Finite Group Databasebeta

← #14737291

Subgroups — #14737291

Order 2816.

640 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079933C211yesmaximal, characteristic
2#13079746C211yesmaximal, characteristic
3#13079162C211yesmaximal, characteristic, complemented
4#13077362C211yesmaximal, characteristic
5#13068140C212yesmaximal, complemented
6#13068116C212yesmaximal, complemented
7#13068016C212yesmaximal, complemented
8#13067992C212yesmaximal, complemented
9#13067271C211yesmaximal, characteristic, complemented
10C2×#10622119C211yesmaximal, characteristic, complemented
11C11×#1565C211yesmaximal, characteristic, complemented
12C2×#66960—21no—
13#10623008C2211yescharacteristic
14#10623001C2211yescharacteristic
15C2×#66922C2211yescharacteristic
16C11×#431C2211yescharacteristic
17C2×C11×C4⋊C8C2211yescharacteristic
18C4×C11×M16C2211yescharacteristic
19#10622742—21no—
20#10622734—21no—
21#10622734—21no—
22#10622727—22no—
23C2×C4⋊(C11⋊C8)C2211yescharacteristic
24#10622464—21no—
25#10622461—21no—
26#10622455C2212yes—
27#10622455C2212yes—
28#10622455C2212yes—
29#10622454C2212yes—
30#10622348—22no—
31#10622319—22no—
32#10622315—22no—
33#10622307—21no—
34#10622301C2212yes—
35C8×D44C2212yes—
36#10622295C2212yes—
37#10622293—21no—
38#10622293C2212yes—
39C11×#335C2212yes—
40C11×#334C2212yes—
41#10622120C2211yescharacteristic
42#10622120C2211yescharacteristic
43#10622119C2212yes—
44#10622119C2212yes—
45#10622119C2211yescharacteristic
46#10622119C2211yescharacteristic
47C2×#4339—21no—
48C22×Dic22—21no—
49C2×C11×M16D411yescharacteristic
50C2×C11×M16D411yescharacteristic
51C22×C8×C11—21no—
52C2×C42×C11C2311yescharacteristic
53#66983—21no—
54#66983D412yes—
55#66979—21no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11—21no—
58#66977—21no—
59#66977—21no—
60C22×C11⋊C8—21no—
61#66960—44no—
62C2×#4314—22no—
63C2×#4313—22no—
64C2×C8×D11—22no—
65#66928—21no—
66#66927D411yescharacteristic
67C4×D44—21no—
68C4×D44C2312yes—
69#66923—21no—
70#66922—21no—
71#66922—21no—
72#66922—21no—
73#66922D411yescharacteristic
74#66922C2312yes—
75#66922C2311yescharacteristic
76#66922C2311yescharacteristic
77C4×Dic22—21no—
78C4×Dic22—21no—
79C11×C4⋊C8—21no—
80C11×C4⋊C8C2311yescharacteristic
81C11×C4⋊C8C2312yes—
82C11×C4⋊C8C2311yescharacteristic
83C11×C22⋊C8—21no—
84C11×#97D412yes—
85C4×C8×C11—21no—
86C4×C8×C11C2312yes—
87#66885—22no—
88#66885—22no—
89#66885—22no—
90(C2×D11)⋊C8—22no—
91(C2×D11)⋊C8—22no—
92#66882—22no—
93#66882—22no—
94#66881—22no—
95#66881—22no—
96#66881—22no—
97#66881—22no—
98#66881—22no—
99#66880—22no—
100C4⋊(C11⋊C8)—21no—
101C4⋊(C11⋊C8)C2311yescharacteristic
102C4⋊(C11⋊C8)C2311yescharacteristic
103#19233—111nomaximal, Sylow
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11#4111yescharacteristic
107C2×C22⋊D11—22no—
108C22×Dic11—41no—
109#4339—42no—
110#4339—42no—
111C2×D44—21no—
112C2×D44—21no—
113C2×D44C2×D412yes—
114C2×C4×D11—22no—
115C2×Dic22—21no—
116C2×Dic22—21no—
117C2×Dic22—21no—
118C2×Dic22—22no—
119C2×Dic22—41no—
120C2×Dic22—82no—
121C11×M16—22no—
122C11×M16SD1614yescomplemented
123C2×C8×C11—22no—
124C2×C8×C11—21no—
125C2×C8×C11—21no—
126C2×C8×C11—81no—
127C2×C8×C11C2×D412yes—
128C2×C8×C11C2×D412yes—
129C42×C11C2×D411yescharacteristic
130C42×C11C2×D411yescharacteristic
131C42×C11#4111yescharacteristic
132C42×C11C2411yescharacteristic
