Finite Group Databasebeta

← #14657162

Subgroups — #14657162

Order 2816.

516 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073785C211yesmaximal, characteristic
2#13069418C211yesmaximal, characteristic, complemented
3#13069379C211yesmaximal, characteristic, complemented
4#13068617C211yesmaximal, characteristic
5C2×#10622119C211yesmaximal, characteristic, complemented
6C2×#10622097C211yesmaximal, characteristic
7C11×#1279C211yesmaximal, characteristic, complemented
8C2×C4×D44C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C2×C11×C4⋊C8C2211yescharacteristic
11C2×C4×C8×C11C2211yescharacteristic
12C4×C11×C4⋊C4C2211yescharacteristic
13C2×#66885—21no—
14C2×#66880—22no—
15#10622600—21no—
16#10622600—21no—
17C2×#66872—21no—
18#10622552—21no—
19#10622549—21no—
20#10622548C2211yescharacteristic
21C2×C4⋊(C11⋊C8)C2211yescharacteristic
22#10622286—22no—
23#10622189—21no—
24#10622167—21no—
25#10622119—22no—
26#10622097—22no—
27C22×D44D411yescharacteristic
28C22×C4×D11—21no—
29C22×Dic22D412yes—
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—21no—
37C2×(C2×D11)⋊C4—22no—
38C2×(C2×D11)⋊C4—22no—
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11—21no—
43C2×C4⋊Dic11—21no—
44C2×C4⋊Dic11D411yescharacteristic
45C22×C11⋊C8—21no—
46C4×D44—21no—
47C4×D44—21no—
48C4×D44—21no—
49C4×D44—21no—
50#66922—21no—
51#66922—21no—
52#66922—21no—
53#66922—21no—
54C11×C4⋊C8—21no—
55C11×C4⋊C8—21no—
56C4×C8×C11—21no—
57C4×C8×C11—21no—
58C11×#95—21no—
59C11⋊#95—22no—
60C11⋊#95—22no—
61#66885—42no—
62#66880—44no—
63#66872—42no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)D412yes—
66#10412—111nomaximal, Sylow
67C23×D11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×Dic11—21no—
74C22×Dic11—22no—
75C22×Dic11—41no—
76C2×D44—21no—
77C2×D44—21no—
78C2×D44—21no—
79C2×D44—21no—
80C2×D44—21no—
81C2×D44SD1612yes—
82C2×C4×D11—41no—
83C2×C4×D11—41no—
84C2×C4×D11—41no—
85C2×C4×D11—41no—
86C2×C4×D11—41no—
87C2×C4×D11—41no—
88C2×Dic22—22no—
89C2×Dic22—22no—
90C2×Dic22—42no—
91C2×Dic22—42no—
92C2×C8×C11—22no—
93C2×C8×C11—41no—
94C2×C8×C11—41no—
95C2×C8×C11—41no—
96C2×C8×C11—41no—
97C2×C8×C11—41no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—21no—
102C42×C11—41no—
103C42×C11—41no—
104C42×C11C2×D411yescharacteristic
105C42×C11#4111yescharacteristic
106C42×C11#4111yescharacteristic
107C42×C11#4111yescharacteristic
108(C2×D11)⋊C4—41no—
109(C2×D11)⋊C4—41no—
110(C2×D11)⋊C4—82no—
111(C2×D11)⋊C4—82no—
112C4⋊Dic11—21no—
113C4⋊Dic11—21no—
114C4⋊Dic11—42no—
115C4⋊Dic11—41no—
116C4⋊Dic11—41no—
117C4⋊Dic11—41no—
118C4⋊Dic11—41no—
119C4⋊Dic11—41no—
120C4⋊Dic11—41no—
121C4⋊Dic11—41no—
122C4⋊Dic11—41no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—41no—
125C2×C11⋊C8—41no—
126#2563—111no—
127#1956—111no—
128#1948—111no—
129#1802—111no—
130C2×#333—111no—
131C2×D4⋊C8—111no—
132#1279D1111yescharacteristic, complemented
133C23×C11#12011yescharacteristic
134C22×D11—22no—
135C22×D11—41no—
136C22×D11—41no—
137C22×D11—41no—
138C22×D11—41no—
139C22×D11—41no—
140C22×D11—41no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11#12111yescharacteristic
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12311yescharacteristic
