Finite Group Databasebeta

← #15754843

Subgroups — #15754843

Order 3328.

756 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13115785C211yesmaximal, characteristic, complemented
2#13114856C211yesmaximal, characteristic, complemented
3#13113521C211yesmaximal, characteristic, complemented
4#13113513C211yesmaximal, characteristic, complemented
5#13113331C211yesmaximal, characteristic, complemented
6#13113223C211yesmaximal, characteristic, complemented
7C13×#3511C211yesmaximal, characteristic
8C13×#556C412yescomplemented
9C13×#555—21no—
10C13×#554—21no—
11C13×#553—22no—
12C13×#548—22no—
13C13×#547C412yescomplemented
14C13×#542—22no—
15C13×#537—21no—
16C13×#533—21no—
17C13×#532—21no—
18C13×#532C2211yescharacteristic
19C2×C13×C4⋊Q8C2211yescharacteristic
20C13×#520—21no—
21C4×C13×#41C2211yescharacteristic
22C2×#88077—21no—
23C4×C4⋊Dic13C2211yescharacteristic
24#11718586C2211yescharacteristic
25#11718585C2211yescharacteristic
26C2×C4⋊#1055C2211yescharacteristic
27#11718139—21no—
28#11718139—22no—
29#11718136—21no—
30#11718129—22no—
31Q8⋊#1055—21no—
32D4⋊#1055—21no—
33#11718124—21no—
34#11718121—22no—
35C2×C13×#41—22no—
36C2×C13×#41—21no—
37C2×C13×#41D411yescharacteristic
38C22×Q8×C13—21no—
39C13×C4⋊Q8—21no—
40C13×C4⋊Q8—21no—
41C13×C4⋊Q8C2×C412yes—
42C13×C4⋊Q8D412yes—
43C13×C4⋊Q8D411yescharacteristic
44C13×#127D411yescharacteristic
45C13×#126—24no—
46C13×#125—22no—
47C13×#124—24no—
48C13×#124—22no—
49C13×#124—21no—
50C13×#123—24no—
51C13×C22⋊Q8—22no—
52C13×C22⋊Q8—24no—
53C13×C22⋊Q8—22no—
54C13×C22⋊Q8—22no—
55C13×#121—22no—
56C13×#121—22no—
57C13×#121—24no—
58C13×#121—22no—
59C13×#121—21no—
60C13×#121D412yes—
61C4×Q8×C13—22no—
62C4×Q8×C13—22no—
63C4×Q8×C13C2×C411yescharacteristic
64C4×Q8×C13D411yescharacteristic
65C4×D4×C13—22no—
66C4×D4×C13—24no—
67C4×D4×C13—22no—
68C4×D4×C13—21no—
69C4×D4×C13—21no—
70C4×D4×C13—21no—
71C4×D4×C13C2×C411yescharacteristic
72C4×D4×C13C2×C412yes—
73C4×D4×C13D411yescharacteristic
74C13×#117—22no—
75C13×#117—22no—
76C13×#117—21no—
77C13×#117D411yescharacteristic
78C2×C13×C4⋊C4—21no—
79C2×C13×C4⋊C4—22no—
80C2×C13×C4⋊C4D412yes—
81C2×C42×C13—21no—
82C2×C42×C13C2311yescharacteristic
83C2×C4⋊Dic13—21no—
84C2×C4×Dic13—21no—
85C2×#6099—21no—
86C22×#1055—21no—
87#88077—42no—
88#88071—21no—
89C22⋊#1055—21no—
90C4⋊#1055—21no—
91C4⋊#1055—21no—
92C4⋊#1055—21no—
93C4⋊#1055—21no—
94C4⋊#1055—21no—
95C4×#1055—21no—
96#8422—131nomaximal, Sylow
97C13×#41—21no—
98C13×#41—21no—
99C13×#41—21no—
100C13×#41—21no—
101C13×#41—41no—
102C13×#41—41no—
103C13×#41—41no—
104C13×#41—41no—
105C13×#41—84no—
106C2×Q8×C13—22no—
107C2×Q8×C13—21no—
108C2×Q8×C13—22no—
109C2×Q8×C13—82no—
110C2×Q8×C13C22⋊C411yescharacteristic
111C2×D4×C13—21no—
112C2×D4×C13—22no—
113C2×D4×C13—24no—
114C2×D4×C13—21no—
115C2×D4×C13—21no—
116C2×D4×C13C22⋊C411yescharacteristic
117C2×D4×C13C22⋊C412yes—
118C22×C4×C13—24no—
