Finite Group Databasebeta

← #15892910

Subgroups — #15892910

Order 3328.

880 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#88184C211yesmaximal, characteristic
2#13117243C211yesmaximal, characteristic, complemented
3#13116395C211yesmaximal, characteristic, complemented
4#13116363C211yesmaximal, characteristic, complemented
5#13116309C211yesmaximal, characteristic, complemented
6#13116259C212yesmaximal, complemented
7#13116241C211yesmaximal, characteristic, complemented
8#13116019C212yesmaximal
9C4×#88058C212yesmaximal, complemented
10C4×#88061C212yesmaximal, complemented
11C4×C13×C22⋊C8C211yesmaximal, characteristic, complemented
12C22×C42×C13C2211yescharacteristic
13C2×#88184C2211yescharacteristic
14C2×C4×C22⋊D13—21no—
15C2×#88180—21no—
16C2×C4×D52C2211yescharacteristic
17C2×C13×C22⋊C8C2212yes—
18C2×C4×C8×C13C2212yes—
19#11718874—21no—
20#11718873—21no—
21#11718873C2212yes—
22#11718873C2211yescharacteristic
23C2×#88061C2212yes—
24C2×#88061C2212yes—
25C2×#88058C2212yes—
26C2×#88058C2212yes—
27#11718601—21no—
28#11718600C2211yescharacteristic
29C4×#6103—21no—
30#11718597—21no—
31#11718596C2211yescharacteristic
32#11718596C2211yescharacteristic
33C4×C4⋊Dic13—21no—
34C4×C4⋊Dic13C2212yes—
35C4×C4⋊Dic13C2211yescharacteristic
36#11718589C2211yescharacteristic
37C13×#336C2211yescharacteristic
38C13×#336C2211yescharacteristic
39#11718143C2212yes—
40#11718143C2212yes—
41#11718143C2212yes—
42#11718143C2212yes—
43C23×C4×C13D411yescharacteristic
44C23×C4×C13D411yescharacteristic
45C23×C4×C13C2311yescharacteristic
46C22×C22⋊D13—21no—
47C22×D52C2311yescharacteristic
48C22×C4×D13—21no—
49C22×C8×C13C2312yes—
50C22×C8×C13C2312yes—
51C2×C42×C13—24no—
52C2×C42×C13D411yescharacteristic
53C2×C42×C13D411yescharacteristic
54C2×C42×C13C2311yescharacteristic
55C2×C42×C13C2311yescharacteristic
56C2×C22⋊Dic13—22no—
57C2×C22⋊Dic13—21no—
58#88184—22no—
59#88184—22no—
60C4×C22⋊D13—44no—
61C2×#6103—21no—
62C2×#6103—21no—
63C2×#6103—21no—
64C2×#6103—21no—
65#88180—44no—
66C2×C4⋊Dic13—21no—
67C2×C4⋊Dic13—21no—
68C2×C4⋊Dic13—21no—
69C2×C4⋊Dic13—21no—
70C2×C4⋊Dic13C2311yescharacteristic
71C2×C4⋊Dic13C2311yescharacteristic
72C2×C4⋊Dic13C2312yes—
73C2×C4⋊Dic13C2312yes—
74C2×C4⋊Dic13C2311yescharacteristic
75C2×#6101—21no—
76C2×C4×Dic13—22no—
77C2×C4×Dic13—21no—
78C4×D52—24no—
79C13×C22⋊C8—24no—
80C4×C8×C13—24no—
81#88071—21no—
82#88071—22no—
83#88071—22no—
84#88071—21no—
85#88071—21no—
86#88061—24no—
87#88061—24no—
88#88058—24no—
89#88058—24no—
90#23754—131nomaximal, Sylow
91C24×C13C2×D411yescharacteristic
92C23×D13—21no—
93C22×C4×C13—22no—
94C22×C4×C13—22no—
95C22×C4×C13—22no—
96C22×C4×C13—22no—
97C22×C4×C13—22no—
98C22×C4×C13—21no—
99C22×C4×C13—21no—
100C22×C4×C13—22no—
101C22×C4×C13—41no—
102C22×C4×C13D814yes—
103C22×C4×C13C2×D411yescharacteristic
104C22×C4×C13C2×D411yescharacteristic
105C22×C4×C13C2×D411yescharacteristic
