Finite Group Databasebeta

← #14910655

Subgroups — #14910655

Order 2816.

548 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081006C211yesmaximal, characteristic
2Q16×C22⋊D11C211yesmaximal, characteristic
3#13070842C211yesmaximal, characteristic, complemented
4#13070818C211yesmaximal, characteristic, complemented
5#13070817C211yesmaximal, characteristic, complemented
6#13070766C211yesmaximal, characteristic, complemented
7#13070707C211yesmaximal, characteristic, complemented
8#13070706C211yesmaximal, characteristic, complemented
9#13070665C211yesmaximal, characteristic, complemented
10#13070551C211yesmaximal, characteristic, complemented
11#13070550C211yesmaximal, characteristic, complemented
12#13070472C211yesmaximal, characteristic, complemented
13C16×C22⋊D11C211yesmaximal, characteristic
14D11×#358C211yesmaximal, characteristic, complemented
15C2×C11×#358C211yesmaximal, characteristic, complemented
16C22×C11×Q16C2211yescharacteristic
17Q8×C22⋊D11—21no—
18C2×Q16×D11C2211yescharacteristic
19#10623042—21no—
20C22×C11×C16C2211yescharacteristic
21C2×C11×#107C2211yescharacteristic
22#10622841—21no—
23#10622801C2211yescharacteristic
24#10622799—21no—
25Q16×Dic11C2211yescharacteristic
26#10622795—21no—
27#10622794C2211yescharacteristic
28C2×#66893C2211yescharacteristic
29C2×#66893C2211yescharacteristic
30#10622729C2211yescharacteristic
31#10622729C2211yescharacteristic
32C8×C22⋊D11C2211yescharacteristic
33#10622583—21no—
34C2×Dic88C2211yescharacteristic
35C2×C16×D11C2211yescharacteristic
36#10622500C2211yescharacteristic
37#10622497—21no—
38D11×#107C2211yescharacteristic
39#10622488—21no—
40#10622487C2211yescharacteristic
41#10622486C2211yescharacteristic
42C11×#358C2211yescharacteristic
43C11×#358C2211yescharacteristic
44C11×#358C2211yescharacteristic
45C11×#358C2211yescharacteristic
46#10622202C2211yescharacteristic
47#10622202C2211yescharacteristic
48C22⋊(C11⋊C16)C2211yescharacteristic
49(C2×D11)⋊C16C2211yescharacteristic
50#10622142C2211yescharacteristic
51#10622141C2211yescharacteristic
52#10622141C2211yescharacteristic
53Dic11⋊C16C2211yescharacteristic
54C16×Dic11C2211yescharacteristic
55#10622130C2211yescharacteristic
56#10622130C2211yescharacteristic
57#10622127C2211yescharacteristic
58#10622127C2211yescharacteristic
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
66C22×C8×C11C2311yescharacteristic
67C2×C11×C4⋊C4—21no—
68#66999—21no—
69#66999—41no—
70Q8×Dic11—21no—
71#66997—21no—
72#66997—41no—
73C2×#4326—21no—
74C2×#4326—21no—
75C4×C22⋊D11—41no—
76C4×C22⋊D11—41no—
77C4×C22⋊D11D411yescharacteristic
78#66977—21no—
79#66977—21no—
80#66977—41no—
81#66977—41no—
82Q16×D11—22no—
83Q16×D11—41no—
84C2×Dic44C2311yescharacteristic
85C2×Dic44C2311yescharacteristic
86C2×C8×D11C2311yescharacteristic
