Finite Group Databasebeta

← #15781621

Subgroups — #15781621

Order 3328.

618 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88067C211yesmaximal, characteristic, complemented
2C2×#11718777C211yesmaximal, characteristic, complemented
3C2×#11718084C211yesmaximal, characteristic, complemented
4C2×#11718154C211yesmaximal, characteristic, complemented
5C2×C22⋊#6090C211yesmaximal, characteristic, complemented
6#13112927C211yesmaximal, characteristic, complemented
7C2×C13×#466C211yesmaximal, characteristic
8C22×C13×D8C2211yescharacteristic
9C23×C8×C13C2211yescharacteristic
10C2×C13×#121—21no—
11C2×#88178—21no—
12C22×Dic52C2211yescharacteristic
13C13×#466—22no—
14C13×#466—22no—
15C2×C13×#107C2211yescharacteristic
16C2×C13×#102—21no—
17C2×#88067—22no—
18C2×#88067—22no—
19C2×#88067—22no—
20#11718777—22no—
21#11718777—22no—
22C2×#88058C2211yescharacteristic
23C2×#88056—21no—
24C22×#6090C2211yescharacteristic
25C22×#6090C2211yescharacteristic
26#11718154—22no—
27C22⋊#6090—22no—
28#11718084—22no—
29C22×D4×C13—21no—
30C22×D4×C13—41no—
31C23×C4×C13D411yescharacteristic
32C22×Dic26—21no—
33C2×C13×D8—21no—
34C2×C13×D8—21no—
35C2×C13×D8—21no—
36C2×C13×D8—21no—
37C2×C13×D8—21no—
38C2×C13×D8D412yes—
39C22×C8×C13—21no—
40C22×C8×C13—21no—
41C22×C8×C13—21no—
42C22×C8×C13—21no—
43C22×C8×C13—21no—
44C22×C8×C13—21no—
45C22×C8×C13D411yescharacteristic
46C22×C8×C13C2311yescharacteristic
47C13×#121—24no—
48C13×#121—42no—
49C2×C13×C4⋊C4—21no—
50C2×C13×C22⋊C4—41no—
51C2×C22⋊Dic13—41no—
52C2×C4⋊Dic13—21no—
53#88178—24no—
54#88178—42no—
55C2×#6101—41no—
56C2×Dic52—21no—
57C2×Dic52—21no—
58C2×Dic52—21no—
59C2×Dic52—21no—
60C2×Dic52—21no—
61C2×Dic52D412yescomplemented
62C13×#107—21no—
63C13×#107D412yes—
64C13×#102—24no—
65#88067—28no—
66#88058—21no—
67#88058D412yescomplemented
68#88056—24no—
69C2×#6090—21no—
70C2×#6090—21no—
71C2×#6090—21no—
72C2×#6090—21no—
73C2×#6090—21no—
74C2×#6090D412yescomplemented
75#13305—131nomaximal, Sylow
76C24×C13—41no—
77C24×C13D811yescharacteristic
78C2×D4×C13—22no—
79C2×D4×C13—44no—
80C2×D4×C13—41no—
81C2×D4×C13—41no—
82C2×D4×C13—41no—
83C2×D4×C13—41no—
84C2×D4×C13—41no—
85C2×D4×C13—82no—
86C2×D4×C13—82no—
87C22×C4×C13—21no—
88C22×C4×C13—21no—
89C22×C4×C13—21no—
90C22×C4×C13—21no—
91C22×C4×C13—21no—
92C22×C4×C13—21no—
93C22×C4×C13—41no—
94C22×C4×C13D811yescharacteristic
95C22×C4×C13C2×D411yescharacteristic
96C22×Dic13—41no—
97C22×Dic13—41no—
98C2×Dic26—22no—
99C2×Dic26—41no—
100C2×Dic26—41no—
101C2×Dic26—41no—
102C2×Dic26—41no—
103C2×Dic26—41no—
104C13×D8—22no—
105C13×D8—22no—
106C13×D8—41no—
107C13×D8—41no—
108C2×C8×C13—21no—
109C2×C8×C13—21no—
110C2×C8×C13—21no—
111C2×C8×C13—41no—
112C2×C8×C13—41no—
113C2×C8×C13—41no—
114C2×C8×C13—41no—
115C2×C8×C13C2×D411yescharacteristic
116C2×C8×C13C2×D411yescharacteristic
117C2×C8×C13C2×D411yescharacteristic
118C2×C8×C13C2×D411yescharacteristic
119C2×C8×C13C2×D411yescharacteristic
120C2×C8×C13#4111yescharacteristic
121C13×C4⋊C4—22no—
122C13×C4⋊C4—41no—
123C13×C22⋊C4—44no—
124C22⋊Dic13—44no—
125C4⋊Dic13—22no—
126C4⋊Dic13—41no—
127#6101—44no—
128Dic52—22no—
129Dic52—22no—
130Dic52—41no—
131Dic52—41no—
132#6090—22no—
133#6090—41no—
134C22×SD32—131no—
135C2×#467—131no—
136C2×#466D1311yescharacteristic
137C2×#358—131no—
138C2×#357—131no—
139C2×C22⋊C16—131no—
140#1380—131no—
141C23×C13—21no—
142C23×C13—21no—
143C23×C13—21no—
144C23×C13—21no—
145C23×C13—21no—
