Finite Group Databasebeta

← #27279539

Subgroups — #27279539

Order 13568.

456 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20283798C211yesmaximal, characteristic
2C2×#16810731C211yesmaximal, characteristic
3#20273111C211yesmaximal, characteristic
4#20273109C211yesmaximal, characteristic
5#20273038C211yesmaximal, characteristic
6#20272560C211yesmaximal, characteristic
7C53×#1275C211yesmaximal, characteristic
8C22×Dic212C411yescharacteristic
9C2×C4×Dic106C2211yescharacteristic
10C2×C4×Dic106C2211yescharacteristic
11#16810753—22no—
12#16810750—22no—
13#16810731—22no—
14#16810731—22no—
15#16810677—22no—
16#16810676C2211yescharacteristic
17#16810676C2211yescharacteristic
18C2×#13133149C411yescharacteristic
19C2×#13133142C411yescharacteristic
20C2×#13133142C411yescharacteristic
21#16810355—22no—
22#16810353—22no—
23#16810348—22no—
24C53×#431C2211yescharacteristic
25C53×#431C2211yescharacteristic
26C2×#97×C53C2211yescharacteristic
27C22×Dic106C2×C411yescharacteristic
28C22×Dic106C2×C411yescharacteristic
29C2×Dic212—22no—
30C2×Dic212—22no—
31C2×Dic212—22no—
32C4×Dic106—21no—
33C4×Dic106—21no—
34C4×Dic106—21no—
35C4×Dic106—21no—
36C4×Dic106—21no—
37C4×Dic106—21no—
38C4×Dic106D412yes—
39C4×Dic106D412yes—
40C2×C4⋊Dic53C2×C411yescharacteristic
41C2×C4⋊Dic53C2×C411yescharacteristic
42C2×#11719919—21no—
43C2×#11719919—21no—
44C2×C4×Dic53—21no—
45C2×C4×Dic53—21no—
46#13133149—22no—
47C4⋊#88322—21no—
48C4⋊#88322—21no—
49#13133146—24no—
50#13133142—22no—
51#13133142—22no—
52C22⋊#88322—21no—
53C22⋊#88322D412yes—
54#13133127—24no—
55C4×#88322—21no—
56C4×#88322—21no—
57C22×C8×C53C2×C411yescharacteristic
58C22×C8×C53C2×C411yescharacteristic
59C2×C42×C53C2311yescharacteristic
60C4⋊C8×C53—21no—
61C4⋊C8×C53—21no—
62C22⋊C8×C53—21no—
63C22⋊C8×C53—21no—
64#97×C53—21no—
65#97×C53—21no—
66C4×C8×C53—21no—
67C4×C8×C53D412yes—
68C22×C4×C53C22×C411yescharacteristic
69C22×C4×C53C2×D411yescharacteristic
70C22×C4×C53#4111yescharacteristic
71C22×Dic53—21no—
72C22×Dic53—21no—
73C22×Dic53—21no—
74C22×Dic53—21no—
75C2×Dic106—21no—
76C2×Dic106—21no—
77C2×Dic106—21no—
78C2×Dic106—21no—
79C2×Dic106—21no—
80C2×Dic106—21no—
81C2×Dic106—21no—
82C2×Dic106—21no—
83C2×Dic106—21no—
84C2×Dic106—21no—
85C2×Dic106C22⋊C412yes—
86C2×Dic106M1612yes—
87C2×C8×C53—21no—
88C2×C8×C53—21no—
89C2×C8×C53—21no—
90C2×C8×C53—22no—
91C2×C8×C53—21no—
92C2×C8×C53—21no—
93C2×C8×C53—41no—
94C2×C8×C53M1612yes—
95C42×C53C2×D411yescharacteristic
96C42×C53C2×D411yescharacteristic
97C42×C53C2×D411yescharacteristic
98C42×C53#4111yescharacteristic
99C4⋊Dic53—21no—
100C4⋊Dic53—21no—
101C4⋊Dic53—21no—
102C4⋊Dic53C22⋊C412yes—
103#11719919—22no—
104#11719919—22no—
105#11719919—41no—
106#11719919—41no—
107C4×Dic53—22no—
108C4×Dic53—22no—
109C4×Dic53—41no—
