Finite Group Databasebeta

← #14672477

Subgroups — #14672477

Order 2816.

618 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66864C211yesmaximal, characteristic, complemented
2C2×#10622729C211yesmaximal, characteristic, complemented
3C2×#10622728C211yesmaximal, characteristic
4C2×#10622141C211yesmaximal, characteristic, complemented
5C2×#10622147C211yesmaximal, characteristic, complemented
6#13066708C211yesmaximal, characteristic, complemented
7C2×C11×C22⋊C16C211yesmaximal, characteristic, complemented
8C23×C8×C11C2211yescharacteristic
9C2×#66983—21no—
10C2×#66977—21no—
11C22×Dic44C2211yescharacteristic
12C22×D88C2211yescharacteristic
13C22×C11×C16C2211yescharacteristic
14C22×C11×C16C2211yescharacteristic
15#10622729—22no—
16#10622729—22no—
17#10622728—22no—
18#10622728—22no—
19C2×#66885—21no—
20C2×#66882C2211yescharacteristic
21C2×#66882C2211yescharacteristic
22C2×#66880—21no—
23C2×#66864—22no—
24C2×#66864—22no—
25C2×#66864—22no—
26C11×C22⋊C16—22no—
27#10622147—22no—
28#10622141—22no—
29C23×C4×C11D411yescharacteristic
30C22×C22⋊D11—41no—
31C22×D44—21no—
32C22×Dic22—21no—
33C22×C8×C11—21no—
34C22×C8×C11—21no—
35C22×C8×C11—21no—
36C22×C8×C11—21no—
37C22×C8×C11—21no—
38C22×C8×C11—21no—
39C22×C8×C11D411yescharacteristic
40C22×C8×C11C2311yescharacteristic
41C2×C22⋊Dic11—41no—
42#66983—24no—
43#66983—42no—
44C2×(C2×D11)⋊C4—41no—
45C2×C4⋊Dic11—21no—
46C2×C4⋊Dic11—21no—
47#66977—24no—
48#66977—42no—
49C2×Dic11⋊C4—41no—
50C2×Dic44—21no—
51C2×Dic44—21no—
52C2×Dic44—21no—
53C2×Dic44—21no—
54C2×Dic44—21no—
55C2×Dic44D412yescomplemented
56C2×D88—21no—
57C2×D88—21no—
58C2×D88—21no—
59C2×D88—21no—
60C2×D88—21no—
61C2×D88D412yes—
62C2×C11×C16—21no—
63C2×C11×C16—21no—
64C2×C11×C16—21no—
65C2×C11×C16—21no—
66C2×C11×C16—21no—
67C2×C11×C16D412yescomplemented
68#66885—24no—
69#66882—21no—
70#66882—21no—
71#66882D412yes—
72#66882D412yescomplemented
73#66880—24no—
74#66864—28no—
75#13305—111nomaximal, Sylow
76C24×C11D811yescharacteristic
77C23×D11—41no—
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11D811yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C2×C22⋊D11—44no—
87C2×C22⋊D11—82no—
88C2×C22⋊D11—82no—
89C22×Dic11—41no—
90C22×Dic11—41no—
91C22×Dic11—41no—
92C2×D44—22no—
93C2×D44—41no—
94C2×D44—41no—
95C2×D44—41no—
96C2×D44—41no—
97C2×D44—41no—
98C2×Dic22—22no—
99C2×Dic22—41no—
100C2×Dic22—41no—
101C2×Dic22—41no—
102C2×Dic22—41no—
103C2×Dic22—41no—
104C2×C8×C11—21no—
105C2×C8×C11—21no—
106C2×C8×C11—21no—
107C2×C8×C11—41no—
108C2×C8×C11—41no—
109C2×C8×C11—41no—
110C2×C8×C11—41no—
111C2×C8×C11C2×D411yescharacteristic
112C2×C8×C11C2×D411yescharacteristic
113C2×C8×C11C2×D411yescharacteristic
114C2×C8×C11C2×D411yescharacteristic
115C2×C8×C11C2×D411yescharacteristic
116C2×C8×C11#4111yescharacteristic
117C22⋊Dic11—44no—
118(C2×D11)⋊C4—44no—
119C4⋊Dic11—22no—
120C4⋊Dic11—22no—
121C4⋊Dic11—41no—
122C4⋊Dic11—41no—
123Dic11⋊C4—44no—
124Dic44—22no—
125Dic44—22no—
126Dic44—41no—
127Dic44—41no—
128D88—22no—
129D88—22no—
130D88—41no—
131D88—41no—
132C11×C16—22no—
133C11×C16—41no—
134C22×SD32—111no—
135C2×#467—111no—
136C2×#466—111no—
137C2×#358—111no—
138C2×#357—111no—
139C2×C22⋊C16D1111yescharacteristic, complemented
140#1380—111no—
141C23×C11—21no—
142C23×C11—21no—
143C23×C11—21no—
144C23×C11—21no—
145C23×C11—21no—
146C23×C11—21no—
147C23×C11SD3212yescomplemented
148C23×C11C2×D811yescharacteristic
