Finite Group Databasebeta

← #14648016

Subgroups — #14648016

Order 2816.

602 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4⋊C4×D44C211yesmaximal, characteristic
2#13068743C211yesmaximal, characteristic, complemented
3#13068613C211yesmaximal, characteristic
4C2×#10622121C211yesmaximal, characteristic
5#13066500C211yesmaximal, characteristic, complemented
6#13066457C211yesmaximal, characteristic, complemented
7C11×#1948C211yesmaximal, characteristic, complemented
8C2×C4⋊C4×D11—21no—
9C2×C4×D44—21no—
10C2×C4×D44C2211yescharacteristic
11C2×C11×#106—21no—
12C2×C11×C4⋊C8C2211yescharacteristic
13C11×#384C2211yescharacteristic
14C4×C11×C4⋊C4C2211yescharacteristic
15#10622600—21no—
16C2×#66873—21no—
17#10622548C2211yescharacteristic
18#10622541—21no—
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C2×C4×C11⋊C8C2211yescharacteristic
21#10622281—22no—
22C11×#340—21no—
23#10622167—21no—
24#10622167—22no—
25#10622121C414yescomplemented
26C22×D44D411yescharacteristic
27C22×C4×D11—21no—
28C22×C4×D11—22no—
29C22×C8×C11—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C42×C11—21no—
36C2×C42×C11C2311yescharacteristic
37C2×(C2×D11)⋊C4—21no—
38C2×(C2×D11)⋊C4—22no—
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11D411yescharacteristic
42C2×C4⋊Dic11D412yes—
43C2×Dic11⋊C4—22no—
44C22×C11⋊C8—21no—
45C22×C11⋊C8—21no—
46C4⋊C4×D11—42no—
47C4⋊C4×D11—42no—
48C4×D44—21no—
49C4×D44—21no—
50C4×D44—42no—
51C4×D44—42no—
52C4×D44C2×C412yes—
53C4×D44Q812yes—
54C11×#106—42no—
55C11×C4⋊C8—21no—
56C11×C4⋊C8C2×C412yescomplemented
57C11×#95—21no—
58C11⋊#95—22no—
59#66873—42no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62C4×C11⋊C8—21no—
63C4×C11⋊C8C2×C412yescomplemented
64#8894—111nomaximal, Sylow
65C23×D11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—41no—
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×Dic11—21no—
73C22×Dic11—22no—
74C2×D44—21no—
75C2×D44—21no—
76C2×D44—21no—
77C2×D44C4⋊C412yes—
78C2×D44SD1612yes—
79C2×D44SD1612yes—
80C2×C4×D11—22no—
81C2×C4×D11—22no—
82C2×C4×D11—44no—
83C2×C4×D11—44no—
84C2×C4×D11—41no—
85C2×C4×D11—41no—
86C2×C4×D11—41no—
87C2×C4×D11—41no—
88C2×C4×D11—82no—
89C2×C8×C11—22no—
90C2×C8×C11—41no—
91C2×C8×C11—41no—
92C11×C4⋊C4—21no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—42no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4D812yes—
101C42×C11—41no—
102C42×C11—41no—
103C42×C11C22×C411yescharacteristic
104C42×C11C2×Q811yescharacteristic
105C42×C11#4111yescharacteristic
106C42×C11#4111yescharacteristic
107(C2×D11)⋊C4—22no—
108(C2×D11)⋊C4—22no—
109(C2×D11)⋊C4—44no—
110C4⋊Dic11—21no—
111C4⋊Dic11—42no—
112C4⋊Dic11—41no—
113C4⋊Dic11—41no—
114C4⋊Dic11—41no—
115C4⋊Dic11—41no—
116C4⋊Dic11C4⋊C412yes—
117Dic11⋊C4—44no—
118C2×C11⋊C8—22no—
119C2×C11⋊C8—41no—
120C2×C11⋊C8—41no—
121C2×C11⋊C8—41no—
122C2×C11⋊C8—41no—
123C2×C11⋊C8—41no—
124D4×C4⋊C4—111no—
125#1948D1111yescharacteristic, complemented
126#1834—111no—
127#1802—111no—
128C2×D4⋊C8—111no—
129#1296—111no—
130#1279—111no—
131C23×C11#12011yescharacteristic
132C22×D11—22no—
133C22×D11—22no—
134C22×D11—22no—
135C22×D11—41no—
136C22×D11—41no—
137C22×D11—41no—
138C22×D11—41no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—22no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—81no—
148C2×C4×C11—81no—
149C2×C4×C11—81no—
150C2×C4×C11C2×C4⋊C411yescharacteristic
