Finite Group Databasebeta

← #14738564

Subgroups — #14738564

Order 2816.

596 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079837C211yesmaximal, characteristic
2#13079643C211yesmaximal, characteristic
3#13077591C211yesmaximal, characteristic
4#13068119C212yesmaximal, complemented
5#13068112C212yesmaximal, complemented
6#13067995C212yesmaximal, complemented
7#13067988C212yesmaximal, complemented
8#13067379C211yesmaximal, characteristic, complemented
9#13067342C211yesmaximal, characteristic, complemented
10#13067333C211yesmaximal, characteristic, complemented
11C2×C11×#498C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14#10623010C2211yescharacteristic
15C11×#498—21no—
16C11×#498—21no—
17C11×#498C2212yes—
18C11×#498C2212yes—
19C2×C11×#106—21no—
20C2×C11×#106—21no—
21C2×C4×C8×C11C2211yescharacteristic
22#10622841—21no—
23#10622840—21no—
24#10622724—21no—
25C8×C22⋊D11—21no—
26#10622704C2212yes—
27#10622703C2212yes—
28#10622702—21no—
29#10622699—21no—
30#10622697C2212yes—
31#10622696C2212yes—
32#10622695—21no—
33#10622693—21no—
34#10622584—21no—
35#10622580—21no—
36#10622539C2211yescharacteristic
37#10622539C2211yescharacteristic
38#10622539C2211yescharacteristic
39#10622303—21no—
40#10622302—21no—
41#10622301C2211yescharacteristic
42C8×D44C2211yescharacteristic
43#10622292C2211yescharacteristic
44C8×Dic22C2211yescharacteristic
45#10622185C2212yes—
46#10622185C2212yes—
47#10622184C2212yes—
48#10622184C2212yes—
49#10622096C2212yes—
50#10622095C2212yes—
51C22×Q8×C11—21no—
52C22×Q8×C11—21no—
53C22×C8×C11D411yescharacteristic
54C22×C8×C11D411yescharacteristic
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8—21no—
57C11×C4⋊Q8—21no—
58C11×C4⋊Q8—21no—
59C11×C4⋊Q8—21no—
60C11×C4⋊Q8—21no—
61C11×C4⋊Q8C2312yes—
62C11×C4⋊Q8C2312yes—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C42×C11C2311yescharacteristic
68C2×#4326—22no—
69C2×#4325—22no—
70#66983D411yescharacteristic
71#66982—21no—
72C4×C22⋊D11—21no—
73#66977D411yescharacteristic
74C2×#4313—21no—
75C2×C8×D11—21no—
76#66929—21no—
77#66928D411yescharacteristic
78C4×D44C2311yescharacteristic
79#66925—21no—
80#66923D411yescharacteristic
81C4×Dic22C2311yescharacteristic
82C11×#106—22no—
83C11×#106—22no—
84C11×#106—22no—
85C11×#106—22no—
86C4×C8×C11D411yescharacteristic
87C4×C8×C11D411yescharacteristic
88C4×C8×C11C2311yescharacteristic
89C4×C8×C11C2311yescharacteristic
90#66899—22no—
91#66899—22no—
92C22⋊(C11⋊C8)—21no—
93C22⋊(C11⋊C8)—21no—
94C22⋊(C11⋊C8)—21no—
95(C2×D11)⋊C8—21no—
96(C2×D11)⋊C8—21no—
97#66879—21no—
98Dic11⋊C8—21no—
99Dic11⋊C8—21no—
100C8×Dic11—21no—
101#66874—22no—
102#66873—22no—
103#66872—22no—
104#66871—22no—
105C4⋊(C11⋊C8)C2311yescharacteristic
106C4⋊(C11⋊C8)C2311yescharacteristic
107C4⋊(C11⋊C8)C2312yes—
108C4⋊(C11⋊C8)C2312yes—
109#66867—21no—
110#66867—21no—
111#66867—21no—
112#19357—111nomaximal, Sylow
113C2×Q8×C11—22no—
114C2×Q8×C11—22no—
115C2×Q8×C11—41no—
116C2×Q8×C11—41no—
117C2×Q8×C11—82no—
118C2×Q8×C11—82no—
119C22×C4×C11—41no—
120C22×C4×C11—41no—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11#4111yescharacteristic
124C2×C22⋊D11—21no—
125C2×D44C2×D411yescharacteristic
126C2×C4×D11—21no—
127C2×Dic22C2×D411yescharacteristic
128C2×C8×C11—22no—
129C2×C8×C11—22no—
130C2×C8×C11C2×D411yescharacteristic
131C2×C8×C11C2×D411yescharacteristic
132C2×C8×C11C2×D411yescharacteristic
133C2×C8×C11C2×D411yescharacteristic
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—41no—
