Finite Group Databasebeta

← #14910836

Subgroups — #14910836

Order 2816.

536 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#13080985C211yesmaximal, characteristic
2D4×Dic44C211yesmaximal, characteristic
3#13070862C211yesmaximal, characteristic, complemented
4#13070825C211yesmaximal, characteristic, complemented
5#13070814C211yesmaximal, characteristic, complemented
6#13070781C211yesmaximal, characteristic, complemented
7#13070724C211yesmaximal, characteristic, complemented
8#13070707C211yesmaximal, characteristic, complemented
9#13070667C211yesmaximal, characteristic, complemented
10#13070552C211yesmaximal, characteristic, complemented
11#13070552C211yesmaximal, characteristic, complemented
12#13070488C211yesmaximal, characteristic, complemented
13#13070337C211yesmaximal, characteristic, complemented
14C2×#10622141C211yesmaximal, characteristic, complemented
15C11×#2168C211yesmaximal, characteristic
16C22×Dic44C2211yescharacteristic
17C22×Dic44C2211yescharacteristic
18#10623072—21no—
19D4×Dic22—21no—
20C2×C11×M32C2211yescharacteristic
21C22×C11×C16C2211yescharacteristic
22C8×D4×C11C2211yescharacteristic
23#10622729C2211yescharacteristic
24#10622729C2211yescharacteristic
25#10622729C2211yescharacteristic
26#10622729C2211yescharacteristic
27#10622719C2211yescharacteristic
28C2×#66882C2211yescharacteristic
29C2×Dic88C2211yescharacteristic
30C2×Dic88C2211yescharacteristic
31C2×Dic88C2211yescharacteristic
32#10622462—21no—
33#10622442—21no—
34#10622352—21no—
35#10622352—21no—
36#10622336—21no—
37#10622334—21no—
38#10622312C2211yescharacteristic
39C4×Dic44C2211yescharacteristic
40C4×Dic44C2211yescharacteristic
41#10622296C2211yescharacteristic
42C11×C4⋊C16C2211yescharacteristic
43C11×C22⋊C16C2211yescharacteristic
44C11×C22⋊C16C2211yescharacteristic
45C11×#346C2211yescharacteristic
46#10622143C2211yescharacteristic
47#10622143C2211yescharacteristic
48#10622142C2211yescharacteristic
49#10622141C2211yescharacteristic
50#10622141C2211yescharacteristic
51#10622141C2211yescharacteristic
52#10622141C2211yescharacteristic
53#10622141C2211yescharacteristic
54#10622141C2211yescharacteristic
55#10622141C2211yescharacteristic
56#10622141C2211yescharacteristic
57#10622141C2211yescharacteristic
58#10622141C2211yescharacteristic
59C22×Dic22—21no—
60C22×Dic22—21no—
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C4×D4×C11D411yescharacteristic
64#66988—41no—
65D4×Dic11—41no—
66#66979—21no—
67C2×C4⋊Dic11—21no—
68#66977—21no—
69#66977—21no—
70#66977—21no—
71#66977—21no—
72C2×Dic44—22no—
73C2×Dic44—22no—
74C2×Dic44—21no—
75C2×Dic44—21no—
76C2×Dic44—21no—
77C2×Dic44—41no—
78C2×Dic44—41no—
79C2×Dic44C2311yescharacteristic
80C2×Dic44C2311yescharacteristic
81C2×Dic44C2311yescharacteristic
82C2×Dic44C2311yescharacteristic
83#66942—41no—
84#66941—41no—
85#66932—41no—
86#66931—41no—
87#66931—41no—
88#66930—41no—
89#66923—21no—
90#66922—21no—
91C4×Dic22—21no—
92C4×Dic22—21no—
