Finite Group Databasebeta

← #15872634

Subgroups — #15872634

Order 3328.

1106 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719433C211yesmaximal, characteristic
2C2×#11718346C211yesmaximal, characteristic
3#13117241C211yesmaximal, characteristic
4#13115798C211yesmaximal, characteristic, complemented
5#13115638C211yesmaximal, characteristic, complemented
6#13115637C211yesmaximal, characteristic, complemented
7#13115147C214yesmaximal
8#13114850C214yesmaximal, complemented
9C13×#1990C211yesmaximal, characteristic, complemented
10C2×C13×C4⋊Q8C2211yescharacteristic
11C2×#88200—21no—
12C2×Q8×Dic13—21no—
13#11719433—24no—
14#11719433C418yescomplemented
15C2×#88151C2212yes—
16C2×#88146—21no—
17C2×#88146C2212yes—
18C2×#88144—21no—
19C2×#88141C2212yes—
20C2×C42×D13C2211yescharacteristic
21C2×#88123C2211yescharacteristic
22C2×C4×C8×C13C2211yescharacteristic
23C13×#384C2211yescharacteristic
24C2×#88060C2212yes—
25C2×#88056C2214yes—
26C2×#88054C2212yes—
27#11718648—21no—
28#11718648—21no—
29#11718638C2212yes—
30C4⋊C4×Dic13—21no—
31C4⋊C4×Dic13—21no—
32C2×#88050C2214yes—
33#11718596C2211yescharacteristic
34C2×C4×#1055C2211yescharacteristic
35#11718346—24no—
36C13×#340C2214yes—
37#11718121C2214yes—
38C22×Q8×C13—21no—
39C22×C4×D13D411yescharacteristic
40C22×C4×D13D411yescharacteristic
41C22×C4×D13C2311yescharacteristic
42C22×Dic26C2312yes—
43C22×C8×C13C2312yes—
44C13×C4⋊Q8—22no—
45C13×C4⋊Q8C2×C414yes—
46C2×C13×C4⋊C4—21no—
47C2×C13×C4⋊C4—21no—
48C2×C13×C4⋊C4—21no—
49C2×C13×C4⋊C4C2312yes—
50C2×C13×C4⋊C4C2312yes—
51C2×C42×C13C2311yescharacteristic
52#88200—28no—
53Q8×Dic13—28no—
54C2×#6103—22no—
55C2×#6103—22no—
56C2×C4⋊Dic13—21no—
57C2×C4⋊Dic13—21no—
58C2×C4⋊Dic13—22no—
59C2×C4⋊Dic13—21no—
60C2×C4⋊Dic13—21no—
61C2×C4⋊Dic13C2312yes—
62C2×#6101—22no—
63C2×C4×Dic13—22no—
64C2×C4×Dic13—22no—
65C2×C4×Dic13D411yescharacteristic
66C2×C4×Dic13D411yescharacteristic
67C2×C4×Dic13C2311yescharacteristic
68C22×#1055C2312yes—
69#88151—24no—
70#88151C2×C418yes—
71#88146—28no—
72#88146—44no—
73#88144—28no—
74#88141—24no—
75#88141C2×C418yes—
76C42×D13C2×C414yes—
77C42×D13D414yes—
78#88123—22no—
79#88123C2×C414yes—
80C4×C8×C13—22no—
81#88071—22no—
82#88071—22no—
83#88060—24no—
84#88056—44no—
85#88054—24no—
86#88050—44no—
87C4×#1055—22no—
88#21864—131nomaximal, Sylow
89C23×D13C2×D411yescharacteristic
90C2×Q8×C13—24no—
91C2×Q8×C13—42no—
92C2×Q8×C13—42no—
93C22×C4×C13—22no—
94C22×C4×C13—22no—
95C22×C4×C13C2×D411yescharacteristic
96C22×C4×C13C2×D411yescharacteristic
97C22×C4×C13C2411yescharacteristic
98C22×Dic13—22no—
