Finite Group Databasebeta

← #14803274

Subgroups — #14803274

Order 2816.

954 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622628C211yesmaximal, characteristic
2C2×C8×Dic22C211yesmaximal, characteristic, complemented
3#13073618C211yesmaximal, characteristic, complemented
4#13073538C211yesmaximal, characteristic, complemented
5#13070005C212yesmaximal, complemented
6#13069925C212yesmaximal, complemented
7#13069479C212yesmaximal, complemented
8#13069422C211yesmaximal, characteristic, complemented
9#13069374C211yesmaximal, characteristic, complemented
10#13069297C212yesmaximal, complemented
11C4×C11×#102C211yesmaximal, characteristic, complemented
12C2×C4×D4×C11C2211yescharacteristic
13C22×#4323C2212yes—
14C2×#66977—21no—
15C2×#66928—21no—
16C2×#66927C2211yescharacteristic
17C2×C4×Dic22C2211yescharacteristic
18C2×C11×#102C2211yescharacteristic
19C2×C11×#102C2211yescharacteristic
20C2×C4×C8×C11C2211yescharacteristic
21C4×C11×C4⋊C4C2211yescharacteristic
22#10622834C2212yes—
23#10622825—21no—
24C2×#66885C2212yes—
25C2×#66885C2212yes—
26C2×Dic11⋊C8C2212yes—
27C2×C8×Dic11C2212yes—
28#10622628—24no—
29#10622601C2212yes—
30#10622601C2212yes—
31#10622586C2212yes—
32C2×#66873C2212yes—
33C2×#66871C2212yes—
34#10622561—22no—
35#10622552—21no—
36#10622548C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38C8×Dic22—24no—
39#10622285—22no—
40C11×#340C2211yescharacteristic
41C11×#340C2211yescharacteristic
42#10622167C2212yes—
43C22×D4×C11C2311yescharacteristic
44C23×C4×C11—21no—
45C22×D44—21no—
46C22×D44—21no—
47C22×D44C2312yes—
48C22×Dic22D411yescharacteristic
49C22×C8×C11C2311yescharacteristic
50C22×C8×C11C2311yescharacteristic
51C4×D4×C11—22no—
52C4×D4×C11—22no—
53C2×C11×C4⋊C4C2311yescharacteristic
54C2×C11×C4⋊C4C2311yescharacteristic
55C2×C11×C4⋊C4C2311yescharacteristic
56C2×C11×C22⋊C4—21no—
57C2×C42×C11—21no—
58C2×C42×C11C2311yescharacteristic
59C2×C22⋊Dic11—22no—
60C2×C22⋊Dic11—22no—
61C2×#4323—24no—
62C2×#4323—24no—
63C2×#4323—42no—
64C2×(C2×D11)⋊C4—22no—
65C2×(C2×D11)⋊C4—22no—
66C2×(C2×D11)⋊C4—22no—
67C2×(C2×D11)⋊C4—22no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11D411yescharacteristic
71C2×C4⋊Dic11C2312yes—
72#66977—44no—
73C2×Dic11⋊C4—22no—
74C2×Dic11⋊C4D412yes—
75C2×C4×Dic11C2312yes—
76C22×C11⋊C8C2312yes—
77#66928—44no—
78#66927—22no—
79#66927—22no—
80C4×Dic22—22no—
81C4×Dic22—22no—
82C11×#102—22no—
83C11×#102—22no—
84C4×C8×C11—22no—
85C11×#95—21no—
86C11⋊#95—22no—
87#66885—24no—
88#66885—42no—
89Dic11⋊C8—24no—
90C8×Dic11—24no—
91#66873—24no—
92#66871—42no—
93C4⋊(C11⋊C8)D414yes—
94#25292—111nomaximal, Sylow
95C24×C11—21no—
96C23×D11—22no—
97C2×D4×C11—21no—
98C2×D4×C11—21no—
99C2×D4×C11—21no—
100C2×D4×C11—21no—
101C2×D4×C11—21no—
102C2×D4×C11#4112yes—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—42no—
107C22×C4×C11—42no—
108C22×C4×C11—42no—
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2411yescharacteristic
