Finite Group Databasebeta

← #14658169

Subgroups — #14658169

Order 2816.

490 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 95 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#13079388C211yesmaximal, characteristic
2#13069602C211yesmaximal, characteristic
3#13069600C211yesmaximal, characteristic
4#13069039C211yesmaximal, characteristic
5#13068794C211yesmaximal, characteristic
6#13066483C211yesmaximal, characteristic
7C11×#1892C211yesmaximal, characteristic
8C23×C8×C11C2211yescharacteristic
9C2×C11×C22⋊Q8C2211yescharacteristic
10C2×#66977C2211yescharacteristic
11C2×C11×#103—21no—
12C11×#380C2211yescharacteristic
13#10622841—21no—
14#10622825C2211yescharacteristic
15C4×C22⋊Dic11C2211yescharacteristic
16C2×C22⋊(C11⋊C8)C2211yescharacteristic
17C2×#66880—21no—
18C2×Dic11⋊C8—21no—
19#10622664—21no—
20#10622664—21no—
21#10622663—21no—
22#10622657—21no—
23#10622583—21no—
24C11×#340—21no—
25#10622189—21no—
26#10622188—21no—
27#10622165—21no—
28#10622165—21no—
29#10622164—21no—
30#10622164—21no—
31C22×Q8×C11D411yescharacteristic
32C23×C4×C11C2311yescharacteristic
33C22×Dic22D411yescharacteristic
34C22×C8×C11—21no—
35C22×C8×C11—21no—
36C22×C8×C11—21no—
37C22×C8×C11—42no—
38C11×C22⋊Q8—21no—
39C11×C22⋊Q8—21no—
40C11×C22⋊Q8—21no—
41C11×C22⋊Q8—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4D411yescharacteristic
45C2×C11×C22⋊C4—21no—
46C2×C11×C22⋊C4—21no—
47C2×C22⋊Dic11—21no—
48C2×C22⋊Dic11—21no—
49C2×C22⋊Dic11D411yescharacteristic
50C2×C22⋊Dic11D411yescharacteristic
51C2×#4326—21no—
52C2×#4326—21no—
53C2×C4⋊Dic11—21no—
54C2×C4⋊Dic11D411yescharacteristic
55#66977—21no—
56#66977—21no—
57#66977—21no—
58#66977—21no—
59C2×Dic11⋊C4—21no—
60C2×C4×Dic11—21no—
61C22×C11⋊C8D411yescharacteristic
62C22×C11⋊C8D411yescharacteristic
63C11×#103—42no—
64C11×#95—21no—
65#66899—21no—
66#66899—21no—
67C11⋊#95—21no—
68C11⋊#95—21no—
69C22⋊(C11⋊C8)—21no—
70C22⋊(C11⋊C8)—21no—
71#66880—42no—
72Dic11⋊C8—42no—
73#66874—21no—
74#66874—21no—
75#66871—21no—
76#66871—21no—
77#10566—111nomaximal, Sylow
78C24×C11C2×D411yescharacteristic
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—41no—
82C2×Q8×C11—41no—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—41no—
86C22×C4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11#4111yescharacteristic
92C22×C4×C11#4111yescharacteristic
93C22×C4×C11#4111yescharacteristic
94C22×Dic11—21no—
95C22×Dic11—21no—
96C22×Dic11—21no—
97C22×Dic11—21no—
98C22×Dic11—41no—
99C2×Dic22—21no—
100C2×Dic22—21no—
101C2×Dic22—41no—
102C2×Dic22—41no—
103C2×C8×C11—22no—
104C2×C8×C11—22no—
105C2×C8×C11—22no—
106C2×C8×C11—41no—
107C2×C8×C11—41no—
108C2×C8×C11—41no—
109C2×C8×C11—41no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C11×C22⋊C4—41no—
117C11×C22⋊C4—41no—
118C11×C22⋊C4—41no—
119C11×C22⋊C4—41no—
120C22⋊Dic11—21no—
121C22⋊Dic11—21no—
122C22⋊Dic11—21no—
123C22⋊Dic11—41no—
124C22⋊Dic11—41no—
125C22⋊Dic11—41no—
126C22⋊Dic11—41no—
127C22⋊Dic11Q1612yescomplemented
128#4326—81no—
129#4326—81no—
130C4⋊Dic11—21no—
131C4⋊Dic11—21no—
132C4⋊Dic11—41no—
133C4⋊Dic11—41no—
134Dic11⋊C4—41no—
135Dic11⋊C4—41no—
136C4×Dic11—41no—
137C4×Dic11—41no—
138C2×C11⋊C8—21no—
139C2×C11⋊C8—21no—
140C2×C11⋊C8—41no—
141C2×C11⋊C8—41no—
142#3189—111no—
143#1996—111no—
144#1996—111no—
