Finite Group Databasebeta

← #14911507

Subgroups — #14911507

Order 2816.

518 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081589C211yesmaximal, characteristic
2#13081507C211yesmaximal, characteristic, complemented
3#13070857C211yesmaximal, characteristic, complemented
4#13070856C211yesmaximal, characteristic, complemented
5#13070838C211yesmaximal, characteristic, complemented
6#13070775C211yesmaximal, characteristic, complemented
7#13070774C211yesmaximal, characteristic, complemented
8#13070751C211yesmaximal, characteristic, complemented
9#13070654C211yesmaximal, characteristic, complemented
10#13070654C211yesmaximal, characteristic, complemented
11#13070523C211yesmaximal, characteristic, complemented
12#13070481C211yesmaximal, characteristic, complemented
13#13070478C211yesmaximal, characteristic, complemented
14SD32×Dic11C211yesmaximal, characteristic, complemented
15C11×#2207C211yesmaximal, characteristic, complemented
16#10623249—21no—
17#10623100—21no—
18C2×C11×SD32C2211yescharacteristic
19C2×C11×SD32C2211yescharacteristic
20C11×#493C2211yescharacteristic
21C4×C11×Q16C2211yescharacteristic
22Q16×Dic11C2211yescharacteristic
23Q16×Dic11C2211yescharacteristic
24C2×#66892C2211yescharacteristic
25#10622764C2211yescharacteristic
26#10622764C2211yescharacteristic
27#10622763—21no—
28#10622763—21no—
29D8×Dic11C2211yescharacteristic
30D8×Dic11C2211yescharacteristic
31#10622685—21no—
32#10622635—21no—
33#10622491C2211yescharacteristic
34#10622487C2211yescharacteristic
35#10622412—21no—
36#10622404—21no—
37C4×D88C2211yescharacteristic
38#10622296C2211yescharacteristic
39C8×Dic22C2211yescharacteristic
40C11×C4⋊C16C2211yescharacteristic
41C11×#357C2211yescharacteristic
42C11×#357C2211yescharacteristic
43#10622202C2211yescharacteristic
44#10622200C2211yescharacteristic
45#10622200C2211yescharacteristic
46#10622200C2211yescharacteristic
47#10622200C2211yescharacteristic
48#10622147C2211yescharacteristic
49#10622147C2211yescharacteristic
50#10622143C2211yescharacteristic
51#10622142C2211yescharacteristic
52#10622140C2211yescharacteristic
53Dic11⋊C16C2211yescharacteristic
54Dic11⋊C16C2211yescharacteristic
55C16×Dic11C2211yescharacteristic
56#10622129C2211yescharacteristic
57#10622127C2211yescharacteristic
58#10622099C2211yescharacteristic
59C2×#4341—41no—
60C2×C11×Q16C2311yescharacteristic
61C2×C11×D8—21no—
62C2×C11×D8C2311yescharacteristic
63C2×C11×D8C2311yescharacteristic
64C11×#127—21no—
65C4×Q8×C11—21no—
66Q8×Dic11—21no—
67Q8×Dic11—21no—
68#66993—21no—
69#66993—21no—
70#66992—41no—
71#66992—41no—
72#66991—41no—
73D4×Dic11—21no—
74D4×Dic11—21no—
75C2×#4323—21no—
76C2×#4323—21no—
77C2×D88C2311yescharacteristic
78#66943—21no—
79#66943—41no—
80#66941—21no—
81#66941—41no—
82C4×D44—21no—
83#66923—21no—
84#66923—41no—
85C4×Dic22—41no—
86C4×Dic22D411yescharacteristic
87C11×SD32—22no—
