Finite Group Databasebeta

← #27283015

Subgroups — #27283015

Order 13568.

510 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11719922C211yesmaximal, characteristic
2#20273461C211yesmaximal, characteristic, complemented
3#20273107C211yesmaximal, characteristic, complemented
4#20273106C211yesmaximal, characteristic, complemented
5#20273035C211yesmaximal, characteristic, complemented
6#20272999C211yesmaximal, characteristic, complemented
7C53×#1460C211yesmaximal, characteristic, complemented
8C22×#11719922C411yescharacteristic
9C2×C4×D212C2211yescharacteristic
10C4×#11719922—21no—
11C4×#11719922—21no—
12C4×#11719922—21no—
13C4×#11719922—21no—
14#16810676C2211yescharacteristic
15#16810676C2211yescharacteristic
16C2×#13133150C411yescharacteristic
17C2×#13133138C411yescharacteristic
18C2×#13133137C411yescharacteristic
19C2×C4×#88322C2211yescharacteristic
20#16810375—21no—
21#16810373—21no—
22#16810352—22no—
23D4⋊#88322—22no—
24#16810346—22no—
25#16810345—21no—
26C8×#88322—21no—
27C2×C4×D4×C53C2211yescharacteristic
28C53×#431C2211yescharacteristic
29C53×#431C2211yescharacteristic
30C53×#323—22no—
31C22×D212C2×C411yescharacteristic
32C22×C4×D53—21no—
33C2×#11719922—21no—
34C2×#11719922—21no—
35C2×#11719922—22no—
36C2×#11719922C814yescomplemented
37C22×#88322C2×C411yescharacteristic
38C22×#88322C2×C411yescharacteristic
39C4×D212—21no—
40C4×D212—21no—
41C4×D212—21no—
42C4×D212—21no—
43C2×C4⋊Dic53C2×C411yescharacteristic
44C2×#11719921—21no—
45#13133150—21no—
46#13133150—21no—
47C4⋊#88322—21no—
48C4⋊#88322D412yes—
49#13133138—21no—
50#13133138—21no—
51#13133137—21no—
52#13133137—21no—
53C22⋊#88322—21no—
54C22⋊#88322—21no—
55C4×#88322—21no—
56C4×#88322—21no—
57C4×#88322D411yescharacteristic
58C4×#88322D411yescharacteristic
59C4×#88322D411yescharacteristic
60C4×#88322D411yescharacteristic
61C22×D4×C53C2×C411yescharacteristic
62C23×C4×C53—21no—
63C4×D4×C53—21no—
64C4×D4×C53—21no—
65C4×D4×C53—21no—
66C4×D4×C53—21no—
67C2×C4⋊C4×C53C2×C411yescharacteristic
68C2×C22⋊C4×C53—21no—
69C2×C42×C53C2311yescharacteristic
70C4⋊C8×C53—21no—
71C4⋊C8×C53—21no—
72C22⋊C8×C53—21no—
73C22⋊C8×C53D412yes—
74C4×C8×C53—21no—
75C4×C8×C53—21no—
76C24×C53—21no—
77C23×D53—21no—
78C2×D4×C53—21no—
79C2×D4×C53—21no—
80C2×D4×C53—21no—
81C2×D4×C53—21no—
82C2×D4×C53—21no—
83C2×D4×C53C2×C812yes—
84C22×C4×C53—21no—
85C22×C4×C53—41no—
86C22×C4×C53—41no—
87C22×C4×C53—82no—
88C22×C4×C53C22×C411yescharacteristic
89C22×C4×C53C2×D411yescharacteristic
90C22×C4×C53#4111yescharacteristic
91C22×Dic53—21no—
92C2×D212—21no—
93C2×D212—21no—
94C2×D212—21no—
95C2×D212—21no—
96C2×D212—21no—
97C2×D212C2×C812yes—
98C2×C4×D53—41no—
99C2×C4×D53—41no—
100C2×C4×D53—82no—
101C2×C8×C53—22no—
102C2×C8×C53—41no—
103C4⋊C4×C53—21no—
104C4⋊C4×C53—21no—
105C22⋊C4×C53—41no—
106C22⋊C4×C53—41no—
107C42×C53C2×D411yescharacteristic
108C42×C53C2×D411yescharacteristic
109C42×C53C2×D411yescharacteristic
110C42×C53#4111yescharacteristic
111#11719922—24no—
112#11719922—24no—
113#11719921—41no—
114#11719921—41no—
115C4⋊Dic53—21no—
116C4⋊Dic53—21no—
117C2×#88322—21no—
118C2×#88322—21no—
119C2×#88322—22no—
120C2×#88322—41no—
121C2×#88322C22⋊C411yescharacteristic
122C2×#88322C22⋊C411yescharacteristic
123C2×#88322C22⋊C411yescharacteristic
124C2×#88322C22⋊C411yescharacteristic
