Finite Group Databasebeta

← #14642889

Subgroups — #14642889

Order 2816.

516 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 83 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#13074979C211yesmaximal, characteristic
2#13070145C211yesmaximal, characteristic, complemented
3#13070093C211yesmaximal, characteristic, complemented
4#13066438C211yesmaximal, characteristic, complemented
5#13066437C211yesmaximal, characteristic, complemented
6#13066436C211yesmaximal, characteristic, complemented
7C11×#2071C211yesmaximal, characteristic, complemented
8C2×#66937—21no—
9C2×#66936—21no—
10C2×C11×#102—21no—
11C11×#390C2211yescharacteristic
12C11×#384C2211yescharacteristic
13#10622836—21no—
14#10622602—21no—
15C2×#66873—21no—
16C2×#66872—21no—
17C2×#66871—21no—
18#10622574—21no—
19#10622561—21no—
20#10622552C2211yescharacteristic
21#10622541C2211yescharacteristic
22C11×#340—21no—
23C11×#336C2211yescharacteristic
24#10622167—21no—
25#10622162C2211yescharacteristic
26#10622162C2211yescharacteristic
27C22×D4×C11D411yescharacteristic
28C22×C22⋊D11—21no—
29C22×C22⋊D11—21no—
30C22×D44D411yescharacteristic
31C22×C4×D11—21no—
32C22×C8×C11—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4D411yescharacteristic
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4—21no—
39C2×C42×C11C2311yescharacteristic
40C2×C22⋊Dic11—21no—
41C2×C22⋊Dic11—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×C4⋊Dic11D411yescharacteristic
46C2×C4⋊Dic11D411yescharacteristic
47C2×C4⋊Dic11D411yescharacteristic
48C2×Dic11⋊C4—21no—
49C2×Dic11⋊C4—21no—
50C22×C11⋊C8—21no—
51C22×C11⋊C8—21no—
52#66937—42no—
53#66937—42no—
54#66936—42no—
55#66936—42no—
56C11×#102—42no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59#66873—42no—
60#66872—42no—
61#66871—42no—
62#7800—111nomaximal, Sylow
63C24×C11—21no—
64C23×D11—21no—
65C2×D4×C11—21no—
66C2×D4×C11—21no—
67C2×D4×C11—41no—
68C2×D4×C11—41no—
69C22×C4×C11—21no—
70C22×C4×C11—41no—
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C2×C22⋊D11—42no—
75C2×C22⋊D11—42no—
76C2×C22⋊D11—42no—
77C2×C22⋊D11—81no—
78C2×C22⋊D11—81no—
79C2×C22⋊D11—81no—
80C22×Dic11—21no—
81C22×Dic11—21no—
82C22×Dic11—21no—
83C2×D44—21no—
84C2×D44—41no—
85C2×D44—41no—
86C2×D44SD1612yes—
87C2×C4×D11—42no—
88C2×C4×D11—42no—
89C2×C4×D11—81no—
90C2×C8×C11—41no—
91C2×C8×C11—41no—
92C2×C8×C11—41no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C11×C22⋊C4—41no—
101C11×C22⋊C4—41no—
102C11×C22⋊C4—41no—
103C11×C22⋊C4—41no—
104C42×C11—41no—
105C22⋊Dic11—42no—
106C22⋊Dic11—81no—
107(C2×D11)⋊C4—42no—
108(C2×D11)⋊C4—41no—
109(C2×D11)⋊C4—41no—
110(C2×D11)⋊C4—41no—
111(C2×D11)⋊C4—41no—
112C4⋊Dic11—21no—
113C4⋊Dic11—41no—
114C4⋊Dic11—41no—
115C4⋊Dic11D812yes—
116Dic11⋊C4—42no—
117Dic11⋊C4—41no—
118Dic11⋊C4—41no—
119C2×C11⋊C8—22no—
120C2×C11⋊C8—22no—
121C2×C11⋊C8—41no—
122C2×C11⋊C8—41no—
123C2×C11⋊C8—41no—
124C2×C11⋊C8—41no—
125#2682—111no—
126#2093—111no—
127#2084—111no—
128#2071D1111yescharacteristic, complemented
129#1271—111no—
130#1270—111no—
131#1270—111no—
132C23×C11—41no—
133C23×C11—41no—