87#66950—21no—
88#66949—41no—
89C4⋊C4×D11—21no—
90#66942—41no—
91#66941—21no—
92#66940—21no—
93C2×C11×C16—41no—
94C2×C11×C16C2311yescharacteristic
95C2×C11×C16C2311yescharacteristic
96C11×#107—21no—
97C11×#107C2311yescharacteristic
98C11×#107C2311yescharacteristic
99#66899—21no—
100#66899—21no—
101C22⋊(C11⋊C8)D411yescharacteristic
102#66893—22no—
103#66893—41no—
104(C2×D11)⋊C8D411yescharacteristic
105#66882C2311yescharacteristic
106#66882C2311yescharacteristic
107#66880—21no—
108#66880—21no—
109Dic11⋊C8D411yescharacteristic
110C8×Dic11C2311yescharacteristic
111C2×C11⋊C16C2311yescharacteristic
112C2×C11⋊C16C2311yescharacteristic
113#66874—21no—
114#66874—21no—
115#66871—21no—
116#66871—21no—
117Dic88—41no—
118C16×D11—41no—
119#33866—111nomaximal, Sylow
120C2×Q8×C11—21no—
121C2×Q8×C11—21no—
122C2×Q8×C11—42no—
123C2×Q8×C11—41no—
124C2×Q8×C11—81no—
125C22×C4×C11—41no—
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—21no—
136C2×Dic22—41no—
137C2×Dic22—41no—
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—21no—
149C11×C4⋊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—41no—
161C4⋊Dic11—41no—
162Dic11⋊C4—41no—
163Dic11⋊C4—41no—
164Dic11⋊C4—41no—
165Dic11⋊C4—41no—
166Dic11⋊C4—41no—
167Dic11⋊C4—41no—
168Dic11⋊C4—41no—
169Dic11⋊C4—41no—
170Dic11⋊C4D811yescharacteristic
171C4×Dic11—41no—
172C4×Dic11—41no—
173C4×Dic11C2×D411yescharacteristic
174C2×C11⋊C8C2×D411yescharacteristic
175C2×C11⋊C8C2×D411yescharacteristic
176Dic44—21no—
177Dic44—21no—
178Dic44—21no—
179Dic44—21no—
180C8×D11—21no—
181C8×D11—21no—
182C11×C16—21no—
183C11×C16—21no—
184C11⋊C16—21no—
185C11⋊C16—21no—
186#3338—111no—
187D4×Q16—111no—
188#2241—111no—
189#2236—111no—
190#2236—111no—
191#2227—111no—
192#2216—111no—
193#2216—111no—
194#2209—111no—
195#2188—111no—
196#2188—111no—
197C4×Q32—111no—
198D4×C16—111no—
199C2×#358—111no—
200C2×#358D1111yescharacteristic, complemented
201C23×C11C2×D811yescharacteristic
202C22×D11C2×D811yescharacteristic
203Q8×C11—22no—
204Q8×C11—41no—
205Q8×C11—41no—
206Q8×C11—41no—
207Q8×C11—82no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—82no—
215C2×C4×C11—161no—
216C2×C4×C11C2×D811yescharacteristic
217C2×C4×C11C22×D411yescharacteristic
218C22⋊D11Q3214yescomplemented
219C2×Dic11—41no—
220C2×Dic11—41no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223C2×Dic11C2×D811yescharacteristic
224C2×Dic11C2×D811yescharacteristic
225C2×Dic11C2×D811yescharacteristic
226C4×D11—21no—
227C4×D11—21no—
228C4×D11—82no—
229C4×D11—161no—
230Dic22—41no—
231Dic22—41no—
232Dic22—41no—
233Dic22—41no—
234Dic22—82no—
235Dic22—161no—
236C8×C11—21no—
237C8×C11C2×#4111yescharacteristic
238C8×C11H(5,𝔽2)11yescharacteristic
239C11⋊C8—21no—
240C11⋊C8—21no—
241C22×Q16—111no—
242C22×Q16C2×D1111yescharacteristic