88C11×SD32—22no—
89C2×C11×C16C2311yescharacteristic
90C2×C11×C16C2311yescharacteristic
91C11×#107C2311yescharacteristic
92C11×#103—21no—
93C4×C8×C11C2311yescharacteristic
94#66899—21no—
95#66899—21no—
96#66896—21no—
97#66896—21no—
98#66892—22no—
99#66885—21no—
100#66882C2311yescharacteristic
101#66882C2311yescharacteristic
102#66882C2311yescharacteristic
103#66881—21no—
104Dic11⋊C8D411yescharacteristic
105Dic11⋊C8D411yescharacteristic
106C8×Dic11C2311yescharacteristic
107C8×Dic11C2311yescharacteristic
108C2×C11⋊C16C2311yescharacteristic
109C2×C11⋊C16C2311yescharacteristic
110#66872—21no—
111#66871—21no—
112C4⋊(C11⋊C8)D411yescharacteristic
113#33935—111nomaximal, Sylow
114C2×Q8×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—41no—
118C2×D4×C11—41no—
119C2×C22⋊D11—41no—
120C2×C22⋊D11—41no—
121C2×C22⋊D11—41no—
122C2×C22⋊D11—41no—
123C22×Dic11—41no—
124C22×Dic11—41no—
125#4341—84no—
126C2×D44—21no—
127C2×C4×D11—41no—
128C2×Dic22—41no—
129C2×Dic22D811yescharacteristic
130C11×Q16—21no—
131C11×Q16#4112yescomplemented
132C11×D8—21no—
133C11×D8—21no—
134C11×D8—21no—
135C11×D8—21no—
136C11×D8—81no—
137C2×C8×C11C2×D411yescharacteristic
138C2×C8×C11C2411yescharacteristic
139C11×C4⋊C4—21no—
140C11×C4⋊C4—41no—
141C42×C11—41no—
142C42×C11C2×D411yescharacteristic
143C22⋊Dic11—41no—
144C22⋊Dic11—41no—
145#4323—81no—
146#4323—81no—
147(C2×D11)⋊C4—41no—
148C4⋊Dic11—21no—
149C4⋊Dic11—21no—
150C4⋊Dic11—21no—
151C4⋊Dic11—41no—
152C4⋊Dic11—41no—
153C4⋊Dic11—41no—
154C4⋊Dic11D811yescharacteristic
155Dic11⋊C4—41no—
156Dic11⋊C4—41no—
157Dic11⋊C4—41no—
158Dic11⋊C4—41no—
159Dic11⋊C4D811yescharacteristic
160Dic11⋊C4D811yescharacteristic
161C4×Dic11—41no—
162C4×Dic11—41no—
163C4×Dic11C2×D411yescharacteristic
164C4×Dic11C2×D411yescharacteristic
165C2×C11⋊C8C2×D411yescharacteristic
166C2×C11⋊C8C2×D411yescharacteristic
167D88—21no—
168D88—21no—
169C11×C16—21no—
170C11×C16—21no—
171C11⋊C16—21no—
172C11⋊C16—21no—
173#3391—111no—
174#3383—111no—
175#2244—111no—
176#2244—111no—
177#2240—111no—
178#2228—111no—
179#2228—111no—
180#2224—111no—
181#2207—111no—
182#2207—111no—
183#2207D1111yescharacteristic, complemented
184#2183—111no—
185#2175—111no—
186#2175—111no—
187C4×SD32—111no—
188C23×C11—41no—
189C23×C11—41no—
190C22×D11—41no—
191Q8×C11—22no—
192Q8×C11—41no—
193D4×C11—41no—
194D4×C11—41no—
195D4×C11—41no—
196D4×C11—41no—
197D4×C11—82no—
198D4×C11—161no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11C2×D811yescharacteristic
202C2×C4×C11C2×D811yescharacteristic
203C2×C4×C11C22×D411yescharacteristic
204C22⋊D11—82no—
205C22⋊D11—82no—
206C22⋊D11—161no—
207C22⋊D11—161no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—82no—
212C2×Dic11—82no—
213C2×Dic11C2×D811yescharacteristic
214C2×Dic11C2×D811yescharacteristic
215C2×Dic11C2×D811yescharacteristic
216C2×Dic11C2×D811yescharacteristic
217D44—41no—
218D44—41no—
