Finite Group Databasebeta

← #14658201

Subgroups — #14658201

Order 2816.

560 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074589C211yesmaximal, characteristic
2#13068804C211yesmaximal, characteristic
3#13066879C211yesmaximal, characteristic
4#13066496C211yesmaximal, characteristic
5#13066494C211yesmaximal, characteristic
6#13066458C211yesmaximal, characteristic
7C11×#1853C211yesmaximal, characteristic
8C22×C11×C4⋊C4C2211yescharacteristic
9C22×Dic11⋊C4—21no—
10C2×C11×#106—21no—
11C2×C11×C22⋊C8C2211yescharacteristic
12C11×#380C2211yescharacteristic
13#10622825C2211yescharacteristic
14C2×C11⋊#95—21no—
15C2×C11⋊#95C2211yescharacteristic
16C2×C11⋊#95C2211yescharacteristic
17C2×C22⋊(C11⋊C8)C2211yescharacteristic
18#10622599—21no—
19#10622597—21no—
20C2×#66871—21no—
21#10622563—21no—
22#10622559—21no—
23#10622274—21no—
24#10622273—21no—
25C11×#340—21no—
26#10622167—21no—
27C23×C4×C11—21no—
28C23×C4×C11C2311yescharacteristic
29C23×Dic11—21no—
30C23×Dic11D411yescharacteristic
31C23×Dic11D411yescharacteristic
32C22×C8×C11—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—42no—
36C2×C11×C4⋊C4D411yescharacteristic
37C2×C11×C4⋊C4D411yescharacteristic
38C2×C11×C22⋊C4—21no—
39C2×C22⋊Dic11—21no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11D411yescharacteristic
43C2×C4⋊Dic11D411yescharacteristic
44C2×Dic11⋊C4—21no—
45C2×Dic11⋊C4—21no—
46C2×Dic11⋊C4—42no—
47C2×Dic11⋊C4—42no—
48C2×Dic11⋊C4—42no—
49C22×C11⋊C8—21no—
50C11×#106—42no—
51C11×C22⋊C8—21no—
52C11×C22⋊C8Q812yes—
53C11×#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95—21no—
62C11⋊#95—42no—
63C11⋊#95Q812yes—
64C22⋊(C11⋊C8)—21no—
65C22⋊(C11⋊C8)Q812yes—
66#66871—42no—
67#10572—111nomaximal, Sylow
68C24×C11C2×D411yescharacteristic
69C22×C4×C11—22no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—41no—
73C22×C4×C11—41no—
74C22×C4×C11—41no—
75C22×C4×C11—41no—
76C22×C4×C11—41no—
77C22×C4×C11—41no—
78C22×C4×C11—41no—
79C22×C4×C11—41no—
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×Q811yescharacteristic
83C22×C4×C11C2×Q811yescharacteristic
84C22×C4×C11C2×Q811yescharacteristic
85C22×C4×C11#4111yescharacteristic
86C22×Dic11—22no—
87C22×Dic11—22no—
88C22×Dic11—21no—
89C22×Dic11—21no—
90C22×Dic11—21no—
91C22×Dic11—21no—
92C22×Dic11—22no—
93C22×Dic11—21no—
94C22×Dic11—21no—
95C22×Dic11—21no—
96C22×Dic11—21no—
97C22×Dic11—41no—
98C22×Dic11—41no—
99C22×Dic11—41no—
100C22×Dic11—41no—
101C22×Dic11—41no—
102C22×Dic11—41no—
103C22×Dic11—41no—
104C22×Dic11—41no—
105C2×C8×C11—22no—
106C2×C8×C11—41no—
107C2×C8×C11—41no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—41no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C11×C22⋊C4—41no—
115C11×C22⋊C4—41no—
116C22⋊Dic11—41no—
117C22⋊Dic11—41no—
118C4⋊Dic11—41no—
119C4⋊Dic11—41no—
120C4⋊Dic11—81no—
121C4⋊Dic11—81no—
122Dic11⋊C4—48no—
123Dic11⋊C4—81no—
124Dic11⋊C4—81no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—41no—
127C2×C11⋊C8—41no—
128#2646—111no—
129#1853D1111yescharacteristic
130#1852—111no—
131#1444—111no—
132#1294—111no—
133#1294—111no—
134#1280—111no—
135C23×C11—21no—
136C23×C11—21no—
137C23×C11—21no—
138C23×C11—21no—
139C23×C11#12011yescharacteristic
140C23×C11C22⋊Q811yescharacteristic
