Finite Group Databasebeta

← #14658167

Subgroups — #14658167

Order 2816.

532 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 95 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#13079374C211yesmaximal, characteristic
2#13069600C211yesmaximal, characteristic, complemented
3#13069451C211yesmaximal, characteristic
4#13069042C211yesmaximal, characteristic
5#13069037C211yesmaximal, characteristic, complemented
6#13068793C211yesmaximal, characteristic, complemented
7C11×#1289C211yesmaximal, characteristic, complemented
8C2×#66983C2211yescharacteristic
9C2×#66977C2211yescharacteristic
10C23×C11⋊C8C2211yescharacteristic
11C2×C11×C22⋊C8C2211yescharacteristic
12C11×#380C2211yescharacteristic
13C11×#380C2211yescharacteristic
14C4×C22⋊Dic11C2211yescharacteristic
15#10622727—21no—
16#10622727—21no—
17C2×Dic11⋊C8—21no—
18C2×#66874—21no—
19C2×#66873—21no—
20C2×#66870—21no—
21C2×#66870—21no—
22#10622351—21no—
23#10622348—21no—
24#10622344—21no—
25#10622334—21no—
26#10622188—21no—
27#10622167—21no—
28#10622167—21no—
29#10622165—21no—
30#10622165—21no—
31C23×C4×C11C2311yescharacteristic
32C22×C22⋊D11—21no—
33C22×D44D411yescharacteristic
34C22×Dic22D411yescharacteristic
35C22×C8×C11D411yescharacteristic
36C22×C8×C11D411yescharacteristic
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4—21no—
41C2×C22⋊Dic11—21no—
42C2×C22⋊Dic11D411yescharacteristic
43C2×C22⋊Dic11D411yescharacteristic
44#66983—21no—
45#66983—21no—
46#66983—21no—
47#66983—21no—
48C2×(C2×D11)⋊C4—21no—
49C2×C4⋊Dic11D411yescharacteristic
50C2×C4⋊Dic11D411yescharacteristic
51#66977—21no—
52#66977—21no—
53#66977—21no—
54#66977—21no—
55C2×Dic11⋊C4—21no—
56C2×C4×Dic11—21no—
57C22×C11⋊C8—21no—
58C22×C11⋊C8—21no—
59C22×C11⋊C8—21no—
60C22×C11⋊C8—42no—
61C2×#4314—21no—
62C2×#4314—21no—
63C11×C22⋊C8—21no—
64C11×C22⋊C8—21no—
65C11×#95—21no—
66C11×#95—21no—
67C11⋊#95—21no—
68#66885—21no—
69#66885—21no—
70#66881—21no—
71#66881—21no—
72#66880—21no—
73#66880—21no—
74Dic11⋊C8—42no—
75#66874—42no—
76#66873—42no—
77#66870—42no—
78#66870—42no—
79#10565—111nomaximal, Sylow
80C24×C11C2×D411yescharacteristic
81C23×D11—21no—
82C22×C4×C11—41no—
83C22×C4×C11—41no—
84C22×C4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11#4111yescharacteristic
90C22×C4×C11#4111yescharacteristic
91C22×C4×C11#4111yescharacteristic
92C2×C22⋊D11—41no—
93C2×C22⋊D11—41no—
94C2×C22⋊D11—41no—
95C2×C22⋊D11—41no—
96C2×C22⋊D11—41no—
97C2×C22⋊D11—41no—
98C22×Dic11—21no—
99C22×Dic11—21no—
100C22×Dic11—21no—
101C22×Dic11—21no—
102C22×Dic11—21no—
103C2×D44—21no—
104C2×D44—21no—
105C2×D44—41no—
106C2×D44—41no—
107C2×Dic22—21no—
108C2×Dic22—21no—
109C2×Dic22—41no—
110C2×Dic22—41no—
111C2×C8×C11—21no—
112C2×C8×C11—21no—
113C2×C8×C11—41no—
114C2×C8×C11—41no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—41no—
119C11×C22⋊C4—41no—
120C11×C22⋊C4—41no—
121C11×C22⋊C4—41no—
122C11×C22⋊C4—41no—
123C22⋊Dic11—21no—
124C22⋊Dic11—21no—
125C22⋊Dic11—21no—
126C22⋊Dic11—41no—
127C22⋊Dic11—41no—
128C22⋊Dic11SD1612yescomplemented
129(C2×D11)⋊C4—41no—
130(C2×D11)⋊C4—41no—
131C4⋊Dic11—21no—
132C4⋊Dic11—21no—
133C4⋊Dic11—21no—
134C4⋊Dic11—21no—
135Dic11⋊C4—41no—
136Dic11⋊C4—41no—
137C4×Dic11—41no—
138C4×Dic11—41no—
139C2×C11⋊C8—22no—
140C2×C11⋊C8—22no—
141C2×C11⋊C8—22no—
