Finite Group Databasebeta

← #14649735

Subgroups — #14649735

Order 2816.

532 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 91 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#13077643C211yesmaximal, characteristic
2#13074536C211yesmaximal, characteristic
3C4×#66870C211yesmaximal, characteristic
4#13067137C211yesmaximal, characteristic, complemented
5#13067135C211yesmaximal, characteristic, complemented
6#13066468C211yesmaximal, characteristic, complemented
7C11×#1284C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊D11C2211yescharacteristic
9C2×#66977C2211yescharacteristic
10C11×#407C2211yescharacteristic
11C11×#381C2211yescharacteristic
12C4×C11×C22⋊C4C2211yescharacteristic
13C4×C22⋊Dic11C2211yescharacteristic
14#10622820C2211yescharacteristic
15#10622740—22no—
16#10622574—21no—
17C2×#66870—21no—
18#10622566—21no—
19#10622341—22no—
20D11×C22⋊C8—21no—
21#10622332—21no—
22#10622287C411yescharacteristic, complemented
23#10622286C411yescharacteristic, complemented
24#10622281—21no—
25#10622274C411yescharacteristic, complemented
26#10622269C411yescharacteristic, complemented
27#10622266—21no—
28#10622165—21no—
29#10622105—22no—
30#10622090—22no—
31C23×C4×C11C2311yescharacteristic
32C22×C22⋊D11D411yescharacteristic
33C22×C4×D11D411yescharacteristic
34C22×Dic22C2×C411yescharacteristic
35C2×C11×M16—21no—
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4—21no—
38C2×C42×C11—21no—
39C2×C22⋊Dic11—21no—
40C2×C22⋊Dic11—21no—
41C2×C22⋊Dic11D411yescharacteristic
42C4×C22⋊D11—21no—
43C4×C22⋊D11—21no—
44C4×C22⋊D11—21no—
45C4×C22⋊D11—21no—
46C2×(C2×D11)⋊C4—21no—
47C2×(C2×D11)⋊C4—21no—
48C2×(C2×D11)⋊C4C2×C411yescharacteristic
49C2×C4⋊Dic11—21no—
50C2×C4⋊Dic11—21no—
51C2×C4⋊Dic11C2×C411yescharacteristic
52#66977—21no—
53#66977—21no—
54#66977—21no—
55#66977—21no—
56C2×Dic11⋊C4—21no—
57C2×Dic11⋊C4C2×C411yescharacteristic
58C2×C4×Dic11—21no—
59C2×C4×Dic11D411yescharacteristic
60C2×#4318—21no—
61C2×C8×D11—22no—
62C11×C22⋊C8—21no—
63C11×C22⋊C8D412yes—
64C11×#95—21no—
65C11×#95—21no—
66C11×#95C2×C411yescharacteristic
67C11×#95C2×C411yescharacteristic
68C11⋊#95—21no—
69C11⋊#95—21no—
70C11⋊#95—21no—
71C11⋊#95—21no—
72C11⋊#95—21no—
73C22⋊(C11⋊C8)—21no—
74C22⋊(C11⋊C8)D412yes—
75(C2×D11)⋊C8—22no—
76#66879—22no—
77Dic11⋊C8—22no—
78#66870—24no—
79#9183—111nomaximal, Sylow
80C24×C11C2×D411yescharacteristic
81C23×D11C22⋊C411yescharacteristic
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—41no—
85C22×C4×C11—81no—
86C22×C4×C11C22×C411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11#4111yescharacteristic
91C22×C4×C11#4111yescharacteristic
92C2×C22⋊D11—21no—
93C2×C22⋊D11—21no—
94C2×C22⋊D11—22no—
95C2×C22⋊D11—41no—
96C22×Dic11—21no—
97C22×Dic11—21no—
98C22×Dic11—41no—
99C22×Dic11C22⋊C411yescharacteristic
100C22×Dic11C22⋊C411yescharacteristic
101C22×Dic11C22⋊C411yescharacteristic
102C2×C4×D11—21no—
103C2×C4×D11—21no—
104C2×C4×D11—81no—
105C2×Dic22—21no—
106C2×Dic22—21no—
107C2×Dic22—81no—
108C11×M16—81no—
109C2×C8×C11—22no—
110C11×C22⋊C4—22no—
111C11×C22⋊C4—41no—
112C11×C22⋊C4—81no—
113C42×C11—81no—
114C22⋊Dic11—22no—
115C22⋊Dic11—21no—
116C22⋊Dic11—21no—
117C22⋊Dic11—41no—
118C22⋊Dic11—41no—
119C22⋊Dic11—41no—
120(C2×D11)⋊C4—21no—
121(C2×D11)⋊C4—21no—
122(C2×D11)⋊C4—42no—
123(C2×D11)⋊C4—81no—
124C4⋊Dic11—21no—
125C4⋊Dic11—21no—
