Finite Group Databasebeta

← #14670540

Subgroups — #14670540

Order 2816.

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

normal subgroups only

This group has 608 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
1C2×#10622174C211yesmaximal, characteristic
2#13069025C211yesmaximal, characteristic
3#13068896C211yesmaximal, characteristic, complemented
4#13068825C211yesmaximal, characteristic, complemented
5#13066741C211yesmaximal, characteristic, complemented
6#13066734C211yesmaximal, characteristic, complemented
7C11×#2375C211yesmaximal, characteristic
8C2×C11×#120C2211yescharacteristic
9#10623329C2211yescharacteristic
10C11×#390—21no—
11C11×#390C2211yescharacteristic
12C11×#388—21no—
13C11×#388—21no—
14C11×#388—21no—
15C11×#386—21no—
16C11×#386C2211yescharacteristic
17C11×#379—21no—
18#10622860—21no—
19C2×#66898C2211yescharacteristic
20C2×#66898C2211yescharacteristic
21C2×#66897C2211yescharacteristic
22#10622823—21no—
23#10622577—21no—
24#10622174C414yescomplemented
25#10622165—21no—
26#10622165—21no—
27#10622161—21no—
28C25×C11D411yescharacteristic
29C22×D4×C11—21no—
30C22×D4×C11C2311yescharacteristic
31C23×C4×C11D411yescharacteristic
32C11×#120—21no—
33C11×#120—21no—
34C11×#120C2×C412yes—
35C11×#120Q812yes—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4D411yescharacteristic
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4—21no—
45C2×C11×C22⋊C4—21no—
46C2×C11×C22⋊C4D411yescharacteristic
47C2×C11×C22⋊C4D411yescharacteristic
48C2×C42×C11—21no—
49C2×C42×C11D411yescharacteristic
50C2×C22⋊Dic11—21no—
51C2×C22⋊Dic11—21no—
52C2×C22⋊Dic11—21no—
53C2×C22⋊Dic11—21no—
54C2×C22⋊Dic11—41no—
55C2×C22⋊Dic11—41no—
56D4×Dic11—41no—
57D4×Dic11—41no—
58#66979—21no—
59C2×Dic11⋊C4—41no—
60C2×#4318—21no—
61C11×#95—21no—
62C11×#95—21no—
63C11×#95—21no—
64#66898—21no—
65#66898—21no—
66#66898—21no—
67#66898C2×C412yes—
68#66897—21no—
69#66897C2×C412yes—
70C11⋊#95—41no—
71#66872—41no—
72#66871—41no—
73#12960—111nomaximal, Sylow
74C24×C11—21no—
75C24×C11—21no—
76C24×C11—41no—
77C24×C11—41no—
78C24×C11—81no—
79C24×C11—81no—
80C24×C11C4⋊C412yescomplemented
81C24×C11C2×D411yescharacteristic
82C24×C11C2×D411yescharacteristic
83C2×D4×C11—22no—
84C2×D4×C11—22no—
85C2×D4×C11—41no—
86C2×D4×C11—41no—
87C2×D4×C11—81no—
88C2×D4×C11—81no—
89C2×D4×C11C22×C411yescharacteristic
90C2×D4×C11C2×Q811yescharacteristic
91C2×D4×C11#4111yescharacteristic
92C2×D4×C11#4111yescharacteristic
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—41no—
99C22×C4×C11—81no—
100C22×C4×C11C2×D411yescharacteristic
101C22×Dic11—21no—
102C22×Dic11—21no—
103C22×Dic11—21no—
104C22×Dic11—21no—
105C22×Dic11—41no—
106C22×Dic11—41no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—81no—
109C11×C22⋊C4—21no—
110C11×C22⋊C4—22no—
111C11×C22⋊C4—22no—
112C11×C22⋊C4—41no—
113C11×C22⋊C4—81no—
114C11×C22⋊C4—81no—
115C11×C22⋊C4—81no—
116C11×C22⋊C4—81no—
117C11×C22⋊C4—81no—
118C11×C22⋊C4—81no—
119C11×C22⋊C4—81no—
120C11×C22⋊C4C4⋊C412yescomplemented
121C42×C11—41no—
122C42×C11—81no—
123C22⋊Dic11—22no—
124C22⋊Dic11—41no—
125C22⋊Dic11—41no—
126C22⋊Dic11—41no—
127C22⋊Dic11—41no—
128C22⋊Dic11—41no—
129C22⋊Dic11—41no—
130C22⋊Dic11—82no—
131C22⋊Dic11—82no—
132C4⋊Dic11—21no—
133C4⋊Dic11—21no—
134Dic11⋊C4—82no—
135C4×Dic11—41no—
136#4318—22no—
137#4318—41no—
138C2×C11⋊C8—41no—
139#2375D1111yescharacteristic
140C2×AΣL(1,𝔽16)—111no—
141#1889—111no—
142#1867—111no—
143#1856—111no—
144#1393—111no—
145#1390—111no—
146C23×C11—21no—
147C23×C11—21no—
148C23×C11—21no—
149C23×C11—21no—
150C23×C11—22no—
151C23×C11—41no—
152C23×C11—41no—
