Finite Group Databasebeta

← #14910164

Subgroups — #14910164

Order 2816.

500 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079266C211yesmaximal, characteristic, complemented
2#13079255C211yesmaximal, characteristic, complemented
3#13070781C211yesmaximal, characteristic, complemented
4#13070774C211yesmaximal, characteristic, complemented
5#13070764C211yesmaximal, characteristic, complemented
6#13070754C211yesmaximal, characteristic, complemented
7#13070729C211yesmaximal, characteristic, complemented
8#13070719C211yesmaximal, characteristic, complemented
9#13070712C211yesmaximal, characteristic, complemented
10#13070702C211yesmaximal, characteristic, complemented
11#13070672C211yesmaximal, characteristic, complemented
12#13070672C211yesmaximal, characteristic, complemented
13#13070657C211yesmaximal, characteristic, complemented
14#13070652C211yesmaximal, characteristic, complemented
15C11×#2151C211yesmaximal, characteristic, complemented
16#10623066—21no—
17#10623065—21no—
18C2×C11×M32C2211yescharacteristic
19C22×C11×C16C2211yescharacteristic
20C11×#405C2211yescharacteristic
21#10622748—21no—
22#10622747—21no—
23#10622729C2211yescharacteristic
24#10622728C2211yescharacteristic
25#10622728C2211yescharacteristic
26#10622728C2211yescharacteristic
27C2×#66864C2211yescharacteristic
28C2×#66864C2211yescharacteristic
29C2×D176C2211yescharacteristic
30C2×D176C2211yescharacteristic
31#10622327—21no—
32#10622326—21no—
33#10622324—21no—
34#10622323—21no—
35C4×Dic44C2211yescharacteristic
36#10622309C2211yescharacteristic
37#10622308C2211yescharacteristic
38C4×D88C2211yescharacteristic
39C4×D88C2211yescharacteristic
40C4×D88C2211yescharacteristic
41#10622296C2211yescharacteristic
42#10622295C2211yescharacteristic
43C11×C4⋊C16C2211yescharacteristic
44C11×C4⋊C16C2211yescharacteristic
45C11×C4⋊C16C2211yescharacteristic
46C11×C4⋊C16C2211yescharacteristic
47#10622147C2211yescharacteristic
48#10622147C2211yescharacteristic
49#10622147C2211yescharacteristic
50#10622147C2211yescharacteristic
51#10622147C2211yescharacteristic
52#10622147C2211yescharacteristic
53#10622143C2211yescharacteristic
54#10622143C2211yescharacteristic
55#10622142C2211yescharacteristic
56#10622142C2211yescharacteristic
57#10622141C2211yescharacteristic
58#10622141C2211yescharacteristic
59C2×C11×M16D411yescharacteristic
60C22×C8×C11C2311yescharacteristic
61C11×#117D411yescharacteristic
62#66983—21no—
63#66983—21no—
64#66983—21no—
65#66977—21no—
66C2×Dic44C2311yescharacteristic
67C2×D88—21no—
68C2×D88C2311yescharacteristic
69C2×D88C2311yescharacteristic
70C2×D88C2311yescharacteristic
71C2×#4314—21no—
72#66951—41no—
73#66949—41no—
74#66947—41no—
75#66947—41no—
76#66938—41no—
77#66937—41no—
78#66937—41no—
79#66936—41no—
80#66928—21no—
81#66927—21no—
82C4×D44—21no—
83C4×D44—21no—
84C4×D44—21no—
85#66923—21no—
86#66922—21no—
87C4×Dic22—21no—
88C11×M32—41no—
89C2×C11×C16—41no—
90C2×C11×C16C2311yescharacteristic