126C4⋊Dic11—42no—
127C4⋊Dic11—81no—
128Dic11⋊C4—21no—
129Dic11⋊C4—21no—
130Dic11⋊C4—41no—
131Dic11⋊C4—41no—
132C4×Dic11—21no—
133C4×Dic11—21no—
134C4×Dic11—81no—
135#4318—81no—
136C2×C11⋊C8—22no—
137C8×D11—82no—
138#2973—111no—
139#2638—111no—
140C4×#99—111no—
141#1508—111no—
142#1508—111no—
143#1284—111no—
144#1284D1111yescharacteristic, complemented
145C23×C11—21no—
146C23×C11—21no—
147C23×C11—41no—
148C23×C11—41no—
149C23×C11C2×C22⋊C411yescharacteristic
150C23×C11#12111yescharacteristic
151C23×C11#12111yescharacteristic
152C22×D11—21no—
153C22×D11—21no—
154C22×D11—41no—
155C22×D11—41no—
156C22×D11#10412yes—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—42no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—81no—
171C2×C4×C11—81no—
172C2×C4×C11C4×D411yescharacteristic
173C2×C4×C11C4×D411yescharacteristic
174C2×C4×C11#12011yescharacteristic
175C2×C4×C11#12311yescharacteristic
176C22⋊D11—42no—
177C22⋊D11—42no—
178C2×Dic11—21no—
179C2×Dic11—21no—
180C2×Dic11—21no—
181C2×Dic11—21no—
182C2×Dic11—21no—
183C2×Dic11—41no—
184C2×Dic11—41no—
185C2×Dic11—41no—
186C2×Dic11—41no—
187C2×Dic11—42no—
188C2×Dic11—41no—
189C2×Dic11—41no—
190C2×Dic11—41no—
191C2×Dic11—41no—
192C2×Dic11—81no—
193C2×Dic11—81no—
194C4×D11—42no—
195C4×D11—81no—
196Dic22—81no—
197Dic22—81no—
198C8×C11—42no—
199C11⋊C8—42no—
200C2×C22⋊Q8—111no—
201C2×C4×D4—111no—
202#435—222no—
203#435—222no—
204#432—221no—
205C2×#99—221no—
206#407—111no—
207#407C2×D1111yescharacteristic
208C2×C22⋊C8—221no—
209#398—111no—
210#397—111no—
211#397—221no—
212#395—111no—
213#394—221no—
214#393—111no—
215#387—221no—
216#385—221no—
217#381C2×D1111yescharacteristic
218C4×C22⋊C4—111no—
219C4×C22⋊C4C2×D1111yescharacteristic
220#342—221no—
221#328—222no—
222#328—222no—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11—21no—
226C22×C11—21no—
227C22×C11—21no—
228C22×C11—21no—
229C22×C11—21no—
230C22×C11—21no—
231C22×C11—81no—
232C22×C11—81no—
233C22×C11#38611yescharacteristic
234C22×C11C2×#10411yescharacteristic
235C22×C11#42111yescharacteristic
236C2×D11—22no—
237C2×D11—41no—
238C2×D11—41no—
239C2×D11—42no—
240C2×D11—81no—
241C4×C11—21no—
242C4×C11—21no—
243C4×C11—21no—
244C4×C11—21no—
245C4×C11—81no—
246C4×C11—81no—
247C4×C11—82no—
248Dic11—41no—
249Dic11—41no—
250Dic11—41no—
251Dic11—82no—
252Dic11—81no—
253Dic11—81no—
254C22×Q8—111no—
255C22×D4—111no—
256C23×C4—111no—
257C23×C4C22×D1111yescharacteristic
258C2×M16—21no—
259C2×M16—221no—
260C22×C8—222no—
261C22⋊Q8—221no—
262C22⋊Q8—221no—
263C22⋊Q8—221no—
264C22⋊Q8—221no—
265C4×D4—221no—
266C4×D4—221no—
267C4×D4—221no—
268C4×D4—221no—
269C2×C4⋊C4—111no—
270C2×C4⋊C4—111no—
271C2×C4⋊C4—221no—
272C2×C4⋊C4—221no—
273C2×C4⋊C4—221no—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—111no—
277C2×C22⋊C4—111no—
278C2×C22⋊C4—221no—
279C2×C22⋊C4—221no—
280C2×C22⋊C4—221no—
281C2×C22⋊C4—221no—
282C2×C42—21no—
283C2×C42—111no—
284C2×C42—221no—
285C4⋊C8—222no—
286#99—224no—
287C22⋊C8—21no—
288C22⋊C8—112no—
289C22⋊C8—222no—
290C22⋊C8—221no—
291C22⋊C8D4412yes—
292#97—222no—
293#95—21no—
294#95—21no—
295#95—221no—
296#95—221no—
297#95—221no—
298#95—221no—
299#95—221no—
300#95C4×D1111yescharacteristic
301#95C4×D1111yescharacteristic
302C2×C11—21no—
303C2×C11—21no—
304C2×C11—41no—
305C2×C11—41no—
306C2×C11#187111yescharacteristic
307C2×C11#190911yescharacteristic
