Finite Group Databasebeta

← #14656285

Subgroups — #14656285

Order 2816.

678 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622307C211yesmaximal, characteristic, complemented
2C2×#10622632C211yesmaximal, characteristic, complemented
3C2×#10622628C211yesmaximal, characteristic
4C2×#10622124C211yesmaximal, characteristic, complemented
5C2×#10622123C211yesmaximal, characteristic, complemented
6#13066451C211yesmaximal, characteristic, complemented
7C11×#1954C211yesmaximal, characteristic, complemented
8C2×C4×D4×C11C2211yescharacteristic
9C22×#4324—21no—
10C22×#4323—21no—
11C2×#66927C2211yescharacteristic
12C2×#66922C2211yescharacteristic
13C2×C11×C4⋊C8C2211yescharacteristic
14C2×C11×C22⋊C8—22no—
15C2×C4×C8×C11C2211yescharacteristic
16C2×#66885—22no—
17#10622632—22no—
18#10622632—22no—
19#10622628—22no—
20#10622628—22no—
21C2×#66874—21no—
22C2×#66873—21no—
23C2×C4⋊(C11⋊C8)C2211yescharacteristic
24C2×C4⋊(C11⋊C8)C2211yescharacteristic
25#10622307—22no—
26#10622307—22no—
27#10622124—22no—
28#10622123—22no—
29C22×D4×C11D411yescharacteristic
30C23×C4×C11—21no—
31C22×D44—21no—
32C22×D44—21no—
33C22×D44—21no—
34C22×Dic22—21no—
35C22×C8×C11—21no—
36C22×C8×C11D412yes—
37C4×D4×C11—21no—
38C4×D4×C11—21no—
39C4×D4×C11—21no—
40C4×D4×C11—21no—
41C2×C11×C4⋊C4D411yescharacteristic
42C2×C11×C22⋊C4—21no—
43C2×C42×C11C2311yescharacteristic
44C2×#4324—24no—
45C2×#4324—42no—
46C2×#4324—42no—
47C2×#4323—24no—
48C2×#4323—42no—
49C2×#4323—42no—
50C2×C4⋊Dic11—21no—
51C2×C4⋊Dic11—21no—
52C22×C11⋊C8—21no—
53C22×C11⋊C8—21no—
54#66927—21no—
55#66927—21no—
56#66927—21no—
57#66927D412yes—
58#66922—21no—
59#66922—21no—
60#66922—21no—
61#66922D412yes—
62C11×C4⋊C8—21no—
63C11×C4⋊C8—21no—
64C11×C22⋊C8—44no—
65C4×C8×C11—21no—
66C4×C8×C11—21no—
67#66885—28no—
68#66874—24no—
69#66873—24no—
70C4⋊(C11⋊C8)—21no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)D412yes—
73C4⋊(C11⋊C8)D412yes—
74#10261—111nomaximal, Sylow
75C24×C11—21no—
76C23×D11—41no—
77C2×D4×C11—21no—
78C2×D4×C11—21no—
79C2×D4×C11—21no—
80C2×D4×C11—21no—
81C2×D4×C11—21no—
82C2×D4×C11D812yes—
83C22×C4×C11—21no—
84C22×C4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11—42no—
87C22×C4×C11—42no—
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11#4111yescharacteristic
91C22×Dic11—41no—
92C2×D44—22no—
93C2×D44—22no—
94C2×D44—22no—
95C2×D44—41no—
96C2×D44—41no—
97C2×D44—41no—
98C2×D44—41no—
99C2×D44—41no—
100C2×D44—42no—
101C2×D44—41no—
102C2×D44—41no—
103C2×D44—42no—
104C2×D44—82no—
105C2×Dic22—22no—
106C2×Dic22—41no—
107C2×Dic22—41no—
108C2×Dic22—41no—
109C2×Dic22—41no—
110C2×Dic22—41no—
111C2×C8×C11—22no—
112C2×C8×C11—22no—
113C2×C8×C11—22no—
114C2×C8×C11—41no—
115C2×C8×C11—42no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—21no—
118C11×C22⋊C4—41no—
119C11×C22⋊C4—41no—
120C42×C11C2×D411yescharacteristic
121C42×C11C2×D411yescharacteristic
122C42×C11C2×D411yescharacteristic
123C42×C11C2×D411yescharacteristic
124#4324—48no—
125#4323—48no—
126C4⋊Dic11—22no—
127C4⋊Dic11—22no—
128C4⋊Dic11—41no—
129C4⋊Dic11—41no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—41no—
133C2×C11⋊C8—41no—
134C2×C11⋊C8—41no—
135C2×C11⋊C8—41no—
136C2×#486—111no—
137C2×#461—111no—
138C2×#459—111no—
139#1954D1111yescharacteristic, complemented
140C2×#332—111no—
141C2×#331—111no—
142#1277—111no—
143C23×C11—22no—
144C23×C11—41no—
145C23×C11—42no—