112C22×Dic11—22no—
113C22×Dic11C2×D412yes—
114C22×Dic11C2×D412yes—
115C2×D44—22no—
116C2×D44—22no—
117C2×D44—22no—
118C2×D44—22no—
119C2×D44—22no—
120C2×D44—22no—
121C2×D44—42no—
122C2×D44—42no—
123C2×D44—42no—
124C2×D44—42no—
125C2×D44—81no—
126C2×D44—81no—
127C2×Dic22—22no—
128C2×Dic22—22no—
129C2×Dic22D814yescomplemented
130C2×C8×C11—21no—
131C2×C8×C11—21no—
132C2×C8×C11—21no—
133C2×C8×C11—21no—
134C2×C8×C11—21no—
135C2×C8×C11#4112yes—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C22⋊C4—42no—
143C42×C11—42no—
144C42×C11C2×D412yes—
145C42×C11#4112yes—
146C22⋊Dic11—44no—
147C22⋊Dic11—82no—
148#4323—48no—
149(C2×D11)⋊C4—44no—
150(C2×D11)⋊C4—44no—
151(C2×D11)⋊C4—82no—
152(C2×D11)⋊C4—82no—
153C4⋊Dic11—22no—
154C4⋊Dic11—22no—
155C4⋊Dic11—22no—
156C4⋊Dic11—42no—
157C4⋊Dic11—81no—
158Dic11⋊C4—24no—
159Dic11⋊C4—44no—
160C4×Dic11—22no—
161C4×Dic11—22no—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—22no—
164C2×C11⋊C8C2×D414yes—
165C2×#459—111no—
166C2×C8×Q8—111no—
167#2548—111no—
168#2538—111no—
169#2067—112no—
170#2054—112no—
171#1970—112no—
172#1957—111no—
173#1947—111no—
174#1934—112no—
175C4×#102D1111yescharacteristic, complemented
176C23×C11—22no—
177C23×C11—41no—
178C23×C11—41no—
179C23×C11—41no—
180C23×C11—41no—
181C23×C11—41no—
182C23×C11—41no—
183C23×C11C22×D411yescharacteristic
184C22×D11—42no—
185C22×D11—42no—
186C22×D11—42no—
187C22×D11—42no—
188C22×D11—42no—
189C22×D11—42no—
190C22×D11—42no—
191D4×C11—22no—
192D4×C11—22no—
193D4×C11—41no—
194D4×C11—41no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—84no—
207C2×C4×C11#12112yes—
208C2×C4×C11#12112yes—
209C2×C4×C11C2×D812yes—
210C2×C4×C11#13512yes—
211C2×C4×C11C22×D411yescharacteristic
212C2×C4×C11C2×#4111yescharacteristic
213C2×C4×C11C2×#4111yescharacteristic
214C2×C4×C11C2×#4111yescharacteristic
215C2×C4×C11H(5,𝔽2)11yescharacteristic
216C2×C4×C112−1+411yescharacteristic
217C2×Dic11—22no—
218C2×Dic11—22no—
219C2×Dic11—22no—
220C2×Dic11—22no—
221C2×Dic11—22no—
222C2×Dic11—42no—
223C2×Dic11—42no—
224C2×Dic11—42no—
225C2×Dic11C2×D814yes—
226D44—42no—
227D44—42no—
228D44—42no—
229D44—42no—
230D44—84no—
231D44—84no—
232Dic22—28no—
233C8×C11—22no—
234C8×C11—41no—
235C11⋊C8—24no—
236C22×D8—112no—
237C2×#127—111no—
238C2×#124—221no—
239C2×C22⋊Q8—221no—
240C2×C4×Q8—111no—
241C2×C4×D4C2×D1111yescharacteristic
242#459—224no—
243C8×Q8—224no—
244C2×#107—112no—
245C2×C4⋊C8—111no—
246C2×C4⋊C8—112no—
247C2×#102—112no—
248C2×#102—112no—
249C2×#102—112no—
250C2×#102C2×D1111yescharacteristic
251C2×#102C2×D1111yescharacteristic
252C2×C4×C8—112no—
253C2×C4×C8C2×D1111yescharacteristic
254#396—222no—
255#394—222no—
256#390—112no—
257#390—112no—
258#390—112no—
259#390—221no—
260#389—112no—
261#384—111no—
262#380—221no—
263C4×C4⋊C4C2×D1111yescharacteristic
264#340—112no—
265#340C2×D1111yescharacteristic
266#340C2×D1111yescharacteristic
267C22×C11—42no—
