Finite Group Databasebeta

← #15918738

Subgroups — #15918738

Order 3328.

990 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718726C211yesmaximal, characteristic, complemented
2C2×#11718740C211yesmaximal, characteristic, complemented
3#13120657C211yesmaximal, characteristic
4#13116171C212yesmaximal, complemented
5#13116166C212yesmaximal, complemented
6#13115810C211yesmaximal, characteristic, complemented
7#13115802C211yesmaximal, characteristic, complemented
8#13115035C212yesmaximal
9#13115029C212yesmaximal
10#13114602C211yesmaximal, characteristic
11C2×C13×#544C211yesmaximal, characteristic
12C13×#544—24no—
13C13×#544—24no—
14C2×C13×C4⋊Q8—21no—
15C2×C13×C4⋊Q8C2211yescharacteristic
16C2×C13×C4⋊Q8C2211yescharacteristic
17C2×C13×#125—21no—
18C2×C13×#125C2211yescharacteristic
19C2×C13×#125C2211yescharacteristic
20C2×C13×C22⋊Q8—21no—
21C2×C13×C22⋊Q8—21no—
22C2×C13×#117C2211yescharacteristic
23C2×C13×#117C2211yescharacteristic
24C22×C13×C4⋊C4C2211yescharacteristic
25C2×#88123C2211yescharacteristic
26#11718873C2212yes—
27C2×C22⋊#1055C2212yes—
28#11718740—24no—
29#11718726—24no—
30#11718647—21no—
31#11718640—21no—
32C2×#88048C2212yes—
33C2×#88048C2212yes—
34C2×#88048C2212yes—
35C2×#88047C2212yes—
36#11718610—21no—
37#11718608—21no—
38#11718597C2211yescharacteristic
39#11718589C2212yes—
40C2×#88043C2211yescharacteristic
41C2×C4×#1055C2211yescharacteristic
42#11718121C2212yes—
43#11718121C2212yes—
44#11718121C2212yes—
45#11718121C2212yes—
46#11718116C2212yes—
47C22×Q8×C13—21no—
48C22×Q8×C13—21no—
49C23×C4×C13—21no—
50C23×C4×C13C2311yescharacteristic
51C22×Dic26—21no—
52C13×C4⋊Q8—28no—
53C13×C4⋊Q8—22no—
54C13×C4⋊Q8—22no—
55C13×C4⋊Q8—22no—
56C13×C4⋊Q8D414yes—
57C13×#125—28no—
58C13×#125—22no—
59C13×#125—22no—
60C13×#125—22no—
61C13×#125D414yes—
62C13×C22⋊Q8—28no—
63C13×C22⋊Q8—28no—
64C13×#117—22no—
65C13×#117—22no—
66C13×#117—22no—
67C13×#117—22no—
68C2×C13×C4⋊C4—21no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—22no—
76C2×C13×C4⋊C4—22no—
77C2×C13×C4⋊C4D411yescharacteristic
78C2×C13×C4⋊C4D411yescharacteristic
79C2×C13×C4⋊C4C2311yescharacteristic
80C2×C13×C4⋊C4C2311yescharacteristic
81C2×C13×C4⋊C4C2311yescharacteristic
82C2×C13×C4⋊C4C2311yescharacteristic
83C2×C13×C22⋊C4—21no—
84C2×C13×C22⋊C4D411yescharacteristic
85C2×C13×C22⋊C4D411yescharacteristic
86C2×C42×C13—21no—
87C2×C42×C13C2311yescharacteristic
88C2×C42×C13C2311yescharacteristic
89C2×C22⋊Dic13—22no—
90C2×C4⋊Dic13—21no—
91C2×C4⋊Dic13C2312yes—
92C2×C4⋊Dic13C2312yes—
93C2×#6101—22no—
94C22×#1055C2312yes—
95C22×#1055C2312yes—
96#88123—22no—
97#88123—22no—
98#88071—22no—
99#88071—21no—
100#88071—21no—
101#88071—22no—
102C22⋊#1055Q818yescomplemented
103#88048—24no—
