Finite Group Databasebeta

← #15862935

Subgroups — #15862935

Order 3328.

1326 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88141C211yesmaximal, characteristic
2C2×#11718379C211yesmaximal, characteristic
3#13117231C211yesmaximal, characteristic
4#13114922C211yesmaximal, characteristic
5#13114850C214yesmaximal, complemented
6#13114772C211yesmaximal, characteristic
7#13114770C211yesmaximal, characteristic
8#13114655C214yesmaximal, complemented
9C13×#1823C211yesmaximal, characteristic
10C23×Dic26C2211yescharacteristic
11C22×C13×C4⋊C4C2211yescharacteristic
12C22×#6101—21no—
13C22×C4×Dic13—21no—
14C22×C4×Dic13C2211yescharacteristic
15C2×#88141—21no—
16C2×#88141—21no—
17C2×#88141—24no—
18C2×#88141C418yescomplemented
19C2×#88141C2212yes—
20C2×#88141C2212yes—
21C2×C13×C22⋊C8C2211yescharacteristic
22C13×#380C2211yescharacteristic
23#11718873C2211yescharacteristic
24C2×C22⋊#1055C2211yescharacteristic
25C2×#88056C2214yes—
26C2×#88054C2212yes—
27C2×C8×Dic13C2212yes—
28#11718638C2212yes—
29C4⋊C4×Dic13C2212yes—
30C2×#88050C2214yes—
31#11718604—21no—
32C22⋊C4×Dic13—21no—
33#11718379—24no—
34#11718312—21no—
35#11718309—21no—
36C13×#340C2214yes—
37#11718121C2214yes—
38C23×C4×C13—21no—
39C23×C4×C13C2311yescharacteristic
40C23×Dic13—21no—
41C23×Dic13D411yescharacteristic
42C23×Dic13D411yescharacteristic
43C22×Dic26—21no—
44C22×Dic26—22no—
45C22×Dic26—28no—
46C22×Dic26C2×C414yes—
47C22×Dic26C2312yes—
48C22×C8×C13C2312yes—
49C2×C13×C4⋊C4—21no—
50C2×C13×C4⋊C4—22no—
51C2×C13×C4⋊C4C2×C414yes—
52C2×C13×C4⋊C4C2312yes—
53C2×C13×C4⋊C4C2312yes—
54C2×C13×C22⋊C4—21no—
55C2×C22⋊Dic13—21no—
56C2×C4⋊Dic13C2312yes—
57C2×#6101—28no—
58C2×#6101—22no—
59C2×#6101—22no—
60C2×C4×Dic13—28no—
61C2×C4×Dic13—22no—
62C2×C4×Dic13—22no—
63C2×C4×Dic13—22no—
64C2×C4×Dic13C2×C414yes—
65C2×C4×Dic13D411yescharacteristic
66C2×C4×Dic13D411yescharacteristic
67C2×C4×Dic13D414yes—
68C2×C4×Dic13C2311yescharacteristic
69C2×C4×Dic13C2311yescharacteristic
70C22×#1055C2312yes—
71#88141—28no—
72#88141—28no—
73#88141—24no—
74#88141—24no—
75#88141C2×C418yes—
76#88141C2×C418yes—
77C13×C22⋊C8—22no—
78C13×#95—21no—
79#88071—21no—
80#88071—22no—
81#88071—22no—
82#88071—22no—
83C22⋊#1055—22no—
84#88056—28no—
85#88054—24no—
86C8×Dic13—24no—
87#88050—28no—
88#20735—131nomaximal, Sylow
89C24×C13C2×D411yescharacteristic
90C22×C4×C13—24no—
91C22×C4×C13—24no—
92C22×C4×C13—22no—
93C22×C4×C13—22no—
94C22×C4×C13—42no—
95C22×C4×C13—42no—
96C22×C4×C13C22×C412yes—
97C22×C4×C13C2×D411yescharacteristic
98C22×C4×C13C2×D412yes—
99C22×C4×C13C2411yescharacteristic
100C22×Dic13—28no—
101C22×Dic13—24no—
102C22×Dic13—22no—
103C22×Dic13—22no—
104C22×Dic13—22no—
105C22×Dic13—24no—
106C22×Dic13—22no—
107C22×Dic13C22⋊C414yes—
108C22×Dic13C22⋊C414yes—
109C22×Dic13C2×D411yescharacteristic
110C22×Dic13C2×D411yescharacteristic
111C22×Dic13C2×D411yescharacteristic
112C22×Dic13C2×D411yescharacteristic
113C2×Dic26—28no—
114C2×Dic26—216no—
115C2×Dic26—24no—
116C2×Dic26—22no—
117C2×Dic26—24no—
118C2×Dic26—216no—
119C2×Dic26C22×C414yes—
120C2×Dic26#4118yes—
121C2×C8×C13—22no—
122C2×C8×C13—24no—
123C13×C4⋊C4—24no—
124C13×C4⋊C4—22no—
125C13×C4⋊C4—24no—
126C13×C4⋊C4C22×C414yes—
127C13×C22⋊C4—42no—
