Finite Group Databasebeta

← #15836979

Subgroups — #15836979

Order 3328.

888 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125984C212yesmaximal, complemented
2#13120657C211yesmaximal, characteristic
3#13113878C214yesmaximal, complemented
4#13113861C214yesmaximal
5#13113400C212yesmaximal, complemented
6#13113150C211yesmaximal, characteristic
7C13×#3458C211yesmaximal, characteristic
8C13×#544—22no—
9C13×#544—22no—
10C13×#544—21no—
11C13×#544C2212yes—
12C13×#543—21no—
13C13×#543C2212yes—
14C13×#533—24no—
15C13×#533—21no—
16C13×#533C2212yes—
17C2×C13×#117—21no—
18C2×C13×#117C2211yescharacteristic
19C2×#88123C2211yescharacteristic
20#11718873—21no—
21#11718742—22no—
22#11718739—22no—
23#11718705C2218yes—
24#11718682—24no—
25#11718647C2212yes—
26#11718640—21no—
27#11718610C2212yes—
28#11718608—21no—
29#11718597C2211yescharacteristic
30#11718589—21no—
31#11718586C2212yes—
32#11718130C2218yes—
33#11718120C2212yes—
34#11718117C2212yes—
35C23×C4×C13D411yescharacteristic
36C22×Dic26—21no—
37C13×C4⋊Q8—24no—
38C13×C4⋊Q8—21no—
39C13×C4⋊Q8—21no—
40C13×C4⋊Q8—24no—
41C13×C4⋊Q8D412yes—
42C13×C4⋊Q8D412yes—
43C13×#125—24no—
44C13×#125—22no—
45C13×#125—24no—
46C13×#125—22no—
47C13×C22⋊Q8—24no—
48C13×C22⋊Q8—24no—
49C13×C22⋊Q8—24no—
50C13×C22⋊Q8—22no—
51C13×C22⋊Q8—22no—
52C13×C22⋊Q8—22no—
53C13×C22⋊Q8—24no—
54C13×C22⋊Q8C2314yes—
55C4×Q8×C13—22no—
56C4×Q8×C13—22no—
57C4×Q8×C13—22no—
58C4×Q8×C13D414yes—
59C13×#117—22no—
60C13×#117—22no—
61C13×#117—22no—
62C13×#117—22no—
63C13×#117—22no—
64C13×#117—22no—
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4—21no—
67C2×C13×C4⋊C4D411yescharacteristic
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C13×C22⋊C4—22no—
70C2×C13×C22⋊C4D411yescharacteristic
71C2×C13×C22⋊C4C2311yescharacteristic
72C2×C42×C13—22no—
73C2×C42×C13D411yescharacteristic
74C2×C42×C13C2311yescharacteristic
75C2×C22⋊Dic13—22no—
76C2×C4⋊Dic13—21no—
77C2×C4⋊Dic13—21no—
78C2×C4⋊Dic13C2312yes—
79C2×#6101—22no—
80#88123—22no—
81#88123—22no—
82#88075—28no—
83#88071—22no—
84#88071—21no—
85#88071—22no—
86#88071C2312yes—
87C22⋊#1055C2314yes—
88#88047—28no—
89C4⋊#1055—22no—
90C4×#1055—22no—
91#18311—131nomaximal, Sylow
92C24×C13C2×D411yescharacteristic
93C2×Q8×C13—22no—
94C2×Q8×C13—22no—
95C2×Q8×C13—22no—
96C2×Q8×C13C2×D414yes—
97C22×C4×C13—21no—
98C22×C4×C13—21no—
99C22×C4×C13—22no—
100C22×C4×C13—22no—
101C22×C4×C13—22no—
102C22×C4×C13Q1614yes—
103C22×C4×C13C2×D411yescharacteristic
104C22×C4×C13C2×D411yescharacteristic
105C22×C4×C13C2×D411yescharacteristic
106C22×C4×C13C2×D411yescharacteristic
107C22×C4×C13C2×D411yescharacteristic
108C22×C4×C13C2411yescharacteristic
109C22×Dic13—22no—
110C22×Dic13—22no—
111C2×Dic26—42no—
112C2×Dic26—82no—
113C13×C4⋊C4—22no—
114C13×C4⋊C4—22no—
115C13×C4⋊C4—22no—
116C13×C4⋊C4—24no—
117C13×C4⋊C4—24no—
118C13×C4⋊C4—22no—
119C13×C4⋊C4—22no—
120C13×C4⋊C4—22no—
121C13×C4⋊C4—22no—
122C13×C4⋊C4—22no—
123C13×C4⋊C4—24no—
124C13×C4⋊C4—22no—
125C13×C4⋊C4—24no—
126C13×C4⋊C4C2×D414yes—
127C13×C22⋊C4—24no—
128C13×C22⋊C4—24no—
129C13×C22⋊C4—22no—
