Finite Group Databasebeta

← #14788693

Subgroups — #14788693

Order 2816.

1084 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623101C211yesmaximal, characteristic, complemented
2C2×#10622632C211yesmaximal, characteristic
3C2×#10622631C211yesmaximal, characteristic
4#13069862C212yesmaximal, complemented
5#13069698C212yesmaximal
6#13069557C211yesmaximal, characteristic, complemented
7#13069435C211yesmaximal, characteristic, complemented
8#13068974C212yesmaximal
9#13068869C212yesmaximal, complemented
10#13068628C211yesmaximal, characteristic, complemented
11C11×#2580C211yesmaximal, characteristic
12C2×C4×Q8×C11C2211yescharacteristic
13C2×C4×D4×C11C2211yescharacteristic
14C2×Q8×Dic11—21no—
15C22×#4324C2211yescharacteristic
16C22×#4324C2212yes—
17#10623101—24no—
18#10623101—24no—
19C2×#66943—22no—
20C2×#66943—21no—
21C2×#66922C2212yes—
22C2×#66922C2211yescharacteristic
23C2×C4×Dic22C2212yes—
24C2×C4×Dic22C2211yescharacteristic
25C11×#399—21no—
26C11×#393—21no—
27C11×#390C2212yes—
28C11×#389C2212yes—
29C11×#385—22no—
30C11×#382C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32#10622632—24no—
33#10622631—24no—
34C2×#66874C2212yes—
35C2×#66874C2211yescharacteristic
36C2×#66874C2212yes—
37C2×#66874C2212yes—
38C2×#66874C2212yes—
39C2×#66871C2211yescharacteristic
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×#66867C2211yescharacteristic
42#10622167C2212yes—
43#10622162C2212yes—
44#10622162C2212yes—
45C22×Q8×C11D411yescharacteristic
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C22×Dic22C2312yes—
49C22×Dic22C2311yescharacteristic
50C4×Q8×C11—22no—
51C4×Q8×C11—22no—
52C4×D4×C11—22no—
53C4×D4×C11—22no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4D412yes—
56C2×C11×C4⋊C4D411yescharacteristic
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C4⋊C4C2312yes—
59C2×C11×C22⋊C4—21no—
60C2×C11×C22⋊C4—22no—
61C2×C11×C22⋊C4—22no—
62C2×C42×C11C2312yes—
63C2×C42×C11C2311yescharacteristic
64Q8×Dic11—28no—
65C2×#4324—22no—
66C2×#4324—22no—
67C2×#4324—24no—
68C2×#4324—24no—
69C2×#4324—22no—
70C2×#4324—42no—
71C2×C4⋊Dic11—22no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11—22no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11C2311yescharacteristic
76C2×Dic11⋊C4—22no—
77C2×Dic11⋊C4—21no—
78C2×C4×Dic11—22no—
79C2×C4×Dic11—21no—
80C22×C11⋊C8C2311yescharacteristic
81C22×C11⋊C8C2312yes—
82C22×C11⋊C8C2311yescharacteristic
83#66943—216no—
84#66943—28no—
85#66922—24no—
86#66922—24no—
87#66922—22no—
88#66922D414yes—
89C4×Dic22—24no—
90C4×Dic22—22no—
91C4×Dic22—24no—
92C4×Dic22D414yes—
93C11×#95—21no—
94C11×#95—21no—
95C11×#95—22no—
96#66896—22no—
97#66874—22no—
98#66874—24no—
99#66874—24no—
100#66874—42no—
101#66874—42no—
102#66871—22no—
103C4⋊(C11⋊C8)—22no—
