Finite Group Databasebeta

← #14910827

Subgroups — #14910827

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#13080979C211yesmaximal, characteristic
2Q16×C22⋊D11C211yesmaximal, characteristic
3#13070860C211yesmaximal, characteristic, complemented
4#13070825C211yesmaximal, characteristic, complemented
5#13070812C211yesmaximal, characteristic, complemented
6#13070782C211yesmaximal, characteristic, complemented
7#13070722C211yesmaximal, characteristic, complemented
8#13070704C211yesmaximal, characteristic, complemented
9#13070664C211yesmaximal, characteristic, complemented
10#13070548C211yesmaximal, characteristic, complemented
11#13070487C211yesmaximal, characteristic, complemented
12#13070444C211yesmaximal, characteristic
13#13070336C211yesmaximal, characteristic, complemented
14D11×#358C211yesmaximal, characteristic, complemented
15C11×#2188C211yesmaximal, characteristic, complemented
16C22×C11×Q16C2211yescharacteristic
17Q8×C22⋊D11—21no—
18C2×Q16×D11C2211yescharacteristic
19#10623170—21no—
20C2×C11×Q32C2211yescharacteristic
21C2×C11×Q32C2211yescharacteristic
22C11×#467C2211yescharacteristic
23#10622841—21no—
24#10622801C2211yescharacteristic
25#10622801C2211yescharacteristic
26#10622799—21no—
27Q16×Dic11C2211yescharacteristic
28Q16×Dic11C2211yescharacteristic
29#10622795—21no—
30#10622794C2211yescharacteristic
31C2×#66893C2211yescharacteristic
32#10622729C2211yescharacteristic
33C8×C22⋊D11C2211yescharacteristic
34#10622719C2211yescharacteristic
35C2×#66876C2211yescharacteristic
36#10622658—21no—
37C2×C16×D11C2211yescharacteristic
38D11×#107C2211yescharacteristic
39#10622491C2211yescharacteristic
40#10622418—21no—
41#10622412—21no—
42C11×#358C2211yescharacteristic
43C11×#358C2211yescharacteristic
44C11×C22⋊C16C2211yescharacteristic
45#10622202C2211yescharacteristic
46#10622202C2211yescharacteristic
47#10622202C2211yescharacteristic
48#10622202C2211yescharacteristic
49#10622202C2211yescharacteristic
50(C2×D11)⋊C16C2211yescharacteristic
51#10622143C2211yescharacteristic
52#10622142C2211yescharacteristic
53#10622141C2211yescharacteristic
54#10622141C2211yescharacteristic
55#10622140C2211yescharacteristic
56Dic11⋊C16C2211yescharacteristic
57#10622130C2211yescharacteristic
58#10622128C2211yescharacteristic
59C22×Q8×C11—21no—
60C2×Q8×D11—21no—
61C2×C11×Q16—22no—
62C2×C11×Q16—21no—
63C2×C11×Q16—41no—
64C2×C11×Q16C2311yescharacteristic
65C2×C11×Q16C2311yescharacteristic
66C2×C11×Q16C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C11×C22⋊Q8—21no—
69#66999—21no—
70#66999—21no—
71#66999—41no—
72Q8×Dic11—21no—
73Q8×Dic11—21no—
74#66997—21no—
75#66997—41no—
76C2×#4326—21no—
77C2×#4326—21no—
78C4×C22⋊D11—41no—
79C4×C22⋊D11D411yescharacteristic
80#66979—21no—
81#66977—21no—
82#66977—41no—
83Q16×D11—22no—
84Q16×D11—41no—
