Finite Group Databasebeta

← #14726763

Subgroups — #14726763

Order 2816.

1002 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082419C211yesmaximal, characteristic
2C2×#10622584C212yesmaximal, complemented
3#13067623C214yesmaximal, complemented
4#13067606C214yesmaximal, complemented
5#13067187C212yesmaximal, complemented
6#13066934C211yesmaximal, characteristic
7C11×#2486C211yesmaximal, characteristic
8C2×C11×#123—21no—
9C2×C4×D4×C11C2211yescharacteristic
10C22×C11×C4⋊C4C2211yescharacteristic
11#10623329—21no—
12C2×#66977—21no—
13C2×#66977C2212yes—
14#10623074—22no—
15#10623070—24no—
16D4×Dic22—22no—
17#10623031C2212yes—
18#10623014—21no—
19#10623014C2212yes—
20#10623001—21no—
21C11×#398C2212yes—
22C11×#397C2212yes—
23C11×#389—21no—
24C11×#381—21no—
25C11×#380—21no—
26C11×#380C2211yescharacteristic
27C2×C22⋊(C11⋊C8)C2212yes—
28#10622584—24no—
29#10622584C2218yes—
30C2×#66874—22no—
31C2×#66872—22no—
32#10622166C2212yes—
33#10622163C2212yes—
34#10622090C2218yes—
35C22×D4×C11D411yescharacteristic
36C23×C4×C11—21no—
37C23×C4×C11D411yescharacteristic
38C23×C4×C11C2311yescharacteristic
39C22×Dic22—21no—
40C22×Dic22D412yes—
41C11×#123—44no—
42C4×D4×C11—22no—
43C4×D4×C11—22no—
44C2×C11×C4⋊C4—22no—
45C2×C11×C4⋊C4—22no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4—22no—
49C2×C11×C4⋊C4C2312yes—
50C2×C11×C4⋊C4C2311yescharacteristic
51C2×C11×C22⋊C4—22no—
52C2×C11×C22⋊C4—21no—
53C2×C11×C22⋊C4D411yescharacteristic
54C2×C11×C22⋊C4C2311yescharacteristic
55C2×C42×C11D411yescharacteristic
56C2×C22⋊Dic11—22no—
57C2×C22⋊Dic11—22no—
58D4×Dic11—24no—
59D4×Dic11—24no—
60#66979—22no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11D412yes—
63#66977—22no—
64#66977—22no—
65#66977—22no—
66#66977—22no—
67#66977—22no—
68#66977—22no—
69#66977D414yes—
70#66977C2314yes—
71C2×Dic11⋊C4—22no—
72C2×Dic11⋊C4—22no—
73C22×C11⋊C8—22no—
74#66943—24no—
75#66941—24no—
76#66931—24no—
77#66931—24no—
78#66931—24no—
79#66931—24no—
80#66923—22no—
81#66922—21no—
82#66922—21no—
83C4×Dic22—22no—
84C4×Dic22—22no—
85C11×#95—22no—
86C11×#95—22no—
87C11×#95C2312yes—
88C22⋊(C11⋊C8)—22no—
89C22⋊(C11⋊C8)C2314yes—
90#66874—28no—
91#66872—28no—
92#18204—111nomaximal, Sylow
93C24×C11C2×D411yescharacteristic
94C24×C11C2×D411yescharacteristic
95C2×D4×C11—22no—
96C2×D4×C11—22no—
97C2×D4×C11SD1614yes—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—42no—
103C22×C4×C11—42no—
104C22×C4×C11—42no—
105C22×C4×C11—42no—
106C22×C4×C11—42no—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D412yes—
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2411yescharacteristic
114C22×Dic11—22no—
115C22×Dic11—22no—
116C22×Dic11—22no—
117C22×Dic11—22no—
118C2×Dic22—22no—
119C2×Dic22—22no—
120C2×Dic22—22no—
121C2×Dic22—44no—
122C2×Dic22—82no—
123C2×Dic22C2×D414yes—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—24no—
126C11×C4⋊C4—42no—
127C11×C4⋊C4—41no—
128C11×C4⋊C4—41no—
129C11×C4⋊C4—44no—
130C11×C22⋊C4—22no—
131C11×C22⋊C4—22no—
132C11×C22⋊C4—42no—
133C11×C22⋊C4—44no—
134C42×C11—21no—
135C42×C11—21no—
136C22⋊Dic11—24no—
137C22⋊Dic11—24no—
138C22⋊Dic11—24no—
139C4⋊Dic11—22no—
140C4⋊Dic11—22no—
141C4⋊Dic11—22no—
142C4⋊Dic11—22no—