104#66867—22no—
105#24199—111nomaximal, Sylow
106C24×C11—21no—
107C2×Q8×C11—22no—
108C2×Q8×C11—24no—
109C2×D4×C11—21no—
110C2×D4×C11—21no—
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11—21no—
114C2×D4×C11#4112yes—
115C22×C4×C11—22no—
116C22×C4×C11—21no—
117C22×C4×C11—42no—
118C22×C4×C11—82no—
119C22×C4×C11C2×D412yes—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2411yescharacteristic
124C22×Dic11—21no—
125C22×Dic11—22no—
126C22×Dic11—21no—
127C2×Dic22—22no—
128C2×Dic22—21no—
129C2×Dic22—22no—
130C2×Dic22—21no—
131C2×Dic22—22no—
132C2×Dic22—21no—
133C2×Dic22—21no—
134C2×Dic22—22no—
135C2×Dic22—21no—
136C2×Dic22—22no—
137C2×Dic22C2×D414yes—
138C2×Dic22C2×D412yes—
139C11×C4⋊C4—24no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—82no—
146C11×C22⋊C4—42no—
147C11×C22⋊C4—44no—
148C11×C22⋊C4—82no—
149C42×C11—22no—
150C42×C11—22no—
151C42×C11C2×D412yes—
152C42×C11C2×D412yes—
153#4324—28no—
154#4324—48no—
155C4⋊Dic11—28no—
156C4⋊Dic11—28no—
157C4⋊Dic11—24no—
158C4⋊Dic11—24no—
159C4⋊Dic11—21no—
160C4⋊Dic11C2×D412yes—
161Dic11⋊C4—28no—
162Dic11⋊C4—24no—
163C4×Dic11—28no—
164C4×Dic11—24no—
165C2×C11⋊C8—21no—
166C2×C11⋊C8—21no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—21no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—21no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—21no—
173C2×C11⋊C8#4112yes—
174C2×#557—111no—
175C2×#461—111no—
176C2×#440—111no—
177#2580D1111yescharacteristic
178#2043—112no—
179#2013—112no—
180#1985—111no—
181#1960—111no—
182#1880—112no—
183#1863—112no—
184#1805—111no—
185C23×C11—22no—
186C23×C11—41no—
187C23×C11—41no—
188C23×C11—42no—
189C23×C11—42no—
190C23×C11C22×D411yescharacteristic
191Q8×C11—28no—
192D4×C11—22no—
193D4×C11—22no—
194D4×C11—41no—
195D4×C11—41no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—41no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—84no—
209C2×C4×C11#12012yes—
210C2×C4×C11#12012yes—
211C2×C4×C11#13714yes—
212C2×C4×C11C22×D411yescharacteristic
213C2×C4×C11C22×D411yescharacteristic
214C2×C4×C11C2×#4111yescharacteristic
215C2×C4×C11C2×#4111yescharacteristic
216C2×C4×C11H(5,𝔽2)11yescharacteristic
217C2×C4×C112−1+411yescharacteristic
218C2×Dic11—22no—
219C2×Dic11—24no—
220C2×Dic11—22no—
221C2×Dic11—41no—
222C2×Dic11—42no—
223C2×Dic11—42no—
224C2×Dic11—41no—
225C2×Dic11—42no—
226Dic22—22no—
227Dic22—22no—
228Dic22—24no—
229Dic22—24no—
230Dic22—42no—
231Dic22—42no—
232Dic22—41no—
233Dic22—41no—
234C11⋊C8—22no—
235C11⋊C8—41no—
236C11⋊C8—42no—
237C22×SD16—111no—
238C22×SD16—112no—
239#557—224no—
240#557—224no—
241C2×C4⋊Q8—111no—
242C2×C4⋊Q8—112no—
243C2×#125—222no—
244C2×#125—221no—
245C2×C4×Q8—111no—
246C2×C4×Q8—112no—
247C2×C4×Q8—221no—
248C2×C4×Q8C2×D1111yescharacteristic
