Finite Group Databasebeta

← #14719870

Subgroups — #14719870

Order 2816.

1034 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077249C212yesmaximal, complemented
2#13066985C218yesmaximal, complemented
3#13066946C212yesmaximal, complemented
4#13066943C212yesmaximal
5C22×C11×#126C211yesmaximal, characteristic
6C2×C11×#126—22no—
7C2×C11×#126—22no—
8C2×C11×#126—22no—
9C2×C11×#126—22no—
10C2×C11×#126C414yes—
11C2×C11×#126C2214yes—
12C22×C11×C4⋊C4C411yescharacteristic
13C22×C11×C4⋊C4C411yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C22⋊C4C411yescharacteristic
16C22×C11×C22⋊C4C411yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19#10622820C2214yes—
20#10622539—22no—
21#10622539C2214yescomplemented
22#10622538—22no—
23#10622538C2214yescomplemented
24#10622537—22no—
25C4×#4318—22no—
26#10622166C2218yescomplemented
27#10622163C2218yes—
28C25×C11C2×C411yescharacteristic
29C23×C4×C11C2×C411yescharacteristic
30C23×C4×C11C2×C411yescharacteristic
31C23×C4×C11C2×C411yescharacteristic
32C23×C4×C11C2×C411yescharacteristic
33C23×C4×C11C2×C411yescharacteristic
34C23×C4×C11C2311yescharacteristic
35C11×#126—24no—
36C11×#126—24no—
37C11×#126—24no—
38C11×#126—24no—
39C11×#126—24no—
40C11×#126—24no—
41C11×#126—24no—
42C11×#126—24no—
43C2×C11×C4⋊C4—22no—
44C2×C11×C4⋊C4—22no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4C2×C414yes—
52C2×C11×C4⋊C4C2×C414yes—
53C2×C11×C4⋊C4C2×C412yes—
54C2×C11×C4⋊C4C2312yes—
55C2×C11×C22⋊C4—22no—
56C2×C11×C22⋊C4—21no—
57C2×C11×C22⋊C4—21no—
58C2×C11×C22⋊C4—21no—
59C2×C11×C22⋊C4—21no—
60C2×C11×C22⋊C4—22no—
61C2×C11×C22⋊C4—22no—
62C2×C11×C22⋊C4—22no—
63C2×C11×C22⋊C4C2×C414yes—
64C2×C11×C22⋊C4C2×C414yes—
65C2×C11×C22⋊C4C2×C412yes—
66C2×C11×C22⋊C4C2312yes—
67C2×C42×C11C2×C412yes—
68C2×C42×C11D412yes—
69C2×C42×C11D412yes—
70C2×C42×C11D412yes—
71C2×C42×C11D412yes—
72C2×C42×C11C2312yes—
73C2×#4318—24no—
74C22⋊(C11⋊C8)—24no—
75C22⋊(C11⋊C8)C2318yes—
76C4⋊(C11⋊C8)—24no—
77C4⋊(C11⋊C8)—24no—
78#66867—24no—
79C4×C11⋊C8—24no—
80#17398—111nomaximal, Sylow
81C24×C11—21no—
82C24×C11—21no—
83C24×C11—42no—
84C24×C11—42no—
85C24×C11—42no—
86C24×C11C22×C411yescharacteristic
87C24×C11C22×C412yes—
88C22×C4×C11—21no—
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—42no—
95C22×C4×C11—42no—
96C22×C4×C11—42no—
97C22×C4×C11—42no—
98C22×C4×C11—42no—
99C22×C4×C11—42no—
100C22×C4×C11C22⋊C412yes—
101C22×C4×C11C22⋊C411yescharacteristic
102C22×C4×C11C22⋊C412yes—
103C22×C4×C11C22⋊C411yescharacteristic
104C22×C4×C11C22⋊C411yescharacteristic
105C22×C4×C11C22⋊C411yescharacteristic
106C22×C4×C11C22×C412yes—
107C22×C4×C11C22×C412yes—
108C22×C4×C11C22×C412yes—
109C22×C4×C11C22×C412yes—
110C22×C4×C11C22×C411yescharacteristic
111C22×C4×C11C22×C412yes—
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2×D412yes—
114C22×C4×C11C2411yescharacteristic
115C11×C4⋊C4—24no—
116C11×C4⋊C4—24no—
117C11×C4⋊C4—24no—
118C11×C4⋊C4—24no—
119C11×C4⋊C4—24no—
120C11×C4⋊C4—24no—
121C11×C22⋊C4—24no—
122C11×C22⋊C4—24no—
123C11×C22⋊C4—24no—
124C11×C22⋊C4—24no—
125C11×C22⋊C4—24no—
126C11×C22⋊C4—24no—
127C42×C11C22⋊C412yes—
