Finite Group Databasebeta

← #14651760

Subgroups — #14651760

Order 2816.

716 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 716 conjugacy classes of subgroups — too many to draw. Only its 103 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#13077061C211yesmaximal, characteristic
2#13071947C211yesmaximal, characteristic
3#13066945C212yesmaximal, complemented
4#13066525C212yesmaximal, complemented
5C11×#1785C211yesmaximal, characteristic
6C22×C11×#41C2211yescharacteristic
7C2×#66988C411yescharacteristic
8C2×#66988C411yescharacteristic
9C22×Dic11⋊C4C2211yescharacteristic
10C22×#4318—21no—
11C2×C11×#101—21no—
12C2×C11×#100—21no—
13C11×#407C2212yes—
14#10622847—24no—
15#10622842—21no—
16#10622835—21no—
17#10622833C411yescharacteristic
18#10622833C411yescharacteristic
19#10622824C2211yescharacteristic
20#10622823—21no—
21#10622823—21no—
22#10622820—21no—
23#10622820C2212yes—
24#10622107—24no—
25C2×C11×#41—22no—
26C2×C11×#41—22no—
27C2×C11×#41—42no—
28C2×C11×#41—42no—
29C22×Q8×C11D411yescharacteristic
30C22×D4×C11C2×C411yescharacteristic
31C22×D4×C11C2×C411yescharacteristic
32C22×D4×C11D411yescharacteristic
33C23×C4×C11D411yescharacteristic
34C23×C4×C11D411yescharacteristic
35C23×C4×C11C2311yescharacteristic
36C23×Dic11C2×C411yescharacteristic
37C23×Dic11C2×C411yescharacteristic
38C2×C11×M16—22no—
39C2×C22⋊Dic11—21no—
40C2×C22⋊Dic11—21no—
41C2×C22⋊Dic11—21no—
42C2×C22⋊Dic11—21no—
43C2×C22⋊Dic11C2×C411yescharacteristic
44C2×C22⋊Dic11C2×C411yescharacteristic
45#66988—42no—
46#66988—42no—
47C2×Dic11⋊C4—21no—
48C2×Dic11⋊C4—21no—
49C2×Dic11⋊C4—21no—
50C2×Dic11⋊C4—21no—
51C2×Dic11⋊C4—22no—
52C2×Dic11⋊C4—22no—
53C2×#4318—22no—
54C2×#4318—22no—
55C2×#4318—42no—
56C2×#4318—42no—
57C22×C11⋊C8—22no—
58C11×#101—42no—
59C11×#100—42no—
60C11×C22⋊C8—22no—
61C11×C22⋊C8—22no—
62C11⋊#95—21no—
63C11⋊#95—21no—
64C11⋊#95—21no—
65C11⋊#95—21no—
66C22⋊(C11⋊C8)—24no—
67C22⋊(C11⋊C8)—22no—
68C22⋊(C11⋊C8)D414yes—
69#9513—111nomaximal, Sylow
70C24×C11C22⋊C411yescharacteristic
71C24×C11C22⋊C411yescharacteristic
72C24×C11C22×C411yescharacteristic
73C11×#41—44no—
74C11×#41—44no—
75C11×#41—48no—
76C2×Q8×C11—22no—
77C2×Q8×C11—22no—
78C2×Q8×C11—41no—
79C2×D4×C11—22no—
80C2×D4×C11—22no—
81C2×D4×C11—22no—
82C2×D4×C11—22no—
83C2×D4×C11—22no—
84C2×D4×C11—22no—
85C2×D4×C11—41no—
86C2×D4×C11—41no—
87C2×D4×C11—41no—
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—41no—
95C22×C4×C11—41no—
96C22×C4×C11—41no—
97C22×C4×C11—41no—
98C22×C4×C11C22⋊C411yescharacteristic
99C22×C4×C11C22⋊C411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D412yes—
103C22×C4×C11#4112yes—
104C22×Dic11—21no—
105C22×Dic11—21no—
106C22×Dic11—21no—
107C22×Dic11—21no—
108C22×Dic11—22no—
109C22×Dic11—22no—
110C22×Dic11—41no—
111C22×Dic11—41no—
112C22×Dic11—42no—
113C11×M16—42no—
114C11×M16—42no—
115C2×C8×C11—42no—
116C22⋊Dic11—41no—
117C22⋊Dic11—41no—
118C22⋊Dic11—42no—
119C22⋊Dic11—42no—
120C22⋊Dic11—42no—
121C22⋊Dic11—42no—
122Dic11⋊C4—42no—
123Dic11⋊C4—42no—
124Dic11⋊C4—41no—
125Dic11⋊C4—42no—
126Dic11⋊C4—41no—
127#4318—44no—
128#4318—42no—
