Finite Group Databasebeta

← #14664116

Subgroups — #14664116

Order 2816.

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

normal subgroups only

This group has 486 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#13074506C211yesmaximal, characteristic
2#13068403C211yesmaximal, characteristic, complemented
3#13066935C211yesmaximal, characteristic, complemented
4#13066640C211yesmaximal, characteristic, complemented
5#13066614C211yesmaximal, characteristic, complemented
6#13066612C211yesmaximal, characteristic, complemented
7C11×#1352C211yesmaximal, characteristic, complemented
8C2×#66948C411yescharacteristic, complemented
9C2×(C22⋊D11)⋊C4C2211yescharacteristic
10C11×#399C2211yescharacteristic
11#10622604—21no—
12#10622603—21no—
13#10622595C411yescharacteristic, complemented
14#10622573—21no—
15#10622573C2211yescharacteristic
16#10622571—21no—
17C2×#66870—21no—
18C22⋊C4×Dic11—21no—
19#10622331—21no—
20#10622285C411yescharacteristic, complemented
21#10622277C411yescharacteristic, complemented
22C11×#342C2211yescharacteristic
23C11×#323C2211yescharacteristic
24#10622164C2211yescharacteristic
25#10622163C2211yescharacteristic
26#10622106—21no—
27C22×C22⋊D11—21no—
28C22×C22⋊D11D411yescharacteristic
29C23×Dic11D411yescharacteristic
30C22×D44—21no—
31C22×D44C2×C411yescharacteristic
32C22×C4×D11C2×C411yescharacteristic
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4C2×C411yescharacteristic
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4C2311yescharacteristic
38C2×C22⋊Dic11—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4D411yescharacteristic
45C2×Dic11⋊C4C2×C411yescharacteristic
46C2×C4×Dic11—41no—
47C2×C4×Dic11D411yescharacteristic
48#66948—41no—
49#66948—41no—
50(C22⋊D11)⋊C4—41no—
51(C22⋊D11)⋊C4—41no—
52C11×C22⋊C8—21no—
53C11×#95C2×C411yescharacteristic
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—41no—
58C11⋊#95C2×C411yescharacteristic
59C22⋊(C11⋊C8)—21no—
60Dic11⋊C8—41no—
61C8×Dic11—41no—
62#66870—24no—
63#11729—111nomaximal, Sylow
64C24×C11C2×D411yescharacteristic
65C23×D11—21no—
66C23×D11C22⋊C411yescharacteristic
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—41no—
70C22×C4×C11C22×C411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C2×C22⋊D11—22no—
73C2×C22⋊D11—21no—
74C2×C22⋊D11—21no—
75C2×C22⋊D11—41no—
76C2×C22⋊D11—41no—
77C2×C22⋊D11—41no—
78C2×C22⋊D11—81no—
79C2×C22⋊D11—81no—
80C22×Dic11—21no—
81C22×Dic11—21no—
82C22×Dic11—21no—
83C22×Dic11—41no—
84C22×Dic11—81no—
85C22×Dic11C22⋊C411yescharacteristic
86C22×Dic11C22⋊C411yescharacteristic
87C22×Dic11C22⋊C411yescharacteristic
88C2×D44—41no—
89C2×D44—42no—
90C2×D44—81no—
91C2×D44—81no—
92C2×D44—81no—
93C2×C4×D11—21no—
94C2×C4×D11—21no—
95C2×C4×D11—81no—
96C2×C8×C11—41no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—81no—
99C11×C22⋊C4—22no—
100C11×C22⋊C4—41no—
101C11×C22⋊C4—41no—
102C11×C22⋊C4—81no—
103C22⋊Dic11—22no—
104C22⋊Dic11—41no—
105(C2×D11)⋊C4—41no—
106(C2×D11)⋊C4—41no—
107(C2×D11)⋊C4—41no—
108(C2×D11)⋊C4—42no—
109(C2×D11)⋊C4—81no—
110(C2×D11)⋊C4—81no—
111(C2×D11)⋊C4—81no—
112Dic11⋊C4—41no—
