Finite Group Databasebeta

← #14657213

Subgroups — #14657213

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#13073570C211yesmaximal, characteristic
2#13069377C211yesmaximal, characteristic, complemented
3#13068613C211yesmaximal, characteristic
4C2×#10622185C211yesmaximal, characteristic, complemented
5C2×#10622097C211yesmaximal, characteristic
6#13066456C211yesmaximal, characteristic, complemented
7C11×#1990C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×#66999—21no—
10C2×#66999—21no—
11C2×C4×D44C2211yescharacteristic
12C2×C4×C8×C11C2211yescharacteristic
13C11×#384C2211yescharacteristic
14#10622605—22no—
15#10622601—21no—
16#10622589—21no—
17C2×#66873—21no—
18C2×#66872—21no—
19C4×C4⋊Dic11C2211yescharacteristic
20C2×C4⋊(C11⋊C8)C2211yescharacteristic
21C2×C4⋊(C11⋊C8)C2211yescharacteristic
22C11×#340—22no—
23#10622185—22no—
24#10622167—21no—
25#10622167—21no—
26#10622097—22no—
27C22×Q8×C11—21no—
28C22×D44D411yescharacteristic
29C22×C4×D11—21no—
30C22×C8×C11—21no—
31C11×C4⋊Q8—21no—
32C11×C4⋊Q8—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4D412yes—
40C2×C42×C11C2311yescharacteristic
41#66999—42no—
42#66999—42no—
43#66999—42no—
44#66999—42no—
45C2×(C2×D11)⋊C4—22no—
46C2×(C2×D11)⋊C4—22no—
47C2×(C2×D11)⋊C4—21no—
48C2×C4⋊Dic11D411yescharacteristic
49C2×C4⋊Dic11D411yescharacteristic
50C2×C4⋊Dic11D411yescharacteristic
51C2×Dic11⋊C4—22no—
52C2×Dic11⋊C4—22no—
53C2×C4×Dic11—21no—
54C22×C11⋊C8—21no—
55C22×C11⋊C8—21no—
56C4×D44—21no—
57C4×D44—21no—
58C4×D44—21no—
59C4×D44—21no—
60C4×C8×C11—21no—
61C4×C8×C11—21no—
62C11⋊#95—21no—
63#66873—42no—
64#66872—42no—
65C4⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)—21no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)D412yes—
69#10420—111nomaximal, Sylow
70C23×D11—21no—
71C2×Q8×C11—41no—
72C2×Q8×C11—41no—
73C2×Q8×C11—41no—
74C2×Q8×C11—41no—
75C2×Q8×C11—41no—
76C2×Q8×C11—41no—
77C22×C4×C11—22no—
78C22×C4×C11—41no—
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×Dic11—21no—
83C22×Dic11—21no—
84C22×Dic11—21no—
85C2×D44—21no—
86C2×D44—21no—
87C2×D44—21no—
88C2×D44—21no—
89C2×D44—21no—
90C2×D44SD1612yes—
91C2×C4×D11—41no—
92C2×C4×D11—41no—
93C2×C4×D11—41no—
94C2×C4×D11—41no—
95C2×C4×D11—41no—
96C2×C4×D11—41no—
97C2×C8×C11—22no—
98C2×C8×C11—41no—
99C2×C8×C11—41no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—42no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—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—21no—
118C4⋊Dic11—21no—
119C4⋊Dic11—21no—
120C4⋊Dic11—21no—
121C4⋊Dic11D812yes—
122C4⋊Dic11SD1612yes—
123Dic11⋊C4—44no—
124Dic11⋊C4—44no—
125C4×Dic11—41no—
126C4×Dic11—41no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—41no—
129C2×C11⋊C8—41no—
130C2×C11⋊C8—41no—
131C2×C11⋊C8—41no—
132C2×C11⋊C8—41no—
133#2542—111no—
134#1990D1111yescharacteristic, complemented
135#1948—111no—
136#1802—111no—
137C2×#332—111no—
138C2×D4⋊C8—111no—
139#1279—111no—
140C23×C11#12011yescharacteristic