85C2×Dic44C2311yescharacteristic
86C2×C8×D11C2311yescharacteristic
87#66945—41no—
88C4⋊C4×D11—21no—
89#66943—21no—
90#66942—41no—
91#66936—41no—
92#66932—41no—
93C11×Q32—22no—
94C11×Q32—41no—
95C2×C11×C16C2311yescharacteristic
96C2×C11×C16C2311yescharacteristic
97C11×#107C2311yescharacteristic
98C11×#103—21no—
99#66899—21no—
100#66899—21no—
101#66899—21no—
102#66899—21no—
103C22⋊(C11⋊C8)D411yescharacteristic
104#66893—41no—
105(C2×D11)⋊C8D411yescharacteristic
106#66882C2311yescharacteristic
107#66882C2311yescharacteristic
108#66882C2311yescharacteristic
109#66881—21no—
110#66880—21no—
111Dic11⋊C8D411yescharacteristic
112C8×Dic11C2311yescharacteristic
113#66876—41no—
114C2×C11⋊C16C2311yescharacteristic
115C2×C11⋊C16C2311yescharacteristic
116#66872—21no—
117#66871—21no—
118C16×D11—41no—
119#33879—111nomaximal, Sylow
120C2×Q8×C11—21no—
121C2×Q8×C11—21no—
122C2×Q8×C11—21no—
123C2×Q8×C11—42no—
124C2×Q8×C11—41no—
125C2×Q8×C11—81no—
126C22×C4×C11—41no—
127C22×C4×C11C2×D411yescharacteristic
128C2×C22⋊D11D811yescharacteristic
129Q8×D11—42no—
130Q8×D11—81no—
131C2×C4×D11—41no—
132C2×C4×D11—41no—
133C2×C4×D11C2×D411yescharacteristic
134C2×Dic22—21no—
135C2×Dic22—41no—
136C11×Q16—21no—
137C11×Q16—21no—
138C11×Q16—21no—
139C11×Q16—21no—
140C11×Q16—21no—
141C11×Q16—42no—
142C11×Q16#4112yes—
143C2×C8×C11—21no—
144C2×C8×C11—21no—
145C2×C8×C11C2×D411yescharacteristic
146C2×C8×C11C2411yescharacteristic
147C11×C4⋊C4—21no—
148C11×C4⋊C4—41no—
149C11×C22⋊C4—41no—
150C22⋊Dic11—41no—
151C22⋊Dic11—41no—
152C22⋊Dic11D811yescharacteristic
153#4326—42no—
154#4326—81no—
155(C2×D11)⋊C4—41no—
156(C2×D11)⋊C4—41no—
157(C2×D11)⋊C4D811yescharacteristic
158C4⋊Dic11—21no—
159C4⋊Dic11—21no—
160C4⋊Dic11—21no—
161C4⋊Dic11—41no—
162C4⋊Dic11—41no—
163C4⋊Dic11—41no—
164Dic11⋊C4—41no—
165Dic11⋊C4—41no—
166Dic11⋊C4—41no—
167Dic11⋊C4—41no—
168Dic11⋊C4—41no—
169Dic11⋊C4—41no—
170Dic11⋊C4—41no—
171Dic11⋊C4D811yescharacteristic
172C4×Dic11—41no—
173C4×Dic11—41no—
174C4×Dic11—41no—
175C4×Dic11C2×D411yescharacteristic
176C2×C11⋊C8C2×D411yescharacteristic
177C2×C11⋊C8C2×D411yescharacteristic
178Dic44—21no—
179Dic44—21no—
180C8×D11—21no—
181C8×D11—21no—
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#2188D1111yescharacteristic, complemented
197#2176—111no—
198#2168—111no—
199#2141—111no—
200C2×#358—111no—
201C23×C11C2×D811yescharacteristic
202C22×D11C2×D811yescharacteristic
203Q8×C11—22no—
204Q8×C11—41no—
205Q8×C11—41no—
206Q8×C11—41no—
207Q8×C11—41no—
208Q8×C11—41no—
209Q8×C11—82no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—82no—
217C2×C4×C11C2×D811yescharacteristic
218C2×C4×C11C22×D411yescharacteristic
219C22⋊D11—22no—
220C2×Dic11—41no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223C2×Dic11—41no—
224C2×Dic11C2×D811yescharacteristic
