Finite Group Databasebeta

← #15764143

Subgroups — #15764143

Order 3328.

790 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718731C211yesmaximal, characteristic, complemented
2C2×#11718668C211yesmaximal, characteristic, complemented
3#13115759C211yesmaximal, characteristic, complemented
4C2×#11718136C211yesmaximal, characteristic, complemented
5C2×D4⋊#1055C211yesmaximal, characteristic, complemented
6#13112677C211yesmaximal, characteristic, complemented
7C13×#2541C211yesmaximal, characteristic
8C2×C13×#127—21no—
9C2×C13×#127C2211yescharacteristic
10C2×C13×#121—22no—
11C2×C4×D4×C13C2211yescharacteristic
12C2×#88123C2211yescharacteristic
13C13×#392—22no—
14C13×#390—21no—
15C4×C13×C4⋊C4C2211yescharacteristic
16C2×#88072—22no—
17C2×#88072—21no—
18#11718731—22no—
19#11718731—22no—
20#11718668—22no—
21#11718668—22no—
22C2×#88050—22no—
23C2×#88047—21no—
24C2×C4⋊#1055C2211yescharacteristic
25C2×C4⋊#1055C2211yescharacteristic
26C2×C4×#1055C2211yescharacteristic
27#11718136—22no—
28D4⋊#1055—22no—
29C22×D4×C13—24no—
30C22×D4×C13—21no—
31C22×D4×C13—21no—
32C22×D4×C13D411yescharacteristic
33C22×D4×C13D412yes—
34C23×C4×C13—21no—
35C22×Dic26—21no—
36C13×#127—21no—
37C13×#127—21no—
38C13×#127—21no—
39C13×#127—21no—
40C13×#127—42no—
41C13×#127—42no—
42C13×#121—44no—
43C13×#121—44no—
44C4×D4×C13—21no—
45C4×D4×C13—21no—
46C4×D4×C13—21no—
47C4×D4×C13—21no—
48C2×C13×C4⋊C4D411yescharacteristic
49C2×C13×C4⋊C4D412yes—
50C2×C13×C22⋊C4—24no—
51C2×C13×C22⋊C4—21no—
52C2×C42×C13—21no—
53C2×C42×C13C2311yescharacteristic
54C2×C4⋊Dic13—21no—
55C2×C4⋊Dic13—21no—
56C22×#1055—21no—
57C22×#1055—21no—
58C22×#1055—21no—
59#88123—21no—
60#88123—21no—
61#88123—21no—
62#88123D412yescomplemented
63C13×#95—21no—
64#88072—24no—
65#88072—28no—
66#88050—44no—
67#88047—24no—
68C4⋊#1055—21no—
69C4⋊#1055—21no—
70C4⋊#1055—21no—
71C4⋊#1055D412yescomplemented
72C4×#1055—21no—
73C4×#1055D412yescomplemented
74#10070—131nomaximal, Sylow
75C24×C13—21no—
76C24×C13—22no—
77C2×D4×C13—21no—
78C2×D4×C13—22no—
79C2×D4×C13—21no—
80C2×D4×C13—22no—
81C2×D4×C13—21no—
82C2×D4×C13—21no—
83C2×D4×C13—21no—
84C2×D4×C13—44no—
85C2×D4×C13—48no—
86C2×D4×C13—48no—
87C2×D4×C13—41no—
88C2×D4×C13—41no—
89C2×D4×C13—41no—
90C2×D4×C13—41no—
91C2×D4×C13—42no—
92C2×D4×C13—41no—
93C2×D4×C13—41no—
94C2×D4×C13—42no—
95C2×D4×C13—41no—
96C2×D4×C13—41no—
97C2×D4×C13—84no—
98C2×D4×C13SD1612yes—
99C22×C4×C13—22no—
100C22×C4×C13—21no—
101C22×C4×C13—41no—
102C22×C4×C13—41no—
103C22×C4×C13—42no—
104C22×C4×C13—42no—
105C22×C4×C13C2×D411yescharacteristic
106C22×C4×C13C2×D411yescharacteristic
107C22×C4×C13C2×D411yescharacteristic
108C22×Dic13—41no—
109C2×Dic26—22no—
110C2×Dic26—42no—
111C2×Dic26—42no—
112C2×Dic26—41no—
113C13×C4⋊C4—22no—
114C13×C4⋊C4—21no—
115C13×C4⋊C4—21no—
116C13×C4⋊C4D814yes—
117C13×C22⋊C4—48no—
118C13×C22⋊C4—41no—
119C13×C22⋊C4—41no—
120C42×C13—41no—
121C42×C13—41no—
122C42×C13C2×D411yescharacteristic
123C42×C13C2×D411yescharacteristic
124C42×C13C2×D411yescharacteristic
125C42×C13#4111yescharacteristic
126C4⋊Dic13—22no—
127C4⋊Dic13—22no—
128C4⋊Dic13—41no—
129C4⋊Dic13—41no—
130C2×#1055—22no—
131C2×#1055—22no—
132C2×#1055—42no—
133C2×#1055—41no—
134C2×#1055—41no—
135C2×#1055—41no—
136C2×#1055—42no—
137C2×#486—131no—
138C2×#474—131no—
139#2541D1311yescharacteristic
140#1981—131no—
141C2×#331—131no—
142C2×D4⋊C8—131no—
143#1279—131no—
144C23×C13—22no—
145C23×C13—41no—
