Finite Group Databasebeta

← #15763197

Subgroups — #15763197

Order 3328.

734 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718704C211yesmaximal, characteristic, complemented
2C2×#11718614C211yesmaximal, characteristic
3#13114920C211yesmaximal, characteristic, complemented
4C2×#11718130C211yesmaximal, characteristic, complemented
5C2×#11718117C211yesmaximal, characteristic
6#13112714C211yesmaximal, characteristic, complemented
7C13×#2626C211yesmaximal, characteristic
8C2×C13×C22⋊Q8C2211yescharacteristic
9C22×C13×C22⋊C4C2211yescharacteristic
10C22×C22⋊Dic13—21no—
11C22×C4⋊Dic13C2211yescharacteristic
12C13×#399—21no—
13C13×#396—22no—
14C13×#393—21no—
15C13×#385—21no—
16C13×#380C2211yescharacteristic
17C13×#379—21no—
18C2×#88075—21no—
19C2×#88071—21no—
20C2×#88071C2211yescharacteristic
21C2×C22⋊#1055C2211yescharacteristic
22C2×C22⋊#1055C2211yescharacteristic
23#11718704—22no—
24#11718704—22no—
25C2×#88048—21no—
26#11718614—22no—
27#11718614—22no—
28#11718130—22no—
29#11718121—22no—
30#11718117—22no—
31C25×C13D411yescharacteristic
32C22×Q8×C13D411yescharacteristic
33C23×C4×C13D411yescharacteristic
34C23×C4×C13C2311yescharacteristic
35C23×Dic13—21no—
36C23×Dic13—21no—
37C13×C22⋊Q8—21no—
38C13×C22⋊Q8—21no—
39C13×C22⋊Q8—21no—
40C13×C22⋊Q8—21no—
41C2×C13×C4⋊C4—21no—
42C2×C13×C4⋊C4—22no—
43C2×C13×C4⋊C4D411yescharacteristic
44C2×C13×C4⋊C4D412yes—
45C2×C13×C22⋊C4—21no—
46C2×C13×C22⋊C4—21no—
47C2×C13×C22⋊C4—21no—
48C2×C13×C22⋊C4—21no—
49C2×C13×C22⋊C4—21no—
50C2×C13×C22⋊C4—21no—
51C2×C13×C22⋊C4—21no—
52C2×C13×C22⋊C4—21no—
53C2×C13×C22⋊C4—22no—
54C2×C13×C22⋊C4—22no—
55C2×C22⋊Dic13—24no—
56C2×C22⋊Dic13—42no—
57C2×C22⋊Dic13—42no—
58C2×C4⋊Dic13—21no—
59C2×C4⋊Dic13—21no—
60C2×C4⋊Dic13—21no—
61C2×C4⋊Dic13—21no—
62C2×C4⋊Dic13—21no—
63C2×C4⋊Dic13D412yes—
64C22×#1055—21no—
65C22×#1055—21no—
66C13×#95—22no—
67C13×#95—21no—
68#88075—24no—
69#88071—24no—
70#88071—21no—
71#88071D412yes—
72C22⋊#1055—21no—
73C22⋊#1055—21no—
74C22⋊#1055—21no—
75C22⋊#1055D412yes—
76#88048—24no—
77#9926—131nomaximal, Sylow
78C24×C13—21no—
79C24×C13—21no—
80C24×C13—21no—
81C24×C13—21no—
82C24×C13—21no—
83C24×C13—21no—
84C24×C13—42no—
85C24×C13—42no—
86C24×C13SD1612yes—
87C24×C13C2×D411yescharacteristic
88C2×Q8×C13—21no—
89C2×Q8×C13—21no—
90C2×Q8×C13—42no—
91C22×C4×C13—21no—
92C22×C4×C13—22no—
93C22×C4×C13—21no—
94C22×C4×C13—21no—
95C22×C4×C13—21no—
96C22×C4×C13—21no—
97C22×C4×C13—42no—
98C22×C4×C13—42no—
99C22×C4×C13C2×D411yescharacteristic
100C22×C4×C13C2×D411yescharacteristic
101C22×C4×C13C2×D411yescharacteristic
102C22×C4×C13C2×D411yescharacteristic
103C22×C4×C13C2×D411yescharacteristic
104C22×C4×C13#4111yescharacteristic
105C22×Dic13—22no—
106C22×Dic13—22no—
107C22×Dic13—42no—
