Finite Group Databasebeta

← #14727627

Subgroups — #14727627

Order 2816.

1064 conjugacy classes of subgroups; only the 187 normal subgroups are shown.

normal subgroups only

This group has 1064 conjugacy classes of subgroups — too many to draw. Only its 187 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623014C211yesmaximal, characteristic
2#13079388C212yesmaximal, complemented
3#13067640C214yesmaximal, complemented
4#13067572C214yesmaximal, complemented
5#13067187C212yesmaximal, complemented
6C2×#10622163C211yesmaximal, characteristic
7C11×#2626C211yesmaximal, characteristic
8C2×C11×C22⋊Q8C2211yescharacteristic
9C22×C11×C22⋊C4C2211yescharacteristic
10C22×C22⋊Dic11—21no—
11C2×#66977—21no—
12C2×#66977C2212yes—
13#10623014—22no—
14#10623014—24no—
15#10623014C2214yes—
16C2×#66931—22no—
17C2×#66931—22no—
18C11×#399C2212yes—
19C11×#396—22no—
20C11×#393C2212yes—
21C11×#385—21no—
22C11×#380C2211yescharacteristic
23C11×#379—21no—
24#10622841C2214yescomplemented
25C2×C22⋊(C11⋊C8)C2212yes—
26#10622664—24no—
27#10622663—22no—
28#10622657—22no—
29#10622583C2214yescomplemented
30#10622163C2214yes—
31#10622090C2218yescomplemented
32C25×C11D411yescharacteristic
33C22×Q8×C11C2311yescharacteristic
34C23×C4×C11D411yescharacteristic
35C23×C4×C11C2311yescharacteristic
36C23×Dic11—21no—
37C23×Dic11—21no—
38C22×Dic22—21no—
39C22×Dic22D412yes—
40C11×C22⋊Q8—22no—
41C11×C22⋊Q8—22no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—22no—
45C2×C11×C4⋊C4C2311yescharacteristic
46C2×C11×C22⋊C4—22no—
47C2×C11×C22⋊C4—22no—
48C2×C11×C22⋊C4—21no—
49C2×C11×C22⋊C4—21no—
50C2×C11×C22⋊C4—22no—
51C2×C11×C22⋊C4—22no—
52C2×C11×C22⋊C4D412yes—
53C2×C11×C22⋊C4C2312yes—
54C2×C22⋊Dic11—22no—
55C2×C22⋊Dic11—24no—
56C2×C22⋊Dic11—24no—
57C2×C22⋊Dic11—22no—
58C2×#4326—24no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11D412yes—
61#66977—24no—
62#66977—22no—
63#66977—22no—
64#66977—24no—
65#66977D414yes—
66#66977C2314yes—
67C2×Dic11⋊C4—22no—
68C2×Dic11⋊C4—22no—
69C22×C11⋊C8—22no—
70#66931—28no—
71#66931—28no—
72#66931—28no—
73#66931—28no—
74C11×#95—22no—
75C11×#95C2312yes—
76#66899—24no—
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—22no—
91C2×Q8×C11—81no—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—22no—
96C22×C4×C11—21no—
97C22×C4×C11—81no—
98C22×C4×C11—81no—
99C22×C4×C11C2×D412yes—
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D412yes—
102C22×C4×C11C2×D412yes—
103C22×C4×C11C2411yescharacteristic
104C22×Dic11—24no—
105C22×Dic11—24no—
106C22×Dic11—22no—
107C22×Dic11—22no—
108C22×Dic11—82no—
109C22×Dic11—82no—
110C2×Dic22—24no—
111C2×Dic22—22no—
112C2×Dic22—82no—
113C2×Dic22—82no—
114C2×Dic22C2×D414yes—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—42no—
117C11×C4⋊C4—81no—
118C11×C4⋊C4—82no—
119C11×C22⋊C4—24no—
120C11×C22⋊C4—24no—
121C11×C22⋊C4—41no—
122C11×C22⋊C4—41no—
123C11×C22⋊C4—42no—
124C11×C22⋊C4—82no—
125C11×C22⋊C4—82no—
126C22⋊Dic11—28no—
127C22⋊Dic11—24no—
128C22⋊Dic11—24no—
129#4326—84no—
130C4⋊Dic11—24no—
131C4⋊Dic11—22no—
132C4⋊Dic11C2×D414yes—
133Dic11⋊C4—28no—
134Dic11⋊C4—24no—
135Dic11⋊C4—24no—
136C2×C11⋊C8—24no—
137C2×C11⋊C8—82no—
138C2×#543—111no—
139#3189—112no—
140#2626D1111yescharacteristic
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—
166C2×C4×C11—22no—
167C2×C4×C11—42no—
168C2×C4×C11—41no—
169C2×C4×C11—42no—
170C2×C4×C11—41no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—42no—
180C2×C4×C11—81no—
181C2×C4×C11#12012yes—
182C2×C4×C11C22×D412yes—
183C2×Dic11—24no—
184C2×Dic11—24no—
185C2×Dic11—44no—
186C2×Dic11—44no—
187C2×Dic11—84no—
188C2×Dic11—84no—
189Dic22—44no—
190Dic22—82no—
191Dic22—84no—
192C11⋊C8—44no—
193#543—114no—
194#543—224no—
195#543—222no—
196C2×C22⋊Q8—112no—
197C2×C22⋊Q8—222no—
198C2×C22⋊Q8—222no—
199C2×C22⋊Q8—221no—
200C2×C22⋊Q8C2×D1111yescharacteristic
201C22×C22⋊C4—221no—
202C22×C22⋊C4C2×D1111yescharacteristic
203#484—114no—
