Finite Group Databasebeta

← #14792690

Subgroups — #14792690

Order 2816.

976 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622659C211yesmaximal, characteristic
2#13077274C211yesmaximal, characteristic, complemented
3C2×#10622614C211yesmaximal, characteristic
4#13069973C212yesmaximal, complemented
5#13069876C212yesmaximal, complemented
6#13069518C212yesmaximal, complemented
7#13069277C212yesmaximal, complemented
8#13069085C211yesmaximal, characteristic, complemented
9#13068820C211yesmaximal, characteristic, complemented
10#13068536C211yesmaximal, characteristic
11C11×#3095C211yesmaximal, characteristic, complemented
12C23×D44C2211yescharacteristic
13C2×C11×C22⋊Q8C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C22×#4325C2212yes—
16C22×#4318C2211yescharacteristic
17C11×#485—21no—
18C11×#485—21no—
19C11×#484—21no—
20C11×#483—21no—
21C11×#428C2211yescharacteristic, complemented
22C11×#428C2211yescharacteristic, complemented
23C11×#419C2211yescharacteristic, complemented
24C11×#419C2211yescharacteristic, complemented
25C11×#407C2211yescharacteristic
26C2×#66900C2212yescomplemented
27#10622820C2211yescharacteristic
28C2×C22⋊(C11⋊C8)C2211yescharacteristic
29C2×#66887C2212yes—
30C2×#66887C2212yes—
31C2×#66886C2212yescomplemented
32#10622659—21no—
33#10622659—21no—
34#10622659—22no—
35#10622614—21no—
36#10622614—21no—
37#10622614C2212yes—
38#10622614C2212yes—
39#10622613—22no—
40#10622612C2212yescomplemented
41#10622610C2212yescomplemented
42C2×#66873—21no—
43C2×#66873—21no—
44C2×#66873C2212yes—
45#10622539—21no—
46#10622538—21no—
47#10622196C2212yescomplemented
48#10622168C2212yescomplemented
49C24×D11—21no—
50C22×Q8×C11C2311yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C22×D44—21no—
53C22×D44—21no—
54C22×D44—24no—
55C22×D44—21no—
56C22×D44—21no—
57C22×D44—21no—
58C22×D44—42no—
59C22×D44C2312yes—
60C2×C11×M16C2311yescharacteristic
61C2×C11×M16C2311yescharacteristic
62C11×C22⋊Q8—21no—
63C11×C22⋊Q8—21no—
64C11×C22⋊Q8—21no—
65C11×C22⋊Q8—21no—
66C11×#117—21no—
67C11×#117—21no—
68C11×#117D411yescharacteristic
69C11×#117D411yescharacteristic
70C11×#117C2311yescharacteristic
71C11×#117C2311yescharacteristic
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C11×C4⋊C4D411yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C42×C11—21no—
79C2×#4325—24no—
80C2×#4325—22no—
81C2×#4325—22no—
82C2×#4325—42no—
83C2×#4318—21no—
84C2×#4318—42no—
85C2×#4318C2312yes—
86C2×#4318C2312yes—
87C22×C11⋊C8—21no—
88C22×C11⋊C8C2312yes—
89C11×#107—21no—
90C11×#107—21no—
91C11×#106—21no—
92C11×#106—21no—
93C11×#103—21no—
94C11×#103—21no—
95C11×#103—21no—
96C11×#103—21no—
97C11×C22⋊C8—21no—
98C11×C22⋊C8—21no—
99#66900—42no—
100C22⋊(C11⋊C8)—21no—
101C22⋊(C11⋊C8)—21no—
102C22⋊(C11⋊C8)D411yescharacteristic
103C22⋊(C11⋊C8)D411yescharacteristic
104C22⋊(C11⋊C8)D412yes—
105#66887—24no—
106#66887—42no—
107#66886—42no—
108#66873—22no—
109#66873—22no—
110#66873—22no—
111#66873—22no—
112#66873—22no—
113#66873—22no—
114C4⋊(C11⋊C8)—22no—
115C4⋊(C11⋊C8)—22no—
116#66867—22no—
117C4×C11⋊C8—22no—
118#24521—111nomaximal, Sylow
