Finite Group Databasebeta

← #14657281

Subgroups — #14657281

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#13073529C211yesmaximal, characteristic
2#13068744C211yesmaximal, characteristic, complemented
3#13068617C211yesmaximal, characteristic, complemented
4#13068616C211yesmaximal, characteristic, complemented
5C2×#10622097C211yesmaximal, characteristic, complemented
6#13066500C211yesmaximal, characteristic, complemented
7C2×C11×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×C4×D4×C11C2211yescharacteristic
9C2×#66991—21no—
10C2×#66983—21no—
11C2×C4×D44C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13C2×C4×C8×C11C2211yescharacteristic
14C2×#66896—21no—
15#10622825—21no—
16C2×#66885—21no—
17#10622600—21no—
18#10622574—22no—
19#10622548C2211yescharacteristic
20#10622548C2211yescharacteristic
21C2×C4⋊(C11⋊C8)C2211yescharacteristic
22C11×D4⋊C8—22no—
23#10622189—21no—
24#10622189—22no—
25#10622167—21no—
26#10622097—22no—
27C22×D4×C11D411yescharacteristic
28C23×C4×C11—21no—
29C22×C22⋊D11—22no—
30C22×D44D411yescharacteristic
31C22×C4×D11—21no—
32C22×C8×C11—21no—
33C22×C8×C11—21no—
34C4×D4×C11—21no—
35C4×D4×C11—21no—
36C4×D4×C11—21no—
37C4×D4×C11—21no—
38C2×C11×C4⋊C4D411yescharacteristic
39C2×C11×C22⋊C4—21no—
40C2×C42×C11C2311yescharacteristic
41C2×C22⋊Dic11—22no—
42#66991—42no—
43#66991—42no—
44#66983—42no—
45#66983—42no—
46C2×(C2×D11)⋊C4—22no—
47C2×(C2×D11)⋊C4—21no—
48C2×C4⋊Dic11—21no—
49C2×C4⋊Dic11—21no—
50C2×C4⋊Dic11—21no—
51C2×C4⋊Dic11—21no—
52C2×C4⋊Dic11—21no—
53C2×C4⋊Dic11D411yescharacteristic
54C2×C4⋊Dic11D412yes—
55C22×C11⋊C8—21no—
56C4×D44—21no—
57C4×D44—21no—
58C4×D44—21no—
59C4×D44—21no—
60C11×C4⋊C8—21no—
61C11×C4⋊C8—21no—
62C4×C8×C11—21no—
63C4×C8×C11D412yescomplemented
64#66896—42no—
65C11⋊#95—22no—
66#66885—42no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)—21no—
69#10431—111nomaximal, Sylow
70C24×C11—21no—
71C23×D11—21no—
72C2×D4×C11—21no—
73C2×D4×C11—21no—
74C2×D4×C11—21no—
75C2×D4×C11—21no—
76C2×D4×C11—21no—
77C2×D4×C11D812yes—
78C22×C4×C11—21no—
79C22×C4×C11—41no—
80C22×C4×C11—41no—
81C22×C4×C11—41no—
82C22×C4×C11—41no—
83C22×C4×C11—41no—
84C22×C4×C11—41no—
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C2×C22⋊D11—44no—
89C2×C22⋊D11—44no—
90C2×C22⋊D11—82no—
91C22×Dic11—21no—
92C22×Dic11—22no—
93C22×Dic11—41no—
94C2×D44—21no—
95C2×D44—21no—
96C2×D44—21no—
97C2×D44—21no—
98C2×D44—21no—
99C2×D44SD1612yes—
100C2×C4×D11—41no—
101C2×C4×D11—41no—
102C2×C4×D11—41no—
103C2×C4×D11—41no—
104C2×C4×D11—41no—
105C2×C4×D11—41no—
106C2×C8×C11—22no—
107C2×C8×C11—41no—
108C2×C8×C11—41no—
109C2×C8×C11—41no—
110C2×C8×C11—41no—
111C2×C8×C11—41no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—21no—
114C11×C22⋊C4—41no—
115C11×C22⋊C4—41no—
116C42×C11C2×D411yescharacteristic
