Finite Group Databasebeta

← #14726702

Subgroups — #14726702

Order 2816.

1174 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082419C211yesmaximal, characteristic
2C2×#10622841C212yesmaximal, complemented
3#13067589C214yesmaximal, complemented
4#13067572C214yesmaximal, complemented
5#13067187C212yesmaximal, complemented
6#13066934C211yesmaximal, characteristic
7C11×#2409C211yesmaximal, characteristic
8C23×Q8×C11C2211yescharacteristic
9C2×C11×C22⋊Q8—21no—
10C2×C4×D4×C11C2211yescharacteristic
11C22×#4326—22no—
12#10623329—21no—
13C2×#66977—21no—
14C2×#66977C2212yes—
15#10623074—22no—
16#10623070—24no—
17D4×Dic22—22no—
18#10623031C2212yes—
19#10623014—21no—
20#10623014C2212yes—
21#10623001—21no—
22C11×#395C2212yes—
23C11×#393C2212yes—
24C11×#391—21no—
25C11×#386—21no—
26C11×#385—21no—
27C11×#380C2211yescharacteristic
28#10622841—24no—
29#10622841C2218yes—
30C2×#66899—22no—
31C2×C22⋊(C11⋊C8)C2212yes—
32#10622166C2212yes—
33#10622163C2212yes—
34#10622090C2218yes—
35C22×Q8×C11—21no—
36C22×Q8×C11—22no—
37C22×Q8×C11—22no—
38C22×Q8×C11—44no—
39C22×Q8×C11C2312yes—
40C22×D4×C11D411yescharacteristic
41C23×C4×C11—21no—
42C23×C4×C11D411yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C22×Dic22—21no—
45C22×Dic22D412yes—
46C11×C22⋊Q8—44no—
47C4×D4×C11—22no—
48C4×D4×C11—22no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4C2311yescharacteristic
52C2×C11×C22⋊C4—21no—
53C2×C11×C22⋊C4—22no—
54C2×C11×C22⋊C4D411yescharacteristic
55C2×C11×C22⋊C4C2311yescharacteristic
56C2×C42×C11D411yescharacteristic
57C2×C22⋊Dic11—22no—
58C2×C22⋊Dic11—22no—
59C2×#4326—28no—
60C2×#4326—48no—
61D4×Dic11—24no—
62D4×Dic11—24no—
63#66979—22no—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11D412yes—
66#66977—22no—
67#66977—22no—
68#66977—22no—
69#66977—22no—
70#66977—22no—
71#66977—22no—
72#66977D414yes—
73#66977C2314yes—
74C2×Dic11⋊C4—22no—
75C2×Dic11⋊C4—22no—
76C22×C11⋊C8—22no—
77#66943—24no—
78#66941—24no—
79#66931—24no—
80#66931—24no—
81#66931—24no—
82#66931—24no—
83#66923—22no—
84#66922—21no—
85#66922—21no—
86C4×Dic22—22no—
87C4×Dic22—22no—
88C11×#95—22no—
89C11×#95—22no—
90C11×#95C2312yes—
91#66899—28no—
92C22⋊(C11⋊C8)—22no—
93C22⋊(C11⋊C8)C2314yes—
94#18197—111nomaximal, Sylow
95C24×C11C2×D411yescharacteristic
96C24×C11C2×D411yescharacteristic
97C2×Q8×C11—24no—
98C2×Q8×C11—28no—
99C2×Q8×C11—24no—
100C2×Q8×C11—44no—
101C2×Q8×C11—44no—
102C2×Q8×C11—42no—
103C2×Q8×C11—48no—
104C2×Q8×C11—41no—
105C2×Q8×C11—41no—
106C2×D4×C11—22no—
107C2×D4×C11—22no—
108C2×D4×C11Q1614yescomplemented
109C22×C4×C11—22no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—22no—
113C22×C4×C11—42no—
114C22×C4×C11—44no—
115C22×C4×C11—42no—
116C22×C4×C11—42no—
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D412yes—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2411yescharacteristic
124C22×Dic11—22no—
125C22×Dic11—22no—
126C22×Dic11—22no—
127C22×Dic11—22no—
128C2×Dic22—22no—
129C2×Dic22—22no—
130C2×Dic22—22no—
131C2×Dic22—44no—
132C2×Dic22—82no—
133C2×Dic22C2×D414yes—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—42no—
136C11×C4⋊C4—44no—
137C11×C22⋊C4—22no—
138C11×C22⋊C4—22no—
139C11×C22⋊C4—44no—
140C11×C22⋊C4—42no—
141C42×C11—21no—
142C42×C11—21no—
143C22⋊Dic11—24no—
144C22⋊Dic11—24no—
145C22⋊Dic11—24no—
146#4326—416no—
147C4⋊Dic11—22no—
148C4⋊Dic11—22no—
149C4⋊Dic11—22no—
150C4⋊Dic11—22no—
151C4⋊Dic11—22no—
152C4⋊Dic11C2×D414yes—
153Dic11⋊C4—24no—
154Dic11⋊C4—24no—
