Finite Group Databasebeta

← #14646758

Subgroups — #14646758

Order 2816.

456 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077311C211yesmaximal, characteristic
2#13068652C211yesmaximal, characteristic, complemented
3#13068639C211yesmaximal, characteristic, complemented
4#13067159C211yesmaximal, characteristic
5#13066523C211yesmaximal, characteristic, complemented
6#13066522C211yesmaximal, characteristic, complemented
7C11×#1513C211yesmaximal, characteristic
8C11×#525C2211yescharacteristic
9C2×#67001C411yescharacteristic, complemented
10C23×C11⋊C8C2211yescharacteristic
11C11×#407C2211yescharacteristic
12C11×#380C2211yescharacteristic
13#10622847C411yescharacteristic, complemented
14#10622825C2211yescharacteristic
15#10622820C2211yescharacteristic
16#10622820C2211yescharacteristic
17C2×#66886—21no—
18#10622624—21no—
19#10622624—21no—
20D4×C11⋊C8—21no—
21D4×C11⋊C8—21no—
22#10622612C411yescharacteristic, complemented
23#10622610C411yescharacteristic, complemented
24C2×#66872—21no—
25C11×#328—21no—
26C11×#327—21no—
27#10622196—21no—
28#10622176—21no—
29#10622175—21no—
30#10622167—21no—
31C2×C11×#41C2×C411yescharacteristic
32C23×C4×C11C2311yescharacteristic
33C2×C11×M16—21no—
34C11×#123—21no—
35C11×C22⋊Q8D411yescharacteristic
36C11×C22⋊Q8Q811yescharacteristic
37C11×#121D411yescharacteristic
38C11×#121Q811yescharacteristic
39C11×#120—21no—
40C4×D4×C11—21no—
41C4×D4×C11—21no—
42C11×#117C2×C411yescharacteristic
43C2×C11×C4⋊C4—21no—
44C2×C11×C22⋊C4—21no—
45C2×C22⋊Dic11—21no—
46#67001—42no—
47C2×C4⋊Dic11—21no—
48C2×#4318—21no—
49C2×#4318—21no—
50C2×#4318C2×C411yescharacteristic
51C2×#4318C2×C411yescharacteristic
52C22×C11⋊C8—21no—
53C22×C11⋊C8—42no—
54C22×C11⋊C8C2×C411yescharacteristic
55C22×C11⋊C8C2×C411yescharacteristic
56C22×C11⋊C8D411yescharacteristic
57C22×C11⋊C8D411yescharacteristic
58C22×C11⋊C8D411yescharacteristic
59C22×C11⋊C8D411yescharacteristic
60C11×C22⋊C8—21no—
61C11×C22⋊C8—21no—
62C11×#95—21no—
63C11⋊#95—21no—
64C22⋊(C11⋊C8)—21no—
65C22⋊(C11⋊C8)—21no—
66C22⋊(C11⋊C8)—21no—
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)—21no—
69C22⋊(C11⋊C8)—21no—
70#66886—42no—
71#66872—42no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)—21no—
74#66867—21no—
75C4×C11⋊C8—21no—
76#8629—111nomaximal, Sylow
77C24×C11#4111yescharacteristic
78C11×#41—41no—
79C11×#41—41no—
80C2×Q8×C11C4⋊C411yescharacteristic
81C2×D4×C11—21no—
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11C4⋊C411yescharacteristic
85C22×C4×C11—21no—
86C22×C4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11—41no—
89C22×C4×C11C22×C411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×Q811yescharacteristic
94C22×C4×C11#4111yescharacteristic
95C22×Dic11—41no—
96C11×M16—41no—
97C11×M16—41no—
98C2×C8×C11—41no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4C4⋊C411yescharacteristic
104C11×C4⋊C4C4⋊C411yescharacteristic
105C11×C22⋊C4—21no—
106C11×C22⋊C4—21no—
107C11×C22⋊C4—21no—
108C11×C22⋊C4—21no—
109C11×C22⋊C4—21no—
110C11×C22⋊C4—81no—
111C42×C11—21no—
112C22⋊Dic11—81no—
113C4⋊Dic11—41no—
114C4⋊Dic11—41no—
115#4318—41no—
116#4318—41no—
117#4318—41no—
