Finite Group Databasebeta

← #14664136

Subgroups — #14664136

Order 2816.

632 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 632 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071834C211yesmaximal, characteristic
2#13068407C211yesmaximal, characteristic, complemented
3#13066933C211yesmaximal, characteristic, complemented
4#13066646C211yesmaximal, characteristic, complemented
5#13066620C211yesmaximal, characteristic, complemented
6#13066618C211yesmaximal, characteristic, complemented
7C11×#1354C211yesmaximal, characteristic, complemented
8C22×#4343C411yescharacteristic
9C2×#66946—21no—
10C2×#66946C2211yescharacteristic
11C11×#395C2211yescharacteristic
12#10622844C411yescharacteristic
13C2×#66887—21no—
14M16×Dic11—21no—
15#10622604—21no—
16#10622604C2211yescharacteristic
17D11×C22⋊C8—21no—
18#10622284—21no—
19#10622284C411yescharacteristic
20#10622279—21no—
21#10622279C411yescharacteristic
22C11×#343C2211yescharacteristic
23C11×#324C2211yescharacteristic
24#10622168C2211yescharacteristic
25#10622166C2211yescharacteristic
26#10622106—21no—
27C22×Q8×C11C2×C411yescharacteristic
28C2×#4343—44no—
29C2×#4343—41no—
30C2×#4343—41no—
31C22×D44—21no—
32C22×D44—21no—
33C22×D44C2×C411yescharacteristic
34C22×D44D411yescharacteristic
35C22×C4×D11—21no—
36C22×C4×D11C2×C411yescharacteristic
37C22×C4×D11D411yescharacteristic
38C2×C11×M16—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4C2311yescharacteristic
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×(C2×D11)⋊C4—21no—
46C2×(C2×D11)⋊C4C2×C411yescharacteristic
47C2×(C2×D11)⋊C4D411yescharacteristic
48C2×C4×Dic11—21no—
49C2×C4×Dic11D411yescharacteristic
50C2×#4318—21no—
51C2×C8×D11—41no—
52#66946—41no—
53#66946—41no—
54#66946—44no—
55C11×C22⋊C8—21no—
56C11×#95—21no—
57C11×#95C2×C411yescharacteristic
58C11⋊#95—21no—
59C11⋊#95C2×C411yescharacteristic
60C22⋊(C11⋊C8)—21no—
61#66887—24no—
62(C2×D11)⋊C8—41no—
63#66879—41no—
64C8×Dic11—41no—
65#11733—111nomaximal, Sylow
66C23×D11—21no—
67C23×D11C22⋊C411yescharacteristic
68C23×D11C22⋊C411yescharacteristic
69C2×Q8×C11—42no—
70C2×Q8×C11—41no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11C22×C411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×Dic11—21no—
77C22×Dic11C22⋊C411yescharacteristic
78C22×Dic11C22⋊C411yescharacteristic
79#4343—44no—
80#4343—44no—
81#4343—44no—
82#4343—44no—
83C2×D44—22no—
84C2×D44—21no—
85C2×D44—21no—
86C2×D44—41no—
87C2×D44—42no—
88C2×D44—42no—
89C2×D44—41no—
90C2×D44—42no—
91C2×D44—42no—
92C2×D44—42no—
93C2×D44—42no—
94C2×D44—42no—
95C2×C4×D11—24no—
96C2×C4×D11—21no—
97C2×C4×D11—21no—
98C2×C4×D11—21no—
99C2×C4×D11—21no—
100C2×C4×D11—42no—
101C2×C4×D11—41no—
102C2×C4×D11—41no—
103C2×C4×D11—42no—
104C2×C4×D11—42no—
105C11×M16—22no—
106C11×M16—41no—
107C2×C8×C11—41no—
108C2×C8×C11—41no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4—42no—
111(C2×D11)⋊C4—41no—
112(C2×D11)⋊C4—41no—
113(C2×D11)⋊C4—42no—
114(C2×D11)⋊C4—42no—
115(C2×D11)⋊C4—42no—
116(C2×D11)⋊C4—42no—
117(C2×D11)⋊C4—41no—
118(C2×D11)⋊C4—41no—
119C4×Dic11—21no—
120C4×Dic11—21no—
121C4×Dic11—42no—
122#4318—22no—
123#4318—41no—
