Finite Group Databasebeta

← #14656093

Subgroups — #14656093

Order 2816.

644 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622696C211yesmaximal, characteristic
2#13073534C211yesmaximal, characteristic
3#13069578C211yesmaximal, characteristic, complemented
4C2×Q8⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
5C2×#10622121C211yesmaximal, characteristic
6#13066500C211yesmaximal, characteristic, complemented
7C2×C11×#475C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C4×Q8×C11C2211yescharacteristic
10C2×#66999—21no—
11C22×#4325—21no—
12C2×C4×D44C2211yescharacteristic
13C11×#475—22no—
14C11×#475—22no—
15C2×C11×#106—21no—
16C2×C11×C4⋊C8C2211yescharacteristic
17C2×C11×#103—21no—
18C2×#66899—21no—
19#10622696—22no—
20#10622696—22no—
21#10622607—22no—
22#10622600—21no—
23#10622552—21no—
24#10622548C2211yescharacteristic
25#10622541—21no—
26C2×C4⋊(C11⋊C8)C2211yescharacteristic
27C2×C4×C11⋊C8C2211yescharacteristic
28Q8⋊(C11⋊C8)—22no—
29#10622167—22no—
30#10622121—22no—
31C22×Q8×C11—21no—
32C22×Q8×C11D411yescharacteristic
33C22×D44D411yescharacteristic
34C22×C4×D11—21no—
35C22×C8×C11—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8D412yes—
40C4×Q8×C11—21no—
41C4×Q8×C11—21no—
42C4×Q8×C11—21no—
43C4×Q8×C11—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4D411yescharacteristic
48C2×C42×C11—21no—
49C2×C42×C11C2311yescharacteristic
50#66999—42no—
51#66999—42no—
52C2×#4325—24no—
53C2×#4325—42no—
54C2×#4325—42no—
55C2×(C2×D11)⋊C4—22no—
56C2×(C2×D11)⋊C4—21no—
57C2×(C2×D11)⋊C4—22no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11D411yescharacteristic
61C2×C4⋊Dic11D412yes—
62C2×Dic11⋊C4—22no—
63C22×C11⋊C8—21no—
64C22×C11⋊C8—21no—
65C4×D44—21no—
66C4×D44—21no—
67C4×D44—21no—
68C4×D44—21no—
69C11×#106—24no—
70C11×C4⋊C8—21no—
71C11×C4⋊C8D412yes—
72C11×#103—24no—
73#66899—24no—
74C11⋊#95—22no—
75C4⋊(C11⋊C8)—21no—
76C4⋊(C11⋊C8)D412yes—
77C4×C11⋊C8—21no—
78C4×C11⋊C8—21no—
79#10232—111nomaximal, Sylow
80C23×D11—21no—
81C2×Q8×C11—21no—
82C2×Q8×C11—21no—
83C2×Q8×C11—22no—
84C2×Q8×C11—21no—
85C2×Q8×C11—21no—
86C2×Q8×C11—21no—
87C2×Q8×C11—41no—
88C2×Q8×C11—41no—
89C2×Q8×C11—41no—
90C2×Q8×C11—41no—
91C2×Q8×C11—41no—
92C2×Q8×C11SD1612yescomplemented
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—41no—
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×Dic11—21no—
100C22×Dic11—22no—
101C2×D44—21no—
102C2×D44—21no—
103C2×D44—21no—
104C2×D44—21no—
105C2×D44—21no—
106C2×D44SD1612yes—
107C2×C4×D11—41no—
108C2×C4×D11—41no—
109C2×C4×D11—41no—
110C2×C4×D11—41no—
111C2×C4×D11—41no—
112C2×C4×D11—41no—
113C2×C8×C11—22no—
114C2×C8×C11—41no—
115C2×C8×C11—41no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—21no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—41no—
121C11×C4⋊C4—41no—
