Finite Group Databasebeta

← #14803268

Subgroups — #14803268

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×#10622456C211yesmaximal, characteristic
2#13073615C211yesmaximal, characteristic, complemented
3#13073534C211yesmaximal, characteristic, complemented
4#13070003C212yesmaximal, complemented
5#13069927C212yesmaximal, complemented
6#13069482C212yesmaximal, complemented
7#13069422C211yesmaximal, characteristic, complemented
8#13069375C211yesmaximal, characteristic, complemented
9#13069299C212yesmaximal, complemented
10C4×#66885C211yesmaximal, characteristic, complemented
11C2×C8×Q8×C11C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13C2×#67000—21no—
14C2×#66999—21no—
15C22×D88C2212yes—
16C2×#66927C2211yescharacteristic
17C2×C4×D44C2211yescharacteristic
18C8×Q8×C11—24no—
19C2×C11×C4⋊C8C2212yes—
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C4×C8×C11C2211yescharacteristic
22C2×C4×C8×C11C2212yes—
23C2×#66885C2212yes—
24C2×#66885C2211yescharacteristic
25C2×#66885C2212yes—
26C2×#66885C2211yescharacteristic
27C2×#66885C2212yes—
28C2×#66882C2212yes—
29#10622607—22no—
30#10622604—22no—
31#10622601—21no—
32#10622600—21no—
33#10622552C2212yes—
34#10622552C2212yes—
35#10622552C2212yes—
36#10622548C2211yescharacteristic
37C4×C4⋊Dic11C2211yescharacteristic
38#10622541C2212yes—
39#10622456—24no—
40#10622189C2212yes—
41#10622189C2211yescharacteristic
42#10622189C2211yescharacteristic
43C22×Q8×C11D411yescharacteristic
44C22×D44—21no—
45C22×D44—21no—
46C22×D44C2312yes—
47C22×D44C2311yescharacteristic
48C22×C4×D11—21no—
49C22×C8×C11C2311yescharacteristic
50C22×C8×C11C2312yes—
51C22×C8×C11C2311yescharacteristic
52C4×Q8×C11—22no—
53C4×Q8×C11—22no—
54C2×C11×C4⋊C4D411yescharacteristic
55C2×C11×C4⋊C4D412yes—
56C2×C42×C11C2312yes—
57C2×C42×C11C2311yescharacteristic
58#67000—44no—
59#66999—44no—
60C2×(C2×D11)⋊C4—21no—
61C2×(C2×D11)⋊C4—22no—
62C2×(C2×D11)⋊C4—22no—
63C2×(C2×D11)⋊C4—22no—
64C2×(C2×D11)⋊C4—22no—
65C2×(C2×D11)⋊C4—22no—
66C2×(C2×D11)⋊C4—22no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11C2311yescharacteristic
70C2×C4⋊Dic11C2312yes—
71C2×C4⋊Dic11C2311yescharacteristic
72C2×C4⋊Dic11C2311yescharacteristic
73C2×Dic11⋊C4—22no—
74C2×C4×Dic11—21no—
75C2×D88—24no—
76C2×D88—24no—
77C2×D88—42no—
78#66927—22no—
79#66927—22no—
80C4×D44—22no—
81C4×D44—22no—
82C11×C4⋊C8—24no—
83C11×C4⋊C8D414yes—
84C4×C8×C11—24no—
85C4×C8×C11—22no—
86C11⋊#95—22no—
87C11⋊#95—21no—
88#66885—22no—
89#66885—24no—
90#66885—22no—
91#66885—24no—
92#66885—42no—
93#66882—42no—
94#25292—111nomaximal, Sylow
95C23×D11—21no—
96C23×D11—22no—
97C2×Q8×C11—22no—
98C2×Q8×C11—22no—
99C2×Q8×C11D814yescomplemented
100C22×C4×C11C2×D412yes—
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D412yes—
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2411yescharacteristic
105C22×Dic11—21no—
106C22×Dic11—21no—
107C22×Dic11—21no—
108C22×Dic11—22no—
109C2×D44—21no—
