Finite Group Databasebeta

← #14661668

Subgroups — #14661668

Order 2816.

778 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622537C211yesmaximal, characteristic
2C2×#10622168C212yesmaximal
3C2×#10622168C212yesmaximal
4#13068310C211yesmaximal, characteristic
5C2×C11×#389C211yesmaximal, characteristic
6C22×C11×C4⋊C4C412yes—
7C22×C11×C4⋊C4C2211yescharacteristic
8C22×C11×C4⋊C4C2211yescharacteristic
9C22×C42×C11C2211yescharacteristic
10C22×#4318C2212yes—
11C22×#4318C2212yes—
12C11×#389—21no—
13C11×#389—21no—
14C11×#389—21no—
15C11×#389—21no—
16C2×C11×#95C412yes—
17#10622537—24no—
18C2×C4⋊(C11⋊C8)—21no—
19C2×C4⋊(C11⋊C8)—21no—
20#10622168—24no—
21#10622168—24no—
22#10622162—21no—
23#10622162—21no—
24C23×C4×C11C2×C411yescharacteristic
25C23×C4×C11C2×C411yescharacteristic
26C23×C4×C11C2×C412yes—
27C23×C4×C11C2×C412yes—
28C23×C4×C11C2311yescharacteristic
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—22no—
34C2×C11×C4⋊C4—22no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—22no—
38C2×C11×C4⋊C4—22no—
39C2×C11×C4⋊C4—44no—
40C2×C11×C4⋊C4D412yes—
41C2×C11×C4⋊C4Q812yes—
42C2×C42×C11—22no—
43C2×C42×C11—22no—
44C2×C42×C11D411yescharacteristic
45C2×C42×C11D411yescharacteristic
46C2×C42×C11D411yescharacteristic
47C2×C42×C11D411yescharacteristic
48C2×#4318—22no—
49C2×#4318—22no—
50C2×#4318—22no—
51C2×#4318—22no—
52C2×#4318—22no—
53C2×#4318—22no—
54C2×#4318—22no—
55C2×#4318—22no—
56C2×#4318—22no—
57C2×#4318—22no—
58C2×#4318D414yes—
59C2×#4318Q814yes—
60C22×C11⋊C8—22no—
61C22×C11⋊C8—22no—
62C11×#95—22no—
63C11×#95—22no—
64C4⋊(C11⋊C8)—24no—
65C4⋊(C11⋊C8)—24no—
66#11204—111nomaximal, Sylow
67C24×C11C22×C411yescharacteristic
68C22×C4×C11—22no—
69C22×C4×C11—22no—
70C22×C4×C11—22no—
71C22×C4×C11—22no—
72C22×C4×C11—22no—
73C22×C4×C11—22no—
74C22×C4×C11—22no—
75C22×C4×C11—24no—
76C22×C4×C11—41no—
77C22×C4×C11—41no—
78C22×C4×C11—42no—
79C22×C4×C11—42no—
80C22×C4×C11—42no—
81C22×C4×C11—42no—
82C22×C4×C11C22⋊C411yescharacteristic
83C22×C4×C11C22⋊C411yescharacteristic
84C22×C4×C11C22⋊C411yescharacteristic
85C22×C4×C11C22⋊C411yescharacteristic
86C22×C4×C11C4⋊C414yes—
87C22×C4×C11C2×D412yes—
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×Q812yes—
92C22×C4×C11C2×Q811yescharacteristic
93C22×C4×C11#4111yescharacteristic
94C22×C4×C11#4111yescharacteristic
95C22×C4×C11#4112yes—
96C22×C4×C11#4112yes—
97C11×C4⋊C4—22no—
98C11×C4⋊C4—22no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—44no—
102C11×C4⋊C4—44no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—42no—
105C11×C4⋊C4—41no—
106C42×C11—21no—
107C42×C11—21no—
108C42×C11—22no—
109C42×C11—22no—
110C42×C11—21no—
111C42×C11—21no—
112#4318—24no—
113#4318—24no—
114#4318—24no—
115#4318—24no—
116#4318—42no—
117#4318—42no—
118#4318—42no—
119#4318—42no—
120C2×C11⋊C8—24no—
121C2×C11⋊C8—24no—
122C2×C11⋊C8—42no—
123C2×C11⋊C8—42no—
124C2×C11⋊C8—42no—
125C2×C11⋊C8—42no—
126C2×#423—111no—
127C2×#389D1111yescharacteristic
128C2×#343—112no—
129C2×#343—112no—
130#1728—111no—
131C23×C11—21no—
132C23×C11—21no—
133C23×C11—21no—
134C23×C11—21no—
135C23×C11C2×C22⋊C411yescharacteristic
136C23×C11C2×C4⋊C411yescharacteristic
137C23×C11#11711yescharacteristic
138C23×C11C4×D412yes—