139C11×C4⋊C4—41no—
140C11×C4⋊C4—41no—
141C11×C4⋊C4—41no—
142C42×C11C2×D411yescharacteristic
143C42×C11C2×D411yescharacteristic
144C42×C11#4111yescharacteristic
145C42×C11C2411yescharacteristic
146C22⋊Dic11—21no—
147#4326—82no—
148#4325—82no—
149(C2×D11)⋊C4—21no—
150(C2×D11)⋊C4—21no—
151(C2×D11)⋊C4—21no—
152(C2×D11)⋊C4—21no—
153C4⋊Dic11C2×D411yescharacteristic
154C4⋊Dic11C2×D411yescharacteristic
155Dic11⋊C4—21no—
156Dic11⋊C4—21no—
157Dic11⋊C4—21no—
158Dic11⋊C4—21no—
159C4×Dic11—21no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—21no—
162C2×C11⋊C8—21no—
163C2×C11⋊C8—22no—
164#4313—42no—
165C8×D11—42no—
166#3238—111no—
167#3218—111no—
168C2×#498D1111yescharacteristic, complemented
169#2966—111no—
170#1692—112no—
171#1691—112no—
172#1672—112no—
173#1671—112no—
174#1568—111no—
175#1558—111no—
176#1556—111no—
177C23×C11#12111yescharacteristic
178C22×D11—21no—
179Q8×C11—42no—
180Q8×C11—42no—
181Q8×C11—82no—
182Q8×C11—82no—
183Q8×C11—82no—
184C2×C4×C11—22no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—22no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—82no—
191C2×C4×C11—82no—
192C2×C4×C11#12111yescharacteristic
193C2×C4×C11#12111yescharacteristic
194C2×C4×C11#12111yescharacteristic
195C2×C4×C11C22×D411yescharacteristic
196C2×C4×C11C22×D411yescharacteristic
197C2×C4×C11C2×#4111yescharacteristic
198C22⋊D11—42no—
199C2×Dic11—21no—
200C2×Dic11—21no—
201C2×Dic11—21no—
202D44—22no—
203C4×D11—41no—
204C4×D11—41no—
205Dic22—22no—
206C8×C11—21no—
207C8×C11—21no—
208C8×C11#13712yes—
209C8×C11#13712yes—
210C11⋊C8—41no—
211C11⋊C8—41no—
212C11⋊C8—42no—
213C11⋊C8—42no—
214C2×C4⋊Q8C2×D1111yescharacteristic
215C2×C4⋊Q8C2×D1111yescharacteristic
216#529—111no—
217#501—221no—
218#498—21no—
219#498—21no—
220#498C2×D1112yes—
221#498C2×D1112yes—
222#497—221no—
223#491—221no—
224#489—221no—
225#483—221no—
226#480—221no—
227#477—112no—
228#476—112no—
229#462—112no—
230#461—112no—
231#451—221no—
232#448—221no—
233#446—111no—
234C8×Q8—111no—
235#436—111no—
236#435—221no—
237C8×D4—111no—
238C8×D4—221no—
239#433—221no—
240#432—111no—
241#432—111no—
242#432—111no—
243C2×#106—21no—
244C2×#106—21no—
245#405—221no—
246C2×C4×C8C2×D1111yescharacteristic
247#335—112no—
248#334—112no—
249#333—112no—
250#333—112no—
251#332—112no—
252#332—112no—
253C22×C11—21no—
254C22×C11—21no—
255C22×C11#47112yes—
256C22×C11C2×#12111yescharacteristic
257C2×D11—41no—
258C2×D11—41no—
259C2×D11—41no—
260C4×C11—21no—
261C4×C11—21no—
262C4×C11—21no—
263C4×C11—21no—
264C4×C11—82no—
265C4×C11—82no—
266C4×C11C2×#13711yescharacteristic
267C4×C11C2×#13711yescharacteristic
268C4×C11#57712yes—
269Dic11—41no—
270Dic11—41no—
271Dic11—41no—
272C22×Q8—21no—
273C22×Q8—21no—
274C2×Q16—222no—
275C2×SD16—222no—
276C2×M16—221no—
277C22×C8—221no—
278C22×C8C22⋊D1111yescharacteristic
279C22×C8C22⋊D1111yescharacteristic
280C4⋊Q8—21no—
281C4⋊Q8—21no—
282C4⋊Q8—21no—
283C4⋊Q8—21no—
284C4⋊Q8—21no—
285C4⋊Q8—21no—
286C4⋊Q8C22×D1112yes—
287C4⋊Q8C22×D1112yes—
288#126—221no—
289#125—111no—
290#124—111no—
291#123—221no—
292C22⋊Q8—111no—
293#121—111no—
294C4×Q8—111no—
295C4×D4—111no—
296C4×D4—221no—
297#117—221no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C42C22×D1111yescharacteristic
303#107—222no—
304#106—22no—
305#106—22no—
306#106—22no—
307#106—22no—
308#106—222no—
309C4⋊C8—111no—
310C4⋊C8—111no—
311C4⋊C8—112no—
312C4⋊C8—112no—
313C4⋊C8—221no—
314C4⋊C8—221no—
315#103—222no—
