Finite Group Databasebeta

← #14672091

Subgroups — #14672091

Order 2816.

602 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 602 conjugacy classes of subgroups — too many to draw. Only its 103 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#13073583C211yesmaximal, characteristic
2C2×#10622111C212yesmaximal, complemented
3C2×#10622112C212yesmaximal
4#13068604C211yesmaximal, characteristic, complemented
5C4×C11×#99C211yesmaximal, characteristic, complemented
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66993C2211yescharacteristic
8C2×#66989C2211yescharacteristic
9C2×#66928C411yescharacteristic, complemented
10C2×C11×#99C2212yes—
11C4×C11×C22⋊C4—21no—
12C2×#66898C2212yes—
13#10622826—21no—
14#10622826—21no—
15#10622825—21no—
16#10622601C411yescharacteristic, complemented
17#10622587C411yescharacteristic, complemented
18#10622574—21no—
19#10622574—21no—
20C4×C4⋊Dic11C411yescharacteristic, complemented
21C11×#342—21no—
22#10622164—21no—
23#10622112—24no—
24#10622111—24no—
25C22×D4×C11C2311yescharacteristic
26C23×C4×C11D411yescharacteristic
27C23×C4×C11D411yescharacteristic
28C22×C22⋊D11—21no—
29C22×C22⋊D11—21no—
30C22×D44C2×C411yescharacteristic
31C22×Dic22C2×C411yescharacteristic
32C4×D4×C11—41no—
33C4×D4×C11—41no—
34C2×C11×C4⋊C4C2×C411yescharacteristic
35C2×C11×C22⋊C4—22no—
36C2×C11×C22⋊C4D411yescharacteristic
37C2×C11×C22⋊C4D411yescharacteristic
38C2×C42×C11—41no—
39C2×C42×C11C2×C411yescharacteristic
40C2×C22⋊Dic11—21no—
41C2×C22⋊Dic11—21no—
42C2×C22⋊Dic11—22no—
43#66993—22no—
44#66993—22no—
45#66989—22no—
46#66989—22no—
47C2×(C2×D11)⋊C4—21no—
48C2×(C2×D11)⋊C4—21no—
49C2×(C2×D11)⋊C4—21no—
50C2×(C2×D11)⋊C4—21no—
51C2×C4⋊Dic11—21no—
52C2×C4⋊Dic11—41no—
53C2×C4×Dic11C2×C411yescharacteristic
54C2×C4×Dic11C2×C411yescharacteristic
55#66928—41no—
56#66928—41no—
57C11×#99—22no—
58C11×#99D414yes—
59C11×#95—41no—
60#66898—22no—
61#66898—22no—
62C11⋊#95—21no—
63C11⋊#95—21no—
64C11⋊#95—21no—
65C11⋊#95—41no—
66#13225—111nomaximal, Sylow
67C24×C11C2×D411yescharacteristic
68C24×C11C2×D411yescharacteristic
69C23×D11—21no—
70C2×D4×C11—41no—
71C2×D4×C11—41no—
72C2×D4×C11C2×D412yes—
73C2×D4×C11#4112yes—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—42no—
79C22×C4×C11—81no—
80C22×C4×C11—81no—
81C22×C4×C11C22⋊C411yescharacteristic
82C22×C4×C11C22⋊C411yescharacteristic
83C22×C4×C11C22⋊C411yescharacteristic
84C22×C4×C11C22⋊C411yescharacteristic
85C22×C4×C11C22×C411yescharacteristic
86C2×C22⋊D11—42no—
87C2×C22⋊D11—42no—
88C2×C22⋊D11—42no—
89C2×C22⋊D11—41no—
90C2×C22⋊D11—41no—
91C2×C22⋊D11—81no—
92C2×C22⋊D11—81no—
93C22×Dic11—21no—
94C22×Dic11—21no—
95C22×Dic11—21no—
96C22×Dic11—42no—
97C2×D44—22no—
98C2×D44—41no—
99C2×D44—41no—
100C2×Dic22—22no—
101C2×Dic22—41no—
102C2×Dic22—41no—
103C11×C4⋊C4—41no—
104C11×C22⋊C4—24no—
105C11×C22⋊C4—41no—
106C11×C22⋊C4—41no—
107C11×C22⋊C4—42no—
108C42×C11—21no—
109C42×C11—21no—
110C42×C11—82no—
111C22⋊Dic11—42no—
112C22⋊Dic11—42no—
113C22⋊Dic11—41no—
114C22⋊Dic11—41no—
115C22⋊Dic11—42no—
116(C2×D11)⋊C4—42no—
117(C2×D11)⋊C4—41no—
118(C2×D11)⋊C4—41no—
119(C2×D11)⋊C4—81no—
120(C2×D11)⋊C4—81no—
121C4⋊Dic11—42no—
122C4⋊Dic11—82no—
123C4×Dic11—22no—
