Finite Group Databasebeta

← #15901326

Subgroups — #15901326

Order 3328.

958 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718631C211yesmaximal, characteristic
2#13118476C211yesmaximal, characteristic
3#13117713C211yesmaximal, characteristic
4#13116227C212yesmaximal, complemented
5#13116081C212yesmaximal, complemented
6#13115757C212yesmaximal, complemented
7#13115480C212yesmaximal, complemented
8#13115259C211yesmaximal, characteristic
9#13115014C211yesmaximal, characteristic
10#13114771C211yesmaximal, characteristic
11C22×C13×#103C211yesmaximal, characteristic
12C23×Q8×C13C2211yescharacteristic
13C23×C8×C13C2211yescharacteristic
14C22×C13×C4⋊C4C2211yescharacteristic
15C2×#88198C2212yes—
16C2×#88178C2211yescharacteristic
17C2×C13×#103—24no—
18C2×C13×#103C2212yes—
19C2×C13×#103C2212yes—
20#11718891C2212yes—
21#11718890—22no—
22C2×#88075C2212yes—
23C2×#88075C2212yes—
24#11718873—21no—
25#11718873C2211yescharacteristic
26#11718871—21no—
27#11718871—21no—
28C4×C22⋊Dic13—21no—
29C4×C22⋊Dic13C2211yescharacteristic
30C2×C22⋊#1055C2211yescharacteristic
31C2×#88056C2212yes—
32C2×#88054C2212yes—
33#11718646C2212yes—
34#11718642—22no—
35C4⋊C4×Dic13C2212yes—
36#11718631—24no—
37C2×#88050C2211yescharacteristic
38C2×#88050C2211yescharacteristic
39C2×#88047C2211yescharacteristic
40C2×#88047C2211yescharacteristic
41#11718143C2212yes—
42#11718142C2212yes—
43C22×Q8×C13—21no—
44C22×Q8×C13—24no—
45C22×Q8×C13—22no—
46C22×Q8×C13—22no—
47C22×Q8×C13—42no—
48C22×Q8×C13C2312yes—
49C23×C4×C13—21no—
50C23×C4×C13—21no—
51C23×C4×C13C2311yescharacteristic
52C22×Dic26C2311yescharacteristic
53C22×C8×C13—22no—
54C22×C8×C13—42no—
55C22×C8×C13C2312yes—
56C2×C13×C4⋊C4—21no—
57C2×C13×C4⋊C4—22no—
58C2×C13×C4⋊C4D414yes—
59C2×C13×C4⋊C4C2311yescharacteristic
60C2×C13×C4⋊C4C2311yescharacteristic
61C2×C22⋊Dic13—21no—
62C2×C22⋊Dic13—21no—
63C2×C22⋊Dic13D411yescharacteristic
64C2×C22⋊Dic13D411yescharacteristic
65#88198—24no—
66#88198—42no—
67C2×C4⋊Dic13—22no—
68C2×C4⋊Dic13C2311yescharacteristic
69C2×C4⋊Dic13C2312yes—
70#88178—22no—
71#88178—22no—
72C2×#6101—21no—
73C2×#6101—22no—
74C2×#6101—22no—
75C2×C4×Dic13—22no—
76C2×C4×Dic13C2312yes—
77C22×#1055C2311yescharacteristic
78C22×#1055C2311yescharacteristic
79C13×#103—24no—
80C13×#103—24no—
81#88075—24no—
82#88075—42no—
83#88071—21no—
84#88071—22no—
85#88071—22no—
86#88071—22no—
87#88071—22no—
88#88071D412yes—
89C22⋊#1055—22no—
90#88056—42no—
91#88054—42no—
92#88050—22no—
93#88050—22no—
94#88047—22no—
95#88047—22no—
96#24482—131nomaximal, Sylow
97C24×C13C2×D411yescharacteristic