119C22×C4×C13—22no—
120C22×C4×C13—21no—
121C22×C4×C13—22no—
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13C2×D411yescharacteristic
125C22×C4×C13C2×D411yescharacteristic
126C22×C4×C13C2×D411yescharacteristic
127C22×Dic13—41no—
128C13×C4⋊C4—24no—
129C13×C4⋊C4—24no—
130C13×C4⋊C4—22no—
131C13×C4⋊C4—21no—
132C13×C4⋊C4—22no—
133C13×C4⋊C4—22no—
134C13×C4⋊C4—21no—
135C13×C4⋊C4—21no—
136C13×C4⋊C4C22⋊C411yescharacteristic
137C13×C4⋊C4C22⋊C414yes—
138C13×C4⋊C4C22⋊C411yescharacteristic
139C13×C4⋊C4C22⋊C412yes—
140C13×C22⋊C4—24no—
141C13×C22⋊C4—24no—
142C13×C22⋊C4—24no—
143C13×C22⋊C4—21no—
144C13×C22⋊C4—21no—
145C13×C22⋊C4—22no—
146C13×C22⋊C4—21no—
147C13×C22⋊C4—22no—
148C42×C13—24no—
149C42×C13—21no—
150C42×C13—21no—
151C42×C13—21no—
152C42×C13C22×C411yescharacteristic
153C42×C13C2×D411yescharacteristic
154C42×C13C2×D411yescharacteristic
155C42×C13C2×D411yescharacteristic
156C4⋊Dic13—22no—
157C4⋊Dic13—41no—
158C4×Dic13—41no—
159C4×Dic13—41no—
160#6099—41no—
161#6099—41no—
162C2×#1055—42no—
163C2×#1055—41no—
164C2×#1055—41no—
165C2×#1055—41no—
166#3511D1311yescharacteristic
167#1987—131no—
168#1806—131no—
169#1549—131no—
170#1547—131no—
171#1502—131no—
172#1477—131no—
173C23×C13—21no—
174C23×C13—22no—
175C23×C13#12011yescharacteristic
176Q8×C13—21no—
177Q8×C13—21no—
178Q8×C13—44no—
179Q8×C13—41no—
180Q8×C13—41no—
181Q8×C13—82no—
182D4×C13—21no—
183D4×C13—21no—
184D4×C13—42no—
185D4×C13—41no—
186D4×C13—42no—
187D4×C13—41no—
188D4×C13—42no—
189D4×C13—41no—
190D4×C13—41no—
191D4×C13—41no—
192D4×C13—41no—
193D4×C13—84no—
194C2×C4×C13—21no—
195C2×C4×C13—21no—
196C2×C4×C13—21no—
197C2×C4×C13—21no—
198C2×C4×C13—22no—
199C2×C4×C13—21no—
200C2×C4×C13—24no—
201C2×C4×C13—41no—
202C2×C4×C13—42no—
203C2×C4×C13—42no—
204C2×C4×C13—42no—
205C2×C4×C13—41no—
206C2×C4×C13—41no—
207C2×C4×C13—41no—
208C2×C4×C13—41no—
209C2×C4×C13—82no—
210C2×C4×C13—84no—
211C2×C4×C13C2×C22⋊C411yescharacteristic
212C2×C4×C13C2×C22⋊C411yescharacteristic
213C2×C4×C13C2×C22⋊C411yescharacteristic
214C2×C4×C13#12011yescharacteristic
215C2×C4×C13#12011yescharacteristic
216C2×C4×C13#12011yescharacteristic
217C2×C4×C13#13511yescharacteristic
218C2×C4×C13#13511yescharacteristic
219C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
220C2×C4×C13#13711yescharacteristic
221C2×Dic13—42no—
222C2×Dic13—81no—
223C2×Dic13—81no—
224#1055—81no—
225#1055—81no—
226#1055—81no—
227#556Dic1312yescomplemented
228#555—21no—
229#554—21no—
230#553—22no—
231#548—22no—
232#547Dic1312yescomplemented
233#542—22no—
234#537—21no—
235#533—21no—
236#532—21no—
237#532C2×D1311yescharacteristic
238C2×C4⋊Q8C2×D1311yescharacteristic
239#520—21no—
240C4×#41C2×D1311yescharacteristic
241#431—131no—
242#423—131no—
243C2×C4⋊C8—131no—
244C2×#104—261no—
245C4×C4⋊C4—131no—
246#340—262no—
247#339—261no—
248#332—261no—
249#332—262no—
250#331—261no—
251#327—262no—
252Q8⋊C8—261no—
