Finite Group Databasebeta

← #14650149

Subgroups — #14650149

Order 2816.

512 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622455C211yesmaximal, characteristic
2M16×D44C211yesmaximal, characteristic
3#13069605C211yesmaximal, characteristic, complemented
4#13067300C211yesmaximal, characteristic, complemented
5#13067042C211yesmaximal, characteristic
6#13066491C211yesmaximal, characteristic, complemented
7C11×#1283C211yesmaximal, characteristic, complemented
8C2×M16×D11—21no—
9C2×C4×D44C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13C4×C11×M16C2211yescharacteristic
14#10622739—21no—
15C2×#66885C412yes—
16C2×#66881C412yes—
17#10622537C2211yescharacteristic
18#10622537C2211yescharacteristic
19#10622455—21no—
20#10622455—21no—
21#10622455—21no—
22#10622455—21no—
23#10622319—22no—
24#10622301—21no—
25C8×D44—21no—
26#10622192—21no—
27#10622192—21no—
28#10622120—22no—
29#10622097—21no—
30#10622097—21no—
31C22×D44C2×C411yescharacteristic
32C22×C4×D11—21no—
33C22×Dic22—21no—
34C2×C11×M16D411yescharacteristic
35C2×C11×M16D411yescharacteristic
36C22×C8×C11C2×C412yes—
37C2×C42×C11C2311yescharacteristic
38C2×(C2×D11)⋊C4—21no—
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11C2×C412yes—
41C2×C4⋊Dic11C2×C411yescharacteristic
42C2×#4318—21no—
43C2×#4318—21no—
44M16×D11—42no—
45M16×D11—42no—
46C2×#4313—22no—
47C2×C8×D11—22no—
48C4×D44—21no—
49C4×D44—21no—
50C4×D44D411yescharacteristic
51C4×D44D411yescharacteristic
52C4×D44D411yescharacteristic
53C4×D44D411yescharacteristic
54#66922—21no—
55#66922—21no—
56#66922—21no—
57#66922—21no—
58C11×C4⋊C8—21no—
59C11×C4⋊C8—21no—
60C11×C4⋊C8—21no—
61C11×C22⋊C8—21no—
62C11×#97—21no—
63C4×C8×C11—21no—
64C4×C8×C11—21no—
65#66885—22no—
66#66885—22no—
67(C2×D11)⋊C8—22no—
68(C2×D11)⋊C8—22no—
69#66881—22no—
70#66881—22no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)D412yes—
75#9249—111nomaximal, Sylow
76C23×D11—21no—
77C22×C4×C11C22×C411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11#4111yescharacteristic
80C22×Dic11—21no—
81C22×Dic11—22no—
82C2×D44—22no—
83C2×D44—21no—
84C2×D44—41no—
85C2×D44C22⋊C411yescharacteristic
86C2×D44C22⋊C411yescharacteristic
87C2×C4×D11—21no—
88C2×C4×D11—21no—
89C2×C4×D11—21no—
90C2×C4×D11—21no—
91C2×C4×D11—41no—
92C2×C4×D11—41no—
93C2×C4×D11—41no—
94C2×C4×D11—41no—
95C2×Dic22—41no—
96C2×Dic22—41no—
97C2×Dic22—82no—
98C11×M16—21no—
99C11×M16—21no—
100C11×M16—21no—
101C11×M16SD1612yes—
102C2×C8×C11—22no—
103C2×C8×C11—21no—
104C2×C8×C11—21no—
105C2×C8×C11—42no—
106C2×C8×C11—41no—
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110C42×C11#4111yescharacteristic
111(C2×D11)⋊C4—21no—
112(C2×D11)⋊C4—21no—
113(C2×D11)⋊C4—21no—
114(C2×D11)⋊C4—21no—
115C4⋊Dic11—22no—
116C4⋊Dic11—21no—
117C4⋊Dic11—22no—
118C4⋊Dic11—41no—
119C4⋊Dic11—41no—
120C4⋊Dic11C22⋊C411yescharacteristic
121C4⋊Dic11C22⋊C411yescharacteristic
122#4318—41no—
123#4318—41no—
124#4318—41no—
125#4318—41no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—41no—
128#4313—44no—
129C8×D11—44no—
130C2×#476—111no—
131D4×M16—111no—
132#1997—111no—
133#1549—111no—
134#1486—111no—
135#1292—111no—
