Finite Group Databasebeta

← #14805646

Subgroups — #14805646

Order 2816.

770 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
1C2×#10622443C211yesmaximal, characteristic
2#13073986C211yesmaximal, characteristic
3#13073605C211yesmaximal, characteristic
4#13070115C212yesmaximal
5#13069995C212yesmaximal
6#13069578C211yesmaximal, characteristic
7#13069380C211yesmaximal, characteristic
8#13069342C212yesmaximal
9#13069289C212yesmaximal
10C4×#66899C211yesmaximal, characteristic
11C2×C11×#475C211yesmaximal, characteristic
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C2×#66997—21no—
15C2×C4×Dic22C2211yescharacteristic
16C11×#475—24no—
17C2×C11×#106C2212yes—
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×#103C2212yes—
20#10622843—21no—
21#10622843C2212yes—
22C2×#66899C2211yescharacteristic
23C2×#66899C2211yescharacteristic
24C2×#66881C2212yes—
25C2×Dic11⋊C8C2212yes—
26C2×C8×Dic11C2212yes—
27#10622597—22no—
28#10622593—22no—
29#10622586C2212yes—
30#10622586C2212yes—
31#10622586C2212yes—
32#10622548C2211yescharacteristic
33C4×C4⋊Dic11C2211yescharacteristic
34#10622542—21no—
35#10622541—21no—
36C2×C4×C11⋊C8C2211yescharacteristic
37#10622443—24no—
38#10622189C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622167C2211yescharacteristic
42#10622167C2211yescharacteristic
43C22×Q8×C11—21no—
44C22×Q8×C11C2311yescharacteristic
45C22×Dic22D411yescharacteristic
46C22×C8×C11C2312yes—
47C11×C4⋊Q8—22no—
48C11×C4⋊Q8—22no—
49C4×Q8×C11—22no—
50C4×Q8×C11—22no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4C2311yescharacteristic
54C2×C11×C4⋊C4C2312yes—
55C2×C42×C11—21no—
56C2×C42×C11C2311yescharacteristic
57#66997—44no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11D411yescharacteristic
61C2×C4⋊Dic11C2312yes—
62C2×C4⋊Dic11C2311yescharacteristic
63C2×C4⋊Dic11C2311yescharacteristic
64C2×Dic11⋊C4—22no—
65C2×Dic11⋊C4—22no—
66C2×Dic11⋊C4—22no—
67C2×Dic11⋊C4D412yes—
68C2×C4×Dic11—21no—
69C2×C4×Dic11C2312yes—
70C22×C11⋊C8C2311yescharacteristic
71C22×C11⋊C8C2311yescharacteristic
72C4×Dic22—22no—
73C4×Dic22—22no—
74C11×#106—24no—
75C11×C4⋊C8D414yes—
76C11×#103—24no—
77#66899—22no—
78#66899Q814yescomplemented
79C11⋊#95—21no—
80C11⋊#95—22no—
81C11⋊#95—22no—
82C11⋊#95—22no—
83C11⋊#95—22no—
84C11⋊#95—22no—
85#66881—24no—
86Dic11⋊C8—24no—
87C8×Dic11—24no—
88C4×C11⋊C8—22no—
89#25472—111nomaximal, Sylow
90C2×Q8×C11—21no—
91C2×Q8×C11—21no—
92C2×Q8×C11—21no—
93C2×Q8×C11—21no—
94C2×Q8×C11—21no—
95C2×Q8×C11—42no—
96C2×Q8×C11—42no—
97C2×Q8×C11—42no—
98C2×Q8×C11C2×Q812yes—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—22no—
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2411yescharacteristic
105C22×Dic11—21no—
106C22×Dic11—21no—
107C22×Dic11—22no—
108C22×Dic11C2×D412yes—
109C22×Dic11C2×D412yes—
110C2×Dic22—22no—
111C2×Dic22—22no—
112C2×Dic22SD1614yes—
113C2×C8×C11—22no—
114C2×C8×C11—22no—
115C2×C8×C11C2×D414yes—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—21no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—42no—
121C11×C4⋊C4—42no—
122C42×C11—42no—
123C42×C11C2×D412yes—
124C42×C11#4112yes—
125C4⋊Dic11—22no—
126C4⋊Dic11—22no—
127C4⋊Dic11—21no—
128C4⋊Dic11—21no—
129C4⋊Dic11—22no—
130C4⋊Dic11—42no—
131C4⋊Dic11—81no—
132C4⋊Dic11C2×Q812yes—
133C4⋊Dic11#4112yes—
134Dic11⋊C4—24no—
135Dic11⋊C4—44no—
