Finite Group Databasebeta

← #15918830

Subgroups — #15918830

Order 3328.

1054 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125383C211yesmaximal, characteristic, complemented
2#13124651C211yesmaximal, characteristic
3#13123232C211yesmaximal, characteristic, complemented
4#13116178C214yesmaximal, complemented
5#13115826C211yesmaximal, characteristic, complemented
6#13115814C211yesmaximal, characteristic, complemented
7#13115062C214yesmaximal
8C4×#88077C211yesmaximal, characteristic
9C13×#3503C211yesmaximal, characteristic
10Q82×C13—21no—
11C13×#557—21no—
12C13×#554—21no—
13C13×#554—22no—
14D4×Q8×C13—22no—
15D4×Q8×C13—21no—
16C13×#544—22no—
17C13×#544C2212yes—
18C13×#533—21no—
19C13×#533C2211yescharacteristic
20C2×C13×C4⋊Q8—21no—
21C2×C13×C4⋊Q8C2211yescharacteristic
22C13×#520C2212yes—
23C4×C13×#41C2211yescharacteristic
24C2×#88198—22no—
25C2×#88123C2211yescharacteristic
26C2×#88077C2212yes—
27#11718893C2212yes—
28#11718740—21no—
29#11718739—21no—
30#11718726—22no—
31#11718682—21no—
32#11718681—21no—
33#11718669—21no—
34#11718668—21no—
35#11718656C2214yes—
36#11718656C2212yes—
37#11718637—22no—
38#11718637C2214yes—
39C42×Dic13C2211yescharacteristic
40#11718585C2211yescharacteristic
41C4×#6099C2211yescharacteristic
42#11718124C2212yes—
43#11718124C2214yes—
44#11718122C2214yes—
45C2×C13×#41C2311yescharacteristic
46C22×Q8×C13—22no—
47C22×Q8×C13D412yes—
48C22×Dic26—21no—
49C13×C4⋊Q8—22no—
50C13×C4⋊Q8—22no—
51C13×C4⋊Q8—24no—
52C13×C4⋊Q8—22no—
53C13×C4⋊Q8—22no—
54C13×C4⋊Q8—21no—
55C13×C4⋊Q8—21no—
56C13×C4⋊Q8—21no—
57C13×C4⋊Q8—21no—
58C13×C4⋊Q8D411yescharacteristic
59C13×C4⋊Q8D411yescharacteristic
60C13×#125—24no—
61C13×#125—22no—
62C13×#125—22no—
63C13×#125D412yes—
64C13×C22⋊Q8—22no—
65C13×C22⋊Q8—22no—
66C13×C22⋊Q8—24no—
67C13×C22⋊Q8—24no—
68C13×C22⋊Q8—21no—
69C13×C22⋊Q8—21no—
70C13×C22⋊Q8—24no—
71C4×Q8×C13—22no—
72C4×Q8×C13—22no—
73C4×Q8×C13—22no—
74C4×Q8×C13—21no—
75C4×Q8×C13—21no—
76C4×Q8×C13D411yescharacteristic
77C4×Q8×C13D411yescharacteristic
78C4×D4×C13—22no—
79C4×D4×C13—21no—
80C4×D4×C13—21no—
81C4×D4×C13—24no—
82C4×D4×C13D411yescharacteristic
83C4×D4×C13D411yescharacteristic
84C13×#117—22no—
85C13×#117—21no—
86C13×#117C2311yescharacteristic
87C13×#117C2312yes—
88C2×C13×C4⋊C4—22no—
89C2×C13×C4⋊C4—22no—
90C2×C13×C4⋊C4D412yes—
91C2×C13×C4⋊C4C2312yes—
92C2×C42×C13—21no—
93C2×C42×C13C2311yescharacteristic
94#88198—48no—
95C2×C4⋊Dic13—21no—
96C2×C4⋊Dic13C2312yes—
97C2×#6101—28no—
98C2×C4×Dic13—21no—
99C2×C4×Dic13—21no—
100C2×C4×Dic13C2312yes—
101C2×#6099C2312yes—
102C2×#6099C2312yes—
103#88123—21no—
104#88123—21no—
105#88123—21no—
106#88123—21no—
107#88077Q818yescomplemented
108#88075—22no—
109#88072—22no—
110#88048—22no—
111#88048—24no—
112#88047—22no—
113#88047—24no—
114C4⋊#1055—21no—
115C4⋊#1055—21no—
116#88043—21no—
117C4×#1055—21no—
118#25830—131nomaximal, Sylow
119C13×#41—22no—
120C13×#41C2×Q814yes—
