Finite Group Databasebeta

← #14654323

Subgroups — #14654323

Order 2816.

830 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 830 conjugacy classes of subgroups — too many to draw. Only its 111 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
1C2×#10622841C211yesmaximal, characteristic, complemented
2C2×#10622840C211yesmaximal, characteristic
3#13074544C211yesmaximal, characteristic
4C2×#10622090C211yesmaximal, characteristic, complemented
5C2×#10622089C211yesmaximal, characteristic
6#13066459C211yesmaximal, characteristic, complemented
7C11×#1446C211yesmaximal, characteristic, complemented
8C23×Q8×C11C2211yescharacteristic
9C22×#4326—21no—
10C22×#4325—21no—
11C2×#66983C2211yescharacteristic
12C2×#66977C2211yescharacteristic
13C2×C11×#95—22no—
14C2×C11×#95C2211yescharacteristic
15C2×C11×#95C2211yescharacteristic
16#10622841—22no—
17#10622841—22no—
18#10622840—22no—
19#10622840—22no—
20C2×#66899—21no—
21C2×#66899—21no—
22#10622826—22no—
23C2×C22⋊(C11⋊C8)C2211yescharacteristic
24C2×C22⋊(C11⋊C8)C2211yescharacteristic
25#10622287—21no—
26#10622286—21no—
27#10622285—21no—
28#10622272—21no—
29#10622090—22no—
30#10622089—22no—
31C22×Q8×C11—21no—
32C22×Q8×C11—21no—
33C22×Q8×C11—21no—
34C22×Q8×C11—21no—
35C22×Q8×C11—21no—
36C22×Q8×C11—44no—
37C22×Q8×C11D412yes—
38C23×C4×C11—21no—
39C23×C4×C11—21no—
40C23×C4×C11D412yes—
41C23×C4×C11C2311yescharacteristic
42C22×C22⋊D11—21no—
43C22×D44D411yescharacteristic
44C22×Dic22D411yescharacteristic
45C2×C22⋊Dic11—21no—
46C2×#4326—24no—
47C2×#4326—44no—
48C2×#4325—24no—
49C2×#4325—44no—
50#66983—21no—
51#66983—21no—
52#66983—21no—
53#66983—21no—
54C2×(C2×D11)⋊C4—21no—
55C2×(C2×D11)⋊C4—22no—
56C2×(C2×D11)⋊C4—22no—
57C2×C4⋊Dic11D411yescharacteristic
58C2×C4⋊Dic11D411yescharacteristic
59#66977—21no—
60#66977—21no—
61#66977—21no—
62#66977—21no—
63C2×Dic11⋊C4—21no—
64C22×C11⋊C8—21no—
65C22×C11⋊C8—21no—
66C11×#95—21no—
67C11×#95—21no—
68C11×#95—21no—
69C11×#95—21no—
70C11×#95—44no—
71#66899—24no—
72#66899—24no—
73C11⋊#95—22no—
74C11⋊#95—22no—
75C22⋊(C11⋊C8)—21no—
76C22⋊(C11⋊C8)—21no—
77C22⋊(C11⋊C8)D412yes—
78C22⋊(C11⋊C8)D412yes—
79#9965—111nomaximal, Sylow
80C24×C11C2×D411yescharacteristic
81C23×D11—21no—
82C2×Q8×C11—24no—
83C2×Q8×C11—24no—
84C2×Q8×C11—22no—
85C2×Q8×C11—22no—
86C2×Q8×C11—44no—
87C2×Q8×C11—42no—
88C2×Q8×C11—42no—
89C2×Q8×C11—44no—
90C2×Q8×C11—44no—
91C2×Q8×C11—44no—
92C2×Q8×C11—41no—
93C2×Q8×C11—41no—
94C22×C4×C11—24no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—42no—
101C22×C4×C11—42no—
102C22×C4×C11—41no—
103C22×C4×C11—41no—
104C22×C4×C11—42no—
105C22×C4×C11—42no—
106C22×C4×C11—42no—
107C22×C4×C11—41no—
108C22×C4×C11—41no—
109C22×C4×C11—42no—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11#4111yescharacteristic
116C2×C22⋊D11—41no—
117C2×C22⋊D11—41no—
118C2×C22⋊D11—42no—
119C2×C22⋊D11—42no—
120C22×Dic11—21no—
121C22×Dic11—21no—
122C22×Dic11—21no—
123C2×D44—21no—
124C2×D44—21no—
125C2×D44—42no—
126C2×Dic22—21no—
127C2×Dic22—21no—
128C2×Dic22—42no—
129C22⋊Dic11—41no—
130C22⋊Dic11—41no—
131#4326—48no—
132#4325—48no—
133(C2×D11)⋊C4—41no—
134(C2×D11)⋊C4—41no—
135(C2×D11)⋊C4—82no—
136(C2×D11)⋊C4—82no—
137C4⋊Dic11—21no—
138C4⋊Dic11—21no—
139C4⋊Dic11—21no—
140C4⋊Dic11—21no—
141Dic11⋊C4—41no—
142Dic11⋊C4—41no—
143C2×C11⋊C8—22no—
144C2×C11⋊C8—22no—
145C2×C11⋊C8—42no—
146C2×C11⋊C8—42no—
147C2×#451—111no—
148C2×#448—111no—
149#2639—111no—
150C2×#328—111no—
151C2×#327—111no—
