Finite Group Databasebeta

← #15766300

Subgroups — #15766300

Order 3328.

572 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
1#13119838C211yesmaximal, characteristic
2#13115641C211yesmaximal, characteristic
3#13114838C211yesmaximal, characteristic, complemented
4C2×#11718077C211yesmaximal, characteristic
5C2×#11718076C211yesmaximal, characteristic, complemented
6#13112677C211yesmaximal, characteristic, complemented
7C13×#1947C211yesmaximal, characteristic, complemented
8C2×#88129—21no—
9C2×#88128C2211yescharacteristic
10C2×C4×Dic26C2211yescharacteristic
11C2×C13×#107—21no—
12C2×C13×C4⋊C8C2211yescharacteristic
13C13×#384C2211yescharacteristic
14C4×C13×C4⋊C4C2211yescharacteristic
15#11718649—21no—
16#11718649—21no—
17C2×#88050—21no—
18C2×#88049—22no—
19#11718600—21no—
20C2×C4⋊#1055C2211yescharacteristic
21C2×C4×#1055C2211yescharacteristic
22#11718333—22no—
23C13×#340—21no—
24#11718121—21no—
25#11718077—22no—
26#11718076—22no—
27C22×D52—21no—
28C22×D52—21no—
29C22×D52D412yes—
30C22×Dic26D411yescharacteristic
31C22×C8×C13—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4D411yescharacteristic
36C2×C13×C4⋊C4D411yescharacteristic
37C2×C42×C13—21no—
38C2×C42×C13C2311yescharacteristic
39C2×#6103—22no—
40C2×#6103—22no—
41C2×#6103—22no—
42C2×#6103—22no—
43C2×C4⋊Dic13D411yescharacteristic
44C2×#6101—21no—
45C2×C4×Dic13—21no—
46C22×#1055—21no—
47C22×#1055—21no—
48#88129—42no—
49#88129—42no—
50#88128—21no—
51#88128—21no—
52#88128—21no—
53#88128—21no—
54C4×Dic26—21no—
55C4×Dic26—21no—
56C4×Dic26—21no—
57C4×Dic26—21no—
58C13×#107—42no—
59C13×C4⋊C8—21no—
60C13×C4⋊C8D412yes—
61C13×#95—21no—
62#88050—42no—
63#88049—44no—
64C4⋊#1055—21no—
65C4⋊#1055—21no—
66C4×#1055—21no—
67C4×#1055—21no—
68#10411—131nomaximal, Sylow
69C23×D13—22no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—41no—
73C22×C4×C13C2×D411yescharacteristic
74C22×C4×C13C2×D411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C22×Dic13—21no—
77C22×Dic13—21no—
78C2×D52—22no—
79C2×D52—22no—
80C2×D52—42no—
81C2×D52—42no—
82C2×D52—41no—
83C2×D52—41no—
84C2×D52—41no—
85C2×D52—41no—
86C2×D52—41no—
87C2×D52—41no—
88C2×D52—41no—
89C2×D52—41no—
90C2×D52—41no—
91C2×D52—41no—
92C2×D52—41no—
93C2×D52—41no—
94C2×Dic26—21no—
95C2×Dic26—21no—
96C2×Dic26—21no—
97C2×Dic26—21no—
98C2×Dic26—21no—
99C2×Dic26D812yes—
100C2×C8×C13—22no—
101C2×C8×C13—41no—
102C2×C8×C13—41no—
103C13×C4⋊C4—21no—
104C13×C4⋊C4—21no—
105C13×C4⋊C4—21no—
106C13×C4⋊C4—21no—
107C13×C4⋊C4—42no—
108C13×C4⋊C4—41no—
109C13×C4⋊C4—41no—
110C13×C4⋊C4—41no—
111C13×C4⋊C4—41no—
112C42×C13—41no—
113C42×C13—41no—
114C42×C13C2×D411yescharacteristic
115C42×C13#4111yescharacteristic
116C42×C13#4111yescharacteristic
117C42×C13#4111yescharacteristic
118#6103—44no—
119#6103—44no—
120#6103—82no—
121#6103—82no—
122C4⋊Dic13—21no—
123C4⋊Dic13—21no—
124#6101—41no—
125#6101—41no—
126C4×Dic13—41no—
127C4×Dic13—41no—
128C2×#1055—22no—
129C2×#1055—41no—
130C2×#1055—41no—
131C2×#1055—41no—
132C2×#1055—41no—
133C2×#1055—41no—
134#2548—131no—
135#1957—131no—
136#1947D1311yescharacteristic, complemented
137#1803—131no—
138C2×#331—131no—
139C2×Q8⋊C8—131no—
140#1279—131no—
141C23×C13#12011yescharacteristic
142C22×D13—42no—
143C22×D13—42no—
144C22×D13—42no—
145C22×D13—42no—
146C22×D13—42no—
147C22×D13—42no—
148C22×D13—42no—
149C2×C4×C13—21no—
150C2×C4×C13—21no—
151C2×C4×C13—41no—
152C2×C4×C13—41no—
153C2×C4×C13—41no—