243#554—221no—
244D4×Q8—221no—
245C2×Q32—111no—
246C2×Q32—111no—
247C2×Q32—111no—
248C22×C16—111no—
249C22×C16C2×D1111yescharacteristic
250#500—111no—
251#494—111no—
252#484—221no—
253#484—221no—
254#477—221no—
255#467—111no—
256#467—111no—
257#467—111no—
258#467—111no—
259#462—221no—
260#451—221no—
261#451—221no—
262C4×Q16—111no—
263C4×Q16—111no—
264C8×D4—111no—
265C2×#107—111no—
266C2×#107C2×D1111yescharacteristic
267#366—111no—
268#366—111no—
269#366—111no—
270C4⋊C16—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
279#358C2×D1111yescharacteristic
280#358C2×D1111yescharacteristic
281C22⋊C16—111no—
282C22⋊C16—111no—
283C4×C16—111no—
284C22×C11—21no—
285C22×C11—21no—
286C22×C11C2×Q3212yes—
287C22×C11C22×D811yescharacteristic
288C2×D11—21no—
289C2×D11—21no—
290C2×D11C2×Q3212yes—
291C4×C11—21no—
292C4×C11—42no—
293C4×C11—81no—
294C4×C11—81no—
295C4×C11—81no—
296C4×C11#54611yescharacteristic
297C4×C11#57711yescharacteristic
298Dic11—21no—
299Dic11—21no—
300Dic11—81no—
301Dic11—81no—
302Dic11—81no—
303Dic11—81no—
304Dic11C2×Q3212yes—
305C22×Q8—21no—
306C22×Q8—221no—
307C2×Q16—22no—
308C2×Q16—21no—
309C2×Q16—41no—
310C2×Q16—111no—
311C2×Q16—111no—
312C2×Q16—221no—
313C2×Q16—221no—
314C2×Q16—222no—
315C2×Q16—441no—
316C2×Q16C22×D1111yescharacteristic
317C2×Q16C22×D1111yescharacteristic
318C22×C8—111no—
319C22×C8C22×D1111yescharacteristic
320C4⋊Q8—221no—
321C4⋊Q8—221no—
322C4⋊Q8—441no—
323#125—441no—
324C22⋊Q8—221no—
325C22⋊Q8—221no—
326C22⋊Q8—221no—
327C22⋊Q8—221no—
328C22⋊Q8—441no—
329C22⋊Q8—441no—
330C22⋊Q8—441no—
331C22⋊Q8—441no—
332C4×Q8—221no—
333C4×Q8—221no—
334C4×D4—111no—
335C4×D4—441no—
336C4×D4—441no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—221no—
339Q32—222no—
340Q32—441no—
341Q32—441no—
342C2×C16—41no—
343C2×C16—111no—
344C2×C16—111no—
345C2×C16—441no—
346C2×C16C22×D1111yescharacteristic
347C2×C16C22×D1111yescharacteristic
348#107—21no—
349#107—111no—
350#107—111no—
351#107—221no—
352#107—221no—
353#107C22×D1111yescharacteristic
354#107C22×D1111yescharacteristic
355C4⋊C8—111no—
356#103—221no—
357#103—221no—
358#103—221no—
359#103—221no—
360#103—221no—
361#103—221no—
362C22⋊C8—111no—
363C22⋊C8—111no—
364C4×C8—111no—
365C2×C11—22no—
366C2×C11#329411yescharacteristic
367C2×C11C22×Q3211yescharacteristic
368C2×C11#341611yescharacteristic
369D11—22no—
370C2×Q8—21no—
371C2×Q8—21no—
372C2×Q8—42no—
373C2×Q8—41no—
374C2×Q8—81no—
375C2×Q8—221no—
376C2×Q8—221no—
377C2×Q8—441no—
378C2×Q8—441no—
379C2×Q8—442no—
380C2×Q8—881no—
381C2×D4—111no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—111no—
385C22×C4—441no—
386C22×C4—441no—
387C22×C4D4×D1111yescharacteristic
388Q16—21no—
389Q16—21no—
390Q16—21no—
391Q16—42no—
392Q16—221no—
393Q16—221no—
394Q16—221no—
395Q16—221no—
