Finite Group Databasebeta

← #14719835

Subgroups — #14719835

Order 2816.

876 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623114C211yesmaximal, characteristic
2#13077699C211yesmaximal, characteristic, complemented
3#13077696C211yesmaximal, characteristic, complemented
4#13066984C214yesmaximal
5#13066970C214yesmaximal, complemented
6#13066940C211yesmaximal, characteristic, complemented
7#13066928C211yesmaximal, characteristic
8#13066928C211yesmaximal, characteristic
9C11×#1461C211yesmaximal, characteristic, complemented
10C2×C4×Q8×C11C2211yescharacteristic
11C2×#66999C411yescharacteristic
12C2×#66997C411yescharacteristic
13#10623114—22no—
14#10623114—22no—
15#10623114—22no—
16#10623114—22no—
17C2×#66951C2212yes—
18C2×#66950C411yescharacteristic
19C2×#66943C411yescharacteristic
20C2×#66942C2212yes—
21C2×#66929C412yes—
22C2×#66925C2211yescharacteristic
23C2×#66923C412yes—
24C2×C4×Dic22C2211yescharacteristic
25C11×#431C2211yescharacteristic
26C11×#431C2211yescharacteristic
27#10622538C2211yescharacteristic
28#10622538C2211yescharacteristic
29#10622444—22no—
30#10622443—22no—
31#10622332C2214yes—
32#10622331C2214yes—
33#10622292—22no—
34C8×Dic22—22no—
35C11×#324C2214yes—
36#10622166C2214yes—
37#10622107C2212yes—
38#10622107C2212yes—
39#10622106C2212yes—
40#10622106C2212yes—
41C22×Q8×C11C2×C411yescharacteristic
42C22×C4×D11C2×C411yescharacteristic
43C22×Dic22C2×C411yescharacteristic
44C4×Q8×C11—21no—
45C4×Q8×C11—21no—
46C4×Q8×C11—21no—
47C4×Q8×C11—21no—
48C2×C11×C4⋊C4C2×C411yescharacteristic
49C2×C11×C4⋊C4C2312yes—
50C2×C42×C11C2×C412yes—
51C2×C42×C11C2311yescharacteristic
52#66999—22no—
53#66999—22no—
54#66997—22no—
55#66997—22no—
56C2×(C2×D11)⋊C4C2×C411yescharacteristic
57C2×(C2×D11)⋊C4C2×C412yes—
58C2×(C2×D11)⋊C4C2×C412yes—
59C2×(C2×D11)⋊C4C2311yescharacteristic
60C2×C4⋊Dic11C2×C412yes—
61C2×C4⋊Dic11C2×C412yes—
62C2×C4⋊Dic11C2×C411yescharacteristic
63C2×Dic11⋊C4C2×C411yescharacteristic
64C2×Dic11⋊C4C2×C412yes—
65C2×Dic11⋊C4C2×C412yes—
66C2×Dic11⋊C4C2×C412yes—
67C2×Dic11⋊C4C2×C412yes—
68C2×Dic11⋊C4C2×C412yes—
69C2×Dic11⋊C4C2311yescharacteristic
70C2×C4×Dic11C2×C411yescharacteristic
71C2×C4×Dic11C2312yes—
72#66951—24no—
73#66951—24no—
74#66950—22no—
75#66950—22no—
76#66943—22no—
77#66943—22no—
78#66942—24no—
79#66942—24no—
80#66929—24no—
81#66929—24no—
82#66925—21no—
83#66925—21no—
84#66925—21no—
85#66925—21no—
86#66923—24no—
87#66923—24no—
88C4×Dic22D412yes—
89C4×Dic22D412yes—
90C4×Dic22D412yes—
91C4×Dic22D412yes—
92C11×C4⋊C8—21no—
93C11×C4⋊C8—21no—
94C11×C22⋊C8C2312yes—
95C11×C22⋊C8C2312yes—
96C4×C8×C11—21no—
97C4×C8×C11—21no—
98C22⋊(C11⋊C8)C2312yes—
99C22⋊(C11⋊C8)C2312yes—
100#66879—24no—
101Dic11⋊C8—24no—
