Finite Group Databasebeta

← #15758556

Subgroups — #15758556

Order 3328.

588 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×#11718494C211yesmaximal, characteristic
2#13123183C211yesmaximal, characteristic
3#13114813C211yesmaximal, characteristic
4C2×#11718138C211yesmaximal, characteristic, complemented
5#13112720C211yesmaximal, characteristic, complemented
6#13112720C211yesmaximal, characteristic, complemented
7C2×C13×#333C211yesmaximal, characteristic, complemented
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×#88200C412yes—
10C2×C42×D13C2211yescharacteristic
11C2×C13×C4⋊C8C2211yescharacteristic
12C2×C13×C4⋊C8C2211yescharacteristic
13#11718891C412yes—
14C2×#88060—21no—
15C2×#88060—21no—
16C2×C8×Dic13—21no—
17#11718648—21no—
18#11718648—21no—
19#11718634—21no—
20#11718634—21no—
21#11718596C2211yescharacteristic
22C2×C4⋊#1055C2211yescharacteristic
23C2×C4⋊#1055C2211yescharacteristic
24#11718494—22no—
25#11718494—22no—
26C13×#333—22no—
27#11718142—21no—
28#11718138—22no—
29C22×Q8×C13C2×C412yes—
30C22×C4×D13C2×C411yescharacteristic
31C22×C4×D13D411yescharacteristic
32C22×C4×D13D411yescharacteristic
33C22×C8×C13—21no—
34C22×C8×C13—21no—
35C13×C4⋊Q8—21no—
36C13×C4⋊Q8—21no—
37C13×C4⋊Q8—21no—
38C13×C4⋊Q8—21no—
39C2×C13×C4⋊C4—21no—
40C2×C13×C4⋊C4—21no—
41C2×C42×C13C2311yescharacteristic
42#88200—44no—
43C2×#6103—22no—
44C2×C4⋊Dic13—21no—
45C2×C4⋊Dic13—21no—
46C2×C4⋊Dic13C2×C412yes—
47C2×#6101—22no—
48C2×C4×Dic13C2×C411yescharacteristic
49C2×C4×Dic13D411yescharacteristic
50C2×C4×Dic13D411yescharacteristic
51C22×#1055—21no—
52C22×#1055—21no—
53C42×D13—21no—
54C42×D13—21no—
55C42×D13—21no—
56C42×D13—21no—
57C13×C4⋊C8—21no—
58C13×C4⋊C8—21no—
59C13×C4⋊C8—21no—
60C13×C4⋊C8D412yes—
61#88071—22no—
62#88071—22no—
63#88060—24no—
64#88060—42no—
65C8×Dic13—24no—
66C4⋊#1055—21no—
67C4⋊#1055—21no—
68C4⋊#1055—21no—
69C4⋊#1055D412yes—
70#9128—131nomaximal, Sylow
71C23×D13C22⋊C411yescharacteristic
72C2×Q8×C13—22no—
73C2×Q8×C13—22no—
74C2×Q8×C13—42no—
75C2×Q8×C13—42no—
76C22×C4×C13—22no—
77C22×C4×C13C22×C411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13C2×D411yescharacteristic
80C22×Dic13—22no—
81C22×Dic13C22⋊C411yescharacteristic
82C22×Dic13C22⋊C411yescharacteristic
83C22×Dic13C22⋊C411yescharacteristic
84C2×C4×D13—21no—
85C2×C4×D13—21no—
86C2×C4×D13—21no—
87C2×C4×D13—21no—
88C2×C4×D13—21no—
89C2×C4×D13—21no—
90C2×C4×D13—21no—
91C2×C4×D13—21no—
92C2×C4×D13—21no—
93C2×C4×D13—21no—
94C2×C4×D13—21no—
95C2×C4×D13—21no—
96C2×C4×D13—22no—
97C2×C4×D13—41no—
98C2×C4×D13SD1612yes—
99C2×C4×D13Q1612yes—
100C2×C8×C13—22no—
101C2×C8×C13—41no—
102C2×C8×C13—41no—
103C2×C8×C13—41no—
104C2×C8×C13—41no—
