Finite Group Databasebeta

← #14666863

Subgroups — #14666863

Order 2816.

596 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 59 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
1#13069780C211yesmaximal, characteristic, complemented
2#13067640C211yesmaximal, characteristic, complemented
3#13067538C211yesmaximal, characteristic, complemented
4#13066640C211yesmaximal, characteristic, complemented
5#13066613C211yesmaximal, characteristic, complemented
6#13066544C211yesmaximal, characteristic, complemented
7C11×#2668C211yesmaximal, characteristic
8C2×C11×#121—21no—
9C2×C11×#120—21no—
10#10623014C2211yescharacteristic
11C11×#399C2211yescharacteristic
12C11×#397—21no—
13C11×#394—21no—
14C11×#392C2211yescharacteristic
15C11×#386—21no—
16C11×#386—21no—
17C11×#379C2211yescharacteristic
18#10622860—21no—
19#10622831—21no—
20#10622583—21no—
21#10622165—21no—
22#10622164C2211yescharacteristic
23#10622163C2211yescharacteristic
24#10622163C2211yescharacteristic
25#10622090—21no—
26#10622090—21no—
27C25×C11D411yescharacteristic
28C22×D4×C11—21no—
29C22×D4×C11—21no—
30C22×D4×C11—21no—
31C22×D4×C11D411yescharacteristic
32C23×C4×C11—21no—
33C11×#121—44no—
34C11×#120—44no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4D411yescharacteristic
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4D411yescharacteristic
45C2×C11×C22⋊C4C2311yescharacteristic
46C2×C22⋊Dic11—21no—
47C2×C22⋊Dic11—21no—
48C2×C22⋊Dic11—41no—
49C2×C22⋊Dic11—41no—
50C2×#4324—41no—
51#66977—21no—
52#66977—21no—
53#66931—41no—
54#66931—41no—
55C11×#95—21no—
56C11×#95—21no—
57C11×#95D411yescharacteristic
58C11×#95D411yescharacteristic
59#66896—41no—
60C22⋊(C11⋊C8)—21no—
61C22⋊(C11⋊C8)—21no—
62#66874—41no—
63#66871—41no—
64#12262—111nomaximal, Sylow
65C24×C11—21no—
66C24×C11—21no—
67C24×C11—21no—
68C24×C11—21no—
69C24×C11—41no—
70C24×C11—42no—
71C24×C11—41no—
72C24×C11—81no—
73C24×C11C2×D411yescharacteristic
74C2×D4×C11—24no—
75C2×D4×C11—41no—
76C2×D4×C11—42no—
77C2×D4×C11—42no—
78C2×D4×C11—42no—
79C2×D4×C11—42no—
80C2×D4×C11—41no—
81C2×D4×C11—41no—
82C2×D4×C11—81no—
83C2×D4×C11—81no—
84C2×D4×C11—81no—
85C2×D4×C11—81no—
86C22×C4×C11—21no—
87C22×C4×C11—21no—
88C22×C4×C11—21no—
89C22×C4×C11—21no—
90C22×C4×C11—42no—
91C22×C4×C11—81no—
92C22×C4×C11—81no—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×Dic11—21no—
96C22×Dic11—21no—
97C22×Dic11—41no—
98C2×Dic22—21no—
99C2×Dic22—21no—
100C11×C4⋊C4—42no—
101C11×C4⋊C4—41no—
102C11×C22⋊C4—41no—
103C11×C22⋊C4—42no—
104C11×C22⋊C4—42no—
105C11×C22⋊C4—42no—
106C11×C22⋊C4—42no—
107C11×C22⋊C4—42no—
108C11×C22⋊C4—41no—
109C11×C22⋊C4—81no—
110C11×C22⋊C4—81no—
111C22⋊Dic11—41no—
112C22⋊Dic11—41no—
113C22⋊Dic11—41no—
114C22⋊Dic11—41no—
115C22⋊Dic11—82no—
116C22⋊Dic11—82no—
117#4324—82no—
118C4⋊Dic11—21no—
119C4⋊Dic11—21no—
120Dic11⋊C4—41no—
121Dic11⋊C4—41no—
122C2×C11⋊C8—41no—
123C2×C11⋊C8—41no—
124#2668D1111yescharacteristic
125#2029—111no—
126#1614—111no—
127#1596—111no—
128#1352—111no—
129#1343—111no—
130#1316—111no—
131C23×C11—21no—
132C23×C11—21no—
133C23×C11—22no—