141C22×D11—22no—
142C22×D11—41no—
143C22×D11—41no—
144C22×D11—41no—
145C22×D11—41no—
146C22×D11—41no—
147C22×D11—41no—
148Q8×C11—81no—
149Q8×C11—81no—
150Q8×C11—81no—
151Q8×C11—81no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—42no—
155C2×C4×C11—42no—
156C2×C4×C11—42no—
157C2×C4×C11—81no—
158C2×C4×C11—81no—
159C2×C4×C11—81no—
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11#12311yescharacteristic
164C2×C4×C11#12311yescharacteristic
165C2×C4×C11#12411yescharacteristic
166C2×C4×C11C2×D811yescharacteristic
167C2×C4×C11C2×SD1611yescharacteristic
168C2×C4×C11C2×SD1611yescharacteristic
169C2×C4×C11#13511yescharacteristic
170C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C11#13711yescharacteristic
173C2×C4×C11#13711yescharacteristic
174C2×Dic11—22no—
175C2×Dic11—22no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11—41no—
181C2×Dic11—41no—
182C2×Dic11—41no—
183D44—22no—
184D44—22no—
185D44—41no—
186D44—41no—
187C4×D11—81no—
188C4×D11—81no—
189C4×D11—81no—
190C4×D11—81no—
191C8×C11—42no—
192C11⋊C8—42no—
193C11⋊C8—81no—
194C2×C4⋊Q8C2×D1111yescharacteristic
195C2×C22⋊Q8—221no—
196C2×C22⋊Q8—221no—
197C2×C4×D4—111no—
198C2×#106—221no—
199C2×C4⋊C8—111no—
200C2×C4⋊C8—111no—
201C2×#102—221no—
202C2×C4×C8C2×D1111yescharacteristic
203#399—222no—
204#390—221no—
205#384—221no—
206#384C2×D1111yescharacteristic
207C4×C4⋊C4—111no—
208#340—22no—
209#340—221no—
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—82no—
230C4×C11—161no—
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—42no—
240Dic11—42no—
241Dic11—81no—
242C22×Q8—21no—
243C22×D4—111no—
244C23×C4—221no—
245C22×C8—21no—
246C22×C8—221no—
247C22×C8—221no—
248C4⋊Q8—21no—
249C4⋊Q8—21no—
250C4⋊Q8—21no—
251C4⋊Q8—21no—
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—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—111no—
265C2×C4⋊C4—111no—
266C2×C4⋊C4—111no—
267C2×C4⋊C4—222no—
268C2×C4⋊C4—222no—
269C2×C4⋊C4C22⋊D1112yes—
270C2×C22⋊C4—222no—
271C2×C22⋊C4—222no—
272C2×C22⋊C4—221no—
273C2×C42—221no—
274C2×C42C22×D1111yescharacteristic
275#106—442no—
276C4⋊C8—112no—
277C4⋊C8—221no—
278C4⋊C8—221no—
279C4⋊C8—221no—
280#102—442no—
281C4×C8—21no—
282C4×C8—21no—
283#95—221no—
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—41no—
294C2×Q8—41no—
295C2×Q8—41no—
296C2×Q8—41no—
297C2×Q8—41no—
298C2×Q8—41no—
299C2×D4—112no—
300C2×D4—221no—
301C2×D4—221no—
302C2×D4—221no—
303C2×D4—221no—
304C2×D4—221no—
305C22×C4—22no—
306C22×C4—41no—
307C22×C4—221no—
308C22×C4—221no—
309C22×C4—221no—
310C22×C4—441no—
311C22×C4—441no—
312C22×C4—441no—
313C22×C4—441no—
314C22×C4—441no—
315C22×C4—441no—
316C22×C4D4×D1111yescharacteristic
317C22×C4D4×D1111yescharacteristic
318C22×C4C2×C22⋊D1111yescharacteristic
319C2×C8—22no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—222no—
323C2×C8—441no—
324C2×C8—441no—
325C2×C8—441no—
326C2×C8—441no—
327C2×C8—441no—
328C4⋊C4—22no—
329C4⋊C4—22no—
330C4⋊C4—42no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—112no—