118#4318—41no—
119#4318—42no—
120C2×C11⋊C8—22no—
121C2×C11⋊C8—22no—
122C2×C11⋊C8—22no—
123C2×C11⋊C8—21no—
124C2×C11⋊C8—21no—
125C2×C11⋊C8—41no—
126C2×C11⋊C8—41no—
127C2×C11⋊C8—41no—
128C2×C11⋊C8—42no—
129C2×C11⋊C8—41no—
130C2×C11⋊C8C22⋊C411yescharacteristic
131C2×C11⋊C8C22⋊C411yescharacteristic
132C2×C11⋊C8C22⋊C411yescharacteristic
133C2×C11⋊C8C22⋊C411yescharacteristic
134#2929—111no—
135#1810—111no—
136#1807—111no—
137#1513—111no—
138#1513D1111yescharacteristic
139#1305—111no—
140#1305—111no—
141C23×C11—21no—
142C23×C11—21no—
143C23×C11—21no—
144C23×C11—41no—
145C23×C11—41no—
146C23×C11#11711yescharacteristic
147C23×C11#12111yescharacteristic
148C23×C11C22⋊Q811yescharacteristic
149Q8×C11—41no—
150D4×C11—41no—
151D4×C11—42no—
152D4×C11—42no—
153D4×C11—41no—
154D4×C11—41no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—81no—
170C2×C4×C11—81no—
171C2×C4×C11—81no—
172C2×C4×C11C2×C22⋊C411yescharacteristic
173C2×C4×C11C2×C4⋊C411yescharacteristic
174C2×C4×C11#12111yescharacteristic
175C2×C4×C11C22⋊Q811yescharacteristic
176C2×Dic11—81no—
177C2×Dic11—81no—
178C2×Dic11—81no—
179C8×C11—81no—
180C11⋊C8—21no—
181C11⋊C8—21no—
182C11⋊C8—21no—
183C11⋊C8—41no—
184C11⋊C8—41no—
185C11⋊C8—81no—
186C11⋊C8#9912yes—
187C2×#131—111no—
188C23×C8—111no—
189#525C2×D1111yescharacteristic
190#435—221no—
191#435—221no—
192C8×D4—221no—
193C8×D4—221no—
194C2×#108—221no—
195C2×#106—221no—
196#424—111no—
197#408—111no—
198#407—111no—
199#407—111no—
200#407C2×D1111yescharacteristic
201#405—111no—
202#380—111no—
203#380C2×D1111yescharacteristic
204#341—221no—
205#340—221no—
206#328—21no—
207#328—221no—
208#327—21no—
209#327—221no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—42no—
219C22×C11—42no—
220C22×C11—41no—
221C22×C11—41no—
222C22×C11—41no—
223C22×C11#38011yescharacteristic
224C22×C11#47111yescharacteristic
225C22×C11#47111yescharacteristic
226C4×C11—21no—
227C4×C11—21no—
228C4×C11—21no—
229C4×C11—41no—
230C4×C11—41no—
231C4×C11—41no—
232C4×C11—161no—
233C4×C11C2×#9911yescharacteristic
234C4×C11#41011yescharacteristic
235Dic11—161no—
236C2×#41C4×D1111yescharacteristic
237C23×C4C22×D1111yescharacteristic
238#131—442no—
239C2×M16—21no—
240C2×M16—111no—
241C2×M16—111no—
242C2×M16—221no—
243C2×M16—221no—
244C22×C8—111no—
245C22×C8—111no—
246C22×C8—111no—
247C22×C8—111no—
248C22×C8—111no—
249C22×C8—111no—
250C22×C8—221no—
251C22×C8—442no—
252#123—21no—
253C22⋊Q8Dic2211yescharacteristic
254C22⋊Q8C22⋊D1111yescharacteristic
255#121Dic2211yescharacteristic
256#121C22⋊D1111yescharacteristic
257#120—21no—
258C4×D4—21no—
259C4×D4—21no—
260#117C4×D1111yescharacteristic
261C2×C4⋊C4—21no—
262C2×C4⋊C4—221no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—221no—
265#108—442no—
266#106—442no—
267C4⋊C8—221no—
268C4⋊C8—221no—
269C22⋊C8—21no—
270C22⋊C8—21no—
271C22⋊C8—221no—
272C22⋊C8—221no—
273C22⋊C8—221no—
274C22⋊C8—221no—
275C22⋊C8—221no—
276C22⋊C8—221no—
277#97—221no—
278C4×C8—221no—
279#95—21no—
280#95—221no—
281C2×C11—21no—
282C2×C11—21no—
283C2×C11—41no—
284C2×C11—41no—
285C2×C11—81no—
286C2×C11#179911yescharacteristic
287C2×C11#181411yescharacteristic