102Dic11⋊C8—24no—
103C8×Dic11—24no—
104C4⋊(C11⋊C8)—21no—
105C4⋊(C11⋊C8)—21no—
106C4×C11⋊C8—21no—
107C4×C11⋊C8—21no—
108#17391—111nomaximal, Sylow
109C23×D11C22×C411yescharacteristic
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C22×C4×C11C22×C412yes—
115C22×C4×C11C22×C412yes—
116C22×C4×C11C22×C411yescharacteristic
117C22×C4×C11C22×C411yescharacteristic
118C22×C4×C11C2411yescharacteristic
119C22×Dic11C22×C411yescharacteristic
120C22×Dic11C22×C412yes—
121C22×Dic11C22×C411yescharacteristic
122C22×Dic11C22×C411yescharacteristic
123C22×Dic11C22×C412yes—
124C2×C4×D11—21no—
125C2×C4×D11—21no—
126C2×C4×D11—22no—
127C2×C4×D11—22no—
128C2×Dic22—22no—
129C2×Dic22—22no—
130C2×Dic22C22⋊C412yes—
131C2×Dic22C22⋊C412yes—
132C2×C8×C11—22no—
133C2×C8×C11—22no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C42×C11—22no—
139C42×C11—22no—
140C42×C11C2×D411yescharacteristic
141C42×C11C2×D411yescharacteristic
142C42×C11C2×D411yescharacteristic
143C42×C11C2×D411yescharacteristic
144(C2×D11)⋊C4—24no—
145(C2×D11)⋊C4—24no—
146(C2×D11)⋊C4—21no—
147(C2×D11)⋊C4—21no—
148(C2×D11)⋊C4—21no—
149(C2×D11)⋊C4—21no—
150C4⋊Dic11—24no—
151C4⋊Dic11—24no—
152C4⋊Dic11C22⋊C412yes—
153C4⋊Dic11C22⋊C412yes—
154Dic11⋊C4—24no—
155Dic11⋊C4—24no—
156Dic11⋊C4—24no—
157Dic11⋊C4—24no—
158Dic11⋊C4—21no—
159Dic11⋊C4—21no—
160Dic11⋊C4—21no—
161Dic11⋊C4—21no—
162Dic11⋊C4C22⋊C414yes—
163Dic11⋊C4C22⋊C414yes—
164C4×Dic11—21no—
165C4×Dic11—21no—
166C4×Dic11C2×D414yes—
167C4×Dic11C2×D414yes—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—22no—
170C2×#541—111no—
171#2983—111no—
172#2982—111no—
173#1473—114no—
174#1470—114no—
175#1461—111no—
176#1461D1111yescharacteristic, complemented
177#1458—111no—
178#1458—111no—
179C23×C11C23×C411yescharacteristic
180C22×D11—21no—
181C22×D11—21no—
182C22×D11—21no—
183C22×D11—41no—
184C22×D11—41no—
185Q8×C11—42no—
186Q8×C11—42no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—42no—
194C2×C4×C11C2×C22⋊C411yescharacteristic
195C2×C4×C11C2×C22⋊C411yescharacteristic
196C2×C4×C11C2×C22⋊C411yescharacteristic
197C2×C4×C11C2×C22⋊C411yescharacteristic
198C2×C4×C11#13112yes—
199C2×C4×C11#13112yes—
200C2×C4×C11C22×D411yescharacteristic
201C2×C4×C11C22×D411yescharacteristic
202C2×Dic11—22no—
203C2×Dic11—22no—
204C2×Dic11—21no—
205C2×Dic11—21no—
206C2×Dic11—21no—
207C2×Dic11—21no—
208C2×Dic11—21no—
209C2×Dic11—42no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11C2×C22⋊C414yes—
213C2×Dic11C2×C22⋊C414yes—
214C4×D11—42no—
215C4×D11—42no—
216Dic22—24no—
217Dic22—24no—
218C8×C11—42no—
219C8×C11—42no—
220C11⋊C8—42no—
221C11⋊C8—42no—
222#541—222no—
223#541—222no—
224#541—222no—
225#541—222no—
226C2×C4⋊Q8—111no—
227C2×#126—112no—
228C2×#126—112no—