142C2×C11⋊C8—41no—
143C2×C11⋊C8—41no—
144C2×C11⋊C8—41no—
145C2×C11⋊C8—41no—
146#4314—81no—
147#4314—81no—
148#3187—111no—
149#1996—111no—
150#1964—111no—
151#1893—111no—
152#1892—111no—
153#1850—111no—
154#1289D1111yescharacteristic, complemented
155C23×C11—41no—
156C23×C11—41no—
157C23×C11#12111yescharacteristic
158C23×C11#12111yescharacteristic
159C23×C11#12111yescharacteristic
160C23×C11C2×SD1611yescharacteristic
161C23×C11#13511yescharacteristic
162C23×C11AGL(1,ℤ/8)11yescharacteristic
163C23×C11#13711yescharacteristic
164C22×D11—41no—
165C22×D11—41no—
166C22×D11—41no—
167C22×D11—81no—
168C22×D11—81no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—21no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—81no—
179C2×C4×C11—81no—
180C2×C4×C11—81no—
181C2×C4×C11—81no—
182C2×C4×C11—81no—
183C2×C4×C11—81no—
184C2×C4×C11#12011yescharacteristic
185C2×C4×C11#12311yescharacteristic
186C2×C4×C11#12311yescharacteristic
187C2×C4×C11#12411yescharacteristic
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—81no—
204C2×Dic11—81no—
205D44—42no—
206D44—41no—
207D44—41no—
208Dic22—42no—
209Dic22—41no—
210Dic22—41no—
211C8×C11—41no—
212C8×C11—41no—
213C11⋊C8—42no—
214C23×C8—111no—
215C2×C22⋊Q8—111no—
216C2×#121—111no—
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—221no—
227C2×#99—221no—
228C2×C22⋊C8C2×D1111yescharacteristic
229#380C2×D1111yescharacteristic
230#380C2×D1111yescharacteristic
231C4×C22⋊C4—111no—
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#39411yescharacteristic
248C22×C11#46011yescharacteristic
249C22×C11#46111yescharacteristic
250C22×C11#46311yescharacteristic
251C22×C11#46411yescharacteristic
252C22×C11#46511yescharacteristic
253C22×C11#46811yescharacteristic
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—161no—
263C4×C11—161no—
264C4×C11B(4,𝔽2)11yescharacteristic
265C4×C11#45811yescharacteristic
266Dic11—42no—
267Dic11—81no—
268Dic11—81no—
269Dic11—81no—
270Dic11—81no—
271C22×Q8—111no—
272C22×D4—111no—
273C22×D4—221no—
274C23×C4C22×D1111yescharacteristic
275C2×SD16—221no—
276C2×SD16—221no—
277C22×C8—221no—
278C22×C8—221no—
279C22×C8—221no—
280C22×C8—442no—
281C22×C8D4411yescharacteristic
282C22×C8D4411yescharacteristic
283C22⋊Q8—221no—
284C22⋊Q8—221no—
285C22⋊Q8—221no—
286C22⋊Q8—221no—
287#121—221no—
288#121—221no—
289#121—221no—
290#121—221no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—111no—
294C2×C4⋊C4—111no—
295C2×C4⋊C4—221no—
296C2×C22⋊C4—21no—
297C2×C22⋊C4—21no—
298C2×C22⋊C4—111no—
299C2×C22⋊C4—111no—
300C2×C22⋊C4—221no—
301C2×C22⋊C4—221no—
302C2×C42—221no—
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—442no—
313#99—442no—
314C22⋊C8—21no—
315C22⋊C8—21no—
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#204411yescharacteristic
326C2×C11#205311yescharacteristic
327C2×C11#205511yescharacteristic
328D11—161no—
329C24—221no—
330C24D4×D1111yescharacteristic
331C2×Q8—221no—
332C2×Q8—221no—
333C2×Q8—441no—
334C2×Q8—441no—
335C2×D4—221no—
336C2×D4—221no—
337C2×D4—441no—
338C2×D4—441no—
339C2×D4—441no—
340C2×D4—441no—
341C2×D4—441no—
342C2×D4—441no—
343C2×D4—441no—
344C2×D4—441no—
345C22×C4—41no—
346C22×C4—41no—
347C22×C4—41no—
348C22×C4—41no—
349C22×C4—221no—
350C22×C4—221no—
351C22×C4—221no—
352C22×C4—221no—
353C22×C4—221no—
