Finite Group Databasebeta

← #14788581

Subgroups — #14788581

Order 2816.

1050 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×#10622703C211yesmaximal, characteristic
2C2×C4×#4326C211yesmaximal, characteristic
3#13073986C211yesmaximal, characteristic
4#13069859C212yesmaximal
5#13069716C212yesmaximal
6#13069553C211yesmaximal, characteristic
7#13069419C211yesmaximal, characteristic
8#13068957C212yesmaximal
9#13068870C212yesmaximal
10#13068621C211yesmaximal, characteristic
11C2×C11×#557C211yesmaximal, characteristic
12C11×#557—24no—
13C11×#557—24no—
14C2×C11×C4⋊Q8C2212yes—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#125—21no—
17C2×C11×#125—22no—
18C2×C4×Q8×C11—21no—
19C2×C4×Q8×C11C2212yes—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×Q8×C11C2211yescharacteristic
22C22×#4326C2211yescharacteristic
23C22×#4326C2212yes—
24C2×C4×Dic22C2211yescharacteristic
25#10622843—21no—
26C2×#66899C2211yescharacteristic
27C2×#66899C2212yes—
28C2×#66899C2212yes—
29C2×#66899C2212yes—
30C2×#66899C2212yes—
31#10622703—24no—
32C4×#4326—24no—
33#10622597—22no—
34#10622586—21no—
35C2×#66874C2211yescharacteristic
36C2×#66871C2211yescharacteristic
37#10622548C2211yescharacteristic
38#10622542C2212yes—
39#10622541C2212yes—
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×C4×C11⋊C8C2211yescharacteristic
42#10622167C2212yes—
43#10622162C2212yes—
44#10622162C2212yes—
45C22×Q8×C11D411yescharacteristic
46C22×Q8×C11C2312yes—
47C22×Q8×C11C2311yescharacteristic
48C22×Dic22C2311yescharacteristic
49C11×C4⋊Q8—24no—
50C11×C4⋊Q8—24no—
51C11×C4⋊Q8—22no—
52C11×C4⋊Q8D414yes—
53C11×#125—216no—
54C11×#125—28no—
55C4×Q8×C11—28no—
56C4×Q8×C11—24no—
57C4×Q8×C11—24no—
58C4×Q8×C11—22no—
59C4×Q8×C11—22no—
60C4×Q8×C11—22no—
61C4×Q8×C11D414yes—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—22no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4D411yescharacteristic
69C2×C11×C4⋊C4D412yes—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C42×C11—22no—
72C2×C42×C11—21no—
73C2×C42×C11C2312yes—
74C2×C42×C11C2311yescharacteristic
75C2×#4326—22no—
76C2×#4326—22no—
77C2×#4326—24no—
78C2×#4326—24no—
79C2×#4326—22no—
80C2×#4326—42no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2312yes—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—22no—
87C2×C4×Dic11—21no—
88C22×C11⋊C8C2311yescharacteristic
89C22×C11⋊C8C2312yes—
90C22×C11⋊C8C2311yescharacteristic
91C4×Dic22—22no—
92C4×Dic22—22no—
93#66899—22no—
94#66899—24no—
95#66899—24no—
96#66899—42no—
97#66899—42no—
98C11⋊#95—22no—
99C11⋊#95—22no—
100C11⋊#95—22no—
101#66874—22no—
102#66871—22no—
103C4⋊(C11⋊C8)—22no—
104C4×C11⋊C8—22no—
105#24191—111nomaximal, Sylow
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11—21no—
