Finite Group Databasebeta

← #14672449

Subgroups — #14672449

Order 2816.

492 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 91 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#13073818C211yesmaximal, characteristic
2#13068602C211yesmaximal, characteristic
3#99×Dic11C211yesmaximal, characteristic
4#13066741C211yesmaximal, characteristic
5#13066740C211yesmaximal, characteristic
6#13066740C211yesmaximal, characteristic
7C11×#1393C211yesmaximal, characteristic
8C2×D4×Dic11C2211yescharacteristic
9C2×#66943C411yescharacteristic, complemented
10C2×C11×#99C2211yescharacteristic
11C2×C11×#99C2211yescharacteristic
12C11×#390C2211yescharacteristic
13#10622834C2211yescharacteristic
14C2×#66898C2211yescharacteristic
15C2×#66898C2211yescharacteristic
16#10622590C411yescharacteristic, complemented
17#10622563—21no—
18#10622563—21no—
19#10622561—21no—
20#10622561—21no—
21#10622555—21no—
22C22⋊C4×Dic11—21no—
23#10622548C411yescharacteristic, complemented
24C4×Dic11⋊C4C411yescharacteristic, complemented
25#10622165—21no—
26#10622165—21no—
27C22×D4×C11C2311yescharacteristic
28C23×Dic11D411yescharacteristic
29C23×Dic11D411yescharacteristic
30C2×C11×C4⋊C4C2×C411yescharacteristic
31C2×C11×C22⋊C4—21no—
32C2×C11×C22⋊C4—21no—
33C2×C11×C22⋊C4—21no—
34C2×C11×C22⋊C4—21no—
35C2×C42×C11C2×C411yescharacteristic
36C2×C22⋊Dic11—21no—
37C2×C22⋊Dic11—21no—
38C2×C22⋊Dic11—21no—
39C2×C22⋊Dic11—21no—
40C2×C22⋊Dic11D411yescharacteristic
41C2×C22⋊Dic11D411yescharacteristic
42D4×Dic11—41no—
43D4×Dic11—41no—
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11—21no—
46C2×C4⋊Dic11—21no—
47C2×C4⋊Dic11C2×C411yescharacteristic
48C2×C4⋊Dic11C2×C411yescharacteristic
49C2×Dic11⋊C4—21no—
50C2×Dic11⋊C4—21no—
51C2×Dic11⋊C4—41no—
52C2×C4×Dic11—41no—
53C2×C4×Dic11C2×C411yescharacteristic
54C2×C4×Dic11C2×C411yescharacteristic
55#66943—41no—
56#66943—41no—
57C11×#99—21no—
58C11×#99—21no—
59C11×#99—21no—
60C11×#99Q812yes—
61#66898—21no—
62#66898—21no—
63#66898—21no—
64#66898Q812yes—
65C11⋊#95—21no—
66C11⋊#95—21no—
67C11⋊#95—21no—
68C11⋊#95—41no—
69C11⋊#95—41no—
70#13300—111nomaximal, Sylow
71C24×C11C2×D411yescharacteristic
72C24×C11C2×D411yescharacteristic
73C2×D4×C11—41no—
74C2×D4×C11—41no—
75C2×D4×C11C2×Q811yescharacteristic
76C2×D4×C11C2×Q811yescharacteristic
77C2×D4×C11#4111yescharacteristic
78C2×D4×C11#4111yescharacteristic
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—41no—
82C22×C4×C11—41no—
83C22×C4×C11C22×C411yescharacteristic
84C22×Dic11—21no—
85C22×Dic11—21no—
86C22×Dic11—21no—
87C22×Dic11—21no—
88C22×Dic11—21no—
89C22×Dic11—21no—
90C22×Dic11—41no—
91C22×Dic11—41no—
92C22×Dic11—81no—
93C22×Dic11—81no—
94C22×Dic11C22⋊C411yescharacteristic
95C22×Dic11C22⋊C411yescharacteristic
96C22×Dic11C22⋊C411yescharacteristic
97C22×Dic11C22⋊C411yescharacteristic
98C11×C4⋊C4—41no—
99C11×C22⋊C4—22no—
100C11×C22⋊C4—42no—
101C11×C22⋊C4—42no—
102C11×C22⋊C4—41no—
103C11×C22⋊C4—41no—
104C11×C22⋊C4—41no—
105C42×C11—41no—
106C22⋊Dic11—22no—
107C22⋊Dic11—41no—
108C22⋊Dic11—41no—
109C22⋊Dic11—41no—
110C22⋊Dic11—41no—
111C22⋊Dic11—41no—
112C22⋊Dic11—81no—
113C22⋊Dic11—81no—
114C4⋊Dic11—41no—
115C4⋊Dic11—41no—
116C4⋊Dic11—41no—
117C4⋊Dic11—41no—
118C4⋊Dic11—81no—
119C4⋊Dic11—81no—
120Dic11⋊C4—42no—
