Finite Group Databasebeta

← #15848405

Subgroups — #15848405

Order 3328.

694 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125954C211yesmaximal, characteristic, complemented
2#13124323C211yesmaximal, characteristic, complemented
3#13123947C211yesmaximal, characteristic, complemented
4#13114278C212yesmaximal, complemented
5#13114271C212yesmaximal, complemented
6#13114228C212yesmaximal, complemented
7#13114223C212yesmaximal, complemented
8#13113610C211yesmaximal, characteristic, complemented
9#13113513C211yesmaximal, characteristic, complemented
10C2×#11718074C211yesmaximal, characteristic, complemented
11C13×#3035C211yesmaximal, characteristic
12C2×C13×#135—21no—
13C13×#532C2211yescharacteristic
14C4×C13×#41C2211yescharacteristic
15C2×#88205—21no—
16C2×#88123C2211yescharacteristic
17C13×#464—21no—
18C13×#463—21no—
19C13×#462C2211yescharacteristic
20C13×#461C2211yescharacteristic
21C13×#460C2211yescharacteristic
22C13×#459C2211yescharacteristic
23C2×C13×C4⋊C8C2211yescharacteristic
24C13×#416—21no—
25#11718739C2212yes—
26#11718731C2212yes—
27#11718694—22no—
28#11718692—21no—
29#11718692C2212yes—
30Q8×#1055C2212yes—
31#11718680—21no—
32#11718680C2212yes—
33D4×#1055—22no—
34D4×#1055C2212yes—
35#11718668—21no—
36#11718668—21no—
37#11718665—21no—
38#11718586—21no—
39#11718586C2211yescharacteristic
40#11718585C2211yescharacteristic
41C2×C4⋊#1055—21no—
42C2×C4⋊#1055C2211yescharacteristic
43#11718139C2212yes—
44#11718136C2212yes—
45#11718074C2212yes—
46#11718074C2212yes—
47#11718071C2212yes—
48#11718071C2212yes—
49C2×C13×#41—21no—
50C2×C13×#41D411yescharacteristic
51C22×Dic26—21no—
52C13×#135—44no—
53C2×C13×Q16—21no—
54C2×C13×SD16—21no—
55C2×C13×SD16—21no—
56C2×C13×D8—21no—
57C22×C8×C13—21no—
58C13×C4⋊Q8C2311yescharacteristic
59C13×#127C2311yescharacteristic
60C13×#124—21no—
61C13×#121—21no—
62C13×#121—21no—
63C4×Q8×C13D411yescharacteristic
64C4×Q8×C13C2311yescharacteristic
65C4×D4×C13—21no—
66C4×D4×C13—21no—
67C4×D4×C13—21no—
68C4×D4×C13—21no—
69C4×D4×C13D411yescharacteristic
70C4×D4×C13C2311yescharacteristic
71C13×#117—21no—
72C13×#117D411yescharacteristic
73C2×C42×C13—21no—
74C2×C42×C13C2311yescharacteristic
75#88205—44no—
76C2×#6107—22no—
77C2×#6105—22no—
78C2×C4⋊Dic13—21no—
79C2×C4⋊Dic13—21no—
80C2×#6099—21no—
81C22×#1055—21no—
82C22×#1055—22no—
83#88123—21no—
84#88123—21no—
85#88123—21no—
86#88123C2312yes—
87C13×C4⋊C8—21no—
88C13×C4⋊C8C2311yescharacteristic
89C13×C4⋊C8C2311yescharacteristic
90C13×#103—21no—
91C13×#103—21no—
92C13×#102—21no—
93C13×#102—21no—
94#88072—22no—
95#88072—22no—
96C22⋊#1055—22no—
97C22⋊#1055D412yes—
98#88050—22no—
99#88050—22no—
100#88047—22no—
101#88047—22no—
102C4⋊#1055—21no—
103C4⋊#1055—21no—
104C4⋊#1055—22no—
105C4⋊#1055D411yescharacteristic
106C4⋊#1055D411yescharacteristic
107C4⋊#1055C2312yes—
108C4⋊#1055C2312yes—