119C24×C11#4111yescharacteristic
120C23×D11—22no—
121C23×D11—44no—
122C23×D11—41no—
123C23×D11—41no—
124C23×D11—82no—
125C23×D11—82no—
126C2×Q8×C11—21no—
127C2×Q8×C11—21no—
128C2×Q8×C11—22no—
129C2×Q8×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11#4111yescharacteristic
141C22×C4×C11C2411yescharacteristic
142C2×D44—24no—
143C2×D44—24no—
144C2×D44—22no—
145C2×D44—22no—
146C2×D44—22no—
147C2×D44—22no—
148C2×D44—22no—
149C2×D44—44no—
150C2×D44—44no—
151C2×D44—44no—
152C2×D44—42no—
153C2×D44—42no—
154C2×D44—41no—
155C2×D44—41no—
156C2×D44#4114yes—
157C11×M16—22no—
158C11×M16—22no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—41no—
166C11×C4⋊C4—41no—
167C11×C4⋊C4C2×D411yescharacteristic
168C11×C4⋊C4C2×D411yescharacteristic
169C11×C4⋊C4C2×D411yescharacteristic
170C11×C4⋊C4C2×D411yescharacteristic
171C11×C22⋊C4—21no—
172C11×C22⋊C4—21no—
173C11×C22⋊C4—21no—
174C11×C22⋊C4—21no—
175C11×C22⋊C4—41no—
176C11×C22⋊C4—41no—
177C42×C11—21no—
178C42×C11—21no—
179C42×C11—21no—
180C42×C11—21no—
181#4325—44no—
182#4325—44no—
183#4318—22no—
184#4318—22no—
185#4318—22no—
186#4318—22no—
187#4318—42no—
188C2×C11⋊C8—22no—
189C2×C11⋊C8—22no—
190C2×C11⋊C8—22no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—42no—
193C2×C11⋊C8C2×D412yes—
194C2×C11⋊C8C2×D412yes—
195#3095D1111yescharacteristic, complemented
196C2×#450—111no—
197#2924—111no—
198C2×#418—111no—
199#2063—112no—
200#2046—112no—
201#1977—112no—
202#1931—112no—
203#1901—111no—
204#1855—111no—
205#1783—111no—
206C23×C11—22no—
207C23×C11—22no—
208C23×C11—41no—
209C23×C11#12111yescharacteristic
210C23×C11#12111yescharacteristic
211C23×C11C2×#4111yescharacteristic
212C22×D11—24no—
213C22×D11—44no—
214C22×D11—44no—
215C22×D11—42no—
216C22×D11—42no—
217C22×D11—82no—
218C22×D11—82no—
219C22×D11—82no—
220C22×D11—816no—
221C22×D11—82no—
222C22×D11—82no—
223C22×D11—82no—
224Q8×C11—41no—
225Q8×C11—41no—
226Q8×C11—42no—
227C2×C4×C11—22no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—42no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—42no—
242C2×C4×C11—81no—
243C2×C4×C11—81no—
244C2×C4×C11#12111yescharacteristic
245C2×C4×C11#12111yescharacteristic
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C2×#4112yes—
249C2×C4×C11H(5,𝔽2)12yes—
250D44—24no—
251D44—24no—
252D44—44no—
253D44—44no—
254D44—42no—
255D44—42no—
256C8×C11—41no—
257C8×C11—41no—
258C11⋊C8—22no—
259C11⋊C8—22no—
260C11⋊C8—42no—
261C11⋊C8—42no—
262C23×D4—111no—
263C22×SD16—112no—
264C22×M16—111no—
265C2×C22⋊Q8C2×D1111yescharacteristic
266C2×#117C2×D1111yescharacteristic
267#485—21no—
268#485—21no—
269#484—21no—
270#483—21no—
271#450—221no—
272#450—221no—
273#450—222no—
274#433—222no—
275#432—221no—
276#431—221no—
277C2×#108—112no—
278#428C2×D1111yescharacteristic, complemented
279#428C2×D1111yescharacteristic, complemented
280#424—112no—
281#419C2×D1111yescharacteristic, complemented
282#419C2×D1111yescharacteristic, complemented
283#418—112no—
284#418—112no—
285#418—221no—
286#418—221no—
287C2×#102—112no—
288C2×#102—221no—
289C2×#102—221no—
290C2×#101—112no—
