Finite Group Databasebeta

← #14670547

Subgroups — #14670547

Order 2816.

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

normal subgroups only

This group has 504 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×#10622177C211yesmaximal, characteristic
2#13069030C211yesmaximal, characteristic
3#13068896C211yesmaximal, characteristic
4#13068825C211yesmaximal, characteristic
5#13066741C211yesmaximal, characteristic
6#13066734C211yesmaximal, characteristic
7C11×#2376C211yesmaximal, characteristic
8C2×C11×#123C2211yescharacteristic
9#10623329C2211yescharacteristic
10C11×#390C2211yescharacteristic
11C11×#389—21no—
12C11×#388—21no—
13C11×#388—21no—
14C11×#387—21no—
15C11×#386C2211yescharacteristic
16C11×#385—21no—
17C11×#380—21no—
18C2×#66898C2211yescharacteristic
19C2×#66898C2211yescharacteristic
20C2×#66897C2211yescharacteristic
21#10622824—21no—
22#10622823—21no—
23#10622577—21no—
24#10622177C414yescomplemented
25#10622165—21no—
26#10622165—21no—
27#10622161—21no—
28C22×D4×C11C2311yescharacteristic
29C23×C4×C11D411yescharacteristic
30C23×C4×C11D411yescharacteristic
31C11×#123—21no—
32C11×#123—21no—
33C11×#123C2×C412yes—
34C11×#123Q812yes—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4D411yescharacteristic
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4D411yescharacteristic
45C2×C11×C22⋊C4D411yescharacteristic
46C2×C42×C11—21no—
47C2×C42×C11D411yescharacteristic
48C2×C22⋊Dic11—21no—
49C2×C22⋊Dic11—21no—
50C2×C22⋊Dic11—21no—
51C2×C22⋊Dic11—21no—
52D4×Dic11—41no—
53D4×Dic11—41no—
54#66979—21no—
55C2×Dic11⋊C4—41no—
56C2×#4318—21no—
57C11×#95—21no—
58C11×#95—21no—
59C11×#95—21no—
60C11×#95—21no—
61C11×#95—21no—
62#66898—21no—
63#66898—21no—
64#66898—21no—
65#66898C2×C412yes—
66#66897—21no—
67#66897C2×C412yes—
68C11⋊#95—41no—
69C11⋊#95—41no—
70C11⋊#95—41no—
71#66872—41no—
72#66871—41no—
73#12961—111nomaximal, Sylow
74C24×C11C2×D411yescharacteristic
75C24×C11C2×D411yescharacteristic
76C2×D4×C11—41no—
77C2×D4×C11—41no—
78C2×D4×C11C22×C411yescharacteristic
79C2×D4×C11C2×Q811yescharacteristic
80C2×D4×C11#4111yescharacteristic
81C2×D4×C11#4111yescharacteristic
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—21no—
88C22×C4×C11—21no—
89C22×C4×C11—41no—
90C22×C4×C11—41no—
91C22×C4×C11—41no—
92C22×C4×C11—81no—
93C22×C4×C11C4⋊C412yescomplemented
94C22×C4×C11C2×D411yescharacteristic
95C22×Dic11—21no—
96C22×Dic11—21no—
97C22×Dic11—21no—
98C22×Dic11—21no—
99C22×Dic11—41no—
100C22×Dic11—41no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—22no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—81no—
105C11×C4⋊C4—81no—
106C11×C4⋊C4—81no—
107C11×C22⋊C4—22no—
108C11×C22⋊C4—22no—
109C11×C22⋊C4—21no—
110C11×C22⋊C4—41no—
111C11×C22⋊C4—81no—
112C11×C22⋊C4—81no—
113C11×C22⋊C4—81no—
114C11×C22⋊C4C4⋊C412yescomplemented
115C42×C11—41no—
116C42×C11—81no—
117C22⋊Dic11—22no—
118C22⋊Dic11—41no—
119C22⋊Dic11—41no—
120C22⋊Dic11—41no—
121C22⋊Dic11—41no—
122C22⋊Dic11—41no—
123C22⋊Dic11—41no—
124C4⋊Dic11—21no—
125C4⋊Dic11—21no—
126Dic11⋊C4—82no—
127C4×Dic11—41no—
