Finite Group Databasebeta

← #14658117

Subgroups — #14658117

Order 2816.

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

normal subgroups only

This group has 474 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#13079369C211yesmaximal, characteristic
2#13069079C211yesmaximal, characteristic
3#13068799C211yesmaximal, characteristic, complemented
4#13067136C211yesmaximal, characteristic, complemented
5#13067133C211yesmaximal, characteristic
6#13066492C211yesmaximal, characteristic, complemented
7C11×#1901C211yesmaximal, characteristic, complemented
8C22×C11×M16C2211yescharacteristic
9C2×C11×C22⋊Q8C2211yescharacteristic
10C2×#66983C2211yescharacteristic
11C2×C11×#101—21no—
12C11×#407C2211yescharacteristic
13#10622840—21no—
14C4×C22⋊Dic11C2211yescharacteristic
15#10622820C2211yescharacteristic
16C2×C22⋊(C11⋊C8)C2211yescharacteristic
17C2×#66887—21no—
18C2×Dic11⋊C8—21no—
19#10622661—21no—
20#10622661—21no—
21#10622659—21no—
22#10622656—21no—
23#10622581—21no—
24C11×#343—21no—
25#10622192—21no—
26#10622188—21no—
27#10622176—21no—
28#10622176—21no—
29#10622108—21no—
30#10622108—21no—
31C22×Q8×C11D411yescharacteristic
32C23×C4×C11C2311yescharacteristic
33C22×C22⋊D11—21no—
34C22×D44D411yescharacteristic
35C2×C11×M16—21no—
36C2×C11×M16—21no—
37C2×C11×M16—21no—
38C2×C11×M16—42no—
39C22×C8×C11—21no—
40C11×C22⋊Q8—21no—
41C11×C22⋊Q8—21no—
42C11×C22⋊Q8—21no—
43C11×C22⋊Q8—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4D411yescharacteristic
46C2×C11×C22⋊C4—21no—
47C2×C22⋊Dic11—21no—
48C2×#4325—21no—
49C2×#4325—21no—
50#66983—21no—
51#66983—21no—
52#66983—21no—
53#66983—21no—
54C2×(C2×D11)⋊C4—21no—
55C2×C4⋊Dic11D411yescharacteristic
56C2×C4×Dic11—21no—
57C2×#4318—21no—
58C22×C11⋊C8D411yescharacteristic
59C22×C11⋊C8D411yescharacteristic
60C11×#101—42no—
61C11×C22⋊C8—21no—
62C11×C22⋊C8—21no—
63#66899—21no—
64#66899—21no—
65C11⋊#95D411yescharacteristic
66C11⋊#95D411yescharacteristic
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)—21no—
69C22⋊(C11⋊C8)—21no—
70C22⋊(C11⋊C8)—21no—
71#66887—42no—
72Dic11⋊C8—42no—
73#66873—21no—
74#66873—21no—
75#66872—21no—
76#66872—21no—
77#10558—111nomaximal, Sylow
78C24×C11#4111yescharacteristic
79C23×D11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—21no—
82C2×Q8×C11—41no—
83C2×Q8×C11—41no—
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11#4111yescharacteristic
93C22×C4×C11#4111yescharacteristic
94C2×C22⋊D11—41no—
95C2×C22⋊D11—41no—
96C2×C22⋊D11—81no—
97C2×C22⋊D11—81no—
98C22×Dic11—21no—
99C22×Dic11—21no—
100C22×Dic11—21no—
101C2×D44—21no—
102C2×D44—21no—
103C2×D44—41no—
104C2×D44—41no—
105C11×M16—22no—
106C11×M16—22no—
107C11×M16—41no—
108C11×M16—41no—
109C11×M16—41no—
110C11×M16—41no—
111C2×C8×C11—22no—
112C2×C8×C11—41no—
113C2×C8×C11—41no—
114C2×C8×C11—41no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—41no—
119C11×C22⋊C4—41no—
120C11×C22⋊C4—41no—
121C22⋊Dic11—42no—
122#4325—81no—
123#4325—81no—
124(C2×D11)⋊C4—41no—
125(C2×D11)⋊C4—41no—
126C4⋊Dic11—21no—
127C4⋊Dic11—21no—
128C4×Dic11—41no—
129C4×Dic11—41no—
130#4318—41no—
