Finite Group Databasebeta

← #14657566

Subgroups — #14657566

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
1C2×#10622456C211yesmaximal, characteristic
2#13069421C211yesmaximal, characteristic, complemented
3#13069409C211yesmaximal, characteristic, complemented
4#13068613C211yesmaximal, characteristic, complemented
5C2×#10622117C211yesmaximal, characteristic, complemented
6C2×#10622123C211yesmaximal, characteristic, complemented
7C11×#1296C211yesmaximal, characteristic, complemented
8C22×D88—21no—
9C2×#66927C2211yescharacteristic
10C2×C4×D44C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13C11×#384C2211yescharacteristic
14C2×#66885—21no—
15C2×(C2×D11)⋊C8—21no—
16C2×(C2×D11)⋊C8—21no—
17C2×#66873—21no—
18C2×#66873—21no—
19C2×#66873—21no—
20C2×C4⋊(C11⋊C8)C2211yescharacteristic
21C2×C4×C11⋊C8C2211yescharacteristic
22#10622456—22no—
23#10622456—22no—
24#10622167—21no—
25#10622123—22no—
26#10622117—22no—
27C22×D44—21no—
28C22×D44—21no—
29C22×D44—21no—
30C22×D44D411yescharacteristic
31C22×C4×D11—21no—
32C22×C8×C11—21no—
33C22×C8×C11—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C42×C11C2311yescharacteristic
38C2×(C2×D11)⋊C4—21no—
39C2×C4⋊Dic11D411yescharacteristic
40C22×C11⋊C8—21no—
41C22×C11⋊C8D411yescharacteristic
42C22×C11⋊C8D411yescharacteristic
43C2×D88—24no—
44C2×D88—42no—
45C2×D88—42no—
46#66927—21no—
47#66927—21no—
48#66927—21no—
49#66927D412yes—
50C4×D44—21no—
51C4×D44—21no—
52C4×D44—21no—
53C4×D44—21no—
54C11×C4⋊C8—21no—
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C11×C4⋊C8D412yes—
58#66885—24no—
59(C2×D11)⋊C8—42no—
60(C2×D11)⋊C8—42no—
61#66873—42no—
62#66873—42no—
63#66873—42no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66C4×C11⋊C8—21no—
67C4×C11⋊C8—21no—
68#10472—111nomaximal, Sylow
69C23×D11—21no—
70C23×D11—41no—
71C22×C4×C11—41no—
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11#4111yescharacteristic
75C22×Dic11—21no—
76C2×D44—21no—
77C2×D44—22no—
78C2×D44—22no—
79C2×D44—21no—
80C2×D44—22no—
81C2×D44—21no—
82C2×D44—21no—
83C2×D44—21no—
84C2×D44—41no—
85C2×D44—41no—
86C2×D44—41no—
87C2×D44—41no—
88C2×D44—41no—
89C2×D44—41no—
90C2×D44—41no—
91C2×D44—41no—
92C2×D44—41no—
93C2×D44—41no—
94C2×D44—41no—
95C2×D44—81no—
96C2×D44—81no—
97C2×D44D812yes—
98C2×C4×D11—41no—
99C2×C4×D11—41no—
100C2×C4×D11—41no—
101C2×C4×D11—41no—
102C2×C4×D11—41no—
103C2×C4×D11—41no—
104C2×C8×C11—22no—
105C2×C8×C11—41no—
106C2×C8×C11—41no—
107C2×C8×C11—41no—
108C2×C8×C11—41no—
109C2×C8×C11—41no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—41no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—81no—
115C42×C11C2×D411yescharacteristic
116C42×C11C2×D411yescharacteristic
117C42×C11#4111yescharacteristic
118C42×C11#4111yescharacteristic
119(C2×D11)⋊C4—41no—
120(C2×D11)⋊C4—41no—
121C4⋊Dic11—21no—
122C4⋊Dic11—21no—
123C2×C11⋊C8—21no—
124C2×C11⋊C8—21no—
125C2×C11⋊C8—21no—
126C2×C11⋊C8—21no—
127C2×C11⋊C8—21no—
128C2×C11⋊C8—41no—
129C2×C11⋊C8—41no—
130C2×C11⋊C8—41no—
131C2×C11⋊C8D812yescomplemented
132D88—48no—
133C2×#459—111no—
134#1957—111no—
135#1954—111no—
136#1802—111no—
137C2×#335—111no—
138C2×#331—111no—
139#1296D1111yescharacteristic, complemented
140C23×C11#12111yescharacteristic
141C22×D11—22no—
142C22×D11—41no—
143C22×D11—41no—
144C22×D11—41no—
145C22×D11—41no—
146C22×D11—41no—
147C22×D11—41no—
148C22×D11—42no—
149C22×D11—81no—
150C22×D11—81no—
151C22×D11—81no—
152C22×D11—81no—
153C22×D11—81no—
154C22×D11—81no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—81no—
