Finite Group Databasebeta

← #14657567

Subgroups — #14657567

Order 2816.

574 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13069423C211yesmaximal, characteristic, complemented
2#13069411C211yesmaximal, characteristic, complemented
3#13068616C211yesmaximal, characteristic, complemented
4C2×#10622118C211yesmaximal, characteristic, complemented
5C2×#10622182C211yesmaximal, characteristic, complemented
6#13066500C211yesmaximal, characteristic, complemented
7C2×C11×#459C211yesmaximal, characteristic
8C22×C11×D8—21no—
9C2×C11×#127C2211yescharacteristic
10C2×C4×D4×C11C2211yescharacteristic
11C11×#459—22no—
12C11×#459—22no—
13C2×C11×C4⋊C8C2211yescharacteristic
14C2×C11×#102—21no—
15C2×#66896—21no—
16C2×#66896—21no—
17C2×#66896—21no—
18C2×C22⋊(C11⋊C8)—21no—
19C2×C22⋊(C11⋊C8)—21no—
20#10622548C2211yescharacteristic
21C2×C4⋊(C11⋊C8)C2211yescharacteristic
22C2×C4⋊(C11⋊C8)C2211yescharacteristic
23C2×C4×C11⋊C8C2211yescharacteristic
24#10622182—22no—
25#10622167—21no—
26#10622118—22no—
27C22×D4×C11—21no—
28C22×D4×C11—21no—
29C22×D4×C11—21no—
30C22×D4×C11D411yescharacteristic
31C23×C4×C11—21no—
32C2×C11×D8—24no—
33C2×C11×D8—42no—
34C2×C11×D8—42no—
35C22×C8×C11—21no—
36C11×#127—21no—
37C11×#127—21no—
38C11×#127—21no—
39C11×#127D412yes—
40C4×D4×C11—21no—
41C4×D4×C11—21no—
42C4×D4×C11—21no—
43C4×D4×C11—21no—
44C2×C11×C4⋊C4D411yescharacteristic
45C2×C11×C22⋊C4—21no—
46C2×C42×C11C2311yescharacteristic
47C2×C4⋊Dic11—21no—
48C2×C4⋊Dic11—21no—
49C2×C4⋊Dic11—21no—
50C22×C11⋊C8—21no—
51C22×C11⋊C8—21no—
52C22×C11⋊C8D411yescharacteristic
53C22×C11⋊C8D411yescharacteristic
54C11×C4⋊C8—21no—
55C11×C4⋊C8D412yes—
56C11×#102—24no—
57#66896—42no—
58#66896—42no—
59#66896—42no—
60C22⋊(C11⋊C8)—42no—
61C22⋊(C11⋊C8)—42no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)—21no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66C4×C11⋊C8—21no—
67C4×C11⋊C8—21no—
68#10473—111nomaximal, Sylow
69C24×C11—21no—
70C24×C11—41no—
71C2×D4×C11—21no—
72C2×D4×C11—22no—
73C2×D4×C11—22no—
74C2×D4×C11—21no—
75C2×D4×C11—22no—
76C2×D4×C11—21no—
77C2×D4×C11—21no—
78C2×D4×C11—21no—
79C2×D4×C11—41no—
80C2×D4×C11—41no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C2×D4×C11—41no—
84C2×D4×C11—41no—
85C2×D4×C11—41no—
86C2×D4×C11—41no—
87C2×D4×C11—41no—
88C2×D4×C11—41no—
89C2×D4×C11—41no—
90C2×D4×C11—81no—
91C2×D4×C11—81no—
92C2×D4×C11SD1612yes—
93C22×C4×C11—21no—
94C22×C4×C11—41no—
95C22×C4×C11—41no—
96C22×C4×C11—41no—
97C22×C4×C11—41no—
98C22×C4×C11—41no—
99C22×C4×C11—41no—
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11#4111yescharacteristic
103C22×Dic11—41no—
104C11×D8—48no—
105C2×C8×C11—22no—
106C2×C8×C11—41no—
107C2×C8×C11—41no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—21no—
110C11×C22⋊C4—41no—
111C11×C22⋊C4—41no—
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C42×C11#4111yescharacteristic
115C42×C11#4111yescharacteristic
116C4⋊Dic11—41no—
117C4⋊Dic11—41no—
118C4⋊Dic11—41no—
119C4⋊Dic11—41no—
120C4⋊Dic11—81no—
121C2×C11⋊C8—21no—
122C2×C11⋊C8—21no—
123C2×C11⋊C8—21no—
124C2×C11⋊C8—21no—
125C2×C11⋊C8—21no—
126C2×C11⋊C8—41no—
127C2×C11⋊C8—41no—
128C2×C11⋊C8—41no—
129C2×C11⋊C8—41no—
130C2×C11⋊C8—41no—
131C2×C11⋊C8—41no—
132C2×C11⋊C8D812yescomplemented
133C2×#459D1111yescharacteristic
134#1957—111no—
135#1954—111no—
136#1802—111no—
137C2×#334—111no—
138C2×#331—111no—
139#1296—111no—
140C23×C11—22no—
141C23×C11—41no—
142C23×C11—41no—
143C23×C11—41no—
144C23×C11—41no—
145C23×C11—41no—
146C23×C11—41no—
147C23×C11—42no—
148C23×C11—81no—
149C23×C11—81no—
150C23×C11—81no—
151C23×C11—81no—
