Finite Group Databasebeta

← #14654421

Subgroups — #14654421

Order 2816.

602 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 602 conjugacy classes of subgroups — too many to draw. Only its 81 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#13078556C211yesmaximal, characteristic, complemented
2#13076638C211yesmaximal, characteristic
3#13068693C211yesmaximal, characteristic, complemented
4#13067146C211yesmaximal, characteristic, complemented
5#13067145C211yesmaximal, characteristic, complemented
6#13066525C211yesmaximal, characteristic, complemented
7C11×#3094C211yesmaximal, characteristic, complemented
8C2×C11×#121C2211yescharacteristic
9C2×C11×#117C2211yescharacteristic
10C2×#66983C2211yescharacteristic
11C11×#482—22no—
12C11×#481—21no—
13C11×#480—21no—
14C11×#428—21no—
15C11×#418—21no—
16C11×#407C2211yescharacteristic
17#10622836—21no—
18#10622836—22no—
19#10622824C2211yescharacteristic
20#10622824C2211yescharacteristic
21#10622820C2211yescharacteristic
22#10622616—22no—
23#10622614—21no—
24#10622608—21no—
25#10622606—21no—
26#10622581—21no—
27#10622580—21no—
28#10622573—21no—
29#10622566—21no—
30#10622175—22no—
31#10622164—22no—
32#10622108—22no—
33C22×D4×C11—21no—
34C22×D4×C11D411yescharacteristic
35C23×C4×C11C2311yescharacteristic
36C22×C22⋊D11—21no—
37C22×C22⋊D11—22no—
38C22×D44D411yescharacteristic
39C2×C11×M16—21no—
40C11×#121—21no—
41C11×#121—21no—
42C11×#121—21no—
43C11×#121—21no—
44C11×#117—21no—
45C11×#117—21no—
46C11×#117—21no—
47C11×#117—21no—
48C2×C11×C4⋊C4D411yescharacteristic
49C2×C11×C4⋊C4D411yescharacteristic, complemented
50C2×C11×C4⋊C4D411yescharacteristic, complemented
51C2×C11×C22⋊C4—21no—
52C2×C11×C22⋊C4—21no—
53C2×C42×C11—21no—
54C2×C22⋊Dic11—21no—
55C2×C22⋊Dic11—22no—
56C2×C22⋊Dic11D412yes—
57#66983—21no—
58#66983—21no—
59#66983—21no—
60#66983—21no—
61C2×(C2×D11)⋊C4—21no—
62C2×(C2×D11)⋊C4—22no—
63C2×C4⋊Dic11D411yescharacteristic
64C2×#4318—21no—
65C11×#107—22no—
66C11×#106—22no—
67C11×#102—22no—
68C11×#102—22no—
69C11×C22⋊C8—21no—
70C11×C22⋊C8D412yescomplemented
71C11⋊#95—22no—
72C11⋊#95—21no—
73C11⋊#95—21no—
74C11⋊#95—21no—
75C11⋊#95—21no—
76C22⋊(C11⋊C8)—21no—
77C22⋊(C11⋊C8)D412yescomplemented
78#66873—22no—
79#66873—22no—
80#66872—22no—
81#66871—22no—
82#9983—111nomaximal, Sylow
83C24×C11—21no—
84C24×C11C2×D411yescharacteristic
85C23×D11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—42no—
89C2×D4×C11—41no—
90C2×D4×C11—41no—
91C2×D4×C11—82no—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—42no—
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11#4111yescharacteristic
102C2×C22⋊D11—41no—
103C2×C22⋊D11—41no—
104C2×C22⋊D11—82no—
105C2×C22⋊D11—82no—
106C2×C22⋊D11—82no—
107C2×C22⋊D11—82no—
108C22×Dic11—22no—
109C22×Dic11—21no—
110C22×Dic11—41no—
111C2×D44—21no—
112C2×D44—21no—
113C2×D44—42no—
114C11×M16—42no—
115C2×C8×C11—22no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—21no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—21no—
122C11×C22⋊C4—41no—
123C11×C22⋊C4—41no—
124C11×C22⋊C4—41no—
125C11×C22⋊C4—41no—
126C42×C11—41no—
127C42×C11—41no—
128C22⋊Dic11—42no—
129C22⋊Dic11—42no—
130C22⋊Dic11—82no—
131(C2×D11)⋊C4—41no—
132(C2×D11)⋊C4—41no—
133(C2×D11)⋊C4—82no—
134C4⋊Dic11—21no—
