Finite Group Databasebeta

← #14908982

Subgroups — #14908982

Order 2816.

544 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079259C211yesmaximal, characteristic
2#13077484C211yesmaximal, characteristic, complemented
3#13070808C211yesmaximal, characteristic, complemented
4#13070804C211yesmaximal, characteristic, complemented
5#13070782C211yesmaximal, characteristic, complemented
6#13070778C211yesmaximal, characteristic, complemented
7#13070654C211yesmaximal, characteristic, complemented
8#13070654C211yesmaximal, characteristic, complemented
9#13070533C211yesmaximal, characteristic, complemented
10#13070483C211yesmaximal, characteristic, complemented
11#13070481C211yesmaximal, characteristic, complemented
12SD32×Dic11C211yesmaximal, characteristic, complemented
13#13070465C211yesmaximal, characteristic, complemented
14#13070420C211yesmaximal, characteristic, complemented
15C11×#2185C211yesmaximal, characteristic, complemented
16C22×C11×Q16C2211yescharacteristic
17#10623343—21no—
18#10623150—21no—
19C2×C11×SD32C2211yescharacteristic
20C2×C11×SD32C2211yescharacteristic
21C11×#466C2211yescharacteristic
22#10622838—21no—
23#10622797—21no—
24#10622797—21no—
25Q16×Dic11C2211yescharacteristic
26Q16×Dic11C2211yescharacteristic
27Q16×Dic11C2211yescharacteristic
28Q16×Dic11C2211yescharacteristic
29C2×#66892C2211yescharacteristic
30C2×#66892C2211yescharacteristic
31#10622764C2211yescharacteristic
32D8×Dic11C2211yescharacteristic
33#10622728C2211yescharacteristic
34#10622719C2211yescharacteristic
35#10622714C2211yescharacteristic
36#10622652—21no—
37#10622491C2211yescharacteristic
38#10622485C2211yescharacteristic
39#10622398—21no—
40#10622377—21no—
41C11×#358C2211yescharacteristic
42C11×#358C2211yescharacteristic
43C11×C22⋊C16C2211yescharacteristic
44#10622202C2211yescharacteristic
45#10622202C2211yescharacteristic
46#10622200C2211yescharacteristic
47#10622200C2211yescharacteristic
48C22⋊(C11⋊C16)C2211yescharacteristic
49#10622147C2211yescharacteristic
50#10622147C2211yescharacteristic
51#10622143C2211yescharacteristic
52#10622142C2211yescharacteristic
53#10622140C2211yescharacteristic
54Dic11⋊C16C2211yescharacteristic
55Dic11⋊C16C2211yescharacteristic
56C16×Dic11C2211yescharacteristic
57#10622128C2211yescharacteristic
58#10622127C2211yescharacteristic
59C22×Q8×C11—21no—
60C2×C11×Q16—22no—
61C2×C11×Q16—22no—
62C2×C11×Q16—21no—
63C2×C11×Q16C2311yescharacteristic
64C2×C11×Q16C2311yescharacteristic
65C2×C11×D8C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C11×#121—21no—
68Q8×Dic11—21no—
69Q8×Dic11—21no—
70Q8×Dic11—21no—
71Q8×Dic11—21no—
72Q8×Dic11—41no—
73Q8×Dic11—41no—
74#66993—21no—
75#66992—41no—
76#66991—41no—
77D4×Dic11—21no—
78C2×#4323—21no—
79#66983—21no—
80#66979—21no—
81#66979—41no—
82#66979—41no—
83#66979D411yescharacteristic
84C2×#4318D411yescharacteristic
85C2×D88C2311yescharacteristic
86#66946—21no—