141C23×C11C4⋊Q811yescharacteristic
142C23×C11#13511yescharacteristic
143C23×C11#13511yescharacteristic
144C23×C11AGL(1,ℤ/8)11yescharacteristic
145C23×C11#13711yescharacteristic
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—42no—
155C2×C4×C11—42no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—42no—
162C2×C4×C11—41no—
163C2×C4×C11—81no—
164C2×C4×C11—81no—
165C2×C4×C11—81no—
166C2×C4×C11—81no—
167C2×C4×C11C22⋊Q811yescharacteristic
168C2×C4×C11C22⋊Q811yescharacteristic
169C2×C4×C11C4⋊Q811yescharacteristic
170C2×C4×C11C4⋊Q811yescharacteristic
171C2×Dic11—24no—
172C2×Dic11—42no—
173C2×Dic11—42no—
174C2×Dic11—42no—
175C2×Dic11—42no—
176C2×Dic11—42no—
177C2×Dic11—42no—
178C2×Dic11—42no—
179C2×Dic11—42no—
180C2×Dic11—41no—
181C2×Dic11—41no—
182C2×Dic11—41no—
183C2×Dic11—41no—
184C2×Dic11—41no—
185C2×Dic11—41no—
186C2×Dic11—41no—
187C2×Dic11—41no—
188C2×Dic11—41no—
189C2×Dic11—41no—
190C2×Dic11—41no—
191C2×Dic11—41no—
192C2×Dic11—81no—
193C2×Dic11—81no—
194C8×C11—42no—
195C11⋊C8—42no—
196C22×C4⋊C4—221no—
197C22×C4⋊C4C2×D1111yescharacteristic
198C2×#107—221no—
199C2×#106—21no—
200C2×C22⋊C8—111no—
201C2×C22⋊C8C2×D1111yescharacteristic
202#400—221no—
203#400—221no—
204#398—221no—
205#398—221no—
206#385—221no—
207#385—221no—
208#380—111no—
209#380C2×D1111yescharacteristic
210C2×#95—111no—
211C2×#95—111no—
212C2×#95—221no—
213#340—21no—
214#340—221no—
215C22×C11—21no—
216C22×C11—21no—
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—21no—
226C22×C11—21no—
227C22×C11#39511yescharacteristic
228C22×C11#44911yescharacteristic
229C22×C11#45211yescharacteristic
230C22×C11#45311yescharacteristic
231C22×C11#45611yescharacteristic
232C22×C11B(4,𝔽2)11yescharacteristic
233C22×C11#45811yescharacteristic
234C22×C11#47811yescharacteristic
235C22×C11#47911yescharacteristic
236C22×C11#49911yescharacteristic
237C22×C11#50111yescharacteristic
238C4×C11—21no—
239C4×C11—21no—
240C4×C11—21no—
241C4×C11—21no—
242C4×C11—82no—
243C4×C11—81no—
244C4×C11—81no—
245Dic11—44no—
246Dic11—81no—
247Dic11—81no—
248Dic11—81no—
249Dic11—81no—
250C23×C4—21no—
251C23×C4—111no—
252C23×C4—111no—
253C23×C4—221no—
254C23×C4C22×D1111yescharacteristic
255C22×C8—21no—
256C22×C8—221no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—42no—
260C2×C4⋊C4—111no—
261C2×C4⋊C4—111no—
262C2×C4⋊C4—221no—
263C2×C4⋊C4—221no—
264C2×C4⋊C4—221no—
265C2×C4⋊C4—221no—
266C2×C4⋊C4—442no—
267C2×C4⋊C4—442no—
268C2×C4⋊C4—442no—
269C2×C4⋊C4C22⋊D1111yescharacteristic
270C2×C4⋊C4C22⋊D1111yescharacteristic
271C2×C22⋊C4—21no—
272C2×C22⋊C4—221no—
273#107—442no—
274#106—42no—
275C22⋊C8—21no—
276C22⋊C8—112no—
277C22⋊C8—221no—
278C22⋊C8Dic2212yes—
279#95—21no—
280#95—112no—
281#95—221no—
282#95—221no—
283#95—221no—
284#95—221no—
285#95—221no—
286#95—221no—
287#95—221no—
288#95—221no—
289#95—442no—
290C2×C11—21no—
291C2×C11—21no—
292C2×C11—21no—
293C2×C11—21no—
294C2×C11#160011yescharacteristic
295C2×C11#160311yescharacteristic
296C2×C11#160911yescharacteristic
297C2×C11#161811yescharacteristic
298C2×C11#205911yescharacteristic
299C2×C11#206011yescharacteristic
300C2×C11#206211yescharacteristic
301C24D4×D1111yescharacteristic
302C22×C4—22no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—222no—
