Finite Group Databasebeta

← #14664796

Subgroups — #14664796

Order 2816.

536 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 77 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#13073514C211yesmaximal, characteristic
2#13068603C211yesmaximal, characteristic, complemented
3#13066931C211yesmaximal, characteristic, complemented
4#13066616C211yesmaximal, characteristic, complemented
5#13066614C211yesmaximal, characteristic, complemented
6#13066612C211yesmaximal, characteristic, complemented
7C11×#1344C211yesmaximal, characteristic, complemented
8C2×#66946C411yescharacteristic, complemented
9C2×#66937—21no—
10C2×(C22⋊D11)⋊C4C2211yescharacteristic
11C11×#397C2211yescharacteristic
12#10622606C411yescharacteristic, complemented
13#10622573C2211yescharacteristic
14#10622571—21no—
15C2×#66870—21no—
16#10622555—21no—
17D11×C22⋊C8—21no—
18#10622284C411yescharacteristic, complemented
19#10622280—21no—
20#10622278—21no—
21#10622263C411yescharacteristic, complemented
22C11×#342C2211yescharacteristic
23C11×#323C2211yescharacteristic
24#10622164C2211yescharacteristic
25#10622163C2211yescharacteristic
26#10622107—21no—
27C22×C22⋊D11—21no—
28C22×C22⋊D11D411yescharacteristic
29C23×Dic11D411yescharacteristic
30C22×D44—21no—
31C22×D44C2×C411yescharacteristic
32C22×C4×D11—21no—
33C22×C4×D11D411yescharacteristic
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)⋊C4C2×C411yescharacteristic
44C2×Dic11⋊C4—21no—
45C2×Dic11⋊C4—41no—
46C2×Dic11⋊C4D411yescharacteristic
47C2×C4×Dic11C2×C411yescharacteristic
48C2×C8×D11—41no—
49#66946—41no—
50#66946—41no—
51#66937—42no—
52#66937—42no—
53(C22⋊D11)⋊C4—41no—
54(C22⋊D11)⋊C4—41no—
55C11×C22⋊C8—21no—
56C11×#95—21no—
57C11×#95C2×C411yescharacteristic
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—41no—
61C11⋊#95C2×C411yescharacteristic
62C22⋊(C11⋊C8)—21no—
63(C2×D11)⋊C8—41no—
64#66870—42no—
65#11875—111nomaximal, Sylow
66C24×C11C2×D411yescharacteristic
67C23×D11—21no—
68C23×D11C22⋊C411yescharacteristic
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—41no—
72C22×C4×C11C22×C411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C2×C22⋊D11—41no—
75C2×C22⋊D11—41no—
76C2×C22⋊D11—42no—
77C2×C22⋊D11—41no—
78C2×C22⋊D11—41no—
79C2×C22⋊D11—81no—
80C2×C22⋊D11D812yes—
81C2×C22⋊D11SD1612yes—
82C22×Dic11—21no—
83C22×Dic11—21no—
84C22×Dic11—21no—
85C22×Dic11—41no—
86C22×Dic11—81no—
87C22×Dic11C22⋊C411yescharacteristic
88C22×Dic11C22⋊C411yescharacteristic
89C22×Dic11C22⋊C411yescharacteristic
90C2×D44—41no—
91C2×D44—42no—
92C2×D44—42no—
93C2×D44—42no—
94C2×D44—81no—
95C2×C4×D11—21no—
96C2×C4×D11—21no—
97C2×C4×D11—42no—
98C2×C4×D11—42no—
99C2×C4×D11—42no—
100C2×C4×D11—81no—
101C2×C8×C11—41no—
102C11×C4⋊C4—41no—
103C11×C22⋊C4—41no—
104C11×C22⋊C4—41no—
105C11×C22⋊C4—41no—
106C11×C22⋊C4—41no—
107C11×C22⋊C4—41no—
108C22⋊Dic11—41no—
109C22⋊Dic11—41no—
110(C2×D11)⋊C4—41no—
111(C2×D11)⋊C4—41no—
112(C2×D11)⋊C4—41no—
113(C2×D11)⋊C4—42no—
114(C2×D11)⋊C4—81no—
115(C2×D11)⋊C4—81no—
116Dic11⋊C4—41no—
117Dic11⋊C4—42no—
118Dic11⋊C4—82no—
119C4×Dic11—21no—
120C4×Dic11—21no—
121C2×C11⋊C8—41no—
122C8×D11—82no—
123#2535—111no—
124#1799—111no—
