Finite Group Databasebeta

← #14642219

Subgroups — #14642219

Order 2816.

572 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 109 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#13076970C211yesmaximal, characteristic
2#13068468C211yesmaximal, characteristic, complemented
3#13068360C211yesmaximal, characteristic, complemented
4#13066437C211yesmaximal, characteristic, complemented
5#13066436C211yesmaximal, characteristic, complemented
6#13066436C211yesmaximal, characteristic, complemented
7C11×#1270C211yesmaximal, characteristic, complemented
8C2×#66993C411yescharacteristic
9C2×#66941C411yescharacteristic
10C2×#66938—21no—
11C2×#66938—21no—
12C11×#390C2211yescharacteristic
13#10622834C411yescharacteristic
14C2×#66879—21no—
15C2×Dic11⋊C8—21no—
16C2×C8×Dic11—21no—
17#10622601C411yescharacteristic
18#10622570—21no—
19#10622570—21no—
20#10622552C2211yescharacteristic
21C42×Dic11C2211yescharacteristic
22C11×#336C2211yescharacteristic
23C11×#336C2211yescharacteristic
24#10622188—21no—
25#10622162C2211yescharacteristic
26#10622162C2211yescharacteristic
27C22×D4×C11C2×C411yescharacteristic
28C22×C22⋊D11—21no—
29C22×C22⋊D11—21no—
30C22×D44C2×C411yescharacteristic
31C22×Dic22—21no—
32C22×C8×C11—21no—
33C22×C8×C11—21no—
34C2×C11×C4⋊C4C2×C411yescharacteristic
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4—21no—
37C2×C42×C11C2311yescharacteristic
38C2×C22⋊Dic11—21no—
39C2×C22⋊Dic11—21no—
40#66993—42no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×C4⋊Dic11C2×C411yescharacteristic
46C2×Dic11⋊C4—21no—
47C2×C4×Dic11C2×C411yescharacteristic
48C2×C4×Dic11C2×C411yescharacteristic
49C2×C4×Dic11D411yescharacteristic
50C2×C4×Dic11D411yescharacteristic
51C2×C4×Dic11D411yescharacteristic
52C2×C4×Dic11D411yescharacteristic
53C22×C11⋊C8—21no—
54C22×C11⋊C8—21no—
55#66941—42no—
56#66938—42no—
57#66938—42no—
58#66938—42no—
59#66938—42no—
60#66879—42no—
61Dic11⋊C8—24no—
62C8×Dic11—24no—
63#7679—111nomaximal, Sylow
64C24×C11—21no—
65C23×D11—21no—
66C2×D4×C11—21no—
67C2×D4×C11—21no—
68C2×D4×C11—41no—
69C2×D4×C11—41no—
70C22×C4×C11—21no—
71C22×C4×C11C22×C411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C2×C22⋊D11—42no—
75C2×C22⋊D11—42no—
76C2×C22⋊D11—42no—
77C2×C22⋊D11—42no—
78C2×C22⋊D11—42no—
79C2×C22⋊D11—42no—
80C22×Dic11—21no—
81C22×Dic11C22⋊C411yescharacteristic
82C22×Dic11C22⋊C411yescharacteristic
83C22×Dic11C22⋊C411yescharacteristic
84C22×Dic11C22⋊C411yescharacteristic
85C2×D44—21no—
86C2×D44—21no—
87C2×D44—41no—
88C2×D44—41no—
89C2×Dic22—42no—
90C2×Dic22—42no—
91C2×Dic22—42no—
92C2×C8×C11—22no—
93C2×C8×C11—22no—
94C2×C8×C11—41no—
95C2×C8×C11—41no—
96C2×C8×C11—41no—
97C2×C8×C11—41no—
98C11×C4⋊C4—41no—
99C11×C22⋊C4—41no—
100C11×C22⋊C4—41no—
101C11×C22⋊C4—41no—
102C11×C22⋊C4—41no—
103C42×C11—41no—
104C22⋊Dic11—42no—
105C22⋊Dic11—42no—
106(C2×D11)⋊C4—42no—
107(C2×D11)⋊C4—42no—
108(C2×D11)⋊C4—41no—
109(C2×D11)⋊C4—41no—
110(C2×D11)⋊C4—41no—
111(C2×D11)⋊C4—41no—
112C4⋊Dic11—41no—
113Dic11⋊C4—42no—
114C4×Dic11—22no—
115C4×Dic11—22no—
116C4×Dic11—22no—
117C4×Dic11—21no—
118C4×Dic11—21no—
119C4×Dic11—21no—
120C4×Dic11—21no—
121C4×Dic11D812yes—
122C4×Dic11SD1612yes—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—41no—
