Finite Group Databasebeta

← #28315647

Subgroups — #28315647

Order 13568.

962 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#20291391C211yesmaximal, characteristic
2#20291391C211yesmaximal, characteristic
3#20290197C214yesmaximal, complemented
4#20290179C214yesmaximal, complemented
5#20290177C214yesmaximal, complemented
6C22×#13133208C211yesmaximal, characteristic
7#16811644C2212yes—
8#16811644C2212yes—
9#16811643C2212yes—
10#16811643C2212yes—
11#16811640—21no—
12#16811640—21no—
13#16811639—21no—
14#16811639—21no—
15#16811626—21no—
16#16811626—21no—
17#16811593—21no—
18#16811593—21no—
19C4×#11719940C2212yes—
20C4×#11719940C2212yes—
21#16811480C22116yescomplemented
22C2×#13133208—21no—
23C2×#13133208—21no—
24C2×#13133208—21no—
25C2×#13133208—21no—
26C2×#13133208—21no—
27C2×#13133208—21no—
28C2×#13133208C412yes—
29C2×#13133208C412yes—
30C2×#13133208C412yes—
31C2×#13133208C2212yes—
32C2×#13133208C2212yes—
33C2×#13133208C2212yes—
34C22×C4⋊Dic53—21no—
35C22×C4⋊Dic53C411yescharacteristic
36C22×#11719919—21no—
37C22×C4×Dic53C2211yescharacteristic
38C22×C4⋊C4×C53C411yescharacteristic
39C2×#11719940—22no—
40C2×#11719940—22no—
41#13133284—22no—
42#13133284—22no—
43C4⋊#88324—22no—
44C4⋊#88324—22no—
45C22⋊#88324—22no—
46C22⋊#88324—22no—
47C22⋊#88324—22no—
48C22⋊#88324—22no—
49#13133272C2314yes—
50#13133272C2314yes—
51C4×#88324—22no—
52C4×#88324—22no—
53C23×Dic53—21no—
54C23×Dic53D411yescharacteristic
55C23×Dic53D411yescharacteristic
56#13133208—22no—
57#13133208—22no—
58#13133208—22no—
59#13133208—22no—
60#13133208—22no—
61#13133208—22no—
62#13133208—22no—
63#13133208—22no—
64#13133208—22no—
65#13133208—22no—
66#13133208—22no—
67#13133208—22no—
68#13133208C2×C414yes—
69#13133208C2×C414yes—
70#13133208C2×C414yes—
71#13133208C2314yes—
72C2×C4⋊Dic53—21no—
73C2×C4⋊Dic53—21no—
74C2×C4⋊Dic53—21no—
75C2×C4⋊Dic53—22no—
76C2×C4⋊Dic53—22no—
77C2×C4⋊Dic53—22no—
78C2×C4⋊Dic53—22no—
79C2×C4⋊Dic53—22no—
80C2×C4⋊Dic53—22no—
81C2×C4⋊Dic53C2×C412yes—
82C2×C4⋊Dic53C2×C412yes—
83C2×C4⋊Dic53C2×C412yes—
84C2×#11719919—22no—
85C2×#11719919—22no—
86C2×#11719919—22no—
87C2×#11719919—22no—
88C2×#11719919—22no—
89C2×#11719919—22no—
90C2×C4×Dic53C2×C411yescharacteristic
91C2×C4×Dic53C2×C411yescharacteristic
92C2×C4×Dic53C2×C411yescharacteristic
93C2×C4×Dic53D411yescharacteristic
94C2×C4×Dic53D411yescharacteristic
95C2×C4×Dic53D411yescharacteristic
96C2×C4×Dic53D411yescharacteristic
97C2×C4×Dic53D411yescharacteristic
98C2×C4×Dic53D411yescharacteristic
99C2×C4×Dic53C2311yescharacteristic
100C2×C4×Dic53C2311yescharacteristic
101C2×C4×Dic53C2311yescharacteristic
102C23×C4×C53—21no—
103C23×C4×C53C2×C411yescharacteristic
104C2×C4⋊C4×C53—21no—
105C2×C4⋊C4×C53—21no—
106C2×C4⋊C4×C53—21no—
107C2×C4⋊C4×C53C2×C412yes—
108C2×C4⋊C4×C53C2×C412yes—
109C2×C4⋊C4×C53C2×C412yes—
110C24×C53C22⋊C411yescharacteristic
111C22×C4×C53—24no—
112C22×C4×C53—22no—
113C22×C4×C53—22no—
114C22×C4×C53—22no—
115C22×C4×C53—44no—
