Finite Group Databasebeta

← #14672054

Subgroups — #14672054

Order 2816.

536 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 93 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#13072921C211yesmaximal, characteristic
2C2×#10622114C211yesmaximal, characteristic
3C2×#10622177C211yesmaximal, characteristic
4C2×#10622110C211yesmaximal, characteristic
5#13068602C211yesmaximal, characteristic
6#100×Dic11C211yesmaximal, characteristic
7C2×C11×#352C211yesmaximal, characteristic
8C2×C11×#123C2211yescharacteristic
9C2×#66988C2211yescharacteristic
10C2×D4×Dic11C2211yescharacteristic
11C22×Dic11⋊C4C411yescharacteristic, complemented
12C2×C11×#100C2211yescharacteristic
13C2×C11×#99C2211yescharacteristic
14C2×#66898C2211yescharacteristic
15C2×#66897C2211yescharacteristic
16#10622824C411yescharacteristic, complemented
17M16×Dic11—21no—
18#10622597—21no—
19#10622585—21no—
20#10622565—21no—
21#10622556C411yescharacteristic, complemented
22#10622555—21no—
23#10622555—21no—
24#10622555C411yescharacteristic, complemented
25C11×#352—22no—
26#10622192—21no—
27#10622177—22no—
28#10622165—21no—
29#10622114—22no—
30#10622110—22no—
31C22×D4×C11C2311yescharacteristic
32C23×C4×C11C2×C411yescharacteristic
33C23×Dic11C2×C411yescharacteristic
34C23×Dic11C2×C411yescharacteristic
35C23×Dic11D411yescharacteristic
36C2×C11×M16—21no—
37C11×#123—21no—
38C11×#123—21no—
39C11×#123—21no—
40C11×#123—21no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4C2×C411yescharacteristic
45C2×C22⋊Dic11—21no—
46C2×C22⋊Dic11—21no—
47C2×C22⋊Dic11C2×C411yescharacteristic
48C2×C22⋊Dic11C2×C411yescharacteristic
49C2×C22⋊Dic11D411yescharacteristic
50#66988—21no—
51#66988—21no—
52#66988—21no—
53#66988—21no—
54D4×Dic11—41no—
55D4×Dic11—41no—
56C2×C4⋊Dic11D411yescharacteristic
57C2×Dic11⋊C4—21no—
58C2×Dic11⋊C4—21no—
59C2×Dic11⋊C4—21no—
60C2×Dic11⋊C4—21no—
61C2×Dic11⋊C4—41no—
62C2×Dic11⋊C4—41no—
63C2×Dic11⋊C4—41no—
64C2×C4×Dic11D411yescharacteristic
65C2×#4318—21no—
66C11×#100—21no—
67C11×#100D412yes—
68C11×#99—21no—
69C11×#99—21no—
70#66898—21no—
71#66898—21no—
72#66897—21no—
73#66897D412yes—
74C11⋊#95—21no—
75C11⋊#95—21no—
76C11⋊#95—21no—
77C11⋊#95—21no—
78C11⋊#95—21no—
79C11⋊#95—41no—
80#66879—41no—
81C8×Dic11—41no—
82#13217—111nomaximal, Sylow
83C24×C11C22×C411yescharacteristic
84C24×C11C2×D411yescharacteristic
85C2×D4×C11—41no—
86C2×D4×C11—41no—
87C2×D4×C11C2×D411yescharacteristic
88C2×D4×C11C2×D411yescharacteristic
89C2×D4×C11#4111yescharacteristic
90C2×D4×C11#4111yescharacteristic
91C22×C4×C11—21no—
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×Dic11—21no—
100C22×Dic11—21no—
101C22×Dic11—21no—
102C22×Dic11—21no—
103C22×Dic11—21no—
104C22×Dic11—21no—
105C22×Dic11—21no—
106C22×Dic11—21no—
107C22×Dic11—41no—
108C22×Dic11—41no—
109C22×Dic11—41no—
110C22×Dic11—42no—
111C22×Dic11—42no—
112C22×Dic11C22⋊C411yescharacteristic
113C22×Dic11C22⋊C411yescharacteristic
114C22×Dic11C22⋊C411yescharacteristic
115C22×Dic11C22⋊C411yescharacteristic
116C11×M16—22no—
117C11×M16—41no—
118C2×C8×C11—41no—
119C11×C4⋊C4—41no—
120C11×C4⋊C4—41no—
121C11×C22⋊C4—21no—
122C11×C22⋊C4—21no—
123C11×C22⋊C4—41no—
124C11×C22⋊C4—41no—
125C11×C22⋊C4—41no—
126C11×C22⋊C4—41no—
127C22⋊Dic11—21no—
128C22⋊Dic11—21no—
129C22⋊Dic11—41no—
130C22⋊Dic11—41no—
131C22⋊Dic11—41no—
132C22⋊Dic11—41no—
133C22⋊Dic11—41no—
134C22⋊Dic11—41no—
135C4⋊Dic11—41no—