110C4×Dic53—41no—
111C2×#88322—22no—
112C2×#88322—41no—
113Dic212—28no—
114C23×C53C4×D411yescharacteristic
115C2×C4×C53—41no—
116C2×C4×C53—41no—
117C2×C4×C53C2×C22⋊C411yescharacteristic
118C2×C4×C53C4×D411yescharacteristic
119C2×C4×C53#12011yescharacteristic
120C2×C4×C53#12111yescharacteristic
121C2×C4×C53#12111yescharacteristic
122C2×C4×C53#12311yescharacteristic
123C2×C4×C53C2×M1611yescharacteristic
124C2×C4×C53C2×M1611yescharacteristic
125C2×C4×C53#13111yescharacteristic
126C2×C4×C53#13111yescharacteristic
127C2×Dic53—22no—
128C2×Dic53—22no—
129C2×Dic53—22no—
130C2×Dic53—41no—
131C2×Dic53—41no—
132C2×Dic53—41no—
133C2×Dic53—41no—
134C2×Dic53—41no—
135C2×Dic53—81no—
136C2×Dic53—81no—
137Dic106—22no—
138Dic106—22no—
139Dic106—22no—
140Dic106—22no—
141Dic106—41no—
142Dic106—41no—
143Dic106—41no—
144Dic106—41no—
145C8×C53—22no—
146C8×C53—42no—
147C8×C53—41no—
148C8×C53—81no—
149#88322—42no—
150#88322—81no—
151#9092—531nomaximal, Sylow
152C22×C53—21no—
153C22×C53—21no—
154C22×C53#38611yescharacteristic
155C22×C53#43511yescharacteristic
156C22×C53#43611yescharacteristic
157C4×C53—21no—
158C4×C53—21no—
159C4×C53—21no—
160C4×C53—21no—
161C4×C53#40711yescharacteristic
162C4×C53#40811yescharacteristic
163C4×C53#43511yescharacteristic
164C4×C53#43611yescharacteristic
165Dic53—42no—
166Dic53—42no—
167Dic53—42no—
168Dic53—81no—
169#2983—531no—
170C2×#441—531no—
171#1479—531no—
172#1479—531no—
173#1461—531no—
174#1281—531no—
175#1275D5311yescharacteristic
176C2×C53—21no—
177C2×C53—21no—
178C2×C53#187011yescharacteristic
179C2×C53#190211yescharacteristic
180C2×C53#190511yescharacteristic
181C22×Q16—531no—
182C2×C4×Q8—531no—
183C2×C4×Q8—531no—
184#446—1062no—
185#446—1062no—
186#441—1062no—
187#441—1062no—
188#432—1062no—
189#431—531no—
190#431—531no—
191#431C2×D5311yescharacteristic
192#431C2×D5311yescharacteristic
193C2×#106—531no—
194C2×#103—531no—
195C2×#103—531no—
196C2×#97C2×D5311yescharacteristic
197Q8⋊C8—1062no—
198Q8⋊C8—1062no—
199#324—1062no—
200C53#909211yescharacteristic, complemented, Sylow
201C22×Q8—531no—
202C22×Q8—531no—
203C2×Q16—1062no—
204C2×Q16—1062no—
205C2×Q16—1062no—
206C22×C8C4×D5311yescharacteristic
207C22×C8C4×D5311yescharacteristic
208C4×Q8—532no—
209C4×Q8—532no—
210C4×Q8—1061no—
211C4×Q8—1061no—
212C4×Q8—1061no—
213C4×Q8—1061no—
214C4×Q8—1061no—
215C4×Q8—1061no—
216C2×C4⋊C4—531no—
217C2×C4⋊C4—531no—
218C2×C4⋊C4—1061no—
219C2×C4⋊C4—1061no—
220C2×C42—1061no—
221C2×C42—1061no—
222C2×C42C22×D5311yescharacteristic
223#106—1062no—
224C4⋊C8—21no—
225C4⋊C8—21no—
226C4⋊C8—1064no—
227C4⋊C8—1061no—
228C4⋊C8—1061no—
229#103—1062no—
230#103—1062no—
231C22⋊C8—21no—
232C22⋊C8—21no—
233C22⋊C8—532no—
234C22⋊C8—1061no—
235#97—21no—
236#97—21no—
237#97—1064no—
238C4×C8—21no—
239C4×C8—1061no—
240C4×C8—1061no—
