Finite Group Databasebeta

← #14782528

Subgroups — #14782528

Order 2816.

1038 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622417C212yesmaximal
2#13071105C211yesmaximal, characteristic
3#13071021C211yesmaximal, characteristic, complemented
4#13070037C212yesmaximal, complemented
5#13070033C212yesmaximal, complemented
6#13070024C211yesmaximal, characteristic, complemented
7#13070021C211yesmaximal, characteristic, complemented
8#13070020C211yesmaximal, characteristic, complemented
9#13068331C212yesmaximal, complemented
10D11×#336C211yesmaximal, characteristic, complemented
11C11×#2072C211yesmaximal, characteristic, complemented
12C22×#4343C2211yescharacteristic
13C22×C8×D11C2212yes—
14C2×#66945C2211yescharacteristic
15C2×#66945C2212yes—
16C2×C42×D11C2211yescharacteristic
17C2×C11×#103C2212yes—
18C11×#391C2211yescharacteristic
19C11×#384C2211yescharacteristic
20#10622843C2211yescharacteristic
21C2×#66899C2212yes—
22C2×#66885C2212yes—
23#10622601C2211yescharacteristic
24#10622600—21no—
25#10622600—21no—
26#10622590C2212yes—
27C4⋊C4×Dic11—21no—
28C4⋊C4×Dic11—21no—
29C2×#66873C2212yes—
30#10622552C2211yescharacteristic
31#10622548C2211yescharacteristic
32#10622417—28no—
33#10622279—21no—
34#10622279—21no—
35#10622278—21no—
36#10622278—21no—
37C11×#340C2212yes—
38C11×#336C2211yescharacteristic
39#10622189C2212yes—
40#10622188C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43#10622162C2211yescharacteristic
44C22×Q8×C11C2311yescharacteristic
45C2×#4343—22no—
46C2×#4343—24no—
47C2×#4343—24no—
48C2×#4343D414yes—
49C22×D44—21no—
50C22×D44C2311yescharacteristic
51C22×C4×D11—21no—
52C22×C4×D11D411yescharacteristic
53C22×C4×D11D411yescharacteristic
54C22×C4×D11C2311yescharacteristic
55C22×C8×C11C2312yes—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C4⋊C4C2312yes—
60C2×C42×C11C2311yescharacteristic
61C2×(C2×D11)⋊C4—21no—
62C2×(C2×D11)⋊C4—22no—
63C2×(C2×D11)⋊C4—21no—
64C2×(C2×D11)⋊C4—21no—
65C2×(C2×D11)⋊C4—21no—
66C2×(C2×D11)⋊C4—21no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11C2312yes—
70C2×C4⋊Dic11C2311yescharacteristic
71C2×C4×Dic11—21no—
72C2×C4×Dic11—22no—
73C2×C4×Dic11D411yescharacteristic
74C2×C4×Dic11D411yescharacteristic
75C2×C4×Dic11C2311yescharacteristic
76C22×C11⋊C8C2312yes—
77C2×C8×D11—24no—
78C2×C8×D11—24no—
79C2×C8×D11—24no—
80#66945—24no—
81#66945—24no—
82#66945—24no—
83C42×D11—24no—
84C11×#103—24no—
85C11×#95—21no—
86C11×#95—21no—
87#66899—24no—
88C11⋊#95—21no—
89C11⋊#95—21no—
90C11⋊#95—22no—
91C11⋊#95—22no—
92#66885—24no—
93#66873—24no—
94#23627—111nomaximal, Sylow
95C23×D11—21no—
96C23×D11C2×D411yescharacteristic
97C2×Q8×C11—21no—
98C2×Q8×C11—22no—
99C2×Q8×C11—22no—
100C2×Q8×C11C2×D412yes—
101C22×C4×C11—21no—
102C22×C4×C11—22no—
103C22×C4×C11—21no—
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2411yescharacteristic
107C22×Dic11—22no—
108C22×Dic11—21no—
109C22×Dic11C2×D411yescharacteristic