253D4⋊C8—261no—
254C22×C13—21no—
255C22×C13—21no—
256C22×C13—41no—
257C22×C13—42no—
258C22×C13—41no—
259C22×C13—42no—
260C22×C13—41no—
261C22×C13—42no—
262C22×C13#37911yescharacteristic
263C22×C13#44911yescharacteristic
264C22×C13#45211yescharacteristic
265C4×C13—21no—
266C4×C13—21no—
267C4×C13—21no—
268C4×C13—41no—
269C4×C13—41no—
270C4×C13—44no—
271C4×C13—41no—
272C4×C13—42no—
273C4×C13#41611yescharacteristic
274C4×C13#41711yescharacteristic
275C4×C13#44911yescharacteristic
276C4×C13#45211yescharacteristic
277C4×C13#45411yescharacteristic
278C4×C13#45611yescharacteristic
279Dic13—82no—
280C2×#41—22no—
281C2×#41—21no—
282C2×#41C22⋊D1311yescharacteristic
283C22×Q8—21no—
284C2×M16—261no—
285C22×C8—261no—
286C4⋊Q8—21no—
287C4⋊Q8—21no—
288C4⋊Q8C2×Dic1312yes—
289C4⋊Q8C22⋊D1312yes—
290C4⋊Q8C22⋊D1311yescharacteristic
291#127C22⋊D1311yescharacteristic
292#126—24no—
293#125—22no—
294#124—24no—
295#124—22no—
296#124—21no—
297#123—24no—
298C22⋊Q8—22no—
299C22⋊Q8—24no—
300C22⋊Q8—22no—
301C22⋊Q8—22no—
302#121—22no—
303#121—22no—
304#121—24no—
305#121—22no—
306#121—21no—
307#121C22⋊D1312yes—
308C4×Q8—22no—
309C4×Q8—22no—
310C4×Q8C2×Dic1311yescharacteristic
311C4×Q8C22⋊D1311yescharacteristic
312C4×D4—22no—
313C4×D4—24no—
314C4×D4—22no—
315C4×D4—21no—
316C4×D4—21no—
317C4×D4—21no—
318C4×D4C2×Dic1311yescharacteristic
319C4×D4C2×Dic1312yes—
320C4×D4C22⋊D1311yescharacteristic
321#117—22no—
322#117—22no—
323#117—21no—
324#117C22⋊D1311yescharacteristic
325C2×C4⋊C4—21no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—261no—
328C2×C4⋊C4C22⋊D1312yes—
329C2×C42—21no—
330C2×C42—261no—
331C2×C42C22×D1311yescharacteristic
332C4⋊C8—261no—
333C4⋊C8—261no—
334C4⋊C8—261no—
335C4⋊C8—261no—
336C4⋊C8—261no—
337#104—522no—
338C22⋊C8—261no—
339C4×C8—261no—
340#95—261no—
341C2×C13—21no—
342C2×C13—21no—
343C2×C13—81no—
344C2×C13—82no—
345C2×C13#178811yescharacteristic
346C2×C13#179311yescharacteristic
347C2×C13#179511yescharacteristic
348#41—21no—
349#41—21no—
350#41—21no—
351#41—21no—
352#41—41no—
353#41—41no—
354#41—41no—
355#41—41no—
356#41—84no—
357C2×Q8—22no—
358C2×Q8—21no—
359C2×Q8—22no—
360C2×Q8—82no—
361C2×Q8C22⋊Dic1311yescharacteristic
362C2×D4—21no—
363C2×D4—22no—
364C2×D4—24no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4C22⋊Dic1311yescharacteristic
368C2×D4C22⋊Dic1312yes—
369C22×C4—24no—
370C22×C4—22no—
371C22×C4—21no—
372C22×C4—22no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—521no—
376C22×C4C2×C22⋊D1311yescharacteristic
377C22×C4C2×C22⋊D1311yescharacteristic
378C22×C4C2×C22⋊D1311yescharacteristic
379M16—521no—
380M16—521no—
381C2×C8—522no—
382C2×C8—521no—
383C2×C8—521no—
384C2×C8—521no—
385C4⋊C4—24no—
386C4⋊C4—24no—
387C4⋊C4—22no—
388C4⋊C4—21no—
389C4⋊C4—22no—
390C4⋊C4—22no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—262no—
394C4⋊C4—521no—
395C4⋊C4C22⋊Dic1311yescharacteristic
