Finite Group Databasebeta

← #15765264

Subgroups — #15765264

Order 3328.

628 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718745C211yesmaximal, characteristic
2#13119754C211yesmaximal, characteristic
3#13115639C211yesmaximal, characteristic, complemented
4C2×Q8⋊#1055C211yesmaximal, characteristic, complemented
5C2×#11718075C211yesmaximal, characteristic
6#13112720C211yesmaximal, characteristic, complemented
7C2×C13×#477C211yesmaximal, characteristic, complemented
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×C4×Q8×C13C2211yescharacteristic
10C2×#88200—21no—
11C2×C4×D52C2211yescharacteristic
12C13×#477—22no—
13C13×#477—22no—
14C2×C13×#107—21no—
15C2×C13×C4⋊C8C2211yescharacteristic
16C2×C13×#103—21no—
17C2×#88075—22no—
18#11718745—22no—
19#11718745—22no—
20#11718655—22no—
21#11718648—21no—
22C2×#88049—21no—
23C2×#88048—21no—
24#11718600—21no—
25#11718596C2211yescharacteristic
26#11718589—21no—
27C2×C4⋊#1055C2211yescharacteristic
28C2×C4×#1055C2211yescharacteristic
29Q8⋊#1055—22no—
30#11718075—22no—
31C22×Q8×C13—21no—
32C22×Q8×C13D411yescharacteristic
33C22×D52D411yescharacteristic
34C22×C4×D13—21no—
35C22×C8×C13—21no—
36C13×C4⋊Q8—21no—
37C13×C4⋊Q8—21no—
38C13×C4⋊Q8—21no—
39C13×C4⋊Q8D412yes—
40C4×Q8×C13—21no—
41C4×Q8×C13—21no—
42C4×Q8×C13—21no—
43C4×Q8×C13—21no—
44C2×C13×C4⋊C4—21no—
45C2×C13×C4⋊C4—21no—
46C2×C13×C4⋊C4—21no—
47C2×C13×C4⋊C4D411yescharacteristic
48C2×C42×C13—21no—
49C2×C42×C13C2311yescharacteristic
50#88200—42no—
51#88200—42no—
52C2×#6103—22no—
53C2×#6103—21no—
54C2×#6103—22no—
55C2×C4⋊Dic13—21no—
56C2×C4⋊Dic13—21no—
57C2×C4⋊Dic13D411yescharacteristic
58C2×C4⋊Dic13D412yes—
59C2×#6101—22no—
60C22×#1055—21no—
61C22×#1055—21no—
62C4×D52—21no—
63C4×D52—21no—
64C4×D52—21no—
65C4×D52—21no—
66C13×#107—24no—
67C13×C4⋊C8—21no—
68C13×C4⋊C8D412yes—
69C13×#103—24no—
70#88075—44no—
71#88071—22no—
72#88049—24no—
73#88048—24no—
74C4⋊#1055—21no—
75C4⋊#1055D412yes—
76C4×#1055—21no—
77C4×#1055—21no—
78#10236—131nomaximal, Sylow
79C23×D13—21no—
80C2×Q8×C13—21no—
81C2×Q8×C13—21no—
82C2×Q8×C13—21no—
83C2×Q8×C13—22no—
84C2×Q8×C13—21no—
85C2×Q8×C13—21no—
86C2×Q8×C13—42no—
87C2×Q8×C13—42no—
88C2×Q8×C13—41no—
89C2×Q8×C13SD1612yes—
90C22×C4×C13—21no—
91C22×C4×C13—21no—
92C22×C4×C13—41no—
93C22×C4×C13C2×D411yescharacteristic
94C22×C4×C13C2×D411yescharacteristic
95C22×C4×C13C2×D411yescharacteristic
96C22×Dic13—21no—
97C22×Dic13—22no—
98C2×D52—21no—
99C2×D52—21no—
100C2×D52—21no—
101C2×D52—21no—
102C2×D52—21no—
103C2×D52Q1612yes—
104C2×C4×D13—41no—
105C2×C4×D13—41no—
106C2×C4×D13—41no—
107C2×C4×D13—41no—
108C2×C4×D13—41no—
109C2×C4×D13—41no—
110C2×C8×C13—22no—
111C2×C8×C13—41no—
112C2×C8×C13—41no—
113C13×C4⋊C4—22no—
114C13×C4⋊C4—21no—
115C13×C4⋊C4—22no—