117C42×C11#4111yescharacteristic
118C42×C11#4111yescharacteristic
119C42×C11#4111yescharacteristic
120C22⋊Dic11—44no—
121(C2×D11)⋊C4—44no—
122(C2×D11)⋊C4—41no—
123(C2×D11)⋊C4—41no—
124C4⋊Dic11—21no—
125C4⋊Dic11—21no—
126C4⋊Dic11—42no—
127C4⋊Dic11—42no—
128C4⋊Dic11—41no—
129C4⋊Dic11—41no—
130C4⋊Dic11—41no—
131C4⋊Dic11—41no—
132C4⋊Dic11—41no—
133C4⋊Dic11—41no—
134C4⋊Dic11—41no—
135C4⋊Dic11—41no—
136C2×C11⋊C8—41no—
137C2×C11⋊C8—41no—
138C2×C11⋊C8—41no—
139#2537—111no—
140#1834—111no—
141#1802—111no—
142#1802—111no—
143C2×D4⋊C8—111no—
144C2×D4⋊C8D1111yescharacteristic, complemented
145#1296—111no—
146C23×C11—22no—
147C23×C11—41no—
148C23×C11—41no—
149C23×C11—41no—
150C23×C11—41no—
151C23×C11—41no—
152C23×C11—41no—
153C23×C11#12011yescharacteristic
154C22×D11—22no—
155C22×D11—41no—
156C22×D11—41no—
157C22×D11—41no—
158C22×D11—41no—
159C22×D11—41no—
160C22×D11—41no—
161D4×C11—22no—
162D4×C11—22no—
163D4×C11—41no—
164D4×C11—41no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—81no—
171C2×C4×C11—81no—
172C2×C4×C11—81no—
173C2×C4×C11—81no—
174C2×C4×C11#12111yescharacteristic
175C2×C4×C11#12111yescharacteristic
176C2×C4×C11#12111yescharacteristic
177C2×C4×C11#12311yescharacteristic
178C2×C4×C11#12311yescharacteristic
179C2×C4×C11#12411yescharacteristic
180C2×C4×C11C2×D811yescharacteristic
181C2×C4×C11C2×SD1611yescharacteristic
182C2×C4×C11#13511yescharacteristic
183C2×C4×C11#13511yescharacteristic
184C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
185C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
186C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
187C2×C4×C11#13711yescharacteristic
188C22⋊D11—88no—
189C2×Dic11—41no—
190C2×Dic11—42no—
191C2×Dic11—41no—
192C2×Dic11—42no—
193C2×Dic11—41no—
194C2×Dic11—42no—
195C2×Dic11—81no—
196C2×Dic11—81no—
197C2×Dic11—81no—
198D44—22no—
199D44—22no—
200D44—41no—
201D44—41no—
202C4×D11—81no—
203C4×D11—81no—
204C4×D11—81no—
205C4×D11—81no—
206C8×C11—42no—
207C8×C11—81no—
208C11⋊C8—81no—
209C2×#121—221no—
210C2×#121—221no—
211C2×C4×D4—111no—
212C2×C4×D4C2×D1111yescharacteristic
213C2×C4⋊C8—111no—
214C2×C4⋊C8C2×D1111yescharacteristic
215C2×#102—221no—
216C2×#102—221no—
217C2×C4×C8C2×D1111yescharacteristic
218#394—222no—
219#384—111no—
220#384—111no—
221#380—221no—
222#380—221no—
223#340—221no—
224#340—222no—
225#340—221no—
226D4⋊C8—22no—
227D4⋊C8—222no—
228C22×C11—42no—
229C22×C11—42no—
230C22×C11—42no—
231C22×C11—81no—
232C22×C11—81no—
233C22×C11—81no—
234C22×C11—81no—
235C22×C11#39411yescharacteristic
236C22×C11#44711yescharacteristic
237C22×C11#44911yescharacteristic
238C22×C11#45011yescharacteristic
239C22×C11#45211yescharacteristic
240C22×C11#45411yescharacteristic
241C22×C11#45511yescharacteristic
242C2×D11—42no—
243C2×D11—42no—
244C2×D11—42no—
245C2×D11—81no—
246C2×D11—81no—