152C23×C11—81no—
153C23×C11—81no—
154C23×C11#12111yescharacteristic
155D4×C11—22no—
156D4×C11—22no—
157D4×C11—41no—
158D4×C11—42no—
159D4×C11—42no—
160D4×C11—42no—
161D4×C11—42no—
162D4×C11—41no—
163D4×C11—82no—
164D4×C11—82no—
165D4×C11—81no—
166D4×C11—81no—
167D4×C11—81no—
168D4×C11—81no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—81no—
175C2×C4×C11—81no—
176C2×C4×C11—81no—
177C2×C4×C11—81no—
178C2×C4×C11#12011yescharacteristic
179C2×C4×C11#12111yescharacteristic
180C2×C4×C11#12111yescharacteristic
181C2×C4×C11#12311yescharacteristic
182C2×C4×C11#12311yescharacteristic
183C2×C4×C11#12411yescharacteristic
184C2×C4×C11C2×D811yescharacteristic
185C2×C4×C11C2×SD1611yescharacteristic
186C2×C4×C11#13511yescharacteristic
187C2×C4×C11#13511yescharacteristic
188C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
189C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
190C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
191C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
192C2×Dic11—81no—
193C2×Dic11—81no—
194C2×Dic11—81no—
195C8×C11—42no—
196C11⋊C8—22no—
197C11⋊C8—41no—
198C11⋊C8—81no—
199C11⋊C8—81no—
200C22×D8—21no—
201C2×#127C2×D1111yescharacteristic
202C2×C4×D4C2×D1111yescharacteristic
203#459—22no—
204#459—22no—
205C2×C4⋊C8—111no—
206C2×C4⋊C8—111no—
207C2×C4⋊C8C2×D1111yescharacteristic
208C2×#102—21no—
209C2×#102—221no—
210C2×#102—221no—
211C2×#102—221no—
212C2×C22⋊C8—221no—
213C2×C22⋊C8—221no—
214C2×C4×C8—111no—
215#384—111no—
216#340—221no—
217#334—222no—
218#331—222no—
219C22×C11—42no—
220C22×C11—42no—
221C22×C11—42no—
222C22×C11—81no—
223C22×C11—81no—
224C22×C11—81no—
225C22×C11—81no—
226C22×C11—82no—
227C22×C11—82no—
228C22×C11—82no—
229C22×C11—161no—
230C22×C11—161no—
231C22×C11—161no—
232C22×C11—161no—
233C22×C11#39411yescharacteristic
234C22×C11#45911yescharacteristic
235C22×C11#46311yescharacteristic
236C22×C11#46511yescharacteristic
237C22×C11#46911yescharacteristic
238C22×C11#47111yescharacteristic
239C22×C11#47211yescharacteristic
240C4×C11—21no—
241C4×C11—21no—
242C4×C11—81no—
243C4×C11#44911yescharacteristic
244C4×C11#45011yescharacteristic
245C4×C11#45911yescharacteristic
246C4×C11#46311yescharacteristic
247C4×C11#46611yescharacteristic
248C4×C11#46911yescharacteristic
249C4×C11#48111yescharacteristic
250C4×C11#48211yescharacteristic
251Dic11—161no—
252C22×D4—21no—
253C22×D4—21no—
254C22×D4—21no—
255C22×D4C22⋊D1111yescharacteristic
256C23×C4—21no—
257C2×D8—24no—
258C2×D8—42no—
259C2×D8—42no—
260C22×C8—21no—
261C22×C8—111no—
262C22×C8—111no—
263C22×C8—221no—
264C22×C8—221no—
265#127—21no—
266#127—21no—
267#127—21no—
268#127C22⋊D1112yes—
269C4×D4—21no—
270C4×D4—21no—
271C4×D4—21no—
272C4×D4—21no—
273C2×C4⋊C4—221no—
274C2×C4⋊C4—221no—
275C2×C4⋊C4—221no—
276C2×C4⋊C4C22⋊D1111yescharacteristic
277C2×C22⋊C4—21no—
278C2×C42C22×D1111yescharacteristic
279C4⋊C8—21no—
280C4⋊C8—221no—
281C4⋊C8—221no—
282C4⋊C8—221no—
283C4⋊C8—221no—
284C4⋊C8C22⋊D1112yes—
285#102—24no—
286#102—442no—
287#102—442no—
288#102—442no—
289C22⋊C8—442no—
290C22⋊C8—442no—
291C4×C8—221no—
292C4×C8—221no—
293C2×C11—82no—
294C2×C11—162no—
295C2×C11#166511yescharacteristic
296C2×C11#167711yescharacteristic
297C2×C11#168711yescharacteristic
298C2×C11#170111yescharacteristic
299C2×C11#203411yescharacteristic
300C2×C11#205111yescharacteristic
301C2×C11#205411yescharacteristic
302C24—21no—
303C24—41no—
304C2×D4—21no—
305C2×D4—21no—
306C2×D4—22no—
307C2×D4—22no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—21no—
311C2×D4—22no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—41no—
