Finite Group Databasebeta

← #14796398

Subgroups — #14796398

Order 2816.

998 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622700C211yesmaximal, characteristic, complemented
2C2×C4×D88C211yesmaximal, characteristic
3#13073570C211yesmaximal, characteristic, complemented
4#13071516C211yesmaximal, characteristic, complemented
5#13070091C212yesmaximal, complemented
6#13070005C212yesmaximal, complemented
7#13069334C211yesmaximal, characteristic, complemented
8#13068965C212yesmaximal
9#13068615C212yesmaximal, complemented
10#13068613C211yesmaximal, characteristic, complemented
11C11×#1990C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×#66999—21no—
14C2×#66999—21no—
15C22×D88C2211yescharacteristic
16C2×#66946C2212yes—
17C2×C4⋊C4×D11—21no—
18C2×C4×D44C2211yescharacteristic
19C2×C4×D44C2211yescharacteristic
20C2×C4×C8×C11C2211yescharacteristic
21C11×#384C2211yescharacteristic
22C2×#66885C2211yescharacteristic
23C2×#66885C2211yescharacteristic
24C2×#66882C2211yescharacteristic
25C2×Dic11⋊C8C2212yes—
26#10622700—24no—
27#10622605—22no—
28#10622602—22no—
29#10622601C2212yes—
30#10622600—21no—
31#10622589C2212yes—
32#10622586C2212yes—
33C2×#66873C2212yes—
34C2×#66873C2212yes—
35C2×#66871C2212yes—
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
59#66999—44no—
60#66999—44no—
61C2×(C2×D11)⋊C4—21no—
62C2×(C2×D11)⋊C4—21no—
63C2×(C2×D11)⋊C4—22no—
64C2×(C2×D11)⋊C4—22no—
65C2×(C2×D11)⋊C4—22no—
66C2×C4⋊Dic11D411yescharacteristic
67C2×C4⋊Dic11D411yescharacteristic
68C2×C4⋊Dic11C2311yescharacteristic
69C2×C4⋊Dic11C2311yescharacteristic
70C2×Dic11⋊C4—22no—
71C2×Dic11⋊C4—22no—
72C2×Dic11⋊C4—22no—
73C2×C4×Dic11C2312yes—
74C22×C11⋊C8C2312yes—
75C2×D88—22no—
76C2×D88—22no—
77C2×D88Q814yescomplemented
78#66946—24no—
79#66946—42no—
80C4⋊C4×D11—44no—
81C4×D44—22no—
82C4×D44—22no—
83C4×D44—22no—
84C4×D44D414yes—
85C4×C8×C11—22no—
86C11⋊#95—22no—
87C11⋊#95D412yes—
88#66885—22no—
89#66885—22no—
90#66882—22no—
91Dic11⋊C8—42no—
92#66873—24no—
93#66873—42no—
94#66871—24no—
95C4⋊(C11⋊C8)—22no—
96#24811—111nomaximal, Sylow
97C23×D11—21no—
98C23×D11—21no—
99C2×Q8×C11—42no—
100C2×Q8×C11—42no—
101C2×Q8×C11—42no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2411yescharacteristic
107C22×Dic11—21no—
108C22×Dic11—21no—
109C22×Dic11C2×D412yes—
110C22×Dic11C2×D412yes—
111C2×D44—21no—
112C2×D44—21no—
113C2×D44—21no—
114C2×D44—21no—
115C2×D44—21no—
116C2×D44—21no—
117C2×D44—21no—
118C2×D44—21no—
119C2×D44C2×D412yes—
120C2×D44C2×Q812yes—
121C2×D44C2×Q812yes—
122C2×D44#4112yes—
123C2×C4×D11—24no—
124C2×C4×D11—44no—
125C2×C4×D11—44no—
126C2×C4×D11—42no—
127C2×C4×D11—42no—
128C2×C4×D11—42no—
129C2×C4×D11—42no—
130C2×C4×D11—42no—
131C2×C4×D11—82no—
132C2×C8×C11—21no—
133C2×C8×C11—21no—
134C2×C8×C11—21no—
135C2×C8×C11—21no—
136C2×C8×C11—21no—
