Finite Group Databasebeta

← #14672078

Subgroups — #14672078

Order 2816.

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

normal subgroups only

This group has 628 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×#10622110C212yesmaximal, complemented
3C2×#10622109C212yesmaximal
4#13068608C211yesmaximal, characteristic, complemented
5C4×C11×#99C211yesmaximal, characteristic, complemented
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66990C2211yescharacteristic
8C2×#66988C2211yescharacteristic
9C22×(C2×D11)⋊C4C411yescharacteristic, complemented
10C2×C11×#99C2212yes—
11C4×C11×C22⋊C4—21no—
12C2×#66897C2212yes—
13#10622826—21no—
14#10622825C411yescharacteristic, complemented
15#10622607—21no—
16#10622574—21no—
17#10622568C411yescharacteristic, complemented
18#10622556C411yescharacteristic, complemented
19#10622553—21no—
20#10622537—21no—
21C11×#342—21no—
22#10622168—21no—
23#10622110—24no—
24#10622109—24no—
25C24×D11C2×C411yescharacteristic
26C22×D4×C11C2311yescharacteristic
27C23×C4×C11C2×C411yescharacteristic
28C23×C4×C11D411yescharacteristic
29C22×C22⋊D11—21no—
30C23×Dic11C2×C411yescharacteristic
31C4×D4×C11—41no—
32C4×D4×C11—41no—
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C11×C22⋊C4—22no—
35C2×C11×C22⋊C4C2×C411yescharacteristic
36C2×C11×C22⋊C4D411yescharacteristic
37C2×C42×C11—41no—
38C2×C42×C11D411yescharacteristic
39C2×C22⋊Dic11—21no—
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×Dic11⋊C4—21no—
55C2×#4318—22no—
56C11×#99—22no—
57C11×#99D414yes—
58C11×#95—41no—
59#66897—22no—
60#66897—22no—
61C11⋊#95—21no—
62C11⋊#95—21no—
63C11⋊#95—21no—
64C4⋊(C11⋊C8)—41no—
65C4⋊(C11⋊C8)—41no—
66#13222—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—42no—
84C22×C4×C11—81no—
85C22×C4×C11—81no—
86C22×C4×C11C22⋊C411yescharacteristic
87C22×C4×C11C22⋊C411yescharacteristic
88C22×C4×C11C22⋊C411yescharacteristic
89C22×C4×C11C22⋊C411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C2×C22⋊D11—42no—
92C2×C22⋊D11—42no—
93C2×C22⋊D11—81no—
94C22×Dic11—21no—
95C22×Dic11—21no—
96C22×Dic11—21no—
97C22×Dic11—22no—
98C22×Dic11—41no—
99C22×Dic11—41no—
100C11×C4⋊C4—41no—
101C11×C22⋊C4—24no—
102C11×C22⋊C4—41no—
103C11×C22⋊C4—41no—
104C11×C22⋊C4—42no—
105C42×C11—21no—
106C42×C11—21no—
107C42×C11—82no—
108C22⋊Dic11—22no—
109C22⋊Dic11—22no—
110C22⋊Dic11—42no—
111(C2×D11)⋊C4—42no—
112(C2×D11)⋊C4—42no—
113(C2×D11)⋊C4—41no—
114(C2×D11)⋊C4—41no—
115(C2×D11)⋊C4—41no—
116(C2×D11)⋊C4—41no—
117(C2×D11)⋊C4—81no—
118C4⋊Dic11—81no—
119Dic11⋊C4—41no—
120Dic11⋊C4—41no—
121#4318—42no—
122#4318—42no—
123C2×C11⋊C8—42no—
124#2534—111no—
125C2×#352—112no—
126C2×AΣL(1,𝔽16)—112no—
127#1800—111no—
128C4×#99D1111yescharacteristic, 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#12112yes—
140C22×D11—22no—
141C22×D11—41no—
142C22×D11—41no—
143C22×D11—41no—
144C22×D11—42no—
145C22×D11—41no—
146C22×D11—41no—
147C22×D11—41no—
148C22×D11—42no—
149C22×D11—84no—
150C22×D11—84no—