314C22×C4—222no—
315C22×C4—222no—
316C22×C4—221no—
317C22×C4—221no—
318C22×C4—221no—
319C22×C4—221no—
320C22×C4—221no—
321C22×C4—221no—
322C22×C4—221no—
323C22×C4—221no—
324C22×C4—441no—
325C22×C4—441no—
326C22×C4—441no—
327C22×C4—441no—
328C22×C4—441no—
329C22×C4—441no—
330C22×C4—441no—
331C22×C4—441no—
332C22×C4C2×Dic2211yescharacteristic
333C22×C4#433911yescharacteristic
334C22×C4D4×D1111yescharacteristic
335C22×C4Q8×D1111yescharacteristic
336C22×C4Q8×D1111yescharacteristic
337C22×C4C2×C22⋊D1111yescharacteristic
338C2×C8—22no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8—222no—
342C2×C8—441no—
343C2×C8—441no—
344C4⋊C4—22no—
345C4⋊C4—22no—
346C4⋊C4—41no—
347C4⋊C4—41no—
348C4⋊C4—41no—
349C4⋊C4—41no—
350C4⋊C4—441no—
351C4⋊C4—441no—
352C4⋊C4—448no—
353C4⋊C4—881no—
354C4⋊C4—881no—
355C4⋊C4—881no—
356C4⋊C4—881no—
357C22⋊C4—41no—
358C22⋊C4—41no—
359C22⋊C4—441no—
360C22⋊C4—441no—
361C11#1057211yescharacteristic, complemented, Sylow
362C23—21no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23#6694111yescharacteristic
367C23#6694911yescharacteristic
368C23#6696711yescharacteristic
369C23#6696811yescharacteristic
370C23#6696911yescharacteristic
371C23#6696911yescharacteristic
372C23#6699011yescharacteristic
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—81no—
394C2×C4—224no—
395C2×C4—442no—
396C2×C4—442no—
397C2×C4—442no—
398C2×C4—442no—
399C2×C4—442no—
400C2×C4—442no—
401C2×C4—442no—
402C2×C4—442no—
403C2×C4—441no—
404C2×C4—441no—
405C2×C4—441no—
406C2×C4—441no—
407C2×C4—441no—
408C2×C4—441no—
409C2×C4—441no—
410C2×C4—441no—
411C2×C4—441no—
412C2×C4—441no—
413C2×C4—441no—
414C2×C4—441no—
415C2×C4—881no—
416C2×C4—881no—
417C2×C4#6694111yescharacteristic
418C2×C4#6694911yescharacteristic
419C2×C4#6697711yescharacteristic
420C2×C4#6699711yescharacteristic
421C8—42no—
422C8—442no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22#1062246911yescharacteristic
436C22#1062247011yescharacteristic
437C22#1062247111yescharacteristic
438C22#1062248411yescharacteristic
439C22#1062259211yescharacteristic
440C22#1062264511yescharacteristic
441C22#1062266611yescharacteristic
442C22#1062278511yescharacteristic
443C22#1062278611yescharacteristic
444C22#1062281111yescharacteristic
445C22#1062281811yescharacteristic
446C4—21no—
447C4—21no—
448C4—21no—
449C4—21no—
450C4—82no—
451C4—81no—
452C4—81no—
453C4—444no—
454C4—881no—
455C4—881no—
456C4—881no—
457C4—881no—
458C2—21no—
459C2—21no—
460C2—21no—
461C2—21no—
462C2#1306756111yescharacteristic
463C2#1306757611yescharacteristic
464C2#1306761211yescharacteristic
465C2#1306766111yescharacteristic
466C2#1306995611yescharacteristic
467C2#1306995911yescharacteristic
468C2#1306996911yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1853C2
socleC23×C11#120
prime radicalC24×C11C2×D4
hypercenter#1853D11
hypocenterC11#10572
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1853

Complements

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

NH ≅ G/Ntype
361. C11#10572semidirect

Maximal subgroups

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

subgroupindex
#130745892
#130688042
#130668792
#130664962
#130664942
#130664582
C11×#18532
#1057211