288C2×C11#181511yescharacteristic
289C24#434111yescharacteristic
290#41—41no—
291#41—41no—
292C2×Q8Dic11⋊C411yescharacteristic
293C2×D4—21no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4Dic11⋊C411yescharacteristic
297C22×C4—21no—
298C22×C4—41no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—441no—
302C22×C4C2×Dic2211yescharacteristic
303C22×C4C2×C4×D1111yescharacteristic
304C22×C4D4×D1111yescharacteristic
305C22×C4D4×D1111yescharacteristic
306C22×C4#434111yescharacteristic
307C22×C4C2×C22⋊D1111yescharacteristic
308M16—41no—
309M16—41no—
310M16—442no—
311M16—441no—
312M16—441no—
313M16—441no—
314M16—441no—
315C2×C8—41no—
316C2×C8—111no—
317C2×C8—111no—
318C2×C8—111no—
319C2×C8—111no—
320C2×C8—222no—
321C2×C8—222no—
322C2×C8—222no—
323C2×C8—221no—
324C2×C8—221no—
325C2×C8—441no—
326C2×C8—441no—
327C2×C8—441no—
328C2×C8—442no—
329C2×C8—441no—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—441no—
335C4⋊C4—441no—
336C4⋊C4Dic11⋊C411yescharacteristic
337C4⋊C4Dic11⋊C411yescharacteristic
338C22⋊C4—21no—
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—21no—
342C22⋊C4—21no—
343C22⋊C4—81no—
344C22⋊C4—881no—
345C42—21no—
346C11#862911yescharacteristic, complemented, Sylow
347C23—21no—
348C23—21no—
349C23—21no—
350C23—41no—
351C23—41no—
352C23#6693011yescharacteristic
353C23#6693111yescharacteristic
354C23#6699211yescharacteristic
355Q8—41no—
356D4—41no—
357D4—42no—
358D4—42no—
359D4—41no—
360D4—41no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—81no—
376C2×C4—81no—
377C2×C4—81no—
378C2×C4—881no—
379C2×C4—881no—
380C2×C4—881no—
381C2×C4#6693111yescharacteristic
382C2×C4C22⋊C4×D1111yescharacteristic
383C2×C4C2×Dic11⋊C411yescharacteristic
384C2×C4#6699211yescharacteristic
385C8—81no—
386C8—112no—
387C8—221no—
388C8—221no—
389C8—221no—
390C8—441no—
391C8—441no—
392C8—881no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—42no—
402C22—42no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22#1062255511yescharacteristic
407C22#1062281311yescharacteristic
408C22#1062281611yescharacteristic
409C4—21no—
410C4—21no—
411C4—21no—
412C4—41no—
413C4—41no—
414C4—41no—
415C4—161no—
416C4—1761no—
417C4#1062235311yescharacteristic
418C4D11×#9911yescharacteristic
419C2—21no—
420C2—21no—
421C2—41no—
422C2—41no—
423C2—81no—
424C2#1306860211yescharacteristic
425C2#1306866811yescharacteristic
426C2#1306867311yescharacteristic
subgroupG/H
centerC22#10622555
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1513C2
socleC22×C11#380
prime radicalC11×#525C22
cosocleC23×C4×C11C23
hypercenter#1513D11
hypocenterC11#8629
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1513

Complements

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

NH ≅ G/Ntype
2. #13068652C2semidirect
3. #13068639C2semidirect
5. #13066523C2semidirect
6. #13066522C2semidirect
9. C2×#67001C4semidirect
13. #10622847C4semidirect
22. #10622612C4semidirect
23. #10622610C4semidirect
346. C11#8629semidirect

Maximal subgroups

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

subgroupindex
#130773112
#130686522
#130686392
#130671592
#130665232
#130665222
C11×#15132
#862911