Finite Group Databasebeta

← #14738509

Subgroups — #14738509

Order 2816.

590 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079999C211yesmaximal, characteristic
2#13079176C211yesmaximal, characteristic
3#13077551C211yesmaximal, characteristic, complemented
4#13068120C212yesmaximal, complemented
5#13068090C212yesmaximal, complemented
6#13068072C212yesmaximal, complemented
7#13068062C212yesmaximal, complemented
8#13067374C211yesmaximal, characteristic, complemented
9#13067354C211yesmaximal, characteristic, complemented
10#13067349C211yesmaximal, characteristic
11C11×#3255C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C11×#533C2211yescharacteristic
14#10623008C2211yescharacteristic
15C11×#475—21no—
16C11×#475C2212yes—
17C11×#470—22no—
18C11×#462—21no—
19C11×#462C2212yes—
20C11×#423C2211yescharacteristic
21#10622701C2211yescharacteristic
22#10622700—21no—
23#10622698C2211yescharacteristic
24#10622696—21no—
25#10622694C2211yescharacteristic
26#10622692C2211yescharacteristic
27#10622662—22no—
28#10622661—21no—
29#10622661—21no—
30#10622640C2212yes—
31C4×#4325—21no—
32C4×#4325—21no—
33#10622637—21no—
34#10622637C2212yes—
35Q8×C11⋊C8—21no—
36Q8×C11⋊C8C2212yes—
37#10622634C2212yes—
38#10622612—21no—
39#10622610—21no—
40#10622537C2211yescharacteristic
41#10622537C2211yescharacteristic
42C2×C4×C11⋊C8C2211yescharacteristic
43#10622185C2212yes—
44#10622185C2212yes—
45#10622123C2212yes—
46#10622119C2212yes—
47#10622117C2212yes—
48#10622117C2212yes—
49C2×#4339—21no—
50C2×C11×Q16—22no—
51C2×C11×M16—21no—
52C11×C4⋊Q8D411yescharacteristic
53C11×C4⋊Q8D411yescharacteristic
54C11×C4⋊Q8C2311yescharacteristic
55C11×C4⋊Q8C2311yescharacteristic
56C11×#125—21no—
57C11×#125—21no—
58C11×C22⋊Q8—21no—
59C11×C22⋊Q8—21no—
60C11×C22⋊Q8—21no—
61C11×C22⋊Q8D412yes—
62C4×Q8×C11—21no—
63C4×Q8×C11—21no—
64C4×Q8×C11—21no—
65C4×Q8×C11C2312yes—
66C11×#117—21no—
67C11×#117—21no—
68C2×C42×C11C2311yescharacteristic
69C2×#4325—22no—
70C2×#4325—21no—
71C2×#4325—21no—
72#66983—21no—
73#66983—21no—
74C2×#4318—21no—
75C2×#4318—21no—
76C22×C11⋊C8D411yescharacteristic
77C22×C11⋊C8D411yescharacteristic
78#66928—21no—
79#66927C2311yescharacteristic
80C4×D44—21no—
81C4×D44—21no—
82#66922C2311yescharacteristic
83C11×#106—22no—
84C11×C4⋊C8—21no—
85C11×C4⋊C8C2312yes—
86C11×#103—22no—
87C11×#103—22no—
88#66899—22no—
89#66899—21no—
90#66899—21no—
91#66873—22no—
92#66873—21no—
93#66873—21no—
94#66872—21no—
95#66872—21no—
96#66871—22no—
97C4⋊(C11⋊C8)—21no—
98C4⋊(C11⋊C8)—21no—
99C4⋊(C11⋊C8)—22no—
100C4⋊(C11⋊C8)—22no—
101C4⋊(C11⋊C8)C2312yes—
102C4⋊(C11⋊C8)C2312yes—
103#66867—22no—
104C4×C11⋊C8—22no—
105C4×C11⋊C8D411yescharacteristic
106C4×C11⋊C8D411yescharacteristic
107C4×C11⋊C8C2311yescharacteristic
108C4×C11⋊C8C2311yescharacteristic
109#19351—111nomaximal, Sylow
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11C2×D412yes—
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11#4111yescharacteristic
117C2×C22⋊D11—41no—
118#4339—82no—
119C2×D44—21no—
120C2×D44—21no—
121C2×D44—21no—
122C2×C4×D11—41no—
123C2×Dic22—21no—
124C11×Q16—82no—
125C11×M16—81no—
126C2×C8×C11—22no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—41no—
137C11×C4⋊C4—41no—
138C11×C4⋊C4C2×D412yes—
139C11×C22⋊C4—22no—
140C11×C22⋊C4—41no—
141C42×C11—22no—
142C42×C11—41no—