153C2×C4×C11#12311yescharacteristic
154C2×C4×C11#12411yescharacteristic
155C2×C4×C11C2×SD1611yescharacteristic
156C2×C4×C11#13511yescharacteristic
157C2×C4×C11#13511yescharacteristic
158C2×C4×C11#13511yescharacteristic
159C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
160C2×C4×C11#13711yescharacteristic
161C2×C4×C11#13711yescharacteristic
162C2×C4×C11#13711yescharacteristic
163C2×Dic11—41no—
164C2×Dic11—42no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11—42no—
168C2×Dic11—42no—
169C2×Dic11—81no—
170C2×Dic11—81no—
171C2×Dic11—81no—
172D44—22no—
173D44—22no—
174D44—41no—
175D44—41no—
176C4×D11—81no—
177C4×D11—81no—
178C4×D11—81no—
179C4×D11—81no—
180Dic22—44no—
181Dic22—82no—
182C8×C11—42no—
183C8×C11—81no—
184C11⋊C8—42no—
185C2×C4⋊Q8—111no—
186C2×C4×D4—111no—
187C2×#106—221no—
188C2×C4⋊C8—111no—
189C2×C4⋊C8C2×D1111yescharacteristic
190C2×#103—222no—
191C2×#102—221no—
192C2×C4×C8C2×D1111yescharacteristic
193#393—222no—
194#390—221no—
195#384—111no—
196#382—221no—
197#380—221no—
198#380—221no—
199C4×C4⋊C4C2×D1111yescharacteristic
200#340—221no—
201#340—221no—
202#333—222no—
203D4⋊C8—222no—
204C22×C11#39411yescharacteristic
205C22×C11#44811yescharacteristic
206C22×C11#44911yescharacteristic
207C22×C11#45211yescharacteristic
208C22×C11#45211yescharacteristic
209C22×C11#45311yescharacteristic
210C22×C11#45511yescharacteristic
211C2×D11—42no—
212C2×D11—42no—
213C2×D11—42no—
214C2×D11—81no—
215C2×D11—81no—
216C2×D11—81no—
217C2×D11—81no—
218C4×C11—21no—
219C4×C11—21no—
220C4×C11—81no—
221C4×C11—81no—
222C4×C11#46311yescharacteristic
223C4×C11#46411yescharacteristic
224C4×C11#46511yescharacteristic
225C4×C11#47011yescharacteristic
226C4×C11#48311yescharacteristic
227C4×C11#48511yescharacteristic
228C4×C11#48811yescharacteristic
229C4×C11#48911yescharacteristic
230Dic11—82no—
231Dic11—81no—
232Dic11—161no—
233C22×Q8—112no—
234C22×D4—111no—
235C23×C4—221no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—221no—
239C4⋊Q8—221no—
240C4⋊Q8—221no—
241C4⋊Q8—221no—
242C4⋊Q8—221no—
243C4×D4—221no—
244C4×D4—221no—
245C4×D4—221no—
246C4×D4—221no—
247C2×C4⋊C4—111no—
248C2×C4⋊C4—221no—
249C2×C4⋊C4—221no—
250C2×C4⋊C4—221no—
251C2×C4⋊C4—221no—
252C2×C4⋊C4—221no—
253C2×C4⋊C4D4411yescharacteristic
254C2×C4⋊C4D4411yescharacteristic
255C2×C22⋊C4—221no—
256C2×C22⋊C4—222no—
257C2×C22⋊C4—222no—
258C2×C42—21no—
259C2×C42C22×D1111yescharacteristic
260#106—442no—
261C4⋊C8—21no—
262C4⋊C8—21no—
263C4⋊C8—112no—
264C4⋊C8—221no—
265#103—444no—
266#102—442no—
267C4×C8—21no—
268C4×C8—21no—
269#95—21no—
270#95—222no—
271#95—222no—
272C2×C11#162211yescharacteristic
273C2×C11#163411yescharacteristic
274C2×C11#164311yescharacteristic
275C2×C11#164611yescharacteristic
276C2×C11#203511yescharacteristic
277C2×C11#203711yescharacteristic
278C2×C11#204211yescharacteristic
279D11—82no—
280C24—221no—
281C2×Q8—222no—
282C2×Q8—222no—
283C2×Q8—442no—
284C2×Q8—442no—
285C2×D4—112no—
286C2×D4—221no—
287C2×D4—221no—
288C2×D4—221no—
289C2×D4—221no—
290C2×D4—221no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—221no—
294C22×C4—222no—
295C22×C4—441no—
296C22×C4—441no—
297C22×C4—441no—
298C22×C4—441no—
299C22×C4—441no—
300C22×C4—441no—
