Finite Group Databasebeta

← #14764094

Subgroups — #14764094

Order 2816.

1010 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622820C211yesmaximal, characteristic
2C2×#10622820C211yesmaximal, characteristic
3#13068821C214yesmaximal, complemented
4#13068820C214yesmaximal, complemented
5#13068656C214yesmaximal, complemented
6C2×C11×#407C211yesmaximal, characteristic
7C24×C4×C11C2211yescharacteristic
8C22×C11×M16C2212yes—
9C22×#4318C2212yes—
10C22×#4318C2212yes—
11C11×#407—21no—
12C11×#407—21no—
13C11×#407C2212yes—
14C11×#407C2212yes—
15C2×C11×C22⋊C8—21no—
16C2×C11×C22⋊C8—21no—
17#10622820—21no—
18#10622820—21no—
19#10622820C412yes—
20#10622820C412yes—
21#10622820C412yes—
22#10622820C412yes—
23#10622820C2212yes—
24#10622820C2212yes—
25C2×C22⋊(C11⋊C8)—21no—
26C2×C22⋊(C11⋊C8)—21no—
27C2×C22⋊(C11⋊C8)C2212yes—
28C2×C22⋊(C11⋊C8)C2212yes—
29C2×#66886C2218yescomplemented
30#10622196C2218yescomplemented
31C25×C11Q811yescharacteristic
32C23×C4×C11—44no—
33C23×C4×C11C2×C411yescharacteristic
34C23×C4×C11C2×C411yescharacteristic
35C23×C4×C11C2×C411yescharacteristic
36C23×C4×C11C2×C411yescharacteristic
37C23×C4×C11D411yescharacteristic
38C23×C4×C11D411yescharacteristic
39C23×C4×C11D411yescharacteristic
40C23×C4×C11D411yescharacteristic
41C23×C4×C11Q811yescharacteristic
42C23×C4×C11Q811yescharacteristic
43C23×C4×C11Q811yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C2×C11×M16—22no—
48C2×C11×M16—44no—
49C2×C11×M16C2314yes—
50C22×C8×C11—22no—
51C2×#4318—22no—
52C2×#4318—44no—
53C2×#4318—44no—
54C2×#4318C2×C414yes—
55C2×#4318C2×C414yes—
56C2×#4318C2314yes—
57C22×C11⋊C8—22no—
58C22×C11⋊C8C2314yes—
59C11×C22⋊C8—22no—
60C11×C22⋊C8—22no—
61C11×C22⋊C8—22no—
62C11×C22⋊C8—22no—
63C22⋊(C11⋊C8)—22no—
64C22⋊(C11⋊C8)—22no—
65C22⋊(C11⋊C8)—22no—
66C22⋊(C11⋊C8)—22no—
67C22⋊(C11⋊C8)C2×C414yes—
68C22⋊(C11⋊C8)C2×C414yes—
69C22⋊(C11⋊C8)C2×C414yes—
70C22⋊(C11⋊C8)C2×C414yes—
71#66886—48no—
72#21949—111nomaximal, Sylow
73C24×C11—42no—
74C24×C11—42no—
75C24×C11—42no—
76C24×C11C4⋊C411yescharacteristic
77C24×C11C4⋊C411yescharacteristic
78C24×C11C4⋊C411yescharacteristic
79C24×C11C4⋊C411yescharacteristic
80C24×C11C2×Q811yescharacteristic
81C24×C11C2×Q811yescharacteristic
82C24×C11C2×Q811yescharacteristic
83C22×C4×C11—24no—
84C22×C4×C11—24no—
85C22×C4×C11—24no—
86C22×C4×C11—42no—
87C22×C4×C11—42no—
88C22×C4×C11—42no—
89C22×C4×C11—42no—
90C22×C4×C11—42no—
91C22×C4×C11—42no—
92C22×C4×C11—42no—
93C22×C4×C11—42no—
94C22×C4×C11—42no—
95C22×C4×C11—42no—
96C22×C4×C11—42no—
97C22×C4×C11C4⋊C411yescharacteristic
98C22×C4×C11C4⋊C411yescharacteristic
99C22×C4×C11C4⋊C411yescharacteristic
100C22×C4×C11C4⋊C411yescharacteristic
101C22×C4×C11C4⋊C411yescharacteristic
102C22×C4×C11C4⋊C411yescharacteristic
