Finite Group Databasebeta

← #14908627

Subgroups — #14908627

Order 2816.

556 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078266C211yesmaximal, characteristic
2#13077212C211yesmaximal, characteristic
3#13070826C211yesmaximal, characteristic, complemented
4#13070825C211yesmaximal, characteristic, complemented
5#13070823C211yesmaximal, characteristic, complemented
6#13070821C211yesmaximal, characteristic, complemented
7#13070820C211yesmaximal, characteristic, complemented
8#13070813C211yesmaximal, characteristic, complemented
9#13070812C211yesmaximal, characteristic, complemented
10#13070401C211yesmaximal, characteristic, complemented
11#13070397C211yesmaximal, characteristic, complemented
12#13070334C211yesmaximal, characteristic, complemented
13D11×#358C211yesmaximal, characteristic, complemented
14#13070228C211yesmaximal, characteristic
15C11×#2236C211yesmaximal, characteristic, complemented
16C2×Q16×D11C2211yescharacteristic
17C2×#66954C2211yescharacteristic
18#10623159—21no—
19#10623035—21no—
20C11×#467C2211yescharacteristic
21C2×C11×#107C2211yescharacteristic
22#10622801C2211yescharacteristic
23#10622729C2211yescharacteristic
24#10622719C2211yescharacteristic
25#10622665—21no—
26#10622577—21no—
27C2×#66862C2211yescharacteristic
28C2×C16×D11C2211yescharacteristic
29#10622500C2211yescharacteristic
30#10622494—21no—
31#10622494—21no—
32#10622493C2211yescharacteristic
33#10622493C2211yescharacteristic
34#10622493C2211yescharacteristic
35D11×#107C2211yescharacteristic
36D11×#107C2211yescharacteristic
37#10622429—21no—
38#10622415—21no—
39C11×#366C2211yescharacteristic
40C11×#366C2211yescharacteristic
41C11×#358C2211yescharacteristic
42C11×#358C2211yescharacteristic
43C11×C22⋊C16C2211yescharacteristic
44#10622202C2211yescharacteristic
45#10622202C2211yescharacteristic
46C22⋊(C11⋊C16)C2211yescharacteristic
47(C2×D11)⋊C16C2211yescharacteristic
48(C2×D11)⋊C16C2211yescharacteristic
49#10622143C2211yescharacteristic
50#10622142C2211yescharacteristic
51#10622141C2211yescharacteristic
52#10622141C2211yescharacteristic
53#10622130C2211yescharacteristic
54#10622130C2211yescharacteristic
55#10622128C2211yescharacteristic
56#10622128C2211yescharacteristic
57#10622128C2211yescharacteristic
58#10622127C2211yescharacteristic
59C2×Q8×D11—21no—
60C2×#4339D411yescharacteristic
61C2×C11×Q16C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C11×C22⋊Q8—21no—
64C2×C11×C4⋊C4—21no—
65#66999—21no—
66C2×#4326—21no—
67C4×C22⋊D11—41no—
68C4×C22⋊D11—41no—
69#66979—21no—
70#66977—21no—
71C2×#4318D411yescharacteristic
72Q16×D11—22no—
73Q16×D11—22no—
74C2×Dic44C2311yescharacteristic
75#66954—22no—
76#66954—22no—
77C2×#4313D411yescharacteristic
78C2×#4313D411yescharacteristic
79C2×C8×D11C2311yescharacteristic
80C2×C8×D11C2311yescharacteristic
81#66950—21no—
82#66947—41no—
83#66946—41no—
84#66945—21no—
85#66945—21no—
86#66945—21no—
