Finite Group Databasebeta

← #14908714

Subgroups — #14908714

Order 2816.

558 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#13079183C211yesmaximal, characteristic, complemented
2C4×#66972C211yesmaximal, characteristic, complemented
3#13070822C211yesmaximal, characteristic, complemented
4#13070805C211yesmaximal, characteristic, complemented
5#13070780C211yesmaximal, characteristic, complemented
6#13070774C211yesmaximal, characteristic, complemented
7#13070668C211yesmaximal, characteristic, complemented
8#13070555C211yesmaximal, characteristic, complemented
9#13070538C211yesmaximal, characteristic
10Q32×Dic11C211yesmaximal, characteristic, complemented
11SD32×Dic11C211yesmaximal, characteristic, complemented
12#13070465C211yesmaximal, characteristic, complemented
13#13070460C211yesmaximal, characteristic, complemented
14#13070414C211yesmaximal, characteristic, complemented
15C11×#2211C211yesmaximal, characteristic, complemented
16C2×#66972C2211yescharacteristic
17#10623211—21no—
18C4×#4343—21no—
19C2×C11×Q32C2211yescharacteristic
20C2×C11×SD32C2211yescharacteristic
21C11×#495C2211yescharacteristic
22C4×C11×Q16C2211yescharacteristic
23#10622801C2211yescharacteristic
24Q16×Dic11C2211yescharacteristic
25Q16×Dic11C2211yescharacteristic
26C2×#66892C2211yescharacteristic
27#10622784—21no—
28SD16×Dic11—21no—
29#10622770C2211yescharacteristic
30D8×Dic11C2211yescharacteristic
31C2×#66890C2211yescharacteristic
32#10622669—21no—
33C4×#4325—21no—
34#10622493C2211yescharacteristic
35#10622485C2211yescharacteristic
36#10622417—21no—
37#10622401—21no—
38C4×D88C2211yescharacteristic
39C4×C8×D11C2211yescharacteristic
40#10622296C2211yescharacteristic
41C11×C4⋊C16C2211yescharacteristic
42C11×#358C2211yescharacteristic
43C11×#357C2211yescharacteristic
44#10622202C2211yescharacteristic
45#10622202C2211yescharacteristic
46#10622202C2211yescharacteristic
47#10622200C2211yescharacteristic
48#10622147C2211yescharacteristic
49#10622147C2211yescharacteristic
50(C2×D11)⋊C16C2211yescharacteristic
51(C2×D11)⋊C16C2211yescharacteristic
52#10622143C2211yescharacteristic
53#10622142C2211yescharacteristic
54C16×Dic11C2211yescharacteristic
55C16×Dic11C2211yescharacteristic
56#10622128C2211yescharacteristic
57#10622127C2211yescharacteristic
58C4⋊(C11⋊C16)C2211yescharacteristic
59C2×#4343—21no—
60C2×C11×Q16C2311yescharacteristic
61C2×C11×Q16C2311yescharacteristic
62C2×C11×SD16—21no—
63C2×C11×D8C2311yescharacteristic
64C11×#124—21no—
65C4×Q8×C11—21no—
66#66999—21no—
67Q8×Dic11—21no—
68Q8×Dic11—21no—
69C2×#4325—21no—
70#66991—21no—
71D4×Dic11—21no—
72#66972—22no—
73#66972—22no—
74C2×D88C2311yescharacteristic
75C2×C8×D11D411yescharacteristic
76C2×C8×D11C2311yescharacteristic
77#66946—21no—
78#66946—41no—
79#66945—21no—
80#66945—41no—
81#66936—41no—
82(C22⋊D11)⋊C4—41no—
83#66932—41no—
84#66930—41no—
