Finite Group Databasebeta

← #14782865

Subgroups — #14782865

Order 2816.

950 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×#10622577C211yesmaximal, characteristic
2C2×#10622537C211yesmaximal, characteristic
3#13071099C211yesmaximal, characteristic
4#13070118C212yesmaximal, complemented
5#13070117C212yesmaximal, complemented
6#13070112C212yesmaximal, complemented
7#13070107C212yesmaximal, complemented
8#13068335C211yesmaximal, characteristic
9#13068335C211yesmaximal, characteristic
10#13068335C211yesmaximal, characteristic
11C2×C11×#389C211yesmaximal, characteristic
12C22×C11×C4⋊C4—21no—
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C42×C11C2211yescharacteristic
16C2×#66979C2211yescharacteristic
17C2×#66979C2211yescharacteristic
18C22×#4318C2211yescharacteristic
19C22×#4318C2211yescharacteristic
20C11×#389—21no—
21C11×#389—21no—
22C11×#389C2212yes—
23C11×#389C2212yes—
24C2×C11×#95—21no—
25#10622823—21no—
26#10622823—21no—
27#10622577—24no—
28C2×#66872C2212yes—
29C2×#66871C2212yes—
30C4×Dic11⋊C4—21no—
31C4×Dic11⋊C4—21no—
32#10622541C2211yescharacteristic
33#10622541C2211yescharacteristic
34#10622541C2211yescharacteristic
35#10622541C2211yescharacteristic
36#10622537—24no—
37C2×C4⋊(C11⋊C8)C2212yes—
38C2×C4⋊(C11⋊C8)C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45C23×C4×C11—21no—
46C23×C4×C11—21no—
47C23×C4×C11D411yescharacteristic
48C23×C4×C11D411yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—44no—
58C2×C11×C4⋊C4Q814yes—
59C2×C11×C4⋊C4C2312yes—
60C2×C11×C4⋊C4C2312yes—
61C2×C42×C11—22no—
62C2×C42×C11—22no—
63C2×C42×C11D411yescharacteristic
64C2×C42×C11D411yescharacteristic
65C2×C42×C11C2311yescharacteristic
66C2×C42×C11C2311yescharacteristic
67C2×C22⋊Dic11—21no—
68C2×C22⋊Dic11—21no—
69#66979—22no—
70#66979—22no—
71#66979—22no—
72#66979Q814yes—
73C2×C4⋊Dic11C2311yescharacteristic
74C2×C4⋊Dic11C2311yescharacteristic
75C2×C4⋊Dic11C2311yescharacteristic
76C2×C4⋊Dic11C2311yescharacteristic
77C2×Dic11⋊C4—21no—
78C2×Dic11⋊C4—21no—
79C2×Dic11⋊C4—21no—
80C2×Dic11⋊C4—21no—
81C2×C4×Dic11—21no—
82C2×C4×Dic11—21no—
83C2×#4318—22no—
84C2×#4318—22no—
85C2×#4318—22no—
86C2×#4318—22no—
87C2×#4318—22no—
88C2×#4318D414yes—
89C22×C11⋊C8C2312yes—
90C22×C11⋊C8C2312yes—
91C11×#95—22no—
92C11×#95—22no—
93C11⋊#95—21no—
94C11⋊#95—21no—
95C11⋊#95—21no—
96C11⋊#95—21no—
97#66872—24no—
98#66871—24no—
99C4⋊(C11⋊C8)—24no—
100C4⋊(C11⋊C8)—24no—
101#23670—111nomaximal, Sylow
102C24×C11C2×D411yescharacteristic
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—24no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—41no—
111C22×C4×C11—41no—
112C22×C4×C11—42no—
113C22×C4×C11—42no—
114C22×C4×C11—42no—
115C22×C4×C11—42no—
116C22×C4×C11—42no—
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2×Q812yes—
124C22×C4×C11C2×Q812yes—
