Finite Group Databasebeta

← #14671307

Subgroups — #14671307

Order 2816.

724 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 724 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072240C211yesmaximal, characteristic
2C2×#10622111C212yesmaximal, complemented
3#13068534C211yesmaximal, characteristic
4#13066740C212yesmaximal, complemented
5C2×C11×#410C211yesmaximal, characteristic
6C22×C11×#41C2211yescharacteristic
7C2×C11×#117—21no—
8C2×#66997C411yescharacteristic, complemented
9C2×#66989C2211yescharacteristic
10C2×#66977C411yescharacteristic, complemented
11C11×#410—24no—
12C2×C11×#99—21no—
13C2×C11×#99C2212yes—
14#10622843C411yescharacteristic, complemented
15#10622835—21no—
16#10622835—21no—
17#10622834C2211yescharacteristic
18C2×#66898—21no—
19C2×#66898C2212yes—
20#10622824—21no—
21#10622823—21no—
22#10622823—21no—
23C4×C22⋊Dic11C411yescharacteristic, complemented
24#10622111—24no—
25C2×C11×#41—22no—
26C2×C11×#41—22no—
27C2×C11×#41—41no—
28C2×C11×#41—41no—
29C2×C11×#41—42no—
30C22×Q8×C11C2×C411yescharacteristic
31C22×D4×C11D411yescharacteristic
32C22×D4×C11D411yescharacteristic
33C22×D4×C11C2311yescharacteristic
34C23×C4×C11C2×C411yescharacteristic
35C23×C4×C11D411yescharacteristic
36C23×C4×C11D411yescharacteristic
37C22×Dic22C2×C411yescharacteristic
38C11×#117—24no—
39C11×#117—42no—
40C2×C11×C4⋊C4—41no—
41C2×C11×C22⋊C4—22no—
42C2×C42×C11—41no—
43C2×C22⋊Dic11—21no—
44C2×C22⋊Dic11—21no—
45C2×C22⋊Dic11—21no—
46C2×C22⋊Dic11—21no—
47C2×C22⋊Dic11—21no—
48C2×C22⋊Dic11—21no—
49C2×C22⋊Dic11—22no—
50#66997—42no—
51#66989—22no—
52#66989—22no—
53C2×C4⋊Dic11C2×C411yescharacteristic
54#66977—41no—
55#66977—41no—
56C2×Dic11⋊C4—21no—
57C2×Dic11⋊C4—21no—
58C2×Dic11⋊C4—21no—
59C2×C4×Dic11C2×C411yescharacteristic
60C2×C4×Dic11C2×C411yescharacteristic
61C11×#99—24no—
62C11×#99—22no—
63C11×#99D414yes—
64#66898—22no—
65#66898—22no—
66#66898—42no—
67C11⋊#95—21no—
68C11⋊#95—21no—
69C11⋊#95—21no—
70C11⋊#95—41no—
71C11⋊#95—41no—
72#13091—111nomaximal, Sylow
73C24×C11C22⋊C411yescharacteristic
74C24×C11C2×D411yescharacteristic
75C24×C11C2×D411yescharacteristic
76C11×#41—44no—
77C11×#41—44no—
78C11×#41—44no—
79C11×#41—44no—
80C2×Q8×C11—22no—
81C2×Q8×C11—22no—
82C2×Q8×C11—41no—
83C2×D4×C11—21no—
84C2×D4×C11—22no—
85C2×D4×C11—21no—
86C2×D4×C11—22no—
87C2×D4×C11—41no—
88C2×D4×C11—41no—
89C2×D4×C11—41no—
90C2×D4×C11—41no—
91C2×D4×C11—41no—
92C2×D4×C11C2×D412yes—
93C2×D4×C11#4112yes—
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—22no—
105C22×C4×C11—41no—
106C22×C4×C11—41no—
107C22×C4×C11—42no—
108C22×C4×C11C22⋊C411yescharacteristic
109C22×C4×C11C22⋊C411yescharacteristic
110C22×C4×C11C22⋊C411yescharacteristic
111C22×C4×C11C22×C411yescharacteristic
112C22×Dic11—21no—
113C22×Dic11—21no—
114C22×Dic11—21no—
115C22×Dic11—21no—
116C22×Dic11—42no—
117C2×Dic22—22no—
118C2×Dic22—41no—
119C2×Dic22—41no—
120C11×C4⋊C4—44no—
121C11×C22⋊C4—24no—
122C11×C22⋊C4—42no—
123C42×C11—44no—
124C22⋊Dic11—42no—
125C22⋊Dic11—42no—
126C22⋊Dic11—42no—
127C22⋊Dic11—42no—
128C22⋊Dic11—42no—
129C22⋊Dic11—41no—
130C22⋊Dic11—42no—
131C22⋊Dic11—42no—
132C22⋊Dic11—41no—
133C4⋊Dic11—41no—
134Dic11⋊C4—42no—
135Dic11⋊C4—41no—
136Dic11⋊C4—41no—
137Dic11⋊C4—42no—