85C4×D44—21no—
86C4×D44—41no—
87C42×D11—41no—
88C42×D11D411yescharacteristic
89#66923—21no—
90C11×Q32—22no—
91C11×SD32—22no—
92C2×C11×C16C2311yescharacteristic
93C2×C11×C16C2311yescharacteristic
94C11×#107C2311yescharacteristic
95C11×#103—21no—
96C4×C8×C11C2311yescharacteristic
97#66899—21no—
98#66899—21no—
99#66899—21no—
100#66896—21no—
101#66896—21no—
102#66892—22no—
103#66890—22no—
104#66885—21no—
105#66882C2311yescharacteristic
106#66882C2311yescharacteristic
107#66882C2311yescharacteristic
108#66881—21no—
109C8×Dic11D411yescharacteristic
110C8×Dic11C2311yescharacteristic
111C2×C11⋊C16C2311yescharacteristic
112C2×C11⋊C16C2311yescharacteristic
113#66873—21no—
114#66872—21no—
115C4×C11⋊C8D411yescharacteristic
116#33662—111nomaximal, Sylow
117C2×Q8×C11—21no—
118C2×Q8×C11—21no—
119C2×D4×C11—21no—
120C2×C22⋊D11—41no—
121C22×Dic11—41no—
122#4343—24no—
123#4343—42no—
124C2×D44—21no—
125C2×D44—41no—
126C2×C4×D11—41no—
127C2×C4×D11—41no—
128C2×C4×D11—41no—
129C2×C4×D11D811yescharacteristic
130C2×C4×D11D811yescharacteristic
131C2×C4×D11C2×D411yescharacteristic
132C11×Q16—21no—
133C11×Q16—21no—
134C11×Q16—21no—
135C11×Q16#4112yes—
136C11×SD16—42no—
137C11×D8—21no—
138C11×D8—21no—
139C2×C8×C11C2×D411yescharacteristic
140C2×C8×C11C2411yescharacteristic
141C11×C4⋊C4—21no—
142C11×C4⋊C4—41no—
143C11×C22⋊C4—41no—
144C11×C22⋊C4—41no—
145C42×C11—41no—
146C42×C11C2×D411yescharacteristic
147C22⋊Dic11—41no—
148C22⋊Dic11—41no—
149#4325—24no—
150(C2×D11)⋊C4—41no—
151(C2×D11)⋊C4—41no—
152(C2×D11)⋊C4—41no—
153(C2×D11)⋊C4—41no—
154C4⋊Dic11—21no—
155C4⋊Dic11—21no—
156C4⋊Dic11—21no—
157C4⋊Dic11—41no—
158C4⋊Dic11—41no—
159Dic11⋊C4—41no—
160Dic11⋊C4—41no—
161Dic11⋊C4—41no—
162C4×Dic11—41no—
163C4×Dic11—41no—
164C4×Dic11—41no—
165C4×Dic11D811yescharacteristic
166C4×Dic11D811yescharacteristic
167C4×Dic11C2×D411yescharacteristic
168C2×C11⋊C8C2×D411yescharacteristic
169C2×C11⋊C8C2×D411yescharacteristic
170D88—21no—
171D88#4112yes—
172C8×D11—21no—
173C8×D11—21no—
174C8×D11—41no—
175C11×C16—21no—
176C11×C16—21no—
177C11⋊C16—21no—
178C11⋊C16—21no—
179#3168—111no—
180C4×#135—111no—
181#2237—111no—
182#2234—111no—
183#2229—111no—
184#2228—111no—
185#2211D1111yescharacteristic, complemented
186#2210—111no—
187#2189—111no—
188#2186—111no—
189C4×Q32—111no—
190C4×SD32—111no—
191C4×SD32—111no—
192C4×D16—111no—
193#2162—111no—
194C23×C11—41no—
195C22×D11—41no—
196C22×D11C2×D811yescharacteristic
197Q8×C11—22no—
198Q8×C11—41no—
199Q8×C11—41no—
200Q8×C11—41no—
201D4×C11—41no—
202D4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11C2×D811yescharacteristic
207C2×C4×C11C2×D811yescharacteristic
208C2×C4×C11C22×D411yescharacteristic
209C22⋊D11—82no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—82no—
214C2×Dic11C2×D811yescharacteristic
215C2×Dic11C2×D811yescharacteristic
216C2×Dic11C2×D811yescharacteristic
