Finite Group Databasebeta

← #14657279

Subgroups — #14657279

Order 2816.

614 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068743C211yesmaximal, characteristic, complemented
2#13068616C211yesmaximal, characteristic, complemented
3#13068616C211yesmaximal, characteristic, complemented
4C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
5C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
6#13066499C211yesmaximal, characteristic, complemented
7C11×#2537C211yesmaximal, characteristic
8C2×C11×#121—21no—
9C2×C11×#121—21no—
10C2×C4×D4×C11C2211yescharacteristic
11C2×C4×D4×C11C2211yescharacteristic
12C11×#394—22no—
13C11×#384C2211yescharacteristic
14C11×#380—21no—
15C11×#380—21no—
16C2×#66896—21no—
17C2×#66896—21no—
18#10622548C2211yescharacteristic
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C2×C4⋊(C11⋊C8)C2211yescharacteristic
21C2×C4×C11⋊C8C2211yescharacteristic
22D4⋊(C11⋊C8)—22no—
23D4⋊(C11⋊C8)—22no—
24#10622167—21no—
25#10622167—21no—
26#10622167—22no—
27C22×D4×C11—22no—
28C22×D4×C11D411yescharacteristic
29C22×D4×C11D411yescharacteristic
30C23×C4×C11—21no—
31C23×C4×C11—21no—
32C11×#121—42no—
33C11×#121—42no—
34C11×#121—42no—
35C11×#121—42no—
36C4×D4×C11—21no—
37C4×D4×C11—21no—
38C4×D4×C11—21no—
39C4×D4×C11—21no—
40C4×D4×C11—21no—
41C4×D4×C11—21no—
42C4×D4×C11—21no—
43C4×D4×C11—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4D411yescharacteristic
47C2×C11×C4⋊C4D411yescharacteristic
48C2×C11×C4⋊C4D412yes—
49C2×C11×C22⋊C4—22no—
50C2×C11×C22⋊C4—22no—
51C2×C11×C22⋊C4—21no—
52C2×C11×C22⋊C4—21no—
53C2×C42×C11C2311yescharacteristic
54C2×C4⋊Dic11—21no—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11—21no—
57C22×C11⋊C8—21no—
58C22×C11⋊C8—21no—
59C22×C11⋊C8—21no—
60C11×#95—22no—
61#66896—42no—
62#66896—42no—
63C4⋊(C11⋊C8)—21no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)—21no—
67C4×C11⋊C8—21no—
68C4×C11⋊C8D412yescomplemented
69#10431—111nomaximal, Sylow
70C24×C11—21no—
71C24×C11—21no—
72C2×D4×C11—21no—
73C2×D4×C11—21no—
74C2×D4×C11—21no—
75C2×D4×C11—21no—
76C2×D4×C11—21no—
77C2×D4×C11—21no—
78C2×D4×C11—21no—
79C2×D4×C11—21no—
80C2×D4×C11—21no—
81C2×D4×C11—21no—
82C2×D4×C11—44no—
83C2×D4×C11—44no—
84C2×D4×C11—82no—
85C2×D4×C11D812yes—
86C2×D4×C11SD1612yes—
87C22×C4×C11—21no—
88C22×C4×C11—21no—
89C22×C4×C11—22no—
90C22×C4×C11—41no—
91C22×C4×C11—41no—
92C22×C4×C11—41no—
93C22×C4×C11—41no—
94C22×C4×C11—41no—
95C22×C4×C11—41no—
96C22×C4×C11—41no—
97C22×C4×C11—41no—
98C22×C4×C11—41no—
99C22×C4×C11—41no—
100C22×C4×C11—41no—
101C22×C4×C11—41no—
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C22×Dic11—41no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—42no—
111C11×C4⋊C4—41no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C11×C22⋊C4—44no—
116C11×C22⋊C4—44no—
117C11×C22⋊C4—41no—
118C11×C22⋊C4—41no—
119C11×C22⋊C4—41no—
120C11×C22⋊C4—41no—
121C42×C11C2×D411yescharacteristic
122C42×C11#4111yescharacteristic
123C42×C11#4111yescharacteristic
124C42×C11#4111yescharacteristic
125C4⋊Dic11—42no—
126C4⋊Dic11—41no—
127C4⋊Dic11—41no—
128C4⋊Dic11—41no—
129C4⋊Dic11—41no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—41no—
132C2×C11⋊C8—41no—
133C2×C11⋊C8—41no—
134C2×C11⋊C8—41no—
135C2×C11⋊C8—41no—
136C2×C11⋊C8—41no—
137C2×C11⋊C8—41no—
138C2×C11⋊C8—41no—
139#2537D1111yescharacteristic
140#1834—111no—
141#1802—111no—
142#1802—111no—
143C2×D4⋊C8—111no—
144C2×D4⋊C8—111no—
145#1296—111no—
146C23×C11—22no—
147C23×C11—22no—
148C23×C11—41no—
149C23×C11—41no—
150C23×C11—41no—
151C23×C11—41no—
152C23×C11—41no—
153C23×C11—41no—
154C23×C11—41no—
155C23×C11—41no—
156C23×C11—41no—
157C23×C11—41no—
158C23×C11—41no—
159C23×C11—41no—
160C23×C11#12011yescharacteristic
161D4×C11—22no—
162D4×C11—22no—
163D4×C11—22no—