116C13×C4⋊C4—21no—
117C13×C4⋊C4—41no—
118C13×C4⋊C4—41no—
119C13×C4⋊C4—41no—
120C13×C4⋊C4—41no—
121C42×C13—41no—
122C42×C13—41no—
123C42×C13C2×D411yescharacteristic
124C42×C13C2×D411yescharacteristic
125C42×C13C2×D411yescharacteristic
126C42×C13#4111yescharacteristic
127#6103—44no—
128#6103—41no—
129#6103—41no—
130#6103—82no—
131C4⋊Dic13—21no—
132C4⋊Dic13—21no—
133C4⋊Dic13—41no—
134C4⋊Dic13—41no—
135C4⋊Dic13—41no—
136C4⋊Dic13—41no—
137C4⋊Dic13—42no—
138#6101—44no—
139C2×#1055—22no—
140C2×#1055—22no—
141C2×#1055—41no—
142C2×#1055—41no—
143C2×#1055—41no—
144C2×#1055—41no—
145C2×#477D1311yescharacteristic, complemented
146C2×#476—131no—
147#2538—131no—
148#1956—131no—
149C2×Q8⋊C8—131no—
150C2×D4⋊C8—131no—
151#1296—131no—
152C23×C13#12011yescharacteristic
153C22×D13—22no—
154C22×D13—41no—
155C22×D13—41no—
156C22×D13—41no—
157C22×D13—41no—
158C22×D13—41no—
159C22×D13—41no—
160Q8×C13—22no—
161Q8×C13—22no—
162Q8×C13—44no—
163Q8×C13—41no—
164Q8×C13—41no—
165Q8×C13—82no—
166C2×C4×C13—21no—
167C2×C4×C13—21no—
168C2×C4×C13—22no—
169C2×C4×C13—41no—
170C2×C4×C13—41no—
171C2×C4×C13—41no—
172C2×C4×C13—42no—
173C2×C4×C13—41no—
174C2×C4×C13—41no—
175C2×C4×C13—81no—
176C2×C4×C13—81no—
177C2×C4×C13#12011yescharacteristic
178C2×C4×C13#12011yescharacteristic
179C2×C4×C13#12111yescharacteristic
180C2×C4×C13#12111yescharacteristic
181C2×C4×C13#12111yescharacteristic
182C2×C4×C13#12711yescharacteristic
183C2×C4×C13C2×SD1611yescharacteristic
184C2×C4×C13C2×Q1611yescharacteristic
185C2×C4×C13#13511yescharacteristic
186C2×C4×C13#13511yescharacteristic
187C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
188C2×C4×C13#13711yescharacteristic
189C2×C4×C13#13711yescharacteristic
190C2×C4×C13#13711yescharacteristic
191C2×Dic13—41no—
192C2×Dic13—41no—
193C2×Dic13—42no—
194C2×Dic13—42no—
195C2×Dic13—41no—
196C2×Dic13—42no—
197D52—22no—
198D52—22no—
199D52—41no—
200D52—41no—
201C4×D13—81no—
202C4×D13—81no—
203C4×D13—81no—
204C4×D13—81no—
205C8×C13—42no—
206#1055—42no—
207#1055—42no—
208C2×C4⋊Q8C2×D1311yescharacteristic
209C2×C22⋊Q8—261no—
210C2×C4×Q8C2×D1311yescharacteristic
211C2×C4×D4—131no—
212#477—22no—
213#477—22no—
214#476—262no—
215#476—262no—
216C2×#107—21no—
217C2×#106—261no—
218C2×C4⋊C8—131no—
219C2×C4⋊C8C2×D1311yescharacteristic
220C2×#103—21no—
221C2×#103—262no—
222C2×#102—261no—
223C2×C4×C8—131no—
224#396—262no—
225#390—261no—
226#389—261no—
227#384—131no—
228#380—261no—
229Q8⋊C8—262no—
230D4⋊C8—262no—
231C22×C13#39211yescharacteristic
232C22×C13#45011yescharacteristic
233C22×C13#45111yescharacteristic
234C22×C13#45211yescharacteristic
235C22×C13#45211yescharacteristic
236C22×C13#45311yescharacteristic
237C22×C13#45411yescharacteristic
238C2×D13—42no—
239C2×D13—42no—