125C2×#88322C2×C812yes—
126C2×#88322M1612yes—
127C23×C53—22no—
128C23×C53—41no—
129C23×C53—41no—
130C23×C53—81no—
131C23×C53—81no—
132C23×C53C4×D411yescharacteristic
133C22×D53—22no—
134C22×D53—41no—
135C22×D53—41no—
136C22×D53—81no—
137C22×D53—81no—
138D4×C53—22no—
139D4×C53—22no—
140D4×C53—41no—
141D4×C53—41no—
142C2×C4×C53—22no—
143C2×C4×C53—41no—
144C2×C4×C53—41no—
145C2×C4×C53—82no—
146C2×C4×C53—82no—
147C2×C4×C53—81no—
148C2×C4×C53C2×C22⋊C411yescharacteristic
149C2×C4×C53C4×D411yescharacteristic
150C2×C4×C53#12111yescharacteristic
151C2×C4×C53#12111yescharacteristic
152C2×C4×C53#12411yescharacteristic
153C2×C4×C53#12711yescharacteristic
154C2×C4×C53C22×C811yescharacteristic
155C2×C4×C53C2×M1611yescharacteristic
156C2×C4×C53#13111yescharacteristic
157C2×C4×C53#13111yescharacteristic
158C2×Dic53—41no—
159C2×Dic53—81no—
160D212—22no—
161D212—22no—
162D212—41no—
163D212—41no—
164C4×D53—82no—
165C4×D53—82no—
166C8×C53—42no—
167C8×C53—81no—
168#88322—21no—
169#88322—21no—
170#88322—42no—
171#88322—81no—
172#88322C22⋊C812yes—
173#88322C22⋊C812yes—
174#9668—531nomaximal, Sylow
175C22×C53—21no—
176C22×C53—21no—
177C22×C53—42no—
178C22×C53—82no—
179C22×C53—82no—
180C22×C53—81no—
181C22×C53—81no—
182C22×C53#39011yescharacteristic
183C22×C53C8×D411yescharacteristic
184C22×C53#43611yescharacteristic
185C2×D53—42no—
186C2×D53—82no—
187C2×D53—81no—
188C2×D53—81no—
189C2×D53—82no—
190C4×C53—21no—
191C4×C53—21no—
192C4×C53—21no—
193C4×C53—81no—
194C4×C53C2×C22⋊C811yescharacteristic
195C4×C53#40811yescharacteristic
196C4×C53C8×D411yescharacteristic
197C4×C53#43611yescharacteristic
198C4×C53#47212yes—
199Dic53—81no—
200C2×C4×D8—531no—
201#1564—531no—
202#1478—531no—
203#1478—531no—
204#1460—531no—
205#1460D5311yescharacteristic, complemented
206#1450—531no—
207C2×C53—21no—
208C2×C53—21no—
209C2×C53—82no—
210C2×C53#195411yescharacteristic
211C2×C53#197611yescharacteristic
212C2×C53#197811yescharacteristic
213D53—82no—
214C22×D8—531no—
215C2×C4×D4—531no—
216C2×C4×D4C2×D5311yescharacteristic
217C4×D8—1061no—
218C4×D8—1061no—
219C4×D8—1061no—
220C4×D8—1061no—
221#431—531no—
222#431—531no—
223#431C2×D5311yescharacteristic
224#431C2×D5311yescharacteristic
225C2×#107—531no—
226C2×#102—531no—
227C2×#102—531no—
228C2×C4×C8—531no—
229#335—1061no—
230#334—1061no—
231D4⋊C8—1062no—
232D4⋊C8—1062no—
233#323—22no—
234#323—1062no—
235#322—1061no—
236C82—1061no—
237C53#966811yescharacteristic, complemented, Sylow
238C22×D4—531no—
239C22×D4C4×D5311yescharacteristic
240C23×C4—21no—
241C23×C4—1061no—
242C2×D8—534no—
243C2×D8—1062no—
244C2×D8—1061no—
245C2×D8—1061no—
246C22×C8—531no—
247C22×C8—531no—
248C4×D4—21no—
249C4×D4—21no—
250C4×D4—21no—
251C4×D4—21no—
252C4×D4—1061no—
253C4×D4—1061no—
254C4×D4—1061no—
255C4×D4—1061no—
256C2×C4⋊C4—531no—
257C2×C4⋊C4C4×D5311yescharacteristic
258C2×C22⋊C4—21no—
259C2×C22⋊C4—1061no—
260C2×C42C22×D5311yescharacteristic
261#107—1061no—
262#107—1061no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8—532no—
266C4⋊C8—1061no—
267#102—1061no—
268#102—1061no—
269#102—1061no—
270#102—1061no—
271C22⋊C8—21no—
272C22⋊C8—1061no—
273C22⋊C8—1061no—
274C22⋊C8C22⋊D5312yes—
275C4×C8—21no—
276C4×C8—21no—
277C4×C8—531no—
278C4×C8—531no—
279C4×C8—531no—
280C4×C8—531no—
