Finite Group Databasebeta

← #15766299

Subgroups — #15766299

Order 3328.

572 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13119835C211yesmaximal, characteristic
2#13115642C211yesmaximal, characteristic
3#13115595C211yesmaximal, characteristic, complemented
4#13114841C211yesmaximal, characteristic, complemented
5C2×#11718077C211yesmaximal, characteristic
6#13112676C211yesmaximal, characteristic, complemented
7C2×C13×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×C4×Q8×C13C2211yescharacteristic
9C2×#88201—21no—
10C2×#88128C2211yescharacteristic
11C2×C13×C4⋊C8C2211yescharacteristic
12C2×C4×C8×C13C2211yescharacteristic
13C2×#88075—21no—
14C2×#88061—22no—
15C2×#88058—21no—
16#11718652—22no—
17#11718649—21no—
18#11718600—21no—
19#11718600—21no—
20#11718596C2211yescharacteristic
21C4×C4⋊Dic13C2211yescharacteristic
22C2×C4⋊#1055C2211yescharacteristic
23C13×Q8⋊C8—22no—
24#11718143—21no—
25#11718121—21no—
26#11718077—22no—
27C22×Q8×C13D411yescharacteristic
28C22×D52—21no—
29C22×D52—21no—
30C22×D52D412yes—
31C22×C8×C13—21no—
32C22×C8×C13—21no—
33C4×Q8×C13—21no—
34C4×Q8×C13—21no—
35C4×Q8×C13—21no—
36C4×Q8×C13—21no—
37C2×C13×C4⋊C4—21no—
38C2×C13×C4⋊C4D411yescharacteristic
39C2×C42×C13—21no—
40C2×C42×C13C2311yescharacteristic
41#88201—42no—
42#88201—42no—
43C2×#6103—22no—
44C2×#6103—22no—
45C2×#6103—22no—
46C2×#6103—22no—
47C2×C4⋊Dic13—21no—
48C2×C4⋊Dic13—21no—
49C2×C4⋊Dic13—21no—
50C2×C4⋊Dic13D411yescharacteristic
51C2×C4⋊Dic13D411yescharacteristic
52C2×C4×Dic13—21no—
53C22×#1055—21no—
54#88128—21no—
55#88128—21no—
56#88128—21no—
57#88128—21no—
58C13×C4⋊C8—21no—
59C13×C4⋊C8D412yes—
60C4×C8×C13—21no—
61C4×C8×C13—21no—
62#88075—42no—
63#88071—21no—
64#88061—44no—
65#88058—42no—
66C4⋊#1055—21no—
67C4⋊#1055—21no—
68#10411—131nomaximal, Sylow
69C23×D13—22no—
70C2×Q8×C13—21no—
71C2×Q8×C13—21no—
72C2×Q8×C13—21no—
73C2×Q8×C13—21no—
74C2×Q8×C13—21no—
75C2×Q8×C13D812yes—
76C22×C4×C13—21no—
77C22×C4×C13—21no—
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13C2×D411yescharacteristic
80C22×C4×C13C2×D411yescharacteristic
81C22×Dic13—21no—
82C22×Dic13—21no—
83C22×Dic13—41no—
84C2×D52—22no—
85C2×D52—22no—
86C2×D52—42no—
87C2×D52—42no—
88C2×D52—41no—
89C2×D52—41no—
90C2×D52—41no—
91C2×D52—41no—
92C2×D52—41no—
93C2×D52—41no—
94C2×D52—41no—
95C2×D52—41no—
96C2×D52—41no—
97C2×D52—41no—
98C2×D52—41no—
99C2×D52—41no—
100C2×C8×C13—22no—
101C2×C8×C13—22no—
102C2×C8×C13—41no—
103C2×C8×C13—41no—
104C2×C8×C13—41no—
105C2×C8×C13—41no—
106C13×C4⋊C4—21no—
107C13×C4⋊C4—21no—
108C13×C4⋊C4—41no—
109C13×C4⋊C4—41no—
110C42×C13—41no—
111C42×C13—41no—
112C42×C13C2×D411yescharacteristic
113C42×C13#4111yescharacteristic
114C42×C13#4111yescharacteristic
115C42×C13#4111yescharacteristic
116#6103—44no—
117#6103—44no—
118#6103—82no—
119#6103—82no—
120C4⋊Dic13—21no—
121C4⋊Dic13—21no—
122C4⋊Dic13—21no—
123C4⋊Dic13—21no—
124C4⋊Dic13—42no—
125C4⋊Dic13—41no—
126C4⋊Dic13—41no—
127C4⋊Dic13—41no—
128C4⋊Dic13—41no—
129C4×Dic13—41no—
130C4×Dic13—41no—
131C2×#1055—41no—
132C2×#1055—41no—
133C2×#1055—41no—
134#2548—131no—
135#1957—131no—
136#1947—131no—
137#1803—131no—
138C2×#331—131no—
139C2×Q8⋊C8D1311yescharacteristic, complemented
140#1279—131no—
141C23×C13#12011yescharacteristic
142C22×D13—42no—
143C22×D13—42no—
144C22×D13—42no—
145C22×D13—42no—
146C22×D13—42no—
147C22×D13—42no—
148C22×D13—42no—
149Q8×C13—22no—
150Q8×C13—22no—
151Q8×C13—41no—
152Q8×C13—41no—
153C2×C4×C13—21no—
154C2×C4×C13—21no—