124C2×C11⋊C8—41no—
125C2×C11⋊C8—41no—
126C8×D11—82no—
127#2388—111no—
128C4×#100—111no—
129#1459—111no—
130#1354—111no—
131#1354D1111yescharacteristic, complemented
132#1345—111no—
133#1345—111no—
134C23×C11C2×C22⋊C411yescharacteristic
135C22×D11—21no—
136C22×D11—21no—
137C22×D11—22no—
138C22×D11—21no—
139C22×D11—21no—
140C22×D11—21no—
141C22×D11—41no—
142C22×D11—41no—
143C22×D11—41no—
144C22×D11—41no—
145C22×D11—41no—
146C22×D11—41no—
147C22×D11—41no—
148C22×D11—41no—
149C22×D11—41no—
150C22×D11—41no—
151C22×D11#10412yes—
152Q8×C11—42no—
153Q8×C11—42no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
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#13511yescharacteristic
167C2×C4×C11#13511yescharacteristic
168C2×Dic11—22no—
169C2×Dic11—21no—
170C2×Dic11—41no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173C2×Dic11—41no—
174C2×Dic11#9911yescharacteristic
175C2×Dic11#9911yescharacteristic
176D44—42no—
177D44—42no—
178D44—42no—
179D44—48no—
180D44—48no—
181D44—42no—
182C4×D11—44no—
183C4×D11—42no—
184C4×D11—42no—
185C4×D11—44no—
186C4×D11—42no—
187C4×D11—81no—
188C8×C11—42no—
189C8×C11—81no—
190C11⋊C8—42no—
191C11⋊C8—81no—
192C22×#41—111no—
193C2×C4×D4—111no—
194C2×C4×D4—221no—
195C2×#100—221no—
196C2×C22⋊C8—221no—
197C4×M16—221no—
198#395C2×D1111yescharacteristic
199#394—111no—
200#394—221no—
201#393—111no—
202#392—111no—
203#392—221no—
204C4×C22⋊C4—111no—
205C4×C22⋊C4—221no—
206#343—111no—
207#343C2×D1111yescharacteristic
208#324—111no—
209#324C2×D1111yescharacteristic
210#323—221no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11C2×#9911yescharacteristic
214C22×C11#41611yescharacteristic
215C22×C11C2×#10411yescharacteristic
216C2×D11—22no—
217C2×D11—41no—
218C2×D11—41no—
219C2×D11—42no—
220C2×D11—42no—
221C2×D11—42no—
222C2×D11—42no—
223C2×D11—41no—
224C2×D11—41no—
225C2×D11—41no—
226C2×D11—81no—
227C2×D11—81no—
228C2×D11—81no—
229C2×D11—81no—
230C2×D11—81no—
231C2×D11—81no—
232C2×D11—81no—
233C4×C11—21no—
234C4×C11—21no—
235C4×C11—42no—
236C4×C11—42no—
237C4×C11—41no—
238C4×C11—41no—
239Dic11—21no—
240Dic11—41no—
241Dic11—81no—
242Dic11AΣL(1,𝔽16)12yes—
243C2×#41—444no—
244C2×#41—441no—
245C2×#41—441no—
246C22×Q8C4×D1111yescharacteristic
247C22×D4—111no—
248C22×D4—111no—
249C22×D4—221no—
250C22×D4—221no—
251C23×C4—111no—
252C23×C4—111no—
253C23×C4—221no—
254C2×M16—21no—
255C2×M16—221no—
256C22×C8—441no—
257C4×D4—441no—
258C4×D4—441no—
259C4×D4—444no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4C22×D1111yescharacteristic
262C2×C22⋊C4—111no—
263C2×C22⋊C4—111no—
264C2×C22⋊C4—221no—
265C2×C22⋊C4—221no—
266C2×C22⋊C4—221no—
267C2×C22⋊C4—221no—
268C2×C22⋊C4—221no—
269C2×C42—111no—
270C2×C42—221no—
271#100—224no—
272C22⋊C8—21no—
273C22⋊C8—221no—
274C22⋊C8—441no—
275#97—441no—
276C4×C8—441no—
277#95—21no—
278#95—111no—
279#95—221no—
280#95C4×D1111yescharacteristic
281C2×C11—21no—
282C2×C11—21no—
283C2×C11#150111yescharacteristic
284C2×C11C2×AΣL(1,𝔽16)11yescharacteristic
285C2×C11#213211yescharacteristic
286D11—42no—
287D11—81no—
288D11—82no—
289C24—111no—
290C24—111no—
291C24—221no—
292#41—444no—
293#41—444no—
294#41—444no—