146C23×C13—21no—
147C23×C13—42no—
148C23×C13—81no—
149C23×C13—81no—
150C23×C13—81no—
151C23×C13—81no—
152C23×C13—81no—
153C23×C13—81no—
154C23×C13SD3212yescomplemented
155C23×C13C2×D811yescharacteristic
156D4×C13—42no—
157D4×C13—42no—
158D4×C13—88no—
159D4×C13—81no—
160D4×C13—81no—
161C2×C4×C13—21no—
162C2×C4×C13—21no—
163C2×C4×C13—21no—
164C2×C4×C13—41no—
165C2×C4×C13—41no—
166C2×C4×C13—41no—
167C2×C4×C13—41no—
168C2×C4×C13—42no—
169C2×C4×C13—81no—
170C2×C4×C13—81no—
171C2×C4×C13#12011yescharacteristic
172C2×C4×C13#12011yescharacteristic
173C2×C4×C13#12111yescharacteristic
174C2×C4×C13#13511yescharacteristic
175C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
176C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
177C2×Dic13—42no—
178C2×Dic13—42no—
179C2×Dic13—81no—
180C2×Dic13—81no—
181C2×Dic13—81no—
182C2×Dic13—81no—
183Dic26—42no—
184Dic26—42no—
185Dic26—81no—
186Dic26—81no—
187C8×C13—41no—
188C8×C13#12011yescharacteristic
189C8×C13#12111yescharacteristic
190C8×C13#12111yescharacteristic
191C8×C13#12711yescharacteristic
192C22×Q16—131no—
193C22×D8C2×D1311yescharacteristic
194C23×C8C2×D1311yescharacteristic
195C2×C22⋊Q8—261no—
196C2×#121—21no—
197C2×SD32—262no—
198C2×SD32—262no—
199C2×SD32—262no—
200C22×C16—131no—
201C22×C16—131no—
202#467—262no—
203#467—262no—
204#466—22no—
205#466—22no—
206C2×#107—131no—
207C2×#107C2×D1311yescharacteristic
208C2×#103—261no—
209C2×#102—21no—
210#358—262no—
211#357—262no—
212C22⋊C16—262no—
213C22×C13—22no—
214C22×C13—22no—
215C22×C13—22no—
216C22×C13—41no—
217C22×C13—41no—
218C22×C13—41no—
219C22×C13—41no—
220C22×C13—82no—
221C22×C13—82no—
222C22×C13—82no—
223C22×C13—161no—
224C22×C13—161no—
225C22×C13—161no—
226C22×C13—161no—
227C22×C13#44711yescharacteristic
228C22×C13#44711yescharacteristic
229C22×C13#46611yescharacteristic
230C22×C13C2×SD3211yescharacteristic
231C22×C13#50811yescharacteristic
232C22×C13#50911yescharacteristic
233C22×C13#51011yescharacteristic
234C4×C13—41no—
235C4×C13—82no—
236C4×C13#39211yescharacteristic
237C4×C13#44911yescharacteristic
238C4×C13#44911yescharacteristic
239C4×C13#46911yescharacteristic
240Dic13—82no—
241Dic13—82no—
242C22×Q8—261no—
243C22×D4—21no—
244C22×D4—41no—
245C23×C4C22⋊D1311yescharacteristic
246C2×Q16—132no—
247C2×Q16—261no—
248C2×Q16—261no—
249C2×Q16—261no—
250C2×Q16—261no—
251C2×Q16—261no—
252C2×D8—21no—
253C2×D8—21no—
254C2×D8—21no—
255C2×D8—21no—
256C2×D8—21no—
257C2×D8C22⋊D1312yes—
258C22×C8—21no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—21no—
264C22×C8C22⋊D1311yescharacteristic
265C22×C8C22×D1311yescharacteristic
266C22⋊Q8—264no—
267C22⋊Q8—522no—
268#121—24no—
269#121—42no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—261no—
272C2×C4⋊C4—521no—
273C2×C22⋊C4—41no—
274C2×C22⋊C4—521no—
275SD32—268no—
276C2×C16—132no—
277C2×C16—261no—
278C2×C16—261no—
279C2×C16—261no—
280C2×C16—261no—
281C2×C16—261no—
282#107—21no—
283#107—132no—
284#107—261no—
285#107C22⋊D1312yes—
286#103—264no—
287#102—24no—
288C2×C13—42no—
289C2×C13—162no—
290C2×C13#199911yescharacteristic
291C2×C13#218511yescharacteristic
292C2×C13#218611yescharacteristic
293C2×C13#218711yescharacteristic
294C2×C13#218911yescharacteristic
295C2×C13#221711yescharacteristic
296C2×C13#222011yescharacteristic
297C24—41no—
298C24#610411yescharacteristic
299C2×Q8—262no—
300C2×Q8—521no—
301C2×Q8—521no—
302C2×Q8—521no—
303C2×Q8—521no—
