Finite Group Databasebeta

← #14664156

Subgroups — #14664156

Order 2816.

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

normal subgroups only

This group has 470 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#13074509C211yesmaximal, characteristic
2#13068407C211yesmaximal, characteristic, complemented
3#13066933C211yesmaximal, characteristic, complemented
4#13066643C211yesmaximal, characteristic, complemented
5#13066620C211yesmaximal, characteristic, complemented
6#13066618C211yesmaximal, characteristic, complemented
7C11×#1353C211yesmaximal, characteristic, complemented
8C2×#66948C411yescharacteristic
9C2×#66946C2211yescharacteristic
10C11×#400C2211yescharacteristic
11C2×#66887—21no—
12M16×Dic11—21no—
13#10622605C411yescharacteristic
14#10622604C2211yescharacteristic
15D11×C22⋊C8—21no—
16#10622285—21no—
17#10622284—21no—
18#10622284C411yescharacteristic
19#10622282—21no—
20#10622278—21no—
21#10622277C411yescharacteristic
22C11×#343C2211yescharacteristic
23C11×#324C2211yescharacteristic
24#10622168C2211yescharacteristic
25#10622166C2211yescharacteristic
26#10622106—21no—
27C22×D44—21no—
28C22×D44—21no—
29C22×D44C2×C411yescharacteristic
30C22×D44D411yescharacteristic
31C22×C4×D11C2×C411yescharacteristic
32C22×C4×D11D411yescharacteristic
33C2×C11×M16—21no—
34C2×C11×C4⋊C4C2×C411yescharacteristic
35C2×C11×C4⋊C4C2311yescharacteristic
36C2×(C2×D11)⋊C4—21no—
37C2×(C2×D11)⋊C4—21no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4C2×C411yescharacteristic
43C2×(C2×D11)⋊C4D411yescharacteristic
44C2×Dic11⋊C4—21no—
45C2×C4×Dic11D411yescharacteristic
46C2×#4318—21no—
47C2×C8×D11—41no—
48#66948—41no—
49#66948—41no—
50#66946—41no—
51#66946—41no—
52C11×C22⋊C8—21no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95C2×C411yescharacteristic
56C11⋊#95—21no—
57C11⋊#95C2×C411yescharacteristic
58C22⋊(C11⋊C8)—21no—
59#66887—24no—
60(C2×D11)⋊C8—41no—
61#66879—41no—
62C8×Dic11—41no—
63#11737—111nomaximal, Sylow
64C23×D11—21no—
65C23×D11C22⋊C411yescharacteristic
66C23×D11C22⋊C411yescharacteristic
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11C22×C411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×Dic11—21no—
73C22×Dic11C22⋊C411yescharacteristic
74C22×Dic11C22⋊C411yescharacteristic
75C2×D44—22no—
76C2×D44—21no—
77C2×D44—21no—
78C2×D44—41no—
79C2×D44—41no—
80C2×D44—42no—
81C2×D44—42no—
82C2×D44—81no—
83C2×D44—81no—
84C2×D44—81no—
85C2×D44—81no—
86C2×D44—81no—
87C2×C4×D11—21no—
88C2×C4×D11—21no—
89C2×C4×D11—21no—
90C2×C4×D11—21no—
91C2×C4×D11—81no—
92C2×C4×D11—81no—
93C11×M16—22no—
94C11×M16—41no—
95C2×C8×C11—41no—
96C2×C8×C11—41no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99(C2×D11)⋊C4—41no—
100(C2×D11)⋊C4—41no—
101(C2×D11)⋊C4—41no—
102(C2×D11)⋊C4—41no—
103(C2×D11)⋊C4—41no—
104(C2×D11)⋊C4—41no—
105(C2×D11)⋊C4—81no—
106(C2×D11)⋊C4—81no—
107(C2×D11)⋊C4—81no—
108(C2×D11)⋊C4—81no—
109Dic11⋊C4—81no—
110C4×Dic11—21no—
