Finite Group Databasebeta

← #14796409

Subgroups — #14796409

Order 2816.

942 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622697C211yesmaximal, characteristic, complemented
2C2×C4×D88C211yesmaximal, characteristic
3#13073790C211yesmaximal, characteristic, complemented
4#13071516C211yesmaximal, characteristic, complemented
5#13070103C212yesmaximal, complemented
6#13069991C212yesmaximal, complemented
7#13069334C211yesmaximal, characteristic, complemented
8#13068965C212yesmaximal
9#13068625C212yesmaximal, complemented
10#13068613C211yesmaximal, characteristic, complemented
11C11×#1990C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C22×D88C2211yescharacteristic
14C2×#66946C2212yes—
15C2×C4⋊C4×D11—21no—
16C2×C4×D44C2211yescharacteristic
17C2×C4×D44C2211yescharacteristic
18C2×C4×C8×C11C2211yescharacteristic
19C11×#384C2211yescharacteristic
20#10622844—22no—
21C2×#66885C2211yescharacteristic
22C2×#66885C2211yescharacteristic
23C2×#66882C2211yescharacteristic
24C2×Dic11⋊C8C2212yes—
25#10622697—24no—
26#10622602—22no—
27#10622601C2212yes—
28#10622600—21no—
29#10622600—21no—
30#10622600—21no—
31#10622590C2212yes—
32#10622586C2212yes—
33C2×#66873C2212yes—
34C2×#66873C2212yes—
35C2×#66872C2212yes—
36C4×C4⋊Dic11C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38C4×D88—24no—
39C11×#340C2212yes—
40C11×#340C2212yes—
41#10622188C2212yes—
42#10622167C2212yes—
43C22×Q8×C11—21no—
44C22×D44C2311yescharacteristic
45C22×D44C2311yescharacteristic
46C22×C4×D11—21no—
47C22×C4×D11—21no—
48C22×C4×D11—22no—
49C22×C8×C11C2311yescharacteristic
50C22×C8×C11C2311yescharacteristic
51C11×C4⋊Q8—22no—
52C11×C4⋊Q8—22no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4C2312yes—
57C2×C11×C4⋊C4C2312yes—
58C2×C42×C11C2311yescharacteristic
59C2×(C2×D11)⋊C4—21no—
60C2×(C2×D11)⋊C4—21no—
61C2×(C2×D11)⋊C4—22no—
62C2×(C2×D11)⋊C4—22no—
63C2×(C2×D11)⋊C4—22no—
64C2×C4⋊Dic11D411yescharacteristic
65C2×C4⋊Dic11D411yescharacteristic
66C2×C4⋊Dic11C2311yescharacteristic
67C2×C4⋊Dic11C2311yescharacteristic
68C2×Dic11⋊C4—22no—
69C2×C4×Dic11C2312yes—
70C22×C11⋊C8C2312yes—
71C2×D88—22no—
72C2×D88—22no—
73C2×D88Q814yescomplemented
74#66946—24no—
75#66946—42no—
76C4⋊C4×D11—44no—
77C4×D44—22no—
78C4×D44—22no—
79C4×D44—22no—
80C4×D44D414yes—
81C4×C8×C11—22no—
82C11⋊#95—22no—
83C11⋊#95—22no—
84C11⋊#95—22no—
85C11⋊#95D412yes—
86#66885—22no—
87#66885—22no—
88#66882—22no—
89Dic11⋊C8—42no—
90#66873—24no—
91#66873—42no—
92#66872—24no—
93C4⋊(C11⋊C8)—22no—
94#24812—111nomaximal, Sylow
95C23×D11—21no—
96C23×D11—21no—
97C2×Q8×C11—42no—
98C2×Q8×C11—81no—
99C2×Q8×C11—81no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2411yescharacteristic
105C22×Dic11—21no—
106C22×Dic11—21no—
107C22×Dic11C2×D412yes—
108C22×Dic11C2×D412yes—
109C2×D44—21no—
110C2×D44—21no—
111C2×D44—21no—
112C2×D44—21no—
113C2×D44—21no—
114C2×D44—21no—
115C2×D44—21no—