128C22⋊Dic13—42no—
129C4⋊Dic13—24no—
130#6101—28no—
131#6101—28no—
132C4×Dic13—28no—
133C4×Dic13—28no—
134C4×Dic13—44no—
135C4×Dic13C22⋊C414yes—
136C4×Dic13C22⋊C414yes—
137C4×Dic13C22×C412yes—
138C4×Dic13C22×C412yes—
139C4×Dic13C2×D412yes—
140C4×Dic13C2×D412yes—
141C2×#1055—22no—
142C2×#1055—24no—
143C22×C4×Q8—131no—
144C2×#431—131no—
145#2283—131no—
146#1823—131no—
147#1823D1311yescharacteristic
148#1805—134no—
149#1787—131no—
150#1787—131no—
151C4×#103—134no—
152C23×C13—22no—
153C23×C13—22no—
154C23×C13C2×C22⋊C412yes—
155C23×C13#13512yes—
156C23×C13#13512yes—
157C23×C13C22×D411yescharacteristic
158C2×C4×C13—22no—
159C2×C4×C13—24no—
160C2×C4×C13—24no—
161C2×C4×C13—24no—
162C2×C4×C13—42no—
163C2×C4×C13—42no—
164C2×C4×C13—48no—
165C2×C4×C13—42no—
166C2×C4×C13—42no—
167C2×C4×C13—42no—
168C2×C4×C13C2×C22⋊C412yes—
169C2×C4×C13C23×C411yescharacteristic
170C2×C4×C13C22×D411yescharacteristic
171C2×C4×C13C2×#4114yes—
172C2×Dic13—216no—
173C2×Dic13—24no—
174C2×Dic13—28no—
175C2×Dic13—21no—
176C2×Dic13—21no—
177C2×Dic13—21no—
178C2×Dic13—21no—
179C2×Dic13—22no—
180C2×Dic13—28no—
181C2×Dic13—28no—
182C2×Dic13—42no—
183C2×Dic13—42no—
184C2×Dic13—42no—
185C2×Dic13C2×C22⋊C412yes—
186C2×Dic13C2×C22⋊C412yes—
187C2×Dic13C2×C22⋊C412yes—
188C2×Dic13C2×C22⋊C412yes—
189C2×Dic13#13714yes—
190Dic26—216no—
191Dic26—24no—
192Dic26—28no—
193Dic26#11718yes—
194C8×C13—42no—
195#1055—42no—
196C23×Q8—131no—
197C2×C4×Q8—138no—
198C2×C4×Q8—132no—
199C2×C4×Q8—132no—
200C2×C4×Q8—261no—
201C2×C4×Q8—261no—
202C2×C4×Q8—264no—
203C22×C4⋊C4—261no—
204C22×C4⋊C4C2×D1311yescharacteristic
205C22×C42—131no—
206C22×C42—261no—
207#431—264no—
208C2×C4⋊C8—132no—
209C2×#103—134no—
210C2×#103—134no—
211C2×C22⋊C8—131no—
212C2×C22⋊C8C2×D1311yescharacteristic
213C2×C4×C8—132no—
214#383—261no—
215#382—132no—
216#381—261no—
217#380—131no—
218#380C2×D1311yescharacteristic
219C4×C4⋊C4—132no—
220C4×C22⋊C4—261no—
221#376—261no—
222#340—134no—
223#340C2×D1314yes—
224C22×C13—24no—
225C22×C13—24no—
226C22×C13—22no—
227C22×C13—22no—
228C22×C13#41614yes—
229C22×C13C22×C22⋊C411yescharacteristic
230C22×C13#52512yes—
231C22×C13C2×#13511yescharacteristic
232C22×C13C2×#13511yescharacteristic
233C22×C13C2×#13712yes—
234C4×C13—22no—
235C4×C13—44no—
236C4×C13—82no—
237C4×C13C2×#11712yes—
238C4×C13#52512yes—
239Dic13—22no—
240Dic13—22no—
241Dic13—22no—
242Dic13—28no—
243Dic13—82no—
244Dic13#41914yes—
245C22×Q8—134no—
246C22×Q8—132no—
247C22×Q8—268no—
248C22×Q8—262no—
249C22×Q8—261no—
250C23×C4—21no—
251C23×C4—131no—
252C23×C4—131no—
253C23×C4—261no—
254C23×C4C22×D1311yescharacteristic
255C22×C8—132no—
256C22×C8C22×D1312yes—
257C4×Q8—138no—
258C4×Q8—138no—
259C4×Q8—268no—
260C4×Q8—268no—
261C4×Q8—264no—
262C4×Q8—264no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—132no—
266C2×C4⋊C4—268no—
267C2×C4⋊C4—262no—
268C2×C4⋊C4—262no—
269C2×C4⋊C4C4×D1314yes—
270C2×C4⋊C4C22×D1312yes—
271C2×C4⋊C4C22×D1312yes—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—261no—
274C2×C42—134no—
275C2×C42—131no—
276C2×C42—131no—
277C2×C42—134no—
278C2×C42—131no—
279C2×C42—131no—
280C2×C42—268no—
281C2×C42—262no—
282C2×C42—262no—
283C2×C42—262no—
284C4⋊C8—264no—
285#103—268no—
286#103—268no—