110C2×Q8×C11—22no—
111C2×Q8×C11—21no—
112C2×Q8×C11—22no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—22no—
116C2×Q8×C11—21no—
117C2×Q8×C11—22no—
118C2×Q8×C11Q1614yescomplemented
119C2×Q8×C11C2×D414yes—
120C2×Q8×C11C2×D412yes—
121C22×C4×C11—21no—
122C22×C4×C11—22no—
123C22×C4×C11—21no—
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2411yescharacteristic
129C22×Dic11—21no—
130C22×Dic11—22no—
131C22×Dic11—21no—
132C2×Dic22—21no—
133C2×Dic22—21no—
134C2×Dic22—21no—
135C2×Dic22—21no—
136C2×Dic22—21no—
137C2×Dic22#4112yes—
138C11×C4⋊C4—28no—
139C11×C4⋊C4—28no—
140C11×C4⋊C4—28no—
141C11×C4⋊C4—24no—
142C11×C4⋊C4—24no—
143C11×C4⋊C4—24no—
144C11×C4⋊C4—24no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4C2×D412yes—
148C42×C11—28no—
149C42×C11—24no—
150C42×C11—22no—
151C42×C11—22no—
152C42×C11C2×D412yes—
153C42×C11C2×D412yes—
154#4326—28no—
155#4326—48no—
156C4⋊Dic11—21no—
157C4⋊Dic11—21no—
158C4⋊Dic11—22no—
159C4⋊Dic11—22no—
160C4⋊Dic11—42no—
161C4⋊Dic11—81no—
162Dic11⋊C4—42no—
163Dic11⋊C4—82no—
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×#557D1111yescharacteristic
175C2×#462—111no—
176C2×C4×Q16—111no—
177#2582—111no—
178#2043—112no—
179#2016—112no—
180#1984—111no—
181#1956—111no—
182#1878—112no—
183#1863—112no—
184#1803—111no—
185C23×C11C22×D411yescharacteristic
186Q8×C11—28no—
187Q8×C11—22no—
188Q8×C11—22no—
189Q8×C11—24no—
190Q8×C11—24no—
191Q8×C11—42no—
192Q8×C11—42no—
193Q8×C11—41no—
194Q8×C11—41no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—24no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—41no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11#12012yes—
212C2×C4×C11#12012yes—
213C2×C4×C11C2×Q1614yes—
214C2×C4×C11C2×Q1612yes—
215C2×C4×C11#13712yes—
216C2×C4×C11C22×D411yescharacteristic
217C2×C4×C11C22×D411yescharacteristic
218C2×C4×C11C2×#4111yescharacteristic
219C2×C4×C11C2×#4111yescharacteristic
220C2×C4×C11H(5,𝔽2)11yescharacteristic
221C2×C4×C112−1+411yescharacteristic
222C2×Dic11—22no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226C2×Dic11—42no—
227C2×Dic11—42no—
228C2×Dic11—41no—
229C2×Dic11—42no—
230C2×Dic11—41no—
231Dic22—22no—
232Dic22—22no—
233Dic22—41no—
234Dic22—41no—
235C11⋊C8—22no—
236C11⋊C8—41no—
237C11⋊C8—42no—
238C22×Q16—111no—
239C22×Q16—112no—
240#557—24no—
241#557—24no—
242C2×C4⋊Q8C2×D1112yes—
243C2×C4⋊Q8C2×D1111yescharacteristic
244C2×#125—21no—
245C2×#125—22no—
246C2×C4×Q8—21no—
247C2×C4×Q8—111no—
248C2×C4×Q8C2×D1112yes—
249C2×C4×Q8C2×D1111yescharacteristic
250C2×C4×Q8C2×D1111yescharacteristic
251#462—224no—
252C4×Q16—224no—
253C2×#107—111no—
254C2×C4⋊C8—111no—
255C2×#103—112no—
256C2×#103—112no—
257C2×#103—111no—
258C2×#103—111no—
259C2×#103—112no—
