Finite Group Databasebeta

← #14809903

Subgroups — #14809903

Order 2816.

1056 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623110C211yesmaximal, characteristic
2C2×#10622693C211yesmaximal, characteristic, complemented
3C2×#10622700C211yesmaximal, characteristic
4#13069954C212yesmaximal, complemented
5#13069944C212yesmaximal, complemented
6#13069573C211yesmaximal, characteristic, complemented
7#13069557C211yesmaximal, characteristic, complemented
8#13068876C212yesmaximal
9#13068862C212yesmaximal
10#13068444C211yesmaximal, characteristic
11C11×#2567C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C2×#66999—21no—
15#10623110—24no—
16#10623110—24no—
17C2×#66949—21no—
18C2×#66949—21no—
19C2×C4⋊C4×D11—21no—
20C2×C4×D44C2211yescharacteristic
21C2×C4×D44C2211yescharacteristic
22C2×C4×D44C2211yescharacteristic
23C2×#66923C2211yescharacteristic
24C2×#66923C2211yescharacteristic
25C2×#66922C2211yescharacteristic
26C11×#395—21no—
27C11×#395—21no—
28C11×#391—21no—
29C11×#389C2212yes—
30C11×#389C2212yes—
31C11×#384—21no—
32C4×C11×C4⋊C4C2211yescharacteristic
33#10622700—24no—
34#10622693—24no—
35C2×#66873C2212yes—
36C2×#66873C2212yes—
37C2×#66872C2212yes—
38C2×#66871C2212yes—
39C2×#66871C2212yes—
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×#66867C2211yescharacteristic
42#10622167C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45#10622162C2212yes—
46#10622162C2212yes—
47C22×Q8×C11—21no—
48C22×Q8×C11D411yescharacteristic
49C22×D44C2311yescharacteristic
50C22×C4×D11—21no—
51C22×C4×D11—21no—
52C22×C4×D11—21no—
53C22×Dic22—21no—
54C11×C4⋊Q8—22no—
55C11×C4⋊Q8—22no—
56C4×Q8×C11—22no—
57C4×Q8×C11—22no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4D411yescharacteristic
62C2×C11×C4⋊C4D411yescharacteristic
63C2×C11×C4⋊C4D411yescharacteristic
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C4⋊C4C2312yes—
66C2×C42×C11—21no—
67C2×C42×C11C2311yescharacteristic
68C2×C42×C11C2311yescharacteristic
69C2×C42×C11C2311yescharacteristic
70#66999—28no—
71C2×(C2×D11)⋊C4—21no—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11C2311yescharacteristic
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2311yescharacteristic
78C2×Dic11⋊C4—21no—
79C2×Dic11⋊C4—21no—
80C2×Dic11⋊C4—21no—
81C2×Dic11⋊C4—21no—
82C22×C11⋊C8C2312yes—
83C22×C11⋊C8C2312yes—
84#66949—28no—
85#66949—28no—
86C4⋊C4×D11—28no—
87C4×D44—22no—
88C4×D44—22no—
89C4×D44—22no—
90C4×D44—22no—
91C4×D44—22no—
92C4×D44D414yes—
93#66923—22no—
94#66923—22no—
95#66923—22no—
96#66923D414yes—
97#66922—22no—
98#66922—22no—
99C11×#95—21no—
100C11×#95—22no—
101C11×#95—22no—
102#66873—24no—
103#66873Q818yescomplemented
104#66872—24no—
105#66871—24no—
106#66871—24no—
107C4⋊(C11⋊C8)—22no—
108#66867—22no—
109#25850—111nomaximal, Sylow
110C23×D11—21no—
111C2×Q8×C11—22no—
112C2×Q8×C11—22no—
113C2×Q8×C11—41no—
114C2×Q8×C11—42no—
115C2×Q8×C11—82no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2411yescharacteristic
125C22×Dic11—21no—
126C22×Dic11—21no—
127C22×Dic11—21no—
128C2×D44—21no—
129C2×D44—22no—
130C2×D44C2×D412yes—
131C2×D44C2×Q814yes—
132C2×C4×D11—24no—
133C2×C4×D11—24no—
134C2×C4×D11—24no—
135C2×C4×D11—42no—
136C2×C4×D11—42no—
137C2×C4×D11—82no—
138C2×C4×D11—82no—
139C2×Dic22—24no—
140C2×Dic22—82no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—42no—
148C11×C4⋊C4—82no—
149C11×C4⋊C4—82no—
150C11×C4⋊C4C2×Q814yes—
151C42×C11—21no—
152C42×C11—21no—
153C42×C11—21no—
154C42×C11—21no—
155C42×C11—42no—
156C42×C11C2×D412yes—
157C42×C11C2×D412yes—
158(C2×D11)⋊C4—24no—
159(C2×D11)⋊C4—24no—
160(C2×D11)⋊C4—24no—
161C4⋊Dic11—24no—
