Finite Group Databasebeta

← #14648331

Subgroups — #14648331

Order 2816.

620 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4325C211yesmaximal, characteristic
2C2×#10622447C211yesmaximal, characteristic
3#13069553C211yesmaximal, characteristic, complemented
4C2×#10622097C211yesmaximal, characteristic
5#13066450C211yesmaximal, characteristic, complemented
6C11⋊#1273C211yesmaximal, characteristic, complemented
7C2×C11×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×C4×Q8×C11C2211yescharacteristic
9C22×#4325C411yescharacteristic
10C22×C8×D11—21no—
11C2×C4×D44C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13C2×C4×C8×C11C2211yescharacteristic
14C2×#66899C411yescharacteristic
15C2×(C2×D11)⋊C8—21no—
16C4×#4325—22no—
17C4×#4325—22no—
18C2×#66873C411yescharacteristic
19C2×#66872C411yescharacteristic
20C2×C4⋊(C11⋊C8)C2211yescharacteristic
21C2×C4×C11⋊C8C2211yescharacteristic
22C2×C4×C11⋊C8C2211yescharacteristic
23#10622447—22no—
24#10622447—22no—
25C11×Q8⋊C8—22no—
26#10622162—21no—
27#10622162—21no—
28#10622097—22no—
29C22×Q8×C11C2×C411yescharacteristic
30C22×D44C2×C411yescharacteristic
31C22×C4×D11—21no—
32C22×C8×C11—21no—
33C22×C8×C11—21no—
34C4×Q8×C11—21no—
35C4×Q8×C11—21no—
36C4×Q8×C11—21no—
37C4×Q8×C11—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4C2×C411yescharacteristic
40C2×C42×C11—21no—
41C2×C42×C11C2311yescharacteristic
42C2×#4325—22no—
43C2×#4325—22no—
44C2×#4325C814yescomplemented
45C2×(C2×D11)⋊C4—21no—
46C2×C4⋊Dic11C2×C411yescharacteristic
47C22×C11⋊C8—21no—
48C22×C11⋊C8C2×C411yescharacteristic
49C22×C11⋊C8C2×C411yescharacteristic
50C22×C11⋊C8D411yescharacteristic
51C22×C11⋊C8D411yescharacteristic
52C2×C8×D11—24no—
53C2×C8×D11—42no—
54C2×C8×D11—42no—
55C4×D44—21no—
56C4×D44—21no—
57C4×D44D412yes—
58C4×D44D412yes—
59C11×C4⋊C8—21no—
60C11×C4⋊C8D412yes—
61C4×C8×C11—21no—
62C4×C8×C11—21no—
63#66899—22no—
64(C2×D11)⋊C8—24no—
65#66873—22no—
66#66872—22no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)—21no—
69C4×C11⋊C8—21no—
70C4×C11⋊C8—21no—
71C4×C11⋊C8—21no—
72C4×C11⋊C8—21no—
73#8945—111nomaximal, Sylow
74C23×D11—21no—
75C2×Q8×C11—21no—
76C2×Q8×C11—21no—
77C2×Q8×C11—21no—
78C2×Q8×C11—21no—
79C2×Q8×C11—21no—
80C2×Q8×C11C2×C812yescomplemented
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11C22×C411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11#4111yescharacteristic
86C22×Dic11—21no—
87C2×D44—21no—
88C2×D44—21no—
89C2×D44—21no—
90C2×D44C22⋊C412yes—
91C2×D44C2×C812yes—
92C2×D44M1612yes—
93C2×C4×D11—22no—
94C2×C4×D11—22no—
95C2×C4×D11—41no—
96C2×C4×D11—41no—
97C2×C4×D11—41no—
98C2×C4×D11—41no—
99C2×C8×C11—22no—
100C2×C8×C11—22no—
101C2×C8×C11—41no—
102C2×C8×C11—41no—
103C2×C8×C11—41no—
104C2×C8×C11—41no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C42×C11—41no—
110C42×C11—41no—
111C42×C11C2×D411yescharacteristic
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C42×C11#4111yescharacteristic
115#4325—28no—
116(C2×D11)⋊C4—22no—
117(C2×D11)⋊C4—22no—
118C4⋊Dic11—21no—
119C4⋊Dic11C22⋊C412yes—
120C2×C11⋊C8—21no—
121C2×C11⋊C8—21no—
122C2×C11⋊C8—21no—
123C2×C11⋊C8—21no—
124C2×C11⋊C8—21no—
125C2×C11⋊C8—21no—
126C2×C11⋊C8—21no—
127C2×C11⋊C8—21no—
128C2×C11⋊C8—21no—
129C2×C11⋊C8—21no—
130C2×C11⋊C8—41no—
131C2×C11⋊C8—41no—
132C2×C11⋊C8—41no—
133C2×C11⋊C8C2×C812yescomplemented
134C2×C11⋊C8SD1612yescomplemented
135C8×D11—48no—
136C2×C4×SD16—111no—
137C2×C8×D4—111no—
138#1984—111no—
139C2×Q8⋊C8D1111yescharacteristic, complemented
140C2×D4⋊C8—111no—
141#1277—111no—
142#1273—111no—
143C23×C11C4×D411yescharacteristic
144C22×D11—22no—
145C22×D11—22no—
