Finite Group Databasebeta

← #14727628

Subgroups — #14727628

Order 2816.

1064 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079388C212yesmaximal, complemented
2#13074421C211yesmaximal, characteristic
3#13067641C214yesmaximal, complemented
4#13067573C214yesmaximal, complemented
5#13067188C212yesmaximal, complemented
6C2×#10622163C211yesmaximal, characteristic
7C2×C11×#543C211yesmaximal, characteristic
8C11×#543—24no—
9C11×#543—22no—
10C11×#543C2214yes—
11C2×C11×C22⋊Q8—22no—
12C2×C11×C22⋊Q8—21no—
13C2×C11×C22⋊Q8—22no—
14C2×C11×C22⋊Q8C2212yes—
15C22×C11×C22⋊C4—21no—
16C22×C11×C22⋊C4C2211yescharacteristic
17C2×#66977C2211yescharacteristic
18#10622860—21no—
19#10622841—22no—
20#10622825C2211yescharacteristic
21#10622823—21no—
22C2×C22⋊(C11⋊C8)C2212yes—
23#10622664—24no—
24#10622663C2214yescomplemented
25#10622657C2214yescomplemented
26#10622583—22no—
27#10622562C2212yes—
28#10622561—22no—
29#10622560C2212yes—
30#10622176C2218yescomplemented
31#10622163C2214yes—
32C25×C11D411yescharacteristic
33C22×Q8×C11—21no—
34C22×Q8×C11D412yes—
35C23×C4×C11—21no—
36C23×C4×C11—21no—
37C23×C4×C11D411yescharacteristic
38C23×C4×C11C2311yescharacteristic
39C22×Dic22C2311yescharacteristic
40C11×C22⋊Q8—28no—
41C11×C22⋊Q8—28no—
42C11×C22⋊Q8—24no—
43C11×C22⋊Q8—28no—
44C11×C22⋊Q8—24no—
45C11×C22⋊Q8—22no—
46C11×C22⋊Q8—22no—
47C11×C22⋊Q8—28no—
48C11×C22⋊Q8D414yes—
49C11×C22⋊Q8C2314yes—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4D412yes—
54C2×C11×C22⋊C4—22no—
55C2×C11×C22⋊C4—24no—
56C2×C11×C22⋊C4—22no—
57C2×C11×C22⋊C4—24no—
58C2×C11×C22⋊C4—22no—
59C2×C11×C22⋊C4—22no—
60C2×C11×C22⋊C4D412yes—
61C2×C11×C22⋊C4C2312yes—
62C2×C22⋊Dic11—21no—
63C2×C22⋊Dic11—21no—
64C2×C22⋊Dic11—22no—
65C2×C22⋊Dic11—22no—
66C2×#4326—24no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11C2311yescharacteristic
69#66977—22no—
70#66977—22no—
71C2×Dic11⋊C4—21no—
72C2×Dic11⋊C4—22no—
73C22×C11⋊C8—22no—
74#66899—24no—
75C11⋊#95—22no—
76C11⋊#95C2312yes—
77C22⋊(C11⋊C8)—22no—
78C22⋊(C11⋊C8)C2314yes—
79#66874—24no—
80#66871—24no—
81#18287—111nomaximal, Sylow
82C24×C11—21no—
83C24×C11—21no—
84C24×C11—22no—
85C24×C11—81no—
86C24×C11—81no—
87C24×C11Q1614yescomplemented
88C24×C11C2×D412yes—
89C24×C11C2×D411yescharacteristic
90C2×Q8×C11—24no—
91C2×Q8×C11—22no—
92C2×Q8×C11—82no—
93C2×Q8×C11—82no—
94C2×Q8×C11C2×D414yes—
95C22×C4×C11—22no—
96C22×C4×C11—21no—
97C22×C4×C11—22no—
98C22×C4×C11—24no—
99C22×C4×C11—24no—
100C22×C4×C11—21no—
101C22×C4×C11—81no—
102C22×C4×C11—81no—
103C22×C4×C11—82no—
104C22×C4×C11—82no—
105C22×C4×C11C2×D412yes—
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D412yes—
108C22×C4×C11C2×D412yes—
109C22×C4×C11C2411yescharacteristic
110C22×Dic11—21no—
111C22×Dic11—22no—
112C22×Dic11—21no—
113C2×Dic22—22no—
114C2×Dic22—81no—
115C11×C4⋊C4—24no—
116C11×C4⋊C4—28no—
117C11×C4⋊C4—24no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—24no—
120C11×C4⋊C4C2×D414yes—
121C11×C22⋊C4—28no—
122C11×C22⋊C4—24no—
123C11×C22⋊C4—24no—
124C11×C22⋊C4—24no—
125C11×C22⋊C4—24no—
126C22⋊Dic11—41no—
127C22⋊Dic11—41no—
128C22⋊Dic11—42no—
129C22⋊Dic11—82no—
130C22⋊Dic11—82no—
131#4326—84no—
132C4⋊Dic11—22no—
133C4⋊Dic11—81no—
