Finite Group Databasebeta

← #14651426

Subgroups — #14651426

Order 2816.

516 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 89 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#13077251C211yesmaximal, characteristic, complemented
2#13073078C211yesmaximal, characteristic
3#13068691C211yesmaximal, characteristic, complemented
4#13067146C211yesmaximal, characteristic
5#13067144C211yesmaximal, characteristic
6#13066469C211yesmaximal, characteristic, complemented
7C11×#1284C211yesmaximal, characteristic, complemented
8C2×#66983C2211yescharacteristic
9C2×#66979C2211yescharacteristic
10C11×#407C2211yescharacteristic
11C11×#381C2211yescharacteristic
12C4×C11×C22⋊C4C2211yescharacteristic
13#10622824C2211yescharacteristic
14#10622820C2211yescharacteristic
15#10622731—21no—
16M16×Dic11—21no—
17#10622574—21no—
18#10622574—21no—
19#10622552C411yescharacteristic, complemented
20#10622552C411yescharacteristic, complemented
21#10622549C411yescharacteristic, complemented
22#10622548C411yescharacteristic, complemented
23#10622333—22no—
24#10622333—22no—
25#10622283—21no—
26#10622283—21no—
27#10622165—21no—
28#10622165—21no—
29#10622108—22no—
30#10622089—22no—
31C23×C4×C11C2311yescharacteristic
32C22×C22⋊D11—21no—
33C22×D44C2×C411yescharacteristic
34C2×C11×M16—21no—
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4—21no—
37C2×C42×C11C2×C411yescharacteristic
38C2×C42×C11C2×C411yescharacteristic
39C2×C22⋊Dic11—21no—
40C2×C22⋊Dic11D411yescharacteristic
41C2×C22⋊Dic11D411yescharacteristic
42#66983—21no—
43#66983—21no—
44#66983—21no—
45#66983—21no—
46C2×(C2×D11)⋊C4—21no—
47C2×(C2×D11)⋊C4—21no—
48C2×(C2×D11)⋊C4—21no—
49C2×(C2×D11)⋊C4—21no—
50C2×(C2×D11)⋊C4—21no—
51#66979—21no—
52#66979—21no—
53#66979—21no—
54#66979—21no—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11C2×C411yescharacteristic
58C2×C4⋊Dic11C2×C411yescharacteristic
59C2×C4⋊Dic11C2×C411yescharacteristic
60C2×C4×Dic11D411yescharacteristic
61C2×C4×Dic11D411yescharacteristic
62C2×#4318—21no—
63C11×C22⋊C8—21no—
64C11×C22⋊C8D412yes—
65C11×#95—21no—
66C11×#95—21no—
67C11×#95—21no—
68C11⋊#95—21no—
69C11⋊#95—21no—
70C11⋊#95—21no—
71C11⋊#95—21no—
72C22⋊(C11⋊C8)—21no—
73C22⋊(C11⋊C8)D412yes—
74#66879—22no—
75Dic11⋊C8—24no—
76C8×Dic11—22no—
77#9446—111nomaximal, Sylow
78C24×C11C2×D411yescharacteristic
79C23×D11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—41no—
83C22×C4×C11—41no—
84C22×C4×C11—41no—
85C22×C4×C11C22×C411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11#4111yescharacteristic
90C22×C4×C11#4111yescharacteristic
91C2×C22⋊D11—41no—
92C2×C22⋊D11—41no—
93C2×C22⋊D11—81no—
94C2×C22⋊D11—81no—
95C22×Dic11—21no—
96C22×Dic11—41no—
97C22×Dic11C22⋊C411yescharacteristic
98C22×Dic11C22⋊C411yescharacteristic
99C22×Dic11C22⋊C411yescharacteristic
100C22×Dic11C22⋊C411yescharacteristic
101C2×D44—21no—
102C2×D44—21no—
103C2×D44—41no—
104C2×D44—41no—
105C11×M16—41no—
106C11×M16—41no—
107C2×C8×C11—22no—
108C11×C22⋊C4—42no—
109C11×C22⋊C4—41no—
110C11×C22⋊C4—41no—
111C42×C11—41no—
112C42×C11—41no—
113C22⋊Dic11—21no—
114C22⋊Dic11—21no—
115C22⋊Dic11—21no—
116C22⋊Dic11—21no—
117C22⋊Dic11—41no—
118C22⋊Dic11—41no—
119(C2×D11)⋊C4—42no—
120(C2×D11)⋊C4—42no—
121(C2×D11)⋊C4—41no—
122(C2×D11)⋊C4—41no—
123(C2×D11)⋊C4—81no—
124(C2×D11)⋊C4—81no—
125C4⋊Dic11—21no—
126C4⋊Dic11—21no—
127C4⋊Dic11—21no—