99C22×Dic13—22no—
100C22×Dic13C2×D411yescharacteristic
101C22×Dic13C2×D411yescharacteristic
102C22×Dic13C2×D411yescharacteristic
103C2×C4×D13—22no—
104C2×C4×D13—22no—
105C2×C4×D13—22no—
106C2×C4×D13—22no—
107C2×C4×D13—22no—
108C2×C4×D13—22no—
109C2×C4×D13C22⋊C414yes—
110C2×C4×D13C22⋊C414yes—
111C2×C4×D13C22×C412yes—
112C2×C4×D13C2×D412yes—
113C2×Dic26—24no—
114C2×Dic26—24no—
115C2×Dic26—22no—
116C2×Dic26C22×C414yes—
117C2×C8×C13—22no—
118C2×C8×C13—22no—
119C2×C8×C13—22no—
120C13×C4⋊C4—24no—
121C13×C4⋊C4—22no—
122C13×C4⋊C4—24no—
123C13×C4⋊C4—42no—
124C13×C4⋊C4—42no—
125C13×C4⋊C4C22×C414yes—
126C42×C13C22×C412yes—
127C42×C13C2×D412yes—
128#6103—28no—
129#6103—44no—
130C4⋊Dic13—24no—
131C4⋊Dic13—24no—
132C4⋊Dic13—28no—
133C4⋊Dic13—24no—
134C4⋊Dic13—42no—
135C4⋊Dic13—42no—
136#6101—28no—
137C4×Dic13—28no—
138C4×Dic13—44no—
139C4×Dic13C22⋊C414yes—
140C4×Dic13C22⋊C414yes—
141C4×Dic13C22×C412yes—
142C4×Dic13C2×D412yes—
143C2×#1055—22no—
144C2×#1055—22no—
145C2×#1055—22no—
146C2×#533—131no—
147C2×#431—131no—
148#2285—131no—
149#1990—131no—
150#1990D1311yescharacteristic, complemented
151#1956—131no—
152#1956—131no—
153#1873—134no—
154#1805—134no—
155C23×C13C22×D411yescharacteristic
156C22×D13—21no—
157C22×D13—21no—
158C22×D13—21no—
159C22×D13—21no—
160C22×D13—21no—
161C22×D13—21no—
162C22×D13C2×C22⋊C412yes—
163Q8×C13—48no—
164C2×C4×C13—24no—
165C2×C4×C13—42no—
166C2×C4×C13—42no—
167C2×C4×C13—42no—
168C2×C4×C13—42no—
169C2×C4×C13—42no—
170C2×C4×C13C2×C22⋊C412yes—
171C2×C4×C13C2×C22⋊C412yes—
172C2×C4×C13#13512yes—
173C2×C4×C13#13512yes—
174C2×C4×C13#13712yes—
175C2×C4×C13#13712yes—
176C2×C4×C13C23×C411yescharacteristic
177C2×C4×C13C22×D411yescharacteristic
178C2×C4×C13H(5,𝔽2)12yes—
179C2×C4×C132−1+412yes—
180C2×Dic13—21no—
181C2×Dic13—21no—
182C2×Dic13—21no—
183C2×Dic13—21no—
184C2×Dic13—21no—
185C2×Dic13—21no—
186C2×Dic13—24no—
187C2×Dic13—42no—
188C2×Dic13—42no—
189C2×Dic13—42no—
190C2×Dic13—42no—
191C2×Dic13—42no—
192C2×Dic13C2×C22⋊C412yes—
193C2×Dic13C2×C22⋊C412yes—
194C2×Dic13C2×C22⋊C412yes—
195C4×D13—24no—
196C4×D13—24no—
197C4×D13—28no—
198C4×D13—28no—
199Dic26—28no—
200Dic26—44no—
201C8×C13—42no—
202#1055—42no—
203#533—138no—
204#533—264no—
205C2×C4⋊Q8—131no—
206C2×C4⋊Q8C2×D1311yescharacteristic
207C2×#125—261no—
208C2×C22⋊Q8—132no—
209C2×C22⋊Q8—261no—
210C2×C4×Q8—132no—
211C2×C4×Q8—261no—
212C2×#117—132no—
213C2×#117—261no—
214C22×C42—131no—
215#431—264no—
216C2×C4⋊C8—132no—
217C2×#103—134no—
218C2×#103—134no—
219C2×C22⋊C8—132no—
220C2×C4×C8—131no—
221C2×C4×C8C2×D1311yescharacteristic
222#384—131no—
