Finite Group Databasebeta

← #16019180

Subgroups — #16019180

Order 3328.

454 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125475C211yesmaximal, characteristic
2#13117123C211yesmaximal, characteristic, complemented
3#13117109C211yesmaximal, characteristic, complemented
4#13117075C211yesmaximal, characteristic, complemented
5#13117070C211yesmaximal, characteristic, complemented
6#13117044C211yesmaximal, characteristic, complemented
7#13117038C211yesmaximal, characteristic, complemented
8#13117027C211yesmaximal, characteristic
9#13117016C211yesmaximal, characteristic
10#13116997C211yesmaximal, characteristic, complemented
11#13116990C211yesmaximal, characteristic, complemented
12#13116985C211yesmaximal, characteristic, complemented
13#13116970C211yesmaximal, characteristic, complemented
14#13116643C211yesmaximal, characteristic, complemented
15C13×#3164C211yesmaximal, characteristic, complemented
16C13×#544—21no—
17#11719239—21no—
18C13×#501—21no—
19C13×#501—21no—
20C13×#500C2211yescharacteristic
21C13×#500C2211yescharacteristic
22C13×#499C2211yescharacteristic
23C13×#499C2211yescharacteristic
24C13×#428—21no—
25C13×#427C2211yescharacteristic
26C2×C13×#107C2211yescharacteristic
27C13×#405C2211yescharacteristic
28#11718795—21no—
29#11718777C2211yescharacteristic
30#11718776C2211yescharacteristic
31#11718375—21no—
32#11718371—21no—
33C4×Dic52C2211yescharacteristic
34#11718357C2211yescharacteristic
35C4×D104C2211yescharacteristic
36#11718343C2211yescharacteristic
37C22⋊#6090C2211yescharacteristic
38C22⋊#6090C2211yescharacteristic
39#11718084C2211yescharacteristic
40#11718084C2211yescharacteristic
41#11718084C2211yescharacteristic
42#11718084C2211yescharacteristic
43#11718083C2211yescharacteristic
44#11718083C2211yescharacteristic
45#11718083C2211yescharacteristic
46#11718083C2211yescharacteristic
47#11718082C2211yescharacteristic
48#11718082C2211yescharacteristic
49#11718081C2211yescharacteristic
50#11718081C2211yescharacteristic
51#11718081C2211yescharacteristic
52#11718081C2211yescharacteristic
53#11718081C2211yescharacteristic
54#11718081C2211yescharacteristic
55C4⋊#6090C2211yescharacteristic
56C4⋊#6090C2211yescharacteristic
57#11718053C2211yescharacteristic
58C4×#6090C2211yescharacteristic
59C2×C13×M16D411yescharacteristic
60C22×C8×C13C2311yescharacteristic
61C13×C4⋊Q8—21no—
62C13×C4⋊Q8—21no—
63C13×C4⋊Q8—41no—
64C13×#125—21no—
65C13×#125—21no—
66C13×#125—41no—
67C13×C22⋊Q8—41no—
68C13×C22⋊Q8—41no—
69C13×#117—21no—
70C13×#117D411yescharacteristic
71C2×C13×C4⋊C4—21no—
72#88184—21no—
73#88178—21no—
74C2×Dic52C2311yescharacteristic
75C2×D104C2311yescharacteristic
76C2×#6095—21no—
77#88152—41no—
78#88150—41no—
79#88139—41no—
80#88137—41no—
81#88129—21no—
82C4×D52—21no—
83#88123—21no—
84C4×Dic26—21no—