116C2×D44—21no—
117C2×D44C2×D412yes—
118C2×D44C2×Q812yes—
119C2×D44C2×Q812yes—
120C2×D44#4112yes—
121C2×C4×D11—24no—
122C2×C4×D11—44no—
123C2×C4×D11—44no—
124C2×C4×D11—42no—
125C2×C4×D11—42no—
126C2×C4×D11—42no—
127C2×C4×D11—42no—
128C2×C4×D11—42no—
129C2×C4×D11—82no—
130C2×C8×C11—21no—
131C2×C8×C11—21no—
132C2×C8×C11—21no—
133C2×C8×C11—21no—
134C2×C8×C11—21no—
135C2×C8×C11C2×Q812yes—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—42no—
141C11×C4⋊C4—42no—
142C11×C4⋊C4—81no—
143C42×C11C2×D412yes—
144C42×C11#4112yes—
145(C2×D11)⋊C4—24no—
146(C2×D11)⋊C4—44no—
147(C2×D11)⋊C4—42no—
148(C2×D11)⋊C4—82no—
149(C2×D11)⋊C4—82no—
150C4⋊Dic11—22no—
151C4⋊Dic11—22no—
152C4⋊Dic11—21no—
153C4⋊Dic11—21no—
154C4⋊Dic11—21no—
155C4⋊Dic11C2×D412yes—
156Dic11⋊C4—44no—
157C4×Dic11—22no—
158C4×Dic11—22no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—22no—
162D88—28no—
163C2×#476—111no—
164C2×C4×D8—111no—
165#2563—111no—
166D4×C4⋊C4—111no—
167#2085—112no—
168#2065—112no—
169#1990D1111yescharacteristic, complemented
170#1939—111no—
171#1879—112no—
172#1804—112no—
173#1802—111no—
174C23×C11C22×D411yescharacteristic
175C22×D11—22no—
176C22×D11—22no—
177C22×D11—22no—
178C22×D11—22no—
179C22×D11—41no—
180C22×D11—41no—
181C22×D11—41no—
182C22×D11—41no—
183C22×D11—41no—
184C22×D11—41no—
185C22×D11—41no—
186C22×D11—41no—
187C22×D11—41no—
188C22×D11—41no—
189Q8×C11—84no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11#12112yes—
199C2×C4×C11#12112yes—
200C2×C4×C11#13512yes—
201C2×C4×C11AGL(1,ℤ/8)12yes—
202C2×C4×C11C22×D411yescharacteristic
203C2×C4×C11C22×Q811yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C2×C4×C11C2×#4111yescharacteristic
206C2×C4×C11H(5,𝔽2)11yescharacteristic
207C2×C4×C112−1+411yescharacteristic
208C2×Dic11—22no—
209C2×Dic11—22no—
210C2×Dic11—22no—
211C2×Dic11—22no—
212C2×Dic11—22no—
213C2×Dic11—22no—
214C2×Dic11—22no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11—41no—
219C2×Dic11—41no—
220D44—22no—
221D44—22no—
222D44—22no—
223D44—22no—
224D44—22no—
225D44—41no—
226D44—41no—
227D44C22⋊Q814yes—
228C4×D11—48no—
229C4×D11—88no—
230C4×D11—84no—
231C8×C11—22no—
232C8×C11—41no—
233C11⋊C8—42no—
234C22×D8—111no—
235C2×C4⋊Q8C2×D1111yescharacteristic
236C2×C4×D4—112no—
237C2×C4×D4—111no—
238C2×C4×D4—111no—
239C22×C4⋊C4—221no—
240#476—224no—
241C4×D8—224no—
242C2×#107—111no—
243C2×#106—112no—
244C2×C4⋊C8—111no—
245C2×C4⋊C8—112no—
246C2×#102—111no—
247C2×#102—111no—
248C2×#102—112no—
249C2×#102—112no—
250C2×C4×C8C2×D1111yescharacteristic
251#393—222no—
252#390—112no—
253#389—112no—
254#385—222no—
255#384C2×D1111yescharacteristic
256#382—112no—
257#380—221no—
258#380—221no—
259#380—221no—
260C4×C4⋊C4—111no—
261#340—112no—
262#340C2×D1112yes—
263#340C2×D1112yes—
264#336—112no—
265C22×C11C2×#12111yescharacteristic
266C22×C11#54611yescharacteristic
267C22×C11D4×Q811yescharacteristic
