Finite Group Databasebeta

← #14651564

Subgroups — #14651564

Order 2816.

576 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 109 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#13077642C211yesmaximal, characteristic
2#13072918C211yesmaximal, characteristic
3#13068702C211yesmaximal, characteristic, complemented
4#13068601C211yesmaximal, characteristic
5#13066484C211yesmaximal, characteristic, complemented
6#13066483C211yesmaximal, characteristic, complemented
7C11×#1823C211yesmaximal, characteristic, complemented
8C22×C11×C4⋊C4C2211yescharacteristic
9C2×#66982—21no—
10C2×C4×C22⋊D11C2211yescharacteristic
11C2×C11×C22⋊C8C2211yescharacteristic
12C11×#380C2211yescharacteristic
13#10622825C2211yescharacteristic
14#10622825C2211yescharacteristic
15#10622824—21no—
16C2×C22⋊(C11⋊C8)C2211yescharacteristic
17#10622724—22no—
18#10622606C412yescomplemented
19#10622600—21no—
20#10622593C412yescomplemented
21#10622586—21no—
22C2×#66870—21no—
23#10622343—22no—
24#10622339—21no—
25#10622332—21no—
26C11×#340—22no—
27#10622167—22no—
28#10622165—21no—
29C23×C4×C11—21no—
30C23×C4×C11C2311yescharacteristic
31C22×C22⋊D11D411yescharacteristic
32C22×C4×D11D411yescharacteristic
33C22×C8×C11D412yes—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4C2×C412yes—
41C2×C11×C22⋊C4—21no—
42C2×C22⋊Dic11—21no—
43C2×C22⋊Dic11—21no—
44C2×C22⋊Dic11D411yescharacteristic
45#66982—42no—
46#66982—42no—
47C4×C22⋊D11—21no—
48C4×C22⋊D11—21no—
49C4×C22⋊D11—21no—
50C4×C22⋊D11—21no—
51C2×(C2×D11)⋊C4—22no—
52C2×(C2×D11)⋊C4C2×C411yescharacteristic
53C2×C4⋊Dic11—21no—
54C2×C4⋊Dic11—21no—
55C2×Dic11⋊C4—22no—
56C2×Dic11⋊C4C2×C411yescharacteristic
57C2×C4×Dic11D411yescharacteristic
58C22×C11⋊C8D412yes—
59C2×#4313—22no—
60C11×C22⋊C8—21no—
61C11×C22⋊C8—21no—
62C11×#95—21no—
63C11⋊#95—22no—
64C11⋊#95—22no—
65C11⋊#95—21no—
66C11⋊#95C2×C412yes—
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)—21no—
69(C2×D11)⋊C8—22no—
70#66879—22no—
71Dic11⋊C8—22no—
72#66870—42no—
73#9474—111nomaximal, Sylow
74C24×C11C2×D411yescharacteristic
75C23×D11C22⋊C411yescharacteristic
76C22×C4×C11—22no—
77C22×C4×C11—42no—
78C22×C4×C11—41no—
79C22×C4×C11—41no—
80C22×C4×C11—41no—
81C22×C4×C11—41no—
82C22×C4×C11—41no—
83C22×C4×C11—41no—
84C22×C4×C11—41no—
85C22×C4×C11C22×C411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11#4111yescharacteristic
90C22×C4×C11#4111yescharacteristic
91C2×C22⋊D11—21no—
92C2×C22⋊D11—21no—
93C2×C22⋊D11—21no—
94C2×C22⋊D11—21no—
95C2×C22⋊D11—21no—
96C2×C22⋊D11—21no—
97C22×Dic11—22no—
98C22×Dic11—41no—
99C22×Dic11C22⋊C411yescharacteristic
100C22×Dic11C22⋊C411yescharacteristic
101C22×Dic11C22⋊C411yescharacteristic
102C2×C4×D11—21no—
103C2×C4×D11—21no—
104C2×C4×D11—42no—
105C2×C8×C11—22no—
106C2×C8×C11—42no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—42no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—41no—
112C11×C22⋊C4—41no—
113C11×C22⋊C4—41no—
114C22⋊Dic11—21no—
115C22⋊Dic11—21no—
116C22⋊Dic11—41no—
117C22⋊Dic11—41no—
118C22⋊Dic11—41no—
119C22⋊Dic11—41no—
120(C2×D11)⋊C4—21no—
121(C2×D11)⋊C4—21no—
122(C2×D11)⋊C4—44no—
123C4⋊Dic11—42no—
124C4⋊Dic11—42no—
125Dic11⋊C4—21no—
126Dic11⋊C4—21no—
127Dic11⋊C4—44no—
128C4×Dic11—21no—
129C4×Dic11—21no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—42no—
132#4313—82no—