129#4318—42no—
130C2×C11⋊C8—24no—
131C2×C11⋊C8—44no—
132#2879—111no—
133#2406—111no—
134#1785D1111yescharacteristic
135#1463—112no—
136#1306—112no—
137C23×C11—21no—
138C23×C11—21no—
139C23×C11—21no—
140C23×C11—21no—
141C23×C11—21no—
142C23×C11—21no—
143C23×C11—21no—
144C23×C11—41no—
145C23×C11—41no—
146C23×C11—41no—
147C23×C11—41no—
148C23×C11—41no—
149C23×C11—41no—
150C23×C11#9912yes—
151C23×C11C2×C22⋊C411yescharacteristic
152C23×C11C4×D412yes—
153Q8×C11—44no—
154D4×C11—44no—
155D4×C11—44no—
156D4×C11—44no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—24no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11—21no—
168C2×C4×C11—21no—
169C2×C4×C11—42no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11#9912yes—
174C2×C4×C11#12011yescharacteristic
175C2×C4×C11#12112yes—
176C2×C4×C11#12311yescharacteristic
177C2×Dic11—22no—
178C2×Dic11—24no—
179C2×Dic11—41no—
180C2×Dic11—42no—
181C2×Dic11—41no—
182C2×Dic11—41no—
183C2×Dic11—41no—
184C2×Dic11—41no—
185C2×Dic11—41no—
186C2×Dic11—41no—
187C2×Dic11—41no—
188C2×Dic11—41no—
189C2×Dic11—41no—
190C2×Dic11—41no—
191C2×Dic11—82no—
192C8×C11—82no—
193C11⋊C8—44no—
194C22×#41C2×D1111yescharacteristic
195C22×M16—221no—
196C2×#123—111no—
197C2×#123—111no—
198C22×C4⋊C4—111no—
199C2×#101—21no—
200C2×#100—21no—
201#408—224no—
202#407—112no—
203#407—221no—
204#407C2×D1112yes—
205#395—221no—
206#394—221no—
207#386—111no—
208#386—111no—
209#385—221no—
210#385—221no—
211#381—111no—
212#324—224no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—22no—
216C22×C11—22no—
217C22×C11—22no—
218C22×C11—22no—
219C22×C11—42no—
220C22×C11—42no—
221C22×C11—42no—
222C22×C11—42no—
223C22×C11—41no—
224C22×C11—41no—
225C22×C11—41no—
226C22×C11—41no—
227C22×C11—41no—
228C22×C11—81no—
229C22×C11—81no—
230C22×C11#38611yescharacteristic
231C22×C11C2×#9911yescharacteristic
232C22×C11C2×#9911yescharacteristic
233C4×C11—21no—
234C4×C11—21no—
235C4×C11—22no—
236C4×C11—22no—
237C4×C11—41no—
238Dic11—42no—
239Dic11—81no—
240Dic11—81no—
241Dic11—81no—
242C2×#41—22no—
243C2×#41—22no—
244C2×#41—42no—
245C2×#41—42no—
246C22×Q8C22⋊D1111yescharacteristic
247C22×D4C4×D1111yescharacteristic
248C22×D4C4×D1111yescharacteristic
249C22×D4C22⋊D1111yescharacteristic
250C23×C4—111no—
251C23×C4—111no—
252C23×C4D4411yescharacteristic
253C23×C4D4411yescharacteristic
254C23×C4C22×D1111yescharacteristic
255C2×M16—22no—
256C2×M16—222no—
257C2×M16—222no—
258C2×M16—442no—
259C2×M16—442no—
260C22×C8—222no—
261#123—442no—
262#123—442no—
263C2×C4⋊C4—221no—
264C2×C4⋊C4—221no—
265C2×C4⋊C4—221no—
266C2×C4⋊C4—222no—
267C2×C4⋊C4—222no—
268C2×C4⋊C4—221no—
269C2×C22⋊C4—111no—
270C2×C22⋊C4—111no—
271C2×C22⋊C4—221no—
272C2×C22⋊C4—221no—
273C2×C22⋊C4—221no—
274C2×C22⋊C4—221no—
275#101—42no—
276#100—42no—
277C22⋊C8—22no—
278C22⋊C8—22no—
279C22⋊C8—114no—
280C22⋊C8—224no—
281C22⋊C8—222no—
282#95—221no—
283#95—221no—
284#95—221no—
285#95—221no—
286C2×C11—21no—
287C2×C11—21no—
288C2×C11—42no—
289C2×C11—42no—
290C2×C11—81no—
291C2×C11#189111yescharacteristic
292C2×C11#189811yescharacteristic
293C2×C11#191511yescharacteristic