109C4×#1055—22no—
110C4×#1055C2312yes—
111#19416—131nomaximal, Sylow
112C13×#41—22no—
113C13×#41—42no—
114C13×#41—42no—
115C13×#41D814yes—
116C2×Q8×C13—21no—
117C2×Q8×C13C2×D411yescharacteristic
118C2×D4×C13—21no—
119C2×D4×C13—21no—
120C2×D4×C13—21no—
121C2×D4×C13—21no—
122C2×D4×C13—41no—
123C2×D4×C13C2×D411yescharacteristic
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—41no—
128C22×C4×C13C2×D411yescharacteristic
129C22×C4×C13C2×D411yescharacteristic
130C22×C4×C13#4111yescharacteristic
131C22×Dic13—41no—
132C2×Dic26—22no—
133C2×Dic26—42no—
134C2×Dic26—42no—
135C2×Dic26—41no—
136C13×Q16—42no—
137C13×SD16—42no—
138C13×SD16—42no—
139C13×D8—42no—
140C2×C8×C13—21no—
141C2×C8×C13—21no—
142C2×C8×C13—42no—
143C13×C4⋊C4—21no—
144C13×C4⋊C4—21no—
145C13×C4⋊C4—21no—
146C13×C4⋊C4—21no—
147C13×C4⋊C4C2×D411yescharacteristic
148C13×C4⋊C4C2×D411yescharacteristic
149C13×C22⋊C4—21no—
150C13×C22⋊C4—21no—
151C13×C22⋊C4—21no—
152C13×C22⋊C4—41no—
153C13×C22⋊C4—41no—
154C42×C13—21no—
155C42×C13—21no—
156C42×C13—21no—
157C42×C13C2×D411yescharacteristic
158C42×C13C2×D411yescharacteristic
159C42×C13#4111yescharacteristic
160C42×C13C2411yescharacteristic
161#6107—44no—
162#6105—44no—
163C4⋊Dic13—22no—
164C4⋊Dic13—22no—
165C4⋊Dic13—41no—
166C4⋊Dic13—41no—
167#6099—42no—
168C2×#1055—22no—
169C2×#1055—22no—
170C2×#1055—82no—
171C2×#1055—81no—
172C2×#1055C2×D412yes—
173C2×#1055C2×D412yes—
174#3226—131no—
175#3039—131no—
176#3035D1311yescharacteristic
177#2988—131no—
178#1682—132no—
179#1681—132no—
180#1674—132no—
181#1673—132no—
182#1571—131no—
183#1547—131no—
184C2×#332—131no—
185C23×C13—21no—
186C23×C13—41no—
187C23×C13#12111yescharacteristic
188Q8×C13—21no—
189Q8×C13—41no—
190Q8×C13—41no—
191Q8×C13C2×D812yes—
192D4×C13—24no—
193D4×C13—21no—
194D4×C13—41no—
195D4×C13—41no—
196D4×C13—41no—
197D4×C13—41no—
198D4×C13—81no—
199D4×C13—82no—
200D4×C13C2×D812yes—
201C2×C4×C13—21no—
202C2×C4×C13—21no—
203C2×C4×C13—21no—
204C2×C4×C13—24no—
205C2×C4×C13—21no—
206C2×C4×C13—21no—
207C2×C4×C13—41no—
208C2×C4×C13—41no—
209C2×C4×C13—41no—
210C2×C4×C13—41no—
211C2×C4×C13—81no—
212C2×C4×C13—82no—
213C2×C4×C13#12111yescharacteristic
214C2×C4×C13#12111yescharacteristic
215C2×C4×C13#12111yescharacteristic
216C2×C4×C13C2×D812yes—
217C2×C4×C13#13512yes—
218C2×C4×C13C22×D411yescharacteristic
219C2×C4×C13C22×D411yescharacteristic
220C2×C4×C13C2×#4111yescharacteristic
221C2×Dic13—42no—
222C2×Dic13—82no—
223Dic26—42no—
224Dic26—42no—
225Dic26—82no—
226C8×C13—41no—
227C8×C13—41no—
228#1055—22no—
229#1055—22no—
230#1055—42no—
231#1055—42no—
232C2×#137—261no—
233C2×#135—21no—
234#532C2×D1311yescharacteristic
235C2×C4⋊Q8—131no—
236C4×#41C2×D1311yescharacteristic
237#500—132no—
238#486—132no—
239#480—262no—
240#474—261no—
241#474—261no—
242#464—21no—
243#463—21no—
244#462—132no—
245#462—261no—