133#2973—111no—
134#2486—111no—
135#1823—111no—
136#1823D1111yescharacteristic, complemented
137#1799—111no—
138#1289—111no—
139#1289—111no—
140C23×C11—41no—
141C23×C11—41no—
142C23×C11C2×C22⋊C411yescharacteristic
143C23×C11#12111yescharacteristic
144C23×C11#12111yescharacteristic
145C23×C11AGL(1,ℤ/8)11yescharacteristic
146C23×C11AGL(1,ℤ/8)11yescharacteristic
147C23×C11AGL(1,ℤ/8)11yescharacteristic
148C23×C11#13711yescharacteristic
149C22×D11—21no—
150C22×D11—21no—
151C22×D11—21no—
152C22×D11—41no—
153C22×D11—41no—
154C2×C4×C11—22no—
155C2×C4×C11—22no—
156C2×C4×C11—22no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—42no—
161C2×C4×C11—42no—
162C2×C4×C11—42no—
163C2×C4×C11—81no—
164C2×C4×C11—81no—
165C2×C4×C11—81no—
166C2×C4×C11—81no—
167C2×C4×C11—81no—
168C2×C4×C11—81no—
169C2×C4×C11—81no—
170C2×C4×C11C4×D411yescharacteristic
171C2×C4×C11C4×D411yescharacteristic
172C2×C4×C11#12011yescharacteristic
173C2×C4×C11#12311yescharacteristic
174C22⋊D11—41no—
175C22⋊D11—41no—
176C22⋊D11—41no—
177C22⋊D11—41no—
178C2×Dic11—21no—
179C2×Dic11—21no—
180C2×Dic11—21no—
181C2×Dic11—21no—
182C2×Dic11—21no—
183C2×Dic11—41no—
184C2×Dic11—41no—
185C2×Dic11—42no—
186C2×Dic11—42no—
187C2×Dic11—42no—
188C2×Dic11—81no—
189C2×Dic11—81no—
190C2×Dic11—81no—
191C4×D11—42no—
192C4×D11—81no—
193C8×C11—42no—
194C11⋊C8—42no—
195C2×#123—221no—
196C2×C4×D4—111no—
197C22×C4⋊C4C2×D1111yescharacteristic
198#435—222no—
199#435—222no—
200#432—221no—
201C2×#99—221no—
202#407—221no—
203C2×C22⋊C8—111no—
204C2×C22⋊C8C2×D1111yescharacteristic
205#398—112no—
206#397—112no—
207#389—221no—
208#381—221no—
209#380—111no—
210#380—111no—
211#380—221no—
212#380C2×D1111yescharacteristic
213#342—221no—
214#340—22no—
215#340—222no—
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×C11#41711yescharacteristic
228C22×C11#41811yescharacteristic
229C22×C11#46811yescharacteristic
230C22×C11#46811yescharacteristic
231C22×C11#46911yescharacteristic
232C22×C11#46911yescharacteristic
233C2×D11—42no—
234C2×D11—41no—
235C2×D11—41no—
236C2×D11—41no—
237C2×D11—81no—
238C4×C11—21no—
239C4×C11—21no—
240C4×C11—21no—
241C4×C11—82no—
242C4×C11—161no—
243C4×C11#45812yes—
244Dic11—41no—
245Dic11—41no—
246Dic11—41no—
247Dic11—82no—
248Dic11—161no—
249C22×D4—111no—
250C23×C4—21no—
251C23×C4—111no—
252C23×C4C22×D1111yescharacteristic
253C2×M16—222no—
254C22×C8—112no—
255C22×C8C22⋊D1112yes—
256#123—442no—
257#123—442no—
258C4×D4—221no—
259C4×D4—221no—
260C4×D4—221no—
261C4×D4—221no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—111no—
269C2×C4⋊C4—222no—
270C2×C4⋊C4—221no—
271C2×C4⋊C4—221no—
272C2×C4⋊C4C4×D1112yes—
273C2×C22⋊C4—21no—
274C2×C22⋊C4—111no—
275C2×C22⋊C4—111no—
276C2×C22⋊C4—222no—
277C2×C22⋊C4—221no—
278C2×C22⋊C4—221no—
279C2×C42—111no—
280C4⋊C8—222no—
281#99—442no—
282C22⋊C8—21no—
283C22⋊C8—21no—
284C22⋊C8—222no—
285C22⋊C8—221no—
286C22⋊C8—221no—
287#97—222no—
288#95—21no—
289#95—112no—
290#95—222no—
291#95—222no—
292#95—221no—
293C2×C11—21no—
294C2×C11—21no—
295C2×C11—21no—
296C2×C11—21no—
297C2×C11—21no—
298C2×C11—21no—
299C2×C11#189011yescharacteristic
300C2×C11#189511yescharacteristic
301C2×C11#190911yescharacteristic
302D11—81no—
303C24—111no—
304C24D4×D1111yescharacteristic
305C2×D4—221no—
306C2×D4—221no—
307C2×D4—221no—
308C2×D4—221no—