111C4×Dic11—21no—
112#4318—22no—
113#4318—41no—
114C2×C11⋊C8—41no—
115C2×C11⋊C8—41no—
116C8×D11—82no—
117#2635—111no—
118C4×#100—111no—
119#1459—111no—
120#1353—111no—
121#1353D1111yescharacteristic, complemented
122#1345—111no—
123#1345—111no—
124C23×C11C2×C22⋊C411yescharacteristic
125C22×D11—21no—
126C22×D11—21no—
127C22×D11—21no—
128C22×D11—21no—
129C22×D11—21no—
130C22×D11—41no—
131C22×D11—41no—
132C22×D11—41no—
133C22×D11—41no—
134C22×D11—41no—
135C22×D11—41no—
136C22×D11—41no—
137C22×D11—41no—
138C22×D11—41no—
139C22×D11—41no—
140C22×D11—41no—
141C22×D11#10412yes—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11#13511yescharacteristic
155C2×C4×C11#13511yescharacteristic
156C2×Dic11—21no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11#9911yescharacteristic
163C2×Dic11#9911yescharacteristic
164D44—42no—
165D44—42no—
166D44—82no—
167D44—84no—
168D44—84no—
169C4×D11—42no—
170C4×D11—81no—
171C4×D11—81no—
172C4×D11—81no—
173C8×C11—42no—
174C8×C11—81no—
175C11⋊C8—42no—
176C11⋊C8—81no—
177C2×#121—111no—
178C2×C4×D4—111no—
179C2×#100—221no—
180C2×C22⋊C8—221no—
181C4×M16—221no—
182#400C2×D1111yescharacteristic
183#399—111no—
184#394—111no—
185#394—221no—
186#392—111no—
187#392—221no—
188#388—221no—
189#386—221no—
190#381—111no—
191#343—111no—
192#343C2×D1111yescharacteristic
193#324—111no—
194#324C2×D1111yescharacteristic
195#323—221no—
196C22×C11—21no—
197C22×C11—21no—
198C22×C11C2×#9911yescharacteristic
199C22×C11#41611yescharacteristic
200C22×C11C2×#10411yescharacteristic
201C2×D11—22no—
202C2×D11—41no—
203C2×D11—41no—
204C2×D11—42no—
205C2×D11—41no—
206C2×D11—41no—
207C2×D11—41no—
208C2×D11—81no—
209C2×D11—81no—
210C2×D11—81no—
211C2×D11—81no—
212C2×D11—81no—
213C2×D11—81no—
214C2×D11—81no—
215C2×D11—81no—
216C2×D11—81no—
217C2×D11—81no—
218C4×C11—21no—
219C4×C11—21no—
220C4×C11—41no—
221C4×C11—41no—
222C4×C11—81no—
223C4×C11—81no—
224Dic11—21no—
225Dic11—21no—
226Dic11—41no—
227Dic11—81no—
228C22×D4—111no—
229C22×D4—111no—
230C22×D4—221no—
231C22×D4—221no—
232C23×C4—111no—
233C23×C4—111no—
234C2×M16—21no—
235C2×M16—221no—
236C22×C8—441no—
237#121—441no—
238#121—441no—
239C4×D4—441no—
240C4×D4—441no—
241C2×C4⋊C4—221no—
242C2×C4⋊C4C4×D1111yescharacteristic
243C2×C4⋊C4C22×D1111yescharacteristic
244C2×C22⋊C4—111no—
245C2×C22⋊C4—111no—
246C2×C22⋊C4—221no—
247C2×C22⋊C4—221no—
248C2×C22⋊C4—221no—
249C2×C22⋊C4—221no—
250C2×C22⋊C4—221no—
251C2×C22⋊C4—221no—
252C2×C42—111no—
253#100—224no—
254C22⋊C8—21no—
255C22⋊C8—221no—
256C22⋊C8—441no—
257#97—441no—
258C4×C8—441no—
259#95—21no—
260#95—21no—
261#95—111no—
262#95—221no—
263#95C4×D1111yescharacteristic
264C2×C11—21no—
265C2×C11—21no—
266C2×C11#150111yescharacteristic
267C2×C11#212111yescharacteristic
268C2×C11#213411yescharacteristic
269D11—42no—
270D11—81no—
271D11—161no—
272C24—111no—
273C24—111no—
274C24—221no—
275C2×D4—222no—
276C2×D4—221no—
277C2×D4—221no—
278C2×D4—441no—
279C2×D4—441no—
