Finite Group Databasebeta

← #14650133

Subgroups — #14650133

Order 2816.

544 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622696C211yesmaximal, characteristic
2#13077351C211yesmaximal, characteristic
3#13069606C211yesmaximal, characteristic, complemented
4#13067042C211yesmaximal, characteristic
5#13066490C211yesmaximal, characteristic, complemented
6#13066465C211yesmaximal, characteristic, complemented
7C11×#1548C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C22×#4325C412yes—
10C2×M16×D11—21no—
11C2×C4×D44C2211yescharacteristic
12C11×#431C2211yescharacteristic
13C11×#423C2211yescharacteristic
14C2×#66899C412yes—
15#10622739—21no—
16#10622696—21no—
17#10622696—21no—
18#10622696—21no—
19#10622696—21no—
20#10622537C2211yescharacteristic
21C2×C4⋊(C11⋊C8)C2211yescharacteristic
22C4×#4318C2211yescharacteristic
23#10622451—21no—
24#10622449—22no—
25#10622447—21no—
26C11×#333—22no—
27#10622168—21no—
28#10622168—21no—
29#10622097—21no—
30#10622097—21no—
31C22×Q8×C11C2×C412yes—
32C22×D44C2×C411yescharacteristic
33C22×C4×D11—21no—
34C2×C11×M16—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—21no—
41C2×C42×C11C2311yescharacteristic
42C2×#4325—22no—
43C2×#4325—22no—
44C2×#4325—44no—
45C2×(C2×D11)⋊C4—21no—
46C2×C4⋊Dic11C2×C411yescharacteristic
47C2×#4318—21no—
48C2×#4318D411yescharacteristic
49C2×#4318D411yescharacteristic
50C22×C11⋊C8C2×C412yes—
51M16×D11—42no—
52M16×D11—42no—
53C2×#4313—22no—
54C2×C8×D11—22no—
55C4×D44—21no—
56C4×D44—21no—
57C4×D44D411yescharacteristic
58C4×D44D411yescharacteristic
59C4×D44D411yescharacteristic
60C4×D44D411yescharacteristic
61C11×C4⋊C8—21no—
62C11×C4⋊C8—21no—
63C11×C4⋊C8D412yes—
64C11×C22⋊C8—21no—
65C4×C8×C11—21no—
66#66899—22no—
67#66899—22no—
68(C2×D11)⋊C8—22no—
69(C2×D11)⋊C8—22no—
70C4⋊(C11⋊C8)—21no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)—21no—
74#66867—21no—
75C4×C11⋊C8—21no—
76#9247—111nomaximal, Sylow
77C23×D11—21no—
78C2×Q8×C11—22no—
79C2×Q8×C11—22no—
80C2×Q8×C11—42no—
81C2×Q8×C11—42no—
82C22×C4×C11—22no—
83C22×C4×C11C22×C411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11#4111yescharacteristic
86C22×Dic11—21no—
87C2×D44—22no—
88C2×D44—21no—
89C2×D44—41no—
90C2×D44C22⋊C411yescharacteristic
91C2×D44C22⋊C411yescharacteristic
92C2×C4×D11—21no—
93C2×C4×D11—21no—
94C2×C4×D11—21no—
95C2×C4×D11—21no—
96C2×C4×D11—41no—
97C2×C4×D11—41no—
98C2×C4×D11—41no—
99C2×C4×D11—41no—
100C11×M16—41no—
101C11×M16—41no—
102C2×C8×C11—22no—
103C2×C8×C11—41no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110C42×C11C2×D411yescharacteristic
111C42×C11#4111yescharacteristic
112#4325—44no—
113#4325—44no—
114(C2×D11)⋊C4—21no—
115(C2×D11)⋊C4—21no—
116(C2×D11)⋊C4—21no—
117(C2×D11)⋊C4—21no—
118C4⋊Dic11—21no—
119C4⋊Dic11C22⋊C411yescharacteristic
120C4⋊Dic11C22⋊C411yescharacteristic
121#4318—21no—
122#4318—21no—
123#4318—21no—
124#4318—41no—
125#4318—41no—
126#4318SD1612yescomplemented
127C2×C11⋊C8—22no—
128C2×C11⋊C8—21no—
129C2×C11⋊C8—21no—
130C2×C11⋊C8—42no—
131C2×C11⋊C8—41no—
132#4313—44no—
133C8×D11—44no—
134C2×#461—111no—
135D4×M16—111no—
136#1997—111no—
137#1548D1111yescharacteristic, complemented
138#1486—111no—
139#1292—111no—