309C2×D4—221no—
310C2×D4—221no—
311C22×C4—22no—
312C22×C4—42no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4—111no—
321C22×C4—111no—
322C22×C4—111no—
323C22×C4—221no—
324C22×C4—221no—
325C22×C4—222no—
326C22×C4—442no—
327C22×C4—441no—
328C22×C4C2×C4×D1111yescharacteristic
329C22×C4#433911yescharacteristic
330C22×C4D4×D1111yescharacteristic
331C22×C4D4×D1111yescharacteristic
332C22×C4#434111yescharacteristic
333C22×C4C2×C22⋊D1111yescharacteristic
334M16—882no—
335C2×C8—22no—
336C2×C8—42no—
337C2×C8—222no—
338C2×C8—442no—
339C4⋊C4—22no—
340C4⋊C4—22no—
341C4⋊C4—42no—
342C4⋊C4—41no—
343C4⋊C4—41no—
344C4⋊C4—221no—
345C4⋊C4—221no—
346C4⋊C4—442no—
347C4⋊C4—442no—
348C4⋊C4—444no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—221no—
352C22⋊C4—221no—
353C22⋊C4—221no—
354C22⋊C4—221no—
355C22⋊C4—444no—
356C22⋊C4—441no—
357C22⋊C4—441no—
358C22⋊C4—441no—
359C22⋊C4—441no—
360C42—221no—
361C42—221no—
362C11#947411yescharacteristic, complemented, Sylow
363C23—41no—
364C23—41no—
365C23—221no—
366C23—221no—
367C23—221no—
368C23—441no—
369C23—441no—
370C23C22⋊C4×D1111yescharacteristic
371C23#6693711yescharacteristic
372C23#6696411yescharacteristic
373C23#6696411yescharacteristic
374C23#6696711yescharacteristic
375C23#6696811yescharacteristic
376C23#6699111yescharacteristic
377D4—441no—
378D4—441no—
379D4—441no—
380D4—441no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—81no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4—221no—
398C2×C4—221no—
399C2×C4—221no—
400C2×C4—221no—
401C2×C4—221no—
402C2×C4—442no—
403C2×C4—441no—
404C2×C4—441no—
405C2×C4—442no—
406C2×C4—442no—
407C2×C4—442no—
408C2×C4—881no—
409C2×C4—881no—
410C2×C4—881no—
411C2×C4—881no—
412C2×C4(C22⋊D11)⋊C411yescharacteristic
413C2×C4#6693611yescharacteristic
414C2×C4C4×C22⋊D1111yescharacteristic
415C2×C4#6699011yescharacteristic
416C8—42no—
417C8—442no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—41no—
425C22—41no—
426C22—41no—
427C22—41no—
428C22—442no—
429C22—441no—
430C22—441no—
431C22—441no—
432C22—881no—
433C22#1062238311yescharacteristic
434C22#1062238411yescharacteristic
435C22#1062239311yescharacteristic
436C22#1062239511yescharacteristic
437C22#1062256911yescharacteristic
438C22#1062277211yescharacteristic
439C22#1062278711yescharacteristic
440C4—21no—
441C4—21no—
442C4—21no—
443C4—82no—
444C4—161no—
445C4—441no—
446C4—441no—
447C4—441no—
448C4—882no—
449C4—1761no—
450C4#1062266612yes—
451C2—21no—
452C2—21no—
453C2—21no—
454C2—21no—
455C2—21no—
456C2—21no—
457C2—881no—
458C2#1306902611yescharacteristic
459C2#1306905111yescharacteristic
460C2#1306913511yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1823C2
socleC22×C11#386
prime radicalC22×C22⋊D11D4
cosocleC23×C4×C11C23
hypercenter#1823D11
hypocenterC11#9474
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1823

Complements

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

NH ≅ G/Ntype
3. #13068702C2semidirect
5. #13066484C2semidirect
6. #13066483C2semidirect
7. C11×#1823C2semidirect
18. #10622606C4semidirect
20. #10622593C4semidirect
136. #1823D11semidirect
362. C11#9474semidirect

Maximal subgroups

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

subgroupindex
#130776422
#130729182
#130687022
#130686012
#130664842
#130664832
C11×#18232
#947411