Finite Group Databasebeta

← #14908415

Subgroups — #14908415

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#13079128C211yesmaximal, characteristic, complemented
2#135×Dic11C211yesmaximal, characteristic
3#13070782C211yesmaximal, characteristic, complemented
4#13070778C211yesmaximal, characteristic, complemented
5#13070775C211yesmaximal, characteristic, complemented
6#13070771C211yesmaximal, characteristic, complemented
7#13070766C211yesmaximal, characteristic, complemented
8#13070761C211yesmaximal, characteristic, complemented
9#13070756C211yesmaximal, characteristic, complemented
10#13070751C211yesmaximal, characteristic, complemented
11#13070400C211yesmaximal, characteristic, complemented
12#13070398C211yesmaximal, characteristic, complemented
13C2×Dic11⋊C16C211yesmaximal, characteristic, complemented
14#13070323C211yesmaximal, characteristic
15C11×#2138C211yesmaximal, characteristic
16C2×C11×#135C2211yescharacteristic
17#41×Dic11—21no—
18#10623048—21no—
19C22×C11×C16C2211yescharacteristic
20C11×#427C2211yescharacteristic
21#10622846—21no—
22Q16×Dic11C2211yescharacteristic
23Q16×Dic11C2211yescharacteristic
24SD16×Dic11—21no—
25SD16×Dic11—21no—
26D8×Dic11C2211yescharacteristic
27D8×Dic11C2211yescharacteristic
28#10622719C2211yescharacteristic
29#10622719C2211yescharacteristic
30C2×C8×Dic11C2211yescharacteristic
31C22×C11⋊C16C2211yescharacteristic
32#10622611—21no—
33#10622491C2211yescharacteristic
34#10622491C2211yescharacteristic
35#10622487C2211yescharacteristic
36#10622487C2211yescharacteristic
37#10622471—21no—
38#10622468—21no—
39C11×#358C2211yescharacteristic
40C11×#358C2211yescharacteristic
41C11×#357C2211yescharacteristic
42C11×#357C2211yescharacteristic
43#10622202C2211yescharacteristic
44#10622202C2211yescharacteristic
45#10622200C2211yescharacteristic
46#10622200C2211yescharacteristic
47#10622143C2211yescharacteristic
48#10622143C2211yescharacteristic
49#10622142C2211yescharacteristic
50#10622142C2211yescharacteristic
51Dic11⋊C16C2211yescharacteristic
52Dic11⋊C16C2211yescharacteristic
53Dic11⋊C16C2211yescharacteristic
54Dic11⋊C16C2211yescharacteristic
55#10622128C2211yescharacteristic
56#10622128C2211yescharacteristic
57#10622127C2211yescharacteristic
58#10622127C2211yescharacteristic
59C2×C11×#41—21no—
60C11×#135—22no—
61C11×#135Q814yescomplemented
62C2×C11×Q16C2311yescharacteristic
63C2×C11×SD16—21no—
64C2×C11×D8C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C11×#117—21no—
67Q8×Dic11—21no—
68Q8×Dic11—21no—
69D4×Dic11—21no—
70D4×Dic11—21no—
71D4×Dic11—41no—
72D4×Dic11—41no—
73#66979—21no—
74#66979—21no—
75#66979—41no—
76C2×C4×Dic11—41no—
77C2×C4×Dic11D411yescharacteristic
78C22×C11⋊C8D411yescharacteristic
79#66943—21no—
80#66943—21no—
81#66941—21no—
82#66941—21no—
83#66931—41no—
84#66931—41no—