93C11×M32—41no—
94C2×C11×C16—41no—
95C2×C11×C16C2311yescharacteristic
96C2×C11×C16C2311yescharacteristic
97C2×C11×C16C2311yescharacteristic
98C2×C11×C16C2311yescharacteristic
99C11×C4⋊C8D411yescharacteristic
100C11×C22⋊C8D411yescharacteristic
101C11×C22⋊C8D411yescharacteristic
102C4×C8×C11C2311yescharacteristic
103#66882—21no—
104#66882C2311yescharacteristic
105#66882C2311yescharacteristic
106#66882C2311yescharacteristic
107#66882C2311yescharacteristic
108#66881—21no—
109#66881—21no—
110#66880—21no—
111#66880—21no—
112#66880—21no—
113#66880—21no—
114#66880—21no—
115#66880—21no—
116Dic88—22no—
117Dic88—41no—
118Dic88—41no—
119#33879—111nomaximal, Sylow
120C2×D4×C11D811yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×Dic11—41no—
124C22×Dic11—41no—
125C22×Dic11—41no—
126C2×Dic22—21no—
127C2×Dic22—21no—
128C2×Dic22—21no—
129C2×Dic22—21no—
130C2×Dic22—42no—
131C2×Dic22—42no—
132C2×Dic22—41no—
133C2×Dic22—41no—
134C2×Dic22—81no—
135C2×Dic22—81no—
136C2×C8×C11—21no—
137C2×C8×C11—21no—
138C2×C8×C11—21no—
139C2×C8×C11—21no—
140C2×C8×C11C2×D411yescharacteristic
141C2×C8×C11C2×D411yescharacteristic
142C2×C8×C11C2×D411yescharacteristic
143C2×C8×C11C2411yescharacteristic
144C11×C4⋊C4D811yescharacteristic
145C11×C22⋊C4D811yescharacteristic
146C11×C22⋊C4D811yescharacteristic
147C42×C11C2×D411yescharacteristic
148C22⋊Dic11—41no—
149C22⋊Dic11—41no—
150C22⋊Dic11—41no—
151C22⋊Dic11—41no—
152C22⋊Dic11—41no—
153C4⋊Dic11—21no—
154C4⋊Dic11—21no—
155C4⋊Dic11—21no—
156C4⋊Dic11—21no—
157C4⋊Dic11—41no—
158C4⋊Dic11—41no—
159C4⋊Dic11—41no—
160Dic11⋊C4—41no—
161Dic11⋊C4—41no—
162Dic11⋊C4—41no—
163Dic11⋊C4—41no—
164Dic11⋊C4—41no—
165Dic11⋊C4—41no—
166Dic11⋊C4—41no—
167Dic11⋊C4—41no—
168C4×Dic11—41no—
169C4×Dic11—41no—
170C4×Dic11—41no—
171Dic44—21no—
172Dic44—21no—
173Dic44—21no—
174Dic44—21no—
175Dic44—21no—
176Dic44—21no—
177Dic44—21no—
178Dic44—42no—
179Dic44—42no—
180Dic44—81no—
181Dic44#4112yes—
182C11×C16—21no—
183C11×C16—21no—
184C11×C16—21no—
185C11×C16—21no—
186#3336—111no—
187D4×Q16—111no—
188#2245—111no—
189#2237—111no—
190#2235—111no—
191#2229—111no—
192#2219—111no—
193#2216—111no—
194#2209—111no—
195#2188—111no—
196#2188—111no—
197#2176—111no—
198#2168D1111yescharacteristic
199#2141—111no—
200C2×#358—111no—
201C23×C11C2×D811yescharacteristic
202C23×C11C2×D811yescharacteristic
203D4×C11—22no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11C2×D811yescharacteristic
209C2×C4×C11C2×D811yescharacteristic
210C2×C4×C11C2×D811yescharacteristic
211C2×C4×C11C2×D811yescharacteristic
212C2×C4×C11C22×D411yescharacteristic
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11—41no—
219C2×Dic11—41no—
220C2×Dic11—41no—
221C2×Dic11—82no—
222C2×Dic11—82no—
223C2×Dic11—82no—
224Dic22—22no—
225Dic22—41no—
226Dic22—41no—
227Dic22—41no—
228Dic22—41no—
229Dic22—41no—
230Dic22—41no—
231Dic22—41no—
232Dic22—82no—
233Dic22—82no—
234C8×C11—21no—
235C8×C11—21no—
236C8×C11—21no—
