Finite Group Databasebeta

← #16798109

Subgroups — #16798109

Order 3328.

1166 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131516C212yesmaximal
2#13130738C212yesmaximal
3#13130703C212yesmaximal, complemented
4#13130702C212yesmaximal, complemented
5#13130670C212yesmaximal
6#13130589C212yesmaximal, complemented
7C4×#88113C212yesmaximal, complemented
8C2×#11719221C211yesmaximal, characteristic
9C23×Dic26C2211yescharacteristic
10C2×C13×#117C411yescharacteristic
11C2×#88180C411yescharacteristic
12#11719221—28no—
13C2×#88141C411yescharacteristic
14C2×#88141C411yescharacteristic
15C2×#88141C2211yescharacteristic
16C2×#88141C2211yescharacteristic
17C2×#88131C411yescharacteristic
18C2×#88131C411yescharacteristic
19C2×#88131C2211yescharacteristic
20C2×#88131C2211yescharacteristic
21C2×C4×Dic26C411yescharacteristic
22C2×C4×Dic26C411yescharacteristic
23C2×C4×Dic26C2211yescharacteristic
24C2×C4×Dic26C2211yescharacteristic
25#11719169C2214yes—
26C2×#88113C2214yes—
27C2×#88113C2214yes—
28#11719129C2214yes—
29C4×#6122C2214yes—
30#11719068—28no—
31#11718291C2214yes—
32#11718291C2214yes—
33C23×C4×C13C2×C411yescharacteristic
34C23×Dic13C2×C411yescharacteristic
35C23×Dic13C2311yescharacteristic
36C22×Dic26—24no—
37C22×Dic26—24no—
38C22×Dic26—24no—
39C22×Dic26C2×C411yescharacteristic
40C22×Dic26C2×C411yescharacteristic
41C22×Dic26C2311yescharacteristic
42C22×Dic26C2311yescharacteristic
43C2×#6122C2318yes—
44C13×#117—24no—
45C2×C13×C4⋊C4C2×C411yescharacteristic
46C2×C13×C4⋊C4C2×C411yescharacteristic
47C2×C13×C22⋊C4C2×C411yescharacteristic
48C2×C13×C22⋊C4C2×C411yescharacteristic
49C2×C42×C13C2×C411yescharacteristic
50C2×C42×C13C2×C411yescharacteristic
51C2×C22⋊Dic13C2×C411yescharacteristic
52C2×C22⋊Dic13C2×C411yescharacteristic
53#88180—24no—
54C2×C4⋊Dic13C2×C411yescharacteristic
55C2×C4⋊Dic13C2×C411yescharacteristic
56C2×#6101C2×C411yescharacteristic
57C2×#6101C2×C411yescharacteristic
58C2×#6101C2×C411yescharacteristic
59C2×#6101C2×C411yescharacteristic
60C2×#6101C2×C411yescharacteristic
61C2×#6101C2×C411yescharacteristic
62C2×#6101C2311yescharacteristic
63C2×#6101C2311yescharacteristic
64C2×C4×Dic13C2×C411yescharacteristic
65C2×C4×Dic13C2×C411yescharacteristic
66C2×C4×Dic13C2×C411yescharacteristic
67C2×C4×Dic13C2×C411yescharacteristic
68C2×C4×Dic13C2×C411yescharacteristic
69C2×C4×Dic13C2×C411yescharacteristic
70C2×C4×Dic13C2×C411yescharacteristic
71C2×C4×Dic13C2×C411yescharacteristic
72C2×C4×Dic13C2311yescharacteristic
73C2×C4×Dic13C2311yescharacteristic
74#88141—24no—
75#88141—24no—
76#88141—24no—
77#88141—24no—
78#88131—24no—
79#88131—24no—
80#88131—24no—
81#88131D418yes—
82C4×Dic26—24no—
83C4×Dic26—24no—
84C4×Dic26—24no—
85C4×Dic26—24no—
86C22⋊#1057—28no—
