Finite Group Databasebeta

← #14664372

Subgroups — #14664372

Order 2816.

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

normal subgroups only

This group has 514 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#13073577C211yesmaximal, characteristic
2#13068407C211yesmaximal, characteristic, complemented
3#13066953C211yesmaximal, characteristic, complemented
4#13066622C211yesmaximal, characteristic, complemented
5#13066620C211yesmaximal, characteristic, complemented
6#13066618C211yesmaximal, characteristic, complemented
7C11×#1346C211yesmaximal, characteristic, complemented
8C2×#66948—21no—
9C2×#66948C411yescharacteristic
10C2×#66946C2211yescharacteristic
11C11×#398C2211yescharacteristic
12C2×#66887—21no—
13M16×Dic11—21no—
14#10622606C411yescharacteristic
15#10622604C2211yescharacteristic
16#10622603—21no—
17#10622339—21no—
18#10622284C411yescharacteristic
19#10622278—21no—
20#10622278—21no—
21D11×#95C411yescharacteristic
22C11×#343C2211yescharacteristic
23C11×#324C2211yescharacteristic
24#10622168C2211yescharacteristic
25#10622166C2211yescharacteristic
26#10622106—21no—
27C22×D44—21no—
28C22×D44—21no—
29C22×D44C2×C411yescharacteristic
30C22×D44D411yescharacteristic
31C22×C4×D11—21no—
32C22×C4×D11C2×C411yescharacteristic
33C22×C4×D11D411yescharacteristic
34C2×C11×M16—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4C2×C411yescharacteristic
37C2×C11×C4⋊C4C2311yescharacteristic
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4C2×C411yescharacteristic
44C2×(C2×D11)⋊C4D411yescharacteristic
45C2×C4×Dic11D411yescharacteristic
46C2×#4318—21no—
47C2×#4313—41no—
48#66948—42no—
49#66948—42no—
50#66948—41no—
51#66948—41no—
52#66946—41no—
53#66946—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#66887—24no—
62(C2×D11)⋊C8—41no—
63#66879—41no—
64C8×Dic11—41no—
65#11783—111nomaximal, Sylow
66C23×D11—21no—
67C23×D11C22⋊C411yescharacteristic
68C23×D11C22⋊C411yescharacteristic
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
77C2×D44—22no—
78C2×D44—21no—
79C2×D44—21no—
80C2×D44—41no—
81C2×D44—42no—
82C2×D44—41no—
83C2×D44—42no—
84C2×D44—42no—
85C2×D44—42no—
86C2×D44—42no—
87C2×D44—81no—
88C2×D44—81no—
89C2×C4×D11—21no—
90C2×C4×D11—21no—
91C2×C4×D11—21no—
92C2×C4×D11—21no—
93C2×C4×D11—42no—
94C2×C4×D11—42no—
95C2×C4×D11—81no—
96C2×C4×D11—81no—
97C2×C4×D11—81no—
98C11×M16—22no—
99C11×M16—41no—
100C2×C8×C11—41no—
101C2×C8×C11—41no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106(C2×D11)⋊C4—41no—
107(C2×D11)⋊C4—41no—
108(C2×D11)⋊C4—42no—
109(C2×D11)⋊C4—42no—
110(C2×D11)⋊C4—41no—
111(C2×D11)⋊C4—41no—
112(C2×D11)⋊C4—41no—
113(C2×D11)⋊C4—41no—
114(C2×D11)⋊C4—81no—
115C4×Dic11—21no—
116C4×Dic11—21no—
117#4318—22no—
118#4318—41no—
119C2×C11⋊C8—41no—
120C2×C11⋊C8—41no—
121#4313—82no—
122#2543—111no—
123C4×#100—111no—
124#1465—111no—
125#1346—111no—
126#1346D1111yescharacteristic, complemented
127#1345—111no—
128#1345—111no—