155Dic11⋊C4—24no—
156Dic11⋊C4—24no—
157C4×Dic11—24no—
158C2×C11⋊C8—24no—
159C2×C11⋊C8—44no—
160#3501—111no—
161C2×#451—112no—
162#2409D1111yescharacteristic
163#1605—114no—
164#1602—114no—
165#1520—112no—
166#1459—111no—
167C23×C11—21no—
168C23×C11—21no—
169C23×C11—41no—
170C23×C11—41no—
171C23×C11—41no—
172C23×C11—41no—
173C23×C11#12012yes—
174C23×C11C2×Q1612yes—
175C23×C11C2×Q1612yescomplemented
176C23×C11#13712yes—
177C23×C11C22×D411yescharacteristic
178Q8×C11—28no—
179Q8×C11—44no—
180Q8×C11—44no—
181Q8×C11—44no—
182D4×C11—28no—
183C2×C4×C11—21no—
184C2×C4×C11—21no—
185C2×C4×C11—24no—
186C2×C4×C11—22no—
187C2×C4×C11—24no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—42no—
191C2×C4×C11—41no—
192C2×C4×C11—42no—
193C2×C4×C11—48no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—81no—
202C2×C4×C11#12011yescharacteristic
203C2×C4×C11#12011yescharacteristic
204C2×C4×C11C2×Q1612yescomplemented
205C2×C4×C11C22×D412yes—
206C2×Dic11—24no—
207C2×Dic11—24no—
208C2×Dic11—82no—
209C2×Dic11—82no—
210C2×Dic11—82no—
211C2×Dic11—82no—
212Dic22—44no—
213Dic22—44no—
214Dic22—82no—
215Dic22—82no—
216C11⋊C8—44no—
217C23×Q8C2×D1111yescharacteristic
218C22×Q16—222no—
219#554—222no—
220#554—224no—
221D4×Q8—222no—
222#544—112no—
223#543—112no—
224#543—221no—
225#533—221no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—112no—
228C2×C22⋊Q8—221no—
229#518—221no—
230C2×C4×D4C2×D1111yescharacteristic
231#451—118no—
232#451—224no—
233C2×#103—222no—
234C2×C22⋊C8—112no—
235#395C2×D1112yes—
236#393C2×D1112yes—
237#391—21no—
238#386—21no—
239#385—21no—
240#380C2×D1111yescharacteristic
241#328—118no—
242#324—112no—
243#323—112no—
244C22×C11—21no—
245C22×C11—22no—
246C22×C11—21no—
247C22×C11—22no—
248C22×C11—22no—
249C22×C11—42no—
250C22×C11—42no—
251C22×C11—42no—
252C22×C11—41no—
253C22×C11—41no—
254C22×C11—81no—
255C22×C11#45114yes—
256C22×C11C2×#12011yescharacteristic
257C22×C11C22×Q1611yescharacteristic
258C22×C11C2×#13711yescharacteristic
259C4×C11—22no—
260C4×C11—21no—
261C4×C11—22no—
262C4×C11—41no—
263C4×C11—44no—
264C4×C11—41no—
265C4×C11—82no—
266C4×C11B(4,𝔽2)12yes—
267Dic11—44no—
268Dic11—44no—
269C22×Q8—21no—
270C22×Q8—22no—
271C22×Q8—22no—
272C22×Q8—44no—
273C22×Q8—112no—
274C22×Q8—221no—
275C22×Q8C22×D1112yes—
276C22×D4C22⋊D1111yescharacteristic
277C23×C4—21no—
278C23×C4C22⋊D1111yescharacteristic
279C23×C4C22×D1111yescharacteristic
280C2×Q16—228no—
281C2×Q16—448no—
282C22×C8—222no—
283C4⋊Q8—221no—
284C4⋊Q8—221no—
285C4⋊Q8—224no—
286#125—222no—
287#125—224no—
288C22⋊Q8—44no—
289C22⋊Q8—114no—
290C22⋊Q8—114no—
291C22⋊Q8—224no—
292C22⋊Q8—224no—
293C22⋊Q8—224no—
294C22⋊Q8—224no—
295C22⋊Q8—222no—
296C22⋊Q8—222no—
297C22⋊Q8—222no—
298C22⋊Q8—222no—
299C22⋊Q8—222no—
300C22⋊Q8—222no—
301C4×Q8—222no—
302C4×Q8—222no—
303C4×D4—22no—
304C4×D4—22no—
305C4×D4—224no—
306C4×D4—224no—
307#117—222no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—112no—
311C2×C4⋊C4—222no—
312C2×C4⋊C4—221no—
313C2×C4⋊C4—222no—
314C2×C4⋊C4C22×D1111yescharacteristic
315C2×C22⋊C4—22no—
316C2×C22⋊C4—21no—
317C2×C22⋊C4—222no—
318C2×C22⋊C4—222no—
319C2×C22⋊C4C22⋊D1111yescharacteristic
320C2×C22⋊C4C22×D1111yescharacteristic
321C2×C42C22⋊D1111yescharacteristic
322#103—228no—
323C22⋊C8—114no—
324C22⋊C8—222no—
325#95—22no—
326#95—22no—
327#95C22×D1112yes—
328C2×C11—21no—
329C2×C11—21no—
330C2×C11—24no—
331C2×C11—42no—
332C2×C11C2×#45111yescharacteristic
333C2×C11#302211yescharacteristic