98C2×Q8×C13—22no—
99C2×Q8×C13—28no—
100C2×Q8×C13—22no—
101C2×Q8×C13—22no—
102C2×Q8×C13—22no—
103C2×Q8×C13—22no—
104C2×Q8×C13—44no—
105C2×Q8×C13—48no—
106C2×Q8×C13—44no—
107C2×Q8×C13—42no—
108C2×Q8×C13#4114yes—
109C22×C4×C13—22no—
110C22×C4×C13—22no—
111C22×C4×C13—21no—
112C22×C4×C13—22no—
113C22×C4×C13—21no—
114C22×C4×C13—24no—
115C22×C4×C13—44no—
116C22×C4×C13—42no—
117C22×C4×C13—82no—
118C22×C4×C13C2×D411yescharacteristic
119C22×C4×C13C2×D412yes—
120C22×C4×C13#4112yes—
121C22×C4×C13C2411yescharacteristic
122C22×Dic13—21no—
123C22×Dic13—22no—
124C22×Dic13—21no—
125C22×Dic13C2×D412yes—
126C22×Dic13C2×D412yes—
127C2×Dic26—21no—
128C2×Dic26—21no—
129C2×Dic26—22no—
130C2×Dic26—22no—
131C2×C8×C13—22no—
132C2×C8×C13—22no—
133C2×C8×C13—22no—
134C2×C8×C13—44no—
135C13×C4⋊C4—24no—
136C13×C4⋊C4—21no—
137C13×C4⋊C4—21no—
138C13×C4⋊C4C2×D412yes—
139C13×C4⋊C4C2×D412yes—
140C22⋊Dic13—22no—
141C22⋊Dic13—42no—
142C22⋊Dic13—42no—
143C22⋊Dic13Q1614yes—
144C4⋊Dic13—21no—
145C4⋊Dic13—22no—
146C4⋊Dic13—21no—
147C4⋊Dic13—22no—
148C4⋊Dic13—82no—
149#6101—44no—
150#6101—44no—
151#6101—42no—
152C4×Dic13—22no—
153C4×Dic13—22no—
154C4×Dic13—82no—
155C2×#1055—21no—
156C2×#1055—21no—
157C2×#1055—22no—
158C2×#1055—22no—
159C2×#484—131no—
160C22×#103D1311yescharacteristic
161#2434—131no—
162#2345—131no—
163#2068—132no—
164#2043—132no—
165#1981—132no—
166#1928—132no—
167#1892—131no—
168#1850—131no—
169#1787—131no—
170C23×C13—22no—
171C23×C13—22no—
172C23×C13#12112yes—
173C23×C13C2×Q1612yes—
174C23×C13#13712yes—
175C23×C13C22×D411yescharacteristic
176Q8×C13—24no—
177Q8×C13—24no—
178Q8×C13—48no—
179Q8×C13—42no—
180Q8×C13—42no—
181C2×C4×C13—22no—
182C2×C4×C13—22no—
183C2×C4×C13—22no—
184C2×C4×C13—24no—
185C2×C4×C13—22no—
186C2×C4×C13—22no—
187C2×C4×C13—24no—
188C2×C4×C13—48no—
189C2×C4×C13—42no—
190C2×C4×C13—42no—
191C2×C4×C13—42no—
192C2×C4×C13—42no—
193C2×C4×C13—84no—
194C2×C4×C13#12112yes—
195C2×C4×C13C22×D411yescharacteristic
196C2×C4×C13C2×#4112yes—
197C2×C4×C13C2×#4111yescharacteristic
198C2×C4×C13H(5,𝔽2)12yes—
199C2×Dic13—22no—
200C2×Dic13—22no—
201C2×Dic13—22no—
202C2×Dic13—22no—
203C2×Dic13—22no—
204C2×Dic13—41no—
205C2×Dic13—41no—
206C2×Dic13—42no—
207C2×Dic13—42no—
208C2×Dic13—42no—
209C2×Dic13—42no—
210C2×Dic13—42no—
211C2×Dic13C2×Q1614yes—
212Dic26—41no—
213Dic26—41no—
214Dic26—42no—
215C8×C13—42no—
216#1055—41no—
217#1055—41no—
218C23×Q8C2×D1311yescharacteristic
219C23×C8C2×D1311yescharacteristic
220C2×C4⋊Q8—132no—
221C2×C22⋊Q8—131no—
222C22×C4⋊C4C2×D1311yescharacteristic
223#484—264no—
224C2×#107—131no—