128C42×C11C22⋊C412yes—
129C42×C11C22⋊C412yes—
130C42×C11C22⋊C412yes—
131C42×C11C2×D412yes—
132C42×C11C2×D412yes—
133C42×C11C2×D412yes—
134C42×C11C2×D412yes—
135#4318—48no—
136C2×C11⋊C8—28no—
137C22×#126D1111yescharacteristic
138#2920—112no—
139#1473—118no—
140#1463—112no—
141#1462—112no—
142C23×C11—22no—
143C23×C11—22no—
144C23×C11—22no—
145C23×C11—22no—
146C23×C11—24no—
147C23×C11—42no—
148C23×C11—42no—
149C23×C11—42no—
150C23×C11—42no—
151C23×C11—42no—
152C23×C11—42no—
153C23×C11—42no—
154C23×C11—42no—
155C23×C11—88no—
156C23×C11C2×C22⋊C411yescharacteristic
157C23×C11C2×C22⋊C411yescharacteristic
158C23×C11C23×C411yescharacteristic
159C2×C4×C11—24no—
160C2×C4×C11—24no—
161C2×C4×C11—24no—
162C2×C4×C11—22no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—24no—
166C2×C4×C11—42no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—41no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11C2×C22⋊C412yes—
184C2×C4×C11C2×C22⋊C412yes—
185C2×C4×C11C2×C22⋊C412yes—
186C2×C4×C11C2×C22⋊C412yes—
187C2×C4×C11C2×C22⋊C412yes—
188C2×C4×C11C22×D412yes—
189C11⋊C8—48no—
190C2×#126—22no—
191C2×#126—22no—
192C2×#126—22no—
193C2×#126—22no—
194C2×#126Dic1114yes—
195C2×#126C2×D1114yes—
196C22×C4⋊C4Dic1111yescharacteristic
197C22×C4⋊C4Dic1111yescharacteristic
198C22×C4⋊C4C2×D1111yescharacteristic
199C22×C22⋊C4Dic1111yescharacteristic
200C22×C22⋊C4Dic1111yescharacteristic
201C22×C22⋊C4C2×D1111yescharacteristic
202C22×C42C2×D1111yescharacteristic
203#432—114no—
204#432—222no—
205#431—114no—
206#431—222no—
207#423—222no—
208#407—114no—
209C4×M16—222no—
210#324—118no—
211#323—118no—
212C22×C11—28no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11—42no—
220C22×C11—42no—
221C22×C11—42no—
222C22×C11—84no—
223C22×C11—84no—
224C22×C11—84no—
225C22×C11#41012yes—
226C22×C11#41312yes—
227C22×C11C22×C22⋊C411yescharacteristic
228C22×C11#56812yes—
229C4×C11—22no—
230C4×C11—22no—
231C4×C11—22no—
232C4×C11—22no—
233C4×C11—22no—
234C4×C11—22no—
235C4×C11—42no—
236C4×C11—42no—
237C4×C11—42no—
238C25C2×Dic1111yescharacteristic
239C23×C4C2×Dic1111yescharacteristic
240C23×C4C2×Dic1111yescharacteristic
241C23×C4C2×Dic1111yescharacteristic
242C23×C4C2×Dic1111yescharacteristic
243C23×C4C2×Dic1111yescharacteristic
244C23×C4C22×D1111yescharacteristic
245C2×M16—224no—
246#126—24no—
247#126—24no—
248#126—24no—
249#126—24no—
250#126—24no—
251#126—24no—
252#126—24no—
253#126—24no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—22no—
262C2×C4⋊C4C2×Dic1114yes—
263C2×C4⋊C4C2×Dic1114yes—
264C2×C4⋊C4C2×Dic1112yes—
265C2×C4⋊C4C22×D1112yes—
266C2×C22⋊C4—22no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—22no—
272C2×C22⋊C4—22no—
273C2×C22⋊C4—22no—
274C2×C22⋊C4C2×Dic1114yes—
275C2×C22⋊C4C2×Dic1114yes—
276C2×C22⋊C4C2×Dic1112yes—
277C2×C22⋊C4C22×D1112yes—
278C2×C42C2×Dic1112yes—
279C2×C42C22⋊D1112yes—
280C2×C42C22⋊D1112yes—
281C2×C42C22⋊D1112yes—
282C2×C42C22⋊D1112yes—
283C2×C42C22×D1112yes—
284C4⋊C8—224no—
285C4⋊C8—224no—
286C22⋊C8—118no—
287C22⋊C8—224no—
288#97—224no—
289C4×C8—224no—
290C2×C11—22no—
291C2×C11—22no—
292C2×C11—22no—