145#1892—111no—
146#1892D1111yescharacteristic
147#1850—111no—
148#1289—111no—
149C23×C11—41no—
150C23×C11—41no—
151C23×C11#12111yescharacteristic
152C23×C11#12111yescharacteristic
153C23×C11#12111yescharacteristic
154C23×C11C2×Q1611yescharacteristic
155C23×C11#13511yescharacteristic
156C23×C11#13711yescharacteristic
157C23×C11#13711yescharacteristic
158Q8×C11—42no—
159Q8×C11—41no—
160Q8×C11—41no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—81no—
173C2×C4×C11—81no—
174C2×C4×C11—81no—
175C2×C4×C11—81no—
176C2×C4×C11—81no—
177C2×C4×C11#12011yescharacteristic
178C2×C4×C11#12311yescharacteristic
179C2×C4×C11#12311yescharacteristic
180C2×C4×C11#12411yescharacteristic
181C2×Dic11—22no—
182C2×Dic11—41no—
183C2×Dic11—41no—
184C2×Dic11—41no—
185C2×Dic11—41no—
186C2×Dic11—41no—
187C2×Dic11—41no—
188C2×Dic11—41no—
189C2×Dic11—81no—
190C2×Dic11—81no—
191C2×Dic11—81no—
192C2×Dic11—81no—
193C2×Dic11—81no—
194Dic22—42no—
195Dic22—41no—
196Dic22—41no—
197C8×C11—42no—
198C11⋊C8—41no—
199C11⋊C8—41no—
200C23×C8C2×D1111yescharacteristic
201C2×C22⋊Q8—111no—
202C2×C22⋊Q8C2×D1111yescharacteristic
203#484—221no—
204#484—221no—
205#467—221no—
206#467—221no—
207#451—221no—
208#451—221no—
209C2×C4⋊C8—221no—
210C2×#103—21no—
211C2×#103—221no—
212C2×C22⋊C8—111no—
213#380—111no—
214#380C2×D1111yescharacteristic
215C4×C22⋊C4—111no—
216#342—221no—
217#342—221no—
218#342—221no—
219#342—221no—
220#340—21no—
221#340—221no—
222#336—221no—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11—21no—
226C22×C11—21no—
227C22×C11—21no—
228C22×C11—21no—
229C22×C11—41no—
230C22×C11—41no—
231C22×C11—41no—
232C22×C11—41no—
233C22×C11#39411yescharacteristic
234C22×C11#46211yescharacteristic
235C22×C11#46211yescharacteristic
236C22×C11#46411yescharacteristic
237C22×C11#46411yescharacteristic
238C22×C11#46711yescharacteristic
239C22×C11#47011yescharacteristic
240C4×C11—21no—
241C4×C11—21no—
242C4×C11—21no—
243C4×C11—81no—
244C4×C11—81no—
245C4×C11—161no—
246C4×C11B(4,𝔽2)11yescharacteristic
247C4×C11#45811yescharacteristic
248Dic11—42no—
249Dic11—81no—
250Dic11—81no—
251Dic11—81no—
252Dic11—161no—
253C22×Q8—111no—
254C22×Q8C22⋊D1111yescharacteristic
255C23×C4C22×D1111yescharacteristic
256C2×Q16—221no—
257C2×Q16—221no—
258C22×C8—21no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—42no—
262C22×C8—111no—
263C22×C8—111no—
264C22⋊Q8—21no—
265C22⋊Q8—21no—
266C22⋊Q8—21no—
267C22⋊Q8—21no—
268C22⋊Q8—221no—
269C22⋊Q8—221no—
270C22⋊Q8—221no—
271C22⋊Q8—221no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—111no—
275C2×C4⋊C4—221no—
276C2×C4⋊C4—221no—
277C2×C4⋊C4C22⋊D1111yescharacteristic
278C2×C22⋊C4—21no—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—111no—
281C2×C22⋊C4—111no—
282C2×C22⋊C4—221no—
283C2×C22⋊C4—221no—
284C2×C42—221no—
285#107—221no—
286#107—221no—
287C4⋊C8—442no—
288#103—42no—
289#103—221no—
290#103—221no—
291#103—221no—
292#103—221no—
293#103—442no—
294C22⋊C8—221no—
295C22⋊C8—221no—
296#95—21no—
297#95—221no—
298#95—221no—
299C2×C11—21no—
300C2×C11—21no—
301C2×C11—21no—
302C2×C11—21no—
303C2×C11—21no—
304C2×C11—21no—
305C2×C11#204411yescharacteristic
306C2×C11#205311yescharacteristic
307C2×C11#205611yescharacteristic
308C24D4×D1111yescharacteristic
309C2×Q8—21no—
310C2×Q8—21no—