246#462C2×D1311yescharacteristic
247#461—132no—
248#461—261no—
249#461C2×D1311yescharacteristic
250#460C2×D1311yescharacteristic
251#459C2×D1311yescharacteristic
252C8×Q8—132no—
253C8×D4—132no—
254C8×D4—262no—
255#431—131no—
256#431—261no—
257#423—131no—
258C2×C4⋊C8—131no—
259C2×C4⋊C8—261no—
260C2×C4⋊C8C2×D1311yescharacteristic
261#419—261no—
262#416—21no—
263#335—132no—
264#335—132no—
265#332—132no—
266#332—132no—
267#332—132no—
268#331—132no—
269C22×C13—21no—
270C22×C13—21no—
271C22×C13—22no—
272C22×C13—41no—
273C22×C13—41no—
274C22×C13—81no—
275C22×C13—81no—
276C22×C13—81no—
277C22×C13#46612yes—
278C22×C13C2×#12111yescharacteristic
279C4×C13—21no—
280C4×C13—22no—
281C4×C13—21no—
282C4×C13—21no—
283C4×C13—41no—
284C4×C13—41no—
285C4×C13—81no—
286C4×C13#46612yes—
287C4×C13C22×D811yescharacteristic
288C4×C13C2×#13511yescharacteristic
289C4×C13#57711yescharacteristic
290C4×C13#57811yescharacteristic
291Dic13—82no—
292C2×#41—21no—
293C2×#41C22⋊D1311yescharacteristic
294C22×Q8—261no—
295#137—524no—
296#135—44no—
297C2×Q16—21no—
298C2×Q16—262no—
299C2×SD16—21no—
300C2×SD16—21no—
301C2×SD16—262no—
302C2×D8—21no—
303C2×M16—261no—
304C22×C8—21no—
305C22×C8—262no—
306C22×C8—261no—
307C4⋊Q8—132no—
308C4⋊Q8—261no—
309C4⋊Q8—261no—
310C4⋊Q8—261no—
311C4⋊Q8C22×D1311yescharacteristic
312#127C22×D1311yescharacteristic
313#124—21no—
314#121—21no—
315#121—21no—
316C4×Q8C22⋊D1311yescharacteristic
317C4×Q8C22×D1311yescharacteristic
318C4×D4—21no—
319C4×D4—21no—
320C4×D4—21no—
321C4×D4—21no—
322C4×D4C22⋊D1311yescharacteristic
323C4×D4C22×D1311yescharacteristic
324#117—21no—
325#117C22⋊D1311yescharacteristic
326C2×C4⋊C4—261no—
327C2×C4⋊C4—261no—
328C2×C42—21no—
329C2×C42C22×D1311yescharacteristic
330#107—262no—
331#107—262no—
332C4⋊C8—21no—
333C4⋊C8—131no—
334C4⋊C8—131no—
335C4⋊C8—132no—
336C4⋊C8—132no—
337C4⋊C8—262no—
338C4⋊C8—261no—
339C4⋊C8—261no—
340C4⋊C8C22×D1311yescharacteristic
341C4⋊C8C22×D1311yescharacteristic
342#103—21no—
343#103—21no—
344#103—262no—
345#103—262no—
346#102—21no—
347#102—21no—
348#102—262no—
349#102—262no—
350C22⋊C8—132no—
351C22⋊C8—262no—
352C4×C8—132no—
353C4×C8—262no—
354C2×C13—22no—
355C2×C13—42no—
356C2×C13—161no—
357C2×C13#304611yescharacteristic
358C2×C13C2×#46611yescharacteristic
359C2×C13#306911yescharacteristic
360#41—22no—
361#41—42no—
362#41—42no—
363#41#610414yes—
364C2×Q8—21no—
365C2×Q8—262no—
366C2×Q8—521no—
367C2×Q8—522no—
368C2×Q8—522no—
369C2×Q8C2×C22⋊D1311yescharacteristic
370C2×D4—21no—
371C2×D4—21no—
372C2×D4—21no—
373C2×D4—21no—
374C2×D4—41no—
375C2×D4C2×C22⋊D1311yescharacteristic
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—41no—
380C22×C4—521no—
381C22×C4D4×D1311yescharacteristic
382C22×C4#612911yescharacteristic
383C22×C4C2×C22⋊D1311yescharacteristic
384Q16—42no—
385Q16—524no—
386SD16—42no—
387SD16—42no—
