Finite Group Databasebeta

← #14649765

Subgroups — #14649765

Order 2816.

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

normal subgroups only

This group has 502 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#13077644C211yesmaximal, characteristic
2#13074487C211yesmaximal, characteristic
3C4×#66887C211yesmaximal, characteristic
4#13067219C211yesmaximal, characteristic, complemented
5#13067217C211yesmaximal, characteristic, complemented
6#13066480C211yesmaximal, characteristic, complemented
7C11×#1288C211yesmaximal, characteristic, complemented
8C2×C4×D44C2211yescharacteristic
9C2×#66923C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C4×C11×M16C2211yescharacteristic
12C11×#383C2211yescharacteristic
13C2×#66887—21no—
14#10622539C2211yescharacteristic
15C4×#4318C2211yescharacteristic
16#10622449—22no—
17#10622339—21no—
18D11×C22⋊C8—21no—
19#10622319—22no—
20#10622290C411yescharacteristic
21#10622290C411yescharacteristic
22#10622287C411yescharacteristic
23#10622287C411yescharacteristic
24#10622285—21no—
25#10622281—21no—
26#10622281—21no—
27#10622274—21no—
28#10622192—21no—
29#10622103—22no—
30#10622103—22no—
31C22×D44D411yescharacteristic
32C22×C4×D11D411yescharacteristic
33C22×C4×D11D411yescharacteristic
34C2×C11×M16—21no—
35C2×C42×C11C2311yescharacteristic
36C2×(C2×D11)⋊C4—21no—
37C2×(C2×D11)⋊C4—21no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4C2×C411yescharacteristic
41C2×(C2×D11)⋊C4C2×C411yescharacteristic
42C2×C4⋊Dic11—21no—
43C2×C4⋊Dic11—21no—
44C2×C4⋊Dic11C2×C411yescharacteristic
45C2×C4⋊Dic11C2×C411yescharacteristic
46C2×C4⋊Dic11D411yescharacteristic
47C2×Dic11⋊C4—21no—
48C2×Dic11⋊C4—21no—
49C2×#4318—21no—
50C2×#4313—22no—
51C2×C8×D11—22no—
52C4×D44—21no—
53C4×D44—21no—
54C4×D44—21no—
55C4×D44—21no—
56#66923—21no—
57#66923—21no—
58#66923—21no—
59#66923—21no—
60C11×C4⋊C8—21no—
61C11×C22⋊C8—21no—
62C11×#97—21no—
63C11×#97D412yes—
64C4×C8×C11—21no—
65C11×#95—21no—
66C11×#95—21no—
67C11×#95C2×C411yescharacteristic
68C11×#95C2×C411yescharacteristic
69C11⋊#95—21no—
70C11⋊#95—21no—
71C22⋊(C11⋊C8)—21no—
72#66887—24no—
73(C2×D11)⋊C8—22no—
74(C2×D11)⋊C8—22no—
75C4⋊(C11⋊C8)—21no—
76#66867—21no—
77#66867D412yes—
78C4×C11⋊C8—21no—
79#9189—111nomaximal, Sylow
80C23×D11C22⋊C411yescharacteristic
81C23×D11C22⋊C411yescharacteristic
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11C22×C411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×Dic11—21no—
88C22×Dic11—21no—
89C22×Dic11C22⋊C411yescharacteristic
90C22×Dic11C22⋊C411yescharacteristic
91C2×D44—22no—
92C2×D44—21no—
93C2×D44—21no—
94C2×D44—41no—
95C2×C4×D11—21no—
96C2×C4×D11—21no—
97C2×C4×D11—21no—
98C2×C4×D11—21no—
99C2×C4×D11—81no—
100C2×C4×D11—81no—
101C11×M16—22no—
102C11×M16—41no—
103C2×C8×C11—22no—
104C2×C8×C11—41no—
105C42×C11C2×D411yescharacteristic
106C42×C11C2×D411yescharacteristic
107C42×C11#4111yescharacteristic
108C42×C11#4111yescharacteristic
109(C2×D11)⋊C4—21no—
110(C2×D11)⋊C4—21no—
111(C2×D11)⋊C4—21no—
112(C2×D11)⋊C4—21no—
113(C2×D11)⋊C4—42no—
114(C2×D11)⋊C4—42no—
115(C2×D11)⋊C4—81no—
116(C2×D11)⋊C4—81no—
117C4⋊Dic11—21no—