121C2×Q8×C13—24no—
122C2×Q8×C13—21no—
123C2×Q8×C13—22no—
124C2×Q8×C13—21no—
125C2×Q8×C13—22no—
126C2×Q8×C13—44no—
127C2×Q8×C13—84no—
128C2×Q8×C13C2×D411yescharacteristic
129C2×D4×C13—21no—
130C2×D4×C13C2×D411yescharacteristic
131C22×C4×C13—21no—
132C22×C4×C13—24no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13C2×D411yescharacteristic
137C22×C4×C13C2×D414yes—
138C22×C4×C13C2411yescharacteristic
139C22×Dic13—22no—
140C22×Dic13—22no—
141C2×Dic26—44no—
142C2×Dic26—41no—
143C2×Dic26—41no—
144C13×C4⋊C4—24no—
145C13×C4⋊C4—24no—
146C13×C4⋊C4—24no—
147C13×C4⋊C4—24no—
148C13×C4⋊C4—21no—
149C13×C4⋊C4—22no—
150C13×C4⋊C4—22no—
151C13×C4⋊C4—21no—
152C13×C4⋊C4—21no—
153C13×C4⋊C4—21no—
154C13×C4⋊C4—22no—
155C13×C4⋊C4—22no—
156C13×C4⋊C4—22no—
157C13×C4⋊C4—22no—
158C13×C4⋊C4C2×D412yes—
159C13×C4⋊C4C2×D412yes—
160C13×C4⋊C4C2×D411yescharacteristic
161C13×C4⋊C4C2×D411yescharacteristic
162C13×C22⋊C4—24no—
163C13×C22⋊C4—22no—
164C13×C22⋊C4—21no—
165C13×C22⋊C4—21no—
166C13×C22⋊C4—21no—
167C42×C13—24no—
168C42×C13—21no—
169C42×C13—21no—
170C42×C13—21no—
171C42×C13—22no—
172C42×C13C2×D411yescharacteristic
173C42×C13C2×D411yescharacteristic
174C42×C13C2×D411yescharacteristic
175C42×C13C2×D411yescharacteristic
176C4⋊Dic13—22no—
177C4⋊Dic13—22no—
178C4⋊Dic13—41no—
179C4⋊Dic13—41no—
180#6101—416no—
181C4×Dic13—24no—
182C4×Dic13—24no—
183C4×Dic13—22no—
184C4×Dic13C2×Q814yescomplemented
185#6099—22no—
186#6099—24no—
187#6099C2×Q814yescomplemented
188C2×#1055—22no—
189C2×#1055—22no—
190#3503D1311yescharacteristic
191#3165—131no—
192#3079—131no—
193#2868—131no—
194#2060—134no—
195#1997—131no—
196#1994—131no—
197#1859—134no—
198C4×#104—131no—
199C23×C13—21no—
200C23×C13C22×D411yescharacteristic
201Q8×C13—21no—
202Q8×C13—44no—
203Q8×C13—42no—
204Q8×C13—42no—
205Q8×C13—82no—
206Q8×C13—84no—
207Q8×C13C4⋊Q812yescomplemented
208D4×C13—24no—
209D4×C13—21no—
210D4×C13C4⋊Q812yescomplemented
211C2×C4×C13—21no—
212C2×C4×C13—24no—
213C2×C4×C13—22no—
214C2×C4×C13—22no—
215C2×C4×C13—22no—
216C2×C4×C13—21no—
217C2×C4×C13—21no—
218C2×C4×C13—24no—
219C2×C4×C13—22no—
220C2×C4×C13—42no—
221C2×C4×C13—42no—
222C2×C4×C13—44no—
223C2×C4×C13—84no—
224C2×C4×C13#12011yescharacteristic
225C2×C4×C13#12011yescharacteristic
226C2×C4×C13#12011yescharacteristic
227C2×C4×C13#12011yescharacteristic
228C2×C4×C13C22×D411yescharacteristic
229C2×C4×C13C22×D411yescharacteristic
230C2×C4×C13C22×Q812yes—
231C2×C4×C132−1+412yes—
232C2×Dic13—24no—
233C2×Dic13—24no—
234C2×Dic13—24no—
235C2×Dic13—44no—
236C2×Dic13—42no—
237Dic26—82no—
238Dic26—82no—
239#1055—24no—
240#1055—42no—
241Q82—21no—
242#557—21no—
243#554—21no—
244#554—22no—
245D4×Q8—22no—
246D4×Q8—21no—
247#544—22no—
248#544C2×D1312yes—
249#533—21no—
250#533C2×D1311yescharacteristic
251C2×C4⋊Q8—21no—
252C2×C4⋊Q8—131no—
253C2×C4⋊Q8—262no—
254C2×C4⋊Q8C2×D1311yescharacteristic
255#520C2×D1312yes—
256C4×#41C2×D1311yescharacteristic
