Finite Group Databasebeta

← #15846873

Subgroups — #15846873

Order 3328.

722 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718355C211yesmaximal, characteristic, complemented
2#13124651C211yesmaximal, characteristic, complemented
3#13124316C211yesmaximal, characteristic
4#13114252C214yesmaximal, complemented
5#13114245C214yesmaximal, complemented
6#13113592C211yesmaximal, characteristic, complemented
7#13113516C211yesmaximal, characteristic, complemented
8#13113503C211yesmaximal, characteristic, complemented
9C8×C13×#41C211yesmaximal, characteristic, complemented
10C4×C13×#41C2211yescharacteristic
11C2×#88203—21no—
12C2×#88128C2211yescharacteristic
13C2×#88123C2211yescharacteristic
14C8×Q8×C13C2212yescomplemented
15C8×D4×C13—22no—
16C8×D4×C13C2212yescomplemented
17C13×#431—21no—
18C13×#431C2211yescharacteristic
19C2×C4×C8×C13—21no—
20C2×C4×C8×C13C2211yescharacteristic
21#11718893—21no—
22C2×#88061—22no—
23#11718688—21no—
24#11718688C2212yes—
25#11718682C2212yescomplemented
26#11718681—21no—
27#11718676—21no—
28#11718676C2212yes—
29#11718669C2212yescomplemented
30#11718668—21no—
31#11718662—21no—
32#11718656—21no—
33#11718585C2211yescharacteristic
34#11718585C2211yescharacteristic
35#11718355—21no—
36#11718355—21no—
37#11718355C2214yes—
38#11718077C2214yes—
39#11718073C2214yescomplemented
40#11718049C2214yescomplemented
41C2×C13×#41D411yescharacteristic
42C22×D52—21no—
43C22×D52—21no—
44C22×D52—21no—
45C22×Dic26—21no—
46C22×C8×C13—22no—
47C22×C8×C13D412yes—
48C4×Q8×C13D411yescharacteristic
49C4×Q8×C13C2311yescharacteristic
50C4×D4×C13—21no—
51C4×D4×C13—21no—
52C4×D4×C13D411yescharacteristic
53C4×D4×C13C2311yescharacteristic
54C13×#117—21no—
55C13×#117D411yescharacteristic
56C2×C42×C13—21no—
57C2×C42×C13C2311yescharacteristic
58#88203—44no—
59C2×#6106—22no—
60C2×#6104—22no—
61C2×C4⋊Dic13—21no—
62C2×C4⋊Dic13—21no—
63C2×#6099—21no—
64C2×#6099—21no—
65#88128—21no—
66#88128—21no—
67#88128—21no—
68#88128C2312yes—
69#88123—21no—
70#88123—21no—
71#88123—21no—
72#88123C2312yes—
73C13×C4⋊C8—22no—
74C13×C4⋊C8C2312yes—
75C13×C22⋊C8—21no—
76C13×C22⋊C8—22no—
77C4×C8×C13—22no—
78C4×C8×C13—21no—
79C4×C8×C13D411yescharacteristic
80C4×C8×C13D411yescharacteristic
81C4×C8×C13C2312yes—
82#88075—22no—
83#88072—22no—
84#88061—24no—
85#88061—24no—
86#88049—22no—
87#88049—22no—
88#88048—22no—
89#88047—22no—
90C4⋊#1055—21no—
91C4⋊#1055—21no—
92C4⋊#1055C2312yes—
93C4⋊#1055C2312yes—
94#19274—131nomaximal, Sylow
95C23×D13—41no—
96C13×#41—22no—
97C13×#41SD1614yes—
98C2×Q8×C13C2×D411yescharacteristic
99C2×D4×C13—21no—
100C2×D4×C13C2×D411yescharacteristic
101C22×C4×C13—21no—
102C22×C4×C13—21no—
103C22×C4×C13—21no—
104C22×C4×C13C2×D411yescharacteristic
105C22×C4×C13C2×D411yescharacteristic
106C22×C4×C13#4111yescharacteristic
107C22×Dic13—41no—
108C2×D52—22no—
109C2×D52—22no—
110C2×D52—22no—
111C2×D52—44no—
112C2×D52—42no—
113C2×D52—42no—
114C2×D52—41no—
115C2×D52—41no—
116C2×D52—41no—
117C2×D52—82no—
118C2×Dic26—22no—
119C2×Dic26—41no—
120C2×Dic26—82no—
121C2×C8×C13—22no—
122C2×C8×C13—42no—
123C2×C8×C13—44no—
124C2×C8×C13C2×D412yes—
125C2×C8×C13C2×D412yes—
126C13×C4⋊C4—21no—
127C13×C4⋊C4—21no—
128C13×C4⋊C4C2×D411yescharacteristic
129C13×C4⋊C4C2×D411yescharacteristic
130C13×C22⋊C4—21no—
131C13×C22⋊C4—21no—
132C13×C22⋊C4—21no—
133C42×C13—21no—
134C42×C13—21no—
135C42×C13—21no—
136C42×C13C2×D411yescharacteristic
137C42×C13C2×D411yescharacteristic
138C42×C13#4111yescharacteristic