118C4⋊Dic11—21no—
119C4⋊Dic11—21no—
120C4⋊Dic11—21no—
121C4⋊Dic11—21no—
122C4⋊Dic11—21no—
123C4⋊Dic11—81no—
124C4⋊Dic11—81no—
125Dic11⋊C4—41no—
126Dic11⋊C4—41no—
127Dic11⋊C4—41no—
128Dic11⋊C4—41no—
129#4318—22no—
130#4318—41no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—41no—
133#4313—82no—
134C8×D11—82no—
135#2973—111no—
136#2633—111no—
137C4×#100—111no—
138#1528—111no—
139#1528—111no—
140#1288—111no—
141#1288D1111yescharacteristic, complemented
142C23×C11C2×C22⋊C411yescharacteristic
143C22×D11—21no—
144C22×D11—21no—
145C22×D11—21no—
146C22×D11—21no—
147C22×D11—21no—
148C22×D11—41no—
149C22×D11—41no—
150C22×D11—41no—
151C22×D11—41no—
152C22×D11#10412yes—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11C4×D411yescharacteristic
164C2×C4×C11C4×D411yescharacteristic
165C2×C4×C11#12011yescharacteristic
166C2×C4×C11#12111yescharacteristic
167C2×C4×C11#12111yescharacteristic
168C2×C4×C11#12311yescharacteristic
169C2×Dic11—21no—
170C2×Dic11—21no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173C2×Dic11—41no—
174C2×Dic11—41no—
175C2×Dic11—41no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179D44—42no—
180D44—42no—
181C4×D11—42no—
182C4×D11—42no—
183C4×D11—81no—
184C4×D11—81no—
185C8×C11—42no—
186C8×C11—42no—
187C11⋊C8—42no—
188C11⋊C8—42no—
189C2×#125—111no—
190C2×C4×D4—111no—
191#435—222no—
192#435—222no—
193#432—111no—
194#432C2×D1111yescharacteristic
195C2×#100—221no—
196#407—221no—
197C2×C22⋊C8—221no—
198C4×M16—111no—
199C4×M16C2×D1111yescharacteristic
200#399—111no—
201#399—111no—
202#398—221no—
203#397—111no—
204#397—111no—
205#394—221no—
206#385—221no—
207#385—221no—
208#383C2×D1111yescharacteristic
209#343—221no—
210#330—222no—
211#330—222no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11#38611yescharacteristic
215C22×C11C2×#10411yescharacteristic
216C22×C11#42111yescharacteristic
217C2×D11—22no—
218C2×D11—41no—
219C2×D11—41no—
220C2×D11—42no—
221C2×D11—42no—
222C2×D11—41no—
223C2×D11—41no—
224C2×D11—41no—
225C2×D11—81no—
226C2×D11—81no—
227C4×C11—21no—
228C4×C11—21no—
229C4×C11—21no—
230C4×C11—21no—
231C4×C11—21no—
232C4×C11—21no—
233C4×C11—81no—
234C4×C11—81no—
235Dic11—41no—
236Dic11—41no—
237Dic11—81no—
238Dic11—81no—
239C22×D4—111no—
240C23×C4—111no—
241C23×C4—111no—
242C2×M16—21no—
243C2×M16—222no—
244C2×M16—221no—
245C22×C8—222no—
246#125—221no—
247#125—221no—
248#125—221no—
249#125—221no—
250C4×D4—221no—
251C4×D4—221no—
252C4×D4—221no—
253C4×D4—221no—
254C2×C4⋊C4—111no—
255C2×C4⋊C4—111no—
256C2×C4⋊C4—111no—
257C2×C4⋊C4—221no—
258C2×C4⋊C4—221no—
259C2×C4⋊C4—221no—
260C2×C4⋊C4—221no—
261C2×C22⋊C4—111no—
262C2×C22⋊C4—111no—
263C2×C22⋊C4—221no—
264C2×C22⋊C4—221no—
265C2×C22⋊C4—221no—
266C2×C22⋊C4—221no—
267C2×C42C22×D1111yescharacteristic
268C4⋊C8—21no—
269C4⋊C8—221no—
270#100—224no—
271C22⋊C8—21no—
272C22⋊C8—222no—
273C22⋊C8—222no—
274C22⋊C8—221no—
275#97—21no—
276#97—112no—
277#97—221no—
278#97D4412yes—
279C4×C8—21no—
280C4×C8—221no—
281#95—21no—
282#95—21no—
283#95—221no—
284#95—221no—
285#95C4×D1111yescharacteristic
286#95C4×D1111yescharacteristic
287C2×C11—21no—
288C2×C11—21no—
