Finite Group Databasebeta

← #15835917

Subgroups — #15835917

Order 3328.

982 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718705C212yesmaximal, complemented
2#13119153C211yesmaximal, characteristic
3#13113878C214yesmaximal, complemented
4#13113861C214yesmaximal, complemented
5#13113408C212yesmaximal, complemented
6#13113154C211yesmaximal, characteristic
7C13×#3501C211yesmaximal, characteristic
8C13×#554—24no—
9C13×#554—22no—
10D4×Q8×C13—22no—
11C13×#544C2212yes—
12C13×#543—21no—
13C13×#543C2212yes—
14C13×#533—21no—
15C2×C13×C22⋊Q8—21no—
16C2×C13×C22⋊Q8C2212yes—
17C13×#518—21no—
18C2×C4×D4×C13C2211yescharacteristic
19C22×C4⋊Dic13C2211yescharacteristic
20C2×#88075—22no—
21#11718881—21no—
22#11718873—21no—
23#11718873C2211yescharacteristic
24C2×C22⋊#1055C2212yes—
25#11718705—24no—
26#11718705C2218yes—
27#11718647C2212yes—
28C2×#88047—22no—
29#11718610C2212yes—
30#11718607—21no—
31#11718589—21no—
32#11718130C2218yes—
33#11718120C2212yes—
34#11718117C2212yes—
35C22×Q8×C13—21no—
36C22×Q8×C13D412yes—
37C22×D4×C13D411yescharacteristic
38C23×C4×C13D411yescharacteristic
39C23×C4×C13C2311yescharacteristic
40C23×Dic13—21no—
41C13×C4⋊Q8—21no—
42C13×C4⋊Q8—21no—
43C13×C4⋊Q8—24no—
44C13×#125—22no—
45C13×#125—24no—
46C13×C22⋊Q8—22no—
47C13×C22⋊Q8—22no—
48C13×C22⋊Q8—24no—
49C13×C22⋊Q8—24no—
50C13×C22⋊Q8—24no—
51C13×C22⋊Q8—22no—
52C13×C22⋊Q8—22no—
53C13×C22⋊Q8—22no—
54C13×C22⋊Q8—22no—
55C13×C22⋊Q8—24no—
56C13×C22⋊Q8D414yes—
57C13×C22⋊Q8C2314yes—
58C4×Q8×C13—22no—
59C4×Q8×C13—22no—
60C4×D4×C13—24no—
61C4×D4×C13—24no—
62C4×D4×C13—22no—
63C4×D4×C13—22no—
64C13×#117—22no—
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4—22no—
67C2×C13×C4⋊C4—22no—
68C2×C13×C4⋊C4D412yes—
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C13×C22⋊C4—22no—
71C2×C13×C22⋊C4—22no—
72C2×C13×C22⋊C4D411yescharacteristic
73C2×C13×C22⋊C4C2311yescharacteristic
74C2×C42×C13D411yescharacteristic
75C2×C22⋊Dic13—21no—
76C2×C22⋊Dic13—22no—
77C2×C4⋊Dic13—22no—
78C2×C4⋊Dic13—22no—
79C2×C4⋊Dic13—21no—
80C2×C4⋊Dic13—21no—
81C2×C4⋊Dic13C2312yes—
82C2×#6101—22no—
83C22×#1055—22no—
84#88075—28no—
85#88071—22no—
86#88071—22no—
87#88071C2312yes—
88C22⋊#1055—22no—
89C22⋊#1055C2314yes—
90#88047—28no—
91#18205—131nomaximal, Sylow
92C24×C13C2×D411yescharacteristic
93C24×C13C2×D411yescharacteristic
94C2×Q8×C13—22no—
95C2×Q8×C13—22no—
96C2×Q8×C13—22no—
97C2×Q8×C13—44no—
98C2×Q8×C13—82no—
99C2×Q8×C13C2×D414yes—
100C2×D4×C13—22no—
101C2×D4×C13—22no—
