Finite Group Databasebeta

← #15755653

Subgroups — #15755653

Order 3328.

698 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#88184C211yesmaximal, characteristic
2C2×#11718062C212yesmaximal
3#13113063C211yesmaximal, characteristic, complemented
4#13112716C212yesmaximal, complemented
5C13×#1797C211yesmaximal, characteristic, complemented
6C22×C42×C13C2211yescharacteristic
7C2×#88184C2211yescharacteristic
8C2×C4×C22⋊D13—21no—
9C2×C4×D52C411yescharacteristic, complemented
10C2×C13×C4⋊C8—21no—
11C2×C13×C22⋊C8C2212yes—
12#11718874—21no—
13#11718873C2211yescharacteristic
14C2×#88071—21no—
15C2×#88071—21no—
16C2×#88071C2212yes—
17#11718601—21no—
18#11718600C411yescharacteristic, complemented
19C4×#6103—21no—
20C4×C4⋊Dic13C411yescharacteristic, complemented
21#11718589C411yescharacteristic, complemented
22C13×#336—21no—
23#11718062—24no—
24C23×C4×C13D411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C23×C4×C13C2311yescharacteristic
27C22×C22⋊D13—21no—
28C23×Dic13—22no—
29C22×D52C2×C411yescharacteristic
30C22×C4×D13—21no—
31C22×C8×C13—22no—
32C2×C42×C13—42no—
33C2×C42×C13C2×C411yescharacteristic
34C2×C42×C13C2×C411yescharacteristic
35C2×C42×C13D411yescharacteristic
36C2×C42×C13D411yescharacteristic
37C2×C22⋊Dic13—21no—
38#88184—21no—
39#88184—21no—
40#88184D412yes—
41#88184Q812yes—
42C4×C22⋊D13—44no—
43C2×#6103—21no—
44C2×#6103—21no—
45C2×#6103—21no—
46C2×#6103—21no—
47C2×C4⋊Dic13C2×C411yescharacteristic
48C2×C4⋊Dic13C2×C411yescharacteristic
49C2×C4⋊Dic13C2×C411yescharacteristic
50C2×#6101—21no—
51C2×C4×Dic13—21no—
52C4×D52—42no—
53C13×C4⋊C8—42no—
54C13×C22⋊C8—22no—
55C13×C22⋊C8—22no—
56#88071—24no—
57#88071—21no—
58#88071—21no—
59#88071—21no—
60#88071—22no—
61#88071—22no—
62#88071—42no—
63#8573—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×D411yescharacteristic
80C22×C4×C13C2×D411yescharacteristic
81C22×C4×C13C2×Q811yescharacteristic
82C22×C4×C13#4111yescharacteristic
83C22×C4×C13#4111yescharacteristic
84C2×C22⋊D13—22no—
85C2×C22⋊D13—22no—
86C2×C22⋊D13—42no—
87C2×C22⋊D13—42no—
88C22×Dic13—21no—
89C22×Dic13—24no—
90C22×Dic13—21no—
91C22×Dic13—21no—
92C22×Dic13—42no—
93C22×Dic13—42no—
94C22×Dic13—42no—
95C22×Dic13—42no—
96C22×Dic13—42no—
97C22×Dic13—42no—
98C2×D52—21no—
99C2×D52—41no—
100C2×D52—41no—
101C2×D52C4⋊C412yes—
102C2×C4×D13—42no—
103C2×C4×D13—42no—
104C2×C4×D13—42no—
105C2×C8×C13—42no—
106C2×C8×C13—42no—
107C2×C8×C13—42no—
108C42×C13—22no—
109C42×C13—22no—
110C42×C13—41no—
111C42×C13—41no—
112C22⋊Dic13—42no—
113#6103—22no—
114#6103—22no—
115#6103—42no—
116#6103—42no—
117#6103—42no—
118C4⋊Dic13—21no—
119C4⋊Dic13—41no—
120C4⋊Dic13—41no—
121C4⋊Dic13C4⋊C412yes—
122#6101—42no—
123C4×Dic13—42no—
124C4×#121—131no—
125#1797D1311yescharacteristic, complemented
126C2×#327—132no—
127#1434—131no—
128#1294—132no—
129C23×C13—21no—
130C23×C13—21no—
131C23×C13—21no—
132C23×C13—21no—
133C23×C13C2×C22⋊C411yescharacteristic
134C23×C13#12111yescharacteristic
135C23×C13C22⋊Q811yescharacteristic
136C23×C13#13512yes—
137C23×C13AGL(1,ℤ/8)12yes—
138C22×D13—22no—
139C22×D13—41no—
140C22×D13—41no—
141C22×D13—41no—
142C22×D13—41no—
143C22×D13—41no—
144C22×D13—41no—
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—21no—
155C2×C4×C13—21no—
156C2×C4×C13—21no—