110C22×Dic11C2×D411yescharacteristic
111C22×Dic11C2×D411yescharacteristic
112#4343—216no—
113#4343—48no—
114C2×D44—24no—
115C2×D44—21no—
116C2×D44—22no—
117C2×D44—22no—
118C2×D44—42no—
119C2×D44—42no—
120C2×D44C2×D412yes—
121C2×C4×D11—24no—
122C2×C4×D11—22no—
123C2×C4×D11—22no—
124C2×C4×D11—22no—
125C2×C4×D11—22no—
126C2×C4×D11—41no—
127C2×C4×D11—41no—
128C2×C4×D11—42no—
129C2×C4×D11—42no—
130C2×C4×D11C2×D412yes—
131C2×C4×D11#4112yes—
132C2×C4×D11#4114yes—
133C2×C4×D11#4114yes—
134C2×C8×C11—22no—
135C2×C8×C11—22no—
136C2×C8×C11—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—42no—
141C11×C4⋊C4—42no—
142C42×C11—22no—
143(C2×D11)⋊C4—42no—
144(C2×D11)⋊C4—42no—
145(C2×D11)⋊C4—44no—
146(C2×D11)⋊C4—42no—
147(C2×D11)⋊C4—42no—
148(C2×D11)⋊C4—42no—
149C4⋊Dic11—22no—
150C4⋊Dic11—22no—
151C4⋊Dic11—22no—
152C4⋊Dic11—42no—
153C4⋊Dic11—42no—
154C4×Dic11—22no—
155C4×Dic11—22no—
156C4×Dic11—22no—
157C4×Dic11—44no—
158C4×Dic11—42no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—22no—
162C8×D11—48no—
163C2×#416—112no—
164#2297—111no—
165#2285—111no—
166#2074—112no—
167#2073—112no—
168#2072—111no—
169#2072D1111yescharacteristic, complemented
170#2071—111no—
171#2071—111no—
172#1735—112no—
173C2×#336—111no—
174C23×C11C22×D411yescharacteristic
175C22×D11—21no—
176C22×D11—21no—
177C22×D11—21no—
178C22×D11—21no—
179C22×D11—22no—
180C22×D11—41no—
181C22×D11—41no—
182C22×D11—41no—
183C22×D11—41no—
184C22×D11—41no—
185C22×D11—41no—
186C22×D11#12112yes—
187C22×D11#12312yes—
188C22×D11#12412yes—
189Q8×C11—24no—
190Q8×C11—42no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—22no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—42no—
199C2×C4×C11—41no—
200C2×C4×C11—42no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—42no—
204C2×C4×C11#13512yes—
205C2×C4×C11#13512yes—
206C2×C4×C11C22×D411yescharacteristic
207C2×C4×C11C2×#4112yes—
208C2×C4×C11C2×#4112yes—
209C2×C4×C11C2×#4111yescharacteristic
210C2×Dic11—21no—
211C2×Dic11—21no—
212C2×Dic11—21no—
213C2×Dic11—21no—
214C2×Dic11—21no—
215C2×Dic11—21no—
216C2×Dic11—42no—
217C2×Dic11—41no—
218C2×Dic11—42no—
219C2×Dic11—41no—
220C2×Dic11—41no—
221C2×Dic11—42no—
222C2×Dic11#12112yes—
223C2×Dic11#12312yes—
224C2×Dic11#12412yes—
225D44—24no—
226D44—48no—
227D44—42no—
228C4×D11—44no—
229C4×D11—44no—
230C4×D11—48no—
231C4×D11#12318yes—
232C4×D11#12618yes—
233C8×C11—42no—
234C11⋊C8—42no—
235C22×#41—111no—
236C23×C8—112no—
237C2×#117—112no—
238C2×#117—111no—
239C22×C42—111no—
240#416—228no—
241C2×#103—112no—
242C2×#103C2×D1112yes—
243C2×#102—112no—
244C2×#102—112no—
245#391—111no—
246#391C2×D1111yescharacteristic
247#390—111no—
248#390—111no—
249#386—221no—
250#386—221no—
251#384—111no—
252#384C2×D1111yescharacteristic
253#382—112no—
254#380—221no—
255#380—221no—
256C4×C4⋊C4—221no—
257C4×C4⋊C4—221no—
258C4×C22⋊C4—221no—
259C4×C22⋊C4—221no—
260#340—112no—
261#340—112no—
262#340—112no—
