Finite Group Databasebeta

← #14647128

Subgroups — #14647128

Order 2816.

592 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#66945C211yesmaximal, characteristic
2#13068593C211yesmaximal, characteristic
3C4×(C2×D11)⋊C8C211yesmaximal, characteristic
4#13066457C211yesmaximal, characteristic, complemented
5#13066456C211yesmaximal, characteristic, complemented
6#13066455C211yesmaximal, characteristic, complemented
7C11×#1279C211yesmaximal, characteristic, complemented
8C2×#66945C411yescharacteristic
9C2×#66945C411yescharacteristic
10C2×C42×D11C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C4×C8×C11C2211yescharacteristic
13C4×C11×C4⋊C4C2211yescharacteristic
14C2×(C2×D11)⋊C8—21no—
15C2×(C2×D11)⋊C8—21no—
16C4⋊C4×Dic11C411yescharacteristic
17C4⋊C4×Dic11C411yescharacteristic
18C4×(C2×D11)⋊C4—21no—
19C4×C4⋊Dic11C2211yescharacteristic
20C42×Dic11—21no—
21C2×C4⋊(C11⋊C8)C2211yescharacteristic
22C2×C4×C11⋊C8C2211yescharacteristic
23#10622279—21no—
24#10622261—21no—
25#10622188—21no—
26#10622188—21no—
27C22×C4×D11C2×C411yescharacteristic
28C22×C4×D11D411yescharacteristic
29C22×C4×D11D411yescharacteristic
30C22×C8×C11—21no—
31C22×C8×C11—21no—
32C2×C11×C4⋊C4C2×C411yescharacteristic
33C2×C11×C4⋊C4C2×C411yescharacteristic
34C2×C42×C11—21no—
35C2×C42×C11C2311yescharacteristic
36C2×(C2×D11)⋊C4—21no—
37C2×(C2×D11)⋊C4—21no—
38C2×C4⋊Dic11C2×C411yescharacteristic
39C2×C4⋊Dic11C2×C411yescharacteristic
40C2×C4×Dic11—21no—
41C2×C4×Dic11—21no—
42C2×C4×Dic11—21no—
43C2×C4×Dic11—21no—
44C2×C4×Dic11—21no—
45C2×C4×Dic11C2×C411yescharacteristic
46C2×C4×Dic11D411yescharacteristic
47C2×C4×Dic11D411yescharacteristic
48C22×C11⋊C8—21no—
49C22×C11⋊C8—21no—
50#66945—22no—
51#66945—22no—
52#66945—22no—
53#66945C814yescomplemented
54C42×D11—21no—
55C42×D11—21no—
56C42×D11—21no—
57C42×D11—21no—
58C11×C4⋊C8—21no—
59C11×C4⋊C8—21no—
60C4×C8×C11—21no—
61C4×C8×C11—21no—
62C11×#95—21no—
63C11⋊#95—21no—
64C11⋊#95—21no—
65C11⋊#95—21no—
66(C2×D11)⋊C8—24no—
67(C2×D11)⋊C8—42no—
68C4⋊(C11⋊C8)—21no—
69C4⋊(C11⋊C8)—21no—
70C4×C11⋊C8—21no—
71C4×C11⋊C8—21no—
72#8708—111nomaximal, Sylow
73C23×D11C22⋊C411yescharacteristic
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11C22×C411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×Dic11—21no—
80C22×Dic11—21no—
81C22×Dic11C22⋊C411yescharacteristic
82C22×Dic11C22⋊C411yescharacteristic
83C22×Dic11C22⋊C411yescharacteristic
84C2×C4×D11—22no—
85C2×C4×D11—21no—
86C2×C4×D11—21no—
87C2×C4×D11—21no—
88C2×C4×D11—21no—
89C2×C4×D11—21no—
90C2×C4×D11—21no—
91C2×C4×D11—21no—
92C2×C4×D11—21no—
93C2×C4×D11—21no—
94C2×C4×D11—21no—
95C2×C4×D11—21no—
96C2×C4×D11—21no—
97C2×C4×D11—41no—
98C2×C4×D11C2×C812yes—
99C2×C4×D11M1612yes—
100C2×C8×C11—22no—
101C2×C8×C11—41no—
102C2×C8×C11—41no—
103C2×C8×C11—41no—
104C2×C8×C11—41no—
