Finite Group Databasebeta

← #14783732

Subgroups — #14783732

Order 2816.

782 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071236C211yesmaximal, characteristic
2#13071232C211yesmaximal, characteristic
3#13070188C212yesmaximal, complemented
4#13070186C212yesmaximal, complemented
5#13070181C212yesmaximal, complemented
6#13070176C212yesmaximal, complemented
7#13068337C211yesmaximal, characteristic
8#13068337C211yesmaximal, characteristic
9C2×#10622189C211yesmaximal, characteristic
10#13068312C211yesmaximal, characteristic
11C11×#1735C211yesmaximal, characteristic
12C23×C8×C11C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C2×#66979C2211yescharacteristic
16C22×C4⋊Dic11C2211yescharacteristic
17C22×C4⋊Dic11C2211yescharacteristic
18C22×#4318C2211yescharacteristic
19#10622590C2212yes—
20#10622589C2212yes—
21#10622586C2212yes—
22#10622586C2212yes—
23#10622559—22no—
24#10622555—22no—
25#10622541—21no—
26#10622541—21no—
27#10622541—21no—
28#10622541—21no—
29C11×#340C2211yescharacteristic
30C11×#340C2211yescharacteristic
31C11×#340C2211yescharacteristic
32C11×#340C2211yescharacteristic
33#10622189C2212yes—
34#10622189C2212yes—
35#10622188C2212yes—
36#10622188C2212yes—
37#10622167C2212yes—
38#10622167C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41C23×C4×C11C2311yescharacteristic
42C23×Dic11—21no—
43C23×Dic11—21no—
44C22×C8×C11—22no—
45C22×C8×C11—22no—
46C22×C8×C11—22no—
47C22×C8×C11C2311yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C11×#117—22no—
50C11×#117—22no—
51C11×#117—22no—
52C11×#117—22no—
53C2×C11×C4⋊C4C2311yescharacteristic
54C2×C11×C4⋊C4C2311yescharacteristic
55C2×C11×C4⋊C4C2311yescharacteristic
56C2×C11×C4⋊C4C2311yescharacteristic
57C2×C11×C22⋊C4—21no—
58C2×C11×C22⋊C4—21no—
59C2×C42×C11—21no—
60C2×C42×C11—21no—
61C2×C22⋊Dic11D412yes—
62#66979—22no—
63#66979—22no—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11—22no—
66C2×C4⋊Dic11—22no—
67C2×C4⋊Dic11—22no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11D411yescharacteristic
70C2×C4⋊Dic11D411yescharacteristic
71C2×C4⋊Dic11Q814yes—
72C2×C4⋊Dic11C2312yes—
73C2×C4⋊Dic11C2312yes—
74C2×Dic11⋊C4—22no—
75C2×Dic11⋊C4—22no—
76C2×Dic11⋊C4—22no—
77C2×Dic11⋊C4—22no—
78C2×C4×Dic11C2312yes—
79C2×#4318—22no—
80C2×#4318—22no—
81C2×#4318—22no—
82C22×C11⋊C8C2312yes—
83C11⋊#95—22no—
84C11⋊#95—22no—
85C11⋊#95—22no—
86C11⋊#95—22no—
87#23749—111nomaximal, Sylow
88C24×C11C2×D411yescharacteristic
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×Q812yes—
95C22×C4×C11#4112yes—
96C22×C4×C11#4112yes—
97C22×C4×C11#4112yes—
98C22×C4×C11#4112yes—
99C22×C4×C11#4112yes—
100C22×C4×C11C2411yescharacteristic
101C22×Dic11—24no—
102C22×Dic11—22no—
103C22×Dic11—22no—
104C22×Dic11—42no—
105C22×Dic11—81no—
106C22×Dic11—81no—
107C22×Dic11—81no—
108C22×Dic11—81no—
109C22×Dic11C2×D412yes—
110C22×Dic11C2×D412yes—
111C2×C8×C11—21no—
112C2×C8×C11—21no—
113C2×C8×C11—21no—
114C2×C8×C11—21no—
115C2×C8×C11—21no—
116C2×C8×C11—21no—
117C2×C8×C11—44no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—21no—
126C11×C22⋊C4—42no—
127C11×C22⋊C4—42no—
128C42×C11—42no—
129C42×C11—42no—
130C22⋊Dic11—24no—
131C4⋊Dic11—24no—
132C4⋊Dic11—22no—
133C4⋊Dic11—22no—
134C4⋊Dic11—22no—
135C4⋊Dic11—22no—
136C4⋊Dic11—22no—
137C4⋊Dic11—42no—
138C4⋊Dic11C2×Q814yes—
139Dic11⋊C4—82no—
140Dic11⋊C4—82no—
141Dic11⋊C4—82no—
142Dic11⋊C4—82no—
143C4×Dic11—22no—
144C4×Dic11—22no—
145#4318—44no—
146C2×C11⋊C8—22no—
147C2×C11⋊C8—22no—