128C4⋊Dic11—21no—
129C4⋊Dic11—21no—
130C4⋊Dic11—21no—
131C4⋊Dic11—81no—
132C4⋊Dic11—81no—
133C4×Dic11—21no—
134C4×Dic11—21no—
135C4×Dic11—21no—
136C4×Dic11—21no—
137#4318—41no—
138#4318—41no—
139C2×C11⋊C8—22no—
140#2921—111no—
141#2500—111no—
142#1820—111no—
143#1510—111no—
144#1510—111no—
145#1284—111no—
146#1284D1111yescharacteristic, complemented
147C23×C11—21no—
148C23×C11—21no—
149C23×C11—41no—
150C23×C11—41no—
151C23×C11C2×C22⋊C411yescharacteristic
152C23×C11#12111yescharacteristic
153C23×C11#12111yescharacteristic
154C22×D11—41no—
155C22×D11—41no—
156C22×D11—41no—
157C22×D11—41no—
158C22×D11—41no—
159C22×D11—41no—
160C22×D11—41no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—22no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—81no—
176C2×C4×C11—81no—
177C2×C4×C11—81no—
178C2×C4×C11C4×D411yescharacteristic
179C2×C4×C11C4×D411yescharacteristic
180C2×C4×C11#12011yescharacteristic
181C2×C4×C11#12311yescharacteristic
182C22⋊D11—82no—
183C22⋊D11—82no—
184C2×Dic11—21no—
185C2×Dic11—21no—
186C2×Dic11—21no—
187C2×Dic11—21no—
188C2×Dic11—41no—
189C2×Dic11—41no—
190C2×Dic11—41no—
191C2×Dic11—41no—
192C2×Dic11—41no—
193C2×Dic11—41no—
194C2×Dic11—41no—
195C2×Dic11—81no—
196C2×Dic11—81no—
197C2×Dic11—81no—
198D44—81no—
199D44—81no—
200C8×C11—42no—
201C11⋊C8—42no—
202C2×#121—111no—
203C2×#117—111no—
204#433—222no—
205#433—222no—
206#423—221no—
207#407—111no—
208#407C2×D1111yescharacteristic
209C4×M16—221no—
210#394—221no—
211#394—221no—
212#390—111no—
213#390—111no—
214#388—221no—
215#388—221no—
216#384—111no—
217#382—111no—
218#381—111no—
219#381C2×D1111yescharacteristic
220C4×C22⋊C4C2×D1111yescharacteristic
221#342—221no—
222#342—221no—
223#327—222no—
224#327—222no—
225C22×C11—21no—
226C22×C11—21no—
227C22×C11—21no—
228C22×C11—21no—
229C22×C11—21no—
230C22×C11—21no—
231C22×C11—21no—
232C22×C11—21no—
233C22×C11—81no—
234C22×C11—81no—
235C22×C11#38611yescharacteristic
236C22×C11#41011yescharacteristic
237C22×C11#41011yescharacteristic
238C2×D11—81no—
239C2×D11—81no—
240C2×D11—81no—
241C2×D11—81no—
242C2×D11—81no—
243C2×D11—81no—
244C2×D11—81no—
245C4×C11—21no—
246C4×C11—21no—
247C4×C11—21no—
248C4×C11—21no—
249C4×C11—42no—
250C4×C11—81no—
251C4×C11—161no—
252Dic11—41no—
253Dic11—41no—
254Dic11—41no—
255Dic11—41no—
256Dic11—81no—
257Dic11—161no—
258C22×D4—111no—
259C22×D4—221no—
260C23×C4C22×D1111yescharacteristic
261C2×M16—21no—
262C2×M16—221no—
263#121—221no—
264#121—221no—
265#121—221no—
266#121—221no—
267#117—221no—
268#117—221no—
269#117—221no—
270#117—221no—
271C2×C4⋊C4—111no—
272C2×C4⋊C4—111no—
273C2×C4⋊C4—111no—
274C2×C4⋊C4—221no—
275C2×C4⋊C4—221no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—21no—
278C2×C22⋊C4—111no—
279C2×C22⋊C4—111no—
280C2×C22⋊C4—221no—
281C2×C22⋊C4—221no—
282C2×C22⋊C4—221no—
283C2×C22⋊C4—221no—
284C2×C22⋊C4—221no—
285C2×C22⋊C4—221no—
286C2×C42—111no—
287C2×C42—111no—
288C2×C42C4×D1111yescharacteristic
289C2×C42C4×D1111yescharacteristic
290C4⋊C8—224no—
291C22⋊C8—21no—
292C22⋊C8—112no—
293C22⋊C8—221no—
294C22⋊C8D4412yes—
295#97—222no—
296C4×C8—222no—
297#95—21no—
298#95—21no—
299#95—21no—
300#95—221no—
301#95—221no—
302#95—221no—
303#95—221no—
304C2×C11—21no—
305C2×C11—21no—
306C2×C11—41no—
307C2×C11—41no—
308C2×C11#188411yescharacteristic
309C2×C11#189911yescharacteristic
310C2×C11#191011yescharacteristic
