Finite Group Databasebeta

← #27276758

Subgroups — #27276758

Order 13568.

682 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11719919C211yesmaximal, characteristic
2#20274695C211yesmaximal, characteristic
3C2×#16810348C212yesmaximal
4#20272557C212yesmaximal
5C53×#1797C211yesmaximal, characteristic
6C22×#11719919C411yescharacteristic
7C22×#11719919C2211yescharacteristic
8C22×C4×Dic53C411yescharacteristic
9C22×C4×Dic53C411yescharacteristic
10C2×C4⋊#88322—21no—
11C2×C22⋊#88322C2212yes—
12C4×#11719919—21no—
13C4×#11719919—21no—
14C4×#11719919—21no—
15C4×#11719919—21no—
16C2×#13133124C411yescharacteristic
17C2×#13133124C2211yescharacteristic
18#16810378—21no—
19#16810348—24no—
20C22×C42×C53C2211yescharacteristic
21C2×C4⋊C8×C53—21no—
22C2×C22⋊C8×C53C2212yes—
23C53×#336—21no—
24C23×Dic53C2×C411yescharacteristic
25C23×Dic53C2×C411yescharacteristic
26C23×Dic53C2×C411yescharacteristic
27C23×Dic53C2×C411yescharacteristic
28C22×#88322—22no—
29C2×#11719919—21no—
30C2×#11719919—21no—
31C2×#11719919—22no—
32C2×#11719919—21no—
33C2×#11719919—21no—
34C2×#11719919—21no—
35C2×#11719919—21no—
36C2×#11719919C814yescomplemented
37C2×#11719919D412yes—
38C2×#11719919Q812yes—
39C2×C4×Dic53—21no—
40C2×C4×Dic53—21no—
41C2×C4×Dic53—21no—
42C2×C4×Dic53—21no—
43C2×C4×Dic53—22no—
44C2×C4×Dic53—22no—
45C2×C4×Dic53—42no—
46C4⋊#88322—42no—
47C22⋊#88322—22no—
48C22⋊#88322—22no—
49#13133124—21no—
50#13133124—21no—
51#13133124—21no—
52#13133124—21no—
53C23×C4×C53C2×C411yescharacteristic
54C23×C4×C53C2×C411yescharacteristic
55C23×C4×C53C2311yescharacteristic
56C22×C8×C53—22no—
57C2×C42×C53—42no—
58C2×C42×C53D411yescharacteristic
59C2×C42×C53D411yescharacteristic
60C2×C42×C53D411yescharacteristic
61C2×C42×C53D411yescharacteristic
62C4⋊C8×C53—42no—
63C22⋊C8×C53—22no—
64C22⋊C8×C53—22no—
65C24×C53C22×C411yescharacteristic
66C22×C4×C53—21no—
67C22×C4×C53—21no—
68C22×C4×C53—22no—
69C22×C4×C53—22no—
70C22×C4×C53—41no—
71C22×C4×C53—41no—
72C22×C4×C53—41no—
73C22×C4×C53—41no—
74C22×C4×C53C22⋊C411yescharacteristic
75C22×C4×C53C22⋊C411yescharacteristic
76C22×C4×C53C22⋊C411yescharacteristic
77C22×C4×C53C22⋊C411yescharacteristic
78C22×C4×C53C2×C812yes—
79C22×C4×C53M1612yes—
80C22×C4×C53C2×D411yescharacteristic
81C22×C4×C53C2×D411yescharacteristic
82C22×C4×C53C2×D411yescharacteristic
83C22×C4×C53C2×Q811yescharacteristic
84C22×C4×C53#4111yescharacteristic
85C22×C4×C53#4111yescharacteristic
86C22×Dic53—21no—
87C22×Dic53—21no—
88C22×Dic53—21no—
89C22×Dic53—21no—
90C22×Dic53—21no—
91C22×Dic53—21no—
92C22×Dic53—21no—
93C22×Dic53—21no—
94C22×Dic53—21no—
95C22×Dic53—21no—
96C22×Dic53—41no—
97C22×Dic53—41no—
98C22×Dic53—41no—
99C22×Dic53—41no—
