Finite Group Databasebeta

← #14796426

Subgroups — #14796426

Order 2816.

838 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622463C211yesmaximal, characteristic, complemented
2C2×C4×#4314C211yesmaximal, characteristic
3#13073785C211yesmaximal, characteristic
4C4⋊C4×Dic22C211yesmaximal, characteristic, complemented
5#13070099C212yesmaximal, complemented
6#13070003C212yesmaximal
7#13069577C211yesmaximal, characteristic, complemented
8#13068970C212yesmaximal
9#13068632C212yesmaximal, complemented
10#13068617C211yesmaximal, characteristic
11C11×#1939C211yesmaximal, characteristic, complemented
12C22×#4314C2211yescharacteristic
13C2×C4×D44C2211yescharacteristic
14C2×#66922C2211yescharacteristic
15C2×C4×Dic22C2212yes—
16C2×C4×Dic22C2211yescharacteristic
17C2×C11×C4⋊C8C2211yescharacteristic
18C2×C11×C4⋊C8C2212yes—
19C2×C4×C8×C11C2211yescharacteristic
20C4×C11×C4⋊C4C2211yescharacteristic
21C2×#66885C2211yescharacteristic
22C2×#66885C2212yes—
23C2×#66882C2212yes—
24C2×#66881C2211yescharacteristic
25C2×#66880C2211yescharacteristic
26C2×#66880C2212yes—
27#10622600—21no—
28#10622600—21no—
29#10622589—21no—
30C4⋊C4×Dic11—21no—
31#10622552C2212yes—
32#10622549C2212yes—
33#10622548C2211yescharacteristic
34#10622541C2212yes—
35#10622463—24no—
36C4×#4314—24no—
37#10622286—22no—
38#10622260—22no—
39C11×#336C2212yes—
40#10622189C2212yes—
41#10622189C2212yes—
42#10622189C2212yes—
43C22×D44C2311yescharacteristic
44C22×C4×D11—21no—
45C22×Dic22—21no—
46C22×Dic22C2311yescharacteristic
47C22×C8×C11C2312yes—
48C22×C8×C11C2311yescharacteristic
49C22×C8×C11C2311yescharacteristic
50C2×C11×C4⋊C4D411yescharacteristic
51C2×C11×C4⋊C4D411yescharacteristic
52C2×C42×C11C2312yes—
53C2×C42×C11C2311yescharacteristic
54C2×(C2×D11)⋊C4—21no—
55C2×(C2×D11)⋊C4—22no—
56C2×(C2×D11)⋊C4—22no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11C2312yes—
61C2×C4⋊Dic11C2312yes—
62C2×C4⋊Dic11C2311yescharacteristic
63C2×C4⋊Dic11C2311yescharacteristic
64C2×Dic11⋊C4—21no—
65C2×Dic11⋊C4—22no—
66C2×Dic11⋊C4—22no—
67C2×C4×Dic11—21no—
68C2×C4×Dic11—22no—
69C2×#4314—22no—
70C2×#4314—22no—
71C2×#4314Q814yescomplemented
72C4×D44—22no—
73C4×D44—22no—
74#66922—22no—
75#66922—22no—
76C4×Dic22—22no—
77C4×Dic22—24no—
78C4×Dic22—42no—
79C4×Dic22D414yes—
80C11×C4⋊C8—22no—
81C11×C4⋊C8—42no—
82C4×C8×C11—22no—
83C11×#95D412yes—
84C11⋊#95—22no—
85C11⋊#95—22no—
86C11⋊#95—22no—
87#66885—22no—
88#66885—42no—
89#66882—24no—
90#66881—22no—
91#66880—22no—
92#66880—24no—
93#24814—111nomaximal, Sylow
94C23×D11—21no—
95C22×C4×C11C2×D412yes—
96C22×C4×C11C2×D412yes—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2411yescharacteristic
100C22×Dic11—21no—
101C22×Dic11—21no—
102C22×Dic11—21no—
103C22×Dic11—22no—
104C22×Dic11—22no—
105C2×D44—21no—
106C2×D44—21no—
