Finite Group Databasebeta

← #16783099

Subgroups — #16783099

Order 3328.

628 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719119C211yesmaximal, characteristic
2#13130726C211yesmaximal, characteristic
3C2×#11718285C212yesmaximal
4#13129674C212yesmaximal
5C2×#11718642C211yesmaximal, characteristic
6C22×C13×C4⋊C4C411yescharacteristic
7C22×C4⋊Dic13C2211yescharacteristic
8C22×C4×Dic13C2211yescharacteristic
9C2×C22⋊#1057C2212yes—
10C2×C22⋊#1057C2212yes—
11#11719119—24no—
12C2×C4⋊#1057—21no—
13C2×C4×#1057—21no—
14C2×#88071C411yescharacteristic
15C2×#88071C411yescharacteristic
16C2×#88071C411yescharacteristic
17C2×#88071C2211yescharacteristic
18#11718642—21no—
19#11718642—21no—
20#11718642—21no—
21#11718642—21no—
22#11718290—21no—
23#11718290—21no—
24#11718285—24no—
25C23×C4×C13C2×C411yescharacteristic
26C23×C4×C13C2×C411yescharacteristic
27C23×C4×C13C2×C411yescharacteristic
28C23×Dic13C2×C411yescharacteristic
29C23×Dic13C2×C411yescharacteristic
30C23×Dic13C2×C411yescharacteristic
31C23×Dic13C2311yescharacteristic
32C22×#1057—22no—
33C22×#1057—22no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4—22no—
37C2×C13×C4⋊C4C814yescomplemented
38C2×C4⋊Dic13—22no—
39C2×C4⋊Dic13—21no—
40C2×C4⋊Dic13—21no—
41C2×C4⋊Dic13—22no—
42C2×C4×Dic13—22no—
43C2×C4×Dic13—22no—
44C2×C4×Dic13D411yescharacteristic
45C2×C4×Dic13D411yescharacteristic
46C2×C4×Dic13D411yescharacteristic
47C2×C4×Dic13D411yescharacteristic
48C22⋊#1057—22no—
49C22⋊#1057—22no—
50C22⋊#1057—22no—
51C22⋊#1057D414yes—
52C4⋊#1057—24no—
53C4×#1057—24no—
54#88071—21no—
55#88071—21no—
56#88071—21no—
57#88071—21no—
58#88071—21no—
59#88071—21no—
60#88071—21no—
61#88071—21no—
62#9082—131nomaximal, Sylow
63C24×C13C22×C411yescharacteristic
64C22×C4×C13—22no—
65C22×C4×C13—22no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—22no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—22no—
72C22×C4×C13—41no—
73C22×C4×C13—41no—
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C2×C812yes—
77C22×C4×C13C2×C812yes—
78C22×C4×C13C2×C812yes—
79C22×C4×C13M1612yes—
80C22×Dic13—22no—
81C22×Dic13—22no—
82C22×Dic13—21no—
83C22×Dic13—21no—
84C22×Dic13—22no—
85C22×Dic13—22no—
86C22×Dic13—41no—
87C22×Dic13—41no—
88C22×Dic13—41no—
89C22×Dic13—41no—
90C22×Dic13—41no—
91C22×Dic13—41no—
92C22×Dic13—41no—
93C22×Dic13C22⋊C411yescharacteristic
94C22×Dic13C22⋊C411yescharacteristic
95C22×Dic13C2×D411yescharacteristic
96C22×Dic13C2×D411yescharacteristic
97C22×Dic13C2×D412yes—
98C22×Dic13#4112yes—
99C2×#1057—24no—
100C2×#1057—42no—
101C2×#1057—42no—
102C2×#1057—42no—
103C2×#1057—42no—
104C2×#1057—42no—
105C13×C4⋊C4—24no—
106C13×C4⋊C4—24no—
107C4⋊Dic13—41no—
108C4⋊Dic13—42no—
109C4⋊Dic13—41no—
110C4×Dic13—21no—
111C4×Dic13—21no—
112C4×Dic13—22no—
113C4×Dic13—22no—
114C4×Dic13—21no—
115C4×Dic13—21no—
116C2×#431—131no—
117C2×#387—131no—
118#1817—131no—
119C2×#324—132no—
120#1280—132no—
121C23×C13—21no—
122C23×C13—21no—
123C23×C13—21no—
