Finite Group Databasebeta

← #15846891

Subgroups — #15846891

Order 3328.

754 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718355C211yesmaximal, characteristic, complemented
2#13124323C211yesmaximal, characteristic, complemented
3#13124316C211yesmaximal, characteristic
4#13114280C214yesmaximal, complemented
5#13114273C214yesmaximal, complemented
6#13113595C211yesmaximal, characteristic, complemented
7#13113507C211yesmaximal, characteristic, complemented
8#13113503C211yesmaximal, characteristic, complemented
9C8×C13×#41C211yesmaximal, characteristic, complemented
10C4×C13×#41C2211yescharacteristic
11C2×#88205—21no—
12C2×#88203—21no—
13C2×#88128C2211yescharacteristic
14C2×#88123C2211yescharacteristic
15C8×Q8×C13C2212yescomplemented
16C8×D4×C13—22no—
17C8×D4×C13C2212yescomplemented
18C13×#431—21no—
19C13×#431C2211yescharacteristic
20C2×C4×C8×C13—21no—
21C2×C4×C8×C13C2211yescharacteristic
22C2×#88061—22no—
23#11718692—21no—
24#11718692C2212yescomplemented
25#11718688—21no—
26#11718688C2212yes—
27#11718680—21no—
28#11718680C2212yescomplemented
29#11718676—21no—
30#11718676C2212yes—
31#11718665—21no—
32#11718662—21no—
33#11718585C2211yescharacteristic
34#11718585C2211yescharacteristic
35#11718355—21no—
36#11718355—21no—
37#11718355C2214yes—
38#11718078C2214yescomplemented
39#11718077C2214yes—
40#11718050C2214yescomplemented
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#88205—44no—
59#88203—44no—
60C2×#6107—22no—
61C2×#6106—22no—
62C2×#6105—22no—
63C2×#6104—22no—
64C2×C4⋊Dic13—21no—
65C2×C4⋊Dic13—21no—
66C2×#6099—21no—
67C2×#6099—21no—
68#88128—21no—
69#88128—21no—
70#88128—21no—
71#88128C2312yes—
72#88123—21no—
73#88123—21no—
74#88123—21no—
75#88123C2312yes—
76C13×C4⋊C8—22no—
77C13×C4⋊C8C2312yes—
78C13×C22⋊C8—21no—
79C13×C22⋊C8—22no—
80C4×C8×C13—22no—
81C4×C8×C13—21no—
82C4×C8×C13D411yescharacteristic
83C4×C8×C13D411yescharacteristic
84C4×C8×C13C2312yes—
85#88061—24no—
86#88061—24no—
87#88050—22no—
88#88050—22no—
89#88049—22no—
90#88049—22no—
91C4⋊#1055—21no—
92C4⋊#1055—21no—
93C4⋊#1055C2312yes—
94C4⋊#1055C2312yes—
95#19276—131nomaximal, Sylow
96C23×D13—41no—
97C13×#41—22no—
98C13×#41D814yes—
99C2×Q8×C13C2×D411yescharacteristic
100C2×D4×C13—21no—
101C2×D4×C13C2×D411yescharacteristic
102C22×C4×C13—21no—
103C22×C4×C13—21no—
104C22×C4×C13—21no—
105C22×C4×C13C2×D411yescharacteristic
106C22×C4×C13C2×D411yescharacteristic
107C22×C4×C13#4111yescharacteristic
108C22×Dic13—41no—
109C2×D52—22no—
110C2×D52—22no—
111C2×D52—22no—
112C2×D52—44no—
113C2×D52—42no—
114C2×D52—42no—
115C2×D52—41no—
116C2×D52—41no—
117C2×D52—41no—
118C2×D52—82no—
119C2×Dic26—22no—
120C2×Dic26—42no—
121C2×Dic26—42no—
122C2×Dic26—41no—
123C2×C8×C13—22no—
124C2×C8×C13—42no—
125C2×C8×C13—44no—
126C2×C8×C13C2×D412yes—
127C2×C8×C13C2×D412yes—
128C13×C4⋊C4—21no—
129C13×C4⋊C4—21no—
130C13×C4⋊C4C2×D411yescharacteristic
131C13×C4⋊C4C2×D411yescharacteristic
132C13×C22⋊C4—21no—
133C13×C22⋊C4—21no—
134C13×C22⋊C4—21no—
135C42×C13—21no—
136C42×C13—21no—
137C42×C13—21no—
138C42×C13C2×D411yescharacteristic
139C42×C13C2×D411yescharacteristic
140C42×C13#4111yescharacteristic
141C42×C13C2411yescharacteristic
142#6107—44no—
143#6106—44no—
144#6105—44no—
145#6104—44no—
146C4⋊Dic13—22no—
147C4⋊Dic13—22no—
148C4⋊Dic13—41no—
149C4⋊Dic13—41no—
150#6099—42no—
151#6099—42no—
152C2×#1055—22no—
153C2×#1055—22no—
