Finite Group Databasebeta

← #14661673

Subgroups — #14661673

Order 2816.

918 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071230C211yesmaximal, characteristic
2C2×#10622164C212yesmaximal
3C2×#10622164C211yesmaximal, characteristic
4C2×#10622165C212yesmaximal
5C11×#2315C211yesmaximal, characteristic
6C22×C11×C22⋊C4C2211yescharacteristic
7C22×C11×C22⋊C4C2211yescharacteristic
8C22×C11×C22⋊C4C2211yescharacteristic
9C22×C22⋊Dic11C2212yes—
10C22×C22⋊Dic11C2212yes—
11C11×#385—22no—
12C11×#385C414yescomplemented
13C11×#380—22no—
14#10622825—22no—
15#10622563—24no—
16#10622165—24no—
17#10622164—22no—
18#10622164—24no—
19C25×C11C2311yescharacteristic
20C23×C4×C11—21no—
21C23×C4×C11C2×C412yes—
22C23×C4×C11D412yes—
23C23×Dic11—22no—
24C23×Dic11—22no—
25C2×C11×C4⋊C4—24no—
26C2×C11×C22⋊C4—22no—
27C2×C11×C22⋊C4—21no—
28C2×C11×C22⋊C4—21no—
29C2×C11×C22⋊C4—21no—
30C2×C11×C22⋊C4—22no—
31C2×C11×C22⋊C4—21no—
32C2×C11×C22⋊C4—21no—
33C2×C11×C22⋊C4—22no—
34C2×C11×C22⋊C4—22no—
35C2×C11×C22⋊C4C2×C412yes—
36C2×C11×C22⋊C4C2×C412yes—
37C2×C11×C22⋊C4D412yes—
38C2×C11×C22⋊C4D412yes—
39C2×C11×C22⋊C4Q812yes—
40C2×C22⋊Dic11—22no—
41C2×C22⋊Dic11—22no—
42C2×C22⋊Dic11—22no—
43C2×C22⋊Dic11—22no—
44C2×C22⋊Dic11—22no—
45C2×C22⋊Dic11—22no—
46C2×C22⋊Dic11—22no—
47C2×C22⋊Dic11—22no—
48C2×C22⋊Dic11—22no—
49C2×C22⋊Dic11—22no—
50C2×C22⋊Dic11D414yes—
51C2×C22⋊Dic11Q814yes—
52C2×C4⋊Dic11—24no—
53C11×#95—24no—
54C11⋊#95—24no—
55#11205—111nomaximal, Sylow
56C24×C11—82no—
57C24×C11C22×C411yescharacteristic
58C24×C11C2×D411yescharacteristic
59C24×C11C2×D411yescharacteristic
60C24×C11C2×D412yes—
61C24×C11C2×D411yescharacteristic
62C24×C11C2×Q811yescharacteristic
63C24×C11C2×Q812yes—
64C24×C11#4112yes—
65C24×C11#4111yescharacteristic
66C24×C11#4111yescharacteristic
67C24×C11#4112yes—
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—24no—
75C22×C4×C11—82no—
76C22×C4×C11—82no—
77C22×C4×C11—82no—
78C22×C4×C11C22⋊C414yes—
79C22×Dic11—24no—
80C22×Dic11—24no—
81C22×Dic11—42no—
82C22×Dic11—42no—
83C22×Dic11—42no—
84C22×Dic11—42no—
85C22×Dic11—84no—
86C22×Dic11—84no—
87C11×C4⋊C4—84no—
88C11×C22⋊C4—22no—
89C11×C22⋊C4—24no—
90C11×C22⋊C4—22no—
91C11×C22⋊C4—24no—
92C11×C22⋊C4—22no—
93C11×C22⋊C4—41no—
94C11×C22⋊C4—42no—
95C11×C22⋊C4—41no—
96C11×C22⋊C4C4⋊C414yescomplemented
97C22⋊Dic11—24no—
98C22⋊Dic11—24no—
99C22⋊Dic11—24no—
100C22⋊Dic11—24no—
101C22⋊Dic11—42no—
102C22⋊Dic11—42no—
103C22⋊Dic11—42no—
104C22⋊Dic11—42no—
105C4⋊Dic11—84no—
106#2315—111no—
107#2315D1111yescharacteristic
108C2×#342—112no—
109C2×#342—112no—
110C2×#342—111no—
111C23×C11—44no—
112C23×C11—44no—
113C23×C11—42no—
114C23×C11—42no—
115C23×C11—42no—
116C23×C11—81no—
117C23×C11—81no—
118C23×C11—82no—
119C23×C11—81no—
120C23×C11—81no—
121C23×C11—82no—
122C23×C11C2×C22⋊C411yescharacteristic
123C23×C11C2×C4⋊C411yescharacteristic
124C23×C11#11711yescharacteristic
125C23×C11C4×D412yes—
126C23×C11C4×Q812yes—
127C23×C11#12011yescharacteristic
128C23×C11#12112yes—
129C23×C11#12111yescharacteristic
130C23×C11#12111yescharacteristic
131C23×C11#12112yes—
132C23×C11C22⋊Q812yes—
133C23×C11C22⋊Q812yes—
134C23×C11C22⋊Q811yescharacteristic
