Finite Group Databasebeta

← #14755945

Subgroups — #14755945

Order 2816.

990 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622577C211yesmaximal, characteristic
2#13071099C211yesmaximal, characteristic
3#13069208C212yesmaximal, complemented
4#13069201C212yesmaximal, complemented
5#13069194C212yesmaximal, complemented
6#13069187C212yesmaximal, complemented
7#13068335C211yesmaximal, characteristic
8#13068335C211yesmaximal, characteristic
9#13068335C211yesmaximal, characteristic
10#13068310C211yesmaximal, characteristic
11C2×C4×C11×C4⋊C4C211yesmaximal, characteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C42×C11—21no—
15C22×C42×C11C2211yescharacteristic
16C2×#66979C2211yescharacteristic
17C2×#66979C2211yescharacteristic
18C22×#4318C2211yescharacteristic
19C22×#4318C2211yescharacteristic
20C4×C11×C4⋊C4—21no—
21C4×C11×C4⋊C4—21no—
22C4×C11×C4⋊C4C2212yes—
23C4×C11×C4⋊C4C2212yes—
24C2×C11×#95—21no—
25#10622823—21no—
26#10622823—21no—
27#10622577C418yescomplemented
28C2×#66872C2212yes—
29C2×#66871C2212yes—
30C4×Dic11⋊C4—21no—
31C4×Dic11⋊C4—21no—
32#10622541C2211yescharacteristic
33#10622541C2211yescharacteristic
34#10622541C2211yescharacteristic
35#10622541C2211yescharacteristic
36#10622167C2212yes—
37#10622167C2212yes—
38#10622167C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42#10622162C2212yes—
43#10622162C2212yes—
44C23×C4×C11—21no—
45C23×C4×C11—21no—
46C23×C4×C11D411yescharacteristic
47C23×C4×C11D411yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4C2×C414yes—
54C2×C11×C4⋊C4Q814yes—
55C2×C11×C4⋊C4C2312yes—
56C2×C11×C4⋊C4C2312yes—
57C2×C42×C11—22no—
58C2×C42×C11—22no—
59C2×C42×C11—22no—
60C2×C42×C11—22no—
61C2×C42×C11—44no—
62C2×C42×C11D411yescharacteristic
63C2×C42×C11D411yescharacteristic
64C2×C42×C11C2311yescharacteristic
65C2×C42×C11C2311yescharacteristic
66C2×C22⋊Dic11—21no—
67C2×C22⋊Dic11—21no—
68#66979—22no—
69#66979—22no—
70#66979—22no—
71#66979C2×C414yes—
72C2×C4⋊Dic11C2311yescharacteristic
73C2×C4⋊Dic11C2311yescharacteristic
74C2×C4⋊Dic11C2311yescharacteristic
75C2×C4⋊Dic11C2311yescharacteristic
76C2×Dic11⋊C4—21no—
77C2×Dic11⋊C4—21no—
78C2×Dic11⋊C4—21no—
79C2×Dic11⋊C4—21no—
80C2×C4×Dic11—21no—
81C2×C4×Dic11—21no—
82C2×#4318—22no—
83C2×#4318—22no—
84C2×#4318—22no—
85C2×#4318—22no—
86C2×#4318—22no—
87C2×#4318C2×C414yes—
88C22×C11⋊C8C2312yes—
89C22×C11⋊C8C2312yes—
90C11×#95—22no—
91C11×#95—22no—
92C11⋊#95—21no—
93C11⋊#95—21no—
94C11⋊#95—21no—
95C11⋊#95—21no—
96#66872C2×C418yescomplemented
97#66871C2×C418yescomplemented
98#21033—111nomaximal, Sylow
99C24×C11C2×D411yescharacteristic
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—24no—
104C22×C4×C11—24no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—41no—
109C22×C4×C11—41no—
110C22×C4×C11—42no—
111C22×C4×C11—42no—
112C22×C4×C11—42no—
113C22×C4×C11—42no—
114C22×C4×C11C22×C412yes—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×Q812yes—
