Finite Group Databasebeta

← #14788691

Subgroups — #14788691

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×#10623098C211yesmaximal, characteristic, complemented
2C2×#10622632C211yesmaximal, characteristic
3#13073970C211yesmaximal, characteristic
4#13069860C212yesmaximal, complemented
5#13069697C212yesmaximal
6#13069556C211yesmaximal, characteristic, complemented
7#13069436C211yesmaximal, characteristic, complemented
8#13068968C212yesmaximal
9#13068867C212yesmaximal, complemented
10#13068631C211yesmaximal, characteristic, complemented
11C2×C11×#440C211yesmaximal, characteristic
12C22×C11×SD16C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×#66997C2212yes—
16C22×#4324C2212yes—
17#10623098—24no—
18#10623098—24no—
19C2×#66942—22no—
20C2×#66940C2212yes—
21C2×#66923—21no—
22C2×#66922C2211yescharacteristic
23C2×C4×Dic22—21no—
24C2×C4×Dic22C2211yescharacteristic
25C11×#440—24no—
26C2×C11×#107C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28C2×C11×#102C2211yescharacteristic
29C2×C11×#97C2211yescharacteristic
30C2×#66899C2212yes—
31#10622834C2212yes—
32#10622823—22no—
33C2×#66880C2212yes—
34C2×#66880C2212yes—
35#10622632—24no—
36#10622586C2212yes—
37C2×#66874C2212yes—
38#10622562—21no—
39#10622560—21no—
40#10622549C2211yescharacteristic
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42#10622188C2212yes—
43#10622188C2212yes—
44#10622167C2212yes—
45C22×Q8×C11C2311yescharacteristic
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C22×Dic22D411yescharacteristic
49C22×Dic22C2312yes—
50C2×C11×SD16—22no—
51C2×C11×SD16—22no—
52C2×C11×SD16—22no—
53C22×C8×C11C2311yescharacteristic
54C22×C8×C11C2311yescharacteristic
55C4×Q8×C11—22no—
56C4×Q8×C11D414yes—
57C4×D4×C11—22no—
58C4×D4×C11—22no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C11×C4⋊C4C2311yescharacteristic
62C2×C11×C22⋊C4—21no—
63C2×C42×C11—21no—
64C2×C42×C11C2311yescharacteristic
65C2×C22⋊Dic11—22no—
66C2×C22⋊Dic11—22no—
67#66997—24no—
68#66997—24no—
69C2×#4324—24no—
70C2×#4324—24no—
71C2×#4324—42no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11—21no—
74C2×C4⋊Dic11D411yescharacteristic
75C2×C4⋊Dic11C2312yes—
76C2×Dic11⋊C4—22no—
77C2×Dic11⋊C4—22no—
78C2×Dic11⋊C4—22no—
79C2×Dic11⋊C4—22no—
80C2×Dic11⋊C4D412yes—
81C2×C4×Dic11—22no—
82C2×C4×Dic11C2312yes—
83C22×C11⋊C8C2312yes—
84#66942—216no—
85#66940—24no—
86#66940—24no—
87#66923—28no—
88#66922—22no—
89#66922D414yes—
90C4×Dic22—28no—
91C4×Dic22—22no—
92C4×Dic22—22no—
93C11×#107—22no—
94C11×#103—22no—
95C11×#102—22no—
96C11×#97—22no—
97#66899—42no—
98C11⋊#95—21no—
99C11⋊#95—21no—
100C11⋊#95—22no—
101#66880—24no—
102#66880—42no—
103#66874—24no—
104C4⋊(C11⋊C8)—22no—
105#24199—111nomaximal, Sylow
106C24×C11—21no—
107C2×Q8×C11—21no—
108C2×Q8×C11—21no—
109C2×Q8×C11—21no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11C2×D412yes—
113C2×D4×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11#4112yes—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—42no—
123C22×C4×C11—82no—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2411yescharacteristic
127C22×Dic11—22no—
128C22×Dic11—22no—
129C22×Dic11C2×D412yes—
130C22×Dic11C2×D412yes—
131C2×Dic22—24no—
132C2×Dic22—22no—
133C2×Dic22—22no—
134C2×Dic22—22no—
135C2×Dic22—22no—
136C2×Dic22—22no—
137C2×Dic22—22no—
138C2×Dic22C2×D414yes—
139C11×SD16—28no—
140C2×C8×C11—21no—
141C2×C8×C11—21no—
142C2×C8×C11—21no—
143C2×C8×C11—21no—
144C2×C8×C11—21no—
145C2×C8×C11#4112yes—
146C11×C4⋊C4—24no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4C2×D412yes—