311C2×Q8—41no—
312C2×Q8—41no—
313C2×Q8—221no—
314C2×Q8—221no—
315C2×Q8—441no—
316C2×Q8—441no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—221no—
323C22×C4—221no—
324C22×C4—221no—
325C22×C4—221no—
326C22×C4—441no—
327C22×C4#433911yescharacteristic
328C22×C4#433911yescharacteristic
329C22×C4D4×D1111yescharacteristic
330C22×C4D4×D1111yescharacteristic
331C22×C4#434111yescharacteristic
332C22×C4C2×C22⋊D1111yescharacteristic
333Q16—881no—
334Q16—881no—
335C2×C8—22no—
336C2×C8—22no—
337C2×C8—22no—
338C2×C8—41no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8—41no—
342C2×C8—221no—
343C2×C8—221no—
344C2×C8—441no—
345C2×C8—441no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—41no—
349C4⋊C4—41no—
350C4⋊C4—41no—
351C4⋊C4—41no—
352C4⋊C4—221no—
353C4⋊C4—221no—
354C4⋊C4—441no—
355C4⋊C4—441no—
356C4⋊C4—441no—
357C4⋊C4—441no—
358C22⋊C4—41no—
359C22⋊C4—41no—
360C22⋊C4—41no—
361C22⋊C4—41no—
362C22⋊C4—112no—
363C22⋊C4—221no—
364C22⋊C4—221no—
365C22⋊C4—221no—
366C22⋊C4—441no—
367C22⋊C4—441no—
368C22⋊C4—441no—
369C22⋊C4—441no—
370C42—441no—
371C42—441no—
372C11#1056611yescharacteristic, complemented, Sylow
373C23—41no—
374C23—41no—
375C23#6693711yescharacteristic
376C23#6693711yescharacteristic
377C23#6696811yescharacteristic
378C23#6696911yescharacteristic
379C23Q16×D1111yescharacteristic
380C23#6697111yescharacteristic
381C23#6699211yescharacteristic
382Q8—42no—
383Q8—41no—
384Q8—41no—
385Q8—442no—
386Q8—441no—
387Q8—441no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—81no—
400C2×C4—81no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—81no—
404C2×C4—222no—
405C2×C4—441no—
406C2×C4—441no—
407C2×C4—441no—
408C2×C4—441no—
409C2×C4—441no—
410C2×C4—441no—
411C2×C4—441no—
412C2×C4—881no—
413C2×C4—881no—
414C2×C4—881no—
415C2×C4—881no—
416C2×C4—881no—
417C2×C4#6693611yescharacteristic
418C2×C4#6693811yescharacteristic
419C2×C4#6698211yescharacteristic
420C2×C4#6699011yescharacteristic
421C8—42no—
422C8—441no—
423C8—441no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—41no—
431C22—41no—
432C22—41no—
433C22—41no—
434C22#1062240611yescharacteristic
435C22#1062241111yescharacteristic
436C22#1062242611yescharacteristic
437C22#1062242911yescharacteristic
438C22#1062257211yescharacteristic
439C22#1062277911yescharacteristic
440C22#1062279511yescharacteristic
441C4—21no—
442C4—21no—
443C4—21no—
444C4—81no—
445C4—81no—
446C4—161no—
447C4—442no—
448C4—881no—
449C4—881no—
450C4—881no—
451C4—1761no—
452C4#1062264511yescharacteristic
453C4#1062266611yescharacteristic
454C2—21no—
455C2—21no—
456C2—21no—
457C2—21no—
458C2—21no—
459C2—21no—
460C2#1306986511yescharacteristic
461C2#1306992011yescharacteristic
462C2#1306993711yescharacteristic
subgroupG/H
centerC22#10622572
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1892C2
socleC22×C11#394
prime radicalC24×C11C2×D4
hypercenter#1892D11
hypocenterC11#10566
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1892

Complements

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

NH ≅ G/Ntype
127. C22⋊Dic11Q16semidirect
372. C11#10566semidirect

Maximal subgroups

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

subgroupindex
#130793882
#130696022
#130696002
#130690392
#130687942
#130664832
C11×#18922
#1056611