Finite Group Databasebeta

← #16795401

Subgroups — #16795401

Order 3328.

660 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131755C211yesmaximal, characteristic, complemented
2#13131751C211yesmaximal, characteristic, complemented
3#13130461C212yesmaximal, complemented
4#13130457C212yesmaximal, complemented
5#13130445C212yesmaximal, complemented
6#13130441C212yesmaximal, complemented
7C2×#11718255C211yesmaximal, characteristic, complemented
8#13130131C211yesmaximal, characteristic, complemented
9#13130131C211yesmaximal, characteristic, complemented
10#13130049C211yesmaximal, characteristic, complemented
11#135×Dic13C211yesmaximal, characteristic
12C2×C13×#135C411yescharacteristic
13#41×Dic13C2211yescharacteristic
14#41×Dic13C2211yescharacteristic
15#11719158C2212yes—
16Q8×#1057C2212yes—
17#11719145C2212yes—
18#11719144—22no—
19D4×#1057—22no—
20D4×#1057C2212yes—
21#11719130—21no—
22#11719129—21no—
23#11719119—21no—
24#11719119C2211yescharacteristic
25#11719119C2211yescharacteristic
26C2×C4⋊#1057—21no—
27C2×C4⋊#1057C2211yescharacteristic
28C2×C4⋊#1057C2211yescharacteristic
29#11718894C411yescharacteristic
30#11718894C411yescharacteristic
31Q16×Dic13C411yescharacteristic
32Q16×Dic13C2211yescharacteristic
33SD16×Dic13C411yescharacteristic
34SD16×Dic13C411yescharacteristic
35SD16×Dic13C2211yescharacteristic
36SD16×Dic13C2211yescharacteristic
37D8×Dic13C411yescharacteristic
38D8×Dic13C2211yescharacteristic
39#11718767C411yescharacteristic
40C2×C8×Dic13C2211yescharacteristic
41Q8⋊#1057C2212yes—
42Q8⋊#1057C2212yes—
43D4⋊#1057C2212yes—
44D4⋊#1057C2212yes—
45#11718255C2212yes—
46#11718255C2212yes—
47#1057⋊C8C2212yes—
48#1057⋊C8C2212yes—
49C2×C13×#41C2×C411yescharacteristic
50C2×C13×#41C2×C411yescharacteristic
51C2×#6122—22no—
52C22×#1057—21no—
53C22×#1057—21no—
54C22×#1057—22no—
55C13×#135—24no—
56C2×C13×Q16C2×C411yescharacteristic
57C2×C13×SD16C2×C411yescharacteristic
58C2×C13×SD16C2×C411yescharacteristic
59C2×C13×D8C2×C411yescharacteristic
60C22×C8×C13C2×C411yescharacteristic
61Q8×Dic13C2×C411yescharacteristic
62Q8×Dic13C2×C411yescharacteristic
63Q8×Dic13C2311yescharacteristic
64Q8×Dic13C2311yescharacteristic
65D4×Dic13—21no—
66D4×Dic13—21no—
67D4×Dic13—21no—
68D4×Dic13—21no—
69D4×Dic13C2×C411yescharacteristic
70D4×Dic13C2×C411yescharacteristic
71D4×Dic13C2311yescharacteristic
72D4×Dic13C2311yescharacteristic
73#88180—21no—
74#88180—21no—
75#88180C2×C411yescharacteristic
76#88180C2×C411yescharacteristic
77C2×C4×Dic13—21no—
78C2×C4×Dic13—21no—
79C2×C4×Dic13C2311yescharacteristic
80C22×#1055C2×C411yescharacteristic
81C22⋊#1057—21no—
82C22⋊#1057—22no—
83C22⋊#1057—22no—
84C22⋊#1057D412yes—
85#88112—22no—
86#88110—22no—
87C4⋊#1057—22no—
88C4⋊#1057—21no—
89C4⋊#1057—21no—
90C4⋊#1057—21no—
91C4⋊#1057D411yescharacteristic
92C4⋊#1057D411yescharacteristic
93C4⋊#1057C2312yes—
94C4⋊#1057C2312yes—
95C4×#1057—22no—
96C4×#1057C2312yes—
97C4×#1057C2312yes—
98#88075C2×C411yescharacteristic
99#88075C2×C411yescharacteristic