134C23×C11—22no—
135C23×C11—41no—
136C23×C11—41no—
137C23×C11—41no—
138C23×C11—41no—
139C23×C11—41no—
140C23×C11—41no—
141C23×C11—41no—
142C23×C11—41no—
143C23×C11—42no—
144C23×C11—42no—
145C23×C11—42no—
146C23×C11—41no—
147C23×C11—41no—
148C23×C11—41no—
149C23×C11—41no—
150C23×C11—41no—
151C23×C11—41no—
152C23×C11—81no—
153C23×C11—82no—
154C23×C11—81no—
155C23×C11—82no—
156C23×C11—84no—
157C23×C11—81no—
158C23×C11#12011yescharacteristic
159C23×C11#13511yescharacteristic
160C23×C11#13711yescharacteristic
161D4×C11—42no—
162D4×C11—84no—
163D4×C11—81no—
164D4×C11—82no—
165D4×C11—82no—
166D4×C11—84no—
167C2×C4×C11—22no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—84no—
184C2×Dic11—41no—
185C2×Dic11—41no—
186C2×Dic11—81no—
187C2×Dic11—81no—
188C2×Dic11—81no—
189C2×Dic11—81no—
190C2×Dic11—81no—
191Dic22—81no—
192Dic22—81no—
193C11⋊C8—81no—
194C11⋊C8—81no—
195#543—111no—
196C2×#121—21no—
197C2×#120—21no—
198#484—221no—
199#450—221no—
200#399C2×D1111yescharacteristic
201#397—21no—
202#394—21no—
203#392C2×D1111yescharacteristic
204#386—21no—
205#386—21no—
206#379—221no—
207#379C2×D1111yescharacteristic
208#342—111no—
209#342—221no—
210#328—221no—
211#328—221no—
212#323—111no—
213#323—111no—
214C22×C11—21no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—41no—
219C22×C11—41no—
220C22×C11—42no—
221C22×C11—42no—
222C22×C11—42no—
223C22×C11—42no—
224C22×C11—41no—
225C22×C11—41no—
226C22×C11—44no—
227C22×C11—42no—
228C22×C11—42no—
229C22×C11—81no—
230C22×C11—81no—
231C22×C11—81no—
232C22×C11—81no—
233C22×C11—81no—
234C22×C11—82no—
235C22×C11—82no—
236C22×C11—82no—
237C22×C11—81no—
238C22×C11—81no—
239C22×C11—81no—
240C22×C11—81no—
241C22×C11#45211yescharacteristic
242C22×C11#45511yescharacteristic
243C22×C11B(4,𝔽2)11yescharacteristic
244C4×C11—42no—
245C4×C11—41no—
246C4×C11—41no—
247C4×C11—81no—
248C4×C11—81no—
249C4×C11—81no—
250Dic11—81no—
251Dic11—81no—
252Dic11—161no—
253C25C22⋊D1111yescharacteristic
254C22×D4—21no—
255C22×D4—21no—
256C22×D4—21no—
257C22×D4C22⋊D1111yescharacteristic
258C23×C4—21no—
259C2×SD16—441no—
260C22⋊Q8—221no—
261C22⋊Q8—221no—
262C22⋊Q8—441no—
263C22⋊Q8—441no—
264#121—44no—
265#120—44no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4C22⋊D1111yescharacteristic
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—21no—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—221no—
276C2×C22⋊C4—221no—
277C2×C22⋊C4—441no—
278C2×C22⋊C4—441no—
279C2×C22⋊C4C22⋊D1111yescharacteristic
280C2×C22⋊C4C22×D1111yescharacteristic
281#107—441no—
282#103—441no—
283#102—441no—
284C22⋊C8—221no—
285C22⋊C8—221no—
286#95—21no—
287#95—21no—
288#95C22⋊D1111yescharacteristic
289#95C22⋊D1111yescharacteristic
290C2×C11—21no—
291C2×C11—21no—
292C2×C11—41no—
293C2×C11—41no—
294C2×C11—82no—
295C2×C11—82no—
296C2×C11#160611yescharacteristic
297C2×C11#219611yescharacteristic
298C2×C11#220011yescharacteristic
299C24—21no—
300C24—21no—
301C24—21no—
302C24—21no—
303C24—41no—
304C24—42no—
305C24—41no—
306C24—81no—
307C24C2×C22⋊D1111yescharacteristic
308C2×Q8—221no—