155C2×C4×C13—22no—
156C2×C4×C13—41no—
157C2×C4×C13—41no—
158C2×C4×C13—41no—
159C2×C4×C13—41no—
160C2×C4×C13—41no—
161C2×C4×C13#12111yescharacteristic
162C2×C4×C13#12111yescharacteristic
163C2×C4×C13#12111yescharacteristic
164C2×C4×C13#12311yescharacteristic
165C2×C4×C13#12311yescharacteristic
166C2×C4×C13#12411yescharacteristic
167C2×C4×C13C2×D811yescharacteristic
168C2×C4×C13#13511yescharacteristic
169C2×C4×C13#13511yescharacteristic
170C2×C4×C13#13511yescharacteristic
171C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C13#13711yescharacteristic
174C2×C4×C13#13711yescharacteristic
175C2×Dic13—41no—
176C2×Dic13—41no—
177C2×Dic13—41no—
178C2×Dic13—41no—
179C2×Dic13—41no—
180C2×Dic13—41no—
181C2×Dic13—81no—
182C2×Dic13—81no—
183C2×Dic13—81no—
184D52—44no—
185D52—82no—
186D52—81no—
187D52—81no—
188D52—81no—
189D52—81no—
190D52—81no—
191D52—81no—
192D52—81no—
193D52—81no—
194C8×C13—42no—
195C8×C13—42no—
196#1055—81no—
197C2×#127—131no—
198C2×#124—261no—
199C2×C4×Q8C2×D1311yescharacteristic
200C2×#107—261no—
201C2×C4⋊C8—131no—
202C2×C4⋊C8C2×D1311yescharacteristic
203C2×#103—261no—
204C2×#102—262no—
205C2×C4×C8C2×D1311yescharacteristic
206#394—262no—
207#390—261no—
208#390—261no—
209#390—261no—
210#384—131no—
211C4×C4⋊C4—131no—
212#340—261no—
213#340—261no—
214#331—262no—
215Q8⋊C8—22no—
216C22×C13#39411yescharacteristic
217C22×C13#44711yescharacteristic
218C22×C13#44911yescharacteristic
219C22×C13#45211yescharacteristic
220C22×C13#45211yescharacteristic
221C22×C13#45311yescharacteristic
222C22×C13#45511yescharacteristic
223C2×D13—82no—
224C2×D13—82no—
225C2×D13—82no—
226C2×D13—82no—
227C2×D13—82no—
228C2×D13—82no—
229C2×D13—82no—
230C4×C13—21no—
231C4×C13—21no—
232C4×C13—42no—
233C4×C13—81no—
234C4×C13#46311yescharacteristic
235C4×C13#46411yescharacteristic
236C4×C13#46611yescharacteristic
237C4×C13#46811yescharacteristic
238C4×C13#48011yescharacteristic
239C4×C13#48211yescharacteristic
240C4×C13#48811yescharacteristic
241C4×C13#48911yescharacteristic
242Dic13—81no—
243Dic13—81no—
244Dic13—161no—
245C22×Q8D5211yescharacteristic
246C22×D4—132no—
247C22×D4—261no—
248C22×D4—261no—
249C22×C8—21no—
250C22×C8—21no—
251C22×C8—261no—
252#127—261no—
253#127—261no—
254#127—261no—
255#127—261no—
256#124—522no—
257#124—522no—
258C4×Q8—21no—
259C4×Q8—21no—
260C4×Q8—21no—
261C4×Q8—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—131no—
264C2×C4⋊C4—131no—
265C2×C4⋊C4—261no—
266C2×C4⋊C4—261no—
267C2×C4⋊C4—261no—
268C2×C4⋊C4D5211yescharacteristic
269C2×C22⋊C4—262no—
270C2×C22⋊C4—262no—
271C2×C22⋊C4—262no—
272C2×C22⋊C4—262no—
273C2×C42—21no—
274C2×C42—261no—
275C2×C42C22×D1311yescharacteristic
276#107—522no—
277C4⋊C8—21no—
278C4⋊C8—261no—
279C4⋊C8—261no—
280C4⋊C8C22⋊D1312yes—
281#103—522no—
282#102—524no—
283C4×C8—21no—
284C4×C8—21no—
285#95—261no—
286C2×C13#162111yescharacteristic
287C2×C13#163011yescharacteristic
288C2×C13#164011yescharacteristic
289C2×C13#164111yescharacteristic
290C2×C13#203311yescharacteristic
291C2×C13#203711yescharacteristic
292C2×C13#204211yescharacteristic
293D13—162no—
294C24—262no—
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8—21no—
298C2×Q8—21no—
299C2×Q8—21no—
300C2×Q8D10412yes—
301C2×D4—262no—
302C2×D4—262no—
303C2×D4—522no—
304C2×D4—522no—
305C2×D4—521no—
306C2×D4—521no—
307C2×D4—521no—
308C2×D4—521no—
309C2×D4—521no—
310C2×D4—521no—
311C2×D4—521no—
312C2×D4—521no—
313C2×D4—521no—
314C2×D4—521no—
315C2×D4—521no—