164D4×C11—22no—
165D4×C11—41no—
166D4×C11—41no—
167D4×C11—41no—
168D4×C11—41no—
169D4×C11—88no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—42no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—42no—
179C2×C4×C11—41no—
180C2×C4×C11—42no—
181C2×C4×C11—81no—
182C2×C4×C11—81no—
183C2×C4×C11—81no—
184C2×C4×C11—81no—
185C2×C4×C11—81no—
186C2×C4×C11—81no—
187C2×C4×C11—81no—
188C2×C4×C11—81no—
189C2×C4×C11#12111yescharacteristic
190C2×C4×C11#12111yescharacteristic
191C2×C4×C11#12111yescharacteristic
192C2×C4×C11#12311yescharacteristic
193C2×C4×C11#12311yescharacteristic
194C2×C4×C11#12411yescharacteristic
195C2×C4×C11C2×D811yescharacteristic
196C2×C4×C11C2×SD1611yescharacteristic
197C2×C4×C11#13511yescharacteristic
198C2×C4×C11#13511yescharacteristic
199C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
200C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
201C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
202C2×C4×C11#13711yescharacteristic
203C2×Dic11—81no—
204C2×Dic11—81no—
205C2×Dic11—81no—
206C11⋊C8—42no—
207C11⋊C8—81no—
208C11⋊C8—81no—
209C2×#121—21no—
210C2×#121—21no—
211C2×C4×D4C2×D1111yescharacteristic
212C2×C4×D4C2×D1111yescharacteristic
213C2×C4⋊C8—111no—
214C2×C4⋊C8—111no—
215C2×#102—221no—
216C2×#102—221no—
217C2×C4×C8—111no—
218#394—22no—
219#384—111no—
220#384C2×D1111yescharacteristic
221#380—21no—
222#380—21no—
223#340—221no—
224#340—221no—
225#340—222no—
226D4⋊C8—222no—
227D4⋊C8—222no—
228C22×C11—42no—
229C22×C11—42no—
230C22×C11—42no—
231C22×C11—42no—
232C22×C11—42no—
233C22×C11—42no—
234C22×C11—81no—
235C22×C11—81no—
236C22×C11—81no—
237C22×C11—81no—
238C22×C11—81no—
239C22×C11—81no—
240C22×C11—81no—
241C22×C11—81no—
242C22×C11#39411yescharacteristic
243C22×C11#44711yescharacteristic
244C22×C11#44911yescharacteristic
245C22×C11#45011yescharacteristic
246C22×C11#45211yescharacteristic
247C22×C11#45411yescharacteristic
248C22×C11#45511yescharacteristic
249C4×C11—21no—
250C4×C11—21no—
251C4×C11—82no—
252C4×C11—81no—
253C4×C11—81no—
254C4×C11#46511yescharacteristic
255C4×C11#46611yescharacteristic
256C4×C11#46811yescharacteristic
257C4×C11#46911yescharacteristic
258C4×C11#48011yescharacteristic
259C4×C11#48111yescharacteristic
260C4×C11#48211yescharacteristic
261C4×C11#48211yescharacteristic
262Dic11—161no—
263C22×D4—22no—
264C22×D4C22⋊D1111yescharacteristic
265C22×D4C22⋊D1111yescharacteristic
266C23×C4—21no—
267C23×C4—21no—
268C22×C8—221no—
269C22×C8—221no—
270C22×C8—221no—
271#121—42no—
272#121—42no—
273#121—42no—
274#121—42no—
275C4×D4—21no—
276C4×D4—21no—
277C4×D4—21no—
278C4×D4—21no—
279C4×D4—21no—
280C4×D4—21no—
281C4×D4—21no—
282C4×D4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—221no—
286C2×C4⋊C4—221no—
287C2×C4⋊C4—221no—
288C2×C4⋊C4C22⋊D1111yescharacteristic
289C2×C4⋊C4C22⋊D1111yescharacteristic
290C2×C4⋊C4C22⋊D1112yes—
291C2×C22⋊C4—22no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—21no—
294C2×C22⋊C4—21no—
295C2×C42C22×D1111yescharacteristic
296C4⋊C8—221no—
297C4⋊C8—221no—
298C4⋊C8—221no—
299C4⋊C8—221no—
300#102—442no—
301#102—442no—
302C4×C8—112no—
303C4×C8—221no—
304#95—22no—
305C2×C11—82no—
306C2×C11—82no—
307C2×C11#162511yescharacteristic
308C2×C11#163511yescharacteristic
309C2×C11#163911yescharacteristic
310C2×C11#164611yescharacteristic
311C2×C11#203311yescharacteristic
312C2×C11#203411yescharacteristic
313C2×C11#204011yescharacteristic
314C24—21no—
315C24—21no—
316C2×D4—21no—
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—21no—
322C2×D4—21no—
323C2×D4—21no—
324C2×D4—21no—
325C2×D4—21no—
326C2×D4—44no—
327C2×D4—44no—
328C2×D4—82no—
329C2×D4#432312yes—
330C2×D4#432412yes—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—22no—
334C22×C4—41no—
335C22×C4—41no—
336C22×C4—41no—
