Finite Group Databasebeta

← #15917344

Subgroups — #15917344

Order 3328.

968 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×#11718726C211yesmaximal, characteristic, complemented
2C2×#11718742C211yesmaximal, characteristic, complemented
3#13120657C211yesmaximal, characteristic
4#13116036C212yesmaximal
5#13116029C212yesmaximal
6#13115802C211yesmaximal, characteristic, complemented
7#13115657C211yesmaximal, characteristic, complemented
8#13115104C212yesmaximal, complemented
9#13115090C212yesmaximal, complemented
10#13114602C211yesmaximal, characteristic
11C2×C13×#541C211yesmaximal, characteristic
12C13×#541—24no—
13C13×#541—24no—
14C2×C13×C4⋊Q8C2211yescharacteristic
15C2×C13×#126—21no—
16C2×C13×#126—21no—
17C2×C13×#125—21no—
18C2×C13×#125—21no—
19C2×C13×#125C2211yescharacteristic
20C2×C13×C22⋊Q8C2211yescharacteristic
21C2×C13×C22⋊Q8C2211yescharacteristic
22C2×C4×Q8×C13C2211yescharacteristic
23C2×C4×Q8×C13C2211yescharacteristic
24C2×C13×#117C2211yescharacteristic
25C2×#88123C2211yescharacteristic
26C2×#88075C2212yes—
27C2×#88075C2212yes—
28C2×#88075C2212yes—
29C2×#88075C2212yes—
30#11718873C2212yes—
31C2×C22⋊#1055C2212yes—
32#11718742—24no—
33#11718726—24no—
34#11718647—21no—
35#11718640—21no—
36C2×#88048C2212yes—
37C2×#88047C2212yes—
38#11718610—21no—
39#11718608—21no—
40#11718597C2211yescharacteristic
41#11718589C2212yes—
42C2×#88043C2211yescharacteristic
43C2×C4×#1055C2211yescharacteristic
44#11718121C2212yes—
45#11718121C2212yes—
46#11718116C2212yes—
47C22×Q8×C13C2311yescharacteristic
48C22×Q8×C13C2311yescharacteristic
49C23×C4×C13C2311yescharacteristic
50C22×Dic26—21no—
51C13×C4⋊Q8—22no—
52C13×C4⋊Q8D414yes—
53C13×#126—28no—
54C13×#126—28no—
55C13×#125—28no—
56C13×#125—28no—
57C13×#125—22no—
58C13×#125D414yes—
59C13×C22⋊Q8—22no—
60C13×C22⋊Q8—22no—
61C13×C22⋊Q8—22no—
62C13×C22⋊Q8—22no—
63C4×Q8×C13—22no—
64C4×Q8×C13—22no—
65C4×Q8×C13—22no—
66C4×Q8×C13—22no—
67C13×#117—22no—
68C13×#117—22no—
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—21no—
76C2×C13×C4⋊C4—21no—
77C2×C13×C4⋊C4D411yescharacteristic
78C2×C13×C4⋊C4D411yescharacteristic
79C2×C13×C4⋊C4C2311yescharacteristic
80C2×C13×C4⋊C4C2311yescharacteristic
81C2×C13×C22⋊C4—21no—
82C2×C13×C22⋊C4—21no—
83C2×C13×C22⋊C4D411yescharacteristic
84C2×C13×C22⋊C4D411yescharacteristic
85C2×C42×C13—21no—
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#88075—24no—
99#88075—24no—
100#88075—24no—
101#88075—24no—
102#88071—22no—
103#88071—21no—
104#88071—21no—
105#88071—22no—
106C22⋊#1055—24no—
107#88048—24no—
108#88047—24no—
109#88043—22no—
110C4×#1055—22no—
111#25686—131nomaximal, Sylow
112C24×C13C2×D411yescharacteristic