87#88113—28no—
88#88113—28no—
89#88112—24no—
90#88110—24no—
91C4⋊#1057—24no—
92C4×#1057—24no—
93#20730—131nomaximal, Sylow
94C24×C13C22×C411yescharacteristic
95C22×C4×C13—22no—
96C22×C4×C13—22no—
97C22×C4×C13—22no—
98C22×C4×C13C22×C411yescharacteristic
99C22×C4×C13C22×C411yescharacteristic
100C22×C4×C13C22×C411yescharacteristic
101C22×C4×C13C22×C411yescharacteristic
102C22×C4×C13C22×C411yescharacteristic
103C22×C4×C13C22×C411yescharacteristic
104C22×Dic13—22no—
105C22×Dic13—22no—
106C22×Dic13—22no—
107C22×Dic13—22no—
108C22×Dic13—22no—
109C22×Dic13C22×C411yescharacteristic
110C22×Dic13C22×C411yescharacteristic
111C22×Dic13C22×C411yescharacteristic
112C22×Dic13C22×C411yescharacteristic
113C22×Dic13C22×C411yescharacteristic
114C22×Dic13C22×C411yescharacteristic
115C22×Dic13C22×C411yescharacteristic
116C22×Dic13C2×D414yes—
117C22×Dic13C2411yescharacteristic
118C2×Dic26—232no—
119C2×Dic26—22no—
120C2×Dic26—22no—
121C2×Dic26—22no—
122C2×Dic26—22no—
123C2×Dic26—22no—
124C2×Dic26—22no—
125C2×Dic26—22no—
126C2×Dic26—22no—
127C2×Dic26—22no—
128C2×Dic26—22no—
129C2×Dic26#4114yes—
130C2×Dic26#4114yes—
131#6122—28no—
132#6122—28no—
133C2×#1057—28no—
134C13×C4⋊C4—22no—
135C13×C4⋊C4—22no—
136C13×C22⋊C4—22no—
137C13×C22⋊C4C22⋊C414yes—
138C42×C13—22no—
139C42×C13—22no—
140C22⋊Dic13—22no—
141C22⋊Dic13C22⋊C414yes—
142C4⋊Dic13—22no—
143C4⋊Dic13—22no—
144#6101—22no—
145#6101—22no—
146#6101—22no—
147#6101—22no—
148#6101—22no—
149#6101—22no—
150#6101C22⋊C414yes—
151#6101C22⋊C414yes—
152C4×Dic13—22no—
153C4×Dic13—22no—
154C4×Dic13—22no—
155C4×Dic13—22no—
156C4×Dic13—22no—
157C4×Dic13—22no—
158C4×Dic13—22no—
159C4×Dic13—22no—
160C4×Dic13C2×D414yes—
161C4×Dic13C2×D414yes—
162C2×#519—131no—
163#2921—132no—
164#1822—132no—
165#1801—132no—
166#1801—132no—
167#1784—132no—
168C4×#101—132no—
169C4×#101—132no—
170C23×C13—21no—
171C23×C13—21no—
172C23×C13—41no—
173C23×C13—41no—
174C23×C13C2×C22⋊C412yes—
175C23×C13C23×C411yescharacteristic
176C2×C4×C13—28no—
177C2×C4×C13—21no—
178C2×C4×C13—21no—
179C2×C4×C13—21no—
180C2×C4×C13—21no—
181C2×C4×C13—21no—
182C2×C4×C13—21no—
183C2×C4×C13—41no—
184C2×C4×C13—41no—
185C2×C4×C13—41no—
186C2×C4×C13—41no—
187C2×C4×C13C2×C22⋊C412yes—
188C2×C4×C13C2×C22⋊C412yes—
189C2×C4×C13#11712yes—
190C2×C4×C13#11712yes—
191C2×Dic13—28no—
192C2×Dic13—21no—
193C2×Dic13—21no—
194C2×Dic13—21no—
195C2×Dic13—21no—
196C2×Dic13—21no—
197C2×Dic13—21no—
198C2×Dic13—28no—
199C2×Dic13—21no—
200C2×Dic13—21no—
201C2×Dic13—41no—
202C2×Dic13—41no—
203C2×Dic13—41no—
204C2×Dic13—41no—
205C2×Dic13C2×C22⋊C412yes—
206C2×Dic13C2×C22⋊C412yes—
207C2×Dic13C2×C22⋊C412yes—
208C2×Dic13#11712yes—
209C2×Dic13#11712yes—
210C2×Dic13C22×D412yes—
211C2×Dic13C2×#4112yes—
212C2×Dic13C2×#4112yes—