125#1459—111no—
126#1344—111no—
127#1344D1111yescharacteristic, complemented
128#1343—111no—
129#1343—111no—
130C23×C11—21no—
131C23×C11—21no—
132C23×C11—41no—
133C23×C11—41no—
134C23×C11C2×C22⋊C411yescharacteristic
135C23×C11C2×D811yescharacteristic
136C23×C11C2×SD1611yescharacteristic
137C22×D11—21no—
138C22×D11—21no—
139C22×D11—22no—
140C22×D11—41no—
141C22×D11—41no—
142C22×D11—41no—
143C22×D11—41no—
144C22×D11—41no—
145C22×D11—41no—
146C22×D11—41no—
147C22×D11—41no—
148C22×D11#10212yes—
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—41no—
159C2×C4×C11—81no—
160C2×C4×C11—81no—
161C2×C4×C11—81no—
162C22⋊D11—42no—
163C22⋊D11—42no—
164C22⋊D11—82no—
165C22⋊D11—82no—
166C2×Dic11—21no—
167C2×Dic11—21no—
168C2×Dic11—21no—
169C2×Dic11—41no—
170C2×Dic11—42no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173C2×Dic11—41no—
174C2×Dic11—41no—
175C2×Dic11—81no—
176C2×Dic11—81no—
177C2×Dic11—81no—
178C2×Dic11—81no—
179C2×Dic11#9911yescharacteristic
180C2×Dic11#9911yescharacteristic
181C2×Dic11#10212yes—
182D44—42no—
183D44—42no—
184D44—84no—
185C4×D11—42no—
186C4×D11—81no—
187C4×D11—84no—
188C8×C11—81no—
189C11⋊C8—81no—
190C2×#121—221no—
191C2×C4×D4—111no—
192C2×C4×D4—111no—
193C2×#99—221no—
194C2×C22⋊C8—221no—
195#397—111no—
196#397C2×D1111yescharacteristic
197#392—111no—
198#392—111no—
199#386—221no—
200#386—221no—
201#382—111no—
202#380—221no—
203#380—221no—
204#342—111no—
205#342C2×D1111yescharacteristic
206#324—221no—
207#323—111no—
208#323C2×D1111yescharacteristic
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—41no—
214C22×C11—41no—
215C22×C11—41no—
216C22×C11—41no—
217C22×C11—81no—
218C22×C11C2×#9911yescharacteristic
219C22×C11C2×#10211yescharacteristic
220C22×C11#42111yescharacteristic
221C2×D11—22no—
222C2×D11—41no—
223C2×D11—41no—
224C2×D11—42no—
225C2×D11—42no—
226C2×D11—42no—
227C2×D11—42no—
228C2×D11—81no—
229C2×D11—81no—
230C2×D11—81no—
231C2×D11—81no—
232C2×D11—81no—
233C4×C11—41no—
234C4×C11—41no—
235C4×C11—81no—
236C4×C11—81no—
237C4×C11—161no—
238Dic11—21no—
239Dic11—21no—
240Dic11—22no—
241Dic11—41no—
242Dic11—81no—
243Dic11—161no—
244C22×D4—111no—
245C22×D4—111no—
246C22×D4—221no—
247C22×D4—221no—
248C23×C4—111no—
249C23×C4—111no—
250C23×C4—221no—
251C22×C8—441no—
252#121—442no—
253#121—442no—
254C4×D4—441no—
255C4×D4—441no—
256C4×D4—441no—
257C4×D4—441no—
258C2×C4⋊C4—111no—
259C2×C4⋊C4—221no—
260C2×C4⋊C4—441no—
261C2×C4⋊C4C4×D1111yescharacteristic
262C2×C22⋊C4—21no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—111no—
265C2×C22⋊C4—221no—
266C2×C22⋊C4—221no—
267C2×C22⋊C4—221no—
268C2×C22⋊C4—221no—
269C2×C22⋊C4—221no—
270C2×C22⋊C4C22×D1111yescharacteristic
271C2×C42—111no—
272#99—442no—
273C22⋊C8—21no—
274C22⋊C8—221no—
275C22⋊C8—441no—
276#95—21no—
277#95—111no—
278#95—221no—
279#95—221no—
280#95—441no—
281#95C4×D1111yescharacteristic
282C2×C11—21no—
283C2×C11—21no—
284C2×C11—41no—
285C2×C11—41no—
286C2×C11#151911yescharacteristic
287C2×C11#212011yescharacteristic
288C2×C11#212711yescharacteristic
289D11—42no—
290D11—82no—
291C24—111no—
292C24—221no—
293C24D4×D1111yescharacteristic
294C2×D4—112no—
295C2×D4—112no—