91C2×C11×C16C2311yescharacteristic
92C2×C11×C16C2311yescharacteristic
93C2×C11×C16C2311yescharacteristic
94C11×#97D411yescharacteristic
95C11×#97D411yescharacteristic
96C4×C8×C11C2311yescharacteristic
97C4×C8×C11C2311yescharacteristic
98#66885—21no—
99#66885—21no—
100#66885—21no—
101#66885—21no—
102#66885—21no—
103#66885—21no—
104#66882—21no—
105#66882C2311yescharacteristic
106#66882C2311yescharacteristic
107#66882C2311yescharacteristic
108#66882C2311yescharacteristic
109#66881—21no—
110#66880—21no—
111#66880—21no—
112#66864—41no—
113#66864—41no—
114D176—41no—
115D176—41no—
116#33823—111nomaximal, Sylow
117C22×C4×C11C2×D411yescharacteristic
118C2×C22⋊D11—41no—
119C2×C22⋊D11—41no—
120C2×C22⋊D11—41no—
121C2×D44—21no—
122C2×D44—21no—
123C2×D44—21no—
124C2×D44—41no—
125C2×D44—41no—
126C2×C4×D11—41no—
127C2×C4×D11—41no—
128C2×C4×D11—41no—
129C2×Dic22—21no—
130C2×Dic22—41no—
131C11×M16—41no—
132C2×C8×C11—21no—
133C2×C8×C11—21no—
134C2×C8×C11C2×D411yescharacteristic
135C2×C8×C11C2×D411yescharacteristic
136C2×C8×C11C2×D411yescharacteristic
137C2×C8×C11C2411yescharacteristic
138C11×C4⋊C4D811yescharacteristic
139C11×C4⋊C4D811yescharacteristic
140C11×C22⋊C4D811yescharacteristic
141C11×C22⋊C4D811yescharacteristic
142C42×C11C2×D411yescharacteristic
143C42×C11C2×D411yescharacteristic
144C22⋊Dic11—41no—
145(C2×D11)⋊C4—41no—
146(C2×D11)⋊C4—41no—
147(C2×D11)⋊C4—41no—
148(C2×D11)⋊C4—41no—
149(C2×D11)⋊C4—41no—
150(C2×D11)⋊C4—41no—
151(C2×D11)⋊C4—41no—
152(C2×D11)⋊C4—41no—
153C4⋊Dic11—21no—
154C4⋊Dic11—21no—
155C4⋊Dic11—21no—
156C4⋊Dic11—21no—
157C4⋊Dic11—41no—
158Dic11⋊C4—41no—
159Dic11⋊C4—41no—
160Dic11⋊C4—41no—
161Dic11⋊C4—41no—
162C4×Dic11—41no—
163Dic44—21no—
164Dic44—21no—
165D88—21no—
166D88—21no—
167D88—21no—
168D88—21no—
169D88—21no—
170D88—21no—
171D88—42no—
172#4314—42no—
173C11×C16—21no—
174C11×C16—21no—
175C11×C16—21no—
176C11×C16—21no—
177#3176—111no—
178#3175—111no—
179#2229—111no—
180#2228—111no—
181#2226—111no—
182#2224—111no—
183#2220—111no—
184#2218—111no—
185#2217—111no—
186#2215—111no—
187#2210—111no—
188#2210—111no—
189#2207—111no—
190#2206—111no—
191#2151D1111yescharacteristic, complemented
192C23×C11C2×D811yescharacteristic
193C22×D11—41no—
194C22×D11—41no—
195C22×D11—41no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11C2×D811yescharacteristic
199C2×C4×C11C2×D811yescharacteristic
200C2×C4×C11C2×D811yescharacteristic
201C2×C4×C11C2×D811yescharacteristic
202C2×C4×C11C2×D811yescharacteristic
203C2×C4×C11C22×D411yescharacteristic
204C22⋊D11—161no—
205C22⋊D11—161no—
206C22⋊D11—161no—
207C2×Dic11—41no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212D44—41no—
213D44—41no—
214D44—41no—
215D44—41no—
216D44—41no—
217D44—41no—
218D44—161no—
219D44—161no—
220C4×D11—161no—
221C4×D11—161no—
222C4×D11—161no—
223Dic22—41no—
224Dic22—41no—
225Dic22—161no—
226C8×C11—21no—
227C8×C11—21no—
228C8×C11—21no—
229C8×C11H(5,𝔽2)11yescharacteristic
230C8×C112−1+411yescharacteristic
231#542—221no—