213Dic26—28no—
214Dic26—28no—
215Dic26—28no—
216Dic26—28no—
217#1057—48no—
218C23×Q8—131no—
219#519—268no—
220C2×C4×Q8—131no—
221C2×C4×Q8—131no—
222C2×C4×Q8—131no—
223C2×C4×Q8—131no—
224C2×C4×Q8—131no—
225C2×C4×Q8—131no—
226C2×C4×Q8—131no—
227C2×C4×Q8—131no—
228C2×#117—131no—
229C2×#117—131no—
230C2×#117—131no—
231C2×#117—131no—
232C2×#117—131no—
233C2×#117#26111yescharacteristic
234#433—268no—
235#423—134no—
236C2×#101—134no—
237C2×#101—134no—
238#407—134no—
239C4×M16—134no—
240#343—134no—
241#343—134no—
242C22×C13—21no—
243C22×C13—21no—
244C22×C13—22no—
245C22×C13—22no—
246C22×C13—22no—
247C22×C13—42no—
248C22×C13—42no—
249C22×C13C22×C22⋊C411yescharacteristic
250C22×C13C2×#11711yescharacteristic
251C22×C13C2×#11711yescharacteristic
252C4×C13—22no—
253C4×C13—22no—
254C4×C13—22no—
255C4×C13—22no—
256C4×C13—41no—
257C4×C13—41no—
258Dic13—22no—
259Dic13—22no—
260Dic13—22no—
261Dic13—22no—
262Dic13—22no—
263Dic13—41no—
264Dic13—41no—
265Dic13#52514yes—
266C22×Q8—131no—
267C22×Q8—131no—
268C22×Q8—131no—
269C22×Q8—131no—
270C22×Q8—264no—
271C22×Q8—264no—
272C22×Q8—264no—
273C23×C4—131no—
274C23×C4—131no—
275C23×C4C2×#26111yescharacteristic
276C2×M16—138no—
277C4×Q8—264no—
278C4×Q8—264no—
279C4×Q8—264no—
280C4×Q8—264no—
281C4×Q8—264no—
282C4×Q8—264no—
283C4×Q8—264no—
284C4×Q8—264no—
285#117—24no—
286#117—138no—
287#117—264no—
288#117—264no—
289#117—264no—
290#117—264no—
291C2×C4⋊C4—131no—
292C2×C4⋊C4—131no—
293C2×C4⋊C4—131no—
294C2×C4⋊C4—131no—
295C2×C4⋊C4—131no—
296C2×C4⋊C4—131no—
297C2×C4⋊C4—131no—
298C2×C4⋊C4—131no—
299C2×C4⋊C4—131no—
300C2×C4⋊C4—131no—
301C2×C4⋊C4C2×#26111yescharacteristic
302C2×C4⋊C4C2×#26111yescharacteristic
303C2×C22⋊C4—131no—
304C2×C22⋊C4—131no—
305C2×C22⋊C4C2×#26111yescharacteristic
306C2×C22⋊C4C2×#26111yescharacteristic
307C2×C42—131no—
308C2×C42—131no—
309C2×C42—131no—
310C2×C42—131no—
311C2×C42—131no—
312C2×C42—131no—
313C2×C42—131no—
314C2×C42—131no—
315C2×C42—131no—
316C2×C42—131no—
317C2×C42C2×#26111yescharacteristic
318C2×C42C2×#26111yescharacteristic
319C4⋊C8—264no—
320C4⋊C8—264no—
321#101—268no—
322#101—268no—
323C22⋊C8—268no—
324#97—264no—
325C4×C8—264no—
326C2×C13—21no—
327C2×C13—21no—
328C2×C13—42no—
329C2×C13#228011yescharacteristic
330C2×C13#288911yescharacteristic
331C2×C13#288911yescharacteristic
332C24C22×#26111yescharacteristic
333C2×Q8—134no—
334C2×Q8—134no—
335C2×Q8—262no—
336C2×Q8—262no—
337C2×Q8—262no—
338C2×Q8—262no—
339C2×Q8—262no—
340C2×Q8—262no—
341C2×Q8—262no—
342C2×Q8—262no—
343C2×Q8—2632no—
344C2×Q8—262no—
345C2×Q8—262no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—131no—
350C22×C4—134no—
351C22×C4—131no—
352C22×C4—131no—
353C22×C4—131no—
354C22×C4—131no—
355C22×C4—131no—
356C22×C4—131no—
