Finite Group Databasebeta

← #14657218

Subgroups — #14657218

Order 2816.

556 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073565C211yesmaximal, characteristic
2#13069577C211yesmaximal, characteristic, complemented
3#13069379C211yesmaximal, characteristic, complemented
4#13068617C211yesmaximal, characteristic
5C2×#10622124C211yesmaximal, characteristic, complemented
6C2×#10622097C211yesmaximal, characteristic
7C11×#1279C211yesmaximal, characteristic, complemented
8C2×#66950—21no—
9C2×#66950—21no—
10C2×C4×D44C2211yescharacteristic
11C2×#66922C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13C2×C4×C8×C11C2211yescharacteristic
14C4×C11×C4⋊C4C2211yescharacteristic
15C2×#66885—21no—
16C2×#66872—21no—
17#10622552—21no—
18#10622548—21no—
19#10622548C2211yescharacteristic
20C2×C4⋊(C11⋊C8)C2211yescharacteristic
21#10622290—22no—
22#10622189—22no—
23#10622189—21no—
24#10622167—21no—
25#10622124—22no—
26#10622097—22no—
27C22×D44D411yescharacteristic
28C22×C4×D11—21no—
29C22×Dic22—21no—
30C22×C8×C11—21no—
31C22×C8×C11—21no—
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C42×C11—21no—
35C2×C42×C11C2311yescharacteristic
36C2×(C2×D11)⋊C4—22no—
37C2×(C2×D11)⋊C4—22no—
38C2×(C2×D11)⋊C4—21no—
39C2×C4⋊Dic11—22no—
40C2×C4⋊Dic11—22no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11—21no—
43C2×C4⋊Dic11—21no—
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11D412yes—
46C2×C4⋊Dic11D411yescharacteristic
47C22×C11⋊C8—21no—
48#66950—42no—
49#66950—42no—
50#66950—42no—
51#66950—42no—
52C4×D44—21no—
53C4×D44—21no—
54C4×D44—21no—
55C4×D44—21no—
56#66922—21no—
57#66922—21no—
58#66922—21no—
59#66922—21no—
60C11×C4⋊C8—21no—
61C11×C4⋊C8—21no—
62C4×C8×C11—21no—
63C4×C8×C11—21no—
64C11×#95—21no—
65#66885—42no—
66#66872—42no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)D412yes—
69#10420—111nomaximal, Sylow
70C23×D11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×Dic11—21no—
77C22×Dic11—22no—
78C22×Dic11—41no—
79C2×D44—21no—
80C2×D44—21no—
81C2×D44—21no—
82C2×D44—21no—
83C2×D44—21no—
84C2×D44SD1612yes—
85C2×C4×D11—41no—
86C2×C4×D11—41no—
87C2×C4×D11—41no—
88C2×C4×D11—41no—
89C2×C4×D11—41no—
90C2×C4×D11—41no—
91C2×Dic22—41no—
92C2×Dic22—41no—
93C2×Dic22—41no—
94C2×Dic22—41no—
95C2×Dic22—41no—
96C2×Dic22—41no—
97C2×C8×C11—22no—
98C2×C8×C11—41no—
99C2×C8×C11—41no—
100C2×C8×C11—41no—
101C2×C8×C11—41no—
102C2×C8×C11—41no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4D812yes—
106C11×C4⋊C4SD1612yes—
107C42×C11—41no—
108C42×C11—41no—
109C42×C11C2×D411yescharacteristic
110C42×C11#4111yescharacteristic
111C42×C11#4111yescharacteristic
112C42×C11#4111yescharacteristic
113(C2×D11)⋊C4—44no—
114(C2×D11)⋊C4—44no—
115(C2×D11)⋊C4—41no—
116(C2×D11)⋊C4—41no—
117C4⋊Dic11—22no—
118C4⋊Dic11—21no—
119C4⋊Dic11—22no—
120C4⋊Dic11—21no—
121C4⋊Dic11—44no—
122C4⋊Dic11—44no—
123C4⋊Dic11—42no—
124C4⋊Dic11—41no—
125C4⋊Dic11—41no—
126C4⋊Dic11—41no—
127C4⋊Dic11—41no—
128C4⋊Dic11—41no—
129C4⋊Dic11—41no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—41no—
132C2×C11⋊C8—41no—
133#2542—111no—
134#1990—111no—
135#1948—111no—
136#1802—111no—
137C2×#332—111no—
138C2×D4⋊C8—111no—
139#1279D1111yescharacteristic, complemented
140C23×C11#12011yescharacteristic
141C22×D11—22no—
142C22×D11—41no—
143C22×D11—41no—
144C22×D11—41no—
145C22×D11—41no—
146C22×D11—41no—
147C22×D11—41no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—22no—