162C4⋊Dic11—21no—
163C4⋊Dic11—21no—
164C4⋊Dic11—21no—
165C4⋊Dic11C2×D412yes—
166C4⋊Dic11C2×D412yes—
167C4⋊Dic11C2×D412yes—
168Dic11⋊C4—24no—
169Dic11⋊C4—24no—
170Dic11⋊C4—24no—
171Dic11⋊C4—24no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—22no—
175C2×C11⋊C8—24no—
176C2×C11⋊C8C2×Q814yes—
177C2×#554—111no—
178C2×#501—111no—
179C2×#474—111no—
180#2567D1111yescharacteristic, complemented
181#2059—112no—
182#2057—112no—
183#1989—111no—
184#1985—111no—
185#1864—112no—
186#1862—112no—
187#1762—111no—
188C23×C11C22×D411yescharacteristic
189C22×D11—22no—
190C22×D11—24no—
191C22×D11—41no—
192C22×D11—41no—
193C22×D11—42no—
194Q8×C11—44no—
195Q8×C11—84no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—22no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—24no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11#12012yes—
215C2×C4×C11#12012yes—
216C2×C4×C11#13712yes—
217C2×C4×C11C22×D411yescharacteristic
218C2×C4×C11C22×D411yescharacteristic
219C2×C4×C11C22×Q812yes—
220C2×C4×C112−1+412yes—
221C2×Dic11—22no—
222C2×Dic11—22no—
223C2×Dic11—22no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226C2×Dic11—42no—
227C2×Dic11—42no—
228D44—22no—
229D44—24no—
230D44C4⋊Q814yes—
231C4×D11—48no—
232C4×D11—84no—
233C4×D11—84no—
234Dic22—84no—
235C11⋊C8—24no—
236C11⋊C8—42no—
237#554—224no—
238#554—224no—
239C2×C4⋊Q8—111no—
240C2×C4⋊Q8C2×D1111yescharacteristic
241C2×#125—111no—
242C2×#125—111no—
243C2×C22⋊Q8—221no—
244C2×C22⋊Q8—221no—
245C2×C22⋊Q8—221no—
246C2×C4×Q8C2×D1111yescharacteristic
247C2×C4×D4—111no—
248C2×C4×D4—111no—
249C2×C4×D4—111no—
250C22×C4⋊C4—221no—
251#501—224no—
252#474—224no—
253C2×#107—112no—
254C2×#107—112no—
255C2×#106—112no—
256C2×C4⋊C8—111no—
257C2×#102—112no—
258C2×#102—112no—
259C2×#97—111no—
260#395—21no—
261#395—21no—
262#391—21no—
263#389C2×D1112yes—
264#389C2×D1112yes—
265#384—21no—
266C4×C4⋊C4C2×D1111yescharacteristic
267#340—112no—
268#340—112no—
269#340—112no—
270#336—112no—
271#336—112no—
272C22×C11C2×#12011yescharacteristic
273C22×C11D4×Q812yes—
274C22×C11C2×#13711yescharacteristic
275C22×C11#57511yescharacteristic
276C22×C11#57612yes—
277C2×D11—24no—
278C2×D11—44no—
279C2×D11—44no—
280C2×D11—42no—
281C2×D11—42no—
282C4×C11—22no—
283C4×C11—22no—
284C4×C11—22no—
285C4×C11—44no—
286C4×C11—41no—
287C4×C11—41no—
288C4×C11—41no—
289C4×C11—82no—
290C4×C11C2×C4⋊Q811yescharacteristic
291C4×C11#53611yescharacteristic
292C4×C11D4×Q812yes—
293Dic11—42no—
294Dic11—42no—
295Dic11—42no—
296C22×Q8—21no—
297C22×Q8—221no—
298C22×Q8C22⋊D1111yescharacteristic
299C22×D4—111no—
300C23×C4—221no—
301C23×C4—221no—
302C23×C4—221no—
303C22×C8—112no—
304C22×C8—112no—
305C4⋊Q8—22no—
306C4⋊Q8—22no—
307C4⋊Q8—222no—
308C4⋊Q8—222no—
309#125—114no—
310#125—222no—
311#125—222no—
312#125—222no—
313C22⋊Q8—228no—
314C22⋊Q8—228no—
315C22⋊Q8—228no—
316C4×Q8—22no—
317C4×Q8—22no—
318C4×D4—114no—
319C4×D4—222no—
320C4×D4—222no—
321C4×D4—222no—
322C4×D4—222no—
323C4×D4—222no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—111no—
328C2×C4⋊C4—111no—
329C2×C4⋊C4—111no—
330C2×C4⋊C4—228no—
331C2×C4⋊C4—221no—
332C2×C4⋊C4—221no—
333C2×C4⋊C4—221no—
334C2×C4⋊C4—221no—
335C2×C4⋊C4—221no—
336C2×C4⋊C4C22⋊D1111yescharacteristic
337C2×C4⋊C4C22⋊D1111yescharacteristic
338C2×C4⋊C4C22⋊D1111yescharacteristic
339C2×C4⋊C4C22×D1112yes—
340C2×C4⋊C4C22×D1112yes—
341C2×C22⋊C4—221no—
342C2×C22⋊C4—221no—
343C2×C22⋊C4—221no—
344C2×C42—21no—
345C2×C42C22×D1111yescharacteristic
346C2×C42C22×D1111yescharacteristic
347C2×C42C22×D1111yescharacteristic
348#107—224no—
349#107—224no—
350#106—224no—
351C4⋊C8—222no—
352#102—118no—
353#102—224no—
