Finite Group Databasebeta

← #14664336

Subgroups — #14664336

Order 2816.

532 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 71 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#13073571C211yesmaximal, characteristic
2#13068403C211yesmaximal, characteristic, complemented
3#13066955C211yesmaximal, characteristic, complemented
4#13066617C211yesmaximal, characteristic, complemented
5#13066615C211yesmaximal, characteristic, complemented
6#13066613C211yesmaximal, characteristic, complemented
7C11×#1343C211yesmaximal, characteristic, complemented
8C2×#66991—21no—
9C2×#66991C411yescharacteristic, complemented
10C2×(C22⋊D11)⋊C4C2211yescharacteristic
11C11×#392C2211yescharacteristic
12#10622835C411yescharacteristic, complemented
13#10622833—21no—
14#10622569—21no—
15C2×#66870—21no—
16#10622566C2211yescharacteristic
17#10622564—21no—
18C22⋊C4×Dic11—21no—
19#10622332—21no—
20D11×#95C411yescharacteristic, complemented
21#10622274C411yescharacteristic, complemented
22C11×#342C2211yescharacteristic
23C11×#323C2211yescharacteristic
24#10622164C2211yescharacteristic
25#10622163C2211yescharacteristic
26#10622106—21no—
27C22×D4×C11—21no—
28C22×D4×C11C2×C411yescharacteristic
29C22×C22⋊D11—21no—
30C22×C22⋊D11D411yescharacteristic
31C23×Dic11D411yescharacteristic
32C22×C4×D11—21no—
33C22×C4×D11C2×C411yescharacteristic
34C2×C11×C22⋊C4—21no—
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4C2311yescharacteristic
37C2×C22⋊Dic11—21no—
38C2×C22⋊Dic11—21no—
39C2×C22⋊Dic11—21no—
40C2×C22⋊Dic11—21no—
41C2×C22⋊Dic11—21no—
42#66991—42no—
43#66991—42no—
44#66991—41no—
45#66991—41no—
46C2×(C2×D11)⋊C4D411yescharacteristic
47C2×C4⋊Dic11—21no—
48C2×C4⋊Dic11C2×C411yescharacteristic
49C2×Dic11⋊C4C2×C411yescharacteristic
50C2×C4×Dic11—41no—
51C2×C4×Dic11D411yescharacteristic
52(C22⋊D11)⋊C4—41no—
53(C22⋊D11)⋊C4—41no—
54C11×C22⋊C8—21no—
55C11×#95C2×C411yescharacteristic
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—41no—
60C11⋊#95C2×C411yescharacteristic
61C22⋊(C11⋊C8)—21no—
62#66879—41no—
63Dic11⋊C8—41no—
64#66870—24no—
65#11775—111nomaximal, Sylow
66C24×C11—21no—
67C24×C11C2×D411yescharacteristic
68C23×D11C22⋊C411yescharacteristic
69C2×D4×C11—42no—
70C2×D4×C11—41no—
71C2×D4×C11—41no—
72C2×D4×C11—41no—
73C2×D4×C11—81no—
74C2×D4×C11—81no—
75C22×C4×C11—21no—
76C22×C4×C11—41no—
77C22×C4×C11C22×C411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C2×C22⋊D11—21no—
80C2×C22⋊D11—21no—
81C2×C22⋊D11—22no—
82C2×C22⋊D11—41no—
83C2×C22⋊D11—42no—
84C2×C22⋊D11—42no—
85C2×C22⋊D11—42no—
86C22×Dic11—21no—
87C22×Dic11—21no—
88C22×Dic11—21no—
89C22×Dic11—21no—
90C22×Dic11—41no—
91C22×Dic11—81no—
92C22×Dic11C22⋊C411yescharacteristic
93C22×Dic11C22⋊C411yescharacteristic
94C22×Dic11C22⋊C411yescharacteristic
95C2×C4×D11—21no—
96C2×C4×D11—21no—
97C2×C4×D11—42no—
98C2×C4×D11—42no—
99C2×C4×D11—81no—
100C2×C4×D11—81no—
101C2×C8×C11—41no—
102C11×C22⋊C4—22no—
103C11×C22⋊C4—41no—
104C11×C22⋊C4—42no—
105C11×C22⋊C4—41no—
106C22⋊Dic11—22no—
107C22⋊Dic11—42no—
108C22⋊Dic11—41no—
109C22⋊Dic11—41no—
110C22⋊Dic11—41no—
111C22⋊Dic11—41no—
112C22⋊Dic11—41no—
113C22⋊Dic11—81no—
114(C2×D11)⋊C4—41no—
115C4⋊Dic11—41no—
116C4⋊Dic11—42no—
117Dic11⋊C4—41no—
118C4×Dic11—21no—