240C2×D13—42no—
241C2×D13—81no—
242C2×D13—81no—
243C2×D13—81no—
244C2×D13—81no—
245C4×C13—21no—
246C4×C13—21no—
247C4×C13—42no—
248C4×C13—81no—
249C4×C13—82no—
250C4×C13#44811yescharacteristic
251C4×C13#44911yescharacteristic
252C4×C13#45111yescharacteristic
253C4×C13#45211yescharacteristic
254C4×C13#46511yescharacteristic
255C4×C13#46711yescharacteristic
256C4×C13#46811yescharacteristic
257C4×C13#47011yescharacteristic
258Dic13—82no—
259Dic13—81no—
260C22×Q8—21no—
261C22×Q8C22⋊D1311yescharacteristic
262C22×D4—131no—
263C23×C4—261no—
264C22×C8—21no—
265C22×C8—261no—
266C22×C8—261no—
267C4⋊Q8—21no—
268C4⋊Q8—21no—
269C4⋊Q8—21no—
270C4⋊Q8C22⋊D1312yes—
271C22⋊Q8—522no—
272C22⋊Q8—522no—
273C4×Q8—21no—
274C4×Q8—21no—
275C4×Q8—21no—
276C4×Q8—21no—
277C4×D4—261no—
278C4×D4—261no—
279C4×D4—261no—
280C4×D4—261no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—131no—
285C2×C4⋊C4—132no—
286C2×C4⋊C4—262no—
287C2×C4⋊C4—261no—
288C2×C4⋊C4—261no—
289C2×C4⋊C4C22⋊D1311yescharacteristic
290C2×C22⋊C4—262no—
291C2×C22⋊C4—261no—
292C2×C22⋊C4—262no—
293C2×C42—21no—
294C2×C42C22×D1311yescharacteristic
295#107—24no—
296#106—264no—
297C4⋊C8—21no—
298C4⋊C8—132no—
299C4⋊C8—261no—
300C4⋊C8C22⋊D1312yes—
301#103—24no—
302#103—524no—
303#102—264no—
304C4×C8—261no—
305C4×C8—261no—
306#95—262no—
307C2×C13#163111yescharacteristic
308C2×C13#163211yescharacteristic
309C2×C13#163711yescharacteristic
310C2×C13#163811yescharacteristic
311C2×C13#200011yescharacteristic
312C2×C13#200111yescharacteristic
313C2×C13#200611yescharacteristic
314D13—82no—
315C24—261no—
316C2×Q8—21no—
317C2×Q8—21no—
318C2×Q8—22no—
319C2×Q8—21no—
320C2×Q8—21no—
321C2×Q8—21no—
322C2×Q8—42no—
323C2×Q8—42no—
324C2×Q8—41no—
325C2×Q8#610612yes—
326C2×D4—132no—
327C2×D4—261no—
328C2×D4—261no—
329C2×D4—261no—
330C2×D4—261no—
331C2×D4—261no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—41no—
335C22×C4—261no—
336C22×C4—262no—
337C22×C4—521no—
338C22×C4—521no—
339C22×C4—521no—
340C22×C4—521no—
341C22×C4—521no—
342C22×C4—521no—
343C22×C4D4×D1311yescharacteristic
344C22×C4D4×D1311yescharacteristic
345C22×C4C2×C22⋊D1311yescharacteristic
346C2×C8—22no—
347C2×C8—41no—
348C2×C8—41no—
349C2×C8—262no—
350C2×C8—262no—
351C2×C8—521no—
352C2×C8—521no—
353C2×C8—521no—
354C2×C8—521no—
355C4⋊C4—22no—
356C4⋊C4—21no—
357C4⋊C4—22no—
358C4⋊C4—21no—
359C4⋊C4—41no—
360C4⋊C4—41no—
361C4⋊C4—41no—
362C4⋊C4—41no—
363C4⋊C4—261no—
364C4⋊C4—261no—
365C4⋊C4—522no—
366C4⋊C4—524no—
367C4⋊C4—521no—
368C4⋊C4—521no—
369C4⋊C4—521no—
370C4⋊C4—521no—
371C22⋊C4—524no—
372C22⋊C4—521no—
373C22⋊C4—521no—
374C22⋊C4—1042no—
375C42—41no—
376C42—41no—
377C42D4×D1311yescharacteristic
378C42#612911yescharacteristic
379C42C2×C22⋊D1311yescharacteristic
