Finite Group Databasebeta

← #15766336

Subgroups — #15766336

Order 3328.

520 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13119831C211yesmaximal, characteristic
2#13115797C211yesmaximal, characteristic, complemented
3#13115594C211yesmaximal, characteristic, complemented
4#13114837C211yesmaximal, characteristic
5C2×#11718074C211yesmaximal, characteristic, complemented
6C2×#11718051C211yesmaximal, characteristic
7C13×#1279C211yesmaximal, characteristic, complemented
8C2×#88129—21no—
9C2×C4×D52C2211yescharacteristic
10C2×#88123C2211yescharacteristic
11C2×C13×C4⋊C8C2211yescharacteristic
12C2×C4×C8×C13C2211yescharacteristic
13C4×C13×C4⋊C4C2211yescharacteristic
14C2×#88061—21no—
15#11718648—21no—
16#11718648—21no—
17C2×#88047—21no—
18#11718596C2211yescharacteristic
19#11718590—21no—
20C2×C4⋊#1055C2211yescharacteristic
21#11718335—22no—
22#11718143—22no—
23#11718143—21no—
24#11718121—21no—
25#11718074—22no—
26#11718051—22no—
27C22×D52D411yescharacteristic
28C22×C4×D13—21no—
29C22×Dic26—21no—
30C22×C8×C13—21no—
31C22×C8×C13—21no—
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C13×C4⋊C4D411yescharacteristic
34C2×C42×C13—21no—
35C2×C42×C13C2311yescharacteristic
36C2×#6103—22no—
37C2×#6103—22no—
38C2×#6103—21no—
39C2×C4⋊Dic13—21no—
40C2×C4⋊Dic13—21no—
41C2×C4⋊Dic13—21no—
42C2×C4⋊Dic13—21no—
43C2×C4⋊Dic13D412yes—
44C2×C4⋊Dic13D411yescharacteristic
45C22×#1055—21no—
46#88129—42no—
47#88129—42no—
48C4×D52—21no—
49C4×D52—21no—
50C4×D52—21no—
51C4×D52—21no—
52#88123—21no—
53#88123—21no—
54#88123—21no—
55#88123—21no—
56C13×C4⋊C8—21no—
57C13×C4⋊C8—21no—
58C4×C8×C13—21no—
59C4×C8×C13—21no—
60C13×#95—21no—
61#88071—22no—
62#88071—22no—
63#88061—42no—
64#88047—42no—
65C4⋊#1055—21no—
66C4⋊#1055D412yes—
67#10416—131nomaximal, Sylow
68C23×D13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13C2×D411yescharacteristic
72C22×C4×C13C2×D411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C22×Dic13—21no—
75C22×Dic13—22no—
76C22×Dic13—41no—
77C2×D52—21no—
78C2×D52—21no—
79C2×D52—21no—
80C2×D52—21no—
81C2×D52—21no—
82C2×D52D812yes—
83C2×C4×D13—41no—
84C2×C4×D13—41no—
85C2×C4×D13—41no—
86C2×C4×D13—41no—
87C2×C4×D13—41no—
88C2×C4×D13—41no—
89C2×Dic26—41no—
90C2×Dic26—41no—
91C2×Dic26—41no—
92C2×Dic26—41no—
93C2×Dic26—41no—
94C2×Dic26—41no—
95C2×C8×C13—22no—
96C2×C8×C13—41no—
97C2×C8×C13—41no—
98C2×C8×C13—41no—
99C2×C8×C13—41no—
100C2×C8×C13—41no—
101C13×C4⋊C4—21no—
102C13×C4⋊C4—21no—
103C13×C4⋊C4—21no—
104C13×C4⋊C4—21no—
105C42×C13—41no—
106C42×C13—41no—
107C42×C13C2×D411yescharacteristic
108C42×C13#4111yescharacteristic
109C42×C13#4111yescharacteristic
110C42×C13#4111yescharacteristic
111#6103—44no—
112#6103—44no—
113#6103—41no—
114#6103—41no—
115C4⋊Dic13—22no—
116C4⋊Dic13—21no—
117C4⋊Dic13—22no—
118C4⋊Dic13—21no—
119C4⋊Dic13—41no—
120C4⋊Dic13—41no—
121C4⋊Dic13—42no—
122C4⋊Dic13—41no—
123C4⋊Dic13—41no—
124C4⋊Dic13—41no—
125C4⋊Dic13—41no—
126C2×#1055—22no—
127C2×#1055—41no—
128C2×#1055—41no—
129#2547—131no—
130#1990—131no—
131#1947—131no—
132#1802—131no—
133C2×#332—131no—
134C2×D4⋊C8—131no—
135#1279D1311yescharacteristic, complemented
136C23×C13#12011yescharacteristic
137C22×D13—22no—
138C22×D13—41no—
139C22×D13—41no—
140C22×D13—41no—
141C22×D13—41no—
142C22×D13—41no—
143C22×D13—41no—
144C2×C4×C13—21no—
145C2×C4×C13—21no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13—41no—
