Finite Group Databasebeta

← #14719939

Subgroups — #14719939

Order 2816.

1012 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
1C2×#10623093C211yesmaximal, characteristic
2#13077644C212yesmaximal, complemented
3#13066974C214yesmaximal, complemented
4#13066961C214yesmaximal, complemented
5#13066957C211yesmaximal, characteristic, complemented
6#13066948C212yesmaximal, complemented
7C11×#1466C211yesmaximal, characteristic, complemented
8C2×C4×D4×C11C2211yescharacteristic
9C2×#66993C411yescharacteristic
10C2×#66991C411yescharacteristic
11C2×#66983C412yes—
12C2×#66982C412yes—
13#10623093—24no—
14#10623093—24no—
15C2×#66948C411yescharacteristic
16C2×#66943C411yescharacteristic
17C2×#66937C2212yes—
18C2×#66936C2212yes—
19C2×C4×D44C2211yescharacteristic
20C2×#66925C2211yescharacteristic
21C11×#432C2212yes—
22#10622539C2212yes—
23#10622449—24no—
24#10622339C2214yes—
25D11×C22⋊C8C2214yes—
26#10622319—24no—
27C11×#323C2214yes—
28#10622163C2214yes—
29#10622107C2214yes—
30#10622106C2214yes—
31C22×D4×C11C2×C411yescharacteristic
32C23×C4×C11C2×C412yes—
33C22×C22⋊D11C2×C412yes—
34C22×C22⋊D11C2×C412yes—
35C22×C22⋊D11C2×C412yes—
36C22×D44C2×C412yes—
37C22×D44C2×C411yescharacteristic
38C22×C4×D11C2×C411yescharacteristic
39C22×C4×D11C2312yes—
40C4×D4×C11—22no—
41C4×D4×C11—22no—
42C2×C11×C4⋊C4C2×C411yescharacteristic
43C2×C11×C22⋊C4C2312yes—
44C2×C42×C11C2311yescharacteristic
45C2×C22⋊Dic11C2×C412yes—
46#66993—24no—
47#66991—24no—
48#66983—24no—
49#66983—24no—
50#66982—24no—
51#66982—24no—
52C2×(C2×D11)⋊C4C2×C411yescharacteristic
53C2×(C2×D11)⋊C4C2×C412yes—
54C2×(C2×D11)⋊C4C2×C412yes—
55C2×(C2×D11)⋊C4C2311yescharacteristic
56C2×C4⋊Dic11C2×C412yes—
57C2×C4⋊Dic11C2×C411yescharacteristic
58C2×Dic11⋊C4C2×C411yescharacteristic
59C2×Dic11⋊C4C2×C412yes—
60C2×Dic11⋊C4C2311yescharacteristic
61C2×C4×Dic11C2×C411yescharacteristic
62C2×#4313—24no—
63C2×C8×D11—24no—
64#66948—24no—
65#66943—24no—
66#66937—24no—
67#66937—24no—
68#66936—24no—
69#66936—24no—
70C4×D44D414yes—
71C4×D44D414yes—
72#66925—22no—
73#66925—22no—
74C11×C4⋊C8—22no—
75C11×C22⋊C8C2314yes—
76C11×#97—22no—
77C22⋊(C11⋊C8)C2314yes—
78(C2×D11)⋊C8—24no—
79(C2×D11)⋊C8—24no—
80C4⋊(C11⋊C8)—22no—
81#66867—22no—
82#17408—111nomaximal, Sylow
83C24×C11C22×C412yes—
84C23×D11C22×C411yescharacteristic
85C23×D11C22×C412yes—
86C2×D4×C11—22no—
87C2×D4×C11—42no—
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11—82no—
91C22×C4×C11C22×C411yescharacteristic
92C22×C4×C11C22×C412yes—
93C22×C4×C11C22×C411yescharacteristic
94C22×C4×C11C2411yescharacteristic
95C2×C22⋊D11—24no—
96C2×C22⋊D11—24no—
97C2×C22⋊D11—24no—
98C2×C22⋊D11—82no—
99C2×C22⋊D11—82no—
100C2×C22⋊D11—82no—
101C22×Dic11C22×C411yescharacteristic
102C22×Dic11C22×C411yescharacteristic
103C22×Dic11C22×C411yescharacteristic
104C22×Dic11C22×C412yes—
105C2×D44—24no—
106C2×D44—42no—
107C2×D44—82no—
108C2×D44C22⋊C414yes—
109C2×C4×D11—22no—
110C2×C4×D11—42no—
111C2×C4×D11—82no—
112C2×C4×D11C2×D414yes—
113C2×C4×D11C2×D414yes—
114C2×C8×C11—24no—
115C11×C4⋊C4—22no—
116C11×C22⋊C4—22no—
117C11×C22⋊C4—22no—
118C42×C11C2×D412yes—
119C42×C11C2×D412yes—