257#501—262no—
258#500—261no—
259#498—261no—
260#477—261no—
261#476—261no—
262#475—261no—
263#474—261no—
264#428—132no—
265#428—134no—
266#423—131no—
267C2×#104—132no—
268#417—132no—
269C4×M16—131no—
270#384—134no—
271#384—262no—
272C43—131no—
273#343—134no—
274#339—132no—
275#339—134no—
276C22×C13—21no—
277C22×C13—21no—
278C22×C13—22no—
279C22×C13—41no—
280C22×C13—41no—
281C22×C13C2×#12011yescharacteristic
282C22×C13D4×Q812yes—
283C4×C13—22no—
284C4×C13—21no—
285C4×C13—21no—
286C4×C13—41no—
287C4×C13—44no—
288C4×C13—42no—
289C4×C13—41no—
290C4×C13—42no—
291C4×C13#45312yes—
292C4×C13#45612yes—
293C4×C13C2×C4⋊Q811yescharacteristic
294C4×C13#53611yescharacteristic
295C4×C13D4×Q812yes—
296Dic13—28no—
297Dic13—82no—
298C2×#41C22×D1311yescharacteristic
299C22×Q8—22no—
300C22×Q8—261no—
301C22×Q8C22⋊D1312yes—
302C2×M16—132no—
303C2×M16—132no—
304C4⋊Q8—22no—
305C4⋊Q8—22no—
306C4⋊Q8—24no—
307C4⋊Q8—22no—
308C4⋊Q8—22no—
309C4⋊Q8—21no—
310C4⋊Q8—21no—
311C4⋊Q8—21no—
312C4⋊Q8—21no—
313C4⋊Q8—261no—
314C4⋊Q8—261no—
315C4⋊Q8—261no—
316C4⋊Q8—261no—
317C4⋊Q8—528no—
318C4⋊Q8C22⋊D1311yescharacteristic
319C4⋊Q8C22⋊D1311yescharacteristic
320#125—24no—
321#125—22no—
322#125—22no—
323#125C22⋊D1312yes—
324C22⋊Q8—22no—
325C22⋊Q8—22no—
326C22⋊Q8—24no—
327C22⋊Q8—24no—
328C22⋊Q8—21no—
329C22⋊Q8—21no—
330C22⋊Q8—24no—
331C4×Q8—22no—
332C4×Q8—22no—
333C4×Q8—22no—
334C4×Q8—21no—
335C4×Q8—21no—
336C4×Q8C22⋊D1311yescharacteristic
337C4×Q8C22⋊D1311yescharacteristic
338C4×D4—22no—
339C4×D4—21no—
340C4×D4—21no—
341C4×D4—24no—
342C4×D4C22⋊D1311yescharacteristic
343C4×D4C22⋊D1311yescharacteristic
344#117—22no—
345#117—21no—
346#117C22×D1311yescharacteristic
347#117C22×D1312yes—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—132no—
351C2×C4⋊C4—261no—
352C2×C4⋊C4—268no—
353C2×C4⋊C4C22⋊D1312yes—
354C2×C4⋊C4C22×D1312yes—
355C2×C42—21no—
356C2×C42—132no—
357C2×C42—261no—
358C2×C42—261no—
359C2×C42C22×D1311yescharacteristic
360#107—262no—
361#107—264no—
362#106—262no—
363#106—264no—
364C4⋊C8—261no—
365C4⋊C8—261no—
366#104—138no—
367#103—262no—
368#102—262no—
369#97—261no—
370C4×C8—261no—
371C2×C13—22no—
372C2×C13—42no—
373C2×C13#243411yescharacteristic
374C2×C13C2×#45311yescharacteristic
375C2×C13C2×#45611yescharacteristic
376#41—22no—
377#41Q8×D1314yes—
378C2×Q8—24no—
379C2×Q8—21no—
380C2×Q8—22no—
381C2×Q8—21no—
382C2×Q8—22no—
383C2×Q8—44no—
384C2×Q8—84no—
385C2×Q8—524no—
386C2×Q8—521no—
387C2×Q8—521no—
388C2×Q8C2×C22⋊D1311yescharacteristic
389C2×D4—21no—
390C2×D4C2×C22⋊D1311yescharacteristic
391C22×C4—21no—
392C22×C4—24no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—262no—
396C22×C4—262no—
397C22×C4C2×C22⋊D1311yescharacteristic
398C22×C4C2×C22⋊D1311yescharacteristic
399C22×C4C2×C22⋊D1314yes—
400C22×C4C23×D1311yescharacteristic
401M16—134no—
402M16—262no—
403M16—264no—
404C2×C8—262no—
405C2×C8—262no—
406C4⋊C4—24no—
407C4⋊C4—24no—