136#1283D1111yescharacteristic, complemented
137C23×C11C4×D411yescharacteristic
138C22×D11—21no—
139C22×D11—21no—
140C22×D11—42no—
141C22×D11—41no—
142C22×D11—41no—
143C22×D11—81no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—41no—
147C2×C4×C11C2×C22⋊C411yescharacteristic
148C2×C4×C11C4×D411yescharacteristic
149C2×C4×C11#12011yescharacteristic
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12311yescharacteristic
153C2×C4×C11C2×SD1611yescharacteristic
154C2×C4×C11#13511yescharacteristic
155C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C11#13711yescharacteristic
157C2×Dic11—21no—
158C2×Dic11—21no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—42no—
162C2×Dic11—82no—
163D44—21no—
164D44—21no—
165D44—21no—
166D44—42no—
167D44#10112yes—
168C4×D11—41no—
169C4×D11—41no—
170C4×D11—41no—
171C4×D11—41no—
172C4×D11—41no—
173C4×D11—41no—
174C4×D11—41no—
175C4×D11—41no—
176Dic22—82no—
177Dic22—82no—
178C8×C11—22no—
179C8×C11—42no—
180C8×C11—41no—
181C8×C11—81no—
182C11⋊C8—42no—
183C11⋊C8—81no—
184C22×M16—221no—
185C2×C4⋊Q8—111no—
186C2×C4×D4—111no—
187#476—221no—
188#476—221no—
189#476—221no—
190#476—221no—
191#436—221no—
192#435—222no—
193C8×D4—221no—
194#431C2×D1111yescharacteristic
195C2×#106—112no—
196#423—111no—
197#423—111no—
198C2×C4⋊C8C2×D1111yescharacteristic
199C2×#102—112no—
200#407—221no—
201C4×M16C2×D1111yescharacteristic
202#343—221no—
203#343—221no—
204#332—222no—
205D4⋊C8—221no—
206D4⋊C8—221no—
207C22×C11—21no—
208C22×C11—21no—
209C22×C11#38611yescharacteristic
210C22×C11C4×SD1611yescharacteristic
211C22×C11#44011yescharacteristic
212C2×D11—22no—
213C2×D11—41no—
214C2×D11—41no—
215C2×D11—41no—
216C2×D11—41no—
217C2×D11—41no—
218C2×D11—82no—
219C2×D11—82no—
220C4×C11—21no—
221C4×C11—21no—
222C4×C11—21no—
223C4×C11C2×#10111yescharacteristic
224C4×C11#41311yescharacteristic
225C4×C11#45011yescharacteristic
226C4×C11#45211yescharacteristic
227C4×C11#46111yescharacteristic
228C4×C11#46311yescharacteristic
229Dic11—41no—
230Dic11—41no—
231Dic11—82no—
232C22×Q8—221no—
233C22×D4—111no—
234C23×C4—221no—
235C2×M16—222no—
236C2×M16—221no—
237C2×M16—221no—
238C2×M16—442no—
239C2×M16—442no—
240C2×M16D4411yescharacteristic
241C2×M16D4411yescharacteristic
242C22×C8—222no—
243C22×C8C4×D1112yes—
244C4⋊Q8—221no—
245C4⋊Q8—221no—
246C4⋊Q8—221no—
247C4⋊Q8—221no—
248C4×D4—111no—
249C4×D4—111no—
250C4×D4—111no—
251C4×D4—111no—
252C4×D4—221no—
253C4×D4—221no—
254C2×C4⋊C4—111no—
255C2×C4⋊C4—112no—
256C2×C4⋊C4—221no—
257C2×C22⋊C4—221no—
258C2×C42C22×D1111yescharacteristic
259#106—222no—
260#106—222no—
261C4⋊C8—21no—
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8—112no—
265C4⋊C8—221no—
266C4⋊C8—221no—
267C4⋊C8—221no—
268#102—222no—
269#102—222no—
270C22⋊C8—21no—
271C22⋊C8—222no—
272C22⋊C8—222no—
273#97—21no—
274C4×C8—21no—
275C4×C8—21no—
276C2×C11—21no—
277C2×C11—21no—
278C2×C11#187711yescharacteristic
279C2×C11#190111yescharacteristic
280C2×C11#190311yescharacteristic
281D11—42no—
282D11—81no—
283C24—221no—
284C2×Q8—441no—
285C2×Q8—441no—
286C2×Q8—882no—
287C2×D4—111no—
288C2×D4—111no—
289C2×D4—222no—
290C2×D4—221no—