388SD16—524no—
389D8—42no—
390M16—522no—
391C2×C8—21no—
392C2×C8—21no—
393C2×C8—42no—
394C2×C8—132no—
395C2×C8—132no—
396C2×C8—262no—
397C2×C8—262no—
398C2×C8—1042no—
399C2×C8—1041no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—262no—
405C4⋊C4—262no—
406C4⋊C4—521no—
407C4⋊C4—521no—
408C4⋊C4C2×C22⋊D1311yescharacteristic
409C4⋊C4C2×C22⋊D1311yescharacteristic
410C22⋊C4—21no—
411C22⋊C4—21no—
412C22⋊C4—21no—
413C22⋊C4—41no—
414C22⋊C4—41no—
415C42—21no—
416C42—21no—
417C42—21no—
418C42D4×D1311yescharacteristic
419C42#612911yescharacteristic
420C42C2×C22⋊D1311yescharacteristic
421C42C23×D1311yescharacteristic
422C13#1941611yescharacteristic, complemented, Sylow
423C23—21no—
424C23—41no—
425C23#8819311yescharacteristic
426Q8—21no—
427Q8—41no—
428Q8—41no—
429Q8—522no—
430Q8—522no—
431Q8—1042no—
432Q8C2×#610412yes—
433D4—24no—
434D4—21no—
435D4—41no—
436D4—41no—
437D4—41no—
438D4—41no—
439D4—81no—
440D4—82no—
441D4C2×#610412yes—
442C2×C4—21no—
443C2×C4—24no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—81no—
453C2×C4—82no—
454C2×C4—522no—
455C2×C4—1042no—
456C2×C4C2×#610412yes—
457C2×C4#8819311yescharacteristic
458C2×C4#8819311yescharacteristic
459C2×C4#8819311yescharacteristic
460C2×C4#8820412yes—
461C2×C4C2×D4×D1311yescharacteristic
462C2×C4C2×#612911yescharacteristic
463C2×C4C22×C22⋊D1311yescharacteristic
464C8—41no—
465C8—41no—
466C8—262no—
467C8—262no—
468C8—522no—
469C8—522no—
470C22—21no—
471C22—21no—
472C22—22no—
473C22—41no—
474C22—41no—
475C22—81no—
476C22—81no—
477C22—81no—
478C22#1171869912yes—
479C22C2×#8819311yescharacteristic
480C4—21no—
481C4—22no—
482C4—21no—
483C4—21no—
484C4—41no—
485C4—41no—
486C4—81no—
487C4—1042no—
488C4#1171869912yes—
489C4#1171947511yescharacteristic
490C4#1171947611yescharacteristic
491C4C22×#610411yescharacteristic
492C4C2×#8820411yescharacteristic
493C2—22no—
494C2—42no—
495C2—161no—
496C2#1312438411yescharacteristic
497C2C2×#1171869911yescharacteristic
498C2#1312457511yescharacteristic
subgroupG/H
centerC22C2×#88193
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
Fitting, prime radicalC13×#3035C2
socleC22×C13C2×#121
hypercenter#3035D13
hypocenterC13#19416
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3035

Complements

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

NH ≅ G/Ntype
1. #13125954C2semidirect
2. #13124323C2semidirect
3. #13123947C2semidirect
4. #13114278C2semidirect
5. #13114271C2semidirect
6. #13114228C2semidirect
7. #13114223C2semidirect
8. #13113610C2semidirect
9. #13113513C2semidirect
10. C2×#11718074C2semidirect
422. C13#19416semidirect

Maximal subgroups

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

subgroupindex
#131259542
#131243232
#131239472
#131142782
#131142712
#131142282
#131142232
#131136102
#131135132
C2×#117180742
C13×#30352
#1941613