Finite Group Databasebeta

← #14648989

Subgroups — #14648989

Order 2816.

488 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077755C211yesmaximal, characteristic, complemented
2#13069415C211yesmaximal, characteristic, complemented
3#13067204C211yesmaximal, characteristic, complemented
4#13067059C211yesmaximal, characteristic, complemented
5#13066516C211yesmaximal, characteristic, complemented
6#13066465C211yesmaximal, characteristic, complemented
7C11×#3105C211yesmaximal, characteristic
8C11×#529C2211yescharacteristic
9C2×C4×D4×C11C2211yescharacteristic
10C11×#484C411yescharacteristic
11C11×#481C411yescharacteristic
12C11×#478—21no—
13C11×#463—21no—
14C11×#450C411yescharacteristic
15C11×#447C411yescharacteristic
16C4×C11×SD16—21no—
17C4×C11×D8—21no—
18C11×#431C2211yescharacteristic
19C2×C22⋊(C11⋊C8)—21no—
20C2×C22⋊(C11⋊C8)—21no—
21#10622637—21no—
22#10622624—21no—
23#10622624—21no—
24D4×C11⋊C8—21no—
25#10622613—21no—
26#10622612—21no—
27#10622539C2211yescharacteristic
28C2×C4⋊(C11⋊C8)C2211yescharacteristic
29C4×#4318C2211yescharacteristic
30C2×#66867C2211yescharacteristic
31#10622181—21no—
32#10622178—21no—
33D4⋊(C11⋊C8)—21no—
34D4⋊(C11⋊C8)—21no—
35C22×D4×C11C2×C411yescharacteristic
36C23×C4×C11—21no—
37C2×C11×SD16—21no—
38C2×C11×D8—21no—
39C11×#126—21no—
40C11×#125D411yescharacteristic
41C11×#124D411yescharacteristic
42C11×#123—21no—
43C11×C22⋊Q8C2×C411yescharacteristic
44C11×#121C2×C411yescharacteristic
45C4×Q8×C11D411yescharacteristic
46C4×D4×C11—21no—
47C4×D4×C11—21no—
48C4×D4×C11—21no—
49C4×D4×C11—21no—
50C4×D4×C11—21no—
51C4×D4×C11D411yescharacteristic
52C11×#117—21no—
53C2×C11×C4⋊C4C2×C411yescharacteristic
54C2×C11×C22⋊C4—21no—
55C2×C42×C11C2311yescharacteristic
56C2×#4318—21no—
57C2×#4318—21no—
58C22×C11⋊C8—21no—
59C22×C11⋊C8—21no—
60C22×C11⋊C8D411yescharacteristic
61C22×C11⋊C8D411yescharacteristic
62C11×#107—21no—
63C11×#106—21no—
64C11×C4⋊C8—21no—
65C11×#103—21no—
66C11×#102—21no—
67C11×#102—21no—
68C11×#102—21no—
69C11×C22⋊C8C2×C411yescharacteristic
70C11×C22⋊C8C2×C411yescharacteristic
71C4×C8×C11—21no—
72C22⋊(C11⋊C8)—21no—
73C22⋊(C11⋊C8)—21no—
74C22⋊(C11⋊C8)—21no—
75C22⋊(C11⋊C8)—42no—
76C22⋊(C11⋊C8)—42no—
77C4⋊(C11⋊C8)—21no—
78C4⋊(C11⋊C8)—21no—
79C4⋊(C11⋊C8)—21no—
80C4⋊(C11⋊C8)—21no—
81C4⋊(C11⋊C8)D411yescharacteristic
82C4⋊(C11⋊C8)D411yescharacteristic
83#66867—21no—
84#66867—21no—
85#66867—21no—
86#66867—21no—
87#66867—21no—
88C4×C11⋊C8—21no—
89C4×C11⋊C8—21no—
90#9052—111nomaximal, Sylow
91C24×C11—21no—
92C2×Q8×C11C22⋊C411yescharacteristic
93C2×D4×C11—21no—
94C2×D4×C11—21no—
95C2×D4×C11—21no—
96C2×D4×C11—42no—
97C2×D4×C11C22⋊C411yescharacteristic
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—41no—
101C22×C4×C11—41no—
102C22×C4×C11—41no—
103C22×C4×C11—41no—
104C22×C4×C11—41no—
105C22×C4×C11—41no—
106C22×C4×C11C22×C411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11#4111yescharacteristic
109C11×SD16—42no—
110C11×D8—42no—
111C2×C8×C11—21no—
112C2×C8×C11—21no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—21no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4C22⋊C411yescharacteristic
120C11×C4⋊C4C22⋊C411yescharacteristic
121C11×C22⋊C4—21no—
122C11×C22⋊C4—21no—
123C11×C22⋊C4—21no—
124C11×C22⋊C4—21no—
125C11×C22⋊C4—21no—
126C11×C22⋊C4—41no—
127C11×C22⋊C4—41no—
128C42×C11—21no—