122C11×C4⋊C4—41no—
123C11×C4⋊C4—41no—
124C42×C11—41no—
125C42×C11—41no—
126C42×C11C2×D411yescharacteristic
127C42×C11C2×D411yescharacteristic
128C42×C11C2×D411yescharacteristic
129C42×C11#4111yescharacteristic
130#4325—48no—
131(C2×D11)⋊C4—44no—
132(C2×D11)⋊C4—41no—
133(C2×D11)⋊C4—41no—
134(C2×D11)⋊C4—82no—
135C4⋊Dic11—21no—
136C4⋊Dic11—21no—
137C4⋊Dic11—42no—
138C4⋊Dic11—41no—
139C4⋊Dic11—41no—
140C4⋊Dic11—41no—
141C4⋊Dic11—41no—
142Dic11⋊C4—44no—
143C2×C11⋊C8—22no—
144C2×C11⋊C8—22no—
145C2×C11⋊C8—41no—
146C2×C11⋊C8—41no—
147C2×C11⋊C8—41no—
148C2×C11⋊C8—41no—
149C2×#475D1111yescharacteristic, complemented
150C2×#461—111no—
151#2538—111no—
152#1990—111no—
153C2×Q8⋊C8—111no—
154C2×D4⋊C8—111no—
155#1296—111no—
156C23×C11#12011yescharacteristic
157C22×D11—22no—
158C22×D11—41no—
159C22×D11—41no—
160C22×D11—41no—
161C22×D11—41no—
162C22×D11—41no—
163C22×D11—41no—
164Q8×C11—22no—
165Q8×C11—22no—
166Q8×C11—41no—
167Q8×C11—41no—
168Q8×C11—42no—
169Q8×C11—42no—
170Q8×C11—81no—
171Q8×C11—81no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—22no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—42no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—81no—
182C2×C4×C11—81no—
183C2×C4×C11#12011yescharacteristic
184C2×C4×C11#12011yescharacteristic
185C2×C4×C11#12111yescharacteristic
186C2×C4×C11#12111yescharacteristic
187C2×C4×C11#12111yescharacteristic
188C2×C4×C11#12711yescharacteristic
189C2×C4×C11C2×SD1611yescharacteristic
190C2×C4×C11C2×SD1611yescharacteristic
191C2×C4×C11#13511yescharacteristic
192C2×C4×C11#13511yescharacteristic
193C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
194C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
195C2×C4×C11#13711yescharacteristic
196C2×C4×C11#13711yescharacteristic
197C2×Dic11—41no—
198C2×Dic11—42no—
199C2×Dic11—41no—
200C2×Dic11—42no—
201C2×Dic11—41no—
202C2×Dic11—42no—
203D44—22no—
204D44—22no—
205D44—41no—
206D44—41no—
207C4×D11—81no—
208C4×D11—81no—
209C4×D11—81no—
210C4×D11—81no—
211C8×C11—42no—
212C11⋊C8—42no—
213C11⋊C8—42no—
214C22×SD16—221no—
215C2×C4⋊Q8C2×D1111yescharacteristic
216C2×C22⋊Q8—221no—
217C2×C4×Q8C2×D1111yescharacteristic
218C2×C4×D4—111no—
219#475—22no—
220#475—22no—
221#461—222no—
222#461—222no—
223C2×#106—21no—
224C2×C4⋊C8—111no—
225C2×C4⋊C8C2×D1111yescharacteristic
226C2×#103—21no—
227C2×#103—221no—
228C2×C4×C8—111no—
229#396—222no—
230#390—221no—
231#389—221no—
232#384—111no—
233#380—221no—
234#340—222no—
235Q8⋊C8—222no—
236D4⋊C8—222no—
237C22×C11#39211yescharacteristic
238C22×C11#44811yescharacteristic
239C22×C11#44911yescharacteristic
240C22×C11#45011yescharacteristic
241C22×C11#45211yescharacteristic
242C22×C11#45511yescharacteristic
243C22×C11#45611yescharacteristic
244C2×D11—42no—
245C2×D11—42no—
246C2×D11—42no—