133C22⋊Dic11—41no—
134(C2×D11)⋊C4—22no—
135(C2×D11)⋊C4—22no—
136C4⋊Dic11—21no—
137C4⋊Dic11—21no—
138C4⋊Dic11—22no—
139C4⋊Dic11—21no—
140C4⋊Dic11—22no—
141C4⋊Dic11—21no—
142C4⋊Dic11—21no—
143C4⋊Dic11—41no—
144C4⋊Dic11—41no—
145C4⋊Dic11C2×D412yes—
146Dic11⋊C4—41no—
147Dic11⋊C4—41no—
148C4×Dic11—41no—
149C2×C11⋊C8—21no—
150C2×C11⋊C8—21no—
151C2×C11⋊C8—42no—
152#4314—82no—
153#4313—44no—
154C8×D11—44no—
155#3246—111no—
156#3227—111no—
157#3165—111no—
158#2935—111no—
159#1695—112no—
160#1691—112no—
161#1675—112no—
162#1671—112no—
163#1565D1111yescharacteristic, complemented
164#1542—111no—
165C2×#333—111no—
166C23×C11#12111yescharacteristic
167C22×D11—22no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—41no—
171C2×C4×C11#12111yescharacteristic
172C2×C4×C11#12111yescharacteristic
173C2×C4×C11#12111yescharacteristic
174C2×C4×C11C2×SD1612yes—
175C2×C4×C11#13712yes—
176C2×C4×C11C22×D411yescharacteristic
177C2×C4×C11C22×D411yescharacteristic
178C2×C4×C11C2×#4111yescharacteristic
179C22⋊D11—44no—
180C2×Dic11—22no—
181C2×Dic11—41no—
182C2×Dic11—41no—
183C2×Dic11—42no—
184C2×Dic11—82no—
185D44—22no—
186D44—22no—
187D44—42no—
188D44—81no—
189C4×D11—42no—
190C4×D11—42no—
191Dic22—42no—
192Dic22—41no—
193Dic22—41no—
194Dic22—82no—
195Dic22—81no—
196Dic22—82no—
197C8×C11—22no—
198C8×C11—42no—
199C8×C11—41no—
200C8×C11—41no—
201C8×C11C2×SD1614yes—
202C11⋊C8—41no—
203C11⋊C8—41no—
204C2×#131—221no—
205#533—111no—
206#532—111no—
207C2×C4⋊Q8—111no—
208#501—222no—
209#500—112no—
210#498—112no—
211#498—221no—
212#486—221no—
213#481—222no—
214#476—112no—
215#476—112no—
216#476—112no—
217#475—221no—
218#465—222no—
219#461—112no—
220#460—221no—
221#436—112no—
222#435—222no—
223C8×D4—112no—
224#431C2×D1111yescharacteristic
225#428—221no—
226#428—221no—
227C2×C4⋊C8—111no—
228C2×C4⋊C8C2×D1111yescharacteristic
229#408—221no—
230C4×M16C2×D1111yescharacteristic
231#335C2×D1112yes—
232#334C2×D1112yes—
233#333—112no—
234#333—112no—
235#333—111no—
236#333—111no—
237#332—111no—
238#332—111no—
239C22×C11—21no—
240C22×C11—21no—
241C22×C11#46112yes—
242C22×C11C2×#12111yescharacteristic
243C2×D11—42no—
244C2×D11—42no—
245C2×D11—42no—
246C4×C11—21no—
247C4×C11—21no—
248C4×C11—21no—
249C4×C11#46112yes—
250C4×C11C22×SD1611yescharacteristic
251C4×C11C2×#13711yescharacteristic
252C4×C11#57711yescharacteristic
253C4×C11#57811yescharacteristic
254Dic11—42no—
255Dic11—81no—
256Dic11—82no—
257Dic11—81no—
258C2×#41—221no—
259C22×Q8—221no—
260C2×SD16—222no—
261#131—444no—
262C2×M16—222no—
263C2×M16D4411yescharacteristic
264C2×M16D4411yescharacteristic
265C22×C8—21no—
266C22×C8—221no—
267C22×C8—222no—
268C4⋊Q8—111no—
269C4⋊Q8—112no—
270C4⋊Q8—111no—
271C4⋊Q8—111no—
272C4⋊Q8—221no—
273C4⋊Q8—221no—
274C4⋊Q8—221no—
275#127—111no—
276#125—221no—
277#124—221no—
278C22⋊Q8—221no—
279C22⋊Q8—221no—
280#121—112no—
281#121—221no—
282C4×Q8—221no—
283C4×Q8—221no—
284C4×D4—112no—
285C4×D4—221no—
286#117—221no—
287C2×C4⋊C4—221no—
288C2×C4⋊C4—221no—
289C2×C42C22×D1111yescharacteristic
290#107—222no—
291#107—222no—
292#106—222no—
293#106—222no—
294#106—222no—
295#106—222no—
296#106—222no—
297C4⋊C8—21no—
298C4⋊C8—111no—
299C4⋊C8—111no—
300C4⋊C8—221no—
301C4⋊C8C22×D1111yescharacteristic
302C4⋊C8C22×D1111yescharacteristic
303C4⋊C8C22×D1112yes—
304#103—222no—
305#102—222no—
306#102—222no—
307#102—222no—