287C22⋊C8—22no—
288C22⋊C8—262no—
289C4×C8—264no—
290#95—21no—
291#95—262no—
292#95—262no—
293#95—262no—
294#95—261no—
295C2×C13—24no—
296C2×C13#228011yescharacteristic
297C2×C13C2×#41611yescharacteristic
298C2×C13C2×#41911yescharacteristic
299C2×C13#310812yes—
300C2×C13#310812yes—
301C24D4×D1311yescharacteristic
302C2×Q8—134no—
303C2×Q8—138no—
304C2×Q8—2616no—
305C2×Q8—268no—
306C2×Q8—2616no—
307C2×Q8—264no—
308C2×Q8—262no—
309C2×Q8—264no—
310C22×C4—24no—
311C22×C4—24no—
312C22×C4—22no—
313C22×C4—22no—
314C22×C4—42no—
315C22×C4—42no—
316C22×C4—131no—
317C22×C4—134no—
318C22×C4—134no—
319C22×C4—131no—
320C22×C4—131no—
321C22×C4—131no—
322C22×C4—264no—
323C22×C4—268no—
324C22×C4—264no—
325C22×C4—262no—
326C22×C4—262no—
327C22×C4—262no—
328C22×C4—262no—
329C22×C4C2×C4×D1312yes—
330C22×C4D4×D1311yescharacteristic
331C22×C4D4×D1312yes—
332C22×C4C23×D1311yescharacteristic
333C2×C8—22no—
334C2×C8—24no—
335C2×C8—262no—
336C2×C8—264no—
337C4⋊C4—24no—
338C4⋊C4—22no—
339C4⋊C4—24no—
340C4⋊C4—268no—
341C4⋊C4—268no—
342C4⋊C4—264no—
343C4⋊C4C2×C4×D1314yes—
344C22⋊C4—42no—
345C22⋊C4—522no—
346C42—134no—
347C42—134no—
348C42—132no—
349C42—132no—
350C42—132no—
351C42—132no—
352C42—268no—
353C42—268no—
354C42—524no—
355C13#2073511yescharacteristic, complemented, Sylow
356C23—22no—
357C23—22no—
358C23C22⋊C4×D1312yes—
359C23#8816612yes—
360C23#8817012yes—
361C23C2×D4×D1311yescharacteristic
362Q8—138no—
363Q8—2616no—
364Q8—264no—
365Q8—268no—
366C2×C4—22no—
367C2×C4—24no—
368C2×C4—24no—
369C2×C4—24no—
370C2×C4—48no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—132no—
377C2×C4—134no—
378C2×C4—132no—
379C2×C4—132no—
380C2×C4—132no—
381C2×C4—268no—
382C2×C4—2616no—
383C2×C4—264no—
384C2×C4—268no—
385C2×C4—261no—
386C2×C4—261no—
387C2×C4—261no—
388C2×C4—261no—
389C2×C4—262no—
390C2×C4—268no—
391C2×C4—522no—
392C2×C4—522no—
393C2×C4—522no—
394C2×C4C22⋊C4×D1312yes—
395C2×C4C22×C4×D1311yescharacteristic
396C2×C4C2×D4×D1311yescharacteristic
397C2×C4#41×D1314yes—
398C8—42no—
399C8—522no—
400C22—22no—
401C22—22no—
402C22—24no—
403C22—24no—
404C22#1171843314yes—
405C22C2×C22⋊C4×D1311yescharacteristic
406C22#1171936112yes—
407C22C2×#8816611yescharacteristic
408C22C2×#8817011yescharacteristic
409C22D13×#13712yes—
410C4—22no—
411C4—44no—
412C4—82no—
413C4—134no—
414C4—262no—
415C4—262no—
416C4—262no—
417C4—268no—
418C4—1042no—
419C4D13×#11712yes—
420C4#1171936112yes—
421C2—24no—
422C2#1311721611yescharacteristic
423C2C2×#1171843311yescharacteristic
424C2D13×#41911yescharacteristic
425C2#1312491312yes—
426C2#1312491912yes—
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1823C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
cosocleC22×C4×C13C24
hypercenter#1823D13
hypocenterC13#20735
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1823

Complements

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

NH ≅ G/Ntype
5. #13114850C2semidirect
8. #13114655C2semidirect
18. C2×#88141C4semidirect
355. C13#20735semidirect

Maximal subgroups

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

subgroupindex
C22×#881412
C2×#117183792
#131172312
#131149222
#131148502
#131147722
#131147702
#131146552
C13×#18232
#2073513