143C4⋊Dic11—22no—
144C4⋊Dic11C2×D414yes—
145Dic11⋊C4—24no—
146Dic11⋊C4—24no—
147Dic11⋊C4—24no—
148Dic11⋊C4—24no—
149C4×Dic11—24no—
150C2×C11⋊C8—24no—
151C2×C11⋊C8—44no—
152#3501—111no—
153C2×#483—112no—
154#2486D1111yescharacteristic
155#1611—114no—
156#1608—114no—
157#1520—112no—
158#1459—111no—
159C23×C11—21no—
160C23×C11—21no—
161C23×C11—41no—
162C23×C11—41no—
163C23×C11—41no—
164C23×C11—41no—
165C23×C11#12012yes—
166C23×C11C2×SD1612yes—
167C23×C11C2×SD1612yes—
168C23×C11#13712yes—
169C23×C11C22×D411yescharacteristic
170D4×C11—28no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—24no—
174C2×C4×C11—22no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—42no—
178C2×C4×C11—41no—
179C2×C4×C11—42no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—81no—
189C2×C4×C11—84no—
190C2×C4×C11#12011yescharacteristic
191C2×C4×C11#12011yescharacteristic
192C2×C4×C11C2×SD1612yes—
193C2×C4×C11C22×D412yes—
194C2×Dic11—24no—
195C2×Dic11—24no—
196C2×Dic11—82no—
197C2×Dic11—82no—
198C2×Dic11—82no—
199C2×Dic11—82no—
200Dic22—44no—
201Dic22—44no—
202Dic22—82no—
203Dic22—82no—
204C11⋊C8—44no—
205#554—222no—
206#554—224no—
207D4×Q8—222no—
208#544—112no—
209#543—112no—
210#543—221no—
211#533—221no—
212C2×#123—21no—
213C2×C22⋊Q8—112no—
214C2×C22⋊Q8—221no—
215#518—221no—
216C2×C4×D4C2×D1111yescharacteristic
217C22×C4⋊C4C2×D1111yescharacteristic
218#483—118no—
219#483—224no—
220C2×#106—222no—
221C2×#103—222no—
222C2×C22⋊C8—112no—
223#398C2×D1112yes—
224#397C2×D1112yes—
225#389—21no—
226#381—21no—
227#380—21no—
228#380C2×D1111yescharacteristic
229#328—118no—
230#324—112no—
231#323—112no—
232C22×C11—21no—
233C22×C11—22no—
234C22×C11—21no—
235C22×C11—22no—
236C22×C11—22no—
237C22×C11—42no—
238C22×C11—42no—
239C22×C11—42no—
240C22×C11—41no—
241C22×C11—41no—
242C22×C11—81no—
243C22×C11#44814yes—
244C22×C11C2×#12011yescharacteristic
245C22×C11C22×SD1611yescharacteristic
246C22×C11C2×#13711yescharacteristic
247C4×C11—22no—
248C4×C11—21no—
249C4×C11—22no—
250C4×C11—41no—
251C4×C11—41no—
252C4×C11—82no—
253C4×C11—82no—
254C4×C11#45812yes—
255Dic11—44no—
256Dic11—44no—
257C22×Q8—112no—
258C22×Q8—221no—
259C22×D4C22⋊D1111yescharacteristic
260C23×C4—21no—
261C23×C4C22⋊D1111yescharacteristic
262C23×C4C22×D1111yescharacteristic
263C22×C8—222no—
264C4⋊Q8—221no—
265C4⋊Q8—221no—
266C4⋊Q8—224no—
267#125—222no—
268#125—224no—
269#123—44no—
270C22⋊Q8—114no—
271C22⋊Q8—114no—
272C22⋊Q8—224no—
273C22⋊Q8—224no—
274C22⋊Q8—224no—
275C22⋊Q8—224no—
276C22⋊Q8—222no—
277C22⋊Q8—222no—
278C22⋊Q8—222no—
279C22⋊Q8—222no—
280C22⋊Q8—222no—
281C22⋊Q8—222no—
282C4×Q8—222no—
283C4×Q8—222no—
284C4×D4—22no—
285C4×D4—22no—
286C4×D4—224no—
287C4×D4—224no—
288#117—222no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—112no—
295C2×C4⋊C4—222no—
296C2×C4⋊C4—221no—
297C2×C4⋊C4—222no—
298C2×C4⋊C4C22×D1112yes—
299C2×C4⋊C4C22×D1111yescharacteristic
300C2×C22⋊C4—22no—
301C2×C22⋊C4—21no—
302C2×C22⋊C4—222no—
303C2×C22⋊C4—222no—
304C2×C22⋊C4C22⋊D1111yescharacteristic
305C2×C22⋊C4C22×D1111yescharacteristic
306C2×C42C22⋊D1111yescharacteristic
307#106—228no—
308#103—228no—
309C22⋊C8—114no—
310C22⋊C8—222no—
311#95—22no—
312#95—22no—
313#95C22×D1112yes—
314C2×C11—21no—