268C22×C11—42no—
269C22×C11—42no—
270C22×C11—81no—
271C22×C11—81no—
272C22×C11—81no—
273C22×C11—81no—
274C22×C11C2×#12111yescharacteristic
275C22×C11#54811yescharacteristic
276C22×C11#55011yescharacteristic
277C22×C11C22×D811yescharacteristic
278C22×C11C2×#13511yescharacteristic
279C22×C11#57611yescharacteristic
280C22×C11#57711yescharacteristic
281C2×D11—82no—
282C2×D11—82no—
283C2×D11—82no—
284C2×D11—82no—
285C2×D11—82no—
286C2×D11—82no—
287C2×D11—82no—
288C4×C11—22no—
289C4×C11—81no—
290C4×C11—81no—
291C4×C11—81no—
292C4×C11#46614yes—
293C4×C11#52911yescharacteristic
294C4×C11#54211yescharacteristic
295C4×C11#54611yescharacteristic
296C4×C11#54811yescharacteristic
297Dic11—24no—
298Dic11—42no—
299Dic11—82no—
300C22×Q8—111no—
301C22×D4—112no—
302C22×D4—221no—
303C22×D4—221no—
304C22×D4C22×D1111yescharacteristic
305C23×C4—21no—
306C2×D8—224no—
307C2×D8—224no—
308C2×D8—442no—
309C22×C8—112no—
310C22×C8C22×D1111yescharacteristic
311C22×C8C22×D1111yescharacteristic
312#127—222no—
313#127—222no—
314#124—444no—
315C22⋊Q8—444no—
316C4×Q8—222no—
317C4×Q8—222no—
318C4×D4—22no—
319C4×D4—22no—
320C2×C4⋊C4—111no—
321C2×C4⋊C4—112no—
322C2×C4⋊C4—112no—
323C2×C4⋊C4—222no—
324C2×C4⋊C4—221no—
325C2×C4⋊C4—221no—
326C2×C4⋊C4C22×D1111yescharacteristic
327C2×C4⋊C4C22×D1111yescharacteristic
328C2×C4⋊C4C22×D1111yescharacteristic
329C2×C22⋊C4—21no—
330C2×C22⋊C4—222no—
331C2×C22⋊C4—222no—
332C2×C22⋊C4—222no—
333C2×C22⋊C4—222no—
334C2×C22⋊C4—222no—
335C2×C22⋊C4—222no—
336C2×C42—21no—
337C2×C42—112no—
338C2×C42C22×D1111yescharacteristic
339#107—442no—
340C4⋊C8—114no—
341C4⋊C8—224no—
342#102—22no—
343#102—22no—
344#102—224no—
345#102—224no—
346#102—442no—
347C4×C8—22no—
348C4×C8—224no—
349#95—21no—
350#95—222no—
351C2×C11—82no—
352C2×C11#242611yescharacteristic
353C2×C11C2×#46611yescharacteristic
354C2×C11#306211yescharacteristic
355C2×C11#335811yescharacteristic
356C2×C11#336111yescharacteristic
357C2×C11#339111yescharacteristic
358C2×C11#339411yescharacteristic
359D11—162no—
360C24—21no—
361C24—222no—
362C2×Q8—114no—
363C2×Q8—222no—
364C2×Q8—222no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4—21no—
369C2×D4—21no—
370C2×D4—222no—
371C2×D4—222no—
372C2×D4—222no—
373C2×D4—222no—
374C2×D4—222no—
375C2×D4—222no—
376C2×D4—442no—
377C2×D4—442no—
378C2×D4—442no—
379C2×D4—442no—
380C2×D4—881no—
381C2×D4—881no—
382C2×D4#433912yes—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—42no—
387C22×C4—42no—
388C22×C4—42no—
389C22×C4—112no—
390C22×C4—112no—
391C22×C4—222no—
392C22×C4D4×D1111yescharacteristic
393C22×C4D4×D1111yescharacteristic
394C22×C4C23×D1111yescharacteristic
395D8—448no—
396C2×C8—21no—
397C2×C8—21no—
398C2×C8—21no—
399C2×C8—21no—
400C2×C8—21no—
401C2×C8—114no—
402C2×C8—222no—
403C2×C8—222no—
404C2×C8#433912yes—
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—224no—
412C4⋊C4—222no—
413C4⋊C4—222no—
414C4⋊C4—222no—
415C4⋊C4—444no—
