Finite Group Databasebeta

← #16785536

Subgroups — #16785536

Order 3328.

802 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718291C212yesmaximal
2C2×#11718291C212yesmaximal
3#13130499C212yesmaximal
4C2×#11718310C211yesmaximal, characteristic
5C22×#6122C2214yes—
6C22×#6101C2211yescharacteristic
7C22×#6101C2211yescharacteristic
8C22×C4×Dic13C411yescharacteristic
9C22×C4×Dic13C411yescharacteristic
10C22×C4×Dic13C2211yescharacteristic
11C2×C13×#95C411yescharacteristic
12C2×#88071C411yescharacteristic
13#11718310—22no—
14#11718310—22no—
15#11718291—24no—
16#11718291C418yescomplemented
17#11718290—22no—
18#11718290—22no—
19C23×C4×C13C2×C411yescharacteristic
20C23×C4×C13C2×C411yescharacteristic
21C23×C4×C13C2×C411yescharacteristic
22C23×Dic13C2×C411yescharacteristic
23C23×Dic13C2×C411yescharacteristic
24C23×Dic13C2×C411yescharacteristic
25C23×Dic13C2311yescharacteristic
26C2×#6122—24no—
27C2×#6122—24no—
28C2×#6122—24no—
29C2×#6122—24no—
30C2×#6122—24no—
31C2×#6122C2×C418yes—
32C22×#1057—24no—
33C2×#6101—22no—
34C2×#6101—22no—
35C2×#6101—22no—
36C2×#6101—22no—
37C2×#6101C2×C414yes—
38C2×#6101D412yes—
39C2×#6101Q812yes—
40C2×C4×Dic13—22no—
41C2×C4×Dic13—22no—
42C2×C4×Dic13—21no—
43C2×C4×Dic13—21no—
44C2×C4×Dic13—21no—
45C2×C4×Dic13—21no—
46C2×C4×Dic13—42no—
47C2×C4×Dic13—42no—
48C2×C4×Dic13D412yes—
49C2×C4×Dic13D412yes—
50C13×#95—22no—
51#88071—22no—
52#10802—131nomaximal, Sylow
53C24×C13C22×C411yescharacteristic
54C22×C4×C13—21no—
55C22×C4×C13—21no—
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—41no—
61C22×C4×C13—41no—
62C22×C4×C13—41no—
63C22×C4×C13—41no—
64C22×C4×C13—41no—
65C22×C4×C13—41no—
66C22×C4×C13C4212yes—
67C22×C4×C13C22⋊C412yes—
68C22×C4×C13C4⋊C412yes—
69C22×Dic13—21no—
70C22×Dic13—21no—
71C22×Dic13—22no—
72C22×Dic13—22no—
73C22×Dic13—21no—
74C22×Dic13—21no—
75C22×Dic13—21no—
76C22×Dic13—21no—
77C22×Dic13—41no—
78C22×Dic13—41no—
79C22×Dic13—41no—
80C22×Dic13—41no—
81C22×Dic13C4212yes—
82C22×Dic13C22⋊C411yescharacteristic
83C22×Dic13C22⋊C411yescharacteristic
84C22×Dic13C4⋊C412yes—
85C22×Dic13C22×C412yes—
86C22×Dic13C2×D411yescharacteristic
87C22×Dic13C2×D412yes—
88C22×Dic13C2×Q811yescharacteristic
89C22×Dic13#4112yes—
90C22×Dic13#4112yes—
91C22×Dic13#4112yes—
92C22×Dic13#4112yes—
93#6122—28no—
94#6122—28no—
95#6122—44no—
96#6122—44no—
97C2×#1057—28no—
98C2×#1057—44no—
99C2×#1057—44no—
100#6101—28no—
101#6101—24no—
102#6101—24no—
103C4×Dic13—24no—
104C4×Dic13—24no—
105C4×Dic13—42no—
106C4×Dic13—42no—
107C4×Dic13—42no—
108C4×Dic13—42no—
109C2×C4×C4⋊C4—131no—
110C2×#343—132no—
111C2×#343—132no—
112#1728—132no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—21no—
117C23×C13C2×C4211yescharacteristic
118C23×C13C2×C22⋊C411yescharacteristic
119C23×C13C2×C4⋊C411yescharacteristic
120C23×C13#11711yescharacteristic
121C23×C13#11711yescharacteristic
122C23×C13#11711yescharacteristic
