Finite Group Databasebeta

← #14672436

Subgroups — #14672436

Order 2816.

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

normal subgroups only

This group has 488 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#13073962C211yesmaximal, characteristic
2#13068606C211yesmaximal, characteristic
3#99×Dic11C211yesmaximal, characteristic
4#13066735C211yesmaximal, characteristic
5#13066734C211yesmaximal, characteristic
6#13066733C211yesmaximal, characteristic
7C11×#1390C211yesmaximal, characteristic
8C2×D4×Dic11C2211yescharacteristic
9C22×Dic11⋊C4C411yescharacteristic, complemented
10C2×C11×#100C2211yescharacteristic
11C2×C11×#99C2211yescharacteristic
12C11×#386C2211yescharacteristic
13#10622833C2211yescharacteristic
14C2×#66898C2211yescharacteristic
15C2×#66897C2211yescharacteristic
16#10622823C411yescharacteristic, complemented
17#10622731—21no—
18#10622563C411yescharacteristic, complemented
19#10622561—21no—
20#10622559—21no—
21#10622555C411yescharacteristic, complemented
22C22⋊C4×Dic11—21no—
23#10622270—21no—
24#10622267—21no—
25#10622192—21no—
26#10622165—21no—
27C22×D4×C11C2311yescharacteristic
28C23×C4×C11C2×C411yescharacteristic
29C23×Dic11C2×C411yescharacteristic
30C23×Dic11C2×C411yescharacteristic
31C23×Dic11D411yescharacteristic
32C2×C11×M16—21no—
33C2×C11×C22⋊C4—21no—
34C2×C11×C22⋊C4—21no—
35C2×C11×C22⋊C4C2×C411yescharacteristic
36C2×C22⋊Dic11—21no—
37C2×C22⋊Dic11—21no—
38C2×C22⋊Dic11C2×C411yescharacteristic
39C2×C22⋊Dic11C2×C411yescharacteristic
40C2×C22⋊Dic11D411yescharacteristic
41D4×Dic11—41no—
42D4×Dic11—41no—
43C2×C4⋊Dic11—21no—
44C2×C4⋊Dic11D411yescharacteristic
45C2×Dic11⋊C4—21no—
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4—21no—
48C2×Dic11⋊C4—21no—
49C2×Dic11⋊C4—41no—
50C2×Dic11⋊C4—41no—
51C2×C4×Dic11—41no—
52C2×C4×Dic11D411yescharacteristic
53C2×#4318—21no—
54C11×#100—21no—
55C11×#100—21no—
56C11×#99—21no—
57C11×#99Q812yes—
58C11×#95—21no—
59#66898—21no—
60#66898Q812yes—
61#66897—21no—
62#66897—21no—
63C11⋊#95—21no—
64C11⋊#95—21no—
65C11⋊#95—21no—
66C11⋊#95—21no—
67C11⋊#95—41no—
68Dic11⋊C8—41no—
69Dic11⋊C8—41no—
70#13297—111nomaximal, Sylow
71C24×C11C22×C411yescharacteristic
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×C11—81no—
84C22×C4×C11C2×D411yescharacteristic
85C22×Dic11—21no—
86C22×Dic11—21no—
87C22×Dic11—21no—
88C22×Dic11—21no—
89C22×Dic11—21no—
90C22×Dic11—21no—
91C22×Dic11—41no—
92C22×Dic11—41no—
93C22×Dic11—42no—
94C22×Dic11—81no—
95C22×Dic11—81no—
96C22×Dic11C22⋊C411yescharacteristic
97C22×Dic11C22⋊C411yescharacteristic
98C22×Dic11C22⋊C411yescharacteristic
99C22×Dic11C22⋊C411yescharacteristic
100C11×M16—41no—
101C11×M16—41no—
102C2×C8×C11—41no—
103C11×C22⋊C4—22no—
104C11×C22⋊C4—41no—
105C11×C22⋊C4—41no—
106C11×C22⋊C4—81no—
107C22⋊Dic11—22no—
108C22⋊Dic11—41no—
109C22⋊Dic11—41no—
110C22⋊Dic11—41no—
111C22⋊Dic11—41no—
112C22⋊Dic11—42no—
113C4⋊Dic11—41no—
114C4⋊Dic11—42no—
115Dic11⋊C4—42no—
116Dic11⋊C4—41no—
117Dic11⋊C4—41no—
118Dic11⋊C4—81no—
119Dic11⋊C4—81no—
120C4×Dic11—21no—
121C4×Dic11—21no—
