Finite Group Databasebeta

← #14664655

Subgroups — #14664655

Order 2816.

432 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 69 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#13074304C211yesmaximal, characteristic
2#13068692C211yesmaximal, characteristic, complemented
3#13066927C211yesmaximal, characteristic, complemented
4#13066637C211yesmaximal, characteristic, complemented
5#13066614C211yesmaximal, characteristic
6#13066612C211yesmaximal, characteristic
7C11×#1351C211yesmaximal, characteristic, complemented
8C2×#67000C411yescharacteristic, complemented
9C2×#66930C2211yescharacteristic
10C11×#393C2211yescharacteristic
11#10622842C411yescharacteristic, complemented
12#10622573C2211yescharacteristic
13#10622571—21no—
14#10622570—21no—
15#10622556—21no—
16#10622331—21no—
17#10622285C411yescharacteristic, complemented
18#10622282—21no—
19#10622282—21no—
20#10622261C411yescharacteristic, complemented
21C11×#342C2211yescharacteristic
22C11×#323C2211yescharacteristic
23#10622165—21no—
24#10622164C2211yescharacteristic
25#10622163C2211yescharacteristic
26#10622107—21no—
27C22×Q8×C11C2×C411yescharacteristic
28C22×C22⋊D11—21no—
29C23×Dic11D411yescharacteristic
30C22×D44C2×C411yescharacteristic
31C2×C11×C22⋊C4—21no—
32C2×C11×C22⋊C4—21no—
33C2×C11×C22⋊C4C2311yescharacteristic
34C2×C22⋊Dic11—21no—
35C2×C22⋊Dic11D411yescharacteristic
36#67000—41no—
37#67000—41no—
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×Dic11⋊C4—21no—
44C2×Dic11⋊C4C2×C411yescharacteristic
45C2×Dic11⋊C4D411yescharacteristic
46C2×C4×Dic11—21no—
47C2×C4×Dic11C2×C411yescharacteristic
48C2×C4×Dic11D411yescharacteristic
49#66930—41no—
50#66930—41no—
51C11×C22⋊C8—21no—
52C11×#95—21no—
53C11×#95C2×C411yescharacteristic
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—41no—
57C11⋊#95—41no—
58C11⋊#95C2×C411yescharacteristic
59C22⋊(C11⋊C8)—21no—
60Dic11⋊C8—41no—
61C8×Dic11—41no—
62#11844—111nomaximal, Sylow
63C24×C11C2×D411yescharacteristic
64C23×D11—21no—
65C2×Q8×C11—41no—
66C2×Q8×C11—81no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—41no—
70C22×C4×C11C22×C411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C2×C22⋊D11—42no—
73C2×C22⋊D11—41no—
74C2×C22⋊D11—41no—
75C2×C22⋊D11—81no—
76C22×Dic11—21no—
77C22×Dic11—21no—
78C22×Dic11—21no—
79C22×Dic11—21no—
80C22×Dic11—21no—
81C22×Dic11—41no—
82C22×Dic11—41no—
83C22×Dic11C22⋊C411yescharacteristic
84C22×Dic11C22⋊C411yescharacteristic
85C22×Dic11C22⋊C411yescharacteristic
86C22×Dic11C22⋊C411yescharacteristic
87C2×D44—41no—
88C2×D44—81no—
89C2×C8×C11—41no—
90C11×C22⋊C4—41no—
91C11×C22⋊C4—41no—
92C11×C22⋊C4—41no—
93C11×C22⋊C4—81no—
94C22⋊Dic11—41no—
95C22⋊Dic11—41no—
96C22⋊Dic11—41no—
97(C2×D11)⋊C4—42no—
98(C2×D11)⋊C4—42no—
99(C2×D11)⋊C4—42no—
100(C2×D11)⋊C4—41no—
101(C2×D11)⋊C4—41no—
102(C2×D11)⋊C4—81no—
103Dic11⋊C4—41no—
104Dic11⋊C4—41no—
105Dic11⋊C4—81no—
