Finite Group Databasebeta

← #14648017

Subgroups — #14648017

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
1#13069379C211yesmaximal, characteristic, complemented
2#13068743C211yesmaximal, characteristic, complemented
3#13068616C211yesmaximal, characteristic
4C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic
5#13066499C211yesmaximal, characteristic, complemented
6#13066457C211yesmaximal, characteristic, complemented
7D4×C11×C4⋊C4C211yesmaximal, characteristic
8C2×C4×D4×C11—21no—
9C2×C4×D4×C11C2211yescharacteristic
10C22×C11×C4⋊C4—21no—
11C11×#389—21no—
12C11×#385—22no—
13C11×#384C2211yescharacteristic
14C11×#380—21no—
15C4×C11×C4⋊C4C2211yescharacteristic
16C2×#66896—21no—
17C2×#66872—21no—
18#10622548C2211yescharacteristic
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C2×C4⋊(C11⋊C8)C2211yescharacteristic
21C2×C4×C11⋊C8C2211yescharacteristic
22D4⋊(C11⋊C8)C414yescomplemented
23#10622167—21no—
24#10622167—21no—
25#10622167—22no—
26C22×D4×C11D411yescharacteristic
27C23×C4×C11—21no—
28C23×C4×C11—22no—
29C4×D4×C11—21no—
30C4×D4×C11—21no—
31C4×D4×C11—42no—
32C4×D4×C11—42no—
33C4×D4×C11C2×C412yes—
34C4×D4×C11Q812yes—
35C2×C11×C4⋊C4—22no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—42no—
39C2×C11×C4⋊C4—42no—
40C2×C11×C4⋊C4D411yescharacteristic
41C2×C11×C4⋊C4D411yescharacteristic
42C2×C11×C4⋊C4D411yescharacteristic
43C2×C11×C4⋊C4D412yes—
44C2×C11×C22⋊C4—21no—
45C2×C11×C22⋊C4—22no—
46C2×C42×C11—21no—
47C2×C42×C11C2311yescharacteristic
48C2×C4⋊Dic11—21no—
49C2×C4⋊Dic11—21no—
50C2×C4⋊Dic11—21no—
51C22×C11⋊C8—21no—
52C22×C11⋊C8—21no—
53C22×C11⋊C8—21no—
54C11×#95—22no—
55C11×#95—21no—
56#66896—42no—
57#66872—42no—
58C4⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)C2×C412yescomplemented
62C4×C11⋊C8—21no—
63C4×C11⋊C8C2×C412yescomplemented
64#8894—111nomaximal, Sylow
65C24×C11—21no—
66C2×D4×C11—21no—
67C2×D4×C11—21no—
68C2×D4×C11—21no—
69C2×D4×C11C4⋊C412yes—
70C2×D4×C11SD1612yes—
71C2×D4×C11SD1612yes—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—22no—
75C22×C4×C11—22no—
76C22×C4×C11—21no—
77C22×C4×C11—22no—
78C22×C4×C11—44no—
79C22×C4×C11—41no—
80C22×C4×C11—41no—
81C22×C4×C11—41no—
82C22×C4×C11—41no—
83C22×C4×C11—44no—
84C22×C4×C11—82no—
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×Dic11—41no—
89C11×C4⋊C4—21no—
90C11×C4⋊C4—21no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4—21no—
93C11×C4⋊C4—44no—
94C11×C4⋊C4—42no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4C4⋊C412yes—
100C11×C4⋊C4D812yes—
101C11×C22⋊C4—22no—
102C11×C22⋊C4—22no—
103C11×C22⋊C4—44no—
104C42×C11—41no—
105C42×C11—41no—
106C42×C11C22×C411yescharacteristic
107C42×C11C2×Q811yescharacteristic
108C42×C11#4111yescharacteristic
109C42×C11#4111yescharacteristic
110C4⋊Dic11—42no—
111C4⋊Dic11—41no—
112C4⋊Dic11—41no—
113C4⋊Dic11—41no—
114C4⋊Dic11—41no—
115C2×C11⋊C8—22no—
116C2×C11⋊C8—22no—
117C2×C11⋊C8—41no—
118C2×C11⋊C8—41no—
119C2×C11⋊C8—41no—
120C2×C11⋊C8—41no—
121C2×C11⋊C8—41no—
122C2×C11⋊C8—41no—
123C2×C11⋊C8—41no—
124D4×C4⋊C4D1111yescharacteristic
125#1948—111no—
126#1834—111no—
127#1802—111no—
128C2×D4⋊C8—111no—
129#1296—111no—
130#1279—111no—
131C23×C11—22no—
132C23×C11—22no—
133C23×C11—22no—
134C23×C11—41no—
135C23×C11—41no—
136C23×C11—41no—
137C23×C11—41no—
138C23×C11#12011yescharacteristic
139D4×C11—22no—
140D4×C11—22no—
141D4×C11—22no—