121Dic11⋊C4—42no—
122Dic11⋊C4—82no—
123C4×Dic11—21no—
124C4×Dic11—21no—
125C4×Dic11—41no—
126C4×Dic11—82no—
127#2566—111no—
128#1799—111no—
129C4×#99—111no—
130#1393—111no—
131#1393—111no—
132#1393—111no—
133#1393D1111yescharacteristic
134C23×C11—21no—
135C23×C11—21no—
136C23×C11—21no—
137C23×C11—21no—
138C23×C11—41no—
139C23×C11—41no—
140C23×C11—41no—
141C23×C11—41no—
142C23×C11C2×C22⋊C411yescharacteristic
143C23×C11C22⋊Q811yescharacteristic
144C23×C11C22⋊Q811yescharacteristic
145C23×C11#12411yescharacteristic
146C23×C11C4⋊Q811yescharacteristic
147D4×C11—41no—
148D4×C11—41no—
149D4×C11—41no—
150D4×C11—41no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—22no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—42no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—81no—
161C2×C4×C11—81no—
162C2×C4×C11—81no—
163C2×C4×C11—81no—
164C2×C4×C11—81no—
165C2×C4×C11C4×Q811yescharacteristic
166C2×C4×C11C4×Q811yescharacteristic
167C2×Dic11—21no—
168C2×Dic11—21no—
169C2×Dic11—21no—
170C2×Dic11—41no—
171C2×Dic11—42no—
172C2×Dic11—42no—
173C2×Dic11—41no—
174C2×Dic11—41no—
175C2×Dic11—41no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—42no—
180C2×Dic11—41no—
181C2×Dic11—41no—
182C2×Dic11—41no—
183C2×Dic11—81no—
184C2×Dic11—81no—
185C2×Dic11—81no—
186C2×Dic11—81no—
187C2×Dic11—81no—
188C2×Dic11—81no—
189C2×Dic11—81no—
190C2×Dic11#9911yescharacteristic
191C2×Dic11#9911yescharacteristic
192C2×#125—111no—
193C2×C4×D4—111no—
194C2×#99—111no—
195C2×#99—111no—
196C2×#99C2×D1111yescharacteristic
197C2×#99C2×D1111yescharacteristic
198#396—221no—
199#396—221no—
200#390—111no—
201#390C2×D1111yescharacteristic
202#385—221no—
203#385—221no—
204#384—111no—
205#382—111no—
206#380—221no—
207C4×C4⋊C4—111no—
208C4×C22⋊C4—221no—
209#342—221no—
210#342—221no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11—41no—
218C22×C11—41no—
219C22×C11—41no—
220C22×C11—41no—
221C22×C11—41no—
222C22×C11—41no—
223C22×C11—41no—
224C22×C11—41no—
225C22×C11—81no—
226C22×C11—81no—
227C22×C11#39111yescharacteristic
228C22×C11C2×#9911yescharacteristic
229C22×C11#41011yescharacteristic
230C4×C11—21no—
231C4×C11—21no—
232C4×C11—42no—
233C4×C11—82no—
234C4×C11—81no—
235C4×C11—161no—
236Dic11—21no—
237Dic11—21no—
238Dic11—41no—
239Dic11—41no—
240Dic11—41no—
241Dic11—81no—
242Dic11—82no—
243Dic11—81no—
244Dic11—161no—
245C22×D4C22×D1111yescharacteristic
246C23×C4—111no—
247C23×C4—111no—
248#125—441no—
249#125—441no—
250C4×D4—441no—
251C4×D4—441no—
252C2×C4⋊C4—111no—
253C2×C4⋊C4—111no—
254C2×C4⋊C4—221no—
255C2×C4⋊C4—221no—
256C2×C4⋊C4—221no—
257C2×C4⋊C4—221no—
258C2×C4⋊C4—221no—
259C2×C4⋊C4—441no—
260C2×C4⋊C4C4×D1111yescharacteristic
261C2×C22⋊C4—21no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—21no—
265C2×C22⋊C4—111no—
266C2×C22⋊C4—111no—
267C2×C22⋊C4—221no—
268C2×C22⋊C4—221no—
269C2×C22⋊C4—221no—
270C2×C22⋊C4—221no—
271C2×C42—111no—
272C2×C42—111no—
273C2×C42—441no—
274C2×C42C4×D1111yescharacteristic
275#99—21no—
276#99—21no—
277#99—21no—
278#99—112no—
279#99—221no—
280#99—221no—
281#99—221no—
282#99Dic2212yes—
283#95—221no—
284#95—221no—
285#95—221no—
286#95—441no—
287#95—441no—
288C2×C11—21no—
289C2×C11—21no—
290C2×C11—41no—
291C2×C11—41no—
292C2×C11—41no—
293C2×C11—41no—