100C22×Dic53—41no—
101C22×Dic53—41no—
102C22×Dic53C4⋊C412yes—
103C22×Dic53C4⋊C412yes—
104C22×Dic53C2×C812yes—
105C22×Dic53C2×C812yes—
106C22×Dic53M1612yes—
107C22×Dic53M1612yes—
108C2×C8×C53—42no—
109C2×C8×C53—42no—
110C2×C8×C53—42no—
111C42×C53—22no—
112C42×C53—22no—
113C42×C53—41no—
114C42×C53—41no—
115#11719919—24no—
116#11719919—24no—
117#11719919—22no—
118#11719919—22no—
119#11719919—22no—
120#11719919—22no—
121C4×Dic53—24no—
122C4×Dic53—24no—
123C4×Dic53—42no—
124C4×Dic53—42no—
125C2×#88322—42no—
126C2×#88322—42no—
127C2×#88322—42no—
128C23×C53—21no—
129C23×C53—21no—
130C23×C53—21no—
131C23×C53—21no—
132C23×C53C2×C22⋊C411yescharacteristic
133C23×C53C2×C4⋊C411yescharacteristic
134C23×C53#11711yescharacteristic
135C23×C53C22×C811yescharacteristic
136C23×C53C2×M1611yescharacteristic
137C23×C53C2×M1611yescharacteristic
138C23×C53C2×M1611yescharacteristic
139C2×C4×C53—24no—
140C2×C4×C53—24no—
141C2×C4×C53—21no—
142C2×C4×C53—21no—
143C2×C4×C53—21no—
144C2×C4×C53—21no—
145C2×C4×C53—21no—
146C2×C4×C53—21no—
147C2×C4×C53—21no—
148C2×C4×C53—21no—
149C2×C4×C53—21no—
150C2×C4×C53—21no—
151C2×C4×C53—21no—
152C2×C4×C53—21no—
153C2×C4×C53—42no—
154C2×C4×C53—42no—
155C2×C4×C53—41no—
156C2×C4×C53—41no—
157C2×C4×C53—41no—
158C2×C4×C53—41no—
159C2×C4×C53C22⋊C812yes—
160C2×C4×C53C22⋊C812yes—
161C2×C4×C53#9912yes—
162C2×C4×C53#10112yes—
163C2×C4×C53#12111yescharacteristic
164C2×C4×C53#12111yescharacteristic
165C2×C4×C53C22⋊Q811yescharacteristic
166C2×C4×C53C22⋊Q811yescharacteristic
167C2×Dic53—22no—
168C2×Dic53—22no—
169C2×Dic53—22no—
170C2×Dic53—22no—
171C2×Dic53—22no—
172C2×Dic53—22no—
173C2×Dic53—22no—
174C2×Dic53—22no—
175C2×Dic53—22no—
176C2×Dic53—42no—
177C2×Dic53—42no—
178C2×Dic53—42no—
179C2×Dic53—41no—
180C2×Dic53—41no—
181C2×Dic53—41no—
182C2×Dic53—41no—
183C2×Dic53—41no—
184C2×Dic53—41no—
185C2×Dic53—42no—
186C2×Dic53—42no—
187C2×Dic53—42no—
188C2×Dic53C4⋊C814yescomplemented
189C8×C53—82no—
190#88322—82no—
191#8560—531nomaximal, Sylow
192C22×C53—21no—
193C22×C53—21no—
194C22×C53—21no—
195C22×C53—21no—
196C22×C53—21no—
197C22×C53—21no—
198C22×C53—21no—
199C22×C53—21no—
200C22×C53—21no—
201C22×C53—21no—
202C22×C53—21no—
203C22×C53—21no—
204C22×C53#38011yescharacteristic
205C22×C53C2×C22⋊C811yescharacteristic
206C22×C53#40711yescharacteristic
207C22×C53C2×#9911yescharacteristic
208C22×C53#41011yescharacteristic
209C22×C53C2×#10111yescharacteristic
210C22×C53#41311yescharacteristic
211C22×C53C2×C4⋊C811yescharacteristic
212C22×C53#42311yescharacteristic
213C22×C53#43111yescharacteristic
214C22×C53#43211yescharacteristic
215C4×C53—21no—
216C4×C53—21no—
217C4×C53—21no—
218C4×C53—21no—
219C4×C53—22no—
220C4×C53—22no—