149C22×D11—42no—
150C22×D11—81no—
151C22×D11—81no—
152C22×D11—81no—
153C22×D11—81no—
154C22×D11—81no—
155C22×D11—81no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11#12011yescharacteristic
164C2×C4×C11#12011yescharacteristic
165C2×C4×C11#12111yescharacteristic
166C2×C4×C11#13511yescharacteristic
167C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
168C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
169C22⋊D11—88no—
170C2×Dic11—42no—
171C2×Dic11—42no—
172C2×Dic11—42no—
173C2×Dic11—81no—
174C2×Dic11—81no—
175C2×Dic11—81no—
176C2×Dic11—81no—
177C2×Dic11—81no—
178C2×Dic11—81no—
179D44—42no—
180D44—42no—
181D44—81no—
182D44—81no—
183Dic22—42no—
184Dic22—42no—
185Dic22—81no—
186Dic22—81no—
187C8×C11—41no—
188C8×C11#12011yescharacteristic
189C8×C11#12111yescharacteristic
190C8×C11#12111yescharacteristic
191C8×C11#12711yescharacteristic
192C22×Q16—111no—
193C22×D8—111no—
194C23×C8C2×D1111yescharacteristic
195C2×C22⋊Q8—221no—
196C2×#121—221no—
197C2×SD32—222no—
198C2×SD32—222no—
199C2×SD32—222no—
200C22×C16C2×D1111yescharacteristic
201C22×C16C2×D1111yescharacteristic
202#467—222no—
203#467—222no—
204#466—222no—
205#466—222no—
206C2×#107—111no—
207C2×#107—111no—
208C2×#103—221no—
209C2×#102—221no—
210#358—222no—
211#357—222no—
212C22⋊C16—22no—
213C22×C11—22no—
214C22×C11—22no—
215C22×C11—22no—
216C22×C11—41no—
217C22×C11—41no—
218C22×C11—41no—
219C22×C11—41no—
220C22×C11#44711yescharacteristic
221C22×C11#44711yescharacteristic
222C22×C11#46611yescharacteristic
223C22×C11C2×SD3211yescharacteristic
224C22×C11#50811yescharacteristic
225C22×C11#50911yescharacteristic
226C22×C11#51011yescharacteristic
227C2×D11—82no—
228C2×D11—82no—
229C2×D11—82no—
230C2×D11—161no—
231C2×D11—161no—
232C2×D11—161no—
233C2×D11—161no—
234C4×C11—41no—
235C4×C11#39211yescharacteristic
236C4×C11#44911yescharacteristic
237C4×C11#44911yescharacteristic
238C4×C11#46911yescharacteristic
239Dic11—82no—
240Dic11—82no—
241Dic11—82no—
242C22×Q8—221no—
243C22×D4—221no—
244C22×D4—441no—
245C23×C4D4411yescharacteristic
246C2×Q16—112no—
247C2×Q16—221no—
248C2×Q16—221no—
249C2×Q16—221no—
250C2×Q16—221no—
251C2×Q16—221no—
252C2×D8—112no—
253C2×D8—221no—
254C2×D8—221no—
255C2×D8—221no—
256C2×D8—221no—
257C2×D8—221no—
258C22×C8—21no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—21no—
264C22×C8D4411yescharacteristic
265C22×C8C22×D1111yescharacteristic
266C22⋊Q8—224no—
267C22⋊Q8—442no—
268#121—224no—
269#121—442no—
270C2×C4⋊C4—221no—
271C2×C4⋊C4—221no—
272C2×C4⋊C4—441no—
273C2×C22⋊C4—441no—
274C2×C22⋊C4—441no—
275SD32—228no—
276C2×C16—21no—
277C2×C16—21no—
278C2×C16—21no—
279C2×C16—21no—
280C2×C16—21no—
281C2×C16C22⋊D1112yescomplemented
282#107—112no—
283#107—112no—
284#107—221no—
285#107—221no—
286#103—224no—
287#102—224no—
288C2×C11—42no—
289C2×C11#199911yescharacteristic
290C2×C11#218511yescharacteristic
291C2×C11#218611yescharacteristic
292C2×C11#218711yescharacteristic
293C2×C11#218911yescharacteristic
294C2×C11#221711yescharacteristic
295C2×C11#222011yescharacteristic
296D11—162no—
297C24—441no—
298C24D8811yescharacteristic
299C2×Q8—222no—
300C2×Q8—441no—
301C2×Q8—441no—
302C2×Q8—441no—
303C2×Q8—441no—
304C2×Q8—441no—
305C2×D4—222no—
306C2×D4—444no—
307C2×D4—441no—
308C2×D4—441no—
309C2×D4—441no—
310C2×D4—441no—
311C2×D4—441no—
312C2×D4—882no—
313C2×D4—882no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—441no—
