Finite Group Databasebeta

← #14668742

Subgroups — #14668742

Order 2816.

854 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622853C211yesmaximal, characteristic
2#13071107C211yesmaximal, characteristic
3#13066740C214yesmaximal, complemented
4C2×C11×#410C211yesmaximal, characteristic
5C22×C11×#41C2211yescharacteristic
6C2×C11×#117—21no—
7C2×#66979—21no—
8C2×#66979C411yescharacteristic, complemented
9C22×C4×Dic11C411yescharacteristic, complemented
10C11×#410—22no—
11C11×#410C414yescomplemented
12C2×C11×#99—21no—
13C2×C11×#99C2212yes—
14#10622853—22no—
15#10622853C414yescomplemented
16#10622843C412yescomplemented
17#10622834C2212yes—
18#10622833—21no—
19#10622833—21no—
20C2×#66898—21no—
21C2×#66898C2212yes—
22C4×C22⋊Dic11—21no—
23C4×C22⋊Dic11—21no—
24C2×C11×#41—42no—
25C2×C11×#41—41no—
26C2×C11×#41—41no—
27C2×C11×#41C2×C412yes—
28C2×C11×#41C2×C412yes—
29C2×C11×#41D412yes—
30C2×C11×#41Q812yes—
31C22×Q8×C11C2×C411yescharacteristic
32C22×D4×C11D411yescharacteristic
33C22×D4×C11D411yescharacteristic
34C22×D4×C11C2311yescharacteristic
35C23×C4×C11C2×C411yescharacteristic
36C23×C4×C11D411yescharacteristic
37C23×C4×C11D411yescharacteristic
38C23×Dic11—21no—
39C11×#117—24no—
40C11×#117—42no—
41C2×C11×C4⋊C4—41no—
42C2×C11×C22⋊C4—22no—
43C2×C42×C11—41no—
44C2×C22⋊Dic11—22no—
45C2×C22⋊Dic11—21no—
46C2×C22⋊Dic11—22no—
47C2×C22⋊Dic11—22no—
48#66979—24no—
49#66979—42no—
50#66979—41no—
51#66979—41no—
52C2×C4⋊Dic11—41no—
53C2×C4⋊Dic11C2×C412yes—
54C2×C4×Dic11—21no—
55C2×C4×Dic11—21no—
56C2×C4×Dic11—41no—
57C2×C4×Dic11—42no—
58C2×C4×Dic11C2×C412yes—
59C11×#99—24no—
60C11×#99—22no—
61C11×#99C2×C414yescomplemented
62#66898—24no—
63#66898—22no—
64#66898C2×C414yescomplemented
65C11⋊#95—22no—
66C11⋊#95—22no—
67#12581—111nomaximal, Sylow
68C24×C11C22⋊C411yescharacteristic
69C24×C11C2×D411yescharacteristic
70C24×C11C2×D411yescharacteristic
71C11×#41—42no—
72C11×#41—42no—
73C11×#41—42no—
74C11×#41—42no—
75C11×#41—42no—
76C11×#41—42no—
77C11×#41—42no—
78C11×#41—42no—
79C2×Q8×C11—41no—
80C2×Q8×C11—41no—
81C2×Q8×C11C4212yes—
82C2×Q8×C11C4⋊C412yes—
83C2×D4×C11—41no—
84C2×D4×C11—41no—
85C2×D4×C11—41no—
86C2×D4×C11—41no—
87C2×D4×C11—41no—
88C2×D4×C11—41no—
89C2×D4×C11C22⋊C412yes—
90C2×D4×C11C22⋊C412yes—
91C2×D4×C11C4⋊C412yes—
92C2×D4×C11C4⋊C412yes—
93C2×D4×C11C22×C411yescharacteristic
94C2×D4×C11C22×C411yescharacteristic
95C2×D4×C11C2×D411yescharacteristic
96C2×D4×C11C2×Q811yescharacteristic
97C22×C4×C11—22no—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11—22no—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11—22no—