151C2×C4×C11—22no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#12111yescharacteristic
159C2×C4×C11#12311yescharacteristic
160C2×C4×C11#12311yescharacteristic
161C2×C4×C11#12411yescharacteristic
162C2×C4×C11C2×D811yescharacteristic
163C2×C4×C11C2×SD1611yescharacteristic
164C2×C4×C11C2×SD1611yescharacteristic
165C2×C4×C11#13511yescharacteristic
166C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
168C2×C4×C11#13711yescharacteristic
169C2×C4×C11#13711yescharacteristic
170C2×Dic11—42no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173C2×Dic11—42no—
174C2×Dic11—41no—
175C2×Dic11—42no—
176C2×Dic11—81no—
177C2×Dic11—81no—
178C2×Dic11—81no—
179D44—22no—
180D44—22no—
181D44—41no—
182D44—41no—
183C4×D11—81no—
184C4×D11—81no—
185C4×D11—81no—
186C4×D11—81no—
187Dic22—81no—
188Dic22—81no—
189Dic22—81no—
190Dic22—81no—
191C8×C11—42no—
192C8×C11—81no—
193C11⋊C8—42no—
194C2×C4⋊Q8—111no—
195C2×C22⋊Q8—221no—
196C2×C22⋊Q8—221no—
197C2×C4×D4—111no—
198C2×#106—221no—
199C2×C4⋊C8—111no—
200C2×C4⋊C8C2×D1111yescharacteristic
201C2×#102—221no—
202C2×C4×C8C2×D1111yescharacteristic
203#399—222no—
204#390—221no—
205#384—111no—
206#384—221no—
207C4×C4⋊C4C2×D1111yescharacteristic
208#340—221no—
209#340—222no—
210#340—221no—
211#332—222no—
212D4⋊C8—222no—
213C22×C11#39411yescharacteristic
214C22×C11#44711yescharacteristic
215C22×C11#44811yescharacteristic
216C22×C11#45011yescharacteristic
217C22×C11#45211yescharacteristic
218C22×C11#45411yescharacteristic
219C22×C11#45611yescharacteristic
220C2×D11—42no—
221C2×D11—42no—
222C2×D11—42no—
223C2×D11—81no—
224C2×D11—81no—
225C2×D11—81no—
226C2×D11—81no—
227C4×C11—21no—
228C4×C11—21no—
229C4×C11—42no—
230C4×C11—42no—
231C4×C11#45911yescharacteristic
232C4×C11#46011yescharacteristic
233C4×C11#46511yescharacteristic
234C4×C11#47011yescharacteristic
235C4×C11#48311yescharacteristic
236C4×C11#48511yescharacteristic
237C4×C11#48611yescharacteristic
238C4×C11#49011yescharacteristic
239Dic11—82no—
240Dic11—81no—
241Dic11—161no—
242C22×Q8—221no—
243C22×D4—111no—
244C23×C4—221no—
245C22×C8—21no—
246C22×C8—21no—
247C22×C8—221no—
248C4⋊Q8—221no—
249C4⋊Q8—221no—
250C4⋊Q8—221no—
251C4⋊Q8—221no—
252C22⋊Q8—442no—
253C22⋊Q8—442no—
254C22⋊Q8—442no—
255C22⋊Q8—442no—
256C4×D4—221no—
257C4×D4—221no—
258C4×D4—221no—
259C4×D4—221no—
260C2×C4⋊C4—111no—
261C2×C4⋊C4—112no—
262C2×C4⋊C4—222no—
263C2×C4⋊C4—222no—
264C2×C4⋊C4—221no—
265C2×C4⋊C4—221no—
266C2×C4⋊C4—221no—
267C2×C4⋊C4—221no—
268C2×C4⋊C4D4411yescharacteristic
269C2×C4⋊C4D4411yescharacteristic
270C2×C22⋊C4—222no—
271C2×C22⋊C4—222no—
272C2×C22⋊C4—221no—
273C2×C42—21no—
274C2×C42C22×D1111yescharacteristic
275#106—442no—
276C4⋊C8—21no—
277C4⋊C8—21no—
278C4⋊C8—112no—
279C4⋊C8—221no—
280#102—442no—
281C4×C8—21no—
282C4×C8—21no—
283#95—21no—
284C2×C11#162711yescharacteristic
285C2×C11#163511yescharacteristic
286C2×C11#164711yescharacteristic
287C2×C11#165111yescharacteristic
288C2×C11#203511yescharacteristic
289C2×C11#203811yescharacteristic
290C2×C11#204111yescharacteristic
291D11—82no—
292C24—221no—
293C2×Q8—441no—
294C2×Q8—441no—
295C2×Q8—441no—
296C2×Q8—441no—
297C2×Q8—441no—
298C2×Q8—441no—
299C2×D4—112no—
300C2×D4—221no—
301C2×D4—221no—
302C2×D4—221no—
303C2×D4—221no—
304C2×D4—221no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—222no—
308C22×C4—221no—
309C22×C4—441no—
310C22×C4—441no—