103C22×C4×C11C4⋊C411yescharacteristic
104C22×C4×C11C4⋊C411yescharacteristic
105C22×C4×C11C4⋊C411yescharacteristic
106C22×C4×C11C4⋊C411yescharacteristic
107C22×C4×C11C4⋊C411yescharacteristic
108C22×C4×C11C4⋊C411yescharacteristic
109C22×C4×C11C22×C411yescharacteristic
110C22×C4×C11C22×C411yescharacteristic
111C22×C4×C11C22×C411yescharacteristic
112C22×C4×C11C22×C411yescharacteristic
113C22×C4×C11C22×C411yescharacteristic
114C22×C4×C11C22×C411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×Q811yescharacteristic
122C22×C4×C11C2×Q811yescharacteristic
123C22×C4×C11C2×Q811yescharacteristic
124C22×C4×C11C2411yescharacteristic
125C11×M16—28no—
126C11×M16—44no—
127C2×C8×C11—24no—
128C2×C8×C11—44no—
129#4318—28no—
130#4318—44no—
131#4318—44no—
132#4318—44no—
133C2×C11⋊C8—24no—
134C2×C11⋊C8—28no—
135C2×C11⋊C8—44no—
136C2×C11⋊C8C22×C418yes—
137C2×#407—111no—
138C2×#407—111no—
139C2×#407D1111yescharacteristic
140#1855—114no—
141#1855—114no—
142#1811—114no—
143C23×C11—22no—
144C23×C11—22no—
145C23×C11—22no—
146C23×C11—22no—
147C23×C11—22no—
148C23×C11—22no—
149C23×C11—22no—
150C23×C11—22no—
151C23×C11—22no—
152C23×C11—41no—
153C23×C11—41no—
154C23×C11—41no—
155C23×C11—41no—
156C23×C11—41no—
157C23×C11—41no—
158C23×C11—41no—
159C23×C11—41no—
160C23×C11—41no—
161C23×C11—41no—
162C23×C11—41no—
163C23×C11—41no—
164C23×C11—416no—
165C23×C11C2×C4⋊C411yescharacteristic
166C23×C11C2×C4⋊C411yescharacteristic
167C23×C11C2×C4⋊C411yescharacteristic
168C23×C11C2×C4⋊C411yescharacteristic
169C23×C11C2×C4⋊C411yescharacteristic
170C23×C11C2×C4⋊C411yescharacteristic
171C23×C11C22×Q811yescharacteristic
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11C2×C4⋊C411yescharacteristic
200C2×C4×C11C2×C4⋊C411yescharacteristic
201C2×C4×C11C2×C4⋊C411yescharacteristic
202C2×C4×C11C2×C4⋊C411yescharacteristic
203C2×C4×C11C2×C4⋊C411yescharacteristic
204C2×C4×C11C2×C4⋊C411yescharacteristic
205C2×C4×C11C23×C411yescharacteristic
206C2×C4×C11C22×D411yescharacteristic
207C2×C4×C11H(5,𝔽2)14yes—
208C8×C11—44no—
209C11⋊C8—28no—
210C11⋊C8—44no—
211C24×C4C2×D1111yescharacteristic
212C22×M16—112no—
213C22×M16—112no—
214C22×M16C2×D1112yes—
215C2×#108—118no—
216#407—21no—
217#407—21no—
218#407—112no—
219#407—112no—
220#407—112no—
221#407—112no—
222#407—112no—
223#407—112no—
224#407—221no—
225#407—221no—
226#407C2×D1112yes—
227#407C2×D1112yes—
228C2×C22⋊C8—21no—
229C2×C22⋊C8—21no—
230C2×C22⋊C8—112no—
231C2×C22⋊C8—112no—
232C2×C22⋊C8—221no—
233C2×C22⋊C8—221no—
234#341—118no—
235C22×C11—21no—
236C22×C11—21no—
237C22×C11—21no—
238C22×C11—21no—
239C22×C11—21no—
240C22×C11—21no—
241C22×C11—21no—
242C22×C11—21no—
243C22×C11—21no—
244C22×C11—21no—
245C22×C11—21no—
246C22×C11—21no—
247C22×C11—21no—
248C22×C11—21no—
