Finite Group Databasebeta

← #15781614

Subgroups — #15781614

Order 3328.

670 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88066C211yesmaximal, characteristic, complemented
2C2×#11718776C211yesmaximal, characteristic, complemented
3C2×#11718154C211yesmaximal, characteristic, complemented
4C2×#11718083C211yesmaximal, characteristic, complemented
5C2×C22⋊#6090C211yesmaximal, characteristic, complemented
6#13112927C211yesmaximal, characteristic, complemented
7C2×C13×#466C211yesmaximal, characteristic, complemented
8C22×C13×D8C2211yescharacteristic
9C23×C8×C13C2211yescharacteristic
10C2×C13×#121—21no—
11C2×#88184—21no—
12C22×D104C2211yescharacteristic
13C13×#466—22no—
14C13×#466—22no—
15C2×C13×#107C2211yescharacteristic
16C2×C13×#102—21no—
17C2×#88066—22no—
18C2×#88066—22no—
19C2×#88066—22no—
20#11718776—22no—
21#11718776—22no—
22C2×#88061—21no—
23C2×#88058C2211yescharacteristic
24C22×#6090C2211yescharacteristic
25C22×#6090C2211yescharacteristic
26#11718154—22no—
27C22⋊#6090—22no—
28#11718083—22no—
29C22×D4×C13—21no—
30C22×D4×C13—41no—
31C23×C4×C13D411yescharacteristic
32C22×C22⋊D13—41no—
33C22×D52—21no—
34C2×C13×D8—21no—
35C2×C13×D8—21no—
36C2×C13×D8—21no—
37C2×C13×D8—21no—
38C2×C13×D8—21no—
39C2×C13×D8D412yescomplemented
40C22×C8×C13—21no—
41C22×C8×C13—21no—
42C22×C8×C13—21no—
43C22×C8×C13—21no—
44C22×C8×C13—21no—
45C22×C8×C13—21no—
46C22×C8×C13D411yescharacteristic
47C22×C8×C13C2311yescharacteristic
48C13×#121—24no—
49C13×#121—42no—
50C2×C13×C4⋊C4—21no—
51C2×C13×C22⋊C4—41no—
52#88184—24no—
53#88184—42no—
54C2×#6103—41no—
55C2×C4⋊Dic13—21no—
56C2×D104—21no—
57C2×D104—21no—
58C2×D104—21no—
59C2×D104—21no—
60C2×D104—21no—
61C2×D104D412yescomplemented
62C13×#107—21no—
63C13×#107D412yescomplemented
64C13×#102—24no—
65#88066—28no—
66#88061—24no—
67#88058—21no—
68#88058D412yescomplemented
69C2×#6090—21no—
70C2×#6090—21no—
71C2×#6090—21no—
72C2×#6090—21no—
73C2×#6090—21no—
74C2×#6090D412yescomplemented
75#13304—131nomaximal, Sylow
76C24×C13—41no—
77C24×C13D811yescharacteristic
78C23×D13—41no—
79C2×D4×C13—22no—
80C2×D4×C13—44no—
81C2×D4×C13—41no—
82C2×D4×C13—41no—
83C2×D4×C13—41no—
84C2×D4×C13—41no—
85C2×D4×C13—41no—
86C2×D4×C13—82no—
87C2×D4×C13—82no—
88C22×C4×C13—21no—
89C22×C4×C13—21no—
90C22×C4×C13—21no—
91C22×C4×C13—21no—
92C22×C4×C13—21no—
93C22×C4×C13—21no—
94C22×C4×C13—41no—
95C22×C4×C13D811yescharacteristic
96C22×C4×C13C2×D411yescharacteristic
97C2×C22⋊D13—44no—
98C2×C22⋊D13—82no—
99C2×C22⋊D13—82no—
100C22×Dic13—41no—
101C2×D52—22no—
102C2×D52—41no—
103C2×D52—41no—
104C2×D52—41no—
105C2×D52—41no—
106C2×D52—41no—
107C13×D8—22no—
108C13×D8—22no—
109C13×D8—41no—
110C13×D8—41no—
111C2×C8×C13—21no—
112C2×C8×C13—21no—
113C2×C8×C13—21no—
114C2×C8×C13—41no—
