Finite Group Databasebeta

← #14658121

Subgroups — #14658121

Order 2816.

474 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 79 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#13079374C211yesmaximal, characteristic
2#13069084C211yesmaximal, characteristic, complemented
3#13069079C211yesmaximal, characteristic
4#13067135C211yesmaximal, characteristic, complemented
5#13067131C211yesmaximal, characteristic
6#13066493C211yesmaximal, characteristic, complemented
7C11×#1851C211yesmaximal, characteristic, complemented
8C22×C11×M16C2211yescharacteristic
9C2×#66983C2211yescharacteristic
10C2×#66977C2211yescharacteristic
11C2×C11×C4⋊C8—21no—
12C2×C11×C22⋊C8C2211yescharacteristic
13C4×C11×C22⋊C4C2211yescharacteristic
14#10622820C2211yescharacteristic
15#10622820C2211yescharacteristic
16C2×#66888—21no—
17C2×#66887—21no—
18#10622727—21no—
19#10622727—21no—
20#10622351—21no—
21#10622348—21no—
22#10622344—21no—
23#10622334—21no—
24C11×#336—21no—
25#10622192—21no—
26#10622192—21no—
27#10622090—21no—
28#10622090—21no—
29#10622089—21no—
30#10622089—21no—
31C23×C4×C11C2311yescharacteristic
32C22×C22⋊D11—21no—
33C22×D44D411yescharacteristic
34C22×Dic22D411yescharacteristic
35C2×C11×M16—21no—
36C2×C11×M16—21no—
37C2×C11×M16—42no—
38C22×C8×C11—21no—
39C22×C8×C11D411yescharacteristic
40C22×C8×C11D411yescharacteristic
41C2×C11×C22⋊C4—21no—
42C2×C42×C11—21no—
43C2×C22⋊Dic11—21no—
44#66983—21no—
45#66983—21no—
46#66983—21no—
47#66983—21no—
48C2×(C2×D11)⋊C4—21no—
49C2×C4⋊Dic11D411yescharacteristic
50C2×C4⋊Dic11D411yescharacteristic
51#66977—21no—
52#66977—21no—
53#66977—21no—
54#66977—21no—
55C2×Dic11⋊C4—21no—
56C2×#4318—21no—
57C2×#4318—21no—
58C2×#4314—21no—
59C2×#4314—21no—
60C11×C4⋊C8—42no—
61C11×C22⋊C8—21no—
62C11×C22⋊C8—21no—
63C11×#95D411yescharacteristic
64C11×#95D411yescharacteristic
65C22⋊(C11⋊C8)—21no—
66C22⋊(C11⋊C8)—21no—
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)—21no—
69#66888—42no—
70#66887—42no—
71#66885—21no—
72#66885—21no—
73#66881—21no—
74#66881—21no—
75#66880—21no—
76#66880—21no—
77#10558—111nomaximal, Sylow
78C24×C11#4111yescharacteristic
79C23×D11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—41no—
83C22×C4×C11—41no—
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11#4111yescharacteristic
89C22×C4×C11#4111yescharacteristic
90C2×C22⋊D11—41no—
91C2×C22⋊D11—41no—
92C2×C22⋊D11—81no—
93C2×C22⋊D11—81no—
94C22×Dic11—21no—
95C22×Dic11—21no—
96C22×Dic11—21no—
97C2×D44—21no—
98C2×D44—21no—
99C2×D44—41no—
100C2×D44—41no—
101C2×Dic22—21no—
102C2×Dic22—21no—
103C2×Dic22—41no—
104C2×Dic22—41no—
105C11×M16—22no—
106C11×M16—22no—
107C11×M16—41no—
108C11×M16—41no—
109C2×C8×C11—22no—
110C2×C8×C11—21no—
111C2×C8×C11—21no—
112C2×C8×C11—41no—
113C2×C8×C11—41no—
114C2×C8×C11—41no—
115C2×C8×C11—41no—
116C11×C22⋊C4—42no—
117C42×C11—41no—
118C42×C11—41no—
119C22⋊Dic11—41no—
120C22⋊Dic11—41no—
121(C2×D11)⋊C4—41no—
122(C2×D11)⋊C4—41no—
123C4⋊Dic11—21no—
124C4⋊Dic11—21no—
125C4⋊Dic11—21no—
126C4⋊Dic11—21no—
127Dic11⋊C4—41no—
128Dic11⋊C4—41no—
129#4318—41no—
130#4318—41no—