85C13×#107—21no—
86C13×#107—21no—
87C13×#107—21no—
88C13×#107C2311yescharacteristic
89C13×#107C2311yescharacteristic
90C13×#107C2311yescharacteristic
91C13×#107C2311yescharacteristic
92C13×#106—21no—
93C13×#106—21no—
94C13×#106—21no—
95C13×#97D411yescharacteristic
96C13×#97D411yescharacteristic
97C4×C8×C13C2311yescharacteristic
98C4×C8×C13C2311yescharacteristic
99#88061—21no—
100#88061—21no—
101#88058—21no—
102#88058C2311yescharacteristic
103#88058C2311yescharacteristic
104#88056—21no—
105#88056—21no—
106C2×#6090C2311yescharacteristic
107C2×#6090C2311yescharacteristic
108C2×#6090C2311yescharacteristic
109C2×#6090C2311yescharacteristic
110#33809—131nomaximal, Sylow
111C2×Q8×C13—41no—
112C2×Q8×C13—41no—
113C22×C4×C13—41no—
114C22×C4×C13C2×D411yescharacteristic
115C2×C22⋊D13—41no—
116C2×D52—21no—
117C2×C4×D13—41no—
118C2×Dic26—21no—
119C2×Dic26—41no—
120C13×M16—22no—
121C2×C8×C13—21no—
122C2×C8×C13—21no—
123C2×C8×C13C2×D411yescharacteristic
124C2×C8×C13C2×D411yescharacteristic
125C2×C8×C13C2×D411yescharacteristic
126C2×C8×C13C2411yescharacteristic
127C13×C4⋊C4—21no—
128C13×C4⋊C4—21no—
129C13×C4⋊C4—21no—
130C13×C4⋊C4—21no—
131C13×C4⋊C4—41no—
132C13×C4⋊C4—41no—
133C13×C4⋊C4—41no—
134C13×C4⋊C4—41no—
135C13×C4⋊C4—41no—
136C13×C4⋊C4—41no—
137C13×C4⋊C4—41no—
138C13×C4⋊C4D811yescharacteristic
139C13×C4⋊C4D811yescharacteristic
140C13×C22⋊C4—41no—
141C13×C22⋊C4D811yescharacteristic
142C13×C22⋊C4D811yescharacteristic
143C42×C13—41no—
144C42×C13C2×D411yescharacteristic
145C42×C13C2×D411yescharacteristic
146C22⋊Dic13—41no—
147#6103—41no—
148#6103—41no—
149#6103—41no—
150#6103—41no—
151C4⋊Dic13—21no—
152C4⋊Dic13—21no—
153C4⋊Dic13—41no—
154#6101—41no—
155#6101—41no—
156C4×Dic13—41no—
157Dic52—21no—
158Dic52—21no—
159D104—21no—
160D104—21no—
161#6095—42no—
162#6090—21no—
163#6090—21no—
164#6090—21no—
165#6090—21no—
166#3175—131no—
167#3164D1311yescharacteristic, complemented
168#2255—131no—
169#2252—131no—
170#2243—131no—
171#2242—131no—
172#2237—131no—
173#2236—131no—
174#2234—131no—
175#2232—131no—
176#2229—131no—
177#2228—131no—
178#2227—131no—
179#2224—131no—
180#2164—131no—
181C23×C13C2×D811yescharacteristic
182C22×D13—41no—
183Q8×C13—161no—
184Q8×C13—161no—
185C2×C4×C13—21no—
186C2×C4×C13—21no—
187C2×C4×C13—41no—
188C2×C4×C13—41no—
189C2×C4×C13—41no—
190C2×C4×C13—41no—
191C2×C4×C13—161no—
192C2×C4×C13C2×D811yescharacteristic
193C2×C4×C13C2×D811yescharacteristic
194C2×C4×C13C2×D811yescharacteristic
195C2×C4×C13C2×D811yescharacteristic
196C2×C4×C13C2×D811yescharacteristic
197C2×C4×C13C22×D411yescharacteristic
198C22⋊D13—161no—
199C2×Dic13—41no—
200C2×Dic13—41no—
201C2×Dic13—41no—
202D52—41no—
203D52—41no—
204C4×D13—161no—
205Dic26—41no—
206Dic26—41no—
207Dic26—161no—
208C8×C13—21no—
209C8×C13—21no—