134Dic11⋊C4—42no—
135Dic11⋊C4—82no—
136C2×C11⋊C8—24no—
137C2×C11⋊C8—82no—
138C2×#543D1111yescharacteristic
139#3189—112no—
140#2626—111no—
141#1614—114no—
142#1602—114no—
143#1520—112no—
144C2×#323—111no—
145C23×C11—22no—
146C23×C11—24no—
147C23×C11—22no—
148C23×C11—24no—
149C23×C11—41no—
150C23×C11—41no—
151C23×C11—42no—
152C23×C11—42no—
153C23×C11—42no—
154C23×C11—42no—
155C23×C11—81no—
156C23×C11—81no—
157C23×C11—84no—
158C23×C11—84no—
159C23×C11#12011yescharacteristic
160C23×C11#12011yescharacteristic
161C23×C11C2×Q1614yes—
162C23×C11C2×Q1612yes—
163C23×C11#13712yes—
164C23×C11C22×D411yescharacteristic
165Q8×C11—44no—
166Q8×C11—82no—
167Q8×C11—84no—
168C2×C4×C11—24no—
169C2×C4×C11—22no—
170C2×C4×C11—24no—
171C2×C4×C11—42no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—44no—
177C2×C4×C11—44no—
178C2×C4×C11—42no—
179C2×C4×C11—81no—
180C2×C4×C11—84no—
181C2×C4×C11—84no—
182C2×C4×C11#12012yes—
183C2×C4×C11C22×D412yes—
184C2×Dic11—42no—
185C2×Dic11—42no—
186C2×Dic11—42no—
187C2×Dic11—42no—
188C2×Dic11—41no—
189C2×Dic11—41no—
190C2×Dic11—42no—
191Dic22—44no—
192C11⋊C8—44no—
193#543—24no—
194#543—22no—
195#543C2×D1114yes—
196C2×C22⋊Q8—22no—
197C2×C22⋊Q8—21no—
198C2×C22⋊Q8—22no—
199C2×C22⋊Q8—111no—
200C2×C22⋊Q8C2×D1112yes—
201C22×C22⋊C4—21no—
202C22×C22⋊C4C2×D1111yescharacteristic
203#484—114no—
204#484—222no—
205#467—224no—
206#451—114no—
207#451—222no—
208C2×C22⋊C8—112no—
209#399—112no—
210#396—222no—
211#393—112no—
212#385—221no—
213#380—111no—
214#379—221no—
215#328—118no—
216#323—114no—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11—21no—
221C22×C11—21no—
222C22×C11—21no—
223C22×C11—24no—
224C22×C11—42no—
225C22×C11—42no—
226C22×C11—44no—
227C22×C11—48no—
228C22×C11—42no—
229C22×C11—42no—
230C22×C11—82no—
231C22×C11—84no—
232C22×C11#45112yes—
233C22×C11#45112yes—
234C22×C11C2×#12011yescharacteristic
235C22×C11C22×Q1611yescharacteristic
236C22×C11C2×#13711yescharacteristic
237C4×C11—22no—
238C4×C11—22no—
239C4×C11—42no—
240C4×C11—44no—
241C4×C11—44no—
242Dic11—82no—
243Dic11—81no—
244Dic11—81no—
245C25C22⋊D1111yescharacteristic
246C22×Q8—21no—
247C22×Q8—111no—
248C22×Q8C22⋊D1112yes—
249C23×C4—21no—
250C23×C4—21no—
251C23×C4C22⋊D1111yescharacteristic
252C23×C4C22×D1111yescharacteristic
253C2×Q16—224no—
254C22×C8—222no—
255C22⋊Q8—28no—
256C22⋊Q8—28no—
257C22⋊Q8—24no—
258C22⋊Q8—28no—
259C22⋊Q8—24no—
260C22⋊Q8—22no—
261C22⋊Q8—22no—
262C22⋊Q8—28no—
263C22⋊Q8—222no—
264C22⋊Q8—222no—
265C22⋊Q8C22⋊D1114yes—
266C22⋊Q8C22×D1114yes—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—111no—
271C2×C4⋊C4—221no—
272C2×C4⋊C4—221no—
273C2×C4⋊C4—222no—
274C2×C4⋊C4C22⋊D1112yes—
275C2×C22⋊C4—22no—
276C2×C22⋊C4—24no—
277C2×C22⋊C4—22no—
278C2×C22⋊C4—24no—
279C2×C22⋊C4—22no—
280C2×C22⋊C4—22no—
281C2×C22⋊C4—221no—
282C2×C22⋊C4—221no—
283C2×C22⋊C4—222no—
284C2×C22⋊C4—222no—
285C2×C22⋊C4C22⋊D1112yes—
286C2×C22⋊C4C22×D1112yes—
287#107—224no—
288#103—224no—
289#103—224no—
290C22⋊C8—114no—
291C22⋊C8—222no—
292#95—112no—
293#95—222no—
294C2×C11—21no—
295C2×C11—21no—
296C2×C11—22no—
297C2×C11—22no—
298C2×C11—44no—
299C2×C11C2×#45111yescharacteristic
300C2×C11#301911yescharacteristic