229C2×#125—112no—
230C2×#125—111no—
231C2×#125—112no—
232C2×C22⋊Q8—111no—
233C2×C22⋊Q8—111no—
234C2×C4×Q8—111no—
235C2×C4×Q8C2×D1111yescharacteristic
236C2×#117—111no—
237#446—222no—
238#446—222no—
239C8×Q8—222no—
240C8×Q8—222no—
241#432—114no—
242#431—111no—
243#431—111no—
244#431—114no—
245#431C2×D1111yescharacteristic
246#431C2×D1111yescharacteristic
247#324—114no—
248#324—112no—
249#324—112no—
250#324C2×D1114yes—
251#323—112no—
252#323—112no—
253C22×C11—21no—
254C22×C11—21no—
255C22×C11C22×C22⋊C411yescharacteristic
256C22×C11C2×#13111yescharacteristic
257C22×C11C2×#13111yescharacteristic
258C2×D11—41no—
259C2×D11—41no—
260C2×D11—41no—
261C2×D11—81no—
262C2×D11—81no—
263C4×C11—21no—
264C4×C11—21no—
265C4×C11—21no—
266C4×C11—21no—
267C4×C11—42no—
268C4×C11—42no—
269C4×C11#40812yes—
270C4×C11#40812yes—
271Dic11—24no—
272Dic11—24no—
273Dic11—41no—
274Dic11—41no—
275Dic11—41no—
276C22×Q8—111no—
277C22×Q8C4×D1111yescharacteristic
278C23×C4—111no—
279C4⋊Q8—222no—
280C4⋊Q8—222no—
281#126—224no—
282#126—224no—
283#126—224no—
284#126—224no—
285#125—224no—
286#125—224no—
287#125—224no—
288#125—224no—
289#125—222no—
290#125—222no—
291C22⋊Q8—222no—
292C22⋊Q8—222no—
293C22⋊Q8—222no—
294C22⋊Q8—222no—
295C4×Q8—21no—
296C4×Q8—21no—
297C4×Q8—21no—
298C4×Q8—21no—
299C4×Q8—112no—
300C4×Q8—112no—
301C4×Q8—112no—
302C4×Q8—112no—
303#117—221no—
304#117—221no—
305#117—221no—
306#117—221no—
307C2×C4⋊C4—111no—
308C2×C4⋊C4—112no—
309C2×C4⋊C4—111no—
310C2×C4⋊C4—112no—
311C2×C4⋊C4—112no—
312C2×C4⋊C4—112no—
313C2×C4⋊C4—112no—
314C2×C4⋊C4—112no—
315C2×C4⋊C4—112no—
316C2×C4⋊C4—111no—
317C2×C4⋊C4C4×D1111yescharacteristic
318C2×C4⋊C4C22×D1112yes—
319C2×C22⋊C4—111no—
320C2×C22⋊C4—112no—
321C2×C22⋊C4—112no—
322C2×C22⋊C4—111no—
323C2×C42—112no—
324C2×C42—111no—
325C2×C42C4×D1112yes—
326C2×C42C22×D1111yescharacteristic
327C4⋊C8—21no—
328C4⋊C8—21no—
329C4⋊C8—224no—
330C4⋊C8—224no—
331C4⋊C8—221no—
332C4⋊C8—221no—
333C22⋊C8—112no—
334C22⋊C8—112no—
335C22⋊C8C22×D1112yes—
336C22⋊C8C22×D1112yes—
337#97—224no—
338C4×C8—21no—
339C4×C8—21no—
340C4×C8—224no—
341C4×C8—221no—
342C4×C8—221no—
343C2×C11—21no—
344C2×C11—21no—
345C2×C11C2×#40811yescharacteristic
346C2×C11#288411yescharacteristic
347C2×C11#288911yescharacteristic
348D11—81no—
349C24—111no—
350C2×Q8—21no—
351C2×Q8—21no—
352C2×Q8—22no—
353C2×Q8—22no—
354C2×Q8—112no—
355C2×Q8—112no—
356C2×Q8—222no—
357C2×Q8—222no—
358C22×C4—112no—
359C22×C4—112no—
360C22×C4—111no—
361C22×C4—111no—
362C22×C4—111no—
363C22×C4—221no—
364C22×C4—221no—
365C22×C4—222no—
366C22×C4—222no—
367C22×C4C2×C4×D1112yes—
368C22×C4C2×C4×D1112yes—
369C22×C4C2×C4×D1111yescharacteristic
370C22×C4C2×C4×D1111yescharacteristic