217D44—22no—
218D44—44no—
219D44—41no—
220C4×D11—21no—
221C4×D11—21no—
222C4×D11—22no—
223C4×D11—41no—
224C4×D11—44no—
225C4×D11—82no—
226C4×D11—82no—
227C8×C11—21no—
228C8×C11C2×#4111yescharacteristic
229C8×C11C2×#4111yescharacteristic
230C11⋊C8—21no—
231C11⋊C8—21no—
232C2×#135—111no—
233#529—221no—
234C4×#41—221no—
235C2×Q32C2×D1111yescharacteristic
236C2×SD32—111no—
237C2×SD32C2×D1111yescharacteristic
238C2×D16—111no—
239#499—111no—
240#495C2×D1111yescharacteristic
241#488—221no—
242#467—111no—
243#466—111no—
244#465—221no—
245C4×Q16—111no—
246C4×Q16—111no—
247C4×Q16C2×D1111yescharacteristic
248C4×SD16—221no—
249C4×SD16—221no—
250C4×SD16—221no—
251C4×D8—111no—
252C4×D8—111no—
253C4×D8—111no—
254#427—111no—
255#416—221no—
256C2×C4×C8—111no—
257#367—111no—
258#367—111no—
259#366—111no—
260#366—111no—
261C4⋊C16—111no—
262C4⋊C16C2×D1111yescharacteristic
263#358—111no—
264#358—111no—
265#358—111no—
266#358C2×D1111yescharacteristic
267#357—111no—
268#357—111no—
269#357—111no—
270#357C2×D1111yescharacteristic
271C22⋊C16—111no—
272C22⋊C16—111no—
273C4×C16—111no—
274C4×C16—111no—
275C22×C11—81no—
276C22×C11—81no—
277C22×C11—81no—
278C22×C11C22×D811yescharacteristic
279C2×D11—21no—
280C2×D11—21no—
281C2×D11—21no—
282C2×D11—42no—
283C2×D11—81no—
284C2×D11—81no—
285C4×C11—21no—
286C4×C11—21no—
287C4×C11—42no—
288C4×C11—81no—
289C4×C11—81no—
290C4×C11#52511yescharacteristic
291C4×C11#57511yescharacteristic
292Dic11—21no—
293Dic11—21no—
294Dic11—81no—
295Dic11—81no—
296Dic11—81no—
297Dic11#50812yes—
298C2×#41—221no—
299#135—222no—
300#135—222no—
301C2×Q16C22×D1111yescharacteristic
302C2×Q16C22×D1111yescharacteristic
303C2×SD16—21no—
304C2×SD16—221no—
305C2×D8—111no—
306C2×D8C22×D1111yescharacteristic
307C22×C8—111no—
308C22×C8—111no—
309#126—441no—
310#125—221no—
311#124—21no—
312#123—441no—
313C22⋊Q8—221no—
314#121—221no—
315C4×Q8—21no—
316C4×Q8—221no—
317C4×Q8—221no—
318C4×D4—221no—
319C4×D4—221no—
320C4×D4—221no—
321C4×D4—441no—
322C4×D4—441no—
323C4×D4—441no—
324#117—221no—
325#117—441no—
326#117—441no—
327C2×C42—111no—
328C2×C42—441no—
329Q32—22no—
330SD32—22no—
331SD32—222no—
332D16—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—21no—
344#103—221no—
345#103—221no—
346#103—221no—
347#102—221no—
348#102—221no—
349#102—221no—
350#102—221no—
351C4×C8—111no—
352C4×C8—111no—
353C4×C8—111no—
354C4×C8C22×D1111yescharacteristic
355C2×C11—161no—
356C2×C11#310011yescharacteristic
357C2×C11C2×#50811yescharacteristic
358C2×C11#341411yescharacteristic
359D11—41no—
360D11—82no—
361#41—224no—
362#41—442no—
363C2×Q8—21no—
364C2×Q8—21no—
365C2×D4—21no—
366C2×D4—221no—
367C2×D4—441no—
368C2×D4—441no—
369C22×C4—111no—
370C22×C4—111no—
371C22×C4—111no—
372C22×C4—441no—
373C22×C4—441no—
374C22×C4—441no—
375C22×C4—441no—
376Q16—21no—
377Q16—21no—
378Q16—21no—
379Q16#434112yes—
380SD16—42no—