337C22×C4—41no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4—41no—
344C22×C4—41no—
345C22×C4—41no—
346C22×C4—441no—
347C22×C4C2×C22⋊D1111yescharacteristic
348C22×C4C2×C22⋊D1111yescharacteristic
349C22×C4C2×C22⋊D1111yescharacteristic
350C2×C8—222no—
351C2×C8—441no—
352C2×C8—441no—
353C2×C8—441no—
354C2×C8—441no—
355C2×C8—441no—
356C2×C8—441no—
357C2×C8—441no—
358C2×C8—441no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—42no—
364C4⋊C4—41no—
365C4⋊C4—41no—
366C4⋊C4—41no—
367C4⋊C4—41no—
368C4⋊C4—442no—
369C4⋊C4—441no—
370C4⋊C4—441no—
371C4⋊C4—441no—
372C4⋊C4—441no—
373C22⋊C4—44no—
374C22⋊C4—44no—
375C22⋊C4—41no—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C22⋊C4—41no—
379C42D4×D1111yescharacteristic
380C42#434111yescharacteristic
381C42#434111yescharacteristic
382C42#434111yescharacteristic
383C11#1043111yescharacteristic, complemented, Sylow
384C23—22no—
385C23—22no—
386C23—41no—
387C23—41no—
388C23—41no—
389C23—41no—
390C23—41no—
391C23—41no—
392C23—41no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23#6700611yescharacteristic
399D4—22no—
400D4—22no—
401D4—22no—
402D4—22no—
403D4—41no—
404D4—41no—
405D4—41no—
406D4—41no—
407D4—88no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—41no—
411C2×C4—42no—
412C2×C4—41no—
413C2×C4—42no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—42no—
419C2×C4—81no—
420C2×C4—81no—
421C2×C4—81no—
422C2×C4—81no—
423C2×C4—81no—
424C2×C4—81no—
425C2×C4—81no—
426C2×C4—81no—
427C2×C4—881no—
428C2×C4—881no—
429C2×C4—881no—
430C2×C4C2×#432311yescharacteristic
431C2×C4#6698511yescharacteristic
432C2×C4#6698511yescharacteristic
433C2×C4C2×#432411yescharacteristic
434C2×C4#6698811yescharacteristic
435C2×C4#6698811yescharacteristic
436C2×C4#6698911yescharacteristic
437C2×C4#6699111yescharacteristic
438C2×C4#6699211yescharacteristic
439C2×C4#6699211yescharacteristic
440C2×C4#6700211yescharacteristic
441C2×C4#6700311yescharacteristic
442C2×C4#6700311yescharacteristic
443C2×C4#6700411yescharacteristic
444C8—442no—
445C8—881no—
446C8—881no—
447C22—42no—
448C22—42no—
449C22—42no—
450C22—42no—
451C22—42no—
452C22—42no—
453C22—81no—
454C22—81no—
455C22—81no—
456C22—81no—
457C22—81no—
458C22—81no—
459C22—81no—
460C22—81no—
461C22#1062283011yescharacteristic
462C22#1062283111yescharacteristic
463C22#1062283511yescharacteristic
464C22#1062285111yescharacteristic
465C22#1062285211yescharacteristic
466C22#1062285511yescharacteristic
467C22#1062285811yescharacteristic
468C4—21no—
469C4—21no—
470C4—82no—
471C4—81no—
472C4—81no—
473C4—1761no—
474C4#1062264611yescharacteristic
475C4#1062264711yescharacteristic
476C4#1062264811yescharacteristic
477C4#1062264811yescharacteristic
478C4#1062265111yescharacteristic
479C4#1062265211yescharacteristic
480C4#1062265411yescharacteristic
481C4#1062265511yescharacteristic
482C2—82no—
483C2—82no—
484C2#1306770511yescharacteristic
485C2#1306776711yescharacteristic
486C2#1306779511yescharacteristic
487C2#1306784411yescharacteristic
488C2#1306979511yescharacteristic
489C2#1306980211yescharacteristic
490C2#1306984211yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
Fitting, prime radicalC11×#2537C2
socleC23×C11#120
hypercenter#2537D11
hypocenterC11#10431
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2537

Complements

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

NH ≅ G/Ntype
1. #13068743C2semidirect
2. #13068616C2semidirect
3. #13068616C2semidirect
4. C2×D4⋊(C11⋊C8)C2semidirect
5. C2×D4⋊(C11⋊C8)C2semidirect
6. #13066499C2semidirect
68. C4×C11⋊C8D4semidirect
383. C11#10431semidirect

Maximal subgroups

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

subgroupindex
#130687432
#130686162
C2×D4⋊(C11⋊C8)2
#130664992
C11×#25372
#1043111