104#88048—24no—
105#88048—24no—
106#88047—24no—
107#88043—22no—
108C4×#1055—22no—
109#25820—131nomaximal, Sylow
110C24×C13C2×D411yescharacteristic
111C2×Q8×C13—24no—
112C2×Q8×C13—24no—
113C2×Q8×C13—82no—
114C2×Q8×C13—82no—
115C22×C4×C13—21no—
116C22×C4×C13—21no—
117C22×C4×C13—22no—
118C22×C4×C13—21no—
119C22×C4×C13—21no—
120C22×C4×C13—21no—
121C22×C4×C13—21no—
122C22×C4×C13—24no—
123C22×C4×C13—82no—
124C22×C4×C13C2×D411yescharacteristic
125C22×C4×C13C2×D411yescharacteristic
126C22×C4×C13C2×D411yescharacteristic
127C22×C4×C13C2×D411yescharacteristic
128C22×C4×C13C2×D411yescharacteristic
129C22×C4×C13C2×Q814yes—
130C22×C4×C13C2411yescharacteristic
131C22×Dic13—22no—
132C22×Dic13—22no—
133C2×Dic26—42no—
134C2×Dic26—82no—
135C13×C4⋊C4—24no—
136C13×C4⋊C4—24no—
137C13×C4⋊C4—24no—
138C13×C4⋊C4—24no—
139C13×C4⋊C4—24no—
140C13×C4⋊C4—24no—
141C13×C4⋊C4—24no—
142C13×C4⋊C4—22no—
143C13×C4⋊C4—22no—
144C13×C4⋊C4—21no—
145C13×C4⋊C4—21no—
146C13×C4⋊C4—21no—
147C13×C4⋊C4—21no—
148C13×C4⋊C4C2×D412yes—
149C13×C4⋊C4C2×D412yes—
150C13×C4⋊C4C2×D412yes—
151C13×C4⋊C4C2×D412yes—
152C13×C22⋊C4—24no—
153C13×C22⋊C4—22no—
154C13×C22⋊C4—22no—
155C42×C13—24no—
156C42×C13—21no—
157C42×C13—21no—
158C42×C13C2×D412yes—
159C42×C13C2×D412yes—
160C22⋊Dic13—82no—
161C4⋊Dic13—22no—
162C4⋊Dic13—22no—
163C4⋊Dic13—24no—
164C4⋊Dic13—42no—
165#6101—82no—
166C2×#1055—22no—
167C2×#1055—22no—
168C2×#1055—22no—
169C2×#1055—22no—
170C2×#1055C2×Q814yes—
171C2×#1055C2×Q814yes—
172C2×#544D1311yescharacteristic
173C2×#501—131no—
174C2×#498—131no—
175#2628—131no—
176#2059—132no—
177#2058—132no—
178#1993—131no—
179#1991—131no—
180#1854—132no—
181#1853—132no—
182#1750—131no—
183C23×C13—21no—
184C23×C13—21no—
185C23×C13—22no—
186C23×C13—22no—
187C23×C13C4⋊Q812yes—
188C23×C13C22×D411yescharacteristic
189Q8×C13—84no—
190Q8×C13—84no—
191C2×C4×C13—21no—
192C2×C4×C13—21no—
193C2×C4×C13—22no—
194C2×C4×C13—22no—
195C2×C4×C13—24no—
196C2×C4×C13—24no—
197C2×C4×C13—21no—
198C2×C4×C13—22no—
199C2×C4×C13—21no—
200C2×C4×C13—22no—
201C2×C4×C13—22no—
202C2×C4×C13—22no—
203C2×C4×C13—22no—
204C2×C4×C13—22no—
205C2×C4×C13—42no—
206C2×C4×C13—42no—
207C2×C4×C13—42no—
208C2×C4×C13—42no—
209C2×C4×C13—84no—
210C2×C4×C13#12012yes—
211C2×C4×C13#12012yes—
212C2×C4×C13C4⋊Q812yes—
213C2×C4×C13C22×D411yescharacteristic
214C2×C4×C13C22×D411yescharacteristic
215C2×C4×C13C22×Q812yes—
216C2×C4×C132−1+412yes—
217C2×Dic13—42no—
218C2×Dic13—42no—
219C2×Dic13—42no—
220C2×Dic13—42no—
221C2×Dic13—42no—
222C2×Dic13—42no—
223Dic26—84no—
224#1055—24no—
225#1055—24no—
226#544—24no—
227#544—24no—
228C2×C4⋊Q8—21no—
229C2×C4⋊Q8—131no—
230C2×C4⋊Q8C2×D1311yescharacteristic
231C2×C4⋊Q8C2×D1311yescharacteristic
232C2×#125—21no—
