Finite Group Databasebeta

← #14648641

Subgroups — #14648641

Order 2816.

500 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#4318C211yesmaximal, characteristic, complemented
2#13069536C211yesmaximal, characteristic
3C4×#66899C211yesmaximal, characteristic, complemented
4#13067067C211yesmaximal, characteristic
5#13066518C211yesmaximal, characteristic, complemented
6#13066452C211yesmaximal, characteristic, complemented
7C11×#3103C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×C4×Q8×C11C2211yescharacteristic
10C11×#481—21no—
11C11×#475C411yescharacteristic, complemented
12C11×#475C411yescharacteristic, complemented
13C11×#460C411yescharacteristic, complemented
14C11×#460C411yescharacteristic, complemented
15C11×#448—21no—
16C4×C11×SD16—21no—
17C4×C11×SD16—21no—
18C11×#431C2211yescharacteristic
19C2×#66901—21no—
20C2×#66901—21no—
21C2×#66899—21no—
22#10622637—21no—
23#10622637—22no—
24Q8×C11⋊C8—21no—
25C4×C4⋊Dic11C2211yescharacteristic
26#10622537—21no—
27#10622537C2211yescharacteristic
28C4×#4318—21no—
29C4×#4318C2211yescharacteristic
30C2×C4×C11⋊C8C2211yescharacteristic
31D4⋊(C11⋊C8)—22no—
32#10622167—21no—
33C2×C11×#41—21no—
34C22×Q8×C11D411yescharacteristic
35C2×C11×SD16—21no—
36C2×C11×SD16—21no—
37C11×C4⋊Q8C2×C411yescharacteristic
38C11×#127C2×C411yescharacteristic
39C11×#124—21no—
40C11×#121—21no—
41C11×#121—21no—
42C4×Q8×C11—21no—
43C4×Q8×C11—21no—
44C4×Q8×C11C2×C411yescharacteristic
45C4×Q8×C11C2×C411yescharacteristic
46C4×Q8×C11D411yescharacteristic
47C4×Q8×C11D411yescharacteristic
48C4×D4×C11—21no—
49C4×D4×C11—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4D411yescharacteristic
52C2×C42×C11—21no—
53C2×C42×C11C2311yescharacteristic
54C2×C4⋊Dic11—21no—
55C2×C4×Dic11—21no—
56C2×#4318—21no—
57C2×#4318D411yescharacteristic
58C2×#4318D411yescharacteristic
59C22×C11⋊C8—21no—
60C11×#106—21no—
61C11×#106—21no—
62C11×C4⋊C8C2×C411yescharacteristic
63C11×C4⋊C8C2×C411yescharacteristic
64C11×#103—21no—
65C11×#103—21no—
66C11×#102—21no—
67C11×#102—21no—
68C11×C22⋊C8—21no—
69C4×C8×C11—21no—
70#66901—42no—
71#66901—42no—
72#66899—24no—
73C11⋊#95—21no—
74C4⋊(C11⋊C8)—22no—
75C4⋊(C11⋊C8)—22no—
76C4⋊(C11⋊C8)—21no—
77C4⋊(C11⋊C8)D412yes—
78#66867—22no—
79#66867—21no—
80C4×C11⋊C8—22no—
81C4×C11⋊C8—21no—
82C4×C11⋊C8—21no—
83C4×C11⋊C8—21no—
84#8992—111nomaximal, Sylow
85C11×#41—41no—
86C11×#41—41no—
87C11×#41—41no—
88C11×#41—41no—
89C2×Q8×C11—21no—
90C2×Q8×C11—22no—
91C2×Q8×C11—21no—
92C2×Q8×C11—41no—
93C2×Q8×C11C22⋊C411yescharacteristic
94C2×Q8×C11C22⋊C411yescharacteristic
95C2×D4×C11—21no—
96C2×D4×C11—21no—
97C2×D4×C11—21no—
98C2×D4×C11—41no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—41no—
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11#4111yescharacteristic
105C22×Dic11—41no—
106C11×SD16—42no—
107C11×SD16—42no—
108C2×C8×C11—21no—
109C2×C8×C11—21no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4C22⋊C411yescharacteristic
118C11×C4⋊C4C22⋊C411yescharacteristic
119C11×C22⋊C4—41no—
120C11×C22⋊C4—41no—
121C42×C11—21no—
122C42×C11—21no—
123C42×C11—21no—
124C42×C11—21no—
125C42×C11C22×C411yescharacteristic
126C42×C11C2×D411yescharacteristic
127C42×C11C2×D411yescharacteristic
128C42×C11#4111yescharacteristic
129C4⋊Dic11—22no—
130C4⋊Dic11—41no—
131C4×Dic11—41no—
132C4×Dic11—41no—
133#4318—21no—
134#4318—21no—
135#4318—21no—
136#4318—41no—
137#4318—41no—
138#4318SD1612yescomplemented
139C2×C11⋊C8—22no—
140C2×C11⋊C8—21no—
141C2×C11⋊C8—21no—
142C2×C11⋊C8—22no—
143C2×C11⋊C8—41no—
