Finite Group Databasebeta

← #14724546

Subgroups — #14724546

Order 2816.

646 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079211C211yesmaximal, characteristic
2#13077591C211yesmaximal, characteristic, complemented
3#13077329C211yesmaximal, characteristic, complemented
4#13067496C212yesmaximal, complemented
5#13067482C212yesmaximal, complemented
6#13067454C212yesmaximal, complemented
7#13067447C212yesmaximal, complemented
8#13067383C211yesmaximal, characteristic, complemented
9#13067086C211yesmaximal, characteristic, complemented
10#13067082C211yesmaximal, characteristic, complemented
11C11×#1451C211yesmaximal, characteristic, complemented
12C2×#66954—21no—
13#10623010C2211yescharacteristic
14#10623008C2211yescharacteristic
15C11×#431C2211yescharacteristic
16C4×C11×M16C2211yescharacteristic
17C2×C4×C8×C11C2211yescharacteristic
18#10622748C412yes—
19#10622747C412yes—
20#10622724—21no—
21#10622723—21no—
22C8×C22⋊D11—21no—
23#10622539C2211yescharacteristic
24#10622537C2211yescharacteristic
25#10622327C411yescharacteristic
26#10622326C411yescharacteristic
27#10622325C411yescharacteristic
28#10622315C411yescharacteristic
29C4×D88C2212yes—
30C4×#4314C2212yes—
31#10622303—21no—
32#10622302—21no—
33#10622301—21no—
34#10622301C2212yes—
35#10622301C2211yescharacteristic
36C8×D44—21no—
37C8×D44C2212yes—
38C8×D44C2211yescharacteristic
39#10622292C2211yescharacteristic
40C8×Dic22C2211yescharacteristic
41C11×#322C2212yes—
42C11×#322C2212yes—
43#10622097C2212yes—
44#10622097C2212yes—
45#10622097C2212yes—
46#10622096C2212yes—
47#10622095C2212yes—
48#10622094C2212yes—
49C2×#4339—21no—
50C2×C11×M16C2×C412yes—
51C22×C8×C11D411yescharacteristic
52C22×C8×C11D411yescharacteristic
53C2×C42×C11C2311yescharacteristic
54#66983—21no—
55#66983C2×C412yes—
56#66983C2×C411yescharacteristic
57#66982—21no—
58C4×C22⋊D11—21no—
59#66977C2×C411yescharacteristic
60C2×#4318—21no—
61C2×D88C2×C412yes—
62C2×#4314C2×C412yes—
63#66954—44no—
64C2×#4313—21no—
65C2×#4313—22no—
66C2×C8×D11—21no—
67C2×C8×D11—22no—
68#66929—21no—
69#66928—21no—
70#66928C2×C411yescharacteristic
71#66927C2×C411yescharacteristic
72C4×D44—21no—
73C4×D44C2312yes—
74C4×D44C2311yescharacteristic
75#66925—21no—
76#66923C2×C411yescharacteristic
77#66922C2×C411yescharacteristic
78C4×Dic22C2311yescharacteristic
79C11×C4⋊C8—21no—
80C11×C22⋊C8—21no—
81C11×#97C2×C411yescharacteristic
82C11×#97C2×C411yescharacteristic
83C4×C8×C11D411yescharacteristic
84C4×C8×C11D411yescharacteristic
85C4×C8×C11C2312yes—
86C4×C8×C11C2312yes—
87C4×C8×C11C2311yescharacteristic
88C4×C8×C11C2311yescharacteristic
89C22⋊(C11⋊C8)—21no—
90#66885C2×C412yes—
91#66885C2×C412yes—
92#66885C2×C412yes—
93(C2×D11)⋊C8—21no—
94(C2×D11)⋊C8—22no—
95(C2×D11)⋊C8—22no—