108C22×Dic13—42no—
109C22×Dic13—41no—
110C22×Dic13—41no—
111C22×Dic13—41no—
112C22×Dic13—41no—
113C22×Dic13—41no—
114C22×Dic13—41no—
115C22×Dic13—41no—
116C22×Dic13—41no—
117C13×C4⋊C4—21no—
118C13×C4⋊C4—21no—
119C13×C4⋊C4—42no—
120C13×C4⋊C4—41no—
121C13×C4⋊C4—41no—
122C13×C4⋊C4—82no—
123C13×C22⋊C4—41no—
124C13×C22⋊C4—41no—
125C13×C22⋊C4—41no—
126C13×C22⋊C4—41no—
127C13×C22⋊C4—41no—
128C13×C22⋊C4—41no—
129C13×C22⋊C4—41no—
130C13×C22⋊C4—41no—
131C13×C22⋊C4—82no—
132C13×C22⋊C4—82no—
133C22⋊Dic13—48no—
134C4⋊Dic13—22no—
135C4⋊Dic13—22no—
136C4⋊Dic13—41no—
137C4⋊Dic13—41no—
138C2×#1055—22no—
139C2×#1055—42no—
140C2×#1055—42no—
141C2×#1055—41no—
142C2×#483—131no—
143#2626D1311yescharacteristic
144C2×#397—131no—
145#1823—131no—
146C2×#328—131no—
147C2×#323—131no—
148#1294—131no—
149C23×C13—22no—
150C23×C13—22no—
151C23×C13—22no—
152C23×C13—22no—
153C23×C13—22no—
154C23×C13—44no—
155C23×C13—44no—
156C23×C13—42no—
157C23×C13—42no—
158C23×C13—41no—
159C23×C13—41no—
160C23×C13—41no—
161C23×C13—42no—
162C23×C13—42no—
163C23×C13—41no—
164C23×C13—82no—
165C23×C13—82no—
166C23×C13—81no—
167C23×C13—81no—
168C23×C13#12011yescharacteristic
169C23×C13#12011yescharacteristic
170C23×C13#12111yescharacteristic
171C23×C13C2×SD1611yescharacteristic
172C23×C13#13511yescharacteristic
173C23×C13AGL(1,ℤ/8)11yescharacteristic
174C23×C13#13711yescharacteristic
175Q8×C13—42no—
176Q8×C13—81no—
177C2×C4×C13—22no—
178C2×C4×C13—22no—
179C2×C4×C13—41no—
180C2×C4×C13—41no—
181C2×C4×C13—41no—
182C2×C4×C13—41no—
183C2×C4×C13—42no—
184C2×C4×C13—41no—
185C2×C4×C13—41no—
186C2×C4×C13—41no—
187C2×C4×C13—42no—
188C2×C4×C13—42no—
189C2×C4×C13—42no—
190C2×C4×C13—42no—
191C2×C4×C13—42no—
192C2×C4×C13—42no—
193C2×C4×C13—81no—
194C2×C4×C13#12011yescharacteristic
195C2×C4×C13#12111yescharacteristic
196C2×C4×C13#12111yescharacteristic
197C2×C4×C13#12711yescharacteristic
198C2×Dic13—42no—
199C2×Dic13—42no—
200C2×Dic13—42no—
201C2×Dic13—42no—
202C2×Dic13—42no—
203C2×Dic13—42no—
204C2×Dic13—82no—
205C2×Dic13—82no—
206C2×Dic13—81no—
207C2×Dic13—81no—
208C2×Dic13—81no—
209C2×Dic13—81no—
210#1055—42no—
211#1055—81no—
212C2×C22⋊Q8C2×D1311yescharacteristic
213C22×C4⋊C4—131no—
214C22×C22⋊C4—261no—
215C22×C22⋊C4C2×D1311yescharacteristic
216#483—262no—
217#483—262no—
218C2×#106—261no—
219C2×#103—261no—
220C2×C22⋊C8—131no—
221C2×C22⋊C8—131no—
222#399—21no—
223#397—262no—
224#397—262no—
225#396—22no—
226#393—21no—
227#385—21no—
228#380C2×D1311yescharacteristic
229#379—21no—
230C2×#95—131no—
231C2×#95—261no—
232#340—262no—
233#328—262no—
234#323—262no—
235C22×C13—22no—
236C22×C13—22no—
237C22×C13—22no—
238C22×C13—22no—
239C22×C13—21no—
240C22×C13—21no—
241C22×C13—21no—
242C22×C13—21no—