136Dic11⋊C4—42no—
137Dic11⋊C4—42no—
138Dic11⋊C4—41no—
139Dic11⋊C4—41no—
140Dic11⋊C4—41no—
141Dic11⋊C4—41no—
142Dic11⋊C4—82no—
143C4×Dic11—21no—
144C4×Dic11—21no—
145#4318—22no—
146#4318—41no—
147C2×C11⋊C8—41no—
148#2486—111no—
149C2×#352—111no—
150C2×#352—111no—
151C2×#352—111no—
152C2×#352D1111yescharacteristic
153#1799—111no—
154C4×#100—111no—
155C23×C11—21no—
156C23×C11—21no—
157C23×C11—21no—
158C23×C11—21no—
159C23×C11—41no—
160C23×C11—41no—
161C23×C11—41no—
162C23×C11—41no—
163C23×C11C2×C22⋊C411yescharacteristic
164C23×C11C4×D411yescharacteristic
165C23×C11C4×D411yescharacteristic
166C23×C11#12411yescharacteristic
167C23×C11#12711yescharacteristic
168D4×C11—41no—
169D4×C11—41no—
170D4×C11—41no—
171D4×C11—41no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—81no—
181C2×C4×C11—81no—
182C2×C4×C11—81no—
183C2×C4×C11—81no—
184C2×C4×C11—81no—
185C2×C4×C11#12111yescharacteristic
186C2×C4×C11#12111yescharacteristic
187C2×Dic11—22no—
188C2×Dic11—21no—
189C2×Dic11—21no—
190C2×Dic11—21no—
191C2×Dic11—42no—
192C2×Dic11—42no—
193C2×Dic11—42no—
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—
205C2×Dic11—81no—
206C2×Dic11—81no—
207C2×Dic11—81no—
208C2×Dic11—81no—
209C2×Dic11#9911yescharacteristic
210C2×Dic11#9911yescharacteristic
211C8×C11—42no—
212C11⋊C8—42no—
213C2×#123—111no—
214C2×#123C2×D1111yescharacteristic
215C2×C4×D4—111no—
216C22×C4⋊C4—111no—
217C2×#100—111no—
218C2×#100C2×D1111yescharacteristic
219C2×#99—111no—
220C2×#99C2×D1111yescharacteristic
221C4×M16—221no—
222#398—221no—
223#397—221no—
224#389—221no—
225#381—111no—
226#381—111no—
227#380—111no—
228#380—221no—
229#380—221no—
230#352—22no—
231#352—222no—
232#352—222no—
233#352—222no—
234#343—221no—
235#342—221no—
236C22×C11—21no—
237C22×C11—21no—
238C22×C11—21no—
239C22×C11—21no—
240C22×C11—21no—
241C22×C11—21no—
242C22×C11—41no—
243C22×C11—41no—
244C22×C11—41no—
245C22×C11—41no—
246C22×C11—42no—
247C22×C11—41no—
248C22×C11—41no—
249C22×C11—41no—
250C22×C11—41no—
251C22×C11—81no—
252C22×C11#39011yescharacteristic
253C22×C11C2×#9911yescharacteristic
254C22×C11#41011yescharacteristic
255C4×C11—21no—
256C4×C11—21no—
257C4×C11—81no—
258C4×C11—81no—
259C4×C11—161no—
260Dic11—21no—
261Dic11—41no—
262Dic11—41no—
263Dic11—41no—
264Dic11—81no—
265Dic11—81no—
266Dic11—161no—
267Dic11#35212yescomplemented
268C22×D4C22×D1111yescharacteristic
269C23×C4—111no—
270C23×C4—111no—
271C23×C4—111no—
272C23×C4C4×D1111yescharacteristic
273C2×M16—21no—
274C2×M16—221no—
275#123—21no—
276#123—21no—
277#123—21no—
278#123—21no—
279#123—221no—
280#123—221no—
281#123—221no—
282#123—221no—
283C4×D4—441no—
284C4×D4—441no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—111no—
287C2×C4⋊C4—221no—
288C2×C4⋊C4—221no—
289C2×C4⋊C4—221no—
290C2×C4⋊C4—221no—
291C2×C4⋊C4—441no—
292C2×C4⋊C4—441no—
293C2×C4⋊C4—441no—
294C2×C22⋊C4—21no—
295C2×C22⋊C4—21no—
296C2×C22⋊C4—111no—
297C2×C22⋊C4—111no—
298C2×C22⋊C4—111no—
299C2×C22⋊C4—221no—
300C2×C22⋊C4—221no—
301C2×C22⋊C4C4×D1111yescharacteristic
302C2×C42—111no—
303#100—21no—
304#100—112no—
305#100—221no—
306#100C22⋊D1112yes—
307#99—21no—
308#99—21no—
309#99—221no—
310#99—221no—
311#97—441no—
312C4×C8—441no—
313#95—221no—
314#95—221no—
315#95—221no—
316#95—221no—
317#95—221no—
318#95—441no—
319C2×C11—21no—
320C2×C11—21no—
321C2×C11—41no—
322C2×C11—41no—
323C2×C11—41no—
324C2×C11—41no—