96(C2×D11)⋊C8—21no—
97#66882C2×C412yes—
98#66881C2×C412yes—
99#66880C2×C412yes—
100#66879—21no—
101Dic11⋊C8—21no—
102Dic11⋊C8—21no—
103C8×Dic11—21no—
104C4⋊(C11⋊C8)—21no—
105C4⋊(C11⋊C8)C2312yes—
106C4⋊(C11⋊C8)C2311yescharacteristic
107C4⋊(C11⋊C8)C2311yescharacteristic
108#66867—21no—
109#17983—111nomaximal, Sylow
110C22×C4×C11C22×C411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11#4111yescharacteristic
113C2×C22⋊D11—21no—
114C2×C22⋊D11—22no—
115#4339—42no—
116#4339—42no—
117C2×D44—21no—
118C2×D44—21no—
119C2×D44C22×C412yes—
120C2×D44C22×C411yescharacteristic
121C2×C4×D11—21no—
122C2×C4×D11—22no—
123C2×Dic22—21no—
124C2×Dic22C22×C411yescharacteristic
125C11×M16—42no—
126C2×C8×C11—22no—
127C2×C8×C11—22no—
128C2×C8×C11—41no—
129C2×C8×C11C22×C412yes—
130C2×C8×C11C22×C412yes—
131C2×C8×C11C2×D411yescharacteristic
132C2×C8×C11C2×D411yescharacteristic
133C2×C8×C11C2×D411yescharacteristic
134C2×C8×C11C2×D411yescharacteristic
135C42×C11C22×C411yescharacteristic
136C42×C11C2×D411yescharacteristic
137C42×C11#4111yescharacteristic
138C42×C11C2411yescharacteristic
139C22⋊Dic11—21no—
140(C2×D11)⋊C4—21no—
141(C2×D11)⋊C4—21no—
142(C2×D11)⋊C4—22no—
143(C2×D11)⋊C4—21no—
144(C2×D11)⋊C4—22no—
145(C2×D11)⋊C4—21no—
146C4⋊Dic11—21no—
147C4⋊Dic11C22×C412yes—
148C4⋊Dic11C22×C411yescharacteristic
149C4⋊Dic11C22×C411yescharacteristic
150Dic11⋊C4—21no—
151Dic11⋊C4—21no—
152Dic11⋊C4—21no—
153Dic11⋊C4—21no—
154C4×Dic11—21no—
155#4318—42no—
156C2×C11⋊C8—21no—
157C2×C11⋊C8—21no—
158C2×C11⋊C8—22no—
159D88—42no—
160#4314—42no—
161#4313—44no—
162#4313—42no—
163C8×D11—42no—
164C8×D11—44no—
165#3171—111no—
166#2966—111no—
167#2931—111no—
168#1588—112no—
169#1586—112no—
170#1582—112no—
171#1581—112no—
172#1569—111no—
173#1496—111no—
174#1495—111no—
175#1451D1111yescharacteristic, complemented
176C23×C11C4×D411yescharacteristic
177C22×D11—21no—
178C22×D11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—41no—
183C2×C4×C11C4×D411yescharacteristic
184C2×C4×C11C4×D411yescharacteristic
185C2×C4×C11C4×D411yescharacteristic
186C2×C4×C11C23×C411yescharacteristic
187C2×C4×C11C22×D411yescharacteristic
188C2×C4×C11C2×#4111yescharacteristic
189C22⋊D11—44no—
190C22⋊D11—42no—
191C2×Dic11—21no—
192C2×Dic11—21no—
193C2×Dic11—21no—
194C2×Dic11—22no—
195D44—22no—
196D44—22no—
197D44—22no—
198D44—42no—
199D44—42no—
200C4×D11—42no—
201C4×D11—41no—
202C4×D11—41no—
203C4×D11—42no—
204Dic22—22no—
205Dic22—42no—
206C8×C11—22no—
207C8×C11—22no—
208C8×C11—21no—
209C8×C11—21no—
210C8×C11—21no—
211C8×C11—42no—
212C8×C11AGL(1,ℤ/8)12yes—
213C11⋊C8—42no—
214C11⋊C8—41no—
215C11⋊C8—41no—
216C2×#131—221no—
217#532—111no—
218#529—111no—
219#501—111no—
220#496—111no—
221#490—111no—
222#489—111no—