204#484—222no—
205#467—224no—
206#451—114no—
207#451—222no—
208C2×C22⋊C8—112no—
209#399C2×D1112yes—
210#396—22no—
211#393C2×D1112yes—
212#385—21no—
213#380C2×D1111yescharacteristic
214#379—21no—
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—82no—
241C4×C11—81no—
242C4×C11—81no—
243Dic11—44no—
244Dic11—44no—
245C25C22⋊D1111yescharacteristic
246C22×Q8—112no—
247C22×Q8—221no—
248C22×Q8C22×D1111yescharacteristic
249C23×C4—221no—
250C23×C4—221no—
251C23×C4C22⋊D1111yescharacteristic
252C23×C4C22×D1111yescharacteristic
253C2×Q16—224no—
254C22×C8—222no—
255C22⋊Q8—22no—
256C22⋊Q8—22no—
257C22⋊Q8—114no—
258C22⋊Q8—114no—
259C22⋊Q8—228no—
260C22⋊Q8—228no—
261C22⋊Q8—228no—
262C22⋊Q8—228no—
263C22⋊Q8—224no—
264C22⋊Q8—222no—
265C22⋊Q8—222no—
266C22⋊Q8—224no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—112no—
271C2×C4⋊C4—222no—
272C2×C4⋊C4—221no—
273C2×C4⋊C4—222no—
274C2×C4⋊C4C22×D1111yescharacteristic
275C2×C22⋊C4—22no—
276C2×C22⋊C4—22no—
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—22no—
280C2×C22⋊C4—22no—
281C2×C22⋊C4—222no—
282C2×C22⋊C4—224no—
283C2×C22⋊C4—222no—
284C2×C22⋊C4—224no—
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—22no—
293#95C22×D1112yes—
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—21no—
304C24—22no—
305C24—81no—
306C24—81no—
307C24#432614yescomplemented
308C24C2×C22⋊D1112yes—
309C24C2×C22⋊D1111yescharacteristic
310C2×Q8—22no—
311C2×Q8—81no—
312C2×Q8—114no—
313C2×Q8—224no—
314C2×Q8—222no—
315C2×Q8—882no—
316C2×Q8—882no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—22no—
321C22×C4—21no—
322C22×C4—81no—
323C22×C4—81no—
324C22×C4—222no—
325C22×C4—222no—
326C22×C4—224no—
327C22×C4—224no—
328C22×C4—882no—
329C22×C4—882no—
330C22×C4D4×D1112yes—
331C22×C4D4×D1112yes—
332C22×C4C2×C22⋊D1112yes—
333C22×C4C2×C22⋊D1111yescharacteristic
334C22×C4C23×D1111yescharacteristic
335Q16—884no—
336C2×C8—224no—
337C2×C8—882no—
338C4⋊C4—22no—
339C4⋊C4—42no—
340C4⋊C4—81no—
341C4⋊C4—82no—
342C4⋊C4—114no—
343C4⋊C4—228no—
344C4⋊C4—224no—
345C4⋊C4—222no—
346C4⋊C4—224no—
347C4⋊C4—224no—
348C22⋊C4—24no—
349C22⋊C4—24no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C22⋊C4—42no—
353C22⋊C4—82no—
354C22⋊C4—82no—
355C22⋊C4—228no—
356C22⋊C4—224no—
357C22⋊C4—224no—
358C11#1828711yescharacteristic, complemented, Sylow
359C23—22no—
360C23—24no—
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#6699011yescharacteristic
374C23#6699011yescharacteristic
375C23C2×#432614yes—
376C23C2×#432612yes—
377C23#6700412yes—
378C23C22×C22⋊D1111yescharacteristic
379Q8—44no—
380Q8—444no—
381Q8—882no—
382Q8—884no—
383C2×C4—22no—
384C2×C4—41no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—42no—
397C2×C4—81no—
398C2×C4—224no—
399C2×C4—224no—
400C2×C4—444no—
401C2×C4—444no—
402C2×C4—884no—
403C2×C4—884no—
404C2×C4#6699012yes—
405C2×C4C2×D4×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#1062266312yes—
423C22#1062266312yes—
424C22C2×#6699011yescharacteristic
425C22C22×#432611yescharacteristic
426C22C2×#6700411yescharacteristic
427C4—22no—
428C4—22no—
429C4—42no—
430C4—82no—
431C4—81no—
432C4—81no—
433C4—444no—
434C4—444no—
435C2—21no—
436C2—21no—
437C2—22no—
438C2—22no—
439C2—44no—
440C2C2×#1062266311yescharacteristic
441C2#1307797211yescharacteristic
442C2#1307801211yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2626C2
socleC22×C11C2×#120
prime radicalC25×C11D4
hypercenter#2626D11
hypocenterC11#18287
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2626

Complements

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

NH ≅ G/Ntype
2. #13079388C2semidirect
3. #13067640C2semidirect
4. #13067572C2semidirect
5. #13067187C2semidirect
24. #10622841C22semidirect
29. #10622583C22semidirect
31. #10622090C22semidirect
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
C2×#106230142
#130793882
#130676402
#130675722
#130671872
C2×#106221632
C11×#26262
#1828711