243C22×C13—44no—
244C22×C13—44no—
245C22×C13—42no—
246C22×C13—82no—
247C22×C13—82no—
248C22×C13—82no—
249C22×C13—82no—
250C22×C13—81no—
251C22×C13—81no—
252C22×C13#39211yescharacteristic
253C22×C13#44811yescharacteristic
254C22×C13#44911yescharacteristic
255C22×C13#45011yescharacteristic
256C22×C13#45211yescharacteristic
257C22×C13#45512yes—
258C22×C13#45812yes—
259C22×C13#46511yescharacteristic
260C22×C13#46811yescharacteristic
261C4×C13—21no—
262C4×C13—21no—
263C4×C13—21no—
264C4×C13—21no—
265C4×C13—82no—
266C4×C13—81no—
267C4×C13—81no—
268C4×C13—81no—
269Dic13—82no—
270Dic13—82no—
271C25C22⋊D1311yescharacteristic
272C22×Q8C22⋊D1311yescharacteristic
273C23×C4—261no—
274C23×C4—261no—
275C23×C4C22⋊D1311yescharacteristic
276C23×C4C22×D1311yescharacteristic
277C22×C8—261no—
278C22×C8—261no—
279C22⋊Q8—21no—
280C22⋊Q8—21no—
281C22⋊Q8—21no—
282C22⋊Q8—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—132no—
286C2×C4⋊C4—261no—
287C2×C4⋊C4—261no—
288C2×C4⋊C4—261no—
289C2×C4⋊C4—261no—
290C2×C4⋊C4—261no—
291C2×C4⋊C4C22⋊D1311yescharacteristic
292C2×C4⋊C4C22⋊D1312yes—
293C2×C22⋊C4—21no—
294C2×C22⋊C4—21no—
295C2×C22⋊C4—21no—
296C2×C22⋊C4—21no—
297C2×C22⋊C4—21no—
298C2×C22⋊C4—21no—
299C2×C22⋊C4—21no—
300C2×C22⋊C4—21no—
301C2×C22⋊C4—22no—
302C2×C22⋊C4—22no—
303C2×C22⋊C4—264no—
304C2×C22⋊C4—522no—
305C2×C22⋊C4—522no—
306#106—264no—
307#103—264no—
308C22⋊C8—132no—
309C22⋊C8—261no—
310C22⋊C8—261no—
311C22⋊C8—261no—
312#95—22no—
313#95—21no—
314#95—132no—
315#95—264no—
316#95—261no—
317C2×C13—21no—
318C2×C13—21no—
319C2×C13—21no—
320C2×C13—21no—
321C2×C13—82no—
322C2×C13#160812yes—
323C2×C13#161212yes—
324C2×C13#200011yescharacteristic
325C2×C13#200411yescharacteristic
326C2×C13#202211yescharacteristic
327C24—21no—
328C24—21no—
329C24—21no—
330C24—21no—
331C24—21no—
332C24—21no—
333C24—42no—
334C24—42no—
335C24#610612yes—
336C24C2×C22⋊D1311yescharacteristic
337C2×Q8—21no—
338C2×Q8—21no—
339C2×Q8—42no—
340C22×C4—21no—
341C22×C4—22no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—42no—
347C22×C4—42no—
348C22×C4—262no—
349C22×C4—262no—
350C22×C4—522no—
351C22×C4—522no—
352C22×C4—521no—
353C22×C4—521no—
354C22×C4—521no—
355C22×C4—521no—
356C22×C4—521no—
357C22×C4—521no—
358C22×C4—521no—
359C22×C4—521no—
360C22×C4D4×D1311yescharacteristic
361C22×C4D4×D1311yescharacteristic
362C22×C4D4×D1311yescharacteristic
363C22×C4#612911yescharacteristic
364C22×C4C2×C22⋊D1311yescharacteristic
365C22×C4C2×C22⋊D1311yescharacteristic
366C2×C8—262no—
367C2×C8—522no—
368C2×C8—522no—
369C2×C8—521no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—42no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—82no—
376C4⋊C4—262no—
377C4⋊C4—262no—
378C4⋊C4—521no—
379C4⋊C4—521no—