121C22×C4×C11#4112yes—
122C22×C4×C11#4112yes—
123C22×C4×C11#4112yes—
124C22×C4×C11#4112yes—
125C22×C4×C11C2411yescharacteristic
126C22×Dic11—21no—
127C22×Dic11—21no—
128C22×Dic11—21no—
129C22×Dic11—21no—
130C11×C4⋊C4—24no—
131C11×C4⋊C4—24no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4C22×C414yes—
135C11×C4⋊C4C2×Q814yes—
136C42×C11—22no—
137C42×C11—22no—
138C42×C11—21no—
139C42×C11—21no—
140C42×C11—21no—
141C42×C11—21no—
142C42×C11—44no—
143C42×C11—44no—
144C22⋊Dic11—24no—
145C22⋊Dic11—42no—
146C4⋊Dic11—21no—
147C4⋊Dic11—21no—
148C4⋊Dic11—21no—
149C4⋊Dic11—21no—
150C4⋊Dic11—21no—
151C4⋊Dic11—21no—
152C4⋊Dic11C22×C412yes—
153C4⋊Dic11C22×C412yes—
154Dic11⋊C4—42no—
155Dic11⋊C4—42no—
156Dic11⋊C4—42no—
157Dic11⋊C4—42no—
158C4×Dic11—24no—
159C4×Dic11—42no—
160#4318—28no—
161#4318—44no—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—22no—
164C2×C11⋊C8—22no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8C22×C414yes—
168C2×#428—111no—
169#2296—111no—
170C2×C4×C4⋊C4D1111yescharacteristic
171#1921—112no—
172#1920—112no—
173#1919—112no—
174#1918—112no—
175#1736—111no—
176#1736—111no—
177#1736—111no—
178#1728—111no—
179C23×C11—21no—
180C23×C11—21no—
181C23×C11—21no—
182C23×C11—21no—
183C23×C11C4×D412yes—
184C23×C11C22⋊Q812yes—
185C23×C11#12312yes—
186C23×C11C22×D411yescharacteristic
187C2×C4×C11—28no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—24no—
193C2×C4×C11—24no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—48no—
201C2×C4×C11—44no—
202C2×C4×C11—48no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11#11714yes—
208C2×C4×C11C4×D412yes—
209C2×C4×C11C4×Q814yes—
210C2×C4×C11C22⋊Q812yes—
211C2×C4×C11#12312yes—
212C2×C4×C11#12514yes—
213C2×C4×C11#12614yes—
214C2×C4×C11AGL(1,ℤ/8)12yes—
215C2×C4×C11#13712yes—
216C2×C4×C11C23×C411yescharacteristic
217C2×C4×C11C22×Q811yescharacteristic
218C2×C4×C11C2×#4111yescharacteristic
219C2×C4×C11C2×#4111yescharacteristic
220C2×C4×C11C2×#4111yescharacteristic
221C2×C4×C11C2×#4111yescharacteristic
222C2×Dic11—22no—
223C2×Dic11—22no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226C2×Dic11—41no—
227C2×Dic11—41no—
228C2×Dic11—41no—
229C2×Dic11—41no—
230C2×Dic11—41no—
231C2×Dic11—41no—
232C2×Dic11—41no—
233C2×Dic11—41no—
234C11⋊C8—24no—
235C11⋊C8—42no—
236C22×M16—111no—
237C22×M16—111no—
238C2×#117—111no—
239C2×#117—111no—
240C22×C4⋊C4C2×D1111yescharacteristic
241C22×C4⋊C4C2×D1111yescharacteristic
242C22×C42—21no—
243C22×C42C2×D1111yescharacteristic
244#428—118no—
245C2×#107—112no—
246C2×#106—112no—
247#389—111no—
248#389—111no—
249#389—111no—
250#389—111no—
251#385—221no—
252#385—221no—
253C4×C4⋊C4—21no—
254C4×C4⋊C4—21no—
255C4×C4⋊C4—221no—
256C4×C4⋊C4—221no—
257C4×C4⋊C4C2×D1112yes—
258C4×C4⋊C4C2×D1112yes—
259C2×#95—21no—
260#340—112no—
261#340—112no—
262#340—112no—
263#340—112no—
264#340—112no—
265#340—112no—
266#336—112no—
267#336—112no—
268C22×C11—22no—
269C22×C11—22no—
270C22×C11—22no—
