Finite Group Databasebeta

← #14651103

Subgroups — #14651103

Order 2816.

618 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 618 conjugacy classes of subgroups — too many to draw. Only its 115 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#13073572C211yesmaximal, characteristic
2#13068604C211yesmaximal, characteristic, complemented
3#13067185C212yesmaximal, complemented
4#13066496C212yesmaximal, complemented
5C11×#2973C211yesmaximal, characteristic, complemented
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66992—21no—
8C2×#66983C2211yescharacteristic
9C11×#435—24no—
10C11×#432—21no—
11C11×#407—21no—
12C2×C11×C22⋊C8C2212yes—
13C2×#66898—21no—
14#10622826—21no—
15#10622825C2212yes—
16C2×C11⋊#95C2211yescharacteristic
17#10622604C411yescharacteristic, complemented
18#10622596C411yescharacteristic, complemented
19#10622573C411yescharacteristic, complemented
20#10622571—21no—
21#10622566C411yescharacteristic, complemented
22#10622553—21no—
23#10622164—21no—
24#10622108—24no—
25C22×D4×C11D411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C23×C4×C11C2311yescharacteristic
28C22×C22⋊D11—21no—
29C22×C22⋊D11—21no—
30C23×Dic11—21no—
31C22×D44C2×C411yescharacteristic
32C2×C11×M16—22no—
33C22×C8×C11—22no—
34C4×D4×C11—22no—
35C4×D4×C11—22no—
36C2×C11×C4⋊C4C2×C411yescharacteristic
37C2×C11×C22⋊C4C2×C411yescharacteristic
38C2×C11×C22⋊C4D411yescharacteristic
39C2×C42×C11D411yescharacteristic
40C2×C22⋊Dic11—21no—
41C2×C22⋊Dic11—22no—
42#66992—44no—
43#66983—22no—
44#66983—22no—
45C2×(C2×D11)⋊C4—21no—
46C2×(C2×D11)⋊C4—21no—
47C2×(C2×D11)⋊C4—21no—
48C2×(C2×D11)⋊C4—21no—
49C2×C4⋊Dic11—22no—
50C2×C4⋊Dic11C2×C411yescharacteristic
51C2×Dic11⋊C4—21no—
52C11×C4⋊C8—22no—
53C11×C22⋊C8—22no—
54C11×C22⋊C8—22no—
55C11×C22⋊C8D414yescomplemented
56C11×#97—22no—
57#66898—42no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95—22no—
62C11⋊#95C2×C411yescharacteristic
63C11⋊#95C2×C411yescharacteristic
64#9386—111nomaximal, Sylow
65C24×C11C22⋊C411yescharacteristic
66C24×C11C2×D411yescharacteristic
67C23×D11—21no—
68C2×D4×C11—22no—
69C2×D4×C11—21no—
70C2×D4×C11—22no—
71C2×D4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—81no—
75C22×C4×C11—81no—
76C22×C4×C11C22⋊C411yescharacteristic
77C22×C4×C11C22⋊C411yescharacteristic
78C22×C4×C11C22⋊C411yescharacteristic
79C22×C4×C11C22×C411yescharacteristic
80C22×C4×C11C2×D412yes—
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11#4112yes—
83C2×C22⋊D11—42no—
84C2×C22⋊D11—42no—
85C2×C22⋊D11—42no—
86C2×C22⋊D11—42no—
87C2×C22⋊D11—41no—
88C2×C22⋊D11—41no—
89C2×C22⋊D11—81no—
90C22×Dic11—21no—
91C22×Dic11—21no—
92C22×Dic11—21no—
93C22×Dic11—42no—
94C22×Dic11—42no—
95C22×Dic11—42no—
96C22×Dic11—81no—
97C2×D44—22no—
98C2×D44—81no—
99C11×M16—82no—
100C2×C8×C11—24no—
101C2×C8×C11—82no—
102C11×C4⋊C4—22no—
103C11×C22⋊C4—22no—
104C11×C22⋊C4—22no—
105C42×C11—21no—
106C42×C11—21no—
107C22⋊Dic11—42no—
108C22⋊Dic11—42no—
109C22⋊Dic11—42no—
110(C2×D11)⋊C4—42no—
111(C2×D11)⋊C4—42no—
112(C2×D11)⋊C4—41no—
113(C2×D11)⋊C4—41no—
114(C2×D11)⋊C4—81no—
115C4⋊Dic11—22no—
116C4⋊Dic11—82no—
117Dic11⋊C4—42no—
118#2973D1111yescharacteristic, complemented