151C22×D11—82no—
152C22×D11—82no—
153D4×C11—42no—
154D4×C11—42no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—41no—
161C2×C4×C11—42no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—44no—
166C2×C4×C11—81no—
167C2×C4×C11—81no—
168C2×C4×C11—81no—
169C2×C4×C11—82no—
170C2×C4×C11—82no—
171C2×C4×C11#9911yescharacteristic
172C2×C4×C11#9911yescharacteristic
173C2×C4×C11#12411yescharacteristic
174C2×C4×C11#12711yescharacteristic
175C22⋊D11—84no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11—41no—
181C2×Dic11—41no—
182C2×Dic11—41no—
183C2×Dic11—41no—
184C2×Dic11—41no—
185C2×Dic11—82no—
186C11⋊C8—82no—
187C2×#123—111no—
188C2×#120—111no—
189C2×C4×D4C2×D1111yescharacteristic
190C22×C22⋊C4—111no—
191#423—221no—
192C2×#100—112no—
193C2×#99C2×D1112yes—
194#396—221no—
195#394—221no—
196#388—221no—
197#386—221no—
198#381—111no—
199#380—111no—
200#379—111no—
201C4×C22⋊C4—21no—
202#352—224no—
203AΣL(1,𝔽16)—224no—
204#343—221no—
205#342—21no—
206C22×C11—21no—
207C22×C11—21no—
208C22×C11—22no—
209C22×C11—22no—
210C22×C11—42no—
211C22×C11—42no—
212C22×C11—42no—
213C22×C11—41no—
214C22×C11—41no—
215C22×C11—41no—
216C22×C11—41no—
217C22×C11—81no—
218C22×C11#39011yescharacteristic
219C22×C11C2×#9911yescharacteristic
220C22×C11#41011yescharacteristic
221C2×D11—42no—
222C2×D11—42no—
223C2×D11—42no—
224C2×D11—81no—
225C2×D11—81no—
226C2×D11—84no—
227C2×D11—81no—
228C2×D11—81no—
229C2×D11—84no—
230C4×C11—21no—
231C4×C11—21no—
232C4×C11—21no—
233C4×C11—21no—
234C4×C11—41no—
235C4×C11—41no—
236C4×C11—41no—
237C4×C11—84no—
238Dic11—81no—
239Dic11—81no—
240Dic11—81no—
241C25—111no—
242C22×D4—221no—
243C22×D4C22×D1111yescharacteristic
244C23×C4—111no—
245C23×C4C4×D1111yescharacteristic
246C23×C4C22⋊D1111yescharacteristic
247C2×M16—222no—
248#123—222no—
249#123—222no—
250#120—222no—
251#120—222no—
252C4×D4—41no—
253C4×D4—41no—
254C2×C4⋊C4—221no—
255C2×C4⋊C4—221no—
256C2×C4⋊C4D4411yescharacteristic
257C2×C22⋊C4—22no—
258C2×C22⋊C4—111no—
259C2×C22⋊C4—111no—
260C2×C22⋊C4—221no—
261C2×C22⋊C4—221no—
262C2×C22⋊C4—221no—
263C2×C22⋊C4—221no—
264C2×C22⋊C4—221no—
265C2×C22⋊C4—221no—
266C2×C22⋊C4—441no—
267C2×C22⋊C4—441no—
268C2×C22⋊C4C4×D1111yescharacteristic
269C2×C22⋊C4C22⋊D1111yescharacteristic
270C2×C42—41no—
271C2×C42D4411yescharacteristic
272C4⋊C8—441no—
273C4⋊C8—441no—
274#100—222no—
275#100—222no—
276#99—22no—
277#99D4414yes—
278#95—41no—
279#95—221no—
280#95—221no—
281#95—221no—
282C2×C11—21no—
283C2×C11—21no—
284C2×C11—42no—
285C2×C11—42no—
286C2×C11#196411yescharacteristic
287C2×C11#212011yescharacteristic
288C2×C11#212111yescharacteristic
289D11—82no—
290C24—221no—
291C24—222no—
292C24—441no—
293C24—441no—
294C24—442no—
295C24—881no—
296C24C2×C4×D1111yescharacteristic
297C24C2×C22⋊D1111yescharacteristic
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—442no—
301C2×D4—442no—
302C2×D4—881no—
303C2×D4C2×D4412yes—
304C2×D4#433912yes—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—42no—