233C2×#125C2×D1311yescharacteristic
234C2×#125C2×D1311yescharacteristic
235C2×C22⋊Q8—21no—
236C2×C22⋊Q8—21no—
237C2×#117C2×D1311yescharacteristic
238C2×#117C2×D1311yescharacteristic
239C22×C4⋊C4C2×D1311yescharacteristic
240#501—264no—
241#498—264no—
242C2×#107—132no—
243C2×#106—132no—
244C2×#106—132no—
245C2×#106—132no—
246C2×C22⋊C8—132no—
247C2×#97—131no—
248C2×C4×C8—131no—
249#400—261no—
250#399—261no—
251#395—261no—
252#393—261no—
253#389—132no—
254#382—131no—
255#380—132no—
256#340—132no—
257#340—132no—
258#340—132no—
259#340—132no—
260#336—132no—
261C22×C13—24no—
262C22×C13—22no—
263C22×C13—42no—
264C22×C13—41no—
265C22×C13—41no—
266C22×C13C2×#12011yescharacteristic
267C22×C13C2×C4⋊Q811yescharacteristic
268C22×C13#53611yescharacteristic
269C22×C13#57712yes—
270C22×C13#57712yes—
271C4×C13—22no—
272C4×C13—22no—
273C4×C13—22no—
274C4×C13—41no—
275C4×C13—42no—
276C4×C13—42no—
277C4×C13—42no—
278C4×C13—41no—
279C4×C13—42no—
280C4×C13D4×Q812yes—
281C4×C13D4×Q812yes—
282Dic13—82no—
283Dic13—82no—
284C22×Q8—21no—
285C22×Q8—21no—
286C22×Q8—261no—
287C23×C4—21no—
288C23×C4C22×D1311yescharacteristic
289C22×C8—132no—
290C22×C8—132no—
291C4⋊Q8—28no—
292C4⋊Q8—22no—
293C4⋊Q8—22no—
294C4⋊Q8—22no—
295C4⋊Q8—262no—
296C4⋊Q8—262no—
297C4⋊Q8C22⋊D1314yes—
298#125—28no—
299#125—22no—
300#125—22no—
301#125—22no—
302#125C22⋊D1314yes—
303C22⋊Q8—28no—
304C22⋊Q8—28no—
305#117—22no—
306#117—22no—
307#117—22no—
308#117—22no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—132no—
319C2×C4⋊C4—132no—
320C2×C4⋊C4—261no—
321C2×C4⋊C4—262no—
322C2×C4⋊C4C22⋊D1311yescharacteristic
323C2×C4⋊C4C22⋊D1311yescharacteristic
324C2×C4⋊C4C22×D1311yescharacteristic
325C2×C4⋊C4C22×D1311yescharacteristic
326C2×C4⋊C4C22×D1311yescharacteristic
327C2×C4⋊C4C22×D1311yescharacteristic
328C2×C22⋊C4—21no—
329C2×C22⋊C4—262no—
330C2×C22⋊C4C22⋊D1311yescharacteristic
331C2×C22⋊C4C22⋊D1311yescharacteristic
332C2×C42—21no—
333C2×C42C22×D1311yescharacteristic
334C2×C42C22×D1311yescharacteristic
335#107—264no—
336#106—264no—
337#106—264no—
338#106—264no—
339C22⋊C8—138no—
340#97—262no—
341C4×C8—262no—
342#95—262no—
343#95—261no—
344#95—261no—
345#95—262no—
346C2×C13—42no—
347C2×C13#243411yescharacteristic
348C2×C13#300911yescharacteristic
349C2×C13#301011yescharacteristic
350C2×C13#316312yes—
351C2×C13#324412yes—
352C24C2×C22⋊D1311yescharacteristic
353C2×Q8—24no—
354C2×Q8—24no—
355C2×Q8—82no—
356C2×Q8—82no—
357C2×Q8—522no—
358C2×Q8—1042no—
359C22×C4—22no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—24no—
367C22×C4—82no—
368C22×C4—262no—
369C22×C4—262no—
370C22×C4Q8×D1314yes—
371C22×C4C2×C22⋊D1311yescharacteristic
372C22×C4C2×C22⋊D1311yescharacteristic
373C22×C4C2×C22⋊D1311yescharacteristic