153C23×C11—41no—
154C23×C11—41no—
155C23×C11—42no—
156C23×C11—41no—
157C23×C11—41no—
158C23×C11—41no—
159C23×C11—41no—
160C23×C11—42no—
161C23×C11—42no—
162C23×C11—41no—
163C23×C11—41no—
164C23×C11—81no—
165C23×C11—82no—
166C23×C11—82no—
167C23×C11—81no—
168C23×C11—81no—
169C23×C11—84no—
170C23×C11C2×C4⋊C411yescharacteristic
171C23×C11C4×D411yescharacteristic
172C23×C11#12011yescharacteristic
173C23×C11C22⋊Q811yescharacteristic
174C23×C11#12311yescharacteristic
175D4×C11—41no—
176D4×C11—41no—
177D4×C11—41no—
178D4×C11—41no—
179D4×C11—82no—
180D4×C11—82no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—22no—
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—42no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—81no—
200C2×C4×C11C4×D411yescharacteristic
201C2×C4×C11C22⋊Q811yescharacteristic
202C2×Dic11—42no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—81no—
206C2×Dic11—81no—
207C2×Dic11—81no—
208C2×Dic11—81no—
209C2×Dic11—81no—
210C2×Dic11—81no—
211C2×Dic11—81no—
212C2×Dic11—81no—
213C2×Dic11—81no—
214C11⋊C8—42no—
215C2×#120C2×D1111yescharacteristic
216#518—111no—
217#428—221no—
218C2×#100—111no—
219C2×#99—111no—
220C2×#99—111no—
221#390—21no—
222#390C2×D1111yescharacteristic
223#388—21no—
224#388—21no—
225#388—21no—
226#386—21no—
227#386C2×D1111yescharacteristic
228#385—221no—
229#379—21no—
230#379—221no—
231AΣL(1,𝔽16)—114no—
232#342—221no—
233#342—221no—
234#339—221no—
235C22×C11—21no—
236C22×C11—21no—
237C22×C11—21no—
238C22×C11—21no—
239C22×C11—21no—
240C22×C11—21no—
241C22×C11—41no—
242C22×C11—41no—
243C22×C11—41no—
244C22×C11—41no—
245C22×C11—42no—
246C22×C11—42no—
247C22×C11—41no—
248C22×C11—41no—
249C22×C11—41no—
250C22×C11—41no—
251C22×C11—44no—
252C22×C11—42no—
253C22×C11—81no—
254C22×C11—81no—
255C22×C11—81no—
256C22×C11—81no—
257C22×C11—82no—
258C22×C11—82no—
259C22×C11—82no—
260C22×C11—81no—
261C22×C11—81no—
262C22×C11#38511yescharacteristic
263C22×C11B(4,𝔽2)11yescharacteristic
264C22×C11#45811yescharacteristic
265C4×C11—21no—
266C4×C11—21no—
267C4×C11—42no—
268C4×C11—81no—
269C4×C11—81no—
270C4×C11—81no—
271C4×C11—81no—
272Dic11—82no—
273Dic11—81no—
274Dic11—81no—
275Dic11—161no—
276C25C22⋊D1111yescharacteristic
277C22×D4—21no—
278C22×D4C22×D1111yescharacteristic
279C23×C4C22⋊D1111yescharacteristic
280C2×M16—221no—
281#120—21no—
282#120—21no—
283#120Dic2212yes—
284#120C4×D1112yes—
285C4×D4—441no—
286C4×D4—441no—
287#117—221no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—441no—
290C2×C4⋊C4C22⋊D1111yescharacteristic
291C2×C22⋊C4—21no—
292C2×C22⋊C4—21no—
293C2×C22⋊C4—21no—
294C2×C22⋊C4—21no—
295C2×C22⋊C4—21no—
296C2×C22⋊C4—21no—
297C2×C22⋊C4—21no—
298C2×C22⋊C4—21no—
299C2×C22⋊C4—221no—
300C2×C22⋊C4—221no—
301C2×C22⋊C4—221no—
302C2×C22⋊C4—221no—
303C2×C22⋊C4—441no—
304C2×C22⋊C4—441no—
305C2×C22⋊C4C22⋊D1111yescharacteristic
306C2×C22⋊C4C22⋊D1111yescharacteristic
307C2×C42—21no—
308C2×C42C22⋊D1111yescharacteristic
309#107—441no—
310#106—441no—
311#100—112no—
312#100—221no—
313#99—112no—
314#99—221no—
315#99—221no—
316#99—221no—
317#95—21no—
318#95—21no—
319#95—21no—
320#95—441no—
321C2×C11—21no—
322C2×C11—21no—
323C2×C11—41no—
324C2×C11—41no—
325C2×C11—41no—
326C2×C11—41no—
327C2×C11—82no—
328C2×C11#186711yescharacteristic
329C2×C11#219911yescharacteristic
330C2×C11#220011yescharacteristic
331C24—21no—
332C24—21no—
333C24—41no—
334C24—41no—
335C24—81no—
336C24—81no—
337C24Dic11⋊C412yescomplemented
338C24C2×C22⋊D1111yescharacteristic
339C24C2×C22⋊D1111yescharacteristic
340C2×D4—22no—
341C2×D4—22no—
342C2×D4—41no—