291C2×#100—112no—
292C2×#100—112no—
293#407—111no—
294#407C2×D1111yescharacteristic
295C2×C22⋊C8—111no—
296#405—112no—
297#343—112no—
298#341—112no—
299C22×C11—21no—
300C22×C11—21no—
301C22×C11—21no—
302C22×C11—21no—
303C22×C11—21no—
304C22×C11—21no—
305C22×C11—21no—
306C22×C11—44no—
307C22×C11#47112yes—
308C22×C11C2×#12111yescharacteristic
309C22×C11#55112yes—
310C2×D11—44no—
311C2×D11—84no—
312C2×D11—88no—
313C2×D11—88no—
314C2×D11—82no—
315C2×D11—82no—
316C2×D11—84no—
317C4×C11—21no—
318C4×C11—21no—
319C4×C11—41no—
320C4×C11—41no—
321C4×C11—41no—
322C4×C11—41no—
323C4×C11—81no—
324C4×C11—81no—
325C4×C11#52511yescharacteristic
326C4×C11#53511yescharacteristic
327C4×C11#54612yes—
328C25—221no—
329C22×Q8C22×D1111yescharacteristic
330C22×D4—112no—
331C22×D4—224no—
332C22×D4—221no—
333C22×D4—221no—
334C22×D4—221no—
335C22×D4—221no—
336C22×D4—221no—
337C22×D4—442no—
338C23×C4C22×D1111yescharacteristic
339C2×SD16—222no—
340C2×SD16—222no—
341C2×SD16—224no—
342C2×SD16—442no—
343C2×M16—112no—
344C2×M16—112no—
345C2×M16—221no—
346C2×M16—442no—
347C2×M16C22×D1111yescharacteristic
348C2×M16C22×D1111yescharacteristic
349C22×C8—112no—
350C22×C8—221no—
351C22⋊Q8—21no—
352C22⋊Q8—21no—
353C22⋊Q8—21no—
354C22⋊Q8—21no—
355#117—21no—
356#117—21no—
357#117C22⋊D1111yescharacteristic
358#117C22⋊D1111yescharacteristic
359#117C22×D1111yescharacteristic
360#117C22×D1111yescharacteristic
361C2×C4⋊C4—21no—
362C2×C4⋊C4C22⋊D1111yescharacteristic
363C2×C4⋊C4C22⋊D1111yescharacteristic
364C2×C4⋊C4C22×D1111yescharacteristic
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C42—21no—
368#108—442no—
369#107—21no—
370#107—21no—
371#106—21no—
372#106—21no—
373C4⋊C8—222no—
374C4⋊C8—222no—
375#103—21no—
376#103—21no—
377#103—21no—
378#103—21no—
379#102—222no—
380#102—222no—
381#102—222no—
382#102—222no—
383#102—222no—
384#102—222no—
385#101—442no—
386#100—224no—
387#100—442no—
388C22⋊C8—21no—
389C22⋊C8—21no—
390C22⋊C8—111no—
391C22⋊C8—111no—
392C22⋊C8—112no—
393C22⋊C8—221no—
394C22⋊C8—221no—
395#97—222no—
396C4×C8—222no—
397C2×C11—22no—
398C2×C11—22no—
399C2×C11—41no—
400C2×C11#241111yescharacteristic
401C2×C11C2×#47111yescharacteristic
402C2×C11#306811yescharacteristic
403D11—84no—
404C24—222no—
405C24—444no—
406C24—441no—
407C24—441no—
408C24—882no—
409C24—882no—
410C24#434111yescharacteristic
411C2×Q8—21no—
412C2×Q8—22no—
413C2×Q8—22no—
414C2×Q8—21no—
415C2×D4—114no—
416C2×D4—224no—
417C2×D4—224no—
418C2×D4—222no—
419C2×D4—222no—
420C2×D4—222no—
421C2×D4—222no—
422C2×D4—222no—
423C2×D4—444no—
424C2×D4—444no—
425C2×D4—444no—
426C2×D4—442no—
427C2×D4—442no—
428C2×D4—441no—
429C2×D4—441no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4D4×D1111yescharacteristic
437C22×C4D4×D1111yescharacteristic
438C22×C4#434111yescharacteristic
439C22×C4C2×C22⋊D1111yescharacteristic
440C22×C4C2×C22⋊D1111yescharacteristic
441C22×C4C23×D1111yescharacteristic
442SD16—444no—
443SD16—444no—
444M16—22no—
445M16—22no—
446M16—222no—
447M16—222no—
448M16—222no—
449M16—222no—
450M16—442no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—112no—