106C22×C4×C13C2×D411yescharacteristic
107C22×C4×C13C2×D411yescharacteristic
108C22×C4×C13C2411yescharacteristic
109C2×C22⋊D13—24no—
110C2×C22⋊D13—42no—
111C2×C22⋊D13—42no—
112C22×Dic13—21no—
113C22×Dic13—22no—
114C22×Dic13—22no—
115C22×Dic13—21no—
116C22×Dic13—21no—
117C2×D52—22no—
118C2×D52—22no—
119C2×D52—21no—
120C2×D52#4112yes—
121C2×C4×D13—42no—
122C2×C4×D13—42no—
123C2×C4×D13—42no—
124C2×C8×C13—22no—
125C2×C8×C13—22no—
126C2×C8×C13—22no—
127C2×C8×C13—22no—
128C2×C8×C13—22no—
129C2×C8×C13#4114yes—
130C42×C13—22no—
131C42×C13—22no—
132C42×C13—22no—
133C42×C13#4114yes—
134C22⋊Dic13—44no—
135C22⋊Dic13—42no—
136#6103—24no—
137#6103—42no—
138#6103—42no—
139#6103—42no—
140C4⋊Dic13—21no—
141C4⋊Dic13—22no—
142C4⋊Dic13—22no—
143C4⋊Dic13—22no—
144C4⋊Dic13—22no—
145C4⋊Dic13—22no—
146C4⋊Dic13—22no—
147C4⋊Dic13—42no—
148C4⋊Dic13—42no—
149C4⋊Dic13—42no—
150C4⋊Dic13—42no—
151C4⋊Dic13#4112yes—
152#6101—42no—
153C4×Dic13—44no—
154C4×Dic13—42no—
155C4×#121—131no—
156#2285—131no—
157#2099—131no—
158#2093—131no—
159#2083—131no—
160#2075—132no—
161#2071—131no—
162#2033—132no—
163C4×#107—132no—
164C4×#102—132no—
165C4×C22⋊C8D1311yescharacteristic, complemented
166C23×C13—21no—
167C23×C13—21no—
168C23×C13—21no—
169C23×C13—21no—
170C23×C13—21no—
171C23×C13—21no—
172C23×C13C2×D812yes—
173C23×C13C22×D411yescharacteristic
174C22×D13—22no—
175C22×D13—41no—
176C22×D13—41no—
177C22×D13—41no—
178C22×D13—41no—
179C22×D13—41no—
180C22×D13—41no—
181C2×C4×C13—21no—
182C2×C4×C13—21no—
183C2×C4×C13—21no—
184C2×C4×C13—21no—
185C2×C4×C13—21no—
186C2×C4×C13—21no—
187C2×C4×C13—28no—
188C2×C4×C13—21no—
189C2×C4×C13—21no—
190C2×C4×C13—21no—
191C2×C4×C13—44no—
192C2×C4×C13—42no—
193C2×C4×C13—42no—
194C2×C4×C13#12312yes—
195C2×C4×C13#12312yes—
196C2×C4×C13C2×D812yes—
197C2×C4×C13C2×D812yes—
198C2×C4×C13#13512yes—
199C2×C4×C13#13712yes—
200C2×C4×C13C2×#4112yes—
201C2×C4×C13C2×#4111yescharacteristic
202C2×C4×C13C2×#4111yescharacteristic
203C2×C4×C13C2×#4112yes—
204C22⋊D13—48no—
205C2×Dic13—22no—
206C2×Dic13—41no—
207C2×Dic13—41no—
208C2×Dic13—41no—
209C2×Dic13—42no—
210C2×Dic13—41no—
211C2×Dic13—42no—
212C2×Dic13—42no—
213C2×Dic13—42no—
214C2×Dic13—41no—
215C2×Dic13—41no—
216C2×Dic13—42no—
217C2×Dic13—41no—
218C2×Dic13—41no—
219C2×Dic13—42no—
220D52—24no—
221D52—42no—
222C4×D13—84no—
223C8×C13—24no—
224C8×C13—42no—
225C2×#121—131no—
226C2×C4×D4—131no—
227C2×C4×D4—261no—
228C2×#117—261no—
229C22×C42C2×D1311yescharacteristic
230C2×#107—132no—
231C2×#107—132no—
232C2×#102—132no—
233C2×#102—132no—
234C2×C22⋊C8C2×D1312yes—
235C2×C4×C8C2×D1312yes—
236#390—131no—
237#389—131no—
238#388—261no—
239#386—261no—
240#384—131no—
241#384—131no—
242#382—261no—
243#380—131no—
244#380—132no—
245#380—261no—
246C4×C4⋊C4—132no—
247C4×C4⋊C4—131no—
248C4×C4⋊C4—261no—
249C4×C22⋊C4—261no—
250#340—132no—
251#340—132no—
252#340—132no—