219C4×D11—82no—
220Dic22—22no—
221Dic22—82no—
222C8×C11—21no—
223C8×C11C2×#4111yescharacteristic
224C8×C112−1+411yescharacteristic
225C11⋊C8—21no—
226C11⋊C8—21no—
227#557—221no—
228#550—221no—
229C2×SD32—111no—
230C2×SD32C2×D1111yescharacteristic
231C2×SD32C2×D1111yescharacteristic
232#500—111no—
233#499—111no—
234#499—111no—
235#493—111no—
236#493—111no—
237#493C2×D1111yescharacteristic
238#479—221no—
239#479—221no—
240#475—221no—
241#459—221no—
242#459—221no—
243#459—221no—
244C8×Q8—111no—
245C4×Q16—111no—
246C4×Q16—111no—
247C4×Q16C2×D1111yescharacteristic
248C4×D8—111no—
249C4×D8—111no—
250C4×D8—111no—
251#367—111no—
252#366—111no—
253#366—111no—
254C4⋊C16—111no—
255C4⋊C16—111no—
256C4⋊C16C2×D1111yescharacteristic
257#358—111no—
258#357—111no—
259#357—111no—
260#357—111no—
261#357—111no—
262#357—111no—
263#357—111no—
264#357—111no—
265#357C2×D1111yescharacteristic
266#357C2×D1111yescharacteristic
267#346—111no—
268#346—111no—
269C4×C16—111no—
270C22×C11—81no—
271C22×C11—81no—
272C22×C11—81no—
273C22×C11—81no—
274C22×C11—81no—
275C22×C11—81no—
276C22×C11C22×D811yescharacteristic
277C2×D11—81no—
278C2×D11—81no—
279C2×D11—81no—
280C4×C11—21no—
281C4×C11—21no—
282C4×C11—42no—
283C4×C11—81no—
284C4×C11#54811yescharacteristic
285C4×C11#57711yescharacteristic
286Dic11—21no—
287Dic11—21no—
288Dic11—21no—
289Dic11—81no—
290Dic11—81no—
291Dic11—81no—
292Dic11#50912yes—
293C2×#41—441no—
294C2×Q16C22×D1111yescharacteristic
295C2×D8—21no—
296C2×D8—111no—
297C2×D8—221no—
298C2×D8—221no—
299C2×D8C22×D1111yescharacteristic
300C2×D8C22×D1111yescharacteristic
301C4⋊Q8—221no—
302C4⋊Q8—441no—
303#127—21no—
304#127—221no—
305#127—221no—
306#125—221no—
307#125—221no—
308#125—441no—
309#125—441no—
310#121—441no—
311#121—441no—
312#121—441no—
313C4×Q8—21no—
314C4×Q8—111no—
315C4×Q8—221no—
316C4×Q8—221no—
317C4×Q8—441no—
318C4×D4—221no—
319C4×D4—221no—
320C4×D4—221no—
321SD32—22no—
322SD32—22no—
323SD32—222no—
324C2×C16—111no—
325C2×C16—111no—
326C2×C16C22×D1111yescharacteristic
327C2×C16C22×D1111yescharacteristic
328#107—111no—
329#107—111no—
330#107—111no—
331#107—221no—
332#107C22×D1111yescharacteristic
333#106—221no—
334#106—221no—
335C4⋊C8—111no—
336C4⋊C8—111no—
337C4⋊C8—111no—
338#103—21no—
339#103—221no—
340#103—221no—
341#102—221no—
342#102—221no—
343#102—221no—
344C4×C8—111no—
345C4×C8—111no—
346C4×C8C22×D1111yescharacteristic
347C2×C11—161no—
348C2×C11—161no—
349C2×C11#335811yescharacteristic
350C2×C11C2×#50911yescharacteristic
351C2×C11#341611yescharacteristic
352D11—161no—
353#41—884no—
354C2×Q8—21no—
355C2×Q8—111no—
356C2×Q8—441no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—41no—
360C2×D4—41no—
361C2×D4—221no—
362C2×D4—441no—
363C2×D4—441no—
364C2×D4—441no—
365C2×D4—441no—
366C22×C4—441no—
367C22×C4—441no—
368C22×C4—441no—
369Q16—21no—
370Q16#434112yescomplemented
371D8—21no—
