Finite Group Databasebeta

← #14650812

Subgroups — #14650812

Order 2816.

520 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 89 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#13079422C211yesmaximal, characteristic
2#13071784C211yesmaximal, characteristic, complemented
3#13069453C211yesmaximal, characteristic
4#13067137C211yesmaximal, characteristic, complemented
5#13066521C211yesmaximal, characteristic, complemented
6#13066468C211yesmaximal, characteristic, complemented
7C11×#1510C211yesmaximal, characteristic
8C2×C11×#121C2211yescharacteristic
9C2×#66977C2211yescharacteristic
10C11×#407C2211yescharacteristic
11C11×#381C2211yescharacteristic
12C2×#66898—21no—
13C2×#66898—21no—
14#10622831C412yescomplemented
15#10622825C2211yescharacteristic
16C4×C22⋊Dic11C2211yescharacteristic
17#10622820C2211yescharacteristic
18#10622655—22no—
19#10622653—21no—
20#10622646—21no—
21#10622583C412yescomplemented
22#10622558—21no—
23#10622557—21no—
24#10622268—21no—
25#10622266—21no—
26#10622260—21no—
27#10622259—21no—
28C11×#327—21no—
29C11×#327—21no—
30#10622105—22no—
31C22×D4×C11—21no—
32C22×D4×C11C2×C411yescharacteristic
33C23×C4×C11C2311yescharacteristic
34C22×Dic22D411yescharacteristic
35C2×C11×M16—21no—
36C11×#121—21no—
37C11×#121—21no—
38C11×#121—21no—
39C11×#121—21no—
40C2×C11×C4⋊C4C2×C411yescharacteristic
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4—21no—
43C2×C22⋊Dic11—21no—
44C2×C22⋊Dic11—21no—
45C2×C22⋊Dic11D411yescharacteristic
46C2×C22⋊Dic11D411yescharacteristic
47C2×#4324—22no—
48C2×C4⋊Dic11—21no—
49C2×C4⋊Dic11D411yescharacteristic
50#66977—21no—
51#66977—21no—
52#66977C2×C412yes—
53#66977D412yes—
54C2×Dic11⋊C4—21no—
55C2×Dic11⋊C4—21no—
56C2×Dic11⋊C4—21no—
57C2×C4×Dic11—21no—
58C2×C4×Dic11—21no—
59C2×C4×Dic11—21no—
60C2×#4318—21no—
61C11×C22⋊C8—21no—
62C11×C22⋊C8—21no—
63C11×#95—21no—
64C11×#95D411yescharacteristic
65C11×#95D411yescharacteristic
66#66898—42no—
67#66898—42no—
68#66896—22no—
69C11⋊#95—21no—
70C11⋊#95—21no—
71C11⋊#95—21no—
72C11⋊#95—21no—
73C11⋊#95—21no—
74C11⋊#95—21no—
75C22⋊(C11⋊C8)—21no—
76C22⋊(C11⋊C8)C2×C412yes—
77#66874—22no—
78#66871—22no—
79#9344—111nomaximal, Sylow
80C24×C11—21no—
81C24×C11C2×D411yescharacteristic
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—41no—
85C2×D4×C11—41no—
86C2×D4×C11—41no—
87C2×D4×C11—41no—
88C2×D4×C11—41no—
89C2×D4×C11—41no—
90C2×D4×C11—81no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—81no—
95C22×C4×C11C22×C411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11#4111yescharacteristic
100C22×C4×C11#4111yescharacteristic
101C22×Dic11—21no—
102C22×Dic11—21no—
103C22×Dic11—21no—
104C22×Dic11—21no—
105C22×Dic11—41no—
106C2×Dic22—21no—
107C2×Dic22—81no—
108C2×Dic22C22⋊C412yes—
109C11×M16—81no—
110C2×C8×C11—41no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—21no—
113C11×C22⋊C4—41no—
114C11×C22⋊C4—41no—
115C11×C22⋊C4—81no—
116C22⋊Dic11—22no—
117C22⋊Dic11—22no—
118C22⋊Dic11—22no—
119C22⋊Dic11—41no—
120C22⋊Dic11—41no—
121C22⋊Dic11—41no—
122#4324—82no—
123C4⋊Dic11—21no—
124C4⋊Dic11—81no—