154C2×#486—131no—
155#3039—131no—
156#3038—131no—
157C8×#41D1311yescharacteristic, complemented
158#1682—134no—
159#1681—134no—
160#1567—131no—
161#1546—131no—
162#1545—131no—
163C23×C13—21no—
164C23×C13#12111yescharacteristic
165C22×D13—42no—
166C22×D13—82no—
167C22×D13—82no—
168C22×D13—82no—
169Q8×C13—21no—
170Q8×C13C2×D812yes—
171D4×C13—24no—
172D4×C13—21no—
173D4×C13C2×D812yes—
174C2×C4×C13—21no—
175C2×C4×C13—22no—
176C2×C4×C13—24no—
177C2×C4×C13—22no—
178C2×C4×C13—21no—
179C2×C4×C13—21no—
180C2×C4×C13—42no—
181C2×C4×C13—42no—
182C2×C4×C13#12111yescharacteristic
183C2×C4×C13#12111yescharacteristic
184C2×C4×C13#12111yescharacteristic
185C2×C4×C13C2×D812yes—
186C2×C4×C13#13512yes—
187C2×C4×C13C22×D411yescharacteristic
188C2×C4×C13C22×D411yescharacteristic
189C2×C4×C13C2×#4111yescharacteristic
190C2×Dic13—42no—
191C2×Dic13—82no—
192D52—42no—
193D52—42no—
194D52—44no—
195D52—82no—
196D52—82no—
197D52—82no—
198D52—82no—
199Dic26—42no—
200Dic26—42no—
201Dic26—82no—
202C8×C13—22no—
203C8×C13—22no—
204C8×C13—42no—
205#1055—42no—
206#1055—42no—
207C2×#137—261no—
208C2×AGL(1,ℤ/8)—261no—
209C2×C4⋊Q8—131no—
210C2×#127—131no—
211C4×#41C2×D1311yescharacteristic
212#486—134no—
213#486—261no—
214#486—261no—
215#462—132no—
216#462—261no—
217#461—132no—
218#461—261no—
219#460—132no—
220#460—261no—
221#459—132no—
222#459—261no—
223C8×Q8C2×D1312yescomplemented
224C8×D4—22no—
225C8×D4C2×D1312yescomplemented
226#431—21no—
227#431C2×D1311yescharacteristic
228#423—131no—
229#423—131no—
230#419—261no—
231#418—261no—
232C2×#102—262no—
233C2×C4×C8—21no—
234C2×C4×C8C2×D1311yescharacteristic
235#335—134no—
236#332—134no—
237#331—134no—
238C22×C13—21no—
239C22×C13—21no—
240C22×C13—22no—
241C22×C13—41no—
242C22×C13—41no—
243C22×C13#46612yes—
244C22×C13C2×#12111yescharacteristic
245C2×D13—82no—
246C2×D13—82no—
247C2×D13—82no—
248C2×D13—164no—
249C4×C13—21no—
250C4×C13—22no—
251C4×C13—21no—
252C4×C13—41no—
253C4×C13—41no—
254C4×C13#46612yes—
255C4×C13#47112yes—
256C4×C13C22×D811yescharacteristic
257C4×C13C2×#13511yescharacteristic
258C4×C13#57512yes—
259Dic13—82no—
260C2×#41D5211yescharacteristic
261C22×Q8—261no—
262C22×D4—261no—
263C22×D4—261no—
264C22×D4—261no—
265#137—524no—
266AGL(1,ℤ/8)—524no—
267C2×Q16—262no—
268C2×SD16—262no—
269C2×SD16—262no—
270C2×D8—262no—
271C2×M16—261no—
272C2×M16—261no—
273C22×C8—22no—
274C22×C8C22⋊D1312yes—
275C4⋊Q8—132no—
276C4⋊Q8—261no—
277C4⋊Q8—261no—
278C4⋊Q8—261no—
279#127—132no—
280#127—261no—
281#127—261no—
282#127—261no—
283C4×Q8D5211yescharacteristic
284C4×Q8C22×D1311yescharacteristic
285C4×D4—21no—
286C4×D4—21no—
287C4×D4D5211yescharacteristic
288C4×D4C22×D1311yescharacteristic
289#117—21no—
290#117D5211yescharacteristic
291C2×C4⋊C4—261no—
292C2×C4⋊C4—261no—
293C2×C42—21no—
294C2×C42C22×D1311yescharacteristic
295C4⋊C8—22no—
296C4⋊C8—132no—
297C4⋊C8—132no—
298C4⋊C8—261no—
299C4⋊C8—261no—
300C4⋊C8C22×D1312yes—
301#103—262no—
302#103—262no—
303#102—264no—
304#102—264no—
305#102—262no—
306#102—262no—
307C22⋊C8—21no—
308C22⋊C8—22no—
309C4×C8—22no—
310C4×C8—21no—
311C4×C8C22⋊D1311yescharacteristic
312C4×C8C22⋊D1311yescharacteristic
313C4×C8C22×D1312yes—
314C2×C13—22no—
315C2×C13—42no—
316C2×C13#304011yescharacteristic
317C2×C13C2×#46611yescharacteristic
318C2×C13C2×#47111yescharacteristic
319D13—162no—
320C24—521no—
321#41—22no—
322#41D10414yes—