247C2×D11—81no—
248C2×D11—81no—
249C4×C11—21no—
250C4×C11—21no—
251C4×C11—81no—
252C4×C11#46511yescharacteristic
253C4×C11#46611yescharacteristic
254C4×C11#46811yescharacteristic
255C4×C11#46911yescharacteristic
256C4×C11#48011yescharacteristic
257C4×C11#48111yescharacteristic
258C4×C11#48211yescharacteristic
259C4×C11#48211yescharacteristic
260Dic11—82no—
261Dic11—81no—
262Dic11—161no—
263C22×D4—111no—
264C22×D4—222no—
265C22×D4D4411yescharacteristic
266C23×C4—21no—
267C23×C4—221no—
268C22×C8—21no—
269C22×C8—21no—
270C22×C8—221no—
271#121—442no—
272#121—442no—
273#121—442no—
274#121—442no—
275C4×D4—21no—
276C4×D4—21no—
277C4×D4—21no—
278C4×D4—21no—
279C4×D4—221no—
280C4×D4—221no—
281C4×D4—221no—
282C4×D4—221no—
283C2×C4⋊C4—111no—
284C2×C4⋊C4—112no—
285C2×C4⋊C4—221no—
286C2×C4⋊C4—221no—
287C2×C4⋊C4—221no—
288C2×C4⋊C4—221no—
289C2×C4⋊C4—221no—
290C2×C4⋊C4D4411yescharacteristic
291C2×C22⋊C4—21no—
292C2×C22⋊C4—222no—
293C2×C22⋊C4—222no—
294C2×C22⋊C4—221no—
295C2×C42C22×D1111yescharacteristic
296C4⋊C8—21no—
297C4⋊C8—21no—
298C4⋊C8—221no—
299C4⋊C8—221no—
300#102—442no—
301#102—442no—
302C4×C8—21no—
303C4×C8C22⋊D1112yescomplemented
304#95—222no—
305C2×C11—82no—
306C2×C11#162511yescharacteristic
307C2×C11#163511yescharacteristic
308C2×C11#163911yescharacteristic
309C2×C11#164611yescharacteristic
310C2×C11#203311yescharacteristic
311C2×C11#203411yescharacteristic
312C2×C11#204011yescharacteristic
313D11—82no—
314C24—21no—
315C24—221no—
316C2×D4—21no—
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—112no—
322C2×D4—221no—
323C2×D4—221no—
324C2×D4—221no—
325C2×D4—221no—
326C2×D4—221no—
327C2×D4—444no—
328C2×D4—444no—
329C2×D4—882no—
330C2×D4D8812yes—
331C22×C4—21no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4—41no—
335C22×C4—41no—
336C22×C4—41no—
337C22×C4—41no—
338C22×C4—221no—
339C22×C4—222no—
340C22×C4—441no—
341C22×C4—441no—
342C22×C4—441no—
343C22×C4—441no—
344C22×C4—441no—
345C22×C4—441no—
346C22×C4—441no—
347C22×C4C2×D4411yescharacteristic
348C22×C4D4×D1111yescharacteristic
349C22×C4D4×D1111yescharacteristic
350C2×C8—22no—
351C2×C8—41no—
352C2×C8—41no—
353C2×C8—41no—
354C2×C8—41no—
355C2×C8—41no—
356C2×C8—441no—
357C2×C8—441no—
358C2×C8—441no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—221no—
362C4⋊C4—221no—
363C4⋊C4—442no—
364C4⋊C4—442no—
365C4⋊C4—441no—
366C4⋊C4—441no—
367C4⋊C4—441no—
368C4⋊C4—441no—
369C4⋊C4—441no—
370C4⋊C4—441no—
371C4⋊C4—441no—
372C4⋊C4—441no—
373C22⋊C4—41no—
374C22⋊C4—41no—
375C22⋊C4—444no—
376C22⋊C4—444no—
377C22⋊C4—441no—
378C22⋊C4—441no—
379C42#433911yescharacteristic
380C42#434111yescharacteristic
381C42#434111yescharacteristic
382C42C2×C22⋊D1111yescharacteristic
383C11#1043111yescharacteristic, complemented, Sylow
384C23—22no—
385C23—41no—
386C23—41no—
387C23—41no—
388C23—41no—