110C2×D44—22no—
111C2×D44—21no—
112C2×D44—21no—
113C2×D44—22no—
114C2×D44—22no—
115C2×D44—22no—
116C2×D44—21no—
117C2×D44—22no—
118C2×D44—21no—
119C2×D44—22no—
120C2×D44—42no—
121C2×D44—42no—
122C2×D44—42no—
123C2×D44—42no—
124C2×D44—81no—
125C2×D44—81no—
126C2×D44#4112yes—
127C2×C4×D11—42no—
128C2×C4×D11—42no—
129C2×C4×D11—42no—
130C2×C8×C11—21no—
131C2×C8×C11—21no—
132C2×C8×C11—22no—
133C2×C8×C11—21no—
134C2×C8×C11—22no—
135C2×C8×C11—21no—
136C2×C8×C11—21no—
137C2×C8×C11C2×D414yes—
138C2×C8×C11#4112yes—
139C11×C4⋊C4—24no—
140C11×C4⋊C4—22no—
141C42×C11—22no—
142C42×C11—22no—
143C42×C11C2×D412yes—
144C42×C11#4112yes—
145(C2×D11)⋊C4—42no—
146(C2×D11)⋊C4—44no—
147(C2×D11)⋊C4—44no—
148(C2×D11)⋊C4—44no—
149(C2×D11)⋊C4—82no—
150(C2×D11)⋊C4—82no—
151(C2×D11)⋊C4—82no—
152C4⋊Dic11—21no—
153C4⋊Dic11—22no—
154C4⋊Dic11—21no—
155C4⋊Dic11—21no—
156C4⋊Dic11—21no—
157C4⋊Dic11—21no—
158C4⋊Dic11—22no—
159C4⋊Dic11—21no—
160C4⋊Dic11—42no—
161C4⋊Dic11—81no—
162Dic11⋊C4—44no—
163C4×Dic11—42no—
164D88—48no—
165C2×#459—111no—
166C2×C8×Q8D1111yescharacteristic, complemented
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×#102—111no—
176C23×C11C22×D411yescharacteristic
177C22×D11—22no—
178C22×D11—41no—
179C22×D11—41no—
180C22×D11—41no—
181C22×D11—41no—
182C22×D11—41no—
183C22×D11—41no—
184C22×D11—42no—
185C22×D11—42no—
186C22×D11—42no—
187C22×D11—42no—
188C22×D11—42no—
189C22×D11—42no—
190C22×D11—42no—
191Q8×C11—28no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11#12112yes—
200C2×C4×C11#12112yes—
201C2×C4×C11C2×D814yes—
202C2×C4×C11C2×D812yes—
203C2×C4×C11#13512yes—
204C2×C4×C11C22×D411yescharacteristic
205C2×C4×C11C2×#4111yescharacteristic
206C2×C4×C11C2×#4111yescharacteristic
207C2×C4×C11C2×#4111yescharacteristic
208C2×C4×C11H(5,𝔽2)11yescharacteristic
209C2×C4×C112−1+411yescharacteristic
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—42no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—42no—
218C2×Dic11—41no—
219C2×Dic11—42no—
220C2×Dic11—41no—
221C2×Dic11—41no—
222D44—22no—
223D44—22no—
224D44—42no—
225D44—41no—
226D44—42no—
227D44—42no—
228D44—41no—
229D44—42no—
230D44—84no—
231D44—84no—
232C4×D11—84no—
233C8×C11—24no—
234C8×C11—22no—
235C8×C11—41no—
236C22×D8—112no—
237C2×#127—111no—
238C2×#124—221no—
239C2×C22⋊Q8—221no—
240C2×C4×Q8C2×D1111yescharacteristic
241C2×C4×D4—111no—
242#459—224no—
243C8×Q8—24no—
244C2×#107—112no—
245C2×C4⋊C8C2×D1112yes—
246C2×C4⋊C8C2×D1111yescharacteristic
247C2×#102—111no—
248C2×#102—112no—
249C2×#102—112no—
250C2×#102—111no—
251C2×#102—112no—
252C2×C4×C8C2×D1112yes—
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⋊C4—111no—
264#340—112no—
265#340—111no—
266#340—111no—
267C22×C11C2×#12111yescharacteristic
268C22×C11#54811yescharacteristic
269C22×C11#55011yescharacteristic
270C22×C11C22×D811yescharacteristic
271C22×C11C2×#13511yescharacteristic
272C22×C11#57611yescharacteristic