223#469—112no—
224#468—112no—
225#446—111no—
226C8×Q8—111no—
227C4×SD16—112no—
228C4×D8—112no—
229#436—111no—
230#436—112no—
231#436—221no—
232#435—221no—
233C8×D4—112no—
234C8×D4—111no—
235C8×D4—221no—
236C8×D4—221no—
237#433—221no—
238#432—111no—
239#431C2×D1111yescharacteristic
240#423—111no—
241#408—221no—
242#405—221no—
243C4×M16C2×D1111yescharacteristic
244C2×C4×C8C2×D1111yescharacteristic
245#335—112no—
246#334—112no—
247Q8⋊C8—112no—
248D4⋊C8—112no—
249D4⋊C8—112no—
250D4⋊C8—112no—
251#322C2×D1112yes—
252#322C2×D1112yes—
253C22×C11—21no—
254C22×C11—21no—
255C22×C11—21no—
256C22×C11C2×C4×D411yescharacteristic
257C2×D11—41no—
258C2×D11—42no—
259C2×D11—41no—
260C2×D11—42no—
261C2×D11—42no—
262C2×D11—41no—
263C4×C11—21no—
264C4×C11—21no—
265C4×C11—21no—
266C4×C11—21no—
267C4×C11#56812yes—
268C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
269C4×C11#57511yescharacteristic
270Dic11—41no—
271Dic11—42no—
272Dic11—41no—
273Dic11—41no—
274C2×#41—221no—
275C2×SD16—112no—
276C2×D8—112no—
277#131—444no—
278C2×M16—221no—
279C2×M16—222no—
280C2×M16—221no—
281C2×M16C4×D1112yes—
282C22×C8—222no—
283C22×C8—221no—
284C22×C8D4411yescharacteristic
285C22×C8D4411yescharacteristic
286C4⋊Q8—111no—
287#127—111no—
288#126—221no—
289#125—111no—
290#124—111no—
291#124—221no—
292#123—221no—
293C22⋊Q8—111no—
294#121—111no—
295#121—112no—
296#121—221no—
297C4×Q8—111no—
298C4×D4—111no—
299C4×D4—112no—
300C4×D4—221no—
301C4×D4—221no—
302#117—221no—
303C2×C42C22×D1111yescharacteristic
304#107—112no—
305#106—112no—
306C4⋊C8—21no—
307C4⋊C8—111no—
308C4⋊C8—111no—
309C4⋊C8—112no—
310C4⋊C8—221no—
311C4⋊C8—221no—
312C4⋊C8—221no—
313#103—112no—
314#102—112no—
315#102—112no—
316#102—112no—
317C22⋊C8—21no—
318C22⋊C8—221no—
319C22⋊C8—222no—
320C22⋊C8—222no—
321C22⋊C8—221no—
322C22⋊C8—221no—
323#97—221no—
324#97—221no—
325#97C4×D1111yescharacteristic
326#97C4×D1111yescharacteristic
327C4×C8—221no—
328C4×C8D4411yescharacteristic
329C4×C8D4411yescharacteristic
330C4×C8C22×D1112yes—
331C4×C8C22×D1112yes—
332C4×C8C22×D1111yescharacteristic
333C4×C8C22×D1111yescharacteristic
334C2×C11—41no—
335C2×C11#293211yescharacteristic
336C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
337C2×C11#295511yescharacteristic
338D11—81no—
339D11—82no—
340#41—442no—
341#41—442no—
342C2×Q8—111no—
343C2×Q8—221no—
344C2×D4—111no—
345C2×D4—112no—
346C2×D4—221no—
347C2×D4—222no—
348C2×D4—221no—
349C2×D4—221no—
350C22×C4—221no—
351C22×C4—222no—
352C22×C4C2×C4×D1111yescharacteristic
353C22×C4C2×D4411yescharacteristic
354C22×C4#433911yescharacteristic
355SD16—442no—
356D8—442no—
357M16—42no—
358M16—444no—
359M16—442no—
360M16—442no—
361C2×C8—22no—
362C2×C8—22no—
363C2×C8—41no—
364C2×C8—221no—
365C2×C8—221no—