143C42×C11C2×D411yescharacteristic
144C42×C11C2×D411yescharacteristic
145C42×C11#4111yescharacteristic
146C42×C11C2411yescharacteristic
147#4325—42no—
148#4325—42no—
149#4325—82no—
150(C2×D11)⋊C4—41no—
151(C2×D11)⋊C4—41no—
152C4⋊Dic11—21no—
153C4⋊Dic11—21no—
154#4318—42no—
155#4318—81no—
156C2×C11⋊C8—22no—
157C2×C11⋊C8—22no—
158C2×C11⋊C8—22no—
159C2×C11⋊C8—41no—
160C2×C11⋊C8C2×D411yescharacteristic
161C2×C11⋊C8C2×D411yescharacteristic
162C2×C11⋊C8C2×D411yescharacteristic
163C2×C11⋊C8C2×D411yescharacteristic
164#3255D1111yescharacteristic, complemented
165#3254—111no—
166#3167—111no—
167#2960—111no—
168#1692—112no—
169#1686—112no—
170#1684—112no—
171#1682—112no—
172#1567—111no—
173#1561—111no—
174#1560—111no—
175C23×C11#12111yescharacteristic
176C22×D11—41no—
177Q8×C11—22no—
178Q8×C11—22no—
179Q8×C11—42no—
180Q8×C11—41no—
181Q8×C11—41no—
182Q8×C11—41no—
183Q8×C11—41no—
184C2×C4×C11—21no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11#12111yescharacteristic
194C2×C4×C11#12111yescharacteristic
195C2×C4×C11#12111yescharacteristic
196C2×C4×C11C22×D411yescharacteristic
197C2×C4×C11C22×D411yescharacteristic
198C2×C4×C11C2×#4111yescharacteristic
199C22⋊D11—82no—
200C2×Dic11—41no—
201D44—41no—
202D44—41no—
203D44—41no—
204D44—41no—
205D44—81no—
206C4×D11—82no—
207Dic22—81no—
208C8×C11—42no—
209C11⋊C8—21no—
210C11⋊C8—21no—
211C11⋊C8—21no—
212C11⋊C8—42no—
213C11⋊C8—42no—
214C11⋊C8#13712yes—
215#533C2×D1111yescharacteristic
216#533C2×D1111yescharacteristic
217#532—111no—
218#498—111no—
219#492—111no—
220#487—111no—
221#486—111no—
222#477—112no—
223#475—21no—
224#475C2×D1112yes—
225#474—221no—
226#470—22no—
227#468—222no—
228#465—221no—
229#465—221no—
230#462—21no—
231#462C2×D1112yes—
232#461—221no—
233#460—112no—
234#446—112no—
235#446—221no—
236C8×Q8—112no—
237C8×Q8—221no—
238C4×SD16—221no—
239C4×SD16—221no—
240#424—221no—
241#423—111no—
242#423—111no—
243#423C2×D1111yescharacteristic
244#405—221no—
245C2×C4×C8—111no—
246#335—112no—
247#335—112no—
248#333—112no—
249#332—112no—
250#332—112no—
251#331—112no—
252C22×C11—21no—
253C22×C11—21no—
254C22×C11—21no—
255C22×C11C2×#12111yescharacteristic
256C2×D11—81no—
257C2×D11—81no—
258C2×D11—81no—
259C4×C11—21no—
260C4×C11—21no—
261C4×C11—21no—
262C4×C11—42no—
263C4×C11—42no—
264C4×C11—81no—
265C4×C11—81no—
266C4×C11#47112yes—
267C4×C11C2×#13711yescharacteristic
268C4×C11#57511yescharacteristic
269C4×C11#57611yescharacteristic
270C4×C11#57811yescharacteristic
271Dic11—81no—
272C2×#41—221no—
273C2×Q16—22no—
274C2×SD16—221no—
275C2×SD16—221no—
276C2×SD16—222no—
277C2×M16—21no—
278C2×M16—221no—
279C2×M16—221no—
280C22×C8—111no—
281C22×C8—111no—
282C4⋊Q8—111no—
283C4⋊Q8C22⋊D1111yescharacteristic
284C4⋊Q8C22⋊D1111yescharacteristic
285C4⋊Q8C22×D1111yescharacteristic
286C4⋊Q8C22×D1111yescharacteristic
287#127—111no—
288#125—21no—
289#125—21no—
290#124—221no—
291C22⋊Q8—21no—
292C22⋊Q8—21no—
293C22⋊Q8—21no—
294C22⋊Q8C22⋊D1112yes—
295#121—221no—
296#121—221no—
297C4×Q8—21no—
298C4×Q8—21no—
299C4×Q8—21no—
300C4×Q8C22×D1112yes—
301C4×D4—221no—
302C4×D4—221no—
303#117—21no—
304#117—21no—
305C2×C42C22×D1111yescharacteristic
306#107—222no—
307#106—22no—
308#106—221no—
309#106—221no—
310C4⋊C8—21no—
311C4⋊C8—112no—
312C4⋊C8—112no—
313C4⋊C8—222no—
314C4⋊C8—222no—
315C4⋊C8—221no—
316C4⋊C8—221no—