142D4×C11#10614yescomplemented
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—22no—
146C2×C4×C11—22no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11—42no—
154C2×C4×C11—42no—
155C2×C4×C11—42no—
156C2×C4×C11—41no—
157C2×C4×C11—42no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—42no—
161C2×C4×C11—88no—
162C2×C4×C11C2×C4⋊C411yescharacteristic
163C2×C4×C11C4×D411yescharacteristic
164C2×C4×C11C4×D411yescharacteristic
165C2×C4×C11C22⋊Q811yescharacteristic
166C2×C4×C11C22⋊Q811yescharacteristic
167C2×C4×C11#12311yescharacteristic
168C2×C4×C11C2×D811yescharacteristic
169C2×C4×C11C2×SD1611yescharacteristic
170C2×C4×C11C2×SD1611yescharacteristic
171C2×C4×C11#13511yescharacteristic
172C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
174C2×C4×C11#13711yescharacteristic
175C2×C4×C11#13711yescharacteristic
176C2×Dic11—81no—
177C2×Dic11—81no—
178C2×Dic11—81no—
179C11⋊C8—42no—
180C11⋊C8—42no—
181C11⋊C8—81no—
182C2×C4×D4—21no—
183C2×C4×D4C2×D1111yescharacteristic
184C22×C4⋊C4—21no—
185C2×#106—221no—
186C2×C4⋊C8—111no—
187C2×C4⋊C8—111no—
188C2×#102—221no—
189C2×C4×C8—111no—
190#389—21no—
191#385—22no—
192#384—111no—
193#384C2×D1111yescharacteristic
194#380—21no—
195C4×C4⋊C4C2×D1111yescharacteristic
196#340—221no—
197#340—222no—
198#340—221no—
199D4⋊C8—114no—
200C22×C11—24no—
201C22×C11—42no—
202C22×C11—42no—
203C22×C11—42no—
204C22×C11—42no—
205C22×C11—42no—
206C22×C11—42no—
207C22×C11#38511yescharacteristic
208C22×C11#44711yescharacteristic
209C22×C11#44811yescharacteristic
210C22×C11#45011yescharacteristic
211C22×C11#45211yescharacteristic
212C22×C11#45411yescharacteristic
213C22×C11#45511yescharacteristic
214C4×C11—21no—
215C4×C11—21no—
216C4×C11—42no—
217C4×C11—42no—
218C4×C11—81no—
219C4×C11—82no—
220C4×C11C2×#10611yescharacteristic
221C4×C11#42811yescharacteristic
222C4×C11C4×D811yescharacteristic
223C4×C11#44011yescharacteristic
224C4×C11#47411yescharacteristic
225C4×C11#47811yescharacteristic
226C4×C11#48111yescharacteristic
227C4×C11#48311yescharacteristic
228Dic11—161no—
229C22×D4C22⋊D1111yescharacteristic
230C23×C4—21no—
231C23×C4—22no—
232C22×C8—221no—
233C22×C8—221no—
234C22×C8—221no—
235C4×D4—21no—
236C4×D4—21no—
237C4×D4—42no—
238C4×D4—42no—
239C4×D4Dic2212yes—
240C4×D4C4×D1112yes—
241C2×C4⋊C4—22no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—42no—
245C2×C4⋊C4—42no—
246C2×C4⋊C4—221no—
247C2×C4⋊C4—221no—
248C2×C4⋊C4—221no—
249C2×C4⋊C4C22⋊D1111yescharacteristic
250C2×C4⋊C4C22⋊D1111yescharacteristic
251C2×C4⋊C4C22⋊D1111yescharacteristic
252C2×C4⋊C4C22⋊D1112yes—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—22no—
255C2×C42—21no—
256C2×C42C22×D1111yescharacteristic
257#106—442no—
258C4⋊C8—112no—
259C4⋊C8—221no—
260C4⋊C8—221no—
261C4⋊C8—221no—
262#102—442no—
263C4×C8—112no—
264C4×C8—221no—
265#95—22no—
266#95—21no—
267C2×C11—44no—
268C2×C11#162711yescharacteristic
269C2×C11#163511yescharacteristic
270C2×C11#163911yescharacteristic
271C2×C11#164311yescharacteristic
272C2×C11#185311yescharacteristic
273C2×C11#186011yescharacteristic
274C2×C11#186211yescharacteristic
275C24—21no—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—21no—
279C2×D4Dic11⋊C412yes—
280C2×D4#432412yes—
281C2×D4#432512yes—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—21no—
287C22×C4—22no—
288C22×C4—44no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—44no—