247C2×D11—81no—
248C2×D11—81no—
249C2×D11—81no—
250C2×D11—81no—
251C4×C11—21no—
252C4×C11—21no—
253C4×C11—42no—
254C4×C11—82no—
255C4×C11—81no—
256C4×C11#44811yescharacteristic
257C4×C11#44911yescharacteristic
258C4×C11#45011yescharacteristic
259C4×C11#45211yescharacteristic
260C4×C11#46511yescharacteristic
261C4×C11#46511yescharacteristic
262C4×C11#46811yescharacteristic
263C4×C11#46811yescharacteristic
264Dic11—82no—
265Dic11—81no—
266C22×Q8—21no—
267C22×Q8C22⋊D1111yescharacteristic
268C22×D4—111no—
269C23×C4—221no—
270C2×SD16—224no—
271C2×SD16—442no—
272C2×SD16—442no—
273C22×C8—21no—
274C22×C8—221no—
275C22×C8—221no—
276C4⋊Q8—21no—
277C4⋊Q8—21no—
278C4⋊Q8—21no—
279C4⋊Q8C22⋊D1112yes—
280C22⋊Q8—442no—
281C22⋊Q8—442no—
282C4×Q8—21no—
283C4×Q8—21no—
284C4×Q8—21no—
285C4×Q8—21no—
286C4×D4—221no—
287C4×D4—221no—
288C4×D4—221no—
289C4×D4—221no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—111no—
294C2×C4⋊C4—112no—
295C2×C4⋊C4—222no—
296C2×C4⋊C4—221no—
297C2×C4⋊C4—221no—
298C2×C4⋊C4C22⋊D1111yescharacteristic
299C2×C22⋊C4—222no—
300C2×C22⋊C4—221no—
301C2×C22⋊C4—222no—
302C2×C42—21no—
303C2×C42C22×D1111yescharacteristic
304#106—24no—
305C4⋊C8—21no—
306C4⋊C8—112no—
307C4⋊C8—221no—
308C4⋊C8C22⋊D1112yes—
309#103—24no—
310#103—224no—
311C4×C8—221no—
312C4×C8—221no—
313#95—222no—
314C2×C11#164211yescharacteristic
315C2×C11#164311yescharacteristic
316C2×C11#165011yescharacteristic
317C2×C11#165111yescharacteristic
318C2×C11#200011yescharacteristic
319C2×C11#200011yescharacteristic
320C2×C11#200711yescharacteristic
321D11—82no—
322C24—221no—
323C2×Q8—21no—
324C2×Q8—22no—
325C2×Q8—21no—
326C2×Q8—21no—
327C2×Q8—21no—
328C2×Q8—21no—
329C2×Q8—41no—
330C2×Q8—41no—
331C2×Q8—41no—
332C2×Q8—41no—
333C2×Q8—41no—
334C2×Q8#432512yescomplemented
335C2×D4—112no—
336C2×D4—221no—
337C2×D4—221no—
338C2×D4—221no—
339C2×D4—221no—
340C2×D4—221no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—41no—
344C22×C4—221no—
345C22×C4—222no—
346C22×C4—441no—
347C22×C4—441no—
348C22×C4—441no—
349C22×C4—441no—
350C22×C4—441no—
351C22×C4—441no—
352C22×C4D4×D1111yescharacteristic
353C22×C4D4×D1111yescharacteristic
354C22×C4C2×C22⋊D1111yescharacteristic
355SD16—448no—
356C2×C8—22no—
357C2×C8—41no—
358C2×C8—41no—
359C2×C8—222no—
360C2×C8—222no—
361C2×C8—441no—
362C2×C8—441no—
363C2×C8—441no—
364C2×C8—441no—
365C4⋊C4—22no—
366C4⋊C4—21no—
367C4⋊C4—22no—
368C4⋊C4—21no—
369C4⋊C4—41no—
370C4⋊C4—41no—
371C4⋊C4—41no—
372C4⋊C4—41no—
373C4⋊C4—221no—
374C4⋊C4—221no—
375C4⋊C4—442no—
376C4⋊C4—444no—
377C4⋊C4—441no—
378C4⋊C4—441no—
379C4⋊C4—441no—
380C4⋊C4—441no—
381C22⋊C4—444no—
382C22⋊C4—441no—
383C22⋊C4—441no—
384C22⋊C4—882no—
385C42—41no—
386C42—41no—
387C42D4×D1111yescharacteristic
388C42#434111yescharacteristic