137C2×C8×C11C2×Q812yes—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—42no—
143C11×C4⋊C4—42no—
144C11×C4⋊C4—81no—
145C42×C11C2×D412yes—
146C42×C11#4112yes—
147(C2×D11)⋊C4—24no—
148(C2×D11)⋊C4—44no—
149(C2×D11)⋊C4—44no—
150(C2×D11)⋊C4—44no—
151(C2×D11)⋊C4—42no—
152C4⋊Dic11—22no—
153C4⋊Dic11—21no—
154C4⋊Dic11—21no—
155C4⋊Dic11—21no—
156C4⋊Dic11D814yescomplemented
157C4⋊Dic11C2×D412yes—
158Dic11⋊C4—44no—
159Dic11⋊C4—44no—
160Dic11⋊C4—44no—
161C4×Dic11—22no—
162C4×Dic11—22no—
163C2×C11⋊C8—22no—
164C2×C11⋊C8—22no—
165C2×C11⋊C8—22no—
166D88—28no—
167C2×#474—111no—
168C2×C4×D8—111no—
169#2542—111no—
170D4×C4⋊C4—111no—
171#2083—112no—
172#2067—112no—
173#1990D1111yescharacteristic, complemented
174#1939—111no—
175#1879—112no—
176#1802—111no—
177#1802—112no—
178C23×C11C22×D411yescharacteristic
179C22×D11—22no—
180C22×D11—22no—
181C22×D11—22no—
182C22×D11—22no—
183C22×D11—41no—
184C22×D11—41no—
185C22×D11—41no—
186C22×D11—41no—
187C22×D11—41no—
188C22×D11—41no—
189C22×D11—41no—
190C22×D11—41no—
191C22×D11—41no—
192C22×D11—41no—
193Q8×C11—84no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11#12112yes—
203C2×C4×C11#12112yes—
204C2×C4×C11C2×D812yes—
205C2×C4×C11AGL(1,ℤ/8)12yes—
206C2×C4×C11C22×D411yescharacteristic
207C2×C4×C11C22×Q811yescharacteristic
208C2×C4×C11C2×#4111yescharacteristic
209C2×C4×C11C2×#4111yescharacteristic
210C2×C4×C11H(5,𝔽2)11yescharacteristic
211C2×C4×C112−1+411yescharacteristic
212C2×Dic11—22no—
213C2×Dic11—22no—
214C2×Dic11—22no—
215C2×Dic11—22no—
216C2×Dic11—22no—
217C2×Dic11—22no—
218C2×Dic11—41no—
219C2×Dic11—41no—
220C2×Dic11—41no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223C2×Dic11C2×D814yes—
224D44—22no—
225D44—22no—
226D44—22no—
227D44—22no—
228D44—22no—
229D44—41no—
230D44—41no—
231D44C22⋊Q814yescomplemented
232C4×D11—48no—
233C4×D11—88no—
234C4×D11—84no—
235C8×C11—22no—
236C8×C11—41no—
237C11⋊C8—42no—
238C22×D8—111no—
239C2×C4⋊Q8C2×D1111yescharacteristic
240C2×C22⋊Q8—221no—
241C2×C22⋊Q8—221no—
242C2×C4×D4—112no—
243C2×C4×D4—111no—
244C2×C4×D4—111no—
245C22×C4⋊C4—221no—
246#474—224no—
247C4×D8—224no—
248C2×#107—111no—
249C2×#107—112no—
250C2×C4⋊C8—111no—
251C2×C4⋊C8—112no—
252C2×#102—111no—
253C2×#102—111no—
254C2×#102—112no—
255C2×#102—112no—
256C2×C4×C8C2×D1111yescharacteristic
257#399—222no—
258#390—112no—
259#389—112no—
260#385—222no—
261#384—112no—
262#384C2×D1111yescharacteristic
263#380—221no—
264C4×C4⋊C4—111no—
265#340—112no—
266#340C2×D1112yes—
267#340C2×D1112yes—
268#336—112no—
269C22×C11C2×#12111yescharacteristic
270C22×C11#54611yescharacteristic
271C22×C11D4×Q811yescharacteristic
272C22×C11C22×D811yescharacteristic
273C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
274C22×C11#57711yescharacteristic
275C22×C11#57811yescharacteristic
276C2×D11—24no—
277C2×D11—42no—
278C2×D11—42no—