152#1446D1111yescharacteristic, complemented
153#1280—111no—
154C23×C11—21no—
155C23×C11—21no—
156C23×C11—22no—
157C23×C11#12011yescharacteristic
158C23×C11#12111yescharacteristic
159C23×C11#12711yescharacteristic
160C23×C11#13512yes—
161C23×C11#13712yes—
162C22×D11—41no—
163C22×D11—42no—
164C22×D11—41no—
165C22×D11—41no—
166C22×D11—42no—
167Q8×C11—24no—
168Q8×C11—24no—
169Q8×C11—42no—
170Q8×C11—42no—
171Q8×C11—44no—
172Q8×C11—44no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—24no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—42no—
181C2×C4×C11—44no—
182C2×C4×C11—42no—
183C2×C4×C11—44no—
184C2×C4×C11—44no—
185C2×C4×C11—42no—
186C2×C4×C11—44no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—82no—
191C2×C4×C11—81no—
192C2×C4×C11—81no—
193C2×C4×C11—82no—
194C2×C4×C11#12011yescharacteristic
195C2×C4×C11#12011yescharacteristic
196C2×C4×C11#12111yescharacteristic
197C2×C4×C11#12111yescharacteristic
198C22⋊D11—82no—
199C22⋊D11—81no—
200C22⋊D11—81no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—42no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—42no—
208D44—42no—
209D44—81no—
210Dic22—42no—
211Dic22—81no—
212C11⋊C8—42no—
213C11⋊C8—42no—
214C23×Q8C2×D1111yescharacteristic
215C22×Q16—221no—
216C22×SD16—221no—
217C2×C22⋊Q8—111no—
218C2×#121—111no—
219#451—222no—
220#451—222no—
221#448—222no—
222#448—222no—
223C2×#103—221no—
224C2×#103—221no—
225C2×C22⋊C8—111no—
226C2×C22⋊C8—111no—
227#400—221no—
228#397—221no—
229#394—221no—
230#393—221no—
231#386—222no—
232C2×#95—22no—
233C2×#95C2×D1111yescharacteristic
234C2×#95C2×D1111yescharacteristic
235#328—222no—
236#327—222no—
237C22×C11—22no—
238C22×C11—22no—
239C22×C11—22no—
240C22×C11—22no—
241C22×C11—21no—
242C22×C11—21no—
243C22×C11—21no—
244C22×C11—21no—
245C22×C11#39211yescharacteristic
246C22×C11#45212yes—
247C22×C11#45511yescharacteristic
248C22×C11#45611yescharacteristic
249C22×C11B(4,𝔽2)12yes—
250C22×C11#46412yes—
251C22×C11#49511yescharacteristic
252C22×C11#49711yescharacteristic
253C2×D11—82no—
254C2×D11—82no—
255C2×D11—81no—
256C2×D11—81no—
257C2×D11—81no—
258C4×C11—21no—
259C4×C11—21no—
260C4×C11—21no—
261C4×C11—21no—
262C4×C11—44no—
263C4×C11—82no—
264C4×C11—82no—
265Dic11—81no—
266Dic11—81no—
267Dic11—81no—
268C22×Q8—21no—
269C22×Q8—21no—
270C22×Q8—21no—
271C22×Q8—21no—
272C22×Q8—21no—
273C22×Q8—44no—
274C22×Q8—111no—
275C22×Q8D4412yes—
276C22×D4—111no—
277C22×D4—221no—
278C23×C4—21no—
279C23×C4—21no—
280C23×C4C22⋊D1112yes—
281C23×C4C22×D1111yescharacteristic
282C2×Q16—224no—
283C2×Q16—444no—
284C2×SD16—224no—
285C2×SD16—444no—
286C22×C8—221no—
287C22×C8—221no—
288C22⋊Q8—221no—
289C22⋊Q8—221no—
290C22⋊Q8—221no—
291C22⋊Q8—221no—
292#121—221no—
293#121—221no—
294#121—221no—
295#121—221no—
296C2×C4⋊C4—111no—
297C2×C4⋊C4—111no—
298C2×C4⋊C4—221no—
299C2×C22⋊C4—221no—
300C2×C22⋊C4—221no—
301C2×C22⋊C4—222no—
302C2×C22⋊C4—222no—
303#103—224no—
304#103—224no—
305C22⋊C8—112no—
306C22⋊C8—112no—
307C22⋊C8—221no—
308C22⋊C8—221no—
309#95—21no—
310#95—21no—
311#95—21no—
312#95—21no—
313#95—44no—
314#95—222no—
315#95—222no—
316C2×C11—21no—
317C2×C11—22no—
318C2×C11—21no—
319C2×C11#160312yes—
320C2×C11#160612yes—
321C2×C11#200711yescharacteristic
322C2×C11#201511yescharacteristic
323C2×C11#202111yescharacteristic
324D11—161no—
325C24—221no—
326C24C2×C22⋊D1111yescharacteristic
327C2×Q8—24no—
328C2×Q8—24no—
329C2×Q8—22no—
330C2×Q8—22no—
331C2×Q8—44no—
332C2×Q8—42no—