100#88075C2×C411yescharacteristic
101#88075C2×C411yescharacteristic
102#88072C2×C411yescharacteristic
103#88072C2×C411yescharacteristic
104#88072C2×C411yescharacteristic
105#88072C2×C411yescharacteristic
106#88058C2×C411yescharacteristic
107#88058C2×C411yescharacteristic
108#88057C2×C411yescharacteristic
109#88057C2×C411yescharacteristic
110C8×Dic13C2×C411yescharacteristic
111C8×Dic13C2×C411yescharacteristic
112C8×Dic13C2311yescharacteristic
113C8×Dic13C2311yescharacteristic
114#17882—131nomaximal, Sylow
115C13×#41—22no—
116C13×#41—22no—
117C13×#41—22no—
118C13×#41M1614yescomplemented
119C2×Q8×C13C22×C411yescharacteristic
120C2×Q8×C13C22×C411yescharacteristic
121C2×D4×C13—21no—
122C2×D4×C13—21no—
123C2×D4×C13C22×C411yescharacteristic
124C2×D4×C13C22×C411yescharacteristic
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13C22×C411yescharacteristic
128C22×Dic13—21no—
129C22×Dic13—21no—
130C22×Dic13—21no—
131C22×Dic13—21no—
132C22×Dic13C2×D411yescharacteristic
133C22×Dic13#4111yescharacteristic
134#6122—82no—
135C2×#1057—22no—
136C2×#1057—22no—
137C2×#1057—22no—
138C2×#1057—82no—
139C2×#1057—81no—
140C2×#1057—81no—
141C2×#1057C2×D412yes—
142C2×#1057C2×D412yes—
143C13×Q16—22no—
144C13×SD16—22no—
145C13×SD16—22no—
146C13×D8—22no—
147C2×C8×C13—22no—
148C2×C8×C13C22×C411yescharacteristic
149C2×C8×C13C22×C411yescharacteristic
150C22⋊Dic13—21no—
151C22⋊Dic13—21no—
152C22⋊Dic13—21no—
153C22⋊Dic13—21no—
154C22⋊Dic13—21no—
155C22⋊Dic13—21no—
156C4⋊Dic13—21no—
157C4⋊Dic13—21no—
158C4⋊Dic13—21no—
159C4⋊Dic13—21no—
160C4⋊Dic13C22×C411yescharacteristic
161C4⋊Dic13C22×C411yescharacteristic
162C4⋊Dic13C22×C411yescharacteristic
163C4⋊Dic13C22×C411yescharacteristic
164C4×Dic13—21no—
165C4×Dic13—21no—
166C4×Dic13—21no—
167C4×Dic13—21no—
168C4×Dic13—21no—
169C4×Dic13—21no—
170C4×Dic13C22×C411yescharacteristic
171C4×Dic13C2×D411yescharacteristic
172C4×Dic13#4111yescharacteristic
173C4×Dic13C2411yescharacteristic
174C2×#1055—22no—
175C2×#1055C22×C411yescharacteristic
176C2×#1055C22×C411yescharacteristic
177#2989—131no—
178#2988—131no—
179C4×#135—131no—
180#1587—132no—
181#1586—132no—
182#1583—132no—
183#1582—132no—
184C2×#334—131no—
185#1477—131no—
186#1477—131no—
187#1452—131no—
188C23×C13—21no—
189C23×C13—21no—
190C23×C13C4×D411yescharacteristic
191Q8×C13—21no—
192Q8×C13—21no—
193Q8×C13—21no—
194Q8×C13C2×M1612yes—
195D4×C13—24no—
196D4×C13—21no—
197D4×C13—21no—
198D4×C13—21no—
199D4×C13—42no—
200D4×C13C2×M1612yes—
201C2×C4×C13—21no—
202C2×C4×C13—24no—
203C2×C4×C13—21no—
204C2×C4×C13—42no—
205C2×C4×C13C4×D411yescharacteristic
206C2×C4×C13C2×M1612yes—
207C2×C4×C13#13112yes—
208C2×C4×C13C23×C411yescharacteristic
209C2×Dic13—21no—
210C2×Dic13—21no—
211C2×Dic13—21no—
212C2×Dic13—21no—
213C2×Dic13—21no—
214C2×Dic13—21no—
215C2×Dic13—41no—
216C2×Dic13—41no—
217C2×Dic13—41no—
218C2×Dic13—41no—
219C2×Dic13—41no—
220C2×Dic13—81no—
221C2×Dic13—81no—
222C2×Dic13C4×D411yescharacteristic
223C2×Dic13C4×D411yescharacteristic