119C4×Dic11—21no—
120C4×Dic11—82no—
121C2×C11⋊C8—41no—
122#2543—111no—
123C4×#99—111no—
124#1466—111no—
125#1344—111no—
126#1344—111no—
127#1343—111no—
128#1343D1111yescharacteristic, complemented
129C23×C11—21no—
130C23×C11—21no—
131C23×C11—41no—
132C23×C11—41no—
133C23×C11—41no—
134C23×C11—41no—
135C23×C11—41no—
136C23×C11—41no—
137C23×C11—41no—
138C23×C11—41no—
139C23×C11—41no—
140C23×C11C2×C22⋊C411yescharacteristic
141C23×C11AGL(1,ℤ/8)11yescharacteristic
142C23×C11AGL(1,ℤ/8)11yescharacteristic
143C22×D11—21no—
144C22×D11—21no—
145C22×D11—41no—
146C22×D11—41no—
147C22×D11#10412yes—
148D4×C11—82no—
149D4×C11—82no—
150D4×C11—82no—
151C2×C4×C11—22no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—42no—
159C2×C4×C11—81no—
160C2×C4×C11—81no—
161C22⋊D11—42no—
162C22⋊D11—42no—
163C22⋊D11—84no—
164C2×Dic11—21no—
165C2×Dic11—21no—
166C2×Dic11—21no—
167C2×Dic11—21no—
168C2×Dic11—41no—
169C2×Dic11—42no—
170C2×Dic11—41no—
171C2×Dic11—42no—
172C2×Dic11—41no—
173C2×Dic11—41no—
174C2×Dic11—41no—
175C2×Dic11—41no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—81no—
179C2×Dic11—81no—
180C2×Dic11—81no—
181C2×Dic11#9911yescharacteristic
182C2×Dic11#9911yescharacteristic
183C4×D11—81no—
184C4×D11—81no—
185C4×D11—84no—
186C8×C11—81no—
187C11⋊C8—81no—
188C2×#121—111no—
189C2×#121—221no—
190C2×C4×D4—111no—
191#432—221no—
192C2×#99—221no—
193#398—111no—
194#397—111no—
195#394—111no—
196#392C2×D1111yescharacteristic
197#388—221no—
198#386—221no—
199#386—221no—
200C4×C22⋊C4—221no—
201C2×#95—111no—
202#342—111no—
203#342C2×D1111yescharacteristic
204#323—111no—
205#323—221no—
206#323C2×D1111yescharacteristic
207C22×C11—21no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—41no—
212C22×C11—41no—
213C22×C11—41no—
214C22×C11—41no—
215C22×C11—81no—
216C22×C11—81no—
217C22×C11—81no—
218C22×C11—81no—
219C22×C11—81no—
220C22×C11—81no—
221C22×C11—81no—
222C22×C11—81no—
223C22×C11C2×#9911yescharacteristic
224C22×C11#41811yescharacteristic
225C22×C11C2×#10411yescharacteristic
226C2×D11—22no—
227C2×D11—42no—
228C2×D11—41no—
229C2×D11—41no—
230C2×D11—42no—
231C4×C11—42no—
232C4×C11—41no—
233C4×C11—41no—
234C4×C11—82no—
235Dic11—21no—
236Dic11—21no—
237Dic11—41no—
238Dic11—41no—
239Dic11—81no—
240Dic11—82no—
241Dic11—81no—
242C22×D4—21no—
243C22×D4—111no—
244C22×D4—221no—
245C22×D4C4×D1111yescharacteristic
246C23×C4—111no—
247C23×C4—111no—
248C23×C4—221no—
249#121—442no—
250#121—442no—
251#121—441no—
252#121—441no—
253C4×D4—441no—
254C4×D4—441no—
255C2×C4⋊C4—111no—
256C2×C4⋊C4—111no—
257C2×C4⋊C4—221no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—111no—
261C2×C22⋊C4—221no—
262C2×C22⋊C4—221no—
263C2×C22⋊C4—221no—
264C2×C22⋊C4—221no—
265C2×C22⋊C4—221no—
266C2×C22⋊C4C22×D1111yescharacteristic
267C2×C42—111no—
268C2×C42—441no—
269C4⋊C8—441no—
270#99—224no—
271C22⋊C8—21no—
272C22⋊C8—221no—
273#97—441no—
274#95—111no—
275#95—221no—
276#95—221no—
277#95—221no—
278#95—441no—
279#95C4×D1111yescharacteristic
280C2×C11—21no—
281C2×C11—21no—
282C2×C11—41no—
283C2×C11—41no—
284C2×C11—161no—
285C2×C11#150711yescharacteristic
286C2×C11#212111yescharacteristic
287C2×C11#212611yescharacteristic
288D11—42no—
289C24—21no—
290C24—111no—
