Finite Group Databasebeta

← #14780326

Subgroups — #14780326

Order 2816.

912 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
1C4×#66993C211yesmaximal, characteristic
2#13068914C211yesmaximal, characteristic, complemented
3#13068913C212yesmaximal, complemented
4#13068912C212yesmaximal, complemented
5#13068911C212yesmaximal, complemented
6#13068910C212yesmaximal, complemented
7#13068910C212yesmaximal, complemented
8#13068758C212yesmaximal, complemented
9C11×#1870C211yesmaximal, characteristic, complemented
10C22×C11×M16C2211yescharacteristic
11C2×C4×D4×C11C2211yescharacteristic
12C2×#66993C411yescharacteristic
13C2×C4×C22⋊D11C2212yes—
14C2×C4×C22⋊D11C2212yes—
15C22×#4318C2211yescharacteristic
16C22×#4313C2212yes—
17C2×C4×D44C2211yescharacteristic
18C2×C11×C22⋊C8C2211yescharacteristic
19C2×C11×C22⋊C8C2212yes—
20#10622834C411yescharacteristic
21C2×C22⋊(C11⋊C8)C2211yescharacteristic
22C2×C22⋊(C11⋊C8)C2212yes—
23C2×(C2×D11)⋊C8C2212yes—
24C2×(C2×D11)⋊C8C2212yes—
25C2×(C2×D11)⋊C8C2212yes—
26#10622601C411yescharacteristic
27#10622589C411yescharacteristic
28#10622570C412yes—
29#10622570C412yes—
30C42×Dic11C2211yescharacteristic
31C11×#336C2212yes—
32#10622188C2212yes—
33#10622188C2212yes—
34#10622188C2212yes—
35#10622188C2212yes—
36#10622162C2212yes—
37C22×D4×C11C2×C411yescharacteristic
38C23×C4×C11C2311yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C22×C22⋊D11C2×C412yes—
41C22×C22⋊D11C2×C412yes—
42C22×D44C2×C411yescharacteristic
43C22×C4×D11C2312yes—
44C2×C11×M16—41no—
45C2×C11×M16—42no—
46C22×C8×C11C2312yes—
47C22×C8×C11C2312yes—
48C4×D4×C11—41no—
49C4×D4×C11—41no—
50C2×C11×C4⋊C4C2×C411yescharacteristic
51C2×C11×C22⋊C4C2×C411yescharacteristic
52C2×C11×C22⋊C4C2×C411yescharacteristic
53C2×C42×C11C2311yescharacteristic
54C2×C22⋊Dic11C2×C412yes—
55C2×C22⋊Dic11C2×C412yes—
56#66993—24no—
57C4×C22⋊D11—42no—
58C4×C22⋊D11—42no—
59C4×C22⋊D11—42no—
60C4×C22⋊D11—42no—
61C2×(C2×D11)⋊C4C2×C412yes—
62C2×(C2×D11)⋊C4C2×C412yes—
63C2×(C2×D11)⋊C4C2×C412yes—
64C2×C4⋊Dic11C2×C411yescharacteristic
65C2×Dic11⋊C4C2×C412yes—
66C2×Dic11⋊C4C2×C412yes—
67C2×C4×Dic11C2×C412yes—
68C2×C4×Dic11C2×C411yescharacteristic
69C2×C4×Dic11C2×C411yescharacteristic
70C2×C4×Dic11C2312yes—
71C2×#4318—41no—
72C2×#4318—42no—
73C22×C11⋊C8C2312yes—
74C22×C11⋊C8C2312yes—
75C2×#4313—42no—
76C2×#4313—42no—
77C2×#4313—42no—
78C4×D44—41no—
79C4×D44—41no—
80C11×C22⋊C8—41no—
81C11×C22⋊C8—42no—
82C22⋊(C11⋊C8)—41no—
83C22⋊(C11⋊C8)—42no—
84(C2×D11)⋊C8—42no—
85(C2×D11)⋊C8—42no—
86(C2×D11)⋊C8—42no—
87#23357—111nomaximal, Sylow
88C24×C11C22×C411yescharacteristic
89C24×C11C22×C411yescharacteristic
90C23×D11C22×C412yes—
91C2×D4×C11—22no—
92C2×D4×C11—41no—
93C2×D4×C11—41no—
94C22×C4×C11—22no—
95C22×C4×C11—21no—
96C22×C4×C11—22no—