124C23×C13—21no—
125C23×C13C2×C22⋊C411yescharacteristic
126C23×C13C4×D412yes—
127C23×C13C22×C811yescharacteristic
128C23×C13C2×M1611yescharacteristic
129C23×C13#13112yes—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—24no—
135C2×C4×C13—24no—
136C2×C4×C13—22no—
137C2×C4×C13—22no—
138C2×C4×C13—24no—
139C2×C4×C13—42no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—42no—
145C2×C4×C13—42no—
146C2×C4×C13C22⋊C812yes—
147C2×C4×C13C22⋊C812yes—
148C2×Dic13—21no—
149C2×Dic13—21no—
150C2×Dic13—21no—
151C2×Dic13—21no—
152C2×Dic13—21no—
153C2×Dic13—21no—
154C2×Dic13—21no—
155C2×Dic13—21no—
156C2×Dic13—21no—
157C2×Dic13—42no—
158C2×Dic13—42no—
159C2×Dic13—44no—
160C2×Dic13—41no—
161C2×Dic13—41no—
162C2×Dic13—41no—
163C2×Dic13—41no—
164C2×Dic13—41no—
165C2×Dic13—41no—
166C2×Dic13—82no—
167C2×Dic13—82no—
168C2×Dic13#10112yes—
169C2×Dic13#12011yescharacteristic
170C2×Dic13#12112yes—
171C2×Dic13#12311yescharacteristic
172#1057—44no—
173#1057—82no—
174C22×C4⋊C4—131no—
175C22×C4⋊C4#26111yescharacteristic
176C22×C42—131no—
177#431—264no—
178C2×C4⋊C8—261no—
179C2×C22⋊C8—132no—
180C2×C22⋊C8—132no—
181C2×C4×C8—261no—
182#387—261no—
183#387—261no—
184#387—261no—
185#387—261no—
186C2×#95—131no—
187C2×#95—131no—
188C2×#95—131no—
189C2×#95—131no—
190#336—261no—
191#336—261no—
192#324—264no—
193C22×C13—22no—
194C22×C13—22no—
195C22×C13—21no—
196C22×C13—21no—
197C22×C13—21no—
198C22×C13—21no—
199C22×C13—22no—
200C22×C13—22no—
201C22×C13#38611yescharacteristic
202C22×C13C2×C22⋊C811yescharacteristic
203C22×C13#40811yescharacteristic
204C22×C13#41011yescharacteristic
205C22×C13#41011yescharacteristic
206C22×C13C2×#10111yescharacteristic
207C22×C13#41311yescharacteristic
208C22×C13C8×D412yes—
209C22×C13#43512yes—
210C4×C13—22no—
211C4×C13—22no—
212C4×C13—42no—
213C4×C13—42no—
214Dic13—21no—
215Dic13—22no—
216Dic13—21no—
217Dic13—22no—
218Dic13—41no—
219Dic13—81no—
220Dic13—81no—
221C23×C4—131no—
222C23×C4—131no—
223C23×C4—131no—
224C23×C4—131no—
225C23×C4C2×#26111yescharacteristic
226C23×C4C2×#26111yescharacteristic
227C23×C4C2×#26111yescharacteristic
228C22×C8—262no—
229C22×C8—262no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—262no—
234C2×C4⋊C4—262no—
235C2×C4⋊C4—261no—
236C2×C4⋊C4—261no—
237C2×C4⋊C4#105714yescomplemented
238C2×C42—131no—
239C2×C42—131no—
240C2×C42—131no—
241C2×C42—131no—
242C2×C42—262no—
243C2×C42—262no—
244C4⋊C8—264no—
245C22⋊C8—134no—
246C22⋊C8—262no—
247C22⋊C8—262no—
248C22⋊C8—262no—
249C4×C8—264no—
250#95—261no—
251#95—261no—
252#95—261no—
253#95—261no—
254#95—261no—
255#95—261no—
256#95—261no—
257#95—261no—
258C2×C13—22no—
259C2×C13—22no—
260C2×C13#145811yescharacteristic
261C2×C13#146111yescharacteristic
262C2×C13#147011yescharacteristic
263C2×C13#147311yescharacteristic
264C2×C13#186911yescharacteristic
265C2×C13#189911yescharacteristic
266C2×C13#190111yescharacteristic
267C24C22×#26111yescharacteristic
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—131no—
