Finite Group Databasebeta

← #14658165

Subgroups — #14658165

Order 2816.

532 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 99 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#13079373C211yesmaximal, characteristic
2#13069601C211yesmaximal, characteristic, complemented
3#13069045C211yesmaximal, characteristic
4#13069037C211yesmaximal, characteristic, complemented
5#13068796C211yesmaximal, characteristic, complemented
6#13066483C211yesmaximal, characteristic, complemented
7C11×#1964C211yesmaximal, characteristic
8C2×C11×#121C2211yescharacteristic
9C2×#66977C2211yescharacteristic
10C23×C11⋊C8C2211yescharacteristic
11C2×C11×#99—21no—
12C2×C11×#99—21no—
13C11×#380C2211yescharacteristic
14C4×C11×C22⋊C4C2211yescharacteristic
15#10622831—21no—
16C2×#66896—21no—
17#10622825C2211yescharacteristic
18C2×C22⋊(C11⋊C8)C2211yescharacteristic
19#10622654—21no—
20#10622654—21no—
21#10622653—21no—
22#10622647—21no—
23#10622584—21no—
24C2×#66874—21no—
25C2×C4⋊(C11⋊C8)—21no—
26#10622167—21no—
27#10622167—21no—
28#10622165—21no—
29#10622165—21no—
30#10622162—21no—
31C22×D4×C11—21no—
32C22×D4×C11D411yescharacteristic
33C23×C4×C11C2311yescharacteristic
34C22×Dic22D411yescharacteristic
35C11×#121—21no—
36C11×#121—21no—
37C11×#121—21no—
38C11×#121—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4D411yescharacteristic
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4D411yescharacteristic
44C2×C11×C22⋊C4D411yescharacteristic
45C2×C42×C11—21no—
46C2×C22⋊Dic11—21no—
47C2×C22⋊Dic11—21no—
48C2×#4324—21no—
49C2×#4324—21no—
50C2×C4⋊Dic11—21no—
51C2×C4⋊Dic11D411yescharacteristic
52#66977—21no—
53#66977—21no—
54#66977—21no—
55#66977—21no—
56C2×Dic11⋊C4—21no—
57C22×C11⋊C8—21no—
58C22×C11⋊C8—21no—
59C22×C11⋊C8—21no—
60C22×C11⋊C8—42no—
61C22×C11⋊C8D411yescharacteristic
62C22×C11⋊C8D411yescharacteristic
63C11×#99—42no—
64C11×#99—42no—
65C11×#95—21no—
66C11×#95—21no—
67#66896—21no—
68#66896—21no—
69#66896—42no—
70C11⋊#95—21no—
71C22⋊(C11⋊C8)—21no—
72C22⋊(C11⋊C8)—21no—
73#66874—21no—
74#66874—21no—
75#66874—42no—
76#66872—21no—
77#66872—21no—
78C4⋊(C11⋊C8)—42no—
79#10565—111nomaximal, Sylow
80C24×C11—21no—
81C24×C11C2×D411yescharacteristic
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—41no—
85C2×D4×C11—41no—
86C2×D4×C11—41no—
87C2×D4×C11—41no—
88C2×D4×C11—41no—
89C2×D4×C11—41no—
90C2×D4×C11—41no—
91C2×D4×C11—41no—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—41no—
96C22×C4×C11—41no—
97C22×C4×C11—41no—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11#4111yescharacteristic
102C22×C4×C11#4111yescharacteristic
103C22×C4×C11#4111yescharacteristic
104C22×Dic11—21no—
105C22×Dic11—21no—
106C22×Dic11—41no—
107C2×Dic22—21no—
108C2×Dic22—21no—
109C2×Dic22—41no—
110C2×Dic22—41no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C11×C22⋊C4—21no—
116C11×C22⋊C4—21no—
117C11×C22⋊C4—21no—
118C11×C22⋊C4—41no—
119C11×C22⋊C4—41no—
120C11×C22⋊C4—41no—
121C11×C22⋊C4—41no—
122C11×C22⋊C4SD1612yescomplemented
123C42×C11—41no—
124C42×C11—41no—
125C22⋊Dic11—41no—
126C22⋊Dic11—41no—
127C22⋊Dic11—41no—
128C22⋊Dic11—41no—
129#4324—81no—
130#4324—81no—
131C4⋊Dic11—21no—
132C4⋊Dic11—21no—
133C4⋊Dic11—41no—
134C4⋊Dic11—41no—
135Dic11⋊C4—41no—
136Dic11⋊C4—41no—
137C2×C11⋊C8—22no—
138C2×C11⋊C8—22no—
139C2×C11⋊C8—22no—
140C2×C11⋊C8—21no—
141C2×C11⋊C8—21no—
142C2×C11⋊C8—41no—
143C2×C11⋊C8—41no—
144C2×C11⋊C8—41no—
145C2×C11⋊C8—41no—
146C2×C11⋊C8—41no—
147C2×C11⋊C8—41no—
148#3187—111no—
149#1996—111no—
150#1964D1111yescharacteristic
