Finite Group Databasebeta

← #14664675

Subgroups — #14664675

Order 2816.

572 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 71 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#13071952C211yesmaximal, characteristic
2#13068695C211yesmaximal, characteristic, complemented
3D11×#324C211yesmaximal, characteristic, complemented
4#13066646C211yesmaximal, characteristic, complemented
5#13066620C211yesmaximal, characteristic, complemented
6#13066618C211yesmaximal, characteristic, complemented
7C11×#1354C211yesmaximal, characteristic, complemented
8C22×#4343C411yescharacteristic
9C2×#66947—21no—
10C2×C4⋊C4×D11C2211yescharacteristic
11C11×#395C2211yescharacteristic
12#10622842C411yescharacteristic
13#10622739—21no—
14#10622604C2211yescharacteristic
15#10622602—21no—
16D11×C22⋊C8—21no—
17#10622285C411yescharacteristic
18#10622281—21no—
19#10622278—21no—
20#10622277C411yescharacteristic
21C11×#343C2211yescharacteristic
22C11×#324C2211yescharacteristic
23#10622192—21no—
24#10622168C2211yescharacteristic
25#10622166C2211yescharacteristic
26#10622107—21no—
27C22×Q8×C11C2×C411yescharacteristic
28C2×#4343—41no—
29C2×#4343—41no—
30C2×#4343—44no—
31C22×D44—21no—
32C22×D44C2×C411yescharacteristic
33C22×C4×D11—21no—
34C22×C4×D11C2×C411yescharacteristic
35C22×C4×D11D411yescharacteristic
36C22×C4×D11D411yescharacteristic
37C2×C11×M16—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4C2311yescharacteristic
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×C4⋊Dic11D411yescharacteristic
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4C2×C411yescharacteristic
48C2×Dic11⋊C4D411yescharacteristic
49C2×#4318—21no—
50C2×C8×D11—41no—
51#66947—44no—
52C4⋊C4×D11—41no—
53C4⋊C4×D11—41no—
54C11×C22⋊C8—21no—
55C11×#95—21no—
56C11×#95C2×C411yescharacteristic
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95C2×C411yescharacteristic
60C22⋊(C11⋊C8)—21no—
61(C2×D11)⋊C8—41no—
62(C2×D11)⋊C8—41no—
63(C2×D11)⋊C8—41no—
64#11848—111nomaximal, Sylow
65C23×D11—21no—
66C23×D11C22⋊C411yescharacteristic
67C2×Q8×C11—42no—
68C2×Q8×C11—41no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11C22×C411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×Dic11—21no—
75C22×Dic11C22⋊C411yescharacteristic
76C22×Dic11C22⋊C411yescharacteristic
77C22×Dic11C22⋊C411yescharacteristic
78#4343—44no—
79#4343—44no—
80#4343—44no—
81#4343—44no—
82C2×D44—24no—
83C2×D44—41no—
84C2×D44—42no—
85C2×D44—42no—
86C2×D44—41no—
87C2×D44—41no—
88C2×C4×D11—21no—
89C2×C4×D11—21no—
90C2×C4×D11—21no—
91C2×C4×D11—21no—
92C2×C4×D11—21no—
93C2×C4×D11—21no—
94C2×C4×D11—21no—
95C2×C4×D11—21no—
96C2×C4×D11—41no—
97C2×C4×D11—42no—
98C2×C4×D11—42no—
99C2×C4×D11—42no—
100C2×C4×D11—42no—
101C2×C4×D11—42no—
102C11×M16—41no—
103C11×M16—41no—
104C2×C8×C11—41no—
105C2×C8×C11—41no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—42no—
108(C2×D11)⋊C4—42no—
109(C2×D11)⋊C4—42no—
110(C2×D11)⋊C4—42no—
111(C2×D11)⋊C4—42no—
112(C2×D11)⋊C4—41no—
113(C2×D11)⋊C4—41no—
114C4⋊Dic11—41no—
115Dic11⋊C4—41no—
116Dic11⋊C4—41no—
117Dic11⋊C4—42no—