323C2×Q8—262no—
324C2×Q8—521no—
325C2×Q8—522no—
326C2×Q8—522no—
327C2×Q8C2×D5211yescharacteristic
328C2×D4—21no—
329C2×D4—262no—
330C2×D4—262no—
331C2×D4—262no—
332C2×D4—524no—
333C2×D4—522no—
334C2×D4—522no—
335C2×D4—521no—
336C2×D4—521no—
337C2×D4—521no—
338C2×D4—1042no—
339C2×D4C2×D5211yescharacteristic
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—521no—
344C22×C4C2×D5211yescharacteristic
345C22×C4#612711yescharacteristic
346C22×C4C2×C22⋊D1311yescharacteristic
347Q16—524no—
348SD16—524no—
349SD16—524no—
350D8—524no—
351M16—522no—
352M16—522no—
353C2×C8—22no—
354C2×C8—42no—
355C2×C8—44no—
356C2×C8—262no—
357C2×C8—262no—
358C2×C8C2×C22⋊D1312yes—
359C2×C8C2×C22⋊D1312yes—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—262no—
363C4⋊C4—262no—
364C4⋊C4—521no—
365C4⋊C4—521no—
366C4⋊C4C2×D5211yescharacteristic
367C4⋊C4C2×D5211yescharacteristic
368C22⋊C4—21no—
369C22⋊C4—21no—
370C22⋊C4—21no—
371C42—21no—
372C42—21no—
373C42—21no—
374C42C2×D5211yescharacteristic
375C42#612711yescharacteristic
376C42C2×C22⋊D1311yescharacteristic
377C42C23×D1311yescharacteristic
378C13#1927611yescharacteristic, complemented, Sylow
379C23—21no—
380C23—522no—
381C23—1042no—
382C23—1042no—
383C23—1042no—
384C23#8818411yescharacteristic
385Q8—21no—
386Q8—522no—
387Q8—522no—
388Q8—1042no—
389Q8C2×D10412yes—
390D4—24no—
391D4—21no—
392D4—522no—
393D4—522no—
394D4—524no—
395D4—1042no—
396D4—1042no—
397D4—1042no—
398D4—1042no—
399D4C2×D10412yes—
400C2×C4—21no—
401C2×C4—22no—
402C2×C4—24no—
403C2×C4—22no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—522no—
409C2×C4—1042no—
410C2×C4C2×D10412yes—
411C2×C4#8815812yes—
412C2×C4#8818411yescharacteristic
413C2×C4#8818411yescharacteristic
414C2×C4#8818411yescharacteristic
415C2×C4C22×D5211yescharacteristic
416C2×C4C2×#612711yescharacteristic
417C2×C4C22×C22⋊D1311yescharacteristic
418C8—22no—
419C8—22no—
420C8—42no—
421C8—522no—
422C8—522no—
423C22—21no—
424C22—21no—
425C22—22no—
426C22—41no—
427C22—41no—
428C22—1042no—
429C22—1042no—
430C22—1042no—
431C22—2084no—
432C22#1171877612yes—
433C22C2×#8818411yescharacteristic
434C4—22no—
435C4—21no—
436C4—21no—
437C4—41no—
438C4—41no—
439C4—1042no—
440C4#1171877612yes—
441C4#1171880212yes—
442C4C22×D10411yescharacteristic
443C4C2×#8815811yescharacteristic
444C4#1171952712yes—
445C2—22no—
446C2—42no—
447C2—2082no—
448C2#1312433011yescharacteristic
449C2C2×#1171877611yescharacteristic
450C2C2×#1171880211yescharacteristic
subgroupG/H
centerC22C2×#88184
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC8×C13×#41C2
socleC22×C13C2×#121
prime radical#13124316C2
hypercenterC8×#41D13
hypocenterC13#19276
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. #13124323C2semidirect
4. #13114280C2semidirect
5. #13114273C2semidirect
6. #13113595C2semidirect
7. #13113507C2semidirect
8. #13113503C2semidirect
9. C8×C13×#41C2semidirect
15. C8×Q8×C13C22semidirect
17. C8×D4×C13C22semidirect
24. #11718692C22semidirect
28. #11718680C22semidirect
38. #11718078C22semidirect
40. #11718050C22semidirect
157. C8×#41D13semidirect
223. C8×Q8C2×D13semidirect
225. C8×D4C2×D13semidirect
378. C13#19276semidirect

Maximal subgroups

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

subgroupindex
C2×#117183552
#131243232
#131243162
#131142802
#131142732
#131135952
#131135072
#131135032
C8×C13×#412
#1927613