357C22×C4—131no—
358C22×C4—262no—
359C22×C4—262no—
360C22×C4—262no—
361C22×C4—262no—
362C22×C4—262no—
363C22×C4C22×#26111yescharacteristic
364C22×C4C22×#26111yescharacteristic
365C22×C4C22×#26111yescharacteristic
366C22×C4C22×#26111yescharacteristic
367C22×C4C22×#26111yescharacteristic
368C22×C4C22×#26111yescharacteristic
369M16—268no—
370M16—268no—
371C2×C8—268no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—134no—
375C4⋊C4—134no—
376C4⋊C4—262no—
377C4⋊C4—262no—
378C4⋊C4—262no—
379C4⋊C4—262no—
380C4⋊C4—262no—
381C4⋊C4—262no—
382C4⋊C4—262no—
383C4⋊C4—262no—
384C22⋊C4—22no—
385C22⋊C4—134no—
386C22⋊C4—262no—
387C22⋊C4C22⋊#26114yes—
388C42—22no—
389C42—22no—
390C42—134no—
391C42—134no—
392C42—262no—
393C42—262no—
394C42—262no—
395C42—262no—
396C42—262no—
397C42—262no—
398C42—262no—
399C42—262no—
400C13#2073011yescharacteristic, complemented, Sylow
401C23—21no—
402C23—21no—
403C23—41no—
404C23—41no—
405C23C2×C22⋊#26112yes—
406C23C23×#26111yescharacteristic
407Q8—268no—
408Q8—268no—
409Q8—268no—
410Q8—268no—
411C2×C4—28no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—132no—
423C2×C4—132no—
424C2×C4—132no—
425C2×C4—132no—
426C2×C4—132no—
427C2×C4—132no—
428C2×C4—132no—
429C2×C4—132no—
430C2×C4—268no—
431C2×C4—268no—
432C2×C4—261no—
433C2×C4—261no—
434C2×C4—261no—
435C2×C4—261no—
436C2×C4—261no—
437C2×C4—261no—
438C2×C4—261no—
439C2×C4—261no—
440C2×C4—521no—
441C2×C4—521no—
442C2×C4—521no—
443C2×C4—521no—
444C2×C4#8823712yes—
445C2×C4#8823712yes—
446C2×C4C2×C22⋊#26112yes—
447C2×C4C2×C22⋊#26112yes—
448C8—528no—
449C22—21no—
450C22—21no—
451C22—22no—
452C22—22no—
453C22—22no—
454C22—42no—
455C22—42no—
456C22C2×#8823711yescharacteristic
457C22C2×#8823711yescharacteristic
458C22C22×C22⋊#26111yescharacteristic
459C4—22no—
460C4—22no—
461C4—22no—
462C4—22no—
463C4—41no—
464C4—41no—
465C4—134no—
466C4—262no—
467C4—262no—
468C4—262no—
469C4—262no—
470C4—262no—
471C4—521no—
472C4—521no—
473C2—21no—
474C2—21no—
475C2—42no—
476C2#1313128011yescharacteristic
477C2#1313144811yescharacteristic
478C2#1313144811yescharacteristic
subgroupG/H
centerC22C22×C22⋊#261
commutatorC23×C13C23×C4
FrattiniC23C23×#261
FittingC2×C13×#117C4
socleC22×C13C22×C22⋊C4
prime radicalC24×C13C22×C4
cosocleC22×Dic13C24
hypercenterC2×#117#261
hypocenterC13#20730
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C22⋊C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
3. #13130703C2semidirect
4. #13130702C2semidirect
6. #13130589C2semidirect
7. C4×#88113C2semidirect
400. C13#20730semidirect

Maximal subgroups

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

subgroupindex
#131315162
#131307382
#131307032
#131307022
#131306702
#131305892
C4×#881132
C2×#117192212
#2073013