Finite Group Databasebeta

← #14788718

Subgroups — #14788718

Order 2816.

1132 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622688C211yesmaximal, characteristic
2C2×#10622643C211yesmaximal, characteristic, complemented
3#13073982C211yesmaximal, characteristic, complemented
4#13069852C212yesmaximal, complemented
5#13069710C212yesmaximal, complemented
6#13069557C211yesmaximal, characteristic, complemented
7#13069441C211yesmaximal, characteristic
8#13068950C212yesmaximal, complemented
9#13068877C212yesmaximal, complemented
10#13068631C211yesmaximal, characteristic, complemented
11C2×C11×#559C211yesmaximal, characteristic
12C11×#559—24no—
13C11×#559—24no—
14C2×C11×#127C2211yescharacteristic
15C2×C11×#124—21no—
16C2×C11×#124C2212yes—
17C2×C11×#123—22no—
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11—21no—
21C2×C4×D4×C11C2212yes—
22C22×#4326C2211yescharacteristic
23C22×#4324C2212yes—
24C2×C4×Dic22C2211yescharacteristic
25#10622842—21no—
26C2×#66899C2211yescharacteristic
27C2×#66899C2212yes—
28C2×#66896C2212yes—
29C2×#66896C2212yes—
30C2×#66896C2212yes—
31#10622688—24no—
32#10622643—24no—
33#10622595—21no—
34#10622591—22no—
35C2×#66874C2211yescharacteristic
36C2×#66872C2211yescharacteristic
37#10622549C2211yescharacteristic
38#10622542C2212yes—
39#10622541C2212yes—
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×#66867C2211yescharacteristic
42#10622167C2212yes—
43#10622162C2212yes—
44#10622162C2212yes—
45C22×Q8×C11D411yescharacteristic
46C22×Q8×C11C2311yescharacteristic
47C22×D4×C11—21no—
48C22×D4×C11—21no—
49C22×D4×C11C2312yes—
50C23×C4×C11—22no—
51C22×Dic22C2311yescharacteristic
52C11×#127—22no—
53C11×#127D414yes—
54C11×#124—28no—
55C11×#124—24no—
56C11×#124—24no—
57C11×#123—216no—
58C4×Q8×C11—22no—
59C4×Q8×C11—22no—
60C4×Q8×C11—22no—
61C4×Q8×C11D414yes—
62C4×D4×C11—28no—
63C4×D4×C11—24no—
64C4×D4×C11—24no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4D412yes—
67C2×C11×C4⋊C4D411yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—22no—
72C2×C42×C11—21no—
73C2×C42×C11C2312yes—
74C2×C42×C11C2311yescharacteristic
75C2×#4326—22no—
76C2×#4326—22no—
77C2×#4326—22no—
78C2×#4324—24no—
79C2×#4324—24no—
80C2×#4324—42no—
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2312yes—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—22no—
85C2×C4×Dic11—21no—
86C22×C11⋊C8C2311yescharacteristic
87C22×C11⋊C8C2312yes—
88C22×C11⋊C8C2311yescharacteristic
89C4×Dic22—22no—
90C4×Dic22—22no—
91#66899—22no—
92#66899—42no—
93#66896—24no—
94#66896—24no—
95#66896—42no—
96C11⋊#95—22no—
97C11⋊#95—22no—
98C11⋊#95—22no—
99C11⋊#95—21no—
100C11⋊#95—21no—
101#66874—22no—
102#66872—22no—
103C4⋊(C11⋊C8)—22no—
104#66867—22no—
105#24202—111nomaximal, Sylow
106C24×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—21no—
109C2×Q8×C11—21no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—42no—
114C2×Q8×C11C2×D412yes—
115C2×D4×C11—24no—
116C2×D4×C11—24no—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C2×D4×C11—22no—
122C2×D4×C11—44no—
123C2×D4×C11—82no—
124C2×D4×C11C2×D414yes—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—28no—
128C22×C4×C11—84no—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2411yescharacteristic
134C22×Dic11—21no—
135C22×Dic11—22no—
136C22×Dic11—21no—
137C2×Dic22—21no—
138C2×Dic22—21no—
139C2×Dic22—21no—
140C2×Dic22—21no—
141C2×Dic22—21no—
142C2×Dic22#4112yes—
143C11×C4⋊C4—24no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—24no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4C2×D412yes—
148C11×C22⋊C4—28no—
149C11×C22⋊C4—28no—
150C11×C22⋊C4—28no—
151C42×C11—24no—
152C42×C11—22no—
153C42×C11—22no—
