Finite Group Databasebeta

← #14908418

Subgroups — #14908418

Order 2816.

546 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079129C211yesmaximal, characteristic, complemented
2C4×#66972C211yesmaximal, characteristic
3#13070780C211yesmaximal, characteristic, complemented
4#13070774C211yesmaximal, characteristic, complemented
5#13070770C211yesmaximal, characteristic, complemented
6#13070766C211yesmaximal, characteristic, complemented
7#13070762C211yesmaximal, characteristic, complemented
8#13070756C211yesmaximal, characteristic, complemented
9#13070752C211yesmaximal, characteristic, complemented
10#13070399C211yesmaximal, characteristic, complemented
11#13070397C211yesmaximal, characteristic, complemented
12D11×C4⋊C16C211yesmaximal, characteristic, complemented
13#13070322C211yesmaximal, characteristic
14#13070322C211yesmaximal, characteristic
15C11×#2229C211yesmaximal, characteristic, complemented
16C2×#66972C2211yescharacteristic
17#10623219—21no—
18C4×#4343—21no—
19C11×#499C2211yescharacteristic
20C4×C11×Q16C2211yescharacteristic
21Q16×Dic11C2211yescharacteristic
22#10622677—21no—
23C4×#4325—21no—
24C2×C16×D11C2211yescharacteristic
25C2×C16×D11C2211yescharacteristic
26#10622493C2211yescharacteristic
27#10622493C2211yescharacteristic
28#10622493C2211yescharacteristic
29#10622487C2211yescharacteristic
30#10622487C2211yescharacteristic
31#10622485C2211yescharacteristic
32#10622473—21no—
33#10622468—21no—
34#10622417—21no—
35#10622401—21no—
36C4×D88C2211yescharacteristic
37C4×C8×D11C2211yescharacteristic
38#10622296C2211yescharacteristic
39C11×#367C2211yescharacteristic
40C11×#366C2211yescharacteristic
41C11×C4⋊C16C2211yescharacteristic
42C11×#358C2211yescharacteristic
43C11×#358C2211yescharacteristic
44#10622202C2211yescharacteristic
45#10622202C2211yescharacteristic
46#10622147C2211yescharacteristic
47#10622147C2211yescharacteristic
48#10622143C2211yescharacteristic
49#10622142C2211yescharacteristic
50Dic11⋊C16C2211yescharacteristic
51Dic11⋊C16C2211yescharacteristic
52#10622129C2211yescharacteristic
53#10622129C2211yescharacteristic
54#10622128C2211yescharacteristic
55#10622128C2211yescharacteristic
56#10622127C2211yescharacteristic
57#10622127C2211yescharacteristic
58C4⋊(C11⋊C16)C2211yescharacteristic
59C2×#4343—21no—
60C2×C11×Q16C2311yescharacteristic
61C11×#125—21no—
62C4×Q8×C11—21no—
63Q8×Dic11—21no—
64C2×#4325—21no—
65#66972—22no—
66#66972Q814yescomplemented
67C2×D88C2311yescharacteristic
68C2×C8×D11D411yescharacteristic
69C2×C8×D11C2311yescharacteristic
70#66949—41no—
71#66949—41no—
72#66946—21no—
73#66946—41no—
74#66945—21no—
75#66945—21no—
76#66945—21no—
77#66945—41no—
78#66941—21no—
79#66941—21no—
80#66940—41no—
81#66940—41no—
82C4×D44—21no—
83C4×D44—41no—
84C42×D11—41no—
85C42×D11D411yescharacteristic
86#66923—21no—
87C2×C11×C16C2311yescharacteristic
88C2×C11×C16C2311yescharacteristic
89C11×#107C2311yescharacteristic
90C11×#107C2311yescharacteristic
91C11×#107C2311yescharacteristic
92C11×#106—21no—
93C11×#103—21no—
94C4×C8×C11C2311yescharacteristic
95#66899—21no—
96#66885—21no—
97#66882C2311yescharacteristic
98#66882C2311yescharacteristic
99#66882C2311yescharacteristic
100#66881—21no—
101C8×Dic11D411yescharacteristic
102C8×Dic11C2311yescharacteristic
103C2×C11⋊C16C2311yescharacteristic
104C2×C11⋊C16C2311yescharacteristic
105#66873—21no—
106#66872—21no—
107#66872—21no—
108#66872—21no—
109#66871—21no—
110#66871—21no—
111C4×C11⋊C8D411yescharacteristic
112C16×D11—22no—
113C16×D11—22no—
114#33626—111nomaximal, Sylow
115C2×Q8×C11—21no—
116#4343—24no—
117#4343—42no—
118C2×D44—21no—
119C2×D44—41no—
120C2×C4×D11—41no—
121C2×C4×D11—41no—
122C2×C4×D11—41no—