87C4⋊C4×D11—21no—
88C4⋊C4×D11—21no—
89#66941—41no—
90#66940—41no—
91#66938—41no—
92#66936—41no—
93C2×C11×C16C2311yescharacteristic
94C2×C11×C16C2311yescharacteristic
95C11×#107—21no—
96C11×#107C2311yescharacteristic
97C11×#107C2311yescharacteristic
98C11×#107C2311yescharacteristic
99C11×#103—21no—
100#66899—21no—
101#66882C2311yescharacteristic
102#66882C2311yescharacteristic
103#66882C2311yescharacteristic
104#66881—21no—
105#66880—21no—
106C2×C11⋊C16C2311yescharacteristic
107C2×C11⋊C16C2311yescharacteristic
108#66874—21no—
109#66872—21no—
110#66872—21no—
111#66872—21no—
112#66871—21no—
113#66871—21no—
114#66862—22no—
115C16×D11—22no—
116#33651—111nomaximal, Sylow
117C2×Q8×C11—21no—
118C22×C4×C11—41no—
119C22×C4×C11C2×D411yescharacteristic
120C2×C22⋊D11D811yescharacteristic
121C2×C22⋊D11D811yescharacteristic
122Q8×D11—42no—
123Q8×D11—42no—
124#4339—22no—
125#4339—22no—
126C2×D44D811yescharacteristic
127C2×C4×D11—41no—
128C2×C4×D11—41no—
129C2×C4×D11—41no—
130C2×C4×D11C2×D411yescharacteristic
131C2×C4×D11C2×D411yescharacteristic
132C2×Dic22—21no—
133C2×Dic22—41no—
134C2×Dic22D811yescharacteristic
135C11×Q16—21no—
136C11×Q16—21no—
137C2×C8×C11—21no—
138C2×C8×C11—21no—
139C2×C8×C11C2×D411yescharacteristic
140C2×C8×C11C2411yescharacteristic
141C11×C4⋊C4—21no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—41no—
145C11×C4⋊C4—41no—
146C11×C22⋊C4—41no—
147C22⋊Dic11—41no—
148C22⋊Dic11—41no—
149#4326—42no—
150(C2×D11)⋊C4—41no—
151(C2×D11)⋊C4—41no—
152(C2×D11)⋊C4—41no—
153(C2×D11)⋊C4—41no—
154(C2×D11)⋊C4—41no—
155C4⋊Dic11—21no—
156C4⋊Dic11—21no—
157C4⋊Dic11—21no—
158C4⋊Dic11—41no—
159Dic11⋊C4—41no—
160Dic11⋊C4—41no—
161Dic11⋊C4—41no—
162Dic11⋊C4—41no—
163C4×Dic11—41no—
164C4×Dic11—41no—
165C4×Dic11—41no—
166C4×Dic11—41no—
167#4318—22no—
168C2×C11⋊C8C2×D411yescharacteristic
169C2×C11⋊C8C2×D411yescharacteristic
170Dic44—21no—
171Dic44—21no—
172#4313—22no—
173#4313—22no—
174C8×D11—21no—
175C8×D11—21no—
176C8×D11#4112yes—
177C8×D11#4112yes—
178C11×C16—21no—
179C11×C16—21no—
180C11⋊C16—21no—
181C11⋊C16—21no—
182#3059—111no—
183#2913—111no—
184#2237—111no—
185#2237—111no—
186#2237—111no—
187#2237—111no—
188#2236—111no—
189#2236D1111yescharacteristic, complemented
190#2235—111no—
191#2235—111no—
192#2159—111no—
193#2158—111no—
194#2141—111no—
195C2×#358—111no—
196#2113—111no—
197C23×C11C2×D811yescharacteristic
198C22×D11C2×D811yescharacteristic
199C22×D11C2×D811yescharacteristic
200Q8×C11—41no—
201Q8×C11—41no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—161no—
209C2×C4×C11C2×D811yescharacteristic
210C2×C4×C11C22×D411yescharacteristic
211C22⋊D11—22no—
212C22⋊D11—22no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11C2×D811yescharacteristic
218C2×Dic11C2×D811yescharacteristic
219D44—22no—
220C4×D11—21no—
221C4×D11—21no—
222C4×D11—82no—
223C4×D11—161no—
224C4×D11—161no—
225C4×D11#12312yes—
226C4×D11#13712yes—
227Dic22—22no—