223#384C2×D1311yescharacteristic
224#382—132no—
225#380—261no—
226#380—261no—
227C4×C4⋊C4—261no—
228C4×C4⋊C4—261no—
229#340—134no—
230#340C2×D1314yes—
231C22×C13C22×C22⋊C411yescharacteristic
232C22×C13#53511yescharacteristic
233C22×C13#53611yescharacteristic
234C22×C13C2×#13511yescharacteristic
235C22×C13C2×#13511yescharacteristic
236C22×C13C2×#13711yescharacteristic
237C22×C13C2×#13711yescharacteristic
238C2×D13—22no—
239C2×D13—22no—
240C2×D13—22no—
241C2×D13—41no—
242C2×D13—41no—
243C2×D13—41no—
244C2×D13—41no—
245C4×C13—44no—
246C4×C13—82no—
247C4×C13#41614yes—
248C4×C13#41914yes—
249C4×C13#52012yes—
250C4×C13#53712yes—
251Dic13—22no—
252Dic13—22no—
253Dic13—22no—
254Dic13—44no—
255Dic13—82no—
256C22×Q8—21no—
257C22×Q8—132no—
258C23×C4—131no—
259C23×C4—131no—
260C23×C4—131no—
261C22×C8—132no—
262C22×C8C22×D1312yes—
263C4⋊Q8—22no—
264C4⋊Q8—134no—
265C4⋊Q8—262no—
266C4⋊Q8C4×D1314yes—
267#125—268no—
268C22⋊Q8—138no—
269C22⋊Q8—264no—
270C22⋊Q8—268no—
271C4×Q8—138no—
272C4×Q8—264no—
273C4×Q8—268no—
274#117—268no—
275#117—524no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—132no—
280C2×C4⋊C4—262no—
281C2×C4⋊C4—262no—
282C2×C4⋊C4—261no—
283C2×C4⋊C4—261no—
284C2×C4⋊C4—261no—
285C2×C4⋊C4—261no—
286C2×C4⋊C4C22×D1312yes—
287C2×C4⋊C4C22×D1312yes—
288C2×C22⋊C4—262no—
289C2×C22⋊C4—262no—
290C2×C42—131no—
291C2×C42—131no—
292C2×C42—131no—
293C2×C42—134no—
294C2×C42—134no—
295C2×C42—262no—
296C2×C42—262no—
297C2×C42C22×D1311yescharacteristic
298C4⋊C8—264no—
299#103—524no—
300#103—524no—
301C22⋊C8—264no—
302C4×C8—22no—
303C4×C8—262no—
304#95—262no—
305#95—262no—
306C2×C13#231111yescharacteristic
307C2×C13C2×#41611yescharacteristic
308C2×C13C2×#41911yescharacteristic
309C2×C13#321011yescharacteristic
310C2×C13#321011yescharacteristic
311C2×C13#323111yescharacteristic
312C2×C13#323111yescharacteristic
313D13—42no—
314C24—131no—
315C2×Q8—24no—
316C2×Q8—42no—
317C2×Q8—42no—
318C2×Q8—134no—
319C2×Q8—262no—
320C2×Q8—264no—
321C2×Q8—264no—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—131no—
325C22×C4—131no—
326C22×C4—131no—
327C22×C4—134no—
328C22×C4—134no—
329C22×C4—132no—
330C22×C4—132no—
331C22×C4—262no—
332C22×C4—262no—
333C22×C4—262no—
334C22×C4—262no—
335C22×C4—262no—
336C22×C4—262no—
337C22×C4—262no—
338C22×C4—262no—
339C22×C4D4×D1311yescharacteristic
340C22×C4D4×D1311yescharacteristic
341C22×C4C23×D1311yescharacteristic
342C2×C8—22no—
343C2×C8—22no—
344C2×C8—22no—
345C2×C8—262no—
346C2×C8—262no—
347C2×C8—262no—
348C4⋊C4—24no—
349C4⋊C4—22no—
350C4⋊C4—24no—
351C4⋊C4—42no—
352C4⋊C4—42no—