115C2×C8×C13—41no—
116C2×C8×C13—41no—
117C2×C8×C13—41no—
118C2×C8×C13C2×D411yescharacteristic
119C2×C8×C13C2×D411yescharacteristic
120C2×C8×C13C2×D411yescharacteristic
121C2×C8×C13C2×D411yescharacteristic
122C2×C8×C13C2×D411yescharacteristic
123C2×C8×C13#4111yescharacteristic
124C13×C4⋊C4—22no—
125C13×C4⋊C4—41no—
126C13×C22⋊C4—44no—
127#6103—44no—
128C4⋊Dic13—22no—
129C4⋊Dic13—41no—
130D104—22no—
131D104—22no—
132D104—41no—
133D104—41no—
134#6090—22no—
135#6090—41no—
136C22×D16—131no—
137C2×#466—131no—
138C2×#466D1311yescharacteristic, complemented
139C2×#357—131no—
140C2×#357—131no—
141C2×C22⋊C16—131no—
142#1380—131no—
143C23×C13—21no—
144C23×C13—21no—
145C23×C13—21no—
146C23×C13—21no—
147C23×C13—21no—
148C23×C13—21no—
149C23×C13—42no—
150C23×C13—81no—
151C23×C13—81no—
152C23×C13—81no—
153C23×C13—81no—
154C23×C13—81no—
155C23×C13—81no—
156C23×C13D1612yescomplemented
157C23×C13C2×D811yescharacteristic
158C22×D13—42no—
159C22×D13—81no—
160C22×D13—81no—
161C22×D13—81no—
162C22×D13—81no—
163C22×D13—81no—
164C22×D13—81no—
165D4×C13—42no—
166D4×C13—42no—
167D4×C13—88no—
168D4×C13—81no—
169D4×C13—81no—
170C2×C4×C13—21no—
171C2×C4×C13—21no—
172C2×C4×C13—21no—
173C2×C4×C13—41no—
174C2×C4×C13—41no—
175C2×C4×C13—41no—
176C2×C4×C13—41no—
177C2×C4×C13—42no—
178C2×C4×C13—81no—
179C2×C4×C13—81no—
180C2×C4×C13#12011yescharacteristic
181C2×C4×C13#12011yescharacteristic
182C2×C4×C13#12111yescharacteristic
183C2×C4×C13#13511yescharacteristic
184C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
185C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
186C22⋊D13—88no—
187C2×Dic13—42no—
188C2×Dic13—81no—
189C2×Dic13—81no—
190D52—42no—
191D52—42no—
192D52—81no—
193D52—81no—
194C8×C13—41no—
195C8×C13#12011yescharacteristic
196C8×C13#12111yescharacteristic
197C8×C13#12111yescharacteristic
198C8×C13#12711yescharacteristic
199C22×D8—131no—
200C22×D8C2×D1311yescharacteristic
201C23×C8C2×D1311yescharacteristic
202C2×#121—21no—
203C2×#121—261no—
204C2×D16—262no—
205C2×D16—262no—
206C2×D16—262no—
207C22×C16—131no—
208C22×C16—131no—
209#466—22no—
210#466—22no—
211#466—262no—
212#466—262no—
213C2×#107—131no—
214C2×#107C2×D1311yescharacteristic
215C2×#102—21no—
216C2×#102—261no—
217#357—262no—
218#357—262no—
219C22⋊C16—262no—
220C22×C13—22no—
221C22×C13—22no—
222C22×C13—22no—
223C22×C13—41no—
224C22×C13—41no—
225C22×C13—41no—
226C22×C13—41no—
227C22×C13—82no—
228C22×C13—82no—
229C22×C13—82no—
230C22×C13—161no—
231C22×C13—161no—
232C22×C13—161no—
233C22×C13—161no—
234C22×C13#44711yescharacteristic
235C22×C13#44711yescharacteristic
236C22×C13#46611yescharacteristic
237C22×C13C2×D1611yescharacteristic
238C22×C13#50811yescharacteristic
239C22×C13#50911yescharacteristic