125C22×C4×C11#4112yes—
126C22×C4×C11#4112yes—
127C22×C4×C11#4112yes—
128C22×C4×C11C2411yescharacteristic
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11—21no—
132C22×Dic11—21no—
133C11×C4⋊C4—24no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—44no—
138C11×C4⋊C4—42no—
139C11×C4⋊C4—44no—
140C11×C4⋊C4C2×Q814yes—
141C42×C11—22no—
142C42×C11—22no—
143C42×C11—21no—
144C42×C11—21no—
145C42×C11—21no—
146C42×C11—21no—
147C22⋊Dic11—24no—
148C22⋊Dic11—42no—
149C4⋊Dic11—21no—
150C4⋊Dic11—21no—
151C4⋊Dic11—21no—
152C4⋊Dic11—21no—
153C4⋊Dic11—21no—
154C4⋊Dic11—21no—
155C4⋊Dic11C2×Q812yes—
156C4⋊Dic11C2×Q812yes—
157Dic11⋊C4—42no—
158Dic11⋊C4—42no—
159Dic11⋊C4—42no—
160Dic11⋊C4—42no—
161C4×Dic11—24no—
162C4×Dic11—42no—
163#4318—28no—
164#4318—44no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8C2×D414yes—
171C2×#428—111no—
172C2×#423—111no—
173#2296—111no—
174C2×#389D1111yescharacteristic
175#2088—112no—
176#2088—112no—
177#2087—112no—
178#2086—112no—
179#1736—111no—
180#1736—111no—
181#1736—111no—
182C23×C11—21no—
183C23×C11—21no—
184C23×C11—21no—
185C23×C11—21no—
186C23×C11#12112yes—
187C23×C11C22⋊Q812yes—
188C23×C11C22⋊Q812yes—
189C23×C11C22×D411yescharacteristic
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—24no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—44no—
202C2×C4×C11—44no—
203C2×C4×C11—48no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—84no—
210C2×C4×C11#12112yes—
211C2×C4×C11C22⋊Q812yes—
212C2×C4×C11C22⋊Q812yes—
213C2×C4×C11#12314yes—
214C2×C4×C11#12514yes—
215C2×C4×C11#12514yes—
216C2×C4×C11C4⋊Q814yes—
217C2×C4×C11AGL(1,ℤ/8)12yes—
218C2×C4×C11#13712yes—
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C22×Q811yescharacteristic
221C2×C4×C11C22×Q811yescharacteristic
222C2×C4×C11C2×#4111yescharacteristic
223C2×C4×C11C2×#4111yescharacteristic
224C2×C4×C11C2×#4111yescharacteristic
225C2×Dic11—22no—
226C2×Dic11—22no—
227C2×Dic11—41no—
228C2×Dic11—41no—
229C2×Dic11—41no—
230C2×Dic11—41no—
231C2×Dic11—41no—
232C2×Dic11—41no—
233C2×Dic11—41no—
234C2×Dic11—41no—
235C2×Dic11—41no—
236C2×Dic11—41no—
237C11⋊C8—24no—
238C11⋊C8—42no—
239C22×M16—111no—
240C22×M16—111no—
241C2×#117—111no—
242C2×#117—111no—
243C22×C4⋊C4—21no—
244C22×C4⋊C4C2×D1111yescharacteristic
245C22×C4⋊C4C2×D1111yescharacteristic
246C22×C42C2×D1111yescharacteristic
247#428—224no—
248C2×#107—112no—
249C2×#106—112no—
250#423—224no—
251C2×C4⋊C8—112no—
252C2×C4⋊C8—112no—
253#389—21no—
254#389—21no—
255#389—111no—
256#389—111no—
257#389—111no—
258#389—111no—
259#389C2×D1112yes—
260#389C2×D1112yes—
261#385—221no—
262#385—221no—
263C4×C4⋊C4—221no—
264C4×C4⋊C4—221no—
265C2×#95—21no—
266#340—112no—
267#340—112no—
268#340—112no—
269#340—112no—
270#340—112no—
271#340—112no—
272C22×C11—22no—
273C22×C11—22no—
274C22×C11—22no—
275C22×C11—22no—
276C22×C11—22no—