268C22×C11C2×#13511yescharacteristic
269C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
270C22×C11#57611yescharacteristic
271C22×C11#57711yescharacteristic
272C2×D11—24no—
273C2×D11—42no—
274C2×D11—42no—
275C2×D11—42no—
276C2×D11—42no—
277C2×D11—42no—
278C2×D11—42no—
279C2×D11—42no—
280C2×D11—42no—
281C2×D11—42no—
282C2×D11—81no—
283C2×D11—81no—
284C2×D11—81no—
285C2×D11—81no—
286C4×C11—22no—
287C4×C11—82no—
288C4×C11—82no—
289C4×C11#46314yes—
290C4×C11C2×C22⋊Q811yescharacteristic
291C4×C11#53711yescharacteristic
292C4×C11#55211yescharacteristic
293C4×C11#55411yescharacteristic
294Dic11—42no—
295Dic11—42no—
296Dic11—42no—
297Dic11—81no—
298C22×Q8—21no—
299C22×D4—111no—
300C22×D4—111no—
301C23×C4—222no—
302C23×C4—221no—
303C23×C4—221no—
304C2×D8—114no—
305C2×D8—222no—
306C2×D8—222no—
307C22×C8—112no—
308C22×C8C22×D1111yescharacteristic
309C22×C8C22×D1111yescharacteristic
310C4⋊Q8—22no—
311C4⋊Q8—22no—
312C4×D4—114no—
313C4×D4—224no—
314C4×D4—222no—
315C4×D4—222no—
316C4×D4—222no—
317C4×D4—442no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—111no—
322C2×C4⋊C4—111no—
323C2×C4⋊C4—111no—
324C2×C4⋊C4—111no—
325C2×C4⋊C4—222no—
326C2×C4⋊C4—444no—
327C2×C4⋊C4C22×D1112yes—
328C2×C4⋊C4C22×D1112yes—
329C2×C22⋊C4—221no—
330C2×C22⋊C4—222no—
331C2×C22⋊C4—221no—
332C2×C22⋊C4—222no—
333C2×C22⋊C4—222no—
334C2×C42—112no—
335C2×C42C22×D1111yescharacteristic
336#107—222no—
337#106—224no—
338C4⋊C8—222no—
339C4⋊C8—442no—
340#102—224no—
341#102—222no—
342#102—222no—
343#102—442no—
344C4×C8—22no—
345#95—112no—
346#95—222no—
347#95—222no—
348#95—222no—
349C2×C11#241711yescharacteristic
350C2×C11C2×#46311yescharacteristic
351C2×C11#304511yescharacteristic
352C2×C11#330311yescharacteristic
353C2×C11#332511yescharacteristic
354C2×C11#338011yescharacteristic
355C2×C11#338411yescharacteristic
356D11—44no—
357D11—82no—
358C24—221no—
359C24—221no—
360C2×Q8—42no—
361C2×Q8—81no—
362C2×Q8—81no—
363C2×D4—112no—
364C2×D4—112no—
365C2×D4—112no—
366C2×D4—112no—
367C2×D4—221no—
368C2×D4—221no—
369C2×D4—221no—
370C2×D4—221no—
371C2×D4—221no—
372C2×D4—221no—
373C2×D4—221no—
374C2×D4—221no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—112no—
378C22×C4—112no—
379C22×C4—221no—
380C22×C4—224no—
381C22×C4—221no—
382C22×C4—444no—
383C22×C4—444no—
384C22×C4—442no—
385C22×C4—442no—
386C22×C4—442no—
387C22×C4—442no—
388C22×C4—442no—
389C22×C4—882no—
390C22×C4D4×D1111yescharacteristic
391C22×C4D4×D1111yescharacteristic
392C22×C4C23×D1111yescharacteristic
393D8—228no—
394C2×C8—21no—
395C2×C8—21no—
396C2×C8—21no—
397C2×C8—21no—
398C2×C8—21no—
399C2×C8—222no—
400C2×C8—222no—
401C2×C8—222no—
402C2×C8Q8×D1112yes—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—22no—
407C4⋊C4—42no—
408C4⋊C4—42no—
409C4⋊C4—81no—
410C4⋊C4—112no—
411C4⋊C4—222no—
412C4⋊C4—222no—
413C4⋊C4—221no—
414C4⋊C4—221no—
415C4⋊C4—221no—