102C2×D4×C13Q1614yes—
103C22×C4×C13—22no—
104C22×C4×C13—22no—
105C22×C4×C13—22no—
106C22×C4×C13—22no—
107C22×C4×C13—21no—
108C22×C4×C13—21no—
109C22×C4×C13—42no—
110C22×C4×C13—42no—
111C22×C4×C13C2×D411yescharacteristic
112C22×C4×C13C2×D412yes—
113C22×C4×C13C2×D411yescharacteristic
114C22×C4×C13C2×D411yescharacteristic
115C22×C4×C13C2×D411yescharacteristic
116C22×C4×C13C2×D412yes—
117C22×C4×C13C2411yescharacteristic
118C22×Dic13—22no—
119C22×Dic13—22no—
120C22×Dic13—42no—
121C22×Dic13—82no—
122C13×C4⋊C4—22no—
123C13×C4⋊C4—24no—
124C13×C4⋊C4—22no—
125C13×C4⋊C4—22no—
126C13×C4⋊C4—24no—
127C13×C4⋊C4—22no—
128C13×C4⋊C4—24no—
129C13×C4⋊C4—22no—
130C13×C4⋊C4—24no—
131C13×C4⋊C4—22no—
132C13×C4⋊C4C2×D414yes—
133C13×C22⋊C4—24no—
134C13×C22⋊C4—24no—
135C13×C22⋊C4—22no—
136C13×C22⋊C4—24no—
137C13×C22⋊C4—22no—
138C42×C13—24no—
139C42×C13—21no—
140C42×C13—21no—
141C22⋊Dic13—42no—
142C22⋊Dic13—82no—
143C4⋊Dic13—24no—
144C4⋊Dic13—42no—
145C4⋊Dic13—41no—
146C4⋊Dic13—41no—
147#6101—82no—
148C2×#1055—24no—
149C2×#1055—44no—
150#3501D1311yescharacteristic
151C2×#484—132no—
152#2487—131no—
153#1617—134no—
154#1614—134no—
155#1520—132no—
156#1459—131no—
157C23×C13—21no—
158C23×C13—21no—
159C23×C13—41no—
160C23×C13—41no—
161C23×C13—41no—
162C23×C13—41no—
163C23×C13#12012yes—
164C23×C13C2×Q1612yes—
165C23×C13C2×Q1612yes—
166C23×C13#13712yes—
167C23×C13C22×D411yescharacteristic
168Q8×C13—44no—
169Q8×C13—44no—
170Q8×C13—82no—
171Q8×C13—82no—
172D4×C13—28no—
173C2×C4×C13—21no—
174C2×C4×C13—21no—
175C2×C4×C13—24no—
176C2×C4×C13—22no—
177C2×C4×C13—21no—
178C2×C4×C13—24no—
179C2×C4×C13—24no—
180C2×C4×C13—21no—
181C2×C4×C13—42no—
182C2×C4×C13—41no—
183C2×C4×C13—42no—
184C2×C4×C13—41no—
185C2×C4×C13—41no—
186C2×C4×C13—81no—
187C2×C4×C13—82no—
188C2×C4×C13—82no—
189C2×C4×C13—82no—
190C2×C4×C13—82no—
191C2×C4×C13#12011yescharacteristic
192C2×C4×C13#12011yescharacteristic
193C2×C4×C13C2×Q1612yes—
194C2×C4×C13C22×D412yes—
195C2×Dic13—42no—
196C2×Dic13—42no—
197C2×Dic13—42no—
198C2×Dic13—42no—
199C2×Dic13—42no—
200C2×Dic13—42no—
201C2×Dic13—84no—
202#1055—44no—
203#554—24no—
204#554—22no—
205D4×Q8—22no—
206#544C2×D1312yes—
207#543—21no—
208#543C2×D1312yes—
209#533—21no—
210C2×C22⋊Q8—21no—
211C2×C22⋊Q8C2×D1312yes—
212#518—21no—
213C2×C4×D4C2×D1311yescharacteristic
214C22×C4⋊C4—131no—
215#484—138no—
216#484—264no—
217C2×#107—262no—
218C2×#103—262no—
219C2×C22⋊C8—132no—
220#400—132no—
221#399—132no—
222#389—261no—
223#386—261no—
224#385—261no—
