Finite Group Databasebeta

← #27303443

Subgroups — #27303443

Order 13568.

482 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811007C211yesmaximal, characteristic
2C2×#16810426C211yesmaximal, characteristic, complemented
3C2×#16810426C211yesmaximal, characteristic, complemented
4C2×#16810423C211yesmaximal, characteristic
5C2×#16810423C211yesmaximal, characteristic
6#20272793C211yesmaximal, characteristic, complemented
7C53×#1942C211yesmaximal, characteristic, complemented
8C22×Dic212C2211yescharacteristic
9C22×#11719913—21no—
10C22×D424C2211yescharacteristic
11C2×#13133205—21no—
12C22×#11719908C2211yescharacteristic
13C22×#11719908C2211yescharacteristic
14#16811007—22no—
15#16811007—22no—
16#16810426—22no—
17#16810426—22no—
18#16810423—22no—
19#16810423—22no—
20C2×#107×C53C2211yescharacteristic
21C2×#107×C53C2211yescharacteristic
22C2×C4×C8×C53C2211yescharacteristic
23C53×#389—21no—
24C53×#340—21no—
25C22×Dic106—21no—
26C22×D212—21no—
27C2×Dic212—21no—
28C2×Dic212—21no—
29C2×Dic212—21no—
30C2×Dic212—21no—
31C2×Dic212—21no—
32C2×Dic212D412yes—
33C2×#11719913—24no—
34C2×#11719913—42no—
35C2×#11719913—42no—
36C2×D424—21no—
37C2×D424—21no—
38C2×D424—21no—
39C2×D424—21no—
40C2×D424—21no—
41C2×D424D412yes—
42#13133205—24no—
43#13133205—42no—
44C2×#11719921—41no—
45C2×#11719921—41no—
46C2×#11719908—21no—
47C2×#11719908—21no—
48C2×#11719908—21no—
49C2×#11719908—21no—
50C2×#11719908—21no—
51C2×#11719908—21no—
52C22×C8×C53D411yescharacteristic
53C22×C8×C53C2311yescharacteristic
54C2×C4⋊C4×C53—21no—
55C2×C4⋊C4×C53—21no—
56C2×C4⋊C4×C53—41no—
57C2×C42×C53D411yescharacteristic
58#107×C53—21no—
59#107×C53—21no—
60#107×C53—21no—
61#107×C53D412yes—
62C4×C8×C53—21no—
63C4×C8×C53—21no—
64#95×C53—41no—
65C23×D53—41no—
66C22×C4×C53—41no—
67C22×C4×C53—41no—
68C22×C4×C53D811yescharacteristic
69C22×C4×C53D811yescharacteristic
70C22×C4×C53C2×D411yescharacteristic
71C22×Dic53—41no—
72C2×D212—22no—
73C2×D212—41no—
74C2×D212—41no—
75C2×D212—41no—
76C2×D212—41no—
77C2×D212—41no—
78C2×Dic106—22no—
79C2×Dic106—41no—
80C2×Dic106—41no—
81C2×Dic106—41no—
82C2×Dic106—41no—
83C2×Dic106—41no—
84C2×C8×C53—21no—
85C2×C8×C53—21no—
86C2×C8×C53SD1612yes—
87C2×C8×C53C2×D411yescharacteristic
88C2×C8×C53C2×D411yescharacteristic
89C2×C8×C53C2×D411yescharacteristic
90C2×C8×C53#4111yescharacteristic
91C2×C8×C53#4111yescharacteristic
92C2×C8×C53#4111yescharacteristic
93C4⋊C4×C53—22no—
94C4⋊C4×C53—41no—
95C4⋊C4×C53—41no—
96C4⋊C4×C53—41no—
97C4⋊C4×C53—82no—
98C42×C53—21no—
99C42×C53—21no—
100#11719921—44no—
101#11719921—44no—
102Dic212—22no—
103Dic212—22no—
104Dic212—41no—
105Dic212—41no—
106D424—22no—
107D424—22no—
108D424—41no—
109D424—41no—
110#11719913—48no—
111#11719908—41no—
112#11719908—41no—
113C23×C53C2×D811yescharacteristic
114C22×D53—42no—
115C22×D53—81no—
116C22×D53—81no—
117C22×D53—81no—
118C22×D53—81no—
119C22×D53—81no—
120C22×D53—81no—
121C2×C4×C53—21no—
122C2×C4×C53—21no—
123C2×C4×C53—21no—
124C2×C4×C53—21no—
125C2×C4×C53—21no—
126C2×C4×C53—21no—
127C2×C4×C53—42no—