126C2×C11⋊C8—41no—
127C2×C11⋊C8—41no—
128C2×C11⋊C8—41no—
129#2858—111no—
130#1767—111no—
131#1744—111no—
132#1270—111no—
133#1270—111no—
134#1270—111no—
135#1270D1111yescharacteristic, complemented
136C23×C11—41no—
137C23×C11—41no—
138C23×C11—41no—
139C23×C11—41no—
140C23×C11—41no—
141C23×C11—41no—
142C23×C11—41no—
143C23×C11C2×C22⋊C411yescharacteristic
144C22×D11—41no—
145C22×D11—41no—
146C22×D11—41no—
147C22×D11—41no—
148C22×D11—41no—
149C22×D11—41no—
150C22×D11—41no—
151D4×C11—81no—
152D4×C11—81no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11#13111yescharacteristic
163C2×C4×C11#13111yescharacteristic
164C2×C4×C11C2×D811yescharacteristic
165C2×C4×C11C2×SD1611yescharacteristic
166C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
168C22⋊D11—84no—
169C22⋊D11—84no—
170C2×Dic11—21no—
171C2×Dic11—21no—
172C2×Dic11—21no—
173C2×Dic11—21no—
174C2×Dic11—21no—
175C2×Dic11—21no—
176C2×Dic11—21no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11#10012yes—
181C2×Dic11#10212yes—
182C2×Dic11#10212yes—
183C2×Dic11#10412yes—
184C2×Dic11#10412yes—
185D44—81no—
186D44—81no—
187Dic22—84no—
188C8×C11—42no—
189C8×C11—42no—
190C11⋊C8—42no—
191C11⋊C8—42no—
192C2×C4⋊Q8—111no—
193C2×#127—111no—
194C2×#124—221no—
195C2×#124—221no—
196C2×C4⋊C8—221no—
197C2×#97—221no—
198C2×C4×C8—221no—
199#390—111no—
200#390—111no—
201#390—111no—
202#390—221no—
203#390—221no—
204#390C2×D1111yescharacteristic
205C43—111no—
206#336—111no—
207#336—111no—
208#336—221no—
209#336C2×D1111yescharacteristic
210#336C2×D1111yescharacteristic
211C22×C11—81no—
212C22×C11—81no—
213C22×C11—81no—
214C22×C11—81no—
215C22×C11—81no—
216C22×C11—81no—
217C22×C11—81no—
218C22×C11#40811yescharacteristic
219C22×C11#41011yescharacteristic
220C22×C11C2×#10011yescharacteristic
221C22×C11C2×#10211yescharacteristic
222C22×C11#41811yescharacteristic
223C22×C11C2×#10411yescharacteristic
224C22×C11C2×#10411yescharacteristic
225C2×D11—81no—
226C2×D11—81no—
227C2×D11—81no—
228C2×D11—81no—
229C2×D11—81no—
230C2×D11—81no—
231C2×D11—81no—
232C4×C11—21no—
233C4×C11—21no—
234C4×C11—21no—
235C4×C11—21no—
236C4×C11—21no—
237C4×C11—21no—
238C4×C11—81no—
239Dic11—22no—
240Dic11—22no—
241Dic11—41no—
242Dic11—81no—
243Dic11#32914yes—
244C22×Q8—221no—
245C22×D4—111no—
246C22×D4—221no—
247C22×D4—221no—
248C22×D4C4×D1111yescharacteristic
249C22×C8—21no—
250C22×C8—21no—
251C22×C8—221no—
252C22×C8—221no—
253C4⋊Q8—442no—
254#127—442no—
255#124—442no—
256#124—442no—
257#124—442no—
258#124—442no—
259C2×C4⋊C4—111no—
260C2×C4⋊C4—221no—
261C2×C4⋊C4C4×D1111yescharacteristic
262C2×C22⋊C4—21no—
263C2×C22⋊C4—21no—
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×C42—111no—
271C2×C42—111no—
272C2×C42—111no—
273C2×C42—111no—
274C2×C42—111no—
275C2×C42—111no—
276C2×C42C22×D1111yescharacteristic
277C4⋊C8—224no—
278#97—442no—
279C4×C8—224no—
280C2×C11—161no—
281C2×C11#146911yescharacteristic
282C2×C11#148411yescharacteristic
283C2×C11#149211yescharacteristic
284C2×C11#150211yescharacteristic
285C2×C11#150511yescharacteristic
286C2×C11C2×#32911yescharacteristic
287C2×C11#154511yescharacteristic
288D11—161no—
289C24—21no—
290C24—221no—
291C2×Q8—442no—
292C2×Q8—442no—
293C2×Q8—442no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—221no—
