Finite Group Databasebeta

← #14765817

Subgroups — #14765817

Order 2816.

848 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622697C211yesmaximal, characteristic
2#13071080C211yesmaximal, characteristic
3#13069565C211yesmaximal, characteristic, complemented
4#13069377C211yesmaximal, characteristic, complemented
5#13069341C212yesmaximal, complemented
6#13069298C212yesmaximal
7#13069243C212yesmaximal
8#13069194C212yesmaximal, complemented
9#13068613C211yesmaximal, characteristic
10C4×C4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
11C4×C11×C4⋊Q8C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×Q8×C11—21no—
14C2×C4×D44C2211yescharacteristic
15C2×#66925—21no—
16C11×#391—21no—
17C11×#389—21no—
18C11×#389C2212yes—
19C11×#384C2211yescharacteristic
20C4×C11×C4⋊C4—21no—
21C4×C11×C4⋊C4C2212yes—
22C43×C11C2211yescharacteristic
23#10622697C418yescomplemented
24C2×#66873C2212yes—
25C2×#66873C2212yes—
26C2×#66872C2212yes—
27C2×#66872C2212yes—
28#10622553—21no—
29#10622553—21no—
30#10622552C2211yescharacteristic
31#10622552C2211yescharacteristic
32C4×(C2×D11)⋊C4—21no—
33C4×C4⋊Dic11C2211yescharacteristic
34#10622541C2211yescharacteristic
35#10622541C2211yescharacteristic
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38C2×C4×C11⋊C8C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43#10622162C2212yes—
44C22×Q8×C11—21no—
45C22×D44C2311yescharacteristic
46C22×C4×D11—21no—
47C11×C4⋊Q8—22no—
48C11×C4⋊Q8C2×C414yes—
49C4×Q8×C11—44no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4C2312yes—
55C2×C11×C4⋊C4C2312yes—
56C2×C42×C11—22no—
57C2×C42×C11D411yescharacteristic
58C2×C42×C11D411yescharacteristic
59C2×C42×C11D411yescharacteristic
60C2×C42×C11D411yescharacteristic
61C2×C42×C11C2311yescharacteristic
62C2×C42×C11C2311yescharacteristic
63C2×C42×C11C2311yescharacteristic
64C2×(C2×D11)⋊C4—21no—
65C2×(C2×D11)⋊C4—21no—
66C2×(C2×D11)⋊C4—21no—
67C2×(C2×D11)⋊C4—21no—
68C2×(C2×D11)⋊C4—21no—
69C2×C4⋊Dic11C2311yescharacteristic
70C2×C4⋊Dic11C2311yescharacteristic
71C2×C4⋊Dic11C2311yescharacteristic
72C2×Dic11⋊C4—21no—
73C2×Dic11⋊C4—21no—
74C2×C4×Dic11—21no—
75C22×C11⋊C8C2312yes—
76C22×C11⋊C8C2312yes—
77C4×D44—22no—
78C4×D44C2×C414yes—
79#66925—44no—
80C11×#95—22no—
81C11×#95—22no—
82C11⋊#95—21no—
83C11⋊#95—21no—
84C11⋊#95—21no—
85#66873—42no—
86#66873C2×C418yes—
87#66872—42no—
88#66872C2×C418yes—
89C4⋊(C11⋊C8)—22no—
90C4⋊(C11⋊C8)C2×C414yes—
91C4×C11⋊C8—42no—
92#22111—111nomaximal, Sylow
93C23×D11—21no—
94C2×Q8×C11—24no—
95C2×Q8×C11—42no—
96C2×Q8×C11—42no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2411yescharacteristic
106C22×Dic11—21no—
107C22×Dic11—21no—
108C22×Dic11—21no—
109C2×D44—21no—
110C2×D44—21no—
111C2×D44—21no—
112C2×D44—21no—