225C2×#107—131no—
226C2×C4⋊C8—132no—
227C2×#103—24no—
228C2×#103—132no—
229C2×#103—131no—
230C2×#103—131no—
231C2×#103—132no—
232C2×#103—132no—
233C2×#103C2×D1312yes—
234C2×#103C2×D1312yes—
235C2×C22⋊C8—131no—
236#395—262no—
237#391—132no—
238#389—132no—
239#387—262no—
240#385—261no—
241#385—261no—
242#380—131no—
243#380—261no—
244C4×C4⋊C4—132no—
245C4×C22⋊C4—131no—
246C4×C22⋊C4—261no—
247#340—132no—
248#336—132no—
249C22×C13—22no—
250C22×C13—22no—
251C22×C13—24no—
252C22×C13—24no—
253C22×C13#46214yes—
254C22×C13C2×#12111yescharacteristic
255C22×C13#54612yes—
256C22×C13C22×Q1611yescharacteristic
257C22×C13C2×#13711yescharacteristic
258C22×C13#57712yes—
259C4×C13—22no—
260C4×C13—44no—
261C4×C13—42no—
262C4×C13—42no—
263C4×C13#52511yescharacteristic
264C4×C13#53511yescharacteristic
265C4×C13#55112yes—
266Dic13—24no—
267Dic13—42no—
268Dic13—81no—
269Dic13—81no—
270Dic13—82no—
271C22×Q8—21no—
272C22×Q8—24no—
273C22×Q8—22no—
274C22×Q8—22no—
275C22×Q8—42no—
276C22×Q8—131no—
277C22×Q8C22×D1312yes—
278C23×C4—21no—
279C23×C4—21no—
280C23×C4C22×D1311yescharacteristic
281C22×C8—22no—
282C22×C8—42no—
283C22×C8—131no—
284C22×C8—131no—
285C22×C8C22×D1312yes—
286C4⋊Q8—264no—
287C4⋊Q8—522no—
288C22⋊Q8—262no—
289C22⋊Q8—262no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—131no—
293C2×C4⋊C4—132no—
294C2×C4⋊C4—262no—
295C2×C4⋊C4—262no—
296C2×C4⋊C4—261no—
297C2×C4⋊C4—262no—
298C2×C4⋊C4C22⋊D1314yes—
299C2×C4⋊C4C22×D1311yescharacteristic
300C2×C4⋊C4C22×D1311yescharacteristic
301C2×C22⋊C4—131no—
302C2×C22⋊C4—131no—
303C2×C22⋊C4—261no—
304C2×C22⋊C4—261no—
305C2×C42—132no—
306C2×C42—262no—
307#107—262no—
308#107—262no—
309C4⋊C8—522no—
310#103—24no—
311#103—24no—
312#103—264no—
313#103—262no—
314#103—262no—
315#103—522no—
316#103—522no—
317C22⋊C8—262no—
318#95—132no—
319#95—262no—
320#95—262no—
321#95—262no—
322#95—262no—
323#95—261no—
324C2×C13—24no—
325C2×C13#241111yescharacteristic
326C2×C13C2×#46211yescharacteristic
327C2×C13#304211yescharacteristic
328C2×C13#329912yes—
329C2×C13#332012yes—
330C24D4×D1311yescharacteristic
331C2×Q8—22no—
332C2×Q8—28no—
333C2×Q8—22no—
334C2×Q8—22no—
335C2×Q8—22no—
336C2×Q8—22no—
337C2×Q8—44no—
338C2×Q8—48no—
339C2×Q8—44no—
340C2×Q8—42no—
341C2×Q8—262no—
342C2×Q8—261no—
343C2×Q8—262no—
344C2×Q8—261no—
345C2×Q8#612714yes—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—22no—
351C22×C4—24no—
352C22×C4—44no—
353C22×C4—42no—
354C22×C4—82no—
355C22×C4—132no—
356C22×C4—132no—
357C22×C4—261no—
358C22×C4—262no—
359C22×C4—261no—
360C22×C4D4×D1311yescharacteristic
361C22×C4#612912yes—
