C2×C22⋊C8—132no—
215C2×#97—132no—
216#383—261no—
217#382—132no—
218#381—261no—
219#380—132no—
220C4×C4⋊C4—131no—
221C4×C4⋊C4C2×D1311yescharacteristic
222C4×C22⋊C4—261no—
223#376—261no—
224#340—134no—
225#340—134no—
226#340—134no—
227#340C2×D1314yes—
228C22×C13C22×C22⋊C411yescharacteristic
229C22×C13#53612yes—
230C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
231C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
232C22×C13C2×#13712yes—
233C2×D13—22no—
234C2×D13—22no—
235C2×D13—24no—
236C2×D13—24no—
237C2×D13#41914yes—
238C4×C13—22no—
239C4×C13—44no—
240C4×C13—82no—
241C4×C13#41814yes—
242C4×C13#51912yes—
243C4×C13#53611yescharacteristic
244C4×C13#53611yescharacteristic
245Dic13—22no—
246Dic13—22no—
247Dic13—22no—
248Dic13—44no—
249Dic13—82no—
250C22×Q8—21no—
251C22×Q8—262no—
252C22×Q8—268no—
253C22×Q8—261no—
254C22×Q8—524no—
255C22×Q8—524no—
256C23×C4—131no—
257C23×C4—131no—
258C23×C4—131no—
259C23×C4—262no—
260C22×C8—132no—
261C22×C8C22×D1312yes—
262C4⋊Q8—22no—
263C4⋊Q8—138no—
264C4⋊Q8—134no—
265C4⋊Q8—268no—
266C4⋊Q8—264no—
267C4⋊Q8—268no—
268C4⋊Q8—262no—
269C4⋊Q8C4×D1314yes—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—132no—
272C2×C4⋊C4—138no—
273C2×C4⋊C4—132no—
274C2×C4⋊C4—264no—
275C2×C4⋊C4—268no—
276C2×C4⋊C4—262no—
277C2×C4⋊C4—262no—
278C2×C4⋊C4—261no—
279C2×C4⋊C4C22×D1312yes—
280C2×C4⋊C4C22×D1312yes—
281C2×C22⋊C4—262no—
282C2×C42—21no—
283C2×C42—131no—
284C2×C42—131no—
285C2×C42—131no—
286C2×C42—134no—
287C2×C42—134no—
288C2×C42—261no—
289C2×C42C22×D1311yescharacteristic
290C4⋊C8—22no—
291C4⋊C8—262no—
292C22⋊C8—264no—
293#97—264no—
294#95—21no—
295#95—262no—
296#95—262no—
297#95—262no—
298#95—261no—
299C2×C13#231011yescharacteristic
300C2×C13C2×#41811yescharacteristic
301C2×C13C2×#41911yescharacteristic
302C2×C13#323912yes—
303C2×C13#323912yes—
304D13—24no—
305C24—131no—
306C2×Q8—24no—
307C2×Q8—42no—
308C2×Q8—42no—
309C2×Q8—268no—
310C2×Q8—264no—
311C2×Q8—524no—
312C2×Q8—524no—
313C2×Q8—5232no—
314C2×Q8—522no—
315C2×Q8—522no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—131no—
319C22×C4—131no—
320C22×C4—131no—
321C22×C4—134no—
322C22×C4—134no—
323C22×C4—132no—
324C22×C4—132no—
325C22×C4—264no—
326C22×C4—268no—
327C22×C4—262no—
328C22×C4—262no—
329C22×C4—262no—
330C22×C4—262no—
331C22×C4—262no—
332C22×C4—262no—
333C22×C4—524no—
334C22×C4—524no—
335C22×C4D4×D1311yescharacteristic
336C22×C4D4×D1311yescharacteristic
337C22×C4C23×D1311yescharacteristic
338C2×C8—22no—
339C2×C8—24no—
340C2×C8—262no—
341C2×C8—264no—
342C4⋊C4—24no—
343C4⋊C4—22no—
344C4⋊C4—22no—
345C4⋊C4—22no—
346C4⋊C4—134no—
347C4⋊C4—268no—
348C4⋊C4—268no—
349C4⋊C4—264no—
350C4⋊C4—262no—
351C4⋊C4—262no—
352C4⋊C4—262no—
353C4⋊C4C2×C4×D1314yes—
354C22⋊C4—524no—
355C42—42no—
356C42—134no—
357C42—134no—
358C42—132no—
359C42—132no—
360C42—522no—
361C42C2×C4×D1312yes—
362C42D4×D1312yes—
363C13#2184111yescharacteristic, complemented, Sylow
364C23—132no—
365C23—134no—
366C23—261no—
367C23—261no—
368C23—262no—
369C23C2×D4×D1311yescharacteristic
370Q8—48no—
371Q8—5216no—
372Q8—528no—
373C2×C4—22no—
374C2×C4—24no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—132no—
381C2×C4—132no—
382C2×C4—132no—
383C2×C4—268no—
384C2×C4—261no—
385C2×C4—261no—
386C2×C4—262no—
387C2×C4—262no—
388C2×C4—262no—
389C2×C4—268no—
390C2×C4—264no—
391C2×C4—262no—
392C2×C4—264no—
393C2×C4—5216no—
394C2×C4—522no—
395C2×C4—522no—
396C2×C4—522no—
397C2×C4—522no—
398C2×C4—522no—
399C2×C4C22⋊C4×D1312yes—
400C2×C4C22⋊C4×D1312yes—
401C2×C4#8816512yes—
402C2×C4#8816812yes—
403C2×C4C22×C4×D1311yescharacteristic
404C2×C4C2×D4×D1311yescharacteristic
405C2×C4#8825412yes—
406C2×C4#8825712yes—
407C8—42no—
408C8—522no—
409C22—134no—
410C22—262no—
411C22—264no—
412C22—264no—
413C22—262no—
414C22C2×C22⋊C4×D1311yescharacteristic
415C22#1171933312yes—
416C22C2×#8816511yescharacteristic
417C22C2×#8816811yescharacteristic
418C22D13×#13712yes—
419C4—22no—
420C4—44no—
421C4—82no—
422C4—262no—
423C4—262no—
424C4—262no—
425C4—524no—
426C4—1042no—
427C4#1171843114yes—
428C4#1171927712yes—
429C4#1171938011yescharacteristic
430C4#1171942911yescharacteristic
431C2—264no—
432C2#1311741911yescharacteristic
433C2C2×#1171843111yescharacteristic
434C2D13×#41911yescharacteristic
435C2#1312606512yes—
436C2#1312607012yes—
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1988C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
cosocleC22×C4×C13C24
hypercenter#1988D13
hypocenterC13#21841
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1988

Complements

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

NH ≅ G/Ntype
4. #13115807C2semidirect
5. #13115789C2semidirect
6. #13115788C2semidirect
7. #13115787C2semidirect
9. C13×#1988C2semidirect
14. D13×C4⋊Q8C4semidirect
153. #1988D13semidirect
363. C13#21841semidirect

Maximal subgroups

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

subgroupindex
C2×D13×C4⋊Q82
C2×#117184962
#131172322
#131158072
#131157892
#131157882
#131157872
#131149252
C13×#19882
#2184113