Finite Group Databasebeta

← #15761906

Subgroups — #15761906

Order 3328.

668 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123137C211yesmaximal, characteristic
2C2×#11718059C212yesmaximal, complemented
3C2×#11718062C212yesmaximal
4#13113063C211yesmaximal, characteristic, complemented
5C4×C13×C22⋊C8C211yesmaximal, characteristic, complemented
6C22×C42×C13C2211yescharacteristic
7C2×#88184C2211yescharacteristic
8C2×#88178C2211yescharacteristic
9C2×#88129C411yescharacteristic, complemented
10C2×C13×C22⋊C8C2212yes—
11C2×C4×C8×C13—21no—
12#11718874—21no—
13#11718874—21no—
14C2×#88071—21no—
15C2×#88071—21no—
16C2×#88071C2212yes—
17#11718601—21no—
18#11718601—21no—
19#11718600C411yescharacteristic, complemented
20#11718597C411yescharacteristic, complemented
21#11718590C411yescharacteristic, complemented
22C13×#336—21no—
23#11718062—24no—
24#11718059—24no—
25C23×C4×C13D411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C23×C4×C13C2311yescharacteristic
28C22×C22⋊D13—21no—
29C23×Dic13—22no—
30C22×D52C2×C411yescharacteristic
31C22×Dic26C2×C411yescharacteristic
32C22×C8×C13—22no—
33C2×C42×C13—42no—
34C2×C42×C13C2×C411yescharacteristic
35C2×C42×C13C2×C411yescharacteristic
36C2×C42×C13D411yescharacteristic
37C2×C42×C13D411yescharacteristic
38C2×C22⋊Dic13—21no—
39#88184—22no—
40#88184—22no—
41C2×#6103—21no—
42C2×#6103—21no—
43C2×#6103—21no—
44C2×#6103—21no—
45C2×#6103—21no—
46C2×C4⋊Dic13C2×C411yescharacteristic
47C2×C4⋊Dic13C2×C411yescharacteristic
48#88178—22no—
49#88178—22no—
50C2×#6101—21no—
51#88129—42no—
52C13×C22⋊C8—22no—
53C13×C22⋊C8D414yes—
54C4×C8×C13—42no—
55#88071—24no—
56#88071—21no—
57#88071—21no—
58#88071—21no—
59#88071—21no—
60#88071—22no—
61#88071—22no—
62#88071—42no—
63#9681—131nomaximal, Sylow
64C24×C13C2×D411yescharacteristic
65C23×D13—21no—
66C22×C4×C13—22no—
67C22×C4×C13—22no—
68C22×C4×C13—22no—
69C22×C4×C13—22no—
70C22×C4×C13—41no—
71C22×C4×C13—41no—
72C22×C4×C13—41no—
73C22×C4×C13—41no—
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C22⋊C411yescharacteristic
78C22×C4×C13C22×C411yescharacteristic
79C22×C4×C13C2×D412yes—
80C22×C4×C13C2×D411yescharacteristic
81C22×C4×C13#4112yes—
82C2×C22⋊D13—41no—
83C2×C22⋊D13—41no—
84C2×C22⋊D13—42no—
85C2×C22⋊D13—42no—
86C22×Dic13—24no—
87C22×Dic13—21no—
88C22×Dic13—21no—
89C22×Dic13—21no—
90C22×Dic13—42no—
91C22×Dic13—42no—
92C22×Dic13—42no—
93C22×Dic13—42no—
94C22×Dic13—42no—
95C22×Dic13—42no—
96C2×D52—22no—
97C2×D52—41no—
98C2×D52—41no—
99C2×Dic26—22no—
100C2×Dic26—41no—
101C2×Dic26—41no—
102C2×C8×C13—24no—
103C2×C8×C13—42no—
104C2×C8×C13—42no—
105C42×C13—22no—
106C42×C13—22no—
107C42×C13—41no—
108C42×C13—41no—
109C22⋊Dic13—41no—
110C22⋊Dic13—41no—
111#6103—42no—
112#6103—42no—
113#6103—42no—
114#6103—42no—
115#6103—42no—
116C4⋊Dic13—22no—
117C4⋊Dic13—22no—
118#6101—42no—
119#2850—131no—
120C4×C22⋊C8D1311yescharacteristic, complemented
121C2×#328—132no—
122C2×#327—132no—
123#1434—131no—
124C23×C13—21no—
125C23×C13—21no—
126C23×C13—21no—
127C23×C13—21no—
128C23×C13C2×C22⋊C411yescharacteristic
129C23×C13#12411yescharacteristic
130C23×C13#12711yescharacteristic
131C23×C13#13512yes—
132C23×C13#13512yes—
133C22×D13—41no—