107C2×D44—21no—
108C2×D44—21no—
109C2×D44—21no—
110C2×D44C2×Q812yes—
111C2×C4×D11—42no—
112C2×C4×D11—42no—
113C2×C4×D11—42no—
114C2×Dic22—21no—
115C2×Dic22—21no—
116C2×Dic22—21no—
117C2×Dic22—42no—
118C2×Dic22—81no—
119C2×Dic22—81no—
120C2×Dic22C2×D412yes—
121C2×Dic22C2×Q812yes—
122C2×Dic22#4112yes—
123C2×C8×C11—21no—
124C2×C8×C11—22no—
125C2×C8×C11—21no—
126C2×C8×C11—21no—
127C2×C8×C11—22no—
128C2×C8×C11—21no—
129C2×C8×C11—22no—
130C2×C8×C11—21no—
131C2×C8×C11C2×Q812yes—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—22no—
134C42×C11—22no—
135C42×C11—22no—
136C42×C11C2×D412yes—
137C42×C11#4112yes—
138(C2×D11)⋊C4—42no—
139(C2×D11)⋊C4—82no—
140(C2×D11)⋊C4—82no—
141C4⋊Dic11—21no—
142C4⋊Dic11—22no—
143C4⋊Dic11—21no—
144C4⋊Dic11—22no—
145C4⋊Dic11—22no—
146C4⋊Dic11—21no—
147C4⋊Dic11—22no—
148C4⋊Dic11—42no—
149C4⋊Dic11—42no—
150C4⋊Dic11—81no—
151C4⋊Dic11C2×D412yes—
152Dic11⋊C4—24no—
153Dic11⋊C4—44no—
154Dic11⋊C4—82no—
155C4×Dic11—24no—
156C4×Dic11—44no—
157#4314—28no—
158C2×#477—111no—
159C2×C4×SD16—111no—
160#2563—111no—
161Q8×C4⋊C4—111no—
162#2085—112no—
163#2067—112no—
164#1990—111no—
165#1939D1111yescharacteristic, complemented
166#1880—112no—
167#1805—112no—
168#1802—111no—
169C23×C11C22×D411yescharacteristic
170C22×D11—22no—
171C22×D11—41no—
172C22×D11—41no—
173C22×D11—41no—
174C22×D11—41no—
175C22×D11—41no—
176C22×D11—41no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
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#12112yes—
186C2×C4×C11#12112yes—
187C2×C4×C11#13512yes—
188C2×C4×C11#13712yes—
189C2×C4×C11C22×D411yescharacteristic
190C2×C4×C11C22×Q811yescharacteristic
191C2×C4×C11C2×#4111yescharacteristic
192C2×C4×C11C2×#4111yescharacteristic
193C2×C4×C11H(5,𝔽2)11yescharacteristic
194C2×C4×C112−1+411yescharacteristic
195C2×Dic11—22no—
196C2×Dic11—22no—
197C2×Dic11—22no—
198C2×Dic11—22no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—42no—
202C2×Dic11—41no—
203C2×Dic11—42no—
204C2×Dic11—42no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210D44—22no—
211D44—22no—
212D44—41no—
213D44—41no—
214C4×D11—84no—
215Dic22—22no—
216Dic22—22no—
217Dic22—22no—
218Dic22—84no—
219Dic22C22⋊Q814yes—
220C8×C11—22no—
221C8×C11—42no—
222C8×C11—41no—
223C22×SD16—111no—
224C2×C4⋊Q8—111no—
225C2×C4×Q8—111no—
226C2×C4×Q8—112no—
227C2×C4×D4—111no—
228#477—224no—
229C4×SD16—224no—
230C2×#107—112no—
231C2×#106—111no—
232C2×C4⋊C8C2×D1111yescharacteristic
233C2×C4⋊C8C2×D1112yes—
234C2×#103—112no—
235C2×#103—111no—
236C2×#102—111no—
237C2×#102—112no—
238C2×C4×C8C2×D1111yescharacteristic
239#393—222no—
240#390—112no—
241#389—112no—
242#389—222no—
243#384—111no—
244#384—221no—
245#382—112no—
246#380—221no—
247#380—221no—
248C4×C4⋊C4—221no—
249C4×C4⋊C4C2×D1111yescharacteristic
250#340—112no—