408C4⋊C4—24no—
409C4⋊C4—24no—
410C4⋊C4—21no—
411C4⋊C4—22no—
412C4⋊C4—22no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—262no—
421C4⋊C4—262no—
422C4⋊C4—5216no—
423C4⋊C4—521no—
424C4⋊C4—521no—
425C4⋊C4C2×C22⋊D1312yes—
426C4⋊C4C2×C22⋊D1311yescharacteristic
427C4⋊C4C2×C22⋊D1312yes—
428C4⋊C4C2×C22⋊D1311yescharacteristic
429C22⋊C4—24no—
430C22⋊C4—22no—
431C22⋊C4—21no—
432C22⋊C4—21no—
433C22⋊C4—21no—
434C42—24no—
435C42—21no—
436C42—21no—
437C42—21no—
438C42—22no—
439C42—134no—
440C42—264no—
441C42—264no—
442C42—262no—
443C42C2×C22⋊D1311yescharacteristic
444C42C2×C22⋊D1311yescharacteristic
445C42C2×C22⋊D1311yescharacteristic
446C42C2×C22⋊D1311yescharacteristic
447C13#2583011yescharacteristic, complemented, Sylow
448C23—21no—
449C23C22×C22⋊D1311yescharacteristic
450Q8—21no—
451Q8—44no—
452Q8—42no—
453Q8—42no—
454Q8—82no—
455Q8—84no—
456Q8—1042no—
457Q8—1042no—
458Q8#8819812yescomplemented
459D4—24no—
460D4—21no—
461D4#8819812yescomplemented
462C2×C4—21no—
463C2×C4—24no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—24no—
470C2×C4—22no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—44no—
474C2×C4—84no—
475C2×C4—264no—
476C2×C4—264no—
477C2×C4—264no—
478C2×C4—524no—
479C2×C4—522no—
480C2×C4#8820711yescharacteristic
481C2×C4#8820711yescharacteristic
482C2×C4#8820711yescharacteristic
483C2×C4#8820711yescharacteristic
484C2×C4C2×Q8×D1312yes—
485C2×C4#8825412yes—
486C2×C4C22×C22⋊D1311yescharacteristic
487C2×C4C22×C22⋊D1311yescharacteristic
488C8—264no—
489C8—522no—
490C22—21no—
491C22—21no—
492C22—22no—
493C22—41no—
494C22—41no—
495C22Q8×C22⋊D1312yes—
496C22C2×#8820711yescharacteristic
497C4—22no—
498C4—21no—
499C4—21no—
500C4—41no—
501C4—44no—
502C4—42no—
503C4—41no—
504C4—42no—
505C4—268no—
506C4—1042no—
507C4#1171890212yes—
508C4#1171890712yes—
509C4C2×#8819811yescharacteristic
510C4Q8×C22⋊D1312yes—
511C4#1171952111yescharacteristic
512C2—22no—
513C2—42no—
514C2#1311847611yescharacteristic
515C2C2×#1171890211yescharacteristic
516C2C2×#1171890711yescharacteristic
subgroupG/H
centerC22C2×#88207
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#3503C2
socleC22×C13C2×#120
prime radicalC2×C13×#41C23
hypercenter#3503D13
hypocenterC13#25830
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3503

Complements

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

NH ≅ G/Ntype
1. #13125383C2semidirect
3. #13123232C2semidirect
4. #13116178C2semidirect
5. #13115826C2semidirect
6. #13115814C2semidirect
107. #88077Q8semidirect
184. C4×Dic13C2×Q8semidirect
187. #6099C2×Q8semidirect
207. Q8×C13C4⋊Q8semidirect
210. D4×C13C4⋊Q8semidirect
447. C13#25830semidirect
458. Q8#88198semidirect
461. D4#88198semidirect

Maximal subgroups

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

subgroupindex
#131253832
#131246512
#131232322
#131161782
#131158262
#131158142
#131150622
C4×#880772
C13×#35032
#2583013