130C13×C22⋊C4—22no—
131C42×C13—24no—
132C42×C13—24no—
133C42×C13—21no—
134C42×C13—21no—
135C42×C13C2×D412yes—
136C42×C13C2×D412yes—
137C22⋊Dic13—82no—
138C4⋊Dic13—24no—
139C4⋊Dic13—41no—
140C4⋊Dic13—41no—
141C4⋊Dic13—42no—
142#6101—82no—
143C2×#1055—24no—
144#3458D1311yescharacteristic
145#3230—132no—
146#2628—131no—
147#1617—134no—
148#1614—134no—
149#1518—132no—
150#1458—131no—
151C23×C13—21no—
152C23×C13—21no—
153C23×C13—41no—
154C23×C13—41no—
155C23×C13C2×Q1612yes—
156C23×C13C22×D411yescharacteristic
157Q8×C13—44no—
158Q8×C13—82no—
159Q8×C13—82no—
160Q8×C13—82no—
161C2×C4×C13—21no—
162C2×C4×C13—21no—
163C2×C4×C13—24no—
164C2×C4×C13—24no—
165C2×C4×C13—24no—
166C2×C4×C13—21no—
167C2×C4×C13—21no—
168C2×C4×C13—24no—
169C2×C4×C13—41no—
170C2×C4×C13—41no—
171C2×C4×C13—41no—
172C2×C4×C13—41no—
173C2×C4×C13—82no—
174C2×C4×C13—82no—
175C2×C4×C13#12012yes—
176C2×C4×C13#12011yescharacteristic
177C2×C4×C13#12011yescharacteristic
178C2×C4×C13C2×Q1612yes—
179C2×C4×C13C2×Q1612yes—
180C2×C4×C13#13712yes—
181C2×C4×C13C22×D412yes—
182C2×Dic13—42no—
183C2×Dic13—42no—
184C2×Dic13—42no—
185C2×Dic13—42no—
186C2×Dic13—42no—
187C2×Dic13—42no—
188Dic26—84no—
189#1055—44no—
190#544—22no—
191#544—22no—
192#544—21no—
193#544C2×D1312yes—
194#543—21no—
195#543C2×D1312yes—
196#533—24no—
197#533—21no—
198#533C2×D1312yes—
199C2×C4⋊Q8—131no—
200C2×#117—21no—
201C2×#117C2×D1311yescharacteristic
202#500—262no—
203#487—262no—
204#484—138no—
205#477—264no—
206#431—132no—
207#400—132no—
208#399—132no—
209#395—261no—
210#393—261no—
211#389—261no—
212#382—131no—
213#380—261no—
214#328—138no—
215#324—132no—
216#323—132no—
217C22×C13—21no—
218C22×C13—21no—
219C22×C13—22no—
220C22×C13—42no—
221C22×C13—41no—
222C22×C13—41no—
223C22×C13—81no—
224C22×C13C2×#12011yescharacteristic
225C22×C13C22×Q1611yescharacteristic
226C22×C13C2×#13711yescharacteristic
227C4×C13—22no—
228C4×C13—22no—
229C4×C13—22no—
230C4×C13—41no—
231C4×C13—44no—
232C4×C13—41no—
233C4×C13—44no—
234C4×C13#45112yes—
235C4×C13#45112yes—
236Dic13—82no—
237Dic13—82no—
238C22×Q8—261no—
239C23×C4C22⋊D1311yescharacteristic
240C4⋊Q8—24no—
241C4⋊Q8—21no—
242C4⋊Q8—21no—
243C4⋊Q8—24no—
244C4⋊Q8—262no—
245C4⋊Q8—262no—
246C4⋊Q8C22⋊D1312yes—
247C4⋊Q8C22⋊D1312yes—
248#125—24no—
249#125—22no—
250#125—24no—
251#125—22no—
252C22⋊Q8—24no—
253C22⋊Q8—24no—
254C22⋊Q8—24no—
255C22⋊Q8—22no—
256C22⋊Q8—22no—
257C22⋊Q8—22no—
258C22⋊Q8—24no—
259C22⋊Q8C22×D1314yes—
260C4×Q8—22no—
261C4×Q8—22no—
262C4×Q8—22no—
263C4×Q8C22⋊D1314yes—
264#117—22no—
265#117—22no—
266#117—22no—
267#117—22no—
268#117—22no—
269#117—22no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—132no—
273C2×C4⋊C4—261no—
274C2×C4⋊C4—261no—
275C2×C4⋊C4—262no—
276C2×C4⋊C4C22⋊D1311yescharacteristic
277C2×C4⋊C4C22×D1311yescharacteristic
278C2×C22⋊C4—22no—
279C2×C22⋊C4—262no—
280C2×C22⋊C4C22⋊D1311yescharacteristic
281C2×C22⋊C4C22×D1311yescharacteristic
282C2×C42—22no—
283C2×C42C22⋊D1311yescharacteristic
284C2×C42C22×D1311yescharacteristic
285#107—268no—
286C4⋊C8—262no—
287#103—268no—
288C22⋊C8—134no—
