Finite Group Databasebeta

← #14649394

Subgroups — #14649394

Order 2816.

600 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622539C211yesmaximal, characteristic, complemented
2#13068378C211yesmaximal, characteristic, complemented
3C2×#10622178C212yesmaximal, complemented
4#13066497C212yesmaximal, complemented
5C11×#2850C211yesmaximal, characteristic
6C2×C11×#124C2211yescharacteristic
7C2×C11×C22⋊Q8C411yescharacteristic
8C2×C11×#121C411yescharacteristic
9C22×C42×C11C2211yescharacteristic
10C11×#391C411yescharacteristic
11C11×#390C411yescharacteristic
12C11×#388—21no—
13C11×#388—21no—
14C11×#386—21no—
15C11×#386—21no—
16C11×#382C2211yescharacteristic
17C2×C22⋊(C11⋊C8)—21no—
18C2×C22⋊(C11⋊C8)—21no—
19#10622539—24no—
20C2×C4⋊(C11⋊C8)—21no—
21C2×#66867C2212yes—
22C2×#66867C2212yes—
23#10622178—24no—
24#10622162—21no—
25C22×Q8×C11C2×C411yescharacteristic
26C22×D4×C11—21no—
27C22×D4×C11C2×C411yescharacteristic
28C23×C4×C11C2×C411yescharacteristic
29C23×C4×C11D411yescharacteristic
30C23×C4×C11D411yescharacteristic
31C11×#124—22no—
32C11×#124—22no—
33C11×C22⋊Q8—42no—
34C11×#121—42no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4C2×C411yescharacteristic
37C2×C11×C4⋊C4C2×C411yescharacteristic
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4—21no—
44C2×C42×C11—22no—
45C2×C42×C11—22no—
46C2×C42×C11C2×C411yescharacteristic
47C2×C42×C11D411yescharacteristic
48C2×C42×C11D411yescharacteristic
49C2×C42×C11C2311yescharacteristic
50C22×C11⋊C8—22no—
51C22×C11⋊C8—22no—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95—21no—
56C22⋊(C11⋊C8)—24no—
57C22⋊(C11⋊C8)—24no—
58C4⋊(C11⋊C8)—24no—
59#66867—22no—
60#66867—22no—
61#66867—22no—
62#66867D414yescomplemented
63#9124—111nomaximal, Sylow
64C24×C11—21no—
65C24×C11C22⋊C411yescharacteristic
66C2×Q8×C11—22no—
67C2×Q8×C11—41no—
68C2×Q8×C11—41no—
69C2×D4×C11—22no—
70C2×D4×C11—41no—
71C2×D4×C11—41no—
72C2×D4×C11—42no—
73C2×D4×C11—42no—
74C2×D4×C11—42no—
75C22×C4×C11—22no—
76C22×C4×C11—22no—
77C22×C4×C11—22no—
78C22×C4×C11—21no—
79C22×C4×C11—22no—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11C22⋊C411yescharacteristic
89C22×C4×C11C22⋊C411yescharacteristic
90C22×C4×C11C22⋊C411yescharacteristic
91C22×C4×C11C22×C411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C11×C4⋊C4—42no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4—41no—
97C11×C22⋊C4—42no—
98C11×C22⋊C4—42no—
99C11×C22⋊C4—42no—
100C11×C22⋊C4—42no—
101C11×C22⋊C4—41no—
102C11×C22⋊C4—42no—
103C11×C22⋊C4—41no—
104C42×C11—22no—
105C42×C11—21no—
106C42×C11—22no—
107C42×C11—21no—
108C42×C11C2×D412yes—
109C42×C11#4112yes—
110C2×C11⋊C8—24no—
111C2×C11⋊C8—24no—
112C2×C11⋊C8—42no—
113C2×C11⋊C8—42no—
114C2×C11⋊C8—42no—
115C2×C11⋊C8—42no—
116C2×#432—111no—
117#2850D1111yescharacteristic
118#1749—111no—
119C2×#329—112no—
120#1295—112no—
121C23×C11—21no—
122C23×C11—21no—
123C23×C11—21no—
124C23×C11—21no—
125C23×C11—21no—
126C23×C11—21no—
127C23×C11—41no—
128C23×C11—41no—
129C23×C11—41no—
130C23×C11—41no—
131C23×C11—41no—
132C23×C11—41no—
133C23×C11—41no—
134C23×C11#10012yes—
135C23×C11C2×C22⋊C411yescharacteristic
136Q8×C11—82no—
137D4×C11—82no—
138D4×C11—84no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
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—21no—
152C2×C4×C11—21no—
153C2×C4×C11—44no—
154C2×C4×C11—44no—
155C2×C4×C11—42no—
156C2×C4×C11—42no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11#10412yes—
167C2×C4×C11C4×D412yes—
168C2×C4×C11#12011yescharacteristic
169C2×C4×C11#12112yes—
170C2×C4×C11#12311yescharacteristic
171C11⋊C8—44no—
172C11⋊C8—44no—
173C2×#124C2×D1111yescharacteristic
174C2×C22⋊Q8Dic1111yescharacteristic
175C2×#121Dic1111yescharacteristic
176C22×C42C2×D1111yescharacteristic
177#432—224no—
178C2×C4⋊C8—221no—
179C2×C22⋊C8—221no—
180C2×C22⋊C8—221no—
181C2×#97—112no—
182C2×#97—112no—
183#391Dic1111yescharacteristic
184#390Dic1111yescharacteristic
185#388—21no—
186#388—21no—
187#386—21no—
188#386—21no—
189#382C2×D1111yescharacteristic
190#336—221no—
191#329—224no—
192C22×C11—22no—
193C22×C11—22no—
194C22×C11—22no—
195C22×C11—41no—
196C22×C11—41no—
197C22×C11—41no—
198C22×C11—41no—
199C22×C11—81no—
200C22×C11—81no—
201C22×C11—81no—
202C22×C11—81no—
203C22×C11—81no—
204C22×C11—81no—