251#340—112no—
252#340—112no—
253#336C2×D1112yes—
254C22×C11C2×#12111yescharacteristic
255C22×C11#54611yescharacteristic
256C22×C11D4×Q811yescharacteristic
257C22×C11C2×#13511yescharacteristic
258C22×C11C2×#13711yescharacteristic
259C22×C11#57611yescharacteristic
260C22×C11#57711yescharacteristic
261C2×D11—42no—
262C2×D11—42no—
263C2×D11—42no—
264C2×D11—81no—
265C2×D11—81no—
266C2×D11—81no—
267C2×D11—81no—
268C4×C11—22no—
269C4×C11—42no—
270C4×C11—42no—
271C4×C11#46414yes—
272C4×C11C2×C22⋊Q811yescharacteristic
273C4×C11#53711yescharacteristic
274C4×C11#55211yescharacteristic
275C4×C11#55411yescharacteristic
276Dic11—24no—
277Dic11—42no—
278Dic11—81no—
279Dic11—82no—
280Dic11—82no—
281C22×Q8—111no—
282C22×Q8—221no—
283C22×D4—111no—
284C23×C4—221no—
285C2×SD16—114no—
286C2×SD16—222no—
287C2×SD16—222no—
288C22×C8C22×D1112yes—
289C22×C8C22×D1111yescharacteristic
290C22×C8C22×D1111yescharacteristic
291C4⋊Q8—222no—
292C4⋊Q8—222no—
293C4×Q8—114no—
294C4×Q8—224no—
295C4×Q8—222no—
296C4×Q8—442no—
297C4×D4—222no—
298C4×D4—222no—
299C2×C4⋊C4—111no—
300C2×C4⋊C4—111no—
301C2×C4⋊C4—112no—
302C2×C4⋊C4—112no—
303C2×C4⋊C4—221no—
304C2×C4⋊C4—222no—
305C2×C4⋊C4—221no—
306C2×C4⋊C4—221no—
307C2×C4⋊C4—221no—
308C2×C4⋊C4—222no—
309C2×C4⋊C4D4411yescharacteristic
310C2×C4⋊C4D4411yescharacteristic
311C2×C22⋊C4—221no—
312C2×C22⋊C4—222no—
313C2×C22⋊C4—222no—
314C2×C42—221no—
315C2×C42—222no—
316C2×C42C22×D1112yes—
317C2×C42C22×D1111yescharacteristic
318#107—224no—
319#106—222no—
320C4⋊C8—22no—
321C4⋊C8—42no—
322#103—222no—
323#103—224no—
324#102—222no—
325#102—442no—
326C4×C8—22no—
327#95—222no—
328#95—222no—
329#95—222no—
330#95D4412yes—
331C2×C11#241711yescharacteristic
332C2×C11C2×#46411yescharacteristic
333C2×C11#304511yescharacteristic
334C2×C11#330511yescharacteristic
335C2×C11#332911yescharacteristic
336C2×C11#338111yescharacteristic
337C2×C11#338511yescharacteristic
338D11—82no—
339C24—221no—
340C2×Q8—112no—
341C2×Q8—112no—
342C2×Q8—112no—
343C2×Q8—221no—
344C2×Q8—221no—
345C2×Q8—221no—
346C2×Q8—442no—
347C2×Q8—881no—
348C2×Q8—881no—
349C2×D4—112no—
350C2×D4—221no—
351C2×D4—221no—
352C2×D4—221no—
353C2×D4—221no—
354C2×D4—221no—
355C22×C4—221no—
356C22×C4—221no—
357C22×C4—221no—
358C22×C4—222no—
359C22×C4—222no—
360C22×C4—442no—
361C22×C4—442no—
362C22×C4—442no—
363C22×C4C2×D4412yes—
364C22×C4C2×D4412yes—
365C22×C4C2×D4411yescharacteristic
366C22×C4C2×D4411yescharacteristic
367C22×C4C23×D1111yescharacteristic
368SD16—228no—
369C2×C8—21no—
370C2×C8—21no—
371C2×C8—21no—
372C2×C8—22no—
373C2×C8—22no—
374C2×C8—21no—
375C2×C8—22no—
376C2×C8—21no—
377C2×C8Q8×D1112yes—
378C4⋊C4—22no—
379C4⋊C4—22no—
380C4⋊C4—112no—
381C4⋊C4—224no—
382C4⋊C4—221no—
383C4⋊C4—221no—
384C4⋊C4—222no—
385C4⋊C4—222no—
386C4⋊C4—221no—
387C4⋊C4—222no—
