Finite Group Databasebeta

← #14719848

Subgroups — #14719848

Order 2816.

970 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66942C211yesmaximal, characteristic
2#13077245C212yesmaximal
3#13066970C218yesmaximal, complemented
4#13066946C211yesmaximal, characteristic
5#13066945C212yesmaximal
6C11×#1463C211yesmaximal, characteristic
7C22×C11×C4⋊C4C2211yescharacteristic
8C22×C4⋊Dic11C411yescharacteristic
9C22×Dic11⋊C4C411yescharacteristic
10C22×Dic11⋊C4C411yescharacteristic
11C22×Dic11⋊C4C411yescharacteristic
12C22×Dic11⋊C4C2211yescharacteristic
13C22×C4×Dic11C2211yescharacteristic
14C2×#66942—22no—
15C2×#66942—22no—
16C2×#66942—22no—
17C2×#66942—22no—
18C2×#66942C414yes—
19C2×#66942C2214yes—
20C11×#407C2212yes—
21#10622820C2212yes—
22#10622731—22no—
23M16×Dic11—22no—
24#10622332—22no—
25#10622332C2214yes—
26#10622331—22no—
27#10622331C2214yes—
28C11×#324C2214yes—
29#10622166C2214yes—
30#10622107C2218yes—
31C23×C4×C11C2×C411yescharacteristic
32C23×C4×C11C2×C411yescharacteristic
33C23×C4×C11C2311yescharacteristic
34C23×Dic11C2×C411yescharacteristic
35C23×Dic11C2×C411yescharacteristic
36C23×Dic11C2×C411yescharacteristic
37C23×Dic11C2×C411yescharacteristic
38C2×C11×M16—22no—
39C2×C11×C4⋊C4—22no—
40C2×C11×C4⋊C4—22no—
41C2×C11×C4⋊C4C2×C412yes—
42C2×C11×C4⋊C4C2312yes—
43C2×C4⋊Dic11—21no—
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11—22no—
46C2×C4⋊Dic11C2×C414yes—
47C2×Dic11⋊C4—22no—
48C2×Dic11⋊C4—22no—
49C2×Dic11⋊C4—21no—
50C2×Dic11⋊C4—22no—
51C2×Dic11⋊C4—21no—
52C2×Dic11⋊C4—21no—
53C2×Dic11⋊C4—22no—
54C2×Dic11⋊C4—21no—
55C2×Dic11⋊C4—21no—
56C2×Dic11⋊C4—22no—
57C2×Dic11⋊C4—21no—
58C2×Dic11⋊C4C2×C412yes—
59C2×Dic11⋊C4C2×C414yes—
60C2×Dic11⋊C4C2×C414yes—
61C2×Dic11⋊C4C2×C414yes—
62C2×Dic11⋊C4C2312yes—
63C2×C4×Dic11C2×C412yes—
64C2×C4×Dic11D412yes—
65C2×C4×Dic11D412yes—
66C2×C4×Dic11D412yes—
67C2×C4×Dic11D412yes—
68C2×C4×Dic11C2312yes—
69C2×#4318—22no—
70#66942—24no—
71#66942—24no—
72#66942—24no—
73#66942—24no—
74#66942—24no—
75#66942—24no—
76#66942—24no—
77#66942—24no—
78C11×C22⋊C8—22no—
79C11×C22⋊C8C2314yes—
80C22⋊(C11⋊C8)—22no—
81C22⋊(C11⋊C8)C2314yes—
82#66879—24no—
83Dic11⋊C8—24no—
84Dic11⋊C8—24no—
85C8×Dic11—24no—
86#17394—111nomaximal, Sylow
87C24×C11C22×C411yescharacteristic
88C22×C4×C11—21no—
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—42no—
93C22×C4×C11—42no—
94C22×C4×C11—42no—
95C22×C4×C11C22×C412yes—
96C22×C4×C11C22×C412yes—
97C22×C4×C11C22×C411yescharacteristic
98C22×C4×C11C2×D412yes—
99C22×C4×C11C2×D412yes—
100C22×C4×C11C2411yescharacteristic
101C22×Dic11—24no—
102C22×Dic11—21no—
103C22×Dic11—21no—
104C22×Dic11—21no—
105C22×Dic11—21no—
106C22×Dic11—42no—
107C22×Dic11—42no—
108C22×Dic11—42no—
109C22×Dic11C22⋊C412yes—
110C22×Dic11C22⋊C411yescharacteristic
111C22×Dic11C22⋊C411yescharacteristic
112C22×Dic11C22⋊C411yescharacteristic
113C22×Dic11C22⋊C412yes—
114C22×Dic11C22⋊C411yescharacteristic
115C22×Dic11C22×C412yes—
116C22×Dic11C22×C412yes—
117C22×Dic11C22×C412yes—
118C22×Dic11C22×C412yes—
119C11×M16—44no—