225C2×Dic11C2×D811yescharacteristic
226C2×Dic11C2×D811yescharacteristic
227C4×D11—21no—
228C4×D11—21no—
229C4×D11—82no—
230C4×D11—82no—
231Dic22—41no—
232Dic22—41no—
233Dic22—82no—
234C8×C11—21no—
235C8×C11C2×#4111yescharacteristic
236C8×C11H(5,𝔽2)11yescharacteristic
237C11⋊C8—21no—
238C11⋊C8—21no—
239C22×Q16—111no—
240C22×Q16C2×D1111yescharacteristic
241#552—221no—
242D4×Q8—221no—
243C2×Q32—111no—
244C2×Q32C2×D1111yescharacteristic
245C2×Q32C2×D1111yescharacteristic
246C2×M32—111no—
247C22×C16—111no—
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#467C2×D1111yescharacteristic
257#462—221no—
258#451—221no—
259#451—221no—
260C4×Q16—111no—
261C4×Q16—111no—
262C8×D4—111no—
263#427—111no—
264C2×#107—111no—
265#367—111no—
266#367—111no—
267#366—111no—
268C4⋊C16—111no—
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#358C2×D1111yescharacteristic
278#358C2×D1111yescharacteristic
279C22⋊C16—111no—
280C22⋊C16C2×D1111yescharacteristic
281#346—111no—
282C22×C11—21no—
283C22×C11—21no—
284C22×C11—21no—
285C22×C11C22×D811yescharacteristic
286C2×D11—21no—
287C2×D11—21no—
288C2×D11#51012yes—
289C4×C11—21no—
290C4×C11—42no—
291C4×C11—81no—
292C4×C11—81no—
293C4×C11—81no—
294C4×C11#54611yescharacteristic
295C4×C11#57711yescharacteristic
296Dic11—21no—
297Dic11—21no—
298Dic11—21no—
299Dic11—81no—
300Dic11—81no—
301Dic11—81no—
302Dic11—81no—
303C22×Q8—21no—
304C22×Q8—221no—
305C2×Q16—22no—
306C2×Q16—21no—
307C2×Q16—41no—
308C2×Q16—111no—
309C2×Q16—221no—
310C2×Q16—221no—
311C2×Q16—222no—
312C2×Q16—441no—
313C2×Q16C22×D1111yescharacteristic
314C2×Q16C22×D1111yescharacteristic
315C2×Q16C22×D1111yescharacteristic
316C22×C8—111no—
317C22×C8C22×D1111yescharacteristic
318C4⋊Q8—221no—
319C4⋊Q8—441no—
320#126—441no—
321#125—221no—
322#125—441no—
323#123—441no—
324C22⋊Q8—21no—
325C22⋊Q8—221no—
326C22⋊Q8—221no—
327C22⋊Q8—221no—
328C22⋊Q8—441no—
329C22⋊Q8—441no—
330C4×Q8—221no—
331C4×Q8—221no—
332C4×D4—111no—
333C4×D4—441no—
334#117—221no—
335#117—441no—
336C2×C4⋊C4—221no—
337Q32—22no—
338Q32—41no—
339Q32—441no—
340M32—441no—
341C2×C16—111no—
342C2×C16—111no—
343C2×C16—441no—
344C2×C16C22×D1111yescharacteristic
345C2×C16C22×D1111yescharacteristic
346#107—111no—
347#107—111no—
348#107—111no—
349#107—221no—
350#107C22×D1111yescharacteristic
351#106—221no—
352#106—221no—
353C4⋊C8—111no—
354#103—21no—
355#103—221no—
356#103—221no—
357#103—221no—
358#103—221no—
359#103—221no—
360C22⋊C8—111no—
361C22⋊C8—111no—
362C4×C8—111no—
363C2×C11—41no—
364C2×C11#329411yescharacteristic
365C2×C11C2×#51011yescharacteristic
366C2×C11#341711yescharacteristic
367D11—22no—
368C2×Q8—21no—
369C2×Q8—21no—
370C2×Q8—21no—
371C2×Q8—42no—
372C2×Q8—41no—
373C2×Q8—81no—
374C2×Q8—221no—
375C2×Q8—441no—
376C2×Q8—442no—
377C2×Q8—881no—
378C2×D4—111no—
379C22×C4—41no—
380C22×C4—111no—