389C23—41no—
390C23—41no—
391C23—222no—
392C23—441no—
393C23—441no—
394C23—441no—
395C23—441no—
396C23—441no—
397C23—441no—
398C23#6693511yescharacteristic
399D4—22no—
400D4—22no—
401D4—41no—
402D4—41no—
403D4—222no—
404D4—222no—
405D4—441no—
406D4—441no—
407D4—888no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—81no—
414C2×C4—81no—
415C2×C4—81no—
416C2×C4—81no—
417C2×C4—441no—
418C2×C4—441no—
419C2×C4—442no—
420C2×C4—441no—
421C2×C4—442no—
422C2×C4—442no—
423C2×C4—881no—
424C2×C4—881no—
425C2×C4—881no—
426C2×C4—881no—
427C2×C4—881no—
428C2×C4—881no—
429C2×C4—881no—
430C2×C4#6693611yescharacteristic
431C2×C4#6693811yescharacteristic
432C2×C4#6693911yescharacteristic
433C2×C4C2×D8811yescharacteristic
434C2×C4#6695711yescharacteristic
435C2×C4#6696111yescharacteristic
436C2×C4#6696211yescharacteristic
437C2×C4#6696411yescharacteristic
438C2×C4#6696411yescharacteristic
439C2×C4SD16×D1111yescharacteristic
440C2×C4#6696911yescharacteristic
441C2×C4#6698311yescharacteristic
442C2×C4#6699111yescharacteristic
443C2×C4#6699211yescharacteristic
444C8—42no—
445C8—81no—
446C8—881no—
447C22—42no—
448C22—42no—
449C22—42no—
450C22—81no—
451C22—81no—
452C22—81no—
453C22—81no—
454C22—442no—
455C22—442no—
456C22—442no—
457C22—881no—
458C22—881no—
459C22—881no—
460C22—881no—
461C22#1062234511yescharacteristic
462C22#1062234611yescharacteristic
463C22#1062238911yescharacteristic
464C22#1062239411yescharacteristic
465C22#1062243811yescharacteristic
466C22#1062244011yescharacteristic
467C22#1062257411yescharacteristic
468C4—21no—
469C4—21no—
470C4—81no—
471C4—882no—
472C4—881no—
473C4—1761no—
474C4#1062234911yescharacteristic
475C4#1062235011yescharacteristic
476C4#1062239011yescharacteristic
477C4#1062239211yescharacteristic
478C4#1062272811yescharacteristic
479C4#1062274711yescharacteristic
480C4#1062277211yescharacteristic
481C4#1062278411yescharacteristic
482C2—82no—
483C2—882no—
484C2#1306770711yescharacteristic
485C2#1306777011yescharacteristic
486C2#1306779711yescharacteristic
487C2#1306784711yescharacteristic
488C2#1306979911yescharacteristic
489C2#1306980411yescharacteristic
490C2#1306984411yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×D4⋊C8C2
socleC23×C11#120
prime radical#13073529C2
hypercenterC2×D4⋊C8D11
hypocenterC11#10431
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #13068744C2semidirect
3. #13068617C2semidirect
4. #13068616C2semidirect
5. C2×#10622097C2semidirect
6. #13066500C2semidirect
7. C2×C11×D4⋊C8C2semidirect
63. C4×C8×C11D4semidirect
144. C2×D4⋊C8D11semidirect
303. C4×C8C22⋊D11semidirect
383. C11#10431semidirect

Maximal subgroups

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

subgroupindex
#130735292
#130687442
#130686172
#130686162
C2×#106220972
#130665002
C2×C11×D4⋊C82
#1043111