Finite Group Databasebeta

← #14672065

Subgroups — #14672065

Order 2816.

624 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 624 conjugacy classes of subgroups — too many to draw. Only its 103 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#13073502C211yesmaximal, characteristic
2C2×#10622114C212yesmaximal, complemented
3C2×#10622113C212yesmaximal
4#13068604C211yesmaximal, characteristic, complemented
5C4×C11×#100C211yesmaximal, characteristic, complemented
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66990C2211yescharacteristic
8C2×#66988C2211yescharacteristic
9C22×(C2×D11)⋊C4C411yescharacteristic, complemented
10C2×C11×#100C2212yes—
11C4×C11×M16—21no—
12C2×#66898C2212yes—
13#10622826—21no—
14#10622825—21no—
15#10622825C411yescharacteristic, complemented
16#10622607—21no—
17#10622574—21no—
18#10622568C411yescharacteristic, complemented
19#10622556C411yescharacteristic, complemented
20#10622553—21no—
21C11×#343—21no—
22#10622164—21no—
23#10622114—24no—
24#10622113—24no—
25C24×D11C2×C411yescharacteristic
26C22×D4×C11C2311yescharacteristic
27C23×C4×C11C2×C411yescharacteristic
28C23×C4×C11D411yescharacteristic
29C22×C22⋊D11—21no—
30C23×Dic11C2×C411yescharacteristic
31C2×C11×M16—22no—
32C4×D4×C11—41no—
33C4×D4×C11—41no—
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C11×C22⋊C4C2×C411yescharacteristic
36C2×C11×C22⋊C4D411yescharacteristic
37C2×C42×C11D411yescharacteristic
38C2×C22⋊Dic11—21no—
39C2×C22⋊Dic11—22no—
40C2×C22⋊Dic11C2×C411yescharacteristic
41C2×C22⋊Dic11C2×C411yescharacteristic
42#66990—22no—
43#66990—22no—
44#66988—22no—
45#66988—22no—
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—
51C2×(C2×D11)⋊C4—41no—
52C2×(C2×D11)⋊C4—41no—
53C2×C4⋊Dic11—21no—
54C2×C4⋊Dic11—41no—
55C2×Dic11⋊C4—21no—
56C11×#100—22no—
57C11×#100D414yes—
58C11×#97—41no—
59C4×C8×C11—41no—
60#66898—22no—
61#66898—22no—
62C11⋊#95—21no—
63C11⋊#95—21no—
64C11⋊#95—21no—
65C11⋊#95—41no—
66#13219—111nomaximal, Sylow
67C24×C11C22×C411yescharacteristic
68C24×C11C2×D411yescharacteristic
69C23×D11—21no—
70C23×D11—22no—
71C23×D11—42no—
72C23×D11—41no—
73C23×D11—41no—
74C23×D11—81no—
75C2×D4×C11—41no—
76C2×D4×C11—41no—
77C2×D4×C11C2×D412yes—
78C2×D4×C11#4112yes—
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—81no—
84C22×C4×C11—81no—
85C22×C4×C11C22⋊C411yescharacteristic
86C22×C4×C11C22⋊C411yescharacteristic
87C22×C4×C11C22⋊C411yescharacteristic
88C22×C4×C11C22⋊C411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C2×C22⋊D11—42no—
91C2×C22⋊D11—41no—
92C2×C22⋊D11—41no—
93C2×C22⋊D11—81no—
94C22×Dic11—21no—
95C22×Dic11—21no—
96C22×Dic11—21no—
97C22×Dic11—22no—
98C22×Dic11—41no—
99C22×Dic11—41no—
100C22×Dic11—42no—
101C11×M16—24no—
102C11×M16—42no—
103C2×C8×C11—42no—
104C11×C4⋊C4—41no—
105C11×C22⋊C4—41no—
106C11×C22⋊C4—41no—
107C42×C11—21no—
108C42×C11—21no—
109C22⋊Dic11—22no—
110C22⋊Dic11—22no—
111C22⋊Dic11—42no—
112C22⋊Dic11—41no—
113C22⋊Dic11—41no—
114C22⋊Dic11—42no—
115(C2×D11)⋊C4—42no—
116(C2×D11)⋊C4—42no—
117(C2×D11)⋊C4—41no—
118(C2×D11)⋊C4—41no—
119(C2×D11)⋊C4—42no—
120(C2×D11)⋊C4—81no—
121C4⋊Dic11—81no—
122C4⋊Dic11—82no—
123Dic11⋊C4—42no—
124#2534—111no—
125C2×#352—112no—
126C2×AΣL(1,𝔽16)—112no—
127#1799—111no—
128C4×#100D1111yescharacteristic, complemented