371C22×C4C23×D1111yescharacteristic
372C2×C8—22no—
373C2×C8—22no—
374C2×C8—222no—
375C2×C8—222no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—22no—
379C4⋊C4—22no—
380C4⋊C4—112no—
381C4⋊C4—112no—
382C4⋊C4—114no—
383C4⋊C4—114no—
384C4⋊C4—224no—
385C4⋊C4—224no—
386C4⋊C4—224no—
387C4⋊C4—224no—
388C4⋊C4—224no—
389C4⋊C4—224no—
390C4⋊C4—221no—
391C4⋊C4—221no—
392C4⋊C4—221no—
393C4⋊C4—221no—
394C22⋊C4—224no—
395C22⋊C4—224no—
396C22⋊C4—221no—
397C22⋊C4—221no—
398C22⋊C4—221no—
399C22⋊C4—221no—
400C42—22no—
401C42—22no—
402C42—114no—
403C42—114no—
404C42—221no—
405C42—221no—
406C42D4×D1111yescharacteristic
407C42D4×D1111yescharacteristic
408C42D4×D1111yescharacteristic
409C42D4×D1111yescharacteristic
410C11#1739111yescharacteristic, complemented, Sylow
411C23—221no—
412C23—221no—
413C23—221no—
414C23—441no—
415C23—441no—
416C23C22×C4×D1111yescharacteristic
417Q8—42no—
418Q8—42no—
419Q8—224no—
420Q8—224no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—114no—
429C2×C4—114no—
430C2×C4—222no—
431C2×C4—222no—
432C2×C4—221no—
433C2×C4—221no—
434C2×C4—221no—
435C2×C4—221no—
436C2×C4—221no—
437C2×C4—442no—
438C2×C4—442no—
439C2×C4—442no—
440C2×C4—441no—
441C2×C4—441no—
442C2×C4C22⋊C4×D1111yescharacteristic
443C2×C4C22⋊C4×D1111yescharacteristic
444C2×C4C22⋊C4×D1111yescharacteristic
445C2×C4C22⋊C4×D1111yescharacteristic
446C2×C4#6695412yes—
447C2×C4#6696012yes—
448C2×C4C2×D4×D1111yescharacteristic
449C2×C4C2×D4×D1111yescharacteristic
450C8—42no—
451C8—42no—
452C8—442no—
453C8—442no—
454C22—21no—
455C22—21no—
456C22—441no—
457C22—441no—
458C22—441no—
459C22—881no—
460C22—881no—
461C22C2×C22⋊C4×D1111yescharacteristic
462C22C2×#6695411yescharacteristic
463C22C2×#6696011yescharacteristic
464C4—21no—
465C4—21no—
466C4—21no—
467C4—21no—
468C4—42no—
469C4—42no—
470C4—224no—
471C4—224no—
472C4—441no—
473C4—441no—
474C4—441no—
475C4#1062234012yes—
476C4#1062234012yes—
477C2—21no—
478C2—21no—
479C2—881no—
480C2C2×#1062234011yescharacteristic
481C2#1307707811yescharacteristic
482C2#1307709611yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1461C2
socleC22×C11C22×C22⋊C4
prime radicalC23×D11C22×C4
cosocleC22×C4×C11C24
hypercenter#1461D11
hypocenterC11#17391
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1461

Complements

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

NH ≅ G/Ntype
2. #13077699C2semidirect
3. #13077696C2semidirect
5. #13066970C2semidirect
6. #13066940C2semidirect
9. C11×#1461C2semidirect
176. #1461D11semidirect
410. C11#17391semidirect

Maximal subgroups

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

subgroupindex
C2×#106231142
#130776992
#130776962
#130669842
#130669702
#130669402
#130669282
C11×#14612
#1739111