148C2×C11⋊C8—22no—
149#2317—111no—
150#2316—111no—
151#2101—112no—
152#2101—112no—
153#2100—112no—
154#2099—112no—
155#1736—111no—
156#1736—111no—
157#1735D1111yescharacteristic
158C2×#340—111no—
159#1729—111no—
160C23×C11—21no—
161C23×C11—21no—
162C23×C11—21no—
163C23×C11—21no—
164C23×C11C22⋊Q812yes—
165C23×C11#12312yes—
166C23×C11#12412yes—
167C23×C11C22×D411yescharacteristic
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11C22⋊Q812yes—
181C2×C4×C11#12312yes—
182C2×C4×C11#12412yes—
183C2×C4×C11#12514yes—
184C2×C4×C11#12514yes—
185C2×C4×C11#12614yes—
186C2×C4×C11#12614yes—
187C2×C4×C11C22×Q811yescharacteristic
188C2×C4×C11C2×#4111yescharacteristic
189C2×C4×C11C2×#4111yescharacteristic
190C2×C4×C11C2×#4111yescharacteristic
191C2×C4×C11C2×#4111yescharacteristic
192C2×C4×C11C2×#4111yescharacteristic
193C2×Dic11—24no—
194C2×Dic11—22no—
195C2×Dic11—22no—
196C2×Dic11—22no—
197C2×Dic11—22no—
198C2×Dic11—22no—
199C2×Dic11—22no—
200C2×Dic11—42no—
201C2×Dic11—42no—
202C2×Dic11—42no—
203C2×Dic11—42no—
204C2×Dic11—42no—
205C2×Dic11—84no—
206C2×Dic11—84no—
207C8×C11—41no—
208C8×C11—41no—
209C11⋊C8—42no—
210C22×M16—111no—
211C23×C8C2×D1111yescharacteristic
212C2×#117—111no—
213C2×#117C2×D1111yescharacteristic
214C2×#117C2×D1111yescharacteristic
215C22×C4⋊C4—111no—
216C22×C4⋊C4—111no—
217#389—112no—
218#389—112no—
219#389—221no—
220#389—221no—
221#389—221no—
222#389—221no—
223#385—222no—
224#384—112no—
225#382—112no—
226#380—222no—
227#340—112no—
228#340—112no—
229#340—112no—
230#340—112no—
231#340—112no—
232#340—112no—
233#340C2×D1111yescharacteristic
234#340C2×D1111yescharacteristic
235#340C2×D1111yescharacteristic
236#340C2×D1111yescharacteristic
237#336—112no—
238#336—112no—
239C22×C11—22no—
240C22×C11—22no—
241C22×C11—22no—
242C22×C11—22no—
243C22×C11—22no—
244C22×C11—22no—
245C22×C11#40014yes—
246C22×C11C2×C22⋊Q811yescharacteristic
247C22×C11C2×#12311yescharacteristic
248C22×C11C2×#12411yescharacteristic
249C22×C11#57611yescharacteristic
250C22×C11#57711yescharacteristic
251C22×C11#57711yescharacteristic
252C22×C11#57811yescharacteristic
253C4×C11—81no—
254C4×C11—81no—
255C4×C11—81no—
256C4×C11—81no—
257C4×C11#40014yes—
258C4×C11C2×#12511yescharacteristic
259C4×C11C2×#12511yescharacteristic
260C4×C11C2×#12611yescharacteristic
261C4×C11C2×#12611yescharacteristic
262Dic11—44no—
263Dic11—42no—
264Dic11—42no—
265Dic11—82no—
266C23×C4—221no—
267C23×C4—221no—
268C23×C4C22×D1111yescharacteristic
269C2×M16—222no—
270C2×M16—222no—
271C2×M16—222no—
272C22×C8—22no—
273C22×C8—22no—
274C22×C8—22no—
275C22×C8—112no—
276C22×C8C22×D1111yescharacteristic
277C22×C8C22×D1111yescharacteristic
278#117—22no—
279#117—22no—
280#117—22no—
281#117—22no—
282#117—222no—
283#117—222no—
284C2×C4⋊C4—114no—
285C2×C4⋊C4—112no—
286C2×C4⋊C4—111no—
287C2×C4⋊C4—111no—
288C2×C4⋊C4—112no—
289C2×C4⋊C4—222no—
290C2×C4⋊C4—221no—
291C2×C4⋊C4—222no—
292C2×C4⋊C4—222no—
293C2×C4⋊C4—221no—
294C2×C4⋊C4—222no—
295C2×C4⋊C4—222no—
296C2×C4⋊C4—222no—
297C2×C4⋊C4—222no—
298C2×C4⋊C4C22×D1111yescharacteristic
299C2×C4⋊C4C22×D1111yescharacteristic
300C2×C4⋊C4C22×D1111yescharacteristic
301C2×C4⋊C4C22×D1111yescharacteristic
302C2×C22⋊C4—21no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—112no—
305C2×C42—21no—
306C2×C42—21no—
307C2×C42—112no—
308#95—222no—
309#95—222no—
310#95—222no—
311#95—222no—
312C2×C11—24no—
313C2×C11C2×#40011yescharacteristic
314C2×C11#308111yescharacteristic
315C2×C11#308211yescharacteristic