454C2×C8—112no—
455C2×C8—222no—
456C2×C8—222no—
457C2×C8—222no—
458C2×C8—222no—
459C2×C8—442no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4C2×C22⋊D1111yescharacteristic
467C4⋊C4C2×C22⋊D1111yescharacteristic
468C4⋊C4C2×C22⋊D1111yescharacteristic
469C4⋊C4C2×C22⋊D1111yescharacteristic
470C22⋊C4—21no—
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—41no—
475C22⋊C4—41no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—21no—
480C11#2452111yescharacteristic, complemented, Sylow
481C23—22no—
482C23—22no—
483C23—41no—
484C23—224no—
485C23—444no—
486C23—444no—
487C23—442no—
488C23—442no—
489C23—882no—
490C23—882no—
491C23—882no—
492C23—882no—
493C23—882no—
494C23—8816no—
495C23—882no—
496C23#6699211yescharacteristic
497C23#6699211yescharacteristic
498C23C2×#434111yescharacteristic
499Q8—41no—
500Q8—41no—
501Q8—42no—
502D4—224no—
503D4—224no—
504D4—444no—
505D4—444no—
506D4—442no—
507D4—442no—
508C2×C4—22no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—42no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—81no—
524C2×C4—81no—
525C2×C4#6699211yescharacteristic
526C2×C4#6699211yescharacteristic
527C2×C4C2×D4×D1111yescharacteristic
528C2×C4#41×D1112yes—
529C2×C4#6704212yes—
530C2×C4C22×C22⋊D1111yescharacteristic
531C8—41no—
532C8—41no—
533C8—222no—
534C8—222no—
535C8—442no—
536C8—442no—
537C22—21no—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—44no—
545C22—444no—
546C22—884no—
547C22—888no—
548C22—884no—
549C22—888no—
550C22—882no—
551C22—882no—
552C22#1062281612yes—
553C22#1062318912yes—
554C22C2×#6699211yescharacteristic
555C4—21no—
556C4—21no—
557C4—41no—
558C4—41no—
559C4—41no—
560C4—41no—
561C4—81no—
562C4—81no—
563C4#1062318512yes—
564C4#1062335911yescharacteristic
565C4#1062336111yescharacteristic
566C2—22no—
567C2—22no—
568C2—41no—
569C2—884no—
570C2#1307200211yescharacteristic
571C2C2×#1062281611yescharacteristic
572C2#1307834611yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3095C2
socleC22×C11C2×#121
prime radicalC23×D44C22
hypercenter#3095D11
hypocenterC11#24521
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3095

Complements

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

NH ≅ G/Ntype
2. #13077274C2semidirect
4. #13069973C2semidirect
5. #13069876C2semidirect
6. #13069518C2semidirect
7. #13069277C2semidirect
8. #13069085C2semidirect
9. #13068820C2semidirect
11. C11×#3095C2semidirect
21. C11×#428C22semidirect
22. C11×#428C22semidirect
23. C11×#419C22semidirect
24. C11×#419C22semidirect
26. C2×#66900C22semidirect
31. C2×#66886C22semidirect
40. #10622612C22semidirect
41. #10622610C22semidirect
47. #10622196C22semidirect
48. #10622168C22semidirect
195. #3095D11semidirect
278. #428C2×D11semidirect
279. #428C2×D11semidirect
281. #419C2×D11semidirect
282. #419C2×D11semidirect
480. C11#24521semidirect

Maximal subgroups

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

subgroupindex
C2×#106226592
#130772742
C2×#106226142
#130699732
#130698762
#130695182
#130692772
#130690852
#130688202
#130685362
C11×#30952
#2452111