119#2543—111no—
120#1799—111no—
121#1519—112no—
122#1294—112no—
123C23×C11—21no—
124C23×C11—21no—
125C23×C11—21no—
126C23×C11—41no—
127C23×C11—41no—
128C23×C11—41no—
129C23×C11—41no—
130C23×C11C2×C22⋊C411yescharacteristic
131C23×C11#12112yes—
132C23×C11AGL(1,ℤ/8)11yescharacteristic
133C23×C11AGL(1,ℤ/8)12yes—
134C23×C11#13711yescharacteristic
135C22×D11—41no—
136C22×D11—41no—
137C22×D11—41no—
138C22×D11—41no—
139C22×D11—41no—
140C22×D11—41no—
141C22×D11—41no—
142D4×C11—42no—
143D4×C11—42no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—42no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—81no—
157C2×C4×C11C4×D412yes—
158C2×C4×C11#12011yescharacteristic
159C2×C4×C11#12311yescharacteristic
160C22⋊D11—84no—
161C22⋊D11—82no—
162C22⋊D11—82no—
163C2×Dic11—22no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170C2×Dic11—41no—
171C2×Dic11—41no—
172C2×Dic11—84no—
173C2×Dic11—82no—
174C2×Dic11—82no—
175C2×Dic11—82no—
176D44—82no—
177C8×C11—44no—
178C2×#121—111no—
179C2×#121—221no—
180C2×C4×D4C2×D1111yescharacteristic
181#435—24no—
182#432—21no—
183C2×#99—221no—
184#407—21no—
185C2×C22⋊C8C2×D1112yes—
186#398—111no—
187#397—111no—
188#394—111no—
189#392—111no—
190#388—221no—
191#386—221no—
192#386—221no—
193#380—112no—
194C2×#95—111no—
195#342—221no—
196#327—224no—
197C22×C11—21no—
198C22×C11—22no—
199C22×C11—21no—
200C22×C11—22no—
201C22×C11—41no—
202C22×C11—42no—
203C22×C11—41no—
204C22×C11—42no—
205C22×C11—41no—
206C22×C11—41no—
207C22×C11—41no—
208C22×C11—81no—
209C22×C11#38611yescharacteristic
210C22×C11#41711yescharacteristic
211C22×C11#41811yescharacteristic
212C22×C11#46812yes—
213C22×C11#46912yes—
214C2×D11—81no—
215C2×D11—81no—
216C2×D11—81no—
217C2×D11—81no—
218C2×D11—81no—
219C2×D11—81no—
220C2×D11—81no—
221C4×C11—21no—
222C4×C11—21no—
223C4×C11—22no—
224C4×C11—41no—
225C4×C11—41no—
226C4×C11—41no—
227Dic11—42no—
228Dic11—81no—
229Dic11—81no—
230Dic11—162no—
231C22×D4—111no—
232C22×D4—221no—
233C22×D4—221no—
234C22×D4D4411yescharacteristic
235C23×C4—221no—
236C23×C4C22⋊D1111yescharacteristic
237C23×C4C22×D1111yescharacteristic
238C2×M16—22no—
239C22×C8—22no—
240#121—222no—
241#121—222no—
242#121—444no—
243C4×D4—22no—
244C4×D4—22no—
245C2×C4⋊C4—111no—
246C2×C4⋊C4—221no—
247C2×C4⋊C4—222no—
248C2×C4⋊C4C4×D1111yescharacteristic
249C2×C22⋊C4—221no—
250C2×C22⋊C4—221no—
251C2×C22⋊C4—221no—
252C2×C22⋊C4—221no—
253C2×C22⋊C4—222no—
254C2×C22⋊C4—221no—
255C2×C22⋊C4C4×D1111yescharacteristic
256C2×C22⋊C4D4411yescharacteristic
257C2×C42C22⋊D1111yescharacteristic
258C4⋊C8—22no—
259#99—442no—
260C22⋊C8—22no—
261C22⋊C8—22no—
262C22⋊C8C22⋊D1114yescomplemented
263#97—22no—
264#95—111no—
265#95—111no—
266#95—221no—
267#95—221no—
268#95—221no—
269#95—222no—
270C2×C11—21no—
271C2×C11—22no—
272C2×C11—21no—
273C2×C11—22no—
274C2×C11—81no—
275C2×C11#188411yescharacteristic
276C2×C11#189511yescharacteristic
277C2×C11#191311yescharacteristic
278D11—161no—
279C24—221no—
280C24(C2×D11)⋊C411yescharacteristic
281C24C2×D4411yescharacteristic
282C2×D4—21no—
283C2×D4—22no—
284C2×D4—21no—
285C2×D4—22no—
286C2×D4—222no—
287C2×D4—442no—
288C2×D4—442no—