131#4318—41no—
132#4318—41no—
133C2×C11⋊C8—41no—
134C2×C11⋊C8—41no—
135#4314—81no—
136#4314—81no—
137#3187—111no—
138#1901—111no—
139#1900—111no—
140#1851D1111yescharacteristic, complemented
141#1508—111no—
142#1507—111no—
143#1293—111no—
144C23×C11—21no—
145C23×C11—21no—
146C23×C11—41no—
147C23×C11—41no—
148C23×C11#12111yescharacteristic
149C23×C11#12311yescharacteristic
150C23×C11#12311yescharacteristic
151C22×D11—41no—
152C22×D11—42no—
153C22×D11—81no—
154C22×D11—81no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—22no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11#12011yescharacteristic
171C2×C4×C11#12111yescharacteristic
172C2×C4×C11#12111yescharacteristic
173C2×C4×C11#12411yescharacteristic
174C22⋊D11—82no—
175C22⋊D11—81no—
176C22⋊D11—81no—
177C2×Dic11—42no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11—41no—
181C2×Dic11—81no—
182C2×Dic11—81no—
183D44—41no—
184D44—41no—
185D44—81no—
186Dic22—41no—
187Dic22—41no—
188Dic22—81no—
189C8×C11—41no—
190C8×C11—42no—
191C8×C11—41no—
192C11⋊C8—81no—
193C11⋊C8—81no—
194C22×M16C2×D1111yescharacteristic
195C2×C22⋊Q8—111no—
196C2×#121—111no—
197#483—221no—
198#481—221no—
199#465—221no—
200#465—221no—
201#450—221no—
202#448—221no—
203C2×C4⋊C8—21no—
204C2×#101—221no—
205C2×#100—221no—
206#407—111no—
207#407—111no—
208C2×C22⋊C8C2×D1111yescharacteristic
209C4×C22⋊C4C2×D1111yescharacteristic
210#343—221no—
211#343—221no—
212#336—21no—
213#328—221no—
214#328—221no—
215#327—221no—
216#327—221no—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11—21no—
221C22×C11—21no—
222C22×C11—21no—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11—81no—
226C22×C11—81no—
227C22×C11#39411yescharacteristic
228C22×C11#47111yescharacteristic
229C22×C11#47111yescharacteristic
230C2×D11—81no—
231C2×D11—81no—
232C2×D11—81no—
233C2×D11—162no—
234C4×C11—21no—
235C4×C11—21no—
236C4×C11—21no—
237C4×C11—42no—
238C4×C11—81no—
239C4×C11B(4,𝔽2)11yescharacteristic
240C4×C11#45811yescharacteristic
241Dic11—81no—
242Dic11—81no—
243Dic11—81no—
244C22×Q8—111no—
245C22×D4—111no—
246C22×D4—221no—
247C23×C4C22×D1111yescharacteristic
248C2×SD16—221no—
249C2×SD16—221no—
250C2×M16—21no—
251C2×M16—21no—
252C2×M16—42no—
253C2×M16—221no—
254C2×M16—221no—
255C22×C8—21no—
256C22×C8C22⋊D1111yescharacteristic
257C22×C8C22⋊D1111yescharacteristic
258C22⋊Q8—221no—
259C22⋊Q8—221no—
260C22⋊Q8—221no—
261C22⋊Q8—221no—
262#121—221no—
263#121—221no—
264#121—221no—
265#121—221no—
266C2×C4⋊C4—111no—
267C2×C4⋊C4—111no—
268C2×C4⋊C4—221no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—221no—
271C2×C22⋊C4—221no—
272C2×C42—21no—
273#106—221no—
274#106—221no—
275C4⋊C8—42no—
276#103—221no—
277#103—221no—
278#102—221no—
279#102—221no—
280#101—442no—
281#100—442no—
282C22⋊C8—21no—
283C22⋊C8—21no—
284C22⋊C8—221no—
285C22⋊C8—221no—
286C22⋊C8—221no—
287C22⋊C8—221no—
288#95D4411yescharacteristic
289#95D4411yescharacteristic
290C2×C11—21no—
291C2×C11—21no—
292C2×C11—41no—
293C2×C11—41no—
294C2×C11#204411yescharacteristic
295C2×C11#204611yescharacteristic
296C2×C11#205011yescharacteristic