146C22×D11—22no—
147C22×D11—41no—
148C22×D11—41no—
149C22×D11—41no—
150C22×D11—41no—
151Q8×C11—22no—
152Q8×C11—22no—
153Q8×C11—41no—
154Q8×C11—41no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—22no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11C2×C22⋊C411yescharacteristic
164C2×C4×C11C4×D411yescharacteristic
165C2×C4×C11#12011yescharacteristic
166C2×C4×C11#12111yescharacteristic
167C2×C4×C11#12111yescharacteristic
168C2×C4×C11#12311yescharacteristic
169C2×C4×C11C22×C811yescharacteristic
170C2×C4×C11C2×M1611yescharacteristic
171C2×C4×C11#13111yescharacteristic
172C2×C4×C11#13111yescharacteristic
173C2×C4×C11C2×SD1611yescharacteristic
174C2×C4×C11#13511yescharacteristic
175C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
176C2×C4×C11#13711yescharacteristic
177C2×Dic11—22no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180D44—22no—
181D44—22no—
182D44—22no—
183D44C22⋊C814yes—
184C4×D11—42no—
185C4×D11—42no—
186C4×D11—42no—
187C4×D11—42no—
188C8×C11—42no—
189C8×C11—42no—
190C11⋊C8—22no—
191C11⋊C8—22no—
192C11⋊C8—41no—
193C11⋊C8—41no—
194C11⋊C8—81no—
195C22×SD16—111no—
196C23×C8—221no—
197C2×C4×Q8C2×D1111yescharacteristic
198C2×C4×D4—111no—
199C4×SD16—222no—
200C4×SD16—222no—
201C8×D4—222no—
202C8×D4—222no—
203C2×#106—111no—
204C2×C4⋊C8—111no—
205C2×C4⋊C8C2×D1111yescharacteristic
206C2×#103—111no—
207C2×#102—111no—
208C2×C22⋊C8—221no—
209C2×C4×C8—111no—
210C2×C4×C8—111no—
211C2×C4×C8C2×D1111yescharacteristic
212#336—221no—
213#336—221no—
214Q8⋊C8—22no—
215D4⋊C8—222no—
216C22×C11#38611yescharacteristic
217C22×C11C8×D411yescharacteristic
218C22×C11#43511yescharacteristic
219C22×C11C4×SD1611yescharacteristic
220C22×C11#44011yescharacteristic
221C22×C11#44311yescharacteristic
222C22×C11#44411yescharacteristic
223C2×D11—24no—
224C2×D11—42no—
225C2×D11—42no—
226C2×D11—42no—
227C2×D11—42no—
228C2×D11—42no—
229C2×D11—42no—
230C4×C11—21no—
231C4×C11—21no—
232C4×C11—42no—
233C4×C11—81no—
234C4×C11C2×C22⋊C811yescharacteristic
235C4×C11#40811yescharacteristic
236C4×C11C8×D411yescharacteristic
237C4×C11#43511yescharacteristic
238C4×C11#45011yescharacteristic
239C4×C11#45211yescharacteristic
240C4×C11#46111yescharacteristic
241C4×C11#46311yescharacteristic
242Dic11—42no—
243C22×Q8C4×D1111yescharacteristic
244C22×D4—111no—
245C23×C4—221no—
246C2×SD16—114no—
247C2×SD16—222no—
248C2×SD16—222no—
249C22×C8—21no—
250C22×C8—21no—
251C22×C8—111no—
252C22×C8—111no—
253C22×C8—111no—
254C22×C8—111no—
255C22×C8—224no—
256C22×C8—221no—
257C22×C8—442no—
258C22×C8—442no—
259C4×Q8—21no—
260C4×Q8—21no—
261C4×Q8—21no—
262C4×Q8—21no—
263C4×D4—112no—
264C4×D4—112no—
265C4×D4—221no—
266C4×D4—221no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—111no—
269C2×C4⋊C4C4×D1111yescharacteristic
270C2×C22⋊C4—221no—
271C2×C42—21no—
272C2×C42C22×D1111yescharacteristic
273#106—222no—
274C4⋊C8—21no—
275C4⋊C8—221no—
276C4⋊C8—221no—
277C4⋊C8C22⋊D1112yes—
278#103—222no—
279#102—222no—
280C22⋊C8—224no—
281C4×C8—21no—
282C4×C8—21no—
283C4×C8—221no—
284C4×C8—221no—
285C4×C8—221no—
286C4×C8—221no—
287C2×C11C8×SD1611yescharacteristic
288C2×C11SD16⋊C811yescharacteristic
289C2×C11#158211yescharacteristic
290C2×C11#158511yescharacteristic
291C2×C11#186911yescharacteristic
292C2×C11#187611yescharacteristic
293C2×C11#187711yescharacteristic
294D11—44no—
295C24—221no—
296C2×Q8—21no—
297C2×Q8—21no—
298C2×Q8—21no—
299C2×Q8—21no—
300C2×Q8—21no—
301C2×Q8C8×D1112yescomplemented
302C2×D4—112no—
303C2×D4—112no—
304C2×D4—112no—
305C2×D4—221no—
306C2×D4—221no—
307C2×D4—221no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—221no—