97C22×C4×C11—21no—
98C22×C4×C11—22no—
99C22×C4×C11—21no—
100C22×C4×C11—22no—
101C22×C4×C11—21no—
102C22×C4×C11C22×C411yescharacteristic
103C22×C4×C11C22×C411yescharacteristic
104C22×C4×C11C22×C411yescharacteristic
105C22×C4×C11C22×C411yescharacteristic
106C22×C4×C11C2411yescharacteristic
107C2×C22⋊D11—24no—
108C2×C22⋊D11—24no—
109C2×C22⋊D11—42no—
110C2×C22⋊D11—42no—
111C2×C22⋊D11—42no—
112C2×C22⋊D11—42no—
113C22×Dic11C22×C412yes—
114C22×Dic11C22×C412yes—
115C22×Dic11C22×C412yes—
116C2×D44—22no—
117C2×D44—41no—
118C2×D44—41no—
119C2×C4×D11—22no—
120C2×C4×D11—22no—
121C2×C4×D11—22no—
122C2×C4×D11—22no—
123C2×C4×D11—22no—
124C2×C4×D11—22no—
125C11×M16—44no—
126C2×C8×C11—22no—
127C2×C8×C11—22no—
128C2×C8×C11—22no—
129C2×C8×C11—22no—
130C2×C8×C11—22no—
131C2×C8×C11—22no—
132C11×C4⋊C4—41no—
133C11×C22⋊C4—41no—
134C11×C22⋊C4—41no—
135C42×C11—21no—
136C42×C11—21no—
137C22⋊Dic11—42no—
138C22⋊Dic11—42no—
139(C2×D11)⋊C4—42no—
140(C2×D11)⋊C4—42no—
141(C2×D11)⋊C4—42no—
142C4⋊Dic11—41no—
143Dic11⋊C4—42no—
144Dic11⋊C4—42no—
145C4×Dic11—22no—
146C4×Dic11—22no—
147C4×Dic11—41no—
148C4×Dic11—42no—
149C4×Dic11M1614yescomplemented
150#4318—44no—
151C2×C11⋊C8—22no—
152C2×C11⋊C8—22no—
153C2×C11⋊C8—22no—
154C2×C11⋊C8—22no—
155C2×C11⋊C8—22no—
156C2×C11⋊C8—22no—
157#4313—48no—
158C4×#127—111no—
159#1870—112no—
160#1870—112no—
161#1870—112no—
162#1870—112no—
163#1870—112no—
164#1870—111no—
165#1870D1111yescharacteristic, complemented
166#1839—112no—
167C23×C11—22no—
168C23×C11—22no—
169C23×C11—21no—
170C23×C11—21no—
171C23×C11—21no—
172C23×C11—21no—
173C23×C11—22no—
174C23×C11—22no—
175C23×C11—21no—
176C23×C11—21no—
177C23×C11C23×C411yescharacteristic
178C22×D11—22no—
179C22×D11—22no—
180C22×D11—22no—
181C22×D11—22no—
182C22×D11—22no—
183C22×D11—22no—
184C22×D11—22no—
185D4×C11—44no—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—22no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—41no—
200C2×C4×C11C2×M1612yes—
201C2×C4×C11H(5,𝔽2)11yescharacteristic
202C2×C4×C11H(5,𝔽2)11yescharacteristic
203C2×C4×C11H(5,𝔽2)12yes—
204C2×C4×C11H(5,𝔽2)12yes—
205C22⋊D11—48no—
206C22⋊D11—48no—
207C2×Dic11—22no—
208C2×Dic11—22no—
209C2×Dic11—22no—
210C2×Dic11—22no—
211C2×Dic11—22no—
212C2×Dic11—22no—
213C2×Dic11—22no—
214C2×Dic11—22no—
215C2×Dic11C2×M1614yes—
216D44—44no—
217C4×D11—42no—
218C4×D11—42no—
219C4×D11—42no—
220C4×D11—42no—
221C8×C11—42no—
222C8×C11—42no—
223C11⋊C8—42no—
224C11⋊C8—42no—
225C22×M16—111no—
226C22×M16—112no—
227C22×M16C2×D1111yescharacteristic
228C2×#127—111no—
229C2×C4×D4—112no—
230C2×C4×D4—112no—
231C2×C4×D4—111no—
232C2×C4×D4C2×D1111yescharacteristic
233C2×C22⋊C8—111no—
234C2×C22⋊C8—112no—
235C2×C22⋊C8—112no—
236C2×C22⋊C8—112no—
237C2×C22⋊C8—112no—
238C2×C22⋊C8C2×D1111yescharacteristic