146C23×C11—41no—
147C23×C11—42no—
148C23×C11#12111yescharacteristic
149C22×D11—42no—
150C22×D11—82no—
151C22×D11—81no—
152C22×D11—81no—
153C22×D11—82no—
154D4×C11—22no—
155D4×C11—22no—
156D4×C11—41no—
157D4×C11—41no—
158C2×C4×C11—22no—
159C2×C4×C11—41no—
160C2×C4×C11—42no—
161C2×C4×C11—82no—
162C2×C4×C11—81no—
163C2×C4×C11—81no—
164C2×C4×C11#12011yescharacteristic
165C2×C4×C11#12011yescharacteristic
166C2×C4×C11#12011yescharacteristic
167C2×C4×C11#12111yescharacteristic
168C2×C4×C11#12111yescharacteristic
169C2×C4×C11#12711yescharacteristic
170C2×C4×C11C2×D811yescharacteristic
171C2×C4×C11#13511yescharacteristic
172C2×C4×C11#13512yes—
173C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
174C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
175C2×C4×C11AGL(1,ℤ/8)12yes—
176C2×Dic11—42no—
177C2×Dic11—81no—
178C2×Dic11—81no—
179D44—42no—
180D44—42no—
181D44—44no—
182D44—82no—
183D44—82no—
184D44—81no—
185D44—81no—
186D44—81no—
187D44—81no—
188Dic22—42no—
189Dic22—42no—
190Dic22—81no—
191Dic22—81no—
192C8×C11—42no—
193C8×C11—81no—
194C11⋊C8—42no—
195C11⋊C8—42no—
196C22×SD16—221no—
197C22×D8—221no—
198C2×C4⋊Q8—111no—
199C2×#127—111no—
200C2×C4×D4C2×D1111yescharacteristic
201#486—222no—
202#486—222no—
203#461—222no—
204#461—222no—
205#459—222no—
206#459—222no—
207C2×C4⋊C8—111no—
208C2×C4⋊C8—111no—
209C2×C4⋊C8C2×D1111yescharacteristic
210C2×#103—221no—
211C2×#102—222no—
212C2×#102—221no—
213C2×C22⋊C8—22no—
214C2×C4×C8C2×D1111yescharacteristic
215#332—222no—
216#331—222no—
217C22×C11—44no—
218C22×C11—42no—
219C22×C11—82no—
220C22×C11—81no—
221C22×C11—81no—
222C22×C11#39211yescharacteristic
223C22×C11#46312yes—
224C22×C11#46611yescharacteristic
225C22×C11#46911yescharacteristic
226C22×C11#47112yes—
227C2×D11—82no—
228C2×D11—82no—
229C2×D11—82no—
230C2×D11—162no—
231C2×D11—162no—
232C4×C11—21no—
233C4×C11—21no—
234C4×C11—81no—
235C4×C11#44711yescharacteristic
236C4×C11#44711yescharacteristic
237C4×C11#44911yescharacteristic
238C4×C11#44911yescharacteristic
239C4×C11#44912yes—
240C4×C11#49511yescharacteristic
241C4×C11#49611yescharacteristic
242Dic11—82no—
243C22×Q8—221no—
244C22×D4—221no—
245C22×D4—221no—
246C22×D4—221no—
247C22×D4D4411yescharacteristic
248C23×C4—21no—
249C2×SD16—224no—
250C2×SD16—442no—
251C2×SD16—442no—
252C2×D8—224no—
253C2×D8—442no—
254C2×D8—442no—
255C22×C8—21no—
256C22×C8—221no—
257C22×C8—221no—
258C22×C8C22⋊D1112yes—
259C4⋊Q8—112no—
260C4⋊Q8—221no—
261C4⋊Q8—221no—
262C4⋊Q8—221no—
263#127—112no—
264#127—221no—
265#127—221no—
266#127—221no—
267C4×D4—21no—
268C4×D4—21no—
269C4×D4—21no—
270C4×D4—21no—
271C2×C4⋊C4—221no—
272C2×C4⋊C4—221no—
273C2×C4⋊C4D4411yescharacteristic
274C2×C22⋊C4—21no—
275C2×C42C22×D1111yescharacteristic
276C4⋊C8—21no—
277C4⋊C8—21no—
278C4⋊C8—112no—
279C4⋊C8—112no—
280C4⋊C8—221no—
281C4⋊C8—221no—
282#103—224no—
283#102—224no—
284#102—228no—
285C22⋊C8—44no—
286C4×C8—21no—
287C4×C8—21no—
288C2×C11—82no—
289C2×C11#168112yes—
290C2×C11#170112yes—
291C2×C11#199911yescharacteristic
292C2×C11#201211yescharacteristic
293C2×C11#201911yescharacteristic
294D11—162no—
295C24—21no—
296C24—441no—
297C2×Q8—222no—
298C2×Q8—441no—
299C2×Q8—441no—
300C2×Q8—441no—
301C2×Q8—441no—
302C2×Q8—441no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—21no—
306C2×D4—21no—
307C2×D4—21no—
308C2×D4—222no—
309C2×D4—222no—
310C2×D4—222no—
311C2×D4—441no—