151C11×C22⋊C4—42no—
152C42×C11—24no—
153C42×C11C2×D412yes—
154C42×C11C2×D412yes—
155C22⋊Dic11—44no—
156C22⋊Dic11—82no—
157#4324—48no—
158C4⋊Dic11—24no—
159C4⋊Dic11—22no—
160C4⋊Dic11—24no—
161C4⋊Dic11—22no—
162C4⋊Dic11—22no—
163Dic11⋊C4—28no—
164Dic11⋊C4—28no—
165Dic11⋊C4—28no—
166Dic11⋊C4—24no—
167Dic11⋊C4—82no—
168C4×Dic11—28no—
169C4×Dic11—22no—
170C4×Dic11—22no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—22no—
174C2×#557—111no—
175C2×#461—111no—
176C2×#440D1111yescharacteristic
177#2580—111no—
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—22no—
192Q8×C11—22no—
193Q8×C11—41no—
194Q8×C11—41no—
195D4×C11—22no—
196D4×C11—22no—
197D4×C11—41no—
198D4×C11—41no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—42no—
206C2×C4×C11—41no—
207C2×C4×C11—42no—
208C2×C4×C11—84no—
209C2×C4×C11#12012yes—
210C2×C4×C11#12012yes—
211C2×C4×C11C22×D411yescharacteristic
212C2×C4×C11C22×D411yescharacteristic
213C2×C4×C11C2×#4111yescharacteristic
214C2×C4×C11C2×#4111yescharacteristic
215C2×C4×C11H(5,𝔽2)11yescharacteristic
216C2×C4×C112−1+411yescharacteristic
217C2×Dic11—22no—
218C2×Dic11—22no—
219C2×Dic11—22no—
220C2×Dic11—24no—
221C2×Dic11—22no—
222C2×Dic11—22no—
223C2×Dic11—42no—
224C2×Dic11—42no—
225C2×Dic11—42no—
226C2×Dic11—42no—
227C2×Dic11—42no—
228C2×Dic11#13714yes—
229Dic22—28no—
230Dic22—24no—
231Dic22—24no—
232Dic22—42no—
233Dic22—42no—
234C8×C11—22no—
235C8×C11—41no—
236C11⋊C8—42no—
237C22×SD16—112no—
238C22×SD16C2×D1111yescharacteristic
239#557—224no—
240#557—224no—
241C2×C4⋊Q8—112no—
242C2×C4⋊Q8—111no—
243C2×#125—221no—
244C2×#125—222no—
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—24no—
252C2×#107C2×D1111yescharacteristic
253C2×C4⋊C8—111no—
254C2×#103—112no—
255C2×#103—112no—
256C2×#103—112no—
257C2×#103—112no—
258C2×#103C2×D1111yescharacteristic
259C2×#102C2×D1111yescharacteristic
260C2×#97C2×D1111yescharacteristic
261#399—221no—
262#393—221no—
263#390—112no—
264#389—112no—
265#385—222no—
266#382—111no—
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—22no—
282C4×C11—42no—
283C4×C11—42no—
284C4×C11—81no—
285C4×C11#52511yescharacteristic
286C4×C11#53711yescharacteristic
287C4×C11#54611yescharacteristic
288C4×C11#54711yescharacteristic
289Dic11—24no—
290Dic11—44no—
291Dic11—42no—
292Dic11—82no—
293C22×Q8—111no—
294C22×Q8—112no—
295C22×Q8C22×D1111yescharacteristic
296C22×D4C22×D1111yescharacteristic
297C23×C4—21no—
298C2×SD16—22no—
299C2×SD16—22no—
300C2×SD16—22no—
301C2×SD16—224no—
302C2×SD16—224no—
303C2×SD16—442no—
304C22×C8—112no—
305C22×C8C22×D1111yescharacteristic
306C22×C8C22×D1111yescharacteristic
307C4⋊Q8—114no—
308C4⋊Q8—224no—
309C4⋊Q8—224no—
310C4⋊Q8—222no—
311#125—228no—
312#125—2216no—
313C4×Q8—22no—
314C4×Q8—228no—
315C4×Q8—224no—
316C4×Q8—224no—
317C4×Q8—222no—
318C4×Q8—222no—
319C4×Q8C22⋊D1114yes—
320C4×D4—22no—
321C4×D4—22no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—112no—
324C2×C4⋊C4—111no—
325C2×C4⋊C4—112no—
326C2×C4⋊C4—222no—
327C2×C4⋊C4—222no—
328C2×C4⋊C4—222no—
329C2×C4⋊C4—221no—
330C2×C4⋊C4—221no—
331C2×C4⋊C4—222no—
332C2×C4⋊C4C22×D1111yescharacteristic
333C2×C4⋊C4C22×D1111yescharacteristic
334C2×C22⋊C4—21no—
335C2×C22⋊C4—222no—
336C2×C22⋊C4—222no—
337C2×C42—21no—
338C2×C42—112no—
339C2×C42—222no—
340C2×C42C22×D1111yescharacteristic
341#107—22no—
342C4⋊C8—222no—
343#103—22no—
344#103—224no—
345#103—224no—
346#103—442no—
347#103—442no—
348#102—22no—
349#97—22no—
350#95—222no—
351#95—221no—
352#95—221no—
353C2×C11—82no—