232#540—221no—
233C2×SD32—111no—
234C2×SD32—111no—
235C2×D16—111no—
236C2×D16—111no—
237C2×M32C2×D1111yescharacteristic
238C22×C16C2×D1111yescharacteristic
239#500—111no—
240#499—111no—
241#495—111no—
242#493—111no—
243#490—221no—
244#489—221no—
245#469—221no—
246#468—221no—
247#467—111no—
248#466—111no—
249#466—111no—
250#466—111no—
251#442—221no—
252#440—221no—
253C4×Q16—111no—
254C4×D8—111no—
255C4×D8—111no—
256C4×D8—111no—
257#405C2×D1111yescharacteristic
258#367—111no—
259#367—111no—
260#366—111no—
261#366—111no—
262C4⋊C16C2×D1111yescharacteristic
263C4⋊C16C2×D1111yescharacteristic
264C4⋊C16C2×D1111yescharacteristic
265C4⋊C16C2×D1111yescharacteristic
266#358—111no—
267#358—111no—
268#357—111no—
269#357—111no—
270#357—111no—
271#357—111no—
272#357—111no—
273#357—111no—
274C22×C11—21no—
275C22×C11—21no—
276C22×C11—21no—
277C22×C11C22×D811yescharacteristic
278C2×D11—81no—
279C2×D11—81no—
280C2×D11—81no—
281C2×D11—81no—
282C2×D11—81no—
283C2×D11—81no—
284C2×D11—81no—
285C2×D11—81no—
286C2×D11—81no—
287C4×C11—21no—
288C4×C11—21no—
289C4×C11—21no—
290C4×C11—21no—
291C4×C11—21no—
292C4×C11#53711yescharacteristic
293C4×C11#57511yescharacteristic
294Dic11—81no—
295Dic11—81no—
296Dic11—81no—
297Dic11—81no—
298Dic11—81no—
299C2×Q16—111no—
300C2×SD16—221no—
301C2×D8—111no—
302C2×D8—111no—
303C2×D8—111no—
304C2×D8—221no—
305C2×M16D4411yescharacteristic
306C22×C8C22×D1111yescharacteristic
307C4⋊Q8—221no—
308#127—221no—
309#126—441no—
310#125—221no—
311#124—221no—
312#124—441no—
313#123—441no—
314#123—441no—
315#123—441no—
316C22⋊Q8—221no—
317C22⋊Q8—441no—
318#121—221no—
319#121—221no—
320#121—221no—
321#121—441no—
322#121—441no—
323C4×Q8—221no—
324C4×D4—221no—
325C4×D4—221no—
326C4×D4—221no—
327#117D4411yescharacteristic
328SD32—441no—
329SD32—441no—
330D16—441no—
331D16—441no—
332M32—41no—
333C2×C16—41no—
334C2×C16C22×D1111yescharacteristic
335C2×C16C22×D1111yescharacteristic
336C2×C16C22×D1111yescharacteristic
337C2×C16C22×D1111yescharacteristic
338#107—111no—
339#107—111no—
340#107—111no—
341#107—111no—
342#107—221no—
343#106—221no—
344#103—221no—
345#103—221no—
346#102—221no—
347#102—221no—
348#102—221no—
349#102—221no—
350#102—221no—
351#102—221no—
352#97D4411yescharacteristic
353#97D4411yescharacteristic
354C4×C8C22×D1111yescharacteristic
355C4×C8C22×D1111yescharacteristic
356C2×C11—41no—
357C2×C11#324511yescharacteristic
358C2×C11#341511yescharacteristic
359C2×C11#341611yescharacteristic
360D11—161no—
361D11—161no—
362D11—161no—
363C2×Q8—221no—
364C2×Q8—441no—
365C2×D4—221no—
366C2×D4—221no—
367C2×D4—221no—
368C2×D4—441no—
369C2×D4—441no—
370C2×D4—441no—
371C2×D4—441no—
372C2×D4—441no—
373C22×C4—441no—
374C22×C4—441no—
375C22×C4—441no—
376C22×C4C2×D4411yescharacteristic
377Q16—221no—
378Q16—221no—
379SD16—442no—
380D8—221no—
381D8—221no—
382D8—221no—
383D8—221no—
384D8—221no—
385D8—221no—
386D8—442no—
387M16—41no—
388C2×C8—21no—
389C2×C8—21no—
390C2×C8C2×D4411yescharacteristic