294C24(C2×D11)⋊C411yescharacteristic
295C24(C2×D11)⋊C411yescharacteristic
296C24C2×C4×D1111yescharacteristic
297#41—44no—
298#41—44no—
299#41—48no—
300C2×Q8—22no—
301C2×Q8—22no—
302C2×Q8—41no—
303C2×D4—22no—
304C2×D4—22no—
305C2×D4—22no—
306C2×D4—22no—
307C2×D4—22no—
308C2×D4—22no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—41no—
312C22×C4—22no—
313C22×C4—22no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—222no—
323C22×C4—221no—
324C22×C4—221no—
325C22×C4—221no—
326C22×C4—221no—
327C22×C4—222no—
328C22×C4—442no—
329C22×C4—441no—
330C22×C4—441no—
331C22×C4(C2×D11)⋊C411yescharacteristic
332C22×C4(C2×D11)⋊C411yescharacteristic
333C22×C4C2×D4411yescharacteristic
334C22×C4D4×D1112yes—
335C22×C4#434112yes—
336C22×C4C2×C22⋊D1111yescharacteristic
337M16—42no—
338M16—42no—
339M16—444no—
340M16—442no—
341M16—442no—
342C2×C8—42no—
343C2×C8—224no—
344C2×C8—444no—
345C4⋊C4—442no—
346C4⋊C4—442no—
347C4⋊C4—441no—
348C4⋊C4—441no—
349C4⋊C4—442no—
350C22⋊C4—442no—
351C22⋊C4—442no—
352C22⋊C4—442no—
353C22⋊C4—442no—
354C22⋊C4—441no—
355C22⋊C4—441no—
356C11#951311yescharacteristic, complemented, Sylow
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—21no—
363C23—21no—
364C23—41no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23—41no—
370C23#6687012yes—
371C23(C22⋊D11)⋊C412yes—
372C23C2×(C2×D11)⋊C411yescharacteristic
373Q8—44no—
374D4—44no—
375D4—44no—
376D4—44no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—24no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—222no—
394C2×C4—224no—
395C2×C4—441no—
396C2×C4—442no—
397C2×C4—441no—
398C2×C4—441no—
399C2×C4—441no—
400C2×C4—441no—
401C2×C4—441no—
402C2×C4—441no—
403C2×C4—441no—
404C2×C4—441no—
405C2×C4—441no—
406C2×C4—441no—
407C2×C4—882no—
408C2×C4#6687012yes—
409C2×C4#6693511yescharacteristic
410C2×C4#6693911yescharacteristic
411C2×C4#6699212yes—
412C8—82no—
413C8—444no—
414C22—21no—
415C22—21no—
416C22—22no—
417C22—22no—
418C22—22no—
419C22—22no—
420C22—42no—
421C22—42no—
422C22—42no—
423C22—42no—
424C22—41no—
425C22—41no—
426C22—41no—
427C22—41no—
428C22—41no—
429C22—81no—
430C22—81no—
431C22C2×#6687011yescharacteristic
432C22C2×#6687011yescharacteristic
433C22#1062257111yescharacteristic
434C4—22no—
435C4—21no—
436C4—21no—
437C4—22no—
438C4—41no—
439C4—442no—
440C4—881no—
441C4—881no—
442C4—881no—
443C2—21no—
444C2—21no—
445C2—42no—
446C2—42no—
447C2—81no—
448C2#1306903211yescharacteristic
449C2#1306906711yescharacteristic
450C2#1306916611yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC24×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1785C2
socleC22×C11#386
prime radicalC22×C11×#41C22
cosocleC23×C4×C11C23
hypercenter#1785D11
hypocenterC11#9513
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1785

Complements

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

NH ≅ G/Ntype
3. #13066945C2semidirect
4. #13066525C2semidirect
356. C11#9513semidirect

Maximal subgroups

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

subgroupindex
#130770612
#130719472
#130669452
#130665252
C11×#17852
#951311