151C2×C4×C13—41no—
152C2×C4×C13#12111yescharacteristic
153C2×C4×C13#12111yescharacteristic
154C2×C4×C13#12111yescharacteristic
155C2×C4×C13#12311yescharacteristic
156C2×C4×C13#12311yescharacteristic
157C2×C4×C13#12411yescharacteristic
158C2×C4×C13C2×D811yescharacteristic
159C2×C4×C13#13511yescharacteristic
160C2×C4×C13#13511yescharacteristic
161C2×C4×C13#13511yescharacteristic
162C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
163C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C13#13711yescharacteristic
165C2×C4×C13#13711yescharacteristic
166C2×Dic13—42no—
167C2×Dic13—41no—
168C2×Dic13—42no—
169C2×Dic13—41no—
170C2×Dic13—42no—
171C2×Dic13—41no—
172C2×Dic13—81no—
173C2×Dic13—81no—
174C2×Dic13—81no—
175D52—22no—
176D52—22no—
177D52—41no—
178D52—41no—
179C4×D13—81no—
180C4×D13—81no—
181C4×D13—81no—
182C4×D13—81no—
183Dic26—81no—
184Dic26—81no—
185Dic26—81no—
186Dic26—81no—
187C8×C13—42no—
188C8×C13—81no—
189#1055—42no—
190C2×C4⋊Q8—131no—
191C2×#124—261no—
192C2×C4×D4—131no—
193C2×#107—261no—
194C2×C4⋊C8—131no—
195C2×C4⋊C8C2×D1311yescharacteristic
196C2×#102—261no—
197C2×C4×C8C2×D1311yescharacteristic
198#397—262no—
199#391—261no—
200#384—131no—
201#380—261no—
202#380—261no—
203C4×C4⋊C4C2×D1311yescharacteristic
204#340—261no—
205#340—262no—
206#340—261no—
207#332—262no—
208D4⋊C8—262no—
209C22×C13#39411yescharacteristic
210C22×C13#44711yescharacteristic
211C22×C13#44911yescharacteristic
212C22×C13#45211yescharacteristic
213C22×C13#45211yescharacteristic
214C22×C13#45411yescharacteristic
215C22×C13#45611yescharacteristic
216C2×D13—42no—
217C2×D13—42no—
218C2×D13—42no—
219C2×D13—81no—
220C2×D13—81no—
221C2×D13—81no—
222C2×D13—81no—
223C4×C13—21no—
224C4×C13—21no—
225C4×C13—81no—
226C4×C13—81no—
227C4×C13#46311yescharacteristic
228C4×C13#46411yescharacteristic
229C4×C13#46611yescharacteristic
230C4×C13#46811yescharacteristic
231C4×C13#48011yescharacteristic
232C4×C13#48211yescharacteristic
233C4×C13#48811yescharacteristic
234C4×C13#48911yescharacteristic
235Dic13—82no—
236Dic13—81no—
237Dic13—161no—
238C22×Q8—261no—
239C22×D4—131no—
240C23×C4—261no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8—261no—
244C4⋊Q8—261no—
245C4⋊Q8—261no—
246C4⋊Q8—261no—
247C4⋊Q8—261no—
248#124—522no—
249#124—522no—
250C4×D4—261no—
251C4×D4—261no—
252C4×D4—261no—
253C4×D4—261no—
254C2×C4⋊C4—131no—
255C2×C4⋊C4—132no—
256C2×C4⋊C4—261no—
257C2×C4⋊C4—261no—
258C2×C4⋊C4—261no—
259C2×C4⋊C4—261no—
260C2×C4⋊C4D5211yescharacteristic
261C2×C4⋊C4D5211yescharacteristic
262C2×C22⋊C4—262no—
263C2×C22⋊C4—262no—
264C2×C22⋊C4—261no—
265C2×C42—21no—
266C2×C42C22×D1311yescharacteristic
267#107—522no—
268C4⋊C8—21no—
269C4⋊C8—21no—
270C4⋊C8—132no—
271C4⋊C8—261no—
272#102—522no—
273C4×C8—21no—
274C4×C8—21no—
275#95—21no—
276#95—262no—
277#95—262no—
278C2×C13#162511yescharacteristic
279C2×C13#163811yescharacteristic
280C2×C13#164711yescharacteristic
281C2×C13#165211yescharacteristic
282C2×C13#203311yescharacteristic
283C2×C13#203811yescharacteristic
284C2×C13#204211yescharacteristic
285D13—82no—
286C24—261no—
287C2×Q8—521no—
288C2×Q8—521no—
289C2×Q8—521no—
290C2×Q8—521no—
291C2×Q8—521no—
292C2×Q8—521no—
293C2×D4—132no—
294C2×D4—261no—
295C2×D4—261no—
296C2×D4—261no—
297C2×D4—261no—
298C2×D4—261no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—261no—
302C22×C4—262no—
303C22×C4—521no—