105C2×C8×C13—41no—
106C13×C4⋊C4—41no—
107C13×C4⋊C4—41no—
108C13×C4⋊C4—41no—
109C13×C4⋊C4—41no—
110C42×C13C2×D411yescharacteristic
111C42×C13C2×D411yescharacteristic
112C42×C13#4111yescharacteristic
113C42×C13#4111yescharacteristic
114#6103—44no—
115C4⋊Dic13—41no—
116C4⋊Dic13—41no—
117C4⋊Dic13—41no—
118C4⋊Dic13—41no—
119C4⋊Dic13—42no—
120#6101—44no—
121C4×Dic13—21no—
122C4×Dic13—21no—
123C4×Dic13—21no—
124C4×Dic13—21no—
125C4×Dic13—21no—
126C4×Dic13—21no—
127C2×#1055—22no—
128C2×#1055—41no—
129C2×#1055—41no—
130C2×#1055—41no—
131C2×#1055—41no—
132C2×#1055—41no—
133C2×#431—131no—
134#2857—131no—
135#1797—131no—
136C2×#333—131no—
137C2×#333D1311yescharacteristic, complemented
138#1296—131no—
139#1296—131no—
140C23×C13C2×C22⋊C411yescharacteristic
141C22×D13—21no—
142C22×D13—21no—
143C22×D13—21no—
144C22×D13—21no—
145C22×D13—21no—
146C22×D13—21no—
147C22×D13#10312yes—
148Q8×C13—82no—
149Q8×C13—82no—
150C2×C4×C13—21no—
151C2×C4×C13—21no—
152C2×C4×C13—42no—
153C2×C4×C13—42no—
154C2×C4×C13—42no—
155C2×C4×C13C4×D411yescharacteristic
156C2×C4×C13C4×D411yescharacteristic
157C2×C4×C13#12011yescharacteristic
158C2×C4×C13#12111yescharacteristic
159C2×C4×C13#12111yescharacteristic
160C2×C4×C13#12311yescharacteristic
161C2×C4×C13C2×SD1611yescharacteristic
162C2×C4×C13C2×Q1611yescharacteristic
163C2×C4×C13#13511yescharacteristic
164C2×C4×C13#13511yescharacteristic
165C2×C4×C13#13511yescharacteristic
166C2×C4×C13#13511yescharacteristic
167C2×C4×C13#13711yescharacteristic
168C2×C4×C13#13711yescharacteristic
169C2×Dic13—21no—
170C2×Dic13—21no—
171C2×Dic13—21no—
172C2×Dic13—21no—
173C2×Dic13—21no—
174C2×Dic13—21no—
175C2×Dic13—21no—
176C2×Dic13—42no—
177C2×Dic13—42no—
178C2×Dic13—42no—
179C2×Dic13#10012yes—
180C2×Dic13#10312yes—
181C4×D13—22no—
182C4×D13—22no—
183C4×D13—22no—
184C4×D13—22no—
185C4×D13—42no—
186C4×D13—42no—
187C4×D13—41no—
188C4×D13—41no—
189C4×D13—41no—
190C4×D13—41no—
191C8×C13—42no—
192C8×C13—81no—
193#1055—42no—
194#1055—81no—
195C2×C4⋊Q8C2×D1311yescharacteristic
196C2×C22⋊Q8—132no—
197C22×C42—131no—
198#431—262no—
199#431—262no—
200C2×C4⋊C8—131no—
201C2×C4⋊C8—131no—
202C2×C4⋊C8C2×D1311yescharacteristic
203C2×C4⋊C8C2×D1311yescharacteristic
204C2×C22⋊C8—261no—
205C2×C22⋊C8—261no—
206C2×C4×C8—261no—
207#391—132no—
208#389—261no—
209#389—261no—
210#384—131no—
211#380—261no—
212#380—261no—
213#336—261no—
214#333—22no—
215#333—262no—
216C22×C13#38611yescharacteristic
217C22×C13C2×#10011yescharacteristic
218C22×C13#41311yescharacteristic
219C22×C13C2×#10311yescharacteristic
220C22×C13#41611yescharacteristic
221C22×C13#41611yescharacteristic
222C22×C13#41911yescharacteristic
223C2×D13—22no—
224C2×D13—22no—