239C2×C22⋊C8C2×D1112yes—
240#390—111no—
241#390—111no—
242#390—112no—
243#390—112no—
244#384—111no—
245C43—111no—
246#336—112no—
247#336—112no—
248#336—112no—
249#336—112no—
250#336—112no—
251#336C2×D1112yes—
252C22×C11—41no—
253C22×C11—41no—
254C22×C11—41no—
255C22×C11—41no—
256C22×C11—42no—
257C22×C11—42no—
258C22×C11—42no—
259C22×C11—42no—
260C22×C11—41no—
261C22×C11—41no—
262C22×C11#51811yescharacteristic
263C22×C11#51812yes—
264C22×C11C22×M1611yescharacteristic
265C22×C11#56811yescharacteristic
266C22×C11#56812yes—
267C2×D11—42no—
268C2×D11—42no—
269C2×D11—42no—
270C2×D11—42no—
271C2×D11—42no—
272C2×D11—42no—
273C2×D11—42no—
274C4×C11—22no—
275C4×C11—41no—
276C4×C11—41no—
277C4×C11—41no—
278C4×C11#56011yescharacteristic
279C4×C11#56012yes—
280C4×C11#56011yescharacteristic
281Dic11—24no—
282Dic11—42no—
283Dic11—42no—
284C22×D4—112no—
285C22×D4—112no—
286C22×D4—111no—
287C22×D4C4×D1111yescharacteristic
288C23×C4—112no—
289C23×C4C22×D1111yescharacteristic
290C23×C4C22×D1111yescharacteristic
291C2×M16—42no—
292C2×M16—41no—
293C2×M16—442no—
294C2×M16—442no—
295C2×M16—442no—
296C2×M16—441no—
297C2×M16—442no—
298C22×C8—112no—
299C22×C8—112no—
300C22×C8C22×D1112yes—
301C22×C8C22×D1112yes—
302#127—224no—
303C4×D4—41no—
304C4×D4—41no—
305C4×D4—441no—
306C4×D4—441no—
307C4×D4—442no—
308C4×D4—442no—
309C4×D4—442no—
310C4×D4—442no—
311C2×C4⋊C4—112no—
312C2×C4⋊C4—112no—
313C2×C4⋊C4—111no—
314C2×C4⋊C4C4×D1111yescharacteristic
315C2×C22⋊C4—112no—
316C2×C22⋊C4—112no—
317C2×C22⋊C4—112no—
318C2×C22⋊C4—112no—
319C2×C22⋊C4—112no—
320C2×C22⋊C4C4×D1111yescharacteristic
321C2×C22⋊C4C4×D1111yescharacteristic
322C2×C42—111no—
323C2×C42—112no—
324C2×C42—112no—
325C2×C42—111no—
326C2×C42C22×D1111yescharacteristic
327C22⋊C8—42no—
328C22⋊C8—41no—
329C22⋊C8—442no—
330C22⋊C8—442no—
331C22⋊C8—442no—
332C22⋊C8—441no—
333C22⋊C8—442no—
334C2×C11—81no—
335C2×C11—81no—
336C2×C11#238011yescharacteristic
337C2×C11#297512yes—
338C2×C11#297511yescharacteristic
339C2×C11#298012yes—
340C2×C11#298011yescharacteristic
341D11—82no—
342C24—112no—
343C24C2×C4×D1111yescharacteristic
344C24C2×C4×D1111yescharacteristic
345C2×D4—22no—
346C2×D4—41no—
347C2×D4—41no—
348C2×D4—224no—
349C2×D4—224no—
350C2×D4—222no—
351C2×D4—441no—
352C2×D4—441no—
353C2×D4—442no—
354C2×D4—442no—
355C2×D4—442no—
356C2×D4—442no—
357C22×C4—21no—
358C22×C4—22no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—112no—
366C22×C4—112no—
367C22×C4—112no—
368C22×C4—222no—
369C22×C4—222no—
370C22×C4—222no—
371C22×C4—222no—
372C22×C4—222no—
373C22×C4—222no—
374C22×C4C2×C4×D1111yescharacteristic
375C22×C4C2×C4×D1111yescharacteristic
376C22×C4C2×C4×D1111yescharacteristic
377C22×C4C2×C4×D1111yescharacteristic
378C22×C4C23×D1111yescharacteristic
379M16—44no—
380M16—448no—