134C23×C11—41no—
135C23×C11—41no—
136C23×C11—41no—
137C23×C11—41no—
138C23×C11—41no—
139C23×C11#12011yescharacteristic
140C22×D11—22no—
141C22×D11—41no—
142C22×D11—41no—
143C22×D11—41no—
144C22×D11—41no—
145C22×D11—41no—
146C22×D11—41no—
147D4×C11—42no—
148D4×C11—81no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—81no—
159C2×C4×C11—81no—
160C2×C4×C11—81no—
161C2×C4×C11C2×D811yescharacteristic
162C2×C4×C11C2×SD1611yescharacteristic
163C2×C4×C11#13511yescharacteristic
164C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
167C22⋊D11—84no—
168C22⋊D11—84no—
169C2×Dic11—22no—
170C2×Dic11—41no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173C2×Dic11—41no—
174C2×Dic11—41no—
175C2×Dic11—41no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178D44—42no—
179D44—81no—
180C4×D11—84no—
181C8×C11—81no—
182C11⋊C8—42no—
183C11⋊C8—42no—
184C2×#123—221no—
185C2×#121—221no—
186C2×#107—221no—
187C2×#106—221no—
188C2×#102—21no—
189C2×#102—221no—
190#396—221no—
191#394—221no—
192#392—221no—
193#390—111no—
194#390C2×D1111yescharacteristic
195#389—111no—
196#385—221no—
197#384C2×D1111yescharacteristic
198#340—21no—
199#340—221no—
200#336—111no—
201#336—111no—
202#336C2×D1111yescharacteristic
203C22×C11—81no—
204C22×C11—81no—
205C22×C11—81no—
206C22×C11—81no—
207C22×C11—81no—
208C22×C11—81no—
209C22×C11—81no—
210C22×C11#44711yescharacteristic
211C22×C11#44911yescharacteristic
212C22×C11#45011yescharacteristic
213C22×C11#45311yescharacteristic
214C22×C11#45511yescharacteristic
215C22×C11#45611yescharacteristic
216C22×C11#45811yescharacteristic
217C2×D11—42no—
218C2×D11—42no—
219C2×D11—42no—
220C2×D11—81no—
221C2×D11—81no—
222C2×D11—81no—
223C2×D11—81no—
224C4×C11—21no—
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—21no—
228C4×C11—21no—
229C4×C11—21no—
230C4×C11—81no—
231C4×C11—161no—
232Dic11—42no—
233Dic11—81no—
234Dic11—81no—
235C22×D4—111no—
236C22×D4—221no—
237C22×D4—221no—
238C22×D4C22⋊D1111yescharacteristic
239C23×C4—221no—
240C22×C8—21no—
241C22×C8—221no—
242C22×C8—221no—
243#123—442no—
244#123—442no—
245#121—442no—
246#121—442no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—111no—
251C2×C4⋊C4—111no—
252C2×C4⋊C4—111no—
253C2×C4⋊C4—221no—
254C2×C4⋊C4—221no—
255C2×C4⋊C4C22⋊D1111yescharacteristic
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—221no—
259C2×C22⋊C4—221no—
260C2×C22⋊C4—221no—
261C2×C22⋊C4—221no—
262C2×C22⋊C4—221no—
263C2×C42C22×D1111yescharacteristic
264#107—442no—
265#106—442no—
266#102—42no—
267#102—442no—
268#95—221no—
269#95—221no—
270C2×C11—161no—
271C2×C11#161011yescharacteristic
272C2×C11#161211yescharacteristic
273C2×C11#161311yescharacteristic
274C2×C11#162111yescharacteristic
275C2×C11#163911yescharacteristic
276C2×C11#165411yescharacteristic
277C2×C11#166111yescharacteristic
278D11—82no—
279C24—21no—
280C24—221no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—41no—
284C2×D4—41no—
285C2×D4—112no—
286C2×D4—221no—
287C2×D4—441no—
288C2×D4—441no—
289C2×D4—442no—
290C2×D4—442no—
291C2×D4—442no—
292C2×D4—881no—
293C2×D4—881no—