144C2×C11⋊C8—41no—
145#3103D1111yescharacteristic
146Q8×M16—111no—
147#1980—111no—
148C4×#103—111no—
149#1492—111no—
150#1303—111no—
151#1278—111no—
152C23×C11—41no—
153C23×C11#12111yescharacteristic
154Q8×C11—21no—
155Q8×C11—21no—
156Q8×C11—21no—
157Q8×C11—42no—
158Q8×C11—41no—
159Q8×C11—41no—
160Q8×C11#10412yescomplemented
161D4×C11—42no—
162D4×C11—41no—
163D4×C11—41no—
164D4×C11—41no—
165D4×C11—41no—
166D4×C11—81no—
167D4×C11—81no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—41no—
175C2×C4×C11—42no—
176C2×C4×C11—41no—
177C2×C4×C11—81no—
178C2×C4×C11—81no—
179C2×C4×C11—81no—
180C2×C4×C11C2×C22⋊C411yescharacteristic
181C2×C4×C11C4×D411yescharacteristic
182C2×C4×C11C4×D411yescharacteristic
183C2×C4×C11#12011yescharacteristic
184C2×C4×C11#12111yescharacteristic
185C2×C4×C11#12311yescharacteristic
186C2×C4×C11C2×SD1611yescharacteristic
187C2×C4×C11#13511yescharacteristic
188C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
189C2×C4×C11#13711yescharacteristic
190C2×Dic11—42no—
191C2×Dic11—81no—
192C2×Dic11—81no—
193C8×C11—41no—
194C8×C11—41no—
195C11⋊C8—22no—
196C11⋊C8—42no—
197C11⋊C8—41no—
198C11⋊C8—42no—
199#532C2×D1111yescharacteristic
200C2×C4×Q8C2×D1111yescharacteristic
201#481—21no—
202#475Dic1111yescharacteristic, complemented
203#475Dic1111yescharacteristic, complemented
204#460Dic1111yescharacteristic, complemented
205#460Dic1111yescharacteristic, complemented
206#448—21no—
207#446—222no—
208#446—221no—
209C8×Q8—221no—
210C4×SD16—21no—
211C4×SD16—21no—
212#431C2×D1111yescharacteristic
213#423—111no—
214#423—221no—
215C2×#104—221no—
216C2×#104—221no—
217C2×#103—221no—
218C4×M16—111no—
219C4×M16—221no—
220C2×C4×C8—111no—
221C4×C4⋊C4—111no—
222#340—221no—
223D4⋊C8—222no—
224C22×C11—21no—
225C22×C11—21no—
226C22×C11—81no—
227C22×C11—81no—
228C22×C11—81no—
229C22×C11#38611yescharacteristic
230C22×C11#46011yescharacteristic
231C22×C11#46411yescharacteristic
232C4×C11—21no—
233C4×C11—22no—
234C4×C11—21no—
235C4×C11—21no—
236C4×C11—41no—
237C4×C11—41no—
238C4×C11—41no—
239C4×C11—81no—
240C4×C11C2×#10411yescharacteristic
241C4×C11#42111yescharacteristic
242C4×C11C4×SD1611yescharacteristic
243C4×C11#44011yescharacteristic
244C4×C11#44811yescharacteristic
245C4×C11#44911yescharacteristic
246Dic11—82no—
247C2×#41—21no—
248C22×Q8C22⋊D1111yescharacteristic
249C2×SD16—21no—
250C2×SD16—21no—
251C2×M16—111no—
252C2×M16—111no—
253C2×M16—221no—
254C22×C8—221no—
255C4⋊Q8C2×Dic1111yescharacteristic
256#127C2×Dic1111yescharacteristic
257#124—21no—
258#121—21no—
259#121—21no—
260C4×Q8—21no—
261C4×Q8—21no—
262C4×Q8C2×Dic1111yescharacteristic
263C4×Q8C2×Dic1111yescharacteristic
264C4×Q8C22⋊D1111yescharacteristic
265C4×Q8C22⋊D1111yescharacteristic
266C4×D4—21no—
267C4×D4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—221no—
270C2×C4⋊C4C22⋊D1111yescharacteristic
271C2×C42—21no—
272C2×C42—221no—
273C2×C42C22×D1111yescharacteristic
274#106—21no—
275#106—21no—
276C4⋊C8—112no—
277C4⋊C8—222no—
278C4⋊C8—222no—
279C4⋊C8—221no—
280C4⋊C8C2×Dic1111yescharacteristic
281C4⋊C8C2×Dic1111yescharacteristic
282#104—442no—
283#104—442no—
284#103—21no—
285#103—21no—
286#103—224no—
287#102—21no—
288#102—21no—
289C22⋊C8—21no—
290#97—222no—
291#97—221no—
292C4×C8—21no—
293C4×C8—222no—
294C4×C8—221no—
295C4×C8—221no—
296C4×C8—221no—
297#95—221no—
298C2×C11—21no—
299C2×C11—21no—
300C2×C11—161no—
301C2×C11#187111yescharacteristic
302C2×C11#188011yescharacteristic
303C2×C11#188111yescharacteristic
304#41—41no—