85C4×Dic22—41no—
86C4×Dic22—41no—
87C2×C11×C16—22no—
88C2×C11×C16C2311yescharacteristic
89C2×C11×C16C2311yescharacteristic
90C11×#107C2311yescharacteristic
91C11×#107C2311yescharacteristic
92C11×#106—21no—
93#66899—21no—
94#66899—21no—
95#66896—21no—
96#66896—21no—
97#66882C2311yescharacteristic
98#66882C2311yescharacteristic
99#66882C2311yescharacteristic
100#66882C2311yescharacteristic
101#66881—21no—
102#66881—21no—
103C8×Dic11D411yescharacteristic
104C8×Dic11D411yescharacteristic
105C8×Dic11C2311yescharacteristic
106C8×Dic11C2311yescharacteristic
107C2×C11⋊C16—22no—
108C2×C11⋊C16C2311yescharacteristic
109C2×C11⋊C16C2311yescharacteristic
110#66872—21no—
111#66872—21no—
112#66871—21no—
113#66871—21no—
114#33626—111nomaximal, Sylow
115C11×#41—24no—
116C11×#41—42no—
117C2×Q8×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11—41no—
120C22×C4×C11—41no—
121C22×C4×C11C2×D411yescharacteristic
122C22×Dic11—41no—
123C22×Dic11—41no—
124C22×Dic11D811yescharacteristic
125C22×Dic11D811yescharacteristic
126C2×Dic22—41no—
127C2×Dic22—41no—
128C11×Q16—21no—
129C11×Q16C2×Q812yes—
130C11×SD16—24no—
131C11×D8—21no—
132C11×D8C2×Q812yes—
133C2×C8×C11C2×D411yescharacteristic
134C2×C8×C11C2×Q812yes—
135C2×C8×C11#4112yes—
136C2×C8×C11C2411yescharacteristic
137C11×C4⋊C4—21no—
138C11×C4⋊C4—21no—
139C11×C22⋊C4—41no—
140C42×C11—41no—
141C22⋊Dic11—41no—
142C22⋊Dic11—41no—
143C22⋊Dic11—41no—
144C22⋊Dic11—41no—
145C4⋊Dic11—21no—
146C4⋊Dic11—21no—
147C4⋊Dic11—21no—
148C4⋊Dic11—21no—
149C4⋊Dic11—41no—
150C4⋊Dic11—41no—
151C4⋊Dic11—41no—
152C4⋊Dic11—41no—
153Dic11⋊C4—41no—
154Dic11⋊C4—41no—
155Dic11⋊C4—41no—
156Dic11⋊C4—41no—
157C4×Dic11—41no—
158C4×Dic11—41no—
159C4×Dic11—41no—
160C4×Dic11—41no—
161C4×Dic11D811yescharacteristic
162C4×Dic11D811yescharacteristic
163C4×Dic11C2×D411yescharacteristic
164C4×Dic11C2×D411yescharacteristic
165C2×C11⋊C8—22no—
166C2×C11⋊C8C2×D411yescharacteristic
167C2×C11⋊C8C2×D411yescharacteristic
168C11×C16—21no—
169C11×C16—21no—
170C11⋊C16—21no—
171C11⋊C16—21no—
172#3160—111no—
173C4×#135—111no—
174#2229—111no—
175#2229—111no—
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#2138D1111yescharacteristic
187C23×C11—41no—
188C23×C11C2×D811yescharacteristic
189Q8×C11—22no—
190Q8×C11—41no—
191D4×C11—22no—
192D4×C11—44no—
193D4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—44no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11C22⋊Q812yes—
199C2×C4×C11C2×D811yescharacteristic
200C2×C4×C11#13712yes—
201C2×C4×C11C22×D411yescharacteristic
202C2×Dic11—22no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—41no—
208C2×Dic11—82no—
209C2×Dic11—82no—
210C2×Dic11C2×D811yescharacteristic
211C2×Dic11C2×D811yescharacteristic
212C2×Dic11C2×D811yescharacteristic
213C2×Dic11C2×D811yescharacteristic
214Dic22—82no—
215Dic22—82no—