333C2×Q8—42no—
334C2×Q8—44no—
335C2×Q8—44no—
336C2×Q8—44no—
337C2×Q8—41no—
338C2×Q8—41no—
339C2×Q8—221no—
340C2×Q8—221no—
341C2×Q8—442no—
342C2×D4—221no—
343C2×D4—221no—
344C2×D4—442no—
345C2×D4—441no—
346C2×D4—441no—
347C2×D4—442no—
348C2×D4—442no—
349C22×C4—24no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—42no—
356C22×C4—42no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4—42no—
360C22×C4—42no—
361C22×C4—42no—
362C22×C4—41no—
363C22×C4—41no—
364C22×C4—42no—
365C22×C4—221no—
366C22×C4—221no—
367C22×C4—221no—
368C22×C4C2×D4411yescharacteristic
369C22×C4#433911yescharacteristic
370C22×C4D4×D1111yescharacteristic
371C22×C4D4×D1111yescharacteristic
372C22×C4D4×D1111yescharacteristic
373C22×C4D4×D1111yescharacteristic
374Q16—448no—
375SD16—448no—
376C2×C8—222no—
377C2×C8—222no—
378C2×C8—442no—
379C2×C8—442no—
380C4⋊C4—221no—
381C4⋊C4—221no—
382C4⋊C4—221no—
383C4⋊C4—221no—
384C4⋊C4—441no—
385C4⋊C4—441no—
386C22⋊C4—441no—
387C22⋊C4—441no—
388C22⋊C4—441no—
389C22⋊C4—441no—
390C22⋊C4—882no—
391C22⋊C4—882no—
392C11#996511yescharacteristic, complemented, Sylow
393C23—22no—
394C23—21no—
395C23—21no—
396C23—441no—
397C23—442no—
398C23—442no—
399C23—441no—
400C23—441no—
401C23#6698311yescharacteristic
402C23#6699011yescharacteristic
403C23#6699311yescharacteristic
404C23#6699512yes—
405C23#6700312yes—
406Q8—24no—
407Q8—24no—
408Q8—42no—
409Q8—42no—
410Q8—44no—
411Q8—44no—
412Q8—442no—
413Q8—881no—
414D4—442no—
415D4—881no—
416D4—882no—
417D4—881no—
418D4—881no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—24no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—42no—
427C2×C4—44no—
428C2×C4—42no—
429C2×C4—44no—
430C2×C4—44no—
431C2×C4—42no—
432C2×C4—44no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—82no—
437C2×C4—81no—
438C2×C4—81no—
439C2×C4—82no—
440C2×C4—441no—
441C2×C4—441no—
442C2×C4—441no—
443C2×C4—442no—
444C2×C4—442no—
445C2×C4—441no—
446C2×C4—441no—
447C2×C4#6693511yescharacteristic
448C2×C4#6693511yescharacteristic
449C2×C4#6693711yescharacteristic
450C2×C4#6693711yescharacteristic
451C8—442no—
452C8—442no—
453C22—22no—
454C22—22no—
455C22—22no—
456C22—22no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—882no—
462C22—882no—
463C22—881no—
464C22—881no—
465C22—881no—
466C22#1062257311yescharacteristic
467C22#1062264112yes—
468C22#1062264512yes—
469C22#1062266012yes—
470C22#1062267211yescharacteristic
471C22#1062267411yescharacteristic
472C22#1062269911yescharacteristic
473C22#1062270811yescharacteristic
474C4—21no—
475C4—21no—
476C4—21no—
477C4—21no—
478C4—44no—
479C4—82no—
480C4—82no—
481C4—881no—
482C4—881no—
483C4—881no—
484C2—21no—
485C2—22no—
486C2—21no—
487C2—1761no—
488C2#1306757712yes—
489C2#1306759412yes—
490C2#1306966211yescharacteristic
491C2#1306970911yescharacteristic
492C2#1306974211yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1446C2
socleC23×C11#120
prime radicalC2×#66983C22
hypercenter#1446D11
hypocenterC11#9965
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1446

Complements

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

NH ≅ G/Ntype
1. C2×#10622841C2semidirect
4. C2×#10622090C2semidirect
6. #13066459C2semidirect
7. C11×#1446C2semidirect
152. #1446D11semidirect
392. C11#9965semidirect

Maximal subgroups

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

subgroupindex
C2×#106228412
C2×#106228402
#130745442
C2×#106220902
C2×#106220892
#130664592
C11×#14462
#996511