271C22×C11—22no—
272C22×C11—22no—
273C22×C11—22no—
274C22×C11#38714yes—
275C22×C11C2×C4×D411yescharacteristic
276C22×C11C2×C22⋊Q811yescharacteristic
277C22×C11C2×#12311yescharacteristic
278C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
279C22×C11C2×#13711yescharacteristic
280C22×C11#57511yescharacteristic
281C22×C11#57511yescharacteristic
282C4×C11—22no—
283C4×C11—22no—
284C4×C11—44no—
285C4×C11—41no—
286C4×C11—41no—
287C4×C11—44no—
288C4×C11#38714yes—
289C4×C11C2×#11711yescharacteristic
290C4×C11C2×C4×Q811yescharacteristic
291C4×C11C2×#12511yescharacteristic
292C4×C11C2×#12611yescharacteristic
293Dic11—42no—
294Dic11—42no—
295Dic11—81no—
296Dic11—81no—
297C23×C4—21no—
298C23×C4—21no—
299C23×C4C22⋊D1111yescharacteristic
300C23×C4C22⋊D1111yescharacteristic
301C23×C4C22×D1111yescharacteristic
302C2×M16—114no—
303C2×M16—222no—
304C2×M16—222no—
305C2×M16—222no—
306C2×M16—222no—
307C2×M16—222no—
308C22×C8—112no—
309C22×C8—112no—
310#117—114no—
311#117—222no—
312#117—222no—
313#117—222no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—111no—
319C2×C4⋊C4—111no—
320C2×C4⋊C4—111no—
321C2×C4⋊C4—111no—
322C2×C4⋊C4—221no—
323C2×C4⋊C4—221no—
324C2×C4⋊C4—221no—
325C2×C4⋊C4—221no—
326C2×C4⋊C4Dic2214yes—
327C2×C4⋊C4C4×D1114yes—
328C2×C4⋊C4C22×D1112yes—
329C2×C4⋊C4C22×D1112yes—
330C2×C22⋊C4—221no—
331C2×C22⋊C4—221no—
332C2×C42—22no—
333C2×C42—22no—
334C2×C42—22no—
335C2×C42—22no—
336C2×C42—44no—
337C2×C42—221no—
338C2×C42—221no—
339C2×C42C22⋊D1111yescharacteristic
340C2×C42C22⋊D1111yescharacteristic
341C2×C42C22×D1111yescharacteristic
342C2×C42C22×D1111yescharacteristic
343#107—118no—
344#106—118no—
345#95—22no—
346#95—22no—
347#95—221no—
348#95—221no—
349#95—221no—
350#95—221no—
351C2×C11—24no—
352C2×C11C2×#38711yescharacteristic
353C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
354C2×C11C4×#13711yescharacteristic
355C2×C11#307711yescharacteristic
356C2×C11#307811yescharacteristic
357C2×C11#309211yescharacteristic
358C2×C11#309311yescharacteristic
359C24C2×C22⋊D1111yescharacteristic
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—24no—
364C22×C4—24no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—41no—
369C22×C4—41no—
370C22×C4—42no—
371C22×C4—42no—
372C22×C4—42no—
373C22×C4—42no—
374C22×C4—221no—
375C22×C4—221no—
376C22×C4—221no—
377C22×C4—221no—
378C22×C4C2×Dic2212yes—
379C22×C4C2×C4×D1112yes—
380C22×C4#433912yes—
381C22×C4#433912yes—
382C22×C4#433912yes—
383C22×C4#433912yes—
384C22×C4C2×C22⋊D1111yescharacteristic
385C22×C4C2×C22⋊D1111yescharacteristic
386C22×C4C2×C22⋊D1111yescharacteristic
387C22×C4C2×C22⋊D1111yescharacteristic
388C22×C4C2×C22⋊D1111yescharacteristic
389C22×C4C23×D1111yescharacteristic
390M16—228no—
391M16—444no—
392C2×C8—114no—
393C2×C8—222no—
394C2×C8—222no—
395C2×C8—222no—
396C2×C8—222no—
397C2×C8—222no—
398C4⋊C4—24no—
399C4⋊C4—24no—
400C4⋊C4—22no—
401C4⋊C4—22no—
402C4⋊C4—112no—
403C4⋊C4—112no—
404C4⋊C4—221no—