129C23×C11—21no—
130C23×C11—21no—
131C23×C11—21no—
132C23×C11—21no—
133C23×C11—41no—
134C23×C11—41no—
135C23×C11—41no—
136C23×C11—41no—
137C23×C11C2×C22⋊C411yescharacteristic
138C23×C11C4×D412yes—
139C23×C11#12411yescharacteristic
140C23×C11#12711yescharacteristic
141C22×D11—22no—
142C22×D11—41no—
143C22×D11—41no—
144C22×D11—41no—
145C22×D11—42no—
146C22×D11—41no—
147C22×D11—41no—
148C22×D11—41no—
149C22×D11—42no—
150C22×D11—84no—
151C22×D11—84no—
152C22×D11—82no—
153C22×D11—82no—
154D4×C11—42no—
155D4×C11—42no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—41no—
162C2×C4×C11—42no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—81no—
167C2×C4×C11—81no—
168C2×C4×C11—81no—
169C2×C4×C11#9911yescharacteristic
170C2×C4×C11#9911yescharacteristic
171C2×C4×C11#12112yes—
172C22⋊D11—82no—
173C22⋊D11—82no—
174C2×Dic11—41no—
175C2×Dic11—41no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11—41no—
181C2×Dic11—41no—
182C2×Dic11—41no—
183C2×Dic11—82no—
184C2×Dic11—82no—
185C2×Dic11—82no—
186C2×Dic11—82no—
187C8×C11—44no—
188C2×#123—111no—
189C2×#120—111no—
190C2×C4×D4C2×D1111yescharacteristic
191C22×C22⋊C4—111no—
192C2×#100C2×D1112yes—
193C2×#99—112no—
194C4×M16—21no—
195#396—221no—
196#394—221no—
197#388—221no—
198#386—221no—
199#381—111no—
200#380—111no—
201#380—221no—
202#379—111no—
203#352—224no—
204AΣL(1,𝔽16)—224no—
205#343—21no—
206#342—221no—
207C22×C11—21no—
208C22×C11—21no—
209C22×C11—22no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—42no—
213C22×C11—41no—
214C22×C11—41no—
215C22×C11—42no—
216C22×C11—41no—
217C22×C11—41no—
218C22×C11—41no—
219C22×C11—41no—
220C22×C11—81no—
221C22×C11#39011yescharacteristic
222C22×C11C2×#9911yescharacteristic
223C22×C11#41011yescharacteristic
224C2×D11—42no—
225C2×D11—42no—
226C2×D11—42no—
227C2×D11—81no—
228C2×D11—81no—
229C2×D11—84no—
230C2×D11—81no—
231C2×D11—81no—
232C2×D11—84no—
233C4×C11—21no—
234C4×C11—21no—
235C4×C11—22no—
236C4×C11—41no—
237C4×C11—41no—
238C4×C11—41no—
239Dic11—81no—
240Dic11—81no—
241Dic11—81no—
242Dic11—162no—
243C25—111no—
244C22×D4—221no—
245C22×D4C22×D1111yescharacteristic
246C23×C4—111no—
247C23×C4C4×D1111yescharacteristic
248C23×C4D4411yescharacteristic
249C2×M16—22no—
250#123—222no—
251#123—222no—
252#120—222no—
253#120—222no—
254C4×D4—41no—
255C4×D4—41no—
256C2×C4⋊C4—221no—
257C2×C4⋊C4—221no—
258C2×C4⋊C4—441no—
259C2×C4⋊C4C22⋊D1111yescharacteristic
260C2×C22⋊C4—111no—
261C2×C22⋊C4—111no—
262C2×C22⋊C4—221no—
263C2×C22⋊C4—221no—
264C2×C22⋊C4—221no—
265C2×C22⋊C4—221no—
266C2×C22⋊C4—221no—
267C2×C22⋊C4—222no—
268C2×C22⋊C4—221no—
269C2×C22⋊C4—441no—
270C2×C22⋊C4—441no—
271C2×C22⋊C4C4×D1111yescharacteristic
272C2×C22⋊C4D4411yescharacteristic
273C2×C42C22⋊D1111yescharacteristic
274#100—22no—
275#100D4414yes—
276#99—222no—
277#99—222no—
278#97—41no—
279C4×C8—41no—
280#95—221no—
281#95—221no—
282#95—221no—
283#95—441no—
284C2×C11—21no—
285C2×C11—21no—
286C2×C11—41no—
287C2×C11—42no—
288C2×C11—41no—
289C2×C11#196411yescharacteristic
290C2×C11#212011yescharacteristic
291C2×C11#212111yescharacteristic
292D11—82no—
293C24—221no—
294C24—222no—
295C24—441no—
296C24—441no—
297C24—442no—
298C24—881no—
299C24C2×C4×D1111yescharacteristic
300C24C2×D4411yescharacteristic
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—442no—