116C22×C4×C53C22⋊C411yescharacteristic
117C22×C4×C53C22⋊C411yescharacteristic
118C22×C4×C53C22⋊C411yescharacteristic
119C22×C4×C53C22×C411yescharacteristic
120C22×C4×C53C22×C411yescharacteristic
121C22×C4×C53C22×C411yescharacteristic
122C22×Dic53—22no—
123C22×Dic53—22no—
124C22×Dic53—22no—
125C22×Dic53—42no—
126C22×Dic53—42no—
127C22×Dic53—44no—
128C22×Dic53C22⋊C411yescharacteristic
129C22×Dic53C22⋊C411yescharacteristic
130C22×Dic53C22⋊C411yescharacteristic
131C22×Dic53C22⋊C411yescharacteristic
132C22×Dic53C22⋊C411yescharacteristic
133C22×Dic53C22⋊C411yescharacteristic
134C22×Dic53C2×D411yescharacteristic
135C22×Dic53C2×D411yescharacteristic
136C22×Dic53C2×D411yescharacteristic
137C22×Dic53C2×D411yescharacteristic
138C22×Dic53C2×D411yescharacteristic
139C22×Dic53C2×D411yescharacteristic
140#11719940—44no—
141#11719940—44no—
142C2×#88324—24no—
143C2×#88324—24no—
144C4⋊C4×C53—22no—
145C4⋊C4×C53—22no—
146C4⋊C4×C53—22no—
147C4⋊C4×C53C22×C414yes—
148C4⋊Dic53—22no—
149C4⋊Dic53—22no—
150C4⋊Dic53—22no—
151C4⋊Dic53—24no—
152C4⋊Dic53—24no—
153C4⋊Dic53—24no—
154C4⋊Dic53—24no—
155C4⋊Dic53C22×C414yes—
156#11719919—24no—
157#11719919—24no—
158#11719919—24no—
159#11719919—24no—
160C4×Dic53C22⋊C411yescharacteristic
161C4×Dic53C22⋊C411yescharacteristic
162C4×Dic53C22⋊C411yescharacteristic
163C4×Dic53C22⋊C411yescharacteristic
164C4×Dic53C22⋊C411yescharacteristic
165C4×Dic53C22⋊C411yescharacteristic
166C4×Dic53C22×C411yescharacteristic
167C4×Dic53C22×C411yescharacteristic
168C4×Dic53C22×C411yescharacteristic
169C4×Dic53C2×D411yescharacteristic
170C4×Dic53C2×D411yescharacteristic
171C4×Dic53C2×D411yescharacteristic
172C4×Dic53C2×D411yescharacteristic
173C4×Dic53C2×D411yescharacteristic
174C4×Dic53C2×D411yescharacteristic
175C4×Dic53C2411yescharacteristic
176C23×C53—22no—
177C23×C53—22no—
178C23×C53—22no—
179C23×C53C2×C22⋊C411yescharacteristic
180C23×C53C2×C22⋊C411yescharacteristic
181C23×C53C2×C22⋊C411yescharacteristic
182C2×C4×C53—22no—
183C2×C4×C53—22no—
184C2×C4×C53—22no—
185C2×C4×C53—22no—
186C2×C4×C53—22no—
187C2×C4×C53—24no—
188C2×C4×C53—44no—
189C2×C4×C53—44no—
190C2×C4×C53—44no—
191C2×C4×C53#10114yes—
192C2×C4×C53C2×C22⋊C411yescharacteristic
193C2×C4×C53C2×C22⋊C411yescharacteristic
194C2×C4×C53C2×C22⋊C411yescharacteristic
195C2×C4×C53C23×C411yescharacteristic
196C2×Dic53—22no—
197C2×Dic53—22no—
198C2×Dic53—22no—
199C2×Dic53—22no—
200C2×Dic53—24no—
201C2×Dic53—41no—
202C2×Dic53—41no—
203C2×Dic53—41no—
204C2×Dic53—41no—
205C2×Dic53—41no—
206C2×Dic53—41no—
207C2×Dic53—41no—
208C2×Dic53—41no—
209C2×Dic53—44no—
210C2×Dic53—44no—
211C2×Dic53—44no—
212C2×Dic53C2×C22⋊C411yescharacteristic
213C2×Dic53C2×C22⋊C411yescharacteristic
214C2×Dic53C2×C22⋊C411yescharacteristic
215C2×Dic53C2×C22⋊C411yescharacteristic
216C2×Dic53C2×C22⋊C411yescharacteristic
217C2×Dic53C2×C22⋊C411yescharacteristic
218C2×Dic53C22×D411yescharacteristic
219C2×Dic53C22×D411yescharacteristic
220#88324—44no—
221#88324—44no—