291C24D4×D1111yescharacteristic
292C2×D4—41no—
293C2×D4—42no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—81no—
297C2×D4—81no—
298C2×D4—222no—
299C2×D4—221no—
300C2×D4—221no—
301C2×D4—441no—
302C2×D4—442no—
303C2×D4—442no—
304C2×D4—442no—
305C22×C4—21no—
306C22×C4—41no—
307C22×C4—111no—
308C22×C4—111no—
309C22×C4—111no—
310C22×C4—221no—
311C22×C4—221no—
312C22×C4—221no—
313C22×C4—221no—
314C22×C4—221no—
315C22×C4—221no—
316C22×C4—442no—
317C22×C4—442no—
318C22×C4—441no—
319C22×C4—881no—
320C22×C4—881no—
321C22×C4—881no—
322C22×C4C2×C4×D1111yescharacteristic
323C22×C4D4×D1111yescharacteristic
324C2×C8—41no—
325C2×C8—441no—
326C4⋊C4—441no—
327C4⋊C4—441no—
328C4⋊C4—442no—
329C22⋊C4—22no—
330C22⋊C4—41no—
331C22⋊C4—42no—
332C22⋊C4—41no—
333C22⋊C4—222no—
334C22⋊C4—441no—
335C22⋊C4—441no—
336C22⋊C4—441no—
337C22⋊C4—442no—
338C22⋊C4—441no—
339C22⋊C4—441no—
340C22⋊C4—441no—
341C22⋊C4—881no—
342C42—221no—
343C42—221no—
344C42—882no—
345C11#1177511yescharacteristic, complemented, Sylow
346C23—21no—
347C23—21no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23—112no—
358C23—221no—
359C23—221no—
360C23—441no—
361C23—441no—
362C23C22⋊C4×D1111yescharacteristic
363C23#6696411yescharacteristic
364C23#6696711yescharacteristic
365D4—82no—
366D4—82no—
367D4—82no—
368D4—442no—
369D4—442no—
370D4—884no—
371C2×C4—22no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—42no—
379C2×C4—81no—
380C2×C4—81no—
381C2×C4—111no—
382C2×C4—111no—
383C2×C4—221no—
384C2×C4—221no—
385C2×C4—221no—
386C2×C4—221no—
387C2×C4—441no—
388C2×C4—442no—
389C2×C4—441no—
390C2×C4—442no—
391C2×C4—441no—
392C2×C4—441no—
393C2×C4—441no—
394C2×C4—441no—
395C2×C4—441no—
396C2×C4—441no—
397C2×C4—881no—
398C2×C4—881no—
399C2×C4—884no—
400C2×C4—881no—
401C2×C4—881no—
402C2×C4—881no—
403C8—81no—
404C8—881no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—81no—
414C22—81no—
415C22—81no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22—222no—
422C22—442no—
423C22—442no—
424C22—441no—
425C22—441no—
426C22D11×#9911yescharacteristic
427C22#1062238311yescharacteristic
428C22D11×#10411yescharacteristic
429C4—42no—
430C4—41no—
431C4—41no—
432C4—82no—
433C4—221no—
434C4—221no—
435C4—441no—
436C4—441no—
437C4—881no—
438C4—882no—
439C4—881no—
440C2—21no—
441C2—21no—
442C2—41no—
443C2—41no—
444C2—161no—
445C2—442no—
446C2#1306713011yescharacteristic
447C2#1307025911yescharacteristic
448C2#1307027811yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1343C2
socleC22×C11C2×#99
prime radical#13073571C2
cosocleC2×C11×C22⋊C4C23
hypercenter#1343D11
hypocenterC11#11775
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1343

Complements

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

NH ≅ G/Ntype
2. #13068403C2semidirect
3. #13066955C2semidirect
4. #13066617C2semidirect
5. #13066615C2semidirect
6. #13066613C2semidirect
7. C11×#1343C2semidirect
9. C2×#66991C4semidirect
12. #10622835C4semidirect
20. D11×#95C4semidirect
21. #10622274C4semidirect
128. #1343D11semidirect
345. C11#11775semidirect

Maximal subgroups

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

subgroupindex
#130735712
#130684032
#130669552
#130666172
#130666152
#130666132
C11×#13432
#1177511