240C22×C13#50911yescharacteristic
241C2×D13—82no—
242C2×D13—82no—
243C2×D13—82no—
244C2×D13—161no—
245C2×D13—161no—
246C2×D13—161no—
247C2×D13—161no—
248C4×C13—41no—
249C4×C13—82no—
250C4×C13#39211yescharacteristic
251C4×C13#44911yescharacteristic
252C4×C13#44911yescharacteristic
253C4×C13#46911yescharacteristic
254Dic13—82no—
255C22×D4—21no—
256C22×D4—41no—
257C22×D4—261no—
258C22×D4—521no—
259C23×C4C22⋊D1311yescharacteristic
260C2×D8—21no—
261C2×D8—21no—
262C2×D8—21no—
263C2×D8—21no—
264C2×D8—21no—
265C2×D8—132no—
266C2×D8—261no—
267C2×D8—261no—
268C2×D8—261no—
269C2×D8—261no—
270C2×D8—261no—
271C2×D8C22⋊D1312yescomplemented
272C22×C8—21no—
273C22×C8—21no—
274C22×C8—21no—
275C22×C8—21no—
276C22×C8—21no—
277C22×C8—21no—
278C22×C8C22⋊D1311yescharacteristic
279C22×C8C22×D1311yescharacteristic
280#121—24no—
281#121—42no—
282#121—264no—
283#121—522no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—261no—
286C2×C22⋊C4—41no—
287C2×C22⋊C4—521no—
288D16—268no—
289C2×C16—132no—
290C2×C16—261no—
291C2×C16—261no—
292C2×C16—261no—
293C2×C16—261no—
294C2×C16—261no—
295#107—21no—
296#107—132no—
297#107—261no—
298#107C22⋊D1312yescomplemented
299#102—24no—
300#102—264no—
301C2×C13—42no—
302C2×C13—162no—
303C2×C13#199911yescharacteristic
304C2×C13#218411yescharacteristic
305C2×C13#218411yescharacteristic
306C2×C13#218611yescharacteristic
307C2×C13#218611yescharacteristic
308C2×C13#221511yescharacteristic
309C2×C13#221811yescharacteristic
310D13—162no—
311C24—41no—
312C24—521no—
313C24#610411yescharacteristic
314C2×D4—22no—
315C2×D4—44no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—82no—
322C2×D4—82no—
323C2×D4—262no—
324C2×D4—524no—
325C2×D4—521no—
326C2×D4—521no—
327C2×D4—521no—
328C2×D4—521no—
329C2×D4—521no—
330C2×D4—1042no—
331C2×D4—1042no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—41no—
339C22×C4—521no—
340C22×C4#610411yescharacteristic
341C22×C4C2×C22⋊D1311yescharacteristic
342D8—22no—
343D8—22no—
344D8—41no—
345D8—41no—
346D8—262no—
347D8—262no—
348D8—521no—
349D8—521no—
350C2×C8—21no—
351C2×C8—21no—
352C2×C8—21no—
353C2×C8—41no—
354C2×C8—41no—
355C2×C8—41no—
356C2×C8—41no—
357C2×C8D4×D1311yescharacteristic
358C2×C8D4×D1311yescharacteristic
359C2×C8D4×D1311yescharacteristic
360C2×C8#612911yescharacteristic
361C2×C8C2×C22⋊D1311yescharacteristic
362C2×C8C2×C22⋊D1311yescharacteristic
363C4⋊C4—22no—
364C4⋊C4—41no—
365C4⋊C4—262no—
366C4⋊C4—521no—
367C22⋊C4—44no—
368C22⋊C4—524no—
369C16—262no—
370C16—521no—
371C13#1330411yescharacteristic, complemented, Sylow
372C23—21no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—42no—
379C23—81no—
380C23—81no—
381C23—81no—
382C23—81no—
383C23—81no—
384C23—81no—
385C23—522no—
386C23—1041no—
387C23—1041no—