366C2×C8—222no—
367C2×C8—442no—
368C2×C8—444no—
369C2×C8C2×C4×D1112yes—
370C2×C8C2×C4×D1112yes—
371C2×C8C2×D4411yescharacteristic
372C2×C8C2×D4411yescharacteristic
373C2×C8C2×D4411yescharacteristic
374C2×C8C2×D4411yescharacteristic
375C4⋊C4—111no—
376C4⋊C4—111no—
377C4⋊C4—112no—
378C4⋊C4—221no—
379C4⋊C4—221no—
380C4⋊C4—221no—
381C4⋊C4—221no—
382C4⋊C4—221no—
383C22⋊C4—221no—
384C22⋊C4—221no—
385C22⋊C4—221no—
386C22⋊C4—222no—
387C22⋊C4—221no—
388C22⋊C4—222no—
389C22⋊C4—221no—
390C42—221no—
391C42C2×C4×D1111yescharacteristic
392C42C2×D4411yescharacteristic
393C42#433911yescharacteristic
394C42C23×D1111yescharacteristic
395C11#1798311yescharacteristic, complemented, Sylow
396C23—221no—
397C23—222no—
398C23C4×D4411yescharacteristic
399Q8—222no—
400Q8—442no—
401D4—222no—
402D4—222no—
403D4—222no—
404D4—442no—
405D4—442no—
406D4—444no—
407D4—442no—
408C2×C4—22no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—41no—
412C2×C4—221no—
413C2×C4—221no—
414C2×C4—221no—
415C2×C4—222no—
416C2×C4—442no—
417C2×C4—441no—
418C2×C4—441no—
419C2×C4—442no—
420C2×C4C4×D4411yescharacteristic
421C2×C4C4×D4411yescharacteristic
422C2×C4C4×D4411yescharacteristic
423C2×C4C22×C4×D1111yescharacteristic
424C2×C4C22×D4411yescharacteristic
425C2×C4C2×#433911yescharacteristic
426C8—22no—
427C8—22no—
428C8—21no—
429C8—21no—
430C8—21no—
431C8—42no—
432C8—442no—
433C8—441no—
434C8—441no—
435C8#6696112yes—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—442no—
440C22—441no—
441C22—441no—
442C22—442no—
443C22—442no—
444C22—441no—
445C22C2×C4×D4411yescharacteristic
446C4—21no—
447C4—21no—
448C4—21no—
449C4—21no—
450C4—441no—
451C4—441no—
452C4—442no—
453C4—441no—
454C4#1062327612yes—
455C4C2×#6696111yescharacteristic
456C4#1062327911yescharacteristic
457C2—41no—
458C2—882no—
459C2—881no—
460C2#1307733511yescharacteristic
461C2C4×#6696111yescharacteristic
462C2#1307752011yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1451C2
socleC22×C11C2×C4×D4
prime radical#13079211C2
cosocleC42×C11C24
hypercenter#1451D11
hypocenterC11#17983
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C4×C8 ◁ #1451

Complements

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

NH ≅ G/Ntype
2. #13077591C2semidirect
3. #13077329C2semidirect
4. #13067496C2semidirect
5. #13067482C2semidirect
6. #13067454C2semidirect
7. #13067447C2semidirect
8. #13067383C2semidirect
9. #13067086C2semidirect
10. #13067082C2semidirect
11. C11×#1451C2semidirect
175. #1451D11semidirect
395. C11#17983semidirect

Maximal subgroups

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

subgroupindex
#130792112
#130775912
#130773292
#130674962
#130674822
#130674542
#130674472
#130673832
#130670862
#130670822
C11×#14512
#1798311