146C23×C13—42no—
147C23×C13—41no—
148C23×C13—42no—
149C23×C13—42no—
150C23×C13—44no—
151C23×C13—42no—
152C23×C13—42no—
153C23×C13—44no—
154C23×C13#12011yescharacteristic
155D4×C13—22no—
156D4×C13—22no—
157D4×C13—44no—
158D4×C13—41no—
159D4×C13—41no—
160D4×C13—82no—
161D4×C13—816no—
162D4×C13—81no—
163D4×C13—81no—
164D4×C13—82no—
165D4×C13—81no—
166D4×C13—81no—
167D4×C13—81no—
168D4×C13—81no—
169C2×C4×C13—22no—
170C2×C4×C13—24no—
171C2×C4×C13—42no—
172C2×C4×C13—42no—
173C2×C4×C13—41no—
174C2×C4×C13—42no—
175C2×C4×C13—82no—
176C2×C4×C13—81no—
177C2×C4×C13—81no—
178C2×C4×C13#12011yescharacteristic
179C2×C4×C13#12011yescharacteristic
180C2×C4×C13#12111yescharacteristic
181C2×C4×C13#12111yescharacteristic
182C2×C4×C13#12111yescharacteristic
183C2×C4×C13#12711yescharacteristic
184C2×C4×C13C2×D812yes—
185C2×C4×C13C2×SD1611yescharacteristic
186C2×C4×C13#13511yescharacteristic
187C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
188C2×C4×C13AGL(1,ℤ/8)12yes—
189C2×C4×C13#13711yescharacteristic
190C2×Dic13—42no—
191C2×Dic13—82no—
192Dic26—44no—
193Dic26—81no—
194Dic26—81no—
195#1055—42no—
196#1055—42no—
197#1055—81no—
198C2×C4⋊Q8—131no—
199C2×#127—21no—
200C2×#127C2×D1311yescharacteristic
201C2×#121—22no—
202C2×C4×D4C2×D1311yescharacteristic
203#486—262no—
204#486—262no—
205#474—262no—
206#474—262no—
207C2×#107—261no—
208C2×C4⋊C8—131no—
209C2×C4⋊C8—131no—
210C2×#103—262no—
211C2×#102—262no—
212C2×#102—261no—
213C2×C4×C8—131no—
214#392—22no—
215#390—21no—
216C4×C4⋊C4C2×D1311yescharacteristic
217#331—262no—
218D4⋊C8—262no—
219C22×C13—44no—
220C22×C13—42no—
221C22×C13—82no—
222C22×C13—81no—
223C22×C13—81no—
224C22×C13—84no—
225C22×C13—84no—
226C22×C13—82no—
227C22×C13—82no—
228C22×C13—82no—
229C22×C13#39211yescharacteristic
230C22×C13#44712yes—
231C22×C13#45011yescharacteristic
232C22×C13#45211yescharacteristic
233C22×C13#45512yes—
234C4×C13—21no—
235C4×C13—21no—
236C4×C13—44no—
237C4×C13—81no—
238C4×C13#44811yescharacteristic
239C4×C13#44911yescharacteristic
240C4×C13#45912yes—
241C4×C13#46511yescharacteristic
242C4×C13#46811yescharacteristic
243C4×C13#49311yescharacteristic
244C4×C13#49611yescharacteristic
245Dic13—82no—
246C22×Q8—261no—
247C22×D4—24no—
248C22×D4—21no—
249C22×D4—21no—
250C22×D4C22⋊D1311yescharacteristic
251C22×D4C22⋊D1312yes—
252C23×C4—21no—
253C22×C8—261no—
254C22×C8—261no—
255C22×C8—261no—
256C4⋊Q8—132no—
257C4⋊Q8—261no—
258C4⋊Q8—261no—
259C4⋊Q8—261no—
260#127—21no—
261#127—21no—
262#127—21no—
263#127—21no—
264#127—42no—
265#127—42no—
266#121—44no—
267#121—44no—
268C4×D4—21no—
269C4×D4—21no—
270C4×D4—21no—
271C4×D4—21no—
272C2×C4⋊C4—261no—
273C2×C4⋊C4—261no—
274C2×C4⋊C4C22⋊D1311yescharacteristic
275C2×C4⋊C4C22⋊D1312yes—
276C2×C22⋊C4—24no—
277C2×C22⋊C4—21no—
278C2×C42—21no—
279C2×C42C22×D1311yescharacteristic
280#107—264no—
281C4⋊C8—132no—
282C4⋊C8—261no—
283C4⋊C8—261no—
284C4⋊C8—261no—
285#103—524no—
286#102—264no—
287#102—268no—
288C4×C8—132no—
289C4×C8—261no—
290#95—21no—
291C2×C13—82no—
292C2×C13—162no—
293C2×C13#163912yes—
294C2×C13#164112yes—
295C2×C13#200011yescharacteristic
296C2×C13#200411yescharacteristic
297C2×C13#201111yescharacteristic
298C24—21no—
299C24—22no—
300C2×Q8—262no—
301C2×Q8—521no—
302C2×Q8—522no—
303C2×Q8—522no—
304C2×D4—21no—
305C2×D4—21no—
306C2×D4—22no—
307C2×D4—21no—
308C2×D4—22no—
309C2×D4—21no—
310C2×D4—21no—
311C2×D4—44no—
312C2×D4—48no—