354C2×C11#240711yescharacteristic
355C2×C11#300411yescharacteristic
356C2×C11#301011yescharacteristic
357C2×C11#337212yes—
358C2×C11#340012yes—
359C24—21no—
360C2×Q8—21no—
361C2×Q8—21no—
362C2×Q8—21no—
363C2×Q8—21no—
364C2×Q8—21no—
365C2×Q8—114no—
366C2×Q8—224no—
367C2×Q8—222no—
368C2×Q8—222no—
369C2×Q8—222no—
370C2×Q8—222no—
371C2×Q8—222no—
372C2×Q8—222no—
373C2×Q8C2×C22⋊D1112yes—
374C2×D4—21no—
375C2×D4—21no—
376C2×D4—21no—
377C2×D4—21no—
378C2×D4—21no—
379C2×D4#433912yes—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—42no—
384C22×C4—82no—
385C22×C4—112no—
386C22×C4—112no—
387C22×C4—222no—
388C22×C4—222no—
389C22×C4D4×D1111yescharacteristic
390C22×C4D4×D1111yescharacteristic
391C22×C4C23×D1111yescharacteristic
392SD16—28no—
393SD16—448no—
394C2×C8—21no—
395C2×C8—21no—
396C2×C8—21no—
397C2×C8—21no—
398C2×C8—21no—
399C2×C8—222no—
400C2×C8—222no—
401C2×C8—222no—
402C2×C8#433912yes—
403C4⋊C4—24no—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—228no—
408C4⋊C4—228no—
409C4⋊C4—228no—
410C4⋊C4—224no—
411C4⋊C4—222no—
412C4⋊C4—224no—
413C4⋊C4—224no—
414C4⋊C4—222no—
415C4⋊C4—222no—
416C4⋊C4—882no—
417C4⋊C4C2×C22⋊D1112yes—
418C22⋊C4—42no—
419C22⋊C4—444no—
420C22⋊C4—882no—
421C42—24no—
422C42—228no—
423C42—222no—
424C42—222no—
425C42D4×D1112yes—
426C42C2×C22⋊D1112yes—
427C11#2419911yescharacteristic, complemented, Sylow
428C23—22no—
429C23—42no—
430C23—42no—
431C23—41no—
432C23—41no—
433C23C2×D4×D1111yescharacteristic
434Q8—22no—
435Q8—22no—
436Q8—41no—
437Q8—41no—
438Q8—228no—
439Q8—224no—
440Q8—224no—
441Q8—442no—
442Q8—442no—
443D4—22no—
444D4—22no—
445D4—41no—
446D4—41no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—42no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—42no—
455C2×C4—41no—
456C2×C4—84no—
457C2×C4—114no—
458C2×C4—222no—
459C2×C4—222no—
460C2×C4—222no—
461C2×C4—222no—
462C2×C4—222no—
463C2×C4—224no—
464C2×C4—442no—
465C2×C4—442no—
466C2×C4—442no—
467C2×C4—442no—
468C2×C4—442no—
469C2×C4#6699012yes—
470C2×C4#6699012yes—
471C2×C4C2×#433911yescharacteristic
472C2×C4C2×#433911yescharacteristic
473C2×C4C2×D4×D1111yescharacteristic
474C2×C4#6704211yescharacteristic
475C2×C4#6704311yescharacteristic
476C2×C4C22×C22⋊D1111yescharacteristic
477C8—22no—
478C8—41no—
479C8—442no—
480C22—44no—
481C22—42no—
482C22—82no—
483C22—81no—
484C22—81no—
485C22#1062308311yescharacteristic
486C22#1062308411yescharacteristic
487C22#1062330612yes—
488C22D11×#13712yes—
489C22C2×#6699011yescharacteristic
490C4—22no—
491C4—22no—
492C4—42no—
493C4—42no—
494C4—81no—
495C4—224no—
496C4—444no—
497C4—442no—
498C4—882no—
499C4#1062308111yescharacteristic
500C4#1062308211yescharacteristic
501C4#1062332211yescharacteristic
502C4#1062336411yescharacteristic
503C2—82no—
504C2#1307196111yescharacteristic
505C2#1307784811yescharacteristic
506C2#1307790111yescharacteristic
507C2#1308139812yes—
508C2#1308167012yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#440C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenterC2×#440D11
hypocenterC11#24199
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C2×#10623098C2semidirect
4. #13069860C2semidirect
6. #13069556C2semidirect
7. #13069436C2semidirect
9. #13068867C2semidirect
10. #13068631C2semidirect
427. C11#24199semidirect

Maximal subgroups

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

subgroupindex
C2×#106230982
C2×#106226322
#130739702
#130698602
#130696972
#130695562
#130694362
#130689682
#130688672
#130686312
C2×C11×#4402
#2419911