125C4⋊Dic11C22⋊C412yes—
126Dic11⋊C4—22no—
127Dic11⋊C4—22no—
128Dic11⋊C4—81no—
129Dic11⋊C4—81no—
130C4×Dic11—81no—
131C4×Dic11—81no—
132C4×Dic11—81no—
133#4318—81no—
134C2×C11⋊C8—22no—
135#3193—111no—
136#2378—111no—
137#1964—111no—
138#1510D1111yescharacteristic
139#1508—111no—
140#1305—111no—
141#1284—111no—
142C23×C11—21no—
143C23×C11—21no—
144C23×C11—41no—
145C23×C11—41no—
146C23×C11—41no—
147C23×C11—41no—
148C23×C11—41no—
149C23×C11—81no—
150C23×C11—81no—
151C23×C11C4×D411yescharacteristic
152C23×C11#12011yescharacteristic
153C23×C11#12111yescharacteristic
154D4×C11—42no—
155D4×C11—81no—
156D4×C11—81no—
157D4×C11—81no—
158D4×C11—81no—
159D4×C11—81no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11C2×C22⋊C411yescharacteristic
176C2×C4×C11C4×D411yescharacteristic
177C2×C4×C11#12111yescharacteristic
178C2×C4×C11#12311yescharacteristic
179C2×Dic11—22no—
180C2×Dic11—22no—
181C2×Dic11—41no—
182C2×Dic11—41no—
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—
194Dic22—42no—
195Dic22—81no—
196C8×C11—81no—
197C11⋊C8—42no—
198C2×C22⋊Q8—111no—
199C2×#121C2×D1111yescharacteristic
200#484—112no—
201#480—221no—
202#468—222no—
203#450—112no—
204#448—221no—
205C2×#99—221no—
206C2×#99—221no—
207#407—111no—
208#407C2×D1111yescharacteristic
209#391—221no—
210#389—221no—
211#388—221no—
212#388—221no—
213#387—221no—
214#387—221no—
215#381C2×D1111yescharacteristic
216#380—111no—
217C4×C22⋊C4—111no—
218#328—222no—
219#327—21no—
220#327—21no—
221C22×C11—21no—
222C22×C11—21no—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11—21no—
226C22×C11—21no—
227C22×C11—21no—
228C22×C11—21no—
229C22×C11—81no—
230C22×C11—81no—
231C22×C11—81no—
232C22×C11—81no—
233C22×C11—81no—
234C22×C11—161no—
235C22×C11—161no—
236C22×C11#38611yescharacteristic
237C22×C11#45311yescharacteristic
238C22×C11#45411yescharacteristic
239C4×C11—21no—
240C4×C11—21no—
241C4×C11—21no—
242C4×C11—21no—
243C4×C11—81no—
244C4×C11—81no—
245C4×C11—81no—
246Dic11—42no—
247Dic11—42no—
248Dic11—81no—
249Dic11—81no—
250Dic11—82no—
251C22×Q8—111no—
252C22×D4—21no—
253C22×D4C4×D1111yescharacteristic
254C23×C4C22×D1111yescharacteristic
255C2×SD16—222no—
256C2×M16—21no—
257C2×M16—221no—
258C22⋊Q8—112no—
259C22⋊Q8—112no—
260C22⋊Q8—221no—
261C22⋊Q8—221no—
262#121—21no—
263#121—21no—
264#121—21no—
265#121—21no—
266C2×C4⋊C4—111no—
267C2×C4⋊C4—221no—
268C2×C4⋊C4—221no—
269C2×C4⋊C4—221no—
270C2×C4⋊C4—221no—
271C2×C4⋊C4C4×D1111yescharacteristic
272C2×C22⋊C4—21no—
273C2×C22⋊C4—21no—
274C2×C22⋊C4—111no—
275C2×C22⋊C4—111no—
276C2×C22⋊C4—221no—
277C2×C22⋊C4—221no—
278C2×C42—221no—
279C2×C42—221no—
280C2×C42—221no—
281#107—222no—
282#103—222no—
283#102—222no—
284#99—442no—
285#99—442no—
286C22⋊C8—21no—
287C22⋊C8—21no—
288C22⋊C8—112no—
289C22⋊C8—221no—
290#95—21no—
291#95—221no—
292#95—221no—
293#95—221no—
294#95—221no—
295#95—221no—
296#95—221no—
297#95C22⋊D1111yescharacteristic
298#95C22⋊D1111yescharacteristic
299C2×C11—21no—
300C2×C11—21no—
301C2×C11—41no—
302C2×C11—41no—
303C2×C11—161no—
304C2×C11#188311yescharacteristic
305C2×C11#190511yescharacteristic