263#340C2×D1112yes—
264#336—112no—
265#336—111no—
266#336C2×D1111yescharacteristic
267C22×C11C2×#12111yescharacteristic
268C22×C11C2×#12311yescharacteristic
269C22×C11C2×#12411yescharacteristic
270C22×C11C2×#13511yescharacteristic
271C22×C11C2×#13511yescharacteristic
272C22×C11#57511yescharacteristic
273C22×C11#57511yescharacteristic
274C2×D11—22no—
275C2×D11—22no—
276C2×D11—22no—
277C2×D11—22no—
278C2×D11—22no—
279C2×D11—22no—
280C2×D11—42no—
281C2×D11—42no—
282C2×D11—42no—
283C2×D11—81no—
284C2×D11—81no—
285C2×D11—81no—
286C2×D11—81no—
287C2×D11#39714yes—
288C4×C11—22no—
289C4×C11—22no—
290C4×C11—42no—
291C4×C11—81no—
292C4×C11—82no—
293C4×C11C2×#12312yes—
294C4×C11C2×#12612yes—
295Dic11—41no—
296Dic11—41no—
297Dic11—81no—
298Dic11—82no—
299Dic11#39714yes—
300C2×#41—114no—
301C2×#41—222no—
302C2×#41—224no—
303C2×#41—224no—
304C22×Q8C22×D1111yescharacteristic
305C22×D4—111no—
306C22×D4—221no—
307C23×C4—111no—
308C23×C4—111no—
309C23×C4—111no—
310C23×C4—221no—
311C22×C8—112no—
312C22×C8—224no—
313C22×C8—224no—
314C22×C8—224no—
315C22×C8C22×D1112yes—
316#117—224no—
317#117—224no—
318#117—224no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—111no—
322C2×C4⋊C4—112no—
323C2×C4⋊C4—221no—
324C2×C4⋊C4—221no—
325C2×C4⋊C4C22×D1111yescharacteristic
326C2×C4⋊C4C22×D1112yes—
327C2×C22⋊C4—221no—
328C2×C22⋊C4—221no—
329C2×C22⋊C4—222no—
330C2×C22⋊C4—221no—
331C2×C22⋊C4—221no—
332C2×C22⋊C4—221no—
333C2×C42—111no—
334C2×C42—111no—
335C2×C42—111no—
336C2×C42—224no—
337C2×C42—221no—
338C2×C42—222no—
339C2×C42C22×D1111yescharacteristic
340#103—24no—
341#103—224no—
342#102—224no—
343#102—224no—
344#95—21no—
345#95—21no—
346#95—221no—
347#95—221no—
348#95—222no—
349#95—222no—
350C2×C11C2×#39711yescharacteristic
351C2×C11#303511yescharacteristic
352C2×C11#303511yescharacteristic
353C2×C11#309111yescharacteristic
354C2×C11#309111yescharacteristic
355C2×C11#313111yescharacteristic
356C2×C11#313511yescharacteristic
357D11—24no—
358D11—82no—
359C24—111no—
360C24—221no—
361#41—2216no—
362#41—448no—
363C2×Q8—21no—
364C2×Q8—22no—
365C2×Q8—22no—
366C2×Q8D4×D1112yes—
367C2×D4—112no—
368C2×D4—224no—
369C2×D4—222no—
370C2×D4—222no—
371C2×D4—221no—
372C2×D4—442no—
373C2×D4—442no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—111no—
378C22×C4—112no—
379C22×C4—114no—
380C22×C4—112no—
381C22×C4—114no—
382C22×C4—111no—
383C22×C4—111no—
384C22×C4—224no—
385C22×C4—222no—
386C22×C4—222no—
387C22×C4—222no—
388C22×C4—222no—
389C22×C4—221no—
390C22×C4—222no—
391C22×C4—441no—
392C22×C4—441no—
393C22×C4—442no—
394C22×C4—442no—
395C22×C4D4×D1111yescharacteristic
396C22×C4D4×D1111yescharacteristic
397C22×C4C23×D1111yescharacteristic
398C2×C8—22no—
399C2×C8—22no—
400C2×C8—22no—
401C2×C8—222no—
402C2×C8—222no—
403C2×C8—222no—
404C2×C8—448no—
405C4⋊C4—22no—
406C4⋊C4—22no—
407C4⋊C4—22no—
408C4⋊C4—42no—
409C4⋊C4—42no—
410C4⋊C4—222no—
411C4⋊C4—222no—
412C4⋊C4—222no—