221C4×C53—22no—
222C4×C53—22no—
223Dic53—24no—
224Dic53—42no—
225Dic53—42no—
226Dic53—42no—
227C2×C4×C4⋊C4—531no—
228#1797—531no—
229#1797D5311yescharacteristic
230C2×#324—532no—
231#1280—532no—
232C2×C53—21no—
233C2×C53—21no—
234C2×C53—21no—
235C2×C53—21no—
236C2×C53#145911yescharacteristic
237C2×C53#146111yescharacteristic
238C2×C53#146311yescharacteristic
239C2×C53#146411yescharacteristic
240C2×C53#179711yescharacteristic
241C2×C53#179911yescharacteristic
242C2×C53#180111yescharacteristic
243C22×C4⋊C4—531no—
244C22×C4⋊C4—531no—
245C22×C42—531no—
246C22×C42—531no—
247C22×C42C2×D5311yescharacteristic
248C2×C4⋊C8—21no—
249C2×C4⋊C8—1061no—
250C2×C22⋊C8—532no—
251C2×C22⋊C8C2×D5312yes—
252C4×C4⋊C4—1061no—
253C4×C4⋊C4—1061no—
254C4×C4⋊C4—1061no—
255C4×C4⋊C4—1061no—
256C2×#95—531no—
257C2×#95—531no—
258#336—21no—
259#336—1061no—
260#324—1064no—
261C53#856011yescharacteristic, complemented, Sylow
262C23×C4—531no—
263C23×C4—531no—
264C23×C4—531no—
265C23×C4—531no—
266C23×C4C4×D5311yescharacteristic
267C23×C4C4×D5311yescharacteristic
268C23×C4C22×D5311yescharacteristic
269C22×C8—22no—
270C22×C8—1062no—
271C2×C4⋊C4—532no—
272C2×C4⋊C4—532no—
273C2×C4⋊C4—534no—
274C2×C4⋊C4—1061no—
275C2×C4⋊C4—1061no—
276C2×C4⋊C4—1061no—
277C2×C4⋊C4—1061no—
278C2×C4⋊C4—1062no—
279C2×C4⋊C4—1061no—
280C2×C4⋊C4—1061no—
281C2×C42—42no—
282C2×C42—1062no—
283C2×C42—1062no—
284C2×C42—1061no—
285C2×C42—1061no—
286C2×C42—1061no—
287C2×C42—1061no—
288C2×C42—2122no—
289C2×C42D21211yescharacteristic
290C2×C42D21211yescharacteristic
291C2×C42C22⋊D5311yescharacteristic
292C2×C42C22⋊D5311yescharacteristic
293C4⋊C8—42no—
294C4⋊C8—2122no—
295C22⋊C8—22no—
296C22⋊C8—22no—
297C22⋊C8—1062no—
298C22⋊C8—1062no—
299#95—1061no—
300#95—1061no—
301#95—1061no—
302#95—1061no—
303C24C2×C4×D5311yescharacteristic
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—532no—
313C22×C4—532no—
314C22×C4—532no—
315C22×C4—532no—
316C22×C4—532no—
317C22×C4—532no—
318C22×C4—1061no—
319C22×C4—1061no—
320C22×C4—1061no—
321C22×C4—1061no—
322C22×C4—1061no—
323C22×C4—1061no—
324C22×C4—1061no—
325C22×C4—1061no—
326C22×C4—1061no—
327C22×C4—1061no—
328C22×C4—2121no—
329C22×C4—2121no—
330C22×C4—2121no—
331C22×C4—2121no—
332C22×C4—2121no—
333C22×C4—2121no—
334C22×C4C8×D5312yes—
335C22×C4#1171991212yes—
336C22×C4#1171992111yescharacteristic
337C22×C4#1171992111yescharacteristic
338C22×C4#1171992111yescharacteristic
339C22×C4#1171992111yescharacteristic
340C22×C4C2×D21211yescharacteristic
341C22×C4D4×D5311yescharacteristic
342C22×C4#1171994711yescharacteristic
343C22×C4Q8×D5311yescharacteristic
344C22×C4#1171994911yescharacteristic
345C22×C4C2×C22⋊D5311yescharacteristic
346C2×C8—42no—