224C2×Dic13C22×D411yescharacteristic
225C2×Dic13C2×#4111yescharacteristic
226#1057—22no—
227#1057—22no—
228#1057—42no—
229#1057—42no—
230#1057—42no—
231C8×C13—21no—
232C8×C13—21no—
233#1055—21no—
234#1055—21no—
235C2×#135#26111yescharacteristic
236C4×#41—131no—
237C4×#41—131no—
238#446—132no—
239C8×Q8—132no—
240C4×Q16—131no—
241C4×Q16—131no—
242C4×SD16—131no—
243C4×SD16—131no—
244C4×SD16—131no—
245C4×SD16—131no—
246C4×D8—131no—
247C4×D8—131no—
248#436—132no—
249#435—262no—
250C8×D4—132no—
251C8×D4—262no—
252#432—261no—
253#431—131no—
254#431—131no—
255#431—261no—
256#427—131no—
257#423—261no—
258C2×C4⋊C8—131no—
259C2×C4⋊C8—131no—
260C2×C4⋊C8—261no—
261#416—131no—
262#416—131no—
263C2×C4×C8—131no—
264#334—132no—
265#334—132no—
266Q8⋊C8—132no—
267Q8⋊C8—132no—
268D4⋊C8—132no—
269D4⋊C8—132no—
270#322—132no—
271#322—132no—
272C22×C13—21no—
273C22×C13—21no—
274C22×C13—22no—
275C22×C13—41no—
276C22×C13—41no—
277C22×C13—41no—
278C22×C13—41no—
279C22×C13—41no—
280C22×C13#43512yes—
281C22×C13C2×C4×D411yescharacteristic
282C4×C13—22no—
283C4×C13—41no—
284C4×C13#43512yes—
285C4×C13C22×M1611yescharacteristic
286C4×C13C2×#13111yescharacteristic
287Dic13—21no—
288Dic13—21no—
289Dic13—21no—
290Dic13—41no—
291Dic13—41no—
292Dic13—41no—
293Dic13—41no—
294Dic13#57711yescharacteristic
295Dic13#57711yescharacteristic
296C2×#41C2×#26111yescharacteristic
297C2×#41C2×#26111yescharacteristic
298#135—24no—
299C2×Q16C2×#26111yescharacteristic
300C2×SD16C2×#26111yescharacteristic
301C2×SD16C2×#26111yescharacteristic
302C2×D8C2×#26111yescharacteristic
303C2×M16—262no—
304C22×C8—131no—
305C22×C8—262no—
306C22×C8—261no—
307C22×C8—261no—
308C22×C8C2×#26111yescharacteristic
309C4×Q8—131no—
310C4×Q8—131no—
311C4×Q8—131no—
312C4×Q8—131no—
313C4×D4—131no—
314C4×D4—131no—
315C4×D4—131no—
316C4×D4—131no—
317C4×D4—261no—
318C4×D4—261no—
319C4×D4—261no—
320C4×D4—261no—
321#117—131no—
322#117—131no—
323#117—261no—
324#117—261no—
325C2×C42—131no—
326C2×C42—261no—
327C2×C42—261no—
328#107—131no—
329#107—131no—
330#106—131no—
331#106—131no—
332C4⋊C8—131no—
333C4⋊C8—131no—
334C4⋊C8—132no—
335C4⋊C8—132no—
336C4⋊C8—261no—
337C4⋊C8—261no—
338C4⋊C8—261no—
339C4⋊C8—262no—
340C4⋊C8—262no—
341#103—131no—
342#103—131no—
343#103—131no—
344#103—131no—
345#102—131no—
346#102—131no—
347#102—131no—
348#102—131no—
349C22⋊C8—132no—
350C22⋊C8—262no—
351C22⋊C8—262no—
352C22⋊C8—261no—
353#97—262no—
354C4×C8—132no—
355C4×C8—131no—
356C4×C8—131no—
357C4×C8—131no—
358C4×C8—131no—
359C4×C8—132no—
360C4×C8—262no—
361C2×C13—22no—
362C2×C13—42no—
363C2×C13—81no—
364C2×C13C2×#43511yescharacteristic
365C2×C13#295211yescharacteristic
366C2×C13#295711yescharacteristic
367#41—22no—
368#41—22no—
369#41—22no—
370#41#612214yescomplemented
371C2×Q8C22×#26111yescharacteristic
372C2×Q8C22×#26111yescharacteristic
373C2×D4—21no—
374C2×D4—21no—
375C2×D4C22×#26111yescharacteristic
376C2×D4C22×#26111yescharacteristic
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—131no—
380C22×C4—131no—
