Finite Group Databasebeta

← #14653167

Subgroups — #14653167

Order 2816.

478 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079042C211yesmaximal, characteristic
2#13068746C211yesmaximal, characteristic, complemented
3#13067177C211yesmaximal, characteristic, complemented
4#13067176C211yesmaximal, characteristic, complemented
5#13067175C211yesmaximal, characteristic, complemented
6#13066909C211yesmaximal, characteristic, complemented
7C11×#1517C211yesmaximal, characteristic, complemented
8C11×#532C2211yescharacteristic
9C2×#67003—21no—
10C2×#67003—21no—
11#10623008C2211yescharacteristic
12C11×#431C2211yescharacteristic
13C11×#382C2211yescharacteristic
14#10622705C411yescharacteristic, complemented
15#10622698C411yescharacteristic, complemented
16#10622689C411yescharacteristic, complemented
17#10622686C411yescharacteristic, complemented
18#10622672—21no—
19#10622672—21no—
20#10622549C2211yescharacteristic
21#10622538C2211yescharacteristic
22C2×C4×C11⋊C8C2211yescharacteristic
23C11×#327—22no—
24#10622175—22no—
25#10622167—21no—
26#10622167—21no—
27#10622108—22no—
28#10622093—21no—
29#10622092—21no—
30#10622089—22no—
31C2×C11×#41—21no—
32C2×#4339—21no—
33C11×C4⋊Q8C2×C411yescharacteristic
34C11×#127C2×C411yescharacteristic
35C11×#124—21no—
36C11×#121—21no—
37C11×#121—21no—
38C4×D4×C11—21no—
39C4×D4×C11—21no—
40C2×C11×C4⋊C4—21no—
41C2×C42×C11C2311yescharacteristic
42#67003—42no—
43#67003—42no—
44#67003—42no—
45#67003—42no—
46C2×#4326—21no—
47C2×#4326—21no—
48C2×#4325—21no—
49C2×#4325—21no—
50C2×#4324—21no—
51C2×#4324—21no—
52C2×#4323—21no—
53C2×#4323—21no—
54#66983—21no—
55#66983—21no—
56C2×C4⋊Dic11—21no—
57C22×C11⋊C8D411yescharacteristic
58C22×C11⋊C8D411yescharacteristic
59#66928—21no—
60#66927C2×C411yescharacteristic
61C4×D44—21no—
62C4×D44—21no—
63#66922C2×C411yescharacteristic
64C11×C4⋊C8—21no—
65C11×C22⋊C8D412yes—
66C4×C8×C11—21no—
67C11×#95—21no—
68C11×#95—21no—
69C11⋊#95—21no—
70C11⋊#95—21no—
71C22⋊(C11⋊C8)D412yes—
72C4⋊(C11⋊C8)—21no—
73C4×C11⋊C8—21no—
74C4×C11⋊C8C2×C411yescharacteristic
75C4×C11⋊C8C2×C411yescharacteristic
76C4×C11⋊C8D411yescharacteristic
77C4×C11⋊C8D411yescharacteristic
78#9760—111nomaximal, Sylow
79C11×#41—41no—
80C11×#41—41no—
81C11×#41—41no—
82C11×#41—41no—
83C2×Q8×C11—21no—
84C2×D4×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—41no—
88C22×C4×C11—41no—
89C22×C4×C11—41no—
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C2×C22⋊D11—41no—
94C22×Dic11—41no—
95#4339—41no—
96#4339—41no—
97#4339—41no—
98#4339—41no—
99C2×D44—21no—
100C2×D44—21no—
101C2×D44—21no—
102C2×C4×D11—41no—
103C2×Dic22—21no—
104C2×C8×C11—22no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C22⋊C4—41no—
110C11×C22⋊C4—41no—
111C42×C11C22×C411yescharacteristic
112C42×C11C2×D411yescharacteristic
113C42×C11#4111yescharacteristic
114C42×C11#4111yescharacteristic
115#4326—42no—
116#4326—42no—
117#4325—42no—
118#4325—42no—
119#4324—42no—
120#4324—42no—
121#4323—42no—
122#4323—42no—
123(C2×D11)⋊C4—41no—
124(C2×D11)⋊C4—41no—
125C4⋊Dic11—21no—
126C4⋊Dic11—21no—
127C4⋊Dic11—41no—
128C4⋊Dic11—41no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—21no—
131C2×C11⋊C8—21no—
132C2×C11⋊C8—21no—
133C2×C11⋊C8—21no—
134C2×C11⋊C8C22⋊C411yescharacteristic
135C2×C11⋊C8C22⋊C411yescharacteristic