123C23×C13#11711yescharacteristic
124C2×C4×C13—22no—
125C2×C4×C13—22no—
126C2×C4×C13—22no—
127C2×C4×C13—22no—
128C2×C4×C13—22no—
129C2×C4×C13—42no—
130C2×C4×C13—42no—
131C2×C4×C13—42no—
132C2×C4×C13—42no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—42no—
138C2×C4×C13—42no—
139C2×Dic13—24no—
140C2×Dic13—24no—
141C2×Dic13—21no—
142C2×Dic13—21no—
143C2×Dic13—21no—
144C2×Dic13—21no—
145C2×Dic13—22no—
146C2×Dic13—22no—
147C2×Dic13—42no—
148C2×Dic13—42no—
149C2×Dic13—41no—
150C2×Dic13—41no—
151C2×Dic13—41no—
152C2×Dic13—41no—
153C2×Dic13—42no—
154C2×Dic13—42no—
155C2×Dic13#10012yes—
156C2×Dic13#10112yes—
157C2×Dic13#11714yes—
158C2×Dic13C4×D414yes—
159C2×Dic13C4×D412yes—
160C2×Dic13C4×Q812yes—
161C2×Dic13#12112yes—
162C2×Dic13C22⋊Q812yes—
163C2×Dic13#12314yes—
164C2×Dic13#12412yes—
165C2×Dic13#12512yes—
166C2×Dic13#12614yes—
167#1057—48no—
168C22×M16—134no—
169C22×C4⋊C4—131no—
170C22×C4⋊C4—131no—
171C22×C42—131no—
172C22×C42—131no—
173C22×C42—131no—
174C4×C4⋊C4—262no—
175C4×C4⋊C4—262no—
176C2×#95—131no—
177C2×#95#26111yescharacteristic
178#343—138no—
179#343—264no—
180#336—262no—
181#336—262no—
182C22×C13—21no—
183C22×C13—21no—
184C22×C13—21no—
185C22×C13—21no—
186C22×C13—21no—
187C22×C13—21no—
188C22×C13—21no—
189C22×C13—21no—
190C22×C13—21no—
191C22×C13—21no—
192C22×C13—21no—
193C22×C13—21no—
194C22×C13#37611yescharacteristic
195C22×C13C4×C22⋊C411yescharacteristic
196C22×C13C4×C4⋊C411yescharacteristic
197C22×C13#38011yescharacteristic
198C22×C13#38111yescharacteristic
199C22×C13#38211yescharacteristic
200C22×C13#38311yescharacteristic
201C22×C13C2×#10011yescharacteristic
202C22×C13C2×#10111yescharacteristic
203C22×C13#41311yescharacteristic
204C22×C13#41311yescharacteristic
205C4×C13—42no—
206C4×C13—42no—
207C4×C13—42no—
208Dic13—22no—
209Dic13—22no—
210Dic13—42no—
211Dic13—42no—
212Dic13#38714yes—
213Dic13#38814yes—
214C23×C4—131no—
215C23×C4—131no—
216C23×C4—131no—
217C23×C4—131no—
218C23×C4C2×#26111yescharacteristic
219C23×C4C2×#26111yescharacteristic
220C23×C4C2×#26111yescharacteristic
221C2×M16—138no—
222C2×M16—264no—
223C2×M16—264no—
224C2×M16—264no—
225C2×M16—264no—
226C2×M16—264no—
227C22×C8—264no—
228C2×C4⋊C4—134no—
229C2×C4⋊C4—132no—
230C2×C4⋊C4—132no—
231C2×C4⋊C4—262no—
232C2×C4⋊C4—262no—
233C2×C4⋊C4—262no—
234C2×C4⋊C4—262no—
235C2×C42—132no—
236C2×C42—132no—
237C2×C42—262no—
238C2×C42—262no—
239C2×C42—261no—
240C2×C42—261no—
241C2×C42—261no—
242C2×C42—261no—
243C2×C42—522no—
244C2×C42—522no—
245#95—22no—
246#95—262no—
247C2×C13—21no—
248C2×C13—21no—
249C2×C13—21no—
250C2×C13—21no—
251C2×C13#143411yescharacteristic
252C2×C13C4×#10011yescharacteristic
253C2×C13C4×#10111yescharacteristic
254C2×C13#180011yescharacteristic
255C2×C13#180111yescharacteristic
256C2×C13#182111yescharacteristic
257C2×C13#182211yescharacteristic
258C24C22×#26111yescharacteristic
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4—132no—
