Finite Group Databasebeta

← #14647772

Subgroups — #14647772

Order 2816.

612 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071233C211yesmaximal, characteristic
2#13068811C211yesmaximal, characteristic
3#13068808C211yesmaximal, characteristic
4C2×#10622107C211yesmaximal, characteristic
5#13066870C211yesmaximal, characteristic
6#13066495C211yesmaximal, characteristic
7C11×#1294C211yesmaximal, characteristic
8C22×C4⋊Dic11C2211yescharacteristic
9C22×Dic11⋊C4C2211yescharacteristic
10C2×#66930—21no—
11C2×C11×C22⋊C8C2211yescharacteristic
12C11×#380C2211yescharacteristic
13C2×C11×#95C2211yescharacteristic
14#10622825C2211yescharacteristic
15C2×C11⋊#95—21no—
16C2×C11⋊#95—21no—
17C2×C22⋊(C11⋊C8)C2211yescharacteristic
18C2×#66881—21no—
19#10622585—21no—
20#10622585—21no—
21C2×#66872—21no—
22#10622555—21no—
23#10622260—21no—
24#10622260—21no—
25#10622189—21no—
26#10622167—21no—
27#10622107C414yescomplemented
28C23×C4×C11—21no—
29C23×C4×C11C2311yescharacteristic
30C23×Dic11—21no—
31C23×Dic11D411yescharacteristic
32C23×Dic11D411yescharacteristic
33C22×C8×C11—21no—
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C11×C4⋊C4D411yescharacteristic
36C2×C11×C22⋊C4—21no—
37C2×C22⋊Dic11—21no—
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11—42no—
41C2×C4⋊Dic11D411yescharacteristic
42C2×C4⋊Dic11D411yescharacteristic
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C2×Dic11⋊C4—21no—
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4—21no—
48C2×Dic11⋊C4—21no—
49C2×Dic11⋊C4—21no—
50C2×Dic11⋊C4—21no—
51C2×Dic11⋊C4C2×C412yes—
52C2×Dic11⋊C4Q812yes—
53C2×C4×Dic11—21no—
54C2×C4×Dic11—21no—
55C22×C11⋊C8—21no—
56#66930—42no—
57#66930—42no—
58C11×C22⋊C8—21no—
59C11×C22⋊C8C2×C412yes—
60C11×#95—21no—
61C11×#95—21no—
62C11×#95—21no—
63C11⋊#95—21no—
64C11⋊#95—21no—
65C11⋊#95—21no—
66C11⋊#95—42no—
67C11⋊#95—42no—
68C22⋊(C11⋊C8)—21no—
69C22⋊(C11⋊C8)C2×C412yes—
70#66881—42no—
71#66872—42no—
72#8857—111nomaximal, Sylow
73C24×C11C2×D411yescharacteristic
74C22×C4×C11—22no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—41no—
78C22×C4×C11—41no—
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×C11C22×C411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×Q811yescharacteristic
89C22×C4×C11#4111yescharacteristic
90C22×C4×C11#4111yescharacteristic
91C22×Dic11—22no—
92C22×Dic11—21no—
93C22×Dic11—21no—
94C22×Dic11—21no—
95C22×Dic11—21no—
96C22×Dic11—21no—
97C22×Dic11—21no—
98C22×Dic11—21no—
99C22×Dic11—21no—
100C22×Dic11—41no—
101C22×Dic11—41no—
102C22×Dic11—41no—
103C22×Dic11—41no—
104C22×Dic11—41no—
105C22×Dic11—41no—
106C22×Dic11—41no—
107C22×Dic11—41no—
108C22×Dic11C4⋊C412yes—
109C22×Dic11C4⋊C412yes—
110C22×Dic11SD1612yes—
111C22×Dic11SD1612yes—
112C2×C8×C11—22no—
113C2×C8×C11—41no—
114C2×C8×C11—41no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4—41no—
117C11×C22⋊C4—41no—
118C11×C22⋊C4—41no—
119C22⋊Dic11—41no—
120C22⋊Dic11—41no—
121C4⋊Dic11—22no—
122C4⋊Dic11—22no—
123C4⋊Dic11—41no—
124C4⋊Dic11—41no—
125C4⋊Dic11—41no—
126C4⋊Dic11—41no—
127Dic11⋊C4—22no—
128Dic11⋊C4—22no—
129Dic11⋊C4—22no—
130Dic11⋊C4—22no—
131Dic11⋊C4—42no—
132Dic11⋊C4—42no—
133Dic11⋊C4—81no—
134Dic11⋊C4—81no—
135C4×Dic11—42no—
136C4×Dic11—42no—
137C2×C11⋊C8—22no—
138C2×C11⋊C8—41no—
139C2×C11⋊C8—41no—
140#2316—111no—
141#1853—111no—
142#1853—111no—
143C2×#324—111no—
144#1441—111no—
145#1294—111no—
146#1294D1111yescharacteristic
147C23×C11—21no—
148C23×C11—21no—
