Finite Group Databasebeta

← #14650809

Subgroups — #14650809

Order 2816.

576 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 89 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#13079416C211yesmaximal, characteristic
2#13071775C211yesmaximal, characteristic, complemented
3#13069452C211yesmaximal, characteristic, complemented
4#13067144C211yesmaximal, characteristic, complemented
5#13067131C211yesmaximal, characteristic, complemented
6#13066523C211yesmaximal, characteristic, complemented
7C11×#1284C211yesmaximal, characteristic, complemented
8C2×#66983C2211yescharacteristic
9C2×#66983C2211yescharacteristic
10C11×#407C2211yescharacteristic
11C11×#381C2211yescharacteristic
12C4×C11×C22⋊C4C2211yescharacteristic
13#10622825C2211yescharacteristic
14#10622820C2211yescharacteristic
15#10622748—22no—
16#10622570—21no—
17#10622569—21no—
18C2×#66870—21no—
19C2×#66870—21no—
20#10622348—21no—
21#10622348C412yescomplemented
22#10622345—21no—
23#10622345C412yescomplemented
24#10622283—21no—
25#10622281—21no—
26#10622278—21no—
27#10622267—21no—
28#10622089—22no—
29#10622089—21no—
30#10622089—21no—
31C23×C4×C11C2311yescharacteristic
32C22×C22⋊D11—21no—
33C22×C22⋊D11—21no—
34C22×D44C2×C411yescharacteristic, complemented
35C22×D44D411yescharacteristic
36C22×C4×D11—21no—
37C2×C11×M16—21no—
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C42×C11—21no—
41C2×C22⋊Dic11D411yescharacteristic
42C2×C22⋊Dic11D411yescharacteristic
43#66983—21no—
44#66983—21no—
45#66983—21no—
46#66983—21no—
47#66983—21no—
48#66983—21no—
49#66983C2×C412yes—
50#66983D412yes—
51C2×(C2×D11)⋊C4—21no—
52C2×(C2×D11)⋊C4—21no—
53C2×(C2×D11)⋊C4—21no—
54C2×(C2×D11)⋊C4—21no—
55C2×(C2×D11)⋊C4—21no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11C2×C411yescharacteristic, complemented
58C2×C4⋊Dic11D411yescharacteristic
59C2×Dic11⋊C4—21no—
60C2×C4×Dic11—21no—
61C2×#4318—21no—
62C2×D88—22no—
63C11×C22⋊C8—21no—
64C11×C22⋊C8C2×C412yescomplemented
65C11×#95—21no—
66C11×#95—21no—
67C11×#95D411yescharacteristic
68C11×#95D411yescharacteristic
69C11⋊#95—21no—
70C11⋊#95—21no—
71C11⋊#95—21no—
72C22⋊(C11⋊C8)—21no—
73C22⋊(C11⋊C8)—21no—
74#66885—22no—
75#66885—22no—
76#66881—22no—
77#66870—42no—
78#66870—42no—
79#9343—111nomaximal, Sylow
80C24×C11C2×D411yescharacteristic
81C23×D11—21no—
82C23×D11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—41no—
86C22×C4×C11—81no—
87C22×C4×C11C22×C411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11#4111yescharacteristic
92C22×C4×C11#4111yescharacteristic
93C2×C22⋊D11—22no—
94C2×C22⋊D11—22no—
95C2×C22⋊D11—41no—
96C2×C22⋊D11—41no—
97C2×C22⋊D11—41no—
98C2×C22⋊D11—41no—
99C2×C22⋊D11—41no—
100C2×C22⋊D11—41no—
101C2×C22⋊D11—81no—
102C2×C22⋊D11—81no—
103C22×Dic11—21no—
104C22×Dic11—21no—
105C22×Dic11—21no—
106C22×Dic11—21no—
107C2×D44—21no—
108C2×D44—21no—
109C2×D44—21no—
110C2×D44—81no—
111C2×D44—81no—
112C2×D44C22⋊C412yes—
113C2×C4×D11—81no—
114C2×C4×D11—81no—
115C2×C4×D11—81no—
116C11×M16—81no—
117C2×C8×C11—22no—
118C11×C22⋊C4—22no—
119C11×C22⋊C4—41no—
120C11×C22⋊C4—81no—
121C42×C11—81no—
122C22⋊Dic11—41no—
123C22⋊Dic11—41no—
124(C2×D11)⋊C4—22no—
125(C2×D11)⋊C4—22no—
126(C2×D11)⋊C4—41no—
127(C2×D11)⋊C4—41no—
128(C2×D11)⋊C4—81no—
129(C2×D11)⋊C4—81no—
130(C2×D11)⋊C4—81no—
131C4⋊Dic11—21no—
132C4⋊Dic11—21no—
133C4⋊Dic11—21no—
134C4⋊Dic11—81no—
135C4⋊Dic11C22⋊C412yes—
136Dic11⋊C4—81no—
137C4×Dic11—81no—
138#4318—81no—
139C2×C11⋊C8—41no—
