Finite Group Databasebeta

← #14673442

Subgroups — #14673442

Order 2816.

540 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 81 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#13074989C211yesmaximal, characteristic
2#13068899C211yesmaximal, characteristic
3#13068896C211yesmaximal, characteristic
4#13068828C211yesmaximal, characteristic
5#13066740C211yesmaximal, characteristic
6#13066735C211yesmaximal, characteristic
7C11×#1390C211yesmaximal, characteristic
8#10623329C2211yescharacteristic
9C2×#66977—21no—
10C2×#66931—21no—
11C2×C11×#100C2211yescharacteristic
12C2×C11×#99C2211yescharacteristic
13C11×#386C2211yescharacteristic
14#10622834C2211yescharacteristic
15#10622833C2211yescharacteristic
16C2×#66898C2211yescharacteristic
17#10622823—21no—
18#10622734—21no—
19#10622563—21no—
20#10622561—21no—
21#10622561—21no—
22#10622269—21no—
23#10622260—21no—
24#10622193—21no—
25#10622165—21no—
26#10622165—21no—
27C22×D4×C11C2311yescharacteristic
28C23×C4×C11D411yescharacteristic
29C23×Dic11D411yescharacteristic
30C22×Dic22—21no—
31C2×C11×M16—21no—
32C2×C11×C22⋊C4—21no—
33C2×C11×C22⋊C4—21no—
34C2×C11×C22⋊C4D411yescharacteristic
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11—21no—
37C2×C22⋊Dic11—21no—
38C2×C22⋊Dic11—21no—
39C2×C22⋊Dic11—21no—
40C2×C22⋊Dic11—21no—
41C2×C22⋊Dic11D411yescharacteristic
42D4×Dic11—41no—
43D4×Dic11—41no—
44#66979—21no—
45C2×C4⋊Dic11—21no—
46C2×C4⋊Dic11—21no—
47C2×C4⋊Dic11—41no—
48C2×C4⋊Dic11D411yescharacteristic
49#66977—44no—
50C2×Dic11⋊C4—21no—
51C2×Dic11⋊C4—21no—
52C2×Dic11⋊C4—21no—
53C2×Dic11⋊C4—21no—
54C2×Dic11⋊C4—41no—
55C2×C4×Dic11D411yescharacteristic
56#66931—44no—
57C11×#100—21no—
58C11×#100Q812yescomplemented
59C11×#99—21no—
60C11×#99Q812yescomplemented
61C11×#95—21no—
62#66898—21no—
63#66898Q812yescomplemented
64C11⋊#95—21no—
65C11⋊#95—21no—
66C11⋊#95—41no—
67C11⋊#95—41no—
68#66882—41no—
69#66881—41no—
70#13461—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×C11C2×Q811yescharacteristic
78C2×D4×C11#4111yescharacteristic
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—42no—
82C22×C4×C11—41no—
83C22×C4×C11—41no—
84C22×C4×C11C2×D411yescharacteristic
85C22×Dic11—21no—
86C22×Dic11—21no—
87C22×Dic11—21no—
88C22×Dic11—21no—
89C22×Dic11—21no—
90C22×Dic11—21no—
91C22×Dic11—21no—
92C22×Dic11—21no—
93C22×Dic11—41no—
94C22×Dic11—41no—
95C22×Dic11—42no—
96C2×Dic22—42no—
97C2×Dic22—42no—
98C2×Dic22—81no—
99C11×M16—22no—
100C11×M16—41no—
101C2×C8×C11—41no—
102C11×C22⋊C4—22no—
103C11×C22⋊C4—42no—
104C11×C22⋊C4—41no—
105C11×C22⋊C4—41no—
106C22⋊Dic11—22no—
107C22⋊Dic11—41no—
108C22⋊Dic11—41no—
109C22⋊Dic11—41no—
110C22⋊Dic11—41no—
111C22⋊Dic11—42no—
112C22⋊Dic11—42no—
113C22⋊Dic11—42no—
114C22⋊Dic11—41no—
115C4⋊Dic11—21no—
116C4⋊Dic11—21no—
117C4⋊Dic11—41no—
118C4⋊Dic11—42no—
119C4⋊Dic11—42no—
120C4⋊Dic11—82no—
121Dic11⋊C4—24no—
122Dic11⋊C4—42no—
123Dic11⋊C4—42no—
124Dic11⋊C4—81no—
125Dic11⋊C4—82no—
126C4×Dic11—41no—
127C4×Dic11—41no—
128#2683—111no—