237C8×C11C2×#4111yescharacteristic
238C8×C11H(5,𝔽2)11yescharacteristic
239C22×Q16—111no—
240C22×Q16—111no—
241#552—221no—
242D4×Q8—221no—
243C2×Q32—111no—
244C2×Q32—111no—
245C2×Q32—111no—
246C2×M32C2×D1111yescharacteristic
247C22×C16C2×D1111yescharacteristic
248#499—111no—
249#494—111no—
250#485—221no—
251#483—221no—
252#479—221no—
253#467—111no—
254#467—111no—
255#467—111no—
256#467—111no—
257#462—221no—
258#451—221no—
259#451—221no—
260C4×Q16—111no—
261C4×Q16—111no—
262C8×D4C2×D1111yescharacteristic
263#427—111no—
264C2×#107—111no—
265#367—111no—
266#367—111no—
267#366—111no—
268C4⋊C16C2×D1111yescharacteristic
269#358—111no—
270#358—111no—
271#358—111no—
272#358—111no—
273#358—111no—
274#358—111no—
275#358—111no—
276#358—111no—
277#358—111no—
278#358—111no—
279C22⋊C16C2×D1111yescharacteristic
280C22⋊C16C2×D1111yescharacteristic
281#346C2×D1111yescharacteristic
282C22×C11—21no—
283C22×C11—21no—
284C22×C11—21no—
285C22×C11—21no—
286C22×C11—21no—
287C22×C11#51012yes—
288C22×C11C22×D811yescharacteristic
289C4×C11—21no—
290C4×C11—21no—
291C4×C11—21no—
292C4×C11—21no—
293C4×C11#54611yescharacteristic
294C4×C11#57711yescharacteristic
295Dic11—42no—
296Dic11—81no—
297Dic11—81no—
298Dic11—81no—
299Dic11—81no—
300Dic11—81no—
301Dic11—81no—
302Dic11—81no—
303C22×Q8—221no—
304C22×Q8—221no—
305C2×Q16—111no—
306C2×Q16—111no—
307C2×Q16—111no—
308C2×Q16—111no—
309C2×Q16—222no—
310C2×Q16—222no—
311C2×Q16—221no—
312C2×Q16—221no—
313C2×Q16—221no—
314C2×Q16—441no—
315C2×Q16—441no—
316C22×C8C22×D1111yescharacteristic
317C22×C8C22×D1111yescharacteristic
318C4⋊Q8—221no—
319C4⋊Q8—441no—
320#126—441no—
321#125—221no—
322#125—441no—
323#123—441no—
324C22⋊Q8—221no—
325C22⋊Q8—221no—
326C22⋊Q8—221no—
327C22⋊Q8—221no—
328C22⋊Q8—441no—
329C22⋊Q8—441no—
330C4×Q8—221no—
331C4×Q8—221no—
332C4×D4—441no—
333C4×D4D4411yescharacteristic
334#117—221no—
335#117—441no—
336C2×C4⋊C4—221no—
337Q32—222no—
338Q32—441no—
339Q32—441no—
340M32—41no—
341C2×C16—41no—
342C2×C16C22×D1111yescharacteristic
343C2×C16C22×D1111yescharacteristic
344C2×C16C22×D1111yescharacteristic
345C2×C16C22×D1111yescharacteristic
346#107—111no—
347#107—111no—
348#107—111no—
349#107—111no—
350#107—221no—
351#106—221no—
352#106—221no—
353C4⋊C8D4411yescharacteristic
354#103—221no—
355#103—221no—
356#103—221no—
357#103—221no—
358#103—221no—
359#103—221no—
360C22⋊C8D4411yescharacteristic
361C22⋊C8D4411yescharacteristic
362C4×C8C22×D1111yescharacteristic
363C2×C11—22no—
364C2×C11—41no—
365C2×C11#329411yescharacteristic
366C2×C11C2×#51011yescharacteristic
367C2×C11#341711yescharacteristic
368C2×Q8—221no—
369C2×Q8—221no—
370C2×Q8—221no—
371C2×Q8—221no—
372C2×Q8—442no—
373C2×Q8—442no—
374C2×Q8—441no—
375C2×Q8—441no—
376C2×Q8—881no—
377C2×Q8—881no—
378C2×D4D8811yescharacteristic
379C22×C4—441no—
380C22×C4—441no—
381C22×C4—441no—
382C22×C4C2×D4411yescharacteristic
383C22×C4C2×D4411yescharacteristic
384Q16—112no—
385Q16—221no—
386Q16—221no—