113C4×Dic11—21no—
114C4×Dic11—21no—
115C4×Dic11—82no—
116C2×C11⋊C8—41no—
117#2635—111no—
118C4×#99—111no—
119#1460—111no—
120#1352—111no—
121#1352D1111yescharacteristic, complemented
122#1343—111no—
123#1343—111no—
124C23×C11—21no—
125C23×C11—21no—
126C23×C11—41no—
127C23×C11—41no—
128C23×C11C2×C22⋊C411yescharacteristic
129C23×C11#13511yescharacteristic
130C23×C11#13511yescharacteristic
131C22×D11—21no—
132C22×D11—21no—
133C22×D11—21no—
134C22×D11—41no—
135C22×D11—41no—
136C22×D11—41no—
137C22×D11—41no—
138C22×D11—41no—
139C22×D11—41no—
140C22×D11—41no—
141C22×D11—41no—
142C22×D11—41no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—42no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—81no—
155C2×C4×C11—81no—
156C22⋊D11—42no—
157C22⋊D11—42no—
158C22⋊D11—82no—
159C22⋊D11—82no—
160C2×Dic11—21no—
161C2×Dic11—21no—
162C2×Dic11—21no—
163C2×Dic11—41no—
164C2×Dic11—42no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—42no—
169C2×Dic11—41no—
170C2×Dic11—81no—
171C2×Dic11—81no—
172C2×Dic11—81no—
173C2×Dic11#9911yescharacteristic
174C2×Dic11#9911yescharacteristic
175C2×Dic11#10412yes—
176D44—82no—
177D44—84no—
178C4×D11—81no—
179C4×D11—81no—
180C8×C11—81no—
181C11⋊C8—81no—
182C2×#121—111no—
183C2×C4×D4—111no—
184#431—221no—
185C2×#99—221no—
186#400—111no—
187#399C2×D1111yescharacteristic
188#394—111no—
189#394—221no—
190#392—111no—
191#392—221no—
192#388—221no—
193#386—221no—
194#381—111no—
195C4×C22⋊C4—221no—
196#342—111no—
197#342C2×D1111yescharacteristic
198#323—111no—
199#323—221no—
200#323C2×D1111yescharacteristic
201C22×C11—21no—
202C22×C11—21no—
203C22×C11—21no—
204C22×C11—21no—
205C22×C11—41no—
206C22×C11—41no—
207C22×C11—41no—
208C22×C11—41no—
209C22×C11—81no—
210C22×C11C2×#9911yescharacteristic
211C22×C11#41611yescharacteristic
212C22×C11C2×#10411yescharacteristic
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—
224C2×D11—81no—
225C4×C11—41no—
226C4×C11—41no—
227C4×C11—81no—
228C4×C11—82no—
229C4×C11—81no—
230Dic11—21no—
231Dic11—21no—
232Dic11—22no—
233Dic11—41no—
234Dic11—81no—
235Dic11—82no—
236C22×D4—111no—
237C22×D4—111no—
238C22×D4—221no—
239C22×D4—221no—
240C23×C4—111no—
241C23×C4—111no—
242#121—441no—
243#121—441no—
244C4×D4—441no—
245C4×D4—441no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—111no—
248C2×C4⋊C4C4×D1111yescharacteristic
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—111no—
252C2×C22⋊C4—221no—
253C2×C22⋊C4—221no—
254C2×C22⋊C4—221no—
255C2×C22⋊C4—221no—
256C2×C22⋊C4—221no—
257C2×C22⋊C4—221no—
258C2×C22⋊C4C22×D1111yescharacteristic
259C2×C42—111no—
260C2×C42—441no—
261C4⋊C8—441no—
262#99—224no—
263C22⋊C8—21no—
264C22⋊C8—221no—
265C4×C8—441no—
266#95—111no—
267#95—221no—
268#95—221no—
269#95—221no—
270#95—441no—
271#95C4×D1111yescharacteristic
272C2×C11—21no—
273C2×C11—21no—
274C2×C11—41no—
275C2×C11—41no—
276C2×C11#150111yescharacteristic
277C2×C11#212111yescharacteristic
278C2×C11#212811yescharacteristic
279D11—81no—
280D11—161no—
281C24—111no—
282C24—221no—
283C24D4×D1111yescharacteristic
284C2×D4—222no—
285C2×D4—221no—
286C2×D4—221no—
287C2×D4—441no—
288C2×D4—442no—