128C2×C4×C53—81no—
129C2×C4×C53—81no—
130C2×C4×C53—81no—
131C2×C4×C53—81no—
132C2×C4×C53—81no—
133C2×C4×C53#12011yescharacteristic
134C2×C4×C53#12111yescharacteristic
135C2×C4×C53#12411yescharacteristic
136C2×C4×C53C2×SD1611yescharacteristic
137C2×C4×C53AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C53AGL(1,ℤ/8)11yescharacteristic
139C2×Dic53—42no—
140C2×Dic53—81no—
141C2×Dic53—81no—
142D212—42no—
143D212—42no—
144D212—81no—
145D212—81no—
146Dic106—42no—
147Dic106—42no—
148Dic106—81no—
149Dic106—81no—
150C8×C53—22no—
151C8×C53#12111yescharacteristic
152C8×C53#12111yescharacteristic
153C8×C53#12311yescharacteristic
154C8×C53#12311yescharacteristic
155#13408—531nomaximal, Sylow
156C22×C53#44711yescharacteristic
157C22×C53#45911yescharacteristic
158C22×C53#48611yescharacteristic
159C22×C53#50811yescharacteristic
160C22×C53#50811yescharacteristic
161C22×C53#50911yescharacteristic
162C22×C53#51011yescharacteristic
163C2×D53—82no—
164C2×D53—82no—
165C2×D53—82no—
166C2×D53—161no—
167C2×D53—161no—
168C2×D53—161no—
169C2×D53—161no—
170C4×C53—41no—
171C4×C53—41no—
172C4×C53—82no—
173C4×C53—161no—
174C4×C53#39411yescharacteristic
175C4×C53#45011yescharacteristic
176C4×C53#46011yescharacteristic
177C4×C53#49011yescharacteristic
178Dic53—82no—
179C2×#495—531no—
180C2×#358—531no—
181C2×#358—531no—
182C2×#357—531no—
183C2×#357—531no—
184#1942D5311yescharacteristic, complemented
185#1374—531no—
186C2×C53#204111yescharacteristic
187C2×C53#218611yescharacteristic
188C2×C53#218911yescharacteristic
189C2×C53#221011yescharacteristic
190C2×C53#221111yescharacteristic
191C2×C53#224211yescharacteristic
192C2×C53#224311yescharacteristic
193D53—162no—
194C22×Q16—531no—
195C22×SD16—1061no—
196C22×D8—531no—
197C2×#124—1061no—
198C22×C16—531no—
199C22×C16—531no—
200#495—1062no—
201#495—1062no—
202C2×#107C2×D5311yescharacteristic
203C2×#107C2×D5311yescharacteristic
204C2×C4×C8C2×D5311yescharacteristic
205#389—21no—
206#358—1062no—
207#358—1062no—
208#357—1062no—
209#357—1062no—
210#340—21no—
211C53#1340811yescharacteristic, complemented, Sylow
212C22×Q8—1061no—
213C22×D4—1061no—
214C2×Q16—532no—
215C2×Q16—1061no—
216C2×Q16—1061no—
217C2×Q16—1061no—
218C2×Q16—1061no—
219C2×Q16—1061no—
220C2×SD16—1064no—
221C2×SD16—2122no—
222C2×SD16—2122no—
223C2×D8—532no—
224C2×D8—1061no—
225C2×D8—1061no—
226C2×D8—1061no—
227C2×D8—1061no—
228C2×D8—1061no—
229C22×C8C22⋊D5311yescharacteristic
230C22×C8C22×D5311yescharacteristic
231#124—1064no—
232#124—2122no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—41no—
236C2×C22⋊C4—2121no—
237C2×C22⋊C4—2121no—
238C2×C42C22⋊D5311yescharacteristic
239C2×C16—1061no—
240C2×C16—1061no—
241C2×C16—1061no—
242C2×C16—1061no—
243C2×C16—1061no—
244C2×C16—1061no—
245#107—21no—
246#107—21no—
247#107—21no—
248#107D21212yes—
249C4×C8—21no—
250C4×C8—21no—
251#95—41no—
252C24—2121no—
253C2×Q8—1062no—
254C2×Q8—2121no—
255C2×Q8—2121no—
256C2×Q8—2121no—
257C2×Q8—2121no—
258C2×Q8—2121no—
259C2×D4—1062no—
260C2×D4—2121no—
261C2×D4—2121no—