105C2×C8×C11—41no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4C2×C812yes—
109C11×C4⋊C4M1612yes—
110C42×C11—41no—
111C42×C11—41no—
112C42×C11#4111yescharacteristic
113C42×C11#4111yescharacteristic
114C42×C11#4111yescharacteristic
115C42×C11#4111yescharacteristic
116(C2×D11)⋊C4—24no—
117(C2×D11)⋊C4—24no—
118C4⋊Dic11—21no—
119C4⋊Dic11—21no—
120C4⋊Dic11C2×C812yes—
121C4⋊Dic11M1612yes—
122C4×Dic11—24no—
123C4×Dic11—24no—
124C4×Dic11—21no—
125C4×Dic11—21no—
126C4×Dic11—21no—
127C4×Dic11—21no—
128C4×Dic11—21no—
129C4×Dic11—21no—
130C4×Dic11—42no—
131C4×Dic11—42no—
132C4×Dic11—41no—
133C4×Dic11—41no—
134C2×C11⋊C8—22no—
135C2×C11⋊C8—41no—
136C2×C11⋊C8—41no—
137C2×C11⋊C8—41no—
138C2×C11⋊C8—41no—
139C2×C11⋊C8—41no—
140C4×#117—111no—
141#1797—111no—
142C4×C22⋊C8—111no—
143#1279—111no—
144#1279—111no—
145#1279—111no—
146#1279D1111yescharacteristic, complemented
147C23×C11C2×C22⋊C411yescharacteristic
148C22×D11—21no—
149C22×D11—21no—
150C22×D11—21no—
151C22×D11—21no—
152C22×D11—21no—
153C22×D11—21no—
154C22×D11C22⋊C812yes—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11#11711yescharacteristic
164C2×C4×C11#11711yescharacteristic
165C2×C4×C11#12311yescharacteristic
166C2×C4×C11#12311yescharacteristic
167C2×C4×C11#12311yescharacteristic
168C2×C4×C11#12311yescharacteristic
169C2×C4×C11C22×C811yescharacteristic
170C2×C4×C11C2×M1611yescharacteristic
171C2×C4×C11C2×M1611yescharacteristic
172C2×C4×C11C2×M1611yescharacteristic
173C2×C4×C11#13511yescharacteristic
174C2×C4×C11#13511yescharacteristic
175C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
176C2×C4×C11#13711yescharacteristic
177C2×Dic11—21no—
178C2×Dic11—21no—
179C2×Dic11—21no—
180C2×Dic11—21no—
181C2×Dic11—21no—
182C2×Dic11—22no—
183C2×Dic11—22no—
184C2×Dic11—21no—
185C2×Dic11—21no—
186C2×Dic11—41no—
187C2×Dic11—41no—
188C2×Dic11—41no—
189C2×Dic11—41no—
190C2×Dic11C22⋊C812yes—
191C2×Dic11#10412yes—
192C4×D11—22no—
193C4×D11—22no—
194C4×D11—22no—
195C4×D11—22no—
196C4×D11—42no—
197C4×D11—42no—
198C4×D11—41no—
199C4×D11—41no—
200C4×D11—41no—
201C4×D11—41no—
202C8×C11—42no—
203C8×C11—81no—
204C11⋊C8—42no—
205C11⋊C8—81no—
206C2×#117—111no—
207C2×#117—111no—
208C22×C42—111no—
209C2×C4⋊C8—111no—
210C2×C4⋊C8C2×D1111yescharacteristic
211C2×C22⋊C8—221no—
212C2×C22⋊C8—221no—
213C2×C4×C8—111no—
214C2×C4×C8C2×D1111yescharacteristic
215C4×C4⋊C4—111no—
216C4×C4⋊C4—111no—
217C4×C4⋊C4—111no—
218C4×C4⋊C4C2×D1111yescharacteristic
219C4×C22⋊C4—221no—
220C4×C22⋊C4—221no—
221#376—221no—
222C43—221no—
223#336—221no—
224#336—221no—
225C22×C11#38111yescharacteristic
226C22×C11C2×C22⋊C811yescharacteristic
227C22×C11#40711yescharacteristic
228C22×C11#41611yescharacteristic
229C22×C11#41711yescharacteristic
230C22×C11C2×#10411yescharacteristic
231C22×C11#42111yescharacteristic