396C4⋊C4C22⋊Dic1314yes—
397C4⋊C4C22⋊Dic1311yescharacteristic
398C4⋊C4C22⋊Dic1312yes—
399C22⋊C4—24no—
400C22⋊C4—24no—
401C22⋊C4—24no—
402C22⋊C4—21no—
403C22⋊C4—21no—
404C22⋊C4—22no—
405C22⋊C4—21no—
406C22⋊C4—22no—
407C42—24no—
408C42—21no—
409C42—21no—
410C42—21no—
411C42—521no—
412C42—521no—
413C42C22×Dic1311yescharacteristic
414C42C2×C22⋊D1311yescharacteristic
415C42C2×C22⋊D1311yescharacteristic
416C42C2×C22⋊D1311yescharacteristic
417C13#842211yescharacteristic, complemented, Sylow
418C23—21no—
419C23—22no—
420C23#8820711yescharacteristic
421Q8—21no—
422Q8—21no—
423Q8—44no—
424Q8—41no—
425Q8—41no—
426Q8—82no—
427D4—21no—
428D4—21no—
429D4—42no—
430D4—41no—
431D4—42no—
432D4—41no—
433D4—42no—
434D4—41no—
435D4—41no—
436D4—41no—
437D4—41no—
438D4—84no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—22no—
444C2×C4—21no—
445C2×C4—24no—
446C2×C4—41no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—82no—
455C2×C4—84no—
456C2×C4—522no—
457C2×C4—1041no—
458C2×C4—1041no—
459C2×C4#8820311yescharacteristic
460C2×C4#8820411yescharacteristic
461C2×C4#8820411yescharacteristic
462C2×C4#8820511yescharacteristic
463C2×C4C2×C22⋊Dic1311yescharacteristic
464C2×C4C2×C22⋊Dic1311yescharacteristic
465C2×C4C2×C22⋊Dic1311yescharacteristic
466C2×C4#8820711yescharacteristic
467C2×C4#8820711yescharacteristic
468C2×C4#8820711yescharacteristic
469C8—1041no—
470C8—1041no—
471C8—1041no—
472C22—21no—
473C22—21no—
474C22—41no—
475C22—42no—
476C22—41no—
477C22—42no—
478C22—41no—
479C22—42no—
480C22#1171889911yescharacteristic
481C22#1171890011yescharacteristic
482C22#1171890811yescharacteristic
483C4—21no—
484C4—21no—
485C4—21no—
486C4—41no—
487C4—42no—
488C4—41no—
489C4—41no—
490C4—44no—
491C4—1042no—
492C4#1171889311yescharacteristic
493C4#1171889411yescharacteristic
494C4#1171889911yescharacteristic
495C4#1171890011yescharacteristic
496C4#1171890611yescharacteristic
497C4#1171890711yescharacteristic
498C2—21no—
499C2—21no—
500C2—81no—
501C2—82no—
502C2#1311477611yescharacteristic
503C2#1311479511yescharacteristic
504C2#1311480611yescharacteristic
subgroupG/H
centerC22#11718908
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
Fitting, prime radicalC13×#3511C2
socleC22×C13#379
cosocleC2×C42×C13C23
hypercenter#3511D13
hypocenterC13#8422
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3511

Complements

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

NH ≅ G/Ntype
1. #13115785C2semidirect
2. #13114856C2semidirect
3. #13113521C2semidirect
4. #13113513C2semidirect
5. #13113331C2semidirect
6. #13113223C2semidirect
8. C13×#556C4semidirect
13. C13×#547C4semidirect
227. #556Dic13semidirect
232. #547Dic13semidirect
417. C13#8422semidirect

Maximal subgroups

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

subgroupindex
#131157852
#131148562
#131135212
#131135132
#131133312
#131132232
C13×#35112
#842213