338C4⋊C4—112no—
339C4⋊C4—221no—
340C4⋊C4—221no—
341C4⋊C4—221no—
342C4⋊C4—221no—
343C4⋊C4—444no—
344C4⋊C4—444no—
345C22⋊C4—444no—
346C22⋊C4—444no—
347C22⋊C4—441no—
348C22⋊C4—441no—
349C42—441no—
350C42—441no—
351C42#433911yescharacteristic
352C42#433911yescharacteristic
353C42D4×D1111yescharacteristic
354C42#434111yescharacteristic
355C11#1042011yescharacteristic, complemented, Sylow
356C23—222no—
357C23—441no—
358C23—441no—
359C23—441no—
360C23—441no—
361C23—441no—
362C23—441no—
363C23#6699011yescharacteristic
364Q8—81no—
365Q8—81no—
366Q8—81no—
367Q8—81no—
368D4—222no—
369D4—222no—
370D4—441no—
371D4—441no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—81no—
378C2×C4—81no—
379C2×C4—81no—
380C2×C4—222no—
381C2×C4—222no—
382C2×C4—441no—
383C2×C4—441no—
384C2×C4—441no—
385C2×C4—441no—
386C2×C4—441no—
387C2×C4—441no—
388C2×C4—441no—
389C2×C4—881no—
390C2×C4—881no—
391C2×C4—881no—
392C2×C4—881no—
393C2×C4#6693611yescharacteristic
394C2×C4#6693711yescharacteristic
395C2×C4#6693711yescharacteristic
396C2×C4#6693811yescharacteristic
397C2×C4D8×D1111yescharacteristic
398C2×C4#6696411yescharacteristic
399C2×C4SD16×D1111yescharacteristic
400C2×C4SD16×D1111yescharacteristic
401C2×C4#6696711yescharacteristic
402C2×C4#6696811yescharacteristic
403C2×C4#6697111yescharacteristic
404C2×C4#6697211yescharacteristic
405C2×C4#6698211yescharacteristic
406C2×C4#6699211yescharacteristic
407C8—42no—
408C8—442no—
409C8—881no—
410C22—442no—
411C22—442no—
412C22—442no—
413C22—881no—
414C22—881no—
415C22—881no—
416C22—881no—
417C22#1062257211yescharacteristic
418C22#1062267511yescharacteristic
419C22#1062270811yescharacteristic
420C22#1062276911yescharacteristic
421C22#1062278211yescharacteristic
422C22#1062278311yescharacteristic
423C22#1062280011yescharacteristic
424C4—21no—
425C4—21no—
426C4—82no—
427C4—161no—
428C4—442no—
429C4—442no—
430C4—881no—
431C4#1062237311yescharacteristic
432C4#1062237511yescharacteristic
433C4#1062237711yescharacteristic
434C4#1062239911yescharacteristic
435C4#1062241811yescharacteristic
436C4#1062242011yescharacteristic
437C4#1062242711yescharacteristic
438C4#1062242911yescharacteristic
439C2—882no—
440C2#1306771611yescharacteristic
441C2#1306776411yescharacteristic
442C2#1306784811yescharacteristic
443C2#1306787611yescharacteristic
444C2#1306981011yescharacteristic
445C2#1306983311yescharacteristic
446C2#1306984811yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1990C2
socleC23×C11#120
prime radicalC22×D44D4
hypercenter#1990D11
hypocenterC11#10420
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
2. #13069377C2semidirect
4. C2×#10622185C2semidirect
6. #13066456C2semidirect
7. C11×#1990C2semidirect
134. #1990D11semidirect
355. C11#10420semidirect

Maximal subgroups

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

subgroupindex
#130735702
#130693772
#130686132
C2×#106221852
C2×#106220972
#130664562
C11×#19902
#1042011