138C4×Dic11—22no—
139C4×Dic11—41no—
140C2×#410D1111yescharacteristic
141#2432—111no—
142C2×#354—112no—
143#1782—111no—
144#1393—112no—
145C23×C11—21no—
146C23×C11—21no—
147C23×C11—21no—
148C23×C11—21no—
149C23×C11—21no—
150C23×C11—21no—
151C23×C11—21no—
152C23×C11—41no—
153C23×C11—41no—
154C23×C11—41no—
155C23×C11—41no—
156C23×C11—41no—
157C23×C11—41no—
158C23×C11C2×C22⋊C411yescharacteristic
159C23×C11#12011yescharacteristic
160C23×C11#12112yes—
161C23×C11#12311yescharacteristic
162Q8×C11—44no—
163D4×C11—42no—
164D4×C11—42no—
165D4×C11—44no—
166D4×C11—42no—
167D4×C11—42no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—44no—
186C2×C4×C11—82no—
187C2×C4×C11—82no—
188C2×C4×C11#9911yescharacteristic
189C2×C4×C11#9911yescharacteristic
190C2×C4×C11#9912yes—
191C2×C4×C11C4×D412yes—
192C2×Dic11—22no—
193C2×Dic11—41no—
194C2×Dic11—41no—
195C2×Dic11—41no—
196C2×Dic11—41no—
197C2×Dic11—41no—
198C2×Dic11—41no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—82no—
205C2×Dic11—82no—
206C2×Dic11—82no—
207Dic22—82no—
208C22×#41C2×D1111yescharacteristic
209C2×C4⋊Q8—111no—
210C2×#124—111no—
211C2×C22⋊Q8—111no—
212C2×#117—21no—
213#410—24no—
214C2×#99—21no—
215C2×#99—112no—
216C2×#99—221no—
217C2×#99C2×D1112yes—
218#394—221no—
219#394—221no—
220#391—111no—
221#390—111no—
222#385—221no—
223#385—221no—
224#381—221no—
225C4×C22⋊C4—111no—
226#354—224no—
227C22×C11—21no—
228C22×C11—21no—
229C22×C11—21no—
230C22×C11—21no—
231C22×C11—22no—
232C22×C11—41no—
233C22×C11—42no—
234C22×C11—41no—
235C22×C11—41no—
236C22×C11—41no—
237C22×C11—41no—
238C22×C11—41no—
239C22×C11—41no—
240C22×C11—41no—
241C22×C11—41no—
242C22×C11—81no—
243C22×C11—81no—
244C22×C11—81no—
245C22×C11—81no—
246C22×C11#38611yescharacteristic
247C22×C11C2×#9911yescharacteristic
248C22×C11C2×#9911yescharacteristic
249C4×C11—21no—
250C4×C11—21no—
251C4×C11—22no—
252C4×C11—22no—
253C4×C11—41no—
254C4×C11—84no—
255Dic11—42no—
256Dic11—81no—
257Dic11—81no—
258Dic11—81no—
259Dic11—162no—
260C2×#41—22no—
261C2×#41—22no—
262C2×#41—41no—
263C2×#41—41no—
264C2×#41—42no—
265C22×Q8—111no—
266C22×Q8C4×D1111yescharacteristic
267C22×D4D4411yescharacteristic
268C22×D4C22⋊D1111yescharacteristic
269C22×D4C22×D1111yescharacteristic
270C23×C4C4×D1111yescharacteristic
271C23×C4D4411yescharacteristic
272C23×C4C22⋊D1111yescharacteristic
273C4⋊Q8—442no—
274#124—222no—
275#124—222no—
276C22⋊Q8—441no—
277C22⋊Q8—441no—
278#117—24no—
279#117—42no—
280C2×C4⋊C4—41no—
281C2×C4⋊C4—111no—
282C2×C4⋊C4—221no—
283C2×C4⋊C4—221no—
284C2×C4⋊C4—221no—
285C2×C22⋊C4—22no—
286C2×C22⋊C4—221no—
287C2×C22⋊C4—221no—
288C2×C22⋊C4—221no—
289C2×C22⋊C4—221no—
290C2×C22⋊C4—221no—
291C2×C22⋊C4—221no—
292C2×C22⋊C4—222no—
293C2×C42—41no—
294C2×C42—111no—
295C2×C42—111no—
296#99—24no—
297#99—22no—
298#99—222no—
299#99—222no—
300#99—442no—
301#99C22⋊D1114yes—
302#95—221no—
303#95—221no—
304#95—221no—
305#95—441no—
306#95—441no—
307C2×C11—21no—
308C2×C11—21no—
309C2×C11—42no—
310C2×C11—41no—
311C2×C11—41no—
312C2×C11—81no—
313C2×C11#189811yescharacteristic
314C2×C11#212611yescharacteristic
315C2×C11#212911yescharacteristic
316C24(C2×D11)⋊C411yescharacteristic
317C24C2×D4411yescharacteristic