151C2×C4×C11C4×D411yescharacteristic
152C2×C4×C11C4×D411yescharacteristic
153C2×C4×C11C22⋊Q811yescharacteristic
154C2×C4×C11C22⋊Q811yescharacteristic
155C2×C4×C11#12311yescharacteristic
156C2×C4×C11C2×D811yescharacteristic
157C2×C4×C11C2×SD1611yescharacteristic
158C2×C4×C11C2×SD1611yescharacteristic
159C2×C4×C11#13511yescharacteristic
160C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C11#13711yescharacteristic
163C2×C4×C11#13711yescharacteristic
164C2×Dic11—22no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11—42no—
168C2×Dic11—42no—
169C2×Dic11—42no—
170D44—22no—
171D44—22no—
172D44—22no—
173D44#10614yescomplemented
174C4×D11—42no—
175C4×D11—42no—
176C4×D11—42no—
177C4×D11—42no—
178C4×D11—88no—
179C8×C11—42no—
180C11⋊C8—42no—
181C11⋊C8—81no—
182C2×C4×D4—111no—
183C2×C4×D4—221no—
184C22×C4⋊C4—221no—
185C2×#106—21no—
186C2×C4⋊C8—111no—
187C2×C4⋊C8C2×D1111yescharacteristic
188C2×#102—221no—
189C2×C4×C8—111no—
190#389—221no—
191#385—222no—
192#384—111no—
193#384C2×D1111yescharacteristic
194#380—221no—
195C4×C4⋊C4C2×D1111yescharacteristic
196#340—21no—
197#340—221no—
198#340—222no—
199D4⋊C8—114no—
200C22×C11#38511yescharacteristic
201C22×C11#44711yescharacteristic
202C22×C11#44811yescharacteristic
203C22×C11#45011yescharacteristic
204C22×C11#45211yescharacteristic
205C22×C11#45411yescharacteristic
206C22×C11#45511yescharacteristic
207C2×D11—24no—
208C2×D11—42no—
209C2×D11—42no—
210C2×D11—42no—
211C2×D11—42no—
212C2×D11—42no—
213C2×D11—42no—
214C4×C11—21no—
215C4×C11—21no—
216C4×C11—42no—
217C4×C11—81no—
218C4×C11—161no—
219C4×C11C2×#10611yescharacteristic
220C4×C11#42811yescharacteristic
221C4×C11C4×D811yescharacteristic
222C4×C11#44011yescharacteristic
223C4×C11#47411yescharacteristic
224C4×C11#47811yescharacteristic
225C4×C11#48111yescharacteristic
226C4×C11#48311yescharacteristic
227Dic11—42no—
228Dic11—82no—
229C22×D4—111no—
230C23×C4—222no—
231C23×C4—221no—
232C22×C8—21no—
233C22×C8—221no—
234C22×C8—221no—
235C4×D4—112no—
236C4×D4—112no—
237C4×D4—221no—
238C4×D4—221no—
239C4×D4—442no—
240C4×D4—442no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—111no—
245C2×C4⋊C4—112no—
246C2×C4⋊C4—222no—
247C2×C4⋊C4—221no—
248C2×C4⋊C4—221no—
249C2×C4⋊C4—442no—
250C2×C4⋊C4—442no—
251C2×C4⋊C4C22⋊D1111yescharacteristic
252C2×C4⋊C4C22⋊D1111yescharacteristic
253C2×C22⋊C4—221no—
254C2×C22⋊C4—222no—
255C2×C42—21no—
256C2×C42C22×D1111yescharacteristic
257#106—42no—
258C4⋊C8—21no—
259C4⋊C8—221no—
260C4⋊C8—221no—
261C4⋊C8C4×D1112yescomplemented
262#102—442no—
263C4×C8—112no—
264C4×C8—221no—
265#95—21no—
266#95—222no—
267C2×C11#162711yescharacteristic
268C2×C11#163511yescharacteristic
269C2×C11#163911yescharacteristic
270C2×C11#164311yescharacteristic
271C2×C11#185311yescharacteristic
272C2×C11#186011yescharacteristic
273C2×C11#186211yescharacteristic
274D11—44no—
275C24—221no—
276C2×D4—112no—
277C2×D4—112no—
278C2×D4—112no—
279C2×D4—221no—
280C2×D4—221no—
281C2×D4—221no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—41no—
285C22×C4—221no—
286C22×C4—222no—
287C22×C4—222no—
288C22×C4—222no—
289C22×C4—444no—
290C22×C4—444no—
291C22×C4—441no—
292C22×C4—441no—
293C22×C4—441no—
294C22×C4—441no—
295C22×C4—882no—
296C22×C4D4×D1111yescharacteristic
297C22×C4D4×D1111yescharacteristic
298C22×C4C2×C22⋊D1111yescharacteristic
299C2×C8—22no—
300C2×C8—41no—
301C2×C8—41no—
302C2×C8—222no—