260C2×#103—112no—
261C2×C4×C8—111no—
262#398—222no—
263#391—112no—
264#391—221no—
265#389—112no—
266#389—221no—
267#384—111no—
268#340—112no—
269#336—112no—
270#336—112no—
271C22×C11C2×#12011yescharacteristic
272C22×C11#54811yescharacteristic
273C22×C11#55011yescharacteristic
274C22×C11C22×Q1611yescharacteristic
275C22×C11C2×#13711yescharacteristic
276C22×C11#57711yescharacteristic
277C22×C11#57811yescharacteristic
278C4×C11—24no—
279C4×C11—22no—
280C4×C11—42no—
281C4×C11—44no—
282C4×C11—42no—
283C4×C11—42no—
284C4×C11#45114yes—
285C4×C11#52511yescharacteristic
286C4×C11#53711yescharacteristic
287C4×C11#54611yescharacteristic
288C4×C11#54711yescharacteristic
289Dic11—42no—
290Dic11—82no—
291Dic11—81no—
292C22×Q8—111no—
293C22×Q8C22⋊D1111yescharacteristic
294C22×Q8C22×D1112yes—
295C22×Q8C22×D1111yescharacteristic
296C2×Q16—222no—
297C2×Q16—222no—
298C2×Q16—222no—
299C2×Q16—224no—
300C2×Q16—224no—
301C2×Q16—442no—
302C22×C8—111no—
303C22×C8—112no—
304C22×C8—111no—
305C4⋊Q8—24no—
306C4⋊Q8—24no—
307C4⋊Q8—22no—
308C4⋊Q8C22⋊D1114yes—
309#125—216no—
310#125—28no—
311C4×Q8—28no—
312C4×Q8—24no—
313C4×Q8—24no—
314C4×Q8—22no—
315C4×Q8—22no—
316C4×Q8—22no—
317C4×Q8—222no—
318C4×Q8—222no—
319C4×Q8C22⋊D1114yes—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—111no—
327C2×C4⋊C4—112no—
328C2×C4⋊C4—221no—
329C2×C4⋊C4—221no—
330C2×C4⋊C4—221no—
331C2×C4⋊C4—222no—
332C2×C4⋊C4C22⋊D1111yescharacteristic
333C2×C4⋊C4C22⋊D1112yes—
334C2×C4⋊C4C22×D1111yescharacteristic
335C2×C42—22no—
336C2×C42—21no—
337C2×C42—221no—
338C2×C42C22×D1112yes—
339C2×C42C22×D1111yescharacteristic
340#107—222no—
341C4⋊C8—222no—
342#103—224no—
343#103—222no—
344#103—224no—
345#103—222no—
346#103—442no—
347#103—442no—
348C4×C8—222no—
349#95—222no—
350#95—222no—
351#95—222no—
352C2×C11#240711yescharacteristic
353C2×C11C2×#45111yescharacteristic
354C2×C11#301311yescharacteristic
355C2×C11#336311yescharacteristic
356C2×C11#337411yescharacteristic
357C2×C11#339511yescharacteristic
358C2×C11#340011yescharacteristic
359C2×Q8—22no—
360C2×Q8—22no—
361C2×Q8—21no—
362C2×Q8—22no—
363C2×Q8—22no—
364C2×Q8—21no—
365C2×Q8—22no—
366C2×Q8—21no—
367C2×Q8—21no—
368C2×Q8—22no—
369C2×Q8—22no—
370C2×Q8—21no—
371C2×Q8—112no—
372C2×Q8—221no—
373C2×Q8—221no—
374C2×Q8—221no—
375C2×Q8—221no—
376C2×Q8—221no—
377C2×Q8#432614yescomplemented
378C2×Q8C2×C22⋊D1114yes—
379C2×Q8C2×C22⋊D1112yes—
380C22×C4—21no—
381C22×C4—22no—
382C22×C4—21no—
383C22×C4—221no—
384C22×C4—222no—
385C22×C4—221no—
386C22×C4C2×C22⋊D1112yes—
387C22×C4C2×C22⋊D1112yes—
388C22×C4C2×C22⋊D1111yescharacteristic
389C22×C4C2×C22⋊D1111yescharacteristic
390C22×C4C23×D1111yescharacteristic
391Q16—228no—
392Q16—448no—
393C2×C8—112no—
394C2×C8—221no—