311C22×C4—441no—
312C22×C4—441no—
313C22×C4—441no—
314C22×C4—441no—
315C22×C4—441no—
316C22×C4C2×D4411yescharacteristic
317C22×C4D4×D1111yescharacteristic
318C22×C4D4×D1111yescharacteristic
319C2×C8—22no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8—41no—
325C2×C8—222no—
326C2×C8—441no—
327C2×C8—441no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—221no—
331C4⋊C4—222no—
332C4⋊C4—221no—
333C4⋊C4—222no—
334C4⋊C4—444no—
335C4⋊C4—444no—
336C4⋊C4—442no—
337C4⋊C4—441no—
338C4⋊C4—441no—
339C4⋊C4—441no—
340C4⋊C4—441no—
341C4⋊C4—441no—
342C4⋊C4—441no—
343C4⋊C4#431412yes—
344C4⋊C4D8812yes—
345C22⋊C4—444no—
346C22⋊C4—444no—
347C22⋊C4—441no—
348C22⋊C4—441no—
349C42—41no—
350C42—41no—
351C42#433911yescharacteristic
352C42#433911yescharacteristic
353C42D4×D1111yescharacteristic
354C42#434311yescharacteristic
355C11#1042011yescharacteristic, complemented, Sylow
356C23—222no—
357C23—441no—
358C23—441no—
359C23—441no—
360C23—441no—
361C23—441no—
362C23—441no—
363C23#6693511yescharacteristic
364Q8—881no—
365Q8—881no—
366Q8—881no—
367Q8—881no—
368D4—222no—
369D4—222no—
370D4—441no—
371D4—441no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—441no—
381C2×C4—442no—
382C2×C4—442no—
383C2×C4—441no—
384C2×C4—442no—
385C2×C4—441no—
386C2×C4—881no—
387C2×C4—881no—
388C2×C4—881no—
389C2×C4—881no—
390C2×C4—881no—
391C2×C4—881no—
392C2×C4—881no—
393C2×C4#6692811yescharacteristic
394C2×C4#6693711yescharacteristic
395C2×C4#6693711yescharacteristic
396C2×C4#6694711yescharacteristic
397C2×C4#6694711yescharacteristic
398C2×C4#6694811yescharacteristic
399C2×C4C2×#431411yescharacteristic
400C2×C4C2×D8811yescharacteristic
401C2×C4#6696111yescharacteristic
402C2×C4#6696111yescharacteristic
403C2×C4#6696511yescharacteristic
404C2×C4SD16×D1111yescharacteristic
405C2×C4#6696811yescharacteristic
406C2×C4#6697111yescharacteristic
407C8—42no—
408C8—81no—
409C8—442no—
410C22—442no—
411C22—442no—
412C22—442no—
413C22—881no—
414C22—881no—
415C22—881no—
416C22—881no—
417C22#1062228511yescharacteristic
418C22#1062234411yescharacteristic
419C22#1062234511yescharacteristic
420C22#1062239611yescharacteristic
421C22#1062241911yescharacteristic
422C22#1062243911yescharacteristic
423C22#1062244011yescharacteristic
424C4—21no—
425C4—21no—
426C4—42no—
427C4—42no—
428C4—881no—
429C4—882no—
430C4—1761no—
431C4#1062230711yescharacteristic
432C4#1062232611yescharacteristic
433C4#1062239111yescharacteristic
434C4#1062242911yescharacteristic
435C4#1062245611yescharacteristic
436C4#1062246111yescharacteristic
437C4#1062247511yescharacteristic
438C4#1062250111yescharacteristic
439C2—882no—
440C2#1306772111yescharacteristic
441C2#1306776911yescharacteristic
442C2#1306785311yescharacteristic
443C2#1306788211yescharacteristic
444C2#1306981511yescharacteristic
445C2#1306983611yescharacteristic
446C2#1306985111yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1279C2
socleC23×C11#120
prime radicalC22×D44D4
hypercenter#1279D11
hypocenterC11#10420
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
2. #13069577C2semidirect
3. #13069379C2semidirect
5. C2×#10622124C2semidirect
7. C11×#1279C2semidirect
139. #1279D11semidirect
355. C11#10420semidirect

Maximal subgroups

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

subgroupindex
#130735652
#130695772
#130693792
#130686172
C2×#106221242
C2×#106220972
C11×#12792
#1042011