120C2×C8×C11—24no—
121C11×C4⋊C4—24no—
122C11×C4⋊C4—24no—
123C4⋊Dic11—24no—
124C4⋊Dic11—24no—
125Dic11⋊C4—24no—
126Dic11⋊C4—24no—
127Dic11⋊C4—24no—
128Dic11⋊C4—24no—
129Dic11⋊C4—24no—
130Dic11⋊C4—24no—
131Dic11⋊C4—24no—
132Dic11⋊C4—24no—
133C4×Dic11C22⋊C412yes—
134C4×Dic11C22⋊C412yes—
135C4×Dic11C22⋊C412yes—
136C4×Dic11C22⋊C412yes—
137C4×Dic11C2×D412yes—
138C4×Dic11C2×D412yes—
139C4×Dic11C2×D412yes—
140C4×Dic11C2×D412yes—
141#4318—44no—
142C2×C11⋊C8—24no—
143C22×#125—111no—
144#2920—112no—
145#1470—118no—
146#1463—112no—
147#1463—111no—
148#1463D1111yescharacteristic
149C23×C11—22no—
150C23×C11—22no—
151C23×C11—22no—
152C23×C11C2×C22⋊C411yescharacteristic
153C23×C11C2×C22⋊C411yescharacteristic
154C23×C11C23×C411yescharacteristic
155C2×C4×C11—24no—
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—24no—
159C2×C4×C11—41no—
160C2×C4×C11—42no—
161C2×C4×C11—41no—
162C2×C4×C11—42no—
163C2×C4×C11—42no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11C2×C22⋊C412yes—
168C2×C4×C11C22×D412yes—
169C2×Dic11—24no—
170C2×Dic11—22no—
171C2×Dic11—24no—
172C2×Dic11—24no—
173C2×Dic11—22no—
174C2×Dic11—22no—
175C2×Dic11—24no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—42no—
179C2×Dic11—42no—
180C2×Dic11—42no—
181C2×Dic11—42no—
182C2×Dic11—42no—
183C2×Dic11—42no—
184C2×Dic11#10114yes—
185C2×Dic11C2×C22⋊C412yes—
186C2×Dic11C2×C22⋊C412yes—
187C2×Dic11C2×C22⋊C412yes—
188C2×Dic11C2×C22⋊C412yes—
189C8×C11—44no—
190C11⋊C8—44no—
191C2×#125—114no—
192C2×#125—114no—
193C2×#125—222no—
194C2×#125—222no—
195C2×#125—222no—
196C2×#125—222no—
197C22×C4⋊C4—111no—
198C22×C4⋊C4—111no—
199C22×C4⋊C4—111no—
200C22×C4⋊C4—111no—
201C22×C4⋊C4—111no—
202C22×C4⋊C4C2×D1111yescharacteristic
203C22×C42—111no—
204#432—114no—
205#432—222no—
206#431—114no—
207#431—222no—
208#423—222no—
209#407—112no—
210#407C2×D1112yes—
211C4×M16—222no—
212#324—114no—
213#324—118no—
214#324C2×D1114yes—
215C22×C11—28no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11—21no—
221C22×C11—21no—
222C22×C11#41012yes—
223C22×C11C2×#10112yes—
224C22×C11C22×C22⋊C411yescharacteristic
225C22×C11#56812yes—
226C4×C11—22no—
227C4×C11—22no—
228C4×C11—42no—
229C4×C11—42no—
230Dic11—22no—
231Dic11—22no—
232Dic11—22no—
233Dic11—42no—
234Dic11—42no—
235Dic11C2×#10114yes—
236C23×C4—111no—
237C23×C4—111no—
238C23×C4—111no—
239C23×C4—111no—
240C23×C4C4×D1111yescharacteristic
241C23×C4C4×D1111yescharacteristic
242C23×C4C22×D1111yescharacteristic
243C2×M16—22no—
244C2×M16—222no—
245#125—224no—
246#125—224no—
247#125—224no—
248#125—224no—
249#125—224no—
250#125—224no—
251#125—224no—
252#125—224no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—114no—
256C2×C4⋊C4—114no—
257C2×C4⋊C4—114no—
258C2×C4⋊C4—112no—
259C2×C4⋊C4—114no—
260C2×C4⋊C4—112no—
261C2×C4⋊C4—221no—
262C2×C4⋊C4—221no—
263C2×C4⋊C4—222no—
264C2×C4⋊C4—222no—
265C2×C4⋊C4—221no—
266C2×C4⋊C4—221no—
267C2×C4⋊C4—221no—
268C2×C4⋊C4—221no—
269C2×C4⋊C4—222no—
270C2×C4⋊C4—222no—
271C2×C4⋊C4—221no—
272C2×C4⋊C4—221no—
273C2×C4⋊C4—222no—