140#1283—111no—
141C23×C11C4×D411yescharacteristic
142C22×D11—21no—
143C22×D11—21no—
144C22×D11—42no—
145C22×D11—41no—
146C22×D11—41no—
147C22×D11—81no—
148Q8×C11—42no—
149Q8×C11—42no—
150Q8×C11—82no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—41no—
154C2×C4×C11—42no—
155C2×C4×C11—82no—
156C2×C4×C11C2×C22⋊C411yescharacteristic
157C2×C4×C11C4×D411yescharacteristic
158C2×C4×C11#12011yescharacteristic
159C2×C4×C11#12111yescharacteristic
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11#12311yescharacteristic
162C2×C4×C11C2×SD1611yescharacteristic
163C2×C4×C11#13511yescharacteristic
164C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C11#13711yescharacteristic
166C2×Dic11—21no—
167C2×Dic11—21no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170D44—21no—
171D44—21no—
172D44—21no—
173D44—42no—
174D44#10012yes—
175C4×D11—41no—
176C4×D11—41no—
177C4×D11—41no—
178C4×D11—41no—
179C4×D11—41no—
180C4×D11—41no—
181C4×D11—41no—
182C4×D11—41no—
183C8×C11—42no—
184C8×C11—81no—
185C11⋊C8—22no—
186C11⋊C8—42no—
187C11⋊C8—41no—
188C11⋊C8—81no—
189C22×SD16—112no—
190C22×M16—221no—
191C2×C4⋊Q8C2×D1111yescharacteristic
192C2×C4×D4—111no—
193#461—221no—
194#461—221no—
195#461—221no—
196#461—221no—
197#436—221no—
198#435—222no—
199C8×D4—221no—
200#431C2×D1111yescharacteristic
201#423—111no—
202#423C2×D1111yescharacteristic
203C2×C4⋊C8—111no—
204C2×#103—112no—
205#407—221no—
206C4×M16—111no—
207#343—221no—
208#343—221no—
209#333—22no—
210D4⋊C8—221no—
211D4⋊C8—221no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11#38611yescharacteristic
215C22×C11C4×SD1611yescharacteristic
216C22×C11#44011yescharacteristic
217C2×D11—22no—
218C2×D11—41no—
219C2×D11—41no—
220C2×D11—41no—
221C2×D11—41no—
222C2×D11—41no—
223C2×D11—82no—
224C2×D11—82no—
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—21no—
228C4×C11—82no—
229C4×C11C2×#10011yescharacteristic
230C4×C11#41311yescharacteristic
231C4×C11#45011yescharacteristic
232C4×C11#45211yescharacteristic
233C4×C11#46111yescharacteristic
234C4×C11#46311yescharacteristic
235Dic11—41no—
236Dic11—41no—
237C22×Q8C4×D1112yes—
238C22×D4—111no—
239C23×C4—221no—
240C2×SD16—222no—
241C2×SD16—222no—
242C2×SD16—444no—
243C2×M16—21no—
244C2×M16—111no—
245C2×M16—111no—
246C2×M16—222no—
247C2×M16—221no—
248C2×M16—442no—
249C2×M16—442no—
250C22×C8—112no—
251C22×C8—222no—
252C4⋊Q8—21no—
253C4⋊Q8—21no—
254C4⋊Q8—21no—
255C4⋊Q8—21no—
256C4×D4—111no—
257C4×D4—111no—
258C4×D4—111no—
259C4×D4—111no—
260C4×D4—221no—
261C4×D4—221no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—111no—
265C2×C22⋊C4—221no—
266C2×C42C22×D1111yescharacteristic
267C4⋊C8—21no—
268C4⋊C8—21no—
269C4⋊C8—221no—
270C4⋊C8—221no—
271C4⋊C8—221no—
272C4⋊C8—221no—
273C4⋊C8C22⋊D1112yes—
274#103—222no—
275#103—222no—
276C22⋊C8—21no—
277C22⋊C8—222no—
278C22⋊C8—222no—
279#97—221no—
280C4×C8—21no—
281C4×C8—221no—
282C2×C11—21no—
283C2×C11—21no—
284C2×C11#187711yescharacteristic
285C2×C11#190011yescharacteristic
286C2×C11#190211yescharacteristic
287D11—42no—
288D11—81no—
289C24—221no—
290C2×Q8—22no—
291C2×Q8—22no—
292C2×Q8—42no—
293C2×Q8—42no—
294C2×D4—111no—
295C2×D4—111no—
296C2×D4—222no—