228Dic22—41no—
229Dic22—41no—
230Dic22—82no—
231C8×C11—21no—
232C8×C11C2×#4111yescharacteristic
233C8×C11C2×#4111yescharacteristic
234C11⋊C8—21no—
235C11⋊C8#12312yes—
236C22×Q16—111no—
237C2×#131—111no—
238#536—221no—
239#520—221no—
240C2×M32—111no—
241C22×C16—111no—
242#470—221no—
243#470—221no—
244#467—111no—
245#467—111no—
246#467—111no—
247#467C2×D1111yescharacteristic
248#428—221no—
249#428—221no—
250#428—221no—
251#427—111no—
252#427—111no—
253#427—111no—
254#427—111no—
255C2×#107—111no—
256C2×#107—111no—
257C2×#107C2×D1111yescharacteristic
258#419—221no—
259#367—111no—
260#367—111no—
261#367—111no—
262#367—111no—
263#366—111no—
264#366—111no—
265#366C2×D1111yescharacteristic
266#366C2×D1111yescharacteristic
267#358—111no—
268#358—111no—
269#358—111no—
270#358—111no—
271#358—111no—
272#358—111no—
273#358C2×D1111yescharacteristic
274#358C2×D1111yescharacteristic
275C22⋊C16—111no—
276C22⋊C16—111no—
277C22⋊C16—111no—
278C22⋊C16C2×D1111yescharacteristic
279C22×C11—21no—
280C22×C11—21no—
281C22×C11—21no—
282C22×C11C22×D811yescharacteristic
283C2×D11—21no—
284C2×D11—21no—
285C2×D11—21no—
286C2×D11—21no—
287C2×D11—21no—
288C2×D11#48012yes—
289C4×C11—21no—
290C4×C11—81no—
291C4×C11—81no—
292C4×C11—81no—
293C4×C11—81no—
294C4×C11C2×#12311yescharacteristic
295C4×C11C2×#13711yescharacteristic
296Dic11—21no—
297Dic11—81no—
298Dic11—81no—
299Dic11—81no—
300Dic11—81no—
301Dic11#48012yes—
302C2×#41—111no—
303C22×Q8—221no—
304C2×Q16—111no—
305C2×Q16—222no—
306C2×Q16—222no—
307C2×Q16—221no—
308C2×Q16C22×D1111yescharacteristic
309#131—222no—
310#131—222no—
311C2×M16—111no—
312C2×M16—111no—
313C2×M16—111no—
314C22×C8—111no—
315C22×C8—111no—
316C22×C8C22×D1111yescharacteristic
317C4⋊Q8—441no—
318#124—441no—
319#123—441no—
320#123—441no—
321C22⋊Q8—21no—
322C22⋊Q8—221no—
323C22⋊Q8—221no—
324C22⋊Q8—221no—
325C4×Q8—441no—
326C4×D4—441no—
327C4×D4—441no—
328C4×D4—441no—
329#117—221no—
330#117—221no—
331#117—221no—
332#117—221no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—221no—
335C2×C4⋊C4—221no—
336M32—222no—
337C2×C16—111no—
338C2×C16—111no—
339C2×C16—222no—
340C2×C16C22×D1111yescharacteristic
341C2×C16C22×D1111yescharacteristic
342#107—21no—
343#107—111no—
344#107—111no—
345#107—111no—
346#107—221no—
347#107—221no—
348#107C22×D1111yescharacteristic
349#107C22×D1111yescharacteristic
350#107C22×D1111yescharacteristic
351#106—221no—
352#106—221no—
353#106—221no—
354#106—221no—
355#103—21no—
356#103—221no—
357#103—221no—
358#103—221no—
359C2×C11—41no—
360C2×C11C2×#48011yescharacteristic
361C2×C11#341611yescharacteristic
362C2×C11#341711yescharacteristic
363D11—22no—
364D11—41no—
365#41—222no—
366#41—222no—
367C2×Q8—21no—
368C2×Q8—111no—
369C2×Q8—221no—
370C2×Q8—441no—
371C2×Q8—442no—
372C2×Q8—442no—
373C2×D4—111no—
374C2×D4—111no—
375C2×D4—111no—
376C22×C4—41no—
377C22×C4—111no—
378C22×C4—111no—
379C22×C4—441no—