387Q16—221no—
388Q16—221no—
389Q16—221no—
390Q16—221no—
391Q16—221no—
392Q16—442no—
393Q16—442no—
394Q16—881no—
395C2×C8—21no—
396C2×C8—21no—
397C2×C8—21no—
398C2×C8—21no—
399C2×C8C2×D4411yescharacteristic
400C2×C8C2×D4411yescharacteristic
401C2×C8C2×D4411yescharacteristic
402C2×C8C23×D1111yescharacteristic
403C4⋊C4—221no—
404C4⋊C4—221no—
405C4⋊C4—221no—
406C4⋊C4—221no—
407C4⋊C4—441no—
408C4⋊C4—441no—
409C4⋊C4—441no—
410C4⋊C4—441no—
411C4⋊C4—441no—
412C4⋊C4—441no—
413C4⋊C4—441no—
414C4⋊C4—441no—
415C4⋊C4—441no—
416C4⋊C4—441no—
417C4⋊C4—441no—
418C4⋊C4D8811yescharacteristic
419C22⋊C4—441no—
420C22⋊C4—441no—
421C22⋊C4—441no—
422C22⋊C4—441no—
423C22⋊C4—441no—
424C22⋊C4D8811yescharacteristic
425C22⋊C4D8811yescharacteristic
426C42—441no—
427C42—441no—
428C42—441no—
429C42C2×D4411yescharacteristic
430C16—21no—
431C16—21no—
432C16—21no—
433C16—21no—
434C11#3387911yescharacteristic, complemented, Sylow
435C23C2×D8811yescharacteristic
436C23C2×D8811yescharacteristic
437Q8—222no—
438Q8—441no—
439Q8—441no—
440Q8—441no—
441Q8—441no—
442Q8—441no—
443Q8—441no—
444Q8—441no—
445Q8—882no—
446Q8—882no—
447D4—22no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—441no—
453C2×C4—441no—
454C2×C4—441no—
455C2×C4—441no—
456C2×C4—441no—
457C2×C4—441no—
458C2×C4—441no—
459C2×C4—441no—
460C2×C4—882no—
461C2×C4—882no—
462C2×C4—882no—
463C2×C4C2×D8811yescharacteristic
464C2×C4C2×D8811yescharacteristic
465C2×C4C2×D8811yescharacteristic
466C2×C4C2×D8811yescharacteristic
467C2×C4C22×D4411yescharacteristic
468C8—21no—
469C8—21no—
470C8—21no—
471C8#6703711yescharacteristic
472C8#41×D1111yescharacteristic
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22#1062252212yes—
479C22C22×D8811yescharacteristic
480C4—21no—
481C4—21no—
482C4—21no—
483C4—21no—
484C4—442no—
485C4—881no—
486C4—881no—
487C4—881no—
488C4—881no—
489C4—881no—
490C4—881no—
491C4—881no—
492C4#1062308511yescharacteristic
493C4#1062328211yescharacteristic
494C2—22no—
495C2—41no—
496C2#1308043011yescharacteristic
497C2C2×#1062252211yescharacteristic
498C2#1308176911yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2168C2
socleC22×C11C22×D8
prime radicalC2×D4×C11D8
hypercenter#2168D11
hypocenterC11#33879
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #2168

Complements

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

NH ≅ G/Ntype
3. #13070862C2semidirect
4. #13070825C2semidirect
5. #13070814C2semidirect
6. #13070781C2semidirect
7. #13070724C2semidirect
8. #13070707C2semidirect
9. #13070667C2semidirect
10. #13070552C2semidirect
11. #13070552C2semidirect
12. #13070488C2semidirect
13. #13070337C2semidirect
14. C2×#10622141C2semidirect
434. C11#33879semidirect

Maximal subgroups

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

subgroupindex
#130809852
D4×Dic442
#130708622
#130708252
#130708142
#130707812
#130707242
#130707072
#130706672
#130705522
#130704882
#130703372
C2×#106221412
C11×#21682
#3387911