308C22⋊C8—21no—
309C22⋊C8—222no—
310C22⋊C8—222no—
311#97D4412yes—
312C4×C8—21no—
313C4×C8C22×D1112yes—
314C2×C11—22no—
315C2×C11C2×#46111yescharacteristic
316C2×C11#306311yescharacteristic
317C2×C11#306811yescharacteristic
318D11—82no—
319#41—442no—
320#41—442no—
321C2×Q8—221no—
322C2×Q8—221no—
323C2×Q8—221no—
324C2×Q8—222no—
325C2×Q8—441no—
326C2×Q8—882no—
327C2×D4—112no—
328C2×D4—222no—
329C2×D4—221no—
330C2×D4—221no—
331C22×C4—222no—
332C22×C4—441no—
333C22×C4C2×D4411yescharacteristic
334C22×C4D4×D1111yescharacteristic
335C22×C4#434311yescharacteristic
336SD16—882no—
337M16—22no—
338M16—444no—
339M16#431414yescomplemented
340C2×C8—21no—
341C2×C8—21no—
342C2×C8—22no—
343C2×C8—81no—
344C2×C8—221no—
345C2×C8—221no—
346C2×C8—442no—
347C2×C8—444no—
348C2×C8C2×D4412yes—
349C2×C8C2×D4412yes—
350C4⋊C4—112no—
351C4⋊C4—221no—
352C4⋊C4—221no—
353C4⋊C4—222no—
354C4⋊C4—221no—
355C4⋊C4—222no—
356C4⋊C4—221no—
357C4⋊C4—221no—
358C4⋊C4—441no—
359C4⋊C4—441no—
360C4⋊C4—441no—
361C4⋊C4—441no—
362C22⋊C4—222no—
363C22⋊C4—222no—
364C22⋊C4—441no—
365C42—441no—
366C42C2×D4411yescharacteristic
367C42D4×D1111yescharacteristic
368C42#434311yescharacteristic
369C42C23×D1111yescharacteristic
370C11#1923311yescharacteristic, complemented, Sylow
371C23—222no—
372C23#6694811yescharacteristic
373Q8—442no—
374Q8—441no—
375Q8—441no—
376Q8—882no—
377Q8—881no—
378Q8—882no—
379D4—222no—
380D4—222no—
381D4—444no—
382D4—442no—
383D4—881no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—41no—
387C2×C4—222no—
388C2×C4—442no—
389C2×C4—442no—
390C2×C4—441no—
391C2×C4—441no—
392C2×C4—442no—
393C2×C4—882no—
394C2×C4#6694811yescharacteristic
395C2×C4#6694811yescharacteristic
396C2×C4#6694811yescharacteristic
397C2×C4C2×#431412yes—
398C2×C4#6696212yes—
399C2×C4C22×D4411yescharacteristic
400C2×C4C2×D4×D1111yescharacteristic
401C2×C4C2×#434311yescharacteristic
402C8—22no—
403C8—42no—
404C8—41no—
405C8—41no—
406C8—441no—
407C8—441no—
408C8C2×#431414yes—
409C22—21no—
410C22—21no—
411C22—442no—
412C22—442no—
413C22—442no—
414C22#1062245412yes—
415C22C2×#6694811yescharacteristic
416C4—21no—
417C4—21no—
418C4—21no—
419C4—442no—
420C4—881no—
421C4—882no—
422C4—881no—
423C4#1062245412yes—
424C4C22×#431411yescharacteristic
425C4C2×#6696211yescharacteristic
426C4#1062330611yescharacteristic
427C4#1062331011yescharacteristic
428C2—22no—
429C2—882no—
430C2C2×#1062245411yescharacteristic
431C2#1307830811yescharacteristic
432C2#1307834511yescharacteristic
subgroupG/H
centerC22C2×#66948
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1565C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenter#1565D11
hypocenterC11#19233
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1565

Complements

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

NH ≅ G/Ntype
3. #13079162C2semidirect
5. #13068140C2semidirect
6. #13068116C2semidirect
7. #13068016C2semidirect
8. #13067992C2semidirect
9. #13067271C2semidirect
10. C2×#10622119C2semidirect
11. C11×#1565C2semidirect
122. C11×M16SD16semidirect
163. #1565D11semidirect
339. M16#4314semidirect
370. C11#19233semidirect

Maximal subgroups

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

subgroupindex
#130799332
#130797462
#130791622
#130773622
#130681402
#130681162
#130680162
#130679922
#130672712
C2×#106221192
C11×#15652
#1923311