135C23×C11C22⋊Q811yescharacteristic
136C23×C11C22⋊Q812yes—
137C23×C11#12312yes—
138C23×C11#12311yescharacteristic
139C23×C11#12411yescharacteristic
140C23×C11#12512yes—
141C23×C11#12512yes—
142C23×C11#12612yes—
143C23×C11C4⋊Q812yes—
144C23×C11C4⋊Q811yescharacteristic
145C2×C4×C11—24no—
146C2×C4×C11—24no—
147C2×C4×C11—44no—
148C2×C4×C11—44no—
149C2×C4×C11—44no—
150C2×C4×C11—44no—
151C2×C4×C11—42no—
152C2×C4×C11—82no—
153C2×C4×C11—82no—
154C2×C4×C11—82no—
155C2×C4×C11—84no—
156C2×Dic11—48no—
157C2×Dic11—44no—
158C2×Dic11—44no—
159C2×Dic11—84no—
160C2×Dic11—84no—
161C2×Dic11—84no—
162C2×Dic11—84no—
163C2×Dic11—84no—
164C22×C22⋊C4—112no—
165C22×C22⋊C4—112no—
166C22×C22⋊C4C2×D1111yescharacteristic
167C22×C22⋊C4C2×D1111yescharacteristic
168C22×C22⋊C4C2×D1111yescharacteristic
169#385—22no—
170#385—224no—
171#385Dic1114yescomplemented
172#380—22no—
173#380—222no—
174#342—224no—
175#342—224no—
176#342—222no—
177C22×C11—22no—
178C22×C11—22no—
179C22×C11—24no—
180C22×C11—22no—
181C22×C11—24no—
182C22×C11—41no—
183C22×C11—41no—
184C22×C11—41no—
185C22×C11—41no—
186C22×C11—42no—
187C22×C11—41no—
188C22×C11—42no—
189C22×C11—42no—
190C22×C11—41no—
191C22×C11—42no—
192C22×C11—42no—
193C22×C11—42no—
194C22×C11—41no—
195C22×C11—42no—
196C22×C11—42no—
197C22×C11—42no—
198C22×C11—42no—
199C22×C11—41no—
200C22×C11#38011yescharacteristic
201C22×C11#38611yescharacteristic
202C22×C11#38712yes—
203C22×C11#38912yes—
204C22×C11#39111yescharacteristic
205C22×C11#39411yescharacteristic
206C22×C11#39511yescharacteristic
207C22×C11#39612yes—
208C22×C11#39811yescharacteristic
209C22×C11#39812yes—
210C22×C11#40011yescharacteristic
211C4×C11—44no—
212C4×C11—44no—
213C4×C11—82no—
214Dic11—84no—
215Dic11—84no—
216C25C22×D1111yescharacteristic
217C23×C4—21no—
218C23×C4—222no—
219C23×C4—222no—
220C23×C4C2×Dic1112yes—
221C23×C4C22⋊D1112yes—
222C2×C4⋊C4—24no—
223C2×C4⋊C4—224no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—22no—
227C2×C22⋊C4—22no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4—22no—
230C2×C22⋊C4—22no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—114no—
234C2×C22⋊C4—114no—
235C2×C22⋊C4—222no—
236C2×C22⋊C4—222no—
237C2×C22⋊C4—222no—
238C2×C22⋊C4—222no—
239C2×C22⋊C4—222no—
240C2×C22⋊C4—222no—
241C2×C22⋊C4—222no—
242C2×C22⋊C4—222no—
243C2×C22⋊C4—222no—
244C2×C22⋊C4—222no—
245C2×C22⋊C4Dic2212yes—
246C2×C22⋊C4D4412yes—
247C2×C22⋊C4C2×Dic1112yes—
248C2×C22⋊C4C2×Dic1112yes—
249C2×C22⋊C4C22⋊D1112yes—
250#95—24no—
251#95—224no—
252C2×C11—21no—
253C2×C11—22no—
254C2×C11—21no—
255C2×C11—22no—
256C2×C11—22no—
257C2×C11—21no—
258C2×C11—21no—
259C2×C11—21no—
260C2×C11—22no—
261C2×C11—21no—
262C2×C11#144111yescharacteristic
263C2×C11#191312yes—
264C24—82no—
265C24C2×Dic2211yescharacteristic
266C24C2×D4411yescharacteristic
267C24#433911yescharacteristic
268C24#433911yescharacteristic
269C24D4×D1112yes—
270C24#434112yes—
271C24Q8×D1112yes—
272C24#434312yes—
273C24C22×Dic1111yescharacteristic
274C24C2×C22⋊D1111yescharacteristic
275C24C2×C22⋊D1111yescharacteristic
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—24no—
283C22×C4—82no—