210C8×C13#13712yes—
211C8×C132−1+411yescharacteristic
212C8×C132−1+411yescharacteristic
213#544—21no—
214#542—261no—
215#501—21no—
216#501—21no—
217#500—131no—
218#500C2×D1311yescharacteristic
219#500C2×D1311yescharacteristic
220#499C2×D1311yescharacteristic
221#499C2×D1311yescharacteristic
222#495—131no—
223#489—261no—
224#468—261no—
225#467—131no—
226#466—131no—
227#440—261no—
228C4×Q16—131no—
229C4×D8—131no—
230#428—21no—
231#427C2×D1311yescharacteristic
232C2×#107C2×D1311yescharacteristic
233#405C2×D1311yescharacteristic
234#367—131no—
235#367—131no—
236#366—131no—
237#366—131no—
238#366—131no—
239#366—131no—
240#366—131no—
241#366—131no—
242C4⋊C16—131no—
243C4⋊C16—131no—
244#358—131no—
245#358—131no—
246#358—131no—
247#358—131no—
248#357—131no—
249#357—131no—
250#357—131no—
251#357—131no—
252C22⋊C16—131no—
253C22⋊C16—131no—
254#346—131no—
255C4×C16—131no—
256C22×C13—21no—
257C22×C13—21no—
258C22×C13—21no—
259C22×C13C22×D811yescharacteristic
260C2×D13—81no—
261C2×D13—81no—
262C2×D13—81no—
263C4×C13—21no—
264C4×C13—21no—
265C4×C13—21no—
266C4×C13—21no—
267C4×C13—21no—
268C4×C13—81no—
269C4×C13—81no—
270C4×C13—81no—
271C4×C13—81no—
272C4×C13#53611yescharacteristic
273C4×C13C2×#13711yescharacteristic
274Dic13—81no—
275Dic13—81no—
276Dic13—81no—
277C2×Q16—131no—
278C2×SD16—261no—
279C2×D8—131no—
280C2×M16C22⋊D1311yescharacteristic
281C22×C8C22×D1311yescharacteristic
282C4⋊Q8—21no—
283C4⋊Q8—21no—
284C4⋊Q8—41no—
285C4⋊Q8—261no—
286#126—521no—
287#125—21no—
288#125—21no—
289#125—41no—
290#124—261no—
291#124—521no—
292#123—521no—
293C22⋊Q8—41no—
294C22⋊Q8—41no—
295C22⋊Q8—261no—
296C22⋊Q8—521no—
297#121—261no—
298C4×Q8—261no—
299C4×D4—261no—
300#117—21no—
301#117C22⋊D1311yescharacteristic
302C2×C4⋊C4—21no—
303C2×C16—131no—
304C2×C16—131no—
305C2×C16—131no—
306C2×C16—131no—
307#107—21no—
308#107—21no—
309#107—21no—
310#107—131no—
311#107—131no—
312#107—261no—
313#107C22×D1311yescharacteristic
314#107C22×D1311yescharacteristic
315#107C22×D1311yescharacteristic
316#107C22×D1311yescharacteristic
317#106—21no—
318#106—21no—
319#106—21no—
320#103—261no—
321#103—261no—
322#102—261no—
323#102—261no—
324#97C22⋊D1311yescharacteristic
325#97C22⋊D1311yescharacteristic
326C4×C8C22×D1311yescharacteristic
327C4×C8C22×D1311yescharacteristic
328C2×C13—41no—
329C2×C13#322611yescharacteristic
330C2×C13#341511yescharacteristic
331C2×C13#341711yescharacteristic
332D13—161no—
333C2×Q8—41no—
334C2×Q8—41no—
335C2×Q8—261no—
336C2×Q8—521no—
337C2×D4—261no—
338C2×D4—521no—
339C22×C4—41no—
340C22×C4—521no—
341C22×C4C2×C22⋊D1311yescharacteristic
342Q16—261no—
343Q16—261no—
344SD16—522no—
345D8—261no—
346D8—261no—
347M16—22no—
348C2×C8—21no—
349C2×C8—21no—
350C2×C8C2×C22⋊D1311yescharacteristic
351C2×C8C2×C22⋊D1311yescharacteristic