262C2×D4—2121no—
263C2×D4—2121no—
264C2×D4—2121no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—2121no—
268C22×C4#1171992211yescharacteristic
269C22×C4#1171992211yescharacteristic
270C22×C4C2×C22⋊D5311yescharacteristic
271Q16—1062no—
272Q16—1062no—
273Q16—2121no—
274Q16—2121no—
275SD16—2128no—
276D8—1062no—
277D8—1062no—
278D8—2121no—
279D8—2121no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8#1171992412yes—
283C2×C8C2×D21211yescharacteristic
284C2×C8#1171994511yescharacteristic
285C2×C8D4×D5311yescharacteristic
286C2×C8D4×D5311yescharacteristic
287C2×C8#1171994911yescharacteristic
288C2×C8#1171994911yescharacteristic
289C4⋊C4—22no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—82no—
294C22⋊C4—2124no—
295C22⋊C4—2124no—
296C42—21no—
297C42—21no—
298C16—2121no—
299C16—2121no—
300C23—4241no—
301C23—4241no—
302C23—4241no—
303C23—4241no—
304C23—4241no—
305C23—4241no—
306C23—2122no—
307C23C2×#1171992211yescharacteristic
308Q8—4241no—
309Q8—4241no—
310Q8—2122no—
311Q8—2122no—
312D4—4241no—
313D4—4241no—
314D4—2122no—
315D4—2122no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—4241no—
329C2×C4—4241no—
330C2×C4—2122no—
331C2×C4#1313318511yescharacteristic
332C2×C4#1313319111yescharacteristic
333C2×C4#1313320611yescharacteristic
334C2×C4C2×#1171992411yescharacteristic
335C2×C4#1313324211yescharacteristic
336C2×C4#1313324211yescharacteristic
337C8—22no—
338C8#1313319211yescharacteristic
339C8#1313319211yescharacteristic
340C8#1313320211yescharacteristic
341C8#1313320211yescharacteristic
342C22—8481no—
343C22—8481no—
344C22—8481no—
345C22—8481no—
346C22—4242no—
347C22—4242no—
348C22—4242no—
349C22#1681075611yescharacteristic
350C22#1681081811yescharacteristic
351C22#1681097111yescharacteristic
352C22#1681105311yescharacteristic
353C22#1681105311yescharacteristic
354C22#1681105911yescharacteristic
355C22#1681106411yescharacteristic
356C4—41no—
357C4—41no—
358C4—82no—
359C4—161no—
360C4—4242no—
361C4#1681054011yescharacteristic
362C4#1681077311yescharacteristic
363C4#1681082311yescharacteristic
364C4#1681098911yescharacteristic
365C2—8482no—
366C2#2027594911yescharacteristic
367C2#2027663611yescharacteristic
368C2#2027665311yescharacteristic
369C2#2027677011yescharacteristic
370C2#2027677711yescharacteristic
371C2#2027694911yescharacteristic
372C2#2027695411yescharacteristic
subgroupG/H
centerC23C2×#11719922
commutator, cosocleC22×C8×C53C23
FrattiniC22×C8C22×D53
FittingC53×#1942C2
socleC23×C53C2×D8
prime radicalC22×D424C22
hypercenter#1942D53
hypocenterC53#13408
LCSG ▷ C22×C8×C53 ▷ C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ #1942

Complements

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

NH ≅ G/Ntype
2. C2×#16810426C2semidirect
3. C2×#16810426C2semidirect
6. #20272793C2semidirect
7. C53×#1942C2semidirect
184. #1942D53semidirect
211. C53#13408semidirect

Maximal subgroups

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

subgroupindex
C2×#168110072
C2×#168104262
C2×#168104232
#202727932
C53×#19422
#1340853