120C22⋊Dic11—24no—
121(C2×D11)⋊C4—24no—
122(C2×D11)⋊C4—21no—
123(C2×D11)⋊C4—21no—
124(C2×D11)⋊C4—22no—
125(C2×D11)⋊C4C22⋊C414yes—
126(C2×D11)⋊C4C22⋊C414yes—
127C4⋊Dic11—24no—
128C4⋊Dic11C22⋊C414yes—
129Dic11⋊C4—24no—
130Dic11⋊C4—21no—
131Dic11⋊C4—21no—
132Dic11⋊C4—22no—
133C4×Dic11—22no—
134C2×C11⋊C8—24no—
135#4313—84no—
136C8×D11—84no—
137C2×#540—111no—
138#2973—112no—
139#1471—114no—
140#1468—114no—
141#1466—111no—
142#1466D1111yescharacteristic, complemented
143#1464—112no—
144C23×C11—22no—
145C23×C11—24no—
146C23×C11—42no—
147C23×C11—42no—
148C23×C11C23×C411yescharacteristic
149C22×D11—24no—
150C22×D11—21no—
151C22×D11—22no—
152C22×D11—42no—
153C22×D11—42no—
154C22×D11—41no—
155C22×D11—41no—
156C22×D11C2×C22⋊C414yes—
157D4×C11—44no—
158C2×C4×C11—22no—
159C2×C4×C11—22no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—42no—
163C2×C4×C11—82no—
164C2×C4×C11—82no—
165C2×C4×C11C2×C22⋊C412yes—
166C2×C4×C11C2×C22⋊C411yescharacteristic
167C2×C4×C11C2×C22⋊C411yescharacteristic
168C2×C4×C11C22×D412yes—
169C22⋊D11—84no—
170C22⋊D11—84no—
171C22⋊D11—84no—
172C2×Dic11—21no—
173C2×Dic11—21no—
174C2×Dic11—21no—
175C2×Dic11—22no—
176C2×Dic11—42no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11C2×C22⋊C414yes—
180D44—44no—
181D44—84no—
182C4×D11—44no—
183C4×D11—44no—
184C4×D11—44no—
185C8×C11—44no—
186C11⋊C8—44no—
187#540—224no—
188#540—224no—
189C2×#127—111no—
190C2×#125—111no—
191C2×#123—112no—
192C2×#123—112no—
193C2×#121—111no—
194C2×#121—112no—
195C2×#121—111no—
196C2×#121—112no—
197C2×C4×D4—111no—
198C2×C4×D4C2×D1111yescharacteristic
199C2×#117—111no—
200#435—224no—
201#435—224no—
202#432—112no—
203#432C2×D1112yes—
204#407—114no—
205C2×C22⋊C8—114no—
206#324—114no—
207#323—114no—
208#323—114no—
209#323C2×D1114yes—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—42no—
213C22×C11—42no—
214C22×C11—42no—
215C22×C11—84no—
216C22×C11C22×C22⋊C411yescharacteristic
217C22×C11#56812yes—
218C2×D11—24no—
219C2×D11—24no—
220C2×D11—24no—
221C2×D11—41no—
222C2×D11—41no—
223C2×D11—41no—
224C2×D11—84no—
225C2×D11—82no—
226C4×C11—22no—
227C4×C11—22no—
228C4×C11—21no—
229C4×C11—21no—
230C4×C11—42no—
231Dic11—24no—
232Dic11—41no—
233Dic11—41no—
234Dic11—41no—
235C22×D4—112no—
236C22×D4—112no—
237C22×D4—112no—
238C22×D4—111no—
239C22×D4—112no—
240C22×D4C4×D1111yescharacteristic
241C23×C4—112no—
242C23×C4—111no—
243C23×C4C4×D1112yes—
244C2×M16—224no—
245C22×C8—224no—
246#127—224no—
247#125—224no—
248#123—224no—
249#123—224no—
250#123—224no—
251#123—224no—
252#121—224no—
253#121—224no—
254#121—224no—
255#121—224no—
256#121—224no—
257#121—224no—
258C4×D4—22no—
259C4×D4—22no—
260C4×D4—114no—
261C4×D4—114no—
262#117—222no—
263#117—222no—
264C2×C4⋊C4—111no—
265C2×C4⋊C4—111no—
266C2×C4⋊C4—112no—
267C2×C4⋊C4—112no—
268C2×C4⋊C4—111no—
269C2×C4⋊C4C4×D1111yescharacteristic
270C2×C22⋊C4—112no—
271C2×C22⋊C4—112no—
272C2×C22⋊C4—111no—
273C2×C22⋊C4—112no—
274C2×C22⋊C4—111no—
275C2×C22⋊C4C22×D1112yes—
276C2×C42—111no—
277C2×C42C22×D1111yescharacteristic
278C4⋊C8—22no—
279C4⋊C8—222no—
280C22⋊C8—114no—
281C22⋊C8—224no—
282C22⋊C8—224no—
283C22⋊C8C22×D1114yes—