122C4×Dic11—82no—
123#4318—41no—
124#4318—41no—
125C2×C11⋊C8—41no—
126#2579—111no—
127#1800—111no—
128C4×#99—111no—
129#1390—111no—
130#1390—111no—
131#1390—111no—
132#1390D1111yescharacteristic
133C23×C11—21no—
134C23×C11—21no—
135C23×C11—21no—
136C23×C11—21no—
137C23×C11—41no—
138C23×C11—41no—
139C23×C11—41no—
140C23×C11—41no—
141C23×C11C2×C22⋊C411yescharacteristic
142C23×C11C4×Q811yescharacteristic
143C23×C11C4×Q811yescharacteristic
144C23×C11C22⋊Q811yescharacteristic
145C23×C11C22⋊Q811yescharacteristic
146D4×C11—41no—
147D4×C11—41no—
148D4×C11—41no—
149D4×C11—41no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—42no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—81no—
160C2×C4×C11—81no—
161C2×C4×C11—82no—
162C2×C4×C11#12411yescharacteristic
163C2×C4×C11C4⋊Q811yescharacteristic
164C2×Dic11—22no—
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—42no—
177C2×Dic11—41no—
178C2×Dic11—42no—
179C2×Dic11—41no—
180C2×Dic11—41no—
181C2×Dic11—81no—
182C2×Dic11—81no—
183C2×Dic11—81no—
184C2×Dic11—81no—
185C2×Dic11—81no—
186C2×Dic11#9911yescharacteristic
187C2×Dic11#9911yescharacteristic
188C8×C11—81no—
189C11⋊C8—81no—
190C2×C4×D4—111no—
191C22×C4⋊C4—111no—
192#423—221no—
193C2×#100—111no—
194C2×#100C2×D1111yescharacteristic
195C2×#99—111no—
196C2×#99C2×D1111yescharacteristic
197#398—221no—
198#396—221no—
199#387—221no—
200#386—111no—
201#386C2×D1111yescharacteristic
202#385—111no—
203#385—111no—
204#385—221no—
205#380—111no—
206C4×C22⋊C4—221no—
207#343—221no—
208#342—221no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—41no—
216C22×C11—41no—
217C22×C11—41no—
218C22×C11—41no—
219C22×C11—42no—
220C22×C11—41no—
221C22×C11—41no—
222C22×C11—41no—
223C22×C11—41no—
224C22×C11—81no—
225C22×C11#39111yescharacteristic
226C22×C11C2×#9911yescharacteristic
227C22×C11#41011yescharacteristic
228C4×C11—21no—
229C4×C11—21no—
230C4×C11—81no—
231C4×C11—82no—
232C4×C11—81no—
233Dic11—21no—
234Dic11—21no—
235Dic11—41no—
236Dic11—42no—
237Dic11—41no—
238Dic11—41no—
239Dic11—81no—
240Dic11—82no—
241C22×D4C22×D1111yescharacteristic
242C23×C4—111no—
243C23×C4—111no—
244C23×C4—111no—
245C23×C4C4×D1111yescharacteristic
246C2×M16—21no—
247C2×M16—221no—
248C4×D4—441no—
249C4×D4—441no—
250C2×C4⋊C4—111no—
251C2×C4⋊C4—221no—
252C2×C4⋊C4—221no—
253C2×C4⋊C4—221no—
254C2×C4⋊C4—221no—
255C2×C4⋊C4—221no—
256C2×C4⋊C4—441no—
257C2×C4⋊C4—441no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—111no—
261C2×C22⋊C4—111no—
262C2×C22⋊C4—111no—
263C2×C22⋊C4—221no—
264C2×C22⋊C4—221no—
265C2×C22⋊C4C4×D1111yescharacteristic
266C2×C42—111no—
267C2×C42—441no—
268C4⋊C8—441no—
269C4⋊C8—441no—
270#100—21no—
271#100—21no—
272#100—221no—
273#100—221no—
274#99—21no—
275#99—112no—
276#99—221no—
277#99Dic2212yes—
278#95—21no—
279#95—221no—
280#95—221no—
281#95—221no—
282#95—221no—
283#95—441no—
284C2×C11—21no—
285C2×C11—21no—
286C2×C11—41no—
287C2×C11—41no—
288C2×C11—41no—
289C2×C11—41no—
290C2×C11#199611yescharacteristic
291C2×C11#212011yescharacteristic
292C2×C11#212111yescharacteristic