113C2×D44—21no—
114C2×D44C22×C412yes—
115C2×C4×D11—24no—
116C2×C4×D11—42no—
117C2×C4×D11—42no—
118C11×C4⋊C4—24no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—42no—
123C11×C4⋊C4—42no—
124C11×C4⋊C4—44no—
125C11×C4⋊C4C22×C414yes—
126C42×C11—22no—
127C42×C11—22no—
128C42×C11—21no—
129C42×C11—21no—
130C42×C11—21no—
131C42×C11—21no—
132C42×C11—41no—
133C42×C11—44no—
134C42×C11SD1614yes—
135C42×C11C22×C412yes—
136C42×C11#4112yes—
137(C2×D11)⋊C4—24no—
138(C2×D11)⋊C4—42no—
139(C2×D11)⋊C4—42no—
140(C2×D11)⋊C4—42no—
141(C2×D11)⋊C4—42no—
142C4⋊Dic11—21no—
143C4⋊Dic11—21no—
144C4⋊Dic11—21no—
145C4⋊Dic11—21no—
146C4⋊Dic11—21no—
147C4⋊Dic11C22×C412yes—
148Dic11⋊C4—42no—
149Dic11⋊C4—42no—
150C4×Dic11—42no—
151C2×C11⋊C8—22no—
152C2×C11⋊C8—22no—
153C2×C11⋊C8—22no—
154C2×C11⋊C8—22no—
155C2×C11⋊C8—22no—
156C2×C11⋊C8C22×C414yes—
157C2×#476—111no—
158C4×C4⋊Q8D1111yescharacteristic, complemented
159#2293—111no—
160#1987—111no—
161#1948—111no—
162#1941—112no—
163#1934—112no—
164#1926—112no—
165#1919—112no—
166#1802—111no—
167C4×C4⋊C8—111no—
168C23×C11C22×D411yescharacteristic
169C22×D11—22no—
170C22×D11—41no—
171C22×D11—41no—
172C22×D11—41no—
173C22×D11—41no—
174C22×D11—41no—
175C22×D11—41no—
176Q8×C11—48no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—21no—
185C2×C4×C11—24no—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11C4×D412yes—
195C2×C4×C11C4×D412yes—
196C2×C4×C11C2×SD1612yes—
197C2×C4×C11C2×SD1612yes—
198C2×C4×C11C2×SD1612yes—
199C2×C4×C11#13512yes—
200C2×C4×C11AGL(1,ℤ/8)12yes—
201C2×C4×C11C23×C411yescharacteristic
202C2×C4×C11C2×#4111yescharacteristic
203C2×C4×C11H(5,𝔽2)11yescharacteristic
204C2×C4×C112−1+411yescharacteristic
205C2×C4×C112−1+411yescharacteristic
206C2×C4×C112−1+411yescharacteristic
207C2×Dic11—22no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216D44—22no—
217D44—22no—
218D44—41no—
219D44—41no—
220C4×D11—48no—
221C11⋊C8—24no—
222C11⋊C8—42no—
223C2×C4⋊Q8C2×D1111yescharacteristic
224C2×C4×Q8—21no—
225C2×C4×D4—111no—
226C2×#117—221no—
227#476—118no—
228C2×#106—112no—
229C2×#106—112no—
230C2×C4⋊C8—111no—
231C2×C4⋊C8—111no—
232C2×#102—112no—
233C2×#102—112no—
234C2×C4×C8—112no—
235#391—21no—
236#390—111no—
237#390—111no—
238#389—21no—
239#389—111no—
240#389—111no—
241#389C2×D1112yes—
242#388—221no—
243#388—221no—
244#384C2×D1111yescharacteristic
245C4×C4⋊C4—21no—
246C4×C4⋊C4—111no—
247C4×C4⋊C4C2×D1112yes—
248C4×C22⋊C4—221no—
249C43C2×D1111yescharacteristic
250#340—112no—
251#340—112no—
252#340—112no—
253#340—112no—
254#336—112no—
255C22×C11C2×C4×D411yescharacteristic
256C22×C11#53611yescharacteristic
257C22×C11#53711yescharacteristic
258C22×C11C22×SD1611yescharacteristic
259C22×C11C2×#13511yescharacteristic