316C2×D4—521no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—261no—
320C22×C4—261no—
321C22×C4—521no—
322C22×C4C2×D5211yescharacteristic
323C22×C4D4×D1311yescharacteristic
324C22×C4D4×D1311yescharacteristic
325C2×C8—22no—
326C2×C8—22no—
327C2×C8—41no—
328C2×C8—41no—
329C2×C8—41no—
330C2×C8—41no—
331C2×C8—521no—
332C2×C8—521no—
333C2×C8—521no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—261no—
339C4⋊C4—261no—
340C4⋊C4—261no—
341C4⋊C4—261no—
342C4⋊C4—522no—
343C4⋊C4—521no—
344C4⋊C4—521no—
345C4⋊C4—521no—
346C4⋊C4—521no—
347C22⋊C4—524no—
348C22⋊C4—524no—
349C22⋊C4—1042no—
350C22⋊C4—1042no—
351C42—41no—
352C42—41no—
353C42—521no—
354C42—521no—
355C42#612711yescharacteristic
356C42#612911yescharacteristic
357C42#612911yescharacteristic
358C42C2×C22⋊D1311yescharacteristic
359C13#1041111yescharacteristic, complemented, Sylow
360C23—522no—
361C23—522no—
362C23—522no—
363C23—522no—
364C23—522no—
365C23—522no—
366C23—522no—
367C23#8813611yescharacteristic
368Q8—22no—
369Q8—22no—
370Q8—41no—
371Q8—41no—
372D4—524no—
373D4—1042no—
374D4—1041no—
375D4—1041no—
376D4—1041no—
377D4—1041no—
378D4—1041no—
379D4—1041no—
380D4—1041no—
381D4—1041no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—22no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—521no—
391C2×C4—521no—
392C2×C4—521no—
393C2×C4—521no—
394C2×C4—521no—
395C2×C4—521no—
396C2×C4—1041no—
397C2×C4—1041no—
398C2×C4—1041no—
399C2×C4#8813711yescharacteristic
400C2×C4#8813911yescharacteristic
401C2×C4#8814011yescharacteristic
402C2×C4C2×D10411yescharacteristic
403C2×C4#8815811yescharacteristic
404C2×C4#8816211yescharacteristic
405C2×C4#8816311yescharacteristic
406C2×C4#8816811yescharacteristic
407C2×C4#8817011yescharacteristic
408C2×C4#8817211yescharacteristic
409C2×C4#8817311yescharacteristic
410C2×C4#8818411yescharacteristic
411C2×C4#8819211yescharacteristic
412C2×C4#8819311yescharacteristic
413C8—42no—
414C8—42no—
415C8—1041no—
416C22—1042no—
417C22—1042no—
418C22—1042no—
419C22—1042no—
420C22—1042no—
421C22—1042no—
422C22—1042no—
423C22#1171839311yescharacteristic
424C22#1171839411yescharacteristic
425C22#1171847111yescharacteristic
426C22#1171847211yescharacteristic
427C22#1171848311yescharacteristic
428C22#1171848611yescharacteristic
429C22#1171862211yescharacteristic
430C4—21no—
431C4—21no—
432C4—42no—
433C4—81no—
434C4—1041no—
435C4—1041no—
436C4—2081no—
437C4#1171839711yescharacteristic
438C4#1171839811yescharacteristic
439C4#1171845611yescharacteristic
440C4#1171846111yescharacteristic
441C4#1171877611yescharacteristic
442C4#1171879511yescharacteristic
443C4#1171882611yescharacteristic
444C4#1171884611yescharacteristic
445C2—2082no—
446C2#1311390311yescharacteristic
447C2#1311395911yescharacteristic
448C2#1311402511yescharacteristic
449C2#1311403111yescharacteristic
450C2#1311601911yescharacteristic
451C2#1311604511yescharacteristic
452C2#1311607411yescharacteristic
subgroupG/H
centerC23#88136
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC2×C13×Q8⋊C8C2
socleC23×C13#120
prime radicalC2×#88128C22
hypercenterC2×Q8⋊C8D13
hypocenterC13#10411
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
3. #13115595C2semidirect
4. #13114841C2semidirect
6. #13112676C2semidirect
7. C2×C13×Q8⋊C8C2semidirect
139. C2×Q8⋊C8D13semidirect
359. C13#10411semidirect

Maximal subgroups

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

subgroupindex
#131198352
#131156422
#131155952
#131148412
C2×#117180772
#131126762
C2×C13×Q8⋊C82
#1041113