129#1867—111no—
130#1867—111no—
131#1856—111no—
132#1393—111no—
133#1390—111no—
134#1390D1111yescharacteristic
135C23×C11—21no—
136C23×C11—21no—
137C23×C11—21no—
138C23×C11—21no—
139C23×C11—41no—
140C23×C11—41no—
141C23×C11—41no—
142C23×C11—41no—
143C23×C11#12011yescharacteristic
144C23×C11C22⋊Q811yescharacteristic
145C23×C11C22⋊Q811yescharacteristic
146C23×C11C4⋊Q811yescharacteristic
147C23×C11C4⋊Q811yescharacteristic
148D4×C11—41no—
149D4×C11—41no—
150D4×C11—41no—
151D4×C11—41no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—22no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—42no—
158C2×C4×C11—41no—
159C2×C4×C11—42no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—81no—
163C2×C4×C11—81no—
164C2×C4×C11—81no—
165C2×C4×C11C22⋊Q811yescharacteristic
166C2×C4×C11C4⋊Q811yescharacteristic
167C2×Dic11—22no—
168C2×Dic11—22no—
169C2×Dic11—41no—
170C2×Dic11—41no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173C2×Dic11—42no—
174C2×Dic11—41no—
175C2×Dic11—41no—
176C2×Dic11—41no—
177C2×Dic11—42no—
178C2×Dic11—41no—
179C2×Dic11—41no—
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—
190Dic22—84no—
191C8×C11—42no—
192C2×C22⋊Q8—221no—
193C2×C22⋊Q8—221no—
194#518—111no—
195#428—221no—
196C2×#100C2×D1111yescharacteristic
197C2×#99—111no—
198C2×#99C2×D1111yescharacteristic
199#396—221no—
200#396—221no—
201#395—221no—
202#390—111no—
203#389—221no—
204#386—111no—
205#386C2×D1111yescharacteristic
206#385—221no—
207#385—221no—
208#342—221no—
209#342—221no—
210#339—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#39511yescharacteristic
228C22×C11B(4,𝔽2)11yescharacteristic
229C22×C11#45811yescharacteristic
230C4×C11—21no—
231C4×C11—21no—
232C4×C11—42no—
233C4×C11—81no—
234C4×C11—82no—
235Dic11—42no—
236Dic11—42no—
237Dic11—81no—
238Dic11—82no—
239Dic11—81no—
240Dic11—81no—
241Dic11—81no—
242C22×Q8—221no—
243C22×D4C22×D1111yescharacteristic
244C23×C4—111no—
245C23×C4D4411yescharacteristic
246C2×M16—21no—
247C22⋊Q8—444no—
248C22⋊Q8—444no—
249C4×D4—441no—
250C4×D4—441no—
251#117—221no—
252C2×C4⋊C4—111no—
253C2×C4⋊C4—221no—
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⋊C4—441no—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—111no—
264C2×C22⋊C4—221no—
265C2×C22⋊C4—221no—
266C2×C22⋊C4—221no—
267C2×C22⋊C4—221no—
268C2×C22⋊C4—221no—
269C2×C22⋊C4—221no—
270C2×C22⋊C4D4411yescharacteristic
271C2×C42—111no—
272#107—441no—
273#106—441no—
274#100—21no—
275#100Dic2212yescomplemented
276#99—21no—
277#99—112no—
278#99—221no—
279#99Dic2212yescomplemented
280#95—21no—
281#95—221no—
282#95—221no—
283#95—441no—
284#95—441no—
285C2×C11—21no—
286C2×C11—21no—
287C2×C11—41no—
288C2×C11—41no—
289C2×C11—41no—
290C2×C11—41no—
291C2×C11#206211yescharacteristic
292C2×C11#219611yescharacteristic
293C2×C11#220111yescharacteristic
294C24C2×D4411yescharacteristic
295C24D4×D1111yescharacteristic
296C2×Q8—442no—
297C2×Q8—442no—
298C2×Q8—881no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4C2×Dic2211yescharacteristic