158C2×C4×C11—81no—
159C2×C4×C11—81no—
160C2×C4×C11#12011yescharacteristic
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11#12311yescharacteristic
164C2×C4×C11#12311yescharacteristic
165C2×C4×C11#12411yescharacteristic
166C2×C4×C11C2×D811yescharacteristic
167C2×C4×C11C2×D811yescharacteristic
168C2×C4×C11#13511yescharacteristic
169C2×C4×C11#13511yescharacteristic
170C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C11#13711yescharacteristic
174C2×Dic11—41no—
175C2×Dic11—41no—
176C2×Dic11—41no—
177D44—22no—
178D44—22no—
179D44—42no—
180D44—41no—
181D44—42no—
182D44—42no—
183D44—42no—
184D44—41no—
185D44—82no—
186D44—82no—
187D44—81no—
188D44—81no—
189D44—81no—
190D44—81no—
191C4×D11—81no—
192C4×D11—81no—
193C4×D11—81no—
194C4×D11—81no—
195C8×C11—42no—
196C8×C11—81no—
197C11⋊C8—22no—
198C11⋊C8—41no—
199C11⋊C8—81no—
200C22×D8—221no—
201C2×#127—111no—
202C2×C4×D4—111no—
203#459—222no—
204#459—222no—
205C2×C4⋊C8—111no—
206C2×C4⋊C8C2×D1111yescharacteristic
207C2×C4⋊C8C2×D1111yescharacteristic
208C2×#102—221no—
209C2×#102—221no—
210C2×#102—221no—
211C2×#102—221no—
212C2×C22⋊C8—221no—
213C2×C22⋊C8—221no—
214C2×C4×C8—111no—
215#384C2×D1111yescharacteristic
216#340—221no—
217#335—222no—
218#331—222no—
219C22×C11#39411yescharacteristic
220C22×C11#45911yescharacteristic
221C22×C11#46311yescharacteristic
222C22×C11#46611yescharacteristic
223C22×C11#46811yescharacteristic
224C22×C11#47111yescharacteristic
225C22×C11#47211yescharacteristic
226C2×D11—42no—
227C2×D11—42no—
228C2×D11—42no—
229C2×D11—81no—
230C2×D11—81no—
231C2×D11—81no—
232C2×D11—81no—
233C2×D11—82no—
234C2×D11—82no—
235C2×D11—82no—
236C2×D11—161no—
237C2×D11—161no—
238C2×D11—161no—
239C2×D11—161no—
240C4×C11—21no—
241C4×C11—21no—
242C4×C11—161no—
243C4×C11#44711yescharacteristic
244C4×C11#45211yescharacteristic
245C4×C11#45911yescharacteristic
246C4×C11#46311yescharacteristic
247C4×C11#46611yescharacteristic
248C4×C11#46911yescharacteristic
249C4×C11#48011yescharacteristic
250C4×C11#48211yescharacteristic
251Dic11—81no—
252C22×D4—111no—
253C22×D4—221no—
254C22×D4—221no—
255C22×D4—221no—
256C23×C4—221no—
257C2×D8—224no—
258C2×D8—442no—
259C2×D8—442no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—111no—
263C22×C8—111no—
264C22×C8—221no—
265#127—112no—
266#127—221no—
267#127—221no—
268#127—221no—
269C4×D4—221no—
270C4×D4—221no—
271C4×D4—221no—
272C4×D4—221no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—111no—
277C2×C22⋊C4—221no—
278C2×C42C22×D1111yescharacteristic
279C4⋊C8—21no—
280C4⋊C8—21no—
281C4⋊C8—21no—
282C4⋊C8—221no—
283C4⋊C8—221no—
284C4⋊C8D4412yes—
285#102—224no—
286#102—442no—
287#102—442no—
288#102—442no—
289C22⋊C8—442no—
290C22⋊C8—442no—
291C4×C8—221no—
292C4×C8—221no—
293C2×C11#166711yescharacteristic
294C2×C11#168111yescharacteristic
295C2×C11#168511yescharacteristic
296C2×C11#169711yescharacteristic
297C2×C11#203311yescharacteristic
298C2×C11#205111yescharacteristic
299C2×C11#205411yescharacteristic
300D11—82no—
301D11—162no—
302C24—221no—
303C24—441no—
304C2×D4—112no—
305C2×D4—221no—
306C2×D4—222no—
307C2×D4—222no—
308C2×D4—221no—
309C2×D4—222no—
310C2×D4—221no—
311C2×D4—221no—
312C2×D4—221no—
313C2×D4—441no—
314C2×D4—441no—
315C2×D4—441no—
316C2×D4—441no—
317C2×D4—441no—
318C2×D4—441no—
319C2×D4—441no—
320C2×D4—441no—
321C2×D4—441no—
322C2×D4—441no—
323C2×D4—441no—
324C2×D4—881no—
325C2×D4—881no—
326C22×C4—41no—
327C22×C4—221no—
328C22×C4—441no—
329C22×C4—441no—
330C22×C4—441no—
331C22×C4—441no—
332C22×C4—441no—
333C22×C4—441no—