274C2×C4⋊C4—222no—
275C2×C4⋊C4C4×D1112yes—
276C2×C4⋊C4C22×D1112yes—
277C2×C42—112no—
278C2×C42—112no—
279C2×C42—112no—
280C2×C42—112no—
281C2×C42—112no—
282C2×C42—112no—
283C4⋊C8—224no—
284C4⋊C8—224no—
285C22⋊C8—22no—
286C22⋊C8—114no—
287C22⋊C8—222no—
288C22⋊C8C22×D1114yes—
289#97—224no—
290C4×C8—224no—
291C2×C11—22no—
292C2×C11—22no—
293C2×C11—22no—
294C2×C11#287911yescharacteristic
295C2×C11C2×#41011yescharacteristic
296C2×C11C22×#10111yescharacteristic
297C24C2×C4×D1111yescharacteristic
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—42no—
303C22×C4—42no—
304C22×C4—42no—
305C22×C4—111no—
306C22×C4—112no—
307C22×C4—111no—
308C22×C4—112no—
309C22×C4—112no—
310C22×C4—111no—
311C22×C4—111no—
312C22×C4—112no—
313C22×C4—112no—
314C22×C4—112no—
315C22×C4—224no—
316C22×C4—221no—
317C22×C4—221no—
318C22×C4—221no—
319C22×C4—221no—
320C22×C4—442no—
321C22×C4—442no—
322C22×C4—442no—
323C22×C4C2×C4×D1112yes—
324C22×C4C2×C4×D1112yes—
325C22×C4C2×C4×D1111yescharacteristic
326C22×C4D4×D1112yes—
327C22×C4D4×D1112yes—
328C22×C4C23×D1111yescharacteristic
329M16—44no—
330M16—444no—
331C2×C8—24no—
332C2×C8—224no—
333C4⋊C4—24no—
334C4⋊C4—24no—
335C4⋊C4—224no—
336C4⋊C4—224no—
337C4⋊C4—224no—
338C4⋊C4—224no—
339C4⋊C4—224no—
340C4⋊C4—224no—
341C4⋊C4—224no—
342C4⋊C4—224no—
343C4⋊C4—224no—
344C4⋊C4—224no—
345C42—112no—
346C42—112no—
347C42—112no—
348C42—112no—
349C42—112no—
350C42—112no—
351C42—112no—
352C42—112no—
353C11#1739411yescharacteristic, complemented, Sylow
354C23—22no—
355C23—22no—
356C23—22no—
357C23C22⋊C4×D1111yescharacteristic
358C23C22⋊C4×D1111yescharacteristic
359C23C22×C4×D1111yescharacteristic
360C2×C4—24no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—24no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—112no—
373C2×C4—114no—
374C2×C4—112no—
375C2×C4—112no—
376C2×C4—112no—
377C2×C4—224no—
378C2×C4—224no—
379C2×C4—224no—
380C2×C4—222no—
381C2×C4—222no—
382C2×C4—222no—
383C2×C4—224no—
384C2×C4—441no—
385C2×C4—441no—
386C2×C4—442no—
387C2×C4—442no—
388C2×C4—442no—
389C2×C4—442no—
390C2×C4—442no—
391C2×C4—442no—
392C2×C4C22⋊C4×D1112yes—
393C2×C4C2×D4×D1112yes—
394C8—44no—
395C8—444no—
396C22—28no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22#1062235312yes—
404C22D11×#10112yes—
405C22C2×C22⋊C4×D1111yescharacteristic
406C22#1062327612yes—
407C4—22no—
408C4—22no—
409C4—42no—
410C4—42no—
411C4—114no—
412C4—222no—
413C4—222no—
414C4—222no—
415C4—442no—
416C4—442no—
417C2—22no—
418C2—22no—
419C2—22no—
420C2#1307705911yescharacteristic
421C2C2×#1062235311yescharacteristic
422C2C2×D11×#10111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1463C2
socleC22×C11C22×C22⋊C4
prime radicalC24×C11C22×C4
cosocleC22×C4×C11C24
hypercenter#1463D11
hypocenterC11#17394
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
3. #13066970C2semidirect
353. C11#17394semidirect

Maximal subgroups

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

subgroupindex
C22×#669422
#130772452
#130669702
#130669462
#130669452
C11×#14632
#1739411