299C2×D4—221no—
300C2×D4—441no—
301C2×D4—441no—
302C2×D4—442no—
303C2×D4—442no—
304C2×D4—442no—
305C2×D4—442no—
306C2×D4—442no—
307C2×D4—442no—
308C22×C4—21no—
309C22×C4—111no—
310C22×C4—111no—
311C22×C4—111no—
312C22×C4—111no—
313C22×C4—221no—
314C22×C4C2×C4×D1111yescharacteristic
315C22×C4D4×D1111yescharacteristic
316C22×C4D4×D1111yescharacteristic
317C2×C8—22no—
318C2×C8—22no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—222no—
324C2×C8—222no—
325C2×C8—441no—
326C2×C8—441no—
327C2×C8—441no—
328C2×C8—441no—
329C4⋊C4—41no—
330C4⋊C4—441no—
331C4⋊C4—442no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—442no—
337C22⋊C4—442no—
338C22⋊C4—442no—
339C22⋊C4—442no—
340C22⋊C4—441no—
341C22⋊C4—441no—
342C22⋊C4—441no—
343C22⋊C4—441no—
344C42—41no—
345C42—112no—
346C42—112no—
347C42—222no—
348C42—222no—
349C42—222no—
350C42—221no—
351C42—221no—
352C42—221no—
353C42—221no—
354C11#767911yescharacteristic, complemented, Sylow
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—41no—
362C23—441no—
363C23—441no—
364C23—441no—
365C23—441no—
366C23—441no—
367C23—441no—
368C23—441no—
369C23C22⋊C4×D1111yescharacteristic
370Q8—884no—
371D4—81no—
372D4—81no—
373D4—881no—
374D4—881no—
375D4—884no—
376D4—884no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—112no—
387C2×C4—112no—
388C2×C4—112no—
389C2×C4—112no—
390C2×C4—112no—
391C2×C4—221no—
392C2×C4—221no—
393C2×C4—221no—
394C2×C4—221no—
395C2×C4—221no—
396C2×C4—221no—
397C2×C4—221no—
398C2×C4—441no—
399C2×C4—441no—
400C2×C4—441no—
401C2×C4#6695411yescharacteristic
402C2×C4#6696011yescharacteristic
403C2×C4D8×D1111yescharacteristic
404C2×C4#6696411yescharacteristic
405C2×C4SD16×D1111yescharacteristic
406C2×C4#6696711yescharacteristic
407C8—42no—
408C8—42no—
409C8—442no—
410C8—442no—
411C22—81no—
412C22—81no—
413C22—81no—
414C22—81no—
415C22—81no—
416C22—81no—
417C22—81no—
418C22—881no—
419C22—881no—
420C22—881no—
421C22—881no—
422C22—881no—
423C22—881no—
424C22—881no—
425C22#1062234011yescharacteristic
426C22#1062235311yescharacteristic
427C22D11×#10011yescharacteristic
428C22D11×#10211yescharacteristic
429C22#1062238311yescharacteristic
430C22D11×#10411yescharacteristic
431C22D11×#10411yescharacteristic
432C4—21no—
433C4—21no—
434C4—21no—
435C4—21no—
436C4—21no—
437C4—21no—
438C4—81no—
439C4—114no—
440C4—222no—
441C4—222no—
442C4—441no—
443C4—881no—
444C2—161no—
445C2—1761no—
446C2#1306696611yescharacteristic
447C2#1306703111yescharacteristic
448C2#1306706511yescharacteristic
449C2#1306710911yescharacteristic
450C2#1306712211yescharacteristic
451C2D11×#32911yescharacteristic
452C2#1306728211yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1270C2
socleC23×C11C2×C22⋊C4
prime radicalC2×#66993C4
cosocleC2×C42×C11C23
hypercenter#1270D11
hypocenterC11#7679
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #13068468C2semidirect
3. #13068360C2semidirect
4. #13066437C2semidirect
5. #13066436C2semidirect
6. #13066436C2semidirect
7. C11×#1270C2semidirect
135. #1270D11semidirect
354. C11#7679semidirect

Maximal subgroups

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

subgroupindex
#130769702
#130684682
#130683602
#130664372
#130664362
C11×#12702
#767911