396Q16—442no—
397Q16—881no—
398Q16#433912yes—
399C2×C8—21no—
400C2×C8—21no—
401C2×C8—111no—
402C2×C8—111no—
403C2×C8—221no—
404C2×C8—221no—
405C2×C8D4×D1111yescharacteristic
406C2×C8C23×D1111yescharacteristic
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—41no—
410C4⋊C4—111no—
411C4⋊C4—221no—
412C4⋊C4—221no—
413C4⋊C4—441no—
414C4⋊C4—441no—
415C4⋊C4—441no—
416C4⋊C4—441no—
417C4⋊C4—441no—
418C4⋊C4—441no—
419C4⋊C4—441no—
420C4⋊C4—441no—
421C4⋊C4—441no—
422C4⋊C4—441no—
423C22⋊C4—111no—
424C22⋊C4—111no—
425C22⋊C4—441no—
426C22⋊C4—441no—
427C22⋊C4—441no—
428C22⋊C4—441no—
429C42—111no—
430C42—441no—
431C42—441no—
432C16—21no—
433C16—21no—
434C16—221no—
435C16—221no—
436C11#3386611yescharacteristic, complemented, Sylow
437C23—111no—
438C23D8×D1111yescharacteristic
439Q8—22no—
440Q8—41no—
441Q8—41no—
442Q8—41no—
443Q8—82no—
444Q8—441no—
445Q8—441no—
446Q8—441no—
447Q8—441no—
448Q8—882no—
449Q8—1761no—
450D4—114no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—82no—
458C2×C4—111no—
459C2×C4—111no—
460C2×C4—111no—
461C2×C4—161no—
462C2×C4—221no—
463C2×C4—221no—
464C2×C4—441no—
465C2×C4—441no—
466C2×C4—441no—
467C2×C4—441no—
468C2×C4—882no—
469C2×C4—1761no—
470C2×C4D8×D1111yescharacteristic
471C2×C4C2×D4×D1111yescharacteristic
472C8—21no—
473C8—221no—
474C8—221no—
475C8C2×#433911yescharacteristic
476C8#6703711yescharacteristic
477C22—21no—
478C22—21no—
479C22—112no—
480C22—221no—
481C22—221no—
482C22D11×Q3212yes—
483C22C2×D8×D1111yescharacteristic
484C4—21no—
485C4—42no—
486C4—81no—
487C4—81no—
488C4—81no—
489C4—112no—
490C4—221no—
491C4—221no—
492C4—881no—
493C4—881no—
494C4—881no—
495C4—881no—
496C4#1062302111yescharacteristic
497C4#1062329311yescharacteristic
498C2—22no—
499C2—222no—
500C2#1308042511yescharacteristic
501C2C2×D11×Q3211yescharacteristic
502C2#1308175811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#358C2
socleC22×C11C22×D8
prime radicalC2×C22⋊D11D8
hypercenterC2×#358D11
hypocenterC11#33866
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#358

Complements

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

NH ≅ G/Ntype
3. #13070842C2semidirect
4. #13070818C2semidirect
5. #13070817C2semidirect
6. #13070766C2semidirect
7. #13070707C2semidirect
8. #13070706C2semidirect
9. #13070665C2semidirect
10. #13070551C2semidirect
11. #13070550C2semidirect
12. #13070472C2semidirect
14. D11×#358C2semidirect
15. C2×C11×#358C2semidirect
200. C2×#358D11semidirect
218. C22⋊D11Q32semidirect
436. C11#33866semidirect

Maximal subgroups

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

subgroupindex
#130810062
Q16×C22⋊D112
#130708422
#130708182
#130708172
#130707662
#130707072
#130707062
#130706652
#130705512
#130705502
#130704722
C16×C22⋊D112
D11×#3582
C2×C11×#3582
#3386611