277C22×C11—22no—
278C22×C11#39814yes—
279C22×C11C2×#12111yescharacteristic
280C22×C11C2×C22⋊Q811yescharacteristic
281C22×C11C2×C22⋊Q811yescharacteristic
282C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
283C22×C11C2×#13711yescharacteristic
284C22×C11#57511yescharacteristic
285C22×C11#57511yescharacteristic
286C4×C11—22no—
287C4×C11—22no—
288C4×C11—44no—
289C4×C11—41no—
290C4×C11—41no—
291C4×C11—82no—
292C4×C11#39814yes—
293C4×C11C2×#12311yescharacteristic
294C4×C11C2×#12511yescharacteristic
295C4×C11C2×#12511yescharacteristic
296C4×C11C2×C4⋊Q811yescharacteristic
297Dic11—42no—
298Dic11—42no—
299Dic11—81no—
300Dic11—81no—
301C23×C4—21no—
302C23×C4—21no—
303C23×C4C22⋊D1111yescharacteristic
304C23×C4C22⋊D1111yescharacteristic
305C23×C4C22×D1111yescharacteristic
306C2×M16—114no—
307C2×M16—222no—
308C2×M16—222no—
309C2×M16—222no—
310C2×M16—222no—
311C2×M16—222no—
312C22×C8—112no—
313C22×C8—112no—
314#117—114no—
315#117—222no—
316#117—222no—
317#117—222no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—44no—
326C2×C4⋊C4—111no—
327C2×C4⋊C4—111no—
328C2×C4⋊C4—111no—
329C2×C4⋊C4—111no—
330C2×C4⋊C4—221no—
331C2×C4⋊C4—221no—
332C2×C4⋊C4—221no—
333C2×C4⋊C4—221no—
334C2×C4⋊C4Dic2214yes—
335C2×C4⋊C4C22×D1112yes—
336C2×C4⋊C4C22×D1112yes—
337C2×C22⋊C4—221no—
338C2×C22⋊C4—221no—
339C2×C42—22no—
340C2×C42—22no—
341C2×C42—221no—
342C2×C42—221no—
343C2×C42C22⋊D1111yescharacteristic
344C2×C42C22⋊D1111yescharacteristic
345C2×C42C22×D1111yescharacteristic
346C2×C42C22×D1111yescharacteristic
347#107—224no—
348#106—224no—
349C4⋊C8—224no—
350C4⋊C8—224no—
351#95—22no—
352#95—22no—
353#95—221no—
354#95—221no—
355#95—221no—
356#95—221no—
357C2×C11—24no—
358C2×C11C2×#39811yescharacteristic
359C2×C11#305511yescharacteristic
360C2×C11#305611yescharacteristic
361C2×C11#307711yescharacteristic
362C2×C11#307811yescharacteristic
363C2×C11#307911yescharacteristic
364C2×C11#308011yescharacteristic
365C24C2×C22⋊D1111yescharacteristic
366C22×C4—24no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—41no—
374C22×C4—41no—
375C22×C4—42no—
376C22×C4—42no—
377C22×C4—42no—
378C22×C4—42no—
379C22×C4—42no—
380C22×C4—221no—
381C22×C4—221no—
382C22×C4—221no—
383C22×C4—221no—
384C22×C4C2×Dic2212yes—
385C22×C4#433912yes—
386C22×C4D4×D1112yes—
387C22×C4#434112yes—
388C22×C4Q8×D1112yes—
389C22×C4#434312yes—
390C22×C4C2×C22⋊D1111yescharacteristic
391C22×C4C2×C22⋊D1111yescharacteristic
392C22×C4C2×C22⋊D1111yescharacteristic
393C22×C4C2×C22⋊D1111yescharacteristic
394C22×C4C2×C22⋊D1111yescharacteristic
395C22×C4C23×D1111yescharacteristic
396M16—228no—
397M16—444no—
398C2×C8—114no—
399C2×C8—222no—
400C2×C8—222no—
401C2×C8—222no—
402C2×C8—222no—
403C2×C8—222no—
404C4⋊C4—24no—
405C4⋊C4—22no—
406C4⋊C4—22no—
407C4⋊C4—22no—
408C4⋊C4—44no—
409C4⋊C4—44no—
410C4⋊C4—42no—