135C4⋊Dic11—21no—
136#4318—42no—
137C2×C11⋊C8—22no—
138#3094—111no—
139#3094D1111yescharacteristic, complemented
140#2815—111no—
141#1820—111no—
142#1510—111no—
143#1510—111no—
144#1306—111no—
145C23×C11—22no—
146C23×C11—41no—
147C23×C11—41no—
148C23×C11—41no—
149C23×C11—41no—
150C23×C11—42no—
151C23×C11—41no—
152C23×C11—42no—
153C23×C11#12011yescharacteristic
154C23×C11#12111yescharacteristic
155C23×C11#12711yescharacteristic
156C22×D11—41no—
157C22×D11—42no—
158C22×D11—41no—
159C22×D11—41no—
160C22×D11—42no—
161D4×C11—42no—
162D4×C11—81no—
163D4×C11—82no—
164D4×C11—82no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—42no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—81no—
176C2×C4×C11—81no—
177C2×C4×C11#12011yescharacteristic
178C2×C4×C11#12011yescharacteristic
179C2×C4×C11#12111yescharacteristic
180C2×C4×C11#12111yescharacteristic
181C22⋊D11—82no—
182C22⋊D11—82no—
183C22⋊D11—88no—
184C2×Dic11—42no—
185C2×Dic11—42no—
186C2×Dic11—42no—
187C2×Dic11—41no—
188C2×Dic11—42no—
189C2×Dic11—81no—
190C2×Dic11—81no—
191C2×Dic11—81no—
192D44—42no—
193D44—81no—
194C8×C11—42no—
195C11⋊C8—42no—
196C2×#121—111no—
197C2×#121C2×D1111yescharacteristic
198C2×#117C2×D1111yescharacteristic
199#482—22no—
200#482—222no—
201#481—21no—
202#481—221no—
203#480—21no—
204#480—221no—
205#428—21no—
206#428—221no—
207#418—21no—
208#418—221no—
209#407—111no—
210#407C2×D1111yescharacteristic
211#397—221no—
212#397—221no—
213#392—221no—
214#392—222no—
215#392—221no—
216#381—111no—
217#381—111no—
218#342—222no—
219#327—222no—
220#327—222no—
221C22×C11—21no—
222C22×C11—21no—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11—21no—
226C22×C11—21no—
227C22×C11—21no—
228C22×C11—21no—
229C22×C11—82no—
230C22×C11—82no—
231C22×C11—82no—
232C22×C11—81no—
233C22×C11—81no—
234C22×C11—81no—
235C22×C11#39211yescharacteristic
236C22×C11#45812yes—
237C2×D11—82no—
238C2×D11—82no—
239C2×D11—81no—
240C2×D11—81no—
241C2×D11—81no—
242C4×C11—21no—
243C4×C11—21no—
244C4×C11—21no—
245C4×C11—21no—
246C4×C11—81no—
247C4×C11—81no—
248C4×C11—81no—
249Dic11—82no—
250Dic11—81no—
251Dic11—161no—
252C22×D4—21no—
253C22×D4—111no—
254C22×D4—221no—
255C22×D4—222no—
256C22×D4C22⋊D1111yescharacteristic
257C23×C4C22×D1111yescharacteristic
258C2×M16—21no—
259C2×M16—221no—
260#121—21no—
261#121—21no—
262#121—21no—
263#121—21no—
264#121—221no—
265#121—221no—
266#121—221no—
267#121—221no—
268#117—21no—
269#117—21no—
270#117—21no—
271#117—21no—
272C2×C4⋊C4—111no—
273C2×C4⋊C4C22⋊D1111yescharacteristic
274C2×C4⋊C4C22⋊D1111yescharacteristic, complemented
275C2×C4⋊C4C22⋊D1111yescharacteristic, complemented
276C2×C22⋊C4—21no—
277C2×C22⋊C4—21no—
278C2×C22⋊C4—112no—
279C2×C22⋊C4—221no—
280C2×C22⋊C4—221no—
281C2×C22⋊C4—222no—
282C2×C22⋊C4—222no—
283C2×C42—21no—
284#107—22no—
285#107—222no—
286#106—22no—
287#106—222no—
288#102—22no—
289#102—22no—
290#102—222no—
291#102—222no—
292C22⋊C8—21no—
293C22⋊C8—112no—
294C22⋊C8—221no—
295C22⋊C8C22⋊D1112yescomplemented
296#95—222no—
297#95—221no—
298#95—221no—
299#95—221no—
300#95—221no—
301C2×C11—22no—
302C2×C11—41no—
303C2×C11—41no—
304C2×C11—161no—
305C2×C11#200811yescharacteristic
306C2×C11#200811yescharacteristic
307C2×C11#202211yescharacteristic
308D11—161no—