139C42×C13C2411yescharacteristic
140#6106—44no—
141#6104—44no—
142C4⋊Dic13—22no—
143C4⋊Dic13—22no—
144C4⋊Dic13—41no—
145C4⋊Dic13—41no—
146#6099—42no—
147#6099—42no—
148C2×#1055—22no—
149C2×#1055—22no—
150C2×#486—131no—
151#3079—131no—
152#3038—131no—
153C8×#41D1311yescharacteristic, complemented
154#1678—134no—
155#1677—134no—
156#1566—131no—
157#1548—131no—
158#1545—131no—
159C23×C13—21no—
160C23×C13#12111yescharacteristic
161C22×D13—42no—
162C22×D13—82no—
163C22×D13—82no—
164C22×D13—82no—
165Q8×C13—21no—
166Q8×C13C2×SD1612yes—
167D4×C13—24no—
168D4×C13—21no—
169D4×C13C2×SD1612yes—
170C2×C4×C13—21no—
171C2×C4×C13—22no—
172C2×C4×C13—24no—
173C2×C4×C13—22no—
174C2×C4×C13—21no—
175C2×C4×C13—21no—
176C2×C4×C13—42no—
177C2×C4×C13—42no—
178C2×C4×C13#12111yescharacteristic
179C2×C4×C13#12111yescharacteristic
180C2×C4×C13#12111yescharacteristic
181C2×C4×C13C2×SD1612yes—
182C2×C4×C13#13512yes—
183C2×C4×C13C22×D411yescharacteristic
184C2×C4×C13C22×D411yescharacteristic
185C2×C4×C13C2×#4111yescharacteristic
186C2×Dic13—42no—
187C2×Dic13—82no—
188D52—42no—
189D52—42no—
190D52—44no—
191D52—82no—
192D52—82no—
193D52—82no—
194D52—82no—
195Dic26—82no—
196Dic26—82no—
197C8×C13—22no—
198C8×C13—22no—
199C8×C13—42no—
200#1055—42no—
201#1055—42no—
202C2×AGL(1,ℤ/8)—261no—
203C2×C4⋊Q8—131no—
204C2×#127—131no—
205C4×#41C2×D1311yescharacteristic
206#486—134no—
207#486—261no—
208#486—261no—
209#477—132no—
210#476—132no—
211#475—261no—
212#474—261no—
213#460—132no—
214#460—261no—
215#459—132no—
216#459—261no—
217C8×Q8C2×D1312yescomplemented
218C8×D4—22no—
219C8×D4C2×D1312yescomplemented
220#431—21no—
221#431C2×D1311yescharacteristic
222#428—261no—
223#423—131no—
224#423—131no—
225#418—261no—
226#417—261no—
227C2×#102—262no—
228C2×C4×C8—21no—
229C2×C4×C8C2×D1311yescharacteristic
230#334—134no—
231#333—134no—
232#331—134no—
233C22×C13—21no—
234C22×C13—21no—
235C22×C13—22no—
236C22×C13—41no—
237C22×C13—41no—
238C22×C13#46512yes—
239C22×C13C2×#12111yescharacteristic
240C2×D13—82no—
241C2×D13—82no—
242C2×D13—82no—
243C2×D13—164no—
244C4×C13—21no—
245C4×C13—22no—
246C4×C13—21no—
247C4×C13—41no—
248C4×C13—41no—
249C4×C13#46512yes—
250C4×C13#47212yes—
251C4×C13C22×SD1611yescharacteristic
252C4×C13C2×#13511yescharacteristic
253C4×C13#57512yes—
254Dic13—82no—
255C2×#41D5211yescharacteristic
256C22×Q8—261no—
257C22×D4—261no—
258C22×D4—261no—
259C22×D4—261no—
260AGL(1,ℤ/8)—524no—
261C2×SD16—262no—
262C2×D8—262no—
263C2×M16—261no—
264C2×M16—261no—
265C22×C8—22no—
266C22×C8C22⋊D1312yes—
267C4⋊Q8—132no—
268C4⋊Q8—261no—
269C4⋊Q8—261no—
270C4⋊Q8—261no—
271#127—132no—
272#127—261no—
273#127—261no—
274#127—261no—
275C4×Q8D5211yescharacteristic
276C4×Q8C22×D1311yescharacteristic
277C4×D4—21no—
278C4×D4—21no—
279C4×D4D5211yescharacteristic
280C4×D4C22×D1311yescharacteristic
281#117—21no—
282#117D5211yescharacteristic
283C2×C4⋊C4—261no—
284C2×C4⋊C4—261no—
285C2×C42—21no—
286C2×C42C22×D1311yescharacteristic
287#107—262no—
288#106—262no—
289C4⋊C8—22no—
290C4⋊C8—132no—
291C4⋊C8—132no—
292C4⋊C8—261no—
293C4⋊C8—261no—
294C4⋊C8C22×D1312yes—
295#103—262no—
296#102—262no—
297#102—264no—
298#102—264no—
299#102—262no—
300#102—262no—
301C22⋊C8—21no—
302C22⋊C8—22no—
303C4×C8—22no—
304C4×C8—21no—
305C4×C8C22⋊D1311yescharacteristic
306C4×C8C22⋊D1311yescharacteristic
307C4×C8C22×D1312yes—
308C2×C13—22no—
309C2×C13—42no—
310C2×C13#304011yescharacteristic
311C2×C13C2×#46511yescharacteristic
312C2×C13C2×#47211yescharacteristic