129C23×C11C2×C22⋊C411yescharacteristic
130C22×D11—21no—
131C22×D11—21no—
132C22×D11—21no—
133C22×D11—21no—
134C22×D11—21no—
135C22×D11—41no—
136C22×D11—41no—
137C22×D11—41no—
138C22×D11—41no—
139C22×D11—41no—
140C22×D11—41no—
141C22×D11—41no—
142C22×D11—41no—
143C22×D11—41no—
144C22×D11—41no—
145C22×D11—41no—
146C22×D11#10412yes—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—22no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
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—41no—
159C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
160C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
161C2×Dic11—21no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11#9911yescharacteristic
168C2×Dic11#9911yescharacteristic
169D44—42no—
170D44—42no—
171D44—84no—
172D44—82no—
173D44—84no—
174C4×D11—42no—
175C4×D11—81no—
176C4×D11—81no—
177C4×D11—81no—
178C4×D11—84no—
179C8×C11—42no—
180C8×C11—81no—
181C11⋊C8—42no—
182C11⋊C8—81no—
183C2×#121—111no—
184C2×#121—221no—
185C2×C4×D4—111no—
186C2×#100—221no—
187#407—221no—
188C4×M16—221no—
189#398C2×D1111yescharacteristic
190#397—111no—
191#394—111no—
192#392—111no—
193#388—221no—
194#386—221no—
195#386—221no—
196C2×#95—111no—
197#343—111no—
198#343C2×D1111yescharacteristic
199#324—111no—
200#324C2×D1111yescharacteristic
201#323—221no—
202C22×C11—21no—
203C22×C11—21no—
204C22×C11C2×#9911yescharacteristic
205C22×C11#41811yescharacteristic
206C22×C11C2×#10411yescharacteristic
207C2×D11—22no—
208C2×D11—42no—
209C2×D11—41no—
210C2×D11—41no—
211C2×D11—42no—
212C2×D11—42no—
213C2×D11—41no—
214C2×D11—41no—
215C2×D11—41no—
216C2×D11—81no—
217C2×D11—81no—
218C2×D11—81no—
219C2×D11—81no—
220C2×D11—81no—
221C2×D11—81no—
222C2×D11—81no—
223C2×D11—81no—
224C4×C11—21no—
225C4×C11—21no—
226C4×C11—42no—
227C4×C11—41no—
228C4×C11—41no—
229C4×C11—81no—
230Dic11—21no—
231Dic11—21no—
232Dic11—41no—
233Dic11—81no—
234C22×D4—111no—
235C22×D4—111no—
236C22×D4—221no—
237C22×D4—221no—
238C23×C4—111no—
239C23×C4—111no—
240C23×C4—221no—
241C2×M16—21no—
242C2×M16—221no—
243C2×M16—441no—
244#121—442no—
245#121—442no—
246#121—441no—
247#121—441no—
248C4×D4—441no—
249C4×D4—441no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4C4×D1111yescharacteristic
252C2×C4⋊C4C22×D1111yescharacteristic
253C2×C22⋊C4—111no—
254C2×C22⋊C4—111no—
255C2×C22⋊C4—221no—
256C2×C22⋊C4—221no—
257C2×C22⋊C4—221no—
258C2×C22⋊C4—221no—
259C2×C22⋊C4—221no—
260C2×C42—111no—
261#100—224no—
262C22⋊C8—21no—
263C22⋊C8—221no—
264C22⋊C8—441no—
265#97—441no—
266C4×C8—441no—
267#95—21no—
268#95—111no—
269#95—221no—
270#95—221no—
271#95C4×D1111yescharacteristic
272C2×C11—21no—
273C2×C11—21no—
274C2×C11#150711yescharacteristic
275C2×C11#212111yescharacteristic
276C2×C11#213211yescharacteristic
277D11—42no—
278D11—81no—
279D11—161no—
280C24—111no—
281C24—111no—
282C24—221no—
283C2×D4—222no—
284C2×D4—221no—
285C2×D4—221no—
286C2×D4—441no—
287C2×D4—441no—
288C2×D4—442no—