205C22×C11—81no—
206C22×C11#38611yescharacteristic
207C22×C11C2×#10011yescharacteristic
208C22×C11#41311yescharacteristic
209C22×C11C2×#10411yescharacteristic
210C22×C11#42111yescharacteristic
211C22×C11#42111yescharacteristic
212C22×C11#42111yescharacteristic
213C4×C11—22no—
214C4×C11—22no—
215C4×C11—21no—
216C4×C11—21no—
217C4×C11—22no—
218C4×C11—41no—
219C4×C11—41no—
220C4×C11—81no—
221C4×C11—81no—
222C4×C11—81no—
223C22×Q8C2×Dic1111yescharacteristic
224C22×D4—21no—
225C22×D4C2×Dic1111yescharacteristic
226C23×C4C2×Dic1111yescharacteristic
227C23×C4C22⋊D1111yescharacteristic
228C23×C4C22⋊D1111yescharacteristic
229C22×C8—222no—
230C22×C8—222no—
231#124—22no—
232#124—22no—
233C22⋊Q8—42no—
234#121—42no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4C2×Dic1111yescharacteristic
237C2×C4⋊C4C2×Dic1111yescharacteristic
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C42—22no—
245C2×C42—22no—
246C2×C42C2×Dic1111yescharacteristic
247C2×C42C22⋊D1111yescharacteristic
248C2×C42C22⋊D1111yescharacteristic
249C2×C42C22×D1111yescharacteristic
250C4⋊C8—224no—
251C22⋊C8—224no—
252C22⋊C8—224no—
253#97—114no—
254#97—222no—
255#97—222no—
256#97—222no—
257#95—21no—
258#95—21no—
259#95—21no—
260#95—21no—
261C2×C11—42no—
262C2×C11—161no—
263C2×C11#152911yescharacteristic
264C2×C11#153011yescharacteristic
265C2×C11#153311yescharacteristic
266C2×C11#153511yescharacteristic
267C2×C11#187111yescharacteristic
268C2×C11#189711yescharacteristic
269C2×C11#190011yescharacteristic
270C24—21no—
271C24C22⋊Dic1111yescharacteristic
272C2×Q8—22no—
273C2×Q8—41no—
274C2×Q8—41no—
275C2×D4—22no—
276C2×D4—41no—
277C2×D4—41no—
278C2×D4—42no—
279C2×D4—42no—
280C2×D4—42no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—22no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4C22⋊Dic1111yescharacteristic
295C22×C4C22⋊Dic1111yescharacteristic
296C22×C4C22⋊Dic1111yescharacteristic
297C22×C4C22×Dic1111yescharacteristic
298C22×C4C2×C22⋊D1111yescharacteristic
299C22×C4C2×C22⋊D1111yescharacteristic
300C2×C8—224no—
301C2×C8—224no—
302C2×C8—442no—
303C2×C8—442no—
304C2×C8—442no—
305C2×C8—442no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—42no—
309C22⋊C4—42no—
310C22⋊C4—42no—
311C22⋊C4—42no—
312C22⋊C4—42no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—42no—
316C42—22no—
317C42—21no—
318C42—21no—
319C42—22no—
320C42D4×D1112yes—
321C42#434112yes—
322C11#912411yescharacteristic, complemented, Sylow
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23#6689712yes—
337C23C2×C22⋊Dic1111yescharacteristic
338Q8—82no—
339D4—82no—
340D4—84no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—44no—
356C2×C4—44no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4#6690112yes—
369C2×C4D4×Dic1112yes—
370C2×C4#6698811yescharacteristic
371C2×C4#6699011yescharacteristic
372C2×C4#6699212yes—
373C8—444no—
374C8—444no—
375C22—22no—
376C22—22no—
377C22—22no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22—81no—
386C22—81no—
387C22—81no—
388C22—81no—
389C22C2×#6689711yescharacteristic
390C22#1062283311yescharacteristic
391C22C2×#6690111yescharacteristic
392C22#1062284911yescharacteristic
393C22#1062284911yescharacteristic
394C22#1062284911yescharacteristic
395C22#1062285011yescharacteristic
396C4—21no—
397C4—21no—
398C4—22no—
399C4—22no—
400C4—22no—
401C4—41no—
402C4—41no—
403C4—81no—
404C4—81no—
405C4—81no—
406C2—42no—
407C2—161no—
408C2#1306722311yescharacteristic
409C2#1306722711yescharacteristic
410C2#1306724011yescharacteristic
411C2#1306724711yescharacteristic
412C2#1306891911yescharacteristic
413C2#1306906511yescharacteristic
414C2#1306908011yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2850C2
socleC23×C11C2×C22⋊C4
prime radicalC2×C11×#121C4
cosocleC2×C42×C11C23
hypercenter#2850D11
hypocenterC11#9124
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2850

Complements

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

NH ≅ G/Ntype
1. C2×#10622539C2semidirect
2. #13068378C2semidirect
3. C2×#10622178C2semidirect
4. #13066497C2semidirect
62. #66867D4semidirect
322. C11#9124semidirect

Maximal subgroups

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

subgroupindex
C2×#106225392
#130683782
C2×#106221782
#130664972
C11×#28502
#912411