311D11—161no—
312C24—221no—
313C24D4×D1111yescharacteristic
314C2×D4—221no—
315C2×D4—221no—
316C2×D4—441no—
317C2×D4—441no—
318C2×D4—441no—
319C2×D4—441no—
320C2×D4—881no—
321C2×D4—881no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—111no—
328C22×C4—111no—
329C22×C4—111no—
330C22×C4—111no—
331C22×C4—221no—
332C22×C4—441no—
333C22×C4C2×C4×D1111yescharacteristic
334C22×C4C2×D4411yescharacteristic
335C22×C4#433911yescharacteristic
336C22×C4D4×D1111yescharacteristic
337C22×C4D4×D1111yescharacteristic
338C22×C4#434311yescharacteristic
339M16—41no—
340M16—41no—
341M16—441no—
342M16—441no—
343C2×C8—22no—
344C2×C8—222no—
345C4⋊C4—221no—
346C4⋊C4—221no—
347C4⋊C4—221no—
348C4⋊C4—221no—
349C4⋊C4—221no—
350C4⋊C4—221no—
351C4⋊C4—881no—
352C4⋊C4—881no—
353C22⋊C4—42no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C22⋊C4—221no—
357C22⋊C4—221no—
358C22⋊C4—221no—
359C22⋊C4—221no—
360C22⋊C4—442no—
361C22⋊C4—442no—
362C22⋊C4—441no—
363C22⋊C4—441no—
364C22⋊C4—441no—
365C22⋊C4—441no—
366C22⋊C4—881no—
367C22⋊C4—881no—
368C42—41no—
369C42—41no—
370C42—221no—
371C42—221no—
372C42—221no—
373C42—221no—
374C11#944611yescharacteristic, complemented, Sylow
375C23—21no—
376C23—21no—
377C23—41no—
378C23—41no—
379C23—441no—
380C23—441no—
381C23—441no—
382C23—441no—
383C23—441no—
384C23—441no—
385C23—441no—
386C23C22⋊C4×D1111yescharacteristic
387C23#6693711yescharacteristic
388C23#6694811yescharacteristic
389D4—881no—
390D4—881no—
391D4—882no—
392D4—882no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—22no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—81no—
408C2×C4—81no—
409C2×C4—81no—
410C2×C4—221no—
411C2×C4—221no—
412C2×C4—221no—
413C2×C4—221no—
414C2×C4—441no—
415C2×C4—441no—
416C2×C4—441no—
417C2×C4—441no—
418C2×C4—441no—
419C2×C4—441no—
420C2×C4—441no—
421C2×C4—881no—
422C2×C4—881no—
423C2×C4—881no—
424C2×C4C4×D4411yescharacteristic
425C2×C4#6693511yescharacteristic
426C2×C4#6694611yescharacteristic
427C2×C4#6694711yescharacteristic
428C8—42no—
429C8—442no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—81no—
439C22—81no—
440C22—881no—
441C22—881no—
442C22—881no—
443C22—881no—
444C22—881no—
445C22—881no—
446C22—881no—
447C22#1062227811yescharacteristic
448C22#1062235311yescharacteristic
449C22#1062235311yescharacteristic
450C4—21no—
451C4—21no—
452C4—21no—
453C4—21no—
454C4—42no—
455C4—81no—
456C4—161no—
457C4—441no—
458C4—441no—
459C4—441no—
460C4—441no—
461C4—881no—
462C4—1761no—
463C2—21no—
464C2—21no—
465C2—41no—
466C2—41no—
467C2—1761no—
468C2#1306899811yescharacteristic
469C2#1306907311yescharacteristic
470C2#1306914211yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1284C2
socleC22×C11#386
prime radicalC2×#66983C22
cosocleC23×C4×C11C23
hypercenter#1284D11
hypocenterC11#9446
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1284

Complements

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

NH ≅ G/Ntype
1. #13077251C2semidirect
3. #13068691C2semidirect
6. #13066469C2semidirect
7. C11×#1284C2semidirect
19. #10622552C4semidirect
20. #10622552C4semidirect
21. #10622549C4semidirect
22. #10622548C4semidirect
146. #1284D11semidirect
374. C11#9446semidirect

Maximal subgroups

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

subgroupindex
#130772512
#130730782
#130686912
#130671462
#130671442
#130664692
C11×#12842
#944611