372D8—21no—
373D8—21no—
374D8—21no—
375D8—81no—
376D8—221no—
377D8—221no—
378D8—881no—
379D8—881no—
380C2×C8—111no—
381C2×C8—111no—
382C2×C8D4×D1111yescharacteristic
383C2×C8C23×D1111yescharacteristic
384C4⋊C4—21no—
385C4⋊C4—41no—
386C4⋊C4—111no—
387C4⋊C4—111no—
388C4⋊C4—111no—
389C4⋊C4—221no—
390C4⋊C4—221no—
391C4⋊C4—221no—
392C4⋊C4—441no—
393C4⋊C4—441no—
394C4⋊C4—441no—
395C4⋊C4—441no—
396C4⋊C4—441no—
397C4⋊C4—441no—
398C4⋊C4—441no—
399C22⋊C4—441no—
400C22⋊C4—441no—
401C22⋊C4—441no—
402C42—41no—
403C42—111no—
404C42—111no—
405C42—441no—
406C42—441no—
407C42D4×D1111yescharacteristic
408C16—21no—
409C16—21no—
410C16—221no—
411C16—221no—
412C11#3393511yescharacteristic, complemented, Sylow
413C23—41no—
414C23—41no—
415C23—441no—
416Q8—22no—
417Q8—41no—
418Q8—222no—
419Q8—882no—
420D4—41no—
421D4—41no—
422D4—41no—
423D4—41no—
424D4—82no—
425D4—161no—
426D4—441no—
427D4—441no—
428D4—882no—
429D4—882no—
430D4—1761no—
431D4—1761no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—111no—
435C2×C4—111no—
436C2×C4—111no—
437C2×C4—111no—
438C2×C4—441no—
439C2×C4—441no—
440C2×C4—441no—
441C2×C4—882no—
442C2×C4—882no—
443C2×C4—882no—
444C2×C4D8×D1111yescharacteristic
445C2×C4D8×D1111yescharacteristic
446C2×C4C2×D4×D1111yescharacteristic
447C8—21no—
448C8—221no—
449C8—221no—
450C8C2×#434111yescharacteristic
451C8#6704311yescharacteristic
452C22—81no—
453C22—81no—
454C22—81no—
455C22—81no—
456C22—81no—
457C22—81no—
458C22—881no—
459C22—881no—
460C22—881no—
461C22C2×D8×D1111yescharacteristic
462C4—21no—
463C4—21no—
464C4—42no—
465C4—81no—
466C4—112no—
467C4—221no—
468C4—221no—
469C4—221no—
470C4—881no—
471C4—881no—
472C4—881no—
473C4#1062312911yescharacteristic
474C4#1062330611yescharacteristic
475C2—161no—
476C2—161no—
477C2—1761no—
478C2#1308124611yescharacteristic
479C2D11×#50911yescharacteristic
480C2#1308175811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2207C2
socleC22×C11C22×D8
prime radical#13081589C2
hypercenter#2207D11
hypocenterC11#33935
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2207

Complements

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

NH ≅ G/Ntype
2. #13081507C2semidirect
3. #13070857C2semidirect
4. #13070856C2semidirect
5. #13070838C2semidirect
6. #13070775C2semidirect
7. #13070774C2semidirect
8. #13070751C2semidirect
9. #13070654C2semidirect
10. #13070654C2semidirect
11. #13070523C2semidirect
12. #13070481C2semidirect
13. #13070478C2semidirect
14. SD32×Dic11C2semidirect
15. C11×#2207C2semidirect
131. C11×Q16#41semidirect
183. #2207D11semidirect
370. Q16#4341semidirect
412. C11#33935semidirect

Maximal subgroups

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

subgroupindex
#130815892
#130815072
#130708572
#130708562
#130708382
#130707752
#130707742
#130707512
#130706542
#130705232
#130704812
#130704782
SD32×Dic112
C11×#22072
#3393511