272C22×C4—131no—
273C22×C4—131no—
274C22×C4—132no—
275C22×C4—132no—
276C22×C4—132no—
277C22×C4—132no—
278C22×C4—132no—
279C22×C4—131no—
280C22×C4—131no—
281C22×C4—132no—
282C22×C4—132no—
283C22×C4—262no—
284C22×C4—262no—
285C22×C4—261no—
286C22×C4—261no—
287C22×C4—261no—
288C22×C4—261no—
289C22×C4—261no—
290C22×C4—261no—
291C22×C4—521no—
292C22×C4—521no—
293C22×C4—521no—
294C22×C4—521no—
295C22×C4C4×#26112yes—
296C22×C4C4⋊#26112yes—
297C22×C4C22⋊#26112yes—
298M16—268no—
299M16—268no—
300M16—524no—
301M16—524no—
302C2×C8—268no—
303C2×C8—524no—
304C2×C8—524no—
305C4⋊C4—268no—
306C4⋊C4—264no—
307C4⋊C4—264no—
308C42—264no—
309C42—264no—
310C42—522no—
311C42—522no—
312C42—522no—
313C42—522no—
314C13#1080211yescharacteristic, complemented, Sylow
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23C2×C4×#26111yescharacteristic
320C23C2×C4⋊#26111yescharacteristic
321C23#8823711yescharacteristic
322C23#8823711yescharacteristic
323C23#8823711yescharacteristic
324C23#8823711yescharacteristic
325C23C2×C22⋊#26111yescharacteristic
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—134no—
342C2×C4—132no—
343C2×C4—132no—
344C2×C4—132no—
345C2×C4—132no—
346C2×C4—134no—
347C2×C4—134no—
348C2×C4—134no—
349C2×C4—132no—
350C2×C4—132no—
351C2×C4—132no—
352C2×C4—132no—
353C2×C4—264no—
354C2×C4—264no—
355C2×C4—261no—
356C2×C4—261no—
357C2×C4—261no—
358C2×C4—261no—
359C2×C4—262no—
360C2×C4—262no—
361C2×C4—522no—
362C2×C4—522no—
363C2×C4—521no—
364C2×C4—521no—
365C2×C4—521no—
366C2×C4—521no—
367C2×C4—522no—
368C2×C4—522no—
369C8—528no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22#1171905711yescharacteristic
383C22C4×C4⋊#26111yescharacteristic
384C22#1171906011yescharacteristic
385C22#1171906111yescharacteristic
386C22C4×C22⋊#26111yescharacteristic
387C22#1171913511yescharacteristic
388C22#1171913611yescharacteristic
389C22#1171914811yescharacteristic
390C22#1171914811yescharacteristic
391C22D13⋊#10011yescharacteristic
392C22D13⋊#10111yescharacteristic
393C4—42no—
394C4—42no—
395C4—42no—
396C4—134no—
397C4—134no—
398C4—262no—
399C4—262no—
400C4—522no—
401C4—522no—
402C2—21no—
403C2—21no—
404C2—21no—
405C2—21no—
406C2#1313001211yescharacteristic
407C2#1313058611yescharacteristic
408C2#1313058911yescharacteristic
409C2#1313070111yescharacteristic
410C2#1313070311yescharacteristic
411C2#1313073611yescharacteristic
412C2#1313073811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC23×C13C2×C42
FrattiniC24C22×#261
FittingC2×C13×#95C4
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22×C4
cosocleC23×Dic13C23
hypercenterC2×#95#261
hypocenterC13#10802
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
16. #11718291C4semidirect
314. C13#10802semidirect

Maximal subgroups

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

subgroupindex
C2×#117182912
#131304992
C2×#117183102
#1080213