Finite Group Databasebeta

← #14783706

Subgroups — #14783706

Order 2816.

858 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#389C211yesmaximal, characteristic
2#13071021C211yesmaximal, characteristic
3#13070189C212yesmaximal, complemented
4#13070188C212yesmaximal, complemented
5#13070180C211yesmaximal, characteristic, complemented
6#13070179C211yesmaximal, characteristic, complemented
7#13070173C211yesmaximal, characteristic, complemented
8#13068334C212yesmaximal
9#13068334C212yesmaximal
10#13068308C211yesmaximal, characteristic
11C11×#2099C211yesmaximal, characteristic, complemented
12C22×#4313C2212yes—
13C2×#66945C2212yes—
14C2×C4⋊C4×D11—21no—
15C2×C4⋊C4×D11C2211yescharacteristic
16C2×C4⋊C4×D11C2211yescharacteristic
17C2×C42×D11C2211yescharacteristic
18C11×#389C2211yescharacteristic
19C11×#384C2211yescharacteristic
20#10622600—21no—
21#10622600—21no—
22#10622598C2211yescharacteristic
23#10622590C2212yes—
24C4⋊C4×Dic11—21no—
25C4⋊C4×Dic11—21no—
26#10622586C2211yescharacteristic
27#10622585—21no—
28#10622548C2211yescharacteristic
29#10622541C2211yescharacteristic
30D11×#95—21no—
31#10622260—21no—
32C11×#340C2212yes—
33C11×#340C2212yes—
34C11×#336C2211yescharacteristic
35#10622189C2212yes—
36#10622189C2212yes—
37#10622188C2212yes—
38#10622167C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42#10622162C2211yescharacteristic
43C22×C4×D11—21no—
44C22×C4×D11—21no—
45C22×C4×D11D411yescharacteristic
46C22×C4×D11D411yescharacteristic
47C22×C4×D11C2311yescharacteristic
48C22×C8×C11C2312yes—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4C2311yescharacteristic
53C2×C11×C4⋊C4C2312yes—
54C2×C11×C4⋊C4C2311yescharacteristic
55C2×C42×C11C2311yescharacteristic
56C2×(C2×D11)⋊C4—22no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11C2311yescharacteristic
61C2×C4⋊Dic11C2312yes—
62C2×C4⋊Dic11C2311yescharacteristic
63C2×Dic11⋊C4—21no—
64C2×Dic11⋊C4—21no—
65C2×Dic11⋊C4—21no—
66C2×Dic11⋊C4—21no—
67C2×C4×Dic11—22no—
68C2×C4×Dic11D411yescharacteristic
69C2×C4×Dic11D411yescharacteristic
70C2×C4×Dic11C2311yescharacteristic
71C22×C11⋊C8C2312yes—
72C2×#4313—24no—
73C2×#4313—24no—
74C2×#4313—24no—
75#66945—28no—
76C4⋊C4×D11—22no—
77C4⋊C4×D11—24no—
78C4⋊C4×D11—44no—
79C4⋊C4×D11Q814yes—
80C42×D11—24no—
81C11×#95—21no—
82C11⋊#95—21no—
83C11⋊#95—21no—
84C11⋊#95—21no—
85C11⋊#95—22no—
86C11⋊#95—22no—
87#23747—111nomaximal, Sylow
88C23×D11C2×D411yescharacteristic
89C22×C4×C11—21no—
90C22×C4×C11—22no—
91C22×C4×C11—21no—
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2411yescharacteristic
95C22×Dic11—21no—
96C22×Dic11—22no—
97C22×Dic11—21no—
98C22×Dic11C2×D411yescharacteristic
99C22×Dic11C2×D411yescharacteristic
100C22×Dic11C2×D411yescharacteristic
101C2×C4×D11—24no—
102C2×C4×D11—22no—
103C2×C4×D11—22no—
104C2×C4×D11—22no—
105C2×C4×D11—22no—
106C2×C4×D11—41no—
107C2×C4×D11—41no—
108C2×C4×D11—42no—
109C2×C4×D11—42no—
110C2×C4×D11—42no—
111C2×C4×D11—42no—
112C2×C4×D11—42no—
113C2×C4×D11C2×Q812yes—
114C2×C4×D11#4112yes—
115C2×C4×D11#4114yes—
116C2×C4×D11#4114yes—
117C2×C8×C11—22no—
118C2×C8×C11—22no—
119C2×C8×C11—22no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—24no—
123C11×C4⋊C4—42no—
124C11×C4⋊C4—42no—
125C11×C4⋊C4—42no—
126C11×C4⋊C4C2×Q812yes—
127C42×C11—22no—
128(C2×D11)⋊C4—44no—
129C4⋊Dic11—21no—
130C4⋊Dic11—22no—
131C4⋊Dic11—24no—
132C4⋊Dic11—42no—
133C4⋊Dic11—42no—
134C4⋊Dic11—42no—
135C4⋊Dic11C2×Q812yes—
136Dic11⋊C4—24no—
137Dic11⋊C4—42no—
138Dic11⋊C4—42no—
139Dic11⋊C4—42no—
140C4×Dic11—22no—
141C4×Dic11—22no—
