Finite Group Databasebeta

← #14648487

Subgroups — #14648487

Order 2816.

514 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077748C211yesmaximal, characteristic, complemented
2#13069445C211yesmaximal, characteristic, complemented
3C4×#66901C211yesmaximal, characteristic, complemented
4#13067033C211yesmaximal, characteristic, complemented
5#13066507C211yesmaximal, characteristic, complemented
6#13066448C211yesmaximal, characteristic, complemented
7C11×#3106C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C4×C11×#41C2211yescharacteristic
10C11×#482—21no—
11C11×#477C411yescharacteristic, complemented
12C11×#476C411yescharacteristic, complemented
13C11×#460C411yescharacteristic, complemented
14C11×#459C411yescharacteristic, complemented
15C11×#449—21no—
16C4×C11×SD16—21no—
17C4×C11×D8—21no—
18C11×#431C2211yescharacteristic
19C2×#66901—21no—
20C2×#66901—22no—
21Q8×C11⋊C8—21no—
22#10622625—21no—
23#10622625—22no—
24C42×Dic11C2211yescharacteristic
25#10622538—21no—
26#10622538C2211yescharacteristic
27#10622537—21no—
28#10622537C2211yescharacteristic
29C4×#4318C2211yescharacteristic
30D4⋊(C11⋊C8)—21no—
31D4⋊(C11⋊C8)—21no—
32#10622170—21no—
33C2×C11×#41—21no—
34C2×C11×#41D411yescharacteristic
35C2×C11×SD16—21no—
36C2×C11×D8—21no—
37C11×C4⋊Q8C2×C411yescharacteristic
38C11×#127C2×C411yescharacteristic
39C11×#124—21no—
40C11×#121—21no—
41C11×#121—21no—
42C4×Q8×C11C2×C411yescharacteristic
43C4×Q8×C11D411yescharacteristic
44C4×D4×C11—21no—
45C4×D4×C11—21no—
46C4×D4×C11—21no—
47C4×D4×C11—21no—
48C4×D4×C11C2×C411yescharacteristic
49C4×D4×C11D411yescharacteristic
50C11×#117—21no—
51C11×#117D411yescharacteristic
52C2×C42×C11—21no—
53C2×C42×C11C2311yescharacteristic
54C2×C4×Dic11—21no—
55C2×C4×Dic11—21no—
56C2×C4×Dic11—21no—
57C2×#4318—22no—
58C2×#4318—21no—
59C2×#4318D412yes—
60C11×#107—21no—
61C11×#106—21no—
62C11×C4⋊C8C2×C411yescharacteristic
63C11×C4⋊C8C2×C411yescharacteristic
64C11×#103—21no—
65C11×#102—21no—
66C11×#102—21no—
67C11×#102—21no—
68C11×C22⋊C8—21no—
69C4×C8×C11—21no—
70#66901—24no—
71#66901—44no—
72C22⋊(C11⋊C8)—22no—
73C22⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)—22no—
75C4⋊(C11⋊C8)—21no—
76C4⋊(C11⋊C8)—21no—
77C4⋊(C11⋊C8)D411yescharacteristic
78C4⋊(C11⋊C8)D411yescharacteristic
79#66867—21no—
80C4×C11⋊C8—22no—
81C4×C11⋊C8—21no—
82C4×C11⋊C8—21no—
83#8970—111nomaximal, Sylow
84C11×#41—22no—
85C11×#41—41no—
86C11×#41—42no—
87C11×#41—42no—
88C2×Q8×C11—21no—
89C2×Q8×C11C22⋊C411yescharacteristic
90C2×D4×C11—21no—
91C2×D4×C11—21no—
92C2×D4×C11—21no—
93C2×D4×C11—21no—
94C2×D4×C11—41no—
95C2×D4×C11C22⋊C411yescharacteristic
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—41no—
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11#4111yescharacteristic
103C22×Dic11—41no—
104C11×SD16—42no—
105C11×D8—42no—
106C2×C8×C11—21no—
107C2×C8×C11—21no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4C22⋊C411yescharacteristic
113C11×C4⋊C4C22⋊C411yescharacteristic
114C11×C22⋊C4—21no—
115C11×C22⋊C4—21no—
116C11×C22⋊C4—21no—
117C11×C22⋊C4—41no—
118C11×C22⋊C4—41no—
119C42×C11—21no—
120C42×C11—21no—
121C42×C11—21no—
122C42×C11C22×C411yescharacteristic
123C42×C11C2×D411yescharacteristic
124C42×C11C2×D411yescharacteristic
125C42×C11#4111yescharacteristic
126C4×Dic11—22no—
127C4×Dic11—22no—
128C4×Dic11—22no—
129C4×Dic11—41no—
130C4×Dic11—41no—