106C22×C4×C11—42no—
107C22×C4×C11C4212yes—
108C22×C4×C11C22⋊C411yescharacteristic
109C22×C4×C11C22⋊C411yescharacteristic
110C22×C4×C11C22⋊C412yes—
111C22×C4×C11C22⋊C412yes—
112C22×C4×C11C22⋊C411yescharacteristic
113C22×C4×C11C4⋊C412yes—
114C22×C4×C11C4⋊C412yes—
115C22×C4×C11C4⋊C412yes—
116C22×C4×C11C22×C411yescharacteristic
117C22×Dic11—22no—
118C22×Dic11—22no—
119C22×Dic11—42no—
120C22×Dic11—42no—
121C22×Dic11—44no—
122C11×C4⋊C4—44no—
123C11×C22⋊C4—24no—
124C11×C22⋊C4—42no—
125C42×C11—44no—
126C22⋊Dic11—24no—
127C22⋊Dic11—42no—
128C22⋊Dic11—42no—
129C22⋊Dic11—44no—
130C22⋊Dic11—44no—
131C4⋊Dic11—42no—
132C4⋊Dic11—44no—
133C4×Dic11—42no—
134C4×Dic11—44no—
135C4×Dic11—42no—
136C4×Dic11—41no—
137C4×Dic11—41no—
138C2×#410—111no—
139C2×#410D1111yescharacteristic
140#2297—111no—
141#1393—114no—
142C23×C11—21no—
143C23×C11—21no—
144C23×C11—21no—
145C23×C11—21no—
146C23×C11—21no—
147C23×C11—21no—
148C23×C11—42no—
149C23×C11—42no—
150C23×C11—42no—
151C23×C11#9512yes—
152C23×C11C2×C22⋊C411yescharacteristic
153C23×C11C2×C22⋊C411yescharacteristic
154C23×C11C2×C22⋊C411yescharacteristic
155C23×C11C2×C4⋊C411yescharacteristic
156C23×C11C2×C4⋊C411yescharacteristic
157Q8×C11—42no—
158Q8×C11—42no—
159D4×C11—42no—
160D4×C11—42no—
161D4×C11—42no—
162D4×C11—42no—
163D4×C11—41no—
164D4×C11—41no—
165D4×C11—41no—
166D4×C11—41no—
167C2×C4×C11—21no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—44no—
186C2×C4×C11—84no—
187C2×C4×C11#9512yes—
188C2×C4×C11#9512yes—
189C2×C4×C11#9512yes—
190C2×C4×C11#9912yes—
191C2×C4×C11#9911yescharacteristic
192C2×C4×C11#9911yescharacteristic
193C2×C4×C11C2×C4211yescharacteristic
194C2×C4×C11C2×C4⋊C411yescharacteristic
195C2×Dic11—24no—
196C2×Dic11—42no—
197C2×Dic11—48no—
198C2×Dic11—42no—
199C2×Dic11—44no—
200C2×Dic11—42no—
201C2×Dic11—42no—
202C2×Dic11—42no—
203C2×Dic11—84no—
204C22×#41C2×D1111yescharacteristic
205C2×#117—21no—
206C2×#117—111no—
207C2×#117—221no—
208C22×C42—111no—
209#410—22no—
210#410—114no—
211#410—222no—
212#410Dic1114yescomplemented
213C2×#99—21no—
214C2×#99—112no—
215C2×#99—221no—
216C2×#99C2×D1112yes—
217#391—112no—
218#390—112no—
219#386—221no—
220#386—221no—
221C4×C22⋊C4—221no—
222C4×C22⋊C4—221no—
223C22×C11—22no—
224C22×C11—21no—
225C22×C11—22no—
226C22×C11—21no—
227C22×C11—21no—
228C22×C11—21no—
229C22×C11—42no—
230C22×C11—41no—
231C22×C11—41no—
232C22×C11—41no—
233C22×C11—41no—
234C22×C11—42no—
235C22×C11—42no—
236C22×C11—42no—
237C22×C11—42no—
238C22×C11—81no—
239C22×C11—81no—
240C22×C11C2×#9511yescharacteristic