232C2×D11—22no—
233C2×D11—22no—
234C2×D11—22no—
235C2×D11—41no—
236C2×D11—41no—
237C2×D11—41no—
238C2×D11—41no—
239C4×C11—21no—
240C4×C11—21no—
241C4×C11—42no—
242C4×C11—42no—
243C4×C11#43111yescharacteristic
244C4×C11#43111yescharacteristic
245C4×C11#43211yescharacteristic
246C4×C11#43211yescharacteristic
247C4×C11#48211yescharacteristic
248C4×C11#48211yescharacteristic
249C4×C11#48511yescharacteristic
250C4×C11#48511yescharacteristic
251Dic11—22no—
252Dic11—22no—
253Dic11—41no—
254Dic11—42no—
255Dic11—42no—
256C23×C4—111no—
257C23×C4—111no—
258C23×C4—111no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—221no—
262C22×C8—221no—
263#117—114no—
264#117—222no—
265#117—222no—
266#117—222no—
267C2×C4⋊C4—111no—
268C2×C4⋊C4—111no—
269C2×C4⋊C4C4×D1111yescharacteristic
270C2×C4⋊C4C4×D1111yescharacteristic
271C2×C22⋊C4—221no—
272C2×C22⋊C4—221no—
273C2×C42—21no—
274C2×C42—111no—
275C2×C42—111no—
276C2×C42—111no—
277C2×C42—221no—
278C2×C42—221no—
279C2×C42—221no—
280C2×C42—221no—
281C2×C42—221no—
282C2×C42—221no—
283C2×C42—221no—
284C2×C42—221no—
285C2×C42—221no—
286C2×C42C22×D1111yescharacteristic
287C4⋊C8—21no—
288C4⋊C8—21no—
289C4⋊C8—221no—
290C4⋊C8—221no—
291C22⋊C8—224no—
292C22⋊C8—442no—
293C4×C8—21no—
294C4×C8—21no—
295C4×C8—221no—
296C4×C8—221no—
297#95—21no—
298#95—221no—
299#95—221no—
300#95—221no—
301C2×C11#147611yescharacteristic
302C2×C11#147711yescharacteristic
303C2×C11#148811yescharacteristic
304C2×C11#148911yescharacteristic
305C2×C11#181711yescharacteristic
306C2×C11#182511yescharacteristic
307C2×C11#182611yescharacteristic
308D11—42no—
309C24—111no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—111no—
313C22×C4—111no—
314C22×C4—112no—
315C22×C4—112no—
316C22×C4—111no—
317C22×C4—222no—
318C22×C4—221no—
319C22×C4—221no—
320C22×C4—221no—
321C22×C4—221no—
322C22×C4—221no—
323C22×C4—221no—
324C22×C4—221no—
325C22×C4—221no—
326C22×C4—221no—
327C22×C4—221no—
328C22×C4—221no—
329C22×C4—221no—
330C22×C4—221no—
331C22×C4—221no—
332C22×C4—441no—
333C22×C4C2×C4×D1111yescharacteristic
334C22×C4D4×D1111yescharacteristic
335C22×C4D4×D1111yescharacteristic
336C2×C8—22no—
337C2×C8—41no—
338C2×C8—41no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8—41no—
342C2×C8—222no—
343C2×C8—441no—
344C2×C8—441no—
345C2×C8—441no—
346C2×C8—441no—
347C2×C8—441no—
348C4⋊C4—21no—
349C4⋊C4—21no—
350C4⋊C4—112no—
351C4⋊C4—112no—
352C4⋊C4—221no—
353C4⋊C4—221no—
354C4⋊C4C8×D1112yes—
355C4⋊C4#431312yes—
356C22⋊C4—224no—
357C22⋊C4—224no—
358C42—41no—
359C42—41no—
360C42—224no—
361C42—224no—
362C42—221no—
363C42—221no—
364C42—221no—
365C42—221no—
366C42—221no—
367C42—221no—
368C42—442no—
369C42—442no—
370C42—441no—
371C42—441no—
372C42#433911yescharacteristic
373C42#433911yescharacteristic
374C42#434111yescharacteristic