222#17667—531nomaximal, Sylow
223C22×C53—28no—
224C22×C53—21no—
225C22×C53—21no—
226C22×C53—21no—
227C22×C53—21no—
228C22×C53—21no—
229C22×C53—21no—
230C22×C53C2×#10112yes—
231C22×C53#42112yes—
232C22×C53#42112yes—
233C22×C53C22×C22⋊C411yescharacteristic
234C4×C53—21no—
235C4×C53—21no—
236C4×C53—44no—
237C4×C53C2×#10112yes—
238C4×C53C2×#10112yes—
239Dic53—21no—
240Dic53—21no—
241Dic53—21no—
242Dic53—21no—
243Dic53—21no—
244Dic53—21no—
245Dic53—21no—
246Dic53—21no—
247Dic53—44no—
248C22×#125—531no—
249#2920—531no—
250#2920—531no—
251#1534—534no—
252#1528—534no—
253#1528—534no—
254C2×C53—22no—
255C2×C53—22no—
256C2×C53—22no—
257C2×C53C22×#10111yescharacteristic
258C2×C53C2×#42111yescharacteristic
259C2×C53C2×#42111yescharacteristic
260C2×#125—532no—
261C2×#125—532no—
262C2×#125—532no—
263C2×#125—532no—
264C2×#125—532no—
265C2×#125—532no—
266C2×#125—1061no—
267C2×#125—1061no—
268C2×#125—1061no—
269C2×#125—1061no—
270C2×#125—1061no—
271C2×#125—1061no—
272C22×C4⋊C4—531no—
273C22×C4⋊C4—1061no—
274C22×C4⋊C4—1061no—
275C22×C4⋊C4#615711yescharacteristic
276C22×C42—531no—
277#432—532no—
278#432—532no—
279#432—532no—
280#432—532no—
281#431—1061no—
282#431—1061no—
283#431—1061no—
284#431—1061no—
285#423—1061no—
286#423—1061no—
287#407—1061no—
288#407—1061no—
289C4×M16—532no—
290C4×M16—532no—
291#330—5316no—
292C53#1766711yescharacteristic, complemented, Sylow
293C23×C4—21no—
294C23×C4—531no—
295C23×C4—531no—
296C23×C4—1061no—
297C23×C4C2×#615711yescharacteristic
298C2×M16—1062no—
299C2×M16—1062no—
300#125—534no—
301#125—534no—
302#125—534no—
303#125—534no—
304#125—1062no—
305#125—1062no—
306#125—1062no—
307#125—1062no—
308#125—1062no—
309#125—1062no—
310#125—1062no—
311#125—1062no—
312#125—1062no—
313#125—1062no—
314#125—1062no—
315#125—1062no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—532no—
320C2×C4⋊C4—532no—
321C2×C4⋊C4—532no—
322C2×C4⋊C4—1062no—
323C2×C4⋊C4—1062no—
324C2×C4⋊C4—1062no—
325C2×C4⋊C4—1062no—
326C2×C4⋊C4—1062no—
327C2×C4⋊C4—1062no—
328C2×C4⋊C4—1062no—
329C2×C4⋊C4—1062no—
330C2×C4⋊C4—1062no—
331C2×C4⋊C4—1062no—
332C2×C4⋊C4—1062no—
333C2×C4⋊C4—1062no—
334C2×C4⋊C4—1061no—
335C2×C4⋊C4—1061no—
336C2×C4⋊C4—1061no—
337C2×C4⋊C4C2×#615712yes—
338C2×C4⋊C4C2×#615712yes—
339C2×C4⋊C4C2×#615712yes—
340C2×C42—531no—
341C2×C42—531no—
342C2×C42—531no—
343C2×C42—531no—
344C2×C42—531no—
345C2×C42—531no—
346C2×C42—531no—
347C2×C42—531no—
348C2×C42—531no—
349C2×C42—531no—
350C2×C42—531no—
351C2×C42—531no—
352C4⋊C8—1062no—
353C4⋊C8—1062no—
354C4⋊C8—1062no—
355C4⋊C8—1062no—
356C22⋊C8—1062no—
357C22⋊C8—1062no—
358C22⋊C8—1062no—
359C22⋊C8—1062no—
360#97—534no—
361#97—534no—
362C4×C8—1062no—
363C4×C8—1062no—
364C24C22⋊#615711yescharacteristic
365C22×C4—24no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—44no—
370C22×C4—531no—
371C22×C4—531no—
372C22×C4—531no—
373C22×C4—531no—
374C22×C4—531no—
375C22×C4—531no—
376C22×C4—531no—
377C22×C4—531no—
378C22×C4—531no—
379C22×C4—531no—