321C22×C4—441no—
322C22×C4—441no—
323C22×C4D8811yescharacteristic
324C22×C4C2×D4411yescharacteristic
325Q16—222no—
326Q16—222no—
327Q16—441no—
328Q16—441no—
329D8—222no—
330D8—222no—
331D8—441no—
332D8—441no—
333C2×C8—21no—
334C2×C8—21no—
335C2×C8—21no—
336C2×C8—41no—
337C2×C8—41no—
338C2×C8—41no—
339C2×C8—41no—
340C2×C8#433911yescharacteristic
341C2×C8D4×D1111yescharacteristic
342C2×C8D4×D1111yescharacteristic
343C2×C8D4×D1111yescharacteristic
344C2×C8D4×D1111yescharacteristic
345C2×C8C2×C22⋊D1111yescharacteristic
346C4⋊C4—222no—
347C4⋊C4—222no—
348C4⋊C4—444no—
349C4⋊C4—441no—
350C4⋊C4—441no—
351C22⋊C4—444no—
352C22⋊C4—444no—
353C16—22no—
354C16—41no—
355C11#1330511yescharacteristic, complemented, Sylow
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—442no—
363C23—881no—
364C23—881no—
365C23—881no—
366C23—881no—
367C23—881no—
368C23—881no—
369C23#6686412yescomplemented
370C23C2×D8811yescharacteristic
371Q8—442no—
372Q8—442no—
373Q8—881no—
374Q8—881no—
375D4—442no—
376D4—442no—
377D4—888no—
378D4—881no—
379D4—881no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—442no—
388C2×C4—442no—
389C2×C4—442no—
390C2×C4—881no—
391C2×C4—881no—
392C2×C4—881no—
393C2×C4—881no—
394C2×C4—881no—
395C2×C4—881no—
396C2×C4#6693511yescharacteristic
397C2×C4#6693511yescharacteristic
398C2×C4#6695711yescharacteristic
399C2×C4#6696111yescharacteristic
400C2×C4#6696111yescharacteristic
401C2×C4#6698311yescharacteristic
402C8—41no—
403C8#6693711yescharacteristic
404C8#6693711yescharacteristic
405C8#6699011yescharacteristic
406C8#6699311yescharacteristic
407C22—22no—
408C22—22no—
409C22—22no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—882no—
415C22—882no—
416C22—882no—
417C22—1761no—
418C22—1761no—
419C22—1761no—
420C22—1761no—
421C22#1062234511yescharacteristic
422C22#1062234511yescharacteristic
423C22C2×#6686411yescharacteristic
424C22#1062251711yescharacteristic
425C22#1062252111yescharacteristic
426C22#1062252211yescharacteristic
427C22#1062272811yescharacteristic
428C4—41no—
429C4—882no—
430C4—882no—
431C4—882no—
432C4#1062234711yescharacteristic
433C4#1062234711yescharacteristic
434C4#1062257311yescharacteristic
435C4#1062274811yescharacteristic
436C2—42no—
437C2—1762no—
438C2#1306961411yescharacteristic
439C2#1307053511yescharacteristic
440C2#1307054111yescharacteristic
441C2#1307054711yescharacteristic
442C2#1307055811yescharacteristic
443C2#1307071211yescharacteristic
444C2#1307072911yescharacteristic
subgroupG/H
centerC23C2×D88
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC2×C11×C22⋊C16C2
socleC23×C11C2×D8
prime radicalC2×#10622728C2
hypercenterC2×C22⋊C16D11
hypocenterC11#13305
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C2×C22⋊C16

Complements

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

NH ≅ G/Ntype
1. C22×#66864C2semidirect
2. C2×#10622729C2semidirect
4. C2×#10622141C2semidirect
5. C2×#10622147C2semidirect
6. #13066708C2semidirect
7. C2×C11×C22⋊C16C2semidirect
55. C2×Dic44D4semidirect
67. C2×C11×C16D4semidirect
72. #66882D4semidirect
139. C2×C22⋊C16D11semidirect
147. C23×C11SD32semidirect
281. C2×C16C22⋊D11semidirect
355. C11#13305semidirect
369. C23#66864semidirect

Maximal subgroups

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

subgroupindex
C22×#668642
C2×#106227292
C2×#106227282
C2×#106221412
C2×#106221472
#130667082
C2×C11×C22⋊C162
#1330511