216C8×C11C22⋊Q812yes—
217C8×C11C22×Q811yescharacteristic
218C8×C11C2×#4111yescharacteristic
219C11⋊C8—21no—
220C11⋊C8—21no—
221C2×#135C2×D1111yescharacteristic
222#533—221no—
223C4×#41—221no—
224C22×C16—111no—
225C22×C16C2×D1111yescharacteristic
226#500—111no—
227#500—111no—
228#499—111no—
229#499—111no—
230#499—221no—
231#498—221no—
232C4×Q16—111no—
233C4×Q16—111no—
234C4×SD16—221no—
235C4×SD16—221no—
236C4×D8—111no—
237C4×D8—111no—
238#427—111no—
239#427—111no—
240#427—221no—
241#427C2×D1111yescharacteristic
242#416—221no—
243C2×C4×C8—111no—
244#367—111no—
245#367—111no—
246#367—111no—
247#367—111no—
248#366—111no—
249#366—111no—
250#366—111no—
251#366—111no—
252C4⋊C16—111no—
253C4⋊C16—111no—
254C4⋊C16—111no—
255C4⋊C16—111no—
256#358—111no—
257#358—111no—
258#358C2×D1111yescharacteristic
259#358C2×D1111yescharacteristic
260#357—111no—
261#357—111no—
262#357C2×D1111yescharacteristic
263#357C2×D1111yescharacteristic
264C22×C11—21no—
265C22×C11—21no—
266C22×C11—42no—
267C22×C11—81no—
268C22×C11—81no—
269C22×C11#47412yes—
270C22×C11C22×D811yescharacteristic
271C4×C11—42no—
272C4×C11—81no—
273C4×C11—81no—
274C4×C11#47412yes—
275C4×C11C2×C22⋊Q811yescharacteristic
276C4×C11C2×#13711yescharacteristic
277Dic11—21no—
278Dic11—21no—
279Dic11—21no—
280Dic11—81no—
281Dic11—81no—
282Dic11—81no—
283Dic11—81no—
284Dic11#50812yes—
285C2×#41—21no—
286#135—22no—
287#135Dic2214yescomplemented
288C2×Q16C22×D1111yescharacteristic
289C2×SD16—21no—
290C2×D8C22×D1111yescharacteristic
291C22×C8—111no—
292C22×C8C22×D1111yescharacteristic
293C4⋊Q8—221no—
294C4⋊Q8—221no—
295#125—221no—
296#125—221no—
297C22⋊Q8—441no—
298C22⋊Q8—441no—
299C4×Q8—221no—
300C4×Q8—221no—
301C4×Q8—441no—
302C4×Q8—441no—
303C4×D4—221no—
304C4×D4—221no—
305C4×D4—441no—
306C4×D4—441no—
307#117—21no—
308#117—221no—
309#117—221no—
310#117—441no—
311C2×C42—111no—
312C2×C42—441no—
313C2×C16—22no—
314C2×C16—111no—
315C2×C16—111no—
316C2×C16—222no—
317C2×C16C22×D1111yescharacteristic
318C2×C16C22×D1111yescharacteristic
319#107—111no—
320#107—111no—
321#107—111no—
322#107—111no—
323#107—221no—
324#107—221no—
325#107C22×D1111yescharacteristic
326#107C22×D1111yescharacteristic
327#106—21no—
328#106—221no—
329#106—221no—
330#106—221no—
331#106—221no—
332#103—221no—
333#103—221no—
334#102—221no—
335#102—221no—
336C4×C8—111no—
337C4×C8—111no—
338C4×C8—111no—
339C4×C8—111no—
340C2×C11—22no—
341C2×C11—82no—
342C2×C11C2×#47411yescharacteristic
343C2×C11C2×#50811yescharacteristic
344C2×C11#341411yescharacteristic
345#41—24no—
346#41—42no—
347C2×Q8—21no—
348C2×Q8—441no—
349C2×Q8—441no—
350C2×D4—21no—
351C2×D4—41no—
352C22×C4—41no—
353C22×C4—111no—
354C22×C4—111no—
355C22×C4—441no—
356C22×C4—441no—
357C22×C4D4×D1111yescharacteristic
358Q16—21no—
359Q16C2×Dic2212yes—
360SD16—24no—
361D8—21no—
362D8C2×Dic2212yes—