411C4⋊C4—112no—
412C4⋊C4—112no—
413C4⋊C4—221no—
414C4⋊C4—221no—
415C4⋊C4—221no—
416C4⋊C4—221no—
417C4⋊C4—221no—
418C4⋊C4—221no—
419C4⋊C4—442no—
420C4⋊C4—442no—
421C4⋊C4—442no—
422C4⋊C4—442no—
423C4⋊C4C2×Dic2214yes—
424C22⋊C4—224no—
425C22⋊C4—442no—
426C42—22no—
427C42—22no—
428C42—21no—
429C42—21no—
430C42—21no—
431C42—21no—
432C42—224no—
433C42—442no—
434C11#2367011yescharacteristic, complemented, Sylow
435C23—21no—
436C23—21no—
437C23—21no—
438C23—21no—
439C23#6697712yes—
440C23#6699212yes—
441C23#6699912yes—
442C23C22×C22⋊D1111yescharacteristic
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—24no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—44no—
455C2×C4—44no—
456C2×C4—48no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—84no—
463C2×C4—222no—
464C2×C4—222no—
465C2×C4—441no—
466C2×C4—441no—
467C2×C4—441no—
468C2×C4—441no—
469C2×C4—441no—
470C2×C4—441no—
471C2×C4—441no—
472C2×C4—441no—
473C2×C4—441no—
474C2×C4—441no—
475C2×C4#6694114yes—
476C2×C4#6694214yes—
477C2×C4#6694314yes—
478C2×C4#6694714yes—
479C2×C4#6697712yes—
480C2×C4#6698512yes—
481C2×C4#6699212yes—
482C2×C4#6699512yes—
483C2×C4#6699912yes—
484C2×C4C22×Dic2211yescharacteristic
485C2×C4C2×#433911yescharacteristic
486C2×C4C2×D4×D1111yescharacteristic
487C2×C4C2×#434111yescharacteristic
488C2×C4C2×Q8×D1111yescharacteristic
489C2×C4C2×#434311yescharacteristic
490C8—224no—
491C8—442no—
492C22—22no—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—22no—
497C22—22no—
498C22#1062259714yes—
499C22C2×#6697711yescharacteristic
500C22C2×#6698511yescharacteristic
501C22C2×#6699211yescharacteristic
502C22C2×#6699511yescharacteristic
503C22C2×#6699911yescharacteristic
504C22#1062335311yescharacteristic
505C22#1062335311yescharacteristic
506C4—22no—
507C4—22no—
508C4—44no—
509C4—41no—
510C4—41no—
511C4—82no—
512C4—442no—
513C4—442no—
514C4—881no—
515C4—881no—
516C4#1062259714yes—
517C4C2×#6694111yescharacteristic
518C4C2×#6694211yescharacteristic
519C4C2×#6694311yescharacteristic
520C4C2×#6694711yescharacteristic
521C2—24no—
522C2C2×#1062259711yescharacteristic
523C2#1307823111yescharacteristic
524C2#1307824211yescharacteristic
525C2#1307841311yescharacteristic
526C2#1307842111yescharacteristic
527C2#1307842511yescharacteristic
528C2#1307843411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#389C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenterC2×#389D11
hypocenterC11#23670
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
4. #13070118C2semidirect
5. #13070117C2semidirect
6. #13070112C2semidirect
7. #13070107C2semidirect
434. C11#23670semidirect

Maximal subgroups

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

subgroupindex
C2×#106225772
C2×#106225372
#130710992
#130701182
#130701172
#130701122
#130701072
#130683352
C2×C11×#3892
#2367011