313D13—162no—
314C24—521no—
315#41—22no—
316#41#609514yes—
317C2×Q8—262no—
318C2×Q8—521no—
319C2×Q8—1042no—
320C2×Q8C2×D5211yescharacteristic
321C2×D4—21no—
322C2×D4—262no—
323C2×D4—262no—
324C2×D4—262no—
325C2×D4—524no—
326C2×D4—522no—
327C2×D4—522no—
328C2×D4—521no—
329C2×D4—521no—
330C2×D4—521no—
331C2×D4—1042no—
332C2×D4C2×D5211yescharacteristic
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—521no—
337C22×C4C2×D5211yescharacteristic
338C22×C4#612711yescharacteristic
339C22×C4C2×C22⋊D1311yescharacteristic
340SD16—524no—
341D8—524no—
342M16—522no—
343M16—522no—
344C2×C8—22no—
345C2×C8—42no—
346C2×C8—44no—
347C2×C8—262no—
348C2×C8—262no—
349C2×C8C2×C22⋊D1312yes—
350C2×C8C2×C22⋊D1312yes—
351C4⋊C4—21no—
352C4⋊C4—21no—
353C4⋊C4—262no—
354C4⋊C4—262no—
355C4⋊C4—521no—
356C4⋊C4—521no—
357C4⋊C4C2×D5211yescharacteristic
358C4⋊C4C2×D5211yescharacteristic
359C22⋊C4—21no—
360C22⋊C4—21no—
361C22⋊C4—21no—
362C42—21no—
363C42—21no—
364C42—21no—
365C42C2×D5211yescharacteristic
366C42#612711yescharacteristic
367C42C2×C22⋊D1311yescharacteristic
368C42C23×D1311yescharacteristic
369C13#1927411yescharacteristic, complemented, Sylow
370C23—21no—
371C23—522no—
372C23—1042no—
373C23—1042no—
374C23—1042no—
375C23#8818411yescharacteristic
376Q8—21no—
377Q8—1042no—
378Q8—1042no—
379Q8C2×#609512yes—
380D4—24no—
381D4—21no—
382D4—522no—
383D4—522no—
384D4—524no—
385D4—1042no—
386D4—1042no—
387D4—1042no—
388D4—1042no—
389D4C2×#609512yes—
390C2×C4—21no—
391C2×C4—22no—
392C2×C4—24no—
393C2×C4—22no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—522no—
399C2×C4—1042no—
400C2×C4C2×#609512yes—
401C2×C4#8815812yes—
402C2×C4#8818411yescharacteristic
403C2×C4#8818411yescharacteristic
404C2×C4#8818411yescharacteristic
405C2×C4C22×D5211yescharacteristic
406C2×C4C2×#612711yescharacteristic
407C2×C4C22×C22⋊D1311yescharacteristic
408C8—22no—
409C8—22no—
410C8—42no—
411C8—522no—
412C8—522no—
413C22—21no—
414C22—21no—
415C22—22no—
416C22—41no—
417C22—41no—
418C22—1042no—
419C22—1042no—
420C22—1042no—
421C22—2084no—
422C22#1171877512yes—
423C22C2×#8818411yescharacteristic
424C4—22no—
425C4—21no—
426C4—21no—
427C4—41no—
428C4—41no—
429C4—1042no—
430C4#1171877512yes—
431C4#1171880312yes—
432C4C22×#609511yescharacteristic
433C4C2×#8815811yescharacteristic
434C4#1171952712yes—
435C2—22no—
436C2—42no—
437C2—2082no—
438C2#1312433011yescharacteristic
439C2C2×#1171877511yescharacteristic
440C2C2×#1171880311yescharacteristic
subgroupG/H
centerC22C2×#88184
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC8×C13×#41C2
socleC22×C13C2×#121
prime radical#13124316C2
hypercenterC8×#41D13
hypocenterC13#19274
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C8×#41

Complements

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

NH ≅ G/Ntype
1. C2×#11718355C2semidirect
2. #13124651C2semidirect
4. #13114252C2semidirect
5. #13114245C2semidirect
6. #13113592C2semidirect
7. #13113516C2semidirect
8. #13113503C2semidirect
9. C8×C13×#41C2semidirect
14. C8×Q8×C13C22semidirect
16. C8×D4×C13C22semidirect
25. #11718682C22semidirect
29. #11718669C22semidirect
39. #11718073C22semidirect
40. #11718049C22semidirect
153. C8×#41D13semidirect
217. C8×Q8C2×D13semidirect
219. C8×D4C2×D13semidirect
369. C13#19274semidirect

Maximal subgroups

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

subgroupindex
C2×#117183552
#131246512
#131243162
#131142522
#131142452
#131135922
#131135162
#131135032
C8×C13×#412
#1927413