249C2×C4×D4C2×D1111yescharacteristic
250#461—224no—
251#440—224no—
252C2×#107—111no—
253C2×C4⋊C8—111no—
254C2×#103—112no—
255C2×#103—112no—
256C2×#103—111no—
257C2×#103—112no—
258C2×#103—112no—
259C2×#102—111no—
260C2×#97—111no—
261#399—21no—
262#393—21no—
263#390C2×D1112yes—
264#389C2×D1112yes—
265#385—22no—
266#382C2×D1111yescharacteristic
267#340—112no—
268#336—112no—
269#336—112no—
270C22×C11—44no—
271C22×C11—42no—
272C22×C11—82no—
273C22×C11—81no—
274C22×C11—81no—
275C22×C11C2×#12011yescharacteristic
276C22×C11#54811yescharacteristic
277C22×C11#55011yescharacteristic
278C22×C11C2×#13712yes—
279C22×C11#57712yes—
280C4×C11—22no—
281C4×C11—24no—
282C4×C11—22no—
283C4×C11—42no—
284C4×C11—82no—
285C4×C11—81no—
286C4×C11#52511yescharacteristic
287C4×C11#53711yescharacteristic
288C4×C11#54611yescharacteristic
289C4×C11#54711yescharacteristic
290Dic11—42no—
291Dic11—44no—
292Dic11—42no—
293C22×Q8—111no—
294C22×Q8—112no—
295C22×Q8C22⋊D1111yescharacteristic
296C22×D4C22×D1111yescharacteristic
297C23×C4—21no—
298C2×SD16—222no—
299C2×SD16—222no—
300C2×SD16—222no—
301C2×SD16—224no—
302C2×SD16—224no—
303C2×SD16—442no—
304C22×C8—111no—
305C22×C8—112no—
306C22×C8—111no—
307C4⋊Q8—114no—
308C4⋊Q8—224no—
309C4⋊Q8—224no—
310C4⋊Q8—222no—
311#125—2216no—
312#125—228no—
313C4×Q8—22no—
314C4×Q8—22no—
315C4×Q8—114no—
316C4×Q8—224no—
317C4×Q8—224no—
318C4×Q8—228no—
319C4×Q8—222no—
320C4×D4—22no—
321C4×D4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—111no—
324C2×C4⋊C4—222no—
325C2×C4⋊C4—221no—
326C2×C4⋊C4—222no—
327C2×C4⋊C4—221no—
328C2×C4⋊C4—222no—
329C2×C4⋊C4—221no—
330C2×C4⋊C4C22⋊D1112yes—
331C2×C4⋊C4C22⋊D1111yescharacteristic
332C2×C4⋊C4C22×D1111yescharacteristic
333C2×C4⋊C4C22×D1112yes—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—22no—
337C2×C42—222no—
338C2×C42—221no—
339C2×C42C22×D1112yes—
340C2×C42C22×D1111yescharacteristic
341#107—222no—
342C4⋊C8—222no—
343#103—224no—
344#103—222no—
345#103—224no—
346#103—442no—
347#103—442no—
348#102—222no—
349#97—222no—
350#95—21no—
351#95—21no—
352#95—22no—
353C2×C11—82no—
354C2×C11#240711yescharacteristic
355C2×C11#300411yescharacteristic
356C2×C11#301011yescharacteristic
357C2×C11#337212yes—
358C2×C11#340012yes—
359C24—21no—
360C2×Q8—22no—
361C2×Q8—24no—
362C2×Q8—112no—
363C2×Q8—114no—
364C2×Q8—222no—
365C2×Q8—221no—
366C2×Q8—221no—
367C2×Q8—222no—
368C2×Q8—221no—
369C2×Q8—222no—
370C2×Q8—222no—
371C2×Q8—221no—
372C2×Q8—221no—
373C2×Q8—222no—
374C2×D4—21no—
375C2×D4—21no—
376C2×D4—21no—
377C2×D4—21no—
378C2×D4—21no—
379C2×D4#434312yes—
380C22×C4—22no—
381C22×C4—21no—
382C22×C4—42no—
383C22×C4—82no—
384C22×C4—221no—
385C22×C4—222no—
386C22×C4—221no—
387C22×C4C2×C22⋊D1112yes—
388C22×C4C2×C22⋊D1111yescharacteristic
389C22×C4C2×C22⋊D1111yescharacteristic
