Finite Group Databasebeta

← #14664632

Subgroups — #14664632

Order 2816.

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

normal subgroups only

This group has 698 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#13071935C211yesmaximal, characteristic
2#13068690C211yesmaximal, characteristic, complemented
3#13066638C212yesmaximal, complemented
4#13066614C212yesmaximal, complemented
5C2×C11×#323C211yesmaximal, characteristic, complemented
6C22×#4339C411yescharacteristic, complemented
7C22×C11×C22⋊C4C2211yescharacteristic
8C2×#67006—21no—
9C2×C11×C22⋊C8—21no—
10#10622860—21no—
11#10622826—21no—
12#10622824C411yescharacteristic, complemented
13#10622573C411yescharacteristic, complemented
14#10622573C2211yescharacteristic
15#10622569—21no—
16#10622569—21no—
17#10622560C411yescharacteristic, complemented
18#10622560C2211yescharacteristic
19C11×#323—21no—
20C11×#323C2212yes—
21#10622164—21no—
22#10622164C2212yes—
23C25×C11D411yescharacteristic
24C23×C4×C11C2×C411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C22×C22⋊D11—21no—
27C22×C22⋊D11—21no—
28C22×C22⋊D11—21no—
29C2×#4339—41no—
30C2×#4339—41no—
31C2×#4339—44no—
32C22×D44C2×C411yescharacteristic
33C22×C4×D11—21no—
34C22×Dic22C2×C411yescharacteristic
35C22×C8×C11—41no—
36C2×C11×C22⋊C4—41no—
37C2×C11×C22⋊C4—41no—
38C2×C11×C22⋊C4C2×C411yescharacteristic
39C2×C11×C22⋊C4D411yescharacteristic
40C2×C11×C22⋊C4D411yescharacteristic
41C2×C11×C22⋊C4C2311yescharacteristic
42#67006—44no—
43C2×C22⋊Dic11—21no—
44C2×C22⋊Dic11—21no—
45C2×C22⋊Dic11—21no—
46C2×C22⋊Dic11—22no—
47C2×C22⋊Dic11—41no—
48C2×C22⋊Dic11—41no—
49C2×(C2×D11)⋊C4—21no—
50C2×(C2×D11)⋊C4—21no—
51C11×C22⋊C8—22no—
52C11×C22⋊C8—41no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95C2×C411yescharacteristic
57C11⋊#95C2×C411yescharacteristic
58#11839—111nomaximal, Sylow
59C24×C11—21no—
60C24×C11—21no—
61C24×C11—22no—
62C24×C11—41no—
63C24×C11—42no—
64C24×C11—81no—
65C24×C11C22⋊C411yescharacteristic
66C24×C11C22⋊C411yescharacteristic
67C24×C11C2×D411yescharacteristic
68C23×D11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—42no—
74C22×C4×C11—81no—
75C22×C4×C11C22⋊C411yescharacteristic
76C22×C4×C11C22⋊C411yescharacteristic
77C22×C4×C11C22×C411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C2×C22⋊D11—24no—
80C2×C22⋊D11—42no—
81C2×C22⋊D11—42no—
82C2×C22⋊D11—42no—
83C2×C22⋊D11—42no—
84C2×C22⋊D11—41no—
85C2×C22⋊D11—41no—
86C2×C22⋊D11—42no—
87C2×C22⋊D11—81no—
88C2×C22⋊D11—81no—
89C22×Dic11—21no—
90C22×Dic11—21no—
91C22×Dic11—21no—
92C22×Dic11—42no—
93#4339—44no—
94#4339—44no—
95#4339—44no—
96#4339—44no—
97C2×D44—41no—
98C2×D44—42no—
99C2×C4×D11—42no—
100C2×C4×D11—42no—
101C2×C4×D11—42no—
102C2×Dic22—41no—
103C2×Dic22—42no—
104C2×C8×C11—42no—
105C2×C8×C11—82no—
106C11×C22⋊C4—41no—
107C11×C22⋊C4—41no—
108C11×C22⋊C4—41no—
109C11×C22⋊C4—41no—
110C22⋊Dic11—42no—
111C22⋊Dic11—42no—
112C22⋊Dic11—42no—
113C22⋊Dic11—42no—
114C22⋊Dic11—42no—
115C22⋊Dic11—82no—
116C22⋊Dic11—82no—
117(C2×D11)⋊C4—81no—
118(C2×D11)⋊C4—81no—
119#2404—111no—
120#1819—111no—
121C2×#323D1111yescharacteristic, complemented
122#1351—112no—
123#1343—112no—
124C23×C11—22no—
125C23×C11—21no—
126C23×C11—21no—
127C23×C11—21no—
128C23×C11—21no—
129C23×C11—21no—