139C23×C11C4×Q812yes—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—24no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—44no—
152C2×C4×C11—44no—
153C2×C4×C11—44no—
154C2×C4×C11—42no—
155C2×C4×C11—42no—
156C2×C4×C11—44no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
159C2×C4×C11—42no—
160C2×C4×C11—84no—
161C2×C4×C11#10012yes—
162C2×C4×C11#10112yes—
163C2×C4×C11#12011yescharacteristic
164C2×C4×C11#12112yes—
165C2×C4×C11#12111yescharacteristic
166C2×C4×C11#12111yescharacteristic
167C2×C4×C11#12112yes—
168C2×C4×C11C22⋊Q812yes—
169C2×C4×C11C22⋊Q812yes—
170C2×C4×C11C22⋊Q811yescharacteristic
171C2×C4×C11C22⋊Q811yescharacteristic
172C2×C4×C11C22⋊Q812yes—
173C2×C4×C11#12312yes—
174C2×C4×C11#12311yescharacteristic
175C2×C4×C11#12411yescharacteristic
176C2×C4×C11#12512yes—
177C2×C4×C11#12512yes—
178C2×C4×C11#12612yes—
179C2×C4×C11C4⋊Q812yes—
180C2×C4×C11C4⋊Q811yescharacteristic
181C11⋊C8—44no—
182C11⋊C8—44no—
183C22×M16—112no—
184C22×M16—112no—
185C22×C4⋊C4Dic1112yes—
186C22×C4⋊C4C2×D1111yescharacteristic
187C22×C4⋊C4C2×D1111yescharacteristic
188C22×C42C2×D1111yescharacteristic
189#423—224no—
190C2×C4⋊C8—221no—
191C2×C4⋊C8—221no—
192#389—21no—
193#389—21no—
194#389—21no—
195#389—21no—
196C2×#95Dic1112yes—
197#343—224no—
198#343—224no—
199#336—221no—
200#336—221no—
201C22×C11—21no—
202C22×C11—21no—
203C22×C11—21no—
204C22×C11—21no—
205C22×C11—22no—
206C22×C11—22no—
207C22×C11—22no—
208C22×C11—22no—
209C22×C11#38011yescharacteristic
210C22×C11#38611yescharacteristic
211C22×C11#38712yes—
212C22×C11#38912yes—
213C22×C11#39111yescharacteristic
214C22×C11C2×#10011yescharacteristic
215C22×C11C2×#10111yescharacteristic
216C22×C11#41311yescharacteristic
217C22×C11#41311yescharacteristic
218C4×C11—22no—
219C4×C11—22no—
220C4×C11—44no—
221C4×C11—41no—
222C4×C11—41no—
223C4×C11—82no—
224C4×C11#39411yescharacteristic
225C4×C11#39511yescharacteristic
226C4×C11#39612yes—
227C4×C11#39811yescharacteristic
228C4×C11#39812yes—
229C4×C11#40011yescharacteristic
230C23×C4C2×Dic1111yescharacteristic
231C23×C4C2×Dic1111yescharacteristic
232C23×C4C2×Dic1112yes—
233C23×C4C2×Dic1112yes—
234C23×C4C22×D1111yescharacteristic
235C2×M16—114no—
236C2×M16—114no—
237C2×M16—222no—
238C2×M16—222no—
239C2×M16—222no—
240C2×M16—222no—
241C2×M16—222no—
242C2×M16—222no—
243C2×M16—222no—
244C2×M16—222no—
245C2×M16—222no—
246C2×M16—222no—
247C22×C8—222no—
248C22×C8—222no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—44no—
260C2×C4⋊C4Dic2212yes—
261C2×C4⋊C4D4412yes—
262C2×C42—22no—
263C2×C42—22no—
264C2×C42C22⋊D1111yescharacteristic
265C2×C42C22⋊D1111yescharacteristic
266C2×C42C22⋊D1111yescharacteristic
267C2×C42C22⋊D1111yescharacteristic
268C4⋊C8—224no—
269C4⋊C8—224no—
270#95—22no—
271#95—22no—
272C2×C11—22no—
273C2×C11—22no—
274C2×C11#144111yescharacteristic
275C2×C11#180011yescharacteristic
276C2×C11#180111yescharacteristic
277C2×C11#190011yescharacteristic
278C2×C11#190111yescharacteristic
279C2×C11#199711yescharacteristic
280C2×C11#199811yescharacteristic
281C24C22×Dic1111yescharacteristic
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—24no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—42no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4—42no—
296C22×C4C4⋊Dic1114yes—
297C22×C4C22⋊Dic1111yescharacteristic
298C22×C4C22⋊Dic1111yescharacteristic