113C2×Q8×C13—21no—
114C2×Q8×C13—21no—
115C2×Q8×C13—22no—
116C2×Q8×C13—22no—
117C2×Q8×C13—22no—
118C2×Q8×C13—22no—
119C2×Q8×C13C2×D412yes—
120C2×Q8×C13C2×D412yes—
121C22×C4×C13—21no—
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—22no—
128C22×C4×C13—22no—
129C22×C4×C13C2×D411yescharacteristic
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2×D411yescharacteristic
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2×D411yescharacteristic
134C22×C4×C13C2411yescharacteristic
135C22×Dic13—22no—
136C22×Dic13—22no—
137C2×Dic26—42no—
138C2×Dic26—82no—
139C13×C4⋊C4—24no—
140C13×C4⋊C4—24no—
141C13×C4⋊C4—24no—
142C13×C4⋊C4—24no—
143C13×C4⋊C4—24no—
144C13×C4⋊C4—24no—
145C13×C4⋊C4—24no—
146C13×C4⋊C4—24no—
147C13×C4⋊C4—22no—
148C13×C4⋊C4—22no—
149C13×C4⋊C4—21no—
150C13×C4⋊C4—21no—
151C13×C4⋊C4C2×D412yes—
152C13×C4⋊C4C2×D412yes—
153C13×C22⋊C4—24no—
154C13×C22⋊C4—24no—
155C13×C22⋊C4—22no—
156C13×C22⋊C4—22no—
157C42×C13—24no—
158C42×C13—24no—
159C42×C13—21no—
160C42×C13—21no—
161C42×C13C2×D412yes—
162C42×C13C2×D412yes—
163C22⋊Dic13—82no—
164C4⋊Dic13—22no—
165C4⋊Dic13—22no—
166C4⋊Dic13—22no—
167C4⋊Dic13—22no—
168C4⋊Dic13—42no—
169#6101—82no—
170C2×#1055—22no—
171C2×#1055—22no—
172C2×#1055—22no—
173C2×#1055—22no—
174C2×#1055—22no—
175C2×#1055#4114yes—
176C2×#541D1311yescharacteristic
177C2×#501—131no—
178C2×#487—131no—
179#2628—131no—
180#2036—132no—
181#2035—132no—
182#1991—131no—
183#1960—131no—
184#1865—132no—
185#1863—132no—
186#1750—131no—
187C23×C13—21no—
188C23×C13—21no—
189C23×C13—21no—
190C23×C13—22no—
191C23×C13—22no—
192C23×C13C22×D411yescharacteristic
193Q8×C13—24no—
194Q8×C13—24no—
195Q8×C13—42no—
196Q8×C13—42no—
197C2×C4×C13—22no—
198C2×C4×C13—22no—
199C2×C4×C13—21no—
200C2×C4×C13—21no—
201C2×C4×C13—22no—
202C2×C4×C13—22no—
203C2×C4×C13—22no—
204C2×C4×C13—22no—
205C2×C4×C13—21no—
206C2×C4×C13—21no—
207C2×C4×C13—21no—
208C2×C4×C13—22no—
209C2×C4×C13—22no—
210C2×C4×C13—41no—
211C2×C4×C13—41no—
212C2×C4×C13—41no—
213C2×C4×C13—41no—
214C2×C4×C13—42no—
215C2×C4×C13—42no—
216C2×C4×C13—42no—
217C2×C4×C13—42no—
218C2×C4×C13#12012yes—
219C2×C4×C13#12012yes—
220C2×C4×C13C22×D411yescharacteristic
221C2×C4×C13C22×D411yescharacteristic
222C2×C4×C13C2×#4112yes—
223C2×C4×C132−1+412yes—
224C2×Dic13—42no—
225C2×Dic13—42no—
226C2×Dic13—42no—
227C2×Dic13—42no—
228C2×Dic13—42no—
229C2×Dic13—42no—
230Dic26—84no—
231#1055—24no—
232#1055—42no—
233#541—24no—
234#541—24no—
235C2×C4⋊Q8—131no—
236C2×C4⋊Q8C2×D1311yescharacteristic
237C2×#126—21no—
238C2×#126—21no—
239C2×#125—21no—
240C2×#125—21no—
241C2×#125C2×D1311yescharacteristic
242C2×C22⋊Q8C2×D1311yescharacteristic