225C2×D13—22no—
226C2×D13—41no—
227C2×D13—41no—
228C2×D13—41no—
229C2×D13—41no—
230C4×C13—21no—
231C4×C13—21no—
232C4×C13—82no—
233C4×C13#45211yescharacteristic
234C4×C13#45211yescharacteristic
235C4×C13#46511yescharacteristic
236C4×C13#46511yescharacteristic
237C4×C13#46711yescharacteristic
238C4×C13#46711yescharacteristic
239C4×C13#48511yescharacteristic
240C4×C13#48511yescharacteristic
241Dic13—22no—
242Dic13—22no—
243Dic13—41no—
244Dic13—82no—
245C22×Q8C4×D1312yes—
246C23×C4—131no—
247C23×C4—131no—
248C23×C4—131no—
249C22×C8—21no—
250C22×C8—21no—
251C22×C8—261no—
252C22×C8—261no—
253C4⋊Q8—21no—
254C4⋊Q8—21no—
255C4⋊Q8—21no—
256C4⋊Q8—21no—
257C22⋊Q8—524no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—132no—
261C2×C4⋊C4—262no—
262C2×C4⋊C4—261no—
263C2×C4⋊C4—261no—
264C2×C22⋊C4—262no—
265C2×C42—131no—
266C2×C42—131no—
267C2×C42—131no—
268C2×C42—261no—
269C2×C42—261no—
270C2×C42—261no—
271C2×C42—261no—
272C2×C42C22×D1311yescharacteristic
273C4⋊C8—21no—
274C4⋊C8—21no—
275C4⋊C8—21no—
276C4⋊C8—132no—
277C4⋊C8—261no—
278C4⋊C8—261no—
279C4⋊C8—261no—
280C4⋊C8C22⋊D1312yes—
281C22⋊C8—264no—
282C22⋊C8—522no—
283C4×C8—264no—
284#95—262no—
285#95—262no—
286C2×C13#154211yescharacteristic
287C2×C13#154311yescharacteristic
288C2×C13#154811yescharacteristic
289C2×C13#155411yescharacteristic
290C2×C13#187311yescharacteristic
291C2×C13#189211yescharacteristic
292C2×C13#190011yescharacteristic
293D13—42no—
294C24—131no—
295C2×Q8—22no—
296C2×Q8—22no—
297C2×Q8—42no—
298C2×Q8—42no—
299C22×C4—22no—
300C22×C4—131no—
301C22×C4—131no—
302C22×C4—132no—
303C22×C4—132no—
304C22×C4—131no—
305C22×C4—262no—
306C22×C4—261no—
307C22×C4—261no—
308C22×C4—261no—
309C22×C4—261no—
310C22×C4—261no—
311C22×C4—261no—
312C22×C4—261no—
313C22×C4—261no—
314C22×C4—261no—
315C22×C4—261no—
316C22×C4—261no—
317C22×C4—261no—
318C22×C4—262no—
319C22×C4—521no—
320C22×C4C2×C4×D1311yescharacteristic
321C22×C4D4×D1311yescharacteristic
322C22×C4D4×D1311yescharacteristic
323C2×C8—22no—
324C2×C8—41no—
325C2×C8—41no—
326C2×C8—41no—
327C2×C8—41no—
328C2×C8—41no—
329C2×C8—262no—
330C2×C8—521no—
331C2×C8—521no—
332C2×C8—521no—
333C2×C8—521no—
334C2×C8—521no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4—522no—
340C4⋊C4—524no—
341C4⋊C4—521no—
342C4⋊C4—521no—
343C4⋊C4—521no—
344C4⋊C4—521no—
345C22⋊C4—524no—
346C42—261no—
347C42—261no—
348C42—261no—
349C42—261no—
350C42—261no—
351C42—261no—
352C42#612711yescharacteristic
353C42D4×D1311yescharacteristic
354C42#612911yescharacteristic
355C42C2×C22⋊D1311yescharacteristic
356C13#912811yescharacteristic, complemented, Sylow
357C23—132no—
358C23—261no—
359C23—261no—
360C23—261no—
361C23—261no—