380C42C2×C22⋊D1311yescharacteristic
381C13#1023611yescharacteristic, complemented, Sylow
382C23—262no—
383C23—521no—
384C23—521no—
385C23—521no—
386C23—521no—
387C23—521no—
388C23—521no—
389C23#8819111yescharacteristic
390Q8—22no—
391Q8—22no—
392Q8—44no—
393Q8—41no—
394Q8—41no—
395Q8—82no—
396D4—262no—
397D4—262no—
398D4—521no—
399D4—521no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—22no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—42no—
409C2×C4—81no—
410C2×C4—81no—
411C2×C4—522no—
412C2×C4—521no—
413C2×C4—521no—
414C2×C4—522no—
415C2×C4—522no—
416C2×C4—521no—
417C2×C4—1041no—
418C2×C4—1041no—
419C2×C4—1041no—
420C2×C4—1041no—
421C2×C4Q16×D1311yescharacteristic
422C2×C4#8817211yescharacteristic
423C2×C4#8817211yescharacteristic
424C2×C4#8817311yescharacteristic
425C2×C4#8819111yescharacteristic
426C2×C4#8819211yescharacteristic
427C2×C4#8819311yescharacteristic
428C2×C4#8819311yescharacteristic
429C2×C4#8819411yescharacteristic
430C2×C4C2×#610611yescharacteristic
431C2×C4#8819611yescharacteristic
432C2×C4#8820311yescharacteristic
433C2×C4#8820411yescharacteristic
434C2×C4#8820711yescharacteristic
435C8—42no—
436C8—522no—
437C8—522no—
438C22—522no—
439C22—522no—
440C22—522no—
441C22—1041no—
442C22—1041no—
443C22—1041no—
444C22—1041no—
445C22#1171870711yescharacteristic
446C22#1171870811yescharacteristic
447C22#1171884711yescharacteristic
448C22#1171884811yescharacteristic
449C22#1171885911yescharacteristic
450C22#1171886211yescharacteristic
451C22#1171888411yescharacteristic
452C4—21no—
453C4—21no—
454C4—42no—
455C4—81no—
456C4—82no—
457C4—1042no—
458C4—1041no—
459C4#1171870911yescharacteristic
460C4#1171871011yescharacteristic
461C4#1171884711yescharacteristic
462C4#1171884811yescharacteristic
463C4#1171884911yescharacteristic
464C4#1171885011yescharacteristic
465C4#1171888811yescharacteristic
466C4#1171889911yescharacteristic
467C2—1042no—
468C2#1311396111yescharacteristic
469C2#1311396911yescharacteristic
470C2#1311399911yescharacteristic
471C2#1311400711yescharacteristic
472C2#1311583711yescharacteristic
473C2#1311584311yescharacteristic
474C2#1311587611yescharacteristic
subgroupG/H
centerC23#88191
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC2×C13×#477C2
socleC23×C13#120
prime radicalC22×D52D4
hypercenterC2×#477D13
hypocenterC13#10236
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
3. #13115639C2semidirect
4. C2×Q8⋊#1055C2semidirect
6. #13112720C2semidirect
7. C2×C13×#477C2semidirect
145. C2×#477D13semidirect
381. C13#10236semidirect

Maximal subgroups

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

subgroupindex
C2×#117187452
#131197542
#131156392
C2×Q8⋊#10552
C2×#117180752
#131127202
C2×C13×#4772
#1023613