318C24C2×C22⋊D1111yescharacteristic
319#41—44no—
320#41—44no—
321#41—44no—
322#41—44no—
323C2×Q8—22no—
324C2×Q8—22no—
325C2×Q8—41no—
326C2×Q8—222no—
327C2×Q8—441no—
328C2×Q8—441no—
329C2×D4—21no—
330C2×D4—22no—
331C2×D4—21no—
332C2×D4—22no—
333C2×D4—41no—
334C2×D4—41no—
335C2×D4—41no—
336C2×D4—41no—
337C2×D4—41no—
338C2×D4#433912yes—
339C2×D4C2×C22⋊D1112yes—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—22no—
351C22×C4—41no—
352C22×C4—41no—
353C22×C4—42no—
354C22×C4—221no—
355C22×C4—221no—
356C22×C4—221no—
357C22×C4—221no—
358C22×C4—442no—
359C22×C4(C2×D11)⋊C411yescharacteristic
360C22×C4(C2×D11)⋊C411yescharacteristic
361C22×C4(C2×D11)⋊C411yescharacteristic
362C22×C4C2×C4×D1111yescharacteristic
363C4⋊C4—44no—
364C4⋊C4—441no—
365C4⋊C4—442no—
366C4⋊C4—441no—
367C4⋊C4—441no—
368C4⋊C4—442no—
369C22⋊C4—24no—
370C22⋊C4—42no—
371C22⋊C4—442no—
372C22⋊C4—442no—
373C22⋊C4—442no—
374C22⋊C4—442no—
375C22⋊C4—441no—
376C22⋊C4—442no—
377C22⋊C4—441no—
378C22⋊C4—442no—
379C22⋊C4—442no—
380C42—44no—
381C42—222no—
382C42—441no—
383C11#1309111yescharacteristic, complemented, Sylow
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—21no—
391C23—41no—
392C23—41no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23—41no—
397C23C2×(C2×D11)⋊C411yescharacteristic
398C23#6698211yescharacteristic
399C23#6698312yes—
400C23#6700611yescharacteristic
401Q8—44no—
402Q8—882no—
403D4—42no—
404D4—42no—
405D4—44no—
406D4—42no—
407D4—42no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—44no—
426C2×C4—82no—
427C2×C4—82no—
428C2×C4—222no—
429C2×C4—441no—
430C2×C4—441no—
431C2×C4—441no—
432C2×C4—441no—
433C2×C4—441no—
434C2×C4—441no—
435C2×C4—441no—
436C2×C4—441no—
437C2×C4—441no—
438C2×C4—441no—
439C2×C4—441no—
440C2×C4—882no—
441C2×C4—882no—
442C2×C4—882no—
443C2×C4#6687012yes—
444C2×C4#6687011yescharacteristic
445C2×C4#6687011yescharacteristic
446C2×C4C4×C22⋊D1112yes—
447C22—21no—
448C22—21no—
449C22—21no—
450C22—21no—
451C22—22no—
452C22—41no—
453C22—42no—
454C22—41no—
455C22—41no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—81no—
463C22—81no—
464C22—81no—
465C22—81no—
466C22C2×#6687011yescharacteristic
467C22C2×#6687011yescharacteristic
468C22#1062282611yescharacteristic
469C4—21no—
470C4—21no—
471C4—22no—
472C4—22no—
473C4—41no—
474C4—84no—
475C4—442no—
476C4—881no—
477C4—881no—
478C4—881no—
479C4—1762no—
480C2—21no—
481C2—21no—
482C2—41no—
483C2—42no—
484C2—41no—
485C2—81no—
486C2#1306906911yescharacteristic
487C2#1307027911yescharacteristic
488C2#1307029011yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC22×D4C22×D11
FittingC2×C11×#410C2
socleC22×C11C2×#99
prime radicalC22×C11×#41C22
cosocleC22×D4×C11C23
hypercenterC2×#410D11
hypocenterC11#13091
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ C2×#410

Complements

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

NH ≅ G/Ntype
2. C2×#10622111C2semidirect
4. #13066740C2semidirect
8. C2×#66997C4semidirect
10. C2×#66977C4semidirect
14. #10622843C4semidirect
23. C4×C22⋊Dic11C4semidirect
383. C11#13091semidirect

Maximal subgroups

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

subgroupindex
#130722402
C2×#106221112
#130685342
#130667402
C2×C11×#4102
#1309111