289C2×D4—441no—
290C2×D4—441no—
291C2×D4—441no—
292C2×D4—881no—
293C2×D4—881no—
294C2×D4—881no—
295C2×D4—881no—
296C2×D4—881no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—41no—
300C22×C4—111no—
301C22×C4—111no—
302C22×C4—111no—
303C22×C4—221no—
304C22×C4—221no—
305C22×C4—221no—
306C22×C4—221no—
307C22×C4—221no—
308C22×C4—441no—
309C22×C4—881no—
310C22×C4—881no—
311C22×C4C2×C4×D1111yescharacteristic
312C22×C4D4×D1111yescharacteristic
313C2×C8—41no—
314C2×C8—441no—
315C4⋊C4—41no—
316C4⋊C4—81no—
317C4⋊C4—441no—
318C22⋊C4—22no—
319C22⋊C4—41no—
320C22⋊C4—41no—
321C22⋊C4—81no—
322C22⋊C4—222no—
323C22⋊C4—441no—
324C22⋊C4—441no—
325C22⋊C4—441no—
326C22⋊C4—442no—
327C22⋊C4—441no—
328C22⋊C4—881no—
329C22⋊C4—881no—
330C22⋊C4—881no—
331C42—221no—
332C42—221no—
333C42—882no—
334C11#1172911yescharacteristic, complemented, Sylow
335C23—21no—
336C23—21no—
337C23—41no—
338C23—41no—
339C23—221no—
340C23—221no—
341C23—221no—
342C23—441no—
343C23—441no—
344C23—441no—
345C23—441no—
346C23—441no—
347C23—441no—
348C23—441no—
349C23—441no—
350C23—441no—
351C23C22⋊C4×D1111yescharacteristic
352C23#6696911yescharacteristic
353C23#6697211yescharacteristic
354D4—442no—
355D4—442no—
356D4—882no—
357D4—884no—
358D4—882no—
359D4—882no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—42no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4—111no—
374C2×C4—111no—
375C2×C4—112no—
376C2×C4—221no—
377C2×C4—221no—
378C2×C4—221no—
379C2×C4—441no—
380C2×C4—442no—
381C2×C4—441no—
382C2×C4—442no—
383C2×C4—441no—
384C2×C4—441no—
385C2×C4—441no—
386C2×C4—881no—
387C2×C4—881no—
388C2×C4—881no—
389C2×C4—881no—
390C2×C4—881no—
391C8—81no—
392C8—881no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—81no—
402C22—441no—
403C22—441no—
404C22—441no—
405C22—881no—
406C22—881no—
407C22—881no—
408C22—881no—
409C22—881no—
410C22—881no—
411C22—881no—
412C22—881no—
413C22—881no—
414C22D11×#9911yescharacteristic
415C22#1062241711yescharacteristic
416C22D11×#10411yescharacteristic
417C4—41no—
418C4—41no—
419C4—81no—
420C4—82no—
421C4—81no—
422C4—222no—
423C4—221no—
424C4—221no—
425C4—441no—
426C4—881no—
427C4—882no—
428C2—21no—
429C2—21no—
430C2—41no—
431C2—41no—
432C2—881no—
433C2—1761no—
434C2#1306710611yescharacteristic
435C2#1307026111yescharacteristic
436C2#1307028611yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1352C2
socleC22×C11C2×#99
prime radical#13074506C2
cosocleC2×C11×C22⋊C4C23
hypercenter#1352D11
hypocenterC11#11729
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1352

Complements

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

NH ≅ G/Ntype
2. #13068403C2semidirect
3. #13066935C2semidirect
4. #13066640C2semidirect
5. #13066614C2semidirect
6. #13066612C2semidirect
7. C11×#1352C2semidirect
8. C2×#66948C4semidirect
13. #10622595C4semidirect
20. #10622285C4semidirect
21. #10622277C4semidirect
121. #1352D11semidirect
334. C11#11729semidirect

Maximal subgroups

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

subgroupindex
#130745062
#130684032
#130669352
#130666402
#130666142
#130666122
C11×#13522
#1172911