304C2×D4—441no—
305C2×D4—441no—
306C2×D4—881no—
307C2×D4C2×D4412yes—
308C2×D4#433912yes—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—81no—
314C22×C4—81no—
315C22×C4—221no—
316C22×C4—221no—
317C22×C4—221no—
318C22×C4—222no—
319C22×C4—441no—
320C22×C4—441no—
321C22×C4—442no—
322C22×C4(C2×D11)⋊C411yescharacteristic
323C22×C4(C2×D11)⋊C411yescharacteristic
324C22×C4(C2×D11)⋊C411yescharacteristic
325C22×C4(C2×D11)⋊C411yescharacteristic
326C22×C4C2×C22⋊D1111yescharacteristic
327M16—24no—
328M16—42no—
329C2×C8—42no—
330C4⋊C4—41no—
331C4⋊C4—442no—
332C4⋊C4—881no—
333C4⋊C4—882no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—222no—
337C22⋊C4—222no—
338C22⋊C4—442no—
339C22⋊C4—442no—
340C22⋊C4—441no—
341C22⋊C4—441no—
342C22⋊C4—441no—
343C22⋊C4—441no—
344C22⋊C4—442no—
345C22⋊C4—442no—
346C22⋊C4—442no—
347C22⋊C4—881no—
348C42—21no—
349C42—21no—
350C11#1321911yescharacteristic, complemented, Sylow
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—222no—
360C23—441no—
361C23—441no—
362C23—441no—
363C23—442no—
364C23—442no—
365C23—441no—
366C23—441no—
367C23—441no—
368C23—882no—
369C23—884no—
370C23—884no—
371C23—882no—
372C23C4×D4412yes—
373C23#6692711yescharacteristic
374C23#6692811yescharacteristic
375C23C2×(C2×D11)⋊C411yescharacteristic
376D4—42no—
377D4—42no—
378D4—882no—
379D4—882no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—41no—
386C2×C4—42no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—441no—
394C2×C4—441no—
395C2×C4—441no—
396C2×C4—441no—
397C2×C4—441no—
398C2×C4—441no—
399C2×C4—441no—
400C2×C4—441no—
401C2×C4—441no—
402C2×C4—882no—
403C2×C4—882no—
404C2×C4—882no—
405C2×C4—882no—
406C2×C4#6687011yescharacteristic
407C2×C4#6687011yescharacteristic
408C2×C4#6698312yes—
409C8—44no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—22no—
414C22—21no—
415C22—41no—
416C22—41no—
417C22—42no—
418C22—42no—
419C22—41no—
420C22—41no—
421C22—41no—
422C22—41no—
423C22—81no—
424C22—442no—
425C22—442no—
426C22—442no—
427C22—881no—
428C22—881no—
429C22—884no—
430C22—884no—
431C22—881no—
432C22—881no—
433C22#1062255211yescharacteristic
434C22C2×#6687011yescharacteristic
435C22#1062261911yescharacteristic
436C4—22no—
437C4—21no—
438C4—21no—
439C4—41no—
440C4—41no—
441C4—41no—
442C4—881no—
443C4—881no—
444C4—881no—
445C4—1762no—
446C2—21no—
447C2—21no—
448C2—41no—
449C2—42no—
450C2—41no—
451C2—882no—
452C2#1306945211yescharacteristic
453C2#1307025811yescharacteristic
454C2#1307026311yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC24×C11C22×C4
FrattiniC22×D4C22×D11
FittingC4×C11×#100C2
socleC22×C11C2×#99
prime radicalC2×#66990C22
cosocleC22×D4×C11C23
hypercenterC4×#100D11
hypocenterC11#13219
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#100

Complements

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

NH ≅ G/Ntype
2. C2×#10622114C2semidirect
4. #13068604C2semidirect
5. C4×C11×#100C2semidirect
9. C22×(C2×D11)⋊C4C4semidirect
15. #10622825C4semidirect
18. #10622568C4semidirect
19. #10622556C4semidirect
128. C4×#100D11semidirect
350. C11#13219semidirect

Maximal subgroups

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

subgroupindex
#130735022
C2×#106221142
C2×#106221132
#130686042
C4×C11×#1002
#1321911