Finite Group Databasebeta

← #14650340

Subgroups — #14650340

Order 2816.

522 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 107 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#13079391C211yesmaximal, characteristic
2#13071696C211yesmaximal, characteristic
3#13069600C211yesmaximal, characteristic
4#13067187C211yesmaximal, characteristic
5C2×#10622090C211yesmaximal, characteristic
6#13066462C211yesmaximal, characteristic
7C11×#1294C211yesmaximal, characteristic
8C2×#66977C2211yescharacteristic
9C2×#66977C2211yescharacteristic
10C2×C11×C22⋊C8C2211yescharacteristic
11C11×#380C2211yescharacteristic
12C2×C11×#95C2211yescharacteristic
13#10622823—21no—
14C4×C22⋊Dic11—21no—
15C4×C22⋊Dic11C2211yescharacteristic
16C2×C22⋊(C11⋊C8)C2211yescharacteristic
17#10622729—22no—
18#10622352—21no—
19#10622352C412yescomplemented
20#10622335—21no—
21#10622335C412yescomplemented
22#10622266—21no—
23#10622265—21no—
24#10622262—21no—
25#10622259—21no—
26#10622165—21no—
27#10622165—21no—
28#10622090—22no—
29#10622090—21no—
30#10622090—21no—
31C23×C4×C11—21no—
32C23×C4×C11C2311yescharacteristic
33C22×Dic22C2×C411yescharacteristic
34C22×Dic22D411yescharacteristic
35C22×C8×C11—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C22⋊C4—21no—
38C2×C22⋊Dic11—21no—
39C2×C22⋊Dic11—21no—
40C2×C22⋊Dic11D411yescharacteristic
41C2×C22⋊Dic11D411yescharacteristic
42C2×C4⋊Dic11C2×C411yescharacteristic
43C2×C4⋊Dic11D411yescharacteristic
44#66977—21no—
45#66977—21no—
46#66977—21no—
47#66977—21no—
48#66977—21no—
49#66977—21no—
50#66977C2×C412yes—
51#66977D412yes—
52C2×Dic11⋊C4—21no—
53C2×Dic11⋊C4—21no—
54C2×Dic11⋊C4—21no—
55C2×Dic11⋊C4—21no—
56C2×C4×Dic11—21no—
57C2×C4×Dic11—21no—
58C2×C4×Dic11—21no—
59C22×C11⋊C8—21no—
60C2×Dic44—22no—
61C11×C22⋊C8—21no—
62C11×C22⋊C8C2×C412yes—
63C11×#95—21no—
64C11×#95—21no—
65C11×#95D411yescharacteristic
66C11×#95D411yescharacteristic
67C11⋊#95—21no—
68C11⋊#95—21no—
69C11⋊#95—21no—
70C11⋊#95—21no—
71C11⋊#95—21no—
72C22⋊(C11⋊C8)—21no—
73C22⋊(C11⋊C8)—21no—
74#66882—22no—
75#66880—22no—
76#66880—22no—
77#9276—111nomaximal, Sylow
78C24×C11C2×D411yescharacteristic
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—42no—
82C22×C4×C11—41no—
83C22×C4×C11—41no—
84C22×C4×C11—41no—
85C22×C4×C11—81no—
86C22×C4×C11—81no—
87C22×C4×C11C22×C411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11#4111yescharacteristic
92C22×C4×C11#4111yescharacteristic
93C22×Dic11—21no—
94C22×Dic11—21no—
95C22×Dic11—21no—
96C22×Dic11—21no—
97C22×Dic11—21no—
98C22×Dic11—21no—
99C2×Dic22—21no—
100C2×Dic22—21no—
101C2×Dic22—21no—
102C2×Dic22—81no—
103C2×Dic22—81no—
104C2×Dic22C22⋊C412yes—
105C2×C8×C11—22no—
106C2×C8×C11—81no—
107C11×C4⋊C4—81no—
108C11×C22⋊C4—41no—
109C11×C22⋊C4—41no—
110C22⋊Dic11—22no—
111C22⋊Dic11—22no—
112C22⋊Dic11—21no—
113C22⋊Dic11—21no—
114C22⋊Dic11—21no—
115C22⋊Dic11—41no—
116C22⋊Dic11—41no—
117C22⋊Dic11Q1612yescomplemented
118C4⋊Dic11—21no—
119C4⋊Dic11—21no—
120C4⋊Dic11—21no—
121C4⋊Dic11C22⋊C412yes—
122Dic11⋊C4—22no—
123Dic11⋊C4—22no—
124Dic11⋊C4—42no—
125Dic11⋊C4—41no—
126Dic11⋊C4—41no—
127Dic11⋊C4—81no—
128C4×Dic11—42no—
129C4×Dic11—81no—
130C4×Dic11—81no—
131C2×C11⋊C8—41no—