334C22×C4#433911yescharacteristic
335C22×C4D4×D1111yescharacteristic
336C22×C4D4×D1111yescharacteristic
337D8—448no—
338C2×C8—22no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8—41no—
342C2×C8—41no—
343C2×C8—41no—
344C2×C8—112no—
345C2×C8—221no—
346C2×C8—221no—
347C2×C8—221no—
348C2×C8—221no—
349C2×C8—221no—
350C2×C8—441no—
351C2×C8—441no—
352C2×C8—441no—
353C4⋊C4—41no—
354C4⋊C4—41no—
355C4⋊C4—41no—
356C4⋊C4—41no—
357C4⋊C4—81no—
358C4⋊C4—221no—
359C4⋊C4—221no—
360C22⋊C4—441no—
361C22⋊C4—441no—
362C42C2×D4411yescharacteristic
363C42#433911yescharacteristic
364C42D4×D1111yescharacteristic
365C42#434311yescharacteristic
366C11#1047211yescharacteristic, complemented, Sylow
367C23—222no—
368C23—441no—
369C23—441no—
370C23—441no—
371C23—441no—
372C23—441no—
373C23—441no—
374C23—442no—
375C23—881no—
376C23—881no—
377C23—881no—
378C23—881no—
379C23—881no—
380C23—881no—
381C23#6693711yescharacteristic
382D4—222no—
383D4—222no—
384D4—441no—
385D4—442no—
386D4—442no—
387D4—441no—
388D4—442no—
389D4—442no—
390D4—882no—
391D4—882no—
392D4—881no—
393D4—881no—
394D4—881no—
395D4—881no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4—81no—
401C2×C4—441no—
402C2×C4—441no—
403C2×C4—441no—
404C2×C4—881no—
405C2×C4—881no—
406C2×C4—881no—
407C2×C4—881no—
408C2×C4#6692811yescharacteristic
409C2×C4#6693511yescharacteristic
410C2×C4#6693711yescharacteristic
411C2×C4#6694711yescharacteristic
412C2×C4#6694711yescharacteristic
413C2×C4#6694811yescharacteristic
414C2×C4D8×D1111yescharacteristic
415C2×C4D8×D1111yescharacteristic
416C2×C4#6696711yescharacteristic
417C2×C4#6696711yescharacteristic
418C2×C4#6696711yescharacteristic
419C2×C4#6696911yescharacteristic
420C2×C4#6697111yescharacteristic
421C2×C4#6697211yescharacteristic
422C8—42no—
423C8—81no—
424C8—222no—
425C8—441no—
426C8—881no—
427C22—442no—
428C22—442no—
429C22—442no—
430C22—881no—
431C22—881no—
432C22—881no—
433C22—881no—
434C22—882no—
435C22—882no—
436C22—882no—
437C22—1761no—
438C22—1761no—
439C22—1761no—
440C22—1761no—
441C22#1062228511yescharacteristic
442C22#1062236211yescharacteristic
443C22#1062236711yescharacteristic
444C22#1062238811yescharacteristic
445C22#1062239911yescharacteristic
446C22#1062242511yescharacteristic
447C22#1062243211yescharacteristic
448C4—21no—
449C4—21no—
450C4—161no—
451C4—881no—
452C4#1062238611yescharacteristic
453C4#1062239911yescharacteristic
454C4#1062242311yescharacteristic
455C4#1062243211yescharacteristic
456C4#1062247811yescharacteristic
457C4#1062247911yescharacteristic
458C4#1062249511yescharacteristic
459C4#1062249611yescharacteristic
460C2—882no—
461C2—1762no—
462C2#1306797011yescharacteristic
463C2#1306805611yescharacteristic
464C2#1306808411yescharacteristic
465C2#1306815211yescharacteristic
466C2#1306980111yescharacteristic
467C2#1306991111yescharacteristic
468C2#1306992811yescharacteristic
subgroupG/H
centerC23#66937
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1296C2
socleC23×C11#121
prime radicalC2×#10622456C2
hypercenter#1296D11
hypocenterC11#10472
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
2. #13069421C2semidirect
3. #13069409C2semidirect
4. #13068613C2semidirect
5. C2×#10622117C2semidirect
6. C2×#10622123C2semidirect
7. C11×#1296C2semidirect
131. C2×C11⋊C8D8semidirect
139. #1296D11semidirect
366. C11#10472semidirect

Maximal subgroups

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

subgroupindex
C2×#106224562
#130694212
#130694092
#130686132
C2×#106221172
C2×#106221232
C11×#12962
#1047211