301C22×C4—441no—
302C22×C4C2×D4411yescharacteristic
303C22×C4D4×D1111yescharacteristic
304C22×C4D4×D1111yescharacteristic
305C2×C8—22no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—222no—
312C2×C8—441no—
313C2×C8—441no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—221no—
319C4⋊C4—221no—
320C4⋊C4—442no—
321C4⋊C4—441no—
322C4⋊C4—441no—
323C4⋊C4—441no—
324C4⋊C4—441no—
325C4⋊C4—441no—
326C4⋊C4—441no—
327C4⋊C4—441no—
328C4⋊C4—441no—
329C22⋊C4—441no—
330C22⋊C4—441no—
331C22⋊C4—882no—
332C22⋊C4—882no—
333C42—41no—
334C42—41no—
335C42#433911yescharacteristic
336C42#433911yescharacteristic
337C42D4×D1111yescharacteristic
338C42#434311yescharacteristic
339C11#1041211yescharacteristic, complemented, Sylow
340C23—222no—
341C23—441no—
342C23—441no—
343C23—441no—
344C23—441no—
345C23—441no—
346C23—441no—
347C23#6693511yescharacteristic
348Q8—444no—
349Q8—882no—
350D4—222no—
351D4—222no—
352D4—441no—
353D4—441no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—441no—
363C2×C4—442no—
364C2×C4—441no—
365C2×C4—441no—
366C2×C4—442no—
367C2×C4—442no—
368C2×C4—881no—
369C2×C4—881no—
370C2×C4—881no—
371C2×C4—881no—
372C2×C4—881no—
373C2×C4—881no—
374C2×C4—881no—
375C2×C4#6692811yescharacteristic
376C2×C4#6693711yescharacteristic
377C2×C4#6693711yescharacteristic
378C2×C4#6694711yescharacteristic
379C2×C4#6694711yescharacteristic
380C2×C4#6694811yescharacteristic
381C2×C4#6695711yescharacteristic
382C2×C4#6695711yescharacteristic
383C2×C4#6696111yescharacteristic
384C2×C4#6696211yescharacteristic
385C2×C4#6696511yescharacteristic
386C2×C4SD16×D1111yescharacteristic
387C2×C4#6696811yescharacteristic
388C2×C4#6697111yescharacteristic
389C8—42no—
390C8—81no—
391C8—442no—
392C22—442no—
393C22—442no—
394C22—442no—
395C22—881no—
396C22—881no—
397C22—881no—
398C22—881no—
399C22#1062228511yescharacteristic
400C22#1062234611yescharacteristic
401C22#1062234711yescharacteristic
402C22#1062239611yescharacteristic
403C22#1062241911yescharacteristic
404C22#1062243511yescharacteristic
405C22#1062243811yescharacteristic
406C4—21no—
407C4—21no—
408C4—81no—
409C4—81no—
410C4—882no—
411C4—881no—
412C4—1761no—
413C4#1062231011yescharacteristic
414C4#1062232711yescharacteristic
415C4#1062239111yescharacteristic
416C4#1062242911yescharacteristic
417C4#1062245711yescharacteristic
418C4#1062245811yescharacteristic
419C4#1062247511yescharacteristic
420C4#1062250111yescharacteristic
421C2—882no—
422C2#1306769111yescharacteristic
423C2#1306776311yescharacteristic
424C2#1306782611yescharacteristic
425C2#1306784611yescharacteristic
426C2#1306981511yescharacteristic
427C2#1306982911yescharacteristic
428C2#1306985811yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1279C2
socleC23×C11#120
prime radicalC22×D44D4
hypercenter#1279D11
hypocenterC11#10412
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. #13069418C2semidirect
3. #13069379C2semidirect
5. C2×#10622119C2semidirect
7. C11×#1279C2semidirect
132. #1279D11semidirect
339. C11#10412semidirect

Maximal subgroups

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

subgroupindex
#130737852
#130694182
#130693792
#130686172
C2×#106221192
C2×#106220972
C11×#12792
#1041211