347C2×C8—42no—
348C2×C8—42no—
349C2×C8—2122no—
350C2×C8—2122no—
351C2×C8—2122no—
352C4⋊C4—1064no—
353C4⋊C4—1064no—
354C4⋊C4—1062no—
355C4⋊C4—1062no—
356C4⋊C4—1062no—
357C4⋊C4—1062no—
358C42—22no—
359C42—22no—
360C42—41no—
361C42—41no—
362C42—1064no—
363C42—1064no—
364C42—2122no—
365C42—2122no—
366C23—21no—
367C23—21no—
368C23—21no—
369C23—21no—
370C23C2×#1171992111yescharacteristic
371C23C4⋊C4×D5311yescharacteristic
372C23#1313317511yescharacteristic
373C23C2×C8×D5311yescharacteristic
374C23M16×D5311yescharacteristic
375C23M16×D5311yescharacteristic
376C23C2×#1171991211yescharacteristic
377C2×C4—24no—
378C2×C4—24no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—534no—
398C2×C4—1062no—
399C2×C4—1062no—
400C2×C4—1062no—
401C2×C4—1062no—
402C2×C4—1062no—
403C2×C4—1062no—
404C2×C4—1062no—
405C2×C4—1062no—
406C2×C4—1062no—
407C2×C4—2122no—
408C2×C4—2122no—
409C2×C4—2122no—
410C2×C4—2121no—
411C2×C4—2121no—
412C2×C4—2121no—
413C2×C4—2121no—
414C2×C4—2121no—
415C2×C4—2121no—
416C2×C4—2122no—
417C2×C4—2122no—
418C2×C4—2122no—
419C2×C4#1313312912yes—
420C2×C4#1313312912yes—
421C2×C4#1313313112yes—
422C2×C4#1313313512yes—
423C2×C4#1313318811yescharacteristic
424C2×C4#1313319211yescharacteristic
425C2×C4#1313319311yescharacteristic
426C2×C4#1313319711yescharacteristic
427C8—82no—
428C8—4242no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22#1681048011yescharacteristic
442C22C2×#1313312911yescharacteristic
443C22#1681058611yescharacteristic
444C22C2×#1313313111yescharacteristic
445C22#1681059611yescharacteristic
446C22C2×#1313313511yescharacteristic
447C22#1681060511yescharacteristic
448C22C4⋊C8×D5311yescharacteristic
449C22#1681064511yescharacteristic
450C22#1681067511yescharacteristic
451C22#1681067911yescharacteristic
452C4—21no—
453C4—21no—
454C4—21no—
455C4—21no—
456C4—22no—
457C4—22no—
458C4—22no—
459C4—22no—
460C4—1064no—
461C4—2122no—
462C4—2122no—
463C4—2122no—
464C2—21no—
465C2—21no—
466C2—21no—
467C2—21no—
468C2#2027303111yescharacteristic
469C2#2027303811yescharacteristic
470C2#2027304411yescharacteristic
471C2#2027304711yescharacteristic
472C2#2027469211yescharacteristic
473C2#2027470011yescharacteristic
474C2#2027470811yescharacteristic
subgroupG/H
centerC23C2×#11719921
commutatorC23×C53C22×C8
FrattiniC23×C4C22×D53
FittingC53×#1797C2
socleC23×C53C2×C22⋊C4
prime radicalC24×C53C22×C4
cosocleC23×C4×C53C23
hypercenter#1797D53
hypocenterC53#8560
LCSG ▷ C23×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
36. C2×#11719919C8semidirect
188. C2×Dic53C4⋊C8semidirect
261. C53#8560semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#117199192
#202746952
C2×#168103482
#202725572
C53×#17972
#856053