293C24C2×C4×D1111yescharacteristic
294C24D4×D1111yescharacteristic
295C2×D4—41no—
296C2×D4—41no—
297C2×D4C2×Dic2211yescharacteristic
298C2×D4#433911yescharacteristic
299C2×D4#434111yescharacteristic
300C2×D4Q8×D1111yescharacteristic
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—81no—
306C22×C4—111no—
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—441no—
318C22×C4—441no—
319C22×C4—881no—
320C22×C4—881no—
321C22×C4D4×D1111yescharacteristic
322M16—41no—
323M16—41no—
324M16—441no—
325M16—441no—
326C2×C8—41no—
327C2×C8—441no—
328C4⋊C4—441no—
329C4⋊C4—441no—
330C4⋊C4—441no—
331C4⋊C4—442no—
332C4⋊C4—442no—
333C4⋊C4—881no—
334C4⋊C4—881no—
335C22⋊C4—22no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—81no—
339C22⋊C4—222no—
340C22⋊C4—441no—
341C22⋊C4—441no—
342C22⋊C4—442no—
343C22⋊C4—441no—
344C22⋊C4—441no—
345C42—221no—
346C42—221no—
347C42—882no—
348C11#1329711yescharacteristic, complemented, Sylow
349C23—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23C4×Dic2211yescharacteristic
358C23#6693111yescharacteristic
359C23C22⋊C4×D1111yescharacteristic
360C23#6694011yescharacteristic
361C23#6694911yescharacteristic
362D4—41no—
363D4—41no—
364D4—41no—
365D4—41no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—42no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—81no—
376C2×C4—81no—
377C2×C4—82no—
378C2×C4—111no—
379C2×C4—111no—
380C2×C4—222no—
381C2×C4—221no—
382C2×C4—221no—
383C2×C4—221no—
384C2×C4—441no—
385C2×C4—442no—
386C2×C4—441no—
387C2×C4—442no—
388C2×C4—441no—
389C2×C4—441no—
390C2×C4—441no—
391C2×C4—441no—
392C2×C4—442no—
393C2×C4—442no—
394C2×C4—441no—
395C2×C4—441no—
396C2×C4—441no—
397C2×C4—881no—
398C2×C4—881no—
399C2×C4—881no—
400C2×C4—881no—
401C2×C4—881no—
402C2×C4#6693811yescharacteristic
403C2×C4#6694111yescharacteristic
404C8—81no—
405C8—881no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—42no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22—41no—
421C22—81no—
422C22#1062225911yescharacteristic
423C22#1062235311yescharacteristic
424C22D11×#9911yescharacteristic
425C4—21no—
426C4—21no—
427C4—81no—
428C4—82no—
429C4—81no—
430C4—221no—
431C4—221no—
432C4—442no—
433C4—441no—
434C4—441no—
435C4—441no—
436C4—881no—
437C4—882no—
438C2—21no—
439C2—21no—
440C2—41no—
441C2—41no—
442C2—41no—
443C2—41no—
444C2#1306959911yescharacteristic
445C2#1307025611yescharacteristic
446C2#1307025911yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC24×C11C22×C4
FrattiniC22×D4C22×D11
FittingC11×#1390C2
socleC22×C11C2×#99
prime radical, cosocleC22×D4×C11C23
hypercenter#1390D11
hypocenterC11#13297
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #1390

Complements

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

NH ≅ G/Ntype
9. C22×Dic11⋊C4C4semidirect
16. #10622823C4semidirect
18. #10622563C4semidirect
21. #10622555C4semidirect
348. C11#13297semidirect

Maximal subgroups

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

subgroupindex
#130739622
#130686062
#99×Dic112
#130667352
#130667342
#130667332
C11×#13902
#1329711