279C2×D11—42no—
280C2×D11—42no—
281C2×D11—42no—
282C2×D11—42no—
283C2×D11—42no—
284C2×D11—42no—
285C2×D11—42no—
286C2×D11—81no—
287C2×D11—81no—
288C2×D11—81no—
289C2×D11—81no—
290C4×C11—22no—
291C4×C11—82no—
292C4×C11—82no—
293C4×C11#45914yes—
294C4×C11C2×C22⋊Q811yescharacteristic
295C4×C11#53711yescharacteristic
296C4×C11#55211yescharacteristic
297C4×C11#55411yescharacteristic
298Dic11—24no—
299Dic11—42no—
300Dic11—42no—
301Dic11—81no—
302C22×Q8—21no—
303C22×D4—111no—
304C22×D4—111no—
305C23×C4—222no—
306C23×C4—221no—
307C23×C4—221no—
308C2×D8—114no—
309C2×D8—222no—
310C2×D8—222no—
311C22×C8—112no—
312C22×C8C22×D1111yescharacteristic
313C22×C8C22×D1111yescharacteristic
314C4⋊Q8—22no—
315C4⋊Q8—22no—
316C22⋊Q8—444no—
317C22⋊Q8—444no—
318C4×D4—114no—
319C4×D4—224no—
320C4×D4—222no—
321C4×D4—222no—
322C4×D4—222no—
323C4×D4—442no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—111no—
328C2×C4⋊C4—111no—
329C2×C4⋊C4—111no—
330C2×C4⋊C4—111no—
331C2×C4⋊C4—222no—
332C2×C4⋊C4—222no—
333C2×C4⋊C4—222no—
334C2×C4⋊C4—444no—
335C2×C4⋊C4C22×D1112yes—
336C2×C4⋊C4C22×D1112yes—
337C2×C22⋊C4—221no—
338C2×C22⋊C4—222no—
339C2×C22⋊C4—222no—
340C2×C22⋊C4—222no—
341C2×C22⋊C4—221no—
342C2×C42—112no—
343C2×C42C22×D1111yescharacteristic
344#107—224no—
345#107—222no—
346C4⋊C8—222no—
347C4⋊C8—442no—
348#102—224no—
349#102—222no—
350#102—222no—
351#102—442no—
352C4×C8—22no—
353#95—112no—
354#95—222no—
355C2×C11#241711yescharacteristic
356C2×C11C2×#45911yescharacteristic
357C2×C11#304611yescharacteristic
358C2×C11#329411yescharacteristic
359C2×C11#333011yescharacteristic
360C2×C11Q8×D811yescharacteristic
361C2×C11#338411yescharacteristic
362D11—44no—
363D11—82no—
364C24—221no—
365C24—221no—
366C2×Q8—42no—
367C2×Q8—42no—
368C2×Q8—42no—
369C2×D4—112no—
370C2×D4—112no—
371C2×D4—112no—
372C2×D4—112no—
373C2×D4—221no—
374C2×D4—221no—
375C2×D4—221no—
376C2×D4—221no—
377C2×D4—221no—
378C2×D4—221no—
379C2×D4—221no—
380C2×D4—221no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—112no—
384C22×C4—112no—
385C22×C4—221no—
386C22×C4—224no—
387C22×C4—221no—
388C22×C4—444no—
389C22×C4—444no—
390C22×C4—442no—
391C22×C4—442no—
392C22×C4—442no—
393C22×C4—442no—
394C22×C4—442no—
395C22×C4—882no—
396C22×C4D4×D1111yescharacteristic
397C22×C4D4×D1111yescharacteristic
398C22×C4C23×D1111yescharacteristic
399D8—228no—
400C2×C8—21no—
401C2×C8—21no—
402C2×C8—21no—
403C2×C8—21no—
404C2×C8—21no—
405C2×C8—222no—
406C2×C8—222no—
407C2×C8—222no—
408C2×C8Q8×D1112yes—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—22no—
413C4⋊C4—42no—
414C4⋊C4—42no—
415C4⋊C4—81no—
416C4⋊C4—114no—
417C4⋊C4—112no—
418C4⋊C4—222no—
419C4⋊C4—221no—
420C4⋊C4—221no—
421C4⋊C4—221no—
422C4⋊C4—444no—
423C4⋊C4—444no—
424C4⋊C4—444no—
425C22⋊C4—224no—
426C22⋊C4—444no—
427C22⋊C4—444no—
428C22⋊C4—444no—
429C22⋊C4—442no—