390C22×C4C2×C22⋊D1112yes—
391C22×C4C23×D1111yescharacteristic
392SD16—228no—
393SD16—448no—
394C2×C8—112no—
395C2×C8—221no—
396C2×C8—221no—
397C2×C8—221no—
398C2×C8—222no—
399C2×C8—222no—
400C2×C8—221no—
401C2×C8—221no—
402C2×C8—222no—
403C4⋊C4—24no—
404C4⋊C4—22no—
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4—82no—
410C4⋊C4—112no—
411C4⋊C4—228no—
412C4⋊C4—228no—
413C4⋊C4—228no—
414C4⋊C4—224no—
415C4⋊C4—224no—
416C4⋊C4—224no—
417C4⋊C4—221no—
418C22⋊C4—42no—
419C22⋊C4—44no—
420C22⋊C4—82no—
421C42—22no—
422C42—22no—
423C42—228no—
424C42—224no—
425C42D4×D1112yes—
426C42D4×D1112yes—
427C11#2419911yescharacteristic, complemented, Sylow
428C23—22no—
429C23—41no—
430C23—42no—
431C23—41no—
432C23—42no—
433C23C22×C22⋊D1111yescharacteristic
434Q8—28no—
435Q8—222no—
436Q8—222no—
437Q8—224no—
438Q8—224no—
439Q8—442no—
440Q8—442no—
441Q8—441no—
442Q8—441no—
443D4—22no—
444D4—22no—
445D4—41no—
446D4—41no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—84no—
460C2×C4—222no—
461C2×C4—224no—
462C2×C4—222no—
463C2×C4—441no—
464C2×C4—442no—
465C2×C4—442no—
466C2×C4—441no—
467C2×C4—442no—
468C2×C4#6699012yes—
469C2×C4#6699012yes—
470C2×C4#6700414yes—
471C2×C4C2×D4×D1111yescharacteristic
472C2×C4C2×D4×D1111yescharacteristic
473C2×C4C2×#434311yescharacteristic
474C2×C4#6704011yescharacteristic
475C2×C4#41×D1111yescharacteristic
476C2×C4#6704211yescharacteristic
477C8—222no—
478C8—441no—
479C8—442no—
480C22—44no—
481C22—42no—
482C22—82no—
483C22—81no—
484C22—81no—
485C22C2×#6699011yescharacteristic
486C22#1062334811yescharacteristic
487C22C2×#6700412yes—
488C22#1062336511yescharacteristic
489C22#1062336712yes—
490C4—22no—
491C4—24no—
492C4—22no—
493C4—42no—
494C4—82no—
495C4—81no—
496C4—442no—
497C4—444no—
498C4—442no—
499C4#1062315811yescharacteristic
500C4#1062316011yescharacteristic
501C4#1062316111yescharacteristic
502C4#1062316211yescharacteristic
503C2—82no—
504C2#1307196311yescharacteristic
505C2#1307784911yescharacteristic
506C2#1307790011yescharacteristic
507C2#1308139712yes—
508C2#1308166912yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2580C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#2580D11
hypocenterC11#24199
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #2580

Complements

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

NH ≅ G/Ntype
1. C2×#10623101C2semidirect
4. #13069862C2semidirect
6. #13069557C2semidirect
7. #13069435C2semidirect
9. #13068869C2semidirect
10. #13068628C2semidirect
427. C11#24199semidirect

Maximal subgroups

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

subgroupindex
C2×#106231012
C2×#106226322
C2×#106226312
#130698622
#130696982
#130695572
#130694352
#130689742
#130688692
#130686282
C11×#25802
#2419911