149C23×C11—21no—
150C23×C11—21no—
151C23×C11C2×C4⋊C411yescharacteristic
152C23×C11#12011yescharacteristic
153C23×C11#12311yescharacteristic
154C23×C11C2×SD1611yescharacteristic
155C23×C11C2×SD1611yescharacteristic
156C23×C11AGL(1,ℤ/8)11yescharacteristic
157C23×C11#13711yescharacteristic
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—81no—
176C2×C4×C11—81no—
177C2×C4×C11—81no—
178C2×C4×C11—81no—
179C2×C4×C11C4×D411yescharacteristic
180C2×C4×C11C4×D411yescharacteristic
181C2×C4×C11C22⋊Q811yescharacteristic
182C2×C4×C11C22⋊Q811yescharacteristic
183C2×Dic11—22no—
184C2×Dic11—22no—
185C2×Dic11—22no—
186C2×Dic11—22no—
187C2×Dic11—22no—
188C2×Dic11—22no—
189C2×Dic11—22no—
190C2×Dic11—41no—
191C2×Dic11—41no—
192C2×Dic11—42no—
193C2×Dic11—42no—
194C2×Dic11—42no—
195C2×Dic11—41no—
196C2×Dic11—41no—
197C2×Dic11—41no—
198C2×Dic11—41no—
199C2×Dic11—41no—
200C2×Dic11—42no—
201C2×Dic11—41no—
202C2×Dic11—81no—
203C2×Dic11—81no—
204C2×Dic11—81no—
205C2×Dic11—81no—
206C2×Dic11—81no—
207C2×Dic11#10614yescomplemented
208C8×C11—42no—
209C11⋊C8—42no—
210C2×#117—221no—
211C22×C4⋊C4—111no—
212C22×C4⋊C4—111no—
213C2×#106—221no—
214C2×#106—221no—
215C2×C22⋊C8—111no—
216C2×C22⋊C8C2×D1111yescharacteristic
217#389—221no—
218#389—221no—
219#389—221no—
220#389—221no—
221#380—111no—
222#380—221no—
223#380C2×D1111yescharacteristic
224C2×#95—221no—
225C2×#95—221no—
226C2×#95C2×D1111yescharacteristic
227#340—221no—
228#340—221no—
229#324—114no—
230C22×C11—21no—
231C22×C11—21no—
232C22×C11—21no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—21no—
236C22×C11—21no—
237C22×C11—21no—
238C22×C11—21no—
239C22×C11—21no—
240C22×C11—21no—
241C22×C11—21no—
242C22×C11#38511yescharacteristic
243C22×C11C2×#10611yescharacteristic
244C22×C11#42811yescharacteristic
245C22×C11#44811yescharacteristic
246C22×C11#45011yescharacteristic
247C22×C11#45411yescharacteristic
248C22×C11#45611yescharacteristic
249C22×C11B(4,𝔽2)11yescharacteristic
250C22×C11#45811yescharacteristic
251C22×C11#48111yescharacteristic
252C22×C11#48311yescharacteristic
253C4×C11—21no—
254C4×C11—21no—
255C4×C11—21no—
256C4×C11—21no—
257C4×C11—82no—
258C4×C11—81no—
259C4×C11—81no—
260Dic11—24no—
261Dic11—42no—
262Dic11—82no—
263Dic11—81no—
264Dic11—81no—
265C23×C4—21no—
266C23×C4—111no—
267C23×C4—111no—
268C23×C4—221no—
269C23×C4C22×D1111yescharacteristic
270C22×C8—21no—
271C22×C8—221no—
272#117—442no—
273#117—442no—
274C2×C4⋊C4—112no—
275C2×C4⋊C4—112no—
276C2×C4⋊C4—111no—
277C2×C4⋊C4—111no—
278C2×C4⋊C4—221no—
279C2×C4⋊C4—221no—
280C2×C4⋊C4—221no—
281C2×C4⋊C4—221no—
282C2×C4⋊C4—221no—
283C2×C4⋊C4—221no—
284C2×C4⋊C4—221no—
285C2×C4⋊C4—221no—
286C2×C4⋊C4—221no—
287C2×C4⋊C4—221no—
288C2×C4⋊C4—442no—
289C2×C4⋊C4D4411yescharacteristic
290C2×C4⋊C4D4411yescharacteristic
291C2×C22⋊C4—21no—
292C2×C22⋊C4—221no—
293C2×C42—221no—
294C2×C42—221no—
295#106—442no—
296#106—442no—
297C22⋊C8—21no—
298C22⋊C8—112no—
299C22⋊C8—221no—
300C22⋊C8C4×D1112yes—
301#95—21no—
302#95—21no—
303#95—21no—
304#95—221no—
305#95—221no—
306#95—221no—
307#95—442no—
308#95—442no—
309C2×C11—21no—
310C2×C11—21no—
311C2×C11—21no—
312C2×C11—21no—
313C2×C11#159911yescharacteristic
314C2×C11#160411yescharacteristic
315C2×C11#161111yescharacteristic
316C2×C11#161611yescharacteristic
317C2×C11#185311yescharacteristic
318C2×C11#185711yescharacteristic
319C2×C11#186711yescharacteristic
320C24D4×D1111yescharacteristic
321C22×C4—22no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—112no—