136Dic11⋊C4—44no—
137Dic11⋊C4—82no—
138C4×Dic11—22no—
139C4×Dic11—22no—
140C4×Dic11—42no—
141C2×C11⋊C8—21no—
142C2×C11⋊C8—21no—
143C2×C11⋊C8—21no—
144C2×C11⋊C8—21no—
145C2×C11⋊C8—21no—
146C2×C11⋊C8C2×Q812yes—
147C2×#475D1111yescharacteristic
148C2×C8×Q8—111no—
149#2582—111no—
150#2546—111no—
151#2088—112no—
152#2066—112no—
153#1990—111no—
154#1948—111no—
155#1941—112no—
156#1933—112no—
157C4×#103—111no—
158C23×C11C22×D411yescharacteristic
159Q8×C11—22no—
160Q8×C11—22no—
161Q8×C11—41no—
162Q8×C11—41no—
163Q8×C11—84no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—22no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11#12112yes—
176C2×C4×C11#12112yes—
177C2×C4×C11C2×SD1612yes—
178C2×C4×C11#13512yes—
179C2×C4×C11C22×D411yescharacteristic
180C2×C4×C11C22×Q811yescharacteristic
181C2×C4×C11C2×#4111yescharacteristic
182C2×C4×C11C2×#4111yescharacteristic
183C2×C4×C112−1+411yescharacteristic
184C2×C4×C112−1+411yescharacteristic
185C2×Dic11—22no—
186C2×Dic11—22no—
187C2×Dic11—22no—
188C2×Dic11—22no—
189C2×Dic11—22no—
190C2×Dic11—22no—
191C2×Dic11—22no—
192C2×Dic11—41no—
193C2×Dic11—41no—
194C2×Dic11—41no—
195C2×Dic11—41no—
196C2×Dic11—42no—
197C2×Dic11—42no—
198C2×Dic11—42no—
199C2×Dic11C2×SD1614yes—
200Dic22—28no—
201C8×C11—24no—
202C11⋊C8—22no—
203C11⋊C8—41no—
204C2×C4⋊Q8—221no—
205C2×C4⋊Q8C2×D1111yescharacteristic
206C2×C4×Q8—111no—
207C2×C4×Q8C2×D1111yescharacteristic
208#475—24no—
209C8×Q8—224no—
210C2×#106—112no—
211C2×#106C2×D1112yes—
212C2×C4⋊C8—112no—
213C2×C4⋊C8C2×D1111yescharacteristic
214C2×#103—111no—
215C2×#103—111no—
216C2×#103C2×D1112yes—
217C2×C4×C8—112no—
218C2×C4×C8—111no—
219#398—222no—
220#398—222no—
221#391—112no—
222#391—221no—
223#391—221no—
224#389—112no—
225#389—112no—
226#389—112no—
227#389—221no—
228#384—111no—
229C4×C4⋊C4—111no—
230#340—112no—
231#340—112no—
232#340—111no—
233#340—112no—
234#340—111no—
235C22×C11C2×#12111yescharacteristic
236C22×C11#54811yescharacteristic
237C22×C11D4×Q811yescharacteristic
238C22×C11C22×SD1611yescharacteristic
239C22×C11C2×#13511yescharacteristic
240C22×C11#57711yescharacteristic
241C22×C11#57811yescharacteristic
242C4×C11—22no—
243C4×C11—42no—
244C4×C11—82no—
245C4×C11—81no—
246C4×C11#46514yes—
247C4×C11#53311yescharacteristic
248C4×C11#54111yescharacteristic
249C4×C11#54711yescharacteristic
250C4×C11D4×Q811yescharacteristic
251Dic11—24no—
252Dic11—42no—
253Dic11—42no—
254Dic11—42no—
255Dic11—82no—
256C22×Q8—21no—
257C22×Q8—111no—
258C22×Q8C22×D1111yescharacteristic
259C22×C8—111no—
260C22×C8—111no—
261C22×C8C22×D1112yes—
262C4⋊Q8—22no—
263C4⋊Q8—22no—
264C4⋊Q8—444no—
265C4×Q8—22no—
266C4×Q8—22no—
267C4×Q8—222no—
268C4×Q8—222no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—111no—
272C2×C4⋊C4—111no—
273C2×C4⋊C4—111no—
274C2×C4⋊C4—112no—
275C2×C4⋊C4—112no—
276C2×C4⋊C4—222no—
277C2×C4⋊C4—222no—
278C2×C4⋊C4—221no—
279C2×C4⋊C4—222no—
280C2×C4⋊C4—221no—
281C2×C4⋊C4C22×D1111yescharacteristic
282C2×C4⋊C4C22×D1112yes—
283C2×C42—21no—
284C2×C42—112no—
285C2×C42—221no—
286C2×C42C22×D1111yescharacteristic
287#106—24no—
288#106—224no—
289C4⋊C8—224no—
290C4⋊C8C22⋊D1114yes—
291#103—24no—
292#103—114no—
293#103—222no—
294C4×C8—224no—
295C4×C8—222no—
296#95—222no—
297#95—222no—
298#95—222no—
299#95—222no—
300#95—222no—
301#95—221no—