375C42#434311yescharacteristic
376C11#870811yescharacteristic, complemented, Sylow
377C23—112no—
378C23—221no—
379C23—221no—
380C23—221no—
381C23—221no—
382C23—221no—
383C23—221no—
384C23C22⋊C4×D1111yescharacteristic
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—112no—
394C2×C4—112no—
395C2×C4—221no—
396C2×C4—221no—
397C2×C4—221no—
398C2×C4—221no—
399C2×C4—222no—
400C2×C4—222no—
401C2×C4—222no—
402C2×C4—222no—
403C2×C4—221no—
404C2×C4—222no—
405C2×C4—222no—
406C2×C4—221no—
407C2×C4—221no—
408C2×C4—442no—
409C2×C4—442no—
410C2×C4—441no—
411C2×C4—441no—
412C2×C4—441no—
413C2×C4—441no—
414C2×C4—441no—
415C2×C4—441no—
416C2×C4—441no—
417C2×C4—441no—
418C2×C4#6692511yescharacteristic
419C2×C4#6693611yescharacteristic
420C2×C4#6693611yescharacteristic
421C2×C4#6694511yescharacteristic
422C2×C4#6694711yescharacteristic
423C2×C4#6694711yescharacteristic
424C2×C4C2×C8×D1111yescharacteristic
425C2×C4C2×#431311yescharacteristic
426C2×C4M16×D1111yescharacteristic
427C2×C4M16×D1111yescharacteristic
428C2×C4#6696411yescharacteristic
429C2×C4#6696811yescharacteristic
430C2×C4#6696911yescharacteristic
431C2×C4#6697211yescharacteristic
432C8—42no—
433C8—81no—
434C8—442no—
435C8—881no—
436C22—222no—
437C22—222no—
438C22—222no—
439C22—441no—
440C22—441no—
441C22—441no—
442C22—441no—
443C22#1062227711yescharacteristic
444C22D11×C22⋊C811yescharacteristic
445C22#1062233911yescharacteristic
446C22#1062238411yescharacteristic
447C22#1062241711yescharacteristic
448C22D11×#10411yescharacteristic
449C22#1062243411yescharacteristic
450C4—21no—
451C4—21no—
452C4—42no—
453C4—42no—
454C4—222no—
455C4—222no—
456C4—442no—
457C4—441no—
458C4—442no—
459C4#1062229811yescharacteristic
460C4#1062231811yescharacteristic
461C4#1062239211yescharacteristic
462C4#1062242711yescharacteristic
463C4#1062244611yescharacteristic
464C4#1062244811yescharacteristic
465C4#1062248011yescharacteristic
466C4#1062249811yescharacteristic
467C2—442no—
468C2#1306699711yescharacteristic
469C2#1306700011yescharacteristic
470C2#1306704911yescharacteristic
471C2#1306705211yescharacteristic
472C2#1306868311yescharacteristic
473C2#1306871011yescharacteristic
474C2#1306871411yescharacteristic
subgroupG/H
centerC22×C4D4×D11
commutatorC2×C4×C11C22×C8
FrattiniC2×C42C22×D11
FittingC11×#1279C2
socleC23×C11C2×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1279D11
hypocenterC11#8708
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
4. #13066457C2semidirect
5. #13066456C2semidirect
6. #13066455C2semidirect
7. C11×#1279C2semidirect
53. #66945C8semidirect
146. #1279D11semidirect
376. C11#8708semidirect

Maximal subgroups

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

subgroupindex
C4×#669452
#130685932
C4×(C2×D11)⋊C82
#130664572
#130664562
#130664552
C11×#12792
#870811