413C4⋊C4—442no—
414C4⋊C4—442no—
415C22⋊C4—442no—
416C22⋊C4—442no—
417C22⋊C4—444no—
418C22⋊C4—442no—
419C22⋊C4—442no—
420C22⋊C4—442no—
421C42—22no—
422C42—222no—
423C42—222no—
424C42—222no—
425C42—444no—
426C42—442no—
427C11#2362711yescharacteristic, complemented, Sylow
428C23—112no—
429C23—112no—
430C23—112no—
431C23—221no—
432C23—221no—
433C23—221no—
434C23—221no—
435C23—222no—
436C23—441no—
437C23—441no—
438C23—441no—
439C23—441no—
440C23—441no—
441C23—441no—
442C23C2×D4×D1111yescharacteristic
443Q8—24no—
444Q8—42no—
445D4—224no—
446D4—448no—
447D4—442no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—22no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—41no—
457C2×C4—42no—
458C2×C4—41no—
459C2×C4—42no—
460C2×C4—41no—
461C2×C4—112no—
462C2×C4—112no—
463C2×C4—112no—
464C2×C4—118no—
465C2×C4—118no—
466C2×C4—221no—
467C2×C4—221no—
468C2×C4—221no—
469C2×C4—221no—
470C2×C4—221no—
471C2×C4—221no—
472C2×C4—444no—
473C2×C4—444no—
474C2×C4—448no—
475C2×C4—441no—
476C2×C4—441no—
477C2×C4—442no—
478C2×C4—442no—
479C2×C4—442no—
480C2×C4—441no—
481C2×C4#6696912yes—
482C2×C4#6697212yes—
483C2×C4C2×D4×D1111yescharacteristic
484C2×C4#41×D1111yescharacteristic
485C2×C4#41×D1112yes—
486C2×C4#41×D1112yes—
487C8—42no—
488C8—442no—
489C22—114no—
490C22—222no—
491C22—222no—
492C22—222no—
493C22—222no—
494C22—222no—
495C22—222no—
496C22—442no—
497C22—442no—
498C22—442no—
499C22—881no—
500C22—881no—
501C22—881no—
502C22—881no—
503C22D11×#12111yescharacteristic
504C22D11×#12311yescharacteristic
505C22D11×#12411yescharacteristic
506C22C2×#6696911yescharacteristic
507C22C2×#6697211yescharacteristic
508C22#1062330411yescharacteristic
509C22#1062330811yescharacteristic
510C4—22no—
511C4—22no—
512C4—42no—
513C4—82no—
514C4—81no—
515C4—114no—
516C4—441no—
517C4—441no—
518C4—882no—
519C4—881no—
520C4D11×#12312yes—
521C4D11×#12612yes—
522C2—224no—
523C2—882no—
524C2D11×#39711yescharacteristic
525C2#1307806611yescharacteristic
526C2#1307807411yescharacteristic
527C2#1307853011yescharacteristic
528C2#1307853211yescharacteristic
529C2#1307894011yescharacteristic
530C2#1307895811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2072C2
socleC23×C11C22×D4
prime radicalC22×#4343C22
hypercenter#2072D11
hypocenterC11#23627
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2072

Complements

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

NH ≅ G/Ntype
3. #13071021C2semidirect
4. #13070037C2semidirect
5. #13070033C2semidirect
6. #13070024C2semidirect
7. #13070021C2semidirect
8. #13070020C2semidirect
9. #13068331C2semidirect
10. D11×#336C2semidirect
11. C11×#2072C2semidirect
169. #2072D11semidirect
427. C11#23627semidirect

Maximal subgroups

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

subgroupindex
C2×#106224172
#130711052
#130710212
#130700372
#130700332
#130700242
#130700212
#130700202
#130683312
D11×#3362
C11×#20722
#2362711