284C22×C4—82no—
285C22×C4—82no—
286C22×C4—224no—
287C22×C4—224no—
288C22×C4—442no—
289C22×C4—442no—
290C22×C4—442no—
291C22×C4—442no—
292C22×C4—884no—
293C22×C4—884no—
294C22×C4C22⋊Dic1114yes—
295C4⋊C4—84no—
296C4⋊C4—884no—
297C22⋊C4—22no—
298C22⋊C4—22no—
299C22⋊C4—22no—
300C22⋊C4—24no—
301C22⋊C4—24no—
302C22⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—42no—
305C22⋊C4—224no—
306C22⋊C4—224no—
307C22⋊C4—224no—
308C22⋊C4—224no—
309C22⋊C4—442no—
310C22⋊C4—442no—
311C22⋊C4—442no—
312C22⋊C4—442no—
313C22⋊C4C4⋊Dic1114yescomplemented
314C11#1120511yescharacteristic, complemented, Sylow
315C23—42no—
316C23—42no—
317C23—42no—
318C23—44no—
319C23—44no—
320C23—81no—
321C23—81no—
322C23—81no—
323C23—81no—
324C23—82no—
325C23—82no—
326C23#6694112yes—
327C23#6694212yes—
328C23#6694312yes—
329C23#6694712yes—
330C23#6694812yes—
331C23#6694912yes—
332C23#6695012yes—
333C23#6695112yes—
334C23#6697711yescharacteristic
335C23#6697711yescharacteristic
336C23C2×C4⋊Dic1111yescharacteristic
337C23#6697911yescharacteristic
338C23#6698311yescharacteristic
339C23#6698311yescharacteristic
340C23D4×Dic1112yes—
341C23#6698811yescharacteristic
342C23#6699011yescharacteristic
343C23#6699212yes—
344C23#6699711yescharacteristic
345C23Q8×Dic1112yes—
346C23#6699912yes—
347C23#6700011yescharacteristic
348C23C2×C22⋊Dic1111yescharacteristic
349C2×C4—24no—
350C2×C4—24no—
351C2×C4—44no—
352C2×C4—44no—
353C2×C4—44no—
354C2×C4—44no—
355C2×C4—42no—
356C2×C4—82no—
357C2×C4—82no—
358C2×C4—82no—
359C2×C4—84no—
360C2×C4—448no—
361C2×C4—444no—
362C2×C4—444no—
363C2×C4—884no—
364C2×C4—884no—
365C2×C4—884no—
366C2×C4—884no—
367C2×C4—884no—
368C22—22no—
369C22—22no—
370C22—24no—
371C22—22no—
372C22—24no—
373C22—41no—
374C22—41no—
375C22—42no—
376C22—42no—
377C22—42no—
378C22—42no—
379C22—42no—
380C22—42no—
381C22—42no—
382C22—42no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—42no—
389C22—42no—
390C22—41no—
391C22#1062259211yescharacteristic
392C22#1062259412yes—
393C22#1062259611yescharacteristic
394C22#1062259712yes—
395C22#1062259812yes—
396C22#1062259911yescharacteristic
397C22#1062260411yescharacteristic
398C22#1062260712yes—
399C22#1062282511yescharacteristic
400C22#1062283311yescharacteristic
401C22#1062284311yescharacteristic
402C4—44no—
403C4—44no—
404C4—82no—
405C4—884no—
406C4—884no—
407C2—21no—
408C2—21no—
409C2—22no—
410C2—21no—
411C2—21no—
412C2—22no—
413C2—21no—
414C2—22no—
415C2—22no—
416C2—21no—
417C2#1306686911yescharacteristic
418C2#1306915912yes—
subgroupG/H
centerC22#10622833
commutatorC24×C11C22×C4
FrattiniC25C22×D11
FittingC11×#2315C2
socleC22×C11#386
prime radical, cosocleC25×C11C23
hypercenter#2315D11
hypocenterC11#11205
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C25 ◁ #2315

Complements

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

NH ≅ G/Ntype
12. C11×#385C4semidirect
96. C11×C22⋊C4C4⋊C4semidirect
171. #385Dic11semidirect
313. C22⋊C4C4⋊Dic11semidirect
314. C11#11205semidirect

Maximal subgroups

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

subgroupindex
#130712302
C2×#106221642
C2×#106221652
C11×#23152
#1120511