374C22×C4C2×C22⋊D1311yescharacteristic
375C22×C4C2×C22⋊D1311yescharacteristic
376C22×C4C23×D1311yescharacteristic
377C2×C8—134no—
378C2×C8—134no—
379C2×C8—262no—
380C2×C8—262no—
381C2×C8—262no—
382C2×C8—262no—
383C4⋊C4—24no—
384C4⋊C4—24no—
385C4⋊C4—24no—
386C4⋊C4—24no—
387C4⋊C4—24no—
388C4⋊C4—24no—
389C4⋊C4—24no—
390C4⋊C4—22no—
391C4⋊C4—22no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—264no—
397C4⋊C4—262no—
398C4⋊C4—262no—
399C4⋊C4—522no—
400C4⋊C4—1042no—
401C4⋊C4C2×C22⋊D1312yes—
402C4⋊C4C2×C22⋊D1312yes—
403C4⋊C4C2×C22⋊D1312yes—
404C4⋊C4C2×C22⋊D1312yes—
405C22⋊C4—24no—
406C22⋊C4—22no—
407C22⋊C4—22no—
408C22⋊C4—1042no—
409C42—24no—
410C42—21no—
411C42—21no—
412C42C2×C22⋊D1312yes—
413C42C2×C22⋊D1312yes—
414C13#2582011yescharacteristic, complemented, Sylow
415C23—21no—
416C23—22no—
417C23—22no—
418C23—21no—
419C23#8819812yes—
420C23C22×C22⋊D1311yescharacteristic
421Q8—84no—
422Q8—84no—
423Q8—1044no—
424C2×C4—21no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—21no—
428C2×C4—24no—
429C2×C4—24no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—21no—
433C2×C4—22no—
434C2×C4—21no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—84no—
443C2×C4—522no—
444C2×C4—522no—
445C2×C4—522no—
446C2×C4—522no—
447C2×C4—522no—
448C2×C4—522no—
449C2×C4#8819812yes—
450C2×C4#8820712yes—
451C2×C4#8820712yes—
452C2×C4C2×Q8×D1312yes—
453C2×C4#8825412yes—
454C2×C4C22×C22⋊D1311yescharacteristic
455C2×C4C22×C22⋊D1311yescharacteristic
456C8—264no—
457C8—264no—
458C22—22no—
459C22—24no—
460C22—41no—
461C22—41no—
462C22—42no—
463C22C2×#8819811yescharacteristic
464C22#1171952111yescharacteristic
465C22#1171954112yes—
466C22#1171954212yes—
467C22C2×#8820711yescharacteristic
468C4—22no—
469C4—22no—
470C4—22no—
471C4—41no—
472C4—42no—
473C4—42no—
474C4—42no—
475C4—41no—
476C4—42no—
477C4—1042no—
478C4—1042no—
479C4Q8×C22⋊D1312yes—
480C4Q8×C22⋊D1312yes—
481C2—42no—
482C2#1311847611yescharacteristic
483C2#1312411311yescharacteristic
484C2#1312412211yescharacteristic
485C2#1312536212yes—
486C2#1312613412yes—
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#544C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenterC2×#544D13
hypocenterC13#25820
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
1. C2×#11718726C2semidirect
2. C2×#11718740C2semidirect
4. #13116171C2semidirect
5. #13116166C2semidirect
6. #13115810C2semidirect
7. #13115802C2semidirect
102. C22⋊#1055Q8semidirect
414. C13#25820semidirect

Maximal subgroups

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

subgroupindex
C2×#117187262
C2×#117187402
#131206572
#131161712
#131161662
#131158102
#131158022
#131150352
#131150292
#131146022
C2×C13×#5442
#2582013