136C2×C11⋊C8C22⋊C411yescharacteristic
137C2×C11⋊C8C22⋊C411yescharacteristic
138#3147—111no—
139#1835—111no—
140#1517—111no—
141#1517—111no—
142#1517—111no—
143#1517D1111yescharacteristic, complemented
144#1452—111no—
145C23×C11—41no—
146C23×C11#12711yescharacteristic
147C22×D11—41no—
148Q8×C11—41no—
149Q8×C11—41no—
150D4×C11—41no—
151D4×C11—41no—
152D4×C11—81no—
153D4×C11—81no—
154D4×C11—81no—
155D4×C11—81no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—81no—
160C2×C4×C11—81no—
161C2×C4×C11—81no—
162C2×C4×C11—81no—
163C2×C4×C11—81no—
164C2×C4×C11C2×C22⋊C411yescharacteristic
165C2×C4×C11C4×D411yescharacteristic
166C2×C4×C11C4×D411yescharacteristic
167C2×C4×C11#12111yescharacteristic
168C2×C4×C11#12111yescharacteristic
169C2×C4×C11#12411yescharacteristic
170C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
174C22⋊D11—81no—
175C22⋊D11—81no—
176C2×Dic11—41no—
177C2×Dic11—81no—
178C2×Dic11—81no—
179C2×Dic11—81no—
180D44—41no—
181D44—41no—
182D44—81no—
183D44—81no—
184C4×D11—81no—
185C4×D11—81no—
186Dic22—41no—
187Dic22—41no—
188C8×C11—42no—
189C11⋊C8—21no—
190C11⋊C8—21no—
191C11⋊C8—21no—
192C11⋊C8—21no—
193C11⋊C8—42no—
194C2×#135—221no—
195C2×#135—221no—
196#532—111no—
197#532C2×D1111yescharacteristic
198#495—221no—
199#495—221no—
200#494—111no—
201#493—111no—
202#492—111no—
203#492—111no—
204#431—111no—
205#431C2×D1111yescharacteristic
206C2×C4×C8—111no—
207#382—111no—
208#382C2×D1111yescharacteristic
209#340—221no—
210#340—221no—
211#327—22no—
212#327—222no—
213#327—222no—
214#327—222no—
215#322—221no—
216#322—221no—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11—81no—
220C22×C11—81no—
221C22×C11—81no—
222C22×C11#39011yescharacteristic
223C22×C11#49611yescharacteristic
224C22×C11#49611yescharacteristic
225C2×D11—81no—
226C2×D11—81no—
227C2×D11—81no—
228C4×C11—21no—
229C4×C11—21no—
230C4×C11—21no—
231C4×C11—21no—
232C4×C11—81no—
233C4×C11—161no—
234C4×C11#41811yescharacteristic
235C4×C11#41811yescharacteristic
236C4×C11#49011yescharacteristic
237C4×C11#49011yescharacteristic
238Dic11—81no—
239Dic11—161no—
240C2×#41—21no—
241C2×#41—221no—
242#135—442no—
243#135—442no—
244#135—442no—
245#135—442no—
246C2×Q16—221no—
247C2×Q16—221no—
248C2×SD16—221no—
249C2×SD16—221no—
250C2×SD16—221no—
251C2×SD16—221no—
252C2×D8—221no—
253C2×D8—221no—
254C22×C8—111no—
255C22×C8—111no—
256C4⋊Q8—111no—
257C4⋊Q8C4×D1111yescharacteristic
258#127—111no—
259#127C4×D1111yescharacteristic
260#124—21no—
261#124—221no—
262#121—21no—
263#121—21no—
264#121—221no—
265#121—221no—
266C4×D4—21no—
267C4×D4—21no—
268C4×D4—221no—
269C4×D4—221no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—221no—
272C2×C42C22×D1111yescharacteristic
273C4⋊C8—21no—
274C4⋊C8—221no—
275C22⋊C8—112no—
276C22⋊C8C22⋊D1112yes—
277C4×C8—21no—
278C4×C8—111no—
279C4×C8—111no—
280C4×C8—111no—
281C4×C8—111no—
282C4×C8—221no—
283#95—21no—
284#95—21no—
285#95—221no—
286#95—221no—
287C2×C11—21no—
288C2×C11—21no—
289C2×C11—161no—
290C2×C11#196111yescharacteristic
291C2×C11#197611yescharacteristic
292C2×C11#197611yescharacteristic
293D11—161no—
294#41—41no—
295#41—41no—
296#41—41no—
297#41—41no—
298#41—441no—
299#41—441no—
300#41—441no—
301#41—441no—
302C2×Q8—21no—
303C2×Q8—221no—
304C2×D4—21no—
305C2×D4—21no—