273C22×C11#57711yescharacteristic
274C2×D11—42no—
275C2×D11—42no—
276C2×D11—42no—
277C2×D11—81no—
278C2×D11—81no—
279C2×D11—81no—
280C2×D11—81no—
281C2×D11—82no—
282C2×D11—82no—
283C2×D11—82no—
284C2×D11—82no—
285C2×D11—82no—
286C2×D11—82no—
287C2×D11—82no—
288C4×C11—24no—
289C4×C11—22no—
290C4×C11—42no—
291C4×C11#46614yes—
292C4×C11#52911yescharacteristic
293C4×C11#54211yescharacteristic
294C4×C11#54611yescharacteristic
295C4×C11#54811yescharacteristic
296Dic11—81no—
297Dic11—81no—
298Dic11—82no—
299Dic11—81no—
300C22×Q8D4411yescharacteristic
301C22×D4—111no—
302C22×D4—112no—
303C22×D4—221no—
304C22×D4—221no—
305C23×C4—221no—
306C2×D8—224no—
307C2×D8—224no—
308C2×D8—442no—
309C22×C8C22×D1111yescharacteristic
310C22×C8C22×D1111yescharacteristic
311C22×C8C22×D1112yes—
312#127—222no—
313#127—222no—
314#124—444no—
315C22⋊Q8—444no—
316C4×Q8—22no—
317C4×Q8—22no—
318C4×D4—222no—
319C4×D4—222no—
320C2×C4⋊C4—111no—
321C2×C4⋊C4—111no—
322C2×C4⋊C4—111no—
323C2×C4⋊C4—112no—
324C2×C4⋊C4—221no—
325C2×C4⋊C4—222no—
326C2×C4⋊C4—221no—
327C2×C4⋊C4D4411yescharacteristic
328C2×C4⋊C4D4412yes—
329C2×C22⋊C4—221no—
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—221no—
337C2×C42C22×D1112yes—
338C2×C42C22×D1111yescharacteristic
339#107—442no—
340C4⋊C8—24no—
341C4⋊C8C22⋊D1114yes—
342#102—222no—
343#102—222no—
344#102—224no—
345#102—224no—
346#102—442no—
347C4×C8—24no—
348C4×C8—22no—
349#95—221no—
350#95—222no—
351C2×C11#242611yescharacteristic
352C2×C11C2×#46611yescharacteristic
353C2×C11#306211yescharacteristic
354C2×C11#335811yescharacteristic
355C2×C11#336111yescharacteristic
356C2×C11#339111yescharacteristic
357C2×C11#339411yescharacteristic
358D11—82no—
359D11—162no—
360C24—221no—
361C24—222no—
362C2×Q8—22no—
363C2×Q8—22no—
364C2×Q8D8814yescomplemented
365C2×D4—112no—
366C2×D4—221no—
367C2×D4—222no—
368C2×D4—221no—
369C2×D4—222no—
370C2×D4—221no—
371C2×D4—222no—
372C2×D4—222no—
373C2×D4—221no—
374C2×D4—222no—
375C2×D4—221no—
376C2×D4—222no—
377C2×D4—442no—
378C2×D4—442no—
379C2×D4—442no—
380C2×D4—442no—
381C2×D4—881no—
382C2×D4—881no—
383C22×C4—221no—
384C22×C4—221no—
385C22×C4—221no—
386C22×C4—222no—
387C22×C4—442no—
388C22×C4—442no—
389C22×C4—442no—
390C22×C4C2×D4412yes—
391C22×C4C2×D4412yes—
392C22×C4C2×D4411yescharacteristic
393C22×C4C2×D4411yescharacteristic
394C22×C4C23×D1111yescharacteristic
395D8—448no—
396C2×C8—21no—
397C2×C8—22no—
398C2×C8—22no—
399C2×C8—21no—
400C2×C8—21no—
401C2×C8—21no—
402C2×C8—21no—
403C2×C8#434312yes—
404C2×C8C2×C22⋊D1114yes—
405C4⋊C4—24no—
406C4⋊C4—22no—
407C4⋊C4—221no—
408C4⋊C4—221no—
409C4⋊C4—222no—
410C4⋊C4—221no—
411C4⋊C4—221no—
412C4⋊C4—222no—
413C4⋊C4—221no—
414C4⋊C4—221no—
415C4⋊C4—444no—
416C4⋊C4—442no—
417C4⋊C4—881no—
418C22⋊C4—444no—
419C22⋊C4—444no—
420C22⋊C4—444no—
421C22⋊C4—442no—
422C22⋊C4—882no—
423C22⋊C4—882no—
424C22⋊C4—882no—
425C42—22no—
426C42—22no—
427C42—442no—
428C42#433912yes—