131C4×Dic11—41no—
132#4318—22no—
133#4318—42no—
134#4318—41no—
135#4318—82no—
136C2×C11⋊C8—21no—
137C2×C11⋊C8—22no—
138C2×C11⋊C8—21no—
139C2×C11⋊C8—41no—
140#3106D1111yescharacteristic
141#2991—111no—
142#1962—111no—
143C4×#104—111no—
144#1484—111no—
145#1299—111no—
146#1276—111no—
147C23×C11—21no—
148C23×C11—41no—
149C23×C11#12111yescharacteristic
150Q8×C11—21no—
151Q8×C11—42no—
152Q8×C11#10412yescomplemented
153D4×C11—21no—
154D4×C11—21no—
155D4×C11—42no—
156D4×C11—42no—
157D4×C11—41no—
158D4×C11—41no—
159D4×C11—41no—
160D4×C11—41no—
161D4×C11—82no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11—21no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—42no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—81no—
178C2×C4×C11—81no—
179C2×C4×C11C2×C22⋊C411yescharacteristic
180C2×C4×C11C4×D411yescharacteristic
181C2×C4×C11C4×D411yescharacteristic
182C2×C4×C11#12011yescharacteristic
183C2×C4×C11#12111yescharacteristic
184C2×C4×C11#12311yescharacteristic
185C2×Dic11—42no—
186C2×Dic11—42no—
187C2×Dic11—42no—
188C8×C11—41no—
189C8×C11—41no—
190C11⋊C8—42no—
191C11⋊C8—42no—
192C11⋊C8—41no—
193C11⋊C8—41no—
194#532C2×D1111yescharacteristic
195C4×#41C2×D1111yescharacteristic
196#482—21no—
197#477Dic1111yescharacteristic, complemented
198#476Dic1111yescharacteristic, complemented
199#460Dic1111yescharacteristic, complemented
200#459Dic1111yescharacteristic, complemented
201#449—21no—
202C8×Q8—221no—
203C4×SD16—21no—
204C4×D8—21no—
205#436—222no—
206#436—221no—
207#431—111no—
208#431—221no—
209#431C2×D1111yescharacteristic
210#423—111no—
211#423—221no—
212C2×#104—221no—
213C2×#104—222no—
214C4×M16—111no—
215C43—111no—
216#339—221no—
217D4⋊C8—221no—
218D4⋊C8—221no—
219C22×C11—21no—
220C22×C11—21no—
221C22×C11—21no—
222C22×C11—41no—
223C22×C11—41no—
224C22×C11—41no—
225C22×C11—81no—
226C22×C11—81no—
227C22×C11—81no—
228C22×C11#38611yescharacteristic
229C4×C11—21no—
230C4×C11—22no—
231C4×C11—21no—
232C4×C11—21no—
233C4×C11—41no—
234C4×C11—41no—
235C4×C11—81no—
236C4×C11C2×#10411yescharacteristic
237C4×C11#42111yescharacteristic
238C4×C11#44311yescharacteristic
239C4×C11#44411yescharacteristic
240C4×C11#45311yescharacteristic
241C4×C11#45411yescharacteristic
242Dic11—44no—
243C2×#41—21no—
244C2×#41C22⋊D1111yescharacteristic
245C2×SD16—21no—
246C2×D8—21no—
247C2×M16—112no—
248C2×M16—222no—
249C2×M16—221no—
250C4⋊Q8C2×Dic1111yescharacteristic
251#127C2×Dic1111yescharacteristic
252#124—21no—
253#121—21no—
254#121—21no—
255C4×Q8C2×Dic1111yescharacteristic
256C4×Q8C22⋊D1111yescharacteristic
257C4×D4—21no—
258C4×D4—21no—
259C4×D4—21no—
260C4×D4—21no—
261C4×D4C2×Dic1111yescharacteristic
262C4×D4C22⋊D1111yescharacteristic
263#117—21no—
264#117C22⋊D1111yescharacteristic
265C2×C42—21no—
266C2×C42—221no—
267C2×C42—221no—
268C2×C42—221no—
269C2×C42C22×D1111yescharacteristic
270#107—21no—
271#106—21no—
272C4⋊C8—111no—
273C4⋊C8—111no—
274C4⋊C8—222no—
275C4⋊C8—221no—
276C4⋊C8—221no—
277C4⋊C8C2×Dic1111yescharacteristic
278C4⋊C8C2×Dic1111yescharacteristic
279#104—224no—
280#104—444no—
281#103—21no—
282#102—21no—
283#102—21no—
284#102—21no—
285C22⋊C8—21no—
286C22⋊C8—222no—
287C22⋊C8—221no—
288#97—221no—
289C4×C8—21no—
290C4×C8—222no—
291C4×C8—221no—
292C4×C8—221no—
293C2×C11—41no—
294C2×C11—81no—
295C2×C11—161no—
296C2×C11#187111yescharacteristic