305#41—41no—
306#41—41no—
307#41—41no—
308C2×Q8—21no—
309C2×Q8—22no—
310C2×Q8—21no—
311C2×Q8—41no—
312C2×Q8C22⋊Dic1111yescharacteristic
313C2×Q8C22⋊Dic1111yescharacteristic
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—21no—
317C2×D4—41no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—41no—
321C22×C4—441no—
322C22×C4D4×D1111yescharacteristic
323C22×C4#434111yescharacteristic
324C22×C4C2×C22⋊D1111yescharacteristic
325SD16—42no—
326SD16—42no—
327M16—112no—
328M16—221no—
329M16—221no—
330M16—221no—
331M16—441no—
332M16—441no—
333C2×C8—21no—
334C2×C8—21no—
335C2×C8—221no—
336C2×C8—222no—
337C2×C8—222no—
338C2×C8—221no—
339C2×C8—441no—
340C2×C8—441no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—222no—
349C4⋊C4—441no—
350C4⋊C4C22⋊Dic1111yescharacteristic
351C4⋊C4C22⋊Dic1111yescharacteristic
352C22⋊C4—41no—
353C22⋊C4—41no—
354C42—21no—
355C42—21no—
356C42—21no—
357C42—21no—
358C42—441no—
359C42—441no—
360C42D4×D1111yescharacteristic
361C42#434111yescharacteristic
362C42C22×Dic1111yescharacteristic
363C42C2×C22⋊D1111yescharacteristic
364C11#899211yescharacteristic, complemented, Sylow
365C23—41no—
366C23#6699211yescharacteristic
367Q8—21no—
368Q8—21no—
369Q8—21no—
370Q8—42no—
371Q8—41no—
372Q8—41no—
373Q8#6690112yescomplemented
374D4—42no—
375D4—41no—
376D4—41no—
377D4—41no—
378D4—41no—
379D4—81no—
380D4—81no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—41no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—442no—
394C2×C4—881no—
395C2×C4—881no—
396C2×C4SD16×D1111yescharacteristic
397C2×C4#6696711yescharacteristic
398C2×C4#6696811yescharacteristic
399C2×C4#6696911yescharacteristic
400C2×C4D4×Dic1111yescharacteristic
401C2×C4D4×Dic1111yescharacteristic
402C2×C4#6698811yescharacteristic
403C2×C4#6699011yescharacteristic
404C2×C4#6699211yescharacteristic
405C2×C4C2×C22⋊Dic1111yescharacteristic
406C8—41no—
407C8—41no—
408C8—222no—
409C8—442no—
410C8—441no—
411C8—442no—
412C22—21no—
413C22—21no—
414C22—81no—
415C22—81no—
416C22—81no—
417C22#1062277611yescharacteristic
418C22#1062277911yescharacteristic
419C22#1062283311yescharacteristic
420C4—21no—
421C4—22no—
422C4—21no—
423C4—21no—
424C4—41no—
425C4—41no—
426C4—41no—
427C4—81no—
428C4—882no—
429C4SD16×Dic1111yescharacteristic
430C4#1062277711yescharacteristic
431C4#1062278311yescharacteristic
432C4#1062278511yescharacteristic
433C4C2×#6690111yescharacteristic
434C4#1062284911yescharacteristic
435C2—21no—
436C2—21no—
437C2—161no—
438C2#1306891911yescharacteristic
439C2#1306897311yescharacteristic
440C2#1306898011yescharacteristic
subgroupG/H
centerC2×C4#66990
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#3103C2
socleC22×C11#386
prime radicalC11×#532C22
cosocleC2×C42×C11C23
hypercenter#3103D11
hypocenterC11#8992
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3103

Complements

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

NH ≅ G/Ntype
1. Q8×#4318C2semidirect
3. C4×#66899C2semidirect
5. #13066518C2semidirect
6. #13066452C2semidirect
11. C11×#475C4semidirect
12. C11×#475C4semidirect
13. C11×#460C4semidirect
14. C11×#460C4semidirect
138. #4318SD16semidirect
160. Q8×C11#104semidirect
202. #475Dic11semidirect
203. #475Dic11semidirect
204. #460Dic11semidirect
205. #460Dic11semidirect
364. C11#8992semidirect
373. Q8#66901semidirect

Maximal subgroups

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

subgroupindex
Q8×#43182
#130695362
C4×#668992
#130670672
#130665182
#130664522
C11×#31032
#899211