154C2×C4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13—41no—
157C2×C4×C13—81no—
158C2×C4×C13—81no—
159C2×C4×C13—81no—
160C2×C4×C13#12111yescharacteristic
161C2×C4×C13#12111yescharacteristic
162C2×C4×C13#12111yescharacteristic
163C2×C4×C13#12311yescharacteristic
164C2×C4×C13#12311yescharacteristic
165C2×C4×C13#12411yescharacteristic
166C2×C4×C13C2×D811yescharacteristic
167C2×C4×C13#13511yescharacteristic
168C2×C4×C13#13511yescharacteristic
169C2×C4×C13#13511yescharacteristic
170C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C13#13711yescharacteristic
173C2×C4×C13#13711yescharacteristic
174C2×Dic13—22no—
175C2×Dic13—41no—
176C2×Dic13—41no—
177C2×Dic13—41no—
178C2×Dic13—41no—
179C2×Dic13—41no—
180D52—44no—
181D52—82no—
182D52—81no—
183D52—81no—
184D52—81no—
185D52—81no—
186D52—81no—
187D52—81no—
188D52—81no—
189D52—81no—
190Dic26—22no—
191Dic26—22no—
192Dic26—41no—
193Dic26—41no—
194C8×C13—42no—
195#1055—42no—
196#1055—81no—
197C2×#127—131no—
198C2×#124—261no—
199C2×C4×Q8—131no—
200C2×#107—21no—
201C2×C4⋊C8—131no—
202C2×C4⋊C8C2×D1311yescharacteristic
203C2×#103—261no—
204C2×#102—262no—
205C2×C4×C8—131no—
206#394—262no—
207#390—261no—
208#390—261no—
209#390—261no—
210#384C2×D1311yescharacteristic
211C4×C4⋊C4C2×D1311yescharacteristic
212#340—21no—
213#340—261no—
214#331—262no—
215Q8⋊C8—262no—
216C22×C13#39411yescharacteristic
217C22×C13#44711yescharacteristic
218C22×C13#44911yescharacteristic
219C22×C13#45211yescharacteristic
220C22×C13#45211yescharacteristic
221C22×C13#45311yescharacteristic
222C22×C13#45511yescharacteristic
223C2×D13—82no—
224C2×D13—82no—
225C2×D13—82no—
226C2×D13—82no—
227C2×D13—82no—
228C2×D13—82no—
229C2×D13—82no—
230C4×C13—21no—
231C4×C13—21no—
232C4×C13—81no—
233C4×C13—81no—
234C4×C13—161no—
235C4×C13#46311yescharacteristic
236C4×C13#46411yescharacteristic
237C4×C13#46611yescharacteristic
238C4×C13#46811yescharacteristic
239C4×C13#48011yescharacteristic
240C4×C13#48211yescharacteristic
241C4×C13#48811yescharacteristic
242C4×C13#48911yescharacteristic
243Dic13—42no—
244Dic13—81no—
245C22×Q8—131no—
246C22×D4—132no—
247C22×D4—261no—
248C22×D4—261no—
249C22×C8—21no—
250C22×C8—261no—
251C22×C8—261no—
252#127—261no—
253#127—261no—
254#127—261no—
255#127—261no—
256#124—522no—
257#124—522no—
258C4×Q8—261no—
259C4×Q8—261no—
260C4×Q8—261no—
261C4×Q8—261no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—131no—
266C2×C4⋊C4—261no—
267C2×C4⋊C4C22⋊D1311yescharacteristic
268C2×C4⋊C4C22⋊D1311yescharacteristic
269C2×C22⋊C4—262no—
270C2×C22⋊C4—262no—
271C2×C22⋊C4—262no—
272C2×C22⋊C4—262no—
273C2×C42—21no—
274C2×C42—261no—
275C2×C42C22×D1311yescharacteristic
276#107—42no—
277C4⋊C8—21no—
278C4⋊C8—261no—
279C4⋊C8—261no—
280C4⋊C8D5212yes—
281#103—522no—
282#102—524no—
283C4×C8—261no—
284C4×C8—261no—
285#95—21no—
286C2×C13#162111yescharacteristic
287C2×C13#163011yescharacteristic
288C2×C13#164011yescharacteristic
289C2×C13#164111yescharacteristic
290C2×C13#203311yescharacteristic
291C2×C13#203711yescharacteristic
292C2×C13#204211yescharacteristic
293D13—162no—
294C24—262no—
295C2×Q8—132no—
296C2×Q8—261no—
297C2×Q8—261no—
298C2×Q8—261no—
299C2×Q8—261no—
300C2×Q8—261no—
301C2×D4—262no—
302C2×D4—262no—
303C2×D4—522no—
304C2×D4—522no—
305C2×D4—521no—
306C2×D4—521no—
307C2×D4—521no—
308C2×D4—521no—
309C2×D4—521no—
310C2×D4—521no—
311C2×D4—521no—
312C2×D4—521no—
313C2×D4—521no—
314C2×D4—521no—
315C2×D4—521no—