131#4318—41no—
132C2×C11⋊C8—21no—
133C2×C11⋊C8—21no—
134C2×C11⋊C8—41no—
135C2×C11⋊C8—41no—
136C2×C11⋊C8—41no—
137#3187—111no—
138#1901D1111yescharacteristic, complemented
139#1900—111no—
140#1851—111no—
141#1508—111no—
142#1507—111no—
143#1293—111no—
144C23×C11—21no—
145C23×C11—21no—
146C23×C11—41no—
147C23×C11—41no—
148C23×C11#12111yescharacteristic
149C23×C11#12311yescharacteristic
150C23×C11#12311yescharacteristic
151C22×D11—41no—
152C22×D11—42no—
153C22×D11—81no—
154C22×D11—81no—
155Q8×C11—41no—
156Q8×C11—41no—
157Q8×C11—81no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—42no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—81no—
171C2×C4×C11#12011yescharacteristic
172C2×C4×C11#12111yescharacteristic
173C2×C4×C11#12111yescharacteristic
174C2×C4×C11#12411yescharacteristic
175C22⋊D11—82no—
176C22⋊D11—81no—
177C22⋊D11—81no—
178C2×Dic11—22no—
179C2×Dic11—41no—
180C2×Dic11—41no—
181C2×Dic11—41no—
182C2×Dic11—41no—
183C2×Dic11—41no—
184C2×Dic11—41no—
185C2×Dic11—81no—
186D44—41no—
187D44—41no—
188D44—81no—
189C8×C11—42no—
190C8×C11—81no—
191C11⋊C8—41no—
192C11⋊C8—41no—
193C11⋊C8—81no—
194C22×M16C2×D1111yescharacteristic
195C2×C22⋊Q8C2×D1111yescharacteristic
196C2×#121—111no—
197#483—221no—
198#481—221no—
199#465—221no—
200#465—221no—
201#450—221no—
202#448—221no—
203C2×C4⋊C8—221no—
204C2×#101—21no—
205C2×#100—221no—
206#407—111no—
207#407C2×D1111yescharacteristic
208C2×C22⋊C8—111no—
209C4×C22⋊C4—111no—
210#343—21no—
211#343—221no—
212#336—221no—
213#328—221no—
214#328—221no—
215#327—221no—
216#327—221no—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11—21no—
221C22×C11—21no—
222C22×C11—21no—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11—81no—
226C22×C11—81no—
227C22×C11#39411yescharacteristic
228C22×C11#47111yescharacteristic
229C22×C11#47111yescharacteristic
230C2×D11—81no—
231C2×D11—81no—
232C2×D11—81no—
233C2×D11—162no—
234C4×C11—21no—
235C4×C11—21no—
236C4×C11—21no—
237C4×C11—81no—
238C4×C11—81no—
239C4×C11B(4,𝔽2)11yescharacteristic
240C4×C11#45811yescharacteristic
241Dic11—42no—
242Dic11—81no—
243Dic11—81no—
244C22×Q8C22⋊D1111yescharacteristic
245C22×D4—111no—
246C22×D4—221no—
247C23×C4C22×D1111yescharacteristic
248C2×SD16—221no—
249C2×SD16—221no—
250C2×M16—21no—
251C2×M16—21no—
252C2×M16—21no—
253C2×M16—42no—
254C2×M16—221no—
255C22×C8—21no—
256C22×C8—111no—
257C22×C8—111no—
258C22⋊Q8—21no—
259C22⋊Q8—21no—
260C22⋊Q8—21no—
261C22⋊Q8—21no—
262#121—221no—
263#121—221no—
264#121—221no—
265#121—221no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—111no—
268C2×C4⋊C4C22⋊D1111yescharacteristic
269C2×C22⋊C4—21no—
270C2×C22⋊C4—221no—
271C2×C22⋊C4—221no—
272C2×C42—221no—
273#106—221no—
274#106—221no—
275C4⋊C8—442no—
276#103—221no—
277#103—221no—
278#102—221no—
279#102—221no—
280#101—42no—
281#100—442no—
282C22⋊C8—21no—
283C22⋊C8—21no—
284C22⋊C8—221no—
285C22⋊C8—221no—
286C22⋊C8—221no—
287C22⋊C8—221no—
288#95—111no—
289#95—111no—
290C2×C11—21no—
291C2×C11—21no—
292C2×C11—41no—
293C2×C11—41no—
294C2×C11#204411yescharacteristic
295C2×C11#204611yescharacteristic