297C2×D4—221no—
298C2×D4—441no—
299C22×C4—22no—
300C22×C4—221no—
301C22×C4—221no—
302C22×C4—221no—
303C22×C4—221no—
304C22×C4—221no—
305C22×C4—441no—
306C22×C4—441no—
307C22×C4—441no—
308C22×C4—441no—
309C22×C4C2×C4×D1111yescharacteristic
310C22×C4D4×D1111yescharacteristic
311C22×C4#434111yescharacteristic
312SD16—444no—
313SD16—444no—
314M16—41no—
315M16—41no—
316M16—112no—
317M16—221no—
318M16—221no—
319M16—221no—
320M16—444no—
321M16—441no—
322M16—441no—
323C2×C8—22no—
324C2×C8—41no—
325C2×C8—221no—
326C2×C8—222no—
327C2×C8—221no—
328C2×C8—444no—
329C2×C8—442no—
330C2×C8—441no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4—111no—
336C4⋊C4—111no—
337C4⋊C4—221no—
338C22⋊C4—221no—
339C22⋊C4—221no—
340C22⋊C4—221no—
341C22⋊C4—221no—
342C42#433911yescharacteristic
343C42D4×D1111yescharacteristic
344C42D4×D1111yescharacteristic
345C42C2×C22⋊D1111yescharacteristic
346C11#924711yescharacteristic, complemented, Sylow
347C23—221no—
348C23—221no—
349C23—442no—
350C23—441no—
351C23—441no—
352C23—881no—
353C23(C22⋊D11)⋊C411yescharacteristic
354Q8—42no—
355Q8—42no—
356Q8—82no—
357D4—112no—
358D4—221no—
359D4—221no—
360D4—221no—
361D4—442no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—82no—
367C2×C4—221no—
368C2×C4—221no—
369C2×C4—441no—
370C2×C4—441no—
371C2×C4—441no—
372C2×C4—441no—
373C2×C4—441no—
374C2×C4—441no—
375C2×C4—441no—
376C2×C4—441no—
377C2×C4—441no—
378C2×C4—441no—
379C2×C4C22⋊C4×D1111yescharacteristic
380C2×C4#6693611yescharacteristic
381C2×C4#6693711yescharacteristic
382C2×C4SD16×D1111yescharacteristic
383C2×C4#6696711yescharacteristic
384C2×C4#6697111yescharacteristic
385C2×C4#6697211yescharacteristic
386C2×C4C4×C22⋊D1111yescharacteristic
387C2×C4#6699011yescharacteristic
388C2×C4#6699111yescharacteristic
389C8—42no—
390C8—81no—
391C8—222no—
392C8—441no—
393C8—442no—
394C8—881no—
395C22—21no—
396C22—21no—
397C22—222no—
398C22—441no—
399C22—441no—
400C22—441no—
401C22—441no—
402C22—441no—
403C22—882no—
404C22—882no—
405C22#1062240111yescharacteristic
406C22#1062243011yescharacteristic
407C22#1062256911yescharacteristic
408C4—21no—
409C4—21no—
410C4—21no—
411C4—82no—
412C4—441no—
413C4—441no—
414C4D11×#10011yescharacteristic
415C4#1062235811yescharacteristic
416C4#1062243111yescharacteristic
417C4#1062243211yescharacteristic
418C4#1062278211yescharacteristic
419C4#1062280011yescharacteristic
420C2—21no—
421C2—21no—
422C2—442no—
423C2—881no—
424C2#1306894711yescharacteristic
425C2#1306907611yescharacteristic
426C2#1306908611yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1548C2
socleC22×C11#386
prime radicalC22×D44C2×C4
cosocleC2×C42×C11C23
hypercenter#1548D11
hypocenterC11#9247
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1548

Complements

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

NH ≅ G/Ntype
3. #13069606C2semidirect
5. #13066490C2semidirect
6. #13066465C2semidirect
7. C11×#1548C2semidirect
126. #4318SD16semidirect
137. #1548D11semidirect
346. C11#9247semidirect

Maximal subgroups

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

subgroupindex
C2×#106226962
#130773512
#130696062
#130670422
#130664902
#130664652
C11×#15482
#924711