157C2×C4×C13—21no—
158C2×C4×C13—21no—
159C2×C4×C13—41no—
160C2×C4×C13—41no—
161C2×C4×C13—41no—
162C2×C4×C13—41no—
163C2×C4×C13—44no—
164C2×C4×C13—44no—
165C2×C4×C13#9912yes—
166C2×C4×C13#10412yes—
167C2×C4×C13C2×C4⋊C411yescharacteristic
168C2×C4×C13#11711yescharacteristic
169C2×C4×C13#12111yescharacteristic
170C2×C4×C13C22⋊Q811yescharacteristic
171C22⋊D13—44no—
172C22⋊D13—44no—
173C2×Dic13—22no—
174C2×Dic13—41no—
175C2×Dic13—41no—
176C2×Dic13—44no—
177C2×Dic13—44no—
178C2×Dic13—44no—
179C2×Dic13—41no—
180C2×Dic13—41no—
181C2×Dic13—41no—
182C2×Dic13—41no—
183C2×Dic13—41no—
184C2×Dic13—41no—
185C2×Dic13—82no—
186C2×Dic13—82no—
187C2×Dic13—82no—
188C2×Dic13—82no—
189D52—42no—
190D52—42no—
191C4×D13—84no—
192C8×C13—82no—
193C2×#121—131no—
194C2×C4×D4—131no—
195C2×C4×D4—261no—
196C22×C42C2×D1311yescharacteristic
197C2×C4⋊C8—21no—
198C2×C22⋊C8C2×D1312yes—
199#390—131no—
200#389—131no—
201#388—261no—
202#386—261no—
203#380—131no—
204C4×C4⋊C4—131no—
205C4×C22⋊C4—261no—
206C2×#95—132no—
207C2×#95—261no—
208C2×#95—261no—
209#336—21no—
210#327—264no—
211C22×C13—21no—
212C22×C13—21no—
213C22×C13—21no—
214C22×C13—21no—
215C22×C13—22no—
216C22×C13—22no—
217C22×C13—22no—
218C22×C13—22no—
219C22×C13#38011yescharacteristic
220C22×C13C2×#9911yescharacteristic
221C22×C13#41011yescharacteristic
222C22×C13#41611yescharacteristic
223C22×C13#41811yescharacteristic
224C22×C13C2×#10411yescharacteristic
225C22×C13#42111yescharacteristic
226C22×C13#46312yes—
227C22×C13#47812yes—
228C2×D13—42no—
229C2×D13—42no—
230C2×D13—42no—
231C2×D13—81no—
232C2×D13—81no—
233C2×D13—81no—
234C2×D13—81no—
235C4×C13—21no—
236C4×C13—21no—
237C4×C13—21no—
238C4×C13—21no—
239C4×C13—22no—
240C4×C13—22no—
241C4×C13—41no—
242C4×C13—41no—
243Dic13—42no—
244Dic13—84no—
245Dic13—81no—
246Dic13—81no—
247C22×D4—131no—
248C22×D4—261no—
249C23×C4—262no—
250C23×C4—261no—
251C23×C4D5211yescharacteristic
252C23×C4D5211yescharacteristic
253C23×C4C22×D1311yescharacteristic
254C22×C8—22no—
255#121—132no—
256#121—132no—
257#121—261no—
258#121—261no—
259C4×D4—522no—
260C4×D4—524no—
261C2×C4⋊C4—131no—
262C2×C4⋊C4—131no—
263C2×C4⋊C4—131no—
264C2×C4⋊C4—261no—
265C2×C22⋊C4—261no—
266C2×C22⋊C4—261no—
267C2×C22⋊C4—261no—
268C2×C22⋊C4—261no—
269C2×C22⋊C4—261no—
270C2×C42—42no—
271C2×C42—261no—
272C2×C42C4×D1311yescharacteristic
273C2×C42C4×D1311yescharacteristic
274C2×C42C22⋊D1311yescharacteristic
275C2×C42C22⋊D1311yescharacteristic
276C4⋊C8—42no—
277C22⋊C8—22no—
278C22⋊C8—22no—
279#95—264no—
280#95—261no—
281#95—261no—
282#95—261no—
283#95—262no—
284#95—262no—
285#95—522no—
286C2×C13—22no—
287C2×C13—22no—
288C2×C13#150011yescharacteristic
289C2×C13#150711yescharacteristic
290C2×C13#151411yescharacteristic
291C2×C13#151611yescharacteristic
292C2×C13#179911yescharacteristic
293C2×C13#180411yescharacteristic
294C2×C13#180611yescharacteristic
295D13—82no—
296C24—261no—
297C24C2×D5211yescharacteristic
298C2×D4—132no—
299C2×D4—262no—
300C2×D4—262no—
301C2×D4—261no—
302C2×D4—521no—
303C2×D4—521no—
304C2×D4—522no—
305C2×D4—522no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—22no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—261no—
315C22×C4—264no—
316C22×C4—261no—
317C22×C4—261no—
318C22×C4—522no—
319C22×C4—522no—
320C22×C4—522no—