363C2×C8—111no—
364C2×C8—111no—
365C2×C8—222no—
366C2×C8C2×Dic2212yes—
367C2×C8D4×D1111yescharacteristic
368C2×C8#434112yes—
369C2×C8C23×D1111yescharacteristic
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—221no—
373C4⋊C4—221no—
374C4⋊C4—221no—
375C4⋊C4—221no—
376C4⋊C4—441no—
377C4⋊C4—441no—
378C4⋊C4—441no—
379C4⋊C4—441no—
380C4⋊C4—441no—
381C4⋊C4—441no—
382C4⋊C4—441no—
383C4⋊C4—441no—
384C22⋊C4—41no—
385C22⋊C4—441no—
386C22⋊C4—441no—
387C22⋊C4—441no—
388C22⋊C4—441no—
389C42—41no—
390C42—111no—
391C42—111no—
392C42—111no—
393C42—111no—
394C42—441no—
395C42—441no—
396C42—441no—
397C42—441no—
398C16—21no—
399C16—21no—
400C16—221no—
401C16—221no—
402C11#3362611yescharacteristic, complemented, Sylow
403C23—41no—
404C23D8×D1111yescharacteristic
405Q8—22no—
406Q8—41no—
407Q8—882no—
408Q8—882no—
409D4—22no—
410D4—44no—
411D4—41no—
412C2×C4—41no—
413C2×C4—44no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—111no—
417C2×C4—111no—
418C2×C4—111no—
419C2×C4—111no—
420C2×C4—222no—
421C2×C4—441no—
422C2×C4—441no—
423C2×C4—441no—
424C2×C4—441no—
425C2×C4—441no—
426C2×C4—882no—
427C2×C4—882no—
428C2×C4#6693112yes—
429C2×C4D8×D1111yescharacteristic
430C2×C4#6696812yes—
431C2×C4C2×D4×D1111yescharacteristic
432C8—221no—
433C8—221no—
434C8#6693112yes—
435C8C22×Dic2211yescharacteristic
436C8C2×#434111yescharacteristic
437C22—21no—
438C22—21no—
439C22—42no—
440C22—81no—
441C22—81no—
442C22#1062237212yes—
443C22C2×D8×D1111yescharacteristic
444C4—42no—
445C4—81no—
446C4—81no—
447C4—112no—
448C4—221no—
449C4—221no—
450C4—221no—
451C4—881no—
452C4—881no—
453C4—881no—
454C4—881no—
455C4#1062237212yes—
456C4C2×#6693111yescharacteristic
457C4C2×#6696811yescharacteristic
458C2—22no—
459C2—82no—
460C2C2×#1062237211yescharacteristic
461C2D11×#50811yescharacteristic
462C2#1308174911yescharacteristic
subgroupG/H
centerC2×C4D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2138C2
socleC22×C11C22×D8
prime radicalC2×C11×#135C22
hypercenter#2138D11
hypocenterC11#33626
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ #2138

Complements

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

NH ≅ G/Ntype
1. #13079128C2semidirect
3. #13070782C2semidirect
4. #13070778C2semidirect
5. #13070775C2semidirect
6. #13070771C2semidirect
7. #13070766C2semidirect
8. #13070761C2semidirect
9. #13070756C2semidirect
10. #13070751C2semidirect
11. #13070400C2semidirect
12. #13070398C2semidirect
13. C2×Dic11⋊C16C2semidirect
61. C11×#135Q8semidirect
287. #135Dic22semidirect
402. C11#33626semidirect

Maximal subgroups

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

subgroupindex
#130791282
#135×Dic112
#130707822
#130707782
#130707752
#130707712
#130707662
#130707612
#130707562
#130707512
#130704002
#130703982
C2×Dic11⋊C162
#130703232
C11×#21382
#3362611