380C22×C4—531no—
381C22×C4—531no—
382C22×C4—1062no—
383C22×C4—1062no—
384C22×C4—1062no—
385C22×C4—2122no—
386C22×C4—2122no—
387C22×C4—2124no—
388C22×C4C22⋊#615711yescharacteristic
389C22×C4C22⋊#615711yescharacteristic
390C22×C4C22⋊#615711yescharacteristic
391C22×C4C22×#615711yescharacteristic
392C22×C4C22×#615711yescharacteristic
393C22×C4C22×#615711yescharacteristic
394M16—2124no—
395M16—2124no—
396C2×C8—1064no—
397C2×C8—1064no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—22no—
401C4⋊C4—534no—
402C4⋊C4—1064no—
403C4⋊C4—1064no—
404C4⋊C4—1064no—
405C4⋊C4—1064no—
406C4⋊C4—1064no—
407C4⋊C4—1064no—
408C4⋊C4—1064no—
409C4⋊C4—1064no—
410C4⋊C4—1062no—
411C4⋊C4—1062no—
412C4⋊C4—1062no—
413C4⋊C4C22×#615714yes—
414C42—531no—
415C42—531no—
416C42—531no—
417C42—531no—
418C42—531no—
419C42—531no—
420C42—531no—
421C42—531no—
422C42—531no—
423C42—531no—
424C42—531no—
425C42—531no—
426C42—531no—
427C42—531no—
428C42—531no—
429C42—531no—
430C23—22no—
431C23—22no—
432C23—22no—
433C23C2×C22⋊#615711yescharacteristic
434C23C2×C22⋊#615711yescharacteristic
435C23C2×C22⋊#615711yescharacteristic
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—24no—
442C2×C4—44no—
443C2×C4—44no—
444C2×C4—44no—
445C2×C4—531no—
446C2×C4—531no—
447C2×C4—531no—
448C2×C4—531no—
449C2×C4—531no—
450C2×C4—531no—
451C2×C4—531no—
452C2×C4—531no—
453C2×C4—1062no—
454C2×C4—1062no—
455C2×C4—1062no—
456C2×C4—1062no—
457C2×C4—1064no—
458C2×C4—2121no—
459C2×C4—2121no—
460C2×C4—2121no—
461C2×C4—2121no—
462C2×C4—2121no—
463C2×C4—2121no—
464C2×C4—2121no—
465C2×C4—2121no—
466C2×C4—2124no—
467C2×C4—2124no—
468C2×C4—2124no—
469C2×C4#1313327814yes—
470C2×C4C2×C22⋊#615711yescharacteristic
471C2×C4C2×C22⋊#615711yescharacteristic
472C2×C4C2×C22⋊#615711yescharacteristic
473C2×C4C23×#615711yescharacteristic
474C8—2124no—
475C8—2124no—
476C22—28no—
477C22—21no—
478C22—21no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22C2×#1313327812yes—
484C22#1681162112yes—
485C22#1681162212yes—
486C22C22×C22⋊#615711yescharacteristic
487C4—21no—
488C4—21no—
489C4—44no—
490C4—1061no—
491C4—1061no—
492C4—1061no—
493C4—1061no—
494C4—1061no—
495C4—1061no—
496C4—1061no—
497C4—1061no—
498C4—2124no—
499C4C2×#1313327812yes—
500C4C2×#1313327812yes—
501C2—22no—
502C2—22no—
503C2—22no—
504C2C22×#1313327811yescharacteristic
505C2C2×#1681162111yescharacteristic
506C2C2×#1681162211yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6157
commutatorC2×C4×C53C23×C4
FrattiniC2×C4C23×#6157
FittingC22×C4⋊C4×C53C4
socleC22×C53C22×C22⋊C4
prime radicalC24×C53C22⋊C4
cosocleC4×Dic53C24
hypercenterC22×C4⋊C4#6157
hypocenterC53#17667
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #20290197C2semidirect
4. #20290179C2semidirect
5. #20290177C2semidirect
21. #16811480C22semidirect
292. C53#17667semidirect

Maximal subgroups

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

subgroupindex
#202913912
#202901972
#202901792
#202901772
C22×#131332082
#1766753