296C2×C11#205011yescharacteristic
297D11—161no—
298C24—221no—
299C24#433911yescharacteristic
300C2×Q8—21no—
301C2×Q8—21no—
302C2×Q8—41no—
303C2×Q8—41no—
304C2×D4—221no—
305C2×D4—221no—
306C2×D4—441no—
307C2×D4—441no—
308C2×D4—441no—
309C2×D4—441no—
310C2×D4—881no—
311C2×D4—881no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—221no—
317C22×C4—221no—
318C22×C4—221no—
319C22×C4#433911yescharacteristic
320C22×C4D4×D1111yescharacteristic
321C22×C4D4×D1111yescharacteristic
322C22×C4D4×D1111yescharacteristic
323C22×C4#434111yescharacteristic
324C22×C4C2×C22⋊D1111yescharacteristic
325SD16—881no—
326SD16—881no—
327M16—22no—
328M16—22no—
329M16—41no—
330M16—41no—
331M16—41no—
332M16—41no—
333M16—441no—
334M16—441no—
335C2×C8—22no—
336C2×C8—41no—
337C2×C8—41no—
338C2×C8—41no—
339C2×C8—221no—
340C2×C8—221no—
341C2×C8—441no—
342C2×C8—441no—
343C2×C8—441no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—41no—
347C4⋊C4—41no—
348C4⋊C4—221no—
349C4⋊C4—221no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C22⋊C4—442no—
353C22⋊C4—441no—
354C22⋊C4—441no—
355C42—441no—
356C42—441no—
357C11#1055811yescharacteristic, complemented, Sylow
358C23—21no—
359C23—21no—
360C23—41no—
361C23—41no—
362C23—442no—
363C23—441no—
364C23—881no—
365C23—881no—
366C23#6693611yescharacteristic
367C23#6693711yescharacteristic
368C23#6698211yescharacteristic
369Q8—41no—
370Q8—41no—
371Q8—81no—
372D4—441no—
373D4—441no—
374D4—881no—
375D4—882no—
376D4—881no—
377D4—881no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—81no—
391C2×C4—222no—
392C2×C4—441no—
393C2×C4—441no—
394C2×C4—441no—
395C2×C4—441no—
396C2×C4—441no—
397C2×C4—441no—
398C2×C4—881no—
399C2×C4#6693711yescharacteristic
400C2×C4#6693811yescharacteristic
401C2×C4#6699011yescharacteristic
402C2×C4#6699211yescharacteristic
403C8—42no—
404C8—81no—
405C8—441no—
406C8—441no—
407C8—881no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—81no—
417C22—81no—
418C22—881no—
419C22—881no—
420C22—881no—
421C22—1762no—
422C22#1062236711yescharacteristic
423C22#1062236711yescharacteristic
424C22#1062257211yescharacteristic
425C4—21no—
426C4—21no—
427C4—21no—
428C4—81no—
429C4—81no—
430C4—442no—
431C4—881no—
432C4—881no—
433C4#1062264511yescharacteristic
434C4#1062266611yescharacteristic
435C2—21no—
436C2—21no—
437C2—41no—
438C2—41no—
439C2—1761no—
440C2#1306986511yescharacteristic
441C2#1306987511yescharacteristic
442C2#1306990111yescharacteristic
subgroupG/H
centerC22#10622572
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1901C2
socleC22×C11#394
prime radicalC2×#66983C22
hypercenter#1901D11
hypocenterC11#10558
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1901

Complements

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

NH ≅ G/Ntype
3. #13068799C2semidirect
4. #13067136C2semidirect
6. #13066492C2semidirect
7. C11×#1901C2semidirect
138. #1901D11semidirect
357. C11#10558semidirect

Maximal subgroups

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

subgroupindex
#130793692
#130690792
#130687992
#130671362
#130671332
#130664922
C11×#19012
#1055811