129C42×C11C2×D411yescharacteristic
130C42×C11C2×D411yescharacteristic
131C42×C11C2×D411yescharacteristic
132C42×C11#4111yescharacteristic
133#4318—22no—
134#4318—41no—
135#4318—81no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—21no—
138C2×C11⋊C8—21no—
139C2×C11⋊C8—21no—
140C2×C11⋊C8—21no—
141C2×C11⋊C8—41no—
142C2×C11⋊C8—41no—
143C2×C11⋊C8—41no—
144C2×C11⋊C8—41no—
145C2×C11⋊C8—41no—
146C2×C11⋊C8—81no—
147#3105D1111yescharacteristic
148#2992—111no—
149#1955—111no—
150#1524—111no—
151#1490—111no—
152#1302—111no—
153#1283—111no—
154C23×C11—22no—
155C23×C11—21no—
156C23×C11—41no—
157C23×C11—41no—
158C23×C11—41no—
159C23×C11—41no—
160C23×C11—41no—
161C23×C11—41no—
162C23×C11C4×D411yescharacteristic
163Q8×C11—41no—
164D4×C11—22no—
165D4×C11—22no—
166D4×C11—41no—
167D4×C11—41no—
168D4×C11—41no—
169D4×C11—41no—
170D4×C11—41no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—81no—
185C2×C4×C11—81no—
186C2×C4×C11—81no—
187C2×C4×C11—81no—
188C2×C4×C11C2×C22⋊C411yescharacteristic
189C2×C4×C11C4×D411yescharacteristic
190C2×C4×C11#12011yescharacteristic
191C2×C4×C11#12111yescharacteristic
192C2×C4×C11#12111yescharacteristic
193C2×C4×C11#12311yescharacteristic
194C8×C11—41no—
195C8×C11—41no—
196C11⋊C8—42no—
197C11⋊C8—42no—
198C11⋊C8—41no—
199C11⋊C8—41no—
200C11⋊C8—41no—
201C11⋊C8—41no—
202#529C2×D1111yescharacteristic
203C2×C4×D4C2×D1111yescharacteristic
204#484Dic1111yescharacteristic
205#481Dic1111yescharacteristic
206#478—21no—
207#463—21no—
208#450Dic1111yescharacteristic
209#447Dic1111yescharacteristic
210#446—221no—
211C4×SD16—21no—
212C4×D8—21no—
213#435—221no—
214#435—221no—
215C8×D4—221no—
216#433—221no—
217#432—111no—
218#431C2×D1111yescharacteristic
219#424—221no—
220C2×C4⋊C8—111no—
221C2×C22⋊C8—221no—
222C2×C22⋊C8—221no—
223C4×M16—111no—
224C2×#97—111no—
225#330—221no—
226#329—221no—
227D4⋊C8—221no—
228D4⋊C8—221no—
229C22×C11—21no—
230C22×C11—21no—
231C22×C11—42no—
232C22×C11—42no—
233C22×C11—41no—
234C22×C11—41no—
235C22×C11—42no—
236C22×C11—41no—
237C22×C11—81no—
238C22×C11—81no—
239C22×C11—81no—
240C22×C11—81no—
241C22×C11#38611yescharacteristic
242C22×C11#44311yescharacteristic
243C22×C11#44411yescharacteristic
244C4×C11—21no—
245C4×C11—21no—
246C4×C11—21no—
247C4×C11—21no—
248C4×C11—21no—
249C4×C11—41no—
250C4×C11—41no—
251C4×C11—41no—
252C4×C11—81no—
253C4×C11#45311yescharacteristic
254C4×C11#45411yescharacteristic
255C22×D4C2×Dic1111yescharacteristic
256C23×C4—21no—
257C2×SD16—21no—
258C2×D8—21no—
259C2×M16—221no—
260C2×M16—221no—
261C22×C8—111no—
262C22×C8—111no—
263C22×C8—221no—
264C22×C8—221no—
265#126—21no—
266#125C22⋊D1111yescharacteristic
267#124C22⋊D1111yescharacteristic
268#123—21no—
269C22⋊Q8C2×Dic1111yescharacteristic
270#121C2×Dic1111yescharacteristic
271C4×Q8C22⋊D1111yescharacteristic
272C4×D4—21no—
273C4×D4—21no—
274C4×D4—21no—
275C4×D4—21no—
276C4×D4—21no—
277C4×D4C22⋊D1111yescharacteristic
278#117—21no—
279C2×C4⋊C4C2×Dic1111yescharacteristic
280C2×C22⋊C4—21no—
281C2×C42C22×D1111yescharacteristic
282#107—21no—
283#106—21no—
284C4⋊C8—21no—
285C4⋊C8—111no—
286C4⋊C8—111no—
287C4⋊C8—221no—
288C4⋊C8—221no—
289C4⋊C8—221no—
290C4⋊C8—221no—
291#103—21no—
292#102—21no—
293#102—21no—
294#102—21no—
295C22⋊C8—221no—
296C22⋊C8—221no—
297C22⋊C8—221no—
298C22⋊C8—442no—
299C22⋊C8—442no—
300C22⋊C8C2×Dic1111yescharacteristic