294C22×C4—82no—
295C22×C4—441no—
296C22×C4C2×C22⋊D1111yescharacteristic
297C22×C4C2×C22⋊D1111yescharacteristic
298C22×C4C2×C22⋊D1111yescharacteristic
299C2×C8—222no—
300C2×C8—222no—
301C2×C8—441no—
302C2×C8—441no—
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—21no—
312C4⋊C4—42no—
313C4⋊C4—44no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—442no—
319C4⋊C4—441no—
320C4⋊C4—441no—
321C4⋊C4—441no—
322C4⋊C4—441no—
323C4⋊C4Dic11⋊C412yes—
324C4⋊C4#432312yes—
325C22⋊C4—22no—
326C22⋊C4—22no—
327C22⋊C4—44no—
328C42—41no—
329C42—41no—
330C42C2×Dic2211yescharacteristic
331C42C2×C4×D1111yescharacteristic
332C42#433911yescharacteristic
333C42#433911yescharacteristic
334C11#889411yescharacteristic, complemented, Sylow
335C23—22no—
336C23—22no—
337C23—22no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23#6700611yescharacteristic
343D4—22no—
344D4—22no—
345D4—22no—
346D4#6687214yescomplemented
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—41no—
361C2×C4—42no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—41no—
365C2×C4—88no—
366C2×C4—881no—
367C2×C4—881no—
368C2×C4—881no—
369C2×C4C2×Dic11⋊C411yescharacteristic
370C2×C4#6697711yescharacteristic
371C2×C4#6697711yescharacteristic
372C2×C4C4×C22⋊D1111yescharacteristic
373C2×C4C4×C22⋊D1111yescharacteristic
374C2×C4#6698211yescharacteristic
375C2×C4C2×#432311yescharacteristic
376C2×C4#6698511yescharacteristic
377C2×C4#6698511yescharacteristic
378C2×C4C2×#432411yescharacteristic
379C2×C4C2×#432511yescharacteristic
380C2×C4#6699511yescharacteristic
381C2×C4#6700311yescharacteristic
382C2×C4#6700411yescharacteristic
383C8—442no—
384C8—442no—
385C8—881no—
386C22—24no—
387C22—42no—
388C22—42no—
389C22—42no—
390C22—42no—
391C22—42no—
392C22—42no—
393C22#1062282311yescharacteristic
394C22#1062283011yescharacteristic
395C22#1062283111yescharacteristic
396C22#1062284011yescharacteristic
397C22#1062285211yescharacteristic
398C22#1062285511yescharacteristic
399C22#1062285811yescharacteristic
400C4—21no—
401C4—21no—
402C4—42no—
403C4—42no—
404C4—82no—
405C4—81no—
406C4—1761no—
407C4C2×#6687211yescharacteristic
408C4#1062257711yescharacteristic
409C4#1062258111yescharacteristic
410C4#1062258411yescharacteristic
411C4#1062262011yescharacteristic
412C4#1062262211yescharacteristic
413C4C4×#432311yescharacteristic
414C4#1062263111yescharacteristic
415C2—44no—
416C2#1306771911yescharacteristic
417C2#1306776711yescharacteristic
418C2#1306779511yescharacteristic
419C2#1306782311yescharacteristic
420C2#1306880911yescharacteristic
421C2#1306884911yescharacteristic
422C2#1306886311yescharacteristic
subgroupG/H
centerC23#67006
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingD4×C11×C4⋊C4C2
socleC23×C11#120
prime radicalC22×D4×C11D4
cosocleC2×C42×C11C23
hypercenterD4×C4⋊C4D11
hypocenterC11#8894
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #13069379C2semidirect
2. #13068743C2semidirect
5. #13066499C2semidirect
6. #13066457C2semidirect
22. D4⋊(C11⋊C8)C4semidirect
61. C4⋊(C11⋊C8)C2×C4semidirect
63. C4×C11⋊C8C2×C4semidirect
142. D4×C11#106semidirect
334. C11#8894semidirect
346. D4#66872semidirect

Maximal subgroups

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

subgroupindex
#130693792
#130687432
#130686162
C2×D4⋊(C11⋊C8)2
#130664992
#130664572
D4×C11×C4⋊C42
#889411