124C4×Dic11—22no—
125#2544—111no—
126C2×#354—112no—
127C2×#353—112no—
128#1799—111no—
129C4×#99D1111yescharacteristic, complemented
130C23×C11—21no—
131C23×C11—21no—
132C23×C11—21no—
133C23×C11—21no—
134C23×C11—41no—
135C23×C11—41no—
136C23×C11—41no—
137C23×C11—41no—
138C23×C11C2×C22⋊C411yescharacteristic
139C23×C11#12112yes—
140C23×C11#12411yescharacteristic
141C23×C11#12711yescharacteristic
142C22×D11—41no—
143C22×D11—41no—
144C22×D11—41no—
145C22×D11—41no—
146C22×D11—41no—
147C22×D11—41no—
148C22×D11—41no—
149D4×C11—42no—
150D4×C11—42no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—41no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—44no—
163C2×C4×C11—81no—
164C2×C4×C11—81no—
165C2×C4×C11—82no—
166C2×C4×C11—82no—
167C2×C4×C11#9911yescharacteristic
168C2×C4×C11#9911yescharacteristic
169C2×C4×C11C4×D412yes—
170C22⋊D11—84no—
171C22⋊D11—82no—
172C22⋊D11—82no—
173C2×Dic11—22no—
174C2×Dic11—41no—
175C2×Dic11—41no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11—41no—
181C2×Dic11—41no—
182C2×Dic11—82no—
183C2×Dic11—82no—
184C2×Dic11—82no—
185D44—82no—
186Dic22—82no—
187C2×#127—111no—
188C2×#124—111no—
189C2×#124—111no—
190C2×C4×D4C2×D1111yescharacteristic
191C2×#99—112no—
192C2×#99C2×D1112yes—
193#394—221no—
194#394—221no—
195#391—111no—
196#390—111no—
197#386—221no—
198#386—221no—
199#380—221no—
200C4×C4⋊C4—111no—
201C4×C22⋊C4—21no—
202#354—224no—
203#353—224no—
204#342—21no—
205#342—221no—
206C22×C11—21no—
207C22×C11—21no—
208C22×C11—22no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—42no—
212C22×C11—41no—
213C22×C11—41no—
214C22×C11—41no—
215C22×C11—41no—
216C22×C11—41no—
217C22×C11—41no—
218C22×C11—81no—
219C22×C11—81no—
220C22×C11#39011yescharacteristic
221C22×C11C2×#9911yescharacteristic
222C22×C11#41011yescharacteristic
223C2×D11—81no—
224C2×D11—81no—
225C2×D11—81no—
226C2×D11—81no—
227C2×D11—81no—
228C2×D11—81no—
229C2×D11—81no—
230C4×C11—21no—
231C4×C11—21no—
232C4×C11—22no—
233C4×C11—41no—
234C4×C11—41no—
235C4×C11—41no—
236C4×C11—84no—
237Dic11—42no—
238Dic11—81no—
239Dic11—81no—
240Dic11—162no—
241C22×Q8—111no—
242C22×D4—111no—
243C22×D4—221no—
244C22×D4—221no—
245C22×D4C22×D1111yescharacteristic
246C23×C4D4411yescharacteristic
247C23×C4C22⋊D1111yescharacteristic
248#127—222no—
249#127—222no—
250#124—222no—
251#124—222no—
252#124—441no—
253#124—441no—
254C4×D4—41no—
255C4×D4—41no—
256C2×C4⋊C4—221no—
257C2×C4⋊C4—441no—
258C2×C4⋊C4C4×D1111yescharacteristic
259C2×C22⋊C4—22no—
260C2×C22⋊C4—221no—
261C2×C22⋊C4—221no—
262C2×C22⋊C4—221no—
263C2×C22⋊C4—221no—
264C2×C22⋊C4—222no—
265C2×C22⋊C4—221no—
266C2×C22⋊C4—221no—
267C2×C22⋊C4D4411yescharacteristic
268C2×C22⋊C4C22⋊D1111yescharacteristic
269C2×C42—41no—
270C2×C42—111no—
271C2×C42—111no—
272C2×C42C4×D1111yescharacteristic
273#99—22no—
274#99—222no—
275#99—222no—
276#99D4414yes—
277#95—41no—
278#95—221no—
279#95—221no—
280#95—221no—
281#95—441no—
282C2×C11—21no—
283C2×C11—21no—
284C2×C11—41no—
285C2×C11—42no—
286C2×C11—41no—
287C2×C11#196411yescharacteristic
288C2×C11#212611yescharacteristic
289C2×C11#212711yescharacteristic
290D11—161no—
291C24—221no—
292C24C2×D4411yescharacteristic
293C24C2×C22⋊D1111yescharacteristic