306C2×D4—21no—
307C2×D4—41no—
308C2×D4—221no—
309C2×D4—221no—
310C2×D4—221no—
311C2×D4—441no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—441no—
315C22×C4—441no—
316C22×C4D4×D1111yescharacteristic
317C22×C4D4×D1111yescharacteristic
318C22×C4C2×C22⋊D1111yescharacteristic
319Q16—442no—
320Q16—442no—
321SD16—442no—
322SD16—442no—
323SD16—442no—
324SD16—442no—
325D8—442no—
326D8—442no—
327C2×C8—22no—
328C2×C8—111no—
329C2×C8—111no—
330C2×C8—111no—
331C2×C8—111no—
332C2×C8—221no—
333C2×C8—221no—
334C2×C8—221no—
335C2×C8—221no—
336C2×C8—222no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C4⋊C4—221no—
342C4⋊C4—221no—
343C4⋊C4—441no—
344C4⋊C4—441no—
345C22⋊C4—41no—
346C22⋊C4—41no—
347C22⋊C4—441no—
348C22⋊C4—441no—
349C42C2×C4×D1111yescharacteristic
350C42#433911yescharacteristic
351C42D4×D1111yescharacteristic
352C42#434111yescharacteristic
353C11#976011yescharacteristic, complemented, Sylow
354C23—41no—
355C23—441no—
356C23#6699311yescharacteristic
357Q8—41no—
358Q8—41no—
359Q8—441no—
360Q8—441no—
361D4—41no—
362D4—41no—
363D4—81no—
364D4—81no—
365D4—81no—
366D4—81no—
367D4—441no—
368D4—441no—
369D4—881no—
370D4—881no—
371D4—881no—
372D4—881no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—81no—
377C2×C4—81no—
378C2×C4—81no—
379C2×C4—81no—
380C2×C4—81no—
381C2×C4—441no—
382C2×C4—881no—
383C2×C4—881no—
384C2×C4—881no—
385C2×C4—881no—
386C2×C4—881no—
387C2×C4C22⋊C4×D1111yescharacteristic
388C2×C4(C22⋊D11)⋊C411yescharacteristic
389C2×C4#6693711yescharacteristic
390C2×C4#6693811yescharacteristic
391C2×C4#6696411yescharacteristic
392C2×C4#6696411yescharacteristic
393C2×C4#6696711yescharacteristic
394C2×C4#6696711yescharacteristic
395C2×C4C4×C22⋊D1111yescharacteristic
396C2×C4#6699211yescharacteristic
397C8—42no—
398C8—221no—
399C8—221no—
400C8—221no—
401C8—221no—
402C8—442no—
403C22—21no—
404C22—21no—
405C22—81no—
406C22—81no—
407C22—81no—
408C22—881no—
409C22—881no—
410C22—881no—
411C22#1062257011yescharacteristic
412C22#1062276711yescharacteristic
413C22#1062278911yescharacteristic
414C4—21no—
415C4—21no—
416C4—21no—
417C4—21no—
418C4—81no—
419C4—161no—
420C4—881no—
421C4—1761no—
422C4#1062237711yescharacteristic
423C4#1062237711yescharacteristic
424C4#1062238311yescharacteristic
425C4#1062238311yescharacteristic
426C2—21no—
427C2—21no—
428C2—161no—
429C2—1761no—
430C2#1306943811yescharacteristic
431C2#1306951111yescharacteristic
432C2#1306951311yescharacteristic
subgroupG/H
centerC22#10622570
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1517C2
socleC22×C11#390
prime radical#13079042C2
cosocleC2×C42×C11C23
hypercenter#1517D11
hypocenterC11#9760
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1517

Complements

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

NH ≅ G/Ntype
2. #13068746C2semidirect
3. #13067177C2semidirect
4. #13067176C2semidirect
5. #13067175C2semidirect
6. #13066909C2semidirect
7. C11×#1517C2semidirect
14. #10622705C4semidirect
15. #10622698C4semidirect
16. #10622689C4semidirect
17. #10622686C4semidirect
143. #1517D11semidirect
353. C11#9760semidirect

Maximal subgroups

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

subgroupindex
#130790422
#130687462
#130671772
#130671762
#130671752
#130669092
C11×#15172
#976011