293C2×C11—82no—
294C2×C11#287911yescharacteristic
295C2×C11C2×#41011yescharacteristic
296C2×C11C2×#41311yescharacteristic
297C24—21no—
298C24—21no—
299C24—42no—
300C24—42no—
301C24—42no—
302C24C22×Dic1111yescharacteristic
303C24C22×Dic1112yes—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—42no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—42no—
315C22×C4—42no—
316C22×C4C22⋊Dic1112yes—
317C22×C4C22⋊Dic1111yescharacteristic
318C22×C4C22⋊Dic1111yescharacteristic
319C22×C4C22⋊Dic1111yescharacteristic
320C22×C4C22⋊Dic1112yes—
321C22×C4C22⋊Dic1111yescharacteristic
322C22×C4C22×Dic1112yes—
323C22×C4C22×Dic1112yes—
324C22×C4C22×Dic1112yes—
325C22×C4C22×Dic1112yes—
326C22×C4C22×Dic1112yes—
327C22×C4C22×Dic1111yescharacteristic
328C22×C4C2×C22⋊D1112yes—
329C22×C4C2×C22⋊D1112yes—
330C22×C4C23×D1111yescharacteristic
331M16—448no—
332C2×C8—228no—
333C4⋊C4—24no—
334C4⋊C4—24no—
335C4⋊C4—24no—
336C4⋊C4—24no—
337C4⋊C4—24no—
338C4⋊C4—24no—
339C22⋊C4—24no—
340C22⋊C4—24no—
341C22⋊C4—24no—
342C22⋊C4—24no—
343C22⋊C4—24no—
344C22⋊C4—24no—
345C42C22⋊Dic1112yes—
346C42C22⋊Dic1112yes—
347C42C22⋊Dic1112yes—
348C42C22⋊Dic1112yes—
349C42C2×C22⋊D1112yes—
350C42C2×C22⋊D1112yes—
351C42C2×C22⋊D1112yes—
352C42C2×C22⋊D1112yes—
353C11#1739811yescharacteristic, complemented, Sylow
354C23—22no—
355C23—22no—
356C23—22no—
357C23—22no—
358C23—24no—
359C23—42no—
360C23—42no—
361C23—42no—
362C23—42no—
363C23—42no—
364C23—42no—
365C23—42no—
366C23—42no—
367C23—88no—
368C23C2×C22⋊Dic1111yescharacteristic
369C23C2×C22⋊Dic1111yescharacteristic
370C23C23×Dic1111yescharacteristic
371C2×C4—24no—
372C2×C4—24no—
373C2×C4—24no—
374C2×C4—24no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—42no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4C2×C22⋊Dic1112yes—
396C2×C4C2×C22⋊Dic1112yes—
397C2×C4C2×C22⋊Dic1112yes—
398C2×C4C2×C22⋊Dic1112yes—
399C2×C4C2×C22⋊Dic1112yes—
400C2×C4C22×C22⋊D1112yes—
401C8—448no—
402C22—28no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—42no—
410C22—42no—
411C22—42no—
412C22—84no—
413C22—84no—
414C22—84no—
415C22#1062285012yes—
416C22#1062285312yes—
417C22#1062335012yes—
418C22C22×C22⋊Dic1111yescharacteristic
419C4—22no—
420C4—22no—
421C4—22no—
422C4—22no—
423C4—22no—
424C4—22no—
425C4—42no—
426C4—42no—
427C4—42no—
428C2—22no—
429C2—22no—
430C2—22no—
431C2—82no—
432C2#1307706111yescharacteristic
433C2C2×#1062285311yescharacteristic
434C2C2×#1062285011yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×#126C2
socleC22×C11C22×C22⋊C4
prime radicalC25×C11C2×C4
cosocleC22×C4×C11C24
hypercenterC22×#126D11
hypocenterC11#17398
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C42 ◁ C22×#126

Complements

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

NH ≅ G/Ntype
1. #13077249C2semidirect
2. #13066985C2semidirect
3. #13066946C2semidirect
21. #10622539C22semidirect
23. #10622538C22semidirect
26. #10622166C22semidirect
353. C11#17398semidirect

Maximal subgroups

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

subgroupindex
#130772492
#130669852
#130669462
#130669432
C22×C11×#1262
#1739811