321C22×C4—522no—
322C22×C4—522no—
323C22×C4—522no—
324C22×C4—522no—
325C22×C4—522no—
326C22×C4—522no—
327C22×C4#610311yescharacteristic
328C22×C4#610311yescharacteristic
329C22×C4#610311yescharacteristic
330C22×C4#610311yescharacteristic
331C22×C4C2×C4×D1311yescharacteristic
332C22×C4D4×D1311yescharacteristic
333C22×C4#612911yescharacteristic
334C22×C4Q8×D1311yescharacteristic
335C22×C4#613111yescharacteristic
336C22×C4C2×C22⋊D1311yescharacteristic
337C2×C8—42no—
338C2×C8—42no—
339C2×C8—42no—
340C4⋊C4—132no—
341C4⋊C4—261no—
342C4⋊C4—521no—
343C4⋊C4—521no—
344C4⋊C4—522no—
345C22⋊C4—262no—
346C22⋊C4—262no—
347C22⋊C4—522no—
348C22⋊C4—522no—
349C22⋊C4—522no—
350C22⋊C4—522no—
351C42—22no—
352C42—22no—
353C42—41no—
354C42—41no—
355C42—522no—
356C13#857311yescharacteristic, complemented, Sylow
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—262no—
362C23—521no—
363C23—521no—
364C23—521no—
365C23—521no—
366C23—521no—
367C23—521no—
368C23#8814911yescharacteristic
369C23#8815111yescharacteristic
370C23#8815812yes—
371C23#8816212yes—
372C23C2×#610311yescharacteristic
373D4—522no—
374D4—522no—
375D4—524no—
376D4—524no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—44no—
396C2×C4—44no—
397C2×C4—262no—
398C2×C4—521no—
399C2×C4—521no—
400C2×C4—524no—
401C2×C4—524no—
402C2×C4—524no—
403C2×C4—521no—
404C2×C4—521no—
405C2×C4—521no—
406C2×C4—521no—
407C2×C4—521no—
408C2×C4—521no—
409C2×C4—1044no—
410C2×C4—1042no—
411C2×C4—1042no—
412C2×C4—1042no—
413C2×C4—1042no—
414C2×C4#8804612yes—
415C2×C4#8806512yes—
416C2×C4C4⋊C4×D1311yescharacteristic
417C2×C4#8814611yescharacteristic
418C2×C4#8819211yescharacteristic
419C2×C4#8820011yescharacteristic
420C8—82no—
421C22—22no—
422C22—22no—
423C22—22no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—22no—
429C22—522no—
430C22—522no—
431C22—522no—
432C22—1041no—
433C22—1041no—
434C22—1041no—
435C22—1041no—
436C22#1171850512yes—
437C22#1171850812yes—
438C22C2×#8804611yescharacteristic
439C22#1171864811yescharacteristic
440C22#1171866711yescharacteristic
441C22#1171877411yescharacteristic
442C22#1171879211yescharacteristic
443C22C2×#8806511yescharacteristic
444C22#1171880011yescharacteristic
445C4—22no—
446C4—22no—
447C4—21no—
448C4—21no—
449C4—21no—
450C4—21no—
451C4—41no—
452C4—41no—
453C4—522no—
454C4—1044no—
455C4—1041no—
456C4—1041no—
457C2—22no—
458C2—22no—
459C2—1042no—
460C2#1311332311yescharacteristic
461C2#1311335311yescharacteristic
462C2#1311338411yescharacteristic
463C2#1311339311yescharacteristic
464C2#1311482111yescharacteristic
465C2#1311484711yescharacteristic
466C2#1311485311yescharacteristic
subgroupG/H
centerC23C2×#6103
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1797C2
socleC23×C13C2×C22⋊C4
prime radicalC2×#88184C22
cosocleC23×C4×C13C23
hypercenter#1797D13
hypocenterC13#8573
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
3. #13113063C2semidirect
4. #13112716C2semidirect
5. C13×#1797C2semidirect
9. C2×C4×D52C4semidirect
18. #11718600C4semidirect
20. C4×C4⋊Dic13C4semidirect
21. #11718589C4semidirect
125. #1797D13semidirect
356. C13#8573semidirect

Maximal subgroups

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

subgroupindex
C4×#881842
C2×#117180622
#131130632
#131127162
C13×#17972
#857313