130C23×C11—21no—
131C23×C11—21no—
132C23×C11—41no—
133C23×C11—42no—
134C23×C11—42no—
135C23×C11—41no—
136C23×C11—41no—
137C23×C11—41no—
138C23×C11—41no—
139C23×C11—42no—
140C23×C11—42no—
141C23×C11—81no—
142C23×C11—81no—
143C23×C11—84no—
144C23×C11—84no—
145C23×C11#9911yescharacteristic
146C23×C11#9911yescharacteristic
147C23×C11C2×C22⋊C411yescharacteristic
148C23×C11#13512yes—
149C22×D11—22no—
150C22×D11—41no—
151C22×D11—41no—
152C22×D11—41no—
153C22×D11—41no—
154C22×D11—41no—
155C22×D11—41no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—42no—
161C2×C4×C11—42no—
162C2×C4×C11—42no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—81no—
168C22⋊D11—44no—
169C22⋊D11—44no—
170C22⋊D11—84no—
171C22⋊D11—84no—
172C2×Dic11—22no—
173C2×Dic11—41no—
174C2×Dic11—41no—
175C2×Dic11—41no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11—41no—
181C2×Dic11—82no—
182C2×Dic11—82no—
183C2×Dic11—82no—
184D44—42no—
185D44—42no—
186C4×D11—48no—
187Dic22—42no—
188Dic22—42no—
189C8×C11—82no—
190C22×#41—111no—
191C2×#120—221no—
192C22×C22⋊C4C2×D1111yescharacteristic
193C2×C22⋊C8—21no—
194#393—111no—
195#393—111no—
196#392—111no—
197#392—111no—
198#386—221no—
199#386—221no—
200#386—221no—
201#381—111no—
202#379—221no—
203#342—112no—
204#342—221no—
205#323—21no—
206#323C2×D1112yes—
207C22×C11—21no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—22no—
215C22×C11—42no—
216C22×C11—42no—
217C22×C11—42no—
218C22×C11—42no—
219C22×C11—41no—
220C22×C11—41no—
221C22×C11—41no—
222C22×C11—41no—
223C22×C11—41no—
224C22×C11—81no—
225C22×C11—84no—
226C22×C11—81no—
227C22×C11—84no—
228C22×C11AΣL(1,𝔽16)12yes—
229C22×C11C2×#9911yescharacteristic
230C22×C11#41611yescharacteristic
231C22×C11#42111yescharacteristic
232C2×D11—42no—
233C2×D11—42no—
234C2×D11—42no—
235C2×D11—81no—
236C2×D11—81no—
237C2×D11—81no—
238C2×D11—81no—
239C4×C11—41no—
240C4×C11—41no—
241C4×C11—41no—
242C4×C11—41no—
243Dic11—42no—
244Dic11—81no—
245Dic11—81no—
246Dic11—162no—
247C25D4411yescharacteristic
248C2×#41—441no—
249C2×#41—441no—
250C2×#41—444no—
251C22×Q8—111no—
252C22×D4—111no—
253C22×D4—221no—
254C22×D4—221no—
255C22×D4—221no—
256C23×C4—221no—
257C23×C4C4×D1111yescharacteristic
258C23×C4C22⋊D1111yescharacteristic
259C22×C8—41no—
260#120—444no—
261C2×C22⋊C4—41no—
262C2×C22⋊C4—41no—
263C2×C22⋊C4—221no—
264C2×C22⋊C4—221no—
265C2×C22⋊C4—221no—
266C2×C22⋊C4—222no—
267C2×C22⋊C4—221no—
268C2×C22⋊C4—221no—
269C2×C22⋊C4—441no—
270C2×C22⋊C4—441no—
271C2×C22⋊C4C4×D1111yescharacteristic
272C2×C22⋊C4D4411yescharacteristic
273C2×C22⋊C4C22⋊D1111yescharacteristic
274C2×C22⋊C4C22×D1111yescharacteristic
275C22⋊C8—22no—
276C22⋊C8—41no—
277#95—111no—
278#95—111no—
279#95—221no—
280#95—221no—
281#95—221no—
282C2×C11—21no—
283C2×C11—21no—
284C2×C11—22no—
285C2×C11—42no—
286C2×C11—41no—
287C2×C11—81no—
288C2×C11#151611yescharacteristic
289C2×C11C2×AΣL(1,𝔽16)11yescharacteristic
290C2×C11#212711yescharacteristic
291D11—82no—
292C24—21no—
293C24—21no—
294C24—22no—
295C24—41no—
296C24—42no—
297C24—81no—
298C24—221no—
299C24(C2×D11)⋊C411yescharacteristic
300C24(C2×D11)⋊C411yescharacteristic
301C24C2×D4411yescharacteristic
302#41—444no—
303#41—444no—
304#41—444no—
305#41—444no—
306C2×Q8—441no—
307C2×Q8—442no—
308C2×D4—224no—