301C22⋊C8C2×Dic1111yescharacteristic
302#97—221no—
303#97—221no—
304#97—221no—
305#97—221no—
306#97—221no—
307C4×C8—21no—
308C4×C8—221no—
309C4×C8—221no—
310C2×C11—21no—
311C2×C11—21no—
312C2×C11—81no—
313C2×C11—82no—
314C2×C11#187611yescharacteristic
315C2×C11#188311yescharacteristic
316C2×C11#189111yescharacteristic
317C24—21no—
318C2×Q8C22⋊Dic1111yescharacteristic
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—21no—
322C2×D4—42no—
323C2×D4C22⋊Dic1111yescharacteristic
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4D4×D1111yescharacteristic
333C22×C4#434111yescharacteristic
334C22×C4C22×Dic1111yescharacteristic
335SD16—42no—
336D8—42no—
337M16—222no—
338M16—441no—
339M16—881no—
340C2×C8—21no—
341C2×C8—21no—
342C2×C8—222no—
343C2×C8—221no—
344C2×C8—221no—
345C2×C8—221no—
346C2×C8—221no—
347C2×C8—441no—
348C2×C8—441no—
349C2×C8—441no—
350C2×C8—441no—
351C2×C8—441no—
352C2×C8—881no—
353C4⋊C4—21no—
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4C22⋊Dic1111yescharacteristic
360C4⋊C4C22⋊Dic1111yescharacteristic
361C22⋊C4—21no—
362C22⋊C4—21no—
363C22⋊C4—21no—
364C22⋊C4—21no—
365C22⋊C4—21no—
366C22⋊C4—41no—
367C22⋊C4—41no—
368C42—21no—
369C42D4×D1111yescharacteristic
370C42#434111yescharacteristic
371C42C2×C22⋊D1111yescharacteristic
372C42C2×C22⋊D1111yescharacteristic
373C11#905211yescharacteristic, complemented, Sylow
374C23—22no—
375C23—21no—
376C23—41no—
377C23—41no—
378C23—41no—
379C23—41no—
380C23—41no—
381C23—41no—
382C23D4×Dic1111yescharacteristic
383Q8—41no—
384D4—22no—
385D4—22no—
386D4—41no—
387D4—41no—
388D4—41no—
389D4—41no—
390D4—41no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—81no—
405C2×C4—81no—
406C2×C4—81no—
407C2×C4—81no—
408C2×C4D4×Dic1111yescharacteristic
409C2×C4#6698811yescharacteristic
410C2×C4#6699011yescharacteristic
411C2×C4#6699211yescharacteristic
412C2×C4#6699211yescharacteristic
413C2×C4C2×C22⋊Dic1111yescharacteristic
414C8—41no—
415C8—41no—
416C8—442no—
417C8—442no—
418C8—441no—
419C8—441no—
420C8—441no—
421C8—441no—
422C22—21no—
423C22—21no—
424C22—42no—
425C22—42no—
426C22—41no—
427C22—41no—
428C22—42no—
429C22—41no—
430C22—81no—
431C22—81no—
432C22—81no—
433C22—81no—
434C22#1062280911yescharacteristic
435C22#1062281011yescharacteristic
436C22#1062283311yescharacteristic
437C4—21no—
438C4—21no—
439C4—21no—
440C4—21no—
441C4—21no—
442C4—41no—
443C4—41no—
444C4—41no—
445C4—81no—
446C4#1062281111yescharacteristic
447C4#1062281411yescharacteristic
448C2—21no—
449C2—21no—
450C2—82no—
451C2—81no—
452C2#1306894511yescharacteristic
453C2#1306899411yescharacteristic
454C2#1306903511yescharacteristic
subgroupG/H
centerC2×C4#66990
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#3105C2
socleC22×C11#386
prime radicalC11×#447C4
cosocleC2×C42×C11C23
hypercenter#3105D11
hypocenterC11#9052
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3105

Complements

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

NH ≅ G/Ntype
1. #13077755C2semidirect
2. #13069415C2semidirect
3. #13067204C2semidirect
4. #13067059C2semidirect
5. #13066516C2semidirect
6. #13066465C2semidirect
373. C11#9052semidirect

Maximal subgroups

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

subgroupindex
#130777552
#130694152
#130672042
#130670592
#130665162
#130664652
C11×#31052
#905211