380C22×C4—441no—
381C22×C4—441no—
382C22×C4D4×D1111yescharacteristic
383Q16—21no—
384Q16—21no—
385Q16—221no—
386Q16—221no—
387Q16—442no—
388M16—222no—
389M16—222no—
390M16—222no—
391C2×C8—21no—
392C2×C8—21no—
393C2×C8—111no—
394C2×C8—112no—
395C2×C8—112no—
396C2×C8—111no—
397C2×C8—221no—
398C2×C8—221no—
399C2×C8D4×D1111yescharacteristic
400C2×C8C23×D1111yescharacteristic
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—41no—
405C4⋊C4—41no—
406C4⋊C4—221no—
407C4⋊C4—221no—
408C4⋊C4—221no—
409C4⋊C4—441no—
410C4⋊C4—441no—
411C4⋊C4—441no—
412C4⋊C4—441no—
413C4⋊C4—441no—
414C22⋊C4—41no—
415C22⋊C4—441no—
416C22⋊C4—441no—
417C22⋊C4—441no—
418C22⋊C4—441no—
419C22⋊C4—441no—
420C22⋊C4—441no—
421C22⋊C4—441no—
422C42—441no—
423C42—441no—
424C42—441no—
425C42—441no—
426C16—21no—
427C16—21no—
428C16—221no—
429C16—221no—
430C11#3365111yescharacteristic, complemented, Sylow
431C23—111no—
432C23—111no—
433C23D8×D1111yescharacteristic
434Q8—41no—
435Q8—41no—
436Q8—222no—
437Q8—441no—
438Q8—441no—
439Q8—882no—
440D4—222no—
441D4—222no—
442D4—222no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—111no—
450C2×C4—112no—
451C2×C4—112no—
452C2×C4—111no—
453C2×C4—161no—
454C2×C4—221no—
455C2×C4—221no—
456C2×C4—441no—
457C2×C4—441no—
458C2×C4—441no—
459C2×C4—441no—
460C2×C4—882no—
461C2×C4—1761no—
462C2×C4—1761no—
463C2×C4D8×D1111yescharacteristic
464C2×C4C2×D4×D1111yescharacteristic
465C8—21no—
466C8—112no—
467C8—221no—
468C8#41×D1111yescharacteristic
469C8#41×D1111yescharacteristic
470C22—21no—
471C22—21no—
472C22—21no—
473C22—112no—
474C22—221no—
475C22—221no—
476C22—221no—
477C22—221no—
478C22—221no—
479C22C2×D8×D1111yescharacteristic
480C4—21no—
481C4—81no—
482C4—81no—
483C4—81no—
484C4—81no—
485C4—112no—
486C4—221no—
487C4—881no—
488C4—881no—
489C4—881no—
490C4—881no—
491C4D11×#12311yescharacteristic
492C4D11×#13711yescharacteristic
493C2—41no—
494C2—222no—
495C2—441no—
496C2D11×#48011yescharacteristic
497C2#1308176211yescharacteristic
498C2#1308176511yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2236C2
socleC22×C11C22×D8
prime radicalC2×#4339D4
hypercenter#2236D11
hypocenterC11#33651
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2236

Complements

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

NH ≅ G/Ntype
3. #13070826C2semidirect
4. #13070825C2semidirect
5. #13070823C2semidirect
6. #13070821C2semidirect
7. #13070820C2semidirect
8. #13070813C2semidirect
9. #13070812C2semidirect
10. #13070401C2semidirect
11. #13070397C2semidirect
12. #13070334C2semidirect
13. D11×#358C2semidirect
15. C11×#2236C2semidirect
189. #2236D11semidirect
430. C11#33651semidirect

Maximal subgroups

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

subgroupindex
#130782662
#130772122
#130708262
#130708252
#130708232
#130708212
#130708202
#130708132
#130708122
#130704012
#130703972
#130703342
D11×#3582
#130702282
C11×#22362
#3365111