352C2×C8C2×C22⋊D1311yescharacteristic
353C2×C8C23×D1311yescharacteristic
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—41no—
359C4⋊C4—41no—
360C4⋊C4—41no—
361C4⋊C4—41no—
362C4⋊C4—41no—
363C4⋊C4—41no—
364C4⋊C4—41no—
365C4⋊C4—261no—
366C4⋊C4—261no—
367C4⋊C4—521no—
368C4⋊C4—521no—
369C4⋊C4—521no—
370C4⋊C4#610411yescharacteristic
371C4⋊C4#610411yescharacteristic
372C22⋊C4—41no—
373C22⋊C4—521no—
374C22⋊C4—521no—
375C22⋊C4—521no—
376C22⋊C4—521no—
377C22⋊C4—521no—
378C22⋊C4#610411yescharacteristic
379C22⋊C4#610411yescharacteristic
380C42—41no—
381C42—521no—
382C42C2×C22⋊D1311yescharacteristic
383C42C2×C22⋊D1311yescharacteristic
384C16—261no—
385C16—261no—
386C16—261no—
387C16—261no—
388C13#3380911yescharacteristic, complemented, Sylow
389C23—521no—
390C23C2×#610411yescharacteristic
391Q8—161no—
392Q8—161no—
393Q8—521no—
394Q8—521no—
395Q8—2081no—
396D4—521no—
397D4—521no—
398D4—2081no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—161no—
406C2×C4—521no—
407C2×C4—521no—
408C2×C4—521no—
409C2×C4—2081no—
410C2×C4C2×#610411yescharacteristic
411C2×C4C2×#610411yescharacteristic
412C2×C4C2×#610411yescharacteristic
413C2×C4C2×#610411yescharacteristic
414C2×C4C2×#610411yescharacteristic
415C2×C4C22×C22⋊D1311yescharacteristic
416C8—21no—
417C8—21no—
418C8#8819612yes—
419C8#8825411yescharacteristic
420C8#8825411yescharacteristic
421C22—21no—
422C22—21no—
423C22—21no—
424C22—1041no—
425C22—1041no—
426C22—1041no—
427C22C22×#610411yescharacteristic
428C4—21no—
429C4—21no—
430C4—21no—
431C4—21no—
432C4—21no—
433C4—81no—
434C4—81no—
435C4—81no—
436C4—81no—
437C4—1041no—
438C4—1041no—
439C4—1041no—
440C4C2×#8819611yescharacteristic
441C4#1171952111yescharacteristic
442C2—41no—
443C2—2081no—
444C2#1312595711yescharacteristic
445C2#1312797511yescharacteristic
446C2#1312798711yescharacteristic
subgroupG/H
centerC22C22×#6104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC13×#3164C2
socleC22×C13C22×D8
prime radical#11718776C22
hypercenter#3164D13
hypocenterC13#33809
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #3164

Complements

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

NH ≅ G/Ntype
2. #13117123C2semidirect
3. #13117109C2semidirect
4. #13117075C2semidirect
5. #13117070C2semidirect
6. #13117044C2semidirect
7. #13117038C2semidirect
10. #13116997C2semidirect
11. #13116990C2semidirect
12. #13116985C2semidirect
13. #13116970C2semidirect
14. #13116643C2semidirect
15. C13×#3164C2semidirect
167. #3164D13semidirect
388. C13#33809semidirect

Maximal subgroups

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

subgroupindex
#131254752
#131171232
#131171092
#131170752
#131170702
#131170442
#131170382
#131170272
#131170162
#131169972
#131169902
#131169852
#131169702
#131166432
C13×#31642
#3380913