325C2×C11#196411yescharacteristic
326C2×C11C2×#35211yescharacteristic
327C2×C11#212311yescharacteristic
328C24C2×C4×D1111yescharacteristic
329C24D4×D1111yescharacteristic
330C2×D4—41no—
331C2×D4—41no—
332C2×D4#433911yescharacteristic
333C2×D4D4×D1111yescharacteristic
334C2×D4#434111yescharacteristic
335C2×D4C2×C22⋊D1111yescharacteristic
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4—111no—
344C22×C4—111no—
345C22×C4—111no—
346C22×C4—111no—
347C22×C4—221no—
348C22×C4—221no—
349C22×C4—221no—
350C22×C4—221no—
351C22×C4—221no—
352C22×C4—221no—
353C22×C4—221no—
354C22×C4—221no—
355C22×C4—442no—
356C22×C4—442no—
357C22×C4—441no—
358C22×C4—441no—
359C22×C4—441no—
360C22×C4D4×D1111yescharacteristic
361M16—22no—
362M16—41no—
363M16—222no—
364M16—441no—
365C2×C8—41no—
366C2×C8—441no—
367C4⋊C4—41no—
368C4⋊C4—41no—
369C4⋊C4—441no—
370C4⋊C4—441no—
371C4⋊C4—441no—
372C4⋊C4—442no—
373C4⋊C4—442no—
374C4⋊C4—441no—
375C4⋊C4—441no—
376C4⋊C4—882no—
377C22⋊C4—21no—
378C22⋊C4—21no—
379C22⋊C4—41no—
380C22⋊C4—41no—
381C22⋊C4—41no—
382C22⋊C4—41no—
383C22⋊C4—221no—
384C22⋊C4—221no—
385C22⋊C4—441no—
386C22⋊C4—441no—
387C22⋊C4—441no—
388C22⋊C4—441no—
389C22⋊C4—441no—
390C22⋊C4—441no—
391C42—221no—
392C42—221no—
393C11#1321711yescharacteristic, complemented, Sylow
394C23—21no—
395C23—21no—
396C23—21no—
397C23—21no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—41no—
402C23C22⋊C4×D1111yescharacteristic
403C23(C22⋊D11)⋊C411yescharacteristic
404C23#6693811yescharacteristic
405C23C4×C22⋊D1111yescharacteristic
406C23#6699311yescharacteristic
407D4—41no—
408D4—41no—
409D4—41no—
410D4—41no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—81no—
420C2×C4—81no—
421C2×C4—81no—
422C2×C4—81no—
423C2×C4—81no—
424C2×C4—111no—
425C2×C4—111no—
426C2×C4—222no—
427C2×C4—221no—
428C2×C4—221no—
429C2×C4—221no—
430C2×C4—442no—
431C2×C4—442no—
432C2×C4—442no—
433C2×C4—441no—
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—881no—
443C2×C4—881no—
444C2×C4—881no—
445C2×C4—881no—
446C2×C4—881no—
447C2×C4—881no—
448C2×C4#6693711yescharacteristic
449C2×C4#6699211yescharacteristic
450C8—42no—
451C8—442no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—42no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—81no—
468C22#1062235311yescharacteristic
469C22D11×#9911yescharacteristic
470C22#1062257011yescharacteristic
471C4—21no—
472C4—21no—
473C4—81no—
474C4—81no—
475C4—112no—
476C4—161no—
477C4—221no—
478C4—441no—
479C4—441no—
480C4—441no—
481C4—881no—
482C4—881no—
483C4—1761no—
484C2—21no—
485C2—21no—
486C2—41no—
487C2—41no—
488C2—41no—
489C2—41no—
490C2#1306945011yescharacteristic
491C2D11×#35211yescharacteristic
492C2#1307026811yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC24×C11C22×C4
FrattiniC22×D4C22×D11
FittingC2×C11×#352C2
socleC22×C11C2×#99
prime radical, cosocleC22×D4×C11C23
hypercenterC2×#352D11
hypocenterC11#13217
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#352

Complements

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

NH ≅ G/Ntype
11. C22×Dic11⋊C4C4semidirect
16. #10622824C4semidirect
21. #10622556C4semidirect
24. #10622555C4semidirect
267. Dic11#352semidirect
393. C11#13217semidirect

Maximal subgroups

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

subgroupindex
#130729212
C2×#106221142
C2×#106221772
C2×#106221102
#130686022
#100×Dic112
C2×C11×#3522
#1321711