388C4⋊C4—222no—
389C4⋊C4—444no—
390C4⋊C4—442no—
391C4⋊C4—442no—
392C4⋊C4—882no—
393C4⋊C4—881no—
394C22⋊C4—442no—
395C22⋊C4—882no—
396C22⋊C4—882no—
397C42—22no—
398C42—22no—
399C42—224no—
400C42—444no—
401C42D4×D1112yes—
402C42#434312yes—
403C11#2481411yescharacteristic, complemented, Sylow
404C23—222no—
405C23—441no—
406C23—441no—
407C23—441no—
408C23—441no—
409C23—441no—
410C23—441no—
411C23C22×D4411yescharacteristic
412Q8—114no—
413Q8—222no—
414Q8—222no—
415Q8—222no—
416Q8—884no—
417D4—222no—
418D4—222no—
419D4—441no—
420D4—441no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—222no—
430C2×C4—222no—
431C2×C4—222no—
432C2×C4—222no—
433C2×C4—441no—
434C2×C4—441no—
435C2×C4—442no—
436C2×C4—441no—
437C2×C4—441no—
438C2×C4—442no—
439C2×C4—442no—
440C2×C4—442no—
441C2×C4—441no—
442C2×C4—442no—
443C2×C4—442no—
444C2×C4—884no—
445C2×C4#6694812yes—
446C2×C4#6694812yes—
447C2×C4#6695712yes—
448C2×C4#6696212yes—
449C2×C4C2×D4×D1111yescharacteristic
450C2×C4#6703711yescharacteristic
451C2×C4C2×Q8×D1111yescharacteristic
452C2×C4C2×#434311yescharacteristic
453C2×C4#41×D1111yescharacteristic
454C2×C4#6704311yescharacteristic
455C8—22no—
456C8—41no—
457C8—42no—
458C22—442no—
459C22—442no—
460C22—442no—
461C22—881no—
462C22—881no—
463C22—881no—
464C22—881no—
465C22C2×#6694811yescharacteristic
466C22#1062308511yescharacteristic
467C22Q8×D4411yescharacteristic
468C22C2×#6695711yescharacteristic
469C22C2×#6696211yescharacteristic
470C22#1062328211yescharacteristic
471C22#1062328311yescharacteristic
472C4—22no—
473C4—42no—
474C4—42no—
475C4—224no—
476C4—442no—
477C4—881no—
478C4—882no—
479C4—882no—
480C4#1062245814yes—
481C4#1062313911yescharacteristic
482C4D11×C22⋊Q811yescharacteristic
483C4#1062322511yescharacteristic
484C4#1062326111yescharacteristic
485C2—882no—
486C2#1307206511yescharacteristic
487C2C2×#1062245811yescharacteristic
488C2#1307815711yescharacteristic
489C2#1308056711yescharacteristic
490C2#1308091111yescharacteristic
491C2#1308149311yescharacteristic
492C2#1308152811yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1939C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1939D11
hypocenterC11#24814
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1939

Complements

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

NH ≅ G/Ntype
1. C2×#10622463C2semidirect
4. C4⋊C4×Dic22C2semidirect
5. #13070099C2semidirect
7. #13069577C2semidirect
9. #13068632C2semidirect
11. C11×#1939C2semidirect
71. C2×#4314Q8semidirect
165. #1939D11semidirect
403. C11#24814semidirect

Maximal subgroups

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

subgroupindex
C2×#106224632
C2×C4×#43142
#130737852
C4⋊C4×Dic222
#130700992
#130700032
#130695772
#130689702
#130686322
#130686172
C11×#19392
#2481411