241C4×C8D21212yes—
242C2×Q8—532no—
243C2×Q8—532no—
244C2×Q8—1061no—
245C2×Q8—1061no—
246C2×Q8—1061no—
247C2×Q8—1061no—
248C2×Q8—1061no—
249C2×Q8—1061no—
250C2×Q8—1061no—
251C2×Q8—1061no—
252C2×Q8—1061no—
253C2×Q8—1061no—
254C22×C4—1061no—
255C22×C4—1061no—
256C22×C4—1061no—
257C22×C4—1061no—
258C22×C4C2×C4×D5311yescharacteristic
259C22×C4D4×D5311yescharacteristic
260C22×C4#1171994911yescharacteristic
261Q16—1068no—
262C2×C8—21no—
263C2×C8—21no—
264C2×C8—21no—
265C2×C8—22no—
266C2×C8—21no—
267C2×C8—21no—
268C2×C8—41no—
269C2×C8—1062no—
270C2×C8—2121no—
271C2×C8#1171991212yes—
272C4⋊C4—532no—
273C4⋊C4—1061no—
274C4⋊C4—1062no—
275C4⋊C4—1062no—
276C4⋊C4—1061no—
277C4⋊C4—1061no—
278C4⋊C4—2121no—
279C4⋊C4—2121no—
280C42—1062no—
281C42—1062no—
282C42—2121no—
283C42—2121no—
284C42C2×D21211yescharacteristic
285C42#1171994511yescharacteristic
286C42D4×D5311yescharacteristic
287C42D4×D5311yescharacteristic
288C23#1313317911yescharacteristic
289Q8—1062no—
290Q8—1062no—
291Q8—1062no—
292Q8—1062no—
293Q8—2121no—
294Q8—2121no—
295Q8—2121no—
296Q8—2121no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—1062no—
300C2×C4—1062no—
301C2×C4—1062no—
302C2×C4—4241no—
303C2×C4—4241no—
304C2×C4—2121no—
305C2×C4—2121no—
306C2×C4—2121no—
307C2×C4—2121no—
308C2×C4—2121no—
309C2×C4C22⋊C4×D5311yescharacteristic
310C2×C4C4×D21211yescharacteristic
311C2×C4#1313318711yescharacteristic
312C2×C4#1313319011yescharacteristic
313C2×C4#1313319211yescharacteristic
314C2×C4#1313320211yescharacteristic
315C2×C4M16×D5311yescharacteristic
316C2×C4C2×#1171991211yescharacteristic
317C2×C4#1313322311yescharacteristic
318C2×C4#1313322511yescharacteristic
319C8—22no—
320C8—42no—
321C8—41no—
322C8—81no—
323C8—4241no—
324C8—2122no—
325C22—21no—
326C22—21no—
327C22#1681050111yescharacteristic
328C22#1681069311yescharacteristic
329C22#1681070011yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—4241no—
335C4—2122no—
336C4—2122no—
337C4—2122no—
338C4#1681058511yescharacteristic
339C4#1681058811yescharacteristic
340C4#1681069611yescharacteristic
341C4#1681070211yescharacteristic
342C2—21no—
343C2—21no—
344C2#2027501111yescharacteristic
345C2#2027518911yescharacteristic
346C2#2027521011yescharacteristic
subgroupG/H
centerC22#16810501
commutatorC22×C4×C53C22×C4
FrattiniC2×C42C22×D53
FittingC53×#1275C2
socleC22×C53#386
prime radicalC23×C53C4×D4
cosocleC2×C42×C53C23
hypercenter#1275D53
hypocenterC53#9092
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1275

Complements

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

NH ≅ G/Ntype
200. C53#9092semidirect

Maximal subgroups

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

subgroupindex
#202837982
C2×#168107312
#202731112
#202731092
#202730382
#202725602
C53×#12752
#909253