142C4×Dic11—22no—
143C4×Dic11—44no—
144C2×C11⋊C8—22no—
145C2×C11⋊C8—22no—
146C2×C11⋊C8—22no—
147#4313—48no—
148C2×#389—111no—
149#2285—111no—
150#2101—112no—
151#2101—112no—
152#2100—111no—
153#2100—111no—
154#2099—111no—
155#2099D1111yescharacteristic, complemented
156#1736—112no—
157#1736—112no—
158#1728—111no—
159C23×C11C22×D411yescharacteristic
160C22×D11—21no—
161C22×D11—21no—
162C22×D11—21no—
163C22×D11—21no—
164C22×D11C22⋊Q812yes—
165C22×D11#12312yes—
166C22×D11#12412yes—
167C2×C4×C11—21no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—22no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—42no—
176C2×C4×C11—41no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—41no—
180C2×C4×C11AGL(1,ℤ/8)12yes—
181C2×C4×C11#13712yes—
182C2×C4×C11C22×Q811yescharacteristic
183C2×C4×C11C2×#4112yes—
184C2×C4×C11C2×#4112yes—
185C2×C4×C11C2×#4111yescharacteristic
186C2×Dic11—22no—
187C2×Dic11—21no—
188C2×Dic11—21no—
189C2×Dic11—21no—
190C2×Dic11—21no—
191C2×Dic11—21no—
192C2×Dic11—21no—
193C2×Dic11—41no—
194C2×Dic11—41no—
195C2×Dic11—41no—
196C2×Dic11—42no—
197C2×Dic11—41no—
198C2×Dic11—42no—
199C2×Dic11—42no—
200C2×Dic11—41no—
201C2×Dic11C22⋊Q812yes—
202C2×Dic11#12312yes—
203C2×Dic11#12412yes—
204C4×D11—44no—
205C4×D11—44no—
206C4×D11—48no—
207C4×D11—84no—
208C4×D11#12518yes—
209C4×D11#12618yes—
210C8×C11—42no—
211C11⋊C8—42no—
212C22×M16—112no—
213C2×#117—112no—
214C22×C4⋊C4—111no—
215C22×C4⋊C4—111no—
216C22×C4⋊C4—221no—
217C22×C42—111no—
218#389—111no—
219#389—111no—
220#389—111no—
221#389—221no—
222#389—221no—
223#389C2×D1111yescharacteristic
224#384—111no—
225#384C2×D1111yescharacteristic
226#382—112no—
227#380—221no—
228#380—221no—
229C4×C4⋊C4—221no—
230C4×C4⋊C4—221no—
231C2×#95—221no—
232#340—112no—
233#340—112no—
234#340—112no—
235#340—112no—
236#340—112no—
237#340—112no—
238#340C2×D1112yes—
239#340C2×D1112yes—
240#336—112no—
241#336—111no—
242#336C2×D1111yescharacteristic
243C22×C11C2×C22⋊Q811yescharacteristic
244C22×C11C2×#12311yescharacteristic
245C22×C11C2×#12411yescharacteristic
246C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
247C22×C11C2×#13711yescharacteristic
248C22×C11#57511yescharacteristic
249C22×C11#57511yescharacteristic
250C2×D11—22no—
251C2×D11—22no—
252C2×D11—22no—
253C2×D11—22no—
254C2×D11—22no—
255C2×D11—22no—
256C2×D11#40014yes—
257C4×C11—22no—
258C4×C11—22no—
259C4×C11—42no—
260C4×C11—81no—
261C4×C11—82no—
262C4×C11C2×#12512yes—
263C4×C11C2×#12612yes—
264Dic11—42no—
265Dic11—41no—
266Dic11—41no—
267Dic11—81no—
268Dic11—82no—
269Dic11#40014yes—
270C23×C4—111no—
271C23×C4—111no—
272C23×C4—111no—
273C23×C4—221no—
274C23×C4—221no—
275C2×M16—224no—
276C2×M16—224no—
277C2×M16—224no—
278C22×C8—112no—
279C22×C8C22×D1112yes—
280#117—228no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—111no—
285C2×C4⋊C4—114no—
286C2×C4⋊C4—111no—
287C2×C4⋊C4—112no—
288C2×C4⋊C4—222no—
289C2×C4⋊C4—224no—
290C2×C4⋊C4—221no—
291C2×C4⋊C4—221no—
292C2×C4⋊C4—221no—
293C2×C4⋊C4—221no—
294C2×C4⋊C4—221no—
295C2×C4⋊C4—221no—
296C2×C4⋊C4—221no—
297C2×C4⋊C4—444no—
298C2×C4⋊C4C22×D1111yescharacteristic
299C2×C4⋊C4C22×D1112yes—
300C2×C4⋊C4C22×D1111yescharacteristic
301C2×C22⋊C4—222no—
302C2×C42—111no—
303C2×C42—111no—
304C2×C42—111no—
305C2×C42—224no—
306C2×C42—222no—
307C2×C42C22×D1111yescharacteristic
308#95—21no—
309#95—221no—
310#95—221no—
311#95—222no—
312#95—222no—
313#95—221no—
314C2×C11C2×#40011yescharacteristic
315C2×C11#307711yescharacteristic
316C2×C11#307811yescharacteristic
317C2×C11#309411yescharacteristic