362C23—261no—
363C23—261no—
364C23C22⋊C4×D1311yescharacteristic
365Q8—82no—
366Q8—82no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—132no—
373C2×C4—132no—
374C2×C4—261no—
375C2×C4—261no—
376C2×C4—261no—
377C2×C4—261no—
378C2×C4—262no—
379C2×C4—262no—
380C2×C4—262no—
381C2×C4—262no—
382C2×C4—261no—
383C2×C4—261no—
384C2×C4—261no—
385C2×C4—522no—
386C2×C4—522no—
387C2×C4—521no—
388C2×C4—521no—
389C2×C4—521no—
390C2×C4—521no—
391C2×C4—522no—
392C2×C4—522no—
393C2×C4—522no—
394C2×C4#8813511yescharacteristic
395C2×C4#8813711yescharacteristic
396C2×C4#8813811yescharacteristic
397C2×C4SD16×D1311yescharacteristic
398C2×C4#8816911yescharacteristic
399C2×C4#8817011yescharacteristic
400C2×C4#8817011yescharacteristic
401C2×C4Q16×D1311yescharacteristic
402C2×C4#8817211yescharacteristic
403C2×C4#8817311yescharacteristic
404C2×C4#8817311yescharacteristic
405C2×C4C4×C22⋊D1311yescharacteristic
406C2×C4#8819111yescharacteristic
407C2×C4#8819211yescharacteristic
408C8—42no—
409C8—81no—
410C8—522no—
411C8—1041no—
412C22—262no—
413C22—262no—
414C22—262no—
415C22—521no—
416C22—521no—
417C22—521no—
418C22—521no—
419C22D13×#10011yescharacteristic
420C22#1171840611yescharacteristic
421C22D13×#10311yescharacteristic
422C22#1171846311yescharacteristic
423C22#1171846511yescharacteristic
424C22#1171846511yescharacteristic
425C22#1171861711yescharacteristic
426C4—21no—
427C4—21no—
428C4—82no—
429C4—262no—
430C4—262no—
431C4—521no—
432C4—1042no—
433C4#1171846811yescharacteristic
434C4#1171847411yescharacteristic
435C4#1171847511yescharacteristic
436C4#1171847611yescharacteristic
437C4#1171883211yescharacteristic
438C4#1171883411yescharacteristic
439C4#1171884811yescharacteristic
440C4#1171884911yescharacteristic
441C2—522no—
442C2#1311349011yescharacteristic
443C2#1311349711yescharacteristic
444C2#1311351511yescharacteristic
445C2#1311354511yescharacteristic
446C2#1311514511yescharacteristic
447C2#1311525611yescharacteristic
448C2#1311529611yescharacteristic
subgroupG/H
centerC23C22⋊C4×D13
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC2×C13×#333C2
socleC23×C13C2×C22⋊C4
prime radicalC23×D13C22⋊C4
cosocleC2×C42×C13C23
hypercenterC2×#333D13
hypocenterC13#9128
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#333

Complements

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

NH ≅ G/Ntype
4. C2×#11718138C2semidirect
5. #13112720C2semidirect
6. #13112720C2semidirect
7. C2×C13×#333C2semidirect
137. C2×#333D13semidirect
356. C13#9128semidirect

Maximal subgroups

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

subgroupindex
C2×#117184942
#131231832
#131148132
C2×#117181382
#131127202
C2×C13×#3332
#912813