430C42—222no—
431C42—222no—
432C42#433912yes—
433C42D4×D1112yes—
434C11#2481111yescharacteristic, complemented, Sylow
435C23—222no—
436C23—222no—
437C23—222no—
438C23—222no—
439C23—441no—
440C23—441no—
441C23—441no—
442C23—441no—
443C23—441no—
444C23—441no—
445C23—441no—
446C23—441no—
447C23—441no—
448C23—441no—
449C23C2×D4×D1111yescharacteristic
450Q8—84no—
451D4—114no—
452D4—222no—
453D4—222no—
454D4—222no—
455D4—222no—
456D4—222no—
457D4—441no—
458D4—441no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—114no—
468C2×C4—222no—
469C2×C4—222no—
470C2×C4—222no—
471C2×C4—222no—
472C2×C4—222no—
473C2×C4—222no—
474C2×C4—441no—
475C2×C4—441no—
476C2×C4—448no—
477C2×C4—441no—
478C2×C4—441no—
479C2×C4—441no—
480C2×C4—888no—
481C2×C4—884no—
482C2×C4#6693712yes—
483C2×C4#6693712yes—
484C2×C4D8×D1112yes—
485C2×C4#6696712yes—
486C2×C4C2×#433911yescharacteristic
487C2×C4C2×D4×D1111yescharacteristic
488C2×C4C2×Q8×D1111yescharacteristic
489C2×C4#6704011yescharacteristic
490C2×C4#41×D1111yescharacteristic
491C2×C4#6704211yescharacteristic
492C8—22no—
493C8—41no—
494C8—442no—
495C22—224no—
496C22—442no—
497C22—442no—
498C22—442no—
499C22—442no—
500C22—442no—
501C22—442no—
502C22—442no—
503C22—442no—
504C22—442no—
505C22—881no—
506C22—881no—
507C22—881no—
508C22—881no—
509C22C2×#6693711yescharacteristic
510C22#1062320711yescharacteristic
511C22#1062325811yescharacteristic
512C22C2×D8×D1111yescharacteristic
513C22C2×#6696711yescharacteristic
514C22#1062329311yescharacteristic
515C22#1062329711yescharacteristic
516C4—22no—
517C4—82no—
518C4—82no—
519C4—224no—
520C4—442no—
521C4—442no—
522C4—881no—
523C4#1062239914yes—
524C4#1062311011yescharacteristic
525C4#1062311211yescharacteristic
526C4D11×C22⋊Q811yescharacteristic
527C4#1062316011yescharacteristic
528C2—444no—
529C2—882no—
530C2#1307207011yescharacteristic
531C2C2×#1062239911yescharacteristic
532C2#1307817111yescharacteristic
533C2#1308042811yescharacteristic
534C2#1308092011yescharacteristic
535C2#1308146811yescharacteristic
536C2#1308152011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1990C2
socleC23×C11C22×D4
prime radicalC22×D88C22
hypercenter#1990D11
hypocenterC11#24811
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×#10622700C2semidirect
3. #13073570C2semidirect
4. #13071516C2semidirect
5. #13070091C2semidirect
6. #13070005C2semidirect
7. #13069334C2semidirect
9. #13068615C2semidirect
10. #13068613C2semidirect
11. C11×#1990C2semidirect
77. C2×D88Q8semidirect
156. C4⋊Dic11D8semidirect
173. #1990D11semidirect
231. D44C22⋊Q8semidirect
434. C11#24811semidirect

Maximal subgroups

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

subgroupindex
C2×#106227002
C2×C4×D882
#130735702
#130715162
#130700912
#130700052
#130693342
#130689652
#130686152
#130686132
C11×#19902
#2481111