353C4⋊C4—268no—
354C4⋊C4—268no—
355C4⋊C4—264no—
356C4⋊C4—264no—
357C4⋊C4—264no—
358C4⋊C4—522no—
359C4⋊C4—522no—
360C4⋊C4C2×C4×D1314yes—
361C22⋊C4—268no—
362C22⋊C4—524no—
363C42—134no—
364C42—134no—
365C42—132no—
366C42—132no—
367C42—268no—
368C42—524no—
369C42C2×C4×D1312yes—
370C42D4×D1312yes—
371C13#2186411yescharacteristic, complemented, Sylow
372C23—132no—
373C23—261no—
374C23—261no—
375C23—261no—
376C23—261no—
377C23—261no—
378C23—261no—
379C23C2×D4×D1311yescharacteristic
380Q8—48no—
381Q8—268no—
382Q8—524no—
383C2×C4—24no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—132no—
390C2×C4—132no—
391C2×C4—132no—
392C2×C4—261no—
393C2×C4—261no—
394C2×C4—261no—
395C2×C4—261no—
396C2×C4—261no—
397C2×C4—261no—
398C2×C4—268no—
399C2×C4—268no—
400C2×C4—264no—
401C2×C4—264no—
402C2×C4—264no—
403C2×C4—522no—
404C2×C4—522no—
405C2×C4—522no—
406C2×C4—522no—
407C2×C4—522no—
408C2×C4C22⋊C4×D1312yes—
409C2×C4C22⋊C4×D1312yes—
410C2×C4#8816612yes—
411C2×C4#8816912yes—
412C2×C4#8817012yes—
413C2×C4#8817212yes—
414C2×C4C22×C4×D1311yescharacteristic
415C2×C4C2×D4×D1311yescharacteristic
416C2×C4#8825412yes—
417C2×C4#8825612yes—
418C8—42no—
419C8—522no—
420C22—262no—
421C22—262no—
422C22—262no—
423C22—521no—
424C22—521no—
425C22—521no—
426C22—521no—
427C22C2×C22⋊C4×D1311yescharacteristic
428C22#1171937911yescharacteristic
429C22#1171942911yescharacteristic
430C22C2×#8816611yescharacteristic
431C22C2×#8816911yescharacteristic
432C22C2×#8817011yescharacteristic
433C22C2×#8817211yescharacteristic
434C4—44no—
435C4—82no—
436C4—262no—
437C4—262no—
438C4—262no—
439C4—524no—
440C4—1042no—
441C4#1171843314yes—
442C4#1171846314yes—
443C4#1171927912yes—
444C4#1171933412yes—
445C2—522no—
446C2#1311742711yescharacteristic
447C2C2×#1171843311yescharacteristic
448C2C2×#1171846311yescharacteristic
449C2#1312579311yescharacteristic
450C2#1312579511yescharacteristic
451C2#1312599611yescharacteristic
452C2#1312599811yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1990C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
cosocleC22×C4×C13C24
hypercenter#1990D13
hypocenterC13#21864
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
4. #13115798C2semidirect
5. #13115638C2semidirect
6. #13115637C2semidirect
8. #13114850C2semidirect
9. C13×#1990C2semidirect
14. #11719433C4semidirect
150. #1990D13semidirect
371. C13#21864semidirect

Maximal subgroups

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

subgroupindex
C2×#117194332
C2×#117183462
#131172412
#131157982
#131156382
#131156372
#131151472
#131148502
C13×#19902
#2186413