243C2×C22⋊Q8C2×D1311yescharacteristic
244C2×C4×Q8C2×D1311yescharacteristic
245C2×C4×Q8C2×D1311yescharacteristic
246C2×#117C2×D1311yescharacteristic
247#501—264no—
248#487—264no—
249C2×#107—132no—
250C2×#106—132no—
251C2×#103—132no—
252C2×#103—132no—
253C2×#103—132no—
254C2×#103—132no—
255C2×C22⋊C8—132no—
256C2×#97—131no—
257C2×C4×C8—131no—
258#400—261no—
259#399—261no—
260#395—261no—
261#393—261no—
262#389—132no—
263#382—131no—
264#380—132no—
265#340—132no—
266#340—132no—
267#336—132no—
268C22×C13—42no—
269C22×C13—41no—
270C22×C13—42no—
271C22×C13—41no—
272C22×C13—41no—
273C22×C13C2×#12011yescharacteristic
274C22×C13#53211yescharacteristic
275C22×C13#53611yescharacteristic
276C22×C13#57712yes—
277C22×C13#57812yes—
278C4×C13—22no—
279C4×C13—22no—
280C4×C13—41no—
281C4×C13—42no—
282C4×C13—42no—
283C4×C13—41no—
284C4×C13—42no—
285C4×C13—41no—
286C4×C13—42no—
287C4×C13#54712yes—
288C4×C13#54812yes—
289Dic13—82no—
290Dic13—82no—
291C22×Q8—261no—
292C22×Q8C22×D1311yescharacteristic
293C22×Q8C22×D1311yescharacteristic
294C23×C4C22×D1311yescharacteristic
295C22×C8—132no—
296C22×C8—132no—
297C4⋊Q8—22no—
298C4⋊Q8—262no—
299C4⋊Q8—262no—
300C4⋊Q8C22⋊D1314yes—
301#126—28no—
302#126—28no—
303#125—28no—
304#125—28no—
305#125—22no—
306#125C22⋊D1314yes—
307C22⋊Q8—22no—
308C22⋊Q8—22no—
309C22⋊Q8—22no—
310C22⋊Q8—22no—
311C4×Q8—22no—
312C4×Q8—22no—
313C4×Q8—22no—
314C4×Q8—22no—
315#117—22no—
316#117—22no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—132no—
326C2×C4⋊C4—132no—
327C2×C4⋊C4—261no—
328C2×C4⋊C4—262no—
329C2×C4⋊C4C22⋊D1311yescharacteristic
330C2×C4⋊C4C22⋊D1311yescharacteristic
331C2×C4⋊C4C22×D1311yescharacteristic
332C2×C4⋊C4C22×D1311yescharacteristic
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—262no—
336C2×C22⋊C4C22⋊D1311yescharacteristic
337C2×C22⋊C4C22⋊D1311yescharacteristic
338C2×C42—21no—
339C2×C42—21no—
340C2×C42C22×D1311yescharacteristic
341C2×C42C22×D1311yescharacteristic
342#107—264no—
343#106—264no—
344#103—264no—
345#103—264no—
346#103—264no—
347#103—264no—
348C22⋊C8—264no—
349#97—262no—
350C4×C8—262no—
351#95—262no—
352#95—261no—
353#95—261no—
354#95—262no—
355C2×C13—81no—
356C2×C13#243211yescharacteristic
357C2×C13#301011yescharacteristic
358C2×C13#301111yescharacteristic
359C2×C13#317812yes—
360C2×C13#324212yes—
361C24C2×C22⋊D1311yescharacteristic
362C2×Q8—21no—
363C2×Q8—21no—
364C2×Q8—22no—
365C2×Q8—22no—
366C2×Q8—22no—
367C2×Q8—22no—
368C2×Q8—522no—
369C2×Q8—1042no—
370C2×Q8C2×C22⋊D1312yes—
371C2×Q8C2×C22⋊D1312yes—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—262no—
381C22×C4—262no—
382C22×C4C2×C22⋊D1311yescharacteristic
383C22×C4C2×C22⋊D1311yescharacteristic