308C2×C11#191311yescharacteristic
309D11—42no—
310C24—111no—
311C24D4×D1111yescharacteristic
312C2×Q8—221no—
313C2×Q8—221no—
314C2×Q8—881no—
315C2×D4—222no—
316C2×D4—221no—
317C2×D4—221no—
318C2×D4—441no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—41no—
322C22×C4—81no—
323C22×C4—111no—
324C22×C4—111no—
325C22×C4—111no—
326C22×C4—221no—
327C22×C4—221no—
328C22×C4—221no—
329C22×C4—221no—
330C22×C4—441no—
331C22×C4—881no—
332C22×C4C2×C4×D1111yescharacteristic
333C22×C4C2×D4411yescharacteristic
334C22×C4#433911yescharacteristic
335C22×C4D4×D1111yescharacteristic
336C22×C4D4×D1111yescharacteristic
337C22×C4#434311yescharacteristic
338M16—81no—
339M16—881no—
340C2×C8—22no—
341C2×C8—222no—
342C2×C8—882no—
343C4⋊C4—221no—
344C4⋊C4—221no—
345C4⋊C4—221no—
346C4⋊C4—221no—
347C4⋊C4—442no—
348C4⋊C4—441no—
349C4⋊C4—441no—
350C4⋊C4—881no—
351C22⋊C4—22no—
352C22⋊C4—41no—
353C22⋊C4—81no—
354C22⋊C4—221no—
355C22⋊C4—221no—
356C22⋊C4—221no—
357C22⋊C4—221no—
358C22⋊C4—222no—
359C22⋊C4—442no—
360C22⋊C4—441no—
361C22⋊C4—441no—
362C22⋊C4—441no—
363C22⋊C4—881no—
364C42—81no—
365C42—221no—
366C42—221no—
367C42—881no—
368C11#918311yescharacteristic, complemented, Sylow
369C23—21no—
370C23—21no—
371C23—41no—
372C23—41no—
373C23—112no—
374C23—221no—
375C23—221no—
376C23—441no—
377C23—441no—
378C23C22⋊C4×D1111yescharacteristic
379C23#6693711yescharacteristic
380C23#6694811yescharacteristic
381Q8—881no—
382Q8—881no—
383D4—442no—
384D4—442no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—42no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4—221no—
401C2×C4—221no—
402C2×C4—221no—
403C2×C4—221no—
404C2×C4—221no—
405C2×C4—442no—
406C2×C4—441no—
407C2×C4—441no—
408C2×C4—442no—
409C2×C4—441no—
410C2×C4—441no—
411C2×C4—441no—
412C2×C4—441no—
413C2×C4—441no—
414C2×C4—441no—
415C2×C4—881no—
416C2×C4—881no—
417C2×C4—881no—
418C2×C4C4×D4411yescharacteristic
419C2×C4#6693511yescharacteristic
420C2×C4#6694611yescharacteristic
421C2×C4#6694711yescharacteristic
422C8—42no—
423C8—442no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—81no—
433C22—81no—
434C22—222no—
435C22—442no—
436C22—441no—
437C22—441no—
438C22—881no—
439C22#1062227811yescharacteristic
440C22D11×#10411yescharacteristic
441C22#1062243411yescharacteristic
442C4—21no—
443C4—21no—
444C4—21no—
445C4—21no—
446C4—81no—
447C4—81no—
448C4—82no—
449C4—441no—
450C4—441no—
451C4—441no—
452C4—882no—
453C4—881no—
454C4—881no—
455C2—21no—
456C2—21no—
457C2—41no—
458C2—41no—
459C2—442no—
460C2#1306891711yescharacteristic
461C2#1306913711yescharacteristic
462C2#1306915711yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1284C2
socleC22×C11#386
prime radicalC22×C22⋊D11D4
cosocleC23×C4×C11C23
hypercenter#1284D11
hypocenterC11#9183
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1284

Complements

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

NH ≅ G/Ntype
4. #13067137C2semidirect
5. #13067135C2semidirect
6. #13066468C2semidirect
7. C11×#1284C2semidirect
22. #10622287C4semidirect
23. #10622286C4semidirect
25. #10622274C4semidirect
26. #10622269C4semidirect
144. #1284D11semidirect
368. C11#9183semidirect

Maximal subgroups

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

subgroupindex
#130776432
#130745362
C4×#668702
#130671372
#130671352
#130664682
C11×#12842
#918311