253#340—132no—
254#336C2×D1311yescharacteristic
255#336C2×D1311yescharacteristic
256C22×C13—22no—
257C22×C13—22no—
258C22×C13—22no—
259C22×C13—41no—
260C22×C13—41no—
261C22×C13—41no—
262C22×C13—41no—
263C22×C13C2×#12311yescharacteristic
264C22×C13#52511yescharacteristic
265C22×C13#53211yescharacteristic
266C22×C13C22×D811yescharacteristic
267C22×C13C2×#13511yescharacteristic
268C22×C13C2×#13711yescharacteristic
269C22×C13#57511yescharacteristic
270C2×D13—42no—
271C2×D13—42no—
272C2×D13—42no—
273C2×D13—81no—
274C2×D13—81no—
275C2×D13—81no—
276C2×D13—81no—
277C4×C13—22no—
278C4×C13—22no—
279C4×C13—22no—
280C4×C13—41no—
281C4×C13#48014yes—
282C4×C13#52912yes—
283C4×C13#52912yes—
284Dic13—42no—
285Dic13—81no—
286Dic13—82no—
287Dic13—82no—
288Dic13—81no—
289C22×D4—131no—
290C22×D4—261no—
291C23×C4—261no—
292C23×C4D5211yescharacteristic
293C23×C4D5211yescharacteristic
294C23×C4C22×D1311yescharacteristic
295C22×C8C22×D1312yes—
296C22×C8C22×D1312yes—
297#121—262no—
298#121—262no—
299C4×D4—264no—
300C4×D4—524no—
301#117—524no—
302C2×C4⋊C4—131no—
303C2×C4⋊C4—131no—
304C2×C4⋊C4—132no—
305C2×C4⋊C4—132no—
306C2×C4⋊C4—131no—
307C2×C4⋊C4—261no—
308C2×C4⋊C4—261no—
309C2×C4⋊C4—261no—
310C2×C4⋊C4—261no—
311C2×C4⋊C4—261no—
312C2×C22⋊C4—261no—
313C2×C22⋊C4—262no—
314C2×C22⋊C4—261no—
315C2×C22⋊C4—261no—
316C2×C22⋊C4—261no—
317C2×C22⋊C4—261no—
318C2×C42—24no—
319C2×C42—262no—
320C2×C42—261no—
321C2×C42D5211yescharacteristic
322C2×C42D5211yescharacteristic
323C2×C42C22×D1311yescharacteristic
324C2×C42C22×D1311yescharacteristic
325#107—264no—
326#107—264no—
327#102—264no—
328#102—264no—
329C22⋊C8—24no—
330C4×C8—24no—
331#95—261no—
332#95—261no—
333#95—262no—
334#95—261no—
335#95—262no—
336C2×C13—42no—
337C2×C13#239511yescharacteristic
338C2×C13C2×#48011yescharacteristic
339C2×C13#309111yescharacteristic
340C2×C13#310011yescharacteristic
341C2×C13#310711yescharacteristic
342C2×C13#316911yescharacteristic
343C2×C13#317211yescharacteristic
344D13—82no—
345C24—261no—
346C24C2×D5211yescharacteristic
347C2×D4—132no—
348C2×D4—264no—
349C2×D4—262no—
350C2×D4—262no—
351C2×D4—261no—
352C2×D4—522no—
353C2×D4—522no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—41no—
363C22×C4—261no—
364C22×C4—261no—
365C22×C4—262no—
366C22×C4—262no—
367C22×C4—261no—
368C22×C4—522no—
369C22×C4—522no—
370C22×C4—522no—
371C22×C4D10414yes—
372C22×C4C2×D5211yescharacteristic
373C22×C4C2×D5211yescharacteristic
374C22×C4C2×D5211yescharacteristic
375C22×C4C2×D5211yescharacteristic
376C22×C4C2×D5211yescharacteristic
377C22×C4C23×D1311yescharacteristic
378C2×C8—22no—
379C2×C8—22no—
380C2×C8—22no—
381C2×C8—22no—
382C2×C8—22no—
383C2×C8#612714yes—
384C4⋊C4—132no—
385C4⋊C4—261no—
386C4⋊C4—262no—
387C4⋊C4—262no—
388C4⋊C4—262no—
389C4⋊C4—262no—
390C4⋊C4—262no—
391C4⋊C4—262no—
392C4⋊C4—522no—
393C4⋊C4—522no—
394C4⋊C4—522no—
395C4⋊C4—522no—