297C2×C11#187611yescharacteristic
298C2×C11#188311yescharacteristic
299#41—22no—
300#41—41no—
301#41—42no—
302#41—42no—
303C2×Q8—21no—
304C2×Q8C22⋊Dic1111yescharacteristic
305C2×D4—21no—
306C2×D4—21no—
307C2×D4—21no—
308C2×D4—21no—
309C2×D4—41no—
310C2×D4C22⋊Dic1111yescharacteristic
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—41no—
315C22×C4—441no—
316C22×C4D4×D1111yescharacteristic
317C22×C4#434111yescharacteristic
318C22×C4C2×C22⋊D1111yescharacteristic
319SD16—42no—
320D8—42no—
321M16—222no—
322M16—441no—
323M16—442no—
324M16—882no—
325C2×C8—21no—
326C2×C8—21no—
327C2×C8—221no—
328C2×C8—221no—
329C2×C8—222no—
330C2×C8—441no—
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4C22⋊Dic1111yescharacteristic
336C4⋊C4C22⋊Dic1111yescharacteristic
337C22⋊C4—21no—
338C22⋊C4—21no—
339C22⋊C4—21no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C42—21no—
343C42—21no—
344C42—21no—
345C42—222no—
346C42—222no—
347C42—222no—
348C42—441no—
349C42—441no—
350C42—441no—
351C42D4×D1111yescharacteristic
352C42#434111yescharacteristic
353C42C22×Dic1111yescharacteristic
354C42C2×C22⋊D1111yescharacteristic
355C11#897011yescharacteristic, complemented, Sylow
356C23—21no—
357C23—41no—
358C23#6699211yescharacteristic
359Q8—21no—
360Q8—42no—
361Q8#6690112yescomplemented
362D4—21no—
363D4—21no—
364D4—42no—
365D4—42no—
366D4—41no—
367D4—41no—
368D4—41no—
369D4—41no—
370D4—82no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—42no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—442no—
389C2×C4—442no—
390C2×C4—442no—
391C2×C4D4×Dic1111yescharacteristic
392C2×C4D4×Dic1111yescharacteristic
393C2×C4#6698811yescharacteristic
394C2×C4#6699011yescharacteristic
395C2×C4#6699211yescharacteristic
396C2×C4C2×C22⋊Dic1111yescharacteristic
397C8—41no—
398C8—41no—
399C8—442no—
400C8—442no—
401C8—441no—
402C8—441no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—81no—
410C22—81no—
411C22—81no—
412C22#1062283311yescharacteristic
413C4—21no—
414C4—22no—
415C4—21no—
416C4—21no—
417C4—41no—
418C4—41no—
419C4—81no—
420C4—444no—
421C4#1062280911yescharacteristic
422C4#1062281011yescharacteristic
423C4#1062281111yescharacteristic
424C4#1062281411yescharacteristic
425C4C2×#6690111yescharacteristic
426C4#1062284911yescharacteristic
427C2—41no—
428C2—81no—
429C2—161no—
430C2#1306891911yescharacteristic
431C2#1306894511yescharacteristic
432C2#1306899411yescharacteristic
subgroupG/H
centerC2×C4#66990
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
Fitting, prime radicalC11×#3106C2
socleC22×C11#386
cosocleC2×C42×C11C23
hypercenter#3106D11
hypocenterC11#8970
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3106

Complements

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

NH ≅ G/Ntype
1. #13077748C2semidirect
2. #13069445C2semidirect
3. C4×#66901C2semidirect
4. #13067033C2semidirect
5. #13066507C2semidirect
6. #13066448C2semidirect
11. C11×#477C4semidirect
12. C11×#476C4semidirect
13. C11×#460C4semidirect
14. C11×#459C4semidirect
152. Q8×C11#104semidirect
197. #477Dic11semidirect
198. #476Dic11semidirect
199. #460Dic11semidirect
200. #459Dic11semidirect
355. C11#8970semidirect
361. Q8#66901semidirect

Maximal subgroups

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

subgroupindex
#130777482
#130694452
C4×#669012
#130670332
#130665072
#130664482
C11×#31062
#897011