106C4×Dic11—21no—
107C4×Dic11—21no—
108C4×Dic11—21no—
109C4×Dic11—21no—
110C4×Dic11—42no—
111C2×C11⋊C8—41no—
112#2610—111no—
113#1820—111no—
114#1458—111no—
115#1351—111no—
116#1351D1111yescharacteristic, complemented
117#1343—111no—
118#1343—111no—
119C23×C11—21no—
120C23×C11—21no—
121C23×C11—41no—
122C23×C11—41no—
123C23×C11C2×C22⋊C411yescharacteristic
124C23×C11#13511yescharacteristic
125C23×C11#13511yescharacteristic
126C22×D11—41no—
127C22×D11—41no—
128C22×D11—41no—
129C22×D11—41no—
130C22×D11—41no—
131C22×D11—41no—
132C22×D11—41no—
133Q8×C11—82no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—81no—
145C2×C4×C11—81no—
146C2×C4×C11—81no—
147C22⋊D11—82no—
148C22⋊D11—82no—
149C2×Dic11—21no—
150C2×Dic11—21no—
151C2×Dic11—22no—
152C2×Dic11—21no—
153C2×Dic11—21no—
154C2×Dic11—21no—
155C2×Dic11—21no—
156C2×Dic11—21no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—81no—
166C2×Dic11—81no—
167C2×Dic11—81no—
168C2×Dic11#9911yescharacteristic
169C2×Dic11#9911yescharacteristic
170D44—82no—
171C8×C11—81no—
172C11⋊C8—81no—
173C2×#124—111no—
174C2×#117—111no—
175#431—221no—
176#395—111no—
177#394—111no—
178#393C2×D1111yescharacteristic
179#392—111no—
180#390—221no—
181#388—221no—
182#388—221no—
183#386—221no—
184#381—221no—
185#376—111no—
186#342—111no—
187#342—221no—
188#342C2×D1111yescharacteristic
189#324—221no—
190#323—111no—
191#323C2×D1111yescharacteristic
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11—41no—
197C22×C11—41no—
198C22×C11—41no—
199C22×C11—41no—
200C22×C11—81no—
201C22×C11C2×#9911yescharacteristic
202C22×C11#41611yescharacteristic
203C22×C11#42111yescharacteristic
204C2×D11—81no—
205C2×D11—81no—
206C2×D11—81no—
207C2×D11—81no—
208C2×D11—81no—
209C2×D11—81no—
210C2×D11—81no—
211C4×C11—41no—
212C4×C11—41no—
213C4×C11—81no—
214C4×C11—81no—
215C4×C11—161no—
216Dic11—21no—
217Dic11—21no—
218Dic11—42no—
219Dic11—41no—
220Dic11—41no—
221Dic11—41no—
222Dic11—161no—
223C22×Q8C4×D1111yescharacteristic
224C22×D4—111no—
225C22×D4—221no—
226C23×C4—111no—
227#124—441no—
228#124—441no—
229#117—441no—
230#117—441no—
231C2×C4⋊C4—111no—
232C2×C4⋊C4—111no—
233C2×C4⋊C4—221no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—111no—
237C2×C22⋊C4—221no—
238C2×C22⋊C4—221no—
239C2×C22⋊C4—221no—
240C2×C22⋊C4—221no—
241C2×C22⋊C4—221no—
242C2×C22⋊C4—221no—
243C2×C22⋊C4C22×D1111yescharacteristic
244C2×C42—111no—
245C2×C42—111no—
246C2×C42—221no—
247C4⋊C8—441no—
248C22⋊C8—21no—
249C22⋊C8—221no—
250C4×C8—441no—
251#95—21no—
252#95—111no—
253#95—221no—
254#95—221no—
255#95—441no—
256#95—441no—
257#95C4×D1111yescharacteristic
258C2×C11—21no—
259C2×C11—21no—
260C2×C11—41no—
261C2×C11—41no—
262C2×C11#151611yescharacteristic
263C2×C11#212211yescharacteristic
264C2×C11#212611yescharacteristic
265D11—161no—
266C24—221no—
267C24D4×D1111yescharacteristic
268C2×Q8—41no—
269C2×Q8—81no—