279C22×C4—131no—
280C22×C4—131no—
281C22×C4—132no—
282C22×C4—132no—
283C22×C4—131no—
284C22×C4—262no—
285C22×C4—262no—
286C22×C4—261no—
287C22×C4—261no—
288C22×C4—262no—
289C22×C4—262no—
290C22×C4—521no—
291C22×C4—521no—
292C22×C4—521no—
293C22×C4—521no—
294C22×C4—521no—
295C22×C4—521no—
296C22×C4—521no—
297C22×C4C2×#105712yes—
298C22×C4C2×#105712yes—
299C22×C4C2×#105712yes—
300C22×C4#612212yes—
301C22×C4C22⋊#26111yescharacteristic
302C22×C4C22⋊#26111yescharacteristic
303C2×C8—264no—
304C2×C8—522no—
305C2×C8—522no—
306C2×C8—522no—
307C2×C8—522no—
308C2×C8—522no—
309C4⋊C4—24no—
310C4⋊C4—24no—
311C4⋊C4—521no—
312C4⋊C4—522no—
313C4⋊C4—521no—
314C42—261no—
315C42—261no—
316C42—262no—
317C42—262no—
318C42—261no—
319C42—261no—
320C13#908211yescharacteristic, complemented, Sylow
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23#8823812yes—
326C23D4×#26112yes—
327C23C22×#105711yescharacteristic
328C23C2×#612211yescharacteristic
329C23C2×C22⋊#26111yescharacteristic
330C2×C4—24no—
331C2×C4—24no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—24no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—42no—
346C2×C4—131no—
347C2×C4—132no—
348C2×C4—131no—
349C2×C4—132no—
350C2×C4—261no—
351C2×C4—261no—
352C2×C4—261no—
353C2×C4—261no—
354C2×C4—261no—
355C2×C4—261no—
356C2×C4—261no—
357C2×C4—261no—
358C2×C4—261no—
359C2×C4—522no—
360C2×C4—522no—
361C2×C4—524no—
362C2×C4—521no—
363C2×C4—521no—
364C2×C4—521no—
365C2×C4—521no—
366C2×C4—521no—
367C2×C4—521no—
368C2×C4—1042no—
369C2×C4—1042no—
370C2×C4C22⋊#105712yes—
371C2×C4C22⋊#105712yes—
372C8—524no—
373C8—1042no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—22no—
379C22—22no—
380C22—22no—
381C22—22no—
382C22#1171911611yescharacteristic
383C22#1171913211yescharacteristic
384C22D4×#105712yes—
385C22#1171914412yes—
386C22#1171914611yescharacteristic
387C22#1171915011yescharacteristic
388C22#1171915611yescharacteristic
389C22D13⋊#10111yescharacteristic
390C22C2×C22⋊#105711yescharacteristic
391C4—22no—
392C4—22no—
393C4—42no—
394C4—42no—
395C4—261no—
396C4—262no—
397C4—261no—
398C4—262no—
399C4—521no—
400C4—1041no—
401C4—1041no—
402C2—22no—
403C2—22no—
404C2#1313006711yescharacteristic
405C2#1313007911yescharacteristic
406C2#1313010811yescharacteristic
407C2#1313012011yescharacteristic
408C2#1313080911yescharacteristic
409C2#1313086011yescharacteristic
410C2#1313086411yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC23×C13C22×C8
FrattiniC24C22×#261
FittingC22×C13×C4⋊C4C4
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22×C4
cosocleC23×Dic13C23
hypercenterC22×C4⋊C4#261
hypocenterC13#9082
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
37. C2×C13×C4⋊C4C8semidirect
237. C2×C4⋊C4#1057semidirect
320. C13#9082semidirect

Maximal subgroups

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

subgroupindex
C2×#117191192
#131307262
C2×#117182852
#131296742
C2×#117186422
#908213