416C4⋊C4—442no—
417C4⋊C4—881no—
418C22⋊C4—42no—
419C22⋊C4—444no—
420C22⋊C4—444no—
421C22⋊C4—444no—
422C22⋊C4—882no—
423C22⋊C4—882no—
424C22⋊C4—882no—
425C42—42no—
426C42—222no—
427C42—222no—
428C42#433912yes—
429C42D4×D1112yes—
430C11#2529211yescharacteristic, complemented, Sylow
431C23—22no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—41no—
436C23—41no—
437C23—41no—
438C23—442no—
439C23—442no—
440C23—442no—
441C23—442no—
442C23—442no—
443C23—442no—
444C23—442no—
445C23C2×D4×D1111yescharacteristic
446Q8—228no—
447D4—22no—
448D4—22no—
449D4—41no—
450D4—41no—
451D4—442no—
452D4—442no—
453D4—442no—
454D4—442no—
455D4—884no—
456D4—884no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—84no—
469C2×C4—114no—
470C2×C4—222no—
471C2×C4—222no—
472C2×C4—222no—
473C2×C4—222no—
474C2×C4—222no—
475C2×C4—442no—
476C2×C4—442no—
477C2×C4—442no—
478C2×C4#6693712yes—
479C2×C4#6693712yes—
480C2×C4D8×D1112yes—
481C2×C4#6696912yes—
482C2×C4C2×#433911yescharacteristic
483C2×C4C2×#433911yescharacteristic
484C2×C4C2×#433911yescharacteristic
485C2×C4C2×D4×D1111yescharacteristic
486C2×C4#6704211yescharacteristic
487C2×C4#6704311yescharacteristic
488C8—22no—
489C8—41no—
490C8—224no—
491C22—42no—
492C22—42no—
493C22—42no—
494C22—81no—
495C22—81no—
496C22—81no—
497C22—81no—
498C22—882no—
499C22—882no—
500C22—882no—
501C22—882no—
502C22—882no—
503C22—882no—
504C22—882no—
505C22C2×#6693711yescharacteristic
506C22#1062308311yescharacteristic
507C22#1062308411yescharacteristic
508C22C2×D8×D1111yescharacteristic
509C22C2×#6696911yescharacteristic
510C22#1062330011yescharacteristic
511C22#1062330111yescharacteristic
512C4—22no—
513C4—81no—
514C4—81no—
515C4—81no—
516C4—224no—
517C4—442no—
518C4—882no—
519C4#1062238814yes—
520C4#1062301011yescharacteristic
521C4#1062306511yescharacteristic
522C4#1062308111yescharacteristic
523C4#1062308311yescharacteristic
524C2—82no—
525C2—1762no—
526C2#1307218211yescharacteristic
527C2C2×#1062238811yescharacteristic
528C2#1307829911yescharacteristic
529C2#1308124911yescharacteristic
530C2#1308127411yescharacteristic
531C2#1308159011yescharacteristic
532C2#1308161011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×#102C2
socleC23×C11C22×D4
prime radicalC2×#10622628C2
hypercenterC4×#102D11
hypocenterC11#25292
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
2. C2×C8×Dic22C2semidirect
3. #13073618C2semidirect
4. #13073538C2semidirect
5. #13070005C2semidirect
6. #13069925C2semidirect
7. #13069479C2semidirect
8. #13069422C2semidirect
9. #13069374C2semidirect
10. #13069297C2semidirect
11. C4×C11×#102C2semidirect
129. C2×Dic22D8semidirect
175. C4×#102D11semidirect
430. C11#25292semidirect

Maximal subgroups

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

subgroupindex
C2×#106226282
C2×C8×Dic222
#130736182
#130735382
#130700052
#130699252
#130694792
#130694222
#130693742
#130692972
C4×C11×#1022
#2529211