309C24—21no—
310C24—221no—
311C24D4×D1111yescharacteristic
312C2×D4—21no—
313C2×D4—21no—
314C2×D4—42no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—82no—
318C2×D4—221no—
319C2×D4—221no—
320C2×D4—442no—
321C2×D4—441no—
322C2×D4—441no—
323C2×D4—882no—
324C2×D4—882no—
325C2×D4—882no—
326C2×D4—882no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—42no—
331C22×C4—222no—
332C22×C4—221no—
333C22×C4—441no—
334C22×C4D4×D1111yescharacteristic
335C22×C4D4×D1111yescharacteristic
336C22×C4#434111yescharacteristic
337C22×C4C2×C22⋊D1111yescharacteristic
338C22×C4C2×C22⋊D1111yescharacteristic
339C22×C4C2×C22⋊D1111yescharacteristic
340M16—42no—
341M16—442no—
342C2×C8—22no—
343C2×C8—222no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—21no—
350C4⋊C4—221no—
351C4⋊C4—221no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C22⋊C4—441no—
357C22⋊C4—441no—
358C22⋊C4—442no—
359C22⋊C4—442no—
360C22⋊C4—882no—
361C22⋊C4—882no—
362C42—41no—
363C42—41no—
364C11#998311yescharacteristic, complemented, Sylow
365C23—22no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23—42no—
370C23—41no—
371C23—41no—
372C23—42no—
373C23—441no—
374C23—442no—
375C23—441no—
376C23—441no—
377C23—442no—
378C23#6699011yescharacteristic
379C23#6699211yescharacteristic
380C23#6699311yescharacteristic
381D4—42no—
382D4—81no—
383D4—82no—
384D4—82no—
385D4—442no—
386D4—881no—
387D4—882no—
388D4—882no—
389D4—888no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—42no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—81no—
401C2×C4—81no—
402C2×C4—442no—
403C2×C4—442no—
404C2×C4—442no—
405C2×C4—441no—
406C2×C4—442no—
407C2×C4—881no—
408C2×C4—881no—
409C2×C4—881no—
410C2×C4#6699011yescharacteristic
411C2×C4#6699111yescharacteristic
412C2×C4#6699211yescharacteristic
413C2×C4#6700611yescharacteristic
414C8—42no—
415C8—442no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—82no—
425C22—82no—
426C22—82no—
427C22—81no—
428C22—81no—
429C22—81no—
430C22—882no—
431C22—882no—
432C22—881no—
433C22—881no—
434C22—881no—
435C22#1062266612yes—
436C22#1062283611yescharacteristic
437C4—21no—
438C4—21no—
439C4—21no—
440C4—21no—
441C4—81no—
442C4—81no—
443C4—81no—
444C4—882no—
445C4—881no—
446C4—1761no—
447C2—22no—
448C2—41no—
449C2—41no—
450C2—161no—
451C2—1761no—
452C2#1306966611yescharacteristic
453C2#1306966711yescharacteristic
454C2#1306974411yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#3094C2
socleC22×C11#392
prime radical#13076638C2
hypercenter#3094D11
hypocenterC11#9983
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3094

Complements

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

NH ≅ G/Ntype
1. #13078556C2semidirect
3. #13068693C2semidirect
4. #13067146C2semidirect
5. #13067145C2semidirect
6. #13066525C2semidirect
7. C11×#3094C2semidirect
49. C2×C11×C4⋊C4D4semidirect
50. C2×C11×C4⋊C4D4semidirect
70. C11×C22⋊C8D4semidirect
77. C22⋊(C11⋊C8)D4semidirect
139. #3094D11semidirect
274. C2×C4⋊C4C22⋊D11semidirect
275. C2×C4⋊C4C22⋊D11semidirect
295. C22⋊C8C22⋊D11semidirect
364. C11#9983semidirect

Maximal subgroups

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

subgroupindex
#130785562
#130766382
#130686932
#130671462
#130671452
#130665252
C11×#30942
#998311