118#4318—41no—
119#4318—41no—
120C2×C11⋊C8—41no—
121C2×C11⋊C8—41no—
122C8×D11—82no—
123#2406—111no—
124#1821—111no—
125C2×#324—111no—
126#1354—111no—
127#1354D1111yescharacteristic, complemented
128#1345—111no—
129#1345—111no—
130C23×C11C2×C22⋊C411yescharacteristic
131C22×D11—21no—
132C22×D11—21no—
133C22×D11—22no—
134C22×D11—22no—
135C22×D11—41no—
136C22×D11—41no—
137C22×D11—41no—
138C22×D11—41no—
139C22×D11—41no—
140C22×D11—41no—
141C22×D11—41no—
142C22×D11#9911yescharacteristic
143C22×D11#9911yescharacteristic
144Q8×C11—42no—
145Q8×C11—42no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—22no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11#13511yescharacteristic
159C2×C4×C11#13511yescharacteristic
160C2×Dic11—21no—
161C2×Dic11—21no—
162C2×Dic11—21no—
163C2×Dic11—21no—
164C2×Dic11—21no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170D44—44no—
171D44—42no—
172D44—42no—
173D44—44no—
174C4×D11—41no—
175C4×D11—41no—
176C4×D11—41no—
177C4×D11—41no—
178C4×D11—42no—
179C4×D11—48no—
180C4×D11—42no—
181C4×D11—42no—
182C4×D11—81no—
183C8×C11—81no—
184C8×C11—81no—
185C11⋊C8—81no—
186C11⋊C8—81no—
187C22×#41—111no—
188C2×#123—221no—
189C22×C4⋊C4—111no—
190#407—221no—
191C2×C22⋊C8—221no—
192#395—111no—
193#395C2×D1111yescharacteristic
194#394—111no—
195#394—111no—
196#386—221no—
197#385—221no—
198#385—221no—
199#381—111no—
200#343—111no—
201#343—221no—
202#343C2×D1111yescharacteristic
203#324—111no—
204#324—221no—
205#324C2×D1111yescharacteristic
206C22×C11—21no—
207C22×C11—21no—
208C22×C11C2×#9911yescharacteristic
209C22×C11#41611yescharacteristic
210C22×C11#42111yescharacteristic
211C2×D11—21no—
212C2×D11—21no—
213C2×D11—21no—
214C2×D11—21no—
215C2×D11—21no—
216C2×D11—42no—
217C2×D11—42no—
218C2×D11—42no—
219C2×D11—42no—
220C2×D11—42no—
221C2×D11—81no—
222C2×D11—81no—
223C2×D11—81no—
224C2×D11—81no—
225C2×D11AΣL(1,𝔽16)12yes—
226C4×C11—21no—
227C4×C11—21no—
228C4×C11—42no—
229C4×C11—41no—
230C4×C11—41no—
231C4×C11—81no—
232Dic11—41no—
233Dic11—41no—
234Dic11—41no—
235Dic11—81no—
236C2×#41—441no—
237C2×#41—441no—
238C2×#41—444no—
239C22×Q8C4×D1111yescharacteristic
240C22×D4—111no—
241C22×D4—221no—
242C23×C4—111no—
243C23×C4—111no—
244C23×C4—111no—
245C23×C4—221no—
246C2×M16—21no—
247C2×M16—221no—
248C22×C8—441no—
249#123—444no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—111no—
252C2×C4⋊C4—111no—
253C2×C4⋊C4—111no—
254C2×C4⋊C4—221no—
255C2×C4⋊C4—441no—
256C2×C4⋊C4—441no—
257C2×C4⋊C4C22×D1111yescharacteristic
258C2×C22⋊C4—221no—
259C2×C22⋊C4—221no—
260C2×C22⋊C4—221no—
261C2×C22⋊C4—221no—
262C2×C22⋊C4—221no—
263C22⋊C8—21no—
264C22⋊C8—221no—
265C22⋊C8—441no—
266C22⋊C8—441no—
267C22⋊C8—441no—
268#95—21no—
269#95—111no—
270#95—221no—
271#95—221no—
272#95C4×D1111yescharacteristic
273C2×C11—21no—
274C2×C11—21no—
275C2×C11#151611yescharacteristic
276C2×C11C2×AΣL(1,𝔽16)11yescharacteristic
277C2×C11#213311yescharacteristic
278D11—22no—
279D11—41no—
280D11—82no—
281C24—111no—
282C24—221no—
283#41—444no—
284#41—444no—
285#41—444no—
286#41—444no—