294C2×Q8—222no—
295C2×Q8—441no—
296C2×Q8—441no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—222no—
300C2×D4—441no—
301C2×D4—441no—
302C2×D4—442no—
303C2×D4—442no—
304C2×D4—441no—
305C2×D4—441no—
306C2×D4—442no—
307C2×D4—881no—
308C2×D4—881no—
309C2×D4C2×D4412yes—
310C2×D4#433912yes—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—42no—
316C22×C4—81no—
317C22×C4—81no—
318C22×C4—221no—
319C22×C4—221no—
320C22×C4—221no—
321C22×C4—442no—
322C22×C4(C2×D11)⋊C411yescharacteristic
323C22×C4(C2×D11)⋊C411yescharacteristic
324C22×C4(C2×D11)⋊C411yescharacteristic
325C22×C4(C2×D11)⋊C411yescharacteristic
326C22×C4C2×C4×D1111yescharacteristic
327C4⋊C4—41no—
328C4⋊C4—442no—
329C4⋊C4—882no—
330C22⋊C4—24no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—42no—
334C22⋊C4—442no—
335C22⋊C4—441no—
336C22⋊C4—441no—
337C22⋊C4—442no—
338C22⋊C4—441no—
339C22⋊C4—441no—
340C22⋊C4—442no—
341C22⋊C4—442no—
342C22⋊C4—881no—
343C22⋊C4—881no—
344C42—21no—
345C42—21no—
346C42—82no—
347C42—222no—
348C42—222no—
349C11#1322511yescharacteristic, complemented, Sylow
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—441no—
359C23—441no—
360C23—441no—
361C23—441no—
362C23—441no—
363C23—441no—
364C23—441no—
365C23#6692711yescharacteristic
366C23#6692811yescharacteristic
367C23C2×(C2×D11)⋊C411yescharacteristic
368C23#6698312yes—
369Q8—882no—
370D4—42no—
371D4—42no—
372D4—882no—
373D4—882no—
374D4—882no—
375D4—884no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—44no—
388C2×C4—81no—
389C2×C4—81no—
390C2×C4—82no—
391C2×C4—82no—
392C2×C4—222no—
393C2×C4—441no—
394C2×C4—441no—
395C2×C4—441no—
396C2×C4—441no—
397C2×C4—441no—
398C2×C4—441no—
399C2×C4—441no—
400C2×C4—441no—
401C2×C4—882no—
402C2×C4—882no—
403C2×C4—882no—
404C2×C4#6687011yescharacteristic
405C2×C4#6687011yescharacteristic
406C2×C4C4×D4412yes—
407C22—21no—
408C22—21no—
409C22—22no—
410C22—21no—
411C22—21no—
412C22—41no—
413C22—41no—
414C22—42no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—81no—
420C22—81no—
421C22—881no—
422C22—881no—
423C22—881no—
424C22—881no—
425C22—881no—
426C22—881no—
427C22—881no—
428C22#1062255211yescharacteristic
429C22C2×#6687011yescharacteristic
430C22#1062261911yescharacteristic
431C4—22no—
432C4—21no—
433C4—21no—
434C4—41no—
435C4—41no—
436C4—41no—
437C4—84no—
438C4—442no—
439C4—881no—
440C4—881no—
441C4—1762no—
442C2—21no—
443C2—21no—
444C2—42no—
445C2—41no—
446C2—41no—
447C2—1761no—
448C2#1306945211yescharacteristic
449C2#1307027911yescharacteristic
450C2#1307028311yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC22×D4C22×D11
FittingC4×C11×#99C2
socleC22×C11C2×#99
prime radicalC2×#66993C22
cosocleC22×D4×C11C23
hypercenterC4×#99D11
hypocenterC11#13225
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
2. C2×#10622111C2semidirect
4. #13068604C2semidirect
5. C4×C11×#99C2semidirect
9. C2×#66928C4semidirect
16. #10622601C4semidirect
17. #10622587C4semidirect
20. C4×C4⋊Dic11C4semidirect
129. C4×#99D11semidirect
349. C11#13225semidirect

Maximal subgroups

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

subgroupindex
#130735832
C2×#106221112
C2×#106221122
#130686042
C4×C11×#992
#1322511