123C2×C4×D11D811yescharacteristic
124C2×C4×D11D811yescharacteristic
125C2×C4×D11C2×D411yescharacteristic
126C2×Dic22—41no—
127C2×Dic22—41no—
128C11×Q16—21no—
129C11×Q16C2×Q812yes—
130C2×C8×C11C2×D411yescharacteristic
131C2×C8×C11C2411yescharacteristic
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—41no—
136C11×C4⋊C4—41no—
137C11×C4⋊C4—41no—
138C42×C11—41no—
139C42×C11C2×D411yescharacteristic
140#4325—24no—
141(C2×D11)⋊C4—41no—
142(C2×D11)⋊C4—41no—
143(C2×D11)⋊C4—41no—
144(C2×D11)⋊C4—41no—
145(C2×D11)⋊C4—41no—
146C4⋊Dic11—21no—
147C4⋊Dic11—21no—
148C4⋊Dic11—21no—
149C4⋊Dic11—41no—
150Dic11⋊C4—41no—
151Dic11⋊C4—41no—
152Dic11⋊C4—41no—
153Dic11⋊C4—41no—
154C4×Dic11—41no—
155C4×Dic11—41no—
156C4×Dic11—41no—
157C4×Dic11—41no—
158C4×Dic11D811yescharacteristic
159C4×Dic11D811yescharacteristic
160C4×Dic11C2×D411yescharacteristic
161C2×C11⋊C8C2×D411yescharacteristic
162C2×C11⋊C8C2×D411yescharacteristic
163D88—21no—
164D88C2×Q812yes—
165C8×D11—22no—
166C8×D11C2×Q812yes—
167C8×D11#4112yes—
168C11×C16—21no—
169C11×C16—21no—
170C11⋊C16—21no—
171C11⋊C16—21no—
172#3160—111no—
173C4×#135—111no—
174#2229—111no—
175#2229D1111yescharacteristic, complemented
176#2228—111no—
177#2228—111no—
178#2227—111no—
179#2226—111no—
180#2225—111no—
181#2224—111no—
182#2158—111no—
183#2158—111no—
184C2×C4⋊C16—111no—
185#2138—111no—
186#2138—111no—
187C22×D11—41no—
188C22×D11C2×D811yescharacteristic
189Q8×C11—22no—
190Q8×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11C2×D811yescharacteristic
196C2×C4×C11C2×D811yescharacteristic
197C2×C4×C11C22×D411yescharacteristic
198C2×Dic11—41no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11C2×D811yescharacteristic
202C2×Dic11C2×D811yescharacteristic
203C2×Dic11C2×D811yescharacteristic
204D44—22no—
205D44—44no—
206D44—41no—
207C4×D11—22no—
208C4×D11—41no—
209C4×D11—44no—
210C4×D11—82no—
211C4×D11—82no—
212C4×D11C22⋊Q812yes—
213C4×D11#13712yes—
214Dic22—82no—
215Dic22—82no—
216C8×C11—21no—
217C8×C11C22×Q811yescharacteristic
218C8×C11C2×#4111yescharacteristic
219C11⋊C8—21no—
220C11⋊C8C22⋊Q812yes—
221C2×#135—111no—
222#533—221no—
223C4×#41—221no—
224C22×C16—111no—
225C22×C16—111no—
226#500—111no—
227#500—111no—
228#499—111no—
229#499—221no—
230#499C2×D1111yescharacteristic
231#498—221no—
232C4×Q16—111no—
233C4×Q16C2×D1111yescharacteristic
234C4×SD16—221no—
235C4×SD16—221no—
236C4×D8—111no—
237C4×D8—111no—
238#427—111no—
239#427—111no—
240#427—111no—
241#427—221no—
242#416—221no—
243C2×C4×C8—111no—
244#367—111no—
245#367—111no—
246#367—111no—
247#367C2×D1111yescharacteristic
248#366—111no—
249#366—111no—
250#366—111no—
251#366C2×D1111yescharacteristic
252C4⋊C16—111no—
253C4⋊C16—111no—
254C4⋊C16—111no—
255C4⋊C16C2×D1111yescharacteristic
256#358—111no—
257#358—111no—
258#358C2×D1111yescharacteristic
259#358C2×D1111yescharacteristic
260#357—111no—
261#357—111no—
262#357—111no—
263#357—111no—
264C22×C11C22×D811yescharacteristic
265C2×D11—21no—
266C2×D11—21no—
267C2×D11—42no—
268C2×D11—81no—
269C2×D11—81no—
270C2×D11#47412yes—
271C4×C11—21no—
272C4×C11—21no—
273C4×C11—42no—
274C4×C11—81no—
275C4×C11—81no—
276C4×C11—81no—
277C4×C11C2×C22⋊Q811yescharacteristic
278C4×C11C2×#13711yescharacteristic
279Dic11—21no—
280Dic11—81no—
281Dic11—81no—
282Dic11—81no—
283Dic11#47412yes—
284Dic11#50812yes—
285C2×#41—221no—
286#135—114no—
287#135—222no—
288C2×Q16C22×D1111yescharacteristic
289C2×SD16—221no—
290C2×D8—111no—
291C22×C8—111no—
292C22×C8—111no—
293C4⋊Q8—221no—
294C4⋊Q8—221no—
295#125—21no—
296#125—221no—
297C22⋊Q8—441no—
298C22⋊Q8—441no—
299C4×Q8—21no—
300C4×Q8—221no—
301C4×Q8—441no—
302C4×Q8—441no—
303C4×D4—221no—
304C4×D4—221no—
305C4×D4—441no—
306C4×D4—441no—