151#1893—111no—
152#1892—111no—
153#1850—111no—
154#1289—111no—
155C23×C11—41no—
156C23×C11—41no—
157C23×C11—41no—
158C23×C11—41no—
159C23×C11—41no—
160C23×C11—81no—
161C23×C11—81no—
162C23×C11#12111yescharacteristic
163C23×C11#12111yescharacteristic
164C23×C11#12111yescharacteristic
165C23×C11C2×SD1611yescharacteristic
166C23×C11#13511yescharacteristic
167C23×C11AGL(1,ℤ/8)11yescharacteristic
168C23×C11#13711yescharacteristic
169D4×C11—42no—
170D4×C11—41no—
171D4×C11—41no—
172D4×C11—81no—
173D4×C11—81no—
174D4×C11—81no—
175D4×C11—81no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—22no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—81no—
195C2×C4×C11—81no—
196C2×C4×C11—81no—
197C2×C4×C11#12011yescharacteristic
198C2×C4×C11#12311yescharacteristic
199C2×C4×C11#12311yescharacteristic
200C2×C4×C11#12411yescharacteristic
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—81no—
204C2×Dic11—81no—
205C2×Dic11—81no—
206C2×Dic11—81no—
207C2×Dic11—81no—
208Dic22—42no—
209Dic22—41no—
210Dic22—41no—
211C11⋊C8—42no—
212C11⋊C8—41no—
213C11⋊C8—41no—
214C23×C8—111no—
215C2×C22⋊Q8—111no—
216C2×#121C2×D1111yescharacteristic
217#483—221no—
218#481—221no—
219#465—221no—
220#465—221no—
221#450—221no—
222#448—221no—
223C2×C4⋊C8—221no—
224C2×#103—221no—
225C2×#102—221no—
226C2×#99—21no—
227C2×#99—21no—
228C2×C22⋊C8—111no—
229#380—111no—
230#380C2×D1111yescharacteristic
231C4×C22⋊C4C2×D1111yescharacteristic
232#342—221no—
233#342—221no—
234#340—221no—
235#340—221no—
236#336—221no—
237C22×C11—21no—
238C22×C11—21no—
239C22×C11—21no—
240C22×C11—21no—
241C22×C11—21no—
242C22×C11—21no—
243C22×C11—41no—
244C22×C11—41no—
245C22×C11—41no—
246C22×C11—41no—
247C22×C11—81no—
248C22×C11—81no—
249C22×C11—81no—
250C22×C11—161no—
251C22×C11—161no—
252C22×C11#39411yescharacteristic
253C22×C11#46011yescharacteristic
254C22×C11#46111yescharacteristic
255C22×C11#46311yescharacteristic
256C22×C11#46411yescharacteristic
257C22×C11#46511yescharacteristic
258C22×C11#46811yescharacteristic
259C4×C11—21no—
260C4×C11—21no—
261C4×C11—21no—
262C4×C11—42no—
263C4×C11—81no—
264C4×C11—81no—
265C4×C11—161no—
266C4×C11B(4,𝔽2)11yescharacteristic
267C4×C11#45811yescharacteristic
268Dic11—81no—
269Dic11—81no—
270Dic11—161no—
271C22×Q8—111no—
272C22×D4—21no—
273C22×D4D4411yescharacteristic
274C23×C4C22×D1111yescharacteristic
275C2×SD16—221no—
276C2×SD16—221no—
277C22×C8—111no—
278C22×C8—111no—
279C22×C8—221no—
280C22×C8—221no—
281C22×C8—221no—
282C22×C8—442no—
283C22⋊Q8—221no—
284C22⋊Q8—221no—
285C22⋊Q8—221no—
286C22⋊Q8—221no—
287#121—21no—
288#121—21no—
289#121—21no—
290#121—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—111no—
293C2×C4⋊C4—221no—
294C2×C4⋊C4—221no—
295C2×C4⋊C4D4411yescharacteristic
296C2×C22⋊C4—21no—
297C2×C22⋊C4—21no—
298C2×C22⋊C4—221no—
299C2×C22⋊C4—221no—
300C2×C22⋊C4C22⋊D1111yescharacteristic
301C2×C22⋊C4C22⋊D1111yescharacteristic
302C2×C42—21no—
303#106—221no—
304#106—221no—
305C4⋊C8—442no—
306#103—221no—
307#103—221no—
308#103—442no—
309#102—221no—
310#102—221no—
311#102—442no—
312#99—42no—
313#99—42no—
314C22⋊C8—221no—
315C22⋊C8—221no—
316#95—21no—
317#95—21no—
318#95—221no—
319C2×C11—21no—
320C2×C11—21no—
321C2×C11—21no—
322C2×C11—21no—
323C2×C11—21no—
324C2×C11—21no—
325C2×C11—161no—
326C2×C11#204411yescharacteristic
327C2×C11#205311yescharacteristic
328C2×C11#205511yescharacteristic
329C24—21no—
330C24C2×C22⋊D1111yescharacteristic
331C2×Q8—221no—
332C2×Q8—221no—
333C2×Q8—441no—
334C2×Q8—441no—