225#380—131no—
226#380—261no—
227#328—138no—
228#324—132no—
229#323—132no—
230C22×C13—21no—
231C22×C13—22no—
232C22×C13—21no—
233C22×C13—22no—
234C22×C13—22no—
235C22×C13—42no—
236C22×C13—42no—
237C22×C13—42no—
238C22×C13—41no—
239C22×C13—41no—
240C22×C13—81no—
241C22×C13#45114yes—
242C22×C13C2×#12011yescharacteristic
243C22×C13C22×Q1611yescharacteristic
244C22×C13C2×#13711yescharacteristic
245C4×C13—22no—
246C4×C13—22no—
247C4×C13—21no—
248C4×C13—41no—
249C4×C13—44no—
250C4×C13—41no—
251C4×C13—44no—
252C4×C13#45812yes—
253Dic13—82no—
254Dic13—82no—
255C22×Q8—21no—
256C22×Q8C22⋊D1312yes—
257C22×D4C22⋊D1311yescharacteristic
258C23×C4—261no—
259C23×C4C22⋊D1311yescharacteristic
260C23×C4C22×D1311yescharacteristic
261C22×C8—262no—
262C4⋊Q8—21no—
263C4⋊Q8—21no—
264C4⋊Q8—24no—
265#125—22no—
266#125—24no—
267C22⋊Q8—22no—
268C22⋊Q8—22no—
269C22⋊Q8—24no—
270C22⋊Q8—24no—
271C22⋊Q8—24no—
272C22⋊Q8—22no—
273C22⋊Q8—22no—
274C22⋊Q8—22no—
275C22⋊Q8—22no—
276C22⋊Q8—24no—
277C22⋊Q8C22⋊D1314yes—
278C22⋊Q8C22×D1314yes—
279C4×Q8—22no—
280C4×Q8—22no—
281C4×D4—24no—
282C4×D4—24no—
283C4×D4—22no—
284C4×D4—22no—
285#117—22no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—132no—
290C2×C4⋊C4—262no—
291C2×C4⋊C4—262no—
292C2×C4⋊C4—261no—
293C2×C4⋊C4—261no—
294C2×C4⋊C4—262no—
295C2×C4⋊C4C22⋊D1312yes—
296C2×C4⋊C4C22×D1311yescharacteristic
297C2×C22⋊C4—22no—
298C2×C22⋊C4—22no—
299C2×C22⋊C4—261no—
300C2×C22⋊C4—262no—
301C2×C22⋊C4C22⋊D1311yescharacteristic
302C2×C22⋊C4C22×D1311yescharacteristic
303C2×C42C22⋊D1311yescharacteristic
304#107—268no—
305#103—268no—
306C22⋊C8—134no—
307C22⋊C8—262no—
308#95—132no—
309#95—262no—
310#95—262no—
311C2×C13—21no—
312C2×C13—21no—
313C2×C13—24no—
314C2×C13—42no—
315C2×C13C2×#45111yescharacteristic
316C2×C13#302111yescharacteristic
317C2×C13C2×#45811yescharacteristic
318C24C2×C22⋊D1311yescharacteristic
319C24C2×C22⋊D1311yescharacteristic
320C2×Q8—22no—
321C2×Q8—22no—
322C2×Q8—22no—
323C2×Q8—44no—
324C2×Q8—82no—
325C2×Q8C2×C22⋊D1314yes—
326C2×D4—22no—
327C2×D4—22no—
328C2×D4#610714yes—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—42no—
336C22×C4—42no—
337C22×C4—262no—
338C22×C4—262no—
339C22×C4—522no—
340C22×C4—1042no—
341C22×C4C2×C22⋊D1311yescharacteristic
342C22×C4C2×C22⋊D1311yescharacteristic
343C22×C4C2×C22⋊D1312yes—
344C22×C4C2×C22⋊D1311yescharacteristic
345C22×C4C2×C22⋊D1311yescharacteristic
346C22×C4C2×C22⋊D1312yes—
347C22×C4C23×D1311yescharacteristic
348C2×C8—264no—
349C2×C8—524no—