281C4×C8—1061no—
282C4×C8—1061no—
283C24—21no—
284C24—1061no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—532no—
291C2×D4—1061no—
292C2×D4—1061no—
293C2×D4—1061no—
294C2×D4—1061no—
295C2×D4—1061no—
296C2×D4C8×D5312yes—
297C22×C4—21no—
298C22×C4—41no—
299C22×C4—41no—
300C22×C4—82no—
301C22×C4—1061no—
302C22×C4—4242no—
303C22×C4—2121no—
304C22×C4—2121no—
305C22×C4C2×C4×D5311yescharacteristic
306C22×C4#1171994511yescharacteristic
307C22×C4C2×C22⋊D5311yescharacteristic
308D8—1064no—
309D8—1064no—
310C2×C8—22no—
311C2×C8—41no—
312C2×C8—531no—
313C2×C8—531no—
314C2×C8—532no—
315C2×C8—532no—
316C2×C8—531no—
317C2×C8—531no—
318C2×C8—1061no—
319C2×C8—1061no—
320C2×C8—1062no—
321C2×C8—2121no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—1061no—
325C4⋊C4—1061no—
326C22⋊C4—41no—
327C22⋊C4—41no—
328C22⋊C4—2121no—
329C22⋊C4—2121no—
330C42D4×D5311yescharacteristic
331C42D4×D5311yescharacteristic
332C42D4×D5311yescharacteristic
333C42#1171994711yescharacteristic
334C23—22no—
335C23—41no—
336C23—41no—
337C23—81no—
338C23—81no—
339C23—1062no—
340C23—4241no—
341C23—4241no—
342C23—2121no—
343C23—2121no—
344C23C4×C22⋊D5311yescharacteristic
345D4—22no—
346D4—22no—
347D4—41no—
348D4—41no—
349D4—1062no—
350D4—1062no—
351D4—2121no—
352D4—2121no—
353C2×C4—22no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—82no—
357C2×C4—82no—
358C2×C4—81no—
359C2×C4—4242no—
360C2×C4—4242no—
361C2×C4—4241no—
362C2×C4—2121no—
363C2×C4C22⋊C4×D5311yescharacteristic
364C2×C4#1313317711yescharacteristic
365C2×C4#1313318911yescharacteristic
366C2×C4#1313319011yescharacteristic
367C2×C4#1313320311yescharacteristic
368C2×C4#1313321311yescharacteristic
369C2×C4C2×C8×D5311yescharacteristic
370C2×C4M16×D5311yescharacteristic
371C2×C4#1313322311yescharacteristic
372C2×C4#1313322511yescharacteristic
373C8—42no—
374C8—81no—
375C8—532no—
376C8—532no—
377C8—1061no—
378C8—1061no—
379C8—4241no—
380C8—2122no—
381C22—21no—
382C22—21no—
383C22—42no—
384C22—82no—
385C22—82no—
386C22—81no—
387C22—81no—
388C22—4242no—
389C22—4242no—
390C22—4241no—
391C22—4241no—
392C22—2122no—
393C22#1681052311yescharacteristic
394C22C8×C22⋊D5311yescharacteristic
395C22#1681069911yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—81no—
400C4—4241no—
401C4C22⋊C8×D5311yescharacteristic
402C4#1681058811yescharacteristic
403C4#1681068611yescharacteristic
404C4#1681069811yescharacteristic
405C4#1681089212yes—
406C2—21no—
407C2—21no—
408C2—82no—
409C2—4242no—
410C2#2027550711yescharacteristic
411C2#2027561011yescharacteristic
412C2#2027562211yescharacteristic
subgroupG/H
centerC2×C4#13133190
commutatorC2×C4×C53C22×C8
FrattiniC2×C42C22×D53
FittingC53×#1460C2
socleC22×C53#390
prime radicalC22×#11719922C4
cosocleC2×C42×C53C23
hypercenter#1460D53
hypocenterC53#9668
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1460

Complements

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

NH ≅ G/Ntype
2. #20273461C2semidirect
3. #20273107C2semidirect
4. #20273106C2semidirect
5. #20273035C2semidirect
6. #20272999C2semidirect
7. C53×#1460C2semidirect
36. C2×#11719922C8semidirect
205. #1460D53semidirect
237. C53#9668semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#117199222
#202734612
#202731072
#202731062
#202730352
#202729992
C53×#14602
#966853