241C22×C11C2×#9911yescharacteristic
242C22×C11C2×#9911yescharacteristic
243C4×C11—22no—
244C4×C11—22no—
245C4×C11—21no—
246C4×C11—21no—
247C4×C11—84no—
248C4×C11#34212yes—
249C4×C11#34212yes—
250Dic11—44no—
251Dic11—84no—
252Dic11—82no—
253C2×#41—42no—
254C2×#41—41no—
255C2×#41—41no—
256C2×#41Dic2212yes—
257C2×#41C4×D1112yes—
258C2×#41C2×Dic1112yes—
259C2×#41C22⋊D1112yes—
260C22×Q8C4×D1111yescharacteristic
261C22×D4D4411yescharacteristic
262C22×D4C22⋊D1111yescharacteristic
263C22×D4C22×D1111yescharacteristic
264C23×C4—221no—
265C23×C4C4×D1111yescharacteristic
266C23×C4D4411yescharacteristic
267C23×C4C22⋊D1111yescharacteristic
268#117—24no—
269#117—42no—
270#117—224no—
271#117—442no—
272#117—441no—
273#117—441no—
274C2×C4⋊C4—41no—
275C2×C4⋊C4—112no—
276C2×C4⋊C4—441no—
277C2×C22⋊C4—22no—
278C2×C22⋊C4—222no—
279C2×C22⋊C4—221no—
280C2×C22⋊C4—222no—
281C2×C22⋊C4—222no—
282C2×C42—41no—
283C2×C42—112no—
284C2×C42—221no—
285C2×C42—221no—
286C2×C42—441no—
287C2×C42—442no—
288#99—24no—
289#99—22no—
290#99—114no—
291#99—224no—
292#99—222no—
293#99C2×Dic1114yescomplemented
294#95—222no—
295#95—222no—
296C2×C11—21no—
297C2×C11—21no—
298C2×C11—41no—
299C2×C11—41no—
300C2×C11—42no—
301C2×C11—41no—
302C2×C11—41no—
303C2×C11C2×#34211yescharacteristic
304C2×C11#212612yes—
305C24(C2×D11)⋊C411yescharacteristic
306C24C2×D4411yescharacteristic
307C24C2×C22⋊D1111yescharacteristic
308#41—42no—
309#41—42no—
310#41—42no—
311#41—42no—
312#41—42no—
313#41—42no—
314#41—42no—
315#41—42no—
316C2×Q8—41no—
317C2×Q8—41no—
318C2×Q8C4×Dic1112yes—
319C2×Q8Dic11⋊C412yes—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4—41no—
325C2×D4—41no—
326C2×D4Dic11⋊C412yes—
327C2×D4C4⋊Dic1112yes—
328C2×D4(C2×D11)⋊C412yes—
329C2×D4C22⋊Dic1112yes—
330C2×D4C2×Dic2211yescharacteristic
331C2×D4C2×C4×D1111yescharacteristic
332C2×D4C22×Dic1111yescharacteristic
333C2×D4C2×C22⋊D1111yescharacteristic
334C22×C4—22no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—22no—
338C22×C4—21no—
339C22×C4—22no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—42no—
344C22×C4—222no—
345C22×C4—222no—
346C22×C4—444no—
347C22×C4—442no—
348C22×C4—442no—
349C22×C4C4×Dic1112yes—
350C22×C4Dic11⋊C412yes—
351C22×C4Dic11⋊C412yes—
352C22×C4C4⋊Dic1112yes—
353C22×C4(C2×D11)⋊C411yescharacteristic
354C22×C4(C2×D11)⋊C411yescharacteristic
355C22×C4(C2×D11)⋊C412yes—
356C22×C4(C2×D11)⋊C411yescharacteristic
357C22×C4C22⋊Dic1112yes—
358C22×C4C2×C4×D1111yescharacteristic
359C4⋊C4—44no—
360C4⋊C4—442no—
361C4⋊C4—444no—
362C22⋊C4—24no—