318C2×C11#309511yescharacteristic
319C2×C11#314111yescharacteristic
320C2×C11#314211yescharacteristic
321D11—24no—
322C24—111no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—22no—
326C22×C4—111no—
327C22×C4—112no—
328C22×C4—114no—
329C22×C4—112no—
330C22×C4—114no—
331C22×C4—111no—
332C22×C4—111no—
333C22×C4—222no—
334C22×C4—222no—
335C22×C4—224no—
336C22×C4—221no—
337C22×C4—222no—
338C22×C4—222no—
339C22×C4—222no—
340C22×C4—221no—
341C22×C4—441no—
342C22×C4—441no—
343C22×C4—442no—
344C22×C4—442no—
345C22×C4—442no—
346C22×C4—442no—
347C22×C4—442no—
348C22×C4D4×D1111yescharacteristic
349C22×C4D4×D1111yescharacteristic
350C22×C4C23×D1111yescharacteristic
351M16—448no—
352C2×C8—22no—
353C2×C8—22no—
354C2×C8—22no—
355C2×C8—222no—
356C2×C8—222no—
357C2×C8—222no—
358C4⋊C4—21no—
359C4⋊C4—22no—
360C4⋊C4—24no—
361C4⋊C4—42no—
362C4⋊C4—42no—
363C4⋊C4—42no—
364C4⋊C4—112no—
365C4⋊C4—224no—
366C4⋊C4—221no—
367C4⋊C4—222no—
368C4⋊C4—224no—
369C4⋊C4—442no—
370C4⋊C4—442no—
371C4⋊C4—442no—
372C4⋊C4—442no—
373C4⋊C4—442no—
374C4⋊C4—442no—
375C4⋊C4Q8×D1112yes—
376C22⋊C4—444no—
377C42—22no—
378C42—222no—
379C42—222no—
380C42—222no—
381C42—444no—
382C11#2374711yescharacteristic, complemented, Sylow
383C23—112no—
384C23—112no—
385C23—112no—
386C23—221no—
387C23—221no—
388C23—221no—
389C23—221no—
390C23C2×D4×D1111yescharacteristic
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—22no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—42no—
404C2×C4—112no—
405C2×C4—112no—
406C2×C4—112no—
407C2×C4—118no—
408C2×C4—118no—
409C2×C4—221no—
410C2×C4—221no—
411C2×C4—221no—
412C2×C4—221no—
413C2×C4—222no—
414C2×C4—221no—
415C2×C4—221no—
416C2×C4—444no—
417C2×C4—444no—
418C2×C4—448no—
419C2×C4—441no—
420C2×C4—441no—
421C2×C4—441no—
422C2×C4—442no—
423C2×C4—442no—
424C2×C4—441no—
425C2×C4—441no—
426C2×C4—442no—
427C2×C4—884no—
428C2×C4#6696412yes—
429C2×C4#6696812yes—
430C2×C4C2×Q8×D1111yescharacteristic
431C2×C4#41×D1111yescharacteristic
432C2×C4#41×D1112yes—
433C2×C4#41×D1112yes—
434C8—42no—
435C8—442no—
436C22—114no—
437C22—222no—
438C22—222no—
439C22—222no—
440C22—222no—
441C22—222no—
442C22—222no—
443C22D11×C22⋊Q811yescharacteristic
444C22D11×#12311yescharacteristic
445C22D11×#12411yescharacteristic
446C22C2×#6696411yescharacteristic
447C22C2×#6696811yescharacteristic
448C22#1062330811yescharacteristic
449C22#1062330811yescharacteristic
450C4—22no—
451C4—22no—
452C4—42no—
453C4—81no—
454C4—82no—
455C4—114no—
456C4—441no—
457C4—441no—
458C4—442no—
459C4—881no—
460C4—882no—
461C4D11×#12512yes—
462C4D11×#12612yes—
463C2—224no—
464C2D11×#40011yescharacteristic
465C2#1307840811yescharacteristic
466C2#1307841611yescharacteristic
467C2#1307855111yescharacteristic
468C2#1307855911yescharacteristic
469C2#1307900611yescharacteristic
470C2#1307901811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2099C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenter#2099D11
hypocenterC11#23747
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2099

Complements

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

NH ≅ G/Ntype
3. #13070189C2semidirect
4. #13070188C2semidirect
5. #13070180C2semidirect
6. #13070179C2semidirect
7. #13070173C2semidirect
11. C11×#2099C2semidirect
155. #2099D11semidirect
382. C11#23747semidirect

Maximal subgroups

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

subgroupindex
D11×#3892
#130710212
#130701892
#130701882
#130701802
#130701792
#130701732
#130683342
#130683082
C11×#20992
#2374711