128#4318—22no—
129#4318—41no—
130C2×C11⋊C8—41no—
131#2376D1111yescharacteristic
132C2×#352—111no—
133#1890—111no—
134#1867—111no—
135#1856—111no—
136#1393—111no—
137#1390—111no—
138C23×C11—21no—
139C23×C11—21no—
140C23×C11—21no—
141C23×C11—21no—
142C23×C11—41no—
143C23×C11—41no—
144C23×C11—41no—
145C23×C11—41no—
146C23×C11C2×C4⋊C411yescharacteristic
147C23×C11C4×D411yescharacteristic
148C23×C11#12011yescharacteristic
149C23×C11C22⋊Q811yescharacteristic
150C23×C11#12311yescharacteristic
151D4×C11—41no—
152D4×C11—41no—
153D4×C11—41no—
154D4×C11—41no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—42no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—42no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—81no—
178C2×C4×C11—81no—
179C2×C4×C11C4×D411yescharacteristic
180C2×C4×C11C22⋊Q811yescharacteristic
181C2×Dic11—42no—
182C2×Dic11—41no—
183C2×Dic11—41no—
184C2×Dic11—81no—
185C2×Dic11—81no—
186C2×Dic11—81no—
187C2×Dic11—81no—
188C2×Dic11—81no—
189C2×Dic11—81no—
190C2×Dic11—81no—
191C2×Dic11—81no—
192C2×Dic11—81no—
193C11⋊C8—42no—
194C2×#123C2×D1111yescharacteristic
195#518—111no—
196#428—221no—
197C2×#100—111no—
198C2×#99—111no—
199C2×#99—111no—
200#390C2×D1111yescharacteristic
201#389—21no—
202#388—21no—
203#388—21no—
204#387—21no—
205#386C2×D1111yescharacteristic
206#385—21no—
207#385—221no—
208#381—221no—
209#380—21no—
210#352—114no—
211#342—221no—
212#342—221no—
213#339—221no—
214C22×C11—21no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11—41no—
221C22×C11—41no—
222C22×C11—41no—
223C22×C11—41no—
224C22×C11—41no—
225C22×C11—41no—
226C22×C11—41no—
227C22×C11—41no—
228C22×C11—81no—
229C22×C11—81no—
230C22×C11#38511yescharacteristic
231C22×C11B(4,𝔽2)11yescharacteristic
232C22×C11#45811yescharacteristic
233C4×C11—21no—
234C4×C11—21no—
235C4×C11—42no—
236C4×C11—42no—
237C4×C11—81no—
238C4×C11—81no—
239C4×C11—81no—
240C4×C11—81no—
241Dic11—82no—
242Dic11—81no—
243Dic11—81no—
244Dic11—161no—
245C22×D4C22×D1111yescharacteristic
246C23×C4C22⋊D1111yescharacteristic
247C23×C4C22⋊D1111yescharacteristic
248C2×M16—221no—
249#123—21no—
250#123—21no—
251#123Dic2212yes—
252#123C4×D1112yes—
253C4×D4—441no—
254C4×D4—441no—
255#117—221no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—441no—
261C2×C4⋊C4C22⋊D1111yescharacteristic
262C2×C22⋊C4—21no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—21no—
265C2×C22⋊C4—21no—
266C2×C22⋊C4—221no—
267C2×C22⋊C4—221no—
268C2×C22⋊C4—221no—
269C2×C22⋊C4—221no—
270C2×C22⋊C4C22⋊D1111yescharacteristic
271C2×C22⋊C4C22⋊D1111yescharacteristic
272C2×C42—21no—
273C2×C42C22⋊D1111yescharacteristic
274#107—441no—
275#106—441no—
276#100—112no—
277#100—221no—
278#99—112no—
279#99—221no—
280#99—221no—
281#99—221no—
282#95—21no—
283#95—21no—
284#95—21no—
285#95—21no—
286#95—21no—
287#95—441no—
288#95—441no—
289#95—441no—
290C2×C11—21no—
291C2×C11—21no—
292C2×C11—41no—
293C2×C11—41no—
294C2×C11—41no—
295C2×C11—41no—
296C2×C11#186711yescharacteristic
297C2×C11#220011yescharacteristic
298C2×C11#220111yescharacteristic