303C2×C8—441no—
304C2×C8—441no—
305C2×C8—441no—
306C2×C8—441no—
307C2×C8—441no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—42no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—112no—
317C4⋊C4—221no—
318C4⋊C4—442no—
319C4⋊C4—444no—
320C4⋊C4—441no—
321C4⋊C4—441no—
322C4⋊C4—441no—
323C4⋊C4—441no—
324C4⋊C4#432312yes—
325C22⋊C4—222no—
326C22⋊C4—222no—
327C22⋊C4—444no—
328C42—41no—
329C42—41no—
330C42C2×C4×D1111yescharacteristic
331C42#433911yescharacteristic
332C42Q8×D1111yescharacteristic
333C42#434311yescharacteristic
334C11#889411yescharacteristic, complemented, Sylow
335C23—222no—
336C23—222no—
337C23—222no—
338C23—441no—
339C23—441no—
340C23—441no—
341C23—441no—
342C23#6699011yescharacteristic
343D4—114no—
344D4—222no—
345D4—222no—
346D4—222no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—22no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4—81no—
358C2×C4—222no—
359C2×C4—441no—
360C2×C4—441no—
361C2×C4—442no—
362C2×C4—442no—
363C2×C4—442no—
364C2×C4—442no—
365C2×C4—442no—
366C2×C4—442no—
367C2×C4—442no—
368C2×C4—888no—
369C2×C4C4⋊C4×D1111yescharacteristic
370C2×C4#6694611yescharacteristic
371C2×C4#6694711yescharacteristic
372C2×C4#6694911yescharacteristic
373C2×C4SD16×D1111yescharacteristic
374C2×C4SD16×D1111yescharacteristic
375C2×C4#6696711yescharacteristic
376C2×C4#6696811yescharacteristic
377C2×C4C4×C22⋊D1111yescharacteristic
378C2×C4C2×#432311yescharacteristic
379C2×C4#6699511yescharacteristic
380C2×C4#6699911yescharacteristic
381C2×C4#6700211yescharacteristic
382C2×C4#6700311yescharacteristic
383C8—42no—
384C8—442no—
385C8—881no—
386C22—224no—
387C22—442no—
388C22—442no—
389C22—442no—
390C22—442no—
391C22—442no—
392C22—442no—
393C22#1062260211yescharacteristic
394C22#1062264911yescharacteristic
395C22#1062266011yescharacteristic
396C22#1062278211yescharacteristic
397C22#1062278311yescharacteristic
398C22#1062281411yescharacteristic
399C22#1062281511yescharacteristic
400C4—21no—
401C4—21no—
402C4—42no—
403C4—81no—
404C4—161no—
405C4—442no—
406C4—882no—
407C4D11×#10611yescharacteristic
408C4#1062247411yescharacteristic
409C4#1062247511yescharacteristic
410C4#1062247611yescharacteristic
411C4C4×#432311yescharacteristic
412C4#1062263911yescharacteristic
413C4#1062267911yescharacteristic
414C4#1062270011yescharacteristic
415C2—444no—
416C2#1306771711yescharacteristic
417C2#1306776611yescharacteristic
418C2#1306779311yescharacteristic
419C2#1306782211yescharacteristic
420C2#1306880711yescharacteristic
421C2#1306884611yescharacteristic
422C2#1306886211yescharacteristic
subgroupG/H
centerC23#66990
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1948C2
socleC23×C11#120
prime radicalC22×D44D4
cosocleC2×C42×C11C23
hypercenter#1948D11
hypocenterC11#8894
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

Complements

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

NH ≅ G/Ntype
2. #13068743C2semidirect
5. #13066500C2semidirect
6. #13066457C2semidirect
7. C11×#1948C2semidirect
25. #10622121C4semidirect
56. C11×C4⋊C8C2×C4semidirect
63. C4×C11⋊C8C2×C4semidirect
125. #1948D11semidirect
173. D44#106semidirect
261. C4⋊C8C4×D11semidirect
334. C11#8894semidirect

Maximal subgroups

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

subgroupindex
C4⋊C4×D442
#130687432
#130686132
C2×#106221212
#130665002
#130664572
C11×#19482
#889411