335C2×D4—21no—
336C2×D4—21no—
337C2×D4—41no—
338C2×D4—41no—
339C2×D4—41no—
340C2×D4—41no—
341C2×D4—41no—
342C2×D4—41no—
343C2×D4—41no—
344C2×D4—41no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—41no—
349C22×C4—41no—
350C22×C4—41no—
351C22×C4—221no—
352C22×C4—221no—
353C22×C4—441no—
354C22×C4C2×D4411yescharacteristic
355C22×C4#433911yescharacteristic
356C22×C4D4×D1111yescharacteristic
357C22×C4D4×D1111yescharacteristic
358C22×C4#434111yescharacteristic
359C22×C4#434111yescharacteristic
360SD16—881no—
361SD16—881no—
362C2×C8—222no—
363C2×C8—222no—
364C2×C8—222no—
365C2×C8—221no—
366C2×C8—221no—
367C2×C8—441no—
368C2×C8—441no—
369C2×C8—441no—
370C2×C8—441no—
371C2×C8—441no—
372C2×C8—441no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—41no—
376C4⋊C4—41no—
377C4⋊C4—221no—
378C4⋊C4—221no—
379C4⋊C4—441no—
380C4⋊C4—441no—
381C4⋊C4—441no—
382C4⋊C4—441no—
383C22⋊C4—21no—
384C22⋊C4—21no—
385C22⋊C4—21no—
386C22⋊C4—41no—
387C22⋊C4—41no—
388C22⋊C4—41no—
389C22⋊C4—41no—
390C22⋊C4—441no—
391C22⋊C4—441no—
392C22⋊C4—441no—
393C22⋊C4—441no—
394C22⋊C4#432412yescomplemented
395C42—41no—
396C42—41no—
397C11#1056511yescharacteristic, complemented, Sylow
398C23—41no—
399C23—41no—
400C23—41no—
401C23—41no—
402C23—41no—
403C23—81no—
404C23—81no—
405C23#6698311yescharacteristic
406C23#6698511yescharacteristic
407C23C2×#432411yescharacteristic
408C23#6699111yescharacteristic
409C23#6699211yescharacteristic
410C23#6700311yescharacteristic
411C23#6700411yescharacteristic
412Q8—442no—
413Q8—441no—
414Q8—441no—
415D4—42no—
416D4—41no—
417D4—41no—
418D4—81no—
419D4—81no—
420D4—81no—
421D4—81no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—22no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—81no—
441C2×C4—81no—
442C2×C4—81no—
443C2×C4—441no—
444C2×C4—441no—
445C2×C4—881no—
446C2×C4—881no—
447C2×C4—881no—
448C2×C4—881no—
449C2×C4—881no—
450C2×C4#6693511yescharacteristic
451C2×C4#6693611yescharacteristic
452C2×C4#6693811yescharacteristic
453C2×C4#6693911yescharacteristic
454C8—442no—
455C8—441no—
456C8—441no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—81no—
468C22—81no—
469C22—81no—
470C22—161no—
471C22—161no—
472C22#1062257411yescharacteristic
473C22#1062262911yescharacteristic
474C22#1062263211yescharacteristic
475C22#1062265411yescharacteristic
476C22#1062265511yescharacteristic
477C22#1062266711yescharacteristic
478C22#1062268811yescharacteristic
479C4—21no—
480C4—21no—
481C4—21no—
482C4—42no—
483C4—81no—
484C4—81no—
485C4—161no—
486C4—881no—
487C4—881no—
488C4—1761no—
489C4#1062235411yescharacteristic
490C4#1062235511yescharacteristic
491C2—21no—
492C2—21no—
493C2—21no—
494C2—21no—
495C2—21no—
496C2—21no—
497C2—161no—
498C2#1306986611yescharacteristic
499C2#1306992111yescharacteristic
500C2#1306993311yescharacteristic
subgroupG/H
centerC22#10622574
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1964C2
socleC22×C11#394
prime radicalC2×C11×#121C22
hypercenter#1964D11
hypocenterC11#10565
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1964

Complements

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

NH ≅ G/Ntype
2. #13069601C2semidirect
4. #13069037C2semidirect
5. #13068796C2semidirect
6. #13066483C2semidirect
122. C11×C22⋊C4SD16semidirect
394. C22⋊C4#4324semidirect
397. C11#10565semidirect

Maximal subgroups

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

subgroupindex
#130793732
#130696012
#130690452
#130690372
#130687962
#130664832
C11×#19642
#1056511