381M16—444no—
382C2×C8—22no—
383C2×C8—22no—
384C2×C8—22no—
385C2×C8—22no—
386C2×C8—22no—
387C2×C8—22no—
388C2×C8—222no—
389C2×C8—222no—
390C2×C8—222no—
391C2×C8—222no—
392C2×C8—222no—
393C2×C8—222no—
394C4⋊C4—41no—
395C4⋊C4—442no—
396C4⋊C4—442no—
397C4⋊C4—441no—
398C22⋊C4—41no—
399C22⋊C4—41no—
400C22⋊C4—442no—
401C22⋊C4—442no—
402C22⋊C4—442no—
403C22⋊C4—442no—
404C22⋊C4—442no—
405C42—21no—
406C42—21no—
407C42—114no—
408C42—222no—
409C42—222no—
410C42—441no—
411C42—442no—
412C11#2335711yescharacteristic, complemented, Sylow
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—21no—
419C23—22no—
420C23—22no—
421C23—22no—
422C23—22no—
423C23—222no—
424C23—222no—
425C23—222no—
426C23—222no—
427C23—222no—
428C23—222no—
429C23—222no—
430C23C22×C4×D1111yescharacteristic
431D4—44no—
432D4—444no—
433D4—448no—
434D4—448no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—114no—
450C2×C4—222no—
451C2×C4—222no—
452C2×C4—222no—
453C2×C4—222no—
454C2×C4—222no—
455C2×C4—222no—
456C2×C4—222no—
457C2×C4—222no—
458C2×C4—442no—
459C2×C4—442no—
460C2×C4—442no—
461C2×C4—442no—
462C2×C4M16×D1112yes—
463C2×C4#6703712yes—
464C2×C4#6703711yescharacteristic
465C2×C4#6703711yescharacteristic
466C2×C4#6704212yes—
467C8—42no—
468C8—42no—
469C8—442no—
470C8—442no—
471C22—42no—
472C22—42no—
473C22—41no—
474C22—41no—
475C22—41no—
476C22—41no—
477C22—42no—
478C22—42no—
479C22—41no—
480C22—41no—
481C22—442no—
482C22—442no—
483C22—442no—
484C22—442no—
485C22—442no—
486C22—442no—
487C22—442no—
488C22#1062301711yescharacteristic
489C22#1062307612yes—
490C22C2×M16×D1111yescharacteristic
491C22#1062327611yescharacteristic
492C22#1062328112yes—
493C4—22no—
494C4—41no—
495C4—41no—
496C4—41no—
497C4—224no—
498C4—442no—
499C4—442no—
500C4#1062312611yescharacteristic
501C4#1062315112yes—
502C4#1062319711yescharacteristic
503C2—81no—
504C2—81no—
505C2—882no—
506C2#1307179111yescharacteristic
507C2#1307765412yes—
508C2#1307765511yescharacteristic
509C2#1307768412yes—
510C2#1307768511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1870C2
prime radicalC2×#66993C4
cosocleC22×C4×C11C24
hypercenter#1870D11
hypocenterC11#23357
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1870

Complements

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

NH ≅ G/Ntype
2. #13068914C2semidirect
3. #13068913C2semidirect
4. #13068912C2semidirect
5. #13068911C2semidirect
6. #13068910C2semidirect
7. #13068910C2semidirect
8. #13068758C2semidirect
9. C11×#1870C2semidirect
149. C4×Dic11M16semidirect
165. #1870D11semidirect
412. C11#23357semidirect

Maximal subgroups

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

subgroupindex
C4×#669932
#130689142
#130689132
#130689122
#130689112
#130689102
#130687582
C11×#18702
#2335711