354C22×C4C2×D4411yescharacteristic
355C22×C4#433911yescharacteristic
356C22×C4#433911yescharacteristic
357C22×C4D4×D1111yescharacteristic
358C22×C4D4×D1111yescharacteristic
359C22×C4#434311yescharacteristic
360SD16—881no—
361SD16—881no—
362C2×C8—21no—
363C2×C8—21no—
364C2×C8—41no—
365C2×C8—41no—
366C2×C8—222no—
367C2×C8—222no—
368C2×C8—222no—
369C2×C8—441no—
370C2×C8—441no—
371C2×C8—441no—
372C2×C8—441no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4—41no—
377C4⋊C4—221no—
378C4⋊C4—221no—
379C4⋊C4—221no—
380C4⋊C4—221no—
381C4⋊C4—441no—
382C4⋊C4—441no—
383C22⋊C4—41no—
384C22⋊C4—41no—
385C22⋊C4—41no—
386C22⋊C4—41no—
387C22⋊C4—112no—
388C22⋊C4—221no—
389C22⋊C4—221no—
390C22⋊C4—221no—
391C22⋊C4—441no—
392C22⋊C4—441no—
393C22⋊C4—441no—
394C22⋊C4—441no—
395C42—441no—
396C42—441no—
397C11#1056511yescharacteristic, complemented, Sylow
398C23—41no—
399C23—41no—
400C23—441no—
401C23—441no—
402C23—441no—
403C23—881no—
404C23—881no—
405C23#6693711yescharacteristic
406C23#6693711yescharacteristic
407C23#6694811yescharacteristic
408C23#6696411yescharacteristic
409C23SD16×D1111yescharacteristic
410C23#6696911yescharacteristic
411C23#6697111yescharacteristic
412Q8—442no—
413Q8—441no—
414Q8—441no—
415D4—442no—
416D4—441no—
417D4—441no—
418D4—881no—
419D4—881no—
420D4—881no—
421D4—881no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—81no—
432C2×C4—81no—
433C2×C4—81no—
434C2×C4—81no—
435C2×C4—81no—
436C2×C4—81no—
437C2×C4—222no—
438C2×C4—441no—
439C2×C4—441no—
440C2×C4—441no—
441C2×C4—441no—
442C2×C4—441no—
443C2×C4—441no—
444C2×C4—441no—
445C2×C4—441no—
446C2×C4—441no—
447C2×C4—441no—
448C2×C4—881no—
449C2×C4—881no—
450C2×C4#6692811yescharacteristic
451C2×C4#6693511yescharacteristic
452C2×C4#6694711yescharacteristic
453C2×C4#6694711yescharacteristic
454C8—41no—
455C8—41no—
456C8—442no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—881no—
468C22—881no—
469C22—881no—
470C22—1761no—
471C22—1761no—
472C22#1062228511yescharacteristic
473C22#1062237511yescharacteristic
474C22#1062240011yescharacteristic
475C22#1062241111yescharacteristic
476C22#1062243111yescharacteristic
477C22#1062247711yescharacteristic
478C22#1062249911yescharacteristic
479C4—21no—
480C4—21no—
481C4—21no—
482C4—161no—
483C4—161no—
484C4—442no—
485C4—881no—
486C4—881no—
487C4—881no—
488C4—881no—
489C4#1062235411yescharacteristic
490C4#1062235511yescharacteristic
491C2—21no—
492C2—21no—
493C2—21no—
494C2—21no—
495C2—21no—
496C2—21no—
497C2—1761no—
498C2#1306986811yescharacteristic
499C2#1306992311yescharacteristic
500C2#1306993511yescharacteristic
subgroupG/H
centerC22#10622285
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1289C2
socleC22×C11#394
prime radicalC2×#66983C22
hypercenter#1289D11
hypocenterC11#10565
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1289

Complements

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

NH ≅ G/Ntype
2. #13069600C2semidirect
5. #13069037C2semidirect
6. #13068793C2semidirect
7. C11×#1289C2semidirect
128. C22⋊Dic11SD16semidirect
154. #1289D11semidirect
397. C11#10565semidirect

Maximal subgroups

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

subgroupindex
#130793742
#130696002
#130694512
#130690422
#130690372
#130687932
C11×#12892
#1056511