309C2×Q8—221no—
310C2×D4—24no—
311C2×D4—41no—
312C2×D4—42no—
313C2×D4—42no—
314C2×D4—42no—
315C2×D4—42no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—81no—
319C2×D4—81no—
320C2×D4—81no—
321C2×D4—81no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—42no—
327C22×C4—81no—
328C22×C4—81no—
329C22×C4—221no—
330C22×C4—221no—
331C22×C4—441no—
332C22×C4C2×C22⋊D1111yescharacteristic
333C22×C4C2×C22⋊D1111yescharacteristic
334SD16—882no—
335C2×C8—441no—
336C2×C8—441no—
337C4⋊C4—41no—
338C4⋊C4—42no—
339C4⋊C4—221no—
340C4⋊C4—221no—
341C4⋊C4—441no—
342C4⋊C4—441no—
343C22⋊C4—41no—
344C22⋊C4—42no—
345C22⋊C4—42no—
346C22⋊C4—42no—
347C22⋊C4—42no—
348C22⋊C4—42no—
349C22⋊C4—41no—
350C22⋊C4—81no—
351C22⋊C4—81no—
352C22⋊C4—441no—
353C22⋊C4—441no—
354C22⋊C4—441no—
355C22⋊C4—441no—
356C22⋊C4—882no—
357C22⋊C4—882no—
358C11#1226211yescharacteristic, complemented, Sylow
359C23—21no—
360C23—21no—
361C23—22no—
362C23—22no—
363C23—41no—
364C23—41no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23—42no—
372C23—42no—
373C23—42no—
374C23—41no—
375C23—41no—
376C23—41no—
377C23—41no—
378C23—41no—
379C23—41no—
380C23—81no—
381C23—82no—
382C23—81no—
383C23—82no—
384C23—84no—
385C23—81no—
386C23#6700311yescharacteristic
387C23#6700411yescharacteristic
388C23#6700611yescharacteristic
389Q8—881no—
390Q8—881no—
391D4—42no—
392D4—84no—
393D4—81no—
394D4—82no—
395D4—82no—
396D4—84no—
397C2×C4—22no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—84no—
414C2×C4—441no—
415C2×C4—441no—
416C2×C4—881no—
417C2×C4—881no—
418C2×C4—881no—
419C2×C4—881no—
420C2×C4—881no—
421C8—881no—
422C8—881no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—41no—
428C22—41no—
429C22—42no—
430C22—42no—
431C22—42no—
432C22—42no—
433C22—41no—
434C22—41no—
435C22—44no—
436C22—42no—
437C22—42no—
438C22—81no—
439C22—81no—
440C22—81no—
441C22—81no—
442C22—81no—
443C22—82no—
444C22—82no—
445C22—82no—
446C22—81no—
447C22—81no—
448C22—81no—
449C22—81no—
450C22#1062285211yescharacteristic
451C22#1062285511yescharacteristic
452C22#1062285711yescharacteristic
453C4—42no—
454C4—41no—
455C4—41no—
456C4—81no—
457C4—81no—
458C4—81no—
459C4—881no—
460C4—881no—
461C4—1761no—
462C2—21no—
463C2—21no—
464C2—41no—
465C2—41no—
466C2—82no—
467C2—82no—
468C2#1306759611yescharacteristic
469C2#1307060011yescharacteristic
470C2#1307062311yescharacteristic
subgroupG/H
centerC22#10622857
commutator, cosocleC2×C11×C22⋊C4C23
FrattiniC2×C22⋊C4C22×D11
Fitting, prime radicalC11×#2668C2
socleC22×C11B(4,𝔽2)
hypercenter#2668D11
hypocenterC11#12262
LCSG ▷ C2×C11×C22⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2668

Complements

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

NH ≅ G/Ntype
1. #13069780C2semidirect
2. #13067640C2semidirect
3. #13067538C2semidirect
4. #13066640C2semidirect
5. #13066613C2semidirect
6. #13066544C2semidirect
358. C11#12262semidirect

Maximal subgroups

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

subgroupindex
#130697802
#130676402
#130675382
#130666402
#130666132
#130665442
C11×#26682
#1226211