307#117—221no—
308#117—221no—
309#117—221no—
310#117—441no—
311C2×C42—111no—
312C2×C42—441no—
313C2×C16—111no—
314C2×C16—111no—
315C2×C16—222no—
316C2×C16—222no—
317C2×C16C22×D1111yescharacteristic
318C2×C16C22×D1111yescharacteristic
319#107—111no—
320#107—111no—
321#107—111no—
322#107—221no—
323#107—221no—
324#107C22×D1111yescharacteristic
325#107C22×D1111yescharacteristic
326#107C22×D1111yescharacteristic
327#106—21no—
328#106—221no—
329#106—221no—
330#106—221no—
331#106—221no—
332#103—21no—
333#103—221no—
334#102—221no—
335#102—221no—
336C4×C8—111no—
337C4×C8—111no—
338C4×C8—111no—
339C4×C8C22×D1111yescharacteristic
340C2×C11C2×#47411yescharacteristic
341C2×C11C2×#50811yescharacteristic
342C2×C11#341411yescharacteristic
343D11—22no—
344D11—82no—
345#41—224no—
346#41—442no—
347C2×Q8—21no—
348C2×Q8—441no—
349C2×Q8—441no—
350C2×D4—221no—
351C2×D4—441no—
352C22×C4—111no—
353C22×C4—111no—
354C22×C4—111no—
355C22×C4—441no—
356C22×C4—441no—
357C22×C4—441no—
358Q16—21no—
359Q16Q8×D1112yes—
360SD16—224no—
361D8—112no—
362D8—221no—
363C2×C8—111no—
364C2×C8—112no—
365C2×C8—112no—
366C2×C8—111no—
367C2×C8—222no—
368C2×C8D4×D1111yescharacteristic
369C2×C8C23×D1111yescharacteristic
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4—221no—
377C4⋊C4—221no—
378C4⋊C4—221no—
379C4⋊C4—441no—
380C4⋊C4—441no—
381C4⋊C4—441no—
382C4⋊C4—441no—
383C4⋊C4—441no—
384C22⋊C4—441no—
385C22⋊C4—441no—
386C22⋊C4—441no—
387C22⋊C4—441no—
388C22⋊C4—441no—
389C42—41no—
390C42—111no—
391C42—111no—
392C42—111no—
393C42—441no—
394C42—441no—
395C42—441no—
396C42—441no—
397C42D4×D1111yescharacteristic
398C16—21no—
399C16—21no—
400C16—221no—
401C16—221no—
402C11#3362611yescharacteristic, complemented, Sylow
403C23—111no—
404C23—441no—
405Q8—22no—
406Q8—41no—
407Q8—882no—
408Q8—882no—
409D4—222no—
410D4—444no—
411D4—441no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—111no—
417C2×C4—111no—
418C2×C4—112no—
419C2×C4—112no—
420C2×C4—111no—
421C2×C4—222no—
422C2×C4—441no—
423C2×C4—444no—
424C2×C4—441no—
425C2×C4—441no—
426C2×C4—441no—
427C2×C4—882no—
428C2×C4—882no—
429C2×C4D8×D1111yescharacteristic
430C2×C4D8×D1111yescharacteristic
431C2×C4C2×D4×D1111yescharacteristic
432C8—21no—
433C8—112no—
434C8—221no—
435C8C2×Q8×D1111yescharacteristic
436C8#41×D1111yescharacteristic
437C22—112no—
438C22—221no—
439C22—221no—
440C22—442no—
441C22—881no—
442C22—881no—
443C22C2×D8×D1111yescharacteristic
444C4—21no—
445C4—21no—
446C4—42no—
447C4—81no—
448C4—81no—
449C4—81no—
450C4—112no—
451C4—112no—
452C4—221no—
453C4—881no—
454C4—881no—
455C4—881no—
456C4D11×C22⋊Q811yescharacteristic
457C4D11×#13711yescharacteristic
458C2—222no—
459C2—882no—
460C2D11×#47411yescharacteristic
461C2D11×#50811yescharacteristic
462C2#1308175111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2229C2
socleC22×C11C22×D8
prime radicalC2×#66972C22
hypercenter#2229D11
hypocenterC11#33626
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2229

Complements

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

NH ≅ G/Ntype
1. #13079129C2semidirect
3. #13070780C2semidirect
4. #13070774C2semidirect
5. #13070770C2semidirect
6. #13070766C2semidirect
7. #13070762C2semidirect
8. #13070756C2semidirect
9. #13070752C2semidirect
10. #13070399C2semidirect
11. #13070397C2semidirect
12. D11×C4⋊C16C2semidirect
15. C11×#2229C2semidirect
66. #66972Q8semidirect
175. #2229D11semidirect
402. C11#33626semidirect

Maximal subgroups

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

subgroupindex
#130791292
C4×#669722
#130707802
#130707742
#130707702
#130707662
#130707622
#130707562
#130707522
#130703992
#130703972
D11×C4⋊C162
#130703222
C11×#22292
#3362611