416C4⋊C4—444no—
417C22⋊C4—224no—
418C22⋊C4—444no—
419C22⋊C4—442no—
420C22⋊C4—882no—
421C22⋊C4—882no—
422C42—222no—
423C42—222no—
424C42#433912yes—
425C42D4×D1112yes—
426C11#2481211yescharacteristic, complemented, Sylow
427C23—222no—
428C23—222no—
429C23—222no—
430C23—222no—
431C23—441no—
432C23—441no—
433C23—441no—
434C23—441no—
435C23—441no—
436C23—441no—
437C23—441no—
438C23—441no—
439C23—441no—
440C23—441no—
441C23C2×D4×D1111yescharacteristic
442Q8—84no—
443D4—114no—
444D4—222no—
445D4—222no—
446D4—222no—
447D4—222no—
448D4—222no—
449D4—441no—
450D4—441no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—222no—
460C2×C4—222no—
461C2×C4—222no—
462C2×C4—222no—
463C2×C4—222no—
464C2×C4—222no—
465C2×C4—222no—
466C2×C4—441no—
467C2×C4—441no—
468C2×C4—448no—
469C2×C4—441no—
470C2×C4—441no—
471C2×C4—441no—
472C2×C4—888no—
473C2×C4—884no—
474C2×C4#6693712yes—
475C2×C4#6693712yes—
476C2×C4#6696712yes—
477C2×C4#6697212yes—
478C2×C4C2×#433911yescharacteristic
479C2×C4C2×D4×D1111yescharacteristic
480C2×C4C2×Q8×D1111yescharacteristic
481C2×C4#6704011yescharacteristic
482C2×C4#41×D1111yescharacteristic
483C2×C4#6704211yescharacteristic
484C8—22no—
485C8—41no—
486C8—442no—
487C22—224no—
488C22—442no—
489C22—442no—
490C22—442no—
491C22—442no—
492C22—442no—
493C22—442no—
494C22—442no—
495C22—442no—
496C22—442no—
497C22—881no—
498C22—881no—
499C22—881no—
500C22—881no—
501C22C2×#6693711yescharacteristic
502C22#1062320711yescharacteristic
503C22#1062325811yescharacteristic
504C22#1062328811yescharacteristic
505C22C2×#6696711yescharacteristic
506C22#1062329311yescharacteristic
507C22C2×#6697211yescharacteristic
508C4—22no—
509C4—82no—
510C4—82no—
511C4—442no—
512C4—442no—
513C4—442no—
514C4—881no—
515C4#1062243214yes—
516C4#1062311011yescharacteristic
517C4#1062311211yescharacteristic
518C4D11×C22⋊Q811yescharacteristic
519C4#1062316011yescharacteristic
520C2—444no—
521C2—882no—
522C2#1307207011yescharacteristic
523C2C2×#1062243211yescharacteristic
524C2#1307816011yescharacteristic
525C2#1308054311yescharacteristic
526C2#1308085711yescharacteristic
527C2#1308148511yescharacteristic
528C2#1308152011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1990C2
socleC23×C11C22×D4
prime radicalC22×D88C22
hypercenter#1990D11
hypocenterC11#24812
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
1. C2×#10622697C2semidirect
3. #13073790C2semidirect
4. #13071516C2semidirect
5. #13070103C2semidirect
6. #13069991C2semidirect
7. #13069334C2semidirect
9. #13068625C2semidirect
10. #13068613C2semidirect
11. C11×#1990C2semidirect
73. C2×D88Q8semidirect
169. #1990D11semidirect
426. C11#24812semidirect

Maximal subgroups

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

subgroupindex
C2×#106226972
C2×C4×D882
#130737902
#130715162
#130701032
#130699912
#130693342
#130689652
#130686252
#130686132
C11×#19902
#2481211