302C2×C11#242911yescharacteristic
303C2×C11C2×#46511yescharacteristic
304C2×C11#306311yescharacteristic
305C2×C11#335911yescharacteristic
306C2×C11#336511yescharacteristic
307C2×C11Q8×SD1611yescharacteristic
308C2×C11#338311yescharacteristic
309C2×Q8—21no—
310C2×Q8—21no—
311C2×Q8—21no—
312C2×Q8—21no—
313C2×Q8—21no—
314C2×Q8—42no—
315C2×Q8—42no—
316C2×Q8—42no—
317C2×Q8—114no—
318C2×Q8—222no—
319C2×Q8—222no—
320C2×Q8Q8×D1112yes—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—22no—
324C22×C4—112no—
325C22×C4—112no—
326C22×C4—221no—
327C22×C4—221no—
328C22×C4—222no—
329C22×C4D4×D1111yescharacteristic
330C22×C4D4×D1111yescharacteristic
331C22×C4C23×D1111yescharacteristic
332C2×C8—22no—
333C2×C8—22no—
334C2×C8—112no—
335C2×C8—221no—
336C2×C8—221no—
337C2×C8—221no—
338C2×C8—221no—
339C2×C8—221no—
340C2×C8C2×C22⋊D1114yes—
341C4⋊C4—21no—
342C4⋊C4—22no—
343C4⋊C4—22no—
344C4⋊C4—21no—
345C4⋊C4—42no—
346C4⋊C4—42no—
347C4⋊C4—112no—
348C4⋊C4—112no—
349C4⋊C4—224no—
350C4⋊C4—222no—
351C4⋊C4—221no—
352C4⋊C4—221no—
353C4⋊C4—222no—
354C4⋊C4—222no—
355C4⋊C4—444no—
356C4⋊C4—444no—
357C4⋊C4—442no—
358C4⋊C4—881no—
359C4⋊C4—882no—
360C42—42no—
361C42—222no—
362C42—222no—
363C42—442no—
364C42#434112yes—
365C42C2×C22⋊D1112yes—
366C11#2547211yescharacteristic, complemented, Sylow
367C23C2×D4×D1111yescharacteristic
368Q8—22no—
369Q8—22no—
370Q8—41no—
371Q8—41no—
372Q8—84no—
373Q8—228no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—22no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—114no—
386C2×C4—222no—
387C2×C4—222no—
388C2×C4—222no—
389C2×C4—222no—
390C2×C4—222no—
391C2×C4—222no—
392C2×C4—222no—
393C2×C4—441no—
394C2×C4—441no—
395C2×C4—441no—
396C2×C4—441no—
397C2×C4—442no—
398C2×C4—442no—
399C2×C4—442no—
400C2×C4SD16×D1112yes—
401C2×C4#6696912yes—
402C2×C4#6699112yes—
403C2×C4#6699112yes—
404C2×C4C2×#434111yescharacteristic
405C2×C4C2×Q8×D1111yescharacteristic
406C2×C4#6704011yescharacteristic
407C2×C4#41×D1111yescharacteristic
408C2×C4#6704311yescharacteristic
409C2×C4C22×C22⋊D1111yescharacteristic
410C8—24no—
411C8—222no—
412C8—441no—
413C22#1062316311yescharacteristic
414C22#1062316411yescharacteristic
415C22C2×SD16×D1111yescharacteristic
416C22C2×#6696911yescharacteristic
417C22#1062330911yescharacteristic
418C22#1062331011yescharacteristic
419C22C2×#6699111yescharacteristic
420C4—22no—
421C4—42no—
422C4—81no—
423C4—82no—
424C4—224no—
425C4—442no—
426C4—442no—
427C4—442no—
428C4—882no—
429C4#1062278414yes—
430C4#1062315311yescharacteristic
431C4#1062315611yescharacteristic
432C4Q8×C22⋊D1111yescharacteristic
433C4#1062335511yescharacteristic
434C2#1307221111yescharacteristic
435C2C2×#1062278411yescharacteristic
436C2#1307830111yescharacteristic
437C2#1308125711yescharacteristic
438C2#1308131111yescharacteristic
439C2#1308147511yescharacteristic
440C2#1308150611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#475C2
socle, prime radicalC23×C11C22×D4
hypercenterC2×#475D11
hypocenterC11#25472
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
78. #66899Q8semidirect
366. C11#25472semidirect

Maximal subgroups

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

subgroupindex
C2×#106224432
#130739862
#130736052
#130701152
#130699952
#130695782
#130693802
#130693422
#130692892
C4×#668992
C2×C11×#4752
#2547211