384C22×C4C2×C22⋊D1311yescharacteristic
385C22×C4C2×C22⋊D1311yescharacteristic
386C22×C4C2×C22⋊D1311yescharacteristic
387C22×C4C23×D1311yescharacteristic
388C2×C8—134no—
389C2×C8—262no—
390C2×C8—262no—
391C2×C8—262no—
392C2×C8—262no—
393C2×C8—262no—
394C4⋊C4—24no—
395C4⋊C4—24no—
396C4⋊C4—24no—
397C4⋊C4—24no—
398C4⋊C4—24no—
399C4⋊C4—24no—
400C4⋊C4—24no—
401C4⋊C4—24no—
402C4⋊C4—22no—
403C4⋊C4—22no—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—262no—
407C4⋊C4—262no—
408C4⋊C4—262no—
409C4⋊C4—262no—
410C4⋊C4—522no—
411C4⋊C4—1042no—
412C4⋊C4C2×C22⋊D1312yes—
413C4⋊C4C2×C22⋊D1312yes—
414C22⋊C4—24no—
415C22⋊C4—24no—
416C22⋊C4—22no—
417C22⋊C4—22no—
418C22⋊C4—1042no—
419C42—24no—
420C42—24no—
421C42—21no—
422C42—21no—
423C42C2×C22⋊D1312yes—
424C42C2×C22⋊D1312yes—
425C13#2568611yescharacteristic, complemented, Sylow
426C23—21no—
427C23—21no—
428C23—22no—
429C23—22no—
430C23—21no—
431C23C22×C22⋊D1311yescharacteristic
432Q8—24no—
433Q8—24no—
434Q8—42no—
435Q8—42no—
436Q8—1044no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—21no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—522no—
459C2×C4—522no—
460C2×C4—522no—
461C2×C4—522no—
462C2×C4—522no—
463C2×C4—522no—
464C2×C4#8820712yes—
465C2×C4#8820712yes—
466C2×C4#41×D1312yes—
467C2×C4#8825712yes—
468C2×C4C22×C22⋊D1311yescharacteristic
469C2×C4C22×C22⋊D1311yescharacteristic
470C8—264no—
471C8—522no—
472C22—41no—
473C22—41no—
474C22—42no—
475C22—42no—
476C22—41no—
477C22#1171953011yescharacteristic
478C22#1171953711yescharacteristic
479C22#1171954212yes—
480C22#1171954312yes—
481C22C2×#8820711yescharacteristic
482C4—22no—
483C4—22no—
484C4—41no—
485C4—42no—
486C4—41no—
487C4—42no—
488C4—41no—
489C4—42no—
490C4—42no—
491C4—1042no—
492C4—1042no—
493C4#1171952912yes—
494C4#1171953612yes—
495C2—81no—
496C2#1311846011yescharacteristic
497C2#1312412211yescharacteristic
498C2#1312413111yescharacteristic
499C2#1312550612yes—
500C2#1312609812yes—
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#541C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenterC2×#541D13
hypocenterC13#25686
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#541

Complements

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

NH ≅ G/Ntype
1. C2×#11718726C2semidirect
2. C2×#11718742C2semidirect
6. #13115802C2semidirect
7. #13115657C2semidirect
8. #13115104C2semidirect
9. #13115090C2semidirect
425. C13#25686semidirect

Maximal subgroups

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

subgroupindex
C2×#117187262
C2×#117187422
#131206572
#131160362
#131160292
#131158022
#131156572
#131151042
#131150902
#131146022
C2×C13×#5412
#2568613