294C2×D4—881no—
295C22×C4—21no—
296C22×C4—41no—
297C22×C4—221no—
298C22×C4—221no—
299C22×C4—221no—
300C22×C4—442no—
301C22×C4—442no—
302C22×C4—881no—
303C22×C4D4×D1111yescharacteristic
304C22×C4D4×D1111yescharacteristic
305C22×C4C2×C22⋊D1111yescharacteristic
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—222no—
310C2×C8—222no—
311C2×C8—441no—
312C2×C8—441no—
313C2×C8—441no—
314C2×C8—441no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—112no—
323C4⋊C4—221no—
324C4⋊C4—441no—
325C4⋊C4—441no—
326C4⋊C4—442no—
327C4⋊C4—441no—
328C4⋊C4—441no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—442no—
334C22⋊C4—442no—
335C22⋊C4—441no—
336C22⋊C4—441no—
337C22⋊C4—441no—
338C22⋊C4—441no—
339C22⋊C4—881no—
340C42—41no—
341C11#780011yescharacteristic, complemented, Sylow
342C23—41no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—222no—
350C23—441no—
351C23—441no—
352C23—441no—
353C23—441no—
354C23—441no—
355C23—441no—
356C23#6699011yescharacteristic
357D4—42no—
358D4—81no—
359D4—442no—
360D4—881no—
361D4—884no—
362D4—884no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—81no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4—222no—
376C2×C4—441no—
377C2×C4—441no—
378C2×C4—441no—
379C2×C4—441no—
380C2×C4—441no—
381C2×C4—441no—
382C2×C4—441no—
383C2×C4—441no—
384C2×C4—884no—
385C2×C4D8×D1111yescharacteristic
386C2×C4#6696411yescharacteristic
387C2×C4SD16×D1111yescharacteristic
388C2×C4#6696711yescharacteristic
389C2×C4#6698511yescharacteristic
390C2×C4#6700311yescharacteristic
391C8—81no—
392C8—442no—
393C8—442no—
394C22—81no—
395C22—81no—
396C22—81no—
397C22—81no—
398C22—81no—
399C22—81no—
400C22—81no—
401C22—442no—
402C22—442no—
403C22—442no—
404C22—881no—
405C22—881no—
406C22—881no—
407C22—881no—
408C22#1062265011yescharacteristic
409C22#1062266611yescharacteristic
410C22#1062267411yescharacteristic
411C22#1062276911yescharacteristic
412C22#1062278211yescharacteristic
413C22#1062281111yescharacteristic
414C22#1062281811yescharacteristic
415C4—21no—
416C4—21no—
417C4—21no—
418C4—21no—
419C4—21no—
420C4—21no—
421C4—81no—
422C4—161no—
423C4—442no—
424C4—881no—
425C4—881no—
426C2—161no—
427C2—882no—
428C2#1306761711yescharacteristic
429C2#1306762811yescharacteristic
430C2#1306763411yescharacteristic
431C2#1306768011yescharacteristic
432C2#1306779211yescharacteristic
433C2#1306789811yescharacteristic
434C2#1306793211yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2071C2
socleC23×C11#120
prime radical#13074979C2
hypercenter#2071D11
hypocenterC11#7800
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2071

Complements

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

NH ≅ G/Ntype
2. #13070145C2semidirect
3. #13070093C2semidirect
4. #13066438C2semidirect
5. #13066437C2semidirect
6. #13066436C2semidirect
7. C11×#2071C2semidirect
128. #2071D11semidirect
341. C11#7800semidirect

Maximal subgroups

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

subgroupindex
#130749792
#130701452
#130700932
#130664382
#130664372
#130664362
C11×#20712
#780011