249C22×C11—21no—
250C22×C11—21no—
251C22×C11—21no—
252C22×C11—21no—
253C22×C11—44no—
254C22×C11—44no—
255C22×C11—44no—
256C22×C11—44no—
257C22×C11—44no—
258C22×C11—44no—
259C22×C11—44no—
260C22×C11#43012yes—
261C22×C11#43012yes—
262C22×C11C22×C4⋊C411yescharacteristic
263C22×C11#54312yes—
264C4×C11—21no—
265C4×C11—21no—
266C4×C11—21no—
267C4×C11—21no—
268C4×C11—21no—
269C4×C11—21no—
270C4×C11#51812yes—
271C4×C11#53412yes—
272C25Dic2211yescharacteristic
273C23×C4—44no—
274C23×C4Dic2211yescharacteristic
275C23×C4Dic2211yescharacteristic
276C23×C4Dic2211yescharacteristic
277C23×C4C4×D1111yescharacteristic
278C23×C4C4×D1111yescharacteristic
279C23×C4C4×D1111yescharacteristic
280C23×C4C4×D1111yescharacteristic
281C23×C4C22⋊D1111yescharacteristic
282C23×C4C22⋊D1111yescharacteristic
283C23×C4C22⋊D1111yescharacteristic
284C23×C4C22⋊D1111yescharacteristic
285C23×C4C22×D1111yescharacteristic
286C23×C4C22×D1111yescharacteristic
287C23×C4C22×D1111yescharacteristic
288C2×M16—22no—
289C2×M16—44no—
290C2×M16—114no—
291C2×M16—114no—
292C2×M16—114no—
293C2×M16—222no—
294C2×M16—444no—
295C2×M16—444no—
296C2×M16C22×D1114yes—
297C22×C8—22no—
298C22×C8—114no—
299C22×C8—222no—
300#108—448no—
301C22⋊C8—22no—
302C22⋊C8—22no—
303C22⋊C8—22no—
304C22⋊C8—22no—
305C22⋊C8—114no—
306C22⋊C8—114no—
307C22⋊C8—114no—
308C22⋊C8—114no—
309C22⋊C8—222no—
310C22⋊C8—222no—
311C22⋊C8—222no—
312C22⋊C8—222no—
313C2×C11—22no—
314C2×C11—22no—
315C2×C11—22no—
316C2×C11—41no—
317C2×C11—41no—
318C2×C11—41no—
319C2×C11—41no—
320C2×C11#231511yescharacteristic
321C2×C11C2×#43011yescharacteristic
322C2×C11C2×#43011yescharacteristic
323C24—42no—
324C24—42no—
325C24—42no—
326C24Dic11⋊C411yescharacteristic
327C24Dic11⋊C411yescharacteristic
328C24Dic11⋊C411yescharacteristic
329C24Dic11⋊C411yescharacteristic
330C24C2×Dic2211yescharacteristic
331C24C2×Dic2211yescharacteristic
332C24C2×Dic2211yescharacteristic
333C22×C4—24no—
334C22×C4—24no—
335C22×C4—24no—
336C22×C4—42no—
337C22×C4—42no—
338C22×C4—42no—
339C22×C4—42no—
340C22×C4—42no—
341C22×C4—42no—
342C22×C4—42no—
343C22×C4—42no—
344C22×C4—42no—
345C22×C4—42no—
346C22×C4—42no—
347C22×C4Dic11⋊C411yescharacteristic
348C22×C4Dic11⋊C411yescharacteristic
349C22×C4Dic11⋊C411yescharacteristic
350C22×C4Dic11⋊C411yescharacteristic
351C22×C4Dic11⋊C411yescharacteristic
352C22×C4Dic11⋊C411yescharacteristic
353C22×C4Dic11⋊C411yescharacteristic
354C22×C4Dic11⋊C411yescharacteristic
355C22×C4Dic11⋊C411yescharacteristic
356C22×C4Dic11⋊C411yescharacteristic
357C22×C4Dic11⋊C411yescharacteristic
358C22×C4Dic11⋊C411yescharacteristic
359C22×C4C2×Dic2211yescharacteristic
360C22×C4C2×Dic2211yescharacteristic
361C22×C4C2×Dic2211yescharacteristic
362C22×C4C2×C4×D1111yescharacteristic