289C4×C8—262no—
290#95—132no—
291#95—262no—
292#95—261no—
293#95—262no—
294C2×C13—21no—
295C2×C13—21no—
296C2×C13—42no—
297C2×C13C2×#45111yescharacteristic
298C2×C13#302111yescharacteristic
299C2×C13#302811yescharacteristic
300C24C2×C22⋊D1311yescharacteristic
301C2×Q8—22no—
302C2×Q8—22no—
303C2×Q8—22no—
304C2×Q8—522no—
305C2×Q8—1042no—
306C2×Q8C2×C22⋊D1314yes—
307C22×C4—22no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—262no—
313C22×C4—262no—
314C22×C4#610714yes—
315C22×C4C2×C22⋊D1311yescharacteristic
316C22×C4C2×C22⋊D1311yescharacteristic
317C22×C4C2×C22⋊D1311yescharacteristic
318C22×C4C2×C22⋊D1311yescharacteristic
319C22×C4C2×C22⋊D1311yescharacteristic
320C22×C4C23×D1311yescharacteristic
321C2×C8—264no—
322C4⋊C4—22no—
323C4⋊C4—22no—
324C4⋊C4—22no—
325C4⋊C4—24no—
326C4⋊C4—24no—
327C4⋊C4—22no—
328C4⋊C4—22no—
329C4⋊C4—22no—
330C4⋊C4—22no—
331C4⋊C4—22no—
332C4⋊C4—24no—
333C4⋊C4—22no—
334C4⋊C4—24no—
335C4⋊C4—264no—
336C4⋊C4—522no—
337C4⋊C4—521no—
338C4⋊C4—521no—
339C4⋊C4—1042no—
340C4⋊C4C2×C22⋊D1314yes—
341C22⋊C4—24no—
342C22⋊C4—24no—
343C22⋊C4—22no—
344C22⋊C4—22no—
345C22⋊C4—1042no—
346C42—24no—
347C42—24no—
348C42—21no—
349C42—21no—
350C42C2×C22⋊D1312yes—
351C42C2×C22⋊D1312yes—
352C13#1831111yescharacteristic, complemented, Sylow
353C23—21no—
354C23—21no—
355C23—41no—
356C23—41no—
357C23C2×#610712yes—
358C23C22×C22⋊D1311yescharacteristic
359Q8—44no—
360Q8—82no—
361Q8—82no—
362Q8—82no—
363Q8—1044no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—24no—
367C2×C4—24no—
368C2×C4—24no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—24no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—82no—
377C2×C4—82no—
378C2×C4—522no—
379C2×C4—522no—
380C2×C4—522no—
381C2×C4—522no—
382C2×C4—522no—
383C2×C4—522no—
384C2×C4#8819612yes—
385C2×C4C2×#610712yes—
386C2×C4C2×#610712yes—
387C2×C4#8820712yes—
388C2×C4#8820711yescharacteristic
389C2×C4#8820711yescharacteristic
390C2×C4C22×C22⋊D1312yes—
391C8—524no—
392C22—21no—
393C22—21no—
394C22—22no—
395C22—42no—
396C22—41no—
397C22—41no—
398C22—81no—
399C22C2×#8819611yescharacteristic
400C22C22×#610711yescharacteristic
401C22C2×#8820711yescharacteristic
402C4—22no—
403C4—22no—
404C4—22no—
405C4—41no—
406C4—44no—
407C4—41no—
408C4—44no—
409C4—1042no—
410C4—1042no—
411C4#1171888912yes—
412C4#1171888912yes—
413C2—21no—
414C2—21no—
415C2—42no—
416C2C2×#1171888911yescharacteristic
417C2#1312420811yescharacteristic
418C2#1312424211yescharacteristic
subgroupG/H
centerC22C2×#88207
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#3458C2
socleC22×C13C2×#120
prime radicalC24×C13C2×D4
hypercenter#3458D13
hypocenterC13#18311
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3458

Complements

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

NH ≅ G/Ntype
1. #13125984C2semidirect
3. #13113878C2semidirect
5. #13113400C2semidirect
352. C13#18311semidirect

Maximal subgroups

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

subgroupindex
#131259842
#131206572
#131138782
#131138612
#131134002
#131131502
C13×#34582
#1831113