396C4⋊C4—522no—
397C22⋊C4—264no—
398C22⋊C4—524no—
399C22⋊C4—522no—
400C22⋊C4—522no—
401C22⋊C4—522no—
402C22⋊C4—522no—
403C42—22no—
404C42—22no—
405C42—22no—
406C42—524no—
407C42—522no—
408C42#612914yes—
409C13#2375411yescharacteristic, complemented, Sylow
410C23—21no—
411C23—21no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—262no—
417C23—521no—
418C23—521no—
419C23—521no—
420C23—521no—
421C23—521no—
422C23—521no—
423C23C2×D10412yes—
424C23C22×D5211yescharacteristic
425D4—264no—
426D4—528no—
427D4—522no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—28no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—44no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—262no—
442C2×C4—521no—
443C2×C4—521no—
444C2×C4—522no—
445C2×C4—521no—
446C2×C4—521no—
447C2×C4—522no—
448C2×C4—522no—
449C2×C4—521no—
450C2×C4—521no—
451C2×C4—522no—
452C2×C4—521no—
453C2×C4—521no—
454C2×C4—522no—
455C2×C4—522no—
456C2×C4—1044no—
457C2×C4#8814012yes—
458C2×C4#8814012yes—
459C2×C4C2×D10412yes—
460C2×C4C2×D10412yes—
461C2×C4#8815812yes—
462C2×C4#8816312yes—
463C2×C4C2×#612712yes—
464C2×C4C2×#612912yes—
465C2×C4#41×D1311yescharacteristic
466C2×C4#41×D1311yescharacteristic
467C8—24no—
468C8—42no—
469C22—22no—
470C22—22no—
471C22—22no—
472C22—41no—
473C22—41no—
474C22—41no—
475C22—41no—
476C22—522no—
477C22—522no—
478C22—522no—
479C22—1041no—
480C22—1041no—
481C22—1041no—
482C22—1041no—
483C22#1171918211yescharacteristic
484C22C2×#8814011yescharacteristic
485C22#1171922911yescharacteristic
486C22C22×D10411yescharacteristic
487C22C2×#8815811yescharacteristic
488C22C2×#8816311yescharacteristic
489C22#1171945311yescharacteristic
490C4—22no—
491C4—22no—
492C4—22no—
493C4—41no—
494C4—522no—
495C4—1041no—
496C4—1042no—
497C4—1041no—
498C4—1042no—
499C4#1171839714yes—
500C4#1171924312yes—
501C4#1171926212yes—
502C2—42no—
503C2—1042no—
504C2#1311809611yescharacteristic
505C2C2×#1171839711yescharacteristic
506C2#1312475111yescharacteristic
507C2#1312483711yescharacteristic
508C2#1312490811yescharacteristic
509C2#1312541511yescharacteristic
510C2#1312544211yescharacteristic
subgroupG/H
centerC22×C4C2×D52
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC4×C13×C22⋊C8C2
socleC23×C13C22×D4
prime radicalC2×#88184C22
hypercenterC4×C22⋊C8D13
hypocenterC13#23754
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #13117243C2semidirect
3. #13116395C2semidirect
4. #13116363C2semidirect
5. #13116309C2semidirect
6. #13116259C2semidirect
7. #13116241C2semidirect
9. C4×#88058C2semidirect
10. C4×#88061C2semidirect
11. C4×C13×C22⋊C8C2semidirect
165. C4×C22⋊C8D13semidirect
409. C13#23754semidirect

Maximal subgroups

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

subgroupindex
C4×#881842
#131172432
#131163952
#131163632
#131163092
#131162592
#131162412
#131160192
C4×#880582
C4×#880612
C4×C13×C22⋊C82
#2375413