362C22×C4C2×C22⋊D1312yes—
363C22×C4C23×D1311yescharacteristic
364C2×C8—22no—
365C2×C8—22no—
366C2×C8—22no—
367C2×C8—44no—
368C2×C8—262no—
369C2×C8—262no—
370C2×C8—261no—
371C2×C8—261no—
372C4⋊C4—24no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—262no—
376C4⋊C4—261no—
377C4⋊C4—262no—
378C4⋊C4—261no—
379C4⋊C4—524no—
380C4⋊C4—524no—
381C4⋊C4—522no—
382C4⋊C4—1042no—
383C4⋊C4C2×C22⋊D1312yes—
384C4⋊C4C2×C22⋊D1312yes—
385C22⋊C4—134no—
386C22⋊C4—262no—
387C22⋊C4—522no—
388C22⋊C4—522no—
389C42—262no—
390C42—262no—
391C42—1042no—
392C13#2448211yescharacteristic, complemented, Sylow
393C23—22no—
394C23—22no—
395C23Q16×D1312yes—
396C23#8817212yes—
397C23#8819312yes—
398C23C2×D4×D1311yescharacteristic
399Q8—24no—
400Q8—24no—
401Q8—48no—
402Q8—42no—
403Q8—42no—
404Q8—522no—
405Q8—521no—
406Q8—521no—
407C2×C4—22no—
408C2×C4—24no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—24no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—48no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—84no—
420C2×C4—134no—
421C2×C4—262no—
422C2×C4—262no—
423C2×C4—262no—
424C2×C4—262no—
425C2×C4—262no—
426C2×C4—522no—
427C2×C4—522no—
428C2×C4—522no—
429C2×C4—522no—
430C2×C4—522no—
431C2×C4—521no—
432C2×C4—521no—
433C2×C4#8819312yes—
434C2×C4C2×#612712yes—
435C2×C4C2×#612911yescharacteristic
436C2×C4#8825112yes—
437C2×C4C22×C22⋊D1311yescharacteristic
438C8—42no—
439C8—521no—
440C8—521no—
441C22—22no—
442C22—24no—
443C22—24no—
444C22—22no—
445C22#1171884314yes—
446C22#1171919512yes—
447C22#1171946712yes—
448C22C2×Q16×D1311yescharacteristic
449C22C2×#8817211yescharacteristic
450C22C2×#8819311yescharacteristic
451C4—22no—
452C4—44no—
453C4—42no—
454C4—42no—
455C4—264no—
456C4—522no—
457C4—1041no—
458C4—1042no—
459C4—1041no—
460C4#1171920012yes—
461C4#1171949611yescharacteristic
462C4#1171951011yescharacteristic
463C2—24no—
464C2#1311822111yescharacteristic
465C2C2×#1171884311yescharacteristic
466C2#1312434511yescharacteristic
467C2#1312670812yes—
468C2#1312700312yes—
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC22×C13×#103C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenterC22×#103D13
hypocenterC13#24482
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
4. #13116227C2semidirect
5. #13116081C2semidirect
6. #13115757C2semidirect
7. #13115480C2semidirect
392. C13#24482semidirect

Maximal subgroups

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

subgroupindex
C2×#117186312
#131184762
#131177132
#131162272
#131160812
#131157572
#131154802
#131152592
#131150142
#131147712
C22×C13×#1032
#2448213