301C2×C11#302611yescharacteristic
302C24—21no—
303C24—22no—
304C24—21no—
305C24—81no—
306C24—81no—
307C24#432614yescomplemented
308C24C2×C22⋊D1112yes—
309C24C2×C22⋊D1111yescharacteristic
310C2×Q8—24no—
311C2×Q8—22no—
312C2×Q8—82no—
313C2×Q8—82no—
314C2×Q8—222no—
315C2×Q8—881no—
316C2×Q8C2×C22⋊D1114yes—
317C22×C4—22no—
318C22×C4—21no—
319C22×C4—22no—
320C22×C4—24no—
321C22×C4—24no—
322C22×C4—21no—
323C22×C4—81no—
324C22×C4—81no—
325C22×C4—82no—
326C22×C4—82no—
327C22×C4—222no—
328C22×C4—221no—
329C22×C4—221no—
330C22×C4C2×C22⋊D1112yes—
331C22×C4C2×C22⋊D1111yescharacteristic
332C22×C4C2×C22⋊D1112yes—
333C22×C4C2×C22⋊D1112yes—
334C22×C4C23×D1111yescharacteristic
335Q16—884no—
336C2×C8—224no—
337C2×C8—882no—
338C4⋊C4—24no—
339C4⋊C4—28no—
340C4⋊C4—24no—
341C4⋊C4—22no—
342C4⋊C4—24no—
343C4⋊C4—222no—
344C4⋊C4—442no—
345C4⋊C4—882no—
346C4⋊C4—881no—
347C4⋊C4C2×C22⋊D1114yes—
348C22⋊C4—28no—
349C22⋊C4—24no—
350C22⋊C4—24no—
351C22⋊C4—24no—
352C22⋊C4—24no—
353C22⋊C4—442no—
354C22⋊C4—441no—
355C22⋊C4—441no—
356C22⋊C4—882no—
357C22⋊C4—882no—
358C11#1828711yescharacteristic, complemented, Sylow
359C23—24no—
360C23—22no—
361C23—22no—
362C23—24no—
363C23—41no—
364C23—41no—
365C23—42no—
366C23—42no—
367C23—42no—
368C23—42no—
369C23—81no—
370C23—81no—
371C23—84no—
372C23—84no—
373C23#6699512yes—
374C23C2×#432614yes—
375C23C2×#432612yes—
376C23#6700611yescharacteristic
377C23#6700611yescharacteristic
378C23C22×C22⋊D1111yescharacteristic
379Q8—44no—
380Q8—82no—
381Q8—84no—
382Q8—444no—
383C2×C4—24no—
384C2×C4—22no—
385C2×C4—24no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—41no—
390C2×C4—42no—
391C2×C4—44no—
392C2×C4—44no—
393C2×C4—42no—
394C2×C4—81no—
395C2×C4—84no—
396C2×C4—84no—
397C2×C4—442no—
398C2×C4—442no—
399C2×C4—442no—
400C2×C4—442no—
401C2×C4—442no—
402C2×C4—441no—
403C2×C4—441no—
404C2×C4#6700612yes—
405C2×C4C22×C22⋊D1112yes—
406C8—444no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—24no—
414C22—42no—
415C22—42no—
416C22—44no—
417C22—48no—
418C22—42no—
419C22—42no—
420C22—82no—
421C22—84no—
422C22#1062284112yes—
423C22#1062284112yes—
424C22C2×#6699511yescharacteristic
425C22C22×#432611yescharacteristic
426C22C2×#6700611yescharacteristic
427C4—22no—
428C4—22no—
429C4—42no—
430C4—44no—
431C4—44no—
432C4—882no—
433C4—881no—
434C4—881no—
435C2—21no—
436C2—21no—
437C2—22no—
438C2—22no—
439C2—44no—
440C2C2×#1062284111yescharacteristic
441C2#1307797311yescharacteristic
442C2#1307801311yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#543C2
socleC22×C11C2×#120
prime radicalC25×C11D4
hypercenterC2×#543D11
hypocenterC11#18287
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#543

Complements

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

NH ≅ G/Ntype
1. #13079388C2semidirect
3. #13067641C2semidirect
4. #13067573C2semidirect
5. #13067188C2semidirect
24. #10622663C22semidirect
25. #10622657C22semidirect
30. #10622176C22semidirect
87. C24×C11Q16semidirect
307. C24#4326semidirect
358. C11#18287semidirect

Maximal subgroups

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

subgroupindex
#130793882
#130744212
#130676412
#130675732
#130671882
C2×#106221632
C2×C11×#5432
#1828711