87#66943—21no—
88#66939—41no—
89#66936—41no—
90C11×SD32—22no—
91C11×SD32—22no—
92C2×C11×C16C2311yescharacteristic
93C2×C11×C16C2311yescharacteristic
94C11×#107C2311yescharacteristic
95C11×#102—21no—
96#66899—21no—
97#66899—21no—
98#66899—21no—
99#66899—21no—
100#66896—21no—
101#66892—22no—
102#66892—22no—
103#66885—21no—
104#66882C2311yescharacteristic
105#66882C2311yescharacteristic
106#66882C2311yescharacteristic
107#66881—21no—
108#66879D411yescharacteristic
109#66879D411yescharacteristic
110C8×Dic11C2311yescharacteristic
111C8×Dic11C2311yescharacteristic
112C2×C11⋊C16C2311yescharacteristic
113C2×C11⋊C16C2311yescharacteristic
114#66873—21no—
115#66872—21no—
116#33686—111nomaximal, Sylow
117C2×Q8×C11—24no—
118C2×Q8×C11—21no—
119C2×Q8×C11—21no—
120C2×Q8×C11—42no—
121C2×Q8×C11—41no—
122C2×D4×C11—21no—
123C2×D4×C11—41no—
124C22×C4×C11—41no—
125C22×C4×C11C2×D411yescharacteristic
126C2×C22⋊D11—41no—
127C2×C22⋊D11—41no—
128C2×C22⋊D11—41no—
129C22×Dic11—41no—
130C2×D44—21no—
131C2×C4×D11—41no—
132C11×Q16—24no—
133C11×Q16—21no—
134C11×Q16—21no—
135C11×Q16#4112yes—
136C11×Q16#4112yes—
137C11×D8—21no—
138C11×D8—21no—
139C2×C8×C11—21no—
140C2×C8×C11—21no—
141C2×C8×C11C2×D411yescharacteristic
142C2×C8×C11C2411yescharacteristic
143C11×C4⋊C4—21no—
144C11×C22⋊C4—41no—
145C22⋊Dic11—41no—
146C22⋊Dic11—41no—
147C22⋊Dic11D811yescharacteristic
148C22⋊Dic11D811yescharacteristic
149#4323—42no—
150(C2×D11)⋊C4—41no—
151(C2×D11)⋊C4—41no—
152C4⋊Dic11—21no—
153C4⋊Dic11—21no—
154C4⋊Dic11—21no—
155C4⋊Dic11—41no—
156C4⋊Dic11—41no—
157C4⋊Dic11—41no—
158C4⋊Dic11—41no—
159C4⋊Dic11—41no—
160C4⋊Dic11D811yescharacteristic
161C4⋊Dic11D811yescharacteristic
162Dic11⋊C4—41no—
163C4×Dic11—41no—
164C4×Dic11—41no—
165C4×Dic11—41no—
166C4×Dic11—41no—
167C4×Dic11—41no—
168C4×Dic11C2×D411yescharacteristic
169C4×Dic11C2×D411yescharacteristic
170#4318—41no—
171C2×C11⋊C8C2×D411yescharacteristic
172C2×C11⋊C8C2×D411yescharacteristic
173D88—21no—
174D88—21no—
175C11×C16—21no—
176C11×C16—21no—
177C11⋊C16—21no—
178C11⋊C16—21no—
179#3176—111no—
180#2950—111no—
181#2234—111no—
182#2234—111no—
183#2229—111no—
184#2229—111no—
185#2207—111no—
186#2207—111no—
187#2185—111no—
188#2185D1111yescharacteristic, complemented
189#2175—111no—
190#2175—111no—
191C4×SD32—111no—
192C4×SD32—111no—
193#2164—111no—
194C23×C11—41no—
195C23×C11C2×D811yescharacteristic
196C22×D11—41no—
197Q8×C11—22no—
198Q8×C11—22no—
199Q8×C11—44no—
200Q8×C11—41no—
201Q8×C11—41no—
202D4×C11—41no—
203D4×C11—41no—
204D4×C11—161no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—44no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11C2×D811yescharacteristic
212C2×C4×C11C22×D411yescharacteristic
213C22⋊D11—161no—
214C22⋊D11—161no—
215C22⋊D11—161no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11—41no—
219C2×Dic11—161no—
220C2×Dic11C2×D811yescharacteristic
221C2×Dic11C2×D811yescharacteristic