363C22×C4C2×C4×D1111yescharacteristic
364C22×C4C2×C4×D1111yescharacteristic
365C22×C4C2×C4×D1111yescharacteristic
366C22×C4C2×C4×D1111yescharacteristic
367C22×C4C2×C4×D1111yescharacteristic
368C22×C4C2×C22⋊D1111yescharacteristic
369C22×C4C2×C22⋊D1111yescharacteristic
370C22×C4C2×C22⋊D1111yescharacteristic
371C22×C4C2×C22⋊D1111yescharacteristic
372C22×C4C2×C22⋊D1111yescharacteristic
373C22×C4C2×C22⋊D1111yescharacteristic
374C22×C4C23×D1111yescharacteristic
375M16—28no—
376M16—44no—
377M16—228no—
378M16—444no—
379M16—444no—
380M16—444no—
381C2×C8—24no—
382C2×C8—44no—
383C2×C8—118no—
384C2×C8—228no—
385C2×C8—224no—
386C2×C8—444no—
387C11#2194911yescharacteristic, complemented, Sylow
388C23—22no—
389C23—22no—
390C23—22no—
391C23—22no—
392C23—22no—
393C23—22no—
394C23—22no—
395C23—22no—
396C23—22no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—41no—
402C23—41no—
403C23—41no—
404C23—41no—
405C23—41no—
406C23—41no—
407C23—41no—
408C23—41no—
409C23—416no—
410C23C2×Dic11⋊C411yescharacteristic
411C23C2×Dic11⋊C411yescharacteristic
412C23C2×Dic11⋊C411yescharacteristic
413C23C2×Dic11⋊C411yescharacteristic
414C23C2×Dic11⋊C411yescharacteristic
415C23C2×Dic11⋊C411yescharacteristic
416C23C22×Dic2211yescharacteristic
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4C2×Dic11⋊C411yescharacteristic
445C2×C4C2×Dic11⋊C411yescharacteristic
446C2×C4C2×Dic11⋊C411yescharacteristic
447C2×C4C2×Dic11⋊C411yescharacteristic
448C2×C4C2×Dic11⋊C411yescharacteristic
449C2×C4C2×Dic11⋊C411yescharacteristic
450C2×C4C22×C4×D1111yescharacteristic
451C2×C4#6703714yes—
452C2×C4C22×C22⋊D1111yescharacteristic
453C8—44no—
454C8—228no—
455C8—444no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—44no—
475C22—44no—
476C22—44no—
477C22—44no—
478C22—44no—
479C22—44no—
480C22—44no—
481C22#1062273712yes—
482C22#1062273712yes—
483C22#1062301412yes—
484C22C22×Dic11⋊C411yescharacteristic
485C4—21no—
486C4—21no—
487C4—21no—
488C4—21no—
489C4—21no—
490C4—21no—
491C4#1062301712yes—
492C4#1062333512yes—
493C2—22no—
494C2—22no—
495C2—22no—
496C2—41no—
497C2—41no—
498C2—41no—
499C2—41no—
500C2#1307122811yescharacteristic
501C2C2×#1062273711yescharacteristic
502C2C2×#1062273711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#407C2
socleC22×C11C22×C4⋊C4
prime radicalC25×C11Q8
cosocleC22×C4×C11C24
hypercenterC2×#407D11
hypocenterC11#21949
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
3. #13068821C2semidirect
4. #13068820C2semidirect
5. #13068656C2semidirect
29. C2×#66886C22semidirect
30. #10622196C22semidirect
387. C11#21949semidirect

Maximal subgroups

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

subgroupindex
C2×#106228202
#130688212
#130688202
#130686562
C2×C11×#4072
#2194911