291C2×D4—441no—
292C22×C4—221no—
293C22×C4—221no—
294C22×C4—221no—
295C22×C4—221no—
296C22×C4—221no—
297C22×C4—222no—
298C22×C4—441no—
299C22×C4—441no—
300C22×C4—441no—
301C22×C4—441no—
302C22×C4C2×C4×D1111yescharacteristic
303C22×C4C2×D4411yescharacteristic
304C22×C4#433911yescharacteristic
305M16—21no—
306M16—21no—
307M16—21no—
308M16—444no—
309M16—441no—
310M16—441no—
311M16—441no—
312M16—441no—
313M16#431412yes—
314C2×C8—21no—
315C2×C8—22no—
316C2×C8—21no—
317C2×C8—42no—
318C2×C8—41no—
319C2×C8—222no—
320C2×C8—444no—
321C2×C8—441no—
322C4⋊C4—111no—
323C4⋊C4—111no—
324C4⋊C4—221no—
325C4⋊C4—222no—
326C4⋊C4—222no—
327C4⋊C4—441no—
328C4⋊C4—441no—
329C22⋊C4—221no—
330C22⋊C4—221no—
331C22⋊C4—221no—
332C22⋊C4—221no—
333C42D4×D1111yescharacteristic
334C42D4×D1111yescharacteristic
335C42D4×D1111yescharacteristic
336C42#434311yescharacteristic
337C11#924911yescharacteristic, complemented, Sylow
338C23—221no—
339C23—221no—
340C23—442no—
341C23—441no—
342C23—441no—
343C23—881no—
344C23C4×D4411yescharacteristic
345Q8—882no—
346Q8—882no—
347D4—112no—
348D4—221no—
349D4—221no—
350D4—221no—
351D4—442no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—41no—
355C2×C4—221no—
356C2×C4—221no—
357C2×C4—441no—
358C2×C4—441no—
359C2×C4—441no—
360C2×C4—441no—
361C2×C4—441no—
362C2×C4—441no—
363C2×C4—441no—
364C2×C4—441no—
365C2×C4—441no—
366C2×C4—441no—
367C2×C4—442no—
368C2×C4—882no—
369C2×C4C22⋊C4×D1111yescharacteristic
370C2×C4#6693511yescharacteristic
371C2×C4#6693711yescharacteristic
372C2×C4#6694611yescharacteristic
373C2×C4#6694711yescharacteristic
374C2×C4#6694811yescharacteristic
375C2×C4C2×#431411yescharacteristic
376C2×C4#6695711yescharacteristic
377C2×C4#6696111yescharacteristic
378C2×C4#6696211yescharacteristic
379C8—22no—
380C8—41no—
381C8—42no—
382C8—81no—
383C8—442no—
384C8—881no—
385C22—21no—
386C22—21no—
387C22—222no—
388C22—441no—
389C22—441no—
390C22—441no—
391C22—441no—
392C22—441no—
393C22—882no—
394C22—882no—
395C22#1062227811yescharacteristic
396C22C4×#431411yescharacteristic
397C22#1062232311yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—441no—
402C4—441no—
403C4—882no—
404C4#1062234411yescharacteristic
405C4#1062234611yescharacteristic
406C4#1062235811yescharacteristic
407C4D11×#10111yescharacteristic
408C4#1062245411yescharacteristic
409C4#1062245711yescharacteristic
410C2—21no—
411C2—21no—
412C2—442no—
413C2—881no—
414C2#1306894911yescharacteristic
415C2#1306908311yescharacteristic
416C2#1306909511yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1283C2
socleC22×C11#386
prime radicalC22×D44C2×C4
cosocleC2×C42×C11C23
hypercenter#1283D11
hypocenterC11#9249
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1283

Complements

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

NH ≅ G/Ntype
3. #13069605C2semidirect
4. #13067300C2semidirect
6. #13066491C2semidirect
7. C11×#1283C2semidirect
136. #1283D11semidirect
337. C11#9249semidirect

Maximal subgroups

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

subgroupindex
C2×#106224552
M16×D442
#130696052
#130673002
#130670422
#130664912
C11×#12832
#924911