343C2×D4—41no—
344C2×D4—81no—
345C2×D4—81no—
346C2×D4C2×Dic2211yescharacteristic
347C2×D4C2×C4×D1111yescharacteristic
348C2×D4#433911yescharacteristic
349C2×D4#433911yescharacteristic
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—41no—
356C22×C4—81no—
357C22×C4—221no—
358C22×C4—221no—
359C22×C4—221no—
360C22×C4—221no—
361C22×C4—441no—
362C22×C4—441no—
363C22×C4C2×C22⋊D1111yescharacteristic
364M16—222no—
365M16—441no—
366C2×C8—441no—
367C4⋊C4—41no—
368C4⋊C4—81no—
369C4⋊C4—221no—
370C4⋊C4—221no—
371C4⋊C4—882no—
372C22⋊C4—21no—
373C22⋊C4—22no—
374C22⋊C4—22no—
375C22⋊C4—41no—
376C22⋊C4—81no—
377C22⋊C4—81no—
378C22⋊C4—81no—
379C22⋊C4—81no—
380C22⋊C4—81no—
381C22⋊C4—81no—
382C22⋊C4—81no—
383C22⋊C4—222no—
384C22⋊C4—441no—
385C22⋊C4—441no—
386C22⋊C4—441no—
387C22⋊C4—441no—
388C22⋊C4—441no—
389C22⋊C4—441no—
390C22⋊C4—882no—
391C22⋊C4—882no—
392C22⋊C4Dic11⋊C412yescomplemented
393C42—41no—
394C42—81no—
395C42—441no—
396C11#1296011yescharacteristic, complemented, Sylow
397C23—21no—
398C23—21no—
399C23—21no—
400C23—21no—
401C23—22no—
402C23—41no—
403C23—41no—
404C23—41no—
405C23—41no—
406C23—42no—
407C23—41no—
408C23—41no—
409C23—41no—
410C23—41no—
411C23—42no—
412C23—42no—
413C23—41no—
414C23—41no—
415C23—81no—
416C23—82no—
417C23—82no—
418C23—81no—
419C23—81no—
420C23—84no—
421C23C2×Dic11⋊C411yescharacteristic
422C23#6697711yescharacteristic
423C23C4×C22⋊D1111yescharacteristic
424C23#6698211yescharacteristic
425C23#6700611yescharacteristic
426D4—41no—
427D4—41no—
428D4—41no—
429D4—41no—
430D4—82no—
431D4—82no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—22no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—42no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—81no—
451C2×C4—442no—
452C2×C4—441no—
453C2×C4—441no—
454C2×C4—881no—
455C2×C4—881no—
456C2×C4—881no—
457C2×C4—881no—
458C2×C4—881no—
459C2×C4—881no—
460C2×C4—881no—
461C2×C4—881no—
462C2×C4—881no—
463C2×C4#6697711yescharacteristic
464C2×C4C4×C22⋊D1111yescharacteristic
465C8—442no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—41no—
473C22—41no—
474C22—41no—
475C22—41no—
476C22—42no—
477C22—42no—
478C22—41no—
479C22—41no—
480C22—41no—
481C22—41no—
482C22—44no—
483C22—42no—
484C22—81no—
485C22—81no—
486C22—81no—
487C22—81no—
488C22—82no—
489C22—82no—
490C22—82no—
491C22—81no—
492C22—81no—
493C22#1062282311yescharacteristic
494C22#1062285611yescharacteristic
495C22#1062285711yescharacteristic
496C4—21no—
497C4—21no—
498C4—42no—
499C4—81no—
500C4—81no—
501C4—81no—
502C4—81no—
503C4—882no—
504C4—881no—
505C4—881no—
506C4—1761no—
507C2—21no—
508C2—21no—
509C2—41no—
510C2—41no—
511C2—41no—
512C2—41no—
513C2—82no—
514C2#1306889711yescharacteristic
515C2#1307061711yescharacteristic
516C2#1307062311yescharacteristic
subgroupG/H
centerC22#10622857
commutatorC2×D4×C11C22×C4
FrattiniC22×D4C22×D11
FittingC11×#2375C2
socleC22×C11B(4,𝔽2)
prime radicalC2×C11×#120C22
cosocleC22×D4×C11C23
hypercenter#2375D11
hypocenterC11#12960
LCSG ▷ C2×D4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #2375

Complements

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

NH ≅ G/Ntype
3. #13068896C2semidirect
4. #13068825C2semidirect
5. #13066741C2semidirect
6. #13066734C2semidirect
24. #10622174C4semidirect
80. C24×C11C4⋊C4semidirect
120. C11×C22⋊C4C4⋊C4semidirect
337. C24Dic11⋊C4semidirect
392. C22⋊C4Dic11⋊C4semidirect
396. C11#12960semidirect

Maximal subgroups

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

subgroupindex
C2×#106221742
#130690252
#130688962
#130688252
#130667412
#130667342
C11×#23752
#1296011