295#41—444no—
296C2×Q8—42no—
297C2×Q8—41no—
298C2×D4—222no—
299C2×D4—221no—
300C2×D4—221no—
301C2×D4—441no—
302C2×D4—441no—
303C2×D4—442no—
304C2×D4—442no—
305C2×D4—442no—
306C2×D4—442no—
307C2×D4—442no—
308C2×D4—442no—
309C2×D4—442no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—111no—
313C22×C4—111no—
314C22×C4—221no—
315C22×C4—221no—
316C22×C4—221no—
317C22×C4—221no—
318C22×C4—224no—
319C22×C4—221no—
320C22×C4—441no—
321C22×C4—441no—
322C22×C4—442no—
323C22×C4—442no—
324C22×C4—442no—
325C22×C4C2×C4×D1111yescharacteristic
326C22×C4D4×D1111yescharacteristic
327C22×C4D4×D1111yescharacteristic
328M16—22no—
329M16—41no—
330M16—222no—
331M16—441no—
332C2×C8—41no—
333C2×C8—41no—
334C2×C8—441no—
335C2×C8—441no—
336C2×C8—882no—
337C4⋊C4—41no—
338C4⋊C4—42no—
339C22⋊C4—441no—
340C22⋊C4—441no—
341C22⋊C4—442no—
342C22⋊C4—442no—
343C22⋊C4—442no—
344C22⋊C4—442no—
345C22⋊C4—441no—
346C22⋊C4—441no—
347C42—221no—
348C42—221no—
349C42—442no—
350C11#1173311yescharacteristic, complemented, Sylow
351C23—112no—
352C23—222no—
353C23—221no—
354C23—221no—
355C23—221no—
356C23—221no—
357C23—221no—
358C23—441no—
359C23—441no—
360C23—441no—
361C23—441no—
362C23—441no—
363C23—441no—
364C23—441no—
365C23—441no—
366C23—441no—
367C23—441no—
368C23C22⋊C4×D1111yescharacteristic
369Q8—42no—
370Q8—42no—
371D4—442no—
372D4—442no—
373D4—442no—
374D4—448no—
375D4—442no—
376D4—448no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—111no—
390C2×C4—111no—
391C2×C4—222no—
392C2×C4—221no—
393C2×C4—442no—
394C2×C4—444no—
395C2×C4—442no—
396C2×C4—444no—
397C2×C4—442no—
398C2×C4—441no—
399C2×C4—441no—
400C2×C4—441no—
401C2×C4—441no—
402C2×C4—881no—
403C2×C4#6696911yescharacteristic
404C2×C4#6697211yescharacteristic
405C8—42no—
406C8—81no—
407C8—442no—
408C8—881no—
409C22—21no—
410C22—21no—
411C22—222no—
412C22—442no—
413C22—442no—
414C22—442no—
415C22—441no—
416C22—441no—
417C22—441no—
418C22—441no—
419C22—442no—
420C22—441no—
421C22—881no—
422C22—881no—
423C22—881no—
424C22—881no—
425C22—881no—
426C22—881no—
427C22—881no—
428C22D11×#9911yescharacteristic
429C22#1062241711yescharacteristic
430C22D11×#10411yescharacteristic
431C4—21no—
432C4—21no—
433C4—42no—
434C4—41no—
435C4—42no—
436C4—41no—
437C4—112no—
438C4—221no—
439C4—441no—
440C4—881no—
441C2—21no—
442C2—21no—
443C2—442no—
444C2—882no—
445C2—881no—
446C2#1306710611yescharacteristic
447C2D11×AΣL(1,𝔽16)11yescharacteristic
448C2#1307030011yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1354C2
socleC22×C11C2×#99
prime radical#13071834C2
cosocleC2×C11×C4⋊C4C23
hypercenter#1354D11
hypocenterC11#11733
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1354

Complements

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

NH ≅ G/Ntype
2. #13068407C2semidirect
3. #13066933C2semidirect
4. #13066646C2semidirect
5. #13066620C2semidirect
6. #13066618C2semidirect
7. C11×#1354C2semidirect
131. #1354D11semidirect
350. C11#11733semidirect

Maximal subgroups

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

subgroupindex
#130718342
#130684072
#130669332
#130666462
#130666202
#130666182
C11×#13542
#1173311