381SD16—224no—
382D8—21no—
383D8—21no—
384D8—112no—
385D8—221no—
386C2×C8—111no—
387C2×C8—111no—
388C2×C8—221no—
389C2×C8—221no—
390C2×C8—441no—
391C2×C8D4×D1111yescharacteristic
392C2×C8C23×D1111yescharacteristic
393C4⋊C4—21no—
394C4⋊C4—41no—
395C4⋊C4—221no—
396C4⋊C4—221no—
397C4⋊C4—221no—
398C4⋊C4—441no—
399C4⋊C4—441no—
400C4⋊C4—441no—
401C4⋊C4—441no—
402C4⋊C4—441no—
403C22⋊C4—41no—
404C22⋊C4—41no—
405C22⋊C4—441no—
406C22⋊C4—441no—
407C22⋊C4—441no—
408C22⋊C4—441no—
409C22⋊C4—441no—
410C22⋊C4—441no—
411C42—41no—
412C42—111no—
413C42—111no—
414C42—111no—
415C42—441no—
416C42—441no—
417C42—441no—
418C42D4×D1111yescharacteristic
419C16—21no—
420C16—21no—
421C16—221no—
422C16—221no—
423C11#3366211yescharacteristic, complemented, Sylow
424C23—41no—
425C23—111no—
426C23—441no—
427Q8—22no—
428Q8—41no—
429Q8—41no—
430Q8—41no—
431D4—41no—
432D4—41no—
433D4—222no—
434D4—444no—
435D4—441no—
436D4—882no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—111no—
441C2×C4—111no—
442C2×C4—111no—
443C2×C4—222no—
444C2×C4—221no—
445C2×C4—221no—
446C2×C4—441no—
447C2×C4—444no—
448C2×C4—441no—
449C2×C4—441no—
450C2×C4—441no—
451C2×C4—882no—
452C2×C4—882no—
453C2×C4—882no—
454C2×C4D8×D1111yescharacteristic
455C2×C4D8×D1111yescharacteristic
456C2×C4C2×D4×D1111yescharacteristic
457C8—21no—
458C8—221no—
459C8—221no—
460C8C2×#434111yescharacteristic
461C8#41×D1111yescharacteristic
462C22—81no—
463C22—81no—
464C22—81no—
465C22—221no—
466C22—221no—
467C22—221no—
468C22—442no—
469C22—881no—
470C22—881no—
471C22C2×D8×D1111yescharacteristic
472C4—21no—
473C4—21no—
474C4—42no—
475C4—81no—
476C4—81no—
477C4—112no—
478C4—221no—
479C4—221no—
480C4—881no—
481C4—881no—
482C4—881no—
483C4#1062313711yescharacteristic
484C4#1062330411yescharacteristic
485C2—161no—
486C2—441no—
487C2—882no—
488C2#1307861511yescharacteristic
489C2D11×#50811yescharacteristic
490C2#1308175111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2211C2
socleC22×C11C22×D8
prime radical#13070538C2
hypercenter#2211D11
hypocenterC11#33662
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2211

Complements

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

NH ≅ G/Ntype
1. #13079183C2semidirect
2. C4×#66972C2semidirect
3. #13070822C2semidirect
4. #13070805C2semidirect
5. #13070780C2semidirect
6. #13070774C2semidirect
7. #13070668C2semidirect
8. #13070555C2semidirect
10. Q32×Dic11C2semidirect
11. SD32×Dic11C2semidirect
12. #13070465C2semidirect
13. #13070460C2semidirect
14. #13070414C2semidirect
15. C11×#2211C2semidirect
185. #2211D11semidirect
423. C11#33662semidirect

Maximal subgroups

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

subgroupindex
#130791832
C4×#669722
#130708222
#130708052
#130707802
#130707742
#130706682
#130705552
#130705382
Q32×Dic112
SD32×Dic112
#130704652
#130704602
#130704142
C11×#22112
#3366211