311C22×C4—222no—
312C22×C4—222no—
313C22×C4—441no—
314C22×C4—441no—
315C22×C4—441no—
316C22×C4—441no—
317C22×C4C2×C4×D1111yescharacteristic
318C22×C4D4×D1111yescharacteristic
319C22×C4#434111yescharacteristic
320SD16—228no—
321C2×C8—22no—
322C2×C8—22no—
323C2×C8—41no—
324C2×C8—41no—
325C2×C8—41no—
326C2×C8—41no—
327C2×C8—112no—
328C2×C8—112no—
329C2×C8—221no—
330C2×C8—221no—
331C2×C8—221no—
332C2×C8—221no—
333C2×C8—221no—
334C2×C8—221no—
335C2×C8—221no—
336C2×C8—221no—
337C2×C8—221no—
338C2×C8—221no—
339C2×C8—448no—
340C2×C8—441no—
341C2×C8—441no—
342C2×C8—441no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4—112no—
348C4⋊C4—221no—
349C22⋊C4—222no—
350C22⋊C4—222no—
351C42—41no—
352C42—41no—
353C42#433911yescharacteristic
354C42D4×D1111yescharacteristic
355C42D4×D1111yescharacteristic
356C42C2×C22⋊D1111yescharacteristic
357C11#894511yescharacteristic, complemented, Sylow
358C23—222no—
359C23—222no—
360C23—222no—
361C23—441no—
362C23—441no—
363C23—441no—
364C23—441no—
365C23(C22⋊D11)⋊C411yescharacteristic
366Q8—22no—
367Q8—22no—
368Q8—41no—
369Q8—41no—
370D4—114no—
371D4—222no—
372D4—222no—
373D4—222no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—22no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—222no—
383C2×C4—441no—
384C2×C4—441no—
385C2×C4—442no—
386C2×C4—442no—
387C2×C4—442no—
388C2×C4—442no—
389C2×C4C22⋊C4×D1111yescharacteristic
390C2×C4#6693611yescharacteristic
391C2×C4#6693711yescharacteristic
392C2×C4C2×C8×D1111yescharacteristic
393C2×C4#6695411yescharacteristic
394C2×C4M16×D1111yescharacteristic
395C2×C4#6696011yescharacteristic
396C2×C4SD16×D1111yescharacteristic
397C2×C4#6696711yescharacteristic
398C2×C4#6697111yescharacteristic
399C2×C4#6697211yescharacteristic
400C2×C4C4×C22⋊D1111yescharacteristic
401C2×C4#6699011yescharacteristic
402C2×C4#6699111yescharacteristic
403C8—42no—
404C8—42no—
405C8—222no—
406C8—222no—
407C8—441no—
408C8—441no—
409C8—881no—
410C22—224no—
411C22—442no—
412C22—442no—
413C22—442no—
414C22—442no—
415C22—442no—
416C22—442no—
417C22(C22⋊D11)⋊C811yescharacteristic
418C22#1062234111yescharacteristic
419C22#1062240111yescharacteristic
420C22#1062243011yescharacteristic
421C22#1062243611yescharacteristic
422C22#1062243711yescharacteristic
423C22#1062256911yescharacteristic
424C4—21no—
425C4—21no—
426C4—42no—
427C4—81no—
428C4—442no—
429C4D11×C22⋊C811yescharacteristic
430C4#1062234011yescharacteristic
431C4#1062243111yescharacteristic
432C4#1062243211yescharacteristic
433C4C8×C22⋊D1111yescharacteristic
434C4#1062274011yescharacteristic
435C4#1062278211yescharacteristic
436C4#1062280011yescharacteristic
437C2—444no—
438C2#1306741311yescharacteristic
439C2#1306743111yescharacteristic
440C2#1306745511yescharacteristic
441C2#1306747611yescharacteristic
442C2#1306890511yescharacteristic
443C2#1306894011yescharacteristic
444C2#1306894711yescharacteristic
subgroupG/H
centerC22×C4D4×D11
commutatorC2×C4×C11C22×C8
FrattiniC2×C42C22×D11
FittingC2×C11×Q8⋊C8C2
socleC23×C11C4×D4
prime radicalC22×D44C2×C4
cosocleC2×C42×C11C23
hypercenterC2×Q8⋊C8D11
hypocenterC11#8945
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
3. #13069553C2semidirect
5. #13066450C2semidirect
6. C11⋊#1273C2semidirect
7. C2×C11×Q8⋊C8C2semidirect
44. C2×#4325C8semidirect
80. C2×Q8×C11C2×C8semidirect
133. C2×C11⋊C8C2×C8semidirect
134. C2×C11⋊C8SD16semidirect
139. C2×Q8⋊C8D11semidirect
301. C2×Q8C8×D11semidirect
357. C11#8945semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43252
C2×#106224472
#130695532
C2×#106220972
#130664502
C11⋊#12732
C2×C11×Q8⋊C82
#894511