154C42×C11C2×D412yes—
155C42×C11C2×D412yes—
156#4326—28no—
157#4324—48no—
158C4⋊Dic11—21no—
159C4⋊Dic11—21no—
160C4⋊Dic11—22no—
161C4⋊Dic11—22no—
162Dic11⋊C4—44no—
163Dic11⋊C4—42no—
164C4×Dic11—42no—
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×#559D1111yescharacteristic
175C2×#460—111no—
176C2×#441—111no—
177#2581—111no—
178#2042—112no—
179#2015—112no—
180#1985—111no—
181#1961—111no—
182#1877—112no—
183#1864—112no—
184#1805—111no—
185C23×C11—24no—
186C23×C11—42no—
187C23×C11—42no—
188C23×C11—44no—
189C23×C11—44no—
190C23×C11C22×D411yescharacteristic
191Q8×C11—22no—
192Q8×C11—22no—
193Q8×C11—44no—
194Q8×C11—41no—
195Q8×C11—41no—
196D4×C11—24no—
197D4×C11—24no—
198D4×C11—48no—
199D4×C11—42no—
200D4×C11—42no—
201D4×C11—84no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—24no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—42no—
214C2×C4×C11—88no—
215C2×C4×C11#12012yes—
216C2×C4×C11#12012yes—
217C2×C4×C11C22×D411yescharacteristic
218C2×C4×C11C22×D411yescharacteristic
219C2×C4×C11C2×#4111yescharacteristic
220C2×C4×C11C2×#4111yescharacteristic
221C2×C4×C11H(5,𝔽2)11yescharacteristic
222C2×C4×C112−1+411yescharacteristic
223C2×Dic11—22no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226C2×Dic11—41no—
227C2×Dic11—42no—
228C2×Dic11—42no—
229C2×Dic11—42no—
230C2×Dic11—42no—
231Dic22—22no—
232Dic22—22no—
233Dic22—41no—
234Dic22—41no—
235C11⋊C8—22no—
236C11⋊C8—41no—
237C11⋊C8—42no—
238C22×Q16—111no—
239C22×SD16—112no—
240#559—24no—
241#559—24no—
242C2×#127C2×D1111yescharacteristic
243C2×#124—21no—
244C2×#124C2×D1112yes—
245C2×#123—22no—
246C2×C4×Q8—111no—
247C2×C4×Q8C2×D1111yescharacteristic
248C2×C4×Q8C2×D1111yescharacteristic
249C2×C4×D4—21no—
250C2×C4×D4C2×D1112yes—
251#460—224no—
252#441—224no—
253C2×#106—111no—
254C2×C4⋊C8—111no—
255C2×#103—111no—
256C2×#103—111no—
257C2×#103—112no—
258C2×#102—112no—
259C2×#102—112no—
260C2×#102—112no—
261C2×#97—111no—
262#400—221no—
263#395—221no—
264#391—112no—
265#389—112no—
266#387—222no—
267#382—111no—
268#340—112no—
269#336—112no—
270#336—112no—
271C22×C11—44no—
272C22×C11—44no—
273C22×C11—44no—
274C22×C11—84no—
275C22×C11—84no—
276C22×C11C2×#12011yescharacteristic
277C22×C11#54811yescharacteristic
278C22×C11#55011yescharacteristic
279C22×C11#57512yes—
280C22×C11#57712yes—
281C4×C11—22no—
282C4×C11—22no—
283C4×C11—42no—
284C4×C11—42no—
285C4×C11—42no—
286C4×C11—42no—
287C4×C11#52511yescharacteristic
288C4×C11#53711yescharacteristic
289C4×C11#54611yescharacteristic
290C4×C11#54711yescharacteristic
291Dic11—42no—
292Dic11—82no—
293Dic11—81no—
294C22×Q8—111no—
295C22×Q8C22⋊D1111yescharacteristic
296C22×Q8C22×D1111yescharacteristic
297C22×D4—21no—
298C22×D4—21no—
299C22×D4C22×D1112yes—
300C23×C4—22no—
301C2×Q16—222no—
302C2×Q16—222no—
303C2×Q16—222no—
304C2×SD16—224no—
305C2×SD16—224no—
306C2×SD16—442no—
307C22×C8—111no—
308C22×C8—112no—
309C22×C8—111no—
310#127—22no—
311#127C22⋊D1114yes—
312#124—28no—
313#124—24no—
314#124—24no—
315#123—216no—
316C4×Q8—22no—
317C4×Q8—22no—
318C4×Q8—22no—
319C4×Q8—222no—
320C4×Q8—222no—
321C4×Q8C22⋊D1114yes—
322C4×D4—28no—
323C4×D4—24no—
324C4×D4—24no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—111no—
327C2×C4⋊C4—112no—
328C2×C4⋊C4—221no—
329C2×C4⋊C4—222no—
330C2×C4⋊C4C22⋊D1111yescharacteristic
331C2×C4⋊C4C22⋊D1112yes—
332C2×C4⋊C4C22×D1111yescharacteristic
333C2×C22⋊C4—22no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—22no—
336C2×C42—21no—
337C2×C42—221no—
338C2×C42C22×D1112yes—
339C2×C42C22×D1111yescharacteristic
340#106—222no—
341C4⋊C8—222no—
342#103—222no—
343#103—222no—
344#103—442no—
345#102—224no—
346#102—224no—
347#102—442no—