310C22×C4—81no—
311C22×C4—81no—
312C22×C4—221no—
313C22×C4—221no—
314C22×C4—221no—
315C22×C4—222no—
316C22×C4—441no—
317C22×C4—441no—
318C22×C4(C2×D11)⋊C411yescharacteristic
319C22×C4(C2×D11)⋊C411yescharacteristic
320C22×C4(C2×D11)⋊C411yescharacteristic
321C22×C4(C2×D11)⋊C411yescharacteristic
322C22×C4C2×D4411yescharacteristic
323M16—442no—
324M16—442no—
325C2×C8—442no—
326C4⋊C4—41no—
327C4⋊C4—441no—
328C4⋊C4—441no—
329C4⋊C4—881no—
330C22⋊C4—24no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—42no—
334C22⋊C4—222no—
335C22⋊C4—222no—
336C22⋊C4—442no—
337C22⋊C4—442no—
338C22⋊C4—442no—
339C22⋊C4—441no—
340C22⋊C4—441no—
341C22⋊C4—441no—
342C22⋊C4—441no—
343C22⋊C4—881no—
344C42—21no—
345C42—21no—
346C42—82no—
347C11#1322211yescharacteristic, complemented, Sylow
348C23—21no—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—222no—
357C23—441no—
358C23—441no—
359C23—441no—
360C23—442no—
361C23—442no—
362C23—441no—
363C23—441no—
364C23—441no—
365C23—882no—
366C23—884no—
367C23—884no—
368C23—882no—
369C23C4×D4412yes—
370C23C2×(C2×D11)⋊C411yescharacteristic
371C23#6698312yes—
372D4—42no—
373D4—42no—
374D4—884no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—44no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4—82no—
390C2×C4—82no—
391C2×C4—441no—
392C2×C4—441no—
393C2×C4—441no—
394C2×C4—441no—
395C2×C4—441no—
396C2×C4—441no—
397C2×C4—441no—
398C2×C4—441no—
399C2×C4—441no—
400C2×C4—882no—
401C2×C4#6687011yescharacteristic
402C2×C4#6687011yescharacteristic
403C2×C4#6692711yescharacteristic
404C2×C4#6692811yescharacteristic
405C8—882no—
406C22—21no—
407C22—21no—
408C22—22no—
409C22—22no—
410C22—42no—
411C22—42no—
412C22—42no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—81no—
418C22—442no—
419C22—442no—
420C22—442no—
421C22—881no—
422C22—881no—
423C22—884no—
424C22—884no—
425C22—881no—
426C22—881no—
427C22#1062255211yescharacteristic
428C22C2×#6687011yescharacteristic
429C22#1062261911yescharacteristic
430C4—21no—
431C4—21no—
432C4—21no—
433C4—21no—
434C4—41no—
435C4—41no—
436C4—41no—
437C4—84no—
438C4—881no—
439C4—881no—
440C4—881no—
441C2—21no—
442C2—21no—
443C2—42no—
444C2—42no—
445C2—882no—
446C2#1306945211yescharacteristic
447C2#1307025511yescharacteristic
448C2#1307026011yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC24×C11C22×C4
FrattiniC22×D4C22×D11
FittingC4×C11×#99C2
socleC22×C11C2×#99
prime radicalC2×#66990C22
cosocleC22×D4×C11C23
hypercenterC4×#99D11
hypocenterC11#13222
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
2. C2×#10622110C2semidirect
4. #13068608C2semidirect
5. C4×C11×#99C2semidirect
9. C22×(C2×D11)⋊C4C4semidirect
14. #10622825C4semidirect
17. #10622568C4semidirect
18. #10622556C4semidirect
128. C4×#99D11semidirect
347. C11#13222semidirect

Maximal subgroups

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

subgroupindex
#130735022
C2×#106221102
C2×#106221092
#130686082
C4×C11×#992
#1322211