316C2×C11#309811yescharacteristic
317C2×C11#309911yescharacteristic
318C2×C11#313611yescharacteristic
319C2×C11#313711yescharacteristic
320C24D4×D1111yescharacteristic
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—112no—
326C22×C4—112no—
327C22×C4—222no—
328C22×C4—224no—
329C22×C4—222no—
330C22×C4—442no—
331C22×C4—881no—
332C22×C4—881no—
333C22×C4—881no—
334C22×C4—881no—
335C22×C4#433912yes—
336C22×C4#433912yes—
337C22×C4#433912yes—
338C22×C4D4×D1111yescharacteristic
339C22×C4#434112yes—
340C22×C4#434112yes—
341C22×C4Q8×D1112yes—
342C22×C4C23×D1111yescharacteristic
343M16—444no—
344C2×C8—21no—
345C2×C8—21no—
346C2×C8—21no—
347C2×C8—21no—
348C2×C8—21no—
349C2×C8—21no—
350C2×C8—44no—
351C2×C8—222no—
352C2×C8—222no—
353C2×C8—222no—
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—114no—
363C4⋊C4—222no—
364C4⋊C4—222no—
365C4⋊C4—224no—
366C4⋊C4—222no—
367C4⋊C4—222no—
368C4⋊C4—222no—
369C4⋊C4—442no—
370C4⋊C4—882no—
371C4⋊C4—882no—
372C4⋊C4—882no—
373C4⋊C4—882no—
374C22⋊C4—42no—
375C22⋊C4—42no—
376C22⋊C4—224no—
377C42—42no—
378C42—42no—
379C42—222no—
380C42—222no—
381C11#2374911yescharacteristic, complemented, Sylow
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23#6693612yes—
387C23#6693812yes—
388C23#6694912yes—
389C23C2×D4×D1111yescharacteristic
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—222no—
403C2×C4—222no—
404C2×C4—224no—
405C2×C4—222no—
406C2×C4—222no—
407C2×C4—222no—
408C2×C4—222no—
409C2×C4—442no—
410C2×C4—442no—
411C2×C4—442no—
412C2×C4—442no—
413C2×C4—442no—
414C2×C4—884no—
415C2×C4—884no—
416C2×C4#6692914yes—
417C2×C4#6693214yes—
418C2×C4#6693612yes—
419C2×C4#6693812yes—
420C2×C4#6694214yes—
421C2×C4#6694214yes—
422C2×C4#6694912yes—
423C2×C4C2×#433911yescharacteristic
424C2×C4C2×#433911yescharacteristic
425C2×C4C2×#433911yescharacteristic
426C2×C4C2×#434111yescharacteristic
427C2×C4C2×#434111yescharacteristic
428C2×C4C2×Q8×D1111yescharacteristic
429C8—41no—
430C8—41no—
431C8—442no—
432C22—22no—
433C22—22no—
434C22—22no—
435C22—22no—
436C22—22no—
437C22—22no—
438C22#1062227114yes—
439C22C2×#6693611yescharacteristic
440C22C2×#6693811yescharacteristic
441C22C2×#6694911yescharacteristic
442C22#1062330011yescharacteristic
443C22#1062330111yescharacteristic
444C22#1062330111yescharacteristic
445C22#1062330211yescharacteristic
446C4—81no—
447C4—81no—
448C4—81no—
449C4—81no—
450C4—442no—
451C4—442no—
452C4—444no—
453C4—882no—
454C4#1062227114yes—
455C4C2×#6692911yescharacteristic
456C4C2×#6693211yescharacteristic
457C4C2×#6694211yescharacteristic
458C4C2×#6694211yescharacteristic
459C2—24no—
460C2C2×#1062227111yescharacteristic
461C2#1307845011yescharacteristic
462C2#1307846111yescharacteristic
463C2#1307859211yescharacteristic
464C2#1307860311yescharacteristic
465C2#1307897411yescharacteristic
466C2#1307898511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1735C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#1735D11
hypocenterC11#23749
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1735

Complements

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

NH ≅ G/Ntype
3. #13070188C2semidirect
4. #13070186C2semidirect
5. #13070181C2semidirect
6. #13070176C2semidirect
381. C11#23749semidirect

Maximal subgroups

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

subgroupindex
#130712362
#130712322
#130701882
#130701862
#130701812
#130701762
#130683372
C2×#106221892
#130683122
C11×#17352
#2374911