350C4⋊C4—22no—
351C4⋊C4—24no—
352C4⋊C4—22no—
353C4⋊C4—22no—
354C4⋊C4—24no—
355C4⋊C4—22no—
356C4⋊C4—24no—
357C4⋊C4—22no—
358C4⋊C4—24no—
359C4⋊C4—22no—
360C4⋊C4—264no—
361C4⋊C4—522no—
362C4⋊C4—521no—
363C4⋊C4—521no—
364C4⋊C4—1042no—
365C4⋊C4C2×C22⋊D1314yes—
366C22⋊C4—24no—
367C22⋊C4—24no—
368C22⋊C4—22no—
369C22⋊C4—24no—
370C22⋊C4—22no—
371C22⋊C4—522no—
372C22⋊C4—1042no—
373C42—24no—
374C42—21no—
375C42—21no—
376C13#1820511yescharacteristic, complemented, Sylow
377C23—21no—
378C23—21no—
379C23—41no—
380C23—41no—
381C23—41no—
382C23—41no—
383C23#8819612yes—
384C23C2×#610712yes—
385C23C2×#610712yes—
386C23#8820712yes—
387C23C22×C22⋊D1311yescharacteristic
388Q8—44no—
389Q8—44no—
390Q8—82no—
391Q8—82no—
392D4—28no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—22no—
396C2×C4—24no—
397C2×C4—21no—
398C2×C4—24no—
399C2×C4—24no—
400C2×C4—21no—
401C2×C4—42no—
402C2×C4—41no—
403C2×C4—42no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—81no—
407C2×C4—82no—
408C2×C4—82no—
409C2×C4—82no—
410C2×C4—82no—
411C2×C4—522no—
412C2×C4—522no—
413C2×C4—522no—
414C2×C4—522no—
415C2×C4—522no—
416C2×C4—522no—
417C2×C4—1044no—
418C2×C4C2×#610712yes—
419C2×C4#8820711yescharacteristic
420C2×C4#8820711yescharacteristic
421C2×C4C22×C22⋊D1312yes—
422C8—524no—
423C22—21no—
424C22—22no—
425C22—21no—
426C22—22no—
427C22—22no—
428C22—42no—
429C22—42no—
430C22—42no—
431C22—41no—
432C22—41no—
433C22—81no—
434C22#1171888914yes—
435C22C2×#8819611yescharacteristic
436C22C22×#610711yescharacteristic
437C22C2×#8820711yescharacteristic
438C4—22no—
439C4—21no—
440C4—22no—
441C4—41no—
442C4—44no—
443C4—41no—
444C4—44no—
445C4—1042no—
446C4—1042no—
447C4#1171890412yes—
448C2—21no—
449C2—21no—
450C2—24no—
451C2—42no—
452C2C2×#1171888911yescharacteristic
453C2#1312420811yescharacteristic
454C2C2×#1171890411yescharacteristic
subgroupG/H
centerC22C2×#88207
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#3501C2
socleC22×C13C2×#120
prime radicalC22×D4×C13D4
hypercenter#3501D13
hypocenterC13#18205
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3501

Complements

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

NH ≅ G/Ntype
1. C2×#11718705C2semidirect
3. #13113878C2semidirect
4. #13113861C2semidirect
5. #13113408C2semidirect
376. C13#18205semidirect

Maximal subgroups

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

subgroupindex
C2×#117187052
#131191532
#131138782
#131138612
#131134082
#131131542
C13×#35012
#1820513