134C22×D13—41no—
135C22×D13—41no—
136C22×D13—41no—
137C22×D13—41no—
138C22×D13—41no—
139C22×D13—41no—
140C2×C4×C13—21no—
141C2×C4×C13—21no—
142C2×C4×C13—21no—
143C2×C4×C13—21no—
144C2×C4×C13—21no—
145C2×C4×C13—21no—
146C2×C4×C13—21no—
147C2×C4×C13—21no—
148C2×C4×C13—21no—
149C2×C4×C13—21no—
150C2×C4×C13—21no—
151C2×C4×C13—21no—
152C2×C4×C13—21no—
153C2×C4×C13—21no—
154C2×C4×C13—42no—
155C2×C4×C13—42no—
156C2×C4×C13—44no—
157C2×C4×C13—44no—
158C2×C4×C13#9912yes—
159C2×C4×C13#10412yes—
160C2×C4×C13C4×D412yes—
161C2×C4×C13#12112yes—
162C22⋊D13—82no—
163C22⋊D13—82no—
164C2×Dic13—44no—
165C2×Dic13—44no—
166C2×Dic13—44no—
167C2×Dic13—41no—
168C2×Dic13—41no—
169C2×Dic13—41no—
170C2×Dic13—41no—
171C2×Dic13—41no—
172C2×Dic13—41no—
173C2×Dic13—41no—
174C2×Dic13—41no—
175C2×Dic13—41no—
176C2×Dic13—82no—
177C2×Dic13—82no—
178C2×Dic13—82no—
179C2×Dic13—82no—
180D52—82no—
181Dic26—82no—
182C8×C13—44no—
183C2×#124—131no—
184C2×C22⋊Q8—131no—
185C2×#121—131no—
186C22×C42C2×D1311yescharacteristic
187C2×C22⋊C8C2×D1312yes—
188C2×C4×C8—21no—
189#391—131no—
190#390—131no—
191#388—261no—
192#388—261no—
193#386—261no—
194#386—261no—
195#382—131no—
196C2×#95—132no—
197C2×#95—261no—
198C2×#95—261no—
199#336—21no—
200#328—264no—
201#327—264no—
202C22×C13—21no—
203C22×C13—21no—
204C22×C13—21no—
205C22×C13—21no—
206C22×C13—22no—
207C22×C13—22no—
208C22×C13—22no—
209C22×C13—22no—
210C22×C13#39011yescharacteristic
211C22×C13C2×#9911yescharacteristic
212C22×C13#41011yescharacteristic
213C22×C13#41611yescharacteristic
214C22×C13#41611yescharacteristic
215C22×C13C2×#10411yescharacteristic
216C22×C13#42111yescharacteristic
217C22×C13#48812yes—
218C22×C13#49512yes—
219C2×D13—81no—
220C2×D13—81no—
221C2×D13—81no—
222C2×D13—81no—
223C2×D13—81no—
224C2×D13—81no—
225C2×D13—81no—
226C4×C13—22no—
227C4×C13—22no—
228C4×C13—22no—
229C4×C13—22no—
230C4×C13—41no—
231C4×C13—41no—
232Dic13—84no—
233Dic13—81no—
234Dic13—81no—
235Dic13—81no—
236C22×Q8—131no—
237C22×D4—131no—
238C22×D4—261no—
239C23×C4—262no—
240C23×C4D5211yescharacteristic
241C23×C4D5211yescharacteristic
242C23×C4C22×D1311yescharacteristic
243C22×C8—22no—
244#124—522no—
245C22⋊Q8—262no—
246C22⋊Q8—262no—
247#121—262no—
248#121—262no—
249C2×C4⋊C4—131no—
250C2×C4⋊C4—131no—
251C2×C4⋊C4—261no—
252C2×C22⋊C4—261no—
253C2×C22⋊C4—261no—
254C2×C22⋊C4—261no—
255C2×C22⋊C4—261no—
256C2×C22⋊C4—261no—
257C2×C22⋊C4—261no—
258C2×C42—42no—
259C2×C42C4×D1311yescharacteristic
260C2×C42C4×D1311yescharacteristic
261C2×C42C22⋊D1311yescharacteristic
262C2×C42C22⋊D1311yescharacteristic
263C22⋊C8—22no—
264C22⋊C8D5214yes—
265C4×C8—42no—
266#95—264no—
267#95—261no—
268#95—261no—
269#95—261no—
270#95—261no—
271#95—262no—
272#95—262no—
273#95—522no—
274C2×C13—22no—
275C2×C13—22no—
276C2×C13#150011yescharacteristic
277C2×C13#150111yescharacteristic
278C2×C13#151611yescharacteristic
279C2×C13#152111yescharacteristic
280C2×C13#195811yescharacteristic
281C2×C13#196411yescharacteristic
282C2×C13#198011yescharacteristic
283D13—161no—
284C24—261no—
285C24C2×D5211yescharacteristic
286C2×Q8—262no—
287C2×Q8—521no—
288C2×Q8—521no—
289C2×D4—262no—
290C2×D4—521no—
291C2×D4—521no—
292C2×D4—521no—
293C2×D4—521no—