222C2×Dic11C2×D811yescharacteristic
223C2×Dic11C2×D811yescharacteristic
224D44—41no—
225D44—41no—
226C4×D11—161no—
227C8×C11—21no—
228C8×C11C2×#4111yescharacteristic
229C8×C11C2×#4111yescharacteristic
230C11⋊C8—21no—
231C11⋊C8—21no—
232C22×Q16C2×D1111yescharacteristic
233#540—221no—
234#519—221no—
235C2×SD32—111no—
236C2×SD32—111no—
237C2×SD32C2×D1111yescharacteristic
238C2×SD32C2×D1111yescharacteristic
239#499—111no—
240#493—111no—
241#490—221no—
242#469—221no—
243#466—111no—
244#466C2×D1111yescharacteristic
245#442—221no—
246#441—221no—
247#441—221no—
248C4×Q16—111no—
249C4×Q16—111no—
250C4×Q16—111no—
251C4×Q16—111no—
252C4×D8—111no—
253C4×D8—111no—
254#427—111no—
255#419—221no—
256#405—111no—
257#367—111no—
258#367—111no—
259#366—111no—
260#366—111no—
261C4⋊C16—111no—
262C4⋊C16—111no—
263#358—111no—
264#358—111no—
265#358C2×D1111yescharacteristic
266#358C2×D1111yescharacteristic
267#357—111no—
268#357—111no—
269#357—111no—
270#357—111no—
271C22⋊C16—111no—
272C22⋊C16C2×D1111yescharacteristic
273#346—111no—
274C4×C16—111no—
275C22×C11—21no—
276C22×C11—21no—
277C22×C11—21no—
278C22×C11—81no—
279C22×C11—81no—
280C22×C11—81no—
281C22×C11C22×D811yescharacteristic
282C2×D11—81no—
283C2×D11—81no—
284C2×D11—81no—
285C4×C11—21no—
286C4×C11—42no—
287C4×C11—42no—
288C4×C11—81no—
289C4×C11#52511yescharacteristic
290C4×C11#57511yescharacteristic
291Dic11—21no—
292Dic11—21no—
293Dic11—21no—
294Dic11—21no—
295Dic11—81no—
296Dic11—81no—
297Dic11—81no—
298C22×Q8—21no—
299C2×Q16—22no—
300C2×Q16—22no—
301C2×Q16—21no—
302C2×Q16C22×D1111yescharacteristic
303C2×Q16C22×D1111yescharacteristic
304C2×D8—111no—
305C2×D8—221no—
306C2×D8C22×D1111yescharacteristic
307C2×M16—111no—
308C22×C8C22×D1111yescharacteristic
309#127—221no—
310#125—221no—
311#123—441no—
312#123—441no—
313#121—21no—
314#121—221no—
315#121—441no—
316#121—441no—
317C4×Q8—221no—
318C4×Q8—221no—
319C4×Q8—221no—
320C4×Q8—221no—
321C4×Q8—441no—
322C4×Q8—441no—
323C4×D4—221no—
324C4×D4—221no—
325#117—111no—
326#117—221no—
327#117—441no—
328#117—441no—
329SD32—22no—
330SD32—22no—
331SD32—222no—
332SD32—222no—
333C2×C16—111no—
334C2×C16—111no—
335C2×C16C22×D1111yescharacteristic
336C2×C16C22×D1111yescharacteristic
337#107—111no—
338#107—111no—
339#107—111no—
340#107C22×D1111yescharacteristic
341#106—221no—
342#106—221no—
343#103—221no—
344#103—221no—
345#103—221no—
346#103—221no—
347#102—21no—
348#102—221no—
349#102—221no—
350#102—221no—
351#97—111no—
352#97—111no—
353C4×C8—111no—
354C4×C8—111no—
355C2×C11—41no—
356C2×C11—161no—
357C2×C11#310011yescharacteristic
358C2×C11#341611yescharacteristic
359C2×C11#341611yescharacteristic
360D11—161no—
361C2×Q8—24no—
362C2×Q8—21no—
363C2×Q8—21no—
364C2×Q8—42no—
365C2×Q8—41no—
366C2×D4—21no—
367C2×D4—41no—
368C2×D4—221no—
369C2×D4—441no—
370C2×D4—441no—
371C2×D4—441no—
372C22×C4—41no—
373C22×C4—441no—
374C22×C4—441no—
375C22×C4D4×D1111yescharacteristic