306C2×C11#191311yescharacteristic
307C24—21no—
308C24D4×D1111yescharacteristic
309C2×Q8—112no—
310C2×Q8—221no—
311C2×Q8—881no—
312C2×D4—21no—
313C2×D4—21no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—81no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—81no—
325C22×C4—221no—
326C22×C4—221no—
327C22×C4—221no—
328C22×C4—221no—
329C22×C4—441no—
330C22×C4C2×C4×D1111yescharacteristic
331C22×C4#433911yescharacteristic
332C22×C4D4×D1111yescharacteristic
333C22×C4D4×D1111yescharacteristic
334C22×C4#434111yescharacteristic
335C22×C4C2×C22⋊D1111yescharacteristic
336SD16—882no—
337M16—81no—
338M16—881no—
339C2×C8—41no—
340C2×C8—222no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—112no—
344C4⋊C4—221no—
345C4⋊C4—222no—
346C4⋊C4—222no—
347C4⋊C4—881no—
348C4⋊C4—881no—
349C4⋊C4—881no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C22⋊C4—81no—
353C22⋊C4—222no—
354C22⋊C4—222no—
355C22⋊C4—222no—
356C22⋊C4—441no—
357C22⋊C4—441no—
358C22⋊C4—441no—
359C42—881no—
360C42—881no—
361C42—881no—
362C11#934411yescharacteristic, complemented, Sylow
363C23—21no—
364C23—21no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23—41no—
370C23—81no—
371C23—81no—
372C23(C22⋊D11)⋊C411yescharacteristic
373C23#6693711yescharacteristic
374C23#6699011yescharacteristic
375Q8—442no—
376Q8—881no—
377D4—42no—
378D4—81no—
379D4—81no—
380D4—81no—
381D4—81no—
382D4—81no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—222no—
399C2×C4—222no—
400C2×C4—441no—
401C2×C4—441no—
402C2×C4—441no—
403C2×C4—441no—
404C2×C4—441no—
405C2×C4—442no—
406C2×C4—441no—
407C2×C4—441no—
408C2×C4—441no—
409C2×C4—441no—
410C2×C4—441no—
411C2×C4—881no—
412C2×C4—881no—
413C2×C4C22⋊C4×D1111yescharacteristic
414C2×C4#6693611yescharacteristic
415C2×C4C4×C22⋊D1111yescharacteristic
416C2×C4#6699111yescharacteristic
417C8—81no—
418C8—442no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—81no—
428C22—81no—
429C22—81no—
430C22—81no—
431C22—81no—
432C22—161no—
433C22—161no—
434C22#1062256911yescharacteristic
435C22#1062281111yescharacteristic
436C22#1062281411yescharacteristic
437C4—21no—
438C4—21no—
439C4—21no—
440C4—21no—
441C4—81no—
442C4—81no—
443C4—81no—
444C4—442no—
445C4—442no—
446C4—881no—
447C4—881no—
448C4—882no—
449C2—21no—
450C2—21no—
451C2—41no—
452C2—41no—
453C2—161no—
454C2#1306898911yescharacteristic
455C2#1306910711yescharacteristic
456C2#1306915511yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1510C2
socleC22×C11#386
prime radicalC2×C11×#121C22
cosocleC23×C4×C11C23
hypercenter#1510D11
hypocenterC11#9344
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1510

Complements

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

NH ≅ G/Ntype
2. #13071784C2semidirect
4. #13067137C2semidirect
5. #13066521C2semidirect
6. #13066468C2semidirect
14. #10622831C4semidirect
21. #10622583C4semidirect
362. C11#9344semidirect

Maximal subgroups

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

subgroupindex
#130794222
#130717842
#130694532
#130671372
#130665212
#130664682
C11×#15102
#934411