294C2×C11#199611yescharacteristic
295C2×C11#212611yescharacteristic
296C2×C11#212711yescharacteristic
297C24D4×D1111yescharacteristic
298C24D4×D1111yescharacteristic
299C2×D4—41no—
300C2×D4—41no—
301C2×D4C2×Dic2211yescharacteristic
302C2×D4#433911yescharacteristic
303C2×D4#434111yescharacteristic
304C2×D4Q8×D1111yescharacteristic
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—111no—
310C22×C4—111no—
311C22×C4—111no—
312C22×C4—111no—
313C22×C4—221no—
314C22×C4—221no—
315C22×C4—221no—
316C22×C4—221no—
317C22×C4—221no—
318C22×C4—221no—
319C22×C4—441no—
320C22×C4—441no—
321C22×C4—881no—
322C22×C4—881no—
323C22×C4C2×C4×D1111yescharacteristic
324C4⋊C4—41no—
325C4⋊C4—441no—
326C4⋊C4—441no—
327C4⋊C4—442no—
328C4⋊C4—441no—
329C4⋊C4—441no—
330C4⋊C4—442no—
331C4⋊C4—881no—
332C4⋊C4—881no—
333C4⋊C4—882no—
334C22⋊C4—22no—
335C22⋊C4—42no—
336C22⋊C4—42no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—222no—
341C22⋊C4—441no—
342C22⋊C4—441no—
343C22⋊C4—441no—
344C22⋊C4—441no—
345C22⋊C4—441no—
346C22⋊C4—881no—
347C22⋊C4—881no—
348C42—41no—
349C42—221no—
350C42—221no—
351C42—441no—
352C42—882no—
353C11#1330011yescharacteristic, complemented, Sylow
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—41no—
362C23#6693111yescharacteristic
363C23C22⋊C4×D1111yescharacteristic
364C23#6693811yescharacteristic
365C23#6694111yescharacteristic
366C23#6694911yescharacteristic
367D4—41no—
368D4—41no—
369D4—41no—
370D4—41no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—22no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—81no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—111no—
386C2×C4—111no—
387C2×C4—221no—
388C2×C4—221no—
389C2×C4—221no—
390C2×C4—441no—
391C2×C4—442no—
392C2×C4—442no—
393C2×C4—441no—
394C2×C4—441no—
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—881no—
404C2×C4—881no—
405C2×C4—881no—
406C2×C4—881no—
407C2×C4—881no—
408C2×C4—881no—
409C2×C4—881no—
410C2×C4C4×Dic2211yescharacteristic
411C2×C4#6694011yescharacteristic
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—41no—
419C22—41no—
420C22—41no—
421C22—41no—
422C22—41no—
423C22—41no—
424C22—41no—
425C22—41no—
426C22—81no—
427C22—81no—
428C22#1062225911yescharacteristic
429C22#1062235311yescharacteristic
430C22D11×#9911yescharacteristic
431C4—21no—
432C4—21no—
433C4—42no—
434C4—82no—
435C4—81no—
436C4—161no—
437C4—221no—
438C4—221no—
439C4—441no—
440C4—441no—
441C4—441no—
442C4—881no—
443C4—882no—
444C4—881no—
445C4—1761no—
446C2—21no—
447C2—21no—
448C2—41no—
449C2—41no—
450C2—41no—
451C2—41no—
452C2#1306959911yescharacteristic
453C2#1307027811yescharacteristic
454C2#1307028411yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC22×D4C22×D11
FittingC11×#1393C2
socleC22×C11C2×#99
prime radical, cosocleC22×D4×C11C23
hypercenter#1393D11
hypocenterC11#13300
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #1393

Complements

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

NH ≅ G/Ntype
9. C2×#66943C4semidirect
16. #10622590C4semidirect
23. #10622548C4semidirect
24. C4×Dic11⋊C4C4semidirect
353. C11#13300semidirect

Maximal subgroups

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

subgroupindex
#130738182
#130686022
#99×Dic112
#130667412
#130667402
C11×#13932
#1330011