299C24C2×C22⋊D1111yescharacteristic
300C24C2×C22⋊D1111yescharacteristic
301C2×D4—41no—
302C2×D4—41no—
303C2×D4C2×Dic2211yescharacteristic
304C2×D4C2×C4×D1111yescharacteristic
305C2×D4#433911yescharacteristic
306C2×D4#433911yescharacteristic
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—81no—
318C22×C4—221no—
319C22×C4—221no—
320C22×C4—221no—
321C22×C4—221no—
322C22×C4—441no—
323C22×C4—441no—
324C22×C4Dic11⋊C412yescomplemented
325C22×C4C2×C22⋊D1111yescharacteristic
326M16—222no—
327M16—441no—
328C2×C8—441no—
329C4⋊C4—22no—
330C4⋊C4—22no—
331C4⋊C4—41no—
332C4⋊C4—81no—
333C4⋊C4—81no—
334C4⋊C4—81no—
335C4⋊C4—221no—
336C4⋊C4—221no—
337C4⋊C4—882no—
338C22⋊C4—22no—
339C22⋊C4—22no—
340C22⋊C4—21no—
341C22⋊C4—41no—
342C22⋊C4—81no—
343C22⋊C4—81no—
344C22⋊C4—81no—
345C22⋊C4—222no—
346C22⋊C4—441no—
347C22⋊C4—441no—
348C22⋊C4—441no—
349C22⋊C4—441no—
350C22⋊C4—441no—
351C22⋊C4—441no—
352C22⋊C4Dic11⋊C412yescomplemented
353C42—41no—
354C42—81no—
355C42—441no—
356C11#1296111yescharacteristic, complemented, Sylow
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—41no—
362C23—41no—
363C23—41no—
364C23—41no—
365C23C2×Dic11⋊C411yescharacteristic
366C23#6697711yescharacteristic
367C23C4×C22⋊D1111yescharacteristic
368C23#6698211yescharacteristic
369C23#6700611yescharacteristic
370D4—41no—
371D4—41no—
372D4—41no—
373D4—41no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—42no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4—442no—
399C2×C4—441no—
400C2×C4—441no—
401C2×C4—881no—
402C2×C4—881no—
403C2×C4—881no—
404C2×C4—881no—
405C2×C4—881no—
406C2×C4—881no—
407C2×C4—881no—
408C2×C4—881no—
409C2×C4—881no—
410C2×C4#6697711yescharacteristic
411C2×C4C4×C22⋊D1111yescharacteristic
412C8—442no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—41no—
420C22—41no—
421C22—41no—
422C22—41no—
423C22—41no—
424C22—41no—
425C22—41no—
426C22—41no—
427C22—81no—
428C22—81no—
429C22#1062282311yescharacteristic
430C22#1062285611yescharacteristic
431C22#1062285711yescharacteristic
432C4—21no—
433C4—21no—
434C4—42no—
435C4—42no—
436C4—81no—
437C4—81no—
438C4—81no—
439C4—81no—
440C4—882no—
441C4—881no—
442C4—881no—
443C4—1761no—
444C2—21no—
445C2—21no—
446C2—41no—
447C2—41no—
448C2—41no—
449C2—41no—
450C2#1306889711yescharacteristic
451C2#1307062311yescharacteristic
452C2#1307062911yescharacteristic
subgroupG/H
centerC22#10622857
commutatorC2×D4×C11C22×C4
FrattiniC22×D4C22×D11
FittingC11×#2376C2
socleC22×C11B(4,𝔽2)
prime radical, cosocleC22×D4×C11C23
hypercenter#2376D11
hypocenterC11#12961
LCSG ▷ C2×D4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #2376

Complements

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

NH ≅ G/Ntype
24. #10622177C4semidirect
93. C22×C4×C11C4⋊C4semidirect
114. C11×C22⋊C4C4⋊C4semidirect
324. C22×C4Dic11⋊C4semidirect
352. C22⋊C4Dic11⋊C4semidirect
356. C11#12961semidirect

Maximal subgroups

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

subgroupindex
C2×#106221772
#130690302
#130688962
#130688252
#130667412
#130667342
C11×#23762
#1296111