405C4⋊C4—221no—
406C4⋊C4—221no—
407C4⋊C4—221no—
408C4⋊C4—221no—
409C4⋊C4—221no—
410C4⋊C4—442no—
411C4⋊C4—442no—
412C4⋊C4—442no—
413C4⋊C4—442no—
414C4⋊C4C2×Dic2214yes—
415C4⋊C4C2×C4×D1114yes—
416C22⋊C4—224no—
417C22⋊C4—442no—
418C42—22no—
419C42—22no—
420C42—21no—
421C42—21no—
422C42—21no—
423C42—21no—
424C42—44no—
425C42—44no—
426C42—224no—
427C42—442no—
428C11#2103311yescharacteristic, complemented, Sylow
429C23—21no—
430C23—21no—
431C23—21no—
432C23—21no—
433C23#6697712yes—
434C23C4×C22⋊D1112yes—
435C23#6698212yes—
436C23C22×C22⋊D1111yescharacteristic
437C2×C4—28no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—24no—
443C2×C4—24no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—44no—
451C2×C4—48no—
452C2×C4—48no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—222no—
458C2×C4—222no—
459C2×C4—441no—
460C2×C4—441no—
461C2×C4—441no—
462C2×C4—441no—
463C2×C4—441no—
464C2×C4—441no—
465C2×C4—441no—
466C2×C4—441no—
467C2×C4—441no—
468C2×C4—441no—
469C2×C4C4×Dic2214yes—
470C2×C4#6692314yes—
471C2×C4#6692514yes—
472C2×C4#6692914yes—
473C2×C4#6697712yes—
474C2×C4C4×C22⋊D1112yes—
475C2×C4#6698212yes—
476C2×C4#6698512yes—
477C2×C4#6699512yes—
478C2×C4C22×Dic2211yescharacteristic
479C2×C4C22×C4×D1111yescharacteristic
480C2×C4C2×#433911yescharacteristic
481C2×C4C2×#433911yescharacteristic
482C2×C4C2×#433911yescharacteristic
483C2×C4C2×#433911yescharacteristic
484C8—224no—
485C8—442no—
486C22—22no—
487C22—22no—
488C22—22no—
489C22—22no—
490C22—22no—
491C22—22no—
492C22#1062254614yes—
493C22C2×#6697711yescharacteristic
494C22C2×C4×C22⋊D1111yescharacteristic
495C22C2×#6698211yescharacteristic
496C22C2×#6698511yescharacteristic
497C22C2×#6699511yescharacteristic
498C22#1062335311yescharacteristic
499C22#1062335311yescharacteristic
500C4—22no—
501C4—22no—
502C4—41no—
503C4—41no—
504C4—44no—
505C4—44no—
506C4—442no—
507C4—442no—
508C4—881no—
509C4—881no—
510C4#1062254614yes—
511C4C2×C4×Dic2211yescharacteristic
512C4C2×#6692311yescharacteristic
513C4C2×#6692511yescharacteristic
514C4C2×#6692911yescharacteristic
515C2—24no—
516C2C2×#1062254611yescharacteristic
517C2C4×#6698511yescharacteristic
518C2C4×#6699511yescharacteristic
519C2#1307841311yescharacteristic
520C2#1307842111yescharacteristic
521C2#1307853911yescharacteristic
522C2#1307854711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C4×C11×C4⋊C4C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC2×C4×C4⋊C4D11
hypocenterC11#21033
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #13069208C2semidirect
4. #13069201C2semidirect
5. #13069194C2semidirect
6. #13069187C2semidirect
27. #10622577C4semidirect
96. #66872C2×C4semidirect
97. #66871C2×C4semidirect
428. C11#21033semidirect

Maximal subgroups

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

subgroupindex
C2×#106225772
#130710992
#130692082
#130692012
#130691942
#130691872
#130683352
#130683102
C2×C4×C11×C4⋊C42
#2103311