270C2×D4—441no—
271C2×D4—442no—
272C2×D4—441no—
273C2×D4—441no—
274C2×D4—881no—
275C2×D4—881no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—41no—
279C22×C4—111no—
280C22×C4—111no—
281C22×C4—111no—
282C22×C4—111no—
283C22×C4—221no—
284C22×C4—221no—
285C22×C4—221no—
286C22×C4—221no—
287C22×C4—221no—
288C22×C4—441no—
289C22×C4—441no—
290C22×C4C2×C4×D1111yescharacteristic
291C22×C4D4×D1111yescharacteristic
292C2×C8—41no—
293C2×C8—441no—
294C4⋊C4—441no—
295C4⋊C4—441no—
296C4⋊C4—881no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—81no—
301C22⋊C4—441no—
302C22⋊C4—441no—
303C22⋊C4—442no—
304C22⋊C4—442no—
305C22⋊C4—442no—
306C22⋊C4—441no—
307C22⋊C4—441no—
308C22⋊C4—441no—
309C22⋊C4—881no—
310C42—221no—
311C42—221no—
312C42—221no—
313C42—221no—
314C42—442no—
315C11#1184411yescharacteristic, complemented, Sylow
316C23—21no—
317C23—21no—
318C23—41no—
319C23—41no—
320C23—441no—
321C23—441no—
322C23—441no—
323C23—441no—
324C23—441no—
325C23—441no—
326C23—441no—
327C23C22⋊C4×D1111yescharacteristic
328C23#6696911yescharacteristic
329C23#6697211yescharacteristic
330Q8—82no—
331D4—882no—
332D4—882no—
333D4—882no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4—111no—
348C2×C4—111no—
349C2×C4—221no—
350C2×C4—221no—
351C2×C4—222no—
352C2×C4—221no—
353C2×C4—221no—
354C2×C4—221no—
355C2×C4—221no—
356C2×C4—221no—
357C2×C4—441no—
358C2×C4—441no—
359C2×C4—441no—
360C2×C4—441no—
361C2×C4—441no—
362C2×C4—441no—
363C2×C4—441no—
364C2×C4—441no—
365C2×C4—881no—
366C2×C4—881no—
367C2×C4—881no—
368C8—81no—
369C8—881no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—81no—
379C22—881no—
380C22—881no—
381C22—881no—
382C22—881no—
383C22—881no—
384C22—881no—
385C22—881no—
386C22D11×#9911yescharacteristic
387C22#1062241711yescharacteristic
388C22#1062243411yescharacteristic
389C4—41no—
390C4—41no—
391C4—81no—
392C4—81no—
393C4—161no—
394C4—221no—
395C4—221no—
396C4—442no—
397C4—441no—
398C4—441no—
399C4—441no—
400C4—1761no—
401C2—21no—
402C2—21no—
403C2—41no—
404C2—41no—
405C2—1761no—
406C2#1306717111yescharacteristic
407C2#1307026411yescharacteristic
408C2#1307028011yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1351C2
socleC22×C11C2×#99
prime radical#10622573C22
cosocleC2×C11×C22⋊C4C23
hypercenter#1351D11
hypocenterC11#11844
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1351

Complements

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

NH ≅ G/Ntype
2. #13068692C2semidirect
3. #13066927C2semidirect
4. #13066637C2semidirect
7. C11×#1351C2semidirect
8. C2×#67000C4semidirect
11. #10622842C4semidirect
17. #10622285C4semidirect
20. #10622261C4semidirect
116. #1351D11semidirect
315. C11#11844semidirect

Maximal subgroups

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

subgroupindex
#130743042
#130686922
#130669272
#130666372
#130666142
#130666122
C11×#13512
#1184411