388C23—1041no—
389C23—1041no—
390C23—1041no—
391C23—1041no—
392C23#8806612yescomplemented
393C23C2×#610411yescharacteristic
394D4—42no—
395D4—42no—
396D4—88no—
397D4—81no—
398D4—81no—
399D4—522no—
400D4—522no—
401D4—1048no—
402D4—1041no—
403D4—1041no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—42no—
412C2×C4—81no—
413C2×C4—81no—
414C2×C4—522no—
415C2×C4—1041no—
416C2×C4—1041no—
417C2×C4#8818611yescharacteristic
418C2×C4#8819111yescharacteristic
419C2×C4#8819311yescharacteristic
420C2×C4#8820311yescharacteristic
421C2×C4#8820411yescharacteristic
422C2×C4#8820711yescharacteristic
423C8—41no—
424C8#8819111yescharacteristic
425C8#8819211yescharacteristic
426C8#8819311yescharacteristic
427C8#8819411yescharacteristic
428C22—22no—
429C22—22no—
430C22—22no—
431C22—41no—
432C22—41no—
433C22—41no—
434C22—41no—
435C22—82no—
436C22—82no—
437C22—82no—
438C22—161no—
439C22—161no—
440C22—161no—
441C22—161no—
442C22—1042no—
443C22—1042no—
444C22—1042no—
445C22—2081no—
446C22—2081no—
447C22—2081no—
448C22—2081no—
449C22#1171869711yescharacteristic
450C22#1171869911yescharacteristic
451C22C2×#8806611yescharacteristic
452C22#1171880811yescharacteristic
453C22#1171885411yescharacteristic
454C22#1171885511yescharacteristic
455C22#1171887811yescharacteristic
456C4—41no—
457C4—82no—
458C4—1042no—
459C4#1171869811yescharacteristic
460C4#1171870011yescharacteristic
461C4#1171888411yescharacteristic
462C4#1171889911yescharacteristic
463C2—42no—
464C2—162no—
465C2—2082no—
466C2#1311583211yescharacteristic
467C2#1311674711yescharacteristic
468C2#1311674811yescharacteristic
469C2#1311675711yescharacteristic
470C2#1311675911yescharacteristic
471C2#1311692011yescharacteristic
472C2#1311693711yescharacteristic
subgroupG/H
centerC23C2×#6104
commutator, cosocleC22×C8×C13C23
FrattiniC22×C8C22×D13
FittingC2×C13×#466C2
socleC23×C13C2×D8
hypercenterC2×#466D13
hypocenterC13#13304
LCSG ▷ C22×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C2×#466

Complements

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

NH ≅ G/Ntype
1. C22×#88066C2semidirect
2. C2×#11718776C2semidirect
3. C2×#11718154C2semidirect
4. C2×#11718083C2semidirect
5. C2×C22⋊#6090C2semidirect
6. #13112927C2semidirect
7. C2×C13×#466C2semidirect
39. C2×C13×D8D4semidirect
61. C2×D104D4semidirect
63. C13×#107D4semidirect
68. #88058D4semidirect
74. C2×#6090D4semidirect
138. C2×#466D13semidirect
156. C23×C13D16semidirect
271. C2×D8C22⋊D13semidirect
298. #107C22⋊D13semidirect
371. C13#13304semidirect
392. C23#88066semidirect

Maximal subgroups

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

subgroupindex
C22×#880662
C2×#117187762
C2×#117181542
C2×#117180832
C2×C22⋊#60902
#131129272
C2×C13×#4662
#1330413