316#103—222no—
317#103—222no—
318#102—222no—
319C22⋊C8—221no—
320C22⋊C8—221no—
321C22⋊C8—221no—
322C22⋊C8—221no—
323C22⋊C8—221no—
324#97—221no—
325#97—221no—
326#97—221no—
327#97—221no—
328C4×C8—221no—
329C4×C8C22⋊D1111yescharacteristic
330C4×C8C22⋊D1111yescharacteristic
331C4×C8C22×D1111yescharacteristic
332C4×C8C22×D1111yescharacteristic
333C2×C11—22no—
334C2×C11#303911yescharacteristic
335C2×C11#305711yescharacteristic
336C2×C11C2×#47111yescharacteristic
337D11—81no—
338C2×Q8—22no—
339C2×Q8—22no—
340C2×Q8—41no—
341C2×Q8—41no—
342C2×Q8—82no—
343C2×Q8—82no—
344C2×Q8—111no—
345C2×D4—111no—
346C2×D4—221no—
347C22×C4—41no—
348C22×C4—41no—
349C22×C4—221no—
350C22×C4D4×D1111yescharacteristic
351C22×C4#434111yescharacteristic
352C22×C4C2×C22⋊D1111yescharacteristic
353Q16—882no—
354SD16—882no—
355M16—442no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—222no—
359C2×C8—222no—
360C2×C8—221no—
361C2×C8—221no—
362C2×C8—442no—
363C2×C8C2×C22⋊D1111yescharacteristic
364C2×C8C2×C22⋊D1111yescharacteristic
365C2×C8C2×C22⋊D1111yescharacteristic
366C2×C8C2×C22⋊D1111yescharacteristic
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—22no—
371C4⋊C4—41no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—111no—
376C4⋊C4—111no—
377C4⋊C4—221no—
378C4⋊C4—221no—
379C4⋊C4—221no—
380C4⋊C4—221no—
381C22⋊C4—221no—
382C22⋊C4—221no—
383C22⋊C4—221no—
384C22⋊C4—221no—
385C22⋊C4—221no—
386C42—221no—
387C42D4×D1111yescharacteristic
388C42#434111yescharacteristic
389C42C2×C22⋊D1111yescharacteristic
390C42C23×D1111yescharacteristic
391C11#1935711yescharacteristic, complemented, Sylow
392C23—221no—
393C23#6699111yescharacteristic
394Q8—42no—
395Q8—42no—
396Q8—82no—
397Q8—82no—
398Q8—82no—
399Q8—222no—
400D4—222no—
401D4—442no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—82no—
409C2×C4—82no—
410C2×C4—221no—
411C2×C4—221no—
412C2×C4—221no—
413C2×C4—441no—
414C2×C4—441no—
415C2×C4#6699111yescharacteristic
416C2×C4#6699111yescharacteristic
417C2×C4#6699111yescharacteristic
418C2×C4C2×D4×D1111yescharacteristic
419C2×C4C2×#434111yescharacteristic
420C2×C4C22×C22⋊D1111yescharacteristic
421C8—21no—
422C8—21no—
423C8—442no—
424C8—442no—
425C8—441no—
426C8—441no—
427C8#6699512yes—
428C8#6699512yes—
429C22—21no—
430C22—21no—
431C22—441no—
432C22—441no—
433C22—441no—
434C22#1062279012yes—
435C22C2×#6699111yescharacteristic
436C4—21no—
437C4—21no—
438C4—21no—
439C4—21no—
440C4—82no—
441C4—82no—
442C4—441no—
443C4—441no—
444C4—441no—
445C4#1062329312yes—
446C4C2×#6699511yescharacteristic
447C4C2×#6699511yescharacteristic
448C2—22no—
449C2—881no—
450C2#1307809911yescharacteristic
451C2#1307825111yescharacteristic
452C2C2×#1062279011yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#498C2
socleC22×C11C2×#121
prime radical#66983D4
hypercenterC2×#498D11
hypocenterC11#19357
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#498

Complements

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

NH ≅ G/Ntype
4. #13068119C2semidirect
5. #13068112C2semidirect
6. #13067995C2semidirect
7. #13067988C2semidirect
8. #13067379C2semidirect
9. #13067342C2semidirect
10. #13067333C2semidirect
11. C2×C11×#498C2semidirect
168. C2×#498D11semidirect
391. C11#19357semidirect

Maximal subgroups

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

subgroupindex
#130798372
#130796432
#130775912
#130681192
#130681122
#130679952
#130679882
#130673792
#130673422
#130673332
C2×C11×#4982
#1935711