260C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
261C22×C11#57511yescharacteristic
262C2×D11—42no—
263C2×D11—42no—
264C2×D11—42no—
265C2×D11—81no—
266C2×D11—81no—
267C2×D11—81no—
268C2×D11—81no—
269C4×C11—22no—
270C4×C11—22no—
271C4×C11—22no—
272C4×C11—22no—
273C4×C11—44no—
274C4×C11—41no—
275C4×C11—82no—
276C4×C11C4×SD1614yes—
277C4×C11#51911yescharacteristic
278C4×C11#52011yescharacteristic
279C4×C11#54111yescharacteristic
280C4×C11#54211yescharacteristic
281Dic11—42no—
282Dic11—81no—
283Dic11—81no—
284C22×Q8—21no—
285C22×D4—111no—
286C23×C4—221no—
287C22×C8—112no—
288C22×C8—112no—
289C4⋊Q8—22no—
290C4⋊Q8C4×D1114yes—
291C4×Q8—44no—
292C4×D4—114no—
293C4×D4—222no—
294#117—444no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—111no—
300C2×C4⋊C4—111no—
301C2×C4⋊C4—111no—
302C2×C4⋊C4—221no—
303C2×C4⋊C4—221no—
304C2×C4⋊C4C22×D1112yes—
305C2×C4⋊C4C22×D1112yes—
306C2×C22⋊C4—221no—
307C2×C22⋊C4—221no—
308C2×C22⋊C4—221no—
309C2×C22⋊C4—221no—
310C2×C22⋊C4—221no—
311C2×C42—22no—
312C2×C42—221no—
313C2×C42C22⋊D1111yescharacteristic
314C2×C42C22⋊D1111yescharacteristic
315C2×C42C22⋊D1111yescharacteristic
316C2×C42C22⋊D1111yescharacteristic
317C2×C42C22×D1111yescharacteristic
318C2×C42C22×D1111yescharacteristic
319C2×C42C22×D1111yescharacteristic
320#106—118no—
321#106—442no—
322C4⋊C8—114no—
323C4⋊C8—222no—
324#102—118no—
325#102—442no—
326C4×C8—442no—
327#95—22no—
328#95—22no—
329#95—221no—
330#95—221no—
331#95—221no—
332C2×C11#232311yescharacteristic
333C2×C11C2×C4×SD1611yescharacteristic
334C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
335C2×C11#322711yescharacteristic
336C2×C11#323311yescharacteristic
337C2×C11#324611yescharacteristic
338C2×C11#324711yescharacteristic
339D11—82no—
340C24—221no—
341C2×Q8—24no—
342C2×Q8—42no—
343C2×Q8—42no—
344C2×D4—112no—
345C2×D4—221no—
346C2×D4—221no—
347C2×D4—221no—
348C2×D4—221no—
349C2×D4—221no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—221no—
353C22×C4—224no—
354C22×C4—221no—
355C22×C4—221no—
356C22×C4—442no—
357C22×C4—442no—
358C22×C4C2×C22⋊D1111yescharacteristic
359C22×C4C2×C22⋊D1111yescharacteristic
360C22×C4C2×C22⋊D1111yescharacteristic
361C22×C4C2×C22⋊D1111yescharacteristic
362C22×C4C2×C22⋊D1111yescharacteristic
363C22×C4C2×C22⋊D1111yescharacteristic
364C22×C4C23×D1111yescharacteristic
365C2×C8—114no—
366C2×C8—222no—
367C2×C8—222no—
368C2×C8—222no—
369C2×C8—222no—
370C2×C8—222no—
371C4⋊C4—24no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4—42no—
376C4⋊C4—44no—
377C4⋊C4—42no—
378C4⋊C4—112no—
379C4⋊C4—221no—
380C4⋊C4—221no—
381C4⋊C4—221no—
382C4⋊C4—221no—
383C4⋊C4—221no—
384C4⋊C4—442no—
385C4⋊C4—442no—
386C4⋊C4C2×C4×D1114yes—
387C22⋊C4—224no—
388C22⋊C4—442no—
389C22⋊C4—442no—
390C22⋊C4—442no—