132C2×C11⋊C8—81no—
133Dic44—82no—
134#3189—111no—
135#2368—111no—
136#1996—111no—
137#1520—111no—
138C2×#328—111no—
139#1294D1111yescharacteristic
140#1282—111no—
141C23×C11—41no—
142C23×C11—41no—
143C23×C11C4×D411yescharacteristic
144C23×C11#12011yescharacteristic
145C23×C11#12111yescharacteristic
146C23×C11C2×Q1611yescharacteristic
147C23×C11#13511yescharacteristic
148C23×C11#13711yescharacteristic
149C23×C11#13711yescharacteristic
150C2×C4×C11—22no—
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—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—82no—
163C2×C4×C11—82no—
164C2×C4×C11—81no—
165C2×C4×C11—81no—
166C2×C4×C11—81no—
167C2×C4×C11C2×C22⋊C411yescharacteristic
168C2×C4×C11C4×D411yescharacteristic
169C2×C4×C11#12111yescharacteristic
170C2×C4×C11#12311yescharacteristic
171C2×Dic11—22no—
172C2×Dic11—22no—
173C2×Dic11—22no—
174C2×Dic11—41no—
175C2×Dic11—41no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11—41no—
181C2×Dic11—41no—
182C2×Dic11—41no—
183C2×Dic11—41no—
184C2×Dic11—41no—
185C2×Dic11—81no—
186C2×Dic11—81no—
187Dic22—42no—
188Dic22—42no—
189Dic22—81no—
190Dic22—81no—
191C8×C11—42no—
192C11⋊C8—81no—
193C2×C22⋊Q8—111no—
194C2×C22⋊Q8—111no—
195#484—112no—
196#484—221no—
197#467—222no—
198#451—112no—
199#451—221no—
200C2×C22⋊C8—111no—
201C2×C22⋊C8C2×D1111yescharacteristic
202#391—221no—
203#387—221no—
204#387—221no—
205#385—221no—
206#380C2×D1111yescharacteristic
207C4×C4⋊C4—221no—
208C4×C22⋊C4—111no—
209C4×C22⋊C4—221no—
210C2×#95C2×D1111yescharacteristic
211#342—221no—
212#342—221no—
213#328—222no—
214#328—221no—
215#328—221no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11—21no—
221C22×C11—21no—
222C22×C11—41no—
223C22×C11—41no—
224C22×C11—41no—
225C22×C11—41no—
226C22×C11#38611yescharacteristic
227C22×C11C4×Q1611yescharacteristic
228C22×C11#44111yescharacteristic
229C22×C11#45111yescharacteristic
230C22×C11#45211yescharacteristic
231C22×C11#46211yescharacteristic
232C22×C11#46411yescharacteristic
233C4×C11—21no—
234C4×C11—21no—
235C4×C11—21no—
236C4×C11—21no—
237C4×C11—42no—
238C4×C11—81no—
239C4×C11—161no—
240Dic11—42no—
241Dic11—42no—
242Dic11—42no—
243Dic11—81no—
244Dic11—81no—
245Dic11—81no—
246C22×Q8—111no—
247C22×Q8—111no—
248C23×C4—21no—
249C23×C4C22×D1111yescharacteristic
250C2×Q16—222no—
251C22×C8—21no—
252C22×C8—221no—
253C22⋊Q8—112no—
254C22⋊Q8—112no—
255C22⋊Q8—221no—
256C22⋊Q8—221no—
257C22⋊Q8—221no—
258C22⋊Q8—221no—
259C22⋊Q8—221no—
260C22⋊Q8—221no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—111no—
263C2×C4⋊C4—111no—
264C2×C4⋊C4—221no—
265C2×C4⋊C4—221no—
266C2×C4⋊C4—221no—
267C2×C4⋊C4—221no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—111no—
270C2×C22⋊C4—111no—
271C2×C22⋊C4—221no—
272C2×C22⋊C4—221no—
273C2×C42—221no—
274C2×C42—221no—
275C2×C42—221no—
276#107—222no—
277#103—222no—
278#103—222no—
279C22⋊C8—21no—
280C22⋊C8—221no—
281C22⋊C8—221no—
282C22⋊C8C4×D1112yes—
283#95—21no—
284#95—21no—
285#95—221no—
286#95—221no—
287#95—221no—
288#95—221no—
289#95—221no—
290#95D4411yescharacteristic
291#95D4411yescharacteristic
292C2×C11—21no—
293C2×C11—21no—
294C2×C11—21no—
295C2×C11—21no—
296C2×C11—21no—
297C2×C11—21no—