354#97—222no—
355#95—21no—
356#95—22no—
357#95—22no—
358C2×C11#243411yescharacteristic
359C2×C11#300711yescharacteristic
360C2×C11#300811yescharacteristic
361C2×C11#338512yes—
362C2×C11#338912yes—
363D11—44no—
364C24—221no—
365C2×Q8—22no—
366C2×Q8—22no—
367C2×Q8—41no—
368C2×Q8—42no—
369C2×Q8—82no—
370C2×Q8—224no—
371C2×Q8—882no—
372C2×D4—112no—
373C2×D4—114no—
374C2×D4—221no—
375C2×D4—222no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—224no—
379C22×C4—224no—
380C22×C4—221no—
381C22×C4—221no—
382C22×C4—221no—
383C22×C4—224no—
384C22×C4—442no—
385C22×C4—442no—
386C22×C4—882no—
387C22×C4—882no—
388C22×C4C2×C22⋊D1111yescharacteristic
389C22×C4C2×C22⋊D1111yescharacteristic
390C22×C4C2×C22⋊D1111yescharacteristic
391C22×C4C2×C22⋊D1111yescharacteristic
392C22×C4C2×C22⋊D1111yescharacteristic
393C22×C4C2×C22⋊D1111yescharacteristic
394C22×C4C23×D1111yescharacteristic
395C2×C8—114no—
396C2×C8—222no—
397C2×C8—222no—
398C2×C8—222no—
399C2×C8—224no—
400C4⋊C4—22no—
401C4⋊C4—22no—
402C4⋊C4—22no—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—42no—
407C4⋊C4—82no—
408C4⋊C4—82no—
409C4⋊C4—112no—
410C4⋊C4—112no—
411C4⋊C4—112no—
412C4⋊C4—224no—
413C4⋊C4—224no—
414C4⋊C4—224no—
415C4⋊C4—224no—
416C4⋊C4—224no—
417C4⋊C4—221no—
418C4⋊C4—221no—
419C4⋊C4—221no—
420C4⋊C4Q8×D1114yes—
421C22⋊C4—224no—
422C22⋊C4—224no—
423C22⋊C4—224no—
424C42—21no—
425C42—21no—
426C42—21no—
427C42—21no—
428C42—42no—
429C42D4×D1112yes—
430C42D4×D1112yes—
431C11#2585011yescharacteristic, complemented, Sylow
432C23—222no—
433C23—224no—
434C23—441no—
435C23—441no—
436C23—442no—
437C23C22×C22⋊D1111yescharacteristic
438Q8—44no—
439Q8—84no—
440Q8—884no—
441D4—114no—
442D4—222no—
443D4—224no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—22no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—24no—
454C2×C4—21no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—222no—
463C2×C4—222no—
464C2×C4—222no—
465C2×C4—448no—
466C2×C4—441no—
467C2×C4—441no—
468C2×C4—442no—
469C2×C4—442no—
470C2×C4—884no—
471C2×C4—884no—
472C2×C4#6699012yes—
473C2×C4#6699012yes—
474C2×C4#6699512yes—
475C2×C4C2×D4×D1111yescharacteristic
476C2×C4C2×D4×D1111yescharacteristic
477C2×C4C2×Q8×D1112yes—
478C2×C4#6704012yes—
479C8—224no—
480C8—442no—
481C22—224no—
482C22—442no—
483C22—442no—
484C22—444no—
485C22—444no—
486C22C2×#6699011yescharacteristic
487C22C2×#6699511yescharacteristic
488C22Q8×C22⋊D1112yes—
489C22#1062335311yescharacteristic
490C22#1062336612yes—
491C4—22no—
492C4—22no—
493C4—22no—
494C4—41no—
495C4—41no—
496C4—41no—
497C4—44no—
498C4—82no—
499C4—442no—
500C4—442no—
501C4—442no—
502C4D11×C4⋊Q811yescharacteristic
503C4#1062325511yescharacteristic
504C4#1062325812yes—
505C2—444no—
506C2#1307225711yescharacteristic
507C2#1307787411yescharacteristic
508C2#1307788211yescharacteristic
509C2#1308152212yes—
510C2#1308157012yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2567C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#2567D11
hypocenterC11#25850
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #2567

Complements

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

NH ≅ G/Ntype
2. C2×#10622693C2semidirect
4. #13069954C2semidirect
5. #13069944C2semidirect
6. #13069573C2semidirect
7. #13069557C2semidirect
11. C11×#2567C2semidirect
103. #66873Q8semidirect
180. #2567D11semidirect
431. C11#25850semidirect

Maximal subgroups

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

subgroupindex
C2×#106231102
C2×#106226932
C2×#106227002
#130699542
#130699442
#130695732
#130695572
#130688762
#130688622
#130684442
C11×#25672
#2585011