348#97—222no—
349#95—221no—
350#95—221no—
351#95—222no—
352#95—222no—
353#95—222no—
354C2×C11—84no—
355C2×C11#240711yescharacteristic
356C2×C11#300511yescharacteristic
357C2×C11#300911yescharacteristic
358C2×C11#337112yes—
359C2×C11#340112yes—
360C24—22no—
361C2×Q8—22no—
362C2×Q8—21no—
363C2×Q8—21no—
364C2×Q8—21no—
365C2×Q8—21no—
366C2×Q8—21no—
367C2×Q8—42no—
368C2×Q8—112no—
369C2×Q8—221no—
370C2×Q8—221no—
371C2×Q8—221no—
372C2×Q8—221no—
373C2×Q8—221no—
374C2×Q8C2×C22⋊D1112yes—
375C2×D4—24no—
376C2×D4—24no—
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—22no—
381C2×D4—22no—
382C2×D4—44no—
383C2×D4—82no—
384C2×D4C2×C22⋊D1114yes—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—28no—
388C22×C4—84no—
389C22×C4—221no—
390C22×C4—222no—
391C22×C4—221no—
392C22×C4C2×C22⋊D1112yes—
393C22×C4C2×C22⋊D1112yes—
394C22×C4C2×C22⋊D1111yescharacteristic
395C22×C4C2×C22⋊D1111yescharacteristic
396C22×C4C23×D1111yescharacteristic
397Q16—228no—
398SD16—448no—
399C2×C8—112no—
400C2×C8—221no—
401C2×C8—221no—
402C2×C8—222no—
403C2×C8—221no—
404C2×C8—222no—
405C2×C8—221no—
406C2×C8—221no—
407C2×C8—222no—
408C4⋊C4—24no—
409C4⋊C4—22no—
410C4⋊C4—24no—
411C4⋊C4—21no—
412C4⋊C4—222no—
413C4⋊C4—222no—
414C4⋊C4—221no—
415C4⋊C4—221no—
416C4⋊C4—444no—
417C4⋊C4—442no—
418C4⋊C4C2×C22⋊D1112yes—
419C22⋊C4—28no—
420C22⋊C4—28no—
421C22⋊C4—28no—
422C42—24no—
423C42—22no—
424C42—22no—
425C42—442no—
426C42C2×C22⋊D1112yes—
427C42C2×C22⋊D1112yes—
428C11#2420211yescharacteristic, complemented, Sylow
429C23—24no—
430C23—44no—
431C23—42no—
432C23—42no—
433C23—44no—
434C23C22×C22⋊D1111yescharacteristic
435Q8—22no—
436Q8—22no—
437Q8—44no—
438Q8—41no—
439Q8—41no—
440Q8—222no—
441Q8—222no—
442Q8—441no—
443Q8—441no—
444D4—24no—
445D4—24no—
446D4—48no—
447D4—42no—
448D4—42no—
449D4—84no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—24no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—42no—
462C2×C4—88no—
463C2×C4—222no—
464C2×C4—441no—
465C2×C4—441no—
466C2×C4—442no—
467C2×C4—442no—
468C2×C4—442no—
469C2×C4—442no—
470C2×C4—441no—
471C2×C4#6700612yes—
472C2×C4#6700612yes—
473C2×C4#41×D1111yescharacteristic
474C2×C4#41×D1111yescharacteristic
475C2×C4#6704211yescharacteristic
476C2×C4#6704311yescharacteristic
477C2×C4C22×C22⋊D1111yescharacteristic
478C2×C4C22×C22⋊D1111yescharacteristic
479C8—222no—
480C8—442no—
481C8—441no—
482C22—44no—
483C22—44no—
484C22—44no—
485C22—84no—
486C22—84no—
487C22#1062335312yes—
488C22#1062336211yescharacteristic
489C22#1062336511yescharacteristic
490C22#1062336712yes—
491C22C2×#6700611yescharacteristic
492C4—22no—
493C4—22no—
494C4—42no—
495C4—42no—
496C4—42no—
497C4—42no—
498C4—442no—
499C4—882no—
500C4—881no—
501C4#1062335511yescharacteristic
502C4#1062335911yescharacteristic
503C4#1062336011yescharacteristic
504C4#1062336411yescharacteristic
505C2—84no—
506C2#1307195511yescharacteristic
507C2#1307785811yescharacteristic
508C2#1307789311yescharacteristic
509C2#1308137812yes—
510C2#1308167612yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#559C2
socleC23×C11C22×D4
prime radicalC2×C11×#127C22
hypercenterC2×#559D11
hypocenterC11#24202
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
2. C2×#10622643C2semidirect
3. #13073982C2semidirect
4. #13069852C2semidirect
5. #13069710C2semidirect
6. #13069557C2semidirect
8. #13068950C2semidirect
9. #13068877C2semidirect
10. #13068631C2semidirect
428. C11#24202semidirect

Maximal subgroups

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

subgroupindex
C2×#106226882
C2×#106226432
#130739822
#130698522
#130697102
#130695572
#130694412
#130689502
#130688772
#130686312
C2×C11×#5592
#2420211