280C2×D4—442no—
281C2×D4—442no—
282C2×D4—881no—
283C2×D4—881no—
284C2×D4—881no—
285C2×D4—881no—
286C2×D4—881no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—111no—
290C22×C4—111no—
291C22×C4—221no—
292C22×C4—221no—
293C22×C4—221no—
294C22×C4—221no—
295C22×C4—221no—
296C22×C4—881no—
297C22×C4—881no—
298C22×C4C2×C4×D1111yescharacteristic
299C22×C4D4×D1111yescharacteristic
300C22×C4D4×D1111yescharacteristic
301M16—22no—
302M16—41no—
303M16—222no—
304M16—441no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—441no—
308C2×C8—441no—
309C2×C8—882no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—881no—
313C22⋊C4—441no—
314C22⋊C4—441no—
315C22⋊C4—441no—
316C22⋊C4—441no—
317C22⋊C4—441no—
318C22⋊C4—441no—
319C22⋊C4—881no—
320C22⋊C4—881no—
321C22⋊C4—881no—
322C22⋊C4—881no—
323C42—221no—
324C42—221no—
325C11#1173711yescharacteristic, complemented, Sylow
326C23—112no—
327C23—221no—
328C23—221no—
329C23—221no—
330C23—221no—
331C23—221no—
332C23—441no—
333C23—441no—
334C23—441no—
335C23—441no—
336C23—441no—
337C23—441no—
338C23—441no—
339C23—441no—
340C23—441no—
341C23—441no—
342C23—441no—
343C23C22⋊C4×D1111yescharacteristic
344D4—442no—
345D4—442no—
346D4—882no—
347D4—884no—
348D4—884no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—111no—
362C2×C4—111no—
363C2×C4—221no—
364C2×C4—442no—
365C2×C4—441no—
366C2×C4—441no—
367C2×C4—441no—
368C2×C4—441no—
369C2×C4—441no—
370C2×C4—881no—
371C2×C4—881no—
372C2×C4—881no—
373C2×C4#6696911yescharacteristic
374C2×C4#6697211yescharacteristic
375C8—42no—
376C8—81no—
377C8—442no—
378C8—881no—
379C22—21no—
380C22—21no—
381C22—222no—
382C22—442no—
383C22—441no—
384C22—441no—
385C22—441no—
386C22—441no—
387C22—441no—
388C22—881no—
389C22—881no—
390C22—881no—
391C22—881no—
392C22—881no—
393C22—881no—
394C22—881no—
395C22—881no—
396C22—881no—
397C22—881no—
398C22D11×#9911yescharacteristic
399C22#1062241711yescharacteristic
400C22D11×#10411yescharacteristic
401C4—21no—
402C4—21no—
403C4—41no—
404C4—41no—
405C4—81no—
406C4—81no—
407C4—221no—
408C4—221no—
409C4—441no—
410C4—881no—
411C2—21no—
412C2—21no—
413C2—442no—
414C2—881no—
415C2—1761no—
416C2#1306710611yescharacteristic
417C2#1307026111yescharacteristic
418C2#1307030611yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1353C2
socleC22×C11C2×#99
prime radical#13074509C2
cosocleC2×C11×C4⋊C4C23
hypercenter#1353D11
hypocenterC11#11737
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1353

Complements

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

NH ≅ G/Ntype
2. #13068407C2semidirect
3. #13066933C2semidirect
4. #13066643C2semidirect
5. #13066620C2semidirect
6. #13066618C2semidirect
7. C11×#1353C2semidirect
121. #1353D11semidirect
325. C11#11737semidirect

Maximal subgroups

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

subgroupindex
#130745092
#130684072
#130669332
#130666432
#130666202
#130666182
C11×#13532
#1173711