334C2×C11C2×B(4,𝔽2)11yescharacteristic
335C24C2×C22⋊D1111yescharacteristic
336C24C2×C22⋊D1111yescharacteristic
337C2×Q8—24no—
338C2×Q8—28no—
339C2×Q8—24no—
340C2×Q8—44no—
341C2×Q8—42no—
342C2×Q8—44no—
343C2×Q8—48no—
344C2×Q8—41no—
345C2×Q8—41no—
346C2×Q8—114no—
347C2×Q8—222no—
348C2×Q8—222no—
349C2×Q8—222no—
350C2×Q8—444no—
351C2×Q8—882no—
352C2×D4—22no—
353C2×D4—22no—
354C2×D4#432614yescomplemented
355C22×C4—22no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—22no—
359C22×C4—42no—
360C22×C4—44no—
361C22×C4—42no—
362C22×C4—42no—
363C22×C4—222no—
364C22×C4—222no—
365C22×C4—222no—
366C22×C4—222no—
367C22×C4D4×D1112yes—
368C22×C4D4×D1112yes—
369C22×C4C2×C22⋊D1111yescharacteristic
370C22×C4C2×C22⋊D1111yescharacteristic
371C22×C4C2×C22⋊D1111yescharacteristic
372C22×C4C2×C22⋊D1111yescharacteristic
373C22×C4C23×D1111yescharacteristic
374Q16—4416no—
375C2×C8—224no—
376C2×C8—444no—
377C4⋊C4—22no—
378C4⋊C4—42no—
379C4⋊C4—44no—
380C4⋊C4—114no—
381C4⋊C4—222no—
382C4⋊C4—224no—
383C4⋊C4—222no—
384C4⋊C4—222no—
385C4⋊C4—224no—
386C4⋊C4—222no—
387C4⋊C4—222no—
388C4⋊C4—224no—
389C4⋊C4—224no—
390C22⋊C4—22no—
391C22⋊C4—22no—
392C22⋊C4—44no—
393C22⋊C4—42no—
394C22⋊C4—224no—
395C22⋊C4—224no—
396C22⋊C4—224no—
397C42—21no—
398C42—21no—
399C42—224no—
400C11#1819711yescharacteristic, complemented, Sylow
401C23—21no—
402C23—21no—
403C23—41no—
404C23—41no—
405C23—41no—
406C23—41no—
407C23#6699012yes—
408C23C2×#432612yes—
409C23C2×#432612yescomplemented
410C23#6700412yes—
411C23C22×C22⋊D1111yescharacteristic
412Q8—28no—
413Q8—44no—
414Q8—44no—
415Q8—44no—
416Q8—444no—
417Q8—444no—
418Q8—882no—
419Q8—882no—
420D4—28no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—22no—
424C2×C4—24no—
425C2×C4—24no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—42no—
429C2×C4—41no—
430C2×C4—42no—
431C2×C4—48no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—81no—
440C2×C4—224no—
441C2×C4—224no—
442C2×C4—882no—
443C2×C4—882no—
444C2×C4—882no—
445C2×C4—882no—
446C2×C4#6699011yescharacteristic
447C2×C4#6699011yescharacteristic
448C2×C4C2×#432612yescomplemented
449C2×C4C2×D4×D1112yes—
450C8—444no—
451C22—21no—
452C22—22no—
453C22—21no—
454C22—22no—
455C22—22no—
456C22—42no—
457C22—42no—
458C22—42no—
459C22—41no—
460C22—41no—
461C22—81no—
462C22#1062266314yes—
463C22C2×#6699011yescharacteristic
464C22C22×#432611yescharacteristic
465C22C2×#6700411yescharacteristic
466C4—22no—
467C4—22no—
468C4—21no—
469C4—41no—
470C4—44no—
471C4—41no—
472C4—82no—
473C4—444no—
474C4—444no—
475C4#1062264512yes—
476C2—21no—
477C2—21no—
478C2—24no—
479C2—42no—
480C2C2×#1062266311yescharacteristic
481C2#1307799411yescharacteristic
482C2C2×#1062264511yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2409C2
socleC22×C11C2×#120
prime radicalC22×D4×C11D4
hypercenter#2409D11
hypocenterC11#18197
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2409

Complements

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

NH ≅ G/Ntype
2. C2×#10622841C2semidirect
3. #13067589C2semidirect
4. #13067572C2semidirect
5. #13067187C2semidirect
108. C2×D4×C11Q16semidirect
175. C23×C11C2×Q16semidirect
204. C2×C4×C11C2×Q16semidirect
354. C2×D4#4326semidirect
400. C11#18197semidirect
409. C23C2×#4326semidirect
448. C2×C4C2×#4326semidirect

Maximal subgroups

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

subgroupindex
#130824192
C2×#106228412
#130675892
#130675722
#130671872
#130669342
C11×#24092
#1819711