140D88—82no—
141#3192—111no—
142#2377—111no—
143#1964—111no—
144#1510—111no—
145#1507—111no—
146#1305—111no—
147#1284D1111yescharacteristic, complemented
148C23×C11—21no—
149C23×C11—21no—
150C23×C11—41no—
151C23×C11—41no—
152C23×C11C4×D411yescharacteristic
153C23×C11#12011yescharacteristic
154C23×C11#12111yescharacteristic
155C22×D11—22no—
156C22×D11—41no—
157C22×D11—41no—
158C22×D11—41no—
159C22×D11—41no—
160C22×D11—41no—
161C22×D11—41no—
162C22×D11—41no—
163C22×D11—41no—
164C22×D11—41no—
165C22×D11—81no—
166C22×D11—81no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—42no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—81no—
181C2×C4×C11—81no—
182C2×C4×C11C2×C22⋊C411yescharacteristic
183C2×C4×C11C4×D411yescharacteristic
184C2×C4×C11#12111yescharacteristic
185C2×C4×C11#12311yescharacteristic
186C22⋊D11—82no—
187C22⋊D11—82no—
188C22⋊D11—81no—
189C22⋊D11—81no—
190C22⋊D11—81no—
191C22⋊D11—81no—
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—
204D44—42no—
205D44—42no—
206D44—81no—
207D44—81no—
208C4×D11—84no—
209C8×C11—42no—
210C11⋊C8—81no—
211C2×#121—111no—
212C2×#121—111no—
213#481—112no—
214#481—221no—
215#469—222no—
216#447—112no—
217#447—221no—
218C2×#99—221no—
219C2×#99—221no—
220#407—111no—
221#407C2×D1111yescharacteristic
222#390—221no—
223#388—221no—
224#387—221no—
225#386—221no—
226#386—221no—
227#385—221no—
228#381C2×D1111yescharacteristic
229#380—111no—
230C4×C22⋊C4C2×D1111yescharacteristic
231#327—222no—
232#327—221no—
233#327—221no—
234C22×C11—21no—
235C22×C11—21no—
236C22×C11—21no—
237C22×C11—21no—
238C22×C11—21no—
239C22×C11—21no—
240C22×C11—21no—
241C22×C11—21no—
242C22×C11—81no—
243C22×C11—81no—
244C22×C11#38611yescharacteristic
245C22×C11#45311yescharacteristic
246C22×C11#45411yescharacteristic
247C2×D11—42no—
248C2×D11—42no—
249C2×D11—42no—
250C2×D11—81no—
251C2×D11—81no—
252C2×D11—81no—
253C2×D11—81no—
254C2×D11—81no—
255C2×D11—81no—
256C2×D11—81no—
257C2×D11—161no—
258C2×D11—161no—
259C4×C11—21no—
260C4×C11—21no—
261C4×C11—21no—
262C4×C11—21no—
263C4×C11—81no—
264C4×C11—81no—
265C4×C11—82no—
266Dic11—42no—
267Dic11—81no—
268Dic11—81no—
269Dic11—81no—
270C22×D4—111no—
271C22×D4—111no—
272C22×D4—221no—
273C22×D4—221no—
274C23×C4—221no—
275C23×C4C22×D1111yescharacteristic
276C2×D8—222no—
277C2×M16—21no—
278C2×M16—221no—
279#121—112no—
280#121—112no—
281#121—221no—
282#121—221no—
283#121—221no—
284#121—221no—
285#121—221no—
286#121—221no—
287C2×C4⋊C4—111no—
288C2×C4⋊C4—111no—
289C2×C4⋊C4—221no—
290C2×C4⋊C4—221no—
291C2×C22⋊C4—21no—
292C2×C22⋊C4—21no—
293C2×C22⋊C4—111no—
294C2×C22⋊C4—111no—
295C2×C22⋊C4—221no—
296C2×C22⋊C4—221no—
297C2×C22⋊C4—221no—
298C2×C22⋊C4—221no—
299C2×C22⋊C4—221no—
300C2×C42—21no—
301C2×C42—221no—
302#106—222no—
303#102—222no—
304#102—222no—
305#99—442no—
306#99—442no—
307C22⋊C8—21no—
308C22⋊C8—221no—
309C22⋊C8—221no—
310C22⋊C8C4×D1112yescomplemented
311#95—21no—
312#95—21no—
313#95—221no—
314#95—221no—
315#95—221no—
316#95D4411yescharacteristic
317#95D4411yescharacteristic
318C2×C11—21no—
319C2×C11—21no—
320C2×C11—41no—
321C2×C11—41no—
322C2×C11#188311yescharacteristic
323C2×C11#190411yescharacteristic
324C2×C11#191311yescharacteristic
325D11—82no—
326D11—161no—
327C24—221no—
328C24—221no—
329C24D4×D1111yescharacteristic
330C2×D4—112no—
331C2×D4—222no—
332C2×D4—222no—
333C2×D4—221no—
334C2×D4—221no—
335C2×D4—221no—
336C2×D4—441no—
337C2×D4—441no—
338C2×D4—441no—
339C2×D4—441no—