381C22×C4—261no—
382C22×C4—261no—
383C22×C4—261no—
384C22×C4—261no—
385C22×C4C22×#26111yescharacteristic
386Q16—22no—
387SD16—22no—
388SD16—22no—
389D8—22no—
390M16—1042no—
391C2×C8—22no—
392C2×C8—132no—
393C2×C8—132no—
394C2×C8—131no—
395C2×C8—131no—
396C2×C8—262no—
397C2×C8—262no—
398C2×C8—262no—
399C2×C8—262no—
400C2×C8—1042no—
401C2×C8—1041no—
402C2×C8—1041no—
403C2×C8C22×#26111yescharacteristic
404C2×C8C22×#26111yescharacteristic
405C4⋊C4—131no—
406C4⋊C4—131no—
407C4⋊C4—131no—
408C4⋊C4—131no—
409C4⋊C4—261no—
410C4⋊C4—261no—
411C4⋊C4—261no—
412C4⋊C4—261no—
413C22⋊C4—261no—
414C22⋊C4—261no—
415C22⋊C4—261no—
416C22⋊C4—261no—
417C22⋊C4—261no—
418C22⋊C4—261no—
419C42—131no—
420C42—131no—
421C42—131no—
422C42—131no—
423C42—261no—
424C42—261no—
425C42—261no—
426C42—261no—
427C42—261no—
428C42—261no—
429C13#1788211yescharacteristic, complemented, Sylow
430C23—21no—
431C23—21no—
432C23D4×#26111yescharacteristic
433Q8—21no—
434Q8—21no—
435Q8—21no—
436Q8C2×#612212yes—
437D4—24no—
438D4—21no—
439D4—21no—
440D4—21no—
441D4—42no—
442D4C2×#612212yes—
443C2×C4—21no—
444C2×C4—24no—
445C2×C4—21no—
446C2×C4—42no—
447C2×C4—131no—
448C2×C4—131no—
449C2×C4—131no—
450C2×C4—131no—
451C2×C4—261no—
452C2×C4—261no—
453C2×C4—261no—
454C2×C4—261no—
455C2×C4—261no—
456C2×C4—261no—
457C2×C4—521no—
458C2×C4—521no—
459C2×C4—521no—
460C2×C4—521no—
461C2×C4—521no—
462C2×C4—1041no—
463C2×C4—1041no—
464C2×C4#8823812yes—
465C2×C4D4×#26111yescharacteristic
466C2×C4C2×#612212yes—
467C2×C4C23×#26111yescharacteristic
468C8—21no—
469C8—21no—
470C8—262no—
471C8—262no—
472C8—261no—
473C8—261no—
474C8—522no—
475C8—522no—
476C8—522no—
477C22—21no—
478C22—21no—
479C22—22no—
480C22—41no—
481C22—41no—
482C22—41no—
483C22—41no—
484C22—41no—
485C22#1171914412yes—
486C22C2×D4×#26111yescharacteristic
487C4—22no—
488C4—41no—
489C4—131no—
490C4—131no—
491C4—261no—
492C4—261no—
493C4—261no—
494C4—521no—
495C4—521no—
496C4—521no—
497C4—521no—
498C4#1171914412yes—
499C4C2×#8823811yescharacteristic
500C4C22×#612211yescharacteristic
501C2—22no—
502C2—42no—
503C2—81no—
504C2C2×#1171914411yescharacteristic
505C2#1313159911yescharacteristic
506C2#1313161311yescharacteristic
subgroupG/H
centerC22C2×D4×#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
Fitting, prime radicalC2×C13×#135C4
socleC22×C13C2×C4×D4
cosocleC4×Dic13C24
hypercenterC2×#135#261
hypocenterC13#17882
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. #13131755C2semidirect
2. #13131751C2semidirect
3. #13130461C2semidirect
4. #13130457C2semidirect
5. #13130445C2semidirect
6. #13130441C2semidirect
7. C2×#11718255C2semidirect
8. #13130131C2semidirect
9. #13130131C2semidirect
10. #13130049C2semidirect
118. C13×#41M16semidirect
370. #41#6122semidirect
429. C13#17882semidirect

Maximal subgroups

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

subgroupindex
#131317552
#131317512
#131304612
#131304572
#131304452
#131304412
C2×#117182552
#131301312
#131300492
#135×Dic132
#1788213