317C4⋊C8C22×D1112yes—
318#103—22no—
319#103—22no—
320#103—221no—
321#103—221no—
322#103—222no—
323#102—221no—
324#102—221no—
325#102—222no—
326#97—222no—
327C4×C8—111no—
328C4×C8—111no—
329C4×C8—111no—
330C4×C8—111no—
331C4×C8—222no—
332C2×C11—41no—
333C2×C11#303711yescharacteristic
334C2×C11#306111yescharacteristic
335C2×C11C2×#47111yescharacteristic
336D11—161no—
337#41—882no—
338C2×Q8—21no—
339C2×Q8—21no—
340C2×Q8—21no—
341C2×Q8—221no—
342C2×Q8C2×C22⋊D1112yes—
343C2×D4—221no—
344C2×D4—221no—
345C2×D4—221no—
346C2×D4—441no—
347C22×C4—441no—
348C22×C4D4×D1111yescharacteristic
349C22×C4#434111yescharacteristic
350C22×C4C2×C22⋊D1111yescharacteristic
351Q16—82no—
352SD16—442no—
353SD16—442no—
354SD16—882no—
355M16—81no—
356M16—442no—
357M16—881no—
358C2×C8—22no—
359C2×C8—111no—
360C2×C8—111no—
361C2×C8—111no—
362C2×C8—111no—
363C2×C8—222no—
364C2×C8—222no—
365C2×C8—222no—
366C2×C8—441no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—22no—
371C4⋊C4—22no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—41no—
377C4⋊C4—41no—
378C4⋊C4—221no—
379C4⋊C4—221no—
380C4⋊C4C2×C22⋊D1112yes—
381C22⋊C4—22no—
382C22⋊C4—41no—
383C22⋊C4—441no—
384C22⋊C4—441no—
385C42—22no—
386C42—41no—
387C42D4×D1111yescharacteristic
388C42#434111yescharacteristic
389C42C2×C22⋊D1111yescharacteristic
390C42C23×D1111yescharacteristic
391C11#1935111yescharacteristic, complemented, Sylow
392C23—441no—
393C23#6699211yescharacteristic
394Q8—22no—
395Q8—22no—
396Q8—42no—
397Q8—41no—
398Q8—41no—
399Q8—41no—
400Q8—41no—
401Q8—881no—
402D4—441no—
403D4—441no—
404D4—441no—
405D4—441no—
406D4—881no—
407D4—882no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—22no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—441no—
418C2×C4—882no—
419C2×C4#6699211yescharacteristic
420C2×C4#6699211yescharacteristic
421C2×C4#6699211yescharacteristic
422C2×C4C2×D4×D1111yescharacteristic
423C2×C4C2×#434111yescharacteristic
424C2×C4C22×C22⋊D1111yescharacteristic
425C8—42no—
426C8—112no—
427C8—221no—
428C8—221no—
429C8—221no—
430C8—442no—
431C8—442no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—881no—
436C22—881no—
437C22—881no—
438C22C2×#6699211yescharacteristic
439C4—21no—
440C4—21no—
441C4—21no—
442C4—42no—
443C4—42no—
444C4—81no—
445C4—81no—
446C4—881no—
447C4#1062281612yes—
448C4D11×#13711yescharacteristic
449C4#1062330811yescharacteristic
450C4#1062336611yescharacteristic
451C4#1062336911yescharacteristic
452C2—41no—
453C2—1761no—
454C2#1307808511yescharacteristic
455C2#1307828311yescharacteristic
456C2C2×#1062281611yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3255C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenter#3255D11
hypocenterC11#19351
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3255

Complements

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

NH ≅ G/Ntype
3. #13077551C2semidirect
4. #13068120C2semidirect
5. #13068090C2semidirect
6. #13068072C2semidirect
7. #13068062C2semidirect
8. #13067374C2semidirect
9. #13067354C2semidirect
11. C11×#3255C2semidirect
164. #3255D11semidirect
391. C11#19351semidirect

Maximal subgroups

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

subgroupindex
#130799992
#130791762
#130775512
#130681202
#130680902
#130680722
#130680622
#130673742
#130673542
#130673492
C11×#32552
#1935111