391C2×C8C2×D4411yescharacteristic
392C2×C8C2×D4411yescharacteristic
393C2×C8C23×D1111yescharacteristic
394C4⋊C4—221no—
395C4⋊C4—221no—
396C4⋊C4—221no—
397C4⋊C4—221no—
398C4⋊C4—441no—
399C4⋊C4—441no—
400C4⋊C4—441no—
401C4⋊C4—441no—
402C4⋊C4—441no—
403C4⋊C4D8811yescharacteristic
404C4⋊C4D8811yescharacteristic
405C22⋊C4—441no—
406C22⋊C4—441no—
407C22⋊C4—441no—
408C22⋊C4—441no—
409C22⋊C4—441no—
410C22⋊C4—441no—
411C22⋊C4—441no—
412C22⋊C4—441no—
413C22⋊C4—441no—
414C22⋊C4D8811yescharacteristic
415C22⋊C4D8811yescharacteristic
416C42—441no—
417C42C2×D4411yescharacteristic
418C42C2×D4411yescharacteristic
419C16—21no—
420C16—21no—
421C16—21no—
422C16—21no—
423C11#3382311yescharacteristic, complemented, Sylow
424C23—441no—
425C23—441no—
426C23—441no—
427C23C2×D8811yescharacteristic
428Q8—441no—
429Q8—441no—
430Q8—1761no—
431D4—441no—
432D4—441no—
433D4—441no—
434D4—441no—
435D4—441no—
436D4—441no—
437D4—1761no—
438D4—1761no—
439D4—1761no—
440D4—1761no—
441D4—1761no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—441no—
445C2×C4—441no—
446C2×C4—441no—
447C2×C4—441no—
448C2×C4—441no—
449C2×C4—1761no—
450C2×C4—1761no—
451C2×C4—1761no—
452C2×C4C2×D8811yescharacteristic
453C2×C4C2×D8811yescharacteristic
454C2×C4C2×D8811yescharacteristic
455C2×C4C2×D8811yescharacteristic
456C2×C4C2×D8811yescharacteristic
457C2×C4C22×D4411yescharacteristic
458C8—21no—
459C8—21no—
460C8—21no—
461C8#6703711yescharacteristic
462C8#6704011yescharacteristic
463C22—21no—
464C22—21no—
465C22—21no—
466C22—881no—
467C22—881no—
468C22—881no—
469C22—881no—
470C22—881no—
471C22—881no—
472C22—881no—
473C22—881no—
474C22—881no—
475C22C22×D8811yescharacteristic
476C4—21no—
477C4—21no—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—881no—
482C4—881no—
483C4—881no—
484C4—881no—
485C4—881no—
486C4#1062304111yescharacteristic
487C4#1062327911yescharacteristic
488C2—41no—
489C2—1761no—
490C2—1761no—
491C2—1761no—
492C2#1307992611yescharacteristic
493C2#1308175711yescharacteristic
494C2#1308176411yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2151C2
socleC22×C11C22×D8
hypercenter#2151D11
hypocenterC11#33823
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #2151

Complements

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

NH ≅ G/Ntype
1. #13079266C2semidirect
2. #13079255C2semidirect
3. #13070781C2semidirect
4. #13070774C2semidirect
5. #13070764C2semidirect
6. #13070754C2semidirect
7. #13070729C2semidirect
8. #13070719C2semidirect
9. #13070712C2semidirect
10. #13070702C2semidirect
11. #13070672C2semidirect
12. #13070672C2semidirect
13. #13070657C2semidirect
14. #13070652C2semidirect
15. C11×#2151C2semidirect
191. #2151D11semidirect
423. C11#33823semidirect

Maximal subgroups

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

subgroupindex
#130792662
#130792552
#130707812
#130707742
#130707642
#130707542
#130707292
#130707192
#130707122
#130707022
#130706722
#130706572
#130706522
C11×#21512
#3382311