289C2×D4—442no—
290C2×D4—441no—
291C2×D4—441no—
292C2×D4—442no—
293C2×D4—881no—
294C2×D4—881no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—81no—
298C22×C4—81no—
299C22×C4—221no—
300C22×C4—221no—
301C22×C4—221no—
302C22×C4—442no—
303C22×C4—442no—
304C22×C4—442no—
305C22×C4—881no—
306C22×C4(C2×D11)⋊C411yescharacteristic
307C22×C4(C2×D11)⋊C411yescharacteristic
308C22×C4(C2×D11)⋊C411yescharacteristic
309C22×C4C2×C4×D1111yescharacteristic
310C22×C4#433912yes—
311C22×C4C2×C22⋊D1112yes—
312C22×C4C2×C22⋊D1111yescharacteristic
313M16—82no—
314C2×C8—24no—
315C2×C8—82no—
316C4⋊C4—22no—
317C4⋊C4—222no—
318C4⋊C4—442no—
319C4⋊C4—882no—
320C22⋊C4—22no—
321C22⋊C4—22no—
322C22⋊C4—442no—
323C22⋊C4—442no—
324C22⋊C4—442no—
325C22⋊C4—441no—
326C22⋊C4—441no—
327C22⋊C4—442no—
328C22⋊C4—442no—
329C22⋊C4—881no—
330C42—21no—
331C42—21no—
332C11#938611yescharacteristic, complemented, Sylow
333C23—21no—
334C23—21no—
335C23—21no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—441no—
341C23—441no—
342C23—441no—
343C23—441no—
344C23—441no—
345C23—441no—
346C23—441no—
347C23#6696112yes—
348C23#6696111yescharacteristic
349C23#6696211yescharacteristic
350C23C2×(C2×D11)⋊C411yescharacteristic
351C23#6698312yes—
352D4—42no—
353D4—42no—
354D4—882no—
355D4—884no—
356D4—882no—
357D4—882no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—81no—
371C2×C4—222no—
372C2×C4—441no—
373C2×C4—441no—
374C2×C4—441no—
375C2×C4—441no—
376C2×C4—441no—
377C2×C4—441no—
378C2×C4—441no—
379C2×C4—441no—
380C2×C4—884no—
381C2×C4—882no—
382C2×C4—882no—
383C2×C4—882no—
384C2×C4C4×C22⋊D1112yes—
385C2×C4#6698211yescharacteristic
386C2×C4#6700611yescharacteristic
387C8—44no—
388C22—21no—
389C22—22no—
390C22—21no—
391C22—22no—
392C22—42no—
393C22—41no—
394C22—41no—
395C22—42no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—81no—
400C22—881no—
401C22—881no—
402C22—881no—
403C22—881no—
404C22—881no—
405C22—881no—
406C22—881no—
407C22#1062274411yescharacteristic
408C22#1062274611yescharacteristic
409C22#1062274712yes—
410C22#1062274812yes—
411C22#1062282611yescharacteristic
412C4—21no—
413C4—21no—
414C4—22no—
415C4—41no—
416C4—41no—
417C4—41no—
418C4—442no—
419C4—881no—
420C4—881no—
421C4—1762no—
422C2—21no—
423C2—22no—
424C2—21no—
425C2—22no—
426C2—81no—
427C2—1761no—
428C2#1306899911yescharacteristic
429C2#1306905411yescharacteristic
430C2#1306915811yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#2973C2
socleC22×C11#386
prime radical#13073572C2
cosocleC23×C4×C11C23
hypercenter#2973D11
hypocenterC11#9386
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2973

Complements

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

NH ≅ G/Ntype
2. #13068604C2semidirect
3. #13067185C2semidirect
4. #13066496C2semidirect
5. C11×#2973C2semidirect
17. #10622604C4semidirect
18. #10622596C4semidirect
19. #10622573C4semidirect
21. #10622566C4semidirect
55. C11×C22⋊C8D4semidirect
118. #2973D11semidirect
262. C22⋊C8C22⋊D11semidirect
332. C11#9386semidirect

Maximal subgroups

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

subgroupindex
#130735722
#130686042
#130671852
#130664962
C11×#29732
#938611