289C2×D4—442no—
290C2×D4—442no—
291C2×D4—442no—
292C2×D4—442no—
293C2×D4—881no—
294C2×D4—881no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—111no—
298C22×C4—111no—
299C22×C4—221no—
300C22×C4—221no—
301C22×C4—221no—
302C22×C4—221no—
303C22×C4—221no—
304C22×C4—442no—
305C22×C4—442no—
306C22×C4—881no—
307C22×C4—881no—
308C22×C4—881no—
309C22×C4C2×C4×D1111yescharacteristic
310C22×C4D4×D1111yescharacteristic
311C22×C4D4×D1111yescharacteristic
312M16—22no—
313M16—41no—
314M16—222no—
315M16—441no—
316M16—882no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—441no—
320C2×C8—441no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C22⋊C4—441no—
326C22⋊C4—441no—
327C22⋊C4—442no—
328C22⋊C4—441no—
329C22⋊C4—441no—
330C22⋊C4—442no—
331C22⋊C4—441no—
332C22⋊C4—441no—
333C22⋊C4—881no—
334C42—221no—
335C42—221no—
336C11#1178311yescharacteristic, complemented, Sylow
337C23—112no—
338C23—221no—
339C23—221no—
340C23—221no—
341C23—221no—
342C23—221no—
343C23—441no—
344C23—441no—
345C23—441no—
346C23—441no—
347C23—441no—
348C23—441no—
349C23—441no—
350C23—441no—
351C23—441no—
352C23—441no—
353C23—441no—
354C23C22⋊C4×D1111yescharacteristic
355D4—442no—
356D4—442no—
357D4—884no—
358D4—882no—
359D4—884no—
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—111no—
373C2×C4—111no—
374C2×C4—221no—
375C2×C4—442no—
376C2×C4—441no—
377C2×C4—441no—
378C2×C4—441no—
379C2×C4—441no—
380C2×C4—441no—
381C2×C4—881no—
382C2×C4—881no—
383C2×C4—881no—
384C2×C4—884no—
385C2×C4#6696411yescharacteristic
386C2×C4#6696711yescharacteristic
387C8—42no—
388C8—81no—
389C8—442no—
390C8—881no—
391C22—21no—
392C22—21no—
393C22—222no—
394C22—442no—
395C22—442no—
396C22—442no—
397C22—441no—
398C22—441no—
399C22—441no—
400C22—441no—
401C22—441no—
402C22—881no—
403C22—881no—
404C22—881no—
405C22—881no—
406C22—881no—
407C22—881no—
408C22—881no—
409C22—881no—
410C22D11×#9911yescharacteristic
411C22#1062238311yescharacteristic
412C22D11×#10411yescharacteristic
413C4—21no—
414C4—21no—
415C4—42no—
416C4—41no—
417C4—41no—
418C4—81no—
419C4—221no—
420C4—221no—
421C4—441no—
422C4—881no—
423C2—21no—
424C2—21no—
425C2—442no—
426C2—881no—
427C2—1761no—
428C2#1306713011yescharacteristic
429C2#1307026111yescharacteristic
430C2#1307030011yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1346C2
socleC22×C11C2×#99
prime radical#13073577C2
cosocleC2×C11×C4⋊C4C23
hypercenter#1346D11
hypocenterC11#11783
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1346

Complements

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

NH ≅ G/Ntype
2. #13068407C2semidirect
3. #13066953C2semidirect
4. #13066622C2semidirect
5. #13066620C2semidirect
6. #13066618C2semidirect
7. C11×#1346C2semidirect
126. #1346D11semidirect
336. C11#11783semidirect

Maximal subgroups

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

subgroupindex
#130735772
#130684072
#130669532
#130666222
#130666202
#130666182
C11×#13462
#1178311