297D11—161no—
298C24—221no—
299C24#433911yescharacteristic
300C2×Q8—221no—
301C2×Q8—221no—
302C2×Q8—441no—
303C2×Q8—441no—
304C2×D4—221no—
305C2×D4—221no—
306C2×D4—441no—
307C2×D4—441no—
308C2×D4—441no—
309C2×D4—441no—
310C2×D4—881no—
311C2×D4—881no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—221no—
317C22×C4—221no—
318C22×C4—221no—
319C22×C4C2×D4411yescharacteristic
320C22×C4D4×D1111yescharacteristic
321C22×C4D4×D1111yescharacteristic
322C22×C4#434311yescharacteristic
323C22×C4#434311yescharacteristic
324C22×C4C2×C22⋊D1111yescharacteristic
325SD16—881no—
326SD16—881no—
327M16—22no—
328M16—22no—
329M16—41no—
330M16—41no—
331M16—441no—
332M16—441no—
333M16—441no—
334M16—441no—
335C2×C8—22no—
336C2×C8—21no—
337C2×C8—21no—
338C2×C8—41no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8—41no—
342C2×C8—441no—
343C2×C8—441no—
344C4⋊C4—221no—
345C4⋊C4—221no—
346C4⋊C4—221no—
347C4⋊C4—221no—
348C4⋊C4—441no—
349C4⋊C4—441no—
350C22⋊C4—42no—
351C22⋊C4—441no—
352C22⋊C4—441no—
353C22⋊C4—441no—
354C22⋊C4—441no—
355C42—41no—
356C42—41no—
357C11#1055811yescharacteristic, complemented, Sylow
358C23—21no—
359C23—21no—
360C23—41no—
361C23—41no—
362C23—442no—
363C23—441no—
364C23—881no—
365C23—881no—
366C23#6694711yescharacteristic
367C23#6694711yescharacteristic
368C23#6698311yescharacteristic
369Q8—441no—
370Q8—441no—
371Q8—881no—
372D4—441no—
373D4—441no—
374D4—881no—
375D4—882no—
376D4—881no—
377D4—881no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—22no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—442no—
394C2×C4—441no—
395C2×C4—441no—
396C2×C4—441no—
397C2×C4—881no—
398C2×C4—881no—
399C2×C4#6694811yescharacteristic
400C2×C4#6694811yescharacteristic
401C2×C4#6699011yescharacteristic
402C2×C4#6700011yescharacteristic
403C8—42no—
404C8—41no—
405C8—41no—
406C8—881no—
407C8—881no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—81no—
417C22—81no—
418C22—881no—
419C22—881no—
420C22—881no—
421C22—1762no—
422C22#1062260411yescharacteristic
423C22#1062275411yescharacteristic
424C22#1062275411yescharacteristic
425C4—21no—
426C4—21no—
427C4—21no—
428C4—42no—
429C4—81no—
430C4—881no—
431C4—881no—
432C4—881no—
433C4#1062264511yescharacteristic
434C4#1062266611yescharacteristic
435C2—21no—
436C2—21no—
437C2—41no—
438C2—41no—
439C2—1761no—
440C2#1306986711yescharacteristic
441C2#1306987911yescharacteristic
442C2#1306990311yescharacteristic
subgroupG/H
centerC22#10622604
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1851C2
socleC22×C11#394
prime radicalC2×#66983C22
hypercenter#1851D11
hypocenterC11#10558
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1851

Complements

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

NH ≅ G/Ntype
2. #13069084C2semidirect
4. #13067135C2semidirect
6. #13066493C2semidirect
7. C11×#1851C2semidirect
140. #1851D11semidirect
357. C11#10558semidirect

Maximal subgroups

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

subgroupindex
#130793742
#130690842
#130690792
#130671352
#130671312
#130664932
C11×#18512
#1055811