289C2×C11#187111yescharacteristic
290C2×C11#191111yescharacteristic
291C2×C11#191511yescharacteristic
292D11—42no—
293D11—81no—
294C24—111no—
295C24—111no—
296C2×D4—222no—
297C2×D4—221no—
298C2×D4—221no—
299C2×D4—441no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—111no—
303C22×C4—111no—
304C22×C4—221no—
305C22×C4—221no—
306C22×C4—221no—
307C22×C4—221no—
308C22×C4—221no—
309C22×C4—221no—
310C22×C4—881no—
311C22×C4—881no—
312C22×C4C2×C4×D1111yescharacteristic
313C22×C4D4×D1111yescharacteristic
314C22×C4D4×D1111yescharacteristic
315M16—22no—
316M16—41no—
317M16—222no—
318M16—441no—
319M16—882no—
320C2×C8—22no—
321C2×C8—41no—
322C2×C8—222no—
323C2×C8—441no—
324C2×C8—882no—
325C4⋊C4—221no—
326C4⋊C4—221no—
327C4⋊C4—221no—
328C4⋊C4—221no—
329C4⋊C4—221no—
330C4⋊C4—221no—
331C4⋊C4—441no—
332C4⋊C4—441no—
333C4⋊C4—441no—
334C4⋊C4—441no—
335C4⋊C4—881no—
336C4⋊C4—881no—
337C22⋊C4—221no—
338C22⋊C4—221no—
339C22⋊C4—221no—
340C22⋊C4—221no—
341C22⋊C4—442no—
342C22⋊C4—442no—
343C22⋊C4—881no—
344C22⋊C4—881no—
345C42C2×D4411yescharacteristic
346C42#433911yescharacteristic
347C42D4×D1111yescharacteristic
348C42#434311yescharacteristic
349C11#918911yescharacteristic, complemented, Sylow
350C23—112no—
351C23—221no—
352C23—221no—
353C23—221no—
354C23—221no—
355C23—221no—
356C23—441no—
357C23—441no—
358C23—441no—
359C23—441no—
360C23C22⋊C4×D1111yescharacteristic
361D4—442no—
362D4—442no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—221no—
374C2×C4—221no—
375C2×C4—442no—
376C2×C4—442no—
377C2×C4—441no—
378C2×C4—441no—
379C2×C4—441no—
380C2×C4—441no—
381C2×C4—441no—
382C2×C4—441no—
383C2×C4—441no—
384C2×C4—441no—
385C2×C4—881no—
386C2×C4—881no—
387C2×C4C4×D4411yescharacteristic
388C2×C4#6693511yescharacteristic
389C2×C4#6693711yescharacteristic
390C2×C4#6694611yescharacteristic
391C2×C4#6694711yescharacteristic
392C2×C4#6694811yescharacteristic
393C8—42no—
394C8—42no—
395C8—442no—
396C8—442no—
397C22—21no—
398C22—21no—
399C22—222no—
400C22—442no—
401C22—442no—
402C22—441no—
403C22—441no—
404C22—441no—
405C22—441no—
406C22—441no—
407C22—881no—
408C22—881no—
409C22#1062227811yescharacteristic
410C22D11×#10411yescharacteristic
411C22#1062243411yescharacteristic
412C4—21no—
413C4—21no—
414C4—21no—
415C4—21no—
416C4—21no—
417C4—21no—
418C4—81no—
419C4—81no—
420C4—441no—
421C4—441no—
422C4—881no—
423C4—881no—
424C2—21no—
425C2—21no—
426C2—442no—
427C2—881no—
428C2#1306891711yescharacteristic
429C2#1306914711yescharacteristic
430C2#1306916711yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1288C2
socleC22×C11#386
prime radicalC22×D44D4
cosocleC2×C42×C11C23
hypercenter#1288D11
hypocenterC11#9189
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1288

Complements

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

NH ≅ G/Ntype
4. #13067219C2semidirect
5. #13067217C2semidirect
6. #13066480C2semidirect
7. C11×#1288C2semidirect
141. #1288D11semidirect
349. C11#9189semidirect

Maximal subgroups

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

subgroupindex
#130776442
#130744872
C4×#668872
#130672192
#130672172
#130664802
C11×#12882
#918911