376Q16—24no—
377Q16—21no—
378Q16—21no—
379Q16#434112yes—
380Q16#434112yes—
381D8—21no—
382D8—21no—
383D8—221no—
384D8—221no—
385D8—442no—
386M16—441no—
387C2×C8—21no—
388C2×C8—21no—
389C2×C8—111no—
390C2×C8—111no—
391C2×C8D4×D1111yescharacteristic
392C2×C8C23×D1111yescharacteristic
393C4⋊C4—21no—
394C4⋊C4—111no—
395C4⋊C4—111no—
396C4⋊C4—221no—
397C4⋊C4—221no—
398C4⋊C4—221no—
399C4⋊C4—441no—
400C4⋊C4—441no—
401C4⋊C4—441no—
402C4⋊C4—441no—
403C4⋊C4—441no—
404C4⋊C4—441no—
405C22⋊C4—41no—
406C22⋊C4—111no—
407C22⋊C4—111no—
408C22⋊C4—441no—
409C22⋊C4—441no—
410C22⋊C4—441no—
411C22⋊C4—441no—
412C42—111no—
413C42—111no—
414C42—441no—
415C42—441no—
416C42—441no—
417C42—441no—
418C42—441no—
419C16—21no—
420C16—21no—
421C16—221no—
422C16—221no—
423C11#3368611yescharacteristic, complemented, Sylow
424C23—41no—
425C23—441no—
426C23D8×D1111yescharacteristic
427Q8—22no—
428Q8—22no—
429Q8—44no—
430Q8—41no—
431Q8—41no—
432D4—41no—
433D4—41no—
434D4—161no—
435D4—441no—
436D4—441no—
437D4—1761no—
438D4—1761no—
439D4—1761no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—44no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—111no—
447C2×C4—111no—
448C2×C4—111no—
449C2×C4—111no—
450C2×C4—441no—
451C2×C4—441no—
452C2×C4—441no—
453C2×C4—1761no—
454C2×C4—1761no—
455C2×C4D8×D1111yescharacteristic
456C2×C4C2×D4×D1111yescharacteristic
457C8—21no—
458C8—221no—
459C8—221no—
460C8C2×#434111yescharacteristic
461C8C2×#434111yescharacteristic
462C22—21no—
463C22—21no—
464C22—21no—
465C22—81no—
466C22—81no—
467C22—81no—
468C22—881no—
469C22—881no—
470C22—881no—
471C22C2×D8×D1111yescharacteristic
472C4—21no—
473C4—42no—
474C4—42no—
475C4—81no—
476C4—221no—
477C4—221no—
478C4—221no—
479C4—221no—
480C4—881no—
481C4—881no—
482C4—881no—
483C4#1062311711yescharacteristic
484C4#1062330411yescharacteristic
485C2—41no—
486C2—161no—
487C2—1761no—
488C2#1307861111yescharacteristic
489C2#1308175811yescharacteristic
490C2#1308176111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2185C2
socleC22×C11C22×D8
prime radical#13079259C2
hypercenter#2185D11
hypocenterC11#33686
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2185

Complements

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

NH ≅ G/Ntype
2. #13077484C2semidirect
3. #13070808C2semidirect
4. #13070804C2semidirect
5. #13070782C2semidirect
6. #13070778C2semidirect
7. #13070654C2semidirect
8. #13070654C2semidirect
9. #13070533C2semidirect
10. #13070483C2semidirect
11. #13070481C2semidirect
12. SD32×Dic11C2semidirect
13. #13070465C2semidirect
14. #13070420C2semidirect
15. C11×#2185C2semidirect
188. #2185D11semidirect
423. C11#33686semidirect

Maximal subgroups

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

subgroupindex
#130792592
#130774842
#130708082
#130708042
#130707822
#130707782
#130706542
#130705332
#130704832
#130704812
SD32×Dic112
#130704652
#130704202
C11×#21852
#3368611