284#97—22no—
285#97—222no—
286C2×C11—22no—
287C2×C11—82no—
288C2×C11#287911yescharacteristic
289C2×C11#288311yescharacteristic
290C2×C11#288811yescharacteristic
291D11—44no—
292D11—81no—
293C24—112no—
294C24—111no—
295C24C2×C4×D1112yes—
296C2×D4—22no—
297C2×D4—42no—
298C2×D4—114no—
299C2×D4—224no—
300C2×D4—224no—
301C2×D4—224no—
302C2×D4—224no—
303C2×D4—442no—
304C2×D4—882no—
305C2×D4—882no—
306C2×D4—882no—
307C2×D4—882no—
308C22×C4—22no—
309C22×C4—22no—
310C22×C4—82no—
311C22×C4—112no—
312C22×C4—114no—
313C22×C4—114no—
314C22×C4—111no—
315C22×C4—111no—
316C22×C4—111no—
317C22×C4—222no—
318C22×C4—442no—
319C22×C4—882no—
320C22×C4C2×C4×D1111yescharacteristic
321C22×C4C2×C4×D1112yes—
322C22×C4C2×C4×D1111yescharacteristic
323C22×C4C23×D1111yescharacteristic
324M16—884no—
325C2×C8—24no—
326C2×C8—224no—
327C2×C8—884no—
328C4⋊C4—22no—
329C4⋊C4—114no—
330C4⋊C4—224no—
331C4⋊C4—224no—
332C4⋊C4—221no—
333C4⋊C4—221no—
334C4⋊C4—222no—
335C22⋊C4—22no—
336C22⋊C4—22no—
337C22⋊C4—114no—
338C22⋊C4—114no—
339C22⋊C4—224no—
340C22⋊C4—224no—
341C22⋊C4—221no—
342C22⋊C4—221no—
343C22⋊C4—222no—
344C42—222no—
345C42D4×D1112yes—
346C42D4×D1112yes—
347C11#1740811yescharacteristic, complemented, Sylow
348C23—22no—
349C23—24no—
350C23—42no—
351C23—42no—
352C23—114no—
353C23—224no—
354C23—221no—
355C23—222no—
356C23—442no—
357C23—442no—
358C23—441no—
359C23—441no—
360C23C22×C4×D1111yescharacteristic
361D4—44no—
362D4—444no—
363D4—884no—
364D4—884no—
365D4—884no—
366D4—884no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—42no—
372C2×C4—82no—
373C2×C4—82no—
374C2×C4—114no—
375C2×C4—221no—
376C2×C4—221no—
377C2×C4—221no—
378C2×C4—222no—
379C2×C4—444no—
380C2×C4—444no—
381C2×C4—444no—
382C2×C4—442no—
383C2×C4—441no—
384C2×C4—441no—
385C2×C4C22⋊C4×D1112yes—
386C2×C4C22⋊C4×D1111yescharacteristic
387C2×C4C22⋊C4×D1111yescharacteristic
388C2×C4C2×D4×D1112yes—
389C8—44no—
390C8—444no—
391C22—21no—
392C22—21no—
393C22—42no—
394C22—42no—
395C22—42no—
396C22—84no—
397C22—224no—
398C22—224no—
399C22—224no—
400C22—441no—
401C22—441no—
402C22—441no—
403C22—884no—
404C22—882no—
405C22C2×C22⋊C4×D1111yescharacteristic
406C22#1062327612yes—
407C4—22no—
408C4—22no—
409C4—21no—
410C4—21no—
411C4—42no—
412C4—224no—
413C4—441no—
414C4—441no—
415C4—441no—
416C2—22no—
417C2—82no—
418C2—444no—
419C2—881no—
420C2#1307705911yescharacteristic
421C2#1307707511yescharacteristic
422C2#1307709211yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1466C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#10623093C2
cosocleC22×C4×C11C24
hypercenter#1466D11
hypocenterC11#17408
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1466

Complements

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

NH ≅ G/Ntype
2. #13077644C2semidirect
3. #13066974C2semidirect
4. #13066961C2semidirect
5. #13066957C2semidirect
6. #13066948C2semidirect
7. C11×#1466C2semidirect
142. #1466D11semidirect
347. C11#17408semidirect

Maximal subgroups

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

subgroupindex
C2×#106230932
#130776442
#130669742
#130669612
#130669572
#130669482
C11×#14662
#1740811