299C22×C4C22⋊Dic1111yescharacteristic
300C22×C4C22⋊Dic1111yescharacteristic
301C22×C4C2×Dic2211yescharacteristic
302C22×C4C2×D4411yescharacteristic
303C22×C4#433911yescharacteristic
304C22×C4#433911yescharacteristic
305C22×C4D4×D1112yes—
306C22×C4#434112yes—
307C22×C4Q8×D1112yes—
308C22×C4#434312yes—
309C22×C4C2×C22⋊D1111yescharacteristic
310C22×C4C2×C22⋊D1111yescharacteristic
311M16—224no—
312M16—224no—
313M16—224no—
314M16—224no—
315M16—442no—
316M16—442no—
317M16—442no—
318M16—442no—
319C2×C8—224no—
320C2×C8—224no—
321C2×C8—442no—
322C2×C8—442no—
323C2×C8—442no—
324C2×C8—442no—
325C4⋊C4—22no—
326C4⋊C4—22no—
327C4⋊C4—22no—
328C4⋊C4—22no—
329C4⋊C4—44no—
330C4⋊C4—44no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—42no—
334C42—21no—
335C42—21no—
336C42—21no—
337C42—21no—
338C42—22no—
339C42—22no—
340C11#1120411yescharacteristic, complemented, Sylow
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23C2×C4⋊Dic1111yescharacteristic
346C23#6697911yescharacteristic
347C23D4×Dic1112yes—
348C23Q8×Dic1112yes—
349C23C2×C22⋊Dic1111yescharacteristic
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—24no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—44no—
362C2×C4—44no—
363C2×C4—44no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—44no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—84no—
371C2×C4#6689712yes—
372C2×C4#6690012yes—
373C2×C4#6694112yes—
374C2×C4#6694212yes—
375C2×C4#6694312yes—
376C2×C4#6694712yes—
377C2×C4#6694812yes—
378C2×C4#6694912yes—
379C2×C4#6695012yes—
380C2×C4#6695112yes—
381C2×C4#6697711yescharacteristic
382C2×C4#6697711yescharacteristic
383C2×C4#6698311yescharacteristic
384C2×C4#6698311yescharacteristic
385C2×C4#6698811yescharacteristic
386C2×C4#6699011yescharacteristic
387C2×C4#6699212yes—
388C2×C4#6699711yescharacteristic
389C2×C4#6699912yes—
390C2×C4#6700011yescharacteristic
391C8—444no—
392C8—444no—
393C22—22no—
394C22—22no—
395C22—22no—
396C22—22no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22#1062259412yes—
402C22#1062259812yes—
403C22#1062282511yescharacteristic
404C22C2×#6689711yescharacteristic
405C22#1062283311yescharacteristic
406C22C2×#6690011yescharacteristic
407C22#1062284311yescharacteristic
408C22#1062285011yescharacteristic
409C22#1062285011yescharacteristic
410C4—22no—
411C4—22no—
412C4—41no—
413C4—41no—
414C4—44no—
415C4—82no—
416C4#1062259211yescharacteristic
417C4#1062259611yescharacteristic
418C4#1062259712yes—
419C4#1062259911yescharacteristic
420C4#1062260411yescharacteristic
421C4#1062260712yes—
422C2—22no—
423C2—22no—
424C2#1306686911yescharacteristic
425C2#1306860811yescharacteristic
426C2#1306861211yescharacteristic
427C2#1306908011yescharacteristic
428C2#1306908511yescharacteristic
429C2#1306960611yescharacteristic
430C2#1306961011yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutator, prime radicalC24×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#389C2
socleC23×C11C2×C22⋊C4
cosocleC23×C4×C11C23
hypercenterC2×#389D11
hypocenterC11#11204
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
340. C11#11204semidirect

Maximal subgroups

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

subgroupindex
C2×#106225372
C2×#106221682
#130683102
C2×C11×#3892
#1120411