395C2×C8—221no—
396C2×C8—222no—
397C2×C8—221no—
398C2×C8—222no—
399C2×C8—221no—
400C2×C8—221no—
401C2×C8—222no—
402C4⋊C4—28no—
403C4⋊C4—28no—
404C4⋊C4—28no—
405C4⋊C4—24no—
406C4⋊C4—24no—
407C4⋊C4—24no—
408C4⋊C4—24no—
409C4⋊C4—22no—
410C4⋊C4—21no—
411C4⋊C4—222no—
412C4⋊C4—222no—
413C4⋊C4—221no—
414C4⋊C4—221no—
415C4⋊C4—442no—
416C4⋊C4—442no—
417C4⋊C4—882no—
418C4⋊C4—881no—
419C4⋊C4C2×C22⋊D1112yes—
420C42—28no—
421C42—24no—
422C42—22no—
423C42—22no—
424C42—442no—
425C42C2×C22⋊D1112yes—
426C42C2×C22⋊D1112yes—
427C11#2419111yescharacteristic, complemented, Sylow
428C23C22×C22⋊D1111yescharacteristic
429Q8—28no—
430Q8—24no—
431Q8—22no—
432Q8—24no—
433Q8—22no—
434Q8—41no—
435Q8—42no—
436Q8—41no—
437Q8—42no—
438Q8—222no—
439Q8—222no—
440Q8—441no—
441Q8—441no—
442C2×C4—22no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—24no—
451C2×C4—22no—
452C2×C4—42no—
453C2×C4—41no—
454C2×C4—42no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—222no—
459C2×C4—441no—
460C2×C4—441no—
461C2×C4—442no—
462C2×C4—442no—
463C2×C4—442no—
464C2×C4—441no—
465C2×C4—441no—
466C2×C4—441no—
467C2×C4#6699512yes—
468C2×C4C2×#432614yes—
469C2×C4C2×#432612yes—
470C2×C4#6700612yes—
471C2×C4#6700612yes—
472C2×C4#41×D1111yescharacteristic
473C2×C4#41×D1111yescharacteristic
474C2×C4#6704211yescharacteristic
475C2×C4#6704311yescharacteristic
476C2×C4C22×C22⋊D1111yescharacteristic
477C2×C4C22×C22⋊D1111yescharacteristic
478C8—222no—
479C8—442no—
480C8—441no—
481C22C2×#6699511yescharacteristic
482C22C22×#432611yescharacteristic
483C22#1062336211yescharacteristic
484C22#1062336511yescharacteristic
485C22#1062336811yescharacteristic
486C22#1062336911yescharacteristic
487C22C2×#6700611yescharacteristic
488C4—24no—
489C4—22no—
490C4—44no—
491C4—42no—
492C4—42no—
493C4—42no—
494C4—442no—
495C4—882no—
496C4—881no—
497C4#1062284114yes—
498C4#1062335511yescharacteristic
499C4#1062335911yescharacteristic
500C4#1062336011yescharacteristic
501C4#1062336411yescharacteristic
502C2#1307195511yescharacteristic
503C2C2×#1062284111yescharacteristic
504C2#1307793111yescharacteristic
505C2#1308129011yescharacteristic
506C2#1308141511yescharacteristic
507C2#1308161911yescharacteristic
508C2#1308166511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#557C2
socle, prime radicalC23×C11C22×D4
hypercenterC2×#557D11
hypocenterC11#24191
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
118. C2×Q8×C11Q16semidirect
377. C2×Q8#4326semidirect
427. C11#24191semidirect

Maximal subgroups

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

subgroupindex
C2×#106227032
C2×C4×#43262
#130739862
#130698592
#130697162
#130695532
#130694192
#130689572
#130688702
#130686212
C2×C11×#5572
#2419111