304C22×C4—521no—
305C22×C4—521no—
306C22×C4—521no—
307C22×C4—521no—
308C22×C4—521no—
309C22×C4—521no—
310C22×C4C2×D5211yescharacteristic
311C22×C4D4×D1311yescharacteristic
312C22×C4D4×D1311yescharacteristic
313C2×C8—22no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—262no—
320C2×C8—521no—
321C2×C8—521no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—261no—
327C4⋊C4—262no—
328C4⋊C4—261no—
329C4⋊C4—262no—
330C4⋊C4—522no—
331C4⋊C4—521no—
332C4⋊C4—521no—
333C4⋊C4—521no—
334C4⋊C4—521no—
335C4⋊C4—521no—
336C4⋊C4—521no—
337C22⋊C4—524no—
338C22⋊C4—524no—
339C22⋊C4—521no—
340C22⋊C4—521no—
341C42—41no—
342C42—41no—
343C42#612711yescharacteristic
344C42#612711yescharacteristic
345C42D4×D1311yescharacteristic
346C42#613111yescharacteristic
347C13#1041611yescharacteristic, complemented, Sylow
348C23—262no—
349C23—521no—
350C23—521no—
351C23—521no—
352C23—521no—
353C23—521no—
354C23—521no—
355C23#8813611yescharacteristic
356Q8—1041no—
357Q8—1041no—
358Q8—1041no—
359Q8—1041no—
360D4—262no—
361D4—262no—
362D4—521no—
363D4—521no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—522no—
373C2×C4—522no—
374C2×C4—521no—
375C2×C4—522no—
376C2×C4—521no—
377C2×C4—521no—
378C2×C4—1041no—
379C2×C4—1041no—
380C2×C4—1041no—
381C2×C4—1041no—
382C2×C4—1041no—
383C2×C4—1041no—
384C2×C4—1041no—
385C2×C4#8812911yescharacteristic
386C2×C4#8813811yescharacteristic
387C2×C4#8813811yescharacteristic
388C2×C4#8814811yescharacteristic
389C2×C4#8814811yescharacteristic
390C2×C4#8814911yescharacteristic
391C2×C4#8815811yescharacteristic
392C2×C4#8815811yescharacteristic
393C2×C4#8816211yescharacteristic
394C2×C4#8816311yescharacteristic
395C2×C4D8×D1311yescharacteristic
396C2×C4#8816811yescharacteristic
397C2×C4#8817011yescharacteristic
398C2×C4#8817211yescharacteristic
399C8—42no—
400C8—81no—
401C8—522no—
402C22—522no—
403C22—522no—
404C22—522no—
405C22—1041no—
406C22—1041no—
407C22—1041no—
408C22—1041no—
409C22#1171833311yescharacteristic
410C22#1171839411yescharacteristic
411C22#1171839511yescharacteristic
412C22#1171843411yescharacteristic
413C22#1171847111yescharacteristic
414C22#1171848711yescharacteristic
415C22#1171848811yescharacteristic
416C4—21no—
417C4—21no—
418C4—81no—
419C4—81no—
420C4—1042no—
421C4—1041no—
422C4—2081no—
423C4#1171835811yescharacteristic
424C4#1171837511yescharacteristic
425C4#1171843611yescharacteristic
426C4#1171847311yescharacteristic
427C4#1171850511yescharacteristic
428C4#1171850611yescharacteristic
429C4#1171852711yescharacteristic
430C4#1171854311yescharacteristic
431C2—1042no—
432C2#1311392811yescharacteristic
433C2#1311401111yescharacteristic
434C2#1311407411yescharacteristic
435C2#1311410811yescharacteristic
436C2#1311602111yescharacteristic
437C2#1311605611yescharacteristic
438C2#1311607811yescharacteristic
subgroupG/H
centerC23#88136
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1279C2
socleC23×C13#120
prime radicalC22×D52D4
hypercenter#1279D13
hypocenterC13#10416
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
2. #13115797C2semidirect
3. #13115594C2semidirect
5. C2×#11718074C2semidirect
7. C13×#1279C2semidirect
135. #1279D13semidirect
347. C13#10416semidirect

Maximal subgroups

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

subgroupindex
#131198312
#131157972
#131155942
#131148372
C2×#117180742
C2×#117180512
C13×#12792
#1041613