429C42C2×C22⋊D1112yes—
430C11#2529211yescharacteristic, complemented, Sylow
431C23—222no—
432C23—441no—
433C23—441no—
434C23—441no—
435C23—441no—
436C23—441no—
437C23—441no—
438C23—442no—
439C23—442no—
440C23—442no—
441C23—442no—
442C23—442no—
443C23—442no—
444C23—442no—
445C23C22×D4411yescharacteristic
446Q8—28no—
447D4—222no—
448D4—222no—
449D4—441no—
450D4—442no—
451D4—442no—
452D4—442no—
453D4—441no—
454D4—442no—
455D4—884no—
456D4—884no—
457C2×C4—22no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—441no—
465C2×C4—441no—
466C2×C4—442no—
467C2×C4—441no—
468C2×C4—441no—
469C2×C4—441no—
470C2×C4—441no—
471C2×C4—442no—
472C2×C4—441no—
473C2×C4—441no—
474C2×C4—442no—
475C2×C4—441no—
476C2×C4—884no—
477C2×C4C2×D8814yes—
478C2×C4C2×D8812yes—
479C2×C4#6695712yes—
480C2×C4#6698312yes—
481C2×C4#6698312yes—
482C2×C4C2×#433911yescharacteristic
483C2×C4C2×#434311yescharacteristic
484C2×C4#6704011yescharacteristic
485C2×C4#41×D1111yescharacteristic
486C2×C4#6704211yescharacteristic
487C2×C4C22×C22⋊D1111yescharacteristic
488C8—22no—
489C8—24no—
490C8—41no—
491C22—442no—
492C22—442no—
493C22—442no—
494C22—881no—
495C22—881no—
496C22—881no—
497C22—881no—
498C22—882no—
499C22—882no—
500C22—882no—
501C22—882no—
502C22—882no—
503C22—882no—
504C22—882no—
505C22#1062310711yescharacteristic
506C22#1062310811yescharacteristic
507C22C22×D8811yescharacteristic
508C22C2×#6695711yescharacteristic
509C22#1062328211yescharacteristic
510C22#1062328311yescharacteristic
511C22C2×#6698311yescharacteristic
512C4—22no—
513C4—24no—
514C4—42no—
515C4—881no—
516C4—881no—
517C4—881no—
518C4—882no—
519C4#1062272814yes—
520C4#1062311111yescharacteristic
521C4#1062311311yescharacteristic
522C4#1062334811yescharacteristic
523C4#1062336011yescharacteristic
524C2—882no—
525C2—1762no—
526C2#1307217611yescharacteristic
527C2C2×#1062272811yescharacteristic
528C2#1307829611yescharacteristic
529C2#1308125211yescharacteristic
530C2#1308127811yescharacteristic
531C2#1308159111yescharacteristic
532C2#1308161411yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C8×Q8×C11C2
socleC23×C11C22×D4
prime radicalC2×#10622456C2
hypercenterC2×C8×Q8D11
hypocenterC11#25292
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×C8×Q8

Complements

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

NH ≅ G/Ntype
2. #13073615C2semidirect
3. #13073534C2semidirect
4. #13070003C2semidirect
5. #13069927C2semidirect
6. #13069482C2semidirect
7. #13069422C2semidirect
8. #13069375C2semidirect
9. #13069299C2semidirect
10. C4×#66885C2semidirect
11. C2×C8×Q8×C11C2semidirect
99. C2×Q8×C11D8semidirect
166. C2×C8×Q8D11semidirect
364. C2×Q8D88semidirect
430. C11#25292semidirect

Maximal subgroups

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

subgroupindex
C2×#106224562
#130736152
#130735342
#130700032
#130699272
#130694822
#130694222
#130693752
#130692992
C4×#668852
C2×C8×Q8×C112
#2529211