304C2×Q8—521no—
305C2×D4—22no—
306C2×D4—44no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—41no—
312C2×D4—82no—
313C2×D4—82no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—41no—
321C22×C4—521no—
322C22×C4—521no—
323C22×C4#610411yescharacteristic
324C22×C4C2×C22⋊D1311yescharacteristic
325Q16—262no—
326Q16—262no—
327Q16—521no—
328Q16—521no—
329D8—22no—
330D8—22no—
331D8—41no—
332D8—41no—
333C2×C8—21no—
334C2×C8—21no—
335C2×C8—21no—
336C2×C8—41no—
337C2×C8—41no—
338C2×C8—41no—
339C2×C8—41no—
340C2×C8D4×D1311yescharacteristic
341C2×C8D4×D1311yescharacteristic
342C2×C8D4×D1311yescharacteristic
343C2×C8#612911yescharacteristic
344C2×C8C2×C22⋊D1311yescharacteristic
345C2×C8C2×C22⋊D1311yescharacteristic
346C4⋊C4—22no—
347C4⋊C4—41no—
348C4⋊C4—262no—
349C4⋊C4—524no—
350C4⋊C4—521no—
351C22⋊C4—44no—
352C22⋊C4—524no—
353C16—262no—
354C16—521no—
355C13#1330511yescharacteristic, complemented, Sylow
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—42no—
363C23—81no—
364C23—81no—
365C23—81no—
366C23—81no—
367C23—81no—
368C23—81no—
369C23#8806712yescomplemented
370C23C2×#610411yescharacteristic
371Q8—522no—
372Q8—522no—
373Q8—1041no—
374Q8—1041no—
375D4—42no—
376D4—42no—
377D4—88no—
378D4—81no—
379D4—81no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—81no—
389C2×C4—81no—
390C2×C4—522no—
391C2×C4—522no—
392C2×C4—1041no—
393C2×C4—1041no—
394C2×C4—1041no—
395C2×C4—1041no—
396C2×C4#8818611yescharacteristic
397C2×C4#8819111yescharacteristic
398C2×C4#8819311yescharacteristic
399C2×C4#8820311yescharacteristic
400C2×C4#8820411yescharacteristic
401C2×C4#8820711yescharacteristic
402C8—41no—
403C8#8819111yescharacteristic
404C8#8819211yescharacteristic
405C8#8819311yescharacteristic
406C8#8819411yescharacteristic
407C22—22no—
408C22—22no—
409C22—22no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—82no—
415C22—82no—
416C22—82no—
417C22—161no—
418C22—161no—
419C22—161no—
420C22—161no—
421C22#1171869711yescharacteristic
422C22#1171869911yescharacteristic
423C22#1171880811yescharacteristic
424C22C2×#8806711yescharacteristic
425C22#1171885511yescharacteristic
426C22#1171885611yescharacteristic
427C22#1171887811yescharacteristic
428C4—41no—
429C4—82no—
430C4—1042no—
431C4—1042no—
432C4#1171869811yescharacteristic
433C4#1171870011yescharacteristic
434C4#1171888411yescharacteristic
435C4#1171889911yescharacteristic
436C2—42no—
437C2—162no—
438C2#1311583211yescharacteristic
439C2#1311675211yescharacteristic
440C2#1311675711yescharacteristic
441C2#1311676511yescharacteristic
442C2#1311677611yescharacteristic
443C2#1311693011yescharacteristic
444C2#1311694711yescharacteristic
subgroupG/H
centerC23C2×#6104
commutator, cosocleC22×C8×C13C23
FrattiniC22×C8C22×D13
Fitting, prime radicalC2×C13×#466C2
socleC23×C13C2×D8
hypercenterC2×#466D13
hypocenterC13#13305
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×#88067C2semidirect
2. C2×#11718777C2semidirect
3. C2×#11718084C2semidirect
4. C2×#11718154C2semidirect
5. C2×C22⋊#6090C2semidirect
6. #13112927C2semidirect
61. C2×Dic52D4semidirect
67. #88058D4semidirect
74. C2×#6090D4semidirect
154. C23×C13SD32semidirect
355. C13#13305semidirect
369. C23#88067semidirect

Maximal subgroups

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

subgroupindex
C22×#880672
C2×#117187772
C2×#117180842
C2×#117181542
C2×C22⋊#60902
#131129272
C2×C13×#4662
#1330513