298C2×C11#187811yescharacteristic
299C2×C11#190611yescharacteristic
300C2×C11#191311yescharacteristic
301C24D4×D1111yescharacteristic
302C2×Q8—112no—
303C2×Q8—221no—
304C2×Q8—221no—
305C2×Q8—221no—
306C2×Q8—881no—
307C2×Q8—881no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—42no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—81no—
315C22×C4—81no—
316C22×C4—221no—
317C22×C4—221no—
318C22×C4—221no—
319C22×C4—221no—
320C22×C4—221no—
321C22×C4—221no—
322C22×C4C2×C4×D1111yescharacteristic
323C22×C4C2×D4411yescharacteristic
324C22×C4#433911yescharacteristic
325C22×C4D4×D1111yescharacteristic
326C22×C4D4×D1111yescharacteristic
327C22×C4#434311yescharacteristic
328Q16—882no—
329C2×C8—22no—
330C2×C8—81no—
331C2×C8—441no—
332C2×C8—881no—
333C4⋊C4—81no—
334C4⋊C4—112no—
335C4⋊C4—222no—
336C4⋊C4—221no—
337C4⋊C4—222no—
338C4⋊C4—221no—
339C4⋊C4—221no—
340C4⋊C4—442no—
341C4⋊C4—441no—
342C4⋊C4—441no—
343C4⋊C4—881no—
344C22⋊C4—41no—
345C22⋊C4—41no—
346C22⋊C4—112no—
347C22⋊C4—222no—
348C22⋊C4—222no—
349C22⋊C4—221no—
350C22⋊C4—221no—
351C22⋊C4—221no—
352C22⋊C4—441no—
353C22⋊C4—441no—
354C42—442no—
355C42—881no—
356C42—881no—
357C11#927611yescharacteristic, complemented, Sylow
358C23—41no—
359C23—41no—
360C23#6693511yescharacteristic
361C23#6693711yescharacteristic
362C23#6694611yescharacteristic
363C23#6696511yescharacteristic
364C23#6696811yescharacteristic
365C23#6696811yescharacteristic
366C23Q16×D1111yescharacteristic
367Q8—442no—
368Q8—442no—
369Q8—881no—
370Q8—881no—
371C2×C4—22no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—82no—
384C2×C4—82no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—222no—
389C2×C4—222no—
390C2×C4—222no—
391C2×C4—441no—
392C2×C4—441no—
393C2×C4—441no—
394C2×C4—441no—
395C2×C4—441no—
396C2×C4—441no—
397C2×C4—441no—
398C2×C4—441no—
399C2×C4—441no—
400C2×C4—441no—
401C2×C4—441no—
402C2×C4—881no—
403C2×C4—881no—
404C2×C4C4×D4411yescharacteristic
405C2×C4C22⋊C4×D1111yescharacteristic
406C2×C4#6694711yescharacteristic
407C2×C4#6694811yescharacteristic
408C8—42no—
409C8—881no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22#1062227811yescharacteristic
421C22#1062238011yescharacteristic
422C22#1062239611yescharacteristic
423C22#1062240611yescharacteristic
424C22#1062242111yescharacteristic
425C22#1062246611yescharacteristic
426C22#1062248611yescharacteristic
427C4—21no—
428C4—21no—
429C4—21no—
430C4—21no—
431C4—42no—
432C4—81no—
433C4—161no—
434C4—442no—
435C4—442no—
436C4—442no—
437C4—881no—
438C4—881no—
439C4—881no—
440C2—21no—
441C2—21no—
442C2—21no—
443C2—21no—
444C2—21no—
445C2—21no—
446C2#1306895811yescharacteristic
447C2#1306911611yescharacteristic
448C2#1306915711yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1294C2
socleC22×C11#386
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenter#1294D11
hypocenterC11#9276
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
19. #10622352C4semidirect
21. #10622335C4semidirect
117. C22⋊Dic11Q16semidirect
357. C11#9276semidirect

Maximal subgroups

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

subgroupindex
#130793912
#130716962
#130696002
#130671872
C2×#106220902
#130664622
C11×#12942
#927611