333C22×C4—112no—
334C22×C4—112no—
335C22×C4—112no—
336C22×C4—221no—
337C22×C4—221no—
338C22×C4—221no—
339C22×C4—221no—
340C22×C4—221no—
341C22×C4—221no—
342C22×C4—222no—
343C22×C4—221no—
344C22×C4—221no—
345C22×C4—441no—
346C22×C4—441no—
347C22×C4—441no—
348C22×C4—441no—
349C22×C4—441no—
350C22×C4—441no—
351C22×C4—441no—
352C22×C4—441no—
353C22×C4C2×C4×D1111yescharacteristic
354C22×C4C2×D4411yescharacteristic
355C22×C4#433911yescharacteristic
356C22×C4D4×D1111yescharacteristic
357C22×C4#434111yescharacteristic
358C22×C4Q8×D1111yescharacteristic
359C2×C8—22no—
360C2×C8—41no—
361C2×C8—41no—
362C2×C8—222no—
363C2×C8—441no—
364C2×C8—441no—
365C4⋊C4—41no—
366C4⋊C4—41no—
367C4⋊C4—222no—
368C4⋊C4—222no—
369C4⋊C4—222no—
370C4⋊C4—222no—
371C4⋊C4—222no—
372C4⋊C4—222no—
373C4⋊C4—441no—
374C4⋊C4—441no—
375C4⋊C4—441no—
376C4⋊C4—441no—
377C4⋊C4—442no—
378C4⋊C4—442no—
379C4⋊C4—881no—
380C4⋊C4—881no—
381C22⋊C4—41no—
382C22⋊C4—41no—
383C22⋊C4—441no—
384C22⋊C4—441no—
385C42—442no—
386C42—442no—
387C11#885711yescharacteristic, complemented, Sylow
388C23—21no—
389C23—21no—
390C23—21no—
391C23—21no—
392C23#6693511yescharacteristic
393C23#6693611yescharacteristic
394C23C4⋊C4×D1111yescharacteristic
395C23#6696411yescharacteristic
396C23SD16×D1111yescharacteristic
397C23SD16×D1111yescharacteristic
398C23#6697111yescharacteristic
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—81no—
417C2×C4—81no—
418C2×C4—81no—
419C2×C4—81no—
420C2×C4—114no—
421C2×C4—222no—
422C2×C4—222no—
423C2×C4—222no—
424C2×C4—222no—
425C2×C4—222no—
426C2×C4—222no—
427C2×C4—222no—
428C2×C4—441no—
429C2×C4—441no—
430C2×C4—442no—
431C2×C4—442no—
432C2×C4—442no—
433C2×C4—442no—
434C2×C4—441no—
435C2×C4—441no—
436C2×C4—441no—
437C2×C4—441no—
438C2×C4—441no—
439C2×C4—441no—
440C2×C4—881no—
441C2×C4—881no—
442C2×C4—881no—
443C2×C4—881no—
444C2×C4—881no—
445C2×C4C4×D4411yescharacteristic
446C2×C4(C22⋊D11)⋊C411yescharacteristic
447C2×C4#6694911yescharacteristic
448C2×C4#6695011yescharacteristic
449C8—42no—
450C8—442no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22#1062228111yescharacteristic
464C22#1062235411yescharacteristic
465C22#1062235511yescharacteristic
466C22#1062238911yescharacteristic
467C22#1062239011yescharacteristic
468C22#1062241811yescharacteristic
469C22#1062241911yescharacteristic
470C22#1062243911yescharacteristic
471C22#1062244011yescharacteristic
472C22D11×#10611yescharacteristic
473C22#1062249411yescharacteristic
474C4—21no—
475C4—21no—
476C4—21no—
477C4—21no—
478C4—82no—
479C4—81no—
480C4—81no—
481C4—224no—
482C4—442no—
483C4—882no—
484C4—881no—
485C4—881no—
486C2—21no—
487C2—21no—
488C2—21no—
489C2—21no—
490C2#1306755711yescharacteristic
491C2#1306758611yescharacteristic
492C2#1306762511yescharacteristic
493C2#1306765411yescharacteristic
494C2#1306881011yescharacteristic
495C2#1306883211yescharacteristic
496C2#1306889811yescharacteristic
subgroupG/H
centerC23#66935
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1294C2
socleC23×C11#120
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenter#1294D11
hypocenterC11#8857
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
27. #10622107C4semidirect
207. C2×Dic11#106semidirect
387. C11#8857semidirect

Maximal subgroups

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

subgroupindex
#130712332
#130688112
#130688082
C2×#106221072
#130668702
#130664952
C11×#12942
#885711