313C2×D4—48no—
314C2×D4—42no—
315C2×D4—42no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4—84no—
325C2×D4#610512yes—
326C22×C4—22no—
327C22×C4—21no—
328C22×C4—42no—
329C22×C4—42no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—521no—
333C22×C4C2×C22⋊D1311yescharacteristic
334C22×C4C2×C22⋊D1311yescharacteristic
335C22×C4C2×C22⋊D1311yescharacteristic
336C2×C8—262no—
337C2×C8—262no—
338C2×C8—522no—
339C2×C8—521no—
340C2×C8—521no—
341C2×C8—522no—
342C2×C8—521no—
343C4⋊C4—22no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—262no—
347C4⋊C4—262no—
348C4⋊C4—521no—
349C4⋊C4—521no—
350C4⋊C4#610414yes—
351C22⋊C4—48no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C42—41no—
355C42—41no—
356C42D4×D1311yescharacteristic
357C42D4×D1311yescharacteristic
358C42D4×D1311yescharacteristic
359C42#612911yescharacteristic
360C13#1007011yescharacteristic, complemented, Sylow
361C23—22no—
362C23—42no—
363C23—41no—
364C23—41no—
365C23—42no—
366C23—44no—
367C23—42no—
368C23—42no—
369C23—42no—
370C23—44no—
371C23#8820711yescharacteristic
372Q8—524no—
373Q8—1041no—
374Q8—1041no—
375D4—22no—
376D4—22no—
377D4—44no—
378D4—41no—
379D4—41no—
380D4—82no—
381D4—816no—
382D4—81no—
383D4—81no—
384D4—81no—
385D4—81no—
386D4—82no—
387D4—81no—
388D4—81no—
389C2×C4—22no—
390C2×C4—24no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—41no—
395C2×C4—82no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4—522no—
399C2×C4—1042no—
400C2×C4C2×#610412yes—
401C2×C4#8818611yescharacteristic
402C2×C4#8818612yes—
403C2×C4C2×#610511yescharacteristic
404C2×C4#8819111yescharacteristic
405C2×C4#8819111yescharacteristic
406C2×C4#8819211yescharacteristic
407C2×C4#8819311yescharacteristic
408C2×C4#8819311yescharacteristic
409C2×C4#8819411yescharacteristic
410C2×C4#8820411yescharacteristic
411C2×C4#8820511yescharacteristic
412C8—522no—
413C8—522no—
414C8—1041no—
415C22—44no—
416C22—42no—
417C22—81no—
418C22—82no—
419C22—81no—
420C22—82no—
421C22—84no—
422C22—84no—
423C22—82no—
424C22—82no—
425C22#1171887812yes—
426C22#1171887911yescharacteristic
427C22#1171888411yescharacteristic
428C22#1171890011yescharacteristic
429C22#1171890312yes—
430C4—21no—
431C4—21no—
432C4—44no—
433C4—81no—
434C4—1042no—
435C4#1171869811yescharacteristic
436C4#1171870111yescharacteristic
437C4#1171870211yescharacteristic
438C4#1171870311yescharacteristic
439C4#1171873312yes—
440C4#1171873411yescharacteristic
441C4#1171873511yescharacteristic
442C2—82no—
443C2—162no—
444C2#1311401512yes—
445C2#1311402912yes—
446C2#1311583911yescharacteristic
447C2#1311586311yescharacteristic
448C2#1311590711yescharacteristic
subgroupG/H
centerC23#88207
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
Fitting, prime radicalC13×#2541C2
socleC23×C13#120
hypercenter#2541D13
hypocenterC13#10070
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2541

Complements

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

NH ≅ G/Ntype
1. C2×#11718731C2semidirect
2. C2×#11718668C2semidirect
3. #13115759C2semidirect
4. C2×#11718136C2semidirect
5. C2×D4⋊#1055C2semidirect
6. #13112677C2semidirect
62. #88123D4semidirect
71. C4⋊#1055D4semidirect
73. C4×#1055D4semidirect
360. C13#10070semidirect

Maximal subgroups

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

subgroupindex
C2×#117187312
C2×#117186682
#131157592
C2×#117181362
C2×D4⋊#10552
#131126772
C13×#25412
#1007013