294C2×D4—522no—
295C2×D4—522no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—264no—
305C22×C4—261no—
306C22×C4—261no—
307C22×C4—261no—
308C22×C4—522no—
309C22×C4—522no—
310C22×C4—522no—
311C22×C4—522no—
312C22×C4—522no—
313C22×C4—522no—
314C22×C4#610311yescharacteristic
315C22×C4#610311yescharacteristic
316C22×C4#610311yescharacteristic
317C22×C4#610311yescharacteristic
318C22×C4C2×C4×D1311yescharacteristic
319C22×C4C2×D5212yes—
320C22×C4#612712yes—
321C22×C4C2×C22⋊D1311yescharacteristic
322C2×C8—24no—
323C2×C8—42no—
324C2×C8—42no—
325C4⋊C4—262no—
326C4⋊C4—262no—
327C4⋊C4—522no—
328C22⋊C4—522no—
329C22⋊C4—522no—
330C22⋊C4—521no—
331C22⋊C4—521no—
332C22⋊C4—522no—
333C22⋊C4—522no—
334C22⋊C4—522no—
335C42—22no—
336C42—22no—
337C42—41no—
338C42—41no—
339C13#968111yescharacteristic, complemented, Sylow
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—521no—
345C23—521no—
346C23—521no—
347C23—521no—
348C23—521no—
349C23—521no—
350C23—521no—
351C23#8812811yescharacteristic
352C23#8812911yescharacteristic
353C23#8815812yes—
354C23#8815812yes—
355C23C2×#610311yescharacteristic
356Q8—1042no—
357D4—1042no—
358D4—1042no—
359D4—1042no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—44no—
377C2×C4—44no—
378C2×C4—524no—
379C2×C4—524no—
380C2×C4—524no—
381C2×C4—521no—
382C2×C4—521no—
383C2×C4—521no—
384C2×C4—521no—
385C2×C4—521no—
386C2×C4—521no—
387C2×C4—521no—
388C2×C4—521no—
389C2×C4—521no—
390C2×C4—1042no—
391C2×C4—1042no—
392C2×C4—1042no—
393C2×C4—1042no—
394C2×C4#8804612yes—
395C2×C4#8806512yes—
396C2×C4C4×D5212yes—
397C2×C4#8818412yes—
398C8—44no—
399C22—21no—
400C22—21no—
401C22—22no—
402C22—22no—
403C22—21no—
404C22—21no—
405C22—22no—
406C22—22no—
407C22—1041no—
408C22—1041no—
409C22—1041no—
410C22—1041no—
411C22—1041no—
412C22—1041no—
413C22—1041no—
414C22#1171835712yes—
415C22#1171835812yes—
416C22#1171860011yescharacteristic
417C22C2×#8804611yescharacteristic
418C22#1171866711yescharacteristic
419C22#1171877411yescharacteristic
420C22#1171877411yescharacteristic
421C22C2×#8806511yescharacteristic
422C22#1171880011yescharacteristic
423C4—22no—
424C4—22no—
425C4—22no—
426C4—22no—
427C4—41no—
428C4—41no—
429C4—1044no—
430C4—1041no—
431C4—1041no—
432C4—1041no—
433C2—22no—
434C2—22no—
435C2—2081no—
436C2#1311332311yescharacteristic
437C2#1311332811yescharacteristic
438C2#1311339311yescharacteristic
439C2#1311341411yescharacteristic
440C2#1311564711yescharacteristic
441C2#1311567211yescharacteristic
442C2#1311575511yescharacteristic
subgroupG/H
centerC23C2×#6103
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC4×C13×C22⋊C8C2
socleC23×C13C2×C22⋊C4
prime radicalC2×#88184C22
cosocleC23×C4×C13C23
hypercenterC4×C22⋊C8D13
hypocenterC13#9681
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#11718059C2semidirect
4. #13113063C2semidirect
5. C4×C13×C22⋊C8C2semidirect
9. C2×#88129C4semidirect
19. #11718600C4semidirect
20. #11718597C4semidirect
21. #11718590C4semidirect
120. C4×C22⋊C8D13semidirect
339. C13#9681semidirect

Maximal subgroups

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

subgroupindex
#131231372
C2×#117180592
C2×#117180622
#131130632
C4×C13×C22⋊C82
#968113