302C2×D4C2×Dic2211yescharacteristic
303C2×D4#434111yescharacteristic
304C2×D4Q8×D1111yescharacteristic
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—42no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—221no—
311C22×C4—221no—
312C22×C4—221no—
313C22×C4—221no—
314C22×C4—221no—
315C22×C4—221no—
316C22×C4—221no—
317C22×C4—221no—
318C22×C4—442no—
319C22×C4—441no—
320C22×C4—441no—
321C22×C4D4×D1111yescharacteristic
322M16—22no—
323M16—41no—
324C2×C8—41no—
325C4⋊C4—224no—
326C4⋊C4—221no—
327C4⋊C4—221no—
328C4⋊C4—441no—
329C4⋊C4—442no—
330C4⋊C4—442no—
331C4⋊C4—442no—
332C4⋊C4—442no—
333C4⋊C4—881no—
334C4⋊C4—882no—
335C4⋊C4—882no—
336C22⋊C4—22no—
337C22⋊C4—42no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—222no—
341C22⋊C4—442no—
342C22⋊C4—442no—
343C22⋊C4—442no—
344C22⋊C4—441no—
345C22⋊C4—441no—
346C22⋊C4—441no—
347C22⋊C4—441no—
348C22⋊C4—441no—
349C42—441no—
350C42—441no—
351C11#1346111yescharacteristic, complemented, Sylow
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23#6692211yescharacteristic
361C23#6693111yescharacteristic
362C23#6693511yescharacteristic
363C23#6694111yescharacteristic
364C23#6695011yescharacteristic
365Q8—884no—
366D4—41no—
367D4—41no—
368D4—41no—
369D4—41no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—22no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—81no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4—222no—
384C2×C4—222no—
385C2×C4—441no—
386C2×C4—441no—
387C2×C4—441no—
388C2×C4—441no—
389C2×C4—442no—
390C2×C4—442no—
391C2×C4—441no—
392C2×C4—441no—
393C2×C4—441no—
394C2×C4—441no—
395C2×C4—441no—
396C2×C4—441no—
397C2×C4—441no—
398C2×C4—441no—
399C2×C4—881no—
400C2×C4—881no—
401C2×C4—881no—
402C2×C4—881no—
403C2×C4—881no—
404C2×C4—881no—
405C2×C4—881no—
406C2×C4#6693111yescharacteristic
407C2×C4#6694111yescharacteristic
408C8—42no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22—41no—
421C22—41no—
422C22—41no—
423C22—81no—
424C22—81no—
425C22#1062226911yescharacteristic
426C22#1062235411yescharacteristic
427C22#1062235511yescharacteristic
428C4—21no—
429C4—21no—
430C4—42no—
431C4—81no—
432C4—82no—
433C4—442no—
434C4—442no—
435C4—881no—
436C4—882no—
437C4—881no—
438C4—881no—
439C4—881no—
440C2—21no—
441C2—21no—
442C2—41no—
443C2—41no—
444C2—41no—
445C2—41no—
446C2#1306997011yescharacteristic
447C2#1307060111yescharacteristic
448C2#1307063011yescharacteristic
subgroupG/H
centerC22#10622354
commutator, prime radical, cosocleC22×D4×C11C23
FrattiniC22×D4C22×D11
FittingC11×#1390C2
socleC22×C11B(4,𝔽2)
hypercenter#1390D11
hypocenterC11#13461
LCSG ▷ C22×D4×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
58. C11×#100Q8semidirect
60. C11×#99Q8semidirect
63. #66898Q8semidirect
275. #100Dic22semidirect
279. #99Dic22semidirect
351. C11#13461semidirect

Maximal subgroups

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

subgroupindex
#130749892
#130688992
#130688962
#130688282
#130667402
#130667352
C11×#13902
#1346111