380C22⋊C4—41no—
381C22⋊C4—41no—
382C22⋊C4—41no—
383C22⋊C4—41no—
384C22⋊C4—41no—
385C22⋊C4—41no—
386C22⋊C4—41no—
387C22⋊C4—41no—
388C22⋊C4—82no—
389C22⋊C4—82no—
390C22⋊C4—528no—
391C13#992611yescharacteristic, complemented, Sylow
392C23—22no—
393C23—22no—
394C23—22no—
395C23—22no—
396C23—22no—
397C23—44no—
398C23—42no—
399C23—42no—
400C23—44no—
401C23—41no—
402C23—41no—
403C23—41no—
404C23—41no—
405C23—42no—
406C23—42no—
407C23—82no—
408C23—81no—
409C23—81no—
410C23—82no—
411C23#8819111yescharacteristic
412C23#8819311yescharacteristic
413C23C2×#610611yescharacteristic
414C23#8819611yescharacteristic
415C23#8820311yescharacteristic
416C23#8820411yescharacteristic
417C23#8820711yescharacteristic
418Q8—42no—
419Q8—81no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—42no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—81no—
437C2×C4—522no—
438C2×C4—522no—
439C2×C4—522no—
440C2×C4—522no—
441C2×C4—522no—
442C2×C4—522no—
443C2×C4—1042no—
444C2×C4—1042no—
445C2×C4—1041no—
446C2×C4—1041no—
447C2×C4—1041no—
448C2×C4—1041no—
449C2×C4#8819111yescharacteristic
450C2×C4#8819211yescharacteristic
451C2×C4#8819311yescharacteristic
452C2×C4#8819411yescharacteristic
453C8—522no—
454C8—1041no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—22no—
460C22—22no—
461C22—22no—
462C22—22no—
463C22—44no—
464C22—42no—
465C22—44no—
466C22—82no—
467C22—82no—
468C22—82no—
469C22—81no—
470C22—81no—
471C22—82no—
472C22#1171870711yescharacteristic
473C22#1171870811yescharacteristic
474C22#1171870911yescharacteristic
475C22#1171871011yescharacteristic
476C22#1171888411yescharacteristic
477C22#1171888811yescharacteristic
478C22#1171889911yescharacteristic
479C22#1171890312yes—
480C22#1171890412yes—
481C4—21no—
482C4—21no—
483C4—21no—
484C4—21no—
485C4—81no—
486C4—81no—
487C4—81no—
488C4—82no—
489C4—1042no—
490C4—1042no—
491C2—21no—
492C2—21no—
493C2—21no—
494C2—21no—
495C2—82no—
496C2#1311382712yes—
497C2#1311385012yes—
498C2#1311583711yescharacteristic
499C2#1311586311yescharacteristic
500C2#1311596511yescharacteristic
subgroupG/H
centerC23#88207
commutator, cosocleC23×C4×C13C23
FrattiniC23×C4C22×D13
FittingC13×#2626C2
socleC23×C13#120
prime radicalC25×C13D4
hypercenter#2626D13
hypocenterC13#9926
LCSG ▷ C23×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2626

Complements

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

NH ≅ G/Ntype
1. C2×#11718704C2semidirect
3. #13114920C2semidirect
4. C2×#11718130C2semidirect
6. #13112714C2semidirect
391. C13#9926semidirect

Maximal subgroups

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

subgroupindex
C2×#117187042
C2×#117186142
#131149202
C2×#117181302
C2×#117181172
#131127142
C13×#26262
#992613