316C2×D4—521no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—41no—
320C22×C4—261no—
321C22×C4—261no—
322C22×C4D4×D1311yescharacteristic
323C22×C4D4×D1311yescharacteristic
324C22×C4C2×C22⋊D1311yescharacteristic
325C2×C8—22no—
326C2×C8—41no—
327C2×C8—41no—
328C2×C8—262no—
329C2×C8—521no—
330C2×C8—521no—
331C2×C8—521no—
332C2×C8—521no—
333C2×C8—521no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—42no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4—261no—
344C4⋊C4—261no—
345C4⋊C4—521no—
346C4⋊C4—521no—
347C22⋊C4—524no—
348C22⋊C4—524no—
349C22⋊C4—1042no—
350C22⋊C4—1042no—
351C42—41no—
352C42—41no—
353C42—521no—
354C42—521no—
355C42C2×D5211yescharacteristic
356C42#612711yescharacteristic
357C42#613111yescharacteristic
358C42#613111yescharacteristic
359C13#1041111yescharacteristic, complemented, Sylow
360C23—522no—
361C23—522no—
362C23—522no—
363C23—522no—
364C23—522no—
365C23—522no—
366C23—522no—
367C23#8819111yescharacteristic
368Q8—262no—
369Q8—262no—
370Q8—521no—
371Q8—521no—
372D4—524no—
373D4—1042no—
374D4—1041no—
375D4—1041no—
376D4—1041no—
377D4—1041no—
378D4—1041no—
379D4—1041no—
380D4—1041no—
381D4—1041no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—262no—
394C2×C4—521no—
395C2×C4—521no—
396C2×C4—521no—
397C2×C4—521no—
398C2×C4—521no—
399C2×C4#8814811yescharacteristic
400C2×C4#8814811yescharacteristic
401C2×C4#8814911yescharacteristic
402C2×C4#8814911yescharacteristic
403C2×C4D8×D1311yescharacteristic
404C2×C4#8816511yescharacteristic
405C2×C4#8817211yescharacteristic
406C2×C4#8817311yescharacteristic
407C2×C4#8818411yescharacteristic
408C2×C4#8818611yescharacteristic
409C2×C4#8819611yescharacteristic
410C2×C4#8820111yescharacteristic
411C2×C4#8820411yescharacteristic
412C2×C4#8820411yescharacteristic
413C8—42no—
414C8—522no—
415C8—1041no—
416C22—1042no—
417C22—1042no—
418C22—1042no—
419C22—1042no—
420C22—1042no—
421C22—1042no—
422C22—1042no—
423C22#1171865211yescharacteristic
424C22#1171869811yescharacteristic
425C22#1171870811yescharacteristic
426C22#1171881711yescharacteristic
427C22#1171884811yescharacteristic
428C22#1171885911yescharacteristic
429C22#1171886311yescharacteristic
430C4—21no—
431C4—21no—
432C4—81no—
433C4—81no—
434C4—161no—
435C4—522no—
436C4—1041no—
437C4#1171854311yescharacteristic
438C4#1171854411yescharacteristic
439C4#1171854611yescharacteristic
440C4#1171854711yescharacteristic
441C4#1171867711yescharacteristic
442C4#1171868911yescharacteristic
443C4#1171872911yescharacteristic
444C4#1171875011yescharacteristic
445C2—2082no—
446C2#1311390011yescharacteristic
447C2#1311395611yescharacteristic
448C2#1311402011yescharacteristic
449C2#1311402811yescharacteristic
450C2#1311602011yescharacteristic
451C2#1311604811yescharacteristic
452C2#1311607711yescharacteristic
subgroupG/H
centerC23#88191
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1947C2
socleC23×C13#120
prime radicalC2×#88128C22
hypercenter#1947D13
hypocenterC13#10411
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1947

Complements

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

NH ≅ G/Ntype
3. #13114838C2semidirect
5. C2×#11718076C2semidirect
6. #13112677C2semidirect
7. C13×#1947C2semidirect
136. #1947D13semidirect
359. C13#10411semidirect

Maximal subgroups

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

subgroupindex
#131198382
#131156412
#131148382
C2×#117180772
C2×#117180762
#131126772
C13×#19472
#1041113