381C22×C4—441no—
382C22×C4—441no—
383C22×C4D4×D1111yescharacteristic
384Q16—21no—
385Q16—21no—
386Q16—21no—
387Q16—21no—
388Q16—21no—
389Q16—42no—
390Q16—221no—
391Q16—221no—
392Q16—442no—
393Q16—881no—
394Q16#434112yes—
395C2×C8—21no—
396C2×C8—21no—
397C2×C8—111no—
398C2×C8—111no—
399C2×C8—221no—
400C2×C8—221no—
401C2×C8D4×D1111yescharacteristic
402C2×C8C23×D1111yescharacteristic
403C4⋊C4—21no—
404C4⋊C4—41no—
405C4⋊C4—111no—
406C4⋊C4—221no—
407C4⋊C4—221no—
408C4⋊C4—221no—
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⋊C4—441no—
419C22⋊C4—41no—
420C22⋊C4—111no—
421C22⋊C4—111no—
422C22⋊C4—441no—
423C22⋊C4—441no—
424C22⋊C4—441no—
425C22⋊C4—441no—
426C42—111no—
427C42—441no—
428C42—441no—
429C42—441no—
430C16—21no—
431C16—21no—
432C16—221no—
433C16—221no—
434C11#3387911yescharacteristic, complemented, Sylow
435C23—111no—
436C23D8×D1111yescharacteristic
437Q8—22no—
438Q8—41no—
439Q8—41no—
440Q8—41no—
441Q8—41no—
442Q8—41no—
443Q8—82no—
444Q8—441no—
445Q8—441no—
446Q8—882no—
447D4—222no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—82no—
455C2×C4—111no—
456C2×C4—111no—
457C2×C4—111no—
458C2×C4—221no—
459C2×C4—221no—
460C2×C4—441no—
461C2×C4—441no—
462C2×C4—441no—
463C2×C4—441no—
464C2×C4—882no—
465C2×C4—882no—
466C2×C4D8×D1111yescharacteristic
467C2×C4C2×D4×D1111yescharacteristic
468C8—21no—
469C8—221no—
470C8—221no—
471C8C2×#434111yescharacteristic
472C8#6703711yescharacteristic
473C22—21no—
474C22—21no—
475C22—21no—
476C22—112no—
477C22—221no—
478C22—221no—
479C22C2×D8×D1111yescharacteristic
480C4—21no—
481C4—42no—
482C4—81no—
483C4—81no—
484C4—81no—
485C4—221no—
486C4—221no—
487C4—221no—
488C4—881no—
489C4—881no—
490C4—881no—
491C4—881no—
492C4#1062312211yescharacteristic
493C4#1062330611yescharacteristic
494C2—41no—
495C2—222no—
496C2#1308042211yescharacteristic
497C2D11×#51011yescharacteristic
498C2#1308176511yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2188C2
socleC22×C11C22×D8
prime radicalC2×C22⋊D11D8
hypercenter#2188D11
hypocenterC11#33879
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2188

Complements

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

NH ≅ G/Ntype
3. #13070860C2semidirect
4. #13070825C2semidirect
5. #13070812C2semidirect
6. #13070782C2semidirect
7. #13070722C2semidirect
8. #13070704C2semidirect
9. #13070664C2semidirect
10. #13070548C2semidirect
11. #13070487C2semidirect
13. #13070336C2semidirect
14. D11×#358C2semidirect
15. C11×#2188C2semidirect
196. #2188D11semidirect
434. C11#33879semidirect

Maximal subgroups

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

subgroupindex
#130809792
Q16×C22⋊D112
#130708602
#130708252
#130708122
#130707822
#130707222
#130707042
#130706642
#130705482
#130704872
#130704442
#130703362
D11×#3582
C11×#21882
#3387911