389C42C2×C22⋊D1111yescharacteristic
390C42C2×C22⋊D1111yescharacteristic
391C11#1023211yescharacteristic, complemented, Sylow
392C23—222no—
393C23—441no—
394C23—441no—
395C23—441no—
396C23—441no—
397C23—441no—
398C23—441no—
399C23#6699011yescharacteristic
400Q8—22no—
401Q8—22no—
402Q8—41no—
403Q8—41no—
404Q8—42no—
405Q8—42no—
406Q8—81no—
407Q8—81no—
408D4—222no—
409D4—222no—
410D4—441no—
411D4—441no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—22no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—42no—
421C2×C4—81no—
422C2×C4—81no—
423C2×C4—442no—
424C2×C4—442no—
425C2×C4—441no—
426C2×C4—442no—
427C2×C4—441no—
428C2×C4—441no—
429C2×C4—881no—
430C2×C4—881no—
431C2×C4—881no—
432C2×C4—881no—
433C2×C4SD16×D1111yescharacteristic
434C2×C4#6696711yescharacteristic
435C2×C4#6696811yescharacteristic
436C2×C4#6696911yescharacteristic
437C2×C4#6699011yescharacteristic
438C2×C4#6699111yescharacteristic
439C2×C4#6699211yescharacteristic
440C2×C4#6699211yescharacteristic
441C2×C4#6699311yescharacteristic
442C2×C4C2×#432511yescharacteristic
443C2×C4#6699511yescharacteristic
444C2×C4#6700211yescharacteristic
445C2×C4#6700311yescharacteristic
446C2×C4#6700611yescharacteristic
447C8—42no—
448C8—442no—
449C8—442no—
450C22—442no—
451C22—442no—
452C22—442no—
453C22—881no—
454C22—881no—
455C22—881no—
456C22—881no—
457C22#1062265911yescharacteristic
458C22#1062266011yescharacteristic
459C22#1062278311yescharacteristic
460C22#1062278511yescharacteristic
461C22#1062281511yescharacteristic
462C22#1062281811yescharacteristic
463C22#1062283611yescharacteristic
464C4—21no—
465C4—21no—
466C4—42no—
467C4—82no—
468C4—81no—
469C4—882no—
470C4—881no—
471C4#1062266111yescharacteristic
472C4#1062266211yescharacteristic
473C4#1062278211yescharacteristic
474C4#1062278411yescharacteristic
475C4#1062278611yescharacteristic
476C4#1062278711yescharacteristic
477C4#1062284011yescharacteristic
478C4#1062285111yescharacteristic
479C2—882no—
480C2#1306781511yescharacteristic
481C2#1306782211yescharacteristic
482C2#1306787111yescharacteristic
483C2#1306787811yescharacteristic
484C2#1306961611yescharacteristic
485C2#1306961711yescharacteristic
486C2#1306966111yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#475C2
socleC23×C11#120
prime radicalC22×D44D4
hypercenterC2×#475D11
hypocenterC11#10232
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
3. #13069578C2semidirect
4. C2×Q8⋊(C11⋊C8)C2semidirect
6. #13066500C2semidirect
7. C2×C11×#475C2semidirect
92. C2×Q8×C11SD16semidirect
149. C2×#475D11semidirect
334. C2×Q8#4325semidirect
391. C11#10232semidirect

Maximal subgroups

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

subgroupindex
C2×#106226962
#130735342
#130695782
C2×Q8⋊(C11⋊C8)2
C2×#106221212
#130665002
C2×C11×#4752
#1023211