363C22⋊C4—42no—
364C22⋊C4—224no—
365C22⋊C4—444no—
366C22⋊C4—444no—
367C22⋊C4—442no—
368C22⋊C4—442no—
369C42—44no—
370C42—442no—
371C42—444no—
372C42—442no—
373C42—441no—
374C42—441no—
375C11#1258111yescharacteristic, complemented, Sylow
376C23—21no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—42no—
383C23—42no—
384C23—42no—
385C23C11⋊#9512yes—
386C23C2×Dic11⋊C411yescharacteristic
387C23C2×C4⋊Dic1111yescharacteristic
388C23C2×(C2×D11)⋊C411yescharacteristic
389C23C2×(C2×D11)⋊C411yescharacteristic
390C23C2×C22⋊Dic1111yescharacteristic
391Q8—42no—
392Q8—42no—
393D4—42no—
394D4—42no—
395D4—42no—
396D4—42no—
397D4—41no—
398D4—41no—
399D4—41no—
400D4—41no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—44no—
420C2×C4—84no—
421C2×C4—224no—
422C2×C4—442no—
423C2×C4—448no—
424C2×C4—442no—
425C2×C4—444no—
426C2×C4—442no—
427C2×C4—442no—
428C2×C4—442no—
429C2×C4—884no—
430C2×C4#6687011yescharacteristic
431C2×C4#6687012yes—
432C2×C4#6687011yescharacteristic
433C2×C4C11⋊#9512yes—
434C2×C4C11⋊#9512yes—
435C2×C4C11⋊#9512yes—
436C2×C4C2×C4×Dic1111yescharacteristic
437C2×C4C2×Dic11⋊C411yescharacteristic
438C22—22no—
439C22—21no—
440C22—21no—
441C22—22no—
442C22—21no—
443C22—21no—
444C22—42no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—41no—
449C22—42no—
450C22—42no—
451C22—42no—
452C22—42no—
453C22—81no—
454C22—81no—
455C22C2×#6687011yescharacteristic
456C22C2×#6687011yescharacteristic
457C22C2×C11⋊#9511yescharacteristic
458C4—22no—
459C4—22no—
460C4—21no—
461C4—21no—
462C4—84no—
463C4—444no—
464C4—884no—
465C4—882no—
466C4#1062216512yes—
467C4#1062216512yes—
468C2—21no—
469C2—21no—
470C2—41no—
471C2—41no—
472C2—42no—
473C2—41no—
474C2—41no—
475C2C2×#1062216511yescharacteristic
476C2#1307027912yes—
subgroupG/H
centerC2×C4#66870
commutatorC2×C4×C11C2×C42
FrattiniC22×D4C22×D11
FittingC2×C11×#410C2
socleC22×C11C2×#99
prime radicalC22×C11×#41C22
cosocleC22×D4×C11C23
hypercenterC2×#410D11
hypocenterC11#12581
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×#41 ◁ C2×#410

Complements

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

NH ≅ G/Ntype
3. #13066740C2semidirect
8. C2×#66979C4semidirect
9. C22×C4×Dic11C4semidirect
11. C11×#410C4semidirect
15. #10622853C4semidirect
16. #10622843C4semidirect
61. C11×#99C2×C4semidirect
64. #66898C2×C4semidirect
212. #410Dic11semidirect
293. #99C2×Dic11semidirect
375. C11#12581semidirect

Maximal subgroups

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

subgroupindex
C2×#106228532
#130711072
#130667402
C2×C11×#4102
#1258111