312C2×D4—441no—
313C2×D4—441no—
314C2×D4—441no—
315C2×D4—441no—
316C2×D4—441no—
317C2×D4—442no—
318C2×D4—441no—
319C2×D4—442no—
320C2×D4—882no—
321C2×D4D8812yes—
322C22×C4—21no—
323C22×C4—42no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—42no—
327C22×C4—441no—
328C22×C4C2×D4411yescharacteristic
329C22×C4#433911yescharacteristic
330C22×C4C2×C22⋊D1111yescharacteristic
331SD16—448no—
332D8—448no—
333C2×C8—22no—
334C2×C8—22no—
335C2×C8—22no—
336C2×C8—42no—
337C2×C8—41no—
338C2×C8—222no—
339C2×C8—222no—
340C2×C8—441no—
341C2×C8—441no—
342C2×C8—441no—
343C2×C8—441no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—222no—
347C4⋊C4—222no—
348C4⋊C4—441no—
349C4⋊C4—441no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C42D4×D1111yescharacteristic
353C42D4×D1111yescharacteristic
354C42D4×D1111yescharacteristic
355C42D4×D1111yescharacteristic
356C11#1026111yescharacteristic, complemented, Sylow
357C23—22no—
358C23—41no—
359C23—42no—
360C23—41no—
361C23—42no—
362C23—442no—
363C23—881no—
364C23—881no—
365C23—882no—
366C23—882no—
367C23#6698311yescharacteristic
368Q8—442no—
369Q8—442no—
370Q8—881no—
371Q8—881no—
372D4—22no—
373D4—22no—
374D4—41no—
375D4—41no—
376D4—442no—
377D4—442no—
378D4—444no—
379D4—882no—
380D4—882no—
381D4—881no—
382D4—881no—
383D4—881no—
384D4—881no—
385C2×C4—22no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—82no—
389C2×C4—81no—
390C2×C4—81no—
391C2×C4—442no—
392C2×C4—881no—
393C2×C4—881no—
394C2×C4#6693511yescharacteristic
395C2×C4#6693511yescharacteristic
396C2×C4#6693711yescharacteristic
397C2×C4#6693711yescharacteristic
398C2×C4C2×D8811yescharacteristic
399C2×C4#6695711yescharacteristic
400C2×C4#6696111yescharacteristic
401C2×C4#6696111yescharacteristic
402C2×C4#6698512yes—
403C2×C4#6699011yescharacteristic
404C2×C4#6699311yescharacteristic
405C2×C4#6700312yes—
406C8—42no—
407C8—81no—
408C8—442no—
409C8—442no—
410C22—44no—
411C22—42no—
412C22—81no—
413C22—82no—
414C22—81no—
415C22—882no—
416C22—882no—
417C22—882no—
418C22—1762no—
419C22—1762no—
420C22#1062257311yescharacteristic
421C22#1062262912yes—
422C22#1062272811yescharacteristic
423C22#1062274811yescharacteristic
424C22#1062275412yes—
425C4—21no—
426C4—21no—
427C4—81no—
428C4—882no—
429C4#1062234511yescharacteristic
430C4#1062234511yescharacteristic
431C4#1062234711yescharacteristic
432C4#1062234711yescharacteristic
433C4#1062265012yes—
434C4#1062267211yescharacteristic
435C4#1062268711yescharacteristic
436C2—82no—
437C2—1762no—
438C2#1306805312yes—
439C2#1306817712yes—
440C2#1306961411yescharacteristic
441C2#1306969211yescharacteristic
442C2#1306973111yescharacteristic
subgroupG/H
centerC23#66983
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1954C2
socleC23×C11#121
prime radicalC2×#10622628C2
hypercenter#1954D11
hypocenterC11#10261
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1954

Complements

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

NH ≅ G/Ntype
1. C2×#10622307C2semidirect
2. C2×#10622632C2semidirect
4. C2×#10622124C2semidirect
5. C2×#10622123C2semidirect
6. #13066451C2semidirect
7. C11×#1954C2semidirect
139. #1954D11semidirect
356. C11#10261semidirect

Maximal subgroups

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

subgroupindex
C2×#106223072
C2×#106226322
C2×#106226282
C2×#106221242
C2×#106221232
#130664512
C11×#19542
#1026111