309C2×D4—441no—
310C2×D4—442no—
311C2×D4—442no—
312C2×D4—441no—
313C2×D4—441no—
314C2×D4—442no—
315C2×D4—442no—
316C2×D4—442no—
317C2×D4—442no—
318C2×D4—881no—
319C2×D4—881no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—42no—
325C22×C4—81no—
326C22×C4—221no—
327C22×C4—221no—
328C22×C4—221no—
329C22×C4—442no—
330C22×C4—442no—
331C22×C4—442no—
332C22×C4—442no—
333C22×C4(C2×D11)⋊C411yescharacteristic
334C22×C4(C2×D11)⋊C411yescharacteristic
335C22×C4C2×C4×D1111yescharacteristic
336C22×C4C2×C22⋊D1111yescharacteristic
337C2×C8—42no—
338C2×C8—82no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C22⋊C4—442no—
344C22⋊C4—442no—
345C22⋊C4—442no—
346C22⋊C4—442no—
347C22⋊C4—442no—
348C22⋊C4—881no—
349C22⋊C4—881no—
350C22⋊C4—882no—
351C22⋊C4—882no—
352C11#1183911yescharacteristic, complemented, Sylow
353C23—21no—
354C23—21no—
355C23—21no—
356C23—22no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—41no—
362C23—42no—
363C23—42no—
364C23—41no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23—42no—
369C23—42no—
370C23—81no—
371C23—81no—
372C23—84no—
373C23—84no—
374C23—222no—
375C23—441no—
376C23—441no—
377C23—441no—
378C23—441no—
379C23—441no—
380C23—441no—
381C23#6687011yescharacteristic
382C23#6687011yescharacteristic
383C23#6695712yes—
384C23C2×(C2×D11)⋊C411yescharacteristic
385Q8—442no—
386Q8—442no—
387D4—442no—
388D4—442no—
389D4—444no—
390D4—444no—
391D4—884no—
392D4—884no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—81no—
405C2×C4—222no—
406C2×C4—448no—
407C2×C4—441no—
408C2×C4—441no—
409C2×C4—441no—
410C2×C4—441no—
411C2×C4—441no—
412C2×C4—441no—
413C2×C4—441no—
414C2×C4—441no—
415C2×C4—882no—
416C2×C4—882no—
417C2×C4—882no—
418C8—82no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—22no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—42no—
428C22—42no—
429C22—42no—
430C22—42no—
431C22—41no—
432C22—41no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—81no—
437C22—84no—
438C22—81no—
439C22—84no—
440C22—442no—
441C22—442no—
442C22—442no—
443C22—881no—
444C22—881no—
445C22—881no—
446C22—881no—
447C22#1062211312yes—
448C22C2×#6687011yescharacteristic
449C22#1062272611yescharacteristic
450C22#1062275211yescharacteristic
451C4—41no—
452C4—41no—
453C4—41no—
454C4—41no—
455C4—442no—
456C4—881no—
457C4—881no—
458C4—1762no—
459C2—21no—
460C2—21no—
461C2—22no—
462C2—42no—
463C2—41no—
464C2—81no—
465C2—882no—
466C2#1306717311yescharacteristic
467C2C2×#1062211311yescharacteristic
468C2#1307028311yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC2×C11×#323C2
socleC22×C11C2×#99
prime radical#13071935C2
cosocleC2×C11×C22⋊C4C23
hypercenterC2×#323D11
hypocenterC11#11839
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ C2×#323

Complements

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

NH ≅ G/Ntype
2. #13068690C2semidirect
3. #13066638C2semidirect
4. #13066614C2semidirect
5. C2×C11×#323C2semidirect
6. C22×#4339C4semidirect
12. #10622824C4semidirect
13. #10622573C4semidirect
17. #10622560C4semidirect
121. C2×#323D11semidirect
352. C11#11839semidirect

Maximal subgroups

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

subgroupindex
#130719352
#130686902
#130666382
#130666142
C2×C11×#3232
#1183911