323C2×D4—81no—
324C2×D4—81no—
325C2×D4#432412yes—
326C22×C4—21no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—441no—
334C22×C4D4×D1111yescharacteristic
335C22×C4#434111yescharacteristic
336C22×C4C2×C22⋊D1111yescharacteristic
337D8—48no—
338C2×C8—22no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8—112no—
342C2×C8—221no—
343C2×C8—221no—
344C2×C8—221no—
345C2×C8—221no—
346C2×C8—221no—
347C2×C8—441no—
348C2×C8—441no—
349C2×C8—441no—
350C2×C8—441no—
351C2×C8—441no—
352C2×C8—441no—
353C4⋊C4—21no—
354C4⋊C4—21no—
355C4⋊C4—441no—
356C4⋊C4—441no—
357C4⋊C4—441no—
358C4⋊C4—441no—
359C4⋊C4—881no—
360C22⋊C4—41no—
361C22⋊C4—41no—
362C42#434111yescharacteristic
363C42#434111yescharacteristic
364C42C2×C22⋊D1111yescharacteristic
365C42C2×C22⋊D1111yescharacteristic
366C11#1047311yescharacteristic, complemented, Sylow
367C23—22no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23—41no—
372C23—41no—
373C23—41no—
374C23—42no—
375C23—81no—
376C23—81no—
377C23—81no—
378C23—81no—
379C23—81no—
380C23—81no—
381C23#6699211yescharacteristic
382D4—22no—
383D4—22no—
384D4—42no—
385D4—42no—
386D4—42no—
387D4—41no—
388D4—42no—
389D4—41no—
390D4—82no—
391D4—82no—
392D4—81no—
393D4—81no—
394D4—81no—
395D4—81no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—81no—
404C2×C4—81no—
405C2×C4—881no—
406C2×C4—881no—
407C2×C4—881no—
408C2×C4D8×D1111yescharacteristic
409C2×C4#6696411yescharacteristic
410C2×C4#6696411yescharacteristic
411C2×C4#6696511yescharacteristic
412C2×C4#6698511yescharacteristic
413C2×C4C2×#432411yescharacteristic
414C2×C4#6698811yescharacteristic
415C2×C4#6698811yescharacteristic
416C2×C4#6698911yescharacteristic
417C2×C4#6699111yescharacteristic
418C2×C4#6699211yescharacteristic
419C2×C4#6700211yescharacteristic
420C2×C4#6700311yescharacteristic
421C2×C4#6700611yescharacteristic
422C8—42no—
423C8—222no—
424C8—441no—
425C8—881no—
426C8—881no—
427C22—42no—
428C22—42no—
429C22—42no—
430C22—81no—
431C22—81no—
432C22—81no—
433C22—81no—
434C22—82no—
435C22—82no—
436C22—82no—
437C22—161no—
438C22—161no—
439C22—161no—
440C22—161no—
441C22#1062265211yescharacteristic
442C22#1062265411yescharacteristic
443C22#1062276311yescharacteristic
444C22#1062276611yescharacteristic
445C22#1062281211yescharacteristic
446C22#1062281311yescharacteristic
447C22#1062283511yescharacteristic
448C4—21no—
449C4—21no—
450C4—81no—
451C4—1761no—
452C4#1062264711yescharacteristic
453C4#1062264811yescharacteristic
454C4#1062276311yescharacteristic
455C4#1062276611yescharacteristic
456C4#1062277011yescharacteristic
457C4#1062277211yescharacteristic
458C4#1062283111yescharacteristic
459C4#1062285111yescharacteristic
460C2—82no—
461C2—162no—
462C2#1306795511yescharacteristic
463C2#1306802311yescharacteristic
464C2#1306809311yescharacteristic
465C2#1306817511yescharacteristic
466C2#1306980211yescharacteristic
467C2#1306990511yescharacteristic
468C2#1306992411yescharacteristic
subgroupG/H
centerC23#66992
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
Fitting, prime radicalC2×C11×#459C2
socleC23×C11#121
hypercenterC2×#459D11
hypocenterC11#10473
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. #13069423C2semidirect
2. #13069411C2semidirect
3. #13068616C2semidirect
4. C2×#10622118C2semidirect
5. C2×#10622182C2semidirect
6. #13066500C2semidirect
132. C2×C11⋊C8D8semidirect
366. C11#10473semidirect

Maximal subgroups

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

subgroupindex
#130694232
#130694112
#130686162
C2×#106221182
C2×#106221822
#130665002
C2×C11×#4592
#1047311