391C22⋊C4—442no—
392C42—22no—
393C42—22no—
394C42—21no—
395C42—21no—
396C42—21no—
397C42—21no—
398C42—41no—
399C42—44no—
400C42—442no—
401C42#432514yes—
402C42C2×C4×D1112yes—
403C42#433912yes—
404C11#2211111yescharacteristic, complemented, Sylow
405C23—222no—
406C23—441no—
407C23—441no—
408C23—441no—
409C23—441no—
410C23—441no—
411C23—441no—
412C23C22×C22⋊D1111yescharacteristic
413Q8—48no—
414D4—222no—
415D4—222no—
416D4—441no—
417D4—441no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—24no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—222no—
436C2×C4—441no—
437C2×C4—441no—
438C2×C4—448no—
439C2×C4—441no—
440C2×C4—441no—
441C2×C4—441no—
442C2×C4—441no—
443C2×C4—441no—
444C2×C4—441no—
445C2×C4C4×C22⋊D1112yes—
446C2×C4C4×C22⋊D1112yes—
447C2×C4#6698512yes—
448C2×C4C2×#432512yes—
449C2×C4C2×#432512yes—
450C2×C4C2×#432512yes—
451C2×C4#6700312yes—
452C2×C4C22×C4×D1111yescharacteristic
453C2×C4C2×#433911yescharacteristic
454C2×C4#6704011yescharacteristic
455C2×C4#6704011yescharacteristic
456C2×C4#6704211yescharacteristic
457C2×C4#6704311yescharacteristic
458C8—224no—
459C8—442no—
460C22—442no—
461C22—442no—
462C22—442no—
463C22—881no—
464C22—881no—
465C22—881no—
466C22—881no—
467C22C2×C4×C22⋊D1111yescharacteristic
468C22C2×#6698511yescharacteristic
469C22C22×#432511yescharacteristic
470C22#1062334711yescharacteristic
471C22C2×#6700311yescharacteristic
472C22#1062335311yescharacteristic
473C22#1062336411yescharacteristic
474C4—22no—
475C4—22no—
476C4—22no—
477C4—22no—
478C4—44no—
479C4—41no—
480C4—82no—
481C4—442no—
482C4—881no—
483C4—881no—
484C4C4×#432514yes—
485C4#1062310311yescharacteristic
486C4#1062310511yescharacteristic
487C4#1062311311yescharacteristic
488C4#1062311411yescharacteristic
489C2—882no—
490C2#1307129211yescharacteristic
491C2C2×C4×#432511yescharacteristic
492C2C4×#6698511yescharacteristic
493C2#1307974411yescharacteristic
494C2#1307979511yescharacteristic
495C2#1307992811yescharacteristic
496C2#1307993611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×C4⋊Q8C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenterC4×C4⋊Q8D11
hypocenterC11#22111
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C43 ◁ C4×C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. #13069565C2semidirect
4. #13069377C2semidirect
5. #13069341C2semidirect
8. #13069194C2semidirect
10. C4×C4⋊(C11⋊C8)C2semidirect
11. C4×C11×C4⋊Q8C2semidirect
23. #10622697C4semidirect
158. C4×C4⋊Q8D11semidirect
404. C11#22111semidirect

Maximal subgroups

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

subgroupindex
C2×#106226972
#130710802
#130695652
#130693772
#130693412
#130692982
#130692432
#130691942
#130686132
C4×C4⋊(C11⋊C8)2
C4×C11×C4⋊Q82
#2211111