287C2×Q8—42no—
288C2×Q8—41no—
289C2×D4—224no—
290C2×D4—441no—
291C2×D4—441no—
292C2×D4—441no—
293C2×D4—442no—
294C2×D4—442no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—111no—
298C22×C4—111no—
299C22×C4—111no—
300C22×C4—221no—
301C22×C4—221no—
302C22×C4—221no—
303C22×C4—221no—
304C22×C4—221no—
305C22×C4—221no—
306C22×C4—221no—
307C22×C4—221no—
308C22×C4—221no—
309C22×C4—441no—
310C22×C4—442no—
311C22×C4—442no—
312C22×C4—442no—
313C22×C4—442no—
314C22×C4—442no—
315C22×C4C2×C4×D1111yescharacteristic
316C22×C4D4×D1111yescharacteristic
317C22×C4D4×D1111yescharacteristic
318M16—41no—
319M16—41no—
320M16—441no—
321M16—441no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8—441no—
325C2×C8—441no—
326C2×C8—882no—
327C4⋊C4—41no—
328C4⋊C4—42no—
329C4⋊C4—441no—
330C4⋊C4—441no—
331C4⋊C4—441no—
332C4⋊C4—442no—
333C22⋊C4—442no—
334C22⋊C4—442no—
335C22⋊C4—442no—
336C22⋊C4—442no—
337C22⋊C4—441no—
338C22⋊C4—441no—
339C11#1184811yescharacteristic, complemented, Sylow
340C23—111no—
341C23—111no—
342C23—222no—
343C23—222no—
344C23—221no—
345C23—221no—
346C23—441no—
347C23—441no—
348C23—441no—
349C23—441no—
350C23—441no—
351C23—441no—
352C23—441no—
353C23C22⋊C4×D1111yescharacteristic
354Q8—42no—
355Q8—42no—
356D4—444no—
357D4—444no—
358D4—442no—
359D4—442no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—22no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—221no—
373C2×C4—221no—
374C2×C4—221no—
375C2×C4—221no—
376C2×C4—221no—
377C2×C4—441no—
378C2×C4—441no—
379C2×C4—441no—
380C2×C4—441no—
381C2×C4—442no—
382C2×C4—442no—
383C2×C4—442no—
384C2×C4—448no—
385C2×C4—441no—
386C2×C4—441no—
387C2×C4—441no—
388C2×C4—441no—
389C2×C4—441no—
390C2×C4—881no—
391C2×C4#6696911yescharacteristic
392C2×C4#6697211yescharacteristic
393C8—81no—
394C8—81no—
395C8—881no—
396C8—881no—
397C22—21no—
398C22—21no—
399C22—112no—
400C22—221no—
401C22—221no—
402C22—221no—
403C22—221no—
404C22—221no—
405C22—442no—
406C22—442no—
407C22—442no—
408C22—442no—
409C22—442no—
410C22—881no—
411C22—881no—
412C22—881no—
413C22—881no—
414C22D11×#9911yescharacteristic
415C22#1062241711yescharacteristic
416C22#1062243411yescharacteristic
417C4—21no—
418C4—21no—
419C4—41no—
420C4—42no—
421C4—41no—
422C4—81no—
423C4—441no—
424C4—441no—
425C4—441no—
426C4—881no—
427C2—21no—
428C2—21no—
429C2—222no—
430C2—441no—
431C2—882no—
432C2#1306717111yescharacteristic
433C2D11×AΣL(1,𝔽16)11yescharacteristic
434C2#1307030411yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1354C2
socleC22×C11C2×#99
prime radicalC22×#4343C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1354D11
hypocenterC11#11848
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. #13068695C2semidirect
3. D11×#324C2semidirect
4. #13066646C2semidirect
5. #13066620C2semidirect
6. #13066618C2semidirect
7. C11×#1354C2semidirect
127. #1354D11semidirect
339. C11#11848semidirect

Maximal subgroups

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

subgroupindex
#130719522
#130686952
D11×#3242
#130666462
#130666202
#130666182
C11×#13542
#1184811