315C2×C11—21no—
316C2×C11—24no—
317C2×C11—42no—
318C2×C11C2×#44811yescharacteristic
319C2×C11#302211yescharacteristic
320C2×C11C2×#45811yescharacteristic
321C24C2×C22⋊D1111yescharacteristic
322C24C2×C22⋊D1111yescharacteristic
323C2×Q8—114no—
324C2×Q8—222no—
325C2×Q8—222no—
326C2×Q8—222no—
327C2×Q8—444no—
328C2×Q8—882no—
329C2×D4—22no—
330C2×D4—22no—
331C2×D4#432414yes—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—42no—
337C22×C4—42no—
338C22×C4—42no—
339C22×C4—42no—
340C22×C4—42no—
341C22×C4—222no—
342C22×C4—222no—
343C22×C4—222no—
344C22×C4—222no—
345C22×C4D4×D1112yes—
346C22×C4D4×D1112yes—
347C22×C4C2×C22⋊D1111yescharacteristic
348C22×C4C2×C22⋊D1111yescharacteristic
349C22×C4C2×C22⋊D1111yescharacteristic
350C22×C4C2×C22⋊D1111yescharacteristic
351C22×C4C23×D1111yescharacteristic
352C2×C8—224no—
353C2×C8—444no—
354C4⋊C4—22no—
355C4⋊C4—24no—
356C4⋊C4—42no—
357C4⋊C4—44no—
358C4⋊C4—41no—
359C4⋊C4—41no—
360C4⋊C4—114no—
361C4⋊C4—222no—
362C4⋊C4—224no—
363C4⋊C4—222no—
364C4⋊C4—222no—
365C4⋊C4—224no—
366C4⋊C4—222no—
367C4⋊C4—222no—
368C4⋊C4—224no—
369C4⋊C4—224no—
370C22⋊C4—22no—
371C22⋊C4—22no—
372C22⋊C4—42no—
373C22⋊C4—44no—
374C22⋊C4—224no—
375C22⋊C4—224no—
376C22⋊C4—224no—
377C42—21no—
378C42—21no—
379C42—224no—
380C11#1820411yescharacteristic, complemented, Sylow
381C23—21no—
382C23—21no—
383C23—41no—
384C23—41no—
385C23—41no—
386C23—41no—
387C23C2×#432412yes—
388C23C2×#432412yes—
389C23#6699012yes—
390C23#6700412yes—
391C23C22×C22⋊D1111yescharacteristic
392Q8—444no—
393Q8—444no—
394Q8—882no—
395Q8—882no—
396D4—28no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—22no—
400C2×C4—24no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—42no—
404C2×C4—41no—
405C2×C4—42no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—81no—
415C2×C4—84no—
416C2×C4—224no—
417C2×C4—224no—
418C2×C4—882no—
419C2×C4—882no—
420C2×C4—882no—
421C2×C4—882no—
422C2×C4C2×#432412yes—
423C2×C4#6699011yescharacteristic
424C2×C4#6699011yescharacteristic
425C2×C4C2×D4×D1112yes—
426C8—444no—
427C22—21no—
428C22—22no—
429C22—21no—
430C22—22no—
431C22—22no—
432C22—42no—
433C22—42no—
434C22—42no—
435C22—41no—
436C22—41no—
437C22—81no—
438C22#1062265314yes—
439C22C22×#432411yescharacteristic
440C22C2×#6699011yescharacteristic
441C22C2×#6700411yescharacteristic
442C4—22no—
443C4—22no—
444C4—21no—
445C4—41no—
446C4—41no—
447C4—82no—
448C4—82no—
449C4—444no—
450C4—444no—
451C4#1062266612yes—
452C2—21no—
453C2—21no—
454C2—24no—
455C2—42no—
456C2C2×#1062265311yescharacteristic
457C2#1307799411yescharacteristic
458C2C2×#1062266611yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2486C2
socleC22×C11C2×#120
prime radicalC22×D4×C11D4
hypercenter#2486D11
hypocenterC11#18204
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2486

Complements

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

NH ≅ G/Ntype
2. C2×#10622584C2semidirect
3. #13067623C2semidirect
4. #13067606C2semidirect
5. #13067187C2semidirect
380. C11#18204semidirect

Maximal subgroups

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

subgroupindex
#130824192
C2×#106225842
#130676232
#130676062
#130671872
#130669342
C11×#24862
#1820411