340C2×D4—441no—
341C2×D4—441no—
342C2×D4—881no—
343C2×D4—881no—
344C2×D4—881no—
345C2×D4—881no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—41no—
349C22×C4—81no—
350C22×C4—221no—
351C22×C4—221no—
352C22×C4—221no—
353C22×C4—221no—
354C22×C4—881no—
355C22×C4—881no—
356C22×C4—881no—
357C22×C4C2×C4×D1111yescharacteristic
358C22×C4C2×D4411yescharacteristic
359C22×C4#433911yescharacteristic
360C22×C4D4×D1111yescharacteristic
361C22×C4D4×D1111yescharacteristic
362C22×C4#434311yescharacteristic
363D8—882no—
364M16—81no—
365M16—881no—
366C2×C8—22no—
367C2×C8—441no—
368C4⋊C4—112no—
369C4⋊C4—221no—
370C4⋊C4—221no—
371C4⋊C4—221no—
372C4⋊C4—881no—
373C4⋊C4—881no—
374C22⋊C4—22no—
375C22⋊C4—41no—
376C22⋊C4—81no—
377C22⋊C4—222no—
378C22⋊C4—222no—
379C22⋊C4—441no—
380C22⋊C4—441no—
381C22⋊C4—441no—
382C22⋊C4—441no—
383C22⋊C4—881no—
384C22⋊C4—881no—
385C22⋊C4—881no—
386C42—81no—
387C42—881no—
388C11#934311yescharacteristic, complemented, Sylow
389C23—21no—
390C23—21no—
391C23—41no—
392C23—41no—
393C23—222no—
394C23—441no—
395C23—441no—
396C23—441no—
397C23—441no—
398C23—441no—
399C23—441no—
400C23—441no—
401C23—441no—
402C23—441no—
403C23—881no—
404C23—881no—
405C23#6693511yescharacteristic
406C23#6693711yescharacteristic
407C23#6694611yescharacteristic
408D4—442no—
409D4—442no—
410D4—881no—
411D4—881no—
412D4—882no—
413D4—882no—
414D4—881no—
415D4—881no—
416D4—881no—
417D4—881no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—42no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—81no—
432C2×C4—81no—
433C2×C4—222no—
434C2×C4—441no—
435C2×C4—441no—
436C2×C4—441no—
437C2×C4—441no—
438C2×C4—441no—
439C2×C4—441no—
440C2×C4—441no—
441C2×C4—441no—
442C2×C4—441no—
443C2×C4—441no—
444C2×C4—441no—
445C2×C4—884no—
446C2×C4C4×D4411yescharacteristic
447C2×C4C22⋊C4×D1111yescharacteristic
448C2×C4#6694711yescharacteristic
449C2×C4#6694811yescharacteristic
450C8—42no—
451C8—881no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—81no—
461C22—81no—
462C22—442no—
463C22—442no—
464C22—442no—
465C22—881no—
466C22—881no—
467C22—881no—
468C22—881no—
469C22—881no—
470C22—881no—
471C22—881no—
472C22—1761no—
473C22—1761no—
474C22#1062227811yescharacteristic
475C22#1062243511yescharacteristic
476C22#1062244011yescharacteristic
477C4—21no—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—81no—
482C4—81no—
483C4—82no—
484C4—442no—
485C4—881no—
486C4—881no—
487C4—881no—
488C2—21no—
489C2—21no—
490C2—41no—
491C2—41no—
492C2—882no—
493C2—1761no—
494C2#1306899311yescharacteristic
495C2#1306910411yescharacteristic
496C2#1306915711yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1284C2
socleC22×C11#386
prime radical#13079416C2
cosocleC23×C4×C11C23
hypercenter#1284D11
hypocenterC11#9343
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1284

Complements

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

NH ≅ G/Ntype
2. #13071775C2semidirect
3. #13069452C2semidirect
4. #13067144C2semidirect
5. #13067131C2semidirect
6. #13066523C2semidirect
7. C11×#1284C2semidirect
21. #10622348C4semidirect
23. #10622345C4semidirect
34. C22×D44C2×C4semidirect
57. C2×C4⋊Dic11C2×C4semidirect
64. C11×C22⋊C8C2×C4semidirect
147. #1284D11semidirect
310. C22⋊C8C4×D11semidirect
388. C11#9343semidirect

Maximal subgroups

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

subgroupindex
#130794162
#130717752
#130694522
#130671442
#130671312
#130665232
C11×#12842
#934311