296C2×D4—441no—
297C2×D4—442no—
298C2×D4—442no—
299C2×D4—442no—
300C2×D4—441no—
301C2×D4—441no—
302C2×D4—442no—
303C2×D4—441no—
304C2×D4—441no—
305C2×D4—881no—
306C2×D4—881no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—41no—
310C22×C4—111no—
311C22×C4—111no—
312C22×C4—111no—
313C22×C4—221no—
314C22×C4—221no—
315C22×C4—221no—
316C22×C4—221no—
317C22×C4—221no—
318C22×C4—442no—
319C22×C4—442no—
320C22×C4—442no—
321C22×C4—441no—
322C22×C4—881no—
323C22×C4—881no—
324C22×C4C2×C4×D1111yescharacteristic
325C22×C4D4×D1111yescharacteristic
326C2×C8—41no—
327C2×C8—441no—
328C2×C8—882no—
329C4⋊C4—41no—
330C4⋊C4—441no—
331C4⋊C4—442no—
332C4⋊C4—882no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—441no—
339C22⋊C4—441no—
340C22⋊C4—441no—
341C22⋊C4—442no—
342C22⋊C4—441no—
343C22⋊C4—441no—
344C22⋊C4—881no—
345C22⋊C4—881no—
346C42—221no—
347C42—221no—
348C11#1187511yescharacteristic, complemented, Sylow
349C23—21no—
350C23—21no—
351C23—41no—
352C23—41no—
353C23—112no—
354C23—222no—
355C23—221no—
356C23—221no—
357C23—441no—
358C23—441no—
359C23—441no—
360C23—441no—
361C23—441no—
362C23—441no—
363C23—441no—
364C23—441no—
365C23C22⋊C4×D1111yescharacteristic
366C23D8×D1111yescharacteristic
367C23SD16×D1111yescharacteristic
368D4—442no—
369D4—442no—
370D4—442no—
371D4—442no—
372D4—884no—
373D4—882no—
374D4—882no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—111no—
389C2×C4—111no—
390C2×C4—112no—
391C2×C4—221no—
392C2×C4—221no—
393C2×C4—221no—
394C2×C4—442no—
395C2×C4—441no—
396C2×C4—442no—
397C2×C4—441no—
398C2×C4—441no—
399C2×C4—441no—
400C2×C4—441no—
401C2×C4—881no—
402C2×C4—884no—
403C2×C4—881no—
404C2×C4—881no—
405C2×C4—881no—
406C2×C4—881no—
407C8—81no—
408C8—881no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—81no—
418C22—222no—
419C22—442no—
420C22—442no—
421C22—442no—
422C22—441no—
423C22—441no—
424C22—442no—
425C22—881no—
426C22—881no—
427C22—881no—
428C22—881no—
429C22—881no—
430C22D11×#9911yescharacteristic
431C22D11×#10211yescharacteristic
432C22#1062243411yescharacteristic
433C4—41no—
434C4—41no—
435C4—81no—
436C4—81no—
437C4—161no—
438C4—222no—
439C4—221no—
440C4—221no—
441C4—441no—
442C4—881no—
443C4—1761no—
444C2—21no—
445C2—21no—
446C2—41no—
447C2—41no—
448C2—442no—
449C2—882no—
450C2#1306718211yescharacteristic
451C2#1307025611yescharacteristic
452C2#1307028411yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1344C2
socleC22×C11C2×#99
prime radical#13073514C2
cosocleC2×C11×C22⋊C4C23
hypercenter#1344D11
hypocenterC11#11875
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1344

Complements

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

NH ≅ G/Ntype
2. #13068603C2semidirect
3. #13066931C2semidirect
4. #13066616C2semidirect
5. #13066614C2semidirect
6. #13066612C2semidirect
7. C11×#1344C2semidirect
8. C2×#66946C4semidirect
12. #10622606C4semidirect
18. #10622284C4semidirect
21. #10622263C4semidirect
127. #1344D11semidirect
348. C11#11875semidirect

Maximal subgroups

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

subgroupindex
#130735142
#130686032
#130669312
#130666162
#130666142
#130666122
C11×#13442
#1187511